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lfunc_lfunctions • Show schema
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{'Lhash': '2771770014009296091463132489697', 'a10': [2.6375258833958517, 0.0], 'a2': [-1.0, 0.0], 'a3': [2.3537076551995892, 0.0], 'a4': [1.0, 0.0], 'a5': [-2.6375258833958517, 0.0], 'a6': [-2.3537076551995892, 0.0], 'a7': [0.36844642402490924, 0.0], 'a8': [-1.0, 0.0], 'a9': [2.5399397261451484, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 6.883104654234373, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [1.0, 0]]], [431, [[1.0, 0], [1.0, 0]]]], 'bad_primes': [2, 431], 'central_character': '862.1', 'coefficient_field': 'CDF', 'conductor': 862, 'conductor_radical': 862, 'conjugate': '2771770014009296091463132489697', 'degree': 2, 'euler_factors': [[[1.0, 0], [1.0, 0]], [[1.0, 0], [-2.3537076551995892, 0], [3.0, 0]], [[1.0, 0], [2.6375258833958517, 0], [5.0, 0]], [[1.0, 0], [-0.36844642402490924, 0], [7.0, 0]], [[1.0, 0], [4.479506832439951, 0], [11.0, 0]], [[1.0, 0], [3.7284580300959247, 0], [13.0, 0]], 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'5.14906760713632270232202531891201', '6.77113263069635594267433331456770', '7.69114709713630367966700949510897', '8.041241316193251307296836734201098', '8.646444386129235290258477914682117', '9.701374038919174270442661031834477'], 'prelabel': '2-862-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.623567162135243, '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': '2.18654100231582988810685617707', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.95675840162826184742609675172', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.04794207511389660312637262566', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 6.883104654234373, 'bad_primes': [2, 431], 'central_character': '1.1', 'conductor': 862, 'conductor_radical': 862, 'degree': 2, 'index': 30, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/862/2/a/i/1/6'], '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': '2-862-1.1-c1-0-30', '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': '2-862-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.623567162135243, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.18654100231582988810685617707', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2771770014009296091463132489697', 'Lhash_array': ['2771770014009296091463132489697'], 'label': '2-862-1.1-c1-0-30', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/862/2/a/i/1/6'}