Formats: - HTML - YAML - JSON - 2026-09-06T11:37:47.853824
  • lfunc_lfunctions • Show schema
    {'Lhash': 'dirichlet_L_64.27', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [1.0, -2.8163065144692913e-30], 'a3': [0.3826834323650898, 0.9238795325112867], 'a4': [1.0, -2.8163065144692913e-30], 'a5': [-0.9238795325112867, -0.3826834323650898], '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': 6.877755186856001, 'analytic_normalization': 0, 'bad_lfactors': [[2, [1]]], 'bad_primes': [2], 'central_character': '64.27', 'coeff_info': ['x^16 - 1', '0.923879532511287 + 0.382683432365090*I', '\\\\zeta_{16}'], 'conductor': 64, 'conductor_radical': 2, 'conjugate': 'dirichlet_L_64.19', 'degree': 1, 'dirichlet_coefficients': ['a^0', 0, 'a^3', 0, 'a^9', 0, 'a^2', 0, 'a^6', 0, 'a^5', 0, 'a^7', 0, 'a^12', 0, 'a^12', 0, 'a^7', 0, 'a^5', 0, 'a^6', 0, 'a^2', 0, 'a^9', 0, 'a^3', 0, 'a^0', 0, 'a^8', 0, 'a^11', 0, 'a^1', 0, 'a^10', 0, 'a^14', 0, 'a^13', 0, 'a^15', 0, 'a^4', 0, 'a^4', 0, 'a^15', 0, 'a^13', 0, 'a^14', 0, 'a^10', 0, 'a^1', 0, 'a^11', 0, 'a^8', 0, 'a^0', 0, 'a^3', 0, 'a^9', 0, 'a^2', 0, 'a^6', 0, 'a^5', 0, 'a^7', 0, 'a^12', 0, 'a^12', 0, 'a^7', 0, 'a^5', 0, 'a^6', 0, 'a^2', 0, 'a^9', 0, 'a^3', 0, 'a^0', 0, 'a^8', 0, 'a^11', 0], 'euler_factors': [[0], [1, 'a^3'], [1, 'a^9'], [1, 'a^2'], [1, 'a^5'], [1, 'a^7'], [1, 'a^12'], [1, 'a^7'], [1, 'a^6'], [1, 'a^3'], [1, 'a^0'], [1, 'a^1'], [1, 'a^14'], [1, 'a^13'], [1, 'a^4'], [1, 'a^13'], [1, 'a^1'], [1, 'a^11'], [1, 'a^3'], [1, 'a^2'], [1, 'a^6'], [1, 'a^12'], [1, 'a^7'], [1, 'a^2'], [1, 'a^8'], [1, 'a^1']], 'gamma_factors': [[1], []], 'index': 0, 'label': '1-2e6-64.27-r1-0-0', 'leading_term': '0.372322961497483375395073471009+1.04057296828464655599777854964*I', 'load_key': 'dirichlet', 'motivic_weight': 0, 'mu_imag': [0], 'mu_real': [1], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'origin': 'Character/Dirichlet/64/27', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 14}, 'plot_values': [1.1051771305917328, 1.6856082343733396, 2.186432100899002, 2.5340976007048437, 2.628017131810902, 2.3812005908623535, 1.7681066927100717, 0.8588580468418198, -0.1759977455823103, -1.0984818402392857, -1.6705093555348378, -1.7378368629012644, -1.3013254892683521, -0.5436365113017336, 0.2099334978604946, 0.5949196184728338, 0.34587103827829047, -0.5819384095893358, -1.961953486146155, -3.3510247761250596, -4.242957263523329, -4.269057427138474, -3.3640031871478637, -1.8186194090941834, -0.18205528584592987, 0.958881658365767, 1.2339189630532446, 0.6610513650131523, -0.3532361171753519, -1.1995438460024226, -1.3601746796670389, -0.6735267458208065, 0.5686819450526178, 1.7542775647602806, 2.2614750658519385, 1.7964793171599913, 0.5788674842250763, -0.737601603512773, -1.3866701699965764, -0.8969027778707724, 0.6321269993662464, 2.5457018014851966, 3.95196476339426, 4.183733876284127, 3.1548458884984423, 1.4071433209791564, -0.18970592886135285, -0.9248177760510228, -0.6422917995752283, 0.18853794447998615, 0.7796639206676383, 0.5328030810174252, -0.5571578768393717, -1.8609085296892358, -2.480738792300435, -1.8158632451910033, 0.01875577802680109, 2.1940273345506016, 3.6132714690622203, 3.5486382809776846, 2.0794108518377064, 0.051534703370847625, -1.430353322962089, -1.6694752297713882, -0.7826954452650274, 0.41608139532551247, 0.9821487984765817, 0.4855191934176881, -0.6957269693619053, -1.6393268146106559, -1.531783050194609, -0.2695205125570346, 1.4137092721657778, 2.404323037259353, 1.9607759585232374, 0.2509203914134726, -1.7085705126788668, -2.6961599390487527, -2.093170169320894, -0.30656561841082913, 1.4930327996907962, 2.15116985204986, 1.2966297681420205, -0.43469288892644237, -1.874344179784213, -2.1560361855411423, -1.3116910167707785, -0.19706659297247847, 0.19942158649572023, -0.44643179277353806, -1.4948113864641666, -1.7874255661046483, -0.5338427584049311, 2.012118142378835, 4.609187988290971, 5.817357663647725, 4.972838364027938, 2.6461147884683003, 0.24064035563589792, -0.9851887312031906, -0.7621089421593172, 0.09477981548581245, 0.3957614668761193, -0.45972352402473604, -2.0093946813261088, -3.1118335284846155, -2.8879942996673433, -1.4763083191627295, 0.012127109101107786, 0.33284827338886147, -0.8973365347673838, -2.8377474947995553, -4.009963941310509, -3.4113921284975683, -1.3047286457250618, 0.9406273469752515, 1.8540550585748026, 0.9520828012445639, -0.9291159840303815, -2.3110630581878038, -2.2223285091073617, -0.9110160423327227, 0.4361350457679008, 0.7230427917317108, -0.13077686645988315, -1.1386522668228132, -1.1195007665705974, 0.22765135755420382, 1.959981493041242, 2.5840355936003374, 1.2772388401869224, -1.355706266314962, -3.641079164423562, -4.065812990293887, -2.416492226553693, 0.08112201751446135, 1.7326070026282498, 1.6684671921820489, 0.41736805345970535, -0.6808888338911813, -0.6952048109173263, 0.09481039160589749, 0.4999636917168866, -0.44091473630171907, -2.48597361537995, -4.256981876644863, -4.339736152470208, -2.5043409899165954, 0.010477270062970695, 1.4378392934841333, 0.8961977288634808, -0.9016050097783502, -2.2503558719121486, -1.8723289660969975, 0.034229595631705745, 1.996224745445714, 2.5317164235526164, 1.3891156233507342, -0.2989141894129406, -1.055780863126931, -0.3616776623134274, 0.941565773821562, 1.497387184568966, 0.7647265289491779, -0.3876924289321097, -0.40359128931641797, 1.5220295043623802, 4.564370915618943, 6.779763728333814, 6.630509418012049, 4.2395368041496395, 1.2928453808912561, -0.3356399279075066, -0.05836097137309303, 1.1061109889935645, 1.595759597244357, 0.7597154027287191, -0.6099869519044213, -1.1238486707219308, -0.20406965320634557, 1.278342976186598, 1.7660477294140633, 0.5017625498901255, -1.6419873903247217, -2.8106956075106577, -1.7742319360052137, 0.9326520027601847, 3.385915117927087, 3.871068864584287, 2.306393999443467, 0.23526135582697394, -0.5883143738458281, 0.2641389607438592, 1.6156023634241632, 1.8754559524291181, 0.567729379233786, -1.2332879290744305, -1.9526601544498667, -1.0400663767343798, 0.4930392164466754, 1.0574435894871845, 0.07159784226036411, -1.376142818152269, -1.4763910386260695, 0.5720285347531895, 3.6611130262077767, 5.591240565064417, 4.922343212874342, 2.201622539441461, -0.5388803355930472, -1.5441536306273238, -0.7461989963406217, 0.4287822803528235, 0.588168380039392, -0.27344301700372164, -0.893565359756759, -0.1781335237026511, 1.500391838668819, 2.481589292685286, 1.3734534671915533, -1.4918338213046622, -4.153877766990153, -4.67660742687408, -2.8609652049746743, -0.4144682346044304, 0.6028708672671284, -0.3810274803779652, -2.0303655992367577, -2.461598863986394, -1.0597194943574926, 0.9822302460650305, 1.8787715844331487, 0.9996391526793518, -0.5706924289981381, -1.1930707996781293, -0.3761560319436762, 0.7013192513002728, 0.4032094569056319, -1.6047005186079049, -3.8284958493370933, -4.257877410808454, -2.304392288724875, 0.5170075256002836, 1.8804796083440365, 0.735602529102948, -1.7766229706304921, -3.432273045400497, -2.975288833492383, -1.1493411128070297, 0.21895998069100306, 0.09692738822175749, -0.8151198675099559, -0.9888969358422408, 0.16594884120388428, 1.542214158523328, 1.425729864865609, -0.6317480289305271, -3.0906985766500865, -3.6954098077252056, -1.5883090923270822, 1.7864121519256089, 3.91735396935801, 3.452109777129601, 1.295926932492479, -0.43108199699079974, -0.4963495289350771, 0.37077525080063967, 0.4424677516324221, -1.0632737320452803, -3.083388032346787, -3.7797579770039076, -2.460315735237613, -0.3420376248389676, 0.6695168240155971, -0.048592079371132725, -1.1632891087994675, -0.7635822305479929, 1.5686285737892103, 4.122033086614735, 4.581139526947865, 2.258439647695401, -1.1741655415852312, -3.1974929200592905, -2.720962567087444, -0.9040332366094153, 0.20650137081806186, -0.2410754104270545, -1.2302609744144255, -1.2176811966943097, 0.022725656522727008, 1.0710233278391201, 0.43534208294595966, -1.6459431986174884, -3.163659707200405, -2.2442474164774238, 0.8834186421974408, 3.910998871584882, 4.541563743672828, 2.6152087832714064, 0.16620605267977784, -0.619719257285583, 0.5242872988069682, 1.9013335741408977, 1.7743406110964604, 0.1922417393855502, -1.177778500192234, -0.9636065609458101, 0.35344658628939, 0.9400931363028008, -0.34654157572189465, -2.582978609743458, -3.614694475627113, -2.3015316312835776, 0.18101320891553307, 1.4199262680694333, 0.18398395968965578, -2.296043601010423, -3.5340217657337076, -2.270859144596391, 0.2997786470985589, 1.7913258536201748, 1.029309336872657, -0.886125151488694, -1.8860694988450122, -1.1294606363958657, 0.27437642416623464, 0.7289122899536481, 0.11239975703056049, 0.003126171097928838, 1.84184007908953, 5.020137668670649, 7.077282562772343, 5.987277311288015, 2.2407157619540046, -1.4708448891052337, -2.72306183422286, -1.5076464489652013, 0.07095433076495178, 0.12812200702415302, -1.1343127965179076, -1.9317804963659144, -1.0883347376270487, 0.5570904232194869, 1.0811377340088848, -0.3112013934838431, -2.2829700238868043, -2.7478393082109465, -1.1721745892592244, 0.7449313885905666, 0.8426602920056464, -1.1287211178313101, -3.1093812428848513, -2.8158779086711143, -0.15072256747465151, 2.6176791570711595, 3.1165782160952924, 1.2030809771225517, -1.050200225940422, -1.6156096492717142, -0.544655621087437, 0.36443224999223267, -0.2281448729226161, -1.6538719966207176, -2.077984240133012, -0.7484683211440024, 0.952134100567897, 0.9479826308977116, -1.1153491987847817, -3.196128146484371, -2.821585980484146, 0.2987628558345535, 3.802916660928656, 4.917307244695992, 3.100638004004109, 0.36554291344375733, -0.9515078233892067, -0.5076196279056827, 0.08329717892054744, -0.5811846454038081, -1.9507155779692356, -2.1990628291637617, -0.5091863314395257, 1.7161219505796754, 2.2193684439442385, 0.39698094186377475, -1.8672825278902039, -2.090074528250048, 0.1726896026511204, 2.8105161073948994, 3.374539631126085, 1.652763387159725, -0.17548256901759732, 0.051008997690599925, 2.1468762627466833, 3.8502592397361664, 3.3252512336648747, 1.0985578053853056, -0.6635997089183624, -0.619163008744953, 0.3860072729056142, 0.5733169349716076, -0.4198534904357713, -0.9129212458945424, 0.8727989130033452, 4.458789559993583, 7.121180183265621, 6.482830238353184, 2.978053834284167, -0.4993811214658315, -1.446417219852202, -0.08362240775267998, 1.2443818815821288, 0.7929235123156384, -0.8008752110918327, -1.5561853688795038, -0.6473283923921223, 0.5995785735926467, 0.3554766269095381, -1.39464212427097, -2.65904883314031, -1.7105497803731216, 0.7541016445650294, 2.1366551016810944, 0.7116976924460983, -2.3923471786791604, -4.268342521919173, -3.254802316503141, -0.616649447821271, 0.933445270347101, 0.18954107061374395, -1.394553754618863, -1.5450684158820396, 0.18449874150187887, 1.9817390407971311, 1.9704598234732378, 0.414172297539795, -0.652015170456283, 0.09840701375673142, 1.6499067866618367, 1.850201001042948, 0.10376244430550534, -1.6331960275879798, -0.8784671223159464, 2.4982646296471493, 5.8176658092643665, 6.200886722404983, 3.466668793939327, 0.18939303546280306, -1.0627399948410872, -0.2121962804410082, 0.7656105820433794, 0.4495207769576812, -0.411299810710685, -0.11416571605165426, 1.5428352966515109, 2.659985050220817, 1.3641460062359185, -1.783876023104836, -4.041228288022294, -3.3204956591955463, -0.48247335208886727, 1.5543342759945746, 0.9617514371197688, -1.0931750451595166, -1.893663689664813, -0.28464712619321453, 2.0852763160661922, 2.730633070871926, 1.1592536031504197, -0.6978764428554878, -0.8565561250241207, 0.41587409845684414, 1.0754263132433592, -0.08003958147224156, -1.8540075241120695, -2.0924993935059333, -0.438079763336373, 0.958497561864371, -0.20477368366268056, -3.5826096621873007, -6.23755538338904, -5.649967011178626, -2.377561717174566, 0.598153793741139, 1.0680851837357013, -0.26626606235624173, -0.9986624370377601, 0.02606313555110314, 1.512158722682776, 1.5468288980394465, 0.08963804439691293, -0.9856158365754779, -0.3583425438529846, 0.8328509897146069, 0.13500299944971866, -3.2030566422322306, -6.912320861795708, -7.82920194743215, -5.217284431977562, -1.5521614281760623, 0.1330335502634435, -0.6558558506855908, -1.7733643795971294, -1.2559494124680546, 0.3468470810072727, 0.8249982649302184, -0.8163382723218386, -3.001286148784553, -3.394662320311718, -1.6691699539033102, 0.14884264392351382, 0.19604624252418787, -0.9101697270714616, -0.8316419786922465, 1.483697578650698, 4.180389150824657, 4.361561884774761, 1.4134912875449546, -2.0771986323055556, -2.9764309543682956, -0.869845540509724, 1.712772226485069, 2.238747099265512, 0.8036865902928159, -0.48064053235582865, -0.3328652584849162, 0.2096748079802589, -0.5736821352034297, -2.50325866369806, -3.3557617666951454, -1.528306926934881, 1.7016679493268823, 3.2420185560554264, 1.5664914076354628, -1.4832712547937246, -2.6625410167848194, -0.8743429277859877, 1.7443847905206291, 2.3798918641402547, 0.6937762771601138, -1.0661393300219983, -0.9423099817229118, 0.4355839135667309, 0.8548045687455177, -0.5491917045652656, -2.1400891128533845, -1.8580831501142667, 0.06937228543188627, 1.228108377572031, -0.06538016544068075, -2.5634832590722754, -3.3960632461721683, -1.4599802806421915, 1.1467724741803225, 1.4514222806954369, -0.9699067460470256, -3.484422567460729, -3.4027044403359064, -0.959954786465474, 1.1527076226532984, 0.9932188304523724, -0.5816328849950594, -1.3428893045549843, -0.6090182713905944, 0.06414313623067511, -0.7704649220230935, -2.167109561342958, -1.6632257827631678, 1.5559465920341395, 5.113433599668816, 5.677205074715032, 2.5936487741584227, -1.2970438191398959, -2.679135803137142, -1.1641512841637314, 0.7602752712876886, 0.9404403496161191, -0.03350170969431025, -0.0009885527435184352, 1.7029460925213376, 3.235905069767114, 2.5598671070222414, 0.12276793837189622, -1.5384057375581552, -0.8630977510198767, 0.81122422865693, 0.9445853851774988, -0.9132389963478511, -2.3405439791594027, -0.8880247040617049, 2.809533483254556, 5.4682722284936816, 4.741625264702673, 1.7658030567851912, -0.2920586295802635, 0.1318688377127315, 1.5116071302310878, 1.4820402243296167, -0.14243812091430036, -1.3263004890261259, -0.6299170197521825, 0.8419520146642008, 0.921080756954578, -0.6016577757581294, -1.3899204248642132, 0.5988044020308758, 4.257344693886754, 6.128577781920668, 4.172978476708681, 0.12397385344386382, -2.3863944596784132, -1.7506483480825046, 0.20351104349221658, 0.7725601504468105, -0.3876136340226576, -1.2485229417291137, -0.35701523130175083, 1.1806478694263975, 1.2295924201996333, -0.3689566668643625, -1.314420821102414, 0.31276254325978337, 3.4067067922519025, 4.842132911006687, 3.0919097807719336, 0.07128478642423138, -1.1193424525906848, 0.1309476567038366, 1.3136522818645269, -0.025529596681200466, -3.19846971044232, -5.127303717272866, -3.965224888574412, -1.1491531986760422, 0.5090635178553761, 0.1650595353576431, -0.4491130802159258, 0.29290298372691753, 1.5901270001982708, 1.3562748241136382, -0.6553556390203401], 'positive_zeros': ['2.44656998648640938873141572068', '4.27839388472331745266397975185', '5.14235009109848867310069490849', '7.539438837167444740283954970009', '8.645069874168792518400732034874', '9.86526878837809648384843634027', '11.37938296760468068208422681622', '12.38866896518486383423396326418', '14.32979136291977434343983656295', '15.244416958224685984775249779457', '16.11195199447651831410475064466', '17.49731697949468422731345685312', '19.07089761928346224873064405385', '20.19654589051101055135766280229', '21.07545890993728317358027908860', '22.237575377256032388898222713749', '23.47551822105491698892062536599', '24.73510041532990546370813252904', '25.86243587807944487978069027545', '27.26643525620964289475056851352', '27.650456343804704115611823138241', '28.82584783962982068826165365337', '30.66505022846507803303115787116', '31.525045672629872775720854175077', '32.06719031561098739416560107966', '33.74647355252718569401229823103', '34.18891314025999147857127669258', '35.794189192966329681613130630174', '36.72566220263719005623537733538', '38.00502771005023372830022694653', '38.71409202332360548675999253353', '39.64681494916869828859856455232', '40.78527212382066114886988021813', '42.176673408710583047716801030868', '43.22137670062412320155452092829', '44.0272364711465303576426233841', '44.59274315154972373315413083938', '46.24853687764699423665303953583', '47.04049432364350528518813201586', '48.12020603998203084516614425356', '49.31339252014223739531956685792', '50.08697481978525225498980660106', '51.13114559633403764401729432270', '51.66121685572885758478581160787', '53.64294113949134029328178135396', '54.08048205604765388962727222971', '55.16751128155535125128950933560', '55.98034916545451888780137067614', '56.95046653873181520506616786435', '58.026213966782506544739676159621', '59.42219256767525793734420923555', '59.937653874293738239101457508192', '61.03167315992281398706975066868', '62.079766664746460824320570569', '62.82716527410973347530012884825', '63.6853892652627094416576407316', '65.23811093784478799377547751375', '66.11862901928909641163437525936', '66.79043559729682179206209477350', '67.53799023126843808341756921792', '68.600258549887345701055101016352', '70.071800263872953716632623461304', '70.54778323803848691346167780590', '71.71852800666348605008996219858', '72.69254119975821193942875672648', '73.53064437330346435244634092122', '74.14607801381367847079784400042', '75.56237679898922438221605342595', '76.34710784711522892386100205312', '77.732861486742052428101353609896', '78.1624496664716188658343655920', '79.02893615479205061327471617404', '79.92297954977104180989420647048', '81.08488352232286495388676536780', '82.39221551348647732911268425654', '82.9923213864856561708629133715', '83.56434744232845574273020110481', '85.06295592709599255292324965611', '85.61286098442884787633785558501', '86.37594121775661196589331600130', '87.70187670694866363623035053645', '88.95518001093701614002770767584', '89.291389224178958435829095460001', '90.307641516899369617364855989826', '91.01443466332430348914446553809', '92.109344532608272750976996576626', '93.466718869101157746099389163294', '93.956324625986032155172037998224', '95.0335984863868419475096823762', '95.85595664792959850956857682023', '96.50781167256240443873166748886', '97.78785118188532161988065954500', '98.46251302449356202180377792004', '99.6495552021143338951067063458', '100.48138382280069970530288408713', '101.49290458848711672696099913230', '102.242361922890839878001749729786', '102.49870083735369106284154251900', '104.23434503065037385018924726876', '105.29126703217801320520828981359', '105.66827183846239335954641512070', '106.76336802507148408352196029605', '107.45105759731401967675566170065', '108.6094032830823758949769688596', '109.22259843141489960657525574209', '110.327199995403429138177756510291', '111.40079508332789734051256283782', '112.32734169372540356098689034714', '112.752302956357391698796062392493', '113.87234672310396371775102739469', '114.544089178196913831315736093365', '115.600593295551269749464945762186', '116.92806197150503445948418080194', '117.71586305866611030953099278245', '117.92943210645205496382141710351', '119.12895376607188441158931278143', '120.04897961960722875514925544901', '120.91902245735852640513106054364', '122.14083971763833512911153626798', '122.488515559531806685671421706310', '123.91107682817176957558434102166', '124.56507386755612368854761613333', '125.19955883526646137086377769745', '125.8342277906983492937567093689', '127.44197523309046819911803068528', '128.13966876794822673147179818185', '128.909382162431931083614993303587', '129.82799825946454203584391914345', '130.39145806620478788511009036997', '131.46890339187708680542373134774', '132.26446471402583965128897698574', '133.52071051890124349988742746894', '134.09901501994471043017239941174', '134.97334378973487145969620553457', '136.01920295343390834936956318115', '136.5415711500298432108986940418', '137.51461113298541510088015636164', '138.224675799458602572727359648008', '139.71177357889860528658185780324', '140.36404466353582683503488549107', '141.0846658394659957520933198553', '141.591667099489976449196752807049', '142.64428148607752775520177461768', '143.80286401394858877705920231227', '144.52357967266092668005449504769', '145.34832548501905977093697439174', '146.423656101932275465575426314556', '147.09462369134747313743083123005', '147.79877038661080797063756285450', '148.81990449236433389413298505620', '149.349476851484434718656724387719', '150.85362026357070764644745745871', '151.506072873422412083224808593594', '152.18246439518106229866179766518', '153.14229831732488711937935893175', '153.83217421677994645954221847653', '154.39376952552568880185492095769', '156.1776473880197480639015218127', '156.38783624237329634826906972532', '157.42889744674069958975261165271', '158.00706509928048191452682597240', '159.3361016321637819678437062115', '159.75012018756833742791080446425', '160.455569193622075120667030739281', '161.67727067947368589249912422955', '162.59343101390786992523792465170', '163.59619145949178315354187765791', '164.21098480702259553254392333573', '164.54496630706088610013135943130', '165.7720933392505345458847903096', '166.71865251325149971250378015043', '167.596674764623668045232530208784', '168.538538914066469159901445950964', '169.27649363654995778018303517356', '169.906805526036590423998819204428', '170.92674051962792371778338004606', '171.55370920968153369462854411419', '172.65956044308109182528457313833', '173.33523183341317222388996813277', '174.488680103494458233426915896638', '175.20027522875786103431710162581', '176.162973251992490600603220854804', '176.333193277608404638818002422150', '177.37209080693428791394619342812', '178.63342415210230155974601451538', '179.54175856197450378681422692091', '180.29977824558465686314516437130', '180.62530972459835154564468474675', '181.8904563864159142105371769058', '182.65257384319772891199000042698', '183.30606203594003635963325519295', '184.14673196649817540578817385634', '185.54581975897526493217837645219', '185.90553710053216162849197426987', '186.85056461578164467936142619960', '187.62534617843590741612896218437', '188.32805285143991155393198150802', '189.0021875779879441847287918915', '190.32268034621959340665178686855', '191.212158399060639030282738057123', '191.79038563589429029916240869386', '192.567519317215181545362410762118', '193.37339464669461871024250345477', '194.02649022743466271493363606120', '195.32147451093350346816925863959', '195.91440109920632791224966179793', '196.55950035205467574555470732746', '197.97789911744755904526759613565', '198.495763659591831164428503456699', '198.98989135110319332992172059712', '199.90918398918349593591769306627'], 'prelabel': '1-2e6-64.27-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.877755186856001, 'root_angle': 0.390625, 'root_number': '-0.773010453362736960810906609758+0.634393284163645498215171613226*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.390625', 'prec': 20}, 'spectral_label': 'r1-0', 'st_group': 'mu(16)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.820861585559717786957565912744+0.475446994151398019688330548629*I']], 'z1': {'__RealLiteral__': 0, 'data': '2.44656998649', 'prec': 40}, 'z2': {'__RealLiteral__': 0, 'data': '4.27839388472', 'prec': 40}, 'z3': {'__RealLiteral__': 0, 'data': '5.1423500911', 'prec': 37}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 6.877755186856001, 'bad_primes': [2], 'central_character': '64.27', 'conductor': 64, 'conductor_radical': 2, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/64/27'], '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': '1-2e6-64.27-r1-0-0', 'motivic_weight': 0, 'mu_imag': [0], 'mu_real': [1], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'prelabel': '1-2e6-64.27-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.877755186856001, 'root_angle': 0.390625, 'self_dual': False, 'spectral_label': 'r1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.44656998649', 'prec': 40}}
  • lfunc_instances • Show schema
    {'Lhash': 'dirichlet_L_64.27', 'Lhash_array': ['dirichlet_L_64.27'], 'factors': ['1-2e6-64.27-r1-0-0'], 'label': '1-2e6-64.27-r1-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/64/27'}