Hilbert modular form data - 2.2.313.1-4.1-c

Formats: - HTML - YAML - JSON - 2024-05-17T14:37:05.643026

• 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': 3, 'disc': 313, 'field_bad_primes': [313], 'field_label': '2.2.313.1', 'is_CM': 'no', 'is_base_change': 'yes', 'label': '2.2.313.1-4.1-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, -3*w + 28]', -1], ['[2, 2, -3*w - 25]', -1]], 'hecke_eigenvalues': [1, 1, 'e', 'e', '-1/2*e^2 - 1/2*e + 6', '-1/2*e^2 - 1/2*e + 6', '-1/2*e^2 - 1/2*e', '-1/2*e^2 - 1/2*e', '-e^2 + 4', '-e^2 + 4', '-e^2 + 10', '1/2*e^2 + 3/2*e - 8', '1/2*e^2 + 3/2*e - 8', '3/2*e^2 + 3/2*e - 4', '1/2*e^2 - 5/2*e - 6', '1/2*e^2 - 5/2*e - 6', '1/2*e^2 - 1/2*e - 6', '1/2*e^2 - 1/2*e - 6', 'e^2 + 4*e - 12', 'e^2 + 4*e - 12', 'e^2 + 2*e + 2', 'e^2 + 2*e + 2', 'e + 4', 'e + 4', '5/2*e^2 + 1/2*e - 14', '5/2*e^2 + 1/2*e - 14', '-5*e - 2', '-5*e - 2', 'e - 2', 'e - 2', '-5/2*e^2 - 7/2*e + 18', '-5/2*e^2 - 7/2*e + 18', '-3/2*e^2 - 3/2*e + 6', '-3/2*e^2 - 3/2*e + 6', 'e^2 + 14', 'e^2 + 14', '3*e^2 + 3*e - 24', '3*e^2 + 3*e - 24', '-4*e^2 - 5*e + 26', '-4*e^2 - 5*e + 26', '5/2*e^2 - 9/2*e - 16', '5/2*e^2 - 9/2*e - 16', 'e^2 + 7*e - 6', 'e^2 + 7*e - 6', '-1/2*e^2 - 5/2*e + 10', '-1/2*e^2 - 5/2*e + 10', 'e^2 - e + 6', 'e^2 - e + 6', '-3*e^2 - 4*e + 8', '-3*e^2 - 4*e + 8', 'e^2 - 2*e + 6', 'e^2 - 2*e + 6', '-3/2*e^2 - 15/2*e + 20', '-3/2*e^2 - 15/2*e + 20', '3*e^2 + 7*e - 26', '3*e^2 + 7*e - 26', '-e^2 + 8*e + 18', '-e^2 - 8*e + 4', '-e^2 - 8*e + 4', '-2*e^2 + 2*e + 16', '-2*e^2 + 2*e + 16', '-2*e^2 + 8*e + 26', '-e^2 + 2*e + 6', '-e^2 + 2*e + 6', '5/2*e^2 + 15/2*e - 10', '5/2*e^2 + 15/2*e - 10', '-1/2*e^2 + 13/2*e + 16', '-1/2*e^2 + 13/2*e + 16', '6*e^2 + 6*e - 26', '6*e^2 + 6*e - 26', 'e^2 + 8*e', 'e^2 + 8*e', '-7/2*e^2 - 7/2*e + 18', '-7/2*e^2 - 7/2*e + 18', 'e^2 - 16', 'e^2 - 16', '11/2*e^2 + 9/2*e - 28', '11/2*e^2 + 9/2*e - 28', '-1/2*e^2 + 11/2*e + 12', '-1/2*e^2 + 11/2*e + 12', '-9/2*e^2 - 9/2*e + 28', '-9/2*e^2 - 9/2*e + 28', '-5/2*e^2 - 7/2*e + 12', '-5/2*e^2 - 7/2*e + 12', '-e^2 - 5*e + 14', '-e^2 - 5*e + 14', '3/2*e^2 + 11/2*e - 14', '3/2*e^2 + 11/2*e - 14', '7/2*e^2 - 5/2*e - 30', '7/2*e^2 - 5/2*e - 30', '4*e - 8', '4*e - 8', '9/2*e^2 - 13/2*e - 32', '9/2*e^2 - 13/2*e - 32', '15/2*e^2 + 9/2*e - 48', '15/2*e^2 + 9/2*e - 48', '-4*e - 4', '-4*e - 4', '-5*e^2 + 4*e + 42', '4*e^2 - e - 6', '4*e^2 - e - 6', '2*e^2 + 7*e - 24', '2*e^2 + 7*e - 24', '-7/2*e^2 - 3/2*e + 8', '-7/2*e^2 - 3/2*e + 8', '-2*e^2 - 4*e + 18', '-2*e^2 - 4*e + 18', '-11/2*e^2 - 5/2*e + 30', '-11/2*e^2 - 5/2*e + 30', '-3/2*e^2 - 25/2*e + 4', '-3/2*e^2 - 25/2*e + 4', '5*e^2 - 6*e - 32', '5*e^2 - 6*e - 32', '7/2*e^2 - 7/2*e - 40', '7/2*e^2 - 7/2*e - 40', '-3/2*e^2 + 7/2*e + 26', '-3/2*e^2 + 7/2*e + 26', '1/2*e^2 - 7/2*e - 12', '1/2*e^2 - 7/2*e - 12', '3/2*e^2 - 5/2*e - 28', '3/2*e^2 - 5/2*e - 28', '3*e^2 - 6*e - 18', '3*e^2 - 6*e - 18', '2*e^2 - 6*e - 20', '2*e^2 - 6*e - 20', '6*e^2 + 3*e - 30', '6*e^2 + 3*e - 30', '4*e^2 + 7*e - 48', '4*e^2 + 7*e - 48', '-9/2*e^2 + 7/2*e + 8', '-9/2*e^2 + 7/2*e + 8', '-e^2 - 14*e + 6', '-e^2 - 14*e + 6', '9*e^2 + 8*e - 58', '9*e^2 + 8*e - 58', '9/2*e^2 + 7/2*e - 34', '9/2*e^2 + 7/2*e - 34', '-13/2*e^2 - 11/2*e + 22', '-13/2*e^2 - 11/2*e + 22', '-7*e^2 + 2*e + 42', '-7*e^2 + 2*e + 42', '7*e^2 + 15*e - 46', '7*e^2 + 15*e - 46', '-9/2*e^2 - 3/2*e + 50', '-9/2*e^2 - 3/2*e + 50', '-7*e^2 - 4*e + 30', '-7*e^2 - 4*e + 30', '-11/2*e^2 - 5/2*e + 30', '-11/2*e^2 - 5/2*e + 30', '-1/2*e^2 - 17/2*e - 14', '-1/2*e^2 - 17/2*e - 14', '-4*e^2 - 11*e + 20', '-4*e^2 - 11*e + 20', '13/2*e^2 - 3/2*e - 50', '13/2*e^2 - 3/2*e - 50', '1/2*e^2 + 13/2*e + 24', '1/2*e^2 + 13/2*e + 24', '-e^2 - 2*e - 16', '-e^2 - 2*e - 16', '9/2*e^2 + 9/2*e - 30', '9/2*e^2 + 9/2*e - 30', '-19/2*e^2 + 7/2*e + 60', '-19/2*e^2 + 7/2*e + 60', '-4*e^2 - 11*e + 50', '-4*e^2 - 11*e + 50', '-5*e + 40', '-5*e + 40', '-5/2*e^2 - 7/2*e + 64', '5/2*e^2 + 23/2*e + 6', '5/2*e^2 + 23/2*e + 6', '-e^2 + e - 10', '-e^2 + e - 10', '1/2*e^2 - 17/2*e - 30', '1/2*e^2 - 17/2*e - 30', '-4*e^2 - 8*e + 64', '-4*e^2 - 8*e + 64', '-3*e^2 + 22', '-3*e^2 + 22'], 'hecke_polynomial': 'x^3 - 9*x + 4', 'label': '2.2.313.1-4.1-c'}
• hmf_fields •

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

  
  {'degree': 2, 'discriminant': 313, 'ideals': ['[1, 1, 1]', '[2, 2, -3*w + 28]', '[2, 2, -3*w - 25]', '[3, 3, 26*w - 243]', '[3, 3, -26*w - 217]', '[4, 2, 2]', '[4, 4, 159*w + 1327]', '[4, 4, -159*w + 1486]', '[6, 6, 1379*w - 12888]', '[6, 6, w + 8]', '[6, 6, w - 9]', '[6, 6, 1379*w + 11509]', '[8, 4, -6*w + 56]', '[8, 4, -6*w - 50]', '[8, 8, -769*w - 6418]', '[8, 8, 769*w - 7187]', '[9, 3, 3]', '[9, 9, 610*w - 5701]', '[9, 9, 610*w + 5091]', '[11, 11, -2*w - 17]', '[11, 11, -2*w + 19]', '[12, 6, 52*w - 486]', '[12, 6, -52*w - 434]', '[12, 12, w - 10]', '[12, 12, -133*w + 1243]', '[12, 12, -133*w - 1110]', '[12, 12, -w - 9]', '[13, 13, 2148*w + 17927]', '[13, 13, 2148*w - 20075]', '[16, 4, 4]', '[16, 8, 318*w + 2654]', '[16, 8, -318*w + 2972]', '[16, 16, 29*w - 271]', '[16, 16, 29*w + 242]', '[18, 6, -9*w + 84]', '[18, 6, -9*w - 75]', '[18, 18, -451*w - 3764]', '[18, 18, -23*w - 192]', '[18, 18, 23*w - 215]', '[18, 18, -451*w + 4215]', '[19, 19, -292*w + 2729]', '[19, 19, 292*w + 2437]', '[22, 22, 107*w + 893]', '[22, 22, -w - 7]', '[22, 22, w - 8]', '[22, 22, -107*w + 1000]', '[24, 12, 2758*w - 25776]', '[24, 12, 2*w + 16]', '[24, 12, 2*w - 18]', '[24, 12, 2758*w + 23018]', '[24, 24, 55*w - 514]', '[24, 24, -5*w + 47]', '[24, 24, 5*w + 42]', '[24, 24, 55*w + 459]', '[25, 5, -5]', '[26, 26, -81*w - 676]', '[26, 26, 185*w + 1544]', '[26, 26, 185*w - 1729]', '[26, 26, 81*w - 757]', '[27, 9, 78*w - 729]', '[27, 9, -78*w - 651]', '[27, 27, -4*w + 37]', '[27, 27, -4*w - 33]', '[29, 29, 20*w + 167]', '[29, 29, 20*w - 187]', '[32, 8, -12*w + 112]', '[32, 8, -12*w - 100]', '[32, 16, -1538*w - 12836]', '[32, 16, 1538*w - 14374]', '[32, 32, -w - 10]', '[32, 32, w - 11]', '[33, 33, -8*w + 75]', '[33, 33, 928*w + 7745]', '[33, 33, 928*w - 8673]', '[33, 33, -8*w - 67]', '[36, 6, 6]', '[36, 12, 477*w + 3981]', '[36, 12, -477*w + 4458]', '[36, 18, 1220*w - 11402]', '[36, 18, 1220*w + 10182]', '[36, 36, 17*w + 142]', '[36, 36, w + 6]', '[36, 36, w - 7]', '[36, 36, -17*w + 159]', '[38, 38, -11*w + 103]', '[38, 38, -1989*w + 18589]', '[38, 38, 1989*w + 16600]', '[38, 38, -11*w - 92]', '[39, 39, -14*w - 117]', '[39, 39, 32*w + 267]', '[39, 39, -32*w + 299]', '[39, 39, -14*w + 131]', '[44, 22, -4*w - 34]', '[44, 22, -4*w + 38]', '[44, 44, 49*w - 458]', '[44, 44, -5675*w + 53038]', '[44, 44, -5675*w - 47363]', '[44, 44, 49*w + 409]', '[48, 12, 104*w - 972]', '[48, 12, -104*w - 868]', '[48, 24, 2*w - 20]', '[48, 24, -266*w + 2486]', '[48, 24, -266*w - 2220]', '[48, 24, -2*w - 18]', '[48, 48, -w - 5]', '[48, 48, -2917*w - 24345]', '[48, 48, 2917*w - 27262]', '[48, 48, -w + 6]', '[49, 7, -7]', '[50, 10, 15*w - 140]', '[50, 10, 15*w + 125]', '[52, 26, 4296*w + 35854]', '[52, 26, 4296*w - 40150]', '[52, 52, 7*w - 65]', '[52, 52, 3*w - 29]', '[52, 52, 3*w + 26]', '[52, 52, -7*w - 58]', '[54, 18, 4137*w - 38664]', '[54, 18, 3*w + 24]', '[54, 18, 3*w - 27]', '[54, 18, 4137*w + 34527]', '[54, 54, w + 11]', '[54, 54, 211*w + 1761]', '[54, 54, -211*w + 1972]', '[54, 54, -w + 12]', '[57, 57, 344*w - 3215]', '[57, 57, 2*w - 17]', '[57, 57, -2*w - 15]', '[57, 57, 344*w + 2871]', '[58, 58, -w - 4]', '[58, 58, 1061*w - 9916]', '[58, 58, -1061*w - 8855]', '[58, 58, w - 5]', '[64, 8, 8]', '[64, 16, 636*w + 5308]', '[64, 16, -636*w + 5944]', '[64, 32, 58*w - 542]', '[64, 32, 58*w + 484]', '[64, 64, 5*w + 41]', '[64, 64, 5*w - 46]', '[66, 66, -w - 3]', '[66, 66, -35*w - 292]', '[66, 66, 1087*w + 9072]', '[66, 66, 425*w + 3547]', '[66, 66, -425*w + 3972]', '[66, 66, 1087*w - 10159]', '[66, 66, 35*w - 327]', '[66, 66, w - 4]', '[71, 71, -240*w + 2243]', '[71, 71, 240*w + 2003]', '[72, 12, -18*w + 168]', '[72, 12, -18*w - 150]', '[72, 24, -2307*w - 19254]', '[72, 24, 2307*w - 21561]', '[72, 36, -902*w - 7528]', '[72, 36, -46*w - 384]', '[72, 36, 46*w - 430]', '[72, 36, -902*w + 8430]', '[72, 72, -w - 2]', '[72, 72, -7*w - 59]', '[72, 72, 7*w - 66]', '[72, 72, -w + 3]', '[75, 15, -130*w + 1215]', '[75, 15, 130*w + 1085]', '[76, 38, -584*w + 5458]', '[76, 38, 584*w + 4874]', '[76, 76, -w - 1]', '[76, 76, -75*w + 701]', '[76, 76, -75*w - 626]', '[76, 76, w - 2]', '[78, 78, w]', '[78, 78, -w - 12]', '[78, 78, -1697*w + 15860]', '[78, 78, -743*w + 6944]', '[78, 78, 743*w + 6201]', '[78, 78, -1697*w - 14163]', '[78, 78, -w + 13]', '[78, 78, -w + 1]', '[79, 79, -3368*w + 31477]', '[79, 79, -3368*w - 28109]', '[81, 9, 9]', '[81, 27, 1830*w - 17103]', '[81, 27, 1830*w + 15273]', '[81, 81, 10*w - 93]', '[81, 81, 10*w + 83]', '[83, 83, -84*w - 701]', '[83, 83, 84*w - 785]', '[87, 87, -9202*w + 86001]', '[87, 87, 2*w - 21]', '[87, 87, 2*w + 19]', '[87, 87, -9202*w - 76799]', '[88, 44, 214*w + 1786]', '[88, 44, -2*w - 14]', '[88, 44, 2*w - 16]', '[88, 44, -214*w + 2000]', '[88, 88, -237*w - 1978]', '[88, 88, -2599*w - 21691]', '[88, 88, 2599*w - 24290]', '[88, 88, -237*w + 2215]', '[96, 24, 5516*w - 51552]', '[96, 24, 4*w + 32]', '[96, 24, 4*w - 36]', '[96, 24, 5516*w + 46036]', '[96, 48, 110*w - 1028]', '[96, 48, -10*w + 94]', '[96, 48, 10*w + 84]', '[96, 48, 110*w + 918]', '[96, 96, -503*w + 4701]', '[96, 96, -43*w + 402]', '[96, 96, 43*w + 359]', '[96, 96, 503*w + 4198]', '[97, 97, 38*w + 317]', '[97, 97, 38*w - 355]', '[98, 14, 21*w - 196]', '[98, 14, 21*w + 175]', '[99, 33, -6*w - 51]', '[99, 33, -6*w + 57]', '[99, 99, 3686*w + 30763]', '[99, 99, -188*w + 1757]', '[99, 99, 188*w + 1569]', '[99, 99, 3686*w - 34449]', '[100, 10, 10]', '[100, 20, -795*w - 6635]', '[100, 20, 795*w - 7430]', '[103, 103, -136*w - 1135]', '[103, 103, 136*w - 1271]', '[104, 52, -162*w - 1352]', '[104, 52, 370*w + 3088]', '[104, 52, 370*w - 3458]', '[104, 52, 162*w - 1514]', '[104, 104, -w - 13]', '[104, 104, -3*w + 26]', '[104, 104, 3*w + 23]', '[104, 104, -w + 14]', '[107, 107, -1246*w - 10399]', '[107, 107, 1246*w - 11645]', '[108, 18, 156*w - 1458]', '[108, 18, -156*w - 1302]', '[108, 36, 3*w - 30]', '[108, 36, -399*w + 3729]', '[108, 36, -399*w - 3330]', '[108, 36, -3*w - 27]', '[108, 54, -8*w + 74]', '[108, 54, -8*w - 66]', '[108, 108, -7823*w - 65290]', '[108, 108, -61*w + 570]', '[108, 108, -61*w - 509]', '[108, 108, 7823*w - 73113]', '[113, 113, 6*w + 49]', '[113, 113, 6*w - 55]', '[114, 114, 13*w - 121]', '[114, 114, 101*w - 944]', '[114, 114, -5*w + 48]', '[114, 114, 5065*w - 47337]', '[114, 114, 5065*w + 42272]', '[114, 114, -5*w - 43]', '[114, 114, 101*w + 843]', '[114, 114, -13*w - 108]', '[116, 58, 40*w + 334]', '[116, 58, 40*w - 374]', '[116, 116, 1671*w - 15617]', '[116, 116, -13*w - 109]', '[116, 116, -13*w + 122]', '[116, 116, -1671*w - 13946]', '[117, 39, 6444*w + 53781]', '[117, 39, 6444*w - 60225]', '[117, 117, -4*w - 35]', '[117, 117, -2*w + 15]', '[117, 117, 2*w + 13]', '[117, 117, -4*w + 39]', '[121, 11, 11]', '[121, 121, 72*w + 601]', '[121, 121, -72*w + 673]', '[128, 16, -24*w + 224]', '[128, 16, -24*w - 200]', '[128, 32, -3076*w - 25672]', '[128, 32, 3076*w - 28748]', '[128, 64, -2*w - 20]', '[128, 64, 2*w - 22]', '[128, 128, -263*w - 2195]', '[128, 128, 263*w - 2458]', '[132, 66, -16*w + 150]', '[132, 66, 1856*w + 15490]', '[132, 66, 1856*w - 17346]', '[132, 66, -16*w - 134]', '[132, 132, w + 14]', '[132, 132, -41*w - 342]', '[132, 132, -4747*w + 44365]', '[132, 132, 37*w - 346]', '[132, 132, 37*w + 309]', '[132, 132, 4747*w + 39618]', '[132, 132, 41*w - 383]', '[132, 132, w - 15]', '[137, 137, 558*w + 4657]', '[137, 137, -558*w + 5215]', '[139, 139, -2466*w + 23047]', '[139, 139, 2466*w + 20581]', '[142, 142, -12729*w + 118964]', '[142, 142, -9*w - 76]', '[142, 142, -9*w + 85]', '[142, 142, -12729*w - 106235]', '[143, 143, -662*w + 6187]', '[143, 143, -1512*w - 12619]', '[143, 143, -1512*w + 14131]', '[143, 143, 662*w + 5525]', '[144, 12, 12]', '[144, 24, 954*w + 7962]', '[144, 24, -954*w + 8916]', '[144, 36, 2440*w - 22804]', '[144, 36, 2440*w + 20364]', '[144, 48, 87*w - 813]', '[144, 48, 87*w + 726]', '[144, 72, 34*w + 284]', '[144, 72, 2*w + 12]', '[144, 72, 2*w - 14]', '[144, 72, -34*w + 318]', '[144, 144, 373*w - 3486]', '[144, 144, 19*w + 159]', '[144, 144, -19*w + 178]', '[144, 144, 373*w + 3113]', '[147, 21, -182*w + 1701]', '[147, 21, 182*w + 1519]', '[150, 30, -6895*w + 64440]', '[150, 30, -5*w - 40]', '[150, 30, -5*w + 45]', '[150, 30, -6895*w - 57545]', '[151, 151, 16*w - 149]', '[151, 151, 16*w + 133]', '[152, 76, -22*w + 206]', '[152, 76, -3978*w + 37178]', '[152, 76, 3978*w + 33200]', '[152, 76, -22*w - 184]', '[152, 152, 3*w + 22]', '[152, 152, 31*w - 290]', '[152, 152, 31*w + 259]', '[152, 152, -3*w + 25]', '[156, 78, -28*w - 234]', '[156, 78, 64*w + 534]', '[156, 78, -64*w + 598]', '[156, 78, -28*w + 262]', '[156, 156, -1405*w - 11726]', '[156, 156, 3209*w + 26782]', '[156, 156, -11*w - 91]', '[156, 156, 25*w + 209]', '[156, 156, 25*w - 234]', '[156, 156, 11*w - 102]', '[156, 156, -3209*w + 29991]', '[156, 156, -1405*w + 13131]', '[157, 157, -396*w + 3701]', '[157, 157, 396*w + 3305]', '[158, 158, -127*w + 1187]', '[158, 158, 717*w - 6701]', '[158, 158, 717*w + 5984]', '[158, 158, 127*w + 1060]', '[162, 18, -27*w + 252]', '[162, 18, -27*w - 225]', '[162, 54, -1353*w - 11292]', '[162, 54, -69*w - 576]', '[162, 54, 69*w - 645]', '[162, 54, -1353*w + 12645]', '[162, 162, -w - 15]', '[162, 162, -529*w - 4415]', '[162, 162, 529*w - 4944]', '[162, 162, w - 16]', '[163, 163, -4*w + 35]', '[163, 163, -4*w - 31]', '[166, 166, 4455*w + 37181]', '[166, 166, 3*w - 31]', '[166, 166, 3*w + 28]', '[166, 166, 4455*w - 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2124]', '[9966, 9966, -26305*w - 219539]', '[9967, 9967, -54*w - 461]', '[9967, 9967, -54*w + 515]', '[9972, 1662, 12*w - 42]', '[9972, 1662, -12*w - 30]', '[9972, 3324, -11301*w - 94317]', '[9972, 3324, -5577*w + 52122]', '[9972, 3324, 5577*w + 46545]', '[9972, 3324, 11301*w - 105618]', '[9972, 4986, -28904*w - 241230]', '[9972, 4986, 14264*w - 133310]', '[9972, 4986, 14264*w + 119046]', '[9972, 4986, -28904*w + 270134]', '[9972, 9972, -199*w + 1857]', '[9972, 9972, 403*w - 3765]', '[9972, 9972, -19*w - 186]', '[9972, 9972, 7*w + 114]', '[9972, 9972, 7*w - 121]', '[9972, 9972, -19*w + 205]', '[9972, 9972, -403*w - 3362]', '[9972, 9972, 199*w + 1658]', '[9977, 9977, -18*w + 133]', '[9977, 9977, -1854*w - 15473]', '[9977, 9977, 1854*w - 17327]', '[9977, 9977, 18*w + 115]', '[9978, 9978, 6557*w - 61281]', '[9978, 9978, 131*w + 1089]', '[9978, 9978, 343*w + 2861]', '[9978, 9978, -877*w + 8197]', '[9978, 9978, 877*w + 7320]', '[9978, 9978, 343*w - 3204]', '[9978, 9978, 131*w - 1220]', '[9978, 9978, 6557*w + 54724]', '[9981, 3327, -774*w - 6459]', '[9981, 3327, 774*w - 7233]', '[9981, 9981, 148*w - 1387]', '[9981, 9981, -2906*w + 27159]', '[9981, 9981, 2906*w + 24253]', '[9981, 9981, 148*w + 1239]', '[9984, 624, -224*w - 1872]', '[9984, 624, 512*w + 4272]', '[9984, 624, -512*w + 4784]', '[9984, 624, -224*w + 2096]', '[9984, 1248, -11240*w - 93808]', '[9984, 1248, 25672*w + 214256]', '[9984, 1248, -88*w - 728]', '[9984, 1248, 200*w + 1672]', '[9984, 1248, 200*w - 1872]', '[9984, 1248, 88*w - 816]', '[9984, 1248, -25672*w + 239928]', '[9984, 1248, -11240*w + 105048]', '[9984, 2496, -4*w - 104]', '[9984, 2496, 65660*w + 547992]', '[9984, 2496, -20*w + 156]', '[9984, 2496, -28748*w - 239928]', '[9984, 2496, 28748*w - 268676]', '[9984, 2496, 20*w + 136]', '[9984, 2496, 65660*w - 613652]', '[9984, 2496, -4*w + 108]', '[9984, 4992, -22*w - 156]', '[9984, 4992, 46*w - 442]', '[9984, 4992, 5614*w + 46854]', '[9984, 4992, 2458*w - 22972]', '[9984, 4992, -2458*w - 20514]', '[9984, 4992, 5614*w - 52468]', '[9984, 4992, 46*w + 396]', '[9984, 4992, 22*w - 178]', '[9984, 9984, 2341*w + 19538]', '[9984, 9984, -1025*w - 8554]', '[9984, 9984, -961*w + 8982]', '[9984, 9984, 2195*w + 18319]', '[9984, 9984, -2195*w + 20514]', '[9984, 9984, -961*w - 8021]', '[9984, 9984, 1025*w - 9579]', '[9984, 9984, 2341*w - 21879]', '[9987, 9987, 52*w + 423]', '[9987, 9987, -2234*w - 18645]', '[9987, 9987, -2234*w + 20879]', '[9987, 9987, -52*w + 475]', '[9991, 9991, -18*w - 179]', '[9991, 9991, 88600*w + 739447]', '[9991, 9991, -88600*w + 828047]', '[9991, 9991, 18*w - 197]', '[9992, 4996, -18826*w + 175946]', '[9992, 4996, 306*w - 2858]', '[9992, 4996, 306*w + 2552]', '[9992, 4996, 18826*w + 157120]', '[9992, 9992, 147*w - 1370]', '[9992, 9992, 11*w + 134]', '[9992, 9992, -11*w + 145]', '[9992, 9992, 147*w + 1223]', '[9994, 9994, -97695*w + 913048]', '[9994, 9994, -12547*w + 117263]', '[9994, 9994, -459*w + 4291]', '[9994, 9994, -69*w - 584]', '[9994, 9994, -69*w + 653]', '[9994, 9994, -459*w - 3832]', '[9994, 9994, 12547*w + 104716]', '[9994, 9994, -97695*w - 815353]', '[9997, 9997, 21876*w - 204451]', '[9997, 9997, -9578*w - 79937]', '[9997, 9997, 9578*w - 89515]', '[9997, 9997, 21876*w + 182575]', '[9998, 9998, 221*w - 2068]', '[9998, 9998, 203*w - 1900]', '[9998, 9998, -203*w - 1697]', '[9998, 9998, -221*w - 1847]', '[10000, 100, 100]', '[10000, 200, -7950*w - 66350]', '[10000, 200, 7950*w - 74300]', '[10000, 400, -725*w + 6775]', '[10000, 400, -725*w - 6050]'], 'label': '2.2.313.1', 'narrow_class_no': 1, 'primes': ['[2, 2, -3*w + 28]', '[2, 2, -3*w - 25]', '[3, 3, 26*w - 243]', '[3, 3, -26*w - 217]', '[11, 11, -2*w - 17]', '[11, 11, -2*w + 19]', '[13, 13, 2148*w + 17927]', '[13, 13, 2148*w - 20075]', '[19, 19, -292*w + 2729]', '[19, 19, 292*w + 2437]', '[25, 5, -5]', '[29, 29, 20*w + 167]', '[29, 29, 20*w - 187]', '[49, 7, -7]', '[71, 71, -240*w + 2243]', '[71, 71, 240*w + 2003]', '[79, 79, -3368*w + 31477]', '[79, 79, -3368*w - 28109]', '[83, 83, -84*w - 701]', '[83, 83, 84*w - 785]', '[97, 97, 38*w + 317]', '[97, 97, 38*w - 355]', '[103, 103, -136*w - 1135]', '[103, 103, 136*w - 1271]', '[107, 107, -1246*w - 10399]', '[107, 107, 1246*w - 11645]', '[113, 113, 6*w + 49]', '[113, 113, 6*w - 55]', '[137, 137, 558*w + 4657]', '[137, 137, -558*w + 5215]', '[139, 139, -2466*w + 23047]', '[139, 139, 2466*w + 20581]', '[151, 151, 16*w - 149]', '[151, 151, 16*w + 133]', '[157, 157, -396*w + 3701]', '[157, 157, 396*w + 3305]', '[163, 163, -4*w + 35]', '[163, 163, -4*w - 31]', '[173, 173, 1194*w - 11159]', '[173, 173, -1194*w - 9965]', '[181, 181, -12*w + 113]', '[181, 181, -12*w - 101]', '[197, 197, 6126*w - 57253]', '[197, 197, -6126*w - 51127]', '[199, 199, 66*w - 617]', '[199, 199, 66*w + 551]', '[241, 241, -506*w + 4729]', '[241, 241, 506*w + 4223]', '[263, 263, 2*w - 25]', '[263, 263, -2*w - 23]', '[269, 269, -4*w + 41]', '[269, 269, 4*w + 37]', '[277, 277, 2*w - 7]', '[277, 277, -2*w - 5]', '[281, 281, 448*w - 4187]', '[281, 281, 448*w + 3739]', '[289, 17, -17]', '[307, 307, 54*w + 451]', '[307, 307, 54*w - 505]', '[311, 311, 7982*w + 66617]', '[311, 311, 7982*w - 74599]', '[313, 313, 2*w - 1]', '[317, 317, -6*w + 53]', '[317, 317, -6*w - 47]', '[331, 331, -30*w + 281]', '[331, 331, -30*w - 251]', '[337, 337, 48*w - 449]', '[337, 337, 48*w + 401]', '[349, 349, -36*w - 301]', '[349, 349, -36*w + 337]', '[367, 367, 56*w + 467]', '[367, 367, 56*w - 523]', '[379, 379, -13180*w - 109999]', '[379, 379, -13180*w + 123179]', '[383, 383, -118*w - 985]', '[383, 383, -118*w + 1103]', '[389, 389, 18*w - 167]', '[389, 389, -18*w - 149]', '[401, 401, -246*w - 2053]', '[401, 401, 246*w - 2299]', '[409, 409, 350*w + 2921]', '[409, 409, -350*w + 3271]', '[421, 421, -2414*w - 20147]', '[421, 421, 2414*w - 22561]', '[457, 457, 34*w - 317]', '[457, 457, 34*w + 283]', '[463, 463, 6762*w + 56435]', '[463, 463, -6762*w + 63197]', '[479, 479, -5808*w + 54281]', '[479, 479, -5808*w - 48473]', '[487, 487, 3102*w + 25889]', '[487, 487, 3102*w - 28991]', '[509, 509, 102*w + 851]', '[509, 509, 102*w - 953]', '[521, 521, -2200*w - 18361]', '[521, 521, 2200*w - 20561]', '[523, 523, -4*w - 25]', '[523, 523, 4*w - 29]', '[529, 23, -23]', '[541, 541, -228*w - 1903]', '[541, 541, -228*w + 2131]', '[547, 547, -6*w + 61]', '[547, 547, 6*w + 55]', '[569, 569, -9520*w + 88973]', '[569, 569, -9520*w - 79453]', '[577, 577, -11642*w + 108805]', '[577, 577, 11642*w + 97163]', '[587, 587, 2*w - 31]', '[587, 587, -2*w - 29]', '[593, 593, 1616*w - 15103]', '[593, 593, -1616*w - 13487]', '[599, 599, -17794*w + 166301]', '[599, 599, -17794*w - 148507]', '[601, 601, -552*w + 5159]', '[601, 601, 552*w + 4607]', '[607, 607, -3952*w - 32983]', '[607, 607, -3952*w + 36935]', '[613, 613, -12*w - 103]', '[613, 613, -12*w + 115]', '[617, 617, 8*w + 71]', '[617, 617, 8*w - 79]', '[653, 653, -28*w - 235]', '[653, 653, -28*w + 263]', '[659, 659, -12*w - 97]', '[659, 659, -12*w + 109]', '[661, 661, 1090*w + 9097]', '[661, 661, 1090*w - 10187]', '[683, 683, 108*w - 1009]', '[683, 683, 108*w + 901]', '[701, 701, -6*w - 43]', '[701, 701, 6*w - 49]', '[709, 709, -3420*w + 31963]', '[709, 709, -3420*w - 28543]', '[733, 733, 154*w - 1439]', '[733, 733, 154*w + 1285]', '[739, 739, -1350*w + 12617]', '[739, 739, -1350*w - 11267]', '[743, 743, -818*w - 6827]', '[743, 743, -818*w + 7645]', '[769, 769, -10*w + 89]', '[769, 769, -10*w - 79]', '[773, 773, -4*w - 43]', '[773, 773, 4*w - 47]', '[787, 787, -7028*w + 65683]', '[787, 787, -7028*w - 58655]', '[797, 797, -604*w + 5645]', '[797, 797, 604*w + 5041]', '[811, 811, 4*w - 23]', '[811, 811, -4*w - 19]', '[823, 823, 222*w + 1853]', '[823, 823, -222*w + 2075]', '[839, 839, -14400*w + 134581]', '[839, 839, -14400*w - 120181]', '[863, 863, -18696*w - 156035]', '[863, 863, -18696*w + 174731]', '[881, 881, 6*w - 47]', '[881, 881, -6*w - 41]', '[887, 887, -46*w + 431]', '[887, 887, -46*w - 385]', '[907, 907, 52*w - 485]', '[907, 907, 52*w + 433]', '[937, 937, -14*w - 113]', '[937, 937, -14*w + 127]', '[941, 941, 332*w + 2771]', '[941, 941, -332*w + 3103]', '[947, 947, -5172*w - 43165]', '[947, 947, -5172*w + 48337]', '[961, 31, -31]', '[971, 971, 158*w - 1477]', '[971, 971, 158*w + 1319]', '[977, 977, -64*w - 535]', '[977, 977, 64*w - 599]', '[983, 983, 2*w - 37]', '[983, 983, -2*w - 35]', '[991, 991, -870*w + 8131]', '[991, 991, 870*w + 7261]', '[997, 997, -1668*w - 13921]', '[997, 997, 1668*w - 15589]']}
• 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': [], 'class_number': 1, 'cm': False, 'coeffs': [-78, -1, 1], 'conductor': 313, 'degree': 2, 'dirichlet_group': [1, 312], 'disc_abs': 313, 'disc_rad': 313, 'disc_sign': 1, 'frobs': [[2, [[1, 2]]], [3, [[1, 2]]], [5, [[2, 1]]], [7, [[2, 1]]], [11, [[1, 2]]], [13, [[1, 2]]], [17, [[2, 1]]], [19, [[1, 2]]], [23, [[2, 1]]], [29, [[1, 2]]], [31, [[2, 1]]], [37, [[2, 1]]], [41, [[2, 1]]], [43, [[2, 1]]], [47, [[2, 1]]], [53, [[2, 1]]], [59, [[2, 1]]]], 'gal_is_abelian': True, 'gal_is_cyclic': True, 'gal_is_solvable': True, 'galois_disc_exponents': [1], 'galois_label': '2T1', 'galt': 1, 'grd': 17.69180601295413, 'index': 1, 'inessentialp': [], 'is_galois': True, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '2.2.313.1', 'local_algs': ['m313.2.1.1'], 'monogenic': 1, 'num_ram': 1, 'r2': 0, 'ramps': [313], 'rd': 17.691806013, 'regulator': {'__RealLiteral__': 0, 'data': '19.3517605208', 'prec': 44}, 'res': {}, 'subfield_mults': [], 'subfields': [], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( 14341370 a + 119691683 \\)'], 'used_grh': False, 'zk': ['1', 'a']}