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lfunc_lfunctions • Show schema
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{'Lhash': '3487420663875302894608748176154', 'a10': [20.0, 15.491933384829668], 'a2': [-1.7320508075688772, 2.23606797749979], 'a3': [3.4641016151377544, 3.872983346207417], 'a4': [-2.0, -7.745966692414834], 'a5': [0.0, -8.94427190999916], 'a6': [-14.660254037844387, 1.0377627599154646], 'a7': [0.0, -7.745966692414834], 'a8': [20.784609690826528, 8.94427190999916], 'a9': [-3.0, 26.832815729997478], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.7080229200688877, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [1.7320508075688772, -2.23606797749979]]], [3, [[1.0, 0], [-3.4641016151377544, -3.872983346207417]]]], 'bad_primes': [2, 3], 'central_character': '12.11', 'coefficient_field': 'CDF', 'conductor': 12, 'conductor_radical': 6, 'conjugate': '6334040408680555996434569190503', 'degree': 2, 'euler_factors': [[[1.0, 0], [1.7320508075688772, -2.23606797749979]], [[1.0, 0], [-3.4641016151377544, -3.872983346207417]], 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'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '8.826431911939698895359179639394', 'prec': 107}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.7080229200688877, 'bad_primes': [2, 3], 'central_character': '12.11', 'conductor': 12, 'conductor_radical': 6, 'degree': 2, 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/12/4/b/a/11/2'], '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': '2-12-12.11-c3-0-0', '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': '2-12-12.11-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.8414409783632407, 'root_angle': -0.15635507522696812, 'self_dual': False, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '2.75108982179113338574342640129', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '3487420663875302894608748176154', 'Lhash_array': ['3487420663875302894608748176154'], 'label': '2-12-12.11-c3-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/12/4/b/a/11/2'}