-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1084514462759001858665676151978', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': 0, 'a5': 1, 'a6': 0, 'a7': 1, 'a8': 0, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 74.73997629191848, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1]], [5, [1, -1]], [13, [1, -1]]], 'bad_primes': [2, 3, 5, 13], 'central_character': '9360.1', 'coefficient_field': '1.1.1.1', 'conductor': 9360, 'conductor_radical': 390, 'degree': 2, 'euler_factors': [[1], [1], [1, -1], [1, -1, 7], [1, -3, 11], [1, -1], [1, 3, 17], [1, -4, 19], [1, -9, 23], [1, 6, 29], [1, 2, 31], [1, 1, 37], [1, 3, 41], [1, 2, 43], [1, -6, 47], [1, -9, 53], [1, -12, 59], [1, -5, 61], [1, -4, 67], [1, 9, 71], [1, -14, 73], [1, -7, 79], [1, 0, 83], [1, -15, 89], [1, -5, 97], [1, 12, 101], [1, 14, 103], [1, 3, 107], [1, 10, 109], [1, 6, 113]], 'euler_factors_factorization': [[1], [1], [[[1, -1], 1]], [[[1, -1, 7], 1]], [[[1, -3, 11], 1]], [[[1, -1], 1]], [[[1, 3, 17], 1]], [[[1, -4, 19], 1]], [[[1, -9, 23], 1]], [[[1, 6, 29], 1]], [[[1, 2, 31], 1]], [[[1, 1, 37], 1]], [[[1, 3, 41], 1]], [[[1, 2, 43], 1]], [[[1, -6, 47], 1]], [[[1, -9, 53], 1]], [[[1, -12, 59], 1]], [[[1, -5, 61], 1]], [[[1, -4, 67], 1]], [[[1, 9, 71], 1]], [[[1, -14, 73], 1]], [[[1, -7, 79], 1]], [[[1, 0, 83], 1]], [[[1, -15, 89], 1]], [[[1, -5, 97], 1]], [[[1, 12, 101], 1]], [[[1, 14, 103], 1]], [[[1, 3, 107], 1]], [[[1, 10, 109], 1]], [[[1, 6, 113], 1]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 52, 'label': '2-9360-1.1-c1-0-52', 'leading_term': '2.81215612001021163641885334939940000000000000000000000000000000000000000000000000000000000', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/9360/2/a/bu', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.046875', 'prec': 27}, 'plot_values': [2.8121561200102114, 2.8025199582910885, 2.7736009123911485, 2.725374458932697, 2.657823072732473, 2.570969491371901, 2.4649199411803564, 2.3399143433707286, 2.196380120680325, 2.034986070000566, 1.8566928312485294, 1.662796726083842, 1.4549641143740357, 1.2352538762743825, 1.0061261362327387, 0.7704358754250489, 0.5314106143584546, 0.2926118787670888, 0.05788068552869481, -0.16873220068464867, -0.3830499869533522, -0.5808658078108877, -0.7580487117764292, -0.9106570389168652, -1.0350561575741597, -1.1280371923143064, -1.1869331097674574, -1.2097283492955233, -1.1951581056107288, -1.1427934032177791, -1.053108257995985, -0.9275255061965623, -0.7684382984183871, -0.5792048039886227, -0.364114342885663, -0.12832394597298877, 0.12223477729635233, 0.38097763360944326, 0.6408168762589371, 0.8943344332996037, 1.1339755034099703, 1.3522577532845197, 1.541990507297848, 1.6964976072196207, 1.809837072161848, 1.8770103386876864, 1.8941537353317868, 1.8587049657275512, 1.7695377536812213, 1.6270584468619913, 1.4332592788231842, 1.191724137348931, 0.9075840559253264, 0.5874211997081977, 0.23912181348577227, -0.12831961585125326, -0.5050409156089293, -0.8805916571356811, -1.2442439391736215, -1.585325502135972, -1.8935648870558488, -2.159437389961953, -2.374499954435138, -2.5317029362208796, -2.625666895557858, -2.652913242196912, -2.6120386754834835, -2.5038249105272414, -2.331277126718475, -2.099586864426417, -1.8160176607960974, -1.4897144724620563, -1.1314407856417916, -0.7532501571187741, -0.36810165218093527, 0.010568864626518229, 0.3693074822059629, 0.6951152308074252, 0.9759183247253281, 1.2010181120133026, 1.3615032725469323, 1.450607579184924, 1.4639979959575031, 1.3999800057163168, 1.259609782802611, 1.0467060718139891, 0.767758293741088, 0.43173134554051923, 0.04977164053468692, -0.3651770058761157, -0.7988351751205696, -1.2361113518745832, -1.661668172052604, -2.06051012092922, -2.4185698514258016, -2.723269636910273, -2.9640347626101464, -3.132736920012871, -3.224047884150309, -3.2356868676057435, -3.1685488596282996, -3.026705837507191, -2.817277809634146, -2.5501760163950427, -2.237726056267849, -1.8941839883095575, -1.5351633543458845, -1.1769953384027232, -0.8360477294310975, -0.5280307968479886, -0.2673194852046213, -0.0663213883654742, 0.0650812693112315, 0.11998992552084185, 0.0948262413291366, -0.010470279275438987, -0.19239512682164364, -0.44398722620248926, -0.7550913450175841, -1.1127659405850967, -1.5018212117467074, -1.9054659197275616, -2.3060361405598817, -2.6857747811641994, -3.027627663051917, -3.3160204301868896, -3.5375805864698187, -3.681770658784362, -3.7414017836743514, -3.7130018232712767, -3.597018248814355, -3.3978432396981018, -3.123656425510507, -2.7860890950138324, -2.3997221257183656, -1.9814379533849082, -1.5496542103549584, -1.12347284705889, -0.7217832870393412, -0.36236118673724266, -0.061005486045730514, 0.1692444606204631, 0.3187728010527056, 0.38189813113699106, 0.35720405605251304, 0.24767003568875184, 0.060592390266835064, -0.19270474508987614, -0.49735857463559047, -0.8356370585683413, -1.1877595811513064, -1.5328319037925031, -1.8498521100830325, -2.1187399047055795, -2.3213395273044037, -2.442346844173696, -2.4701139277031077, -2.3972895476067526, -2.2212612802106158, -1.9443740797422648, -1.5739107346477745, -1.121831155345911, -0.6042793502636656, -0.04087865378753118, 0.5461533220091419, 1.1330289992094942, 1.6955057364542765, 2.210037298299515, 2.6549051485257005, 3.0112729302997927, 3.264110480843705, 3.4029394984440344, 3.4223612959931904, 3.3223375614506887, 3.108207204418188, 2.790435604236282, 2.3841062241889475, 1.908177917968404, 1.3845436277125092, 0.8369368935241065, 0.28974107079311423, -0.23323810225184846, -0.7099732809337644, -1.12132694479478, -1.4520147158581975, -1.6913688798883608, -1.8338603484467504, -1.8793495855338507, -1.833051059553554, -1.705210850528336, -1.5105123554639968, -1.2672397742708403, -0.9962424222060635, -0.7197541584532949, -0.4601307004146007, -0.23857280311424098, -0.07390488424719674, 0.01852348073920198, 0.027751629008577167, -0.05211481184891217, -0.22150319409799557, -0.4752750491501346, -0.8029382158972526, -1.1891618798426042, -1.6145696749533456, -2.056770291482488, -2.491571333433236, -2.894311271765878, -3.2412368956253763, -3.5108501451655774, -3.6851488769630873, -3.7506909983387526, -3.6994203063452074, -3.5292048481197678, -3.2440540401135043, -2.8539983257895996, -2.3746338619113034, -1.826353566725034, -1.2333037775024196, -0.622121722195156, -0.020522075452601887, 0.5441897440480967, 1.0465947614806577, 1.4645448573686344, 1.780375381634634, 1.9818757498328483, 2.062960729604319, 2.024001504894773, 1.8717945497240578, 1.6191668034104396, 1.2842364612560921, 0.8893686847008195, 0.4598835269413549, 0.022588294383265844, -0.39578248841775004, -0.7701300659935973, -1.0784667743381176, -1.3032171558747765, -1.4322674858085405, -1.4597001168403023, -1.3861667263495396, -1.2188751387922208, -0.9711867325214092, -0.6618442397764687, -0.3138716790046639, 0.04679208191504675, 0.3928482387533902, 0.6972915324792375, 0.9350655262924297, 1.0846216675781981, 1.1292886655550531, 1.0583688462635104, 0.8678933425222539, 0.5609874038416418, 0.14781967177144653, -0.35486634165165687, -0.9246155407416504], 'positive_zeros': ['0.855531060817345502533185246248534', '1.66490175138557801915283281131303', '2.56195451808732782921994607812200', '3.51429039390038698258083509216339', '4.13079279503724531939678824750048', '5.22356039290941648277101975753604', '5.38715995013386388465924737908299', '6.57353231259339783350337621018045', '6.85604766960116319157746602298415', '7.64392931524003403133757951973826'], 'prelabel': '2-9360-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 8.645228527454812, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'trace_hash': 787093918562607497, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.855531060817345502533185246249', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '1.66490175138557801915283281131', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.56195451808732782921994607812', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 74.73997629191848, 'bad_primes': [2, 3, 5, 13], 'central_character': '1.1', 'conductor': 9360, 'conductor_radical': 390, 'degree': 2, 'dirichlet_coefficients': [1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 3, 0, 1, 0, 0, 0, -3, 0, 4, 0, 0, 0, 9, 0, 1, 0, 0, 0, -6, 0, -2, 0, 0, 0, 1, 0, -1, 0, 0, 0, -3, 0, -2, 0, 0, 0, 6, 0, -6, 0, 0, 0, 9, 0, 3, 0, 0, 0, 12, 0, 5, 0, 0, 0, 1, 0, 4, 0, 0, 0, -9, 0, 14, 0, 0, 0, 3, 0, 7, 0, 0, 0, 0, 0, -3, 0, 0, 0, 15, 0, 1, 0, 0, 0, 4, 0, 5, 0, 0, 0], 'euler11': [1, -3, 11], 'euler13': [1, -1, 0], 'euler17': [1, 3, 17], 'euler19': [1, -4, 19], 'euler2': [1, 0, 0], 'euler23': [1, -9, 23], 'euler29': [1, 6, 29], 'euler3': [1, 0, 0], 'euler31': [1, 2, 31], 'euler37': [1, 1, 37], 'euler41': [1, 3, 41], 'euler43': [1, 2, 43], 'euler47': [1, -6, 47], 'euler5': [1, -1, 0], 'euler53': [1, -9, 53], 'euler59': [1, -12, 59], 'euler61': [1, -5, 61], 'euler67': [1, -4, 67], 'euler7': [1, -1, 7], 'euler71': [1, 9, 71], 'euler73': [1, -14, 73], 'euler79': [1, -7, 79], 'euler83': [1, 0, 83], 'euler89': [1, -15, 89], 'euler97': [1, -5, 97], 'euler_factors': [[1, 0, 0], [1, 0, 0], [1, -1, 0], [1, -1, 7], [1, -3, 11], [1, -1, 0], [1, 3, 17], [1, -4, 19], [1, -9, 23], [1, 6, 29], [1, 2, 31], [1, 1, 37], [1, 3, 41], [1, 2, 43], [1, -6, 47], [1, -9, 53], [1, -12, 59], [1, -5, 61], [1, -4, 67], [1, 9, 71], [1, -14, 73], [1, -7, 79], [1, 0, 83], [1, -15, 89], [1, -5, 97]], 'index': 52, 'instance_types': ['ECQ', 'CMF', 'CMF'], 'instance_urls': ['EllipticCurve/Q/9360/bu', 'ModularForm/GL2/Q/holomorphic/9360/2/a/bu/1/1', 'ModularForm/GL2/Q/holomorphic/9360/2/a/bu'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': True, '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': '2-9360-1.1-c1-0-52', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-9360-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 8.645228527454812, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 787093918562607497, 'z1': {'__RealLiteral__': 0, 'data': '0.855531060817345502533185246249', 'prec': 107}}
-
lfunc_instances • Show schema
Hide schema
-
id: 23049073
{'Lhash': '1084514462759001858665676151978', 'Lhash_array': ['1084514462759001858665676151978'], 'label': '2-9360-1.1-c1-0-52', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/9360/2/a/bu'}
-
id: 24588262
{'Lhash': '1084514462759001858665676151978', 'Lhash_array': ['1084514462759001858665676151978'], 'label': '2-9360-1.1-c1-0-52', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/9360/2/a/bu/1/1'}
-
id: 95248
{'Lhash': '787093918562607497', 'Lhash_array': ['787093918562607497'], 'label': '2-9360-1.1-c1-0-52', 'type': 'ECQ', 'url': 'EllipticCurve/Q/9360/bu'}