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lfunc_lfunctions • Show schema
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{'Lhash': '237480763654079474288766695203', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [-1.0, 0.0], 'a4': [0.0, 0.0], 'a5': [-3.201472338219241, 0.0], 'a6': [0.0, 0.0], 'a7': [0.0, 0.0], 'a8': [0.0, 0.0], 'a9': [1.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 37.56162911081031, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [1.0, 0]]], [7, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 3, 7], 'central_character': '4704.1', 'coefficient_field': 'CDF', 'conductor': 4704, 'conductor_radical': 42, 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [3.201472338219241, 0], [5.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [4.249425132382973, 0], [11.0, 0]], [[1.0, 0], [3.153519544055509, 0], [13.0, 0]], [[1.0, 0], [4.402944676438482, 0], [17.0, 0]], [[1.0, 0], [3.153519544055509, 0], [19.0, 0]], [[1.0, 0], [4.402944676438482, 0], [23.0, 0]], [[1.0, 0], 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'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 0, 'label': '2-4704-1.1-c1-0-0', 'leading_term': '0.12310079336053584101731588311092', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/4704/2/a/bs/1/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05078125', 'prec': 34}, 'plot_values': [0.12310079336053584, 0.1140588801024381, 0.08692799239070187, 0.04169954607588064, -0.02161838829461462, -0.10296917683931794, -0.20220609291963312, -0.319043941290748, -0.4530069538931275, -0.6033761930584338, -0.7691396238191586, -0.9489477989526964, -1.1410777872825517, -1.3434076085678073, -1.5534030455672971, -1.768118301302833, -1.9842115625133403, -2.1979761174127392, -2.405387252774539, -2.602164717803389, -2.7838500882226547, -2.9458978950246277, -3.0837789039120986, -3.1930934530457007, 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'5.07923496502479215161310049105974', '6.23427234536028422489273452084082', '6.93285234944250783552437804798644', '7.59099323980563532332917323499325', '8.197965102239569869701563417624211'], 'prelabel': '2-4704-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.128754287031771, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.18733929018873429335510484084', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.94788014867139412214005367440', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.95240405114502665272081899105', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 37.56162911081031, 'bad_primes': [2, 3, 7], 'central_character': '1.1', 'conductor': 4704, 'conductor_radical': 42, 'degree': 2, 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/4704/2/a/bs/1/1'], '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': '2-4704-1.1-c1-0-0', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-4704-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.128754287031771, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.18733929018873429335510484084', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '237480763654079474288766695203', 'Lhash_array': ['237480763654079474288766695203'], 'label': '2-4704-1.1-c1-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/4704/2/a/bs/1/1'}