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lfunc_lfunctions • Show schema
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{'Lhash': '2156299446889456301717955984273', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [2.5007333804258804, 0.0], 'a4': [0.0, 0.0], 'a5': [1.0, 0.0], 'a6': [0.0, 0.0], 'a7': [-2.234592477329116, 0.0], 'a8': [0.0, 0.0], 'a9': [3.2536674399762506, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 48.22964282085338, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [-1.0, 0]]], [151, [[1.0, 0], [1.0, 0]]]], 'bad_primes': [2, 5, 151], 'central_character': '6040.1', 'coefficient_field': 'CDF', 'conductor': 6040, 'conductor_radical': 1510, 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-2.5007333804258804, 0], [3.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [2.234592477329116, 0], [7.0, 0]], [[1.0, 0], [0.5958160715378942, 0], [11.0, 0]], [[1.0, 0], [3.723171574072971, 0], [13.0, 0]], [[1.0, 0], [2.8771243794697714, 0], [17.0, 0]], [[1.0, 0], [4.5418383159838225, 0], [19.0, 0]], 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-5.466301333625891, -6.033013641931799], 'positive_zeros': ['1.70102033360078356689653026280294', '2.52081227440498712392612148022137', '2.99331352791671227635514808124458', '3.87990357094745073975048006281175', '4.67365912486107403837117886806476', '5.58422677153683748734210399718483', '6.49404386003611836324481817772521', '7.15714776073075401770738406504338', '7.67599810439103221898042932742687'], 'prelabel': '2-6040-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.944756498312477, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.70102033360078356689653026280', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.52081227440498712392612148022', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.99331352791671227635514808124', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 48.22964282085338, 'bad_primes': [2, 5, 151], 'central_character': '1.1', 'conductor': 6040, 'conductor_radical': 1510, 'degree': 2, 'index': 140, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/6040/2/a/l/1/9'], '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': '2-6040-1.1-c1-0-140', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'prelabel': '2-6040-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.944756498312477, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.70102033360078356689653026280', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2156299446889456301717955984273', 'Lhash_array': ['2156299446889456301717955984273'], 'label': '2-6040-1.1-c1-0-140', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/6040/2/a/l/1/9'}