LMFDB - Embedded newform 1.100.a.a.1.2

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			1.2
Root			$-1.08597e13$ 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)

$f(q)$	$=$	$q-8.07907e14 q^{2} -6.25114e23 q^{3} +1.88877e28 q^{4} -5.34820e34 q^{5} +5.05034e38 q^{6} +1.04094e42 q^{7} +4.96812e44 q^{8} +2.18975e47 q^{9} +O(q^{10})$	\(q-8.07907e14 q^{2} -6.25114e23 q^{3} +1.88877e28 q^{4} -5.34820e34 q^{5} +5.05034e38 q^{6} +1.04094e42 q^{7} +4.96812e44 q^{8} +2.18975e47 q^{9} +4.32085e49 q^{10} +2.09751e51 q^{11} -1.18070e52 q^{12} -2.27740e55 q^{13} -8.40981e56 q^{14} +3.34324e58 q^{15} -4.13349e59 q^{16} +7.56916e60 q^{17} -1.76912e62 q^{18} +5.81301e62 q^{19} -1.01016e63 q^{20} -6.50706e65 q^{21} -1.69459e66 q^{22} -2.12928e67 q^{23} -3.10564e68 q^{24} +1.28261e69 q^{25} +1.83993e70 q^{26} -2.94946e70 q^{27} +1.96610e70 q^{28} -1.52350e72 q^{29} -2.70102e73 q^{30} +2.72377e73 q^{31} +1.90555e73 q^{32} -1.31118e75 q^{33} -6.11517e75 q^{34} -5.56715e76 q^{35} +4.13595e75 q^{36} +4.28140e77 q^{37} -4.69637e77 q^{38} +1.42363e79 q^{39} -2.65705e79 q^{40} -5.02606e79 q^{41} +5.25709e80 q^{42} -1.05419e81 q^{43} +3.96172e79 q^{44} -1.17112e82 q^{45} +1.72026e82 q^{46} -3.56207e82 q^{47} +2.58391e83 q^{48} +6.21485e83 q^{49} -1.03623e84 q^{50} -4.73159e84 q^{51} -4.30149e83 q^{52} +1.04502e85 q^{53} +2.38289e85 q^{54} -1.12179e86 q^{55} +5.17151e86 q^{56} -3.63379e86 q^{57} +1.23085e87 q^{58} +3.60957e87 q^{59} +6.31462e86 q^{60} -9.18510e87 q^{61} -2.20055e88 q^{62} +2.27940e89 q^{63} +2.46596e89 q^{64} +1.21800e90 q^{65} +1.05931e90 q^{66} -1.79075e90 q^{67} +1.42964e89 q^{68} +1.33104e91 q^{69} +4.49774e91 q^{70} -3.40784e91 q^{71} +1.08790e92 q^{72} +1.68443e92 q^{73} -3.45898e92 q^{74} -8.01775e92 q^{75} +1.09795e91 q^{76} +2.18338e93 q^{77} -1.15016e94 q^{78} -1.45180e94 q^{79} +2.21068e94 q^{80} -1.91808e94 q^{81} +4.06058e94 q^{82} -9.55043e94 q^{83} -1.22904e94 q^{84} -4.04814e95 q^{85} +8.51687e95 q^{86} +9.52362e95 q^{87} +1.04207e96 q^{88} +4.74685e96 q^{89} +9.46159e96 q^{90} -2.37063e97 q^{91} -4.02173e95 q^{92} -1.70267e97 q^{93} +2.87782e97 q^{94} -3.10891e97 q^{95} -1.19119e97 q^{96} -1.76496e98 q^{97} -5.02102e98 q^{98} +4.59303e98 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−8.07907e14	−1.01479	−0.507395	−	0.861713i	$-0.669392\pi$
$2$	−8.07907e14	−1.01479	−0.507395	+	0.861713i	$0.669392\pi$
$3$	−6.25114e23	−1.50819	−0.754097	−	0.656763i	$-0.771925\pi$
$3$	−6.25114e23	−1.50819	−0.754097	+	0.656763i	$0.771925\pi$
$4$	1.88877e28	0.0297996
$5$	−5.34820e34	−1.34646	−0.673229	−	0.739434i	$-0.735093\pi$
$5$	−5.34820e34	−1.34646	−0.673229	+	0.739434i	$0.735093\pi$
$6$	5.05034e38	1.53050
$7$	1.04094e42	1.53134	0.765671	−	0.643232i	$-0.222407\pi$
$7$	1.04094e42	1.53134	0.765671	+	0.643232i	$0.222407\pi$
$8$	4.96812e44	0.984550
$9$	2.18975e47	1.27465
$10$	4.32085e49	1.36637
$11$	2.09751e51	0.592606	0.296303	−	0.955094i	$-0.404246\pi$
$11$	2.09751e51	0.592606	0.296303	+	0.955094i	$0.404246\pi$
$12$	−1.18070e52	−0.0449436
$13$	−2.27740e55	−1.64909	−0.824543	−	0.565799i	$-0.808568\pi$
$13$	−2.27740e55	−1.64909	−0.824543	+	0.565799i	$0.808568\pi$
$14$	−8.40981e56	−1.55399
$15$	3.34324e58	2.03072
$16$	−4.13349e59	−1.02891
$17$	7.56916e60	0.937187	0.468593	−	0.883414i	$-0.344761\pi$
$17$	7.56916e60	0.937187	0.468593	+	0.883414i	$0.344761\pi$
$18$	−1.76912e62	−1.29350
$19$	5.81301e62	0.292481	0.146240	−	0.989249i	$-0.453283\pi$
$19$	5.81301e62	0.292481	0.146240	+	0.989249i	$0.453283\pi$
$20$	−1.01016e63	−0.0401239
$21$	−6.50706e65	−2.30956
$22$	−1.69459e66	−0.601371
$23$	−2.12928e67	−0.836961	−0.418481	−	0.908226i	$-0.637437\pi$
$23$	−2.12928e67	−0.836961	−0.418481	+	0.908226i	$0.637437\pi$
$24$	−3.10564e68	−1.48489
$25$	1.28261e69	0.812948
$26$	1.83993e70	1.67348
$27$	−2.94946e70	−0.414225
$28$	1.96610e70	0.0456334
$29$	−1.52350e72	−0.622504	−0.311252	−	0.950327i	$-0.600748\pi$
$29$	−1.52350e72	−0.622504	−0.311252	+	0.950327i	$0.600748\pi$
$30$	−2.70102e73	−2.06075
$31$	2.72377e73	0.409984	0.204992	−	0.978764i	$-0.434283\pi$
$31$	2.72377e73	0.409984	0.204992	+	0.978764i	$0.434283\pi$
$32$	1.90555e73	0.0595796
$33$	−1.31118e75	−0.893765
$34$	−6.11517e75	−0.951048
$35$	−5.56715e76	−2.06189
$36$	4.13595e75	0.0379841
$37$	4.28140e77	1.01298	0.506490	−	0.862246i	$-0.330943\pi$
$37$	4.28140e77	1.01298	0.506490	+	0.862246i	$0.330943\pi$
$38$	−4.69637e77	−0.296807
$39$	1.42363e79	2.48714
$40$	−2.65705e79	−1.32566
$41$	−5.02606e79	−0.738629	−0.369315	−	0.929304i	$-0.620407\pi$
$41$	−5.02606e79	−0.738629	−0.369315	+	0.929304i	$0.620407\pi$
$42$	5.25709e80	2.34372
$43$	−1.05419e81	−1.46633	−0.733163	−	0.680053i	$-0.761957\pi$
$43$	−1.05419e81	−1.46633	−0.733163	+	0.680053i	$0.761957\pi$
$44$	3.96172e79	0.0176594
$45$	−1.17112e82	−1.71626
$46$	1.72026e82	0.849340
$47$	−3.56207e82	−0.606539	−0.303269	−	0.952905i	$-0.598078\pi$
$47$	−3.56207e82	−0.606539	−0.303269	+	0.952905i	$0.598078\pi$
$48$	2.58391e83	1.55180
$49$	6.21485e83	1.34501
$50$	−1.03623e84	−0.824972
$51$	−4.73159e84	−1.41346
$52$	−4.30149e83	−0.0491421
$53$	1.04502e85	0.465019	0.232510	−	0.972594i	$-0.425306\pi$
$53$	1.04502e85	0.465019	0.232510	+	0.972594i	$0.425306\pi$
$54$	2.38289e85	0.420351
$55$	−1.12179e86	−0.797919
$56$	5.17151e86	1.50768
$57$	−3.63379e86	−0.441118
$58$	1.23085e87	0.631711
$59$	3.60957e87	0.794841	0.397421	−	0.917637i	$-0.369905\pi$
$59$	3.60957e87	0.794841	0.397421	+	0.917637i	$0.369905\pi$
$60$	6.31462e86	0.0605146
$61$	−9.18510e87	−0.388380	−0.194190	−	0.980964i	$-0.562208\pi$
$61$	−9.18510e87	−0.388380	−0.194190	+	0.980964i	$0.562208\pi$
$62$	−2.20055e88	−0.416048
$63$	2.27940e89	1.95192
$64$	2.46596e89	0.968451
$65$	1.21800e90	2.22042
$66$	1.05931e90	0.906984
$67$	−1.79075e90	−0.728336	−0.364168	−	0.931333i	$-0.618647\pi$
$67$	−1.79075e90	−0.728336	−0.364168	+	0.931333i	$0.618647\pi$
$68$	1.42964e89	0.0279278
$69$	1.33104e91	1.26230
$70$	4.49774e91	2.09238
$71$	−3.40784e91	−0.785581	−0.392791	−	0.919628i	$-0.628490\pi$
$71$	−3.40784e91	−0.785581	−0.392791	+	0.919628i	$0.628490\pi$
$72$	1.08790e92	1.25496
$73$	1.68443e92	0.981681	0.490841	−	0.871249i	$-0.336690\pi$
$73$	1.68443e92	0.981681	0.490841	+	0.871249i	$0.336690\pi$
$74$	−3.45898e92	−1.02796
$75$	−8.01775e92	−1.22608
$76$	1.09795e91	0.00871582
$77$	2.18338e93	0.907483
$78$	−1.15016e94	−2.52393
$79$	−1.45180e94	−1.69576	−0.847880	−	0.530188i	$-0.822121\pi$
$79$	−1.45180e94	−1.69576	−0.847880	+	0.530188i	$0.822121\pi$
$80$	2.21068e94	1.38539
$81$	−1.91808e94	−0.649918
$82$	4.06058e94	0.749554
$83$	−9.55043e94	−0.967515	−0.483757	−	0.875202i	$-0.660728\pi$
$83$	−9.55043e94	−0.967515	−0.483757	+	0.875202i	$0.660728\pi$
$84$	−1.22904e94	−0.0688240
$85$	−4.04814e95	−1.26188
$86$	8.51687e95	1.48801
$87$	9.52362e95	0.938856
$88$	1.04207e96	0.583451
$89$	4.74685e96	1.51915	0.759575	−	0.650420i	$-0.225407\pi$
$89$	4.74685e96	1.51915	0.759575	+	0.650420i	$0.225407\pi$
$90$	9.46159e96	1.74165
$91$	−2.37063e97	−2.52531
$92$	−4.02173e95	−0.0249411
$93$	−1.70267e97	−0.618335
$94$	2.87782e97	0.615510
$95$	−3.10891e97	−0.393813
$96$	−1.19119e97	−0.0898575
$97$	−1.76496e98	−0.797138	−0.398569	−	0.917138i	$-0.630493\pi$
$97$	−1.76496e98	−0.797138	−0.398569	+	0.917138i	$0.630493\pi$
$98$	−5.02102e98	−1.36490
$99$	4.59303e98	0.755365
$100$	2.42255e97	0.0242255
$101$	−1.80045e99	−1.10020	−0.550100	−	0.835099i	$-0.685411\pi$
$101$	−1.80045e99	−1.10020	−0.550100	+	0.835099i	$0.685411\pi$
$102$	3.82268e99	1.43436
$103$	2.19638e99	0.508470	0.254235	−	0.967143i	$-0.418176\pi$
$103$	2.19638e99	0.508470	0.254235	+	0.967143i	$0.418176\pi$
$104$	−1.13144e100	−1.62361
$105$	3.48011e100	3.10973
$106$	−8.44282e99	−0.471897
$107$	3.98740e100	1.40021	0.700105	−	0.714040i	$-0.253136\pi$
$107$	3.98740e100	1.40021	0.700105	+	0.714040i	$0.253136\pi$
$108$	−5.57086e98	−0.0123437
$109$	−1.23890e101	−1.73950	−0.869752	−	0.493490i	$-0.835721\pi$
$109$	−1.23890e101	−1.73950	−0.869752	+	0.493490i	$0.835721\pi$
$110$	9.06303e100	0.809721
$111$	−2.67637e101	−1.52777
$112$	−4.30271e101	−1.57562
$113$	2.58068e101	0.608626	0.304313	−	0.952572i	$-0.401573\pi$
$113$	2.58068e101	0.608626	0.304313	+	0.952572i	$0.401573\pi$
$114$	2.93576e101	0.447642
$115$	1.13878e102	1.12693
$116$	−2.87755e100	−0.0185504
$117$	−4.98694e102	−2.10201
$118$	−2.91619e102	−0.806597
$119$	7.87903e102	1.43515
$120$	1.66096e103	1.99935
$121$	−8.12828e102	−0.648818
$122$	7.42070e102	0.394124
$123$	3.14186e103	1.11400
$124$	5.14459e101	0.0122174
$125$	1.57834e103	0.251857
$126$	−1.84154e104	−1.98079
$127$	−5.80100e103	−0.421909	−0.210955	−	0.977496i	$-0.567657\pi$
$127$	−5.80100e103	−0.421909	−0.210955	+	0.977496i	$0.567657\pi$
$128$	−2.11305e104	−1.04235
$129$	6.58989e104	2.21150
$130$	−9.84030e104	−2.25327
$131$	−4.72094e103	−0.0739775	−0.0369888	−	0.999316i	$-0.511777\pi$
$131$	−4.72094e103	−0.0739775	−0.0369888	+	0.999316i	$0.511777\pi$
$132$	−2.47653e103	−0.0266339
$133$	6.05098e104	0.447888
$134$	1.44676e105	0.739108
$135$	1.57743e105	0.557736
$136$	3.76045e105	0.922707
$137$	8.22650e104	0.140458	0.0702291	−	0.997531i	$-0.477627\pi$
$137$	8.22650e104	0.140458	0.0702291	+	0.997531i	$0.477627\pi$
$138$	−1.07536e106	−1.28097
$139$	2.00751e105	0.167273	0.0836363	−	0.996496i	$-0.473347\pi$
$139$	2.00751e105	0.167273	0.0836363	+	0.996496i	$0.473347\pi$
$140$	−1.05151e105	−0.0614434
$141$	2.22670e106	0.914778
$142$	2.75322e106	0.797200
$143$	−4.77687e106	−0.977259
$144$	−9.05133e106	−1.31150
$145$	8.14799e106	0.838175
$146$	−1.36086e107	−0.996201
$147$	−3.88499e107	−2.02853
$148$	8.08661e105	0.0301864
$149$	4.62813e107	1.23790	0.618949	−	0.785431i	$-0.287559\pi$
$149$	4.62813e107	1.23790	0.618949	+	0.785431i	$0.287559\pi$
$150$	6.47760e107	1.24422
$151$	4.88809e107	0.675741	0.337871	−	0.941193i	$-0.390293\pi$
$151$	4.88809e107	0.675741	0.337871	+	0.941193i	$0.390293\pi$
$152$	2.88797e107	0.287962
$153$	1.65746e108	1.19458
$154$	−1.76397e108	−0.920905
$155$	−1.45673e108	−0.552026
$156$	2.68893e107	0.0741159
$157$	−6.14624e108	−1.23474	−0.617372	−	0.786671i	$-0.711803\pi$
$157$	−6.14624e108	−1.23474	−0.617372	+	0.786671i	$0.711803\pi$
$158$	1.17291e109	1.72084
$159$	−6.53259e108	−0.701339
$160$	−1.01913e108	−0.0802214
$161$	−2.21645e109	−1.28167
$162$	1.54963e109	0.659531
$163$	−4.38649e109	−1.37667	−0.688337	−	0.725391i	$-0.741659\pi$
$163$	−4.38649e109	−1.37667	−0.688337	+	0.725391i	$0.741659\pi$
$164$	−9.49309e107	−0.0220109
$165$	7.01248e109	1.20342
$166$	7.71586e109	0.981825
$167$	−3.84603e108	−0.0363536	−0.0181768	−	0.999835i	$-0.505786\pi$
$167$	−3.84603e108	−0.0363536	−0.0181768	+	0.999835i	$0.505786\pi$
$168$	−3.23278e110	−2.27388
$169$	3.27937e110	1.71948
$170$	3.27052e110	1.28055
$171$	1.27290e110	0.372811
$172$	−1.99113e109	−0.0436959
$173$	−2.45949e110	−0.405101	−0.202550	−	0.979272i	$-0.564923\pi$
$173$	−2.45949e110	−0.405101	−0.202550	+	0.979272i	$0.564923\pi$
$174$	−7.69420e110	−0.952742
$175$	1.33511e111	1.24490
$176$	−8.67005e110	−0.609739
$177$	−2.25639e111	−1.19877
$178$	−3.83501e111	−1.54162
$179$	−1.92441e111	−0.586235	−0.293118	−	0.956076i	$-0.594693\pi$
$179$	−1.92441e111	−0.586235	−0.293118	+	0.956076i	$0.594693\pi$
$180$	−2.21199e110	−0.0511439
$181$	6.58943e111	1.15813	0.579066	−	0.815280i	$-0.303417\pi$
$181$	6.58943e111	1.15813	0.579066	+	0.815280i	$0.303417\pi$
$182$	1.91525e112	2.56267
$183$	5.74174e111	0.585753
$184$	−1.05785e112	−0.824030
$185$	−2.28978e112	−1.36393
$186$	1.37560e112	0.627480
$187$	1.58764e112	0.555383
$188$	−6.72795e110	−0.0180746
$189$	−3.07021e112	−0.634320
$190$	2.51171e112	0.399638
$191$	8.08456e112	0.991984	0.495992	−	0.868327i	$-0.334805\pi$
$191$	8.08456e112	0.991984	0.495992	+	0.868327i	$0.334805\pi$
$192$	−1.54151e113	−1.46061
$193$	7.36960e112	0.539954	0.269977	−	0.962867i	$-0.412984\pi$
$193$	7.36960e112	0.539954	0.269977	+	0.962867i	$0.412984\pi$
$194$	1.42592e113	0.808928
$195$	−7.61389e113	−3.34883
$196$	1.17385e112	0.0400807
$197$	4.97328e113	1.31997	0.659986	−	0.751278i	$-0.270562\pi$
$197$	4.97328e113	1.31997	0.659986	+	0.751278i	$0.270562\pi$
$198$	−3.71074e113	−0.766537
$199$	−2.78506e112	−0.0448340	−0.0224170	−	0.999749i	$-0.507136\pi$
$199$	−2.78506e112	−0.0448340	−0.0224170	+	0.999749i	$0.507136\pi$
$200$	6.37214e113	0.800388
$201$	1.11942e114	1.09847
$202$	1.45459e114	1.11647
$203$	−1.58587e114	−0.953266
$204$	−8.93691e112	−0.0421205
$205$	2.68804e114	0.994533
$206$	−1.77447e114	−0.515990
$207$	−4.66260e114	−1.06683
$208$	9.41362e114	1.69676
$209$	1.21928e114	0.173326
$210$	−2.81160e115	−3.15572
$211$	−5.80811e114	−0.515292	−0.257646	−	0.966239i	$-0.582947\pi$
$211$	−5.80811e114	−0.515292	−0.257646	+	0.966239i	$0.582947\pi$
$212$	1.97381e113	0.0138574
$213$	2.13029e115	1.18481
$214$	−3.22145e115	−1.42092
$215$	5.63802e115	1.97435
$216$	−1.46533e115	−0.407825
$217$	2.83528e115	0.627825
$218$	1.00092e116	1.76523
$219$	−1.05296e116	−1.48057
$220$	−2.11881e114	−0.0237777
$221$	−1.72380e116	−1.54550
$222$	2.16225e116	1.55037
$223$	2.54735e115	0.146217	0.0731085	−	0.997324i	$-0.476708\pi$
$223$	2.54735e115	0.146217	0.0731085	+	0.997324i	$0.476708\pi$
$224$	1.98357e115	0.0912367
$225$	2.80859e116	1.03622
$226$	−2.08495e116	−0.617628
$227$	−4.14427e116	−0.986661	−0.493330	−	0.869842i	$-0.664221\pi$
$227$	−4.14427e116	−0.986661	−0.493330	+	0.869842i	$0.664221\pi$
$228$	−6.86341e114	−0.0131451
$229$	3.44964e116	0.532007	0.266004	−	0.963972i	$-0.414297\pi$
$229$	3.44964e116	0.532007	0.266004	+	0.963972i	$0.414297\pi$
$230$	−9.20031e116	−1.14360
$231$	−1.36486e117	−1.36866
$232$	−7.56894e116	−0.612886
$233$	−4.72400e116	−0.309166	−0.154583	−	0.987980i	$-0.549403\pi$
$233$	−4.72400e116	−0.309166	−0.154583	+	0.987980i	$0.549403\pi$
$234$	4.02898e117	2.13310
$235$	1.90507e117	0.816679
$236$	6.81766e115	0.0236860
$237$	9.07538e117	2.55753
$238$	−6.36552e117	−1.45638
$239$	4.44466e117	0.826309	0.413155	−	0.910661i	$-0.364427\pi$
$239$	4.44466e117	0.826309	0.413155	+	0.910661i	$0.364427\pi$
$240$	−1.38193e118	−2.08943
$241$	−3.63833e117	−0.447774	−0.223887	−	0.974615i	$-0.571875\pi$
$241$	−3.63833e117	−0.447774	−0.223887	+	0.974615i	$0.571875\pi$
$242$	6.56689e117	0.658414
$243$	1.70572e118	1.39443
$244$	−1.73486e116	−0.0115736
$245$	−3.32383e118	−1.81100
$246$	−2.53833e118	−1.13047
$247$	−1.32385e118	−0.482326
$248$	1.35320e118	0.403649
$249$	5.97011e118	1.45920
$250$	−1.27515e118	−0.255582
$251$	−1.95394e118	−0.321412	−0.160706	−	0.987002i	$-0.551377\pi$
$251$	−1.95394e118	−0.321412	−0.160706	+	0.987002i	$0.551377\pi$
$252$	4.30527e117	0.0581666
$253$	−4.46619e118	−0.495989
$254$	4.68667e118	0.428149
$255$	2.53055e119	1.90316
$256$	1.44154e118	0.0893202
$257$	−2.37517e117	−0.0121341	−0.00606703	−	0.999982i	$-0.501931\pi$
$257$	−2.37517e117	−0.0121341	−0.00606703	+	0.999982i	$0.501931\pi$
$258$	−5.32402e119	−2.24421
$259$	4.45668e119	1.55122
$260$	2.30053e118	0.0661678
$261$	−3.33609e119	−0.793474
$262$	3.81408e118	0.0750717
$263$	1.10544e120	1.80187	0.900936	−	0.433953i	$-0.142882\pi$
$263$	1.10544e120	1.80187	0.900936	+	0.433953i	$0.142882\pi$
$264$	−6.51412e119	−0.879957
$265$	−5.58900e119	−0.626129
$266$	−4.88863e119	−0.454513
$267$	−2.96733e120	−2.29117
$268$	−3.38232e118	−0.0217041
$269$	2.00803e120	1.07160	0.535799	−	0.844346i	$-0.320010\pi$
$269$	2.00803e120	1.07160	0.535799	+	0.844346i	$0.320010\pi$
$270$	−1.27442e120	−0.565985
$271$	2.80889e120	1.03885	0.519427	−	0.854515i	$-0.326145\pi$
$271$	2.80889e120	1.03885	0.519427	+	0.854515i	$0.326145\pi$
$272$	−3.12871e120	−0.964282
$273$	1.48192e121	3.80867
$274$	−6.64624e119	−0.142536
$275$	2.69028e120	0.481758
$276$	2.51404e119	0.0376160
$277$	−1.50203e121	−1.87902	−0.939508	−	0.342527i	$-0.888717\pi$
$277$	−1.50203e121	−1.87902	−0.939508	+	0.342527i	$0.888717\pi$
$278$	−1.62188e120	−0.169747
$279$	5.96438e120	0.522585
$280$	−2.76583e121	−2.03003
$281$	2.99881e121	1.84495	0.922477	−	0.386051i	$-0.126161\pi$
$281$	2.99881e121	1.84495	0.922477	+	0.386051i	$0.126161\pi$
$282$	−1.79897e121	−0.928308
$283$	−1.70172e121	−0.736989	−0.368494	−	0.929630i	$-0.620127\pi$
$283$	−1.70172e121	−0.736989	−0.368494	+	0.929630i	$0.620127\pi$
$284$	−6.43664e119	−0.0234100
$285$	1.94343e121	0.593947
$286$	3.85926e121	0.991713
$287$	−5.23182e121	−1.13109
$288$	4.17269e120	0.0759431
$289$	−7.93719e120	−0.121681
$290$	−6.58282e121	−0.850572
$291$	1.10330e122	1.20224
$292$	3.18150e120	0.0292537
$293$	−1.98159e121	−0.153839	−0.0769194	−	0.997037i	$-0.524508\pi$
$293$	−1.98159e121	−0.153839	−0.0769194	+	0.997037i	$0.524508\pi$
$294$	3.13871e122	2.05854
$295$	−1.93047e122	−1.07022
$296$	2.12705e122	0.997330
$297$	−6.18652e121	−0.245472
$298$	−3.73910e122	−1.25621
$299$	4.84923e122	1.38022
$300$	−1.51437e121	−0.0365368
$301$	−1.09735e123	−2.24545
$302$	−3.94912e122	−0.685736
$303$	1.12548e123	1.65932
$304$	−2.40280e122	−0.300937
$305$	4.91238e122	0.522937
$306$	−1.33907e123	−1.21225
$307$	−1.02449e123	−0.789146	−0.394573	−	0.918865i	$-0.629107\pi$
$307$	−1.02449e123	−0.789146	−0.394573	+	0.918865i	$0.629107\pi$
$308$	4.12391e121	0.0270426
$309$	−1.37299e123	−0.766871
$310$	1.17690e123	0.560190
$311$	3.00513e123	1.21962	0.609809	−	0.792549i	$-0.291246\pi$
$311$	3.00513e123	1.21962	0.609809	+	0.792549i	$0.291246\pi$
$312$	7.07279e123	2.44872
$313$	4.89961e122	0.144783	0.0723914	−	0.997376i	$-0.476937\pi$
$313$	4.89961e122	0.144783	0.0723914	+	0.997376i	$0.476937\pi$
$314$	4.96559e123	1.25301
$315$	−1.21907e124	−2.62818
$316$	−2.74211e122	−0.0505330
$317$	1.19280e123	0.187991	0.0939953	−	0.995573i	$-0.470036\pi$
$317$	1.19280e123	0.187991	0.0939953	+	0.995573i	$0.470036\pi$
$318$	5.27773e123	0.711712
$319$	−3.19556e123	−0.368900
$320$	−1.31885e124	−1.30398
$321$	−2.49258e124	−2.11179
$322$	1.79069e124	1.30063
$323$	4.39996e123	0.274109
$324$	−3.62282e122	−0.0193673
$325$	−2.92101e124	−1.34062
$326$	3.54388e124	1.39703
$327$	7.74455e124	2.62351
$328$	−2.49701e124	−0.727217
$329$	−3.70790e124	−0.928819
$330$	−5.66543e124	−1.22122
$331$	−3.31109e124	−0.614448	−0.307224	−	0.951637i	$-0.599400\pi$
$331$	−3.31109e124	−0.614448	−0.307224	+	0.951637i	$0.599400\pi$
$332$	−1.80386e123	−0.0288316
$333$	9.37522e124	1.29119
$334$	3.10723e123	0.0368912
$335$	9.57728e124	0.980673
$336$	2.68969e125	2.37633
$337$	−3.63832e124	−0.277473	−0.138736	−	0.990329i	$-0.544304\pi$
$337$	−3.63832e124	−0.277473	−0.138736	+	0.990329i	$0.544304\pi$
$338$	−2.64942e125	−1.74492
$339$	−1.61322e125	−0.917927
$340$	−7.64603e123	−0.0376036
$341$	5.71314e124	0.242959
$342$	−1.02839e125	−0.378325
$343$	1.65944e125	0.528326
$344$	−5.23734e125	−1.44367
$345$	−7.11870e125	−1.69963
$346$	1.98704e125	0.411092
$347$	6.52952e125	1.17104	0.585520	−	0.810658i	$-0.300890\pi$
$347$	6.52952e125	1.17104	0.585520	+	0.810658i	$0.300890\pi$
$348$	1.79880e124	0.0279776
$349$	1.16874e126	1.57710	0.788550	−	0.614971i	$-0.210832\pi$
$349$	1.16874e126	1.57710	0.788550	+	0.614971i	$0.210832\pi$
$350$	−1.07865e126	−1.26331
$351$	6.71710e125	0.683092
$352$	3.99692e124	0.0353072
$353$	−2.47958e125	−0.190340	−0.0951699	−	0.995461i	$-0.530339\pi$
$353$	−2.47958e125	−0.190340	−0.0951699	+	0.995461i	$0.530339\pi$
$354$	1.82295e126	1.21651
$355$	1.82258e126	1.05775
$356$	8.96574e124	0.0452701
$357$	−4.92529e126	−2.16449
$358$	1.55474e126	0.594906
$359$	5.55205e126	1.85045	0.925227	−	0.379415i	$-0.123875\pi$
$359$	5.55205e126	1.85045	0.925227	+	0.379415i	$0.123875\pi$
$360$	−5.81829e126	−1.68975
$361$	−3.61218e126	−0.914455
$362$	−5.32364e126	−1.17526
$363$	5.08110e126	0.978543
$364$	−4.47759e125	−0.0752534
$365$	−9.00866e126	−1.32179
$366$	−4.63879e126	−0.594416
$367$	1.35337e127	1.51511	0.757556	−	0.652770i	$-0.226393\pi$
$367$	1.35337e127	1.51511	0.757556	+	0.652770i	$0.226393\pi$
$368$	8.80137e126	0.861159
$369$	−1.10058e127	−0.941493
$370$	1.84993e127	1.38411
$371$	1.08781e127	0.712103
$372$	−3.21595e125	−0.0184261
$373$	−1.50969e127	−0.757359	−0.378680	−	0.925528i	$-0.623622\pi$
$373$	−1.50969e127	−0.757359	−0.378680	+	0.925528i	$0.623622\pi$
$374$	−1.28266e127	−0.563597
$375$	−9.86641e126	−0.379849
$376$	−1.76968e127	−0.597168
$377$	3.46962e127	1.02656
$378$	2.48044e127	0.643701
$379$	4.64800e127	1.05834	0.529170	−	0.848516i	$-0.322503\pi$
$379$	4.64800e127	1.05834	0.529170	+	0.848516i	$0.322503\pi$
$380$	−5.87204e125	−0.0117355
$381$	3.62629e127	0.636321
$382$	−6.53157e127	−1.00666
$383$	−1.07340e128	−1.45353	−0.726764	−	0.686887i	$-0.758977\pi$
$383$	−1.07340e128	−1.45353	−0.726764	+	0.686887i	$0.758977\pi$
$384$	1.32089e128	1.57207
$385$	−1.16772e128	−1.22189
$386$	−5.95395e127	−0.547941
$387$	−2.30842e128	−1.86905
$388$	−3.33361e126	−0.0237544
$389$	−2.23369e128	−1.40126	−0.700629	−	0.713525i	$-0.747097\pi$
$389$	−2.23369e128	−1.40126	−0.700629	+	0.713525i	$0.747097\pi$
$390$	6.15131e128	3.39836
$391$	−1.61169e128	−0.784389
$392$	3.08762e128	1.32423
$393$	2.95113e127	0.111572
$394$	−4.01795e128	−1.33949
$395$	7.76450e128	2.28327
$396$	8.67520e126	0.0225096
$397$	4.30347e128	0.985573	0.492787	−	0.870150i	$-0.335978\pi$
$397$	4.30347e128	0.985573	0.492787	+	0.870150i	$0.335978\pi$
$398$	2.25007e127	0.0454971
$399$	−3.78256e128	−0.675503
$400$	−5.30164e128	−0.836452
$401$	−8.89726e127	−0.124054	−0.0620269	−	0.998074i	$-0.519756\pi$
$401$	−8.89726e127	−0.124054	−0.0620269	+	0.998074i	$0.519756\pi$
$402$	−9.04388e128	−1.11472
$403$	−6.20311e128	−0.676098
$404$	−3.40064e127	−0.0327856
$405$	1.02583e129	0.875087
$406$	1.28124e129	0.967365
$407$	8.98029e128	0.600298
$408$	−2.35071e129	−1.39162
$409$	−1.55592e129	−0.815986	−0.407993	−	0.912985i	$-0.633771\pi$
$409$	−1.55592e129	−0.815986	−0.407993	+	0.912985i	$0.633771\pi$
$410$	−2.17168e129	−1.00924
$411$	−5.14250e128	−0.211838
$412$	4.14847e127	0.0151522
$413$	3.75734e129	1.21717
$414$	3.76695e129	1.08261
$415$	5.10777e129	1.30272
$416$	−4.33971e128	−0.0982518
$417$	−1.25492e129	−0.252279
$418$	−9.85068e128	−0.175890
$419$	−8.70069e129	−1.38026	−0.690128	−	0.723688i	$-0.742446\pi$
$419$	−8.70069e129	−1.38026	−0.690128	+	0.723688i	$0.742446\pi$
$420$	6.57314e128	0.0926686
$421$	7.29058e129	0.913689	0.456844	−	0.889547i	$-0.348980\pi$
$421$	7.29058e129	0.913689	0.456844	+	0.889547i	$0.348980\pi$
$422$	4.69241e129	0.522913
$423$	−7.80005e129	−0.773125
$424$	5.19181e129	0.457835
$425$	9.70825e129	0.761884
$426$	−1.72108e130	−1.20233
$427$	−9.56113e129	−0.594743
$428$	7.53131e128	0.0417257
$429$	2.98609e130	1.47390
$430$	−4.55500e130	−2.00355
$431$	−1.66220e130	−0.651715	−0.325858	−	0.945419i	$-0.605653\pi$
$431$	−1.66220e130	−0.651715	−0.325858	+	0.945419i	$0.605653\pi$
$432$	1.21916e130	0.426201
$433$	2.50831e130	0.782041	0.391021	−	0.920382i	$-0.372122\pi$
$433$	2.50831e130	0.782041	0.391021	+	0.920382i	$0.372122\pi$
$434$	−2.29064e130	−0.637111
$435$	−5.09343e130	−1.26413
$436$	−2.34001e129	−0.0518365
$437$	−1.23775e130	−0.244795
$438$	8.50693e130	1.50246
$439$	1.24041e131	1.95692	0.978459	−	0.206439i	$-0.0661876\pi$
$439$	1.24041e131	1.95692	0.978459	+	0.206439i	$0.0661876\pi$
$440$	−5.57320e130	−0.785592
$441$	1.36090e131	1.71441
$442$	1.39267e131	1.56836
$443$	−7.59379e130	−0.764670	−0.382335	−	0.924024i	$-0.624880\pi$
$443$	−7.59379e130	−0.764670	−0.382335	+	0.924024i	$0.624880\pi$
$444$	−5.05505e129	−0.0455270
$445$	−2.53871e131	−2.04547
$446$	−2.05802e130	−0.148380
$447$	−2.89311e131	−1.86699
$448$	2.56691e131	1.48303
$449$	−4.72636e130	−0.244530	−0.122265	−	0.992497i	$-0.539016\pi$
$449$	−4.72636e130	−0.244530	−0.122265	+	0.992497i	$0.539016\pi$
$450$	−2.26908e131	−1.05155
$451$	−1.05422e131	−0.437716
$452$	4.87432e129	0.0181368
$453$	−3.05561e131	−1.01915
$454$	3.34818e131	1.00125
$455$	1.26786e132	3.40023
$456$	−1.80531e131	−0.434303
$457$	−6.40318e131	−1.38211	−0.691057	−	0.722800i	$-0.742855\pi$
$457$	−6.40318e131	−1.38211	−0.691057	+	0.722800i	$0.742855\pi$
$458$	−2.78699e131	−0.539876
$459$	−2.23249e131	−0.388206
$460$	2.15091e130	0.0335822
$461$	3.82608e130	0.0536486	0.0268243	−	0.999640i	$-0.491461\pi$
$461$	3.82608e130	0.0536486	0.0268243	+	0.999640i	$0.491461\pi$
$462$	1.10268e132	1.38890
$463$	−7.47605e131	−0.846084	−0.423042	−	0.906110i	$-0.639038\pi$
$463$	−7.47605e131	−0.846084	−0.423042	+	0.906110i	$0.639038\pi$
$464$	6.29738e131	0.640501
$465$	9.10621e131	0.832562
$466$	3.81655e131	0.313739
$467$	−2.45570e131	−0.181548	−0.0907738	−	0.995872i	$-0.528934\pi$
$467$	−2.45570e131	−0.181548	−0.0907738	+	0.995872i	$0.528934\pi$
$468$	−9.41921e130	−0.0626390
$469$	−1.86406e132	−1.11533
$470$	−1.53912e132	−0.828758
$471$	3.84210e132	1.86223
$472$	1.79328e132	0.782561
$473$	−2.21118e132	−0.868954
$474$	−7.33206e132	−2.59536
$475$	7.45580e131	0.237772
$476$	1.48817e131	0.0427670
$477$	2.28834e132	0.592736
$478$	−3.59087e132	−0.838531
$479$	4.41628e132	0.929926	0.464963	−	0.885330i	$-0.346068\pi$
$479$	4.41628e132	0.929926	0.464963	+	0.885330i	$0.346068\pi$
$480$	6.37072e131	0.120989
$481$	−9.75047e132	−1.67049
$482$	2.93943e132	0.454397
$483$	1.38554e133	1.93301
$484$	−1.53525e131	−0.0193345
$485$	9.43935e132	1.07331
$486$	−1.37806e133	−1.41505
$487$	−4.96534e132	−0.460538	−0.230269	−	0.973127i	$-0.573961\pi$
$487$	−4.96534e132	−0.460538	−0.230269	+	0.973127i	$0.573961\pi$
$488$	−4.56327e132	−0.382380
$489$	2.74206e133	2.07629
$490$	2.68534e133	1.83778
$491$	−1.83058e133	−1.13254	−0.566272	−	0.824219i	$-0.691615\pi$
$491$	−1.83058e133	−1.13254	−0.566272	+	0.824219i	$0.691615\pi$
$492$	5.93426e131	0.0331966
$493$	−1.15316e133	−0.583402
$494$	1.06955e133	0.489460
$495$	−2.45645e133	−1.01707
$496$	−1.12587e133	−0.421837
$497$	−3.54735e133	−1.20299
$498$	−4.82329e133	−1.48078
$499$	−6.66198e132	−0.185194	−0.0925969	−	0.995704i	$-0.529517\pi$
$499$	−6.66198e132	−0.185194	−0.0925969	+	0.995704i	$0.529517\pi$
$500$	2.98112e131	0.00750524
$501$	2.40421e132	0.0548282
$502$	1.57860e133	0.326166
$503$	3.62557e133	0.678831	0.339415	−	0.940637i	$-0.389771\pi$
$503$	3.62557e133	0.678831	0.339415	+	0.940637i	$0.389771\pi$
$504$	1.13243e134	1.92177
$505$	9.62915e133	1.48137
$506$	3.60827e133	0.503324
$507$	−2.04998e134	−2.59332
$508$	−1.09568e132	−0.0125727
$509$	7.69318e133	0.800895	0.400448	−	0.916320i	$-0.368855\pi$
$509$	7.69318e133	0.800895	0.400448	+	0.916320i	$0.368855\pi$
$510$	−2.04445e134	−1.93131
$511$	1.75339e134	1.50329
$512$	1.22284e134	0.951713
$513$	−1.71452e133	−0.121153
$514$	1.91892e132	0.0123135
$515$	−1.17467e134	−0.684633
$516$	1.24468e133	0.0659019
$517$	−7.47148e133	−0.359439
$518$	−3.60058e134	−1.57416
$519$	1.53746e134	0.610971
$520$	6.05117e134	2.18612
$521$	5.97459e133	0.196264	0.0981320	−	0.995173i	$-0.468713\pi$
$521$	5.97459e133	0.196264	0.0981320	+	0.995173i	$0.468713\pi$
$522$	2.69525e134	0.805210
$523$	−6.42395e134	−1.74570	−0.872848	−	0.487992i	$-0.837729\pi$
$523$	−6.42395e134	−1.74570	−0.872848	+	0.487992i	$0.837729\pi$
$524$	−8.91680e131	−0.00220450
$525$	−8.34599e134	−1.87755
$526$	−8.93088e134	−1.82852
$527$	2.06167e134	0.384231
$528$	5.41977e134	0.919605
$529$	−1.93841e134	−0.299496
$530$	4.51539e134	0.635389
$531$	7.90405e134	1.01314
$532$	1.14289e133	0.0133469
$533$	1.14463e135	1.21806
$534$	2.39732e135	2.32506
$535$	−2.13254e135	−1.88532
$536$	−8.89665e134	−0.717083
$537$	1.20297e135	0.884157
$538$	−1.62230e135	−1.08745
$539$	1.30357e135	0.797061
$540$	2.97941e133	0.0166203
$541$	2.18254e135	1.11096	0.555478	−	0.831531i	$-0.312535\pi$
$541$	2.18254e135	1.11096	0.555478	+	0.831531i	$0.312535\pi$
$542$	−2.26932e135	−1.05422
$543$	−4.11915e135	−1.74669
$544$	1.44234e134	0.0558372
$545$	6.62590e135	2.34217
$546$	−1.19725e136	−3.86500
$547$	4.99112e135	1.47172	0.735861	−	0.677133i	$-0.236778\pi$
$547$	4.99112e135	1.47172	0.735861	+	0.677133i	$0.236778\pi$
$548$	1.55380e133	0.00418560
$549$	−2.01131e135	−0.495049
$550$	−2.17350e135	−0.488884
$551$	−8.85612e134	−0.182070
$552$	6.61279e135	1.24280
$553$	−1.51123e136	−2.59679
$554$	1.21350e136	1.90681
$555$	1.43138e136	2.05708
$556$	3.79173e133	0.00498466
$557$	−1.15307e136	−1.38683	−0.693413	−	0.720540i	$-0.743894\pi$
$557$	−1.15307e136	−1.38683	−0.693413	+	0.720540i	$0.743894\pi$
$558$	−4.81866e135	−0.530315
$559$	2.40081e136	2.41810
$560$	2.30118e136	2.12150
$561$	−9.92456e135	−0.837625
$562$	−2.42276e136	−1.87224
$563$	−2.52431e135	−0.178639	−0.0893195	−	0.996003i	$-0.528469\pi$
$563$	−2.52431e135	−0.178639	−0.0893195	+	0.996003i	$0.528469\pi$
$564$	4.20574e134	0.0272600
$565$	−1.38020e136	−0.819490
$566$	1.37483e136	0.747889
$567$	−1.99661e136	−0.995247
$568$	−1.69306e136	−0.773444
$569$	3.76548e136	1.57675	0.788376	−	0.615194i	$-0.210922\pi$
$569$	3.76548e136	1.57675	0.788376	+	0.615194i	$0.210922\pi$
$570$	−1.57011e136	−0.602731
$571$	1.10009e136	0.387204	0.193602	−	0.981080i	$-0.437983\pi$
$571$	1.10009e136	0.387204	0.193602	+	0.981080i	$0.437983\pi$
$572$	−9.02243e134	−0.0291219
$573$	−5.05377e136	−1.49610
$574$	4.22682e136	1.14782
$575$	−2.73103e136	−0.680406
$576$	5.39984e136	1.23444
$577$	6.82183e134	0.0143119	0.00715596	−	0.999974i	$-0.497722\pi$
$577$	6.82183e134	0.0143119	0.00715596	+	0.999974i	$0.497722\pi$
$578$	6.41251e135	0.123481
$579$	−4.60684e136	−0.814356
$580$	1.53897e135	0.0249773
$581$	−9.94142e136	−1.48160
$582$	−8.91363e136	−1.22002
$583$	2.19195e136	0.275573
$584$	8.36844e136	0.966515
$585$	2.66712e137	2.83026
$586$	1.60094e136	0.156114
$587$	1.36891e137	1.22684	0.613420	−	0.789757i	$-0.289793\pi$
$587$	1.36891e137	1.22684	0.613420	+	0.789757i	$0.289793\pi$
$588$	−7.33788e135	−0.0604495
$589$	1.58333e136	0.119912
$590$	1.55964e137	1.08605
$591$	−3.10887e137	−1.99077
$592$	−1.76972e137	−1.04227
$593$	4.29487e136	0.232671	0.116336	−	0.993210i	$-0.462885\pi$
$593$	4.29487e136	0.232671	0.116336	+	0.993210i	$0.462885\pi$
$594$	4.99813e136	0.249103
$595$	−4.21387e137	−1.93237
$596$	8.74149e135	0.0368889
$597$	1.74098e136	0.0676184
$598$	−3.91772e137	−1.40064
$599$	2.61243e137	0.859837	0.429918	−	0.902868i	$-0.358542\pi$
$599$	2.61243e137	0.859837	0.429918	+	0.902868i	$0.358542\pi$
$600$	−3.98332e137	−1.20714
$601$	1.68204e137	0.469406	0.234703	−	0.972067i	$-0.424588\pi$
$601$	1.68204e137	0.469406	0.234703	+	0.972067i	$0.424588\pi$
$602$	8.86554e137	2.27866
$603$	−3.92129e137	−0.928372
$604$	9.23250e135	0.0201368
$605$	4.34717e137	0.873606
$606$	−9.09286e137	−1.68386
$607$	8.63579e137	1.47388	0.736939	−	0.675959i	$-0.236270\pi$
$607$	8.63579e137	1.47388	0.736939	+	0.675959i	$0.236270\pi$
$608$	1.10770e136	0.0174259
$609$	9.91351e137	1.43771
$610$	−3.96874e137	−0.530672
$611$	8.11226e137	1.00023
$612$	3.13057e136	0.0355981
$613$	−1.66331e138	−1.74453	−0.872267	−	0.489030i	$-0.837351\pi$
$613$	−1.66331e138	−1.74453	−0.872267	+	0.489030i	$0.837351\pi$
$614$	8.27690e137	0.800818
$615$	−1.68033e138	−1.49995
$616$	1.08473e138	0.893462
$617$	3.11873e137	0.237062	0.118531	−	0.992950i	$-0.462181\pi$
$617$	3.11873e137	0.237062	0.118531	+	0.992950i	$0.462181\pi$
$618$	1.10925e138	0.778213
$619$	−1.59657e138	−1.03395	−0.516975	−	0.856001i	$-0.672942\pi$
$619$	−1.59657e138	−1.03395	−0.516975	+	0.856001i	$0.672942\pi$
$620$	−2.75143e136	−0.0164501
$621$	6.28023e137	0.346690
$622$	−2.42786e138	−1.23766
$623$	4.94118e138	2.32634
$624$	−5.88458e138	−2.55905
$625$	−2.86772e138	−1.15206
$626$	−3.95843e137	−0.146924
$627$	−7.62192e137	−0.261409
$628$	−1.16089e137	−0.0367949
$629$	3.24066e138	0.949351
$630$	9.84893e138	2.66706
$631$	6.03984e137	0.151207	0.0756036	−	0.997138i	$-0.475912\pi$
$631$	6.03984e137	0.151207	0.0756036	+	0.997138i	$0.475912\pi$
$632$	−7.21269e138	−1.66956
$633$	3.63073e138	0.777160
$634$	−9.63675e137	−0.190771
$635$	3.10249e138	0.568083
$636$	−1.23386e137	−0.0208996
$637$	−1.41537e139	−2.21803
$638$	2.58171e138	0.374356
$639$	−7.46233e138	−1.00134
$640$	1.13010e139	1.40349
$641$	1.01381e139	1.16543	0.582715	−	0.812677i	$-0.301990\pi$
$641$	1.01381e139	1.16543	0.582715	+	0.812677i	$0.301990\pi$
$642$	2.01377e139	2.14302
$643$	9.96851e138	0.982171	0.491086	−	0.871111i	$-0.336600\pi$
$643$	9.96851e138	0.982171	0.491086	+	0.871111i	$0.336600\pi$
$644$	−4.18638e137	−0.0381934
$645$	−3.52441e139	−2.97770
$646$	−3.55475e138	−0.278163
$647$	−6.19850e138	−0.449288	−0.224644	−	0.974441i	$-0.572122\pi$
$647$	−6.19850e138	−0.449288	−0.224644	+	0.974441i	$0.572122\pi$
$648$	−9.52926e138	−0.639877
$649$	7.57110e138	0.471028
$650$	2.35990e139	1.36045
$651$	−1.77237e139	−0.946882
$652$	−8.28509e137	−0.0410243
$653$	−2.82576e139	−1.29698	−0.648490	−	0.761224i	$-0.724599\pi$
$653$	−2.82576e139	−1.29698	−0.648490	+	0.761224i	$0.724599\pi$
$654$	−6.25687e139	−2.66231
$655$	2.52486e138	0.0996076
$656$	2.07752e139	0.759984
$657$	3.68848e139	1.25130
$658$	2.99564e139	0.942556
$659$	−7.20616e138	−0.210318	−0.105159	−	0.994455i	$-0.533535\pi$
$659$	−7.20616e138	−0.210318	−0.105159	+	0.994455i	$0.533535\pi$
$660$	1.32450e138	0.0358614
$661$	6.32637e139	1.58921	0.794607	−	0.607124i	$-0.207677\pi$
$661$	6.32637e139	1.58921	0.794607	+	0.607124i	$0.207677\pi$
$662$	2.67505e139	0.623536
$663$	1.07757e140	2.33092
$664$	−4.74477e139	−0.952567
$665$	−3.23619e139	−0.603063
$666$	−7.57430e139	−1.31029
$667$	3.24396e139	0.521011
$668$	−7.26428e136	−0.00108332
$669$	−1.59238e139	−0.220524
$670$	−7.73755e139	−0.995178
$671$	−1.92658e139	−0.230157
$672$	−1.23995e139	−0.137603
$673$	−6.18271e139	−0.637431	−0.318715	−	0.947850i	$-0.603251\pi$
$673$	−6.18271e139	−0.637431	−0.318715	+	0.947850i	$0.603251\pi$
$674$	2.93942e139	0.281577
$675$	−3.78299e139	−0.336743
$676$	6.19399e138	0.0512400
$677$	1.42063e140	1.09230	0.546149	−	0.837688i	$-0.316093\pi$
$677$	1.42063e140	1.09230	0.546149	+	0.837688i	$0.316093\pi$
$678$	1.30333e140	0.931503
$679$	−1.83721e140	−1.22069
$680$	−2.01117e140	−1.24239
$681$	2.59064e140	1.48808
$682$	−4.61568e139	−0.246552
$683$	−8.50662e139	−0.422603	−0.211301	−	0.977421i	$-0.567770\pi$
$683$	−8.50662e139	−0.422603	−0.211301	+	0.977421i	$0.567770\pi$
$684$	2.40423e138	0.0111096
$685$	−4.39970e139	−0.189121
$686$	−1.34067e140	−0.536140
$687$	−2.15642e140	−0.802370
$688$	4.35749e140	1.50872
$689$	−2.37994e140	−0.766856
$690$	5.75124e140	1.72477
$691$	3.02651e140	0.844849	0.422424	−	0.906398i	$-0.361179\pi$
$691$	3.02651e140	0.844849	0.422424	+	0.906398i	$0.361179\pi$
$692$	−4.64542e138	−0.0120718
$693$	4.78106e140	1.15672
$694$	−5.27524e140	−1.18836
$695$	−1.07366e140	−0.225225
$696$	4.73145e140	0.924351
$697$	−3.80430e140	−0.692233
$698$	−9.44233e140	−1.60043
$699$	2.95304e140	0.466283
$700$	2.52173e139	0.0370976
$701$	5.69693e140	0.780907	0.390453	−	0.920623i	$-0.372318\pi$
$701$	5.69693e140	0.780907	0.390453	+	0.920623i	$0.372318\pi$
$702$	−5.42679e140	−0.693195
$703$	2.48878e140	0.296277
$704$	5.17238e140	0.573910
$705$	−1.19089e141	−1.23171
$706$	2.00327e140	0.193155
$707$	−1.87415e141	−1.68478
$708$	−4.26181e139	−0.0357230
$709$	2.01503e141	1.57504	0.787521	−	0.616288i	$-0.211364\pi$
$709$	2.01503e141	1.57504	0.787521	+	0.616288i	$0.211364\pi$
$710$	−1.47248e141	−1.07340
$711$	−3.17907e141	−2.16150
$712$	2.35829e141	1.49568
$713$	−5.79968e140	−0.343140
$714$	3.97918e141	2.19650
$715$	2.55477e141	1.31584
$716$	−3.63477e139	−0.0174696
$717$	−2.77842e141	−1.24623
$718$	−4.48554e141	−1.87782
$719$	1.94708e141	0.760858	0.380429	−	0.924810i	$-0.375776\pi$
$719$	1.94708e141	0.760858	0.380429	+	0.924810i	$0.375776\pi$
$720$	4.84083e141	1.76588
$721$	2.28630e141	0.778641
$722$	2.91830e141	0.927980
$723$	2.27437e141	0.675330
$724$	1.24459e140	0.0345119
$725$	−1.95405e141	−0.506063
$726$	−4.10506e141	−0.993016
$727$	3.56143e141	0.804768	0.402384	−	0.915471i	$-0.368182\pi$
$727$	3.56143e141	0.804768	0.402384	+	0.915471i	$0.368182\pi$
$728$	−1.17776e142	−2.48630
$729$	−7.36755e141	−1.45315
$730$	7.27815e141	1.34134
$731$	−7.97933e141	−1.37422
$732$	1.08448e140	0.0174552
$733$	−4.84702e141	−0.729168	−0.364584	−	0.931170i	$-0.618789\pi$
$733$	−4.84702e141	−0.729168	−0.364584	+	0.931170i	$0.618789\pi$
$734$	−1.09339e142	−1.53752
$735$	2.07777e142	2.73134
$736$	−4.05746e140	−0.0498658
$737$	−3.75611e141	−0.431616
$738$	8.89167e141	0.955418
$739$	1.59774e142	1.60548	0.802741	−	0.596327i	$-0.203374\pi$
$739$	1.59774e142	1.60548	0.802741	+	0.596327i	$0.203374\pi$
$740$	−4.32488e140	−0.0406447
$741$	8.27560e141	0.727442
$742$	−8.78846e141	−0.722636
$743$	1.52776e141	0.117519	0.0587596	−	0.998272i	$-0.481285\pi$
$743$	1.52776e141	0.117519	0.0587596	+	0.998272i	$0.481285\pi$
$744$	−8.45906e141	−0.608782
$745$	−2.47522e142	−1.66678
$746$	1.21969e142	0.768561
$747$	−2.09131e142	−1.23324
$748$	2.99869e140	0.0165502
$749$	4.15064e142	2.14420
$750$	7.97114e141	0.385468
$751$	4.42922e141	0.200516	0.100258	−	0.994961i	$-0.468033\pi$
$751$	4.42922e141	0.200516	0.100258	+	0.994961i	$0.468033\pi$
$752$	1.47238e142	0.624075
$753$	1.22144e142	0.484752
$754$	−2.80313e142	−1.04175
$755$	−2.61425e142	−0.909857
$756$	−5.79893e140	−0.0189025
$757$	2.38490e142	0.728154	0.364077	−	0.931369i	$-0.381384\pi$
$757$	2.38490e142	0.728154	0.364077	+	0.931369i	$0.381384\pi$
$758$	−3.75515e142	−1.07399
$759$	2.79188e142	0.748047
$760$	−1.54455e142	−0.387729
$761$	8.03086e142	1.88896	0.944478	−	0.328575i	$-0.106569\pi$
$761$	8.03086e142	1.88896	0.944478	+	0.328575i	$0.106569\pi$
$762$	−2.92970e142	−0.645732
$763$	−1.28962e143	−2.66377
$764$	1.52699e141	0.0295607
$765$	−8.86443e142	−1.60846
$766$	8.67209e142	1.47503
$767$	−8.22042e142	−1.31076
$768$	−9.01130e141	−0.134712
$769$	2.40818e142	0.337548	0.168774	−	0.985655i	$-0.446019\pi$
$769$	2.40818e142	0.337548	0.168774	+	0.985655i	$0.446019\pi$
$770$	9.43406e142	1.23996
$771$	1.48476e141	0.0183005
$772$	1.39195e141	0.0160904
$773$	1.54781e143	1.67816	0.839081	−	0.544006i	$-0.183093\pi$
$773$	1.54781e143	1.67816	0.839081	+	0.544006i	$0.183093\pi$
$774$	1.86498e143	1.89670
$775$	3.49352e142	0.333296
$776$	−8.76852e142	−0.784822
$777$	−2.78593e143	−2.33954
$778$	1.80462e143	1.42198
$779$	−2.92165e142	−0.216035
$780$	−1.43809e142	−0.0997939
$781$	−7.14798e142	−0.465540
$782$	1.30209e143	0.795990
$783$	4.49350e142	0.257856
$784$	−2.56891e143	−1.38389
$785$	3.28714e143	1.66253
$786$	−2.38424e142	−0.113223
$787$	7.24195e142	0.322929	0.161464	−	0.986879i	$-0.448378\pi$
$787$	7.24195e142	0.322929	0.161464	+	0.986879i	$0.448378\pi$
$788$	9.39340e141	0.0393346
$789$	−6.91023e143	−2.71757
$790$	−6.27299e143	−2.31704
$791$	2.68633e143	0.932015
$792$	2.28187e143	0.743695
$793$	2.09181e143	0.640472
$794$	−3.47680e143	−1.00015
$795$	3.49376e143	0.944323
$796$	−5.26035e140	−0.00133604
$797$	−3.49451e143	−0.834064	−0.417032	−	0.908892i	$-0.636930\pi$
$797$	−3.49451e143	−0.834064	−0.417032	+	0.908892i	$0.636930\pi$
$798$	3.05595e143	0.685493
$799$	−2.69619e143	−0.568440
$800$	2.44408e142	0.0484351
$801$	1.03944e144	1.93638
$802$	7.18815e142	0.125889
$803$	3.53310e143	0.581751
$804$	2.11433e142	0.0327340
$805$	1.18540e144	1.72572
$806$	5.01154e143	0.686098
$807$	−1.25525e144	−1.61618
$808$	−8.94483e143	−1.08320
$809$	−8.08683e143	−0.921142	−0.460571	−	0.887623i	$-0.652355\pi$
$809$	−8.08683e143	−0.921142	−0.460571	+	0.887623i	$0.652355\pi$
$810$	−8.28774e143	−0.888030
$811$	1.45395e144	1.46561	0.732804	−	0.680440i	$-0.238211\pi$
$811$	1.45395e144	1.46561	0.732804	+	0.680440i	$0.238211\pi$
$812$	−2.99535e142	−0.0284070
$813$	−1.75588e144	−1.56679
$814$	−7.25524e143	−0.609177
$815$	2.34599e144	1.85363
$816$	1.95580e144	1.45432
$817$	−6.12801e143	−0.428872
$818$	1.25704e144	0.828055
$819$	−5.19110e144	−3.21889
$820$	5.07710e142	0.0296367
$821$	1.10763e144	0.608707	0.304353	−	0.952559i	$-0.401560\pi$
$821$	1.10763e144	0.608707	0.304353	+	0.952559i	$0.401560\pi$
$822$	4.15466e143	0.214971
$823$	1.65657e144	0.807082	0.403541	−	0.914962i	$-0.367779\pi$
$823$	1.65657e144	0.807082	0.403541	+	0.914962i	$0.367779\pi$
$824$	1.09119e144	0.500614
$825$	−1.68173e144	−0.726585
$826$	−3.03558e144	−1.23518
$827$	−8.08801e143	−0.309970	−0.154985	−	0.987917i	$-0.549533\pi$
$827$	−8.08801e143	−0.309970	−0.154985	+	0.987917i	$0.549533\pi$
$828$	−8.80660e142	−0.0317912
$829$	−8.46576e143	−0.287884	−0.143942	−	0.989586i	$-0.545978\pi$
$829$	−8.46576e143	−0.287884	−0.143942	+	0.989586i	$0.545978\pi$
$830$	−4.12660e144	−1.32199
$831$	9.38941e144	2.83392
$832$	−5.61598e144	−1.59706
$833$	4.70412e144	1.26052
$834$	1.01386e144	0.256011
$835$	2.05693e143	0.0489485
$836$	2.30295e142	0.00516505
$837$	−8.03365e143	−0.169825
$838$	7.02934e144	1.40067
$839$	7.17447e144	1.34764	0.673819	−	0.738897i	$-0.264653\pi$
$839$	7.17447e144	1.34764	0.673819	+	0.738897i	$0.264653\pi$
$840$	1.72896e145	3.06168
$841$	−3.66860e144	−0.612489
$842$	−5.89011e144	−0.927203
$843$	−1.87460e145	−2.78255
$844$	−1.09702e143	−0.0153555
$845$	−1.75387e145	−2.31521
$846$	6.30172e144	0.784559
$847$	−8.46104e144	−0.993562
$848$	−4.31960e144	−0.478464
$849$	1.06377e145	1.11152
$850$	−7.84336e144	−0.773153
$851$	−9.11632e144	−0.847825
$852$	4.02364e143	0.0353068
$853$	1.90585e145	1.57802	0.789008	−	0.614383i	$-0.210595\pi$
$853$	1.90585e145	1.57802	0.789008	+	0.614383i	$0.210595\pi$
$854$	7.72450e144	0.603539
$855$	−6.80775e144	−0.501974
$856$	1.98099e145	1.37858
$857$	−9.71866e144	−0.638345	−0.319173	−	0.947697i	$-0.603405\pi$
$857$	−9.71866e144	−0.638345	−0.319173	+	0.947697i	$0.603405\pi$
$858$	−2.41248e145	−1.49570
$859$	−1.03916e145	−0.608162	−0.304081	−	0.952646i	$-0.598349\pi$
$859$	−1.03916e145	−0.608162	−0.304081	+	0.952646i	$0.598349\pi$
$860$	1.06490e144	0.0588347
$861$	3.27048e145	1.70591
$862$	1.34290e145	0.661355
$863$	1.64409e145	0.764524	0.382262	−	0.924054i	$-0.375145\pi$
$863$	1.64409e145	0.764524	0.382262	+	0.924054i	$0.375145\pi$
$864$	−5.62035e143	−0.0246793
$865$	1.31539e145	0.545451
$866$	−2.02648e145	−0.793608
$867$	4.96165e144	0.183519
$868$	5.35520e143	0.0187089
$869$	−3.04516e145	−1.00492
$870$	4.11501e145	1.28283
$871$	4.07825e145	1.20109
$872$	−6.15501e145	−1.71263
$873$	−3.86482e145	−1.01607
$874$	9.99989e144	0.248416
$875$	1.64295e145	0.385679
$876$	−1.98880e144	−0.0441203
$877$	2.71326e145	0.568868	0.284434	−	0.958696i	$-0.408194\pi$
$877$	2.71326e145	0.568868	0.284434	+	0.958696i	$0.408194\pi$
$878$	−1.00214e146	−1.98586
$879$	1.23872e145	0.232019
$880$	4.63692e145	0.820988
$881$	3.37734e145	0.565285	0.282643	−	0.959225i	$-0.408789\pi$
$881$	3.37734e145	0.565285	0.282643	+	0.959225i	$0.408789\pi$
$882$	−1.09948e146	−1.73977
$883$	−8.87978e145	−1.32846	−0.664228	−	0.747530i	$-0.731240\pi$
$883$	−8.87978e145	−1.32846	−0.664228	+	0.747530i	$0.731240\pi$
$884$	−3.25587e144	−0.0460553
$885$	1.20676e146	1.61410
$886$	6.13507e145	0.775980
$887$	3.89765e145	0.466213	0.233106	−	0.972451i	$-0.425111\pi$
$887$	3.89765e145	0.466213	0.233106	+	0.972451i	$0.425111\pi$
$888$	−1.32965e146	−1.50417
$889$	−6.03849e145	−0.646087
$890$	2.05104e146	2.07572
$891$	−4.02320e145	−0.385146
$892$	4.81137e143	0.00435721
$893$	−2.07063e145	−0.177401
$894$	2.33736e146	1.89461
$895$	1.02921e146	0.789341
$896$	−2.19955e146	−1.59620
$897$	−3.03132e146	−2.08164
$898$	3.81846e145	0.248147
$899$	−4.14967e145	−0.255216
$900$	5.30479e144	0.0308791
$901$	7.90995e145	0.435810
$902$	8.51712e145	0.444190
$903$	6.85967e146	3.38657
$904$	1.28211e146	0.599223
$905$	−3.52416e146	−1.55938
$906$	2.46865e146	1.03422
$907$	3.51901e144	0.0139592	0.00697959	−	0.999976i	$-0.497778\pi$
$907$	3.51901e144	0.0139592	0.00697959	+	0.999976i	$0.497778\pi$
$908$	−7.82759e144	−0.0294021
$909$	−3.94253e146	−1.40237
$910$	−1.02432e147	−3.45052
$911$	−1.59160e146	−0.507777	−0.253889	−	0.967233i	$-0.581710\pi$
$911$	−1.59160e146	−0.507777	−0.253889	+	0.967233i	$0.581710\pi$
$912$	1.50203e146	0.453871
$913$	−2.00321e146	−0.573355
$914$	5.17317e146	1.40256
$915$	−3.07080e146	−0.788691
$916$	6.51559e144	0.0158536
$917$	−4.91421e145	−0.113285
$918$	1.80365e146	0.393948
$919$	−9.00682e146	−1.86403	−0.932017	−	0.362414i	$-0.881953\pi$
$919$	−9.00682e146	−1.86403	−0.932017	+	0.362414i	$0.881953\pi$
$920$	5.65761e146	1.10952
$921$	6.40422e146	1.19018
$922$	−3.09112e145	−0.0544421
$923$	7.76102e146	1.29549
$924$	−2.57792e145	−0.0407855
$925$	5.49136e146	0.823501
$926$	6.03995e146	0.858598
$927$	4.80953e146	0.648120
$928$	−2.90311e145	−0.0370885
$929$	1.53541e146	0.185972	0.0929860	−	0.995667i	$-0.470359\pi$
$929$	1.53541e146	0.185972	0.0929860	+	0.995667i	$0.470359\pi$
$930$	−7.35697e146	−0.844876
$931$	3.61270e146	0.393389
$932$	−8.92258e144	−0.00921303
$933$	−1.87855e147	−1.83942
$934$	1.98398e146	0.184233
$935$	−8.49102e146	−0.747799
$936$	−2.47757e147	−2.06953
$937$	1.74425e147	1.38197	0.690986	−	0.722868i	$-0.257177\pi$
$937$	1.74425e147	1.38197	0.690986	+	0.722868i	$0.257177\pi$
$938$	1.50598e147	1.13183
$939$	−3.06282e146	−0.218361
$940$	3.59824e145	0.0243367
$941$	1.20711e147	0.774571	0.387285	−	0.921960i	$-0.373413\pi$
$941$	1.20711e147	0.774571	0.387285	+	0.921960i	$0.373413\pi$
$942$	−3.10406e147	−1.88978
$943$	1.07019e147	0.618204
$944$	−1.49201e147	−0.817821
$945$	1.64201e147	0.854085
$946$	1.78642e147	0.881806
$947$	−7.36570e146	−0.345057	−0.172528	−	0.985005i	$-0.555194\pi$
$947$	−7.36570e146	−0.345057	−0.172528	+	0.985005i	$0.555194\pi$
$948$	1.71413e146	0.0762135
$949$	−3.83611e147	−1.61888
$950$	−6.02359e146	−0.241289
$951$	−7.45639e146	−0.283526
$952$	3.91440e147	1.41298
$953$	4.39421e147	1.50585	0.752926	−	0.658105i	$-0.228642\pi$
$953$	4.39421e147	1.50585	0.752926	+	0.658105i	$0.228642\pi$
$954$	−1.84877e147	−0.601503
$955$	−4.32379e147	−1.33566
$956$	8.39496e145	0.0246237
$957$	1.99759e147	0.556372
$958$	−3.56794e147	−0.943680
$959$	8.56328e146	0.215090
$960$	8.24430e147	1.96665
$961$	−3.67186e147	−0.831913
$962$	7.87747e147	1.69520
$963$	8.73143e147	1.78478
$964$	−6.87199e145	−0.0133435
$965$	−3.94141e147	−0.727026
$966$	−1.11938e148	−1.96160
$967$	1.58992e147	0.264707	0.132353	−	0.991203i	$-0.457747\pi$
$967$	1.58992e147	0.264707	0.132353	+	0.991203i	$0.457747\pi$
$968$	−4.03823e147	−0.638794
$969$	−2.75048e147	−0.413410
$970$	−7.62612e147	−1.08919
$971$	5.64423e146	0.0766042	0.0383021	−	0.999266i	$-0.487805\pi$
$971$	5.64423e146	0.0766042	0.0383021	+	0.999266i	$0.487805\pi$
$972$	3.22171e146	0.0415534
$973$	2.08969e147	0.256151
$974$	4.01153e147	0.467350
$975$	1.82596e148	2.02192
$976$	3.79665e147	0.399609
$977$	−1.49810e148	−1.49885	−0.749426	−	0.662088i	$-0.769671\pi$
$977$	−1.49810e148	−1.49885	−0.749426	+	0.662088i	$0.769671\pi$
$978$	−2.21533e148	−2.10700
$979$	9.95658e147	0.900257
$980$	−6.27797e146	−0.0539670
$981$	−2.71289e148	−2.21726
$982$	1.47894e148	1.14929
$983$	−6.38884e147	−0.472088	−0.236044	−	0.971742i	$-0.575851\pi$
$983$	−6.38884e147	−0.472088	−0.236044	+	0.971742i	$0.575851\pi$
$984$	1.56091e148	1.09678
$985$	−2.65981e148	−1.77729
$986$	9.31648e147	0.592031
$987$	2.31786e148	1.40084
$988$	−2.50046e146	−0.0143731
$989$	2.24467e148	1.22726
$990$	1.98458e148	1.03211
$991$	−2.13988e148	−1.05863	−0.529314	−	0.848426i	$-0.677551\pi$
$991$	−2.13988e148	−1.05863	−0.529314	+	0.848426i	$0.677551\pi$
$992$	5.19029e146	0.0244266
$993$	2.06981e148	0.926706
$994$	2.86593e148	1.22079
$995$	1.48951e147	0.0603671
$996$	1.12762e147	0.0434836
$997$	−2.33106e148	−0.855350	−0.427675	−	0.903933i	$-0.640667\pi$
$997$	−2.33106e148	−0.855350	−0.427675	+	0.903933i	$0.640667\pi$
$998$	5.38226e147	0.187933
$999$	−1.26278e148	−0.419601

Twists

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

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

\(f(q)\)	\(=\)	\(q-8.07907e14 q^{2} -6.25114e23 q^{3} +1.88877e28 q^{4} -5.34820e34 q^{5} +5.05034e38 q^{6} +1.04094e42 q^{7} +4.96812e44 q^{8} +2.18975e47 q^{9} +O(q^{10})\)	\(q-8.07907e14 q^{2} -6.25114e23 q^{3} +1.88877e28 q^{4} -5.34820e34 q^{5} +5.05034e38 q^{6} +1.04094e42 q^{7} +4.96812e44 q^{8} +2.18975e47 q^{9} +4.32085e49 q^{10} +2.09751e51 q^{11} -1.18070e52 q^{12} -2.27740e55 q^{13} -8.40981e56 q^{14} +3.34324e58 q^{15} -4.13349e59 q^{16} +7.56916e60 q^{17} -1.76912e62 q^{18} +5.81301e62 q^{19} -1.01016e63 q^{20} -6.50706e65 q^{21} -1.69459e66 q^{22} -2.12928e67 q^{23} -3.10564e68 q^{24} +1.28261e69 q^{25} +1.83993e70 q^{26} -2.94946e70 q^{27} +1.96610e70 q^{28} -1.52350e72 q^{29} -2.70102e73 q^{30} +2.72377e73 q^{31} +1.90555e73 q^{32} -1.31118e75 q^{33} -6.11517e75 q^{34} -5.56715e76 q^{35} +4.13595e75 q^{36} +4.28140e77 q^{37} -4.69637e77 q^{38} +1.42363e79 q^{39} -2.65705e79 q^{40} -5.02606e79 q^{41} +5.25709e80 q^{42} -1.05419e81 q^{43} +3.96172e79 q^{44} -1.17112e82 q^{45} +1.72026e82 q^{46} -3.56207e82 q^{47} +2.58391e83 q^{48} +6.21485e83 q^{49} -1.03623e84 q^{50} -4.73159e84 q^{51} -4.30149e83 q^{52} +1.04502e85 q^{53} +2.38289e85 q^{54} -1.12179e86 q^{55} +5.17151e86 q^{56} -3.63379e86 q^{57} +1.23085e87 q^{58} +3.60957e87 q^{59} +6.31462e86 q^{60} -9.18510e87 q^{61} -2.20055e88 q^{62} +2.27940e89 q^{63} +2.46596e89 q^{64} +1.21800e90 q^{65} +1.05931e90 q^{66} -1.79075e90 q^{67} +1.42964e89 q^{68} +1.33104e91 q^{69} +4.49774e91 q^{70} -3.40784e91 q^{71} +1.08790e92 q^{72} +1.68443e92 q^{73} -3.45898e92 q^{74} -8.01775e92 q^{75} +1.09795e91 q^{76} +2.18338e93 q^{77} -1.15016e94 q^{78} -1.45180e94 q^{79} +2.21068e94 q^{80} -1.91808e94 q^{81} +4.06058e94 q^{82} -9.55043e94 q^{83} -1.22904e94 q^{84} -4.04814e95 q^{85} +8.51687e95 q^{86} +9.52362e95 q^{87} +1.04207e96 q^{88} +4.74685e96 q^{89} +9.46159e96 q^{90} -2.37063e97 q^{91} -4.02173e95 q^{92} -1.70267e97 q^{93} +2.87782e97 q^{94} -3.10891e97 q^{95} -1.19119e97 q^{96} -1.76496e98 q^{97} -5.02102e98 q^{98} +4.59303e98 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 208040616902520 q^{2} - 28\!\cdots\!20 q^{3}+ \cdots + 15\!\cdots\!76 q^{9}+O(q^{10}) \) 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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more