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lfunc_lfunctions • Show schema
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{'Lhash': '1902110771606868727600547383683', 'a10': [7433.1532763823525, 18939.36566974121], 'a2': [9.698627506175791, 42.4924635067435], 'a3': [-28.185400323436767, -26.15222965778302], 'a4': [-1250.2500190023397, 602.0886763151573], 'a5': [461.59089889861434, -69.57363362222274], 'a6': [837.9129655038603, -1451.3078285733939], 'a7': [1972.9645983400244, 3417.2749258596446], 'a8': [-23796.36572776303, -29839.698803130923], 'a9': [-1360.434756742625, -18153.74021540703], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 22.14654095504655, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '4.5', 'prec': 10}, 'bad_lfactors': [[43, [[1.0, 0], [2933639.8978836252, 22225804.122379653]]]], 'bad_primes': [43], 'central_character': '43.10', 'coefficient_field': 'CDF', 'conductor': 43, 'conductor_radical': 43, 'conjugate': '346311341100786171798628214738', 'degree': 2, 'euler_factors': [[[1.0, 0], [-9.698627506175791, -42.4924635067435], [-461.2960603660386, 222.14847442818976]], 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'0.9999224456665436 - 0.012454021528727592*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.001982170329901064', 'prec': 70}, 'spectral_label': 'c9-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.50050082512043170439709643447523', 'prec': 113}, 'z2': {'__RealLiteral__': 0, 'data': '2.71929447141924153078971128444492', 'prec': 113}, 'z3': {'__RealLiteral__': 0, 'data': '4.40900855778570975371332832884848', 'prec': 113}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 22.14654095504655, 'bad_primes': [43], 'central_character': '43.10', 'conductor': 43, 'conductor_radical': 43, 'degree': 2, 'index': 17, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/43/10/g/a/10/32'], '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': '2-43-43.10-c9-0-17', 'motivic_weight': 9, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [9], 'order_of_vanishing': 0, 'prelabel': '2-43-43.10-c9-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.706011151181705, 'root_angle': -0.001982170329901064, 'self_dual': False, 'spectral_label': 'c9-0', 'z1': {'__RealLiteral__': 0, 'data': '1.50050082512043170439709643447523', 'prec': 113}}
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lfunc_instances • Show schema
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{'Lhash': '1902110771606868727600547383683', 'Lhash_array': ['1902110771606868727600547383683'], 'label': '2-43-43.10-c9-0-17', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/43/10/g/a/10/32'}