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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': 1, 'A4': 0, 'A5': -1, 'A6': 0, 'A7': 4, 'A8': 0, 'A9': 1, 'Lhash': '2074612337621526111', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [0.5773502691896258, 0], 'a4': [0.0, 0], 'a5': [-0.4472135954999579, 0], 'a6': [0.0, 0], 'a7': [1.5118578920369088, 0], 'a8': [0.0, 0], 'a9': [0.3333333333333333, 0], 'algebraic': True, 'analytic_conductor': 1507.2561885536893, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, -1]], [5, [1, 1]], [11, [1]], [13, [1, 1]]], 'bad_primes': [2, 3, 5, 11, 13], 'central_character': '188760.1', 'coefficient_field': '1.1.1.1', 'conductor': 188760, 'conductor_radical': 4290, 'degree': 2, 'euler_factors': [[1], [1, -1], [1, 1], [1, -4, 7], [1], [1, 1], [1, -2, 17], [1, -4, 19], [1, -6, 23], [1, -2, 29], [1, 8, 31], [1, -6, 37], [1, -10, 41], [1, 8, 43], [1, -12, 47], [1, -8, 53], [1, -4, 59], [1, -2, 61], [1, 6, 67], [1, -8, 71], [1, -10, 73], [1, 0, 79], [1, 12, 83], [1, -6, 89], [1, 4, 97]], 'gamma_factors': [[], [0]], 'index': 36, 'label': '2-188760-1.1-c1-0-36', 'leading_term': '5.30934175715', 'load_key': 'Cremona', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'origin': 'EllipticCurve/Q/188760/ca', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [5.309341757148325, 4.339820584900361, 1.987370481091958, -0.1972682483142393, -0.6072205928457081, 0.7403022058014725, 1.829387769143096, 0.8548545635589472, -1.284088502235236, -1.875792369561591, -0.1887149010254531, 1.108641530283019, -0.3327245042260493, -2.748159939530729, -2.633146298092116, -0.2681182929631697, 0.5222782001866613, -1.369524875280949, -2.359223881608159, -0.392929833172826, 1.245983028522349, -0.01518071643736176, -0.5606916607001383, 3.233608555493018, 7.044319537641668, 4.282758178190656, -2.638638899924389, -5.268756393069093, -2.12655881846141, 0.4720517656796869, 0.03706188486625021, 0.3189279886066632, 2.007734411912277, 1.560865742571932, -0.287476714995316, 0.5256186832341594, 2.318164064330695, 0.6319276201046237, -1.57321471516874, 1.112387807249536, 4.720185941084962, 2.371737845119079, -2.263368137297152, -1.939216771212742, 0.477170852268787, -0.6498343547237677, -1.765470509650064, 0.90170635366527, 2.000385331964598, -1.117300008508908, -1.528116518384524, 2.482038329800261, 2.801807875404179, -1.61780808804159, -2.369304740348802, 1.046523722293408, 1.343040431156789, -0.8599911422004717, -0.3765569041165768, 0.5915435096070986, -0.2881404543018308, 1.098679986593281, 3.812390075179793, 1.519283171241148, -2.252232990875412, 0.1414321933888591, 3.323599680260526, 0.0780658997949056, -2.55501694318623, 0.8768900504518581, 2.016936542177502, -2.135943068434059, -2.893280389750575, 0.1629756111646984, 0.06688607805259048, -0.04833985598904668, 4.165516132954594, 5.622196489421135, 1.468768583062471, -0.2372016474328542, 1.224110311996853, -0.1961361294630151, -1.550305379816717, 0.6153827175494776, 0.7657839614094633, -1.281862407718455, -0.03252723534660999, -0.139132686714287, -5.491947907090617, -6.161155552702413, 0.1275503304597855, 0.7560056452483462, -4.335282725181353, -3.372908139354528, 0.7274030151384197, -0.3295041165871359, -1.273358099287226, 0.8667323339633023, -0.1237386904167045, -1.887297361259187, 0.4389599936456412, 0.8957490974358873, -1.037025817376347, 2.658140357558415, 7.140672942833703, 3.649494165066797, -0.577998757935639, 0.5017240995032433, 0.7057438193175395, -0.005295281393607734, 1.662804271147913, 0.2302683797663571, -2.787194570022916, 0.8724486809590765, 3.986841811058757, -0.8643149122917354, -1.739500092744074, 4.815093374375479, 4.655615246052606, -1.13533158713417, -0.5902637516617811], 'positive_zeros': ['0.7191450143950601', '1.135122293832302', '1.849025502620934', '2.522765654587343', '2.966350283966996', '3.782242371550832', '4.093373601135998', '4.788368029824703', '5.247996274985481', '5.562562249581583', '6.402135229388248', '7.166040227738488', '7.512657771878659', '7.681681190681212', '8.443835429358759', '8.683084715430059', '9.299803786189477', '9.686335512172352', '10.36251308075037', '10.92407716811888', '11.17666665447128', '11.68194469528614', '12.16973480834744', '12.60446276448050', '13.15992321665426', '13.67112605909631', '14.13851927575878', '14.55762268959971', '14.91623426486517', '15.13876654908515', '15.82866805847984', '16.24250578280596', '16.75397132802386', '17.19910029552802', '17.63150651027585', '18.23196939027213', '18.51093487350836', '18.75498172493650', '19.61343343765945', '19.79631572529952'], 'prelabel': '2-188760-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 38.82339743703131, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 2074612337621526111, 'z1': {'__RealLiteral__': 0, 'data': '0.7191450143950601', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.135122293832302', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '1.849025502620934', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1507.2561885536893, 'bad_primes': [2, 3, 5, 11, 13], 'central_character': '1.1', 'conductor': 188760, 'conductor_radical': 4290, 'degree': 2, 'dirichlet_coefficients': [1, 0, 1, 0, -1, 0, 4, 0, 1, 0, 0, 0, -1, 0, -1, 0, 2, 0, 4, 0, 4, 0, 6, 0, 1, 0, 1, 0, 2, 0, -8, 0, 0, 0, -4, 0, 6, 0, -1, 0, 10, 0, -8, 0, -1, 0, 12, 0, 9, 0, 2, 0, 8, 0, 0, 0, 4, 0, 4, 0, 2, 0, 4, 0, 1, 0, -6, 0, 6, 0, 8, 0, 10, 0, 1, 0, 0, 0, 0, 0, 1, 0, -12, 0, -2, 0, 2, 0, 6, 0, -4, 0, -8, 0, -4, 0, -4, 0, 0, 0], 'euler11': [1, 0, 0], 'euler13': [1, 1, 0], 'euler17': [1, -2, 17], 'euler19': [1, -4, 19], 'euler2': [1, 0, 0], 'euler23': [1, -6, 23], 'euler29': [1, -2, 29], 'euler3': [1, -1, 0], 'euler31': [1, 8, 31], 'euler37': [1, -6, 37], 'euler41': [1, -10, 41], 'euler43': [1, 8, 43], 'euler47': [1, -12, 47], 'euler5': [1, 1, 0], 'euler53': [1, -8, 53], 'euler59': [1, -4, 59], 'euler61': [1, -2, 61], 'euler67': [1, 6, 67], 'euler7': [1, -4, 7], 'euler71': [1, -8, 71], 'euler73': [1, -10, 73], 'euler79': [1, 0, 79], 'euler83': [1, 12, 83], 'euler89': [1, -6, 89], 'euler97': [1, 4, 97], 'euler_factors': [[1, 0, 0], [1, -1, 0], [1, 1, 0], [1, -4, 7], [1, 0, 0], [1, 1, 0], [1, -2, 17], [1, -4, 19], [1, -6, 23], [1, -2, 29], [1, 8, 31], [1, -6, 37], [1, -10, 41], [1, 8, 43], [1, -12, 47], [1, -8, 53], [1, -4, 59], [1, -2, 61], [1, 6, 67], [1, -8, 71], [1, -10, 73], [1, 0, 79], [1, 12, 83], [1, -6, 89], [1, 4, 97]], 'index': 36, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/188760/ca'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': False, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': True, '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': '2-188760-1.1-c1-0-36', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-188760-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 38.82339743703131, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 2074612337621526111, 'z1': {'__RealLiteral__': 0, 'data': '0.7191450143950601', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '2074612337621526111', 'Lhash_array': ['2074612337621526111'], 'label': '2-188760-1.1-c1-0-36', 'type': 'ECQ', 'url': 'EllipticCurve/Q/188760/ca'}