LMFDB - Embedded newform 1.100.a.a.1.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1,100,Mod(1,1)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1.1"); S:= CuspForms(chi, 100); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1, base_ring=CyclotomicField(1)) chi = DirichletCharacter(H, H._module([])) N = Newforms(chi, 100, names="a")

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

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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			1.1
Root			$-2.10181e13$ of defining polynomial
Character	$\chi$	$=$	1.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-1.53931e15 q^{2} +1.09471e23 q^{3} +1.73565e30 q^{4} -1.42424e34 q^{5} -1.68510e38 q^{6} -4.25157e41 q^{7} -1.69606e45 q^{8} -1.59809e47 q^{9} +2.19235e49 q^{10} -5.04571e51 q^{11} +1.90004e53 q^{12} -1.33313e55 q^{13} +6.54449e56 q^{14} -1.55913e57 q^{15} +1.51066e60 q^{16} +8.54293e60 q^{17} +2.45995e62 q^{18} -3.57926e63 q^{19} -2.47199e64 q^{20} -4.65425e64 q^{21} +7.76692e66 q^{22} -1.32632e67 q^{23} -1.85670e68 q^{24} -1.37488e69 q^{25} +2.05211e70 q^{26} -3.63008e70 q^{27} -7.37926e71 q^{28} -1.57811e71 q^{29} +2.39999e72 q^{30} -3.89706e73 q^{31} -1.25037e75 q^{32} -5.52360e74 q^{33} -1.31502e76 q^{34} +6.05525e75 q^{35} -2.77372e77 q^{36} -1.80202e77 q^{37} +5.50960e78 q^{38} -1.45940e78 q^{39} +2.41559e79 q^{40} +2.13003e79 q^{41} +7.16433e79 q^{42} +8.43003e79 q^{43} -8.75761e81 q^{44} +2.27606e81 q^{45} +2.04162e82 q^{46} +2.19872e82 q^{47} +1.65374e83 q^{48} -2.81310e83 q^{49} +2.11636e84 q^{50} +9.35205e83 q^{51} -2.31386e85 q^{52} -2.60808e85 q^{53} +5.58782e85 q^{54} +7.18630e85 q^{55} +7.21091e86 q^{56} -3.91826e86 q^{57} +2.42920e86 q^{58} +3.91766e87 q^{59} -2.70611e87 q^{60} -3.67456e88 q^{61} +5.99879e88 q^{62} +6.79437e88 q^{63} +9.67216e89 q^{64} +1.89870e89 q^{65} +8.50254e89 q^{66} -3.53225e90 q^{67} +1.48276e91 q^{68} -1.45194e90 q^{69} -9.32092e90 q^{70} +1.43616e91 q^{71} +2.71045e92 q^{72} -5.96639e91 q^{73} +2.77387e92 q^{74} -1.50509e92 q^{75} -6.21236e93 q^{76} +2.14522e93 q^{77} +2.24647e93 q^{78} -1.81922e93 q^{79} -2.15154e94 q^{80} +2.34800e94 q^{81} -3.27878e94 q^{82} -6.69942e93 q^{83} -8.07816e94 q^{84} -1.21672e95 q^{85} -1.29764e95 q^{86} -1.72758e94 q^{87} +8.55782e96 q^{88} -5.60112e95 q^{89} -3.50356e96 q^{90} +5.66791e96 q^{91} -2.30203e97 q^{92} -4.26616e96 q^{93} -3.38451e97 q^{94} +5.09772e97 q^{95} -1.36880e98 q^{96} -2.13029e98 q^{97} +4.33023e98 q^{98} +8.06348e98 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 208040616902520 q^{2} - 28\!\cdots\!20 q^{3} + 28\!\cdots\!24 q^{4} - 48\!\cdots\!60 q^{5} - 77\!\cdots\!44 q^{6} - 56\!\cdots\!00 q^{7} + 59\!\cdots\!60 q^{8} + 15\!\cdots\!76 q^{9} - 20\!\cdots\!60 q^{10}+ \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

Coefficient data

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

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

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

$2$	−1.53931e15	−1.93349	−0.966744	−	0.255744i	$-0.917680\pi$
$2$	−1.53931e15	−1.93349	−0.966744	+	0.255744i	$0.917680\pi$
$3$	1.09471e23	0.264118	0.132059	−	0.991242i	$-0.457841\pi$
$3$	1.09471e23	0.264118	0.132059	+	0.991242i	$0.457841\pi$
$4$	1.73565e30	2.73838
$5$	−1.42424e34	−0.358565	−0.179282	−	0.983798i	$-0.557378\pi$
$5$	−1.42424e34	−0.358565	−0.179282	+	0.983798i	$0.557378\pi$
$6$	−1.68510e38	−0.510669
$7$	−4.25157e41	−0.625455	−0.312728	−	0.949843i	$-0.601243\pi$
$7$	−4.25157e41	−0.625455	−0.312728	+	0.949843i	$0.601243\pi$
$8$	−1.69606e45	−3.36114
$9$	−1.59809e47	−0.930242
$10$	2.19235e49	0.693281
$11$	−5.04571e51	−1.42556	−0.712778	−	0.701390i	$-0.752563\pi$
$11$	−5.04571e51	−1.42556	−0.712778	+	0.701390i	$0.752563\pi$
$12$	1.90004e53	0.723255
$13$	−1.33313e55	−0.965334	−0.482667	−	0.875804i	$-0.660332\pi$
$13$	−1.33313e55	−0.965334	−0.482667	+	0.875804i	$0.660332\pi$
$14$	6.54449e56	1.20931
$15$	−1.55913e57	−0.0947034
$16$	1.51066e60	3.76034
$17$	8.54293e60	1.05776	0.528878	−	0.848698i	$-0.322613\pi$
$17$	8.54293e60	1.05776	0.528878	+	0.848698i	$0.322613\pi$
$18$	2.45995e62	1.79861
$19$	−3.57926e63	−1.80090	−0.900451	−	0.434957i	$-0.856763\pi$
$19$	−3.57926e63	−1.80090	−0.900451	+	0.434957i	$0.856763\pi$
$20$	−2.47199e64	−0.981887
$21$	−4.65425e64	−0.165194
$22$	7.76692e66	2.75630
$23$	−1.32632e67	−0.521340	−0.260670	−	0.965428i	$-0.583943\pi$
$23$	−1.32632e67	−0.521340	−0.260670	+	0.965428i	$0.583943\pi$
$24$	−1.85670e68	−0.887737
$25$	−1.37488e69	−0.871431
$26$	2.05211e70	1.86646
$27$	−3.63008e70	−0.509811
$28$	−7.37926e71	−1.71273
$29$	−1.57811e71	−0.0644817	−0.0322409	−	0.999480i	$-0.510264\pi$
$29$	−1.57811e71	−0.0644817	−0.0322409	+	0.999480i	$0.510264\pi$
$30$	2.39999e72	0.183108
$31$	−3.89706e73	−0.586588	−0.293294	−	0.956022i	$-0.594752\pi$
$31$	−3.89706e73	−0.586588	−0.293294	+	0.956022i	$0.594752\pi$
$32$	−1.25037e75	−3.90944
$33$	−5.52360e74	−0.376515
$34$	−1.31502e76	−2.04516
$35$	6.05525e75	0.224266
$36$	−2.77372e77	−2.54735
$37$	−1.80202e77	−0.426357	−0.213179	−	0.977013i	$-0.568382\pi$
$37$	−1.80202e77	−0.426357	−0.213179	+	0.977013i	$0.568382\pi$
$38$	5.50960e78	3.48202
$39$	−1.45940e78	−0.254962
$40$	2.41559e79	1.20519
$41$	2.13003e79	0.313029	0.156514	−	0.987676i	$-0.449974\pi$
$41$	2.13003e79	0.313029	0.156514	+	0.987676i	$0.449974\pi$
$42$	7.16433e79	0.319401
$43$	8.43003e79	0.117257	0.0586287	−	0.998280i	$-0.481327\pi$
$43$	8.43003e79	0.117257	0.0586287	+	0.998280i	$0.481327\pi$
$44$	−8.75761e81	−3.90371
$45$	2.27606e81	0.333552
$46$	2.04162e82	1.00800
$47$	2.19872e82	0.374391	0.187195	−	0.982323i	$-0.440060\pi$
$47$	2.19872e82	0.374391	0.187195	+	0.982323i	$0.440060\pi$
$48$	1.65374e83	0.993174
$49$	−2.81310e83	−0.608805
$50$	2.11636e84	1.68490
$51$	9.35205e83	0.279372
$52$	−2.31386e85	−2.64345
$53$	−2.60808e85	−1.16056	−0.580278	−	0.814418i	$-0.697056\pi$
$53$	−2.60808e85	−1.16056	−0.580278	+	0.814418i	$0.697056\pi$
$54$	5.58782e85	0.985715
$55$	7.18630e85	0.511154
$56$	7.21091e86	2.10224
$57$	−3.91826e86	−0.475651
$58$	2.42920e86	0.124675
$59$	3.91766e87	0.862684	0.431342	−	0.902188i	$-0.358040\pi$
$59$	3.91766e87	0.862684	0.431342	+	0.902188i	$0.358040\pi$
$60$	−2.70611e87	−0.259334
$61$	−3.67456e88	−1.55374	−0.776869	−	0.629662i	$-0.783193\pi$
$61$	−3.67456e88	−1.55374	−0.776869	+	0.629662i	$0.783193\pi$
$62$	5.99879e88	1.13416
$63$	6.79437e88	0.581825
$64$	9.67216e89	3.79852
$65$	1.89870e89	0.346135
$66$	8.50254e89	0.727987
$67$	−3.53225e90	−1.43664	−0.718322	−	0.695711i	$-0.755089\pi$
$67$	−3.53225e90	−1.43664	−0.718322	+	0.695711i	$0.755089\pi$
$68$	1.48276e91	2.89654
$69$	−1.45194e90	−0.137695
$70$	−9.32092e90	−0.433617
$71$	1.43616e91	0.331065	0.165533	−	0.986204i	$-0.447066\pi$
$71$	1.43616e91	0.331065	0.165533	+	0.986204i	$0.447066\pi$
$72$	2.71045e92	3.12667
$73$	−5.96639e91	−0.347720	−0.173860	−	0.984770i	$-0.555624\pi$
$73$	−5.96639e91	−0.347720	−0.173860	+	0.984770i	$0.555624\pi$
$74$	2.77387e92	0.824357
$75$	−1.50509e92	−0.230161
$76$	−6.21236e93	−4.93155
$77$	2.14522e93	0.891622
$78$	2.24647e93	0.492966
$79$	−1.81922e93	−0.212493	−0.106247	−	0.994340i	$-0.533883\pi$
$79$	−1.81922e93	−0.212493	−0.106247	+	0.994340i	$0.533883\pi$
$80$	−2.15154e94	−1.34833
$81$	2.34800e94	0.795591
$82$	−3.27878e94	−0.605238
$83$	−6.69942e93	−0.0678690	−0.0339345	−	0.999424i	$-0.510804\pi$
$83$	−6.69942e93	−0.0678690	−0.0339345	+	0.999424i	$0.510804\pi$
$84$	−8.07816e94	−0.452364
$85$	−1.21672e95	−0.379274
$86$	−1.29764e95	−0.226716
$87$	−1.72758e94	−0.0170308
$88$	8.55782e96	4.79149
$89$	−5.60112e95	−0.179254	−0.0896271	−	0.995975i	$-0.528568\pi$
$89$	−5.60112e95	−0.179254	−0.0896271	+	0.995975i	$0.528568\pi$
$90$	−3.50356e96	−0.644919
$91$	5.66791e96	0.603774
$92$	−2.30203e97	−1.42763
$93$	−4.26616e96	−0.154929
$94$	−3.38451e97	−0.723881
$95$	5.09772e97	0.645740
$96$	−1.36880e98	−1.03255
$97$	−2.13029e98	−0.962139	−0.481070	−	0.876682i	$-0.659752\pi$
$97$	−2.13029e98	−0.962139	−0.481070	+	0.876682i	$0.659752\pi$
$98$	4.33023e98	1.17712
$99$	8.06348e98	1.32611
$100$	−2.38631e99	−2.38631
$101$	−1.55937e99	−0.952888	−0.476444	−	0.879205i	$-0.658075\pi$
$101$	−1.55937e99	−0.952888	−0.476444	+	0.879205i	$0.658075\pi$
$102$	−1.43957e99	−0.540163
$103$	2.08933e99	0.483686	0.241843	−	0.970315i	$-0.422248\pi$
$103$	2.08933e99	0.483686	0.241843	+	0.970315i	$0.422248\pi$
$104$	2.26107e100	3.24462
$105$	6.62876e98	0.0592328
$106$	4.01465e100	2.24392
$107$	−4.67376e100	−1.64123	−0.820615	−	0.571481i	$-0.806369\pi$
$107$	−4.67376e100	−1.64123	−0.820615	+	0.571481i	$0.806369\pi$
$108$	−6.30056e100	−1.39606
$109$	9.73243e100	1.36650	0.683250	−	0.730185i	$-0.260566\pi$
$109$	9.73243e100	1.36650	0.683250	+	0.730185i	$0.260566\pi$
$110$	−1.10620e101	−0.988311
$111$	−1.97269e100	−0.112609
$112$	−6.42268e101	−2.35193
$113$	2.10873e101	0.497323	0.248661	−	0.968591i	$-0.420009\pi$
$113$	2.10873e101	0.497323	0.248661	+	0.968591i	$0.420009\pi$
$114$	6.03142e101	0.919665
$115$	1.88900e101	0.186934
$116$	−2.73905e101	−0.176575
$117$	2.13046e102	0.897994
$118$	−6.03049e102	−1.66799
$119$	−3.63209e102	−0.661579
$120$	2.64438e102	0.318311
$121$	1.29314e103	1.03221
$122$	5.65629e103	3.00414
$123$	2.33177e102	0.0826765
$124$	−6.76395e103	−1.60630
$125$	4.20521e103	0.671030
$126$	−1.04587e104	−1.12495
$127$	1.76385e104	1.28285	0.641426	−	0.767185i	$-0.278343\pi$
$127$	1.76385e104	1.28285	0.641426	+	0.767185i	$0.278343\pi$
$128$	−6.96330e104	−3.43496
$129$	9.22846e102	0.0309698
$130$	−2.92269e104	−0.669248
$131$	8.92579e104	1.39868	0.699338	−	0.714791i	$-0.253478\pi$
$131$	8.92579e104	1.39868	0.699338	+	0.714791i	$0.253478\pi$
$132$	−9.58706e104	−1.03104
$133$	1.52175e105	1.12638
$134$	5.43724e105	2.77773
$135$	5.17010e104	0.182800
$136$	−1.44893e106	−3.55526
$137$	3.33189e105	0.568883	0.284441	−	0.958693i	$-0.408192\pi$
$137$	3.33189e105	0.568883	0.284441	+	0.958693i	$0.408192\pi$
$138$	2.23499e105	0.266232
$139$	1.60870e106	1.34043	0.670213	−	0.742169i	$-0.266203\pi$
$139$	1.60870e106	1.34043	0.670213	+	0.742169i	$0.266203\pi$
$140$	1.05098e106	0.614126
$141$	2.40696e105	0.0988834
$142$	−2.21069e106	−0.640111
$143$	6.72660e106	1.37614
$144$	−2.41416e107	−3.49803
$145$	2.24761e105	0.0231209
$146$	9.18413e106	0.672313
$147$	−3.07953e106	−0.160796
$148$	−3.12768e107	−1.16753
$149$	−7.50937e106	−0.200855	−0.100428	−	0.994944i	$-0.532021\pi$
$149$	−7.50937e106	−0.200855	−0.100428	+	0.994944i	$0.532021\pi$
$150$	2.31681e107	0.445013
$151$	−4.40125e107	−0.608439	−0.304219	−	0.952602i	$-0.598396\pi$
$151$	−4.40125e107	−0.608439	−0.304219	+	0.952602i	$0.598396\pi$
$152$	6.07063e108	6.05308
$153$	−1.36523e108	−0.983968
$154$	−3.30216e108	−1.72394
$155$	5.55035e107	0.210330
$156$	−2.53301e108	−0.698183
$157$	−7.75028e108	−1.55699	−0.778493	−	0.627653i	$-0.784016\pi$
$157$	−7.75028e108	−1.55699	−0.778493	+	0.627653i	$0.784016\pi$
$158$	2.80035e108	0.410854
$159$	−2.85510e108	−0.306524
$160$	1.78083e109	1.40179
$161$	5.63895e108	0.326075
$162$	−3.61431e109	−1.53827
$163$	−2.45335e109	−0.769968	−0.384984	−	0.922923i	$-0.625793\pi$
$163$	−2.45335e109	−0.769968	−0.384984	+	0.922923i	$0.625793\pi$
$164$	3.69699e109	0.857192
$165$	7.86693e108	0.135005
$166$	1.03125e109	0.131224
$167$	−9.13307e109	−0.863280	−0.431640	−	0.902046i	$-0.642065\pi$
$167$	−9.13307e109	−0.863280	−0.431640	+	0.902046i	$0.642065\pi$
$168$	7.89387e109	0.555240
$169$	−1.29936e109	−0.0681300
$170$	1.87291e110	0.733322
$171$	5.71997e110	1.67527
$172$	1.46316e110	0.321096
$173$	−7.23256e108	−0.0119127	−0.00595635	−	0.999982i	$-0.501896\pi$
$173$	−7.23256e108	−0.0119127	−0.00595635	+	0.999982i	$0.501896\pi$
$174$	2.65928e109	0.0329288
$175$	5.84538e110	0.545041
$176$	−7.62235e111	−5.36058
$177$	4.28871e110	0.227850
$178$	8.62186e110	0.346586
$179$	1.89280e111	0.576607	0.288303	−	0.957539i	$-0.406909\pi$
$179$	1.89280e111	0.576607	0.288303	+	0.957539i	$0.406909\pi$
$180$	3.95045e111	0.913392
$181$	7.66036e111	1.34636	0.673178	−	0.739481i	$-0.264929\pi$
$181$	7.66036e111	1.34636	0.673178	+	0.739481i	$0.264929\pi$
$182$	−8.72468e111	−1.16739
$183$	−4.02258e111	−0.410370
$184$	2.24952e112	1.75229
$185$	2.56651e111	0.152877
$186$	6.56695e111	0.299553
$187$	−4.31051e112	−1.50789
$188$	3.81621e112	1.02522
$189$	1.54335e112	0.318864
$190$	−7.84699e112	−1.24853
$191$	−6.08896e112	−0.747121	−0.373561	−	0.927606i	$-0.621863\pi$
$191$	−6.08896e112	−0.747121	−0.373561	+	0.927606i	$0.621863\pi$
$192$	1.05882e113	1.00326
$193$	−7.56005e112	−0.553908	−0.276954	−	0.960883i	$-0.589325\pi$
$193$	−7.56005e112	−0.553908	−0.276954	+	0.960883i	$0.589325\pi$
$194$	3.27918e113	1.86029
$195$	2.07853e112	0.0914204
$196$	−4.88256e113	−1.66714
$197$	−4.51135e113	−1.19737	−0.598685	−	0.800984i	$-0.704310\pi$
$197$	−4.51135e113	−1.19737	−0.598685	+	0.800984i	$0.704310\pi$
$198$	−1.24122e114	−2.56402
$199$	5.34960e113	0.861181	0.430590	−	0.902547i	$-0.358305\pi$
$199$	5.34960e113	0.861181	0.430590	+	0.902547i	$0.358305\pi$
$200$	2.33187e114	2.92900
$201$	−3.86680e113	−0.379443
$202$	2.40036e114	1.84240
$203$	6.70945e112	0.0403304
$204$	1.62319e114	0.765027
$205$	−3.03367e113	−0.112241
$206$	−3.21612e114	−0.935201
$207$	2.11957e114	0.484972
$208$	−2.01391e115	−3.62999
$209$	1.80599e115	2.56729
$210$	−1.02037e114	−0.114526
$211$	−6.81741e114	−0.604836	−0.302418	−	0.953175i	$-0.597794\pi$
$211$	−6.81741e114	−0.604836	−0.302418	+	0.953175i	$0.597794\pi$
$212$	−4.52673e115	−3.17804
$213$	1.57218e114	0.0874402
$214$	7.19438e115	3.17330
$215$	−1.20064e114	−0.0420444
$216$	6.15682e115	1.71355
$217$	1.65686e115	0.366885
$218$	−1.49812e116	−2.64211
$219$	−6.53148e114	−0.0918392
$220$	1.24729e116	1.39973
$221$	−1.13889e116	−1.02109
$222$	3.03659e115	0.217728
$223$	−1.16918e116	−0.671105	−0.335553	−	0.942021i	$-0.608923\pi$
$223$	−1.16918e116	−0.671105	−0.335553	+	0.942021i	$0.608923\pi$
$224$	5.31604e116	2.44518
$225$	2.19717e116	0.810642
$226$	−3.24599e116	−0.961568
$227$	−1.47452e116	−0.351051	−0.175526	−	0.984475i	$-0.556162\pi$
$227$	−1.47452e116	−0.351051	−0.175526	+	0.984475i	$0.556162\pi$
$228$	−6.80075e116	−1.30251
$229$	−6.46968e116	−0.997760	−0.498880	−	0.866671i	$-0.666255\pi$
$229$	−6.46968e116	−0.997760	−0.498880	+	0.866671i	$0.666255\pi$
$230$	−2.90776e116	−0.361435
$231$	2.34840e116	0.235493
$232$	2.67657e116	0.216732
$233$	1.37974e117	0.902983	0.451492	−	0.892275i	$-0.350892\pi$
$233$	1.37974e117	0.902983	0.451492	+	0.892275i	$0.350892\pi$
$234$	−3.27944e117	−1.73626
$235$	−3.13150e116	−0.134243
$236$	6.79970e117	2.36236
$237$	−1.99153e116	−0.0561233
$238$	5.59091e117	1.27916
$239$	4.89334e117	0.909722	0.454861	−	0.890562i	$-0.349689\pi$
$239$	4.89334e117	0.909722	0.454861	+	0.890562i	$0.349689\pi$
$240$	−2.35532e117	−0.356117
$241$	6.47362e117	0.796717	0.398358	−	0.917230i	$-0.369580\pi$
$241$	6.47362e117	0.796717	0.398358	+	0.917230i	$0.369580\pi$
$242$	−1.99054e118	−1.99577
$243$	8.80659e117	0.719941
$244$	−6.37776e118	−4.25473
$245$	4.00652e117	0.218296
$246$	−3.58932e117	−0.159854
$247$	4.77163e118	1.73847
$248$	6.60964e118	1.97160
$249$	−7.33393e116	−0.0179254
$250$	−6.47312e118	−1.29743
$251$	−6.92152e118	−1.13855	−0.569275	−	0.822147i	$-0.692776\pi$
$251$	−6.92152e118	−1.13855	−0.569275	+	0.822147i	$0.692776\pi$
$252$	1.17927e119	1.59326
$253$	6.69223e118	0.743199
$254$	−2.71511e119	−2.48038
$255$	−1.33196e118	−0.100173
$256$	4.58823e119	2.84293
$257$	−1.47015e119	−0.751057	−0.375529	−	0.926811i	$-0.622539\pi$
$257$	−1.47015e119	−0.751057	−0.375529	+	0.926811i	$0.622539\pi$
$258$	−1.42055e118	−0.0598798
$259$	7.66141e118	0.266668
$260$	3.29549e119	0.947849
$261$	2.52196e118	0.0599836
$262$	−1.37396e120	−2.70433
$263$	6.72240e119	1.09576	0.547879	−	0.836558i	$-0.315435\pi$
$263$	6.72240e119	1.09576	0.547879	+	0.836558i	$0.315435\pi$
$264$	9.36834e119	1.26552
$265$	3.71454e119	0.416135
$266$	−2.34244e120	−2.17785
$267$	−6.13161e118	−0.0473442
$268$	−6.13077e120	−3.93408
$269$	3.58420e120	1.91273	0.956366	−	0.292171i	$-0.0943777\pi$
$269$	3.58420e120	1.91273	0.956366	+	0.292171i	$0.0943777\pi$
$270$	−7.95839e119	−0.353443
$271$	1.94223e120	0.718326	0.359163	−	0.933275i	$-0.383062\pi$
$271$	1.94223e120	0.718326	0.359163	+	0.933275i	$0.383062\pi$
$272$	1.29055e121	3.97752
$273$	6.20473e119	0.159467
$274$	−5.12882e120	−1.09993
$275$	6.93722e120	1.24227
$276$	−2.52007e120	−0.377061
$277$	3.85718e120	0.482527	0.241264	−	0.970460i	$-0.422438\pi$
$277$	3.85718e120	0.482527	0.241264	+	0.970460i	$0.422438\pi$
$278$	−2.47629e121	−2.59170
$279$	6.22784e120	0.545669
$280$	−1.02701e121	−0.753790
$281$	5.10363e120	0.313990	0.156995	−	0.987599i	$-0.449819\pi$
$281$	5.10363e120	0.313990	0.156995	+	0.987599i	$0.449819\pi$
$282$	−3.70506e120	−0.191190
$283$	−1.19050e121	−0.515587	−0.257793	−	0.966200i	$-0.582995\pi$
$283$	−1.19050e121	−0.515587	−0.257793	+	0.966200i	$0.582995\pi$
$284$	2.49267e121	0.906582
$285$	5.58054e120	0.170552
$286$	−1.03543e122	−2.66075
$287$	−9.05596e120	−0.195786
$288$	1.99820e122	3.63673
$289$	7.75228e120	0.118846
$290$	−3.45977e120	−0.0447040
$291$	−2.33206e121	−0.254118
$292$	−1.03556e122	−0.952190
$293$	−1.17765e122	−0.914259	−0.457130	−	0.889400i	$-0.651122\pi$
$293$	−1.17765e122	−0.914259	−0.457130	+	0.889400i	$0.651122\pi$
$294$	4.74036e121	0.310898
$295$	−5.57968e121	−0.309328
$296$	3.05633e122	1.43305
$297$	1.83163e122	0.726765
$298$	1.15593e122	0.388352
$299$	1.76816e122	0.503267
$300$	−2.61232e122	−0.630267
$301$	−3.58409e121	−0.0733393
$302$	6.77489e122	1.17641
$303$	−1.70706e122	−0.251675
$304$	−5.40704e123	−6.77201
$305$	5.23345e122	0.557116
$306$	2.10152e123	1.90249
$307$	−2.98902e122	−0.230239	−0.115120	−	0.993352i	$-0.536725\pi$
$307$	−2.98902e122	−0.230239	−0.115120	+	0.993352i	$0.536725\pi$
$308$	3.72336e123	2.44160
$309$	2.28721e122	0.127750
$310$	−8.54372e122	−0.406671
$311$	5.98572e122	0.242928	0.121464	−	0.992596i	$-0.461241\pi$
$311$	5.98572e122	0.242928	0.121464	+	0.992596i	$0.461241\pi$
$312$	2.47522e123	0.856963
$313$	−4.50272e123	−1.33055	−0.665274	−	0.746599i	$-0.731685\pi$
$313$	−4.50272e123	−1.33055	−0.665274	+	0.746599i	$0.731685\pi$
$314$	1.19301e124	3.01041
$315$	−9.67681e122	−0.208622
$316$	−3.15755e123	−0.581887
$317$	−9.72485e123	−1.53267	−0.766336	−	0.642440i	$-0.777922\pi$
$317$	−9.72485e123	−1.53267	−0.766336	+	0.642440i	$0.777922\pi$
$318$	4.39489e123	0.592660
$319$	7.96269e122	0.0919223
$320$	−1.37755e124	−1.36202
$321$	−5.11642e123	−0.433478
$322$	−8.68009e123	−0.630462
$323$	−3.05774e124	−1.90491
$324$	4.07532e124	2.17863
$325$	1.83289e124	0.841222
$326$	3.77647e124	1.48872
$327$	1.06542e124	0.360917
$328$	−3.61265e124	−1.05213
$329$	−9.34800e123	−0.234165
$330$	−1.21097e124	−0.261031
$331$	−7.03877e124	−1.30620	−0.653102	−	0.757270i	$-0.726533\pi$
$331$	−7.03877e124	−1.30620	−0.653102	+	0.757270i	$0.726533\pi$
$332$	−1.16279e124	−0.185851
$333$	2.87978e124	0.396615
$334$	1.40586e125	1.66914
$335$	5.03077e124	0.515130
$336$	−7.03098e124	−0.621186
$337$	1.61739e125	1.23349	0.616744	−	0.787164i	$-0.288451\pi$
$337$	1.61739e125	1.23349	0.616744	+	0.787164i	$0.288451\pi$
$338$	2.00012e124	0.131729
$339$	2.30845e124	0.131352
$340$	−2.11180e125	−1.03860
$341$	1.96634e125	0.836215
$342$	−8.80481e125	−3.23912
$343$	3.16052e125	1.00624
$344$	−1.42978e125	−0.394119
$345$	2.06791e124	0.0493726
$346$	1.11332e124	0.0230331
$347$	5.65213e124	0.101369	0.0506843	−	0.998715i	$-0.483860\pi$
$347$	5.65213e124	0.101369	0.0506843	+	0.998715i	$0.483860\pi$
$348$	−2.99848e124	−0.0466367
$349$	−1.31636e126	−1.77630	−0.888152	−	0.459550i	$-0.848011\pi$
$349$	−1.31636e126	−1.77630	−0.888152	+	0.459550i	$0.848011\pi$
$350$	−8.99786e125	−1.05383
$351$	4.83938e125	0.492138
$352$	6.30901e126	5.57313
$353$	1.02761e126	0.788823	0.394411	−	0.918934i	$-0.370949\pi$
$353$	1.02761e126	0.788823	0.394411	+	0.918934i	$0.370949\pi$
$354$	−6.60166e125	−0.440546
$355$	−2.04543e125	−0.118708
$356$	−9.72160e125	−0.490866
$357$	−3.97609e125	−0.174735
$358$	−2.91361e126	−1.11486
$359$	−5.03591e126	−1.67843	−0.839213	−	0.543802i	$-0.816984\pi$
$359$	−5.03591e126	−1.67843	−0.839213	+	0.543802i	$0.816984\pi$
$360$	−3.86032e126	−1.12111
$361$	8.86102e126	2.24325
$362$	−1.17917e127	−2.60316
$363$	1.41561e126	0.272625
$364$	9.83753e126	1.65336
$365$	8.49757e125	0.124680
$366$	6.19201e126	0.793446
$367$	8.30488e126	0.929744	0.464872	−	0.885378i	$-0.346100\pi$
$367$	8.30488e126	0.929744	0.464872	+	0.885378i	$0.346100\pi$
$368$	−2.00362e127	−1.96042
$369$	−3.40397e126	−0.291192
$370$	−3.95065e126	−0.295586
$371$	1.10885e127	0.725876
$372$	−7.40458e126	−0.424253
$373$	−1.36455e127	−0.684544	−0.342272	−	0.939601i	$-0.611196\pi$
$373$	−1.36455e127	−0.684544	−0.342272	+	0.939601i	$0.611196\pi$
$374$	6.63522e127	2.91549
$375$	4.60349e126	0.177231
$376$	−3.72915e127	−1.25838
$377$	2.10383e126	0.0622464
$378$	−2.37570e127	−0.616521
$379$	−2.89152e127	−0.658394	−0.329197	−	0.944261i	$-0.606778\pi$
$379$	−2.89152e127	−0.658394	−0.329197	+	0.944261i	$0.606778\pi$
$380$	8.84789e127	1.76828
$381$	1.93090e127	0.338824
$382$	9.37280e127	1.44455
$383$	−1.41040e128	−1.90987	−0.954937	−	0.296810i	$-0.904077\pi$
$383$	−1.41040e128	−1.90987	−0.954937	+	0.296810i	$0.904077\pi$
$384$	−7.62281e127	−0.907235
$385$	−3.05531e127	−0.319704
$386$	1.16373e128	1.07098
$387$	−1.34719e127	−0.109078
$388$	−3.69745e128	−2.63470
$389$	−1.19485e128	−0.749562	−0.374781	−	0.927113i	$-0.622282\pi$
$389$	−1.19485e128	−0.749562	−0.374781	+	0.927113i	$0.622282\pi$
$390$	−3.19951e127	−0.176760
$391$	−1.13307e128	−0.551450
$392$	4.77117e128	2.04628
$393$	9.77117e127	0.369416
$394$	6.94438e128	2.31510
$395$	2.59101e127	0.0761927
$396$	1.39954e129	3.63140
$397$	−8.36626e128	−1.91602	−0.958012	−	0.286727i	$-0.907433\pi$
$397$	−8.36626e128	−1.91602	−0.958012	+	0.286727i	$0.907433\pi$
$398$	−8.23470e128	−1.66508
$399$	1.66588e128	0.297498
$400$	−2.07697e129	−3.27688
$401$	1.41593e129	1.97421	0.987107	−	0.160059i	$-0.0511685\pi$
$401$	1.41593e129	1.97421	0.987107	+	0.160059i	$0.0511685\pi$
$402$	5.95221e128	0.733650
$403$	5.19530e128	0.566254
$404$	−2.70653e129	−2.60937
$405$	−3.34412e128	−0.285271
$406$	−1.03279e128	−0.0779784
$407$	9.09246e128	0.607796
$408$	−1.58616e129	−0.939008
$409$	1.37636e129	0.721819	0.360909	−	0.932601i	$-0.382466\pi$
$409$	1.37636e129	0.721819	0.360909	+	0.932601i	$0.382466\pi$
$410$	4.66976e128	0.217017
$411$	3.64746e128	0.150252
$412$	3.62635e129	1.32452
$413$	−1.66562e129	−0.539571
$414$	−3.26268e129	−0.937688
$415$	9.54158e127	0.0243354
$416$	1.66691e130	3.77392
$417$	1.76107e129	0.354031
$418$	−2.77998e130	−4.96382
$419$	1.18071e129	0.187305	0.0936526	−	0.995605i	$-0.470146\pi$
$419$	1.18071e129	0.187305	0.0936526	+	0.995605i	$0.470146\pi$
$420$	1.15052e129	0.162202
$421$	−9.31891e128	−0.116789	−0.0583944	−	0.998294i	$-0.518598\pi$
$421$	−9.31891e128	−0.116789	−0.0583944	+	0.998294i	$0.518598\pi$
$422$	1.04941e130	1.16944
$423$	−3.51374e129	−0.348274
$424$	4.42346e130	3.90079
$425$	−1.17455e130	−0.921761
$426$	−2.42007e129	−0.169065
$427$	1.56226e130	0.971794
$428$	−8.11204e130	−4.49431
$429$	7.36370e129	0.363463
$430$	1.84816e129	0.0812924
$431$	8.65057e129	0.339172	0.169586	−	0.985515i	$-0.445757\pi$
$431$	8.65057e129	0.339172	0.169586	+	0.985515i	$0.445757\pi$
$432$	−5.48381e130	−1.91707
$433$	−8.67048e129	−0.270329	−0.135164	−	0.990823i	$-0.543156\pi$
$433$	−8.67048e129	−0.270329	−0.135164	+	0.990823i	$0.543156\pi$
$434$	−2.55043e130	−0.709368
$435$	2.46048e128	0.00610664
$436$	1.68921e131	3.74199
$437$	4.74725e130	0.938881
$438$	1.00540e130	0.177570
$439$	−2.50512e130	−0.395216	−0.197608	−	0.980281i	$-0.563317\pi$
$439$	−2.50512e130	−0.395216	−0.197608	+	0.980281i	$0.563317\pi$
$440$	−1.21884e131	−1.71806
$441$	4.49557e130	0.566336
$442$	1.75310e131	1.97426
$443$	−2.67742e130	−0.269607	−0.134804	−	0.990872i	$-0.543040\pi$
$443$	−2.67742e130	−0.269607	−0.134804	+	0.990872i	$0.543040\pi$
$444$	−3.42391e130	−0.308365
$445$	7.97733e129	0.0642743
$446$	1.79973e131	1.29758
$447$	−8.22060e129	−0.0530495
$448$	−4.11219e131	−2.37581
$449$	−2.52889e131	−1.30839	−0.654194	−	0.756327i	$-0.726992\pi$
$449$	−2.52889e131	−1.30839	−0.654194	+	0.756327i	$0.726992\pi$
$450$	−3.38213e131	−1.56737
$451$	−1.07475e131	−0.446240
$452$	3.66003e131	1.36186
$453$	−4.81810e130	−0.160700
$454$	2.26974e131	0.678754
$455$	−8.07246e130	−0.216492
$456$	6.64560e131	1.59873
$457$	−3.01784e131	−0.651395	−0.325698	−	0.945474i	$-0.605599\pi$
$457$	−3.01784e131	−0.651395	−0.325698	+	0.945474i	$0.605599\pi$
$458$	9.95885e131	1.92916
$459$	−3.10115e131	−0.539256
$460$	3.27865e131	0.511896
$461$	−2.92541e131	−0.410196	−0.205098	−	0.978741i	$-0.565751\pi$
$461$	−2.92541e131	−0.410196	−0.205098	+	0.978741i	$0.565751\pi$
$462$	−3.61491e131	−0.455324
$463$	−9.30561e131	−1.05314	−0.526569	−	0.850132i	$-0.676522\pi$
$463$	−9.30561e131	−1.05314	−0.526569	+	0.850132i	$0.676522\pi$
$464$	−2.38399e131	−0.242473
$465$	6.07604e130	0.0555519
$466$	−2.12385e132	−1.74591
$467$	2.03544e132	1.50478	0.752388	−	0.658720i	$-0.228902\pi$
$467$	2.03544e132	1.50478	0.752388	+	0.658720i	$0.228902\pi$
$468$	3.69774e132	2.45905
$469$	1.50176e132	0.898557
$470$	4.82035e131	0.259558
$471$	−8.48433e131	−0.411228
$472$	−6.64457e132	−2.89960
$473$	−4.25355e131	−0.167157
$474$	3.06558e131	0.108514
$475$	4.92104e132	1.56936
$476$	−6.30405e132	−1.81165
$477$	4.16794e132	1.07960
$478$	−7.53237e132	−1.75894
$479$	−5.32664e131	−0.112162	−0.0560810	−	0.998426i	$-0.517860\pi$
$479$	−5.32664e131	−0.112162	−0.0560810	+	0.998426i	$0.517860\pi$
$480$	1.94949e132	0.370238
$481$	2.40233e132	0.411577
$482$	−9.96492e132	−1.54044
$483$	6.17302e131	0.0861222
$484$	2.24444e133	2.82658
$485$	3.03404e132	0.344989
$486$	−1.35561e133	−1.39200
$487$	−1.86038e133	−1.72552	−0.862758	−	0.505617i	$-0.831265\pi$
$487$	−1.86038e133	−1.72552	−0.862758	+	0.505617i	$0.831265\pi$
$488$	6.23226e133	5.22233
$489$	−2.68571e132	−0.203362
$490$	−6.16728e132	−0.422073
$491$	1.36922e133	0.847106	0.423553	−	0.905871i	$-0.360783\pi$
$491$	1.36922e133	0.847106	0.423553	+	0.905871i	$0.360783\pi$
$492$	4.04714e132	0.226400
$493$	−1.34817e132	−0.0682059
$494$	−7.34503e133	−3.36132
$495$	−1.14843e133	−0.475497
$496$	−5.88713e133	−2.20577
$497$	−6.10592e132	−0.207066
$498$	1.12892e132	0.0346586
$499$	−3.35713e132	−0.0933236	−0.0466618	−	0.998911i	$-0.514858\pi$
$499$	−3.35713e132	−0.0933236	−0.0466618	+	0.998911i	$0.514858\pi$
$500$	7.29878e133	1.83753
$501$	−9.99809e132	−0.228008
$502$	1.06544e134	2.20137
$503$	5.31160e133	0.994512	0.497256	−	0.867604i	$-0.334341\pi$
$503$	5.31160e133	0.994512	0.497256	+	0.867604i	$0.334341\pi$
$504$	−1.15237e134	−1.95559
$505$	2.22092e133	0.341672
$506$	−1.03014e134	−1.43697
$507$	−1.42243e132	−0.0179943
$508$	3.06143e134	3.51294
$509$	−1.65463e134	−1.72255	−0.861273	−	0.508143i	$-0.830332\pi$
$509$	−1.65463e134	−1.72255	−0.861273	+	0.508143i	$0.830332\pi$
$510$	2.05029e133	0.193683
$511$	2.53665e133	0.217484
$512$	−2.64920e134	−2.06182
$513$	1.29930e134	0.918120
$514$	2.26302e134	1.45216
$515$	−2.97570e133	−0.173433
$516$	1.60174e133	0.0848071
$517$	−1.10941e134	−0.533715
$518$	−1.17933e134	−0.515599
$519$	−7.91757e131	−0.00314636
$520$	−3.22031e134	−1.16341
$521$	6.72181e133	0.220810	0.110405	−	0.993887i	$-0.464785\pi$
$521$	6.72181e133	0.220810	0.110405	+	0.993887i	$0.464785\pi$
$522$	−3.88207e133	−0.115978
$523$	−1.66421e134	−0.452246	−0.226123	−	0.974099i	$-0.572605\pi$
$523$	−1.66421e134	−0.452246	−0.226123	+	0.974099i	$0.572605\pi$
$524$	1.54921e135	3.83011
$525$	6.39901e133	0.143955
$526$	−1.03479e135	−2.11864
$527$	−3.32923e134	−0.620467
$528$	−8.34428e134	−1.41583
$529$	−4.71313e134	−0.728205
$530$	−5.71783e134	−0.804592
$531$	−6.26075e134	−0.802505
$532$	2.64123e135	3.08447
$533$	−2.83961e134	−0.302177
$534$	9.43846e133	0.0915396
$535$	6.65656e134	0.588488
$536$	5.99091e135	4.82876
$537$	2.07207e134	0.152292
$538$	−5.51720e135	−3.69825
$539$	1.41941e135	0.867886
$540$	8.97351e134	0.500577
$541$	1.65804e135	0.843978	0.421989	−	0.906601i	$-0.361332\pi$
$541$	1.65804e135	0.843978	0.421989	+	0.906601i	$0.361332\pi$
$542$	−2.98970e135	−1.38887
$543$	8.38589e134	0.355597
$544$	−1.06818e136	−4.13524
$545$	−1.38613e135	−0.489979
$546$	−9.55101e134	−0.308328
$547$	2.22724e135	0.656740	0.328370	−	0.944549i	$-0.393501\pi$
$547$	2.22724e135	0.656740	0.328370	+	0.944549i	$0.393501\pi$
$548$	5.78301e135	1.55782
$549$	5.87225e135	1.44535
$550$	−1.06785e136	−2.40192
$551$	5.64847e134	0.116125
$552$	2.46257e135	0.462812
$553$	7.73456e134	0.132905
$554$	−5.93741e135	−0.932961
$555$	2.80958e134	0.0403775
$556$	2.79215e136	3.67060
$557$	4.12341e135	0.495934	0.247967	−	0.968768i	$-0.420238\pi$
$557$	4.12341e135	0.495934	0.247967	+	0.968768i	$0.420238\pi$
$558$	−9.58658e135	−1.05504
$559$	−1.12384e135	−0.113193
$560$	9.14743e135	0.843319
$561$	−4.71877e135	−0.398261
$562$	−7.85607e135	−0.607097
$563$	−1.98383e136	−1.40391	−0.701955	−	0.712221i	$-0.747689\pi$
$563$	−1.98383e136	−1.40391	−0.701955	+	0.712221i	$0.747689\pi$
$564$	4.17765e135	0.270780
$565$	−3.00334e135	−0.178322
$566$	1.83255e136	0.996881
$567$	−9.98270e135	−0.497607
$568$	−2.43580e136	−1.11276
$569$	−9.86907e135	−0.413256	−0.206628	−	0.978420i	$-0.566249\pi$
$569$	−9.86907e135	−0.413256	−0.206628	+	0.978420i	$0.566249\pi$
$570$	−8.59019e135	−0.329760
$571$	−8.98219e134	−0.0316151	−0.0158076	−	0.999875i	$-0.505032\pi$
$571$	−8.98219e134	−0.0316151	−0.0158076	+	0.999875i	$0.505032\pi$
$572$	1.16751e137	3.76839
$573$	−6.66566e135	−0.197328
$574$	1.39399e136	0.378549
$575$	1.82353e136	0.454312
$576$	−1.54569e137	−3.53355
$577$	−5.82852e136	−1.22280	−0.611400	−	0.791322i	$-0.709393\pi$
$577$	−5.82852e136	−1.22280	−0.611400	+	0.791322i	$0.709393\pi$
$578$	−1.19332e136	−0.229788
$579$	−8.27608e135	−0.146297
$580$	3.90107e135	0.0633137
$581$	2.84830e135	0.0424490
$582$	3.58976e136	0.491335
$583$	1.31596e137	1.65444
$584$	1.01193e137	1.16874
$585$	−3.03429e136	−0.321989
$586$	1.81277e137	1.76771
$587$	−1.52532e137	−1.36702	−0.683511	−	0.729941i	$-0.739548\pi$
$587$	−1.52532e137	−1.36702	−0.683511	+	0.729941i	$0.739548\pi$
$588$	−5.34500e136	−0.440322
$589$	1.39486e137	1.05639
$590$	8.58887e136	0.598083
$591$	−4.93863e136	−0.316247
$592$	−2.72224e137	−1.60325
$593$	2.39449e137	1.29720	0.648599	−	0.761130i	$-0.275355\pi$
$593$	2.39449e137	1.29720	0.648599	+	0.761130i	$0.275355\pi$
$594$	−2.81945e137	−1.40519
$595$	5.17296e136	0.237219
$596$	−1.30337e137	−0.550018
$597$	5.85628e136	0.227453
$598$	−2.72175e137	−0.973061
$599$	−3.10264e137	−1.02118	−0.510591	−	0.859824i	$-0.670573\pi$
$599$	−3.10264e137	−1.02118	−0.510591	+	0.859824i	$0.670573\pi$
$600$	2.55273e137	0.773601
$601$	−5.55438e137	−1.55006	−0.775031	−	0.631923i	$-0.782266\pi$
$601$	−5.55438e137	−1.55006	−0.775031	+	0.631923i	$0.782266\pi$
$602$	5.51703e136	0.141801
$603$	5.64484e137	1.33643
$604$	−7.63904e137	−1.66614
$605$	−1.84173e137	−0.370114
$606$	2.62770e137	0.486611
$607$	2.49301e137	0.425485	0.212742	−	0.977108i	$-0.431761\pi$
$607$	2.49301e137	0.425485	0.212742	+	0.977108i	$0.431761\pi$
$608$	4.47540e138	7.04053
$609$	7.34491e135	0.0106520
$610$	−8.05591e137	−1.07718
$611$	−2.93118e137	−0.361412
$612$	−2.36957e138	−2.69448
$613$	−1.14723e137	−0.120325	−0.0601625	−	0.998189i	$-0.519162\pi$
$613$	−1.14723e137	−0.120325	−0.0601625	+	0.998189i	$0.519162\pi$
$614$	4.60103e137	0.445165
$615$	−3.32099e136	−0.0296449
$616$	−3.63842e138	−2.99686
$617$	1.08609e138	0.825560	0.412780	−	0.910831i	$-0.364558\pi$
$617$	1.08609e138	0.825560	0.412780	+	0.910831i	$0.364558\pi$
$618$	−3.52073e137	−0.247003
$619$	1.41284e138	0.914968	0.457484	−	0.889218i	$-0.348751\pi$
$619$	1.41284e138	0.914968	0.457484	+	0.889218i	$0.348751\pi$
$620$	9.63349e137	0.575963
$621$	4.81465e137	0.265785
$622$	−9.21389e137	−0.469698
$623$	2.38135e137	0.112116
$624$	−2.20465e138	−0.958745
$625$	1.57025e138	0.630824
$626$	6.93109e138	2.57260
$627$	1.97704e138	0.678066
$628$	−1.34518e139	−4.26362
$629$	−1.53945e138	−0.450982
$630$	1.48956e138	0.403368
$631$	−3.56283e138	−0.891953	−0.445976	−	0.895045i	$-0.647144\pi$
$631$	−3.56283e138	−0.891953	−0.445976	+	0.895045i	$0.647144\pi$
$632$	3.08551e138	0.714219
$633$	−7.46310e137	−0.159748
$634$	1.49696e139	2.96340
$635$	−2.51214e138	−0.459986
$636$	−4.95547e138	−0.839378
$637$	3.75023e138	0.587701
$638$	−1.22571e138	−0.177731
$639$	−2.29510e138	−0.307971
$640$	9.91741e138	1.23166
$641$	−1.38569e139	−1.59292	−0.796461	−	0.604690i	$-0.793297\pi$
$641$	−1.38569e139	−1.59292	−0.796461	+	0.604690i	$0.793297\pi$
$642$	7.87577e138	0.838126
$643$	−4.00774e138	−0.394872	−0.197436	−	0.980316i	$-0.563262\pi$
$643$	−4.00774e138	−0.394872	−0.197436	+	0.980316i	$0.563262\pi$
$644$	9.78726e138	0.892916
$645$	−1.31435e137	−0.0111047
$646$	4.70681e139	3.68313
$647$	−6.39338e138	−0.463414	−0.231707	−	0.972786i	$-0.574431\pi$
$647$	−6.39338e138	−0.463414	−0.231707	+	0.972786i	$0.574431\pi$
$648$	−3.98235e139	−2.67409
$649$	−1.97674e139	−1.22980
$650$	−2.82139e139	−1.62649
$651$	1.81379e138	0.0969009
$652$	−4.25816e139	−2.10846
$653$	2.80881e139	1.28920	0.644599	−	0.764521i	$-0.277024\pi$
$653$	2.80881e139	1.28920	0.644599	+	0.764521i	$0.277024\pi$
$654$	−1.64001e139	−0.697829
$655$	−1.27125e139	−0.501516
$656$	3.21775e139	1.17710
$657$	9.53480e138	0.323464
$658$	1.43895e139	0.452755
$659$	4.04659e138	0.118103	0.0590515	−	0.998255i	$-0.481192\pi$
$659$	4.04659e138	0.118103	0.0590515	+	0.998255i	$0.481192\pi$
$660$	1.36543e139	0.369695
$661$	5.46130e139	1.37191	0.685953	−	0.727646i	$-0.259386\pi$
$661$	5.46130e139	1.37191	0.685953	+	0.727646i	$0.259386\pi$
$662$	1.08349e140	2.52553
$663$	−1.24675e139	−0.269687
$664$	1.13626e139	0.228117
$665$	−2.16733e139	−0.403882
$666$	−4.43288e139	−0.766852
$667$	2.09308e138	0.0336169
$668$	−1.58519e140	−2.36399
$669$	−1.27992e139	−0.177251
$670$	−7.74393e139	−0.995998
$671$	1.85407e140	2.21494
$672$	5.81954e139	0.645817
$673$	2.88994e139	0.297950	0.148975	−	0.988841i	$-0.452403\pi$
$673$	2.88994e139	0.297950	0.148975	+	0.988841i	$0.452403\pi$
$674$	−2.48967e140	−2.38494
$675$	4.99091e139	0.444266
$676$	−2.25524e139	−0.186566
$677$	−1.30300e140	−1.00185	−0.500927	−	0.865490i	$-0.667007\pi$
$677$	−1.30300e140	−1.00185	−0.500927	+	0.865490i	$0.667007\pi$
$678$	−3.55343e139	−0.253967
$679$	9.05708e139	0.601775
$680$	2.06362e140	1.27479
$681$	−1.61417e139	−0.0927189
$682$	−3.02682e140	−1.61681
$683$	−1.78510e140	−0.886824	−0.443412	−	0.896318i	$-0.646232\pi$
$683$	−1.78510e140	−0.886824	−0.443412	+	0.896318i	$0.646232\pi$
$684$	9.92788e140	4.58754
$685$	−4.74541e139	−0.203981
$686$	−4.86503e140	−1.94555
$687$	−7.08243e139	−0.263526
$688$	1.27349e140	0.440928
$689$	3.47692e140	1.12032
$690$	−3.18316e139	−0.0954614
$691$	−3.94939e140	−1.10247	−0.551235	−	0.834350i	$-0.685843\pi$
$691$	−3.94939e140	−1.10247	−0.551235	+	0.834350i	$0.685843\pi$
$692$	−1.25532e139	−0.0326215
$693$	−3.42824e140	−0.829424
$694$	−8.70039e139	−0.195995
$695$	−2.29118e140	−0.480630
$696$	2.93007e139	0.0572428
$697$	1.81967e140	0.331108
$698$	2.02629e141	3.43446
$699$	1.51042e140	0.238494
$700$	1.01456e141	1.49253
$701$	9.14278e139	0.125325	0.0626623	−	0.998035i	$-0.480041\pi$
$701$	9.14278e139	0.125325	0.0626623	+	0.998035i	$0.480041\pi$
$702$	−7.44931e140	−0.951544
$703$	6.44989e140	0.767828
$704$	−4.88029e141	−5.41501
$705$	−3.42809e139	−0.0354561
$706$	−1.58181e141	−1.52518
$707$	6.62978e140	0.595989
$708$	7.44371e140	0.623941
$709$	−9.83283e140	−0.768581	−0.384291	−	0.923212i	$-0.625554\pi$
$709$	−9.83283e140	−0.768581	−0.384291	+	0.923212i	$0.625554\pi$
$710$	3.14855e140	0.229521
$711$	2.90728e140	0.197670
$712$	9.49982e140	0.602498
$713$	5.16875e140	0.305812
$714$	6.12044e140	0.337848
$715$	−9.58029e140	−0.493435
$716$	3.28525e141	1.57897
$717$	5.35679e140	0.240274
$718$	7.75183e141	3.24522
$719$	−4.55372e141	−1.77945	−0.889727	−	0.456494i	$-0.849105\pi$
$719$	−4.55372e141	−1.77945	−0.889727	+	0.456494i	$0.849105\pi$
$720$	3.43835e141	1.25427
$721$	−8.88291e140	−0.302524
$722$	−1.36399e142	−4.33730
$723$	7.08676e140	0.210427
$724$	1.32957e142	3.68683
$725$	2.16971e140	0.0561914
$726$	−2.17907e141	−0.527118
$727$	2.67121e141	0.603608	0.301804	−	0.953370i	$-0.402411\pi$
$727$	2.67121e141	0.603608	0.301804	+	0.953370i	$0.402411\pi$
$728$	−9.61310e141	−2.02937
$729$	−3.06962e141	−0.605442
$730$	−1.30804e141	−0.241068
$731$	7.20172e140	0.124030
$732$	−6.98181e141	−1.12375
$733$	−7.44783e141	−1.12043	−0.560213	−	0.828349i	$-0.689281\pi$
$733$	−7.44783e141	−1.12043	−0.560213	+	0.828349i	$0.689281\pi$
$734$	−1.27838e142	−1.79765
$735$	4.38599e140	0.0576560
$736$	1.65839e142	2.03815
$737$	1.78227e142	2.04802
$738$	5.23976e141	0.563017
$739$	6.83854e141	0.687169	0.343585	−	0.939122i	$-0.388359\pi$
$739$	6.83854e141	0.687169	0.343585	+	0.939122i	$0.388359\pi$
$740$	4.45457e141	0.418635
$741$	5.22356e141	0.459162
$742$	−1.70686e142	−1.40347
$743$	−1.02755e142	−0.790420	−0.395210	−	0.918591i	$-0.629328\pi$
$743$	−1.02755e142	−0.790420	−0.395210	+	0.918591i	$0.629328\pi$
$744$	7.23566e141	0.520736
$745$	1.06951e141	0.0720197
$746$	2.10046e142	1.32356
$747$	1.07062e141	0.0631346
$748$	−7.48156e142	−4.12917
$749$	1.98708e142	1.02652
$750$	−7.08621e141	−0.342674
$751$	2.68344e142	1.21483	0.607413	−	0.794386i	$-0.292207\pi$
$751$	2.68344e142	1.21483	0.607413	+	0.794386i	$0.292207\pi$
$752$	3.32151e142	1.40784
$753$	−7.57707e141	−0.300711
$754$	−3.23845e141	−0.120353
$755$	6.26843e141	0.218165
$756$	2.67873e142	0.873172
$757$	−7.90246e141	−0.241277	−0.120639	−	0.992697i	$-0.538494\pi$
$757$	−7.90246e141	−0.241277	−0.120639	+	0.992697i	$0.538494\pi$
$758$	4.45096e142	1.27300
$759$	7.32606e141	0.196292
$760$	−8.64604e142	−2.17042
$761$	−2.76766e142	−0.650988	−0.325494	−	0.945544i	$-0.605531\pi$
$761$	−2.76766e142	−0.650988	−0.325494	+	0.945544i	$0.605531\pi$
$762$	−2.97226e142	−0.655113
$763$	−4.13781e142	−0.854684
$764$	−1.05683e143	−2.04590
$765$	1.94442e142	0.352816
$766$	2.17105e143	3.69272
$767$	−5.22276e142	−0.832779
$768$	5.02279e142	0.750870
$769$	−1.15768e143	−1.62269	−0.811347	−	0.584566i	$-0.801265\pi$
$769$	−1.15768e143	−1.62269	−0.811347	+	0.584566i	$0.801265\pi$
$770$	4.70307e142	0.618145
$771$	−1.60939e142	−0.198368
$772$	−1.31216e143	−1.51681
$773$	−2.07069e142	−0.224507	−0.112253	−	0.993680i	$-0.535807\pi$
$773$	−2.07069e142	−0.224507	−0.112253	+	0.993680i	$0.535807\pi$
$774$	2.07375e142	0.210901
$775$	5.35798e142	0.511171
$776$	3.61310e143	3.23388
$777$	8.38704e141	0.0704317
$778$	1.83924e143	1.44927
$779$	−7.62392e142	−0.563734
$780$	3.60761e142	0.250344
$781$	−7.24643e142	−0.471952
$782$	1.74414e143	1.06622
$783$	5.72866e141	0.0328735
$784$	−4.24963e143	−2.28932
$785$	1.10383e143	0.558280
$786$	−1.50409e143	−0.714261
$787$	1.34529e143	0.599885	0.299943	−	0.953957i	$-0.403032\pi$
$787$	1.34529e143	0.599885	0.299943	+	0.953957i	$0.403032\pi$
$788$	−7.83015e143	−3.27886
$789$	7.35909e142	0.289409
$790$	−3.98837e142	−0.147318
$791$	−8.96542e142	−0.311053
$792$	−1.36761e144	−4.45724
$793$	4.89867e143	1.49988
$794$	1.28783e144	3.70461
$795$	4.06635e142	0.109909
$796$	9.28506e143	2.35824
$797$	−3.26321e143	−0.778859	−0.389429	−	0.921056i	$-0.627328\pi$
$797$	−3.26321e143	−0.778859	−0.389429	+	0.921056i	$0.627328\pi$
$798$	−2.56430e143	−0.575209
$799$	1.87835e143	0.396014
$800$	1.71911e144	3.40681
$801$	8.95106e142	0.166750
$802$	−2.17955e144	−3.81712
$803$	3.01047e143	0.495695
$804$	−6.71143e143	−1.03906
$805$	−8.03121e142	−0.116919
$806$	−7.99719e143	−1.09485
$807$	3.92367e143	0.505187
$808$	2.64479e144	3.20279
$809$	−9.17846e143	−1.04549	−0.522743	−	0.852490i	$-0.675091\pi$
$809$	−9.17846e143	−1.04549	−0.522743	+	0.852490i	$0.675091\pi$
$810$	5.14764e143	0.551569
$811$	−7.89187e143	−0.795513	−0.397757	−	0.917491i	$-0.630211\pi$
$811$	−7.89187e143	−0.795513	−0.397757	+	0.917491i	$0.630211\pi$
$812$	1.16453e143	0.110440
$813$	2.12619e143	0.189723
$814$	−1.39961e144	−1.17517
$815$	3.49415e143	0.276083
$816$	1.41278e144	1.05054
$817$	−3.01733e143	−0.211169
$818$	−2.11865e144	−1.39563
$819$	−9.05781e143	−0.561655
$820$	−5.26540e143	−0.307359
$821$	3.00742e144	1.65275	0.826376	−	0.563118i	$-0.190398\pi$
$821$	3.00742e144	1.65275	0.826376	+	0.563118i	$0.190398\pi$
$822$	−5.61458e143	−0.290511
$823$	1.16005e144	0.565178	0.282589	−	0.959241i	$-0.408807\pi$
$823$	1.16005e144	0.565178	0.282589	+	0.959241i	$0.408807\pi$
$824$	−3.54362e144	−1.62574
$825$	7.59426e143	0.328107
$826$	2.56391e144	1.04325
$827$	−3.90585e144	−1.49690	−0.748450	−	0.663192i	$-0.769201\pi$
$827$	−3.90585e144	−1.49690	−0.748450	+	0.663192i	$0.769201\pi$
$828$	3.67885e144	1.32804
$829$	4.28000e143	0.145544	0.0727720	−	0.997349i	$-0.476815\pi$
$829$	4.28000e143	0.145544	0.0727720	+	0.997349i	$0.476815\pi$
$830$	−1.46875e143	−0.0470523
$831$	4.22251e143	0.127444
$832$	−1.28943e145	−3.66685
$833$	−2.40321e144	−0.643967
$834$	−2.71083e144	−0.684514
$835$	1.30077e144	0.309542
$836$	3.13458e145	7.03021
$837$	1.41466e144	0.299049
$838$	−1.81748e144	−0.362152
$839$	5.82834e144	1.09478	0.547391	−	0.836877i	$-0.315621\pi$
$839$	5.82834e144	1.09478	0.547391	+	0.836877i	$0.315621\pi$
$840$	−1.12428e144	−0.199089
$841$	−5.96475e144	−0.995842
$842$	1.43447e144	0.225810
$843$	5.58700e143	0.0829304
$844$	−1.18327e145	−1.65627
$845$	1.85060e143	0.0244290
$846$	5.40874e144	0.673384
$847$	−5.49786e144	−0.645601
$848$	−3.93993e145	−4.36409
$849$	−1.30326e144	−0.136176
$850$	1.80799e145	1.78221
$851$	2.39005e144	0.222277
$852$	2.72876e144	0.239445
$853$	−1.78007e145	−1.47388	−0.736938	−	0.675960i	$-0.763729\pi$
$853$	−1.78007e145	−1.47388	−0.736938	+	0.675960i	$0.763729\pi$
$854$	−2.40481e145	−1.87895
$855$	−8.14660e144	−0.600695
$856$	7.92697e145	5.51640
$857$	7.01094e143	0.0460496	0.0230248	−	0.999735i	$-0.492670\pi$
$857$	7.01094e143	0.0460496	0.0230248	+	0.999735i	$0.492670\pi$
$858$	−1.13350e145	−0.702751
$859$	1.71574e145	1.00413	0.502064	−	0.864830i	$-0.332574\pi$
$859$	1.71574e145	1.00413	0.502064	+	0.864830i	$0.332574\pi$
$860$	−2.08389e144	−0.115134
$861$	−9.91367e143	−0.0517105
$862$	−1.33159e145	−0.655785
$863$	−2.85672e145	−1.32841	−0.664206	−	0.747549i	$-0.731230\pi$
$863$	−2.85672e145	−1.32841	−0.664206	+	0.747549i	$0.731230\pi$
$864$	4.53894e145	1.99308
$865$	1.03009e143	0.00427147
$866$	1.33466e145	0.522678
$867$	8.48651e143	0.0313895
$868$	2.87574e145	1.00467
$869$	9.17928e144	0.302921
$870$	−3.78745e143	−0.0118071
$871$	4.70896e145	1.38684
$872$	−1.65068e146	−4.59299
$873$	3.40439e145	0.895022
$874$	−7.30749e145	−1.81532
$875$	−1.78787e145	−0.419699
$876$	−1.13364e145	−0.251490
$877$	−8.76907e143	−0.0183854	−0.00919271	−	0.999958i	$-0.502926\pi$
$877$	−8.76907e143	−0.0183854	−0.00919271	+	0.999958i	$0.502926\pi$
$878$	3.85616e145	0.764145
$879$	−1.28919e145	−0.241472
$880$	1.08561e146	1.92212
$881$	1.00378e146	1.68008	0.840041	−	0.542523i	$-0.182531\pi$
$881$	1.00378e146	1.68008	0.840041	+	0.542523i	$0.182531\pi$
$882$	−6.92008e145	−1.09500
$883$	6.84113e145	1.02347	0.511733	−	0.859145i	$-0.329004\pi$
$883$	6.84113e145	1.02347	0.511733	+	0.859145i	$0.329004\pi$
$884$	−1.97671e146	−2.79612
$885$	−6.10815e144	−0.0816992
$886$	4.12138e145	0.521283
$887$	1.28947e146	1.54238	0.771192	−	0.636603i	$-0.219661\pi$
$887$	1.28947e146	1.54238	0.771192	+	0.636603i	$0.219661\pi$
$888$	3.34580e145	0.378493
$889$	−7.49912e145	−0.802367
$890$	−1.22796e145	−0.124274
$891$	−1.18473e146	−1.13416
$892$	−2.02929e146	−1.83774
$893$	−7.86978e145	−0.674241
$894$	1.26541e145	0.102571
$895$	−2.69580e145	−0.206751
$896$	2.96050e146	2.14841
$897$	1.93563e145	0.132922
$898$	3.89275e146	2.52975
$899$	6.14999e144	0.0378242
$900$	3.81353e146	2.21984
$901$	−2.22807e146	−1.22758
$902$	1.65437e146	0.862800
$903$	−3.92354e144	−0.0193702
$904$	−3.57653e146	−1.67157
$905$	−1.09102e146	−0.482756
$906$	7.41655e145	0.310711
$907$	−3.83792e146	−1.52242	−0.761210	−	0.648505i	$-0.775395\pi$
$907$	−3.83792e146	−1.52242	−0.761210	+	0.648505i	$0.775395\pi$
$908$	−2.55926e146	−0.961311
$909$	2.49201e146	0.886416
$910$	1.24260e146	0.418585
$911$	−6.33858e145	−0.202224	−0.101112	−	0.994875i	$-0.532240\pi$
$911$	−6.33858e145	−0.202224	−0.101112	+	0.994875i	$0.532240\pi$
$912$	−5.91916e146	−1.78861
$913$	3.38033e145	0.0967511
$914$	4.64540e146	1.25947
$915$	5.72912e145	0.147144
$916$	−1.12291e147	−2.73225
$917$	−3.79486e146	−0.874810
$918$	4.77364e146	1.04265
$919$	8.77393e146	1.81583	0.907917	−	0.419150i	$-0.137672\pi$
$919$	8.77393e146	1.81583	0.907917	+	0.419150i	$0.137672\pi$
$920$	−3.20385e146	−0.628311
$921$	−3.27212e145	−0.0608103
$922$	4.50312e146	0.793109
$923$	−1.91459e146	−0.319588
$924$	4.07601e146	0.644870
$925$	2.47755e146	0.371541
$926$	1.43242e147	2.03623
$927$	−3.33892e146	−0.449945
$928$	1.97322e146	0.252088
$929$	−3.48231e146	−0.421783	−0.210892	−	0.977509i	$-0.567637\pi$
$929$	−3.48231e146	−0.421783	−0.210892	+	0.977509i	$0.567637\pi$
$930$	−9.35291e145	−0.107409
$931$	1.00688e147	1.09640
$932$	2.39476e147	2.47271
$933$	6.55264e145	0.0641616
$934$	−3.13317e147	−2.90947
$935$	6.13920e146	0.540676
$936$	−3.61339e147	−3.01828
$937$	−7.60769e146	−0.602758	−0.301379	−	0.953504i	$-0.597447\pi$
$937$	−7.60769e146	−0.602758	−0.301379	+	0.953504i	$0.597447\pi$
$938$	−2.31168e147	−1.73735
$939$	−4.92919e146	−0.351422
$940$	−5.43520e146	−0.367610
$941$	8.96692e146	0.575383	0.287691	−	0.957723i	$-0.407112\pi$
$941$	8.96692e146	0.575383	0.287691	+	0.957723i	$0.407112\pi$
$942$	1.30600e147	0.795105
$943$	−2.82510e146	−0.163194
$944$	5.91825e147	3.24399
$945$	−2.19810e146	−0.114334
$946$	6.54754e146	0.323196
$947$	1.17443e147	0.550180	0.275090	−	0.961418i	$-0.411292\pi$
$947$	1.17443e147	0.550180	0.275090	+	0.961418i	$0.411292\pi$
$948$	−3.45660e146	−0.153687
$949$	7.95399e146	0.335666
$950$	−7.57501e147	−3.03434
$951$	−1.06459e147	−0.404806
$952$	6.16023e147	2.22366
$953$	−2.75038e147	−0.942527	−0.471264	−	0.881992i	$-0.656202\pi$
$953$	−2.75038e147	−0.942527	−0.471264	+	0.881992i	$0.656202\pi$
$954$	−6.41576e147	−2.08739
$955$	8.67213e146	0.267892
$956$	8.49314e147	2.49117
$957$	8.71685e145	0.0242783
$958$	8.19936e146	0.216864
$959$	−1.41658e147	−0.355811
$960$	−1.50802e147	−0.359733
$961$	−2.89504e147	−0.655914
$962$	−3.69794e147	−0.795780
$963$	7.46907e147	1.52674
$964$	1.12360e148	2.18171
$965$	1.07673e147	0.198612
$966$	−9.50220e146	−0.166516
$967$	8.89246e147	1.48051	0.740255	−	0.672326i	$-0.234705\pi$
$967$	8.89246e147	1.48051	0.740255	+	0.672326i	$0.234705\pi$
$968$	−2.19323e148	−3.46940
$969$	−3.34734e147	−0.503122
$970$	−4.67034e147	−0.667033
$971$	6.23935e146	0.0846813	0.0423406	−	0.999103i	$-0.486519\pi$
$971$	6.23935e146	0.0846813	0.0423406	+	0.999103i	$0.486519\pi$
$972$	1.52852e148	1.97147
$973$	−6.83951e147	−0.838377
$974$	2.86371e148	3.33627
$975$	2.00649e147	0.222182
$976$	−5.55100e148	−5.84259
$977$	9.53759e147	0.954241	0.477120	−	0.878838i	$-0.341681\pi$
$977$	9.53759e147	0.954241	0.477120	+	0.878838i	$0.341681\pi$
$978$	4.13414e147	0.393199
$979$	2.82616e147	0.255537
$980$	6.95394e147	0.597778
$981$	−1.55532e148	−1.27117
$982$	−2.10765e148	−1.63787
$983$	−1.49619e148	−1.10558	−0.552788	−	0.833322i	$-0.686436\pi$
$983$	−1.49619e148	−1.10558	−0.552788	+	0.833322i	$0.686436\pi$
$984$	−3.95481e147	−0.277887
$985$	6.42525e147	0.429335
$986$	2.07525e147	0.131875
$987$	−1.02334e147	−0.0618471
$988$	8.28190e148	4.76060
$989$	−1.11809e147	−0.0611310
$990$	1.76779e148	0.919368
$991$	−1.65465e148	−0.818577	−0.409289	−	0.912405i	$-0.634223\pi$
$991$	−1.65465e148	−0.818577	−0.409289	+	0.912405i	$0.634223\pi$
$992$	4.87277e148	2.29323
$993$	−7.70543e147	−0.344992
$994$	9.39891e147	0.400361
$995$	−7.61912e147	−0.308789
$996$	−1.27292e147	−0.0490866
$997$	−3.26412e148	−1.19772	−0.598860	−	0.800854i	$-0.704379\pi$
$997$	−3.26412e148	−1.19772	−0.598860	+	0.800854i	$0.704379\pi$
$998$	5.16767e147	0.180440
$999$	6.54147e147	0.217362

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1.100.a.a.1.1	✓	8
3.2	odd	2		9.100.a.d.1.8		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1.100.a.a.1.1	✓	8	1.1	even	1	trivial
9.100.a.d.1.8		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 $\F_{q}$
Belyi maps

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

\(f(q)\)	\(=\)	\(q-1.53931e15 q^{2} +1.09471e23 q^{3} +1.73565e30 q^{4} -1.42424e34 q^{5} -1.68510e38 q^{6} -4.25157e41 q^{7} -1.69606e45 q^{8} -1.59809e47 q^{9} +2.19235e49 q^{10} -5.04571e51 q^{11} +1.90004e53 q^{12} -1.33313e55 q^{13} +6.54449e56 q^{14} -1.55913e57 q^{15} +1.51066e60 q^{16} +8.54293e60 q^{17} +2.45995e62 q^{18} -3.57926e63 q^{19} -2.47199e64 q^{20} -4.65425e64 q^{21} +7.76692e66 q^{22} -1.32632e67 q^{23} -1.85670e68 q^{24} -1.37488e69 q^{25} +2.05211e70 q^{26} -3.63008e70 q^{27} -7.37926e71 q^{28} -1.57811e71 q^{29} +2.39999e72 q^{30} -3.89706e73 q^{31} -1.25037e75 q^{32} -5.52360e74 q^{33} -1.31502e76 q^{34} +6.05525e75 q^{35} -2.77372e77 q^{36} -1.80202e77 q^{37} +5.50960e78 q^{38} -1.45940e78 q^{39} +2.41559e79 q^{40} +2.13003e79 q^{41} +7.16433e79 q^{42} +8.43003e79 q^{43} -8.75761e81 q^{44} +2.27606e81 q^{45} +2.04162e82 q^{46} +2.19872e82 q^{47} +1.65374e83 q^{48} -2.81310e83 q^{49} +2.11636e84 q^{50} +9.35205e83 q^{51} -2.31386e85 q^{52} -2.60808e85 q^{53} +5.58782e85 q^{54} +7.18630e85 q^{55} +7.21091e86 q^{56} -3.91826e86 q^{57} +2.42920e86 q^{58} +3.91766e87 q^{59} -2.70611e87 q^{60} -3.67456e88 q^{61} +5.99879e88 q^{62} +6.79437e88 q^{63} +9.67216e89 q^{64} +1.89870e89 q^{65} +8.50254e89 q^{66} -3.53225e90 q^{67} +1.48276e91 q^{68} -1.45194e90 q^{69} -9.32092e90 q^{70} +1.43616e91 q^{71} +2.71045e92 q^{72} -5.96639e91 q^{73} +2.77387e92 q^{74} -1.50509e92 q^{75} -6.21236e93 q^{76} +2.14522e93 q^{77} +2.24647e93 q^{78} -1.81922e93 q^{79} -2.15154e94 q^{80} +2.34800e94 q^{81} -3.27878e94 q^{82} -6.69942e93 q^{83} -8.07816e94 q^{84} -1.21672e95 q^{85} -1.29764e95 q^{86} -1.72758e94 q^{87} +8.55782e96 q^{88} -5.60112e95 q^{89} -3.50356e96 q^{90} +5.66791e96 q^{91} -2.30203e97 q^{92} -4.26616e96 q^{93} -3.38451e97 q^{94} +5.09772e97 q^{95} -1.36880e98 q^{96} -2.13029e98 q^{97} +4.33023e98 q^{98} +8.06348e98 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 208040616902520 q^{2} - 28\!\cdots\!20 q^{3} + 28\!\cdots\!24 q^{4} - 48\!\cdots\!60 q^{5} - 77\!\cdots\!44 q^{6} - 56\!\cdots\!00 q^{7} + 59\!\cdots\!60 q^{8} + 15\!\cdots\!76 q^{9} - 20\!\cdots\!60 q^{10}+ \cdots - 13\!\cdots\!08 q^{99}+O(q^{100}) \) 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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