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lfunc_lfunctions • Show schema
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{'Lhash': '187163013821008161642125992315', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0.43982005497711135, 0.7617906814080937], 'a4': [0, 0], 'a5': [0, 3.767839590487884], 'a6': [0, 0], 'a7': [-0.8660254037844386, -0.5], 'a8': [0, 0], 'a9': [1.1131166384798614, -1.927974572597398], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 11.62621853429843, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [0.8660254037844386, 0.5]]], [13, [[1.0, 0], [3.1233832351750177, 1.8012432279477526]]]], 'bad_primes': [2, 7, 13], 'central_character': '1456.673', 'coefficient_field': 'CDF', 'conductor': 1456, 'conductor_radical': 182, 'conjugate': '2896446300292696500209208491488', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-0.43982005497711135, -0.7617906814080937], [-1.5, 2.598076211353316]], [[1.0, 0], [0, -3.767839590487884], [-5.0, 0]], [[1.0, 0], [0.8660254037844386, 0.5]], [[1.0, 0], 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'0.4176092532951635158959767997481601196154333973223153760', '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/1456/2/cc/e/673/4', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05078125', 'prec': 34}, 'plot_values': [0.4176092532951635, 0.270709778436462, 0.1272742813277373, -0.012823441746407599, -0.1496344754046032, -0.2831070691840654, -0.4130646747178344, -0.5391905438326323, -0.6610193049797303, -0.7779355771908663, -0.8891793856851749, -0.9938579253383545, -1.090963076018055, -1.1793939949099002, -1.257984077529642, -1.3255315725644106, -1.3808331400637741, -1.4227196461946172, -1.45009348387365, -1.4619666944046348, -1.4574991413855136, -1.43603595752232, -1.3971434518880095, -1.3406426345481803, -1.2666394924138231, -1.1755511394912974, -1.0681269706986374, -0.9454639747621824, 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'7.62650381059138361998522086790835', '8.354828379647136102983654727639037', '8.835344239944422329511976135769339'], 'prelabel': '2-1456-13.10-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.4097241141034313, 'root_angle': 0.8372590432362068, 'root_number': '-0.87212587670872582865264463761411330178010238909643473242 + 0.4892815704428650919618237424418473051027840962854245249*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.4186295216181034', 'prec': 60}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.14764558450673324199627511630', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.67437830919185873259077326876', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.54040680759841533910898804432', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 11.62621853429843, 'bad_primes': [2, 7, 13], 'central_character': '13.10', 'conductor': 1456, 'conductor_radical': 182, 'degree': 2, 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1456/2/cc/e/673/4'], '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': '2-1456-13.10-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': '2-1456-13.10-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.4097241141034313, 'root_angle': 0.4186295216181034, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.14764558450673324199627511630', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '187163013821008161642125992315', 'Lhash_array': ['187163013821008161642125992315'], 'label': '2-1456-13.10-c1-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1456/2/cc/e/673/4'}