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lfunc_lfunctions • Show schema
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{'Lhash': '34552818676419157893472090723', 'a10': [0.0, 0.0], 'a2': [-7.658490924025172, 0.0], 'a3': [-9.0, 0.0], 'a4': [26.652483233375936, 0.0], 'a5': [0.0, 0.0], 'a6': [68.92641831622655, 0.0], 'a7': [-112.19726755430972, 0.0], 'a8': [40.953908623262826, 0.0], 'a9': [81.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 132.31665134570906, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '2.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [9.0, 0]]], [5, [[1.0, 0], [0, 0]]], [11, [[1.0, 0], [-121.0, 0]]]], 'bad_primes': [3, 5, 11], 'central_character': '825.1', 'coefficient_field': 'CDF', 'conductor': 825, 'conductor_radical': 165, 'degree': 2, 'euler_factors': [[[1.0, 0], [7.658490924025172, 0], [32.0, 0]], [[1.0, 0], [9.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [112.19726755430972, 0], [16807.0, 0]], [[1.0, 0], [-121.0, 0]], [[1.0, 0], [849.13288923174, 0], [371293.0, 0]], [[1.0, 0], [608.3815156974536, 0], [1419857.0, 0]], [[1.0, 0], [2245.323401689118, 0], 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'positive_zeros': ['0.02725736781901749989292177856272', '1.54861738227629546742183803823283', '2.60870248003433204662357243770217', '4.14480254928421061589739535821370', '5.06921449591583008370168892295488', '6.52908334995014873859659992622011', '6.80424852123398875521884048993929', '7.933096532698632543856558750646171', '8.727349179193450997366978954436729', '9.608237261138686642362566754265083'], 'prelabel': '2-825-1.1-c5-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 11.502897519569105, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c5-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.02725736781901749989292177856', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.54861738227629546742183803823', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.60870248003433204662357243770', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 132.31665134570906, 'bad_primes': [3, 5, 11], 'central_character': '1.1', 'conductor': 825, 'conductor_radical': 165, 'degree': 2, 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/825/6/a/u/1/3'], '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': '2-825-1.1-c5-0-0', 'motivic_weight': 5, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [5], 'order_of_vanishing': 0, 'prelabel': '2-825-1.1-c5-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 11.502897519569105, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c5-0', 'z1': {'__RealLiteral__': 0, 'data': '0.02725736781901749989292177856', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '34552818676419157893472090723', 'Lhash_array': ['34552818676419157893472090723'], 'label': '2-825-1.1-c5-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/825/6/a/u/1/3'}