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lfunc_lfunctions • Show schema
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{'Lhash': '1325959886360877638805979145696', 'a10': [-0.5, 0.8660254037844386], 'a2': [0.9781476007338057, -0.20791169081775934], 'a3': [0.03992632017644873, 0.3798735614747138], 'a4': [0.9135454576426009, -0.4067366430758002], 'a5': [-0.6691306063588582, 0.7431448254773942], 'a6': [0.11803398874989485, 0.36327126400268045], 'a7': [-2.6361079096601494, 0.22568803385912728], 'a8': [0.8090169943749475, -0.5877852522924731], 'a9': [2.791732990536766, -0.5934011655692634], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 6.148480955638592, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.9781476007338057, 0.20791169081775934]]], [5, [[1.0, 0], [0.6691306063588582, -0.7431448254773942]]], [7, [[1.0, 0], [2.6361079096601494, -0.22568803385912728]]], [11, [[1.0, 0], [-3.190027950917674, -0.9075911372220338]]]], 'bad_primes': [2, 5, 7, 11], 'central_character': '770.361', 'coefficient_field': 'CDF', 'conductor': 770, 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[1.6909830056250525, 5.2043105580553535], [-67.14841053312064, 48.78617594027527]], [[1.0, 0], [8.97213595499958, 15.540195326474782], [-44.5, 77.07626093681505]], [[1.0, 0], [1.0172209268743164, -3.1306841003112362], [-78.4746484543699, -57.01516947236989]], [[1.0, 0], [-0.9850512242115453, -1.0940102173571595], [-10.557374790033, 100.44671143219561]], [[1.0, 0], [-1.1439879243355588, 10.884318043358116], [-100.74920287558199, -21.414904154229212]], [[1.0, 0], [-14.648191521326469, -6.52179505318783], [71.59697488039782, 79.51649632608118]], [[1.0, 0], [6.5901699437494745, -11.414509173087419], [-54.5, -94.39676901250381]], [[1.0, 0], [-10.326237921249264, 7.502451004089263], [34.91892036436906, -107.46938634135235]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 10, 'label': '2-770-77.53-c1-0-10', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 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-0.20001430711811594, 'root_number': '0.8089905742933904 - 0.5878216146965424*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.100007153559', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.04599791624139187913089583826', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.88896899847007200052025211651', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.72029081255057368913043989703', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 6.148480955638592, 'bad_primes': [2, 5, 7, 11], 'central_character': '77.53', 'conductor': 770, 'conductor_radical': 770, 'degree': 2, 'index': 10, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/770/2/bg/a/361/1'], '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': '2-770-77.53-c1-0-10', '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': '2-770-77.53-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.4796130657097675, 'root_angle': -0.10000715355905797, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.04599791624139187913089583826', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1325959886360877638805979145696', 'Lhash_array': ['1325959886360877638805979145696'], 'label': '2-770-77.53-c1-0-10', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/770/2/bg/a/361/1'}