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lfunc_lfunctions • Show schema
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{'Lhash': '1643806394173303032273253981243,1886248032697649829754210889177', 'a10': 0, 'a2': 0, 'a3': -2, 'a4': 0, 'a5': 2, 'a6': 0, 'a7': 2, 'a8': 0, 'a9': 3, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1942.819122738756, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, 2, 1]], [5, [1, -2, 1]], [23, [1, -2, 1]]], 'bad_primes': [2, 3, 5, 23], 'central_character': '5520.1', 'coefficient_field': '1.1.1.1', 'conductor': 30470400, 'conductor_radical': 690, 'degree': 4, 'euler_factors': [[1], [1, 2, 1], [1, -2, 1], [1, -2, 15, -14, 49], [1, -4, 8, -44, 121], [1, 8, 40, 104, 169], [1, 6, 41, 102, 289], [1, 0, -12, 0, 361], [1, -2, 1], [1, 6, 49, 174, 841], [1, -10, 55, -310, 961], [1, 6, 83, 222, 1369], [1, 6, 89, 246, 1681], [1, 4, 90, 172, 1849], [1, 8, 108, 376, 2209], [1, 10, 129, 530, 2809], [1, -10, 93, -590, 3481], [1, 12, 108, 732, 3721], [1, 10, 127, 670, 4489], [1, -10, 117, -710, 5041], [1, 0, -96, 0, 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4.094624831799788], 'positive_zeros': ['1.29673460011563917580190857718854', '1.48798733054522071923383153399903', '2.03660463170726851993443952445145', '2.38698678545669935520309868641991', '3.06259212135660160400564661163182', '3.39035498720159624891161968549261', '4.27045187131788394301113708874079', '4.41599738224735621597318883960574', '4.80062121280810881805876208081219', '5.01550542870153924814862024250946', '5.40689523529663712690479257581316', '5.73200606517624761887001746110080', '6.46213577116685072095103128847921', '6.47135976633997813671930328080396', '6.81829885701393525496777589447406', '6.99634598576095783817616187693188', '7.71143626023053175143171229733890', '7.74953599290933879962266125460857'], 'prelabel': '4-5520e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 6.639082912251269, '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': 816501235918425331, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.29673460011563917580190857719', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.48798733054522071923383153400', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.03660463170726851993443952445', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1942.819122738756, 'bad_primes': [2, 3, 5, 23], 'central_character': '1.1', 'conductor': 30470400, 'conductor_radical': 690, 'degree': 4, 'dirichlet_coefficients': [1, 0, -2, 0, 2, 0, 2, 0, 3, 0, 4, 0, -8, 0, -4, 0, -6, 0, 0, 0, -4, 0, 2, 0, 3, 0, -4, 0, -6, 0, 10, 0, -8, 0, 4, 0, -6, 0, 16, 0, -6, 0, -4, 0, 6, 0, -8, 0, -11, 0, 12, 0, -10, 0, 8, 0, 0, 0, 10, 0, -12, 0, 6, 0, -16, 0, -10, 0, -4, 0, 10, 0, 0, 0, -6, 0, 8, 0, 0, 0, 5, 0, -18, 0, -12, 0, 12, 0, -16, 0, -16, 0, -20, 0, 0, 0, -8, 0, 12, 0], 'euler11': [1, -4, 8, -44, 121], 'euler13': [1, 8, 40, 104, 169], 'euler17': [1, 6, 41, 102, 289], 'euler19': [1, 0, -12, 0, 361], 'euler2': [1, 0, 0, 0, 0], 'euler23': [1, -2, 1, 0, 0], 'euler29': [1, 6, 49, 174, 841], 'euler3': [1, 2, 1, 0, 0], 'euler31': [1, -10, 55, -310, 961], 'euler37': [1, 6, 83, 222, 1369], 'euler41': [1, 6, 89, 246, 1681], 'euler43': [1, 4, 90, 172, 1849], 'euler47': [1, 8, 108, 376, 2209], 'euler5': [1, -2, 1, 0, 0], 'euler53': [1, 10, 129, 530, 2809], 'euler59': [1, -10, 93, -590, 3481], 'euler61': [1, 12, 108, 732, 3721], 'euler67': [1, 10, 127, 670, 4489], 'euler7': [1, -2, 15, -14, 49], 'euler71': [1, -10, 117, -710, 5041], 'euler73': [1, 0, -96, 0, 5329], 'euler79': [1, 0, 126, 0, 6241], 'euler83': [1, 18, 197, 1494, 6889], 'euler89': [1, 16, 234, 1424, 7921], 'euler97': [1, 8, 202, 776, 9409], 'euler_factors': [[1, 0, 0, 0, 0], [1, 2, 1, 0, 0], [1, -2, 1, 0, 0], [1, -2, 15, -14, 49], [1, -4, 8, -44, 121], [1, 8, 40, 104, 169], [1, 6, 41, 102, 289], [1, 0, -12, 0, 361], [1, -2, 1, 0, 0], [1, 6, 49, 174, 841], [1, -10, 55, -310, 961], [1, 6, 83, 222, 1369], [1, 6, 89, 246, 1681], [1, 4, 90, 172, 1849], [1, 8, 108, 376, 2209], [1, 10, 129, 530, 2809], [1, -10, 93, -590, 3481], [1, 12, 108, 732, 3721], [1, 10, 127, 670, 4489], [1, -10, 117, -710, 5041], [1, 0, -96, 0, 5329], [1, 0, 126, 0, 6241], [1, 18, 197, 1494, 6889], [1, 16, 234, 1424, 7921], [1, 8, 202, 776, 9409]], 'index': 9, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/5520/2/a/bk'], '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': '4-5520e2-1.1-c1e2-0-9', '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': '4-5520e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 6.639082912251269, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 816501235918425331, 'z1': {'__RealLiteral__': 0, 'data': '1.29673460011563917580190857719', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1643806394173303032273253981243,1886248032697649829754210889177', 'Lhash_array': ['1643806394173303032273253981243', '1886248032697649829754210889177'], 'label': '4-5520e2-1.1-c1e2-0-9', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/5520/2/a/bk'}