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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': -2, 'A3': 3, 'A4': 2, 'A5': 0, 'A6': -6, 'A7': 1, 'A8': 0, 'A9': 6, 'Lhash': '458412309968540338', 'a10': [0.0, 0], 'a2': [-1.414213562373095, 0], 'a3': [1.7320508075688774, 0], 'a4': [1.0, 0], 'a5': [0.0, 0], 'a6': [-2.4494897427831783, 0], 'a7': [0.3779644730092272, 0], 'a8': [0.0, 0], 'a9': [2.0, 0], 'algebraic': True, 'analytic_conductor': 273.2880009178322, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[5, [1]], [37, [1]]], 'bad_primes': [5, 37], 'central_character': '34225.1', 'coefficient_field': '1.1.1.1', 'conductor': 34225, 'conductor_radical': 185, 'degree': 2, 'euler_factors': [[1, 2, 2], [1, -3, 3], [1], [1, -1, 7], [1, 5, 11], [1, 2, 13], [1, 0, 17], [1, 0, 19], [1, -2, 23], [1, 6, 29], [1, -4, 31], [1], [1, 9, 41], [1, -2, 43], [1, -9, 47], [1, 1, 53], [1, 8, 59], [1, -8, 61], [1, 8, 67], [1, -9, 71], [1, -1, 73], [1, 4, 79], [1, -15, 83], [1, 4, 89], [1, -4, 97]], 'gamma_factors': [[], [0]], 'index': 8, 'label': '2-185e2-1.1-c1-0-8', 'leading_term': '4.91631791139', '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': 1, 'origin': 'EllipticCurve/Q/34225/c', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [0.0, 1.144438565682133, 1.783761682576974, 1.520927120886844, 0.3952760632056844, -0.9113660608280492, -1.465099817351927, -0.9317770365732628, -0.04059200295784065, 0.0797336735947233, -0.7499554172358892, -1.28410291431343, -0.2364720681426447, 1.722662674588584, 2.000757489444481, -1.050740599227704, -5.404337589927234, -6.693789624337348, -3.231406180476837, 0.9813318744543232, -0.05656529872801006, -7.082451201769034, -13.42453710854608, -11.70004716238846, -2.221823041924217, 7.028347512232707, 9.098430767925228, 4.943644851079416, 0.6387048031779352, -0.342534923635037, 0.3576761226554719, 0.3048023379159503, -0.205762144262868, 0.026622659887232, 0.4552647634609577, 0.06413104356764074, -0.4037749760884628, 0.1708655715536597, 0.8946086854869832, 0.4091655680192484, -0.2178520998570677, 0.7153488847252186, 1.662762678143113, -0.06836415395885327, -2.292709461695483, 0.5315437796935593, 7.771545943134198, 10.52266539655948, 3.559528333479763, -5.678889119066338, -6.586439774215081, -0.2134591999644742, 3.484691547862464, 1.194356087501799, -0.5385536058001359, 1.899664279495917, 3.36624567541959, 0.2908849996350422, -2.505781571600663, -0.6695153935335476, 2.020275308064993, 1.125845744516088, -0.4577182980198245, 0.9984683260952228, 2.137518164648363, -1.048308150030611, -4.670031782298405, -3.278258634824149, 0.2506448061145236, -0.1560081102553576, -3.143749969318983, -3.183210350999951, -0.5701573927224765, 0.3716064528016305, -0.4151438464067303, -0.1733220590899645, 0.4419186033800216, -0.3218339349837249, -0.7744619233518445, 0.3946708905289405, 0.7460524495096582, -0.5812912692807451, -0.7013678579034421, 0.2912719822828439, -0.7370484205481009, -1.023176516895775, 4.80524909369098, 10.76299054188751, 5.424385390282012, -5.365698245583038, -2.315135116819459, 15.2933233446279, 24.4091508653456, 13.53690935416366, -0.3434109448348484, -0.9403422401072221, 4.385289302182842, 3.320983580264166, -0.9103021978100515, -0.8722843087957531, 0.8754260474964523, 0.06821637207265689, -0.8722596243185853, -0.0081649842859596, 0.3032051788538021, -0.2943690399365406, -0.007566845585063043, 0.1615010022521837, -0.5963750139993702, -0.03859590768615432, 1.197158366708721, -0.5245194661458225, -2.954153948876151, -0.8197322448204197, 2.544994968565046, 0.8599276290775282, -1.609104983019052, 1.450386259909889, 4.106863002406126, -0.2155477892028123, -4.279519267586071], 'positive_zeros': ['1.071012726527684', '2.016121581401957', '2.287126256220979', '3.031191200693463', '3.686354422774425', '4.672645125050427', '4.996908218077302', '6.051168246591496', '7.073845592528331', '7.375651259153501', '7.878134393030590', '8.238111601065694', '8.772973053818475', '9.204167625888170', '9.863050165904891', '10.11015786669984', '10.74404485652910', '11.22702567378086', '12.08568022574822', '12.75813308784845', '13.35149762478085', '13.59041395500666', '14.26753474674523', '14.79876956505917', '15.38332815413334', '15.63417541494859', '16.19166883733377', '16.97381458083153', '17.23476732639365', '18.07270645671752', '18.37309139982240', '18.79841459950894', '19.17720236498270', '19.67861915754301'], 'prelabel': '2-185e2-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 16.531424648766126, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 458412309968540338, 'z1': {'__RealLiteral__': 0, 'data': '1.071012726527684', 'prec': 57}, 'z2': {'__RealLiteral__': 0, 'data': '2.016121581401957', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '2.287126256220979', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 273.2880009178322, 'bad_primes': [5, 37], 'central_character': '1.1', 'conductor': 34225, 'conductor_radical': 185, 'degree': 2, 'dirichlet_coefficients': [1, -2, 3, 2, 0, -6, 1, 0, 6, 0, -5, 6, -2, -2, 0, -4, 0, -12, 0, 0, 3, 10, 2, 0, 0, 4, 9, 2, -6, 0, 4, 8, -15, 0, 0, 12, 0, 0, -6, 0, -9, -6, 2, -10, 0, -4, 9, -12, -6, 0, 0, -4, -1, -18, 0, 0, 0, 12, -8, 0, 8, -8, 6, -8, 0, 30, -8, 0, 6, 0, 9, 0, 1, 0, 0, 0, -5, 12, -4, 0, 9, 18, 15, 6, 0, -4, -18, 0, -4, 0, -2, 4, 12, -18, 0, 24, 4, 12, -30, 0], 'euler11': [1, 5, 11], 'euler13': [1, 2, 13], 'euler17': [1, 0, 17], 'euler19': [1, 0, 19], 'euler2': [1, 2, 2], 'euler23': [1, -2, 23], 'euler29': [1, 6, 29], 'euler3': [1, -3, 3], 'euler31': [1, -4, 31], 'euler37': [1, 0, 0], 'euler41': [1, 9, 41], 'euler43': [1, -2, 43], 'euler47': [1, -9, 47], 'euler5': [1, 0, 0], 'euler53': [1, 1, 53], 'euler59': [1, 8, 59], 'euler61': [1, -8, 61], 'euler67': [1, 8, 67], 'euler7': [1, -1, 7], 'euler71': [1, -9, 71], 'euler73': [1, -1, 73], 'euler79': [1, 4, 79], 'euler83': [1, -15, 83], 'euler89': [1, 4, 89], 'euler97': [1, -4, 97], 'euler_factors': [[1, 2, 2], [1, -3, 3], [1, 0, 0], [1, -1, 7], [1, 5, 11], [1, 2, 13], [1, 0, 17], [1, 0, 19], [1, -2, 23], [1, 6, 29], [1, -4, 31], [1, 0, 0], [1, 9, 41], [1, -2, 43], [1, -9, 47], [1, 1, 53], [1, 8, 59], [1, -8, 61], [1, 8, 67], [1, -9, 71], [1, -1, 73], [1, 4, 79], [1, -15, 83], [1, 4, 89], [1, -4, 97]], 'index': 8, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/34225/c'], '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': '2-185e2-1.1-c1-0-8', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'prelabel': '2-185e2-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 16.531424648766126, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 458412309968540338, 'z1': {'__RealLiteral__': 0, 'data': '1.071012726527684', 'prec': 57}}
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lfunc_instances • Show schema
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{'Lhash': '458412309968540338', 'Lhash_array': ['458412309968540338'], 'label': '2-185e2-1.1-c1-0-8', 'type': 'ECQ', 'url': 'EllipticCurve/Q/34225/c'}