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lfunc_lfunctions • Show schema
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{'Lhash': '559627370229608087572098876526,1066742726479218182947984484032', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': 0, 'a5': -3, 'a6': 0, 'a7': 2, 'a8': 0, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 4839.382476071137, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1]], [11, [1]]], 'bad_primes': [2, 3, 11], 'central_character': '8712.1', 'coefficient_field': '1.1.1.1', 'conductor': 75898944, 'conductor_radical': 66, 'degree': 4, 'euler_factors': [[1], [1], [1, 3, 8, 15, 25], [1, -2, -2, -14, 49], [1], [1, -2, 10, -26, 169], [1, -4, 38, -68, 289], [1, -8, 54, -152, 361], [1, 9, 62, 207, 529], [1, 2, 42, 58, 841], [1, 7, 70, 217, 961], [1, 11, 100, 407, 1369], [1, -6, 74, -246, 1681], [1, -6, 78, -258, 1849], [1, 16, 158, 752, 2209], [1, 8, 54, 424, 2809], [1, -5, 18, -295, 3481], [1, -6, 114, -366, 3721], [1, -15, 186, -1005, 4489], [1, -5, 110, -355, 5041], [1, 2, 130, 146, 5329], [1, -14, 190, -1106, 6241], 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0.7182973810702247, 0.4841274680745713, 0.21619644233770957, -0.06935839757841775], 'positive_zeros': ['0.44146815386578294920970869460031', '0.841511632848326255381804365900732', '1.59139422094954619345736616726874', '1.87019642571345915445113381773971', '2.33754167438792186562776983420787', '3.06936253573987295863097995127486', '3.57948479042599992143172610232769', '3.58910511603259224570815072355584', '3.86629603531077187530636678048573', '4.34087531986733407334779298907070', '4.95346993736919533949863942037759', '5.13260006245767723164161409460328', '5.44034047253880150875150526335170', '5.77503212644068543761214247224897', '6.33467667536438441401040690893658', '6.48405108424065690282867098688222', '7.12442818796937239745216254711199', '7.38468642085246602758979611203063', '7.72036104928894808309883722388599', '7.83759616300998346646168961788118'], 'prelabel': '4-8712e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 8.340603709620755, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1e2-0', 'trace_hash': 106666917600751009, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.44146815386578294920970869460', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '0.841511632848326255381804365901', 'prec': 107}, 'z3': {'__RealLiteral__': 0, 'data': '1.59139422094954619345736616727', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 4839.382476071137, 'bad_primes': [2, 3, 11], 'central_character': '1.1', 'conductor': 75898944, 'conductor_radical': 66, 'degree': 4, 'dirichlet_coefficients': [1, 0, 0, 0, -3, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 4, 0, 8, 0, 0, 0, -9, 0, 1, 0, 0, 0, -2, 0, -7, 0, 0, 0, -6, 0, -11, 0, 0, 0, 6, 0, 6, 0, 0, 0, -16, 0, 6, 0, 0, 0, -8, 0, 0, 0, 0, 0, 5, 0, 6, 0, 0, 0, -6, 0, 15, 0, 0, 0, 5, 0, -2, 0, 0, 0, 0, 0, 14, 0, 0, 0, 10, 0, -12, 0, 0, 0, 7, 0, 4, 0, 0, 0, -24, 0, 27, 0, 0, 0], 'euler11': [1, 0, 0, 0, 0], 'euler13': [1, -2, 10, -26, 169], 'euler17': [1, -4, 38, -68, 289], 'euler19': [1, -8, 54, -152, 361], 'euler2': [1, 0, 0, 0, 0], 'euler23': [1, 9, 62, 207, 529], 'euler29': [1, 2, 42, 58, 841], 'euler3': [1, 0, 0, 0, 0], 'euler31': [1, 7, 70, 217, 961], 'euler37': [1, 11, 100, 407, 1369], 'euler41': [1, -6, 74, -246, 1681], 'euler43': [1, -6, 78, -258, 1849], 'euler47': [1, 16, 158, 752, 2209], 'euler5': [1, 3, 8, 15, 25], 'euler53': [1, 8, 54, 424, 2809], 'euler59': [1, -5, 18, -295, 3481], 'euler61': [1, -6, 114, -366, 3721], 'euler67': [1, -15, 186, -1005, 4489], 'euler7': [1, -2, -2, -14, 49], 'euler71': [1, -5, 110, -355, 5041], 'euler73': [1, 2, 130, 146, 5329], 'euler79': [1, -14, 190, -1106, 6241], 'euler83': [1, -10, 174, -830, 6889], 'euler89': [1, -7, 152, -623, 7921], 'euler97': [1, -27, 372, -2619, 9409], 'euler_factors': [[1, 0, 0, 0, 0], [1, 0, 0, 0, 0], [1, 3, 8, 15, 25], [1, -2, -2, -14, 49], [1, 0, 0, 0, 0], [1, -2, 10, -26, 169], [1, -4, 38, -68, 289], [1, -8, 54, -152, 361], [1, 9, 62, 207, 529], [1, 2, 42, 58, 841], [1, 7, 70, 217, 961], [1, 11, 100, 407, 1369], [1, -6, 74, -246, 1681], [1, -6, 78, -258, 1849], [1, 16, 158, 752, 2209], [1, 8, 54, 424, 2809], [1, -5, 18, -295, 3481], [1, -6, 114, -366, 3721], [1, -15, 186, -1005, 4489], [1, -5, 110, -355, 5041], [1, 2, 130, 146, 5329], [1, -14, 190, -1106, 6241], [1, -10, 174, -830, 6889], [1, -7, 152, -623, 7921], [1, -27, 372, -2619, 9409]], 'index': 3, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/8712/2/a/bb'], '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': '4-8712e2-1.1-c1e2-0-3', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1, 1], 'order_of_vanishing': 0, 'prelabel': '4-8712e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 8.340603709620755, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 106666917600751009, 'z1': {'__RealLiteral__': 0, 'data': '0.44146815386578294920970869460', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '559627370229608087572098876526,1066742726479218182947984484032', 'Lhash_array': ['559627370229608087572098876526', '1066742726479218182947984484032'], 'factors': ['2-8712-1.1-c1-0-12', '2-8712-1.1-c1-0-51'], 'label': '4-8712e2-1.1-c1e2-0-3', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/8712/2/a/bb'}