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lfunc_lfunctions • Show schema
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{'Lhash': '438322649881178157740746937462', 'a10': [-97.42724123465794, -88.45152151843527], 'a2': [-1.7259412844797024, -5.3871260132401355], 'a3': [0.0, 0.0], 'a4': [-26.04225336505711, 18.595726381891396], 'a5': [20.145412198827863, -11.630959155929236], 'a6': [0.0, 0.0], 'a7': [-156.8324529732869, -90.54725894179651], 'a8': [145.1249215506155, 108.19776866889488], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 17.32145253980191, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '2.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [1.7259412844797024, 5.3871260132401355]]], [3, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 3], 'central_character': '108.35', 'coefficient_field': 'CDF', 'conductor': 108, 'conductor_radical': 6, 'conjugate': '1644405734048240434544484957234', 'degree': 2, 'euler_factors': [[[1.0, 0], [1.7259412844797024, 5.3871260132401355]], [[1.0, 0], [0, 0]], [[1.0, 0], [-20.145412198827863, 11.630959155929236], [1562.5, 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'6.80048897382477978420810004660303', '8.286976078830759387662938372875055', '9.425248688913022236512421287563821', '10.00914589946958039875641658207624', '11.61368235149391411251545486278983', '13.03375311471187094551837559254516'], 'prelabel': '2-108-36.11-c5-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.161904917198603, 'root_angle': -0.20570349717352485, 'root_number': '0.7983557168468333 - 0.6021861418016683*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.102851748587', 'prec': 50}, 'spectral_label': 'c5-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.34577560236413882418469056040', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.76743512704028931539572202865', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.74292428488645437860306875927', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 17.32145253980191, 'bad_primes': [2, 3], 'central_character': '36.11', 'conductor': 108, 'conductor_radical': 6, 'degree': 2, 'index': 5, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/108/6/h/a/35/12'], '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': '2-108-36.11-c5-0-5', 'motivic_weight': 5, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [5], 'order_of_vanishing': 0, 'prelabel': '2-108-36.11-c5-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.161904917198603, 'root_angle': -0.10285174858676242, 'self_dual': False, 'spectral_label': 'c5-0', 'z1': {'__RealLiteral__': 0, 'data': '0.34577560236413882418469056040', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '438322649881178157740746937462', 'Lhash_array': ['438322649881178157740746937462'], 'label': '2-108-36.11-c5-0-5', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/108/6/h/a/35/12'}