Database - lfunc_search (L-function search data)

Formats: - HTML - YAML - JSON - 2026-07-28T17:59:21.471015

Query: /api/lfunc_search/?_offset=0

Column	Type
algebraic	boolean
analytic_conductor	double precision
bad_primes	bigint[]
central_character	text
conductor	numeric
conductor_radical	bigint
degree	smallint
dirichlet_coefficients	numeric[]
euler11	numeric[]
euler13	numeric[]
euler17	numeric[]
euler19	numeric[]
euler2	numeric[]
euler23	numeric[]
euler29	numeric[]
euler3	numeric[]
euler31	numeric[]
euler37	numeric[]
euler41	numeric[]
euler43	numeric[]
euler47	numeric[]
euler5	numeric[]
euler53	numeric[]
euler59	numeric[]
euler61	numeric[]
euler67	numeric[]
euler7	numeric[]
euler71	numeric[]
euler73	numeric[]
euler79	numeric[]
euler83	numeric[]
euler89	numeric[]
euler97	numeric[]
euler_factors	numeric[]
index	smallint
instance_types	text[]
instance_urls	text[]
is_instance_Artin	boolean
is_instance_BMF	boolean
is_instance_CMF	boolean
is_instance_DIR	boolean
is_instance_ECNF	boolean
is_instance_ECQ	boolean
is_instance_G2Q	boolean
is_instance_HMF	boolean
is_instance_MaassGL3	boolean
is_instance_MaassGL4	boolean
is_instance_MaassGSp4	boolean
is_instance_NF	boolean
label	text
motivic_weight	smallint
mu_imag	numeric[]
mu_real	smallint[]
nu_imag	numeric[]
nu_real_doubled	smallint[]
order_of_vanishing	smallint
prelabel	text
primitive	boolean
rational	boolean
root_analytic_conductor	double precision
root_angle	double precision
self_dual	boolean
spectral_label	text
trace_hash	bigint
z1	numeric

{'algebraic': True, 'analytic_conductor': 45198215.92454344, 'bad_primes': [2, 3, 7], 'central_character': '1.1', 'conductor': 2734666915254600153252096, 'conductor_radical': 42, 'degree': 16, 'dirichlet_coefficients': [1, 0, 0, 2, 0, 0, -8, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, -24, 0, 0, 0, 0, 0, -4, 0, 0, -16, 0, 0, 12, 0, 0, 0, 0, 0, -16, 0, 0, 0, 0, 0, -16, 0, 0, 0, 0, 0, 12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -24, 0, 0, -2, 0, 0, 40, 0, 0, 0, 0, 0, 24, 0, 0, -48, 0, 0, 28, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -60, 0, 0, -8], 'euler11': [1, 0, -52, 0, 1498, 0, -27664, 0, 361795, 0, -3347344, 0, 21932218, 0, -92121172, 0, 214358881], 'euler13': [1, 0, 40, 0, 862, 0, 16000, 0, 245683, 0, 2704000, 0, 24619582, 0, 193072360, 0, 815730721], 'euler17': [1, 0, -32, 0, 478, 0, 1024, 0, -81341, 0, 295936, 0, 39923038, 0, -772402208, 0, 6975757441], 'euler19': [1, 24, 328, 3264, 26110, 176904, 1043584, 5433864, 25126003, 103243416, 376733824, 1213384536, 3402681310, 8081987136, 15431048968, 21452921736, 16983563041], 'euler2': [1, 0, -2, 0, 3, 0, -2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0], 'euler23': [1, 0, -112, 0, 6820, 0, -265552, 0, 7270534, 0, -140477008, 0, 1908515620, 0, -16580019568, 0, 78310985281], 'euler29': [1, 0, 62, 0, 1849, 0, 19406, 0, 39940, 0, 16320446, 0, 1307762569, 0, 36879045902, 0, 500246412961], 'euler3': [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'euler31': [1, -12, 82, -408, 385, -1512, 51586, -655068, 5497828, -20307108, 49574146, -45043992, 355555585, -11680693608, 72775301842, -330151369332, 852891037441], 'euler37': [1, 16, 48, -160, 2702, 22224, -54272, 598384, 12519891, 22140208, -74298368, 1125712272, 5063983022, -11095033120, 123154867632, 1518910034128, 3512479453921], 'euler41': [1, 0, -20, 0, 1546, 0, 90160, 0, -2184845, 0, 151558960, 0, 4368626506, 0, -95002084820, 0, 7984925229121], 'euler43': [1, 16, 24, -352, 5054, 38544, -182912, 629392, 24542739, 27063856, -338204288, 3064517808, 17278620254, -51746971936, 151712713176, 4349097777712, 11688200277601], 'euler47': [1, 0, -152, 0, 13198, 0, -834176, 0, 42212419, 0, -1842694784, 0, 64402029838, 0, -1638440730008, 0, 23811286661761], 'euler5': [1, 0, 4, 0, -38, 0, 16, 0, 1891, 0, 400, 0, -23750, 0, 62500, 0, 390625], 'euler53': [1, 0, 158, 0, 13753, 0, 883694, 0, 47672164, 0, 2482296446, 0, 108517785193, 0, 3501969058382, 0, 62259690411361], 'euler59': [1, 0, -38, 0, -4727, 0, 30058, 0, 20937316, 0, 104631898, 0, -57278765447, 0, -1602860278358, 0, 146830437604321], 'euler61': [1, 24, 496, 7296, 99022, 1102248, 11405824, 102041592, 854498995, 6224537112, 42441071104, 250189353288, 1371042867502, 6162174612096, 25554105683056, 75425828064504, 191707312997281], 'euler67': [1, -40, 732, -10640, 154490, -1870680, 18641392, -180193480, 1615010499, -12072963160, 83681208688, -562631328840, 3113146683290, -14365331138480, 66215535747708, -242428464212920, 406067677556641], 'euler7': [1, 8, 52, 200, 646, 1400, 2548, 2744, 2401, 0, 0, 0, 0, 0, 0, 0, 0], 'euler71': [1, 0, -352, 0, 61444, 0, -7136800, 0, 595198150, 0, -35976608800, 0, 1561395327364, 0, -45091299940192, 0, 645753531245761], 'euler73': [1, -24, 508, -7584, 103978, -1207224, 13214320, -127218552, 1159585075, -9286954296, 70419111280, -469630658808, 2952792302698, -15722174961312, 76877786954812, -265137564458328, 806460091894081], 'euler79': [1, -28, 210, -1064, 40193, -466536, 1431682, -27656860, 497431332, -2184891940, 8935127362, -230020442904, 1565520605633, -3273988008536, 51048365659410, -537709451612452, 1517108809906561], 'euler83': [1, 0, -278, 0, 44473, 0, -5291174, 0, 496693924, 0, -36450897686, 0, 2110613909833, 0, -90889423796582, 0, 2252292232139041], 'euler89': [1, 0, -140, 0, -1142, 0, -686000, 0, 212236723, 0, -5433806000, 0, -71651639222, 0, -69577380734540, 0, 3936588805702081], 'euler97': [1, 60, 1990, 47400, 897457, 14220360, 193945750, 2311375380, 24244292068, 224203411860, 1824835561750, 12978538622280, 79451222938417, 407039928181800, 1657614289808710, 4847897068686780, 7837433594376961], 'euler_factors': [[1, 0, -2, 0, 3, 0, -2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 4, 0, -38, 0, 16, 0, 1891, 0, 400, 0, -23750, 0, 62500, 0, 390625], [1, 8, 52, 200, 646, 1400, 2548, 2744, 2401, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, -52, 0, 1498, 0, -27664, 0, 361795, 0, -3347344, 0, 21932218, 0, -92121172, 0, 214358881], [1, 0, 40, 0, 862, 0, 16000, 0, 245683, 0, 2704000, 0, 24619582, 0, 193072360, 0, 815730721], [1, 0, -32, 0, 478, 0, 1024, 0, -81341, 0, 295936, 0, 39923038, 0, -772402208, 0, 6975757441], [1, 24, 328, 3264, 26110, 176904, 1043584, 5433864, 25126003, 103243416, 376733824, 1213384536, 3402681310, 8081987136, 15431048968, 21452921736, 16983563041], [1, 0, -112, 0, 6820, 0, -265552, 0, 7270534, 0, -140477008, 0, 1908515620, 0, -16580019568, 0, 78310985281], [1, 0, 62, 0, 1849, 0, 19406, 0, 39940, 0, 16320446, 0, 1307762569, 0, 36879045902, 0, 500246412961], [1, -12, 82, -408, 385, -1512, 51586, -655068, 5497828, -20307108, 49574146, -45043992, 355555585, -11680693608, 72775301842, -330151369332, 852891037441], [1, 16, 48, -160, 2702, 22224, -54272, 598384, 12519891, 22140208, -74298368, 1125712272, 5063983022, -11095033120, 123154867632, 1518910034128, 3512479453921], [1, 0, -20, 0, 1546, 0, 90160, 0, -2184845, 0, 151558960, 0, 4368626506, 0, -95002084820, 0, 7984925229121], [1, 16, 24, -352, 5054, 38544, -182912, 629392, 24542739, 27063856, -338204288, 3064517808, 17278620254, -51746971936, 151712713176, 4349097777712, 11688200277601], [1, 0, -152, 0, 13198, 0, -834176, 0, 42212419, 0, -1842694784, 0, 64402029838, 0, -1638440730008, 0, 23811286661761], [1, 0, 158, 0, 13753, 0, 883694, 0, 47672164, 0, 2482296446, 0, 108517785193, 0, 3501969058382, 0, 62259690411361], [1, 0, -38, 0, -4727, 0, 30058, 0, 20937316, 0, 104631898, 0, -57278765447, 0, -1602860278358, 0, 146830437604321], [1, 24, 496, 7296, 99022, 1102248, 11405824, 102041592, 854498995, 6224537112, 42441071104, 250189353288, 1371042867502, 6162174612096, 25554105683056, 75425828064504, 191707312997281], [1, -40, 732, -10640, 154490, -1870680, 18641392, -180193480, 1615010499, -12072963160, 83681208688, -562631328840, 3113146683290, -14365331138480, 66215535747708, -242428464212920, 406067677556641], [1, 0, -352, 0, 61444, 0, -7136800, 0, 595198150, 0, -35976608800, 0, 1561395327364, 0, -45091299940192, 0, 645753531245761], [1, -24, 508, -7584, 103978, -1207224, 13214320, -127218552, 1159585075, -9286954296, 70419111280, -469630658808, 2952792302698, -15722174961312, 76877786954812, -265137564458328, 806460091894081], [1, -28, 210, -1064, 40193, -466536, 1431682, -27656860, 497431332, -2184891940, 8935127362, -230020442904, 1565520605633, -3273988008536, 51048365659410, -537709451612452, 1517108809906561], [1, 0, -278, 0, 44473, 0, -5291174, 0, 496693924, 0, -36450897686, 0, 2110613909833, 0, -90889423796582, 0, 2252292232139041], [1, 0, -140, 0, -1142, 0, -686000, 0, 212236723, 0, -5433806000, 0, -71651639222, 0, -69577380734540, 0, 3936588805702081], [1, 60, 1990, 47400, 897457, 14220360, 193945750, 2311375380, 24244292068, 224203411860, 1824835561750, 12978538622280, 79451222938417, 407039928181800, 1657614289808710, 4847897068686780, 7837433594376961]], 'id': 23571400, 'index': 2, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1134/2/t/e'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': False, 'is_instance_G2Q': False, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '16-1134e8-1.1-c1e8-0-2', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1, 1, 1, 1, 1, 1, 1, 1], 'order_of_vanishing': 0, 'prelabel': '16-1134e8-1.1-c1e8-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 3.00915861815445, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e8-0', 'trace_hash': 1034817602746479228, 'z1': {'__RealLiteral__': 0, 'data': '0.11716644861599742430740308123', 'prec': 103}}