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lfunc_lfunctions • Show schema
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{'Lhash': '2105369796217090166678077521292', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, 0], 'a4': [0, 0], 'a5': [0, -324.4916501007782], 'a6': [0, 0], 'a7': [956.9604428798726, 0], 'a8': [0, 0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 89.9668873394271, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '3.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 3], 'central_character': '288.145', 'coefficient_field': 'CDF', 'conductor': 288, 'conductor_radical': 6, 'conjugate': '8788569952136956270057722025', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 324.4916501007782], [-78125.0, 0]], [[1.0, 0], [-956.9604428798726, 0], [823543.0, 0]], [[1.0, 0], [0, -5452.204150097201], [-19487171.0, 0]], [[1.0, 0], [0, 6289.376774764119], [-62748517.0, 0]], [[1.0, 0], [34587.28789035768, 0], [410338673.0, 0]], [[1.0, 0], [0, -14595.640731435673], [-893871739.0, 0]], [[1.0, 0], 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-1.2692369553347564, -0.9098155604112421, -0.5267528662306417], 'positive_zeros': ['1.66084392326879090507353123227801', '2.74905175919918062335940748358981', '3.96058232578594535571834582775274', '5.14771507170683438146214607248603', '6.44220810204391801722733248321552', '7.11099124764168262966228790106814', '8.362108303672253250773397974996746', '9.077158143003600146507266343876133', '10.54234957680665203228118903201233', '11.15350406965528913200002403366810'], 'prelabel': '2-288-8.5-c7-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 9.48508762950702, 'root_angle': -0.8281942758292274, 'root_number': '-0.85784047717503851393454625920804312487402793957523307 - 0.51391605902141472815401776392289043162568087508778958*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.4140971379146138', 'prec': 64}, 'spectral_label': 'c7-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.66084392326879090507353123228', 'prec': 103}, 'z2': 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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 89.9668873394271, 'bad_primes': [2, 3], 'central_character': '8.5', 'conductor': 288, 'conductor_radical': 6, 'degree': 2, 'index': 32, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/288/8/d/b/145/2'], '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': '2-288-8.5-c7-0-32', 'motivic_weight': 7, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [7], 'order_of_vanishing': 0, 'prelabel': '2-288-8.5-c7-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 9.48508762950702, 'root_angle': -0.4140971379146137, 'self_dual': False, 'spectral_label': 'c7-0', 'z1': {'__RealLiteral__': 0, 'data': '1.66084392326879090507353123228', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2105369796217090166678077521292', 'Lhash_array': ['2105369796217090166678077521292'], 'label': '2-288-8.5-c7-0-32', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/288/8/d/b/145/2'}