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lfunc_lfunctions • Show schema
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{'Lhash': '1061758836253195472537551163732', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [0.3166809768890286, -1.702854415056264], 'a4': [0.0, 0.0], 'a5': [1.860878567454226, 3.2231362255467078], 'a6': [0.0, 0.0], 'a7': [-2.4642858405443335, 0.9629617313749844], 'a8': [0.0, 0.0], 'a9': [-2.799426317753221, -1.078523199319626], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 5.365947015830044, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [-0.3166809768890286, 1.702854415056264]]], [7, [[1.0, 0], [2.4642858405443335, -0.9629617313749844]]]], 'bad_primes': [2, 3, 7], 'central_character': '672.431', 'coefficient_field': 'CDF', 'conductor': 672, 'conductor_radical': 42, 'conjugate': '2251060089578993789142473713573', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-0.3166809768890286, 1.702854415056264]], [[1.0, 0], [-1.860878567454226, -3.2231362255467078], [-2.5, 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'10.10783388076486413057338976660825'], 'prelabel': '2-672-168.11-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.3164513843010055, 'root_angle': -0.13139990633928164, 'root_number': '0.6781087940137588 - 0.7349615387768299*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.131399906339', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.837580036693103826920049868236', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '2.76734572074057912662956547442', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.90008674401551924220999918728', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 5.365947015830044, 'bad_primes': [2, 3, 7], 'central_character': '168.11', 'conductor': 672, 'conductor_radical': 42, 'degree': 2, 'index': 5, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/672/2/bd/a/431/16'], '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': '2-672-168.11-c1-0-5', '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': '2-672-168.11-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.3164513843010055, 'root_angle': -0.13139990633928164, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.837580036693103826920049868236', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1061758836253195472537551163732', 'Lhash_array': ['1061758836253195472537551163732'], 'factors': ['2-672-168.11-c1-0-5'], 'label': '2-672-168.11-c1-0-5', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/672/2/bd/a/431/16'}