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lfunc_lfunctions • Show schema
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{'Lhash': '1459119221735334244488102444632,1783641925543960843059138057783', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': 0, 'a5': 2, 'a6': 0, 'a7': -2, 'a8': 0, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 5846.857224180202, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1]], [7, [1, 2, 1]], [19, [1, -2, 1]]], 'bad_primes': [2, 3, 7, 19], 'central_character': '9576.1', 'coefficient_field': '1.1.1.1', 'conductor': 91699776, 'conductor_radical': 798, 'degree': 4, 'euler_factors': [[1], [1], [1, -2, 6, -10, 25], [1, 2, 1], [1, 0, 2, 0, 121], [1, 0, 6, 0, 169], [1, 2, 30, 34, 289], [1, -2, 1], [1, 8, 42, 184, 529], [1, 10, 78, 290, 841], [1, -4, 46, -124, 961], [1, 0, 54, 0, 1369], [1, -4, 86, -164, 1681], [1, -16, 150, -688, 1849], [1, -2, 90, -94, 2209], [1, -2, 102, -106, 2809], [1, -8, 134, -472, 3481], [1, 16, 166, 976, 3721], [1, 12, 150, 804, 4489], [1, 6, 146, 426, 5041], [1, 0, 126, 0, 5329], [1, 24, 302, 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'1.40704538397475749011271734053890', '2.21113185854446894071579297139156', '2.21713228050150796281853352126011', '2.81445499711354156946386247002357', '3.09453400936313081601225809344481', '3.81719112521580628574694423563830', '3.93676998670209969985001390485437', '4.35195028037816390684284027779313', '4.62231608038667603239056930204534', '5.34994363652599251282863156396506', '5.58549832141792829673213412357894', '5.95676842864901874450457831268523', '5.98090463534957735751113656080450', '6.36711393436554598551836789273214', '6.81734263652294456454082607282734', '7.31632370874229010607916925332233', '7.41899486715441144324200888190771'], 'prelabel': '4-9576e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 8.744412214413165, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c1e2-0', 'trace_hash': 297177626810559999, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.15104211008351401609105827360', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.40704538397475749011271734054', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.21113185854446894071579297139', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 5846.857224180202, 'bad_primes': [2, 3, 7, 19], 'central_character': '1.1', 'conductor': 91699776, 'conductor_radical': 798, 'degree': 4, 'dirichlet_coefficients': [1, 0, 0, 0, 2, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 2, 0, 0, 0, -8, 0, -2, 0, 0, 0, -10, 0, 4, 0, 0, 0, -4, 0, 0, 0, 0, 0, 4, 0, 16, 0, 0, 0, 2, 0, 3, 0, 0, 0, 2, 0, 0, 0, 0, 0, 8, 0, -16, 0, 0, 0, 0, 0, -12, 0, 0, 0, -6, 0, 0, 0, 0, 0, 0, 0, -24, 0, 0, 0, -2, 0, -4, 0, 0, 0, -4, 0, 0, 0, 0, 0, 4, 0, 16, 0, 0, 0], 'euler11': [1, 0, 2, 0, 121], 'euler13': [1, 0, 6, 0, 169], 'euler17': [1, 2, 30, 34, 289], 'euler19': [1, -2, 1, 0, 0], 'euler2': [1, 0, 0, 0, 0], 'euler23': [1, 8, 42, 184, 529], 'euler29': [1, 10, 78, 290, 841], 'euler3': [1, 0, 0, 0, 0], 'euler31': [1, -4, 46, -124, 961], 'euler37': [1, 0, 54, 0, 1369], 'euler41': [1, -4, 86, -164, 1681], 'euler43': [1, -16, 150, -688, 1849], 'euler47': [1, -2, 90, -94, 2209], 'euler5': [1, -2, 6, -10, 25], 'euler53': [1, -2, 102, -106, 2809], 'euler59': [1, -8, 134, -472, 3481], 'euler61': [1, 16, 166, 976, 3721], 'euler67': [1, 12, 150, 804, 4489], 'euler7': [1, 2, 1, 0, 0], 'euler71': [1, 6, 146, 426, 5041], 'euler73': [1, 0, 126, 0, 5329], 'euler79': [1, 24, 302, 1896, 6241], 'euler83': [1, 2, 122, 166, 6889], 'euler89': [1, 4, 102, 356, 7921], 'euler97': [1, -16, 238, -1552, 9409], 'euler_factors': [[1, 0, 0, 0, 0], [1, 0, 0, 0, 0], [1, -2, 6, -10, 25], [1, 2, 1, 0, 0], [1, 0, 2, 0, 121], [1, 0, 6, 0, 169], [1, 2, 30, 34, 289], [1, -2, 1, 0, 0], [1, 8, 42, 184, 529], [1, 10, 78, 290, 841], [1, -4, 46, -124, 961], [1, 0, 54, 0, 1369], [1, -4, 86, -164, 1681], [1, -16, 150, -688, 1849], [1, -2, 90, -94, 2209], [1, -2, 102, -106, 2809], [1, -8, 134, -472, 3481], [1, 16, 166, 976, 3721], [1, 12, 150, 804, 4489], [1, 6, 146, 426, 5041], [1, 0, 126, 0, 5329], [1, 24, 302, 1896, 6241], [1, 2, 122, 166, 6889], [1, 4, 102, 356, 7921], [1, -16, 238, -1552, 9409]], 'index': 17, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/9576/2/a/bq'], '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': '4-9576e2-1.1-c1e2-0-17', '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': 2, 'prelabel': '4-9576e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 8.744412214413165, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 297177626810559999, 'z1': {'__RealLiteral__': 0, 'data': '1.15104211008351401609105827360', 'prec': 103}}
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{'Lhash': '1459119221735334244488102444632,1783641925543960843059138057783', 'Lhash_array': ['1459119221735334244488102444632', '1783641925543960843059138057783'], 'label': '4-9576e2-1.1-c1e2-0-17', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/9576/2/a/bq'}