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lfunc_lfunctions • Show schema
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{'Lhash': '1011951910873453734205062913880', 'a10': [116.72766999631601, -66.75791331652655], 'a2': [-3.8033635569738244, -3.8033635569738244], 'a3': [0.0, 0.0], 'a4': [0.0, 12.931148693033164], 'a5': [-6.569153320639729, 24.121488856410338], 'a6': [0.0, 0.0], 'a7': [16.61489056308844, 16.61489056308844], 'a8': [-11.671957222689155, 11.671957222689155], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 4.651648338772996, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '2.0', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [6.569153320639729, -24.121488856410338]]]], 'bad_primes': [3, 5], 'central_character': '45.37', 'coefficient_field': 'CDF', 'conductor': 45, 'conductor_radical': 15, 'conjugate': '2169504209119061296307924907961', 'degree': 2, 'euler_factors': [[[1.0, 0], [3.8033635569738244, 3.8033635569738244], [0, 16.0]], [[1.0, 0], [0, 0]], [[1.0, 0], [6.569153320639729, -24.121488856410338]], [[1.0, 0], 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'0.958902891012048 - 0.2837344632023689*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.0457867117015', 'prec': 54}, 'spectral_label': 'c4-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.798289300451765372052626030605', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '4.34401598142625114555860784365', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '6.29602641274894401920615070815', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 4.651648338772996, 'bad_primes': [3, 5], 'central_character': '5.2', 'conductor': 45, 'conductor_radical': 15, 'degree': 2, 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/45/5/g/e/37/1'], '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': '2-45-5.2-c4-0-0', 'motivic_weight': 4, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [4], 'order_of_vanishing': 0, 'prelabel': '2-45-5.2-c4-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.156768030821348, 'root_angle': -0.04578671170153696, 'self_dual': False, 'spectral_label': 'c4-0', 'z1': {'__RealLiteral__': 0, 'data': '0.798289300451765372052626030605', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1011951910873453734205062913880', 'Lhash_array': ['1011951910873453734205062913880'], 'label': '2-45-5.2-c4-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/45/5/g/e/37/1'}