Hilbert modular form data - 2.2.440.1-4.1-c

Formats: - HTML - YAML - JSON - 2024-05-16T22:41:00.161501

• 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': 2, 'dimension': 4, 'disc': 440, 'field_bad_primes': [2, 5, 11], 'field_label': '2.2.440.1', 'is_CM': 'no', 'is_base_change': 'no', 'label': '2.2.440.1-4.1-c', 'label_nsuffix': 2, 'label_suffix': 'c', 'level_bad_primes': [2], 'level_ideal': '[4, 2, 2]', 'level_label': '4.1', 'level_norm': 4, 'parallel_weight': 2, 'short_label': '4.1-c', 'weight': '[2, 2]'}
• hmf_hecke •

  Column	Type
  AL_eigenvalues	jsonb
  hecke_eigenvalues	jsonb
  hecke_polynomial	text
  label	text

  
  {'AL_eigenvalues': [['[2, 2, w]', -1]], 'hecke_eigenvalues': [0, '-1/32*e^3 + 3/2*e', 0, -2, '-1/32*e^3 + 5/2*e', '1/32*e^3 - 5/2*e', '5/64*e^3 - 15/4*e', '5/64*e^3 - 15/4*e', '1/4*e^2 - 8', '-1/4*e^2 + 8', '-1/32*e^3 + 3/2*e', '-1/32*e^3 + 3/2*e', '1/64*e^3 - 5/4*e', '-1/64*e^3 + 5/4*e', '-3/64*e^3 + 9/4*e', '-3/64*e^3 + 9/4*e', -12, 0, 0, -2, -2, '1/8*e^2 - 4', '-1/8*e^2 + 4', '1/32*e^3 - 5/2*e', '-1/32*e^3 + 5/2*e', '-1/4*e^2 + 8', '1/4*e^2 - 8', '5/64*e^3 - 25/4*e', '-5/64*e^3 + 25/4*e', 2, 2, '-1/4*e^2 + 8', '1/4*e^2 - 8', '7/64*e^3 - 21/4*e', '7/64*e^3 - 21/4*e', '-1/64*e^3 + 5/4*e', '1/64*e^3 - 5/4*e', '1/8*e^2 - 4', '-1/8*e^2 + 4', '3/8*e^2 - 12', '-3/8*e^2 + 12', '-1/2*e^2 + 16', '1/2*e^2 - 16', '-1/32*e^3 + 3/2*e', '-1/32*e^3 + 3/2*e', 6, 2, 2, '-1/32*e^3 + 5/2*e', '1/32*e^3 - 5/2*e', '19/64*e^3 - 57/4*e', '19/64*e^3 - 57/4*e', '-7/64*e^3 + 35/4*e', '7/64*e^3 - 35/4*e', '-3/32*e^3 + 15/2*e', '3/32*e^3 - 15/2*e', '1/4*e^2 - 8', '-1/4*e^2 + 8', -26, -26, '3/4*e^2 - 24', '-3/4*e^2 + 24', '-1/64*e^3 + 5/4*e', '1/64*e^3 - 5/4*e', '-1/64*e^3 + 5/4*e', '1/64*e^3 - 5/4*e', '-1/4*e^3 + 12*e', '-1/4*e^3 + 12*e', 6, 6, '-1/8*e^3 + 10*e', '1/8*e^3 - 10*e', '-7/64*e^3 + 35/4*e', '7/64*e^3 - 35/4*e', '1/4*e^2 - 8', '-1/4*e^2 + 8', '-e^2 + 32', 'e^2 - 32', -2, '-7/64*e^3 + 21/4*e', '-7/64*e^3 + 21/4*e', -14, -14, '9/64*e^3 - 27/4*e', '9/64*e^3 - 27/4*e', '1/8*e^3 - 6*e', '1/8*e^3 - 6*e', 22, 22, -26, -26, '-1/4*e^2 + 8', '1/4*e^2 - 8', 0, 0, -16, -16, '1/8*e^3 - 10*e', '-1/8*e^3 + 10*e', '3/4*e^2 - 24', '-3/4*e^2 + 24', '-1/64*e^3 + 3/4*e', '-1/64*e^3 + 3/4*e', '3/2*e^2 - 48', '-3/2*e^2 + 48', '-19/64*e^3 + 57/4*e', '-19/64*e^3 + 57/4*e', -6, -6, -34, -34, '-1/64*e^3 + 5/4*e', '1/64*e^3 - 5/4*e', '-1/4*e^2 + 8', '1/4*e^2 - 8', '11/64*e^3 - 55/4*e', '-11/64*e^3 + 55/4*e', '3/64*e^3 - 15/4*e', '-3/64*e^3 + 15/4*e', '3/16*e^3 - 15*e', '-3/16*e^3 + 15*e', -14, -14, -40, -40, '-3/64*e^3 + 9/4*e', '-3/64*e^3 + 9/4*e', '1/16*e^3 - 3*e', '1/16*e^3 - 3*e', '-5/32*e^3 + 25/2*e', '5/32*e^3 - 25/2*e', -42, -42, '-1/8*e^2 + 4', '1/8*e^2 - 4', '-13/64*e^3 + 39/4*e', '-13/64*e^3 + 39/4*e', '1/32*e^3 - 3/2*e', '1/32*e^3 - 3/2*e', '-1/2*e^3 + 24*e', '-1/2*e^3 + 24*e', '19/64*e^3 - 95/4*e', '-19/64*e^3 + 95/4*e', '-3/8*e^3 + 18*e', '-3/8*e^3 + 18*e', '15/8*e^2 - 60', '-15/8*e^2 + 60', '-25/64*e^3 + 75/4*e', '-25/64*e^3 + 75/4*e', '13/64*e^3 - 65/4*e', '-13/64*e^3 + 65/4*e', '1/4*e^3 - 20*e', '-1/4*e^3 + 20*e', -22, -22, '17/64*e^3 - 51/4*e', '17/64*e^3 - 51/4*e', 52, 52, '1/4*e^2 - 8', '-1/4*e^2 + 8', -8, -8, '-5/32*e^3 + 25/2*e', '5/32*e^3 - 25/2*e', '5/4*e^2 - 40', '-5/4*e^2 + 40', '-1/4*e^3 + 20*e', '1/4*e^3 - 20*e', 14, 22, 22, '-33/64*e^3 + 99/4*e', '-33/64*e^3 + 99/4*e'], 'hecke_polynomial': 'x^4 - 64*x^2 + 256', 'label': '2.2.440.1-4.1-c'}
• hmf_fields •

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

  
  {'degree': 2, 'discriminant': 440, 'ideals': ['[1, 1, 1]', '[2, 2, w]', '[4, 2, 2]', '[5, 5, w]', '[8, 4, 2*w]', '[9, 3, 3]', '[10, 10, w - 10]', '[11, 11, -w + 11]', '[16, 4, 4]', '[17, 17, w + 5]', '[17, 17, w + 12]', '[18, 6, 3*w]', '[20, 10, 2*w]', '[22, 22, w]', '[23, 23, w + 8]', '[23, 23, w + 15]', '[25, 5, 5]', '[29, 29, w + 9]', '[29, 29, -w + 9]', '[32, 8, 4*w]', '[34, 34, -w - 12]', '[34, 34, -w + 12]', '[36, 6, 6]', '[37, 37, w + 6]', '[37, 37, w + 31]', '[40, 20, 2*w - 20]', '[43, 43, w + 14]', '[43, 43, w + 29]', '[44, 22, -2*w + 22]', '[45, 15, 3*w]', '[46, 46, w + 8]', '[46, 46, w - 8]', '[47, 47, w + 4]', '[47, 47, w + 43]', '[49, 7, -7]', '[50, 10, 5*w]', '[53, 53, w + 2]', '[53, 53, w + 51]', '[55, 55, w]', '[58, 58, w + 20]', '[58, 58, w + 38]', '[59, 59, -w - 13]', '[59, 59, w - 13]', '[61, 61, -w - 7]', '[61, 61, w - 7]', '[64, 8, 8]', '[68, 34, 2*w + 10]', '[68, 34, 2*w + 24]', '[72, 12, 6*w]', '[73, 73, w + 16]', '[73, 73, w + 57]', '[74, 74, -w - 6]', '[74, 74, w - 6]', '[79, 79, -2*w + 19]', '[79, 79, -4*w + 41]', '[80, 20, 4*w]', '[81, 9, 9]', '[83, 83, w + 39]', '[83, 83, w + 44]', '[85, 85, w + 5]', '[85, 85, -w + 5]', '[86, 86, -w - 14]', '[86, 86, w - 14]', '[88, 44, 2*w]', '[89, 89, 2*w - 23]', '[89, 89, 4*w - 43]', '[90, 30, 3*w - 30]', '[92, 46, 2*w + 16]', '[92, 46, 2*w + 30]', '[94, 94, -w - 4]', '[94, 94, w - 4]', '[98, 14, 7*w]', '[99, 33, -3*w + 33]', '[100, 10, 10]', '[101, 101, -w - 3]', '[101, 101, w - 3]', '[103, 103, w + 25]', '[103, 103, w + 78]', '[106, 106, -w - 2]', '[106, 106, w - 2]', '[107, 107, w + 18]', '[107, 107, w + 89]', '[109, 109, -w - 1]', '[109, 109, w - 1]', '[110, 110, w]', '[115, 115, w + 15]', '[115, 115, -w + 15]', '[116, 58, 2*w + 18]', '[116, 58, -2*w + 18]', '[118, 118, w + 46]', '[118, 118, w + 72]', '[121, 11, 11]', '[122, 122, w + 54]', '[122, 122, w + 68]', '[125, 25, 5*w]', '[128, 16, 8*w]', '[136, 68, -2*w - 24]', '[136, 68, -2*w + 24]', '[144, 12, 12]', '[145, 145, w + 20]', '[145, 145, w + 125]', '[146, 146, -w - 16]', '[146, 146, w - 16]', '[148, 74, 2*w + 12]', '[148, 74, 2*w + 62]', '[149, 149, -3*w + 29]', '[149, 149, -5*w + 51]', '[151, 151, 2*w - 17]', '[151, 151, -2*w - 17]', '[153, 51, 3*w + 15]', '[153, 51, 3*w + 36]', '[157, 157, w + 61]', '[157, 157, w + 96]', '[158, 158, w + 30]', '[158, 158, w + 128]', '[160, 40, 4*w - 40]', '[162, 18, 9*w]', '[166, 166, 3*w - 34]', '[166, 166, -5*w + 54]', '[169, 13, -13]', '[170, 170, w + 80]', '[170, 170, w + 90]', '[172, 86, 2*w + 28]', '[172, 86, 2*w + 58]', '[176, 44, -4*w + 44]', '[178, 178, w + 56]', '[178, 178, w + 122]', '[179, 179, -w - 17]', '[179, 179, w - 17]', '[180, 30, 6*w]', '[184, 92, 2*w + 16]', '[184, 92, 2*w - 16]', '[185, 185, 2*w - 25]', '[185, 185, -8*w + 85]', '[187, 187, w + 22]', '[187, 187, w + 165]', '[188, 94, 2*w + 8]', '[188, 94, 2*w + 86]', '[193, 193, w + 66]', '[193, 193, w + 127]', '[196, 14, -14]', '[198, 66, 3*w]', '[200, 20, 10*w]', '[202, 202, w + 98]', '[202, 202, w + 104]', '[206, 206, -7*w + 72]', '[206, 206, -3*w + 28]', '[207, 69, 3*w + 24]', '[207, 69, 3*w + 45]', '[212, 106, 2*w + 4]', '[212, 106, 2*w + 102]', '[214, 214, -w - 18]', '[214, 214, w - 18]', '[215, 215, -2*w + 15]', '[215, 215, -12*w + 125]', '[218, 218, w + 108]', '[218, 218, w + 110]', '[220, 110, 2*w]', '[223, 223, w + 35]', '[223, 223, w + 188]', '[225, 15, 15]', '[227, 227, w + 63]', '[227, 227, w + 164]', '[230, 230, w + 100]', '[230, 230, w + 130]', '[232, 116, 2*w + 40]', '[232, 116, 2*w + 76]', '[233, 233, w + 24]', '[233, 233, w + 209]', '[235, 235, -7*w + 75]', '[235, 235, 3*w - 35]', '[236, 118, -2*w - 26]', '[236, 118, 2*w - 26]', '[239, 239, -4*w + 39]', '[239, 239, -6*w + 61]', '[242, 22, 11*w]', '[244, 122, -2*w - 14]', '[244, 122, 2*w - 14]', '[245, 35, 7*w]', '[250, 50, 5*w - 50]', '[251, 251, -w - 19]', '[251, 251, w - 19]', '[253, 253, w + 77]', '[253, 253, w + 176]', '[256, 16, 16]', '[261, 87, 3*w + 27]', '[261, 87, -3*w + 27]', '[265, 265, 4*w - 45]', '[265, 265, -6*w + 65]', '[271, 271, 2*w - 13]', '[271, 271, -2*w - 13]', '[272, 68, 4*w + 20]', '[272, 68, 4*w + 48]', '[275, 55, -5*w + 55]', '[283, 283, w + 26]', '[283, 283, w + 257]', '[288, 24, 12*w]', '[289, 17, 17]', '[289, 289, -2*w + 27]', '[289, 289, 2*w + 27]', '[290, 290, -w - 20]', '[290, 290, -w + 20]', '[292, 146, 2*w + 32]', '[292, 146, 2*w + 114]', '[295, 295, w + 105]', '[295, 295, w + 190]', '[296, 148, -2*w - 12]', '[296, 148, 2*w - 12]', '[298, 298, w + 40]', '[298, 298, w + 258]', '[302, 302, w + 84]', '[302, 302, w + 218]', '[305, 305, w + 115]', '[305, 305, w + 190]', '[306, 102, -3*w - 36]', '[306, 102, -3*w + 36]', '[307, 307, w + 73]', '[307, 307, w + 234]', '[314, 314, -3*w + 26]', '[314, 314, 3*w + 26]', '[316, 158, -4*w + 38]', '[316, 158, -8*w + 82]', '[317, 317, w + 136]', '[317, 317, w + 181]', '[319, 319, 2*w - 11]', '[319, 319, -2*w - 11]', '[320, 40, 8*w]', '[324, 18, 18]', '[331, 331, -w - 21]', '[331, 331, w - 21]', '[332, 166, 2*w + 78]', '[332, 166, 2*w + 88]', '[333, 111, 3*w + 18]', '[333, 111, 3*w + 93]', '[337, 337, w + 28]', '[337, 337, w + 309]', '[338, 26, 13*w]', '[340, 170, 2*w + 10]', '[340, 170, -2*w + 10]', '[344, 172, -2*w - 28]', '[344, 172, 2*w - 28]', '[347, 347, w + 88]', '[347, 347, w + 259]', '[349, 349, -5*w + 49]', '[349, 349, -7*w + 71]', '[352, 88, 4*w]', '[356, 178, 4*w - 46]', '[356, 178, 8*w - 86]', '[358, 358, w + 162]', '[358, 358, w + 196]', '[359, 359, 2*w - 9]', '[359, 359, -2*w - 9]', '[360, 60, 6*w - 60]', '[361, 19, -19]', '[365, 365, -13*w + 135]', '[365, 365, -3*w + 25]', '[367, 367, w + 117]', '[367, 367, w + 250]', '[368, 92, 4*w + 32]', '[368, 92, 4*w + 60]', '[370, 370, w + 80]', '[370, 370, w + 290]', '[374, 374, w + 22]', '[374, 374, w - 22]', '[376, 188, -2*w - 8]', '[376, 188, 2*w - 8]', '[379, 379, 3*w - 37]', '[379, 379, -3*w - 37]', '[383, 383, w + 45]', '[383, 383, w + 338]', '[386, 386, 5*w - 56]', '[386, 386, -7*w + 76]', '[387, 129, 3*w + 42]', '[387, 129, 3*w + 87]', '[391, 391, 4*w + 37]', '[391, 391, 2*w - 7]', '[391, 391, -2*w - 7]', '[391, 391, -4*w + 37]', '[392, 28, 14*w]', '[395, 395, w + 30]', '[395, 395, w + 365]', '[396, 66, -6*w + 66]', '[397, 397, w + 137]', '[397, 397, w + 260]', '[400, 20, 20]', '[401, 401, 2*w - 29]', '[401, 401, -2*w - 29]', '[404, 202, -2*w - 6]', '[404, 202, 2*w - 6]', '[405, 45, 9*w]', '[407, 407, w + 154]', '[407, 407, w + 253]', '[412, 206, 2*w + 50]', '[412, 206, 2*w + 156]', '[414, 138, 3*w + 24]', '[414, 138, 3*w - 24]', '[415, 415, 2*w - 5]', '[415, 415, -2*w - 5]', '[419, 419, -w - 23]', '[419, 419, w - 23]', '[423, 141, 3*w + 12]', '[423, 141, 3*w + 129]', '[424, 212, -2*w - 4]', '[424, 212, 2*w - 4]', '[425, 85, 5*w + 25]', '[425, 85, 5*w + 60]', '[428, 214, 2*w + 36]', '[428, 214, 2*w + 178]', '[430, 430, w + 100]', '[430, 430, w + 330]', '[431, 431, 2*w - 3]', '[431, 431, -2*w - 3]', '[436, 218, -2*w - 2]', '[436, 218, 2*w - 2]', '[439, 439, 2*w - 1]', '[439, 439, -2*w - 1]', '[440, 220, 2*w]', '[441, 21, -21]', '[445, 445, w + 145]', '[445, 445, w + 300]', '[446, 446, -9*w + 92]', '[446, 446, -5*w + 48]', '[449, 449, 10*w - 107]', '[449, 449, -4*w + 47]', '[450, 30, 15*w]', '[454, 454, -3*w - 38]', '[454, 454, 3*w - 38]', '[457, 457, w + 32]', '[457, 457, w + 425]', '[460, 230, 2*w + 30]', '[460, 230, -2*w + 30]', '[461, 461, 3*w - 23]', '[461, 461, -3*w - 23]', '[463, 463, w + 157]', '[463, 463, w + 306]', '[464, 116, 4*w + 36]', '[464, 116, -4*w + 36]', '[466, 466, -w - 24]', '[466, 466, w - 24]', '[470, 470, w + 90]', '[470, 470, w + 380]', '[472, 236, 2*w + 92]', '[472, 236, 2*w + 144]', '[473, 473, w + 143]', '[473, 473, w + 330]', '[477, 159, 3*w + 6]', '[477, 159, 3*w + 153]', '[478, 478, w + 50]', '[478, 478, w + 428]', '[479, 479, -6*w + 59]', '[479, 479, -8*w + 81]', '[484, 22, 22]', '[487, 487, w + 161]', '[487, 487, w + 326]', '[488, 244, 2*w + 108]', '[488, 244, 2*w + 136]', '[490, 70, -7*w + 70]', '[493, 493, w + 107]', '[493, 493, w + 165]', '[493, 493, w + 328]', '[493, 493, w + 386]', '[495, 165, 3*w]', '[499, 499, 9*w - 97]', '[499, 499, 5*w - 57]', '[500, 50, 10*w]', '[502, 502, w + 232]', '[502, 502, w + 270]', '[505, 505, w + 205]', '[505, 505, w + 300]', '[506, 506, 3*w + 22]', '[506, 506, 3*w - 22]', '[512, 32, 16*w]', '[515, 515, -w - 25]', '[515, 515, w - 25]', '[517, 517, w + 231]', '[517, 517, w + 286]', '[521, 521, 2*w - 31]', '[521, 521, -2*w - 31]', '[522, 174, 3*w + 60]', '[522, 174, 3*w + 114]', '[523, 523, w + 34]', '[523, 523, w + 489]', '[529, 23, 23]', '[529, 529, -6*w + 67]', '[529, 529, 6*w + 67]', '[530, 530, w + 210]', '[530, 530, w + 320]', '[531, 177, -3*w - 39]', '[531, 177, 3*w - 39]', '[535, 535, -4*w + 35]', '[535, 535, -14*w + 145]', '[539, 77, 7*w - 77]', '[541, 541, 5*w - 47]', '[541, 541, -11*w + 113]', '[542, 542, w + 142]', '[542, 542, w + 400]', '[544, 136, -4*w - 48]', '[544, 136, -4*w + 48]', '[545, 545, w + 110]', '[545, 545, w + 435]', '[547, 547, w + 97]', '[547, 547, w + 450]', '[549, 183, -3*w - 21]', '[549, 183, 3*w - 21]', '[550, 110, 5*w]', '[563, 563, w + 203]', '[563, 563, w + 360]', '[566, 566, -w - 26]', '[566, 566, w - 26]', '[575, 115, 5*w + 40]', '[575, 115, 5*w + 75]', '[576, 24, 24]', '[578, 34, 17*w]', '[578, 578, w + 158]', '[578, 578, w + 420]', '[580, 290, 2*w + 40]', '[580, 290, 2*w + 250]', '[583, 583, w + 55]', '[583, 583, w + 528]', '[584, 292, -2*w - 32]', '[584, 292, 2*w - 32]', '[590, 590, -3*w + 20]', '[590, 590, -23*w + 240]', '[592, 148, 4*w + 24]', '[592, 148, 4*w + 124]', '[593, 593, w + 36]', '[593, 593, w + 557]', '[596, 298, -6*w + 58]', '[596, 298, -10*w + 102]', '[604, 302, 4*w - 34]', '[604, 302, -4*w - 34]', '[605, 55, 11*w]', '[610, 610, 3*w - 40]', '[610, 610, -17*w + 180]', '[612, 102, 6*w + 30]', '[612, 102, 6*w + 72]', '[614, 614, 5*w - 58]', '[614, 614, -11*w + 118]', '[619, 619, -w - 27]', '[619, 619, w - 27]', '[625, 25, 25]', '[628, 314, 2*w + 122]', '[628, 314, 2*w + 192]', '[629, 629, 9*w + 91]', '[629, 629, -3*w - 19]', '[629, 629, -3*w + 19]', '[629, 629, 9*w - 91]', '[632, 316, 2*w + 60]', '[632, 316, 2*w + 256]', '[634, 634, -13*w + 134]', '[634, 634, -5*w + 46]', '[638, 638, w + 154]', '[638, 638, w + 484]', '[640, 80, 8*w - 80]', '[641, 641, 4*w - 49]', '[641, 641, -4*w - 49]', '[647, 647, w + 194]', '[647, 647, w + 453]', '[648, 36, 18*w]', '[649, 649, 2*w - 33]', '[649, 649, 24*w - 253]', '[653, 653, w + 123]', '[653, 653, w + 530]', '[657, 219, 3*w + 48]', '[657, 219, 3*w + 171]', '[662, 662, w + 310]', '[662, 662, w + 352]', '[664, 332, 6*w - 68]', '[664, 332, -10*w + 108]', '[666, 222, -3*w - 18]', '[666, 222, 3*w - 18]', '[667, 667, w + 38]', '[667, 667, w + 107]', '[667, 667, w + 560]', '[667, 667, w + 629]', '[671, 671, 18*w - 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136]', '[9664, 1208, -16*w - 136]', '[9668, 4834, 2*w + 1312]', '[9668, 4834, 2*w + 3522]', '[9675, 645, 15*w + 210]', '[9675, 645, 15*w + 435]', '[9679, 9679, 14*w - 109]', '[9679, 9679, -14*w - 109]', '[9680, 220, 44*w]', '[9682, 9682, w + 3012]', '[9682, 9682, w + 4610]', '[9682, 9682, w + 5072]', '[9682, 9682, w + 6670]', '[9689, 9689, -4*w - 107]', '[9689, 9689, 4*w - 107]', '[9691, 9691, -w - 99]', '[9691, 9691, w - 99]', '[9692, 4846, 2*w + 2186]', '[9692, 4846, 2*w + 2660]', '[9697, 9697, w + 462]', '[9697, 9697, w + 9235]', '[9701, 9701, -39*w + 397]', '[9701, 9701, -47*w + 483]', '[9701, 9701, 21*w - 197]', '[9701, 9701, -25*w + 243]', '[9702, 462, 21*w]', '[9704, 4852, -10*w - 36]', '[9704, 4852, 10*w - 36]', '[9710, 9710, -11*w + 60]', '[9710, 9710, -111*w + 1160]', '[9719, 9719, 18*w - 161]', '[9719, 9719, -18*w - 161]', '[9722, 9722, w + 2080]', '[9722, 9722, w + 7642]', '[9729, 3243, -18*w - 213]', '[9729, 3243, 6*w - 117]', '[9729, 3243, 6*w + 117]', '[9729, 3243, -18*w + 213]', '[9733, 9733, w + 3495]', '[9733, 9733, w + 6238]', '[9736, 4868, -10*w - 144]', '[9736, 4868, 10*w - 144]', '[9738, 3246, 3*w + 1002]', '[9738, 3246, 3*w + 2244]', '[9739, 9739, 7*w - 123]', '[9739, 9739, -7*w - 123]', '[9740, 4870, -34*w + 370]', '[9740, 4870, 26*w - 290]', '[9745, 9745, w + 140]', '[9745, 9745, w + 9605]', '[9752, 4876, 2*w + 844]', '[9752, 4876, 2*w + 1488]', '[9752, 4876, 2*w + 3388]', '[9752, 4876, 2*w + 4032]', '[9754, 9754, 13*w - 94]', '[9754, 9754, -13*w - 94]', '[9756, 1626, 12*w - 78]', '[9756, 1626, -12*w - 78]', '[9760, 2440, 12*w - 160]', '[9760, 2440, -68*w + 720]', '[9761, 9761, 22*w - 251]', '[9761, 9761, 2*w - 101]', '[9761, 9761, -2*w - 101]', '[9761, 9761, 40*w - 431]', '[9769, 9769, -14*w - 177]', '[9769, 9769, 14*w - 177]', '[9773, 9773, w + 2050]', '[9773, 9773, w + 2387]', '[9773, 9773, w + 7386]', '[9773, 9773, w + 7723]', '[9775, 1955, 20*w + 185]', '[9775, 1955, 10*w - 35]', '[9775, 1955, -10*w - 35]', '[9775, 1955, -20*w + 185]', '[9778, 9778, w + 2408]', '[9778, 9778, w + 7370]', '[9781, 9781, 19*w - 173]', '[9781, 9781, -19*w - 173]', '[9783, 3261, 3*w + 1290]', '[9783, 3261, 3*w + 1971]', '[9787, 9787, w + 4217]', '[9787, 9787, w + 5570]', '[9788, 4894, 2*w + 1708]', '[9788, 4894, 2*w + 3186]', '[9790, 9790, -23*w + 220]', '[9790, 9790, -43*w + 440]', '[9792, 408, 24*w + 120]', '[9792, 408, 24*w + 288]', '[9794, 9794, -5*w - 112]', '[9794, 9794, 11*w - 152]', '[9794, 9794, -11*w - 152]', '[9794, 9794, 5*w - 112]', '[9800, 140, 70*w]', '[9801, 99, 99]', '[9802, 754, 13*w + 260]', '[9802, 754, 13*w + 494]', '[9803, 9803, w + 2225]', '[9803, 9803, w + 7578]', '[9805, 9805, w + 475]', '[9805, 9805, w + 1005]', '[9805, 9805, w + 8800]', '[9805, 9805, w + 9330]', '[9810, 3270, 27*w - 300]', '[9810, 3270, -33*w + 360]', '[9812, 4906, 2*w + 1408]', '[9812, 4906, 2*w + 3498]', '[9824, 2456, 20*w - 232]', '[9824, 2456, -44*w + 472]', '[9826, 578, 17*w + 204]', '[9826, 578, 17*w - 204]', '[9826, 9826, -3*w - 104]', '[9826, 9826, -3*w + 104]', '[9829, 9829, -11*w - 59]', '[9829, 9829, 11*w - 59]', '[9830, 9830, w + 3140]', '[9830, 9830, w + 6690]', '[9832, 4916, 2*w + 476]', '[9832, 4916, 2*w + 4440]', '[9833, 9833, w + 2561]', '[9833, 9833, w + 7272]', '[9837, 3279, 3*w + 756]', '[9837, 3279, 3*w + 2523]', '[9838, 9838, w + 1766]', '[9838, 9838, w + 8072]', '[9844, 4922, -26*w - 254]', '[9844, 4922, -10*w + 34]', '[9844, 4922, -10*w - 34]', '[9844, 4922, -26*w + 254]', '[9845, 9845, w + 2310]', '[9845, 9845, w + 7535]', '[9846, 3282, 15*w + 186]', '[9846, 3282, -15*w + 186]', '[9848, 4924, 2*w + 604]', '[9848, 4924, 2*w + 4320]', '[9859, 9859, -9*w - 137]', '[9859, 9859, 9*w - 137]', '[9860, 4930, -28*w + 310]', '[9860, 4930, 8*w - 130]', '[9860, 4930, -8*w - 130]', '[9860, 4930, 28*w + 310]', '[9862, 9862, w + 4860]', '[9862, 9862, w + 5002]', '[9865, 9865, -54*w + 575]', '[9865, 9865, 16*w - 195]', '[9866, 9866, 15*w - 122]', '[9866, 9866, 71*w - 738]', '[9873, 3291, 3*w + 144]', '[9873, 3291, 3*w + 3147]', '[9875, 1975, 5*w + 150]', '[9875, 1975, 5*w + 1825]', '[9878, 9878, w + 1672]', '[9878, 9878, w + 8206]', '[9882, 1098, 9*w + 486]', '[9882, 1098, 9*w + 612]', '[9886, 9886, -17*w + 148]', '[9886, 9886, 17*w + 148]', '[9887, 9887, w + 1728]', '[9887, 9887, w + 8159]', '[9890, 9890, -w - 100]', '[9890, 9890, 29*w - 320]', '[9890, 9890, -29*w - 320]', '[9890, 9890, w - 100]', '[9896, 4948, -14*w - 108]', '[9896, 4948, 14*w - 108]', '[9898, 1414, 7*w + 686]', '[9898, 1414, 7*w + 728]', '[9900, 330, -30*w + 330]', '[9904, 2476, -4*w - 108]', '[9904, 2476, 4*w - 108]', '[9907, 9907, w + 3586]', '[9907, 9907, w + 6321]', '[9911, 9911, 10*w - 33]', '[9911, 9911, -12*w - 77]', '[9911, 9911, -12*w + 77]', '[9911, 9911, 10*w + 33]', '[9913, 9913, w + 1510]', '[9913, 9913, w + 3665]', '[9913, 9913, w + 6248]', '[9913, 9913, w + 8403]', '[9925, 1985, 5*w + 685]', '[9925, 1985, 5*w + 1300]', '[9927, 3309, 3*w + 225]', '[9927, 3309, 3*w + 3084]', '[9928, 4964, 2*w + 908]', '[9928, 4964, 2*w + 1200]', '[9928, 4964, 2*w + 3764]', '[9928, 4964, 2*w + 4056]', '[9931, 9931, 23*w - 261]', '[9931, 9931, 39*w - 421]', '[9935, 9935, -66*w + 685]', '[9935, 9935, -16*w + 135]', '[9941, 9941, 13*w - 93]', '[9941, 9941, -13*w - 93]', '[9946, 9946, -11*w - 58]', '[9946, 9946, 11*w - 58]', '[9964, 4982, -2*w - 102]', '[9964, 4982, -6*w - 118]', '[9964, 4982, 6*w - 118]', '[9964, 4982, 2*w - 102]', '[9965, 9965, -27*w + 265]', '[9965, 9965, -37*w + 375]', '[9967, 9967, w + 4238]', '[9967, 9967, w + 5729]', '[9971, 767, -13*w - 169]', '[9971, 767, 13*w - 169]', '[9976, 4988, -46*w - 472]', '[9976, 4988, -10*w - 32]', '[9976, 4988, 10*w - 32]', '[9976, 4988, 46*w - 472]', '[9980, 4990, 2*w + 1420]', '[9980, 4990, 2*w + 3570]', '[9986, 9986, 7*w - 124]', '[9986, 9986, -7*w - 124]', '[9988, 4994, 2*w + 1034]', '[9988, 4994, 2*w + 3960]', '[9995, 9995, w + 2240]', '[9995, 9995, w + 7755]', '[9999, 3333, -24*w + 231]', '[9999, 3333, 42*w - 429]', '[10000, 100, 100]'], 'label': '2.2.440.1', 'narrow_class_no': 4, 'primes': ['[2, 2, w]', '[5, 5, w]', '[9, 3, 3]', '[11, 11, -w + 11]', '[17, 17, w + 5]', '[17, 17, w + 12]', '[23, 23, w + 8]', '[23, 23, w + 15]', '[29, 29, w + 9]', '[29, 29, -w + 9]', '[37, 37, w + 6]', '[37, 37, w + 31]', '[43, 43, w + 14]', '[43, 43, w + 29]', '[47, 47, w + 4]', '[47, 47, w + 43]', '[49, 7, -7]', '[53, 53, w + 2]', '[53, 53, w + 51]', '[59, 59, -w - 13]', '[59, 59, w - 13]', '[61, 61, -w - 7]', '[61, 61, w - 7]', '[73, 73, w + 16]', '[73, 73, w + 57]', '[79, 79, -2*w + 19]', '[79, 79, -4*w + 41]', '[83, 83, w + 39]', '[83, 83, w + 44]', '[89, 89, 2*w - 23]', '[89, 89, 4*w - 43]', '[101, 101, -w - 3]', '[101, 101, w - 3]', '[103, 103, w + 25]', '[103, 103, w + 78]', '[107, 107, w + 18]', '[107, 107, w + 89]', '[109, 109, -w - 1]', '[109, 109, w - 1]', '[149, 149, -3*w + 29]', '[149, 149, -5*w + 51]', '[151, 151, 2*w - 17]', '[151, 151, -2*w - 17]', '[157, 157, w + 61]', '[157, 157, w + 96]', '[169, 13, -13]', '[179, 179, -w - 17]', '[179, 179, w - 17]', '[193, 193, w + 66]', '[193, 193, w + 127]', '[223, 223, w + 35]', '[223, 223, w + 188]', '[227, 227, w + 63]', '[227, 227, w + 164]', '[233, 233, w + 24]', '[233, 233, w + 209]', '[239, 239, -4*w + 39]', '[239, 239, -6*w + 61]', '[251, 251, -w - 19]', '[251, 251, w - 19]', '[271, 271, 2*w - 13]', '[271, 271, -2*w - 13]', '[283, 283, w + 26]', '[283, 283, w + 257]', '[307, 307, w + 73]', '[307, 307, w + 234]', '[317, 317, w + 136]', '[317, 317, w + 181]', '[331, 331, -w - 21]', '[331, 331, w - 21]', '[337, 337, w + 28]', '[337, 337, w + 309]', '[347, 347, w + 88]', '[347, 347, w + 259]', '[349, 349, -5*w + 49]', '[349, 349, -7*w + 71]', '[359, 359, 2*w - 9]', '[359, 359, -2*w - 9]', '[361, 19, -19]', '[367, 367, w + 117]', '[367, 367, w + 250]', '[379, 379, 3*w - 37]', '[379, 379, -3*w - 37]', '[383, 383, w + 45]', '[383, 383, w + 338]', '[397, 397, w + 137]', '[397, 397, w + 260]', '[401, 401, 2*w - 29]', '[401, 401, -2*w - 29]', '[419, 419, -w - 23]', '[419, 419, w - 23]', '[431, 431, 2*w - 3]', '[431, 431, -2*w - 3]', '[439, 439, 2*w - 1]', '[439, 439, -2*w - 1]', '[449, 449, 10*w - 107]', '[449, 449, -4*w + 47]', '[457, 457, w + 32]', '[457, 457, w + 425]', '[461, 461, 3*w - 23]', '[461, 461, -3*w - 23]', '[463, 463, w + 157]', '[463, 463, w + 306]', '[479, 479, -6*w + 59]', '[479, 479, -8*w + 81]', '[487, 487, w + 161]', '[487, 487, w + 326]', '[499, 499, 9*w - 97]', '[499, 499, 5*w - 57]', '[521, 521, 2*w - 31]', '[521, 521, -2*w - 31]', '[523, 523, w + 34]', '[523, 523, w + 489]', '[541, 541, 5*w - 47]', '[541, 541, -11*w + 113]', '[547, 547, w + 97]', '[547, 547, w + 450]', '[563, 563, w + 203]', '[563, 563, w + 360]', '[593, 593, w + 36]', '[593, 593, w + 557]', '[619, 619, -w - 27]', '[619, 619, w - 27]', '[641, 641, 4*w - 49]', '[641, 641, -4*w - 49]', '[647, 647, w + 194]', '[647, 647, w + 453]', '[653, 653, w + 123]', '[653, 653, w + 530]', '[673, 673, w + 282]', '[673, 673, w + 391]', '[691, 691, -3*w - 41]', '[691, 691, 3*w - 41]', '[701, 701, 3*w - 17]', '[701, 701, -3*w - 17]', '[727, 727, w + 298]', '[727, 727, w + 429]', '[757, 757, w + 346]', '[757, 757, w + 411]', '[773, 773, w + 212]', '[773, 773, w + 561]', '[787, 787, w + 132]', '[787, 787, w + 655]', '[797, 797, w + 312]', '[797, 797, w + 485]', '[821, 821, -3*w - 13]', '[821, 821, 3*w - 13]', '[823, 823, w + 65]', '[823, 823, w + 758]', '[827, 827, w + 42]', '[827, 827, w + 785]', '[857, 857, w + 303]', '[857, 857, w + 554]', '[859, 859, 3*w - 43]', '[859, 859, -3*w - 43]', '[863, 863, w + 179]', '[863, 863, w + 684]', '[881, 881, 8*w - 89]', '[881, 881, 10*w - 109]', '[919, 919, -4*w - 29]', '[919, 919, 4*w - 29]', '[929, 929, 2*w - 37]', '[929, 929, -2*w - 37]', '[937, 937, w + 201]', '[937, 937, w + 736]', '[941, 941, -3*w - 7]', '[941, 941, 3*w - 7]', '[953, 953, w + 412]', '[953, 953, w + 541]', '[961, 31, -31]', '[971, 971, 5*w - 61]', '[971, 971, -5*w - 61]', '[983, 983, w + 191]', '[983, 983, w + 792]']}
• 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[]
  minimal_sibling	numeric[]
  monogenic	smallint
  num_ram	smallint
  r2	smallint
  ramps	numeric[]
  rd	double precision
  regulator	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': [2], 'class_number': 2, 'cm': False, 'coeffs': [-110, 0, 1], 'conductor': 440, 'degree': 2, 'dirichlet_group': [1, 219], 'disc_abs': 440, 'disc_rad': 110, 'disc_sign': 1, 'frobs': [[2, [0]], [3, [[2, 1]]], [5, [0]], [7, [[2, 1]]], [11, [0]], [13, [[2, 1]]], [17, [[1, 2]]], [19, [[2, 1]]], [23, [[1, 2]]], [29, [[1, 2]]], [31, [[2, 1]]], [37, [[1, 2]]], [41, [[2, 1]]], [43, [[1, 2]]], [47, [[1, 2]]], [53, [[1, 2]]], [59, [[1, 2]]]], 'gal_is_abelian': True, 'gal_is_cyclic': True, 'gal_is_solvable': True, 'galois_disc_exponents': [3, 1, 1], 'galois_label': '2T1', 'galt': 1, 'grd': 20.97617696340303, 'index': 1, 'inessentialp': [], 'is_galois': True, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '2.2.440.1', 'local_algs': ['2.2.3.3', '5.2.1.2', '11.2.1.2'], 'monogenic': 1, 'num_ram': 3, 'r2': 0, 'ramps': [2, 5, 11], 'rd': 20.9761769634, 'regulator': {'__RealLiteral__': 0, 'data': '3.7371022422', 'prec': 40}, 'res': {}, 'subfield_mults': [], 'subfields': [], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( 2 a - 21 \\)'], 'used_grh': False, 'zk': ['1', 'a']}