Hilbert modular form data - 2.2.5.1-361.1-a

Formats: - HTML - YAML - JSON - 2025-06-12T21:09:24.993288

• 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': 1, 'disc': 5, 'field_bad_primes': [5], 'field_label': '2.2.5.1', 'is_CM': 'no', 'is_base_change': 'yes', 'label': '2.2.5.1-361.1-a', 'label_nsuffix': 0, 'label_suffix': 'a', 'level_bad_primes': [19], 'level_ideal': '[361, 19, 19]', 'level_label': '361.1', 'level_norm': 361, 'parallel_weight': 2, 'short_label': '361.1-a', 'weight': '[2, 2]'}
• hmf_hecke •

  Column	Type
  AL_eigenvalues	jsonb
  hecke_eigenvalues	jsonb
  hecke_polynomial	text
  label	text

  
  {'AL_eigenvalues': [['[19, 19, -4*w + 3]', -1], ['[19, 19, -4*w + 1]', -1]], 'hecke_eigenvalues': [-4, 3, -2, 3, 3, 1, 1, 6, 6, -4, -4, -6, -6, -13, -6, -6, -1, -1, 6, 6, 8, 8, 12, 12, 6, 6, -16, -16, -15, -15, -13, -13, 21, 21, -10, -10, -10, -18, -18, 2, 2, 3, 3, 11, 11, 14, 14, 5, 5, 15, 15, -10, -10, 21, 21, 24, 24, -16, -16, 6, 6, -25, -3, -3, -28, -28, 17, 17, 15, 15, -34, -34, 15, 15, 12, 12, -4, -4, -12, -12, 8, 8, -24, -24, -10, -10, 0, 0, 9, 9, -12, -12, 12, 12, 5, 5, 0, 0, 0, 0, -46, -25, -25, -24, -24, -4, -4, -36, -36, 26, 26, 44, 44, 11, 11, 0, 0, -30, -30, 32, 32, 17, 17, 6, 6, 26, 26, 15, 15, 11, 11, 32, 32, 33, 33, 23, 23, -9, -9, -16, -16, 33, 33, -16, -16, 18, 18, -49, -49, -27, -27, -6, -6, 20, 20, -18, -18, -18, -18, 60, 60, -34, -34, 20, 20, 30, 30, -40, -40, -24, -24, -4, -4, 27, 27, 44, 44, 33, 33, -1, -1, -24, -24, -15, -15, 50, 50, 36, 36, 56, 56, -18, -18, 5, 5, 36, 36, -10, -10, -10, -10, 60, 60, -7, -7, 9, 9, 14, 14, 18, 18, -66, -66, -10, -10, -60, -60, -70, 14, 14, 14, 14, 66, 66, 71, 71, 24, 24, 3, 3, -52, -52, 68, 68, -30, -30, -31, -31, -24, -24, -60, -60, -7, -7, 38, 38, 21, 21, 0, 0, 32, 32, 51, 51, -64, -64, 12, 12, 29, 29, -13, -13, -64, -64, 36, 36, 39, 39, 32, 32, -49, -49, 44, 44, -34, -34, 15, 15, -4, -4, -85, -10, -10, 3, 3, -1, -1, 72, 72, -42, -42, -30, -30, -30, -30, 8, 8, -48, -48, -25, -25, 5, 5, 14, 14, -45, -45, -30, -30, -48, -48, -16, -16, -3, -3, 48, 48, -3, -3, 62, 62, 66, 66, -52, -52, 20, 20, -85, 71, 71, -64, -64, -61, -61, 20, 20, 59, 59, 54, 54, -64, -64, 24, 24, 2, 2, -72, -72, -22, -22, 27, 27, -40, -40, 48, 48, -12, -12, 42, 42, 48, 48, -16, -16, -12, -12, 74, 74, -54, -54, 59, 59, 12, 12, -72, -72, 75, 75, -78, -78, -22, -22, -64, -64, -46, -46, 0, 0, -30, -30, 20, 20, -42, -42, 50, 50, 66, 66, -76, -76, 48, 48, -43, -43, 66, 66, 38, 21, 21, -19, -19, -90, -90, -96, -96, 72, 72, 18, 18, -93, -93, -61, -61, 45, 45, 50, 50, -27, -27, 23, 23, -9, -9, 17, 17, -34, -34, -7, -7, 57, 57, -4, -4, -6, -6, -109, -109, 92, 92, -94, -94, -102, -102, 39, 39, 30, 30, 8, 8, -72, -72, 2, 2, -4, -4, -12, -12, 44, 44, -28, -28, -6, -6, 65, 65, 6, 6, 86, 86, 96, 96, -3, -3, 8, 8, 24, 24, 12, 12, -49, -49, 24, 24, 26, 26, -52, -52, -34, -34, 9, 9, 77, 77, 41, 41, 80, 80, 66, 66, 14, 14, -75, -75, 93, 93, -7, -7, -30, -30, -70, -70, -108, -108, -112, -112, -18, -18, 17, 17, -21, -21, 84, 84, -6, -6, -27, -27, 110, 110, -105, -105, 59, 59, 18, 18, 35, 35, -114, -114, 51, 51, -18, -18, -10, -10, 6, 6, -25, -25, -12, -12, -45, -45, -94, -94, 80, 80, -91, -91, -21, -21, -43, -43, -28, -28, -72, -72, 89, 89, -45, -45, -34, -34, 78, 78, -18, -18, -67, -67, 90, 90, -114, -114, -124, -124, 54, 54, -30, -30, 9, 9, 114, 114, 68, 68, -33, -33, -57, -57, -118, 65, 65, -94, -94, 107, 107, 56, 56, -85, -85, 50, 50, 108, 108, 80, 80, 105, 105, 45, 45, -45, -45, 23, 23, 81, 81, 80, 80, 11, 11, 120, 120, -76, -76, 8, 8, 65, 65, 21, 21, -66, -66, -94, -94, 48, 48, -42, -42, 56, 56, 38, 38, -4, -4, -30, -30, 62, 62, 69, 69, 3, 3, 45, 45, -16, -16, -30, -30, 60, 60, 107, 107, 44, 44, -60, -60, 131, 131, -114, -114, 62, 62, -129, -129, 93, 93, -33, -33, 62, 62, -72, -72, -97, -120, -120, -114, -114, -30, -30, -115, -115, -112, -112, -30, -30, 68, 68, 18, 18, -91, -91, -84, -84, 123, 123, 59, 59, 12, 12, -10, -10, 20, 20, -72, -72, 108, 108, -127, -127, 0, 0, 80, 80, 63, 63, 38, 38, -130, -130, -48, -48, 42, 42, -10, -10, -70, -70, -58, -58, -117, -117, -37, -37, -1, -1, 69, 69, 20, 20, 141, 141, -70, -70, 66, 66, 140, 140, 45, 45, 72, 72, 135, 135, 93, 93, -76, -76, -54, -54, -19, -19, 60, 60, -142, -142, -66, -66, -40, -40, 53, 53, -52, -52, 84, 84, -115, -115, 6, 6, 107, 107, -24, -24, 146, 146, 90, 90, 36, 36, -126, -126, 8, 8, -64, -64, 6, 6, -148, -148, 96, 96, 80, 80, 71, 71, 2, 2, 102, 102, 45, 45, -4, -4, -24, -24, 24, 24, -16, -16, -105, -105, 159, 159, 131, 131, 39, 39, -70, -70, 92, 92, 75, 75, -4, -4, 54, 54, -148, -148, -48, -48, -27, -27, -138, -138, -130, -130, 60, 60, -10, -10, 38, 38, -120, -120, -22, -22, -22, 84, 84, 42, 42, 146, 146, -108, -108, 122, 122, 21, 21, 26, 26, -105, -105, 18, 18, -115, -115, -121, -121, 51, 51, 114, 114, -120, -120, -43, -43, -129, -129, -40, -40, 6, 6, 110, 110, -138, -138, 20, 20, -139, -139, 156, 156, -18, -18, 125, 125, -37, -37, -40, -40, -84, -84, -109, -109, -18, -18, -16, -16, -48, -48, 102, 102, 69, 69, -37, -37, 105, 105, 20, 20, 48, 48, 50, 50, -118, -118, -136, -136, -162, -162, -34, -34, -130, -130, -108, -108, 77, 77, 128, 128, 56, 56, 14, 14, -54, -54, -138, -138, -76, -76, -93, -93, -168, -168, -114, -114, -85, -85, -42, -42, 38, 38, -90, -90, -76, -76, -144, -144, 39, 39, -28, -28, 83, 83, -72, -72, -82, -82, -63, -63, 17, 17, 146, 146, 155, 155, -132, -132, 50, 50, -135, -135, -55, -55, -15, -15, -40, -40, 14, 14, -141, -141, 182, 182, 158, 158, 42, 42, 98, 98, -34, -34, 150, 150, -19, -19, 134, 134, 14, 14, -175, -175, 12, 12, 80, 80, 92, 92, 63, 63, -105, -105, -22, -22, 120, 120, -19, -19, -16, -16, 21, 21, -130, -130, -4, -4, 150, 150, -25, -25, 132, 132, 155, 155, 54, 54, 177, 177, -70, -70, -31, -31, -132, -132, -102, -102, -10, -10, 18, 18, -142, -142, 81, 81, 33, 33, -51, -51, 77, 77, -90, -90, 128, 128, -124, -124, -118, -118, -48, -48, 2, 2, 74, 74, 96, 96, -18, -18, 57, 57, -163, -163, 78, 78, 24, 24, 77, 77, 90, 90, 134, 134, 105, 105, 131, 131, -130, 48, 48, -10, -10, 45, 45, -154, -154, 66, 66, -81, -81, -108, -108, -55, -55, -84, -84, -99, -99, 168, 168, 89, 89, -37, -37, -78, -78, 29, 29, -43, -43, 149, 149, 86, 86, 132, 132, -114, -114, 20, 20, 101, 101, -162, -162, -4, -4, -28, -28, 183, 183, -151, -151, 137, 137, 81, 81, -45, -45, -85, -85, -10, -10, 74, 74, -15, -15, -22, -22, -45, -45, 32, 32], 'hecke_polynomial': 'x', 'label': '2.2.5.1-361.1-a'}
• hmf_fields •

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

  
  {'degree': 2, 'discriminant': 5, 'ideals': ['[1, 1, 1]', '[4, 2, 2]', '[5, 5, -2*w + 1]', '[9, 3, 3]', '[11, 11, -3*w + 2]', '[11, 11, -3*w + 1]', '[16, 4, 4]', '[19, 19, -4*w + 3]', '[19, 19, -4*w + 1]', '[20, 10, -4*w + 2]', '[25, 5, 5]', '[29, 29, w + 5]', '[29, 29, -w + 6]', '[31, 31, -5*w + 2]', '[31, 31, -5*w + 3]', '[36, 6, 6]', '[41, 41, -6*w + 5]', '[41, 41, w - 7]', '[44, 22, -6*w + 4]', '[44, 22, -6*w + 2]', '[45, 15, -6*w + 3]', '[49, 7, -7]', '[55, 55, w + 7]', '[55, 55, -w + 8]', '[59, 59, 2*w - 9]', '[59, 59, 7*w - 5]', '[61, 61, 3*w - 10]', '[61, 61, -3*w - 7]', '[64, 8, 8]', '[71, 71, -8*w + 7]', '[71, 71, w - 9]', '[76, 38, -8*w + 6]', '[76, 38, -8*w + 2]', '[79, 79, 8*w - 5]', '[79, 79, 3*w - 11]', '[80, 20, -8*w + 4]', '[81, 9, 9]', '[89, 89, -10*w - 1]', '[89, 89, 10*w - 11]', '[95, 95, -2*w + 11]', '[95, 95, 2*w + 9]', '[99, 33, -9*w + 6]', '[99, 33, -9*w + 3]', '[100, 10, 10]', '[101, 101, 4*w - 13]', '[101, 101, 5*w - 14]', '[109, 109, -11*w - 1]', '[109, 109, 11*w - 12]', '[116, 58, 2*w + 10]', '[116, 58, -2*w + 12]', '[121, 11, 11]', '[121, 121, -10*w + 3]', '[121, 121, -10*w + 7]', '[124, 62, -10*w + 4]', '[124, 62, -10*w + 6]', '[125, 25, -10*w + 5]', '[131, 131, -12*w - 1]', '[131, 131, 12*w - 13]', '[139, 139, 2*w - 13]', '[139, 139, -11*w + 9]', '[144, 12, 12]', '[145, 145, -11*w + 8]', '[145, 145, -11*w + 3]', '[149, 149, 7*w - 18]', '[149, 149, 4*w - 15]', '[151, 151, 5*w - 16]', '[151, 151, 6*w - 17]', '[155, 155, w + 12]', '[155, 155, -w + 13]', '[164, 82, -12*w + 10]', '[164, 82, 2*w - 14]', '[169, 13, -13]', '[171, 57, -12*w + 9]', '[171, 57, -12*w + 3]', '[176, 44, -12*w + 8]', '[176, 44, -12*w + 4]', '[179, 179, 7*w - 19]', '[179, 179, 5*w - 17]', '[180, 30, -12*w + 6]', '[181, 181, -14*w - 1]', '[181, 181, 14*w - 15]', '[191, 191, 2*w - 15]', '[191, 191, -13*w + 11]', '[196, 14, -14]', '[199, 199, 3*w - 16]', '[199, 199, -13*w + 10]', '[205, 205, -4*w + 17]', '[205, 205, 13*w - 9]', '[209, 209, w + 14]', '[209, 209, -13*w + 5]', '[209, 209, -13*w + 8]', '[209, 209, -w + 15]', '[211, 211, 6*w - 19]', '[211, 211, 7*w - 20]', '[220, 110, 2*w + 14]', '[220, 110, -2*w + 16]', '[225, 15, 15]', '[229, 229, -14*w + 11]', '[229, 229, 3*w - 17]', '[236, 118, 4*w - 18]', '[236, 118, 14*w - 10]', '[239, 239, -16*w - 1]', '[239, 239, 16*w - 17]', '[241, 241, 9*w - 23]', '[241, 241, 5*w - 19]', '[244, 122, 6*w - 20]', '[244, 122, -6*w - 14]', '[245, 35, 14*w - 7]', '[251, 251, 2*w - 17]', '[251, 251, -15*w + 13]', '[256, 16, 16]', '[261, 87, 3*w + 15]', '[261, 87, -3*w + 18]', '[269, 269, 15*w - 11]', '[269, 269, 4*w - 19]', '[271, 271, -17*w - 1]', '[271, 271, 17*w - 18]', '[275, 55, -15*w + 10]', '[275, 55, -15*w + 5]', '[279, 93, -15*w + 6]', '[279, 93, -15*w + 9]', '[281, 281, 7*w - 22]', '[281, 281, 8*w - 23]', '[284, 142, -16*w + 14]', '[284, 142, 2*w - 18]', '[289, 17, -17]', '[295, 295, 3*w - 19]', '[295, 295, 16*w - 13]', '[304, 76, -16*w + 12]', '[304, 76, -16*w + 4]', '[305, 305, 17*w - 16]', '[305, 305, 17*w - 1]', '[311, 311, 5*w - 21]', '[311, 311, 16*w - 11]', '[316, 158, 16*w - 10]', '[316, 158, 6*w - 22]', '[319, 319, -16*w + 9]', '[319, 319, -2*w + 19]', '[319, 319, 2*w + 17]', '[319, 319, -16*w + 7]', '[320, 40, -16*w + 8]', '[324, 18, 18]', '[331, 331, -17*w + 14]', '[331, 331, 3*w - 20]', '[341, 341, w + 18]', '[341, 341, -4*w + 21]', '[341, 341, 4*w + 17]', '[341, 341, -w + 19]', '[349, 349, 17*w - 12]', '[349, 349, 5*w - 22]', '[355, 355, 17*w - 11]', '[355, 355, -6*w + 23]', '[356, 178, -20*w - 2]', '[356, 178, 20*w - 22]', '[359, 359, 10*w - 27]', '[359, 359, 7*w - 24]', '[361, 19, 19]', '[361, 361, -17*w + 8]', '[361, 361, -17*w + 9]', '[369, 123, -18*w + 15]', '[369, 123, 3*w - 21]', '[379, 379, -20*w - 1]', '[379, 379, 20*w - 21]', '[380, 190, -4*w + 22]', '[380, 190, 4*w + 18]', '[389, 389, 5*w - 23]', '[389, 389, 18*w - 13]', '[395, 395, 2*w - 21]', '[395, 395, 19*w - 17]', '[396, 66, -18*w + 12]', '[396, 66, -18*w + 6]', '[400, 20, 20]', '[401, 401, 7*w - 25]', '[401, 401, 11*w - 29]', '[404, 202, 8*w - 26]', '[404, 202, 10*w - 28]', '[405, 45, -18*w + 9]', '[409, 409, 3*w - 22]', '[409, 409, -19*w + 16]', '[419, 419, -21*w - 1]', '[419, 419, 21*w - 22]', '[421, 421, -19*w + 15]', '[421, 421, 4*w - 23]', '[431, 431, 19*w - 14]', '[431, 431, 5*w - 24]', '[436, 218, -22*w - 2]', '[436, 218, 22*w - 24]', '[439, 439, 6*w - 25]', '[439, 439, 19*w - 13]', '[441, 21, -21]', '[445, 445, 12*w + 19]', '[445, 445, 12*w - 31]', '[449, 449, 8*w - 27]', '[449, 449, 11*w - 30]', '[451, 451, -9*w + 28]', '[451, 451, 20*w - 17]', '[451, 451, -3*w + 23]', '[451, 451, 19*w - 10]', '[461, 461, -22*w - 1]', '[461, 461, 22*w - 23]', '[464, 116, 4*w + 20]', '[464, 116, -4*w + 24]', '[475, 95, -20*w + 15]', '[475, 95, -20*w + 5]', '[479, 479, 23*w - 25]', '[479, 479, -23*w - 2]', '[484, 22, 22]', '[484, 242, -20*w + 6]', '[484, 242, -20*w + 14]', '[491, 491, 13*w - 33]', '[491, 491, 7*w - 27]', '[495, 165, 3*w + 21]', '[495, 165, -3*w + 24]', '[496, 124, -20*w + 8]', '[496, 124, -20*w + 12]', '[499, 499, 11*w - 31]', '[499, 499, 9*w - 29]', '[500, 50, -20*w + 10]', '[505, 505, 22*w - 21]', '[505, 505, 23*w - 24]', '[509, 509, 4*w - 25]', '[509, 509, -21*w + 17]', '[521, 521, 5*w - 26]', '[521, 521, 21*w - 16]', '[524, 262, -24*w - 2]', '[524, 262, 24*w - 26]', '[529, 23, -23]', '[531, 177, 6*w - 27]', '[531, 177, 21*w - 15]', '[539, 77, 21*w - 14]', '[539, 77, 21*w - 7]', '[541, 541, 25*w - 28]', '[541, 541, -25*w - 3]', '[545, 545, 13*w - 34]', '[545, 545, 13*w + 21]', '[549, 183, 9*w - 30]', '[549, 183, -9*w - 21]', '[551, 551, w + 23]', '[551, 551, -21*w + 10]', '[551, 551, -21*w + 11]', '[551, 551, -w + 24]', '[556, 278, 4*w - 26]', '[556, 278, -22*w + 18]', '[569, 569, -22*w + 17]', '[569, 569, 5*w - 27]', '[571, 571, 25*w - 27]', '[571, 571, -25*w - 2]', '[576, 24, 24]', '[580, 290, -22*w + 16]', '[580, 290, -22*w + 6]', '[589, 589, -22*w + 7]', '[589, 589, 3*w + 23]', '[589, 589, -3*w + 26]', '[589, 589, -22*w + 15]', '[596, 298, 14*w - 36]', '[596, 298, 8*w - 30]', '[599, 599, -25*w - 1]', '[599, 599, 25*w - 26]', '[601, 601, 13*w - 35]', '[601, 601, 9*w - 31]', '[604, 302, 10*w - 32]', '[604, 302, 12*w - 34]', '[605, 55, -22*w + 11]', '[605, 605, 4*w + 23]', '[605, 605, -4*w + 27]', '[619, 619, 5*w - 28]', '[619, 619, -23*w + 18]', '[620, 310, 2*w + 24]', '[620, 310, -2*w + 26]', '[625, 25, 25]', '[631, 631, 23*w - 17]', '[631, 631, 6*w - 29]', '[639, 213, -24*w + 21]', '[639, 213, 3*w - 27]', '[641, 641, 23*w - 16]', '[641, 641, 7*w - 30]', '[649, 649, 25*w - 24]', '[649, 649, 23*w - 15]', '[649, 649, 8*w - 31]', '[649, 649, w - 26]', '[655, 655, 14*w + 23]', '[655, 655, 14*w - 37]', '[656, 164, -24*w + 20]', '[656, 164, 4*w - 28]', '[659, 659, 13*w - 36]', '[659, 659, 10*w - 33]', '[661, 661, 11*w - 34]', '[661, 661, 12*w - 35]', '[671, 671, 24*w - 19]', '[671, 671, 27*w - 29]', '[671, 671, 27*w + 2]', '[671, 671, 24*w - 5]', '[676, 26, -26]', '[684, 114, -24*w + 18]', '[684, 114, -24*w + 6]', '[691, 691, 28*w - 31]', '[691, 691, -28*w - 3]', '[695, 695, 24*w - 17]', '[695, 695, -7*w + 31]', '[701, 701, -27*w - 1]', '[701, 701, 27*w - 28]', '[704, 88, -24*w + 16]', '[704, 88, -24*w + 8]', '[709, 709, 4*w - 29]', '[709, 709, -25*w + 21]', '[711, 237, 24*w - 15]', '[711, 237, 9*w - 33]', '[716, 358, 14*w - 38]', '[716, 358, 10*w - 34]', '[719, 719, 13*w - 37]', '[719, 719, 11*w - 35]', '[720, 60, -24*w + 12]', '[724, 362, -28*w - 2]', '[724, 362, 28*w - 30]', '[725, 145, 5*w + 25]', '[725, 145, -5*w + 30]', '[729, 27, 27]', '[739, 739, 6*w - 31]', '[739, 739, 25*w - 19]', '[745, 745, 26*w - 23]', '[745, 745, 29*w - 32]', '[751, 751, 7*w - 32]', '[751, 751, 25*w - 18]', '[755, 755, 27*w - 26]', '[755, 755, 28*w - 29]', '[761, 761, 8*w - 33]', '[761, 761, 25*w - 17]', '[764, 382, 4*w - 30]', '[764, 382, -26*w + 22]', '[769, 769, 9*w - 34]', '[769, 769, 16*w - 41]', '[775, 155, -25*w + 10]', '[775, 155, -25*w + 15]', '[779, 779, 25*w - 11]', '[779, 779, -2*w + 29]', '[779, 779, 27*w - 25]', '[779, 779, -14*w + 39]', '[781, 781, 25*w - 12]', '[781, 781, -5*w + 31]', '[781, 781, 26*w - 21]', '[781, 781, -13*w + 38]', '[784, 28, -28]', '[796, 398, 6*w - 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98]', '[7649, 7649, -81*w + 64]', '[7669, 7669, 28*w - 107]', '[7669, 7669, 51*w - 130]', '[7681, 7681, 94*w - 105]', '[7681, 7681, -94*w - 11]', '[7691, 7691, 50*w - 129]', '[7691, 7691, 29*w - 108]', '[7699, 7699, 91*w - 97]', '[7699, 7699, -91*w - 6]', '[7741, 7741, -95*w - 12]', '[7741, 7741, 95*w - 107]', '[7759, 7759, 46*w - 125]', '[7759, 7759, 33*w - 112]', '[7789, 7789, 43*w - 122]', '[7789, 7789, 36*w - 115]', '[7829, 7829, -82*w + 65]', '[7829, 7829, 17*w - 99]', '[7841, 7841, -93*w - 8]', '[7841, 7841, 93*w - 101]', '[7879, 7879, 29*w - 109]', '[7879, 7879, 51*w - 131]', '[7901, 7901, -91*w - 4]', '[7901, 7901, 91*w - 95]', '[7919, 7919, 49*w - 129]', '[7919, 7919, 31*w - 111]', '[7949, 7949, -93*w - 7]', '[7949, 7949, 93*w - 100]', '[7951, 7951, 47*w - 127]', '[7951, 7951, 33*w - 113]', '[8009, 8009, -90*w - 1]', '[8009, 8009, 90*w - 91]', '[8011, 8011, 17*w - 100]', '[8011, 8011, -83*w + 66]', '[8039, 8039, -96*w - 11]', '[8039, 8039, 96*w - 107]', '[8059, 8059, 18*w - 101]', '[8059, 8059, -83*w + 65]', '[8069, 8069, 52*w - 133]', '[8069, 8069, 29*w - 110]', '[8081, 8081, 82*w - 59]', '[8081, 8081, 23*w - 105]', '[8089, 8089, 95*w - 104]', '[8089, 8089, -95*w - 9]', '[8101, 8101, 97*w - 109]', '[8101, 8101, -97*w - 12]', '[8111, 8111, 50*w - 131]', '[8111, 8111, 31*w - 112]', '[8161, 8161, 98*w - 111]', '[8161, 8161, -98*w - 13]', '[8171, 8171, 35*w - 116]', '[8171, 8171, 46*w - 127]', '[8179, 8179, -92*w - 3]', '[8179, 8179, 92*w - 95]', '[8191, 8191, 83*w - 62]', '[8191, 8191, 21*w - 104]', '[8209, 8209, 27*w - 109]', '[8209, 8209, 55*w - 137]', '[8219, 8219, 14*w - 99]', '[8219, 8219, -85*w + 71]', '[8221, 8221, 97*w - 108]', '[8221, 8221, -97*w - 11]', '[8231, 8231, 83*w - 61]', '[8231, 8231, 22*w - 105]', '[8269, 8269, 23*w - 106]', '[8269, 8269, 83*w - 60]', '[8291, 8291, -84*w + 65]', '[8291, 8291, 19*w - 103]', '[8311, 8311, 95*w - 102]', '[8311, 8311, -95*w - 7]', '[8329, 8329, -85*w + 69]', '[8329, 8329, 16*w - 101]', '[8369, 8369, 35*w - 117]', '[8369, 8369, 47*w - 129]', '[8389, 8389, 37*w - 119]', '[8389, 8389, 45*w - 127]', '[8419, 8419, -95*w - 6]', '[8419, 8419, 95*w - 101]', '[8429, 8429, 55*w - 138]', '[8429, 8429, 28*w - 111]', '[8431, 8431, 18*w - 103]', '[8431, 8431, -85*w + 67]', '[8461, 8461, -86*w + 71]', '[8461, 8461, 15*w - 101]', '[8501, 8501, 31*w - 114]', '[8501, 8501, 52*w - 135]', '[8521, 8521, 51*w - 134]', '[8521, 8521, 32*w - 115]', '[8539, 8539, 33*w - 116]', '[8539, 8539, 50*w - 133]', '[8581, 8581, 47*w - 130]', '[8581, 8581, 36*w - 119]', '[8599, 8599, 38*w - 121]', '[8599, 8599, 45*w - 128]', '[8609, 8609, 43*w - 126]', '[8609, 8609, 40*w - 123]', '[8629, 8629, -95*w - 4]', '[8629, 8629, 95*w - 99]', '[8641, 8641, -98*w - 9]', '[8641, 8641, 98*w - 107]', '[8669, 8669, 19*w - 105]', '[8669, 8669, -86*w + 67]', '[8681, 8681, -97*w - 7]', '[8681, 8681, 97*w - 104]', '[8689, 8689, 85*w - 61]', '[8689, 8689, 24*w - 109]', '[8699, 8699, 53*w - 137]', '[8699, 8699, 31*w - 115]', '[8719, 8719, 101*w - 114]', '[8719, 8719, -101*w - 13]', '[8731, 8731, -95*w - 3]', '[8731, 8731, 95*w - 98]', '[8741, 8741, -94*w - 1]', '[8741, 8741, 94*w - 95]', '[8761, 8761, 86*w - 65]', '[8761, 8761, 21*w - 107]', '[8779, 8779, 100*w - 111]', '[8779, 8779, -100*w - 11]', '[8819, 8819, 43*w - 127]', '[8819, 8819, 41*w - 125]', '[8821, 8821, 28*w - 113]', '[8821, 8821, 57*w - 142]', '[8831, 8831, 95*w - 97]', '[8831, 8831, -95*w - 2]', '[8839, 8839, 15*w - 103]', '[8839, 8839, -88*w + 73]', '[8849, 8849, 29*w - 114]', '[8849, 8849, 56*w - 141]', '[8861, 8861, 19*w - 106]', '[8861, 8861, -87*w + 68]', '[8929, 8929, -95*w - 1]', '[8929, 8929, 95*w - 96]', '[8941, 8941, 33*w - 118]', '[8941, 8941, 52*w - 137]', '[8951, 8951, 17*w - 105]', '[8951, 8951, -88*w + 71]', '[8969, 8969, -101*w - 11]', '[8969, 8969, 101*w - 112]', '[8971, 8971, 103*w - 117]', '[8971, 8971, -103*w - 14]', '[8999, 8999, 87*w - 65]', '[8999, 8999, 22*w - 109]', '[9001, 9001, 48*w - 133]', '[9001, 9001, 37*w - 122]', '[9011, 9011, 38*w - 123]', '[9011, 9011, 47*w - 132]', '[9029, 9029, 41*w - 126]', '[9029, 9029, 44*w - 129]', '[9041, 9041, 23*w - 110]', '[9041, 9041, 87*w - 64]', '[9049, 9049, 57*w - 143]', '[9049, 9049, 29*w - 115]', '[9059, 9059, 99*w - 106]', '[9059, 9059, -99*w - 7]', '[9091, 9091, 101*w - 111]', '[9091, 9091, -101*w - 10]', '[9109, 9109, 97*w - 100]', '[9109, 9109, -97*w - 3]', '[9151, 9151, 88*w - 67]', '[9151, 9151, 21*w - 109]', '[9161, 9161, 102*w - 113]', '[9161, 9161, -102*w - 11]', '[9181, 9181, 35*w - 121]', '[9181, 9181, 51*w - 137]', '[9199, 9199, -89*w + 71]', '[9199, 9199, 18*w - 107]', '[9209, 9209, 49*w - 135]', '[9209, 9209, 37*w - 123]', '[9221, 9221, 59*w - 146]', '[9221, 9221, 28*w - 115]', '[9239, 9239, 88*w - 65]', '[9239, 9239, 23*w - 111]', '[9241, 9241, 45*w - 131]', '[9241, 9241, 41*w - 127]', '[9281, 9281, -99*w - 5]', '[9281, 9281, 99*w - 104]', '[9311, 9311, -97*w - 1]', '[9311, 9311, 97*w - 98]', '[9319, 9319, 25*w - 113]', '[9319, 9319, 88*w - 63]', '[9341, 9341, 17*w - 107]', '[9341, 9341, -90*w + 73]', '[9349, 9349, -89*w + 68]', '[9349, 9349, 21*w - 110]', '[9371, 9371, 34*w - 121]', '[9371, 9371, 53*w - 140]', '[9391, 9391, 27*w - 115]', '[9391, 9391, 88*w - 61]', '[9409, 97, -97]', '[9419, 9419, 50*w - 137]', '[9419, 9419, 37*w - 124]', '[9421, 9421, 106*w - 121]', '[9421, 9421, -106*w - 15]', '[9431, 9431, 38*w - 125]', '[9431, 9431, 49*w - 136]', '[9439, 9439, 89*w - 66]', '[9439, 9439, 23*w - 112]', '[9461, 9461, 43*w - 130]', '[9461, 9461, 44*w - 131]', '[9479, 9479, -103*w - 10]', '[9479, 9479, 103*w - 113]', '[9491, 9491, 105*w - 118]', '[9491, 9491, -105*w - 13]', '[9511, 9511, 31*w - 119]', '[9511, 9511, 57*w - 145]', '[9521, 9521, 25*w - 114]', '[9521, 9521, 89*w - 64]', '[9539, 9539, 17*w - 108]', '[9539, 9539, -91*w + 74]', '[9551, 9551, -104*w - 11]', '[9551, 9551, 104*w - 115]', '[9601, 9601, -103*w - 9]', '[9601, 9601, 103*w - 112]', '[9619, 9619, -107*w - 15]', '[9619, 9619, 107*w - 122]', '[9629, 9629, 61*w - 150]', '[9629, 9629, 28*w - 117]', '[9631, 9631, 37*w - 125]', '[9631, 9631, 51*w - 139]', '[9649, 9649, -91*w + 72]', '[9649, 9649, 19*w - 110]', '[9661, 9661, 60*w - 149]', '[9661, 9661, 29*w - 118]', '[9679, 9679, 45*w - 133]', '[9679, 9679, 43*w - 131]', '[9689, 9689, -106*w - 13]', '[9689, 9689, 106*w - 119]', '[9719, 9719, 58*w - 147]', '[9719, 9719, 31*w - 120]', '[9721, 9721, -103*w - 8]', '[9721, 9721, 103*w - 111]', '[9739, 9739, 17*w - 109]', '[9739, 9739, -92*w + 75]', '[9749, 9749, 105*w - 116]', '[9749, 9749, -105*w - 11]', '[9769, 9769, 56*w - 145]', '[9769, 9769, 33*w - 122]', '[9781, 9781, 101*w - 105]', '[9781, 9781, -101*w - 4]', '[9791, 9791, 34*w - 123]', '[9791, 9791, 55*w - 144]', '[9811, 9811, 54*w - 143]', '[9811, 9811, 35*w - 124]', '[9829, 9829, 36*w - 125]', '[9829, 9829, 53*w - 142]', '[9839, 9839, 103*w - 110]', '[9839, 9839, -103*w - 7]', '[9851, 9851, 19*w - 111]', '[9851, 9851, -92*w + 73]', '[9859, 9859, 38*w - 127]', '[9859, 9859, 51*w - 140]', '[9871, 9871, 50*w - 139]', '[9871, 9871, 39*w - 128]', '[9901, 9901, 44*w - 133]', '[9901, 9901, 45*w - 134]', '[9929, 9929, 31*w - 121]', '[9929, 9929, 59*w - 149]', '[9931, 9931, 25*w - 116]', '[9931, 9931, 91*w - 66]', '[9941, 9941, -93*w + 76]', '[9941, 9941, 17*w - 110]', '[9949, 9949, -106*w - 11]', '[9949, 9949, 106*w - 117]']}
• 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
  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, -1, 1], 'conductor': 5, 'degree': 2, 'dirichlet_group': [1, 4], 'disc_abs': 5, 'disc_rad': 5, 'disc_sign': 1, 'frobs': [[2, [[2, 1]]], [3, [[2, 1]]], [5, [0]], [7, [[2, 1]]], [11, [[1, 2]]], [13, [[2, 1]]], [17, [[2, 1]]], [19, [[1, 2]]], [23, [[2, 1]]], [29, [[1, 2]]], [31, [[1, 2]]], [37, [[2, 1]]], [41, [[1, 2]]], [43, [[2, 1]]], [47, [[2, 1]]], [53, [[2, 1]]], [59, [[1, 2]]]], 'gal_is_abelian': True, 'gal_is_cyclic': True, 'gal_is_solvable': True, 'galois_disc_exponents': [1], 'galois_label': '2T1', 'galt': 1, 'grd': 2.23606797749979, 'index': 1, 'inessentialp': [], 'is_galois': True, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '2.2.5.1', 'local_algs': ['5.2.1.1'], 'monogenic': 1, 'num_ram': 1, 'r2': 0, 'ramps': [5], 'rd': 2.2360679775, 'regulator': {'__RealLiteral__': 0, 'data': '0.48121182506', 'prec': 44}, 'res': {}, 'subfield_mults': [], 'subfields': [], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( a \\)'], 'used_grh': False, 'zk': ['1', 'a']}