LMFDB - Embedded newform 1.100.a.a.1.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1,100,Mod(1,1)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1, base_ring=CyclotomicField(1))

chi = DirichletCharacter(H, H._module([]))

N = Newforms(chi, 100, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("1.1");

S:= CuspForms(chi, 100);

N := Newforms(S);

Level:	$ N $	$=$	$ 1 $
Weight:	$ k $	$=$	$ 100 $
Character orbit:	$[\chi]$	$=$	1.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	yes
Analytic conductor:	$62.0676682981$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} + \cdots + 23\!\cdots\!00 $ x^8 - x^7 - 765795356833478153590815019x^6 - 847018239936508469063593510315947812341x^5 + 166266085475297433798436838383182406675010433940631891x^4 + 383003540937606521762330014068972951053203782113187882011683494365x^3 - 11669647006531450010063357990045396397379108481887224639799570451704082949635225x^2 - 23238142613948580473684129972228711535824919000337506052734804657134844164338957751998110375x + 236649725056018508613975268945421267815761184396120868241489878887556709696071978474081515546520542830000
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	multiple of $ 2^{109}\cdot 3^{44}\cdot 5^{13}\cdot 7^{9}\cdot 11^{3}\cdot 13\cdot 17 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Root			$1.56804e13$ of defining polynomial
Character	$\chi$	$=$	1.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.10299e15 q^{2} +5.08811e23 q^{3} +5.82752e29 q^{4} +3.48045e34 q^{5} +5.61211e38 q^{6} +4.01523e41 q^{7} -5.63335e43 q^{8} +8.70965e46 q^{9} +O(q^{10})$	\(q+1.10299e15 q^{2} +5.08811e23 q^{3} +5.82752e29 q^{4} +3.48045e34 q^{5} +5.61211e38 q^{6} +4.01523e41 q^{7} -5.63335e43 q^{8} +8.70965e46 q^{9} +3.83889e49 q^{10} +4.15197e51 q^{11} +2.96511e53 q^{12} -4.59067e54 q^{13} +4.42874e56 q^{14} +1.77089e58 q^{15} -4.31498e59 q^{16} +1.61313e61 q^{17} +9.60661e61 q^{18} -2.54791e63 q^{19} +2.02824e64 q^{20} +2.04300e65 q^{21} +4.57956e66 q^{22} +2.64606e67 q^{23} -2.86631e67 q^{24} -3.66366e68 q^{25} -5.06345e69 q^{26} -4.30943e70 q^{27} +2.33988e71 q^{28} +1.04939e72 q^{29} +1.95327e73 q^{30} +1.04509e74 q^{31} -4.40230e74 q^{32} +2.11257e75 q^{33} +1.77925e76 q^{34} +1.39748e76 q^{35} +5.07556e76 q^{36} +1.95635e76 q^{37} -2.81031e78 q^{38} -2.33579e78 q^{39} -1.96066e78 q^{40} -7.32415e79 q^{41} +2.25339e80 q^{42} -3.18946e80 q^{43} +2.41957e81 q^{44} +3.03135e81 q^{45} +2.91856e82 q^{46} -8.27217e82 q^{47} -2.19551e83 q^{48} -3.00847e83 q^{49} -4.04096e83 q^{50} +8.20777e84 q^{51} -2.67522e84 q^{52} +8.37221e84 q^{53} -4.75324e85 q^{54} +1.44507e86 q^{55} -2.26192e85 q^{56} -1.29641e87 q^{57} +1.15746e87 q^{58} +4.40637e87 q^{59} +1.03199e88 q^{60} +2.09373e87 q^{61} +1.15272e89 q^{62} +3.49712e88 q^{63} -2.12073e89 q^{64} -1.59776e89 q^{65} +2.33013e90 q^{66} +2.84981e90 q^{67} +9.40052e90 q^{68} +1.34634e91 q^{69} +1.54140e91 q^{70} -5.10722e91 q^{71} -4.90645e90 q^{72} +1.71803e92 q^{73} +2.15783e91 q^{74} -1.86411e92 q^{75} -1.48480e93 q^{76} +1.66711e93 q^{77} -2.57634e93 q^{78} -7.83106e93 q^{79} -1.50181e94 q^{80} -3.68894e94 q^{81} -8.07843e94 q^{82} +1.37202e95 q^{83} +1.19056e95 q^{84} +5.61441e95 q^{85} -3.51793e95 q^{86} +5.33943e95 q^{87} -2.33895e95 q^{88} +4.51907e95 q^{89} +3.34354e96 q^{90} -1.84326e96 q^{91} +1.54199e97 q^{92} +5.31752e97 q^{93} -9.12409e97 q^{94} -8.86788e97 q^{95} -2.23994e98 q^{96} +1.05705e98 q^{97} -3.31830e98 q^{98} +3.61622e98 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 208040616902520 q^{2} - 28\!\cdots\!20 q^{3}+ \cdots + 15\!\cdots\!76 q^{9}+O(q^{10}) $ 8 * q - 208040616902520 * q^2 - 282956306495420632223520 * q^3 + 2874573971021731526732655093824 * q^4 - 48829879146635109942685521105004560 * q^5 - 77942153094234171155671704171199405344 * q^6 - 56830940560713017104682273454607970657600 * q^7 + 592603013041539183163433278232078795937538560 * q^8 + 15585042525631880727258151421002821416820695976 * q^9	$ 8 q - 208040616902520 q^{2} - 28\!\cdots\!20 q^{3}+ \cdots - 13\!\cdots\!08 q^{99}+O(q^{100}) $ 8 * q - 208040616902520 * q^2 - 282956306495420632223520 * q^3 + 2874573971021731526732655093824 * q^4 - 48829879146635109942685521105004560 * q^5 - 77942153094234171155671704171199405344 * q^6 - 56830940560713017104682273454607970657600 * q^7 + 592603013041539183163433278232078795937538560 * q^8 + 15585042525631880727258151421002821416820695976 * q^9 - 20961738819400631174675750189416259674325116377360 * q^10 + 668605620058921294359176615672652323197376366725536 * q^11 - 260751428362765138428103958747533086169389679507011840 * q^12 - 5313129021153651674083973849295770678848247690376073040 * q^13 - 275891262636795191856274681125121829106120036919920873792 * q^14 + 39601076201132911228470767893146157937452742673766616546880 * q^15 + 1686978001168411473373901309719868789822314791151035737182208 * q^16 + 29870581004484716934093126001838988402381517134653878061066640 * q^17 + 104619592562318909205389831941745992324800916717508145002954280 * q^18 - 2584541347057387315132230533073883085094549482599567538462153120 * q^19 - 87020910945991395973478129409062640628123700866757624264022986880 * q^20 + 720725986617461186277876616197863336884455731162862159407836416 * q^21 + 6448630494375222037284713151002631218361976067562272720681828806560 * q^22 - 591705231800483702926418342143069697446663268741979110571049882560 * q^23 - 786094952626208255303024343193893163353569305701641632350239286773760 * q^24 + 716804381062067209680195080749365299641535704320602348503400092268600 * q^25 + 34654632463607194325743429354208471986051789816879940147342898057153456 * q^26 + 13869683363495491009982193176608883185849831807068440771218044677979840 * q^27 - 1135994339501291724748966539673012720374432727977564592829456188165859840 * q^28 - 439009994693767454184499584774890376667926937141064013921655743937571280 * q^29 + 23517293722912668382363618879896733566643340714874843272431473003480521280 * q^30 - 42796079732631926995692344425065773646038440365668203549397431930127162624 * q^31 - 284044778854068845159282113651411076631875258269403845301648101866131128320 * q^32 - 1184428676639946519273358190717309258531732537332484528437733831641965671040 * q^33 + 11470334814206853457708153296668381286712583035391282441563479133450208961168 * q^34 - 13317873075112713679215664096634074386516466958921311305188860496632195839360 * q^35 - 224326234591498863152148578877455893579609783196337897663675145770615318305472 * q^36 + 7013041648409278763731742859978750449729753703775477297667583228204170683120 * q^37 + 4097267709666535974097951231260487171744232792996835026005028682857459985875040 * q^38 + 3086772337289173445407063166797596998267422181270693039748051240117483908526912 * q^39 - 61154477845927513224255221208858320971333500267390856556166248662272460823577600 * q^40 + 16836611518887404247693904661111767446154336367366992887095255319045118001938896 * q^41 + 586782577486516292654880709693602500520055556295982039518980517393750164948778240 * q^42 - 115479509651193412125043402629710680178430977878852566804453976757651553792322400 * q^43 - 4823674089938931277708865059630293953738849935605913988972972769383583829463937792 * q^44 - 4204225762790416656941382640299001599040327829208847740401216426127468587838672720 * q^45 + 41220575732227465405339930795314328162570779910219577393801310430729179103724398656 * q^46 + 28878226575287510694522520507929237505491250714878620920990009419290436045018975360 * q^47 - 270645616492149970234041108687889002599221246648694105429287982543953957103033794560 * q^48 - 14382803175556111227730750647629461517090856222687609645964147941666232976982659256 * q^49 + 2538900041031429584911497444199766832786695308479217204477072876574482801521012636600 * q^50 - 1711868817156841452117007804086601271536721152787522351736690290031659132307369497664 * q^51 - 199691168563235615231272208715487263769590246824861808533841002609282642680495606400 * q^52 - 30091820242734525213832735040802634061423162425240717202059443809754039115425881976720 * q^53 + 136432908322968282680263912195201284966825652472631606906205576348979246713807692108480 * q^54 + 226099583633880167546966079422139027647924161654010953637858494806538127768993139084480 * q^55 + 323037227302956226932352973051969540564093713359973342312103259763994205180305378488320 * q^56 - 273423384330404631781757518792671605280054294102341216713398337934356290096852147342720 * q^57 + 5713973478801321937231450378714667908258440100056694714036585358012358074567853731219760 * q^58 + 14607245332654695346837714400351649175544087130678579822473040904252509022932739720811040 * q^59 + 53008257791762983739773607116394245193846456713938833829846630209166818928009302295114240 * q^60 + 38323682921378832161349805479389921828014992489778724538462200957929376165086831637164336 * q^61 + 201697385927609334439920541372343666252345396922224455072723131310512431934088015943381760 * q^62 + 659857333915856699600072965534847901170546674796116288100652182111732663513752207410870720 * q^63 + 2567569508313686836352267062189989701299823975229681223291764819542997452948800142018084864 * q^64 + 2649617703605055039617798586548537725956903247199823944158672914229112797191302156162117280 * q^65 + 7971156345834212651621212324655177899942634890685144307138793590710555397223588657590125952 * q^66 + 11538024122310165476577023936338470394129524138300592332780359783942082451772953721242543840 * q^67 + 56045208748154976002290739488865109707859265886693431912946708486067523902076046154608254080 * q^68 + 54550768708090409722131753417710688638608175085564682877064185400954540597503860451967981312 * q^69 + 143889269423962258520958611175254488367329101991613194841590826662727327088381209016536883840 * q^70 + 52677154721705052088453955375369863850612862186345822027042426779160256515633503076296638656 * q^71 + 365038759307175377119135471724071125896012767600977654405238165616233444129512164397555141120 * q^72 + 506688790556979736999516532365405438114465768501506115275379047447697188620686370699300754640 * q^73 - 399134575097952393052355140371514479012153174980660646654807435656154590439317636650100727312 * q^74 - 2324004895287993423141911565246677610480036000604538705092119528699965986086154360593593272800 * q^75 - 6633935918720327036715040118664821987731317587536782451991725427750234686044104260504536239360 * q^76 - 6461585481973245548189356793856436395182994379442713381123224045549509062132894968864516460800 * q^77 - 28556176219359102115465270938556084350909705495286117230117205751412922131522017940137826091200 * q^78 - 30611582035787076807516826687485094690084083072098723290730859803828786802497884290624307556480 * q^79 - 127732467855339073698199167907855646502900419187610712488908375947950612344972404753625834332160 * q^80 - 105098591020590401711840147132548556253048052082258241572206720930835350937368467193794679663032 * q^81 - 68830371209738349493630432122952083611773652840970378016560437888326646942049769865516365685040 * q^82 + 22938542661502254568160041367746263129225779762371870743525183586562110235427022830971680103520 * q^83 + 361795660381091268015394970465025503071664436510904020432798379164529165144740663778138523854848 * q^84 - 65747002822668948096103688317539312015762969670721483634214688263171509401935169398146161091360 * q^85 + 2926007787385729535219437868096352598169987790407590983846487590337872781868895638215544350378656 * q^86 + 4145530857628120059159343787991300967686349677839106320836691853415365479077514876503669002112320 * q^87 + 13379567436970727806886279611606134975535418870618956336086465570267315661188646758052286051051520 * q^88 + 13262749235321210784149676214189766161707478948372569815117556700615668825668004121877579168519760 * q^89 + 18562789747759155399933926620841126049267839227249440162668332587565567838001478928890860138613680 * q^90 - 6466499581384229905399040912443724309264614193875257390824803270602537852945701184143169943974784 * q^91 - 3605940592933441273788896348672120936868261799818064643016984038777885904937799268971010435816960 * q^92 - 6218230725998946523812046145774116878209214952116357458146814759754757343477151669356631201623040 * q^93 - 111501057917354496628976353847689989005658650697758014190949880350502870630016419857891186452986752 * q^94 - 310841228909329722722502224651860795134807193058850708412373586195233672473563873013656113819102400 * q^95 - 967769551108604066125272773812882212494392412979843145463542262778370585211900025491604732868952064 * q^96 - 870148289336425543686683480565613230312583210673688585087479722135977346731183581578056793848665840 * q^97 - 1259902767579045380431363502561233259244081818944281851461225234703715688976807437199140410707221560 * q^98 - 137018494226539733211453518241879004188470623376815926515879377141376994388427950391858832640432608 * q^99

Display 100 coefficients 10 coefficients

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 $

$2$	1.10299e15	1.38543	0.692716	−	0.721211i	$-0.256414\pi$
$2$	1.10299e15	1.38543	0.692716	+	0.721211i	$0.256414\pi$
$3$	5.08811e23	1.22759	0.613797	−	0.789464i	$-0.289641\pi$
$3$	5.08811e23	1.22759	0.613797	+	0.789464i	$0.289641\pi$
$4$	5.82752e29	0.919420
$5$	3.48045e34	0.876235	0.438118	−	0.898918i	$-0.355645\pi$
$5$	3.48045e34	0.876235	0.438118	+	0.898918i	$0.355645\pi$
$6$	5.61211e38	1.70075
$7$	4.01523e41	0.590687	0.295344	−	0.955391i	$-0.404566\pi$
$7$	4.01523e41	0.590687	0.295344	+	0.955391i	$0.404566\pi$
$8$	−5.63335e43	−0.111638
$9$	8.70965e46	0.506986
$10$	3.83889e49	1.21396
$11$	4.15197e51	1.17305	0.586524	−	0.809932i	$-0.300496\pi$
$11$	4.15197e51	1.17305	0.586524	+	0.809932i	$0.300496\pi$
$12$	2.96511e53	1.12867
$13$	−4.59067e54	−0.332415	−0.166207	−	0.986091i	$-0.553152\pi$
$13$	−4.59067e54	−0.332415	−0.166207	+	0.986091i	$0.553152\pi$
$14$	4.42874e56	0.818357
$15$	1.77089e58	1.07566
$16$	−4.31498e59	−1.07409
$17$	1.61313e61	1.99732	0.998658	−	0.0517994i	$-0.0164956\pi$
$17$	1.61313e61	1.99732	0.998658	+	0.0517994i	$0.0164956\pi$
$18$	9.60661e61	0.702395
$19$	−2.54791e63	−1.28198	−0.640989	−	0.767550i	$-0.721476\pi$
$19$	−2.54791e63	−1.28198	−0.640989	+	0.767550i	$0.721476\pi$
$20$	2.02824e64	0.805628
$21$	2.04300e65	0.725124
$22$	4.57956e66	1.62518
$23$	2.64606e67	1.04009	0.520045	−	0.854139i	$-0.325915\pi$
$23$	2.64606e67	1.04009	0.520045	+	0.854139i	$0.325915\pi$
$24$	−2.86631e67	−0.137046
$25$	−3.66366e68	−0.232212
$26$	−5.06345e69	−0.460538
$27$	−4.30943e70	−0.605220
$28$	2.33988e71	0.543090
$29$	1.04939e72	0.428782	0.214391	−	0.976748i	$-0.431223\pi$
$29$	1.04939e72	0.428782	0.214391	+	0.976748i	$0.431223\pi$
$30$	1.95327e73	1.49025
$31$	1.04509e74	1.57307	0.786536	−	0.617545i	$-0.211873\pi$
$31$	1.04509e74	1.57307	0.786536	+	0.617545i	$0.211873\pi$
$32$	−4.40230e74	−1.37644
$33$	2.11257e75	1.44003
$34$	1.77925e76	2.76714
$35$	1.39748e76	0.517581
$36$	5.07556e76	0.466133
$37$	1.95635e76	0.0462873	0.0231436	−	0.999732i	$-0.492632\pi$
$37$	1.95635e76	0.0462873	0.0231436	+	0.999732i	$0.492632\pi$
$38$	−2.81031e78	−1.77609
$39$	−2.33579e78	−0.408070
$40$	−1.96066e78	−0.0978213
$41$	−7.32415e79	−1.07636	−0.538179	−	0.842831i	$-0.680887\pi$
$41$	−7.32415e79	−1.07636	−0.538179	+	0.842831i	$0.680887\pi$
$42$	2.25339e80	1.00461
$43$	−3.18946e80	−0.443638	−0.221819	−	0.975088i	$-0.571199\pi$
$43$	−3.18946e80	−0.443638	−0.221819	+	0.975088i	$0.571199\pi$
$44$	2.41957e81	1.07852
$45$	3.03135e81	0.444239
$46$	2.91856e82	1.44097
$47$	−8.27217e82	−1.40856	−0.704281	−	0.709922i	$-0.748730\pi$
$47$	−8.27217e82	−1.40856	−0.704281	+	0.709922i	$0.748730\pi$
$48$	−2.19551e83	−1.31854
$49$	−3.00847e83	−0.651089
$50$	−4.04096e83	−0.321714
$51$	8.20777e84	2.45189
$52$	−2.67522e84	−0.305629
$53$	8.37221e84	0.372550	0.186275	−	0.982498i	$-0.440358\pi$
$53$	8.37221e84	0.372550	0.186275	+	0.982498i	$0.440358\pi$
$54$	−4.75324e85	−0.838491
$55$	1.44507e86	1.02787
$56$	−2.26192e85	−0.0659432
$57$	−1.29641e87	−1.57375
$58$	1.15746e87	0.594049
$59$	4.40637e87	0.970302	0.485151	−	0.874430i	$-0.338765\pi$
$59$	4.40637e87	0.970302	0.485151	+	0.874430i	$0.338765\pi$
$60$	1.03199e88	0.988984
$61$	2.09373e87	0.0885307	0.0442653	−	0.999020i	$-0.485905\pi$
$61$	2.09373e87	0.0885307	0.0442653	+	0.999020i	$0.485905\pi$
$62$	1.15272e89	2.17938
$63$	3.49712e88	0.299470
$64$	−2.12073e89	−0.832870
$65$	−1.59776e89	−0.291274
$66$	2.33013e90	1.99506
$67$	2.84981e90	1.15908	0.579540	−	0.814944i	$-0.303232\pi$
$67$	2.84981e90	1.15908	0.579540	+	0.814944i	$0.303232\pi$
$68$	9.40052e90	1.83637
$69$	1.34634e91	1.27681
$70$	1.54140e91	0.717073
$71$	−5.10722e91	−1.17733	−0.588663	−	0.808379i	$-0.700345\pi$
$71$	−5.10722e91	−1.17733	−0.588663	+	0.808379i	$0.700345\pi$
$72$	−4.90645e90	−0.0565990
$73$	1.71803e92	1.00127	0.500634	−	0.865659i	$-0.333100\pi$
$73$	1.71803e92	1.00127	0.500634	+	0.865659i	$0.333100\pi$
$74$	2.15783e91	0.0641279
$75$	−1.86411e92	−0.285062
$76$	−1.48480e93	−1.17868
$77$	1.66711e93	0.692905
$78$	−2.57634e93	−0.565354
$79$	−7.83106e93	−0.914702	−0.457351	−	0.889286i	$-0.651202\pi$
$79$	−7.83106e93	−0.914702	−0.457351	+	0.889286i	$0.651202\pi$
$80$	−1.50181e94	−0.941153
$81$	−3.68894e94	−1.24995
$82$	−8.07843e94	−1.49122
$83$	1.37202e95	1.38994	0.694968	−	0.719041i	$-0.255418\pi$
$83$	1.37202e95	1.38994	0.694968	+	0.719041i	$0.255418\pi$
$84$	1.19056e95	0.666693
$85$	5.61441e95	1.75012
$86$	−3.51793e95	−0.614630
$87$	5.33943e95	0.526371
$88$	−2.33895e95	−0.130957
$89$	4.51907e95	0.144625	0.0723125	−	0.997382i	$-0.476962\pi$
$89$	4.51907e95	0.144625	0.0723125	+	0.997382i	$0.476962\pi$
$90$	3.34354e96	0.615463
$91$	−1.84326e96	−0.196353
$92$	1.54199e97	0.956280
$93$	5.31752e97	1.93109
$94$	−9.12409e97	−1.95146
$95$	−8.86788e97	−1.12331
$96$	−2.23994e98	−1.68970
$97$	1.05705e98	0.477415	0.238708	−	0.971092i	$-0.423276\pi$
$97$	1.05705e98	0.477415	0.238708	+	0.971092i	$0.423276\pi$
$98$	−3.31830e98	−0.902038
$99$	3.61622e98	0.594720
$100$	−2.13500e98	−0.213500
$101$	−2.19279e99	−1.33995	−0.669975	−	0.742383i	$-0.733695\pi$
$101$	−2.19279e99	−1.33995	−0.669975	+	0.742383i	$0.733695\pi$
$102$	9.05305e99	3.39693
$103$	−3.03255e99	−0.702046	−0.351023	−	0.936367i	$-0.614166\pi$
$103$	−3.03255e99	−0.702046	−0.351023	+	0.936367i	$0.614166\pi$
$104$	2.58609e98	0.0371102
$105$	7.11055e99	0.635379
$106$	9.23443e99	0.516143
$107$	−1.73760e100	−0.610174	−0.305087	−	0.952324i	$-0.598686\pi$
$107$	−1.73760e100	−0.610174	−0.305087	+	0.952324i	$0.598686\pi$
$108$	−2.51133e100	−0.556452
$109$	2.62017e100	0.367890	0.183945	−	0.982937i	$-0.441113\pi$
$109$	2.62017e100	0.367890	0.183945	+	0.982937i	$0.441113\pi$
$110$	1.59390e101	1.42404
$111$	9.95414e99	0.0568220
$112$	−1.73256e101	−0.634450
$113$	−8.19638e101	−1.93303	−0.966516	−	0.256608i	$-0.917395\pi$
$113$	−8.19638e101	−1.93303	−0.966516	+	0.256608i	$0.917395\pi$
$114$	−1.42992e102	−2.18032
$115$	9.20948e101	0.911364
$116$	6.11535e101	0.394231
$117$	−3.99831e101	−0.168530
$118$	4.86017e102	1.34429
$119$	6.47707e102	1.17979
$120$	−9.97608e101	−0.120085
$121$	4.71101e102	0.376044
$122$	2.30935e102	0.122653
$123$	−3.72661e103	−1.32133
$124$	6.09026e103	1.44631
$125$	−6.76631e103	−1.07971
$126$	3.85728e103	0.414896
$127$	−4.94055e103	−0.359328	−0.179664	−	0.983728i	$-0.557501\pi$
$127$	−4.94055e103	−0.359328	−0.179664	+	0.983728i	$0.557501\pi$
$128$	4.51153e103	0.222551
$129$	−1.62283e104	−0.544608
$130$	−1.76231e104	−0.403540
$131$	−1.15128e105	−1.80406	−0.902031	−	0.431671i	$-0.857924\pi$
$131$	−1.15128e105	−1.80406	−0.902031	+	0.431671i	$0.857924\pi$
$132$	1.23110e105	1.32399
$133$	−1.02304e105	−0.757248
$134$	3.14330e105	1.60583
$135$	−1.49988e105	−0.530315
$136$	−9.08731e104	−0.222977
$137$	6.01427e105	1.02687	0.513435	−	0.858129i	$-0.328373\pi$
$137$	6.01427e105	1.02687	0.513435	+	0.858129i	$0.328373\pi$
$138$	1.48500e106	1.76893
$139$	3.42864e105	0.285686	0.142843	−	0.989745i	$-0.454376\pi$
$139$	3.42864e105	0.285686	0.142843	+	0.989745i	$0.454376\pi$
$140$	8.14385e105	0.475874
$141$	−4.20898e106	−1.72914
$142$	−5.63319e106	−1.63110
$143$	−1.90603e106	−0.389939
$144$	−3.75819e106	−0.544547
$145$	3.65236e106	0.375714
$146$	1.89497e107	1.38719
$147$	−1.53074e107	−0.799272
$148$	1.14007e106	0.0425575
$149$	3.06873e107	0.820803	0.410401	−	0.911905i	$-0.365389\pi$
$149$	3.06873e107	0.820803	0.410401	+	0.911905i	$0.365389\pi$
$150$	−2.05609e107	−0.394934
$151$	−8.49431e107	−1.17427	−0.587137	−	0.809488i	$-0.699745\pi$
$151$	−8.49431e107	−1.17427	−0.587137	+	0.809488i	$0.699745\pi$
$152$	1.43533e107	0.143118
$153$	1.40498e108	1.01261
$154$	1.83880e108	0.959972
$155$	3.63738e108	1.37838
$156$	−1.36118e108	−0.375188
$157$	−1.98869e108	−0.399517	−0.199758	−	0.979845i	$-0.564016\pi$
$157$	−1.98869e108	−0.399517	−0.199758	+	0.979845i	$0.564016\pi$
$158$	−8.63755e108	−1.26726
$159$	4.25988e108	0.457340
$160$	−1.53220e109	−1.20608
$161$	1.06245e109	0.614369
$162$	−4.06885e109	−1.73172
$163$	6.03161e108	0.189298	0.0946492	−	0.995511i	$-0.469827\pi$
$163$	6.03161e108	0.189298	0.0946492	+	0.995511i	$0.469827\pi$
$164$	−4.26816e109	−0.989624
$165$	7.35270e109	1.26180
$166$	1.51332e110	1.92566
$167$	−5.54548e108	−0.0524172	−0.0262086	−	0.999656i	$-0.508343\pi$
$167$	−5.54548e108	−0.0524172	−0.0262086	+	0.999656i	$0.508343\pi$
$168$	−1.15089e109	−0.0809515
$169$	−1.69644e110	−0.889500
$170$	6.19261e110	2.42467
$171$	−2.21914e110	−0.649946
$172$	−1.85866e110	−0.407890
$173$	−8.88018e110	−1.46265	−0.731324	−	0.682030i	$-0.761097\pi$
$173$	−8.88018e110	−1.46265	−0.731324	+	0.682030i	$0.761097\pi$
$174$	5.88931e110	0.729250
$175$	−1.47104e110	−0.137165
$176$	−1.79157e111	−1.25996
$177$	2.24201e111	1.19114
$178$	4.98446e110	0.200368
$179$	−1.92226e111	−0.585580	−0.292790	−	0.956177i	$-0.594584\pi$
$179$	−1.92226e111	−0.585580	−0.292790	+	0.956177i	$0.594584\pi$
$180$	1.76653e111	0.408442
$181$	−7.30596e111	−1.28407	−0.642034	−	0.766676i	$-0.721909\pi$
$181$	−7.30596e111	−1.28407	−0.642034	+	0.766676i	$0.721909\pi$
$182$	−2.03309e111	−0.272034
$183$	1.06531e111	0.108680
$184$	−1.49062e111	−0.116114
$185$	6.80900e110	0.0405586
$186$	5.86515e112	2.67540
$187$	6.69765e112	2.34295
$188$	−4.82062e112	−1.29506
$189$	−1.73034e112	−0.357496
$190$	−9.78114e112	−1.55628
$191$	−2.33258e112	−0.286210	−0.143105	−	0.989708i	$-0.545709\pi$
$191$	−2.33258e112	−0.286210	−0.143105	+	0.989708i	$0.545709\pi$
$192$	−1.07905e113	−1.02243
$193$	−3.33996e112	−0.244712	−0.122356	−	0.992486i	$-0.539045\pi$
$193$	−3.33996e112	−0.244712	−0.122356	+	0.992486i	$0.539045\pi$
$194$	1.16591e113	0.661426
$195$	−8.12960e112	−0.357566
$196$	−1.75319e113	−0.598624
$197$	1.32367e113	0.351320	0.175660	−	0.984451i	$-0.443794\pi$
$197$	1.32367e113	0.351320	0.175660	+	0.984451i	$0.443794\pi$
$198$	3.98863e113	0.823943
$199$	7.61666e112	0.122613	0.0613066	−	0.998119i	$-0.480473\pi$
$199$	7.61666e112	0.122613	0.0613066	+	0.998119i	$0.480473\pi$
$200$	2.06387e112	0.0259237
$201$	1.45002e114	1.42288
$202$	−2.41861e114	−1.85641
$203$	4.21355e113	0.253276
$204$	4.78309e114	2.25432
$205$	−2.54914e114	−0.943142
$206$	−3.34486e114	−0.972637
$207$	2.30462e114	0.527312
$208$	1.98087e114	0.357042
$209$	−1.05788e115	−1.50382
$210$	7.84284e114	0.880274
$211$	5.15108e113	0.0457000	0.0228500	−	0.999739i	$-0.492726\pi$
$211$	5.15108e113	0.0457000	0.0228500	+	0.999739i	$0.492726\pi$
$212$	4.87892e114	0.342530
$213$	−2.59861e115	−1.44528
$214$	−1.91655e115	−0.845354
$215$	−1.11008e115	−0.388731
$216$	2.42766e114	0.0675657
$217$	4.19626e115	0.929193
$218$	2.89001e115	0.509686
$219$	8.74155e115	1.22915
$220$	8.42119e115	0.945041
$221$	−7.40533e115	−0.663937
$222$	1.09793e115	0.0787230
$223$	2.49061e116	1.42960	0.714801	−	0.699327i	$-0.246517\pi$
$223$	2.49061e116	1.42960	0.714801	+	0.699327i	$0.246517\pi$
$224$	−1.76763e116	−0.813043
$225$	−3.19092e115	−0.117728
$226$	−9.04048e116	−2.67808
$227$	−3.50484e115	−0.0834426	−0.0417213	−	0.999129i	$-0.513284\pi$
$227$	−3.50484e115	−0.0834426	−0.0417213	+	0.999129i	$0.513284\pi$
$228$	−7.55482e116	−1.44694
$229$	5.34125e116	0.823733	0.411866	−	0.911244i	$-0.364877\pi$
$229$	5.34125e116	0.823733	0.411866	+	0.911244i	$0.364877\pi$
$230$	1.01579e117	1.26263
$231$	8.48245e116	0.850606
$232$	−5.91160e115	−0.0478685
$233$	1.99231e116	0.130389	0.0651943	−	0.997873i	$-0.479233\pi$
$233$	1.99231e116	0.130389	0.0651943	+	0.997873i	$0.479233\pi$
$234$	−4.41008e116	−0.233486
$235$	−2.87909e117	−1.23423
$236$	2.56782e117	0.892115
$237$	−3.98453e117	−1.12288
$238$	7.14412e117	1.63452
$239$	5.17876e117	0.962785	0.481393	−	0.876505i	$-0.340131\pi$
$239$	5.17876e117	0.962785	0.481393	+	0.876505i	$0.340131\pi$
$240$	−7.64137e117	−1.15535
$241$	9.47196e117	1.16572	0.582862	−	0.812571i	$-0.301933\pi$
$241$	9.47196e117	1.16572	0.582862	+	0.812571i	$0.301933\pi$
$242$	5.19618e117	0.520983
$243$	−1.13665e118	−0.929212
$244$	1.22012e117	0.0813969
$245$	−1.04708e118	−0.570507
$246$	−4.11040e118	−1.83061
$247$	1.16966e118	0.426149
$248$	−5.88734e117	−0.175615
$249$	6.98099e118	1.70628
$250$	−7.46314e118	−1.49586
$251$	−7.15202e118	−1.17647	−0.588233	−	0.808692i	$-0.700176\pi$
$251$	−7.15202e118	−1.17647	−0.588233	+	0.808692i	$0.700176\pi$
$252$	2.03795e118	0.275339
$253$	1.09863e119	1.22008
$254$	−5.44936e118	−0.497825
$255$	2.85668e119	2.14843
$256$	1.84179e119	1.14120
$257$	−1.30448e118	−0.0666421	−0.0333210	−	0.999445i	$-0.510608\pi$
$257$	−1.30448e118	−0.0666421	−0.0333210	+	0.999445i	$0.510608\pi$
$258$	−1.78996e119	−0.754516
$259$	7.85521e117	0.0273413
$260$	−9.31099e118	−0.267803
$261$	9.13983e118	0.217387
$262$	−1.26984e120	−2.49940
$263$	2.20154e119	0.358853	0.179427	−	0.983771i	$-0.442576\pi$
$263$	2.20154e119	0.358853	0.179427	+	0.983771i	$0.442576\pi$
$264$	−1.19008e119	−0.160762
$265$	2.91391e119	0.326441
$266$	−1.12840e120	−1.04912
$267$	2.29935e119	0.177541
$268$	1.66073e120	1.06568
$269$	3.21526e120	1.71585	0.857923	−	0.513778i	$-0.171754\pi$
$269$	3.21526e120	1.71585	0.857923	+	0.513778i	$0.171754\pi$
$270$	−1.65434e120	−0.734716
$271$	1.21597e120	0.449721	0.224860	−	0.974391i	$-0.427807\pi$
$271$	1.21597e120	0.449721	0.224860	+	0.974391i	$0.427807\pi$
$272$	−6.96060e120	−2.14529
$273$	−9.37872e119	−0.241042
$274$	6.63366e120	1.42266
$275$	−1.52114e120	−0.272396
$276$	7.84584e120	1.17392
$277$	−4.15037e120	−0.519204	−0.259602	−	0.965716i	$-0.583591\pi$
$277$	−4.15037e120	−0.519204	−0.259602	+	0.965716i	$0.583591\pi$
$278$	3.78173e120	0.395798
$279$	9.10233e120	0.797526
$280$	−7.87252e119	−0.0577818
$281$	6.12157e120	0.376617	0.188309	−	0.982110i	$-0.439699\pi$
$281$	6.12157e120	0.376617	0.188309	+	0.982110i	$0.439699\pi$
$282$	−4.64244e121	−2.39561
$283$	3.43700e121	1.48851	0.744254	−	0.667897i	$-0.232805\pi$
$283$	3.43700e121	1.48851	0.744254	+	0.667897i	$0.232805\pi$
$284$	−2.97624e121	−1.08246
$285$	−4.51208e121	−1.37897
$286$	−2.10233e121	−0.540234
$287$	−2.94082e121	−0.635791
$288$	−3.83425e121	−0.697834
$289$	1.94988e122	2.98927
$290$	4.02850e121	0.520526
$291$	5.37841e121	0.586072
$292$	1.00119e122	0.920585
$293$	−5.59008e121	−0.433981	−0.216990	−	0.976174i	$-0.569624\pi$
$293$	−5.59008e121	−0.433981	−0.216990	+	0.976174i	$0.569624\pi$
$294$	−1.68839e122	−1.10734
$295$	1.53362e122	0.850213
$296$	−1.10208e120	−0.00516743
$297$	−1.78926e122	−0.709953
$298$	3.38477e122	1.13717
$299$	−1.21472e122	−0.345742
$300$	−1.08631e122	−0.262092
$301$	−1.28064e122	−0.262051
$302$	−9.36910e122	−1.62688
$303$	−1.11572e123	−1.64491
$304$	1.09942e123	1.37696
$305$	7.28713e121	0.0775737
$306$	1.54967e123	1.40290
$307$	−5.97976e122	−0.460611	−0.230305	−	0.973118i	$-0.573973\pi$
$307$	−5.97976e122	−0.460611	−0.230305	+	0.973118i	$0.573973\pi$
$308$	9.71512e122	0.637071
$309$	−1.54300e123	−0.861827
$310$	4.01197e123	1.90965
$311$	−4.38353e123	−1.77903	−0.889517	−	0.456902i	$-0.848959\pi$
$311$	−4.38353e123	−1.77903	−0.889517	+	0.456902i	$0.848959\pi$
$312$	1.31583e122	0.0455562
$313$	2.54398e123	0.751743	0.375872	−	0.926672i	$-0.377343\pi$
$313$	2.54398e123	0.751743	0.375872	+	0.926672i	$0.377343\pi$
$314$	−2.19350e123	−0.553503
$315$	1.21716e123	0.262406
$316$	−4.56356e123	−0.840995
$317$	1.14694e124	1.80762	0.903812	−	0.427930i	$-0.140757\pi$
$317$	1.14694e124	1.80762	0.903812	+	0.427930i	$0.140757\pi$
$318$	4.69858e123	0.633613
$319$	4.35704e123	0.502983
$320$	−7.38111e123	−0.729790
$321$	−8.84112e123	−0.749046
$322$	1.17187e124	0.851165
$323$	−4.11010e124	−2.56051
$324$	−2.14974e124	−1.14923
$325$	1.68187e123	0.0771907
$326$	6.65278e123	0.262260
$327$	1.33317e124	0.451619
$328$	4.12595e123	0.120163
$329$	−3.32147e124	−0.832019
$330$	8.10992e124	1.74814
$331$	3.54437e124	0.657739	0.328870	−	0.944375i	$-0.393332\pi$
$331$	3.54437e124	0.657739	0.328870	+	0.944375i	$0.393332\pi$
$332$	7.99547e124	1.27794
$333$	1.70391e123	0.0234670
$334$	−6.11658e123	−0.0726204
$335$	9.91863e124	1.01563
$336$	−8.81548e124	−0.778846
$337$	−8.25306e124	−0.629412	−0.314706	−	0.949189i	$-0.601906\pi$
$337$	−8.25306e124	−0.629412	−0.314706	+	0.949189i	$0.601906\pi$
$338$	−1.87115e125	−1.23234
$339$	−4.17041e125	−2.37298
$340$	3.27181e125	1.60909
$341$	4.33917e125	1.84529
$342$	−2.44768e125	−0.900455
$343$	−3.06328e125	−0.975277
$344$	1.79674e124	0.0495270
$345$	4.68589e125	1.11879
$346$	−9.79471e125	−2.02640
$347$	5.17889e125	0.928811	0.464406	−	0.885623i	$-0.346268\pi$
$347$	5.17889e125	0.928811	0.464406	+	0.885623i	$0.346268\pi$
$348$	3.11156e125	0.483956
$349$	3.31187e125	0.446905	0.223452	−	0.974715i	$-0.428267\pi$
$349$	3.31187e125	0.446905	0.223452	+	0.974715i	$0.428267\pi$
$350$	−1.62254e125	−0.190032
$351$	1.97832e125	0.201184
$352$	−1.82782e126	−1.61463
$353$	1.54525e126	1.18618	0.593090	−	0.805136i	$-0.297908\pi$
$353$	1.54525e126	1.18618	0.593090	+	0.805136i	$0.297908\pi$
$354$	2.47291e126	1.65024
$355$	−1.77755e126	−1.03161
$356$	2.63349e125	0.132971
$357$	3.29561e126	1.44830
$358$	−2.12022e126	−0.811281
$359$	−1.73202e126	−0.577267	−0.288634	−	0.957440i	$-0.593201\pi$
$359$	−1.73202e126	−0.577267	−0.288634	+	0.957440i	$0.593201\pi$
$360$	−1.70767e125	−0.0495941
$361$	2.54176e126	0.643469
$362$	−8.05837e126	−1.77899
$363$	2.39702e126	0.461629
$364$	−1.07416e126	−0.180531
$365$	5.97954e126	0.877346
$366$	1.17503e126	0.150568
$367$	−1.50576e127	−1.68572	−0.842862	−	0.538130i	$-0.819131\pi$
$367$	−1.50576e127	−1.68572	−0.842862	+	0.538130i	$0.819131\pi$
$368$	−1.14177e127	−1.11715
$369$	−6.37908e126	−0.545698
$370$	7.51022e125	0.0561911
$371$	3.36164e126	0.220061
$372$	3.09879e127	1.77548
$373$	1.89859e127	0.952454	0.476227	−	0.879322i	$-0.342004\pi$
$373$	1.89859e127	0.952454	0.476227	+	0.879322i	$0.342004\pi$
$374$	7.38741e127	3.24599
$375$	−3.44277e127	−1.32544
$376$	4.66001e126	0.157249
$377$	−4.81742e126	−0.142534
$378$	−1.90854e127	−0.495286
$379$	−4.27405e127	−0.973192	−0.486596	−	0.873627i	$-0.661762\pi$
$379$	−4.27405e127	−0.973192	−0.486596	+	0.873627i	$0.661762\pi$
$380$	−5.16777e127	−1.03280
$381$	−2.51381e127	−0.441109
$382$	−2.57280e127	−0.396524
$383$	−5.50225e126	−0.0745077	−0.0372539	−	0.999306i	$-0.511861\pi$
$383$	−5.50225e126	−0.0745077	−0.0372539	+	0.999306i	$0.511861\pi$
$384$	2.29552e127	0.273203
$385$	5.80231e127	0.607148
$386$	−3.68393e127	−0.339031
$387$	−2.77791e127	−0.224919
$388$	6.16000e127	0.438945
$389$	−4.38034e126	−0.0274791	−0.0137396	−	0.999906i	$-0.504374\pi$
$389$	−4.38034e126	−0.0274791	−0.0137396	+	0.999906i	$0.504374\pi$
$390$	−8.96683e127	−0.495383
$391$	4.26842e128	2.07739
$392$	1.69478e127	0.0726863
$393$	−5.85784e128	−2.21466
$394$	1.45999e128	0.486730
$395$	−2.72557e128	−0.801494
$396$	2.10736e128	0.546797
$397$	8.51362e128	1.94977	0.974886	−	0.222704i	$-0.0714882\pi$
$397$	8.51362e128	1.94977	0.974886	+	0.222704i	$0.0714882\pi$
$398$	8.40107e127	0.169872
$399$	−5.20537e128	−0.929593
$400$	1.58086e128	0.249416
$401$	−2.09822e128	−0.292553	−0.146277	−	0.989244i	$-0.546729\pi$
$401$	−2.09822e128	−0.292553	−0.146277	+	0.989244i	$0.546729\pi$
$402$	1.59935e129	1.97130
$403$	−4.79765e128	−0.522912
$404$	−1.27785e129	−1.23198
$405$	−1.28392e129	−1.09525
$406$	4.64749e128	0.350897
$407$	8.12271e127	0.0542973
$408$	−4.62373e128	−0.273725
$409$	−1.75510e129	−0.920445	−0.460222	−	0.887804i	$-0.652230\pi$
$409$	−1.75510e129	−0.920445	−0.460222	+	0.887804i	$0.652230\pi$
$410$	−2.81166e129	−1.30666
$411$	3.06013e129	1.26058
$412$	−1.76722e129	−0.645475
$413$	1.76926e129	0.573145
$414$	2.54196e129	0.730554
$415$	4.77525e129	1.21791
$416$	2.02095e129	0.457548
$417$	1.74453e129	0.350706
$418$	−1.16683e130	−2.08344
$419$	8.40238e129	1.33293	0.666466	−	0.745535i	$-0.267806\pi$
$419$	8.40238e129	1.33293	0.666466	+	0.745535i	$0.267806\pi$
$420$	4.14369e129	0.584180
$421$	8.11468e129	1.01697	0.508484	−	0.861071i	$-0.330206\pi$
$421$	8.11468e129	1.01697	0.508484	+	0.861071i	$0.330206\pi$
$422$	5.68156e128	0.0633143
$423$	−7.20477e129	−0.714121
$424$	−4.71636e128	−0.0415908
$425$	−5.90994e129	−0.463800
$426$	−2.86623e130	−2.00233
$427$	8.40681e128	0.0522939
$428$	−1.01259e130	−0.561006
$429$	−9.69811e129	−0.478687
$430$	−1.22440e130	−0.538561
$431$	3.74452e130	1.46815	0.734076	−	0.679067i	$-0.237616\pi$
$431$	3.74452e130	1.46815	0.734076	+	0.679067i	$0.237616\pi$
$432$	1.85951e130	0.650059
$433$	−2.69953e130	−0.841662	−0.420831	−	0.907139i	$-0.638261\pi$
$433$	−2.69953e130	−0.841662	−0.420831	+	0.907139i	$0.638261\pi$
$434$	4.62842e130	1.28733
$435$	1.85836e130	0.461224
$436$	1.52691e130	0.338245
$437$	−6.74191e130	−1.33337
$438$	9.64180e130	1.70290
$439$	−2.59741e130	−0.409776	−0.204888	−	0.978785i	$-0.565683\pi$
$439$	−2.59741e130	−0.409776	−0.204888	+	0.978785i	$0.565683\pi$
$440$	−8.14061e129	−0.114749
$441$	−2.62027e130	−0.330093
$442$	−8.16797e130	−0.919839
$443$	−4.45692e130	−0.448798	−0.224399	−	0.974497i	$-0.572042\pi$
$443$	−4.45692e130	−0.448798	−0.224399	+	0.974497i	$0.572042\pi$
$444$	5.80079e129	0.0522433
$445$	1.57284e130	0.126726
$446$	2.74711e131	1.98062
$447$	1.56141e131	1.00761
$448$	−8.51523e130	−0.491966
$449$	1.18550e131	0.613350	0.306675	−	0.951814i	$-0.400784\pi$
$449$	1.18550e131	0.613350	0.306675	+	0.951814i	$0.400784\pi$
$450$	−3.51953e130	−0.163104
$451$	−3.04096e131	−1.26262
$452$	−4.77645e131	−1.77727
$453$	−4.32200e131	−1.44153
$454$	−3.86579e130	−0.115604
$455$	−6.41539e130	−0.172052
$456$	7.30311e130	0.175690
$457$	6.69746e131	1.44563	0.722817	−	0.691040i	$-0.242847\pi$
$457$	6.69746e131	1.44563	0.722817	+	0.691040i	$0.242847\pi$
$458$	5.89132e131	1.14123
$459$	−6.95165e131	−1.20882
$460$	5.36684e131	0.837926
$461$	−1.64209e130	−0.0230251	−0.0115126	−	0.999934i	$-0.503665\pi$
$461$	−1.64209e130	−0.0230251	−0.0115126	+	0.999934i	$0.503665\pi$
$462$	9.35602e131	1.17846
$463$	−1.16391e131	−0.131723	−0.0658613	−	0.997829i	$-0.520979\pi$
$463$	−1.16391e131	−0.131723	−0.0658613	+	0.997829i	$0.520979\pi$
$464$	−4.52810e131	−0.460550
$465$	1.85074e132	1.69209
$466$	2.19749e131	0.180644
$467$	−9.11847e131	−0.674119	−0.337059	−	0.941483i	$-0.609432\pi$
$467$	−9.11847e131	−0.674119	−0.337059	+	0.941483i	$0.609432\pi$
$468$	−2.33002e131	−0.154950
$469$	1.14426e132	0.684654
$470$	−3.17560e132	−1.70994
$471$	−1.01187e132	−0.490444
$472$	−2.48227e131	−0.108323
$473$	−1.32425e132	−0.520409
$474$	−4.39488e132	−1.55568
$475$	9.33467e131	0.297691
$476$	3.77452e132	1.08472
$477$	7.29190e131	0.188878
$478$	5.71209e132	1.33387
$479$	−4.15670e132	−0.875267	−0.437633	−	0.899154i	$-0.644183\pi$
$479$	−4.15670e132	−0.875267	−0.437633	+	0.899154i	$0.644183\pi$
$480$	−7.79601e132	−1.48058
$481$	−8.98098e130	−0.0153866
$482$	1.04474e133	1.61503
$483$	5.40588e132	0.754195
$484$	2.74535e132	0.345742
$485$	3.67903e132	0.418328
$486$	−1.25370e133	−1.28736
$487$	9.19381e132	0.852731	0.426365	−	0.904551i	$-0.359794\pi$
$487$	9.19381e132	0.852731	0.426365	+	0.904551i	$0.359794\pi$
$488$	−1.17947e131	−0.00988340
$489$	3.06895e132	0.232381
$490$	−1.15492e133	−0.790398
$491$	1.78007e132	0.110129	0.0550645	−	0.998483i	$-0.482464\pi$
$491$	1.78007e132	0.110129	0.0550645	+	0.998483i	$0.482464\pi$
$492$	−2.17169e133	−1.21486
$493$	1.69280e133	0.856413
$494$	1.29012e133	0.590400
$495$	1.25861e133	0.521114
$496$	−4.50953e133	−1.68962
$497$	−2.05067e133	−0.695431
$498$	7.69993e133	2.36393
$499$	−3.96462e132	−0.110211	−0.0551055	−	0.998481i	$-0.517550\pi$
$499$	−3.96462e132	−0.110211	−0.0551055	+	0.998481i	$0.517550\pi$
$500$	−3.94308e133	−0.992705
$501$	−2.82160e132	−0.0643470
$502$	−7.88857e133	−1.62991
$503$	3.04523e133	0.570170	0.285085	−	0.958502i	$-0.407978\pi$
$503$	3.04523e133	0.570170	0.285085	+	0.958502i	$0.407978\pi$
$504$	−1.97005e132	−0.0334323
$505$	−7.63190e133	−1.17411
$506$	1.21178e134	1.69033
$507$	−8.63167e133	−1.09195
$508$	−2.87912e133	−0.330374
$509$	−3.35095e133	−0.348849	−0.174425	−	0.984671i	$-0.555807\pi$
$509$	−3.35095e133	−0.348849	−0.174425	+	0.984671i	$0.555807\pi$
$510$	3.15087e134	2.97651
$511$	6.89830e133	0.591436
$512$	1.74551e134	1.35850
$513$	1.09800e134	0.775880
$514$	−1.43883e133	−0.0923280
$515$	−1.05547e134	−0.615157
$516$	−9.45710e133	−0.500723
$517$	−3.43458e134	−1.65231
$518$	8.66418e132	0.0378795
$519$	−4.51834e134	−1.79554
$520$	9.00076e132	0.0325173
$521$	−1.60835e134	−0.528339	−0.264169	−	0.964476i	$-0.585098\pi$
$521$	−1.60835e134	−0.528339	−0.264169	+	0.964476i	$0.585098\pi$
$522$	1.00811e134	0.301174
$523$	3.40915e134	0.926430	0.463215	−	0.886246i	$-0.346696\pi$
$523$	3.40915e134	0.926430	0.463215	+	0.886246i	$0.346696\pi$
$524$	−6.70910e134	−1.65869
$525$	−7.48483e133	−0.168382
$526$	2.42827e134	0.497166
$527$	1.68586e135	3.14192
$528$	−9.11569e134	−1.54671
$529$	5.29361e133	0.0817892
$530$	3.21400e134	0.452262
$531$	3.83780e134	0.491930
$532$	−5.96181e134	−0.696229
$533$	3.36228e134	0.357797
$534$	2.53615e134	0.245970
$535$	−6.04765e134	−0.534656
$536$	−1.60540e134	−0.129398
$537$	−9.78066e134	−0.718855
$538$	3.54639e135	2.37719
$539$	−1.24911e135	−0.763759
$540$	−8.74056e134	−0.487583
$541$	2.76601e135	1.40795	0.703977	−	0.710223i	$-0.251406\pi$
$541$	2.76601e135	1.40795	0.703977	+	0.710223i	$0.251406\pi$
$542$	1.34120e135	0.623057
$543$	−3.71735e135	−1.57631
$544$	−7.10147e135	−2.74918
$545$	9.11938e134	0.322358
$546$	−1.03446e135	−0.333947
$547$	5.22581e135	1.54092	0.770461	−	0.637487i	$-0.220026\pi$
$547$	5.22581e135	1.54092	0.770461	+	0.637487i	$0.220026\pi$
$548$	3.50483e135	0.944124
$549$	1.82356e134	0.0448838
$550$	−1.67779e135	−0.377386
$551$	−2.67376e135	−0.549690
$552$	−7.58443e134	−0.142541
$553$	−3.14435e135	−0.540303
$554$	−4.57779e135	−0.719321
$555$	3.46449e134	0.0497894
$556$	1.99804e135	0.262665
$557$	7.97165e132	0.000958774 0	0.000479387	−	1.00000i	$-0.499847\pi$
$557$	7.97165e132	0.000958774 0	0.000479387		1.00000i	$0.499847\pi$
$558$	1.00397e136	1.10492
$559$	1.46418e135	0.147472
$560$	−6.03011e135	−0.555927
$561$	3.40784e136	2.87619
$562$	6.75201e135	0.521777
$563$	1.04266e135	0.0737866	0.0368933	−	0.999319i	$-0.488254\pi$
$563$	1.04266e135	0.0737866	0.0368933	+	0.999319i	$0.488254\pi$
$564$	−2.45279e136	−1.58981
$565$	−2.85271e136	−1.69379
$566$	3.79096e136	2.06222
$567$	−1.48119e136	−0.738330
$568$	2.87708e135	0.131435
$569$	4.03177e136	1.68826	0.844128	−	0.536142i	$-0.180119\pi$
$569$	4.03177e136	1.68826	0.844128	+	0.536142i	$0.180119\pi$
$570$	−4.97676e136	−1.91047
$571$	−4.29426e136	−1.51147	−0.755737	−	0.654876i	$-0.772721\pi$
$571$	−4.29426e136	−1.51147	−0.755737	+	0.654876i	$0.772721\pi$
$572$	−1.11074e136	−0.358518
$573$	−1.18684e136	−0.351350
$574$	−3.24368e136	−0.880844
$575$	−9.69425e135	−0.241521
$576$	−1.84708e136	−0.422254
$577$	−5.63827e136	−1.18289	−0.591444	−	0.806346i	$-0.701442\pi$
$577$	−5.63827e136	−1.18289	−0.591444	+	0.806346i	$0.701442\pi$
$578$	2.15069e137	4.14142
$579$	−1.69941e136	−0.300407
$580$	2.12842e136	0.345439
$581$	5.50898e136	0.821018
$582$	5.93231e136	0.811962
$583$	3.47612e136	0.437019
$584$	−9.67829e135	−0.111780
$585$	−1.39159e136	−0.147672
$586$	−6.16577e136	−0.601251
$587$	1.07351e136	0.0962103	0.0481052	−	0.998842i	$-0.484682\pi$
$587$	1.07351e136	0.0962103	0.0481052	+	0.998842i	$0.484682\pi$
$588$	−8.92044e136	−0.734867
$589$	−2.66279e137	−2.01664
$590$	1.69156e137	1.17791
$591$	6.73501e136	0.431278
$592$	−8.44162e135	−0.0497166
$593$	−3.56133e136	−0.192932	−0.0964662	−	0.995336i	$-0.530754\pi$
$593$	−3.56133e136	−0.192932	−0.0964662	+	0.995336i	$0.530754\pi$
$594$	−1.97353e137	−0.983591
$595$	2.25432e137	1.03377
$596$	1.78831e137	0.754662
$597$	3.87544e136	0.150519
$598$	−1.33982e137	−0.479001
$599$	−6.88222e136	−0.226517	−0.113259	−	0.993566i	$-0.536129\pi$
$599$	−6.88222e136	−0.226517	−0.113259	+	0.993566i	$0.536129\pi$
$600$	1.05012e136	0.0318238
$601$	−2.75734e137	−0.769492	−0.384746	−	0.923023i	$-0.625711\pi$
$601$	−2.75734e137	−0.769492	−0.384746	+	0.923023i	$0.625711\pi$
$602$	−1.41253e137	−0.363054
$603$	2.48208e137	0.587637
$604$	−4.95007e137	−1.07965
$605$	1.63965e137	0.329503
$606$	−1.23062e138	−2.27892
$607$	9.05341e137	1.54515	0.772577	−	0.634921i	$-0.218967\pi$
$607$	9.05341e137	1.54515	0.772577	+	0.634921i	$0.218967\pi$
$608$	1.12167e138	1.76456
$609$	2.14390e137	0.310920
$610$	8.03760e136	0.107473
$611$	3.79748e137	0.468227
$612$	8.18752e137	0.931015
$613$	5.14384e137	0.539503	0.269751	−	0.962930i	$-0.413058\pi$
$613$	5.14384e137	0.539503	0.269751	+	0.962930i	$0.413058\pi$
$614$	−6.59559e137	−0.638145
$615$	−1.29703e138	−1.15780
$616$	−9.39143e136	−0.0773547
$617$	1.33983e138	1.01843	0.509217	−	0.860638i	$-0.329935\pi$
$617$	1.33983e138	1.01843	0.509217	+	0.860638i	$0.329935\pi$
$618$	−1.70190e138	−1.19400
$619$	9.45093e137	0.612051	0.306025	−	0.952023i	$-0.401001\pi$
$619$	9.45093e137	0.612051	0.306025	+	0.952023i	$0.401001\pi$
$620$	2.11969e138	1.26731
$621$	−1.14030e138	−0.629484
$622$	−4.83496e138	−2.46473
$623$	1.81451e137	0.0854281
$624$	1.00789e138	0.438303
$625$	−1.77696e138	−0.713866
$626$	2.80598e138	1.04149
$627$	−5.38263e138	−1.84608
$628$	−1.15891e138	−0.367324
$629$	3.15584e137	0.0924503
$630$	1.34251e138	0.363546
$631$	1.76920e138	0.442917	0.221459	−	0.975170i	$-0.428918\pi$
$631$	1.76920e138	0.442917	0.221459	+	0.975170i	$0.428918\pi$
$632$	4.41151e137	0.102116
$633$	2.62093e137	0.0561011
$634$	1.26506e139	2.50434
$635$	−1.71954e138	−0.314856
$636$	2.48245e138	0.420488
$637$	1.38109e138	0.216432
$638$	4.80576e138	0.696848
$639$	−4.44821e138	−0.596888
$640$	1.57022e138	0.195007
$641$	7.74463e138	0.890283	0.445141	−	0.895460i	$-0.353153\pi$
$641$	7.74463e138	0.890283	0.445141	+	0.895460i	$0.353153\pi$
$642$	−9.75163e138	−1.03775
$643$	−1.61228e139	−1.58854	−0.794270	−	0.607565i	$-0.792146\pi$
$643$	−1.61228e139	−1.58854	−0.794270	+	0.607565i	$0.792146\pi$
$644$	6.19146e138	0.564863
$645$	−5.64820e138	−0.477204
$646$	−4.53338e139	−3.54742
$647$	2.22446e139	1.61237	0.806183	−	0.591667i	$-0.201530\pi$
$647$	2.22446e139	1.61237	0.806183	+	0.591667i	$0.201530\pi$
$648$	2.07811e138	0.139542
$649$	1.82951e139	1.13821
$650$	1.85507e138	0.106942
$651$	2.13511e139	1.14067
$652$	3.51493e138	0.174045
$653$	−3.34083e139	−1.53339	−0.766693	−	0.642014i	$-0.778099\pi$
$653$	−3.34083e139	−1.53339	−0.766693	+	0.642014i	$0.778099\pi$
$654$	1.47047e139	0.625688
$655$	−4.00697e139	−1.58078
$656$	3.16036e139	1.15610
$657$	1.49635e139	0.507629
$658$	−3.66353e139	−1.15271
$659$	4.50577e138	0.131505	0.0657523	−	0.997836i	$-0.479055\pi$
$659$	4.50577e138	0.131505	0.0657523	+	0.997836i	$0.479055\pi$
$660$	4.28480e139	1.16013
$661$	−1.65851e139	−0.416627	−0.208313	−	0.978062i	$-0.566797\pi$
$661$	−1.65851e139	−0.416627	−0.208313	+	0.978062i	$0.566797\pi$
$662$	3.90939e139	0.911253
$663$	−3.76792e139	−0.815045
$664$	−7.72907e138	−0.155170
$665$	−3.56066e139	−0.663528
$666$	1.87939e138	0.0325120
$667$	2.77675e139	0.445973
$668$	−3.23164e138	−0.0481934
$669$	1.26725e140	1.75497
$670$	1.09401e140	1.40708
$671$	8.69310e138	0.103851
$672$	−8.99388e139	−0.998086
$673$	7.92793e139	0.817361	0.408681	−	0.912677i	$-0.365989\pi$
$673$	7.92793e139	0.817361	0.408681	+	0.912677i	$0.365989\pi$
$674$	−9.10300e139	−0.872007
$675$	1.57883e139	0.140539
$676$	−9.88602e139	−0.817824
$677$	−1.84106e140	−1.41556	−0.707782	−	0.706431i	$-0.750304\pi$
$677$	−1.84106e140	−1.41556	−0.707782	+	0.706431i	$0.750304\pi$
$678$	−4.59990e140	−3.28760
$679$	4.24431e139	0.282003
$680$	−3.16280e139	−0.195380
$681$	−1.78330e139	−0.102434
$682$	4.78604e140	2.55652
$683$	1.78435e140	0.886453	0.443226	−	0.896410i	$-0.353834\pi$
$683$	1.78435e140	0.886453	0.443226	+	0.896410i	$0.353834\pi$
$684$	−1.29321e140	−0.597573
$685$	2.09324e140	0.899779
$686$	−3.37876e140	−1.35118
$687$	2.71769e140	1.01121
$688$	1.37625e140	0.476506
$689$	−3.84341e139	−0.123841
$690$	5.16847e140	1.55000
$691$	−1.54549e139	−0.0431423	−0.0215712	−	0.999767i	$-0.506867\pi$
$691$	−1.54549e139	−0.0431423	−0.0215712	+	0.999767i	$0.506867\pi$
$692$	−5.17494e140	−1.34479
$693$	1.45200e140	0.351293
$694$	5.71224e140	1.28680
$695$	1.19332e140	0.250328
$696$	−3.00789e139	−0.0587630
$697$	−1.18148e141	−2.14982
$698$	3.65295e140	0.619156
$699$	1.01371e140	0.160064
$700$	−8.57253e139	−0.126112
$701$	−6.49846e140	−0.890776	−0.445388	−	0.895338i	$-0.646934\pi$
$701$	−6.49846e140	−0.890776	−0.445388	+	0.895338i	$0.646934\pi$
$702$	2.18206e140	0.278727
$703$	−4.98461e139	−0.0593393
$704$	−8.80521e140	−0.976997
$705$	−1.46491e141	−1.51513
$706$	1.70439e141	1.64337
$707$	−8.80455e140	−0.791492
$708$	1.30654e141	1.09515
$709$	7.59801e140	0.593897	0.296949	−	0.954893i	$-0.404031\pi$
$709$	7.59801e140	0.593897	0.296949	+	0.954893i	$0.404031\pi$
$710$	−1.96061e141	−1.42923
$711$	−6.82058e140	−0.463741
$712$	−2.54575e139	−0.0161457
$713$	2.76536e141	1.63614
$714$	3.63501e141	2.00652
$715$	−6.63386e140	−0.341678
$716$	−1.12020e141	−0.538394
$717$	2.63501e141	1.18191
$718$	−1.91039e141	−0.799764
$719$	−4.00928e141	−1.56670	−0.783351	−	0.621580i	$-0.786491\pi$
$719$	−4.00928e141	−1.56670	−0.783351	+	0.621580i	$0.786491\pi$
$720$	−1.30802e141	−0.477152
$721$	−1.21764e141	−0.414690
$722$	2.80352e141	0.891481
$723$	4.81944e141	1.43104
$724$	−4.25756e141	−1.18060
$725$	−3.84461e140	−0.0995683
$726$	2.64387e141	0.639555
$727$	2.02396e141	0.457351	0.228675	−	0.973503i	$-0.426561\pi$
$727$	2.02396e141	0.457351	0.228675	+	0.973503i	$0.426561\pi$
$728$	1.03837e140	0.0219205
$729$	5.53937e140	0.109257
$730$	6.59534e141	1.21550
$731$	−5.14500e141	−0.886085
$732$	6.20813e140	0.0999223
$733$	1.17408e141	0.176624	0.0883121	−	0.996093i	$-0.471853\pi$
$733$	1.17408e141	0.176624	0.0883121	+	0.996093i	$0.471853\pi$
$734$	−1.66083e142	−2.33545
$735$	−5.32769e141	−0.700350
$736$	−1.16487e142	−1.43162
$737$	1.18323e142	1.35966
$738$	−7.03603e141	−0.756028
$739$	3.03022e140	0.0304491	0.0152245	−	0.999884i	$-0.495154\pi$
$739$	3.03022e140	0.0304491	0.0152245	+	0.999884i	$0.495154\pi$
$740$	3.96795e140	0.0372903
$741$	5.95137e141	0.523137
$742$	3.70784e141	0.304879
$743$	1.10741e141	0.0851850	0.0425925	−	0.999093i	$-0.486438\pi$
$743$	1.10741e141	0.0851850	0.0425925	+	0.999093i	$0.486438\pi$
$744$	−2.99555e141	−0.215584
$745$	1.06806e142	0.719216
$746$	2.09412e142	1.31956
$747$	1.19498e142	0.704679
$748$	3.90306e142	2.15415
$749$	−6.97688e141	−0.360422
$750$	−3.79733e142	−1.83631
$751$	9.96847e141	0.451286	0.225643	−	0.974210i	$-0.427552\pi$
$751$	9.96847e141	0.451286	0.225643	+	0.974210i	$0.427552\pi$
$752$	3.56942e142	1.51292
$753$	−3.63903e142	−1.44422
$754$	−5.31354e141	−0.197471
$755$	−2.95641e142	−1.02894
$756$	−1.00836e142	−0.328689
$757$	−2.89776e142	−0.884742	−0.442371	−	0.896832i	$-0.645863\pi$
$757$	−2.89776e142	−0.884742	−0.442371	+	0.896832i	$0.645863\pi$
$758$	−4.71421e142	−1.34829
$759$	5.58998e142	1.49776
$760$	4.99559e141	0.125405
$761$	−3.50793e142	−0.825107	−0.412553	−	0.910933i	$-0.635363\pi$
$761$	−3.50793e142	−0.825107	−0.412553	+	0.910933i	$0.635363\pi$
$762$	−2.77269e142	−0.611126
$763$	1.05206e142	0.217308
$764$	−1.35931e142	−0.263147
$765$	4.88995e142	0.887286
$766$	−6.06891e141	−0.103225
$767$	−2.02282e142	−0.322543
$768$	9.37123e142	1.40093
$769$	1.75426e142	0.245889	0.122945	−	0.992414i	$-0.460766\pi$
$769$	1.75426e142	0.245889	0.122945	+	0.992414i	$0.460766\pi$
$770$	6.39986e142	0.841162
$771$	−6.63735e141	−0.0818094
$772$	−1.94637e142	−0.224993
$773$	−3.85368e142	−0.417821	−0.208910	−	0.977935i	$-0.566992\pi$
$773$	−3.85368e142	−0.417821	−0.208910	+	0.977935i	$0.566992\pi$
$774$	−3.06399e142	−0.311609
$775$	−3.82884e142	−0.365286
$776$	−5.95476e141	−0.0532977
$777$	3.99682e141	0.0335640
$778$	−4.83146e141	−0.0380704
$779$	1.86613e143	1.37987
$780$	−4.73754e142	−0.328753
$781$	−2.12050e143	−1.38106
$782$	4.70801e143	2.87808
$783$	−4.52228e142	−0.259508
$784$	1.29815e143	0.699326
$785$	−6.92155e142	−0.350071
$786$	−6.46111e143	−3.06825
$787$	6.75596e142	0.301257	0.150629	−	0.988590i	$-0.451870\pi$
$787$	6.75596e142	0.301257	0.150629	+	0.988590i	$0.451870\pi$
$788$	7.71373e142	0.323011
$789$	1.12017e143	0.440526
$790$	−3.00626e143	−1.11042
$791$	−3.29103e143	−1.14182
$792$	−2.03714e142	−0.0663934
$793$	−9.61163e141	−0.0294289
$794$	9.39039e143	2.70128
$795$	1.48263e143	0.400738
$796$	4.43862e142	0.112733
$797$	1.25539e143	0.299636	0.149818	−	0.988714i	$-0.452131\pi$
$797$	1.25539e143	0.299636	0.149818	+	0.988714i	$0.452131\pi$
$798$	−5.74144e143	−1.28789
$799$	−1.33441e144	−2.81334
$800$	1.61285e143	0.319625
$801$	3.93595e142	0.0733229
$802$	−2.31431e143	−0.405313
$803$	7.13322e143	1.17454
$804$	8.44999e143	1.30822
$805$	3.69782e143	0.538331
$806$	−5.29174e143	−0.724459
$807$	1.63596e144	2.10636
$808$	1.23528e143	0.149590
$809$	1.55169e144	1.76748	0.883738	−	0.467982i	$-0.155019\pi$
$809$	1.55169e144	1.76748	0.883738	+	0.467982i	$0.155019\pi$
$810$	−1.41614e144	−1.51740
$811$	−6.37117e143	−0.642224	−0.321112	−	0.947041i	$-0.604057\pi$
$811$	−6.37117e143	−0.642224	−0.321112	+	0.947041i	$0.604057\pi$
$812$	2.45545e143	0.232867
$813$	6.18699e143	0.552074
$814$	8.95924e142	0.0752251
$815$	2.09927e143	0.165870
$816$	−3.54163e144	−2.63354
$817$	8.12646e143	0.568735
$818$	−1.93585e144	−1.27521
$819$	−1.60542e143	−0.0995484
$820$	−1.48551e144	−0.867144
$821$	−3.16124e144	−1.73729	−0.868643	−	0.495438i	$-0.835008\pi$
$821$	−3.16124e144	−1.73729	−0.868643	+	0.495438i	$0.835008\pi$
$822$	3.37528e144	1.74644
$823$	−1.50137e144	−0.731469	−0.365734	−	0.930719i	$-0.619182\pi$
$823$	−1.50137e144	−0.731469	−0.365734	+	0.930719i	$0.619182\pi$
$824$	1.70834e143	0.0783751
$825$	−7.73973e143	−0.334391
$826$	1.95147e144	0.794053
$827$	1.73199e144	0.663777	0.331889	−	0.943319i	$-0.392314\pi$
$827$	1.73199e144	0.663777	0.331889	+	0.943319i	$0.392314\pi$
$828$	1.34302e144	0.484821
$829$	5.09573e144	1.73283	0.866417	−	0.499321i	$-0.166417\pi$
$829$	5.09573e144	1.73283	0.866417	+	0.499321i	$0.166417\pi$
$830$	5.26703e144	1.68733
$831$	−2.11175e144	−0.637371
$832$	9.73559e143	0.276858
$833$	−4.85304e144	−1.30043
$834$	1.92419e144	0.485879
$835$	−1.93008e143	−0.0459298
$836$	−6.16484e144	−1.38265
$837$	−4.50373e144	−0.952055
$838$	9.26771e144	1.84669
$839$	−3.68702e144	−0.692561	−0.346281	−	0.938131i	$-0.612555\pi$
$839$	−3.68702e144	−0.692561	−0.346281	+	0.938131i	$0.612555\pi$
$840$	−4.00563e143	−0.0709326
$841$	−4.88843e144	−0.816146
$842$	8.95037e144	1.40894
$843$	3.11473e144	0.462333
$844$	3.00180e143	0.0420175
$845$	−5.90437e144	−0.779412
$846$	−7.94676e144	−0.989366
$847$	1.89158e144	0.222124
$848$	−3.61259e144	−0.400151
$849$	1.74878e145	1.82728
$850$	−6.51858e144	−0.642563
$851$	5.17662e143	0.0481430
$852$	−1.51435e145	−1.32882
$853$	4.10700e144	0.340054	0.170027	−	0.985439i	$-0.445614\pi$
$853$	4.10700e144	0.340054	0.170027	+	0.985439i	$0.445614\pi$
$854$	9.27259e143	0.0724497
$855$	−7.72361e144	−0.569505
$856$	9.78854e143	0.0681187
$857$	8.50296e144	0.558495	0.279248	−	0.960219i	$-0.409915\pi$
$857$	8.50296e144	0.558495	0.279248	+	0.960219i	$0.409915\pi$
$858$	−1.06969e145	−0.663187
$859$	−4.29194e144	−0.251184	−0.125592	−	0.992082i	$-0.540083\pi$
$859$	−4.29194e144	−0.251184	−0.125592	+	0.992082i	$0.540083\pi$
$860$	−6.46900e144	−0.357407
$861$	−1.49632e145	−0.780492
$862$	4.13015e145	2.03402
$863$	4.28210e144	0.199123	0.0995617	−	0.995031i	$-0.468256\pi$
$863$	4.28210e144	0.199123	0.0995617	+	0.995031i	$0.468256\pi$
$864$	1.89714e145	0.833047
$865$	−3.09071e145	−1.28162
$866$	−2.97754e145	−1.16606
$867$	9.92121e145	3.66961
$868$	2.44538e145	0.854319
$869$	−3.25143e145	−1.07299
$870$	2.04975e145	0.638995
$871$	−1.30825e145	−0.385295
$872$	−1.47603e144	−0.0410706
$873$	9.20656e144	0.242043
$874$	−7.43623e145	−1.84730
$875$	−2.71683e145	−0.637769
$876$	5.09415e145	1.13010
$877$	3.55541e145	0.745435	0.372717	−	0.927945i	$-0.378426\pi$
$877$	3.55541e145	0.745435	0.372717	+	0.927945i	$0.378426\pi$
$878$	−2.86490e145	−0.567716
$879$	−2.84429e145	−0.532752
$880$	−6.23546e145	−1.10402
$881$	−5.70823e145	−0.955420	−0.477710	−	0.878518i	$-0.658533\pi$
$881$	−5.70823e145	−0.955420	−0.477710	+	0.878518i	$0.658533\pi$
$882$	−2.89012e145	−0.457321
$883$	4.29336e145	0.642307	0.321153	−	0.947027i	$-0.395929\pi$
$883$	4.29336e145	0.642307	0.321153	+	0.947027i	$0.395929\pi$
$884$	−4.31547e145	−0.610437
$885$	7.80322e145	1.04372
$886$	−4.91592e145	−0.621778
$887$	4.52883e145	0.541709	0.270855	−	0.962620i	$-0.412694\pi$
$887$	4.52883e145	0.541709	0.270855	+	0.962620i	$0.412694\pi$
$888$	−5.60752e143	−0.00634350
$889$	−1.98375e145	−0.212251
$890$	1.73482e145	0.175569
$891$	−1.53164e146	−1.46625
$892$	1.45141e146	1.31441
$893$	2.10767e146	1.80574
$894$	1.72221e146	1.39598
$895$	−6.69033e145	−0.513106
$896$	1.81148e145	0.131458
$897$	−6.18062e145	−0.424430
$898$	1.30759e146	0.849754
$899$	1.09671e146	0.674505
$900$	−1.85951e145	−0.108242
$901$	1.35054e146	0.744100
$902$	−3.35414e146	−1.74927
$903$	−6.51606e145	−0.321693
$904$	4.61731e145	0.215800
$905$	−2.54281e146	−1.12515
$906$	−4.76710e146	−1.99714
$907$	6.85298e145	0.271844	0.135922	−	0.990720i	$-0.456600\pi$
$907$	6.85298e145	0.271844	0.135922	+	0.990720i	$0.456600\pi$
$908$	−2.04245e145	−0.0767188
$909$	−1.90984e146	−0.679337
$910$	−7.07608e145	−0.238366
$911$	−3.05037e146	−0.973178	−0.486589	−	0.873631i	$-0.661759\pi$
$911$	−3.05037e146	−0.973178	−0.486589	+	0.873631i	$0.661759\pi$
$912$	5.59396e146	1.69034
$913$	5.69658e146	1.63046
$914$	7.38720e146	2.00283
$915$	3.70777e145	0.0952290
$916$	3.11262e146	0.757356
$917$	−4.62265e146	−1.06564
$918$	−7.66757e146	−1.67473
$919$	−4.78824e146	−0.990965	−0.495482	−	0.868618i	$-0.665009\pi$
$919$	−4.78824e146	−0.990965	−0.495482	+	0.868618i	$0.665009\pi$
$920$	−5.18803e145	−0.101743
$921$	−3.04257e146	−0.565443
$922$	−1.81121e145	−0.0318997
$923$	2.34456e146	0.391361
$924$	4.94316e146	0.782064
$925$	−7.16741e144	−0.0107485
$926$	−1.28378e146	−0.182493
$927$	−2.64125e146	−0.355928
$928$	−4.61974e146	−0.590191
$929$	1.03258e147	1.25068	0.625341	−	0.780352i	$-0.284960\pi$
$929$	1.03258e147	1.25068	0.625341	+	0.780352i	$0.284960\pi$
$930$	2.04134e147	2.34428
$931$	7.66531e146	0.834681
$932$	1.16102e146	0.119882
$933$	−2.23039e147	−2.18393
$934$	−1.00575e147	−0.933945
$935$	2.33109e147	2.05297
$936$	2.25239e145	0.0188144
$937$	−1.50781e147	−1.19464	−0.597321	−	0.802002i	$-0.703768\pi$
$937$	−1.50781e147	−1.19464	−0.597321	+	0.802002i	$0.703768\pi$
$938$	1.26211e147	0.948540
$939$	1.29441e147	0.922835
$940$	−1.67780e147	−1.13478
$941$	−3.47608e146	−0.223050	−0.111525	−	0.993762i	$-0.535574\pi$
$941$	−3.47608e146	−0.223050	−0.111525	+	0.993762i	$0.535574\pi$
$942$	−1.11608e147	−0.679477
$943$	−1.93801e147	−1.11951
$944$	−1.90134e147	−1.04219
$945$	−6.02236e146	−0.313251
$946$	−1.46063e147	−0.720991
$947$	1.83504e147	0.859650	0.429825	−	0.902912i	$-0.358575\pi$
$947$	1.83504e147	0.859650	0.429825	+	0.902912i	$0.358575\pi$
$948$	−2.32199e147	−1.03240
$949$	−7.88693e146	−0.332836
$950$	1.02960e147	0.412430
$951$	5.83577e147	2.21903
$952$	−3.64876e146	−0.131709
$953$	1.85480e147	0.635621	0.317811	−	0.948154i	$-0.397052\pi$
$953$	1.85480e147	0.635621	0.317811	+	0.948154i	$0.397052\pi$
$954$	8.04286e146	0.261677
$955$	−8.11844e146	−0.250787
$956$	3.01793e147	0.885204
$957$	2.21691e147	0.617458
$958$	−4.58478e147	−1.21262
$959$	2.41487e147	0.606559
$960$	−3.75559e147	−0.895886
$961$	6.50831e147	1.47455
$962$	−9.90589e145	−0.0213171
$963$	−1.51339e147	−0.309350
$964$	5.51980e147	1.07179
$965$	−1.16246e147	−0.214425
$966$	5.96261e147	1.04489
$967$	−3.14774e147	−0.524069	−0.262035	−	0.965058i	$-0.584393\pi$
$967$	−3.14774e147	−0.524069	−0.262035	+	0.965058i	$0.584393\pi$
$968$	−2.65388e146	−0.0419808
$969$	−2.09126e148	−3.14327
$970$	4.05791e147	0.579565
$971$	−8.63030e147	−1.17132	−0.585658	−	0.810558i	$-0.699164\pi$
$971$	−8.63030e147	−1.17132	−0.585658	+	0.810558i	$0.699164\pi$
$972$	−6.62382e147	−0.854336
$973$	1.37668e147	0.168751
$974$	1.01406e148	1.18140
$975$	8.55752e146	0.0947588
$976$	−9.03440e146	−0.0950896
$977$	−3.09347e147	−0.309503	−0.154751	−	0.987953i	$-0.549458\pi$
$977$	−3.09347e147	−0.309503	−0.154751	+	0.987953i	$0.549458\pi$
$978$	3.38501e147	0.321949
$979$	1.87630e147	0.169652
$980$	−6.10190e147	−0.524535
$981$	2.28208e147	0.186515
$982$	1.96339e147	0.152576
$983$	1.70783e147	0.126196	0.0630980	−	0.998007i	$-0.479902\pi$
$983$	1.70783e147	0.126196	0.0630980	+	0.998007i	$0.479902\pi$
$984$	2.09933e147	0.147511
$985$	4.60699e147	0.307839
$986$	1.86714e148	1.18650
$987$	−1.69000e148	−1.02138
$988$	6.81622e147	0.391810
$989$	−8.43950e147	−0.461424
$990$	1.38823e148	0.721968
$991$	3.67747e148	1.81929	0.909647	−	0.415382i	$-0.136352\pi$
$991$	3.67747e148	1.81929	0.909647	+	0.415382i	$0.136352\pi$
$992$	−4.60079e148	−2.16523
$993$	1.80342e148	0.807437
$994$	−2.26186e148	−0.963473
$995$	2.65094e147	0.107438
$996$	4.06819e148	1.56879
$997$	−5.02869e148	−1.84521	−0.922603	−	0.385750i	$-0.873943\pi$
$997$	−5.02869e148	−1.84521	−0.922603	+	0.385750i	$0.873943\pi$
$998$	−4.37292e147	−0.152690
$999$	−8.43077e146	−0.0280140

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1.100.a.a.1.7	✓	8
3.2	odd	2		9.100.a.d.1.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1.100.a.a.1.7	✓	8	1.1	even	1	trivial
9.100.a.d.1.2		8	3.2	odd	2

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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 1 \)
Weight:	\( k \)	\(=\)	\( 100 \)
Character orbit:	\([\chi]\)	\(=\)	1.a (trivial)

\(f(q)\)	\(=\)	\(q+1.10299e15 q^{2} +5.08811e23 q^{3} +5.82752e29 q^{4} +3.48045e34 q^{5} +5.61211e38 q^{6} +4.01523e41 q^{7} -5.63335e43 q^{8} +8.70965e46 q^{9} +O(q^{10})\)	\(q+1.10299e15 q^{2} +5.08811e23 q^{3} +5.82752e29 q^{4} +3.48045e34 q^{5} +5.61211e38 q^{6} +4.01523e41 q^{7} -5.63335e43 q^{8} +8.70965e46 q^{9} +3.83889e49 q^{10} +4.15197e51 q^{11} +2.96511e53 q^{12} -4.59067e54 q^{13} +4.42874e56 q^{14} +1.77089e58 q^{15} -4.31498e59 q^{16} +1.61313e61 q^{17} +9.60661e61 q^{18} -2.54791e63 q^{19} +2.02824e64 q^{20} +2.04300e65 q^{21} +4.57956e66 q^{22} +2.64606e67 q^{23} -2.86631e67 q^{24} -3.66366e68 q^{25} -5.06345e69 q^{26} -4.30943e70 q^{27} +2.33988e71 q^{28} +1.04939e72 q^{29} +1.95327e73 q^{30} +1.04509e74 q^{31} -4.40230e74 q^{32} +2.11257e75 q^{33} +1.77925e76 q^{34} +1.39748e76 q^{35} +5.07556e76 q^{36} +1.95635e76 q^{37} -2.81031e78 q^{38} -2.33579e78 q^{39} -1.96066e78 q^{40} -7.32415e79 q^{41} +2.25339e80 q^{42} -3.18946e80 q^{43} +2.41957e81 q^{44} +3.03135e81 q^{45} +2.91856e82 q^{46} -8.27217e82 q^{47} -2.19551e83 q^{48} -3.00847e83 q^{49} -4.04096e83 q^{50} +8.20777e84 q^{51} -2.67522e84 q^{52} +8.37221e84 q^{53} -4.75324e85 q^{54} +1.44507e86 q^{55} -2.26192e85 q^{56} -1.29641e87 q^{57} +1.15746e87 q^{58} +4.40637e87 q^{59} +1.03199e88 q^{60} +2.09373e87 q^{61} +1.15272e89 q^{62} +3.49712e88 q^{63} -2.12073e89 q^{64} -1.59776e89 q^{65} +2.33013e90 q^{66} +2.84981e90 q^{67} +9.40052e90 q^{68} +1.34634e91 q^{69} +1.54140e91 q^{70} -5.10722e91 q^{71} -4.90645e90 q^{72} +1.71803e92 q^{73} +2.15783e91 q^{74} -1.86411e92 q^{75} -1.48480e93 q^{76} +1.66711e93 q^{77} -2.57634e93 q^{78} -7.83106e93 q^{79} -1.50181e94 q^{80} -3.68894e94 q^{81} -8.07843e94 q^{82} +1.37202e95 q^{83} +1.19056e95 q^{84} +5.61441e95 q^{85} -3.51793e95 q^{86} +5.33943e95 q^{87} -2.33895e95 q^{88} +4.51907e95 q^{89} +3.34354e96 q^{90} -1.84326e96 q^{91} +1.54199e97 q^{92} +5.31752e97 q^{93} -9.12409e97 q^{94} -8.86788e97 q^{95} -2.23994e98 q^{96} +1.05705e98 q^{97} -3.31830e98 q^{98} +3.61622e98 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 208040616902520 q^{2} - 28\!\cdots\!20 q^{3}+ \cdots + 15\!\cdots\!76 q^{9}+O(q^{10}) \) 8 * q - 208040616902520 * q^2 - 282956306495420632223520 * q^3 + 2874573971021731526732655093824 * q^4 - 48829879146635109942685521105004560 * q^5 - 77942153094234171155671704171199405344 * q^6 - 56830940560713017104682273454607970657600 * q^7 + 592603013041539183163433278232078795937538560 * q^8 + 15585042525631880727258151421002821416820695976 * q^9	\( 8 q - 208040616902520 q^{2} - 28\!\cdots\!20 q^{3}+ \cdots - 13\!\cdots\!08 q^{99}+O(q^{100}) \) 8 * q - 208040616902520 * q^2 - 282956306495420632223520 * q^3 + 2874573971021731526732655093824 * q^4 - 48829879146635109942685521105004560 * q^5 - 77942153094234171155671704171199405344 * q^6 - 56830940560713017104682273454607970657600 * q^7 + 592603013041539183163433278232078795937538560 * q^8 + 15585042525631880727258151421002821416820695976 * q^9 - 20961738819400631174675750189416259674325116377360 * q^10 + 668605620058921294359176615672652323197376366725536 * q^11 - 260751428362765138428103958747533086169389679507011840 * q^12 - 5313129021153651674083973849295770678848247690376073040 * q^13 - 275891262636795191856274681125121829106120036919920873792 * q^14 + 39601076201132911228470767893146157937452742673766616546880 * q^15 + 1686978001168411473373901309719868789822314791151035737182208 * q^16 + 29870581004484716934093126001838988402381517134653878061066640 * q^17 + 104619592562318909205389831941745992324800916717508145002954280 * q^18 - 2584541347057387315132230533073883085094549482599567538462153120 * q^19 - 87020910945991395973478129409062640628123700866757624264022986880 * q^20 + 720725986617461186277876616197863336884455731162862159407836416 * q^21 + 6448630494375222037284713151002631218361976067562272720681828806560 * q^22 - 591705231800483702926418342143069697446663268741979110571049882560 * q^23 - 786094952626208255303024343193893163353569305701641632350239286773760 * q^24 + 716804381062067209680195080749365299641535704320602348503400092268600 * q^25 + 34654632463607194325743429354208471986051789816879940147342898057153456 * q^26 + 13869683363495491009982193176608883185849831807068440771218044677979840 * q^27 - 1135994339501291724748966539673012720374432727977564592829456188165859840 * q^28 - 439009994693767454184499584774890376667926937141064013921655743937571280 * q^29 + 23517293722912668382363618879896733566643340714874843272431473003480521280 * q^30 - 42796079732631926995692344425065773646038440365668203549397431930127162624 * q^31 - 284044778854068845159282113651411076631875258269403845301648101866131128320 * q^32 - 1184428676639946519273358190717309258531732537332484528437733831641965671040 * q^33 + 11470334814206853457708153296668381286712583035391282441563479133450208961168 * q^34 - 13317873075112713679215664096634074386516466958921311305188860496632195839360 * q^35 - 224326234591498863152148578877455893579609783196337897663675145770615318305472 * q^36 + 7013041648409278763731742859978750449729753703775477297667583228204170683120 * q^37 + 4097267709666535974097951231260487171744232792996835026005028682857459985875040 * q^38 + 3086772337289173445407063166797596998267422181270693039748051240117483908526912 * q^39 - 61154477845927513224255221208858320971333500267390856556166248662272460823577600 * q^40 + 16836611518887404247693904661111767446154336367366992887095255319045118001938896 * q^41 + 586782577486516292654880709693602500520055556295982039518980517393750164948778240 * q^42 - 115479509651193412125043402629710680178430977878852566804453976757651553792322400 * q^43 - 4823674089938931277708865059630293953738849935605913988972972769383583829463937792 * q^44 - 4204225762790416656941382640299001599040327829208847740401216426127468587838672720 * q^45 + 41220575732227465405339930795314328162570779910219577393801310430729179103724398656 * q^46 + 28878226575287510694522520507929237505491250714878620920990009419290436045018975360 * q^47 - 270645616492149970234041108687889002599221246648694105429287982543953957103033794560 * q^48 - 14382803175556111227730750647629461517090856222687609645964147941666232976982659256 * q^49 + 2538900041031429584911497444199766832786695308479217204477072876574482801521012636600 * q^50 - 1711868817156841452117007804086601271536721152787522351736690290031659132307369497664 * q^51 - 199691168563235615231272208715487263769590246824861808533841002609282642680495606400 * q^52 - 30091820242734525213832735040802634061423162425240717202059443809754039115425881976720 * q^53 + 136432908322968282680263912195201284966825652472631606906205576348979246713807692108480 * q^54 + 226099583633880167546966079422139027647924161654010953637858494806538127768993139084480 * q^55 + 323037227302956226932352973051969540564093713359973342312103259763994205180305378488320 * q^56 - 273423384330404631781757518792671605280054294102341216713398337934356290096852147342720 * q^57 + 5713973478801321937231450378714667908258440100056694714036585358012358074567853731219760 * q^58 + 14607245332654695346837714400351649175544087130678579822473040904252509022932739720811040 * q^59 + 53008257791762983739773607116394245193846456713938833829846630209166818928009302295114240 * q^60 + 38323682921378832161349805479389921828014992489778724538462200957929376165086831637164336 * q^61 + 201697385927609334439920541372343666252345396922224455072723131310512431934088015943381760 * q^62 + 659857333915856699600072965534847901170546674796116288100652182111732663513752207410870720 * q^63 + 2567569508313686836352267062189989701299823975229681223291764819542997452948800142018084864 * q^64 + 2649617703605055039617798586548537725956903247199823944158672914229112797191302156162117280 * q^65 + 7971156345834212651621212324655177899942634890685144307138793590710555397223588657590125952 * q^66 + 11538024122310165476577023936338470394129524138300592332780359783942082451772953721242543840 * q^67 + 56045208748154976002290739488865109707859265886693431912946708486067523902076046154608254080 * q^68 + 54550768708090409722131753417710688638608175085564682877064185400954540597503860451967981312 * q^69 + 143889269423962258520958611175254488367329101991613194841590826662727327088381209016536883840 * q^70 + 52677154721705052088453955375369863850612862186345822027042426779160256515633503076296638656 * q^71 + 365038759307175377119135471724071125896012767600977654405238165616233444129512164397555141120 * q^72 + 506688790556979736999516532365405438114465768501506115275379047447697188620686370699300754640 * q^73 - 399134575097952393052355140371514479012153174980660646654807435656154590439317636650100727312 * q^74 - 2324004895287993423141911565246677610480036000604538705092119528699965986086154360593593272800 * q^75 - 6633935918720327036715040118664821987731317587536782451991725427750234686044104260504536239360 * q^76 - 6461585481973245548189356793856436395182994379442713381123224045549509062132894968864516460800 * q^77 - 28556176219359102115465270938556084350909705495286117230117205751412922131522017940137826091200 * q^78 - 30611582035787076807516826687485094690084083072098723290730859803828786802497884290624307556480 * q^79 - 127732467855339073698199167907855646502900419187610712488908375947950612344972404753625834332160 * q^80 - 105098591020590401711840147132548556253048052082258241572206720930835350937368467193794679663032 * q^81 - 68830371209738349493630432122952083611773652840970378016560437888326646942049769865516365685040 * q^82 + 22938542661502254568160041367746263129225779762371870743525183586562110235427022830971680103520 * q^83 + 361795660381091268015394970465025503071664436510904020432798379164529165144740663778138523854848 * q^84 - 65747002822668948096103688317539312015762969670721483634214688263171509401935169398146161091360 * q^85 + 2926007787385729535219437868096352598169987790407590983846487590337872781868895638215544350378656 * q^86 + 4145530857628120059159343787991300967686349677839106320836691853415365479077514876503669002112320 * q^87 + 13379567436970727806886279611606134975535418870618956336086465570267315661188646758052286051051520 * q^88 + 13262749235321210784149676214189766161707478948372569815117556700615668825668004121877579168519760 * q^89 + 18562789747759155399933926620841126049267839227249440162668332587565567838001478928890860138613680 * q^90 - 6466499581384229905399040912443724309264614193875257390824803270602537852945701184143169943974784 * q^91 - 3605940592933441273788896348672120936868261799818064643016984038777885904937799268971010435816960 * q^92 - 6218230725998946523812046145774116878209214952116357458146814759754757343477151669356631201623040 * q^93 - 111501057917354496628976353847689989005658650697758014190949880350502870630016419857891186452986752 * q^94 - 310841228909329722722502224651860795134807193058850708412373586195233672473563873013656113819102400 * q^95 - 967769551108604066125272773812882212494392412979843145463542262778370585211900025491604732868952064 * q^96 - 870148289336425543686683480565613230312583210673688585087479722135977346731183581578056793848665840 * q^97 - 1259902767579045380431363502561233259244081818944281851461225234703715688976807437199140410707221560 * q^98 - 137018494226539733211453518241879004188470623376815926515879377141376994388427950391858832640432608 * q^99

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