-
lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_1544.1283', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [1.0, -2.8163065144692913e-30], 'a3': [-0.3826834323650898, 0.9238795325112867], 'a4': [1.0, -2.8163065144692913e-30], 'a5': [-0.9951847266721969, -0.0980171403295606], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [0.7071067811865476, 0.7071067811865476], 'a8': [1.0, -2.8163065144692913e-30], 'a9': [-0.7071067811865476, -0.7071067811865476], 'algebraic': True, 'analytic_conductor': 7.170305855403121, 'analytic_normalization': 0, 'bad_lfactors': [[2, [1]], [193, [1]]], 'bad_primes': [2, 193], 'central_character': '1544.1283', 'coeff_info': ['x^64 - 1', '0.995184726672197 + 0.0980171403295606*I', '\\\\zeta_{64}'], 'conductor': 1544, 'conductor_radical': 386, 'conjugate': 'dirichlet_L_1544.491', 'degree': 1, 'dirichlet_coefficients': ['a^0', 0, 'a^20', 0, 'a^33', 0, 'a^72', 0, 'a^40', 0, 'a^55', 0, 'a^45', 0, 'a^53', 0, 'a^31', 0, 'a^17', 0, 'a^92', 0, 'a^66', 0, 'a^2', 0, 'a^60', 0, 'a^91', 0, 'a^50', 0, 'a^11', 0, 'a^41', 0, 'a^37', 0, 'a^65', 0, 'a^23', 0, 'a^24', 0, 'a^73', 0, 'a^61', 0, 'a^16', 0, 'a^51', 0, 'a^45', 0, 'a^88', 0, 'a^37', 0, 'a^20', 0, 'a^79', 0, 'a^48', 0, 'a^14', 0, 'a^18', 0, 'a^86', 0, 'a^81', 0, 'a^27', 0, 'a^22', 0, 'a^63', 0, 'a^71', 0, 'a^16', 0, 'a^58', 0, 'a^0', 0, 'a^47', 0, 'a^19', 0, 'a^53', 0, 'a^70', 0, 'a^50', 0, 'a^30', 0, 'a^31', 0], 'euler_factors': [[0], [1, 'a^20'], [1, 'a^33'], [1, 'a^72'], [1, 'a^55'], [1, 'a^45'], [1, 'a^31'], [1, 'a^17'], [1, 'a^66'], [1, 'a^91'], [1, 'a^50'], [1, 'a^37'], [1, 'a^23'], [1, 'a^24'], [1, 'a^61'], [1, 'a^45'], [1, 'a^20'], [1, 'a^79'], [1, 'a^18'], [1, 'a^81'], [1, 'a^27'], [1, 'a^71'], [1, 'a^58'], [1, 'a^19'], [1, 'a^30'], [1, 'a^38']], 'gamma_factors': [[0], []], 'index': 0, 'label': '1-1544-1544.1283-r0-0-0', 'leading_term': '0.0237664965285204673744700178986+0.463255368509058779722393207204*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/1544/1283', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'plot_values': [0.4638646168977585, 1.2339642463822988, 1.8543305517422666, 1.4637898785140269, -0.39794045071855577, -3.006698980058901, -4.732466911236176, -4.27124564026586, -1.8546244963035052, 0.7566398612526959, 1.7162537088839218, 0.7453782010393255, -0.6587278238222087, -0.8004539715150862, 0.41481111199767606, 1.4372699554925121, 0.9476216028240154, -0.431713724884228, -0.7094067484725113, 1.0450043786428351, 3.2188180449498573, 3.1470788932017117, 0.17579797234190267, -3.2550665994248265, -4.060675617972107, -1.8804611279495391, 0.5895652454548586, 0.8097003423201634, -0.6575227438656135, -1.0750349315511574, 0.8256422478798969, 3.115579655313189, 3.104423749883779, 0.8049676482376361, -1.1187356672485245, -0.8532524918575519, 0.3301831036530559, 0.16522550035098432, -1.1128671260751464, -0.9267986213869579, 1.7328555926016815, 4.0717161311670536, 2.5437906687926057, -2.40155455933977, -6.279543224602871, -5.709879876674534, -2.2377068121210923, 0.049334437840886994, -0.269085552517482, -0.8966820212667319, 0.1281331197441663, 1.4731984427338054, 0.8960812599491006, -0.887165716174241, -0.9911339826265849, 1.1314045859216217, 2.370910251824658, 0.3286661831566583, -2.802131851340711, -2.8846345717453445, 0.3428695024161912, 2.6599849574402845, 1.1244873434428266, -1.9344516393706814, -2.406368813815731, -0.22661654452227592, 0.9258384308730983, -0.6732281322518765, -2.3812494667756976, -1.5073986063283655, 0.5337930602137618, 0.6752801558195581, -0.7823799404736839, -0.7014750431231784, 1.5637040559609778, 2.6866793650575516, 0.509640245936239, -2.1761017277920693, -1.5996031181381398, 1.006881555630835, 0.8763562768804294, -3.09536417467635, -6.26405080538646, -4.666098865556815, -0.46777273008602416, 1.496073749136467, 0.4459294230437483, -0.44382841679192153, 0.1805311306702906, 0.20475547497392022, -1.2564111682896912, -1.4936881259619632, 1.1874152551684474, 3.577806094711283, 1.7978954245431646, -2.3069283180109417, -3.133064160370253, 0.5766736386975642, 3.8312170195296877, 2.7519141508689065, -0.15040758115018688, -0.6392667804518343, 0.588601620575951, -0.14701530380971506, -2.791308334785537, -3.521620997584098, -1.306855657728589, 0.18755939555809778, -1.3514981049921353, -3.1181532483180767, -2.058801297784229, 0.04884976363263048, 0.13220139061123026, -0.1977905530206066, 2.8973700386401706, 8.078680812569102, 9.298765195069038, 4.580614230993131, -0.6327386929114914, -1.2077065916756118, 0.894768445467393, 1.005805840734498, -0.6413567246632008, -0.4189928176248573, 1.7118444423672787, 2.1665057301765085, 0.2340742473058325, -0.797975836745682, 0.12767326018610958, -0.21695163059175337, -2.9773231582619233, -3.803024567518686, 0.4176040095408408, 5.409486010181056, 5.064906573094631, 0.5435147201022418, -1.7474814258350369, 0.03800523347697829, 1.4267842402875428, -0.15343563541242738, -1.5956999027957213, -0.4518568607626271, 0.6536571500614473, -0.6874210789138417, -1.7585477233622973, 0.4680914718128722, 3.3630269132870034, 2.6812410919266685, -0.1339662994807108, -0.48367994522888647, 1.2210172071017986, 0.37635181932200795, -3.1163678669300787, -3.8360162317442863, -0.026393591784084763, 2.775485605645002, 0.43062949770717784, -3.23110212036609, -2.8719381256992493, 0.09467534756316057, 0.9596199234089987, -0.29270421237385513, -0.3988735143612361, 0.41648989759139077, -0.43864984984014743, -1.5552976310150188, 0.8127316701569429, 4.956261774002368, 4.7096215517670075, -0.5854446688603474, -4.081811213062366, -1.8450803140810663, 1.3815987930590825, 0.5310374704668606, -1.8647088800051277, -1.1894578713765986, 1.0571316297436584, 0.7801995911728754, -0.896837800324316, -0.11004762007266247, 2.1092801647468775, 1.6647248475677405, -0.7942719145993641, -1.0521671554539291, 0.4857837053408964, -0.7196693999496938, -4.424686235443809, -4.9425842861705, -0.9615055928051365, 1.6678184330079016, -0.19652382976696645, -1.7335712992779058, 1.082387433866533, 4.311668433726708, 3.046117471882594, -0.26345441893728044, -0.7212670957198756, 0.5612152658870462, -0.32114685946756755, -2.2638161653674778, -1.6894686972505006, 0.11332383244023245, -0.4693159890387005, -1.9049510769204354, -0.36857519148384144, 1.7102281851854646, -1.4759966101589492, -8.189176981682552, -10.01596521537994, -4.66279127803908, 0.7094457244967483, 0.9448894036139466, -0.6668167123039079, -0.33420479091625666, 0.05977379360421611, -1.1327062856226953, -0.7913641307962936, 2.5459908866796503, 4.382528346907763, 1.7660454469320512, -1.056454549017741, -0.09606535779459152, 1.368283819787326, -0.46068231765877476, -2.1000914145806413, 0.8554709285356935, 4.80151627220922, 3.826795223840408, 0.15351739969943454, 0.12041106421998787, 2.9723891239092683, 2.788412249593925, -0.6004703885413556, -1.8621269745960283, -0.11019020830519223, 0.4231711001135088, -0.9355723159469282, -0.7861931764227179, 0.453350788862005, -0.9115804416105446, -3.33342380641506, -1.3599061223758608, 3.7766420219951415, 4.53845322016707, -0.34562405569082566, -3.409864802058977, -1.0307634815498883, 1.246623989457698, -0.5802303835439505, -2.416227206011328, -0.6951858765198511, 1.220682835589565, 0.27602545031080133, -0.6971511948459117, 0.33571626421541206, 0.1577230937914917, -2.3852156651102443, -2.530139725534217, 1.476025066843567, 3.5663934142991347, -0.01240756358550178, -3.6575403867828964, -2.091069968551076, 0.7156737190727634, -0.41433240723197506, -2.4336010397408105, -0.7589895895150359, 1.515652709935752, -0.29823985382901347, -3.26268517019131, -2.3353642908282404, 0.342271838945351, 0.13099255179687672, -1.3497937857339446, -0.433724378147336, 0.8800521283929018, -0.308264132592223, -0.8494574655851982, 2.0210605141583513, 3.074022720595623, -2.6515545904043214, -9.41060165993682, -8.639298760417379, -2.5166729477812826, 0.53388491626701, -0.5140577046302021, -0.5455075911541984, 0.7781539143174437, -0.05802860205011888, -1.8230442617607785, -0.9633574096168636, 0.4398509783434133, -1.3350215314405567, -3.263568796735247, -0.7612197361741125, 2.7439387104329778, 1.4016247414972263, -2.0800026414807045, -1.5064007146136933, 0.958635016794515, -0.8945123557862359, -4.993208452475303, -4.4415076214721685, -0.12467580958301668, 1.4415276298888329, -0.011967116681558154, 0.21755526899653949, 1.5252058355135207, -0.14874608771480827, -2.988861715898596, -2.325406602798316, 0.010025169137471543, -0.5935307957322479, -2.166824156231725, -0.6558607858867455, 0.6932442402526569, -2.786620377648733, -6.618878299736352, -3.912930010157103, 1.806851301419758, 2.175600071907222, -1.8004364493684382, -2.7705144179862797, -0.2818612623021293, 0.5108477556729543, -0.4137130360172301, 0.481971398840583, 1.805694607468557, 0.5783324420462552, -0.3958744226441944, 1.776891579031176, 2.55613704475148, -1.9986094185312127, -6.041277555955396, -3.1422159574522364, 2.0079390481194244, 1.735577434892397, -1.6328100082310322, -1.6864892276328145, 0.1783564535415091, -0.3497632026608246, -0.673336084703876, 2.879231535080085, 6.113107979151917, 4.023581910860596, 0.10527999058925004, -0.4976388525692982, 0.20393224851533945, -0.6419978117804422, -0.045174322502715386, 3.1909159681003616, 3.4466266716879166, -1.1965398700553764, -3.360708066799245, 0.944471487935364, 4.615172045209513, 2.1776159863148883, -0.8118464403153549, 1.0472329963677411, 3.4644056531788068, 1.8661608494899384, -0.3407137538104423, 0.052148182796946135, 0.031755921379523724, -1.6569914646992325, -1.1093298603631654, 1.6389203897476998, 1.2445906260315216, -1.9301056189067842, -1.4620564134947838, 2.1278932972171076, 1.1170039789330568, -4.64948944218963, -6.498727604051295, -2.374807213250581, 0.2975002693948069, -1.2278577632432048, -1.695899375965785, 0.26085666500772936, 0.2844268199118403, -1.304789924749666, -0.060430939847225605, 2.3999114999132733, 1.056172362140896, -1.8215143420720148, -0.6715475679614646, 2.249671804350167, 1.6268512912319077, -0.11360510948373168, 1.2920050596425658, 1.6842411309781458, -3.5258385118203885, -8.320743517977842, -5.549240847801946, 0.0986389917426947, 0.6279491567216811, -1.75981839988401, -1.0750903580112685, 1.006535566984522, 0.6030396820447851, -0.1621214535528418, 0.6310825595399595, -0.31998874040504693, -3.1786984003062777, -2.347427109742657, 1.9910286593669044, 1.9752137531380203, -3.3678720496217154, -5.154657885472722, -0.5758592459297961, 2.476788605197644, 0.48136662047154993, -0.6355640451366416, 1.387883537991931, 1.4823629411076022, -1.041842484242778, -1.095059474657648, 0.9813306427910826, 0.1390943258550963, -2.349375321240001, -1.4635183850093347, 0.8082087376929135, -0.18114403717711342, -1.4608370844341036, 1.1131713618092047, 2.83169800769485, -1.0731435471663477, -4.740425611343792, -2.0043603509716412, 1.8284095467351997, 0.26629220593380615, -2.474153195466582, -0.9274945305208475, 1.0989995816663545, -0.4526513620338649, -1.5289538631247652, 0.7883502266560027, 2.108829598459902, 0.33701269293143593, -0.4116406071064994, 0.4929167740816173, -0.5699388582369209, -0.9626573862551108, 5.088557068332689, 12.79767593049352, 11.717691688736814, 3.4314646229796715, -1.2062793427385483, -0.20004191298057045, -0.25186397283106693, -2.0833933658225026, -1.2459252465118713, 0.7266952047460133, -0.07802813530350992, -0.7831149828794852, 1.8314493836266548, 3.3734312879077852, 0.7629849577471705, -0.6486464826253348, 2.0521782542914764, 2.976212460737771, -0.3650199887734822, -1.711939524410862, 0.7937264320371318, 0.6865165876881258, -2.6915193070385364, -1.7683235334608032, 3.843203717741485, 5.505359127568402, 1.500340102390505, -0.8472944536875797, 0.46217832854208263, 0.6794163670799526, -0.25222746633256005, 0.9900252967465485, 2.0443656741756717, -0.011617800835664206, -0.8117622254507956, 2.3919251955158525, 3.1903435789284673, -1.7913366244590896, -4.824840954651355, -1.3520220894326895, 1.1207239563168145, -2.275248846345484, -4.7524271378241725, -1.786913492091261, 0.876782437646693, -0.3186906727120712, -1.0429976414655484, 0.07312232512920319, -0.6031541664363221, -1.676772942387725, 1.0682240106043377, 4.193200657294349, 2.279641796913758, -0.7330114740361909, 0.5207307966343643, 1.3291178085705244, -3.245136557587432, -7.023049910025567, -4.1284552820021645, -0.22952677821543632, -0.8387190048579821, -1.3495910238191675, 1.4106582859115018, 1.8759314023079594, -1.9413083169054848, -3.4630049469681294, -0.5786250829706389, 0.9290382817419104, -0.3642784224728543, -0.3738405701943142, 0.06271521570611469, -2.015106599784531, -2.5309739346734617, 1.7834225251282525, 3.728083330243855, -2.069659063432987, -7.182275304791324, -3.4632363345865125, 2.6911092307097553, 2.8470079213704254, 0.2280255761452842, -0.035270407266485726, -0.44613852447272323, -2.3225060819003005, -1.6219488551842185, 0.9540164240534856, -0.01813323086880192, -2.891040948157422, -1.8337110797921021, 0.5835976902036032, -1.2553349234861426, -3.496094153117411, -0.7682346522505779, 1.5981953214646907, -2.028716116771056, -5.51838432546575, -2.833262543699498, 0.46674741350602394, -0.7106352390097406, -1.3802927394210616, 1.5630527323021446, 2.7148146553822574, 0.31250155096698917, -0.2450582199362921, 1.483136807875125, 0.6291849955803325, -1.4238758490636365, -0.1995036889607891, 1.1382879734080698, -1.2399130075093996, -1.8574509484491366, 3.1130319440613143, 5.921753954174287, 1.3895439392970113, -2.4577143124349248, 0.3851721818639404, 3.2118386240835135, 0.9113248410512984, -1.127805523166849, 0.30449105403012955, 0.7603672561345707, -0.6888567956252671, -0.26562600362806804, 0.6823984713260823, -0.617420302392936, 0.46158690226951193, 6.804387453936048, 10.288724264839706, 5.296130418670239, -0.25253198101308666, 0.4939005370821485, 2.0572876336051875, 0.16133226690800032, 0.05985457958401569, 3.22590712777268, 3.017397145527447, -1.037852601893877, -1.856746035654546, 0.6105316915050211, 0.2413350025118535, -1.881257164729851, -0.9058657213913909, 0.5644785756542727, -1.093951704721994, -1.9272803164984351, 0.021201613392995686, -0.8356654114316187, -4.516037886254431, -2.730614361650221, 4.0806899752215795, 5.175676647636845, -0.7934038018593363, -3.6769909203266855, -0.8541908389510081, 0.7178137357124694, -0.0855006491666038, 0.9299574469605643, 1.9135051435264123, -0.19524366250795588, -1.2265885758566002, 1.3278331944742365, 2.189478497498702, 0.008482231557673112, 0.618583061219029, 3.115146809282222, 0.12417220963001047, -5.683033190019366, -4.4960594902354085, 1.8401953974269352, 3.3225643559482996, 0.2779668136946383, -0.1871284153666381, 0.755962828586597, -1.0185874355716975, -1.9207421502611046, 0.732520267802649, 1.5775811249696856, -1.160345353499277, -1.3504285364324056, 1.7252980094460417, 1.9252493397238082, -0.1874914481505124, 0.6210013794964528, 1.4944318065894688, -2.01004932831781, -3.872487416261834, 1.1291104130744487, 5.032220221239961, 1.0550324392866386, -3.4861364164631063, -1.837015582019912, 0.5502998096669816, -0.7845492757348194, -1.4116301751024758, 0.31121448642777993, 0.38306392612998375, -0.5048241891050782, 0.3969848136279365], 'positive_zeros': ['1.197852516083647797086890990094', '2.70855373851064720592570082067', '3.58755230860259249164357848367', '4.28499075120621649622137493057', '5.21012364650964396501493936670', '5.788475090586520741311238029182', '6.88945331551209357669311124232', '8.029200662830755598295974778570', '8.61833290232776742773198038712', '9.270928092749388499408758102578', '10.413526246226012046531488792818', '11.14616320612331137607105435613', '11.60774732218656369787197910881', '12.321971172698758547137040290812', '13.29723459100448438887140998256', '14.670637168958067520796019186580', '14.90762328088515556482126521801', '15.600302277962501376365812311593', '16.4023162801674037205067481295', '17.04052859029588798025616802409', '17.842955479506581693894127892628', '18.72061574969769047188694782552', '19.48297824909757252922503613674', '20.3440084747234019542762889869', '20.84318104028570076227763369807', '21.77933369447667374341878899101', '22.33574206399760480323237553712', '22.927327685761806295637515834994', '23.79893993677469347380076031388', '24.559313484705436367611089395573', '25.08986278044450362080210450902', '26.29154979627542593227757400306', '26.97298915617033132344438296016', '27.431651674417995567677614048258', '27.87108395270609273710517878322', '28.63802696728908605451578631718', '29.508519104592335181589090633851', '30.27295142450037573304426459498', '31.22868224038298572307127615803', '31.71719328669390243708359348790', '32.16566148964954563614837381084', '33.32779999501094201651852419252', '33.531898424993364635990337003491', '34.67632864281641980207327552511', '35.04764424274157549645651281212', '35.36026643449312902248900184341', '36.82103613234143470444700254672', '37.36365255583407491704817024891', '37.99699887815202837495434678449', '38.507038890811395812985603869617', '39.41154341421923633159901955309', '39.960541969016838383516855189184', '40.27242471743721542789219616184', '41.22751222879674259138437514659', '42.2280075447607832101183227663', '42.80774036821204037864285424751', '43.416427654421544049966880194647', '44.14215913652220159991757357125', '44.57527618135696447486854736062', '45.26899859691855318069819764449', '46.23118324391158394814079420264', '46.65402065722730820125537054584', '47.22648858170591613759246111675', '48.12682840343423790728362933392', '48.78189102240445296206085266502', '49.67577865619232403790314958849', '50.23917820915865763119323961788', '50.7542951193234303851200364177', '51.160705565040451205452244145003', '51.81005304254101807988992462650', '52.78101689675033860182818830146', '53.58460629598030300617229651156', '54.12332763822235140159562331050', '54.83735159179928736024412467769', '55.441327951209455955148564568102', '55.95280128034125473195393840933', '56.76661232487838501057441698380', '57.38318639706581670773957762945', '57.7301344099750331706916448617', '58.82129828122325514332352186529', '59.35368240743463077912991460057', '59.91587291382696843470724014971', '60.90473872304136385510873704750', '61.406491186845715929495360388339', '61.823969304883983306998149522704', '62.77981538840222580124680476459', '63.02892891505553629383805124498', '63.7896789243541738013718097722', '64.2909293697523770904105047872', '65.56157256938931022805967960831', '66.09547168770876849826775910972', '66.68069204472901771296784456603', '66.90281613723167707197526074985', '67.592514629138160245033877985712', '68.59211487218936357134781555266', '69.07597202603150964125657133760', '69.63603248167284453605358594761', '70.25340534560743510632418523453', '71.26976238371580898036172871566', '71.54566894070100340003967487050', '72.44390523723815045154479917489', '73.14452809713488432910225704396', '73.54662963268128719070452753771', '74.2283631704417182308029312678', '74.56751957650846161299458860370', '75.39653086108247980180012117060', '76.23018649028104118352839067320', '76.96880082227748354302497250745', '77.43659311681965731476914648337', '78.20594778044570944872843304370', '78.80134041939648113924908654345', '79.29245897021211259047638930154', '79.71328176979570949655969417191', '80.52351915780886234790130236630', '81.24923038282436553608798738632', '82.07152440898064053269941643672', '82.44936948491747764745664955216', '83.20173388140252545880460667046', '83.722715314037179651431481317231', '84.631673262562845103795296165141', '85.0239920330059202802865151521', '85.69625527829107448484757870943', '86.196658375564417141518819193540', '86.686029872903193833235254399583', '87.39017614201958319566198411340', '88.62540390369975157967837516152', '88.95078666022588664651156688966', '89.49198259964384173163423202553', '89.99097919663022024500056829232', '90.78107469729125451969206528311', '91.08367542896229493068857859063', '91.93004691614907493860164534938', '92.6119990017409242947894547187', '93.28566250066635328939411924192', '93.67613258007313429493058876121', '94.697914808019491040615252055791', '95.30941173038798923054807862859', '95.57536361366612572155556743922', '96.23517441995086468039068880823', '97.18500526218459611846777571544', '97.38884112283221392548823776563', '98.207417175947548364592267308653', '98.548477396734117248495061368437', '99.573818687985517238851292104158', '100.17346222870454597039276024927', '100.978257062234016063361379696192', '101.40613720519045738886242334608', '101.78473362332823048350887008563', '102.59725870149002972478448339852', '102.9074270688118420855032916241', '103.641827393169835448252269427270', '104.54405500526905199918030854169', '105.15141657194681655771498564702', '105.889734723530502888029580662073', '106.16844652312946733198075749452', '106.65442752057143018008693198199', '107.8257312024800696662058290083', '108.28361959428418151643221585376', '108.55878488845587436484353613904', '109.068263807895060595690859615138', '109.92774240736118702492600254539', '110.573060772855511943478306965360', '111.4267842719357857073773138739', '111.77131220790839405499456263387', '112.72954263316479184521920176404', '113.107524587821202010137672546576', '113.44523576821431945964528811743', '114.18653926228194432768058267381', '114.8085337016973803785953187843', '115.43621102408619302036424860703', '116.00633277007383299849841160588', '117.08791157372722329332108679195', '117.305946382093779662761095336490', '118.07984183016284851531439986912', '118.49044139728670721239153048895', '119.06916898195940661578615382729', '119.784736185297175856063497744218', '120.37593674923756244629466489472', '121.19410458342201028386073266242', '121.346483948329682856440816562665', '122.01072779930861471091661806342', '123.11694390312444329128556479196', '123.51655842061003963703973741508', '124.200146185292891618723601795598', '124.847043976042760923950574427302', '125.09449632227184415179517390609', '125.5835551862240853338358179797', '126.4169204038183997853274902309', '127.00364231648758815153980823770', '127.84702003130558818373880803253', '128.49610381994399534290135419203', '128.87192737020199960249646052696', '129.55737540572097557991617410533', '130.15270846759413486556675692037', '130.64132450036410663423975670438', '131.41922151317227500667858433434', '131.84946579531447547096271274152', '132.40061073489167559915763728144', '133.06272980447149370028793481928', '133.87879989868644658537740032893', '134.39809069211065830789668230357', '135.099076812495678877508349958292', '135.566027128058182455286144669677', '136.16455302523006133805965857113', '136.93189509517473165569183819828', '137.319718654595082923902963405209', '137.71513907286384064687271603397', '138.2108513496691890549310207951', '139.54377372432774910309202613631', '140.04737243490723500598473205051', '140.2577116991053053221892868903', '141.101659307460835020254378812761', '141.54843017183661067674914051961', '142.00443242303781414754514449682', '142.89305399632029158526413202947', '143.2329994792985363362915909660', '144.03140151111610729577881332639', '144.59499570317494778640940334995', '145.0688800228592165329999348660', '145.731511466822816022030572121869', '146.68758476143842831279282098572', '147.099569752830716830410105938968', '147.68158745081074015006691433200', '147.94837359230436339835507206278', '148.74857879969831393805569290493', '149.16821957751280397459621129867', '149.90497853842173640772222846582', '150.72288038404544233903466071767', '151.08659683014347660121341751155', '152.02730933313954917029077130736', '152.4474587208706804997627019790', '153.09624855933027769070494175582', '153.3057150071755595954898402553', '153.97939938866974904889494886308', '154.883659594597921371080238170387', '155.246235779087154593177805156651', '155.751885634529750452986932499997', '156.946868997291214557544544534443', '156.991878158261282055168618603418', '157.67104494688732465861066657547', '158.29433537795231748806761657370', '159.123167784325925013219573872370', '159.60549609286162140137314602107', '160.12220169715037016705845663815', '160.33353112671245168313674257733', '161.14067242198718697728745569156', '161.78955069292889889171730373590', '162.65361027067043801572859566204', '163.49095035183555908539854488537', '163.77657397808684327711498665940', '163.93256749060320233720954178270', '164.86492227626496845385673042512', '165.310625693344658644279059838198', '166.131478882834399488212439668801', '166.43433361529566300486814683888', '167.2466419941763330119547881284', '167.68571599011819004755974037012', '168.665773171257336846032489931059', '168.95938840527901290354107057248', '169.54310489803886012705330653609', '170.3574199012928900620095801545', '170.67454488388002310098648768125', '171.327527625234174706820199404503', '171.90073649693075458747865143003', '172.37293508725962038362668189090', '172.956433502435514150035923435727', '173.823549896282526308552659961020', '174.348359334365980749022132569362', '175.08730097895004359232620056612', '175.57460436007534764744513436290', '176.09712097007986184398250393252', '176.6175296305394910424760030069', '177.06724341536208777986603275948', '177.46215149024027760580727291368', '178.72147387587476258138409470607', '179.001398021655768487084274044479', '179.71222676684694782602026556303', '179.99161250237481482002051801994', '180.854607802805254738655385010909', '181.47647501614411695604759403802', '181.90723159085447042908012913761', '182.62989424750415554209052715354', '182.97190904161973314360156223238', '183.74581042739500096909823265621', '183.963909439030111636021497865477', '184.8145946864257898535617826408', '185.58574759332221933427801331596', '186.34167451604390241472075258460', '186.82194298579757340819600619981', '186.99078956356980813801549258370', '187.78973464240254769414281332550', '188.29888135446280762470953891989', '189.06409422581322829065254194928', '189.29067950630155615560988699464', '190.00634260419180621895982201695', '190.84058116961887313747355854269', '191.60052720991137490548131867532', '191.91867879019296398052094856213', '192.366820810418368187308514582303', '193.05038614239094106845478979170', '193.62689245749543892761296923203', '194.203781769928397286507156580369', '194.956449801554019280141817953761', '195.20822089460653510726594904550', '195.79313018095795341843235701332', '196.50857445217680870392655481105', '197.240649208059376084169301459522', '197.99611412326608469312760521476', '198.31486291064599897309432653146', '199.00333513375801679550236248063', '199.47222270968237098169753065485', '199.89006838429185176108527918306'], 'prelabel': '1-1544-1544.1283-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 7.170305855403121, 'root_angle': 0.483683979500552, 'root_number': '-0.994749775969495544570336069268+0.102337105727289475706000548030*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.483683979501', 'prec': 47}, 'spectral_label': 'r0-0', 'st_group': 'mu(64)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.669257961557147549871713761880+0.250211949772236931231366564567*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.19785251608', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '2.70855373851', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.5875523086', 'prec': 40}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 7.170305855403121, 'bad_primes': [2, 193], 'central_character': '1544.1283', 'conductor': 1544, 'conductor_radical': 386, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/1544/1283'], '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': '1-1544-1544.1283-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': '1-1544-1544.1283-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 7.170305855403121, 'root_angle': 0.483683979500552, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.19785251608', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_1544.1283', 'Lhash_array': ['dirichlet_L_1544.1283'], 'factors': ['1-1544-1544.1283-r0-0-0'], 'label': '1-1544-1544.1283-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/1544/1283'}
Lfunction data - 1-1544-1544.1283-r0-0-0