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Label Polynomial Discriminant Galois group Class group
27.9.675...923.1 x27 - 18x23 - 18x22 - 18x21 + 18x20 + 135x19 + 219x18 - 162x17 + 324x16 - 153x15 - 81x14 - 675x13 - 630x12 - 540x11 - 513x10 - 405x9 + 27x8 + 243x7 + 387x6 + 162x5 - 81x4 - 135x3 + 27x - 3 \( -\,3^{73} \) $C_9\times S_3$ (as 27T12) trivial (GRH)
27.9.218...752.1 x27 - 18x25 - 9x24 + 135x23 + 63x22 - 642x21 - 135x20 + 2133x19 + 336x18 - 6156x17 - 270x16 + 15525x15 - 4347x14 - 26667x13 + 16194x12 + 26730x11 - 24912x10 - 13179x9 + 19197x8 + 693x7 - 6957x6 + 1917x5 + 648x4 - 507x3 + 135x2 - 18x + 1 \( -\,2^{18}\cdot 3^{69} \) $C_9\times S_3$ (as 27T12) trivial (GRH)
27.1.437...027.1 x27 - x - 1 \( -\,23\cdot 3539\cdot 535391\cdot 10033918834509020645502251401 \) $S_{27}$ (as 27T2392) trivial (GRH)
27.1.449...579.1 x27 + x - 1 \( -\,151\cdot 144512650291622071\cdot 20602820982951053299 \) $S_{27}$ (as 27T2392) trivial (GRH)
27.9.656...256.1 x27 - 9x26 + 27x25 - 24x24 - 9x23 - 63x22 + 273x21 + 144x20 - 2376x19 + 4050x18 - 396x17 - 3465x16 - 141x15 + 441x14 + 17019x13 - 33225x12 + 12852x11 + 17379x10 - 14277x9 + 1188x8 + 1143x7 - 501x6 + 891x5 + 216x4 + 129x3 + 18x2 + 9x - 1 \( -\,2^{18}\cdot 3^{70} \) $C_9\times S_3$ (as 27T12) trivial (GRH)
27.1.800...063.1 x27 - 9x26 + 41x25 - 116x24 + 234x23 - 347x22 + 380x21 - 274x20 + 118x19 - 121x18 + 474x17 - 1071x16 + 1556x15 - 1531x14 + 964x13 - 256x12 + 122x11 - 700x10 + 1761x9 - 2620x8 + 2840x7 - 2483x6 + 1678x5 - 860x4 + 463x3 - 60x2 + 44x - 1 \( -\,983^{13} \) $D_{27}$ (as 27T8) trivial (GRH)
27.9.162...375.1 x27 - 9x25 + 54x23 - 63x22 - 267x21 + 513x20 + 468x19 - 981x18 - 972x17 - 1107x16 + 9846x15 - 4860x14 - 24624x13 + 41403x12 - 9909x11 - 43317x10 + 67377x9 - 45441x8 - 4905x7 + 46368x6 - 47520x5 + 19584x4 + 1146x3 - 3483x2 + 594x + 107 \( -\,3^{69}\cdot 5^{9} \) $C_9\times S_3$ (as 27T12) trivial (GRH)
27.1.321...296.1 x27 - 10x26 + 38x25 - 52x24 - 84x23 + 458x22 - 715x21 + 40x20 + 1948x19 - 3756x18 + 1448x17 + 4952x16 - 7109x15 + 94x14 + 4978x13 - 2352x12 - 1300x11 + 2422x10 + 639x9 - 3848x8 - 28x7 + 1728x6 + 572x5 - 368x4 - 244x3 + 48x2 + 32x - 16 \( -\,2^{18}\cdot 419^{13} \) $D_{27}$ (as 27T8) trivial (GRH)
27.1.149...191.1 x27 - 4x26 + 14x25 - 10x24 + 37x22 - 3x21 - x20 + 139x19 - 26x18 + 76x17 + 144x16 - 117x15 - 101x14 + 12x13 - 340x12 + x11 + 205x10 + 307x9 + 774x8 + 909x7 + 892x6 + 864x5 + 521x4 + 327x3 + 86x2 + 71x + 1 \( -\,1231^{13} \) $D_{27}$ (as 27T8) trivial (GRH)
27.9.177...912.1 x27 - 18x25 + 189x23 - 63x22 - 1062x21 + 648x20 + 4464x19 - 2679x18 - 14499x17 + 7092x16 + 36963x15 - 21411x14 - 74187x13 + 24255x12 + 61398x11 - 36351x10 - 17520x9 + 66663x8 + 42507x7 - 11583x6 - 18603x5 - 10539x4 - 6327x3 - 2835x2 - 639x - 53 \( -\,2^{18}\cdot 3^{73} \) $C_9\times S_3$ (as 27T12) trivial (GRH)
27.9.177...912.2 x27 - 9x26 + 36x25 - 54x24 - 180x23 + 1296x22 - 3699x21 + 5184x20 + 1737x19 - 28278x18 + 81630x17 - 152073x16 + 206037x15 - 206640x14 + 143748x13 - 36954x12 - 70929x11 + 125325x10 - 106329x9 + 53154x8 - 10548x7 - 9594x6 + 13185x5 - 9180x4 + 4068x3 - 1053x2 - 207x + 163 \( -\,2^{18}\cdot 3^{73} \) $C_9\times S_3$ (as 27T12) trivial (GRH)
27.1.252...624.1 x27 - 9x26 + 45x25 - 154x24 + 444x23 - 1140x22 + 2734x21 - 5824x20 + 11115x19 - 18567x18 + 29531x17 - 43306x16 + 56712x15 - 56676x14 + 52570x13 - 50872x12 + 59685x11 - 40721x10 + 10893x9 + 10490x8 - 13378x7 + 7126x6 - 3604x5 - 204x4 + 1348x3 - 376x2 + 8x + 8 \( -\,2^{18}\cdot 491^{13} \) $D_{27}$ (as 27T8) $[2]$ (GRH)
27.1.786...199.1 x27 - x26 + 6x25 - 31x24 + 97x23 - 269x22 + 599x21 - 994x20 + 1307x19 - 1298x18 + 592x17 + 817x16 - 2461x15 + 4001x14 - 4903x13 + 4315x12 - 2279x11 - 512x10 + 3872x9 - 6814x8 + 7826x7 - 7115x6 + 5689x5 - 3842x4 + 1951x3 - 627x2 + 101x - 1 \( -\,1399^{13} \) $D_{27}$ (as 27T8) $[2]$ (GRH)
27.1.149...032.1 x27 - 7x26 + 21x25 - 50x24 + 110x23 - 244x22 + 734x21 - 2140x20 + 5743x19 - 13591x18 + 28791x17 - 54584x16 + 93410x15 - 138060x14 + 176010x13 - 189870x12 + 169389x11 - 127135x10 + 89765x9 - 72912x8 + 70628x7 - 65648x6 + 50256x5 - 29876x4 + 13340x3 - 4224x2 + 848x - 80 \( -\,2^{18}\cdot 563^{13} \) $D_{27}$ (as 27T8) $[2]$ (GRH)
27.1.476...207.1 x27 - 3x26 - 11x25 + 17x24 + 38x23 + x22 + 157x21 + 384x20 + 124x19 - 139x18 + 318x17 + 1284x16 + 1757x15 - 73x14 - 3289x13 - 3942x12 - 2202x11 - 2459x10 - 3813x9 - 1971x8 + 2174x7 + 7281x6 + 9348x5 + 4444x4 - 209x3 - 325x2 + 132x + 1 \( -\,1607^{13} \) $D_{27}$ (as 27T8) trivial (GRH)
27.1.154...079.1 x27 - 6x26 + 31x25 - 80x24 + 117x23 - 51x22 - 243x21 + 807x20 - 1350x19 + 966x18 + 1935x17 - 9345x16 + 23103x15 - 43548x14 + 68751x13 - 94575x12 + 115269x11 - 125268x10 + 121785x9 - 105567x8 + 81027x7 - 54357x6 + 31122x5 - 14664x4 + 5393x3 - 1350x2 + 179x - 1 \( -\,1759^{13} \) $D_{27}$ (as 27T8) trivial (GRH)
27.1.363...239.1 x27 - 2x26 + x25 + 18x24 + 107x23 + 180x22 + 332x21 + 290x20 + 295x19 - 179x18 - 772x17 - 1774x16 - 2092x15 - 2320x14 - 811x13 + 489x12 + 3551x11 + 5424x10 + 7617x9 + 6962x8 + 6380x7 + 2824x6 + 2291x5 - 521x4 + 623x3 - 221x2 + 207x - 1 \( -\,1879^{13} \) $D_{27}$ (as 27T8) $[4]$ (GRH)
27.1.813...999.1 x27 - 11x26 + 70x25 - 273x24 + 723x23 - 1456x22 + 2649x21 - 4775x20 + 8022x19 - 11719x18 + 15552x17 - 20687x16 + 27099x15 - 31222x14 + 31020x13 - 30638x12 + 32802x11 - 31588x10 + 22446x9 - 12521x8 + 9384x7 - 8740x6 + 4644x5 - 254x4 - 460x3 - 287x2 + 245x + 1 \( -\,1999^{13} \) $D_{27}$ (as 27T8) $[5]$ (GRH)
27.1.536...079.1 x27 - 5x26 + 4x25 - 53x24 + 12x23 - 178x22 + 281x21 - 251x20 + 1170x19 - 548x18 + 1924x17 - 3164x16 + 1182x15 - 5392x14 + 2732x13 - 5123x12 + 7843x11 + 5402x10 + 11272x9 - 9146x8 - 13685x7 - 8959x6 + 8451x5 + 8381x4 + 1087x3 - 2808x2 - 714x - 59 \( -\,31^{13}\cdot 89^{13} \) $D_{27}$ (as 27T8) trivial (GRH)
27.27.706...369.1 x27 - 27x25 + 324x23 - 2277x21 + 10395x19 - 32319x17 + 69768x15 - 104652x13 + 107406x11 - 72930x9 + 30888x7 - 7371x5 + 819x3 - 27x - 1 \( 3^{94} \) $C_{27}$ (as 27T1) trivial (GRH)
27.1.826...731.1 x27 + 2x - 1 \( -\,229351\cdot 3602603985935124183594095692605319901381 \) $S_{27}$ (as 27T2392) trivial (GRH)
27.1.124...951.1 x27 - 13x26 + 64x25 - 128x24 - 64x23 + 1031x22 - 3598x21 + 9810x20 - 21567x19 + 36061x18 - 52129x17 + 97285x16 - 181966x15 + 235897x14 - 374052x13 + 634209x12 - 258724x11 + 64070x10 - 1005397x9 + 111021x8 + 1266741x7 + 944398x6 - 1133842x5 - 1337690x4 + 643480x3 + 1031258x2 - 50650x + 12587 \( -\,7^{18}\cdot 199^{13} \) $D_{27}$ (as 27T8) $[3, 3]$ (GRH)
27.1.128...351.1 x27 - 4x26 + 28x25 - 42x24 + 71x23 + 267x22 - 142x21 + 385x20 + 2210x19 + 2329x18 - 3315x17 + 15117x16 + 19014x15 - 23157x14 + 44479x13 + 77004x12 - 41903x11 + 19829x10 + 208952x9 - 35302x8 - 53453x7 + 258838x6 - 35701x5 + 60990x4 - 5393x3 + 76227x2 + 19031x + 2209 \( -\,13^{13}\cdot 227^{13} \) $D_{27}$ (as 27T8) trivial (GRH)
27.1.490...711.1 x27 - 3x26 + 15x25 - 53x24 + 106x23 - 298x22 + 714x21 - 199x20 + 2747x19 + 4180x18 + 4767x17 + 27487x16 - 7928x15 + 93863x14 - 80586x13 + 257840x12 - 253867x11 + 459460x10 - 363114x9 + 981160x8 + 143119x7 - 202978x6 + 143097x5 + 629777x4 + 25669x3 - 205103x2 - 65505x + 40293 \( -\,3271^{13} \) $D_{27}$ (as 27T8) $[2]$ (GRH)
27.27.797...529.1 x27 - x26 - 42x25 + 37x24 + 728x23 - 564x22 - 6817x21 + 4664x20 + 37948x19 - 23103x18 - 130429x17 + 71289x16 + 279661x15 - 138143x14 - 372684x13 + 166778x12 + 305327x11 - 124486x10 - 150120x9 + 56020x8 + 42107x7 - 14253x6 - 6122x5 + 1790x4 + 395x3 - 85x2 - 10x + 1 \( 7^{18}\cdot 19^{24} \) $C_3\times C_9$ (as 27T2) trivial (GRH)
27.1.201...127.1 x27 - 9x26 + 43x25 - 96x24 + 144x23 - 267x22 + 429x21 + 20x20 - 947x19 + 1263x18 + 1070x17 - 4443x16 + 3518x15 + 4729x14 - 7874x13 + 2497x12 + 13136x11 - 1996x10 - 8600x9 + 6002x8 + 17843x7 - 14482x6 + 6811x5 + 47488x4 + 900x3 - 46897x2 + 24633x + 2075 \( -\,7^{13}\cdot 521^{13} \) $D_{27}$ (as 27T8) trivial (GRH)
27.1.219...911.1 x27 - 8x26 + 46x25 - 158x24 + 412x23 - 651x22 + 948x21 - 1384x20 + 7521x19 - 22249x18 + 61004x17 - 97499x16 + 110127x15 + 98440x14 - 785239x13 + 2068135x12 - 3012058x11 + 444932x10 + 9236470x9 - 28098698x8 + 53493798x7 - 76988059x6 + 87553666x5 - 79021445x4 + 56695661x3 - 30768538x2 + 10754601x - 1715933 \( -\,3671^{13} \) $D_{27}$ (as 27T8) trivial (GRH)
27.1.281...936.1 x27 - 4x - 4 \( -\,2^{26}\cdot 263\cdot 1592403079552126010285410393405129573 \) $S_{27}$ (as 27T2392) trivial (GRH)
27.1.289...864.1 x27 - 2x - 2 \( -\,2^{26}\cdot 239\cdot 911\cdot 1492637\cdot 10924843\cdot 125481509\cdot 967669291801 \) $S_{27}$ (as 27T2392) trivial (GRH)
27.1.297...016.1 x27 - x - 2 \( -\,2^{27}\cdot 47\cdot 4717303065439408933563627808093088051 \) $S_{27}$ (as 27T2392) trivial (GRH)
27.1.297...783.1 x27 - x - 4 \( -\,167\cdot 359\cdot 10245289151\cdot 48446943180119740684317685671961 \) $S_{27}$ (as 27T2392) trivial (GRH)
27.1.297...792.1 x27 - 2 \( -\,2^{26}\cdot 3^{81} \) $C_9.(C_9\times S_3)$ (as 27T176) trivial (GRH)
27.1.305...720.1 x27 + 2x - 2 \( -\,2^{26}\cdot 5\cdot 7\cdot 11\cdot 80071\cdot 14783591491235038142928766927013 \) $S_{27}$ (as 27T2392) trivial (GRH)
27.1.314...648.1 x27 + 4x - 4 \( -\,2^{26}\cdot 1831\cdot 255625869232040633091991440618651397 \) $S_{27}$ (as 27T2392) trivial (GRH)
27.27.503...521.1 x27 - 45x25 + 837x23 - 8430x21 + 50652x19 - 193x18 - 188811x17 + 2934x16 + 441720x15 - 15822x14 - 646731x13 + 37506x12 + 585063x11 - 42453x10 - 319331x9 + 24462x8 + 99963x7 - 7245x6 - 16119x5 + 1080x4 + 1059x3 - 81x2 - 18x + 1 \( 3^{66}\cdot 7^{18} \) $C_3\times C_9$ (as 27T2) trivial (GRH)
27.1.556...943.1 x27 - 6x26 + 27x25 - 119x24 + 469x23 - 1488x22 + 4228x21 - 11600x20 + 26558x19 - 54959x18 + 133324x17 - 272188x16 + 522791x15 - 983894x14 + 1639478x13 - 2435791x12 + 3557436x11 - 4633264x10 + 5404652x9 - 6079977x8 + 6195381x7 - 5327698x6 + 4651935x5 - 3835566x4 + 2476602x3 - 1723599x2 + 1364445x - 459999 \( -\,3943^{13} \) $D_{27}$ (as 27T8) trivial (GRH)
27.27.735...441.1 x27 - 51x25 - 4x24 + 1080x23 + 156x22 - 12356x21 - 2448x20 + 83283x19 + 19984x18 - 339003x17 - 91596x16 + 825846x15 + 238428x14 - 1168977x13 - 344712x12 + 930681x11 + 259620x10 - 414755x9 - 102465x8 + 101628x7 + 20920x6 - 12933x5 - 2085x4 + 755x3 + 90x2 - 15x - 1 \( 3^{36}\cdot 19^{24} \) $C_3\times C_9$ (as 27T2) trivial (GRH)
27.1.108...375.1 x27 - 8x26 + 11x25 + 79x24 - 318x23 + 272x22 + 1817x21 - 11487x20 + 27792x19 - 5214x18 - 88324x17 + 101476x16 + 384139x15 - 2894444x14 + 8285833x13 - 7065937x12 - 6208737x11 - 6594753x10 + 51530498x9 - 40765921x8 + 72314518x7 - 318855243x6 + 340132420x5 + 140246505x4 - 148040525x3 - 594053575x2 + 805097125x - 295863625 \( -\,5^{13}\cdot 7^{18}\cdot 67^{13} \) $D_{27}$ (as 27T8) $[3]$ (GRH)
27.1.356...663.1 x27 - 10x26 + 80x25 - 447x24 + 1863x23 - 6240x22 + 15201x21 - 25896x20 + 26931x19 + 29922x18 - 2157x17 + 228x16 + 1150141x15 - 1553359x14 + 3361193x13 - 357518x12 - 4399792x11 - 5659177x10 - 7694789x9 - 6381628x8 + 25148690x7 + 37280366x6 + 10154644x5 - 4374482x4 + 5689374x3 + 3195477x2 - 2094606x + 247941 \( -\,7^{18}\cdot 367^{13} \) $D_{27}$ (as 27T8) $[3]$ (GRH)
27.1.155...607.1 x27 + 18x25 - 54x24 + 81x23 - 729x22 + 711x21 - 2322x20 + 7389x19 - 646x18 + 36288x17 - 20349x16 + 36072x15 - 256311x14 - 65700x13 - 942516x12 + 444744x11 - 558486x10 + 4867412x9 + 1228689x8 + 12312063x7 - 3080772x6 + 6516828x5 - 31451760x4 - 20430663x3 - 52842915x2 - 27379269x - 39209779 \( -\,3^{66}\cdot 23^{13} \) $D_{27}$ (as 27T8) $[9]$ (GRH)
27.1.199...291.1 x27 - 2x26 + 16x25 + 62x24 + 342x23 + 1648x22 + 6094x21 + 15834x20 + 34184x19 + 61822x18 + 112334x17 + 237408x16 + 637440x15 + 1828206x14 + 5099608x13 + 12463122x12 + 26430338x11 + 48978608x10 + 80603954x9 + 116977534x8 + 149538616x7 + 167922122x6 + 164525402x5 + 137815936x4 + 94764543x3 + 50090044x2 + 17954520x + 3418472 \( -\,7^{18}\cdot 419^{13} \) $D_{27}$ (as 27T8) $[3]$ (GRH)
27.1.432...211.1 x27 - 3x - 3 \( -\,3^{27}\cdot 71\cdot 337\cdot 14619373\cdot 78563389\cdot 206180539890995287 \) $S_{27}$ (as 27T2392) trivial (GRH)
27.3.469...109.1 x27 - 3x - 1 \( 3^{27}\cdot 11\cdot 29\cdot 318911\cdot 7780103222533\cdot 7777884788734331 \) $S_{27}$ (as 27T2392) $[2]$ (GRH)
27.1.469...715.1 x27 + 3x - 1 \( -\,3^{27}\cdot 5\cdot 29573\cdot 718375177076041\cdot 57954924238599673 \) $S_{27}$ (as 27T2392) trivial (GRH)
27.1.469...704.1 x27 + 3x - 2 \( -\,2^{27}\cdot 3^{27}\cdot 1592729\cdot 28815787221263522142841 \) $S_{27}$ (as 27T2392) trivial (GRH)
27.1.863...271.1 x27 - 9x26 + 51x25 - 157x24 + 381x23 + 94x22 - 4772x21 + 22385x20 - 19633x19 - 132957x18 + 462384x17 + 49228x16 - 4729835x15 + 16673567x14 - 15312382x13 - 102305328x12 + 361800096x11 - 196173035x10 - 890969729x9 + 1569260108x8 - 437613721x7 - 1278467664x6 + 2134193061x5 - 1922367953x4 + 1085805378x3 - 524572351x2 + 152402636x - 24878621 \( -\,13^{18}\cdot 199^{13} \) $D_{27}$ (as 27T8) $[3]$ (GRH)
27.1.100...375.1 x27 - 82x24 - 9x23 + 195x22 + 2387x21 + 810x20 - 11814x19 - 33683x18 + 2520x17 + 230379x16 + 441880x15 - 1170738x14 - 529926x13 - 6335185x12 + 26111763x11 - 28861455x10 + 54201969x9 - 172123947x8 + 231730104x7 - 172770969x6 + 271759050x5 - 338641350x4 + 41402575x3 + 177368400x2 - 96664125x + 14269375 \( -\,3^{36}\cdot 5^{13}\cdot 67^{13} \) $D_{27}$ (as 27T8) $[3]$ (GRH)
27.1.119...311.1 x27 - 9x26 + 56x25 - 273x24 + 1290x23 - 5604x22 + 24003x21 - 98346x20 + 381168x19 - 1383408x18 + 4700958x17 - 15265944x16 + 47759673x15 - 142609974x14 + 403676163x13 - 1071234237x12 + 2616260829x11 - 5766916275x10 + 11330239941x9 - 19648861461x8 + 29452821249x7 - 36679431165x6 + 35809916697x5 - 25389897726x4 + 11811942110x3 - 3328128234x2 + 1063555192x - 565863243 \( -\,19^{24}\cdot 31^{13} \) $D_{27}$ (as 27T8) $[9]$ (GRH)
27.27.550...809.1 x27 - 6x26 - 47x25 + 302x24 + 943x23 - 6448x22 - 10567x21 + 76481x20 + 71695x19 - 556066x18 - 291044x17 + 2587104x16 + 603975x15 - 7811439x14 - 35156x13 + 15161145x12 - 2848142x11 - 18230502x10 + 6439289x9 + 12558384x8 - 6282221x7 - 4210683x6 + 2778704x5 + 421825x4 - 457387x3 + 20126x2 + 21522x - 2699 \( 13^{18}\cdot 19^{24} \) $C_3\times C_9$ (as 27T2) trivial (GRH)
27.1.929...947.1 x27 - 11x26 + 7x25 + 393x24 - 1777x23 - 1339x22 + 33149x21 - 122161x20 + 301221x19 - 901165x18 + 2771309x17 - 5696089x16 + 7240134x15 - 11573472x14 + 45471960x13 - 153604016x12 + 357338624x11 - 615897728x10 + 876134656x9 - 1154442240x8 + 1414654976x7 - 1520924672x6 + 1526870016x5 - 1494863872x4 + 1216438272x3 - 684785664x2 + 248741888x - 73596928 \( -\,7^{18}\cdot 563^{13} \) $D_{27}$ (as 27T8) $[6]$ (GRH)
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