-
lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_2001.500', 'a10': [0.37796670142890654, -0.9258191900208981], 'a2': [-0.9179165852537594, -0.3967734145782425], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [0.6851417149678442, 0.7284097956582691], 'a5': [0.020398537391405354, 0.9997919281892065], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [0.37796670142890654, 0.9258191900208981], 'a8': [-0.3398893015826167, -0.9404654500138115], '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': '2001.500', 'coeff_info': ['x^154 - 1', '0.999167799344583 + 0.0407885860615856*I', '\\\\zeta_{154}'], 'conductor': 2001, 'conductor_radical': 2001, 'conjugate': 'dirichlet_L_2001.1997', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^87', 0, 'a^20', 'a^38', 0, 'a^29', 'a^107', 0, 'a^125', 'a^12', 0, 'a^26', 'a^116', 0, 'a^40', 'a^112', 0, 'a^97', 'a^58', 0, 'a^99', 0, 0, 'a^76', 'a^113', 0, 'a^49', 0, 0, 'a^52', 'a^127', 0, 'a^45', 'a^67', 0, 'a^149', 'a^30', 0, 'a^145', 'a^49', 0, 'a^25', 'a^32', 0, 0, 'a^33', 0, 'a^58', 'a^9', 0, 'a^46', 'a^150', 0, 'a^50', 'a^136', 0, 0, 'a^147', 0, 'a^85', 'a^139', 0, 'a^60', 'a^64', 0, 'a^65', 'a^132', 0, 'a^0', 'a^131', 0, 'a^130', 'a^82', 0, 'a^117', 'a^41', 0, 'a^37', 'a^78', 0, 'a^136', 'a^6', 0, 'a^150', 'a^112', 0, 'a^119', 'a^80', 0, 'a^55', 0, 0, 'a^120', 'a^135', 0, 'a^27', 'a^145', 0, 'a^96'], 'euler_factors': [[1, 'a^87'], [0], [1, 'a^38'], [1, 'a^29'], [1, 'a^12'], [1, 'a^26'], [1, 'a^112'], [1, 'a^97'], [0], [0], [1, 'a^52'], [1, 'a^149'], [1, 'a^49'], [1, 'a^25'], [1, 'a^33'], [1, 'a^150'], [1, 'a^147'], [1, 'a^85'], [1, 'a^65'], [1, 'a^131'], [1, 'a^130'], [1, 'a^37'], [1, 'a^6'], [1, 'a^80'], [1, 'a^27'], [1, 'a^39']], 'gamma_factors': [[0], []], 'index': 0, 'label': '1-2001-2001.500-r0-0-0', 'leading_term': '0.565408961397346909065751053170+0.844489927352248689849707276208*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/2001/500', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'plot_values': [1.0162925420506794, 1.6244409459221025, 1.9857987772803403, 1.4592114625680477, 0.14216561396794772, -0.9919547328525647, -1.000053932842407, -0.04334085021477854, 0.5860792727375242, -0.1972706586763029, -1.8305865842093862, -2.3287210667115126, -0.39292325203113665, 2.6768336692329475, 3.6848038144716266, 0.6936042778777552, -4.543094516259746, -7.828281476872221, -6.5773348070954505, -2.423084457388004, 0.6211975414334033, 0.48080779573450844, -1.0880656330962437, -1.1154764317535029, 0.7995170752801306, 2.226029105973502, 1.2901808074449488, -0.8441705164131103, -1.6489379263756998, -0.6688265625641212, 0.03993292968216501, -0.9821398403424892, -2.416092294779696, -2.0853578723621147, -0.20594009578024006, 0.8717133658519881, 0.17206883724052963, -0.42124372146083233, 0.7619473691355108, 2.014141568901656, 0.25421887355501, -3.9959240577866115, -6.039280879012489, -2.720244968037597, 2.9368939078817426, 5.0120669884890505, 2.074347324758459, -1.2416991383932774, -0.6726597009710706, 2.1328753447287245, 2.5328238788686455, -0.23579008600126825, -2.1622889076316802, -0.49144913425096365, 2.4052813396969697, 2.759005641320205, 0.7403887630490251, -0.48415008957037015, 0.14611433730707696, 0.5163270037484993, -0.5425470217534438, -1.1996504039877725, -0.09493878941484189, 0.7722680486515343, -0.8807374996903512, -3.37779263160295, -3.126035585580961, -0.28972992848894147, 1.1616460744324293, -0.3150621063588607, -1.2845156120486751, 0.852959276825952, 2.7980870299761316, -0.028815547249618323, -5.587715447535473, -6.813730774340069, -1.4719209235783925, 4.250042942385812, 4.11837677856705, -0.05979730825250418, -2.183503280241549, -0.8618127438738458, 0.0006135590746547943, -1.499254744612769, -2.557151647781852, -1.1480297188559558, 0.40608456371814766, -0.2919132681568271, -1.5266980869339464, -0.7555052406788498, 0.681059202651475, -0.015763790968345417, -1.8148234948368178, -1.3721993136856738, 0.9814630941802573, 1.480178622108227, -0.6034841167141819, -1.6549189083167373, -0.30506737100004233, -0.1947918987493964, -3.0926473017581775, -4.0501810275435925, 1.4814887418131253, 8.964671883764298, 9.59504944084018, 2.67981633996144, -3.3715234101789395, -3.029203291923247, -0.11289473835070639, 0.024341738566647793, -1.3930874627839094, -0.5995511315232366, 1.3571084655258434, 0.9703671769648778, -0.9051197673573983, -0.5368614574893227, 1.776962253099172, 2.0917898409720177, -0.2164738568373175, -1.4849706613924267, -0.26524172788944367, 0.6697803153247138, -0.0208755613362702, -0.11047615628130962, 0.7235136653722186, -0.9899822200134409, -5.744366980984286, -7.947006238493909, -4.15713779131608, 0.5013279035054458, -0.03026877150230422, -2.8693517409396323, -1.1472181075165093, 3.988077290886916, 4.791755250116189, -0.3113684835123792, -4.132212925225373, -2.3884585184376803, 0.2952140014845625, -0.6928726923168064, -2.482654281955486, -0.9512193013920914, 1.7344277756518167, 1.524360784513134, -0.2722336740092508, -0.1049078878393, 1.1348714426901474, 0.5258401023242883, -0.7968614902183372, -0.017971617626848187, 1.4298339313446151, 0.5236716499162577, -0.9897261702662274, 0.4994760604825609, 3.0908616010660452, 2.166340368197725, -0.7940902777680819, -0.2676060618615572, 2.89855229567006, 2.079232313325739, -3.1425465993145036, -5.058231698235377, -0.7072417564131016, 2.733554941770052, 0.09447113358317144, -3.0419675464374714, -0.17027149711875572, 5.086744625378129, 5.452077415102958, 1.6789326460505658, -0.35707419411645874, 0.17359918089662404, -0.09396385161894202, -1.0529876114123655, -0.2599166096633135, 0.7677011548225849, -1.0338639005190775, -3.6198654509435535, -2.840025087208301, -0.0914252264279509, 0.24034879325524053, -1.116894586958741, -0.31600401795435273, 1.6530965110269888, 1.1028175175958324, -0.3441047247578287, 1.1448277288717856, 2.322894187978947, -3.040950996790889, -11.462393044013679, -12.378408953366433, -4.529762172747906, 1.5937226608830593, 0.10317730505048038, -2.736686991242019, -1.1061963682489018, 1.2147087269772672, -0.22162227359233408, -2.247237891568239, -1.1749852001237284, 0.11302793865493002, -1.3926423283136806, -2.5971317452752287, -0.6223450308502478, 1.3836566501490088, 0.4658318859893189, -0.6315565061642214, 0.5286765415282992, 1.2035050354839778, -0.3664536836028061, -0.8598323351752393, 1.179202417043995, 1.7148886912857395, -0.6491060187845152, -1.1693643433214875, 1.246911276681442, 0.08130867858382593, -6.6054502040752405, -9.86911137194458, -3.743868598433978, 4.009944058316288, 4.10583386698058, -0.11809995722344296, -0.6379921841715782, 1.3714154218723176, 0.4196599471278937, -1.5534300358292317, 0.4486792655942501, 3.8712806327635625, 3.0221317996023114, -0.47215573505452907, -1.2313638761646988, 0.2514469363895172, 0.2847113527028231, -0.32662044781969324, 0.6509157568166758, 1.059363802320374, -0.9514413933956338, -1.955066808139278, 0.11398080608138986, 0.8764941654849867, -2.196101432933013, -4.02202745170662, -1.4337112162535914, 0.16128061453271852, -2.832214520789693, -4.662077552596709, -1.452859065666846, 0.21650397853129286, -4.440490960421207, -7.834668572797278, -2.5346589115227056, 5.111938973953952, 5.369805305327722, 0.5967486224320777, -1.0789206787198533, 0.2713243691269183, -0.09757000094928495, -1.1775930428886667, 0.16141694032590462, 1.4375816375435895, -0.3535753628738733, -2.1396253556869698, -0.9129855320624659, 0.3819749063025207, -0.46603838202361036, -0.1838031543997556, 2.4346884089539276, 2.9628692599885094, 0.27158733910949795, -0.5388429699110825, 1.736966994641367, 1.9784840051751529, -0.25869996663879075, 0.5274041599502314, 3.050371370272965, -0.8742554345910276, -10.084353155266983, -12.644446382857, -5.21721875425041, 1.1704115936804005, -0.2771424947791731, -2.7526516637318825, -0.44712065770780873, 2.072191935339422, 0.8368827381639028, -0.5076816320030795, 0.1781095176375957, -0.5285359921754493, -2.810390785130905, -2.1538767062601227, 1.0791813396294756, 1.5916028775926692, -0.6740047826553022, -0.9591495349507979, 0.6627581945214909, 0.5044425626693697, -0.4432352142010826, 0.3976677730528424, 0.2537025646132554, -2.7893103305914893, -3.2027722637435088, 1.8712957236987422, 4.382017415239831, -1.426213263207603, -7.324929284567635, -4.735682266800139, 0.5504733724116787, 0.031553504769938144, -2.2388476978767353, 0.6420899098582358, 4.380102179143625, 2.4555242228411904, -1.1040897423838463, -0.20842917194825056, 1.903824923348746, 0.5034129227817705, -1.2601772523834411, 0.0726043143761868, 1.218247692839592, -0.15696237828442125, -0.7180015101430655, 0.5568513964529945, 0.0697850813871368, -1.9249033408888039, -1.399079032822241, 0.3583857526405174, -0.8939707946226028, -2.682758519248596, -0.5868355522410279, 1.3550274178779613, -2.0745201848093036, -5.563852906013624, -2.5974549106356903, 1.1616855751678223, -1.6780852871197, -5.3927083130923545, -1.9440915751354169, 3.113585548770459, 1.010471938836051, -3.9029677667868556, -3.220955742737062, 0.11719016274730693, -0.5499975879652873, -2.576170330361554, -0.9860180652966054, 1.3726732636013481, 0.7790676751953358, -0.1556173076884648, 0.47514081395782004, 0.07470959055924481, -0.7836892457467368, 1.8061733570248322, 5.637246766369702, 4.716767702516062, 0.625017691718347, -0.5504536186837539, 0.41999525963170603, -0.22915558923798743, 0.07680250848169767, 3.3761323421766285, 3.571484242487143, -1.7126473999002096, -2.814909869861504, 5.433924700950196, 11.941927160614364, 7.435016144940344, 0.10709122708071303, 0.06271634380221659, 2.910986626827439, 1.4389194325547887, -1.031913474204678, -0.21459016716457302, 0.20622612594616546, -1.9435733245946087, -2.275074262330868, -0.02433913092991668, -0.14894851304353213, -2.572705346645118, -2.2860658266661327, 0.043433935740933814, 0.014465224612343931, -1.0241429518466123, 0.010921719974545925, 0.34509641929067175, -1.905563075912177, -2.126282294021648, 0.8794350189517616, 0.9408870606629932, -2.5332394421927926, -2.244266879406062, 1.0114892284156347, -2.3631194132831945, -11.024340057040352, -11.878899031596891, -2.9310055697073203, 3.2447127963362155, 1.5213746568282118, -0.3830869971442744, 0.5287773145398244, -0.7303064745565525, -3.297112970384377, -1.5575485106068456, 2.1180878193084474, 1.5341145646312102, -1.1277395755897375, -0.6650758242926089, 0.8105756572502502, -0.03603895175265193, -0.534918933813374, 0.8437429926251221, 0.8460470520920587, -0.18512143703852063, 1.529274656414501, 3.4806144486756816, 0.8961761064466578, -1.932627808251949, 0.982479180217119, 4.446159609505883, 1.7948630775202368, -1.600421923653321, 0.10947236158013739, 0.3946266830153, -5.6633416285087135, -9.143643695024002, -3.8722003800321207, 0.8626706149523625, -2.3356798048638776, -5.901786118378663, -3.0862915448493475, 0.4797241824277374, -0.011016467833499782, -0.5497424012124996, 0.686881015266855, 0.0778392886331316, -1.6410842020609366, -0.6517211945068977, 0.8153157351233047, -0.6625070852552698, -1.572303557797665, 0.8886586369097199, 2.256173982541932, 0.48715344565066354, 0.20694236358873536, 1.6542088380380953, -0.20517262887907783, -3.2646330920093165, -1.3176471662197868, 1.918627130981473, -0.3994638610223776, -2.754953532395123, 2.333499992522024, 7.155872692667733, 2.018277376647585, -5.443554593275844, -3.774938737999912, 2.14815501628099, 2.4306083948142176, -0.3027226129451906, -0.03135557720649622, 0.56471423270223, -1.0675678858896824, -1.085708766394033, 0.8986736571590924, 0.3070190231627303, -1.6389386828309747, -0.09099079184644898, 2.530941855928127, 1.5089857515313683, -0.25729075299827475, 0.7438886661536561, 1.1013361578827972, -0.8187808347528307, -0.9775927093644814, 0.05264129500960722, -2.0001809240627613, -2.892285957607985, 3.4543516290428578, 9.135136336470492, 3.5089152912716677, -6.05565649874382, -5.9792766590873425, 0.23633462258348267, 1.3959481567217373, -0.7170252585348129, 0.3438413001534759, 0.6436113346634754, -3.7040949157385255, -6.03864365821244, -2.3360564799405585, 0.7881390366869927, -0.2957696209956257, -0.868970819250166, 0.17199038573586412, -0.8771377536072279, -2.395124875558231, -0.790510683975141, 0.8835905732821777, -0.287992511828186, -0.7517382113954042, 0.3902989613143755, -1.2181212961648014, -3.8176294608582717, -1.3659113813353434, 2.6863809782911474, 1.152316500380806, -1.5667070562842538, 1.241660326669653, 3.0472025205252824, -2.7604627257970225, -7.2106831034018555, -2.1661019576096763, 3.6440344834974514, 1.8575218748127416, -0.7178026562840105, 1.6063129461723706, 2.3506222604089873, -1.495085075455176, -2.9056951360722554, -0.008305637106293322, 1.0918644608732935, -0.19125718039731096, 0.3865781191924343, 1.414228104609561, 0.21124430936580563, -0.30095066967920375, 0.6061192597414663, -1.3487513532948547, -4.62514779698755, -3.0031017189587317, 1.1805471437470585, 1.1083779820315205, -0.9318372963243401, -0.06431074609625456, 0.20766594491880158, -1.701406348915515, 1.1759976285884275, 7.909158583118335, 6.1543877338543425, -4.42515548246391, -8.335060749422272, -1.4342232617804362, 3.0974883352106644, 0.11944527464720836, -1.57503090608017, 0.5665578918462582, 0.5436346222109021, -1.203937234727598, -0.5086114407314999, -0.15417167788519281, -2.523861364284886, -2.685768784709562, 0.7572110044812294, 1.9435711278161842, 0.0773750115934675, 0.029375790707825, 0.8801716044310277, -0.8100914611635148, -1.8297109165409875, 0.13040735891398877, 0.2988605986539632, -1.9129863992865215, -0.780056595027339, 1.3797083200286933, -2.69437016618732, -7.505424715547131, -2.94553816834702, 4.461426042783854, 2.681807258082818, -2.680987068737602, -0.3764553675966637, 4.509271400367653, 2.669919981989571, -1.2334586184853968, -0.6995819500469029, 0.026843679622208017, -1.810942799097691, -1.438175097092456, 0.7427058455710098, -0.8585045642245333, -3.9720094914783486, -2.7648759108053365, 0.09433564018978532, 0.14793866509966835, -0.041613187937607043, 1.0403444357344414, 0.3782209649885897, -0.42536385717915876, 2.0319431133911454, 2.963747511185735, -1.5153089080740407, -3.9876052850381685, -0.1075242630531985, 1.5190184656412216, -2.5343205318131186, -2.774954740595507, 2.386913667878176, 2.275805590915195, -3.32211685569313, -3.3535680630640563, 1.2684721318704715, 0.24155604756768156, -4.100739323518873, -2.493589968656184, 1.8508259044201483, 1.2394052537003488, -1.1423163837337043, -0.36913511834377755, 0.4612702829559244, -0.2658542173058171, 0.5175614023019295, 1.1285433570268173, -1.576467298368658, -3.244593162200963, -0.5495687972647568, 1.1628781764730591, -0.5128250881741286, -0.4409420118972235, 1.2967091803926922, -0.07778912342123745, -1.2069522288529486, 2.3505000352910823, 3.610875003963485, -2.091753718844307, -5.123041788344201, -0.7888837720454105, -0.08786711104182399, -6.622454403650728, -7.842897388957758, -0.2543607845230582, 3.7718678275335016, 0.41346424441515783, -1.150518429059791, 0.9315423175105091, 0.7704853812313243, -0.4749040515642589, 0.7362827199528769, 0.9377550010363438, -1.33532251376552, -1.2322839563485133, 0.8361792374898696], 'positive_zeros': ['1.28137337282506230845734340462', '2.20047369518612541924991087194', '2.768195954636572904538098918652', '3.79047161526324317642545536156', '4.73186932938013441872821728809', '6.15324452890302306689751747110', '6.65788481516380114221349290056', '7.38616752267224625567556803855', '8.309347067327662261673918687787', '9.28697032721168885617746242598', '9.41933802029129366336460308855', '10.660313491359530145538203264220', '11.29996829927424999666678094723', '11.7262201245836656824404378440', '12.52176105686246574648332778794', '13.58274716253576457034917365582', '14.53931541978514123922106473090', '15.0774769750721242276324834096', '15.91436976922871693523002648766', '16.611882381792579862299952283899', '17.6257045911156057035512303219', '18.07717750080442333860085166001', '18.62003676587365874482443274969', '19.39444413281955866218440672757', '19.886836390360602675682140466919', '20.97056867458518845028074626868', '21.51406014635963011529564162716', '22.096480311221636502029047093689', '22.81077403596942864268991754700', '23.81626409909440668936017460602', '24.6828565571000778874091026798', '25.522467770495753205891706610450', '25.62539699891072376575598887147', '26.75045141796824978444829855484', '27.124722593158787240726447697917', '27.949910294822310948695035090489', '28.43477527660909819851873957041', '29.24435559091179293179650073868', '29.91995378041519577092905389917', '30.69906633312033915893589062399', '30.89501582017996230608703071451', '31.81528407516374952401751434298', '32.921352825424058563019669053326', '33.76912805988096613701903999580', '34.06796407704630013790578279403', '34.77427943621507139208205251988', '35.463318451206299672618663376464', '36.01551611856741346160809126295', '36.84793158434431207943751458682', '37.5521214339751555949796686725', '38.117226064607063206857181579344', '38.478695384332244918455727227899', '38.96384033085646774850938712461', '40.259807179245526527538334452121', '40.62177067884984303019280534067', '41.32239338717570551641746819003', '42.171065347652739791747860846443', '43.06157545876946410438047861526', '43.333809669081231707824673217767', '44.159162160660484555767701762068', '44.93830556729122894041030056937', '45.33727356759863461047173353659', '46.038965078840598436574256719657', '46.56570504185573491098864342020', '47.26936320990006096882950511380', '47.75559677050021608340615167539', '48.64981491321295567901194297524', '49.090922451499679944353011291775', '49.82180590596886733997603405729', '50.66605477170399189155761306844', '51.25661386391764507483963705133', '51.88465457296179641259861038797', '53.004029473154646241259349607019', '53.36031929492922886159410047639', '53.72117536581071381363965040229', '54.426440688277621532026764644811', '54.879843196038555952148477861643', '55.9521495480307228566551622203', '56.305772748205418851445348816493', '56.92048461095044325880634631965', '57.69021906980313146739790262284', '57.96423351987149477591562001334', '58.62331144171262572298711918403', '59.87320952198180639419335587005', '60.321027848258069686426407406052', '61.04831734284419639829958393130', '61.53676268135788160899964372966', '62.40791477075646326704772831695', '62.569254547222641720441301095546', '63.50691281442254599452895991318', '64.146821641734994483757618897014', '64.58581398918512179434557563739', '65.25071495828546940847133506819', '65.77763067329467834044967993463', '66.48338330122211372037400000094', '67.03202461366391126466368645366', '67.50536285184280945251813513926', '68.566917841993657062009434770323', '69.363642384571813515240168529738', '69.78086126631488810018770409653', '70.36345153802548226193051784339', '70.89972344433285688785532258776', '71.82532651920503970969714711540', '72.43956320067898446387160679182', '72.91126982609541036634961044470', '73.28189140237190330637207026264', '73.93896353658455015082685807451', '74.67294977100704587409939613406', '75.11972195252970542418486746554', '76.10562576046316810931751501333', '76.28844467970816218765869298844', '77.32316111092053699456138650987', '77.53155297735581795825356803231', '78.52825861779720311731401249490', '79.423996003056810922316541302025', '79.930362697011732252565592193735', '80.29085330322848449076677150841', '80.91382999005484043295523311751', '81.52085273332140109237901013292', '82.34298501772129614856317568827', '82.685447470708190653402095021803', '83.153638530405740687137744695558', '84.09603191792275352645323900604', '84.46778621099612305297647595059', '85.26649672967031816772354843918', '85.56050877646659467154167700344', '86.21468902819566092193397202353', '87.40225750563833520166070991328', '87.78875267237892568623007901555', '88.47583870615246814016857621440', '89.19353873678530235394011099799', '89.61693774932739576922920050871', '89.904015449832893065439416337244', '90.8280975384743638785471982845', '91.46810212461819996694872586353', '92.052007736779851019236305816759', '92.624381121200535625332704064564', '93.023870041504999476112847332828', '93.47417408491725999947510323310', '94.275631800851381359708953735179', '94.94402940265706417679316111646', '95.887698277336390998684431189981', '96.25325779765991245000715058464', '96.83284284447977597795054313702', '97.684284211748339081846303709370', '98.14874227623824083876830139911', '98.81080654020645452823306782952', '99.36425278526110495939915618033', '99.9713888743882469124174168103', '100.490970867985653907362778111926', '100.94882788883633165576512580190', '101.77620402257706509528269013547', '102.061834488872182549672785764367', '102.86776338670371458973959875764', '103.300149286727927144638474709948', '104.22879996254658391284637623111', '104.576846990172208465760012844116', '105.40865799157220013515429104190', '105.99464333675428536514577182838', '106.85634973896294549265459407144', '107.11110888049598230032587688352', '107.915487415221660465835052861324', '108.62616970208281653110443281180', '108.869044614555152535481301820344', '109.39275940593912346387580189896', '109.84333617523041895407015397740', '111.00582209347384678162683776025', '111.4080781162992127811171677407', '111.81031434304894948187735589191', '112.17626943005217941034492481507', '113.03169029571783849347530670174', '113.57402521299642912067581179611', '114.69561687251598178620991555411', '114.993660226334449451440498781753', '115.7678031641286302270324417965', '116.294046957620936682627586015368', '116.6065960558659705677289671765', '117.5042446092367785476021427154', '117.788360724918347929496125242', '118.7415996622721988008157045903', '119.0659552890583802076193310382', '119.685227450243117148039006222656', '120.06593096438236031555402671443', '120.84635099626890119363714634636', '121.34155609611208100757267967091', '122.0635460260439696538809454466', '122.38380742689576739208554928566', '123.539791010235394832568055798837', '124.23602240530803325792331431064', '124.529695936901547416373437475695', '124.91077690011267037700390265484', '125.741403979158289749299923990775', '126.40919290150612409492919199288', '126.98214262734869639356175787366', '127.4919991666586652493649690238', '127.95092778100069032777712631839', '128.64217589952098538329112887170', '128.84873602622123951827737253480', '129.75487980966809244264631043477', '130.247581509007537686191861471551', '131.05983115140553080962509518495', '131.55025687236851608175136458308', '131.90799006042455532637082569006', '133.011413175878779001824402007418', '133.28563091732361426644427723020', '134.30158847735999504760178005958', '134.68514878967876424366731820827', '135.14436275559871236895967681691', '135.63755458677428199251763342326', '136.34539817023585071967760816894', '136.780194391710706736847364634635', '137.40813179818785946556897929352', '138.235136279608292588767542215146', '138.3785385527887787277878139004', '139.044847140747916827939367207454', '139.78439624942738962667179879083', '140.28292226162640135229861663524', '140.83447175178979793745849452926', '141.632284235676581011064080060924', '142.37014059543489968455738601007', '143.07421029105426600159815583367', '143.44452505013467555998019970723', '143.88195065999064421417836312067', '144.537588696199607853672146998522', '145.04162017952820782516432569380', '145.63392473990381742166045151826', '146.47006216825512304015473516449', '146.72074326342807138547796806207', '147.37333706059395441904690924906', '148.0504700270096005100304205528', '148.15966354483675651478154875003', '148.92853260125969262489505920028', '149.78925763099015566921920627010', '150.61004149283632505301321087264', '151.116856071961458587079757872', '151.510184528011025131069780381047', '151.94277018111054402335787883931', '152.99013452709314093545921871679', '153.385881594148403463811320194951', '153.98661143222567243346458275980', '154.21617540541021163456363553204', '155.09917188267221244415908052034', '155.5712551392463888049613472807', '156.11894993374687867178283973840', '156.41836334200691660265810246211', '157.27379318130873213012131148071', '157.90523259946781254735043573367', '158.34610889160484289612582080609', '158.94646074203393287658062139727', '159.7753011033888237783950596483', '160.46888363160410587048957794761', '160.774354051719684132349407934372', '161.4533600400668879608900801354', '162.188381236614436230010680223602', '162.75285546969915010280311340073', '163.03997084823614102568940265601', '163.794618688059385666224696963579', '164.15687866915982966498090575687', '164.55066931712966837854609747434', '165.51872327673001014803466140632', '166.077515193296573768869989802020', '166.57511530706336376414735220075', '166.91287823642688477189017549229', '167.437091472907031363730897702209', '168.31117850900456236787331495180', '169.12045015981586661480652731174', '169.697060467866252279484212686847', '170.2324594674500320387601313257', '170.710448938954755659976268134627', '171.38323212179734076559848164879', '171.5176945739171397896123702013', '172.43331747174290101399040387448', '173.14124404894133326160756283360', '173.429860100078514684740168086551', '173.95279966787812026302115636408', '174.66781802662481073405535625593', '175.0456003406847978287239257037', '175.70136010547609548272866452067', '176.10557118879841233721625398708', '176.97945472850136520751416597784', '177.6309809148723865152792065771', '178.14515180371966712942236157614', '178.93174582789536630257911810544', '179.51485312724375775865580779595', '179.695578906593742158987776780206', '180.490488087696005455739735581214', '180.85431012028397393892066049456', '181.85763241636755788862671300370', '182.24445398476089378019299412208', '182.51537212093244182878372976576', '183.19920566944212581001825542751', '183.529020723285240715617693791144', '184.28741828308031139733353667839', '185.007369637515989147925093858279', '185.45017148731880101171441268926', '186.107311863535880486546397506302', '186.69130146908883333465710380616', '187.39964236241145720403346445692', '187.82901391026831229126105905677', '188.59460009822162755652893375682', '189.193961296345415261384383879816', '189.76064991585333881230729599709', '190.1893301531302573331894900272', '190.50993871539520646817355452385', '191.102633835888503886915637306750', '191.92788472677049434414095413616', '192.41603647759156152143033704761', '192.88200275137998341050140605338', '193.42803662669755171283884641631', '193.891326760972726960635080475078', '194.591093868592949940003995766096', '195.37067375192291038248212866577', '195.61823959812553325495747295543', '196.572514348784083007820184694137', '197.221329462542566369881818876021', '197.67751169455704320630292055387', '198.26600689069265111523778897738', '198.61300230716938281261160684278', '199.19932142237196063815827615654', '199.85233871369115661834292877871'], 'prelabel': '1-2001-2001.500-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 9.292604933071013, 'root_angle': 0.6244068459613231, 'root_number': '-0.380961167129783397328142235526+0.924591038859404716205929906258*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.312203422981', 'prec': 47}, 'spectral_label': 'r0-0', 'st_group': 'mu(154)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.745164151290420223259870669716+0.231196577171973540904706093243*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.28137337283', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '2.20047369519', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.76819595464', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 9.292604933071013, 'bad_primes': [3, 23, 29], 'central_character': '2001.500', 'conductor': 2001, 'conductor_radical': 2001, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/2001/500'], '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': '1-2001-2001.500-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': '1-2001-2001.500-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 9.292604933071013, 'root_angle': 0.31220342298066156, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.28137337283', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_2001.500', 'Lhash_array': ['dirichlet_L_2001.500'], 'label': '1-2001-2001.500-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/2001/500'}
Lfunction data - 1-2001-2001.500-r0-0-0