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lfunc_lfunctions • Show schema
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{'Lhash': '2034602864957002207648577704281', 'a10': [1.1642535005111074, 9.791166207433048e-61], 'a2': [1.0786642207469255, -0.7836954298104039], 'a3': [0.30901699437494745, 0.9510565162951535], 'a4': [-0.06869601433603664, 0.21142459239157516], 'a5': [0.7064420922732758, 0.5132602236096222], 'a6': [1.0786642207469255, 0.7836954298104039], 'a7': [-0.30901699437494745, 0.9510565162951535], 'a8': [0.9156186937884163, 2.8179845802025185], 'a9': [-0.8090169943749475, 0.5877852522924731], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.8445442866915778, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [-0.30901699437494745, -0.9510565162951535]]], [7, [[1.0, 0], [0.30901699437494745, -0.9510565162951535]]], [11, [[1.0, 0], [-1.7951434983248904, 2.788809749771733]]]], 'bad_primes': [3, 7, 11], 'central_character': '231.190', 'coefficient_field': 'CDF', 'conductor': 231, 'conductor_radical': 231, 'conjugate': 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'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.60501865781524480009267735357', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.72436087744063251370772324857', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.88409802316470882149364909442', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.8445442866915778, 'bad_primes': [3, 7, 11], 'central_character': '11.3', 'conductor': 231, 'conductor_radical': 231, 'degree': 2, 'index': 6, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/231/2/j/g/190/4'], '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': '2-231-11.3-c1-0-6', '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': '2-231-11.3-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.3581400099737795, 'root_angle': -0.05519073497233909, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.60501865781524480009267735357', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2034602864957002207648577704281', 'Lhash_array': ['2034602864957002207648577704281'], 'label': '2-231-11.3-c1-0-6', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/231/2/j/g/190/4'}