-
lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_287.207', 'a10': [0.6691306063588582, -0.7431448254773942], 'a2': [0.10452846326765347, 0.9945218953682733], 'a3': [-0.8660254037844386, 0.5], 'a4': [-0.9781476007338057, 0.20791169081775934], 'a5': [-0.6691306063588582, -0.7431448254773942], 'a6': [-0.5877852522924731, -0.8090169943749475], 'a7': [1.0, -2.8163065144692913e-30], 'a8': [-0.30901699437494745, -0.9510565162951535], 'a9': [0.5, -0.8660254037844386], 'algebraic': True, 'analytic_conductor': 1.3328223966973418, 'analytic_normalization': 0, 'bad_lfactors': [[7, [1]], [41, [1]]], 'bad_primes': [7, 41], 'central_character': '287.207', 'coeff_info': ['x^60 - 1', '0.994521895368273 + 0.104528463267653*I', '\\\\zeta_{60}'], 'conductor': 287, 'conductor_radical': 287, 'conjugate': 'dirichlet_L_287.226', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^14', 'a^25', 'a^28', 'a^38', 'a^39', 0, 'a^42', 'a^50', 'a^52', 'a^37', 'a^53', 'a^9', 0, 'a^3', 'a^56', 'a^7', 'a^4', 'a^11', 'a^6', 0, 'a^51', 'a^44', 'a^7', 'a^16', 'a^23', 'a^15', 0, 'a^33', 'a^17', 'a^52', 'a^10', 'a^2', 'a^21', 0, 'a^18', 'a^8', 'a^25', 'a^34', 'a^20', 0, 0, 'a^54', 'a^5', 'a^28', 'a^58', 'a^59', 'a^21', 0, 'a^30', 'a^32', 'a^37', 'a^13', 'a^29', 'a^15', 0, 'a^36', 'a^47', 'a^4', 'a^31', 'a^26', 'a^6', 0, 'a^24', 'a^47', 'a^16', 'a^43', 'a^35', 'a^9', 0, 'a^57', 'a^32', 'a^10', 'a^22', 'a^41', 'a^39', 0, 'a^48', 'a^5', 'a^34', 'a^40', 0, 'a^0', 0, 'a^45', 'a^8', 'a^58', 'a^19', 'a^41', 'a^42', 0, 'a^12', 'a^17', 'a^13', 'a^49', 'a^35', 'a^3', 0, 'a^27', 'a^44'], 'euler_factors': [[1, 'a^14'], [1, 'a^25'], [1, 'a^38'], [0], [1, 'a^37'], [1, 'a^9'], [1, 'a^7'], [1, 'a^11'], [1, 'a^44'], [1, 'a^33'], [1, 'a^52'], [1, 'a^8'], [0], [1, 'a^54'], [1, 'a^59'], [1, 'a^13'], [1, 'a^4'], [1, 'a^26'], [1, 'a^43'], [1, 'a^57'], [1, 'a^10'], [1, 'a^5'], [1, 'a^0'], [1, 'a^41'], [1, 'a^3'], [1, 'a^31']], 'gamma_factors': [[0], []], 'index': 0, 'label': '1-287-287.207-r0-0-0', 'leading_term': '0.544964959697564300930264102017+0.454644629437755368079213975343*I', 'load_key': 'dirichlet', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [0], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'origin': 'Character/Dirichlet/287/207', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'plot_values': [0.7097101847759844, 0.7959679195143152, 0.6153788448060903, -0.2785833018516117, -2.077256316202266, -4.542730351304009, -7.013111791007107, -8.61959177226418, -8.671609219107973, -7.037198854914238, -4.291709056328038, -1.4964004237006476, 0.32298841865732336, 0.7177428408397253, 0.03870273748546381, -0.8310018408581401, -1.0864465781379464, -0.5504156277091911, 0.2356651060418072, 0.4693600056526348, -0.23037869707558656, -1.4472040277894687, -2.233773679890286, -1.8626486570786038, -0.4795184466200993, 0.9117421975068921, 1.2037881782396753, 0.12466850305219372, -1.4270604790082304, -2.0192540253287303, -0.8674280286311402, 1.394738233404388, 3.071739655908103, 2.712235536561533, 0.3452776933115502, -2.416776356251148, -3.592438625280599, -2.424457339243923, -0.018775348204784305, 1.5621111168793917, 1.0325674183748532, -1.0262696767072799, -2.6782332013331747, -2.3200270306349937, -0.0717963114591985, 2.3532662463285092, 3.1644249245935354, 2.0115686343947834, 0.14639191580260746, -0.848091237539696, -0.49522816918195695, 0.34319822313195536, 0.5805245375084034, 0.1449463936250102, 0.01358080286547438, 0.9910390433763582, 2.5687994173237603, 3.2202596914453707, 2.014129405671839, -0.07733793097966625, -0.7124744881309375, 1.6715559706905083, 6.079890700750927, 9.427339262741231, 9.074887178613663, 5.18382514996599, 0.6475200809167291, -1.4147642454704374, -0.2904680254010173, 1.998566149564813, 2.8565667772447076, 1.5540817288671538, -0.40549768656341406, -1.1412244278414814, -0.371793184349945, 0.5529751085982656, 0.42607529324738813, -0.3432298887447624, -0.2538392473160638, 1.3758751957911852, 3.3470169078997776, 3.69722281638437, 1.8479292862871537, -0.6289064166583513, -1.585611813398947, -0.5528645101641001, 0.8329897840110722, 0.7476667795827776, -0.7093639091697925, -1.6667565572798677, -0.8178663257775761, 0.7331392047797324, 0.42519995227792584, -2.805811176454336, -6.818222899052962, -7.951396502911778, -4.619091871592452, 0.9136719119503758, 4.5426085712383015, 4.131956789394015, 1.2351409382571645, -0.8901626823060969, -0.6600680661817795, 0.6666786511953718, 0.9690976115616449, -0.16406687824195074, -1.2194092808316952, -0.8703877431266339, 0.34286985355169664, 0.8080817450114277, -0.01218487872905326, -0.8873801298902675, -0.5076177172386787, 0.6268334987058799, 0.6978220683827878, -0.9433261661224464, -2.4204825515822788, -1.180707995378731, 2.76381033300052, 6.082528847450531, 5.218868084889286, 0.2140659465764541, -5.020822143953047, -6.501191054694322, -4.003068366785799, -0.835334221810328, -0.015848476485419146, -1.2684407500781476, -2.056114269374269, -1.0394888720796898, 0.3450046595426047, -0.043920172189193064, -2.10662417112624, -3.4433651151604163, -2.2605338770791987, 0.39686014778063733, 1.867117018199419, 1.013889192124247, -0.5979744533638378, -0.8463850719962793, 0.3091289918052252, 1.0413089503109458, 0.3048391453332617, -0.676980849638999, -0.13178865104953474, 1.6182498772685932, 2.28655839008061, 0.6733620229433845, -1.2778028234291186, -0.4717903099625098, 3.3330461229646704, 6.51219214562372, 5.318717011103372, 0.31441423899791276, -3.8091118992844173, -3.1104694449553594, 1.4733303886102203, 5.371979473429832, 5.3704707690240365, 2.5593378968188603, 0.2615655610704002, 0.0023876721311445756, 0.44097080905738645, -0.05206758319093056, -1.0623521686022412, -1.0766367384354343, 0.0033935854181330713, 0.5745337743344249, -0.2289216266838803, -0.9089243704418857, 0.5835369354965775, 3.7685950973815947, 5.592455396393387, 3.9592202689446276, 0.4780625675641803, -1.3153178429019938, -0.2669609357226257, 1.035592229864202, -0.2466315823466788, -3.248266127094411, -4.1821332586792055, -1.0913031762407082, 3.4068408069556053, 4.98971326176124, 2.6416966860061017, -0.3952361121448554, -0.7891424527436883, 0.9585496706756859, 1.6685824776052773, -0.09263181900997035, -2.191276476122617, -1.9050839432419782, 0.4501307777617345, 2.0401681499026103, 1.2853636689398404, -0.255947545574169, -0.2550993320010728, 1.21590750407929, 2.036398867794059, 1.1688234084923812, -0.003967289854933154, 0.037799918763921664, 0.5771477651362834, -0.05275160095129356, -1.2227953780859517, 0.11270411814130014, 5.303351285913754, 10.87123968812673, 11.283074080942272, 5.166281038711911, -2.5229842104298448, -5.47858431458564, -2.5558720507954, 1.7403997970731566, 2.930463586475432, 1.2141265584054535, -0.1221772684831158, 0.44978510151356993, 1.201094259885667, 0.3490269383553374, -1.114587121221227, -0.9783193518327622, 0.7861439513591477, 1.8795180156242242, 1.0134806003187353, -0.1890110269725951, 0.39828389130534647, 2.132478936733838, 2.3308158954859612, 0.16411966028633926, -1.8672064133332242, -1.2500045639349682, 0.9302765463343219, 1.3112499707379117, -1.072615816342252, -3.2702085433777377, -2.4087941203397616, 0.1907222325555521, 0.6496695436954202, -2.0591542831778553, -4.368846613847673, -2.743274862746228, 1.3731799604679564, 3.060100183599707, 0.1239042404871307, -4.089053155284635, -4.890591046314205, -1.8779499507043798, 1.1582660288072617, 1.345014286526238, -0.18366626237982533, -0.7792862174873557, -0.10261913702999148, 0.1214183705107139, -0.6518445967717924, -0.8680619696992031, 0.3837585740845951, 1.5084095841607539, 0.686154119715729, -1.0134234131152993, -0.7760239478219086, 1.6818599748040792, 3.04935213045103, 0.8681602395026078, -2.3764447210314805, -1.7666779064102487, 3.536628371464628, 8.447378485162467, 7.766033804399905, 2.4342298213787283, -1.7994781117928698, -1.419555621208253, 1.2635703810649792, 2.066418211726722, 0.4385839197774791, -0.7771537534695416, -0.04376511747572135, 0.921539039370418, 0.3939429872900554, -0.3436709512573229, 0.9963553318091027, 3.7516836222188075, 4.618607308960316, 2.1341444503797513, -1.1140464114105078, -1.8595970362098537, -0.3298040414102833, 0.6596324834271577, 0.04680122123029706, -0.28239683406973365, 0.963587795263013, 1.990759127535887, 0.7172130553320402, -1.293746650805975, -0.35269429040069583, 3.6979266609525476, 5.912146522853573, 2.0742602501519856, -5.323431279727636, -9.32057165809717, -6.579974625905756, -0.9791746910322314, 1.6950271381484012, 0.6084440705935541, -0.4707959004692008, 0.8046148932101037, 2.4702870989643744, 1.8666520362842776, -0.29401106931134113, -1.295832895157572, -0.5288954042909171, 0.0938624214136992, -0.3878468867177504, -0.48497970610506075, 0.8721221868543322, 2.007141393105254, 0.9686107937853643, -0.8142181145583505, 0.06677984438908127, 3.770004632583534, 5.940972471014053, 3.2062185634269893, -1.8322007403383864, -3.490624360650748, -0.30738245712321755, 3.220641419880756, 2.854231006244493, 0.06092289065384826, -0.7292412309571603, 1.2928169396311098, 2.4626057392422247, 0.4093222843368222, -2.3001389205689113, -1.9493119085989288, 0.8808355410505271, 2.2403464287244907, 0.5460964938753439, -1.3972873062554259, -0.7835732509086345, 1.2090460620564034, 1.600585050727839, 0.20591227737036483, -0.4452876518638848, 0.6336097021255038, 1.3860560927261953, 0.2603470939023425, -1.0845017044896408, -0.4649670667809041, 1.0233578293807013, 0.5233160868566293, -1.7477192494599612, -2.275442107843096, 0.07140159056059939, 0.9232132149080996, -4.286619779411307, -13.122411718230682, -17.573622299760512, -13.288722333849595, -4.718891496448371, 0.5124142222252317, 0.30557370008669305, -1.2595547497911603, -0.6964985238194792, 0.851064311296752, 0.921290967337706, -0.04294487986143784, -0.05040332440485027, 0.6336014452921148, -0.03608452485097539, -1.9733346770578812, -2.445071760032964, -0.31600433670703354, 1.6755757783646665, 0.7183505817550365, -1.7377258053527624, -1.9904281861045243, 0.3474498065741458, 1.7834317183641144, 0.41144808247083337, -1.0749453556577366, 0.2231635716669213, 2.2748258297497843, 0.6051238510166537, -4.7359928784613015, -8.240712853965872, -6.066307239591202, -1.1639204234453757, 1.0179010784978892, -0.03517257123529503, -0.04782877592034564, 3.010546781515067, 5.728659698524298, 4.454699871281897, 0.7954194124498857, -0.7542080173871056, 0.8418449975336106, 2.3137741327369956, 1.3772991729239796, -0.2617046276906615, -0.25539740892850593, 0.6874906631435326, 0.555994905406942, -0.30810355846346416, -0.08256218539326328, 0.8184212435755884, 0.12736088606799886, -1.7356855724285722, -0.8361810346636519, 4.488942364119532, 9.507523043430098, 8.116766448671466, 1.1561862269623773, -3.918080153944264, -2.356245616990916, 2.1838450338107527, 3.2364518936300186, 0.16413854019002605, -2.1209856969151293, -0.8462037712097126, 1.2382444793458673, 0.9104002809343996, -0.6772897240120324, -0.5727814158052777, 0.9267763071010496, 1.0519503339498772, -0.5380588303941984, -1.0889349597967577, 0.5832541029627771, 1.954361492402623, 0.9276652133652585, -0.47703600291979587, 0.8271611615666716, 3.845568662183787, 4.623907334180205, 2.14666339253306, -0.2566131719518414, -0.2092171812756829, 0.28729466936936743, -1.1288494062419587, -2.44795860684936, -0.188630985391477, 4.1279552578821805, 4.747297239229867, -0.12205296888901149, -4.705002820254305, -2.8899110205932965, 3.467926615357808, 7.001568733931919, 4.489551958838657, 0.156795171449625, -1.0610746911240292, 0.30069812572028004, 0.825313823167761, -0.02265353093547728, -0.08908327621062641, 0.9300950569946611, 0.884371282513029, -0.7574008497305332, -1.6154990264666746, -0.38227840224175846, 0.8011613668848996, -0.017930187238923305, -1.000473937025877, 0.4719014905462381, 2.731069495031676, 1.6593956116566688, -2.4282541423506445, -3.896761976729345, 0.3704605269451618, 5.661115403877286, 5.277062469561059, -0.3164826364463378, -4.237691730681507, -2.626485520537261, 0.9398978295980525, 1.6506528453009488, 0.10768837633431674, -0.15320311653492052, 0.9979359316257037, 0.6029277631137167, -1.6116598945164655, -2.163954531144242, 0.5166881449833716, 3.0474623582109346, 1.9318049393798784, -1.244924193450976, -2.375665339401877, -0.8591682172402179, 0.34423791900830086, -0.025675548608915758, 0.019002831505451335, 1.4336407615664462, 2.0143458581605636, 0.4535190057435613, -0.635086113138854, 1.1563258713665259, 3.1095304353525157, 0.7714286615435766, -4.41520567091072, -5.586390690962472, 0.08426253249492079, 6.554426329407505, 6.562578266731032, 1.202457750887743, -2.2084703582192406, -0.39133718136780565, 2.468022902956354, 1.9667928973100934, -0.4346807446413052, -0.9321212257300012, 0.47072356808464044, 0.8965323677156838, -0.19839331484280925, -0.6632889492596721, 0.04494522372152393, 0.07037829747234924, -0.7762166726157042, 0.1010121341303633, 3.4081987409233774, 5.4455562855789115, 3.1309729878837866, -0.8288629447767781, -1.4566646318268452, 1.0952503575387236, 1.9329071754344167, -0.7222118433805718, -2.648984234458321, -0.4614179551693378, 2.7655312811126365, 2.2991341851325995, -0.5722712461394321, -0.42245475246533215, 3.6143041593170375, 6.108338917836261, 3.4316082241296293, -0.9182375628251813, -1.812287168138235, 0.1350775323468722, 0.5615709745917861, -1.3239971068268774, -2.0141585263002835, 0.005289832324497212, 1.751191756632466, 0.8120145236105328, -0.8817278063173609, -0.6759538305105346, 0.40511548722765883, -0.05967383192127374, -1.3411566630514398, -0.9517911977971424, 0.6038047267029364, 0.574931405874274, -0.7022893223000451, 0.19182189862811028, 3.0422803685162867, 1.9399238404993828, -6.486644362996248, -16.028279693243753, -17.060365256372044, -8.690965626010158, 0.1819518386452052, 2.3428755131433467, -0.058686802014792004, -1.1467172741288045, 0.009968978921897107, 0.321758234148931, -0.7187698146399488, -0.48212322784414785, 1.452775279476341, 2.2188409175849184, 0.7569399900804537, -0.16666473000515744, 1.1622813158347935, 2.12365532723844, 0.1025737618380455, -2.755655941119984, -2.6856424500650657, -0.2961032689478139, 0.6892144780563907, -0.1929238814489617, 0.3497730407190792, 2.9899927112080276, 3.699587594822502, 0.2616481667310686, -3.3003250369631716, -2.4966015131807096, 0.4486959867775316, -0.018898757607926416, -3.763805820646982, -4.8827689387133155, -1.0936903995166414, 2.3282638386003387, 0.5509490177452514, -3.397081508187736, -3.334994888673748, 0.8537859884526982, 3.651771733197661, 2.3900234649155823, 0.2209086466959376, 0.15880797001601415, 0.8794272154987598, 0.32624323707469505, -0.43525710378820237, 0.19945702341105304, 0.9478446294299336, 0.17952973384430992, -0.38279738971931127, 1.5534648950336702, 3.855635459326279, 2.4128738779425563, -1.6738637798738276, -2.460327593846858, 1.8790980937501351, 5.4130661880852715, 2.9448072792225854, -1.9548991327640695, -2.147510316953589, 2.3734971237843423, 4.728567863584255, 1.6060657372043439, -2.4128900163107048, -2.5186124791611584, -0.4119803526336589, -0.15367435444796573, -1.3459717364572743, -0.9136621639423912, 0.7989684707191902, 0.726742796585677, -1.0163580898727371, -0.9395363741440976, 1.643113068227266, 2.922940711918118, 0.7458092154759832, -1.7088138338629513, -1.0411930111173013, 1.0622811849376095, 1.0994826834682432, -0.4034432859201269, -0.530437472651473, 0.3958089503334053, -0.21322687401170162], 'positive_zeros': ['0.86738957173492508055880768808', '3.67234015863215428730378235088', '4.38784937218387349783127465834', '5.5217436530651229571288160736', '6.17950087796733698580158121548', '7.5948527687931061956907872368', '8.46239043556711076950183408547', '9.5018119141284181814189893124', '10.66168960400515102867538313741', '11.877521930995236614975978276031', '12.66896496953795132949024061421', '13.75832910833102392739658613434', '15.02878384056625535441935077755', '15.8010749232092648072315140072', '16.67637188886548336444484385135', '16.86303186824986084322804470253', '18.424101061520601528220489380294', '18.89349332474547077108528618320', '20.6843483257411938399568454648', '21.29018373873407787135446988495', '22.42629706654194777464148637857', '23.22850770584845639766558847448', '23.91848799848116487328039185436', '24.447208876761775920321217510237', '25.84850338620479433457458351624', '26.67027839487520499638039759626', '27.362435785601798575703642522161', '28.2761266431920026799730743489', '28.811286861431286657854815260302', '30.25940006557858279665070614001', '31.39323666464472950795876739134', '32.02797959462503937615307799543', '32.77636339721538552187163333743', '33.659591090866231730231617692689', '34.37166690715820371893711799168', '35.137471087000395726179032922412', '35.78613213145705796108432236645', '36.671123591737095982608861694466', '37.82374863196853873229997464072', '39.24855788363837484511962872590', '39.36547133236997676626178143511', '40.5210284216888892411943163056', '40.92816698933653463573090814746', '42.13926315561718190999747031494', '42.99539780402240675390613237118', '43.67678584032146858169973254160', '44.45272820101641013537321856317', '45.02753064647854371441787598821', '46.02693699194251633963222577086', '46.613204250146827271425740729766', '47.830522793399805026862437234070', '48.65990076939241444387919539728', '50.087850672467006653006240660187', '50.31085088715953973858335698793', '50.92092061968926438261833097567', '51.87406332697097885884793742298', '52.437249128073062634730554751107', '53.050780773373783566199774254848', '54.42492622868960437301571115289', '55.04619574165731362912966477145', '55.59480798277481757085593290655', '56.63519290014304593303545929305', '57.75799690362221189885296604630', '58.28076630612224566937459496352', '59.05083807928662539992602668334', '59.944519217034846591367775072980', '60.87090271012854998425741881312', '61.31797891520626495980072775940', '62.498140264353851068818673715121', '62.79208216939749841259507633162', '63.42456612052645881112154059166', '64.05197579474024657925363447442', '65.51126655981699502369611906711', '66.42154570495014893375227238035', '67.43209336534799048628020083910', '67.66538256387101018531534363581', '68.505337949295342545269848583388', '69.24802724748740598869670099792', '70.23308443024556032663044275281', '70.52958700973614104372275267736', '71.581660840003410542072073664318', '72.36309066921968995484024956445', '73.00963467019912054752514682388', '74.03553247921776329179017811992', '74.4784381518484156482550103635', '75.519267352556040870862105107294', '76.25862025111215615663963737347', '77.35350156733818822952320202352', '78.08571733232897044735090492108', '78.796167623523335246759695675061', '79.13316821955998605926708644227', '79.92472808526953383549110045121', '80.74151055221535938447249212105', '81.36564343766839603210077612348', '82.26197020875111074626643382103', '82.93879810674425515745277326776', '84.20669538871808690724285510849', '84.851062356761773592524702291306', '85.69906379088747548678166503353', '86.260526674426260583550943015', '86.99000509540135840105013856605', '87.3410605665592816946257675922', '88.62682570873809039591816554414', '89.438421612336184052181059723473', '90.016605280037505558247928373336', '90.420109108794010727363420592171', '91.34604472396580279773471211580', '91.909667447881388170128979729100', '92.903427119249769317977643780992', '94.13174985646635968150006415184', '94.80104656022346106385848776699', '95.17519192704780359471855293396', '96.20539182735689350855737683408', '97.07083098664563342260009807727', '97.30525542800882477525446602422', '97.9560396524602485417816577585', '98.89732514326818290619552506338', '99.36724859444993217938613284155', '100.5045371704230854648962964212', '101.27198869965695700936019528779', '102.19551226473341009831325567724', '102.640974094821846935223759558341', '103.47785736779637289803904225649', '104.28127447818670644082984621767', '105.06866841502621536840421925960', '105.74534886583816063797892049537', '106.60897377641579138590606853631', '107.04145195871592484025915009979', '107.8594692286264027512671116126', '108.52563012548166874489924502322', '109.141844239028234592983986962432', '109.99161144800622411468331431774', '110.41063938067337287662865099779', '112.12945993373806994612667533411', '112.55155528212761231601413977798', '113.254289469656607228480027094190', '114.04464717353481367211951644890', '114.3981932128812230680701670', '114.99300475506383943930589450215', '115.97394465846843869755552862816', '116.65176171051949583219353426435', '117.458404162410341022262843714418', '118.18563152493051324094437589941', '118.720850419293512115379208115066', '119.418047360337736909957607632297', '120.72523451834135929562352928878', '121.24171940304966514953295823484', '121.57108156428519337190106497032', '122.89993618665783790538750599171', '123.31429427894275025184912152432', '124.3069367323366592793994905092', '124.77052673815881321839584508051', '125.49797916031457584631967543307', '125.964740558429055134818801988567', '126.584603633929014539456676286658', '127.25449433040641036535294821982', '128.48781870658137239611199685943', '129.21852507430095896172784113493', '130.01439999042334669153943610270', '130.73172694622216053476926653875', '131.41677919380861032816378560543', '131.99766024591849945533934616442', '132.714192845839289588488157766296', '133.35104421250091084612687288248', '134.224619953278857998187081965664', '134.575756219017647508348545905304', '135.88223916396735872263252335299', '136.323698811396928096189976671685', '136.67431097674637284432695807669', '137.51416708543497409652556961631', '138.43123971944104814275431550544', '139.21112471881961123465695027128', '140.328218299745481336825095902925', '140.87485987926195284529046781397', '141.55378551970769666690458680000', '141.9097643509841672355814387136', '142.68254001259576008622957603584', '143.507511397961441024550373869297', '144.05871675702976364870452621968', '144.62684118613626651761038882341', '145.447015480544122206127472601966', '146.23086225336729102614710757425', '147.17111400051752415431946987310', '148.028889710240219760909533329', '148.7761874325417360437452137499', '149.111637769749518693767833238186', '149.78239491079266673404507879274', '150.5778392295292463556260457178', '151.43615265612082240527454641963', '152.35475744211269582049739096184', '152.79903902516837145654378641220', '153.11812875126778673263478747468', '154.137777748845421975270573053571', '154.54061851539489716125246285675', '155.36140411320790883973933370203', '156.24653101735876543707309983861', '157.258964057110974554216159461780', '157.84814135867903644406867603884', '158.68552057414946349178699395260', '159.27617351325502220149693466789', '159.94842097224048732535399674370', '160.605330088101425135185742360483', '160.96678338776671931140721149339', '161.548936495860515203527382914879', '162.73443221281138961233825431266', '163.31435592868937629105196822843', '163.99377522343906318475853470772', '164.72609065886844655558483796852', '165.55358195778921877275220549950', '165.98228810037310155801514420288', '167.107895646677165180625522832577', '167.79008955681266112818955065278', '168.23845566671105974610835860580', '169.06185581243200857148090045706', '169.816215986605083257176798006686', '170.48385854671819889174863491407', '170.92300801082619172595619968211', '171.74416112136288151197330440530', '172.31920060513162090462354312381', '172.78756243427845766189920512188', '173.534975484783820153954834937494', '174.990645590831556168791769961069', '175.6176789979028653606232917197', '176.24744905189783985453255893003', '176.67070846877700012853197353256', '177.27788748747335727189893391896', '178.287978530638381890142877031097', '178.51840027683030295864108444121', '179.38505681487938634175699008090', '180.35688954779522477872467306688', '180.8694795179901778000414011741', '181.185424634157784501333146412320', '182.20549368566232179836928850426', '183.063785286867127812485702553944', '183.435413973594146394052719904509', '184.447424723945219717758232839928', '185.04169965068179788001809344737', '185.87927177757615744092257490658', '186.94798980280591956259856494385', '187.11620029958714764841575853007', '187.90923442384149547110860669295', '188.37997204376540233218436672197', '189.1097244300911306291758355243', '189.48316880056479743051352025173', '190.49391484634873816746189519309', '191.13812021090056349634492389950', '192.048675408985450772997113880713', '192.66257794031809825889702102957', '193.54359798912667698524734069615', '194.48868341200412857186417921192', '194.6267491525177101036956386850', '195.47178632628587003961465357718', '196.071124462800203941941500419693', '196.69338716609954839537756567084', '197.57462876146666740159000190299', '198.26816337708501071416822125611', '198.97125147324048386165393787504', '199.53603799619372713050386270914', '199.95238162463344601623047798054'], 'prelabel': '1-287-287.207-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.3328223966973418, 'root_angle': 0.44263361185375855, 'root_number': '0.179247808732975953578173999540+0.983803955605193970838067843007*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.221316805927', 'prec': 47}, 'spectral_label': 'r0-0', 'st_group': 'mu(60)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.615172657448180508129698247783+0.348019031548787591026613446459*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.867389571735', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '3.67234015863', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '4.38784937218', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 1.3328223966973418, 'bad_primes': [7, 41], 'central_character': '287.207', 'conductor': 287, 'conductor_radical': 287, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/287/207'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': False, 'is_instance_DIR': True, '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': '1-287-287.207-r0-0-0', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [0], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'prelabel': '1-287-287.207-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.3328223966973418, 'root_angle': 0.22131680592687927, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.867389571735', 'prec': 47}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_287.207', 'Lhash_array': ['dirichlet_L_287.207'], 'label': '1-287-287.207-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/287/207'}
Lfunction data - 1-287-287.207-r0-0-0