LMFDB - Embedded newform 1.102.a.a.1.1

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			1.1
Root			$2.71282e13$ 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)

$f(q)$	$=$	$q-2.65868e15 q^{2} -2.23967e24 q^{3} +4.53328e30 q^{4} +2.85912e35 q^{5} +5.95456e39 q^{6} +3.30273e41 q^{7} -5.31200e45 q^{8} +3.46997e48 q^{9} +O(q^{10})$	\(q-2.65868e15 q^{2} -2.23967e24 q^{3} +4.53328e30 q^{4} +2.85912e35 q^{5} +5.95456e39 q^{6} +3.30273e41 q^{7} -5.31200e45 q^{8} +3.46997e48 q^{9} -7.60148e50 q^{10} -4.96610e52 q^{11} -1.01530e55 q^{12} +5.64410e55 q^{13} -8.78091e56 q^{14} -6.40347e59 q^{15} +2.62967e60 q^{16} -1.94858e61 q^{17} -9.22556e63 q^{18} +3.52128e64 q^{19} +1.29612e66 q^{20} -7.39702e65 q^{21} +1.32033e68 q^{22} -1.63800e68 q^{23} +1.18971e70 q^{24} +4.23025e70 q^{25} -1.50059e71 q^{26} -4.30876e72 q^{27} +1.49722e72 q^{28} -5.40160e73 q^{29} +1.70248e75 q^{30} -3.00633e75 q^{31} +6.47607e75 q^{32} +1.11224e77 q^{33} +5.18065e76 q^{34} +9.44290e76 q^{35} +1.57304e79 q^{36} +2.08004e79 q^{37} -9.36197e79 q^{38} -1.26409e80 q^{39} -1.51876e81 q^{40} +6.19514e80 q^{41} +1.96663e81 q^{42} -1.29205e82 q^{43} -2.25127e83 q^{44} +9.92107e83 q^{45} +4.35492e83 q^{46} +3.59319e84 q^{47} -5.88958e84 q^{48} -2.25323e85 q^{49} -1.12469e86 q^{50} +4.36417e85 q^{51} +2.55863e86 q^{52} -9.51793e86 q^{53} +1.14556e88 q^{54} -1.41987e88 q^{55} -1.75441e87 q^{56} -7.88650e88 q^{57} +1.43611e89 q^{58} +2.90108e89 q^{59} -2.90288e90 q^{60} +9.18299e89 q^{61} +7.99286e90 q^{62} +1.14604e90 q^{63} -2.38848e91 q^{64} +1.61371e91 q^{65} -2.95709e92 q^{66} -1.99314e92 q^{67} -8.83346e91 q^{68} +3.66857e92 q^{69} -2.51057e92 q^{70} -1.96946e93 q^{71} -1.84325e94 q^{72} +2.27832e94 q^{73} -5.53017e94 q^{74} -9.47435e94 q^{75} +1.59630e95 q^{76} -1.64017e94 q^{77} +3.36081e95 q^{78} +2.24448e95 q^{79} +7.51853e95 q^{80} +4.28516e96 q^{81} -1.64709e96 q^{82} +1.11393e96 q^{83} -3.35328e96 q^{84} -5.57122e96 q^{85} +3.43516e97 q^{86} +1.20978e98 q^{87} +2.63799e98 q^{88} -1.83015e98 q^{89} -2.63770e99 q^{90} +1.86409e97 q^{91} -7.42551e98 q^{92} +6.73317e99 q^{93} -9.55315e99 q^{94} +1.00678e100 q^{95} -1.45042e100 q^{96} +2.50182e100 q^{97} +5.99061e100 q^{98} -1.72322e101 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.65868e15	−1.66975	−0.834875	−	0.550440i	$-0.814460\pi$
$2$	−2.65868e15	−1.66975	−0.834875	+	0.550440i	$0.814460\pi$
$3$	−2.23967e24	−1.80119	−0.900596	−	0.434657i	$-0.856870\pi$
$3$	−2.23967e24	−1.80119	−0.900596	+	0.434657i	$0.856870\pi$
$4$	4.53328e30	1.78807
$5$	2.85912e35	1.43962	0.719808	−	0.694173i	$-0.244230\pi$
$5$	2.85912e35	1.43962	0.719808	+	0.694173i	$0.244230\pi$
$6$	5.95456e39	3.00754
$7$	3.30273e41	0.0694100	0.0347050	−	0.999398i	$-0.488951\pi$
$7$	3.30273e41	0.0694100	0.0347050	+	0.999398i	$0.488951\pi$
$8$	−5.31200e45	−1.31587
$9$	3.46997e48	2.24429
$10$	−7.60148e50	−2.40380
$11$	−4.96610e52	−1.27551	−0.637756	−	0.770238i	$-0.720137\pi$
$11$	−4.96610e52	−1.27551	−0.637756	+	0.770238i	$0.720137\pi$
$12$	−1.01530e55	−3.22065
$13$	5.64410e55	0.314380	0.157190	−	0.987568i	$-0.449756\pi$
$13$	5.64410e55	0.314380	0.157190	+	0.987568i	$0.449756\pi$
$14$	−8.78091e56	−0.115897
$15$	−6.40347e59	−2.59303
$16$	2.62967e60	0.409112
$17$	−1.94858e61	−0.141921	−0.0709606	−	0.997479i	$-0.522606\pi$
$17$	−1.94858e61	−0.141921	−0.0709606	+	0.997479i	$0.522606\pi$
$18$	−9.22556e63	−3.74741
$19$	3.52128e64	0.932490	0.466245	−	0.884656i	$-0.345606\pi$
$19$	3.52128e64	0.932490	0.466245	+	0.884656i	$0.345606\pi$
$20$	1.29612e66	2.57413
$21$	−7.39702e65	−0.125021
$22$	1.32033e68	2.12979
$23$	−1.63800e68	−0.279935	−0.139968	−	0.990156i	$-0.544700\pi$
$23$	−1.63800e68	−0.279935	−0.139968	+	0.990156i	$0.544700\pi$
$24$	1.18971e70	2.37014
$25$	4.23025e70	1.07250
$26$	−1.50059e71	−0.524936
$27$	−4.30876e72	−2.24121
$28$	1.49722e72	0.124110
$29$	−5.40160e73	−0.761068	−0.380534	−	0.924767i	$-0.624260\pi$
$29$	−5.40160e73	−0.761068	−0.380534	+	0.924767i	$0.624260\pi$
$30$	1.70248e75	4.32971
$31$	−3.00633e75	−1.45972	−0.729862	−	0.683595i	$-0.760416\pi$
$31$	−3.00633e75	−1.45972	−0.729862	+	0.683595i	$0.760416\pi$
$32$	6.47607e75	0.632758
$33$	1.11224e77	2.29744
$34$	5.18065e76	0.236973
$35$	9.44290e76	0.0999238
$36$	1.57304e79	4.01294
$37$	2.08004e79	1.33010	0.665052	−	0.746797i	$-0.268410\pi$
$37$	2.08004e79	1.33010	0.665052	+	0.746797i	$0.268410\pi$
$38$	−9.36197e79	−1.55703
$39$	−1.26409e80	−0.566259
$40$	−1.51876e81	−1.89435
$41$	6.19514e80	0.222058	0.111029	−	0.993817i	$-0.464585\pi$
$41$	6.19514e80	0.222058	0.111029	+	0.993817i	$0.464585\pi$
$42$	1.96663e81	0.208753
$43$	−1.29205e82	−0.417950	−0.208975	−	0.977921i	$-0.567013\pi$
$43$	−1.29205e82	−0.417950	−0.208975	+	0.977921i	$0.567013\pi$
$44$	−2.25127e83	−2.28070
$45$	9.92107e83	3.23092
$46$	4.35492e83	0.467422
$47$	3.59319e84	1.30178	0.650891	−	0.759171i	$-0.274395\pi$
$47$	3.59319e84	1.30178	0.650891	+	0.759171i	$0.274395\pi$
$48$	−5.88958e84	−0.736889
$49$	−2.25323e85	−0.995182
$50$	−1.12469e86	−1.79080
$51$	4.36417e85	0.255627
$52$	2.55863e86	0.562132
$53$	−9.51793e86	−0.799118	−0.399559	−	0.916707i	$-0.630837\pi$
$53$	−9.51793e86	−0.799118	−0.399559	+	0.916707i	$0.630837\pi$
$54$	1.14556e88	3.74226
$55$	−1.41987e88	−1.83625
$56$	−1.75441e87	−0.0913347
$57$	−7.88650e88	−1.67959
$58$	1.43611e89	1.27079
$59$	2.90108e89	1.08276	0.541382	−	0.840777i	$-0.317901\pi$
$59$	2.90108e89	1.08276	0.541382	+	0.840777i	$0.317901\pi$
$60$	−2.90288e90	−4.63650
$61$	9.18299e89	0.636543	0.318271	−	0.948000i	$-0.396898\pi$
$61$	9.18299e89	0.636543	0.318271	+	0.948000i	$0.396898\pi$
$62$	7.99286e90	2.43737
$63$	1.14604e90	0.155776
$64$	−2.38848e91	−1.46566
$65$	1.61371e91	0.452587
$66$	−2.95709e92	−3.83616
$67$	−1.99314e92	−1.20993	−0.604966	−	0.796251i	$-0.706813\pi$
$67$	−1.99314e92	−1.20993	−0.604966	+	0.796251i	$0.706813\pi$
$68$	−8.83346e91	−0.253764
$69$	3.66857e92	0.504218
$70$	−2.51057e92	−0.166848
$71$	−1.96946e93	−0.639442	−0.319721	−	0.947512i	$-0.603589\pi$
$71$	−1.96946e93	−0.639442	−0.319721	+	0.947512i	$0.603589\pi$
$72$	−1.84325e94	−2.95320
$73$	2.27832e94	1.81891	0.909453	−	0.415806i	$-0.136501\pi$
$73$	2.27832e94	1.81891	0.909453	+	0.415806i	$0.136501\pi$
$74$	−5.53017e94	−2.22094
$75$	−9.47435e94	−1.93177
$76$	1.59630e95	1.66735
$77$	−1.64017e94	−0.0885334
$78$	3.36081e95	0.945511
$79$	2.24448e95	0.331854	0.165927	−	0.986138i	$-0.446938\pi$
$79$	2.24448e95	0.331854	0.165927	+	0.986138i	$0.446938\pi$
$80$	7.51853e95	0.588964
$81$	4.28516e96	1.79256
$82$	−1.64709e96	−0.370782
$83$	1.11393e96	0.135961	0.0679805	−	0.997687i	$-0.478344\pi$
$83$	1.11393e96	0.135961	0.0679805	+	0.997687i	$0.478344\pi$
$84$	−3.35328e96	−0.223545
$85$	−5.57122e96	−0.204312
$86$	3.43516e97	0.697871
$87$	1.20978e98	1.37083
$88$	2.63799e98	1.67841
$89$	−1.83015e98	−0.658099	−0.329050	−	0.944313i	$-0.606728\pi$
$89$	−1.83015e98	−0.658099	−0.329050	+	0.944313i	$0.606728\pi$
$90$	−2.63770e99	−5.39483
$91$	1.86409e97	0.0218211
$92$	−7.42551e98	−0.500543
$93$	6.73317e99	2.62924
$94$	−9.55315e99	−2.17365
$95$	1.00678e100	1.34243
$96$	−1.45042e100	−1.13972
$97$	2.50182e100	1.16489	0.582443	−	0.812872i	$-0.302097\pi$
$97$	2.50182e100	1.16489	0.582443	+	0.812872i	$0.302097\pi$
$98$	5.99061e100	1.66171
$99$	−1.72322e101	−2.86262
$100$	1.91769e101	1.91769
$101$	1.66188e101	1.00547	0.502735	−	0.864441i	$-0.332327\pi$
$101$	1.66188e101	1.00547	0.502735	+	0.864441i	$0.332327\pi$
$102$	−1.16029e101	−0.426834
$103$	4.49375e101	1.01002	0.505009	−	0.863114i	$-0.331489\pi$
$103$	4.49375e101	1.01002	0.505009	+	0.863114i	$0.331489\pi$
$104$	−2.99814e101	−0.413684
$105$	−2.11489e101	−0.179982
$106$	2.53051e102	1.33433
$107$	−1.40440e102	−0.460903	−0.230451	−	0.973084i	$-0.574020\pi$
$107$	−1.40440e102	−0.460903	−0.230451	+	0.973084i	$0.574020\pi$
$108$	−1.95329e103	−4.00743
$109$	−7.42040e102	−0.955849	−0.477924	−	0.878401i	$-0.658611\pi$
$109$	−7.42040e102	−0.955849	−0.477924	+	0.878401i	$0.658611\pi$
$110$	3.77497e103	3.06608
$111$	−4.65860e103	−2.39577
$112$	8.68509e101	0.0283964
$113$	5.70765e103	1.19123	0.595615	−	0.803270i	$-0.296908\pi$
$113$	5.70765e103	1.19123	0.595615	+	0.803270i	$0.296908\pi$
$114$	2.09677e104	2.80450
$115$	−4.68323e103	−0.403000
$116$	−2.44870e104	−1.36084
$117$	1.95849e104	0.705561
$118$	−7.71305e104	−1.80794
$119$	−6.43563e102	−0.00985075
$120$	3.40152e105	3.41209
$121$	9.50347e104	0.626933
$122$	−2.44147e105	−1.06287
$123$	−1.38751e105	−0.399969
$124$	−1.36285e106	−2.61008
$125$	8.17554e104	0.104366
$126$	−3.04695e105	−0.260108
$127$	−2.11472e106	−1.21106	−0.605528	−	0.795824i	$-0.707038\pi$
$127$	−2.11472e106	−1.21106	−0.605528	+	0.795824i	$0.707038\pi$
$128$	4.70833e106	1.81453
$129$	2.89377e106	0.752808
$130$	−4.29035e106	−0.755707
$131$	−1.59542e107	−1.90843	−0.954213	−	0.299129i	$-0.903304\pi$
$131$	−1.59542e107	−1.90843	−0.954213	+	0.299129i	$0.903304\pi$
$132$	5.04210e107	4.10798
$133$	1.16299e106	0.0647242
$134$	5.29913e107	2.02028
$135$	−1.23193e108	−3.22648
$136$	1.03508e107	0.186750
$137$	−5.11141e107	−0.637018	−0.318509	−	0.947920i	$-0.603182\pi$
$137$	−5.11141e107	−0.637018	−0.318509	+	0.947920i	$0.603182\pi$
$138$	−9.75356e107	−0.841917
$139$	3.25384e108	1.95051	0.975256	−	0.221078i	$-0.0709575\pi$
$139$	3.25384e108	1.95051	0.975256	+	0.221078i	$0.0709575\pi$
$140$	4.28073e107	0.178670
$141$	−8.04755e108	−2.34476
$142$	5.23617e108	1.06771
$143$	−2.80291e108	−0.400996
$144$	9.12488e108	0.918166
$145$	−1.54438e109	−1.09565
$146$	−6.05733e109	−3.03712
$147$	5.04647e109	1.79251
$148$	9.42943e109	2.37831
$149$	−2.84162e109	−0.510104	−0.255052	−	0.966927i	$-0.582093\pi$
$149$	−2.84162e109	−0.510104	−0.255052	+	0.966927i	$0.582093\pi$
$150$	2.51893e110	3.22558
$151$	−5.37944e109	−0.492494	−0.246247	−	0.969207i	$-0.579197\pi$
$151$	−5.37944e109	−0.492494	−0.246247	+	0.969207i	$0.579197\pi$
$152$	−1.87051e110	−1.22704
$153$	−6.76152e109	−0.318513
$154$	4.36069e109	0.147829
$155$	−8.59544e110	−2.10144
$156$	−5.73048e110	−1.01251
$157$	6.87958e110	0.880298	0.440149	−	0.897925i	$-0.354926\pi$
$157$	6.87958e110	0.880298	0.440149	+	0.897925i	$0.354926\pi$
$158$	−5.96734e110	−0.554113
$159$	2.13170e111	1.43937
$160$	1.85158e111	0.910928
$161$	−5.40987e109	−0.0194303
$162$	−1.13929e112	−2.99312
$163$	2.92192e111	0.562594	0.281297	−	0.959621i	$-0.409235\pi$
$163$	2.92192e111	0.562594	0.281297	+	0.959621i	$0.409235\pi$
$164$	2.80843e111	0.397054
$165$	3.18003e112	3.30744
$166$	−2.96158e111	−0.227021
$167$	−2.55509e112	−1.44619	−0.723094	−	0.690749i	$-0.757281\pi$
$167$	−2.55509e112	−1.44619	−0.723094	+	0.690749i	$0.757281\pi$
$168$	3.92929e111	0.164511
$169$	−2.90458e112	−0.901165
$170$	1.48121e112	0.341150
$171$	1.22188e113	2.09278
$172$	−5.85725e112	−0.747321
$173$	−5.66260e110	−0.00539122	−0.00269561	−	0.999996i	$-0.500858\pi$
$173$	−5.66260e110	−0.00539122	−0.00269561	+	0.999996i	$0.500858\pi$
$174$	−3.21641e113	−2.28894
$175$	1.39714e112	0.0744420
$176$	−1.30592e113	−0.521827
$177$	−6.49746e113	−1.95026
$178$	4.86579e113	1.09886
$179$	−3.56632e113	−0.606936	−0.303468	−	0.952842i	$-0.598145\pi$
$179$	−3.56632e113	−0.606936	−0.303468	+	0.952842i	$0.598145\pi$
$180$	4.49750e114	5.77710
$181$	−1.18458e114	−1.15026	−0.575131	−	0.818061i	$-0.695049\pi$
$181$	−1.18458e114	−1.15026	−0.575131	+	0.818061i	$0.695049\pi$
$182$	−4.95603e112	−0.0364358
$183$	−2.05668e114	−1.14654
$184$	8.70105e113	0.368359
$185$	5.94709e114	1.91484
$186$	−1.79014e115	−4.39018
$187$	9.67683e113	0.181022
$188$	1.62889e115	2.32767
$189$	−1.42307e114	−0.155562
$190$	−2.67670e115	−2.24152
$191$	−2.94775e114	−0.189367	−0.0946837	−	0.995507i	$-0.530184\pi$
$191$	−2.94775e114	−0.189367	−0.0946837	+	0.995507i	$0.530184\pi$
$192$	5.34940e115	2.63993
$193$	1.45178e115	0.551134	0.275567	−	0.961282i	$-0.411134\pi$
$193$	1.45178e115	0.551134	0.275567	+	0.961282i	$0.411134\pi$
$194$	−6.65154e115	−1.94507
$195$	−3.61418e115	−0.815196
$196$	−1.02145e116	−1.77945
$197$	−3.67802e115	−0.495529	−0.247765	−	0.968820i	$-0.579696\pi$
$197$	−3.67802e115	−0.495529	−0.247765	+	0.968820i	$0.579696\pi$
$198$	4.58150e116	4.77987
$199$	4.98786e115	0.403491	0.201746	−	0.979438i	$-0.435339\pi$
$199$	4.98786e115	0.403491	0.201746	+	0.979438i	$0.435339\pi$
$200$	−2.24711e116	−1.41127
$201$	4.46398e116	2.17932
$202$	−4.41840e116	−1.67888
$203$	−1.78400e115	−0.0528257
$204$	1.97840e116	0.457078
$205$	1.77126e116	0.319679
$206$	−1.19475e117	−1.68648
$207$	−5.68381e116	−0.628257
$208$	1.48421e116	0.128617
$209$	−1.74870e117	−1.18940
$210$	5.62283e116	0.300525
$211$	2.38874e117	1.00439	0.502197	−	0.864753i	$-0.332525\pi$
$211$	2.38874e117	1.00439	0.502197	+	0.864753i	$0.332525\pi$
$212$	−4.31475e117	−1.42888
$213$	4.41094e117	1.15176
$214$	3.73385e117	0.769593
$215$	−3.69414e117	−0.601687
$216$	2.28881e118	2.94915
$217$	−9.92909e116	−0.101319
$218$	1.97285e118	1.59603
$219$	−5.10268e118	−3.27620
$220$	−6.43666e118	−3.28333
$221$	−1.09980e117	−0.0446172
$222$	1.23857e119	4.00034
$223$	−3.35176e118	−0.862734	−0.431367	−	0.902177i	$-0.641969\pi$
$223$	−3.35176e118	−0.862734	−0.431367	+	0.902177i	$0.641969\pi$
$224$	2.13887e117	0.0439197
$225$	1.46789e119	2.40700
$226$	−1.51748e119	−1.98906
$227$	−5.26256e118	−0.551939	−0.275969	−	0.961166i	$-0.588999\pi$
$227$	−5.26256e118	−0.551939	−0.275969	+	0.961166i	$0.588999\pi$
$228$	−3.57518e119	−3.00322
$229$	7.34834e118	0.494877	0.247439	−	0.968904i	$-0.420411\pi$
$229$	7.34834e118	0.494877	0.247439	+	0.968904i	$0.420411\pi$
$230$	1.24512e119	0.672909
$231$	3.67343e118	0.159466
$232$	2.86933e119	1.00147
$233$	2.38643e119	0.670307	0.335154	−	0.942163i	$-0.391212\pi$
$233$	2.38643e119	0.670307	0.335154	+	0.942163i	$0.391212\pi$
$234$	−5.20699e119	−1.17811
$235$	1.02734e120	1.87407
$236$	1.31514e120	1.93605
$237$	−5.02688e119	−0.597732
$238$	1.71103e118	0.0164483
$239$	−1.95496e120	−1.52070	−0.760352	−	0.649511i	$-0.774974\pi$
$239$	−1.95496e120	−1.52070	−0.760352	+	0.649511i	$0.774974\pi$
$240$	−1.68390e120	−1.06084
$241$	1.17898e120	0.602066	0.301033	−	0.953614i	$-0.402669\pi$
$241$	1.17898e120	0.602066	0.301033	+	0.953614i	$0.402669\pi$
$242$	−2.52667e120	−1.04682
$243$	−2.93540e120	−0.987531
$244$	4.16291e120	1.13818
$245$	−6.44224e120	−1.43268
$246$	3.68894e120	0.667849
$247$	1.98745e120	0.293156
$248$	1.59696e121	1.92081
$249$	−2.49483e120	−0.244892
$250$	−2.17361e120	−0.174266
$251$	−1.91657e121	−1.25603	−0.628017	−	0.778200i	$-0.716133\pi$
$251$	−1.91657e121	−1.25603	−0.628017	+	0.778200i	$0.716133\pi$
$252$	5.19532e120	0.278538
$253$	8.13446e120	0.357061
$254$	5.62236e121	2.02216
$255$	1.24777e121	0.368005
$256$	−6.46242e121	−1.56415
$257$	−4.00544e120	−0.0796211	−0.0398105	−	0.999207i	$-0.512675\pi$
$257$	−4.00544e120	−0.0796211	−0.0398105	+	0.999207i	$0.512675\pi$
$258$	−7.69362e121	−1.25700
$259$	6.86982e120	0.0923225
$260$	7.31542e121	0.809255
$261$	−1.87434e122	−1.70806
$262$	4.24172e122	3.18659
$263$	1.20762e122	0.748452	0.374226	−	0.927337i	$-0.377908\pi$
$263$	1.20762e122	0.748452	0.374226	+	0.927337i	$0.377908\pi$
$264$	−5.90822e122	−3.02314
$265$	−2.72129e122	−1.15042
$266$	−3.09201e121	−0.108073
$267$	4.09893e122	1.18536
$268$	−9.03548e122	−2.16344
$269$	−7.02503e122	−1.39366	−0.696832	−	0.717234i	$-0.745408\pi$
$269$	−7.02503e122	−1.39366	−0.696832	+	0.717234i	$0.745408\pi$
$270$	3.27530e123	5.38742
$271$	4.75544e122	0.648995	0.324497	−	0.945887i	$-0.394805\pi$
$271$	4.75544e122	0.648995	0.324497	+	0.945887i	$0.394805\pi$
$272$	−5.12411e121	−0.0580616
$273$	−4.17495e121	−0.0393041
$274$	1.35896e123	1.06366
$275$	−2.10078e123	−1.36798
$276$	1.66307e123	0.901574
$277$	4.65434e122	0.210198	0.105099	−	0.994462i	$-0.466484\pi$
$277$	4.65434e122	0.210198	0.105099	+	0.994462i	$0.466484\pi$
$278$	−8.65092e123	−3.25687
$279$	−1.04319e124	−3.27605
$280$	−5.01606e122	−0.131487
$281$	8.19421e123	1.79406	0.897032	−	0.441966i	$-0.145719\pi$
$281$	8.19421e123	1.79406	0.897032	+	0.441966i	$0.145719\pi$
$282$	2.13959e124	3.91516
$283$	2.01371e123	0.308164	0.154082	−	0.988058i	$-0.450758\pi$
$283$	2.01371e123	0.308164	0.154082	+	0.988058i	$0.450758\pi$
$284$	−8.92813e123	−1.14336
$285$	−2.25484e124	−2.41797
$286$	7.45205e123	0.669563
$287$	2.04609e122	0.0154131
$288$	2.24718e124	1.42009
$289$	−1.84716e124	−0.979858
$290$	4.10601e124	1.82945
$291$	−5.60324e124	−2.09818
$292$	1.03283e125	3.25232
$293$	−2.49149e124	−0.660154	−0.330077	−	0.943954i	$-0.607075\pi$
$293$	−2.49149e124	−0.660154	−0.330077	+	0.943954i	$0.607075\pi$
$294$	−1.34170e125	−2.99305
$295$	8.29454e124	1.55876
$296$	−1.10492e125	−1.75025
$297$	2.13978e125	2.85869
$298$	7.55496e124	0.851747
$299$	−9.24502e123	−0.0880061
$300$	−4.29499e125	−3.45413
$301$	−4.26731e123	−0.0290099
$302$	1.43022e125	0.822342
$303$	−3.72205e125	−1.81104
$304$	9.25981e124	0.381493
$305$	2.62553e125	0.916378
$306$	1.79767e125	0.531837
$307$	1.07629e125	0.270049	0.135024	−	0.990842i	$-0.456889\pi$
$307$	1.07629e125	0.270049	0.135024	+	0.990842i	$0.456889\pi$
$308$	−7.43535e124	−0.158303
$309$	−1.00645e126	−1.81924
$310$	2.28525e126	3.50888
$311$	−2.71674e125	−0.354527	−0.177263	−	0.984163i	$-0.556724\pi$
$311$	−2.71674e125	−0.354527	−0.177263	+	0.984163i	$0.556724\pi$
$312$	6.71484e125	0.745124
$313$	1.08086e126	1.02043	0.510214	−	0.860048i	$-0.329566\pi$
$313$	1.08086e126	1.02043	0.510214	+	0.860048i	$0.329566\pi$
$314$	−1.82906e126	−1.46988
$315$	3.27666e125	0.224258
$316$	1.01748e126	0.593376
$317$	−3.10015e126	−1.54131	−0.770656	−	0.637252i	$-0.780071\pi$
$317$	−3.10015e126	−1.54131	−0.770656	+	0.637252i	$0.780071\pi$
$318$	−5.66751e126	−2.40338
$319$	2.68249e126	0.970751
$320$	−6.82894e126	−2.10999
$321$	3.14538e126	0.830175
$322$	1.43831e125	0.0324438
$323$	−6.86150e125	−0.132340
$324$	1.94258e127	3.20521
$325$	2.38759e126	0.337171
$326$	−7.76846e126	−0.939391
$327$	1.66192e127	1.72167
$328$	−3.29086e126	−0.292200
$329$	1.18673e126	0.0903567
$330$	−8.45468e127	−5.52259
$331$	2.31485e127	1.29780	0.648902	−	0.760872i	$-0.275228\pi$
$331$	2.31485e127	1.29780	0.648902	+	0.760872i	$0.275228\pi$
$332$	5.04976e126	0.243107
$333$	7.21770e127	2.98514
$334$	6.79318e127	2.41477
$335$	−5.69863e127	−1.74184
$336$	−1.94517e126	−0.0511474
$337$	−5.17085e127	−1.17018	−0.585089	−	0.810969i	$-0.698940\pi$
$337$	−5.17085e127	−1.17018	−0.585089	+	0.810969i	$0.698940\pi$
$338$	7.72234e127	1.50472
$339$	−1.27832e128	−2.14563
$340$	−2.52559e127	−0.365323
$341$	1.49297e128	1.86190
$342$	−3.24858e128	−3.49442
$343$	−1.49196e127	−0.138486
$344$	6.86339e127	0.549968
$345$	1.04889e128	0.725880
$346$	1.50550e126	0.00900200
$347$	−1.81398e128	−0.937549	−0.468775	−	0.883318i	$-0.655304\pi$
$347$	−1.81398e128	−0.937549	−0.468775	+	0.883318i	$0.655304\pi$
$348$	5.48426e128	2.45113
$349$	3.13313e128	1.21142	0.605710	−	0.795686i	$-0.292889\pi$
$349$	3.13313e128	1.21142	0.605710	+	0.795686i	$0.292889\pi$
$350$	−3.71454e127	−0.124299
$351$	−2.43191e128	−0.704592
$352$	−3.21608e128	−0.807090
$353$	−1.25997e128	−0.273992	−0.136996	−	0.990572i	$-0.543745\pi$
$353$	−1.25997e128	−0.273992	−0.136996	+	0.990572i	$0.543745\pi$
$354$	1.72747e129	3.25645
$355$	−5.63093e128	−0.920551
$356$	−8.29659e128	−1.17672
$357$	1.44137e127	0.0177431
$358$	9.48172e128	1.01343
$359$	−7.76594e128	−0.720982	−0.360491	−	0.932763i	$-0.617391\pi$
$359$	−7.76594e128	−0.720982	−0.360491	+	0.932763i	$0.617391\pi$
$360$	−5.27007e129	−4.25148
$361$	−1.86036e128	−0.130462
$362$	3.14942e129	1.92065
$363$	−2.12846e129	−1.12923
$364$	8.45046e127	0.0390176
$365$	6.51399e129	2.61853
$366$	5.46807e129	1.91443
$367$	−4.50811e129	−1.37518	−0.687588	−	0.726101i	$-0.741331\pi$
$367$	−4.50811e129	−1.37518	−0.687588	+	0.726101i	$0.741331\pi$
$368$	−4.30739e128	−0.114525
$369$	2.14970e129	0.498363
$370$	−1.58114e130	−3.19730
$371$	−3.14352e128	−0.0554668
$372$	3.05234e130	4.70126
$373$	−7.42600e129	−0.998754	−0.499377	−	0.866385i	$-0.666438\pi$
$373$	−7.42600e129	−0.998754	−0.499377	+	0.866385i	$0.666438\pi$
$374$	−2.57276e129	−0.302262
$375$	−1.83105e129	−0.187984
$376$	−1.90870e130	−1.71298
$377$	−3.04871e129	−0.239265
$378$	3.78349e129	0.259750
$379$	−1.86901e130	−1.12288	−0.561439	−	0.827518i	$-0.689752\pi$
$379$	−1.86901e130	−1.12288	−0.561439	+	0.827518i	$0.689752\pi$
$380$	4.56400e130	2.40035
$381$	4.73626e130	2.18135
$382$	7.83712e129	0.316196
$383$	−3.78544e130	−1.33838	−0.669188	−	0.743093i	$-0.733358\pi$
$383$	−3.78544e130	−1.33838	−0.669188	+	0.743093i	$0.733358\pi$
$384$	−1.05451e131	−3.26831
$385$	−4.68944e129	−0.127454
$386$	−3.85982e130	−0.920256
$387$	−4.48340e130	−0.938001
$388$	1.13415e131	2.08289
$389$	−9.11393e130	−1.46977	−0.734887	−	0.678189i	$-0.762765\pi$
$389$	−9.11393e130	−1.46977	−0.734887	+	0.678189i	$0.762765\pi$
$390$	9.60895e130	1.36117
$391$	3.19177e129	0.0397288
$392$	1.19691e131	1.30953
$393$	3.57321e131	3.43744
$394$	9.77868e130	0.827410
$395$	6.41722e130	0.477742
$396$	−7.81186e131	−5.11856
$397$	2.61893e131	1.51079	0.755393	−	0.655272i	$-0.227446\pi$
$397$	2.61893e131	1.51079	0.755393	+	0.655272i	$0.227446\pi$
$398$	−1.32611e131	−0.673729
$399$	−2.60470e130	−0.116581
$400$	1.11242e131	0.438771
$401$	4.94826e130	0.172053	0.0860265	−	0.996293i	$-0.472583\pi$
$401$	4.94826e130	0.172053	0.0860265	+	0.996293i	$0.472583\pi$
$402$	−1.18683e132	−3.63892
$403$	−1.69680e131	−0.458908
$404$	7.53375e131	1.79785
$405$	1.22518e132	2.58060
$406$	4.74309e130	0.0882057
$407$	−1.03297e132	−1.69656
$408$	−2.31824e131	−0.336373
$409$	−7.74861e131	−0.993566	−0.496783	−	0.867875i	$-0.665485\pi$
$409$	−7.74861e131	−0.993566	−0.496783	+	0.867875i	$0.665485\pi$
$410$	−4.70923e131	−0.533783
$411$	1.14479e132	1.14739
$412$	2.03715e132	1.80598
$413$	9.58149e130	0.0751546
$414$	1.51114e132	1.04903
$415$	3.18486e131	0.195732
$416$	3.65515e131	0.198926
$417$	−7.28752e132	−3.51325
$418$	4.64925e132	1.98601
$419$	5.87287e131	0.222353	0.111176	−	0.993801i	$-0.464538\pi$
$419$	5.87287e131	0.222353	0.111176	+	0.993801i	$0.464538\pi$
$420$	−9.58741e131	−0.321820
$421$	−3.52135e132	−1.04825	−0.524123	−	0.851643i	$-0.675607\pi$
$421$	−3.52135e132	−1.04825	−0.524123	+	0.851643i	$0.675607\pi$
$422$	−6.35089e132	−1.67709
$423$	1.24683e133	2.92158
$424$	5.05592e132	1.05154
$425$	−8.24298e131	−0.152210
$426$	−1.17273e133	−1.92315
$427$	3.03290e131	0.0441824
$428$	−6.36653e132	−0.824124
$429$	6.27759e132	0.722271
$430$	9.82153e132	1.00467
$431$	−1.61351e133	−1.46781	−0.733905	−	0.679252i	$-0.762304\pi$
$431$	−1.61351e133	−1.46781	−0.733905	+	0.679252i	$0.762304\pi$
$432$	−1.13306e133	−0.916905
$433$	−9.85490e132	−0.709600	−0.354800	−	0.934942i	$-0.615451\pi$
$433$	−9.85490e132	−0.709600	−0.354800	+	0.934942i	$0.615451\pi$
$434$	2.63983e132	0.169178
$435$	3.45890e133	1.97347
$436$	−3.36388e133	−1.70912
$437$	−5.76786e132	−0.261037
$438$	1.35664e134	5.47044
$439$	−3.01466e133	−1.08338	−0.541689	−	0.840579i	$-0.682215\pi$
$439$	−3.01466e133	−1.08338	−0.541689	+	0.840579i	$0.682215\pi$
$440$	7.54233e133	2.41627
$441$	−7.81864e133	−2.23348
$442$	2.92401e132	0.0744996
$443$	3.73898e133	0.849894	0.424947	−	0.905218i	$-0.360293\pi$
$443$	3.73898e133	0.849894	0.424947	+	0.905218i	$0.360293\pi$
$444$	−2.11188e134	−4.28380
$445$	−5.23262e133	−0.947411
$446$	8.91125e133	1.44055
$447$	6.36428e133	0.918796
$448$	−7.88850e132	−0.101731
$449$	−4.28883e132	−0.0494195	−0.0247098	−	0.999695i	$-0.507866\pi$
$449$	−4.28883e132	−0.0494195	−0.0247098	+	0.999695i	$0.507866\pi$
$450$	−3.90264e134	−4.01908
$451$	−3.07657e133	−0.283238
$452$	2.58744e134	2.13000
$453$	1.20481e134	0.887076
$454$	1.39915e134	0.921600
$455$	5.32966e132	0.0314141
$456$	4.18931e134	2.21013
$457$	4.13841e133	0.195464	0.0977318	−	0.995213i	$-0.468841\pi$
$457$	4.13841e133	0.195464	0.0977318	+	0.995213i	$0.468841\pi$
$458$	−1.95369e134	−0.826322
$459$	8.39597e133	0.318075
$460$	−2.12304e134	−0.720590
$461$	−5.95323e134	−1.81074	−0.905369	−	0.424625i	$-0.860406\pi$
$461$	−5.95323e134	−1.81074	−0.905369	+	0.424625i	$0.860406\pi$
$462$	−9.76648e133	−0.266268
$463$	−3.95798e134	−0.967461	−0.483731	−	0.875217i	$-0.660719\pi$
$463$	−3.95798e134	−0.967461	−0.483731	+	0.875217i	$0.660719\pi$
$464$	−1.42044e134	−0.311362
$465$	1.92509e135	3.78510
$466$	−6.34474e134	−1.11925
$467$	1.18548e135	1.87668	0.938341	−	0.345712i	$-0.112363\pi$
$467$	1.18548e135	1.87668	0.938341	+	0.345712i	$0.112363\pi$
$468$	8.87838e134	1.26159
$469$	−6.58282e133	−0.0839814
$470$	−2.73136e135	−3.12922
$471$	−1.54080e135	−1.58559
$472$	−1.54105e135	−1.42478
$473$	6.41647e134	0.533100
$474$	1.33649e135	0.998064
$475$	1.48959e135	1.00009
$476$	−2.91745e133	−0.0176138
$477$	−3.30270e135	−1.79346
$478$	5.19763e135	2.53920
$479$	4.57007e134	0.200900	0.100450	−	0.994942i	$-0.467972\pi$
$479$	4.57007e134	0.200900	0.100450	+	0.994942i	$0.467972\pi$
$480$	−4.14693e135	−1.64076
$481$	1.17400e135	0.418158
$482$	−3.13452e135	−1.00530
$483$	1.21163e134	0.0349977
$484$	4.30819e135	1.12100
$485$	7.15299e135	1.67699
$486$	7.80430e135	1.64893
$487$	−7.30705e135	−1.39165	−0.695824	−	0.718212i	$-0.744961\pi$
$487$	−7.30705e135	−1.39165	−0.695824	+	0.718212i	$0.744961\pi$
$488$	−4.87800e135	−0.837609
$489$	−6.54414e135	−1.01334
$490$	1.71279e136	2.39222
$491$	4.01652e135	0.506098	0.253049	−	0.967453i	$-0.418567\pi$
$491$	4.01652e135	0.506098	0.253049	+	0.967453i	$0.418567\pi$
$492$	−6.28996e135	−0.715171
$493$	1.05254e135	0.108012
$494$	−5.28399e135	−0.489498
$495$	−4.92690e136	−4.12108
$496$	−7.90564e135	−0.597190
$497$	−6.50460e134	−0.0443837
$498$	6.63296e135	0.408908
$499$	−6.63017e135	−0.369358	−0.184679	−	0.982799i	$-0.559125\pi$
$499$	−6.63017e135	−0.369358	−0.184679	+	0.982799i	$0.559125\pi$
$500$	3.70620e135	0.186614
$501$	5.72256e136	2.60486
$502$	5.09554e136	2.09726
$503$	−2.86457e136	−1.06629	−0.533145	−	0.846024i	$-0.678990\pi$
$503$	−2.86457e136	−1.06629	−0.533145	+	0.846024i	$0.678990\pi$
$504$	−6.08776e135	−0.204982
$505$	4.75150e136	1.44749
$506$	−2.16269e136	−0.596203
$507$	6.50529e136	1.62317
$508$	−9.58662e136	−2.16545
$509$	−1.28096e136	−0.261991	−0.130996	−	0.991383i	$-0.541817\pi$
$509$	−1.28096e136	−0.261991	−0.130996	+	0.991383i	$0.541817\pi$
$510$	−3.31741e136	−0.614477
$511$	7.52468e135	0.126250
$512$	5.24450e136	0.797207
$513$	−1.51724e137	−2.08991
$514$	1.06492e136	0.132947
$515$	1.28482e137	1.45404
$516$	1.31183e137	1.34607
$517$	−1.78441e137	−1.66044
$518$	−1.82647e136	−0.154155
$519$	1.26823e135	0.00971063
$520$	−8.57204e136	−0.595546
$521$	7.26006e136	0.457757	0.228878	−	0.973455i	$-0.426494\pi$
$521$	7.26006e136	0.457757	0.228878	+	0.973455i	$0.426494\pi$
$522$	4.98327e137	2.85203
$523$	−1.02612e137	−0.533167	−0.266584	−	0.963812i	$-0.585895\pi$
$523$	−1.02612e137	−0.533167	−0.266584	+	0.963812i	$0.585895\pi$
$524$	−7.23250e137	−3.41239
$525$	−3.12912e136	−0.134084
$526$	−3.21067e137	−1.24973
$527$	5.85806e136	0.207166
$528$	2.92482e137	0.939911
$529$	−3.15552e137	−0.921636
$530$	7.23504e137	1.92092
$531$	1.00667e138	2.43004
$532$	5.27214e136	0.115731
$533$	3.49660e136	0.0698107
$534$	−1.08977e138	−1.97926
$535$	−4.01534e137	−0.663524
$536$	1.05876e138	1.59212
$537$	7.98738e137	1.09321
$538$	1.86773e138	2.32707
$539$	1.11897e138	1.26937
$540$	−5.58467e138	−5.76916
$541$	−1.45489e138	−1.36889	−0.684446	−	0.729064i	$-0.739956\pi$
$541$	−1.45489e138	−1.36889	−0.684446	+	0.729064i	$0.739956\pi$
$542$	−1.26432e138	−1.08366
$543$	2.65307e138	2.07184
$544$	−1.26191e137	−0.0898017
$545$	−2.12158e138	−1.37606
$546$	1.10999e137	0.0656279
$547$	1.17665e138	0.634292	0.317146	−	0.948377i	$-0.397276\pi$
$547$	1.17665e138	0.634292	0.317146	+	0.948377i	$0.397276\pi$
$548$	−2.31715e138	−1.13903
$549$	3.18648e138	1.42859
$550$	5.58532e138	2.28419
$551$	−1.90206e138	−0.709688
$552$	−1.94874e138	−0.663486
$553$	7.41290e136	0.0230340
$554$	−1.23744e138	−0.350979
$555$	−1.33195e139	−3.44899
$556$	1.47506e139	3.48764
$557$	−3.44720e138	−0.744354	−0.372177	−	0.928162i	$-0.621389\pi$
$557$	−3.44720e138	−0.744354	−0.372177	+	0.928162i	$0.621389\pi$
$558$	2.77350e139	5.47018
$559$	−7.29248e137	−0.131395
$560$	2.48317e137	0.0408800
$561$	−2.16729e138	−0.326056
$562$	−2.17858e139	−2.99564
$563$	−2.08998e138	−0.262705	−0.131353	−	0.991336i	$-0.541932\pi$
$563$	−2.08998e138	−0.262705	−0.131353	+	0.991336i	$0.541932\pi$
$564$	−3.64818e139	−4.19258
$565$	1.63188e139	1.71491
$566$	−5.35381e138	−0.514556
$567$	1.41527e138	0.124421
$568$	1.04618e139	0.841423
$569$	−8.60079e138	−0.632949	−0.316475	−	0.948601i	$-0.602499\pi$
$569$	−8.60079e138	−0.632949	−0.316475	+	0.948601i	$0.602499\pi$
$570$	5.99491e139	4.03741
$571$	−9.38577e138	−0.578557	−0.289279	−	0.957245i	$-0.593415\pi$
$571$	−9.38577e138	−0.578557	−0.289279	+	0.957245i	$0.593415\pi$
$572$	−1.27064e139	−0.717007
$573$	6.60197e138	0.341087
$574$	−5.43990e137	−0.0257360
$575$	−6.92915e138	−0.300230
$576$	−8.28796e139	−3.28937
$577$	2.84386e139	1.03402	0.517010	−	0.855979i	$-0.327045\pi$
$577$	2.84386e139	1.03402	0.517010	+	0.855979i	$0.327045\pi$
$578$	4.91101e139	1.63612
$579$	−3.25151e139	−0.992698
$580$	−7.00111e139	−1.95909
$581$	3.67901e137	0.00943705
$582$	1.48972e140	3.50344
$583$	4.72670e139	1.01929
$584$	−1.21024e140	−2.39345
$585$	5.59955e139	1.01574
$586$	6.62409e139	1.10229
$587$	−1.57271e139	−0.240118	−0.120059	−	0.992767i	$-0.538308\pi$
$587$	−1.57271e139	−0.240118	−0.120059	+	0.992767i	$0.538308\pi$
$588$	2.28771e140	3.20513
$589$	−1.05861e140	−1.36118
$590$	−2.20525e140	−2.60275
$591$	8.23753e139	0.892544
$592$	5.46982e139	0.544161
$593$	9.51778e139	0.869508	0.434754	−	0.900549i	$-0.356835\pi$
$593$	9.51778e139	0.869508	0.434754	+	0.900549i	$0.356835\pi$
$594$	−5.68898e140	−4.77330
$595$	−1.84002e138	−0.0141813
$596$	−1.28819e140	−0.912100
$597$	−1.11711e140	−0.726765
$598$	2.45796e139	0.146948
$599$	1.75385e140	0.963692	0.481846	−	0.876256i	$-0.339966\pi$
$599$	1.75385e140	0.963692	0.481846	+	0.876256i	$0.339966\pi$
$600$	5.03277e140	2.54196
$601$	2.44735e140	1.13641	0.568205	−	0.822887i	$-0.307638\pi$
$601$	2.44735e140	1.13641	0.568205	+	0.822887i	$0.307638\pi$
$602$	1.13454e139	0.0484393
$603$	−6.91616e140	−2.71544
$604$	−2.43865e140	−0.880611
$605$	2.71715e140	0.902542
$606$	9.89573e140	3.02399
$607$	2.18152e140	0.613382	0.306691	−	0.951809i	$-0.400778\pi$
$607$	2.18152e140	0.613382	0.306691	+	0.951809i	$0.400778\pi$
$608$	2.28041e140	0.590040
$609$	3.99557e139	0.0951493
$610$	−6.98044e140	−1.53012
$611$	2.02803e140	0.409255
$612$	−3.06519e140	−0.569522
$613$	−3.77369e140	−0.645672	−0.322836	−	0.946455i	$-0.604636\pi$
$613$	−3.77369e140	−0.645672	−0.322836	+	0.946455i	$0.604636\pi$
$614$	−2.86152e140	−0.450914
$615$	−3.96704e140	−0.575802
$616$	8.71257e139	0.116499
$617$	−1.61490e141	−1.98950	−0.994752	−	0.102315i	$-0.967375\pi$
$617$	−1.61490e141	−1.98950	−0.994752	+	0.102315i	$0.967375\pi$
$618$	2.67583e141	3.03767
$619$	1.70112e141	1.77974	0.889869	−	0.456217i	$-0.150796\pi$
$619$	1.70112e141	1.77974	0.889869	+	0.456217i	$0.150796\pi$
$620$	−3.89656e141	−3.75752
$621$	7.05775e140	0.627394
$622$	7.22296e140	0.591971
$623$	−6.04450e139	−0.0456787
$624$	−3.32414e140	−0.231663
$625$	−1.43479e141	−0.922248
$626$	−2.87367e141	−1.70386
$627$	3.91652e141	2.14234
$628$	3.11871e141	1.57403
$629$	−4.05313e140	−0.188770
$630$	−8.71160e140	−0.374455
$631$	1.57092e141	0.623265	0.311632	−	0.950203i	$-0.399124\pi$
$631$	1.57092e141	0.623265	0.311632	+	0.950203i	$0.399124\pi$
$632$	−1.19226e141	−0.436677
$633$	−5.34997e141	−1.80911
$634$	8.24232e141	2.57361
$635$	−6.04623e141	−1.74346
$636$	9.66360e141	2.57368
$637$	−1.27174e141	−0.312866
$638$	−7.13188e141	−1.62091
$639$	−6.83398e141	−1.43510
$640$	1.34617e142	2.61222
$641$	9.21834e139	0.0165319	0.00826594	−	0.999966i	$-0.497369\pi$
$641$	9.21834e139	0.0165319	0.00826594	+	0.999966i	$0.497369\pi$
$642$	−8.36257e141	−1.38618
$643$	6.37723e141	0.977187	0.488594	−	0.872511i	$-0.337510\pi$
$643$	6.37723e141	0.977187	0.488594	+	0.872511i	$0.337510\pi$
$644$	−2.45245e140	−0.0347427
$645$	8.27364e141	1.08375
$646$	1.82425e141	0.220975
$647$	5.48721e141	0.614732	0.307366	−	0.951591i	$-0.400552\pi$
$647$	5.48721e141	0.614732	0.307366	+	0.951591i	$0.400552\pi$
$648$	−2.27627e142	−2.35878
$649$	−1.44071e142	−1.38108
$650$	−6.34785e141	−0.562992
$651$	2.22378e141	0.182496
$652$	1.32459e142	1.00595
$653$	2.39345e141	0.168232	0.0841161	−	0.996456i	$-0.473193\pi$
$653$	2.39345e141	0.168232	0.0841161	+	0.996456i	$0.473193\pi$
$654$	−4.41852e142	−2.87475
$655$	−4.56150e142	−2.74740
$656$	1.62912e141	0.0908465
$657$	7.90571e142	4.08216
$658$	−3.15515e141	−0.150873
$659$	4.27600e142	1.89376	0.946879	−	0.321591i	$-0.104218\pi$
$659$	4.27600e142	1.89376	0.946879	+	0.321591i	$0.104218\pi$
$660$	1.44160e143	5.91391
$661$	−1.93362e141	−0.0734849	−0.0367424	−	0.999325i	$-0.511698\pi$
$661$	−1.93362e141	−0.0734849	−0.0367424	+	0.999325i	$0.511698\pi$
$662$	−6.15445e142	−2.16701
$663$	2.46318e141	0.0803642
$664$	−5.91719e141	−0.178907
$665$	3.32511e141	0.0931780
$666$	−1.91896e143	−4.98444
$667$	8.84781e141	0.213050
$668$	−1.15830e143	−2.58588
$669$	7.50682e142	1.55395
$670$	1.51508e143	2.90843
$671$	−4.56037e142	−0.811918
$672$	−4.79036e141	−0.0791078
$673$	6.44088e141	0.0986698	0.0493349	−	0.998782i	$-0.484290\pi$
$673$	6.44088e141	0.0986698	0.0493349	+	0.998782i	$0.484290\pi$
$674$	1.37476e143	1.95390
$675$	−1.82272e143	−2.40369
$676$	−1.31673e143	−1.61134
$677$	−1.37829e143	−1.56536	−0.782680	−	0.622424i	$-0.786148\pi$
$677$	−1.37829e143	−1.56536	−0.782680	+	0.622424i	$0.786148\pi$
$678$	3.39865e143	3.58267
$679$	8.26283e141	0.0808547
$680$	2.95943e142	0.268849
$681$	1.17864e143	0.994148
$682$	−3.96934e143	−3.10890
$683$	−2.02521e142	−0.147307	−0.0736537	−	0.997284i	$-0.523466\pi$
$683$	−2.02521e142	−0.147307	−0.0736537	+	0.997284i	$0.523466\pi$
$684$	5.53911e143	3.74203
$685$	−1.46141e143	−0.917062
$686$	3.96665e142	0.231236
$687$	−1.64578e143	−0.891369
$688$	−3.39768e142	−0.170988
$689$	−5.37201e142	−0.251227
$690$	−2.78866e143	−1.21204
$691$	3.53577e143	1.42837	0.714187	−	0.699955i	$-0.246797\pi$
$691$	3.53577e143	1.42837	0.714187	+	0.699955i	$0.246797\pi$
$692$	−2.56702e141	−0.00963986
$693$	−5.69134e142	−0.198695
$694$	4.82280e143	1.56547
$695$	9.30311e143	2.80799
$696$	−6.42634e143	−1.80383
$697$	−1.20717e142	−0.0315148
$698$	−8.33000e143	−2.02277
$699$	−5.34480e143	−1.20735
$700$	6.33362e142	0.133107
$701$	−4.97697e143	−0.973207	−0.486603	−	0.873623i	$-0.661764\pi$
$701$	−4.97697e143	−0.973207	−0.486603	+	0.873623i	$0.661764\pi$
$702$	6.46567e143	1.17649
$703$	7.32442e143	1.24031
$704$	1.18614e144	1.86947
$705$	−2.30089e144	−3.37556
$706$	3.34986e143	0.457499
$707$	5.48873e142	0.0697897
$708$	−2.94548e144	−3.48720
$709$	4.41508e143	0.486748	0.243374	−	0.969933i	$-0.421746\pi$
$709$	4.41508e143	0.486748	0.243374	+	0.969933i	$0.421746\pi$
$710$	1.49708e144	1.53709
$711$	7.78827e143	0.744777
$712$	9.72176e143	0.865974
$713$	4.92436e143	0.408628
$714$	−3.83213e142	−0.0296265
$715$	−8.01386e143	−0.577280
$716$	−1.61672e144	−1.08524
$717$	4.37847e144	2.73908
$718$	2.06472e144	1.20386
$719$	−1.90598e144	−1.03588	−0.517940	−	0.855417i	$-0.673301\pi$
$719$	−1.90598e144	−1.03588	−0.517940	+	0.855417i	$0.673301\pi$
$720$	2.60891e144	1.32181
$721$	1.48417e143	0.0701054
$722$	4.94611e143	0.217839
$723$	−2.64051e144	−1.08444
$724$	−5.37004e144	−2.05674
$725$	−2.28501e144	−0.816242
$726$	5.65890e144	1.88552
$727$	1.74840e144	0.543441	0.271721	−	0.962376i	$-0.412407\pi$
$727$	1.74840e144	0.543441	0.271721	+	0.962376i	$0.412407\pi$
$728$	−9.90206e142	−0.0287138
$729$	−5.10998e142	−0.0138255
$730$	−1.73186e145	−4.37229
$731$	2.51767e143	0.0593159
$732$	−9.32353e144	−2.05008
$733$	−2.17870e144	−0.447142	−0.223571	−	0.974688i	$-0.571772\pi$
$733$	−2.17870e144	−0.447142	−0.223571	+	0.974688i	$0.571772\pi$
$734$	1.19856e145	2.29620
$735$	1.44285e145	2.58053
$736$	−1.06078e144	−0.177131
$737$	9.89815e144	1.54328
$738$	−5.71536e144	−0.832142
$739$	2.47719e144	0.336833	0.168417	−	0.985716i	$-0.446135\pi$
$739$	2.47719e144	0.336833	0.168417	+	0.985716i	$0.446135\pi$
$740$	2.69598e145	3.42386
$741$	−4.45122e144	−0.528031
$742$	8.35761e143	0.0926157
$743$	−1.41653e145	−1.46653	−0.733266	−	0.679942i	$-0.762005\pi$
$743$	−1.41653e145	−1.46653	−0.733266	+	0.679942i	$0.762005\pi$
$744$	−3.57666e145	−3.45975
$745$	−8.12452e144	−0.734355
$746$	1.97434e145	1.66767
$747$	3.86531e144	0.305136
$748$	4.38678e144	0.323680
$749$	−4.63835e143	−0.0319913
$750$	4.86817e144	0.313886
$751$	−2.99869e145	−1.80765	−0.903827	−	0.427898i	$-0.859254\pi$
$751$	−2.99869e145	−1.80765	−0.903827	+	0.427898i	$0.859254\pi$
$752$	9.44890e144	0.532574
$753$	4.29247e145	2.26236
$754$	8.10556e144	0.399512
$755$	−1.53804e145	−0.709002
$756$	−6.45118e144	−0.278156
$757$	2.01628e145	0.813223	0.406611	−	0.913601i	$-0.366710\pi$
$757$	2.01628e145	0.813223	0.406611	+	0.913601i	$0.366710\pi$
$758$	4.96911e145	1.87492
$759$	−1.82185e145	−0.643136
$760$	−5.34800e145	−1.76646
$761$	−2.47328e145	−0.764449	−0.382225	−	0.924069i	$-0.624842\pi$
$761$	−2.47328e145	−0.764449	−0.382225	+	0.924069i	$0.624842\pi$
$762$	−1.25922e146	−3.64230
$763$	−2.45076e144	−0.0663455
$764$	−1.33630e145	−0.338601
$765$	−1.93320e145	−0.458536
$766$	1.00643e146	2.23475
$767$	1.63740e145	0.340399
$768$	1.44737e146	2.81733
$769$	−6.52736e145	−1.18976	−0.594878	−	0.803816i	$-0.702799\pi$
$769$	−6.52736e145	−1.18976	−0.594878	+	0.803816i	$0.702799\pi$
$770$	1.24677e145	0.212816
$771$	8.97086e144	0.143413
$772$	6.58134e145	0.985463
$773$	−1.86502e145	−0.261589	−0.130794	−	0.991410i	$-0.541753\pi$
$773$	−1.86502e145	−0.261589	−0.130794	+	0.991410i	$0.541753\pi$
$774$	1.19199e146	1.56623
$775$	−1.27175e146	−1.56555
$776$	−1.32897e146	−1.53284
$777$	−1.53861e145	−0.166291
$778$	2.42310e146	2.45416
$779$	2.18149e145	0.207067
$780$	−1.63841e146	−1.45762
$781$	9.78055e145	0.815616
$782$	−8.48590e144	−0.0663371
$783$	2.32742e146	1.70571
$784$	−5.92523e145	−0.407141
$785$	1.96695e146	1.26729
$786$	−9.50004e146	−5.73967
$787$	1.31860e146	0.747117	0.373558	−	0.927607i	$-0.378138\pi$
$787$	1.31860e146	0.747117	0.373558	+	0.927607i	$0.378138\pi$
$788$	−1.66735e146	−0.886039
$789$	−2.70466e146	−1.34811
$790$	−1.70613e146	−0.797710
$791$	1.88508e145	0.0826833
$792$	9.15376e146	3.76685
$793$	5.18297e145	0.200116
$794$	−6.96289e146	−2.52263
$795$	6.09478e146	2.07213
$796$	2.26114e146	0.721468
$797$	2.99469e146	0.896823	0.448412	−	0.893827i	$-0.351990\pi$
$797$	2.99469e146	0.896823	0.448412	+	0.893827i	$0.351990\pi$
$798$	6.92507e145	0.194661
$799$	−7.00161e145	−0.184751
$800$	2.73954e146	0.678630
$801$	−6.35058e146	−1.47697
$802$	−1.31559e146	−0.287285
$803$	−1.13144e147	−2.32004
$804$	2.02365e147	3.89677
$805$	−1.54675e145	−0.0279722
$806$	4.51125e146	0.766262
$807$	1.57337e147	2.51026
$808$	−8.82788e146	−1.32307
$809$	−5.73712e146	−0.807781	−0.403891	−	0.914807i	$-0.632342\pi$
$809$	−5.73712e146	−0.807781	−0.403891	+	0.914807i	$0.632342\pi$
$810$	−3.25735e147	−4.30895
$811$	−6.28300e146	−0.780933	−0.390466	−	0.920617i	$-0.627686\pi$
$811$	−6.28300e146	−0.780933	−0.390466	+	0.920617i	$0.627686\pi$
$812$	−8.08739e145	−0.0944558
$813$	−1.06506e147	−1.16896
$814$	2.74634e147	2.83284
$815$	8.35412e146	0.809919
$816$	1.14763e146	0.104580
$817$	−4.54969e146	−0.389734
$818$	2.06011e147	1.65901
$819$	6.46836e145	0.0489730
$820$	8.02965e146	0.571606
$821$	−1.21835e147	−0.815533	−0.407767	−	0.913086i	$-0.633692\pi$
$821$	−1.21835e147	−0.815533	−0.407767	+	0.913086i	$0.633692\pi$
$822$	−3.04362e147	−1.91586
$823$	−1.61951e145	−0.00958719	−0.00479359	−	0.999989i	$-0.501526\pi$
$823$	−1.61951e145	−0.00958719	−0.00479359	+	0.999989i	$0.501526\pi$
$824$	−2.38708e147	−1.32905
$825$	4.70506e147	2.46400
$826$	−2.54741e146	−0.125489
$827$	−1.74500e147	−0.808662	−0.404331	−	0.914613i	$-0.632496\pi$
$827$	−1.74500e147	−0.808662	−0.404331	+	0.914613i	$0.632496\pi$
$828$	−2.57663e147	−1.12336
$829$	1.16559e147	0.478125	0.239063	−	0.971004i	$-0.423160\pi$
$829$	1.16559e147	0.478125	0.239063	+	0.971004i	$0.423160\pi$
$830$	−8.46752e146	−0.326823
$831$	−1.04242e147	−0.378608
$832$	−1.34808e147	−0.460774
$833$	4.39059e146	0.141237
$834$	1.93752e148	5.86624
$835$	−7.30531e147	−2.08196
$836$	−7.92737e147	−2.12673
$837$	1.29536e148	3.27155
$838$	−1.56141e147	−0.371273
$839$	2.66604e147	0.596880	0.298440	−	0.954428i	$-0.403534\pi$
$839$	2.66604e147	0.596880	0.298440	+	0.954428i	$0.403534\pi$
$840$	1.12343e147	0.236833
$841$	−2.11958e147	−0.420776
$842$	9.36214e147	1.75031
$843$	−1.83523e148	−3.23145
$844$	1.08288e148	1.79592
$845$	−8.30453e147	−1.29733
$846$	−3.31492e148	−4.87831
$847$	3.13874e146	0.0435154
$848$	−2.50290e147	−0.326929
$849$	−4.51003e147	−0.555062
$850$	2.19154e147	0.254153
$851$	−3.40711e147	−0.372343
$852$	1.99960e148	2.05942
$853$	1.18019e148	1.14558	0.572790	−	0.819702i	$-0.305861\pi$
$853$	1.18019e148	1.14558	0.572790	+	0.819702i	$0.305861\pi$
$854$	−8.06350e146	−0.0737736
$855$	3.49349e148	3.01280
$856$	7.46016e147	0.606489
$857$	−1.85191e148	−1.41934	−0.709672	−	0.704532i	$-0.751157\pi$
$857$	−1.85191e148	−1.41934	−0.709672	+	0.704532i	$0.751157\pi$
$858$	−1.66901e148	−1.20601
$859$	5.32758e147	0.362974	0.181487	−	0.983393i	$-0.441909\pi$
$859$	5.32758e147	0.362974	0.181487	+	0.983393i	$0.441909\pi$
$860$	−1.67466e148	−1.07586
$861$	−4.58256e146	−0.0277619
$862$	4.28981e148	2.45088
$863$	−7.09562e147	−0.382336	−0.191168	−	0.981557i	$-0.561228\pi$
$863$	−7.09562e147	−0.382336	−0.191168	+	0.981557i	$0.561228\pi$
$864$	−2.79038e148	−1.41814
$865$	−1.61900e146	−0.00776130
$866$	2.62010e148	1.18485
$867$	4.13702e148	1.76491
$868$	−4.50114e147	−0.181166
$869$	−1.11463e148	−0.423284
$870$	−9.19610e148	−3.29520
$871$	−1.12495e148	−0.380379
$872$	3.94172e148	1.25777
$873$	8.68125e148	2.61434
$874$	1.53349e148	0.435867
$875$	2.70016e146	0.00724407
$876$	−2.31319e149	−5.85806
$877$	−5.98242e148	−1.43020	−0.715101	−	0.699021i	$-0.753619\pi$
$877$	−5.98242e148	−1.43020	−0.715101	+	0.699021i	$0.753619\pi$
$878$	8.01501e148	1.80897
$879$	5.58012e148	1.18906
$880$	−3.73378e148	−0.751231
$881$	−5.93085e147	−0.112677	−0.0563383	−	0.998412i	$-0.517943\pi$
$881$	−5.93085e147	−0.112677	−0.0563383	+	0.998412i	$0.517943\pi$
$882$	2.07873e149	3.72935
$883$	1.68283e148	0.285118	0.142559	−	0.989786i	$-0.454467\pi$
$883$	1.68283e148	0.285118	0.142559	+	0.989786i	$0.454467\pi$
$884$	−4.98569e147	−0.0797785
$885$	−1.85770e149	−2.80763
$886$	−9.94075e148	−1.41911
$887$	6.72744e148	0.907208	0.453604	−	0.891203i	$-0.350138\pi$
$887$	6.72744e148	0.907208	0.453604	+	0.891203i	$0.350138\pi$
$888$	2.47465e149	3.15253
$889$	−6.98434e147	−0.0840595
$890$	1.39119e149	1.58194
$891$	−2.12805e149	−2.28643
$892$	−1.51945e149	−1.54262
$893$	1.26526e149	1.21390
$894$	−1.69206e149	−1.53416
$895$	−1.01965e149	−0.873755
$896$	1.55503e148	0.125946
$897$	2.07058e148	0.158516
$898$	1.14026e148	0.0825183
$899$	1.62390e149	1.11095
$900$	6.65434e149	4.30386
$901$	1.85464e148	0.113412
$902$	8.17962e148	0.472937
$903$	9.55735e147	0.0522524
$904$	−3.03190e149	−1.56751
$905$	−3.38686e149	−1.65594
$906$	−3.20322e149	−1.48120
$907$	−2.64086e149	−1.15499	−0.577494	−	0.816395i	$-0.695969\pi$
$907$	−2.64086e149	−1.15499	−0.577494	+	0.816395i	$0.695969\pi$
$908$	−2.38567e149	−0.986903
$909$	5.76666e149	2.25657
$910$	−1.41699e148	−0.0524536
$911$	6.18346e148	0.216548	0.108274	−	0.994121i	$-0.465468\pi$
$911$	6.18346e148	0.216548	0.108274	+	0.994121i	$0.465468\pi$
$912$	−2.07389e149	−0.687141
$913$	−5.53189e148	−0.173420
$914$	−1.10027e149	−0.326375
$915$	−5.88030e149	−1.65057
$916$	3.33121e149	0.884873
$917$	−5.26925e148	−0.132464
$918$	−2.23222e149	−0.531106
$919$	5.43382e148	0.122369	0.0611845	−	0.998126i	$-0.480512\pi$
$919$	5.43382e148	0.122369	0.0611845	+	0.998126i	$0.480512\pi$
$920$	2.48773e149	0.530296
$921$	−2.41053e149	−0.486409
$922$	1.58277e150	3.02348
$923$	−1.11158e149	−0.201028
$924$	1.66527e149	0.285135
$925$	8.79911e149	1.42653
$926$	1.05230e150	1.61542
$927$	1.55932e150	2.26678
$928$	−3.49811e149	−0.481571
$929$	8.18039e149	1.06655	0.533274	−	0.845942i	$-0.320961\pi$
$929$	8.18039e149	1.06655	0.533274	+	0.845942i	$0.320961\pi$
$930$	−5.11821e150	−6.32017
$931$	−7.93425e149	−0.927998
$932$	1.08183e150	1.19855
$933$	6.08460e149	0.638571
$934$	−3.15180e150	−3.13359
$935$	2.76672e149	0.260603
$936$	−1.04035e150	−0.928428
$937$	1.21825e150	1.03011	0.515057	−	0.857156i	$-0.327771\pi$
$937$	1.21825e150	1.03011	0.515057	+	0.857156i	$0.327771\pi$
$938$	1.75016e149	0.140228
$939$	−2.42078e150	−1.83799
$940$	4.65720e150	3.35095
$941$	−2.26501e150	−1.54452	−0.772261	−	0.635306i	$-0.780874\pi$
$941$	−2.26501e150	−1.54452	−0.772261	+	0.635306i	$0.780874\pi$
$942$	4.09649e150	2.64753
$943$	−1.01476e149	−0.0621619
$944$	7.62888e149	0.442971
$945$	−4.06872e149	−0.223950
$946$	−1.70594e150	−0.890144
$947$	−2.06929e150	−1.02364	−0.511820	−	0.859093i	$-0.671028\pi$
$947$	−2.06929e150	−1.02364	−0.511820	+	0.859093i	$0.671028\pi$
$948$	−2.27883e150	−1.06878
$949$	1.28591e150	0.571828
$950$	−3.96035e150	−1.66990
$951$	6.94331e150	2.77620
$952$	3.41861e148	0.0129623
$953$	−5.31863e149	−0.191253	−0.0956265	−	0.995417i	$-0.530485\pi$
$953$	−5.31863e149	−0.191253	−0.0956265	+	0.995417i	$0.530485\pi$
$954$	8.78082e150	2.99462
$955$	−8.42796e149	−0.272617
$956$	−8.86241e150	−2.71912
$957$	−6.00788e150	−1.74851
$958$	−1.21504e150	−0.335453
$959$	−1.68816e149	−0.0442155
$960$	1.52946e151	3.80049
$961$	4.79639e150	1.13079
$962$	−3.12128e150	−0.698219
$963$	−4.87323e150	−1.03440
$964$	5.34463e150	1.07653
$965$	4.15081e150	0.793421
$966$	−3.22134e149	−0.0584375
$967$	−6.29354e150	−1.08357	−0.541786	−	0.840516i	$-0.682252\pi$
$967$	−6.29354e150	−1.08357	−0.541786	+	0.840516i	$0.682252\pi$
$968$	−5.04824e150	−0.824963
$969$	1.53675e150	0.238370
$970$	−1.90175e151	−2.80015
$971$	6.77300e150	0.946694	0.473347	−	0.880876i	$-0.343046\pi$
$971$	6.77300e150	0.946694	0.473347	+	0.880876i	$0.343046\pi$
$972$	−1.33070e151	−1.76577
$973$	1.07466e150	0.135385
$974$	1.94271e151	2.32371
$975$	−5.34742e150	−0.607311
$976$	2.41482e150	0.260417
$977$	6.16617e150	0.631451	0.315726	−	0.948851i	$-0.397752\pi$
$977$	6.16617e150	0.631451	0.315726	+	0.948851i	$0.397752\pi$
$978$	1.73988e151	1.69202
$979$	9.08871e150	0.839414
$980$	−2.92045e151	−2.56173
$981$	−2.57486e151	−2.14520
$982$	−1.06787e151	−0.845057
$983$	9.36727e150	0.704142	0.352071	−	0.935973i	$-0.385478\pi$
$983$	9.36727e150	0.704142	0.352071	+	0.935973i	$0.385478\pi$
$984$	7.37043e150	0.526308
$985$	−1.05159e151	−0.713372
$986$	−2.79838e150	−0.180352
$987$	−2.65789e150	−0.162750
$988$	9.00966e150	0.524183
$989$	2.11638e150	0.116999
$990$	1.30991e152	6.88118
$991$	8.64302e150	0.431465	0.215733	−	0.976452i	$-0.430786\pi$
$991$	8.64302e150	0.431465	0.215733	+	0.976452i	$0.430786\pi$
$992$	−1.94692e151	−0.923651
$993$	−5.18449e151	−2.33759
$994$	1.72937e150	0.0741096
$995$	1.42609e151	0.580873
$996$	−1.13098e151	−0.437882
$997$	3.72625e151	1.37141	0.685703	−	0.727881i	$-0.259495\pi$
$997$	3.72625e151	1.37141	0.685703	+	0.727881i	$0.259495\pi$
$998$	1.76275e151	0.616735
$999$	−8.96242e151	−2.98104

Twists

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

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q-2.65868e15 q^{2} -2.23967e24 q^{3} +4.53328e30 q^{4} +2.85912e35 q^{5} +5.95456e39 q^{6} +3.30273e41 q^{7} -5.31200e45 q^{8} +3.46997e48 q^{9} +O(q^{10})\)	\(q-2.65868e15 q^{2} -2.23967e24 q^{3} +4.53328e30 q^{4} +2.85912e35 q^{5} +5.95456e39 q^{6} +3.30273e41 q^{7} -5.31200e45 q^{8} +3.46997e48 q^{9} -7.60148e50 q^{10} -4.96610e52 q^{11} -1.01530e55 q^{12} +5.64410e55 q^{13} -8.78091e56 q^{14} -6.40347e59 q^{15} +2.62967e60 q^{16} -1.94858e61 q^{17} -9.22556e63 q^{18} +3.52128e64 q^{19} +1.29612e66 q^{20} -7.39702e65 q^{21} +1.32033e68 q^{22} -1.63800e68 q^{23} +1.18971e70 q^{24} +4.23025e70 q^{25} -1.50059e71 q^{26} -4.30876e72 q^{27} +1.49722e72 q^{28} -5.40160e73 q^{29} +1.70248e75 q^{30} -3.00633e75 q^{31} +6.47607e75 q^{32} +1.11224e77 q^{33} +5.18065e76 q^{34} +9.44290e76 q^{35} +1.57304e79 q^{36} +2.08004e79 q^{37} -9.36197e79 q^{38} -1.26409e80 q^{39} -1.51876e81 q^{40} +6.19514e80 q^{41} +1.96663e81 q^{42} -1.29205e82 q^{43} -2.25127e83 q^{44} +9.92107e83 q^{45} +4.35492e83 q^{46} +3.59319e84 q^{47} -5.88958e84 q^{48} -2.25323e85 q^{49} -1.12469e86 q^{50} +4.36417e85 q^{51} +2.55863e86 q^{52} -9.51793e86 q^{53} +1.14556e88 q^{54} -1.41987e88 q^{55} -1.75441e87 q^{56} -7.88650e88 q^{57} +1.43611e89 q^{58} +2.90108e89 q^{59} -2.90288e90 q^{60} +9.18299e89 q^{61} +7.99286e90 q^{62} +1.14604e90 q^{63} -2.38848e91 q^{64} +1.61371e91 q^{65} -2.95709e92 q^{66} -1.99314e92 q^{67} -8.83346e91 q^{68} +3.66857e92 q^{69} -2.51057e92 q^{70} -1.96946e93 q^{71} -1.84325e94 q^{72} +2.27832e94 q^{73} -5.53017e94 q^{74} -9.47435e94 q^{75} +1.59630e95 q^{76} -1.64017e94 q^{77} +3.36081e95 q^{78} +2.24448e95 q^{79} +7.51853e95 q^{80} +4.28516e96 q^{81} -1.64709e96 q^{82} +1.11393e96 q^{83} -3.35328e96 q^{84} -5.57122e96 q^{85} +3.43516e97 q^{86} +1.20978e98 q^{87} +2.63799e98 q^{88} -1.83015e98 q^{89} -2.63770e99 q^{90} +1.86409e97 q^{91} -7.42551e98 q^{92} +6.73317e99 q^{93} -9.55315e99 q^{94} +1.00678e100 q^{95} -1.45042e100 q^{96} +2.50182e100 q^{97} +5.99061e100 q^{98} -1.72322e101 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 434989091795040 q^{2} - 12\!\cdots\!60 q^{3}+ \cdots + 52\!\cdots\!84 q^{9}+O(q^{10}) \) 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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