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lfunc_lfunctions • Show schema
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{'Lhash': '2377203950673427096150964153177', 'a10': [-1.2841816470586054, 5.301628438145034], 'a2': [2.356399230142752, 0.6313952707620697], 'a3': [1.5487785780848544, -0.7754256354193201], 'a4': [3.4219065363077696, 1.9756386598790308], 'a5': [0.05400159687117193, 2.2354158064072474], 'a6': [4.139140728092169, -0.8493209006746603], 'a7': [0.0, 0.0], 'a8': [3.365961102432382, 3.365961102432382], 'a9': [1.7974301678690874, -2.4019252260705586], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 5.869004548564111, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [-1.5487785780848544, 0.7754256354193201]]], [5, [[1.0, 0], [-0.05400159687117193, -2.2354158064072474]]], [7, [[1.0, 0], [0, 0]]]], 'bad_primes': [3, 5, 7], 'central_character': '735.557', 'coefficient_field': 'CDF', 'conductor': 735, 'conductor_radical': 105, 'conjugate': '2958722071881104433332218614735', 'degree': 2, 'euler_factors': [[[1.0, 0], 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'3.92770586734981815708925979590655', '4.74209753470522569694622369275922', '5.24419010228761397195053235748096', '6.46605356952020749402191871008624', '7.78730699133631540782771616469454', '8.488868988382008205293892660805291', '9.685519445337878563101614119217611', '10.37433494819173380184427041291310'], 'prelabel': '2-735-105.32-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.422602845817719, 'root_angle': -0.2053294074410335, 'root_number': '0.7990628771153607 - 0.6012474685319864*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.102664703721', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.87528326042320519549139945855', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.81082443367346819022158755380', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.92770586734981815708925979591', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 5.869004548564111, 'bad_primes': [3, 5, 7], 'central_character': '105.32', 'conductor': 735, 'conductor_radical': 105, 'degree': 2, 'index': 54, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/735/2/y/i/557/12'], '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': '2-735-105.32-c1-0-54', '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': '2-735-105.32-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.422602845817719, 'root_angle': -0.10266470372051675, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.87528326042320519549139945855', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2377203950673427096150964153177', 'Lhash_array': ['2377203950673427096150964153177'], 'label': '2-735-105.32-c1-0-54', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/735/2/y/i/557/12'}