-
lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_1225.666', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [-0.5508969814521025, 0.8345732537213026], 'a3': [0.4738686624729987, -0.880595531856738], 'a4': [-0.3930250316539236, -0.9195277725514507], 'a5': [1.0, -2.8163065144692913e-30], 'a6': [0.4738686624729987, 0.880595531856738], 'a7': [1.0, -2.8163065144692913e-30], 'a8': [0.9839295885986297, 0.17855689479863665], 'a9': [-0.5508969814521025, -0.8345732537213026], 'algebraic': True, 'analytic_conductor': 5.6888760834642635, 'analytic_normalization': 0, 'bad_lfactors': [[5, [1]], [7, [1]]], 'bad_primes': [5, 7], 'central_character': '1225.666', 'coeff_info': ['x^35 - 1', '0.983929588598630 + 0.178556894798637*I', '\\\\zeta_{35}'], 'conductor': 1225, 'conductor_radical': 35, 'conjugate': 'dirichlet_L_1225.561', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^12', 'a^29', 'a^24', 0, 'a^6', 0, 'a^1', 'a^23', 0, 'a^12', 'a^18', 'a^33', 0, 0, 'a^13', 'a^11', 'a^0', 'a^21', 0, 0, 'a^24', 'a^17', 'a^30', 0, 'a^10', 'a^17', 0, 'a^4', 0, 'a^21', 'a^25', 'a^6', 'a^23', 0, 'a^12', 'a^18', 'a^33', 'a^27', 0, 'a^8', 0, 'a^20', 'a^1', 0, 'a^29', 'a^19', 'a^7', 0, 0, 'a^5', 'a^22', 'a^24', 'a^29', 0, 0, 'a^15', 'a^16', 'a^13', 0, 'a^32', 'a^33', 0, 'a^2', 0, 'a^18', 'a^21', 'a^0', 'a^11', 0, 'a^24', 'a^24', 'a^2', 'a^30', 0, 'a^10', 0, 'a^4', 'a^14', 0, 'a^11', 'a^20', 'a^16', 0, 0, 'a^32', 'a^33', 'a^13', 'a^2', 0, 0, 'a^6', 'a^15', 'a^31', 0, 'a^19', 'a^14', 0, 'a^0', 0], 'euler_factors': [[1, 'a^12'], [1, 'a^29'], [0], [0], [1, 'a^12'], [1, 'a^33'], [1, 'a^11'], [1, 'a^21'], [1, 'a^17'], [1, 'a^4'], [1, 'a^21'], [1, 'a^18'], [1, 'a^8'], [1, 'a^20'], [1, 'a^19'], [1, 'a^24'], [1, 'a^13'], [1, 'a^32'], [1, 'a^21'], [1, 'a^24'], [1, 'a^2'], [1, 'a^14'], [1, 'a^16'], [1, 'a^2'], [1, 'a^14'], [1, 'a^15']], 'gamma_factors': [[0], []], 'index': 0, 'label': '1-35e2-1225.666-r0-0-0', 'leading_term': '0.000144606699970867106603968980029+0.0102513990397660077971567884705*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/1225/666', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'plot_values': [0.010252418903370525, -0.7548702618514089, -1.526637141997644, -1.7310745916946684, -0.9685167678215894, 0.293603395241389, 0.8566219995567445, -0.2529494824224582, -2.715305883184163, -4.779895329462637, -4.489705090259539, -1.4396152198123793, 2.524031484521859, 4.567399050951827, 3.2220192695045893, -0.27656329305483496, -3.0385966041474948, -3.094377512255432, -1.0476498992033454, 0.8003316567149491, 0.8922977562531029, -0.16997945281931315, -0.6627027154227573, 0.10655595104295727, 1.095400760970446, 1.0407182604444685, 0.20307542662338338, 0.026550750364908598, 1.0612770488796113, 1.9073174696736588, 0.8647162451778317, -1.561232266073418, -2.690915878684531, -0.7725603623114438, 2.400611283897229, 2.941711765897475, -0.7356920201766584, -5.656356498410949, -7.193153909239767, -4.091169717844944, 0.24023791142447154, 1.7296549632308402, 0.13872545257126467, -1.2821913301816956, -0.22971682285925854, 1.9013079987574522, 2.286167968607402, 0.6360779188804692, -0.541915195735234, 0.401232828591553, 1.8627574568066556, 1.2347543959304461, -1.3301767412511538, -2.9336686743482074, -1.7724455019258665, 0.5236295063994619, 1.2708373533408932, 0.366338690879169, 0.00305231734458503, 1.0671553541951955, 1.7263896627360298, 0.4289616764176157, -1.2901656374660877, -0.8760041689844701, 0.9714175453590057, 0.5165611022511197, -3.6081931746330485, -7.209146037146551, -4.965468754984681, 2.5090274295337767, 8.461694502754577, 7.602205174608616, 2.0140729861233977, -2.0176677505299665, -1.6836229479615485, 0.1819398196181721, 0.24774476676417992, -0.8609135225954901, -0.6207926785594486, 0.9866787136700399, 1.659749948533845, 0.6733698498659585, -0.1171972007651671, 0.31648536048760667, 0.24440322497641595, -1.753114033456714, -3.655193446555838, -2.457643219664005, 1.0122274244113934, 2.6641361859274375, 0.9940914019876227, -0.510285204171154, 1.4293771582579256, 4.592765782022721, 4.185915194113385, 0.061513087410876535, -2.6246471878110413, -0.6837197613222347, 2.581473655105004, 2.3811555957961326, -0.5349075830346547, -1.3393884373794984, 1.3678238198594057, 3.544769082110877, 2.0594452940303185, -0.5736403511657028, -0.25823737195991325, 2.3933053931434802, 3.2604602216708756, 1.1377976256349724, -0.7778030908165628, -0.1785192161841465, 1.094117274693314, 0.6639978425280717, -0.4427508075722941, -0.04090633764364428, 1.142026328090597, 0.9112041933530477, -0.03299346274753284, 1.003304741588181, 3.453784637148689, 3.367233656254407, 0.13373225291428856, -0.7095719015086026, 5.083488607124288, 12.921773596569242, 14.03002316550193, 6.951482138805435, -0.46679064463555586, -1.5366671406165608, 1.4369716394089411, 2.319993537557209, 0.168795688765052, -1.193594056642308, -0.35043165538947935, 0.09611547183121523, -1.0885000796196023, -1.5974782246866717, -0.150450765759371, 0.8674863118564797, -0.3165455847782894, -1.349263784450986, 0.3010196583945918, 2.513305467942156, 1.5823082606628618, -1.5108001443052645, -2.391063825509267, -0.366326026666881, 0.6048483856106714, -1.2033476981254327, -2.374948546315903, -0.6211944732123209, 0.6656415329466447, -1.8973698184924117, -5.019620893385198, -3.154648496460957, 2.2890219005082275, 4.279893336050608, 0.7824487395393647, -2.140655564135997, 0.13382900899288355, 3.7871332010179524, 2.96190124331036, -1.1721884569768473, -2.91367511066274, -0.9838191459364537, 0.6750840190963463, 0.10548767817305929, -0.2984490808269962, 0.8609921277599308, 1.4745333896359767, 0.38865388630619435, -0.1854777659671318, 0.9841081361732279, 1.532071824202282, 0.0621241130343307, -0.6994721921410965, 0.8863928418175251, 0.8164658080794238, -4.599156968915216, -10.94114317782103, -10.435667587023904, -3.669170649683094, 0.4857526907927407, -2.275663760350875, -5.880212671507503, -3.9267939575615287, 0.820807751814627, 1.9591095643075613, -0.4264339502378679, -1.421285228416833, -0.04559950927897711, 0.3988151317228773, -0.5358807477419114, 0.2925822074605091, 2.9534426957007303, 3.3762100880558035, 0.40298475290279706, -1.8363761315745313, -0.8568842795962338, 0.20216145307735542, -1.4341014865167836, -3.163582001753695, -1.9252752119713108, 0.20199320248137456, -0.014427807624456022, -1.068128232907925, -0.10225216866131027, 0.989430895897607, -0.9535308578513643, -3.19324111294031, -0.7374165019938201, 3.859736423673595, 2.547543322415131, -5.300542508660312, -10.262169315086352, -6.35576102400243, 0.34366690975655056, 1.484629887700534, -1.5990100519474382, -2.147445919104826, 0.6451395119528976, 2.0093899209796775, 0.6109829125258821, -0.30622407947974467, 0.273056845227966, 0.03726784251563654, -1.087194370043401, -0.5565925468378653, 1.298490758912079, 1.3926881238561681, -0.0012514257495053968, 0.5761292943642926, 2.654657307227358, 1.6474549614548535, -2.4562217565279725, -3.4234677977794643, 1.0225211984844051, 4.517658524890379, 2.2493970971443096, -0.9575728568148534, 0.97201278237963, 4.787385416440128, 3.5441422205166457, -1.4923301199723789, -3.30694009320253, -0.9759163144338932, -0.031819585020184456, -1.9143409986513618, -2.094952254641667, 0.595353474700103, 1.4320047538215557, -1.3486419778105476, -3.0627856170631236, -0.9395696427290403, 1.1613653581496646, -0.008099856679160253, -1.6180302328260179, -0.6178769019844187, 0.8412297968707352, 0.23607797916759438, -0.5115823385630615, 0.40617753032339565, 0.5766670193665879, -1.419665754129932, -2.099272765744149, 0.34373508046097956, 1.335548687472833, -1.7198087205355312, -2.281453995401279, 5.632333189381393, 15.307750346133469, 15.01428087125388, 5.234850442894562, -2.276060709985036, -1.7984202341690616, 0.6316617443503619, -0.33991059020883324, -1.8134890708383242, -0.5404046312554046, 0.8594874284966183, -0.11040921299552892, -1.0631783732260485, -0.14598549805688316, 0.27799015063029436, -0.8921328867460787, -0.6892975680418193, 1.6281054937996957, 1.9985549139563685, -0.8812000946943341, -2.1453380546965732, 0.7835868560858746, 3.2177415386862718, 1.5940793908156048, -0.2255354339339796, 1.1982025838587778, 1.8860719413005702, -1.7529715559837904, -4.89641858175588, -2.2222610192707495, 2.1493367302296025, 1.6307763851942316, -1.1323421536833562, 0.5550391423138452, 4.725658879965918, 3.989395760099499, -1.115263396557698, -2.971061578335149, -0.006674955375894946, 1.643886058516637, -0.32575680801574836, -1.3282850868422014, 0.6077184619826772, 1.6278762274787895, 0.018504587000939265, -1.016351562865459, -0.20210957925374623, -0.12101343162897571, -1.0792764044134033, -0.5466647388286126, 0.6240389219587554, -0.7733056031440204, -2.9033629756218753, -1.1913986810233026, 1.9992134846818068, 0.05507312248902456, -4.865830601923922, -2.9973081313476078, 6.433636403971335, 11.756536734423825, 6.443632954580018, -1.2967950476098637, -2.369540105166698, 0.4745367624421667, 0.8366337705489049, -0.0809942470453938, 1.422395108307223, 3.1386945615476294, 1.7779971821364964, -0.24684724828549254, -0.014171686042349604, 0.030613683632832518, -2.193784777117282, -3.1575415673699143, -0.47943342288786295, 1.5613897955931966, -0.4703868545928356, -2.7279259331154035, -1.3448792001661236, 0.6661458956144318, 0.0204647235740978, -0.4400283930037515, 1.6361165582298902, 2.5474100936705892, 0.2505730236490262, -0.3090580260528934, 3.2698651174795583, 4.519569431010329, -0.5149685576924848, -4.363103856321924, -0.17195928324110926, 5.68540277847475, 3.8834540267358197, -2.2915753670113466, -3.291972943085247, 0.7557278369937778, 2.342493988539213, 0.24312087663490972, -0.5903544198801519, 0.5418416156825249, 0.24555012868646953, -1.0464466217424293, -0.4402488685888322, 0.8929420877931882, 0.4132193181851821, -0.12609255810189607, 1.2439247208700774, 1.7421461606693451, -0.21404861572384037, -0.19252293799623488, 3.870923567697101, 5.7211518283405365, 1.3940504205040412, -2.2148219011850916, 1.1939874827893093, 5.5288347818613905, 2.737760520892741, -2.7958900587944537, -2.1840330887013635, 2.5238300690604016, 3.25202796787635, 0.4350353238587237, 0.24990591862132006, 2.2066672395286306, 1.4425296654262674, -0.8332071178893712, -0.3586607830962802, 0.8237521862638187, -1.5019261898822398, -4.478871623315308, -3.006399039610906, 0.5720824604198241, 0.9624656862206685, -0.6204477910200459, -0.2982807884503279, 0.3806851421547569, -1.3670518836066083, -2.868117662337676, -1.3318396383827165, 0.2783868227141585, -0.3303706850011171, -0.021599193882906997, 1.5175370776467203, -1.761738159014898, -10.099556920346078, -13.023104960916854, -5.576146862400947, 1.6506450507930397, -1.0597651882034798, -7.050620025852634, -5.579241223541242, 0.6485263345299216, 2.5002786418342873, 0.18236999122212555, -0.22077199910841636, 1.234748359270334, 0.8772778467126696, -0.1983107579142572, 0.4357244958041141, 0.7073858443503638, -0.9740697551917343, -1.5205089274572468, 0.24919720325035458, 0.526121668493342, -1.3529055716508451, -0.7130678964702792, 2.5911656359808286, 2.474490741508427, -1.5948119226128643, -2.579830969361546, 0.8907217735639545, 1.719635679907514, -1.8049754267121638, -2.7026094996934837, 0.5465861498108766, 0.5684954085891302, -4.194681134294329, -5.604852375760947, -0.9573911432342552, 2.098480234985549, -0.009052225740761284, -1.3413806093190765, 0.5475608982408385, -0.005496916247999698, -4.379244407280757, -5.907701267317931, -2.2906686654135684, 0.4999655041865769, -0.4110846036046433, -1.0489612858403061, 0.07711490524272263, -0.125107450388869, -1.4746557212069409, -0.8165324299315168, 0.6464391404489146, -0.17355418356862307, -1.2344026108844093, 0.057425253429890084, 0.40757943923580997, -1.7943970025869962, -0.06320663012608702, 8.231617241085642, 12.7081007901858, 5.374442578324742, -4.360878668564935, -3.921164633602057, 2.595340821204413, 3.400102982571799, -1.0735501809629366, -2.2706435802516833, 0.2067259998931158, 0.7889023505639535, -0.14037706273536013, 0.950852620193129, 2.1968574059345714, 0.8381859578515726, -0.4362912894186015, 0.3000976060701454, -0.41440925985392957, -3.457016445829745, -3.8078849080653807, -0.4328506171336919, 0.8637072904119308, -1.4427796568888887, -1.8824378158964186, 0.6746349196542201, 1.0884834648671453, -0.8229375590340365, 0.057190898884295835, 2.664828811280688, 1.4461616198741138, -1.216800188124025, 1.313448663954726, 5.717244784202055, 3.6169429763614316, -1.9493817770580304, -1.2607934609049951, 3.841725776922327, 3.276579463603592, -2.597643405395932, -4.335736380769932, -0.7553684465860702, 0.9117929387051533, -0.5257961669917175, -0.11459795666668796, 1.949484433288187, 1.630010502890026, -0.06501256466719957, -0.00967055973106182, 0.2564195789884916, -0.979216424415165, -1.0978543381074877, 0.43246023612263, -0.1912075809630086, -2.3261428100996895, -0.6832196071544743, 3.0405072520443506, 1.554541863241361, -2.9396768206425876, -0.6473793185836334, 6.982605473663472, 7.667106586349371, -0.2728718241929395, -4.927953873967999, -1.6359878164604023, 1.1883256788843315, -0.6782684381811928, -1.5819900595009306, 0.4795312306340517, 0.7415502381550009, -0.946212586022728, -0.05412796025527958, 2.134498940780952, 1.0076487027383951, -1.3365802518773828, -0.5461048285203737, 0.47883266948756076, -2.2371053622069774, -4.7147752887216186, -2.521922994363427, 0.5669586557711036, 0.3582209304032589, -0.4202486899478468, 0.2611881427809559, -0.6900139985222937, -2.94682475102566, -1.7227294047203567, 1.4266710959430249, 0.2222241573277157, -2.8534687779598262, -0.2786610359438578, 3.877638669737551, -0.95837680153955, -11.065082897073863, -12.121047948870192, -3.080496388473641, 3.0136257928188996, 1.2978878165826326, -0.5736599715291917, 0.7446728501404312, 0.7016384383796208, -1.1648492613238275, -0.8239485018846071, 0.871069011905478, 0.5549074737330382, -0.1786648162328566, 0.7951246029093331, 0.9152385399521722, -0.5724048699383841, 0.09992900046424441, 2.2899822584349785, 0.5344053819332755, -3.7416587851345784, -3.400170664768697, 0.1517674441280842, -1.0012107108987873, -5.2731533118429, -4.305215711917638, -0.079828872252, -1.482720118385849, -6.384382019742553, -5.3792471593219, 0.1017527242175249, 1.2332696336662055, -1.3462337374684323, -1.0429314847313522, 0.3993492051514489, -2.034324969834218, -4.568821667845449, -2.016185510346545, 1.2062373901481949, -0.15678427200441578, -2.1119405137055227, -0.4737615293800885, 0.8326557731791229, -1.1085222364960878, -2.221137244254955, -0.5670065750469913, 0.16627386931658983, -0.6077683184319811, 0.1251824779583103, 0.9032606997310032, -1.0391527065687463, -2.1130814180723143, 0.43185043293704695, 1.0786950129813357, -2.1828138506330097, 0.03387462004131323, 11.295510351859521, 18.129183783332326, 10.681258312001487, -0.25378536810445607, -1.6056206840748004, 2.024770026431015, 1.071629147209805, -1.8248899148707585, -0.8271151421855931, 1.1144714655787307, 0.3251710368729245, -0.3195914557988009, 0.6236955331212883, 0.13362570953192815, -1.118629511406154, 0.34404963189563903, 2.2421385754279064, 0.701414678870862, -0.9822838985848228, 0.8183480831751818, 1.6302224094118858, -1.8132924485885644, -3.7110073969871467], 'positive_zeros': ['0.0044024926666677412020801970', '1.48654412299517116484295124943', '2.14531356131146591070678408774', '3.54759184982026642735008929682', '4.66383989034938545155587706009', '5.774178745549643645331255086176', '6.51369662973582062023093179924', '7.15810748646298567759839150191', '8.23251962085641366065164128577', '8.41982526425338393397549857378', '9.4918998433838274962666540631', '10.38605163428188843197749462368', '11.20388482478301279021527414538', '12.47836991733242577012711564089', '13.145424992342154743008715918', '13.78337456609537591075337418042', '14.80215275087306988062946760414', '15.23338392335362039013287492495', '16.09845591269583330032328040946', '17.107406772164873106243845000373', '17.9616487957992460742100497354', '18.12293556025383265570786593034', '19.12832872090166798741154076750', '19.83123061609637069889779736989', '20.368011000087937196315248379295', '21.46630575864445860659276935780', '22.619094838225441543842046989074', '23.39625716270534493088840799549', '23.82149784331366778970524499412', '24.50480432106770242368693721170', '25.52115522633426580269524851201', '25.77779150788701926604164541634', '26.30985805186697977681804359398', '27.4089390129623531339667048899', '28.266929036271842114467876007590', '28.589593809459124324739224248365', '29.6918887539609141786372532678', '30.37062453656441102983305826563', '31.1907341779459366985302852457', '31.74478072956149782189286169852', '32.72383638000930603975904189230', '33.16130035961647566546073720287', '34.206073179617274181381303371487', '34.72414358494561268763328585670', '35.4746498144945962128726788272', '35.94805246534749411205675990112', '36.848255953043847535301588828', '36.97250797222979110775038205899', '38.13817981631940769548140080533', '38.50595138826410577929565869433', '39.97078707211902014266861675486', '40.48123972779535615633988146924', '41.272225159790698603862481362596', '41.98390610644248966667185059999', '42.23219903574578348618469431953', '43.151572933910830873193182706121', '43.69312593633668637906742101610', '44.33892933312720409266853573741', '45.158953151104980433347741267041', '45.99209030241265267840734885054', '46.39220049054981154531316667922', '47.27267643772019034252163466055', '47.6354571721177799682085054886', '48.61831177842678059110442180258', '49.430404151643946833952621836915', '49.98990524397490374259850870996', '50.84807062546929496042211012061', '51.696968530346183414650323867972', '52.22048015121329478547975341118', '52.61258512918187541775288979103', '53.54247891197261290572306242818', '53.831734412688523478110918447271', '54.69865298904268405091763855081', '55.16738955449472898329250926070', '55.6993421680062939089770450774', '57.0947249013207192726835910622', '57.31880187759505469953079380230', '58.374549204082806987392479356782', '59.010197206932253539240563423008', '59.697522053814253259977005859135', '60.13397658439866526799420563949', '60.58075630065736767942451209541', '61.5996692208000621767317725908', '62.357681803435169206280510385416', '62.586808318039482549307765902927', '63.70416011503855942054713781493', '64.05894395812188277994155320575', '64.70569273096294793595908934423', '65.20897189869826851862182092218', '65.98398463762971084301778742245', '66.6791958584218880238263998748', '67.79061834770235083850516219980', '68.282938698195600372484088159757', '68.99546254701444314356727915352', '69.816753418776232319661732828692', '70.188785243339512637008119049786', '70.63595915446314913685011868271', '71.34385444284320335161355491353', '72.18705762585267099920536943879', '72.3799540040622380662226128062', '73.25636307060692924674390838709', '74.00377190273646877698000642179', '74.86515980033985632019482255130', '75.23283498530230046272785002220', '76.154750884201763351222351432378', '77.0444357689244326550770835031', '77.17626998400890338869192154397', '78.059420533787920377372284394925', '78.62258677278765796839177099592', '79.47495034827474276659432355140', '79.998850840854730555784876722343', '80.72633173852909390967776782580', '81.309348653671214498574894478558', '81.77004428488867770202444228457', '82.30062056498695116978645362039', '83.0871428202534093464830143986', '83.601801914793132717150257291205', '84.190471994666610953426067096799', '85.49005962192507409269561600135', '86.13078149711636948996068743465', '86.51123921669062540484514276182', '87.27032889427182733903529379217', '87.79085451621090748305252571544', '88.476499726455259746777043470302', '88.8453527180897811714095068291', '89.47984508764308038439534744370', '90.2275896846669237718018891368', '90.87301887931123114144958182058', '91.781001506344583591217787345528', '91.99258401271519129219138670704', '92.69352906037991414033581076088', '93.574774982657434094439504667369', '94.22103318988899294596243336874', '94.64330406090805700064086887412', '95.55551480505857592649329200655', '96.2506120301629252203556726084', '96.8335997025689283454105277518', '97.41905061823153546313654119123', '98.12796033343268514755343292779', '98.83753480057852798016644721429', '99.00561480838373210869191824854', '99.80015435684622433628938897151', '100.20989344139918456045896901754', '101.03556785560648874874954911261', '101.566013265643797903572701631989', '102.300161641771921979911514886751', '103.368299432074425630119124725918', '104.002326911351730775607070589167', '104.60495655794180173351960994374', '104.750019941364913297824545519396', '105.87461247476243959014100395032', '106.25518293850155018680760773302', '106.56997756716109498873156490384', '107.54497980664737056772077588830', '108.07842794611757258391632340428', '108.91851258113274577443831060214', '109.379695529216723224698484202207', '109.782746312375066643361326738205', '110.657650576274906437774176364473', '110.97958666396662973023180967463', '111.84965572485910415731499331669', '112.50761364000025582927200015333', '113.31276003968600922339992179978', '114.00555297225561050303624280215', '114.72367028038827739162995944084', '115.167546247948465587289717338720', '115.67881257222937130445122050499', '116.3348051251649582551468093002', '117.001556762316551333753711065992', '117.24300343901633399301934081326', '118.09230272595904634433691726412', '118.46010211836199029314683940124', '119.45425169610374499602858784412', '119.932377791261487888175183998849', '120.762087406789761708174407177048', '121.39231685724247501492604121947', '122.26344239528808611958031964204', '122.447452990537012913665139097865', '123.30088745882188940527659711700', '123.8119064001102787338082508510', '124.23267711151073916482203261907', '125.24970358564005959029570314556', '125.79942435479190330768093819772', '126.32631124060995316671469869839', '126.67695762445385071234272723837', '127.707927762191414171803577302724', '128.01535569811806878827566302258', '128.44166912898004123358508813875', '128.96894740381415271165867306235', '130.20051234155474617013556871265', '130.57185942801569472587151151693', '131.524911728777921793569590154869', '132.2164708144719076053470801509', '132.55058435469818804515455322891', '133.33758463429766845713091636014', '133.61742417944240456146114421097', '134.21664248472828304354890543266', '134.95770475572615349817265228920', '135.40843491224701157622079824721', '136.0096508628471503563586637549', '136.75649277659575430940279109384', '137.4247827381944349701878165757', '137.97941902337535010900391145819', '138.69690654767727567383528145505', '139.11086702099821075576729048597', '140.05857672818767498391815787850', '140.62403914983041804486695724448', '141.166232354894285237040662769604', '141.56195657977797243934872404412', '142.70448902188206628095130549315', '143.04413598550491366880102011283', '143.72616438151807722689854654402', '144.03066339282357726673522611653', '144.82927398393499793596965405233', '145.279900217858605483548100801975', '145.92694642276668597643028093655', '146.32095435036699590301666460273', '146.878403004505151008216128575043', '147.96178925181006807166997550279', '148.61889798688061258523652003093', '149.29843994071049969840746121368', '149.972080626091217177012992663614', '150.539162136175858108604290185438', '150.74430116784351712377614777260', '151.70361641068936098594704293171', '152.08678140782243940355159045635', '152.43785210087978325789443462521', '153.48016323171350337250879828871', '153.89067164656483714149785471621', '154.60592801927243327430528603675', '155.16901147771817622730728680058', '155.61837929410529691749310359393', '156.38444749768317739968455828279', '156.7849203089405484976544057772', '157.68607623730157468319207633990', '158.202733500062806481765906021237', '158.92631980363743784439760753292', '159.75750872095241469304609630372', '160.20448323528086674179714642187', '160.64294157643847078864309174223', '161.5437405475889471168592255141', '161.879036502062167198070727239707', '162.27700179454110785856557339219', '163.02706340724178207749696248414', '163.40896795875109524239276591973', '164.11476889457071608852339420370', '164.784924761113431542148856340179', '165.34144420599686590084620972872', '166.23994404714400180164255571457', '166.99353569294661614756555976217', '167.419044524397492610241003453878', '168.05530866345018585008225294263', '168.566981602654288863657632780611', '169.06939584694595913907755848198', '169.79856648164485825470100690701', '170.401824599249712241493391371879', '170.723357329257178885324029715875', '171.78968727708998014816098974138', '172.27465409648231057354106715640', '172.69812126594318649546187482294', '173.01072539689999814415756703198', '173.900479933568569438748799977120', '174.39413372813739302916241954599', '175.01624588411726799661146785100', '175.5930504363583964984785682873', '176.67171721205613860330554054328', '177.32854169133240113348855955201', '177.67141994447339227153483905203', '178.24020182326016148921577463109', '178.88488530418405182289475621263', '179.53206622543135186758639449300', '179.788697352319689714519952976933', '180.49834955160794865032283680945', '180.92340071368687731841289802377', '181.60087716632732126468488889210', '182.479643744742840735103229082356', '182.72127491176105542792288717296', '183.760940865383660756110762452135', '183.93370212328885854454251519570', '184.99281825338984294277213084501', '185.46051242335100443512888469255', '186.098330151945891078532677373174', '186.360423420699399799668740546025', '187.341743100785339391489451244058', '187.79537892178742491422053754151', '188.49844982584213364818245391869', '188.92191299374016210429417808541', '189.80464506870124017788183141847', '190.07472302888124514134438695982', '190.5982639242543962071871120070', '191.12087758180307605559423618241', '191.82979383336667106351350594065', '192.302421393594242549696088411646', '192.811132065696785850687545715548', '194.05147424519719238738834705411', '194.5031360029791690847645690148', '195.09603262336225099716774629484', '195.72604615095150777323961688142', '196.32451319738860752948461464166', '196.68393936901734904341272462340', '197.21396275219445608493535345229', '197.77030023810869993187472187972', '198.521200106810564994885546319010', '198.96150593185865532561152143439', '199.54993192295151548603213554181'], 'prelabel': '1-35e2-1225.666-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.6888760834642635, 'root_angle': 0.9910204081632653, 'root_number': '-0.999602118138722286549434446748+0.0282064782023543854460252102850*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.495510204082', 'prec': 50}, 'spectral_label': 'r0-0', 'st_group': 'mu(35)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.679255084440183162738751373829+0.0341136320449919765903309172336*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.00440249266667', 'prec': 54}, 'z2': {'__RealLiteral__': 0, 'data': '1.486544123', 'prec': 37}, 'z3': {'__RealLiteral__': 0, 'data': '2.14531356131', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 5.6888760834642635, 'bad_primes': [5, 7], 'central_character': '1225.666', 'conductor': 1225, 'conductor_radical': 35, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/1225/666'], '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': '1-35e2-1225.666-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': '1-35e2-1225.666-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.6888760834642635, 'root_angle': 0.49551020408163265, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.00440249266667', 'prec': 54}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_1225.666', 'Lhash_array': ['dirichlet_L_1225.666'], 'label': '1-35e2-1225.666-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/1225/666'}
Lfunction data - 1-35e2-1225.666-r0-0-0