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lfunc_lfunctions • Show schema
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{'Lhash': '1725919824345250473851567284411', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [0.0, -1.0], 'a4': [0.0, 0.0], 'a5': [1.4811943040920157, -1.6751308705666461], 'a6': [0.0, 0.0], 'a7': [0.0, 1.0], 'a8': [0.0, 0.0], 'a9': [-1.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 6.7074337697875555, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 1.0]]], [5, [[1.0, 0], [-1.4811943040920157, 1.6751308705666461]]], [7, [[1.0, 0], [0, -1.0]]]], 'bad_primes': [2, 3, 5, 7], 'central_character': '840.169', 'coefficient_field': 'CDF', 'conductor': 840, 'conductor_radical': 210, 'conjugate': '1555868327961217127950185626545', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 1.0]], [[1.0, 0], [-1.4811943040920157, 1.6751308705666461]], [[1.0, 0], [0, -1.0]], [[1.0, 0], [-6.312650349317323, 0], [11.0, 0]], [[1.0, 0], [0, -6.962388608184031], [-13.0, 0]], [[1.0, 0], [0, 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'6.13530627668238524049406606585692', '6.54248915374155041465876171310532', '7.83785398821685713588484082067965', '8.675763376275315525465793646312544', '9.694058932568530371278911765725565', '10.29564324884027229897433882873598'], 'prelabel': '2-840-5.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.5898713809352687, 'root_angle': 0.23046639297904453, 'root_number': '0.7491412995590845 + 0.6624102303670484*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.11523319649', 'prec': 44}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.36151067497188397762866344712', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.03815599890933320957317920990', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.73835875176629263664898565403', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 6.7074337697875555, 'bad_primes': [2, 3, 5, 7], 'central_character': '5.4', 'conductor': 840, 'conductor_radical': 210, 'degree': 2, 'index': 12, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/840/2/t/d/169/3'], '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': '2-840-5.4-c1-0-12', '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': '2-840-5.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.5898713809352687, 'root_angle': 0.11523319648952227, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.36151067497188397762866344712', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1725919824345250473851567284411', 'Lhash_array': ['1725919824345250473851567284411'], 'label': '2-840-5.4-c1-0-12', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/840/2/t/d/169/3'}