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lfunc_lfunctions • Show schema
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{'Lhash': '1803437029799446161248859985913', 'a10': [1.9162532255602118, -2.515546377137596], 'a2': [1.100559722079924, 0.8881262850154593], 'a3': [1.2423989354267284, -1.5018023293008713], 'a4': [0.4224634037292783, 1.9548720348169781], 'a5': [-0.06258587067700315, -2.235191940033697], 'a6': [2.7011243506351796, -0.5494160031266473], 'a7': [2.7046595490084133, 0.8787971590772431], 'a8': [-1.271227031765381, 2.526654276649059], 'a9': [-0.14971117778688056, -0.784813478103501], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 7.985040202128042, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-1.100559722079924, -0.8881262850154593]]], [5, [[1.0, 0], [0.06258587067700315, 2.235191940033697]]]], 'bad_primes': [2, 5], 'central_character': '1000.789', 'coefficient_field': 'CDF', 'conductor': 1000, 'conductor_radical': 10, 'conjugate': '2153399956773848617339954328760', 'degree': 2, 'euler_factors': [[[1.0, 0], 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'root_analytic_conductor': 2.8257813436513524, 'root_angle': -0.06317622438637137, 'root_number': '0.9222452362986687 - 0.3866053855346723*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.0631762243864', 'prec': 54}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.42266096783668394116389254366', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.07010348070351065303204036867', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.39160171101150717260900993313', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 7.985040202128042, 'bad_primes': [2, 5], 'central_character': '1000.789', 'conductor': 1000, 'conductor_radical': 10, 'degree': 2, 'index': 90, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1000/2/bd/a/789/116'], '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': '2-10e3-1000.789-c1-0-90', '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': '2-10e3-1000.789-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.8257813436513524, 'root_angle': -0.06317622438637137, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.42266096783668394116389254366', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1803437029799446161248859985913', 'Lhash_array': ['1803437029799446161248859985913'], 'factors': ['2-10e3-1000.789-c1-0-90'], 'label': '2-10e3-1000.789-c1-0-90', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1000/2/bd/a/789/116'}