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lfunc_lfunctions • Show schema
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{'Lhash': '1217097647486395944104936117988', 'a10': [1.0, 0.0], 'a2': [-1.0, 0.0], 'a3': [0.7846772635624373, 0.0], 'a4': [1.0, 0.0], 'a5': [-1.0, 0.0], 'a6': [-0.7846772635624373, 0.0], 'a7': [1.8292643314180368, 0.0], 'a8': [-1.0, 0.0], 'a9': [-2.3842815920481653, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 17.806639650745534, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [1.0, 0]]], [5, [[1.0, 0], [1.0, 0]]], [223, [[1.0, 0], [-1.0, 0]]]], 'bad_primes': [2, 5, 223], 'central_character': '2230.1', 'coefficient_field': 'CDF', 'conductor': 2230, 'conductor_radical': 2230, 'degree': 2, 'euler_factors': [[[1.0, 0], [1.0, 0]], [[1.0, 0], [-0.7846772635624373, 0], [3.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [-1.8292643314180368, 0], [7.0, 0]], [[1.0, 0], [-4.311096727247487, 0], [11.0, 0]], [[1.0, 0], [-5.095372801904178, 0], [13.0, 0]], [[1.0, 0], [-3.845063607071411, 0], [17.0, 0]], [[1.0, 0], 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'7.81496209688094435798229584076847', '8.337939058393808271450993561049032', '8.983875687215023774382979228234181'], 'prelabel': '2-2230-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.219791422658889, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.960120751938482228088285269763', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '1.95964887739689678342218725550', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.30109953622184619990634970887', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 17.806639650745534, 'bad_primes': [2, 5, 223], 'central_character': '1.1', 'conductor': 2230, 'conductor_radical': 2230, 'degree': 2, 'index': 16, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/2230/2/a/p/1/4'], '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': '2-2230-1.1-c1-0-16', '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': '2-2230-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.219791422658889, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.960120751938482228088285269763', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1217097647486395944104936117988', 'Lhash_array': ['1217097647486395944104936117988'], 'label': '2-2230-1.1-c1-0-16', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2230/2/a/p/1/4'}