-
hmf_forms • Show schema
{'deg': 3, 'dimension': 17, 'disc': 1573, 'field_bad_primes': [11, 13], 'field_label': '3.3.1573.1', 'is_CM': 'no', 'is_base_change': 'no', 'label': '3.3.1573.1-11.1-e', 'label_nsuffix': 4, 'label_suffix': 'e', 'level_bad_primes': [11], 'level_ideal': '[11, 11, -w^2 + 5]', 'level_label': '11.1', 'level_norm': 11, 'parallel_weight': 2, 'short_label': '11.1-e', 'weight': '[2, 2, 2]'} -
hmf_hecke • Show schema
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2934886565/2534492*e^11 - 793334556/633623*e^10 + 6923126719/1267246*e^9 + 5098740529/2534492*e^8 - 16377617757/1267246*e^7 - 1237090261/1267246*e^6 + 38589870457/2534492*e^5 - 60740623/1267246*e^4 - 5115111403/633623*e^3 + 21196879/1267246*e^2 + 776254224/633623*e - 116002731/633623', '1374617/2534492*e^16 - 1379675/1267246*e^15 - 37303929/2534492*e^14 + 71659387/2534492*e^13 + 401178939/2534492*e^12 - 178478749/633623*e^11 - 550304005/633623*e^10 + 3408747925/2534492*e^9 + 1672348235/633623*e^8 - 3994953939/1267246*e^7 - 11461961295/2534492*e^6 + 2132381177/633623*e^5 + 2473667411/633623*e^4 - 801368556/633623*e^3 - 670987682/633623*e^2 + 133864275/633623*e + 19309108/633623', '1875761/1900869*e^16 - 29364131/7603476*e^15 - 84224605/3801738*e^14 + 768683531/7603476*e^13 + 1280380511/7603476*e^12 - 7795947787/7603476*e^11 - 502335493/1267246*e^10 + 9695351048/1900869*e^9 - 5994423325/7603476*e^8 - 25076405306/1900869*e^7 + 5834704395/1267246*e^6 + 135808354697/7603476*e^5 - 22719061733/3801738*e^4 - 14568953911/1267246*e^3 + 8782079281/3801738*e^2 + 3998455493/1900869*e - 298888934/633623', '8585213/7603476*e^16 - 18361357/3801738*e^15 - 185227241/7603476*e^14 + 951029597/7603476*e^13 + 1286333111/7603476*e^12 - 4750730405/3801738*e^11 - 315996873/1267246*e^10 + 46265872451/7603476*e^9 - 3180167173/1900869*e^8 - 58118381929/3801738*e^7 + 16201165129/2534492*e^6 + 38140602125/1900869*e^5 - 13495432825/1900869*e^4 - 15923652131/1267246*e^3 + 4303219088/1900869*e^2 + 4094314343/1900869*e - 301867562/633623'], 'hecke_polynomial': 'x^17 - 4*x^16 - 22*x^15 + 103*x^14 + 160*x^13 - 1019*x^12 - 309*x^11 + 4873*x^10 - 1166*x^9 - 11821*x^8 + 5385*x^7 + 14542*x^6 - 7055*x^5 - 8208*x^4 + 3394*x^3 + 1198*x^2 - 660*x + 72', 'label': '3.3.1573.1-11.1-e'} -
hmf_fields • Show schema
{'degree': 3, 'discriminant': 1573, 'ideals': ['[1, 1, 1]', '[2, 2, -w]', '[4, 2, w^2 - w - 7]', '[4, 4, w + 2]', '[5, 5, w - 1]', '[7, 7, w + 1]', '[8, 2, 2]', '[8, 8, w - 2]', '[10, 10, -w^2 + 6]', '[11, 11, -w^2 + 5]', '[13, 13, w + 3]', '[13, 13, -2*w + 1]', '[14, 14, -w^2 + 4*w - 2]', '[16, 4, -2*w]', '[16, 4, -w^2 + 3*w + 1]', '[16, 16, -w^2 + 2*w]', '[19, 19, 2*w^2 - w - 15]', '[20, 10, -w^2 + w + 5]', '[20, 20, w^2 - 2*w - 4]', '[22, 22, w - 4]', '[25, 5, w^2 - 7]', '[25, 25, -2*w^2 + 2*w + 15]', '[26, 26, w^2 + w - 4]', '[26, 26, w^2 - 2*w - 2]', '[27, 3, 3]', '[28, 14, w^2 - w - 9]', '[28, 28, -w^2 + 8]', '[31, 31, w^2 - 2*w - 1]', '[32, 4, 2*w^2 - 2*w - 14]', '[32, 8, 2*w + 4]', '[32, 32, w^2 - 4]', '[35, 35, w^2 - 1]', '[37, 37, -3*w^2 + 2*w + 23]', '[38, 38, -w^2 + w + 4]', '[40, 10, 2*w - 2]', '[40, 40, w^2 - 3*w + 2]', '[41, 41, -2*w - 1]', '[44, 22, w^2 - w - 1]', '[44, 44, -w^2 + 4*w]', '[47, 47, w^2 - 3]', '[49, 7, w^2 - 2*w - 5]', '[49, 49, -2*w + 5]', '[50, 10, -w^2 + 2]', '[50, 50, -w - 4]', '[52, 26, -w^2 + w - 1]', '[52, 26, w^2 - w - 3]', '[52, 52, -w^2 + 3*w + 2]', '[52, 52, -3*w^2 + 2*w + 20]', '[54, 6, -3*w]', '[55, 55, -2*w - 3]', '[56, 14, 2*w + 2]', '[56, 56, w^2 - w - 2]', '[59, 59, 2*w - 3]', '[62, 62, w^2 - 6*w + 2]', '[64, 4, 4]', '[64, 8, w^2 + w - 5]', '[64, 16, 2*w - 4]', '[64, 64, -w^2 - 3*w + 2]', '[65, 65, w^2 - 2*w - 9]', '[65, 65, w^2 + 2*w - 3]', '[67, 67, w - 5]', '[70, 70, -3*w^2 + 3*w + 20]', '[71, 71, w^2 - 2*w - 11]', '[73, 73, w^2 + 1]', '[74, 74, w^2 - 2*w - 6]', '[76, 38, w^2 + w + 1]', '[76, 76, 3*w - 2]', '[77, 77, -2*w^2 + w + 17]', '[80, 20, -2*w^2 + 12]', '[80, 20, 3*w^2 - 9*w + 1]', '[80, 80, w^2 - w - 10]', '[82, 82, 2*w^2 + w]', '[83, 83, -4*w^2 + 3*w + 27]', '[88, 22, -2*w^2 + 10]', '[88, 88, w^2 - 2*w - 8]', '[89, 89, w^2 - 2*w - 7]', '[91, 91, -2*w^2 + 2*w + 11]', '[91, 91, -2*w^2 - w + 1]', '[94, 94, -w^2 - 4*w + 2]', '[95, 95, -w^2 + 11]', '[97, 97, w^2 - 6*w + 1]', '[98, 14, w^2 - 2*w + 2]', '[98, 98, 2*w^2 - 5*w]', '[100, 10, w^2 - 5*w + 3]', '[100, 20, 3*w^2 - 16]', '[100, 50, w^2 - 3*w - 3]', '[100, 100, -2*w^2 + 5*w + 2]', '[104, 26, 2*w + 6]', '[104, 26, -4*w + 2]', '[104, 104, 3*w^2 - 3*w - 22]', '[104, 104, w^2 + w - 6]', '[108, 6, 3*w^2 - 3*w - 21]', '[108, 12, 3*w + 6]', '[109, 109, -w^2 + 4*w + 1]', '[110, 110, w^2 - 5*w + 4]', '[112, 28, w^2 - 3*w + 3]', '[112, 28, -2*w^2 + 8*w - 4]', '[112, 112, -3*w^2 + w + 18]', '[113, 113, -w - 5]', '[113, 113, -3*w - 1]', '[113, 113, 2*w^2 - 3*w - 11]', '[118, 118, -2*w^2 + 3*w]', '[121, 11, -2*w^2 + 5*w + 1]', '[124, 62, -w^2 - w + 11]', '[124, 124, w^2 + 2*w - 4]', '[125, 5, 5]', '[125, 125, 2*w^2 - w - 11]', '[128, 8, -4*w]', '[128, 8, -2*w^2 + 6*w + 2]', '[128, 32, -2*w^2 + 4*w]', '[128, 128, 3*w^2 - 2*w - 24]', '[130, 130, w^2 + 2*w + 2]', '[130, 130, -2*w^2 + 7*w]', '[133, 133, 3*w^2 - 2*w - 19]', '[134, 134, -w^2 + 5*w]', '[135, 15, 3*w - 3]', '[137, 137, -2*w^2 + 3*w + 17]', '[140, 70, -w^2 - w + 7]', '[140, 140, w - 6]', '[142, 142, w^2 + 4*w + 2]', '[143, 143, 2*w^2 - 6*w + 3]', '[143, 143, -2*w^2 + 4*w + 5]', '[146, 146, -3*w - 8]', '[148, 74, -w^2 + 5*w - 7]', '[148, 148, w^2 - w + 2]', '[149, 149, 2*w^2 - 13]', '[151, 151, -2*w^2 + 1]', '[152, 38, 4*w^2 - 2*w - 30]', '[152, 152, -2*w^2 - w + 10]', '[154, 154, w^2 - 3*w - 4]', '[155, 155, -2*w^2 + 8*w - 1]', '[160, 20, -2*w^2 + 2*w + 10]', '[160, 40, 2*w^2 - 4*w - 8]', '[160, 160, 3*w + 2]', '[163, 163, 2*w^2 + w - 7]', '[164, 82, -w^2 + w + 11]', '[164, 164, -2*w^2 - 5*w - 2]', '[166, 166, w^2 + w - 8]', '[167, 167, 2*w^2 - 5*w - 5]', '[169, 13, w^2 - 4*w + 5]', '[169, 13, -4*w^2 + 2*w + 29]', '[169, 169, 3*w + 5]', '[175, 35, 2*w^2 - 9]', '[175, 175, -2*w^2 + 3*w + 19]', '[176, 44, -w^2 - w + 9]', '[176, 44, 2*w - 8]', '[176, 176, w^2 + w + 2]', '[178, 178, w^2 + 2]', '[182, 182, 3*w - 4]', '[182, 182, 2*w^2 - 3*w - 12]', '[185, 185, 2*w^2 - 17]', '[188, 94, -3*w^2 + w + 21]', '[188, 188, 3*w^2 + 4*w - 8]', '[189, 21, 3*w + 3]', '[190, 190, w^2 - 4*w - 2]', '[191, 191, -6*w^2 + 4*w + 41]', '[191, 191, 4*w^2 - 12*w + 1]', '[191, 191, 3*w - 7]', '[193, 193, w^2 + 2*w - 5]', '[194, 194, 3*w + 4]', '[196, 14, -5*w^2 + 3*w + 39]', '[196, 28, w^2 - 2*w - 12]', '[196, 98, w^2 - 3*w - 11]', '[196, 196, -2*w^2 + w + 10]', '[197, 197, -4*w^2 + 4*w + 27]', '[200, 10, 2*w^2 - 14]', '[200, 40, -w^2 + 12]', '[200, 50, -4*w^2 + 4*w + 30]', '[200, 200, 4*w^2 - 3*w - 26]', '[205, 205, -2*w^2 + w + 1]', '[208, 52, -w^2 + 3*w + 5]', '[208, 52, 2*w^2 + 2*w - 8]', '[208, 52, -3*w^2 + w + 23]', '[208, 52, 2*w^2 - 4*w - 4]', '[208, 208, w + 6]', '[208, 208, -2*w^2 - w + 2]', '[209, 209, -w^2 + 2*w - 3]', '[211, 211, -10*w^2 + 8*w + 69]', '[211, 211, 3*w - 5]', '[211, 211, 2*w^2 - 4*w - 1]', '[216, 6, 6]', '[216, 24, 3*w - 6]', '[217, 217, 4*w - 3]', '[218, 218, 2*w^2 - 3*w - 16]', '[220, 110, -3*w^2 + 3*w + 25]', '[220, 220, 3*w^2 - w - 22]', '[223, 223, 2*w^2 - 3*w - 7]', '[224, 28, 2*w^2 - 2*w - 18]', '[224, 56, -2*w^2 + 16]', '[224, 224, 2*w^2 + 3*w - 6]', '[226, 226, 3*w^2 + w]', '[226, 226, w^2 + 5*w]', '[226, 226, w^2 - 3*w + 4]', '[227, 227, 2*w^2 - 15]', '[229, 229, -2*w - 7]', '[233, 233, 2*w^2 - 3*w - 13]', '[233, 233, -w^2 - 4*w + 3]', '[233, 233, 2*w^2 - 2*w - 9]', '[235, 235, 4*w + 1]', '[236, 118, -3*w^2 + 3*w + 17]', '[236, 236, 2*w^2 + w - 6]', '[239, 239, -5*w^2 + 4*w + 33]', '[241, 241, -2*w^2 + 2*w + 1]', '[242, 22, 3*w^2 - 2*w - 18]', '[245, 35, -2*w^2 + 4*w + 3]', '[245, 245, -2*w^2 + 7*w - 5]', '[247, 247, 2*w^2 - 3*w - 1]', '[247, 247, w - 7]', '[248, 62, 2*w^2 - 4*w - 2]', '[248, 248, -3*w^2 + 10*w]', '[250, 10, -5*w]', '[250, 250, -w^2 - 3*w + 4]', '[256, 8, 4*w^2 - 4*w - 28]', '[256, 16, -5*w^2 + 3*w + 33]', '[256, 16, 4*w + 8]', '[256, 64, 2*w^2 - 8]', '[256, 256, -w^2 + 3*w + 6]', '[257, 257, 2*w^2 - 6*w - 3]', '[257, 257, 2*w^2 - 3*w - 15]', '[257, 257, -w^2 - 2*w - 3]', '[259, 259, -4*w^2 + 4*w + 29]', '[260, 130, -w^2 + 5*w + 1]', '[260, 130, -3*w^2 + w + 17]', '[260, 260, 2*w^2 - 3*w - 14]', '[260, 260, 3*w^2 - 8*w]', '[266, 266, -w^2 - 2*w + 6]', '[268, 134, -5*w^2 + 5*w + 33]', '[268, 268, w^2 - 3*w - 10]', '[269, 269, 2*w^2 - w - 9]', '[269, 269, 2*w^2 + w - 11]', '[269, 269, -2*w^2 + 7*w + 1]', '[270, 30, -3*w^2 + 18]', '[271, 271, -7*w^2 + 6*w + 49]', '[274, 274, -w^2 - 3*w - 4]', '[275, 55, -2*w^2 - 1]', '[275, 275, -2*w^2 - w + 3]', '[277, 277, -3*w^2 + 2*w + 25]', '[277, 277, 3*w^2 - 8*w - 1]', '[277, 277, 2*w^2 - 4*w - 9]', '[280, 70, 2*w^2 - 2]', '[280, 280, -w^2 + 6*w]', '[281, 281, w^2 - 4*w - 3]', '[283, 283, 4*w^2 - 2*w - 25]', '[283, 283, -3*w^2 + 10*w - 5]', '[283, 283, 2*w^2 + w - 5]', '[284, 142, -11*w^2 + 9*w + 81]', '[284, 284, w^2 - 8*w - 24]', '[286, 286, -2*w^2 + 9*w - 4]', '[286, 286, w^2 - w - 12]', '[287, 287, -2*w^2 - 3*w - 1]', '[292, 146, w^2 - 3*w - 7]', '[292, 292, -2*w^2 + 3*w + 6]', '[293, 293, -5*w + 3]', '[295, 295, 2*w^2 - 5*w + 3]', '[296, 74, -6*w^2 + 4*w + 46]', '[296, 296, w^2 - 3*w - 14]', '[297, 33, -3*w^2 + 15]', '[298, 298, -2*w^2 - w + 4]', '[302, 302, 3*w^2 + 3*w - 8]', '[304, 76, -2*w^2 + 2*w + 8]', '[304, 76, w^2 - 3*w - 9]', '[304, 304, 2*w^2 - 5*w - 6]', '[307, 307, -4*w^2 + 2*w + 33]', '[308, 154, w^2 + 5*w - 3]', '[308, 308, 2*w^2 - 3*w + 2]', '[310, 310, w^2 - 3*w - 8]', '[317, 317, 2*w^2 + w + 1]', '[320, 20, 4*w - 4]', '[320, 40, w^2 + w + 3]', '[320, 80, 2*w^2 - 6*w + 4]', '[320, 320, 2*w^2 - 5*w - 22]', '[325, 65, 4*w^2 - 23]', '[325, 65, -w^2 - 3]', '[325, 325, 2*w^2 + 2*w + 1]', '[325, 325, -2*w^2 + 7]', '[326, 326, -3*w^2 - 7*w + 4]', '[328, 82, -4*w - 2]', '[328, 328, -2*w^2 + 3*w + 2]', '[329, 329, 2*w^2 + 4*w - 5]', '[331, 331, 2*w - 9]', '[332, 166, 3*w^2 - 7*w - 5]', '[332, 332, -2*w^2 + w + 2]', '[334, 334, -7*w^2 + 6*w + 50]', '[335, 335, w^2 - 6*w + 5]', '[337, 337, -10*w^2 + 6*w + 75]', '[337, 337, w^2 + 2*w - 7]', '[337, 337, -8*w^2 + 6*w + 55]', '[338, 26, 4*w^2 - 3*w - 32]', '[338, 26, 2*w^2 - w - 8]', '[338, 338, -w^2 + 6*w - 6]', '[341, 341, -w - 7]', '[343, 7, 7]', '[343, 343, -2*w^2 + 3*w + 5]', '[347, 347, w^2 - 13]', '[347, 347, 2*w^2 - 4*w - 19]', '[347, 347, -5*w^2 + 4*w + 39]', '[349, 349, 2*w^2 - 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14*w - 12]', '[9990, 1110, -6*w^2 + 9*w + 12]', '[9992, 2498, -8*w^2 - 4*w + 6]', '[9992, 2498, 2*w^2 - 12*w - 34]', '[9992, 2498, -4*w - 22]', '[9992, 9992, -2*w^2 - 7*w + 22]', '[9992, 9992, 2*w^2 - 21*w + 2]', '[9992, 9992, -7*w^2 + 2*w + 32]', '[9995, 9995, 3*w^2 + 6*w + 11]', '[9995, 9995, -6*w^2 + 7*w + 19]', '[9995, 9995, -10*w^2 + 7*w + 83]', '[9997, 9997, w^2 + 24*w - 9]', '[9997, 9997, -4*w^2 - 12*w - 13]', '[9998, 9998, 2*w^2 + 17*w]', '[10000, 100, -9*w^2 - 5*w + 33]', '[10000, 100, 2*w^2 - 10*w - 24]', '[10000, 100, -10*w^2 + 60]', '[10000, 100, 15*w^2 - 45*w + 5]', '[10000, 400, -6*w^2 + 5*w + 22]', '[10000, 400, 5*w^2 - 5*w - 50]', '[10000, 2500, -6*w^2 - 4]', '[10000, 2500, 5*w^2 - 19*w + 19]', '[10000, 10000, 3*w^2 - 23*w + 10]'], 'label': '3.3.1573.1', 'narrow_class_no': 1, 'primes': ['[2, 2, -w]', '[4, 2, w^2 - w - 7]', '[5, 5, w - 1]', '[7, 7, w + 1]', '[11, 11, -w^2 + 5]', '[13, 13, w + 3]', '[13, 13, -2*w + 1]', '[19, 19, 2*w^2 - w - 15]', '[25, 5, w^2 - 7]', '[27, 3, 3]', '[31, 31, w^2 - 2*w - 1]', '[37, 37, -3*w^2 + 2*w + 23]', '[41, 41, -2*w - 1]', '[47, 47, w^2 - 3]', '[49, 7, w^2 - 2*w - 5]', '[59, 59, 2*w - 3]', '[67, 67, w - 5]', '[71, 71, w^2 - 2*w - 11]', '[73, 73, w^2 + 1]', '[83, 83, -4*w^2 + 3*w + 27]', '[89, 89, w^2 - 2*w - 7]', '[97, 97, w^2 - 6*w + 1]', '[109, 109, -w^2 + 4*w + 1]', '[113, 113, -w - 5]', '[113, 113, -3*w - 1]', '[113, 113, 2*w^2 - 3*w - 11]', '[137, 137, -2*w^2 + 3*w + 17]', '[149, 149, 2*w^2 - 13]', '[151, 151, -2*w^2 + 1]', '[163, 163, 2*w^2 + w - 7]', '[167, 167, 2*w^2 - 5*w - 5]', '[191, 191, -6*w^2 + 4*w + 41]', '[191, 191, 4*w^2 - 12*w + 1]', '[191, 191, 3*w - 7]', '[193, 193, w^2 + 2*w - 5]', '[197, 197, -4*w^2 + 4*w + 27]', '[211, 211, -10*w^2 + 8*w + 69]', '[211, 211, 3*w - 5]', '[211, 211, 2*w^2 - 4*w - 1]', '[223, 223, 2*w^2 - 3*w - 7]', '[227, 227, 2*w^2 - 15]', '[229, 229, -2*w - 7]', '[233, 233, 2*w^2 - 3*w - 13]', '[233, 233, -w^2 - 4*w + 3]', '[233, 233, 2*w^2 - 2*w - 9]', '[239, 239, -5*w^2 + 4*w + 33]', '[241, 241, -2*w^2 + 2*w + 1]', '[257, 257, 2*w^2 - 6*w - 3]', '[257, 257, 2*w^2 - 3*w - 15]', '[257, 257, -w^2 - 2*w - 3]', '[269, 269, 2*w^2 - w - 9]', '[269, 269, 2*w^2 + w - 11]', '[269, 269, -2*w^2 + 7*w + 1]', '[271, 271, -7*w^2 + 6*w + 49]', '[277, 277, -3*w^2 + 2*w + 25]', '[277, 277, 3*w^2 - 8*w - 1]', '[277, 277, 2*w^2 - 4*w - 9]', '[281, 281, w^2 - 4*w - 3]', '[283, 283, 4*w^2 - 2*w - 25]', '[283, 283, -3*w^2 + 10*w - 5]', '[283, 283, 2*w^2 + w - 5]', '[293, 293, -5*w + 3]', '[307, 307, -4*w^2 + 2*w + 33]', '[317, 317, 2*w^2 + w + 1]', '[331, 331, 2*w - 9]', '[337, 337, -10*w^2 + 6*w + 75]', '[337, 337, w^2 + 2*w - 7]', '[337, 337, -8*w^2 + 6*w + 55]', '[347, 347, w^2 - 13]', '[347, 347, 2*w^2 - 4*w - 19]', '[347, 347, -5*w^2 + 4*w + 39]', '[349, 349, 2*w^2 - w - 19]', '[353, 353, -8*w^2 + 7*w + 55]', '[359, 359, -4*w^2 + 3*w + 25]', '[361, 19, -w^2 - 6*w + 3]', '[367, 367, 2*w^2 - 3*w - 3]', '[367, 367, 2*w^2 - 2*w - 7]', '[367, 367, w^2 - 2*w - 13]', '[373, 373, -4*w - 7]', '[373, 373, 3*w^2 - 2*w - 17]', '[373, 373, -11*w^2 + 8*w + 77]', '[379, 379, -7*w + 3]', '[383, 383, w^2 + 2*w - 17]', '[397, 397, 2*w^2 - w - 7]', '[401, 401, -4*w - 3]', '[409, 409, 12*w^2 - 7*w - 91]', '[419, 419, 5*w + 1]', '[419, 419, 2*w^2 - 2*w - 3]', '[419, 419, -7*w^2 + 4*w + 51]', '[421, 421, w^2 - 4*w - 13]', '[431, 431, 3*w^2 - 19]', '[449, 449, w^2 + 2*w - 9]', '[457, 457, -8*w^2 + 7*w + 59]', '[461, 461, 2*w^2 - w - 5]', '[463, 463, -4*w - 5]', '[479, 479, -4*w^2 + 4*w + 23]', '[487, 487, -3*w^2 + 4*w + 23]', '[499, 499, 2*w^2 - 4*w - 11]', '[509, 509, 4*w - 7]', '[541, 541, -w^2 + 4*w - 7]', '[557, 557, -2*w^2 - w + 19]', '[569, 569, 8*w - 1]', '[569, 569, -w^2 + 2*w - 5]', '[569, 569, 2*w^2 - 6*w + 5]', '[577, 577, -w^2 + 6*w - 11]', '[587, 587, w - 9]', '[593, 593, 2*w^2 - 8*w - 1]', '[599, 599, 4*w^2 - 10*w - 5]', '[599, 599, 2*w^2 - 6*w - 5]', '[599, 599, -4*w^2 + 3*w + 33]', '[613, 613, -3*w^2 - 2*w + 3]', '[617, 617, 2*w^2 - 3*w + 3]', '[619, 619, -10*w^2 + 7*w + 75]', '[631, 631, 3*w^2 + 1]', '[643, 643, -10*w^2 + 7*w + 69]', '[661, 661, 2*w^2 - 7*w - 3]', '[673, 673, 5*w - 13]', '[673, 673, -w^2 - 2*w - 5]', '[673, 673, 2*w^2 + 2*w - 11]', '[677, 677, 6*w + 1]', '[677, 677, 2*w^2 + w - 17]', '[677, 677, 3*w^2 - 2*w - 15]', '[683, 683, 3*w^2 - 25]', '[691, 691, -5*w - 9]', '[701, 701, -5*w^2 + 2*w + 37]', '[701, 701, -3*w^2 + 4*w + 1]', '[701, 701, w^2 - 4*w - 9]', '[709, 709, -6*w^2 + 4*w + 39]', '[727, 727, 2*w^2 - 3*w - 21]', '[727, 727, -8*w^2 + 6*w + 61]', '[727, 727, 2*w^2 - 4*w - 15]', '[733, 733, 2*w^2 + 2*w - 23]', '[739, 739, -4*w^2 + w + 31]', '[743, 743, 2*w^2 + 4*w - 7]', '[751, 751, 4*w^2 + 2*w - 19]', '[751, 751, -4*w^2 + w + 29]', '[751, 751, -6*w^2 + 6*w + 41]', '[761, 761, -10*w^2 + 6*w + 77]', '[769, 769, -w^2 - 5]', '[773, 773, -3*w^2 + 2*w + 27]', '[787, 787, -10*w^2 + 6*w + 73]', '[797, 797, -5*w^2 + 6*w + 31]', '[797, 797, 3*w^2 - 6*w - 5]', '[797, 797, 2*w - 11]', '[811, 811, 4*w^2 - 16*w + 9]', '[821, 821, 4*w^2 - 8*w - 15]', '[827, 827, -2*w^2 + 9*w - 11]', '[839, 839, -3*w^2 + 8*w + 7]', '[853, 853, -6*w + 5]', '[863, 863, -w^2 + 8*w - 13]', '[877, 877, 5*w - 7]', '[881, 881, -7*w^2 + 6*w + 45]', '[881, 881, -2*w^2 + 10*w - 7]', '[881, 881, 3*w^2 - 4*w - 11]', '[883, 883, 9*w - 1]', '[883, 883, 2*w^2 - w + 3]', '[883, 883, -2*w^2 + 8*w - 9]', '[887, 887, 4*w^2 - 5*w - 27]', '[887, 887, -2*w^2 + 5*w - 5]', '[887, 887, -5*w - 7]', '[929, 929, w^2 + 4*w - 7]', '[941, 941, -2*w^2 + 2*w + 21]', '[947, 947, -3*w - 11]', '[961, 31, -4*w^2 + w + 21]', '[967, 967, -2*w^2 + 11*w - 13]', '[977, 977, 5*w^2 - 16*w - 1]', '[983, 983, 2*w^2 + 2*w - 13]', '[997, 997, 3*w^2 - 2*w - 13]', '[997, 997, -2*w^2 - w - 3]', '[997, 997, -4*w^2 + 4*w + 21]']} -
nf_fields • Show schema
{'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [2, -7, -1, 1], 'conductor': 0, 'degree': 3, 'dirichlet_group': [], 'disc_abs': 1573, 'disc_rad': 143, 'disc_sign': 1, 'frobs': [[2, [[2, 1], [1, 1]]], [3, [[3, 1]]], [5, [[2, 1], [1, 1]]], [7, [[2, 1], [1, 1]]], [11, [0]], [13, [0]], [17, [[3, 1]]], [19, [[2, 1], [1, 1]]], [23, [[3, 1]]], [29, [[3, 1]]], [31, [[2, 1], [1, 1]]], [37, [[2, 1], [1, 1]]], [41, [[2, 1], [1, 1]]], [43, [[3, 1]]], [47, [[2, 1], [1, 1]]], [53, [[3, 1]]], [59, [[2, 1], [1, 1]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [4, 3], 'galois_label': '3T2', 'galt': 2, 'grd': 17.833371889561775, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '3.3.1573.1', 'local_algs': ['11.3.2.1', '13.1.0.1', '13.2.1.1'], 'monogenic': 1, 'num_ram': 2, 'r2': 0, 'ramps': [11, 13], 'rd': 11.6299069738, 'regulator': {'__RealLiteral__': 0, 'data': '8.44494130232', 'prec': 44}, 'res': {'gal': ['-4,-20,5,29,-12,-3,1']}, 'subfield_mults': [], 'subfields': [], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( a - 3 \\)', '\\( a^{2} - 4 a + 1 \\)'], 'unitsGmodule': [[4, 1], [5, 1]], 'used_grh': False, 'zk': ['1', 'a', 'a^2']}
Hilbert modular form data - 3.3.1573.1-11.1-e