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lfunc_lfunctions • Show schema
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{'Lhash': '434417567265917957153591619121,1197526928165054170834353749738', 'a10': 0, 'a2': 0, 'a3': 2, 'a4': 0, 'a5': 0, 'a6': 0, 'a7': 0, 'a8': 0, 'a9': -1, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 4742.1109376785225, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [7, [1]], [11, [1, 2, 1]]], 'bad_primes': [2, 7, 11], 'central_character': '8624.1', 'coefficient_field': '1.1.1.1', 'conductor': 74373376, 'conductor_radical': 154, 'degree': 4, 'euler_factors': [[1], [1, -2, 5, -6, 9], [1, 0, 8, 0, 25], [1], [1, 2, 1], [1, -2, 19, -26, 169], [1, -4, 38, -68, 289], [1, 8, 52, 152, 361], [1, 8, 60, 184, 529], [1, -2, 59, -58, 841], [1, 8, 46, 248, 961], [1, 4, 28, 148, 1369], [1, 4, 68, 164, 1681], [1, -16, 150, -688, 1849], [1, -4, 90, -188, 2209], [1, -8, 120, -424, 2809], [1, -6, 125, -354, 3481], [1, -22, 235, -1342, 3721], [1, 2, 85, 134, 4489], [1, -20, 224, -1420, 5041], [1, -4, 148, -292, 5329], [1, 2, 109, 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['0.34269503535730182617994507305667', '0.944682176578822211001332908348241', '1.83365561692902300189506176843518', '2.20091586010092612134459616997875', '2.35028366247862087940960895787867', '2.64086360797039109863525206751531', '3.57543358182465510441565210953186', '3.61109909799597930746788294503566', '3.90179990463991841946929649492631', '4.10273578298198848765686338612723', '4.91303227161931492959890328581333', '5.20322444694246075737809028837245', '5.56966206939268821343513742455568', '5.92984732464335701416633897244478', '6.26554259254879213121100767061867', '6.36212405314112440706095947757217', '7.21557792825137379895327732378388', '7.28252216463144750559730115489503', '7.73065640091985532299721706342607', '7.984685916907702346841095873630716'], 'prelabel': '4-8624e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 8.2983725334039, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1e2-0', 'trace_hash': 2112711879537326524, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.34269503535730182617994507306', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '0.944682176578822211001332908348', 'prec': 107}, 'z3': {'__RealLiteral__': 0, 'data': '1.83365561692902300189506176844', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 4742.1109376785225, 'bad_primes': [2, 7, 11], 'central_character': '1.1', 'conductor': 74373376, 'conductor_radical': 154, 'degree': 4, 'dirichlet_coefficients': [1, 0, 2, 0, 0, 0, 0, 0, -1, 0, -2, 0, 2, 0, 0, 0, 4, 0, -8, 0, 0, 0, -8, 0, -8, 0, -6, 0, 2, 0, -8, 0, -4, 0, 0, 0, -4, 0, 4, 0, -4, 0, 16, 0, 0, 0, 4, 0, 0, 0, 8, 0, 8, 0, 0, 0, -16, 0, 6, 0, 22, 0, 0, 0, 0, 0, -2, 0, -16, 0, 20, 0, 4, 0, -16, 0, 0, 0, -2, 0, -4, 0, -4, 0, 0, 0, 4, 0, 24, 0, 0, 0, -16, 0, 0, 0, 26, 0, 2, 0], 'euler11': [1, 2, 1, 0, 0], 'euler13': [1, -2, 19, -26, 169], 'euler17': [1, -4, 38, -68, 289], 'euler19': [1, 8, 52, 152, 361], 'euler2': [1, 0, 0, 0, 0], 'euler23': [1, 8, 60, 184, 529], 'euler29': [1, -2, 59, -58, 841], 'euler3': [1, -2, 5, -6, 9], 'euler31': [1, 8, 46, 248, 961], 'euler37': [1, 4, 28, 148, 1369], 'euler41': [1, 4, 68, 164, 1681], 'euler43': [1, -16, 150, -688, 1849], 'euler47': [1, -4, 90, -188, 2209], 'euler5': [1, 0, 8, 0, 25], 'euler53': [1, -8, 120, -424, 2809], 'euler59': [1, -6, 125, -354, 3481], 'euler61': [1, -22, 235, -1342, 3721], 'euler67': [1, 2, 85, 134, 4489], 'euler7': [1, 0, 0, 0, 0], 'euler71': [1, -20, 224, -1420, 5041], 'euler73': [1, -4, 148, -292, 5329], 'euler79': [1, 2, 109, 158, 6241], 'euler83': [1, 4, 98, 332, 6889], 'euler89': [1, -24, 314, -2136, 7921], 'euler97': [1, -26, 355, -2522, 9409], 'euler_factors': [[1, 0, 0, 0, 0], [1, -2, 5, -6, 9], [1, 0, 8, 0, 25], [1, 0, 0, 0, 0], [1, 2, 1, 0, 0], [1, -2, 19, -26, 169], [1, -4, 38, -68, 289], [1, 8, 52, 152, 361], [1, 8, 60, 184, 529], [1, -2, 59, -58, 841], [1, 8, 46, 248, 961], [1, 4, 28, 148, 1369], [1, 4, 68, 164, 1681], [1, -16, 150, -688, 1849], [1, -4, 90, -188, 2209], [1, -8, 120, -424, 2809], [1, -6, 125, -354, 3481], [1, -22, 235, -1342, 3721], [1, 2, 85, 134, 4489], [1, -20, 224, -1420, 5041], [1, -4, 148, -292, 5329], [1, 2, 109, 158, 6241], [1, 4, 98, 332, 6889], [1, -24, 314, -2136, 7921], [1, -26, 355, -2522, 9409]], 'index': 4, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/8624/2/a/cd'], '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': '4-8624e2-1.1-c1e2-0-4', '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': '4-8624e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 8.2983725334039, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 2112711879537326524, 'z1': {'__RealLiteral__': 0, 'data': '0.34269503535730182617994507306', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '434417567265917957153591619121,1197526928165054170834353749738', 'Lhash_array': ['434417567265917957153591619121', '1197526928165054170834353749738'], 'factors': ['2-8624-1.1-c1-0-13', '2-8624-1.1-c1-0-103'], 'label': '4-8624e2-1.1-c1e2-0-4', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/8624/2/a/cd'}