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lfunc_lfunctions • Show schema
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{'Lhash': '1655722336831344252543673654418', 'a10': -1, 'a2': -1, 'a3': 1, 'a4': 1, 'a5': 1, 'a6': -1, 'a7': -1, 'a8': -1, 'a9': 1, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 4.359831950361911, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, 1]], [3, [1, -1]], [7, [1, 1]], [13, [1, 1]]], 'bad_primes': [2, 3, 7, 13], 'central_character': '546.1', 'coefficient_field': '1.1.1.1', 'conductor': 546, 'conductor_radical': 546, 'degree': 2, 'euler_factors': [[1, 1], [1, -1], [1, -1, 5], [1, 1], [1, -3, 11], [1, 1], [1, -5, 17], [1, -1, 19], [1, -3, 23], [1, -5, 29], [1, -4, 31], [1, 5, 37], [1, 8, 41], [1, 1, 43], [1, -8, 47], [1, -6, 53], [1, 0, 59], [1, -13, 61], [1, 10, 67], [1, -8, 71], [1, 15, 73], [1, -6, 79], [1, 2, 83], [1, 2, 89], [1, 2, 97], [1, 16, 101], [1, -1, 103], [1, 6, 107], [1, 7, 109], [1, 6, 113]], 'euler_factors_factorization': [[[[1, 1], 1]], [[[1, -1], 1]], [[[1, -1, 5], 1]], [[[1, 1], 1]], [[[1, -3, 11], 1]], [[[1, 1], 1]], [[[1, -5, 17], 1]], [[[1, -1, 19], 1]], [[[1, -3, 23], 1]], [[[1, -5, 29], 1]], [[[1, -4, 31], 1]], [[[1, 5, 37], 1]], [[[1, 8, 41], 1]], [[[1, 1, 43], 1]], [[[1, -8, 47], 1]], [[[1, -6, 53], 1]], [[[1, 0, 59], 1]], [[[1, -13, 61], 1]], [[[1, 10, 67], 1]], [[[1, -8, 71], 1]], [[[1, 15, 73], 1]], [[[1, -6, 79], 1]], [[[1, 2, 83], 1]], [[[1, 2, 89], 1]], [[[1, 2, 97], 1]], [[[1, 16, 101], 1]], [[[1, -1, 103], 1]], [[[1, 6, 107], 1]], [[[1, 7, 109], 1]], [[[1, 6, 113], 1]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 4, 'label': '2-546-1.1-c1-0-4', 'load_key': 'CMFs-workshop', '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': 'ModularForm/GL2/Q/holomorphic/546/2/a/c', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [1.4270848852578462, 1.421897037708074, 1.4046003626241879, 1.3703589359108712, 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{'__RealLiteral__': 0, 'data': '2.71288319524339209617944628177', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.81468304746563960569702394948', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 4.359831950361911, 'bad_primes': [2, 3, 7, 13], 'central_character': '1.1', 'conductor': 546, 'conductor_radical': 546, 'degree': 2, 'dirichlet_coefficients': [1, -1, 1, 1, 1, -1, -1, -1, 1, -1, 3, 1, -1, 1, 1, 1, 5, -1, 1, 1, -1, -3, 3, -1, -4, 1, 1, -1, 5, -1, 4, -1, 3, -5, -1, 1, -5, -1, -1, -1, -8, 1, -1, 3, 1, -3, 8, 1, 1, 4, 5, -1, 6, -1, 3, 1, 1, -5, 0, 1, 13, -4, -1, 1, -1, -3, -10, 5, 3, 1, 8, -1, -15, 5, -4, 1, -3, 1, 6, 1, 1, 8, -2, -1, 5, 1, 5, -3, -2, -1, 1, 3, 4, -8, 1, -1, -2, -1, 3, -4], 'euler11': [1, -3, 11], 'euler13': [1, 1, 0], 'euler17': [1, -5, 17], 'euler19': [1, -1, 19], 'euler2': [1, 1, 0], 'euler23': [1, -3, 23], 'euler29': [1, -5, 29], 'euler3': [1, -1, 0], 'euler31': [1, -4, 31], 'euler37': [1, 5, 37], 'euler41': [1, 8, 41], 'euler43': [1, 1, 43], 'euler47': [1, -8, 47], 'euler5': [1, -1, 5], 'euler53': [1, -6, 53], 'euler59': [1, 0, 59], 'euler61': [1, -13, 61], 'euler67': [1, 10, 67], 'euler7': [1, 1, 0], 'euler71': [1, -8, 71], 'euler73': [1, 15, 73], 'euler79': [1, -6, 79], 'euler83': [1, 2, 83], 'euler89': [1, 2, 89], 'euler97': [1, 2, 97], 'euler_factors': [[1, 1, 0], [1, -1, 0], [1, -1, 5], [1, 1, 0], [1, -3, 11], [1, 1, 0], [1, -5, 17], [1, -1, 19], [1, -3, 23], [1, -5, 29], [1, -4, 31], [1, 5, 37], [1, 8, 41], [1, 1, 43], [1, -8, 47], [1, -6, 53], [1, 0, 59], [1, -13, 61], [1, 10, 67], [1, -8, 71], [1, 15, 73], [1, -6, 79], [1, 2, 83], [1, 2, 89], [1, 2, 97]], 'index': 4, 'instance_types': ['ECQ', 'CMF', 'CMF'], 'instance_urls': ['EllipticCurve/Q/546/c', 'ModularForm/GL2/Q/holomorphic/546/2/a/c/1/1', 'ModularForm/GL2/Q/holomorphic/546/2/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': '2-546-1.1-c1-0-4', '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': '2-546-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 2.0880210608042034, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 126823583312347391, 'z1': {'__RealLiteral__': 0, 'data': '1.30613462142742324235177250713', 'prec': 103}}
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lfunc_instances • Show schema
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id: 11538245
{'Lhash': '1655722336831344252543673654418', 'Lhash_array': ['1655722336831344252543673654418'], 'label': '2-546-1.1-c1-0-4', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/546/2/a/c'}
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id: 24549675
{'Lhash': '1655722336831344252543673654418', 'Lhash_array': ['1655722336831344252543673654418'], 'label': '2-546-1.1-c1-0-4', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/546/2/a/c/1/1'}
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id: 102182
{'Lhash': '126823583312347391', 'Lhash_array': ['126823583312347391'], 'label': '2-546-1.1-c1-0-4', 'type': 'ECQ', 'url': 'EllipticCurve/Q/546/c'}