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lfunc_lfunctions • Show schema
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{'Lhash': '1972710620881051837320935822646', 'a10': [-36676944625311777000, 0.0], 'a2': [-524288.0, 0.0], 'a3': [2111614217.9112473, 0.0], 'a4': [274877906944.0, 0.0], 'a5': [69955720186828.19, 0.0], 'a6': [-1107093995080252.0, 0.0], 'a7': [55880017704055290, 0.0], 'a8': [-144115188075855870, 0.0], 'a9': [406359452265952300, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 19.26791027794951, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '19.5', 'prec': 14}, 'bad_lfactors': [[2, [[1.0, 0], [524288.0, 0]]]], 'bad_primes': [2], 'central_character': '2.1', 'coefficient_field': 'CDF', 'conductor': 2, 'conductor_radical': 2, 'conjugate': '1972710620881051837320935822646', 'degree': 2, 'euler_factors': [[[1.0, 0], [524288.0, 0]], [[1.0, 0], [-2111614217.9112473, 0], [4052555153018976000, 0]], [[1.0, 0], [-69955720186828.19, 0], [1818989403545856400000000000, 0]], [[1.0, 0], [-55880017704055290, 0], [909543680129861200000000000000000, 0]], [[1.0, 0], 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['1.55619428612733078561671947901778', '2.46169254640360669407218558478609', '5.40983787226348957427096627134057', '7.87724456721961639461677820872105', '9.120765272067143291108306653761161', '10.78877334774693993085290941082456', '13.61714537646484465701077158764987', '14.80190207193498400660355503033606', '17.34455450695660601251387542759169', '18.36942423794841135476684376942700'], 'prelabel': '2-2-1.1-c39-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.389522784762543, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c39-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.55619428612733078561671947902', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.46169254640360669407218558479', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.40983787226348957427096627134', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 19.26791027794951, 'bad_primes': [2], 'central_character': '1.1', 'conductor': 2, 'conductor_radical': 2, 'degree': 2, 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/2/40/a/b/1/2'], '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': '2-2-1.1-c39-0-1', 'motivic_weight': 39, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [39], 'order_of_vanishing': 0, 'prelabel': '2-2-1.1-c39-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.389522784762543, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c39-0', 'z1': {'__RealLiteral__': 0, 'data': '1.55619428612733078561671947902', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1972710620881051837320935822646', 'Lhash_array': ['1972710620881051837320935822646'], 'label': '2-2-1.1-c39-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2/40/a/b/1/2'}