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lfunc_lfunctions • Show schema
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{'Lhash': '1869610901809388547331447712839', 'a10': [0.13198279993216047, -0.32686628185877914], 'a2': [0.0, 0.15764582182482068], 'a3': [0.0, 0.8294606157415517], 'a4': [1.9751477948611769, 0.0], 'a5': [-2.0734217886345236, -0.83721089721504], 'a6': [-0.13076100043989872, 0.0], 'a7': [0.0, -1.0], 'a8': [0.0, 0.626665440996014], 'a9': [2.311995086933646, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 6.427957362713074, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[5, [[1.0, 0], [2.0734217886345236, 0.83721089721504]]], [7, [[1.0, 0], [0, 1.0]]], [23, [[1.0, 0], [0, -1.0]]]], 'bad_primes': [5, 7, 23], 'central_character': '805.484', 'coefficient_field': 'CDF', 'conductor': 805, 'conductor_radical': 805, 'conjugate': '1185426524007345556396323905934', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, -0.15764582182482068], [-2.0, 0]], [[1.0, 0], [0, -0.8294606157415517], [-3.0, 0]], [[1.0, 0], [2.0734217886345236, 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'positive_zeros': ['1.47486294841242646777086412074144', '2.63919761108261397323599226277312', '3.69960736154139734675439754155995', '4.90516020350389619483209665527482', '6.24318327092212392134216722277374', '6.95800532031559201367062760208732', '7.60189893494166443297654164713750', '8.300176375849741599928453135846605', '9.633370827995553792665451548512376', '10.45292018943335916781840214950704'], 'prelabel': '2-805-5.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.535341665873275, 'root_angle': 0.12215545231996215, 'root_number': '0.9272624130831992 + 0.37441209553528376*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.06107772616', 'prec': 44}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.47486294841242646777086412074', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.63919761108261397323599226277', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.69960736154139734675439754156', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 6.427957362713074, 'bad_primes': [5, 7, 23], 'central_character': '5.4', 'conductor': 805, 'conductor_radical': 805, 'degree': 2, 'index': 40, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/805/2/c/c/484/22'], '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': '2-805-5.4-c1-0-40', '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': '2-805-5.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.535341665873275, 'root_angle': 0.061077726159981076, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.47486294841242646777086412074', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1869610901809388547331447712839', 'Lhash_array': ['1869610901809388547331447712839'], 'label': '2-805-5.4-c1-0-40', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/805/2/c/c/484/22'}