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lfunc_lfunctions • Show schema
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{'Lhash': '3444021051711639743327179836373', 'a10': 0, 'a2': 1, 'a3': 0, 'a4': -1, 'a5': 0, 'a6': 0, 'a7': -2, 'a8': -3, 'a9': -3, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3.79289409601082, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[5, [1]], [19, [1, -1]]], 'bad_primes': [5, 19], 'central_character': '475.1', 'coefficient_field': '1.1.1.1', 'conductor': 475, 'conductor_radical': 95, 'degree': 2, 'euler_factors': [[1, -1, 2], [1, 0, 3], [1], [1, 2, 7], [1, 4, 11], [1, -2, 13], [1, 4, 17], [1, -1], [1, -6, 23], [1, 6, 29], [1, 4, 31], [1, -10, 37], [1, 10, 41], [1, 2, 43], [1, -6, 47], [1, 10, 53], [1, 0, 59], [1, -2, 61], [1, 8, 67], [1, -4, 71], [1, 4, 73], [1, -4, 79], [1, -18, 83], [1, 2, 89], [1, 6, 97], [1, 6, 101], [1, 16, 103], [1, -4, 107], [1, -6, 109], [1, 6, 113]], 'euler_factors_factorization': [[[[1, -1, 2], 1]], [[[1, 0, 3], 1]], [1], [[[1, 2, 7], 1]], [[[1, 4, 11], 1]], [[[1, -2, 13], 1]], [[[1, 4, 17], 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0.07596798446555719, -0.32269261579619796, -0.49025950164179044, -0.3310622278454458, 0.10290705655640546, 0.6295042181400129], 'positive_zeros': ['2.71685356445346523746983648242638', '3.56253018952603651968369317882082', '4.88960236344040300877313120060307', '5.66703630365227380430433843993478', '6.56197008088421338178147885328515', '7.910634270974764100222562199419539', '8.884496394435335630734933815789511', '9.497197103514413153205439327665785', '10.75372555761590942712128571002548'], 'prelabel': '2-475-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 1.9475353901818626, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c1-0', 'trace_hash': 1893259189855563151, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.71685356445346523746983648243', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.56253018952603651968369317882', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.88960236344040300877313120060', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 3.79289409601082, 'bad_primes': [5, 19], 'central_character': '1.1', 'conductor': 475, 'conductor_radical': 95, 'degree': 2, 'dirichlet_coefficients': [1, 1, 0, -1, 0, 0, -2, -3, -3, 0, -4, 0, 2, -2, 0, -1, -4, -3, 1, 0, 0, -4, 6, 0, 0, 2, 0, 2, -6, 0, -4, 5, 0, -4, 0, 3, 10, 1, 0, 0, -10, 0, -2, 4, 0, 6, 6, 0, -3, 0, 0, -2, -10, 0, 0, 6, 0, -6, 0, 0, 2, -4, 6, 7, 0, 0, -8, 4, 0, 0, 4, 9, -4, 10, 0, -1, 8, 0, 4, 0, 9, -10, 18, 0, 0, -2, 0, 12, -2, 0, -4, -6, 0, 6, 0, 0, -6, -3, 12, 0], 'euler11': [1, 4, 11], 'euler13': [1, -2, 13], 'euler17': [1, 4, 17], 'euler19': [1, -1, 0], 'euler2': [1, -1, 2], 'euler23': [1, -6, 23], 'euler29': [1, 6, 29], 'euler3': [1, 0, 3], 'euler31': [1, 4, 31], 'euler37': [1, -10, 37], 'euler41': [1, 10, 41], 'euler43': [1, 2, 43], 'euler47': [1, -6, 47], 'euler5': [1, 0, 0], 'euler53': [1, 10, 53], 'euler59': [1, 0, 59], 'euler61': [1, -2, 61], 'euler67': [1, 8, 67], 'euler7': [1, 2, 7], 'euler71': [1, -4, 71], 'euler73': [1, 4, 73], 'euler79': [1, -4, 79], 'euler83': [1, -18, 83], 'euler89': [1, 2, 89], 'euler97': [1, 6, 97], 'euler_factors': [[1, -1, 2], [1, 0, 3], [1, 0, 0], [1, 2, 7], [1, 4, 11], [1, -2, 13], [1, 4, 17], [1, -1, 0], [1, -6, 23], [1, 6, 29], [1, 4, 31], [1, -10, 37], [1, 10, 41], [1, 2, 43], [1, -6, 47], [1, 10, 53], [1, 0, 59], [1, -2, 61], [1, 8, 67], [1, -4, 71], [1, 4, 73], [1, -4, 79], [1, -18, 83], [1, 2, 89], [1, 6, 97]], 'index': 26, 'instance_types': ['ECQ', 'CMF', 'CMF'], 'instance_urls': ['EllipticCurve/Q/475/c', 'ModularForm/GL2/Q/holomorphic/475/2/a/c/1/1', 'ModularForm/GL2/Q/holomorphic/475/2/a/c'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, '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': '2-475-1.1-c1-0-26', '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': '2-475-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 1.9475353901818626, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1893259189855563151, 'z1': {'__RealLiteral__': 0, 'data': '2.71685356445346523746983648243', 'prec': 103}}
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lfunc_instances • Show schema
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id: 10997797
{'Lhash': '3444021051711639743327179836373', 'Lhash_array': ['3444021051711639743327179836373'], 'label': '2-475-1.1-c1-0-26', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/475/2/a/c'}
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id: 24549480
{'Lhash': '3444021051711639743327179836373', 'Lhash_array': ['3444021051711639743327179836373'], 'label': '2-475-1.1-c1-0-26', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/475/2/a/c/1/1'}
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id: 40453
{'Lhash': '1893259189855563151', 'Lhash_array': ['1893259189855563151'], 'label': '2-475-1.1-c1-0-26', 'type': 'ECQ', 'url': 'EllipticCurve/Q/475/c'}