LMFDB - Embedded newform 1.100.a.a.1.8

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			1.8
Root			$2.16174e13$ 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)

$f(q)$	$=$	\(q+1.53045e15 q^{2} -3.78025e23 q^{3} +1.70845e30 q^{4} -5.47796e34 q^{5} -5.78549e38 q^{6} -5.03791e41 q^{7} +1.64466e45 q^{8} -2.88893e46 q^{9} -8.38375e49 q^{10} +3.39044e50 q^{11} -6.45838e53 q^{12} +1.35923e55 q^{13} -7.71028e56 q^{14} +2.07081e58 q^{15} +1.43421e60 q^{16} +1.35236e61 q^{17} -4.42136e61 q^{18} +1.25642e63 q^{19} -9.35884e64 q^{20} +1.90446e65 q^{21} +5.18889e65 q^{22} +5.45698e66 q^{23} -6.21724e68 q^{24} +1.42309e69 q^{25} +2.08023e70 q^{26} +7.58628e70 q^{27} -8.60704e71 q^{28} +1.00507e72 q^{29} +3.16927e73 q^{30} -5.43714e73 q^{31} +1.15256e75 q^{32} -1.28167e74 q^{33} +2.06972e76 q^{34} +2.75975e76 q^{35} -4.93560e76 q^{36} -2.04705e77 q^{37} +1.92288e78 q^{38} -5.13823e78 q^{39} -9.00940e79 q^{40} +5.05152e79 q^{41} +2.91468e80 q^{42} +9.21616e80 q^{43} +5.79240e80 q^{44} +1.58254e81 q^{45} +8.35164e81 q^{46} +4.56701e82 q^{47} -5.42169e83 q^{48} -2.08262e83 q^{49} +2.17796e84 q^{50} -5.11227e84 q^{51} +2.32218e85 q^{52} -2.37631e85 q^{53} +1.16104e86 q^{54} -1.85727e85 q^{55} -8.28567e86 q^{56} -4.74957e86 q^{57} +1.53821e87 q^{58} +1.52955e87 q^{59} +3.53788e88 q^{60} +1.15621e88 q^{61} -8.32127e88 q^{62} +1.45542e88 q^{63} +8.54901e89 q^{64} -7.44581e89 q^{65} -1.96153e89 q^{66} +1.58442e90 q^{67} +2.31045e91 q^{68} -2.06288e90 q^{69} +4.22366e91 q^{70} -7.68861e91 q^{71} -4.75131e91 q^{72} +2.31521e92 q^{73} -3.13290e92 q^{74} -5.37963e92 q^{75} +2.14653e93 q^{76} -1.70807e92 q^{77} -7.86381e93 q^{78} +1.21213e94 q^{79} -7.85657e94 q^{80} -2.37151e94 q^{81} +7.73109e94 q^{82} +6.01316e94 q^{83} +3.25368e95 q^{84} -7.40819e95 q^{85} +1.41049e96 q^{86} -3.79942e95 q^{87} +5.57612e95 q^{88} +1.16422e96 q^{89} +2.42201e96 q^{90} -6.84768e96 q^{91} +9.32300e96 q^{92} +2.05538e97 q^{93} +6.98958e97 q^{94} -6.88260e97 q^{95} -4.35698e98 q^{96} -1.98012e98 q^{97} -3.18735e98 q^{98} -9.79473e96 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	1.53045e15	1.92236	0.961179	−	0.275925i	$-0.0889841\pi$
$2$	1.53045e15	1.92236	0.961179	+	0.275925i	$0.0889841\pi$
$3$	−3.78025e23	−0.912051	−0.456025	−	0.889967i	$-0.650727\pi$
$3$	−3.78025e23	−0.912051	−0.456025	+	0.889967i	$0.650727\pi$
$4$	1.70845e30	2.69546
$5$	−5.47796e34	−1.37913	−0.689563	−	0.724226i	$-0.742197\pi$
$5$	−5.47796e34	−1.37913	−0.689563	+	0.724226i	$0.742197\pi$
$6$	−5.78549e38	−1.75329
$7$	−5.03791e41	−0.741136	−0.370568	−	0.928805i	$-0.620837\pi$
$7$	−5.03791e41	−0.741136	−0.370568	+	0.928805i	$0.620837\pi$
$8$	1.64466e45	3.25929
$9$	−2.88893e46	−0.168164
$10$	−8.38375e49	−2.65117
$11$	3.39044e50	0.0957895	0.0478947	−	0.998852i	$-0.484749\pi$
$11$	3.39044e50	0.0957895	0.0478947	+	0.998852i	$0.484749\pi$
$12$	−6.45838e53	−2.45840
$13$	1.35923e55	0.984231	0.492115	−	0.870530i	$-0.336224\pi$
$13$	1.35923e55	0.984231	0.492115	+	0.870530i	$0.336224\pi$
$14$	−7.71028e56	−1.42473
$15$	2.07081e58	1.25783
$16$	1.43421e60	3.57005
$17$	1.35236e61	1.67445	0.837224	−	0.546860i	$-0.184177\pi$
$17$	1.35236e61	1.67445	0.837224	+	0.546860i	$0.184177\pi$
$18$	−4.42136e61	−0.323271
$19$	1.25642e63	0.632165	0.316082	−	0.948732i	$-0.397632\pi$
$19$	1.25642e63	0.632165	0.316082	+	0.948732i	$0.397632\pi$
$20$	−9.35884e64	−3.71738
$21$	1.90446e65	0.675953
$22$	5.18889e65	0.184142
$23$	5.45698e66	0.214499	0.107249	−	0.994232i	$-0.465796\pi$
$23$	5.45698e66	0.214499	0.107249	+	0.994232i	$0.465796\pi$
$24$	−6.21724e68	−2.97263
$25$	1.42309e69	0.901988
$26$	2.08023e70	1.89204
$27$	7.58628e70	1.06542
$28$	−8.60704e71	−1.99770
$29$	1.00507e72	0.410672	0.205336	−	0.978692i	$-0.434171\pi$
$29$	1.00507e72	0.410672	0.205336	+	0.978692i	$0.434171\pi$
$30$	3.16927e73	2.41800
$31$	−5.43714e73	−0.818402	−0.409201	−	0.912444i	$-0.634193\pi$
$31$	−5.43714e73	−0.818402	−0.409201	+	0.912444i	$0.634193\pi$
$32$	1.15256e75	3.60364
$33$	−1.28167e74	−0.0873648
$34$	2.06972e76	3.21889
$35$	2.75975e76	1.02212
$36$	−4.93560e76	−0.453279
$37$	−2.04705e77	−0.484331	−0.242166	−	0.970235i	$-0.577858\pi$
$37$	−2.04705e77	−0.484331	−0.242166	+	0.970235i	$0.577858\pi$
$38$	1.92288e78	1.21525
$39$	−5.13823e78	−0.897668
$40$	−9.00940e79	−4.49497
$41$	5.05152e79	0.742371	0.371185	−	0.928559i	$-0.378951\pi$
$41$	5.05152e79	0.742371	0.371185	+	0.928559i	$0.378951\pi$
$42$	2.91468e80	1.29942
$43$	9.21616e80	1.28192	0.640961	−	0.767573i	$-0.278536\pi$
$43$	9.21616e80	1.28192	0.640961	+	0.767573i	$0.278536\pi$
$44$	5.79240e80	0.258197
$45$	1.58254e81	0.231919
$46$	8.35164e81	0.412344
$47$	4.56701e82	0.777656	0.388828	−	0.921310i	$-0.372880\pi$
$47$	4.56701e82	0.777656	0.388828	+	0.921310i	$0.372880\pi$
$48$	−5.42169e83	−3.25607
$49$	−2.08262e83	−0.450718
$50$	2.17796e84	1.73394
$51$	−5.11227e84	−1.52718
$52$	2.32218e85	2.65296
$53$	−2.37631e85	−1.05742	−0.528709	−	0.848803i	$-0.677324\pi$
$53$	−2.37631e85	−1.05742	−0.528709	+	0.848803i	$0.677324\pi$
$54$	1.16104e86	2.04813
$55$	−1.85727e85	−0.132106
$56$	−8.28567e86	−2.41557
$57$	−4.74957e86	−0.576566
$58$	1.53821e87	0.789459
$59$	1.52955e87	0.336813	0.168407	−	0.985718i	$-0.446138\pi$
$59$	1.52955e87	0.336813	0.168407	+	0.985718i	$0.446138\pi$
$60$	3.53788e88	3.39044
$61$	1.15621e88	0.488889	0.244444	−	0.969663i	$-0.421394\pi$
$61$	1.15621e88	0.488889	0.244444	+	0.969663i	$0.421394\pi$
$62$	−8.32127e88	−1.57326
$63$	1.45542e88	0.124632
$64$	8.54901e89	3.35743
$65$	−7.44581e89	−1.35738
$66$	−1.96153e89	−0.167946
$67$	1.58442e90	0.644419	0.322209	−	0.946668i	$-0.395574\pi$
$67$	1.58442e90	0.644419	0.322209	+	0.946668i	$0.395574\pi$
$68$	2.31045e91	4.51341
$69$	−2.06288e90	−0.195634
$70$	4.22366e91	1.96488
$71$	−7.68861e91	−1.77239	−0.886195	−	0.463312i	$-0.846661\pi$
$71$	−7.68861e91	−1.77239	−0.886195	+	0.463312i	$0.846661\pi$
$72$	−4.75131e91	−0.548094
$73$	2.31521e92	1.34930	0.674651	−	0.738137i	$-0.264294\pi$
$73$	2.31521e92	1.34930	0.674651	+	0.738137i	$0.264294\pi$
$74$	−3.13290e92	−0.931058
$75$	−5.37963e92	−0.822658
$76$	2.14653e93	1.70398
$77$	−1.70807e92	−0.0709930
$78$	−7.86381e93	−1.72564
$79$	1.21213e94	1.41582	0.707912	−	0.706300i	$-0.249637\pi$
$79$	1.21213e94	1.41582	0.707912	+	0.706300i	$0.249637\pi$
$80$	−7.85657e94	−4.92355
$81$	−2.37151e94	−0.803557
$82$	7.73109e94	1.42710
$83$	6.01316e94	0.609169	0.304584	−	0.952485i	$-0.401482\pi$
$83$	6.01316e94	0.609169	0.304584	+	0.952485i	$0.401482\pi$
$84$	3.25368e95	1.82201
$85$	−7.40819e95	−2.30927
$86$	1.41049e96	2.46431
$87$	−3.79942e95	−0.374554
$88$	5.57612e95	0.312205
$89$	1.16422e96	0.372587	0.186294	−	0.982494i	$-0.440352\pi$
$89$	1.16422e96	0.372587	0.186294	+	0.982494i	$0.440352\pi$
$90$	2.42201e96	0.445832
$91$	−6.84768e96	−0.729449
$92$	9.32300e96	0.578173
$93$	2.05538e97	0.746424
$94$	6.98958e97	1.49493
$95$	−6.88260e97	−0.871834
$96$	−4.35698e98	−3.28670
$97$	−1.98012e98	−0.894315	−0.447157	−	0.894455i	$-0.647564\pi$
$97$	−1.98012e98	−0.894315	−0.447157	+	0.894455i	$0.647564\pi$
$98$	−3.18735e98	−0.866441
$99$	−9.79473e96	−0.0161083
$100$	2.43127e99	2.43127
$101$	2.17919e99	1.33164	0.665821	−	0.746112i	$-0.268082\pi$
$101$	2.17919e99	1.33164	0.665821	+	0.746112i	$0.268082\pi$
$102$	−7.82408e99	−2.93579
$103$	4.44175e99	1.02828	0.514140	−	0.857706i	$-0.328111\pi$
$103$	4.44175e99	1.02828	0.514140	+	0.857706i	$0.328111\pi$
$104$	2.23547e100	3.20789
$105$	−1.04326e100	−0.932225
$106$	−3.63682e100	−2.03274
$107$	−1.98838e100	−0.698235	−0.349118	−	0.937079i	$-0.613519\pi$
$107$	−1.98838e100	−0.698235	−0.349118	+	0.937079i	$0.613519\pi$
$108$	1.29608e101	2.87181
$109$	3.73079e100	0.523829	0.261914	−	0.965091i	$-0.415646\pi$
$109$	3.73079e100	0.523829	0.261914	+	0.965091i	$0.415646\pi$
$110$	−2.84246e100	−0.253954
$111$	7.73836e100	0.441734
$112$	−7.22545e101	−2.64590
$113$	−1.45152e101	−0.342327	−0.171163	−	0.985243i	$-0.554753\pi$
$113$	−1.45152e101	−0.342327	−0.171163	+	0.985243i	$0.554753\pi$
$114$	−7.26898e101	−1.10837
$115$	−2.98932e101	−0.295821
$116$	1.71711e102	1.10695
$117$	−3.92672e101	−0.165512
$118$	2.34090e102	0.647475
$119$	−6.81309e102	−1.24099
$120$	3.40578e103	4.09964
$121$	−1.24129e103	−0.990824
$122$	1.76952e103	0.939819
$123$	−1.90960e103	−0.677080
$124$	−9.28910e103	−2.20597
$125$	8.47091e102	0.135171
$126$	2.22744e103	0.239588
$127$	−4.41405e102	−0.0321035	−0.0160518	−	0.999871i	$-0.505110\pi$
$127$	−4.41405e102	−0.0321035	−0.0160518	+	0.999871i	$0.505110\pi$
$128$	5.77858e104	2.85055
$129$	−3.48394e104	−1.16918
$130$	−1.13954e105	−2.60937
$131$	−1.64894e104	−0.258390	−0.129195	−	0.991619i	$-0.541239\pi$
$131$	−1.64894e104	−0.258390	−0.129195	+	0.991619i	$0.541239\pi$
$132$	−2.18967e104	−0.235489
$133$	−6.32972e104	−0.468520
$134$	2.42488e105	1.23880
$135$	−4.15574e105	−1.46935
$136$	2.22418e106	5.45750
$137$	−9.80328e105	−1.67380	−0.836900	−	0.547356i	$-0.815634\pi$
$137$	−9.80328e105	−1.67380	−0.836900	+	0.547356i	$0.815634\pi$
$138$	−3.15713e105	−0.376078
$139$	−8.10620e105	−0.675437	−0.337719	−	0.941247i	$-0.609655\pi$
$139$	−8.10620e105	−0.675437	−0.337719	+	0.941247i	$0.609655\pi$
$140$	4.71490e106	2.75508
$141$	−1.72644e106	−0.709262
$142$	−1.17670e107	−3.40717
$143$	4.60838e105	0.0942789
$144$	−4.14334e106	−0.600354
$145$	−5.50573e106	−0.566369
$146$	3.54332e107	2.59384
$147$	7.87284e106	0.411077
$148$	−3.49728e107	−1.30550
$149$	8.40473e106	0.224804	0.112402	−	0.993663i	$-0.464146\pi$
$149$	8.40473e106	0.224804	0.112402	+	0.993663i	$0.464146\pi$
$150$	−8.23325e107	−1.58144
$151$	4.48798e107	0.620429	0.310214	−	0.950667i	$-0.399599\pi$
$151$	4.48798e107	0.620429	0.310214	+	0.950667i	$0.399599\pi$
$152$	2.06638e108	2.06041
$153$	−3.90688e107	−0.281582
$154$	−2.61412e107	−0.136474
$155$	2.97845e108	1.12868
$156$	−8.77843e108	−2.41963
$157$	5.26096e108	1.05690	0.528448	−	0.848966i	$-0.322774\pi$
$157$	5.26096e108	1.05690	0.528448	+	0.848966i	$0.322774\pi$
$158$	1.85511e109	2.72172
$159$	8.98304e108	0.964419
$160$	−6.31370e109	−4.96987
$161$	−2.74918e108	−0.158973
$162$	−3.62948e109	−1.54472
$163$	−1.62766e109	−0.510832	−0.255416	−	0.966831i	$-0.582212\pi$
$163$	−1.62766e109	−0.510832	−0.255416	+	0.966831i	$0.582212\pi$
$164$	8.63027e109	2.00103
$165$	7.02095e108	0.120487
$166$	9.20285e109	1.17104
$167$	7.07232e109	0.668493	0.334246	−	0.942486i	$-0.391518\pi$
$167$	7.07232e109	0.668493	0.334246	+	0.942486i	$0.391518\pi$
$168$	3.13219e110	2.20313
$169$	−5.96753e108	−0.0312898
$170$	−1.13379e111	−4.43925
$171$	−3.62970e109	−0.106307
$172$	1.57454e111	3.45537
$173$	−3.85205e110	−0.634468	−0.317234	−	0.948347i	$-0.602754\pi$
$173$	−3.85205e110	−0.634468	−0.317234	+	0.948347i	$0.602754\pi$
$174$	−5.81482e110	−0.720027
$175$	−7.16938e110	−0.668495
$176$	4.86261e110	0.341974
$177$	−5.78208e110	−0.307190
$178$	1.78177e111	0.716246
$179$	−5.75408e111	−1.75288	−0.876438	−	0.481516i	$-0.840086\pi$
$179$	−5.75408e111	−1.75288	−0.876438	+	0.481516i	$0.840086\pi$
$180$	2.70370e111	0.625129
$181$	3.72717e111	0.655073	0.327537	−	0.944838i	$-0.393782\pi$
$181$	3.72717e111	0.655073	0.327537	+	0.944838i	$0.393782\pi$
$182$	−1.04800e112	−1.40226
$183$	−4.37077e111	−0.445891
$184$	8.97490e111	0.699113
$185$	1.12136e112	0.667953
$186$	3.14565e112	1.43489
$187$	4.58510e111	0.160394
$188$	7.80251e112	2.09614
$189$	−3.82190e112	−0.789624
$190$	−1.05335e113	−1.67598
$191$	4.34088e112	0.532630	0.266315	−	0.963886i	$-0.414194\pi$
$191$	4.34088e112	0.532630	0.266315	+	0.963886i	$0.414194\pi$
$192$	−3.23174e113	−3.06215
$193$	1.95579e113	1.43296	0.716482	−	0.697606i	$-0.245751\pi$
$193$	1.95579e113	1.43296	0.716482	+	0.697606i	$0.245751\pi$
$194$	−3.03047e113	−1.71919
$195$	2.81471e113	1.23800
$196$	−3.55806e113	−1.21489
$197$	7.24923e113	1.92404	0.962019	−	0.272983i	$-0.0880104\pi$
$197$	7.24923e113	1.92404	0.962019	+	0.272983i	$0.0880104\pi$
$198$	−1.49903e112	−0.0309660
$199$	−1.15217e114	−1.85477	−0.927386	−	0.374106i	$-0.877950\pi$
$199$	−1.15217e114	−1.85477	−0.927386	+	0.374106i	$0.877950\pi$
$200$	2.34050e114	2.93984
$201$	−5.98952e113	−0.587743
$202$	3.33514e114	2.55989
$203$	−5.06346e113	−0.304364
$204$	−8.73408e114	−4.11646
$205$	−2.76720e114	−1.02382
$206$	6.79788e114	1.97672
$207$	−1.57648e113	−0.0360710
$208$	1.94943e115	3.51376
$209$	4.25980e113	0.0605547
$210$	−1.59665e115	−1.79207
$211$	−8.28477e114	−0.735019	−0.367510	−	0.930020i	$-0.619790\pi$
$211$	−8.28477e114	−0.735019	−0.367510	+	0.930020i	$0.619790\pi$
$212$	−4.05981e115	−2.85023
$213$	2.90649e115	1.61651
$214$	−3.04311e115	−1.34226
$215$	−5.04858e115	−1.76793
$216$	1.24769e116	3.47252
$217$	2.73919e115	0.606547
$218$	5.70979e115	1.00699
$219$	−8.75209e115	−1.23063
$220$	−3.17305e115	−0.356086
$221$	1.83817e116	1.64804
$222$	1.18432e116	0.849172
$223$	1.89839e116	1.08967	0.544834	−	0.838544i	$-0.316593\pi$
$223$	1.89839e116	1.08967	0.544834	+	0.838544i	$0.316593\pi$
$224$	−5.80652e116	−2.67079
$225$	−4.11119e115	−0.151682
$226$	−2.22148e116	−0.658074
$227$	5.86128e114	0.0139544	0.00697722	−	0.999976i	$-0.497779\pi$
$227$	5.86128e114	0.0139544	0.00697722	+	0.999976i	$0.497779\pi$
$228$	−8.11442e116	−1.55411
$229$	4.00083e116	0.617012	0.308506	−	0.951222i	$-0.400171\pi$
$229$	4.00083e116	0.617012	0.308506	+	0.951222i	$0.400171\pi$
$230$	−4.57500e116	−0.568674
$231$	6.45695e115	0.0647492
$232$	1.65300e117	1.33850
$233$	2.69064e117	1.76091	0.880457	−	0.474126i	$-0.157236\pi$
$233$	2.69064e117	1.76091	0.880457	+	0.474126i	$0.157236\pi$
$234$	−6.00965e116	−0.318174
$235$	−2.50179e117	−1.07249
$236$	2.61316e117	0.907867
$237$	−4.58217e117	−1.29130
$238$	−1.04271e118	−2.38563
$239$	8.77480e117	1.63133	0.815664	−	0.578526i	$-0.196372\pi$
$239$	8.77480e117	1.63133	0.815664	+	0.578526i	$0.196372\pi$
$240$	2.96998e118	4.49053
$241$	−1.15369e118	−1.41986	−0.709928	−	0.704274i	$-0.751273\pi$
$241$	−1.15369e118	−1.41986	−0.709928	+	0.704274i	$0.751273\pi$
$242$	−1.89973e118	−1.90472
$243$	−4.06775e117	−0.332540
$244$	1.97533e118	1.31778
$245$	1.14085e118	0.621596
$246$	−2.92255e118	−1.30159
$247$	1.70776e118	0.622196
$248$	−8.94226e118	−2.66741
$249$	−2.27313e118	−0.555592
$250$	1.29643e118	0.259848
$251$	2.16880e118	0.356756	0.178378	−	0.983962i	$-0.442915\pi$
$251$	2.16880e118	0.356756	0.178378	+	0.983962i	$0.442915\pi$
$252$	2.48651e118	0.335942
$253$	1.85016e117	0.0205467
$254$	−6.75548e117	−0.0617145
$255$	2.80048e119	2.10617
$256$	3.42526e119	2.12234
$257$	2.79031e119	1.42548	0.712742	−	0.701426i	$-0.247453\pi$
$257$	2.79031e119	1.42548	0.712742	+	0.701426i	$0.247453\pi$
$258$	−5.33200e119	−2.24758
$259$	1.03128e119	0.358955
$260$	−1.27208e120	−3.65876
$261$	−2.90358e118	−0.0690602
$262$	−2.52362e119	−0.496719
$263$	7.99032e119	1.30243	0.651216	−	0.758893i	$-0.274259\pi$
$263$	7.99032e119	1.30243	0.651216	+	0.758893i	$0.274259\pi$
$264$	−2.10792e119	−0.284747
$265$	1.30173e120	1.45831
$266$	−9.68732e119	−0.900663
$267$	−4.40103e119	−0.339818
$268$	2.70691e120	1.73701
$269$	−2.89810e120	−1.54659	−0.773295	−	0.634046i	$-0.781393\pi$
$269$	−2.89810e120	−1.54659	−0.773295	+	0.634046i	$0.781393\pi$
$270$	−6.36015e120	−2.82463
$271$	−7.18785e119	−0.265839	−0.132920	−	0.991127i	$-0.542435\pi$
$271$	−7.18785e119	−0.265839	−0.132920	+	0.991127i	$0.542435\pi$
$272$	1.93958e121	5.97787
$273$	2.58860e120	0.665294
$274$	−1.50034e121	−3.21764
$275$	4.82488e119	0.0864009
$276$	−3.52433e120	−0.527323
$277$	6.62161e120	0.828352	0.414176	−	0.910197i	$-0.364070\pi$
$277$	6.62161e120	0.828352	0.414176	+	0.910197i	$0.364070\pi$
$278$	−1.24061e121	−1.29843
$279$	1.57075e120	0.137626
$280$	4.53886e121	3.33138
$281$	8.40733e120	0.517244	0.258622	−	0.965979i	$-0.416732\pi$
$281$	8.40733e120	0.517244	0.258622	+	0.965979i	$0.416732\pi$
$282$	−2.64224e121	−1.36346
$283$	1.41547e121	0.613015	0.306508	−	0.951868i	$-0.400839\pi$
$283$	1.41547e121	0.613015	0.306508	+	0.951868i	$0.400839\pi$
$284$	−1.31356e122	−4.77741
$285$	2.60180e121	0.795157
$286$	7.05290e120	0.181238
$287$	−2.54491e121	−0.550198
$288$	−3.32968e121	−0.606002
$289$	1.17659e122	1.80377
$290$	−8.42625e121	−1.08876
$291$	7.48535e121	0.815660
$292$	3.95543e122	3.63699
$293$	−9.54465e121	−0.740990	−0.370495	−	0.928834i	$-0.620812\pi$
$293$	−9.54465e121	−0.740990	−0.370495	+	0.928834i	$0.620812\pi$
$294$	1.20490e122	0.790238
$295$	−8.37881e121	−0.464507
$296$	−3.36670e122	−1.57857
$297$	2.57208e121	0.102056
$298$	1.28630e122	0.432153
$299$	7.41730e121	0.211116
$300$	−9.19083e122	−2.21744
$301$	−4.64303e122	−0.950079
$302$	6.86863e122	1.19269
$303$	−8.23789e122	−1.21452
$304$	1.80197e123	2.25686
$305$	−6.33368e122	−0.674239
$306$	−5.97929e122	−0.541301
$307$	1.63291e123	1.25781	0.628903	−	0.777483i	$-0.283504\pi$
$307$	1.63291e123	1.25781	0.628903	+	0.777483i	$0.283504\pi$
$308$	−2.91816e122	−0.191359
$309$	−1.67909e123	−0.937843
$310$	4.55836e123	2.16973
$311$	5.34818e122	0.217054	0.108527	−	0.994094i	$-0.465387\pi$
$311$	5.34818e122	0.217054	0.108527	+	0.994094i	$0.465387\pi$
$312$	−8.45066e123	−2.92576
$313$	−5.67018e123	−1.67553	−0.837765	−	0.546031i	$-0.816138\pi$
$313$	−5.67018e123	−1.67553	−0.837765	+	0.546031i	$0.816138\pi$
$314$	8.05164e123	2.03173
$315$	−7.97273e122	−0.171884
$316$	2.07087e124	3.81630
$317$	−6.49875e123	−1.02423	−0.512113	−	0.858918i	$-0.671137\pi$
$317$	−6.49875e123	−1.02423	−0.512113	+	0.858918i	$0.671137\pi$
$318$	1.37481e124	1.85396
$319$	3.40762e122	0.0393381
$320$	−4.68311e124	−4.63032
$321$	7.51657e123	0.636826
$322$	−4.20749e123	−0.305603
$323$	1.69913e124	1.05853
$324$	−4.05161e124	−2.16596
$325$	1.93430e124	0.887764
$326$	−2.49106e124	−0.982003
$327$	−1.41033e124	−0.477758
$328$	8.30804e124	2.41960
$329$	−2.30082e124	−0.576349
$330$	1.07452e124	0.231619
$331$	−4.48538e124	−0.832365	−0.416183	−	0.909281i	$-0.636632\pi$
$331$	−4.48538e124	−0.832365	−0.416183	+	0.909281i	$0.636632\pi$
$332$	1.02732e125	1.64199
$333$	5.91377e123	0.0814470
$334$	1.08238e125	1.28508
$335$	−8.67941e124	−0.888735
$336$	2.73140e125	2.41319
$337$	−1.15425e125	−0.880276	−0.440138	−	0.897930i	$-0.645070\pi$
$337$	−1.15425e125	−0.880276	−0.440138	+	0.897930i	$0.645070\pi$
$338$	−9.13301e123	−0.0601502
$339$	5.48712e124	0.312219
$340$	−1.26565e126	−6.22456
$341$	−1.84343e124	−0.0783943
$342$	−5.55507e124	−0.204361
$343$	3.37707e125	1.07518
$344$	1.51575e126	4.17815
$345$	1.13004e125	0.269804
$346$	−5.89537e125	−1.21967
$347$	2.03399e125	0.364787	0.182393	−	0.983226i	$-0.441616\pi$
$347$	2.03399e125	0.364787	0.182393	+	0.983226i	$0.441616\pi$
$348$	−6.49113e125	−1.00960
$349$	−2.16999e124	−0.0292819	−0.0146409	−	0.999893i	$-0.504661\pi$
$349$	−2.16999e124	−0.0292819	−0.0146409	+	0.999893i	$0.504661\pi$
$350$	−1.09724e126	−1.28509
$351$	1.03115e126	1.04862
$352$	3.90769e125	0.345190
$353$	−1.28686e126	−0.987834	−0.493917	−	0.869509i	$-0.664435\pi$
$353$	−1.28686e126	−0.987834	−0.493917	+	0.869509i	$0.664435\pi$
$354$	−8.84919e125	−0.590530
$355$	4.21179e126	2.44435
$356$	1.98901e126	1.00429
$357$	2.57552e126	1.13185
$358$	−8.80633e126	−3.36965
$359$	1.70618e126	0.568656	0.284328	−	0.958727i	$-0.408230\pi$
$359$	1.70618e126	0.568656	0.284328	+	0.958727i	$0.408230\pi$
$360$	2.60275e126	0.755891
$361$	−2.37150e126	−0.600368
$362$	5.70425e126	1.25929
$363$	4.69238e126	0.903682
$364$	−1.16989e127	−1.96620
$365$	−1.26826e127	−1.86086
$366$	−6.68924e126	−0.857163
$367$	−8.66487e126	−0.970045	−0.485022	−	0.874502i	$-0.661189\pi$
$367$	−8.66487e126	−0.970045	−0.485022	+	0.874502i	$0.661189\pi$
$368$	7.82648e126	0.765772
$369$	−1.45935e126	−0.124840
$370$	1.71619e127	1.28405
$371$	1.19716e127	0.783691
$372$	3.51151e127	2.01196
$373$	−2.23251e127	−1.11997	−0.559984	−	0.828503i	$-0.689193\pi$
$373$	−2.23251e127	−1.11997	−0.559984	+	0.828503i	$0.689193\pi$
$374$	7.01727e126	0.308336
$375$	−3.20222e126	−0.123283
$376$	7.51119e127	2.53460
$377$	1.36612e127	0.404196
$378$	−5.84923e127	−1.51794
$379$	−5.42523e127	−1.23531	−0.617657	−	0.786448i	$-0.711918\pi$
$379$	−5.42523e127	−1.23531	−0.617657	+	0.786448i	$0.711918\pi$
$380$	−1.17586e128	−2.35000
$381$	1.66862e126	0.0292801
$382$	6.64350e127	1.02391
$383$	9.41348e127	1.27471	0.637354	−	0.770571i	$-0.280029\pi$
$383$	9.41348e127	1.27471	0.637354	+	0.770571i	$0.280029\pi$
$384$	−2.18445e128	−2.59984
$385$	9.35676e126	0.0979083
$386$	2.99324e128	2.75467
$387$	−2.66249e127	−0.215573
$388$	−3.38294e128	−2.41059
$389$	−1.24505e128	−0.781055	−0.390527	−	0.920591i	$-0.627707\pi$
$389$	−1.24505e128	−0.781055	−0.390527	+	0.920591i	$0.627707\pi$
$390$	4.30777e128	2.37987
$391$	7.37982e127	0.359167
$392$	−3.42521e128	−1.46902
$393$	6.23342e127	0.235665
$394$	1.10946e129	3.69869
$395$	−6.64002e128	−1.95260
$396$	−1.67338e127	−0.0434194
$397$	2.44394e128	0.559707	0.279854	−	0.960043i	$-0.409714\pi$
$397$	2.44394e128	0.559707	0.279854	+	0.960043i	$0.409714\pi$
$398$	−1.76334e129	−3.56554
$399$	2.39279e128	0.427314
$400$	2.04101e129	3.22014
$401$	−4.98178e128	−0.694606	−0.347303	−	0.937753i	$-0.612902\pi$
$401$	−4.98178e128	−0.694606	−0.347303	+	0.937753i	$0.612902\pi$
$402$	−9.16666e128	−1.12985
$403$	−7.39032e128	−0.805497
$404$	3.72304e129	3.58939
$405$	1.29910e129	1.10821
$406$	−7.74937e128	−0.585097
$407$	−6.94038e127	−0.0463938
$408$	−8.40797e129	−4.97752
$409$	−2.01644e129	−1.05750	−0.528751	−	0.848777i	$-0.677339\pi$
$409$	−2.01644e129	−1.05750	−0.528751	+	0.848777i	$0.677339\pi$
$410$	−4.23506e129	−1.96815
$411$	3.70589e129	1.52659
$412$	7.58852e129	2.77169
$413$	−7.70574e128	−0.249624
$414$	−2.41273e128	−0.0693413
$415$	−3.29399e129	−0.840120
$416$	1.56660e130	3.54681
$417$	3.06435e129	0.616033
$418$	6.51941e128	0.116408
$419$	6.71617e129	1.06544	0.532718	−	0.846293i	$-0.321171\pi$
$419$	6.71617e129	1.06544	0.532718	+	0.846293i	$0.321171\pi$
$420$	−1.78235e130	−2.51278
$421$	1.14119e130	1.43019	0.715096	−	0.699026i	$-0.246383\pi$
$421$	1.14119e130	1.43019	0.715096	+	0.699026i	$0.246383\pi$
$422$	−1.26794e130	−1.41297
$423$	−1.31938e129	−0.130774
$424$	−3.90822e130	−3.44643
$425$	1.92453e130	1.51033
$426$	4.44824e130	3.10751
$427$	−5.82489e129	−0.362333
$428$	−3.39705e130	−1.88207
$429$	−1.74209e129	−0.0859871
$430$	−7.72660e130	−3.39860
$431$	−1.24856e130	−0.489535	−0.244767	−	0.969582i	$-0.578712\pi$
$431$	−1.24856e130	−0.489535	−0.244767	+	0.969582i	$0.578712\pi$
$432$	1.08804e131	3.80362
$433$	−7.01159e129	−0.218608	−0.109304	−	0.994008i	$-0.534862\pi$
$433$	−7.01159e129	−0.218608	−0.109304	+	0.994008i	$0.534862\pi$
$434$	4.19219e130	1.16600
$435$	2.08131e130	0.516557
$436$	6.37388e130	1.41196
$437$	6.85624e129	0.135599
$438$	−1.33946e131	−2.36571
$439$	−9.90834e130	−1.56317	−0.781586	−	0.623797i	$-0.785589\pi$
$439$	−9.90834e130	−1.56317	−0.781586	+	0.623797i	$0.785589\pi$
$440$	−3.05458e130	−0.430570
$441$	6.01655e129	0.0757944
$442$	2.81323e131	3.16813
$443$	−1.72237e131	−1.73437	−0.867184	−	0.497988i	$-0.834073\pi$
$443$	−1.72237e131	−1.73437	−0.867184	+	0.497988i	$0.834073\pi$
$444$	1.32206e131	1.19068
$445$	−6.37753e130	−0.513845
$446$	2.90539e131	2.09473
$447$	−3.17720e130	−0.205032
$448$	−4.30692e131	−2.48831
$449$	1.78929e131	0.925736	0.462868	−	0.886427i	$-0.346820\pi$
$449$	1.78929e131	0.925736	0.462868	+	0.886427i	$0.346820\pi$
$450$	−6.29198e130	−0.291587
$451$	1.71268e130	0.0711113
$452$	−2.47986e131	−0.922728
$453$	−1.69657e131	−0.565862
$454$	8.97039e129	0.0268254
$455$	3.75114e131	1.00600
$456$	−7.81144e131	−1.87919
$457$	−4.33551e131	−0.935811	−0.467906	−	0.883778i	$-0.654991\pi$
$457$	−4.33551e131	−0.935811	−0.467906	+	0.883778i	$0.654991\pi$
$458$	6.12307e131	1.18612
$459$	1.02594e132	1.78400
$460$	−5.10710e131	−0.797374
$461$	−4.19594e131	−0.588346	−0.294173	−	0.955752i	$-0.595044\pi$
$461$	−4.19594e131	−0.588346	−0.294173	+	0.955752i	$0.595044\pi$
$462$	9.88204e130	0.124471
$463$	1.22882e132	1.39069	0.695343	−	0.718678i	$-0.255253\pi$
$463$	1.22882e132	1.39069	0.695343	+	0.718678i	$0.255253\pi$
$464$	1.44148e132	1.46612
$465$	−1.12593e132	−1.02941
$466$	4.11790e132	3.38511
$467$	−1.48691e132	−1.09925	−0.549627	−	0.835410i	$-0.685230\pi$
$467$	−1.48691e132	−1.09925	−0.549627	+	0.835410i	$0.685230\pi$
$468$	−6.70861e131	−0.446132
$469$	−7.98219e131	−0.477602
$470$	−3.82886e132	−2.06170
$471$	−1.98878e132	−0.963942
$472$	2.51559e132	1.09777
$473$	3.12468e131	0.122795
$474$	−7.01279e132	−2.48235
$475$	1.78799e132	0.570205
$476$	−1.16398e133	−3.34505
$477$	6.86498e131	0.177820
$478$	1.34294e133	3.13600
$479$	6.76263e132	1.42399	0.711996	−	0.702183i	$-0.247791\pi$
$479$	6.76263e132	1.42399	0.711996	+	0.702183i	$0.247791\pi$
$480$	2.38674e133	4.53277
$481$	−2.78241e132	−0.476694
$482$	−1.76566e133	−2.72947
$483$	1.03926e132	0.144991
$484$	−2.12068e133	−2.67073
$485$	1.08470e133	1.23337
$486$	−6.22549e132	−0.639261
$487$	−1.20139e133	−1.11430	−0.557150	−	0.830412i	$-0.688105\pi$
$487$	−1.20139e133	−1.11430	−0.557150	+	0.830412i	$0.688105\pi$
$488$	1.90158e133	1.59343
$489$	6.15298e132	0.465905
$490$	1.74602e133	1.19493
$491$	9.61080e132	0.594601	0.297301	−	0.954784i	$-0.403914\pi$
$491$	9.61080e132	0.594601	0.297301	+	0.954784i	$0.403914\pi$
$492$	−3.26246e133	−1.82504
$493$	1.35922e133	0.687649
$494$	2.61364e133	1.19608
$495$	5.36552e131	0.0222154
$496$	−7.79802e133	−2.92174
$497$	3.87345e133	1.31358
$498$	−3.47891e133	−1.06805
$499$	−5.04892e132	−0.140353	−0.0701764	−	0.997535i	$-0.522356\pi$
$499$	−5.04892e132	−0.140353	−0.0701764	+	0.997535i	$0.522356\pi$
$500$	1.44721e133	0.364349
$501$	−2.67352e133	−0.609699
$502$	3.31925e133	0.685812
$503$	6.30668e132	0.118082	0.0590412	−	0.998256i	$-0.481196\pi$
$503$	6.30668e132	0.118082	0.0590412	+	0.998256i	$0.481196\pi$
$504$	2.39367e133	0.406212
$505$	−1.19375e134	−1.83650
$506$	2.83157e132	0.0394982
$507$	2.25588e132	0.0285379
$508$	−7.54119e132	−0.0865339
$509$	−8.79618e133	−0.915723	−0.457861	−	0.889024i	$-0.651384\pi$
$509$	−8.79618e133	−0.915723	−0.457861	+	0.889024i	$0.651384\pi$
$510$	4.28600e134	4.04882
$511$	−1.16638e134	−1.00002
$512$	1.57957e134	1.22935
$513$	9.53153e133	0.673524
$514$	4.27043e134	2.74029
$515$	−2.43317e134	−1.41813
$516$	−5.95215e134	−3.15147
$517$	1.54841e133	0.0744913
$518$	1.57833e134	0.690041
$519$	1.45617e134	0.578667
$520$	−1.22458e135	−4.42408
$521$	1.32044e134	0.433762	0.216881	−	0.976198i	$-0.430412\pi$
$521$	1.32044e134	0.433762	0.216881	+	0.976198i	$0.430412\pi$
$522$	−4.44378e133	−0.132759
$523$	2.65366e134	0.721127	0.360563	−	0.932735i	$-0.382584\pi$
$523$	2.65366e134	0.721127	0.360563	+	0.932735i	$0.382584\pi$
$524$	−2.81714e134	−0.696481
$525$	2.71021e134	0.609702
$526$	1.22288e135	2.50374
$527$	−7.35299e134	−1.37037
$528$	−1.83819e134	−0.311897
$529$	−6.17447e134	−0.953990
$530$	1.99224e135	2.80340
$531$	−4.41876e133	−0.0566398
$532$	−1.08140e135	−1.26288
$533$	6.86617e134	0.730664
$534$	−6.73556e134	−0.653253
$535$	1.08923e135	0.962954
$536$	2.60584e135	2.10035
$537$	2.17519e135	1.59871
$538$	−4.43539e135	−2.97310
$539$	−7.06100e133	−0.0431740
$540$	−7.09988e135	−3.96059
$541$	3.44420e133	0.0175317	0.00876584	−	0.999962i	$-0.497210\pi$
$541$	3.44420e133	0.0175317	0.00876584	+	0.999962i	$0.497210\pi$
$542$	−1.10006e135	−0.511038
$543$	−1.40897e135	−0.597460
$544$	1.55868e136	6.03410
$545$	−2.04371e135	−0.722426
$546$	3.96172e135	1.27893
$547$	2.76369e135	0.814924	0.407462	−	0.913222i	$-0.366414\pi$
$547$	2.76369e135	0.814924	0.407462	+	0.913222i	$0.366414\pi$
$548$	−1.67484e136	−4.51166
$549$	−3.34021e134	−0.0822134
$550$	7.38424e134	0.166094
$551$	1.26279e135	0.259612
$552$	−3.39274e135	−0.637626
$553$	−6.10663e135	−1.04932
$554$	1.01340e136	1.59239
$555$	−4.23904e135	−0.609207
$556$	−1.38491e136	−1.82062
$557$	2.67649e135	0.321909	0.160954	−	0.986962i	$-0.448543\pi$
$557$	2.67649e135	0.321909	0.160954	+	0.986962i	$0.448543\pi$
$558$	2.40396e135	0.264566
$559$	1.25269e136	1.26171
$560$	3.95807e136	3.64902
$561$	−1.73328e135	−0.146288
$562$	1.28670e136	0.994328
$563$	−1.81161e135	−0.128204	−0.0641018	−	0.997943i	$-0.520418\pi$
$563$	−1.81161e135	−0.128204	−0.0641018	+	0.997943i	$0.520418\pi$
$564$	−2.94955e136	−1.91179
$565$	7.95138e135	0.472111
$566$	2.16630e136	1.17844
$567$	1.19475e136	0.595545
$568$	−1.26452e137	−5.77673
$569$	−2.24332e136	−0.939364	−0.469682	−	0.882836i	$-0.655631\pi$
$569$	−2.24332e136	−0.939364	−0.469682	+	0.882836i	$0.655631\pi$
$570$	3.98192e136	1.52858
$571$	3.51829e136	1.23835	0.619175	−	0.785253i	$-0.287467\pi$
$571$	3.51829e136	1.23835	0.619175	+	0.785253i	$0.287467\pi$
$572$	7.87320e135	0.254125
$573$	−1.64096e136	−0.485786
$574$	−3.89486e136	−1.05768
$575$	7.76576e135	0.193475
$576$	−2.46975e136	−0.564598
$577$	−1.55007e136	−0.325198	−0.162599	−	0.986692i	$-0.551988\pi$
$577$	−1.55007e136	−0.325198	−0.162599	+	0.986692i	$0.551988\pi$
$578$	1.80071e137	3.46750
$579$	−7.39338e136	−1.30694
$580$	−9.40628e136	−1.52662
$581$	−3.02938e136	−0.451477
$582$	1.14560e137	1.56799
$583$	−8.05672e135	−0.101290
$584$	3.80774e137	4.39776
$585$	2.15104e136	0.228262
$586$	−1.46076e137	−1.42445
$587$	−1.71523e137	−1.53722	−0.768612	−	0.639715i	$-0.779052\pi$
$587$	−1.71523e137	−1.53722	−0.768612	+	0.639715i	$0.779052\pi$
$588$	1.34504e137	1.10804
$589$	−6.83131e136	−0.517365
$590$	−1.28234e137	−0.892950
$591$	−2.74039e137	−1.75482
$592$	−2.93590e137	−1.72909
$593$	8.05225e136	0.436224	0.218112	−	0.975924i	$-0.430010\pi$
$593$	8.05225e136	0.436224	0.218112	+	0.975924i	$0.430010\pi$
$594$	3.93644e136	0.196189
$595$	3.73218e137	1.71149
$596$	1.43591e137	0.605950
$597$	4.35551e137	1.69165
$598$	1.13518e137	0.405841
$599$	−7.96716e134	−0.00262226	−0.00131113	−	0.999999i	$-0.500417\pi$
$599$	−7.96716e134	−0.00262226	−0.00131113	+	0.999999i	$0.500417\pi$
$600$	−8.84767e137	−2.68128
$601$	3.64301e136	0.101666	0.0508328	−	0.998707i	$-0.483812\pi$
$601$	3.64301e136	0.101666	0.0508328	+	0.998707i	$0.483812\pi$
$602$	−7.10592e137	−1.82639
$603$	−4.57728e136	−0.108368
$604$	7.66749e137	1.67234
$605$	6.79973e137	1.36647
$606$	−1.26077e138	−2.33475
$607$	−3.79526e137	−0.647742	−0.323871	−	0.946101i	$-0.604984\pi$
$607$	−3.79526e137	−0.647742	−0.323871	+	0.946101i	$0.604984\pi$
$608$	1.44810e138	2.27809
$609$	1.91411e137	0.277595
$610$	−9.69338e137	−1.29613
$611$	6.20761e137	0.765393
$612$	−6.67472e137	−0.758993
$613$	7.88707e137	0.827222	0.413611	−	0.910454i	$-0.364267\pi$
$613$	7.88707e137	0.827222	0.413611	+	0.910454i	$0.364267\pi$
$614$	2.49909e138	2.41796
$615$	1.04607e138	0.933778
$616$	−2.80920e137	−0.231386
$617$	−2.38821e138	−1.81534	−0.907669	−	0.419686i	$-0.862140\pi$
$617$	−2.38821e138	−1.81534	−0.907669	+	0.419686i	$0.862140\pi$
$618$	−2.56977e138	−1.80287
$619$	−5.05657e137	−0.327468	−0.163734	−	0.986505i	$-0.552354\pi$
$619$	−5.05657e137	−0.327468	−0.163734	+	0.986505i	$0.552354\pi$
$620$	5.08853e138	3.04231
$621$	4.13982e137	0.228532
$622$	8.18513e137	0.417255
$623$	−5.86522e137	−0.276138
$624$	−7.36933e138	−3.20472
$625$	−2.70927e138	−1.08841
$626$	−8.67793e138	−3.22097
$627$	−1.61031e137	−0.0552289
$628$	8.98810e138	2.84882
$629$	−2.76835e138	−0.810987
$630$	−1.22019e138	−0.330422
$631$	3.09437e138	0.774675	0.387337	−	0.921938i	$-0.373395\pi$
$631$	3.09437e138	0.774675	0.387337	+	0.921938i	$0.373395\pi$
$632$	1.99355e139	4.61458
$633$	3.13185e138	0.670375
$634$	−9.94601e138	−1.96893
$635$	2.41800e137	0.0442748
$636$	1.53471e139	2.59956
$637$	−2.83076e138	−0.443610
$638$	5.21520e137	0.0756219
$639$	2.22118e138	0.298052
$640$	−3.16549e139	−3.93126
$641$	−6.73340e138	−0.774037	−0.387019	−	0.922072i	$-0.626495\pi$
$641$	−6.73340e138	−0.774037	−0.387019	+	0.922072i	$0.626495\pi$
$642$	1.15037e139	1.22421
$643$	−1.27251e139	−1.25377	−0.626886	−	0.779111i	$-0.715671\pi$
$643$	−1.27251e139	−1.25377	−0.626886	+	0.779111i	$0.715671\pi$
$644$	−4.69685e138	−0.428505
$645$	1.90849e139	1.61244
$646$	2.60043e139	2.03487
$647$	1.19529e138	0.0866385	0.0433193	−	0.999061i	$-0.486207\pi$
$647$	1.19529e138	0.0866385	0.0433193	+	0.999061i	$0.486207\pi$
$648$	−3.90034e139	−2.61902
$649$	5.18584e137	0.0322631
$650$	2.96035e139	1.70660
$651$	−1.03548e139	−0.553202
$652$	−2.78079e139	−1.37693
$653$	−1.20430e139	−0.552757	−0.276378	−	0.961049i	$-0.589134\pi$
$653$	−1.20430e139	−0.552757	−0.276378	+	0.961049i	$0.589134\pi$
$654$	−2.15845e139	−0.918423
$655$	9.03284e138	0.356353
$656$	7.24496e139	2.65030
$657$	−6.68848e138	−0.226904
$658$	−3.52129e139	−1.10795
$659$	5.62756e139	1.64245	0.821226	−	0.570604i	$-0.193291\pi$
$659$	5.62756e139	1.64245	0.821226	+	0.570604i	$0.193291\pi$
$660$	1.19950e139	0.324768
$661$	−2.00126e139	−0.502726	−0.251363	−	0.967893i	$-0.580879\pi$
$661$	−2.00126e139	−0.502726	−0.251363	+	0.967893i	$0.580879\pi$
$662$	−6.86466e139	−1.60010
$663$	−6.94876e139	−1.50310
$664$	9.88963e139	1.98545
$665$	3.46740e139	0.646148
$666$	9.05073e138	0.156570
$667$	5.48465e138	0.0880887
$668$	1.20827e140	1.80190
$669$	−7.17638e139	−0.993832
$670$	−1.32834e140	−1.70847
$671$	3.92006e138	0.0468304
$672$	2.19501e140	2.43589
$673$	−1.49675e139	−0.154313	−0.0771567	−	0.997019i	$-0.524584\pi$
$673$	−1.49675e139	−0.154313	−0.0771567	+	0.997019i	$0.524584\pi$
$674$	−1.76652e140	−1.69221
$675$	1.07959e140	0.961000
$676$	−1.01952e139	−0.0843405
$677$	9.71420e139	0.746910	0.373455	−	0.927648i	$-0.378173\pi$
$677$	9.71420e139	0.746910	0.373455	+	0.927648i	$0.378173\pi$
$678$	8.39777e139	0.600197
$679$	9.97567e139	0.662809
$680$	−1.21840e141	−7.52658
$681$	−2.21571e138	−0.0127271
$682$	−2.82127e139	−0.150702
$683$	3.53001e139	0.175368	0.0876841	−	0.996148i	$-0.472053\pi$
$683$	3.53001e139	0.175368	0.0876841	+	0.996148i	$0.472053\pi$
$684$	−6.20116e139	−0.286547
$685$	5.37020e140	2.30838
$686$	5.16843e140	2.06688
$687$	−1.51241e140	−0.562746
$688$	1.32180e141	4.57653
$689$	−3.22995e140	−1.04074
$690$	1.72947e140	0.518659
$691$	−3.59525e140	−1.00361	−0.501805	−	0.864981i	$-0.667331\pi$
$691$	−3.59525e140	−1.00361	−0.501805	+	0.864981i	$0.667331\pi$
$692$	−6.58104e140	−1.71018
$693$	4.93450e138	0.0119385
$694$	3.11291e140	0.701251
$695$	4.44055e140	0.931513
$696$	−6.24876e140	−1.22078
$697$	6.83148e140	1.24306
$698$	−3.32106e139	−0.0562903
$699$	−1.01713e141	−1.60604
$700$	−1.22485e141	−1.80190
$701$	−7.99761e140	−1.09627	−0.548136	−	0.836389i	$-0.684662\pi$
$701$	−7.99761e140	−1.09627	−0.548136	+	0.836389i	$0.684662\pi$
$702$	1.57812e141	2.01583
$703$	−2.57194e140	−0.306177
$704$	2.89849e140	0.321606
$705$	9.45740e140	0.978161
$706$	−1.96948e141	−1.89897
$707$	−1.09786e141	−0.986927
$708$	−9.87841e140	−0.828020
$709$	−1.05994e141	−0.828499	−0.414249	−	0.910163i	$-0.635956\pi$
$709$	−1.05994e141	−0.828499	−0.414249	+	0.910163i	$0.635956\pi$
$710$	6.44593e141	4.69891
$711$	−3.50177e140	−0.238091
$712$	1.91474e141	1.21437
$713$	−2.96704e140	−0.175546
$714$	3.94171e141	2.17582
$715$	−2.52445e140	−0.130022
$716$	−9.83057e141	−4.72481
$717$	−3.31710e141	−1.48785
$718$	2.61122e141	1.09316
$719$	1.41416e141	0.552610	0.276305	−	0.961070i	$-0.410890\pi$
$719$	1.41416e141	0.552610	0.276305	+	0.961070i	$0.410890\pi$
$720$	2.26971e141	0.827964
$721$	−2.23772e141	−0.762095
$722$	−3.62947e141	−1.15412
$723$	4.36123e141	1.29498
$724$	6.36769e141	1.76573
$725$	1.43030e141	0.370421
$726$	7.18146e141	1.73720
$727$	4.32554e141	0.977434	0.488717	−	0.872443i	$-0.337465\pi$
$727$	4.32554e141	0.977434	0.488717	+	0.872443i	$0.337465\pi$
$728$	−1.12621e142	−2.37748
$729$	5.61179e141	1.10685
$730$	−1.94102e142	−3.57723
$731$	1.24636e142	2.14651
$732$	−7.46725e141	−1.20188
$733$	−6.82569e140	−0.102683	−0.0513417	−	0.998681i	$-0.516350\pi$
$733$	−6.82569e140	−0.102683	−0.0513417	+	0.998681i	$0.516350\pi$
$734$	−1.32611e142	−1.86477
$735$	−4.31271e141	−0.566927
$736$	6.28952e141	0.772976
$737$	5.37188e140	0.0617285
$738$	−2.23346e141	−0.239987
$739$	−1.20685e142	−1.21270	−0.606351	−	0.795197i	$-0.707367\pi$
$739$	−1.20685e142	−1.21270	−0.606351	+	0.795197i	$0.707367\pi$
$740$	1.91580e142	1.80044
$741$	−6.45576e141	−0.567474
$742$	1.83220e142	1.50653
$743$	−4.25888e141	−0.327604	−0.163802	−	0.986493i	$-0.552376\pi$
$743$	−4.25888e141	−0.327604	−0.163802	+	0.986493i	$0.552376\pi$
$744$	3.38040e142	2.43281
$745$	−4.60408e141	−0.310032
$746$	−3.41674e142	−2.15298
$747$	−1.73716e141	−0.102440
$748$	7.83342e141	0.432337
$749$	1.00173e142	0.517487
$750$	−4.90084e141	−0.236994
$751$	2.19964e142	0.995805	0.497903	−	0.867233i	$-0.334104\pi$
$751$	2.19964e142	0.995805	0.497903	+	0.867233i	$0.334104\pi$
$752$	6.55006e142	2.77627
$753$	−8.19863e141	−0.325379
$754$	2.09078e142	0.777010
$755$	−2.45850e142	−0.855649
$756$	−6.52954e142	−2.12840
$757$	1.00052e142	0.305477	0.152739	−	0.988267i	$-0.451191\pi$
$757$	1.00052e142	0.305477	0.152739	+	0.988267i	$0.451191\pi$
$758$	−8.30305e142	−2.37472
$759$	−6.99406e140	−0.0187396
$760$	−1.13196e143	−2.84156
$761$	1.61830e142	0.380643	0.190322	−	0.981722i	$-0.439047\pi$
$761$	1.61830e142	0.380643	0.190322	+	0.981722i	$0.439047\pi$
$762$	2.55374e141	0.0562868
$763$	−1.87954e142	−0.388228
$764$	7.41618e142	1.43569
$765$	2.14017e142	0.388336
$766$	1.44069e143	2.45045
$767$	2.07901e142	0.331502
$768$	−1.29483e143	−1.93568
$769$	8.43517e142	1.18233	0.591166	−	0.806550i	$-0.298668\pi$
$769$	8.43517e142	1.18233	0.591166	+	0.806550i	$0.298668\pi$
$770$	1.43201e142	0.188215
$771$	−1.05481e143	−1.30011
$772$	3.34137e143	3.86250
$773$	9.74495e141	0.105656	0.0528281	−	0.998604i	$-0.483176\pi$
$773$	9.74495e141	0.105656	0.0528281	+	0.998604i	$0.483176\pi$
$774$	−4.07480e142	−0.414409
$775$	−7.73752e142	−0.738189
$776$	−3.25663e143	−2.91483
$777$	−3.89852e142	−0.327385
$778$	−1.90549e143	−1.50147
$779$	6.34681e142	0.469301
$780$	4.80879e143	3.33697
$781$	−2.60677e142	−0.169776
$782$	1.12944e143	0.690448
$783$	7.62474e142	0.437540
$784$	−2.98693e143	−1.60909
$785$	−2.88193e143	−1.45759
$786$	9.53994e142	0.453033
$787$	−3.01956e142	−0.134646	−0.0673232	−	0.997731i	$-0.521446\pi$
$787$	−3.01956e142	−0.134646	−0.0673232	+	0.997731i	$0.521446\pi$
$788$	1.23850e144	5.18617
$789$	−3.02055e143	−1.18788
$790$	−1.01622e144	−3.75360
$791$	7.31264e142	0.253711
$792$	−1.61090e142	−0.0525016
$793$	1.57156e143	0.481179
$794$	3.74033e143	1.07596
$795$	−4.92088e143	−1.33006
$796$	−1.96843e144	−4.99947
$797$	5.12809e143	1.22397	0.611983	−	0.790871i	$-0.290372\pi$
$797$	5.12809e143	1.22397	0.611983	+	0.790871i	$0.290372\pi$
$798$	3.66205e143	0.821450
$799$	6.17625e143	1.30214
$800$	1.64020e144	3.25044
$801$	−3.36334e142	−0.0626557
$802$	−7.62437e143	−1.33528
$803$	7.84958e142	0.129249
$804$	−1.02328e144	−1.58424
$805$	1.50599e143	0.219243
$806$	−1.13105e144	−1.54845
$807$	1.09555e144	1.41057
$808$	3.58403e144	4.34020
$809$	−9.40204e143	−1.07095	−0.535476	−	0.844550i	$-0.679868\pi$
$809$	−9.40204e143	−1.07095	−0.535476	+	0.844550i	$0.679868\pi$
$810$	1.98822e144	2.13037
$811$	−1.60630e143	−0.161918	−0.0809589	−	0.996717i	$-0.525798\pi$
$811$	−1.60630e143	−0.161918	−0.0809589	+	0.996717i	$0.525798\pi$
$812$	−8.65067e143	−0.820401
$813$	2.71719e143	0.242459
$814$	−1.06219e143	−0.0891855
$815$	8.91628e143	0.704502
$816$	−7.33210e144	−5.45212
$817$	1.15793e144	0.810386
$818$	−3.08606e144	−2.03290
$819$	1.97825e143	0.122667
$820$	−4.72763e144	−2.75968
$821$	2.53844e143	0.139502	0.0697510	−	0.997564i	$-0.477780\pi$
$821$	2.53844e143	0.139502	0.0697510	+	0.997564i	$0.477780\pi$
$822$	5.67168e144	2.93465
$823$	7.78322e143	0.379199	0.189600	−	0.981862i	$-0.439281\pi$
$823$	7.78322e143	0.379199	0.189600	+	0.981862i	$0.439281\pi$
$824$	7.30518e144	3.35146
$825$	−1.82393e143	−0.0788020
$826$	−1.17932e144	−0.479867
$827$	−3.39972e144	−1.30293	−0.651465	−	0.758679i	$-0.725845\pi$
$827$	−3.39972e144	−1.30293	−0.651465	+	0.758679i	$0.725845\pi$
$828$	−2.69335e143	−0.0972279
$829$	2.41240e144	0.820352	0.410176	−	0.912006i	$-0.365467\pi$
$829$	2.41240e144	0.820352	0.410176	+	0.912006i	$0.365467\pi$
$830$	−5.04129e144	−1.61501
$831$	−2.50314e144	−0.755499
$832$	1.16201e145	3.30449
$833$	−2.81646e144	−0.754703
$834$	4.68984e144	1.18424
$835$	−3.87419e144	−0.921935
$836$	7.27766e143	0.163223
$837$	−4.12477e144	−0.871946
$838$	1.02788e145	2.04815
$839$	6.01468e144	1.12978	0.564892	−	0.825165i	$-0.308918\pi$
$839$	6.01468e144	1.12978	0.564892	+	0.825165i	$0.308918\pi$
$840$	−1.71580e145	−3.03839
$841$	−4.97949e144	−0.831348
$842$	1.74654e145	2.74934
$843$	−3.17819e144	−0.471753
$844$	−1.41541e145	−1.98122
$845$	3.26899e143	0.0431526
$846$	−2.01924e144	−0.251394
$847$	6.25350e144	0.734336
$848$	−3.40813e145	−3.77504
$849$	−5.35083e144	−0.559101
$850$	2.94539e145	2.90340
$851$	−1.11707e144	−0.103888
$852$	4.96560e145	4.35724
$853$	−9.81627e144	−0.812773	−0.406387	−	0.913701i	$-0.633211\pi$
$853$	−9.81627e144	−0.812773	−0.406387	+	0.913701i	$0.633211\pi$
$854$	−8.91470e144	−0.696534
$855$	1.98833e144	0.146611
$856$	−3.27021e145	−2.27575
$857$	2.73893e145	1.79900	0.899500	−	0.436921i	$-0.143931\pi$
$857$	2.73893e145	1.79900	0.899500	+	0.436921i	$0.143931\pi$
$858$	−2.66617e144	−0.165298
$859$	−3.74728e144	−0.219308	−0.109654	−	0.993970i	$-0.534974\pi$
$859$	−3.74728e144	−0.219308	−0.109654	+	0.993970i	$0.534974\pi$
$860$	−8.62526e145	−4.76539
$861$	9.62041e144	0.501808
$862$	−1.91085e145	−0.941061
$863$	1.65113e145	0.767800	0.383900	−	0.923375i	$-0.374581\pi$
$863$	1.65113e145	0.767800	0.383900	+	0.923375i	$0.374581\pi$
$864$	8.74368e145	3.83940
$865$	2.11014e145	0.875011
$866$	−1.07309e145	−0.420243
$867$	−4.44781e145	−1.64513
$868$	4.67977e145	1.63493
$869$	4.10966e144	0.135621
$870$	3.18534e145	0.993007
$871$	2.15359e145	0.634257
$872$	6.13589e145	1.70731
$873$	5.72042e144	0.150391
$874$	1.04931e145	0.260669
$875$	−4.26757e144	−0.100180
$876$	−1.49525e146	−3.31712
$877$	−3.97875e145	−0.834194	−0.417097	−	0.908862i	$-0.636953\pi$
$877$	−3.97875e145	−0.834194	−0.417097	+	0.908862i	$0.636953\pi$
$878$	−1.51642e146	−3.00498
$879$	3.60812e145	0.675821
$880$	−2.66372e145	−0.471624
$881$	−7.80490e144	−0.130635	−0.0653175	−	0.997865i	$-0.520806\pi$
$881$	−7.80490e144	−0.130635	−0.0653175	+	0.997865i	$0.520806\pi$
$882$	9.20803e144	0.145704
$883$	−8.91950e145	−1.33440	−0.667200	−	0.744879i	$-0.732507\pi$
$883$	−8.91950e145	−1.33440	−0.667200	+	0.744879i	$0.732507\pi$
$884$	3.14043e146	4.44224
$885$	3.16740e145	0.423654
$886$	−2.63600e146	−3.33408
$887$	−1.24815e145	−0.149295	−0.0746476	−	0.997210i	$-0.523783\pi$
$887$	−1.24815e145	−0.149295	−0.0746476	+	0.997210i	$0.523783\pi$
$888$	1.27270e146	1.43974
$889$	2.22376e144	0.0237931
$890$	−9.76049e145	−0.987794
$891$	−8.04046e144	−0.0769723
$892$	3.24330e146	2.93716
$893$	5.73806e145	0.491607
$894$	−4.86255e145	−0.394146
$895$	3.15206e146	2.41744
$896$	−2.91120e146	−2.11264
$897$	−2.80393e145	−0.192549
$898$	2.73842e146	1.77960
$899$	−5.46471e145	−0.336095
$900$	−7.02378e145	−0.408852
$901$	−3.21363e146	−1.77059
$902$	2.62118e145	0.136701
$903$	1.75518e146	0.866520
$904$	−2.38726e146	−1.11574
$905$	−2.04173e146	−0.903428
$906$	−2.59651e146	−1.08779
$907$	1.51060e146	0.599222	0.299611	−	0.954061i	$-0.403143\pi$
$907$	1.51060e146	0.599222	0.299611	+	0.954061i	$0.403143\pi$
$908$	1.00137e145	0.0376136
$909$	−6.29553e145	−0.223934
$910$	5.74093e146	1.93390
$911$	1.98446e146	0.633114	0.316557	−	0.948574i	$-0.397473\pi$
$911$	1.98446e146	0.633114	0.316557	+	0.948574i	$0.397473\pi$
$912$	−6.81190e146	−2.05837
$913$	2.03872e145	0.0583519
$914$	−6.63528e146	−1.79896
$915$	2.39429e146	0.614940
$916$	6.83522e146	1.66313
$917$	8.30723e145	0.191502
$918$	1.57015e147	3.42948
$919$	−5.31643e146	−1.10028	−0.550139	−	0.835073i	$-0.685425\pi$
$919$	−5.31643e146	−1.10028	−0.550139	+	0.835073i	$0.685425\pi$
$920$	−4.91642e146	−0.964165
$921$	−6.17283e146	−1.14718
$922$	−6.42167e146	−1.13101
$923$	−1.04506e147	−1.74444
$924$	1.10314e146	0.174529
$925$	−2.91312e146	−0.436861
$926$	1.88065e147	2.67340
$927$	−1.28319e146	−0.172920
$928$	1.15841e147	1.47991
$929$	2.64769e146	0.320692	0.160346	−	0.987061i	$-0.448739\pi$
$929$	2.64769e146	0.320692	0.160346	+	0.987061i	$0.448739\pi$
$930$	−1.72318e147	−1.97890
$931$	−2.61664e146	−0.284928
$932$	4.59684e147	4.74648
$933$	−2.02175e146	−0.197964
$934$	−2.27564e147	−2.11316
$935$	−2.51170e146	−0.221204
$936$	−6.45813e146	−0.539451
$937$	1.40872e147	1.11613	0.558065	−	0.829797i	$-0.311544\pi$
$937$	1.40872e147	1.11613	0.558065	+	0.829797i	$0.311544\pi$
$938$	−1.22163e147	−0.918122
$939$	2.14347e147	1.52817
$940$	−4.27419e147	−2.89084
$941$	9.51031e146	0.610250	0.305125	−	0.952312i	$-0.401302\pi$
$941$	9.51031e146	0.610250	0.305125	+	0.952312i	$0.401302\pi$
$942$	−3.04372e147	−1.85304
$943$	2.75660e146	0.159238
$944$	2.19370e147	1.20244
$945$	2.09362e147	1.08899
$946$	4.78217e146	0.236055
$947$	−6.54607e146	−0.306660	−0.153330	−	0.988175i	$-0.549000\pi$
$947$	−6.54607e146	−0.306660	−0.153330	+	0.988175i	$0.549000\pi$
$948$	−7.82842e147	−3.48066
$949$	3.14690e147	1.32802
$950$	2.73643e147	1.09614
$951$	2.45669e147	0.934147
$952$	−1.12052e148	−4.04475
$953$	−4.80790e147	−1.64762	−0.823810	−	0.566866i	$-0.808156\pi$
$953$	−4.80790e147	−1.64762	−0.823810	+	0.566866i	$0.808156\pi$
$954$	1.05065e147	0.341833
$955$	−2.37792e147	−0.734564
$956$	1.49913e148	4.39718
$957$	−1.28817e146	−0.0358783
$958$	1.03499e148	2.73742
$959$	4.93881e147	1.24051
$960$	1.77034e148	4.22308
$961$	−1.45750e147	−0.330218
$962$	−4.25833e147	−0.916376
$963$	5.74428e146	0.117418
$964$	−1.97102e148	−3.82717
$965$	−1.07137e148	−1.97624
$966$	1.59054e147	0.278725
$967$	−7.61407e145	−0.0126767	−0.00633835	−	0.999980i	$-0.502018\pi$
$967$	−7.61407e145	−0.0126767	−0.00633835	+	0.999980i	$0.502018\pi$
$968$	−2.04150e148	−3.22938
$969$	−6.42314e147	−0.965430
$970$	1.66008e148	2.37098
$971$	1.32460e148	1.79776	0.898880	−	0.438194i	$-0.144382\pi$
$971$	1.32460e148	1.79776	0.898880	+	0.438194i	$0.144382\pi$
$972$	−6.94956e147	−0.896349
$973$	4.08384e147	0.500591
$974$	−1.83867e148	−2.14208
$975$	−7.31215e147	−0.809686
$976$	1.65825e148	1.74536
$977$	1.87992e146	0.0188086	0.00940432	−	0.999956i	$-0.497006\pi$
$977$	1.87992e146	0.0188086	0.00940432	+	0.999956i	$0.497006\pi$
$978$	9.41683e147	0.895636
$979$	3.94720e146	0.0356899
$980$	1.94909e148	1.67549
$981$	−1.07780e147	−0.0880891
$982$	1.47089e148	1.14304
$983$	−8.95210e147	−0.661494	−0.330747	−	0.943719i	$-0.607301\pi$
$983$	−8.95210e147	−0.661494	−0.330747	+	0.943719i	$0.607301\pi$
$984$	−3.14065e148	−2.20680
$985$	−3.97110e148	−2.65349
$986$	2.08022e148	1.32191
$987$	8.69768e147	0.525659
$988$	2.91762e148	1.67711
$989$	5.02925e147	0.274971
$990$	8.21166e146	0.0427060
$991$	−1.39056e146	−0.00687927	−0.00343964	−	0.999994i	$-0.501095\pi$
$991$	−1.39056e146	−0.00687927	−0.00343964	+	0.999994i	$0.501095\pi$
$992$	−6.26665e148	−2.94922
$993$	1.69559e148	0.759159
$994$	5.92813e148	2.52518
$995$	6.31156e148	2.55796
$996$	−3.88353e148	−1.49758
$997$	−3.62634e148	−1.33063	−0.665316	−	0.746562i	$-0.731703\pi$
$997$	−3.62634e148	−1.33063	−0.665316	+	0.746562i	$0.731703\pi$
$998$	−7.72712e147	−0.269808
$999$	−1.55295e148	−0.516018

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1.100.a.a.1.8	✓	8	1.1	even	1	trivial
9.100.a.d.1.1		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)

\(f(q)\)	\(=\)	\(q+1.53045e15 q^{2} -3.78025e23 q^{3} +1.70845e30 q^{4} -5.47796e34 q^{5} -5.78549e38 q^{6} -5.03791e41 q^{7} +1.64466e45 q^{8} -2.88893e46 q^{9} -8.38375e49 q^{10} +3.39044e50 q^{11} -6.45838e53 q^{12} +1.35923e55 q^{13} -7.71028e56 q^{14} +2.07081e58 q^{15} +1.43421e60 q^{16} +1.35236e61 q^{17} -4.42136e61 q^{18} +1.25642e63 q^{19} -9.35884e64 q^{20} +1.90446e65 q^{21} +5.18889e65 q^{22} +5.45698e66 q^{23} -6.21724e68 q^{24} +1.42309e69 q^{25} +2.08023e70 q^{26} +7.58628e70 q^{27} -8.60704e71 q^{28} +1.00507e72 q^{29} +3.16927e73 q^{30} -5.43714e73 q^{31} +1.15256e75 q^{32} -1.28167e74 q^{33} +2.06972e76 q^{34} +2.75975e76 q^{35} -4.93560e76 q^{36} -2.04705e77 q^{37} +1.92288e78 q^{38} -5.13823e78 q^{39} -9.00940e79 q^{40} +5.05152e79 q^{41} +2.91468e80 q^{42} +9.21616e80 q^{43} +5.79240e80 q^{44} +1.58254e81 q^{45} +8.35164e81 q^{46} +4.56701e82 q^{47} -5.42169e83 q^{48} -2.08262e83 q^{49} +2.17796e84 q^{50} -5.11227e84 q^{51} +2.32218e85 q^{52} -2.37631e85 q^{53} +1.16104e86 q^{54} -1.85727e85 q^{55} -8.28567e86 q^{56} -4.74957e86 q^{57} +1.53821e87 q^{58} +1.52955e87 q^{59} +3.53788e88 q^{60} +1.15621e88 q^{61} -8.32127e88 q^{62} +1.45542e88 q^{63} +8.54901e89 q^{64} -7.44581e89 q^{65} -1.96153e89 q^{66} +1.58442e90 q^{67} +2.31045e91 q^{68} -2.06288e90 q^{69} +4.22366e91 q^{70} -7.68861e91 q^{71} -4.75131e91 q^{72} +2.31521e92 q^{73} -3.13290e92 q^{74} -5.37963e92 q^{75} +2.14653e93 q^{76} -1.70807e92 q^{77} -7.86381e93 q^{78} +1.21213e94 q^{79} -7.85657e94 q^{80} -2.37151e94 q^{81} +7.73109e94 q^{82} +6.01316e94 q^{83} +3.25368e95 q^{84} -7.40819e95 q^{85} +1.41049e96 q^{86} -3.79942e95 q^{87} +5.57612e95 q^{88} +1.16422e96 q^{89} +2.42201e96 q^{90} -6.84768e96 q^{91} +9.32300e96 q^{92} +2.05538e97 q^{93} +6.98958e97 q^{94} -6.88260e97 q^{95} -4.35698e98 q^{96} -1.98012e98 q^{97} -3.18735e98 q^{98} -9.79473e96 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 208040616902520 q^{2} - 28\!\cdots\!20 q^{3} + 28\!\cdots\!24 q^{4} - 48\!\cdots\!60 q^{5} - 77\!\cdots\!44 q^{6} - 56\!\cdots\!00 q^{7} + 59\!\cdots\!60 q^{8} + 15\!\cdots\!76 q^{9} - 20\!\cdots\!60 q^{10}+ \cdots - 13\!\cdots\!08 q^{99}+O(q^{100}) \) 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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