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lfunc_lfunctions • Show schema
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{'Lhash': '3892598544348762261820842570541', 'a10': 1, 'a2': 1, 'a3': -1, 'a4': 1, 'a5': 1, 'a6': -1, 'a7': -2, 'a8': 1, 'a9': -2, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.46313233172342644, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, -1]], [29, [1, 1]]], 'bad_primes': [2, 29], 'central_character': '58.1', 'coefficient_field': '1.1.1.1', 'conductor': 58, 'conductor_radical': 58, 'degree': 2, 'euler_factors': [[1, -1], [1, 1, 3], [1, -1, 5], [1, 2, 7], [1, 3, 11], [1, 1, 13], [1, -8, 17], [1, 0, 19], [1, -4, 23], [1, 1], [1, 3, 31], [1, -8, 37], [1, -2, 41], [1, 11, 43], [1, -13, 47], [1, 11, 53], [1, 0, 59], [1, 8, 61], [1, 12, 67], [1, -2, 71], [1, -4, 73], [1, -15, 79], [1, -4, 83], [1, 10, 89], [1, 2, 97], [1, 8, 101], [1, -14, 103], [1, 2, 107], [1, -5, 109], [1, 6, 113]], 'euler_factors_factorization': [[[[1, -1], 1]], [[[1, 1, 3], 1]], [[[1, -1, 5], 1]], [[[1, 2, 7], 1]], [[[1, 3, 11], 1]], [[[1, 1, 13], 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3.200469088811479, 2.7601889978433296, 2.0598675759850793, 1.2486891431205318, 0.49225059964947776, -0.06124156118975026, -0.3110897979998223, -0.22425918653869645, 0.15868017918201396], 'positive_zeros': ['3.07071881135695746551942332894698', '5.25136790623537531107690201815860', '6.11658999858863662469236119804230', '7.71436185563727090632996745083086', '9.633495492381883994739439375568316', '10.74800585012115946663581328742246', '12.00978753036483029980569259297615', '12.92256133309152763022923630908415', '13.99719858770620348924737003172946', '15.09322040009074974335092601729420'], 'prelabel': '2-58-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 0.6805382661712907, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c1-0', 'trace_hash': 708012337630994629, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '3.07071881135695746551942332895', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '5.25136790623537531107690201816', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '6.11658999858863662469236119804', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.46313233172342644, 'bad_primes': [2, 29], 'central_character': '1.1', 'conductor': 58, 'conductor_radical': 58, 'degree': 2, 'dirichlet_coefficients': [1, 1, -1, 1, 1, -1, -2, 1, -2, 1, -3, -1, -1, -2, -1, 1, 8, -2, 0, 1, 2, -3, 4, -1, -4, -1, 5, -2, -1, -1, -3, 1, 3, 8, -2, -2, 8, 0, 1, 1, 2, 2, -11, -3, -2, 4, 13, -1, -3, -4, -8, -1, -11, 5, -3, -2, 0, -1, 0, -1, -8, -3, 4, 1, -1, 3, -12, 8, -4, -2, 2, -2, 4, 8, 4, 0, 6, 1, 15, 1, 1, 2, 4, 2, 8, -11, 1, -3, -10, -2, 2, 4, 3, 13, 0, -1, -2, -3, 6, -4], 'euler11': [1, 3, 11], 'euler13': [1, 1, 13], 'euler17': [1, -8, 17], 'euler19': [1, 0, 19], 'euler2': [1, -1, 0], 'euler23': [1, -4, 23], 'euler29': [1, 1, 0], 'euler3': [1, 1, 3], 'euler31': [1, 3, 31], 'euler37': [1, -8, 37], 'euler41': [1, -2, 41], 'euler43': [1, 11, 43], 'euler47': [1, -13, 47], 'euler5': [1, -1, 5], 'euler53': [1, 11, 53], 'euler59': [1, 0, 59], 'euler61': [1, 8, 61], 'euler67': [1, 12, 67], 'euler7': [1, 2, 7], 'euler71': [1, -2, 71], 'euler73': [1, -4, 73], 'euler79': [1, -15, 79], 'euler83': [1, -4, 83], 'euler89': [1, 10, 89], 'euler97': [1, 2, 97], 'euler_factors': [[1, -1, 0], [1, 1, 3], [1, -1, 5], [1, 2, 7], [1, 3, 11], [1, 1, 13], [1, -8, 17], [1, 0, 19], [1, -4, 23], [1, 1, 0], [1, 3, 31], [1, -8, 37], [1, -2, 41], [1, 11, 43], [1, -13, 47], [1, 11, 53], [1, 0, 59], [1, 8, 61], [1, 12, 67], [1, -2, 71], [1, -4, 73], [1, -15, 79], [1, -4, 83], [1, 10, 89], [1, 2, 97]], 'index': 0, 'instance_types': ['ECQ', 'CMF', 'CMF'], 'instance_urls': ['EllipticCurve/Q/58/b', 'ModularForm/GL2/Q/holomorphic/58/2/a/b/1/1', 'ModularForm/GL2/Q/holomorphic/58/2/a/b'], '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': '2-58-1.1-c1-0-0', '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': '2-58-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 0.6805382661712907, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 708012337630994629, 'z1': {'__RealLiteral__': 0, 'data': '3.07071881135695746551942332895', 'prec': 103}}
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lfunc_instances • Show schema
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id: 9957120
{'Lhash': '3892598544348762261820842570541', 'Lhash_array': ['3892598544348762261820842570541'], 'label': '2-58-1.1-c1-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/58/2/a/b'}
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id: 24546213
{'Lhash': '3892598544348762261820842570541', 'Lhash_array': ['3892598544348762261820842570541'], 'label': '2-58-1.1-c1-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/58/2/a/b/1/1'}
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id: 21964
{'Lhash': '708012337630994629', 'Lhash_array': ['708012337630994629'], 'label': '2-58-1.1-c1-0-0', 'type': 'ECQ', 'url': 'EllipticCurve/Q/58/b'}