LMFDB - Embedded newform 1.102.a.a.1.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1,102,Mod(1,1)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1, base_ring=CyclotomicField(1))

chi = DirichletCharacter(H, H._module([]))

N = Newforms(chi, 102, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("1.1");

S:= CuspForms(chi, 102);

N := Newforms(S);

Level:	$ N $	$=$	$ 1 $
Weight:	$ k $	$=$	$ 102 $
Character orbit:	$[\chi]$	$=$	1.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$64.6006978936$
Analytic rank:	$1$
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 + 14\!\cdots\!00 $ x^8 - x^7 - 1587875693797102871013870264x^6 - 1330672377046512025083958312008691941376x^5 + 791445357227345439680707260473135602197341722594809856x^4 + 1619878418527606484256994450085468366256752280708006567605868625920x^3 - 123437551313054499723143526216928211228510769023293658451121904309621876706508800x^2 - 461414543589146449205827365849494496729755778377708510322901762861807152038306434693201920000x + 1491743821439154656522591042817873299711189313438184985174364653060384818799349544894763946517463040000000
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	multiple of $ 2^{119}\cdot 3^{37}\cdot 5^{14}\cdot 7^{7}\cdot 11^{2}\cdot 13^{2}\cdot 17^{2} $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.8
Root			$-2.72721e13$ 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)

$f(q)$	$=$	$q+2.56375e15 q^{2} -2.60728e23 q^{3} +4.03750e30 q^{4} +2.88877e35 q^{5} -6.68439e38 q^{6} -6.25978e42 q^{7} +3.85125e45 q^{8} -1.47815e48 q^{9} +O(q^{10})$	\(q+2.56375e15 q^{2} -2.60728e23 q^{3} +4.03750e30 q^{4} +2.88877e35 q^{5} -6.68439e38 q^{6} -6.25978e42 q^{7} +3.85125e45 q^{8} -1.47815e48 q^{9} +7.40607e50 q^{10} -2.44501e52 q^{11} -1.05269e54 q^{12} -8.21796e55 q^{13} -1.60485e58 q^{14} -7.53182e58 q^{15} -3.62648e59 q^{16} -1.73969e62 q^{17} -3.78961e63 q^{18} -3.05406e64 q^{19} +1.16634e66 q^{20} +1.63210e66 q^{21} -6.26838e67 q^{22} +2.17017e68 q^{23} -1.00413e69 q^{24} +4.40068e70 q^{25} -2.10688e71 q^{26} +7.88515e71 q^{27} -2.52738e73 q^{28} +1.39854e74 q^{29} -1.93097e74 q^{30} -3.23973e75 q^{31} -1.06938e76 q^{32} +6.37481e75 q^{33} -4.46012e77 q^{34} -1.80831e78 q^{35} -5.96804e78 q^{36} +1.43241e79 q^{37} -7.82984e79 q^{38} +2.14265e79 q^{39} +1.11254e81 q^{40} +4.24481e81 q^{41} +4.18428e81 q^{42} +1.21927e82 q^{43} -9.87171e82 q^{44} -4.27005e83 q^{45} +5.56377e83 q^{46} -3.72383e84 q^{47} +9.45523e82 q^{48} +1.65435e85 q^{49} +1.12822e86 q^{50} +4.53585e85 q^{51} -3.31800e86 q^{52} -1.31257e87 q^{53} +2.02155e87 q^{54} -7.06306e87 q^{55} -2.41080e88 q^{56} +7.96278e87 q^{57} +3.58550e89 q^{58} -2.92483e89 q^{59} -3.04097e89 q^{60} -4.65268e89 q^{61} -8.30584e90 q^{62} +9.25292e90 q^{63} -2.64968e91 q^{64} -2.37398e91 q^{65} +1.63434e91 q^{66} +1.13200e92 q^{67} -7.02398e92 q^{68} -5.65824e91 q^{69} -4.63604e93 q^{70} -1.95260e93 q^{71} -5.69273e93 q^{72} -9.13236e93 q^{73} +3.67234e94 q^{74} -1.14738e94 q^{75} -1.23308e95 q^{76} +1.53052e95 q^{77} +5.49321e94 q^{78} -4.27479e95 q^{79} -1.04761e95 q^{80} +2.07983e96 q^{81} +1.08826e97 q^{82} +1.25026e97 q^{83} +6.58959e96 q^{84} -5.02556e97 q^{85} +3.12590e97 q^{86} -3.64638e97 q^{87} -9.41633e97 q^{88} +1.65813e98 q^{89} -1.09473e99 q^{90} +5.14426e98 q^{91} +8.76206e98 q^{92} +8.44686e98 q^{93} -9.54696e99 q^{94} -8.82247e99 q^{95} +2.78817e99 q^{96} +1.54750e100 q^{97} +4.24133e100 q^{98} +3.61410e100 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 434989091795040 q^{2} - 12\!\cdots\!60 q^{3}+ \cdots + 52\!\cdots\!84 q^{9}+O(q^{10}) $ 8 * q - 434989091795040 * q^2 - 1209375896611771518910560 * q^3 + 9008967123164113911511576503296 * q^4 + 38238791540232828026421308589217200 * q^5 + 2477260046146272006672820535971480695936 * q^6 - 5786789720778120168956257648884421874283200 * q^7 - 6101688461407407841888405145259998920458731520 * q^8 + 5273640617280587177839635242070674204864681879784 * q^9	$ 8 q - 434989091795040 q^{2} - 12\!\cdots\!60 q^{3}+ \cdots + 22\!\cdots\!08 q^{99}+O(q^{100}) $ 8 * q - 434989091795040 * q^2 - 1209375896611771518910560 * q^3 + 9008967123164113911511576503296 * q^4 + 38238791540232828026421308589217200 * q^5 + 2477260046146272006672820535971480695936 * q^6 - 5786789720778120168956257648884421874283200 * q^7 - 6101688461407407841888405145259998920458731520 * q^8 + 5273640617280587177839635242070674204864681879784 * q^9 - 376167658847177398692429835067300112512860198593600 * q^10 + 4622006661480385115355021397632645270205791478300896 * q^11 - 7273290781506553143908216801865849714958844187989422080 * q^12 + 250316830865150221699601352256397536965043294984328650480 * q^13 - 4856789037716039923353321450215036970203737520869624889088 * q^14 - 296460708185002952419818874947342543917521978696100167156800 * q^15 - 10662656154906175558835021484824464714661655552497093859868672 * q^16 - 397968518694853312322660892941326449007299986932512193696587120 * q^17 - 7270968925217398747066352706388703938040714138623386028515252960 * q^18 - 21387776045417165942123954421061470474744368808488511816400717280 * q^19 + 1745002690168409059221421019241581897927614179506161156200285542400 * q^20 + 4030935126807879780648600654579655736182360851489572706466859540736 * q^21 + 61357881995862711169740037407631980426480577127973320405539739944320 * q^22 - 1366243345208606848425464574347748611753917469593153677393324561698880 * q^23 + 10457354719000260635321058863018299052737315743164922361342586480885760 * q^24 + 77471873089568593564333770877949420045843582630742632687744142562715000 * q^25 - 97549630676937426518340388130407212490384846814009484188479115327886144 * q^26 - 5951874968930013487417142282111771144801435961988629201748805497863184320 * q^27 + 9217624035174751886516129105576165061663773766415040330328487084880404480 * q^28 + 15465799862710125255662370242568323665682807414567501281109138719156160880 * q^29 + 1101689156065505631051293671607641382064945196508526428823375711603202118400 * q^30 - 6594370386043135339784923725045360443937393326734068279132668478779615001344 * q^31 + 12265519409733718324179959581296851912742484455832107241543734281342036213760 * q^32 + 43813172582105581329585760338258562815639759809845990212191452867766348215680 * q^33 + 9531455444774917507766540524882635666895777953789094347547215472626183995712 * q^34 - 1122850631208004175280217132184898888977788452428069383882586628450512616297600 * q^35 + 1966242586607976986737003826554029255087710066072863106322127653222050407339008 * q^36 + 39729696767983511833540209209183332457877293383323859312175998401968644864715440 * q^37 - 70873740526925065519455012686645778106113298999572267198467188879790467046148480 * q^38 - 269289195198196884798470270521708844679404215685249767615656452740889673105306432 * q^39 - 763642761360299050617237751714968411270996317577517686387843428508400019349504000 * q^40 + 5607291724825101314952096252772109505395882457063737303656079003304969203257094736 * q^41 + 3008066923831569706716293907931878334959183836053498604235677758281531565332526080 * q^42 - 28642921955044714117801359306021921736063108483729021321044095944585527287681223200 * q^43 - 207838425393205175674959052733026300855796348257745356716186803699782799277851086848 * q^44 + 712633045382921242540931880134776511927082560144290402835715503414563529286220047600 * q^45 + 1088094260619851586903932234100844276278561023621942541398958535856528393570339218176 * q^46 - 4595399220200007631460417274797048154524720407021496316223236391731855709593438718080 * q^47 - 58354182581817955899154335674671016574355963424701638945735582725996041826866298880 * q^48 + 12068461406676719302337658501270392621238416595305390197216228129207599916872005856456 * q^49 - 40493179837482260394665357435432250163405353367416857829233726008281167215503492420000 * q^50 + 117646730044094759803745147399491979694134742922341911657750530682089815486256248611136 * q^51 - 736020167800817028850658909331852777746165402605863935107936992324104798352324258252800 * q^52 + 131026696145917691346168139299202731343660174597285772716290345361212508775951813313840 * q^53 + 6803608957095266771149163140167539716357850176039815317805755392633822625226741503089920 * q^54 - 14585157967675450217148723878599628333971210001615112897255333178063634767400530051473600 * q^55 - 23665562342657326400415121984960944704012341384928617813498515591030351969339927087022080 * q^56 - 66899487754306674554237314096607510056291565049587799982155034523058479948455991635655040 * q^57 + 29173417521771002425120779628349939892591335515731485644911210555324770598093888308326080 * q^58 + 212583149562022564923669670483574922097682552074321909615339251529169016840977455874187360 * q^59 - 3455800135608334392541843481344001808338357411235959344412061781382196941870275476295065600 * q^60 - 3390796423636162146406492296389682436951029380958058095674208836333532599894943317230895504 * q^61 - 5878859817222970028213836429448832127296537243368792127423103234889716583457526212133370880 * q^62 - 20171938924061808002384576493874339158887341995607670819297079343133751793255425885494984640 * q^63 - 74870090698021647967203019932764377907062372989513317693678846896652408519412785858115272704 * q^64 - 161067075283368767182138254547148962244907084326790507487294907612770451283405321317426536800 * q^65 - 745278055170676259198413344675313071673593040227005461838089798951153726758412015071955911168 * q^66 - 618774503558862942537948810466095132313460919373052732511642097824837019429997681150398682720 * q^67 - 2182412150351293808121583165511486752102068977919329447376923905220322529537335456462676162560 * q^68 - 5393950442083315109606578094475120918497802785657891521452512469623636760248087300551286537472 * q^69 - 12923520657540473465038555822652190723092643731233782501675276653712048411292540691873715571200 * q^70 - 15797470289857673806303846655911576507977904169297655042639265226995032204172380517793831135424 * q^71 - 55126715113590704564504537983251285080485074916503283789364546398928839504287032847376708239360 * q^72 - 20462651635605668591994589976366754984142669867347912050159975933828495442291952971923777071280 * q^73 - 142953411935712165334538916257020870493984381200782662943456748743148514063783881306064429441088 * q^74 - 204312291750914950304829914412770260373631281822544572731633720960361618548975517964814619460000 * q^75 + 64556217054886497186737063238064337992823205997653378371004031509089422583081356800943896432640 * q^76 + 250231448169383959900618348975396989794902211753647918986458150866408618577007907131029306438400 * q^77 + 1260981709052401111398092363772739439414079820346824747462408082793911096042108256417770344646400 * q^78 + 1474556321278768744579716979675929750918930811984805387023357390321899878561204701118206999166080 * q^79 + 6033438037435277941170744030808192554572458649979375320464765273747209092446481051552234550067200 * q^80 + 14613214105102112111129469132612601529386527627758931132459526147171392070559192290643105065182408 * q^81 + 30083863369214129982421840097969977845328701273986110579467106900080547794123383776302929686086720 * q^82 + 33762254529254022439253159341806143692643909652777369725086142424861011401680843403961249425712160 * q^83 + 57799153837692447414380568170128797835929379783304235587752969314531310322308849537769529417695232 * q^84 + 17314966267116570951109803841412092095679328201414316724042066880549149931729490643535478494114400 * q^85 + 67989564188024628582959760637462873453376851598916319417912395832044408164663357850732592560556416 * q^86 + 2586434133428712948881772736535019341274237946379240114707154003676967765014837223291966941531840 * q^87 - 363099602372059077387783242048689913608334478213970275423791339756517232974574737922754584123146240 * q^88 - 620007165949691950044675276484549383308720953973642955804615855186521697520022438525123333812557360 * q^89 - 4716676146177962028099989697458384454375488041754925418224025761569034561814581975790426208019028800 * q^90 - 3685711793015793225308940042728501386995879977832891226647110522985454537354035281338855172828873344 * q^91 - 4618779932089713137770970202224414792688843158843334085630908366025929325979388063902511470793400320 * q^92 - 3975022445092224432029728046757042348886229630318622378634497589784647142077875089398179428115102720 * q^93 - 17371370943540992303713705925513939673302729250250795188383540356993592041601425149438637190677682688 * q^94 - 2642077700832720169247174948884057845373174576960370774287679094739730873649398763127258995555528000 * q^95 + 4679875418673156206717240026356824763600126819048403120235276936002238426687957733980747642601209856 * q^96 + 64020476116668335744724892375903667651900818166631138467214326399663196857065619648203365824701173520 * q^97 + 202971561788470754768820264959327860776947519106194867162872422213964707447467488105939520314595817120 * q^98 + 225914901454627435116272921386700923755368861971179328902362103653753469396751969300619190223813523808 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	2.56375e15	1.61013	0.805064	−	0.593188i	$-0.202131\pi$
$2$	2.56375e15	1.61013	0.805064	+	0.593188i	$0.202131\pi$
$3$	−2.60728e23	−0.209683	−0.104842	−	0.994489i	$-0.533434\pi$
$3$	−2.60728e23	−0.209683	−0.104842	+	0.994489i	$0.533434\pi$
$4$	4.03750e30	1.59251
$5$	2.88877e35	1.45455	0.727273	−	0.686348i	$-0.240787\pi$
$5$	2.88877e35	1.45455	0.727273	+	0.686348i	$0.240787\pi$
$6$	−6.68439e38	−0.337617
$7$	−6.25978e42	−1.31555	−0.657776	−	0.753214i	$-0.728503\pi$
$7$	−6.25978e42	−1.31555	−0.657776	+	0.753214i	$0.728503\pi$
$8$	3.85125e45	0.954019
$9$	−1.47815e48	−0.956033
$10$	7.40607e50	2.34201
$11$	−2.44501e52	−0.627986	−0.313993	−	0.949425i	$-0.601667\pi$
$11$	−2.44501e52	−0.627986	−0.313993	+	0.949425i	$0.601667\pi$
$12$	−1.05269e54	−0.333923
$13$	−8.21796e55	−0.457746	−0.228873	−	0.973456i	$-0.573504\pi$
$13$	−8.21796e55	−0.457746	−0.228873	+	0.973456i	$0.573504\pi$
$14$	−1.60485e58	−2.11821
$15$	−7.53182e58	−0.304994
$16$	−3.62648e59	−0.0564191
$17$	−1.73969e62	−1.26707	−0.633535	−	0.773714i	$-0.718397\pi$
$17$	−1.73969e62	−1.26707	−0.633535	+	0.773714i	$0.718397\pi$
$18$	−3.78961e63	−1.53934
$19$	−3.05406e64	−0.808762	−0.404381	−	0.914591i	$-0.632513\pi$
$19$	−3.05406e64	−0.808762	−0.404381	+	0.914591i	$0.632513\pi$
$20$	1.16634e66	2.31638
$21$	1.63210e66	0.275849
$22$	−6.26838e67	−1.01114
$23$	2.17017e68	0.370884	0.185442	−	0.982655i	$-0.440628\pi$
$23$	2.17017e68	0.370884	0.185442	+	0.982655i	$0.440628\pi$
$24$	−1.00413e69	−0.200042
$25$	4.40068e70	1.11571
$26$	−2.10688e71	−0.737030
$27$	7.88515e71	0.410147
$28$	−2.52738e73	−2.09503
$29$	1.39854e74	1.97050	0.985249	−	0.171125i	$-0.0547401\pi$
$29$	1.39854e74	1.97050	0.985249	+	0.171125i	$0.0547401\pi$
$30$	−1.93097e74	−0.491079
$31$	−3.23973e75	−1.57305	−0.786526	−	0.617557i	$-0.788122\pi$
$31$	−3.23973e75	−1.57305	−0.786526	+	0.617557i	$0.788122\pi$
$32$	−1.06938e76	−1.04486
$33$	6.37481e75	0.131678
$34$	−4.46012e77	−2.04015
$35$	−1.80831e78	−1.91353
$36$	−5.96804e78	−1.52249
$37$	1.43241e79	0.915968	0.457984	−	0.888960i	$-0.348572\pi$
$37$	1.43241e79	0.915968	0.457984	+	0.888960i	$0.348572\pi$
$38$	−7.82984e79	−1.30221
$39$	2.14265e79	0.0959817
$40$	1.11254e81	1.38766
$41$	4.24481e81	1.52151	0.760753	−	0.649041i	$-0.224830\pi$
$41$	4.24481e81	1.52151	0.760753	+	0.649041i	$0.224830\pi$
$42$	4.18428e81	0.444152
$43$	1.21927e82	0.394405	0.197202	−	0.980363i	$-0.436814\pi$
$43$	1.21927e82	0.394405	0.197202	+	0.980363i	$0.436814\pi$
$44$	−9.87171e82	−1.00007
$45$	−4.27005e83	−1.39059
$46$	5.56377e83	0.597171
$47$	−3.72383e84	−1.34911	−0.674556	−	0.738223i	$-0.735665\pi$
$47$	−3.72383e84	−1.34911	−0.674556	+	0.738223i	$0.735665\pi$
$48$	9.45523e82	0.0118301
$49$	1.65435e85	0.730677
$50$	1.12822e86	1.79643
$51$	4.53585e85	0.265683
$52$	−3.31800e86	−0.728966
$53$	−1.31257e87	−1.10203	−0.551013	−	0.834497i	$-0.685758\pi$
$53$	−1.31257e87	−1.10203	−0.551013	+	0.834497i	$0.685758\pi$
$54$	2.02155e87	0.660389
$55$	−7.06306e87	−0.913434
$56$	−2.41080e88	−1.25506
$57$	7.96278e87	0.169584
$58$	3.58550e89	3.17275
$59$	−2.92483e89	−1.09163	−0.545813	−	0.837907i	$-0.683779\pi$
$59$	−2.92483e89	−1.09163	−0.545813	+	0.837907i	$0.683779\pi$
$60$	−3.04097e89	−0.485706
$61$	−4.65268e89	−0.322513	−0.161256	−	0.986913i	$-0.551555\pi$
$61$	−4.65268e89	−0.322513	−0.161256	+	0.986913i	$0.551555\pi$
$62$	−8.30584e90	−2.53281
$63$	9.25292e90	1.25771
$64$	−2.64968e91	−1.62594
$65$	−2.37398e91	−0.665813
$66$	1.63434e91	0.212018
$67$	1.13200e92	0.687180	0.343590	−	0.939120i	$-0.388357\pi$
$67$	1.13200e92	0.687180	0.343590	+	0.939120i	$0.388357\pi$
$68$	−7.02398e92	−2.01782
$69$	−5.65824e91	−0.0777682
$70$	−4.63604e93	−3.08103
$71$	−1.95260e93	−0.633967	−0.316984	−	0.948431i	$-0.602670\pi$
$71$	−1.95260e93	−0.633967	−0.316984	+	0.948431i	$0.602670\pi$
$72$	−5.69273e93	−0.912073
$73$	−9.13236e93	−0.729086	−0.364543	−	0.931187i	$-0.618775\pi$
$73$	−9.13236e93	−0.729086	−0.364543	+	0.931187i	$0.618775\pi$
$74$	3.67234e94	1.47483
$75$	−1.14738e94	−0.233945
$76$	−1.23308e95	−1.28796
$77$	1.53052e95	0.826148
$78$	5.49321e94	0.154543
$79$	−4.27479e95	−0.632043	−0.316022	−	0.948752i	$-0.602347\pi$
$79$	−4.27479e95	−0.632043	−0.316022	+	0.948752i	$0.602347\pi$
$80$	−1.04761e95	−0.0820642
$81$	2.07983e96	0.870032
$82$	1.08826e97	2.44982
$83$	1.25026e97	1.52601	0.763005	−	0.646392i	$-0.223723\pi$
$83$	1.25026e97	1.52601	0.763005	+	0.646392i	$0.223723\pi$
$84$	6.58959e96	0.439293
$85$	−5.02556e97	−1.84301
$86$	3.12590e97	0.635042
$87$	−3.64638e97	−0.413180
$88$	−9.41633e97	−0.599110
$89$	1.65813e98	0.596242	0.298121	−	0.954528i	$-0.403640\pi$
$89$	1.65813e98	0.596242	0.298121	+	0.954528i	$0.403640\pi$
$90$	−1.09473e99	−2.23903
$91$	5.14426e98	0.602189
$92$	8.76206e98	0.590638
$93$	8.44686e98	0.329842
$94$	−9.54696e99	−2.17224
$95$	−8.82247e99	−1.17638
$96$	2.78817e99	0.219090
$97$	1.54750e100	0.720539	0.360269	−	0.932848i	$-0.382685\pi$
$97$	1.54750e100	0.720539	0.360269	+	0.932848i	$0.382685\pi$
$98$	4.24133e100	1.17648
$99$	3.61410e100	0.600375
$100$	1.77677e101	1.77677
$101$	−3.42264e100	−0.207077	−0.103538	−	0.994625i	$-0.533016\pi$
$101$	−3.42264e100	−0.207077	−0.103538	+	0.994625i	$0.533016\pi$
$102$	1.16288e101	0.427784
$103$	−3.65070e101	−0.820534	−0.410267	−	0.911965i	$-0.634564\pi$
$103$	−3.65070e101	−0.820534	−0.410267	+	0.911965i	$0.634564\pi$
$104$	−3.16494e101	−0.436699
$105$	4.71475e101	0.401235
$106$	−3.36510e102	−1.77440
$107$	1.09596e102	0.359679	0.179839	−	0.983696i	$-0.442442\pi$
$107$	1.09596e102	0.359679	0.179839	+	0.983696i	$0.442442\pi$
$108$	3.18363e102	0.653164
$109$	1.89257e102	0.243788	0.121894	−	0.992543i	$-0.461103\pi$
$109$	1.89257e102	0.243788	0.121894	+	0.992543i	$0.461103\pi$
$110$	−1.81079e103	−1.47075
$111$	−3.73469e102	−0.192063
$112$	2.27010e102	0.0742223
$113$	−6.23836e103	−1.30199	−0.650997	−	0.759080i	$-0.725649\pi$
$113$	−6.23836e103	−1.30199	−0.650997	+	0.759080i	$0.725649\pi$
$114$	2.04145e103	0.273052
$115$	6.26913e103	0.539469
$116$	5.64660e104	3.13804
$117$	1.21474e104	0.437621
$118$	−7.49853e104	−1.75766
$119$	1.08901e105	1.66690
$120$	−2.90069e104	−0.290970
$121$	−9.18061e104	−0.605634
$122$	−1.19283e105	−0.519287
$123$	−1.10674e105	−0.319034
$124$	−1.30804e106	−2.50510
$125$	1.31837e105	0.168300
$126$	2.37221e106	2.02508
$127$	1.87262e106	1.07241	0.536205	−	0.844088i	$-0.319857\pi$
$127$	1.87262e106	1.07241	0.536205	+	0.844088i	$0.319857\pi$
$128$	−4.08190e106	−1.57311
$129$	−3.17897e105	−0.0827001
$130$	−6.08628e106	−1.07204
$131$	5.76238e106	0.689290	0.344645	−	0.938733i	$-0.387999\pi$
$131$	5.76238e106	0.689290	0.344645	+	0.938733i	$0.387999\pi$
$132$	2.57383e106	0.209699
$133$	1.91177e107	1.06397
$134$	2.90217e107	1.10645
$135$	2.27784e107	0.596578
$136$	−6.69997e107	−1.20881
$137$	7.34857e107	0.915829	0.457914	−	0.888996i	$-0.348597\pi$
$137$	7.34857e107	0.915829	0.457914	+	0.888996i	$0.348597\pi$
$138$	−1.45063e107	−0.125217
$139$	8.70128e106	0.0521598	0.0260799	−	0.999660i	$-0.491698\pi$
$139$	8.70128e106	0.0521598	0.0260799	+	0.999660i	$0.491698\pi$
$140$	−7.30103e108	−3.04732
$141$	9.70906e107	0.282886
$142$	−5.00597e108	−1.02077
$143$	2.00930e108	0.287458
$144$	5.36049e107	0.0539385
$145$	4.04006e109	2.86618
$146$	−2.34131e109	−1.17392
$147$	−4.31335e108	−0.153211
$148$	5.78335e109	1.45869
$149$	−3.67441e109	−0.659600	−0.329800	−	0.944051i	$-0.606981\pi$
$149$	−3.67441e109	−0.659600	−0.329800	+	0.944051i	$0.606981\pi$
$150$	−2.94159e109	−0.376681
$151$	4.20738e109	0.385191	0.192595	−	0.981278i	$-0.438309\pi$
$151$	4.20738e109	0.385191	0.192595	+	0.981278i	$0.438309\pi$
$152$	−1.17619e110	−0.771574
$153$	2.57153e110	1.21136
$154$	3.92387e110	1.33020
$155$	−9.35883e110	−2.28808
$156$	8.65094e109	0.152852
$157$	2.25516e110	0.288566	0.144283	−	0.989536i	$-0.453912\pi$
$157$	2.25516e110	0.288566	0.144283	+	0.989536i	$0.453912\pi$
$158$	−1.09595e111	−1.01767
$159$	3.42224e110	0.231076
$160$	−3.08919e111	−1.51980
$161$	−1.35848e111	−0.487918
$162$	5.33217e111	1.40086
$163$	−5.79305e111	−1.11541	−0.557703	−	0.830040i	$-0.688317\pi$
$163$	−5.79305e111	−1.11541	−0.557703	+	0.830040i	$0.688317\pi$
$164$	1.71384e112	2.42302
$165$	1.84154e111	0.191532
$166$	3.20536e112	2.45707
$167$	−2.04226e112	−1.15592	−0.577961	−	0.816064i	$-0.696152\pi$
$167$	−2.04226e112	−1.15592	−0.577961	+	0.816064i	$0.696152\pi$
$168$	6.28561e111	0.263165
$169$	−2.54779e112	−0.790468
$170$	−1.28843e113	−2.96749
$171$	4.51437e112	0.773203
$172$	4.92279e112	0.628094
$173$	1.08886e113	1.03668	0.518340	−	0.855174i	$-0.326550\pi$
$173$	1.08886e113	1.03668	0.518340	+	0.855174i	$0.326550\pi$
$174$	−9.34840e112	−0.665273
$175$	−2.75473e113	−1.46777
$176$	8.86677e111	0.0354304
$177$	7.62584e112	0.228896
$178$	4.25102e113	0.960026
$179$	8.45466e113	1.43886	0.719429	−	0.694566i	$-0.244403\pi$
$179$	8.45466e113	1.43886	0.719429	+	0.694566i	$0.244403\pi$
$180$	−1.72403e114	−2.21454
$181$	−2.55677e113	−0.248269	−0.124135	−	0.992265i	$-0.539615\pi$
$181$	−2.55677e113	−0.248269	−0.124135	+	0.992265i	$0.539615\pi$
$182$	1.31886e114	0.969601
$183$	1.21308e113	0.0676255
$184$	8.35787e113	0.353831
$185$	4.13790e114	1.33232
$186$	2.16556e114	0.531089
$187$	4.25355e114	0.795702
$188$	−1.50350e115	−2.14848
$189$	−4.93593e114	−0.539570
$190$	−2.26186e115	−1.89413
$191$	7.87385e114	0.505827	0.252914	−	0.967489i	$-0.418611\pi$
$191$	7.87385e114	0.505827	0.252914	+	0.967489i	$0.418611\pi$
$192$	6.90844e114	0.340932
$193$	−4.31049e115	−1.63637	−0.818187	−	0.574952i	$-0.805021\pi$
$193$	−4.31049e115	−1.63637	−0.818187	+	0.574952i	$0.805021\pi$
$194$	3.96739e115	1.16016
$195$	6.18962e114	0.139610
$196$	6.67943e115	1.16361
$197$	1.14002e115	0.153591	0.0767957	−	0.997047i	$-0.475531\pi$
$197$	1.14002e115	0.153591	0.0767957	+	0.997047i	$0.475531\pi$
$198$	9.26563e115	0.966680
$199$	−5.38798e115	−0.435859	−0.217929	−	0.975965i	$-0.569930\pi$
$199$	−5.38798e115	−0.435859	−0.217929	+	0.975965i	$0.569930\pi$
$200$	1.69481e116	1.06440
$201$	−2.95145e115	−0.144090
$202$	−8.77478e115	−0.333420
$203$	−8.75456e116	−2.59229
$204$	1.83135e116	0.423104
$205$	1.22623e117	2.21310
$206$	−9.35948e116	−1.32116
$207$	−3.20785e116	−0.354578
$208$	2.98023e115	0.0258256
$209$	7.46720e116	0.507891
$210$	1.20874e117	0.646040
$211$	−2.73700e117	−1.15083	−0.575414	−	0.817862i	$-0.695159\pi$
$211$	−2.73700e117	−1.15083	−0.575414	+	0.817862i	$0.695159\pi$
$212$	−5.29950e117	−1.75499
$213$	5.09097e116	0.132932
$214$	2.80977e117	0.579129
$215$	3.52218e117	0.573680
$216$	3.03676e117	0.391288
$217$	2.02800e118	2.06943
$218$	4.85206e117	0.392530
$219$	2.38106e117	0.152877
$220$	−2.85171e118	−1.45465
$221$	1.42967e118	0.579997
$222$	−9.57479e117	−0.309246
$223$	−5.94409e118	−1.52999	−0.764997	−	0.644034i	$-0.777259\pi$
$223$	−5.94409e118	−1.52999	−0.764997	+	0.644034i	$0.777259\pi$
$224$	6.69409e118	1.37457
$225$	−6.50489e118	−1.06665
$226$	−1.59936e119	−2.09638
$227$	1.51279e118	0.158662	0.0793309	−	0.996848i	$-0.474722\pi$
$227$	1.51279e118	0.158662	0.0793309	+	0.996848i	$0.474722\pi$
$228$	3.21497e118	0.270064
$229$	1.06684e119	0.718465	0.359232	−	0.933248i	$-0.383039\pi$
$229$	1.06684e119	0.718465	0.359232	+	0.933248i	$0.383039\pi$
$230$	1.60725e119	0.868614
$231$	−3.99049e118	−0.173229
$232$	5.38612e119	1.87989
$233$	2.66360e118	0.0748160	0.0374080	−	0.999300i	$-0.488090\pi$
$233$	2.66360e118	0.0748160	0.0374080	+	0.999300i	$0.488090\pi$
$234$	3.11429e119	0.704625
$235$	−1.07573e120	−1.96235
$236$	−1.18090e120	−1.73843
$237$	1.11456e119	0.132529
$238$	2.79194e120	2.68392
$239$	−1.14147e119	−0.0887912	−0.0443956	−	0.999014i	$-0.514136\pi$
$239$	−1.14147e119	−0.0887912	−0.0443956	+	0.999014i	$0.514136\pi$
$240$	2.73140e118	0.0172075
$241$	−4.01998e119	−0.205288	−0.102644	−	0.994718i	$-0.532730\pi$
$241$	−4.01998e119	−0.205288	−0.102644	+	0.994718i	$0.532730\pi$
$242$	−2.35368e120	−0.975148
$243$	−1.76142e120	−0.592578
$244$	−1.87852e120	−0.513605
$245$	4.77904e120	1.06280
$246$	−2.83740e120	−0.513686
$247$	2.50982e120	0.370208
$248$	−1.24770e121	−1.50072
$249$	−3.25978e120	−0.319979
$250$	3.37998e120	0.270984
$251$	6.98915e120	0.458038	0.229019	−	0.973422i	$-0.426448\pi$
$251$	6.98915e120	0.458038	0.229019	+	0.973422i	$0.426448\pi$
$252$	3.73586e121	2.00292
$253$	−5.30609e120	−0.232910
$254$	4.80092e121	1.72672
$255$	1.31030e121	0.386449
$256$	−3.74723e121	−0.906969
$257$	−1.41846e121	−0.281964	−0.140982	−	0.990012i	$-0.545026\pi$
$257$	−1.41846e121	−0.281964	−0.140982	+	0.990012i	$0.545026\pi$
$258$	−8.15007e120	−0.133158
$259$	−8.96657e121	−1.20500
$260$	−9.58493e121	−1.06032
$261$	−2.06726e122	−1.88386
$262$	1.47733e122	1.10984
$263$	2.18472e122	1.35403	0.677017	−	0.735967i	$-0.263272\pi$
$263$	2.18472e122	1.35403	0.677017	+	0.735967i	$0.263272\pi$
$264$	2.45510e121	0.125623
$265$	−3.79172e122	−1.60295
$266$	4.90130e122	1.71313
$267$	−4.32320e121	−0.125022
$268$	4.57046e122	1.09434
$269$	−5.08484e122	−1.00876	−0.504379	−	0.863482i	$-0.668279\pi$
$269$	−5.08484e122	−1.00876	−0.504379	+	0.863482i	$0.668279\pi$
$270$	5.83980e122	0.960567
$271$	−5.98554e122	−0.816872	−0.408436	−	0.912787i	$-0.633926\pi$
$271$	−5.98554e122	−0.816872	−0.408436	+	0.912787i	$0.633926\pi$
$272$	6.30894e121	0.0714870
$273$	−1.34125e122	−0.126269
$274$	1.88399e123	1.47460
$275$	−1.07597e123	−0.700647
$276$	−2.28451e122	−0.123847
$277$	−1.50383e123	−0.679156	−0.339578	−	0.940578i	$-0.610284\pi$
$277$	−1.50383e123	−0.679156	−0.339578	+	0.940578i	$0.610284\pi$
$278$	2.23079e122	0.0839839
$279$	4.78882e123	1.50389
$280$	−6.96423e123	−1.82555
$281$	2.37882e123	0.520827	0.260413	−	0.965497i	$-0.416141\pi$
$281$	2.37882e123	0.520827	0.260413	+	0.965497i	$0.416141\pi$
$282$	2.48916e123	0.455483
$283$	−8.85918e123	−1.35575	−0.677874	−	0.735178i	$-0.737098\pi$
$283$	−8.85918e123	−1.35575	−0.677874	+	0.735178i	$0.737098\pi$
$284$	−7.88362e123	−1.00960
$285$	2.30026e123	0.246668
$286$	5.15133e123	0.462844
$287$	−2.65716e124	−2.00162
$288$	1.58071e124	0.998921
$289$	1.14139e124	0.605468
$290$	1.03577e125	4.61492
$291$	−4.03475e123	−0.151085
$292$	−3.68719e124	−1.16108
$293$	−7.86213e123	−0.208317	−0.104159	−	0.994561i	$-0.533215\pi$
$293$	−7.86213e123	−0.208317	−0.104159	+	0.994561i	$0.533215\pi$
$294$	−1.10583e124	−0.246689
$295$	−8.44916e124	−1.58782
$296$	5.51656e124	0.873851
$297$	−1.92792e124	−0.257567
$298$	−9.42025e124	−1.06204
$299$	−1.78344e124	−0.169771
$300$	−4.63254e124	−0.372560
$301$	−7.63235e124	−0.518860
$302$	1.07867e125	0.620207
$303$	8.92376e123	0.0434205
$304$	1.10755e124	0.0456296
$305$	−1.34405e125	−0.469110
$306$	6.59274e125	1.95045
$307$	5.07790e124	0.127408	0.0637039	−	0.997969i	$-0.479709\pi$
$307$	5.07790e124	0.127408	0.0637039	+	0.997969i	$0.479709\pi$
$308$	6.17947e125	1.31565
$309$	9.51839e124	0.172052
$310$	−2.39937e126	−3.68410
$311$	8.66949e125	1.13134	0.565671	−	0.824631i	$-0.308617\pi$
$311$	8.66949e125	1.13134	0.565671	+	0.824631i	$0.308617\pi$
$312$	8.25187e124	0.0915684
$313$	−2.59518e125	−0.245007	−0.122504	−	0.992468i	$-0.539092\pi$
$313$	−2.59518e125	−0.245007	−0.122504	+	0.992468i	$0.539092\pi$
$314$	5.78167e125	0.464629
$315$	2.67295e126	1.82940
$316$	−1.72594e126	−1.00654
$317$	2.15142e126	1.06963	0.534813	−	0.844971i	$-0.320382\pi$
$317$	2.15142e126	1.06963	0.534813	+	0.844971i	$0.320382\pi$
$318$	8.77375e125	0.372062
$319$	−3.41944e126	−1.23744
$320$	−7.65431e126	−2.36501
$321$	−2.85748e125	−0.0754186
$322$	−3.48280e126	−0.785610
$323$	5.31311e126	1.02476
$324$	8.39732e126	1.38554
$325$	−3.61647e126	−0.510710
$326$	−1.48519e127	−1.79595
$327$	−4.93444e125	−0.0511183
$328$	1.63478e127	1.45155
$329$	2.33104e127	1.77483
$330$	4.72123e126	0.308391
$331$	−1.15240e127	−0.646085	−0.323042	−	0.946385i	$-0.604706\pi$
$331$	−1.15240e127	−0.646085	−0.323042	+	0.946385i	$0.604706\pi$
$332$	5.04793e127	2.43019
$333$	−2.11732e127	−0.875696
$334$	−5.23583e127	−1.86118
$335$	3.27010e127	0.999536
$336$	−5.91877e125	−0.0155632
$337$	−3.11810e127	−0.705635	−0.352817	−	0.935692i	$-0.614776\pi$
$337$	−3.11810e127	−0.705635	−0.352817	+	0.935692i	$0.614776\pi$
$338$	−6.53188e127	−1.27275
$339$	1.62651e127	0.273006
$340$	−2.02907e128	−2.93502
$341$	7.92116e127	0.987854
$342$	1.15737e128	1.24496
$343$	3.81711e127	0.354308
$344$	4.69570e127	0.376270
$345$	−1.63453e127	−0.113118
$346$	2.79157e128	1.66919
$347$	−1.04259e128	−0.538858	−0.269429	−	0.963020i	$-0.586835\pi$
$347$	−1.04259e128	−0.538858	−0.269429	+	0.963020i	$0.586835\pi$
$348$	−1.47222e128	−0.657995
$349$	4.27486e128	1.65287	0.826433	−	0.563036i	$-0.190367\pi$
$349$	4.27486e128	1.65287	0.826433	+	0.563036i	$0.190367\pi$
$350$	−7.06243e128	−2.36330
$351$	−6.47999e127	−0.187743
$352$	2.61464e128	0.656157
$353$	3.37741e128	0.734449	0.367224	−	0.930132i	$-0.380308\pi$
$353$	3.37741e128	0.734449	0.367224	+	0.930132i	$0.380308\pi$
$354$	1.95507e128	0.368551
$355$	−5.64061e128	−0.922135
$356$	6.69469e128	0.949523
$357$	−2.83934e128	−0.349520
$358$	2.16756e129	2.31675
$359$	−2.13662e129	−1.98362	−0.991810	−	0.127724i	$-0.959233\pi$
$359$	−2.13662e129	−1.98362	−0.991810	+	0.127724i	$0.959233\pi$
$360$	−1.64450e129	−1.32665
$361$	−4.93253e128	−0.345904
$362$	−6.55490e128	−0.399745
$363$	2.39364e128	0.126991
$364$	2.07699e129	0.958993
$365$	−2.63813e129	−1.06049
$366$	3.11004e128	0.108886
$367$	−8.11750e128	−0.247620	−0.123810	−	0.992306i	$-0.539511\pi$
$367$	−8.11750e128	−0.247620	−0.123810	+	0.992306i	$0.539511\pi$
$368$	−7.87009e127	−0.0209250
$369$	−6.27449e129	−1.45461
$370$	1.06085e130	2.14520
$371$	8.21641e129	1.44977
$372$	3.41042e129	0.525278
$373$	4.08727e129	0.549714	0.274857	−	0.961485i	$-0.411369\pi$
$373$	4.08727e129	0.549714	0.274857	+	0.961485i	$0.411369\pi$
$374$	1.09050e130	1.28118
$375$	−3.43736e128	−0.0352896
$376$	−1.43414e130	−1.28708
$377$	−1.14932e130	−0.901989
$378$	−1.26545e130	−0.868777
$379$	−5.94249e129	−0.357017	−0.178508	−	0.983938i	$-0.557127\pi$
$379$	−5.94249e129	−0.357017	−0.178508	+	0.983938i	$0.557127\pi$
$380$	−3.56207e130	−1.87340
$381$	−4.88243e129	−0.224867
$382$	2.01866e130	0.814447
$383$	3.05852e130	1.08137	0.540684	−	0.841226i	$-0.318166\pi$
$383$	3.05852e130	1.08137	0.540684	+	0.841226i	$0.318166\pi$
$384$	1.06426e130	0.329855
$385$	4.42132e130	1.20167
$386$	−1.10510e131	−2.63477
$387$	−1.80227e130	−0.377064
$388$	6.24801e130	1.14747
$389$	7.76173e130	1.25171	0.625855	−	0.779940i	$-0.284750\pi$
$389$	7.76173e130	1.25171	0.625855	+	0.779940i	$0.284750\pi$
$390$	1.58686e130	0.224790
$391$	−3.77542e130	−0.469937
$392$	6.37131e130	0.697080
$393$	−1.50241e130	−0.144532
$394$	2.92271e130	0.247302
$395$	−1.23489e131	−0.919336
$396$	1.45919e131	0.956104
$397$	−1.13551e131	−0.655044	−0.327522	−	0.944844i	$-0.606214\pi$
$397$	−1.13551e131	−0.655044	−0.327522	+	0.944844i	$0.606214\pi$
$398$	−1.38134e131	−0.701789
$399$	−4.98452e130	−0.223096
$400$	−1.59590e130	−0.0629471
$401$	4.48151e131	1.55824	0.779119	−	0.626876i	$-0.215667\pi$
$401$	4.48151e131	1.55824	0.779119	+	0.626876i	$0.215667\pi$
$402$	−7.56677e130	−0.232004
$403$	2.66240e131	0.720059
$404$	−1.38189e131	−0.329772
$405$	6.00816e131	1.26550
$406$	−2.24445e132	−4.17392
$407$	−3.50225e131	−0.575215
$408$	1.74687e131	0.253467
$409$	−1.25927e132	−1.61469	−0.807347	−	0.590077i	$-0.799098\pi$
$409$	−1.25927e132	−1.61469	−0.807347	+	0.590077i	$0.799098\pi$
$410$	3.14374e132	3.56338
$411$	−1.91598e131	−0.192034
$412$	−1.47397e132	−1.30671
$413$	1.83088e132	1.43609
$414$	−8.22411e131	−0.570916
$415$	3.61172e132	2.21965
$416$	8.78813e131	0.478281
$417$	−2.26866e130	−0.0109370
$418$	1.91440e132	0.817769
$419$	−2.46484e132	−0.933214	−0.466607	−	0.884465i	$-0.654524\pi$
$419$	−2.46484e132	−0.933214	−0.466607	+	0.884465i	$0.654524\pi$
$420$	1.90358e132	0.638972
$421$	−4.71464e132	−1.40347	−0.701734	−	0.712439i	$-0.747590\pi$
$421$	−4.71464e132	−1.40347	−0.701734	+	0.712439i	$0.747590\pi$
$422$	−7.01697e132	−1.85298
$423$	5.50440e132	1.28980
$424$	−5.05504e132	−1.05135
$425$	−7.65582e132	−1.41368
$426$	1.30520e132	0.214038
$427$	2.91248e132	0.424282
$428$	4.42494e132	0.572793
$429$	−5.23879e131	−0.0602751
$430$	9.02999e132	0.923699
$431$	−1.67772e133	−1.52622	−0.763111	−	0.646268i	$-0.776329\pi$
$431$	−1.67772e133	−1.52622	−0.763111	+	0.646268i	$0.776329\pi$
$432$	−2.85953e131	−0.0231401
$433$	−6.18307e129	−0.000445211 0	−0.000222605	−	1.00000i	$-0.500071\pi$
$433$	−6.18307e129	−0.000445211 0	−0.000222605		1.00000i	$0.500071\pi$
$434$	5.19927e133	3.33205
$435$	−1.05336e133	−0.600990
$436$	7.64123e132	0.388236
$437$	−6.62784e132	−0.299957
$438$	6.10443e132	0.246152
$439$	−3.77735e133	−1.35747	−0.678733	−	0.734385i	$-0.737470\pi$
$439$	−3.77735e133	−1.35747	−0.678733	+	0.734385i	$0.737470\pi$
$440$	−2.72016e133	−0.871433
$441$	−2.44538e133	−0.698551
$442$	3.66531e133	0.933869
$443$	6.56580e133	1.49245	0.746224	−	0.665695i	$-0.231865\pi$
$443$	6.56580e133	1.49245	0.746224	+	0.665695i	$0.231865\pi$
$444$	−1.50788e133	−0.305863
$445$	4.78995e133	0.867262
$446$	−1.52391e134	−2.46348
$447$	9.58019e132	0.138307
$448$	1.65864e134	2.13901
$449$	7.19767e133	0.829377	0.414688	−	0.909963i	$-0.363891\pi$
$449$	7.19767e133	0.829377	0.414688	+	0.909963i	$0.363891\pi$
$450$	−1.66769e134	−1.71745
$451$	−1.03786e134	−0.955484
$452$	−2.51874e134	−2.07344
$453$	−1.09698e133	−0.0807681
$454$	3.87840e133	0.255466
$455$	1.48606e134	0.875912
$456$	3.06666e133	0.161786
$457$	1.64631e134	0.777576	0.388788	−	0.921327i	$-0.372894\pi$
$457$	1.64631e134	0.777576	0.388788	+	0.921327i	$0.372894\pi$
$458$	2.73509e134	1.15682
$459$	−1.37177e134	−0.519686
$460$	2.53116e134	0.859110
$461$	−1.97585e134	−0.600976	−0.300488	−	0.953786i	$-0.597150\pi$
$461$	−1.97585e134	−0.600976	−0.300488	+	0.953786i	$0.597150\pi$
$462$	−1.02306e134	−0.278921
$463$	5.15727e134	1.26061	0.630303	−	0.776349i	$-0.282930\pi$
$463$	5.15727e134	1.26061	0.630303	+	0.776349i	$0.282930\pi$
$464$	−5.07178e133	−0.111174
$465$	2.44010e134	0.479771
$466$	6.82879e133	0.120463
$467$	2.94920e133	0.0466876	0.0233438	−	0.999727i	$-0.492569\pi$
$467$	2.94920e133	0.0466876	0.0233438	+	0.999727i	$0.492569\pi$
$468$	4.90451e134	0.696916
$469$	−7.08610e134	−0.904021
$470$	−2.75790e135	−3.15963
$471$	−5.87984e133	−0.0605075
$472$	−1.12642e135	−1.04143
$473$	−2.98112e134	−0.247681
$474$	2.85744e134	0.213388
$475$	−1.34400e135	−0.902340
$476$	4.39686e135	2.65455
$477$	1.94018e135	1.05357
$478$	−2.92643e134	−0.142965
$479$	2.46547e135	1.08382	0.541909	−	0.840437i	$-0.317702\pi$
$479$	2.46547e135	1.08382	0.541909	+	0.840437i	$0.317702\pi$
$480$	8.05438e134	0.318676
$481$	−1.17715e135	−0.419281
$482$	−1.03062e135	−0.330540
$483$	3.54193e134	0.102308
$484$	−3.70667e135	−0.964479
$485$	4.47036e135	1.04806
$486$	−4.51583e135	−0.954127
$487$	1.02728e134	0.0195649	0.00978245	−	0.999952i	$-0.496886\pi$
$487$	1.02728e134	0.0195649	0.00978245	+	0.999952i	$0.496886\pi$
$488$	−1.79186e135	−0.307683
$489$	1.51041e135	0.233882
$490$	1.22522e136	1.71125
$491$	−8.92443e134	−0.112451	−0.0562257	−	0.998418i	$-0.517907\pi$
$491$	−8.92443e134	−0.112451	−0.0562257	+	0.998418i	$0.517907\pi$
$492$	−4.46846e135	−0.508066
$493$	−2.43302e136	−2.49676
$494$	6.43453e135	0.596082
$495$	1.04403e136	0.873273
$496$	1.17488e135	0.0887502
$497$	1.22229e136	0.834017
$498$	−8.35725e135	−0.515207
$499$	−3.42871e136	−1.91009	−0.955044	−	0.296464i	$-0.904192\pi$
$499$	−3.42871e136	−1.91009	−0.955044	+	0.296464i	$0.904192\pi$
$500$	5.32293e135	0.268019
$501$	5.32473e135	0.242378
$502$	1.79184e136	0.737499
$503$	−4.02932e136	−1.49985	−0.749926	−	0.661522i	$-0.769911\pi$
$503$	−4.02932e136	−1.49985	−0.749926	+	0.661522i	$0.769911\pi$
$504$	3.56353e136	1.19988
$505$	−9.88721e135	−0.301203
$506$	−1.36035e136	−0.375015
$507$	6.64278e135	0.165748
$508$	7.56069e136	1.70783
$509$	1.18185e136	0.241721	0.120861	−	0.992669i	$-0.461435\pi$
$509$	1.18185e136	0.241721	0.120861	+	0.992669i	$0.461435\pi$
$510$	3.35928e136	0.622232
$511$	5.71666e136	0.959151
$512$	7.41901e135	0.112775
$513$	−2.40817e136	−0.331711
$514$	−3.63657e136	−0.453999
$515$	−1.05460e137	−1.19350
$516$	−1.28351e136	−0.131701
$517$	9.10480e136	0.847223
$518$	−2.29880e137	−1.94021
$519$	−2.83897e136	−0.217374
$520$	−9.14278e136	−0.635199
$521$	9.59448e136	0.604946	0.302473	−	0.953158i	$-0.402188\pi$
$521$	9.59448e136	0.604946	0.302473	+	0.953158i	$0.402188\pi$
$522$	−5.29993e137	−3.03326
$523$	1.10209e137	0.572642	0.286321	−	0.958134i	$-0.407568\pi$
$523$	1.10209e137	0.572642	0.286321	+	0.958134i	$0.407568\pi$
$524$	2.32656e137	1.09770
$525$	7.18234e136	0.307766
$526$	5.60106e137	2.18017
$527$	5.63612e137	1.99317
$528$	−2.31181e135	−0.00742915
$529$	−2.95286e137	−0.862445
$530$	−9.72100e137	−2.58095
$531$	4.32335e137	1.04363
$532$	7.71878e137	1.69438
$533$	−3.48837e137	−0.696464
$534$	−1.10836e137	−0.201301
$535$	3.16598e137	0.523170
$536$	4.35963e137	0.655583
$537$	−2.20436e137	−0.301704
$538$	−1.30362e138	−1.62423
$539$	−4.04490e137	−0.458855
$540$	9.19676e137	0.950058
$541$	−6.70930e137	−0.631270	−0.315635	−	0.948881i	$-0.602218\pi$
$541$	−6.70930e137	−0.631270	−0.315635	+	0.948881i	$0.602218\pi$
$542$	−1.53454e138	−1.31527
$543$	6.66619e136	0.0520579
$544$	1.86039e138	1.32391
$545$	5.46719e137	0.354601
$546$	−3.43863e137	−0.203309
$547$	−8.05553e137	−0.434244	−0.217122	−	0.976144i	$-0.569667\pi$
$547$	−8.05553e137	−0.434244	−0.217122	+	0.976144i	$0.569667\pi$
$548$	2.96698e138	1.45847
$549$	6.87738e137	0.308333
$550$	−2.75852e138	−1.12813
$551$	−4.27123e138	−1.59366
$552$	−2.17913e137	−0.0741924
$553$	2.67592e138	0.831486
$554$	−3.85543e138	−1.09353
$555$	−1.07887e138	−0.279365
$556$	3.51314e137	0.0830651
$557$	6.47956e138	1.39913	0.699565	−	0.714569i	$-0.253377\pi$
$557$	6.47956e138	1.39913	0.699565	+	0.714569i	$0.253377\pi$
$558$	1.22773e139	2.42145
$559$	−1.00199e138	−0.180537
$560$	6.55778e137	0.107960
$561$	−1.10902e138	−0.166845
$562$	6.09870e138	0.838598
$563$	4.45055e138	0.559423	0.279711	−	0.960084i	$-0.409761\pi$
$563$	4.45055e138	0.559423	0.279711	+	0.960084i	$0.409761\pi$
$564$	3.92003e138	0.450500
$565$	−1.80212e139	−1.89381
$566$	−2.27127e139	−2.18293
$567$	−1.30193e139	−1.14457
$568$	−7.51995e138	−0.604817
$569$	1.34965e139	0.993237	0.496618	−	0.867969i	$-0.334575\pi$
$569$	1.34965e139	0.993237	0.496618	+	0.867969i	$0.334575\pi$
$570$	5.89729e138	0.397166
$571$	1.08594e139	0.669396	0.334698	−	0.942325i	$-0.391366\pi$
$571$	1.08594e139	0.669396	0.334698	+	0.942325i	$0.391366\pi$
$572$	8.11253e138	0.457780
$573$	−2.05293e138	−0.106063
$574$	−6.81229e139	−3.22287
$575$	9.55024e138	0.413798
$576$	3.91663e139	1.55445
$577$	−2.62894e139	−0.955876	−0.477938	−	0.878394i	$-0.658616\pi$
$577$	−2.62894e139	−0.955876	−0.477938	+	0.878394i	$0.658616\pi$
$578$	2.92622e139	0.974881
$579$	1.12386e139	0.343120
$580$	1.63117e140	4.56443
$581$	−7.82637e139	−2.00755
$582$	−1.03441e139	−0.243266
$583$	3.20925e139	0.692056
$584$	−3.51710e139	−0.695562
$585$	3.50911e139	0.636540
$586$	−2.01565e139	−0.335417
$587$	−1.05231e140	−1.60664	−0.803321	−	0.595546i	$-0.796936\pi$
$587$	−1.05231e140	−1.60664	−0.803321	+	0.595546i	$0.796936\pi$
$588$	−1.74151e139	−0.243990
$589$	9.89432e139	1.27222
$590$	−2.16615e140	−2.55660
$591$	−2.97234e138	−0.0322055
$592$	−5.19461e138	−0.0516781
$593$	6.79702e139	0.620950	0.310475	−	0.950582i	$-0.399512\pi$
$593$	6.79702e139	0.620950	0.310475	+	0.950582i	$0.399512\pi$
$594$	−4.94271e139	−0.414715
$595$	3.14589e140	2.42458
$596$	−1.48354e140	−1.05042
$597$	1.40480e139	0.0913923
$598$	−4.57229e139	−0.273353
$599$	−1.50842e140	−0.828835	−0.414417	−	0.910087i	$-0.636015\pi$
$599$	−1.50842e140	−0.828835	−0.414417	+	0.910087i	$0.636015\pi$
$600$	−4.41884e139	−0.223188
$601$	3.83968e140	1.78293	0.891464	−	0.453091i	$-0.149679\pi$
$601$	3.83968e140	1.78293	0.891464	+	0.453091i	$0.149679\pi$
$602$	−1.95674e140	−0.835431
$603$	−1.67328e140	−0.656967
$604$	1.69873e140	0.613421
$605$	−2.65207e140	−0.880923
$606$	2.28783e139	0.0699126
$607$	8.64913e139	0.243189	0.121594	−	0.992580i	$-0.461199\pi$
$607$	8.64913e139	0.243189	0.121594	+	0.992580i	$0.461199\pi$
$608$	3.26595e140	0.845044
$609$	2.28255e140	0.543560
$610$	−3.44581e140	−0.755327
$611$	3.06023e140	0.617551
$612$	1.03825e141	1.92911
$613$	−7.96669e140	−1.36309	−0.681544	−	0.731777i	$-0.738691\pi$
$613$	−7.96669e140	−1.36309	−0.681544	+	0.731777i	$0.738691\pi$
$614$	1.30184e140	0.205143
$615$	−3.19712e140	−0.464050
$616$	5.89441e140	0.788160
$617$	4.02335e140	0.495664	0.247832	−	0.968803i	$-0.420282\pi$
$617$	4.02335e140	0.495664	0.247832	+	0.968803i	$0.420282\pi$
$618$	2.44027e140	0.277026
$619$	−8.10256e140	−0.847705	−0.423852	−	0.905731i	$-0.639322\pi$
$619$	−8.10256e140	−0.847705	−0.423852	+	0.905731i	$0.639322\pi$
$620$	−3.77862e141	−3.64379
$621$	1.71121e140	0.152117
$622$	2.22264e141	1.82161
$623$	−1.03795e141	−0.784388
$624$	−7.77027e138	−0.00541520
$625$	−1.35492e141	−0.870906
$626$	−6.65339e140	−0.394493
$627$	−1.94691e140	−0.106496
$628$	9.10522e140	0.459545
$629$	−2.49195e141	−1.16060
$630$	6.85278e141	2.94557
$631$	1.26653e141	0.502496	0.251248	−	0.967923i	$-0.419159\pi$
$631$	1.26653e141	0.502496	0.251248	+	0.967923i	$0.419159\pi$
$632$	−1.64633e141	−0.602981
$633$	7.13610e140	0.241309
$634$	5.51569e141	1.72223
$635$	5.40956e141	1.55987
$636$	1.38173e141	0.367991
$637$	−1.35954e141	−0.334465
$638$	−8.76658e141	−1.99244
$639$	2.88624e141	0.606094
$640$	−1.17917e142	−2.28816
$641$	2.46708e141	0.442438	0.221219	−	0.975224i	$-0.428996\pi$
$641$	2.46708e141	0.442438	0.221219	+	0.975224i	$0.428996\pi$
$642$	−7.32585e140	−0.121434
$643$	−1.00891e142	−1.54596	−0.772981	−	0.634430i	$-0.781235\pi$
$643$	−1.00891e142	−1.54596	−0.772981	+	0.634430i	$0.781235\pi$
$644$	−5.48486e141	−0.777015
$645$	−9.18331e140	−0.120291
$646$	1.36215e142	1.64999
$647$	5.47711e141	0.613600	0.306800	−	0.951774i	$-0.400742\pi$
$647$	5.47711e141	0.613600	0.306800	+	0.951774i	$0.400742\pi$
$648$	8.00995e141	0.830027
$649$	7.15123e141	0.685526
$650$	−9.27170e141	−0.822309
$651$	−5.28755e141	−0.433925
$652$	−2.33894e142	−1.77630
$653$	−1.55247e141	−0.109121	−0.0545605	−	0.998510i	$-0.517376\pi$
$653$	−1.55247e141	−0.109121	−0.0545605	+	0.998510i	$0.517376\pi$
$654$	−1.26507e141	−0.0823070
$655$	1.66462e142	1.00260
$656$	−1.53937e141	−0.0858420
$657$	1.34990e142	0.697030
$658$	5.97619e142	2.85770
$659$	−3.76071e142	−1.66554	−0.832772	−	0.553616i	$-0.813248\pi$
$659$	−3.76071e142	−1.66554	−0.832772	+	0.553616i	$0.813248\pi$
$660$	7.43519e141	0.305017
$661$	−3.14082e142	−1.19363	−0.596815	−	0.802379i	$-0.703567\pi$
$661$	−3.14082e142	−1.19363	−0.596815	+	0.802379i	$0.703567\pi$
$662$	−2.95446e142	−1.04028
$663$	−3.72754e141	−0.121616
$664$	4.81507e142	1.45584
$665$	5.52267e142	1.54759
$666$	−5.42828e142	−1.40998
$667$	3.03508e142	0.730827
$668$	−8.24561e142	−1.84082
$669$	1.54979e142	0.320814
$670$	8.38371e142	1.60938
$671$	1.13758e142	0.202533
$672$	−1.74533e142	−0.288224
$673$	5.72017e142	0.876290	0.438145	−	0.898904i	$-0.355636\pi$
$673$	5.72017e142	0.876290	0.438145	+	0.898904i	$0.355636\pi$
$674$	−7.99402e142	−1.13616
$675$	3.47000e142	0.457604
$676$	−1.02867e143	−1.25883
$677$	−1.68388e143	−1.91242	−0.956211	−	0.292679i	$-0.905453\pi$
$677$	−1.68388e143	−1.91242	−0.956211	+	0.292679i	$0.905453\pi$
$678$	4.16997e142	0.439575
$679$	−9.68699e142	−0.947906
$680$	−1.93547e143	−1.75827
$681$	−3.94426e141	−0.0332687
$682$	2.03078e143	1.59057
$683$	9.75485e142	0.709537	0.354769	−	0.934954i	$-0.384560\pi$
$683$	9.75485e142	0.709537	0.354769	+	0.934954i	$0.384560\pi$
$684$	1.82268e143	1.23133
$685$	2.12283e143	1.33212
$686$	9.78610e142	0.570482
$687$	−2.78153e142	−0.150650
$688$	−4.42165e141	−0.0222520
$689$	1.07867e143	0.504448
$690$	−4.19053e142	−0.182134
$691$	−9.67210e142	−0.390732	−0.195366	−	0.980730i	$-0.562590\pi$
$691$	−9.67210e142	−0.390732	−0.195366	+	0.980730i	$0.562590\pi$
$692$	4.39628e143	1.65093
$693$	−2.26235e143	−0.789824
$694$	−2.67293e143	−0.867630
$695$	2.51360e142	0.0758689
$696$	−1.40431e143	−0.394182
$697$	−7.38465e143	−1.92786
$698$	1.09596e144	2.66132
$699$	−6.94473e141	−0.0156877
$700$	−1.11222e144	−2.33744
$701$	−6.48692e143	−1.26847	−0.634233	−	0.773142i	$-0.718684\pi$
$701$	−6.48692e143	−1.26847	−0.634233	+	0.773142i	$0.718684\pi$
$702$	−1.66130e143	−0.302291
$703$	−4.37467e143	−0.740800
$704$	6.47849e143	1.02107
$705$	2.80472e143	0.411471
$706$	8.65883e143	1.18256
$707$	2.14250e143	0.272420
$708$	3.07893e143	0.364519
$709$	8.63719e143	0.952221	0.476111	−	0.879385i	$-0.342046\pi$
$709$	8.63719e143	0.952221	0.476111	+	0.879385i	$0.342046\pi$
$710$	−1.44611e144	−1.48476
$711$	6.31880e143	0.604254
$712$	6.38586e143	0.568826
$713$	−7.03077e143	−0.583420
$714$	−7.27935e143	−0.562772
$715$	5.80440e143	0.418121
$716$	3.41357e144	2.29140
$717$	2.97612e142	0.0186180
$718$	−5.47776e144	−3.19388
$719$	1.28977e143	0.0700975	0.0350488	−	0.999386i	$-0.488841\pi$
$719$	1.28977e143	0.0700975	0.0350488	+	0.999386i	$0.488841\pi$
$720$	1.54852e143	0.0784561
$721$	2.28526e144	1.07946
$722$	−1.26457e144	−0.556950
$723$	1.04812e143	0.0430454
$724$	−1.03229e144	−0.395372
$725$	6.15453e144	2.19850
$726$	6.13668e143	0.204472
$727$	−1.32206e144	−0.410925	−0.205462	−	0.978665i	$-0.565870\pi$
$727$	−1.32206e144	−0.410925	−0.205462	+	0.978665i	$0.565870\pi$
$728$	1.98118e144	0.574500
$729$	−2.75645e144	−0.745778
$730$	−6.76350e144	−1.70752
$731$	−2.12115e144	−0.499739
$732$	4.89782e143	0.107694
$733$	2.44219e144	0.501220	0.250610	−	0.968088i	$-0.419369\pi$
$733$	2.44219e144	0.501220	0.250610	+	0.968088i	$0.419369\pi$
$734$	−2.08112e144	−0.398700
$735$	−1.24603e144	−0.222852
$736$	−2.32074e144	−0.387523
$737$	−2.76776e144	−0.431539
$738$	−1.60862e145	−2.34211
$739$	6.04415e144	0.821847	0.410924	−	0.911670i	$-0.365206\pi$
$739$	6.04415e144	0.821847	0.410924	+	0.911670i	$0.365206\pi$
$740$	1.67068e145	2.12173
$741$	−6.54378e143	−0.0776264
$742$	2.10648e145	2.33432
$743$	4.51166e144	0.467091	0.233546	−	0.972346i	$-0.424967\pi$
$743$	4.51166e144	0.467091	0.233546	+	0.972346i	$0.424967\pi$
$744$	3.25310e144	0.314676
$745$	−1.06145e145	−0.959419
$746$	1.04787e145	0.885110
$747$	−1.84808e145	−1.45892
$748$	1.71737e145	1.26716
$749$	−6.86048e144	−0.473176
$750$	−8.81253e143	−0.0568207
$751$	1.45207e145	0.875326	0.437663	−	0.899139i	$-0.355806\pi$
$751$	1.45207e145	0.875326	0.437663	+	0.899139i	$0.355806\pi$
$752$	1.35044e144	0.0761157
$753$	−1.82226e144	−0.0960428
$754$	−2.94655e145	−1.45232
$755$	1.21542e145	0.560278
$756$	−1.99288e145	−0.859271
$757$	−1.20161e145	−0.484641	−0.242320	−	0.970196i	$-0.577909\pi$
$757$	−1.20161e145	−0.484641	−0.242320	+	0.970196i	$0.577909\pi$
$758$	−1.52351e145	−0.574843
$759$	1.38344e144	0.0488373
$760$	−3.39775e145	−1.12229
$761$	−3.90026e145	−1.20550	−0.602751	−	0.797929i	$-0.705929\pi$
$761$	−3.90026e145	−1.20550	−0.602751	+	0.797929i	$0.705929\pi$
$762$	−1.25173e145	−0.362064
$763$	−1.18470e145	−0.320716
$764$	3.17906e145	0.805536
$765$	7.42855e145	1.76198
$766$	7.84127e145	1.74114
$767$	2.40362e145	0.499688
$768$	9.77007e144	0.190176
$769$	4.51695e144	0.0823313	0.0411656	−	0.999152i	$-0.486893\pi$
$769$	4.51695e144	0.0823313	0.0411656	+	0.999152i	$0.486893\pi$
$770$	1.13351e146	1.93484
$771$	3.69831e144	0.0591232
$772$	−1.74036e146	−2.60594
$773$	1.00998e145	0.141661	0.0708303	−	0.997488i	$-0.477435\pi$
$773$	1.00998e145	0.141661	0.0708303	+	0.997488i	$0.477435\pi$
$774$	−4.62055e145	−0.607121
$775$	−1.42570e146	−1.75506
$776$	5.95979e145	0.687408
$777$	2.33783e145	0.252669
$778$	1.98991e146	2.01541
$779$	−1.29639e146	−1.23054
$780$	2.49906e145	0.222330
$781$	4.77412e145	0.398122
$782$	−9.67923e145	−0.756658
$783$	1.10277e146	0.808195
$784$	−5.99947e144	−0.0412241
$785$	6.51465e145	0.419733
$786$	−3.85180e145	−0.232716
$787$	−2.76862e146	−1.56870	−0.784350	−	0.620319i	$-0.787003\pi$
$787$	−2.76862e146	−1.56870	−0.784350	+	0.620319i	$0.787003\pi$
$788$	4.60281e145	0.244596
$789$	−5.69615e145	−0.283918
$790$	−3.16594e146	−1.48025
$791$	3.90508e146	1.71284
$792$	1.39188e146	0.572769
$793$	3.82356e145	0.147629
$794$	−2.91116e146	−1.05470
$795$	9.88605e145	0.336111
$796$	−2.17540e146	−0.694110
$797$	−1.73951e146	−0.520932	−0.260466	−	0.965483i	$-0.583876\pi$
$797$	−1.73951e146	−0.520932	−0.260466	+	0.965483i	$0.583876\pi$
$798$	−1.27791e146	−0.359214
$799$	6.47831e146	1.70942
$800$	−4.70601e146	−1.16576
$801$	−2.45097e146	−0.570027
$802$	1.14895e147	2.50896
$803$	2.23287e146	0.457855
$804$	−1.19165e146	−0.229465
$805$	−3.92434e146	−0.709699
$806$	6.82571e146	1.15939
$807$	1.32576e146	0.211520
$808$	−1.31814e146	−0.197555
$809$	6.19950e146	0.872883	0.436442	−	0.899733i	$-0.356239\pi$
$809$	6.19950e146	0.872883	0.436442	+	0.899733i	$0.356239\pi$
$810$	1.54034e147	2.03762
$811$	9.95522e146	1.23736	0.618682	−	0.785641i	$-0.287667\pi$
$811$	9.95522e146	1.23736	0.618682	+	0.785641i	$0.287667\pi$
$812$	−3.53465e147	−4.12826
$813$	1.56059e146	0.171284
$814$	−8.97889e146	−0.926169
$815$	−1.67348e147	−1.62241
$816$	−1.64492e145	−0.0149896
$817$	−3.72372e146	−0.318980
$818$	−3.22844e147	−2.59986
$819$	−7.60401e146	−0.575713
$820$	4.95089e147	3.52439
$821$	1.00145e147	0.670349	0.335174	−	0.942156i	$-0.391205\pi$
$821$	1.00145e147	0.670349	0.335174	+	0.942156i	$0.391205\pi$
$822$	−4.91208e146	−0.309199
$823$	−3.42968e146	−0.203031	−0.101515	−	0.994834i	$-0.532369\pi$
$823$	−3.42968e146	−0.203031	−0.101515	+	0.994834i	$0.532369\pi$
$824$	−1.40598e147	−0.782805
$825$	2.80535e146	0.146914
$826$	4.69391e147	2.31229
$827$	−2.19408e147	−1.01677	−0.508386	−	0.861129i	$-0.669758\pi$
$827$	−2.19408e147	−1.01677	−0.508386	+	0.861129i	$0.669758\pi$
$828$	−1.29517e147	−0.564669
$829$	−1.42397e147	−0.584113	−0.292057	−	0.956401i	$-0.594340\pi$
$829$	−1.42397e147	−0.584113	−0.292057	+	0.956401i	$0.594340\pi$
$830$	9.25953e147	3.57393
$831$	3.92089e146	0.142408
$832$	2.17750e147	0.744268
$833$	−2.87805e147	−0.925819
$834$	−5.81628e145	−0.0176100
$835$	−5.89961e147	−1.68134
$836$	3.01488e147	0.808822
$837$	−2.55457e147	−0.645183
$838$	−6.31924e147	−1.50259
$839$	2.17760e147	0.487528	0.243764	−	0.969835i	$-0.421618\pi$
$839$	2.17760e147	0.487528	0.243764	+	0.969835i	$0.421618\pi$
$840$	1.81577e147	0.382786
$841$	1.45219e148	2.88287
$842$	−1.20871e148	−2.25976
$843$	−6.20225e146	−0.109209
$844$	−1.10506e148	−1.83271
$845$	−7.35997e147	−1.14977
$846$	1.41119e148	2.07674
$847$	5.74686e147	0.796743
$848$	4.76001e146	0.0621753
$849$	2.30983e147	0.284277
$850$	−1.96276e148	−2.27620
$851$	3.10858e147	0.339718
$852$	2.05548e147	0.211696
$853$	2.39847e147	0.232814	0.116407	−	0.993202i	$-0.462862\pi$
$853$	2.39847e147	0.232814	0.116407	+	0.993202i	$0.462862\pi$
$854$	7.46685e147	0.683149
$855$	1.30410e148	1.12466
$856$	4.22082e147	0.343140
$857$	−1.77495e148	−1.36037	−0.680183	−	0.733042i	$-0.738100\pi$
$857$	−1.77495e148	−1.36037	−0.680183	+	0.733042i	$0.738100\pi$
$858$	−1.34309e147	−0.0970506
$859$	−1.76032e148	−1.19933	−0.599664	−	0.800252i	$-0.704699\pi$
$859$	−1.76032e148	−1.19933	−0.599664	+	0.800252i	$0.704699\pi$
$860$	1.42208e148	0.913592
$861$	6.92795e147	0.419706
$862$	−4.30125e148	−2.45741
$863$	2.64645e148	1.42600	0.712998	−	0.701166i	$-0.247337\pi$
$863$	2.64645e148	1.42600	0.712998	+	0.701166i	$0.247337\pi$
$864$	−8.43223e147	−0.428547
$865$	3.14547e148	1.50790
$866$	−1.58518e145	−0.000716846 0
$867$	−2.97591e147	−0.126957
$868$	8.18803e148	3.29559
$869$	1.04519e148	0.396914
$870$	−2.70054e148	−0.967671
$871$	−9.30277e147	−0.314554
$872$	7.28874e147	0.232579
$873$	−2.28744e148	−0.688859
$874$	−1.69921e148	−0.482969
$875$	−8.25273e147	−0.221407
$876$	9.61352e147	0.243458
$877$	−7.77572e148	−1.85892	−0.929461	−	0.368920i	$-0.879728\pi$
$877$	−7.77572e148	−1.85892	−0.929461	+	0.368920i	$0.879728\pi$
$878$	−9.68416e148	−2.18569
$879$	2.04987e147	0.0436806
$880$	2.56141e147	0.0515351
$881$	5.10744e148	0.970332	0.485166	−	0.874422i	$-0.338759\pi$
$881$	5.10744e148	0.970332	0.485166	+	0.874422i	$0.338759\pi$
$882$	−6.26934e148	−1.12476
$883$	−4.89678e148	−0.829650	−0.414825	−	0.909901i	$-0.636157\pi$
$883$	−4.89678e148	−0.829650	−0.414825	+	0.909901i	$0.636157\pi$
$884$	5.77228e148	0.923652
$885$	2.20293e148	0.332940
$886$	1.68330e149	2.40303
$887$	8.91966e148	1.20283	0.601416	−	0.798936i	$-0.294603\pi$
$887$	8.91966e148	1.20283	0.601416	+	0.798936i	$0.294603\pi$
$888$	−1.43832e148	−0.183232
$889$	−1.17222e149	−1.41081
$890$	1.22802e149	1.39640
$891$	−5.08521e148	−0.546367
$892$	−2.39992e149	−2.43653
$893$	1.13728e149	1.09111
$894$	2.45612e148	0.222692
$895$	2.44236e149	2.09289
$896$	2.55518e149	2.06951
$897$	4.64992e147	0.0355981
$898$	1.84530e149	1.33540
$899$	−4.53089e149	−3.09970
$900$	−2.62635e149	−1.69865
$901$	2.28347e149	1.39634
$902$	−2.66081e149	−1.53845
$903$	1.98996e148	0.108796
$904$	−2.40255e149	−1.24213
$905$	−7.38591e148	−0.361119
$906$	−2.81238e148	−0.130047
$907$	−2.11629e149	−0.925567	−0.462784	−	0.886471i	$-0.653149\pi$
$907$	−2.11629e149	−0.925567	−0.462784	+	0.886471i	$0.653149\pi$
$908$	6.10787e148	0.252671
$909$	5.05919e148	0.197972
$910$	3.80988e149	1.41033
$911$	2.22931e149	0.780715	0.390358	−	0.920663i	$-0.372351\pi$
$911$	2.22931e149	0.780715	0.390358	+	0.920663i	$0.372351\pi$
$912$	−2.88768e147	−0.00956776
$913$	−3.05690e149	−0.958312
$914$	4.22072e149	1.25200
$915$	3.50432e148	0.0983644
$916$	4.30734e149	1.14416
$917$	−3.60712e149	−0.906796
$918$	−3.51687e149	−0.836760
$919$	−4.28888e149	−0.965852	−0.482926	−	0.875661i	$-0.660426\pi$
$919$	−4.28888e149	−0.965852	−0.482926	+	0.875661i	$0.660426\pi$
$920$	2.41440e149	0.514663
$921$	−1.32395e148	−0.0267153
$922$	−5.06558e149	−0.967648
$923$	1.60464e149	0.290196
$924$	−1.61116e149	−0.275870
$925$	6.30358e149	1.02195
$926$	1.32219e150	2.02974
$927$	5.39630e149	0.784457
$928$	−1.49557e150	−2.05890
$929$	1.69023e149	0.220370	0.110185	−	0.993911i	$-0.464856\pi$
$929$	1.69023e149	0.220370	0.110185	+	0.993911i	$0.464856\pi$
$930$	6.25581e149	0.772493
$931$	−5.05249e149	−0.590944
$932$	1.07543e149	0.119145
$933$	−2.26038e149	−0.237223
$934$	7.56099e148	0.0751729
$935$	1.22875e150	1.15739
$936$	4.67827e149	0.417498
$937$	−1.59055e148	−0.0134492	−0.00672461	−	0.999977i	$-0.502141\pi$
$937$	−1.59055e148	−0.0134492	−0.00672461	+	0.999977i	$0.502141\pi$
$938$	−1.81670e150	−1.45559
$939$	6.76636e148	0.0513739
$940$	−4.34325e150	−3.12506
$941$	2.35520e150	1.60602	0.803012	−	0.595962i	$-0.203229\pi$
$941$	2.35520e150	1.60602	0.803012	+	0.595962i	$0.203229\pi$
$942$	−1.50744e149	−0.0974248
$943$	9.21198e149	0.564303
$944$	1.06068e149	0.0615886
$945$	−1.42588e150	−0.784830
$946$	−7.64284e149	−0.398797
$947$	−1.39047e150	−0.687838	−0.343919	−	0.938999i	$-0.611755\pi$
$947$	−1.39047e150	−0.687838	−0.343919	+	0.938999i	$0.611755\pi$
$948$	4.50001e149	0.211054
$949$	7.50494e149	0.333736
$950$	−3.44566e150	−1.45288
$951$	−5.60934e149	−0.224283
$952$	4.19403e150	1.59025
$953$	9.30332e149	0.334539	0.167269	−	0.985911i	$-0.446505\pi$
$953$	9.30332e149	0.334539	0.167269	+	0.985911i	$0.446505\pi$
$954$	4.97414e150	1.69639
$955$	2.27457e150	0.735749
$956$	−4.60867e149	−0.141401
$957$	8.91543e149	0.259471
$958$	6.32084e150	1.74509
$959$	−4.60004e150	−1.20482
$960$	1.99569e150	0.495902
$961$	6.25422e150	1.47449
$962$	−3.01791e150	−0.675096
$963$	−1.62000e150	−0.343865
$964$	−1.62307e150	−0.326923
$965$	−1.24520e151	−2.38018
$966$	9.08062e149	0.164729
$967$	−5.17125e150	−0.890345	−0.445172	−	0.895445i	$-0.646858\pi$
$967$	−5.17125e150	−0.890345	−0.445172	+	0.895445i	$0.646858\pi$
$968$	−3.53568e150	−0.577786
$969$	−1.38527e150	−0.214875
$970$	1.14609e151	1.68751
$971$	−1.02064e151	−1.42660	−0.713302	−	0.700857i	$-0.752801\pi$
$971$	−1.02064e151	−1.42660	−0.713302	+	0.700857i	$0.752801\pi$
$972$	−7.11172e150	−0.943688
$973$	−5.44681e149	−0.0686189
$974$	2.63370e149	0.0315020
$975$	9.42912e149	0.107087
$976$	1.68729e149	0.0181959
$977$	1.19151e151	1.22017	0.610087	−	0.792334i	$-0.291134\pi$
$977$	1.19151e151	1.22017	0.610087	+	0.792334i	$0.291134\pi$
$978$	3.87230e150	0.376580
$979$	−4.05414e150	−0.374432
$980$	1.92953e151	1.69253
$981$	−2.79750e150	−0.233070
$982$	−2.28800e150	−0.181061
$983$	2.64030e151	1.98473	0.992364	−	0.123343i	$-0.0393617\pi$
$983$	2.64030e151	1.98473	0.992364	+	0.123343i	$0.0393617\pi$
$984$	−4.26233e150	−0.304365
$985$	3.29324e150	0.223406
$986$	−6.23766e151	−4.02010
$987$	−6.07766e150	−0.372152
$988$	1.01334e151	0.589560
$989$	2.64602e150	0.146279
$990$	2.67663e151	1.40608
$991$	−1.12820e151	−0.563205	−0.281603	−	0.959531i	$-0.590866\pi$
$991$	−1.12820e151	−0.563205	−0.281603	+	0.959531i	$0.590866\pi$
$992$	3.46450e151	1.64362
$993$	3.00462e150	0.135473
$994$	3.13363e151	1.34287
$995$	−1.55646e151	−0.633977
$996$	−1.31613e151	−0.509570
$997$	1.50434e151	0.553656	0.276828	−	0.960920i	$-0.410717\pi$
$997$	1.50434e151	0.553656	0.276828	+	0.960920i	$0.410717\pi$
$998$	−8.79035e151	−3.07549
$999$	1.12948e151	0.375682

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1.102.a.a.1.8	✓	8
3.2	odd	2		9.102.a.b.1.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1.102.a.a.1.8	✓	8	1.1	even	1	trivial
9.102.a.b.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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 1 \)
Weight:	\( k \)	\(=\)	\( 102 \)
Character orbit:	\([\chi]\)	\(=\)	1.a (trivial)

\(f(q)\)	\(=\)	\(q+2.56375e15 q^{2} -2.60728e23 q^{3} +4.03750e30 q^{4} +2.88877e35 q^{5} -6.68439e38 q^{6} -6.25978e42 q^{7} +3.85125e45 q^{8} -1.47815e48 q^{9} +O(q^{10})\)	\(q+2.56375e15 q^{2} -2.60728e23 q^{3} +4.03750e30 q^{4} +2.88877e35 q^{5} -6.68439e38 q^{6} -6.25978e42 q^{7} +3.85125e45 q^{8} -1.47815e48 q^{9} +7.40607e50 q^{10} -2.44501e52 q^{11} -1.05269e54 q^{12} -8.21796e55 q^{13} -1.60485e58 q^{14} -7.53182e58 q^{15} -3.62648e59 q^{16} -1.73969e62 q^{17} -3.78961e63 q^{18} -3.05406e64 q^{19} +1.16634e66 q^{20} +1.63210e66 q^{21} -6.26838e67 q^{22} +2.17017e68 q^{23} -1.00413e69 q^{24} +4.40068e70 q^{25} -2.10688e71 q^{26} +7.88515e71 q^{27} -2.52738e73 q^{28} +1.39854e74 q^{29} -1.93097e74 q^{30} -3.23973e75 q^{31} -1.06938e76 q^{32} +6.37481e75 q^{33} -4.46012e77 q^{34} -1.80831e78 q^{35} -5.96804e78 q^{36} +1.43241e79 q^{37} -7.82984e79 q^{38} +2.14265e79 q^{39} +1.11254e81 q^{40} +4.24481e81 q^{41} +4.18428e81 q^{42} +1.21927e82 q^{43} -9.87171e82 q^{44} -4.27005e83 q^{45} +5.56377e83 q^{46} -3.72383e84 q^{47} +9.45523e82 q^{48} +1.65435e85 q^{49} +1.12822e86 q^{50} +4.53585e85 q^{51} -3.31800e86 q^{52} -1.31257e87 q^{53} +2.02155e87 q^{54} -7.06306e87 q^{55} -2.41080e88 q^{56} +7.96278e87 q^{57} +3.58550e89 q^{58} -2.92483e89 q^{59} -3.04097e89 q^{60} -4.65268e89 q^{61} -8.30584e90 q^{62} +9.25292e90 q^{63} -2.64968e91 q^{64} -2.37398e91 q^{65} +1.63434e91 q^{66} +1.13200e92 q^{67} -7.02398e92 q^{68} -5.65824e91 q^{69} -4.63604e93 q^{70} -1.95260e93 q^{71} -5.69273e93 q^{72} -9.13236e93 q^{73} +3.67234e94 q^{74} -1.14738e94 q^{75} -1.23308e95 q^{76} +1.53052e95 q^{77} +5.49321e94 q^{78} -4.27479e95 q^{79} -1.04761e95 q^{80} +2.07983e96 q^{81} +1.08826e97 q^{82} +1.25026e97 q^{83} +6.58959e96 q^{84} -5.02556e97 q^{85} +3.12590e97 q^{86} -3.64638e97 q^{87} -9.41633e97 q^{88} +1.65813e98 q^{89} -1.09473e99 q^{90} +5.14426e98 q^{91} +8.76206e98 q^{92} +8.44686e98 q^{93} -9.54696e99 q^{94} -8.82247e99 q^{95} +2.78817e99 q^{96} +1.54750e100 q^{97} +4.24133e100 q^{98} +3.61410e100 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 434989091795040 q^{2} - 12\!\cdots\!60 q^{3}+ \cdots + 52\!\cdots\!84 q^{9}+O(q^{10}) \) 8 * q - 434989091795040 * q^2 - 1209375896611771518910560 * q^3 + 9008967123164113911511576503296 * q^4 + 38238791540232828026421308589217200 * q^5 + 2477260046146272006672820535971480695936 * q^6 - 5786789720778120168956257648884421874283200 * q^7 - 6101688461407407841888405145259998920458731520 * q^8 + 5273640617280587177839635242070674204864681879784 * q^9	\( 8 q - 434989091795040 q^{2} - 12\!\cdots\!60 q^{3}+ \cdots + 22\!\cdots\!08 q^{99}+O(q^{100}) \) 8 * q - 434989091795040 * q^2 - 1209375896611771518910560 * q^3 + 9008967123164113911511576503296 * q^4 + 38238791540232828026421308589217200 * q^5 + 2477260046146272006672820535971480695936 * q^6 - 5786789720778120168956257648884421874283200 * q^7 - 6101688461407407841888405145259998920458731520 * q^8 + 5273640617280587177839635242070674204864681879784 * q^9 - 376167658847177398692429835067300112512860198593600 * q^10 + 4622006661480385115355021397632645270205791478300896 * q^11 - 7273290781506553143908216801865849714958844187989422080 * q^12 + 250316830865150221699601352256397536965043294984328650480 * q^13 - 4856789037716039923353321450215036970203737520869624889088 * q^14 - 296460708185002952419818874947342543917521978696100167156800 * q^15 - 10662656154906175558835021484824464714661655552497093859868672 * q^16 - 397968518694853312322660892941326449007299986932512193696587120 * q^17 - 7270968925217398747066352706388703938040714138623386028515252960 * q^18 - 21387776045417165942123954421061470474744368808488511816400717280 * q^19 + 1745002690168409059221421019241581897927614179506161156200285542400 * q^20 + 4030935126807879780648600654579655736182360851489572706466859540736 * q^21 + 61357881995862711169740037407631980426480577127973320405539739944320 * q^22 - 1366243345208606848425464574347748611753917469593153677393324561698880 * q^23 + 10457354719000260635321058863018299052737315743164922361342586480885760 * q^24 + 77471873089568593564333770877949420045843582630742632687744142562715000 * q^25 - 97549630676937426518340388130407212490384846814009484188479115327886144 * q^26 - 5951874968930013487417142282111771144801435961988629201748805497863184320 * q^27 + 9217624035174751886516129105576165061663773766415040330328487084880404480 * q^28 + 15465799862710125255662370242568323665682807414567501281109138719156160880 * q^29 + 1101689156065505631051293671607641382064945196508526428823375711603202118400 * q^30 - 6594370386043135339784923725045360443937393326734068279132668478779615001344 * q^31 + 12265519409733718324179959581296851912742484455832107241543734281342036213760 * q^32 + 43813172582105581329585760338258562815639759809845990212191452867766348215680 * q^33 + 9531455444774917507766540524882635666895777953789094347547215472626183995712 * q^34 - 1122850631208004175280217132184898888977788452428069383882586628450512616297600 * q^35 + 1966242586607976986737003826554029255087710066072863106322127653222050407339008 * q^36 + 39729696767983511833540209209183332457877293383323859312175998401968644864715440 * q^37 - 70873740526925065519455012686645778106113298999572267198467188879790467046148480 * q^38 - 269289195198196884798470270521708844679404215685249767615656452740889673105306432 * q^39 - 763642761360299050617237751714968411270996317577517686387843428508400019349504000 * q^40 + 5607291724825101314952096252772109505395882457063737303656079003304969203257094736 * q^41 + 3008066923831569706716293907931878334959183836053498604235677758281531565332526080 * q^42 - 28642921955044714117801359306021921736063108483729021321044095944585527287681223200 * q^43 - 207838425393205175674959052733026300855796348257745356716186803699782799277851086848 * q^44 + 712633045382921242540931880134776511927082560144290402835715503414563529286220047600 * q^45 + 1088094260619851586903932234100844276278561023621942541398958535856528393570339218176 * q^46 - 4595399220200007631460417274797048154524720407021496316223236391731855709593438718080 * q^47 - 58354182581817955899154335674671016574355963424701638945735582725996041826866298880 * q^48 + 12068461406676719302337658501270392621238416595305390197216228129207599916872005856456 * q^49 - 40493179837482260394665357435432250163405353367416857829233726008281167215503492420000 * q^50 + 117646730044094759803745147399491979694134742922341911657750530682089815486256248611136 * q^51 - 736020167800817028850658909331852777746165402605863935107936992324104798352324258252800 * q^52 + 131026696145917691346168139299202731343660174597285772716290345361212508775951813313840 * q^53 + 6803608957095266771149163140167539716357850176039815317805755392633822625226741503089920 * q^54 - 14585157967675450217148723878599628333971210001615112897255333178063634767400530051473600 * q^55 - 23665562342657326400415121984960944704012341384928617813498515591030351969339927087022080 * q^56 - 66899487754306674554237314096607510056291565049587799982155034523058479948455991635655040 * q^57 + 29173417521771002425120779628349939892591335515731485644911210555324770598093888308326080 * q^58 + 212583149562022564923669670483574922097682552074321909615339251529169016840977455874187360 * q^59 - 3455800135608334392541843481344001808338357411235959344412061781382196941870275476295065600 * q^60 - 3390796423636162146406492296389682436951029380958058095674208836333532599894943317230895504 * q^61 - 5878859817222970028213836429448832127296537243368792127423103234889716583457526212133370880 * q^62 - 20171938924061808002384576493874339158887341995607670819297079343133751793255425885494984640 * q^63 - 74870090698021647967203019932764377907062372989513317693678846896652408519412785858115272704 * q^64 - 161067075283368767182138254547148962244907084326790507487294907612770451283405321317426536800 * q^65 - 745278055170676259198413344675313071673593040227005461838089798951153726758412015071955911168 * q^66 - 618774503558862942537948810466095132313460919373052732511642097824837019429997681150398682720 * q^67 - 2182412150351293808121583165511486752102068977919329447376923905220322529537335456462676162560 * q^68 - 5393950442083315109606578094475120918497802785657891521452512469623636760248087300551286537472 * q^69 - 12923520657540473465038555822652190723092643731233782501675276653712048411292540691873715571200 * q^70 - 15797470289857673806303846655911576507977904169297655042639265226995032204172380517793831135424 * q^71 - 55126715113590704564504537983251285080485074916503283789364546398928839504287032847376708239360 * q^72 - 20462651635605668591994589976366754984142669867347912050159975933828495442291952971923777071280 * q^73 - 142953411935712165334538916257020870493984381200782662943456748743148514063783881306064429441088 * q^74 - 204312291750914950304829914412770260373631281822544572731633720960361618548975517964814619460000 * q^75 + 64556217054886497186737063238064337992823205997653378371004031509089422583081356800943896432640 * q^76 + 250231448169383959900618348975396989794902211753647918986458150866408618577007907131029306438400 * q^77 + 1260981709052401111398092363772739439414079820346824747462408082793911096042108256417770344646400 * q^78 + 1474556321278768744579716979675929750918930811984805387023357390321899878561204701118206999166080 * q^79 + 6033438037435277941170744030808192554572458649979375320464765273747209092446481051552234550067200 * q^80 + 14613214105102112111129469132612601529386527627758931132459526147171392070559192290643105065182408 * q^81 + 30083863369214129982421840097969977845328701273986110579467106900080547794123383776302929686086720 * q^82 + 33762254529254022439253159341806143692643909652777369725086142424861011401680843403961249425712160 * q^83 + 57799153837692447414380568170128797835929379783304235587752969314531310322308849537769529417695232 * q^84 + 17314966267116570951109803841412092095679328201414316724042066880549149931729490643535478494114400 * q^85 + 67989564188024628582959760637462873453376851598916319417912395832044408164663357850732592560556416 * q^86 + 2586434133428712948881772736535019341274237946379240114707154003676967765014837223291966941531840 * q^87 - 363099602372059077387783242048689913608334478213970275423791339756517232974574737922754584123146240 * q^88 - 620007165949691950044675276484549383308720953973642955804615855186521697520022438525123333812557360 * q^89 - 4716676146177962028099989697458384454375488041754925418224025761569034561814581975790426208019028800 * q^90 - 3685711793015793225308940042728501386995879977832891226647110522985454537354035281338855172828873344 * q^91 - 4618779932089713137770970202224414792688843158843334085630908366025929325979388063902511470793400320 * q^92 - 3975022445092224432029728046757042348886229630318622378634497589784647142077875089398179428115102720 * q^93 - 17371370943540992303713705925513939673302729250250795188383540356993592041601425149438637190677682688 * q^94 - 2642077700832720169247174948884057845373174576960370774287679094739730873649398763127258995555528000 * q^95 + 4679875418673156206717240026356824763600126819048403120235276936002238426687957733980747642601209856 * q^96 + 64020476116668335744724892375903667651900818166631138467214326399663196857065619648203365824701173520 * q^97 + 202971561788470754768820264959327860776947519106194867162872422213964707447467488105939520314595817120 * q^98 + 225914901454627435116272921386700923755368861971179328902362103653753469396751969300619190223813523808 * q^99

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