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lfunc_lfunctions • Show schema
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{'Lhash': '1582938512944148847951889934914', 'a10': [-2.5, 1.9364916731037085], 'a2': [0.8660254037844386, 1.118033988749895], 'a3': [-1.7320508075688772, 0.0], 'a4': [-0.5, 1.9364916731037085], 'a5': [0.0, 2.23606797749979], 'a6': [-1.5, -1.9364916731037085], 'a7': [0.0, 0.0], 'a8': [-2.598076211353316, 1.118033988749895], 'a9': [3.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.9582048242553651, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.8660254037844386, -1.118033988749895]]], [3, [[1.0, 0], [1.7320508075688772, 0]]], [5, [[1.0, 0], [0, -2.23606797749979]]]], 'bad_primes': [2, 3, 5], 'central_character': '120.59', 'coefficient_field': 'CDF', 'conductor': 120, 'conductor_radical': 30, 'conjugate': '4190912138178646068257864979362', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.8660254037844386, -1.118033988749895]], [[1.0, 0], [1.7320508075688772, 0]], [[1.0, 0], [0, -2.23606797749979]], [[1.0, 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'9.426464548989252731432720387645700', '10.09576733678791506577609402592257', '11.54758214659964146686361762609132', '11.95630402599732234585551874834172', '12.97161248345628890331946702714011'], 'prelabel': '2-120-120.59-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.9788793716568784, 'root_angle': -0.6293540651172507, 'root_number': '-0.3952847075210475 - 0.9185586535436917*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.314677032559', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.24871830823032357325157849446', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.78898483280470033170864145423', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.19345208285814782747346326183', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.9582048242553651, 'bad_primes': [2, 3, 5], 'central_character': '120.59', 'conductor': 120, 'conductor_radical': 30, 'degree': 2, 'index': 2, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/120/2/m/a/59/4'], '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': '2-120-120.59-c1-0-2', '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': '2-120-120.59-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.9788793716568784, 'root_angle': -0.31467703255862534, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.24871830823032357325157849446', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1582938512944148847951889934914', 'Lhash_array': ['1582938512944148847951889934914'], 'label': '2-120-120.59-c1-0-2', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/120/2/m/a/59/4'}