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lfunc_lfunctions • Show schema
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{'Lhash': '1033704171536635282025703012457', 'a10': [0.0, -3.1622776601683795], 'a2': [1.4142135623730951, 0.0], 'a3': [-3.7937940645904713, 0.0], 'a4': [2.0, 0.0], 'a5': [0.0, -2.23606797749979], 'a6': [-5.365235018994394, 0.0], 'a7': [0.0, 7.101795608806756], 'a8': [2.8284271247461903, 0.0], 'a9': [5.392873404521889, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 6.267046080286829, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-1.4142135623730951, 0]]], [5, [[1.0, 0], [0, 2.23606797749979]]], [23, [[1.0, 0], [-20.02800108721293, -11.308367364504814]]]], 'bad_primes': [2, 5, 23], 'central_character': '230.91', 'coefficient_field': 'CDF', 'conductor': 230, 'conductor_radical': 230, 'conjugate': '2109256957924694103658979113472', 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.4142135623730951, 0]], [[1.0, 0], [3.7937940645904713, 0], [9.0, 0]], [[1.0, 0], [0, 2.23606797749979]], [[1.0, 0], [0, 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'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.45438297097648479535958495247', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 6.267046080286829, 'bad_primes': [2, 5, 23], 'central_character': '23.22', 'conductor': 230, 'conductor_radical': 230, 'degree': 2, 'index': 4, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/230/3/d/a/91/9'], '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': '2-230-23.22-c2-0-4', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [2], 'order_of_vanishing': 0, 'prelabel': '2-230-23.22-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.5034068946711057, 'root_angle': -0.1681936581204217, 'self_dual': False, 'spectral_label': 'c2-0', 'z1': {'__RealLiteral__': 0, 'data': '0.815448808489126174446673234449', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1033704171536635282025703012457', 'Lhash_array': ['1033704171536635282025703012457'], 'label': '2-230-23.22-c2-0-4', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/230/3/d/a/91/9'}