Hilbert modular form data - 3.3.148.1-25.2-b

Formats: - HTML - YAML - JSON - 2025-12-28T14:26:51.496213

• hmf_forms •

  Column	Type
  deg	smallint
  dimension	integer
  disc	bigint
  field_bad_primes	integer[]
  field_label	text
  is_CM	text
  is_base_change	text
  label	text
  label_nsuffix	smallint
  label_suffix	text
  level_bad_primes	integer[]
  level_ideal	text
  level_label	text
  level_norm	integer
  parallel_weight	smallint
  short_label	text
  weight	text

  
  {'deg': 3, 'dimension': 1, 'disc': 148, 'field_bad_primes': [2, 37], 'field_label': '3.3.148.1', 'is_CM': 'no', 'is_base_change': 'no', 'label': '3.3.148.1-25.2-b', 'label_nsuffix': 1, 'label_suffix': 'b', 'level_bad_primes': [5], 'level_ideal': '[25, 25, -2*w^2 + 3]', 'level_label': '25.2', 'level_norm': 25, 'parallel_weight': 2, 'short_label': '25.2-b', 'weight': '[2, 2, 2]'}
• hmf_hecke •

  Column	Type
  AL_eigenvalues	jsonb
  hecke_eigenvalues	jsonb
  hecke_polynomial	text
  label	text

  
  {'AL_eigenvalues': [['[5, 5, -w^2 + w + 1]', -1]], 'hecke_eigenvalues': [-2, 0, 4, -2, 0, 4, -4, 8, 0, -8, 8, -2, 4, 0, -8, 8, -12, 8, 0, 10, -2, -16, 8, -12, 8, -10, -16, 12, -12, 8, -12, 0, 0, 0, 12, -8, -8, -16, 8, 10, 0, 12, 4, 20, 8, -26, -6, 4, -20, -8, 12, -2, 10, 0, -20, -22, -8, -16, 20, -6, 24, -26, -8, -6, 28, 18, -22, -8, 24, 8, 0, 10, -20, -36, 12, -32, -32, 8, 4, 10, 12, -10, -28, -8, -20, -30, 38, 12, -16, 8, 0, 8, -8, 32, 12, 40, -16, 4, -40, 32, 8, 18, 24, 0, -2, -32, 22, -38, -38, -32, 32, -16, 48, 14, 2, 24, -28, -8, -8, 2, -20, -32, -42, 40, 8, -40, -16, 4, 44, 48, -50, 40, 40, -40, 32, -6, -12, 40, 24, -56, -16, 8, 38, 38, 2, 12, 52, -16, -32, 32, 0, 30, 40, 20, 22, 42, 2, -12, 32, 48, 12, 32, 12, -32, -8, -42], 'hecke_polynomial': 'x', 'label': '3.3.148.1-25.2-b'}
• hmf_fields •

  Column	Type
  degree	smallint
  discriminant	bigint
  ideals	jsonb
  label	text
  narrow_class_no	smallint
  primes	jsonb

  
  {'degree': 3, 'discriminant': 148, 'ideals': ['[1, 1, 1]', '[2, 2, w - 1]', '[4, 2, -w^2 + 3]', '[5, 5, -w^2 + w + 1]', '[8, 2, -2]', '[10, 10, w^2 + w - 2]', '[13, 13, -w^2 + 2*w + 2]', '[16, 4, -2*w + 2]', '[17, 17, 2*w + 1]', '[19, 19, -w^2 + 2*w + 4]', '[20, 10, -w^2 + 2*w + 3]', '[23, 23, -w^2 - w + 3]', '[25, 5, -2*w^2 + w + 4]', '[25, 25, -2*w^2 + 3]', '[26, 26, -w - 3]', '[27, 3, 3]', '[29, 29, w^2 - 3*w - 1]', '[31, 31, 2*w^2 - 2*w - 3]', '[32, 4, 2*w^2 - 6]', '[34, 34, w^2 + w - 4]', '[37, 37, w^2 + w - 5]', '[37, 37, w - 4]', '[38, 38, 2*w^2 - w - 3]', '[40, 10, 2*w^2 - 2*w - 2]', '[43, 43, 2*w^2 - w - 2]', '[46, 46, 2*w^2 - 3*w - 5]', '[50, 10, w^2 - 3*w - 2]', '[50, 50, w^2 - w - 6]', '[52, 26, -w^2 - 2*w + 3]', '[54, 6, 3*w - 3]', '[58, 58, w^2 + w + 2]', '[59, 59, 2*w^2 - 3*w - 6]', '[61, 61, -3*w^2 + 4*w + 4]', '[62, 62, -2*w^2 - w + 5]', '[64, 4, 4]', '[65, 65, -3*w + 4]', '[67, 67, -w - 4]', '[67, 67, -3*w^2 + 8]', '[67, 67, w^2 - 3*w - 3]', '[68, 34, w^2 - 2*w + 3]', '[74, 74, w^2 - 3*w + 4]', '[74, 74, w^2 - 5*w + 4]', '[76, 38, -w^2 + 7]', '[79, 79, w^2 + 2*w - 4]', '[80, 20, -2*w^2 - 2*w + 4]', '[85, 85, -3*w^2 + 2*w + 6]', '[86, 86, -w^2 + 5*w]', '[89, 89, 3*w^2 - 3*w - 5]', '[92, 46, -3*w^2 + 4*w + 3]', '[95, 95, -2*w^2 - w + 6]', '[97, 97, -3*w^2 + 4]', '[100, 10, -w^2 - 2*w + 7]', '[100, 50, -w^2 - 2*w + 5]', '[103, 103, -w^2 + w - 3]', '[104, 26, 2*w^2 - 4*w - 4]', '[107, 107, 3*w^2 - w - 5]', '[107, 107, w^2 - w - 7]', '[107, 107, -2*w - 5]', '[108, 6, -3*w^2 + 9]', '[109, 109, w^2 + 2*w - 6]', '[113, 113, -2*w^2 + 5*w + 2]', '[115, 115, -w^2 + 4*w + 2]', '[116, 58, 3*w^2 - 2*w - 5]', '[118, 118, -3*w^2 + 3*w + 4]', '[122, 122, -4*w^2 + 9*w + 1]', '[124, 62, -w^2 - 3]', '[125, 5, 5]', '[125, 125, w^2 + w + 3]', '[128, 8, 4*w - 4]', '[130, 130, 3*w^2 - w - 4]', '[131, 131, -5*w^2 + 3*w + 13]', '[134, 134, -w - 5]', '[134, 134, -3*w^2 + 3*w + 2]', '[134, 134, -w^2 - 3*w + 4]', '[135, 15, -3*w^2 + 3*w + 3]', '[136, 34, -4*w - 2]', '[137, 137, 2*w^2 - 4*w - 5]', '[137, 137, 2*w^2 + w - 8]', '[137, 137, 3*w^2 - 10]', '[139, 139, -w^2 + 2*w - 4]', '[139, 139, 4*w^2 - 2*w - 9]', '[139, 139, 3*w^2 - 2*w - 4]', '[145, 145, -4*w - 3]', '[148, 74, 3*w^2 - 2*w - 13]', '[148, 74, 3*w^2 - 11]', '[151, 151, w^2 - 8]', '[151, 151, 4*w - 5]', '[151, 151, w^2 + w - 9]', '[152, 38, 2*w^2 - 4*w - 8]', '[155, 155, -w^2 + 3*w - 5]', '[158, 158, 2*w^2 - 3*w + 3]', '[160, 20, 2*w^2 - 4*w - 6]', '[163, 163, w - 6]', '[167, 167, 2*w^2 - 4*w - 7]', '[169, 13, w^2 - 4*w - 4]', '[169, 169, -2*w + 7]', '[170, 170, 2*w^2 - 5*w - 3]', '[172, 86, w^2 - 4*w - 5]', '[178, 178, -3*w^2 + 7*w + 2]', '[179, 179, w^2 + 3*w - 5]', '[184, 46, 2*w^2 + 2*w - 6]', '[185, 185, 3*w^2 - 6*w - 4]', '[185, 185, 4*w^2 - 6*w - 3]', '[190, 190, -w^2 + w - 4]', '[191, 191, 4*w^2 - 4*w - 7]', '[193, 193, 4*w^2 - 3*w - 8]', '[194, 194, -5*w - 1]', '[199, 199, w^2 + 3*w - 9]', '[200, 10, 4*w^2 - 2*w - 8]', '[200, 50, 4*w^2 - 6]', '[206, 206, w^2 - 7*w + 4]', '[208, 52, 2*w + 6]', '[214, 214, -w^2 + 5*w + 2]', '[214, 214, -w^2 - 3*w + 6]', '[214, 214, w^2 - 5*w + 8]', '[215, 215, -2*w^2 + 2*w - 3]', '[216, 6, -6]', '[218, 218, 2*w^2 - 5*w + 5]', '[221, 221, w^2 + 4]', '[226, 226, 5*w^2 - 9*w]', '[227, 227, 2*w^2 - 5*w - 4]', '[230, 230, w^2 + 3*w - 8]', '[232, 58, -2*w^2 + 6*w + 2]', '[233, 233, -w - 6]', '[233, 233, w^2 + 3*w - 7]', '[233, 233, 2*w^2 + 2*w - 7]', '[236, 118, 7*w^2 - 4*w - 19]', '[239, 239, 3*w^2 + w - 9]', '[241, 241, -5*w^2 + w + 15]', '[244, 122, 5*w^2 - 6*w - 13]', '[247, 247, -2*w^2 + 2*w + 11]', '[248, 62, -4*w^2 + 4*w + 6]', '[250, 10, 5*w - 5]', '[250, 250, 4*w^2 - 3*w - 7]', '[251, 251, 4*w^2 - 5*w - 4]', '[256, 8, -4*w^2 + 12]', '[257, 257, 4*w^2 - 2*w - 7]', '[260, 130, -w^2 + 9]', '[262, 262, 3*w^2 - 5*w - 8]', '[268, 134, 5*w^2 - 13]', '[268, 134, -w^2 - 4*w + 5]', '[268, 134, 5*w^2 - 2*w - 11]', '[269, 269, 4*w^2 - w - 6]', '[269, 269, w^2 - 5*w - 3]', '[269, 269, 2*w^2 + 2*w - 11]', '[270, 30, 3*w^2 + 3*w - 6]', '[272, 68, -2*w^2 - 2*w + 8]', '[274, 274, w^2 - 3*w + 6]', '[274, 274, -4*w^2 + 5*w + 3]', '[274, 274, -w + 7]', '[277, 277, 4*w^2 + w - 10]', '[278, 278, -2*w^2 + 5*w + 5]', '[278, 278, 2*w^2 - 9*w + 5]', '[278, 278, -2*w^2 + 7*w + 1]', '[281, 281, -w^2 + 7*w - 5]', '[283, 283, -3*w^2 + 5*w + 11]', '[289, 17, 4*w^2 - 6*w - 9]', '[289, 289, -5*w + 6]', '[290, 290, -3*w^2 - w + 10]', '[293, 293, 3*w^2 - 5*w - 9]', '[293, 293, 4*w^2 - 4*w - 5]', '[293, 293, 2*w^2 + 3*w - 6]', '[295, 295, 2*w^2 + 2*w - 9]', '[296, 74, -2*w^2 - 2*w + 10]', '[296, 74, -2*w + 8]', '[299, 299, -4*w^2 + 3*w + 6]', '[302, 302, -5*w + 7]', '[302, 302, 4*w^2 - 9*w + 5]', '[302, 302, w^2 - 7*w + 8]', '[304, 76, -4*w^2 + 2*w + 6]', '[305, 305, -2*w^2 + 7*w - 8]', '[310, 310, -w^2 + 5*w + 4]', '[311, 311, 4*w^2 - 13]', '[313, 313, -w^2 + w - 5]', '[316, 158, w^2 - 2*w - 9]', '[317, 317, w^2 - w - 9]', '[317, 317, 2*w^2 - 5*w - 6]', '[317, 317, 2*w^2 - 6*w - 3]', '[320, 20, -4*w^2 + 4*w + 4]', '[323, 323, -4*w^2 + 4*w + 3]', '[325, 65, -3*w^2 - w + 11]', '[325, 325, -3*w^2 - 2*w + 8]', '[326, 326, w^2 - 7*w + 6]', '[331, 331, w^2 - 5*w - 5]', '[334, 334, -4*w^2 + 3*w + 5]', '[335, 335, w^2 + 4*w - 6]', '[335, 335, -2*w^2 + 5*w + 8]', '[335, 335, 4*w^2 - 2*w - 5]', '[338, 26, -4*w^2 + 3*w + 3]', '[338, 338, 2*w^2 - 5*w - 7]', '[340, 170, w^2 + 2*w + 5]', '[343, 7, -7]', '[344, 86, -4*w^2 + 2*w + 4]', '[347, 347, -5*w^2 + 7*w + 11]', '[349, 349, -2*w - 7]', '[349, 349, 4*w^2 - 15]', '[349, 349, 6*w - 5]', '[351, 39, -3*w^2 + 6*w + 6]', '[353, 353, 2*w^2 - w - 12]', '[356, 178, 5*w^2 - 6*w - 15]', '[358, 358, 3*w^2 - 5*w + 4]', '[361, 19, 4*w^2 + 2*w - 9]', '[361, 361, -5*w^2 + 4*w + 10]', '[367, 367, 5*w^2 - 2*w - 10]', '[367, 367, 2*w^2 - 3*w - 12]', '[367, 367, -5*w^2 + 6*w + 16]', '[368, 92, -4*w^2 + 6*w + 10]', '[370, 370, w + 7]', '[370, 370, -2*w^2 - 3*w + 7]', '[377, 377, 5*w^2 - w - 9]', '[380, 190, -5*w^2 + 6*w + 7]', '[382, 382, -4*w^2 + 9*w + 3]', '[383, 383, -7*w^2 + 4*w + 18]', '[386, 386, -3*w^2 + 7*w + 4]', '[388, 194, -5*w^2 + 4*w + 1]', '[389, 389, -w^2 + 2*w - 6]', '[391, 391, -4*w^2 + 8*w + 5]', '[395, 395, 2*w^2 - 7*w - 2]', '[398, 398, 3*w^2 - 9*w + 8]', '[400, 20, -2*w^2 + 6*w + 4]', '[400, 100, -2*w^2 + 2*w + 12]', '[401, 401, 6*w^2 - 3*w - 14]', '[403, 403, w^2 + 4*w - 10]', '[409, 409, w^2 - 7*w - 1]', '[412, 206, 3*w^2 + 2*w - 9]', '[416, 52, 2*w^2 + 4*w - 6]', '[421, 421, w^2 + 4*w - 8]', '[425, 85, -4*w^2 - 3*w + 8]', '[425, 425, -w + 8]', '[428, 214, 3*w^2 - 6*w - 13]', '[428, 214, 7*w^2 - 2*w - 21]', '[428, 214, 7*w^2 - 4*w - 27]', '[430, 430, 2*w^2 + 7*w + 1]', '[431, 431, 4*w^2 - 6*w - 11]', '[432, 12, -6*w + 6]', '[436, 218, 3*w^2 - 2*w - 15]', '[437, 437, w^2 - 3*w + 7]', '[439, 439, 2*w^2 + 3*w - 8]', '[442, 442, 5*w^2 - 5*w - 8]', '[445, 445, -w^2 + 4*w - 8]', '[449, 449, w^2 + w - 11]', '[452, 226, -5*w^2 + 4*w + 9]', '[454, 454, -5*w^2 + 7*w + 2]', '[457, 457, -4*w^2 - 4*w + 7]', '[459, 51, 6*w + 3]', '[460, 230, -5*w^2 + 2*w + 9]', '[461, 461, 3*w^2 + 2*w - 16]', '[463, 463, 5*w^2 - 6*w - 6]', '[464, 116, -2*w^2 - 2*w - 4]', '[466, 466, -w^2 - 5*w + 6]', '[466, 466, 3*w^2 - 7*w + 6]', '[466, 466, 2*w^2 - 3*w + 5]', '[467, 467, 2*w - 9]', '[472, 118, -4*w^2 + 6*w + 12]', '[475, 95, -4*w^2 + 7*w + 8]', '[475, 475, -2*w^2 + 6*w + 5]', '[478, 478, w^2 - w + 6]', '[479, 479, 4*w^2 + w - 12]', '[481, 481, 6*w^2 - 7*w - 10]', '[481, 481, 5*w^2 - 9*w - 7]', '[482, 482, w^2 - w - 10]', '[485, 485, 2*w^2 + w + 4]', '[487, 487, 5*w^2 - 3*w - 9]', '[488, 122, -6*w^2 + 8*w + 8]', '[491, 491, w^2 - 2*w - 10]', '[491, 491, 3*w^2 + 2*w - 10]', '[491, 491, w^2 - 6*w - 8]', '[493, 493, 3*w^2 - 6*w - 8]', '[494, 494, 2*w^2 + 3*w - 9]', '[496, 124, 4*w^2 + 2*w - 10]', '[499, 499, 3*w^2 - 7*w - 5]', '[500, 10, -5*w^2 + 15]', '[500, 250, -3*w^2 + 8*w + 3]', '[502, 502, -5*w^2 + 13*w]', '[503, 503, w^2 - 6*w - 4]', '[512, 8, -8]', '[513, 57, -3*w^2 + 6*w + 12]', '[514, 514, -2*w^2 + 7*w + 3]', '[515, 515, 5*w^2 - 6*w - 2]', '[520, 130, 6*w - 8]', '[523, 523, 5*w^2 - 5*w - 7]', '[524, 262, -5*w^2 + 6*w + 5]', '[527, 527, 2*w^2 + 4*w - 7]', '[529, 23, 2*w^2 + 3*w - 10]', '[529, 529, w^2 + 2*w + 6]', '[535, 535, 5*w^2 - 4*w - 8]', '[535, 535, -w^2 - 6]', '[535, 535, 6*w^2 - 10*w - 9]', '[536, 134, 2*w + 8]', '[536, 134, 6*w^2 - 16]', '[536, 134, -2*w^2 + 6*w + 6]', '[538, 538, -5*w^2 + 5*w + 2]', '[538, 538, 2*w^2 - 7*w + 9]', '[538, 538, -w^2 + 7*w + 2]', '[540, 30, -3*w^2 + 6*w + 9]', '[541, 541, 5*w^2 - 2*w - 8]', '[544, 68, -2*w^2 + 4*w - 6]', '[545, 545, 4*w^2 - 9*w - 4]', '[547, 547, 6*w^2 - 4*w - 13]', '[548, 274, 7*w^2 - 4*w - 17]', '[548, 274, 5*w^2 - 4*w - 21]', '[548, 274, 7*w^2 - 6*w - 27]', '[551, 551, -w - 8]', '[554, 554, w^2 + w + 6]', '[556, 278, 3*w^2 + 2*w - 11]', '[556, 278, 5*w^2 - 6*w - 3]', '[556, 278, 3*w^2 - 6*w - 11]', '[557, 557, 5*w^2 - 6*w - 4]', '[559, 559, w^2 + 5*w - 7]', '[562, 562, -4*w^2 - w + 13]', '[563, 563, 3*w^2 - 6*w - 10]', '[565, 565, 2*w^2 - 10*w + 7]', '[566, 566, 5*w^2 - 3*w - 8]', '[569, 569, 5*w^2 - 7*w - 13]', '[575, 115, -2*w^2 + 6*w + 9]', '[575, 575, -6*w^2 + 6*w + 11]', '[577, 577, 2*w^2 - 6*w - 7]', '[578, 34, -6*w^2 + 9*w + 5]', '[578, 578, 5*w^2 - w - 6]', '[580, 290, -w^2 + 2*w - 7]', '[586, 586, -4*w^2 + 11*w + 1]', '[586, 586, 3*w^2 - 3*w + 4]', '[586, 586, -5*w^2 + 5*w + 6]', '[587, 587, 5*w^2 - 8*w - 10]', '[589, 589, 5*w^2 - 16]', '[590, 590, -6*w^2 + w + 11]', '[592, 148, -2*w^2 + 6*w - 8]', '[592, 148, -2*w^2 + 10*w - 8]', '[598, 598, 3*w^2 - 9*w - 2]', '[601, 601, 6*w^2 - 5*w - 12]', '[601, 601, -7*w - 2]', '[601, 601, 5*w^2 - 3*w - 3]', '[604, 302, 7*w^2 - 2*w - 23]', '[604, 302, w^2 - 11]', '[604, 302, 7*w^2 - 2*w - 25]', '[607, 607, 3*w^2 + 2*w - 14]', '[608, 76, 2*w^2 - 14]', '[610, 610, -3*w^2 + 7*w + 6]', '[620, 310, 3*w^2 + 2*w - 13]', '[621, 69, -3*w^2 - 3*w + 9]', '[622, 622, -w + 9]', '[625, 25, -6*w^2 + 8*w + 7]', '[625, 25, -5*w^2 + 5*w + 5]', '[625, 625, -4*w^2 - w + 14]', '[626, 626, w^2 - 9*w + 6]', '[629, 629, 2*w^2 - 7*w - 4]', '[629, 629, 5*w^2 - 3*w - 7]', '[631, 631, 4*w^2 + 2*w - 11]', '[632, 158, -2*w^2 - 4*w + 8]', '[634, 634, -w^2 - 5*w + 8]', '[634, 634, -6*w^2 + 9*w + 1]', '[634, 634, -5*w^2 + 5*w + 4]', '[640, 40, 4*w^2 + 4*w - 8]', '[643, 643, 5*w^2 - 2*w - 6]', '[646, 646, 7*w^2 - 3*w - 16]', '[647, 647, 3*w^2 - 8*w - 4]', '[650, 130, -w^2 + 3*w - 8]', '[650, 650, -2*w^2 + w - 5]', '[652, 326, 5*w^2 - 17]', '[653, 653, 5*w^2 - 4*w - 6]', '[655, 655, -3*w^2 + 2*w + 16]', '[661, 661, w^2 - 3*w - 11]', '[662, 662, -5*w^2 + 3*w + 4]', '[667, 667, 5*w^2 - 4*w - 4]', '[668, 334, 9*w^2 - 4*w - 23]', '[670, 670, -6*w^2 - w + 7]', '[670, 670, 5*w^2 - 3*w - 6]', '[670, 670, -6*w^2 - 5*w + 9]', '[675, 15, -6*w^2 + 3*w + 12]', '[675, 75, -6*w^2 + 9]', '[676, 26, 7*w^2 - 2*w - 15]', '[676, 338, -5*w^2 + 4*w + 5]', '[680, 170, 6*w^2 - 4*w - 12]', '[683, 683, 5*w^2 - 3*w - 5]', '[685, 685, 4*w^2 - 8*w - 7]', '[685, 685, 4*w^2 - 7*w - 10]', '[685, 685, w^2 + 5*w - 9]', '[686, 14, -7*w + 7]', '[688, 172, 2*w^2 - 10*w]', '[691, 691, -12*w^2 + 7*w + 34]', '[691, 691, -w^2 + w - 7]', '[691, 691, -w^2 - 5*w + 11]', '[694, 694, -7*w^2 + 11*w + 6]', '[695, 695, w^2 - w - 11]', '[695, 695, 6*w^2 - 9*w - 2]', '[695, 695, -2*w^2 + 3*w - 6]', '[698, 698, -3*w + 11]', '[698, 698, -2*w^2 - 5*w + 7]', '[698, 698, -5*w^2 + 11*w + 4]', '[701, 701, -5*w^2 + 7*w + 17]', '[702, 78, -3*w - 9]', '[703, 703, 5*w^2 - 7*w - 15]', '[703, 703, 8*w^2 - 5*w - 20]', '[706, 706, -w^2 - 5*w + 10]', '[709, 709, 5*w^2 - 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18]', '[9818, 9818, 8*w^2 + 5*w - 29]', '[9820, 4910, 9*w^2 - 16*w - 33]', '[9820, 4910, 15*w^2 - 8*w - 31]', '[9820, 4910, -9*w^2 - 22*w - 3]', '[9826, 34, -17*w^2 + 17*w + 34]', '[9826, 9826, -4*w^2 + 11*w - 19]', '[9827, 9827, -15*w^2 + 13*w + 29]', '[9827, 9827, -16*w + 21]', '[9827, 9827, -6*w^2 - 7*w + 28]', '[9829, 9829, -w^2 - 8*w - 20]', '[9832, 2458, -14*w^2 + 2*w + 22]', '[9836, 4918, 19*w^2 - 6*w - 61]', '[9838, 9838, 2*w^2 + w - 27]', '[9841, 9841, -4*w^2 - 12*w + 39]', '[9844, 4922, 21*w^2 - 34*w - 29]', '[9844, 4922, 15*w^2 - 16*w - 25]', '[9844, 4922, -w^2 + 4*w - 21]', '[9851, 9851, 11*w^2 - 20*w - 20]', '[9851, 9851, 3*w^2 - 9*w - 29]', '[9851, 9851, 7*w^2 - 2*w - 40]', '[9853, 9853, -12*w^2 + 11*w + 52]', '[9857, 9857, 13*w^2 - 7*w - 7]', '[9859, 9859, w^2 - 20*w - 2]', '[9860, 4930, 5*w^2 - 4*w - 33]', '[9865, 9865, 7*w^2 + 8*w - 22]', '[9865, 9865, 13*w^2 - 15*w - 7]', '[9865, 9865, 16*w - 23]', '[9871, 9871, 14*w^2 - 18*w - 49]', '[9875, 395, 5*w^2 + 10*w - 20]', '[9875, 9875, 8*w^2 + 13*w - 16]', '[9880, 2470, 14*w^2 - 10*w - 26]', '[9883, 9883, -2*w - 21]', '[9883, 9883, w^2 - 16*w - 14]', '[9883, 9883, -16*w^2 + 2*w + 47]', '[9886, 9886, 4*w^2 - 13*w + 21]', '[9887, 9887, -3*w^2 + 5*w - 17]', '[9890, 9890, -8*w^2 + 21*w + 9]', '[9892, 4946, 9*w^2 - 16*w - 27]', '[9895, 9895, 4*w^2 - 16*w - 13]', '[9896, 2474, -14*w^2 + 20*w + 32]', '[9896, 2474, -6*w^2 + 16*w + 28]', '[9896, 2474, -10*w^2 + 18*w + 22]', '[9901, 9901, -w^2 - w - 19]', '[9908, 4954, -9*w^2 + 4*w + 45]', '[9909, 1101, 15*w^2 - 6*w - 30]', '[9909, 1101, 6*w^2 - 9*w - 36]', '[9909, 1101, -15*w^2 + 18*w + 48]', '[9910, 9910, 3*w^2 - 3*w - 28]', '[9913, 9913, 15*w^2 - 9*w - 31]', '[9914, 9914, 4*w^2 - 5*w + 15]', '[9914, 9914, -13*w^2 + 13*w + 6]', '[9914, 9914, -11*w^2 + 27*w + 6]', '[9916, 4958, 3*w^2 - 8*w + 19]', '[9916, 4958, 17*w^2 - 12*w - 39]', '[9916, 4958, 15*w^2 - 2*w - 47]', '[9916, 4958, -3*w^2 - 2*w - 15]', '[9916, 4958, w^2 - 16*w - 13]', '[9916, 4958, 21*w^2 - 18*w - 79]', '[9920, 620, -4*w^2 + 12*w - 20]', '[9923, 9923, 9*w^2 + 8*w - 22]', '[9923, 9923, -19*w^2 + 11*w + 47]', '[9923, 9923, 10*w^2 + 7*w - 24]', '[9929, 9929, 2*w^2 - 19*w - 4]', '[9931, 9931, 4*w^2 + 10*w - 23]', '[9932, 4966, 7*w^2 - 18*w - 13]', '[9934, 9934, 10*w^2 + 3*w - 33]', '[9934, 9934, 5*w^2 - w + 12]', '[9934, 9934, -6*w^2 - 7*w + 29]', '[9936, 276, -12*w^2 + 18*w + 30]', '[9937, 9937, 12*w^2 + w - 38]', '[9943, 9943, -12*w^2 + 9*w + 52]', '[9946, 9946, 14*w^2 - 5*w - 25]', '[9947, 203, -7*w^2 + 21*w + 7]', '[9950, 1990, -16*w^2 + 23*w + 17]', '[9950, 9950, -12*w^2 - w + 51]', '[9952, 1244, -18*w^2 + 16*w + 70]', '[9953, 9953, 13*w^2 - 12*w - 18]', '[9953, 9953, 13*w^2 - 10*w - 20]', '[9953, 9953, 8*w^2 - 20*w - 11]', '[9953, 9953, 11*w^2 + 4*w - 30]', '[9953, 9953, -4*w - 21]', '[9953, 9953, 8*w^2 - 16*w - 23]', '[9956, 4978, -9*w^2 - 4*w + 31]', '[9958, 9958, 4*w^2 + w - 33]', '[9962, 9962, -16*w^2 + 11*w + 35]', '[9962, 9962, -9*w^2 + 19*w + 16]', '[9962, 9962, 2*w^2 + w + 17]', '[9965, 9965, 6*w^2 + 7*w - 30]', '[9967, 9967, 3*w^2 - 6*w - 28]', '[9970, 9970, -13*w^2 - 9*w + 24]', '[9971, 767, 5*w^2 - 7*w - 33]', '[9971, 9971, 16*w^2 - 21*w - 38]', '[9973, 9973, 6*w^2 - 16*w - 17]', '[9974, 9974, 6*w^2 - 3*w + 11]', '[9976, 2494, 20*w - 14]', '[9979, 9979, -w^2 + 2*w - 20]', '[9980, 4990, w^2 + 2*w - 25]', '[9986, 9986, -3*w + 23]', '[9990, 1110, 3*w + 21]', '[9990, 1110, -6*w^2 - 9*w + 21]', '[9991, 9991, 12*w^2 + 2*w - 35]', '[9997, 9997, 15*w^2 - 23*w - 9]', '[9998, 9998, 9*w^2 - 17*w - 22]', '[9998, 9998, -15*w^2 + 15*w + 2]', '[9998, 9998, 8*w^2 - 19*w + 17]', '[10000, 100, -8*w^2 - 6*w + 26]', '[10000, 100, -10*w^2 - 10*w + 20]', '[10000, 2500, 2*w^2 - 6*w + 20]'], 'label': '3.3.148.1', 'narrow_class_no': 1, 'primes': ['[2, 2, w - 1]', '[5, 5, -w^2 + w + 1]', '[13, 13, -w^2 + 2*w + 2]', '[17, 17, 2*w + 1]', '[19, 19, -w^2 + 2*w + 4]', '[23, 23, -w^2 - w + 3]', '[25, 5, -2*w^2 + w + 4]', '[27, 3, 3]', '[29, 29, w^2 - 3*w - 1]', '[31, 31, 2*w^2 - 2*w - 3]', '[37, 37, w^2 + w - 5]', '[37, 37, w - 4]', '[43, 43, 2*w^2 - w - 2]', '[59, 59, 2*w^2 - 3*w - 6]', '[61, 61, -3*w^2 + 4*w + 4]', '[67, 67, -w - 4]', '[67, 67, -3*w^2 + 8]', '[67, 67, w^2 - 3*w - 3]', '[79, 79, w^2 + 2*w - 4]', '[89, 89, 3*w^2 - 3*w - 5]', '[97, 97, -3*w^2 + 4]', '[103, 103, -w^2 + w - 3]', '[107, 107, 3*w^2 - w - 5]', '[107, 107, w^2 - w - 7]', '[107, 107, -2*w - 5]', '[109, 109, w^2 + 2*w - 6]', '[113, 113, -2*w^2 + 5*w + 2]', '[131, 131, -5*w^2 + 3*w + 13]', '[137, 137, 2*w^2 - 4*w - 5]', '[137, 137, 2*w^2 + w - 8]', '[137, 137, 3*w^2 - 10]', '[139, 139, -w^2 + 2*w - 4]', '[139, 139, 4*w^2 - 2*w - 9]', '[139, 139, 3*w^2 - 2*w - 4]', '[151, 151, w^2 - 8]', '[151, 151, 4*w - 5]', '[151, 151, w^2 + w - 9]', '[163, 163, w - 6]', '[167, 167, 2*w^2 - 4*w - 7]', '[169, 13, w^2 - 4*w - 4]', '[179, 179, w^2 + 3*w - 5]', '[191, 191, 4*w^2 - 4*w - 7]', '[193, 193, 4*w^2 - 3*w - 8]', '[199, 199, w^2 + 3*w - 9]', '[227, 227, 2*w^2 - 5*w - 4]', '[233, 233, -w - 6]', '[233, 233, w^2 + 3*w - 7]', '[233, 233, 2*w^2 + 2*w - 7]', '[239, 239, 3*w^2 + w - 9]', '[241, 241, -5*w^2 + w + 15]', '[251, 251, 4*w^2 - 5*w - 4]', '[257, 257, 4*w^2 - 2*w - 7]', '[269, 269, 4*w^2 - w - 6]', '[269, 269, w^2 - 5*w - 3]', '[269, 269, 2*w^2 + 2*w - 11]', '[277, 277, 4*w^2 + w - 10]', '[281, 281, -w^2 + 7*w - 5]', '[283, 283, -3*w^2 + 5*w + 11]', '[289, 17, 4*w^2 - 6*w - 9]', '[293, 293, 3*w^2 - 5*w - 9]', '[293, 293, 4*w^2 - 4*w - 5]', '[293, 293, 2*w^2 + 3*w - 6]', '[311, 311, 4*w^2 - 13]', '[313, 313, -w^2 + w - 5]', '[317, 317, w^2 - w - 9]', '[317, 317, 2*w^2 - 5*w - 6]', '[317, 317, 2*w^2 - 6*w - 3]', '[331, 331, w^2 - 5*w - 5]', '[343, 7, -7]', '[347, 347, -5*w^2 + 7*w + 11]', '[349, 349, -2*w - 7]', '[349, 349, 4*w^2 - 15]', '[349, 349, 6*w - 5]', '[353, 353, 2*w^2 - w - 12]', '[361, 19, 4*w^2 + 2*w - 9]', '[367, 367, 5*w^2 - 2*w - 10]', '[367, 367, 2*w^2 - 3*w - 12]', '[367, 367, -5*w^2 + 6*w + 16]', '[383, 383, -7*w^2 + 4*w + 18]', '[389, 389, -w^2 + 2*w - 6]', '[401, 401, 6*w^2 - 3*w - 14]', '[409, 409, w^2 - 7*w - 1]', '[421, 421, w^2 + 4*w - 8]', '[431, 431, 4*w^2 - 6*w - 11]', '[439, 439, 2*w^2 + 3*w - 8]', '[449, 449, w^2 + w - 11]', '[457, 457, -4*w^2 - 4*w + 7]', '[461, 461, 3*w^2 + 2*w - 16]', '[463, 463, 5*w^2 - 6*w - 6]', '[467, 467, 2*w - 9]', '[479, 479, 4*w^2 + w - 12]', '[487, 487, 5*w^2 - 3*w - 9]', '[491, 491, w^2 - 2*w - 10]', '[491, 491, 3*w^2 + 2*w - 10]', '[491, 491, w^2 - 6*w - 8]', '[499, 499, 3*w^2 - 7*w - 5]', '[503, 503, w^2 - 6*w - 4]', '[523, 523, 5*w^2 - 5*w - 7]', '[529, 23, 2*w^2 + 3*w - 10]', '[541, 541, 5*w^2 - 2*w - 8]', '[547, 547, 6*w^2 - 4*w - 13]', '[557, 557, 5*w^2 - 6*w - 4]', '[563, 563, 3*w^2 - 6*w - 10]', '[569, 569, 5*w^2 - 7*w - 13]', '[577, 577, 2*w^2 - 6*w - 7]', '[587, 587, 5*w^2 - 8*w - 10]', '[601, 601, 6*w^2 - 5*w - 12]', '[601, 601, -7*w - 2]', '[601, 601, 5*w^2 - 3*w - 3]', '[607, 607, 3*w^2 + 2*w - 14]', '[631, 631, 4*w^2 + 2*w - 11]', '[643, 643, 5*w^2 - 2*w - 6]', '[647, 647, 3*w^2 - 8*w - 4]', '[653, 653, 5*w^2 - 4*w - 6]', '[661, 661, w^2 - 3*w - 11]', '[683, 683, 5*w^2 - 3*w - 5]', '[691, 691, -12*w^2 + 7*w + 34]', '[691, 691, -w^2 + w - 7]', '[691, 691, -w^2 - 5*w + 11]', '[701, 701, -5*w^2 + 7*w + 17]', '[709, 709, 5*w^2 - 10*w - 6]', '[727, 727, 6*w^2 - w - 10]', '[757, 757, -7*w^2 + 8*w + 12]', '[769, 769, 7*w - 8]', '[797, 797, -2*w^2 + 4*w - 7]', '[809, 809, 6*w^2 - 4*w - 11]', '[823, 823, 2*w^2 - 7*w - 6]', '[823, 823, -3*w^2 - 4]', '[823, 823, -w^2 + 2*w - 8]', '[827, 827, 3*w^2 - 7*w - 13]', '[829, 829, -5*w^2 + 4*w + 22]', '[839, 839, 5*w^2 + w - 15]', '[839, 839, -9*w^2 + 5*w + 23]', '[839, 839, 7*w^2 - 3*w - 15]', '[841, 29, 4*w^2 - 7*w - 14]', '[853, 853, 3*w^2 + 3*w - 17]', '[857, 857, 2*w^2 + 4*w - 13]', '[859, 859, 6*w^2 - 5*w - 10]', '[863, 863, w^2 + 6*w - 8]', '[863, 863, 5*w^2 - 9*w - 9]', '[863, 863, -2*w^2 + 5*w - 8]', '[877, 877, 2*w^2 - 15]', '[877, 877, 4*w^2 + 2*w - 13]', '[877, 877, 7*w^2 - 5*w - 15]', '[881, 881, 7*w^2 - 2*w - 14]', '[881, 881, 5*w^2 - 8*w - 12]', '[881, 881, 7*w^2 - 7*w - 13]', '[883, 883, w^2 - 7*w - 7]', '[907, 907, 4*w^2 - 9*w - 6]', '[911, 911, -10*w^2 + 5*w + 26]', '[919, 919, -w^2 + 3*w - 9]', '[929, 929, 6*w^2 - w - 8]', '[929, 929, 2*w^2 - 7*w - 8]', '[929, 929, -7*w^2 + 11*w + 1]', '[941, 941, 6*w^2 - 7*w - 6]', '[941, 941, 3*w^2 - 8*w - 6]', '[941, 941, 6*w^2 + w - 16]', '[947, 947, w^2 + w - 13]', '[961, 31, 6*w^2 - 2*w - 9]', '[967, 967, -w^2 + 4*w - 10]', '[971, 971, 4*w^2 - 8*w - 9]', '[971, 971, w^2 + 2*w - 14]', '[971, 971, 4*w^2 - 5*w - 20]', '[977, 977, 3*w^2 + 3*w - 13]', '[991, 991, -9*w^2 + 10*w + 32]', '[997, 997, w^2 - 2*w - 12]']}
• nf_fields •

  Column	Type
  class_group	jsonb
  class_number	numeric
  cm	boolean
  coeffs	numeric[]
  conductor	numeric
  degree	smallint
  disc_abs	numeric
  disc_rad	numeric
  disc_sign	smallint
  embeddings_gen_imag	double precision[]
  embeddings_gen_real	double precision[]
  gal_is_abelian	boolean
  gal_is_cyclic	boolean
  gal_is_solvable	boolean
  galois_disc_exponents	numeric[]
  galois_label	text
  galt	integer
  grd	double precision
  index	integer
  inessentialp	integer[]
  is_galois	boolean
  is_minimal_sibling	boolean
  iso_number	smallint
  label	text
  local_algs	text[]
  maximal_cm_subfield	numeric[]
  minimal_sibling	numeric[]
  monogenic	smallint
  narrow_class_group	bigint[]
  narrow_class_number	bigint
  num_ram	smallint
  r2	smallint
  ramps	numeric[]
  rd	double precision
  regulator	numeric
  relative_class_number	numeric
  subfield_mults	integer[]
  subfields	text[]
  torsion_order	smallint
  used_grh	boolean
  dirichlet_group	bigint[]
  frobs	jsonb
  res	jsonb
  source	text
  subfield_inclusions	smallint[]
  torsion_gen	text
  units	jsonb
  unitsGmodule	jsonb
  unitsType	text
  zk	jsonb

  
  {'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [1, -3, -1, 1], 'conductor': 0, 'degree': 3, 'dirichlet_group': [], 'disc_abs': 148, 'disc_rad': 74, 'disc_sign': 1, 'frobs': [[2, [0]], [3, [[3, 1]]], [5, [[2, 1], [1, 1]]], [7, [[3, 1]]], [11, [[3, 1]]], [13, [[2, 1], [1, 1]]], [17, [[2, 1], [1, 1]]], [19, [[2, 1], [1, 1]]], [23, [[2, 1], [1, 1]]], [29, [[2, 1], [1, 1]]], [31, [[2, 1], [1, 1]]], [37, [0]], [41, [[3, 1]]], [43, [[2, 1], [1, 1]]], [47, [[3, 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': 9.65578363946814, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '3.3.148.1', 'local_algs': ['2.1.3.2a1.1', '37.1.1.0a1.1', '37.1.2.1a1.1'], 'monogenic': 1, 'narrow_class_group': [], 'narrow_class_number': 1, 'num_ram': 2, 'r2': 0, 'ramps': [2, 37], 'rd': 5.28957247269, 'regulator': {'__RealLiteral__': 0, 'data': '1.66233652077', 'prec': 44}, 'res': {'gal': ['1,-5,0,9,-2,-3,1']}, 'subfield_mults': [], 'subfields': [], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( a \\)', '\\( a^{2} - 2 \\)'], 'unitsGmodule': [[4, 1], [5, 1]], 'used_grh': False, 'zk': ['1', 'a', 'a^2']}