-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '2874488743318931398457247519139', 'a10': [-0.116060951649927, 1.5487257694374634], 'a2': [1.0053944319124821, 0.8017753047807464], 'a3': [0.5484108105550571, 3.638467991830885], 'a4': [-0.5221094114608938, -2.287510794584303], 'a5': [0.6803345008240557, 0.9978674397251192], 'a6': [-2.3658646077525325, 4.097797704456399], 'a7': [-2.4992061330731734, 1.4429173336901604], 'a8': [3.54095103316597, -7.352860584584059], 'a9': [-4.33753965836895, 1.3379537914590753], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.1716651367492767, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 10}, 'bad_lfactors': [[43, [[1.0, 0], [-41.899551107807994, -9.665796240568392]]]], 'bad_primes': [43], 'central_character': '43.19', 'coefficient_field': 'CDF', 'conductor': 43, 'conductor_radical': 43, 'conjugate': '4676046441568384158149282274004', 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.0053944319124821, -0.8017753047807464], [0.8900837358252576, 3.8997116487272945]], [[1.0, 0], [-0.5484108105550571, -3.638467991830885], [-8.600155252075266, 2.652796569698138]], [[1.0, 0], [-0.6803345008240557, -0.9978674397251192], [-9.133525609159875, 23.271843716105106]], [[1.0, 0], [2.4992061330731734, -1.4429173336901604], [24.5, -42.4352447854375]], [[1.0, 0], [-2.007350105153523, 8.794775449843714], [-109.01723301619272, -52.49993243322453]], [[1.0, 0], [0.5326190943663467, 7.107307884461277], [-167.11240963204673, 25.18814298377348]], [[1.0, 0], [10.540774706519313, 7.1865785101016035], [105.58355604188816, 269.02251335817505]], [[1.0, 0], [9.823188907771293, -31.845996275134613], [-298.2721975280742, -203.35854096096756]], [[1.0, 0], [7.088020574525967, 6.576721982194346], [39.53221950721843, 527.5208087088442]], [[1.0, 0], [5.075469810599677, -33.673541976096615], [-803.6367296661443, -247.88910167957044]], [[1.0, 0], [-14.677635782586941, -37.398006057125876], [-704.462848828463, 653.6460009978535]], [[1.0, 0], [24.16684712482989, 13.952735692985069], [684.5, 1185.5887777808964]], [[1.0, 0], [-0.23290609970290815, 0.29205501142716206], [-374.05768998056453, -1638.8538203776454]], [[1.0, 0], [-41.899551107807994, -9.665796240568392]], [[1.0, 0], [14.623013422579195, 64.06760789832363], [-1990.2402291964438, 958.4491797106859]], [[1.0, 0], [-7.316764980980461, 97.63544339306803], [-2777.625790866386, -418.659725688874]], [[1.0, 0], [37.761241409996146, -18.18485543771796], [2170.3680002702513, -2721.555390471212]], [[1.0, 0], [-32.101828537011485, -12.599039277697832], [2727.686015078784, 2530.922757245591]], [[1.0, 0], [-66.68094325494734, -20.56834700609337], [3708.985857904501, 2528.743740647599]], [[1.0, 0], [-26.410915045387647, -28.46419686594456], [-376.7144017691647, 5026.904341590329]], [[1.0, 0], [-22.366960748546884, 1.6761719868171516], [5269.47947295371, -794.2462364528336]], [[1.0, 0], [4.695026903601123, 8.13202513993993], [-3120.5, 5404.864545018681]], [[1.0, 0], [-142.84440535010725, 21.530329879826127], [6582.941059060723, -2030.568396516719]], [[1.0, 0], [8.928406179128041, 59.23610453255478], [-7569.09219463202, 2334.7557365087723]], [[1.0, 0], [25.3516375448503, -111.07278143477285], [-8477.216078093861, -4082.4121013571043]], [[1.0, 0], [-41.69315334649377, 38.68559285879664], [762.3216846751138, -10172.475935045219]], [[1.0, 0], [75.77673283009675, 51.66370166185908], [3875.902927503085, 9875.639599366363]], [[1.0, 0], [-81.95674327258759, -102.77050546782947], [-2547.642172865844, 11161.949666569699]], [[1.0, 0], [88.54205424592224, 82.15502034525984], [887.8682419003065, 11847.778314309602]], [[1.0, 0], [-22.618311761560335, -46.96740832722377], [-7961.341279934169, 9983.206199634273]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 1, 'label': '2-43-43.19-c2-0-1', 'load_key': 'CMFs-workshop', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [2], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/43/3/h/a/19/4', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [1.3785637538858064, 1.339441951888805, 1.3062976807759334, 1.277601015780262, 1.2515167597449521, 1.2259741229832222, 1.1987391342977936, 1.1674863862563565, 1.1298693677427798, 1.0835908109501042, 1.0264755822881324, 0.9565486264595687, 0.872119602958008, 0.7718744879723534, 0.654972844927936, 0.5211478879623693, 0.370804990305912, 0.2051129966294211, 0.026081643923761288, -0.16338235894264222, -0.35944842745443023, -0.5573721472945175, -0.751549463478512, -0.9356210430926837, -1.1026310526803547, -1.245242164944196, -1.3560055759816187, -1.4276812531277154, -1.45359967897157, -1.4280522006860836, -1.3466929819248084, -1.2069317815194838, -1.0082936786218988, -0.7527197743079244, -0.44478216494809786, -0.09178740822305882, 0.29625447164261764, 0.70681352467089, 1.1251871219535807, 1.5350132252836701, 1.918941545920691, 2.25944289097827, 2.539724973273928, 2.7447112963407867, 2.862029345855661, 2.8829462035107585, 2.8031848167383715, 2.623553379000415, 2.3503242875289807, 1.9953083631531388, 1.5755845030562246, 1.1128643404237646, 0.6324950019195759, 0.16212942652689472, -0.2698787402289983, -0.6362719530595392, -0.9127699209064076, -1.0799095021162077, -1.1247070288670642, -1.0420054203678797, -0.8353777785158252, -0.5174797066431127, -0.10977401596153205, 0.3584075274417533, 0.8514525138308541, 1.3296410698378225, 1.751786355548802, 2.0781768382248993, 2.2736157724418224, 2.31032756581874, 2.170491862798784, 1.848176745779336, 1.3504734616422287, 0.6976858100258073, -0.07750482900717036, -0.9318973529814184, -1.8145631416049584, -2.670397754043806, -3.444179669770977, -4.084822668511299, -4.549471220764131, -4.807080248246368, -4.841144977559549, -4.651303651876549, -4.2536227110379645, -3.679484633445297, -2.973124003666574, -2.187986336776547, -1.3822042639951273, -0.6135842479202044, 0.06543739027409334, 0.6123866439594318, 0.9984332241601114, 1.210773749091712, 1.2534445979489717, 1.1464422339288387, 0.9231997479153395, 0.626643470336204, 0.3042141719030447, 0.002365260909428654, -0.23887061045272903, -0.39063684117837927, -0.4387687610790207, -0.38562265890322994, -0.2499412792047572, -0.06469101859357136, 0.12696243506297836, 0.2771474986591782, 0.3396630245808008, 0.2765146692825604, 0.06382805633900289, -0.303616348184106, -0.8098626149218803, -1.4177070559358276, -2.071242250284133, -2.700882689011413, -3.230431863510319, -3.58547884955768, -3.7022092398517144, -3.5356095347271865, -3.0660547501949744, -2.303402008616462, -1.2879595992222315, -0.08803825971825084, 1.2058165704307426, 2.4894108555977392, 3.655442728399446, 4.604856998105872, 5.257720100728123, 5.562320288046586, 5.501354659776764, 5.09436882247067, 4.396035891472141, 3.4903521216210533, 2.481328152979227, 1.4812047097271297, 0.5975600651700531, -0.07914444124374913, -0.48604487839658794, -0.5950514437180593, -0.41577504399279536, 0.006225003723663342, 0.5957114800040788, 1.2578109176942018, 1.8905735825441854, 2.3984439297433724, 2.704882106848218, 2.7624562930733294, 2.5590327480225157, 2.1191911974743887, 1.500625483656074, 0.785970580769689, 0.07113453899484667, -0.5482822787600623, -0.9906027026755841, -1.199805572181668, -1.1536884952124098, -0.8672483031974668, -0.39072672922134644, 0.19747581596724417, 0.8020706047183852, 1.3247611279259757, 1.6787470634629078, 1.8017323474469158, 1.6654935012878205, 1.280531253108881, 0.6950262948027157, -0.01184824756342662, -0.7413597461976651, -1.389764184885087, -1.8638336908753186, -2.095032346308076, -2.0501629613427865, -1.7367975467485097, -1.2025655523200978, -0.5282976020807845, 0.18402928621287315, 0.8267724300939737, 1.3031850221916728, 1.5424919571460183, 1.5110886547311206, 1.2180280093997204, 0.7138220317745004, 0.08262404130603182, -0.5710854338713097, -1.1392788854358833, -1.5279914024375278, -1.6729237096447547, -1.550456385995292, -1.1821729265607221, -0.631999133654924, 0.003747547526113398, 0.6119305655155434, 1.0813502846213505, 1.3216456075055665, 1.2791860499329295, 0.9472003040331339, 0.3682589322368361, -0.37155676957648387, -1.1560997270555384, -1.8582161008211235, -2.361405872524325, -2.5805260379853787, -2.4780054307974537, -2.0726590476429148, -1.4393177366030963, -0.6989563604448596, -0.0005771696395415649, 0.5024740302694879, 0.6780560574129862, 0.4384973129210712, -0.2423402432198844, -1.3212277256503477, -2.688577063601137, -4.182170957940311, -5.609736332683322, -6.776985608996589, -7.516773517484915, -7.714737590159296, -7.327271422935592, -6.3888575246060295, -5.00747755169984, -3.34874703929002, -1.6112680089586449, 0.002857459857004999, 1.317607792941962, 2.2079619880465176, 2.6161966854263037, 2.5570627137179662, 2.111233568602737, 1.4084080973660769, 0.6031928666002953, -0.15192030422820116, -0.7317408039782656, -1.0574051018966812, -1.1061018893327936, -0.9100961861497175, -0.5456317762825506, -0.11414863737149968, 0.2803560548111736, 0.5533284251425864, 0.6567119542266345, 0.5877566933251783, 0.38793115226902514, 0.13225718889909016, -0.0886885564184085, -0.19036289834427975, -0.11491191499112303, 0.15351858113641975, 0.5822368732668974, 1.093938544531566, 1.580737915114573, 1.925830924136303, 2.028660063809471, 1.8285546566064983, 1.3218910535412634, 0.568877661350115], 'positive_zeros': ['2.26757179210218087341650772700943', '4.40546673915176591699095301486616', '6.67020498871332939214961037750710', '7.78045748469532619206420834895571', '9.238169266080401911132423051917308', '11.23693192280845388219016494865837', '12.37606673359763896396738835872932', '13.16615104570854194455078739885406', '13.77597700451059039692652523257405', '15.38368798665498752122008150464069'], 'prelabel': '2-43-43.19-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.0824348187070096, 'root_angle': -0.31342708658996155, 'root_number': '0.5531462011669855 - 0.8330841975061901*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.156713543295', 'prec': 50}, 'spectral_label': 'c2-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.26757179210218087341650772701', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.40546673915176591699095301487', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '6.67020498871332939214961037751', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 1.1716651367492767, 'bad_primes': [43], 'central_character': '43.19', 'conductor': 43, 'conductor_radical': 43, 'degree': 2, 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/43/3/h/a/19/4'], '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': '2-43-43.19-c2-0-1', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [2], 'order_of_vanishing': 0, 'prelabel': '2-43-43.19-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.0824348187070096, 'root_angle': -0.15671354329498077, 'self_dual': False, 'spectral_label': 'c2-0', 'z1': {'__RealLiteral__': 0, 'data': '2.26757179210218087341650772701', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '2874488743318931398457247519139', 'Lhash_array': ['2874488743318931398457247519139'], 'label': '2-43-43.19-c2-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/43/3/h/a/19/4'}