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lfunc_lfunctions • Show schema
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{'Lhash': '150973501296620304551141270940', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, -12.0], 'a4': [0, 0], 'a5': [0, 54.0], 'a6': [0, 0], 'a7': [-88.0, 0], 'a8': [0, 0], 'a9': [99.0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 41.05825787212305, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '2.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]]], 'bad_primes': [2], 'central_character': '256.129', 'coefficient_field': 'CDF', 'conductor': 256, 'conductor_radical': 2, 'conjugate': '1868712121076026483450721578825', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 12.0], [-243.0, 0]], [[1.0, 0], [0, -54.0], [-3125.0, 0]], [[1.0, 0], [88.0, 0], [16807.0, 0]], [[1.0, 0], [0, 540.0], [-161051.0, 0]], [[1.0, 0], [0, -418.0], [-371293.0, 0]], [[1.0, 0], [-594.0, 0], [1419857.0, 0]], [[1.0, 0], [0, -836.0], [-2476099.0, 0]], [[1.0, 0], [4104.0, 0], [6436343.0, 0]], [[1.0, 0], [0, -594.0], [-20511149.0, 0]], [[1.0, 0], [4256.0, 0], [28629151.0, 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'9.126851443848936814166943575674156', '9.869342503231410947193766446648222', '10.42232115203152666088650875086968'], 'prelabel': '2-2e8-8.5-c5-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.407671798096642, 'root_angle': -0.75, 'root_number': '-0.70710678118654752440084436210484903928483593768847404 - 0.70710678118654752440084436210484903928483593768847404*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.375', 'prec': 20}, 'spectral_label': 'c5-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.11909709289723749298048491877', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.76578556463569406586695507691', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.51872166651258097621825353372', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 41.05825787212305, 'bad_primes': [2], 'central_character': '8.5', 'conductor': 256, 'conductor_radical': 2, 'degree': 2, 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/256/6/b/c/129/1'], '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': '2-2e8-8.5-c5-0-1', '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': '2-2e8-8.5-c5-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.407671798096642, 'root_angle': -0.375, 'self_dual': False, 'spectral_label': 'c5-0', 'z1': {'__RealLiteral__': 0, 'data': '0.11909709289723749298048491877', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '150973501296620304551141270940', 'Lhash_array': ['150973501296620304551141270940'], 'label': '2-2e8-8.5-c5-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/256/6/b/c/129/1'}