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lfunc_lfunctions • Show schema
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{'Lhash': '2552071642355983373899729773599', 'a10': [-130.69197751793115, -15.578973055804726], 'a2': [5.617086929936378, 0.6695777934922243], 'a3': [-15.718914233641494, 0.0], 'a4': [31.103331156924167, 7.522153344801625], 'a5': [-23.266860411471576, 0.0], 'a6': [-88.29450769457853, -10.52503590865519], 'a7': [0.0, -110.03748740283051], 'a8': [169.67344808011924, 63.07868908437366], 'a9': [4.084264684577124, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 12.189170305786531, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '2.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-5.617086929936378, -0.6695777934922243]]], [19, [[1.0, 0], [257.4518164908913, 1552.3587092503913]]]], 'bad_primes': [2, 19], 'central_character': '76.75', 'coefficient_field': 'CDF', 'conductor': 76, 'conductor_radical': 38, 'conjugate': '713076919460727395392639909923', 'degree': 2, 'euler_factors': [[[1.0, 0], [-5.617086929936378, -0.6695777934922243]], [[1.0, 0], [15.718914233641494, 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'spectral_label': 'c5-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.01322954597781533771666534228', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.03681784886748282966161692365', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.33261951572008441992497608333', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 12.189170305786531, 'bad_primes': [2, 19], 'central_character': '76.75', 'conductor': 76, 'conductor_radical': 38, 'degree': 2, 'index': 38, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/76/6/d/a/75/48'], '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': '2-76-76.75-c5-0-38', 'motivic_weight': 5, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [5], 'order_of_vanishing': 0, 'prelabel': '2-76-76.75-c5-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.4912992289098526, 'root_angle': 0.26160846428017454, 'self_dual': False, 'spectral_label': 'c5-0', 'z1': {'__RealLiteral__': 0, 'data': '2.01322954597781533771666534228', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2552071642355983373899729773599', 'Lhash_array': ['2552071642355983373899729773599'], 'label': '2-76-76.75-c5-0-38', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/76/6/d/a/75/48'}