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lfunc_lfunctions • Show schema
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{'Lhash': '820320487824332176553545871920,1131745679406686120387961976061', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': 0, 'a5': 0, 'a6': 0, 'a7': 0, 'a8': 0, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1353.876826855227, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1]]], 'bad_primes': [2, 3], 'central_character': '4608.1', 'coefficient_field': '1.1.1.1', 'conductor': 21233664, 'conductor_radical': 6, 'degree': 4, 'euler_factors': [[1], [1], [1, 0, -2, 0, 25], [1, 0, -12, 0, 49], [1, 0, 22, 0, 121], [1, 4, 30, 52, 169], [1, 0, -32, 0, 289], [1, 0, -30, 0, 361], [1, -12, 82, -276, 529], [1, 0, -26, 0, 841], [1, 0, 36, 0, 961], [1, -4, 78, -148, 1369], [1, 0, -64, 0, 1681], [1, 0, -14, 0, 1849], [1, -20, 194, -940, 2209], [1, 0, -74, 0, 2809], [1, -24, 262, -1416, 3481], [1, 20, 222, 1220, 3721], [1, 0, -102, 0, 4489], [1, -4, 146, -284, 5041], [1, 20, 246, 1460, 5329], [1, 0, 4, 0, 6241], [1, -8, 182, -664, 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['0.64711876259644467384693553226549', '0.892789921136727431852781688923567', '1.67080124538445968311198073427412', '2.36503840258358066388202104256522', '2.71322142207489615024343636440696', '2.89387165350341469181261838314841', '3.67320386780717945841491230456256', '3.90067216209622636299953080181407', '4.55579746025051230656506941527520', '4.79630525312801323286761518690333', '5.07564062504294069323065310652712', '5.68554834163475471066921613941085', '5.82619666635213650403729242705700', '6.28344220831121769811173796880333', '6.91035365787776931389898515052413', '7.16182202388232032733600562585479', '7.40308398296919935030251549439596', '7.47226591349202500757507217900722', '8.243407613607398816545171528552165', '8.541348756136689073782896055379046'], 'prelabel': '4-4608e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 6.065893606996913, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1e2-0', 'trace_hash': 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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1353.876826855227, 'bad_primes': [2, 3], 'central_character': '1.1', 'conductor': 21233664, 'conductor_radical': 6, 'degree': 4, 'dirichlet_coefficients': [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 12, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 20, 0, 12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 24, 0, -20, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, -20, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 24, 0, 0, 0], 'euler11': [1, 0, 22, 0, 121], 'euler13': [1, 4, 30, 52, 169], 'euler17': [1, 0, -32, 0, 289], 'euler19': [1, 0, -30, 0, 361], 'euler2': [1, 0, 0, 0, 0], 'euler23': [1, -12, 82, -276, 529], 'euler29': [1, 0, -26, 0, 841], 'euler3': [1, 0, 0, 0, 0], 'euler31': [1, 0, 36, 0, 961], 'euler37': [1, -4, 78, -148, 1369], 'euler41': [1, 0, -64, 0, 1681], 'euler43': [1, 0, -14, 0, 1849], 'euler47': [1, -20, 194, -940, 2209], 'euler5': [1, 0, -2, 0, 25], 'euler53': [1, 0, -74, 0, 2809], 'euler59': [1, -24, 262, -1416, 3481], 'euler61': [1, 20, 222, 1220, 3721], 'euler67': [1, 0, -102, 0, 4489], 'euler7': [1, 0, -12, 0, 49], 'euler71': [1, -4, 146, -284, 5041], 'euler73': [1, 20, 246, 1460, 5329], 'euler79': [1, 0, 4, 0, 6241], 'euler83': [1, -8, 182, -664, 6889], 'euler89': [1, 0, -80, 0, 7921], 'euler97': [1, -24, 338, -2328, 9409], 'euler_factors': [[1, 0, 0, 0, 0], [1, 0, 0, 0, 0], [1, 0, -2, 0, 25], [1, 0, -12, 0, 49], [1, 0, 22, 0, 121], [1, 4, 30, 52, 169], [1, 0, -32, 0, 289], [1, 0, -30, 0, 361], [1, -12, 82, -276, 529], [1, 0, -26, 0, 841], [1, 0, 36, 0, 961], [1, -4, 78, -148, 1369], [1, 0, -64, 0, 1681], [1, 0, -14, 0, 1849], [1, -20, 194, -940, 2209], [1, 0, -74, 0, 2809], [1, -24, 262, -1416, 3481], [1, 20, 222, 1220, 3721], [1, 0, -102, 0, 4489], [1, -4, 146, -284, 5041], [1, 20, 246, 1460, 5329], [1, 0, 4, 0, 6241], [1, -8, 182, -664, 6889], [1, 0, -80, 0, 7921], [1, -24, 338, -2328, 9409]], 'index': 34, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/4608/2/c/d'], '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': '4-4608e2-1.1-c1e2-0-34', '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': '4-4608e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 6.065893606996913, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 1463597798696650190, 'z1': {'__RealLiteral__': 0, 'data': '0.64711876259644467384693553227', 'prec': 103}}
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{'Lhash': '820320487824332176553545871920,1131745679406686120387961976061', 'Lhash_array': ['820320487824332176553545871920', '1131745679406686120387961976061'], 'label': '4-4608e2-1.1-c1e2-0-34', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/4608/2/c/d'}