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Label Polynomial Discriminant Galois group Class group
29.1.186...489.1 x29 - x28 + 7x27 + 7x26 + 29x25 + 70x24 + 115x23 + 217x22 + 336x21 + 447x20 + 628x19 + 758x18 + 820x17 + 951x16 + 953x15 + 866x14 + 839x13 + 574x12 + 405x11 + 413x10 + 349x9 + 268x8 + 247x7 - 13x6 - 6x5 + 265x4 + 95x3 - 98x2 + 32x + 1 \( 887^{14} \) $D_{29}$ (as 29T2) trivial (GRH)
29.1.253...733.1 x29 - x - 1 \( 41393681953973\cdot 61230132484136034758796880121 \) $S_{29}$ (as 29T8) trivial (GRH)
29.1.756...121.1 x29 - 9x28 + 56x27 - 308x26 + 1574x25 - 7243x24 + 28966x23 - 99448x22 + 293090x21 - 744900x20 + 1641343x19 - 3148829x18 + 5274672x17 - 7725970x16 + 9897023x15 - 11084677x14 + 10859104x13 - 9337717x12 + 7122047x11 - 4916951x10 + 3150459x9 - 1890622x8 + 1028653x7 - 470622x6 + 165361x5 - 41848x4 + 8324x3 - 1810x2 + 323x - 1 \( 23^{14}\cdot 97^{14} \) $D_{29}$ (as 29T2) trivial (GRH)
29.1.107...689.1 x29 - 12x28 + 55x27 - 97x26 + 34x25 + 11x24 + 138x23 - 214x22 + 43x21 + 224x20 - 104x19 - 50x18 + 748x17 - 1490x16 + 1965x15 - 460x14 - 575x13 + 2189x12 - 1286x11 - 53x10 + 3178x9 - 2804x8 + 3117x7 - 748x6 + 585x5 + 965x4 + 480x3 + 353x2 + 369x - 1 \( 2287^{14} \) $D_{29}$ (as 29T2) trivial (GRH)
29.1.123...441.1 x29 - 8x28 + 6x27 + 45x26 + 49x25 - 158x24 - 252x23 - 117x22 + 459x21 + 1008x20 + 2232x19 + 2691x18 + 1728x17 - 2718x16 - 7677x15 - 13104x14 - 15537x13 - 15042x12 - 6534x11 + 6768x10 + 22065x9 + 32523x8 + 38385x7 + 37197x6 + 29657x5 + 17606x4 + 7536x3 + 1998x2 + 377x - 1 \( 2311^{14} \) $D_{29}$ (as 29T2) trivial (GRH)
29.1.190...729.1 x29 - 8x28 + 42x27 - 91x26 + 71x25 - 172x24 + 980x23 - 2477x22 + 4032x21 - 5998x20 + 8995x19 - 12396x18 + 15464x17 - 17477x16 + 17661x15 - 16777x14 + 14899x13 - 10749x12 + 6197x11 - 2594x10 - 1233x9 + 2318x8 - 113x7 - 855x6 + 1459x5 - 2625x4 + 2079x3 - 978x2 + 419x + 1 \( 2383^{14} \) $D_{29}$ (as 29T2) trivial (GRH)
29.1.358...441.1 x29 - x28 - 7x27 - 50x26 + 119x25 + 495x24 + 59x23 - 530x22 + 637x21 + 2591x20 + 2977x19 + 1178x18 + 2213x17 + 5385x16 + 5965x15 + 6650x14 + 10883x13 + 16281x12 + 23955x11 + 21146x10 - 8059x9 - 7103x8 + 28957x7 + 37734x6 + 35524x5 + 2552x4 - 22800x3 - 19616x2 - 17024x - 11776 \( 2939^{14} \) $D_{29}$ (as 29T2) trivial (GRH)
29.1.894...288.1 x29 + 4x - 4 \( 2^{28}\cdot 27325532669\cdot 1219981524656697632736241282817 \) $S_{29}$ (as 29T8) trivial (GRH)
29.1.177...701.1 x29 + 2x - 1 \( 461801\cdot 20212226753\cdot 3536300443131271\cdot 539109057311673427 \) $S_{29}$ (as 29T8) trivial (GRH)
29.1.261...256.1 x29 - 4x - 4 \( 2^{28}\cdot 53\cdot 179\cdot 10267119471732676863546062197607495323 \) $S_{29}$ (as 29T8) trivial (GRH)
29.29.383...121.1 x29 - x28 - 28x27 + 27x26 + 351x25 - 325x24 - 2600x23 + 2300x22 + 12650x21 - 10626x20 - 42504x19 + 33649x18 + 100947x17 - 74613x16 - 170544x15 + 116280x14 + 203490x13 - 125970x12 - 167960x11 + 92378x10 + 92378x9 - 43758x8 - 31824x7 + 12376x6 + 6188x5 - 1820x4 - 560x3 + 105x2 + 15x - 1 \( 59^{28} \) $C_{29}$ (as 29T1) trivial (GRH)
29.1.506...201.1 x29 - 11x28 + 45x27 - 70x26 + 66x25 - 800x24 + 4130x23 - 11632x22 + 26627x21 - 43970x20 + 56823x19 - 114622x18 + 216543x17 - 400317x16 + 743290x15 - 1619073x14 + 3038554x13 - 4110770x12 + 3834768x11 - 1791942x10 - 198548x9 + 1096532x8 - 913725x7 + 101442x6 + 212195x5 - 352802x4 + 186129x3 - 93243x2 + 23048x - 4757 \( 53^{14}\cdot 67^{14} \) $D_{29}$ (as 29T2) trivial (GRH)
29.1.574...129.1 x29 - x28 + 18x27 + 12x26 + 179x25 + 123x24 + 1662x23 - 196x22 + 11119x21 - 9104x20 + 47466x19 - 44547x18 + 83114x17 - 23886x16 - 121329x15 + 248495x14 - 275546x13 - 188738x12 + 573921x11 - 476142x10 + 379865x9 - 32019x8 + 20658x7 - 6163x6 - 27930x5 + 2012x4 - 1404x3 + 2898x2 - 594x + 81 \( 3583^{14} \) $D_{29}$ (as 29T2) trivial (GRH)
29.1.771...361.1 x29 - 7x28 + 47x27 - 186x26 + 710x25 - 970x24 + 1144x23 + 2298x22 - 8465x21 + 16505x20 - 20589x19 + 3590x18 + 30661x17 - 81803x16 + 117497x15 - 94780x14 + 10260x13 + 127678x12 - 249606x11 + 245472x10 - 99463x9 - 191187x8 + 582067x7 - 785770x6 + 915704x5 - 793384x4 + 541792x3 - 324448x2 + 144320x - 23552 \( 3659^{14} \) $D_{29}$ (as 29T2) trivial (GRH)
29.1.142...409.1 x29 - x28 + 33x27 - 64x26 + 535x25 - 1144x24 + 5145x23 - 10327x22 + 31220x21 - 55583x20 + 124455x19 - 188951x18 + 323227x17 - 411652x16 + 521736x15 - 591430x14 + 489137x13 - 738131x12 + 175881x11 - 1211717x10 + 917449x9 - 3034006x8 + 2818536x7 - 6798367x6 + 6818314x5 - 8408506x4 + 7552950x3 - 8000650x2 + 5448750x - 1749375 \( 3823^{14} \) $D_{29}$ (as 29T2) trivial (GRH)
29.1.671...632.1 x29 - 2x - 2 \( 2^{28}\cdot 3\cdot 11\cdot 563\cdot 134635615853097819303336173003083422943 \) $S_{29}$ (as 29T8) trivial (GRH)
29.1.689...128.1 x29 - x - 2 \( 2^{28}\cdot 23\cdot 2505541501481\cdot 44556647066894154934970530051 \) $S_{29}$ (as 29T8) trivial (GRH)
29.1.689...608.1 x29 - x - 4 \( 2^{30}\cdot 13\cdot 3373\cdot 84163\cdot 173940633187564199922371542429441 \) $S_{29}$ (as 29T8) trivial (GRH)
29.1.689...864.1 x29 - 2 \( 2^{28}\cdot 29^{29} \) $F_{29}$ (as 29T6) trivial (GRH)
29.1.707...096.1 x29 + 2x - 2 \( 2^{28}\cdot 499\cdot 541\cdot 695389\cdot 2739817\cdot 5913513689\cdot 866002650952007 \) $S_{29}$ (as 29T8) trivial (GRH)
29.3.227...419.1 x29 - 3x - 1 \( -\,19\cdot 157273\cdot 116400694409\cdot 6540002603845429295048615140626894593 \) $S_{29}$ (as 29T8) trivial (GRH)
29.1.227...357.1 x29 + 3x - 1 \( 17\cdot 41\cdot 74959\cdot 160217\cdot 2662789\cdot 25396823\cdot 76318073627\cdot 52654144463043283 \) $S_{29}$ (as 29T8) trivial (GRH)
29.1.227...752.1 x29 + 3x - 2 \( 2^{28}\cdot 8447\cdot 1003530236440432082546482634511606676653811 \) $S_{29}$ (as 29T8) trivial (GRH)
29.1.564...821.1 x29 - 3x - 3 \( 3^{28}\cdot 13\cdot 41\cdot 389\cdot 1619\cdot 4483\cdot 202067\cdot 1052207903\cdot 7714356793195489 \) $S_{29}$ (as 29T8) trivial (GRH)
29.1.565...237.1 x29 + 4x - 1 \( 3\cdot 258439534144219859900797151\cdot 72911782755634284235524422729 \) $S_{29}$ (as 29T8) $[2]$ (GRH)
29.1.587...477.1 x29 - 2x - 3 \( 43\cdot 907\cdot 40322333\cdot 5439157486181\cdot 6867266657725622021109001049749 \) $S_{29}$ (as 29T8) trivial (GRH)
29.1.587...973.1 x29 - x - 3 \( 179\cdot 373\cdot 277813\cdot 42259019123\cdot 2243721410717\cdot 33399064272490942843393 \) $S_{29}$ (as 29T8) trivial (GRH)
29.1.587...709.1 x29 - 3 \( 3^{28}\cdot 29^{29} \) $F_{29}$ (as 29T6) trivial (GRH)
29.1.587...445.1 x29 + x - 3 \( 5\cdot 11\cdot 16381\cdot 127865750920013\cdot 1994744457920647\cdot 255618611114956521989 \) $S_{29}$ (as 29T8) trivial (GRH)
29.1.610...597.1 x29 + 3x - 3 \( 3^{28}\cdot 119533\cdot 419161\cdot 53232187366908496998206741390729 \) $S_{29}$ (as 29T8) trivial (GRH)
29.3.955...720.1 x29 - 4x - 2 \( -\,2^{28}\cdot 5\cdot 7117946375474536827576691201119166250278405717399 \) $S_{29}$ (as 29T8) trivial (GRH)
29.3.955...115.1 x29 - 4x - 1 \( -\,5\cdot 71\cdot 1070754779627347\cdot 25133111119629637924203464052947473855979 \) $S_{29}$ (as 29T8) trivial (GRH)
29.1.955...448.1 x29 + 4x - 2 \( 2^{28}\cdot 3\cdot 3783589506654278873\cdot 3135447344393691704372001950407 \) $S_{29}$ (as 29T8) trivial (GRH)
29.1.961...293.1 x29 + 4x - 3 \( 3744524429\cdot 8675517281441\cdot 295892994260421814018306476982622737 \) $S_{29}$ (as 29T8) trivial (GRH)
29.1.462...688.1 x29 - 2x - 4 \( 2^{54}\cdot 3\cdot 151\cdot 1208109059\cdot 4691779529989938182463888683491 \) $S_{29}$ (as 29T8) trivial (GRH)
29.1.462...304.1 x29 + 2x - 4 \( 2^{54}\cdot 853\cdot 133051\cdot 22624279891052931716065193190632827 \) $S_{29}$ (as 29T8) trivial (GRH)
29.1.185...096.1 x29 - 3x - 4 \( 2^{57}\cdot 71\cdot 14785399\cdot 5818658096101217\cdot 210180474110289901 \) $S_{29}$ (as 29T8) trivial (GRH)
29.1.185...720.1 x29 + x - 4 \( 2^{57}\cdot 3\cdot 5\cdot 5205763\cdot 56893477\cdot 288984011824906401353807959 \) $S_{29}$ (as 29T8) trivial (GRH)
29.1.154...216.1 x29 + 5x - 2 \( 2^{26}\cdot 337\cdot 709\cdot 224066062071001\cdot 7834502381769247\cdot 54834197285853919 \) $S_{29}$ (as 29T8) trivial (GRH)
29.3.617...291.1 x29 - 5x - 3 \( -\,17\cdot 640949\cdot 12442531\cdot 15716663\cdot 2897406320048726202827323835684675345659 \) $S_{29}$ (as 29T8) n/a
29.3.617...136.1 x29 - 5x - 2 \( -\,2^{28}\cdot 3\cdot 47\cdot 19231\cdot 1239599\cdot 17156593\cdot 53138329\cdot 7505402452445630661805687 \) $S_{29}$ (as 29T8) trivial (GRH)
29.3.617...531.1 x29 - 5x - 1 \( -\,3\cdot 9533\cdot 2608914479\cdot 82745486276580889140961704645736700550611234411 \) $S_{29}$ (as 29T8) n/a
29.1.617...709.1 x29 + 5x - 3 \( 23\cdot 79\cdot 107\cdot 931421\cdot 23882194037539\cdot 1427579104021681143732218630118134569 \) $S_{29}$ (as 29T8) trivial (GRH)
29.1.635...984.1 x29 + 5x - 4 \( 2^{57}\cdot 37\cdot 1397743\cdot 853179068682579746198218224556362467 \) $S_{29}$ (as 29T8) n/a
29.1.994...125.1 x29 - 5x - 5 \( 5^{28}\cdot 17\cdot 401\cdot 578483771\cdot 67676598636720696780695919103 \) $S_{29}$ (as 29T8) trivial (GRH)
29.1.956...541.1 x29 - 4x - 5 \( 167\cdot 239\cdot 2396317230277599875767474796578857341345192958863605625557 \) $S_{29}$ (as 29T8) n/a
29.1.956...237.1 x29 - 3x - 5 \( 42691141\cdot 481626857\cdot 2939004407579\cdot 35136939022453\cdot 45049443348110236823 \) $S_{29}$ (as 29T8) trivial (GRH)
29.1.956...893.1 x29 - 2x - 5 \( 3\cdot 43\cdot 57617873845633\cdot 10667339907787007\cdot 1206421276967288581188470646307 \) $S_{29}$ (as 29T8) n/a
29.1.956...389.1 x29 - x - 5 \( 7976611\cdot 37252257474505795723\cdot 321907467498837092682537183194821213 \) $S_{29}$ (as 29T8) n/a
29.1.956...125.1 x29 - 5 \( 5^{28}\cdot 29^{29} \) $F_{29}$ (as 29T6) trivial (GRH)
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