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lfunc_lfunctions • Show schema
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{'Lhash': '1973724613302606985569975828389', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [0.0, -1.0], 'a4': [0.0, 0.0], 'a5': [0.0, 0.0], 'a6': [0.0, 0.0], 'a7': [1.4142135623730951, 0.0], 'a8': [0.0, 0.0], 'a9': [-1.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.5331277188085835, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 1.0]]]], 'bad_primes': [2, 3], 'central_character': '3072.2561', 'coefficient_field': 'CDF', 'conductor': 3072, 'conductor_radical': 6, 'conjugate': '1149033805660123534084113911042', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 1.0]], [[1.0, 0], [0, 0], [1.0, 0]], [[1.0, 0], [-1.4142135623730951, 0], [1.0, 0]], [[1.0, 0], [0, 0], [1.0, 0]], [[1.0, 0], [0, 1.4142135623730951], [-1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [0, 0], [1.0, 0]], [[1.0, 0], 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1.2381953475960825, 'root_angle': 0.5, 'root_number': '1*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.55699418510688602566762805720', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.56914851219594839747133108948', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.77997225217468893239435086849', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.5331277188085835, 'bad_primes': [2, 3], 'central_character': '24.5', 'conductor': 3072, 'conductor_radical': 6, 'degree': 2, 'index': 3, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/3072/1/h/a/2561/2'], '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': '2-3072-24.5-c0-0-3', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'prelabel': '2-3072-24.5-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.2381953475960825, 'root_angle': 0.25, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.55699418510688602566762805720', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1973724613302606985569975828389', 'Lhash_array': ['1973724613302606985569975828389'], 'label': '2-3072-24.5-c0-0-3', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/3072/1/h/a/2561/2'}