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hmf_forms • Show schema
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{'deg': 2, 'dimension': 1, 'disc': 301, 'field_bad_primes': [7, 43], 'field_label': '2.2.301.1', 'is_CM': 'no', 'is_base_change': 'yes', 'label': '2.2.301.1-28.1-b', 'label_nsuffix': 1, 'label_suffix': 'b', 'level_bad_primes': [2, 7], 'level_ideal': '[28, 14, -46*w - 376]', 'level_label': '28.1', 'level_norm': 28, 'parallel_weight': 2, 'short_label': '28.1-b', 'weight': '[2, 2]'}
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hmf_hecke • Show schema
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{'AL_eigenvalues': [['[4, 2, 2]', -1], ['[7, 7, -23*w - 188]', -1]], 'hecke_eigenvalues': [-2, -2, 1, 0, 0, 1, 0, 0, 2, 2, 0, 0, 8, 6, 6, 8, 8, -4, -4, 2, 2, 8, 8, -6, -6, 12, 12, 2, 2, -16, -16, 18, 18, -4, -4, -10, 14, 14, -18, -18, 20, 20, 8, 8, 18, 18, 24, 24, -10, -10, 18, 18, -6, -6, 2, -10, -10, 6, 6, 14, 14, -28, -28, -24, -24, -16, -16, 36, 36, -18, -18, 14, 14, 6, 6, 24, 24, -34, -34, -12, -12, -6, -6, -16, -16, 0, 0, 6, 6, 2, 2, 38, 38, 8, 8, 6, 6, 6, 6, 2, 2, -42, -42, -6, -6, -24, -24, 26, 26, 32, 32, 2, 2, 6, 6, -12, -12, -24, -24, -12, -12, -12, -12, -46, -46, 18, 18, -46, -46, 44, 44, -40, -40, -18, -18, 24, 24, 6, 6, 2, 2, 6, 6, -40, -40, -36, -36, 56, 56, 12, 12, -22, 14, 14, -22, -22, 20, 20, -36, -36, 44, 44, 56, 56, 6, 6, 2, 2, 24, 24, -46, 32, 32, -6, -6, -36, -36, 8, 8], 'hecke_polynomial': 'x', 'label': '2.2.301.1-28.1-b'}
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hmf_fields • Show schema
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{'degree': 2, 'discriminant': 301, 'ideals': ['[1, 1, 1]', '[3, 3, w - 9]', '[3, 3, w + 8]', '[4, 2, 2]', '[5, 5, -6*w + 55]', '[5, 5, -6*w - 49]', '[7, 7, -23*w - 188]', '[9, 3, 3]', '[9, 9, -17*w + 156]', '[9, 9, 17*w + 139]', '[11, 11, 5*w - 46]', '[11, 11, -5*w - 41]', '[12, 6, 2*w - 18]', '[12, 6, 2*w + 16]', '[15, 15, -11*w - 90]', '[15, 15, w - 10]', '[15, 15, -w - 9]', '[15, 15, 11*w - 101]', '[16, 4, 4]', '[19, 19, w + 7]', '[19, 19, -w + 8]', '[20, 10, -12*w + 110]', '[20, 10, -12*w - 98]', '[21, 21, -4*w - 33]', '[21, 21, 4*w - 37]', '[23, 23, 2*w - 19]', '[23, 23, 2*w + 17]', '[25, 5, 5]', '[25, 25, 3*w + 25]', '[25, 25, -3*w + 28]', '[27, 9, 3*w - 27]', '[27, 9, 3*w + 24]', '[27, 27, 7*w + 57]', '[27, 27, 7*w - 64]', '[28, 14, -46*w - 376]', '[33, 33, -w - 6]', '[33, 33, -29*w - 237]', '[33, 33, -29*w + 266]', '[33, 33, -w + 7]', '[35, 35, w + 10]', '[35, 35, -w + 11]', '[36, 6, 6]', '[36, 18, -34*w + 312]', '[36, 18, 34*w + 278]', '[43, 43, 57*w - 523]', '[44, 22, 10*w - 92]', '[44, 22, -10*w - 82]', '[45, 15, -18*w + 165]', '[45, 15, -18*w - 147]', '[45, 45, -w - 5]', '[45, 45, -2*w + 17]', '[45, 45, -2*w - 15]', '[45, 45, -w + 6]', '[48, 12, 4*w - 36]', '[48, 12, 4*w + 32]', '[49, 7, 7]', '[53, 53, 28*w - 257]', '[53, 53, 28*w + 229]', '[55, 55, w + 4]', '[55, 55, 8*w + 65]', '[55, 55, 8*w - 73]', '[55, 55, w - 5]', '[57, 57, -w - 11]', '[57, 57, 16*w + 131]', '[57, 57, 16*w - 147]', '[57, 57, -w + 12]', '[60, 30, -22*w - 180]', '[60, 30, 2*w - 20]', '[60, 30, -2*w - 18]', '[60, 30, 22*w - 202]', '[61, 61, -13*w + 119]', '[61, 61, 13*w + 106]', '[63, 21, -69*w - 564]', '[63, 63, -w - 3]', '[63, 63, -w + 4]', '[64, 8, 8]', '[67, 67, -9*w + 83]', '[67, 67, -9*w - 74]', '[69, 69, -w - 2]', '[69, 69, 35*w + 286]', '[69, 69, -35*w + 321]', '[69, 69, w - 3]', '[73, 73, -w - 1]', '[73, 73, w - 2]', '[75, 15, 5*w - 45]', '[75, 15, 5*w + 40]', '[75, 75, w]', '[75, 75, 52*w - 477]', '[75, 75, 52*w + 425]', '[75, 75, w - 1]', '[76, 38, 2*w + 14]', '[76, 38, -2*w + 16]', '[77, 77, 3*w - 26]', '[77, 77, 3*w + 23]', '[79, 79, 3*w + 26]', '[79, 79, 3*w - 29]', '[80, 20, -24*w + 220]', '[80, 20, -24*w - 196]', '[81, 9, 9]', '[81, 27, -51*w + 468]', '[81, 27, 51*w + 417]', '[81, 81, w + 12]', '[81, 81, -w + 13]', '[84, 42, -8*w - 66]', '[84, 42, 8*w - 74]', '[89, 89, -9*w - 73]', '[89, 89, -9*w + 82]', '[92, 46, 4*w - 38]', '[92, 46, 4*w + 34]', '[95, 95, 74*w + 605]', '[95, 95, 7*w - 65]', '[95, 95, 7*w + 58]', '[95, 95, 74*w - 679]', '[99, 33, 15*w - 138]', '[99, 33, -15*w - 123]', '[99, 99, 2*w - 21]', '[99, 99, -5*w - 42]', '[99, 99, 5*w - 47]', '[99, 99, -2*w - 19]', '[100, 10, 10]', '[100, 50, 6*w + 50]', '[100, 50, -6*w + 56]', '[105, 105, 19*w - 174]', '[105, 105, 2*w - 15]', '[105, 105, 2*w + 13]', '[105, 105, 19*w + 155]', '[107, 107, -w - 13]', '[107, 107, w - 14]', '[108, 18, 6*w - 54]', '[108, 18, 6*w + 48]', '[108, 54, 14*w + 114]', '[108, 54, 14*w - 128]', '[109, 109, 45*w - 413]', '[109, 109, -45*w - 368]', '[112, 28, -92*w - 752]', '[115, 115, -4*w + 35]', '[115, 115, 41*w + 335]', '[115, 115, -41*w + 376]', '[115, 115, 4*w + 31]', '[121, 11, 11]', '[121, 121, 21*w + 172]', '[121, 121, -21*w + 193]', '[125, 25, -30*w + 275]', '[125, 25, -30*w - 245]', '[125, 125, -3*w - 22]', '[125, 125, -3*w + 25]', '[127, 127, 39*w + 319]', '[127, 127, 39*w - 358]', '[129, 129, -10*w - 81]', '[129, 129, -10*w + 91]', '[131, 131, 132*w + 1079]', '[131, 131, 75*w + 613]', '[132, 66, -2*w - 12]', '[132, 66, -58*w - 474]', '[132, 66, -58*w + 532]', '[132, 66, -2*w + 14]', '[133, 133, 27*w - 248]', '[133, 133, 27*w + 221]', '[135, 45, -33*w - 270]', '[135, 45, 3*w - 30]', '[135, 45, -3*w - 27]', '[135, 45, 33*w - 303]', '[135, 135, -w - 14]', '[135, 135, 14*w - 129]', '[135, 135, -14*w - 115]', '[135, 135, w - 15]', '[140, 70, 2*w + 20]', '[140, 70, -2*w + 22]', '[144, 12, 12]', '[144, 36, -68*w + 624]', '[144, 36, 68*w + 556]', '[147, 21, 7*w - 63]', '[147, 21, 7*w + 56]', '[157, 157, 2*w - 13]', '[157, 157, -2*w - 11]', '[159, 159, -5*w + 44]', '[159, 159, 25*w - 229]', '[159, 159, -25*w - 204]', '[159, 159, 5*w + 39]', '[161, 161, -15*w + 137]', '[161, 161, 15*w + 122]', '[165, 165, w + 15]', '[165, 165, 91*w + 744]', '[165, 165, 4*w + 35]', '[165, 165, 13*w + 107]', '[165, 165, -13*w + 120]', '[165, 165, -4*w + 39]', '[165, 165, -91*w + 835]', '[165, 165, -w + 16]', '[169, 13, -13]', '[171, 57, 3*w + 21]', '[171, 57, -3*w + 24]', '[171, 171, -47*w - 384]', '[171, 171, -20*w - 163]', '[171, 171, 20*w - 183]', '[171, 171, 47*w - 431]', '[172, 86, 114*w - 1046]', '[175, 35, -115*w - 940]', '[175, 175, -11*w - 89]', '[175, 175, -11*w + 100]', '[176, 44, 20*w - 184]', '[176, 44, -20*w - 164]', '[180, 30, -36*w + 330]', '[180, 30, -36*w - 294]', '[180, 90, -2*w - 10]', '[180, 90, -4*w + 34]', '[180, 90, -4*w - 30]', '[180, 90, -2*w + 12]', '[183, 183, -62*w + 569]', '[183, 183, 2*w - 23]', '[183, 183, 2*w + 21]', '[183, 183, -62*w - 507]', '[189, 63, -12*w - 99]', '[189, 63, 12*w - 111]', '[189, 189, 5*w - 48]', '[189, 189, -5*w - 43]', '[192, 24, 8*w - 72]', '[192, 24, 8*w + 64]', '[193, 193, -3*w + 31]', '[193, 193, -3*w - 28]', '[196, 14, 14]', '[197, 197, -w - 16]', '[197, 197, w - 17]', '[199, 199, 235*w + 1921]', '[199, 199, 64*w + 523]', '[201, 201, -155*w - 1267]', '[201, 201, 2*w - 11]', '[201, 201, -2*w - 9]', '[201, 201, 155*w - 1422]', '[207, 69, 6*w - 57]', '[207, 69, 6*w + 51]', '[207, 207, -26*w - 213]', '[207, 207, -11*w + 102]', '[207, 207, -11*w - 91]', '[207, 207, -26*w + 239]', '[209, 209, -6*w + 53]', '[209, 209, -195*w + 1789]', '[209, 209, 195*w + 1594]', '[209, 209, 6*w + 47]', '[212, 106, 56*w - 514]', '[212, 106, 56*w + 458]', '[215, 215, 3*w - 23]', '[215, 215, 3*w + 20]', '[219, 219, 7*w + 59]', '[219, 219, -10*w - 83]', '[219, 219, -10*w + 93]', '[219, 219, 7*w - 66]', '[220, 110, 2*w + 8]', '[220, 110, 16*w + 130]', '[220, 110, 16*w - 146]', '[220, 110, 2*w - 10]', '[223, 223, -31*w + 284]', '[223, 223, 31*w + 253]', '[225, 15, 15]', '[225, 45, -85*w + 780]', '[225, 45, 85*w + 695]', '[225, 75, 9*w + 75]', '[225, 75, -9*w + 84]', '[225, 225, -19*w + 175]', '[225, 225, -8*w + 75]', '[225, 225, 8*w + 67]', '[225, 225, 19*w + 156]', '[227, 227, -12*w - 97]', '[227, 227, -12*w + 109]', '[228, 114, -2*w - 22]', '[228, 114, 32*w + 262]', '[228, 114, 32*w - 294]', '[228, 114, -2*w + 24]', '[231, 231, w + 17]', '[231, 231, 50*w + 409]', '[231, 231, -50*w + 459]', '[231, 231, -w + 18]', '[237, 237, 53*w + 433]', '[237, 237, 2*w - 9]', '[237, 237, -2*w - 7]', '[237, 237, -53*w + 486]', '[239, 239, -38*w + 349]', '[239, 239, -38*w - 311]', '[240, 60, -44*w - 360]', '[240, 60, 4*w - 40]', '[240, 60, -4*w - 36]', '[240, 60, 44*w - 404]', '[241, 241, -5*w - 38]', '[241, 241, -5*w + 43]', '[243, 27, 9*w - 81]', '[243, 27, 9*w + 72]', '[243, 81, 21*w + 171]', '[243, 81, 21*w - 192]', '[243, 243, 4*w + 29]', '[243, 243, 4*w - 33]', '[244, 122, -26*w + 238]', '[244, 122, 26*w + 212]', '[245, 35, -42*w + 385]', '[245, 35, -42*w - 343]', '[252, 42, -138*w - 1128]', '[252, 126, -2*w - 6]', '[252, 126, -2*w + 8]', '[253, 253, 108*w + 883]', '[253, 253, 3*w + 29]', '[253, 253, 3*w - 32]', '[253, 253, 108*w - 991]', '[256, 16, 16]', '[257, 257, -3*w - 19]', '[257, 257, 3*w - 22]', '[265, 265, -7*w + 62]', '[265, 265, 2*w - 7]', '[265, 265, -2*w - 5]', '[265, 265, 7*w + 55]', '[267, 267, -w - 18]', '[267, 267, -154*w - 1259]', '[267, 267, 154*w - 1413]', '[267, 267, w - 19]', '[268, 134, -18*w + 166]', '[268, 134, -18*w - 148]', '[275, 55, 25*w - 230]', '[275, 55, -25*w - 205]', '[275, 275, 79*w - 725]', '[275, 275, 2*w - 25]', '[275, 275, -2*w - 23]', '[275, 275, -79*w - 646]', '[276, 138, -2*w - 4]', '[276, 138, 70*w + 572]', '[276, 138, -70*w + 642]', '[276, 138, 2*w - 6]', '[281, 281, 5*w + 44]', '[281, 281, 5*w - 49]', '[285, 285, 13*w + 105]', '[285, 285, -121*w + 1110]', '[285, 285, 17*w - 155]', '[285, 285, -2*w + 5]', '[285, 285, 2*w + 3]', '[285, 285, -17*w - 138]', '[285, 285, 121*w + 989]', '[285, 285, -13*w + 118]', '[289, 17, -17]', '[292, 146, -2*w - 2]', '[292, 146, 2*w - 4]', '[297, 99, -3*w - 18]', '[297, 99, -87*w - 711]', '[297, 99, -87*w + 798]', '[297, 99, -3*w + 21]', '[297, 297, -37*w + 339]', '[297, 297, -2*w + 3]', '[297, 297, -2*w - 1]', '[297, 297, -37*w - 302]', '[300, 30, 10*w - 90]', '[300, 30, 10*w + 80]', '[300, 150, 2*w]', '[300, 150, 104*w - 954]', '[300, 150, 104*w + 850]', '[300, 150, 2*w - 2]', '[301, 301, 2*w - 1]', '[304, 76, 4*w + 28]', '[304, 76, -4*w + 32]', '[305, 305, w + 19]', '[305, 305, 17*w + 140]', '[305, 305, 17*w - 157]', '[305, 305, w - 20]', '[308, 154, 6*w - 52]', '[308, 154, 6*w + 46]', '[313, 313, 59*w + 482]', '[313, 313, 59*w - 541]', '[315, 105, 3*w + 30]', '[315, 105, -3*w + 33]', '[315, 315, 31*w + 254]', '[315, 315, 73*w + 597]', '[315, 315, -73*w + 670]', '[315, 315, -31*w + 285]', '[316, 158, 6*w + 52]', '[316, 158, 6*w - 58]', '[317, 317, -4*w + 41]', '[317, 317, -4*w - 37]', '[320, 40, -48*w + 440]', '[320, 40, -48*w - 392]', '[321, 321, -22*w + 201]', '[321, 321, -5*w + 42]', '[321, 321, -5*w - 37]', '[321, 321, -22*w - 179]', '[324, 18, 18]', '[324, 54, -102*w + 936]', '[324, 54, 102*w + 834]', '[324, 162, 2*w + 24]', '[324, 162, -2*w + 26]', '[327, 327, -8*w + 71]', '[327, 327, -32*w - 261]', '[327, 327, -32*w + 293]', '[327, 327, -8*w - 63]', '[335, 335, -27*w - 220]', '[335, 335, 3*w - 20]', '[335, 335, -3*w - 17]', '[335, 335, 27*w - 247]', '[336, 84, -16*w - 132]', '[336, 84, 16*w - 148]', '[337, 337, 24*w - 221]', '[337, 337, 24*w + 197]', '[343, 49, -161*w - 1316]', '[345, 345, -w - 20]', '[345, 345, 7*w - 67]', '[345, 345, 67*w - 615]', '[345, 345, -37*w + 340]', '[345, 345, -37*w - 303]', '[345, 345, 67*w + 548]', '[345, 345, 7*w + 60]', '[345, 345, -w + 21]', '[349, 349, -14*w - 113]', '[349, 349, -14*w + 127]', '[356, 178, -18*w - 146]', '[356, 178, -18*w + 164]', '[359, 359, -125*w - 1022]', '[359, 359, 125*w - 1147]', '[361, 19, 19]', '[361, 361, -15*w + 139]', '[361, 361, -15*w - 124]', '[363, 33, 11*w - 99]', '[363, 33, 11*w + 88]', '[363, 363, 4*w - 31]', '[363, 363, 76*w - 697]', '[363, 363, 76*w + 621]', '[363, 363, 4*w + 27]', '[365, 365, 61*w + 499]', '[365, 365, -43*w - 352]', '[365, 365, -43*w + 395]', '[365, 365, 61*w - 560]', '[368, 92, 8*w - 76]', '[368, 92, 8*w + 68]', '[371, 371, 3*w + 16]', '[371, 371, -3*w + 19]', '[375, 75, -55*w - 450]', '[375, 75, 5*w - 50]', '[375, 75, -5*w - 45]', '[375, 75, 55*w - 505]', '[375, 375, 49*w - 450]', '[375, 375, 2*w - 27]', '[375, 375, -2*w - 25]', '[375, 375, -49*w - 401]', '[379, 379, 3*w - 34]', '[379, 379, -3*w - 31]', '[380, 190, 148*w + 1210]', '[380, 190, 14*w - 130]', '[380, 190, 14*w + 116]', '[380, 190, 148*w - 1358]', '[381, 381, 43*w - 394]', '[381, 381, 7*w + 54]', '[381, 381, -7*w + 61]', '[381, 381, -43*w - 351]', '[383, 383, 201*w + 1643]', '[383, 383, 144*w + 1177]', '[385, 385, 96*w - 881]', '[385, 385, -9*w - 76]', '[385, 385, 9*w - 85]', '[385, 385, -96*w - 785]', '[387, 129, 171*w - 1569]', '[387, 387, -w - 21]', '[387, 387, w - 22]', '[393, 393, 13*w + 108]', '[393, 393, 23*w + 189]', '[393, 393, -23*w + 212]', '[393, 393, -13*w + 121]', '[395, 395, -9*w + 80]', '[395, 395, -93*w + 853]', '[395, 395, 93*w + 760]', '[395, 395, 9*w + 71]', '[396, 66, 30*w - 276]', '[396, 66, -30*w - 246]', '[396, 198, 4*w - 42]', '[396, 198, -10*w - 84]', '[396, 198, 10*w - 94]', '[396, 198, -4*w - 38]', '[399, 399, -65*w - 531]', '[399, 399, 5*w + 36]', '[399, 399, -5*w + 41]', '[399, 399, 464*w + 3793]', '[400, 20, 20]', '[400, 100, 12*w + 100]', '[400, 100, -12*w + 112]', '[401, 401, -11*w + 103]', '[401, 401, 11*w + 92]', '[405, 45, -54*w + 495]', '[405, 45, -54*w - 441]', '[405, 135, -3*w - 15]', '[405, 135, -6*w + 51]', '[405, 135, -6*w - 45]', '[405, 135, -3*w + 18]', '[405, 405, -23*w - 187]', '[405, 405, -127*w - 1038]', '[405, 405, -127*w + 1165]', '[405, 405, -23*w + 210]', '[409, 409, 110*w + 899]', '[409, 409, 110*w - 1009]', '[419, 419, -15*w - 121]', '[419, 419, -15*w + 136]', '[420, 210, 38*w - 348]', '[420, 210, 4*w - 30]', '[420, 210, 4*w + 26]', '[420, 210, 38*w + 310]', '[427, 427, 6*w + 53]', '[427, 427, 6*w - 59]', '[428, 214, -2*w - 26]', '[428, 214, 2*w - 28]', '[431, 431, -w - 22]', '[431, 431, w - 23]', '[432, 36, 12*w - 108]', '[432, 36, 12*w + 96]', '[432, 108, 28*w + 228]', '[432, 108, 28*w - 256]', '[433, 433, -19*w + 173]', '[433, 433, -19*w - 154]', '[436, 218, 90*w - 826]', '[436, 218, -90*w - 736]', '[437, 437, 3*w - 17]', '[437, 437, -33*w + 302]', '[437, 437, -33*w - 269]', '[437, 437, -3*w - 14]', '[441, 21, 21]', '[441, 63, -119*w + 1092]', '[441, 63, 119*w + 973]', '[443, 443, -22*w + 203]', '[443, 443, -22*w - 181]', '[445, 445, 36*w + 295]', '[445, 445, 3*w + 32]', '[445, 445, -3*w + 35]', '[445, 445, -36*w + 331]', '[448, 56, -184*w - 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197]', '[9872, 2468, -64*w - 532]', '[9872, 2468, -64*w + 596]', '[9873, 3291, 189*w + 1542]', '[9873, 3291, 189*w - 1731]', '[9873, 9873, 41*w - 362]', '[9873, 9873, 19*w - 141]', '[9873, 9873, 19*w + 122]', '[9873, 9873, 41*w + 321]', '[9875, 1975, -45*w + 400]', '[9875, 1975, -465*w + 4265]', '[9875, 1975, 465*w + 3800]', '[9875, 1975, 45*w + 355]', '[9875, 9875, -12*w - 25]', '[9875, 9875, -153*w - 1247]', '[9875, 9875, 153*w - 1400]', '[9875, 9875, 12*w - 37]', '[9876, 4938, -52*w + 466]', '[9876, 4938, -148*w - 1206]', '[9876, 4938, -148*w + 1354]', '[9876, 4938, -52*w - 414]', '[9885, 9885, -7*w + 120]', '[9885, 9885, -316*w + 2901]', '[9885, 9885, 29*w + 256]', '[9885, 9885, 107*w + 880]', '[9885, 9885, -107*w + 987]', '[9885, 9885, -29*w + 285]', '[9885, 9885, 316*w + 2585]', '[9885, 9885, 7*w + 113]', '[9891, 3297, 2025*w + 16554]', '[9891, 3297, -369*w - 3018]', '[9891, 9891, 5*w - 111]', '[9891, 9891, 19*w - 202]', '[9891, 9891, 19*w + 183]', '[9891, 9891, 5*w + 106]', '[9897, 9897, -43*w - 338]', '[9897, 9897, -77*w - 622]', '[9897, 9897, -77*w + 699]', '[9897, 9897, -43*w + 381]', '[9899, 9899, 35*w - 337]', '[9899, 9899, 10*w - 137]', '[9899, 9899, -10*w - 127]', '[9899, 9899, 35*w + 302]', '[9900, 330, 150*w - 1380]', '[9900, 330, -150*w - 1230]', '[9900, 990, 20*w - 210]', '[9900, 990, -50*w - 420]', '[9900, 990, 50*w - 470]', '[9900, 990, -20*w - 190]', '[9900, 1650, 474*w - 4350]', '[9900, 1650, 12*w - 150]', '[9900, 1650, -12*w - 138]', '[9900, 1650, -474*w - 3876]', '[9900, 4950, -2*w - 100]', '[9900, 4950, 532*w - 4882]', '[9900, 4950, -226*w - 1850]', '[9900, 4950, 14*w - 164]', '[9900, 4950, -14*w - 150]', '[9900, 4950, 226*w - 2076]', '[9900, 4950, -532*w - 4350]', '[9900, 4950, 2*w - 102]', '[9907, 9907, 9*w - 131]', '[9907, 9907, -9*w - 122]', '[9908, 4954, -36*w - 278]', '[9908, 4954, -36*w + 314]', '[9913, 9913, -63*w - 524]', '[9913, 9913, 27*w - 268]', '[9913, 9913, 27*w + 241]', '[9913, 9913, -63*w + 587]', '[9921, 9921, -79*w - 653]', '[9921, 9921, 40*w + 341]', '[9921, 9921, 40*w - 381]', '[9921, 9921, -79*w + 732]', '[9924, 4962, -110*w - 894]', '[9924, 4962, -70*w + 634]', '[9924, 4962, -70*w - 564]', '[9924, 4962, -110*w + 1004]', '[9929, 9929, -21*w - 142]', '[9929, 9929, 21*w - 163]', '[9933, 9933, 13*w - 157]', '[9933, 9933, 503*w - 4616]', '[9933, 9933, -503*w - 4113]', '[9933, 9933, -13*w - 144]', '[9936, 828, -12*w - 24]', '[9936, 828, 420*w + 3432]', '[9936, 828, -420*w + 3852]', '[9936, 828, 12*w - 36]', '[9936, 2484, 760*w - 6972]', '[9936, 2484, -20*w - 132]', '[9936, 2484, 20*w - 152]', '[9936, 2484, -760*w - 6212]', '[9937, 9937, -711*w - 5813]', '[9937, 9937, 51*w - 479]', '[9937, 9937, 51*w + 428]', '[9937, 9937, 1056*w + 8633]', '[9948, 4974, 62*w + 516]', '[9948, 4974, 122*w + 1002]', '[9948, 4974, -122*w + 1124]', '[9948, 4974, -62*w + 578]', '[9949, 9949, -195*w + 1792]', '[9949, 9949, -195*w - 1597]', '[9956, 4978, -176*w - 1442]', '[9956, 4978, 310*w - 2846]', '[9956, 4978, 310*w + 2536]', '[9956, 4978, -176*w + 1618]', '[9959, 9959, -15*w - 76]', '[9959, 9959, 669*w + 5468]', '[9959, 9959, 1125*w + 9196]', '[9959, 9959, 15*w - 91]', '[9961, 9961, 13*w + 46]', '[9961, 9961, 13*w - 59]', '[9967, 9967, -97*w + 884]', '[9967, 9967, -97*w - 787]', '[9968, 2492, 52*w + 436]', '[9968, 2492, -52*w + 488]', '[9969, 9969, -232*w + 2131]', '[9969, 9969, -32*w + 311]', '[9969, 9969, 32*w + 279]', '[9969, 9969, 232*w + 1899]', '[9975, 1995, -325*w - 2655]', '[9975, 1995, 25*w + 180]', '[9975, 1995, -25*w + 205]', '[9975, 1995, 2320*w + 18965]', '[9975, 9975, 32*w - 275]', '[9975, 9975, 221*w + 1804]', '[9975, 9975, -17*w - 100]', '[9975, 9975, 248*w + 2025]', '[9975, 9975, -248*w + 2273]', '[9975, 9975, 17*w - 117]', '[9975, 9975, -221*w + 2025]', '[9975, 9975, -32*w - 243]', '[9977, 9977, 61*w + 508]', '[9977, 9977, 16*w + 163]', '[9977, 9977, -16*w + 179]', '[9977, 9977, -61*w + 569]', '[9981, 3327, -18*w - 111]', '[9981, 3327, 18*w - 129]', '[9981, 9981, 1565*w - 14358]', '[9981, 9981, 205*w + 1673]', '[9981, 9981, -205*w + 1878]', '[9981, 9981, -1565*w - 12793]', '[9988, 4994, 364*w + 2974]', '[9988, 4994, 14*w - 76]', '[9988, 4994, 14*w + 62]', '[9988, 4994, 364*w - 3338]', '[9989, 9989, 163*w + 1336]', '[9989, 9989, -163*w + 1499]', '[9993, 9993, -53*w + 497]', '[9993, 9993, 143*w + 1173]', '[9993, 9993, -143*w + 1316]', '[9993, 9993, 53*w + 444]', '[9995, 9995, 12*w - 35]', '[9995, 9995, 81*w - 736]', '[9995, 9995, -81*w - 655]', '[9995, 9995, -12*w - 23]', '[10000, 100, 100]', '[10000, 500, 60*w + 500]', '[10000, 500, -60*w + 560]', '[10000, 2500, 636*w + 5200]', '[10000, 2500, -636*w + 5836]'], 'label': '2.2.301.1', 'narrow_class_no': 2, 'primes': ['[3, 3, w - 9]', '[3, 3, w + 8]', '[4, 2, 2]', '[5, 5, -6*w + 55]', '[5, 5, -6*w - 49]', '[7, 7, -23*w - 188]', '[11, 11, 5*w - 46]', '[11, 11, -5*w - 41]', '[19, 19, w + 7]', '[19, 19, -w + 8]', '[23, 23, 2*w - 19]', '[23, 23, 2*w + 17]', '[43, 43, 57*w - 523]', '[53, 53, 28*w - 257]', '[53, 53, 28*w + 229]', '[61, 61, -13*w + 119]', '[61, 61, 13*w + 106]', '[67, 67, -9*w + 83]', '[67, 67, -9*w - 74]', '[73, 73, -w - 1]', '[73, 73, w - 2]', '[79, 79, 3*w + 26]', '[79, 79, 3*w - 29]', '[89, 89, -9*w - 73]', '[89, 89, -9*w + 82]', '[107, 107, -w - 13]', '[107, 107, w - 14]', '[109, 109, 45*w - 413]', '[109, 109, -45*w - 368]', '[127, 127, 39*w + 319]', '[127, 127, 39*w - 358]', '[131, 131, 132*w + 1079]', '[131, 131, 75*w + 613]', '[157, 157, 2*w - 13]', '[157, 157, -2*w - 11]', '[169, 13, -13]', '[193, 193, -3*w + 31]', '[193, 193, -3*w - 28]', '[197, 197, -w - 16]', '[197, 197, w - 17]', '[199, 199, 235*w + 1921]', '[199, 199, 64*w + 523]', '[223, 223, -31*w + 284]', '[223, 223, 31*w + 253]', '[227, 227, -12*w - 97]', '[227, 227, -12*w + 109]', '[239, 239, -38*w + 349]', '[239, 239, -38*w - 311]', '[241, 241, -5*w - 38]', '[241, 241, -5*w + 43]', '[257, 257, -3*w - 19]', '[257, 257, 3*w - 22]', '[281, 281, 5*w + 44]', '[281, 281, 5*w - 49]', '[289, 17, -17]', '[313, 313, 59*w + 482]', '[313, 313, 59*w - 541]', '[317, 317, -4*w + 41]', '[317, 317, -4*w - 37]', '[337, 337, 24*w - 221]', '[337, 337, 24*w + 197]', '[349, 349, -14*w - 113]', '[349, 349, -14*w + 127]', '[359, 359, -125*w - 1022]', '[359, 359, 125*w - 1147]', '[379, 379, 3*w - 34]', '[379, 379, -3*w - 31]', '[383, 383, 201*w + 1643]', '[383, 383, 144*w + 1177]', '[401, 401, -11*w + 103]', '[401, 401, 11*w + 92]', '[409, 409, 110*w + 899]', '[409, 409, 110*w - 1009]', '[419, 419, -15*w - 121]', '[419, 419, -15*w + 136]', '[431, 431, -w - 22]', '[431, 431, w - 23]', '[433, 433, -19*w + 173]', '[433, 433, -19*w - 154]', '[443, 443, -22*w + 203]', '[443, 443, -22*w - 181]', '[467, 467, -3*w - 13]', '[467, 467, 3*w - 16]', '[487, 487, -21*w - 173]', '[487, 487, -21*w + 194]', '[503, 503, 99*w + 809]', '[503, 503, 99*w - 908]', '[521, 521, 3*w - 14]', '[521, 521, -3*w - 11]', '[523, 523, 44*w + 359]', '[523, 523, 44*w - 403]', '[541, 541, 60*w - 551]', '[541, 541, -60*w - 491]', '[547, 547, 9*w - 86]', '[547, 547, 9*w + 77]', '[557, 557, -19*w + 176]', '[557, 557, -19*w - 157]', '[569, 569, 5*w + 47]', '[569, 569, -5*w + 52]', '[577, 577, -17*w - 137]', '[577, 577, -17*w + 154]', '[587, 587, 3*w - 11]', '[587, 587, -3*w - 8]', '[593, 593, -6*w - 43]', '[593, 593, -6*w + 49]', '[599, 599, 2*w - 31]', '[599, 599, -2*w - 29]', '[601, 601, 77*w + 629]', '[601, 601, 77*w - 706]', '[607, 607, -7*w + 59]', '[607, 607, -7*w - 52]', '[613, 613, 12*w - 113]', '[613, 613, 12*w + 101]', '[617, 617, -16*w - 133]', '[617, 617, -16*w + 149]', '[647, 647, -3*w - 4]', '[647, 647, 3*w - 7]', '[659, 659, -383*w - 3131]', '[659, 659, -130*w - 1063]', '[677, 677, 3*w - 2]', '[677, 677, 3*w - 1]', '[683, 683, -53*w + 487]', '[683, 683, -53*w - 434]', '[691, 691, 5*w - 37]', '[691, 691, -5*w - 32]', '[701, 701, 89*w - 817]', '[701, 701, 89*w + 728]', '[709, 709, -33*w - 271]', '[709, 709, -33*w + 304]', '[727, 727, -13*w + 116]', '[727, 727, -13*w - 103]', '[733, 733, -11*w - 86]', '[733, 733, -11*w + 97]', '[761, 761, 270*w + 2207]', '[761, 761, 213*w + 1741]', '[773, 773, 6*w - 47]', '[773, 773, -6*w - 41]', '[809, 809, 8*w + 71]', '[809, 809, 8*w - 79]', '[811, 811, -100*w + 917]', '[811, 811, 100*w + 817]', '[821, 821, -4*w - 43]', '[821, 821, 4*w - 47]', '[823, 823, -423*w - 3458]', '[823, 823, -147*w - 1202]', '[827, 827, 199*w - 1826]', '[827, 827, -199*w - 1627]', '[829, 829, 179*w + 1463]', '[829, 829, 179*w - 1642]', '[839, 839, -9*w - 68]', '[839, 839, -9*w + 77]', '[841, 29, -29]', '[859, 859, -20*w - 161]', '[859, 859, -20*w + 181]', '[877, 877, 9*w - 88]', '[877, 877, 9*w + 79]', '[883, 883, -3*w - 38]', '[883, 883, 3*w - 41]', '[887, 887, -117*w - 956]', '[887, 887, 117*w - 1073]', '[907, 907, -141*w - 1153]', '[907, 907, 141*w - 1294]', '[919, 919, -30*w + 277]', '[919, 919, -30*w - 247]', '[929, 929, -15*w + 134]', '[929, 929, -15*w - 119]', '[937, 937, -37*w - 301]', '[937, 937, -37*w + 338]', '[947, 947, 94*w + 769]', '[947, 947, 94*w - 863]', '[961, 31, -31]', '[967, 967, -51*w - 418]', '[967, 967, -51*w + 469]', '[977, 977, -29*w - 239]', '[977, 977, -29*w + 268]', '[983, 983, -9*w + 76]', '[983, 983, -9*w - 67]', '[997, 997, 202*w - 1853]', '[997, 997, 202*w + 1651]']}
-
nf_fields • Show schema
Hide schema
{'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [-75, -1, 1], 'conductor': 301, 'degree': 2, 'dirichlet_group': [1, 300], 'disc_abs': 301, 'disc_rad': 301, 'disc_sign': 1, 'frobs': [[2, [[2, 1]]], [3, [[1, 2]]], [5, [[1, 2]]], [7, [0]], [11, [[1, 2]]], [13, [[2, 1]]], [17, [[2, 1]]], [19, [[1, 2]]], [23, [[1, 2]]], [29, [[2, 1]]], [31, [[2, 1]]], [37, [[2, 1]]], [41, [[2, 1]]], [43, [0]], [47, [[2, 1]]], [53, [[1, 2]]], [59, [[2, 1]]]], 'gal_is_abelian': True, 'gal_is_cyclic': True, 'gal_is_solvable': True, 'galois_disc_exponents': [1, 1], 'galois_label': '2T1', 'galt': 1, 'grd': 17.349351572897472, 'index': 1, 'inessentialp': [], 'is_galois': True, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '2.2.301.1', 'local_algs': ['7.2.1.1', '43.2.1.2'], 'monogenic': 1, 'num_ram': 2, 'r2': 0, 'ramps': [7, 43], 'rd': 17.3493515729, 'regulator': {'__RealLiteral__': 0, 'data': '10.0321006181', 'prec': 44}, 'res': {}, 'subfield_mults': [], 'subfields': [], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( 1311 a + 10717 \\)'], 'used_grh': False, 'zk': ['1', 'a']}