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lfunc_lfunctions • Show schema
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{'Lhash': '1651082834653088214062984270924', 'a10': [1.6189500386222506, 0], 'a2': [0, -2.031506006339283], 'a3': [0, 0], 'a4': [-0.12701665379258312, 0], 'a5': [0, 0.796921118406907], 'a6': [0, 0], 'a7': [1.1270166537925832, 0], 'a8': [0, -7.867988930272382], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 29.673100788836337, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [11, [[1.0, 0], [0, 0]]]], 'bad_primes': [3, 11], 'central_character': '1089.485', 'coefficient_field': 'CDF', 'conductor': 1089, 'conductor_radical': 33, 'conjugate': '927049468559207994813597415516', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 2.031506006339283], [-4.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, -0.796921118406907], [-25.0, 0]], [[1.0, 0], [-1.1270166537925832, 0], [49.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-9.254033307585166, 0], [169.0, 0]], [[1.0, 0], [0, 11.751372268510229], [-289.0, 0]], [[1.0, 0], 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'3.95885043340886240044830897365403', '5.07283945756648761354538654417431', '5.87088183753429079739816207086557', '6.54315366785966387002567814429155', '7.54147887558552401734663583693420', '8.071560499136874244042512489399096', '8.934396497701073461979033432646423', '9.743267452171918107243365327854811'], 'prelabel': '2-33e2-3.2-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.447302156924686, 'root_angle': 0.6959132760153036, 'root_number': '-0.5773502691896257645091487805019574556476017512701268761 + 0.8164965809277260327324280249019637973219824935522233762*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.3479566380076518', 'prec': 60}, 'spectral_label': 'c2-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.30247469953930932776155304065', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.66940524547278730847312609424', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.95885043340886240044830897365', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 29.673100788836337, 'bad_primes': [3, 11], 'central_character': '3.2', 'conductor': 1089, 'conductor_radical': 33, 'degree': 2, 'index': 51, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1089/3/b/d/485/2'], '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': '2-33e2-3.2-c2-0-51', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [2], 'order_of_vanishing': 0, 'prelabel': '2-33e2-3.2-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.447302156924686, 'root_angle': 0.3479566380076518, 'self_dual': False, 'spectral_label': 'c2-0', 'z1': {'__RealLiteral__': 0, 'data': '1.30247469953930932776155304065', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1651082834653088214062984270924', 'Lhash_array': ['1651082834653088214062984270924'], 'label': '2-33e2-3.2-c2-0-51', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1089/3/b/d/485/2'}