Reduction domains for unary positive quadratic forms over cyclic cubic field

Introduction

NB! This section is under construction!

Based on results by T. Shintani, On evaluation of zeta functions of totally real algebraic number fields at non-positive integers, myself Some results on reduction of unary positive quadratic forms over totally real cyclic number fields and tables of number fields (available at ftp://megrez.math.u-bordeaux.fr/pub/numberfields/) computed by Henri Cohen, et al. the explicit descriptions of reduction domain is computed for a certain cubic cyclic number fields with discriminant < 2.106. These reduction domains was computed using algebraic number theory software KASH.

# of suitable cubic cyclic numberfields with discriminant < 2.106 = 156
# of cubic cyclic numberfields with discriminant < 2.106 = 225

These inequalities is given with respect to the integral basis.


Also available as LaTeX, DVI, PS, gzipped PS, PDF file.

Polynomials

x3-219*x+730, x3-x2-132*x+544, x3+x2-290*x+1613, x3-x2-24*x+27, x3-x2-184*x-41, x3-x2-422*x+3144, x3+x2-112*x+25, x3+x2-442*x-344, x3-x2-464*x+3921, x3-273*x+1547, x3-x2-42*x-80, x3+x2-384*x-427, x3-x2-162*x+505, x3-x2-94*x-304, x3-417*x+973, x3+x2-122*x+435, x3-93*x-217, x3+x2-142*x-680, x3-x2-14*x-8, x3+x2-410*x-1003, x3+x2-226*x-176, x3+x2-324*x-1009, x3-x2-34*x+61, x3+x2-192*x+171, x3-x2-316*x+2144, x3-x2-100*x-223, x3+x2-180*x+521, x3+x2-226*x+503, x3+x2-166*x+536, x3+x2-184*x-512, x3+x2-160*x+677, x3-201*x-1072, x3-x2-64*x-143, x3-x2-462*x-3185, x3+x2-186*x-207, x3-x2-366*x+2605, x3+x2-284*x+1011, x3+x2-252*x+729, x3-x2-386*x-1760, x3+x2-344*x+1913, x3-x2-190*x+719, x3+x2-146*x-504, x3-x2-286*x+509, x3-x2-272*x+1755, x3-x2-50*x+123, x3+x2-444*x+1728, x3-x2-262*x+991, x3+x2-296*x+461, x3-399*x-665, x3+x2-264*x+1028, x3-x2-70*x+125, x3-471*x-1727, x3-x2-234*x+729, x3-x2-362*x+2335, x3-327*x+2071, x3-453*x-3473, x3-x2-316*x-703, x3-x2-246*x+520, x3-3*x-1, x3-x2-296*x+1317, x3-x2-336*x+1719, x3-291*x+1358, x3-327*x+1853, x3+x2-324*x-36, x3+x2-430*x-3347, x3-x2-140*x+343, x3-x2-22*x-5, x3-x2-52*x-64, x3-x2-346*x-2155, x3+x2-464*x+3044, x3-183*x-854, x3+x2-322*x+1361, x3+x2-380*x+972, x3-453*x+604, x3+x2-342*x+2016, x3-x2-270*x-1592, x3-x2-76*x+212, x3-x2-170*x-776, x3-x2-224*x+997, x3-x2-60*x+67, x3-x2-444*x+3604, x3-291*x+485, x3-399*x-2926, x3+x2-400*x+2491, x3-x2-210*x+1075, x3+x2-230*x+128, x3-x2-30*x+64, x3-x2-66*x-59, x3-183*x-793, x3+x2-204*x+999, x3-x2-44*x-69, x3-x2-152*x+220, x3-417*x+2224, x3-x2-82*x+64, x3+x2-206*x+321, x3+x2-276*x-307, x3+x2-294*x+1439, x3+x2-134*x-597, x3-x2-352*x-1840, x3+x2-420*x-1728, x3-x2-382*x+2209, x3+x2-156*x+608, x3+x2-366*x+1791, x3-57*x-152, x3-273*x-728, x3+x2-196*x-349, x3+x2-372*x+2565, x3+x2-244*x+1276, x3+x2-350*x-2608, x3-x2-390*x-347, x3-x2-170*x+757, x3+x2-446*x+248, x3+x2-256*x-1481, x3-x2-100*x+379, x3-x2-86*x-48, x3-x2-200*x-512, x3-111*x-370, x3-x2-74*x+256, x3-x2-10*x+8, x3-309*x-2060, x3+x2-134*x+209, x3+x2-274*x+61, x3-x2-92*x-236, x3-39*x-26, x3-x2-432*x+1345, x3-201*x-737, x3+x2-302*x-739, x3-129*x+215, x3+x2-374*x+1331, x3+x2-462*x-976, x3-x2-44*x+64, x3-x2-382*x-85, x3-x2-420*x+2989, x3-x2-30*x-27, x3-237*x+1027, x3+x2-342*x+989, x3+x2-416*x+2313, x3+x2-196*x+829, x3-x2-434*x+2799, x3-x2-102*x+216, x3-x2-240*x+988, x3-x2-330*x+2349, x3-x2-90*x-261, x3-x2-220*x+1273, x3-309*x+721, x3-x2-466*x-3368, x3+x2-136*x-515, x3+x2-450*x+1301, x3+x2-412*x+1741, x3-x2-290*x+1000, x3+x2-174*x-891, x3-x2-160*x-196, x3+x2-234*x-1432, x3-21*x-28, x3+x2-426*x-2179, x3-237*x+316,

Inequalities

Q(x), x3-3*x-1=0

Integral basis 1, x, x2
Fundamental units u1=-1-3x1+2x2, u2=1+2x1+x2,
h=1 Regulator R=0.8492874506461925286447620049
2 a1 -4 a2 +5 a3 >= 0
2 a1 +5 a2 +8 a3 >= 0
a1 + a2 +4 a3 >= 0
a1 + a2 + a3 >= 0
a1 -2 a2 + a3 >= 0
2 a1 - a2 - a3 >= 0

Q(x), x3-x2-10*x+8=0

Integral basis 1, w1=x, w2=(x+x2)/2
Fundamental units u1=-47+24w1+40w2, u2=41-64w1+24w2,
h=1 Regulator R=12.19578191258585233051463551
296 a1 +233 a2 +207 a3 >= 0
296 a1 +977 a2 +2098 a3 >= 0
40 a1 +34 a2 +33 a3 >= 0
40 a1 +127 a2 +281 a3 >= 0
40 a1 -121 a2 +126 a3 >= 0
296 a1 -914 a2 +951 a3 >= 0

Q(x), x3-x2-14*x-8=0

Integral basis 1, w1=x, w2=(x+x2)/2
Fundamental units u1=81-40w1+8w2, u2=-7-16w1+24w2,
h=1 Regulator R=18.92186438293808262342272012
2856 a1 +12863 a2 +35393 a3 >= 0
2856 a1 -1757 a2 -340 a3 >= 0
40 a1 +42 a2 +157 a3 >= 0
40 a1 -87 a2 +71 a3 >= 0
40 a1 +85 a2 +372 a3 >= 0
2856 a1 -8250 a2 +7787 a3 >= 0

Q(x), x3-21*x-28=0

Integral basis 1, w1=x, w2=(x+x2)/2
Fundamental units u1=305+232w1+112w2, u2=9+8w1+8w2,
h=3, Classgroup C3 Regulator R=12.59418895691867653136947785
136 a1 +700 a2 +2149 a3 >= 0
136 a1 -203 a2 +49 a3 >= 0
8 a1 -7 a2 +14 a3 >= 0
8 a1 -28 a2 +35 a3 >= 0
8 a1 +35 a2 +119 a3 >= 0
136 a1 -497 a2 +658 a3 >= 0

Q(x), x3-x2-22*x-5=0

Integral basis 1, w1=x, w2=(2+x2)/3
Fundamental units u1=-20-93w1+51w2, u2=-17+51w1+42w2,
h=1 Regulator R=19.70332998041830482933379908
8202 a1 +43604 a2 +82725 a3 >= 0
8202 a1 -1889 a2 +5608 a3 >= 0
237 a1 +12 a2 +271 a3 >= 0
237 a1 -926 a2 +1410 a3 >= 0
237 a1 +1151 a2 +2348 a3 >= 0
8202 a1 -33513 a2 +51101 a3 >= 0

Q(x), x3-x2-24*x+27=0

Integral basis 1, w1=x, w2=(2x+x2)/3
Fundamental units u1=1309-1908w1+720w2, u2=205-288w1+108w2,
h=1 Regulator R=19.24797029940890064434198409
1188 a1 -5882 a2 +5783 a3 >= 0
1188 a1 +5725 a2 +13010 a3 >= 0
180 a1 +863 a2 +1969 a3 >= 0
180 a1 +206 a2 +217 a3 >= 0
180 a1 -889 a2 +874 a3 >= 0
1188 a1 +1345 a2 +1403 a3 >= 0

Q(x), x3-x2-30*x+64=0

Integral basis 1, w1=x, w2=(x+x2)/2
Fundamental units u1=953-696w1+176w2, u2=-279+48w1+40w2,
h=3, Classgroup C3 Regulator R=15.62229944748534262473751525
136 a1 -804 a2 +1973 a3 >= 0
136 a1 +327 a2 +556 a3 >= 0
8 a1 -45 a2 +113 a3 >= 0
8 a1 +20 a2 +35 a3 >= 0
8 a1 +33 a2 +100 a3 >= 0
136 a1 +613 a2 +1687 a3 >= 0

Q(x), x3-x2-30*x-27=0

Integral basis 1, w1=x, w2=(2x+x2)/3
Fundamental units u1=1+3w2, u2=34+27w1+24w2,
h=3, Classgroup C3 Regulator R=7.949577968545347777131492885
30 a1 -29 a2 -11 a3 >= 0
30 a1 +192 a2 +535 a3 >= 0
3 a1 + a2 +8 a3 >= 0
3 a1 +14 a2 +47 a3 >= 0
3 a1 -12 a2 +8 a3 >= 0
30 a1 -133 a2 +106 a3 >= 0

Q(x), x3-x2-34*x+61=0

Integral basis 1, w1=x, w2=(2+x2)/3
Fundamental units u1=5143-4638w1+1947w2, u2=-590+183w1+132w2,
h=1 Regulator R=23.58908050081116618385703581
19821 a1 -121834 a2 +262819 a3 >= 0
19821 a1 +37404 a2 +36734 a3 >= 0
570 a1 -3415 a2 +7428 a3 >= 0
570 a1 +1117 a2 +1145 a3 >= 0
570 a1 +2868 a2 +5677 a3 >= 0
19821 a1 +104251 a2 +195972 a3 >= 0

Q(x), x3-39*x-26=0

Integral basis 1, w1=x, w2=(-2+x+x2)/4
Fundamental units u1=-95-15848w1+8752w2, u2=3377+3144w1+2264w2,
h=3, Classgroup C3 Regulator R=26.70303632025880428032112171
168 a1 -956 a2 +1077 a3 >= 0
712 a1 -481 a2 -395 a3 >= 0
1843402806584 a1 +12083292069589 a2 +21900266908760 a3 >= 0

Q(x), x3-x2-42*x-80=0

Integral basis 1, w1=x, w2=(x+x2)/2
Fundamental units u1=287961+34392w1-16352w2, u2=-129911-45680w1+14664w2,
h=1 Regulator R=87.96911073676017576678629030
302690632 a1 +2346045126 a2 +10264694293 a3 >= 0
302690632 a1 -708419301 a2 +474785120 a3 >= 0
24392 a1 +172257 a2 +773333 a3 >= 0
24392 a1 -60534 a2 +48163 a3 >= 0
24392 a1 -87331 a2 +227360 a3 >= 0
302690632 a1 -1334935193 a2 +2276217763 a3 >= 0

Q(x), x3-x2-44*x-69=0

Integral basis 1, w1=x, w2=(x+x2)/3
Fundamental units u1=-53-27w1+12w2, u2=25+9w1+3w2,
h=3, Classgroup C3 Regulator R=10.86734885727000595191293004
30 a1 -53 a2 +13 a3 >= 0
30 a1 -151 a2 +202 a3 >= 0
3 a1 -6 a2 +2 a3 >= 0
3 a1 -13 a2 +23 a3 >= 0
3 a1 +22 a2 +65 a3 >= 0
30 a1 +234 a2 +685 a3 >= 0

Q(x), x3-x2-44*x+64=0

Integral basis 1, w1=x, w2=(-1x+x2)/4
Fundamental units u1=4281-3112w1+1824w2, u2=12625-9184w1+5384w2,
h=3, Classgroup C3 Regulator R=32.47072061139040132442117460
968 a1 +6142 a2 +8207 a3 >= 0
968 a1 -6605 a2 +12918 a3 >= 0
328 a1 +2081 a2 +2781 a3 >= 0
328 a1 -2238 a2 +4377 a3 >= 0
328 a1 +485 a2 +58 a3 >= 0
968 a1 +1431 a2 +171 a3 >= 0

Q(x), x3-x2-50*x+123=0

Integral basis 1, w1=x, w2=(x+x2)/3
Fundamental units u1=-251+120w1+69w2, u2=16-69w1+51w2,
h=1 Regulator R=31.69949245209034520756959095
143481 a1 -1096904 a2 +2429589 a3 >= 0
143481 a1 +389087 a2 +481387 a3 >= 0
570 a1 +492 a2 +3289 a3 >= 0
570 a1 +3059 a2 +6762 a3 >= 0
570 a1 -2981 a2 +9329 a3 >= 0
143481 a1 +851298 a2 +1967378 a3 >= 0

Q(x), x3-x2-52*x-64=0

Integral basis 1, w1=x, w2=(-1x+x2)/4
Fundamental units u1=4785769+5085432w1+2466664w2, u2=-13697711-7552096w1+5085432w2,
h=1 Regulator R=94.44812385100544064606737409
94609176 a1 -123604885 a2 +71273009 a3 >= 0
94609176 a1 +780209575 a2 +1413478098 a3 >= 0
10447000 a1 -13648774 a2 +7870171 a3 >= 0
10447000 a1 +86152829 a2 +156080055 a3 >= 0
10447000 a1 -62057055 a2 +107671774 a3 >= 0
94609176 a1 -561995514 a2 +975087469 a3 >= 0

Q(x), x3-57*x-152=0

Integral basis 1, w1=x, w2=(x+x2)/2
Fundamental units u1=72929+31648w1+8288w2, u2=10689+4640w1+1216w2,
h=3, Classgroup C3 Regulator R=39.66830406438365192904415015
2400 a1 +20729 a2 +99883 a3 >= 0
2400 a1 -7904 a2 +9063 a3 >= 0
352 a1 -1159 a2 +1330 a3 >= 0
352 a1 -1881 a2 +4085 a3 >= 0
352 a1 +3040 a2 +14649 a3 >= 0
2400 a1 -12825 a2 +27854 a3 >= 0

Q(x), x3-x2-60*x+67=0

Integral basis 1, w1=x, w2=(2+3x+x2)/5
Fundamental units u1=2692+133w1-210w2, u2=319-210w1+77w2,
h=1 Regulator R=32.47751711169280281137395414
476171 a1 -3712806 a2 +3752628 a3 >= 0
476171 a1 +3656066 a2 +7998345 a3 >= 0
2746 a1 +18231 a2 +44493 a3 >= 0
2746 a1 +4294 a2 +6483 a3 >= 0
2746 a1 -19779 a2 +20420 a3 >= 0
476171 a1 +532911 a2 +629473 a3 >= 0

Q(x), x3-x2-64*x-143=0

Integral basis 1, w1=x, w2=(2+x2)/3
Fundamental units u1=840802+536220w1+191211w2, u2=14926+9531w1+3405w2,
h=1 Regulator R=53.86198908997784825896584043
3887706 a1 +36595023 a2 +117414892 a3 >= 0
3887706 a1 -10203038 a2 +11517529 a3 >= 0
69177 a1 -181328 a2 +205439 a3 >= 0
69177 a1 -400383 a2 +818600 a3 >= 0
69177 a1 +650888 a2 +2088926 a3 >= 0
3887706 a1 -22504279 a2 +46014349 a3 >= 0

Q(x), x3-x2-66*x-59=0

Integral basis 1, w1=x, w2=(4+x2)/5
Fundamental units u1=-85459-57880w1+35540w2, u2=1621+5140w1+3200w2,
h=1 Regulator R=28.64286795638920762266472298
180 a1 -1277 a2 +1960 a3 >= 0
740 a1 -682 a2 +719 a3 >= 0
7818549921580 a1 +70611562696705 a2 +133797487524861 a3 >= 0

Q(x), x3-x2-70*x+125=0

Integral basis 1, w1=x, w2=(4x+x2)/5
Fundamental units u1=254-265w1+108w2, u2=-344+108w1+157w2,
h=1 Regulator R=34.06923354371849868546897005
643291 a1 +1173988 a2 +1367660 a3 >= 0
643291 a1 -5595947 a2 +5258922 a3 >= 0
3626 a1 +4655 a2 +8817 a3 >= 0
3626 a1 -28472 a2 +31605 a3 >= 0
3626 a1 +27443 a2 +64732 a3 >= 0
643291 a1 +5065250 a2 +12028857 a3 >= 0

Q(x), x3-x2-74*x+256=0

Integral basis 1, w1=x, w2=(x+x2)/2
Fundamental units u1=13783617033-5941602688w1+1028639864w2, u2=3605612145-1554244776w1+269078600w2,
h=1 Regulator R=153.8026043227643232660396209
14069654776 a1 -134398234569 a2 +574710216746 a3 >= 0
14069654776 a1 +88570612777 a2 +323068033191 a3 >= 0
3680435832 a1 +23168902296 a2 +84510329825 a3 >= 0
3680435832 a1 +15668336321 a2 +41185756694 a3 >= 0
3680435832 a1 -35156802785 a2 +150336600881 a3 >= 0
14069654776 a1 +59897276568 a2 +157445858263 a3 >= 0

Q(x), x3-x2-76*x+212=0

Integral basis 1, w1=x, w2=(-2+x+x2)/4
Fundamental units u1=44511257-20803168w1+7276536w2, u2=-138611495+28079704w1+20803168w2,
h=1 Regulator R=138.3254025994310389070381185
24919951256 a1 +184385928929 a2 +374710315666 a3 >= 0
24919951256 a1 +75670900594 a2 +63902536805 a3 >= 0
47745304 a1 +144981715 a2 +122434679 a3 >= 0
47745304 a1 -450508969 a2 +926216206 a3 >= 0
47745304 a1 +353272558 a2 +717925363 a3 >= 0
24919951256 a1 -235136878267 a2 +483425344001 a3 >= 0

Q(x), x3-x2-82*x+64=0

Integral basis 1, w1=x, w2=(2+3x+x2)/6
Fundamental units u1=-5768663+3327096w1+3856656w2, u2=2854033-7183752w1+3327096w2,
h=3, Classgroup C3 Regulator R=100.3760789091464984457497068
77901288 a1 +60673560 a2 +64179827 a3 >= 0
77901288 a1 +714833053 a2 +1476618205 a3 >= 0
4077672 a1 +3175909 a2 +3359448 a3 >= 0
4077672 a1 +37417272 a2 +77292229 a3 >= 0
4077672 a1 -36515509 a2 +37600811 a3 >= 0
77901288 a1 -697605325 a2 +718339320 a3 >= 0

Q(x), x3-x2-86*x-48=0

Integral basis 1, w1=x, w2=(x+x2)/6
Fundamental units u1=-2316287-4286184w1+2454600w2, u2=1459273+2454600w1+1831584w2,
h=3, Classgroup C3 Regulator R=110.3884905796799952283130493
463383096 a1 +4652823019 a2 +8561958697 a3 >= 0
463383096 a1 -261312186 a2 -18992059 a3 >= 0
2497848 a1 -1408511 a2 -102234 a3 >= 0
2497848 a1 -21174355 a2 +26386991 a3 >= 0
2497848 a1 +25080714 a2 +46152835 a3 >= 0
463383096 a1 -3928127737 a2 +4895143146 a3 >= 0

Q(x), x3-x2-90*x-261=0

Integral basis 1, w1=x, w2=(2x+x2)/3
Fundamental units u1=49681+3168w1-1737w2, u2=-24182-5823w1+2043w2,
h=1 Regulator R=73.34615687350845203165964396
42680070 a1 +476312313 a2 +2089433489 a3 >= 0
42680070 a1 -150424780 a2 +76439527 a3 >= 0
5139 a1 +39653 a2 +194736 a3 >= 0
5139 a1 -21864 a2 +19399 a3 >= 0
5139 a1 -12650 a2 +99344 a3 >= 0
42680070 a1 -283207463 a2 +437611254 a3 >= 0

Q(x), x3-x2-92*x-236=0

Integral basis 1, w1=x, w2=(-2+x+x2)/4
Fundamental units u1=73345+28968w1+12664w2, u2=-2615-784w1+344w2,
h=4, Classgroup C2xC2
102360 a1 +1141289 a2 +3415399 a3 >= 0
102360 a1 -300219 a2 +93892 a3 >= 0
856 a1 +9334 a2 +28075 a3 >= 0
856 a1 -2577 a2 +929 a3 >= 0
856 a1 -5901 a2 +9516 a3 >= 0
102360 a1 -738710 a2 +1096909 a3 >= 0

Q(x), x3-93*x-217=0

Integral basis 1, w1=x, w2=(3+4x+x2)/5
Fundamental units u1=-39-68w1+24w2, u2=13+4w1+20w2,
h=3, Classgroup C3 Regulator R=24.49110593182112945993695341
7348 a1 +78244 a2 +233629 a3 >= 0
7348 a1 -18383 a2 -1103 a3 >= 0
68 a1 -31 a2 +326 a3 >= 0
68 a1 -496 a2 +419 a3 >= 0
68 a1 +527 a2 +1907 a3 >= 0
7348 a1 -59861 a2 +54046 a3 >= 0

Q(x), x3-x2-94*x-304=0

Integral basis 1, w1=x, w2=(x+x2)/2
Fundamental units u1=210610425+75499424w1+15916360w2, u2=1481215073+530984552w1+111939144w2,
h=1 Regulator R=127.2286661530003359746916222
1951106056 a1 -8250722303 a2 +13319722946 a3 >= 0
1951106056 a1 +22412397881 a2 +139932050901 a3 >= 0
277423112 a1 -1173150494 a2 +1893899655 a3 >= 0
277423112 a1 +3186765335 a2 +19896604206 a3 >= 0
277423112 a1 -1736191729 a2 +4564691779 a3 >= 0
1951106056 a1 -12210569522 a2 +32103301473 a3 >= 0

Q(x), x3-x2-100*x+379=0

Integral basis 1, w1=x, w2=(2+x2)/3
Fundamental units u1=73-36w1+12w2, u2=4117-1548w1+384w2,
h=3, Classgroup C3 Regulator R=21.430625417039775390878717932090
444 a1 +1997 a2 +3289 a3 >= 0
444 a1 -4926 a2 +18511 a3 >= 0
12 a1 +47 a2 +104 a3 >= 0
12 a1 -125 a2 +491 a3 >= 0
12 a1 +90 a2 +233 a3 >= 0
444 a1 +3373 a2 +8836 a3 >= 0

Q(x), x3-x2-100*x-223=0

Integral basis 1, w1=x, w2=(2+3x+x2)/5
Fundamental units u1=759+323w1+217w2, u2=-102-41w1+18w2,
h=3, Classgroup C3 Regulator R=16.84781379310228438605590660563
1673 a1 +19148 a2 +55973 a3 >= 0
1673 a1 -4072 a2 +202 a3 >= 0
58 a1 +607 a2 +1801 a3 >= 0
58 a1 -167 a2 +38 a3 >= 0
58 a1 -382 a2 +597 a3 >= 0
1673 a1 -13403 a2 +14091 a3 >= 0

Q(x), x3-x2-102*x+216=0

Integral basis 1, w1=x, w2=(5x+x2)/6
Fundamental units u1=11082557780881-8994473896752w1+3255755776128w2, u2=-21968746129199+3255755776128w1+5738718120624w2,
h=1 Regulator R=394.91105244262068094423952891434
357651153315706032 a1 +3363347596285087738 a2 +8074270429378870481 a3 >= 0
357651153315706032 a1 +776760146621016391 a2 +928466243503384646 a3 >= 0
2879263575216 a1 +6253292301185 a2 +7474599283255 a3 >= 0
2879263575216 a1 -30450592345306 a2 +28297870601407 a3 >= 0
2879263575216 a1 +27076563619337 a2 +65001755247898 a3 >= 0
357651153315706032 a1 -3782456589590398097 a2 +3515053693167455993 a3 >= 0

Q(x), x3-111*x-370=0

Integral basis 1, w1=x, w2=(-2+x+x2)/4
Fundamental units u1=-3458639-718440w1+316424w2, u2=696337+230832w1+85592w2,
h=3, Classgroup C3 Regulator R=120.59350822882493395077641044891
1099922328 a1 +13109155241 a2 +41786892751 a3 >= 0
1099922328 a1 -4230019635 a2 +2459427028 a3 >= 0
93208 a1 -355866 a2 +214283 a3 >= 0
93208 a1 -751729 a2 +1281881 a3 >= 0
93208 a1 +1107595 a2 +3537068 a3 >= 0
1099922328 a1 -8879135606 a2 +15149485933 a3 >= 0

Q(x), x3+x2-112*x+25=0

Integral basis 1, w1=x, w2=(6+5x+x2)/7
Fundamental units u1=192770+6083w1-11417w2, u2=-2908-11417w1+5334w2,
h=1 Regulator R=72.68306274444104265018069993582
293780371 a1 +2930716249 a2 +6521817399 a3 >= 0
293780371 a1 +65736698 a2 +300867832 a3 >= 0
184046 a1 +1820347 a2 +4051688 a3 >= 0
184046 a1 +22789 a2 +204159 a3 >= 0
184046 a1 -2027182 a2 +2001717 a3 >= 0
293780371 a1 -3290233318 a2 +3165847383 a3 >= 0

Q(x), x3+x2-122*x+435=0

Integral basis 1, w1=x, w2=(2x+x2)/3
Fundamental units u1=-1076633894+121700241w1+55911012w2, u2=2143483384-75667446w1-65789229w2,
h=1 Regulator R=168.93577699676642865602754963004
1467234924357 a1 -19045385717996 a2 +69709038388376 a3 >= 0
1467234924357 a1 +11048309712741 a2 +35096874325796 a3 >= 0
392396682 a1 -5093464277 a2 +18642926095 a3 >= 0
392396682 a1 +2954751404 a2 +9386275201 a3 >= 0
392396682 a1 +1746316191 a2 +3754929946 a3 >= 0
1467234924357 a1 +6529841080898 a2 +14040116158745 a3 >= 0

Q(x), x3-129*x+215=0

Integral basis 1, w1=x, w2=(5+6x+x2)/7
Fundamental units u1=-194+15w1+65w2, u2=456-80w1+15w2,
h=3, Classgroup C3 Regulator R=33.087791690242886152148809965896
38105 a1 +64973 a2 +98733 a3 >= 0
38105 a1 +396632 a2 +956970 a3 >= 0
130 a1 +430 a2 +873 a3 >= 0
130 a1 +817 a2 +2937 a3 >= 0
130 a1 -1247 a2 +1260 a3 >= 0
38105 a1 -461605 a2 +430392 a3 >= 0

Q(x), x3-x2-132*x+544=0

Integral basis 1, w1=x, w2=(-1x+x2)/4
Fundamental units u1=-3007+560w1+232w2, u2=217-136w1+96w2,
h=4, Classgroup C2xC2
544472 a1 -6930235 a2 +23785164 a3 >= 0
544472 a1 +2598162 a2 +2449987 a3 >= 0
856 a1 +2535 a2 +7319 a3 >= 0
856 a1 +7299 a2 +14068 a3 >= 0
856 a1 -8978 a2 +35109 a3 >= 0
544472 a1 +4876545 a2 +9700001 a3 >= 0

Q(x), x3+x2-134*x+209=0

Integral basis 1, w1=x, w2=(6+x2)/7
Fundamental units u1=619-703w1+418w2, u2=-2668+1121w1+703w2,
h=3, Classgroup C3 Regulator R=20.50462790802070203037918734866
1515 a1 -19353 a2 +36608 a3 >= 0
1515 a1 +15398 a2 +23650 a3 >= 0
206 a1 -2621 a2 +4975 a3 >= 0
206 a1 +2091 a2 +3208 a3 >= 0
206 a1 +324 a2 +263 a3 >= 0
1515 a1 +2440 a2 +1857 a3 >= 0

Q(x), x3+x2-134*x-597=0

Integral basis 1, w1=x, w2=(2x+x2)/3
Fundamental units u1=289+60w1+12w2, u2=-1955-264w1+84w2,
h=3, Classgroup C3 Regulator R=24.236588254065746324762823702465
444 a1 -3775 a2 +8181 a3 >= 0
444 a1 -2411 a2 +2756 a3 >= 0
12 a1 -66 a2 +77 a3 >= 0
12 a1 +151 a2 +759 a3 >= 0
12 a1 -97 a2 +232 a3 >= 0
444 a1 +5742 a2 +28579 a3 >= 0

Q(x), x3+x2-136*x-515=0

Integral basis 1, w1=x, w2=(3x+x2)/5
Fundamental units u1=-874612-188531w1+81381w2, u2=23763246+6363854w1+2949955w2,
h=1 Regulator R=75.261694306484984240538046505745
224223451 a1 -942346579 a2 +226674237 a3 >= 0
224223451 a1 +2867001302 a2 +9051901594 a3 >= 0
1959266 a1 +25049971 a2 +79091138 a3 >= 0
1959266 a1 -18774379 a2 +24727267 a3 >= 0
1959266 a1 -8234858 a2 +1981959 a3 >= 0
224223451 a1 -2148878174 a2 +2829490523 a3 >= 0

Q(x), x3-x2-140*x+343=0

Integral basis 1, w1=x, w2=(6x+x2)/7
Fundamental units u1=1167114-824341w1+296625w2, u2=-21971+2751w1+4907w2,
h=1 Regulator R=54.326349550677430857082786114557
14838623 a1 -184792458 a2 +170364744 a3 >= 0
14838623 a1 +37375978 a2 +45485619 a3 >= 0
138022 a1 -1717281 a2 +1583742 a3 >= 0
138022 a1 +348566 a2 +425571 a3 >= 0
138022 a1 +1506737 a2 +3649589 a3 >= 0
14838623 a1 +162255103 a2 +392533180 a3 >= 0

Q(x), x3+x2-142*x-680=0

Integral basis 1, w1=x, w2=(x+x2)/2
Fundamental units u1=8782321+2316160w1+345800w2, u2=-138943719-13760040w1+3353560w2,
h=3, Classgroup C3 Regulator R=124.75844977906453871239245680422
1735556360 a1 -14242422427 a2 +51317281838 a3 >= 0
1735556360 a1 -10737843839 a2 +27848463857 a3 >= 0
1828360 a1 -11312066 a2 +29337895 a3 >= 0
1828360 a1 +24487187 a2 +176226322 a3 >= 0
1828360 a1 -15003481 a2 +54062903 a3 >= 0
1735556360 a1 +23244709906 a2 +167283257425 a3 >= 0

Q(x), x3+x2-146*x-504=0

Integral basis 1, w1=x, w2=(5x+x2)/6
Fundamental units u1=7250250427807315825+1712377540978778448w1+1130015717004316224w2, u2=90019061216679265969+5102424691991727120w1-3972408974987410896w2,
h=1 Regulator R=687.76076944877659291469518727873
150897438472328310471600 a1 -1567122263730177087664122 a2 +1406582870151601426624231 a3 >= 0
150897438472328310471600 a1 +1975570943582374323935275 a2 +5957052222869804379144997 a3 >= 0
1547481836638548912 a1 -16071135888493184399 a2 +14424773974448140460 a3 >= 0
1547481836638548912 a1 +20259854528579177754 a2 +61090699803289144745 a3 >= 0
1547481836638548912 a1 -5736200476724542267 a2 -1236345619086937429 a3 >= 0
150897438472328310471600 a1 -559346118324525546742753 a2 -120558046349646903132428 a3 >= 0

Q(x), x3-x2-152*x+220=0

Integral basis 1, w1=x, w2=(-2-3x+x2)/8
Fundamental units u1=197839708352793-4575277050192w1-10598046982744w2, u2=11184542907369-6022769932552w1+4575277050192w2,
h=1 Regulator R=419.156440285244805885569506787094
10250315290245842792 a1 -128446513900804383621 a2 +246799979187930635980 a3 >= 0
10250315290245842792 a1 +123796195704980522476 a2 +137904416969019817441 a3 >= 0
24602013705832 a1 +297126049695767 a2 +330987512673533 a3 >= 0
24602013705832 a1 +35763348203549 a2 -13063219723500 a3 >= 0
24602013705832 a1 -308287384193484 a2 +592350214165751 a3 >= 0
10250315290245842792 a1 +14900633486069703937 a2 -5442730417854270117 a3 >= 0

Q(x), x3+x2-156*x+608=0

Integral basis 1, w1=x, w2=(x+x2)/4
Fundamental units u1=1011105-37712w1-30984w2, u2=-394151+55240w1+24256w2,
h=3, Classgroup C3 Regulator R=105.200837052743820765335830708180
2265419256 a1 +20075200247 a2 +49493312200 a3 >= 0
2265419256 a1 -33008231294 a2 +111984332197 a3 >= 0
81784 a1 -1106743 a2 +3942821 a3 >= 0
81784 a1 +315265 a2 +704376 a3 >= 0
81784 a1 +709694 a2 +1731955 a3 >= 0
2265419256 a1 +10667611791 a2 +15225057571 a3 >= 0

Q(x), x3-x2-160*x-196=0

Integral basis 1, w1=x, w2=(-6+x+x2)/8
Fundamental units u1=-8028983-9743032w1+5788784w2, u2=10031201+5788784w1+3954248w2,
h=3, Classgroup C3 Regulator R=109.89948222057948276722880688854
716220040 a1 +9820472936 a2 +17522108369 a3 >= 0
716220040 a1 -893005047 a2 -509612416 a3 >= 0
23267976 a1 -29011167 a2 -16555783 a3 >= 0
23267976 a1 -266760328 a2 +331494855 a3 >= 0
23267976 a1 +319039471 a2 +569244016 a3 >= 0
716220040 a1 -8211247849 a2 +10203865567 a3 >= 0

Q(x), x3+x2-160*x+677=0

Integral basis 1, w1=x, w2=(2+x2)/3
Fundamental units u1=56851-18057w1+3912w2, u2=3151-1005w1+219w2,
h=3, Classgroup C3 Regulator R=36.88300673664573824136204518454
205005 a1 -3043801 a2 +15200792 a3 >= 0
205005 a1 +1105786 a2 +2124807 a3 >= 0
11442 a1 +61602 a2 +118949 a3 >= 0
11442 a1 +96715 a2 +280084 a3 >= 0
11442 a1 -169759 a2 +848145 a3 >= 0
205005 a1 +1733010 a2 +5019946 a3 >= 0

Q(x), x3-x2-162*x+505=0

Integral basis 1, w1=x, w2=(6+x2)/7
Fundamental units u1=5402490-2540908w1+1216703w2, u2=-18325698+3757611w1+2540908w2,
h=1 Regulator R=95.441592332053825616328766204468
984721511 a1 +3216669321 a2 +2345118424 a3 >= 0
984721511 a1 -13410425752 a2 +26934022118 a3 >= 0
73285006 a1 +239390947 a2 +174528847 a3 >= 0
73285006 a1 -998031249 a2 +2004485404 a3 >= 0
73285006 a1 +831925308 a2 +1411951043 a3 >= 0
984721511 a1 +11178477942 a2 +18972213497 a3 >= 0

Q(x), x3+x2-166*x+536=0

Integral basis 1, w1=x, w2=(2+3x+x2)/6
Fundamental units u1=191604836605129-1942639670184w1-7554711672696w2, u2=-51009341551127+7554711672696w1+5612072002512w2,
h=1 Regulator R=688.409837020286150281155394927433
8084489393416031952004392 a1 -119122534252458736575891975 a2 +235672717510565469494269531 a3 >= 0
8084489393416031952004392 a1 +28970625823381842217701500 a2 +34482764222445870512191473 a3 >= 0
6403887325608 a1 -93387754857547 a2 +185361151190476 a3 >= 0
6403887325608 a1 +23296575528015 a2 +28286104329005 a3 >= 0
6403887325608 a1 +63687292003924 a2 +144970434714567 a3 >= 0
8084489393416031952004392 a1 +82067419035660862406186083 a2 +182575924298286449305784948 a3 >= 0

Q(x), x3-x2-170*x-776=0

Integral basis 1, w1=x, w2=(x+x2)/2
Fundamental units u1=18756985+4959168w1+742472w2, u2=-375762663-40387752w1+7929056w2,
h=3, Classgroup C3 Regulator R=101.0350870127338837973134148040442
2281672 a1 -18680685 a2 +67131646 a3 >= 0
2281672 a1 -14080754 a2 +36407505 a3 >= 0
322248 a1 -1988671 a2 +5141951 a3 >= 0
322248 a1 +4949253 a2 +40481234 a3 >= 0
322248 a1 -2638334 a2 +9481223 a3 >= 0
2281672 a1 +35043111 a2 +286626761 a3 >= 0

Q(x), x3-x2-170*x+757=0

Integral basis 1, w1=x, w2=(2+3x+x2)/5
Fundamental units u1=8713-3180w1+863w2, u2=-3631+307w1+242w2,
h=3, Classgroup C3 Regulator R=26.459419997346071079323158909036
1142 a1 -16473 a2 +38094 a3 >= 0
1142 a1 +5787 a2 +9793 a3 >= 0
87 a1 -1252 a2 +2898 a3 >= 0
87 a1 +442 a2 +749 a3 >= 0
87 a1 +897 a2 +2443 a3 >= 0
1142 a1 +11828 a2 +32053 a3 >= 0

Q(x), x3+x2-174*x-891=0

Integral basis 1, w1=x, w2=(x+x2)/3
Fundamental units u1=7268934214+1789493508w1+362478987w2, u2=362270089+89185014w1+18065277w2,
h=1 Regulator R=138.0148391137191902573971135403903
6896096847 a1 +102134366250 a2 +538263769426 a3 >= 0
6896096847 a1 -43983203204 a2 +78847004375 a3 >= 0
343688598 a1 -2192040725 a2 +3929587701 a3 >= 0
343688598 a1 -3241834044 a2 +9112227959 a3 >= 0
343688598 a1 +5090186171 a2 +26826061708 a3 >= 0
6896096847 a1 -65047259893 a2 +182836460451 a3 >= 0

Q(x), x3+x2-180*x+521=0

Integral basis 1, w1=x, w2=(4+2x+x2)/7
Fundamental units u1=-6339+1268w1+880w2, u2=31057-388w1-1268w2,
h=1 Regulator R=43.80434691906428735456808100033
789356 a1 -11959178 a2 +22918135 a3 >= 0
789356 a1 +8709727 a2 +16668503 a3 >= 0
6588 a1 -99035 a2 +191046 a3 >= 0
6588 a1 +72462 a2 +138569 a3 >= 0
6588 a1 +19985 a2 +19549 a3 >= 0
789356 a1 +2460095 a2 +2249230 a3 >= 0

Q(x), x3-183*x-854=0

Integral basis 1, w1=x, w2=(-2-1x+x2)/4
Fundamental units u1=104476497+3260072w1-2803384w2, u2=6674337+1890008w1+456688w2,
h=3, Classgroup C3 Regulator R=159.0325289389203666630737878804057
2289337880 a1 +35341881523 a2 +126418314627 a3 >= 0
2289337880 a1 -22396296704 a2 +59229424515 a3 >= 0
41752 a1 -407509 a2 +1081302 a3 >= 0
41752 a1 -236251 a2 +372549 a3 >= 0
41752 a1 +643760 a2 +2303829 a3 >= 0
2289337880 a1 -12945584819 a2 +20392670058 a3 >= 0

Q(x), x3-183*x-793=0

Integral basis 1, w1=x, w2=(3+x+x2)/5
Fundamental units u1=3393+991w1+345w2, u2=49673+14591w1+5094w2,
h=3, Classgroup C3 Regulator R=36.388689356871342565280372088844
2902 a1 -29873 a2 +57268 a3 >= 0
2902 a1 +44464 a2 +146887 a3 >= 0
197 a1 -2026 a2 +3890 a3 >= 0
197 a1 +3017 a2 +9968 a3 >= 0
197 a1 -991 a2 +917 a3 >= 0
2902 a1 -14591 a2 +13495 a3 >= 0

Q(x), x3+x2-184*x-512=0

Integral basis 1, w1=x, w2=(x+x2)/8
Fundamental units u1=-506752823-153800328w1+98703312w2, u2=26029513+10441992w1+5828808w2,
h=3, Classgroup C3 Regulator R=108.63945884080618256882246076669
132245592 a1 -1648529520 a2 +2362686323 a3 >= 0
132245592 a1 -379002443 a2 +88397509 a3 >= 0
13990488 a1 -174400763 a2 +249952632 a3 >= 0
13990488 a1 -40095312 a2 +9351733 a3 >= 0
13990488 a1 +200505587 a2 +384258083 a3 >= 0
132245592 a1 +1895286371 a2 +3632213400 a3 >= 0

Q(x), x3-x2-184*x-41=0

Integral basis 1, w1=x, w2=(-1-6x+x2)/9
Fundamental units u1=14182+69903w1+32814w2, u2=-3084674-11340144w1+12826917w2,
h=3, Classgroup C3 Regulator R=79.442793869614046335840930135728
164160837 a1 -36633662 a2 +7090675 a3 >= 0
164160837 a1 -2127000206 a2 +4461885586 a3 >= 0
475002 a1 -6153055 a2 +12907424 a3 >= 0
475002 a1 +6732398 a2 +6070685 a3 >= 0
475002 a1 -104341 a2 +21971 a3 >= 0
164160837 a1 +2327794705 a2 +2097457219 a3 >= 0

Q(x), x3+x2-186*x-207=0

Integral basis 1, w1=x, w2=(-3-5x+x2)/9
Fundamental units u1=-42803-26481w1+31458w2, u2=53356+57939w1+26481w2,
h=3, Classgroup C3 Regulator R=64.88583589126561949584428514729
14888226 a1 -16580439 a2 +6300265 a3 >= 0
14888226 a1 -202134899 a2 +412262276 a3 >= 0
395949 a1 -441110 a2 +167883 a3 >= 0
395949 a1 -5375403 a2 +10963850 a3 >= 0
395949 a1 +5420564 a2 +5102176 a3 >= 0
14888226 a1 +203827112 a2 +191854725 a3 >= 0

Q(x), x3-x2-190*x+719=0

Integral basis 1, w1=x, w2=(+x+x2)/7
Fundamental units u1=-16560+2665w1+1887w2, u2=5289-1887w1+778w2,
h=1 Regulator R=42.67637074749197730434371212918
1913174 a1 +7742297 a2 +5855264 a3 >= 0
1913174 a1 +22752745 a2 +42179429 a3 >= 0
56767 a1 +230002 a2 +174331 a3 >= 0
56767 a1 +674240 a2 +1251808 a3 >= 0
56767 a1 -847475 a2 +1696046 a3 >= 0
1913174 a1 -28581868 a2 +57189877 a3 >= 0

Q(x), x3+x2-192*x+171=0

Integral basis 1, w1=x, w2=(-6-2x+x2)/9
Fundamental units u1=582487378-12322233w1-28445697w2, u2=-13035179+28445697w1+16123464w2,
h=1 Regulator R=161.89423093076138126676842756660
861445304658 a1 +11093714621222 a2 +12834337664591 a3 >= 0
861445304658 a1 -12729263325259 a2 +23153948886434 a3 >= 0
197836929 a1 -2923324076 a2 +5317448653 a3 >= 0
197836929 a1 +177755500 a2 -153607070 a3 >= 0
197836929 a1 +2547731647 a2 +2947472506 a3 >= 0
861445304658 a1 +774103399379 a2 -669029060047 a3 >= 0

Q(x), x3+x2-196*x-349=0

Integral basis 1, w1=x, w2=(-1-6x+x2)/9
Fundamental units u1=-231143-61266w1+84081w2, u2=27334+23052w1+9717w2,
h=3, Classgroup C3 Regulator R=49.74541103365350680448437666445
53814 a1 -729605 a2 +1579524 a3 >= 0
53814 a1 -96523 a2 +77605 a3 >= 0
8535 a1 -115716 a2 +250513 a3 >= 0
8535 a1 -15307 a2 +12309 a3 >= 0
8535 a1 +122488 a2 +112718 a3 >= 0
53814 a1 +772314 a2 +710687 a3 >= 0

Q(x), x3+x2-196*x+829=0

Integral basis 1, w1=x, w2=(4+x2)/5
Fundamental units u1=21-10w1+5w2, u2=1036-335w1+110w2,
h=3, Classgroup C3 Regulator R=17.133712086804606820755708555560
130 a1 +649 a2 +751 a3 >= 0
130 a1 -2110 a2 +6951 a3 >= 0
5 a1 +19 a2 +42 a3 >= 0
5 a1 -74 a2 +259 a3 >= 0
5 a1 +50 a2 +104 a3 >= 0
130 a1 +1331 a2 +2828 a3 >= 0

Q(x), x3-x2-200*x-512=0

Integral basis 1, w1=x, w2=(-1x+x2)/8
Fundamental units u1=3761465939929+1823808153352w1+926025934424w2, u2=-87616763558519-24897279612312w1+16512945910112w2,
h=1 Regulator R=270.150412103981426523558747414844
67237465652216 a1 -181141508822391 a2 +83643363412899 a3 >= 0
67237465652216 a1 -811014578200166 a2 +1324178424910063 a3 >= 0
7426187836792 a1 -89574265443661 a2 +146251760345522 a3 >= 0
7426187836792 a1 +117007020400511 a2 +215819458669125 a3 >= 0
7426187836792 a1 -20006567120058 a2 +9238172824953 a3 >= 0
67237465652216 a1 +1059393552674773 a2 +1954051494287838 a3 >= 0

Q(x), x3-201*x-737=0

Integral basis 1, w1=x, w2=(6+5x+x2)/7
Fundamental units u1=11835+3113w1+2028w2, u2=-50425-12310w1+5141w2,
h=3, Classgroup C3 Regulator R=42.247649407175605540669789167096
5059 a1 -59503 a2 +61814 a3 >= 0
5059 a1 -20137 a2 +1403 a3 >= 0
782 a1 -3113 a2 +217 a3 >= 0
782 a1 +12310 a2 +37147 a3 >= 0
782 a1 -9197 a2 +9556 a3 >= 0
5059 a1 +79640 a2 +240323 a3 >= 0

Q(x), x3-201*x-1072=0

Integral basis 1, w1=x, w2=(x+x2)/2
Fundamental units u1=3440826273+187427872w1-45949920w2, u2=119092769+27808960w1+3628192w2,
h=3, Classgroup C3 Regulator R=114.55938739747898518442965023054
535520 a1 -4911499 a2 +20067053 a3 >= 0
535520 a1 -3833209 a2 +11802296 a3 >= 0
168928 a1 -1549316 a2 +6330085 a3 >= 0
168928 a1 -1209173 a2 +3722995 a3 >= 0
168928 a1 +2758489 a2 +23901448 a3 >= 0
535520 a1 +8744708 a2 +75770171 a3 >= 0

Q(x), x3+x2-204*x+999=0

Integral basis 1, w1=x, w2=(x+x2)/3
Fundamental units u1=-939492176+83020491w1+26508051w2, u2=69526858-19515375w1+3496338w2,
h=1 Regulator R=150.84862025343603689026898799574
234174098889 a1 -3921307477313 a2 +20580675880559 a3 >= 0
234174098889 a1 +1486906902496 a2 +3642713167700 a3 >= 0
234532638 a1 +1489175795 a2 +3648314494 a3 >= 0
234532638 a1 +2203594193 a2 +7635956119 a3 >= 0
234532638 a1 -3927302626 a2 +20612168155 a3 >= 0
234174098889 a1 +2200226475928 a2 +7624288400645 a3 >= 0

Q(x), x3+x2-206*x+321=0

Integral basis 1, w1=x, w2=(-6-1x+x2)/9
Fundamental units u1=4387271167-2234683149w1+1482931725w2, u2=-29081258642+23228524941w1+13962821601w2,
h=1 Regulator R=170.0129301122090985581274564551687
167963949858 a1 +267069372665 a2 -94466903138 a3 >= 0
167963949858 a1 +2178892828485 a2 +2786528620535 a3 >= 0
26881830849 a1 +348721428026 a2 +445970644836 a3 >= 0
26881830849 a1 -418346440976 a2 +751948890761 a3 >= 0
26881830849 a1 +42743182101 a2 -15118978241 a3 >= 0
167963949858 a1 -2613926151008 a2 +4698352076355 a3 >= 0

Q(x), x3-x2-210*x+1075=0

Integral basis 1, w1=x, w2=(4x+x2)/5
Fundamental units u1=-14524+925w1+760w2, u2=2896-760w1+165w2,
h=1 Regulator R=47.72418403123679298313574370500
1410815 a1 +8403414 a2 +16733572 a3 >= 0
1410815 a1 +15776649 a2 +47906234 a3 >= 0
4390 a1 +26493 a2 +53501 a3 >= 0
4390 a1 +47316 a2 +149413 a3 >= 0
4390 a1 -69419 a2 +170236 a3 >= 0
1410815 a1 -22769248 a2 +55279469 a3 >= 0

Q(x), x3-219*x+730=0

Integral basis 1, w1=x, w2=(-2+x+x2)/8
Fundamental units u1=470897-172976w1+80232w2, u2=-1198495+253208w1+172976w2,
h=9, Classgroup C3xC3
33836824 a1 +430099721 a2 +728677712 a3 >= 0
33836824 a1 +119614880 a2 +59348231 a3 >= 0
239384 a1 +846289 a2 +419983 a3 >= 0
239384 a1 -3888929 a2 +7351552 a3 >= 0
239384 a1 +3042640 a2 +5155201 a3 >= 0
33836824 a1 -549714601 a2 +1039162553 a3 >= 0

Q(x), x3-x2-220*x+1273=0

Integral basis 1, w1=x, w2=(2+x2)/3
Fundamental units u1=-403345164278+30351368139w1+9707793693w2, u2=30352961065-7251819573w1+1227987060w2,
h=1 Regulator R=233.439377120402248490408944767288
119957034966474 a1 +880109443907186 a2 +2232388215650205 a3 >= 0
119957034966474 a1 +1245092235918411 a2 +4387776720394064 a3 >= 0
88925711853 a1 +652436591108 a2 +1654898457851 a3 >= 0
88925711853 a1 +923003073328 a2 +3252716037102 a3 >= 0
88925711853 a1 -1486513952583 a2 +8342316571144 a3 >= 0
119957034966474 a1 -2005244644859123 a2 +11253433273960357 a3 >= 0

Q(x), x3-x2-224*x+997=0

Integral basis 1, w1=x, w2=(6+2x+x2)/7
Fundamental units u1=862-574w1+343w2, u2=-4794+917w1+574w2,
h=1 Regulator R=60.80969381779724007104507037071
9106349 a1 +44230677 a2 +51133330 a3 >= 0
9106349 a1 -149206348 a2 +314421698 a3 >= 0
3570 a1 +8593 a2 +31947 a3 >= 0
3570 a1 -46593 a2 +120110 a3 >= 0
3570 a1 +41570 a2 +87133 a3 >= 0
9106349 a1 +114082020 a2 +244570355 a3 >= 0

Q(x), x3+x2-226*x+503=0

Integral basis 1, w1=x, w2=(-1+x2)/9
Fundamental units u1=-85715+32892w1+20820w2, u2=105361-52008w1+30156w2,
h=3, Classgroup C3 Regulator R=49.065148122430251159131005875231
22332 a1 +51435 a2 +10681 a3 >= 0
22332 a1 -368963 a2 +674840 a3 >= 0
8940 a1 -147704 a2 +270153 a3 >= 0
8940 a1 +118173 a2 +172571 a3 >= 0
8940 a1 +20591 a2 +4276 a3 >= 0
22332 a1 +295196 a2 +431079 a3 >= 0

Q(x), x3+x2-226*x-176=0

Integral basis 1, w1=x, w2=(4+5x+x2)/10
Fundamental units u1=-26735-32784w1+17120w2, u2=272209+381904w1+349456w2,
h=12, Classgroup C6xC2
147408 a1 -114708 a2 +10535 a3 >= 0
147408 a1 +2200585 a2 +4444405 a3 >= 0
6608 a1 +98645 a2 +199228 a3 >= 0
6608 a1 -100108 a2 +104265 a3 >= 0
6608 a1 -5145 a2 +475 a3 >= 0
147408 a1 -2233285 a2 +2325828 a3 >= 0

Q(x), x3+x2-230*x+128=0

Integral basis 1, w1=x, w2=(2+7x+x2)/10
Fundamental units u1=-14995019343+1241919280w1+22982992368w2, u2=716106533265+22982992368w1-24224911648w2,
h=1 Regulator R=540.96883911971627306055941738388
13256552956128465076336 a1 +7405595280581478651499 a2 +8248930922667180875439 a3 >= 0
13256552956128465076336 a1 -211261511655969738997436 a2 +191442699061345497493541 a3 >= 0
63186916976 a1 -700659423889 a2 +655885195636 a3 >= 0
63186916976 a1 +345553947909 a2 +1648463178529 a3 >= 0
63186916976 a1 +291918559004 a2 +602249806731 a3 >= 0
13256552956128465076336 a1 +190599363419259795269601 a2 +410109805997896715142476 a3 >= 0

Q(x), x3-x2-234*x+729=0

Integral basis 1, w1=x, w2=(-1x+x2)/9
Fundamental units u1=8140-2934w1+1629w2, u2=196-27w1+9w2,
h=12, Classgroup C6xC2
1863 a1 -30200 a2 +57748 a3 >= 0
1863 a1 +26077 a2 +37657 a3 >= 0
18 a1 +191 a2 +386 a3 >= 0
18 a1 +80 a2 +53 a3 >= 0
18 a1 -253 a2 +497 a3 >= 0
1863 a1 +5986 a2 +1471 a3 >= 0

Q(x), x3+x2-234*x-1432=0

Integral basis 1, w1=x, w2=(x+x2)/2
Fundamental units u1=3988221801+184832232w1-45377128w2, u2=-2964167671-213590760w1+42053408w2,
h=3, Classgroup C3 Regulator R=160.57107626149267130194750901210
11614953880 a1 +200991780589 a2 +1839534042387 a3 >= 0
11614953880 a1 -94621170958 a2 +338104892099 a3 >= 0
7642008 a1 +132241407 a2 +1210312070 a3 >= 0
7642008 a1 -62255605 a2 +222454805 a3 >= 0
7642008 a1 -77627810 a2 +355462997 a3 >= 0
11614953880 a1 -117985563511 a2 +540260273434 a3 >= 0

Q(x), x3-237*x+316=0

Integral basis 1, w1=x, w2=(2+7x+x2)/10
Fundamental units u1=-4833087+1577448w1+2054240w2, u2=-126655+41352w1+53848w2,
h=12, Classgroup C6xC2
3504344 a1 +51440218 a2 +112218043 a3 >= 0
3504344 a1 -56148539 a2 +51361183 a3 >= 0
91864 a1 -1471849 a2 +1346426 a3 >= 0
91864 a1 +123398 a2 +121373 a3 >= 0
91864 a1 +1348451 a2 +2941673 a3 >= 0
3504344 a1 +4708321 a2 +4629286 a3 >= 0

Q(x), x3-237*x+1027=0

Integral basis 1, w1=x, w2=(3+3x+x2)/7
Fundamental units u1=501-315w1+175w2, u2=15796-175w1-490w2,
h=3, Classgroup C3 Regulator R=52.474727275760031605898181185357
1174330 a1 +5636729 a2 +6784168 a3 >= 0
1174330 a1 +14588693 a2 +32646319 a3 >= 0
905 a1 +10507 a2 +23027 a3 >= 0
905 a1 -12719 a2 +31322 a3 >= 0
905 a1 +2212 a2 +8096 a3 >= 0
1174330 a1 -20225422 a2 +41598283 a3 >= 0

Q(x), x3-x2-240*x+988=0

Integral basis 1, w1=x, w2=(-6+x+x2)/8
Fundamental units u1=132119857-1429120w1-4817736w2, u2=12000473-3388616w1+1429120w2,
h=3, Classgroup C3 Regulator R=183.74793771909757326794054332931
369104931976 a1 -6198729804009 a2 +11960974940962 a3 >= 0
369104931976 a1 +4947981233418 a2 +8632847210111 a3 >= 0
1312520 a1 +17498049 a2 +30726889 a3 >= 0
1312520 a1 +5789009 a2 +2963342 a3 >= 0
1312520 a1 -21974538 a2 +42435929 a3 >= 0
369104931976 a1 +1619853502567 a2 +814263903535 a3 >= 0

Q(x), x3+x2-244*x+1276=0

Integral basis 1, w1=x, w2=(-2-1x+x2)/4
Fundamental units u1=-27809162433808027271+2991418451913015520w1+945125032062163832w2, u2=52941405972437352393-2358380131303899736w1-1101168387788687856w2,
h=1 Regulator R=695.348679422079484357787837494279
200618646109962060406712 a1 -3656724595093114290398489 a2 +17476872777571134027747130 a3 >= 0
200618646109962060406712 a1 +2138677742986423030681672 a2 +5064818564422365554215241 a3 >= 0
317513899161190072 a1 -5787402651048708385 a2 +27660190756690722611 a3 >= 0
317513899161190072 a1 +3384829488145702961 a2 +8015956253898012310 a3 >= 0
317513899161190072 a1 +2085059263741815352 a2 +2743034787915263791 a3 >= 0
200618646109962060406712 a1 +1317428205996729199310105 a2 +1733164837311909727249781 a3 >= 0

Q(x), x3-x2-246*x+520=0

Integral basis 1, w1=x, w2=(7x+x2)/10
Fundamental units u1=1032408768726830401-777129807060821504w1+321331214378495520w2, u2=18929116326134398305+455798592682325984w1-777129807060821504w2,
h=1 Regulator R=623.268317229293453402427086678173
9533415466243799108128 a1 +20352374728003718262159 a2 +18591581069681442630094 a3 >= 0
9533415466243799108128 a1 +143476481856463142208082 a2 +316363504044367646200289 a3 >= 0
574583038063888928 a1 +8647389083976038817 a2 +19067364044920919567 a3 >= 0
574583038063888928 a1 -9299452397834807791 a2 +8541265295163453874 a3 >= 0
574583038063888928 a1 +1226646351922657902 a2 +1120522563110072959 a3 >= 0
9533415466243799108128 a1 -154295441118223061362113 a2 +141715688198140866576017 a3 >= 0

Q(x), x3+x2-252*x+729=0

Integral basis 1, w1=x, w2=(x+x2)/9
Fundamental units u1=-312612104+79236783w1+52462026w2, u2=122983981-52462026w1+26774757w2,
h=1 Regulator R=121.73337231643082595144233026541
2400888357 a1 +7301518334 a2 +3278522570 a3 >= 0
2400888357 a1 +32635949522 a2 +52918397117 a3 >= 0
640266786 a1 +1947162475 a2 +874313515 a3 >= 0
640266786 a1 +8703326158 a2 +14112231409 a3 >= 0
640266786 a1 -11290755419 a2 +20868395092 a3 >= 0
2400888357 a1 -42338356213 a2 +78252828305 a3 >= 0

Q(x), x3+x2-256*x-1481=0

Integral basis 1, w1=x, w2=(4+x2)/5
Fundamental units u1=54963665+13208601w1+3492440w2, u2=-424038411-36894522w1+16701041w2,
h=1 Regulator R=131.95044815568536659400714653125
10924034618 a1 -74990692363 a2 +111697596772 a3 >= 0
10924034618 a1 +195652922495 a2 +709580398875 a3 >= 0
74055513 a1 -508371560 a2 +757214308 a3 >= 0
74055513 a1 +1326357087 a2 +4810341082 a3 >= 0
74055513 a1 -892041040 a2 +2208273475 a3 >= 0
10924034618 a1 -131586264750 a2 +325745639243 a3 >= 0

Q(x), x3-x2-262*x+991=0

Integral basis 1, w1=x, w2=(-1+x2)/9
Fundamental units u1=-402812339+79699668w1+53491404w2, u2=169058725-53491404w1+26208264w2,
h=1 Regulator R=122.80855825425077562726141121918
701191524 a1 +2776396079 a2 +1143562281 a3 >= 0
701191524 a1 +10103872120 a2 +16099035035 a3 >= 0
164480340 a1 +651266535 a2 +268248416 a3 >= 0
164480340 a1 +2370091849 a2 +3776392995 a3 >= 0
164480340 a1 -2856878044 a2 +5495218309 a3 >= 0
701191524 a1 -12179076675 a2 +23426511076 a3 >= 0

Q(x), x3+x2-264*x+1028=0

Integral basis 1, w1=x, w2=(-2-5x+x2)/8
Fundamental units u1=3013634793-645103752w1+416447168w2, u2=90460161-19364048w1+12500472w2,
h=3, Classgroup C3 Regulator R=129.83447583640907460040439741491
4646440152 a1 -85459745190 a2 +248728243817 a3 >= 0
4646440152 a1 +61046815283 a2 +60941357816 a3 >= 0
139471960 a1 +1832439053 a2 +1829273833 a3 >= 0
139471960 a1 +593329766 a2 -90187425 a3 >= 0
139471960 a1 -2565240779 a2 +7466062952 a3 >= 0
4646440152 a1 +19766489755 a2 -3004551601 a3 >= 0

Q(x), x3-x2-270*x-1592=0

Integral basis 1, w1=x, w2=(x+x2)/2
Fundamental units u1=-26550318107802935-2055430263502784w1+338436849269848w2, u2=1024108686294745+214391009851368w1+24809167883696w2,
h=1 Regulator R=569.60543145844829695521675495126
32772622598216589788856 a1 -266657624640310263032817 a2 +951514009851208759717910 a3 >= 0
32772622598216589788856 a1 -332531030949989563504516 a2 +1520765881131638936718421 a3 >= 0
1251250195652152 a1 -10180918668289669 a2 +36328557145152011 a3 >= 0
1251250195652152 a1 -12695948062499351 a2 +58062445768834442 a3 >= 0
1251250195652152 a1 +24128116926441172 a2 +244697800107746739 a3 >= 0
32772622598216589788856 a1 +631961278188516416326189 a2 +6409100833133848136343645 a3 >= 0

Q(x), x3-x2-272*x+1755=0

Integral basis 1, w1=x, w2=(x+x2)/3
Fundamental units u1=49407829-10832640w1+1574391w2, u2=-721402484+43518657w1+13981422w2,
h=3, Classgroup C3 Regulator R=132.425924667038904654816367747529
29938445337 a1 +339436688494 a2 +1395969528135 a3 >= 0
29938445337 a1 +248597739566 a2 +770953703702 a3 >= 0
141310002 a1 +1173386037 a2 +3638916827 a3 >= 0
141310002 a1 -2634221221 a2 +15490497750 a3 >= 0
141310002 a1 +1602145186 a2 +6589005787 a3 >= 0
29938445337 a1 -558095982723 a2 +3281873819497 a3 >= 0

Q(x), x3-273*x-728=0

Integral basis 1, w1=x, w2=(8+x+x2)/10
Fundamental units u1=1328337+670840w1+401104w2, u2=29316249+401104w1-1071944w2,
h=9, Classgroup C3xC3
473165848 a1 -7088050424 a2 +10287666149 a3 >= 0
473165848 a1 +8385565461 a2 +16078201536 a3 >= 0
372888 a1 -5585307 a2 +8107621 a3 >= 0
372888 a1 +6608056 a2 +12670179 a3 >= 0
372888 a1 -1022749 a2 +476816 a3 >= 0
473165848 a1 -1297515037 a2 +604585651 a3 >= 0

Q(x), x3-273*x+1547=0

Integral basis 1, w1=x, w2=(3+x+x2)/5
Fundamental units u1=141-25w1+5w2, u2=2531-635w1+160w2,
h=9, Classgroup C3xC3
130 a1 +1561 a2 +4138 a3 >= 0
130 a1 -2450 a2 +8821 a3 >= 0
5 a1 +56 a2 +164 a3 >= 0
5 a1 -91 a2 +332 a3 >= 0
5 a1 +35 a2 +59 a3 >= 0
130 a1 +889 a2 +1471 a3 >= 0

Q(x), x3+x2-274*x+61=0

Integral basis 1, w1=x, w2=(10+7x+x2)/11
Fundamental units u1=-34255612+24639371w1+27254348w2, u2=-321261905+231077143w1+255601371w2,
h=1 Regulator R=123.0084979998921435570458822648067
12096408431 a1 -207664251262 a2 +202943266256 a3 >= 0
12096408431 a1 +192872165760 a2 +413303194589 a3 >= 0
1289819886 a1 -22142893009 a2 +21639502667 a3 >= 0
1289819886 a1 +20565637728 a2 +44069831071 a3 >= 0
1289819886 a1 +287435395 a2 +1361300334 a3 >= 0
12096408431 a1 +2695677071 a2 +12766777567 a3 >= 0

Q(x), x3+x2-276*x-307=0

Integral basis 1, w1=x, w2=(8+5x+x2)/11
Fundamental units u1=30866445+37516802w1+32582155w2, u2=2532570+3078212w1+2673329w2,
h=1 Regulator R=101.495475562859056917674653770921
1749354590 a1 +29154703207 a2 +58696360176 a3 >= 0
1749354590 a1 -28957332146 a2 +31685753681 a3 >= 0
143532603 a1 -2375916611 a2 +2599781121 a3 >= 0
143532603 a1 -159726870 a2 +47943373 a3 >= 0
143532603 a1 +2392110878 a2 +4815970862 a3 >= 0
1749354590 a1 -1946725651 a2 +584324823 a3 >= 0

Q(x), x3+x2-284*x+1011=0

Integral basis 1, w1=x, w2=(-3+2x+x2)/9
Fundamental units u1=1989121-22155w1-67620w2, u2=126001-45465w1+22155w2,
h=4, Classgroup C2xC2
598046190 a1 +8417248683 a2 +14834399452 a3 >= 0
598046190 a1 +2275429462 a2 +1268245655 a3 >= 0
17115 a1 +237400 a2 +416832 a3 >= 0
17115 a1 +57417 a2 +47483 a3 >= 0
17115 a1 -311932 a2 +596815 a3 >= 0
598046190 a1 -11290724335 a2 +20976218673 a3 >= 0

Q(x), x3-x2-286*x+509=0

Integral basis 1, w1=x, w2=(+7x+x2)/11
Fundamental units u1=22582+299w1-780w2, u2=664-780w1+481w2,
h=1 Regulator R=64.085351242954853253190136451257
8053383 a1 +132720740 a2 +284032049 a3 >= 0
8053383 a1 +14403798 a2 +12240154 a3 >= 0
2054 a1 +28459 a2 +60053 a3 >= 0
2054 a1 -3324 a2 +8513 a3 >= 0
2054 a1 -23081 a2 +40296 a3 >= 0
8053383 a1 -139071155 a2 +130557096 a3 >= 0

Q(x), x3-x2-290*x+1000=0

Integral basis 1, w1=x, w2=(9x+x2)/10
Fundamental units u1=82885057818641-42112277669312w1+14992692763312w2, u2=-174645477798431+14992692763312w1+27119584906000w2,
h=3, Classgroup C3 Regulator R=325.65935769504100502479514948211
1090800947595536 a1 +16938353793508713 a2 +41547010162675742 a3 >= 0
1090800947595536 a1 +3883438364851845 a2 +4877665158402007 a3 >= 0
68194485551376 a1 +242784058856318 a2 +304940939868405 a3 >= 0
68194485551376 a1 -1233538344464057 a2 +1121105652171202 a3 >= 0
68194485551376 a1 +1058948771159115 a2 +2597428055491577 a3 >= 0
1090800947595536 a1 -19730991210765022 a2 +17932580587058875 a3 >= 0

Q(x), x3+x2-290*x+1613=0

Integral basis 1, w1=x, w2=(2+2x+x2)/5
Fundamental units u1=35876-905w1-740w2, u2=-14669+1315w1+575w2,
h=3, Classgroup C3 Regulator R=55.84964291883745973479275251419
5840715 a1 +69911466 a2 +197664350 a3 >= 0
5840715 a1 -115540112 a2 +413239463 a3 >= 0
4390 a1 -77821 a2 +300118 a3 >= 0
4390 a1 +22344 a2 +71045 a3 >= 0
4390 a1 +51087 a2 +142467 a3 >= 0
5840715 a1 +39787931 a2 +72459842 a3 >= 0

Q(x), x3-291*x+485=0

Integral basis 1, w1=x, w2=(4+8x+x2)/11
Fundamental units u1=48159+1271w1-1562w2, u2=14805-1562w1+291w2,
h=3, Classgroup C3 Regulator R=76.74535903665502115500040035774
200933497 a1 -3584224205 a2 +3278621855 a3 >= 0
200933497 a1 +3246043114 a2 +7201027151 a3 >= 0
20042 a1 +179741 a2 +635557 a3 >= 0
20042 a1 +95060 a2 +181015 a3 >= 0
20042 a1 -274801 a2 +265696 a3 >= 0
200933497 a1 +338181091 a2 +370759832 a3 >= 0

Q(x), x3-291*x+1358=0

Integral basis 1, w1=x, w2=(-2-5x+x2)/8
Fundamental units u1=12551804308353-2402029242464w1+1369139473552w2, u2=-45096897510783+8911476905584w1+3771168716016w2,
h=3, Classgroup C3 Regulator R=288.303769039692602087373996858375
40969956136336 a1 +210209823364663 a2 -6804806486088 a3 >= 0
40969956136336 a1 -779873930393489 a2 +2332816984694379 a3 >= 0
2838196979600 a1 +14562302282438 a2 -471403512141 a3 >= 0
2838196979600 a1 -54025828740103 a2 +161606082708168 a3 >= 0
2838196979600 a1 +39463526457665 a2 +43215503335173 a3 >= 0
40969956136336 a1 +569664107028826 a2 +623824663607901 a3 >= 0

Q(x), x3+x2-294*x+1439=0

Integral basis 1, w1=x, w2=(6+5x+x2)/7
Fundamental units u1=-553670+43855w1+33663w2, u2=1650497-10192w1-43855w2,
h=1 Regulator R=98.175725834100938581600947219789
7058686231 a1 -138830628093 a2 +296961055145 a3 >= 0
7058686231 a1 +92259154446 a2 +244214688115 a3 >= 0
1190150 a1 -23212848 a2 +50025467 a3 >= 0
1190150 a1 +15511117 a2 +41025931 a3 >= 0
1190150 a1 +6511581 a2 +11301502 a3 >= 0
7058686231 a1 +39512787416 a2 +65871272606 a3 >= 0

Q(x), x3-x2-296*x+1317=0

Integral basis 1, w1=x, w2=(-6+x+x2)/9
Fundamental units u1=541741-146061w1+63648w2, u2=88333-23814w1+10377w2,
h=3, Classgroup C3 Regulator R=54.074164850746208747476655647865
264411 a1 -4932173 a2 +9498139 a3 >= 0
264411 a1 +3945508 a2 +6803707 a3 >= 0
43110 a1 +643274 a2 +1109291 a3 >= 0
43110 a1 +203981 a2 +101165 a3 >= 0
43110 a1 -804145 a2 +1548584 a3 >= 0
264411 a1 +1251076 a2 +620458 a3 >= 0

Q(x), x3+x2-296*x+461=0

Integral basis 1, w1=x, w2=(7+9x+x2)/11
Fundamental units u1=-7150+1554w1+2179w2, u2=75-113w1+48w2,
h=3, Classgroup C3 Regulator R=25.97705806654270627044170837094
13834 a1 +219205 a2 +503898 a3 >= 0
13834 a1 +21847 a2 +29807 a3 >= 0
425 a1 +6674 a2 +15327 a3 >= 0
425 a1 +578 a2 +976 a3 >= 0
425 a1 -7677 a2 +7072 a3 >= 0
13834 a1 -254886 a2 +227165 a3 >= 0

Q(x), x3+x2-302*x-739=0

Integral basis 1, w1=x, w2=(+3x+x2)/11
Fundamental units u1=25802+10256w1+7029w2, u2=5342909+2141051w1+1469506w2,
h=1 Regulator R=66.93752020061887902656325808439
94710503 a1 -1567442548 a2 +1939389660 a3 >= 0
94710503 a1 +1707332651 a2 +3272231602 a3 >= 0
453742 a1 -7502180 a2 +9294233 a3 >= 0
453742 a1 +8175315 a2 +15669536 a3 >= 0
453742 a1 -1126877 a2 -7959 a3 >= 0
94710503 a1 -234600606 a2 -2543597 a3 >= 0

Q(x), x3-309*x-2060=0

Integral basis 1, w1=x, w2=(x+x2)/2
Fundamental units u1=-2559164831911-167914008776w1+27670498008w2, u2=3335732892721+149698614408w1-29561518736w2,
h=3, Classgroup C3 Regulator R=331.53236516996631046575382029806
349456374449848 a1 -3189816863468623 a2 +12963320243429049 a3 >= 0
349456374449848 a1 +7081602007562180 a2 +75293801750238801 a3 >= 0
353029688 a1 +7154002093 a2 +76063635762 a3 >= 0
353029688 a1 -3931567433 a2 +19926655359 a3 >= 0
353029688 a1 -3222434660 a2 +13095882471 a3 >= 0
349456374449848 a1 -3891785144093557 a2 +19724897711335182 a3 >= 0

Q(x), x3-309*x+721=0

Integral basis 1, w1=x, w2=(3+9x+x2)/11
Fundamental units u1=296256-229624w1+91365w2, u2=4852-3709w1+1474w2,
h=3, Classgroup C3 Regulator R=49.163271459923916757501246265034
19730 a1 -367883 a2 +327976 a3 >= 0
19730 a1 +320989 a2 +742753 a3 >= 0
319 a1 +5183 a2 +12005 a3 >= 0
319 a1 +761 a2 +878 a3 >= 0
319 a1 -5944 a2 +5300 a3 >= 0
19730 a1 +46894 a2 +53881 a3 >= 0

Q(x), x3-x2-316*x+2144=0

Integral basis 1, w1=x, w2=(-1x+x2)/4
Fundamental units u1=7089-240w1-112w2, u2=24785-4656w1+928w2,
h=12, Classgroup C6xC2
1040 a1 +13073 a2 +37813 a3 >= 0
1040 a1 -20872 a2 +109937 a3 >= 0
16 a1 -311 a2 +1670 a3 >= 0
16 a1 +127 a2 +283 a3 >= 0
16 a1 +200 a2 +575 a3 >= 0
1040 a1 +8839 a2 +16570 a3 >= 0

Q(x), x3-x2-316*x-703=0

Integral basis 1, w1=x, w2=(5+x+x2)/11
Fundamental units u1=-118-42w1+31w2, u2=251+31w1+11w2,
h=3, Classgroup C3 Regulator R=28.88852976726552016079151141727
18027 a1 -41076 a2 +12964 a3 >= 0
18027 a1 -288473 a2 +401616 a3 >= 0
110 a1 -450 a2 +387 a3 >= 0
110 a1 -1253 a2 +2650 a3 >= 0
110 a1 +1813 a2 +3453 a3 >= 0
18027 a1 +347576 a2 +649013 a3 >= 0

Q(x), x3+x2-322*x+1361=0

Integral basis 1, w1=x, w2=(-1-6x+x2)/9
Fundamental units u1=-45196338671+10638447489w1+4423931394w2, u2=13580050567-2633346693w1+1790584701w2,
h=1 Regulator R=273.58850145090345044730887829166
5136523821855930 a1 +23592917770557449 a2 -4258643476176508 a3 >= 0
5136523821855930 a1 +75212855837748000 a2 +71656633657351769 a3 >= 0
57431865621 a1 +263794517252 a2 -47615777762 a3 >= 0
57431865621 a1 +840959652541 a2 +801199639615 a3 >= 0
57431865621 a1 -1162186035414 a2 +3381510462859 a3 >= 0
5136523821855930 a1 -103942297430161379 a2 +302431724992451699 a3 >= 0

Q(x), x3+x2-324*x-1009=0

Integral basis 1, w1=x, w2=(8+2x+x2)/11
Fundamental units u1=5076+2010w1+1235w2, u2=-528559-137460w1+85195w2,
h=3, Classgroup C3 Regulator R=46.61388088318667655777884395826
107105 a1 -340853 a2 +114532 a3 >= 0
107105 a1 -1793820 a2 +2482953 a3 >= 0
2530 a1 -42358 a2 +58625 a3 >= 0
2530 a1 +47853 a2 +92958 a3 >= 0
2530 a1 -8025 a2 +2747 a3 >= 0
107105 a1 +2027568 a2 +3935920 a3 >= 0

Q(x), x3+x2-324*x-36=0

Integral basis 1, w1=x, w2=(6+7x+x2)/12
Fundamental units u1=-4837187630598983+14159872656787632w1+14694041614391160w2, u2=793720059924051313+14694041614391160w1-28853914271178792w2,
h=3, Classgroup C3 Regulator R=523.53203226827143031007791870231
14657144334866217960 a1 -270463735250001468481 a2 +265456673463850434236 a3 >= 0
14657144334866217960 a1 +257434666351393761477 a2 +534292333277593391761 a3 >= 0
4639886031207912 a1 -85618376845044628 a2 +84033334390104909 a3 >= 0
4639886031207912 a1 +81493876642199209 a2 +169136325406787044 a3 >= 0
4639886031207912 a1 -515385828362493 a2 +2024071919543207 a3 >= 0
14657144334866217960 a1 -1628075436258510956 a2 +6393931676198161803 a3 >= 0

Q(x), x3-327*x+2071=0

Integral basis 1, w1=x, w2=(2+2x+x2)/5
Fundamental units u1=65823-4032w1-355w2, u2=196371-2967w1-3322w2,
h=3, Classgroup C3 Regulator R=90.74073405181031319018773934351
391723379 a1 +5054620158 a2 +15223040889 a3 >= 0
391723379 a1 -8096452529 a2 +30386901363 a3 >= 0
16734 a1 +107801 a2 +774991 a3 >= 0
16734 a1 -254297 a2 +1098394 a3 >= 0
16734 a1 +146496 a2 +335503 a3 >= 0
391723379 a1 +3041832371 a2 +6097543776 a3 >= 0

Q(x), x3-327*x+1853=0

Integral basis 1, w1=x, w2=(6+5x+x2)/7
Fundamental units u1=-123829+7946w1+6235w2, u2=20939-6235w1+1711w2,
h=3, Classgroup C3 Regulator R=58.93741229652034957511486242267
112723 a1 +733897 a2 +1303421 a3 >= 0
112723 a1 +1569818 a2 +4341033 a3 >= 0
870 a1 +5668 a2 +10073 a3 >= 0
870 a1 +12099 a2 +33508 a3 >= 0
870 a1 -17767 a2 +39939 a3 >= 0
112723 a1 -2303715 a2 +5176954 a3 >= 0

Q(x), x3-x2-330*x+2349=0

Integral basis 1, w1=x, w2=(2x+x2)/3
Fundamental units u1=488283826-100841013w1+12826296w2, u2=11759928700-291466098w1-139319901w2,
h=1 Regulator R=216.176819021948233021264164511507
102624261396849 a1 +1262715036172052 a2 +6020732437692256 a3 >= 0
102624261396849 a1 -2112057941444737 a2 +13081026262428352 a3 >= 0
1399540626 a1 +17219500345 a2 +82109552867 a3 >= 0
1399540626 a1 -28802506952 a2 +178390520573 a3 >= 0
1399540626 a1 +12982547233 a2 +48798404906 a3 >= 0
102624261396849 a1 +951967166669534 a2 +3578203068583021 a3 >= 0

Q(x), x3-x2-336*x+1719=0

Integral basis 1, w1=x, w2=(-6+2x+x2)/9
Fundamental units u1=930208-7713w1-27450w2, u2=-229730+27450w1+19737w2,
h=4, Classgroup C2xC2
28175949 a1 +437154506 a2 +831975254 a3 >= 0
28175949 a1 -564731035 a2 +1113377282 a3 >= 0
259686 a1 -5203625 a2 +10261189 a3 >= 0
259686 a1 +1434586 a2 +1028839 a3 >= 0
259686 a1 +4028725 a2 +7667050 a3 >= 0
28175949 a1 +155752478 a2 +111491741 a3 >= 0

Q(x), x3+x2-342*x+2016=0

Integral basis 1, w1=x, w2=(x+x2)/6
Fundamental units u1=-533441880113015+46907952142680w1+21138561562368w2, u2=72713395012729-16507732544424w1+4630829017944w2,
h=3, Classgroup C3 Regulator R=635.84793870154958891431380992114
45268014679569618174456 a1 -968388240945242853181250 a2 +3291281855493148539408191 a3 >= 0
45268014679569618174456 a1 +320411169541413039409181 a2 +431385147336989598038897 a3 >= 0
2444110338552 a1 +17297947540059 a2 +23295094388848 a3 >= 0
2444110338552 a1 +32541093057458 a2 +77633047347577 a3 >= 0
2444110338552 a1 -52283150936069 a2 +177700436858503 a3 >= 0
45268014679569618174456 a1 +602709056724260195597613 a2 +1437886670640798334440896 a3 >= 0

Q(x), x3+x2-342*x+989=0

Integral basis 1, w1=x, w2=(10+x2)/11
Fundamental units u1=4354-2164w1+1235w2, u2=604-11w1-17w2,
h=3, Classgroup C3 Regulator R=24.73305792489996980763759008794
7346 a1 -148941 a2 +281192 a3 >= 0
7346 a1 +119580 a2 +183627 a3 >= 0
55 a1 -624 a2 +1929 a3 >= 0
55 a1 +719 a2 +1060 a3 >= 0
55 a1 -150 a2 +586 a3 >= 0
7346 a1 +22015 a2 +12671 a3 >= 0

Q(x), x3+x2-344*x+1913=0

Integral basis 1, w1=x, w2=(+6x+x2)/7
Fundamental units u1=223176-1016w1-5225w2, u2=18239-4209w1+1016w2,
h=1 Regulator R=75.358347735327155809363815933604
445421918 a1 -9501305901 a2 +20872882091 a3 >= 0
445421918 a1 +6173958797 a2 +17580848480 a3 >= 0
158491 a1 +2096154 a2 +6276829 a3 >= 0
158491 a1 +1046626 a2 +1928932 a3 >= 0
158491 a1 -3301271 a2 +7326357 a3 >= 0
445421918 a1 +2881925186 a2 +5197617393 a3 >= 0

Q(x), x3-x2-346*x-2155=0

Integral basis 1, w1=x, w2=(2x+x2)/5
Fundamental units u1=39182707+1512687w1-703981w2, u2=2086956+389806w1+104725w2,
h=1 Regulator R=109.291143324469303675815989988122
14424979971 a1 -185701401086 a2 +403848496481 a3 >= 0
14424979971 a1 -111702219987 a2 +128316037648 a3 >= 0
21207446 a1 -273012696 a2 +593720545 a3 >= 0
21207446 a1 -164203421 a2 +188712111 a3 >= 0
21207446 a1 +458423563 a2 +2165402338 a3 >= 0
14424979971 a1 +311828601044 a2 +1472907681840 a3 >= 0

Q(x), x3+x2-350*x-2608=0

Integral basis 1, w1=x, w2=(x+x2)/2
Fundamental units u1=2899185922259929+113855978905032w1-22500499353920w2, u2=253978600324345+43968179067288w1+4138509960200w2,
h=1 Regulator R=302.177609513864395985897933819371
38686537642424 a1 -469190595743374 a2 +2610578095115211 a3 >= 0
38686537642424 a1 +822023690126999 a2 +9144320488184401 a3 >= 0
12652268107192 a1 +268839362521417 a2 +2990611244251644 a3 >= 0
12652268107192 a1 -128044835632706 a2 +583904095963709 a3 >= 0
12652268107192 a1 -153446794995903 a2 +853778497301847 a3 >= 0
38686537642424 a1 -391519632026049 a2 +1785389591548788 a3 >= 0

Q(x), x3-x2-352*x-1840=0

Integral basis 1, w1=x, w2=(-4-5x+x2)/8
Fundamental units u1=661092274305+187100115872w1+58857328592w2, u2=-2870848440943-245957444464w1+187100115872w2,
h=3, Classgroup C3 Regulator R=318.67745096718942668492415947423
10342167485304656 a1 -61167618325313019 a2 +78279826189788996 a3 >= 0
10342167485304656 a1 +221643030884046028 a2 +450056102147263377 a3 >= 0
452006699856 a1 -2673344144943 a2 +3421237035973 a3 >= 0
452006699856 a1 +9686957259851 a2 +19669800710876 a3 >= 0
452006699856 a1 -6561606415052 a2 +15781538440767 a3 >= 0
10342167485304656 a1 -150133245073428353 a2 +361090475399148043 a3 >= 0

Q(x), x3-x2-362*x+2335=0

Integral basis 1, w1=x, w2=(4+5x+x2)/7
Fundamental units u1=-33976801765835+1848084467721w1+1470162836883w2, u2=284631855109456-73133443236543w1+18799761117264w2,
h=1 Regulator R=285.193450609481697761899783514144
924512266840602 a1 +6870472140464231 a2 +12729717213844554 a3 >= 0
924512266840602 a1 -19628212125576516 a2 +46040181591373957 a3 >= 0
18584979959937 a1 -394575542247193 a2 +925521361821511 a3 >= 0
18584979959937 a1 +275047063223716 a2 +788587757581209 a3 >= 0
18584979959937 a1 +138113458983414 a2 +255898756350602 a3 >= 0
924512266840602 a1 +13682252251952887 a2 +39228401479885301 a3 >= 0

Q(x), x3-x2-366*x+2605=0

Integral basis 1, w1=x, w2=(2x+x2)/5
Fundamental units u1=626132-127369w1+25921w2, u2=742696-14234w1-12435w2,
h=3, Classgroup C3 Regulator R=51.72583494257468159371936689885
35423 a1 -764028 a2 +2990204 a3 >= 0
35423 a1 +490449 a2 +1554280 a3 >= 0
2458 a1 -53013 a2 +207487 a3 >= 0
2458 a1 +34032 a2 +107849 a3 >= 0
2458 a1 +21439 a2 +45990 a3 >= 0
35423 a1 +309002 a2 +662697 a3 >= 0

Q(x), x3+x2-366*x+1791=0

Integral basis 1, w1=x, w2=(-3-5x+x2)/9
Fundamental units u1=-59755130+11135169w1+4709148w2, u2=16327147-2992275w1+1716873w2,
h=3, Classgroup C3 Regulator R=116.257544481109824393581049478232
30946413 a1 -671098048 a2 +1979550677 a3 >= 0
30946413 a1 +167252157 a2 -2797054 a3 >= 0
405606 a1 +2192123 a2 -36650 a3 >= 0
405606 a1 +6198160 a2 +6945325 a3 >= 0
405606 a1 -8795889 a2 +25945411 a3 >= 0
30946413 a1 +472899478 a2 +529905830 a3 >= 0

Q(x), x3+x2-372*x+2565=0

Integral basis 1, w1=x, w2=(x+x2)/3
Fundamental units u1=66929807840431-2235703198185w1-724639145400w2, u2=2504751196846-477496097460w1+61785761985w2,
h=1 Regulator R=573.55922108714998452471530768156
61761240348551287691310 a1 -1392457980912907305935713 a2 +10000550971863665415474653 a3 >= 0
61761240348551287691310 a1 +758755320543737906980094 a2 +3360097166970609981011447 a3 >= 0
1554307910685 a1 +19002711175306 a2 +84846846583075 a3 >= 0
1554307910685 a1 +14401731432823 a2 +49289303858887 a3 >= 0
1554307910685 a1 -34958750518814 a2 +251332211407918 a3 >= 0
61761240348551287691310 a1 +571941420020618111264309 a2 +1956139467606443950958780 a3 >= 0

Q(x), x3+x2-374*x+1331=0

Integral basis 1, w1=x, w2=(x+x2)/11
Fundamental units u1=-871451952+181631959w1+119992643w2, u2=5884281935-61639316w1-181631959w2,
h=1 Regulator R=256.280698207315923086642450626108
8435234737465211 a1 +31509870772432723 a2 +13565016826143763 a3 >= 0
8435234737465211 a1 -180445382135556090 a2 +334510675587358009 a3 >= 0
5363511906 a1 -114695979984 a2 +212637483811 a3 >= 0
5363511906 a1 +89276709973 a2 +143416531943 a3 >= 0
5363511906 a1 +20055758105 a2 +8664793854 a3 >= 0
8435234737465211 a1 +140500276625658156 a2 +225520269734132576 a3 >= 0

Q(x), x3+x2-380*x+972=0

Integral basis 1, w1=x, w2=(6+11x+x2)/12
Fundamental units u1=314404460059097833-244998363232733448w1+94396384248855936w2, u2=7686692520405208345+150601978983877512w1-244998363232733448w2,
h=3, Classgroup C3 Regulator R=690.80817964029328604784767351997
1000362193661079749766120 a1 +2624477484630129672376002 a2 +3479734476354985214886469 a3 >= 0
1000362193661079749766120 a1 +17527871590527689530202051 a2 +42160317335701573697432693 a3 >= 0
301232513972366952 a1 +5278053146404953893 a2 +12695460165704288106 a3 >= 0
301232513972366952 a1 -6369577372284582114 a2 +5535591081512444723 a3 >= 0
301232513972366952 a1 +790291711907261269 a2 +1047829647014752099 a3 >= 0
1000362193661079749766120 a1 -21152711268818898952344173 a2 +18383128582252545072712518 a3 >= 0

Q(x), x3-x2-382*x-85=0

Integral basis 1, w1=x, w2=(12+5x+x2)/13
Fundamental units u1=-25369-38363w1+20002w2, u2=-904587+1645516w1+1510847w2,
h=3, Classgroup C3 Regulator R=68.76199960833815132895492094391
2502818 a1 -557307 a2 +2105489 a3 >= 0
2502818 a1 +50453689 a2 +99952742 a3 >= 0
30423 a1 +613246 a2 +1214890 a3 >= 0
30423 a1 -576007 a2 +645699 a3 >= 0
30423 a1 -6816 a2 +25637 a3 >= 0
2502818 a1 -47393564 a2 +53116485 a3 >= 0

Q(x), x3-x2-382*x+2209=0

Integral basis 1, w1=x, w2=(-1-6x+x2)/9
Fundamental units u1=48334-7704w1+4197w2, u2=-2651+414w1+177w2,
h=12, Classgroup C6xC2
4413 a1 -94970 a2 +289910 a3 >= 0
4413 a1 +28007 a2 +587 a3 >= 0
66 a1 -1404 a2 +4297 a3 >= 0
66 a1 +425 a2 +19 a3 >= 0
66 a1 +1045 a2 +1228 a3 >= 0
4413 a1 +71376 a2 +80195 a3 >= 0

Q(x), x3+x2-384*x-427=0

Integral basis 1, w1=x, w2=(10+6x+x2)/13
Fundamental units u1=-162892361-125464112w1+66473385w2, u2=498820690+622876190w1+552761373w2,
h=1 Regulator R=134.89755928929733908027319917900
34592029630 a1 -38478137877 a2 +12142483407 a3 >= 0
34592029630 a1 +679698109193 a2 +1367652593546 a3 >= 0
3691663511 a1 +72537423510 a2 +145955967846 a3 >= 0
3691663511 a1 -72122697626 a2 +77939659615 a3 >= 0
3691663511 a1 -4106389395 a2 +1295846710 a3 >= 0
34592029630 a1 -675812000946 a2 +730318730477 a3 >= 0

Q(x), x3-x2-386*x-1760=0

Integral basis 1, w1=x, w2=(7x+x2)/10
Fundamental units u1=121854295777+21538321056w1+15291759264w2, u2=1859316106561+67413598848w1-52121839584w2,
h=3, Classgroup C3 Regulator R=378.52980604505245638359987017412
202782400120382496 a1 -1000485148999567271 a2 -206721552252548723 a3 >= 0
202782400120382496 a1 -3275311257262976581 a2 +2997516294866535586 a3 >= 0
16456858656 a1 -265807300812 a2 +243262189775 a3 >= 0
16456858656 a1 +363455324999 a2 +1057140950867 a3 >= 0
16456858656 a1 -81191165531 a2 -16768165474 a3 >= 0
202782400120382496 a1 +4478578806382926348 a2 +13026232466775847825 a3 >= 0

Q(x), x3-x2-390*x-347=0

Integral basis 1, w1=x, w2=(7+4x+x2)/13
Fundamental units u1=247262+396214w1+328697w2, u2=-774381-724911w1+396214w2,
h=1 Regulator R=118.400800902286449499651011957498
46386381438 a1 -41451841821 a2 +15072271991 a3 >= 0
46386381438 a1 +959041738207 a2 +1845317525146 a3 >= 0
21517211 a1 -19181732 a2 +7076569 a3 >= 0
21517211 a1 +444784862 a2 +855947350 a3 >= 0
21517211 a1 -404085919 a2 +471043163 a3 >= 0
46386381438 a1 -871203514948 a2 +1015565852019 a3 >= 0

Q(x), x3-399*x-2926=0

Integral basis 1, w1=x, w2=(-2-1x+x2)/4
Fundamental units u1=737+112w1+16w2, u2=-7711-448w1+144w2,
h=36, Classgroup C6xC6
1040 a1 -14041 a2 +50381 a3 >= 0
1040 a1 -9823 a2 +25130 a3 >= 0
16 a1 -152 a2 +391 a3 >= 0
16 a1 +361 a2 +1987 a3 >= 0
16 a1 -209 a2 +790 a3 >= 0
1040 a1 +23864 a2 +130409 a3 >= 0

Q(x), x3-399*x-665=0

Integral basis 1, w1=x, w2=(7+4x+x2)/13
Fundamental units u1=-13929-7683w1+4327w2, u2=1226+821w1+637w2,
h=9, Classgroup C3xC3
10991 a1 -209741 a2 +249260 a3 >= 0
10991 a1 -18449 a2 +2621 a3 >= 0
2086 a1 -39805 a2 +47302 a3 >= 0
2086 a1 -3496 a2 +505 a3 >= 0
2086 a1 +43301 a2 +83611 a3 >= 0
10991 a1 +228190 a2 +440552 a3 >= 0

Q(x), x3+x2-400*x+2491=0

Integral basis 1, w1=x, w2=(6+x2)/7
Fundamental units u1=672849489-16327835w1-13672573w2, u2=38719186-8362049w1+2655262w2,
h=1 Regulator R=158.69005209779327125867714565123
2013248873955 a1 +29568506775096 a2 +63764426509241 a3 >= 0
2013248873955 a1 +14816227200092 a2 +17302496035010 a3 >= 0
435185258 a1 +6391514859 a2 +13783255400 a3 >= 0
435185258 a1 +3202545197 a2 +3740434551 a3 >= 0
435185258 a1 -10029245314 a2 +33392985235 a3 >= 0
2013248873955 a1 -46397982849143 a2 +154483195708484 a3 >= 0

Q(x), x3+x2-410*x-1003=0

Integral basis 1, w1=x, w2=(5+4x+x2)/13
Fundamental units u1=9744948+130683w1-307000w2, u2=-711709-307000w1+176317w2,
h=1 Regulator R=139.264284490141253490708002367960
587571313651 a1 -11421247848182 a2 +13789214870639 a3 >= 0
587571313651 a1 +12283893818499 a2 +23760245434853 a3 >= 0
9456158 a1 +195169023 a2 +381327295 a3 >= 0
9456158 a1 -21877204 a2 +3410295 a3 >= 0
9456158 a1 -182747977 a2 +220456522 a3 >= 0
587571313651 a1 -1450217283968 a2 +55103768172 a3 >= 0

Q(x), x3+x2-412*x+1741=0

Integral basis 1, w1=x, w2=(8+2x+x2)/11
Fundamental units u1=39213341-346739w1-1091189w2, u2=2173952-744450w1+346739w2,
h=1 Regulator R=112.243986799112960282587535303222
18089185715 a1 +309743449498 a2 +551634294291 a3 >= 0
18089185715 a1 +81315465701 a2 +61170727676 a3 >= 0
33965206 a1 +581583910 a2 +1035763123 a3 >= 0
33965206 a1 +152667767 a2 +114878473 a3 >= 0
33965206 a1 -768216883 a2 +1464679266 a3 >= 0
18089185715 a1 -409148100914 a2 +780062278088 a3 >= 0

Q(x), x3+x2-416*x+2313=0

Integral basis 1, w1=x, w2=(-4x+x2)/9
Fundamental units u1=4548545245-831419064w1+410842356w2, u2=68120032981-2063946132w1-1653103776w2,
h=1 Regulator R=171.437933275477773155227140521927
70568796036 a1 +440119995427 a2 +109382083736 a3 >= 0
70568796036 a1 +1127441806490 a2 +1500310866053 a3 >= 0
4390449492 a1 +70143981249 a2 +93342092365 a3 >= 0
4390449492 a1 -101916570103 a2 +308164485604 a3 >= 0
4390449492 a1 +27382139362 a2 +6805224787 a3 >= 0
70568796036 a1 -1638130597953 a2 +4953205081559 a3 >= 0

Q(x), x3-417*x+2224=0

Integral basis 1, w1=x, w2=(2+3x+x2)/10
Fundamental units u1=-1564813289139231+162639793808888w1+117074303405928w2, u2=6267181432875617-45565490402960w1-162639793808888w2,
h=3, Classgroup C3 Regulator R=555.385049058384862405646964936241
533465068328816375224 a1 -12106261308899430497401 a2 +23948321619024521494701 a3 >= 0
533465068328816375224 a1 +9011299705817662988429 a2 +18031983516288626015244 a3 >= 0
19468945525304 a1 -441821130827948 a2 +874000184997681 a3 >= 0
19468945525304 a1 +328869710289169 a2 +658081895247291 a3 >= 0
19468945525304 a1 +112951420538779 a2 +103309343880564 a3 >= 0
533465068328816375224 a1 +3094961603081767508972 a2 +2830760604307428008871 a3 >= 0

Q(x), x3-417*x+973=0

Integral basis 1, w1=x, w2=(8+10x+x2)/13
Fundamental units u1=1817+132w1+52w2, u2=57-184w1+132w2,
h=3, Classgroup C3 Regulator R=51.282919857242896154259546665204
1253908 a1 -26959189 a2 +24620411 a3 >= 0
1253908 a1 +2965565 a2 +3592352 a3 >= 0
740 a1 -2780 a2 +5299 a3 >= 0
740 a1 +10981 a2 +24481 a3 >= 0
740 a1 -8201 a2 +19060 a3 >= 0
1253908 a1 +23993624 a2 +54545165 a3 >= 0

Q(x), x3-x2-420*x+2989=0

Integral basis 1, w1=x, w2=(6x+x2)/7
Fundamental units u1=630053-145012w1+33880w2, u2=-1273179+57512w1+46620w2,
h=3, Classgroup C3 Regulator R=56.59379534306801249362765624537
1461156 a1 -33549860 a2 +81292083 a3 >= 0
1461156 a1 +12165173 a2 +24896380 a3 >= 0
469748 a1 -10785955 a2 +26134623 a3 >= 0
469748 a1 +3911000 a2 +8003965 a3 >= 0
469748 a1 +7344703 a2 +22700920 a3 >= 0
1461156 a1 +22845843 a2 +70611413 a3 >= 0

Q(x), x3+x2-420*x-1728=0

Integral basis 1, w1=x, w2=(x+x2)/12
Fundamental units u1=134569+36792w1+20160w2, u2=-284759-56952w1+36792w2,
h=21, Classgroup C21 Regulator R=90.406825793363396246292757987046
4575816 a1 -85071566 a2 +124711809 a3 >= 0
4575816 a1 -19468041 a2 +5279977 a3 >= 0
3528 a1 -15047 a2 +4138 a3 >= 0
3528 a1 +77006 a2 +146631 a3 >= 0
3528 a1 -65487 a2 +96191 a3 >= 0
4575816 a1 +99963791 a2 +190315334 a3 >= 0

Q(x), x3-x2-422*x+3144=0

Integral basis 1, w1=x, w2=(x+x2)/6
Fundamental units u1=102793-2016w1-1752w2, u2=-51239+3240w1+1488w2,
h=36, Classgroup C6xC6
1789224 a1 -41378035 a2 +152590082 a3 >= 0
1789224 a1 +16048740 a2 +26666753 a3 >= 0
2472 a1 -56191 a2 +208675 a3 >= 0
2472 a1 +22363 a2 +37630 a3 >= 0
2472 a1 +36300 a2 +102247 a3 >= 0
1789224 a1 +27118519 a2 +73023749 a3 >= 0

Q(x), x3+x2-426*x-2179=0

Integral basis 1, w1=x, w2=(5+10x+x2)/11
Fundamental units u1=-15743-5883w1+2222w2, u2=6837+783w1+1439w2,
h=1 Regulator R=83.78781358340271590770541885436
1454431238 a1 +32553634175 a2 +96494212736 a3 >= 0
1454431238 a1 -7882699040 a2 -2621121027 a3 >= 0
131967 a1 -377808 a2 +589204 a3 >= 0
131967 a1 -2218289 a2 +1590661 a3 >= 0
131967 a1 +2464130 a2 +8113561 a3 >= 0
1454431238 a1 -26125366373 a2 +19572544855 a3 >= 0

Q(x), x3+x2-430*x-3347=0

Integral basis 1, w1=x, w2=(2+2x+x2)/5
Fundamental units u1=59543093+1824124w1-854992w2, u2=-33870851-2336696w1+740852w2,
h=1 Regulator R=119.88483617646450884113458016451
12788785364 a1 +299749343486 a2 +1530147425625 a3 >= 0
12788785364 a1 -123638941309 a2 +194722325008 a3 >= 0
7222884 a1 +169278589 a2 +864154529 a3 >= 0
7222884 a1 -69831394 a2 +109985895 a3 >= 0
7222884 a1 -106670079 a2 +275418508 a3 >= 0
12788785364 a1 -188899187541 a2 +487590117339 a3 >= 0

Q(x), x3-x2-432*x+1345=0

Integral basis 1, w1=x, w2=(3+10x+x2)/13
Fundamental units u1=4686088-2671883w1+1096801w2, u2=-7411176+1096801w1+1575082w2,
h=1 Regulator R=198.482121774536840651201703953822
124015930411571 a1 +392330388155792 a2 +425885216357642 a3 >= 0
124015930411571 a1 -2694795640852712 a2 +2460036011310341 a3 >= 0
85968846 a1 +235433101 a2 +319299460 a3 >= 0
85968846 a1 -1807448253 a2 +1741850357 a3 >= 0
85968846 a1 +1657983998 a2 +3784731711 a3 >= 0
124015930411571 a1 +2426481183108491 a2 +5547162040318845 a3 >= 0

Q(x), x3-x2-434*x+2799=0

Integral basis 1, w1=x, w2=(-5x+x2)/9
Fundamental units u1=13754347264152640-2162023346022615w1+1020324949544964w2, u2=181910614442737828-5222998194657507w1-4202673245112543w2,
h=1 Regulator R=586.423284837441681322191258617378
99244681080481166933757 a1 +713075005501395561905270 a2 +173120339492806098813742 a3 >= 0
99244681080481166933757 a1 +1675804125160281286189699 a2 +2213100674916511617595795 a3 >= 0
45684071200917282 a1 +771402095693498163 a2 +1018729142010323660 a3 >= 0
45684071200917282 a1 -1053958983767049680 a2 +3287251357889900867 a3 >= 0
45684071200917282 a1 +328240959274468799 a2 +79690335387834545 a3 >= 0
99244681080481166933757 a1 -2289634449581195681161212 a2 +7141268369316874309231135 a3 >= 0

Q(x), x3+x2-442*x-344=0

Integral basis 1, w1=x, w2=(6+7x+x2)/14
Fundamental units u1=-2551864721614124919507703-3109385526152949945958568w1+1604003948943384781884432w2, u2=1661520936520099369209+2372742796198447117608w1+2226854425892642243944w2,
h=1 Regulator R=808.56920502405763759951222389415
12263755511710900153504888 a1 -259246082927322698010059888 a2 +267079779553614979642865227 a3 >= 0
12263755511710900153504888 a1 -9540913807686076419262579 a2 +1015624522631028947785069 a3 >= 0
18141312908811369325304 a1 -383492993339370949795651 a2 +395081086529467673412824 a3 >= 0
18141312908811369325304 a1 -14113515444428917581440 a2 +1502375210050257779597 a3 >= 0
18141312908811369325304 a1 +379465195874988498051787 a2 +764460564424409705627035 a3 >= 0
12263755511710900153504888 a1 +256523241223297874275817579 a2 +516784948673251601233662536 a3 >= 0

Q(x), x3-x2-444*x+3604=0

Integral basis 1, w1=x, w2=(-2+x+x2)/4
Fundamental units u1=4028752897-682594696w1+105443304w2, u2=111488329-18889560w1+2917952w2,
h=12, Classgroup C6xC2
4338329272 a1 -103661268605 a2 +591143447541 a3 >= 0
4338329272 a1 +45215053674 a2 +126944990175 a3 >= 0
120055352 a1 +1251244013 a2 +3512971596 a3 >= 0
120055352 a1 +1737447765 a2 +6660444531 a3 >= 0
120055352 a1 -2868636426 a2 +16358816665 a3 >= 0
4338329272 a1 +62784544203 a2 +240682331396 a3 >= 0

Q(x), x3+x2-444*x+1728=0

Integral basis 1, w1=x, w2=(x+x2)/12
Fundamental units u1=951365952275700841-298142614581722040w1+153742949007914568w2, u2=-2360483072487763919+451885563589636608w1+298142614581722040w2,
h=3, Classgroup C3 Regulator R=698.63506015719071158008477398313
1163133535474917902631912 a1 +4748730941878565571624971 a2 +2011366487707881990025555 a3 >= 0
1163133535474917902631912 a1 -27066971899165065575772245 a2 +50233445808684529667313162 a3 >= 0
605384112416437608 a1 +2471604659887373022 a2 +1046869752071834917 a3 >= 0
605384112416437608 a1 -14087733058339105283 a2 +26145347096446234853 a3 >= 0
605384112416437608 a1 +11010744286035294653 a2 +17606207470298313222 a3 >= 0
1163133535474917902631912 a1 +21155107421811582101515362 a2 +33827069328751513137422771 a3 >= 0

Q(x), x3+x2-446*x+248=0

Integral basis 1, w1=x, w2=(4+9x+x2)/14
Fundamental units u1=-5560103+4234184w1+4806128w2, u2=-115545743+87991184w1+99876856w2,
h=9, Classgroup C3xC3
744686296 a1 -16301996088 a2 +15223519531 a3 >= 0
744686296 a1 +15142417107 a2 +31940408304 a3 >= 0
35834712 a1 -784460869 a2 +732564147 a3 >= 0
35834712 a1 +728661352 a2 +1536989821 a3 >= 0
35834712 a1 +19964805 a2 +23867600 a3 >= 0
744686296 a1 +414892685 a2 +495995109 a3 >= 0

Q(x), x3+x2-450*x+1301=0

Integral basis 1, w1=x, w2=(7+12x+x2)/13
Fundamental units u1=-77427+8268w1+13364w2, u2=31513-21632w1+8268w2,
h=3, Classgroup C3 Regulator R=52.64401384642058869569500308719
91780 a1 +272481 a2 +363167 a3 >= 0
91780 a1 +1747773 a2 +4222974 a3 >= 0
13364 a1 +39678 a2 +52885 a3 >= 0
13364 a1 +254487 a2 +614901 a3 >= 0
13364 a1 -307529 a2 +267694 a3 >= 0
91780 a1 -2112034 a2 +1838459 a3 >= 0

Q(x), x3-453*x-3473=0

Integral basis 1, w1=x, w2=(3+x+x2)/5
Fundamental units u1=1380626+231805w1+49525w2, u2=227537321+38211040w1+8164905w2,
h=3, Classgroup C3 Regulator R=94.64888741503914243549837126281
961055 a1 -14174132 a2 +39551280 a3 >= 0
961055 a1 +23449321 a2 +119697129 a3 >= 0
5830 a1 -85981 a2 +239934 a3 >= 0
5830 a1 +142247 a2 +726105 a3 >= 0
5830 a1 -56266 a2 +100851 a3 >= 0
961055 a1 -9275189 a2 +16624656 a3 >= 0

Q(x), x3-453*x+604=0

Integral basis 1, w1=x, w2=(6+9x+x2)/14
Fundamental units u1=21975565338333073-31527993262594552w1+14274588397298056w2, u2=1029632361855970449+17253404865296496w1-31527993262594552w2,
h=3, Classgroup C3 Regulator R=564.081579162649897894260439639558
8931051792255676312 a1 +11955360724721854037 a2 +12656310301343852885 a3 >= 0
8931051792255676312 a1 +183826829128281025979 a2 +392265329282627758880 a3 >= 0
278159362648088 a1 +5725322707486576 a2 +12217180744244317 a3 >= 0
278159362648088 a1 -6097674765986381 a2 +5747153919758131 a3 >= 0
278159362648088 a1 +372352058499805 a2 +394183270771360 a3 >= 0
8931051792255676312 a1 -195782189853002880016 a2 +184527778704903024827 a3 >= 0

Q(x), x3+x2-462*x-976=0

Integral basis 1, w1=x, w2=(6+5x+x2)/14
Fundamental units u1=38885838457+511464200w1-1169162336w2, u2=1400590465+657698136w1+511464200w2,
h=3, Classgroup C3 Regulator R=296.418049734538984669242303636524
16066601363791080 a1 -335538322956907326 a2 +387582982543922447 a3 >= 0
16066601363791080 a1 -34117752540518687 a2 -124244130231173 a3 >= 0
4726521832 a1 -98701715837 a2 +114010090466 a3 >= 0
4726521832 a1 -10026610162 a2 -18323863 a3 >= 0
4726521832 a1 +104001804167 a2 +202685196141 a3 >= 0
16066601363791080 a1 +353589474133634933 a2 +689003552960311086 a3 >= 0

Q(x), x3-x2-462*x-3185=0

Integral basis 1, w1=x, w2=(6x+x2)/7
Fundamental units u1=653956+90685w1+35700w2, u2=10891596+431270w1-197785w2,
h=3, Classgroup C3 Regulator R=99.52592719901185629053993495388
1116196255 a1 -9222876486 a2 +2981325340 a3 >= 0
1116196255 a1 -17346484167 a2 +23642543372 a3 >= 0
1360130 a1 -21136203 a2 +28806337 a3 >= 0
1360130 a1 +33729356 a2 +148440635 a3 >= 0
1360130 a1 -11233023 a2 +3650318 a3 >= 0
1116196255 a1 +27685556908 a2 +121830233203 a3 >= 0

Q(x), x3-x2-464*x+3921=0

Integral basis 1, w1=x, w2=(x+x2)/3
Fundamental units u1=593851-98238w1+11127w2, u2=16607770-439365w1-142746w2,
h=3, Classgroup C3 Regulator R=70.81403781031425649504518157105
20479593 a1 +230064532 a2 +938190977 a3 >= 0
20479593 a1 +291908160 a2 +1484217724 a3 >= 0
1710894 a1 +24386419 a2 +123993501 a3 >= 0
1710894 a1 -41895307 a2 +328005316 a3 >= 0
1710894 a1 +19219782 a2 +78378323 a3 >= 0
20479593 a1 -501493099 a2 +3926265129 a3 >= 0

Q(x), x3+x2-464*x+3044=0

Integral basis 1, w1=x, w2=(-6-1x+x2)/8
Fundamental units u1=-918398105879+90610871416w1+40088111168w2, u2=168345342297-29653462088w1+10434649080w2,
h=3, Classgroup C3 Regulator R=253.339520086212484208486785396165
124125208334360 a1 -3070188856394586 a2 +9783170932452903 a3 >= 0
124125208334360 a1 +949839488707589 a2 +696729571603505 a3 >= 0
215529935512 a1 +1649293050187 a2 +1209795192328 a3 >= 0
215529935512 a1 +3466226321242 a2 +6373204278401 a3 >= 0
215529935512 a1 -5331049306941 a2 +16987413177639 a3 >= 0
124125208334360 a1 +1996224159352637 a2 +3670373246060632 a3 >= 0

Q(x), x3-x2-466*x-3368=0

Integral basis 1, w1=x, w2=(2+3x+x2)/6
Fundamental units u1=-2190690225045465335-185717977900470168w1+58369844559056064w2, u2=4362434419925710033+148565021788018056w1-68978288782358040w2,
h=4, Classgroup C2xC2
623289462463138970616 a1 +15590486104667843705434 a2 +72997756269937822013921 a3 >= 0
623289462463138970616 a1 -9405732012518908131021 a2 +19161052652731206813787 a3 >= 0
100261539280622328 a1 +2507865492880184269 a2 +11742324952410832740 a3 >= 0
100261539280622328 a1 -1512993924058103146 a2 +3082222224017613559 a3 >= 0
100261539280622328 a1 -894610029541458795 a2 +916514490629259197 a3 >= 0
623289462463138970616 a1 -5561464629685796603797 a2 +5697636684043789559004 a3 >= 0

Q(x), x3-471*x-1727=0

Integral basis 1, w1=x, w2=(11+x+x2)/13
Fundamental units u1=5842+17w1-140w2, u2=1917+123w1+17w2,
h=3, Classgroup C3 Regulator R=47.63408012167307997739519870257
2736050 a1 +63872467 a2 +121927417 a3 >= 0
2736050 a1 -53526167 a2 +78747550 a3 >= 0
2341 a1 -24649 a2 +75167 a3 >= 0
2341 a1 -16642 a2 +17234 a3 >= 0
2341 a1 +41291 a2 +83174 a3 >= 0
2736050 a1 -10346300 a2 +4528783 a3 >= 0

Alar Leibak
Last modified: 17.05.2002