Hilbert modular form data - 3.3.1957.1-11.1-a

Formats: - HTML - YAML - JSON - 2024-05-01T08:46:48.095497

• 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': 1957, 'field_bad_primes': [19, 103], 'field_label': '3.3.1957.1', 'is_CM': 'no', 'is_base_change': 'no', 'label': '3.3.1957.1-11.1-a', 'label_nsuffix': 0, 'label_suffix': 'a', 'level_bad_primes': [11], 'level_ideal': '[11, 11, 10*w + 4]', 'level_label': '11.1', 'level_norm': 11, 'parallel_weight': 2, 'short_label': '11.1-a', 'weight': '[2, 2, 2]'}
• hmf_hecke •

  Column	Type
  AL_eigenvalues	jsonb
  hecke_eigenvalues	jsonb
  hecke_polynomial	text
  label	text

  
  {'AL_eigenvalues': [['[11, 11, 10*w + 4]', -1]], 'hecke_eigenvalues': [1, 3, 2, 1, 2, 2, -2, 6, -4, 4, -2, -4, -6, 6, -4, 0, -4, 10, 8, 2, 6, 8, -8, 20, -2, 2, 10, 18, 6, 6, -10, 14, 24, 6, -20, 0, 6, -14, -18, 6, -8, 8, -12, 4, 12, 6, -26, 6, -14, 12, -16, -6, 8, 2, 12, -12, 12, -28, 30, 18, -8, -4, 12, -4, 10, -14, 24, 8, 8, -10, -4, -20, 4, -6, 2, 18, 26, -26, 16, -26, 30, -14, -4, 10, 8, 16, 24, -40, -8, -28, 24, 16, 24, 14, -4, -12, -2, -4, -20, -44, -14, 6, -6, -2, -10, -48, -22, 30, -14, -12, 22, 2, -38, -42, 6, 20, -18, -14, -22, -30, -42, 26, 0, 0, 30, 24, -8, 0, 32, 38, 14, -26, -28, 26, -18, 6, 38, -10, 8, -48, 14, -30, 6, 10, 26, -4, -48, -40, -40, -46, -18, -14, 34, -4, 4, -44, -48, 12, -32, -22, -18, -12, 6, -40, 2, -24, 32, 58], 'hecke_polynomial': 'x', 'label': '3.3.1957.1-11.1-a'}
• hmf_fields •

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

  
  {'degree': 3, 'discriminant': 1957, 'ideals': ['[1, 1, 1]', '[2, 2, w^2]', '[4, 2, w^2 + w + 1]', '[4, 4, -w + 2]', '[5, 5, w]', '[8, 2, 2]', '[8, 8, w^2 + w + 6]', '[10, 10, w]', '[11, 11, 10*w + 4]', '[13, 13, 12*w^2 + w + 7]', '[16, 4, 2*w]', '[16, 4, -w^2 - w + 7]', '[16, 16, w + 2]', '[17, 17, w + 1]', '[17, 17, 16*w^2 + 16]', '[17, 17, 16*w^2 + 16*w + 8]', '[19, 19, 18*w^2 + 18*w + 1]', '[19, 19, -w^2 + 7]', '[20, 10, -w^2 - w + 5]', '[20, 20, 19*w + 10]', '[22, 22, -w + 4]', '[25, 5, 4*w^2 + w + 4]', '[25, 25, -w^2 - 2*w + 5]', '[26, 26, -w^2 - w + 4]', '[27, 3, -3]', '[29, 29, w + 7]', '[32, 4, 2*w^2 + 2*w + 2]', '[32, 8, -2*w + 4]', '[32, 32, 31*w + 14]', '[34, 34, w + 4]', '[34, 34, w^2 + 33*w + 32]', '[34, 34, -w^2 - w + 8]', '[38, 38, w^2 + w + 20]', '[38, 38, -w^2 + 6]', '[40, 10, 2*w^2 + 2*w]', '[40, 40, -w^2 - w + 10]', '[41, 41, 40*w^2 + 18]', '[43, 43, w^2 - 11]', '[44, 22, -w^2 - w + 9]', '[44, 44, w^2 + w + 2]', '[47, 47, 2*w^2 + 2*w - 13]', '[50, 10, -w^2 + w + 4]', '[50, 50, w + 10]', '[52, 26, -w^2 + w + 7]', '[52, 52, 51*w^2 + w + 46]', '[54, 6, 3*w]', '[55, 55, -w^2 + 5]', '[58, 58, w^2 + 2*w - 6]', '[59, 59, w^2 - 3]', '[64, 4, 4]', '[64, 8, w^2 + 5*w + 5]', '[64, 16, 14*w^2 + 14*w + 4]', '[64, 64, -w^2 + 4]', '[65, 65, -w + 5]', '[68, 34, w^2 + 3*w + 19]', '[68, 34, -w^2 + w + 3]', '[68, 34, w^2 + 3*w - 3]', '[68, 68, -w^2 + w + 2]', '[68, 68, 67*w^2 + 16]', '[68, 68, w^2 + w + 26]', '[73, 73, w^2 + 2*w - 1]', '[76, 38, w^2 + w - 1]', '[76, 38, 37*w^2 + 35*w + 21]', '[76, 76, -w^2 + 2*w + 4]', '[76, 76, w^2 + 75*w + 46]', '[79, 79, w^2 + 37]', '[80, 20, 2*w]', '[80, 20, w^2 + w + 5]', '[80, 80, w^2 + 79*w + 10]', '[82, 82, -w^2 + w + 8]', '[85, 85, w^2 + w]', '[85, 85, 2*w + 5]', '[85, 85, -2*w^2 + 15]', '[86, 86, 85*w^2 + 85*w + 76]', '[88, 22, 2*w^2 + 12]', '[88, 88, -2*w^2 - w + 14]', '[94, 94, w + 6]', '[95, 95, w + 5]', '[95, 95, 94*w^2 + w + 15]', '[97, 97, w^2 + 2*w - 7]', '[100, 10, -w^2 + w + 9]', '[100, 20, 19*w^2 + 16*w + 4]', '[100, 50, w^2 + w + 35]', '[100, 100, -w^2 + w + 10]', '[101, 101, 3*w^2 + 2*w - 21]', '[103, 103, 2*w^2 + 2*w - 11]', '[103, 103, w + 85]', '[104, 26, 24*w^2 + 24]', '[104, 104, -w^2 + 12]', '[107, 107, w^2 + 88]', '[108, 6, 3*w^2 + 3*w + 3]', '[108, 12, 3*w - 6]', '[109, 109, 2*w + 7]', '[109, 109, w^2 + 108*w + 47]', '[109, 109, w + 93]', '[110, 110, 109*w^2 + 60]', '[113, 113, -2*w - 1]', '[113, 113, 112*w^2 + w + 59]', '[113, 113, w^2 + 112*w + 70]', '[116, 58, -w^2 - 3*w - 1]', '[116, 116, w^2 + w + 74]', '[118, 118, 117*w^2 + 62]', '[121, 11, 10*w^2 + 8*w + 8]', '[121, 121, -2*w^2 - 3*w + 11]', '[125, 5, 5]', '[125, 125, w + 10]', '[128, 8, 4*w]', '[128, 8, -2*w^2 - 2*w + 14]', '[128, 32, 2*w + 4]', '[128, 128, w + 114]', '[130, 130, w^2 + w + 100]', '[135, 15, 12*w^2]', '[136, 34, 2*w + 2]', '[136, 34, 32*w^2 + 2*w + 6]', '[136, 34, 2*w + 22]', '[136, 136, 135*w + 118]', '[136, 136, -w^2 - 2*w + 8]', '[136, 136, -w + 6]', '[143, 143, 2*w + 3]', '[145, 145, -2*w^2 - 5*w + 5]', '[146, 146, 145*w^2 + w + 100]', '[152, 38, 2*w^2 + 2*w + 36]', '[152, 38, -2*w^2 + 14]', '[152, 152, w^2 + 151*w + 42]', '[152, 152, -w^2 + 3*w + 2]', '[157, 157, 2*w^2 + w - 13]', '[158, 158, -w^2 + 3*w - 4]', '[160, 20, -2*w^2 - 2*w + 10]', '[160, 40, 38*w^2 + 38*w + 20]', '[160, 160, w^2 + 2*w]', '[164, 82, -3*w^2 - w + 23]', '[164, 164, 163*w^2 + w + 90]', '[167, 167, w^2 + 153]', '[169, 13, 12*w^2 + 9*w + 2]', '[169, 169, -w^2 - 2*w + 9]', '[170, 170, w^2 + w]', '[170, 170, w + 130]', '[170, 170, 169*w^2 + 169*w + 80]', '[172, 86, w^2 + w + 53]', '[172, 172, w^2 + 2*w - 12]', '[176, 44, 43*w^2 + 39*w + 3]', '[176, 44, -2*w + 8]', '[176, 176, w^2 + 28]', '[179, 179, w^2 + 112]', '[187, 187, 186*w^2 + w + 155]', '[187, 187, 3*w - 1]', '[187, 187, -2*w^2 - 2*w + 7]', '[188, 94, 93*w^2 + 91*w + 65]', '[188, 188, -w - 6]', '[190, 190, 189*w^2 + 120]', '[190, 190, -w^2 - 2*w + 10]', '[191, 191, w^2 + 165]', '[193, 193, w^2 + w + 36]', '[193, 193, w^2 + 2*w - 11]', '[193, 193, w^2 + w + 121]', '[194, 194, 193*w^2 + w + 120]', '[197, 197, 2*w^2 + 2*w - 9]', '[199, 199, w^2 - 13]', '[200, 10, 2*w^2 + 8*w + 2]', '[200, 40, -2*w^2 + 7*w - 2]', '[200, 50, -2*w^2 - 4*w + 10]', '[200, 200, 199*w^2 + 100]', '[202, 202, 201*w + 36]', '[205, 205, -2*w^2 - 2*w + 15]', '[206, 206, w^2 + 205*w + 182]', '[206, 206, 2*w^2 - w - 12]', '[208, 52, -2*w^2 - 2*w + 8]', '[208, 52, 51*w^2 + 3*w + 23]', '[208, 208, 207*w^2 + 207*w + 82]', '[209, 209, -2*w^2 + w + 17]', '[209, 209, w^2 + 50]', '[214, 214, -3*w - 8]', '[215, 215, 214*w^2 + 140]', '[216, 6, 6]', '[216, 24, 21*w + 18]', '[218, 218, w^2 + 124]', '[218, 218, -w^2 - 3*w + 16]', '[218, 218, w^2 - 2*w - 6]', '[220, 110, w^2 + 3*w + 5]', '[220, 220, -w^2 + 4*w]', '[221, 221, w^2 + 1]', '[221, 221, 220*w^2 + 220*w + 17]', '[221, 221, -4*w + 7]', '[223, 223, w + 187]', '[226, 226, w^2 - 2*w - 14]', '[226, 226, 2*w^2 + w - 12]', '[226, 226, 225*w^2 + 225*w + 28]', '[227, 227, 2*w^2 - 13]', '[227, 227, w^2 + w + 99]', '[227, 227, w^2 + 60]', '[232, 58, 56*w + 44]', '[232, 232, -w^2 + w - 2]', '[233, 233, 232*w^2 + 178]', '[235, 235, w^2 + 234*w + 5]', '[236, 118, 117*w^2 + w + 51]', '[236, 236, w^2 - 6*w + 4]', '[241, 241, w + 85]', '[241, 241, w^2 + 240*w + 104]', '[241, 241, w - 7]', '[242, 22, w^2 + 3*w - 8]', '[242, 242, w^2 + 241*w + 32]', '[247, 247, w + 8]', '[247, 247, -2*w^2 - 2*w + 21]', '[250, 10, 5*w^2 + 5*w]', '[250, 250, -3*w^2 - 3*w + 20]', '[251, 251, 4*w^2 + 3*w - 27]', '[256, 8, 4*w^2 + 4*w + 4]', '[256, 16, -w^2 + 3*w + 3]', '[256, 16, -4*w + 8]', '[256, 64, 2*w^2 + 56]', '[256, 256, -2*w^2 - w + 22]', '[260, 130, w^2 + 3*w + 25]', '[260, 260, -3*w^2 - 2*w + 20]', '[263, 263, w^2 + 116]', '[269, 269, 268*w + 104]', '[270, 30, -3*w]', '[271, 271, w + 72]', '[272, 68, -3*w^2 - 3*w + 17]', '[272, 68, 2*w + 8]', '[272, 68, w^2 + 65*w + 57]', '[272, 68, 66*w^2 + 2*w + 4]', '[272, 68, 67*w^2 + 63*w + 15]', '[272, 68, -2*w^2 - 2*w + 16]', '[272, 272, w^2 + 3*w + 2]', '[272, 272, w^2 + w + 94]', '[272, 272, w^2 + 188]', '[275, 55, -2*w^2 + 2*w + 13]', '[275, 275, 274*w^2 + 225]', '[277, 277, w^2 + 276*w + 88]', '[283, 283, w^2 + 4*w - 3]', '[286, 286, 285*w^2 + w + 254]', '[289, 17, 16*w^2 + 12*w + 13]', '[289, 17, -w^2 + 2*w + 7]', '[289, 17, 16*w^2 + 5*w + 6]', '[289, 289, -2*w^2 + 2*w + 9]', '[289, 289, w^2 + 2*w + 1]', '[289, 289, -2*w^2 - w + 11]', '[290, 290, w + 210]', '[292, 146, w^2 + 3*w + 105]', '[292, 292, -w^2 - 4*w + 8]', '[295, 295, w^2 + 294*w + 185]', '[297, 33, 30*w + 12]', '[304, 76, 2*w + 16]', '[304, 76, w^2 + 5*w + 57]', '[304, 76, w^2 + w + 1]', '[304, 76, -2*w^2 + 12]', '[304, 304, -2*w^2 - w + 6]', '[304, 304, w^2 + 303*w + 122]', '[307, 307, 2*w^2 - w - 11]', '[307, 307, w + 133]', '[307, 307, 306*w^2 + w + 284]', '[314, 314, 313*w^2 + w + 96]', '[316, 158, w^2 + 3*w - 9]', '[316, 316, w + 90]', '[317, 317, 2*w^2 - 4*w - 3]', '[319, 319, -w - 7]', '[320, 20, 4*w^2]', '[320, 40, w^2 - 3*w + 5]', '[320, 80, -2*w^2 - 2*w + 20]', '[320, 320, w + 50]', '[323, 323, -2*w^2 - 4*w + 11]', '[323, 323, -2*w^2 - 2*w + 17]', '[323, 323, -2*w + 9]', '[323, 323, 322*w^2 + 121]', '[323, 323, w^2 + 322*w + 236]', '[323, 323, 322*w^2 + w + 224]', '[325, 65, -w^2 - 4*w + 19]', '[325, 325, 324*w^2 + w + 85]', '[328, 82, 80*w^2 + 36]', '[328, 328, -2*w^2 + 3*w + 6]', '[334, 334, w^2 - 14]', '[337, 337, w^2 - 2*w - 13]', '[338, 26, 2*w^2 - 5*w - 4]', '[338, 338, 337*w^2 + 116]', '[340, 170, -w^2 - 3*w + 15]', '[340, 170, w^2 + w + 145]', '[340, 170, w^2 + 3*w + 115]', '[340, 340, -2*w^2 - w + 10]', '[340, 340, w^2 + 339*w + 270]', '[340, 340, w^2 + 4*w]', '[343, 7, -7]', '[344, 86, 2*w^2 - 22]', '[344, 344, 343*w^2 + 343*w + 162]', '[347, 347, 3*w - 11]', '[347, 347, -3*w - 1]', '[347, 347, 3*w + 7]', '[349, 349, 348*w^2 + 348*w + 191]', '[351, 39, 3*w^2 + 3]', '[352, 44, -2*w^2 - 2*w + 18]', '[352, 88, 86*w^2 + 2*w + 68]', '[352, 352, -w^2 + 2*w + 8]', '[353, 353, 2*w^2 + 2*w - 19]', '[358, 358, -5*w + 8]', '[359, 359, w^2 + 4*w - 1]', '[359, 359, w^2 + 210]', '[359, 359, 358*w^2 + 346]', '[361, 19, 18*w^2 + 6*w + 17]', '[361, 19, -2*w^2 - w + 7]', '[361, 361, -w^2 + 4*w + 1]', '[365, 365, 364*w^2 + w + 100]', '[373, 373, 2*w^2 + w - 9]', '[374, 374, -w^2 + 3*w + 4]', '[374, 374, 373*w^2 + 373*w + 42]', '[374, 374, 373*w^2 + w + 122]', '[376, 94, 4*w^2 + 4*w - 26]', '[376, 376, 375*w^2 + w + 230]', '[377, 377, 2*w^2 - 11]', '[379, 379, 3*w^2 + 2*w - 29]', '[379, 379, w^2 + w + 148]', '[379, 379, 378*w^2 + 378*w + 323]', '[380, 190, w^2 + w + 75]', '[380, 190, -w^2 + w + 15]', '[380, 380, -w^2 - 3*w + 10]', '[380, 380, 379*w^2 + w + 110]', '[382, 382, 2*w^2 + w - 8]', '[386, 386, -w^2 - 2]', '[386, 386, w^2 + 385*w + 70]', '[386, 386, w - 8]', '[388, 194, 193*w^2 + 191*w + 131]', '[388, 388, -w^2 + 2*w - 4]', '[389, 389, w^2 + w + 25]', '[394, 394, w^2 + 252]', '[395, 395, 2*w^2 - 5]', '[397, 397, 396*w^2 + 118]', '[398, 398, w^2 + 397*w + 336]', '[400, 20, 19*w^2 + 11*w + 19]', '[400, 20, -2*w^2 + 2*w + 8]', '[400, 80, w^2 + 79*w + 26]', '[400, 100, 98*w + 80]', '[400, 100, -w^2 - w + 15]', '[400, 400, -2*w^2 + w + 10]', '[401, 401, w^2 - 2*w - 9]', '[404, 202, 201*w^2 + 201*w + 19]', '[404, 404, w^2 - 2*w - 12]', '[409, 409, 4*w^2 - w - 33]', '[410, 410, w^2 + 310]', '[412, 206, w^2 + 3*w + 13]', '[412, 206, 3*w^2 - w - 27]', '[412, 412, -3*w - 2]', '[412, 412, 411*w^2 + 411*w + 342]', '[416, 52, -2*w^2 + 2*w + 14]', '[416, 104, 102*w^2 + 102*w + 60]', '[416, 416, -w^2 - 3*w + 14]', '[418, 418, w + 62]', '[418, 418, -3*w^2 - 3*w + 16]', '[421, 421, 3*w^2 + 2*w - 19]', '[425, 85, 84*w^2 + 81*w + 14]', '[425, 85, w^2 - 6*w + 11]', '[425, 85, -w^2 - 4*w + 9]', '[425, 425, -2*w^2 + 3*w + 5]', '[425, 425, w + 310]', '[425, 425, w^2 + 100]', '[428, 214, w^2 + 3*w - 11]', '[428, 428, w + 74]', '[430, 430, w^2 - 2*w - 10]', '[431, 431, -w^2 + 2*w + 17]', '[432, 12, 6*w^2]', '[432, 12, 3*w^2 + 3*w - 21]', '[432, 48, -3*w - 6]', '[433, 433, 432*w^2 + 79]', '[433, 433, w^2 + 432*w + 7]', '[433, 433, w^2 - 2*w - 11]', '[436, 218, 217*w^2 + 217*w + 145]', '[436, 218, -3*w^2 - w + 31]', '[436, 218, 3*w^2 + w - 21]', '[436, 436, -2*w^2 - 3*w + 14]', '[436, 436, w^2 + w + 70]', '[436, 436, w^2 + 180]', '[440, 110, -2*w^2 + 10]', '[440, 440, 439*w^2 + 439*w + 130]', '[442, 442, -3*w^2 - 6*w + 14]', '[442, 442, 441*w^2 + w + 98]', '[442, 442, 441*w^2 + 220]', '[443, 443, 4*w^2 + 2*w - 29]', '[446, 446, 2*w^2 + 3*w - 24]', '[451, 451, -4*w^2 + 31]', '[452, 226, w^2 + 225*w + 197]', '[452, 226, w^2 + 3*w - 13]', '[452, 226, w^2 - 3*w - 17]', '[452, 452, 2*w^2 - 3*w - 2]', '[452, 452, w^2 + w + 190]', '[452, 452, 451*w^2 + 451*w + 182]', '[454, 454, 453*w + 410]', '[454, 454, w^2 + 3*w - 12]', '[454, 454, 2*w^2 - w - 4]', '[457, 457, 2*w^2 + w - 23]', '[459, 51, -3*w - 3]', '[459, 51, 48*w^2 + 3*w + 9]', '[459, 51, 3*w + 33]', '[463, 463, 462*w^2 + 422]', '[464, 116, w^2 + w + 45]', '[464, 116, 2*w^2 + 4*w - 12]', '[464, 464, 463*w^2 + 463*w + 274]', '[466, 466, -w^2 - 2*w - 2]', '[470, 470, 4*w^2 + 5*w - 20]', '[472, 118, 2*w^2 - 6]', '[472, 472, 471*w + 70]', '[473, 473, w^2 + w + 354]', '[475, 95, -2*w^2 + 2*w + 3]', '[475, 95, w^2 + 94*w + 61]', '[475, 475, 3*w + 5]', '[475, 475, w + 385]', '[479, 479, 2*w^2 - w - 9]', '[482, 482, -3*w - 4]', '[482, 482, 481*w^2 + 290]', '[482, 482, 2*w^2 - 3*w - 4]', '[484, 22, -w^2 - 3*w - 3]', '[484, 44, w^2 + 14*w + 36]', '[484, 242, 241*w^2 + 241*w + 119]', '[484, 484, w^2 + w + 2]', '[485, 485, 484*w + 415]', '[487, 487, 2*w^2 - 9]', '[487, 487, 2*w^2 - 2*w - 7]', '[487, 487, -2*w - 9]', '[493, 493, -4*w + 1]', '[493, 493, 6*w^2 + 10*w - 21]', '[493, 493, 492*w + 254]', '[494, 494, w + 8]', '[494, 494, 493*w^2 + w + 410]', '[499, 499, -5*w^2 - 4*w + 33]', '[500, 10, 5*w^2 + 5*w + 5]', '[500, 20, -5*w + 10]', '[500, 250, -w^2 + 3*w + 5]', '[500, 500, 499*w + 490]', '[502, 502, w^2 + w + 228]', '[503, 503, w^2 + 2*w - 17]', '[503, 503, 502*w^2 + 502*w + 499]', '[503, 503, 502*w^2 + 216]', '[505, 505, w^2 + w + 385]', '[509, 509, 2*w^2 - 7]', '[512, 8, 8]', '[512, 16, 14*w^2 + 6*w + 6]', '[512, 32, 28*w^2 + 16]', '[512, 128, -2*w^2 + 8]', '[512, 512, w^2 + 511*w + 202]', '[513, 57, 3*w + 15]', '[513, 57, 3*w^2 - 21]', '[515, 515, 514*w^2 + w + 230]', '[515, 515, w^2 - 15]', '[517, 517, w^2 + 105]', '[520, 130, -2*w + 10]', '[520, 520, 519*w^2 + w + 150]', '[523, 523, w^2 + 104]', '[526, 526, w^2 - 4*w - 2]', '[533, 533, -3*w^2 - 2*w + 33]', '[535, 535, 2*w^2 - w - 5]', '[538, 538, 2*w^2 - w - 8]', '[540, 30, 3*w^2 + 3*w - 15]', '[540, 60, 3*w^2]', '[542, 542, -w^2 - 4*w + 18]', '[544, 68, 66*w^2 + 2*w + 38]', '[544, 68, -2*w^2 + 2*w + 6]', '[544, 68, 2*w^2 + 6*w - 6]', '[544, 136, -2*w^2 + 2*w + 4]', '[544, 136, 2*w + 76]', '[544, 136, 134*w^2 + 72]', '[544, 544, 543*w^2 + 543*w + 306]', '[544, 544, w^2 - 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79]', '[1892, 1892, w^2 + 1891*w + 54]', '[1894, 1894, w + 290]', '[1895, 1895, w^2 + 1894*w + 1820]', '[1895, 1895, 8*w^2 + 12*w - 35]', '[1895, 1895, 3*w^2 + 4*w - 25]', '[1898, 1898, -10*w^2 - 17*w + 36]', '[1900, 190, 189*w^2 + 181*w + 189]', '[1900, 190, -3*w^2 + 3*w + 7]', '[1900, 380, 379*w^2 + 371*w + 334]', '[1900, 380, -w^2 - 4*w + 24]', '[1900, 950, 949*w^2 + 947*w + 895]', '[1900, 950, -5*w^2 + w + 35]', '[1900, 1900, -3*w^2 + w + 10]', '[1900, 1900, 1899*w^2 + w + 410]', '[1901, 1901, w^2 + 1900*w + 347]', '[1906, 1906, 5*w^2 + w - 36]', '[1907, 1907, 3*w^2 + 6*w - 19]', '[1910, 1910, 1909*w^2 + w + 70]', '[1913, 1913, 1912*w^2 + 1678]', '[1916, 958, 957*w^2 + 955*w + 943]', '[1916, 1916, 3*w^2 - 11*w + 2]', '[1919, 1919, 10*w^2 - w - 97]', '[1919, 1919, 1918*w^2 + 690]', '[1921, 1921, 2*w^2 + w - 27]', '[1921, 1921, 1920*w^2 + w + 1611]', '[1921, 1921, 4*w^2 + 4*w - 31]', '[1921, 1921, w + 735]', '[1921, 1921, w + 1004]', '[1921, 1921, 6*w^2 + 11*w - 27]', '[1921, 1921, w + 1650]', '[1921, 1921, -2*w^2 - 3*w - 1]', '[1921, 1921, w - 13]', '[1927, 1927, w^2 + 1926*w + 1509]', '[1928, 482, 480*w^2 + 2*w + 160]', '[1928, 482, 480*w^2 + 2*w + 274]', '[1928, 482, 2*w - 14]', '[1928, 1928, 3*w^2 - 2*w - 8]', '[1928, 1928, 1927*w^2 + 772]', '[1928, 1928, -3*w - 14]', '[1930, 1930, 1929*w + 1510]', '[1930, 1930, 1929*w + 780]', '[1930, 1930, 3*w^2 - 2*w - 10]', '[1933, 1933, w^2 + w + 607]', '[1934, 1934, w^2 + 1778]', '[1936, 44, 43*w^2 + 19*w + 19]', '[1936, 44, 2*w^2 + 6*w - 16]', '[1936, 176, 175*w^2 + 173*w + 30]', '[1936, 484, 2*w^2 + 482*w + 64]', '[1936, 484, -w^2 + 7*w - 1]', '[1936, 1936, -5*w^2 + 36]', '[1940, 970, -3*w^2 - 9*w + 5]', '[1940, 1940, w^2 + 1939*w + 850]', '[1945, 1945, 8*w - 15]', '[1948, 974, 973*w^2 + 971*w + 901]', '[1948, 974, w^2 + 3*w + 277]', '[1948, 974, w^2 + 973*w + 97]', '[1948, 1948, 2*w^2 - 9*w + 2]', '[1948, 1948, 4*w^2 - 15*w + 6]', '[1948, 1948, 2*w^2 + 5*w - 18]', '[1949, 1949, 4*w - 17]', '[1951, 1951, -w^2 - 6*w - 1]', '[1954, 1954, w^2 + 1418]', '[1957, 1957, w^2 + 1956*w + 388]', '[1957, 1957, 1956*w + 1151]', '[1957, 1957, 8*w^2 + 3*w - 71]', '[1957, 1957, 3*w^2 - 2*w - 37]', '[1966, 1966, -w^2 - 6*w - 2]', '[1969, 1969, w^2 - 4*w + 11]', '[1970, 1970, 4*w^2 + 9*w - 20]', '[1971, 219, 3*w^2 + 6*w - 3]', '[1972, 986, 985*w^2 + 985*w + 709]', '[1972, 986, w^2 + 3*w + 813]', '[1972, 986, -5*w^2 - 13*w + 9]', '[1972, 1972, -w^2 - 4*w - 8]', '[1972, 1972, 7*w^2 + 11*w - 34]', '[1972, 1972, 1971*w^2 + w + 1158]', '[1973, 1973, w^2 + 1972*w + 1640]', '[1973, 1973, 1972*w^2 + w + 1620]', '[1973, 1973, 2*w^2 - 5*w - 9]', '[1975, 395, 2*w^2 - 7*w - 3]', '[1975, 1975, 1974*w^2 + 200]', '[1976, 494, 492*w^2 + 492*w + 112]', '[1976, 494, -4*w^2 - 4*w + 42]', '[1976, 1976, 1975*w + 1838]', '[1976, 1976, -w^2 - 6*w + 16]', '[1982, 1982, w^2 + 1981*w + 944]', '[1985, 1985, 4*w^2 + w - 25]', '[1987, 1987, 6*w^2 + 4*w - 47]', '[1987, 1987, -5*w^2 + 2*w + 33]', '[1987, 1987, -2*w - 13]', '[1990, 1990, w^2 - 4*w - 10]', '[1994, 1994, -3*w^2 - 9*w + 8]', '[1996, 998, w^2 + 997*w + 177]', '[1996, 1996, -w^2 + 4*w + 16]', '[1999, 1999, w^2 + 1998*w + 172]', '[2000, 20, 10*w^2]', '[2000, 20, -5*w^2 + 15*w - 5]', '[2000, 80, -5*w^2 + 5*w + 30]', '[2000, 500, -6*w^2 - 6*w + 40]', '[2000, 500, w^2 + 5*w + 325]', '[2000, 2000, 1999*w^2 + w + 1110]', '[2003, 2003, 2002*w^2 + w + 1378]', '[2005, 2005, w^2 + 10]', '[2006, 2006, -5*w - 4]', '[2006, 2006, 5*w^2 + 6*w - 22]', '[2006, 2006, w^2 + 764]', '[2008, 502, 8*w^2 + 6*w - 54]', '[2008, 2008, 2007*w^2 + 2007*w + 274]', '[2011, 2011, 2*w^2 + 5*w - 27]', '[2012, 1006, w^2 + 3*w + 519]', '[2012, 1006, 5*w^2 + 7*w - 29]', '[2012, 1006, -w^2 - 3*w - 7]', '[2012, 2012, w^2 + w + 26]', '[2012, 2012, w^2 + w + 1010]', '[2012, 2012, -w^2 + 12*w - 24]', '[2017, 2017, 2016*w^2 + w + 111]', '[2018, 2018, 2017*w^2 + w + 1704]', '[2020, 1010, -w^2 - 11*w - 25]', '[2020, 2020, w^2 + 2019*w + 1770]', '[2021, 2021, 4*w^2 - 3*w - 21]', '[2026, 2026, 4*w^2 - 9*w - 4]', '[2029, 2029, 5*w - 19]', '[2033, 2033, 2032*w^2 + 2032*w + 1443]', '[2033, 2033, 2*w^2 - 4*w - 13]', '[2036, 1018, w^2 + 3*w + 849]', '[2036, 2036, 2*w^2 - 11*w + 6]', '[2038, 2038, 3*w^2 + 4*w - 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10]', '[2180, 2180, -4*w^2 + 7*w + 10]', '[2182, 2182, 2181*w^2 + w + 2070]', '[2186, 2186, 2185*w^2 + w + 652]', '[2188, 1094, 1093*w^2 + 1093*w + 763]', '[2188, 2188, 5*w^2 - 13*w - 2]', '[2189, 2189, 2188*w + 1742]', '[2194, 2194, w + 554]', '[2194, 2194, -4*w^2 - 5*w + 28]', '[2194, 2194, w^2 - 4*w - 14]', '[2197, 13, 13]', '[2197, 2197, w^2 + 2196*w + 1267]', '[2200, 110, -4*w^2 + 4*w + 26]', '[2200, 440, 439*w^2 + w + 254]', '[2200, 550, 2*w^2 + 548*w + 130]', '[2200, 2200, -4*w^2 + 3*w + 30]', '[2203, 2203, 4*w^2 + 3*w - 19]', '[2203, 2203, 2202*w^2 + 252]', '[2203, 2203, 2202*w^2 + 2202*w + 948]', '[2204, 1102, 5*w^2 + 11*w - 23]', '[2204, 1102, w^2 + w + 683]', '[2204, 2204, -5*w - 6]', '[2204, 2204, 2203*w^2 + 2203*w + 854]', '[2206, 2206, 2205*w + 116]', '[2209, 47, 6*w^2 + 5*w - 37]', '[2209, 2209, w^2 - 4*w - 13]', '[2210, 2210, w + 970]', '[2210, 2210, -3*w^2 - 4*w + 30]', '[2210, 2210, -w^2 + w + 20]', '[2214, 246, -3*w^2 + 3*w + 24]', '[2215, 2215, 2214*w^2 + 2214*w + 1585]', '[2216, 554, 2*w^2 + 330]', '[2216, 2216, -3*w^2 - 4*w + 28]', '[2218, 2218, 5*w^2 + 2*w - 34]', '[2218, 2218, 2217*w^2 + 2217*w + 2150]', '[2218, 2218, -5*w - 8]', '[2222, 2222, 7*w^2 + 2*w - 54]', '[2228, 1114, w^2 + 3*w + 1045]', '[2228, 2228, 2*w^2 + 5*w - 26]', '[2230, 2230, 2229*w + 1820]', '[2236, 1118, 9*w^2 - w - 77]', '[2236, 2236, 2235*w^2 + w + 462]', '[2237, 2237, w + 1090]', '[2237, 2237, 2236*w^2 + 2180]', '[2237, 2237, -5*w - 7]', '[2239, 2239, -w - 13]', '[2239, 2239, 2*w^2 + 6*w - 17]', '[2239, 2239, 3*w^2 + 4*w - 29]', '[2242, 2242, w + 1110]', '[2242, 2242, -w^2 + w - 8]', '[2243, 2243, 2242*w^2 + 2242*w + 421]', '[2246, 2246, 4*w^2 - w - 24]', '[2251, 2251, w^2 + 1575]', '[2255, 2255, w^2 + 105]', '[2260, 1130, 1129*w^2 + 1127*w + 95]', '[2260, 1130, 5*w^2 + 9*w - 25]', '[2260, 1130, w^2 + w + 755]', '[2260, 2260, 2259*w + 2090]', '[2260, 2260, 3*w^2 + 6*w - 20]', '[2260, 2260, -w^2 - 5*w - 10]', '[2264, 566, 2*w^2 + 8*w - 6]', '[2264, 2264, 2263*w^2 + w + 830]', '[2266, 2266, 4*w^2 + w - 24]', '[2266, 2266, 2265*w^2 + w + 100]', '[2267, 2267, 2266*w + 2151]', '[2267, 2267, -2*w^2 + 4*w + 33]', '[2267, 2267, 2266*w^2 + 2266*w + 1646]', '[2269, 2269, 2268*w^2 + 2268*w + 812]', '[2269, 2269, 2268*w + 1682]', '[2269, 2269, 2*w^2 - 2*w - 29]', '[2270, 2270, w^2 + 1630]', '[2270, 2270, 2*w^2 + 5*w - 20]', '[2270, 2270, w + 1940]', '[2273, 2273, -w^2 + 2*w - 9]', '[2281, 2281, -w^2 - 2*w - 7]', '[2281, 2281, 4*w^2 + 7*w - 23]', '[2281, 2281, 5*w^2 + 8*w - 27]', '[2284, 1142, 5*w^2 - 3*w - 53]', '[2284, 1142, 1141*w^2 + w + 971]', '[2284, 1142, -w^2 - w - 7]', '[2284, 2284, 3*w^2 - 13*w + 6]', '[2284, 2284, 2283*w^2 + 2283*w + 1706]', '[2284, 2284, w + 1818]', '[2285, 2285, 2284*w^2 + w + 430]', '[2287, 2287, w^2 - 2*w - 21]', '[2288, 572, -7*w^2 + w + 53]', '[2288, 572, 2*w^2 + 570*w + 64]', '[2288, 2288, -3*w^2 - 3*w + 38]', '[2291, 2291, 4*w^2 - 3*w - 43]', '[2295, 255, 3*w + 105]', '[2295, 255, -6*w - 15]', '[2295, 255, 6*w^2 - 45]', '[2297, 2297, 2*w^2 - 8*w - 1]', '[2299, 209, 4*w^2 + 12*w - 21]', '[2299, 209, 208*w^2 + 8*w + 52]', '[2299, 2299, -2*w^2 + 4*w + 27]', '[2299, 2299, w^2 + 2298*w + 274]', '[2302, 2302, -3*w + 16]', '[2302, 2302, 2301*w + 1082]', '[2302, 2302, 3*w^2 + 8*w - 18]', '[2308, 1154, 1153*w^2 + w + 649]', '[2308, 2308, -w^2 + 11*w - 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28]', '[9721, 9721, 4*w^2 - 6*w - 59]', '[9721, 9721, 9720*w + 3519]', '[9721, 9721, 9720*w^2 + 6903]', '[9722, 9722, 9721*w^2 + 7068]', '[9724, 4862, -3*w^2 - 9*w + 29]', '[9724, 4862, w^2 - 7*w + 23]', '[9724, 4862, 4861*w^2 + 4859*w + 3823]', '[9724, 9724, -3*w^2 - 11*w + 26]', '[9724, 9724, 9723*w^2 + 9723*w + 1538]', '[9724, 9724, 9723*w^2 + 9723*w + 4398]', '[9725, 1945, 4*w^2 + 6*w - 1]', '[9725, 9725, w^2 + 9724*w + 515]', '[9728, 152, 144*w + 112]', '[9728, 152, -8*w^2 + 56]', '[9728, 304, -2*w^2 - 10*w + 38]', '[9728, 304, 138*w^2 + 50*w + 194]', '[9728, 608, 604*w^2 + 604*w + 72]', '[9728, 608, -4*w^2 + 12*w + 8]', '[9728, 2432, -2*w^2 - 2*w + 36]', '[9728, 2432, 2*w + 2404]', '[9728, 9728, w^2 + 316]', '[9728, 9728, w^2 - 16*w + 28]', '[9733, 9733, 9732*w^2 + 3544]', '[9736, 2434, 4*w^2 - 8*w - 58]', '[9736, 9736, 9735*w^2 + 9460]', '[9739, 9739, 7*w^2 - 4*w - 57]', '[9740, 4870, -w^2 + 17*w - 25]', '[9740, 4870, -w^2 - w - 15]', '[9740, 4870, -3*w^2 - 7*w - 5]', '[9740, 9740, 9739*w^2 + 6960]', '[9740, 9740, w^2 + w + 6190]', '[9740, 9740, 9739*w^2 + 5960]', '[9743, 9743, 9742*w^2 + 9742*w + 5757]', '[9745, 9745, w^2 + w + 8870]', '[9746, 9746, 10*w^2 + w - 76]', '[9747, 57, 54*w^2 + 18*w + 51]', '[9747, 57, 6*w^2 + 3*w - 21]', '[9747, 1083, 3*w^2 - 12*w - 3]', '[9754, 9754, w^2 + 9753*w + 7200]', '[9755, 9755, 9754*w^2 + 4270]', '[9757, 9757, 6*w^2 + 7*w - 47]', '[9761, 9761, 2*w^2 + 10*w - 27]', '[9761, 9761, w^2 + 9760*w + 7020]', '[9761, 9761, w + 8750]', '[9763, 9763, 6*w^2 - w - 67]', '[9767, 9767, w + 6705]', '[9770, 9770, 6*w^2 + 9*w - 40]', '[9773, 9773, w + 6126]', '[9776, 2444, -10*w^2 - 26*w + 16]', '[9776, 2444, 2443*w^2 + 3*w + 1323]', '[9776, 9776, 9775*w^2 + w + 982]', '[9778, 9778, -7*w^2 - 6*w + 34]', '[9781, 9781, 12*w^2 + 11*w - 81]', '[9781, 9781, 6*w^2 + w - 33]', '[9781, 9781, 6*w^2 + 6*w - 73]', '[9784, 2446, 2*w^2 + 2390]', '[9784, 9784, -w^2 + 28]', '[9785, 9785, 14*w^2 + 17*w - 75]', '[9785, 9785, 12*w^2 + w - 95]', '[9785, 9785, 9784*w^2 + 710]', '[9785, 9785, 9784*w^2 + 2590]', '[9787, 9787, 7*w^2 - 8*w - 41]', '[9791, 9791, 4*w^2 + 9*w - 31]', '[9797, 9797, -2*w^2 + 8*w - 19]', '[9802, 754, w^2 + 17*w + 128]', '[9802, 9802, -3*w^2 - 5*w - 4]', '[9803, 9803, 9802*w + 7961]', '[9806, 9806, 9805*w + 48]', '[9809, 9809, w^2 + w + 3949]', '[9809, 9809, w^2 - 8*w - 9]', '[9809, 9809, 9808*w + 1740]', '[9812, 4906, w^2 + w + 3797]', '[9812, 9812, 5*w^2 + 7*w - 42]', '[9817, 9817, w^2 + 9443]', '[9818, 9818, 9817*w^2 + 9817*w + 5104]', '[9818, 9818, w^2 - w - 28]', '[9818, 9818, 8*w^2 - 7*w - 52]', '[9823, 9823, w^2 + 5275]', '[9823, 9823, 20*w^2 + 7*w - 161]', '[9824, 1228, 2*w^2 + 2*w + 106]', '[9824, 1228, 14*w^2 + 10*w - 102]', '[9824, 1228, -10*w^2 - 6*w + 82]', '[9824, 2456, 2*w^2 + 928]', '[9824, 2456, 6*w^2 - 18*w - 4]', '[9824, 2456, 2*w^2 + 2454*w + 1196]', '[9824, 9824, -4*w^2 + 5*w + 42]', '[9824, 9824, w^2 + 9823*w + 5194]', '[9824, 9824, 2*w^2 - 9*w - 42]', '[9826, 34, 17*w^2 + 17*w]', '[9826, 578, -3*w^2 + 6*w + 38]', '[9826, 578, 577*w^2 + 573*w + 166]', '[9826, 578, -4*w^2 - 3*w + 52]', '[9826, 578, -8*w^2 - 11*w + 48]', '[9826, 578, 577*w^2 + 566*w + 210]', '[9826, 578, -8*w^2 - w + 56]', '[9826, 9826, 9825*w^2 + 9825*w + 646]', '[9826, 9826, -11*w^2 + 2*w + 82]', '[9826, 9826, -7*w^2 + 5*w + 52]', '[9829, 9829, 4*w^2 - 3*w - 53]', '[9830, 9830, w^2 + 9320]', '[9832, 2458, 2*w^2 + 408]', '[9832, 2458, 4*w^2 + 8*w - 34]', '[9832, 2458, 2*w^2 + 1906]', '[9832, 9832, 4*w^2 - 7*w - 54]', '[9832, 9832, w^2 + w + 8318]', '[9832, 9832, 3*w^2 + 13*w + 6]', '[9838, 9838, 6*w^2 + 3*w - 28]', '[9839, 9839, 6*w^2 - 9*w - 17]', '[9845, 9845, w^2 + w + 3225]', '[9848, 2462, 2460*w^2 + 1634]', '[9848, 9848, -11*w^2 - 7*w + 86]', '[9850, 1970, -w^2 + w - 16]', '[9850, 9850, 9849*w + 1340]', '[9853, 9853, w^2 + w + 7066]', '[9854, 9854, 9853*w + 8364]', '[9854, 9854, 4*w^2 - 5*w - 36]', '[9854, 9854, w^2 + w + 906]', '[9855, 1095, 1092*w^2 + 3*w + 300]', '[9857, 9857, w^2 + 6752]', '[9859, 9859, w^2 + 51]', '[9860, 4930, w^2 + 3*w + 4235]', '[9860, 4930, -3*w^2 - w - 5]', '[9860, 4930, 7*w^2 + 15*w - 35]', '[9860, 9860, 9*w^2 + 20*w - 40]', '[9860, 9860, w^2 + 5200]', '[9860, 9860, w^2 + 1140]', '[9865, 9865, w^2 + 2*w + 15]', '[9865, 9865, 11*w^2 + 16*w - 45]', '[9865, 9865, 9864*w + 680]', '[9866, 9866, 2*w^2 - 7*w - 16]', '[9872, 2468, 2*w^2 + 2466*w + 444]', '[9872, 2468, -3*w^2 - 11*w - 11]', '[9872, 9872, 10*w^2 + 13*w - 46]', '[9874, 9874, 5*w^2 - 18*w + 2]', '[9875, 395, 5*w^2 + 185]', '[9875, 9875, -2*w^2 - 9*w - 15]', '[9880, 2470, -8*w^2 + 4*w + 50]', '[9880, 2470, 2468*w^2 + 2468*w + 1750]', '[9880, 9880, 9879*w + 8390]', '[9880, 9880, 3*w^2 + 13*w - 10]', '[9881, 9881, w^2 + w + 4523]', '[9881, 9881, -12*w^2 - 8*w + 91]', '[9881, 9881, 4*w^2 + 2*w - 51]', '[9883, 9883, w^2 + 9882*w + 6823]', '[9887, 9887, 2*w^2 + 11*w - 3]', '[9892, 4946, w^2 + w + 951]', '[9892, 9892, 3*w^2 + 15*w - 26]', '[9893, 9893, 6*w^2 + 5*w - 71]', '[9896, 2474, 8*w^2 + 6*w - 78]', '[9896, 9896, w^2 + w + 3438]', '[9901, 9901, w + 2901]', '[9907, 9907, 9906*w^2 + w + 6961]', '[9908, 4954, w^2 + 4953*w + 4885]', '[9908, 9908, 6*w^2 - 11*w - 2]', '[9910, 9910, -2*w^2 - 5*w + 40]', '[9922, 902, 901*w^2 + 888*w + 404]', '[9922, 9922, -9*w^2 - 6*w + 58]', '[9923, 9923, 9922*w^2 + 1368]', '[9925, 1985, -9*w^2 + 4*w + 71]', '[9925, 9925, w^2 + 7425]', '[9928, 2482, 2480*w^2 + 134]', '[9928, 2482, 8*w^2 + 20*w - 22]', '[9928, 2482, 2480*w + 80]', '[9928, 9928, -9*w^2 - 17*w + 42]', '[9928, 9928, 3*w^2 + 4*w + 4]', '[9928, 9928, 9927*w^2 + w + 9590]', '[9931, 9931, 9930*w^2 + 9930*w + 2117]', '[9931, 9931, 4*w^2 - 11*w - 11]', '[9931, 9931, 9930*w + 1088]', '[9932, 4966, 4965*w^2 + 4965*w + 173]', '[9932, 9932, -8*w^2 - 13*w + 18]', '[9934, 9934, 6*w^2 + w - 16]', '[9935, 9935, 9934*w^2 + 3025]', '[9935, 9935, 9934*w^2 + 6500]', '[9935, 9935, w^2 + w + 8450]', '[9937, 9937, 10*w^2 + 13*w - 33]', '[9937, 9937, w^2 + 9936*w + 3405]', '[9938, 9938, 9937*w^2 + 9937*w + 8440]', '[9941, 9941, w^2 + 9940*w + 548]', '[9944, 2486, 6*w^2 - 4*w - 58]', '[9944, 2486, 2*w + 2148]', '[9944, 2486, 6*w^2 + 12*w - 34]', '[9944, 9944, 8*w^2 + 9*w - 54]', '[9944, 9944, w + 5298]', '[9944, 9944, w + 9786]', '[9946, 9946, -8*w^2 - 7*w + 44]', '[9947, 203, 196*w^2 + 140]', '[9949, 9949, 11*w^2 + 10*w - 67]', '[9950, 1990, 8*w^2 - 3*w - 52]', '[9950, 9950, w^2 + 9949*w + 9490]', '[9967, 9967, w + 1099]', '[9967, 9967, w^2 + w + 7625]', '[9967, 9967, 6*w^2 + 2*w - 31]', '[9970, 9970, w^2 + 7700]', '[9971, 767, 766*w^2 + 9*w + 730]', '[9971, 9971, -11*w + 3]', '[9973, 9973, 8*w^2 + 2*w - 83]', '[9974, 9974, 9973*w^2 + 7152]', '[9976, 2494, 2*w^2 + 1526]', '[9976, 9976, -w + 22]', '[9977, 9977, 9976*w^2 + w + 1123]', '[9980, 4990, 5*w^2 + 23*w + 25]', '[9980, 9980, 9979*w^2 + w + 6310]', '[9986, 9986, w^2 + 11*w - 4]', '[9988, 4994, 9*w^2 - 3*w - 77]', '[9988, 4994, 4993*w^2 + 4993*w + 1263]', '[9988, 4994, 4993*w^2 + 4991*w + 3427]', '[9988, 9988, 7*w^2 - 18*w + 4]', '[9988, 9988, 7*w^2 + 14*w - 36]', '[9988, 9988, w + 7762]', '[9991, 9991, 6*w^2 - 6*w - 41]', '[9991, 9991, w^2 + 9990*w + 2887]', '[9992, 2498, 2*w^2 + 2496*w + 116]', '[9992, 9992, -3*w^2 + 24*w - 28]', '[9994, 9994, 3*w^2 + 9*w - 44]', '[9994, 9994, w + 8840]', '[9995, 9995, 3*w^2 - 6*w - 25]', '[9997, 9997, 6*w^2 - 3*w - 31]', '[9998, 9998, -9*w - 4]', '[10000, 100, 10*w]', '[10000, 100, 9*w^2 + w - 91]', '[10000, 100, 5*w^2 + 85*w + 25]', '[10000, 100, 2*w^2 + 78*w + 52]', '[10000, 400, 9*w^2 + w - 66]', '[10000, 400, 5*w + 250]', '[10000, 2500, 2*w + 520]', '[10000, 2500, -5*w^2 - 9*w + 35]', '[10000, 10000, w^2 + 10*w]'], 'label': '3.3.1957.1', 'narrow_class_no': 4, 'primes': ['[2, 2, w^2]', '[4, 2, w^2 + w + 1]', '[5, 5, w]', '[11, 11, 10*w + 4]', '[13, 13, 12*w^2 + w + 7]', '[17, 17, w + 1]', '[17, 17, 16*w^2 + 16]', '[17, 17, 16*w^2 + 16*w + 8]', '[19, 19, 18*w^2 + 18*w + 1]', '[19, 19, -w^2 + 7]', '[25, 5, 4*w^2 + w + 4]', '[27, 3, -3]', '[29, 29, w + 7]', '[41, 41, 40*w^2 + 18]', '[43, 43, w^2 - 11]', '[47, 47, 2*w^2 + 2*w - 13]', '[59, 59, w^2 - 3]', '[73, 73, w^2 + 2*w - 1]', '[79, 79, w^2 + 37]', '[97, 97, w^2 + 2*w - 7]', '[101, 101, 3*w^2 + 2*w - 21]', '[103, 103, 2*w^2 + 2*w - 11]', '[103, 103, w + 85]', '[107, 107, w^2 + 88]', '[109, 109, 2*w + 7]', '[109, 109, w^2 + 108*w + 47]', '[109, 109, w + 93]', '[113, 113, -2*w - 1]', '[113, 113, 112*w^2 + w + 59]', '[113, 113, w^2 + 112*w + 70]', '[121, 11, 10*w^2 + 8*w + 8]', '[157, 157, 2*w^2 + w - 13]', '[167, 167, w^2 + 153]', '[169, 13, 12*w^2 + 9*w + 2]', '[179, 179, w^2 + 112]', '[191, 191, w^2 + 165]', '[193, 193, w^2 + w + 36]', '[193, 193, w^2 + 2*w - 11]', '[193, 193, w^2 + w + 121]', '[197, 197, 2*w^2 + 2*w - 9]', '[199, 199, w^2 - 13]', '[223, 223, w + 187]', '[227, 227, 2*w^2 - 13]', '[227, 227, w^2 + w + 99]', '[227, 227, w^2 + 60]', '[233, 233, 232*w^2 + 178]', '[241, 241, w + 85]', '[241, 241, w^2 + 240*w + 104]', '[241, 241, w - 7]', '[251, 251, 4*w^2 + 3*w - 27]', '[263, 263, w^2 + 116]', '[269, 269, 268*w + 104]', '[271, 271, w + 72]', '[277, 277, w^2 + 276*w + 88]', '[283, 283, w^2 + 4*w - 3]', '[307, 307, 2*w^2 - w - 11]', '[307, 307, w + 133]', '[307, 307, 306*w^2 + w + 284]', '[317, 317, 2*w^2 - 4*w - 3]', '[337, 337, w^2 - 2*w - 13]', '[343, 7, -7]', '[347, 347, 3*w - 11]', '[347, 347, -3*w - 1]', '[347, 347, 3*w + 7]', '[349, 349, 348*w^2 + 348*w + 191]', '[353, 353, 2*w^2 + 2*w - 19]', '[359, 359, w^2 + 4*w - 1]', '[359, 359, w^2 + 210]', '[359, 359, 358*w^2 + 346]', '[373, 373, 2*w^2 + w - 9]', '[379, 379, 3*w^2 + 2*w - 29]', '[379, 379, w^2 + w + 148]', '[379, 379, 378*w^2 + 378*w + 323]', '[389, 389, w^2 + w + 25]', '[397, 397, 396*w^2 + 118]', '[401, 401, w^2 - 2*w - 9]', '[409, 409, 4*w^2 - w - 33]', '[421, 421, 3*w^2 + 2*w - 19]', '[431, 431, -w^2 + 2*w + 17]', '[433, 433, 432*w^2 + 79]', '[433, 433, w^2 + 432*w + 7]', '[433, 433, w^2 - 2*w - 11]', '[443, 443, 4*w^2 + 2*w - 29]', '[457, 457, 2*w^2 + w - 23]', '[463, 463, 462*w^2 + 422]', '[479, 479, 2*w^2 - w - 9]', '[487, 487, 2*w^2 - 9]', '[487, 487, 2*w^2 - 2*w - 7]', '[487, 487, -2*w - 9]', '[499, 499, -5*w^2 - 4*w + 33]', '[503, 503, w^2 + 2*w - 17]', '[503, 503, 502*w^2 + 502*w + 499]', '[503, 503, 502*w^2 + 216]', '[509, 509, 2*w^2 - 7]', '[523, 523, w^2 + 104]', '[547, 547, 2*w^2 - 3*w - 11]', '[557, 557, 2*w^2 - 23]', '[571, 571, 570*w^2 + 176]', '[571, 571, 2*w^2 - w - 7]', '[571, 571, w^2 + 335]', '[577, 577, w - 9]', '[593, 593, 592*w^2 + w + 454]', '[601, 601, -w^2 - 3]', '[601, 601, 600*w^2 + 578]', '[601, 601, 600*w^2 + 45]', '[607, 607, w^2 + 360]', '[617, 617, 2*w^2 + 4*w - 13]', '[641, 641, 640*w^2 + w + 224]', '[653, 653, w + 511]', '[659, 659, 3*w^2 + 4*w - 19]', '[661, 661, w^2 + 4*w - 11]', '[661, 661, 660*w + 380]', '[661, 661, w^2 + 406]', '[673, 673, w^2 + w + 121]', '[677, 677, -3*w^2 + 2*w + 17]', '[691, 691, w^2 + 690*w + 451]', '[701, 701, -4*w^2 - 4*w + 27]', '[701, 701, 700*w^2 + 700*w + 286]', '[701, 701, w^2 + 700*w + 680]', '[709, 709, w^2 + w + 323]', '[709, 709, w^2 - 4*w - 3]', '[709, 709, w^2 + 708*w + 321]', '[719, 719, -w - 9]', '[727, 727, 726*w^2 + 126]', '[733, 733, 2*w^2 + 3*w - 17]', '[743, 743, w^2 + w + 556]', '[743, 743, 2*w^2 - 2*w - 17]', '[743, 743, w + 731]', '[751, 751, 750*w^2 + 750*w + 484]', '[761, 761, w^2 + 760*w + 725]', '[769, 769, w^2 + w + 442]', '[773, 773, 2*w - 11]', '[787, 787, 3*w^2 - 2*w - 23]', '[797, 797, w^2 + w + 454]', '[809, 809, w + 115]', '[821, 821, 2*w^2 - 2*w - 19]', '[821, 821, 2*w^2 + 3*w - 21]', '[821, 821, 4*w^2 + 3*w - 31]', '[823, 823, w^2 + 822*w + 164]', '[839, 839, w^2 + 436]', '[841, 29, w^2 + 21*w + 18]', '[853, 853, 852*w + 654]', '[853, 853, 3*w^2 - 19]', '[853, 853, 852*w^2 + 787]', '[857, 857, 3*w^2 + 8*w - 9]', '[859, 859, 858*w^2 + 85]', '[863, 863, 2*w^2 + 5*w - 13]', '[863, 863, 862*w^2 + 862*w + 92]', '[863, 863, w^2 + 862*w + 118]', '[877, 877, 876*w^2 + 876*w + 132]', '[877, 877, 2*w^2 - 4*w - 9]', '[877, 877, 876*w^2 + w + 641]', '[881, 881, -4*w^2 - w + 29]', '[883, 883, w + 163]', '[883, 883, 4*w + 9]', '[883, 883, w + 496]', '[887, 887, w^2 + 886*w + 311]', '[907, 907, 3*w - 13]', '[919, 919, w^2 + w + 131]', '[937, 937, 4*w^2 - 29]', '[941, 941, 4*w^2 + 5*w - 17]', '[947, 947, 3*w^2 - 2*w - 31]', '[953, 953, w^2 + w + 603]', '[967, 967, 2*w^2 - 3*w - 13]', '[977, 977, -2*w^2 - 7*w + 13]', '[983, 983, 982*w^2 + w + 923]', '[991, 991, -4*w^2 + 2*w + 31]', '[997, 997, w + 645]']}
• 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': [10, -9, -1, 1], 'conductor': 0, 'degree': 3, 'dirichlet_group': [], 'disc_abs': 1957, 'disc_rad': 1957, 'disc_sign': 1, 'frobs': [[2, [[2, 1], [1, 1]]], [3, [[3, 1]]], [5, [[2, 1], [1, 1]]], [7, [[3, 1]]], [11, [[2, 1], [1, 1]]], [13, [[2, 1], [1, 1]]], [17, [[1, 3]]], [19, [0]], [23, [[3, 1]]], [29, [[2, 1], [1, 1]]], [31, [[3, 1]]], [37, [[3, 1]]], [41, [[2, 1], [1, 1]]], [43, [[2, 1], [1, 1]]], [47, [[2, 1], [1, 1]]], [53, [[3, 1]]], [59, [[2, 1], [1, 1]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [3, 3], 'galois_label': '3T2', 'galt': 2, 'grd': 44.23799272118933, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '3.3.1957.1', 'local_algs': ['19.1.0.1', '19.2.1.2', '103.1.0.1', '103.2.1.1'], 'monogenic': 1, 'num_ram': 2, 'r2': 0, 'ramps': [19, 103], 'rd': 12.5082612057, 'regulator': {'__RealLiteral__': 0, 'data': '4.5514507373', 'prec': 40}, 'res': {'gal': ['68,248,111,-90,-49,0,1']}, 'subfield_mults': [], 'subfields': [], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( a - 1 \\)', '\\( a - 3 \\)'], 'unitsGmodule': [[3, 1], [5, 1]], 'used_grh': False, 'zk': ['1', 'a', 'a^2']}