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lfunc_lfunctions • Show schema
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{'Lhash': '1529039489617897066111535497531', 'a10': [-2.4955076566049246, 0.0], 'a2': [-2.4955076566049246, 0.0], 'a3': [-2.8268383953119516, 0.0], 'a4': [4.227558464173802, 0.0], 'a5': [1.0, 0.0], 'a6': [7.054396859485753, 0.0], 'a7': [-1.9052124122569258, 0.0], 'a8': [-5.558889202880829, 0.0], 'a9': [4.991015313209849, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 6.747358970798196, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[5, [[1.0, 0], [-1.0, 0]]], [13, [[1.0, 0], [0, 0]]]], 'bad_primes': [5, 13], 'central_character': '845.1', 'coefficient_field': 'CDF', 'conductor': 845, 'conductor_radical': 65, 'conjugate': '1529039489617897066111535497531', 'degree': 2, 'euler_factors': [[[1.0, 0], [2.4955076566049246, 0], [2.0, 0]], [[1.0, 0], [2.8268383953119516, 0], [3.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [1.9052124122569258, 0], [7.0, 0]], [[1.0, 0], [1.0693893301548232, 0], [11.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], 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'4.61727994784162460116145434128520', '5.82446743820835504560652361209837', '6.51600577856408276116416099403082', '7.02635831294781775116190016916780', '8.207598342618240121616733112498050', '9.105080116997518109552901283336384', '9.968835118545899550969547747504293'], 'prelabel': '2-845-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.5975678953201964, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.20619947589864816191587014973', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.68174683659477742947105495160', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.61727994784162460116145434129', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 6.747358970798196, 'bad_primes': [5, 13], 'central_character': '1.1', 'conductor': 845, 'conductor_radical': 65, 'degree': 2, 'index': 18, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/845/2/a/l/1/1'], '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': '2-845-1.1-c1-0-18', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'prelabel': '2-845-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.5975678953201964, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.20619947589864816191587014973', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1529039489617897066111535497531', 'Lhash_array': ['1529039489617897066111535497531'], 'label': '2-845-1.1-c1-0-18', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/845/2/a/l/1/1'}