LMFDB - Embedded newform 3.72.a.a.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3,72,Mod(1,3)]

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

lf = mfeigenbasis(mf)

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")

//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);

Level:	$ N $	$=$	$ 3 $
Weight:	$ k $	$=$	$ 72 $
Character orbit:	$[\chi]$	$=$	3.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:	$95.7738481683$
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			1.4
Root			$-1.95252e9$ 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)

$f(q)$	$=$	$q+4.18503e10 q^{2} +5.00315e16 q^{3} -6.09737e20 q^{4} +3.60424e24 q^{5} +2.09383e27 q^{6} -2.88017e29 q^{7} -1.24334e32 q^{8} +2.50316e33 q^{9} +O(q^{10})$	\(q+4.18503e10 q^{2} +5.00315e16 q^{3} -6.09737e20 q^{4} +3.60424e24 q^{5} +2.09383e27 q^{6} -2.88017e29 q^{7} -1.24334e32 q^{8} +2.50316e33 q^{9} +1.50838e35 q^{10} -5.61398e36 q^{11} -3.05061e37 q^{12} +6.27691e39 q^{13} -1.20536e40 q^{14} +1.80326e41 q^{15} -3.76371e42 q^{16} -3.37490e43 q^{17} +1.04758e44 q^{18} -1.62566e45 q^{19} -2.19764e45 q^{20} -1.44099e46 q^{21} -2.34947e47 q^{22} +2.44863e48 q^{23} -6.22061e48 q^{24} -2.93611e49 q^{25} +2.62690e50 q^{26} +1.25237e50 q^{27} +1.75615e50 q^{28} -7.51765e51 q^{29} +7.54668e51 q^{30} -8.42126e52 q^{31} +1.36063e53 q^{32} -2.80876e53 q^{33} -1.41240e54 q^{34} -1.03808e54 q^{35} -1.52627e54 q^{36} -3.32996e55 q^{37} -6.80344e55 q^{38} +3.14044e56 q^{39} -4.48129e56 q^{40} +1.15174e57 q^{41} -6.03059e56 q^{42} -5.54624e57 q^{43} +3.42305e57 q^{44} +9.02197e57 q^{45} +1.02476e59 q^{46} -3.31405e59 q^{47} -1.88304e59 q^{48} -9.21572e59 q^{49} -1.22877e60 q^{50} -1.68851e60 q^{51} -3.82727e60 q^{52} -1.27195e61 q^{53} +5.24119e60 q^{54} -2.02341e61 q^{55} +3.58102e61 q^{56} -8.13344e61 q^{57} -3.14616e62 q^{58} -2.69101e62 q^{59} -1.09951e62 q^{60} +3.49397e63 q^{61} -3.52432e63 q^{62} -7.20951e62 q^{63} +1.45811e64 q^{64} +2.26235e64 q^{65} -1.17547e64 q^{66} +1.08655e64 q^{67} +2.05780e64 q^{68} +1.22509e65 q^{69} -4.34440e64 q^{70} -3.78830e65 q^{71} -3.11227e65 q^{72} -9.02098e65 q^{73} -1.39360e66 q^{74} -1.46898e66 q^{75} +9.91227e65 q^{76} +1.61692e66 q^{77} +1.31428e67 q^{78} -1.18442e67 q^{79} -1.35653e67 q^{80} +6.26579e66 q^{81} +4.82008e67 q^{82} +9.45075e67 q^{83} +8.78627e66 q^{84} -1.21639e68 q^{85} -2.32112e68 q^{86} -3.76120e68 q^{87} +6.98007e68 q^{88} -1.49773e69 q^{89} +3.77572e68 q^{90} -1.80786e69 q^{91} -1.49302e69 q^{92} -4.21328e69 q^{93} -1.38694e70 q^{94} -5.85927e69 q^{95} +6.80744e69 q^{96} -2.78454e70 q^{97} -3.85680e70 q^{98} -1.40527e70 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q - 25051277688 q^{2} + 25\!\cdots\!35 q^{3}+ \cdots + 12\!\cdots\!45 q^{9}+O(q^{10}) $ 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	$ 5 q - 25051277688 q^{2} + 25\!\cdots\!35 q^{3}+ \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

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 $

$2$	4.18503e10	0.861259	0.430629	−	0.902529i	$-0.358292\pi$
$2$	4.18503e10	0.861259	0.430629	+	0.902529i	$0.358292\pi$
$3$	5.00315e16	0.577350
$3$	5.00315e16	0.577350
$4$	−6.09737e20	−0.258234
$5$	3.60424e24	0.553832	0.276916	−	0.960894i	$-0.410688\pi$
$5$	3.60424e24	0.553832	0.276916	+	0.960894i	$0.410688\pi$
$6$	2.09383e27	0.497248
$7$	−2.88017e29	−0.287367	−0.143684	−	0.989624i	$-0.545895\pi$
$7$	−2.88017e29	−0.287367	−0.143684	+	0.989624i	$0.545895\pi$
$8$	−1.24334e32	−1.08366
$9$	2.50316e33	0.333333
$10$	1.50838e35	0.476993
$11$	−5.61398e36	−0.602324	−0.301162	−	0.953573i	$-0.597375\pi$
$11$	−5.61398e36	−0.602324	−0.301162	+	0.953573i	$0.597375\pi$
$12$	−3.05061e37	−0.149091
$13$	6.27691e39	1.78960	0.894802	−	0.446463i	$-0.147317\pi$
$13$	6.27691e39	1.78960	0.894802	+	0.446463i	$0.147317\pi$
$14$	−1.20536e40	−0.247498
$15$	1.80326e41	0.319755
$16$	−3.76371e42	−0.675082
$17$	−3.37490e43	−0.703597	−0.351798	−	0.936076i	$-0.614430\pi$
$17$	−3.37490e43	−0.703597	−0.351798	+	0.936076i	$0.614430\pi$
$18$	1.04758e44	0.287086
$19$	−1.62566e45	−0.653548	−0.326774	−	0.945103i	$-0.605962\pi$
$19$	−1.62566e45	−0.653548	−0.326774	+	0.945103i	$0.605962\pi$
$20$	−2.19764e45	−0.143018
$21$	−1.44099e46	−0.165912
$22$	−2.34947e47	−0.518757
$23$	2.44863e48	1.11580	0.557899	−	0.829909i	$-0.311608\pi$
$23$	2.44863e48	1.11580	0.557899	+	0.829909i	$0.311608\pi$
$24$	−6.22061e48	−0.625654
$25$	−2.93611e49	−0.693270
$26$	2.62690e50	1.54131
$27$	1.25237e50	0.192450
$28$	1.75615e50	0.0742079
$29$	−7.51765e51	−0.914015	−0.457007	−	0.889463i	$-0.651079\pi$
$29$	−7.51765e51	−0.914015	−0.457007	+	0.889463i	$0.651079\pi$
$30$	7.54668e51	0.275392
$31$	−8.42126e52	−0.959482	−0.479741	−	0.877410i	$-0.659269\pi$
$31$	−8.42126e52	−0.959482	−0.479741	+	0.877410i	$0.659269\pi$
$32$	1.36063e53	0.502245
$33$	−2.80876e53	−0.347752
$34$	−1.41240e54	−0.605979
$35$	−1.03808e54	−0.159153
$36$	−1.52627e54	−0.0860779
$37$	−3.32996e55	−0.710031	−0.355016	−	0.934860i	$-0.615524\pi$
$37$	−3.32996e55	−0.710031	−0.355016	+	0.934860i	$0.615524\pi$
$38$	−6.80344e55	−0.562874
$39$	3.14044e56	1.03323
$40$	−4.48129e56	−0.600168
$41$	1.15174e57	0.641991	0.320995	−	0.947081i	$-0.395983\pi$
$41$	1.15174e57	0.641991	0.320995	+	0.947081i	$0.395983\pi$
$42$	−6.03059e56	−0.142893
$43$	−5.54624e57	−0.569991	−0.284996	−	0.958529i	$-0.591992\pi$
$43$	−5.54624e57	−0.569991	−0.284996	+	0.958529i	$0.591992\pi$
$44$	3.42305e57	0.155540
$45$	9.02197e57	0.184611
$46$	1.02476e59	0.960991
$47$	−3.31405e59	−1.44839	−0.724193	−	0.689597i	$-0.757788\pi$
$47$	−3.31405e59	−1.44839	−0.724193	+	0.689597i	$0.757788\pi$
$48$	−1.88304e59	−0.389759
$49$	−9.21572e59	−0.917420
$50$	−1.22877e60	−0.597084
$51$	−1.68851e60	−0.406222
$52$	−3.82727e60	−0.462136
$53$	−1.27195e61	−0.781049	−0.390524	−	0.920593i	$-0.627706\pi$
$53$	−1.27195e61	−0.781049	−0.390524	+	0.920593i	$0.627706\pi$
$54$	5.24119e60	0.165749
$55$	−2.02341e61	−0.333587
$56$	3.58102e61	0.311410
$57$	−8.13344e61	−0.377326
$58$	−3.14616e62	−0.787203
$59$	−2.69101e62	−0.367002	−0.183501	−	0.983020i	$-0.558743\pi$
$59$	−2.69101e62	−0.367002	−0.183501	+	0.983020i	$0.558743\pi$
$60$	−1.09951e62	−0.0825716
$61$	3.49397e63	1.45918	0.729591	−	0.683884i	$-0.239710\pi$
$61$	3.49397e63	1.45918	0.729591	+	0.683884i	$0.239710\pi$
$62$	−3.52432e63	−0.826362
$63$	−7.20951e62	−0.0957891
$64$	1.45811e64	1.10764
$65$	2.26235e64	0.991141
$66$	−1.17547e64	−0.299504
$67$	1.08655e64	0.162328	0.0811641	−	0.996701i	$-0.474136\pi$
$67$	1.08655e64	0.162328	0.0811641	+	0.996701i	$0.474136\pi$
$68$	2.05780e64	0.181692
$69$	1.22509e65	0.644207
$70$	−4.34440e64	−0.137072
$71$	−3.78830e65	−0.722393	−0.361196	−	0.932490i	$-0.617632\pi$
$71$	−3.78830e65	−0.722393	−0.361196	+	0.932490i	$0.617632\pi$
$72$	−3.11227e65	−0.361222
$73$	−9.02098e65	−0.641641	−0.320820	−	0.947140i	$-0.603959\pi$
$73$	−9.02098e65	−0.641641	−0.320820	+	0.947140i	$0.603959\pi$
$74$	−1.39360e66	−0.611520
$75$	−1.46898e66	−0.400259
$76$	9.91227e65	0.168768
$77$	1.61692e66	0.173088
$78$	1.31428e67	0.889877
$79$	−1.18442e67	−0.510203	−0.255102	−	0.966914i	$-0.582109\pi$
$79$	−1.18442e67	−0.510203	−0.255102	+	0.966914i	$0.582109\pi$
$80$	−1.35653e67	−0.373882
$81$	6.26579e66	0.111111
$82$	4.82008e67	0.552920
$83$	9.45075e67	0.705008	0.352504	−	0.935810i	$-0.385330\pi$
$83$	9.45075e67	0.705008	0.352504	+	0.935810i	$0.385330\pi$
$84$	8.78627e66	0.0428440
$85$	−1.21639e68	−0.389675
$86$	−2.32112e68	−0.490910
$87$	−3.76120e68	−0.527707
$88$	6.98007e68	0.652717
$89$	−1.49773e69	−0.937750	−0.468875	−	0.883265i	$-0.655341\pi$
$89$	−1.49773e69	−0.937750	−0.468875	+	0.883265i	$0.655341\pi$
$90$	3.77572e68	0.158998
$91$	−1.80786e69	−0.514274
$92$	−1.49302e69	−0.288137
$93$	−4.21328e69	−0.553957
$94$	−1.38694e70	−1.24744
$95$	−5.85927e69	−0.361956
$96$	6.80744e69	0.289971
$97$	−2.78454e70	−0.821027	−0.410513	−	0.911855i	$-0.634650\pi$
$97$	−2.78454e70	−0.821027	−0.410513	+	0.911855i	$0.634650\pi$
$98$	−3.85680e70	−0.790136
$99$	−1.40527e70	−0.200775
$100$	1.79026e70	0.179026
$101$	1.66688e71	1.17083	0.585416	−	0.810733i	$-0.300931\pi$
$101$	1.66688e71	1.17083	0.585416	+	0.810733i	$0.300931\pi$
$102$	−7.06648e70	−0.349862
$103$	−2.86116e71	−1.00189	−0.500946	−	0.865478i	$-0.667015\pi$
$103$	−2.86116e71	−1.00189	−0.500946	+	0.865478i	$0.667015\pi$
$104$	−7.80433e71	−1.93933
$105$	−5.19368e70	−0.0918872
$106$	−5.32316e71	−0.672685
$107$	−1.57777e72	−1.42863	−0.714314	−	0.699825i	$-0.753261\pi$
$107$	−1.57777e72	−1.42863	−0.714314	+	0.699825i	$0.753261\pi$
$108$	−7.63615e70	−0.0496971
$109$	−3.56670e72	−1.67350	−0.836750	−	0.547585i	$-0.815547\pi$
$109$	−3.56670e72	−1.67350	−0.836750	+	0.547585i	$0.815547\pi$
$110$	−8.46803e71	−0.287304
$111$	−1.66603e72	−0.409937
$112$	1.08401e72	0.193996
$113$	−8.31344e72	−1.08517	−0.542583	−	0.840002i	$-0.682554\pi$
$113$	−8.31344e72	−1.08517	−0.542583	+	0.840002i	$0.682554\pi$
$114$	−3.40387e72	−0.324975
$115$	8.82546e72	0.617965
$116$	4.58379e72	0.236029
$117$	1.57121e73	0.596535
$118$	−1.12619e73	−0.316083
$119$	9.72027e72	0.202191
$120$	−2.24206e73	−0.346507
$121$	−5.53554e73	−0.637206
$122$	1.46223e74	1.25673
$123$	5.76235e73	0.370653
$124$	5.13475e73	0.247771
$125$	−2.58470e74	−0.937788
$126$	−3.01720e73	−0.0824992
$127$	7.22731e74	1.49260	0.746302	−	0.665608i	$-0.231828\pi$
$127$	7.22731e74	1.49260	0.746302	+	0.665608i	$0.231828\pi$
$128$	2.88952e74	0.451723
$129$	−2.77487e74	−0.329085
$130$	9.46799e74	0.853628
$131$	1.91321e75	1.31411	0.657056	−	0.753842i	$-0.271801\pi$
$131$	1.91321e75	1.31411	0.657056	+	0.753842i	$0.271801\pi$
$132$	1.71261e74	0.0898013
$133$	4.68218e74	0.187808
$134$	4.54724e74	0.139807
$135$	4.51383e74	0.106585
$136$	4.19614e75	0.762463
$137$	−3.09929e75	−0.434192	−0.217096	−	0.976150i	$-0.569658\pi$
$137$	−3.09929e75	−0.434192	−0.217096	+	0.976150i	$0.569658\pi$
$138$	5.12703e75	0.554828
$139$	6.45255e75	0.540388	0.270194	−	0.962806i	$-0.412912\pi$
$139$	6.45255e75	0.540388	0.270194	+	0.962806i	$0.412912\pi$
$140$	6.32957e74	0.0410988
$141$	−1.65807e76	−0.836226
$142$	−1.58542e76	−0.622167
$143$	−3.52384e76	−1.07792
$144$	−9.42114e75	−0.225027
$145$	−2.70954e76	−0.506211
$146$	−3.77530e76	−0.552619
$147$	−4.61076e76	−0.529673
$148$	2.03040e76	0.183354
$149$	−1.90351e77	−1.35345	−0.676725	−	0.736236i	$-0.736601\pi$
$149$	−1.90351e77	−1.35345	−0.676725	+	0.736236i	$0.736601\pi$
$150$	−6.14773e76	−0.344727
$151$	1.44929e77	0.641908	0.320954	−	0.947095i	$-0.395997\pi$
$151$	1.44929e77	0.641908	0.320954	+	0.947095i	$0.395997\pi$
$152$	2.02125e77	0.708227
$153$	−8.44789e76	−0.234532
$154$	6.76685e76	0.149074
$155$	−3.03522e77	−0.531392
$156$	−1.91484e77	−0.266814
$157$	1.38149e78	1.53430	0.767152	−	0.641465i	$-0.221673\pi$
$157$	1.38149e78	1.53430	0.767152	+	0.641465i	$0.221673\pi$
$158$	−4.95682e77	−0.439417
$159$	−6.36378e77	−0.450939
$160$	4.90403e77	0.278159
$161$	−7.05248e77	−0.320644
$162$	2.62225e77	0.0956954
$163$	8.24445e77	0.241825	0.120913	−	0.992663i	$-0.461418\pi$
$163$	8.24445e77	0.241825	0.120913	+	0.992663i	$0.461418\pi$
$164$	−7.02261e77	−0.165784
$165$	−1.01234e78	−0.192596
$166$	3.95516e78	0.607194
$167$	1.25264e79	1.55379	0.776894	−	0.629631i	$-0.216794\pi$
$167$	1.25264e79	1.55379	0.776894	+	0.629631i	$0.216794\pi$
$168$	1.79164e78	0.179792
$169$	2.70975e79	2.20268
$170$	−5.09064e78	−0.335611
$171$	−4.06928e78	−0.217849
$172$	3.38175e78	0.147191
$173$	−2.09442e79	−0.742039	−0.371019	−	0.928625i	$-0.620992\pi$
$173$	−2.09442e79	−0.742039	−0.371019	+	0.928625i	$0.620992\pi$
$174$	−1.57407e79	−0.454492
$175$	8.45649e78	0.199223
$176$	2.11294e79	0.406618
$177$	−1.34635e79	−0.211889
$178$	−6.26802e79	−0.807645
$179$	−5.32029e79	−0.561892	−0.280946	−	0.959724i	$-0.590648\pi$
$179$	−5.32029e79	−0.561892	−0.280946	+	0.959724i	$0.590648\pi$
$180$	−5.50103e78	−0.0476727
$181$	−1.79961e80	−1.28112	−0.640560	−	0.767908i	$-0.721298\pi$
$181$	−1.79961e80	−1.28112	−0.640560	+	0.767908i	$0.721298\pi$
$182$	−7.56593e79	−0.442923
$183$	1.74808e80	0.842459
$184$	−3.04448e80	−1.20915
$185$	−1.20020e80	−0.393238
$186$	−1.76327e80	−0.477100
$187$	1.89466e80	0.423793
$188$	2.02070e80	0.374022
$189$	−3.60703e79	−0.0553039
$190$	−2.45212e80	−0.311738
$191$	5.21941e80	0.550728	0.275364	−	0.961340i	$-0.411202\pi$
$191$	5.21941e80	0.550728	0.275364	+	0.961340i	$0.411202\pi$
$192$	7.29513e80	0.639499
$193$	2.72577e80	0.198703	0.0993514	−	0.995052i	$-0.468323\pi$
$193$	2.72577e80	0.198703	0.0993514	+	0.995052i	$0.468323\pi$
$194$	−1.16534e81	−0.707116
$195$	1.13189e81	0.572235
$196$	5.61916e80	0.236909
$197$	4.71812e81	1.66042	0.830209	−	0.557452i	$-0.188221\pi$
$197$	4.71812e81	1.66042	0.830209	+	0.557452i	$0.188221\pi$
$198$	−5.88108e80	−0.172919
$199$	−6.76907e81	−1.66435	−0.832175	−	0.554513i	$-0.812905\pi$
$199$	−6.76907e81	−1.66435	−0.832175	+	0.554513i	$0.812905\pi$
$200$	3.65058e81	0.751272
$201$	5.43618e80	0.0937203
$202$	6.97593e81	1.00839
$203$	2.16521e81	0.262658
$204$	1.02955e81	0.104900
$205$	4.15116e81	0.355555
$206$	−1.19740e82	−0.862889
$207$	6.12931e81	0.371933
$208$	−2.36244e82	−1.20813
$209$	9.12643e81	0.393648
$210$	−2.17357e81	−0.0791386
$211$	5.60759e82	1.72484	0.862420	−	0.506193i	$-0.168948\pi$
$211$	5.60759e82	1.72484	0.862420	+	0.506193i	$0.168948\pi$
$212$	7.75558e81	0.201693
$213$	−1.89535e82	−0.417074
$214$	−6.60301e82	−1.23042
$215$	−1.99900e82	−0.315680
$216$	−1.55712e82	−0.208551
$217$	2.42546e82	0.275724
$218$	−1.49267e83	−1.44132
$219$	−4.51333e82	−0.370451
$220$	1.23375e82	0.0861433
$221$	−2.11839e83	−1.25916
$222$	−6.97238e82	−0.353061
$223$	1.59979e83	0.690622	0.345311	−	0.938488i	$-0.387773\pi$
$223$	1.59979e83	0.690622	0.345311	+	0.938488i	$0.387773\pi$
$224$	−3.91884e82	−0.144329
$225$	−7.34954e82	−0.231090
$226$	−3.47920e83	−0.934608
$227$	5.86027e83	1.34586	0.672929	−	0.739707i	$-0.265036\pi$
$227$	5.86027e83	1.34586	0.672929	+	0.739707i	$0.265036\pi$
$228$	4.95926e82	0.0974383
$229$	9.19975e83	1.54745	0.773724	−	0.633522i	$-0.218392\pi$
$229$	9.19975e83	1.54745	0.773724	+	0.633522i	$0.218392\pi$
$230$	3.69348e83	0.532228
$231$	8.08970e82	0.0999325
$232$	9.34698e83	0.990485
$233$	4.87947e83	0.443851	0.221926	−	0.975064i	$-0.428766\pi$
$233$	4.87947e83	0.443851	0.221926	+	0.975064i	$0.428766\pi$
$234$	6.57555e83	0.513771
$235$	−1.19446e84	−0.802163
$236$	1.64081e83	0.0947722
$237$	−5.92583e83	−0.294566
$238$	4.06796e83	0.174138
$239$	8.23919e83	0.303920	0.151960	−	0.988387i	$-0.451442\pi$
$239$	8.23919e83	0.303920	0.151960	+	0.988387i	$0.451442\pi$
$240$	−6.78692e83	−0.215861
$241$	6.22022e83	0.170687	0.0853435	−	0.996352i	$-0.472801\pi$
$241$	6.22022e83	0.170687	0.0853435	+	0.996352i	$0.472801\pi$
$242$	−2.31664e84	−0.548799
$243$	3.13487e83	0.0641500
$244$	−2.13040e84	−0.376810
$245$	−3.32156e84	−0.508097
$246$	2.41156e84	0.319228
$247$	−1.02041e85	−1.16959
$248$	1.04705e85	1.03976
$249$	4.72835e84	0.407036
$250$	−1.08170e85	−0.807677
$251$	−7.44660e84	−0.482549	−0.241274	−	0.970457i	$-0.577565\pi$
$251$	−7.44660e84	−0.482549	−0.241274	+	0.970457i	$0.577565\pi$
$252$	4.39590e83	0.0247360
$253$	−1.37466e85	−0.672072
$254$	3.02465e85	1.28552
$255$	−6.08580e84	−0.224979
$256$	−2.23358e85	−0.718594
$257$	−3.55460e85	−0.995784	−0.497892	−	0.867239i	$-0.665892\pi$
$257$	−3.55460e85	−0.995784	−0.497892	+	0.867239i	$0.665892\pi$
$258$	−1.16129e85	−0.283427
$259$	9.59083e84	0.204040
$260$	−1.37944e85	−0.255946
$261$	−1.88178e85	−0.304672
$262$	8.00685e85	1.13179
$263$	8.15900e85	1.00741	0.503707	−	0.863875i	$-0.331969\pi$
$263$	8.15900e85	1.00741	0.503707	+	0.863875i	$0.331969\pi$
$264$	3.49224e85	0.376847
$265$	−4.58442e85	−0.432570
$266$	1.95950e85	0.161751
$267$	−7.49335e85	−0.541410
$268$	−6.62510e84	−0.0419186
$269$	4.54114e85	0.251744	0.125872	−	0.992047i	$-0.459827\pi$
$269$	4.54114e85	0.251744	0.125872	+	0.992047i	$0.459827\pi$
$270$	1.88905e85	0.0917973
$271$	4.10752e86	1.75053	0.875265	−	0.483643i	$-0.160687\pi$
$271$	4.10752e86	1.75053	0.875265	+	0.483643i	$0.160687\pi$
$272$	1.27021e86	0.474985
$273$	−9.04498e85	−0.296916
$274$	−1.29706e86	−0.373951
$275$	1.64833e86	0.417573
$276$	−7.46983e85	−0.166356
$277$	4.24433e86	0.831338	0.415669	−	0.909516i	$-0.363547\pi$
$277$	4.24433e86	0.831338	0.415669	+	0.909516i	$0.363547\pi$
$278$	2.70041e86	0.465414
$279$	−2.10797e86	−0.319827
$280$	1.29069e86	0.172469
$281$	−2.05094e86	−0.241478	−0.120739	−	0.992684i	$-0.538526\pi$
$281$	−2.05094e86	−0.241478	−0.120739	+	0.992684i	$0.538526\pi$
$282$	−6.93906e86	−0.720207
$283$	−1.99962e87	−1.83033	−0.915164	−	0.403083i	$-0.867939\pi$
$283$	−1.99962e87	−1.83033	−0.915164	+	0.403083i	$0.867939\pi$
$284$	2.30987e86	0.186546
$285$	−2.93148e86	−0.208975
$286$	−1.47474e87	−0.928369
$287$	−3.31721e86	−0.184487
$288$	3.40587e86	0.167415
$289$	−1.16178e87	−0.504951
$290$	−1.13395e87	−0.435978
$291$	−1.39315e87	−0.474020
$292$	5.50042e86	0.165693
$293$	5.05428e87	1.34852	0.674262	−	0.738492i	$-0.264462\pi$
$293$	5.05428e87	1.34852	0.674262	+	0.738492i	$0.264462\pi$
$294$	−1.92962e87	−0.456185
$295$	−9.69902e86	−0.203257
$296$	4.14026e87	0.769435
$297$	−7.03076e86	−0.115917
$298$	−7.96623e87	−1.16567
$299$	1.53699e88	1.99684
$300$	8.95693e86	0.103361
$301$	1.59741e87	0.163797
$302$	6.06530e87	0.552848
$303$	8.33964e87	0.675981
$304$	6.11851e87	0.441198
$305$	1.25931e88	0.808142
$306$	−3.53547e87	−0.201993
$307$	−3.14487e88	−1.60026	−0.800130	−	0.599827i	$-0.795236\pi$
$307$	−3.14487e88	−1.60026	−0.800130	+	0.599827i	$0.795236\pi$
$308$	−9.85896e86	−0.0446972
$309$	−1.43148e88	−0.578443
$310$	−1.27025e88	−0.457666
$311$	4.90236e88	1.57547	0.787737	−	0.616012i	$-0.211253\pi$
$311$	4.90236e88	1.57547	0.787737	+	0.616012i	$0.211253\pi$
$312$	−3.90462e88	−1.11967
$313$	1.68400e87	0.0431040	0.0215520	−	0.999768i	$-0.493139\pi$
$313$	1.68400e87	0.0431040	0.0215520	+	0.999768i	$0.493139\pi$
$314$	5.78159e88	1.32143
$315$	−2.59848e87	−0.0530511
$316$	7.22184e87	0.131752
$317$	−4.92873e88	−0.803769	−0.401885	−	0.915690i	$-0.631645\pi$
$317$	−4.92873e88	−0.803769	−0.401885	+	0.915690i	$0.631645\pi$
$318$	−2.66326e88	−0.388375
$319$	4.22039e88	0.550533
$320$	5.25536e88	0.613449
$321$	−7.89382e88	−0.824819
$322$	−2.95148e88	−0.276157
$323$	5.48644e88	0.459834
$324$	−3.82048e87	−0.0286926
$325$	−1.84297e89	−1.24068
$326$	3.45033e88	0.208274
$327$	−1.78447e89	−0.966196
$328$	−1.43201e89	−0.695703
$329$	9.54500e88	0.416219
$330$	−4.23669e88	−0.165875
$331$	−2.21455e89	−0.778737	−0.389368	−	0.921082i	$-0.627307\pi$
$331$	−2.21455e89	−0.778737	−0.389368	+	0.921082i	$0.627307\pi$
$332$	−5.76247e88	−0.182057
$333$	−8.33540e88	−0.236677
$334$	5.24234e89	1.33821
$335$	3.91618e88	0.0899026
$336$	5.42347e88	0.112004
$337$	−1.35287e89	−0.251416	−0.125708	−	0.992067i	$-0.540120\pi$
$337$	−1.35287e89	−0.251416	−0.125708	+	0.992067i	$0.540120\pi$
$338$	1.13404e90	1.89708
$339$	−4.15934e89	−0.626521
$340$	7.41680e88	0.100627
$341$	4.72767e89	0.577919
$342$	−1.70301e89	−0.187625
$343$	5.54748e89	0.551004
$344$	6.89585e89	0.617679
$345$	4.41551e89	0.356782
$346$	−8.76519e89	−0.639087
$347$	2.21712e90	1.45913	0.729564	−	0.683912i	$-0.239723\pi$
$347$	2.21712e90	1.45913	0.729564	+	0.683912i	$0.239723\pi$
$348$	2.29334e89	0.136272
$349$	−1.51931e90	−0.815350	−0.407675	−	0.913127i	$-0.633660\pi$
$349$	−1.51931e90	−0.815350	−0.407675	+	0.913127i	$0.633660\pi$
$350$	3.53907e89	0.171583
$351$	7.86100e89	0.344409
$352$	−7.63854e89	−0.302514
$353$	−3.24038e90	−1.16036	−0.580182	−	0.814487i	$-0.697018\pi$
$353$	−3.24038e90	−1.16036	−0.580182	+	0.814487i	$0.697018\pi$
$354$	−5.63452e89	−0.182491
$355$	−1.36539e90	−0.400084
$356$	9.13219e89	0.242159
$357$	4.86320e89	0.116735
$358$	−2.22656e90	−0.483934
$359$	−3.09344e89	−0.0608960	−0.0304480	−	0.999536i	$-0.509693\pi$
$359$	−3.09344e89	−0.0608960	−0.0304480	+	0.999536i	$0.509693\pi$
$360$	−1.12174e90	−0.200056
$361$	−3.54459e90	−0.572875
$362$	−7.53144e90	−1.10338
$363$	−2.76952e90	−0.367891
$364$	1.10232e90	0.132803
$365$	−3.25137e90	−0.355361
$366$	7.31578e90	0.725575
$367$	5.53062e90	0.497884	0.248942	−	0.968518i	$-0.419917\pi$
$367$	5.53062e90	0.497884	0.248942	+	0.968518i	$0.419917\pi$
$368$	−9.21594e90	−0.753255
$369$	2.88299e90	0.213997
$370$	−5.02285e90	−0.338680
$371$	3.66344e90	0.224448
$372$	2.56900e90	0.143050
$373$	3.70854e91	1.87732	0.938662	−	0.344838i	$-0.112066\pi$
$373$	3.70854e91	1.87732	0.938662	+	0.344838i	$0.112066\pi$
$374$	7.92920e90	0.364996
$375$	−1.29316e91	−0.541432
$376$	4.12048e91	1.56957
$377$	−4.71876e91	−1.63572
$378$	−1.50955e90	−0.0476309
$379$	−3.67269e90	−0.105510	−0.0527549	−	0.998607i	$-0.516800\pi$
$379$	−3.67269e90	−0.105510	−0.0527549	+	0.998607i	$0.516800\pi$
$380$	3.57262e90	0.0934692
$381$	3.61593e91	0.861755
$382$	2.18434e91	0.474319
$383$	−2.53155e91	−0.500992	−0.250496	−	0.968118i	$-0.580594\pi$
$383$	−2.53155e91	−0.500992	−0.250496	+	0.968118i	$0.580594\pi$
$384$	1.44567e91	0.260803
$385$	5.82776e90	0.0958619
$386$	1.14074e91	0.171135
$387$	−1.38831e91	−0.189997
$388$	1.69784e91	0.212017
$389$	−1.64757e92	−1.87773	−0.938866	−	0.344284i	$-0.888122\pi$
$389$	−1.64757e92	−1.87773	−0.938866	+	0.344284i	$0.888122\pi$
$390$	4.73698e91	0.492843
$391$	−8.26389e91	−0.785072
$392$	1.14583e92	0.994176
$393$	9.57210e91	0.758703
$394$	1.97455e92	1.43005
$395$	−4.26892e91	−0.282567
$396$	8.56843e90	0.0518468
$397$	−3.68895e91	−0.204099	−0.102049	−	0.994779i	$-0.532540\pi$
$397$	−3.68895e91	−0.204099	−0.102049	+	0.994779i	$0.532540\pi$
$398$	−2.83288e92	−1.43344
$399$	2.34257e91	0.108431
$400$	1.10507e92	0.468014
$401$	−3.14764e92	−1.22000	−0.610001	−	0.792401i	$-0.708831\pi$
$401$	−3.14764e92	−1.22000	−0.610001	+	0.792401i	$0.708831\pi$
$402$	2.27506e91	0.0807174
$403$	−5.28595e92	−1.71709
$404$	−1.01636e92	−0.302349
$405$	2.25834e91	0.0615369
$406$	9.06146e91	0.226216
$407$	1.86943e92	0.427669
$408$	2.09939e92	0.440208
$409$	−7.79338e92	−1.49813	−0.749063	−	0.662498i	$-0.769496\pi$
$409$	−7.79338e92	−1.49813	−0.749063	+	0.662498i	$0.769496\pi$
$410$	1.73727e92	0.306225
$411$	−1.55062e92	−0.250681
$412$	1.74456e92	0.258722
$413$	7.75055e91	0.105464
$414$	2.56513e92	0.320330
$415$	3.40627e92	0.390456
$416$	8.54055e92	0.898819
$417$	3.22831e92	0.311993
$418$	3.81944e92	0.339032
$419$	−1.24468e93	−1.01499	−0.507493	−	0.861656i	$-0.669428\pi$
$419$	−1.24468e93	−1.01499	−0.507493	+	0.861656i	$0.669428\pi$
$420$	3.16678e91	0.0237284
$421$	2.37051e93	1.63240	0.816201	−	0.577768i	$-0.196076\pi$
$421$	2.37051e93	1.63240	0.816201	+	0.577768i	$0.196076\pi$
$422$	2.34679e93	1.48553
$423$	−8.29557e92	−0.482795
$424$	1.58147e93	0.846395
$425$	9.90908e92	0.487782
$426$	−7.93208e92	−0.359208
$427$	−1.00632e93	−0.419321
$428$	9.62024e92	0.368920
$429$	−1.76303e93	−0.622338
$430$	−8.36585e92	−0.271882
$431$	−2.83378e93	−0.848054	−0.424027	−	0.905650i	$-0.639384\pi$
$431$	−2.83378e93	−0.848054	−0.424027	+	0.905650i	$0.639384\pi$
$432$	−4.71354e92	−0.129920
$433$	−4.31274e93	−1.09505	−0.547524	−	0.836790i	$-0.684430\pi$
$433$	−4.31274e93	−1.09505	−0.547524	+	0.836790i	$0.684430\pi$
$434$	1.01506e93	0.237469
$435$	−1.35562e93	−0.292261
$436$	2.17475e93	0.432154
$437$	−3.98065e93	−0.729228
$438$	−1.88884e93	−0.319055
$439$	−2.01386e93	−0.313717	−0.156858	−	0.987621i	$-0.550137\pi$
$439$	−2.01386e93	−0.313717	−0.156858	+	0.987621i	$0.550137\pi$
$440$	2.51578e93	0.361496
$441$	−2.30684e93	−0.305807
$442$	−8.86554e93	−1.08446
$443$	1.46307e94	1.65170	0.825851	−	0.563888i	$-0.190695\pi$
$443$	1.46307e94	1.65170	0.825851	+	0.563888i	$0.190695\pi$
$444$	1.01584e93	0.105859
$445$	−5.39816e93	−0.519356
$446$	6.69517e93	0.594804
$447$	−9.52354e93	−0.781414
$448$	−4.19959e93	−0.318301
$449$	1.86648e93	0.130701	0.0653503	−	0.997862i	$-0.479184\pi$
$449$	1.86648e93	0.130701	0.0653503	+	0.997862i	$0.479184\pi$
$450$	−3.07580e93	−0.199028
$451$	−6.46586e93	−0.386686
$452$	5.06901e93	0.280226
$453$	7.25100e93	0.370606
$454$	2.45254e94	1.15913
$455$	−6.51594e93	−0.284821
$456$	1.01126e94	0.408895
$457$	−3.36889e94	−1.26027	−0.630133	−	0.776487i	$-0.717000\pi$
$457$	−3.36889e94	−1.26027	−0.630133	+	0.776487i	$0.717000\pi$
$458$	3.85012e94	1.33275
$459$	−4.22661e93	−0.135407
$460$	−5.38121e93	−0.159579
$461$	4.87607e94	1.33871	0.669356	−	0.742942i	$-0.266570\pi$
$461$	4.87607e94	1.33871	0.669356	+	0.742942i	$0.266570\pi$
$462$	3.38556e93	0.0860678
$463$	−7.20350e93	−0.169597	−0.0847985	−	0.996398i	$-0.527025\pi$
$463$	−7.20350e93	−0.169597	−0.0847985	+	0.996398i	$0.527025\pi$
$464$	2.82942e94	0.617034
$465$	−1.51857e94	−0.306799
$466$	2.04207e94	0.382271
$467$	−6.63009e94	−1.15019	−0.575096	−	0.818086i	$-0.695035\pi$
$467$	−6.63009e94	−1.15019	−0.575096	+	0.818086i	$0.695035\pi$
$468$	−9.58024e93	−0.154045
$469$	−3.12945e93	−0.0466478
$470$	−4.99885e94	−0.690870
$471$	6.91183e94	0.885831
$472$	3.34583e94	0.397707
$473$	3.11364e94	0.343320
$474$	−2.47997e94	−0.253697
$475$	4.77312e94	0.453085
$476$	−5.92681e93	−0.0522125
$477$	−3.18390e94	−0.260350
$478$	3.44812e94	0.261753
$479$	−1.25215e95	−0.882563	−0.441281	−	0.897369i	$-0.645476\pi$
$479$	−1.25215e95	−0.882563	−0.441281	+	0.897369i	$0.645476\pi$
$480$	2.45356e94	0.160595
$481$	−2.09018e95	−1.27067
$482$	2.60318e94	0.147006
$483$	−3.52846e94	−0.185124
$484$	3.37523e94	0.164548
$485$	−1.00362e95	−0.454711
$486$	1.31195e94	0.0552498
$487$	3.67021e95	1.43685	0.718427	−	0.695602i	$-0.244862\pi$
$487$	3.67021e95	1.43685	0.718427	+	0.695602i	$0.244862\pi$
$488$	−4.34418e95	−1.58126
$489$	4.12483e94	0.139618
$490$	−1.39008e95	−0.437603
$491$	−4.18498e95	−1.22546	−0.612731	−	0.790291i	$-0.709929\pi$
$491$	−4.18498e95	−1.22546	−0.612731	+	0.790291i	$0.709929\pi$
$492$	−3.51352e94	−0.0957152
$493$	2.53713e95	0.643098
$494$	−4.27046e95	−1.00732
$495$	−5.06491e94	−0.111196
$496$	3.16951e95	0.647729
$497$	1.09109e95	0.207592
$498$	1.97883e95	0.350563
$499$	5.04732e95	0.832705	0.416353	−	0.909203i	$-0.363308\pi$
$499$	5.04732e95	0.832705	0.416353	+	0.909203i	$0.363308\pi$
$500$	1.57599e95	0.242168
$501$	6.26716e95	0.897080
$502$	−3.11642e95	−0.415599
$503$	7.32477e95	0.910187	0.455094	−	0.890444i	$-0.349606\pi$
$503$	7.32477e95	0.910187	0.455094	+	0.890444i	$0.349606\pi$
$504$	8.96386e94	0.103803
$505$	6.00782e95	0.648445
$506$	−5.75298e95	−0.578828
$507$	1.35573e96	1.27172
$508$	−4.40676e95	−0.385441
$509$	2.12176e96	1.73067	0.865335	−	0.501194i	$-0.167106\pi$
$509$	2.12176e96	1.73067	0.865335	+	0.501194i	$0.167106\pi$
$510$	−2.54693e95	−0.193765
$511$	2.59819e95	0.184387
$512$	−1.61703e96	−1.07062
$513$	−2.03593e95	−0.125775
$514$	−1.48761e96	−0.857627
$515$	−1.03123e96	−0.554880
$516$	1.69194e95	0.0849808
$517$	1.86050e96	0.872398
$518$	4.01379e95	0.175731
$519$	−1.04787e96	−0.428416
$520$	−2.81286e96	−1.07406
$521$	−2.84114e96	−1.01333	−0.506667	−	0.862142i	$-0.669123\pi$
$521$	−2.84114e96	−1.01333	−0.506667	+	0.862142i	$0.669123\pi$
$522$	−7.87532e95	−0.262401
$523$	−5.12801e96	−1.59639	−0.798194	−	0.602400i	$-0.794211\pi$
$523$	−5.12801e96	−1.59639	−0.798194	+	0.602400i	$0.794211\pi$
$524$	−1.16656e96	−0.339348
$525$	4.23091e95	0.115021
$526$	3.41457e96	0.867644
$527$	2.84209e96	0.675088
$528$	1.05713e96	0.234761
$529$	1.17992e96	0.245006
$530$	−1.91859e96	−0.372555
$531$	−6.73600e95	−0.122334
$532$	−2.85490e95	−0.0484984
$533$	7.22939e96	1.14891
$534$	−3.13599e96	−0.466294
$535$	−5.68665e96	−0.791220
$536$	−1.35095e96	−0.175909
$537$	−2.66182e96	−0.324409
$538$	1.90048e96	0.216816
$539$	5.17368e96	0.552584
$540$	−2.75225e95	−0.0275239
$541$	1.22282e97	1.14514	0.572569	−	0.819856i	$-0.305947\pi$
$541$	1.22282e97	1.14514	0.572569	+	0.819856i	$0.305947\pi$
$542$	1.71901e97	1.50766
$543$	−9.00375e96	−0.739656
$544$	−4.59198e96	−0.353378
$545$	−1.28552e97	−0.926838
$546$	−3.78535e96	−0.255721
$547$	2.69709e96	0.170744	0.0853721	−	0.996349i	$-0.472792\pi$
$547$	2.69709e96	0.170744	0.0853721	+	0.996349i	$0.472792\pi$
$548$	1.88975e96	0.112123
$549$	8.74594e96	0.486394
$550$	6.89829e96	0.359638
$551$	1.22212e97	0.597352
$552$	−1.52320e97	−0.698104
$553$	3.41132e96	0.146616
$554$	1.77627e97	0.715997
$555$	−6.00476e96	−0.227036
$556$	−3.93436e96	−0.139547
$557$	3.83934e97	1.27761	0.638803	−	0.769370i	$-0.279430\pi$
$557$	3.83934e97	1.27761	0.638803	+	0.769370i	$0.279430\pi$
$558$	−8.82192e96	−0.275454
$559$	−3.48132e97	−1.02006
$560$	3.90703e96	0.107441
$561$	9.47928e96	0.244677
$562$	−8.58323e96	−0.207975
$563$	3.30625e97	0.752122	0.376061	−	0.926595i	$-0.377278\pi$
$563$	3.30625e97	0.752122	0.376061	+	0.926595i	$0.377278\pi$
$564$	1.01099e97	0.215942
$565$	−2.99636e97	−0.601000
$566$	−8.36846e97	−1.57638
$567$	−1.80465e96	−0.0319297
$568$	4.71014e97	0.782831
$569$	1.28106e97	0.200025	0.100013	−	0.994986i	$-0.468112\pi$
$569$	1.28106e97	0.200025	0.100013	+	0.994986i	$0.468112\pi$
$570$	−1.22683e97	−0.179982
$571$	−1.01641e98	−1.40116	−0.700581	−	0.713573i	$-0.747076\pi$
$571$	−1.01641e98	−1.40116	−0.700581	+	0.713573i	$0.747076\pi$
$572$	2.14862e97	0.278356
$573$	2.61135e97	0.317963
$574$	−1.38826e97	−0.158891
$575$	−7.18946e97	−0.773549
$576$	3.64987e97	0.369215
$577$	−1.35029e98	−1.28436	−0.642179	−	0.766554i	$-0.721970\pi$
$577$	−1.35029e98	−1.28436	−0.642179	+	0.766554i	$0.721970\pi$
$578$	−4.86207e97	−0.434894
$579$	1.36374e97	0.114721
$580$	1.65211e97	0.130721
$581$	−2.72197e97	−0.202596
$582$	−5.83037e97	−0.408254
$583$	7.14072e97	0.470444
$584$	1.12161e98	0.695323
$585$	5.66301e97	0.330380
$586$	2.11523e98	1.16143
$587$	−1.01005e98	−0.522021	−0.261011	−	0.965336i	$-0.584056\pi$
$587$	−1.01005e98	−0.522021	−0.261011	+	0.965336i	$0.584056\pi$
$588$	2.81135e97	0.136779
$589$	1.36901e98	0.627067
$590$	−4.05907e97	−0.175057
$591$	2.36055e98	0.958643
$592$	1.25330e98	0.479329
$593$	−2.91757e98	−1.05095	−0.525473	−	0.850810i	$-0.676112\pi$
$593$	−2.91757e98	−1.05095	−0.525473	+	0.850810i	$0.676112\pi$
$594$	−2.94239e97	−0.0998348
$595$	3.50342e97	0.111980
$596$	1.16064e98	0.349506
$597$	−3.38667e98	−0.960913
$598$	6.43233e98	1.71979
$599$	6.91114e96	0.0174140	0.00870698	−	0.999962i	$-0.497228\pi$
$599$	6.91114e96	0.0174140	0.00870698	+	0.999962i	$0.497228\pi$
$600$	1.82644e98	0.433747
$601$	4.25206e98	0.951822	0.475911	−	0.879493i	$-0.342118\pi$
$601$	4.25206e98	0.951822	0.475911	+	0.879493i	$0.342118\pi$
$602$	6.68520e97	0.141071
$603$	2.71980e97	0.0541094
$604$	−8.83684e97	−0.165762
$605$	−1.99514e98	−0.352905
$606$	3.49016e98	0.582194
$607$	−5.97624e98	−0.940221	−0.470110	−	0.882608i	$-0.655786\pi$
$607$	−5.97624e98	−0.940221	−0.470110	+	0.882608i	$0.655786\pi$
$608$	−2.21192e98	−0.328241
$609$	1.08329e98	0.151646
$610$	5.27024e98	0.696019
$611$	−2.08020e99	−2.59204
$612$	5.15100e97	0.0605642
$613$	−1.14599e99	−1.27155	−0.635775	−	0.771874i	$-0.719320\pi$
$613$	−1.14599e99	−1.27155	−0.635775	+	0.771874i	$0.719320\pi$
$614$	−1.31614e99	−1.37824
$615$	2.07689e98	0.205280
$616$	−2.01038e98	−0.187570
$617$	1.63325e99	1.43856	0.719282	−	0.694719i	$-0.244471\pi$
$617$	1.63325e99	1.43856	0.719282	+	0.694719i	$0.244471\pi$
$618$	−5.99080e98	−0.498189
$619$	−1.43959e99	−1.13037	−0.565186	−	0.824964i	$-0.691195\pi$
$619$	−1.43959e99	−1.13037	−0.565186	+	0.824964i	$0.691195\pi$
$620$	1.85069e98	0.137223
$621$	3.06659e98	0.214736
$622$	2.05165e99	1.35689
$623$	4.31370e98	0.269479
$624$	−1.18197e99	−0.697513
$625$	3.11905e98	0.173893
$626$	7.04758e97	0.0371237
$627$	4.56609e98	0.227273
$628$	−8.42348e98	−0.396209
$629$	1.12383e99	0.499576
$630$	−1.08747e98	−0.0456907
$631$	1.45678e99	0.578565	0.289282	−	0.957244i	$-0.406583\pi$
$631$	1.45678e99	0.578565	0.289282	+	0.957244i	$0.406583\pi$
$632$	1.47263e99	0.552889
$633$	2.80556e99	0.995837
$634$	−2.06269e99	−0.692253
$635$	2.60489e99	0.826652
$636$	3.88023e98	0.116448
$637$	−5.78462e99	−1.64182
$638$	1.76625e99	0.474151
$639$	−9.48271e98	−0.240798
$640$	1.04145e99	0.250179
$641$	3.23439e99	0.735077	0.367538	−	0.930008i	$-0.380201\pi$
$641$	3.23439e99	0.735077	0.367538	+	0.930008i	$0.380201\pi$
$642$	−3.30359e99	−0.710382
$643$	−1.39405e99	−0.283653	−0.141826	−	0.989892i	$-0.545298\pi$
$643$	−1.39405e99	−0.283653	−0.141826	+	0.989892i	$0.545298\pi$
$644$	4.30016e98	0.0828011
$645$	−1.00013e99	−0.182258
$646$	2.29609e99	0.396036
$647$	8.52776e99	1.39230	0.696150	−	0.717896i	$-0.254895\pi$
$647$	8.52776e99	1.39230	0.696150	+	0.717896i	$0.254895\pi$
$648$	−7.79050e98	−0.120407
$649$	1.51072e99	0.221054
$650$	−7.71289e99	−1.06854
$651$	1.21350e99	0.159189
$652$	−5.02695e98	−0.0624475
$653$	1.70768e99	0.200903	0.100452	−	0.994942i	$-0.467971\pi$
$653$	1.70768e99	0.200903	0.100452	+	0.994942i	$0.467971\pi$
$654$	−7.46807e99	−0.832144
$655$	6.89568e99	0.727798
$656$	−4.33482e99	−0.433396
$657$	−2.25809e99	−0.213880
$658$	3.99461e99	0.358472
$659$	1.87814e100	1.59696	0.798482	−	0.602019i	$-0.205637\pi$
$659$	1.87814e100	1.59696	0.798482	+	0.602019i	$0.205637\pi$
$660$	6.17264e98	0.0497349
$661$	−2.51964e99	−0.192392	−0.0961960	−	0.995362i	$-0.530668\pi$
$661$	−2.51964e99	−0.192392	−0.0961960	+	0.995362i	$0.530668\pi$
$662$	−9.26793e99	−0.670694
$663$	−1.05986e100	−0.726976
$664$	−1.17505e100	−0.763992
$665$	1.68757e99	0.104014
$666$	−3.48839e99	−0.203840
$667$	−1.84080e100	−1.01986
$668$	−7.63782e99	−0.401241
$669$	8.00400e99	0.398731
$670$	1.63893e99	0.0774294
$671$	−1.96150e100	−0.878901
$672$	−1.96066e99	−0.0833282
$673$	1.50667e100	0.607413	0.303707	−	0.952766i	$-0.401776\pi$
$673$	1.50667e100	0.607413	0.303707	+	0.952766i	$0.401776\pi$
$674$	−5.66178e99	−0.216534
$675$	−3.67709e99	−0.133420
$676$	−1.65224e100	−0.568807
$677$	−3.89120e99	−0.127112	−0.0635560	−	0.997978i	$-0.520244\pi$
$677$	−3.89120e99	−0.127112	−0.0635560	+	0.997978i	$0.520244\pi$
$678$	−1.74070e100	−0.539596
$679$	8.01995e99	0.235936
$680$	1.51239e100	0.422277
$681$	2.93198e100	0.777032
$682$	1.97854e100	0.497738
$683$	5.42209e100	1.29489	0.647443	−	0.762113i	$-0.275838\pi$
$683$	5.42209e100	1.29489	0.647443	+	0.762113i	$0.275838\pi$
$684$	2.48119e99	0.0562560
$685$	−1.11706e100	−0.240469
$686$	2.32164e100	0.474557
$687$	4.60278e100	0.893420
$688$	2.08744e100	0.384791
$689$	−7.98394e100	−1.39777
$690$	1.84791e100	0.307282
$691$	4.80379e99	0.0758776	0.0379388	−	0.999280i	$-0.487921\pi$
$691$	4.80379e99	0.0758776	0.0379388	+	0.999280i	$0.487921\pi$
$692$	1.27704e100	0.191619
$693$	4.04740e99	0.0576961
$694$	9.27872e100	1.25669
$695$	2.32565e100	0.299285
$696$	4.67644e100	0.571857
$697$	−3.88702e100	−0.451703
$698$	−6.35836e100	−0.702227
$699$	2.44128e100	0.256258
$700$	−5.15624e99	−0.0514461
$701$	−5.33306e100	−0.505809	−0.252904	−	0.967491i	$-0.581386\pi$
$701$	−5.33306e100	−0.505809	−0.252904	+	0.967491i	$0.581386\pi$
$702$	3.28985e100	0.296626
$703$	5.41338e100	0.464039
$704$	−8.18578e100	−0.667161
$705$	−5.97607e100	−0.463129
$706$	−1.35611e101	−0.999373
$707$	−4.80089e100	−0.336459
$708$	8.20921e99	0.0547168
$709$	−8.55329e100	−0.542240	−0.271120	−	0.962546i	$-0.587394\pi$
$709$	−8.55329e100	−0.542240	−0.271120	+	0.962546i	$0.587394\pi$
$710$	−5.71422e100	−0.344576
$711$	−2.96478e100	−0.170068
$712$	1.86218e101	1.01621
$713$	−2.06206e101	−1.07059
$714$	2.03526e100	0.100539
$715$	−1.27008e101	−0.596988
$716$	3.24398e100	0.145100
$717$	4.12219e100	0.175468
$718$	−1.29461e100	−0.0524472
$719$	−1.88406e101	−0.726474	−0.363237	−	0.931697i	$-0.618328\pi$
$719$	−1.88406e101	−0.726474	−0.363237	+	0.931697i	$0.618328\pi$
$720$	−3.39560e100	−0.124627
$721$	8.24063e100	0.287911
$722$	−1.48342e101	−0.493394
$723$	3.11207e100	0.0985462
$724$	1.09729e101	0.330829
$725$	2.20727e101	0.633659
$726$	−1.15905e101	−0.316849
$727$	2.73927e101	0.713120	0.356560	−	0.934272i	$-0.383949\pi$
$727$	2.73927e101	0.713120	0.356560	+	0.934272i	$0.383949\pi$
$728$	2.24778e101	0.557300
$729$	1.56842e100	0.0370370
$730$	−1.36071e101	−0.306058
$731$	1.87180e101	0.401044
$732$	−1.06587e101	−0.217551
$733$	6.09866e101	1.18589	0.592944	−	0.805244i	$-0.297966\pi$
$733$	6.09866e101	1.18589	0.592944	+	0.805244i	$0.297966\pi$
$734$	2.31458e101	0.428807
$735$	−1.66183e101	−0.293350
$736$	3.33168e101	0.560404
$737$	−6.09987e100	−0.0977742
$738$	1.20654e101	0.184307
$739$	−2.99677e101	−0.436291	−0.218145	−	0.975916i	$-0.570001\pi$
$739$	−2.99677e101	−0.436291	−0.218145	+	0.975916i	$0.570001\pi$
$740$	7.31804e100	0.101547
$741$	−5.10529e101	−0.675264
$742$	1.53316e101	0.193308
$743$	−3.35033e101	−0.402703	−0.201352	−	0.979519i	$-0.564533\pi$
$743$	−3.35033e101	−0.402703	−0.201352	+	0.979519i	$0.564533\pi$
$744$	5.23854e101	0.600304
$745$	−6.86069e101	−0.749584
$746$	1.55203e102	1.61686
$747$	2.36567e101	0.235003
$748$	−1.15524e101	−0.109438
$749$	4.54424e101	0.410541
$750$	−5.41193e101	−0.466313
$751$	−1.73959e102	−1.42965	−0.714824	−	0.699304i	$-0.753493\pi$
$751$	−1.73959e102	−1.42965	−0.714824	+	0.699304i	$0.753493\pi$
$752$	1.24731e102	0.977779
$753$	−3.72565e101	−0.278600
$754$	−1.97481e102	−1.40878
$755$	5.22357e101	0.355509
$756$	2.19934e100	0.0142813
$757$	−1.01574e102	−0.629331	−0.314666	−	0.949203i	$-0.601892\pi$
$757$	−1.01574e102	−0.629331	−0.314666	+	0.949203i	$0.601892\pi$
$758$	−1.53703e101	−0.0908712
$759$	−6.87762e101	−0.388021
$760$	7.28506e101	0.392239
$761$	1.38910e102	0.713804	0.356902	−	0.934142i	$-0.383833\pi$
$761$	1.38910e102	0.713804	0.356902	+	0.934142i	$0.383833\pi$
$762$	1.51328e102	0.742194
$763$	1.02727e102	0.480909
$764$	−3.18247e101	−0.142217
$765$	−3.04482e101	−0.129892
$766$	−1.05946e102	−0.431483
$767$	−1.68912e102	−0.656788
$768$	−1.11750e102	−0.414880
$769$	−6.89068e100	−0.0244274	−0.0122137	−	0.999925i	$-0.503888\pi$
$769$	−6.89068e100	−0.0244274	−0.0122137	+	0.999925i	$0.503888\pi$
$770$	2.43893e101	0.0825619
$771$	−1.77842e102	−0.574916
$772$	−1.66200e101	−0.0513118
$773$	−2.59844e102	−0.766198	−0.383099	−	0.923707i	$-0.625143\pi$
$773$	−2.59844e102	−0.766198	−0.383099	+	0.923707i	$0.625143\pi$
$774$	−5.81011e101	−0.163637
$775$	2.47257e102	0.665180
$776$	3.46213e102	0.889717
$777$	4.79844e101	0.117802
$778$	−6.89513e102	−1.61721
$779$	−1.87234e102	−0.419572
$780$	−6.90154e101	−0.147770
$781$	2.12674e102	0.435115
$782$	−3.45846e102	−0.676150
$783$	−9.41486e101	−0.175902
$784$	3.46852e102	0.619333
$785$	4.97923e102	0.849747
$786$	4.00595e102	0.653440
$787$	5.10362e102	0.795747	0.397874	−	0.917440i	$-0.369748\pi$
$787$	5.10362e102	0.795747	0.397874	+	0.917440i	$0.369748\pi$
$788$	−2.87681e102	−0.428776
$789$	4.08208e102	0.581631
$790$	−1.78656e102	−0.243363
$791$	2.39441e102	0.311841
$792$	1.74722e102	0.217572
$793$	2.19313e103	2.61136
$794$	−1.54384e102	−0.175782
$795$	−2.29366e102	−0.249744
$796$	4.12735e102	0.429792
$797$	−2.80084e102	−0.278944	−0.139472	−	0.990226i	$-0.544541\pi$
$797$	−2.80084e102	−0.278944	−0.139472	+	0.990226i	$0.544541\pi$
$798$	9.80370e101	0.0933873
$799$	1.11846e103	1.01908
$800$	−3.99496e102	−0.348191
$801$	−3.74904e102	−0.312583
$802$	−1.31730e103	−1.05074
$803$	5.06435e102	0.386476
$804$	−3.31464e101	−0.0242017
$805$	−2.54188e102	−0.177583
$806$	−2.21218e103	−1.47886
$807$	2.27200e102	0.145344
$808$	−2.07249e103	−1.26879
$809$	−1.41795e103	−0.830782	−0.415391	−	0.909643i	$-0.636355\pi$
$809$	−1.41795e103	−0.830782	−0.415391	+	0.909643i	$0.636355\pi$
$810$	9.45121e101	0.0529992
$811$	−1.23533e103	−0.663045	−0.331522	−	0.943447i	$-0.607562\pi$
$811$	−1.23533e103	−0.663045	−0.331522	+	0.943447i	$0.607562\pi$
$812$	−1.32021e102	−0.0678271
$813$	2.05506e103	1.01067
$814$	7.82362e102	0.368333
$815$	2.97150e102	0.133931
$816$	6.35507e102	0.274233
$817$	9.01631e102	0.372517
$818$	−3.26155e103	−1.29027
$819$	−4.52534e102	−0.171425
$820$	−2.53111e102	−0.0918163
$821$	−3.75661e103	−1.30501	−0.652505	−	0.757784i	$-0.726282\pi$
$821$	−3.75661e103	−1.30501	−0.652505	+	0.757784i	$0.726282\pi$
$822$	−6.48939e102	−0.215901
$823$	−2.89356e103	−0.922016	−0.461008	−	0.887396i	$-0.652512\pi$
$823$	−2.89356e103	−0.922016	−0.461008	+	0.887396i	$0.652512\pi$
$824$	3.55739e103	1.08572
$825$	8.24683e102	0.241086
$826$	3.24363e102	0.0908320
$827$	2.75668e103	0.739504	0.369752	−	0.929130i	$-0.379443\pi$
$827$	2.75668e103	0.739504	0.369752	+	0.929130i	$0.379443\pi$
$828$	−3.73727e102	−0.0960456
$829$	−5.01809e103	−1.23553	−0.617764	−	0.786364i	$-0.711961\pi$
$829$	−5.01809e103	−1.23553	−0.617764	+	0.786364i	$0.711961\pi$
$830$	1.42554e103	0.336284
$831$	2.12351e103	0.479973
$832$	9.15241e103	1.98224
$833$	3.11021e103	0.645494
$834$	1.35106e103	0.268707
$835$	4.51482e103	0.860538
$836$	−5.56472e102	−0.101653
$837$	−1.05465e103	−0.184652
$838$	−5.20903e103	−0.874166
$839$	−5.48130e103	−0.881727	−0.440864	−	0.897574i	$-0.645328\pi$
$839$	−5.48130e103	−0.881727	−0.440864	+	0.897574i	$0.645328\pi$
$840$	6.45750e102	0.0995749
$841$	−1.11334e103	−0.164577
$842$	9.92065e103	1.40592
$843$	−1.02612e103	−0.139417
$844$	−3.41916e103	−0.445412
$845$	9.76660e103	1.21992
$846$	−3.47172e103	−0.415812
$847$	1.59433e103	0.183112
$848$	4.78726e103	0.527271
$849$	−1.00044e104	−1.05674
$850$	4.14698e103	0.420107
$851$	−8.15385e103	−0.792252
$852$	1.15566e103	0.107703
$853$	1.50307e103	0.134366	0.0671828	−	0.997741i	$-0.478599\pi$
$853$	1.50307e103	0.134366	0.0671828	+	0.997741i	$0.478599\pi$
$854$	−4.21148e103	−0.361144
$855$	−1.46667e103	−0.120652
$856$	1.96170e104	1.54815
$857$	8.99997e103	0.681431	0.340716	−	0.940166i	$-0.389331\pi$
$857$	8.99997e103	0.681431	0.340716	+	0.940166i	$0.389331\pi$
$858$	−7.37834e103	−0.535994
$859$	−1.31001e104	−0.913097	−0.456549	−	0.889698i	$-0.650915\pi$
$859$	−1.31001e104	−0.913097	−0.456549	+	0.889698i	$0.650915\pi$
$860$	1.21886e103	0.0815191
$861$	−1.65965e103	−0.106514
$862$	−1.18595e104	−0.730394
$863$	−3.68488e103	−0.217791	−0.108896	−	0.994053i	$-0.534731\pi$
$863$	−3.68488e103	−0.217791	−0.108896	+	0.994053i	$0.534731\pi$
$864$	1.70401e103	0.0966571
$865$	−7.54878e103	−0.410965
$866$	−1.80490e104	−0.943120
$867$	−5.81255e103	−0.291534
$868$	−1.47889e103	−0.0712012
$869$	6.64930e103	0.307308
$870$	−5.67333e103	−0.251712
$871$	6.82018e103	0.290503
$872$	4.43461e104	1.81351
$873$	−6.97014e103	−0.273676
$874$	−1.66591e104	−0.628054
$875$	7.44436e103	0.269489
$876$	2.75195e103	0.0956631
$877$	−5.44471e104	−1.81756	−0.908782	−	0.417272i	$-0.862986\pi$
$877$	−5.44471e104	−1.81756	−0.908782	+	0.417272i	$0.862986\pi$
$878$	−8.42805e103	−0.270191
$879$	2.52873e104	0.778571
$880$	7.61552e103	0.225198
$881$	−2.54084e104	−0.721659	−0.360829	−	0.932632i	$-0.617506\pi$
$881$	−2.54084e104	−0.721659	−0.360829	+	0.932632i	$0.617506\pi$
$882$	−9.65418e103	−0.263379
$883$	−7.75414e102	−0.0203202	−0.0101601	−	0.999948i	$-0.503234\pi$
$883$	−7.75414e102	−0.0203202	−0.0101601	+	0.999948i	$0.503234\pi$
$884$	1.29166e104	0.325158
$885$	−4.85257e103	−0.117351
$886$	6.12297e104	1.42254
$887$	−7.86417e103	−0.175535	−0.0877676	−	0.996141i	$-0.527973\pi$
$887$	−7.86417e103	−0.175535	−0.0877676	+	0.996141i	$0.527973\pi$
$888$	2.07144e104	0.444234
$889$	−2.08159e104	−0.428925
$890$	−2.25915e104	−0.447300
$891$	−3.51760e103	−0.0669249
$892$	−9.75451e103	−0.178342
$893$	5.38752e104	0.946590
$894$	−3.98563e104	−0.673000
$895$	−1.91756e104	−0.311194
$896$	−8.32231e103	−0.129810
$897$	7.68978e104	1.15287
$898$	7.81126e103	0.112567
$899$	6.33080e104	0.876980
$900$	4.48129e103	0.0596752
$901$	4.29271e104	0.549543
$902$	−2.70598e104	−0.333037
$903$	7.99208e103	0.0945682
$904$	1.03364e105	1.17596
$905$	−6.48624e104	−0.709526
$906$	3.03457e104	0.319187
$907$	6.00998e104	0.607875	0.303938	−	0.952692i	$-0.401699\pi$
$907$	6.00998e104	0.607875	0.303938	+	0.952692i	$0.401699\pi$
$908$	−3.57322e104	−0.347546
$909$	4.17245e104	0.390278
$910$	−2.72694e104	−0.245305
$911$	5.06333e104	0.438060	0.219030	−	0.975718i	$-0.429711\pi$
$911$	5.06333e104	0.438060	0.219030	+	0.975718i	$0.429711\pi$
$912$	3.06119e104	0.254726
$913$	−5.30563e104	−0.424643
$914$	−1.40989e105	−1.08541
$915$	6.30051e104	0.466581
$916$	−5.60943e104	−0.399603
$917$	−5.51038e104	−0.377633
$918$	−1.76885e104	−0.116621
$919$	−6.53019e104	−0.414214	−0.207107	−	0.978318i	$-0.566405\pi$
$919$	−6.53019e104	−0.414214	−0.207107	+	0.978318i	$0.566405\pi$
$920$	−1.09730e105	−0.669667
$921$	−1.57343e105	−0.923910
$922$	2.04065e105	1.15298
$923$	−2.37788e105	−1.29280
$924$	−4.93259e103	−0.0258060
$925$	9.77712e104	0.492243
$926$	−3.01468e104	−0.146067
$927$	−7.16194e104	−0.333964
$928$	−1.02287e105	−0.459059
$929$	−3.92430e105	−1.69514	−0.847568	−	0.530688i	$-0.821934\pi$
$929$	−3.92430e105	−1.69514	−0.847568	+	0.530688i	$0.821934\pi$
$930$	−6.35525e104	−0.264234
$931$	1.49816e105	0.599578
$932$	−2.97520e104	−0.114617
$933$	2.45273e105	0.909600
$934$	−2.77471e105	−0.990612
$935$	6.82880e104	0.234710
$936$	−1.95354e105	−0.646444
$937$	2.26212e105	0.720709	0.360354	−	0.932815i	$-0.382656\pi$
$937$	2.26212e105	0.720709	0.360354	+	0.932815i	$0.382656\pi$
$938$	−1.30968e104	−0.0401758
$939$	8.42531e103	0.0248861
$940$	7.28307e104	0.207146
$941$	4.92894e105	1.34996	0.674981	−	0.737835i	$-0.264152\pi$
$941$	4.92894e105	1.34996	0.674981	+	0.737835i	$0.264152\pi$
$942$	2.89262e105	0.762929
$943$	2.82020e105	0.716332
$944$	1.01282e105	0.247756
$945$	−1.30006e104	−0.0306291
$946$	1.30307e105	0.295687
$947$	6.20973e105	1.35721	0.678607	−	0.734502i	$-0.262584\pi$
$947$	6.20973e105	1.35721	0.678607	+	0.734502i	$0.262584\pi$
$948$	3.61320e104	0.0760669
$949$	−5.66239e105	−1.14828
$950$	1.99757e105	0.390223
$951$	−2.46592e105	−0.464057
$952$	−1.20856e105	−0.219107
$953$	7.29710e105	1.27454	0.637268	−	0.770642i	$-0.280064\pi$
$953$	7.29710e105	1.27454	0.637268	+	0.770642i	$0.280064\pi$
$954$	−1.33247e105	−0.224228
$955$	1.88120e105	0.305011
$956$	−5.02374e104	−0.0784823
$957$	2.11153e105	0.317850
$958$	−5.24028e105	−0.760115
$959$	8.92646e104	0.124772
$960$	2.62934e105	0.354175
$961$	−6.11605e104	−0.0793946
$962$	−8.74748e105	−1.09438
$963$	−3.94940e105	−0.476209
$964$	−3.79270e104	−0.0440771
$965$	9.82431e104	0.110048
$966$	−1.47667e105	−0.159440
$967$	−6.77106e105	−0.704720	−0.352360	−	0.935865i	$-0.614621\pi$
$967$	−6.77106e105	−0.704720	−0.352360	+	0.935865i	$0.614621\pi$
$968$	6.88255e105	0.690517
$969$	2.74495e105	0.265485
$970$	−4.20016e105	−0.391624
$971$	−7.68162e105	−0.690510	−0.345255	−	0.938509i	$-0.612208\pi$
$971$	−7.68162e105	−0.690510	−0.345255	+	0.938509i	$0.612208\pi$
$972$	−1.91145e104	−0.0165657
$973$	−1.85844e105	−0.155290
$974$	1.53599e106	1.23750
$975$	−9.22067e105	−0.716306
$976$	−1.31503e106	−0.985067
$977$	2.31753e106	1.67405	0.837025	−	0.547164i	$-0.184293\pi$
$977$	2.31753e106	1.67405	0.837025	+	0.547164i	$0.184293\pi$
$978$	1.72625e105	0.120247
$979$	8.40820e105	0.564829
$980$	2.02528e105	0.131208
$981$	−8.92800e105	−0.557833
$982$	−1.75142e106	−1.05544
$983$	−2.57093e106	−1.49431	−0.747153	−	0.664652i	$-0.768580\pi$
$983$	−2.57093e106	−1.49431	−0.747153	+	0.664652i	$0.768580\pi$
$984$	−7.16455e105	−0.401664
$985$	1.70052e106	0.919594
$986$	1.06180e106	0.553873
$987$	4.77551e105	0.240304
$988$	6.22184e105	0.302028
$989$	−1.35807e106	−0.635995
$990$	−2.11968e105	−0.0957681
$991$	6.19251e105	0.269930	0.134965	−	0.990850i	$-0.456908\pi$
$991$	6.19251e105	0.269930	0.134965	+	0.990850i	$0.456908\pi$
$992$	−1.14582e106	−0.481895
$993$	−1.10797e106	−0.449604
$994$	4.56626e105	0.178790
$995$	−2.43973e106	−0.921771
$996$	−2.88305e105	−0.105111
$997$	−2.15469e106	−0.758064	−0.379032	−	0.925384i	$-0.623743\pi$
$997$	−2.15469e106	−0.758064	−0.379032	+	0.925384i	$0.623743\pi$
$998$	2.11232e106	0.717174
$999$	−4.17033e105	−0.136646

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3.72.a.a.1.4	✓	5
3.2	odd	2		9.72.a.a.1.2		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3.72.a.a.1.4	✓	5	1.1	even	1	trivial
9.72.a.a.1.2		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 $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+4.18503e10 q^{2} +5.00315e16 q^{3} -6.09737e20 q^{4} +3.60424e24 q^{5} +2.09383e27 q^{6} -2.88017e29 q^{7} -1.24334e32 q^{8} +2.50316e33 q^{9} +O(q^{10})\)	\(q+4.18503e10 q^{2} +5.00315e16 q^{3} -6.09737e20 q^{4} +3.60424e24 q^{5} +2.09383e27 q^{6} -2.88017e29 q^{7} -1.24334e32 q^{8} +2.50316e33 q^{9} +1.50838e35 q^{10} -5.61398e36 q^{11} -3.05061e37 q^{12} +6.27691e39 q^{13} -1.20536e40 q^{14} +1.80326e41 q^{15} -3.76371e42 q^{16} -3.37490e43 q^{17} +1.04758e44 q^{18} -1.62566e45 q^{19} -2.19764e45 q^{20} -1.44099e46 q^{21} -2.34947e47 q^{22} +2.44863e48 q^{23} -6.22061e48 q^{24} -2.93611e49 q^{25} +2.62690e50 q^{26} +1.25237e50 q^{27} +1.75615e50 q^{28} -7.51765e51 q^{29} +7.54668e51 q^{30} -8.42126e52 q^{31} +1.36063e53 q^{32} -2.80876e53 q^{33} -1.41240e54 q^{34} -1.03808e54 q^{35} -1.52627e54 q^{36} -3.32996e55 q^{37} -6.80344e55 q^{38} +3.14044e56 q^{39} -4.48129e56 q^{40} +1.15174e57 q^{41} -6.03059e56 q^{42} -5.54624e57 q^{43} +3.42305e57 q^{44} +9.02197e57 q^{45} +1.02476e59 q^{46} -3.31405e59 q^{47} -1.88304e59 q^{48} -9.21572e59 q^{49} -1.22877e60 q^{50} -1.68851e60 q^{51} -3.82727e60 q^{52} -1.27195e61 q^{53} +5.24119e60 q^{54} -2.02341e61 q^{55} +3.58102e61 q^{56} -8.13344e61 q^{57} -3.14616e62 q^{58} -2.69101e62 q^{59} -1.09951e62 q^{60} +3.49397e63 q^{61} -3.52432e63 q^{62} -7.20951e62 q^{63} +1.45811e64 q^{64} +2.26235e64 q^{65} -1.17547e64 q^{66} +1.08655e64 q^{67} +2.05780e64 q^{68} +1.22509e65 q^{69} -4.34440e64 q^{70} -3.78830e65 q^{71} -3.11227e65 q^{72} -9.02098e65 q^{73} -1.39360e66 q^{74} -1.46898e66 q^{75} +9.91227e65 q^{76} +1.61692e66 q^{77} +1.31428e67 q^{78} -1.18442e67 q^{79} -1.35653e67 q^{80} +6.26579e66 q^{81} +4.82008e67 q^{82} +9.45075e67 q^{83} +8.78627e66 q^{84} -1.21639e68 q^{85} -2.32112e68 q^{86} -3.76120e68 q^{87} +6.98007e68 q^{88} -1.49773e69 q^{89} +3.77572e68 q^{90} -1.80786e69 q^{91} -1.49302e69 q^{92} -4.21328e69 q^{93} -1.38694e70 q^{94} -5.85927e69 q^{95} +6.80744e69 q^{96} -2.78454e70 q^{97} -3.85680e70 q^{98} -1.40527e70 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q - 25051277688 q^{2} + 25\!\cdots\!35 q^{3}+ \cdots + 12\!\cdots\!45 q^{9}+O(q^{10}) \) 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	\( 5 q - 25051277688 q^{2} + 25\!\cdots\!35 q^{3}+ \cdots + 33\!\cdots\!88 q^{99}+O(q^{100}) \) 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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