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Label Polynomial Discriminant Galois group Class group Regulator
29.1.186...489.1 $x^{29} - x^{28} + 7 x^{27} + 7 x^{26} + 29 x^{25} + 70 x^{24} + 115 x^{23} + 217 x^{22} + 336 x^{21} + 447 x^{20} + 628 x^{19} + 758 x^{18} + 820 x^{17} + 951 x^{16} + 953 x^{15} + 866 x^{14} + 839 x^{13} + 574 x^{12} + 405 x^{11} + 413 x^{10} + 349 x^{9} + 268 x^{8} + 247 x^{7} - 13 x^{6} - 6 x^{5} + 265 x^{4} + 95 x^{3} - 98 x^{2} + 32 x + 1$ $887^{14}$ $D_{29}$ (as 29T2) trivial $961536136.7336683$
29.1.253...733.1 $x^{29} - x - 1$ $41393681953973\cdot 61230132484136034758796880121$ $S_{29}$ (as 29T8) trivial $3449310408.0836196$
29.1.756...121.1 $x^{29} - 9 x^{28} + 56 x^{27} - 308 x^{26} + 1574 x^{25} - 7243 x^{24} + 28966 x^{23} - 99448 x^{22} + 293090 x^{21} - 744900 x^{20} + 1641343 x^{19} - 3148829 x^{18} + 5274672 x^{17} - 7725970 x^{16} + 9897023 x^{15} - 11084677 x^{14} + 10859104 x^{13} - 9337717 x^{12} + 7122047 x^{11} - 4916951 x^{10} + 3150459 x^{9} - 1890622 x^{8} + 1028653 x^{7} - 470622 x^{6} + 165361 x^{5} - 41848 x^{4} + 8324 x^{3} - 1810 x^{2} + 323 x - 1$ $23^{14}\cdot 97^{14}$ $D_{29}$ (as 29T2) trivial $737823739010.7355$
29.1.107...689.1 $x^{29} - 12 x^{28} + 55 x^{27} - 97 x^{26} + 34 x^{25} + 11 x^{24} + 138 x^{23} - 214 x^{22} + 43 x^{21} + 224 x^{20} - 104 x^{19} - 50 x^{18} + 748 x^{17} - 1490 x^{16} + 1965 x^{15} - 460 x^{14} - 575 x^{13} + 2189 x^{12} - 1286 x^{11} - 53 x^{10} + 3178 x^{9} - 2804 x^{8} + 3117 x^{7} - 748 x^{6} + 585 x^{5} + 965 x^{4} + 480 x^{3} + 353 x^{2} + 369 x - 1$ $2287^{14}$ $D_{29}$ (as 29T2) trivial $4657227595142.479$
29.1.123...441.1 $x^{29} - 8 x^{28} + 6 x^{27} + 45 x^{26} + 49 x^{25} - 158 x^{24} - 252 x^{23} - 117 x^{22} + 459 x^{21} + 1008 x^{20} + 2232 x^{19} + 2691 x^{18} + 1728 x^{17} - 2718 x^{16} - 7677 x^{15} - 13104 x^{14} - 15537 x^{13} - 15042 x^{12} - 6534 x^{11} + 6768 x^{10} + 22065 x^{9} + 32523 x^{8} + 38385 x^{7} + 37197 x^{6} + 29657 x^{5} + 17606 x^{4} + 7536 x^{3} + 1998 x^{2} + 377 x - 1$ $2311^{14}$ $D_{29}$ (as 29T2) trivial $4095120529090.4673$
29.1.190...729.1 $x^{29} - 8 x^{28} + 42 x^{27} - 91 x^{26} + 71 x^{25} - 172 x^{24} + 980 x^{23} - 2477 x^{22} + 4032 x^{21} - 5998 x^{20} + 8995 x^{19} - 12396 x^{18} + 15464 x^{17} - 17477 x^{16} + 17661 x^{15} - 16777 x^{14} + 14899 x^{13} - 10749 x^{12} + 6197 x^{11} - 2594 x^{10} - 1233 x^{9} + 2318 x^{8} - 113 x^{7} - 855 x^{6} + 1459 x^{5} - 2625 x^{4} + 2079 x^{3} - 978 x^{2} + 419 x + 1$ $2383^{14}$ $D_{29}$ (as 29T2) trivial $6346995452652.517$
29.1.358...441.1 $x^{29} - x^{28} - 7 x^{27} - 50 x^{26} + 119 x^{25} + 495 x^{24} + 59 x^{23} - 530 x^{22} + 637 x^{21} + 2591 x^{20} + 2977 x^{19} + 1178 x^{18} + 2213 x^{17} + 5385 x^{16} + 5965 x^{15} + 6650 x^{14} + 10883 x^{13} + 16281 x^{12} + 23955 x^{11} + 21146 x^{10} - 8059 x^{9} - 7103 x^{8} + 28957 x^{7} + 37734 x^{6} + 35524 x^{5} + 2552 x^{4} - 22800 x^{3} - 19616 x^{2} - 17024 x - 11776$ $2939^{14}$ $D_{29}$ (as 29T2) trivial $191758984500558.16$
29.1.894...288.1 $x^{29} + 4 x - 4$ $2^{28}\cdot 27325532669\cdot 12\!\cdots\!17$ $S_{29}$ (as 29T8) trivial $20818517115126.277$
29.1.177...701.1 $x^{29} + 2 x - 1$ $461801\cdot 20212226753\cdot 3536300443131271\cdot 539109057311673427$ $S_{29}$ (as 29T8) trivial $19372925588185.117$
29.1.261...256.1 $x^{29} - 4 x - 4$ $2^{28}\cdot 53\cdot 179\cdot 10\!\cdots\!23$ $S_{29}$ (as 29T8) trivial $28349352931361.156$
29.29.383...121.1 $x^{29} - x^{28} - 28 x^{27} + 27 x^{26} + 351 x^{25} - 325 x^{24} - 2600 x^{23} + 2300 x^{22} + 12650 x^{21} - 10626 x^{20} - 42504 x^{19} + 33649 x^{18} + 100947 x^{17} - 74613 x^{16} - 170544 x^{15} + 116280 x^{14} + 203490 x^{13} - 125970 x^{12} - 167960 x^{11} + 92378 x^{10} + 92378 x^{9} - 43758 x^{8} - 31824 x^{7} + 12376 x^{6} + 6188 x^{5} - 1820 x^{4} - 560 x^{3} + 105 x^{2} + 15 x - 1$ $59^{28}$ $C_{29}$ (as 29T1) trivial $2275980944744796.5$
29.1.506...201.1 $x^{29} - 11 x^{28} + 45 x^{27} - 70 x^{26} + 66 x^{25} - 800 x^{24} + 4130 x^{23} - 11632 x^{22} + 26627 x^{21} - 43970 x^{20} + 56823 x^{19} - 114622 x^{18} + 216543 x^{17} - 400317 x^{16} + 743290 x^{15} - 1619073 x^{14} + 3038554 x^{13} - 4110770 x^{12} + 3834768 x^{11} - 1791942 x^{10} - 198548 x^{9} + 1096532 x^{8} - 913725 x^{7} + 101442 x^{6} + 212195 x^{5} - 352802 x^{4} + 186129 x^{3} - 93243 x^{2} + 23048 x - 4757$ $53^{14}\cdot 67^{14}$ $D_{29}$ (as 29T2) trivial $21909985755609.77$
29.1.574...129.1 $x^{29} - x^{28} + 18 x^{27} + 12 x^{26} + 179 x^{25} + 123 x^{24} + 1662 x^{23} - 196 x^{22} + 11119 x^{21} - 9104 x^{20} + 47466 x^{19} - 44547 x^{18} + 83114 x^{17} - 23886 x^{16} - 121329 x^{15} + 248495 x^{14} - 275546 x^{13} - 188738 x^{12} + 573921 x^{11} - 476142 x^{10} + 379865 x^{9} - 32019 x^{8} + 20658 x^{7} - 6163 x^{6} - 27930 x^{5} + 2012 x^{4} - 1404 x^{3} + 2898 x^{2} - 594 x + 81$ $3583^{14}$ $D_{29}$ (as 29T2) trivial $133207857013622.31$
29.1.771...361.1 $x^{29} - 7 x^{28} + 47 x^{27} - 186 x^{26} + 710 x^{25} - 970 x^{24} + 1144 x^{23} + 2298 x^{22} - 8465 x^{21} + 16505 x^{20} - 20589 x^{19} + 3590 x^{18} + 30661 x^{17} - 81803 x^{16} + 117497 x^{15} - 94780 x^{14} + 10260 x^{13} + 127678 x^{12} - 249606 x^{11} + 245472 x^{10} - 99463 x^{9} - 191187 x^{8} + 582067 x^{7} - 785770 x^{6} + 915704 x^{5} - 793384 x^{4} + 541792 x^{3} - 324448 x^{2} + 144320 x - 23552$ $3659^{14}$ $D_{29}$ (as 29T2) trivial $1075559501191057.0$
29.1.142...409.1 $x^{29} - x^{28} + 33 x^{27} - 64 x^{26} + 535 x^{25} - 1144 x^{24} + 5145 x^{23} - 10327 x^{22} + 31220 x^{21} - 55583 x^{20} + 124455 x^{19} - 188951 x^{18} + 323227 x^{17} - 411652 x^{16} + 521736 x^{15} - 591430 x^{14} + 489137 x^{13} - 738131 x^{12} + 175881 x^{11} - 1211717 x^{10} + 917449 x^{9} - 3034006 x^{8} + 2818536 x^{7} - 6798367 x^{6} + 6818314 x^{5} - 8408506 x^{4} + 7552950 x^{3} - 8000650 x^{2} + 5448750 x - 1749375$ $3823^{14}$ $D_{29}$ (as 29T2) trivial $254102374099303.56$
29.1.671...632.1 $x^{29} - 2 x - 2$ $2^{28}\cdot 3\cdot 11\cdot 563\cdot 13\!\cdots\!43$ $S_{29}$ (as 29T8) trivial $167099208611677.7$
29.1.689...128.1 $x^{29} - x - 2$ $2^{28}\cdot 23\cdot 2505541501481\cdot 44556647066894154934970530051$ $S_{29}$ (as 29T8) trivial $261495167861816.16$
29.1.689...608.1 $x^{29} - x - 4$ $2^{30}\cdot 13\cdot 3373\cdot 84163\cdot 17\!\cdots\!41$ $S_{29}$ (as 29T8) trivial $216030725427151.9$
29.1.689...864.1 $x^{29} - 2$ $2^{28}\cdot 29^{29}$ $F_{29}$ (as 29T6) trivial $170509022606467.78$
29.1.707...096.1 $x^{29} + 2 x - 2$ $2^{28}\cdot 499\cdot 541\cdot 695389\cdot 2739817\cdot 5913513689\cdot 866002650952007$ $S_{29}$ (as 29T8) trivial $88931326459060.03$
29.3.227...419.1 $x^{29} - 3 x - 1$ $-\,19\cdot 157273\cdot 116400694409\cdot 65\!\cdots\!93$ $S_{29}$ (as 29T8) trivial $6315065032809016.0$
29.1.227...357.1 $x^{29} + 3 x - 1$ $17\cdot 41\cdot 74959\cdot 160217\cdot 2662789\cdot 25396823\cdot 76318073627\cdot 52654144463043283$ $S_{29}$ (as 29T8) trivial $6546753152959768.0$
29.1.227...752.1 $x^{29} + 3 x - 2$ $2^{28}\cdot 8447\cdot 10\!\cdots\!11$ $S_{29}$ (as 29T8) trivial $23857799922719012$
29.1.564...821.1 $x^{29} - 3 x - 3$ $3^{28}\cdot 13\cdot 41\cdot 389\cdot 1619\cdot 4483\cdot 202067\cdot 1052207903\cdot 7714356793195489$ $S_{29}$ (as 29T8) trivial $29272458686891230$
29.1.565...237.1 $x^{29} + 4 x - 1$ $3\cdot 258439534144219859900797151\cdot 72911782755634284235524422729$ $S_{29}$ (as 29T8) $[2]$ $20099249152408180$
29.1.587...477.1 $x^{29} - 2 x - 3$ $43\cdot 907\cdot 40322333\cdot 5439157486181\cdot 68\!\cdots\!49$ $S_{29}$ (as 29T8) trivial $47730899898626100$
29.1.587...973.1 $x^{29} - x - 3$ $179\cdot 373\cdot 277813\cdot 42259019123\cdot 2243721410717\cdot 33399064272490942843393$ $S_{29}$ (as 29T8) trivial $46185846405204810$
29.1.587...709.1 $x^{29} - 3$ $3^{28}\cdot 29^{29}$ $F_{29}$ (as 29T6) trivial $49661461097293670$
29.1.587...445.1 $x^{29} + x - 3$ $5\cdot 11\cdot 16381\cdot 127865750920013\cdot 1994744457920647\cdot 255618611114956521989$ $S_{29}$ (as 29T8) trivial $42821205896121990$
29.1.610...597.1 $x^{29} + 3 x - 3$ $3^{28}\cdot 119533\cdot 419161\cdot 53\!\cdots\!29$ $S_{29}$ (as 29T8) trivial $34353828610448830$
29.3.955...720.1 $x^{29} - 4 x - 2$ $-\,2^{28}\cdot 5\cdot 71\!\cdots\!99$ $S_{29}$ (as 29T8) trivial $819283530647138000$
29.3.955...115.1 $x^{29} - 4 x - 1$ $-\,5\cdot 71\cdot 1070754779627347\cdot 25\!\cdots\!79$ $S_{29}$ (as 29T8) trivial $440767023565659140$
29.1.955...448.1 $x^{29} + 4 x - 2$ $2^{28}\cdot 3\cdot 3783589506654278873\cdot 31\!\cdots\!07$ $S_{29}$ (as 29T8) trivial $489687221548003600$
29.1.961...293.1 $x^{29} + 4 x - 3$ $3744524429\cdot 8675517281441\cdot 29\!\cdots\!37$ $S_{29}$ (as 29T8) trivial $632109057751709300$
29.1.462...688.1 $x^{29} - 2 x - 4$ $2^{54}\cdot 3\cdot 151\cdot 1208109059\cdot 46\!\cdots\!91$ $S_{29}$ (as 29T8) trivial $2408495413358637000$
29.1.462...304.1 $x^{29} + 2 x - 4$ $2^{54}\cdot 853\cdot 133051\cdot 22\!\cdots\!27$ $S_{29}$ (as 29T8) trivial $2017302844328075800$
29.1.185...096.1 $x^{29} - 3 x - 4$ $2^{57}\cdot 71\cdot 14785399\cdot 5818658096101217\cdot 210180474110289901$ $S_{29}$ (as 29T8) trivial $6702753215427773000$
29.1.185...720.1 $x^{29} + x - 4$ $2^{57}\cdot 3\cdot 5\cdot 5205763\cdot 56893477\cdot 288984011824906401353807959$ $S_{29}$ (as 29T8) trivial $7158511448931481000$
29.1.154...216.1 $x^{29} + 5 x - 2$ $2^{26}\cdot 337\cdot 709\cdot 224066062071001\cdot 7834502381769247\cdot 54834197285853919$ $S_{29}$ (as 29T8) trivial $22143705810942657000$
29.3.617...291.1 $x^{29} - 5 x - 3$ $-\,17\cdot 640949\cdot 12442531\cdot 15716663\cdot 28\!\cdots\!59$ $S_{29}$ (as 29T8) not computed
29.3.617...136.1 $x^{29} - 5 x - 2$ $-\,2^{28}\cdot 3\cdot 47\cdot 19231\cdot 1239599\cdot 17156593\cdot 53138329\cdot 7505402452445630661805687$ $S_{29}$ (as 29T8) trivial $48016386518967206000$
29.3.617...531.1 $x^{29} - 5 x - 1$ $-\,3\cdot 9533\cdot 2608914479\cdot 82\!\cdots\!11$ $S_{29}$ (as 29T8) not computed
29.1.617...709.1 $x^{29} + 5 x - 3$ $23\cdot 79\cdot 107\cdot 931421\cdot 23882194037539\cdot 14\!\cdots\!69$ $S_{29}$ (as 29T8) trivial $21861542052281573000$
29.1.635...984.1 $x^{29} + 5 x - 4$ $2^{57}\cdot 37\cdot 1397743\cdot 85\!\cdots\!67$ $S_{29}$ (as 29T8) not computed
29.1.994...125.1 $x^{29} - 5 x - 5$ $5^{28}\cdot 17\cdot 401\cdot 578483771\cdot 67676598636720696780695919103$ $S_{29}$ (as 29T8) trivial $13281089874686380000$
29.1.956...541.1 $x^{29} - 4 x - 5$ $167\cdot 239\cdot 23\!\cdots\!57$ $S_{29}$ (as 29T8) not computed
29.1.956...237.1 $x^{29} - 3 x - 5$ $42691141\cdot 481626857\cdot 2939004407579\cdot 35136939022453\cdot 45049443348110236823$ $S_{29}$ (as 29T8) trivial $46446705639915990000$
29.1.956...893.1 $x^{29} - 2 x - 5$ $3\cdot 43\cdot 57617873845633\cdot 10667339907787007\cdot 12\!\cdots\!07$ $S_{29}$ (as 29T8) not computed
29.1.956...389.1 $x^{29} - x - 5$ $7976611\cdot 37252257474505795723\cdot 32\!\cdots\!13$ $S_{29}$ (as 29T8) not computed
29.1.956...125.1 $x^{29} - 5$ $5^{28}\cdot 29^{29}$ $F_{29}$ (as 29T6) trivial $64731836915276810000$
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