LMFDB - Embedded newform 2.88.a.b.1.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [2,88,Mod(1,2)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("2.1"); S:= CuspForms(chi, 88); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(2, base_ring=CyclotomicField(1)) chi = DirichletCharacter(H, H._module([])) N = Newforms(chi, 88, names="a")

Level:	$ N $	$=$	$ 2 $
Weight:	$ k $	$=$	$ 88 $
Character orbit:	$[\chi]$	$=$	2.a (trivial)

Newform invariants

comment:select newform

sage:traces = [4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$95.8667262922$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\mathbb{Q}[x]/(x^{4} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 2 x^{3} + \cdots + 13\!\cdots\!68 $ x^4 - 2x^3 - 281103089248735483936525960163617359x^2 - 12802046688892212650602531506830185803155982810145588*x + 13431538901013885043865389957038837902382364731827315409437340098095268
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{45}\cdot 3^{15}\cdot 5^{4}\cdot 7^{2}\cdot 11\cdot 17\cdot 29 $
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$-3.01536e17$ of defining polynomial
Character	$\chi$	$=$	2.1

$q$-expansion

comment:q-expansion

sage:f.q_expansion() # note that sage often uses an isomorphic number field

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-8.79609e12 q^{2} +6.79758e20 q^{3} +7.73713e25 q^{4} -4.34651e30 q^{5} -5.97921e33 q^{6} -6.14091e36 q^{7} -6.80565e38 q^{8} +1.38813e41 q^{9} +3.82323e43 q^{10} -1.67749e44 q^{11} +5.25937e46 q^{12} -5.67978e48 q^{13} +5.40160e49 q^{14} -2.95458e51 q^{15} +5.98631e51 q^{16} -3.24957e53 q^{17} -1.22101e54 q^{18} -3.75237e55 q^{19} -3.36295e56 q^{20} -4.17433e57 q^{21} +1.47553e57 q^{22} -8.77213e56 q^{23} -4.62619e59 q^{24} +1.24298e61 q^{25} +4.99599e61 q^{26} -1.25378e62 q^{27} -4.75130e62 q^{28} -3.59415e63 q^{29} +2.59887e64 q^{30} +8.67588e64 q^{31} -5.26561e64 q^{32} -1.14029e65 q^{33} +2.85835e66 q^{34} +2.66916e67 q^{35} +1.07401e67 q^{36} +1.92264e68 q^{37} +3.30062e68 q^{38} -3.86088e69 q^{39} +2.95808e69 q^{40} -2.04884e70 q^{41} +3.67178e70 q^{42} -7.22234e70 q^{43} -1.29789e70 q^{44} -6.03351e71 q^{45} +7.71605e69 q^{46} +4.35922e72 q^{47} +4.06924e72 q^{48} +4.32746e72 q^{49} -1.09334e74 q^{50} -2.20892e74 q^{51} -4.39452e74 q^{52} -1.03415e75 q^{53} +1.10284e75 q^{54} +7.29122e74 q^{55} +4.17929e75 q^{56} -2.55070e76 q^{57} +3.16145e76 q^{58} +1.10058e77 q^{59} -2.28599e77 q^{60} +4.36957e77 q^{61} -7.63139e77 q^{62} -8.52436e77 q^{63} +4.63168e77 q^{64} +2.46873e79 q^{65} +1.00301e78 q^{66} -4.97389e79 q^{67} -2.51423e79 q^{68} -5.96292e77 q^{69} -2.34781e80 q^{70} +2.94585e80 q^{71} -9.44710e79 q^{72} -7.53278e80 q^{73} -1.69118e81 q^{74} +8.44928e81 q^{75} -2.90325e81 q^{76} +1.03013e81 q^{77} +3.39606e82 q^{78} -2.58168e82 q^{79} -2.60196e82 q^{80} -1.30099e83 q^{81} +1.80218e83 q^{82} -6.62340e82 q^{83} -3.22973e83 q^{84} +1.41243e84 q^{85} +6.35284e83 q^{86} -2.44315e84 q^{87} +1.14164e83 q^{88} -8.08787e84 q^{89} +5.30713e84 q^{90} +3.48790e85 q^{91} -6.78711e82 q^{92} +5.89750e85 q^{93} -3.83441e85 q^{94} +1.63097e86 q^{95} -3.57934e85 q^{96} +7.41293e85 q^{97} -3.80648e85 q^{98} -2.32856e85 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 35184372088832 q^{2} + 40\!\cdots\!28 q^{3} + 30\!\cdots\!56 q^{4} - 40\!\cdots\!60 q^{5} - 35\!\cdots\!24 q^{6} + 85\!\cdots\!04 q^{7} - 27\!\cdots\!48 q^{8} + 82\!\cdots\!48 q^{9} + 35\!\cdots\!80 q^{10}+ \cdots + 22\!\cdots\!76 q^{99}+O(q^{100}) $ 4 * q - 35184372088832 * q^2 + 403237985254067182128 * q^3 + 309485009821345068724781056 * q^4 - 4037922390733497835169570162760 * q^5 - 3546918828382512738768149884698624 * q^6 + 8582179387397492406597229487230375904 * q^7 - 2722258935367507707706996859454145691648 * q^8 + 820135434884318664352221575507492568732948 * q^9 + 35517940965348365626859729845107910854574080 * q^10 + 2970616434026495781757184460756379040517208848 * q^11 + 31199027956673594964608194726311446315419041792 * q^12 - 1767394568818848613362028589161957028533441611112 * q^13 - 75489648224824411010546555477731971328955260076032 * q^14 + 3370976843124805373452544557684295582910726697502880 * q^15 + 23945242826029513411849172299223580994042798784118784 * q^16 - 702353032002195299447255515013113779135644499293109816 * q^17 - 7213987576051478951188874632704563580254297738585309184 * q^18 + 38051210330377980576900552965948384772060949611758270960 * q^19 - 312419112688496434410317985513745659312699567327821168640 * q^20 - 2960768946346244712423575885216855505816696171119080255872 * q^21 - 26129818486996871127304316256231512888117802859237038096384 * q^22 + 267410844513343534387094489566271409098947974355011539188128 * q^23 - 274429552109368924814832586348763817236857825346144736116736 * q^24 + 26866935732372298920001618987293695975686810093231631671755100 * q^25 + 15546167034275791140382436144471296993092547711081656715575296 * q^26 + 98351974670575379028284146601861806526822489553847883125490400 * q^27 + 664013967999314535695892002534007752932295679741402958744518656 * q^28 - 936377285291713459807588765220376016646503474372565915415382440 * q^29 - 29651425887834852403903990749669038123824799034099618745983959040 * q^30 + 119463507882721430244886842916392661099853847057206322986794525568 * q^31 - 210624583337114373395836055367340864637790190801098222508621955072 * q^32 - 975951433415384517573045287992141578476030063995050605617360966464 * q^33 + 6177962603921142192805661314942895498269819437765021241050270793728 * q^34 + 14105085028850567766840711566409137394874532315214531645239547531840 * q^35 + 63454905780001617731151046382612710619432714548573512194720658358272 * q^36 + 182087106643248709136261820106869557597167548749803025400276539121464 * q^37 - 334701985673606721323645108291715305922613643471269213861286961479680 * q^38 - 5157167650299694789254850025641525408739411563899847457339313757250784 * q^39 + 2748067577123698321827685975535901419950085077291708477942376033157120 * q^40 + 5499251594717860286021866958065054045901150247706209838765933372175208 * q^41 + 26043199069326335451693431452427559455621627547084532573326442418405376 * q^42 - 157807090931211109929865823295822094205785343123733495078770527721821552 * q^43 + 229840314065034778104010119086398472312972227124835062038272769756495872 * q^44 - 1370445036354823659067923168385609449595471872659192002945296358462825320 * q^45 - 2352170663486569504369914341681047401963148037857733129248014646193946624 * q^46 - 11700969700600051870794491472787906623524149540240126773037581150641555136 * q^47 + 2413907868396886727226140291242059049083751312718584875630451012128473088 * q^48 + 45608750768809825384693277965554885824930550141562503946687984691665533732 * q^49 - 236324065923630760668657815178197122585685320681456781276991408990637260800 * q^50 - 914883468555652107825206155517190576830844787740672822262980556765469169312 * q^51 - 136745531372273324016576733538944106078280970896210682631976284458024173568 * q^52 - 3205407327892231366350098762423033970241498041998526172742677864692608514312 * q^53 - 865113118120226050927175001395744751092084611954848335836798017458090803200 * q^54 - 10009926131406218736826424103970095109094189414661383153140158173941128709920 * q^55 - 5840728630567416793561662980979737449788739679624018831289026246209278312448 * q^56 + 24760562583447132282306921710743074800398451150699602451361304490068034752320 * q^57 + 8236461705308510473577685400040524235406303263089755599489781422351733227520 * q^58 - 81401388903576961577929700275194040780233584053778446123485310614164754536880 * q^59 + 260816700350501796503049467891128405126358446664151554703502613334842482360320 * q^60 + 908111889319782669823282318823295371554753169091641506977419705876741077882328 * q^61 - 1050812128095696376586514967647428079039044942828517372626320439677738647814144 * q^62 + 7137835102413627130280079665652016586382162073538425059614697312278117344350048 * q^63 + 1852673427797059126777135760139006525652319754650249024631321344126610074238976 * q^64 + 11407211919915638593357605065156231994296813060854399078385375214171172364857680 * q^65 + 8584559593478959280621500012652850349171438888492092327918713325137577495232512 * q^66 - 65059771693644954593974794228917141656005263924052931483321156753263176566322896 * q^67 - 54341933751812724902023253670568124974314494093364989057139191298059718491111424 * q^68 - 144323666676858272713465642347149842097884989245184653886655055101689375583845504 * q^69 - 124069639999923005500646624090308971041908232841505948959254386145464972707102720 * q^70 - 183272612160344892942190287282961718510131375557583525213035115209249713064136992 * q^71 - 558155253956338317275929527602177423655680841848067355296117578760944212116504576 * q^72 + 354182538046550765754528347144724476790476600029207619306415675742769571814637288 * q^73 - 1601655128178723932025775974507397068426901430503198065737820251919877020961472512 * q^74 + 710386439551323791969874648476083944602337020291621916942901745237698809202501200 * q^75 + 2944069800702774064027323538684509525361173924971530627370715914294143730780733440 * q^76 + 39316760279456924611775164190833990669200449799501752350802186925973327788597118848 * q^77 + 45362926383157972415756683406366951526581873158623352931657948697548800307937411072 * q^78 + 15689408650300008287770111864298279692820798574497171271867094782550105530843081920 * q^79 - 24172258039693807695503348146758763873414302432021545297363850106765398076513320960 * q^80 - 196590592451401107987710944406206415161857917104016937408869683425180184810203702876 * q^81 - 48371928579663987252349183028740936842481506637169603120359663272770590191611019264 * q^82 + 111926752599709260117886233216331177095176580206068162806299107496899925996223203568 * q^83 - 229078401609675258913891688255885614430188449105962531942162006259872232223914590208 * q^84 - 891497844731417844264766892389844899904478293183670323386186444763703698463839596560 * q^85 + 1388085851394969400976659588554077855842466084275351230019781346209556380442549026816 * q^86 + 2027498154029213080175869882525768385333184769847411190333977363043382754362186713120 * q^87 - 2021696782769547651193529032558892722193566089333659035337753899891686714980356325376 * q^88 - 1111763274969003683091618237538433748811411444468148051875571331333583253595104867160 * q^89 + 12054562021600253271129669326554918303828197627410649510778436683009490086217184706560 * q^90 + 79630263055292573954918630151432006426386375686727482380289693283976606755116980321088 * q^91 + 20689911960136575706111408504507326985128933416561732998791094227623959804415198625792 * q^92 + 121552396376548026998325328889505560359171182104366398760596365823334350324441379006976 * q^93 + 102922817936515347171258282828953462563508237397083710417081191671708730834331304460288 * q^94 + 360329377379389097240594968925389763617374668200294178024200943546627617266362721242400 * q^95 - 21232958157458842504504822471050360495135888697596704547293213652627233307394314338304 * q^96 + 84654632295309208342666811638631082612402959416215649507302559581340331556342797429384 * q^97 - 401178814389151860471251451603139889379513741986404607571754642978513123633817249120256 * q^98 + 2203878007770692926523827334498155512549713414229081953932986276578630523661724303178576 * q^99

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−8.79609e12	−0.707107
$2$	−8.79609e12	−0.707107
$3$	6.79758e20	1.19558	0.597791	−	0.801652i	$-0.296045\pi$
$3$	6.79758e20	1.19558	0.597791	+	0.801652i	$0.296045\pi$
$4$	7.73713e25	0.500000
$5$	−4.34651e30	−1.70980	−0.854901	−	0.518791i	$-0.826382\pi$
$5$	−4.34651e30	−1.70980	−0.854901	+	0.518791i	$0.826382\pi$
$6$	−5.97921e33	−0.845404
$7$	−6.14091e36	−1.06284	−0.531420	−	0.847108i	$-0.678341\pi$
$7$	−6.14091e36	−1.06284	−0.531420	+	0.847108i	$0.678341\pi$
$8$	−6.80565e38	−0.353553
$9$	1.38813e41	0.429418
$10$	3.82323e43	1.20901
$11$	−1.67749e44	−0.0839610	−0.0419805	−	0.999118i	$-0.513367\pi$
$11$	−1.67749e44	−0.0839610	−0.0419805	+	0.999118i	$0.513367\pi$
$12$	5.25937e46	0.597791
$13$	−5.67978e48	−1.98516	−0.992581	−	0.121583i	$-0.961203\pi$
$13$	−5.67978e48	−1.98516	−0.992581	+	0.121583i	$0.961203\pi$
$14$	5.40160e49	0.751542
$15$	−2.95458e51	−2.04421
$16$	5.98631e51	0.250000
$17$	−3.24957e53	−0.971176	−0.485588	−	0.874188i	$-0.661394\pi$
$17$	−3.24957e53	−0.971176	−0.485588	+	0.874188i	$0.661394\pi$
$18$	−1.22101e54	−0.303644
$19$	−3.75237e55	−0.888227	−0.444113	−	0.895971i	$-0.646481\pi$
$19$	−3.75237e55	−0.888227	−0.444113	+	0.895971i	$0.646481\pi$
$20$	−3.36295e56	−0.854901
$21$	−4.17433e57	−1.27071
$22$	1.47553e57	0.0593694
$23$	−8.77213e56	−0.00510439	−0.00255220	−	0.999997i	$-0.500812\pi$
$23$	−8.77213e56	−0.00510439	−0.00255220	+	0.999997i	$0.500812\pi$
$24$	−4.62619e59	−0.422702
$25$	1.24298e61	1.92342
$26$	4.99599e61	1.40372
$27$	−1.25378e62	−0.682178
$28$	−4.75130e62	−0.531420
$29$	−3.59415e63	−0.873542	−0.436771	−	0.899573i	$-0.643878\pi$
$29$	−3.59415e63	−0.873542	−0.436771	+	0.899573i	$0.643878\pi$
$30$	2.59887e64	1.44547
$31$	8.67588e64	1.15899	0.579495	−	0.814976i	$-0.303250\pi$
$31$	8.67588e64	1.15899	0.579495	+	0.814976i	$0.303250\pi$
$32$	−5.26561e64	−0.176777
$33$	−1.14029e65	−0.100382
$34$	2.85835e66	0.686725
$35$	2.66916e67	1.81725
$36$	1.07401e67	0.214709
$37$	1.92264e68	1.16714	0.583571	−	0.812062i	$-0.301655\pi$
$37$	1.92264e68	1.16714	0.583571	+	0.812062i	$0.301655\pi$
$38$	3.30062e68	0.628071
$39$	−3.86088e69	−2.37343
$40$	2.95808e69	0.604506
$41$	−2.04884e70	−1.43025	−0.715124	−	0.698998i	$-0.753630\pi$
$41$	−2.04884e70	−1.43025	−0.715124	+	0.698998i	$0.753630\pi$
$42$	3.67178e70	0.898530
$43$	−7.22234e70	−0.635039	−0.317519	−	0.948252i	$-0.602850\pi$
$43$	−7.22234e70	−0.635039	−0.317519	+	0.948252i	$0.602850\pi$
$44$	−1.29789e70	−0.0419805
$45$	−6.03351e71	−0.734219
$46$	7.71605e69	0.00360935
$47$	4.35922e72	0.800115	0.400057	−	0.916490i	$-0.368990\pi$
$47$	4.35922e72	0.800115	0.400057	+	0.916490i	$0.368990\pi$
$48$	4.06924e72	0.298896
$49$	4.32746e72	0.129630
$50$	−1.09334e74	−1.36007
$51$	−2.20892e74	−1.16112
$52$	−4.39452e74	−0.992581
$53$	−1.03415e75	−1.01996	−0.509979	−	0.860187i	$-0.670347\pi$
$53$	−1.03415e75	−1.01996	−0.509979	+	0.860187i	$0.670347\pi$
$54$	1.10284e75	0.482373
$55$	7.29122e74	0.143557
$56$	4.17929e75	0.375771
$57$	−2.55070e76	−1.06195
$58$	3.16145e76	0.617687
$59$	1.10058e77	1.02225	0.511126	−	0.859506i	$-0.329228\pi$
$59$	1.10058e77	1.02225	0.511126	+	0.859506i	$0.329228\pi$
$60$	−2.28599e77	−1.02210
$61$	4.36957e77	0.951898	0.475949	−	0.879473i	$-0.342105\pi$
$61$	4.36957e77	0.951898	0.475949	+	0.879473i	$0.342105\pi$
$62$	−7.63139e77	−0.819530
$63$	−8.52436e77	−0.456402
$64$	4.63168e77	0.125000
$65$	2.46873e79	3.39424
$66$	1.00301e78	0.0709810
$67$	−4.97389e79	−1.82996	−0.914982	−	0.403495i	$-0.867795\pi$
$67$	−4.97389e79	−1.82996	−0.914982	+	0.403495i	$0.867795\pi$
$68$	−2.51423e79	−0.485588
$69$	−5.96292e77	−0.00610272
$70$	−2.34781e80	−1.28499
$71$	2.94585e80	0.869907	0.434954	−	0.900453i	$-0.356765\pi$
$71$	2.94585e80	0.869907	0.434954	+	0.900453i	$0.356765\pi$
$72$	−9.44710e79	−0.151822
$73$	−7.53278e80	−0.664371	−0.332186	−	0.943214i	$-0.607786\pi$
$73$	−7.53278e80	−0.664371	−0.332186	+	0.943214i	$0.607786\pi$
$74$	−1.69118e81	−0.825294
$75$	8.44928e81	2.29961
$76$	−2.90325e81	−0.444113
$77$	1.03013e81	0.0892371
$78$	3.39606e82	1.67827
$79$	−2.58168e82	−0.733035	−0.366517	−	0.930411i	$-0.619450\pi$
$79$	−2.58168e82	−0.733035	−0.366517	+	0.930411i	$0.619450\pi$
$80$	−2.60196e82	−0.427451
$81$	−1.30099e83	−1.24502
$82$	1.80218e83	1.01134
$83$	−6.62340e82	−0.219373	−0.109687	−	0.993966i	$-0.534985\pi$
$83$	−6.62340e82	−0.219373	−0.109687	+	0.993966i	$0.534985\pi$
$84$	−3.22973e83	−0.635357
$85$	1.41243e84	1.66052
$86$	6.35284e83	0.449040
$87$	−2.44315e84	−1.04439
$88$	1.14164e83	0.0296847
$89$	−8.08787e84	−1.28638	−0.643190	−	0.765707i	$-0.722389\pi$
$89$	−8.08787e84	−1.28638	−0.643190	+	0.765707i	$0.722389\pi$
$90$	5.30713e84	0.519171
$91$	3.48790e85	2.10991
$92$	−6.78711e82	−0.00255220
$93$	5.89750e85	1.38567
$94$	−3.83441e85	−0.565767
$95$	1.63097e86	1.51869
$96$	−3.57934e85	−0.211351
$97$	7.41293e85	0.278881	0.139441	−	0.990230i	$-0.455470\pi$
$97$	7.41293e85	0.278881	0.139441	+	0.990230i	$0.455470\pi$
$98$	−3.80648e85	−0.0916619
$99$	−2.32856e85	−0.0360543
$100$	9.61712e86	0.961712
$101$	−2.60860e86	−0.169210	−0.0846052	−	0.996415i	$-0.526963\pi$
$101$	−2.60860e86	−0.169210	−0.0846052	+	0.996415i	$0.526963\pi$
$102$	1.94299e87	0.821036
$103$	4.72641e87	1.30651	0.653255	−	0.757138i	$-0.273403\pi$
$103$	4.72641e87	1.30651	0.653255	+	0.757138i	$0.273403\pi$
$104$	3.86546e87	0.701861
$105$	1.81438e88	2.17267
$106$	9.09645e87	0.721219
$107$	1.61333e88	0.850214	0.425107	−	0.905143i	$-0.360237\pi$
$107$	1.61333e88	0.850214	0.425107	+	0.905143i	$0.360237\pi$
$108$	−9.70066e87	−0.341089
$109$	−1.41091e88	−0.332237	−0.166118	−	0.986106i	$-0.553123\pi$
$109$	−1.41091e88	−0.332237	−0.166118	+	0.986106i	$0.553123\pi$
$110$	−6.41343e87	−0.101510
$111$	1.30693e89	1.39541
$112$	−3.67614e88	−0.265710
$113$	1.00725e89	0.494568	0.247284	−	0.968943i	$-0.420462\pi$
$113$	1.00725e89	0.494568	0.247284	+	0.968943i	$0.420462\pi$
$114$	2.24362e89	0.750911
$115$	3.81282e87	0.00872751
$116$	−2.78084e89	−0.436771
$117$	−7.88426e89	−0.852464
$118$	−9.68079e89	−0.722842
$119$	1.99553e90	1.03220
$120$	2.01078e90	0.722737
$121$	−3.96361e90	−0.992951
$122$	−3.84351e90	−0.673094
$123$	−1.39272e91	−1.70998
$124$	6.71264e90	0.579495
$125$	−2.59378e91	−1.57887
$126$	7.49810e90	0.322725
$127$	8.95680e90	0.273332	0.136666	−	0.990617i	$-0.456361\pi$
$127$	8.95680e90	0.273332	0.136666	+	0.990617i	$0.456361\pi$
$128$	−4.07407e90	−0.0883883
$129$	−4.90944e91	−0.759241
$130$	−2.17151e92	−2.40009
$131$	1.37183e90	0.0108643	0.00543213	−	0.999985i	$-0.498271\pi$
$131$	1.37183e90	0.0108643	0.00543213	+	0.999985i	$0.498271\pi$
$132$	−8.82253e90	−0.0501911
$133$	2.30430e92	0.944043
$134$	4.37508e92	1.29398
$135$	5.44958e92	1.16639
$136$	2.21154e92	0.343362
$137$	8.10926e92	0.915454	0.457727	−	0.889093i	$-0.348664\pi$
$137$	8.10926e92	0.915454	0.457727	+	0.889093i	$0.348664\pi$
$138$	5.24504e90	0.00431528
$139$	−3.11537e93	−1.87226	−0.936129	−	0.351657i	$-0.885618\pi$
$139$	−3.11537e93	−1.87226	−0.936129	+	0.351657i	$0.885618\pi$
$140$	2.06516e93	0.908623
$141$	2.96322e93	0.956603
$142$	−2.59120e93	−0.615117
$143$	9.52777e92	0.166676
$144$	8.30975e92	0.107354
$145$	1.56220e94	1.49358
$146$	6.62590e93	0.469782
$147$	2.94163e93	0.154983
$148$	1.48757e94	0.583571
$149$	−1.64118e94	−0.480345	−0.240172	−	0.970730i	$-0.577204\pi$
$149$	−1.64118e94	−0.480345	−0.240172	+	0.970730i	$0.577204\pi$
$150$	−7.43206e94	−1.62607
$151$	−7.33524e93	−0.120204	−0.0601018	−	0.998192i	$-0.519143\pi$
$151$	−7.33524e93	−0.120204	−0.0601018	+	0.998192i	$0.519143\pi$
$152$	2.55373e94	0.314036
$153$	−4.51081e94	−0.417040
$154$	−9.06112e93	−0.0631002
$155$	−3.77098e95	−1.98165
$156$	−2.98721e95	−1.18671
$157$	3.00151e95	0.903034	0.451517	−	0.892262i	$-0.350883\pi$
$157$	3.00151e95	0.903034	0.451517	+	0.892262i	$0.350883\pi$
$158$	2.27087e95	0.518334
$159$	−7.02969e95	−1.21944
$160$	2.28871e95	0.302253
$161$	5.38689e93	0.00542516
$162$	1.14436e96	0.880361
$163$	1.45478e95	0.0856319	0.0428160	−	0.999083i	$-0.486367\pi$
$163$	1.45478e95	0.0856319	0.0428160	+	0.999083i	$0.486367\pi$
$164$	−1.58522e96	−0.715124
$165$	4.95627e95	0.171634
$166$	5.82600e95	0.155120
$167$	3.66655e96	0.751781	0.375891	−	0.926664i	$-0.377337\pi$
$167$	3.66655e96	0.751781	0.375891	+	0.926664i	$0.377337\pi$
$168$	2.84090e96	0.449265
$169$	2.40740e97	2.94087
$170$	−1.24239e97	−1.17416
$171$	−5.20876e96	−0.381420
$172$	−5.58802e96	−0.317519
$173$	1.01328e97	0.447429	0.223715	−	0.974655i	$-0.428182\pi$
$173$	1.01328e97	0.447429	0.223715	+	0.974655i	$0.428182\pi$
$174$	2.14902e97	0.738496
$175$	−7.63305e97	−2.04429
$176$	−1.00420e96	−0.0209902
$177$	7.48126e97	1.22219
$178$	7.11417e97	0.909608
$179$	−9.68670e97	−0.970665	−0.485332	−	0.874330i	$-0.661301\pi$
$179$	−9.68670e97	−0.970665	−0.485332	+	0.874330i	$0.661301\pi$
$180$	−4.66820e97	−0.367110
$181$	4.41829e97	0.273046	0.136523	−	0.990637i	$-0.456407\pi$
$181$	4.41829e97	0.273046	0.136523	+	0.990637i	$0.456407\pi$
$182$	−3.06799e98	−1.49193
$183$	2.97025e98	1.13807
$184$	5.97000e95	0.00180468
$185$	−8.35680e98	−1.99558
$186$	−5.18749e98	−0.979816
$187$	5.45111e97	0.0815409
$188$	3.37279e98	0.400057
$189$	7.69936e98	0.725047
$190$	−1.43462e99	−1.07388
$191$	−2.08156e99	−1.24005	−0.620023	−	0.784584i	$-0.712877\pi$
$191$	−2.08156e99	−1.24005	−0.620023	+	0.784584i	$0.712877\pi$
$192$	3.14842e98	0.149448
$193$	4.86239e99	1.84123	0.920613	−	0.390476i	$-0.127689\pi$
$193$	4.86239e99	1.84123	0.920613	+	0.390476i	$0.127689\pi$
$194$	−6.52048e98	−0.197199
$195$	1.67814e100	4.05809
$196$	3.34821e98	0.0648148
$197$	−7.68392e99	−1.19207	−0.596036	−	0.802958i	$-0.703258\pi$
$197$	−7.68392e99	−1.19207	−0.596036	+	0.802958i	$0.703258\pi$
$198$	2.04823e98	0.0254943
$199$	1.02187e100	1.02161	0.510805	−	0.859696i	$-0.329347\pi$
$199$	1.02187e100	1.02161	0.510805	+	0.859696i	$0.329347\pi$
$200$	−8.45931e99	−0.680033
$201$	−3.38104e100	−2.18787
$202$	2.29455e99	0.119650
$203$	2.20714e100	0.928436
$204$	−1.70907e100	−0.580560
$205$	8.90533e100	2.44544
$206$	−4.15740e100	−0.923842
$207$	−1.21768e98	−0.00219192
$208$	−3.40010e100	−0.496291
$209$	6.29455e99	0.0745764
$210$	−1.59594e101	−1.53631
$211$	−1.41371e101	−1.10681	−0.553405	−	0.832912i	$-0.686672\pi$
$211$	−1.41371e101	−1.10681	−0.553405	+	0.832912i	$0.686672\pi$
$212$	−8.00133e100	−0.509979
$213$	2.00247e101	1.04005
$214$	−1.41910e101	−0.601192
$215$	3.13920e101	1.08579
$216$	8.53279e100	0.241186
$217$	−5.32778e101	−1.23182
$218$	1.24105e101	0.234927
$219$	−5.12047e101	−0.794311
$220$	5.64131e100	0.0717783
$221$	1.84569e102	1.92794
$222$	−1.14959e102	−0.986707
$223$	1.25702e102	0.887318	0.443659	−	0.896196i	$-0.353680\pi$
$223$	1.25702e102	0.887318	0.443659	+	0.896196i	$0.353680\pi$
$224$	3.23357e101	0.187885
$225$	1.72542e102	0.825952
$226$	−8.85988e101	−0.349712
$227$	3.80337e101	0.123892	0.0619460	−	0.998080i	$-0.480269\pi$
$227$	3.80337e101	0.123892	0.0619460	+	0.998080i	$0.480269\pi$
$228$	−1.97351e102	−0.530974
$229$	8.36483e102	1.86043	0.930216	−	0.367012i	$-0.119619\pi$
$229$	8.36483e102	1.86043	0.930216	+	0.367012i	$0.119619\pi$
$230$	−3.35379e100	−0.00617128
$231$	7.00239e101	0.106690
$232$	2.44605e102	0.308844
$233$	−8.88439e102	−0.930347	−0.465174	−	0.885219i	$-0.654008\pi$
$233$	−8.88439e102	−0.930347	−0.465174	+	0.885219i	$0.654008\pi$
$234$	6.93507e102	0.602783
$235$	−1.89474e103	−1.36804
$236$	8.51531e102	0.511126
$237$	−1.75492e103	−0.876404
$238$	−1.75529e103	−0.729879
$239$	−3.24132e103	−1.12309	−0.561543	−	0.827448i	$-0.689792\pi$
$239$	−3.24132e103	−1.12309	−0.561543	+	0.827448i	$0.689792\pi$
$240$	−1.76870e103	−0.511052
$241$	−8.70686e102	−0.209952	−0.104976	−	0.994475i	$-0.533477\pi$
$241$	−8.70686e102	−0.209952	−0.104976	+	0.994475i	$0.533477\pi$
$242$	3.48643e103	0.702122
$243$	−4.79063e103	−0.806343
$244$	3.38079e103	0.475949
$245$	−1.88094e103	−0.221641
$246$	1.22505e104	1.20914
$247$	2.13126e104	1.76327
$248$	−5.90450e103	−0.409765
$249$	−4.50230e103	−0.262279
$250$	2.28151e104	1.11643
$251$	−4.39463e104	−1.80765	−0.903826	−	0.427899i	$-0.859254\pi$
$251$	−4.39463e104	−1.80765	−0.903826	+	0.427899i	$0.859254\pi$
$252$	−6.59540e103	−0.228201
$253$	1.47151e101	0.000428570 0
$254$	−7.87849e103	−0.193275
$255$	9.60110e104	1.98529
$256$	3.58359e103	0.0625000
$257$	−1.16147e104	−0.170969	−0.0854845	−	0.996340i	$-0.527244\pi$
$257$	−1.16147e104	−0.170969	−0.0854845	+	0.996340i	$0.527244\pi$
$258$	4.31839e104	0.536865
$259$	−1.18068e105	−1.24049
$260$	1.91008e105	1.69712
$261$	−4.98914e104	−0.375114
$262$	−1.20668e103	−0.00768219
$263$	−2.03499e105	−1.09771	−0.548854	−	0.835918i	$-0.684936\pi$
$263$	−2.03499e105	−1.09771	−0.548854	+	0.835918i	$0.684936\pi$
$264$	7.76038e103	0.0354905
$265$	4.49493e105	1.74393
$266$	−2.02688e105	−0.667539
$267$	−5.49780e105	−1.53797
$268$	−3.84836e105	−0.914982
$269$	6.30450e104	0.127475	0.0637377	−	0.997967i	$-0.479698\pi$
$269$	6.30450e104	0.127475	0.0637377	+	0.997967i	$0.479698\pi$
$270$	−4.79350e105	−0.824762
$271$	−1.07946e106	−1.58140	−0.790702	−	0.612201i	$-0.790284\pi$
$271$	−1.07946e106	−1.58140	−0.790702	+	0.612201i	$0.790284\pi$
$272$	−1.94529e105	−0.242794
$273$	2.37093e106	2.52257
$274$	−7.13298e105	−0.647324
$275$	−2.08509e105	−0.161493
$276$	−4.61359e103	−0.00305136
$277$	1.47619e106	0.834206	0.417103	−	0.908859i	$-0.363045\pi$
$277$	1.47619e106	0.834206	0.417103	+	0.908859i	$0.363045\pi$
$278$	2.74031e106	1.32389
$279$	1.20432e106	0.497691
$280$	−1.81653e106	−0.642494
$281$	9.25713e105	0.280383	0.140191	−	0.990124i	$-0.455228\pi$
$281$	9.25713e105	0.280383	0.140191	+	0.990124i	$0.455228\pi$
$282$	−2.60647e106	−0.676421
$283$	−3.98245e106	−0.886014	−0.443007	−	0.896518i	$-0.646088\pi$
$283$	−3.98245e106	−0.886014	−0.443007	+	0.896518i	$0.646088\pi$
$284$	2.27924e106	0.434954
$285$	1.10867e107	1.81572
$286$	−8.38071e105	−0.117858
$287$	1.25818e107	1.52012
$288$	−7.30934e105	−0.0759110
$289$	−6.36125e105	−0.0568181
$290$	−1.37413e107	−1.05612
$291$	5.03899e106	0.333426
$292$	−5.82821e106	−0.332186
$293$	−2.68188e107	−1.31734	−0.658671	−	0.752431i	$-0.728881\pi$
$293$	−2.68188e107	−1.31734	−0.658671	+	0.752431i	$0.728881\pi$
$294$	−2.58748e106	−0.109589
$295$	−4.78368e107	−1.74785
$296$	−1.30848e107	−0.412647
$297$	2.10320e106	0.0572764
$298$	1.44360e107	0.339655
$299$	4.98238e105	0.0101331
$300$	6.53731e107	1.14981
$301$	4.43517e107	0.674945
$302$	6.45215e106	0.0849967
$303$	−1.77321e107	−0.202305
$304$	−2.24628e107	−0.222057
$305$	−1.89924e108	−1.62756
$306$	3.96775e107	0.294892
$307$	−8.89009e105	−0.00573307	−0.00286653	−	0.999996i	$-0.500912\pi$
$307$	−8.89009e105	−0.00573307	−0.00286653	+	0.999996i	$0.500912\pi$
$308$	7.97025e106	0.0446186
$309$	3.21282e108	1.56204
$310$	3.31699e108	1.40123
$311$	−5.40290e108	−1.98404	−0.992019	−	0.126092i	$-0.959757\pi$
$311$	−5.40290e108	−1.98404	−0.992019	+	0.126092i	$0.959757\pi$
$312$	2.62758e108	0.839133
$313$	4.76789e107	0.132479	0.0662395	−	0.997804i	$-0.478900\pi$
$313$	4.76789e107	0.132479	0.0662395	+	0.997804i	$0.478900\pi$
$314$	−2.64015e108	−0.638542
$315$	3.70512e108	0.780358
$316$	−1.99748e108	−0.366517
$317$	2.69748e108	0.431400	0.215700	−	0.976460i	$-0.430797\pi$
$317$	2.69748e108	0.431400	0.215700	+	0.976460i	$0.430797\pi$
$318$	6.18338e108	0.862276
$319$	6.02915e107	0.0733434
$320$	−2.01317e108	−0.213725
$321$	1.09667e109	1.01650
$322$	−4.73836e106	−0.00383616
$323$	1.21936e109	0.862624
$324$	−1.00659e109	−0.622509
$325$	−7.05988e109	−3.81831
$326$	−1.27964e108	−0.0605509
$327$	−9.59079e108	−0.397216
$328$	1.39437e109	0.505669
$329$	−2.67696e109	−0.850394
$330$	−4.35958e108	−0.121363
$331$	−1.71383e109	−0.418264	−0.209132	−	0.977887i	$-0.567064\pi$
$331$	−1.71383e109	−0.418264	−0.209132	+	0.977887i	$0.567064\pi$
$332$	−5.12460e108	−0.109687
$333$	2.66887e109	0.501191
$334$	−3.22513e109	−0.531590
$335$	2.16191e110	3.12888
$336$	−2.49888e109	−0.317678
$337$	6.65487e109	0.743428	0.371714	−	0.928347i	$-0.378770\pi$
$337$	6.65487e109	0.743428	0.371714	+	0.928347i	$0.378770\pi$
$338$	−2.11757e110	−2.07951
$339$	6.84687e109	0.591297
$340$	1.09281e110	0.830259
$341$	−1.45537e109	−0.0973100
$342$	4.58167e109	0.269705
$343$	1.78429e110	0.925065
$344$	4.91527e109	0.224520
$345$	2.59179e108	0.0104345
$346$	−8.91291e109	−0.316380
$347$	−2.01042e110	−0.629442	−0.314721	−	0.949184i	$-0.601911\pi$
$347$	−2.01042e110	−0.629442	−0.314721	+	0.949184i	$0.601911\pi$
$348$	−1.89030e110	−0.522196
$349$	−1.74762e110	−0.426128	−0.213064	−	0.977038i	$-0.568344\pi$
$349$	−1.74762e110	−0.426128	−0.213064	+	0.977038i	$0.568344\pi$
$350$	6.71410e110	1.44553
$351$	7.12121e110	1.35424
$352$	8.83300e108	0.0148423
$353$	−7.32946e110	−1.08861	−0.544305	−	0.838888i	$-0.683206\pi$
$353$	−7.32946e110	−1.08861	−0.544305	+	0.838888i	$0.683206\pi$
$354$	−6.58059e110	−0.864217
$355$	−1.28042e111	−1.48737
$356$	−6.25769e110	−0.643190
$357$	1.35648e111	1.23409
$358$	8.52051e110	0.686363
$359$	−1.90191e111	−1.35701	−0.678504	−	0.734597i	$-0.737371\pi$
$359$	−1.90191e111	−1.35701	−0.678504	+	0.734597i	$0.737371\pi$
$360$	4.10619e110	0.259586
$361$	−3.76666e110	−0.211054
$362$	−3.88637e110	−0.193073
$363$	−2.69430e111	−1.18715
$364$	2.69864e111	1.05496
$365$	3.27413e111	1.13594
$366$	−2.61266e111	−0.804739
$367$	−8.77524e110	−0.240041	−0.120020	−	0.992771i	$-0.538296\pi$
$367$	−8.77524e110	−0.240041	−0.120020	+	0.992771i	$0.538296\pi$
$368$	−5.25127e108	−0.00127610
$369$	−2.84405e111	−0.614173
$370$	7.35072e111	1.41109
$371$	6.35060e111	1.08405
$372$	4.56297e111	0.692835
$373$	−1.65638e111	−0.223782	−0.111891	−	0.993720i	$-0.535691\pi$
$373$	−1.65638e111	−0.223782	−0.111891	+	0.993720i	$0.535691\pi$
$374$	−4.79485e110	−0.0576581
$375$	−1.76314e112	−1.88767
$376$	−2.96673e111	−0.282883
$377$	2.04140e112	1.73412
$378$	−6.77243e111	−0.512685
$379$	2.06576e111	0.139404	0.0697020	−	0.997568i	$-0.477795\pi$
$379$	2.06576e111	0.139404	0.0697020	+	0.997568i	$0.477795\pi$
$380$	1.26190e112	0.759346
$381$	6.08846e111	0.326792
$382$	1.83096e112	0.876845
$383$	1.82527e112	0.780154	0.390077	−	0.920782i	$-0.372448\pi$
$383$	1.82527e112	0.780154	0.390077	+	0.920782i	$0.372448\pi$
$384$	−2.76938e111	−0.105676
$385$	−4.47748e111	−0.152578
$386$	−4.27701e112	−1.30194
$387$	−1.00255e112	−0.272697
$388$	5.73548e111	0.139441
$389$	−7.71428e112	−1.67682	−0.838412	−	0.545036i	$-0.816516\pi$
$389$	−7.71428e112	−1.67682	−0.838412	+	0.545036i	$0.816516\pi$
$390$	−1.47610e113	−2.86950
$391$	2.85056e110	0.00495726
$392$	−2.94512e111	−0.0458310
$393$	9.32514e110	0.0129891
$394$	6.75885e112	0.842922
$395$	1.12213e113	1.25334
$396$	−1.80164e111	−0.0180272
$397$	2.71833e112	0.243734	0.121867	−	0.992546i	$-0.461112\pi$
$397$	2.71833e112	0.243734	0.121867	+	0.992546i	$0.461112\pi$
$398$	−8.98843e112	−0.722388
$399$	1.56636e113	1.12868
$400$	7.44089e112	0.480856
$401$	3.71194e112	0.215189	0.107595	−	0.994195i	$-0.465685\pi$
$401$	3.71194e112	0.215189	0.107595	+	0.994195i	$0.465685\pi$
$402$	2.97400e113	1.54706
$403$	−4.92771e113	−2.30079
$404$	−2.01830e112	−0.0846052
$405$	5.65477e113	2.12873
$406$	−1.94142e113	−0.656503
$407$	−3.22521e112	−0.0979944
$408$	1.50331e113	0.410518
$409$	2.69444e113	0.661463	0.330731	−	0.943725i	$-0.392705\pi$
$409$	2.69444e113	0.661463	0.330731	+	0.943725i	$0.392705\pi$
$410$	−7.83321e113	−1.72919
$411$	5.51233e113	1.09450
$412$	3.65689e113	0.653255
$413$	−6.75855e113	−1.08649
$414$	1.07108e111	0.00154992
$415$	2.87887e113	0.375085
$416$	2.99076e113	0.350930
$417$	−2.11770e114	−2.23844
$418$	−5.53675e112	−0.0527335
$419$	1.79211e113	0.153834	0.0769172	−	0.997037i	$-0.475492\pi$
$419$	1.79211e113	0.153834	0.0769172	+	0.997037i	$0.475492\pi$
$420$	1.40381e114	1.08633
$421$	−5.75048e113	−0.401266	−0.200633	−	0.979666i	$-0.564300\pi$
$421$	−5.75048e113	−0.401266	−0.200633	+	0.979666i	$0.564300\pi$
$422$	1.24351e114	0.782633
$423$	6.05115e113	0.343583
$424$	7.03804e113	0.360609
$425$	−4.03916e114	−1.86798
$426$	−1.76139e114	−0.735424
$427$	−2.68331e114	−1.01172
$428$	1.24825e114	0.425107
$429$	6.47657e113	0.199275
$430$	−2.76127e114	−0.767770
$431$	−9.56120e113	−0.240298	−0.120149	−	0.992756i	$-0.538337\pi$
$431$	−9.56120e113	−0.240298	−0.120149	+	0.992756i	$0.538337\pi$
$432$	−7.50552e113	−0.170545
$433$	3.13984e114	0.645185	0.322593	−	0.946538i	$-0.395446\pi$
$433$	3.13984e114	0.645185	0.322593	+	0.946538i	$0.395446\pi$
$434$	4.68637e114	0.871030
$435$	1.06192e115	1.78570
$436$	−1.09164e114	−0.166118
$437$	3.29163e112	0.00453386
$438$	4.50401e114	0.561663
$439$	5.69276e114	0.642860	0.321430	−	0.946933i	$-0.395836\pi$
$439$	5.69276e114	0.642860	0.321430	+	0.946933i	$0.395836\pi$
$440$	−4.96215e113	−0.0507550
$441$	6.00707e113	0.0556652
$442$	−1.62348e115	−1.36326
$443$	−1.38988e115	−1.05783	−0.528916	−	0.848674i	$-0.677401\pi$
$443$	−1.38988e115	−1.05783	−0.528916	+	0.848674i	$0.677401\pi$
$444$	1.01119e115	0.697707
$445$	3.51541e115	2.19945
$446$	−1.10568e115	−0.627428
$447$	−1.11560e115	−0.574292
$448$	−2.84428e114	−0.132855
$449$	2.77553e115	1.17660	0.588301	−	0.808642i	$-0.299797\pi$
$449$	2.77553e115	1.17660	0.588301	+	0.808642i	$0.299797\pi$
$450$	−1.51769e115	−0.584036
$451$	3.43691e114	0.120085
$452$	7.79323e114	0.247284
$453$	−4.98619e114	−0.143713
$454$	−3.34548e114	−0.0876049
$455$	−1.51602e116	−3.60753
$456$	1.73592e115	0.375455
$457$	3.56524e115	0.701026	0.350513	−	0.936558i	$-0.386007\pi$
$457$	3.56524e115	0.701026	0.350513	+	0.936558i	$0.386007\pi$
$458$	−7.35779e115	−1.31552
$459$	4.07425e115	0.662515
$460$	2.95003e113	0.00436375
$461$	−1.04237e115	−0.140292	−0.0701459	−	0.997537i	$-0.522346\pi$
$461$	−1.04237e115	−0.140292	−0.0701459	+	0.997537i	$0.522346\pi$
$462$	−6.15937e114	−0.0754415
$463$	1.16992e116	1.30432	0.652158	−	0.758083i	$-0.273864\pi$
$463$	1.16992e116	1.30432	0.652158	+	0.758083i	$0.273864\pi$
$464$	−2.15157e115	−0.218385
$465$	−2.56336e116	−2.36922
$466$	7.81479e115	0.657855
$467$	1.39877e116	1.07266	0.536329	−	0.844009i	$-0.319811\pi$
$467$	1.39877e116	1.07266	0.536329	+	0.844009i	$0.319811\pi$
$468$	−6.10015e115	−0.426232
$469$	3.05442e116	1.94496
$470$	1.66663e116	0.967349
$471$	2.04030e116	1.07965
$472$	−7.49014e115	−0.361421
$473$	1.21154e115	0.0533185
$474$	1.54364e116	0.619711
$475$	−4.66413e116	−1.70844
$476$	1.54397e116	0.516102
$477$	−1.43553e116	−0.437988
$478$	2.85109e116	0.794142
$479$	−1.00387e115	−0.0255318	−0.0127659	−	0.999919i	$-0.504064\pi$
$479$	−1.00387e115	−0.0255318	−0.0127659	+	0.999919i	$0.504064\pi$
$480$	1.55577e116	0.361369
$481$	−1.09202e117	−2.31697
$482$	7.65864e115	0.148459
$483$	3.66178e114	0.00648622
$484$	−3.06670e116	−0.496475
$485$	−3.22204e116	−0.476832
$486$	4.21389e116	0.570171
$487$	1.12491e117	1.39190	0.695951	−	0.718089i	$-0.254983\pi$
$487$	1.12491e117	1.39190	0.695951	+	0.718089i	$0.254983\pi$
$488$	−2.97377e116	−0.336547
$489$	9.88896e115	0.102380
$490$	1.65449e116	0.156724
$491$	−5.79970e115	−0.0502760	−0.0251380	−	0.999684i	$-0.508003\pi$
$491$	−5.79970e115	−0.0502760	−0.0251380	+	0.999684i	$0.508003\pi$
$492$	−1.07756e117	−0.854990
$493$	1.16795e117	0.848363
$494$	−1.87468e117	−1.24682
$495$	1.01211e116	0.0616458
$496$	5.19365e116	0.289748
$497$	−1.80902e117	−0.924573
$498$	3.96027e116	0.185459
$499$	−3.63625e117	−1.56056	−0.780280	−	0.625431i	$-0.784923\pi$
$499$	−3.63625e117	−1.56056	−0.780280	+	0.625431i	$0.784923\pi$
$500$	−2.00684e117	−0.789436
$501$	2.49237e117	0.898817
$502$	3.86555e117	1.27820
$503$	−2.85130e117	−0.864639	−0.432320	−	0.901720i	$-0.642305\pi$
$503$	−2.85130e117	−0.864639	−0.432320	+	0.901720i	$0.642305\pi$
$504$	5.80138e116	0.161363
$505$	1.13383e117	0.289316
$506$	−1.29436e114	−0.000303045 0
$507$	1.63645e118	3.51605
$508$	6.92999e116	0.136666
$509$	3.25229e117	0.588798	0.294399	−	0.955683i	$-0.404881\pi$
$509$	3.25229e117	0.588798	0.294399	+	0.955683i	$0.404881\pi$
$510$	−8.44522e117	−1.40381
$511$	4.62581e117	0.706121
$512$	−3.15216e116	−0.0441942
$513$	4.70465e117	0.605929
$514$	1.02164e117	0.120893
$515$	−2.05434e118	−2.23387
$516$	−3.79850e117	−0.379621
$517$	−7.31254e116	−0.0671784
$518$	1.03854e118	0.877156
$519$	6.88786e117	0.534939
$520$	−1.68013e118	−1.20004
$521$	1.64709e118	1.08212	0.541061	−	0.840983i	$-0.318023\pi$
$521$	1.64709e118	1.08212	0.541061	+	0.840983i	$0.318023\pi$
$522$	4.38849e117	0.265246
$523$	−5.02802e117	−0.279623	−0.139812	−	0.990178i	$-0.544650\pi$
$523$	−5.02802e117	−0.279623	−0.139812	+	0.990178i	$0.544650\pi$
$524$	1.06140e116	0.00543213
$525$	−5.18863e118	−2.44412
$526$	1.78999e118	0.776196
$527$	−2.81929e118	−1.12558
$528$	−6.82610e116	−0.0250956
$529$	−2.95332e118	−0.999974
$530$	−3.95379e118	−1.23314
$531$	1.52774e118	0.438973
$532$	1.78286e118	0.472022
$533$	1.16370e119	2.83927
$534$	4.83591e118	1.08751
$535$	−7.01235e118	−1.45370
$536$	3.38506e118	0.646990
$537$	−6.58461e118	−1.16051
$538$	−5.54550e117	−0.0901387
$539$	−7.25927e116	−0.0108838
$540$	4.21641e118	0.583195
$541$	−2.13071e118	−0.271921	−0.135961	−	0.990714i	$-0.543412\pi$
$541$	−2.13071e118	−0.271921	−0.135961	+	0.990714i	$0.543412\pi$
$542$	9.49504e118	1.11822
$543$	3.00337e118	0.326450
$544$	1.71110e118	0.171681
$545$	6.13255e118	0.568059
$546$	−2.08549e119	−1.78373
$547$	1.34728e119	1.06416	0.532081	−	0.846693i	$-0.321410\pi$
$547$	1.34728e119	1.06416	0.532081	+	0.846693i	$0.321410\pi$
$548$	6.27424e118	0.457727
$549$	6.06551e118	0.408762
$550$	1.83406e118	0.114192
$551$	1.34866e119	0.775903
$552$	4.05816e116	0.00215764
$553$	1.58539e119	0.779099
$554$	−1.29847e119	−0.589873
$555$	−5.68060e119	−2.38588
$556$	−2.41040e119	−0.936129
$557$	−3.44921e119	−1.23885	−0.619425	−	0.785056i	$-0.712634\pi$
$557$	−3.44921e119	−1.23885	−0.619425	+	0.785056i	$0.712634\pi$
$558$	−1.05933e119	−0.351921
$559$	4.10213e119	1.26065
$560$	1.59784e119	0.454312
$561$	3.70544e118	0.0974888
$562$	−8.14266e118	−0.198261
$563$	−2.42804e119	−0.547193	−0.273597	−	0.961845i	$-0.588213\pi$
$563$	−2.42804e119	−0.547193	−0.273597	+	0.961845i	$0.588213\pi$
$564$	2.29268e119	0.478302
$565$	−4.37803e119	−0.845613
$566$	3.50300e119	0.626507
$567$	7.98926e119	1.32326
$568$	−2.00484e119	−0.307559
$569$	5.63770e119	0.801158	0.400579	−	0.916262i	$-0.368809\pi$
$569$	5.63770e119	0.801158	0.400579	+	0.916262i	$0.368809\pi$
$570$	−9.75193e119	−1.28391
$571$	4.88454e119	0.595872	0.297936	−	0.954586i	$-0.403702\pi$
$571$	4.88454e119	0.595872	0.297936	+	0.954586i	$0.403702\pi$
$572$	7.37175e118	0.0833381
$573$	−1.41496e120	−1.48258
$574$	−1.10670e120	−1.07489
$575$	−1.09036e118	−0.00981791
$576$	6.42936e118	0.0536772
$577$	−5.04417e119	−0.390519	−0.195259	−	0.980752i	$-0.562555\pi$
$577$	−5.04417e119	−0.390519	−0.195259	+	0.980752i	$0.562555\pi$
$578$	5.59542e118	0.0401764
$579$	3.30525e120	2.20134
$580$	1.20870e120	0.746792
$581$	4.06737e119	0.233159
$582$	−4.43235e119	−0.235767
$583$	1.73477e119	0.0856366
$584$	5.12655e119	0.234891
$585$	3.42690e120	1.45754
$586$	2.35901e120	0.931501
$587$	−2.12080e120	−0.777574	−0.388787	−	0.921328i	$-0.627106\pi$
$587$	−2.12080e120	−0.777574	−0.388787	+	0.921328i	$0.627106\pi$
$588$	2.27597e119	0.0774914
$589$	−3.25551e120	−1.02945
$590$	4.20777e120	1.23592
$591$	−5.22321e120	−1.42522
$592$	1.15095e120	0.291786
$593$	1.30159e120	0.306616	0.153308	−	0.988178i	$-0.451007\pi$
$593$	1.30159e120	0.306616	0.153308	+	0.988178i	$0.451007\pi$
$594$	−1.85000e119	−0.0405005
$595$	−8.67361e120	−1.76487
$596$	−1.26980e120	−0.240172
$597$	6.94622e120	1.22142
$598$	−4.38255e118	−0.00716515
$599$	−7.74342e120	−1.17724	−0.588622	−	0.808409i	$-0.700329\pi$
$599$	−7.74342e120	−1.17724	−0.588622	+	0.808409i	$0.700329\pi$
$600$	−5.75028e120	−0.813036
$601$	−1.31041e121	−1.72333	−0.861666	−	0.507476i	$-0.830579\pi$
$601$	−1.31041e121	−1.72333	−0.861666	+	0.507476i	$0.830579\pi$
$602$	−3.90122e120	−0.477258
$603$	−6.90439e120	−0.785819
$604$	−5.67537e119	−0.0601018
$605$	1.72279e121	1.69775
$606$	1.55974e120	0.143051
$607$	1.37063e121	1.17007	0.585037	−	0.811007i	$-0.301080\pi$
$607$	1.37063e121	1.17007	0.585037	+	0.811007i	$0.301080\pi$
$608$	1.97585e120	0.157018
$609$	1.50032e121	1.11002
$610$	1.67059e121	1.15086
$611$	−2.47595e121	−1.58836
$612$	−3.49007e120	−0.208520
$613$	−6.82621e120	−0.379882	−0.189941	−	0.981795i	$-0.560830\pi$
$613$	−6.82621e120	−0.379882	−0.189941	+	0.981795i	$0.560830\pi$
$614$	7.81981e118	0.00405389
$615$	6.05347e121	2.92373
$616$	−7.01070e119	−0.0315501
$617$	−2.05628e121	−0.862339	−0.431169	−	0.902271i	$-0.641899\pi$
$617$	−2.05628e121	−0.862339	−0.431169	+	0.902271i	$0.641899\pi$
$618$	−2.82602e121	−1.10453
$619$	−6.45845e120	−0.235280	−0.117640	−	0.993056i	$-0.537533\pi$
$619$	−6.45845e120	−0.235280	−0.117640	+	0.993056i	$0.537533\pi$
$620$	−2.91766e121	−0.990823
$621$	1.09983e119	0.00348211
$622$	4.75244e121	1.40293
$623$	4.96669e121	1.36722
$624$	−2.31124e121	−0.593356
$625$	3.24130e121	0.776136
$626$	−4.19388e120	−0.0936768
$627$	4.27877e120	0.0891622
$628$	2.32230e121	0.451517
$629$	−6.24776e121	−1.13350
$630$	−3.25906e121	−0.551796
$631$	5.17905e121	0.818414	0.409207	−	0.912441i	$-0.365805\pi$
$631$	5.17905e121	0.818414	0.409207	+	0.912441i	$0.365805\pi$
$632$	1.75700e121	0.259167
$633$	−9.60979e121	−1.32328
$634$	−2.37273e121	−0.305046
$635$	−3.89309e121	−0.467344
$636$	−5.43896e121	−0.609722
$637$	−2.45791e121	−0.257336
$638$	−5.30330e120	−0.0518616
$639$	4.08922e121	0.373554
$640$	1.77080e121	0.151127
$641$	1.99649e121	0.159200	0.0796000	−	0.996827i	$-0.474636\pi$
$641$	1.99649e121	0.159200	0.0796000	+	0.996827i	$0.474636\pi$
$642$	−9.64642e121	−0.718774
$643$	−5.25293e121	−0.365783	−0.182892	−	0.983133i	$-0.558546\pi$
$643$	−5.25293e121	−0.365783	−0.182892	+	0.983133i	$0.558546\pi$
$644$	4.16790e119	0.00271258
$645$	2.13390e122	1.29815
$646$	−1.07256e122	−0.609967
$647$	−1.13292e122	−0.602372	−0.301186	−	0.953565i	$-0.597382\pi$
$647$	−1.13292e122	−0.602372	−0.301186	+	0.953565i	$0.597382\pi$
$648$	8.85408e121	0.440180
$649$	−1.84621e121	−0.0858293
$650$	6.20994e122	2.69995
$651$	−3.62160e122	−1.47274
$652$	1.12558e121	0.0428160
$653$	−1.52725e122	−0.543484	−0.271742	−	0.962370i	$-0.587600\pi$
$653$	−1.52725e122	−0.543484	−0.271742	+	0.962370i	$0.587600\pi$
$654$	8.43615e121	0.280874
$655$	−5.96269e120	−0.0185757
$656$	−1.22650e122	−0.357562
$657$	−1.04565e122	−0.285293
$658$	2.35468e122	0.601320
$659$	2.37599e121	0.0567974	0.0283987	−	0.999597i	$-0.490959\pi$
$659$	2.37599e121	0.0567974	0.0283987	+	0.999597i	$0.490959\pi$
$660$	3.83472e121	0.0858169
$661$	3.81809e122	0.799988	0.399994	−	0.916518i	$-0.369012\pi$
$661$	3.81809e122	0.799988	0.399994	+	0.916518i	$0.369012\pi$
$662$	1.50750e122	0.295758
$663$	1.25462e123	2.30501
$664$	4.50765e121	0.0775602
$665$	−1.00157e123	−1.61413
$666$	−2.34756e122	−0.354396
$667$	3.15284e120	0.00445890
$668$	2.83686e122	0.375891
$669$	8.54466e122	1.06086
$670$	−1.90164e123	−2.21245
$671$	−7.32990e121	−0.0799223
$672$	2.19804e122	0.224632
$673$	1.42889e121	0.0136881	0.00684404	−	0.999977i	$-0.497821\pi$
$673$	1.42889e121	0.0136881	0.00684404	+	0.999977i	$0.497821\pi$
$674$	−5.85368e122	−0.525683
$675$	−1.55843e123	−1.31212
$676$	1.86263e123	1.47044
$677$	1.05374e122	0.0780056	0.0390028	−	0.999239i	$-0.487582\pi$
$677$	1.05374e122	0.0780056	0.0390028	+	0.999239i	$0.487582\pi$
$678$	−6.02257e122	−0.418110
$679$	−4.55221e122	−0.296406
$680$	−9.61250e122	−0.587082
$681$	2.58537e122	0.148123
$682$	1.28016e122	0.0688086
$683$	−3.43584e123	−1.73274	−0.866368	−	0.499406i	$-0.833552\pi$
$683$	−3.43584e123	−1.73274	−0.866368	+	0.499406i	$0.833552\pi$
$684$	−4.03008e122	−0.190710
$685$	−3.52470e123	−1.56525
$686$	−1.56948e123	−0.654120
$687$	5.68606e123	2.22430
$688$	−4.32352e122	−0.158760
$689$	5.87373e123	2.02478
$690$	−2.27977e121	−0.00737827
$691$	−1.70370e123	−0.517723	−0.258861	−	0.965914i	$-0.583347\pi$
$691$	−1.70370e123	−0.517723	−0.258861	+	0.965914i	$0.583347\pi$
$692$	7.83988e122	0.223715
$693$	1.42995e122	0.0383200
$694$	1.76839e123	0.445083
$695$	1.35410e124	3.20119
$696$	1.66272e123	0.369248
$697$	6.65786e123	1.38902
$698$	1.53722e123	0.301318
$699$	−6.03923e123	−1.11231
$700$	−5.90579e123	−1.02215
$701$	−4.92673e123	−0.801354	−0.400677	−	0.916219i	$-0.631225\pi$
$701$	−4.92673e123	−0.801354	−0.400677	+	0.916219i	$0.631225\pi$
$702$	−6.26388e123	−0.957589
$703$	−7.21447e123	−1.03669
$704$	−7.76959e121	−0.0104951
$705$	−1.28797e124	−1.63560
$706$	6.44706e123	0.769763
$707$	1.60192e123	0.179844
$708$	5.78835e123	0.611094
$709$	5.10798e123	0.507152	0.253576	−	0.967315i	$-0.418393\pi$
$709$	5.10798e123	0.507152	0.253576	+	0.967315i	$0.418393\pi$
$710$	1.12627e124	1.05173
$711$	−3.58370e123	−0.314778
$712$	5.50432e123	0.454804
$713$	−7.61060e121	−0.00591595
$714$	−1.19317e124	−0.872630
$715$	−4.14126e123	−0.284983
$716$	−7.49472e123	−0.485332
$717$	−2.20331e124	−1.34274
$718$	1.67294e124	0.959550
$719$	2.26289e124	1.22168	0.610838	−	0.791756i	$-0.290833\pi$
$719$	2.26289e124	1.22168	0.610838	+	0.791756i	$0.290833\pi$
$720$	−3.61185e123	−0.183555
$721$	−2.90245e124	−1.38861
$722$	3.31318e123	0.149237
$723$	−5.91856e123	−0.251015
$724$	3.41849e123	0.136523
$725$	−4.46747e124	−1.68019
$726$	2.36993e124	0.839445
$727$	3.42993e124	1.14430	0.572148	−	0.820150i	$-0.306110\pi$
$727$	3.42993e124	1.14430	0.572148	+	0.820150i	$0.306110\pi$
$728$	−2.37375e124	−0.745966
$729$	9.49083e123	0.280968
$730$	−2.87996e124	−0.803234
$731$	2.34695e124	0.616734
$732$	2.29812e124	0.569037
$733$	1.43402e124	0.334606	0.167303	−	0.985906i	$-0.446494\pi$
$733$	1.43402e124	0.334606	0.167303	+	0.985906i	$0.446494\pi$
$734$	7.71878e123	0.169735
$735$	−1.27858e124	−0.264990
$736$	4.61907e121	0.000902338 0
$737$	8.34364e123	0.153646
$738$	2.50166e124	0.434286
$739$	7.78279e124	1.27380	0.636901	−	0.770945i	$-0.280216\pi$
$739$	7.78279e124	1.27380	0.636901	+	0.770945i	$0.280216\pi$
$740$	−6.46576e124	−0.997791
$741$	1.44874e125	2.10814
$742$	−5.58605e124	−0.766540
$743$	−2.58291e124	−0.334269	−0.167135	−	0.985934i	$-0.553451\pi$
$743$	−2.58291e124	−0.334269	−0.167135	+	0.985934i	$0.553451\pi$
$744$	−4.01363e124	−0.489908
$745$	7.13340e124	0.821294
$746$	1.45697e124	0.158238
$747$	−9.19411e123	−0.0942027
$748$	4.21759e123	0.0407704
$749$	−9.90730e124	−0.903641
$750$	1.55087e125	1.33479
$751$	−2.30593e124	−0.187287	−0.0936437	−	0.995606i	$-0.529851\pi$
$751$	−2.30593e124	−0.187287	−0.0936437	+	0.995606i	$0.529851\pi$
$752$	2.60957e124	0.200029
$753$	−2.98728e125	−2.16120
$754$	−1.79564e125	−1.22621
$755$	3.18827e124	0.205524
$756$	5.95709e124	0.362523
$757$	−9.18840e124	−0.527921	−0.263960	−	0.964533i	$-0.585029\pi$
$757$	−9.18840e124	−0.527921	−0.263960	+	0.964533i	$0.585029\pi$
$758$	−1.81707e124	−0.0985735
$759$	1.00027e122	0.000512391 0
$760$	−1.10998e125	−0.536939
$761$	3.76863e125	1.72167	0.860836	−	0.508882i	$-0.169941\pi$
$761$	3.76863e125	1.72167	0.860836	+	0.508882i	$0.169941\pi$
$762$	−5.35546e124	−0.231076
$763$	8.66429e124	0.353115
$764$	−1.61053e125	−0.620023
$765$	1.96063e125	0.713056
$766$	−1.60552e125	−0.551652
$767$	−6.25105e125	−2.02934
$768$	2.43597e124	0.0747239
$769$	−6.07976e124	−0.176234	−0.0881172	−	0.996110i	$-0.528085\pi$
$769$	−6.07976e124	−0.176234	−0.0881172	+	0.996110i	$0.528085\pi$
$770$	3.93843e124	0.107889
$771$	−7.89519e124	−0.204408
$772$	3.76210e125	0.920613
$773$	−3.51499e125	−0.813048	−0.406524	−	0.913640i	$-0.633259\pi$
$773$	−3.51499e125	−0.813048	−0.406524	+	0.913640i	$0.633259\pi$
$774$	8.81854e124	0.192826
$775$	1.07840e126	2.22923
$776$	−5.04498e124	−0.0985994
$777$	−8.02575e125	−1.48310
$778$	6.78555e125	1.18569
$779$	7.68802e125	1.27038
$780$	1.29839e126	2.02904
$781$	−4.94163e124	−0.0730383
$782$	−2.50738e123	−0.00350531
$783$	4.50628e125	0.595911
$784$	2.59055e124	0.0324074
$785$	−1.30461e126	−1.54401
$786$	−8.20248e123	−0.00918469
$787$	1.32282e126	1.40152	0.700760	−	0.713397i	$-0.252845\pi$
$787$	1.32282e126	1.40152	0.700760	+	0.713397i	$0.252845\pi$
$788$	−5.94515e125	−0.596036
$789$	−1.38330e126	−1.31240
$790$	−9.87038e125	−0.886248
$791$	−6.18544e125	−0.525647
$792$	1.58474e124	0.0127471
$793$	−2.48182e126	−1.88967
$794$	−2.39107e125	−0.172346
$795$	3.05547e126	2.08501
$796$	7.90631e125	0.510805
$797$	1.08117e126	0.661391	0.330695	−	0.943738i	$-0.392717\pi$
$797$	1.08117e126	0.661391	0.330695	+	0.943738i	$0.392717\pi$
$798$	−1.37779e126	−0.798098
$799$	−1.41656e126	−0.777052
$800$	−6.54507e125	−0.340017
$801$	−1.12270e126	−0.552394
$802$	−3.26506e125	−0.152162
$803$	1.26361e125	0.0557813
$804$	−2.61595e126	−1.09394
$805$	−2.34142e124	−0.00927594
$806$	4.33446e126	1.62690
$807$	4.28553e125	0.152407
$808$	1.77532e125	0.0598249
$809$	2.96592e126	0.947105	0.473553	−	0.880766i	$-0.342971\pi$
$809$	2.96592e126	0.947105	0.473553	+	0.880766i	$0.342971\pi$
$810$	−4.97399e126	−1.50524
$811$	6.41505e126	1.83990	0.919948	−	0.392041i	$-0.128231\pi$
$811$	6.41505e126	1.83990	0.919948	+	0.392041i	$0.128231\pi$
$812$	1.70769e126	0.464218
$813$	−7.33772e126	−1.89070
$814$	2.83693e125	0.0692925
$815$	−6.32321e125	−0.146414
$816$	−1.32233e126	−0.290280
$817$	2.71009e126	0.564058
$818$	−2.37006e126	−0.467725
$819$	4.84165e126	0.906033
$820$	6.89017e126	1.22272
$821$	3.31218e126	0.557425	0.278712	−	0.960375i	$-0.410092\pi$
$821$	3.31218e126	0.557425	0.278712	+	0.960375i	$0.410092\pi$
$822$	−4.84870e126	−0.773929
$823$	−1.05403e127	−1.59573	−0.797866	−	0.602834i	$-0.794038\pi$
$823$	−1.05403e127	−1.59573	−0.797866	+	0.602834i	$0.794038\pi$
$824$	−3.21663e126	−0.461921
$825$	−1.41736e126	−0.193078
$826$	5.94488e126	0.768265
$827$	1.14898e127	1.40871	0.704355	−	0.709848i	$-0.251236\pi$
$827$	1.14898e127	1.40871	0.704355	+	0.709848i	$0.251236\pi$
$828$	−9.42136e123	−0.00109596
$829$	4.87003e126	0.537538	0.268769	−	0.963205i	$-0.413383\pi$
$829$	4.87003e126	0.537538	0.268769	+	0.963205i	$0.413383\pi$
$830$	−2.53228e126	−0.265225
$831$	1.00345e127	0.997363
$832$	−2.63070e126	−0.248145
$833$	−1.40624e126	−0.125893
$834$	1.86275e127	1.58282
$835$	−1.59367e127	−1.28540
$836$	4.87017e125	0.0372882
$837$	−1.08777e127	−0.790639
$838$	−1.57635e126	−0.108777
$839$	1.75408e127	1.14922	0.574612	−	0.818426i	$-0.305153\pi$
$839$	1.75408e127	1.14922	0.574612	+	0.818426i	$0.305153\pi$
$840$	−1.23480e127	−0.768154
$841$	−4.01084e126	−0.236925
$842$	5.05817e126	0.283738
$843$	6.29260e126	0.335221
$844$	−1.09380e127	−0.553405
$845$	−1.04638e128	−5.02831
$846$	−5.32265e126	−0.242950
$847$	2.43402e127	1.05535
$848$	−6.19073e126	−0.254989
$849$	−2.70710e127	−1.05930
$850$	3.55288e127	1.32086
$851$	−1.68657e125	−0.00595755
$852$	1.54933e127	0.520023
$853$	1.69728e127	0.541340	0.270670	−	0.962672i	$-0.412755\pi$
$853$	1.69728e127	0.541340	0.270670	+	0.962672i	$0.412755\pi$
$854$	2.36027e127	0.715391
$855$	2.26399e127	0.652153
$856$	−1.09797e127	−0.300596
$857$	−5.74056e126	−0.149379	−0.0746893	−	0.997207i	$-0.523797\pi$
$857$	−5.74056e126	−0.149379	−0.0746893	+	0.997207i	$0.523797\pi$
$858$	−5.69685e126	−0.140909
$859$	4.40138e127	1.03487	0.517436	−	0.855722i	$-0.326887\pi$
$859$	4.40138e127	1.03487	0.517436	+	0.855722i	$0.326887\pi$
$860$	2.42884e127	0.542895
$861$	8.55256e127	1.81743
$862$	8.41012e126	0.169917
$863$	−8.05777e127	−1.54791	−0.773954	−	0.633242i	$-0.781724\pi$
$863$	−8.05777e127	−1.54791	−0.773954	+	0.633242i	$0.781724\pi$
$864$	6.60193e126	0.120593
$865$	−4.40424e127	−0.765016
$866$	−2.76183e127	−0.456215
$867$	−4.32411e126	−0.0679307
$868$	−4.12217e127	−0.615911
$869$	4.33074e126	0.0615463
$870$	−9.34075e127	−1.26268
$871$	2.82506e128	3.63278
$872$	9.60218e126	0.117463
$873$	1.02901e127	0.119756
$874$	−2.89534e125	−0.00320592
$875$	1.59282e128	1.67809
$876$	−3.96177e127	−0.397155
$877$	7.51738e127	0.717107	0.358554	−	0.933509i	$-0.383270\pi$
$877$	7.51738e127	0.717107	0.358554	+	0.933509i	$0.383270\pi$
$878$	−5.00741e127	−0.454571
$879$	−1.82303e128	−1.57499
$880$	4.36475e126	0.0358892
$881$	−2.43356e128	−1.90454	−0.952269	−	0.305260i	$-0.901257\pi$
$881$	−2.43356e128	−1.90454	−0.952269	+	0.305260i	$0.901257\pi$
$882$	−5.28387e126	−0.0393612
$883$	−1.48219e128	−1.05103	−0.525514	−	0.850785i	$-0.676127\pi$
$883$	−1.48219e128	−1.05103	−0.525514	+	0.850785i	$0.676127\pi$
$884$	1.42803e128	0.963971
$885$	−3.25174e128	−2.08970
$886$	1.22255e128	0.748000
$887$	2.74514e128	1.59914	0.799571	−	0.600571i	$-0.205060\pi$
$887$	2.74514e128	1.59914	0.799571	+	0.600571i	$0.205060\pi$
$888$	−8.89452e127	−0.493354
$889$	−5.50029e127	−0.290509
$890$	−3.09218e128	−1.55525
$891$	2.18239e127	0.104533
$892$	9.72569e127	0.443659
$893$	−1.63574e128	−0.710683
$894$	9.81295e127	0.406086
$895$	4.21034e128	1.65964
$896$	2.50185e127	0.0939427
$897$	3.38681e126	0.0121149
$898$	−2.44138e128	−0.831983
$899$	−3.11825e128	−1.01243
$900$	1.33498e128	0.412976
$901$	3.36053e128	0.990558
$902$	−3.02314e127	−0.0849129
$903$	3.01484e128	0.806952
$904$	−6.85500e127	−0.174856
$905$	−1.92042e128	−0.466856
$906$	4.38590e127	0.101621
$907$	3.46143e128	0.764432	0.382216	−	0.924073i	$-0.375161\pi$
$907$	3.46143e128	0.764432	0.382216	+	0.924073i	$0.375161\pi$
$908$	2.94271e127	0.0619460
$909$	−3.62106e127	−0.0726620
$910$	1.33351e129	2.55091
$911$	−2.70114e128	−0.492603	−0.246302	−	0.969193i	$-0.579215\pi$
$911$	−2.70114e128	−0.492603	−0.246302	+	0.969193i	$0.579215\pi$
$912$	−1.52693e128	−0.265487
$913$	1.11107e127	0.0184188
$914$	−3.13602e128	−0.495700
$915$	−1.29102e129	−1.94588
$916$	6.47198e128	0.930216
$917$	−8.42430e126	−0.0115470
$918$	−3.58375e128	−0.468469
$919$	3.58249e128	0.446642	0.223321	−	0.974745i	$-0.428310\pi$
$919$	3.58249e128	0.446642	0.223321	+	0.974745i	$0.428310\pi$
$920$	−2.59487e126	−0.00308564
$921$	−6.04311e126	−0.00685435
$922$	9.16879e127	0.0992012
$923$	−1.67318e129	−1.72691
$924$	5.41784e127	0.0533452
$925$	2.38981e129	2.24491
$926$	−1.02907e129	−0.922291
$927$	6.56086e128	0.561038
$928$	1.89254e128	0.154422
$929$	9.35136e128	0.728100	0.364050	−	0.931379i	$-0.381394\pi$
$929$	9.35136e128	0.728100	0.364050	+	0.931379i	$0.381394\pi$
$930$	2.25475e129	1.67529
$931$	−1.62382e128	−0.115140
$932$	−6.87397e128	−0.465174
$933$	−3.67266e129	−2.37208
$934$	−1.23037e129	−0.758483
$935$	−2.36933e128	−0.139419
$936$	5.36575e128	0.301391
$937$	−1.71167e129	−0.917800	−0.458900	−	0.888488i	$-0.651756\pi$
$937$	−1.71167e129	−0.917800	−0.458900	+	0.888488i	$0.651756\pi$
$938$	−2.68670e129	−1.37529
$939$	3.24101e128	0.158390
$940$	−1.46599e129	−0.684019
$941$	3.74042e129	1.66637	0.833186	−	0.552993i	$-0.186514\pi$
$941$	3.74042e129	1.66637	0.833186	+	0.552993i	$0.186514\pi$
$942$	−1.79466e129	−0.763429
$943$	1.79727e127	0.00730055
$944$	6.58840e128	0.255563
$945$	−3.34654e129	−1.23969
$946$	−1.06568e128	−0.0377019
$947$	9.42721e128	0.318536	0.159268	−	0.987235i	$-0.449087\pi$
$947$	9.42721e128	0.318536	0.159268	+	0.987235i	$0.449087\pi$
$948$	−1.35780e129	−0.438202
$949$	4.27846e129	1.31889
$950$	4.10261e129	1.20805
$951$	1.83363e129	0.515774
$952$	−1.35809e129	−0.364939
$953$	3.58993e129	0.921606	0.460803	−	0.887503i	$-0.347562\pi$
$953$	3.58993e129	0.921606	0.460803	+	0.887503i	$0.347562\pi$
$954$	1.26270e129	0.309704
$955$	9.04753e129	2.12023
$956$	−2.50785e129	−0.561543
$957$	4.09836e128	0.0876881
$958$	8.83010e127	0.0180537
$959$	−4.97982e129	−0.972982
$960$	−1.36847e129	−0.255526
$961$	1.92349e129	0.343260
$962$	9.60551e129	1.63834
$963$	2.23950e129	0.365097
$964$	−6.73661e128	−0.104976
$965$	−2.11345e130	−3.14813
$966$	−3.22093e127	−0.00458645
$967$	−1.70160e129	−0.231635	−0.115818	−	0.993270i	$-0.536949\pi$
$967$	−1.70160e129	−0.231635	−0.115818	+	0.993270i	$0.536949\pi$
$968$	2.69750e129	0.351061
$969$	8.28868e129	1.03134
$970$	2.83414e129	0.337171
$971$	2.60034e129	0.295796	0.147898	−	0.989003i	$-0.452749\pi$
$971$	2.60034e129	0.295796	0.147898	+	0.989003i	$0.452749\pi$
$972$	−3.70657e129	−0.403172
$973$	1.91312e130	1.98991
$974$	−9.89483e129	−0.984224
$975$	−4.79901e130	−4.56510
$976$	2.61576e129	0.237975
$977$	−7.15565e129	−0.622637	−0.311319	−	0.950306i	$-0.600771\pi$
$977$	−7.15565e129	−0.622637	−0.311319	+	0.950306i	$0.600771\pi$
$978$	−8.69842e128	−0.0723936
$979$	1.35673e129	0.108006
$980$	−1.45531e129	−0.110820
$981$	−1.95853e129	−0.142668
$982$	5.10147e128	0.0355505
$983$	6.64428e129	0.442966	0.221483	−	0.975164i	$-0.428910\pi$
$983$	6.64428e129	0.442966	0.221483	+	0.975164i	$0.428910\pi$
$984$	9.47835e129	0.604569
$985$	3.33983e130	2.03821
$986$	−1.02734e130	−0.599883
$987$	−1.81968e130	−1.01672
$988$	1.64899e130	0.881637
$989$	6.33553e127	0.00324149
$990$	−8.90265e128	−0.0435901
$991$	8.82385e129	0.413480	0.206740	−	0.978396i	$-0.433715\pi$
$991$	8.82385e129	0.413480	0.206740	+	0.978396i	$0.433715\pi$
$992$	−4.56839e129	−0.204883
$993$	−1.16499e130	−0.500070
$994$	1.59123e130	0.653772
$995$	−4.44156e130	−1.74675
$996$	−3.48349e129	−0.131139
$997$	2.88307e130	1.03900	0.519500	−	0.854470i	$-0.326118\pi$
$997$	2.88307e130	1.03900	0.519500	+	0.854470i	$0.326118\pi$
$998$	3.19848e130	1.10348
$999$	−2.41057e130	−0.796199

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2.88.a.b.1.3	✓	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2.88.a.b.1.3	✓	4	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 2 \)
Weight:	\( k \)	\(=\)	\( 88 \)
Character orbit:	\([\chi]\)	\(=\)	2.a (trivial)

\(f(q)\)	\(=\)	\(q-8.79609e12 q^{2} +6.79758e20 q^{3} +7.73713e25 q^{4} -4.34651e30 q^{5} -5.97921e33 q^{6} -6.14091e36 q^{7} -6.80565e38 q^{8} +1.38813e41 q^{9} +3.82323e43 q^{10} -1.67749e44 q^{11} +5.25937e46 q^{12} -5.67978e48 q^{13} +5.40160e49 q^{14} -2.95458e51 q^{15} +5.98631e51 q^{16} -3.24957e53 q^{17} -1.22101e54 q^{18} -3.75237e55 q^{19} -3.36295e56 q^{20} -4.17433e57 q^{21} +1.47553e57 q^{22} -8.77213e56 q^{23} -4.62619e59 q^{24} +1.24298e61 q^{25} +4.99599e61 q^{26} -1.25378e62 q^{27} -4.75130e62 q^{28} -3.59415e63 q^{29} +2.59887e64 q^{30} +8.67588e64 q^{31} -5.26561e64 q^{32} -1.14029e65 q^{33} +2.85835e66 q^{34} +2.66916e67 q^{35} +1.07401e67 q^{36} +1.92264e68 q^{37} +3.30062e68 q^{38} -3.86088e69 q^{39} +2.95808e69 q^{40} -2.04884e70 q^{41} +3.67178e70 q^{42} -7.22234e70 q^{43} -1.29789e70 q^{44} -6.03351e71 q^{45} +7.71605e69 q^{46} +4.35922e72 q^{47} +4.06924e72 q^{48} +4.32746e72 q^{49} -1.09334e74 q^{50} -2.20892e74 q^{51} -4.39452e74 q^{52} -1.03415e75 q^{53} +1.10284e75 q^{54} +7.29122e74 q^{55} +4.17929e75 q^{56} -2.55070e76 q^{57} +3.16145e76 q^{58} +1.10058e77 q^{59} -2.28599e77 q^{60} +4.36957e77 q^{61} -7.63139e77 q^{62} -8.52436e77 q^{63} +4.63168e77 q^{64} +2.46873e79 q^{65} +1.00301e78 q^{66} -4.97389e79 q^{67} -2.51423e79 q^{68} -5.96292e77 q^{69} -2.34781e80 q^{70} +2.94585e80 q^{71} -9.44710e79 q^{72} -7.53278e80 q^{73} -1.69118e81 q^{74} +8.44928e81 q^{75} -2.90325e81 q^{76} +1.03013e81 q^{77} +3.39606e82 q^{78} -2.58168e82 q^{79} -2.60196e82 q^{80} -1.30099e83 q^{81} +1.80218e83 q^{82} -6.62340e82 q^{83} -3.22973e83 q^{84} +1.41243e84 q^{85} +6.35284e83 q^{86} -2.44315e84 q^{87} +1.14164e83 q^{88} -8.08787e84 q^{89} +5.30713e84 q^{90} +3.48790e85 q^{91} -6.78711e82 q^{92} +5.89750e85 q^{93} -3.83441e85 q^{94} +1.63097e86 q^{95} -3.57934e85 q^{96} +7.41293e85 q^{97} -3.80648e85 q^{98} -2.32856e85 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 35184372088832 q^{2} + 40\!\cdots\!28 q^{3} + 30\!\cdots\!56 q^{4} - 40\!\cdots\!60 q^{5} - 35\!\cdots\!24 q^{6} + 85\!\cdots\!04 q^{7} - 27\!\cdots\!48 q^{8} + 82\!\cdots\!48 q^{9} + 35\!\cdots\!80 q^{10}+ \cdots + 22\!\cdots\!76 q^{99}+O(q^{100}) \) 4 * q - 35184372088832 * q^2 + 403237985254067182128 * q^3 + 309485009821345068724781056 * q^4 - 4037922390733497835169570162760 * q^5 - 3546918828382512738768149884698624 * q^6 + 8582179387397492406597229487230375904 * q^7 - 2722258935367507707706996859454145691648 * q^8 + 820135434884318664352221575507492568732948 * q^9 + 35517940965348365626859729845107910854574080 * q^10 + 2970616434026495781757184460756379040517208848 * q^11 + 31199027956673594964608194726311446315419041792 * q^12 - 1767394568818848613362028589161957028533441611112 * q^13 - 75489648224824411010546555477731971328955260076032 * q^14 + 3370976843124805373452544557684295582910726697502880 * q^15 + 23945242826029513411849172299223580994042798784118784 * q^16 - 702353032002195299447255515013113779135644499293109816 * q^17 - 7213987576051478951188874632704563580254297738585309184 * q^18 + 38051210330377980576900552965948384772060949611758270960 * q^19 - 312419112688496434410317985513745659312699567327821168640 * q^20 - 2960768946346244712423575885216855505816696171119080255872 * q^21 - 26129818486996871127304316256231512888117802859237038096384 * q^22 + 267410844513343534387094489566271409098947974355011539188128 * q^23 - 274429552109368924814832586348763817236857825346144736116736 * q^24 + 26866935732372298920001618987293695975686810093231631671755100 * q^25 + 15546167034275791140382436144471296993092547711081656715575296 * q^26 + 98351974670575379028284146601861806526822489553847883125490400 * q^27 + 664013967999314535695892002534007752932295679741402958744518656 * q^28 - 936377285291713459807588765220376016646503474372565915415382440 * q^29 - 29651425887834852403903990749669038123824799034099618745983959040 * q^30 + 119463507882721430244886842916392661099853847057206322986794525568 * q^31 - 210624583337114373395836055367340864637790190801098222508621955072 * q^32 - 975951433415384517573045287992141578476030063995050605617360966464 * q^33 + 6177962603921142192805661314942895498269819437765021241050270793728 * q^34 + 14105085028850567766840711566409137394874532315214531645239547531840 * q^35 + 63454905780001617731151046382612710619432714548573512194720658358272 * q^36 + 182087106643248709136261820106869557597167548749803025400276539121464 * q^37 - 334701985673606721323645108291715305922613643471269213861286961479680 * q^38 - 5157167650299694789254850025641525408739411563899847457339313757250784 * q^39 + 2748067577123698321827685975535901419950085077291708477942376033157120 * q^40 + 5499251594717860286021866958065054045901150247706209838765933372175208 * q^41 + 26043199069326335451693431452427559455621627547084532573326442418405376 * q^42 - 157807090931211109929865823295822094205785343123733495078770527721821552 * q^43 + 229840314065034778104010119086398472312972227124835062038272769756495872 * q^44 - 1370445036354823659067923168385609449595471872659192002945296358462825320 * q^45 - 2352170663486569504369914341681047401963148037857733129248014646193946624 * q^46 - 11700969700600051870794491472787906623524149540240126773037581150641555136 * q^47 + 2413907868396886727226140291242059049083751312718584875630451012128473088 * q^48 + 45608750768809825384693277965554885824930550141562503946687984691665533732 * q^49 - 236324065923630760668657815178197122585685320681456781276991408990637260800 * q^50 - 914883468555652107825206155517190576830844787740672822262980556765469169312 * q^51 - 136745531372273324016576733538944106078280970896210682631976284458024173568 * q^52 - 3205407327892231366350098762423033970241498041998526172742677864692608514312 * q^53 - 865113118120226050927175001395744751092084611954848335836798017458090803200 * q^54 - 10009926131406218736826424103970095109094189414661383153140158173941128709920 * q^55 - 5840728630567416793561662980979737449788739679624018831289026246209278312448 * q^56 + 24760562583447132282306921710743074800398451150699602451361304490068034752320 * q^57 + 8236461705308510473577685400040524235406303263089755599489781422351733227520 * q^58 - 81401388903576961577929700275194040780233584053778446123485310614164754536880 * q^59 + 260816700350501796503049467891128405126358446664151554703502613334842482360320 * q^60 + 908111889319782669823282318823295371554753169091641506977419705876741077882328 * q^61 - 1050812128095696376586514967647428079039044942828517372626320439677738647814144 * q^62 + 7137835102413627130280079665652016586382162073538425059614697312278117344350048 * q^63 + 1852673427797059126777135760139006525652319754650249024631321344126610074238976 * q^64 + 11407211919915638593357605065156231994296813060854399078385375214171172364857680 * q^65 + 8584559593478959280621500012652850349171438888492092327918713325137577495232512 * q^66 - 65059771693644954593974794228917141656005263924052931483321156753263176566322896 * q^67 - 54341933751812724902023253670568124974314494093364989057139191298059718491111424 * q^68 - 144323666676858272713465642347149842097884989245184653886655055101689375583845504 * q^69 - 124069639999923005500646624090308971041908232841505948959254386145464972707102720 * q^70 - 183272612160344892942190287282961718510131375557583525213035115209249713064136992 * q^71 - 558155253956338317275929527602177423655680841848067355296117578760944212116504576 * q^72 + 354182538046550765754528347144724476790476600029207619306415675742769571814637288 * q^73 - 1601655128178723932025775974507397068426901430503198065737820251919877020961472512 * q^74 + 710386439551323791969874648476083944602337020291621916942901745237698809202501200 * q^75 + 2944069800702774064027323538684509525361173924971530627370715914294143730780733440 * q^76 + 39316760279456924611775164190833990669200449799501752350802186925973327788597118848 * q^77 + 45362926383157972415756683406366951526581873158623352931657948697548800307937411072 * q^78 + 15689408650300008287770111864298279692820798574497171271867094782550105530843081920 * q^79 - 24172258039693807695503348146758763873414302432021545297363850106765398076513320960 * q^80 - 196590592451401107987710944406206415161857917104016937408869683425180184810203702876 * q^81 - 48371928579663987252349183028740936842481506637169603120359663272770590191611019264 * q^82 + 111926752599709260117886233216331177095176580206068162806299107496899925996223203568 * q^83 - 229078401609675258913891688255885614430188449105962531942162006259872232223914590208 * q^84 - 891497844731417844264766892389844899904478293183670323386186444763703698463839596560 * q^85 + 1388085851394969400976659588554077855842466084275351230019781346209556380442549026816 * q^86 + 2027498154029213080175869882525768385333184769847411190333977363043382754362186713120 * q^87 - 2021696782769547651193529032558892722193566089333659035337753899891686714980356325376 * q^88 - 1111763274969003683091618237538433748811411444468148051875571331333583253595104867160 * q^89 + 12054562021600253271129669326554918303828197627410649510778436683009490086217184706560 * q^90 + 79630263055292573954918630151432006426386375686727482380289693283976606755116980321088 * q^91 + 20689911960136575706111408504507326985128933416561732998791094227623959804415198625792 * q^92 + 121552396376548026998325328889505560359171182104366398760596365823334350324441379006976 * q^93 + 102922817936515347171258282828953462563508237397083710417081191671708730834331304460288 * q^94 + 360329377379389097240594968925389763617374668200294178024200943546627617266362721242400 * q^95 - 21232958157458842504504822471050360495135888697596704547293213652627233307394314338304 * q^96 + 84654632295309208342666811638631082612402959416215649507302559581340331556342797429384 * q^97 - 401178814389151860471251451603139889379513741986404607571754642978513123633817249120256 * q^98 + 2203878007770692926523827334498155512549713414229081953932986276578630523661724303178576 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more