LMFDB - Embedded newform 896.2.u.c.113.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [896,2,Mod(113,896)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(896, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([0, 1, 0]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("896.113");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 896 = 2^{7} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	896.u (of order $8$, degree $4$, not minimal)

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:	no
Analytic conductor:	$7.15459602111$
Analytic rank:	$0$
Dimension:	$52$
Relative dimension:	$13$ over $\Q(\zeta_{8})$
Twist minimal:	no (minimal twist has level 224)
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			113.11
Character	$\chi$	$=$	896.113
Dual form			896.2.u.c.785.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.728858 + 1.75962i) q^{3} +(-1.90564 - 0.789342i) q^{5} +(0.707107 + 0.707107i) q^{7} +(-0.443707 + 0.443707i) q^{9} +O(q^{10})$	\(q+(0.728858 + 1.75962i) q^{3} +(-1.90564 - 0.789342i) q^{5} +(0.707107 + 0.707107i) q^{7} +(-0.443707 + 0.443707i) q^{9} +(0.169776 - 0.409876i) q^{11} +(-6.57396 + 2.72302i) q^{13} -3.92852i q^{15} +4.21228i q^{17} +(-2.17381 + 0.900420i) q^{19} +(-0.728858 + 1.75962i) q^{21} +(-5.31621 + 5.31621i) q^{23} +(-0.527131 - 0.527131i) q^{25} +(4.17470 + 1.72922i) q^{27} +(-0.456042 - 1.10098i) q^{29} +6.66083 q^{31} +0.844970 q^{33} +(-0.789342 - 1.90564i) q^{35} +(-9.92246 - 4.11002i) q^{37} +(-9.58297 - 9.58297i) q^{39} +(-0.956704 + 0.956704i) q^{41} +(-0.928127 + 2.24070i) q^{43} +(1.19578 - 0.495309i) q^{45} +9.63410i q^{47} +1.00000i q^{49} +(-7.41202 + 3.07016i) q^{51} +(0.292157 - 0.705330i) q^{53} +(-0.647065 + 0.647065i) q^{55} +(-3.16879 - 3.16879i) q^{57} +(-1.43916 - 0.596121i) q^{59} +(-0.685011 - 1.65376i) q^{61} -0.627497 q^{63} +14.6770 q^{65} +(1.78032 + 4.29807i) q^{67} +(-13.2293 - 5.47974i) q^{69} +(-1.97151 - 1.97151i) q^{71} +(7.73559 - 7.73559i) q^{73} +(0.543346 - 1.31175i) q^{75} +(0.409876 - 0.169776i) q^{77} -14.3965i q^{79} +10.4887i q^{81} +(-8.94779 + 3.70630i) q^{83} +(3.32493 - 8.02710i) q^{85} +(1.60492 - 1.60492i) q^{87} +(-2.74699 - 2.74699i) q^{89} +(-6.57396 - 2.72302i) q^{91} +(4.85480 + 11.7205i) q^{93} +4.85323 q^{95} -8.89601 q^{97} +(0.106534 + 0.257196i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 52 q+O(q^{10}) $ 52 * q	$ 52 q + 20 q^{23} + 24 q^{27} - 48 q^{33} + 24 q^{39} + 44 q^{43} + 40 q^{45} - 16 q^{51} - 36 q^{53} - 32 q^{55} - 32 q^{61} - 68 q^{63} + 80 q^{65} - 28 q^{67} - 32 q^{69} - 32 q^{75} - 12 q^{77} + 64 q^{85} + 56 q^{87} + 64 q^{95} - 72 q^{97} + 64 q^{99}+O(q^{100}) $ 52 * q + 20 * q^23 + 24 * q^27 - 48 * q^33 + 24 * q^39 + 44 * q^43 + 40 * q^45 - 16 * q^51 - 36 * q^53 - 32 * q^55 - 32 * q^61 - 68 * q^63 + 80 * q^65 - 28 * q^67 - 32 * q^69 - 32 * q^75 - 12 * q^77 + 64 * q^85 + 56 * q^87 + 64 * q^95 - 72 * q^97 + 64 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/896\mathbb{Z}\right)^\times$.

$n$	$127$	$129$	$645$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{8}\right)$

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 $

$2$		0			0
$2$		0			0
$3$	0.728858	+	1.75962i	0.420807	+	1.01592i	0.982110	+	0.188307i	$0.0603000\pi$
$3$	0.728858	+	1.75962i	0.420807	+	1.01592i	−0.561304	+	0.827610i	$0.689700\pi$
$4$		0			0
$5$	−1.90564	−	0.789342i	−0.852228	−	0.353004i	−0.0865650	−	0.996246i	$-0.527589\pi$
$5$	−1.90564	−	0.789342i	−0.852228	−	0.353004i	−0.765663	+	0.643242i	$0.777589\pi$
$6$		0			0
$7$	0.707107	+	0.707107i	0.267261	+	0.267261i
$7$	0.707107	+	0.707107i	0.267261	+	0.267261i
$8$		0			0
$9$	−0.443707	+	0.443707i	−0.147902	+	0.147902i
$10$		0			0
$11$	0.169776	−	0.409876i	0.0511895	−	0.123582i	−0.896216	−	0.443618i	$-0.853695\pi$
$11$	0.169776	−	0.409876i	0.0511895	−	0.123582i	0.947406	+	0.320035i	$0.103695\pi$
$12$		0			0
$13$	−6.57396	+	2.72302i	−1.82329	+	0.755231i	−0.849571	+	0.527475i	$0.823139\pi$
$13$	−6.57396	+	2.72302i	−1.82329	+	0.755231i	−0.973718	+	0.227756i	$0.926861\pi$
$14$		0			0
$15$		−	3.92852i		−	1.01434i
$16$		0			0
$17$			4.21228i			1.02163i	0.859691	+	0.510814i	$0.170656\pi$
$17$			4.21228i			1.02163i	−0.859691	+	0.510814i	$0.829344\pi$
$18$		0			0
$19$	−2.17381	+	0.900420i	−0.498705	+	0.206571i	−0.617834	−	0.786308i	$-0.711990\pi$
$19$	−2.17381	+	0.900420i	−0.498705	+	0.206571i	0.119129	+	0.992879i	$0.461990\pi$
$20$		0			0
$21$	−0.728858	+	1.75962i	−0.159050	+	0.383981i
$22$		0			0
$23$	−5.31621	+	5.31621i	−1.10851	+	1.10851i	−0.115159	+	0.993347i	$0.536738\pi$
$23$	−5.31621	+	5.31621i	−1.10851	+	1.10851i	−0.993347	+	0.115159i	$0.963262\pi$
$24$		0			0
$25$	−0.527131	−	0.527131i	−0.105426	−	0.105426i
$26$		0			0
$27$	4.17470	+	1.72922i	0.803422	+	0.332788i
$28$		0			0
$29$	−0.456042	−	1.10098i	−0.0846849	−	0.204448i	0.875864	−	0.482557i	$-0.160292\pi$
$29$	−0.456042	−	1.10098i	−0.0846849	−	0.204448i	−0.960549	+	0.278110i	$0.910292\pi$
$30$		0			0
$31$	6.66083			1.19632			0.598160	−	0.801377i	$-0.295899\pi$
$31$	6.66083			1.19632			0.598160	+	0.801377i	$0.295899\pi$
$32$		0			0
$33$	0.844970			0.147090
$34$		0			0
$35$	−0.789342	−	1.90564i	−0.133423	−	0.322112i
$36$		0			0
$37$	−9.92246	−	4.11002i	−1.63124	−	0.675683i	−0.635871	−	0.771795i	$-0.719359\pi$
$37$	−9.92246	−	4.11002i	−1.63124	−	0.675683i	−0.995370	+	0.0961125i	$0.969359\pi$
$38$		0			0
$39$	−9.58297	−	9.58297i	−1.53450	−	1.53450i
$40$		0			0
$41$	−0.956704	+	0.956704i	−0.149412	+	0.149412i	−0.777855	−	0.628443i	$-0.783692\pi$
$41$	−0.956704	+	0.956704i	−0.149412	+	0.149412i	0.628443	+	0.777855i	$0.283692\pi$
$42$		0			0
$43$	−0.928127	+	2.24070i	−0.141538	+	0.341703i	−0.978713	−	0.205231i	$-0.934205\pi$
$43$	−0.928127	+	2.24070i	−0.141538	+	0.341703i	0.837175	+	0.546934i	$0.184205\pi$
$44$		0			0
$45$	1.19578	−	0.495309i	0.178257	−	0.0738364i
$46$		0			0
$47$			9.63410i			1.40528i	0.711546	+	0.702639i	$0.247995\pi$
$47$			9.63410i			1.40528i	−0.711546	+	0.702639i	$0.752005\pi$
$48$		0			0
$49$			1.00000i			0.142857i
$50$		0			0
$51$	−7.41202	+	3.07016i	−1.03789	+	0.429908i
$52$		0			0
$53$	0.292157	−	0.705330i	0.0401309	−	0.0968845i	−0.902543	−	0.430599i	$-0.858302\pi$
$53$	0.292157	−	0.705330i	0.0401309	−	0.0968845i	0.942674	+	0.333715i	$0.108302\pi$
$54$		0			0
$55$	−0.647065	+	0.647065i	−0.0872503	+	0.0872503i
$56$		0			0
$57$	−3.16879	−	3.16879i	−0.419717	−	0.419717i
$58$		0			0
$59$	−1.43916	−	0.596121i	−0.187363	−	0.0776084i	0.287029	−	0.957922i	$-0.407332\pi$
$59$	−1.43916	−	0.596121i	−0.187363	−	0.0776084i	−0.474393	+	0.880313i	$0.657332\pi$
$60$		0			0
$61$	−0.685011	−	1.65376i	−0.0877066	−	0.211743i	0.873940	−	0.486034i	$-0.161557\pi$
$61$	−0.685011	−	1.65376i	−0.0877066	−	0.211743i	−0.961647	+	0.274291i	$0.911557\pi$
$62$		0			0
$63$	−0.627497			−0.0790572
$64$		0			0
$65$	14.6770			1.82046
$66$		0			0
$67$	1.78032	+	4.29807i	0.217501	+	0.525093i	0.994540	−	0.104359i	$-0.0332792\pi$
$67$	1.78032	+	4.29807i	0.217501	+	0.525093i	−0.777039	+	0.629453i	$0.783279\pi$
$68$		0			0
$69$	−13.2293	−	5.47974i	−1.59262	−	0.659684i
$70$		0			0
$71$	−1.97151	−	1.97151i	−0.233975	−	0.233975i	0.580374	−	0.814350i	$-0.302906\pi$
$71$	−1.97151	−	1.97151i	−0.233975	−	0.233975i	−0.814350	+	0.580374i	$0.802906\pi$
$72$		0			0
$73$	7.73559	−	7.73559i	0.905382	−	0.905382i	−0.0905133	−	0.995895i	$-0.528851\pi$
$73$	7.73559	−	7.73559i	0.905382	−	0.905382i	0.995895	+	0.0905133i	$0.0288508\pi$
$74$		0			0
$75$	0.543346	−	1.31175i	0.0627402	−	0.151468i
$76$		0			0
$77$	0.409876	−	0.169776i	0.0467097	−	0.0193478i
$78$		0			0
$79$		−	14.3965i		−	1.61973i	−0.586615	−	0.809866i	$-0.699540\pi$
$79$		−	14.3965i		−	1.61973i	0.586615	−	0.809866i	$-0.300460\pi$
$80$		0			0
$81$			10.4887i			1.16542i
$82$		0			0
$83$	−8.94779	+	3.70630i	−0.982148	+	0.406819i	−0.815221	−	0.579150i	$-0.803384\pi$
$83$	−8.94779	+	3.70630i	−0.982148	+	0.406819i	−0.166927	+	0.985969i	$0.553384\pi$
$84$		0			0
$85$	3.32493	−	8.02710i	0.360640	−	0.870661i
$86$		0			0
$87$	1.60492	−	1.60492i	0.172066	−	0.172066i
$88$		0			0
$89$	−2.74699	−	2.74699i	−0.291181	−	0.291181i	0.546366	−	0.837547i	$-0.316011\pi$
$89$	−2.74699	−	2.74699i	−0.291181	−	0.291181i	−0.837547	+	0.546366i	$0.816011\pi$
$90$		0			0
$91$	−6.57396	−	2.72302i	−0.689138	−	0.285450i
$92$		0			0
$93$	4.85480	+	11.7205i	0.503419	+	1.21536i
$94$		0			0
$95$	4.85323			0.497931
$96$		0			0
$97$	−8.89601			−0.903253			−0.451627	−	0.892207i	$-0.649156\pi$
$97$	−8.89601			−0.903253			−0.451627	+	0.892207i	$0.649156\pi$
$98$		0			0
$99$	0.106534	+	0.257196i	0.0107071	+	0.0258492i
$100$		0			0
$101$	12.1195	+	5.02007i	1.20594	+	0.499515i	0.892913	−	0.450230i	$-0.148658\pi$
$101$	12.1195	+	5.02007i	1.20594	+	0.499515i	0.313024	+	0.949745i	$0.398658\pi$
$102$		0			0
$103$	3.41949	+	3.41949i	0.336932	+	0.336932i	0.855211	−	0.518279i	$-0.173427\pi$
$103$	3.41949	+	3.41949i	0.336932	+	0.336932i	−0.518279	+	0.855211i	$0.673427\pi$
$104$		0			0
$105$	2.77788	−	2.77788i	0.271094	−	0.271094i
$106$		0			0
$107$	−1.82825	+	4.41378i	−0.176743	+	0.426696i	−0.987280	−	0.158992i	$-0.949176\pi$
$107$	−1.82825	+	4.41378i	−0.176743	+	0.426696i	0.810536	+	0.585688i	$0.199176\pi$
$108$		0			0
$109$	15.0687	−	6.24168i	1.44332	−	0.597845i	0.482723	−	0.875773i	$-0.339648\pi$
$109$	15.0687	−	6.24168i	1.44332	−	0.597845i	0.960602	+	0.277929i	$0.0896479\pi$
$110$		0			0
$111$		−	20.4554i		−	1.94154i
$112$		0			0
$113$		−	3.33893i		−	0.314100i	−0.987591	−	0.157050i	$-0.949802\pi$
$113$		−	3.33893i		−	0.314100i	0.987591	−	0.157050i	$-0.0501984\pi$
$114$		0			0
$115$	14.3271	−	5.93447i	1.33601	−	0.553393i
$116$		0			0
$117$	1.70869	−	4.12514i	0.157968	−	0.381369i
$118$		0			0
$119$	−2.97853	+	2.97853i	−0.273042	+	0.273042i
$120$		0			0
$121$	7.63900	+	7.63900i	0.694455	+	0.694455i
$122$		0			0
$123$	−2.38074	−	0.986133i	−0.214664	−	0.0889166i
$124$		0			0
$125$	4.53514	+	10.9488i	0.405636	+	0.979291i
$126$		0			0
$127$	12.1086			1.07446			0.537232	−	0.843434i	$-0.319470\pi$
$127$	12.1086			1.07446			0.537232	+	0.843434i	$0.319470\pi$
$128$		0			0
$129$	−4.61925			−0.406702
$130$		0			0
$131$	6.90778	+	16.6769i	0.603536	+	1.45706i	0.869918	+	0.493197i	$0.164172\pi$
$131$	6.90778	+	16.6769i	0.603536	+	1.45706i	−0.266382	+	0.963868i	$0.585828\pi$
$132$		0			0
$133$	−2.17381	−	0.900420i	−0.188493	−	0.0780763i
$134$		0			0
$135$	−6.59054	−	6.59054i	−0.567223	−	0.567223i
$136$		0			0
$137$	−5.27482	+	5.27482i	−0.450659	+	0.450659i	−0.895573	−	0.444914i	$-0.853234\pi$
$137$	−5.27482	+	5.27482i	−0.450659	+	0.450659i	0.444914	+	0.895573i	$0.353234\pi$
$138$		0			0
$139$	−1.01653	+	2.45412i	−0.0862209	+	0.208156i	−0.961109	−	0.276170i	$-0.910935\pi$
$139$	−1.01653	+	2.45412i	−0.0862209	+	0.208156i	0.874888	+	0.484325i	$0.160935\pi$
$140$		0			0
$141$	−16.9524	+	7.02190i	−1.42765	+	0.591350i
$142$		0			0
$143$			3.15682i			0.263986i
$144$		0			0
$145$			2.45805i			0.204130i
$146$		0			0
$147$	−1.75962	+	0.728858i	−0.145131	+	0.0601152i
$148$		0			0
$149$	−6.54152	+	15.7926i	−0.535902	+	1.29378i	0.391659	+	0.920110i	$0.371901\pi$
$149$	−6.54152	+	15.7926i	−0.535902	+	1.29378i	−0.927561	+	0.373671i	$0.878099\pi$
$150$		0			0
$151$	−1.89795	+	1.89795i	−0.154453	+	0.154453i	−0.780103	−	0.625651i	$-0.784834\pi$
$151$	−1.89795	+	1.89795i	−0.154453	+	0.154453i	0.625651	+	0.780103i	$0.284834\pi$
$152$		0			0
$153$	−1.86902	−	1.86902i	−0.151101	−	0.151101i
$154$		0			0
$155$	−12.6931	−	5.25767i	−1.01954	−	0.422306i
$156$		0			0
$157$	4.32831	+	10.4495i	0.345437	+	0.833959i	0.997147	+	0.0754901i	$0.0240521\pi$
$157$	4.32831	+	10.4495i	0.345437	+	0.833959i	−0.651710	+	0.758469i	$0.725948\pi$
$158$		0			0
$159$	1.45405			0.115314
$160$		0			0
$161$	−7.51825			−0.592521
$162$		0			0
$163$	2.67988	+	6.46979i	0.209904	+	0.506753i	0.993408	−	0.114634i	$-0.0365694\pi$
$163$	2.67988	+	6.46979i	0.209904	+	0.506753i	−0.783504	+	0.621387i	$0.786569\pi$
$164$		0			0
$165$	−1.61021	−	0.666970i	−0.125355	−	0.0519235i
$166$		0			0
$167$	2.51531	+	2.51531i	0.194641	+	0.194641i	0.797698	−	0.603057i	$-0.206051\pi$
$167$	2.51531	+	2.51531i	0.194641	+	0.194641i	−0.603057	+	0.797698i	$0.706051\pi$
$168$		0			0
$169$	26.6097	−	26.6097i	2.04690	−	2.04690i
$170$		0			0
$171$	0.565011	−	1.36406i	0.0432074	−	0.104312i
$172$		0			0
$173$	0.983007	−	0.407175i	0.0747367	−	0.0309569i	−0.345002	−	0.938602i	$-0.612122\pi$
$173$	0.983007	−	0.407175i	0.0747367	−	0.0309569i	0.419739	+	0.907645i	$0.362122\pi$
$174$		0			0
$175$		−	0.745476i		−	0.0563527i
$176$		0			0
$177$		−	2.96687i		−	0.223004i
$178$		0			0
$179$	−0.638569	+	0.264504i	−0.0477289	+	0.0197699i	−0.406420	−	0.913686i	$-0.633223\pi$
$179$	−0.638569	+	0.264504i	−0.0477289	+	0.0197699i	0.358691	+	0.933456i	$0.383223\pi$
$180$		0			0
$181$	6.11642	−	14.7664i	0.454630	−	1.09757i	−0.515912	−	0.856642i	$-0.672547\pi$
$181$	6.11642	−	14.7664i	0.454630	−	1.09757i	0.970542	−	0.240933i	$-0.0774533\pi$
$182$		0			0
$183$	2.41072	−	2.41072i	0.178205	−	0.178205i
$184$		0			0
$185$	15.6644	+	15.6644i	1.15167	+	1.15167i
$186$		0			0
$187$	1.72652	+	0.715146i	0.126255	+	0.0522967i
$188$		0			0
$189$	1.72922	+	4.17470i	0.125782	+	0.303665i
$190$		0			0
$191$	15.7812			1.14189			0.570943	−	0.820989i	$-0.306578\pi$
$191$	15.7812			1.14189			0.570943	+	0.820989i	$0.306578\pi$
$192$		0			0
$193$	−9.56507			−0.688508			−0.344254	−	0.938876i	$-0.611868\pi$
$193$	−9.56507			−0.688508			−0.344254	+	0.938876i	$0.611868\pi$
$194$		0			0
$195$	10.6975	+	25.8259i	0.766061	+	1.84943i
$196$		0			0
$197$	−16.3663	−	6.77914i	−1.16605	−	0.482994i	−0.286165	−	0.958180i	$-0.592381\pi$
$197$	−16.3663	−	6.77914i	−1.16605	−	0.482994i	−0.879885	+	0.475187i	$0.842381\pi$
$198$		0			0
$199$	9.85196	+	9.85196i	0.698387	+	0.698387i	0.964063	−	0.265675i	$-0.0855950\pi$
$199$	9.85196	+	9.85196i	0.698387	+	0.698387i	−0.265675	+	0.964063i	$0.585595\pi$
$200$		0			0
$201$	−6.26537	+	6.26537i	−0.441925	+	0.441925i
$202$		0			0
$203$	0.456042	−	1.10098i	0.0320079	−	0.0772739i
$204$		0			0
$205$	2.57830	−	1.06797i	0.180076	−	0.0745900i
$206$		0			0
$207$		−	4.71768i		−	0.327901i
$208$		0			0
$209$			1.04386i			0.0722054i
$210$		0			0
$211$	11.0361	−	4.57132i	0.759759	−	0.314703i	0.0310428	−	0.999518i	$-0.490117\pi$
$211$	11.0361	−	4.57132i	0.759759	−	0.314703i	0.728717	+	0.684815i	$0.240117\pi$
$212$		0			0
$213$	2.03216	−	4.90607i	0.139241	−	0.336158i
$214$		0			0
$215$	3.53735	−	3.53735i	0.241245	−	0.241245i
$216$		0			0
$217$	4.70992	+	4.70992i	0.319730	+	0.319730i
$218$		0			0
$219$	19.2498	+	7.97354i	1.30078	+	0.538802i
$220$		0			0
$221$	−11.4701	−	27.6914i	−0.771566	−	1.86272i
$222$		0			0
$223$	−19.0506			−1.27572			−0.637862	−	0.770151i	$-0.720181\pi$
$223$	−19.0506			−1.27572			−0.637862	+	0.770151i	$0.720181\pi$
$224$		0			0
$225$	0.467783			0.0311856
$226$		0			0
$227$	−0.260108	−	0.627957i	−0.0172640	−	0.0416790i	0.915012	−	0.403426i	$-0.132181\pi$
$227$	−0.260108	−	0.627957i	−0.0172640	−	0.0416790i	−0.932276	+	0.361747i	$0.882181\pi$
$228$		0			0
$229$	−4.38285	−	1.81544i	−0.289627	−	0.119967i	0.233140	−	0.972443i	$-0.425100\pi$
$229$	−4.38285	−	1.81544i	−0.289627	−	0.119967i	−0.522767	+	0.852476i	$0.675100\pi$
$230$		0			0
$231$	0.597484	+	0.597484i	0.0393115	+	0.0393115i
$232$		0			0
$233$	16.2472	−	16.2472i	1.06439	−	1.06439i	0.0666108	−	0.997779i	$-0.478781\pi$
$233$	16.2472	−	16.2472i	1.06439	−	1.06439i	0.997779	−	0.0666108i	$-0.0212186\pi$
$234$		0			0
$235$	7.60460	−	18.3591i	0.496070	−	1.19762i
$236$		0			0
$237$	25.3323	−	10.4930i	1.64551	−	0.681594i
$238$		0			0
$239$			22.8156i			1.47582i	0.674901	+	0.737908i	$0.264186\pi$
$239$			22.8156i			1.47582i	−0.674901	+	0.737908i	$0.735814\pi$
$240$		0			0
$241$			17.7780i			1.14518i	0.819842	+	0.572589i	$0.194061\pi$
$241$			17.7780i			1.14518i	−0.819842	+	0.572589i	$0.805939\pi$
$242$		0			0
$243$	−5.93208	+	2.45715i	−0.380543	+	0.157626i
$244$		0			0
$245$	0.789342	−	1.90564i	0.0504292	−	0.121747i
$246$		0			0
$247$	11.8387	−	11.8387i	0.753275	−	0.753275i
$248$		0			0
$249$	−13.0433	−	13.0433i	−0.826589	−	0.826589i
$250$		0			0
$251$	−8.29059	−	3.43408i	−0.523298	−	0.216757i	0.105367	−	0.994433i	$-0.466398\pi$
$251$	−8.29059	−	3.43408i	−0.523298	−	0.216757i	−0.628665	+	0.777676i	$0.716398\pi$
$252$		0			0
$253$	1.27642	+	3.08155i	0.0802480	+	0.193736i
$254$		0			0
$255$	16.5480			1.03628
$256$		0			0
$257$	−2.00120			−0.124832			−0.0624158	−	0.998050i	$-0.519880\pi$
$257$	−2.00120			−0.124832			−0.0624158	+	0.998050i	$0.519880\pi$
$258$		0			0
$259$	−4.11002	−	9.92246i	−0.255384	−	0.616551i
$260$		0			0
$261$	0.690864	+	0.286165i	0.0427634	+	0.0177132i
$262$		0			0
$263$	−18.1955	−	18.1955i	−1.12198	−	1.12198i	−0.991443	−	0.130540i	$-0.958329\pi$
$263$	−18.1955	−	18.1955i	−1.12198	−	1.12198i	−0.130540	−	0.991443i	$-0.541671\pi$
$264$		0			0
$265$	−1.11349	+	1.11349i	−0.0684013	+	0.0684013i
$266$		0			0
$267$	2.83150	−	6.83583i	0.173285	−	0.418346i
$268$		0			0
$269$	21.6150	−	8.95325i	1.31789	−	0.545889i	0.390715	−	0.920512i	$-0.372228\pi$
$269$	21.6150	−	8.95325i	1.31789	−	0.545889i	0.927177	+	0.374623i	$0.122228\pi$
$270$		0			0
$271$			5.54732i			0.336975i	0.985704	+	0.168488i	$0.0538884\pi$
$271$			5.54732i			0.336975i	−0.985704	+	0.168488i	$0.946112\pi$
$272$		0			0
$273$		−	13.5524i		−	0.820227i
$274$		0			0
$275$	−0.305553	+	0.126564i	−0.0184255	+	0.00763210i
$276$		0			0
$277$	−8.92032	+	21.5356i	−0.535970	+	1.29395i	0.391545	+	0.920159i	$0.371941\pi$
$277$	−8.92032	+	21.5356i	−0.535970	+	1.29395i	−0.927515	+	0.373787i	$0.878059\pi$
$278$		0			0
$279$	−2.95546	+	2.95546i	−0.176939	+	0.176939i
$280$		0			0
$281$	−5.78721	−	5.78721i	−0.345236	−	0.345236i	0.513096	−	0.858331i	$-0.328499\pi$
$281$	−5.78721	−	5.78721i	−0.345236	−	0.345236i	−0.858331	+	0.513096i	$0.828499\pi$
$282$		0			0
$283$	−10.0592	−	4.16665i	−0.597957	−	0.247682i	0.0631127	−	0.998006i	$-0.479897\pi$
$283$	−10.0592	−	4.16665i	−0.597957	−	0.247682i	−0.661070	+	0.750325i	$0.729897\pi$
$284$		0			0
$285$	3.53732	+	8.53984i	0.209533	+	0.505857i
$286$		0			0
$287$	−1.35298			−0.0798641
$288$		0			0
$289$	−0.743332			−0.0437254
$290$		0			0
$291$	−6.48393	−	15.6536i	−0.380095	−	0.917630i
$292$		0			0
$293$	12.1635	+	5.03829i	0.710600	+	0.294340i	0.708553	−	0.705658i	$-0.249348\pi$
$293$	12.1635	+	5.03829i	0.710600	+	0.294340i	0.00204717	+	0.999998i	$0.499348\pi$
$294$		0			0
$295$	2.27199	+	2.27199i	0.132280	+	0.132280i
$296$		0			0
$297$	1.41753	−	1.41753i	0.0822535	−	0.0822535i
$298$		0			0
$299$	20.4724	−	49.4247i	1.18395	−	2.85830i
$300$		0			0
$301$	−2.24070	+	0.928127i	−0.129152	+	0.0534964i
$302$		0			0
$303$			24.9847i			1.43533i
$304$		0			0
$305$			3.69218i			0.211414i
$306$		0			0
$307$	27.1788	−	11.2578i	1.55118	−	0.642518i	0.567647	−	0.823272i	$-0.307854\pi$
$307$	27.1788	−	11.2578i	1.55118	−	0.642518i	0.983528	+	0.180754i	$0.0578539\pi$
$308$		0			0
$309$	−3.52468	+	8.50932i	−0.200512	+	0.484079i
$310$		0			0
$311$	−15.3897	+	15.3897i	−0.872672	+	0.872672i	−0.992763	−	0.120091i	$-0.961681\pi$
$311$	−15.3897	+	15.3897i	−0.872672	+	0.872672i	0.120091	+	0.992763i	$0.461681\pi$
$312$		0			0
$313$	−23.0132	−	23.0132i	−1.30078	−	1.30078i	−0.927864	−	0.372919i	$-0.878357\pi$
$313$	−23.0132	−	23.0132i	−1.30078	−	1.30078i	−0.372919	−	0.927864i	$-0.621643\pi$
$314$		0			0
$315$	1.19578	+	0.495309i	0.0673747	+	0.0279075i
$316$		0			0
$317$	−6.22337	−	15.0245i	−0.349539	−	0.843862i	−0.996674	−	0.0814869i	$-0.974033\pi$
$317$	−6.22337	−	15.0245i	−0.349539	−	0.843862i	0.647135	−	0.762375i	$-0.275967\pi$
$318$		0			0
$319$	−0.528692			−0.0296011
$320$		0			0
$321$	−9.09911			−0.507863
$322$		0			0
$323$	−3.79282	−	9.15669i	−0.211038	−	0.509492i
$324$		0			0
$325$	4.90073	+	2.02995i	0.271843	+	0.112601i
$326$		0			0
$327$	21.9660	+	21.9660i	1.21472	+	1.21472i
$328$		0			0
$329$	−6.81234	+	6.81234i	−0.375576	+	0.375576i
$330$		0			0
$331$	10.5213	−	25.4007i	0.578305	−	1.39615i	−0.316029	−	0.948750i	$-0.602350\pi$
$331$	10.5213	−	25.4007i	0.578305	−	1.39615i	0.894333	−	0.447401i	$-0.147650\pi$
$332$		0			0
$333$	6.22631	−	2.57902i	0.341200	−	0.141330i
$334$		0			0
$335$		−	9.59586i		−	0.524278i
$336$		0			0
$337$			16.8771i			0.919356i	0.888086	+	0.459678i	$0.152035\pi$
$337$			16.8771i			0.919356i	−0.888086	+	0.459678i	$0.847965\pi$
$338$		0			0
$339$	5.87525	−	2.43361i	0.319100	−	0.132175i
$340$		0			0
$341$	1.13085	−	2.73012i	0.0612390	−	0.147844i
$342$		0			0
$343$	−0.707107	+	0.707107i	−0.0381802	+	0.0381802i
$344$		0			0
$345$	20.8848	+	20.8848i	1.12440	+	1.12440i
$346$		0			0
$347$	16.2716	+	6.73990i	0.873503	+	0.361817i	0.773974	−	0.633218i	$-0.218266\pi$
$347$	16.2716	+	6.73990i	0.873503	+	0.361817i	0.0995294	+	0.995035i	$0.468266\pi$
$348$		0			0
$349$	−7.30348	−	17.6322i	−0.390946	−	0.943828i	−0.989734	−	0.142920i	$-0.954351\pi$
$349$	−7.30348	−	17.6322i	−0.390946	−	0.943828i	0.598788	−	0.800908i	$-0.295649\pi$
$350$		0			0
$351$	−32.1530			−1.71620
$352$		0			0
$353$	−15.3494			−0.816964			−0.408482	−	0.912766i	$-0.633942\pi$
$353$	−15.3494			−0.816964			−0.408482	+	0.912766i	$0.633942\pi$
$354$		0			0
$355$	2.20080	+	5.31319i	0.116806	+	0.281995i
$356$		0			0
$357$	−7.41202	−	3.07016i	−0.392286	−	0.162490i
$358$		0			0
$359$	12.3204	+	12.3204i	0.650248	+	0.650248i	0.953053	−	0.302805i	$-0.0979230\pi$
$359$	12.3204	+	12.3204i	0.650248	+	0.650248i	−0.302805	+	0.953053i	$0.597923\pi$
$360$		0			0
$361$	−9.52035	+	9.52035i	−0.501071	+	0.501071i
$362$		0			0
$363$	−7.87399	+	19.0095i	−0.413277	+	0.997739i
$364$		0			0
$365$	−20.8473	+	8.63522i	−1.09120	+	0.451988i
$366$		0			0
$367$			7.93564i			0.414237i	0.978316	+	0.207119i	$0.0664086\pi$
$367$			7.93564i			0.414237i	−0.978316	+	0.207119i	$0.933591\pi$
$368$		0			0
$369$		−	0.848993i		−	0.0441968i
$370$		0			0
$371$	0.705330	−	0.292157i	0.0366189	−	0.0151680i
$372$		0			0
$373$	−8.02652	+	19.3777i	−0.415597	+	1.00334i	0.568011	+	0.823021i	$0.307713\pi$
$373$	−8.02652	+	19.3777i	−0.415597	+	1.00334i	−0.983608	+	0.180320i	$0.942287\pi$
$374$		0			0
$375$	−15.9603	+	15.9603i	−0.824184	+	0.824184i
$376$		0			0
$377$	5.99601	+	5.99601i	0.308810	+	0.308810i
$378$		0			0
$379$	−34.0618	−	14.1088i	−1.74964	−	0.724723i	−0.997866	−	0.0652976i	$-0.979200\pi$
$379$	−34.0618	−	14.1088i	−1.74964	−	0.724723i	−0.751770	−	0.659425i	$-0.770800\pi$
$380$		0			0
$381$	8.82545	+	21.3065i	0.452142	+	1.09157i
$382$		0			0
$383$	5.39944			0.275899			0.137949	−	0.990439i	$-0.455949\pi$
$383$	5.39944			0.275899			0.137949	+	0.990439i	$0.455949\pi$
$384$		0			0
$385$	−0.915088			−0.0466372
$386$		0			0
$387$	−0.582397	−	1.40603i	−0.0296049	−	0.0714725i
$388$		0			0
$389$	23.9996	+	9.94096i	1.21683	+	0.504027i	0.896400	−	0.443246i	$-0.146173\pi$
$389$	23.9996	+	9.94096i	1.21683	+	0.504027i	0.320428	+	0.947273i	$0.396173\pi$
$390$		0			0
$391$	−22.3934	−	22.3934i	−1.13248	−	1.13248i
$392$		0			0
$393$	−24.3101	+	24.3101i	−1.22628	+	1.22628i
$394$		0			0
$395$	−11.3638	+	27.4345i	−0.571772	+	1.38038i
$396$		0			0
$397$	4.70957	−	1.95077i	0.236366	−	0.0979062i	−0.261356	−	0.965242i	$-0.584170\pi$
$397$	4.70957	−	1.95077i	0.236366	−	0.0979062i	0.497723	+	0.867336i	$0.334170\pi$
$398$		0			0
$399$		−	4.48135i		−	0.224348i
$400$		0			0
$401$		−	6.77249i		−	0.338202i	−0.985599	−	0.169101i	$-0.945914\pi$
$401$		−	6.77249i		−	0.338202i	0.985599	−	0.169101i	$-0.0540864\pi$
$402$		0			0
$403$	−43.7880	+	18.1376i	−2.18124	+	0.903498i
$404$		0			0
$405$	8.27920	−	19.9878i	0.411397	−	0.993200i
$406$		0			0
$407$	−3.36920	+	3.36920i	−0.167005	+	0.167005i
$408$		0			0
$409$	−5.83145	−	5.83145i	−0.288347	−	0.288347i	0.548080	−	0.836426i	$-0.315359\pi$
$409$	−5.83145	−	5.83145i	−0.288347	−	0.288347i	−0.836426	+	0.548080i	$0.815359\pi$
$410$		0			0
$411$	−13.1263	−	5.43709i	−0.647472	−	0.268192i
$412$		0			0
$413$	−0.596121	−	1.43916i	−0.0293332	−	0.0708166i
$414$		0			0
$415$	19.9768			0.980623
$416$		0			0
$417$	−5.05922			−0.247751
$418$		0			0
$419$	−0.0959286	−	0.231592i	−0.00468642	−	0.0113140i	0.921519	−	0.388333i	$-0.126949\pi$
$419$	−0.0959286	−	0.231592i	−0.00468642	−	0.0113140i	−0.926205	+	0.377019i	$0.876949\pi$
$420$		0			0
$421$	9.84629	+	4.07847i	0.479879	+	0.198772i	0.609492	−	0.792792i	$-0.291374\pi$
$421$	9.84629	+	4.07847i	0.479879	+	0.198772i	−0.129613	+	0.991565i	$0.541374\pi$
$422$		0			0
$423$	−4.27472	−	4.27472i	−0.207844	−	0.207844i
$424$		0			0
$425$	2.22042	−	2.22042i	0.107706	−	0.107706i
$426$		0			0
$427$	0.685011	−	1.65376i	0.0331500	−	0.0800311i
$428$		0			0
$429$	−5.55480	+	2.30087i	−0.268188	+	0.111087i
$430$		0			0
$431$			33.0800i			1.59341i	0.604370	+	0.796704i	$0.293425\pi$
$431$			33.0800i			1.59341i	−0.604370	+	0.796704i	$0.706575\pi$
$432$		0			0
$433$			9.51683i			0.457350i	0.973503	+	0.228675i	$0.0734393\pi$
$433$			9.51683i			0.457350i	−0.973503	+	0.228675i	$0.926561\pi$
$434$		0			0
$435$	−4.32524	+	1.79157i	−0.207379	+	0.0858993i
$436$		0			0
$437$	6.76959	−	16.3432i	0.323833	−	0.781803i
$438$		0			0
$439$	−5.37450	+	5.37450i	−0.256511	+	0.256511i	−0.823633	−	0.567123i	$-0.808057\pi$
$439$	−5.37450	+	5.37450i	−0.256511	+	0.256511i	0.567123	+	0.823633i	$0.308057\pi$
$440$		0			0
$441$	−0.443707	−	0.443707i	−0.0211289	−	0.0211289i
$442$		0			0
$443$	−29.8270	−	12.3547i	−1.41712	−	0.586991i	−0.462986	−	0.886365i	$-0.653222\pi$
$443$	−29.8270	−	12.3547i	−1.41712	−	0.586991i	−0.954136	+	0.299374i	$0.903222\pi$
$444$		0			0
$445$	3.06646	+	7.40310i	0.145364	+	0.350941i
$446$		0			0
$447$	−32.5568			−1.53989
$448$		0			0
$449$	−25.3005			−1.19400			−0.597002	−	0.802240i	$-0.703641\pi$
$449$	−25.3005			−1.19400			−0.597002	+	0.802240i	$0.703641\pi$
$450$		0			0
$451$	0.229705	+	0.554556i	0.0108164	+	0.0261130i
$452$		0			0
$453$	−4.72300	−	1.95633i	−0.221906	−	0.0919165i
$454$		0			0
$455$	10.3782	+	10.3782i	0.486538	+	0.486538i
$456$		0			0
$457$	7.80621	−	7.80621i	0.365159	−	0.365159i	−0.500549	−	0.865708i	$-0.666869\pi$
$457$	7.80621	−	7.80621i	0.365159	−	0.365159i	0.865708	+	0.500549i	$0.166869\pi$
$458$		0			0
$459$	−7.28396	+	17.5850i	−0.339986	+	0.820799i
$460$		0			0
$461$	−8.65557	+	3.58525i	−0.403130	+	0.166982i	−0.575030	−	0.818133i	$-0.695010\pi$
$461$	−8.65557	+	3.58525i	−0.403130	+	0.166982i	0.171900	+	0.985114i	$0.445010\pi$
$462$		0			0
$463$		−	10.3643i		−	0.481671i	−0.970566	−	0.240836i	$-0.922579\pi$
$463$		−	10.3643i		−	0.481671i	0.970566	−	0.240836i	$-0.0774215\pi$
$464$		0			0
$465$		−	26.1672i		−	1.21347i
$466$		0			0
$467$	−26.4671	+	10.9630i	−1.22475	+	0.507308i	−0.898917	−	0.438119i	$-0.855645\pi$
$467$	−26.4671	+	10.9630i	−1.22475	+	0.507308i	−0.325833	+	0.945427i	$0.605645\pi$
$468$		0			0
$469$	−1.78032	+	4.29807i	−0.0822075	+	0.198467i
$470$		0			0
$471$	−15.2324	+	15.2324i	−0.701871	+	0.701871i
$472$		0			0
$473$	0.760835	+	0.760835i	0.0349832	+	0.0349832i
$474$		0			0
$475$	1.62052	+	0.671241i	0.0743545	+	0.0307987i
$476$		0			0
$477$	0.183328	+	0.442592i	0.00839400	+	0.0202649i
$478$		0			0
$479$	−27.8801			−1.27388			−0.636938	−	0.770915i	$-0.719799\pi$
$479$	−27.8801			−1.27388			−0.636938	+	0.770915i	$0.719799\pi$
$480$		0			0
$481$	76.4215			3.48452
$482$		0			0
$483$	−5.47974	−	13.2293i	−0.249337	−	0.601953i
$484$		0			0
$485$	16.9526	+	7.02199i	0.769778	+	0.318852i
$486$		0			0
$487$	−16.3512	−	16.3512i	−0.740942	−	0.740942i	0.231817	−	0.972759i	$-0.425533\pi$
$487$	−16.3512	−	16.3512i	−0.740942	−	0.740942i	−0.972759	+	0.231817i	$0.925533\pi$
$488$		0			0
$489$	−9.43113	+	9.43113i	−0.426490	+	0.426490i
$490$		0			0
$491$	−4.09732	+	9.89181i	−0.184910	+	0.446411i	−0.988966	−	0.148142i	$-0.952671\pi$
$491$	−4.09732	+	9.89181i	−0.184910	+	0.446411i	0.804057	+	0.594553i	$0.202671\pi$
$492$		0			0
$493$	4.63765	−	1.92098i	0.208869	−	0.0865166i
$494$		0			0
$495$		−	0.574215i		−	0.0258090i
$496$		0			0
$497$		−	2.78814i		−	0.125065i
$498$		0			0
$499$	29.7832	−	12.3366i	1.33328	−	0.552262i	0.401689	−	0.915776i	$-0.368423\pi$
$499$	29.7832	−	12.3366i	1.33328	−	0.552262i	0.931589	+	0.363514i	$0.118423\pi$
$500$		0			0
$501$	−2.59269	+	6.25930i	−0.115833	+	0.279645i
$502$		0			0
$503$	15.0442	−	15.0442i	0.670787	−	0.670787i	−0.287110	−	0.957898i	$-0.592695\pi$
$503$	15.0442	−	15.0442i	0.670787	−	0.670787i	0.957898	+	0.287110i	$0.0926946\pi$
$504$		0			0
$505$	−19.1329	−	19.1329i	−0.851402	−	0.851402i
$506$		0			0
$507$	66.2177	+	27.4283i	2.94083	+	1.21813i
$508$		0			0
$509$	12.7267	+	30.7250i	0.564101	+	1.36186i	0.906460	+	0.422292i	$0.138774\pi$
$509$	12.7267	+	30.7250i	0.564101	+	1.36186i	−0.342359	+	0.939569i	$0.611226\pi$
$510$		0			0
$511$	10.9398			0.483947
$512$		0			0
$513$	−10.6320			−0.469415
$514$		0			0
$515$	−3.81717	−	9.21546i	−0.168205	−	0.406082i
$516$		0			0
$517$	3.94879	+	1.63564i	0.173668	+	0.0719355i
$518$		0			0
$519$	1.43295	+	1.43295i	0.0628994	+	0.0628994i
$520$		0			0
$521$	−32.0101	+	32.0101i	−1.40239	+	1.40239i	−0.609933	+	0.792453i	$0.708804\pi$
$521$	−32.0101	+	32.0101i	−1.40239	+	1.40239i	−0.792453	+	0.609933i	$0.791196\pi$
$522$		0			0
$523$	1.99768	−	4.82282i	0.0873523	−	0.210887i	−0.874166	−	0.485626i	$-0.838592\pi$
$523$	1.99768	−	4.82282i	0.0873523	−	0.210887i	0.961519	+	0.274739i	$0.0885915\pi$
$524$		0			0
$525$	1.31175	−	0.543346i	0.0572496	−	0.0237136i
$526$		0			0
$527$			28.0573i			1.22220i
$528$		0			0
$529$		−	33.5241i		−	1.45757i
$530$		0			0
$531$	0.903071	−	0.374064i	0.0391899	−	0.0162330i
$532$		0			0
$533$	3.68421	−	8.89446i	0.159581	−	0.385262i
$534$		0			0
$535$	6.96797	−	6.96797i	0.301251	−	0.301251i
$536$		0			0
$537$	−0.930853	−	0.930853i	−0.0401693	−	0.0401693i
$538$		0			0
$539$	0.409876	+	0.169776i	0.0176546	+	0.00731279i
$540$		0			0
$541$	−7.71409	−	18.6235i	−0.331654	−	0.800685i	−0.998461	−	0.0554541i	$-0.982339\pi$
$541$	−7.71409	−	18.6235i	−0.331654	−	0.800685i	0.666807	−	0.745231i	$-0.267661\pi$
$542$		0			0
$543$	30.4412			1.30636
$544$		0			0
$545$	−33.6424			−1.44108
$546$		0			0
$547$	2.04499	+	4.93705i	0.0874376	+	0.211093i	0.961550	−	0.274631i	$-0.0885558\pi$
$547$	2.04499	+	4.93705i	0.0874376	+	0.211093i	−0.874112	+	0.485725i	$0.838556\pi$
$548$		0			0
$549$	1.03773	+	0.429842i	0.0442892	+	0.0183452i
$550$		0			0
$551$	1.98270	+	1.98270i	0.0844657	+	0.0844657i
$552$		0			0
$553$	10.1799	−	10.1799i	0.432891	−	0.432891i
$554$		0			0
$555$	−16.1463	+	38.9806i	−0.685372	+	1.65463i
$556$		0			0
$557$	20.0988	−	8.32518i	0.851612	−	0.352749i	0.0861909	−	0.996279i	$-0.472531\pi$
$557$	20.0988	−	8.32518i	0.851612	−	0.352749i	0.765422	+	0.643529i	$0.222531\pi$
$558$		0			0
$559$		−	17.2576i		−	0.729917i
$560$		0			0
$561$			3.55925i			0.150272i
$562$		0			0
$563$	3.70612	−	1.53512i	0.156194	−	0.0646978i	−0.303217	−	0.952922i	$-0.598061\pi$
$563$	3.70612	−	1.53512i	0.156194	−	0.0646978i	0.459411	+	0.888224i	$0.348061\pi$
$564$		0			0
$565$	−2.63556	+	6.36280i	−0.110879	+	0.267685i
$566$		0			0
$567$	−7.41666	+	7.41666i	−0.311470	+	0.311470i
$568$		0			0
$569$	−26.0371	−	26.0371i	−1.09153	−	1.09153i	−0.995365	−	0.0961662i	$-0.969342\pi$
$569$	−26.0371	−	26.0371i	−1.09153	−	1.09153i	−0.0961662	−	0.995365i	$-0.530658\pi$
$570$		0			0
$571$	26.7936	+	11.0983i	1.12128	+	0.464448i	0.864807	−	0.502104i	$-0.167441\pi$
$571$	26.7936	+	11.0983i	1.12128	+	0.464448i	0.256470	+	0.966552i	$0.417441\pi$
$572$		0			0
$573$	11.5023	+	27.7689i	0.480514	+	1.16006i
$574$		0			0
$575$	5.60468			0.233731
$576$		0			0
$577$	−6.70881			−0.279291			−0.139646	−	0.990202i	$-0.544596\pi$
$577$	−6.70881			−0.279291			−0.139646	+	0.990202i	$0.544596\pi$
$578$		0			0
$579$	−6.97158	−	16.8309i	−0.289729	−	0.699467i
$580$		0			0
$581$	−8.94779	−	3.70630i	−0.371217	−	0.153763i
$582$		0			0
$583$	−0.239497	−	0.239497i	−0.00991894	−	0.00991894i
$584$		0			0
$585$	−6.51229	+	6.51229i	−0.269250	+	0.269250i
$586$		0			0
$587$	8.32601	−	20.1008i	0.343651	−	0.829647i	−0.653689	−	0.756763i	$-0.726780\pi$
$587$	8.32601	−	20.1008i	0.343651	−	0.829647i	0.997340	−	0.0728841i	$-0.0232203\pi$
$588$		0			0
$589$	−14.4794	+	5.99754i	−0.596611	+	0.247124i
$590$		0			0
$591$		−	33.7395i		−	1.38786i
$592$		0			0
$593$			20.0166i			0.821982i	0.911639	+	0.410991i	$0.134817\pi$
$593$			20.0166i			0.821982i	−0.911639	+	0.410991i	$0.865183\pi$
$594$		0			0
$595$	8.02710	−	3.32493i	0.329079	−	0.136309i
$596$		0			0
$597$	−10.1550	+	24.5164i	−0.415617	+	1.00339i
$598$		0			0
$599$	7.86491	−	7.86491i	0.321352	−	0.321352i	−0.527934	−	0.849286i	$-0.677033\pi$
$599$	7.86491	−	7.86491i	0.321352	−	0.321352i	0.849286	+	0.527934i	$0.177033\pi$
$600$		0			0
$601$	−4.39998	−	4.39998i	−0.179479	−	0.179479i	0.611650	−	0.791129i	$-0.290506\pi$
$601$	−4.39998	−	4.39998i	−0.179479	−	0.179479i	−0.791129	+	0.611650i	$0.790506\pi$
$602$		0			0
$603$	−2.69703	−	1.11714i	−0.109831	−	0.0454937i
$604$		0			0
$605$	−8.52740	−	20.5870i	−0.346688	−	0.836979i
$606$		0			0
$607$	−34.5188			−1.40107			−0.700537	−	0.713616i	$-0.747056\pi$
$607$	−34.5188			−1.40107			−0.700537	+	0.713616i	$0.747056\pi$
$608$		0			0
$609$	2.26970			0.0919730
$610$		0			0
$611$	−26.2339	−	63.3342i	−1.06131	−	2.56223i
$612$		0			0
$613$	−42.6387	−	17.6615i	−1.72216	−	0.713343i	−0.999761	−	0.0218699i	$-0.993038\pi$
$613$	−42.6387	−	17.6615i	−1.72216	−	0.713343i	−0.722402	−	0.691473i	$-0.756962\pi$
$614$		0			0
$615$	3.75843	+	3.75843i	0.151555	+	0.151555i
$616$		0			0
$617$	−2.52196	+	2.52196i	−0.101530	+	0.101530i	−0.756047	−	0.654517i	$-0.772872\pi$
$617$	−2.52196	+	2.52196i	−0.101530	+	0.101530i	0.654517	+	0.756047i	$0.272872\pi$
$618$		0			0
$619$	−9.78737	+	23.6288i	−0.393388	+	0.949722i	0.595809	+	0.803126i	$0.296832\pi$
$619$	−9.78737	+	23.6288i	−0.393388	+	0.949722i	−0.989197	+	0.146596i	$0.953168\pi$
$620$		0			0
$621$	−31.3865	+	13.0007i	−1.25950	+	0.521700i
$622$		0			0
$623$		−	3.88484i		−	0.155643i
$624$		0			0
$625$		−	20.7169i		−	0.828676i
$626$		0			0
$627$	−1.83680	+	0.760828i	−0.0733547	+	0.0303845i
$628$		0			0
$629$	17.3126	−	41.7962i	0.690297	−	1.66652i
$630$		0			0
$631$	3.76778	−	3.76778i	0.149993	−	0.149993i	−0.628122	−	0.778115i	$-0.716176\pi$
$631$	3.76778	−	3.76778i	0.149993	−	0.149993i	0.778115	+	0.628122i	$0.216176\pi$
$632$		0			0
$633$	16.0876	+	16.0876i	0.639424	+	0.639424i
$634$		0			0
$635$	−23.0746	−	9.55782i	−0.915689	−	0.379291i
$636$		0			0
$637$	−2.72302	−	6.57396i	−0.107890	−	0.260470i
$638$		0			0
$639$	1.74955			0.0692111
$640$		0			0
$641$	10.2128			0.403381			0.201690	−	0.979449i	$-0.435357\pi$
$641$	10.2128			0.403381			0.201690	+	0.979449i	$0.435357\pi$
$642$		0			0
$643$	3.35653	+	8.10339i	0.132369	+	0.319566i	0.976142	−	0.217134i	$-0.0696707\pi$
$643$	3.35653	+	8.10339i	0.132369	+	0.319566i	−0.843773	+	0.536700i	$0.819671\pi$
$644$		0			0
$645$	8.80262	+	3.64617i	0.346603	+	0.143568i
$646$		0			0
$647$	15.7646	+	15.7646i	0.619769	+	0.619769i	0.945472	−	0.325703i	$-0.105601\pi$
$647$	15.7646	+	15.7646i	0.619769	+	0.619769i	−0.325703	+	0.945472i	$0.605601\pi$
$648$		0			0
$649$	−0.488672	+	0.488672i	−0.0191821	+	0.0191821i
$650$		0			0
$651$	−4.85480	+	11.7205i	−0.190275	+	0.459364i
$652$		0			0
$653$	−10.7261	+	4.44291i	−0.419746	+	0.173864i	−0.582552	−	0.812794i	$-0.697946\pi$
$653$	−10.7261	+	4.44291i	−0.419746	+	0.173864i	0.162806	+	0.986658i	$0.447946\pi$
$654$		0			0
$655$		−	37.2327i		−	1.45480i
$656$		0			0
$657$			6.86467i			0.267816i
$658$		0			0
$659$	−2.79606	+	1.15817i	−0.108919	+	0.0451158i	−0.436478	−	0.899715i	$-0.643774\pi$
$659$	−2.79606	+	1.15817i	−0.108919	+	0.0451158i	0.327558	+	0.944831i	$0.393774\pi$
$660$		0			0
$661$	−4.96193	+	11.9792i	−0.192997	+	0.465935i	−0.990523	−	0.137350i	$-0.956142\pi$
$661$	−4.96193	+	11.9792i	−0.192997	+	0.465935i	0.797526	+	0.603285i	$0.206142\pi$
$662$		0			0
$663$	40.3662	−	40.3662i	1.56769	−	1.56769i
$664$		0			0
$665$	3.43175	+	3.43175i	0.133078	+	0.133078i
$666$		0			0
$667$	8.27747	+	3.42864i	0.320505	+	0.132758i
$668$		0			0
$669$	−13.8852	−	33.5219i	−0.536833	−	1.29603i
$670$		0			0
$671$	−0.794136			−0.0306573
$672$		0			0
$673$	23.7872			0.916929			0.458464	−	0.888713i	$-0.348400\pi$
$673$	23.7872			0.916929			0.458464	+	0.888713i	$0.348400\pi$
$674$		0			0
$675$	−1.28909	−	3.11214i	−0.0496171	−	0.119786i
$676$		0			0
$677$	41.9806	+	17.3889i	1.61344	+	0.668310i	0.993235	−	0.116126i	$-0.0370476\pi$
$677$	41.9806	+	17.3889i	1.61344	+	0.668310i	0.620210	+	0.784436i	$0.287048\pi$
$678$		0			0
$679$	−6.29043	−	6.29043i	−0.241405	−	0.241405i
$680$		0			0
$681$	0.915383	−	0.915383i	0.0350776	−	0.0350776i
$682$		0			0
$683$	−7.73249	+	18.6679i	−0.295876	+	0.714307i	0.704116	+	0.710085i	$0.251344\pi$
$683$	−7.73249	+	18.6679i	−0.295876	+	0.714307i	−0.999991	+	0.00422127i	$0.998656\pi$
$684$		0			0
$685$	14.2156	−	5.88828i	0.543148	−	0.224979i
$686$		0			0
$687$		−	9.03535i		−	0.344720i
$688$		0			0
$689$			5.43236i			0.206957i
$690$		0			0
$691$	20.7884	−	8.61084i	0.790828	−	0.327572i	0.0495519	−	0.998772i	$-0.484221\pi$
$691$	20.7884	−	8.61084i	0.790828	−	0.327572i	0.741277	+	0.671200i	$0.234221\pi$
$692$		0			0
$693$	−0.106534	+	0.257196i	−0.00404690	+	0.00977007i
$694$		0			0
$695$	3.87428	−	3.87428i	0.146960	−	0.146960i
$696$		0			0
$697$	−4.02991	−	4.02991i	−0.152644	−	0.152644i
$698$		0			0
$699$	40.4308	+	16.7470i	1.52923	+	0.633429i
$700$		0			0
$701$	7.91976	+	19.1200i	0.299125	+	0.722152i	0.999961	+	0.00882942i	$0.00281053\pi$
$701$	7.91976	+	19.1200i	0.299125	+	0.722152i	−0.700836	+	0.713323i	$0.747189\pi$
$702$		0			0
$703$	25.2702			0.953085
$704$		0			0
$705$	37.8478			1.42543
$706$		0			0
$707$	5.02007	+	12.1195i	0.188799	+	0.455801i
$708$		0			0
$709$	−4.95465	−	2.05228i	−0.186076	−	0.0770751i	0.287700	−	0.957721i	$-0.407109\pi$
$709$	−4.95465	−	2.05228i	−0.186076	−	0.0770751i	−0.473776	+	0.880645i	$0.657109\pi$
$710$		0			0
$711$	6.38783	+	6.38783i	0.239562	+	0.239562i
$712$		0			0
$713$	−35.4104	+	35.4104i	−1.32613	+	1.32613i
$714$		0			0
$715$	2.49181	−	6.01576i	0.0931883	−	0.224977i
$716$		0			0
$717$	−40.1467	+	16.6293i	−1.49931	+	0.621033i
$718$		0			0
$719$			17.3138i			0.645696i	0.946451	+	0.322848i	$0.104640\pi$
$719$			17.3138i			0.645696i	−0.946451	+	0.322848i	$0.895360\pi$
$720$		0			0
$721$			4.83589i			0.180098i
$722$		0			0
$723$	−31.2824	+	12.9576i	−1.16341	+	0.481899i
$724$		0			0
$725$	−0.339968	+	0.820756i	−0.0126261	+	0.0304821i
$726$		0			0
$727$	−2.48739	+	2.48739i	−0.0922521	+	0.0922521i	−0.751727	−	0.659475i	$-0.770779\pi$
$727$	−2.48739	+	2.48739i	−0.0922521	+	0.0922521i	0.659475	+	0.751727i	$0.270779\pi$
$728$		0			0
$729$	13.6027	+	13.6027i	0.503803	+	0.503803i
$730$		0			0
$731$	−9.43845	−	3.90953i	−0.349094	−	0.144599i
$732$		0			0
$733$	−1.95033	−	4.70852i	−0.0720372	−	0.173913i	0.883760	−	0.467941i	$-0.155004\pi$
$733$	−1.95033	−	4.70852i	−0.0720372	−	0.173913i	−0.955797	+	0.294028i	$0.905004\pi$
$734$		0			0
$735$	3.92852			0.144906
$736$		0			0
$737$	2.06393			0.0760260
$738$		0			0
$739$	4.17133	+	10.0705i	0.153445	+	0.370448i	0.981844	−	0.189690i	$-0.0607481\pi$
$739$	4.17133	+	10.0705i	0.153445	+	0.370448i	−0.828399	+	0.560138i	$0.810748\pi$
$740$		0			0
$741$	29.4602	+	12.2028i	1.08225	+	0.448282i
$742$		0			0
$743$	27.5681	+	27.5681i	1.01137	+	1.01137i	0.999935	+	0.0114402i	$0.00364162\pi$
$743$	27.5681	+	27.5681i	1.01137	+	1.01137i	0.0114402	+	0.999935i	$0.496358\pi$
$744$		0			0
$745$	24.9316	−	24.9316i	0.913421	−	0.913421i
$746$		0			0
$747$	2.32569	−	5.61471i	0.0850925	−	0.205432i
$748$		0			0
$749$	−4.41378	+	1.82825i	−0.161276	+	0.0668027i
$750$		0			0
$751$		−	9.68438i		−	0.353388i	−0.984266	−	0.176694i	$-0.943460\pi$
$751$		−	9.68438i		−	0.353388i	0.984266	−	0.176694i	$-0.0565403\pi$
$752$		0			0
$753$		−	17.0912i		−	0.622840i
$754$		0			0
$755$	5.11494	−	2.11868i	0.186152	−	0.0771065i
$756$		0			0
$757$	5.50389	−	13.2876i	0.200042	−	0.482945i	−0.791744	−	0.610853i	$-0.790826\pi$
$757$	5.50389	−	13.2876i	0.200042	−	0.482945i	0.991786	+	0.127909i	$0.0408265\pi$
$758$		0			0
$759$	−4.49203	+	4.49203i	−0.163051	+	0.163051i
$760$		0			0
$761$	−10.7427	−	10.7427i	−0.389422	−	0.389422i	0.485059	−	0.874481i	$-0.338798\pi$
$761$	−10.7427	−	10.7427i	−0.389422	−	0.389422i	−0.874481	+	0.485059i	$0.838798\pi$
$762$		0			0
$763$	15.0687	+	6.24168i	0.545525	+	0.225964i
$764$		0			0
$765$	2.08638	+	5.03698i	0.0754334	+	0.182112i
$766$		0			0
$767$	11.0843			0.400230
$768$		0			0
$769$	−23.5384			−0.848815			−0.424408	−	0.905471i	$-0.639518\pi$
$769$	−23.5384			−0.848815			−0.424408	+	0.905471i	$0.639518\pi$
$770$		0			0
$771$	−1.45859	−	3.52136i	−0.0525299	−	0.126819i
$772$		0			0
$773$	−7.12169	−	2.94990i	−0.256149	−	0.106101i	0.250914	−	0.968009i	$-0.419269\pi$
$773$	−7.12169	−	2.94990i	−0.256149	−	0.106101i	−0.507063	+	0.861909i	$0.669269\pi$
$774$		0			0
$775$	−3.51113	−	3.51113i	−0.126123	−	0.126123i
$776$		0			0
$777$	14.4641	−	14.4641i	0.518898	−	0.518898i
$778$		0			0
$779$	1.21825	−	2.94112i	0.0436485	−	0.105377i
$780$		0			0
$781$	−1.14279	+	0.473360i	−0.0408923	+	0.0169382i
$782$		0			0
$783$		−	5.38488i		−	0.192440i
$784$		0			0
$785$		−	23.3295i		−	0.832664i
$786$		0			0
$787$	22.2486	−	9.21567i	0.793077	−	0.328503i	0.0508971	−	0.998704i	$-0.483792\pi$
$787$	22.2486	−	9.21567i	0.793077	−	0.328503i	0.742180	+	0.670201i	$0.233792\pi$
$788$		0			0
$789$	18.7552	−	45.2791i	0.667704	−	1.61198i
$790$		0			0
$791$	2.36098	−	2.36098i	0.0839468	−	0.0839468i
$792$		0			0
$793$	9.00647	+	9.00647i	0.319829	+	0.319829i
$794$		0			0
$795$	−2.77090	−	1.14775i	−0.0982738	−	0.0407063i
$796$		0			0
$797$	−7.36365	−	17.7774i	−0.260834	−	0.629709i	0.738157	−	0.674629i	$-0.235696\pi$
$797$	−7.36365	−	17.7774i	−0.260834	−	0.629709i	−0.998991	+	0.0449207i	$0.985696\pi$
$798$		0			0
$799$	−40.5816			−1.43567
$800$		0			0
$801$	2.43772			0.0861327
$802$		0			0
$803$	−1.85731	−	4.48395i	−0.0655432	−	0.158235i
$804$		0			0
$805$	14.3271	+	5.93447i	0.504963	+	0.209163i
$806$		0			0
$807$	31.5086	+	31.5086i	1.10916	+	1.10916i
$808$		0			0
$809$	−12.5167	+	12.5167i	−0.440065	+	0.440065i	−0.892034	−	0.451969i	$-0.850722\pi$
$809$	−12.5167	+	12.5167i	−0.440065	+	0.440065i	0.451969	+	0.892034i	$0.350722\pi$
$810$		0			0
$811$	−14.6882	+	35.4605i	−0.515773	+	1.24519i	0.424704	+	0.905332i	$0.360378\pi$
$811$	−14.6882	+	35.4605i	−0.515773	+	1.24519i	−0.940478	+	0.339855i	$0.889622\pi$
$812$		0			0
$813$	−9.76117	+	4.04321i	−0.342339	+	0.141802i
$814$		0			0
$815$		−	14.4444i		−	0.505967i
$816$		0			0
$817$		−	5.70655i		−	0.199647i
$818$		0			0
$819$	4.12514	−	1.70869i	0.144144	−	0.0597064i
$820$		0			0
$821$	7.74340	−	18.6942i	0.270247	−	0.652433i	−0.729247	−	0.684250i	$-0.760130\pi$
$821$	7.74340	−	18.6942i	0.270247	−	0.652433i	0.999494	+	0.0318175i	$0.0101295\pi$
$822$		0			0
$823$	−5.40198	+	5.40198i	−0.188301	+	0.188301i	−0.794961	−	0.606660i	$-0.792509\pi$
$823$	−5.40198	+	5.40198i	−0.188301	+	0.188301i	0.606660	+	0.794961i	$0.292509\pi$
$824$		0			0
$825$	−0.445410	−	0.445410i	−0.0155072	−	0.0155072i
$826$		0			0
$827$	9.97222	+	4.13063i	0.346768	+	0.143636i	0.549268	−	0.835646i	$-0.314907\pi$
$827$	9.97222	+	4.13063i	0.346768	+	0.143636i	−0.202500	+	0.979282i	$0.564907\pi$
$828$		0			0
$829$	−5.90110	−	14.2465i	−0.204954	−	0.494802i	0.787661	−	0.616108i	$-0.211292\pi$
$829$	−5.90110	−	14.2465i	−0.204954	−	0.494802i	−0.992615	+	0.121306i	$0.961292\pi$
$830$		0			0
$831$	−44.3960			−1.54008
$832$		0			0
$833$	−4.21228			−0.145947
$834$		0			0
$835$	−2.80784	−	6.77872i	−0.0971692	−	0.234587i
$836$		0			0
$837$	27.8070	+	11.5180i	0.961150	+	0.398121i
$838$		0			0
$839$	3.63604	+	3.63604i	0.125530	+	0.125530i	0.767081	−	0.641551i	$-0.221709\pi$
$839$	3.63604	+	3.63604i	0.125530	+	0.125530i	−0.641551	+	0.767081i	$0.721709\pi$
$840$		0			0
$841$	19.5019	−	19.5019i	0.672480	−	0.672480i
$842$		0			0
$843$	5.96523	−	14.4013i	0.205453	−	0.496009i
$844$		0			0
$845$	−71.7127	+	29.7044i	−2.46699	+	1.02186i
$846$		0			0
$847$			10.8032i			0.371202i
$848$		0			0
$849$		−	20.7373i		−	0.711701i
$850$		0			0
$851$	74.5996	−	30.9001i	2.55724	−	1.05924i
$852$		0			0
$853$	3.01879	−	7.28800i	0.103361	−	0.249536i	−0.863735	−	0.503946i	$-0.831881\pi$
$853$	3.01879	−	7.28800i	0.103361	−	0.249536i	0.967097	+	0.254410i	$0.0818811\pi$
$854$		0			0
$855$	−2.15341	+	2.15341i	−0.0736452	+	0.0736452i
$856$		0			0
$857$	36.5654	+	36.5654i	1.24905	+	1.24905i	0.956139	+	0.292912i	$0.0946245\pi$
$857$	36.5654	+	36.5654i	1.24905	+	1.24905i	0.292912	+	0.956139i	$0.405376\pi$
$858$		0			0
$859$	0.677537	+	0.280645i	0.0231173	+	0.00957548i	0.394212	−	0.919019i	$-0.371018\pi$
$859$	0.677537	+	0.280645i	0.0231173	+	0.00957548i	−0.371095	+	0.928595i	$0.621018\pi$
$860$		0			0
$861$	−0.986133	−	2.38074i	−0.0336073	−	0.0811353i
$862$		0			0
$863$	23.5068			0.800179			0.400090	−	0.916476i	$-0.368979\pi$
$863$	23.5068			0.800179			0.400090	+	0.916476i	$0.368979\pi$
$864$		0			0
$865$	−2.19466			−0.0746206
$866$		0			0
$867$	−0.541784	−	1.30798i	−0.0183999	−	0.0444214i
$868$		0			0
$869$	−5.90078	−	2.44418i	−0.200170	−	0.0829132i
$870$		0			0
$871$	−23.4075	−	23.4075i	−0.793133	−	0.793133i
$872$		0			0
$873$	3.94722	−	3.94722i	0.133593	−	0.133593i
$874$		0			0
$875$	−4.53514	+	10.9488i	−0.153316	+	0.370137i
$876$		0			0
$877$	49.7858	−	20.6219i	1.68115	−	0.696353i	0.681766	−	0.731570i	$-0.261212\pi$
$877$	49.7858	−	20.6219i	1.68115	−	0.696353i	0.999380	+	0.0352169i	$0.0112122\pi$
$878$		0			0
$879$			25.0754i			0.845771i
$880$		0			0
$881$			15.4649i			0.521024i	0.965471	+	0.260512i	$0.0838914\pi$
$881$			15.4649i			0.521024i	−0.965471	+	0.260512i	$0.916109\pi$
$882$		0			0
$883$	−32.9445	+	13.6461i	−1.10867	+	0.459227i	−0.860480	−	0.509484i	$-0.829836\pi$
$883$	−32.9445	+	13.6461i	−1.10867	+	0.459227i	−0.248191	+	0.968711i	$0.579836\pi$
$884$		0			0
$885$	−2.34187	+	5.65379i	−0.0787213	+	0.190050i
$886$		0			0
$887$	39.5426	−	39.5426i	1.32771	−	1.32771i	0.420346	−	0.907364i	$-0.361909\pi$
$887$	39.5426	−	39.5426i	1.32771	−	1.32771i	0.907364	−	0.420346i	$-0.138091\pi$
$888$		0			0
$889$	8.56207	+	8.56207i	0.287163	+	0.287163i
$890$		0			0
$891$	4.29909	+	1.78074i	0.144025	+	0.0596570i
$892$		0			0
$893$	−8.67474	−	20.9427i	−0.290289	−	0.700820i
$894$		0			0
$895$	1.42567			0.0476548
$896$		0			0
$897$	101.890			3.40201
$898$		0			0
$899$	−3.03762	−	7.33346i	−0.101310	−	0.244585i
$900$		0			0
$901$	2.97105	+	1.23065i	0.0989800	+	0.0409989i
$902$		0			0
$903$	−3.26630	−	3.26630i	−0.108696	−	0.108696i
$904$		0			0
$905$	−23.3114	+	23.3114i	−0.774897	+	0.774897i
$906$		0			0
$907$	−14.0309	+	33.8736i	−0.465888	+	1.12475i	0.500053	+	0.865995i	$0.333314\pi$
$907$	−14.0309	+	33.8736i	−0.465888	+	1.12475i	−0.965942	+	0.258759i	$0.916686\pi$
$908$		0			0
$909$	−7.60496	+	3.15008i	−0.252240	+	0.104481i
$910$		0			0
$911$			17.3478i			0.574759i	0.957817	+	0.287379i	$0.0927841\pi$
$911$			17.3478i			0.574759i	−0.957817	+	0.287379i	$0.907216\pi$
$912$		0			0
$913$			4.29673i			0.142201i
$914$		0			0
$915$	−6.49684	+	2.69108i	−0.214779	+	0.0889643i
$916$		0			0
$917$	−6.90778	+	16.6769i	−0.228115	+	0.550719i
$918$		0			0
$919$	−35.4755	+	35.4755i	−1.17023	+	1.17023i	−0.188072	+	0.982155i	$0.560224\pi$
$919$	−35.4755	+	35.4755i	−1.17023	+	1.17023i	−0.982155	+	0.188072i	$0.939776\pi$
$920$		0			0
$921$	39.6190	+	39.6190i	1.30549	+	1.30549i
$922$		0			0
$923$	18.3291	+	7.59217i	0.603310	+	0.249899i
$924$		0			0
$925$	3.06392	+	7.39695i	0.100741	+	0.243210i
$926$		0			0
$927$	−3.03450			−0.0996662
$928$		0			0
$929$	2.13757			0.0701315			0.0350658	−	0.999385i	$-0.488836\pi$
$929$	2.13757			0.0701315			0.0350658	+	0.999385i	$0.488836\pi$
$930$		0			0
$931$	−0.900420	−	2.17381i	−0.0295101	−	0.0712436i
$932$		0			0
$933$	−38.2970	−	15.8632i	−1.25379	−	0.519336i
$934$		0			0
$935$	−2.72562	−	2.72562i	−0.0891374	−	0.0891374i
$936$		0			0
$937$	−4.26446	+	4.26446i	−0.139314	+	0.139314i	−0.773324	−	0.634010i	$-0.781408\pi$
$937$	−4.26446	+	4.26446i	−0.139314	+	0.139314i	0.634010	+	0.773324i	$0.281408\pi$
$938$		0			0
$939$	23.7211	−	57.2678i	0.774109	−	1.86887i
$940$		0			0
$941$	51.8250	−	21.4666i	1.68945	−	0.699791i	0.689740	−	0.724057i	$-0.257725\pi$
$941$	51.8250	−	21.4666i	1.68945	−	0.699791i	0.999706	+	0.0242657i	$0.00772479\pi$
$942$		0			0
$943$		−	10.1721i		−	0.331248i
$944$		0			0
$945$		−	9.32043i		−	0.303194i
$946$		0			0
$947$	−14.4952	+	6.00410i	−0.471030	+	0.195107i	−0.605555	−	0.795803i	$-0.707049\pi$
$947$	−14.4952	+	6.00410i	−0.471030	+	0.195107i	0.134525	+	0.990910i	$0.457049\pi$
$948$		0			0
$949$	−29.7893	+	71.9176i	−0.967000	+	2.33455i
$950$		0			0
$951$	21.9015	−	21.9015i	0.710205	−	0.710205i
$952$		0			0
$953$	32.1278	+	32.1278i	1.04072	+	1.04072i	0.999135	+	0.0415867i	$0.0132413\pi$
$953$	32.1278	+	32.1278i	1.04072	+	1.04072i	0.0415867	+	0.999135i	$0.486759\pi$
$954$		0			0
$955$	−30.0733	−	12.4568i	−0.973148	−	0.403091i
$956$		0			0
$957$	−0.385342	−	0.930298i	−0.0124563	−	0.0300722i
$958$		0			0
$959$	−7.45973			−0.240887
$960$		0			0
$961$	13.3666			0.431182
$962$		0			0
$963$	−1.14722	−	2.76963i	−0.0369686	−	0.0892502i
$964$		0			0
$965$	18.2276	+	7.55011i	0.586766	+	0.243047i
$966$		0			0
$967$	30.7141	+	30.7141i	0.987699	+	0.987699i	0.999925	−	0.0122261i	$-0.00389179\pi$
$967$	30.7141	+	30.7141i	0.987699	+	0.987699i	−0.0122261	+	0.999925i	$0.503892\pi$
$968$		0			0
$969$	13.3479	−	13.3479i	0.428795	−	0.428795i
$970$		0			0
$971$	−15.9158	+	38.4240i	−0.510761	+	1.23309i	0.432681	+	0.901547i	$0.357568\pi$
$971$	−15.9158	+	38.4240i	−0.510761	+	1.23309i	−0.943442	+	0.331539i	$0.892432\pi$
$972$		0			0
$973$	−2.45412	+	1.01653i	−0.0786755	+	0.0325884i
$974$		0			0
$975$			10.1030i			0.323554i
$976$		0			0
$977$		−	0.781423i		−	0.0249999i	−0.999922	−	0.0125000i	$-0.996021\pi$
$977$		−	0.781423i		−	0.0249999i	0.999922	−	0.0125000i	$-0.00397897\pi$
$978$		0			0
$979$	−1.59230	+	0.659553i	−0.0508902	+	0.0210794i
$980$		0			0
$981$	−3.91663	+	9.45559i	−0.125048	+	0.301894i
$982$		0			0
$983$	7.77311	−	7.77311i	0.247924	−	0.247924i	−0.572194	−	0.820118i	$-0.693908\pi$
$983$	7.77311	−	7.77311i	0.247924	−	0.247924i	0.820118	+	0.572194i	$0.193908\pi$
$984$		0			0
$985$	25.8372	+	25.8372i	0.823242	+	0.823242i
$986$		0			0
$987$	−16.9524	−	7.02190i	−0.539600	−	0.223509i
$988$		0			0
$989$	−6.97790	−	16.8461i	−0.221884	−	0.535676i
$990$		0			0
$991$	−0.193808			−0.00615652			−0.00307826	−	0.999995i	$-0.500980\pi$
$991$	−0.193808			−0.00615652			−0.00307826	+	0.999995i	$0.500980\pi$
$992$		0			0
$993$	52.3642			1.66173
$994$		0			0
$995$	−10.9977	−	26.5509i	−0.348651	−	0.841719i
$996$		0			0
$997$	−31.2010	−	12.9239i	−0.988146	−	0.409303i	−0.170709	−	0.985321i	$-0.554606\pi$
$997$	−31.2010	−	12.9239i	−0.988146	−	0.409303i	−0.817437	+	0.576018i	$0.804606\pi$
$998$		0			0
$999$	−34.3162	−	34.3162i	−1.08572	−	1.08572i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	896.2.u.c.113.11		52
4.3	odd	2		224.2.u.c.197.5	yes	52
32.13	even	8	inner	896.2.u.c.785.11		52
32.19	odd	8		224.2.u.c.141.5	✓	52

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
224.2.u.c.141.5	✓	52	32.19	odd	8
224.2.u.c.197.5	yes	52	4.3	odd	2
896.2.u.c.113.11		52	1.1	even	1	trivial
896.2.u.c.785.11		52	32.13	even	8	inner

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:	\( N \)	\(=\)	\( 896 = 2^{7} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	896.u (of order \(8\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.728858 + 1.75962i) q^{3} +(-1.90564 - 0.789342i) q^{5} +(0.707107 + 0.707107i) q^{7} +(-0.443707 + 0.443707i) q^{9} +O(q^{10})\)	\(q+(0.728858 + 1.75962i) q^{3} +(-1.90564 - 0.789342i) q^{5} +(0.707107 + 0.707107i) q^{7} +(-0.443707 + 0.443707i) q^{9} +(0.169776 - 0.409876i) q^{11} +(-6.57396 + 2.72302i) q^{13} -3.92852i q^{15} +4.21228i q^{17} +(-2.17381 + 0.900420i) q^{19} +(-0.728858 + 1.75962i) q^{21} +(-5.31621 + 5.31621i) q^{23} +(-0.527131 - 0.527131i) q^{25} +(4.17470 + 1.72922i) q^{27} +(-0.456042 - 1.10098i) q^{29} +6.66083 q^{31} +0.844970 q^{33} +(-0.789342 - 1.90564i) q^{35} +(-9.92246 - 4.11002i) q^{37} +(-9.58297 - 9.58297i) q^{39} +(-0.956704 + 0.956704i) q^{41} +(-0.928127 + 2.24070i) q^{43} +(1.19578 - 0.495309i) q^{45} +9.63410i q^{47} +1.00000i q^{49} +(-7.41202 + 3.07016i) q^{51} +(0.292157 - 0.705330i) q^{53} +(-0.647065 + 0.647065i) q^{55} +(-3.16879 - 3.16879i) q^{57} +(-1.43916 - 0.596121i) q^{59} +(-0.685011 - 1.65376i) q^{61} -0.627497 q^{63} +14.6770 q^{65} +(1.78032 + 4.29807i) q^{67} +(-13.2293 - 5.47974i) q^{69} +(-1.97151 - 1.97151i) q^{71} +(7.73559 - 7.73559i) q^{73} +(0.543346 - 1.31175i) q^{75} +(0.409876 - 0.169776i) q^{77} -14.3965i q^{79} +10.4887i q^{81} +(-8.94779 + 3.70630i) q^{83} +(3.32493 - 8.02710i) q^{85} +(1.60492 - 1.60492i) q^{87} +(-2.74699 - 2.74699i) q^{89} +(-6.57396 - 2.72302i) q^{91} +(4.85480 + 11.7205i) q^{93} +4.85323 q^{95} -8.89601 q^{97} +(0.106534 + 0.257196i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 52 q+O(q^{10}) \) 52 * q	\( 52 q + 20 q^{23} + 24 q^{27} - 48 q^{33} + 24 q^{39} + 44 q^{43} + 40 q^{45} - 16 q^{51} - 36 q^{53} - 32 q^{55} - 32 q^{61} - 68 q^{63} + 80 q^{65} - 28 q^{67} - 32 q^{69} - 32 q^{75} - 12 q^{77} + 64 q^{85} + 56 q^{87} + 64 q^{95} - 72 q^{97} + 64 q^{99}+O(q^{100}) \) 52 * q + 20 * q^23 + 24 * q^27 - 48 * q^33 + 24 * q^39 + 44 * q^43 + 40 * q^45 - 16 * q^51 - 36 * q^53 - 32 * q^55 - 32 * q^61 - 68 * q^63 + 80 * q^65 - 28 * q^67 - 32 * q^69 - 32 * q^75 - 12 * q^77 + 64 * q^85 + 56 * q^87 + 64 * q^95 - 72 * q^97 + 64 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more