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lfunc_lfunctions • Show schema
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{'Lhash': '2469419901141978692739698737733', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [5.158266621186976, -0.6263269631337115], 'a4': [4.5445179738492465, -6.583870927149251], 'a5': [0.0, 0.0], 'a6': [0.0, 0.0], 'a7': [-29.538857746040357, 3.586666689644453], 'a8': [0.0, 0.0], 'a9': [26.215429070503404, -6.46152293576406], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 13.983452671360531, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [-5.158266621186976, 0.6263269631337115]]], [79, [[1.0, 0], [353.40576597068565, -606.74818877247]]]], 'bad_primes': [3, 79], 'central_character': '237.41', 'coefficient_field': 'CDF', 'conductor': 237, 'conductor_radical': 237, 'conjugate': '1116671804866560838588897625821', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0], [-4.5445179738492465, 6.583870927149251]], [[1.0, 0], [-5.158266621186976, 0.6263269631337115]], [[1.0, 0], [0, 0], [93.56384352138764, 82.8903322800994]], 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'9.637204851336089534862452252662682', '11.00538965644459869236607601367127', '12.06128134457152692536243150374932'], 'prelabel': '2-237-237.41-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.7394455031943616, 'root_angle': 0.4675343823825208, 'root_number': '0.10181700228942624 + 0.9948031453733924*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.233767191191', 'prec': 47}, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.94802881858564279571639666081', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.47617774370563333735753648968', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.80042859166343207258647310784', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 13.983452671360531, 'bad_primes': [3, 79], 'central_character': '237.41', 'conductor': 237, 'conductor_radical': 237, 'degree': 2, 'index': 69, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/237/4/l/a/41/2'], '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': '2-237-237.41-c3-0-69', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'prelabel': '2-237-237.41-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.7394455031943616, 'root_angle': 0.2337671911912604, 'self_dual': False, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '1.94802881858564279571639666081', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2469419901141978692739698737733', 'Lhash_array': ['2469419901141978692739698737733'], 'label': '2-237-237.41-c3-0-69', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/237/4/l/a/41/2'}