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hmf_forms • Show schema
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{'deg': 2, 'dimension': 4, 'disc': 184, 'field_bad_primes': [2, 23], 'field_label': '2.2.184.1', 'is_CM': 'no', 'is_base_change': 'no', 'label': '2.2.184.1-8.1-g', 'label_nsuffix': 6, 'label_suffix': 'g', 'level_bad_primes': [2], 'level_ideal': '[8, 4, 46*w - 312]', 'level_label': '8.1', 'level_norm': 8, 'parallel_weight': 2, 'short_label': '8.1-g', 'weight': '[2, 2]'}
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hmf_hecke • Show schema
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{'AL_eigenvalues': [['[2, 2, 23*w - 156]', 1]], 'hecke_eigenvalues': [0, '1/2*e^3 - e^2 - 7/2*e + 4', 'e', 'e - 1', '-1/2*e^3 + e^2 + 7/2*e - 3', '-1/2*e^3 + e^2 + 7/2*e - 5', 'e + 1', '-2*e^2 + 2*e + 8', '-e^2 - e + 8', 'e^3 - 3*e^2 - 6*e + 8', 'e^3 - 9*e + 1', '-2*e^2 + 4*e + 9', '-3/2*e^3 + 2*e^2 + 23/2*e - 11', '-e^2 + 4*e + 7', '-1/2*e^3 + 13/2*e - 3', 'e^3 - e^2 - 9*e + 1', '1/2*e^3 - 2*e^2 + 3/2*e + 9', '-2*e^3 + 3*e^2 + 14*e - 13', '3/2*e^3 - 3*e^2 - 19/2*e + 9', '1/2*e^3 - e^2 - 1/2*e + 1', '-1/2*e^3 - e^2 + 17/2*e + 2', '-3/2*e^3 + e^2 + 27/2*e - 2', 'e^3 - 3*e^2 - 6*e + 10', '-e^2 - e + 6', 'e^3 + e^2 - 11*e - 3', '1/2*e^3 + 2*e^2 - 17/2*e - 9', '-2*e^3 + 4*e^2 + 10*e - 12', '-2*e^3 + 4*e^2 + 9*e - 6', '-5/2*e^3 + 5*e^2 + 27/2*e - 10', '3/2*e^3 - e^2 - 25/2*e + 8', '-2*e^2 + 5*e + 12', '-3*e^3 + 4*e^2 + 15*e - 2', '4*e^3 - 10*e^2 - 20*e + 26', '2*e - 14', '-e^3 + 2*e^2 + 7*e + 6', '-1/2*e^3 + 11/2*e + 13', '1/2*e^3 - 11/2*e + 13', '5/2*e^3 - 5*e^2 - 25/2*e + 5', '3/2*e^3 - 3*e^2 - 13/2*e + 2', '2*e^3 - 4*e^2 - 11*e + 6', 'e^3 - 6*e^2 + 15', '-3/2*e^3 - e^2 + 25/2*e + 13', '-3/2*e^3 + 4*e^2 + 17/2*e - 12', '1/2*e^3 - 3/2*e - 4', '5/2*e^3 - 5*e^2 - 45/2*e + 17', '-5/2*e^3 + 5*e^2 + 45/2*e - 23', '-9/2*e^3 + 10*e^2 + 39/2*e - 28', '11/2*e^3 - 10*e^2 - 61/2*e + 28', '-3/2*e^3 + 4*e^2 + 15/2*e - 5', '-e^3 + e^2 + 5*e + 7', 'e^3 - 11*e + 12', 'e^3 - 11*e - 12', '2*e^2 + 2*e - 5', '2*e^3 - 6*e^2 - 12*e + 27', '3/2*e^3 - 5*e^2 - 7/2*e + 17', '5/2*e^3 - 3*e^2 - 33/2*e + 9', '-e^3 + 2*e^2 + 9*e - 20', '-e^3 + 2*e^2 + 9*e + 4', '7/2*e^3 - 7*e^2 - 35/2*e + 14', '6*e^2 - 8*e - 18', 'e^3 + 4*e^2 - 13*e - 22', '-e^3 - e^2 + 13*e + 13', '3/2*e^3 - 31/2*e + 9', '1/2*e^3 - 19/2*e - 7', '-5/2*e^3 + 4*e^2 + 39/2*e - 23', '-e^3 + 5*e^2 - 5*e - 25', '-9/2*e^3 + 6*e^2 + 65/2*e - 29', 'e^3 + e^2 - 3*e - 24', '7/2*e^3 - 10*e^2 - 39/2*e + 20', '-3/2*e^3 + 2*e^2 + 11/2*e - 9', '3*e^3 - 7*e^2 - 17*e + 29', '-3*e^3 + 6*e^2 + 15*e - 22', '-1/2*e^3 + 5*e^2 - 1/2*e - 5', '4*e^2 - 3*e - 31', '2*e^3 - 6*e^2 - 9*e + 17', '-3/2*e^3 + e^2 + 17/2*e + 3', '2*e^3 - 6*e^2 - 2*e + 10', '-5*e^3 + 8*e^2 + 33*e - 18', '-e^3 + e + 22', '4*e^3 - 10*e^2 - 24*e + 18', '-7/2*e^3 + 5*e^2 + 51/2*e - 25', '-1/2*e^3 + 3*e^2 - 11/2*e - 17', '-5/2*e^3 + 5*e^2 + 35/2*e - 27', '5*e + 7', '-5*e^3 + 9*e^2 + 23*e - 15', '13/2*e^3 - 14*e^2 - 69/2*e + 35', '3/2*e^3 - e^2 - 37/2*e + 4', '-3*e^3 + 4*e^2 + 26*e - 16', '1/2*e^3 + e^2 - 13/2*e - 18', '-1/2*e^3 - e^2 + 13/2*e - 10', '-3*e^3 + 9*e^2 + 16*e - 28', 'e^3 + e^2 - 4*e - 12', '3/2*e^3 - 2*e^2 - 21/2*e + 7', '1/2*e^3 - 2*e^2 + 1/2*e + 7', '6*e^3 - 12*e^2 - 35*e + 44', '7/2*e^3 - 7*e^2 - 25/2*e + 24', '1/2*e^3 + 2*e^2 - 33/2*e - 1', '5*e^3 - 7*e^2 - 39*e + 21', '3/2*e^3 - 3*e^2 - 45/2*e + 20', '-6*e^3 + 12*e^2 + 45*e - 40', '3/2*e^3 - 6*e^2 - 15/2*e + 43', '-3*e^2 - 7', '-3/2*e^3 + 5*e^2 + 15/2*e - 29', '-1/2*e^3 - e^2 + 5/2*e - 5', '-5/2*e^3 + 4*e^2 + 35/2*e - 25', '-1/2*e^3 + 2*e^2 - 5/2*e - 17', '3*e^3 - 10*e^2 - 15*e + 40', 'e^3 + 2*e^2 - 5*e - 8', '-9/2*e^3 + 5*e^2 + 65/2*e - 27', '-3/2*e^3 + 7*e^2 - 5/2*e - 35', '-13/2*e^3 + 11*e^2 + 99/2*e - 33', '-e^3 + 22*e - 11', '-2*e - 26', 'e^3 - 2*e^2 - 7*e + 34', '-3/2*e^3 + 4*e^2 + 15/2*e - 21', 'e^3 - e^2 - 5*e + 9', '6*e^3 - 7*e^2 - 30*e - 6', '17/2*e^3 - 22*e^2 - 85/2*e + 54', '5/2*e^3 - 4*e^2 - 37/2*e + 17', 'e^2 - 6*e - 5', '6*e^3 - 12*e^2 - 41*e + 38', '1/2*e^3 - e^2 + 17/2*e - 6', '-2*e^3 + 9*e^2 + 14*e - 47', '5/2*e^3 - 10*e^2 - 33/2*e + 29', '-3/2*e^3 + e^2 + 17/2*e + 23', '2*e^3 - 6*e^2 - 9*e - 3', '1/2*e^3 + e^2 - 7/2*e + 1', '-e^3 + 4*e^2 + 4*e - 21', '-7/2*e^3 + 4*e^2 + 57/2*e - 14', '-1/2*e^3 - 2*e^2 + 27/2*e + 6', '-5*e^3 + 6*e^2 + 32*e - 15', '7/2*e^3 - 11*e^2 - 21/2*e + 35', '9/2*e^3 - 3*e^2 - 71/2*e - 4', 'e^3 - 8*e^2 + 8*e + 16', '-2*e^3 + 5*e^2 - 3*e - 16', '8*e^3 - 15*e^2 - 53*e + 56', '4*e^2 - 14*e - 2', '5*e^3 - 6*e^2 - 39*e + 10', 'e^3 - 3*e^2 + 14', '-3*e^3 + 5*e^2 + 20*e - 22', '7/2*e^3 - 9*e^2 - 59/2*e + 37', '-7/2*e^3 + 9*e^2 + 59/2*e - 35', '-e^3 + 3*e^2 + 3*e - 1', '3/2*e^3 - 2*e^2 - 19/2*e - 3', '-9/2*e^3 + 14*e^2 + 53/2*e - 57', '5*e^2 + 4*e - 19', '-4*e^2 - 4*e + 20', '-4*e^3 + 12*e^2 + 24*e - 44', '13/2*e^3 - 11*e^2 - 87/2*e + 42', '2*e^3 - 6*e^2 + e + 22', '-e^3 + 7*e^2 - 16', 'e^3 + 3*e^2 - 10*e - 24', '-9/2*e^3 + 9*e^2 + 45/2*e - 39', '3/2*e^3 - 3*e^2 - 23/2*e - 11', '-1/2*e^3 + e^2 + 13/2*e - 27', '11/2*e^3 - 11*e^2 - 61/2*e + 38', '4*e^3 - 8*e^2 - 17*e + 26', '5*e^3 - 11*e^2 - 33*e + 15', '1/2*e^3 + 11/2*e - 29', '1/2*e^3 - 3*e^2 - 9/2*e + 22', '3/2*e^3 - 5*e^2 - 19/2*e + 10', '-15/2*e^3 + 22*e^2 + 93/2*e - 58', '-1/2*e^3 + 8*e^2 + 23/2*e - 62', '-5/2*e^3 + 25/2*e - 4', '-5*e^3 + 15*e^2 + 25*e - 64', '-2*e^2 - 5*e + 43', '7/2*e^3 - 9*e^2 - 45/2*e + 1', '7/2*e^3 - 7*e^2 - 25/2*e + 24', '6*e^3 - 12*e^2 - 35*e + 44', '3*e^3 - 6*e^2 - 15*e + 1', '-5/2*e^3 + 8*e^2 + 49/2*e - 55', '-5*e^3 + 13*e^2 + 37*e - 29'], 'hecke_polynomial': 'x^4 - 3*x^3 - 5*x^2 + 13*x - 2', 'label': '2.2.184.1-8.1-g'}
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hmf_fields • Show schema
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{'degree': 2, 'discriminant': 184, 'ideals': ['[1, 1, 1]', '[2, 2, 23*w - 156]', '[3, 3, -w - 7]', '[3, 3, w - 7]', '[4, 2, 2]', '[5, 5, -9*w + 61]', '[5, 5, -9*w - 61]', '[6, 6, 5*w + 34]', '[6, 6, -5*w + 34]', '[7, 7, 4*w - 27]', '[7, 7, 4*w + 27]', '[8, 4, 46*w - 312]', '[9, 3, 3]', '[9, 9, 14*w + 95]', '[9, 9, -14*w + 95]', '[10, 10, w - 6]', '[10, 10, w + 6]', '[12, 6, -2*w - 14]', '[12, 6, 2*w - 14]', '[14, 14, -3*w - 20]', '[14, 14, -3*w + 20]', '[15, 15, 2*w - 13]', '[15, 15, 32*w - 217]', '[15, 15, 32*w + 217]', '[15, 15, 2*w + 13]', '[16, 4, 4]', '[18, 6, 69*w - 468]', '[18, 18, -w - 8]', '[18, 18, w - 8]', '[20, 10, -18*w + 122]', '[20, 10, -18*w - 122]', '[21, 21, -55*w + 373]', '[21, 21, -w - 5]', '[21, 21, -w + 5]', '[21, 21, -55*w - 373]', '[23, 23, 78*w - 529]', '[24, 12, 10*w + 68]', '[24, 12, -10*w + 68]', '[25, 5, 5]', '[25, 25, 6*w + 41]', '[25, 25, -6*w + 41]', '[27, 9, -3*w - 21]', '[27, 9, 3*w - 21]', '[27, 27, 37*w - 251]', '[27, 27, -37*w - 251]', '[28, 14, 8*w - 54]', '[28, 14, 8*w + 54]', '[30, 30, -w - 4]', '[30, 30, -13*w + 88]', '[30, 30, -13*w - 88]', '[30, 30, -w + 4]', '[32, 8, 92*w - 624]', '[35, 35, -w - 9]', '[35, 35, -19*w - 129]', '[35, 35, 19*w - 129]', '[35, 35, w - 9]', '[36, 6, 6]', '[36, 18, 28*w + 190]', '[36, 18, -28*w + 190]', '[37, 37, -w - 3]', '[37, 37, w - 3]', '[40, 20, 2*w - 12]', '[40, 20, 2*w + 12]', '[41, 41, -2*w + 15]', '[41, 41, 2*w + 15]', '[42, 42, w + 2]', '[42, 42, 41*w + 278]', '[42, 42, 41*w - 278]', '[42, 42, w - 2]', '[45, 15, -27*w + 183]', '[45, 15, -27*w - 183]', '[45, 45, -w - 1]', '[45, 45, -7*w + 47]', '[45, 45, -7*w - 47]', '[45, 45, -w + 1]', '[46, 46, -w]', '[48, 12, -4*w - 28]', '[48, 12, 4*w - 28]', '[49, 7, 7]', '[49, 49, -60*w + 407]', '[49, 49, 60*w + 407]', '[50, 10, 115*w - 780]', '[50, 50, -7*w - 48]', '[50, 50, 7*w - 48]', '[53, 53, -3*w - 19]', '[53, 53, 3*w - 19]', '[54, 18, 15*w + 102]', '[54, 18, -15*w + 102]', '[54, 54, w + 10]', '[54, 54, -w + 10]', '[56, 28, -6*w - 40]', '[56, 28, -6*w + 40]', '[59, 59, 11*w - 75]', '[59, 59, -11*w - 75]', '[60, 30, 4*w - 26]', '[60, 30, 64*w - 434]', '[60, 30, 64*w + 434]', '[60, 30, 4*w + 26]', '[61, 61, -5*w + 33]', '[61, 61, 5*w + 33]', '[63, 21, 12*w - 81]', '[63, 21, 12*w + 81]', '[63, 63, 22*w - 149]', '[63, 63, 2*w - 11]', '[63, 63, 2*w + 11]', '[63, 63, 22*w + 149]', '[64, 8, 8]', '[69, 69, -17*w - 115]', '[69, 69, -17*w + 115]', '[70, 70, -3*w + 22]', '[70, 70, 51*w + 346]', '[70, 70, -51*w + 346]', '[70, 70, 3*w + 22]', '[72, 12, 138*w - 936]', '[72, 36, -2*w - 16]', '[72, 36, 2*w - 16]', '[73, 73, -24*w - 163]', '[73, 73, -24*w + 163]', '[74, 74, -225*w + 1526]', '[74, 74, 87*w - 590]', '[75, 15, -5*w - 35]', '[75, 15, 5*w - 35]', '[75, 75, -w - 11]', '[75, 75, 83*w - 563]', '[75, 75, -83*w - 563]', '[75, 75, w - 11]', '[79, 79, 50*w + 339]', '[79, 79, 50*w - 339]', '[80, 20, -36*w + 244]', '[80, 20, -36*w - 244]', '[81, 9, 9]', '[81, 27, 42*w + 285]', '[81, 27, -42*w + 285]', '[81, 81, 8*w + 55]', '[81, 81, -8*w + 55]', '[82, 82, 33*w - 224]', '[82, 82, -33*w - 224]', '[84, 42, -110*w + 746]', '[84, 42, -2*w - 10]', '[84, 42, -2*w + 10]', '[84, 42, -110*w - 746]', '[90, 30, 3*w - 18]', '[90, 30, 3*w + 18]', '[90, 90, 11*w - 74]', '[90, 90, 133*w + 902]', '[90, 90, 133*w - 902]', '[90, 90, 11*w + 74]', '[92, 46, 156*w - 1058]', '[96, 24, 20*w + 136]', '[96, 24, -20*w + 136]', '[98, 14, 161*w - 1092]', '[98, 98, -w - 12]', '[98, 98, w - 12]', '[100, 10, 10]', '[100, 50, 12*w + 82]', '[100, 50, -12*w + 82]', '[103, 103, 2*w - 9]', '[103, 103, -2*w - 9]', '[105, 105, -106*w + 719]', '[105, 105, -4*w + 29]', '[105, 105, -16*w + 109]', '[105, 105, -2*w + 17]', '[105, 105, 2*w + 17]', '[105, 105, 16*w + 109]', '[105, 105, 4*w + 29]', '[105, 105, 106*w + 719]', '[106, 106, 31*w - 210]', '[106, 106, -31*w - 210]', '[108, 18, -6*w - 42]', '[108, 18, 6*w - 42]', '[108, 54, 74*w - 502]', '[108, 54, -74*w - 502]', '[109, 109, 73*w - 495]', '[109, 109, -395*w + 2679]', '[111, 111, -4*w - 25]', '[111, 111, 10*w + 67]', '[111, 111, -10*w + 67]', '[111, 111, 4*w - 25]', '[112, 28, 16*w - 108]', '[112, 28, 16*w + 108]', '[115, 115, -3*w - 23]', '[115, 115, 3*w - 23]', '[118, 118, 9*w + 62]', '[118, 118, -9*w + 62]', '[120, 60, -2*w - 8]', '[120, 60, -26*w + 176]', '[120, 60, -26*w - 176]', '[120, 60, -2*w + 8]', '[121, 11, -11]', '[122, 122, 21*w + 142]', '[122, 122, -21*w + 142]', '[123, 123, -w - 13]', '[123, 123, -29*w - 197]', '[123, 123, 29*w - 197]', '[123, 123, w - 13]', '[125, 25, -45*w + 305]', '[125, 25, -45*w - 305]', '[125, 125, -3*w + 17]', '[125, 125, -3*w - 17]', '[126, 42, -9*w - 60]', '[126, 42, -9*w + 60]', '[126, 126, -59*w - 400]', '[126, 126, -5*w + 32]', '[126, 126, -5*w - 32]', '[126, 126, -59*w + 400]', '[128, 16, 184*w - 1248]', '[131, 131, 65*w + 441]', '[131, 131, 65*w - 441]', '[135, 45, 6*w - 39]', '[135, 45, 96*w - 651]', '[135, 45, 96*w + 651]', '[135, 45, 6*w + 39]', '[135, 135, 8*w - 53]', '[135, 135, 2*w - 7]', '[135, 135, 2*w + 7]', '[135, 135, 8*w + 53]', '[138, 138, 7*w + 46]', '[138, 138, 7*w - 46]', '[139, 139, -129*w + 875]', '[139, 139, -285*w + 1933]', '[140, 70, -2*w - 18]', '[140, 70, -38*w - 258]', '[140, 70, 38*w - 258]', '[140, 70, 2*w - 18]', '[144, 12, 12]', '[144, 36, 56*w + 380]', '[144, 36, -56*w + 380]', '[146, 146, -5*w + 36]', '[146, 146, -5*w - 36]', '[147, 21, -7*w - 49]', '[147, 21, 7*w - 49]', '[147, 147, 47*w - 319]', '[147, 147, 13*w - 89]', '[147, 147, -13*w - 89]', '[147, 147, -47*w - 319]', '[148, 74, -2*w - 6]', '[148, 74, 2*w - 6]', '[149, 149, 15*w - 101]', '[149, 149, 15*w + 101]', '[150, 30, 25*w + 170]', '[150, 30, -25*w + 170]', '[150, 150, w + 14]', '[150, 150, 97*w + 658]', '[150, 150, -97*w + 658]', '[150, 150, -w + 14]', '[157, 157, -349*w + 2367]', '[157, 157, 119*w - 807]', '[158, 158, -3*w - 16]', '[158, 158, -3*w + 16]', '[159, 159, -40*w + 271]', '[159, 159, 2*w - 5]', '[159, 159, -2*w - 5]', '[159, 159, 40*w + 271]', '[160, 40, 4*w - 24]', '[160, 40, 4*w + 24]', '[161, 161, 10*w + 69]', '[161, 161, -10*w + 69]', '[162, 18, 207*w - 1404]', '[162, 54, -3*w - 24]', '[162, 54, 3*w - 24]', '[162, 162, -17*w - 116]', '[162, 162, 17*w - 116]', '[163, 163, 21*w - 143]', '[163, 163, -21*w - 143]', '[164, 82, -4*w + 30]', '[164, 82, 4*w + 30]', '[168, 84, 2*w + 4]', '[168, 84, 82*w + 556]', '[168, 84, 82*w - 556]', '[168, 84, 2*w - 4]', '[169, 13, -13]', '[175, 35, 20*w - 135]', '[175, 35, 20*w + 135]', '[175, 175, 142*w - 963]', '[175, 175, 2*w - 3]', '[175, 175, 2*w + 3]', '[175, 175, 142*w + 963]', '[177, 177, -152*w + 1031]', '[177, 177, -2*w + 19]', '[177, 177, 2*w + 19]', '[177, 177, -308*w + 2089]', '[179, 179, -w - 15]', '[179, 179, w - 15]', '[180, 30, -54*w + 366]', '[180, 30, -54*w - 366]', '[180, 90, -2*w - 2]', '[180, 90, -14*w + 94]', '[180, 90, -14*w - 94]', '[180, 90, -2*w + 2]', '[181, 181, 35*w + 237]', '[181, 181, 35*w - 237]', '[183, 183, -68*w - 461]', '[183, 183, 2*w - 1]', '[183, 183, -2*w - 1]', '[183, 183, 68*w - 461]', '[184, 92, -2*w]', '[185, 185, -34*w - 231]', '[185, 185, 88*w - 597]', '[185, 185, 88*w + 597]', '[185, 185, -34*w + 231]', '[189, 63, -165*w + 1119]', '[189, 63, -3*w - 15]', '[189, 63, -3*w + 15]', '[189, 63, -165*w - 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3]', '[727, 727, -4*w - 3]', '[733, 733, -7*w - 39]', '[733, 733, 7*w - 39]', '[739, 739, -21*w + 145]', '[739, 739, 21*w + 145]', '[743, 743, 18*w + 119]', '[743, 743, -18*w + 119]', '[751, 751, 16*w - 105]', '[751, 751, -16*w - 105]', '[757, 757, -89*w - 603]', '[757, 757, -89*w + 603]', '[761, 761, -740*w + 5019]', '[761, 761, -272*w + 1845]', '[773, 773, 27*w + 181]', '[773, 773, -27*w + 181]', '[797, 797, -39*w + 263]', '[797, 797, -39*w - 263]', '[809, 809, 64*w + 435]', '[809, 809, -64*w + 435]', '[811, 811, -3*w - 35]', '[811, 811, 3*w - 35]', '[839, 839, 270*w - 1831]', '[839, 839, -822*w + 5575]', '[841, 29, -29]', '[857, 857, 32*w + 219]', '[857, 857, -32*w + 219]', '[859, 859, -405*w + 2747]', '[859, 859, -561*w + 3805]', '[883, 883, -231*w + 1567]', '[883, 883, -1011*w + 6857]', '[911, 911, -54*w + 365]', '[911, 911, -54*w - 365]', '[919, 919, 8*w - 45]', '[919, 919, -8*w - 45]', '[929, 929, 40*w - 273]', '[929, 929, 40*w + 273]', '[941, 941, 15*w - 97]', '[941, 941, -15*w - 97]', '[947, 947, -23*w + 159]', '[947, 947, 23*w + 159]', '[961, 31, -31]', '[983, 983, 168*w + 1139]', '[983, 983, 168*w - 1139]']}
-
nf_fields • Show schema
Hide schema
{'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [-46, 0, 1], 'conductor': 184, 'degree': 2, 'dirichlet_group': [1, 91], 'disc_abs': 184, 'disc_rad': 46, 'disc_sign': 1, 'frobs': [[2, [0]], [3, [[1, 2]]], [5, [[1, 2]]], [7, [[1, 2]]], [11, [[2, 1]]], [13, [[2, 1]]], [17, [[2, 1]]], [19, [[2, 1]]], [23, [0]], [29, [[2, 1]]], [31, [[2, 1]]], [37, [[1, 2]]], [41, [[1, 2]]], [43, [[2, 1]]], [47, [[2, 1]]], [53, [[1, 2]]], [59, [[1, 2]]]], 'gal_is_abelian': True, 'gal_is_cyclic': True, 'gal_is_solvable': True, 'galois_disc_exponents': [3, 1], 'galois_label': '2T1', 'galt': 1, 'grd': 13.564659966250536, 'index': 1, 'inessentialp': [], 'is_galois': True, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '2.2.184.1', 'local_algs': ['2.2.3.3', '23.2.1.1'], 'monogenic': 1, 'num_ram': 2, 'r2': 0, 'ramps': [2, 23], 'rd': 13.5646599663, 'regulator': {'__RealLiteral__': 0, 'data': '10.7928181024', 'prec': 44}, 'res': {}, 'subfield_mults': [], 'subfields': [], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( 3588 a + 24335 \\)'], 'used_grh': False, 'zk': ['1', 'a']}