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lfunc_lfunctions • Show schema
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{'Lhash': '1873383523679840353777583805842', 'a10': [2.2111251939626713, 5.406316040763771], 'a2': [-1.8470876469728261, 1.8470876469728261], 'a3': [0.7071067811865476, -0.7071067811865476], 'a4': [0.0, -4.823465551199224], 'a5': [0.8649267001589412, -2.0620140162841194], 'a6': [0.0, 2.612176401240778], 'a7': [0.0, 0.0], 'a8': [5.215188341273408, 5.215188341273408], 'a9': [0.0, -1.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 5.869004548564111, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [-0.7071067811865476, 0.7071067811865476]]], [5, [[1.0, 0], [-0.8649267001589412, 2.0620140162841194]]], [7, [[1.0, 0], [0, 0]]]], 'bad_primes': [3, 5, 7], 'central_character': '735.538', 'coefficient_field': 'CDF', 'conductor': 735, 'conductor_radical': 105, 'conjugate': '1036158774118232132991358284895', 'degree': 2, 'euler_factors': [[[1.0, 0], [1.8470876469728261, -1.8470876469728261], [0, -2.0]], [[1.0, 0], 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'sign_arg': {'__RealLiteral__': 0, 'data': '0.051335019518', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.47783902231620766653357219892', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.55433003317044837206110110681', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.48397149009364133718360803954', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 5.869004548564111, 'bad_primes': [3, 5, 7], 'central_character': '35.13', 'conductor': 735, 'conductor_radical': 105, 'degree': 2, 'index': 25, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/735/2/m/b/538/1'], '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': '2-735-35.13-c1-0-25', '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': '2-735-35.13-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.422602845817719, 'root_angle': 0.05133501951800192, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.47783902231620766653357219892', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1873383523679840353777583805842', 'Lhash_array': ['1873383523679840353777583805842'], 'label': '2-735-35.13-c1-0-25', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/735/2/m/b/538/1'}