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lfunc_lfunctions • Show schema
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{'Lhash': '711421117499365781630781345709', 'a10': [4356.07967462993, 0.0], 'a2': [-8.0, 0.0], 'a3': [31.019292596434994, 0.0], 'a4': [64.0, 0.0], 'a5': [-544.5099593287413, 0.0], 'a6': [-248.15434077147995, 0.0], 'a7': [-1685.4358988500903, 0.0], 'a8': [-512.0, 0.0], 'a9': [-1224.803486816753, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 23.11649188582502, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '3.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [8.0, 0]]], [37, [[1.0, 0], [50653.0, 0]]]], 'bad_primes': [2, 37], 'central_character': '74.1', 'coefficient_field': 'CDF', 'conductor': 74, 'conductor_radical': 74, 'degree': 2, 'euler_factors': [[[1.0, 0], [8.0, 0]], [[1.0, 0], [-31.019292596434994, 0], [2187.0, 0]], [[1.0, 0], [544.5099593287413, 0], [78125.0, 0]], [[1.0, 0], [1685.4358988500903, 0], [823543.0, 0]], [[1.0, 0], [-5629.716468670372, 0], [19487171.0, 0]], [[1.0, 0], [-5228.813934117642, 0], [62748517.0, 0]], [[1.0, 0], [12575.53314740744, 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'3.77905155872665571343701753993', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 23.11649188582502, 'bad_primes': [2, 37], 'central_character': '1.1', 'conductor': 74, 'conductor_radical': 74, 'degree': 2, 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/74/8/a/c/1/4'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': False, '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': '2-74-1.1-c7-0-1', 'motivic_weight': 7, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [7], 'order_of_vanishing': 0, 'prelabel': '2-74-1.1-c7-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.807961302446706, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c7-0', 'z1': {'__RealLiteral__': 0, 'data': '0.56121230674389349300985486201', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '711421117499365781630781345709', 'Lhash_array': ['711421117499365781630781345709'], 'label': '2-74-1.1-c7-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/74/8/a/c/1/4'}