Database - lfunc_search (L-function search data)

Formats: - HTML - YAML - JSON - 2026-04-29T15:59:52.019059

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': 42831.74153291534, 'bad_primes': [5, 19], 'central_character': '1.1', 'conductor': 2591486059722900390625, 'conductor_radical': 95, 'degree': 16, 'dirichlet_coefficients': [1, 0, 0, 0, 0, 0, 0, 0, 4, 0, 8, 0, 0, 0, 0, -6, 0, 0, -8, 0, 0, 0, 0, 0, 0, 0, 0, 0, -8, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 32, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 40, 0, 0, 4, 0, 0, 0, 0, 0, 0, -40, 0, 0, 0, 0, 0, 0, 0, 32, 0, 4, 0, 0, 0, 0, 0, 0, 0, -8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 32, 0], 'euler11': [1, -8, 72, -424, 2428, -11176, 49208, -183752, 659686, -2021272, 5954168, -14875256, 35548348, -68285624, 127552392, -155897368, 214358881], 'euler13': [1, 0, -52, 0, 1420, 0, -27916, 0, 417622, 0, -4717804, 0, 40556620, 0, -250994068, 0, 815730721], 'euler17': [1, 0, -56, 0, 1180, 0, -9864, 0, 38854, 0, -2850696, 0, 98554780, 0, -1351703864, 0, 6975757441], 'euler19': [1, 8, 28, 56, 70, 56, 28, 8, 1, 0, 0, 0, 0, 0, 0, 0, 0], 'euler2': [1, 0, 0, 0, 6, 0, -4, 0, 17, 0, -16, 0, 96, 0, 0, 0, 256], 'euler23': [1, 0, -72, 0, 3324, 0, -112888, 0, 2951366, 0, -59717752, 0, 930191484, 0, -10658584008, 0, 78310985281], 'euler29': [1, 8, 184, 1336, 16188, 100936, 872520, 4527800, 30940838, 131306200, 733789320, 2461728104, 11449464828, 27402895064, 109447491064, 137999010472, 500246412961], 'euler3': [1, 0, -4, 0, 12, 0, -60, 0, 214, 0, -540, 0, 972, 0, -2916, 0, 6561], 'euler31': [1, -8, 104, -72, 1148, 19672, 84056, -148200, 7764102, -4594200, 80777816, 586048552, 1060202108, -2061298872, 92300382824, -220100912888, 852891037441], 'euler37': [1, 0, -212, 0, 20748, 0, -1267308, 0, 54701334, 0, -1734944652, 0, 38885092428, 0, -543933998708, 0, 3512479453921], 'euler41': [1, -32, 696, -10912, 139228, -1472608, 13380488, -104869088, 719459590, -4299632608, 22492600328, -101493615968, 393425052508, -1264222865312, 3306072551736, -6232136764192, 7984925229121], 'euler43': [1, 0, -296, 0, 40092, 0, -3238872, 0, 170514342, 0, -5988674328, 0, 137066569692, 0, -1871123462504, 0, 11688200277601], 'euler47': [1, 0, -104, 0, 7100, 0, -362840, 0, 15690118, 0, -801513560, 0, 34645735100, 0, -1121038394216, 0, 23811286661761], 'euler5': [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'euler53': [1, 0, -324, 0, 49836, 0, -4722364, 0, 301404374, 0, -13265120476, 0, 393230011116, 0, -7181253005796, 0, 62259690411361], 'euler59': [1, 0, 344, 448, 55868, 103488, 5768488, 10433920, 408831462, 615601280, 20080106728, 21254261952, 676972724348, 320286085952, 14510103572504, 0, 146830437604321], 'euler61': [1, -40, 1000, -17944, 261884, -3205864, 34218264, -320034328, 2659012134, -19522094008, 127326160344, -727670216584, 3626004224444, -15155436025144, 51520374361000, -125709713440840, 191707312997281], 'euler67': [1, 0, -228, 0, 17356, 0, 3172, 0, -58243754, 0, 14239108, 0, 349742856076, 0, -20624511134532, 0, 406067677556641], 'euler7': [1, 0, -8, 0, 60, 0, -312, 0, 198, 0, -15288, 0, 144060, 0, -941192, 0, 5764801], 'euler71': [1, 40, 1032, 19112, 290428, 3727304, 42165560, 421063624, 3765161542, 29895517304, 212556587960, 1334043101944, 7380263689468, 34482431356312, 132199493006472, 363804806335640, 645753531245761], 'euler73': [1, 0, -312, 0, 52060, 0, -5937416, 0, 497988358, 0, -31640489864, 0, 1478412426460, 0, -47216278602168, 0, 806460091894081], 'euler79': [1, -32, 952, -17760, 308380, -4129120, 51975432, -536623136, 5227209926, -42393227744, 324378671112, -2035817195680, 12011425978780, -54648521646240, 231419257655992, -614525087557088, 1517108809906561], 'euler83': [1, 0, -520, 0, 127324, 0, -19097976, 0, 1915966182, 0, -131565956664, 0, 6042583263004, 0, -170008994151880, 0, 2252292232139041], 'euler89': [1, 8, 440, 4184, 99164, 925960, 15176584, 121086744, 1625421702, 10776720216, 120213721864, 652773095240, 6221771586524, 23363704734616, 218671768022840, 353850679164232, 3936588805702081], 'euler97': [1, 0, -324, 0, 47308, 0, -4899740, 0, 476587702, 0, -46101653660, 0, 4188143225548, 0, -269882929596996, 0, 7837433594376961], 'euler_factors': [[1, 0, 0, 0, 6, 0, -4, 0, 17, 0, -16, 0, 96, 0, 0, 0, 256], [1, 0, -4, 0, 12, 0, -60, 0, 214, 0, -540, 0, 972, 0, -2916, 0, 6561], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, -8, 0, 60, 0, -312, 0, 198, 0, -15288, 0, 144060, 0, -941192, 0, 5764801], [1, -8, 72, -424, 2428, -11176, 49208, -183752, 659686, -2021272, 5954168, -14875256, 35548348, -68285624, 127552392, -155897368, 214358881], [1, 0, -52, 0, 1420, 0, -27916, 0, 417622, 0, -4717804, 0, 40556620, 0, -250994068, 0, 815730721], [1, 0, -56, 0, 1180, 0, -9864, 0, 38854, 0, -2850696, 0, 98554780, 0, -1351703864, 0, 6975757441], [1, 8, 28, 56, 70, 56, 28, 8, 1, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, -72, 0, 3324, 0, -112888, 0, 2951366, 0, -59717752, 0, 930191484, 0, -10658584008, 0, 78310985281], [1, 8, 184, 1336, 16188, 100936, 872520, 4527800, 30940838, 131306200, 733789320, 2461728104, 11449464828, 27402895064, 109447491064, 137999010472, 500246412961], [1, -8, 104, -72, 1148, 19672, 84056, -148200, 7764102, -4594200, 80777816, 586048552, 1060202108, -2061298872, 92300382824, -220100912888, 852891037441], [1, 0, -212, 0, 20748, 0, -1267308, 0, 54701334, 0, -1734944652, 0, 38885092428, 0, -543933998708, 0, 3512479453921], [1, -32, 696, -10912, 139228, -1472608, 13380488, -104869088, 719459590, -4299632608, 22492600328, -101493615968, 393425052508, -1264222865312, 3306072551736, -6232136764192, 7984925229121], [1, 0, -296, 0, 40092, 0, -3238872, 0, 170514342, 0, -5988674328, 0, 137066569692, 0, -1871123462504, 0, 11688200277601], [1, 0, -104, 0, 7100, 0, -362840, 0, 15690118, 0, -801513560, 0, 34645735100, 0, -1121038394216, 0, 23811286661761], [1, 0, -324, 0, 49836, 0, -4722364, 0, 301404374, 0, -13265120476, 0, 393230011116, 0, -7181253005796, 0, 62259690411361], [1, 0, 344, 448, 55868, 103488, 5768488, 10433920, 408831462, 615601280, 20080106728, 21254261952, 676972724348, 320286085952, 14510103572504, 0, 146830437604321], [1, -40, 1000, -17944, 261884, -3205864, 34218264, -320034328, 2659012134, -19522094008, 127326160344, -727670216584, 3626004224444, -15155436025144, 51520374361000, -125709713440840, 191707312997281], [1, 0, -228, 0, 17356, 0, 3172, 0, -58243754, 0, 14239108, 0, 349742856076, 0, -20624511134532, 0, 406067677556641], [1, 40, 1032, 19112, 290428, 3727304, 42165560, 421063624, 3765161542, 29895517304, 212556587960, 1334043101944, 7380263689468, 34482431356312, 132199493006472, 363804806335640, 645753531245761], [1, 0, -312, 0, 52060, 0, -5937416, 0, 497988358, 0, -31640489864, 0, 1478412426460, 0, -47216278602168, 0, 806460091894081], [1, -32, 952, -17760, 308380, -4129120, 51975432, -536623136, 5227209926, -42393227744, 324378671112, -2035817195680, 12011425978780, -54648521646240, 231419257655992, -614525087557088, 1517108809906561], [1, 0, -520, 0, 127324, 0, -19097976, 0, 1915966182, 0, -131565956664, 0, 6042583263004, 0, -170008994151880, 0, 2252292232139041], [1, 8, 440, 4184, 99164, 925960, 15176584, 121086744, 1625421702, 10776720216, 120213721864, 652773095240, 6221771586524, 23363704734616, 218671768022840, 353850679164232, 3936588805702081], [1, 0, -324, 0, 47308, 0, -4899740, 0, 476587702, 0, -46101653660, 0, 4188143225548, 0, -269882929596996, 0, 7837433594376961]], 'id': 10634438, 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/475/2/b/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': '16-475e8-1.1-c1e8-0-1', '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': '16-475e8-1.1-c1e8-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 1.9475353901818626, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e8-0', 'trace_hash': 623828748891625394, 'z1': {'__RealLiteral__': 0, 'data': '0.60555899744086569538930769682', 'prec': 103}}