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lfunc_lfunctions • Show schema
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{'Lhash': '1267505935981607142453149370809', 'a10': [0, 0], 'a2': [0, 0], 'a3': [-1.4142135623730951, 1.0], 'a4': [0, 0], 'a5': [2.414213562373095, -2.414213562373095], 'a6': [0, 0], 'a7': [1.0, 0], 'a8': [0, 0], 'a9': [1.0, -2.8284271247461903], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 10.731894031660088, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [1.4142135623730951, -1.0]]], [7, [[1.0, 0], [-1.0, 0]]]], 'bad_primes': [2, 3, 7], 'central_character': '1344.911', 'coefficient_field': 'CDF', 'conductor': 1344, 'conductor_radical': 42, 'conjugate': '1397513838755976982534978728803', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [1.4142135623730951, -1.0]], [[1.0, 0], [-2.414213562373095, 2.414213562373095], [0, -5.0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [-1.82842712474619, -1.82842712474619], [0, 11.0]], [[1.0, 0], [1.5857864376269049, -1.5857864376269049], [0, 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'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '2.31050775647320779079563945715', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.15897096146462715546894523367', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 10.731894031660088, 'bad_primes': [2, 3, 7], 'central_character': '48.11', 'conductor': 1344, 'conductor_radical': 42, 'degree': 2, 'index': 25, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1344/2/s/a/911/1'], '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': '2-1344-48.11-c1-0-25', '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': '2-1344-48.11-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.2759569642564124, 'root_angle': -0.035456638007651815, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.999885880031456449031433174620', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1267505935981607142453149370809', 'Lhash_array': ['1267505935981607142453149370809'], 'label': '2-1344-48.11-c1-0-25', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1344/2/s/a/911/1'}