LMFDB - Embedded newform 1.100.a.a.1.4

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			1.4
Root			$-8.46093e12$ 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)

$f(q)$	$=$	$q-6.35192e14 q^{2} +5.52801e23 q^{3} -2.30357e29 q^{4} +4.78100e33 q^{5} -3.51135e38 q^{6} +7.17401e41 q^{7} +5.48921e44 q^{8} +1.33796e47 q^{9} +O(q^{10})$	\(q-6.35192e14 q^{2} +5.52801e23 q^{3} -2.30357e29 q^{4} +4.78100e33 q^{5} -3.51135e38 q^{6} +7.17401e41 q^{7} +5.48921e44 q^{8} +1.33796e47 q^{9} -3.03685e48 q^{10} -4.28029e51 q^{11} -1.27341e53 q^{12} +1.83718e55 q^{13} -4.55687e56 q^{14} +2.64294e57 q^{15} -2.02664e59 q^{16} +6.21642e59 q^{17} -8.49864e61 q^{18} +2.46616e63 q^{19} -1.10133e63 q^{20} +3.96580e65 q^{21} +2.71880e66 q^{22} +1.40807e67 q^{23} +3.03444e68 q^{24} -1.55486e69 q^{25} -1.16696e70 q^{26} -2.10043e70 q^{27} -1.65258e71 q^{28} +2.85339e72 q^{29} -1.67877e72 q^{30} -7.00608e73 q^{31} -2.19189e74 q^{32} -2.36615e75 q^{33} -3.94862e74 q^{34} +3.42989e75 q^{35} -3.08209e76 q^{36} -5.39350e76 q^{37} -1.56649e78 q^{38} +1.01560e79 q^{39} +2.62439e78 q^{40} +1.04979e80 q^{41} -2.51904e80 q^{42} -1.06727e81 q^{43} +9.85993e80 q^{44} +6.39681e80 q^{45} -8.94393e81 q^{46} +6.71187e82 q^{47} -1.12033e83 q^{48} +5.25966e82 q^{49} +9.87637e83 q^{50} +3.43644e83 q^{51} -4.23207e84 q^{52} -2.07277e85 q^{53} +1.33417e85 q^{54} -2.04640e85 q^{55} +3.93797e86 q^{56} +1.36330e87 q^{57} -1.81245e87 q^{58} -1.47079e87 q^{59} -6.08819e86 q^{60} +2.22361e88 q^{61} +4.45021e88 q^{62} +9.59858e88 q^{63} +2.67681e89 q^{64} +8.78357e88 q^{65} +1.50296e90 q^{66} +4.24589e90 q^{67} -1.43199e89 q^{68} +7.78381e90 q^{69} -2.17864e90 q^{70} +4.39297e91 q^{71} +7.34437e91 q^{72} +1.41929e92 q^{73} +3.42591e91 q^{74} -8.59530e92 q^{75} -5.68097e92 q^{76} -3.07068e93 q^{77} -6.45099e93 q^{78} +1.10262e94 q^{79} -9.68938e92 q^{80} -3.45964e94 q^{81} -6.66819e94 q^{82} +8.17771e94 q^{83} -9.13549e94 q^{84} +2.97207e93 q^{85} +6.77920e95 q^{86} +1.57736e96 q^{87} -2.34954e96 q^{88} +5.46832e96 q^{89} -4.06320e95 q^{90} +1.31800e97 q^{91} -3.24358e96 q^{92} -3.87297e97 q^{93} -4.26333e97 q^{94} +1.17907e97 q^{95} -1.21168e98 q^{96} +1.47493e98 q^{97} -3.34089e97 q^{98} -5.72687e98 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−6.35192e14	−0.797848	−0.398924	−	0.916984i	$-0.630616\pi$
$2$	−6.35192e14	−0.797848	−0.398924	+	0.916984i	$0.630616\pi$
$3$	5.52801e23	1.33373	0.666863	−	0.745180i	$-0.267637\pi$
$3$	5.52801e23	1.33373	0.666863	+	0.745180i	$0.267637\pi$
$4$	−2.30357e29	−0.363439
$5$	4.78100e33	0.120366	0.0601829	−	0.998187i	$-0.480832\pi$
$5$	4.78100e33	0.120366	0.0601829	+	0.998187i	$0.480832\pi$
$6$	−3.51135e38	−1.06411
$7$	7.17401e41	1.05538	0.527690	−	0.849437i	$-0.323058\pi$
$7$	7.17401e41	1.05538	0.527690	+	0.849437i	$0.323058\pi$
$8$	5.48921e44	1.08782
$9$	1.33796e47	0.778826
$10$	−3.03685e48	−0.0960336
$11$	−4.28029e51	−1.20930	−0.604652	−	0.796490i	$-0.706688\pi$
$11$	−4.28029e51	−1.20930	−0.604652	+	0.796490i	$0.706688\pi$
$12$	−1.27341e53	−0.484728
$13$	1.83718e55	1.33032	0.665161	−	0.746700i	$-0.268363\pi$
$13$	1.83718e55	1.33032	0.665161	+	0.746700i	$0.268363\pi$
$14$	−4.55687e56	−0.842033
$15$	2.64294e57	0.160535
$16$	−2.02664e59	−0.504474
$17$	6.21642e59	0.0769695	0.0384847	−	0.999259i	$-0.487747\pi$
$17$	6.21642e59	0.0769695	0.0384847	+	0.999259i	$0.487747\pi$
$18$	−8.49864e61	−0.621385
$19$	2.46616e63	1.24085	0.620424	−	0.784267i	$-0.286961\pi$
$19$	2.46616e63	1.24085	0.620424	+	0.784267i	$0.286961\pi$
$20$	−1.10133e63	−0.0437456
$21$	3.96580e65	1.40759
$22$	2.71880e66	0.964840
$23$	1.40807e67	0.553472	0.276736	−	0.960946i	$-0.410747\pi$
$23$	1.40807e67	0.553472	0.276736	+	0.960946i	$0.410747\pi$
$24$	3.03444e68	1.45085
$25$	−1.55486e69	−0.985512
$26$	−1.16696e70	−1.06139
$27$	−2.10043e70	−0.294986
$28$	−1.65258e71	−0.383566
$29$	2.85339e72	1.16590	0.582948	−	0.812509i	$-0.301899\pi$
$29$	2.85339e72	1.16590	0.582948	+	0.812509i	$0.301899\pi$
$30$	−1.67877e72	−0.128083
$31$	−7.00608e73	−1.05456	−0.527280	−	0.849692i	$-0.676788\pi$
$31$	−7.00608e73	−1.05456	−0.527280	+	0.849692i	$0.676788\pi$
$32$	−2.19189e74	−0.685324
$33$	−2.36615e75	−1.61288
$34$	−3.94862e74	−0.0614099
$35$	3.42989e75	0.127032
$36$	−3.08209e76	−0.283056
$37$	−5.39350e76	−0.127610	−0.0638051	−	0.997962i	$-0.520324\pi$
$37$	−5.39350e76	−0.127610	−0.0638051	+	0.997962i	$0.520324\pi$
$38$	−1.56649e78	−0.990008
$39$	1.01560e79	1.77428
$40$	2.62439e78	0.130936
$41$	1.04979e80	1.54277	0.771387	−	0.636367i	$-0.219564\pi$
$41$	1.04979e80	1.54277	0.771387	+	0.636367i	$0.219564\pi$
$42$	−2.51904e80	−1.12304
$43$	−1.06727e81	−1.48452	−0.742258	−	0.670115i	$-0.766245\pi$
$43$	−1.06727e81	−1.48452	−0.742258	+	0.670115i	$0.766245\pi$
$44$	9.85993e80	0.439508
$45$	6.39681e80	0.0937440
$46$	−8.94393e81	−0.441586
$47$	6.71187e82	1.14288	0.571439	−	0.820645i	$-0.306385\pi$
$47$	6.71187e82	1.14288	0.571439	+	0.820645i	$0.306385\pi$
$48$	−1.12033e83	−0.672830
$49$	5.25966e82	0.113829
$50$	9.87637e83	0.786289
$51$	3.43644e83	0.102656
$52$	−4.23207e84	−0.483490
$53$	−2.07277e85	−0.922351	−0.461176	−	0.887309i	$-0.652572\pi$
$53$	−2.07277e85	−0.922351	−0.461176	+	0.887309i	$0.652572\pi$
$54$	1.33417e85	0.235354
$55$	−2.04640e85	−0.145559
$56$	3.93797e86	1.14806
$57$	1.36330e87	1.65495
$58$	−1.81245e87	−0.930208
$59$	−1.47079e87	−0.323874	−0.161937	−	0.986801i	$-0.551774\pi$
$59$	−1.47079e87	−0.323874	−0.161937	+	0.986801i	$0.551774\pi$
$60$	−6.08819e86	−0.0583447
$61$	2.22361e88	0.940227	0.470113	−	0.882606i	$-0.344213\pi$
$61$	2.22361e88	0.940227	0.470113	+	0.882606i	$0.344213\pi$
$62$	4.45021e88	0.841379
$63$	9.59858e88	0.821958
$64$	2.67681e89	1.05126
$65$	8.78357e88	0.160125
$66$	1.50296e90	1.28683
$67$	4.24589e90	1.72689	0.863447	−	0.504439i	$-0.168301\pi$
$67$	4.24589e90	1.72689	0.863447	+	0.504439i	$0.168301\pi$
$68$	−1.43199e89	−0.0279737
$69$	7.78381e90	0.738180
$70$	−2.17864e90	−0.101352
$71$	4.39297e91	1.01268	0.506338	−	0.862335i	$-0.330999\pi$
$71$	4.39297e91	1.01268	0.506338	+	0.862335i	$0.330999\pi$
$72$	7.34437e91	0.847220
$73$	1.41929e92	0.827158	0.413579	−	0.910468i	$-0.364279\pi$
$73$	1.41929e92	0.827158	0.413579	+	0.910468i	$0.364279\pi$
$74$	3.42591e91	0.101814
$75$	−8.59530e92	−1.31440
$76$	−5.68097e92	−0.450972
$77$	−3.07068e93	−1.27628
$78$	−6.45099e93	−1.41561
$79$	1.10262e94	1.28791	0.643954	−	0.765064i	$-0.277293\pi$
$79$	1.10262e94	1.28791	0.643954	+	0.765064i	$0.277293\pi$
$80$	−9.68938e92	−0.0607214
$81$	−3.45964e94	−1.17226
$82$	−6.66819e94	−1.23090
$83$	8.17771e94	0.828449	0.414225	−	0.910175i	$-0.364053\pi$
$83$	8.17771e94	0.828449	0.414225	+	0.910175i	$0.364053\pi$
$84$	−9.13549e94	−0.511572
$85$	2.97207e93	0.00926449
$86$	6.77920e95	1.18442
$87$	1.57736e96	1.55499
$88$	−2.34954e96	−1.31550
$89$	5.46832e96	1.75004	0.875021	−	0.484084i	$-0.160847\pi$
$89$	5.46832e96	1.75004	0.875021	+	0.484084i	$0.160847\pi$
$90$	−4.06320e95	−0.0747935
$91$	1.31800e97	1.40400
$92$	−3.24358e96	−0.201153
$93$	−3.87297e97	−1.40649
$94$	−4.26333e97	−0.911842
$95$	1.17907e97	0.149356
$96$	−1.21168e98	−0.914034
$97$	1.47493e98	0.666147	0.333074	−	0.942901i	$-0.391914\pi$
$97$	1.47493e98	0.666147	0.333074	+	0.942901i	$0.391914\pi$
$98$	−3.34089e97	−0.0908180
$99$	−5.72687e98	−0.941837
$100$	3.58173e98	0.358173
$101$	−2.19745e99	−1.34280	−0.671399	−	0.741096i	$-0.734306\pi$
$101$	−2.19745e99	−1.34280	−0.671399	+	0.741096i	$0.734306\pi$
$102$	−2.18280e98	−0.0819040
$103$	6.33137e99	1.46573	0.732867	−	0.680372i	$-0.238182\pi$
$103$	6.33137e99	1.46573	0.732867	+	0.680372i	$0.238182\pi$
$104$	1.00847e100	1.44715
$105$	1.89605e99	0.169426
$106$	1.31661e100	0.735896
$107$	−1.03383e98	−0.00363037	−0.00181518	−	0.999998i	$-0.500578\pi$
$107$	−1.03383e98	−0.00363037	−0.00181518	+	0.999998i	$0.500578\pi$
$108$	4.83847e99	0.107209
$109$	−9.53267e100	−1.33845	−0.669226	−	0.743059i	$-0.733374\pi$
$109$	−9.53267e100	−1.33845	−0.669226	+	0.743059i	$0.733374\pi$
$110$	1.29986e100	0.116134
$111$	−2.98153e100	−0.170197
$112$	−1.45392e101	−0.532412
$113$	9.98386e100	0.235459	0.117730	−	0.993046i	$-0.462438\pi$
$113$	9.98386e100	0.235459	0.117730	+	0.993046i	$0.462438\pi$
$114$	−8.65955e101	−1.32040
$115$	6.73196e100	0.0666191
$116$	−6.57297e101	−0.423732
$117$	2.45809e102	1.03609
$118$	9.34233e101	0.258402
$119$	4.45966e101	0.0812321
$120$	1.45077e102	0.174633
$121$	5.79304e102	0.462414
$122$	−1.41242e103	−0.750158
$123$	5.80326e103	2.05764
$124$	1.61390e103	0.383268
$125$	−1.49769e103	−0.238988
$126$	−6.09694e103	−0.655797
$127$	−1.47749e104	−1.07458	−0.537290	−	0.843397i	$-0.680552\pi$
$127$	−1.47749e104	−1.07458	−0.537290	+	0.843397i	$0.680552\pi$
$128$	−3.11011e103	−0.153420
$129$	−5.89987e104	−1.97994
$130$	−5.57925e103	−0.127756
$131$	6.80569e104	1.06646	0.533228	−	0.845971i	$-0.320979\pi$
$131$	6.80569e104	1.06646	0.533228	+	0.845971i	$0.320979\pi$
$132$	5.45058e104	0.586183
$133$	1.76923e105	1.30957
$134$	−2.69695e105	−1.37780
$135$	−1.00421e104	−0.0355062
$136$	3.41232e104	0.0837287
$137$	1.02712e106	1.75368	0.876842	−	0.480779i	$-0.159646\pi$
$137$	1.02712e106	1.75368	0.876842	+	0.480779i	$0.159646\pi$
$138$	−4.94421e105	−0.588955
$139$	6.25716e104	0.0521369	0.0260684	−	0.999660i	$-0.491701\pi$
$139$	6.25716e104	0.0521369	0.0260684	+	0.999660i	$0.491701\pi$
$140$	−7.90099e104	−0.0461683
$141$	3.71033e106	1.52429
$142$	−2.79038e106	−0.807961
$143$	−7.86367e106	−1.60876
$144$	−2.71158e106	−0.392897
$145$	1.36420e106	0.140334
$146$	−9.01519e106	−0.659946
$147$	2.90755e106	0.151816
$148$	1.24243e106	0.0463785
$149$	−2.05767e107	−0.550371	−0.275186	−	0.961391i	$-0.588739\pi$
$149$	−2.05767e107	−0.550371	−0.275186	+	0.961391i	$0.588739\pi$
$150$	5.45967e107	1.04869
$151$	−1.39849e107	−0.193331	−0.0966656	−	0.995317i	$-0.530818\pi$
$151$	−1.39849e107	−0.193331	−0.0966656	+	0.995317i	$0.530818\pi$
$152$	1.35373e108	1.34981
$153$	8.31734e106	0.0599458
$154$	1.95047e108	1.01827
$155$	−3.34961e107	−0.126933
$156$	−2.33949e108	−0.644844
$157$	9.42457e107	0.189334	0.0946671	−	0.995509i	$-0.469821\pi$
$157$	9.42457e107	0.189334	0.0946671	+	0.995509i	$0.469821\pi$
$158$	−7.00376e108	−1.02756
$159$	−1.14583e109	−1.23016
$160$	−1.04794e108	−0.0824896
$161$	1.01015e109	0.584123
$162$	2.19754e109	0.935282
$163$	−1.24559e109	−0.390920	−0.195460	−	0.980712i	$-0.562620\pi$
$163$	−1.24559e109	−0.390920	−0.195460	+	0.980712i	$0.562620\pi$
$164$	−2.41826e109	−0.560704
$165$	−1.13125e109	−0.194136
$166$	−5.19441e109	−0.660977
$167$	−1.07955e109	−0.102042	−0.0510210	−	0.998698i	$-0.516248\pi$
$167$	−1.07955e109	−0.102042	−0.0510210	+	0.998698i	$0.516248\pi$
$168$	2.17691e110	1.53120
$169$	1.46806e110	0.769754
$170$	−1.88783e108	−0.00739166
$171$	3.29964e110	0.966404
$172$	2.45852e110	0.539530
$173$	−3.82210e110	−0.629535	−0.314767	−	0.949169i	$-0.601927\pi$
$173$	−3.82210e110	−0.629535	−0.314767	+	0.949169i	$0.601927\pi$
$174$	−1.00192e111	−1.24064
$175$	−1.11546e111	−1.04009
$176$	8.67462e110	0.610061
$177$	−8.13054e110	−0.431959
$178$	−3.47343e111	−1.39627
$179$	3.96007e111	1.20636	0.603181	−	0.797604i	$-0.293900\pi$
$179$	3.96007e111	1.20636	0.603181	+	0.797604i	$0.293900\pi$
$180$	−1.47355e110	−0.0340702
$181$	1.58825e111	0.279144	0.139572	−	0.990212i	$-0.455427\pi$
$181$	1.58825e111	0.279144	0.139572	+	0.990212i	$0.455427\pi$
$182$	−8.37181e111	−1.12017
$183$	1.22922e112	1.25401
$184$	7.72918e111	0.602076
$185$	−2.57863e110	−0.0153599
$186$	2.46008e112	1.12217
$187$	−2.66081e111	−0.0930794
$188$	−1.54612e112	−0.415366
$189$	−1.50685e112	−0.311322
$190$	−7.48937e111	−0.119163
$191$	−6.80786e112	−0.835332	−0.417666	−	0.908601i	$-0.637152\pi$
$191$	−6.80786e112	−0.835332	−0.417666	+	0.908601i	$0.637152\pi$
$192$	1.47974e113	1.40209
$193$	−1.68613e113	−1.23539	−0.617695	−	0.786418i	$-0.711933\pi$
$193$	−1.68613e113	−1.23539	−0.617695	+	0.786418i	$0.711933\pi$
$194$	−9.36863e112	−0.531484
$195$	4.85556e112	0.213563
$196$	−1.21160e112	−0.0413698
$197$	−5.12796e112	−0.136103	−0.0680514	−	0.997682i	$-0.521678\pi$
$197$	−5.12796e112	−0.136103	−0.0680514	+	0.997682i	$0.521678\pi$
$198$	3.63766e113	0.751442
$199$	−1.06312e114	−1.71141	−0.855706	−	0.517462i	$-0.826877\pi$
$199$	−1.06312e114	−1.71141	−0.855706	+	0.517462i	$0.826877\pi$
$200$	−8.53498e113	−1.07206
$201$	2.34713e114	2.30320
$202$	1.39580e114	1.07135
$203$	2.04702e114	1.23046
$204$	−7.91607e112	−0.0373092
$205$	5.01905e113	0.185697
$206$	−4.02163e114	−1.16943
$207$	1.88394e114	0.431058
$208$	−3.72332e114	−0.671112
$209$	−1.05559e115	−1.50056
$210$	−1.20435e114	−0.135176
$211$	−7.10050e114	−0.629952	−0.314976	−	0.949100i	$-0.601996\pi$
$211$	−7.10050e114	−0.629952	−0.314976	+	0.949100i	$0.601996\pi$
$212$	4.77477e114	0.335218
$213$	2.42844e115	1.35063
$214$	6.56678e112	0.00289648
$215$	−5.10260e114	−0.178685
$216$	−1.15297e115	−0.320890
$217$	−5.02617e115	−1.11296
$218$	6.05507e115	1.06788
$219$	7.84583e115	1.10320
$220$	4.71403e114	0.0529017
$221$	1.14207e115	0.102394
$222$	1.89385e115	0.135791
$223$	1.44072e116	0.826968	0.413484	−	0.910511i	$-0.364312\pi$
$223$	1.44072e116	0.826968	0.413484	+	0.910511i	$0.364312\pi$
$224$	−1.57247e116	−0.723277
$225$	−2.08035e116	−0.767542
$226$	−6.34167e115	−0.187861
$227$	1.08411e116	0.258104	0.129052	−	0.991638i	$-0.458807\pi$
$227$	1.08411e116	0.258104	0.129052	+	0.991638i	$0.458807\pi$
$228$	−3.14045e116	−0.601473
$229$	7.20332e114	0.0111090	0.00555452	−	0.999985i	$-0.498232\pi$
$229$	7.20332e114	0.0111090	0.00555452	+	0.999985i	$0.498232\pi$
$230$	−4.27609e115	−0.0531519
$231$	−1.69748e117	−1.70220
$232$	1.56628e117	1.26828
$233$	6.41136e116	0.419597	0.209798	−	0.977745i	$-0.432719\pi$
$233$	6.41136e116	0.419597	0.209798	+	0.977745i	$0.432719\pi$
$234$	−1.56136e117	−0.826641
$235$	3.20894e116	0.137563
$236$	3.38806e116	0.117708
$237$	6.09530e117	1.71772
$238$	−2.83274e116	−0.0648109
$239$	7.73521e117	1.43806	0.719028	−	0.694981i	$-0.244587\pi$
$239$	7.73521e117	1.43806	0.719028	+	0.694981i	$0.244587\pi$
$240$	−5.35630e116	−0.0809857
$241$	−3.95024e117	−0.486161	−0.243081	−	0.970006i	$-0.578158\pi$
$241$	−3.95024e117	−0.486161	−0.243081	+	0.970006i	$0.578158\pi$
$242$	−3.67969e117	−0.368936
$243$	−1.55166e118	−1.26848
$244$	−5.12224e117	−0.341715
$245$	2.51464e116	0.0137011
$246$	−3.68618e118	−1.64168
$247$	4.53079e118	1.65073
$248$	−3.84579e118	−1.14717
$249$	4.52064e118	1.10492
$250$	9.51319e117	0.190676
$251$	2.73413e118	0.449748	0.224874	−	0.974388i	$-0.427803\pi$
$251$	2.73413e118	0.449748	0.224874	+	0.974388i	$0.427803\pi$
$252$	−2.21110e118	−0.298731
$253$	−6.02693e118	−0.669315
$254$	9.38487e118	0.857352
$255$	1.64296e117	0.0123563
$256$	−1.49908e119	−0.928852
$257$	1.20758e119	0.616914	0.308457	−	0.951238i	$-0.400187\pi$
$257$	1.20758e119	0.616914	0.308457	+	0.951238i	$0.400187\pi$
$258$	3.74755e119	1.57969
$259$	−3.86931e118	−0.134677
$260$	−2.02335e118	−0.0581957
$261$	3.81773e119	0.908030
$262$	−4.32292e119	−0.850870
$263$	−4.34863e119	−0.708831	−0.354415	−	0.935088i	$-0.615320\pi$
$263$	−4.34863e119	−0.708831	−0.354415	+	0.935088i	$0.615320\pi$
$264$	−1.29883e120	−1.75452
$265$	−9.90992e118	−0.111020
$266$	−1.12380e120	−1.04483
$267$	3.02289e120	2.33408
$268$	−9.78069e119	−0.627620
$269$	−9.76348e119	−0.521035	−0.260517	−	0.965469i	$-0.583893\pi$
$269$	−9.76348e119	−0.521035	−0.260517	+	0.965469i	$0.583893\pi$
$270$	6.37868e118	0.0283285
$271$	1.56757e120	0.579760	0.289880	−	0.957063i	$-0.406385\pi$
$271$	1.56757e120	0.579760	0.289880	+	0.957063i	$0.406385\pi$
$272$	−1.25985e119	−0.0388291
$273$	7.28590e120	1.87255
$274$	−6.52416e120	−1.39917
$275$	6.65527e120	1.19178
$276$	−1.79305e120	−0.268283
$277$	5.93593e120	0.742575	0.371288	−	0.928518i	$-0.378916\pi$
$277$	5.93593e120	0.742575	0.371288	+	0.928518i	$0.378916\pi$
$278$	−3.97450e119	−0.0415973
$279$	−9.37389e120	−0.821319
$280$	1.88274e120	0.138187
$281$	7.89022e120	0.485430	0.242715	−	0.970098i	$-0.421962\pi$
$281$	7.89022e120	0.485430	0.242715	+	0.970098i	$0.421962\pi$
$282$	−2.35677e121	−1.21615
$283$	−4.49520e121	−1.94680	−0.973398	−	0.229119i	$-0.926415\pi$
$283$	−4.49520e121	−1.94680	−0.973398	+	0.229119i	$0.926415\pi$
$284$	−1.01195e121	−0.368045
$285$	6.51792e120	0.199200
$286$	4.99494e121	1.28355
$287$	7.53122e121	1.62821
$288$	−2.93268e121	−0.533748
$289$	−6.48429e121	−0.994076
$290$	−8.66531e120	−0.111965
$291$	8.15342e121	0.888458
$292$	−3.26942e121	−0.300621
$293$	7.86692e121	0.610742	0.305371	−	0.952234i	$-0.401220\pi$
$293$	7.86692e121	0.610742	0.305371	+	0.952234i	$0.401220\pi$
$294$	−1.84685e121	−0.121126
$295$	−7.03184e120	−0.0389834
$296$	−2.96061e121	−0.138817
$297$	8.99043e121	0.356727
$298$	1.30702e122	0.439112
$299$	2.58688e122	0.736295
$300$	1.97999e122	0.477705
$301$	−7.65659e122	−1.56673
$302$	8.88312e121	0.154249
$303$	−1.21475e123	−1.79092
$304$	−4.99803e122	−0.625975
$305$	1.06311e122	0.113171
$306$	−5.28311e121	−0.0478276
$307$	−7.69349e122	−0.592616	−0.296308	−	0.955092i	$-0.595756\pi$
$307$	−7.69349e122	−0.592616	−0.296308	+	0.955092i	$0.595756\pi$
$308$	7.07353e122	0.463848
$309$	3.49999e123	1.95489
$310$	2.12764e122	0.101273
$311$	−1.52052e123	−0.617097	−0.308549	−	0.951209i	$-0.599843\pi$
$311$	−1.52052e123	−0.617097	−0.308549	+	0.951209i	$0.599843\pi$
$312$	5.57483e123	1.93010
$313$	−1.43262e123	−0.423337	−0.211669	−	0.977341i	$-0.567890\pi$
$313$	−1.43262e123	−0.423337	−0.211669	+	0.977341i	$0.567890\pi$
$314$	−5.98641e122	−0.151060
$315$	4.58908e122	0.0989357
$316$	−2.53996e123	−0.468076
$317$	−2.28087e123	−0.359474	−0.179737	−	0.983715i	$-0.557525\pi$
$317$	−2.28087e123	−0.359474	−0.179737	+	0.983715i	$0.557525\pi$
$318$	7.27823e123	0.981484
$319$	−1.22133e124	−1.40992
$320$	1.27978e123	0.126536
$321$	−5.71500e121	−0.00484192
$322$	−6.41638e123	−0.466042
$323$	1.53307e123	0.0955074
$324$	7.96951e123	0.426043
$325$	−2.85657e124	−1.31105
$326$	7.91186e123	0.311894
$327$	−5.26967e124	−1.78513
$328$	5.76253e124	1.67825
$329$	4.81511e124	1.20617
$330$	7.18564e123	0.154891
$331$	2.82060e124	0.523427	0.261713	−	0.965146i	$-0.415712\pi$
$331$	2.82060e124	0.523427	0.261713	+	0.965146i	$0.415712\pi$
$332$	−1.88379e124	−0.301091
$333$	−7.21632e123	−0.0993862
$334$	6.85723e123	0.0814139
$335$	2.02996e124	0.207859
$336$	−8.03727e124	−0.710092
$337$	1.07275e125	0.818124	0.409062	−	0.912507i	$-0.365856\pi$
$337$	1.07275e125	0.818124	0.409062	+	0.912507i	$0.365856\pi$
$338$	−9.32500e124	−0.614147
$339$	5.51909e124	0.314038
$340$	−6.84635e122	−0.00336708
$341$	2.99881e125	1.27528
$342$	−2.09590e125	−0.771044
$343$	−2.93755e125	−0.935248
$344$	−5.85846e125	−1.61488
$345$	3.72144e124	0.0888516
$346$	2.42777e125	0.502273
$347$	−6.42710e125	−1.15267	−0.576336	−	0.817213i	$-0.695518\pi$
$347$	−6.42710e125	−1.15267	−0.576336	+	0.817213i	$0.695518\pi$
$348$	−3.63354e125	−0.565142
$349$	1.13997e126	1.53827	0.769137	−	0.639084i	$-0.220686\pi$
$349$	1.13997e126	1.53827	0.769137	+	0.639084i	$0.220686\pi$
$350$	7.08532e125	0.829834
$351$	−3.85887e125	−0.392426
$352$	9.38194e125	0.828764
$353$	1.99335e126	1.53015	0.765077	−	0.643938i	$-0.222701\pi$
$353$	1.99335e126	1.53015	0.765077	+	0.643938i	$0.222701\pi$
$354$	5.16445e125	0.344638
$355$	2.10028e125	0.121892
$356$	−1.25966e126	−0.636033
$357$	2.46531e125	0.108341
$358$	−2.51540e126	−0.962493
$359$	−4.67436e126	−1.55792	−0.778962	−	0.627071i	$-0.784254\pi$
$359$	−4.67436e126	−1.55792	−0.778962	+	0.627071i	$0.784254\pi$
$360$	3.51134e125	0.101976
$361$	2.13187e126	0.539702
$362$	−1.00884e126	−0.222714
$363$	3.20240e126	0.616733
$364$	−3.03610e126	−0.510266
$365$	6.78560e125	0.0995615
$366$	−7.80788e126	−1.00051
$367$	3.65948e126	0.409684	0.204842	−	0.978795i	$-0.434332\pi$
$367$	3.65948e126	0.409684	0.204842	+	0.978795i	$0.434332\pi$
$368$	−2.85365e126	−0.279212
$369$	1.40458e127	1.20155
$370$	1.63793e125	0.0122549
$371$	−1.48701e127	−0.973432
$372$	8.92164e126	0.511175
$373$	2.24034e126	0.112390	0.0561948	−	0.998420i	$-0.482103\pi$
$373$	2.24034e126	0.112390	0.0561948	+	0.998420i	$0.482103\pi$
$374$	1.69012e126	0.0742632
$375$	−8.27924e126	−0.318744
$376$	3.68429e127	1.24324
$377$	5.24219e127	1.55102
$378$	9.57137e126	0.248388
$379$	−6.54906e127	−1.49121	−0.745604	−	0.666390i	$-0.767839\pi$
$379$	−6.54906e127	−1.49121	−0.745604	+	0.666390i	$0.767839\pi$
$380$	−2.71607e126	−0.0542816
$381$	−8.16755e127	−1.43320
$382$	4.32430e127	0.666468
$383$	−3.40621e127	−0.461246	−0.230623	−	0.973043i	$-0.574076\pi$
$383$	−3.40621e127	−0.461246	−0.230623	+	0.973043i	$0.574076\pi$
$384$	−1.71927e127	−0.204620
$385$	−1.46809e127	−0.153620
$386$	1.07102e128	0.985654
$387$	−1.42797e128	−1.15618
$388$	−3.39760e127	−0.242104
$389$	−4.92678e127	−0.309071	−0.154535	−	0.987987i	$-0.549388\pi$
$389$	−4.92678e127	−0.309071	−0.154535	+	0.987987i	$0.549388\pi$
$390$	−3.08421e127	−0.170391
$391$	8.75313e126	0.0426004
$392$	2.88714e127	0.123825
$393$	3.76219e128	1.42236
$394$	3.25724e127	0.108589
$395$	5.27163e127	0.155020
$396$	1.31922e128	0.342300
$397$	−4.30304e128	−0.985475	−0.492738	−	0.870178i	$-0.664004\pi$
$397$	−4.30304e128	−0.985475	−0.492738	+	0.870178i	$0.664004\pi$
$398$	6.75284e128	1.36545
$399$	9.78031e128	1.74660
$400$	3.15116e128	0.497165
$401$	−8.24021e128	−1.14893	−0.574463	−	0.818531i	$-0.694789\pi$
$401$	−8.24021e128	−1.14893	−0.574463	+	0.818531i	$0.694789\pi$
$402$	−1.49088e129	−1.83761
$403$	−1.28715e129	−1.40290
$404$	5.06197e128	0.488025
$405$	−1.65405e128	−0.141100
$406$	−1.30025e129	−0.981723
$407$	2.30858e128	0.154319
$408$	1.88634e128	0.111671
$409$	6.48708e128	0.340209	0.170104	−	0.985426i	$-0.445590\pi$
$409$	6.48708e128	0.340209	0.170104	+	0.985426i	$0.445590\pi$
$410$	−3.18806e128	−0.148158
$411$	5.67791e129	2.33893
$412$	−1.45847e129	−0.532704
$413$	−1.05515e129	−0.341810
$414$	−1.19667e129	−0.343919
$415$	3.90976e128	0.0997170
$416$	−4.02691e129	−0.911700
$417$	3.45897e128	0.0695363
$418$	6.70501e129	1.19722
$419$	2.72255e128	0.0431899	0.0215949	−	0.999767i	$-0.493126\pi$
$419$	2.72255e128	0.0431899	0.0215949	+	0.999767i	$0.493126\pi$
$420$	−4.36767e128	−0.0615759
$421$	2.90866e129	0.364526	0.182263	−	0.983250i	$-0.441658\pi$
$421$	2.90866e129	0.364526	0.182263	+	0.983250i	$0.441658\pi$
$422$	4.51018e129	0.502606
$423$	8.98025e129	0.890103
$424$	−1.13779e130	−1.00335
$425$	−9.66568e128	−0.0758543
$426$	−1.54252e130	−1.07760
$427$	1.59522e130	0.992297
$428$	2.38149e127	0.00131942
$429$	−4.34705e130	−2.14565
$430$	3.24113e129	0.142563
$431$	−2.25690e130	−0.884885	−0.442443	−	0.896797i	$-0.645888\pi$
$431$	−2.25690e130	−0.884885	−0.442443	+	0.896797i	$0.645888\pi$
$432$	4.25681e129	0.148812
$433$	−2.54795e129	−0.0794402	−0.0397201	−	0.999211i	$-0.512647\pi$
$433$	−2.54795e129	−0.0794402	−0.0397201	+	0.999211i	$0.512647\pi$
$434$	3.19258e130	0.887975
$435$	7.54133e129	0.187167
$436$	2.19591e130	0.486445
$437$	3.47252e130	0.686774
$438$	−4.98360e130	−0.880187
$439$	9.49204e130	1.49750	0.748749	−	0.662854i	$-0.230655\pi$
$439$	9.49204e130	1.49750	0.748749	+	0.662854i	$0.230655\pi$
$440$	−1.12332e130	−0.158341
$441$	7.03724e129	0.0886528
$442$	−7.25433e129	−0.0816949
$443$	3.91044e130	0.393769	0.196884	−	0.980427i	$-0.436918\pi$
$443$	3.91044e130	0.393769	0.196884	+	0.980427i	$0.436918\pi$
$444$	6.86816e129	0.0618562
$445$	2.61440e130	0.210645
$446$	−9.15133e130	−0.659795
$447$	−1.13748e131	−0.734044
$448$	1.92035e131	1.10948
$449$	−2.39649e131	−1.23988	−0.619942	−	0.784648i	$-0.712844\pi$
$449$	−2.39649e131	−1.23988	−0.619942	+	0.784648i	$0.712844\pi$
$450$	1.32142e131	0.612382
$451$	−4.49341e131	−1.86568
$452$	−2.29985e130	−0.0855750
$453$	−7.73089e130	−0.257851
$454$	−6.88619e130	−0.205927
$455$	6.30134e130	0.168993
$456$	7.48343e131	1.80028
$457$	−3.49347e131	−0.754058	−0.377029	−	0.926202i	$-0.623054\pi$
$457$	−3.49347e131	−0.754058	−0.377029	+	0.926202i	$0.623054\pi$
$458$	−4.57549e129	−0.00886332
$459$	−1.30571e130	−0.0227049
$460$	−1.55075e130	−0.0242120
$461$	1.04090e132	1.45953	0.729763	−	0.683700i	$-0.239630\pi$
$461$	1.04090e132	1.45953	0.729763	+	0.683700i	$0.239630\pi$
$462$	1.07822e132	1.35810
$463$	−5.02279e131	−0.568442	−0.284221	−	0.958759i	$-0.591735\pi$
$463$	−5.02279e131	−0.568442	−0.284221	+	0.958759i	$0.591735\pi$
$464$	−5.78280e131	−0.588164
$465$	−1.85167e131	−0.169294
$466$	−4.07244e131	−0.334774
$467$	−1.70721e132	−1.26213	−0.631063	−	0.775732i	$-0.717381\pi$
$467$	−1.70721e132	−1.26213	−0.631063	+	0.775732i	$0.717381\pi$
$468$	−5.66236e131	−0.376555
$469$	3.04601e132	1.82253
$470$	−2.03830e131	−0.109755
$471$	5.20991e131	0.252520
$472$	−8.07348e131	−0.352315
$473$	4.56821e132	1.79523
$474$	−3.87168e132	−1.37048
$475$	−3.83455e132	−1.22287
$476$	−1.02731e131	−0.0295229
$477$	−2.77330e132	−0.718351
$478$	−4.91334e132	−1.14735
$479$	3.83145e132	0.806780	0.403390	−	0.915028i	$-0.367832\pi$
$479$	3.83145e132	0.806780	0.403390	+	0.915028i	$0.367832\pi$
$480$	−5.79305e131	−0.110018
$481$	−9.90885e131	−0.169763
$482$	2.50916e132	0.387883
$483$	5.58411e132	0.779061
$484$	−1.33447e132	−0.168059
$485$	7.05163e131	0.0801814
$486$	9.85599e132	1.01206
$487$	1.80462e133	1.67380	0.836899	−	0.547357i	$-0.184366\pi$
$487$	1.80462e133	1.67380	0.836899	+	0.547357i	$0.184366\pi$
$488$	1.22059e133	1.02279
$489$	−6.88561e132	−0.521380
$490$	−1.59728e131	−0.0109314
$491$	−2.45128e133	−1.51656	−0.758278	−	0.651932i	$-0.773959\pi$
$491$	−2.45128e133	−1.51656	−0.758278	+	0.651932i	$0.773959\pi$
$492$	−1.33682e133	−0.747825
$493$	1.77378e132	0.0897384
$494$	−2.87792e133	−1.31703
$495$	−2.73802e132	−0.113365
$496$	1.41988e133	0.531998
$497$	3.15152e133	1.06876
$498$	−2.87148e133	−0.881562
$499$	−1.55318e133	−0.431763	−0.215881	−	0.976420i	$-0.569262\pi$
$499$	−1.55318e133	−0.431763	−0.215881	+	0.976420i	$0.569262\pi$
$500$	3.45002e132	0.0868574
$501$	−5.96778e132	−0.136096
$502$	−1.73669e133	−0.358831
$503$	−2.78490e133	−0.521428	−0.260714	−	0.965416i	$-0.583958\pi$
$503$	−2.78490e133	−0.521428	−0.260714	+	0.965416i	$0.583958\pi$
$504$	5.26886e133	0.894140
$505$	−1.05060e133	−0.161627
$506$	3.82826e133	0.534012
$507$	8.11545e133	1.02664
$508$	3.40349e133	0.390544
$509$	−1.07405e134	−1.11814	−0.559069	−	0.829121i	$-0.688841\pi$
$509$	−1.07405e134	−1.11814	−0.559069	+	0.829121i	$0.688841\pi$
$510$	−1.04360e132	−0.00985845
$511$	1.01820e134	0.872966
$512$	1.14933e134	0.894502
$513$	−5.17999e133	−0.366032
$514$	−7.67042e133	−0.492203
$515$	3.02703e133	0.176424
$516$	1.35907e134	0.719586
$517$	−2.87288e134	−1.38209
$518$	2.45775e133	0.107452
$519$	−2.11286e134	−0.839627
$520$	4.82149e133	0.174187
$521$	−1.16339e133	−0.0382170	−0.0191085	−	0.999817i	$-0.506083\pi$
$521$	−1.16339e133	−0.0382170	−0.0191085	+	0.999817i	$0.506083\pi$
$522$	−2.42499e134	−0.724470
$523$	5.33559e134	1.44994	0.724968	−	0.688782i	$-0.241854\pi$
$523$	5.33559e134	1.44994	0.724968	+	0.688782i	$0.241854\pi$
$524$	−1.56774e134	−0.387592
$525$	−6.16628e134	−1.38720
$526$	2.76221e134	0.565539
$527$	−4.35527e133	−0.0811689
$528$	4.79534e134	0.813655
$529$	−4.48960e134	−0.693669
$530$	6.29470e133	0.0885767
$531$	−1.96786e134	−0.252241
$532$	−4.07553e134	−0.475947
$533$	1.92866e135	2.05238
$534$	−1.92012e135	−1.86224
$535$	−4.94272e131	−0.000436972 0
$536$	2.33066e135	1.87854
$537$	2.18913e135	1.60896
$538$	6.20168e134	0.415707
$539$	−2.25129e134	−0.137653
$540$	2.31327e133	0.0129043
$541$	−3.29734e135	−1.67841	−0.839206	−	0.543813i	$-0.816980\pi$
$541$	−3.29734e135	−1.67841	−0.839206	+	0.543813i	$0.816980\pi$
$542$	−9.95711e134	−0.462560
$543$	8.77984e134	0.372302
$544$	−1.36257e134	−0.0527490
$545$	−4.55756e134	−0.161104
$546$	−4.62795e135	−1.49401
$547$	−3.86846e135	−1.14069	−0.570343	−	0.821407i	$-0.693190\pi$
$547$	−3.86846e135	−1.14069	−0.570343	+	0.821407i	$0.693190\pi$
$548$	−2.36603e135	−0.637357
$549$	2.97512e135	0.732273
$550$	−4.22737e135	−0.950861
$551$	7.03692e135	1.44670
$552$	4.27270e135	0.803004
$553$	7.91022e135	1.35923
$554$	−3.77046e135	−0.592462
$555$	−1.42547e134	−0.0204859
$556$	−1.44138e134	−0.0189486
$557$	1.15768e136	1.39237	0.696187	−	0.717861i	$-0.254879\pi$
$557$	1.15768e136	1.39237	0.696187	+	0.717861i	$0.254879\pi$
$558$	5.95422e135	0.655288
$559$	−1.96077e136	−1.97488
$560$	−6.95118e134	−0.0640842
$561$	−1.47090e135	−0.124142
$562$	−5.01180e135	−0.387299
$563$	1.78356e136	1.26219	0.631093	−	0.775707i	$-0.282607\pi$
$563$	1.78356e136	1.26219	0.631093	+	0.775707i	$0.282607\pi$
$564$	−8.54699e135	−0.553985
$565$	4.77328e134	0.0283412
$566$	2.85532e136	1.55325
$567$	−2.48195e136	−1.23718
$568$	2.41140e136	1.10160
$569$	−3.80404e136	−1.59290	−0.796448	−	0.604706i	$-0.793290\pi$
$569$	−3.80404e136	−1.59290	−0.796448	+	0.604706i	$0.793290\pi$
$570$	−4.14013e135	−0.158931
$571$	−7.68310e134	−0.0270426	−0.0135213	−	0.999909i	$-0.504304\pi$
$571$	−7.68310e134	−0.0270426	−0.0135213	+	0.999909i	$0.504304\pi$
$572$	1.81145e136	0.584686
$573$	−3.76339e136	−1.11410
$574$	−4.78377e136	−1.29907
$575$	−2.18935e136	−0.545453
$576$	3.58148e136	0.818747
$577$	6.19183e136	1.29902	0.649511	−	0.760352i	$-0.274974\pi$
$577$	6.19183e136	1.29902	0.649511	+	0.760352i	$0.274974\pi$
$578$	4.11877e136	0.793121
$579$	−9.32094e136	−1.64767
$580$	−3.14253e135	−0.0510028
$581$	5.86670e136	0.874330
$582$	−5.17899e136	−0.708854
$583$	8.87207e136	1.11540
$584$	7.79076e136	0.899796
$585$	1.17521e136	0.124710
$586$	−4.99700e136	−0.487279
$587$	1.23004e137	1.10239	0.551193	−	0.834378i	$-0.314173\pi$
$587$	1.23004e137	1.10239	0.551193	+	0.834378i	$0.314173\pi$
$588$	−6.69773e135	−0.0551759
$589$	−1.72781e137	−1.30855
$590$	4.46657e135	0.0311028
$591$	−2.83474e136	−0.181524
$592$	1.09307e136	0.0643760
$593$	2.69659e137	1.46086	0.730428	−	0.682990i	$-0.239321\pi$
$593$	2.69659e137	1.46086	0.730428	+	0.682990i	$0.239321\pi$
$594$	−5.71064e136	−0.284614
$595$	2.13216e135	0.00977757
$596$	4.73998e136	0.200026
$597$	−5.87693e137	−2.28256
$598$	−1.64316e137	−0.587451
$599$	1.08030e137	0.355563	0.177782	−	0.984070i	$-0.443108\pi$
$599$	1.08030e137	0.355563	0.177782	+	0.984070i	$0.443108\pi$
$600$	−4.71815e137	−1.42983
$601$	−4.60281e137	−1.28451	−0.642253	−	0.766492i	$-0.722000\pi$
$601$	−4.60281e137	−1.28451	−0.642253	+	0.766492i	$0.722000\pi$
$602$	4.86340e137	1.25001
$603$	5.68085e137	1.34495
$604$	3.22152e136	0.0702640
$605$	2.76965e136	0.0556588
$606$	7.71600e137	1.42889
$607$	−2.91059e137	−0.496753	−0.248376	−	0.968664i	$-0.579897\pi$
$607$	−2.91059e137	−0.496753	−0.248376	+	0.968664i	$0.579897\pi$
$608$	−5.40557e137	−0.850382
$609$	1.13160e138	1.64110
$610$	−6.75278e136	−0.0902934
$611$	1.23309e138	1.52039
$612$	−1.91596e136	−0.0217866
$613$	−1.15094e138	−1.20715	−0.603574	−	0.797307i	$-0.706257\pi$
$613$	−1.15094e138	−1.20715	−0.603574	+	0.797307i	$0.706257\pi$
$614$	4.88684e137	0.472818
$615$	2.77454e137	0.247669
$616$	−1.68556e138	−1.38835
$617$	1.31552e138	0.999959	0.499979	−	0.866037i	$-0.333341\pi$
$617$	1.31552e138	0.999959	0.499979	+	0.866037i	$0.333341\pi$
$618$	−2.22316e138	−1.55970
$619$	−1.90304e138	−1.23243	−0.616213	−	0.787579i	$-0.711334\pi$
$619$	−1.90304e138	−1.23243	−0.616213	+	0.787579i	$0.711334\pi$
$620$	7.71604e136	0.0461324
$621$	−2.95754e137	−0.163266
$622$	9.65823e137	0.492350
$623$	3.92298e138	1.84696
$624$	−2.05825e138	−0.895079
$625$	2.38154e138	0.956746
$626$	9.09989e137	0.337759
$627$	−5.83530e138	−2.00134
$628$	−2.17101e137	−0.0688114
$629$	−3.35283e136	−0.00982209
$630$	−2.91494e137	−0.0789356
$631$	−2.84804e138	−0.713006	−0.356503	−	0.934294i	$-0.616031\pi$
$631$	−2.84804e138	−0.713006	−0.356503	+	0.934294i	$0.616031\pi$
$632$	6.05252e138	1.40101
$633$	−3.92516e138	−0.840184
$634$	1.44879e138	0.286805
$635$	−7.06385e137	−0.129343
$636$	2.63950e138	0.447089
$637$	9.66296e137	0.151429
$638$	7.75780e138	1.12490
$639$	5.87764e138	0.788698
$640$	−1.48694e137	−0.0184665
$641$	5.29537e138	0.608728	0.304364	−	0.952556i	$-0.401556\pi$
$641$	5.29537e138	0.608728	0.304364	+	0.952556i	$0.401556\pi$
$642$	3.63012e136	0.00386311
$643$	−4.95979e138	−0.488675	−0.244338	−	0.969690i	$-0.578571\pi$
$643$	−4.95979e138	−0.488675	−0.244338	+	0.969690i	$0.578571\pi$
$644$	−2.32695e138	−0.212293
$645$	−2.82072e138	−0.238317
$646$	−9.73793e137	−0.0762003
$647$	−1.78830e139	−1.29622	−0.648110	−	0.761547i	$-0.724440\pi$
$647$	−1.78830e139	−1.29622	−0.648110	+	0.761547i	$0.724440\pi$
$648$	−1.89907e139	−1.27520
$649$	6.29540e138	0.391662
$650$	1.81447e139	1.04602
$651$	−2.77847e139	−1.48439
$652$	2.86929e138	0.142075
$653$	−1.57648e139	−0.723581	−0.361790	−	0.932259i	$-0.617834\pi$
$653$	−1.57648e139	−0.723581	−0.361790	+	0.932259i	$0.617834\pi$
$654$	3.34725e139	1.42426
$655$	3.25380e138	0.128365
$656$	−2.12755e139	−0.778288
$657$	1.89895e139	0.644212
$658$	−3.05852e139	−0.962341
$659$	5.39763e139	1.57534	0.787672	−	0.616095i	$-0.211286\pi$
$659$	5.39763e139	1.57534	0.787672	+	0.616095i	$0.211286\pi$
$660$	2.60592e138	0.0705564
$661$	2.09841e138	0.0527130	0.0263565	−	0.999653i	$-0.491609\pi$
$661$	2.09841e138	0.0527130	0.0263565	+	0.999653i	$0.491609\pi$
$662$	−1.79162e139	−0.417615
$663$	6.31337e138	0.136566
$664$	4.48892e139	0.901201
$665$	8.45867e138	0.157627
$666$	4.58375e138	0.0792951
$667$	4.01776e139	0.645290
$668$	2.48682e138	0.0370860
$669$	7.96431e139	1.10295
$670$	−1.28941e139	−0.165840
$671$	−9.51771e139	−1.13702
$672$	−8.69262e139	−0.964654
$673$	−1.00567e140	−1.03683	−0.518417	−	0.855128i	$-0.673479\pi$
$673$	−1.00567e140	−1.03683	−0.518417	+	0.855128i	$0.673479\pi$
$674$	−6.81403e139	−0.652739
$675$	3.26588e139	0.290712
$676$	−3.38178e139	−0.279758
$677$	−8.13596e138	−0.0625561	−0.0312780	−	0.999511i	$-0.509958\pi$
$677$	−8.13596e138	−0.0625561	−0.0312780	+	0.999511i	$0.509958\pi$
$678$	−3.50568e139	−0.250555
$679$	1.05812e140	0.703039
$680$	1.63143e138	0.0100781
$681$	5.99298e139	0.344240
$682$	−1.90482e140	−1.01748
$683$	2.57595e140	1.27971	0.639856	−	0.768495i	$-0.278994\pi$
$683$	2.57595e140	1.27971	0.639856	+	0.768495i	$0.278994\pi$
$684$	−7.60094e139	−0.351229
$685$	4.91064e139	0.211084
$686$	1.86591e140	0.746186
$687$	3.98200e138	0.0148164
$688$	2.16297e140	0.748899
$689$	−3.80806e140	−1.22702
$690$	−2.36383e139	−0.0708901
$691$	−9.27520e138	−0.0258917	−0.0129458	−	0.999916i	$-0.504121\pi$
$691$	−9.27520e138	−0.0258917	−0.0129458	+	0.999916i	$0.504121\pi$
$692$	8.80446e139	0.228797
$693$	−4.10847e140	−0.993996
$694$	4.08244e140	0.919657
$695$	2.99155e138	0.00627550
$696$	8.65844e140	1.69154
$697$	6.52594e139	0.118746
$698$	−7.24098e140	−1.22731
$699$	3.54421e140	0.559627
$700$	2.56954e140	0.378009
$701$	−2.52502e140	−0.346116	−0.173058	−	0.984912i	$-0.555365\pi$
$701$	−2.52502e140	−0.346116	−0.173058	+	0.984912i	$0.555365\pi$
$702$	2.45112e140	0.313096
$703$	−1.33013e140	−0.158345
$704$	−1.14575e141	−1.27129
$705$	1.77391e140	0.183472
$706$	−1.26616e141	−1.22083
$707$	−1.57645e141	−1.41716
$708$	1.87292e140	0.156991
$709$	−6.75405e140	−0.527929	−0.263965	−	0.964532i	$-0.585030\pi$
$709$	−6.75405e140	−0.527929	−0.263965	+	0.964532i	$0.585030\pi$
$710$	−1.33408e140	−0.0972509
$711$	1.47527e141	1.00306
$712$	3.00168e141	1.90373
$713$	−9.86503e140	−0.583669
$714$	−1.56594e140	−0.0864399
$715$	−3.75962e140	−0.193640
$716$	−9.12228e140	−0.438439
$717$	4.27603e141	1.91797
$718$	2.96911e141	1.24299
$719$	−1.58276e141	−0.618494	−0.309247	−	0.950982i	$-0.600077\pi$
$719$	−1.58276e141	−0.618494	−0.309247	+	0.950982i	$0.600077\pi$
$720$	−1.29640e140	−0.0472914
$721$	4.54213e141	1.54691
$722$	−1.35415e141	−0.430600
$723$	−2.18370e141	−0.648406
$724$	−3.65863e140	−0.101452
$725$	−4.43663e141	−1.14900
$726$	−2.03414e141	−0.492060
$727$	−5.79704e141	−1.30994	−0.654972	−	0.755653i	$-0.727320\pi$
$727$	−5.79704e141	−1.30994	−0.654972	+	0.755653i	$0.727320\pi$
$728$	7.23477e141	1.52729
$729$	−2.63416e141	−0.519553
$730$	−4.31016e140	−0.0794350
$731$	−6.63458e140	−0.114262
$732$	−2.83158e141	−0.455754
$733$	1.16688e142	1.75541	0.877704	−	0.479203i	$-0.159074\pi$
$733$	1.16688e142	1.75541	0.877704	+	0.479203i	$0.159074\pi$
$734$	−2.32447e141	−0.326865
$735$	1.39010e140	0.0182735
$736$	−3.08633e141	−0.379307
$737$	−1.81736e142	−2.08834
$738$	−8.92180e141	−0.958656
$739$	3.28180e141	0.329771	0.164885	−	0.986313i	$-0.447275\pi$
$739$	3.28180e141	0.329771	0.164885	+	0.986313i	$0.447275\pi$
$740$	5.94005e139	0.00558239
$741$	2.50463e142	2.20162
$742$	9.44537e141	0.776650
$743$	1.89490e142	1.45761	0.728804	−	0.684722i	$-0.240076\pi$
$743$	1.89490e142	1.45761	0.728804	+	0.684722i	$0.240076\pi$
$744$	−2.12596e142	−1.53001
$745$	−9.83772e140	−0.0662459
$746$	−1.42304e141	−0.0896699
$747$	1.09415e142	0.645218
$748$	6.12934e140	0.0338287
$749$	−7.41668e139	−0.00383142
$750$	5.25890e141	0.254310
$751$	1.03779e142	0.469821	0.234911	−	0.972017i	$-0.424520\pi$
$751$	1.03779e142	0.469821	0.234911	+	0.972017i	$0.424520\pi$
$752$	−1.36026e142	−0.576552
$753$	1.51143e142	0.599841
$754$	−3.32980e142	−1.23747
$755$	−6.68620e140	−0.0232705
$756$	3.47112e141	0.113147
$757$	−3.88944e142	−1.18752	−0.593761	−	0.804642i	$-0.702357\pi$
$757$	−3.88944e142	−1.18752	−0.593761	+	0.804642i	$0.702357\pi$
$758$	4.15991e142	1.18976
$759$	−3.33169e142	−0.892683
$760$	6.47217e141	0.162472
$761$	3.97513e141	0.0934998	0.0467499	−	0.998907i	$-0.485114\pi$
$761$	3.97513e141	0.0934998	0.0467499	+	0.998907i	$0.485114\pi$
$762$	5.18796e142	1.14347
$763$	−6.83875e142	−1.41258
$764$	1.56824e142	0.303592
$765$	3.97652e140	0.00721543
$766$	2.16360e142	0.368004
$767$	−2.70211e142	−0.430856
$768$	−8.28693e142	−1.23883
$769$	−8.11742e142	−1.13780	−0.568898	−	0.822408i	$-0.692630\pi$
$769$	−8.11742e142	−1.13780	−0.568898	+	0.822408i	$0.692630\pi$
$770$	9.32521e141	0.122565
$771$	6.67549e142	0.822794
$772$	3.88411e142	0.448989
$773$	−2.42740e142	−0.263182	−0.131591	−	0.991304i	$-0.542009\pi$
$773$	−2.42740e142	−0.263182	−0.131591	+	0.991304i	$0.542009\pi$
$774$	9.07032e142	0.922455
$775$	1.08935e143	1.03928
$776$	8.09620e142	0.724646
$777$	−2.13896e142	−0.179623
$778$	3.12945e142	0.246592
$779$	2.58896e143	1.91435
$780$	−1.11851e142	−0.0776172
$781$	−1.88032e143	−1.22463
$782$	−5.55992e141	−0.0339887
$783$	−5.99333e142	−0.343923
$784$	−1.06595e142	−0.0574236
$785$	4.50589e141	0.0227894
$786$	−2.38971e143	−1.13483
$787$	−2.62605e143	−1.17099	−0.585495	−	0.810676i	$-0.699100\pi$
$787$	−2.62605e143	−1.17099	−0.585495	+	0.810676i	$0.699100\pi$
$788$	1.18126e142	0.0494650
$789$	−2.40393e143	−0.945386
$790$	−3.34849e142	−0.123683
$791$	7.16244e142	0.248499
$792$	−3.14360e143	−1.02455
$793$	4.08519e143	1.25080
$794$	2.73326e143	0.786259
$795$	−5.47822e142	−0.148070
$796$	2.44897e143	0.621993
$797$	1.28773e143	0.307353	0.153676	−	0.988121i	$-0.450889\pi$
$797$	1.28773e143	0.307353	0.153676	+	0.988121i	$0.450889\pi$
$798$	−6.21237e143	−1.39352
$799$	4.17238e142	0.0879667
$800$	3.40810e143	0.675395
$801$	7.31642e143	1.36298
$802$	5.23411e143	0.916667
$803$	−6.07495e143	−1.00028
$804$	−5.40677e143	−0.837074
$805$	4.82952e142	0.0703085
$806$	8.17584e143	1.11930
$807$	−5.39726e143	−0.694918
$808$	−1.20623e144	−1.46072
$809$	1.11053e144	1.26496	0.632480	−	0.774577i	$-0.282037\pi$
$809$	1.11053e144	1.26496	0.632480	+	0.774577i	$0.282037\pi$
$810$	1.05064e143	0.112576
$811$	8.45956e143	0.852738	0.426369	−	0.904549i	$-0.359793\pi$
$811$	8.45956e143	0.852738	0.426369	+	0.904549i	$0.359793\pi$
$812$	−4.71546e143	−0.447198
$813$	8.66557e143	0.773241
$814$	−1.46639e143	−0.123123
$815$	−5.95514e142	−0.0470534
$816$	−6.96444e142	−0.0517873
$817$	−2.63205e144	−1.84206
$818$	−4.12054e143	−0.271435
$819$	1.76343e144	1.09347
$820$	−1.15617e143	−0.0674896
$821$	−6.59073e143	−0.362199	−0.181100	−	0.983465i	$-0.557966\pi$
$821$	−6.59073e143	−0.362199	−0.181100	+	0.983465i	$0.557966\pi$
$822$	−3.60656e144	−1.86611
$823$	−2.78185e144	−1.35532	−0.677659	−	0.735376i	$-0.737006\pi$
$823$	−2.78185e144	−1.35532	−0.677659	+	0.735376i	$0.737006\pi$
$824$	3.47542e144	1.59445
$825$	3.67904e144	1.58951
$826$	6.70220e143	0.272713
$827$	−1.77490e144	−0.680224	−0.340112	−	0.940385i	$-0.610465\pi$
$827$	−1.77490e144	−0.680224	−0.340112	+	0.940385i	$0.610465\pi$
$828$	−4.33979e143	−0.156663
$829$	−3.01951e144	−1.02680	−0.513401	−	0.858149i	$-0.671615\pi$
$829$	−3.01951e144	−1.02680	−0.513401	+	0.858149i	$0.671615\pi$
$830$	−2.48345e143	−0.0795590
$831$	3.28139e144	0.990392
$832$	4.91779e144	1.39851
$833$	3.26962e142	0.00876133
$834$	−2.19711e143	−0.0554794
$835$	−5.16134e142	−0.0122824
$836$	2.43162e144	0.545362
$837$	1.47158e144	0.311080
$838$	−1.72934e143	−0.0344589
$839$	−5.39996e144	−1.01432	−0.507158	−	0.861853i	$-0.669304\pi$
$839$	−5.39996e144	−1.01432	−0.507158	+	0.861853i	$0.669304\pi$
$840$	1.04078e144	0.184304
$841$	2.15216e144	0.359313
$842$	−1.84756e144	−0.290837
$843$	4.36172e144	0.647430
$844$	1.63565e144	0.228949
$845$	7.01879e143	0.0926521
$846$	−5.70418e144	−0.710167
$847$	4.15594e144	0.488023
$848$	4.20077e144	0.465302
$849$	−2.48495e145	−2.59649
$850$	6.13956e143	0.0605202
$851$	−7.59441e143	−0.0706287
$852$	−5.59407e144	−0.490872
$853$	−6.84782e144	−0.566990	−0.283495	−	0.958974i	$-0.591494\pi$
$853$	−6.84782e144	−0.566990	−0.283495	+	0.958974i	$0.591494\pi$
$854$	−1.01327e145	−0.791702
$855$	1.57756e144	0.116322
$856$	−5.67489e142	−0.00394917
$857$	−1.02135e145	−0.670847	−0.335423	−	0.942068i	$-0.608879\pi$
$857$	−1.02135e145	−0.670847	−0.335423	+	0.942068i	$0.608879\pi$
$858$	2.76121e145	1.71190
$859$	7.08758e144	0.414798	0.207399	−	0.978256i	$-0.433500\pi$
$859$	7.08758e144	0.414798	0.207399	+	0.978256i	$0.433500\pi$
$860$	1.17542e144	0.0649410
$861$	4.16326e145	2.17159
$862$	1.43356e145	0.706004
$863$	2.17911e144	0.101331	0.0506657	−	0.998716i	$-0.483866\pi$
$863$	2.17911e144	0.101331	0.0506657	+	0.998716i	$0.483866\pi$
$864$	4.60391e144	0.202161
$865$	−1.82734e144	−0.0757745
$866$	1.61844e144	0.0633812
$867$	−3.58452e145	−1.32582
$868$	1.15781e145	0.404494
$869$	−4.71953e145	−1.55747
$870$	−4.79019e144	−0.149331
$871$	7.80047e145	2.29732
$872$	−5.23268e145	−1.45599
$873$	1.97340e145	0.518813
$874$	−2.20572e145	−0.547941
$875$	−1.07444e145	−0.252223
$876$	−1.80734e145	−0.400946
$877$	−3.74826e144	−0.0785868	−0.0392934	−	0.999228i	$-0.512511\pi$
$877$	−3.74826e144	−0.0785868	−0.0392934	+	0.999228i	$0.512511\pi$
$878$	−6.02927e145	−1.19477
$879$	4.34884e145	0.814562
$880$	4.14733e144	0.0734306
$881$	5.19942e145	0.870257	0.435128	−	0.900368i	$-0.356703\pi$
$881$	5.19942e145	0.870257	0.435128	+	0.900368i	$0.356703\pi$
$882$	−4.47000e144	−0.0707314
$883$	4.62338e145	0.691679	0.345840	−	0.938294i	$-0.387594\pi$
$883$	4.62338e145	0.691679	0.345840	+	0.938294i	$0.387594\pi$
$884$	−2.63083e144	−0.0372140
$885$	−3.88721e144	−0.0519931
$886$	−2.48388e145	−0.314167
$887$	−1.43128e146	−1.71201	−0.856003	−	0.516970i	$-0.827060\pi$
$887$	−1.43128e146	−1.71201	−0.856003	+	0.516970i	$0.827060\pi$
$888$	−1.63663e145	−0.185143
$889$	−1.05995e146	−1.13409
$890$	−1.66065e145	−0.168063
$891$	1.48083e146	1.41761
$892$	−3.31879e145	−0.300552
$893$	1.65526e146	1.41814
$894$	7.22520e145	0.585656
$895$	1.89331e145	0.145205
$896$	−2.23120e145	−0.161917
$897$	1.43003e146	0.982016
$898$	1.52223e146	0.989239
$899$	−1.99911e146	−1.22951
$900$	4.79223e145	0.278955
$901$	−1.28852e145	−0.0709929
$902$	2.85418e146	1.48853
$903$	−4.23257e146	−2.08959
$904$	5.48035e145	0.256136
$905$	7.59340e144	0.0335994
$906$	4.91060e145	0.205726
$907$	3.01781e144	0.0119710	0.00598551	−	0.999982i	$-0.498095\pi$
$907$	3.01781e144	0.0119710	0.00598551	+	0.999982i	$0.498095\pi$
$908$	−2.49732e145	−0.0938049
$909$	−2.94011e146	−1.04581
$910$	−4.00256e145	−0.134831
$911$	−1.50370e146	−0.479735	−0.239867	−	0.970806i	$-0.577104\pi$
$911$	−1.50370e146	−0.479735	−0.239867	+	0.970806i	$0.577104\pi$
$912$	−2.76292e146	−0.834879
$913$	−3.50029e146	−1.00185
$914$	2.21902e146	0.601623
$915$	5.87688e145	0.150939
$916$	−1.65933e144	−0.00403745
$917$	4.88241e146	1.12552
$918$	8.29377e144	0.0181150
$919$	1.41586e146	0.293023	0.146511	−	0.989209i	$-0.453195\pi$
$919$	1.41586e146	0.293023	0.146511	+	0.989209i	$0.453195\pi$
$920$	3.69532e145	0.0724694
$921$	−4.25297e146	−0.790388
$922$	−6.61169e146	−1.16448
$923$	8.07069e146	1.34718
$924$	3.91025e146	0.618646
$925$	8.38616e145	0.125761
$926$	3.19043e146	0.453530
$927$	8.47115e146	1.14155
$928$	−6.25432e146	−0.799016
$929$	5.22749e146	0.633163	0.316582	−	0.948565i	$-0.397465\pi$
$929$	5.22749e146	0.633163	0.316582	+	0.948565i	$0.397465\pi$
$930$	1.17616e146	0.135071
$931$	1.29712e146	0.141244
$932$	−1.47690e146	−0.152498
$933$	−8.40546e146	−0.823039
$934$	1.08441e147	1.00698
$935$	−1.27213e145	−0.0112036
$936$	1.34930e147	1.12707
$937$	−1.60122e147	−1.26865	−0.634323	−	0.773068i	$-0.718721\pi$
$937$	−1.60122e147	−1.26865	−0.634323	+	0.773068i	$0.718721\pi$
$938$	−1.93480e147	−1.45410
$939$	−7.91954e146	−0.564616
$940$	−7.39202e145	−0.0499959
$941$	−1.91684e147	−1.22998	−0.614991	−	0.788535i	$-0.710840\pi$
$941$	−1.91684e147	−1.22998	−0.614991	+	0.788535i	$0.710840\pi$
$942$	−3.30929e146	−0.201472
$943$	1.47818e147	0.853881
$944$	2.98077e146	0.163386
$945$	−7.20424e145	−0.0374726
$946$	−2.90169e147	−1.43232
$947$	2.73651e147	1.28195	0.640977	−	0.767560i	$-0.278529\pi$
$947$	2.73651e147	1.28195	0.640977	+	0.767560i	$0.278529\pi$
$948$	−1.40409e147	−0.624285
$949$	2.60749e147	1.10039
$950$	2.43567e147	0.975664
$951$	−1.26087e147	−0.479439
$952$	2.44800e146	0.0883656
$953$	2.47189e147	0.847092	0.423546	−	0.905875i	$-0.360785\pi$
$953$	2.47189e147	0.847092	0.423546	+	0.905875i	$0.360785\pi$
$954$	1.76158e147	0.573135
$955$	−3.25484e146	−0.100545
$956$	−1.78186e147	−0.522645
$957$	−6.75154e147	−1.88045
$958$	−2.43370e147	−0.643687
$959$	7.36854e147	1.85080
$960$	7.07465e146	0.168764
$961$	4.94770e146	0.112097
$962$	6.29402e146	0.135445
$963$	−1.38322e145	−0.00282742
$964$	9.09965e146	0.176690
$965$	−8.06138e146	−0.148699
$966$	−3.54698e147	−0.621572
$967$	6.45804e147	1.07520	0.537601	−	0.843199i	$-0.319331\pi$
$967$	6.45804e147	1.07520	0.537601	+	0.843199i	$0.319331\pi$
$968$	3.17992e147	0.503021
$969$	8.47482e146	0.127381
$970$	−4.47914e146	−0.0639725
$971$	2.08792e147	0.283375	0.141688	−	0.989911i	$-0.454747\pi$
$971$	2.08792e147	0.283375	0.141688	+	0.989911i	$0.454747\pi$
$972$	3.57434e147	0.461016
$973$	4.48890e146	0.0550242
$974$	−1.14628e148	−1.33544
$975$	−1.57911e148	−1.74858
$976$	−4.50648e147	−0.474320
$977$	−5.05077e146	−0.0505332	−0.0252666	−	0.999681i	$-0.508043\pi$
$977$	−5.05077e146	−0.0505332	−0.0252666	+	0.999681i	$0.508043\pi$
$978$	4.37369e147	0.415982
$979$	−2.34060e148	−2.11633
$980$	−5.79265e145	−0.00497951
$981$	−1.27544e148	−1.04242
$982$	1.55703e148	1.20998
$983$	5.89442e147	0.435554	0.217777	−	0.975999i	$-0.430119\pi$
$983$	5.89442e147	0.435554	0.217777	+	0.975999i	$0.430119\pi$
$984$	3.18553e148	2.23833
$985$	−2.45168e146	−0.0163821
$986$	−1.12669e147	−0.0715976
$987$	2.66180e148	1.60870
$988$	−1.04370e148	−0.599938
$989$	−1.50278e148	−0.821637
$990$	1.73917e147	0.0904480
$991$	1.85304e148	0.916726	0.458363	−	0.888765i	$-0.348436\pi$
$991$	1.85304e148	0.916726	0.458363	+	0.888765i	$0.348436\pi$
$992$	1.53566e148	0.722715
$993$	1.55923e148	0.698108
$994$	−2.00182e148	−0.852706
$995$	−5.08277e147	−0.205996
$996$	−1.04136e148	−0.401572
$997$	1.00934e148	0.370363	0.185182	−	0.982704i	$-0.440713\pi$
$997$	1.00934e148	0.370363	0.185182	+	0.982704i	$0.440713\pi$
$998$	9.86568e147	0.344481
$999$	1.13286e147	0.0376432

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1.100.a.a.1.4	✓	8
3.2	odd	2		9.100.a.d.1.5		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1.100.a.a.1.4	✓	8	1.1	even	1	trivial
9.100.a.d.1.5		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)

\(f(q)\)	\(=\)	\(q-6.35192e14 q^{2} +5.52801e23 q^{3} -2.30357e29 q^{4} +4.78100e33 q^{5} -3.51135e38 q^{6} +7.17401e41 q^{7} +5.48921e44 q^{8} +1.33796e47 q^{9} +O(q^{10})\)	\(q-6.35192e14 q^{2} +5.52801e23 q^{3} -2.30357e29 q^{4} +4.78100e33 q^{5} -3.51135e38 q^{6} +7.17401e41 q^{7} +5.48921e44 q^{8} +1.33796e47 q^{9} -3.03685e48 q^{10} -4.28029e51 q^{11} -1.27341e53 q^{12} +1.83718e55 q^{13} -4.55687e56 q^{14} +2.64294e57 q^{15} -2.02664e59 q^{16} +6.21642e59 q^{17} -8.49864e61 q^{18} +2.46616e63 q^{19} -1.10133e63 q^{20} +3.96580e65 q^{21} +2.71880e66 q^{22} +1.40807e67 q^{23} +3.03444e68 q^{24} -1.55486e69 q^{25} -1.16696e70 q^{26} -2.10043e70 q^{27} -1.65258e71 q^{28} +2.85339e72 q^{29} -1.67877e72 q^{30} -7.00608e73 q^{31} -2.19189e74 q^{32} -2.36615e75 q^{33} -3.94862e74 q^{34} +3.42989e75 q^{35} -3.08209e76 q^{36} -5.39350e76 q^{37} -1.56649e78 q^{38} +1.01560e79 q^{39} +2.62439e78 q^{40} +1.04979e80 q^{41} -2.51904e80 q^{42} -1.06727e81 q^{43} +9.85993e80 q^{44} +6.39681e80 q^{45} -8.94393e81 q^{46} +6.71187e82 q^{47} -1.12033e83 q^{48} +5.25966e82 q^{49} +9.87637e83 q^{50} +3.43644e83 q^{51} -4.23207e84 q^{52} -2.07277e85 q^{53} +1.33417e85 q^{54} -2.04640e85 q^{55} +3.93797e86 q^{56} +1.36330e87 q^{57} -1.81245e87 q^{58} -1.47079e87 q^{59} -6.08819e86 q^{60} +2.22361e88 q^{61} +4.45021e88 q^{62} +9.59858e88 q^{63} +2.67681e89 q^{64} +8.78357e88 q^{65} +1.50296e90 q^{66} +4.24589e90 q^{67} -1.43199e89 q^{68} +7.78381e90 q^{69} -2.17864e90 q^{70} +4.39297e91 q^{71} +7.34437e91 q^{72} +1.41929e92 q^{73} +3.42591e91 q^{74} -8.59530e92 q^{75} -5.68097e92 q^{76} -3.07068e93 q^{77} -6.45099e93 q^{78} +1.10262e94 q^{79} -9.68938e92 q^{80} -3.45964e94 q^{81} -6.66819e94 q^{82} +8.17771e94 q^{83} -9.13549e94 q^{84} +2.97207e93 q^{85} +6.77920e95 q^{86} +1.57736e96 q^{87} -2.34954e96 q^{88} +5.46832e96 q^{89} -4.06320e95 q^{90} +1.31800e97 q^{91} -3.24358e96 q^{92} -3.87297e97 q^{93} -4.26333e97 q^{94} +1.17907e97 q^{95} -1.21168e98 q^{96} +1.47493e98 q^{97} -3.34089e97 q^{98} -5.72687e98 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 208040616902520 q^{2} - 28\!\cdots\!20 q^{3}+ \cdots + 15\!\cdots\!76 q^{9}+O(q^{10}) \) 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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