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lfunc_lfunctions • Show schema
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{'Lhash': '2693809077420243164410589901846', 'a10': [1.3771259613472022, 2.846668945729999], 'a2': [1.3098556537382124, -0.5331774248503404], 'a3': [-0.6673045986041588, 1.5983443223166098], 'a4': [1.4314436672599193, -1.3967709287715981], 'a5': [0.14302830424727483, 2.231488943325543], 'a6': [-0.021871591450233572, 2.4493920946813383], 'a7': [0.5827719754125508, -0.5827719754125508], 'a8': [1.130257853659907, -2.592781746356623], 'a9': [-2.1094091453634847, -2.133165032869443], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.9582048242553651, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-1.3098556537382124, 0.5331774248503404]]], [3, [[1.0, 0], [0.6673045986041588, -1.5983443223166098]]], [5, [[1.0, 0], [-0.14302830424727483, -2.231488943325543]]]], 'bad_primes': [2, 3, 5], 'central_character': '120.53', 'coefficient_field': 'CDF', 'conductor': 120, 'conductor_radical': 30, 'conjugate': 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0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/120/2/w/c/53/14', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [1.5297383850023163, 1.5163136785702191, 1.519508409919189, 1.5356080016240647, 1.559623439871615, 1.5857053286163876, 1.6075089949387569, 1.6184783449633688, 1.612069017430059, 1.5819510420114846, 1.5222260533934397, 1.4276789455946572, 1.2940681250957065, 1.1184456825654592, 0.8994891721637637, 0.6378197125597816, 0.3362763751292571, 0.00011422571698832067, -0.36290686047437076, -0.7425730548825951, -1.1264321142504785, -1.500190014803005, -1.8482933977131693, -2.1546881262311977, -2.4037278548305676, -2.5811892219588373, -2.675333526703524, -2.6779402164240222, -2.5852270107182176, -2.398566800716398, -2.124914150243525, -1.7768654076878663, -1.372296587897065, -0.9335519463942887, -0.4861922318799277, -0.05735265365762325, 0.3261966196859924, 0.6401541318278806, 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'root_analytic_conductor': 0.9788793716568784, 'root_angle': -0.0874217650426307, 'root_number': '0.9625219226588657 - 0.27120388714227645*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.0437108825213', 'prec': 54}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.12504066730631169563215257345', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.39260441000675668994751170338', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.57711097469134798338048569281', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.9582048242553651, 'bad_primes': [2, 3, 5], 'central_character': '120.53', 'conductor': 120, 'conductor_radical': 30, 'degree': 2, 'index': 9, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/120/2/w/c/53/14'], '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': '2-120-120.53-c1-0-9', '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': '2-120-120.53-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.9788793716568784, 'root_angle': -0.04371088252131535, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.12504066730631169563215257345', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2693809077420243164410589901846', 'Lhash_array': ['2693809077420243164410589901846'], 'label': '2-120-120.53-c1-0-9', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/120/2/w/c/53/14'}