LMFDB - Embedded newform 1.100.a.a.1.5

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			1.5
Root			$4.33987e12$ 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)

$f(q)$	$=$	\(q+2.86466e14 q^{2} +2.01536e23 q^{3} -5.51763e29 q^{4} -4.79915e34 q^{5} +5.77333e37 q^{6} -6.92478e41 q^{7} -3.39630e44 q^{8} -1.31176e47 q^{9} -1.37479e49 q^{10} +1.55674e51 q^{11} -1.11200e53 q^{12} -2.14548e55 q^{13} -1.98371e56 q^{14} -9.67203e57 q^{15} +2.52429e59 q^{16} -1.39488e61 q^{17} -3.75773e61 q^{18} +1.51628e63 q^{19} +2.64799e64 q^{20} -1.39560e65 q^{21} +4.45952e65 q^{22} +2.55387e67 q^{23} -6.84479e67 q^{24} +7.25462e68 q^{25} -6.14606e69 q^{26} -6.10591e70 q^{27} +3.82084e71 q^{28} +1.39180e72 q^{29} -2.77071e72 q^{30} -1.44293e73 q^{31} +2.87578e74 q^{32} +3.13740e74 q^{33} -3.99585e75 q^{34} +3.32331e76 q^{35} +7.23778e76 q^{36} -5.19313e77 q^{37} +4.34363e77 q^{38} -4.32392e78 q^{39} +1.62994e79 q^{40} -3.58403e79 q^{41} -3.99790e79 q^{42} +2.84099e80 q^{43} -8.58951e80 q^{44} +6.29531e81 q^{45} +7.31597e81 q^{46} -7.73779e82 q^{47} +5.08736e82 q^{48} +1.74580e82 q^{49} +2.07820e83 q^{50} -2.81119e84 q^{51} +1.18380e85 q^{52} +1.89817e84 q^{53} -1.74913e85 q^{54} -7.47103e85 q^{55} +2.35187e86 q^{56} +3.05587e86 q^{57} +3.98704e86 q^{58} -2.13540e87 q^{59} +5.33667e87 q^{60} +4.67707e88 q^{61} -4.13350e87 q^{62} +9.08362e88 q^{63} -7.76144e88 q^{64} +1.02965e90 q^{65} +8.98757e88 q^{66} +3.33536e90 q^{67} +7.69642e90 q^{68} +5.14698e90 q^{69} +9.52013e90 q^{70} +2.25284e91 q^{71} +4.45512e91 q^{72} +2.47879e90 q^{73} -1.48765e92 q^{74} +1.46207e92 q^{75} -8.36629e92 q^{76} -1.07801e93 q^{77} -1.23866e93 q^{78} -1.29965e94 q^{79} -1.21144e94 q^{80} +1.02293e94 q^{81} -1.02670e94 q^{82} -1.54205e95 q^{83} +7.70038e94 q^{84} +6.69423e95 q^{85} +8.13847e94 q^{86} +2.80499e95 q^{87} -5.28716e95 q^{88} +2.29359e96 q^{89} +1.80339e96 q^{90} +1.48570e97 q^{91} -1.40913e97 q^{92} -2.90803e96 q^{93} -2.21661e97 q^{94} -7.27688e97 q^{95} +5.79575e97 q^{96} -3.70442e98 q^{97} +5.00113e96 q^{98} -2.04206e98 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	2.86466e14	0.359822	0.179911	−	0.983683i	$-0.442419\pi$
$2$	2.86466e14	0.359822	0.179911	+	0.983683i	$0.442419\pi$
$3$	2.01536e23	0.486241	0.243120	−	0.969996i	$-0.421829\pi$
$3$	2.01536e23	0.486241	0.243120	+	0.969996i	$0.421829\pi$
$4$	−5.51763e29	−0.870528
$5$	−4.79915e34	−1.20823	−0.604114	−	0.796898i	$-0.706473\pi$
$5$	−4.79915e34	−1.20823	−0.604114	+	0.796898i	$0.706473\pi$
$6$	5.77333e37	0.174960
$7$	−6.92478e41	−1.01872	−0.509358	−	0.860555i	$-0.670117\pi$
$7$	−6.92478e41	−1.01872	−0.509358	+	0.860555i	$0.670117\pi$
$8$	−3.39630e44	−0.673057
$9$	−1.31176e47	−0.763570
$10$	−1.37479e49	−0.434747
$11$	1.55674e51	0.439823	0.219912	−	0.975520i	$-0.429423\pi$
$11$	1.55674e51	0.439823	0.219912	+	0.975520i	$0.429423\pi$
$12$	−1.11200e53	−0.423286
$13$	−2.14548e55	−1.55356	−0.776781	−	0.629771i	$-0.783149\pi$
$13$	−2.14548e55	−1.55356	−0.776781	+	0.629771i	$0.783149\pi$
$14$	−1.98371e56	−0.366557
$15$	−9.67203e57	−0.587490
$16$	2.52429e59	0.628347
$17$	−1.39488e61	−1.72709	−0.863545	−	0.504272i	$-0.831761\pi$
$17$	−1.39488e61	−1.72709	−0.863545	+	0.504272i	$0.831761\pi$
$18$	−3.75773e61	−0.274749
$19$	1.51628e63	0.762917	0.381459	−	0.924386i	$-0.375422\pi$
$19$	1.51628e63	0.762917	0.381459	+	0.924386i	$0.375422\pi$
$20$	2.64799e64	1.05180
$21$	−1.39560e65	−0.495341
$22$	4.45952e65	0.158258
$23$	2.55387e67	1.00386	0.501928	−	0.864910i	$-0.332624\pi$
$23$	2.55387e67	1.00386	0.501928	+	0.864910i	$0.332624\pi$
$24$	−6.84479e67	−0.327268
$25$	7.25462e68	0.459816
$26$	−6.14606e69	−0.559006
$27$	−6.10591e70	−0.857520
$28$	3.82084e71	0.886821
$29$	1.39180e72	0.568692	0.284346	−	0.958722i	$-0.408224\pi$
$29$	1.39180e72	0.568692	0.284346	+	0.958722i	$0.408224\pi$
$30$	−2.77071e72	−0.211392
$31$	−1.44293e73	−0.217191	−0.108595	−	0.994086i	$-0.534635\pi$
$31$	−1.44293e73	−0.217191	−0.108595	+	0.994086i	$0.534635\pi$
$32$	2.87578e74	0.899150
$33$	3.13740e74	0.213860
$34$	−3.99585e75	−0.621445
$35$	3.32331e76	1.23084
$36$	7.23778e76	0.664709
$37$	−5.19313e77	−1.22869	−0.614347	−	0.789036i	$-0.710580\pi$
$37$	−5.19313e77	−1.22869	−0.614347	+	0.789036i	$0.710580\pi$
$38$	4.34363e77	0.274514
$39$	−4.32392e78	−0.755405
$40$	1.62994e79	0.813207
$41$	−3.58403e79	−0.526709	−0.263354	−	0.964699i	$-0.584829\pi$
$41$	−3.58403e79	−0.526709	−0.263354	+	0.964699i	$0.584829\pi$
$42$	−3.99790e79	−0.178235
$43$	2.84099e80	0.395168	0.197584	−	0.980286i	$-0.436690\pi$
$43$	2.84099e80	0.395168	0.197584	+	0.980286i	$0.436690\pi$
$44$	−8.58951e80	−0.382878
$45$	6.29531e81	0.922567
$46$	7.31597e81	0.361209
$47$	−7.73779e82	−1.31757	−0.658784	−	0.752332i	$-0.728929\pi$
$47$	−7.73779e82	−1.31757	−0.658784	+	0.752332i	$0.728929\pi$
$48$	5.08736e82	0.305528
$49$	1.74580e82	0.0377824
$50$	2.07820e83	0.165452
$51$	−2.81119e84	−0.839782
$52$	1.18380e85	1.35242
$53$	1.89817e84	0.0844655	0.0422328	−	0.999108i	$-0.486553\pi$
$53$	1.89817e84	0.0844655	0.0422328	+	0.999108i	$0.486553\pi$
$54$	−1.74913e85	−0.308555
$55$	−7.47103e85	−0.531407
$56$	2.35187e86	0.685654
$57$	3.05587e86	0.370962
$58$	3.98704e86	0.204628
$59$	−2.13540e87	−0.470224	−0.235112	−	0.971968i	$-0.575546\pi$
$59$	−2.13540e87	−0.470224	−0.235112	+	0.971968i	$0.575546\pi$
$60$	5.33667e87	0.511427
$61$	4.67707e88	1.97764	0.988819	−	0.149121i	$-0.0476444\pi$
$61$	4.67707e88	1.97764	0.988819	+	0.149121i	$0.0476444\pi$
$62$	−4.13350e87	−0.0781501
$63$	9.08362e88	0.777861
$64$	−7.76144e88	−0.304813
$65$	1.02965e90	1.87706
$66$	8.98757e88	0.0769515
$67$	3.33536e90	1.35656	0.678282	−	0.734802i	$-0.262725\pi$
$67$	3.33536e90	1.35656	0.678282	+	0.734802i	$0.262725\pi$
$68$	7.69642e90	1.50348
$69$	5.14698e90	0.488116
$70$	9.52013e90	0.442884
$71$	2.25284e91	0.519328	0.259664	−	0.965699i	$-0.416388\pi$
$71$	2.25284e91	0.519328	0.259664	+	0.965699i	$0.416388\pi$
$72$	4.45512e91	0.513926
$73$	2.47879e90	0.0144464	0.00722319	−	0.999974i	$-0.497701\pi$
$73$	2.47879e90	0.0144464	0.00722319	+	0.999974i	$0.497701\pi$
$74$	−1.48765e92	−0.442111
$75$	1.46207e92	0.223581
$76$	−8.36629e92	−0.664141
$77$	−1.07801e93	−0.448055
$78$	−1.23866e93	−0.271812
$79$	−1.29965e94	−1.51805	−0.759025	−	0.651062i	$-0.774324\pi$
$79$	−1.29965e94	−1.51805	−0.759025	+	0.651062i	$0.774324\pi$
$80$	−1.21144e94	−0.759187
$81$	1.02293e94	0.346609
$82$	−1.02670e94	−0.189521
$83$	−1.54205e95	−1.56219	−0.781094	−	0.624414i	$-0.785338\pi$
$83$	−1.54205e95	−1.56219	−0.781094	+	0.624414i	$0.785338\pi$
$84$	7.70038e94	0.431209
$85$	6.69423e95	2.08672
$86$	8.13847e94	0.142190
$87$	2.80499e95	0.276521
$88$	−5.28716e95	−0.296026
$89$	2.29359e96	0.734025	0.367013	−	0.930216i	$-0.380381\pi$
$89$	2.29359e96	0.734025	0.367013	+	0.930216i	$0.380381\pi$
$90$	1.80339e96	0.331960
$91$	1.48570e97	1.58264
$92$	−1.40913e97	−0.873884
$93$	−2.90803e96	−0.105607
$94$	−2.21661e97	−0.474090
$95$	−7.27688e97	−0.921778
$96$	5.79575e97	0.437204
$97$	−3.70442e98	−1.67309	−0.836545	−	0.547898i	$-0.815428\pi$
$97$	−3.70442e98	−1.67309	−0.836545	+	0.547898i	$0.815428\pi$
$98$	5.00113e96	0.0135949
$99$	−2.04206e98	−0.335836
$100$	−4.00283e98	−0.400283
$101$	2.07787e99	1.26972	0.634862	−	0.772625i	$-0.281057\pi$
$101$	2.07787e99	1.26972	0.634862	+	0.772625i	$0.281057\pi$
$102$	−8.05310e98	−0.302172
$103$	1.09026e99	0.252399	0.126200	−	0.992005i	$-0.459722\pi$
$103$	1.09026e99	0.252399	0.126200	+	0.992005i	$0.459722\pi$
$104$	7.28670e99	1.04564
$105$	6.69767e99	0.598486
$106$	5.43760e98	0.0303926
$107$	−1.04962e100	−0.368583	−0.184292	−	0.982872i	$-0.558999\pi$
$107$	−1.04962e100	−0.368583	−0.184292	+	0.982872i	$0.558999\pi$
$108$	3.36901e100	0.746495
$109$	−5.13800e99	−0.0721410	−0.0360705	−	0.999349i	$-0.511484\pi$
$109$	−5.13800e99	−0.0721410	−0.0360705	+	0.999349i	$0.511484\pi$
$110$	−2.14019e100	−0.191212
$111$	−1.04660e101	−0.597441
$112$	−1.74801e101	−0.640107
$113$	−1.99419e101	−0.470309	−0.235154	−	0.971958i	$-0.575560\pi$
$113$	−1.99419e101	−0.470309	−0.235154	+	0.971958i	$0.575560\pi$
$114$	8.75401e100	0.133480
$115$	−1.22564e102	−1.21289
$116$	−7.67945e101	−0.495062
$117$	2.81435e102	1.18625
$118$	−6.11719e101	−0.169197
$119$	9.65924e102	1.75941
$120$	3.28492e102	0.395414
$121$	−1.01044e103	−0.806556
$122$	1.33982e103	0.711598
$123$	−7.22312e102	−0.256107
$124$	7.96155e102	0.189071
$125$	4.09012e103	0.652666
$126$	2.60215e103	0.279891
$127$	−2.58406e104	−1.87940	−0.939700	−	0.342001i	$-0.888895\pi$
$127$	−2.58406e104	−1.87940	−0.939700	+	0.342001i	$0.888895\pi$
$128$	−2.04508e104	−1.00883
$129$	5.72564e103	0.192147
$130$	2.94959e104	0.675407
$131$	−3.18081e104	−0.498434	−0.249217	−	0.968448i	$-0.580173\pi$
$131$	−3.18081e104	−0.498434	−0.249217	+	0.968448i	$0.580173\pi$
$132$	−1.73110e104	−0.186171
$133$	−1.04999e105	−0.777196
$134$	9.55467e104	0.488122
$135$	2.93032e105	1.03608
$136$	4.73743e105	1.16243
$137$	−3.08427e105	−0.526605	−0.263302	−	0.964713i	$-0.584812\pi$
$137$	−3.08427e105	−0.526605	−0.263302	+	0.964713i	$0.584812\pi$
$138$	1.47443e105	0.175635
$139$	1.94625e106	1.62168	0.810841	−	0.585266i	$-0.199010\pi$
$139$	1.94625e106	1.62168	0.810841	+	0.585266i	$0.199010\pi$
$140$	−1.83368e106	−1.07148
$141$	−1.55945e106	−0.640656
$142$	6.45360e105	0.186866
$143$	−3.33995e106	−0.683292
$144$	−3.31125e106	−0.479787
$145$	−6.67947e106	−0.687109
$146$	7.10089e104	0.00519812
$147$	3.51843e105	0.0183713
$148$	2.86537e107	1.06961
$149$	−3.53752e107	−0.946192	−0.473096	−	0.881011i	$-0.656864\pi$
$149$	−3.53752e107	−0.946192	−0.473096	+	0.881011i	$0.656864\pi$
$150$	4.18833e106	0.0804495
$151$	7.26718e107	1.00463	0.502316	−	0.864684i	$-0.332481\pi$
$151$	7.26718e107	1.00463	0.502316	+	0.864684i	$0.332481\pi$
$152$	−5.14976e107	−0.513487
$153$	1.82974e108	1.31875
$154$	−3.08812e107	−0.161220
$155$	6.92484e107	0.262416
$156$	2.38578e108	0.657602
$157$	−2.65806e108	−0.533988	−0.266994	−	0.963698i	$-0.586030\pi$
$157$	−2.65806e108	−0.533988	−0.266994	+	0.963698i	$0.586030\pi$
$158$	−3.72306e108	−0.546228
$159$	3.82550e107	0.0410706
$160$	−1.38013e109	−1.08638
$161$	−1.76850e109	−1.02264
$162$	2.93036e108	0.124717
$163$	1.62131e109	0.508838	0.254419	−	0.967094i	$-0.418116\pi$
$163$	1.62131e109	0.508838	0.254419	+	0.967094i	$0.418116\pi$
$164$	1.97753e109	0.458515
$165$	−1.50568e109	−0.258392
$166$	−4.41745e109	−0.562110
$167$	6.73702e109	0.636800	0.318400	−	0.947957i	$-0.396855\pi$
$167$	6.73702e109	0.636800	0.318400	+	0.947957i	$0.396855\pi$
$168$	4.73987e109	0.333393
$169$	2.69591e110	1.41356
$170$	1.91767e110	0.750848
$171$	−1.98899e110	−0.582541
$172$	−1.56755e110	−0.344005
$173$	−4.92610e110	−0.811374	−0.405687	−	0.914012i	$-0.632968\pi$
$173$	−4.92610e110	−0.811374	−0.405687	+	0.914012i	$0.632968\pi$
$174$	8.03533e109	0.0994984
$175$	−5.02366e110	−0.468422
$176$	3.92966e110	0.276362
$177$	−4.30361e110	−0.228642
$178$	6.57036e110	0.264119
$179$	−3.43689e111	−1.04698	−0.523492	−	0.852030i	$-0.675371\pi$
$179$	−3.43689e111	−1.04698	−0.523492	+	0.852030i	$0.675371\pi$
$180$	−3.47352e111	−0.803120
$181$	1.56523e111	0.275099	0.137549	−	0.990495i	$-0.456077\pi$
$181$	1.56523e111	0.275099	0.137549	+	0.990495i	$0.456077\pi$
$182$	4.25602e111	0.569468
$183$	9.42599e111	0.961608
$184$	−8.67372e111	−0.675652
$185$	2.49226e112	1.48454
$186$	−8.33051e110	−0.0379998
$187$	−2.17146e112	−0.759614
$188$	4.26943e112	1.14698
$189$	4.22821e112	0.873569
$190$	−2.08458e112	−0.331676
$191$	−1.50997e113	−1.85275	−0.926377	−	0.376598i	$-0.877094\pi$
$191$	−1.50997e113	−1.85275	−0.926377	+	0.376598i	$0.877094\pi$
$192$	−1.56421e112	−0.148213
$193$	−7.52564e112	−0.551387	−0.275693	−	0.961246i	$-0.588907\pi$
$193$	−7.52564e112	−0.551387	−0.275693	+	0.961246i	$0.588907\pi$
$194$	−1.06119e113	−0.602015
$195$	2.07512e113	0.912702
$196$	−9.63269e111	−0.0328906
$197$	−2.61400e113	−0.693789	−0.346895	−	0.937904i	$-0.612764\pi$
$197$	−2.61400e113	−0.693789	−0.346895	+	0.937904i	$0.612764\pi$
$198$	−5.84981e112	−0.120841
$199$	7.26456e113	1.16945	0.584725	−	0.811231i	$-0.301202\pi$
$199$	7.26456e113	1.16945	0.584725	+	0.811231i	$0.301202\pi$
$200$	−2.46389e113	−0.309482
$201$	6.72197e113	0.659617
$202$	5.95237e113	0.456875
$203$	−9.63793e113	−0.579335
$204$	1.55111e114	0.731054
$205$	1.72003e114	0.636384
$206$	3.12322e113	0.0908188
$207$	−3.35006e114	−0.766514
$208$	−5.41581e114	−0.976176
$209$	2.36046e114	0.335549
$210$	1.91865e114	0.215348
$211$	−1.36428e115	−1.21038	−0.605190	−	0.796081i	$-0.706903\pi$
$211$	−1.36428e115	−1.21038	−0.605190	+	0.796081i	$0.706903\pi$
$212$	−1.04734e114	−0.0735296
$213$	4.54029e114	0.252518
$214$	−3.00680e114	−0.132624
$215$	−1.36344e115	−0.477453
$216$	2.07375e115	0.577160
$217$	9.99198e114	0.221256
$218$	−1.47186e114	−0.0259579
$219$	4.99567e113	0.00702442
$220$	4.12223e115	0.462605
$221$	2.99269e116	2.68314
$222$	−2.99816e115	−0.214972
$223$	−1.88560e116	−1.08233	−0.541164	−	0.840917i	$-0.682016\pi$
$223$	−1.88560e116	−1.08233	−0.541164	+	0.840917i	$0.682016\pi$
$224$	−1.99142e116	−0.915979
$225$	−9.51628e115	−0.351102
$226$	−5.71267e115	−0.169228
$227$	−1.87429e116	−0.446228	−0.223114	−	0.974792i	$-0.571622\pi$
$227$	−1.87429e116	−0.446228	−0.223114	+	0.974792i	$0.571622\pi$
$228$	−1.68611e116	−0.322932
$229$	5.20732e116	0.803078	0.401539	−	0.915842i	$-0.368475\pi$
$229$	5.20732e116	0.803078	0.401539	+	0.915842i	$0.368475\pi$
$230$	−3.51104e116	−0.436423
$231$	−2.17258e116	−0.217863
$232$	−4.72698e116	−0.382762
$233$	−7.31940e116	−0.479024	−0.239512	−	0.970893i	$-0.576987\pi$
$233$	−7.31940e116	−0.479024	−0.239512	+	0.970893i	$0.576987\pi$
$234$	8.06214e116	0.426840
$235$	3.71348e117	1.59192
$236$	1.17824e117	0.409344
$237$	−2.61927e117	−0.738138
$238$	2.76704e117	0.633076
$239$	−4.11127e116	−0.0764329	−0.0382165	−	0.999269i	$-0.512168\pi$
$239$	−4.11127e116	−0.0764329	−0.0382165	+	0.999269i	$0.512168\pi$
$240$	−2.44150e117	−0.369148
$241$	6.44827e117	0.793596	0.396798	−	0.917906i	$-0.370121\pi$
$241$	6.44827e117	0.793596	0.396798	+	0.917906i	$0.370121\pi$
$242$	−2.89456e117	−0.290217
$243$	1.25511e118	1.02606
$244$	−2.58063e118	−1.72159
$245$	−8.37837e116	−0.0456498
$246$	−2.06918e117	−0.0921530
$247$	−3.25316e118	−1.18524
$248$	4.90063e117	0.146182
$249$	−3.10780e118	−0.759600
$250$	1.17168e118	0.234844
$251$	1.09110e119	1.79479	0.897396	−	0.441226i	$-0.145456\pi$
$251$	1.09110e119	1.79479	0.897396	+	0.441226i	$0.145456\pi$
$252$	−5.01200e118	−0.677150
$253$	3.97571e118	0.441519
$254$	−7.40246e118	−0.676249
$255$	1.34913e119	1.01465
$256$	−9.39066e117	−0.0581859
$257$	1.79659e119	0.917823	0.458911	−	0.888482i	$-0.348240\pi$
$257$	1.79659e119	0.917823	0.458911	+	0.888482i	$0.348240\pi$
$258$	1.64020e118	0.0691387
$259$	3.59613e119	1.25169
$260$	−5.68121e119	−1.63403
$261$	−1.82570e119	−0.434236
$262$	−9.11192e118	−0.179348
$263$	−4.33923e119	−0.707299	−0.353650	−	0.935378i	$-0.615059\pi$
$263$	−4.33923e119	−0.707299	−0.353650	+	0.935378i	$0.615059\pi$
$264$	−1.06556e119	−0.143940
$265$	−9.10960e118	−0.102054
$266$	−3.00787e119	−0.279652
$267$	4.62243e119	0.356913
$268$	−1.84033e120	−1.18093
$269$	2.31687e120	1.23642	0.618208	−	0.786015i	$-0.287859\pi$
$269$	2.31687e120	1.23642	0.618208	+	0.786015i	$0.287859\pi$
$270$	8.39435e119	0.372804
$271$	2.02469e120	0.748821	0.374410	−	0.927263i	$-0.377845\pi$
$271$	2.02469e120	0.748821	0.374410	+	0.927263i	$0.377845\pi$
$272$	−3.52108e120	−1.08521
$273$	2.99422e120	0.769544
$274$	−8.83538e119	−0.189484
$275$	1.12935e120	0.202238
$276$	−2.83991e120	−0.424918
$277$	1.08848e121	1.36167	0.680836	−	0.732436i	$-0.261617\pi$
$277$	1.08848e121	1.36167	0.680836	+	0.732436i	$0.261617\pi$
$278$	5.57534e120	0.583517
$279$	1.89277e120	0.165840
$280$	−1.12870e121	−0.828427
$281$	−1.65497e121	−1.01819	−0.509094	−	0.860711i	$-0.670020\pi$
$281$	−1.65497e121	−1.01819	−0.509094	+	0.860711i	$0.670020\pi$
$282$	−4.46728e120	−0.230522
$283$	−4.53692e120	−0.196486	−0.0982432	−	0.995162i	$-0.531322\pi$
$283$	−4.53692e120	−0.196486	−0.0982432	+	0.995162i	$0.531322\pi$
$284$	−1.24303e121	−0.452089
$285$	−1.46656e121	−0.448206
$286$	−9.56782e120	−0.245864
$287$	2.48186e121	0.536566
$288$	−3.77233e121	−0.686564
$289$	1.29339e122	1.98284
$290$	−1.91344e121	−0.247237
$291$	−7.46576e121	−0.813525
$292$	−1.36771e120	−0.0125760
$293$	1.79667e122	1.39483	0.697415	−	0.716668i	$-0.254334\pi$
$293$	1.79667e122	1.39483	0.697415	+	0.716668i	$0.254334\pi$
$294$	1.00791e120	0.00661041
$295$	1.02481e122	0.568138
$296$	1.76374e122	0.826981
$297$	−9.50531e121	−0.377157
$298$	−1.01338e122	−0.340461
$299$	−5.47928e122	−1.55955
$300$	−8.06715e121	−0.194634
$301$	−1.96733e122	−0.402564
$302$	2.08180e122	0.361489
$303$	4.18766e122	0.617392
$304$	3.82754e122	0.479377
$305$	−2.24459e123	−2.38944
$306$	5.24158e122	0.474517
$307$	3.36933e119	0.000259534 0	0.000129767	−	1.00000i	$-0.499959\pi$
$307$	3.36933e119	0.000259534 0	0.000129767		1.00000i	$0.499959\pi$
$308$	5.94805e122	0.390044
$309$	2.19727e122	0.122727
$310$	1.98373e122	0.0944232
$311$	2.85284e123	1.15781	0.578907	−	0.815394i	$-0.303479\pi$
$311$	2.85284e123	1.15781	0.578907	+	0.815394i	$0.303479\pi$
$312$	1.46854e123	0.508431
$313$	9.19803e121	0.0271800	0.0135900	−	0.999908i	$-0.495674\pi$
$313$	9.19803e121	0.0271800	0.0135900	+	0.999908i	$0.495674\pi$
$314$	−7.61442e122	−0.192141
$315$	−4.35937e123	−0.939834
$316$	7.17099e123	1.32150
$317$	−4.99463e123	−0.787172	−0.393586	−	0.919288i	$-0.628766\pi$
$317$	−4.99463e123	−0.787172	−0.393586	+	0.919288i	$0.628766\pi$
$318$	1.09588e122	0.0147781
$319$	2.16667e123	0.250124
$320$	3.72483e123	0.368284
$321$	−2.11537e123	−0.179220
$322$	−5.06615e123	−0.367970
$323$	−2.11503e124	−1.31763
$324$	−5.64417e123	−0.301733
$325$	−1.55646e124	−0.714353
$326$	4.64449e123	0.183091
$327$	−1.03549e123	−0.0350779
$328$	1.21724e124	0.354505
$329$	5.35825e124	1.34223
$330$	−4.31327e123	−0.0929750
$331$	−2.71673e124	−0.504152	−0.252076	−	0.967707i	$-0.581113\pi$
$331$	−2.71673e124	−0.504152	−0.252076	+	0.967707i	$0.581113\pi$
$332$	8.50846e124	1.35993
$333$	6.81211e124	0.938193
$334$	1.92993e124	0.229135
$335$	−1.60069e125	−1.63904
$336$	−3.52289e124	−0.311246
$337$	1.28573e125	0.980550	0.490275	−	0.871568i	$-0.336896\pi$
$337$	1.28573e125	0.980550	0.490275	+	0.871568i	$0.336896\pi$
$338$	7.72284e124	0.508628
$339$	−4.01902e124	−0.228683
$340$	−3.69363e125	−1.81655
$341$	−2.24627e124	−0.0955256
$342$	−5.69779e124	−0.209611
$343$	3.07883e125	0.980227
$344$	−9.64887e124	−0.265971
$345$	−2.47011e125	−0.589755
$346$	−1.41116e125	−0.291950
$347$	−1.50266e125	−0.269496	−0.134748	−	0.990880i	$-0.543022\pi$
$347$	−1.50266e125	−0.269496	−0.134748	+	0.990880i	$0.543022\pi$
$348$	−1.54769e125	−0.240719
$349$	5.17125e125	0.697809	0.348905	−	0.937158i	$-0.386554\pi$
$349$	5.17125e125	0.697809	0.348905	+	0.937158i	$0.386554\pi$
$350$	−1.43911e125	−0.168549
$351$	1.31001e126	1.33221
$352$	4.47685e125	0.395467
$353$	7.00287e125	0.537561	0.268781	−	0.963201i	$-0.413379\pi$
$353$	7.00287e125	0.537561	0.268781	+	0.963201i	$0.413379\pi$
$354$	−1.23284e125	−0.0822706
$355$	−1.08117e126	−0.627467
$356$	−1.26552e126	−0.638990
$357$	1.94669e126	0.855499
$358$	−9.84550e125	−0.376728
$359$	3.38663e126	1.12874	0.564368	−	0.825523i	$-0.309120\pi$
$359$	3.38663e126	1.12874	0.564368	+	0.825523i	$0.309120\pi$
$360$	−2.13808e126	−0.620940
$361$	−1.65097e126	−0.417957
$362$	4.48385e125	0.0989867
$363$	−2.03640e126	−0.392180
$364$	−8.19753e126	−1.37773
$365$	−1.18961e125	−0.0174545
$366$	2.70022e126	0.346008
$367$	−9.71020e126	−1.08707	−0.543536	−	0.839386i	$-0.682915\pi$
$367$	−9.71020e126	−1.08707	−0.543536	+	0.839386i	$0.682915\pi$
$368$	6.44671e126	0.630770
$369$	4.70137e126	0.402179
$370$	7.13947e126	0.534171
$371$	−1.31444e126	−0.0860464
$372$	1.60454e126	0.0919339
$373$	2.06903e127	1.03796	0.518980	−	0.854786i	$-0.326312\pi$
$373$	2.06903e127	1.03796	0.518980	+	0.854786i	$0.326312\pi$
$374$	−6.22050e126	−0.273326
$375$	8.24309e126	0.317353
$376$	2.62799e127	0.886799
$377$	−2.98609e127	−0.883498
$378$	1.21124e127	0.314329
$379$	7.13227e126	0.162400	0.0812002	−	0.996698i	$-0.474125\pi$
$379$	7.13227e126	0.162400	0.0812002	+	0.996698i	$0.474125\pi$
$380$	4.01511e127	0.802434
$381$	−5.20783e127	−0.913841
$382$	−4.32556e127	−0.666662
$383$	−1.17016e128	−1.58456	−0.792278	−	0.610160i	$-0.791105\pi$
$383$	−1.17016e128	−1.58456	−0.792278	+	0.610160i	$0.791105\pi$
$384$	−4.12159e127	−0.490534
$385$	5.17352e127	0.541353
$386$	−2.15584e127	−0.198401
$387$	−3.72669e127	−0.301738
$388$	2.04396e128	1.45647
$389$	1.08825e128	0.682691	0.341345	−	0.939938i	$-0.389117\pi$
$389$	1.08825e128	0.682691	0.341345	+	0.939938i	$0.389117\pi$
$390$	5.94450e127	0.328410
$391$	−3.56234e128	−1.73375
$392$	−5.92928e126	−0.0254297
$393$	−6.41048e127	−0.242359
$394$	−7.48821e127	−0.249641
$395$	6.23722e128	1.83415
$396$	1.12673e128	0.292354
$397$	1.78683e128	0.409216	0.204608	−	0.978844i	$-0.434408\pi$
$397$	1.78683e128	0.409216	0.204608	+	0.978844i	$0.434408\pi$
$398$	2.08105e128	0.420794
$399$	−2.11612e128	−0.377905
$400$	1.83127e128	0.288924
$401$	−6.41533e128	−0.894484	−0.447242	−	0.894413i	$-0.647594\pi$
$401$	−6.41533e128	−0.894484	−0.447242	+	0.894413i	$0.647594\pi$
$402$	1.92561e128	0.237345
$403$	3.09578e128	0.337420
$404$	−1.14649e129	−1.10533
$405$	−4.90922e128	−0.418782
$406$	−2.76094e128	−0.208458
$407$	−8.08435e128	−0.540408
$408$	9.54765e128	0.565221
$409$	−9.06187e128	−0.475241	−0.237621	−	0.971358i	$-0.576367\pi$
$409$	−9.06187e128	−0.475241	−0.237621	+	0.971358i	$0.576367\pi$
$410$	4.92729e128	0.228985
$411$	−6.21593e128	−0.256057
$412$	−6.01565e128	−0.219721
$413$	1.47872e129	0.479025
$414$	−9.59676e128	−0.275809
$415$	7.40053e129	1.88748
$416$	−6.16994e129	−1.39689
$417$	3.92240e129	0.788529
$418$	6.76191e128	0.120738
$419$	1.07548e130	1.70611	0.853055	−	0.521821i	$-0.174747\pi$
$419$	1.07548e130	1.70611	0.853055	+	0.521821i	$0.174747\pi$
$420$	−3.69553e129	−0.520998
$421$	−4.44148e129	−0.556626	−0.278313	−	0.960490i	$-0.589775\pi$
$421$	−4.44148e129	−0.556626	−0.278313	+	0.960490i	$0.589775\pi$
$422$	−3.90819e129	−0.435522
$423$	1.01501e130	1.00606
$424$	−6.44676e128	−0.0568501
$425$	−1.01193e130	−0.794144
$426$	1.30064e129	0.0908617
$427$	−3.23877e130	−2.01465
$428$	5.79142e129	0.320862
$429$	−6.73122e129	−0.332245
$430$	−3.90577e129	−0.171798
$431$	1.43411e130	0.562285	0.281142	−	0.959666i	$-0.409287\pi$
$431$	1.43411e130	0.562285	0.281142	+	0.959666i	$0.409287\pi$
$432$	−1.54131e130	−0.538820
$433$	3.50235e130	1.09196	0.545982	−	0.837797i	$-0.316157\pi$
$433$	3.50235e130	1.09196	0.545982	+	0.837797i	$0.316157\pi$
$434$	2.86236e129	0.0796127
$435$	−1.34616e130	−0.334101
$436$	2.83495e129	0.0628008
$437$	3.87240e130	0.765859
$438$	1.43109e128	0.00252754
$439$	−3.20537e130	−0.505690	−0.252845	−	0.967507i	$-0.581366\pi$
$439$	−3.20537e130	−0.505690	−0.252845	+	0.967507i	$0.581366\pi$
$440$	2.53739e130	0.357667
$441$	−2.29007e129	−0.0288495
$442$	8.57302e130	0.965454
$443$	3.56275e130	0.358757	0.179379	−	0.983780i	$-0.442591\pi$
$443$	3.56275e130	0.358757	0.179379	+	0.983780i	$0.442591\pi$
$444$	5.77477e130	0.520089
$445$	−1.10073e131	−0.886870
$446$	−5.40160e130	−0.389446
$447$	−7.12940e130	−0.460077
$448$	5.37463e130	0.310518
$449$	−1.31807e131	−0.681936	−0.340968	−	0.940075i	$-0.610755\pi$
$449$	−1.31807e131	−0.681936	−0.340968	+	0.940075i	$0.610755\pi$
$450$	−2.72609e130	−0.126334
$451$	−5.57940e130	−0.231659
$452$	1.10032e131	0.409417
$453$	1.46460e131	0.488493
$454$	−5.36919e130	−0.160563
$455$	−7.13009e131	−1.91219
$456$	−1.03786e131	−0.249678
$457$	−2.21686e131	−0.478505	−0.239252	−	0.970957i	$-0.576902\pi$
$457$	−2.21686e131	−0.478505	−0.239252	+	0.970957i	$0.576902\pi$
$458$	1.49172e131	0.288965
$459$	8.51701e131	1.48101
$460$	6.76263e131	1.05585
$461$	2.50995e131	0.351940	0.175970	−	0.984396i	$-0.443694\pi$
$461$	2.50995e131	0.351940	0.175970	+	0.984396i	$0.443694\pi$
$462$	−6.22369e130	−0.0783918
$463$	2.98626e131	0.337962	0.168981	−	0.985619i	$-0.445952\pi$
$463$	2.98626e131	0.337962	0.168981	+	0.985619i	$0.445952\pi$
$464$	3.51331e131	0.357336
$465$	1.39561e131	0.127598
$466$	−2.09676e131	−0.172363
$467$	8.36468e131	0.618392	0.309196	−	0.950998i	$-0.399940\pi$
$467$	8.36468e131	0.618392	0.309196	+	0.950998i	$0.399940\pi$
$468$	−1.55285e132	−1.03267
$469$	−2.30967e132	−1.38195
$470$	1.06379e132	0.572809
$471$	−5.35695e131	−0.259647
$472$	7.25247e131	0.316488
$473$	4.42269e131	0.173804
$474$	−7.50331e131	−0.265598
$475$	1.10001e132	0.350802
$476$	−5.32961e132	−1.53162
$477$	−2.48993e131	−0.0644953
$478$	−1.17774e131	−0.0275022
$479$	−3.09756e132	−0.652247	−0.326123	−	0.945327i	$-0.605743\pi$
$479$	−3.09756e132	−0.652247	−0.326123	+	0.945327i	$0.605743\pi$
$480$	−2.78147e132	−0.528242
$481$	1.11418e133	1.90885
$482$	1.84721e132	0.285553
$483$	−3.56417e132	−0.497251
$484$	5.57523e132	0.702129
$485$	1.77781e133	2.02148
$486$	3.59545e132	0.369197
$487$	−1.43917e133	−1.33484	−0.667418	−	0.744683i	$-0.732601\pi$
$487$	−1.43917e133	−1.33484	−0.667418	+	0.744683i	$0.732601\pi$
$488$	−1.58847e133	−1.33106
$489$	3.26753e132	0.247418
$490$	−2.40012e131	−0.0164258
$491$	2.27807e133	1.40940	0.704699	−	0.709507i	$-0.251082\pi$
$491$	2.27807e133	1.40940	0.704699	+	0.709507i	$0.251082\pi$
$492$	3.98545e132	0.222949
$493$	−1.94140e133	−0.982182
$494$	−9.31918e132	−0.426475
$495$	9.80016e132	0.405766
$496$	−3.64237e132	−0.136471
$497$	−1.56004e133	−0.529048
$498$	−8.90277e132	−0.273321
$499$	−1.75564e133	−0.488044	−0.244022	−	0.969770i	$-0.578467\pi$
$499$	−1.75564e133	−0.488044	−0.244022	+	0.969770i	$0.578467\pi$
$500$	−2.25678e133	−0.568164
$501$	1.35776e133	0.309638
$502$	3.12562e133	0.645806
$503$	2.26721e133	0.424498	0.212249	−	0.977216i	$-0.431921\pi$
$503$	2.26721e133	0.424498	0.212249	+	0.977216i	$0.431921\pi$
$504$	−3.08507e133	−0.523545
$505$	−9.97199e133	−1.53412
$506$	1.13891e133	0.158868
$507$	5.43323e133	0.687328
$508$	1.42579e134	1.63607
$509$	1.50518e133	0.156696	0.0783481	−	0.996926i	$-0.475035\pi$
$509$	1.50518e133	0.156696	0.0783481	+	0.996926i	$0.475035\pi$
$510$	3.86480e133	0.365093
$511$	−1.71651e132	−0.0147167
$512$	1.26932e134	0.987892
$513$	−9.25830e133	−0.654217
$514$	5.14661e133	0.330253
$515$	−5.23233e133	−0.304956
$516$	−3.15919e133	−0.167269
$517$	−1.20457e134	−0.579497
$518$	1.03017e134	0.450386
$519$	−9.92789e133	−0.394523
$520$	−3.49700e134	−1.26337
$521$	2.78816e133	0.0915905	0.0457952	−	0.998951i	$-0.485418\pi$
$521$	2.78816e133	0.0915905	0.0457952	+	0.998951i	$0.485418\pi$
$522$	−5.23002e133	−0.156248
$523$	−1.88184e134	−0.511387	−0.255694	−	0.966758i	$-0.582304\pi$
$523$	−1.88184e134	−0.511387	−0.255694	+	0.966758i	$0.582304\pi$
$524$	1.75505e134	0.433901
$525$	−1.01245e134	−0.227766
$526$	−1.24304e134	−0.254502
$527$	2.01271e134	0.375108
$528$	7.91969e133	0.134378
$529$	5.00049e132	0.00772603
$530$	−2.60959e133	−0.0367211
$531$	2.80113e134	0.359049
$532$	5.79348e134	0.676571
$533$	7.68946e134	0.818274
$534$	1.32417e134	0.128425
$535$	5.03729e134	0.445333
$536$	−1.13279e135	−0.913046
$537$	−6.92658e134	−0.509087
$538$	6.63705e134	0.444890
$539$	2.71776e133	0.0166176
$540$	−1.61684e135	−0.901936
$541$	2.89315e135	1.47267	0.736337	−	0.676615i	$-0.236554\pi$
$541$	2.89315e135	1.47267	0.736337	+	0.676615i	$0.236554\pi$
$542$	5.80003e134	0.269442
$543$	3.15451e134	0.133764
$544$	−4.01137e135	−1.55291
$545$	2.46580e134	0.0871628
$546$	8.57742e134	0.276899
$547$	−4.76347e135	−1.40459	−0.702297	−	0.711884i	$-0.747842\pi$
$547$	−4.76347e135	−1.40459	−0.702297	+	0.711884i	$0.747842\pi$
$548$	1.70179e135	0.458424
$549$	−6.13517e135	−1.51006
$550$	3.23521e134	0.0727696
$551$	2.11037e135	0.433865
$552$	−1.74807e135	−0.328530
$553$	8.99980e135	1.54646
$554$	3.11813e135	0.489960
$555$	5.02281e135	0.721845
$556$	−1.07387e136	−1.41172
$557$	6.56024e135	0.789019	0.394510	−	0.918892i	$-0.370914\pi$
$557$	6.56024e135	0.789019	0.394510	+	0.918892i	$0.370914\pi$
$558$	5.42214e134	0.0596730
$559$	−6.09530e135	−0.613918
$560$	8.38898e135	0.773396
$561$	−4.37629e135	−0.369355
$562$	−4.74093e135	−0.366367
$563$	1.74627e136	1.23579	0.617896	−	0.786260i	$-0.287985\pi$
$563$	1.74627e136	1.23579	0.617896	+	0.786260i	$0.287985\pi$
$564$	8.60445e135	0.557709
$565$	9.57041e135	0.568241
$566$	−1.29967e135	−0.0707001
$567$	−7.08360e135	−0.353096
$568$	−7.65132e135	−0.349537
$569$	−2.60131e136	−1.08927	−0.544635	−	0.838673i	$-0.683332\pi$
$569$	−2.60131e136	−1.08927	−0.544635	+	0.838673i	$0.683332\pi$
$570$	−4.20118e135	−0.161275
$571$	−4.79163e136	−1.68654	−0.843268	−	0.537493i	$-0.819371\pi$
$571$	−4.79163e136	−1.68654	−0.843268	+	0.537493i	$0.819371\pi$
$572$	1.84286e136	0.594825
$573$	−3.04315e136	−0.900884
$574$	7.10968e135	0.193068
$575$	1.85274e136	0.461589
$576$	1.01811e136	0.232746
$577$	−2.53022e136	−0.530831	−0.265415	−	0.964134i	$-0.585509\pi$
$577$	−2.53022e136	−0.530831	−0.265415	+	0.964134i	$0.585509\pi$
$578$	3.70513e136	0.713470
$579$	−1.51669e136	−0.268107
$580$	3.68548e136	0.598148
$581$	1.06784e137	1.59143
$582$	−2.13868e136	−0.292724
$583$	2.95496e135	0.0371499
$584$	−8.41873e134	−0.00972324
$585$	−1.35065e137	−1.43326
$586$	5.14684e136	0.501891
$587$	1.70706e137	1.52990	0.764948	−	0.644092i	$-0.222765\pi$
$587$	1.70706e137	1.52990	0.764948	+	0.644092i	$0.222765\pi$
$588$	−1.94134e135	−0.0159928
$589$	−2.18789e136	−0.165699
$590$	2.93573e136	0.204429
$591$	−5.26816e136	−0.337349
$592$	−1.31089e137	−0.772046
$593$	7.61876e136	0.412740	0.206370	−	0.978474i	$-0.433835\pi$
$593$	7.61876e136	0.412740	0.206370	+	0.978474i	$0.433835\pi$
$594$	−2.72295e136	−0.135709
$595$	−4.63561e137	−2.12577
$596$	1.95187e137	0.823687
$597$	1.46407e137	0.568635
$598$	−1.56963e137	−0.561161
$599$	1.91129e137	0.629071	0.314535	−	0.949246i	$-0.398151\pi$
$599$	1.91129e137	0.629071	0.314535	+	0.949246i	$0.398151\pi$
$600$	−4.96563e136	−0.150483
$601$	−6.32287e136	−0.176452	−0.0882262	−	0.996100i	$-0.528120\pi$
$601$	−6.32287e136	−0.176452	−0.0882262	+	0.996100i	$0.528120\pi$
$602$	−5.63571e136	−0.144851
$603$	−4.37518e137	−1.03583
$604$	−4.00976e137	−0.874560
$605$	4.84925e137	0.974503
$606$	1.19962e137	0.222151
$607$	8.01601e137	1.36810	0.684051	−	0.729434i	$-0.260217\pi$
$607$	8.01601e137	1.36810	0.684051	+	0.729434i	$0.260217\pi$
$608$	4.36051e137	0.685977
$609$	−1.94239e137	−0.281696
$610$	−6.42999e137	−0.859773
$611$	1.66013e138	2.04692
$612$	−1.00958e138	−1.14801
$613$	3.02896e137	0.317687	0.158844	−	0.987304i	$-0.449223\pi$
$613$	3.02896e137	0.317687	0.158844	+	0.987304i	$0.449223\pi$
$614$	9.65198e133	9.33861e−5 0
$615$	3.46648e137	0.309436
$616$	3.66124e137	0.301567
$617$	−7.78262e137	−0.591575	−0.295788	−	0.955254i	$-0.595582\pi$
$617$	−7.78262e137	−0.591575	−0.295788	+	0.955254i	$0.595582\pi$
$618$	6.29443e136	0.0441598
$619$	1.49252e137	0.0966572	0.0483286	−	0.998831i	$-0.484611\pi$
$619$	1.49252e137	0.0966572	0.0483286	+	0.998831i	$0.484611\pi$
$620$	−3.82087e137	−0.228441
$621$	−1.55937e138	−0.860826
$622$	8.17242e137	0.416607
$623$	−1.58826e138	−0.747763
$624$	−1.09148e138	−0.474657
$625$	−3.10749e138	−1.24839
$626$	2.63492e136	0.00977998
$627$	4.75719e137	0.163157
$628$	1.46662e138	0.464851
$629$	7.24379e138	2.12206
$630$	−1.24881e138	−0.338173
$631$	−7.38843e138	−1.84969	−0.924844	−	0.380346i	$-0.875805\pi$
$631$	−7.38843e138	−1.84969	−0.924844	+	0.380346i	$0.875805\pi$
$632$	4.41401e138	1.02173
$633$	−2.74952e138	−0.588537
$634$	−1.43079e138	−0.283242
$635$	1.24013e139	2.27074
$636$	−2.11077e137	−0.0357531
$637$	−3.74559e137	−0.0586973
$638$	6.20678e137	0.0900000
$639$	−2.95517e138	−0.396543
$640$	9.81466e138	1.21890
$641$	2.38758e138	0.274464	0.137232	−	0.990539i	$-0.456179\pi$
$641$	2.38758e138	0.274464	0.137232	+	0.990539i	$0.456179\pi$
$642$	−6.05981e137	−0.0644874
$643$	−1.42797e139	−1.40694	−0.703471	−	0.710724i	$-0.748368\pi$
$643$	−1.42797e139	−1.40694	−0.703471	+	0.710724i	$0.748368\pi$
$644$	9.75793e138	0.890240
$645$	−2.74782e138	−0.232157
$646$	−6.05885e138	−0.474111
$647$	−2.03156e139	−1.47254	−0.736272	−	0.676686i	$-0.763416\pi$
$647$	−2.03156e139	−1.47254	−0.736272	+	0.676686i	$0.763416\pi$
$648$	−3.47420e138	−0.233287
$649$	−3.32427e138	−0.206816
$650$	−4.45873e138	−0.257040
$651$	2.01375e138	0.107584
$652$	−8.94578e138	−0.442957
$653$	3.32057e139	1.52409	0.762044	−	0.647526i	$-0.224196\pi$
$653$	3.32057e139	1.52409	0.762044	+	0.647526i	$0.224196\pi$
$654$	−2.96633e137	−0.0126218
$655$	1.52652e139	0.602223
$656$	−9.04711e138	−0.330956
$657$	−3.25157e137	−0.0110308
$658$	1.53496e139	0.482963
$659$	−5.05125e139	−1.47425	−0.737124	−	0.675757i	$-0.763817\pi$
$659$	−5.05125e139	−1.47425	−0.737124	+	0.675757i	$0.763817\pi$
$660$	8.30780e138	0.224937
$661$	−3.47031e139	−0.871757	−0.435879	−	0.900005i	$-0.643562\pi$
$661$	−3.47031e139	−0.871757	−0.435879	+	0.900005i	$0.643562\pi$
$662$	−7.78251e138	−0.181405
$663$	6.03135e139	1.30465
$664$	5.23727e139	1.05144
$665$	5.03908e139	0.939030
$666$	1.95144e139	0.337583
$667$	3.55449e139	0.570884
$668$	−3.71724e139	−0.554352
$669$	−3.80017e139	−0.526272
$670$	−4.58543e139	−0.589763
$671$	7.28097e139	0.869811
$672$	−4.01343e139	−0.445386
$673$	−1.04366e140	−1.07600	−0.538001	−	0.842944i	$-0.680820\pi$
$673$	−1.04366e140	−1.07600	−0.538001	+	0.842944i	$0.680820\pi$
$674$	3.68318e139	0.352824
$675$	−4.42960e139	−0.394301
$676$	−1.48750e140	−1.23054
$677$	1.63497e139	0.125710	0.0628552	−	0.998023i	$-0.479979\pi$
$677$	1.63497e139	0.125710	0.0628552	+	0.998023i	$0.479979\pi$
$678$	−1.15131e139	−0.0822854
$679$	2.56523e140	1.70440
$680$	−2.27356e140	−1.40448
$681$	−3.77738e139	−0.216974
$682$	−6.43478e138	−0.0343722
$683$	−1.91884e140	−0.953265	−0.476633	−	0.879103i	$-0.658143\pi$
$683$	−1.91884e140	−0.953265	−0.476633	+	0.879103i	$0.658143\pi$
$684$	1.09745e140	0.507118
$685$	1.48019e140	0.636259
$686$	8.81978e139	0.352707
$687$	1.04946e140	0.390490
$688$	7.17149e139	0.248303
$689$	−4.07249e139	−0.131222
$690$	−7.07603e139	−0.212207
$691$	5.50389e140	1.53641	0.768203	−	0.640206i	$-0.221151\pi$
$691$	5.50389e140	1.53641	0.768203	+	0.640206i	$0.221151\pi$
$692$	2.71804e140	0.706324
$693$	1.41408e140	0.342121
$694$	−4.30461e139	−0.0969706
$695$	−9.34034e140	−1.95936
$696$	−9.52659e139	−0.186115
$697$	4.99929e140	0.909673
$698$	1.48138e140	0.251087
$699$	−1.47513e140	−0.232921
$700$	2.77187e140	0.407774
$701$	−1.30656e141	−1.79096	−0.895482	−	0.445098i	$-0.853169\pi$
$701$	−1.30656e141	−1.79096	−0.895482	+	0.445098i	$0.853169\pi$
$702$	3.75273e140	0.479359
$703$	−7.87426e140	−0.937392
$704$	−1.20825e140	−0.134064
$705$	7.48402e140	0.774058
$706$	2.00608e140	0.193426
$707$	−1.43888e141	−1.29349
$708$	2.37457e140	0.199040
$709$	−3.58096e140	−0.279905	−0.139952	−	0.990158i	$-0.544695\pi$
$709$	−3.58096e140	−0.279905	−0.139952	+	0.990158i	$0.544695\pi$
$710$	−3.09718e140	−0.225776
$711$	1.70483e141	1.15914
$712$	−7.78974e140	−0.494041
$713$	−3.68506e140	−0.218028
$714$	5.57659e140	0.307828
$715$	1.60289e141	0.825573
$716$	1.89635e141	0.911430
$717$	−8.28572e139	−0.0371648
$718$	9.70153e140	0.406144
$719$	−2.27670e141	−0.889665	−0.444832	−	0.895614i	$-0.646737\pi$
$719$	−2.27670e141	−0.889665	−0.444832	+	0.895614i	$0.646737\pi$
$720$	1.58912e141	0.579692
$721$	−7.54982e140	−0.257123
$722$	−4.72945e140	−0.150390
$723$	1.29956e141	0.385879
$724$	−8.63636e140	−0.239481
$725$	1.00970e141	0.261493
$726$	−5.83360e140	−0.141115
$727$	3.97311e141	0.897796	0.448898	−	0.893583i	$-0.351817\pi$
$727$	3.97311e141	0.897796	0.448898	+	0.893583i	$0.351817\pi$
$728$	−5.04588e141	−1.06521
$729$	7.72176e140	0.152301
$730$	−3.40782e139	−0.00628052
$731$	−3.96284e141	−0.682491
$732$	−5.20091e141	−0.837107
$733$	−1.69430e141	−0.254884	−0.127442	−	0.991846i	$-0.540677\pi$
$733$	−1.69430e141	−0.254884	−0.127442	+	0.991846i	$0.540677\pi$
$734$	−2.78164e141	−0.391152
$735$	−1.68855e140	−0.0221968
$736$	7.34438e141	0.902617
$737$	5.19229e141	0.596648
$738$	1.34678e141	0.144713
$739$	−6.64582e141	−0.667804	−0.333902	−	0.942608i	$-0.608365\pi$
$739$	−6.64582e141	−0.667804	−0.333902	+	0.942608i	$0.608365\pi$
$740$	−1.37514e142	−1.29234
$741$	−6.55630e141	−0.576312
$742$	−3.76542e140	−0.0309614
$743$	1.43356e142	1.10273	0.551364	−	0.834265i	$-0.314108\pi$
$743$	1.43356e142	1.10273	0.551364	+	0.834265i	$0.314108\pi$
$744$	9.87655e140	0.0710796
$745$	1.69771e142	1.14322
$746$	5.92707e141	0.373481
$747$	2.02279e142	1.19284
$748$	1.19813e142	0.661265
$749$	7.26840e141	0.375482
$750$	2.36136e141	0.114191
$751$	−2.22287e142	−1.00632	−0.503161	−	0.864193i	$-0.667830\pi$
$751$	−2.22287e142	−1.00632	−0.503161	+	0.864193i	$0.667830\pi$
$752$	−1.95324e142	−0.827890
$753$	2.19896e142	0.872701
$754$	−8.55411e141	−0.317902
$755$	−3.48763e142	−1.21382
$756$	−2.33297e142	−0.760466
$757$	−3.03014e141	−0.0925160	−0.0462580	−	0.998930i	$-0.514730\pi$
$757$	−3.03014e141	−0.0925160	−0.0462580	+	0.998930i	$0.514730\pi$
$758$	2.04315e141	0.0584352
$759$	8.01251e141	0.214685
$760$	2.47145e142	0.620410
$761$	−3.72039e142	−0.875079	−0.437540	−	0.899199i	$-0.644150\pi$
$761$	−3.72039e142	−0.875079	−0.437540	+	0.899199i	$0.644150\pi$
$762$	−1.49186e142	−0.328820
$763$	3.55795e141	0.0734912
$764$	8.33147e142	1.61287
$765$	−8.78120e142	−1.59336
$766$	−3.35212e142	−0.570158
$767$	4.58146e142	0.730523
$768$	−1.89256e141	−0.0282924
$769$	−6.63743e142	−0.930349	−0.465174	−	0.885219i	$-0.654008\pi$
$769$	−6.63743e142	−0.930349	−0.465174	+	0.885219i	$0.654008\pi$
$770$	1.48204e142	0.194791
$771$	3.62078e142	0.446283
$772$	4.15237e142	0.479998
$773$	8.24179e142	0.893587	0.446793	−	0.894637i	$-0.352566\pi$
$773$	8.24179e142	0.893587	0.446793	+	0.894637i	$0.352566\pi$
$774$	−1.06757e142	−0.108572
$775$	−1.04679e142	−0.0998678
$776$	1.25813e143	1.12609
$777$	7.24751e142	0.608623
$778$	3.11747e142	0.245647
$779$	−5.43440e142	−0.401835
$780$	−1.14497e143	−0.794533
$781$	3.50708e142	0.228412
$782$	−1.02049e143	−0.623841
$783$	−8.49822e142	−0.487664
$784$	4.40691e141	0.0237405
$785$	1.27564e143	0.645179
$786$	−1.83638e142	−0.0872062
$787$	−2.45354e143	−1.09407	−0.547034	−	0.837111i	$-0.684243\pi$
$787$	−2.45354e143	−1.09407	−0.547034	+	0.837111i	$0.684243\pi$
$788$	1.44231e143	0.603963
$789$	−8.74513e142	−0.343918
$790$	1.78675e143	0.659968
$791$	1.38093e143	0.479111
$792$	6.93546e142	0.226037
$793$	−1.00346e144	−3.07238
$794$	5.11864e142	0.147245
$795$	−1.83592e142	−0.0496226
$796$	−4.00831e143	−1.01804
$797$	4.52195e143	1.07929	0.539646	−	0.841892i	$-0.318558\pi$
$797$	4.52195e143	1.07929	0.539646	+	0.841892i	$0.318558\pi$
$798$	−6.06196e142	−0.135978
$799$	1.07933e144	2.27556
$800$	2.08627e143	0.413444
$801$	−3.00863e143	−0.560480
$802$	−1.83777e143	−0.321855
$803$	3.85884e141	0.00635385
$804$	−3.70893e143	−0.574215
$805$	8.48730e143	1.23559
$806$	8.86835e142	0.121411
$807$	4.66935e143	0.601196
$808$	−7.05706e143	−0.854598
$809$	1.26235e144	1.43789	0.718946	−	0.695066i	$-0.244625\pi$
$809$	1.26235e144	1.43789	0.718946	+	0.695066i	$0.244625\pi$
$810$	−1.40632e143	−0.150687
$811$	−9.23607e143	−0.931011	−0.465506	−	0.885045i	$-0.654128\pi$
$811$	−9.23607e143	−0.931011	−0.465506	+	0.885045i	$0.654128\pi$
$812$	5.31785e143	0.504328
$813$	4.08048e143	0.364107
$814$	−2.31589e143	−0.194451
$815$	−7.78090e143	−0.614792
$816$	−7.09625e143	−0.527675
$817$	4.30776e143	0.301480
$818$	−2.59591e143	−0.171002
$819$	−1.94887e144	−1.20846
$820$	−9.49047e143	−0.553990
$821$	−4.63326e143	−0.254625	−0.127312	−	0.991863i	$-0.540635\pi$
$821$	−4.63326e143	−0.254625	−0.127312	+	0.991863i	$0.540635\pi$
$822$	−1.78065e143	−0.0921348
$823$	3.30495e143	0.161018	0.0805088	−	0.996754i	$-0.474345\pi$
$823$	3.30495e143	0.161018	0.0805088	+	0.996754i	$0.474345\pi$
$824$	−3.70286e143	−0.169879
$825$	2.27606e143	0.0983362
$826$	4.23602e143	0.172364
$827$	6.42093e142	0.0246079	0.0123040	−	0.999924i	$-0.496083\pi$
$827$	6.42093e142	0.0246079	0.0123040	+	0.999924i	$0.496083\pi$
$828$	1.84844e144	0.667272
$829$	−1.76717e143	−0.0600939	−0.0300469	−	0.999548i	$-0.509566\pi$
$829$	−1.76717e143	−0.0600939	−0.0300469	+	0.999548i	$0.509566\pi$
$830$	2.12000e144	0.679157
$831$	2.19369e144	0.662101
$832$	1.66520e144	0.473546
$833$	−2.43519e143	−0.0652536
$834$	1.12363e144	0.283730
$835$	−3.23320e144	−0.769399
$836$	−1.30241e144	−0.292105
$837$	8.81041e143	0.186245
$838$	3.08087e144	0.613896
$839$	4.47862e144	0.841254	0.420627	−	0.907234i	$-0.361810\pi$
$839$	4.47862e144	0.841254	0.420627	+	0.907234i	$0.361810\pi$
$840$	−2.27473e144	−0.402815
$841$	−4.05254e144	−0.676590
$842$	−1.27233e144	−0.200286
$843$	−3.33538e144	−0.495085
$844$	7.52759e144	1.05367
$845$	−1.29381e145	−1.70790
$846$	2.90765e144	0.362001
$847$	6.99707e144	0.821651
$848$	4.79153e143	0.0530737
$849$	−9.14354e143	−0.0955397
$850$	−2.89884e144	−0.285750
$851$	−1.32626e145	−1.23343
$852$	−2.50516e144	−0.219824
$853$	5.43353e144	0.449889	0.224945	−	0.974372i	$-0.427780\pi$
$853$	5.43353e144	0.449889	0.224945	+	0.974372i	$0.427780\pi$
$854$	−9.27796e144	−0.724916
$855$	9.54548e144	0.703842
$856$	3.56483e144	0.248078
$857$	−1.93165e145	−1.26876	−0.634378	−	0.773023i	$-0.718744\pi$
$857$	−1.93165e145	−1.26876	−0.634378	+	0.773023i	$0.718744\pi$
$858$	−1.92826e144	−0.119549
$859$	6.16032e144	0.360530	0.180265	−	0.983618i	$-0.442304\pi$
$859$	6.16032e144	0.360530	0.180265	+	0.983618i	$0.442304\pi$
$860$	7.52293e144	0.415636
$861$	5.00185e144	0.260901
$862$	4.10822e144	0.202322
$863$	3.34826e145	1.55699	0.778493	−	0.627653i	$-0.215984\pi$
$863$	3.34826e145	1.55699	0.778493	+	0.627653i	$0.215984\pi$
$864$	−1.75593e145	−0.771039
$865$	2.36411e145	0.980325
$866$	1.00330e145	0.392913
$867$	2.60666e145	0.964138
$868$	−5.51320e144	−0.192609
$869$	−2.02322e145	−0.667673
$870$	−3.85628e144	−0.120217
$871$	−7.15596e145	−2.10751
$872$	1.74502e144	0.0485550
$873$	4.85930e145	1.27752
$874$	1.10931e145	0.275573
$875$	−2.83232e145	−0.664881
$876$	−2.75643e143	−0.00611495
$877$	1.75895e145	0.368785	0.184393	−	0.982853i	$-0.440968\pi$
$877$	1.75895e145	0.368785	0.184393	+	0.982853i	$0.440968\pi$
$878$	−9.18228e144	−0.181958
$879$	3.62095e145	0.678223
$880$	−1.88590e145	−0.333908
$881$	−4.32841e145	−0.724470	−0.362235	−	0.932087i	$-0.617986\pi$
$881$	−4.32841e145	−0.724470	−0.362235	+	0.932087i	$0.617986\pi$
$882$	−6.56026e143	−0.0103807
$883$	−7.42579e145	−1.11093	−0.555467	−	0.831539i	$-0.687460\pi$
$883$	−7.42579e145	−1.11093	−0.555467	+	0.831539i	$0.687460\pi$
$884$	−1.65125e146	−2.33575
$885$	2.06537e145	0.276252
$886$	1.02060e145	0.129089
$887$	6.27848e145	0.750991	0.375496	−	0.926824i	$-0.377472\pi$
$887$	6.27848e145	0.750991	0.375496	+	0.926824i	$0.377472\pi$
$888$	3.55459e145	0.402112
$889$	1.78941e146	1.91457
$890$	−3.15321e145	−0.319116
$891$	1.59244e145	0.152446
$892$	1.04040e146	0.942198
$893$	−1.17327e146	−1.00520
$894$	−2.04233e145	−0.165546
$895$	1.64941e146	1.26500
$896$	1.41618e146	1.02771
$897$	−1.10428e146	−0.758318
$898$	−3.77581e145	−0.245376
$899$	−2.00827e145	−0.123515
$900$	5.25073e145	0.305644
$901$	−2.64772e145	−0.145880
$902$	−1.59831e145	−0.0833559
$903$	−3.96488e145	−0.195743
$904$	6.77287e145	0.316545
$905$	−7.51177e145	−0.332382
$906$	4.19558e145	0.175771
$907$	−2.30882e146	−0.915862	−0.457931	−	0.888988i	$-0.651409\pi$
$907$	−2.30882e146	−0.915862	−0.457931	+	0.888988i	$0.651409\pi$
$908$	1.03416e146	0.388454
$909$	−2.72565e146	−0.969524
$910$	−2.04253e146	−0.688048
$911$	3.63913e146	1.16102	0.580508	−	0.814255i	$-0.302854\pi$
$911$	3.63913e146	1.16102	0.580508	+	0.814255i	$0.302854\pi$
$912$	7.71388e145	0.233093
$913$	−2.40057e146	−0.687086
$914$	−6.35054e145	−0.172177
$915$	−4.52368e146	−1.16184
$916$	−2.87321e146	−0.699102
$917$	2.20264e146	0.507763
$918$	2.43983e146	0.532902
$919$	6.10053e146	1.26255	0.631277	−	0.775557i	$-0.282531\pi$
$919$	6.10053e146	1.26255	0.631277	+	0.775557i	$0.282531\pi$
$920$	4.16265e146	0.816342
$921$	6.79043e142	0.000126196 0
$922$	7.19013e145	0.126636
$923$	−4.83342e146	−0.806808
$924$	1.19875e146	0.189655
$925$	−3.76741e146	−0.564973
$926$	8.55460e145	0.121606
$927$	−1.43016e146	−0.192724
$928$	4.00252e146	0.511339
$929$	4.77493e146	0.578347	0.289174	−	0.957277i	$-0.406619\pi$
$929$	4.77493e146	0.578347	0.289174	+	0.957277i	$0.406619\pi$
$930$	3.99794e145	0.0459124
$931$	2.64714e145	0.0288248
$932$	4.03857e146	0.417004
$933$	5.74952e146	0.562977
$934$	2.39619e146	0.222511
$935$	1.04212e147	0.917787
$936$	−9.55837e146	−0.798416
$937$	−5.64932e146	−0.447596	−0.223798	−	0.974636i	$-0.571846\pi$
$937$	−5.64932e146	−0.447596	−0.223798	+	0.974636i	$0.571846\pi$
$938$	−6.61640e146	−0.497257
$939$	1.85374e145	0.0132160
$940$	−2.04896e147	−1.38581
$941$	1.66307e146	0.106715	0.0533575	−	0.998575i	$-0.483008\pi$
$941$	1.66307e146	0.106715	0.0533575	+	0.998575i	$0.483008\pi$
$942$	−1.53458e146	−0.0934266
$943$	−9.15315e146	−0.528739
$944$	−5.39037e146	−0.295464
$945$	−2.02918e147	−1.05547
$946$	1.26695e146	0.0625385
$947$	1.95971e147	0.918051	0.459026	−	0.888423i	$-0.348199\pi$
$947$	1.95971e147	0.918051	0.459026	+	0.888423i	$0.348199\pi$
$948$	1.44522e147	0.642570
$949$	−5.31820e145	−0.0224433
$950$	3.15114e146	0.126226
$951$	−1.00660e147	−0.382755
$952$	−3.28057e147	−1.18419
$953$	1.82910e147	0.626816	0.313408	−	0.949619i	$-0.398529\pi$
$953$	1.82910e147	0.626816	0.313408	+	0.949619i	$0.398529\pi$
$954$	−7.13281e145	−0.0232068
$955$	7.24659e147	2.23855
$956$	2.26845e146	0.0665370
$957$	4.36664e146	0.121620
$958$	−8.87345e146	−0.234693
$959$	2.13579e147	0.536460
$960$	7.50689e146	0.179075
$961$	−4.20554e147	−0.952828
$962$	3.19173e147	0.686847
$963$	1.37685e147	0.281439
$964$	−3.55791e147	−0.690847
$965$	3.61167e147	0.666201
$966$	−1.02101e147	−0.178922
$967$	−4.78838e147	−0.797221	−0.398610	−	0.917120i	$-0.630507\pi$
$967$	−4.78838e147	−0.797221	−0.398610	+	0.917120i	$0.630507\pi$
$968$	3.43176e147	0.542858
$969$	−4.26256e147	−0.640684
$970$	5.09281e147	0.727372
$971$	6.24694e147	0.847843	0.423922	−	0.905699i	$-0.360653\pi$
$971$	6.24694e147	0.847843	0.423922	+	0.905699i	$0.360653\pi$
$972$	−6.92522e147	−0.893210
$973$	−1.34774e148	−1.65203
$974$	−4.12272e147	−0.480303
$975$	−3.13684e147	−0.347347
$976$	1.18063e148	1.24264
$977$	−1.55966e148	−1.56045	−0.780224	−	0.625500i	$-0.784895\pi$
$977$	−1.55966e148	−1.56045	−0.780224	+	0.625500i	$0.784895\pi$
$978$	9.36034e146	0.0890263
$979$	3.57053e147	0.322841
$980$	4.62287e146	0.0397394
$981$	6.73980e146	0.0550847
$982$	6.52589e147	0.507132
$983$	−8.87816e147	−0.656031	−0.328015	−	0.944672i	$-0.606380\pi$
$983$	−8.87816e147	−0.656031	−0.328015	+	0.944672i	$0.606380\pi$
$984$	2.45319e147	0.172375
$985$	1.25450e148	0.838256
$986$	−5.56144e147	−0.353411
$987$	1.07988e148	0.652646
$988$	1.79497e148	1.03178
$989$	7.25553e147	0.396692
$990$	2.80741e147	0.146004
$991$	−1.06594e147	−0.0527336	−0.0263668	−	0.999652i	$-0.508394\pi$
$991$	−1.06594e147	−0.0527336	−0.0263668	+	0.999652i	$0.508394\pi$
$992$	−4.14956e147	−0.195287
$993$	−5.47521e147	−0.245139
$994$	−4.46898e147	−0.190363
$995$	−3.48637e148	−1.41296
$996$	1.71477e148	0.661253
$997$	6.57506e147	0.241262	0.120631	−	0.992697i	$-0.461508\pi$
$997$	6.57506e147	0.241262	0.120631	+	0.992697i	$0.461508\pi$
$998$	−5.02931e147	−0.175609
$999$	3.17088e148	1.05363

Twists

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

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

\(f(q)\)	\(=\)	\(q+2.86466e14 q^{2} +2.01536e23 q^{3} -5.51763e29 q^{4} -4.79915e34 q^{5} +5.77333e37 q^{6} -6.92478e41 q^{7} -3.39630e44 q^{8} -1.31176e47 q^{9} -1.37479e49 q^{10} +1.55674e51 q^{11} -1.11200e53 q^{12} -2.14548e55 q^{13} -1.98371e56 q^{14} -9.67203e57 q^{15} +2.52429e59 q^{16} -1.39488e61 q^{17} -3.75773e61 q^{18} +1.51628e63 q^{19} +2.64799e64 q^{20} -1.39560e65 q^{21} +4.45952e65 q^{22} +2.55387e67 q^{23} -6.84479e67 q^{24} +7.25462e68 q^{25} -6.14606e69 q^{26} -6.10591e70 q^{27} +3.82084e71 q^{28} +1.39180e72 q^{29} -2.77071e72 q^{30} -1.44293e73 q^{31} +2.87578e74 q^{32} +3.13740e74 q^{33} -3.99585e75 q^{34} +3.32331e76 q^{35} +7.23778e76 q^{36} -5.19313e77 q^{37} +4.34363e77 q^{38} -4.32392e78 q^{39} +1.62994e79 q^{40} -3.58403e79 q^{41} -3.99790e79 q^{42} +2.84099e80 q^{43} -8.58951e80 q^{44} +6.29531e81 q^{45} +7.31597e81 q^{46} -7.73779e82 q^{47} +5.08736e82 q^{48} +1.74580e82 q^{49} +2.07820e83 q^{50} -2.81119e84 q^{51} +1.18380e85 q^{52} +1.89817e84 q^{53} -1.74913e85 q^{54} -7.47103e85 q^{55} +2.35187e86 q^{56} +3.05587e86 q^{57} +3.98704e86 q^{58} -2.13540e87 q^{59} +5.33667e87 q^{60} +4.67707e88 q^{61} -4.13350e87 q^{62} +9.08362e88 q^{63} -7.76144e88 q^{64} +1.02965e90 q^{65} +8.98757e88 q^{66} +3.33536e90 q^{67} +7.69642e90 q^{68} +5.14698e90 q^{69} +9.52013e90 q^{70} +2.25284e91 q^{71} +4.45512e91 q^{72} +2.47879e90 q^{73} -1.48765e92 q^{74} +1.46207e92 q^{75} -8.36629e92 q^{76} -1.07801e93 q^{77} -1.23866e93 q^{78} -1.29965e94 q^{79} -1.21144e94 q^{80} +1.02293e94 q^{81} -1.02670e94 q^{82} -1.54205e95 q^{83} +7.70038e94 q^{84} +6.69423e95 q^{85} +8.13847e94 q^{86} +2.80499e95 q^{87} -5.28716e95 q^{88} +2.29359e96 q^{89} +1.80339e96 q^{90} +1.48570e97 q^{91} -1.40913e97 q^{92} -2.90803e96 q^{93} -2.21661e97 q^{94} -7.27688e97 q^{95} +5.79575e97 q^{96} -3.70442e98 q^{97} +5.00113e96 q^{98} -2.04206e98 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 208040616902520 q^{2} - 28\!\cdots\!20 q^{3} + 28\!\cdots\!24 q^{4} - 48\!\cdots\!60 q^{5} - 77\!\cdots\!44 q^{6} - 56\!\cdots\!00 q^{7} + 59\!\cdots\!60 q^{8} + 15\!\cdots\!76 q^{9} - 20\!\cdots\!60 q^{10}+ \cdots - 13\!\cdots\!08 q^{99}+O(q^{100}) \) 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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