-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': 'dirichlet_L_2001.845', 'a10': [-0.8185014665785935, -0.5745044379364633], 'a2': [0.2621016829391022, 0.96504026226914], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [-0.8626054156009807, 0.5058773536894683], 'a5': [-0.768950525339362, 0.6393082899355514], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [0.8185014665785935, -0.5745044379364633], 'a8': [-0.7142823452219036, -0.6998576507435618], 'a9': [1.0, -2.8163065144692913e-30], 'algebraic': True, 'analytic_conductor': 9.292604933071013, 'analytic_normalization': 0, 'bad_lfactors': [[3, [1]], [23, [1]], [29, [1]]], 'bad_primes': [3, 23, 29], 'central_character': '2001.845', 'coeff_info': ['x^154 - 1', '0.999167799344583 + 0.0407885860615856*I', '\\\\zeta_{154}'], 'conductor': 2001, 'conductor_radical': 2001, 'conjugate': 'dirichlet_L_2001.341', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^32', 0, 'a^64', 'a^60', 0, 'a^139', 'a^96', 0, 'a^92', 'a^23', 0, 'a^114', 'a^17', 0, 'a^128', 'a^35', 0, 'a^64', 'a^124', 0, 'a^55', 0, 0, 'a^120', 'a^146', 0, 'a^49', 0, 0, 'a^151', 'a^6', 0, 'a^67', 'a^45', 0, 'a^138', 'a^96', 0, 'a^2', 'a^126', 0, 'a^80', 'a^87', 0, 0, 'a^44', 0, 'a^124', 'a^152', 0, 'a^24', 'a^18', 0, 'a^83', 'a^81', 0, 0, 'a^147', 0, 'a^118', 'a^29', 0, 'a^38', 'a^20', 0, 'a^131', 'a^99', 0, 'a^77', 'a^65', 0, 'a^31', 'a^16', 0, 'a^128', 'a^8', 0, 'a^26', 'a^34', 0, 'a^4', 'a^50', 0, 'a^95', 'a^112', 0, 'a^119', 'a^25', 0, 'a^99', 0, 0, 'a^76', 'a^124', 0, 'a^148', 'a^2', 0, 'a^30'], 'euler_factors': [[1, 'a^32'], [0], [1, 'a^60'], [1, 'a^139'], [1, 'a^23'], [1, 'a^114'], [1, 'a^35'], [1, 'a^64'], [0], [0], [1, 'a^151'], [1, 'a^138'], [1, 'a^126'], [1, 'a^80'], [1, 'a^44'], [1, 'a^18'], [1, 'a^147'], [1, 'a^118'], [1, 'a^131'], [1, 'a^65'], [1, 'a^31'], [1, 'a^26'], [1, 'a^50'], [1, 'a^25'], [1, 'a^148'], [1, 'a^94']], 'gamma_factors': [[0], []], 'index': 0, 'label': '1-2001-2001.845-r0-0-0', 'leading_term': '0.779827066122750026085112516735+1.29446006684665569652059626385*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/2001/845', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'plot_values': [1.5112104809450808, 1.9082254493789454, 1.5703955427886198, -0.3375974576251516, -3.325158447308753, -5.507182697420144, -4.985889561349431, -1.6139837079227883, 2.5137402682136503, 4.610111438948521, 3.590621479274706, 1.006309607654968, -0.5655914276917219, -0.12575567432489707, 0.9119803387680174, 0.5901652988473365, -1.1589029634637986, -2.4063013655064016, -1.6182599473209014, 0.3786753374930672, 1.3660152285164975, 0.47619737558209735, -0.8075029717434973, -0.7291369878832835, 0.36343143274314127, 0.6632685321793453, -0.21667745023435078, -0.2807148812319211, 2.0851837071825177, 5.182486854620714, 5.394236535092457, 1.811838046278538, -1.9490242578930395, -1.8013915391858697, 1.628808560248528, 3.5707553775623193, 1.1197693286105066, -3.01265347879368, -4.046450090962619, -1.3427351842819344, 0.9950948985743917, -0.20858160177249252, -3.098027480948054, -3.682585992751537, -1.3297019199273876, 0.8460549911380775, 0.7047277540674158, -0.30046148076785634, -0.10704798372663309, 0.5205552849926388, -0.4202863538369558, -2.3421871115010915, -2.499890778922377, -0.31034408303557126, 1.4084176128732988, 0.6698318338515233, -0.5278989927868015, 0.5294813294642863, 2.4897193037005363, 1.630103261825164, -1.9479553070491469, -3.4787306708822583, -0.37114268846992593, 3.272497150122101, 2.0201338453850743, -2.886543721876282, -4.881798784990064, -1.2686859615947481, 3.077671668504026, 2.7865574156388595, -0.7770648110527933, -2.4106564534547257, -0.8158301392004289, 0.6238980204022826, 0.013763869109453155, -0.5052590464217201, 0.6911199242081321, 1.5725557002220854, 0.18419183444953469, -1.5234190712688627, -0.7672564912728406, 1.212078062706973, 1.0688117378692663, -0.9674636960311739, -1.438346788481176, 0.37238395242468547, 1.205063446948115, -0.3009444707199691, -1.0406457253597434, 0.5361366641513975, 0.04713352351789514, -6.500288057898164, -14.637221483463875, -15.568362233272586, -7.996821705314138, -0.055552427443412544, 1.771631111376487, 0.10929792516684234, 0.32491476145372467, 1.90031016194304, 1.015920173841119, -1.7138888192254829, -2.0985164178665943, 0.27285176705112824, 1.3596817655369722, -0.3690292632527224, -1.6650449597182284, -0.4939617748191628, 0.6841219279938637, -0.14009362597108851, -0.8416840380262129, 0.5049607799904401, 1.6682079010346034, 0.4835073001943342, -0.5477318024833384, 1.3959637493251502, 3.4985454433837564, 1.4619889057455797, -2.369437549685607, -1.829746105632085, 2.563277455272288, 3.3513022504770222, -2.065793589760971, -6.725763089031925, -4.766621983137298, -0.21217742120270439, 0.1933723235729721, -2.4252232908516977, -2.3572785552563484, 0.47283737609354115, 1.113463899630915, -1.2315271931675142, -2.133619129248677, -0.07024246800740262, 1.3195001978356125, 0.1953992931779964, -0.6363877728614334, 0.3880847451568025, 0.815482682265906, -0.40713330729109465, -0.4949819820118288, 1.341628828557887, 1.3392103541157976, -1.949304426632995, -3.867230175555249, -1.2446747865705592, 1.6678592036100963, 0.37309472975864905, -1.9802268565588235, -0.759870279694181, 0.6998694885715586, -3.5728810284611328, -10.341135472657838, -10.37995472221661, -2.924438821053383, 2.7554608360547195, 1.4063937587091588, -1.7870006451085516, -1.4224118560682264, 0.22872168237352208, -0.32269671514691894, -1.1232246783944027, 0.25734581090327596, 1.3986451519178034, 0.0148692645061141, -1.1168249511461041, 0.5607991556752745, 2.1832358543939674, 0.8012005281859701, -0.951264172998289, 0.014674887222963479, 1.291977079176836, -0.02233263549857284, -1.2990839697240653, 0.23304146151775734, 1.1390537381934496, -1.7164069743352517, -3.271319980626853, 2.1647389286916368, 9.485649963803132, 9.139153912864149, 2.3236086223348664, -1.0115802010113073, 1.7840041543691585, 3.317094194119432, 0.008862208190491438, -2.5887641434271615, -0.7580636379622633, 1.4263099306570655, 0.6448929442732503, -0.2993311808920398, 0.4602913460065454, -0.21464915493830383, -3.418400647845111, -4.786001578338904, -2.162027584302044, 0.4703230304286681, 0.3476205125371426, 0.0599998434507527, 1.0594235071022342, 0.6346901238466737, -1.3481560792423026, -0.8163844976081757, 1.9442287948733874, 0.9680375328979542, -4.144986656542114, -5.36024714016359, 0.2565540304847393, 4.2229782472218105, 0.4359683447621837, -4.637043273372891, -3.4593399981153046, 0.28414359826423596, 0.0029046398935734697, -1.6842783215916908, 0.7591998395237481, 4.460467190780303, 3.4573739866481707, -0.28278125784620683, -0.9583586890362819, 0.7656707327621993, 0.5831441368987036, -0.8573040622207841, -0.5511251300826128, 0.1653175057281427, -0.7982976493489189, -0.8459340320444362, 1.978465468967461, 3.6754959719233655, 1.2336126359633732, -1.2773735901689174, -0.3787067903813259, 0.21367764954434282, -2.1841805361335207, -2.6218532984953535, 1.7171465931845717, 3.943228928875813, -0.9933368875989301, -5.998067277965737, -3.4750361854686083, 1.2735256903351533, -0.3340629251871241, -5.053946954020945, -4.4750804339373556, 0.025394307382131286, 1.245413909352323, -0.5879412090053006, -0.23740146103994672, 1.7327193514853754, 1.3132424740101964, -0.2688612130772797, 0.2694201502616143, 1.137993998544738, -0.14066512765296288, -0.7233992508231011, 1.6049611267088657, 2.857458324497494, 0.2731145051971263, -1.89107181483501, -0.5103221934144602, 0.6769484290108917, -0.48471948379356805, 0.06986086443545031, 2.9179682292170015, 1.8475638355752266, -3.355057836009861, -3.137434881300818, 5.352109404942963, 10.866871294710306, 5.652055944048113, -2.1822666187741304, -2.9478397818864166, 0.18912579778683403, 0.4217236829243085, -0.6623194998582316, 0.34255301198315363, 0.5909444750395989, -1.8887574441420547, -2.629022511482942, 0.5845639199088304, 2.7921610057401645, 1.154533917949974, -0.3324788479974802, 0.5476487017064711, 0.7677791438758856, -0.12534456020477242, 1.0394207022720123, 3.0363051614977765, 1.7878858599890886, -0.4436220539680844, 1.2941801196215568, 3.886161642608646, 1.5309871743528531, -1.549492755418119, 2.171840680307161, 8.103500438939562, 6.196584292572409, -0.917438494480738, -2.4587151009537984, 1.6436371180881255, 2.6106436204911603, -0.1484060505559046, 0.1137767363607318, 2.9488452960346794, 2.2047538811450487, -1.177660655484168, -1.497070495206698, 0.36531624090091447, -0.05025597351304362, -1.2514708909410959, 0.14315780328607644, 1.6841124033612105, 0.5119187373848245, -0.5055110177627585, 0.5958104908882875, 0.583245592093945, -0.9638986841099855, 0.39777938555210396, 3.7081913644693367, 2.29843524620926, -3.0119674900295776, -3.9498315350495616, -0.19236474969021114, 0.24421203928827795, -2.831383735876264, -1.7900363795333178, 1.9977639644643275, -0.8135375070098098, -8.874011802126162, -10.556346400602592, -3.9446953100238487, 0.9324036556408423, 0.1207087880352273, -0.4968560099704895, 1.0751597772536743, 0.8265305003994967, -0.9279759314666308, -0.5356056858331077, 0.4394192875515145, -1.0136264194672022, -2.007125124318691, 0.06646437876549366, 1.1529724881767531, -1.2592958182135783, -2.5133663618671083, -0.2768824242007813, 0.8796180349716184, -0.5210944549495761, -0.4651970389222049, -0.055471461345071124, -4.362135860533287, -9.420918594691349, -6.533830980501397, 0.4301493424673779, -0.25155836237211127, -7.105329746054058, -7.924458884924562, -1.669563312506272, 1.3226802742850563, -0.9659386158506134, -1.0753478291808778, 1.819092992964144, 1.9549768751404042, -0.06517096955407495, 0.477116382595842, 1.872153127661166, 0.4681090843831473, -0.8520143633639924, 0.7586456911287661, 1.4802908278287983, -0.8362014157705134, -1.7127369437300535, 0.4532770153005214, 1.1678017028744014, -0.347856468671773, -0.3291866213417379, 0.04741073855894688, -2.399721520595872, -3.15899687038568, 2.1682218202511083, 5.965770524760138, 0.4239782779572519, -6.562729453170849, -4.140279924746856, 2.3753619000701476, 2.2304731910250646, -1.678400673064579, -1.2604053534541209, 0.7577523201576799, -1.0067435642477356, -2.3237334781547547, 1.0384098982836616, 3.6187029426366357, 1.1831696600649513, -1.214421128825053, -0.014249785691548788, 0.9349163203514061, 0.046528061109133684, 0.5952058580249707, 1.9960264111617652, 0.9769418822358982, -0.34845247192128814, 0.7285463392321567, 0.22053058755160238, -4.0858849814914455, -5.884460477758089, -2.126334070436384, 0.39898851626779475, -1.2830465401473932, -1.026837023315824, 1.3733575848688648, -2.241942970536172, -10.200372678009497, -10.283072334457728, -1.6705995553265396, 2.9432963707285165, -0.19608121547081328, -2.0678185648129856, -0.1158735602795761, -0.8650377749005904, -4.174320346551022, -3.6879356347035137, -0.4055348166605946, 0.16171558086581364, -0.7951073223551308, 0.058220518496701144, 0.3886128048938639, -1.1044780610397558, -0.454222278445338, 2.3911312665181543, 2.2521938974769666, -0.22785650137871338, 0.3021940320127331, 2.196168740933447, 0.5240988762034811, -1.6397561198526942, -0.029342423567535022, 0.6903007790307045, -2.4640422353957474, -2.095719448107459, 4.185062525584437, 5.348341045200854, -2.9764307963065075, -8.147139566688622, -2.4851309958003003, 3.8064721642649575, 2.284290355167122, -0.9414987321047696, -0.33174452327145015, 0.2905555368751507, -0.655413785403688, 0.3069156766638044, 1.5178562695070792, -1.0869304831649707, -3.8341302472701537, -1.7588051195292609, 1.3398502426686907, 0.8612797089922513, -0.20831976171235694, 0.44281052558179, -0.15409203208069897, -1.4088703428418143, 0.5652530815291001, 2.86459304777937, 0.7819516463340959, -0.923952726199563, 2.504859577808468, 3.6758451776771475, -3.0233219428024776, -7.859152141380402, -2.91590014145189, 2.606846910083566, 0.10697137944616927, -3.095092323791667, -0.2210099102571986, 2.2377085405449755, -0.16550529632882321, -1.1067873537397195, 1.797389582147256, 2.3268030526585237, -0.3309477571658295, -0.5800773171426609, 0.952249629716163, -0.214904253928043, -1.8845768776306366, -0.6249012077554413, 0.29252440674336855, -1.2418528974986367, -1.3968016249973068, 0.17197678239437092, -0.48433716298272067, -1.2416828935987014, 2.1293358211247893, 4.728533984769171, 1.3824775520585368, -1.1807167151792277, 2.7063062252602728, 4.990801277553134, -0.09921766028843254, -3.7556516039797794, -0.5450068228196783, 0.737529977822486, -3.8381671447670325, -4.902454916734281, 0.3208128647680735, 1.9938458520400228, -2.513102643233028, -4.467690672129548, -1.5493785241040667, 0.13235966121041817, -0.17637570409689288, 0.8205702453674056, 1.3043805106154156, -0.16405826017077826, 0.431770755044393, 3.207937048515282, 2.6314631789454683, -0.5988571522516323, -0.6413647594343971, 1.0538244481918086, -0.18763921536883243, -1.1969334212813316, 1.31404385124893, 2.243937324787045, -0.07845153360539235, 1.1703741646737482, 4.871358199478952, 0.6110031949160986, -9.290351346465252, -10.065443254504073, -1.0041972449151495, 3.482769393917227, 0.08775543593327323, -1.3009317576553765, 0.9507706649982677, 0.3883345477364851, -1.6216174212630186, -0.3276262589968305, 0.8905401249120145, -1.2660370363349782, -2.2754093136725673, -0.285186469518631, -5.2706992686239165e-06, -1.4685559731810964, -0.39209046535487324, 1.155208171519319, -0.6518344971106551, -1.9853202798513583, 0.30095760620103884, 1.4980734993117861, -0.16373471038787196, -0.14932192636403932, 0.24373488162255086, -3.3040192864887143, -4.00392504555553, 5.747415302382306, 15.598247877121484, 12.001271994801096, 1.878585921943627, -1.1170375878741532, 0.11087664111188368, -2.4674675947547633, -4.519615715626241, -1.3745786634428576, 0.8628207292596594, -0.8994102844489882, -0.7875217523838316, 1.6889462952423564, 0.5445857888609632, -2.755006698213364, -2.297385109487345, -0.1312691773646277, -0.5629994006599284, -1.1290348035221869, -0.09005358875816262, -0.34657282182932814, -0.5432491594141177, 2.735928197388469, 4.772425390353274, 0.8813274862397408, -2.359830851818903, 0.24449382220556587, 1.8017276139928307, -1.0136200882472222, -0.29739429234851883, 4.40855982874166, 2.810719555128976, -3.964636277384883, -3.5918432717479623, 2.8260654847925983, 2.9565151744567015, -2.453036420462467, -3.100959077329598, 0.004964886527491251, -0.08459591076408113, -0.8744166541838385, 1.5128160139718339, 2.6765551323440127, 0.4708194611227564, -0.3562866249307768, 0.5881400827091434, -0.4834140755659995, -1.5277404311776661, 0.15105744944110497, 0.27600346256960356, -2.6639229345958224, -2.834474315459271, -0.0021641000297241723, -0.3519516695278914, -2.2065544205542844, 0.01684375246879192, 1.8256036017421144, -1.720608861344612, -3.391435833305336, 0.6044345297081455, -0.03398511590999687, -8.224668531408415, -10.228379685599347, -1.3840334787752362, 4.671524519578024, 1.6883258774632486, -0.868115697619078, 0.9284308095243565, 1.216387600099172, -0.05053993340560585, 1.08605348426334, 1.9093544530943485, 0.28969107763611396, 0.7954986187339214, 3.6009913757498566, 2.846449440153272, -0.2728581835437282, 0.1937000955051638, 2.1900243138827022, 1.1788445422790534, -0.08220382544587287, 0.26487430300095777, -1.0010132648067058, -1.3633123386143846, 4.100792059500673, 8.518996474649377], 'positive_zeros': ['0.89674336711172021664135903980', '2.30426380762749743702995721171', '3.58805712654987518547631326517', '4.09677790847183452620705777306', '4.80891611119606439916423652190', '5.87631379114182858589898437634', '6.662522464206211170029484446415', '7.3961932611536494171904378449', '8.05582842415036865170807150525', '8.50049783096506238634339556376', '9.8155949235836103042880312726', '10.48874849371474430246160789812', '11.33088352806576169156457252498', '12.32311040607976844988375993352', '12.78798203316559894384946920396', '13.90671992766165439858069407342', '14.57141490186873377295648851837', '15.04111856256926421527374063466', '15.54524673541776234913109888301', '16.601296119339473032388609257228', '17.32169771141175766470741478303', '17.726167465733011873075360167775', '18.58833183474756844983160114323', '19.40068283858139235568790004915', '20.13460685887628911190242055296', '21.01371189060095880454151683983', '21.80683421911907683326812707091', '22.627541195589758793151792040229', '23.12895817240086639573653579133', '23.60882434468453433375457985582', '24.40155822240280885834850244402', '25.112825334864382189989435023571', '25.792660449241208608338966602288', '26.50505923840998689682567227239', '27.136677649274032631865201598676', '27.720088305296533359981666072143', '28.1292309335831075316420410747', '29.69085475272870753949100048314', '30.342489530670419246728866004837', '30.54606618102371280581574193974', '31.36558870355154255072475992802', '32.15361887277109184336091396752', '32.76084095914566997954449099767', '33.52685972144847678252087175930', '34.02981161426959341306189105206', '34.6020472886569408514602656681', '35.39821130257551474547848783140', '35.76796964545800737168553113242', '36.67061747613671845619458886970', '37.32368785946652838038366576426', '38.02687047125826646509088633279', '39.085036337806419713428384825856', '39.402529063506010018183052968927', '40.25769304284582031601170248061', '40.79038096994720781949088378960', '41.57148539857743232051668339727', '42.22679230809318493383375078622', '42.72016023006039485683532691271', '43.34329720720654689421707090261', '43.84856281458716845363102601563', '44.52337935864630352397082491236', '45.414016310227564445404639882355', '45.97683380984046026871155018726', '46.65617151480260029325562952330', '46.979500520805015298388629070667', '48.24501352919130959394901156248', '48.866550092251930955314800395503', '49.61684076823973041151389278295', '49.92045310292199014134908868493', '50.583856026266301863094020308920', '51.252312386255777747265369704886', '51.80229912646348804775707405352', '52.60724005580702121539011172600', '53.12257417350777396426265136539', '53.74667097835353062800022281653', '54.341944754863319496115531259421', '54.84896028207457593200022877072', '55.53688964580912856200184874417', '56.69628353237474100513906196090', '57.0331674657542658827882687927', '57.81316033581658454151184826886', '58.51693584041936973727385231637', '59.202386063437133629582812583284', '59.532657385403411785605630928110', '59.969094371644785367102570290394', '61.16158607992228767488217116305', '61.728070398380095887699213948', '61.833854585005615698336807519458', '62.59982552472965967937799065350', '63.21718413186170822784656129633', '63.81800755413475144321802511945', '64.67552438111594614475674590970', '65.33415857671343431584758983554', '66.21435389252601064879466262351', '66.56291613279839973445186880659', '67.12949534406391640493038863776', '68.0955778154015863605527315896', '68.60695608040278854399004728359', '69.17658097841940235136527500537', '69.85370544112794465778734120150', '70.10238253765033789593010628313', '70.744249970866014596088465239386', '71.67661856806242497385528448760', '72.26045215041398140816057713101', '72.546345558109775757894660351205', '73.33180603298002397386753689193', '74.0170834674804842285364745882', '74.88645969039092408189980130812', '75.289850992058893739263532111047', '76.24787730960306860334223710186', '76.77021194195286348493435111476', '77.2245023745903651217934067884', '78.045508875336321464106053156473', '78.373727817891975468485424949720', '79.0372297412686517997482562907', '79.50400839910960351576798349423', '80.337749954749242089836256435831', '81.014155953569045233372417951138', '81.45140414758266912846561220390', '81.86578413170069822081129731450', '82.61524152948437569240732071229', '83.261351113632917407271367380442', '84.266745002669024587659448580380', '84.975095230347591781566895937954', '85.40394901582703143937352528481', '85.86570978859117677234934714327', '86.34650927901275438786934924373', '87.14000785229886342256665314805', '87.987873799024093211132736697260', '88.29555373540115743401158812144', '88.98901927585179233213086678103', '89.18728113144059538620850910792', '90.20950433557054771968755880232', '90.48581730415442224055073802905', '91.36134306928789618515783949651', '91.7610569816176362825888769642', '92.76602403463575012230151636516', '93.31869488972607634447942804274', '94.04206907751373785627561678754', '94.36063219989031272821587055990', '95.193720503457694762952160166437', '95.85966923228221763458850492587', '96.2400829565527910389725137489', '96.855361764667773774997212230633', '97.591552017232213551689646456876', '97.98763566891556974150690666483', '98.54855560045924052096144249849', '99.02298639207806527937370079455', '99.822849632742378726633685254705', '100.64413966651358466714432894238', '100.9664772278559083012601847919', '101.69173961888667888939377633176', '102.149420765376439318681777618999', '103.33069591553014660438993022466', '103.77102598015736900230337710253', '104.17466347611783469571016728928', '104.821876477571771263777397364579', '105.42726790256095502213806974613', '105.775384642806419799886039252524', '106.55445184675872677327275080139', '107.053902208862617430023653852358', '107.84694060357781430251840668525', '108.33045490830552071917650289079', '108.87466506499630865833366335777', '109.050231766610702549115343987444', '110.28521068834659506304477491705', '110.6105150786183842580510762300', '111.658729190235768489531179996621', '112.07583575325407052771403139004', '112.61989826512329300240452552836', '113.42128241985661338139291165834', '113.65695964948161293322131955272', '114.440894250362039411495635410336', '114.88982237317549552463549064291', '115.527661094287013284415580900331', '116.19039841630128154149157162311', '116.79920033135320961085308820769', '117.292052281828837500892506325701', '117.5135000847469176371110407820', '118.335421861012977078564996760384', '119.07760613591211634473227879300', '119.86781881415477885151496456163', '120.47532686588592134287818252674', '121.08639226171915618895570262678', '121.44789381692707411351165356527', '122.11357830281100889660622093912', '122.91970401710695584877520180999', '123.43981908545522726403176204512', '124.08792189308713904111051082042', '124.210980640545587934202126764920', '125.16712396639328471319953203629', '125.467090763406966788280017923211', '125.9601814199026078873842312683', '127.06203471697465681747745642898', '127.307850636799535641708573354800', '127.925639263773801335737334101914', '128.326883933555299950591245939126', '129.439340080900842232404454997531', '129.98522516647508887671723144155', '130.650079159993033247042827050995', '130.8185143378002996151205453343', '131.93520027292227052589486525063', '132.2329254508994203175160521810', '132.79853160678300997127946502609', '133.21914789109819315124062746208', '133.802699001501950805663014819208', '134.647687178380045081016506829133', '134.95496223915944638067215584287', '135.67770904847766912334991760066', '136.25376297691657162323731824434', '136.651920722535353148501171961156', '137.30550207535420777238455089039', '138.02937280356061661580381734487', '138.84386914897808128108058887307', '139.55796493769268232622006719519', '140.07165436078336907833343821440', '140.41260125098370119346163424811', '140.88770464126637382163676837667', '141.47216090559695691484332633141', '142.333446697085895262822477441715', '142.99561107906126106210976625351', '143.264457985509539202992572137230', '143.71964019851289498236713171511', '144.31982759532247864378301233051', '145.07551300322843037396278856561', '145.43759440026373378642914345801', '146.13492227447400429941362039075', '146.99859354411209446247622916907', '147.506790748039625183244604911621', '148.14102625409654519986708345437', '148.73311239855390774321465417346', '149.19982334460978299190761661364', '149.956795441913702025621228886005', '150.41503500256883300421606573100', '150.90845283070238560506114478662', '151.67312707104209362932195382605', '151.963381885158702981642555528324', '152.76318084142848481529128812657', '153.02817332303311522066022325637', '153.59342912887598656373591248982', '154.47193245032273881867585455653', '154.82852706094901175799293898121', '155.62020680679929150047532978948', '156.29309201252388623010567717006', '156.63338025313872412633007912883', '157.48120120893959750626170302297', '157.97137791535811626433956395916', '158.97370595103207449690306380701', '159.19616733779244735215719515207', '159.48725140849190086463917169220', '160.273881825058166234200220684520', '160.561502109108882351988924274245', '161.493052861204706410520289134825', '161.972189454486031230859689340470', '162.473676337724180724539836352356', '162.99016189956599588600110558974', '163.73592260204122018811382117094', '163.94569848182622626553033222226', '164.70764267053939846808257777895', '165.66116964619057402397941827542', '166.256992544753698005232300689610', '166.74158047242762437912593874425', '167.23641441833426906465274242623', '167.85636631944667634975417187969', '168.29001646916313178631593636132', '169.11523056120929631246939262774', '169.37499876745313960227196485454', '170.052911475474806968698685219456', '170.54875690703512781994533498025', '171.21690976023171289960706180785', '171.842779345498363434782602077415', '172.22443956327411151614911955290', '172.54041405150742596883163359232', '173.28824327005833005020203818899', '174.46822496556158631271241470097', '174.91551687845521174749669376947', '175.049558843531201940356028866276', '176.05507482375023282860377901924', '176.4330989644551597592461947701', '176.97063554568283332508753653177', '177.548140253635737908960799293558', '178.49564548227539086876432169803', '178.56721826304820054116050957917', '179.416481715280619183394569597672', '179.56038195081096649158604481916', '180.081329205696126344376906112344', '180.99070587934400726597287038506', '181.54210176508467948010171889679', '182.0828682646589361707250045218', '182.521725925977326476122187997161', '183.25065019173931189297176937829', '183.9200899264295734612766170901', '184.54300008551932244674305619113', '185.31174896672802864871608601272', '185.60816983849279825515837659420', '186.08685043816747818851006633859', '186.9465432174965076463128275514', '187.296598450820506079879242056216', '187.73064901765952121631139849342', '188.41342887602715603953036454167', '188.78815259501860212655611173483', '189.687840293275135080282860287202', '189.94780811204135439250906246', '190.62351941549694831761641212434', '191.13108139713859596649766113182', '191.8290887781174188337906719973', '192.18565229615279454394640435329', '193.169204811978194343069192761311', '193.87993659472956660854610184528', '194.24494950570577758123981628992', '194.96516877093117929456393847782', '195.08515143179341453872284426467', '196.04043877347625024001474330110', '196.07829102547183666262379491818', '197.14799189232126648228048559724', '197.472867747123924522989650621003', '198.368382500411156696139854538469', '198.54554387819764881266635219374', '198.884413777465473174278168258967', '199.48788763155205759954923467756'], 'prelabel': '1-2001-2001.845-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 9.292604933071013, 'root_angle': 0.6548200100393662, 'root_number': '-0.467430009663017118283332111228+0.884030082104920071835709371701*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.32741000502', 'prec': 44}, 'spectral_label': 'r0-0', 'st_group': 'mu(154)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.876385860170485040450933025649+0.631434925624317524318970815449*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.896743367112', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '2.30426380763', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.58805712655', 'prec': 44}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 9.292604933071013, 'bad_primes': [3, 23, 29], 'central_character': '2001.845', 'conductor': 2001, 'conductor_radical': 2001, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/2001/845'], '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': '1-2001-2001.845-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': '1-2001-2001.845-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 9.292604933071013, 'root_angle': 0.3274100050196831, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.896743367112', 'prec': 47}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': 'dirichlet_L_2001.845', 'Lhash_array': ['dirichlet_L_2001.845'], 'label': '1-2001-2001.845-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/2001/845'}