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lfunc_lfunctions • Show schema
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{'Lhash': '2378675084619172407157677651658', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, 0], 'a4': [0, 0], 'a5': [-0.19433935161259985, 0.08049799514073248], 'a6': [0, 0], 'a7': [-1.7631669397699925, -0.7303276591805969], 'a8': [0, 0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 9.773689207404724, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 0]]], [17, [[1.0, 0], [4.075213053234173, -0.626608786045815]]]], 'bad_primes': [2, 3, 17], 'central_character': '1224.865', 'coefficient_field': 'CDF', 'conductor': 1224, 'conductor_radical': 102, 'conjugate': '72493683233570917186013390004', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0.19433935161259985, -0.08049799514073248], [3.5355339059327378, -3.5355339059327378]], [[1.0, 0], [1.7631669397699925, 0.7303276591805969], [4.949747468305833, 4.949747468305833]], [[1.0, 0], 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-79.90306627407988]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 22, 'label': '2-1224-17.15-c1-0-22', 'leading_term': '0.144061040357384076034101978909646420418519482529399668', '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/1224/2/bq/c/865/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 'prec': 34}, 'plot_values': [0.14406104035738407, 0.29172596701649267, 0.4396278744680236, 0.5878679814613241, 0.7364114296752572, 0.8850347262355315, 1.033284045200478, 1.180446112646286, 1.3255324590252702, 1.4672770308445087, 1.6041465792508762, 1.7343628900838939, 1.855935747160059, 1.9667054654252265, 2.064393830126039, 2.1466622819327856, 2.211176163502066, 2.255673775225565, 2.27803887577175, 2.2763751150658367, 2.249080717916389, 2.194921562694145, 2.113100639093754, 2.003321739206433, 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'6.67197043006146292225290878651743', '7.61017030431864684126486436353697', '8.712054211757516953428113995209182', '9.249791287085917028317828069840183', '9.949068967962198841350963388477755'], 'prelabel': '2-1224-17.15-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.1262900069258968, 'root_angle': 0.9756152063694437, 'root_number': '-0.99706711175477245746877443846635460847746537982277608120 + 0.0765321805320878804555052578818747017915136861795788179*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.4878076031847219', 'prec': 60}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.87644378047934720040101358116', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.96825939437664641426028244298', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.12504563291512671957755401355', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 9.773689207404724, 'bad_primes': [2, 3, 17], 'central_character': '17.15', 'conductor': 1224, 'conductor_radical': 102, 'degree': 2, 'index': 22, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1224/2/bq/c/865/2'], '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': '2-1224-17.15-c1-0-22', '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': '2-1224-17.15-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.1262900069258968, 'root_angle': 0.4878076031847218, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.87644378047934720040101358116', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2378675084619172407157677651658', 'Lhash_array': ['2378675084619172407157677651658'], 'label': '2-1224-17.15-c1-0-22', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1224/2/bq/c/865/2'}