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lfunc_lfunctions • Show schema
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{'Lhash': '2181197629305707208389109872214', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [3.0, 0.0], 'a4': [0.0, 0.0], 'a5': [0.0, 0.0], 'a6': [0.0, 0.0], 'a7': [22.209372712298546, 0.0], 'a8': [0.0, 0.0], 'a9': [9.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 70.80229200688878, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [-3.0, 0]]], [5, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 3, 5], 'central_character': '1200.1', 'coefficient_field': 'CDF', 'conductor': 1200, 'conductor_radical': 30, 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-3.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-22.209372712298546, 0], [343.0, 0]], [[1.0, 0], [-1.790627287701454, 0], [1331.0, 0]], [[1.0, 0], [58.209372712298546, 0], [2197.0, 0]], [[1.0, 0], [18.984378812835757, 0], [4913.0, 0]], [[1.0, 0], [104.83749084919418, 0], [6859.0, 0]], [[1.0, 0], [49.612496949731394, 0], [12167.0, 0]], 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'6.60614180145211059896373100982567', '7.54485599088918513206111052288510', '8.073413254060382002252391792765200', '8.932228356681616004460172006327991'], 'prelabel': '2-1200-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.414409783632408, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.72066153632002513608749342338', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.35605267086697107036003493447', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.74636879365726534589709906161', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 70.80229200688878, 'bad_primes': [2, 3, 5], 'central_character': '1.1', 'conductor': 1200, 'conductor_radical': 30, 'degree': 2, 'index': 56, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1200/4/a/bt/1/2'], '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': '2-1200-1.1-c3-0-56', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 1, 'prelabel': '2-1200-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.414409783632408, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '1.72066153632002513608749342338', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2181197629305707208389109872214', 'Lhash_array': ['2181197629305707208389109872214'], 'label': '2-1200-1.1-c3-0-56', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1200/4/a/bt/1/2'}