LMFDB - Embedded newform 3.72.a.a.1.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [3,72,Mod(1,3)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("3.1"); S:= CuspForms(chi, 72); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(3, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0])) N = Newforms(chi, 72, names="a")

Level:	$ N $	$=$	$ 3 $
Weight:	$ k $	$=$	$ 72 $
Character orbit:	$[\chi]$	$=$	3.a (trivial)

Newform invariants

comment:select newform

sage:traces = [5] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	yes
Analytic conductor:	$95.7738481683$
Analytic rank:	$1$
Dimension:	$5$
Coefficient field:	$\mathbb{Q}[x]/(x^{5} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - 2 x^{4} + \cdots - 10\!\cdots\!54 $ x^5 - 2x^4 - 11794880527205841026x^3 - 1576914464895109132006308600x^2 + 21982147283297468753929167380086357881x - 10487125185557323126488817758602332290924256254
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{36}\cdot 3^{20}\cdot 5^{4}\cdot 7^{2} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$6.47992e8$ of defining polynomial
Character	$\chi$	$=$	3.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-2.05621e10 q^{2} +5.00315e16 q^{3} -1.93838e21 q^{4} -6.43665e24 q^{5} -1.02875e27 q^{6} +4.31786e29 q^{7} +8.84080e31 q^{8} +2.50316e33 q^{9} +1.32351e35 q^{10} -1.03462e37 q^{11} -9.69804e37 q^{12} -1.12453e39 q^{13} -8.87841e39 q^{14} -3.22036e41 q^{15} +2.75903e42 q^{16} +2.79729e43 q^{17} -5.14700e43 q^{18} +1.59912e45 q^{19} +1.24767e46 q^{20} +2.16029e46 q^{21} +2.12740e47 q^{22} +1.17659e48 q^{23} +4.42319e48 q^{24} -9.21131e47 q^{25} +2.31226e49 q^{26} +1.25237e50 q^{27} -8.36967e50 q^{28} +1.13318e52 q^{29} +6.62172e51 q^{30} -8.82218e52 q^{31} -2.65479e53 q^{32} -5.17638e53 q^{33} -5.75180e53 q^{34} -2.77926e54 q^{35} -4.85208e54 q^{36} +5.62400e55 q^{37} -3.28811e55 q^{38} -5.62619e55 q^{39} -5.69052e56 q^{40} -1.33250e56 q^{41} -4.44201e56 q^{42} +1.13532e58 q^{43} +2.00550e58 q^{44} -1.61119e58 q^{45} -2.41931e58 q^{46} +1.12423e59 q^{47} +1.38039e59 q^{48} -8.18086e59 q^{49} +1.89403e58 q^{50} +1.39953e60 q^{51} +2.17977e60 q^{52} +8.51201e60 q^{53} -2.57513e60 q^{54} +6.65951e61 q^{55} +3.81733e61 q^{56} +8.00063e61 q^{57} -2.33006e62 q^{58} -1.21168e62 q^{59} +6.24229e62 q^{60} -4.10214e63 q^{61} +1.81402e63 q^{62} +1.08083e63 q^{63} -1.05578e63 q^{64} +7.23820e63 q^{65} +1.06437e64 q^{66} -5.67761e64 q^{67} -5.42222e64 q^{68} +5.88665e64 q^{69} +5.71472e64 q^{70} -1.78276e65 q^{71} +2.21299e65 q^{72} +1.82157e66 q^{73} -1.15641e66 q^{74} -4.60856e64 q^{75} -3.09970e66 q^{76} -4.46736e66 q^{77} +1.15686e66 q^{78} +3.72892e67 q^{79} -1.77589e67 q^{80} +6.26579e66 q^{81} +2.73989e66 q^{82} -2.02166e68 q^{83} -4.18748e67 q^{84} -1.80052e68 q^{85} -2.33446e68 q^{86} +5.66950e68 q^{87} -9.14690e68 q^{88} +2.01594e69 q^{89} +3.31295e68 q^{90} -4.85555e68 q^{91} -2.28068e69 q^{92} -4.41387e69 q^{93} -2.31165e69 q^{94} -1.02930e70 q^{95} -1.32823e70 q^{96} -4.57132e70 q^{97} +1.68215e70 q^{98} -2.58982e70 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q - 25051277688 q^{2} + 25\!\cdots\!35 q^{3} + 19\!\cdots\!24 q^{4} + 14\!\cdots\!30 q^{5} - 12\!\cdots\!16 q^{6} - 12\!\cdots\!52 q^{7} - 15\!\cdots\!48 q^{8} + 12\!\cdots\!45 q^{9} - 30\!\cdots\!60 q^{10}+ \cdots + 33\!\cdots\!88 q^{99}+O(q^{100}) $ 5 * q - 25051277688 * q^2 + 250157725494998535 * q^3 + 1907299462927273154624 * q^4 + 1422573866433399534277830 * q^5 - 1253354129434737111087637416 * q^6 - 1261222231854515600228814346952 * q^7 - 151958919976138936299686009691648 * q^8 + 12515777524966208006577859930429245 * q^9 - 308853354401574193552393248717551760 * q^10 + 1357894937151168401938494740936725812 * q^11 + 95425139096743786553920018696741695168 * q^12 - 3732312012481108743024076959256483425602 * q^13 + 178792454794792302794525709930294541693632 * q^14 + 71173568555121014264963983054791626595810 * q^15 - 2761767053096261549691112453399712883798016 * q^16 - 277325542902069263625709674624672840731910 * q^17 - 62707243651831565917830179941990275506237112 * q^18 + 2937432205918421125744856768913127977845719948 * q^19 - 24911205133324082416992380941498137854677077120 * q^20 - 63100896972890262121533046345756354145644343064 * q^21 + 981344865457378177927521236701073576051567611680 * q^22 - 4228346897979680919198407557464543114207597141624 * q^23 - 7602739557981482671404075764718702187632312347136 * q^24 + 19633070396484105587134362494981426945191834668275 * q^25 - 163733269614894222914401413204168398319516301314000 * q^26 + 626183687689393767209300272665229846333060639231215 * q^27 - 5768362424640263225567110092226485193092350431463936 * q^28 - 3697116438725251267139482122013539208885912739684274 * q^29 - 15452410529719698927278278181356603942084949997334320 * q^30 + 74551273173252500835223325068153865117486542141504384 * q^31 - 639756106869108826481408208267665768107401476101865472 * q^32 + 67937581787782054618912973363008350989516300927337084 * q^33 - 6217683238533672509931589234500437242788961796499134832 * q^34 - 13153074146721234298498045726570273336863567981003778800 * q^35 + 4774267150297056921454723864735495027586024236315315776 * q^36 - 160060519909409459305929258566699075666754182654348019002 * q^37 - 91685642067030133239673763998240213415299939628290081056 * q^38 - 186733336775986949394712651065025829961603412074954298614 * q^39 + 755753872880123511491678719028119895299413298470522117120 * q^40 + 2279706853693741369685932186247543106805520151549660884994 * q^41 + 8945262765426517501413121912547804713065475672808851765824 * q^42 + 6754858585968454689741824956150275855563744863320129251092 * q^43 + 10256422900727914711051439828948913719762767210529399343360 * q^44 + 3560923605022284438744581203359299419628800805488597427670 * q^45 + 215917478684214015835970415365801427523995942249450992649024 * q^46 - 468036949346743446524224540083033087921443712918743092678704 * q^47 - 138175472869917128113923965027114211523442937794848631181312 * q^48 - 1155203275623883178356241428680618202323141234160855611430803 * q^49 - 662361288254569744891489750838385910624551591076930373305800 * q^50 - 13875025406809456447127343535570692796264334304266755550370 * q^51 + 4686563330803028488195038486432142239675010588344800750934400 * q^52 + 16850153365054699278877708172474268895458775724356533295576086 * q^53 - 3137340288800574070947321989342157748567014121664790760526184 * q^54 + 69903604802785515177733563130194024072223641855144712529201880 * q^55 + 263561757691935735991107069426454954646910606378160826135654400 * q^56 + 146964271885661680599941817303782740393713518895988426056055236 * q^57 - 393766572647074503603427367357535096204856933671806739961414992 * q^58 - 390335442004059371501204897784396685449449222429047305160362108 * q^59 - 1246346083098336838245443167057803985933179433056389614496403840 * q^60 + 725074488292223066537782289903828567460896102224114882556804878 * q^61 - 9988959008617311972392577438833349328275372968547435398535343104 * q^62 - 3157035372686493241148598970419764570521041257808979169543482248 * q^63 - 2023851072198628197882474312831161597933729151994298498048327680 * q^64 + 13140351800845565438471290641483435252971725075901777919813259620 * q^65 + 49098199893802616037233646095483883838218857898857856047009777760 * q^66 + 66714375177521017736160888158122274402157076957263686329132696540 * q^67 + 122874398781837608005594402142092581637778609572473879627701828736 * q^68 - 211550728520485918988863794593760397778492966928452183274813504168 * q^69 - 293285886544485684750990625097245178785454325664385364335258966400 * q^70 + 182228903943633461999697286426491914806644676121035292409010095000 * q^71 - 380376807071099648078549525700513940155076932645648351218946289152 * q^72 - 3126186443395793129070092762366126842796181422188167587986966103774 * q^73 - 909089362115793434062323439709786862714999800511985114251226742928 * q^74 + 982272846973530587229764561497340393007528047854257425826667195425 * q^75 + 17344875012173690040537707411833679809662138514060794984773183596288 * q^76 + 10495163179741456456758662728922622402868815939129112668959031953376 * q^77 - 8191828462944258702008436357306371395699406819716356341809714998000 * q^78 - 27301301517941598101728732493241199802996555070508118978972462370800 * q^79 + 17453171390087969064834561314810599922914790489604475485575264133120 * q^80 + 31328937410889851896281120971709651661033472234053326374297990254005 * q^81 - 211476001448904287369943798857320633308142594733381306800142859557424 * q^82 - 118340201116022360513322067378331477940966167749075029048364461271476 * q^83 - 288600084795764628291001658833202352097198631523538446517373245066752 * q^84 - 353749028745389735175606474209594334673616946227279830960229574948180 * q^85 - 598599366027984305586625758611411918350192525004808831847227328355808 * q^86 - 184972447840335595586879350012403335749718574814304198079640398507718 * q^87 + 884266222865559755895490832763056324497872985335575213438267918764032 * q^88 + 922002192851420225703931949240660524744080828362964363768621192185298 * q^89 - 773107974305929069152539888281824938594397222395836929970148461044240 * q^90 - 8079212959404027614418440109956770906886889649154860574373249888569776 * q^91 - 13670577861982746620628593404236014523694130242253442181460174526039552 * q^92 + 3729915385955429492528971192901332630862445897595761204245366555215488 * q^93 - 13436976700690544599208201928250305890032773609106302404839902759345024 * q^94 - 61508953507577523131201535405733284550943470497632040479599939746271320 * q^95 - 32007986513182294493504227608086345487918910401219597611766423881416704 * q^96 - 149876371240369823947413564997445008107894647331408877752554402308756310 * q^97 - 164242038075013607742967230335294726637154516016956449921881670478527288 * q^98 + 3399022187132399007137561865025534669344410724594880911844979606234388 * q^99

Coefficient data

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

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

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

$2$	−2.05621e10	−0.423157	−0.211579	−	0.977361i	$-0.567860\pi$
$2$	−2.05621e10	−0.423157	−0.211579	+	0.977361i	$0.567860\pi$
$3$	5.00315e16	0.577350
$3$	5.00315e16	0.577350
$4$	−1.93838e21	−0.820938
$5$	−6.43665e24	−0.989065	−0.494533	−	0.869159i	$-0.664661\pi$
$5$	−6.43665e24	−0.989065	−0.494533	+	0.869159i	$0.664661\pi$
$6$	−1.02875e27	−0.244310
$7$	4.31786e29	0.430812	0.215406	−	0.976525i	$-0.430892\pi$
$7$	4.31786e29	0.430812	0.215406	+	0.976525i	$0.430892\pi$
$8$	8.84080e31	0.770543
$9$	2.50316e33	0.333333
$10$	1.32351e35	0.418530
$11$	−1.03462e37	−1.11005	−0.555024	−	0.831834i	$-0.687291\pi$
$11$	−1.03462e37	−1.11005	−0.555024	+	0.831834i	$0.687291\pi$
$12$	−9.69804e37	−0.473969
$13$	−1.12453e39	−0.320613	−0.160307	−	0.987067i	$-0.551248\pi$
$13$	−1.12453e39	−0.320613	−0.160307	+	0.987067i	$0.551248\pi$
$14$	−8.87841e39	−0.182301
$15$	−3.22036e41	−0.571037
$16$	2.75903e42	0.494877
$17$	2.79729e43	0.583177	0.291589	−	0.956544i	$-0.405816\pi$
$17$	2.79729e43	0.583177	0.291589	+	0.956544i	$0.405816\pi$
$18$	−5.14700e43	−0.141052
$19$	1.59912e45	0.642876	0.321438	−	0.946931i	$-0.395834\pi$
$19$	1.59912e45	0.642876	0.321438	+	0.946931i	$0.395834\pi$
$20$	1.24767e46	0.811961
$21$	2.16029e46	0.248730
$22$	2.12740e47	0.469725
$23$	1.17659e48	0.536150	0.268075	−	0.963398i	$-0.413612\pi$
$23$	1.17659e48	0.536150	0.268075	+	0.963398i	$0.413612\pi$
$24$	4.42319e48	0.444873
$25$	−9.21131e47	−0.0217496
$26$	2.31226e49	0.135670
$27$	1.25237e50	0.192450
$28$	−8.36967e50	−0.353670
$29$	1.13318e52	1.37775	0.688877	−	0.724878i	$-0.258104\pi$
$29$	1.13318e52	1.37775	0.688877	+	0.724878i	$0.258104\pi$
$30$	6.62172e51	0.241639
$31$	−8.82218e52	−1.00516	−0.502581	−	0.864530i	$-0.667616\pi$
$31$	−8.82218e52	−1.00516	−0.502581	+	0.864530i	$0.667616\pi$
$32$	−2.65479e53	−0.979954
$33$	−5.17638e53	−0.640887
$34$	−5.75180e53	−0.246776
$35$	−2.77926e54	−0.426101
$36$	−4.85208e54	−0.273646
$37$	5.62400e55	1.19918	0.599590	−	0.800308i	$-0.295330\pi$
$37$	5.62400e55	1.19918	0.599590	+	0.800308i	$0.295330\pi$
$38$	−3.28811e55	−0.272038
$39$	−5.62619e55	−0.185106
$40$	−5.69052e56	−0.762118
$41$	−1.33250e56	−0.0742743	−0.0371372	−	0.999310i	$-0.511824\pi$
$41$	−1.33250e56	−0.0742743	−0.0371372	+	0.999310i	$0.511824\pi$
$42$	−4.44201e56	−0.105252
$43$	1.13532e58	1.16678	0.583391	−	0.812191i	$-0.301725\pi$
$43$	1.13532e58	1.16678	0.583391	+	0.812191i	$0.301725\pi$
$44$	2.00550e58	0.911281
$45$	−1.61119e58	−0.329688
$46$	−2.41931e58	−0.226876
$47$	1.12423e59	0.491340	0.245670	−	0.969353i	$-0.420992\pi$
$47$	1.12423e59	0.491340	0.245670	+	0.969353i	$0.420992\pi$
$48$	1.38039e59	0.285717
$49$	−8.18086e59	−0.814401
$50$	1.89403e58	0.00920350
$51$	1.39953e60	0.336698
$52$	2.17977e60	0.263203
$53$	8.51201e60	0.522684	0.261342	−	0.965246i	$-0.415835\pi$
$53$	8.51201e60	0.522684	0.261342	+	0.965246i	$0.415835\pi$
$54$	−2.57513e60	−0.0814367
$55$	6.65951e61	1.09791
$56$	3.81733e61	0.331959
$57$	8.00063e61	0.371165
$58$	−2.33006e62	−0.583007
$59$	−1.21168e62	−0.165250	−0.0826252	−	0.996581i	$-0.526330\pi$
$59$	−1.21168e62	−0.165250	−0.0826252	+	0.996581i	$0.526330\pi$
$60$	6.24229e62	0.468786
$61$	−4.10214e63	−1.71317	−0.856586	−	0.516004i	$-0.827419\pi$
$61$	−4.10214e63	−1.71317	−0.856586	+	0.516004i	$0.827419\pi$
$62$	1.81402e63	0.425342
$63$	1.08083e63	0.143604
$64$	−1.05578e63	−0.0802022
$65$	7.23820e63	0.317107
$66$	1.06437e64	0.271196
$67$	−5.67761e64	−0.848223	−0.424112	−	0.905610i	$-0.639414\pi$
$67$	−5.67761e64	−0.848223	−0.424112	+	0.905610i	$0.639414\pi$
$68$	−5.42222e64	−0.478752
$69$	5.88665e64	0.309546
$70$	5.71472e64	0.180308
$71$	−1.78276e65	−0.339954	−0.169977	−	0.985448i	$-0.554369\pi$
$71$	−1.78276e65	−0.339954	−0.169977	+	0.985448i	$0.554369\pi$
$72$	2.21299e65	0.256848
$73$	1.82157e66	1.29564	0.647819	−	0.761794i	$-0.275681\pi$
$73$	1.82157e66	1.29564	0.647819	+	0.761794i	$0.275681\pi$
$74$	−1.15641e66	−0.507442
$75$	−4.60856e64	−0.0125571
$76$	−3.09970e66	−0.527761
$77$	−4.46736e66	−0.478222
$78$	1.15686e66	0.0783290
$79$	3.72892e67	1.60628	0.803140	−	0.595791i	$-0.203161\pi$
$79$	3.72892e67	1.60628	0.803140	+	0.595791i	$0.203161\pi$
$80$	−1.77589e67	−0.489466
$81$	6.26579e66	0.111111
$82$	2.73989e66	0.0314297
$83$	−2.02166e68	−1.50812	−0.754060	−	0.656806i	$-0.771907\pi$
$83$	−2.02166e68	−1.50812	−0.754060	+	0.656806i	$0.771907\pi$
$84$	−4.18748e67	−0.204192
$85$	−1.80052e68	−0.576801
$86$	−2.33446e68	−0.493732
$87$	5.66950e68	0.795447
$88$	−9.14690e68	−0.855340
$89$	2.01594e69	1.26221	0.631105	−	0.775697i	$-0.282602\pi$
$89$	2.01594e69	1.26221	0.631105	+	0.775697i	$0.282602\pi$
$90$	3.31295e68	0.139510
$91$	−4.85555e68	−0.138124
$92$	−2.28068e69	−0.440146
$93$	−4.41387e69	−0.580330
$94$	−2.31165e69	−0.207914
$95$	−1.02930e70	−0.635847
$96$	−1.32823e70	−0.565777
$97$	−4.57132e70	−1.34786	−0.673931	−	0.738795i	$-0.735395\pi$
$97$	−4.57132e70	−1.34786	−0.673931	+	0.738795i	$0.735395\pi$
$98$	1.68215e70	0.344620
$99$	−2.58982e70	−0.370016
$100$	1.78551e69	0.0178551
$101$	−2.30611e71	−1.61984	−0.809919	−	0.586542i	$-0.800489\pi$
$101$	−2.30611e71	−1.61984	−0.809919	+	0.586542i	$0.800489\pi$
$102$	−2.87772e70	−0.142476
$103$	−3.04898e71	−1.06766	−0.533831	−	0.845591i	$-0.679248\pi$
$103$	−3.04898e71	−1.06766	−0.533831	+	0.845591i	$0.679248\pi$
$104$	−9.94173e70	−0.247046
$105$	−1.39050e71	−0.246010
$106$	−1.75025e71	−0.221177
$107$	−1.23450e72	−1.11781	−0.558903	−	0.829233i	$-0.688778\pi$
$107$	−1.23450e72	−1.11781	−0.558903	+	0.829233i	$0.688778\pi$
$108$	−2.42757e71	−0.157990
$109$	−3.68560e72	−1.72929	−0.864645	−	0.502383i	$-0.832457\pi$
$109$	−3.68560e72	−1.72929	−0.864645	+	0.502383i	$0.832457\pi$
$110$	−1.36933e72	−0.464589
$111$	2.81377e72	0.692347
$112$	1.19131e72	0.213199
$113$	−4.37947e72	−0.571659	−0.285829	−	0.958281i	$-0.592269\pi$
$113$	−4.37947e72	−0.571659	−0.285829	+	0.958281i	$0.592269\pi$
$114$	−1.64509e72	−0.157061
$115$	−7.57329e72	−0.530287
$116$	−2.19655e73	−1.13105
$117$	−2.81487e72	−0.106871
$118$	2.49147e72	0.0699269
$119$	1.20783e73	0.251240
$120$	−2.84705e73	−0.440009
$121$	2.01724e73	0.232207
$122$	8.43484e73	0.724941
$123$	−6.66668e72	−0.0428823
$124$	1.71008e74	0.825175
$125$	2.78532e74	1.01058
$126$	−2.22240e73	−0.0607671
$127$	6.93356e73	0.143194	0.0715968	−	0.997434i	$-0.477190\pi$
$127$	6.93356e73	0.143194	0.0715968	+	0.997434i	$0.477190\pi$
$128$	6.48553e74	1.01389
$129$	5.68020e74	0.673642
$130$	−1.48832e74	−0.134186
$131$	7.14182e74	0.490544	0.245272	−	0.969454i	$-0.421123\pi$
$131$	7.14182e74	0.490544	0.245272	+	0.969454i	$0.421123\pi$
$132$	1.00338e75	0.526128
$133$	6.90476e74	0.276959
$134$	1.16743e75	0.358932
$135$	−8.06106e74	−0.190346
$136$	2.47303e75	0.449363
$137$	−1.01049e76	−1.41564	−0.707820	−	0.706392i	$-0.750321\pi$
$137$	−1.01049e76	−1.41564	−0.707820	+	0.706392i	$0.750321\pi$
$138$	−1.21042e75	−0.130987
$139$	2.20784e75	0.184902	0.0924510	−	0.995717i	$-0.470530\pi$
$139$	2.20784e75	0.184902	0.0924510	+	0.995717i	$0.470530\pi$
$140$	5.38727e75	0.349803
$141$	5.62471e75	0.283675
$142$	3.66572e75	0.143854
$143$	1.16346e76	0.355896
$144$	6.90628e75	0.164959
$145$	−7.29392e76	−1.36269
$146$	−3.74552e76	−0.548259
$147$	−4.09301e76	−0.470195
$148$	−1.09015e77	−0.984452
$149$	−1.12055e77	−0.796746	−0.398373	−	0.917223i	$-0.630425\pi$
$149$	−1.12055e77	−0.796746	−0.398373	+	0.917223i	$0.630425\pi$
$150$	9.47615e74	0.00531364
$151$	−2.69028e77	−1.19156	−0.595780	−	0.803148i	$-0.703157\pi$
$151$	−2.69028e77	−1.19156	−0.595780	+	0.803148i	$0.703157\pi$
$152$	1.41375e77	0.495364
$153$	7.00205e76	0.194392
$154$	9.18581e76	0.202363
$155$	5.67853e77	0.994171
$156$	1.09057e77	0.151961
$157$	−1.26925e78	−1.40964	−0.704821	−	0.709385i	$-0.748973\pi$
$157$	−1.26925e78	−1.40964	−0.704821	+	0.709385i	$0.748973\pi$
$158$	−7.66743e77	−0.679709
$159$	4.25869e77	0.301772
$160$	1.70880e78	0.969239
$161$	5.08034e77	0.230980
$162$	−1.28838e77	−0.0470175
$163$	4.30092e78	1.26154	0.630770	−	0.775970i	$-0.282739\pi$
$163$	4.30092e78	1.26154	0.630770	+	0.775970i	$0.282739\pi$
$164$	2.58289e77	0.0609746
$165$	3.33186e78	0.633879
$166$	4.15695e78	0.638172
$167$	7.45816e78	0.925118	0.462559	−	0.886589i	$-0.346931\pi$
$167$	7.45816e78	0.925118	0.462559	+	0.886589i	$0.346931\pi$
$168$	1.90987e78	0.191657
$169$	−1.10375e79	−0.897207
$170$	3.70224e78	0.244077
$171$	4.00284e78	0.214292
$172$	−2.20070e79	−0.957856
$173$	2.93224e79	1.03888	0.519438	−	0.854508i	$-0.326141\pi$
$173$	2.93224e79	1.03888	0.519438	+	0.854508i	$0.326141\pi$
$174$	−1.16577e79	−0.336599
$175$	−3.97731e77	−0.00936999
$176$	−2.85456e79	−0.549337
$177$	−6.06224e78	−0.0954074
$178$	−4.14518e79	−0.534113
$179$	−5.61348e79	−0.592856	−0.296428	−	0.955055i	$-0.595795\pi$
$179$	−5.61348e79	−0.592856	−0.296428	+	0.955055i	$0.595795\pi$
$180$	3.12312e79	0.270654
$181$	5.40924e79	0.385076	0.192538	−	0.981290i	$-0.438328\pi$
$181$	5.40924e79	0.385076	0.192538	+	0.981290i	$0.438328\pi$
$182$	9.98402e78	0.0584482
$183$	−2.05236e80	−0.989100
$184$	1.04020e80	0.413127
$185$	−3.61997e80	−1.18607
$186$	9.07584e79	0.245571
$187$	−2.89414e80	−0.647355
$188$	−2.17920e80	−0.403360
$189$	5.40755e79	0.0829099
$190$	2.11645e80	0.269063
$191$	−4.64288e80	−0.489895	−0.244947	−	0.969536i	$-0.578771\pi$
$191$	−4.64288e80	−0.489895	−0.244947	+	0.969536i	$0.578771\pi$
$192$	−5.28225e79	−0.0463047
$193$	−2.52043e80	−0.183734	−0.0918670	−	0.995771i	$-0.529283\pi$
$193$	−2.52043e80	−0.183734	−0.0918670	+	0.995771i	$0.529283\pi$
$194$	9.39958e80	0.570357
$195$	3.62138e80	0.183082
$196$	1.58577e81	0.668572
$197$	2.77270e81	0.975780	0.487890	−	0.872905i	$-0.337767\pi$
$197$	2.77270e81	0.975780	0.487890	+	0.872905i	$0.337767\pi$
$198$	5.32521e80	0.156575
$199$	3.83538e81	0.943027	0.471514	−	0.881859i	$-0.343708\pi$
$199$	3.83538e81	0.943027	0.471514	+	0.881859i	$0.343708\pi$
$200$	−8.14353e79	−0.0167590
$201$	−2.84060e81	−0.489722
$202$	4.74184e81	0.685446
$203$	4.89293e81	0.593553
$204$	−2.71282e81	−0.276408
$205$	8.57681e80	0.0734622
$206$	6.26934e81	0.451789
$207$	2.94518e81	0.178717
$208$	−3.10261e81	−0.158664
$209$	−1.65448e82	−0.713624
$210$	2.85917e81	0.104101
$211$	−3.76862e82	−1.15919	−0.579596	−	0.814904i	$-0.696789\pi$
$211$	−3.76862e82	−1.15919	−0.579596	+	0.814904i	$0.696789\pi$
$212$	−1.64996e82	−0.429091
$213$	−8.91941e81	−0.196273
$214$	2.53838e82	0.473008
$215$	−7.30769e82	−1.15402
$216$	1.10719e82	0.148291
$217$	−3.80929e82	−0.433036
$218$	7.57836e82	0.731762
$219$	9.11358e82	0.748037
$220$	−1.29087e83	−0.901316
$221$	−3.14563e82	−0.186974
$222$	−5.78570e82	−0.292972
$223$	−2.26378e83	−0.977264	−0.488632	−	0.872490i	$-0.662504\pi$
$223$	−2.26378e83	−0.977264	−0.488632	+	0.872490i	$0.662504\pi$
$224$	−1.14630e83	−0.422176
$225$	−2.30573e81	−0.00724986
$226$	9.00509e82	0.241902
$227$	5.11719e83	1.17520	0.587602	−	0.809150i	$-0.300072\pi$
$227$	5.11719e83	1.17520	0.587602	+	0.809150i	$0.300072\pi$
$228$	−1.55083e83	−0.304703
$229$	4.72950e83	0.795528	0.397764	−	0.917488i	$-0.369786\pi$
$229$	4.72950e83	0.795528	0.397764	+	0.917488i	$0.369786\pi$
$230$	1.55723e83	0.224395
$231$	−2.23509e83	−0.276102
$232$	1.00183e84	1.06162
$233$	6.20872e83	0.564764	0.282382	−	0.959302i	$-0.408875\pi$
$233$	6.20872e83	0.564764	0.282382	+	0.959302i	$0.408875\pi$
$234$	5.78795e82	0.0452233
$235$	−7.23630e83	−0.485968
$236$	2.34871e83	0.135660
$237$	1.86564e84	0.927386
$238$	−2.48355e83	−0.106314
$239$	−6.72639e83	−0.248117	−0.124059	−	0.992275i	$-0.539591\pi$
$239$	−6.72639e83	−0.248117	−0.124059	+	0.992275i	$0.539591\pi$
$240$	−8.88507e83	−0.282593
$241$	−1.99795e84	−0.548252	−0.274126	−	0.961694i	$-0.588389\pi$
$241$	−1.99795e84	−0.548252	−0.274126	+	0.961694i	$0.588389\pi$
$242$	−4.14785e83	−0.0982602
$243$	3.13487e83	0.0641500
$244$	7.95152e84	1.40641
$245$	5.26574e84	0.805496
$246$	1.37081e83	0.0181460
$247$	−1.79825e84	−0.206115
$248$	−7.79951e84	−0.774521
$249$	−1.01147e85	−0.870713
$250$	−5.72719e84	−0.427633
$251$	−2.65267e85	−1.71896	−0.859480	−	0.511169i	$-0.829213\pi$
$251$	−2.65267e85	−1.71896	−0.859480	+	0.511169i	$0.829213\pi$
$252$	−2.09506e84	−0.117890
$253$	−1.21733e85	−0.595152
$254$	−1.42568e84	−0.0605935
$255$	−9.00827e84	−0.333016
$256$	−1.08427e85	−0.348834
$257$	4.24592e85	1.18945	0.594724	−	0.803930i	$-0.297261\pi$
$257$	4.24592e85	1.18945	0.594724	+	0.803930i	$0.297261\pi$
$258$	−1.16797e85	−0.285057
$259$	2.42836e85	0.516621
$260$	−1.40304e85	−0.260325
$261$	2.83654e85	0.459251
$262$	−1.46851e85	−0.207577
$263$	1.50287e86	1.85563	0.927816	−	0.373038i	$-0.121684\pi$
$263$	1.50287e86	1.85563	0.927816	+	0.373038i	$0.121684\pi$
$264$	−4.57633e85	−0.493831
$265$	−5.47889e85	−0.516968
$266$	−1.41976e85	−0.117197
$267$	1.00860e86	0.728737
$268$	1.10054e86	0.696339
$269$	6.91704e85	0.383455	0.191727	−	0.981448i	$-0.438591\pi$
$269$	6.91704e85	0.383455	0.191727	+	0.981448i	$0.438591\pi$
$270$	1.65752e85	0.0805462
$271$	−6.25012e85	−0.266366	−0.133183	−	0.991091i	$-0.542520\pi$
$271$	−6.25012e85	−0.266366	−0.133183	+	0.991091i	$0.542520\pi$
$272$	7.71781e85	0.288601
$273$	−2.42931e85	−0.0797460
$274$	2.07778e86	0.599039
$275$	9.53023e84	0.0241431
$276$	−1.14106e86	−0.254118
$277$	−3.12921e86	−0.612918	−0.306459	−	0.951884i	$-0.599144\pi$
$277$	−3.12921e86	−0.612918	−0.306459	+	0.951884i	$0.599144\pi$
$278$	−4.53977e85	−0.0782427
$279$	−2.20833e86	−0.335054
$280$	−2.45708e86	−0.328330
$281$	1.07871e87	1.27007	0.635037	−	0.772482i	$-0.280985\pi$
$281$	1.07871e87	1.27007	0.635037	+	0.772482i	$0.280985\pi$
$282$	−1.15656e86	−0.120039
$283$	−1.17930e87	−1.07946	−0.539729	−	0.841839i	$-0.681473\pi$
$283$	−1.17930e87	−1.07946	−0.539729	+	0.841839i	$0.681473\pi$
$284$	3.45567e86	0.279081
$285$	−5.14973e86	−0.367106
$286$	−2.39232e86	−0.150600
$287$	−5.75353e85	−0.0319983
$288$	−6.64535e86	−0.326651
$289$	−1.51829e87	−0.659904
$290$	1.49978e87	0.576632
$291$	−2.28710e87	−0.778188
$292$	−3.53090e87	−1.06364
$293$	−1.69373e86	−0.0451901	−0.0225950	−	0.999745i	$-0.507193\pi$
$293$	−1.69373e86	−0.0451901	−0.0225950	+	0.999745i	$0.507193\pi$
$294$	8.41608e86	0.198966
$295$	7.79919e86	0.163444
$296$	4.97207e87	0.924020
$297$	−1.29573e87	−0.213629
$298$	2.30409e87	0.337149
$299$	−1.32311e87	−0.171897
$300$	8.93316e85	0.0103086
$301$	4.90217e87	0.502664
$302$	5.53177e87	0.504217
$303$	−1.15378e88	−0.935214
$304$	4.41201e87	0.318145
$305$	2.64040e88	1.69444
$306$	−1.43977e87	−0.0822586
$307$	1.50981e88	0.768264	0.384132	−	0.923278i	$-0.374501\pi$
$307$	1.50981e88	0.768264	0.384132	+	0.923278i	$0.374501\pi$
$308$	8.65946e87	0.392591
$309$	−1.52545e88	−0.616414
$310$	−1.16762e88	−0.420691
$311$	3.95108e88	1.26976	0.634881	−	0.772610i	$-0.281049\pi$
$311$	3.95108e88	1.26976	0.634881	+	0.772610i	$0.281049\pi$
$312$	−4.97400e87	−0.142632
$313$	−3.96054e88	−1.01375	−0.506875	−	0.862020i	$-0.669199\pi$
$313$	−3.96054e88	−1.01375	−0.506875	+	0.862020i	$0.669199\pi$
$314$	2.60984e88	0.596500
$315$	−6.95691e87	−0.142034
$316$	−7.22808e88	−1.31866
$317$	8.65682e88	1.41174	0.705869	−	0.708342i	$-0.250557\pi$
$317$	8.65682e88	1.41174	0.705869	+	0.708342i	$0.250557\pi$
$318$	−8.75675e87	−0.127697
$319$	−1.17242e89	−1.52937
$320$	6.79572e87	0.0793252
$321$	−6.17638e88	−0.645365
$322$	−1.04462e88	−0.0977409
$323$	4.47319e88	0.374911
$324$	−1.21455e88	−0.0912153
$325$	1.03584e87	0.00697320
$326$	−8.84358e88	−0.533830
$327$	−1.84396e89	−0.998406
$328$	−1.17803e88	−0.0572316
$329$	4.85428e88	0.211675
$330$	−6.85098e88	−0.268230
$331$	−3.38783e89	−1.19132	−0.595660	−	0.803237i	$-0.703109\pi$
$331$	−3.38783e89	−1.19132	−0.595660	+	0.803237i	$0.703109\pi$
$332$	3.91876e89	1.23807
$333$	1.40777e89	0.399726
$334$	−1.53355e89	−0.391470
$335$	3.65448e89	0.838948
$336$	5.96031e88	0.123091
$337$	5.88470e89	1.09361	0.546805	−	0.837260i	$-0.315844\pi$
$337$	5.88470e89	1.09361	0.546805	+	0.837260i	$0.315844\pi$
$338$	2.26954e89	0.379660
$339$	−2.19112e89	−0.330047
$340$	3.49010e89	0.473517
$341$	9.12764e89	1.11578
$342$	−8.23066e88	−0.0906793
$343$	−7.86978e89	−0.781666
$344$	1.00372e90	0.899056
$345$	−3.78903e89	−0.306162
$346$	−6.02930e89	−0.439608
$347$	−6.92123e89	−0.455498	−0.227749	−	0.973720i	$-0.573137\pi$
$347$	−6.92123e89	−0.455498	−0.227749	+	0.973720i	$0.573137\pi$
$348$	−1.09897e90	−0.653012
$349$	−7.95083e89	−0.426688	−0.213344	−	0.976977i	$-0.568435\pi$
$349$	−7.95083e89	−0.426688	−0.213344	+	0.976977i	$0.568435\pi$
$350$	8.17817e87	0.00396498
$351$	−1.40832e89	−0.0617020
$352$	2.74671e90	1.08780
$353$	4.54547e90	1.62771	0.813854	−	0.581070i	$-0.197366\pi$
$353$	4.54547e90	1.62771	0.813854	+	0.581070i	$0.197366\pi$
$354$	1.24652e89	0.0403723
$355$	1.14750e90	0.336237
$356$	−3.90766e90	−1.03620
$357$	6.04296e89	0.145053
$358$	1.15425e90	0.250871
$359$	−9.02810e90	−1.77723	−0.888615	−	0.458654i	$-0.848332\pi$
$359$	−9.02810e90	−1.77723	−0.888615	+	0.458654i	$0.848332\pi$
$360$	−1.42442e90	−0.254039
$361$	−3.63019e90	−0.586710
$362$	−1.11225e90	−0.162948
$363$	1.00925e90	0.134065
$364$	9.41193e89	0.113391
$365$	−1.17248e91	−1.28147
$366$	4.22008e90	0.418545
$367$	−1.36021e91	−1.22450	−0.612251	−	0.790663i	$-0.709736\pi$
$367$	−1.36021e91	−1.22450	−0.612251	+	0.790663i	$0.709736\pi$
$368$	3.24624e90	0.265328
$369$	−3.33544e89	−0.0247581
$370$	7.44342e90	0.501893
$371$	3.67537e90	0.225179
$372$	8.55579e90	0.476415
$373$	1.01818e90	0.0515422	0.0257711	−	0.999668i	$-0.491796\pi$
$373$	1.01818e90	0.0515422	0.0257711	+	0.999668i	$0.491796\pi$
$374$	5.95095e90	0.273933
$375$	1.39354e91	0.583457
$376$	9.93912e90	0.378599
$377$	−1.27430e91	−0.441726
$378$	−1.11190e90	−0.0350839
$379$	2.51275e91	0.721868	0.360934	−	0.932591i	$-0.382458\pi$
$379$	2.51275e91	0.721868	0.360934	+	0.932591i	$0.382458\pi$
$380$	1.99517e91	0.521991
$381$	3.46896e90	0.0826729
$382$	9.54672e90	0.207303
$383$	−3.74261e91	−0.740658	−0.370329	−	0.928901i	$-0.620755\pi$
$383$	−3.74261e91	−0.740658	−0.370329	+	0.928901i	$0.620755\pi$
$384$	3.24481e91	0.585371
$385$	2.87548e91	0.472993
$386$	5.18252e90	0.0777484
$387$	2.84189e91	0.388927
$388$	8.86098e91	1.10651
$389$	−1.01443e92	−1.15615	−0.578073	−	0.815985i	$-0.696195\pi$
$389$	−1.01443e92	−1.15615	−0.578073	+	0.815985i	$0.696195\pi$
$390$	−7.44631e90	−0.0774725
$391$	3.29126e91	0.312671
$392$	−7.23254e91	−0.627531
$393$	3.57316e91	0.283216
$394$	−5.70125e91	−0.412909
$395$	−2.40018e92	−1.58872
$396$	5.02007e91	0.303760
$397$	−1.02196e92	−0.565419	−0.282709	−	0.959206i	$-0.591233\pi$
$397$	−1.02196e92	−0.565419	−0.282709	+	0.959206i	$0.591233\pi$
$398$	−7.88633e91	−0.399049
$399$	3.45456e91	0.159902
$400$	−2.54143e90	−0.0107634
$401$	−2.77072e92	−1.07391	−0.536954	−	0.843612i	$-0.680425\pi$
$401$	−2.77072e92	−1.07391	−0.536954	+	0.843612i	$0.680425\pi$
$402$	5.84085e91	0.207229
$403$	9.92079e91	0.322268
$404$	4.47013e92	1.32979
$405$	−4.03307e91	−0.109896
$406$	−1.00609e92	−0.251166
$407$	−5.81872e92	−1.33115
$408$	1.23729e92	0.259440
$409$	−7.85763e91	−0.151048	−0.0755239	−	0.997144i	$-0.524063\pi$
$409$	−7.85763e91	−0.151048	−0.0755239	+	0.997144i	$0.524063\pi$
$410$	−1.76357e91	−0.0310861
$411$	−5.05565e92	−0.817321
$412$	5.91010e92	0.876483
$413$	−5.23188e91	−0.0711919
$414$	−6.05590e91	−0.0756253
$415$	1.30127e93	1.49163
$416$	2.98538e92	0.314186
$417$	1.10462e92	0.106753
$418$	3.40196e92	0.301975
$419$	1.53284e93	1.24997	0.624984	−	0.780638i	$-0.285106\pi$
$419$	1.53284e93	1.24997	0.624984	+	0.780638i	$0.285106\pi$
$420$	2.69533e92	0.201959
$421$	−2.73838e93	−1.88573	−0.942864	−	0.333179i	$-0.891879\pi$
$421$	−2.73838e93	−1.88573	−0.942864	+	0.333179i	$0.891879\pi$
$422$	7.74906e92	0.490520
$423$	2.81413e92	0.163780
$424$	7.52530e92	0.402750
$425$	−2.57667e91	−0.0126839
$426$	1.83401e92	0.0830543
$427$	−1.77124e93	−0.738055
$428$	2.39293e93	0.917649
$429$	5.82098e92	0.205477
$430$	1.50261e93	0.488334
$431$	−1.97815e93	−0.591994	−0.295997	−	0.955189i	$-0.595652\pi$
$431$	−1.97815e93	−0.591994	−0.295997	+	0.955189i	$0.595652\pi$
$432$	3.45532e92	0.0952391
$433$	−5.62822e93	−1.42906	−0.714530	−	0.699605i	$-0.753359\pi$
$433$	−5.62822e93	−1.42906	−0.714530	+	0.699605i	$0.753359\pi$
$434$	7.83269e92	0.183242
$435$	−3.64926e93	−0.786749
$436$	7.14412e93	1.41964
$437$	1.88150e93	0.344678
$438$	−1.87394e93	−0.316537
$439$	−1.12111e94	−1.74646	−0.873229	−	0.487310i	$-0.837978\pi$
$439$	−1.12111e94	−1.74646	−0.873229	+	0.487310i	$0.837978\pi$
$440$	5.88754e93	0.845987
$441$	−2.04780e93	−0.271467
$442$	6.46807e92	0.0791196
$443$	7.36596e92	0.0831566	0.0415783	−	0.999135i	$-0.486761\pi$
$443$	7.36596e92	0.0831566	0.0415783	+	0.999135i	$0.486761\pi$
$444$	−5.45418e93	−0.568374
$445$	−1.29759e94	−1.24841
$446$	4.65480e93	0.413537
$447$	−5.60630e93	−0.460002
$448$	−4.55873e92	−0.0345521
$449$	5.66884e93	0.396962	0.198481	−	0.980105i	$-0.436399\pi$
$449$	5.66884e93	0.396962	0.198481	+	0.980105i	$0.436399\pi$
$450$	4.74106e91	0.00306783
$451$	1.37863e93	0.0824481
$452$	8.48910e93	0.469296
$453$	−1.34599e94	−0.687948
$454$	−1.05220e94	−0.497297
$455$	3.12535e93	0.136614
$456$	7.07319e93	0.285998
$457$	2.57670e94	0.963916	0.481958	−	0.876194i	$-0.339926\pi$
$457$	2.57670e94	0.963916	0.481958	+	0.876194i	$0.339926\pi$
$458$	−9.72482e93	−0.336633
$459$	3.50323e93	0.112233
$460$	1.46800e94	0.435333
$461$	4.29540e94	1.17929	0.589645	−	0.807663i	$-0.299268\pi$
$461$	4.29540e94	1.17929	0.589645	+	0.807663i	$0.299268\pi$
$462$	4.59580e93	0.116835
$463$	4.18743e94	0.985876	0.492938	−	0.870065i	$-0.335923\pi$
$463$	4.18743e94	0.985876	0.492938	+	0.870065i	$0.335923\pi$
$464$	3.12649e94	0.681819
$465$	2.84106e94	0.573985
$466$	−1.27664e94	−0.238984
$467$	−3.31055e93	−0.0574315	−0.0287158	−	0.999588i	$-0.509142\pi$
$467$	−3.31055e93	−0.0574315	−0.0287158	+	0.999588i	$0.509142\pi$
$468$	5.45630e93	0.0877345
$469$	−2.45151e94	−0.365425
$470$	1.48793e94	0.205641
$471$	−6.35024e94	−0.813857
$472$	−1.07122e94	−0.127333
$473$	−1.17463e95	−1.29518
$474$	−3.83613e94	−0.392430
$475$	−1.47300e93	−0.0139823
$476$	−2.34124e94	−0.206252
$477$	2.13069e94	0.174228
$478$	1.38309e94	0.104993
$479$	−1.85594e95	−1.30814	−0.654069	−	0.756435i	$-0.726939\pi$
$479$	−1.85594e95	−1.30814	−0.654069	+	0.756435i	$0.726939\pi$
$480$	8.54937e94	0.559590
$481$	−6.32435e94	−0.384473
$482$	4.10820e94	0.231997
$483$	2.54177e94	0.133356
$484$	−3.91018e94	−0.190628
$485$	2.94240e95	1.33312
$486$	−6.44594e93	−0.0271456
$487$	−1.18747e95	−0.464885	−0.232443	−	0.972610i	$-0.574672\pi$
$487$	−1.18747e95	−0.464885	−0.232443	+	0.972610i	$0.574672\pi$
$488$	−3.62662e95	−1.32007
$489$	2.15182e95	0.728351
$490$	−1.08274e95	−0.340851
$491$	−4.61391e95	−1.35107	−0.675533	−	0.737330i	$-0.736086\pi$
$491$	−4.61391e95	−1.35107	−0.675533	+	0.737330i	$0.736086\pi$
$492$	1.29226e94	0.0352037
$493$	3.16985e95	0.803475
$494$	3.69758e94	0.0872189
$495$	1.66698e95	0.365970
$496$	−2.43407e95	−0.497431
$497$	−7.69769e94	−0.146457
$498$	2.07979e95	0.368449
$499$	7.10119e95	1.17155	0.585777	−	0.810473i	$-0.300790\pi$
$499$	7.10119e95	1.17155	0.585777	+	0.810473i	$0.300790\pi$
$500$	−5.39902e95	−0.829621
$501$	3.73143e95	0.534117
$502$	5.45443e95	0.727391
$503$	2.17519e95	0.270292	0.135146	−	0.990826i	$-0.456850\pi$
$503$	2.17519e95	0.270292	0.135146	+	0.990826i	$0.456850\pi$
$504$	9.55538e94	0.110653
$505$	1.48436e96	1.60213
$506$	2.50307e95	0.251843
$507$	−5.52223e95	−0.518003
$508$	−1.34399e95	−0.117553
$509$	−1.18373e96	−0.965539	−0.482769	−	0.875748i	$-0.660369\pi$
$509$	−1.18373e96	−0.965539	−0.482769	+	0.875748i	$0.660369\pi$
$510$	1.85229e95	0.140918
$511$	7.86527e95	0.558177
$512$	−1.30840e96	−0.866281
$513$	2.00268e95	0.123722
$514$	−8.73048e95	−0.503324
$515$	1.96252e96	1.05599
$516$	−1.10104e96	−0.553018
$517$	−1.16316e96	−0.545411
$518$	−4.99322e95	−0.218612
$519$	1.46705e96	0.599795
$520$	6.39915e95	0.244345
$521$	2.20858e96	0.787724	0.393862	−	0.919170i	$-0.371139\pi$
$521$	2.20858e96	0.787724	0.393862	+	0.919170i	$0.371139\pi$
$522$	−5.83251e95	−0.194336
$523$	−1.71963e96	−0.535333	−0.267667	−	0.963512i	$-0.586253\pi$
$523$	−1.71963e96	−0.535333	−0.267667	+	0.963512i	$0.586253\pi$
$524$	−1.38436e96	−0.402706
$525$	−1.98991e94	−0.00540976
$526$	−3.09021e96	−0.785224
$527$	−2.46782e96	−0.586188
$528$	−1.42818e96	−0.317160
$529$	−3.43153e96	−0.712543
$530$	1.12657e96	0.218759
$531$	−3.03303e95	−0.0550835
$532$	−1.33841e96	−0.227366
$533$	1.49843e95	0.0238133
$534$	−2.07390e96	−0.308371
$535$	7.94604e96	1.10558
$536$	−5.01946e96	−0.653593
$537$	−2.80851e96	−0.342286
$538$	−1.42229e96	−0.162262
$539$	8.46411e96	0.904024
$540$	1.56254e96	0.156262
$541$	4.62986e96	0.433575	0.216788	−	0.976219i	$-0.430442\pi$
$541$	4.62986e96	0.433575	0.216788	+	0.976219i	$0.430442\pi$
$542$	1.28515e96	0.112715
$543$	2.70632e96	0.222324
$544$	−7.42621e96	−0.571487
$545$	2.37230e97	1.71038
$546$	4.99516e95	0.0337451
$547$	−1.88303e97	−1.19209	−0.596043	−	0.802953i	$-0.703261\pi$
$547$	−1.88303e97	−1.19209	−0.596043	+	0.802953i	$0.703261\pi$
$548$	1.95872e97	1.16215
$549$	−1.02683e97	−0.571057
$550$	−1.95961e95	−0.0102163
$551$	1.81209e97	0.885726
$552$	5.20427e96	0.238519
$553$	1.61009e97	0.692005
$554$	6.43430e96	0.259361
$555$	−1.81113e97	−0.684776
$556$	−4.27964e96	−0.151793
$557$	3.83468e97	1.27605	0.638027	−	0.770014i	$-0.279751\pi$
$557$	3.83468e97	1.27605	0.638027	+	0.770014i	$0.279751\pi$
$558$	4.54078e96	0.141781
$559$	−1.27670e97	−0.374086
$560$	−7.66805e96	−0.210868
$561$	−1.44798e97	−0.373751
$562$	−2.21804e97	−0.537441
$563$	−5.42588e97	−1.23430	−0.617152	−	0.786844i	$-0.711714\pi$
$563$	−5.42588e97	−1.23430	−0.617152	+	0.786844i	$0.711714\pi$
$564$	−1.09029e97	−0.232880
$565$	2.81891e97	0.565408
$566$	2.42488e97	0.456780
$567$	2.70548e96	0.0478680
$568$	−1.57610e97	−0.261950
$569$	−1.17545e98	−1.83535	−0.917677	−	0.397328i	$-0.869937\pi$
$569$	−1.17545e98	−1.83535	−0.917677	+	0.397328i	$0.869937\pi$
$570$	1.05889e97	0.155344
$571$	−8.24006e97	−1.13592	−0.567961	−	0.823056i	$-0.692267\pi$
$571$	−8.24006e97	−1.13592	−0.567961	+	0.823056i	$0.692267\pi$
$572$	−2.25524e97	−0.292169
$573$	−2.32290e97	−0.282841
$574$	1.18304e96	0.0135403
$575$	−1.08379e96	−0.0116610
$576$	−2.64279e96	−0.0267341
$577$	1.61133e98	1.53265	0.766326	−	0.642452i	$-0.222083\pi$
$577$	1.61133e98	1.53265	0.766326	+	0.642452i	$0.222083\pi$
$578$	3.12191e97	0.279243
$579$	−1.26101e97	−0.106079
$580$	1.41384e98	1.11868
$581$	−8.72924e97	−0.649717
$582$	4.70276e97	0.329296
$583$	−8.80673e97	−0.580204
$584$	1.61041e98	0.998345
$585$	1.81183e97	0.105702
$586$	3.48265e96	0.0191225
$587$	−2.32660e98	−1.20246	−0.601228	−	0.799078i	$-0.705322\pi$
$587$	−2.32660e98	−1.20246	−0.601228	+	0.799078i	$0.705322\pi$
$588$	7.93383e97	0.386001
$589$	−1.41077e98	−0.646195
$590$	−1.60367e97	−0.0691623
$591$	1.38723e98	0.563367
$592$	1.55168e98	0.593446
$593$	2.35123e98	0.846940	0.423470	−	0.905910i	$-0.360812\pi$
$593$	2.35123e98	0.846940	0.423470	+	0.905910i	$0.360812\pi$
$594$	2.66428e97	0.0903986
$595$	−7.77438e97	−0.248493
$596$	2.17206e98	0.654079
$597$	1.91890e98	0.544457
$598$	2.72058e97	0.0727394
$599$	−5.98305e98	−1.50754	−0.753772	−	0.657136i	$-0.771768\pi$
$599$	−5.98305e98	−1.50754	−0.753772	+	0.657136i	$0.771768\pi$
$600$	−4.07433e96	−0.00967581
$601$	2.46247e98	0.551222	0.275611	−	0.961269i	$-0.411120\pi$
$601$	2.46247e98	0.551222	0.275611	+	0.961269i	$0.411120\pi$
$602$	−1.00799e98	−0.212706
$603$	−1.42119e98	−0.282741
$604$	5.21480e98	0.978197
$605$	−1.29842e98	−0.229668
$606$	2.37242e98	0.395743
$607$	3.58896e98	0.564638	0.282319	−	0.959321i	$-0.408896\pi$
$607$	3.58896e98	0.564638	0.282319	+	0.959321i	$0.408896\pi$
$608$	−4.24532e98	−0.629989
$609$	2.44801e98	0.342688
$610$	−5.42921e98	−0.717014
$611$	−1.26423e98	−0.157530
$612$	−1.35727e98	−0.159584
$613$	2.98052e98	0.330708	0.165354	−	0.986234i	$-0.447123\pi$
$613$	2.98052e98	0.330708	0.165354	+	0.986234i	$0.447123\pi$
$614$	−3.10448e98	−0.325097
$615$	4.29111e97	0.0424134
$616$	−3.94950e98	−0.368491
$617$	−1.51606e99	−1.33534	−0.667670	−	0.744457i	$-0.732708\pi$
$617$	−1.51606e99	−1.33534	−0.667670	+	0.744457i	$0.732708\pi$
$618$	3.13665e98	0.260840
$619$	−9.30578e98	−0.730693	−0.365346	−	0.930872i	$-0.619049\pi$
$619$	−9.30578e98	−0.730693	−0.365346	+	0.930872i	$0.619049\pi$
$620$	−1.10072e99	−0.816152
$621$	1.47352e98	0.103182
$622$	−8.12424e98	−0.537309
$623$	8.70453e98	0.543776
$624$	−1.55228e98	−0.0916047
$625$	−1.75380e99	−0.977777
$626$	8.14370e98	0.428976
$627$	−8.27764e98	−0.412011
$628$	2.46029e99	1.15723
$629$	1.57320e99	0.699334
$630$	1.43048e98	0.0601027
$631$	2.74731e99	1.09110	0.545550	−	0.838078i	$-0.316321\pi$
$631$	2.74731e99	1.09110	0.545550	+	0.838078i	$0.316321\pi$
$632$	3.29666e99	1.23771
$633$	−1.88550e99	−0.669259
$634$	−1.78002e99	−0.597388
$635$	−4.46289e98	−0.141628
$636$	−8.25498e98	−0.247736
$637$	9.19961e98	0.261108
$638$	2.41074e99	0.647166
$639$	−4.46252e98	−0.113318
$640$	−4.17451e99	−1.00281
$641$	1.25416e99	0.285032	0.142516	−	0.989793i	$-0.454481\pi$
$641$	1.25416e99	0.285032	0.142516	+	0.989793i	$0.454481\pi$
$642$	1.26999e99	0.273091
$643$	9.41159e99	1.91502	0.957510	−	0.288400i	$-0.0931233\pi$
$643$	9.41159e99	1.91502	0.957510	+	0.288400i	$0.0931233\pi$
$644$	−9.84766e98	−0.189620
$645$	−3.65615e99	−0.666276
$646$	−9.19781e98	−0.158646
$647$	5.81388e99	0.949215	0.474607	−	0.880198i	$-0.342590\pi$
$647$	5.81388e99	0.949215	0.474607	+	0.880198i	$0.342590\pi$
$648$	5.53946e98	0.0856159
$649$	1.25364e99	0.183436
$650$	−2.12990e97	−0.00295076
$651$	−1.90585e99	−0.250013
$652$	−8.33684e99	−1.03565
$653$	1.14795e100	1.35054	0.675268	−	0.737573i	$-0.264028\pi$
$653$	1.14795e100	1.35054	0.675268	+	0.737573i	$0.264028\pi$
$654$	3.79157e99	0.422483
$655$	−4.59694e99	−0.485180
$656$	−3.67640e98	−0.0367566
$657$	4.55967e99	0.431879
$658$	−9.98140e98	−0.0895720
$659$	−1.28525e100	−1.09283	−0.546417	−	0.837514i	$-0.684008\pi$
$659$	−1.28525e100	−1.09283	−0.546417	+	0.837514i	$0.684008\pi$
$660$	−6.45842e99	−0.520375
$661$	−2.50553e100	−1.91314	−0.956571	−	0.291501i	$-0.905845\pi$
$661$	−2.50553e100	−1.91314	−0.956571	+	0.291501i	$0.905845\pi$
$662$	6.96608e99	0.504116
$663$	−1.57381e99	−0.107950
$664$	−1.78731e100	−1.16207
$665$	−4.44436e99	−0.273930
$666$	−2.89468e99	−0.169147
$667$	1.33329e100	0.738683
$668$	−1.44568e100	−0.759464
$669$	−1.13261e100	−0.564224
$670$	−7.51437e99	−0.355007
$671$	4.24417e100	1.90170
$672$	−5.73512e99	−0.243744
$673$	2.51439e100	1.01367	0.506837	−	0.862042i	$-0.330814\pi$
$673$	2.51439e100	1.01367	0.506837	+	0.862042i	$0.330814\pi$
$674$	−1.21002e100	−0.462769
$675$	−1.15359e98	−0.00418571
$676$	2.13949e100	0.736551
$677$	1.83479e100	0.599360	0.299680	−	0.954040i	$-0.403120\pi$
$677$	1.83479e100	0.599360	0.299680	+	0.954040i	$0.403120\pi$
$678$	4.50539e99	0.139662
$679$	−1.97383e100	−0.580675
$680$	−1.59180e100	−0.444450
$681$	2.56021e100	0.678505
$682$	−1.87683e100	−0.472150
$683$	−3.84076e100	−0.917237	−0.458619	−	0.888633i	$-0.651656\pi$
$683$	−3.84076e100	−0.917237	−0.458619	+	0.888633i	$0.651656\pi$
$684$	−7.75904e99	−0.175920
$685$	6.50419e100	1.40016
$686$	1.61819e100	0.330768
$687$	2.36624e100	0.459298
$688$	3.13240e100	0.577414
$689$	−9.57200e99	−0.167579
$690$	7.79104e99	0.129555
$691$	4.41005e100	0.696583	0.348292	−	0.937386i	$-0.386762\pi$
$691$	4.41005e100	0.696583	0.348292	+	0.937386i	$0.386762\pi$
$692$	−5.68382e100	−0.852852
$693$	−1.11825e100	−0.159407
$694$	1.42315e100	0.192747
$695$	−1.42111e100	−0.182880
$696$	5.01229e100	0.612926
$697$	−3.72737e99	−0.0433151
$698$	1.63486e100	0.180556
$699$	3.10632e100	0.326067
$700$	7.70956e98	0.00769218
$701$	−1.21602e101	−1.15333	−0.576663	−	0.816982i	$-0.695645\pi$
$701$	−1.21602e101	−1.15333	−0.576663	+	0.816982i	$0.695645\pi$
$702$	2.89580e99	0.0261097
$703$	8.99343e100	0.770924
$704$	1.09234e100	0.0890283
$705$	−3.62043e100	−0.280574
$706$	−9.34642e100	−0.688776
$707$	−9.95747e100	−0.697846
$708$	1.17510e100	0.0783235
$709$	−1.60637e101	−1.01837	−0.509184	−	0.860657i	$-0.670053\pi$
$709$	−1.60637e101	−1.01837	−0.509184	+	0.860657i	$0.670053\pi$
$710$	−2.35949e100	−0.142281
$711$	9.33406e100	0.535427
$712$	1.78225e101	0.972587
$713$	−1.03801e101	−0.538917
$714$	−1.24256e100	−0.0613804
$715$	−7.48881e100	−0.352005
$716$	1.08811e101	0.486698
$717$	−3.36532e100	−0.143251
$718$	1.85636e101	0.752048
$719$	−3.09787e101	−1.19450	−0.597252	−	0.802054i	$-0.703741\pi$
$719$	−3.09787e101	−1.19450	−0.597252	+	0.802054i	$0.703741\pi$
$720$	−4.44534e100	−0.163155
$721$	−1.31651e101	−0.459961
$722$	7.46442e100	0.248271
$723$	−9.99606e100	−0.316533
$724$	−1.04852e101	−0.316124
$725$	−1.04381e100	−0.0299656
$726$	−2.07523e100	−0.0567306
$727$	−4.73980e101	−1.23392	−0.616962	−	0.786993i	$-0.711637\pi$
$727$	−4.73980e101	−1.23392	−0.616962	+	0.786993i	$0.711637\pi$
$728$	−4.29270e100	−0.106431
$729$	1.56842e100	0.0370370
$730$	2.41086e101	0.542264
$731$	3.17583e101	0.680441
$732$	3.97827e101	0.811990
$733$	−2.17449e100	−0.0422831	−0.0211416	−	0.999776i	$-0.506730\pi$
$733$	−2.17449e100	−0.0422831	−0.0211416	+	0.999776i	$0.506730\pi$
$734$	2.79687e101	0.518157
$735$	2.63453e101	0.465053
$736$	−3.12359e101	−0.525402
$737$	5.87419e101	0.941569
$738$	6.85836e99	0.0104766
$739$	8.53447e101	1.24251	0.621254	−	0.783609i	$-0.286624\pi$
$739$	8.53447e101	1.24251	0.621254	+	0.783609i	$0.286624\pi$
$740$	7.01690e101	0.973687
$741$	−8.99693e100	−0.119000
$742$	−7.55731e100	−0.0952859
$743$	−9.28234e99	−0.0111572	−0.00557859	−	0.999984i	$-0.501776\pi$
$743$	−9.28234e99	−0.0111572	−0.00557859	+	0.999984i	$0.501776\pi$
$744$	−3.90222e101	−0.447170
$745$	7.21262e101	0.788034
$746$	−2.09360e100	−0.0218105
$747$	−5.06053e101	−0.502707
$748$	5.60996e101	0.531438
$749$	−5.33039e101	−0.481564
$750$	−2.86540e101	−0.246894
$751$	−1.57728e102	−1.29625	−0.648127	−	0.761532i	$-0.724447\pi$
$751$	−1.57728e102	−1.29625	−0.648127	+	0.761532i	$0.724447\pi$
$752$	3.10179e101	0.243153
$753$	−1.32717e102	−0.992442
$754$	2.62022e101	0.186920
$755$	1.73164e102	1.17853
$756$	−1.04819e101	−0.0680638
$757$	−1.02229e102	−0.633387	−0.316693	−	0.948528i	$-0.602573\pi$
$757$	−1.02229e102	−0.633387	−0.316693	+	0.948528i	$0.602573\pi$
$758$	−5.16674e101	−0.305464
$759$	−6.09047e101	−0.343611
$760$	−9.09980e101	−0.489947
$761$	6.40901e100	0.0329333	0.0164667	−	0.999864i	$-0.494758\pi$
$761$	6.40901e100	0.0329333	0.0164667	+	0.999864i	$0.494758\pi$
$762$	−7.13291e100	−0.0349837
$763$	−1.59139e102	−0.744999
$764$	8.99969e101	0.402173
$765$	−4.50698e101	−0.192267
$766$	7.69557e101	0.313415
$767$	1.36257e101	0.0529815
$768$	−5.42477e101	−0.201399
$769$	−2.93171e102	−1.03929	−0.519645	−	0.854382i	$-0.673936\pi$
$769$	−2.93171e102	−1.03929	−0.519645	+	0.854382i	$0.673936\pi$
$770$	−5.91259e101	−0.200151
$771$	2.12430e102	0.686728
$772$	4.88556e101	0.150834
$773$	1.62052e102	0.477840	0.238920	−	0.971039i	$-0.423207\pi$
$773$	1.62052e102	0.477840	0.238920	+	0.971039i	$0.423207\pi$
$774$	−5.84352e101	−0.164577
$775$	8.12638e100	0.0218618
$776$	−4.04141e102	−1.03859
$777$	1.21495e102	0.298271
$778$	2.08589e102	0.489232
$779$	−2.13082e101	−0.0477492
$780$	−7.01963e101	−0.150299
$781$	1.84448e102	0.377366
$782$	−6.76751e101	−0.132309
$783$	1.41916e102	0.265149
$784$	−2.25712e102	−0.403028
$785$	8.16971e102	1.39423
$786$	−7.34716e101	−0.119845
$787$	5.77893e102	0.901041	0.450521	−	0.892766i	$-0.351238\pi$
$787$	5.77893e102	0.901041	0.450521	+	0.892766i	$0.351238\pi$
$788$	−5.37456e102	−0.801055
$789$	7.51908e102	1.07135
$790$	4.93526e102	0.672277
$791$	−1.89099e102	−0.246277
$792$	−2.28961e102	−0.285113
$793$	4.61297e102	0.549265
$794$	2.10136e102	0.239261
$795$	−2.74117e102	−0.298472
$796$	−7.43444e102	−0.774167
$797$	4.03612e102	0.401970	0.200985	−	0.979594i	$-0.435586\pi$
$797$	4.03612e102	0.401970	0.200985	+	0.979594i	$0.435586\pi$
$798$	−7.10329e101	−0.0676638
$799$	3.14480e102	0.286539
$800$	2.44541e101	0.0213136
$801$	5.04620e102	0.420737
$802$	5.69717e102	0.454432
$803$	−1.88464e103	−1.43822
$804$	5.50617e102	0.402031
$805$	−3.27004e102	−0.228454
$806$	−2.03992e102	−0.136370
$807$	3.46070e102	0.221388
$808$	−2.03879e103	−1.24816
$809$	−3.10627e102	−0.181998	−0.0909990	−	0.995851i	$-0.529006\pi$
$809$	−3.10627e102	−0.181998	−0.0909990	+	0.995851i	$0.529006\pi$
$810$	8.29283e101	0.0465034
$811$	−4.60707e102	−0.247277	−0.123639	−	0.992327i	$-0.539456\pi$
$811$	−4.60707e102	−0.247277	−0.123639	+	0.992327i	$0.539456\pi$
$812$	−9.48438e102	−0.487271
$813$	−3.12703e102	−0.153786
$814$	1.19645e103	0.563285
$815$	−2.76835e103	−1.24775
$816$	3.86134e102	0.166624
$817$	1.81552e103	0.750097
$818$	1.61569e102	0.0639170
$819$	−1.21542e102	−0.0460414
$820$	−1.66252e102	−0.0603079
$821$	−8.27269e102	−0.287386	−0.143693	−	0.989622i	$-0.545898\pi$
$821$	−8.27269e102	−0.287386	−0.143693	+	0.989622i	$0.545898\pi$
$822$	1.03955e103	0.345855
$823$	2.47530e103	0.788741	0.394370	−	0.918952i	$-0.370963\pi$
$823$	2.47530e103	0.788741	0.394370	+	0.918952i	$0.370963\pi$
$824$	−2.69554e103	−0.822679
$825$	4.76812e101	0.0139390
$826$	1.07578e102	0.0301254
$827$	1.18072e103	0.316739	0.158370	−	0.987380i	$-0.449376\pi$
$827$	1.18072e103	0.316739	0.158370	+	0.987380i	$0.449376\pi$
$828$	−5.70890e102	−0.146715
$829$	1.03978e103	0.256009	0.128004	−	0.991774i	$-0.459143\pi$
$829$	1.03978e103	0.256009	0.128004	+	0.991774i	$0.459143\pi$
$830$	−2.67569e103	−0.631194
$831$	−1.56559e103	−0.353869
$832$	1.18726e102	0.0257139
$833$	−2.28842e103	−0.474940
$834$	−2.27132e102	−0.0451734
$835$	−4.80056e103	−0.915002
$836$	3.20703e103	0.585841
$837$	−1.10486e103	−0.193443
$838$	−3.15183e103	−0.528933
$839$	8.89695e103	1.43117	0.715586	−	0.698525i	$-0.246160\pi$
$839$	8.89695e103	1.43117	0.715586	+	0.698525i	$0.246160\pi$
$840$	−1.22932e103	−0.189561
$841$	6.07623e103	0.898207
$842$	5.63067e103	0.797959
$843$	5.39694e103	0.733278
$844$	7.30503e103	0.951624
$845$	7.10446e103	0.887397
$846$	−5.78643e102	−0.0693047
$847$	8.71014e102	0.100038
$848$	2.34849e103	0.258664
$849$	−5.90022e103	−0.623225
$850$	5.29816e101	0.00536727
$851$	6.61713e103	0.642940
$852$	1.72892e103	0.161128
$853$	−1.37178e104	−1.22629	−0.613146	−	0.789970i	$-0.710096\pi$
$853$	−1.37178e104	−1.22629	−0.613146	+	0.789970i	$0.710096\pi$
$854$	3.64204e103	0.312314
$855$	−2.57649e103	−0.211949
$856$	−1.09139e104	−0.861318
$857$	−3.43783e103	−0.260294	−0.130147	−	0.991495i	$-0.541545\pi$
$857$	−3.43783e103	−0.260294	−0.130147	+	0.991495i	$0.541545\pi$
$858$	−1.19691e103	−0.0869490
$859$	−1.63637e104	−1.14057	−0.570287	−	0.821446i	$-0.693168\pi$
$859$	−1.63637e104	−1.14057	−0.570287	+	0.821446i	$0.693168\pi$
$860$	1.41651e104	0.947382
$861$	−2.87858e102	−0.0184742
$862$	4.06749e103	0.250506
$863$	3.60240e103	0.212916	0.106458	−	0.994317i	$-0.466049\pi$
$863$	3.60240e103	0.212916	0.106458	+	0.994317i	$0.466049\pi$
$864$	−3.32477e103	−0.188592
$865$	−1.88738e104	−1.02752
$866$	1.15728e104	0.604717
$867$	−7.59623e103	−0.380996
$868$	7.38388e103	0.355496
$869$	−3.85803e104	−1.78305
$870$	7.50363e103	0.332919
$871$	6.38463e103	0.271952
$872$	−3.25837e104	−1.33249
$873$	−1.14427e104	−0.449287
$874$	−3.86876e103	−0.145853
$875$	1.20266e104	0.435369
$876$	−1.76656e104	−0.614092
$877$	3.01223e104	1.00555	0.502774	−	0.864418i	$-0.332313\pi$
$877$	3.01223e104	1.00555	0.502774	+	0.864418i	$0.332313\pi$
$878$	2.30524e104	0.739027
$879$	−8.47398e102	−0.0260905
$880$	1.83738e104	0.543330
$881$	−3.21497e104	−0.913130	−0.456565	−	0.889690i	$-0.650920\pi$
$881$	−3.21497e104	−0.913130	−0.456565	+	0.889690i	$0.650920\pi$
$882$	4.21069e103	0.114873
$883$	−5.75696e104	−1.50865	−0.754324	−	0.656502i	$-0.772035\pi$
$883$	−5.75696e104	−1.50865	−0.754324	+	0.656502i	$0.772035\pi$
$884$	6.09744e103	0.153494
$885$	3.90205e103	0.0943642
$886$	−1.51459e103	−0.0351883
$887$	8.00577e104	1.78696	0.893479	−	0.449104i	$-0.148257\pi$
$887$	8.00577e104	1.78696	0.893479	+	0.449104i	$0.148257\pi$
$888$	2.48760e104	0.533483
$889$	2.99381e103	0.0616896
$890$	2.66811e104	0.528273
$891$	−6.48273e103	−0.123339
$892$	4.38808e104	0.802273
$893$	1.79778e104	0.315871
$894$	1.15277e104	0.194653
$895$	3.61320e104	0.586373
$896$	2.80036e104	0.436797
$897$	−6.61971e103	−0.0992446
$898$	−1.16563e104	−0.167978
$899$	−9.99716e104	−1.38487
$900$	4.46940e102	0.00595169
$901$	2.38106e104	0.304817
$902$	−2.83475e103	−0.0348885
$903$	2.45263e104	0.290213
$904$	−3.87180e104	−0.440488
$905$	−3.48174e104	−0.380865
$906$	2.76763e104	0.291110
$907$	1.24094e105	1.25514	0.627571	−	0.778559i	$-0.284049\pi$
$907$	1.24094e105	1.25514	0.627571	+	0.778559i	$0.284049\pi$
$908$	−9.91908e104	−0.964770
$909$	−5.77256e104	−0.539946
$910$	−6.42637e103	−0.0578091
$911$	−1.45373e105	−1.25771	−0.628857	−	0.777521i	$-0.716477\pi$
$911$	−1.45373e105	−1.25771	−0.628857	+	0.777521i	$0.716477\pi$
$912$	2.20740e104	0.183681
$913$	2.09166e105	1.67409
$914$	−5.29823e104	−0.407888
$915$	1.32103e105	0.978285
$916$	−9.16759e104	−0.653079
$917$	3.08374e104	0.211332
$918$	−7.20337e103	−0.0474920
$919$	−6.50781e104	−0.412795	−0.206397	−	0.978468i	$-0.566174\pi$
$919$	−6.50781e104	−0.412795	−0.206397	+	0.978468i	$0.566174\pi$
$920$	−6.69540e104	−0.408609
$921$	7.55382e104	0.443557
$922$	−8.83222e104	−0.499025
$923$	2.00476e104	0.108994
$924$	4.33246e104	0.226662
$925$	−5.18044e103	−0.0260817
$926$	−8.61022e104	−0.417181
$927$	−7.63208e104	−0.355887
$928$	−3.00837e105	−1.35014
$929$	−1.71049e105	−0.738861	−0.369431	−	0.929258i	$-0.620447\pi$
$929$	−1.71049e105	−0.738861	−0.369431	+	0.929258i	$0.620447\pi$
$930$	−5.84180e104	−0.242886
$931$	−1.30822e105	−0.523559
$932$	−1.20349e105	−0.463636
$933$	1.97679e105	0.733097
$934$	6.80717e103	0.0243026
$935$	1.86286e105	0.640277
$936$	−2.48857e104	−0.0823488
$937$	2.03025e105	0.646835	0.323417	−	0.946256i	$-0.395168\pi$
$937$	2.03025e105	0.646835	0.323417	+	0.946256i	$0.395168\pi$
$938$	5.04082e104	0.154632
$939$	−1.98152e105	−0.585289
$940$	1.40267e105	0.398949
$941$	3.53562e105	0.968352	0.484176	−	0.874971i	$-0.339119\pi$
$941$	3.53562e105	0.968352	0.484176	+	0.874971i	$0.339119\pi$
$942$	1.30574e105	0.344390
$943$	−1.56780e104	−0.0398222
$944$	−3.34307e104	−0.0817786
$945$	−3.48065e104	−0.0820033
$946$	2.41529e105	0.548067
$947$	2.88782e105	0.631170	0.315585	−	0.948897i	$-0.397799\pi$
$947$	2.88782e105	0.631170	0.315585	+	0.948897i	$0.397799\pi$
$948$	−3.61632e105	−0.761326
$949$	−2.04840e105	−0.415399
$950$	3.02878e103	0.00591671
$951$	4.33114e105	0.815068
$952$	1.06782e105	0.193591
$953$	3.65620e105	0.638604	0.319302	−	0.947653i	$-0.396552\pi$
$953$	3.65620e105	0.638604	0.319302	+	0.947653i	$0.396552\pi$
$954$	−4.38114e104	−0.0737258
$955$	2.98846e105	0.484538
$956$	1.30383e105	0.203689
$957$	−5.86579e105	−0.882985
$958$	3.81620e105	0.553548
$959$	−4.36316e105	−0.609875
$960$	3.40000e104	0.0457984
$961$	7.97302e103	0.0103501
$962$	1.30042e105	0.162692
$963$	−3.09014e105	−0.372602
$964$	3.87280e105	0.450081
$965$	1.62231e105	0.181725
$966$	−5.22641e104	−0.0564307
$967$	−5.40345e105	−0.562382	−0.281191	−	0.959652i	$-0.590729\pi$
$967$	−5.40345e105	−0.562382	−0.281191	+	0.959652i	$0.590729\pi$
$968$	1.78340e105	0.178926
$969$	2.23801e105	0.216455
$970$	−6.05018e105	−0.564121
$971$	1.95441e106	1.75684	0.878420	−	0.477889i	$-0.158598\pi$
$971$	1.95441e106	1.75684	0.878420	+	0.477889i	$0.158598\pi$
$972$	−6.07658e104	−0.0526632
$973$	9.53313e104	0.0796581
$974$	2.44169e105	0.196720
$975$	5.18245e103	0.00402598
$976$	−1.13179e106	−0.847809
$977$	−1.44045e106	−1.04050	−0.520248	−	0.854015i	$-0.674161\pi$
$977$	−1.44045e106	−1.04050	−0.520248	+	0.854015i	$0.674161\pi$
$978$	−4.42458e105	−0.308207
$979$	−2.08573e106	−1.40111
$980$	−1.02070e106	−0.661262
$981$	−9.22564e105	−0.576430
$982$	9.48716e105	0.571713
$983$	1.17402e106	0.682382	0.341191	−	0.939994i	$-0.389170\pi$
$983$	1.17402e106	0.682382	0.341191	+	0.939994i	$0.389170\pi$
$984$	−5.89388e104	−0.0330427
$985$	−1.78469e106	−0.965110
$986$	−6.51786e105	−0.339996
$987$	2.42867e105	0.122211
$988$	3.48570e105	0.169207
$989$	1.33581e106	0.625570
$990$	−3.42765e105	−0.154863
$991$	−2.56434e106	−1.11779	−0.558897	−	0.829237i	$-0.688775\pi$
$991$	−2.56434e106	−1.11779	−0.558897	+	0.829237i	$0.688775\pi$
$992$	2.34210e106	0.985012
$993$	−1.69499e106	−0.687809
$994$	1.58280e105	0.0619742
$995$	−2.46870e106	−0.932716
$996$	1.96061e106	0.714802
$997$	3.02413e106	1.06395	0.531976	−	0.846759i	$-0.321450\pi$
$997$	3.02413e106	1.06395	0.531976	+	0.846759i	$0.321450\pi$
$998$	−1.46015e106	−0.495751
$999$	7.04332e105	0.230782

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3.72.a.a.1.3	✓	5
3.2	odd	2		9.72.a.a.1.3		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3.72.a.a.1.3	✓	5	1.1	even	1	trivial
9.72.a.a.1.3		5	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 3 \)
Weight:	\( k \)	\(=\)	\( 72 \)
Character orbit:	\([\chi]\)	\(=\)	3.a (trivial)

\(f(q)\)	\(=\)	\(q-2.05621e10 q^{2} +5.00315e16 q^{3} -1.93838e21 q^{4} -6.43665e24 q^{5} -1.02875e27 q^{6} +4.31786e29 q^{7} +8.84080e31 q^{8} +2.50316e33 q^{9} +1.32351e35 q^{10} -1.03462e37 q^{11} -9.69804e37 q^{12} -1.12453e39 q^{13} -8.87841e39 q^{14} -3.22036e41 q^{15} +2.75903e42 q^{16} +2.79729e43 q^{17} -5.14700e43 q^{18} +1.59912e45 q^{19} +1.24767e46 q^{20} +2.16029e46 q^{21} +2.12740e47 q^{22} +1.17659e48 q^{23} +4.42319e48 q^{24} -9.21131e47 q^{25} +2.31226e49 q^{26} +1.25237e50 q^{27} -8.36967e50 q^{28} +1.13318e52 q^{29} +6.62172e51 q^{30} -8.82218e52 q^{31} -2.65479e53 q^{32} -5.17638e53 q^{33} -5.75180e53 q^{34} -2.77926e54 q^{35} -4.85208e54 q^{36} +5.62400e55 q^{37} -3.28811e55 q^{38} -5.62619e55 q^{39} -5.69052e56 q^{40} -1.33250e56 q^{41} -4.44201e56 q^{42} +1.13532e58 q^{43} +2.00550e58 q^{44} -1.61119e58 q^{45} -2.41931e58 q^{46} +1.12423e59 q^{47} +1.38039e59 q^{48} -8.18086e59 q^{49} +1.89403e58 q^{50} +1.39953e60 q^{51} +2.17977e60 q^{52} +8.51201e60 q^{53} -2.57513e60 q^{54} +6.65951e61 q^{55} +3.81733e61 q^{56} +8.00063e61 q^{57} -2.33006e62 q^{58} -1.21168e62 q^{59} +6.24229e62 q^{60} -4.10214e63 q^{61} +1.81402e63 q^{62} +1.08083e63 q^{63} -1.05578e63 q^{64} +7.23820e63 q^{65} +1.06437e64 q^{66} -5.67761e64 q^{67} -5.42222e64 q^{68} +5.88665e64 q^{69} +5.71472e64 q^{70} -1.78276e65 q^{71} +2.21299e65 q^{72} +1.82157e66 q^{73} -1.15641e66 q^{74} -4.60856e64 q^{75} -3.09970e66 q^{76} -4.46736e66 q^{77} +1.15686e66 q^{78} +3.72892e67 q^{79} -1.77589e67 q^{80} +6.26579e66 q^{81} +2.73989e66 q^{82} -2.02166e68 q^{83} -4.18748e67 q^{84} -1.80052e68 q^{85} -2.33446e68 q^{86} +5.66950e68 q^{87} -9.14690e68 q^{88} +2.01594e69 q^{89} +3.31295e68 q^{90} -4.85555e68 q^{91} -2.28068e69 q^{92} -4.41387e69 q^{93} -2.31165e69 q^{94} -1.02930e70 q^{95} -1.32823e70 q^{96} -4.57132e70 q^{97} +1.68215e70 q^{98} -2.58982e70 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q - 25051277688 q^{2} + 25\!\cdots\!35 q^{3} + 19\!\cdots\!24 q^{4} + 14\!\cdots\!30 q^{5} - 12\!\cdots\!16 q^{6} - 12\!\cdots\!52 q^{7} - 15\!\cdots\!48 q^{8} + 12\!\cdots\!45 q^{9} - 30\!\cdots\!60 q^{10}+ \cdots + 33\!\cdots\!88 q^{99}+O(q^{100}) \) 5 * q - 25051277688 * q^2 + 250157725494998535 * q^3 + 1907299462927273154624 * q^4 + 1422573866433399534277830 * q^5 - 1253354129434737111087637416 * q^6 - 1261222231854515600228814346952 * q^7 - 151958919976138936299686009691648 * q^8 + 12515777524966208006577859930429245 * q^9 - 308853354401574193552393248717551760 * q^10 + 1357894937151168401938494740936725812 * q^11 + 95425139096743786553920018696741695168 * q^12 - 3732312012481108743024076959256483425602 * q^13 + 178792454794792302794525709930294541693632 * q^14 + 71173568555121014264963983054791626595810 * q^15 - 2761767053096261549691112453399712883798016 * q^16 - 277325542902069263625709674624672840731910 * q^17 - 62707243651831565917830179941990275506237112 * q^18 + 2937432205918421125744856768913127977845719948 * q^19 - 24911205133324082416992380941498137854677077120 * q^20 - 63100896972890262121533046345756354145644343064 * q^21 + 981344865457378177927521236701073576051567611680 * q^22 - 4228346897979680919198407557464543114207597141624 * q^23 - 7602739557981482671404075764718702187632312347136 * q^24 + 19633070396484105587134362494981426945191834668275 * q^25 - 163733269614894222914401413204168398319516301314000 * q^26 + 626183687689393767209300272665229846333060639231215 * q^27 - 5768362424640263225567110092226485193092350431463936 * q^28 - 3697116438725251267139482122013539208885912739684274 * q^29 - 15452410529719698927278278181356603942084949997334320 * q^30 + 74551273173252500835223325068153865117486542141504384 * q^31 - 639756106869108826481408208267665768107401476101865472 * q^32 + 67937581787782054618912973363008350989516300927337084 * q^33 - 6217683238533672509931589234500437242788961796499134832 * q^34 - 13153074146721234298498045726570273336863567981003778800 * q^35 + 4774267150297056921454723864735495027586024236315315776 * q^36 - 160060519909409459305929258566699075666754182654348019002 * q^37 - 91685642067030133239673763998240213415299939628290081056 * q^38 - 186733336775986949394712651065025829961603412074954298614 * q^39 + 755753872880123511491678719028119895299413298470522117120 * q^40 + 2279706853693741369685932186247543106805520151549660884994 * q^41 + 8945262765426517501413121912547804713065475672808851765824 * q^42 + 6754858585968454689741824956150275855563744863320129251092 * q^43 + 10256422900727914711051439828948913719762767210529399343360 * q^44 + 3560923605022284438744581203359299419628800805488597427670 * q^45 + 215917478684214015835970415365801427523995942249450992649024 * q^46 - 468036949346743446524224540083033087921443712918743092678704 * q^47 - 138175472869917128113923965027114211523442937794848631181312 * q^48 - 1155203275623883178356241428680618202323141234160855611430803 * q^49 - 662361288254569744891489750838385910624551591076930373305800 * q^50 - 13875025406809456447127343535570692796264334304266755550370 * q^51 + 4686563330803028488195038486432142239675010588344800750934400 * q^52 + 16850153365054699278877708172474268895458775724356533295576086 * q^53 - 3137340288800574070947321989342157748567014121664790760526184 * q^54 + 69903604802785515177733563130194024072223641855144712529201880 * q^55 + 263561757691935735991107069426454954646910606378160826135654400 * q^56 + 146964271885661680599941817303782740393713518895988426056055236 * q^57 - 393766572647074503603427367357535096204856933671806739961414992 * q^58 - 390335442004059371501204897784396685449449222429047305160362108 * q^59 - 1246346083098336838245443167057803985933179433056389614496403840 * q^60 + 725074488292223066537782289903828567460896102224114882556804878 * q^61 - 9988959008617311972392577438833349328275372968547435398535343104 * q^62 - 3157035372686493241148598970419764570521041257808979169543482248 * q^63 - 2023851072198628197882474312831161597933729151994298498048327680 * q^64 + 13140351800845565438471290641483435252971725075901777919813259620 * q^65 + 49098199893802616037233646095483883838218857898857856047009777760 * q^66 + 66714375177521017736160888158122274402157076957263686329132696540 * q^67 + 122874398781837608005594402142092581637778609572473879627701828736 * q^68 - 211550728520485918988863794593760397778492966928452183274813504168 * q^69 - 293285886544485684750990625097245178785454325664385364335258966400 * q^70 + 182228903943633461999697286426491914806644676121035292409010095000 * q^71 - 380376807071099648078549525700513940155076932645648351218946289152 * q^72 - 3126186443395793129070092762366126842796181422188167587986966103774 * q^73 - 909089362115793434062323439709786862714999800511985114251226742928 * q^74 + 982272846973530587229764561497340393007528047854257425826667195425 * q^75 + 17344875012173690040537707411833679809662138514060794984773183596288 * q^76 + 10495163179741456456758662728922622402868815939129112668959031953376 * q^77 - 8191828462944258702008436357306371395699406819716356341809714998000 * q^78 - 27301301517941598101728732493241199802996555070508118978972462370800 * q^79 + 17453171390087969064834561314810599922914790489604475485575264133120 * q^80 + 31328937410889851896281120971709651661033472234053326374297990254005 * q^81 - 211476001448904287369943798857320633308142594733381306800142859557424 * q^82 - 118340201116022360513322067378331477940966167749075029048364461271476 * q^83 - 288600084795764628291001658833202352097198631523538446517373245066752 * q^84 - 353749028745389735175606474209594334673616946227279830960229574948180 * q^85 - 598599366027984305586625758611411918350192525004808831847227328355808 * q^86 - 184972447840335595586879350012403335749718574814304198079640398507718 * q^87 + 884266222865559755895490832763056324497872985335575213438267918764032 * q^88 + 922002192851420225703931949240660524744080828362964363768621192185298 * q^89 - 773107974305929069152539888281824938594397222395836929970148461044240 * q^90 - 8079212959404027614418440109956770906886889649154860574373249888569776 * q^91 - 13670577861982746620628593404236014523694130242253442181460174526039552 * q^92 + 3729915385955429492528971192901332630862445897595761204245366555215488 * q^93 - 13436976700690544599208201928250305890032773609106302404839902759345024 * q^94 - 61508953507577523131201535405733284550943470497632040479599939746271320 * q^95 - 32007986513182294493504227608086345487918910401219597611766423881416704 * q^96 - 149876371240369823947413564997445008107894647331408877752554402308756310 * q^97 - 164242038075013607742967230335294726637154516016956449921881670478527288 * q^98 + 3399022187132399007137561865025534669344410724594880911844979606234388 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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