-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '3803457287082480108844058271425', 'a10': [-0.7788339764869813, -0.4496600059787853], 'a2': [0.0, -0.2938694600161684], 'a3': [-1.6524922780358262, -0.5189116216004083], 'a4': [1.9136407404698055, 0.0], 'a5': [1.5301352034132618, -2.6502719147615084], 'a6': [-0.1524922780358263, 0.48561701342727637], 'a7': [-1.417625364298396, 2.233906516955855], 'a8': [0.0, -1.1500994910991393], 'a9': [2.4614614579360694, 1.7149948953554468], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.5030575327340666, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [1.6524922780358262, 0.5189116216004083]]], [7, [[1.0, 0], [1.417625364298396, -2.233906516955855]]]], 'bad_primes': [3, 7], 'central_character': '63.38', 'coefficient_field': 'CDF', 'conductor': 63, 'conductor_radical': 21, 'conjugate': '2614415313912745995798890474477', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0.2938694600161684], [-2.0, 0]], [[1.0, 0], [1.6524922780358262, 0.5189116216004083]], [[1.0, 0], [-1.5301352034132618, 2.6502719147615084], [-2.5, -4.330127018922194]], [[1.0, 0], [1.417625364298396, -2.233906516955855]], [[1.0, 0], [3.3744457345332988, -1.9482371531985845], [5.5, -9.526279441628825]], [[1.0, 0], [2.029347770428808, -1.1716444815364393], [6.5, -11.258330249197702]], [[1.0, 0], [1.682627481449088, -2.914396288081479], [-8.5, -14.722431864335457]], [[1.0, 0], [-2.206963040165652, 1.274190705331194], [9.5, -16.454482671904334]], [[1.0, 0], [-2.581408774698951, -1.4903770509609013], [11.5, 19.91858428704209]], [[1.0, 0], [3.672409121930312, 2.1202663951209026], [14.5, 25.11473670974872]], [[1.0, 0], [0, 0.4727349242607551], [-31.0, 0]], [[1.0, 0], [3.8939462694544082, 6.744512780638325], [-18.5, 32.04293994002423]], [[1.0, 0], [-3.1273692863348086, -5.416762497962308], [-20.5, 35.50704155516198]], [[1.0, 0], [-2.0619082397778414, 3.5713298318401328], [-21.5, -37.239092362730865]], [[1.0, 0], [4.05387602513825, 0], [47.0, 0]], [[1.0, 0], [-4.99439305129618, -2.883514172604646], [26.5, 45.89934640057525]], [[1.0, 0], [4.687046196271167, 0], [59.0, 0]], [[1.0, 0], [0, -1.600183814267619], [-61.0, 0]], [[1.0, 0], [-1.5756616240556314, 0], [67.0, 0]], [[1.0, 0], [0, 13.613225837521439], [-71.0, 0]], [[1.0, 0], [0.8564520634516299, 0.494472829381809], [36.5, 63.21985447626402]], [[1.0, 0], [9.278153455345826, 0], [79.0, 0]], [[1.0, 0], [-5.493605618311727, 9.515204047661747], [-41.5, -71.88010851410841]], [[1.0, 0], [2.158485858826812, 3.738607174906982], [-44.5, 77.07626093681505]], [[1.0, 0], [-4.9879653795117065, -2.8798031545696174], [48.5, 84.00446416709055]], [[1.0, 0], [-8.578999016839267, -14.859262175249059], [-50.5, 87.4685657822283]], [[1.0, 0], [-8.50422353862638, -4.909915749274693], [51.5, 89.20061658979718]], [[1.0, 0], [3.005012211712244, -1.7349446093501768], [53.5, -92.66471820493493]], [[1.0, 0], [-0.6110659422578358, 1.0583972587655215], [-54.5, -94.39676901250381]], [[1.0, 0], [1.8768080334866601, -1.0835756233507754], [56.5, -97.86087062764156]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 3, 'label': '2-63-63.38-c1-0-3', '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/63/2/i/b/38/3', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [0.8397596763098477, 0.867468503457964, 0.9080733419893563, 0.9614605173427127, 1.0267551793012157, 1.1024475804340668, 1.1865048552893651, 1.2764407202882875, 1.369344156615895, 1.46188407051277, 1.5503104107700298, 1.6304691815052377, 1.697843993573004, 1.7476323972086785, 1.7748616547786962, 1.7745455879445382, 1.741881306174667, 1.6724817404447345, 1.5626368638286712, 1.4095933083077403, 1.2118389171021138, 0.9693758145815751, 0.683963096671253, 0.3593085414827352, 0.0011881188656668016, -0.3825271738771974, -0.7819552660672192, -1.1854117502597301, -1.5797514582767684, -1.9508432791133385, -2.284169504390518, -2.565530838440551, -2.7818276333558027, -2.9218776639759247, -2.977221724174078, -2.942861451504524, -2.8178700162896035, -2.605816499150053, -2.3149496014225317, -1.9580961824068348, -1.5522450278306756, -1.1178058224579452, -0.6775566465393535, -0.2553190790774093, 0.12557363279712905, 0.44392504507520303, 0.6823294115832763, 0.8287051662991471, 0.8775760467285046, 0.8309720808397109, 0.6988382122644478, 0.49886549794379315, 0.25569776471411465, -0.0004865785172254715, -0.235965247594141, -0.41592855023110814, -0.5072433583436586, -0.4813228808841228, -0.3168701573109118, -0.0022503271938096566, 0.46274530188390534, 1.0659498474645224, 1.7828397636147275, 2.5776031356664464, 3.405250797164445, 4.214667870341179, 4.952407732150588, 5.566944452227543, 6.013032937364616, 6.255786962091391, 6.27408068038958, 6.062912980774876, 5.6344464744253155, 5.017540289642253, 4.255730417697935, 3.403761675199283, 2.5229271509302045, 1.6756084591107123, 0.9195174074001208, 0.3022027556050137, -0.14360594554900638, -0.4032973693362155, -0.481911681132836, -0.4036630681084889, -0.2094083792372662, 0.04776065497695301, 0.30840802097338643, 0.513546331847421, 0.6116173222362137, 0.5648829739477617, 0.3544725804874369, -0.016558578645285107, -0.5226113091598009, -1.1175607674155104, -1.739310251336365, -2.3164769227184485, -2.7765318193736777, -3.0545062065338215, -3.1012594181725692, -2.890300243415406, -2.4222724658709787, -1.7264487056651863, -0.8589038100470129, 0.10257492832936133, 1.0663828577626737, 1.9369745429882208, 2.6256147524577074, 3.060736819899706, 3.196632082756644, 3.019345236575353, 2.54895149151762, 1.8378117276851875, 0.9648933260183354, 0.02674671163910515, -0.8738243303627856, -1.6400285209135852, -2.192752775849707, -2.48012080923333, -2.4836682076249863, -2.2202672099958196, -1.739475864665724, -1.1165913947523094, -0.44227615762930267, 0.18988554518338255, 0.6962227299649586, 1.014432082459545, 1.1120282774362458, 0.9905517300830687, 0.6848693637626322, 0.25759297163709294, -0.21065125913320837, -0.6337418158539491, -0.9335600476498175, -1.0524597528575461, -0.962793086284168, -0.6719597748803434, -0.22207336270634623, 0.31587402591968, 0.8526300202825374, 1.2946037375243082, 1.5590447081651633, 1.5881563005411135, 1.3598899041588683, 0.8935855210239669, 0.24934546527936494, -0.4790471747197803, -1.1768588659099994, -1.7250650034066166, -2.0185325824377145, -1.9829789120150765, -1.588030780212273, -0.8542003268975058, 0.14755291604803314, 1.3039082967152422, 2.4739763998200637, 3.5087800456746625, 4.272606671748714, 4.663027857102483, 4.6264848606795494, 4.166934193255796, 3.346057462649522, 2.274818216923659, 1.0974995216321481, -0.029435252008196817, -0.9604489868538747, -1.5824209713450132, -1.8311307159602326, -1.7000922242345529, -1.2402881997172555, -0.5508081549861095, 0.2381228467000898, 0.9869725091311502, 1.5700025114267266, 1.8958102900390092, 1.921870370974173, 1.6606137284738558, 1.1759983204470719, 0.5711418569839122, -0.03086447535184764, -0.5096342108931529, -0.7696771518126174, -0.7581578860941626, -0.4750012981346888, 0.026565477661277148, 0.6492699839850002, 1.269332781680042, 1.7592496752042575, 2.0117706736594925, 1.9607237417693681, 1.594804856186954, 0.9616429361749318, 0.16115329149724486, -0.6708789738897354, -1.3862382468800987, -1.8506416862746786, -1.968290655875163, -1.700088058484553, -1.0720480752829973, -0.17213894519364878, 0.8641187101541135, 1.87690040655485, 2.7100915755108046, 3.239015193197903, 3.3927657108387175, 3.1669340870196128, 2.624207962558007, 1.8825402045965918, 1.0928969534939348, 0.41058990102641063, -0.03451712334296217, -0.16332066236586384, 0.03656103166767477, 0.5073727416486471, 1.1312294011347572, 1.7518864614847716, 2.204341385016792, 2.3467648402393313, 2.088711898834799, 1.4101648161224838, 0.36761942192370295, -0.9141510689351908, -2.263290867535978, -3.491136502964897, -4.4258885530542535, -4.943269082149133, -4.988266592312251, -4.583747461636995, -3.824245869326728, -2.8561480431493624, -1.848191428902008, -0.9581617834155501, -0.3024838618709095, 0.06512190399065668, 0.16152534653405556, 0.0669285832489021, -0.09612266868800712, -0.19317277911884256, -0.11139562009230382, 0.2108941612702975, 0.7652328907619189, 1.46896224466693, 2.177611812924625, 2.7117908407152638, 2.893579518333745, 2.585256486479666, 1.7224508565001162, 0.3346568643253533, -1.4516325486803765, -3.428564846126879, -5.3390029428607315, -6.919345871780924, -7.94511810977638, -8.270619798193533, -7.854935239204708, -6.769165340825643, -5.183383692228083, -3.3357902074289183], 'positive_zeros': ['3.00039875845733903013171643652611', '5.45680076696329972759554524964254', '6.62475830661277071773764655941831', '7.37571900340829696696909684182609', '9.953752903307945170536960757705462', '10.60275541283919301518139920193688', '11.37031778377928747430200946894621', '12.86189340238821977191177340364574', '14.12857254033226387288263045699476', '15.33548301858673616280553698363067'], 'prelabel': '2-63-63.38-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.7092654881876508, 'root_angle': 0.11111984767843577, 'root_number': '0.766009157121537 + 0.6428296595568318*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.111119847678', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '3.00039875845733903013171643653', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '5.45680076696329972759554524964', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '6.62475830661277071773764655942', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 0.5030575327340666, 'bad_primes': [3, 7], 'central_character': '63.38', 'conductor': 63, 'conductor_radical': 21, 'degree': 2, 'index': 3, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/63/2/i/b/38/3'], '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': '2-63-63.38-c1-0-3', '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': '2-63-63.38-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.7092654881876508, 'root_angle': 0.11111984767843577, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '3.00039875845733903013171643653', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '3803457287082480108844058271425', 'Lhash_array': ['3803457287082480108844058271425'], 'factors': ['2-63-63.38-c1-0-3'], 'label': '2-63-63.38-c1-0-3', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/63/2/i/b/38/3'}