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lfunc_lfunctions • Show schema
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{'Lhash': '1113612902458501232587807918871', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [-1.0, 1.4142135623730951], 'a4': [0.0, 0.0], 'a5': [-1.224744871391589, -0.7071067811865476], 'a6': [0.0, 0.0], 'a7': [-4.449489742783178, 0.0], 'a8': [0.0, 0.0], 'a9': [-1.0, -2.8284271247461903], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 7.282356664340774, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [1.0, -1.4142135623730951]]], [19, [[1.0, 0], [-4.174234614174767, 1.255294939775204]]]], 'bad_primes': [2, 3, 19], 'central_character': '912.65', 'coefficient_field': 'CDF', 'conductor': 912, 'conductor_radical': 114, 'conjugate': '686727905017025120724151587460', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [1.0, -1.4142135623730951]], [[1.0, 0], [1.224744871391589, 0.7071067811865476], [2.5, 4.330127018922194]], [[1.0, 0], [4.449489742783178, 0], [7.0, 0]], [[1.0, 0], [0, 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2.698584196266771, 'root_angle': 0.07176805218599522, 'root_number': '0.9746900369061594 + 0.22356057782147037*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.035884026093', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.878485682299211605384982184465', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '2.85249934357193251255091010165', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.41827953563966253234003387937', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 7.282356664340774, 'bad_primes': [2, 3, 19], 'central_character': '57.8', 'conductor': 912, 'conductor_radical': 114, 'degree': 2, 'index': 12, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/912/2/bn/g/65/2'], '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': '2-912-57.8-c1-0-12', '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': '2-912-57.8-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.698584196266771, 'root_angle': 0.03588402609299761, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.878485682299211605384982184465', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1113612902458501232587807918871', 'Lhash_array': ['1113612902458501232587807918871'], 'label': '2-912-57.8-c1-0-12', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/912/2/bn/g/65/2'}