Table lfunc_lfunctions
L-functions
{'Lhash': '419921230196139277487495330896,1569412084645377016671054373667', 'a10': -40, 'a2': 4, 'a3': 3, 'a4': 12, 'a5': -10, 'a6': 12, 'a7': -12, 'a8': 32, 'a9': -29, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3896.758371100149, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 7}, 'bad_lfactors': [[2, [1, -4, 4]], [23, [1]]], 'bad_primes': [2, 23], 'central_character': '1058.1', 'coefficient_field': '1.1.1.1', 'conductor': 1119364, 'conductor_radical': 46, 'degree': 4, 'euler_factors': [[1, -4, 4], [1, -3, 38, -81, 729], [1, 10, 202, 1250, 15625], [1, 12, 430, 4116, 117649], [1, -12, 2698, -15972, 1771561], [1, 51, 2836, 112047, 4826809], [1, -66, 10258, -324258, 24137569], [1, -16, 6482, -109744, 47045881], [1], [1, 57, 29716, 1390173, 594823321], [1, 17, -27234, 506447, 887503681], [1, 206, 85562, 10434518, 2565726409], [1, -373, 157276, -25707533, 4750104241], [1, 314, 60950, 24965198, 6321363049], [1, -859, 380710, -89183957, 10779215329], [1, 50, 272026, 7443850, 22164361129], [1, -612, 438694, -125691948, 42180533641], [1, -1062, 674530, -241053822, 51520374361], [1, -844, 722378, -253843972, 90458382169], [1, -399, 747574, -142806489, 128100283921], [1, 1277, 1185552, 496774709, 151334226289], [1, 122, 977462, 60150758, 243087455521], [1, 1802, 1946542, 1030360174, 326940373369], [1, 2046, 2450554, 1442366574, 496981290961], [1, -910, 662234, -830532430, 832972004929], [1, -1608, 1548070, -1656724008, 1061520150601], [1, -92, 1869582, -100530884, 1194052296529], [1, -1108, 2640202, -1357347644, 1500730351849], [1, 604, 155754, 782197516, 1677100110841], [1, -302, 2882242, -435754894, 2081951752609]], 'euler_factors_factorization': [[[[1, -2], 2]], [[[1, -3, 38, -81, 729], 1]], [[[1, 10, 202, 1250, 15625], 1]], [[[1, 12, 430, 4116, 117649], 1]], [[[1, -6, 1331], 2]], [[[1, 51, 2836, 112047, 4826809], 1]], [[[1, -66, 10258, -324258, 24137569], 1]], [[[1, -16, 6482, -109744, 47045881], 1]], [1], [[[1, 57, 29716, 1390173, 594823321], 1]], [[[1, 17, -27234, 506447, 887503681], 1]], [[[1, 206, 85562, 10434518, 2565726409], 1]], [[[1, -373, 157276, -25707533, 4750104241], 1]], [[[1, 314, 60950, 24965198, 6321363049], 1]], [[[1, -859, 380710, -89183957, 10779215329], 1]], [[[1, 50, 272026, 7443850, 22164361129], 1]], [[[1, -612, 438694, -125691948, 42180533641], 1]], [[[1, -1062, 674530, -241053822, 51520374361], 1]], [[[1, -844, 722378, -253843972, 90458382169], 1]], [[[1, -399, 747574, -142806489, 128100283921], 1]], [[[1, 1277, 1185552, 496774709, 151334226289], 1]], [[[1, 122, 977462, 60150758, 243087455521], 1]], [[[1, 1802, 1946542, 1030360174, 326940373369], 1]], [[[1, 2046, 2450554, 1442366574, 496981290961], 1]], [[[1, -910, 662234, -830532430, 832972004929], 1]], [[[1, -1608, 1548070, -1656724008, 1061520150601], 1]], [[[1, -92, 1869582, -100530884, 1194052296529], 1]], [[[1, -1108, 2640202, -1357347644, 1500730351849], 1]], [[[1, 604, 155754, 782197516, 1677100110841], 1]], [[[1, -302, 2882242, -435754894, 2081951752609], 1]]], 'gamma_factors': [[], [0, 0]], 'group': 'GL2', 'id': 20180199, 'index': 1, 'label': '4-1058e2-1.1-c3e2-0-1', 'leading_term': '3.30635389489463830700501271208474805143484576944990022041741944900000000000000000000000000', 'load_key': 'CMFs-workshop', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0, 0], 'nu_real_doubled': [3, 3], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/1058/4/a/j', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.029296875', 'prec': 27}, 'plot_values': [3.306353894894638, 3.2662885201192515, 3.189397430565183, 3.047312063482348, 2.8439504560239226, 2.589411760141889, 2.286079224727911, 1.9354617027636702, 1.541893466414835, 1.1105472266714798, 0.646555161192355, 0.15534490478977342, -0.3570876521814701, -0.8844553004266081, -1.4202163588377374, -1.9576965120426015, -2.4900682964158958, -3.010510657715684, -3.5122207459953785, -3.988557277570498, -4.433061243985537, -4.839590966294311, -5.202354386384698, -5.516028195367828, -5.77579706650923, -5.977453208139953, -6.117438299597727, -6.192919510047544, -6.201828672012806, -6.142911979193828, -6.015760276253448, -5.820830950353082, -5.559462816171321, -5.2338704076534945, -4.847136978682519, -4.403183335663334, -3.906733024593214, -3.3632599147007403, -2.778920743172833, -2.160487710873822, -1.5152451990070785, -0.8509154949092504, -0.17551861567045943, 0.5026992405797006, 1.175441352967327, 1.8344187881119218, 2.47155747432802, 3.0790325594068526, 3.64950022098717, 4.176097987929915, 4.6526922810299896, 5.073836129624176, 5.435021649049956, 5.7325889654882864, 5.963971815999607, 6.127554638459218, 6.222899406275192, 6.250551557889882, 6.212237156075453, 6.11062235527895, 5.949472013363744, 5.7333713945908595, 5.467840359413759, 5.15902960773042, 4.813788317873699, 4.43935007537451, 4.043356012035477, 3.633547299072314, 3.2177500588523666, 2.803591659773625, 2.398457500958687, 2.0092471712820448, 1.64231620595044, 1.3032854453303717, 0.9969826476089017, 0.7273142444553882, 0.4972219822557297, 0.30862102229217286, 0.16238543533242022, 0.05835068106502001, -0.004661165949695722, -0.028782540096607623, -0.01702886871027204, 0.026803217294967537, 0.09825496407807424, 0.19233234653114195, 0.303668296701884, 0.4266540765562618, 0.5556347910840604, 0.6850241264552125, 0.809518759878671, 0.9241769620502038, 1.0246345288496583, 1.10713161640591, 1.1687118435405033, 1.207187493745079, 1.2213047271584276, 1.210644378856265, 1.1757397593854944, 1.1179179341655099, 1.039362072769411, 0.9429054177648781, 0.8320369760885301, 0.7106664635450984, 0.5830795017499778, 0.4536958359148463, 0.32698715647832344, 0.20725221829750645, 0.09851597675349652, 0.004343575089842459, -0.07225718728470669, -0.12896562751339985, -0.16421989172562923, -0.17728019478965035, -0.16825488172163502, -0.13809559194896606, -0.08856346515996069, -0.022164016780840668, 0.057952704572781434, 0.14810108164974536, 0.24422259337146557, 0.3420154135990716, 0.43714710688015684, 0.5253778587722882, 0.6028020872533483, 0.66593817372406, 0.7119721144784359, 0.7387903942455984, 0.7451966624166513, 0.7308717491006586, 0.6965364429948029, 0.6438327316486311, 0.5754121162641798, 0.49474363754162143, 0.40611718744546144, 0.31439512868373976, 0.2249325534828098, 0.14329860063247118, 0.07512889147604768, 0.025848440152571355, 0.0004836297216262635, 0.0034197588314795217, 0.038208977665364414, 0.10739149985347918, 0.2123402750712503, 0.3531659547484789, 0.5286376929931432, 0.7361791064809542, 0.9718972178579474, 1.2306616028877797, 1.5062607707019444, 1.7915416375465882, 2.0786961029101882, 2.359425304261622, 2.6253410369798904, 2.868111128590728, 3.0799433255396726, 3.2536662418388014, 3.383250097404181, 3.4637828613205035, 3.4919750894051194, 3.4660028639643676, 3.385944471920346, 3.2534792064951334, 3.07221218764367, 2.8472387195438023, 2.5853293663700105, 2.294390341589952, 1.983501977663785, 1.6623232796616727, 1.3410001425630456, 1.0295736921801957, 0.7377964097807517, 0.4746069182759107, 0.2479089420900093, 0.06416867108561894, -0.07177985071255186, -0.15697438120817347, -0.19043045586488971, -0.17320072116596855, -0.10834193169381519, -0.0008037997465314773, 0.14277227858115507, 0.3142978309185453, 0.5046088317224824, 0.703783958032537, 0.9016589521447177, 1.0881443383184275, 1.2538286025626424, 1.3902180929252657, 1.4903558919897109, 1.548916024035241, 1.562757113954403, 1.5308241071002067, 1.4545615073320457, 1.3376057459792414, 1.1860019873869432, 1.0077045345817588, 0.8125715865910785, 0.611724066598781, 0.417329921648924, 0.24189776383589545, 0.09790043530735708, -0.0029060662949958334, -0.04993745018500633, -0.034347502925798835, 0.0505419809757178, 0.2088619677026278, 0.4418996438431574, 0.7479477633065338, 1.122237132677269, 1.5570154781301835, 2.041774845361881, 2.5635174248843056, 3.107301091376354, 3.6566106004018875, 4.194195428908775, 4.702437432699503, 5.164407744873814, 5.5641120275821265, 5.887655714883684, 6.1232583957409386, 6.262396194367538, 6.299507176192414, 6.232980614852667, 6.064521641829254, 5.7998804898296825, 5.447899820993644, 5.020919762113639, 4.533586295227997, 4.0029233655324905, 3.447025687820827, 2.8848480930522156, 2.334932524360839, 1.815016624830164, 1.34094676291707, 0.9262428764853657, 0.5813252730921679, 0.3131836894248518, 0.12499813920026762, 0.0160438053759628, -0.01827747951055908, 0.01379314106942772, 0.10076086092399483, 0.22846166017652425, 0.38069373434600834, 0.5401149684522636, 0.6889559914039444, 0.8101241543532435, 0.8878201019829502, 0.9086931861920834, 0.862197497906598, 0.7416223640044514, 0.5440684113786302, 0.27118859219982955, -0.07126678202379183, -0.4731182772360793, -0.920613940708804, -1.3965552718341658, -1.881448091835177, -2.3540487600686917, -2.792641336863176, -3.1758814597482607, -3.484001053081248, -3.699759422097845, -3.8093832938177044, -3.803398245931291, -3.677156480032304, -3.431325788572597, -3.0719336916847455, -2.610337721909784, -2.0628094709350515, -1.449892999876775, -0.7956486436749947, -0.12641242014794624, 0.5301014797392104, 1.1465170121342376, 1.696590724415608, 2.1571865536743426, 2.508721905336735, 2.7371250728332908, 2.8337342080712555, 2.796951676525845, 2.6314851367326946, 2.349457026035608, 1.9689918517933216, 1.514631581094967, 1.0153944678061135, 0.5044737887787886, 0.016998005846650743, -0.4108709242494356, -0.7441797707086851, -0.9504445838760501, -1.0015856962928855, -0.8752181604727252, -0.5560155536776329, -0.03667041115308729, 0.6814778541229878, 1.5881379403156388, 2.66420233953135, 3.882326432355019, 5.207705023895808, 6.599620329346072, 8.012600821813233, 9.398856626132234, 10.709467928528513, 11.89746785335116, 12.91867541944768, 13.735065401124583, 14.3149000080494, 14.635966629013017, 14.684769322573892, 14.459231965177246, 13.966868335106733, 13.226639431431554, 12.266201924115329, 11.12275937414593, 9.839659891626544, 8.466264803213912, 7.054294743073625, 5.6569219219196185, 4.325323630579433, 3.107350782564715, 2.044725130534567, 1.1717182460729498, 0.5133251239151491, 0.08438708651216541, -0.11109305391825924, -0.08003514780849562, 0.16013867485554348, 0.5824082219835152, 1.1514462940675296, 1.8255125288413991, 2.5582233295961707, 3.301239009982016, 4.006035202311713, 4.627024635177427, 5.122856185522998, 5.4595180587884515, 5.610783893714154, 5.560837135679596, 5.303649594758168, 4.844750269988212, 4.1995290422173746, 3.3939321218332354, 2.461892093353717, 1.4449363203539451, 0.38911353327057363, -0.6562886913889647, -1.6418546625857762, -2.5198437487901644, -3.2468686792936032, -3.785745182070898, -4.107357888540273, -4.192069488010231, -4.03055981309443, -3.6243888325786897, -2.9858028118345312, -2.137204845936344, -1.1101312718872693, 0.05641065425554003, 1.3174248719339883, 2.624550567207618, 3.9275387719883836, 5.177491748782972, 6.3278711918366755, 7.337901816303707, 8.17274301428294, 8.806590950222567, 9.221814288610886, 9.411365687763922, 9.376890317378571, 9.130207656481225, 8.690606315958107, 8.085347876683013, 7.34652131798244, 6.5107118050692545, 5.6158707415237235, 4.700444247418595, 3.800704775534206, 2.949716067916859, 2.175473216392119, 1.5000783483337161, 0.9388703627783497, 0.5001022972780124, 0.18504575182880148, -0.011681850102604014, -0.1012381397878851, -0.09959875019111865, -0.02623878780446435, 0.09727872514057138, 0.2486667839031155, 0.40649795342831896, 0.5512472011997093, 0.6667288485217872, 0.740556011818932, 0.7651538400928688, 0.7375280528890584, 0.6596848351352758, 0.5377696244842146, 0.3818708357080586, 0.20473384305266973, 0.0210763584103709, -0.15383051845901227, -0.3050888485046074, -0.41942182147484725, -0.48603721626072394, -0.4974634331230442, -0.4500597166711116, -0.34431971299031544, -0.18482251689345397, 0.019969758774453856, 0.2583931293518127, 0.5161267203454213, 0.7774296702087208, 1.0257720948461708, 1.2454213086554229, 1.421875618320695, 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['0.33125944177404730716119450430324', '1.23804783775814731569978738582365', '2.34072548798957623618095641440225', '2.41622505267621646785079040693469', '3.19485007537141727028766007010327', '3.43630114505786450113944420019390', '4.10281934384568286500270804329337', '4.12402195399918356516420951914679', '5.13947473697960181784982474679607', '5.30291954364579518552346116379971', '5.94615463452940117249173152937127', '6.02081332635586191243956338995281', '7.03898872870363543965092292199323', '7.08243983359730221808075956664164', '7.46503660551754130113534982360627', '8.032903282833144726859367335107925', '8.467875463698441746435313366815648', '8.673592385011692908770459838435132', '9.559732455942510734189188122112123', '9.622103011906143264368873513861834'], 'prelabel': '4-1058e2-1.1-c3e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 7.900887341689767, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c3e2-0', 'trace_hash': 1244890091454804505, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.33125944177404730716119450430', 'prec': 97}, 'z2': {'__RealLiteral__': 0, 'data': '1.23804783775814731569978738582', 'prec': 100}, 'z3': {'__RealLiteral__': 0, 'data': '2.34072548798957623618095641440', 'prec': 100}}