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lfunc_lfunctions • Show schema
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{'Lhash': '2737469944039504274676626871753', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [3.23606797749979, 0.0], 'a4': [0.0, 0.0], 'a5': [-1.2360679774997898, 0.0], 'a6': [0.0, 0.0], 'a7': [-1.0, 0.0], 'a8': [0.0, 0.0], 'a9': [7.47213595499958, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.7886490052766815, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [1.0, 0]]]], 'bad_primes': [2, 7], 'central_character': '224.1', 'coefficient_field': 'CDF', 'conductor': 224, 'conductor_radical': 14, 'conjugate': '2737469944039504274676626871753', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-3.23606797749979, 0], [3.0, 0]], [[1.0, 0], [1.2360679774997898, 0], [5.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [2.4721359549995796, 0], [11.0, 0]], [[1.0, 0], [-5.23606797749979, 0], [13.0, 0]], [[1.0, 0], [4.47213595499958, 0], [17.0, 0]], [[1.0, 0], [3.23606797749979, 0], [19.0, 0]], 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'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 4, 'label': '2-224-1.1-c1-0-4', '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/224/2/a/d/1/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [1.886282611613162, 1.8940384180017338, 1.9158860292489506, 1.9477730308439363, 1.9835566093144221, 2.0157043558364256, 2.03599514976118, 2.036146679699984, 2.0083714302634847, 1.9458937372890595, 1.8434544020553882, 1.6978066784388985, 1.5081830516526222, 1.276692926664859, 1.0085992270241282, 0.7124173356495754, 0.39978282912837687, 0.08504509255206871, -0.2154379959981601, -0.484304156098146, -0.7044588830301911, -0.8605510618448247, -0.9405529605995516, -0.9373144191559015, -0.8499373873847529, -0.6848050197350679, -0.4561031121804269, -0.1856935718958516, 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'10.13066451433255203489171863316473', '11.14940950384920267977657764595422', '12.69184392290246865848785566472929'], 'prelabel': '2-224-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.3374038302908666, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.15948301807031587246528686001', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.45664727824938054196263640486', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.29668658677344589822753768806', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.7886490052766815, 'bad_primes': [2, 7], 'central_character': '1.1', 'conductor': 224, 'conductor_radical': 14, 'degree': 2, 'index': 4, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/224/2/a/d/1/2'], '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': '2-224-1.1-c1-0-4', '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': '2-224-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.3374038302908666, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.15948301807031587246528686001', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2737469944039504274676626871753', 'Lhash_array': ['2737469944039504274676626871753'], 'label': '2-224-1.1-c1-0-4', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/224/2/a/d/1/2'}