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lfunc_lfunctions • Show schema
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{'Lhash': '2663631326580290074048988995143', 'a10': [-46.980041871302205, -22.372499894430288], 'a2': [-3.7652962189585226, 2.735647833611152], 'a3': [0.9270509831248422, -2.853169548885461], 'a4': [4.221550591962379, -12.99259675823506], 'a5': [5.340902688221366, 9.822156508371764], 'a6': [4.314645533792068, 13.279113528098582], 'a7': [-26.044513640038623, 0.0], 'a8': [8.142059269145442, 25.0586817713541], 'a9': [-7.281152949374527, -5.2900672706322585], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 4.425143250430549, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [-0.9270509831248422, 2.853169548885461]]], [5, [[1.0, 0], [-5.340902688221366, -9.822156508371764]]]], 'bad_primes': [3, 5], 'central_character': '75.61', 'coefficient_field': 'CDF', 'conductor': 75, 'conductor_radical': 15, 'conjugate': '129641429574655280437236556076', 'degree': 2, 'euler_factors': [[[1.0, 0], [3.7652962189585226, 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'prec': 47}, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.10123461946117215141554996427', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.89692856782256680636782397563', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '6.09372038626848118563720842922', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 4.425143250430549, 'bad_primes': [3, 5], 'central_character': '25.11', 'conductor': 75, 'conductor_radical': 15, 'degree': 2, 'index': 9, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/75/4/g/b/61/1'], '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': '2-75-25.11-c3-0-9', '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': '2-75-25.11-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.103602445908102, 'root_angle': 0.32146883490670997, 'self_dual': False, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '2.10123461946117215141554996427', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2663631326580290074048988995143', 'Lhash_array': ['2663631326580290074048988995143'], 'label': '2-75-25.11-c3-0-9', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/75/4/g/b/61/1'}