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lfunc_lfunctions • Show schema
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{'Lhash': '606845084129093070845980380971', 'a10': [-3.5615528128088303, 0.0], 'a2': [0.0, 1.0], 'a3': [-1.0, 0.0], 'a4': [-1.0, 0.0], 'a5': [0.0, 3.5615528128088303], 'a6': [0.0, -1.0], 'a7': [0.0, -1.0], 'a8': [0.0, -1.0], 'a9': [1.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 4.359831950361911, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, -1.0]]], [3, [[1.0, 0], [1.0, 0]]], [7, [[1.0, 0], [0, 1.0]]], [13, [[1.0, 0], [-3.5615528128088303, 0.5615528128088303]]]], 'bad_primes': [2, 3, 7, 13], 'central_character': '546.337', 'coefficient_field': 'CDF', 'conductor': 546, 'conductor_radical': 546, 'conjugate': '2781323121228696368913214866126', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, -1.0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [0, -3.5615528128088303], [-5.0, 0]], [[1.0, 0], [0, 1.0]], [[1.0, 0], [0, -5.56155281280883], [-11.0, 0]], [[1.0, 0], [-3.5615528128088303, 0.5615528128088303]], [[1.0, 0], 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'6.27230941465201258216522956179664', '8.131688311889702758146594966131823', '8.742248087836666161869673482762392', '9.268648105364263272621926553472683', '10.63773064596333522986362743562188'], 'prelabel': '2-546-13.12-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.0880210608042034, 'root_angle': 0.9502216301683548, 'root_number': '-0.9877970220657875 + 0.15574672772794373*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.475110815084', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.47871636239499742434539236738', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.80185961144397048832004952143', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.64149204114418432137774574141', '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': '13.12', 'conductor': 546, 'conductor_radical': 546, 'degree': 2, 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/546/2/c/e/337/4'], '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': '2-546-13.12-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': '2-546-13.12-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.0880210608042034, 'root_angle': 0.4751108150841774, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.47871636239499742434539236738', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '606845084129093070845980380971', 'Lhash_array': ['606845084129093070845980380971'], 'label': '2-546-13.12-c1-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/546/2/c/e/337/4'}