-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '566456462411584803881134141748', 'a10': [0.0, 0.0], 'a2': [-1.0, 0.0], 'a3': [0.0, 0.0], 'a4': [1.0, 0.0], 'a5': [0.0, 0.0], 'a6': [0.0, 0.0], 'a7': [1.0783777456217782, 0.0], 'a8': [-1.0, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 68.27209372819476, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [1.0, 0]]], [3, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [0, 0]]], [19, [[1.0, 0], [-1.0, 0]]]], 'bad_primes': [2, 3, 5, 19], 'central_character': '8550.1', 'coefficient_field': 'CDF', 'conductor': 8550, 'conductor_radical': 570, 'degree': 2, 'euler_factors': [[[1.0, 0], [1.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-1.0783777456217782, 0], [7.0, 0]], [[1.0, 0], [6.340172973252067, 0], [11.0, 0]], [[1.0, 0], [3.4185507188738455, 0], [13.0, 0]], [[1.0, 0], [5.4185507188738455, 0], [17.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [-6.340172973252067, 0], [23.0, 0]], [[1.0, 0], [-0.34017297325206747, 0], [29.0, 0]], [[1.0, 0], [-1.0783777456217782, 0], [31.0, 0]], [[1.0, 0], [3.4185507188738455, 0], [37.0, 0]], [[1.0, 0], [7.601968200882356, 0], [41.0, 0]], [[1.0, 0], [-11.17727441099976, 0], [43.0, 0]], [[1.0, 0], [6.340172973252067, 0], [47.0, 0]], [[1.0, 0], [-6.0, 0], [53.0, 0]], [[1.0, 0], [0.7382047723697108, 0], [59.0, 0]], [[1.0, 0], [2.680345946504135, 0], [61.0, 0]], [[1.0, 0], [2.8371014377476915, 0], [67.0, 0]], [[1.0, 0], [-2.8371014377476915, 0], [71.0, 0]], [[1.0, 0], [6.837101437747691, 0], [73.0, 0]], [[1.0, 0], [1.0783777456217782, 0], [79.0, 0]], [[1.0, 0], [-0.8949602636132673, 0], [83.0, 0]], [[1.0, 0], [6.921622254378222, 0], [89.0, 0]], [[1.0, 0], [-3.6598270267479327, 0], [97.0, 0]], [[1.0, 0], [19.601968200882357, 0], [101.0, 0]], [[1.0, 0], [-11.758723692125914, 0], [103.0, 0]], [[1.0, 0], [-6.1567554912435565, 0], [107.0, 0]], [[1.0, 0], [-17.91547918336947, 0], [109.0, 0]], [[1.0, 0], [13.203936401764713, 0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 7, 'label': '2-8550-1.1-c1-0-7', 'leading_term': '0.74450755855493626583250127417285', '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/8550/2/a/ce/1/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.046875', 'prec': 27}, 'plot_values': [0.7445075585549362, 0.7360731305862329, 0.7107887121183051, 0.6687160630358072, 0.6099749421988933, 0.5347670296476511, 0.44340690605551103, 0.3363578405954422, 0.2142698255143032, 0.07801716235138573, -0.07126706423303786, -0.23216212121509786, -0.4029385948064157, -0.5815470707217387, -0.7656180164762444, -0.9524739381445824, -1.1391544535352833, -1.3224544874145125, -1.498975356733681, -1.665188077985242, -1.817507798360604, -1.952377832254877, -2.066361381783532, -2.1562386433927356, -2.219106663306729, -2.252479014847274, -2.254382143774246, -2.2234450770075926, -2.158979127987387, -2.06104426964093, -1.9304989923838545, -1.7690307258302393, -1.5791642814800328, -1.36424626815865, -1.128404036613489, -0.8764784140544027, -0.6139302785499036, -0.3467218775305283, -0.08117469047019175, 0.176193454324752, 0.41884840544414903, 0.6404324088104298, 0.8349643132919988, 0.997041406603457, 1.1220365299232693, 1.2062838013206332, 1.247246163741191, 1.2436580833006852, 1.195637071794401, 1.1047582998714889, 0.9740874020115731, 0.8081676399731288, 0.6129588670794853, 0.3957271915435237, 0.1648858340307405, -0.07021063432668807, -0.29951475639037783, -0.5125717278245826, -0.6988347541810129, -0.8480014901339568, -0.9503615564917435, -0.9971441346898973, -0.9808539694411261, -0.895583814153097, -0.7372914658351526, -0.5040300787164004, -0.19612142615059877, 0.18373681001323497, 0.6304368299854153, 1.1365045190408967, 1.6922237180382755, 2.2858407105273297, 2.903845828406575, 3.5313261880162052, 4.152380741268275, 4.75058617159045, 5.309499791587175, 5.813183613392024, 6.246732259750785, 6.596786446708549, 6.852013462787675, 7.003536439167057, 7.0452952710663865, 6.974323806602959, 6.790930332716638, 6.498771397639559, 6.104812528429906, 5.619173318300364, 5.054858538467314, 4.4273812225272176, 3.7542879155419917, 3.054600306808716, 2.348191107113364, 1.6551151281247787, 0.9949189280121509, 0.3859539791447089, -0.15528100596912778, -0.6147432496346746, -0.9813705420133146, -1.2475055777099615, -1.4092014661471253, -1.4663939529105434, -1.4229306654084917, -1.2864530139189143, -1.0681320416205606, -0.7822653056435745, -0.4457475529038721, -0.07743329242646754, 0.30258587159813094, 0.6737623106775444, 1.0159020223624737, 1.3099711844727098, 1.5388673375630453, 1.6881236349897046, 1.7465166399894236, 1.7065514679156735, 1.564802566374988, 1.3220939396386713, 0.9835089504459088, 0.5582267244486213, 0.05918936002456304, -0.4973886921240486, -1.0926508788341336, -1.7058440166075866, -2.315149287980805, -2.898564942484555, -3.4348041390403496, -3.9041701547955947, -4.289371594635272, -4.576242285211955, -4.75433417344595, -4.817356645299502, -4.763442040186006, -4.595224501283943, -4.319727361697339, -3.9480626708562023, -3.4949548404928144, -2.978108353073524, -2.4174466558025074, -1.8342554159675293, -1.2502679387050866, -0.6867335062502888, -0.16351052110796946, 0.3017744604893588, 0.6944634302033518, 1.003465522609494, 1.2216898332508352, 1.3462923343714759, 1.3787253459118882, 1.3245872478468603, 1.1932795626875075, 0.997487743706008, 0.7525105275047604, 0.4754701257939553, 0.18444146336406367, -0.10245719459127829, -0.36796777191626573, -0.5965456624331377, -0.7751205946336877, -0.8937272601659794, -0.945974158977836, -0.9293270268880015, -0.8451923918894563, -0.6987968105349491, -0.49886767245167357, -0.25713161071889273, 0.012344000086187896, 0.29393272997340886, 0.5713136265761763, 0.8283736501118394, 1.0501007258445503, 1.2234202137626926, 1.337930135243578, 1.386495397905671, 1.3656683033562076, 1.2759114729274472, 1.1216095477414412, 0.9108670954822361, 0.6551015164406946, 0.3684507894752825, 0.06702604364795016, -0.23195237054468737, -0.5110898921026531, -0.753774016284366, -0.9451001939307241, -1.0727166945212256, -1.127541465059445, -1.104310311475148, -1.001924321786894, -0.8235749151467, -0.5766367027571101, -0.2723308671954622, 0.0748256635536963, 0.4477580372733907, 0.8277204498774486, 1.1952856965912315, 1.5313844199244464, 1.818337671743692, 2.0408259583735857, 2.1867406212481404, 2.2478691292857227, 2.2203743606959465, 2.1050388097186863, 1.9072573066981922, 1.6367756154201774, 1.3071864210146305, 0.9352079600577808, 0.5397830939213072, 0.14104725985107966, -0.24077818256310238, -0.58650566265472, -0.879050987400056, -1.1043915466951952, -1.2523573056210648, -1.317207456492248, -1.2979571450987426, -1.1984324639212345, -1.0270471774377041, -0.7963105669775411, -0.522091455636387, -0.2226779930760746, 0.08231471238815286, 0.3731272924125461, 0.6310609828964938, 0.8396339742796465, 0.9856201081877406, 1.0599063722178879, 1.0581150504664525, 0.9809491443332381, 0.8342351183234549, 0.6286543102986204, 0.37917250984208045, 0.10419521364797688, -0.1755071402206071, -0.4380450840968197, -0.6617568515153109, -0.8265780106011722, -0.9153528897821563, -0.9150081768214492, -0.8175152712014945, -0.6205786249256567, -0.3280018996154429, 0.050298462510419854, 0.4986426745129263, 0.996289392042779, 1.518458234330399, 2.0376218031784847, 2.5249988720155065, 2.952166911945576, 3.292703080298065, 3.523758855164313, 3.6274750086041303, 3.592150612020226, 3.4130919788567984, 3.093084279191552, 2.6424491300489112, 2.07867465657166], 'positive_zeros': ['0.44685535770629483631864430846595', '1.79581902305663366305092530817800', '2.56409794199333565931121708535173', '3.11902141056990383847453744543482', '4.48585639664261130236534176268091', '5.02521117219958121031058577034409', '5.63019648636041995016179304689968', '6.67199170811667325021736370538579', '7.24862451452729884646877695215912', '7.77916823049008533927076673519800'], 'prelabel': '2-8550-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.262692885990303, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.44685535770629483631864430847', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.79581902305663366305092530818', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.56409794199333565931121708535', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 68.27209372819476, 'bad_primes': [2, 3, 5, 19], 'central_character': '1.1', 'conductor': 8550, 'conductor_radical': 570, 'degree': 2, 'index': 7, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/8550/2/a/ce/1/2'], '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': '2-8550-1.1-c1-0-7', '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': '2-8550-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.262692885990303, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.44685535770629483631864430847', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '566456462411584803881134141748', 'Lhash_array': ['566456462411584803881134141748'], 'label': '2-8550-1.1-c1-0-7', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/8550/2/a/ce/1/2'}