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lfunc_lfunctions • Show schema
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{'Lhash': '3789403210615977708169909222421', 'a10': [13.019156600841612, 1.3380444588483518], 'a2': [-1.5513875245483204, 1.2622189781000104], 'a3': [2.102775049096641, 2.102775049096641], 'a4': [0.8136065026483308, -3.9163815517449714], 'a5': [-4.627213005296662, -4.627213005296662], 'a6': [-5.916381551744972, -0.6080564044550493], 'a7': [3.0488759124000415, 0.0], 'a8': [3.681112141993261, 7.102775049096641], 'a9': [0.0, -0.15667418579323988], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.4359684229764751, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [1.5513875245483204, -1.2622189781000104]]]], 'bad_primes': [2], 'central_character': '16.11', 'coefficient_field': 'CDF', 'conductor': 16, 'conductor_radical': 2, 'conjugate': '6029166860115706837328664412793', 'degree': 2, 'euler_factors': [[[1.0, 0], [1.5513875245483204, -1.2622189781000104]], [[1.0, 0], [-2.102775049096641, -2.102775049096641], [0, 9.0]], 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'root_number': '0.7189989718862474 - 0.6950111354694393*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.12230029047', 'prec': 47}, 'spectral_label': 'c2-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.98931204697392862733797842527', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '7.49795545202933616860365622989', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '8.200020929716778120328955933920', 'prec': 107}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.4359684229764751, 'bad_primes': [2], 'central_character': '16.11', 'conductor': 16, 'conductor_radical': 2, 'degree': 2, 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/16/3/f/a/11/1'], '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': '2-2e4-16.11-c2-0-0', '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': '2-2e4-16.11-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.6602790493242043, 'root_angle': -0.1223002904702875, 'self_dual': False, 'spectral_label': 'c2-0', 'z1': {'__RealLiteral__': 0, 'data': '2.98931204697392862733797842527', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '3789403210615977708169909222421', 'Lhash_array': ['3789403210615977708169909222421'], 'factors': ['2-2e4-16.11-c2-0-0'], 'label': '2-2e4-16.11-c2-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/16/3/f/a/11/1'}