LMFDB - Embedded newform 864.2.bi.a.95.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [864,2,Mod(95,864)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("864.95"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(864, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([9, 0, 17])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 864 = 2^{5} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	864.bi (of order $18$, degree $6$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$6.89907473464$
Analytic rank:	$0$
Dimension:	$216$
Relative dimension:	$36$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			95.4
Character	$\chi$	$=$	864.95
Dual form			864.2.bi.a.191.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.68666 - 0.393943i) q^{3} +(2.16279 - 2.57751i) q^{5} +(0.669796 - 1.84025i) q^{7} +(2.68962 + 1.32889i) q^{9} +(1.89402 - 1.58927i) q^{11} +(0.180867 - 1.02575i) q^{13} +(-4.66328 + 3.49537i) q^{15} +(5.43212 + 3.13624i) q^{17} +(1.67078 - 0.964625i) q^{19} +(-1.85467 + 2.84001i) q^{21} +(-6.31451 + 2.29829i) q^{23} +(-1.09767 - 6.22522i) q^{25} +(-4.01296 - 3.30094i) q^{27} +(-0.537761 + 0.0948218i) q^{29} +(-0.559626 - 1.53756i) q^{31} +(-3.82063 + 1.93442i) q^{33} +(-3.29464 - 5.70648i) q^{35} +(3.88295 - 6.72546i) q^{37} +(-0.709147 + 1.65884i) q^{39} +(-9.41682 - 1.66044i) q^{41} +(7.42054 + 8.84345i) q^{43} +(9.24232 - 4.05842i) q^{45} +(6.49706 + 2.36474i) q^{47} +(2.42442 + 2.03433i) q^{49} +(-7.92662 - 7.42970i) q^{51} -9.38676i q^{53} -8.31911i q^{55} +(-3.19804 + 0.968800i) q^{57} +(-5.19772 - 4.36140i) q^{59} +(-9.81295 - 3.57162i) q^{61} +(4.24699 - 4.05948i) q^{63} +(-2.25271 - 2.68467i) q^{65} +(3.04602 + 0.537096i) q^{67} +(11.5558 - 1.38888i) q^{69} +(2.06166 - 3.57091i) q^{71} +(-0.332546 - 0.575987i) q^{73} +(-0.600979 + 10.9322i) q^{75} +(-1.65604 - 4.54995i) q^{77} +(-6.07165 + 1.07060i) q^{79} +(5.46810 + 7.14842i) q^{81} +(-2.83924 - 16.1021i) q^{83} +(19.8322 - 7.21834i) q^{85} +(0.944372 + 0.0519152i) q^{87} +(-14.7688 + 8.52677i) q^{89} +(-1.76649 - 1.01988i) q^{91} +(0.338186 + 2.81379i) q^{93} +(1.12721 - 6.39274i) q^{95} +(-0.273025 + 0.229095i) q^{97} +(7.20615 - 1.75758i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 216 q - 24 q^{29} + 36 q^{33} + 36 q^{41} - 24 q^{45} + 12 q^{57} + 48 q^{65} + 48 q^{69} + 48 q^{77} + 48 q^{81} + 36 q^{89} - 144 q^{93} - 36 q^{97}+O(q^{100}) $ 216 * q - 24 * q^29 + 36 * q^33 + 36 * q^41 - 24 * q^45 + 12 * q^57 + 48 * q^65 + 48 * q^69 + 48 * q^77 + 48 * q^81 + 36 * q^89 - 144 * q^93 - 36 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/864\mathbb{Z}\right)^\times$.

$n$	$325$	$353$	$703$
$\chi(n)$	$1$	$e\left(\frac{17}{18}\right)$	$-1$

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
$3$	−1.68666	−	0.393943i	−0.973791	−	0.227443i
$3$	−1.68666	−	0.393943i	−0.973791	−	0.227443i
$4$		0			0
$5$	2.16279	−	2.57751i	0.967230	−	1.15270i	−0.0210087	−	0.999779i	$-0.506688\pi$
$5$	2.16279	−	2.57751i	0.967230	−	1.15270i	0.988239	−	0.152920i	$-0.0488678\pi$
$6$		0			0
$7$	0.669796	−	1.84025i	0.253159	−	0.695549i	−0.746390	−	0.665509i	$-0.768214\pi$
$7$	0.669796	−	1.84025i	0.253159	−	0.695549i	0.999549	−	0.0300395i	$-0.00956332\pi$
$8$		0			0
$9$	2.68962	+	1.32889i	0.896540	+	0.442964i
$10$		0			0
$11$	1.89402	−	1.58927i	0.571067	−	0.479182i	−0.310933	−	0.950432i	$-0.600641\pi$
$11$	1.89402	−	1.58927i	0.571067	−	0.479182i	0.882000	+	0.471250i	$0.156197\pi$
$12$		0			0
$13$	0.180867	−	1.02575i	0.0501636	−	0.284492i	−0.949399	−	0.314073i	$-0.898306\pi$
$13$	0.180867	−	1.02575i	0.0501636	−	0.284492i	0.999562	+	0.0295814i	$0.00941742\pi$
$14$		0			0
$15$	−4.66328	+	3.49537i	−1.20405	+	0.902500i
$16$		0			0
$17$	5.43212	+	3.13624i	1.31748	+	0.760649i	0.983323	−	0.181868i	$-0.0582142\pi$
$17$	5.43212	+	3.13624i	1.31748	+	0.760649i	0.334160	+	0.942516i	$0.391548\pi$
$18$		0			0
$19$	1.67078	−	0.964625i	0.383303	−	0.221300i	−0.295951	−	0.955203i	$-0.595637\pi$
$19$	1.67078	−	0.964625i	0.383303	−	0.221300i	0.679254	+	0.733903i	$0.262303\pi$
$20$		0			0
$21$	−1.85467	+	2.84001i	−0.404722	+	0.619740i
$22$		0			0
$23$	−6.31451	+	2.29829i	−1.31667	+	0.479227i	−0.902389	−	0.430923i	$-0.858188\pi$
$23$	−6.31451	+	2.29829i	−1.31667	+	0.479227i	−0.414278	+	0.910150i	$0.635966\pi$
$24$		0			0
$25$	−1.09767	−	6.22522i	−0.219535	−	1.24504i
$26$		0			0
$27$	−4.01296	−	3.30094i	−0.772294	−	0.635266i
$28$		0			0
$29$	−0.537761	+	0.0948218i	−0.0998597	+	0.0176080i	−0.223355	−	0.974737i	$-0.571701\pi$
$29$	−0.537761	+	0.0948218i	−0.0998597	+	0.0176080i	0.123495	+	0.992345i	$0.460590\pi$
$30$		0			0
$31$	−0.559626	−	1.53756i	−0.100512	−	0.276154i	0.879237	−	0.476385i	$-0.158053\pi$
$31$	−0.559626	−	1.53756i	−0.100512	−	0.276154i	−0.979749	+	0.200231i	$0.935831\pi$
$32$		0			0
$33$	−3.82063	+	1.93442i	−0.665087	+	0.336739i
$34$		0			0
$35$	−3.29464	−	5.70648i	−0.556896	−	0.964572i
$36$		0			0
$37$	3.88295	−	6.72546i	0.638353	−	1.10566i	−0.347441	−	0.937702i	$-0.612949\pi$
$37$	3.88295	−	6.72546i	0.638353	−	1.10566i	0.985794	−	0.167958i	$-0.0537173\pi$
$38$		0			0
$39$	−0.709147	+	1.65884i	−0.113554	+	0.265626i
$40$		0			0
$41$	−9.41682	−	1.66044i	−1.47066	−	0.259317i	−0.619821	−	0.784743i	$-0.712795\pi$
$41$	−9.41682	−	1.66044i	−1.47066	−	0.259317i	−0.850839	+	0.525426i	$0.823906\pi$
$42$		0			0
$43$	7.42054	+	8.84345i	1.13162	+	1.34861i	0.929314	+	0.369292i	$0.120400\pi$
$43$	7.42054	+	8.84345i	1.13162	+	1.34861i	0.202308	+	0.979322i	$0.435156\pi$
$44$		0			0
$45$	9.24232	−	4.05842i	1.37776	−	0.604993i
$46$		0			0
$47$	6.49706	+	2.36474i	0.947693	+	0.344932i	0.769199	−	0.639009i	$-0.220655\pi$
$47$	6.49706	+	2.36474i	0.947693	+	0.344932i	0.178494	+	0.983941i	$0.442878\pi$
$48$		0			0
$49$	2.42442	+	2.03433i	0.346346	+	0.290619i
$50$		0			0
$51$	−7.92662	−	7.42970i	−1.10995	−	1.04037i
$52$		0			0
$53$		−	9.38676i		−	1.28937i	−0.764448	−	0.644685i	$-0.776988\pi$
$53$		−	9.38676i		−	1.28937i	0.764448	−	0.644685i	$-0.223012\pi$
$54$		0			0
$55$		−	8.31911i		−	1.12175i
$56$		0			0
$57$	−3.19804	+	0.968800i	−0.423591	+	0.128321i
$58$		0			0
$59$	−5.19772	−	4.36140i	−0.676685	−	0.567806i	0.238351	−	0.971179i	$-0.423393\pi$
$59$	−5.19772	−	4.36140i	−0.676685	−	0.567806i	−0.915036	+	0.403373i	$0.867838\pi$
$60$		0			0
$61$	−9.81295	−	3.57162i	−1.25642	−	0.457299i	−0.373854	−	0.927488i	$-0.621964\pi$
$61$	−9.81295	−	3.57162i	−1.25642	−	0.457299i	−0.882566	+	0.470188i	$0.844186\pi$
$62$		0			0
$63$	4.24699	−	4.05948i	0.535070	−	0.511447i
$64$		0			0
$65$	−2.25271	−	2.68467i	−0.279414	−	0.332992i
$66$		0			0
$67$	3.04602	+	0.537096i	0.372131	+	0.0656167i	0.356586	−	0.934262i	$-0.383941\pi$
$67$	3.04602	+	0.537096i	0.372131	+	0.0656167i	0.0155447	+	0.999879i	$0.495052\pi$
$68$		0			0
$69$	11.5558	−	1.38888i	1.39116	−	0.167201i
$70$		0			0
$71$	2.06166	−	3.57091i	0.244675	−	0.423789i	−0.717366	−	0.696697i	$-0.754652\pi$
$71$	2.06166	−	3.57091i	0.244675	−	0.423789i	0.962040	+	0.272908i	$0.0879856\pi$
$72$		0			0
$73$	−0.332546	−	0.575987i	−0.0389216	−	0.0674142i	0.845908	−	0.533328i	$-0.179059\pi$
$73$	−0.332546	−	0.575987i	−0.0389216	−	0.0674142i	−0.884830	+	0.465914i	$0.845726\pi$
$74$		0			0
$75$	−0.600979	+	10.9322i	−0.0693951	+	1.26234i
$76$		0			0
$77$	−1.65604	−	4.54995i	−0.188724	−	0.518514i
$78$		0			0
$79$	−6.07165	+	1.07060i	−0.683114	+	0.120451i	−0.504427	−	0.863454i	$-0.668296\pi$
$79$	−6.07165	+	1.07060i	−0.683114	+	0.120451i	−0.178687	+	0.983906i	$0.557185\pi$
$80$		0			0
$81$	5.46810	+	7.14842i	0.607566	+	0.794269i
$82$		0			0
$83$	−2.83924	−	16.1021i	−0.311647	−	1.76744i	−0.590435	−	0.807085i	$-0.701044\pi$
$83$	−2.83924	−	16.1021i	−0.311647	−	1.76744i	0.278788	−	0.960353i	$-0.410067\pi$
$84$		0			0
$85$	19.8322	−	7.21834i	2.15111	−	0.782939i
$86$		0			0
$87$	0.944372	+	0.0519152i	0.101247	+	0.00556589i
$88$		0			0
$89$	−14.7688	+	8.52677i	−1.56549	+	0.903836i	−0.568805	+	0.822472i	$0.692594\pi$
$89$	−14.7688	+	8.52677i	−1.56549	+	0.903836i	−0.996684	+	0.0813636i	$0.974073\pi$
$90$		0			0
$91$	−1.76649	−	1.01988i	−0.185178	−	0.106913i
$92$		0			0
$93$	0.338186	+	2.81379i	0.0350683	+	0.291777i
$94$		0			0
$95$	1.12721	−	6.39274i	0.115650	−	0.655882i
$96$		0			0
$97$	−0.273025	+	0.229095i	−0.0277215	+	0.0232611i	−0.656543	−	0.754289i	$-0.727982\pi$
$97$	−0.273025	+	0.229095i	−0.0277215	+	0.0232611i	0.628822	+	0.777550i	$0.283538\pi$
$98$		0			0
$99$	7.20615	−	1.75758i	0.724245	−	0.176644i
$100$		0			0
$101$	−5.51402	+	15.1497i	−0.548666	+	1.50745i	0.286847	+	0.957976i	$0.407393\pi$
$101$	−5.51402	+	15.1497i	−0.548666	+	1.50745i	−0.835513	+	0.549471i	$0.814829\pi$
$102$		0			0
$103$	5.54743	−	6.61117i	0.546605	−	0.651418i	−0.420050	−	0.907501i	$-0.637987\pi$
$103$	5.54743	−	6.61117i	0.546605	−	0.651418i	0.966655	+	0.256083i	$0.0824319\pi$
$104$		0			0
$105$	3.30890	+	10.9228i	0.322915	+	1.06595i
$106$		0			0
$107$	8.53972			0.825566			0.412783	−	0.910829i	$-0.364557\pi$
$107$	8.53972			0.825566			0.412783	+	0.910829i	$0.364557\pi$
$108$		0			0
$109$	11.1336			1.06640			0.533202	−	0.845988i	$-0.320989\pi$
$109$	11.1336			1.06640			0.533202	+	0.845988i	$0.320989\pi$
$110$		0			0
$111$	−9.19865	+	9.81389i	−0.873097	+	0.931493i
$112$		0			0
$113$	−3.29505	+	3.92689i	−0.309973	+	0.369411i	−0.898430	−	0.439118i	$-0.855291\pi$
$113$	−3.29505	+	3.92689i	−0.309973	+	0.369411i	0.588457	+	0.808528i	$0.299736\pi$
$114$		0			0
$115$	−7.73309	+	21.2465i	−0.721114	+	1.98124i
$116$		0			0
$117$	1.84957	−	2.51852i	0.170993	−	0.232837i
$118$		0			0
$119$	9.40987	−	7.89581i	0.862601	−	0.723808i
$120$		0			0
$121$	−0.848607	+	4.81269i	−0.0771460	+	0.437517i
$122$		0			0
$123$	15.2288	+	6.51028i	1.37314	+	0.587012i
$124$		0			0
$125$	−3.85002	−	2.22281i	−0.344356	−	0.198814i
$126$		0			0
$127$	3.37987	−	1.95137i	0.299915	−	0.173156i	−0.342490	−	0.939522i	$-0.611270\pi$
$127$	3.37987	−	1.95137i	0.299915	−	0.173156i	0.642405	+	0.766365i	$0.277937\pi$
$128$		0			0
$129$	−9.03208	−	17.8391i	−0.795231	−	1.57065i
$130$		0			0
$131$	−11.8404	+	4.30957i	−1.03450	+	0.376528i	−0.802794	−	0.596257i	$-0.796654\pi$
$131$	−11.8404	+	4.30957i	−1.03450	+	0.376528i	−0.231710	+	0.972785i	$0.574432\pi$
$132$		0			0
$133$	−0.656069	−	3.72075i	−0.0568884	−	0.322630i
$134$		0			0
$135$	−17.1874	+	3.20421i	−1.47926	+	0.275775i
$136$		0			0
$137$	1.71331	−	0.302103i	0.146378	−	0.0258104i	−0.0999790	−	0.994990i	$-0.531878\pi$
$137$	1.71331	−	0.302103i	0.146378	−	0.0258104i	0.246357	+	0.969179i	$0.420766\pi$
$138$		0			0
$139$	4.40691	+	12.1079i	0.373789	+	1.02698i	0.973884	+	0.227048i	$0.0729074\pi$
$139$	4.40691	+	12.1079i	0.373789	+	1.02698i	−0.600095	+	0.799929i	$0.704870\pi$
$140$		0			0
$141$	−10.0267	−	6.54796i	−0.844403	−	0.551438i
$142$		0			0
$143$	−1.28763	−	2.23023i	−0.107677	−	0.186501i
$144$		0			0
$145$	−0.918660	+	1.59117i	−0.0762906	+	0.132139i
$146$		0			0
$147$	−3.28776	−	4.38630i	−0.271170	−	0.361776i
$148$		0			0
$149$	−15.4657	−	2.72702i	−1.26700	−	0.223406i	−0.500549	−	0.865708i	$-0.666868\pi$
$149$	−15.4657	−	2.72702i	−1.26700	−	0.223406i	−0.766452	+	0.642302i	$0.777980\pi$
$150$		0			0
$151$	11.5469	+	13.7611i	0.939676	+	1.11986i	0.992620	+	0.121265i	$0.0386951\pi$
$151$	11.5469	+	13.7611i	0.939676	+	1.11986i	−0.0529439	+	0.998597i	$0.516860\pi$
$152$		0			0
$153$	10.4426	+	15.6540i	0.844235	+	1.26555i
$154$		0			0
$155$	−5.17344	−	1.88298i	−0.415540	−	0.151244i
$156$		0			0
$157$	−9.03307	−	7.57964i	−0.720917	−	0.604921i	0.206722	−	0.978400i	$-0.433721\pi$
$157$	−9.03307	−	7.57964i	−0.720917	−	0.604921i	−0.927639	+	0.373478i	$0.878165\pi$
$158$		0			0
$159$	−3.69784	+	15.8322i	−0.293258	+	1.25558i
$160$		0			0
$161$			13.1597i			1.03713i
$162$		0			0
$163$			10.8683i			0.851273i	0.904894	+	0.425637i	$0.139950\pi$
$163$			10.8683i			0.851273i	−0.904894	+	0.425637i	$0.860050\pi$
$164$		0			0
$165$	−3.27725	+	14.0315i	−0.255134	+	1.09235i
$166$		0			0
$167$	0.347865	+	0.291893i	0.0269186	+	0.0225874i	0.656148	−	0.754633i	$-0.272185\pi$
$167$	0.347865	+	0.291893i	0.0269186	+	0.0225874i	−0.629229	+	0.777220i	$0.716629\pi$
$168$		0			0
$169$	11.1966	+	4.07521i	0.861273	+	0.313478i
$170$		0			0
$171$	5.77564	−	0.374189i	0.441674	−	0.0286150i
$172$		0			0
$173$	10.0308	+	11.9542i	0.762627	+	0.908864i	0.998011	−	0.0630389i	$-0.0200792\pi$
$173$	10.0308	+	11.9542i	0.762627	+	0.908864i	−0.235384	+	0.971902i	$0.575635\pi$
$174$		0			0
$175$	−12.1912	−	2.14963i	−0.921565	−	0.162497i
$176$		0			0
$177$	7.04862	+	9.40379i	0.529807	+	0.706832i
$178$		0			0
$179$	−11.2557	+	19.4954i	−0.841289	+	1.45715i	0.0475171	+	0.998870i	$0.484869\pi$
$179$	−11.2557	+	19.4954i	−0.841289	+	1.45715i	−0.888806	+	0.458284i	$0.848464\pi$
$180$		0			0
$181$	5.91867	+	10.2514i	0.439932	+	0.761984i	0.997684	−	0.0680237i	$-0.0216693\pi$
$181$	5.91867	+	10.2514i	0.439932	+	0.761984i	−0.557752	+	0.830008i	$0.688336\pi$
$182$		0			0
$183$	15.1441	+	9.88984i	1.11948	+	0.731078i
$184$		0			0
$185$	−8.93698	−	24.5541i	−0.657059	−	1.80526i
$186$		0			0
$187$	15.2728	−	2.69301i	1.11686	−	0.196933i
$188$		0			0
$189$	−8.76241	+	5.17388i	−0.637371	+	0.376345i
$190$		0			0
$191$	−0.907792	−	5.14835i	−0.0656855	−	0.372521i	−0.999876	−	0.0157466i	$-0.994988\pi$
$191$	−0.907792	−	5.14835i	−0.0656855	−	0.372521i	0.934190	−	0.356775i	$-0.116124\pi$
$192$		0			0
$193$	−4.64049	+	1.68900i	−0.334030	+	0.121577i	−0.503590	−	0.863943i	$-0.667988\pi$
$193$	−4.64049	+	1.68900i	−0.334030	+	0.121577i	0.169560	+	0.985520i	$0.445765\pi$
$194$		0			0
$195$	2.74193	+	5.41555i	0.196354	+	0.387816i
$196$		0			0
$197$	−15.2867	+	8.82581i	−1.08914	+	0.628813i	−0.933346	−	0.358978i	$-0.883125\pi$
$197$	−15.2867	+	8.82581i	−1.08914	+	0.628813i	−0.155789	+	0.987790i	$0.549792\pi$
$198$		0			0
$199$	23.2442	+	13.4200i	1.64773	+	0.951320i	0.977970	+	0.208746i	$0.0669382\pi$
$199$	23.2442	+	13.4200i	1.64773	+	0.951320i	0.669764	+	0.742574i	$0.266395\pi$
$200$		0			0
$201$	−4.92601	−	2.10585i	−0.347454	−	0.148535i
$202$		0			0
$203$	−0.185694	+	1.05313i	−0.0130332	+	0.0739149i
$204$		0			0
$205$	−24.6464	+	20.6808i	−1.72138	+	1.44441i
$206$		0			0
$207$	−20.0378	−	2.20976i	−1.39272	−	0.153589i
$208$		0			0
$209$	1.63144	−	4.48233i	0.112849	−	0.310049i
$210$		0			0
$211$	6.76909	−	8.06709i	0.466004	−	0.555361i	−0.480943	−	0.876752i	$-0.659706\pi$
$211$	6.76909	−	8.06709i	0.466004	−	0.555361i	0.946947	+	0.321390i	$0.104150\pi$
$212$		0			0
$213$	−4.88405	+	5.21072i	−0.334650	+	0.357032i
$214$		0			0
$215$	38.8432			2.64908
$216$		0			0
$217$	−3.20433			−0.217524
$218$		0			0
$219$	0.333986	+	1.10250i	0.0225687	+	0.0744998i
$220$		0			0
$221$	4.19948	−	5.00475i	0.282488	−	0.336656i
$222$		0			0
$223$	5.75983	−	15.8250i	0.385707	−	1.05972i	−0.583208	−	0.812323i	$-0.698203\pi$
$223$	5.75983	−	15.8250i	0.385707	−	1.05972i	0.968914	−	0.247397i	$-0.0795752\pi$
$224$		0			0
$225$	5.32031	−	18.2021i	0.354687	−	1.21348i
$226$		0			0
$227$	−4.14756	+	3.48022i	−0.275283	+	0.230990i	−0.769968	−	0.638082i	$-0.779728\pi$
$227$	−4.14756	+	3.48022i	−0.275283	+	0.230990i	0.494685	+	0.869072i	$0.335284\pi$
$228$		0			0
$229$	4.07759	−	23.1251i	0.269454	−	1.52815i	−0.486589	−	0.873631i	$-0.661759\pi$
$229$	4.07759	−	23.1251i	0.269454	−	1.52815i	0.756044	−	0.654521i	$-0.227130\pi$
$230$		0			0
$231$	1.00076	+	8.32658i	0.0658453	+	0.547849i
$232$		0			0
$233$	2.34851	+	1.35591i	0.153856	+	0.0888287i	0.574951	−	0.818188i	$-0.305021\pi$
$233$	2.34851	+	1.35591i	0.153856	+	0.0888287i	−0.421096	+	0.907016i	$0.638354\pi$
$234$		0			0
$235$	20.1469	−	11.6318i	1.31424	−	0.758777i
$236$		0			0
$237$	10.6625	+	0.586154i	0.692607	+	0.0380748i
$238$		0			0
$239$	13.2738	−	4.83125i	0.858608	−	0.312508i	0.125063	−	0.992149i	$-0.460087\pi$
$239$	13.2738	−	4.83125i	0.858608	−	0.312508i	0.733545	+	0.679641i	$0.237864\pi$
$240$		0			0
$241$	−2.77584	−	15.7426i	−0.178808	−	1.01407i	−0.933656	−	0.358170i	$-0.883401\pi$
$241$	−2.77584	−	15.7426i	−0.178808	−	1.01407i	0.754849	−	0.655899i	$-0.227710\pi$
$242$		0			0
$243$	−6.40673	−	14.2110i	−0.410992	−	0.911639i
$244$		0			0
$245$	10.4870	−	1.84915i	0.669992	−	0.118138i
$246$		0			0
$247$	−0.687274	−	1.88827i	−0.0437302	−	0.120148i
$248$		0			0
$249$	−1.55449	+	28.2773i	−0.0985119	+	1.79200i
$250$		0			0
$251$	−6.49840	−	11.2556i	−0.410176	−	0.710445i	0.584733	−	0.811226i	$-0.301199\pi$
$251$	−6.49840	−	11.2556i	−0.410176	−	0.710445i	−0.994909	+	0.100781i	$0.967866\pi$
$252$		0			0
$253$	−8.30718	+	14.3885i	−0.522268	+	0.904595i
$254$		0			0
$255$	−36.2938	+	4.36210i	−2.27280	+	0.273166i
$256$		0			0
$257$	28.5374	+	5.03191i	1.78011	+	0.313882i	0.964374	−	0.264541i	$-0.0852205\pi$
$257$	28.5374	+	5.03191i	1.78011	+	0.313882i	0.815737	+	0.578423i	$0.196332\pi$
$258$		0			0
$259$	−9.77575	−	11.6503i	−0.607435	−	0.723913i
$260$		0			0
$261$	−1.57238	−	0.459591i	−0.0973279	−	0.0284480i
$262$		0			0
$263$	0.0560482	+	0.0203999i	0.00345608	+	0.00125791i	0.343748	−	0.939062i	$-0.388304\pi$
$263$	0.0560482	+	0.0203999i	0.00345608	+	0.00125791i	−0.340292	+	0.940320i	$0.610526\pi$
$264$		0			0
$265$	−24.1945	−	20.3016i	−1.48626	−	1.24712i
$266$		0			0
$267$	28.2689	−	8.56367i	1.73003	−	0.524088i
$268$		0			0
$269$		−	11.6327i		−	0.709260i	−0.935007	−	0.354630i	$-0.884607\pi$
$269$		−	11.6327i		−	0.709260i	0.935007	−	0.354630i	$-0.115393\pi$
$270$		0			0
$271$		−	11.1574i		−	0.677766i	−0.940829	−	0.338883i	$-0.889951\pi$
$271$		−	11.1574i		−	0.677766i	0.940829	−	0.338883i	$-0.110049\pi$
$272$		0			0
$273$	2.57769	+	2.41609i	0.156009	+	0.146228i
$274$		0			0
$275$	−11.9725	−	10.0462i	−0.721972	−	0.605806i
$276$		0			0
$277$	−4.48291	−	1.63165i	−0.269352	−	0.0980361i	0.203813	−	0.979010i	$-0.434666\pi$
$277$	−4.48291	−	1.63165i	−0.269352	−	0.0980361i	−0.473165	+	0.880974i	$0.656889\pi$
$278$		0			0
$279$	0.538069	−	4.87913i	0.0322134	−	0.292106i
$280$		0			0
$281$	−1.62414	−	1.93557i	−0.0968878	−	0.115466i	0.715422	−	0.698693i	$-0.246235\pi$
$281$	−1.62414	−	1.93557i	−0.0968878	−	0.115466i	−0.812310	+	0.583226i	$0.801790\pi$
$282$		0			0
$283$	−26.7101	−	4.70971i	−1.58775	−	0.279963i	−0.691118	−	0.722742i	$-0.742882\pi$
$283$	−26.7101	−	4.70971i	−1.58775	−	0.279963i	−0.896631	+	0.442779i	$0.853993\pi$
$284$		0			0
$285$	−4.41959	+	10.3383i	−0.261794	+	0.612388i
$286$		0			0
$287$	−9.36297	+	16.2171i	−0.552678	+	0.957267i
$288$		0			0
$289$	11.1720	+	19.3504i	0.657174	+	1.13826i
$290$		0			0
$291$	0.550749	−	0.278848i	0.0322855	−	0.0163464i
$292$		0			0
$293$	3.39495	+	9.32754i	0.198335	+	0.544921i	0.998494	−	0.0548675i	$-0.0174736\pi$
$293$	3.39495	+	9.32754i	0.198335	+	0.544921i	−0.800159	+	0.599788i	$0.795251\pi$
$294$		0			0
$295$	−22.4832	+	3.96439i	−1.30902	+	0.230816i
$296$		0			0
$297$	−12.8467	+	0.125633i	−0.745440	+	0.00728996i
$298$		0			0
$299$	1.21539	+	6.89279i	0.0702875	+	0.398620i
$300$		0			0
$301$	21.2444	−	7.73233i	1.22451	−	0.445684i
$302$		0			0
$303$	15.2684	−	23.3801i	0.877144	−	1.34315i
$304$		0			0
$305$	−30.4293	+	17.5684i	−1.74238	+	1.00596i
$306$		0			0
$307$	22.8366	+	13.1847i	1.30335	+	0.752491i	0.980978	−	0.194120i	$-0.0621852\pi$
$307$	22.8366	+	13.1847i	1.30335	+	0.752491i	0.322376	+	0.946612i	$0.395519\pi$
$308$		0			0
$309$	−11.9610	+	8.96541i	−0.680440	+	0.510024i
$310$		0			0
$311$	−4.56457	+	25.8870i	−0.258833	+	1.46792i	0.527205	+	0.849738i	$0.323240\pi$
$311$	−4.56457	+	25.8870i	−0.258833	+	1.46792i	−0.786038	+	0.618178i	$0.787871\pi$
$312$		0			0
$313$	11.4160	−	9.57918i	0.645272	−	0.541447i	−0.260360	−	0.965511i	$-0.583841\pi$
$313$	11.4160	−	9.57918i	0.645272	−	0.541447i	0.905632	+	0.424064i	$0.139397\pi$
$314$		0			0
$315$	−1.27803	−	19.7265i	−0.0720088	−	1.11146i
$316$		0			0
$317$	4.71602	−	12.9572i	0.264878	−	0.727747i	−0.733943	−	0.679211i	$-0.762322\pi$
$317$	4.71602	−	12.9572i	0.264878	−	0.727747i	0.998821	−	0.0485359i	$-0.0154555\pi$
$318$		0			0
$319$	−0.867831	+	1.03424i	−0.0485892	+	0.0579063i
$320$		0			0
$321$	−14.4036	−	3.36416i	−0.803929	−	0.187769i
$322$		0			0
$323$	12.1012			0.673327
$324$		0			0
$325$	−6.58404			−0.365217
$326$		0			0
$327$	−18.7785	−	4.38599i	−1.03846	−	0.242546i
$328$		0			0
$329$	8.70340	−	10.3723i	0.479834	−	0.571844i
$330$		0			0
$331$	−3.92538	+	10.7849i	−0.215759	+	0.592792i	−0.999603	−	0.0281650i	$-0.991034\pi$
$331$	−3.92538	+	10.7849i	−0.215759	+	0.592792i	0.783845	+	0.620957i	$0.213256\pi$
$332$		0			0
$333$	19.3811	−	12.9289i	1.06208	−	0.708500i
$334$		0			0
$335$	7.97228	−	6.68954i	0.435572	−	0.365489i
$336$		0			0
$337$	3.98329	−	22.5904i	0.216984	−	1.23058i	−0.660447	−	0.750873i	$-0.729633\pi$
$337$	3.98329	−	22.5904i	0.216984	−	1.23058i	0.877430	−	0.479704i	$-0.159256\pi$
$338$		0			0
$339$	7.10459	−	5.32525i	0.385868	−	0.289228i
$340$		0			0
$341$	−3.50353	−	2.02277i	−0.189727	−	0.109539i
$342$		0			0
$343$	17.2394	−	9.95318i	0.930841	−	0.537421i
$344$		0			0
$345$	21.4129	−	32.7891i	1.15283	−	1.76531i
$346$		0			0
$347$	2.51636	−	0.915879i	0.135085	−	0.0491670i	−0.273593	−	0.961846i	$-0.588212\pi$
$347$	2.51636	−	0.915879i	0.135085	−	0.0491670i	0.408678	+	0.912679i	$0.365990\pi$
$348$		0			0
$349$	2.66673	+	15.1238i	0.142747	+	0.809558i	0.969149	+	0.246477i	$0.0792730\pi$
$349$	2.66673	+	15.1238i	0.142747	+	0.809558i	−0.826402	+	0.563081i	$0.809616\pi$
$350$		0			0
$351$	−4.11175	+	3.51925i	−0.219469	+	0.187844i
$352$		0			0
$353$	16.3565	−	2.88410i	0.870571	−	0.153505i	0.279520	−	0.960140i	$-0.409825\pi$
$353$	16.3565	−	2.88410i	0.870571	−	0.153505i	0.591050	+	0.806635i	$0.298713\pi$
$354$		0			0
$355$	−4.74512	−	13.0371i	−0.251845	−	0.691937i
$356$		0			0
$357$	−18.9817	+	9.61058i	−1.00462	+	0.508646i
$358$		0			0
$359$	17.2448	+	29.8689i	0.910146	+	1.57642i	0.813856	+	0.581066i	$0.197364\pi$
$359$	17.2448	+	29.8689i	0.910146	+	1.57642i	0.0962901	+	0.995353i	$0.469302\pi$
$360$		0			0
$361$	−7.63900	+	13.2311i	−0.402052	+	0.696375i
$362$		0			0
$363$	3.32723	−	7.78305i	0.174634	−	0.408504i
$364$		0			0
$365$	−2.20384	−	0.388597i	−0.115354	−	0.0203401i
$366$		0			0
$367$	12.2133	+	14.5552i	0.637528	+	0.759776i	0.983978	−	0.178292i	$-0.0570572\pi$
$367$	12.2133	+	14.5552i	0.637528	+	0.759776i	−0.346449	+	0.938069i	$0.612613\pi$
$368$		0			0
$369$	−23.1211	−	16.9799i	−1.20364	−	0.883937i
$370$		0			0
$371$	−17.2740	−	6.28721i	−0.896820	−	0.326416i
$372$		0			0
$373$	1.96086	+	1.64536i	0.101530	+	0.0851935i	0.692139	−	0.721764i	$-0.256668\pi$
$373$	1.96086	+	1.64536i	0.101530	+	0.0851935i	−0.590610	+	0.806957i	$0.701113\pi$
$374$		0			0
$375$	5.61800	+	5.26580i	0.290112	+	0.271925i
$376$		0			0
$377$			0.568758i			0.0292925i
$378$		0			0
$379$			4.89256i			0.251314i	0.992074	+	0.125657i	$0.0401038\pi$
$379$			4.89256i			0.251314i	−0.992074	+	0.125657i	$0.959896\pi$
$380$		0			0
$381$	−6.46941	+	1.95982i	−0.331438	+	0.100404i
$382$		0			0
$383$	−4.40255	−	3.69418i	−0.224960	−	0.188764i	0.523341	−	0.852123i	$-0.324685\pi$
$383$	−4.40255	−	3.69418i	−0.224960	−	0.188764i	−0.748301	+	0.663360i	$0.769130\pi$
$384$		0			0
$385$	−15.3092	−	5.57210i	−0.780231	−	0.283981i
$386$		0			0
$387$	8.20643	+	33.6466i	0.417156	+	1.71035i
$388$		0			0
$389$	18.2064	+	21.6976i	0.923102	+	1.10011i	0.994715	+	0.102677i	$0.0327409\pi$
$389$	18.2064	+	21.6976i	0.923102	+	1.10011i	−0.0716130	+	0.997432i	$0.522815\pi$
$390$		0			0
$391$	−41.5092	−	7.31919i	−2.09921	−	0.370147i
$392$		0			0
$393$	21.6685	−	2.60431i	1.09303	−	0.131370i
$394$		0			0
$395$	−10.3722	+	17.9652i	−0.521884	+	0.903930i
$396$		0			0
$397$	−10.5332	−	18.2440i	−0.528645	−	0.915641i	−0.999442	−	0.0333990i	$-0.989367\pi$
$397$	−10.5332	−	18.2440i	−0.528645	−	0.915641i	0.470797	−	0.882242i	$-0.343967\pi$
$398$		0			0
$399$	−0.359200	+	6.53408i	−0.0179825	+	0.327113i
$400$		0			0
$401$	1.37143	+	3.76797i	0.0684859	+	0.188163i	0.969214	−	0.246220i	$-0.0791885\pi$
$401$	1.37143	+	3.76797i	0.0684859	+	0.188163i	−0.900728	+	0.434383i	$0.856966\pi$
$402$		0			0
$403$	−1.67837	+	0.295942i	−0.0836055	+	0.0147419i
$404$		0			0
$405$	30.2515	+	1.36645i	1.50321	+	0.0678993i
$406$		0			0
$407$	−3.33420	−	18.9092i	−0.165270	−	0.937294i
$408$		0			0
$409$	19.4654	−	7.08482i	0.962501	−	0.350322i	0.187488	−	0.982267i	$-0.439965\pi$
$409$	19.4654	−	7.08482i	0.962501	−	0.350322i	0.775013	+	0.631945i	$0.217743\pi$
$410$		0			0
$411$	−3.00878	−	0.165402i	−0.148412	−	0.00815868i
$412$		0			0
$413$	−11.5075	+	6.64384i	−0.566246	+	0.326922i
$414$		0			0
$415$	−47.6442	−	27.5074i	−2.33876	−	1.35028i
$416$		0			0
$417$	−2.66313	−	22.1579i	−0.130414	−	1.08508i
$418$		0			0
$419$	−0.345977	+	1.96213i	−0.0169021	+	0.0958565i	−0.992092	−	0.125514i	$-0.959942\pi$
$419$	−0.345977	+	1.96213i	−0.0169021	+	0.0958565i	0.975190	+	0.221371i	$0.0710531\pi$
$420$		0			0
$421$	−10.7781	+	9.04393i	−0.525294	+	0.440774i	−0.866473	−	0.499224i	$-0.833618\pi$
$421$	−10.7781	+	9.04393i	−0.525294	+	0.440774i	0.341179	+	0.939999i	$0.389174\pi$
$422$		0			0
$423$	14.3321	+	14.9941i	0.696852	+	0.729039i
$424$		0			0
$425$	13.5611	−	37.2587i	0.657808	−	1.80731i
$426$		0			0
$427$	−13.1453	+	15.6660i	−0.636148	+	0.758132i
$428$		0			0
$429$	1.29320	+	4.26889i	0.0624362	+	0.206104i
$430$		0			0
$431$	−26.3094			−1.26728			−0.633640	−	0.773628i	$-0.718440\pi$
$431$	−26.3094			−1.26728			−0.633640	+	0.773628i	$0.718440\pi$
$432$		0			0
$433$	32.5596			1.56471			0.782356	−	0.622831i	$-0.214018\pi$
$433$	32.5596			1.56471			0.782356	+	0.622831i	$0.214018\pi$
$434$		0			0
$435$	2.17629	−	2.32185i	0.104345	−	0.111324i
$436$		0			0
$437$	−8.33317	+	9.93108i	−0.398629	+	0.475068i
$438$		0			0
$439$	6.01640	−	16.5299i	0.287147	−	0.788930i	−0.709315	−	0.704891i	$-0.750996\pi$
$439$	6.01640	−	16.5299i	0.287147	−	0.788930i	0.996462	−	0.0840387i	$-0.0267820\pi$
$440$		0			0
$441$	3.81736	+	8.69337i	0.181779	+	0.413970i
$442$		0			0
$443$	12.1579	−	10.2017i	0.577637	−	0.484695i	−0.306533	−	0.951860i	$-0.599169\pi$
$443$	12.1579	−	10.2017i	0.577637	−	0.484695i	0.884170	+	0.467165i	$0.154725\pi$
$444$		0			0
$445$	−9.96396	+	56.5084i	−0.472337	+	2.67876i
$446$		0			0
$447$	25.0111	+	10.6922i	1.18298	+	0.505721i
$448$		0			0
$449$	5.02068	+	2.89869i	0.236940	+	0.136798i	0.613770	−	0.789485i	$-0.289652\pi$
$449$	5.02068	+	2.89869i	0.236940	+	0.136798i	−0.376829	+	0.926283i	$0.622986\pi$
$450$		0			0
$451$	−20.4745	+	11.8210i	−0.964106	+	0.556627i
$452$		0			0
$453$	−14.0546	−	27.7591i	−0.660344	−	1.30424i
$454$		0			0
$455$	−6.44931	+	2.34736i	−0.302349	+	0.110046i
$456$		0			0
$457$	2.88673	+	16.3715i	0.135035	+	0.765824i	0.974835	+	0.222928i	$0.0715614\pi$
$457$	2.88673	+	16.3715i	0.135035	+	0.765824i	−0.839800	+	0.542897i	$0.817328\pi$
$458$		0			0
$459$	−11.4463	−	30.5167i	−0.534269	−	1.42440i
$460$		0			0
$461$	23.3809	−	4.12268i	1.08896	−	0.192013i	0.399784	−	0.916609i	$-0.369085\pi$
$461$	23.3809	−	4.12268i	1.08896	−	0.192013i	0.689173	+	0.724597i	$0.257974\pi$
$462$		0			0
$463$	−3.26628	−	8.97403i	−0.151797	−	0.417058i	0.840365	−	0.542022i	$-0.182341\pi$
$463$	−3.26628	−	8.97403i	−0.151797	−	0.417058i	−0.992161	+	0.124963i	$0.960119\pi$
$464$		0			0
$465$	7.98402	+	5.21397i	0.370250	+	0.241792i
$466$		0			0
$467$	6.66327	+	11.5411i	0.308339	+	0.534059i	0.977999	−	0.208608i	$-0.0668934\pi$
$467$	6.66327	+	11.5411i	0.308339	+	0.534059i	−0.669660	+	0.742668i	$0.733560\pi$
$468$		0			0
$469$	3.02860	−	5.24569i	0.139848	−	0.242224i
$470$		0			0
$471$	12.2497	+	16.3428i	0.564438	+	0.753035i
$472$		0			0
$473$	28.1092	+	4.95642i	1.29246	+	0.227896i
$474$		0			0
$475$	−7.83897	−	9.34212i	−0.359677	−	0.428646i
$476$		0			0
$477$	12.4740	−	25.2468i	0.571144	−	1.15597i
$478$		0			0
$479$	−21.6497	−	7.87983i	−0.989199	−	0.360039i	−0.203789	−	0.979015i	$-0.565326\pi$
$479$	−21.6497	−	7.87983i	−0.989199	−	0.360039i	−0.785410	+	0.618976i	$0.787548\pi$
$480$		0			0
$481$	−6.19634	−	5.19935i	−0.282529	−	0.237070i
$482$		0			0
$483$	5.18415	−	22.1958i	0.235887	−	1.00994i
$484$		0			0
$485$			1.19921i			0.0544533i
$486$		0			0
$487$			7.69134i			0.348528i	0.984699	+	0.174264i	$0.0557546\pi$
$487$			7.69134i			0.348528i	−0.984699	+	0.174264i	$0.944245\pi$
$488$		0			0
$489$	4.28150	−	18.3311i	0.193616	−	0.828963i
$490$		0			0
$491$	−3.58124	−	3.00502i	−0.161619	−	0.135615i	0.558392	−	0.829578i	$-0.311419\pi$
$491$	−3.58124	−	3.00502i	−0.161619	−	0.135615i	−0.720011	+	0.693963i	$0.755863\pi$
$492$		0			0
$493$	−3.21857	−	1.17146i	−0.144957	−	0.0527600i
$494$		0			0
$495$	11.0552	−	22.3752i	0.496894	−	1.00569i
$496$		0			0
$497$	−5.19046	−	6.18575i	−0.232824	−	0.277469i
$498$		0			0
$499$	−34.9171	−	6.15682i	−1.56310	−	0.275617i	−0.675898	−	0.736995i	$-0.736244\pi$
$499$	−34.9171	−	6.15682i	−1.56310	−	0.275617i	−0.887204	+	0.461378i	$0.847355\pi$
$500$		0			0
$501$	−0.471739	−	0.629362i	−0.0210758	−	0.0281178i
$502$		0			0
$503$	7.15888	−	12.3995i	0.319199	−	0.552868i	−0.661122	−	0.750278i	$-0.729920\pi$
$503$	7.15888	−	12.3995i	0.319199	−	0.552868i	0.980321	+	0.197410i	$0.0632529\pi$
$504$		0			0
$505$	27.1228	+	46.9780i	1.20695	+	2.09049i
$506$		0			0
$507$	−17.2793	−	11.2843i	−0.767402	−	0.501153i
$508$		0			0
$509$	−9.87587	−	27.1337i	−0.437740	−	1.20268i	−0.940959	−	0.338522i	$-0.890073\pi$
$509$	−9.87587	−	27.1337i	−0.437740	−	1.20268i	0.503219	−	0.864159i	$-0.332149\pi$
$510$		0			0
$511$	−1.28270	+	0.226174i	−0.0567432	+	0.0100054i
$512$		0			0
$513$	−9.88893	−	1.64414i	−0.436607	−	0.0725907i
$514$		0			0
$515$	−5.04245	−	28.5972i	−0.222197	−	1.26014i
$516$		0			0
$517$	16.0637	−	5.84672i	0.706482	−	0.257138i
$518$		0			0
$519$	−12.2092	−	24.1142i	−0.535925	−	1.05850i
$520$		0			0
$521$	10.3473	−	5.97403i	0.453324	−	0.261727i	−0.255909	−	0.966701i	$-0.582375\pi$
$521$	10.3473	−	5.97403i	0.453324	−	0.261727i	0.709233	+	0.704974i	$0.249041\pi$
$522$		0			0
$523$	9.97812	+	5.76087i	0.436313	+	0.251905i	0.702032	−	0.712145i	$-0.252276\pi$
$523$	9.97812	+	5.76087i	0.436313	+	0.251905i	−0.265720	+	0.964050i	$0.585610\pi$
$524$		0			0
$525$	19.7155	+	8.42831i	0.860454	+	0.367841i
$526$		0			0
$527$	1.78219	−	10.1073i	0.0776336	−	0.440282i
$528$		0			0
$529$	16.9719	−	14.2411i	0.737908	−	0.619178i
$530$		0			0
$531$	−8.18405	−	18.6377i	−0.355157	−	0.808808i
$532$		0			0
$533$	−3.40639	+	9.35898i	−0.147547	+	0.405382i
$534$		0			0
$535$	18.4696	−	22.0113i	0.798512	−	0.951630i
$536$		0			0
$537$	26.6645	−	28.4479i	1.15066	−	1.22762i
$538$		0			0
$539$	7.82499			0.337046
$540$		0			0
$541$	−17.0505			−0.733059			−0.366529	−	0.930406i	$-0.619454\pi$
$541$	−17.0505			−0.733059			−0.366529	+	0.930406i	$0.619454\pi$
$542$		0			0
$543$	−5.94429	−	19.6223i	−0.255094	−	0.842073i
$544$		0			0
$545$	24.0796	−	28.6970i	1.03146	−	1.22924i
$546$		0			0
$547$	−11.5059	+	31.6122i	−0.491957	+	1.35164i	0.406929	+	0.913460i	$0.366600\pi$
$547$	−11.5059	+	31.6122i	−0.491957	+	1.35164i	−0.898886	+	0.438182i	$0.855623\pi$
$548$		0			0
$549$	−21.6468	−	22.6466i	−0.923863	−	0.966535i
$550$		0			0
$551$	−0.807013	+	0.677164i	−0.0343799	+	0.0288482i
$552$		0			0
$553$	−2.09660	+	11.8904i	−0.0891567	+	0.505633i
$554$		0			0
$555$	5.40069	+	44.9350i	0.229246	+	1.90739i
$556$		0			0
$557$	10.1878	+	5.88192i	0.431670	+	0.249225i	0.700058	−	0.714086i	$-0.253158\pi$
$557$	10.1878	+	5.88192i	0.431670	+	0.249225i	−0.268388	+	0.963311i	$0.586491\pi$
$558$		0			0
$559$	10.4133	−	6.01212i	0.440436	−	0.254286i
$560$		0			0
$561$	−26.8209	−	1.47443i	−1.13238	−	0.0622506i
$562$		0			0
$563$	−37.4911	+	13.6457i	−1.58006	+	0.575096i	−0.975218	−	0.221247i	$-0.928987\pi$
$563$	−37.4911	+	13.6457i	−1.58006	+	0.575096i	−0.604845	+	0.796343i	$0.706765\pi$
$564$		0			0
$565$	2.99511	+	16.9861i	0.126005	+	0.714611i
$566$		0			0
$567$	16.8174	−	5.27468i	0.706264	−	0.221516i
$568$		0			0
$569$	−10.4774	+	1.84745i	−0.439235	+	0.0774490i	−0.388893	−	0.921283i	$-0.627142\pi$
$569$	−10.4774	+	1.84745i	−0.439235	+	0.0774490i	−0.0503422	+	0.998732i	$0.516031\pi$
$570$		0			0
$571$	14.2334	+	39.1059i	0.595649	+	1.63653i	0.759845	+	0.650104i	$0.225275\pi$
$571$	14.2334	+	39.1059i	0.595649	+	1.63653i	−0.164196	+	0.986428i	$0.552503\pi$
$572$		0			0
$573$	−0.497019	+	9.04111i	−0.0207633	+	0.377698i
$574$		0			0
$575$	21.2387	+	36.7864i	0.885713	+	1.53410i
$576$		0			0
$577$	−19.2973	+	33.4239i	−0.803357	+	1.39146i	0.114037	+	0.993477i	$0.463622\pi$
$577$	−19.2973	+	33.4239i	−0.803357	+	1.39146i	−0.917394	+	0.397979i	$0.869712\pi$
$578$		0			0
$579$	8.49229	−	1.02068i	0.352927	−	0.0424179i
$580$		0			0
$581$	−31.5336	−	5.56023i	−1.30824	−	0.230677i
$582$		0			0
$583$	−14.9181	−	17.7787i	−0.617844	−	0.736317i
$584$		0			0
$585$	−2.49128	−	10.2143i	−0.103002	−	0.422311i
$586$		0			0
$587$	25.7747	+	9.38123i	1.06384	+	0.387205i	0.813869	−	0.581049i	$-0.197358\pi$
$587$	25.7747	+	9.38123i	1.06384	+	0.387205i	0.249968	+	0.968254i	$0.419580\pi$
$588$		0			0
$589$	−2.41818	−	2.02909i	−0.0996394	−	0.0836074i
$590$		0			0
$591$	29.2603	−	8.86400i	1.20361	−	0.364616i
$592$		0			0
$593$			23.8547i			0.979596i	0.871836	+	0.489798i	$0.162929\pi$
$593$			23.8547i			0.979596i	−0.871836	+	0.489798i	$0.837071\pi$
$594$		0			0
$595$		−	41.3311i		−	1.69441i
$596$		0			0
$597$	−33.9182	−	31.7918i	−1.38818	−	1.30115i
$598$		0			0
$599$	−4.61252	−	3.87037i	−0.188463	−	0.158139i	0.543675	−	0.839296i	$-0.317033\pi$
$599$	−4.61252	−	3.87037i	−0.188463	−	0.158139i	−0.732137	+	0.681157i	$0.761477\pi$
$600$		0			0
$601$	−40.7708	−	14.8394i	−1.66308	−	0.605310i	−0.672234	−	0.740339i	$-0.734665\pi$
$601$	−40.7708	−	14.8394i	−1.66308	−	0.605310i	−0.990842	+	0.135029i	$0.956887\pi$
$602$		0			0
$603$	7.47889	+	5.49241i	0.304564	+	0.223668i
$604$		0			0
$605$	10.5694	+	12.5961i	0.429708	+	0.512106i
$606$		0			0
$607$	−17.4742	−	3.08117i	−0.709254	−	0.125061i	−0.192628	−	0.981272i	$-0.561701\pi$
$607$	−17.4742	−	3.08117i	−0.709254	−	0.125061i	−0.516626	+	0.856211i	$0.672812\pi$
$608$		0			0
$609$	0.728073	−	1.70311i	0.0295030	−	0.0690134i
$610$		0			0
$611$	3.60073	−	6.23665i	0.145670	−	0.252308i
$612$		0			0
$613$	−0.365561	−	0.633169i	−0.0147649	−	0.0255735i	0.858549	−	0.512732i	$-0.171367\pi$
$613$	−0.365561	−	0.633169i	−0.0147649	−	0.0255735i	−0.873313	+	0.487159i	$0.838033\pi$
$614$		0			0
$615$	49.7171	−	25.1721i	2.00479	−	1.01504i
$616$		0			0
$617$	2.90099	+	7.97039i	0.116789	+	0.320876i	0.984290	−	0.176560i	$-0.0564971\pi$
$617$	2.90099	+	7.97039i	0.116789	+	0.320876i	−0.867501	+	0.497436i	$0.834275\pi$
$618$		0			0
$619$	22.1687	−	3.90894i	0.891036	−	0.157114i	0.290655	−	0.956828i	$-0.406127\pi$
$619$	22.1687	−	3.90894i	0.891036	−	0.157114i	0.600381	+	0.799714i	$0.295016\pi$
$620$		0			0
$621$	32.9264	+	11.6209i	1.32129	+	0.466329i
$622$		0			0
$623$	5.79930	+	32.8895i	0.232344	+	1.31769i
$624$		0			0
$625$	15.6440	−	5.69397i	0.625762	−	0.227759i
$626$		0			0
$627$	−4.51745	+	6.91746i	−0.180410	+	0.276257i
$628$		0			0
$629$	42.1853	−	24.3557i	1.68204	−	0.971125i
$630$		0			0
$631$	6.96833	+	4.02317i	0.277405	+	0.160160i	0.632248	−	0.774766i	$-0.282132\pi$
$631$	6.96833	+	4.02317i	0.277405	+	0.160160i	−0.354843	+	0.934926i	$0.615466\pi$
$632$		0			0
$633$	−14.5951	+	10.9398i	−0.580103	+	0.434817i
$634$		0			0
$635$	2.28028	−	12.9321i	0.0904900	−	0.513194i
$636$		0			0
$637$	2.52521	−	2.11891i	0.100053	−	0.0839541i
$638$		0			0
$639$	10.2904	−	6.86465i	0.407083	−	0.271561i
$640$		0			0
$641$	−10.8473	+	29.8028i	−0.428444	+	1.17714i	0.518313	+	0.855191i	$0.326560\pi$
$641$	−10.8473	+	29.8028i	−0.428444	+	1.17714i	−0.946757	+	0.321949i	$0.895662\pi$
$642$		0			0
$643$	20.9258	−	24.9384i	0.825234	−	0.983476i	−0.174765	−	0.984610i	$-0.555917\pi$
$643$	20.9258	−	24.9384i	0.825234	−	0.983476i	0.999999	+	0.00113439i	$0.000361087\pi$
$644$		0			0
$645$	−65.5151	−	15.3020i	−2.57966	−	0.602515i
$646$		0			0
$647$	−40.2717			−1.58324			−0.791621	−	0.611012i	$-0.790763\pi$
$647$	−40.2717			−1.58324			−0.791621	+	0.611012i	$0.790763\pi$
$648$		0			0
$649$	−16.7760			−0.658515
$650$		0			0
$651$	5.40460	+	1.26232i	0.211823	+	0.0494742i
$652$		0			0
$653$	−3.55771	+	4.23991i	−0.139224	+	0.165921i	−0.831151	−	0.556047i	$-0.812318\pi$
$653$	−3.55771	+	4.23991i	−0.139224	+	0.165921i	0.691927	+	0.721967i	$0.256762\pi$
$654$		0			0
$655$	−14.5004	+	39.8396i	−0.566578	+	1.55666i
$656$		0			0
$657$	−0.128999	−	1.99110i	−0.00503271	−	0.0776804i
$658$		0			0
$659$	11.0903	−	9.30591i	0.432019	−	0.362507i	−0.400694	−	0.916212i	$-0.631231\pi$
$659$	11.0903	−	9.30591i	0.432019	−	0.362507i	0.832713	+	0.553705i	$0.186787\pi$
$660$		0			0
$661$	−1.52635	+	8.65635i	−0.0593681	+	0.336693i	−0.999996	−	0.00274570i	$-0.999126\pi$
$661$	−1.52635	+	8.65635i	−0.0593681	+	0.336693i	0.940628	+	0.339439i	$0.110237\pi$
$662$		0			0
$663$	−9.05467	+	6.78694i	−0.351654	+	0.263583i
$664$		0			0
$665$	−11.0092	−	6.35619i	−0.426920	−	0.246482i
$666$		0			0
$667$	3.17777	−	1.83469i	0.123044	−	0.0710393i
$668$		0			0
$669$	−15.9490	+	24.4223i	−0.616624	+	0.944220i
$670$		0			0
$671$	−24.2622	+	8.83070i	−0.936630	+	0.340905i
$672$		0			0
$673$	−0.896280	−	5.08305i	−0.0345490	−	0.195937i	0.962648	−	0.270755i	$-0.0872735\pi$
$673$	−0.896280	−	5.08305i	−0.0345490	−	0.195937i	−0.997197	+	0.0748181i	$0.976162\pi$
$674$		0			0
$675$	−16.1441	+	28.6049i	−0.621388	+	1.10100i
$676$		0			0
$677$	17.9488	−	3.16485i	0.689828	−	0.121635i	0.182264	−	0.983250i	$-0.441657\pi$
$677$	17.9488	−	3.16485i	0.689828	−	0.121635i	0.507564	+	0.861614i	$0.330546\pi$
$678$		0			0
$679$	0.238721	+	0.655880i	0.00916127	+	0.0251704i
$680$		0			0
$681$	8.36652	−	4.23603i	0.320606	−	0.162325i
$682$		0			0
$683$	−2.90442	−	5.03061i	−0.111135	−	0.192491i	0.805093	−	0.593148i	$-0.202115\pi$
$683$	−2.90442	−	5.03061i	−0.111135	−	0.192491i	−0.916228	+	0.400657i	$0.868782\pi$
$684$		0			0
$685$	2.92686	−	5.06947i	0.111829	−	0.193694i
$686$		0			0
$687$	−15.9875	+	37.3978i	−0.609960	+	1.42682i
$688$		0			0
$689$	−9.62846	−	1.69776i	−0.366815	−	0.0646794i
$690$		0			0
$691$	0.751798	+	0.895957i	0.0285997	+	0.0340838i	0.780155	−	0.625587i	$-0.215140\pi$
$691$	0.751798	+	0.895957i	0.0285997	+	0.0340838i	−0.751555	+	0.659670i	$0.770696\pi$
$692$		0			0
$693$	1.59225	−	14.4383i	0.0604847	−	0.548466i
$694$		0			0
$695$	40.7395	+	14.8280i	1.54534	+	0.562456i
$696$		0			0
$697$	−45.9458	−	38.5531i	−1.74032	−	1.46030i
$698$		0			0
$699$	−3.42697	−	3.21213i	−0.129620	−	0.121494i
$700$		0			0
$701$		−	3.20626i		−	0.121099i	−0.998165	−	0.0605494i	$-0.980715\pi$
$701$		−	3.20626i		−	0.121099i	0.998165	−	0.0605494i	$-0.0192853\pi$
$702$		0			0
$703$		−	14.9824i		−	0.565071i
$704$		0			0
$705$	−38.5632	+	11.6822i	−1.45237	+	0.439976i
$706$		0			0
$707$	24.1859	+	20.2943i	0.909603	+	0.763248i
$708$		0			0
$709$	1.36441	+	0.496603i	0.0512413	+	0.0186503i	0.367514	−	0.930018i	$-0.380209\pi$
$709$	1.36441	+	0.496603i	0.0512413	+	0.0186503i	−0.316272	+	0.948668i	$0.602431\pi$
$710$		0			0
$711$	−17.7531	−	5.18907i	−0.665795	−	0.194605i
$712$		0			0
$713$	7.06753	+	8.42275i	0.264681	+	0.315435i
$714$		0			0
$715$	−8.53332	−	1.50465i	−0.319128	−	0.0562709i
$716$		0			0
$717$	−24.2915	+	2.91957i	−0.907183	+	0.109033i
$718$		0			0
$719$	8.38430	−	14.5220i	0.312682	−	0.541580i	−0.666260	−	0.745719i	$-0.732106\pi$
$719$	8.38430	−	14.5220i	0.312682	−	0.541580i	0.978942	+	0.204139i	$0.0654394\pi$
$720$		0			0
$721$	−8.45056	−	14.6368i	−0.314715	−	0.545103i
$722$		0			0
$723$	−1.51978	+	27.6458i	−0.0565213	+	1.02816i
$724$		0			0
$725$	1.18057	+	3.24360i	0.0438453	+	0.120464i
$726$		0			0
$727$	−37.2096	+	6.56105i	−1.38003	+	0.243336i	−0.813911	−	0.580990i	$-0.802666\pi$
$727$	−37.2096	+	6.56105i	−1.38003	+	0.243336i	−0.566116	+	0.824326i	$0.691555\pi$
$728$		0			0
$729$	5.20762	+	26.4930i	0.192875	+	0.981223i
$730$		0			0
$731$	12.5741	+	71.3112i	0.465070	+	2.63754i
$732$		0			0
$733$	29.3794	−	10.6932i	1.08515	−	0.394964i	0.263330	−	0.964706i	$-0.415179\pi$
$733$	29.3794	−	10.6932i	1.08515	−	0.394964i	0.821824	+	0.569742i	$0.192957\pi$
$734$		0			0
$735$	−18.4165	−	1.01241i	−0.679302	−	0.0373434i
$736$		0			0
$737$	6.62280	−	3.82368i	0.243954	−	0.140847i
$738$		0			0
$739$	−29.4171	−	16.9840i	−1.08213	−	0.624765i	−0.150656	−	0.988586i	$-0.548139\pi$
$739$	−29.4171	−	16.9840i	−1.08213	−	0.624765i	−0.931469	+	0.363821i	$0.881472\pi$
$740$		0			0
$741$	0.415325	+	3.45561i	0.0152574	+	0.126945i
$742$		0			0
$743$	−1.19531	+	6.77896i	−0.0438518	+	0.248696i	−0.998852	−	0.0479104i	$-0.984744\pi$
$743$	−1.19531	+	6.77896i	−0.0438518	+	0.248696i	0.955000	+	0.296606i	$0.0958549\pi$
$744$		0			0
$745$	−40.4781	+	33.9651i	−1.48300	+	1.24439i
$746$		0			0
$747$	13.7615	−	47.0816i	0.503507	−	1.72263i
$748$		0			0
$749$	5.71987	−	15.7152i	0.209000	−	0.574221i
$750$		0			0
$751$	14.1290	−	16.8383i	0.515576	−	0.614439i	−0.443953	−	0.896050i	$-0.646424\pi$
$751$	14.1290	−	16.8383i	0.515576	−	0.614439i	0.959529	+	0.281611i	$0.0908687\pi$
$752$		0			0
$753$	6.52653	+	21.5443i	0.237840	+	0.785117i
$754$		0			0
$755$	60.4431			2.19975
$756$		0			0
$757$	−25.1474			−0.913997			−0.456999	−	0.889467i	$-0.651076\pi$
$757$	−25.1474			−0.913997			−0.456999	+	0.889467i	$0.651076\pi$
$758$		0			0
$759$	19.6796	−	20.9958i	0.714324	−	0.762100i
$760$		0			0
$761$	16.3531	−	19.4888i	0.592798	−	0.706469i	−0.383343	−	0.923606i	$-0.625227\pi$
$761$	16.3531	−	19.4888i	0.592798	−	0.706469i	0.976141	+	0.217137i	$0.0696719\pi$
$762$		0			0
$763$	7.45723	−	20.4886i	0.269970	−	0.741736i
$764$		0			0
$765$	62.9336	+	6.94029i	2.27537	+	0.250927i
$766$		0			0
$767$	−5.41380	+	4.54272i	−0.195481	+	0.164028i
$768$		0			0
$769$	−7.03963	+	39.9237i	−0.253856	+	1.43969i	0.545138	+	0.838347i	$0.316477\pi$
$769$	−7.03963	+	39.9237i	−0.253856	+	1.43969i	−0.798993	+	0.601340i	$0.794634\pi$
$770$		0			0
$771$	−46.1504	−	19.7292i	−1.66207	−	0.710529i
$772$		0			0
$773$	43.1837	+	24.9321i	1.55321	+	0.896745i	0.997878	+	0.0651151i	$0.0207415\pi$
$773$	43.1837	+	24.9321i	1.55321	+	0.896745i	0.555330	+	0.831630i	$0.312592\pi$
$774$		0			0
$775$	−8.95735	+	5.17153i	−0.321758	+	0.185767i
$776$		0			0
$777$	11.8988	+	23.5011i	0.426866	+	0.843097i
$778$		0			0
$779$	−17.3351	+	6.30947i	−0.621096	+	0.226060i
$780$		0			0
$781$	−1.77030	−	10.0399i	−0.0633464	−	0.359256i
$782$		0			0
$783$	2.47101	+	1.39460i	0.0883068	+	0.0498389i
$784$		0			0
$785$	−39.0733	+	6.88968i	−1.39459	+	0.245903i
$786$		0			0
$787$	−2.62375	−	7.20870i	−0.0935266	−	0.256962i	0.884104	−	0.467289i	$-0.154769\pi$
$787$	−2.62375	−	7.20870i	−0.0935266	−	0.256962i	−0.977631	+	0.210327i	$0.932547\pi$
$788$		0			0
$789$	−0.0864977	−	0.0564874i	−0.00307940	−	0.00201100i
$790$		0			0
$791$	5.01944	+	8.69393i	0.178471	+	0.309121i
$792$		0			0
$793$	−5.43843	+	9.41964i	−0.193124	+	0.334501i
$794$		0			0
$795$	32.8102	+	43.7731i	1.16366	+	1.55247i
$796$		0			0
$797$	−42.1998	−	7.44096i	−1.49479	−	0.263572i	−0.634320	−	0.773070i	$-0.718720\pi$
$797$	−42.1998	−	7.44096i	−1.49479	−	0.263572i	−0.860472	+	0.509498i	$0.829831\pi$
$798$		0			0
$799$	27.8764	+	33.2218i	0.986197	+	1.17530i
$800$		0			0
$801$	−51.0536	+	3.30763i	−1.80389	+	0.116869i
$802$		0			0
$803$	−1.54525	−	0.562424i	−0.0545306	−	0.0198475i
$804$		0			0
$805$	33.9192	+	28.4616i	1.19550	+	1.00314i
$806$		0			0
$807$	−4.58263	+	19.6204i	−0.161316	+	0.690671i
$808$		0			0
$809$			1.75268i			0.0616208i	0.999525	+	0.0308104i	$0.00980881\pi$
$809$			1.75268i			0.0616208i	−0.999525	+	0.0308104i	$0.990191\pi$
$810$		0			0
$811$		−	18.3348i		−	0.643822i	−0.946770	−	0.321911i	$-0.895675\pi$
$811$		−	18.3348i		−	0.643822i	0.946770	−	0.321911i	$-0.104325\pi$
$812$		0			0
$813$	−4.39539	+	18.8188i	−0.154153	+	0.660003i
$814$		0			0
$815$	28.0133	+	23.5059i	0.981262	+	0.823377i
$816$		0			0
$817$	20.9287	+	7.61742i	0.732203	+	0.266500i
$818$		0			0
$819$	−3.39587	−	5.09057i	−0.118661	−	0.177879i
$820$		0			0
$821$	16.3897	+	19.5324i	0.572003	+	0.681687i	0.972041	−	0.234812i	$-0.0754474\pi$
$821$	16.3897	+	19.5324i	0.572003	+	0.681687i	−0.400038	+	0.916499i	$0.631003\pi$
$822$		0			0
$823$	30.4900	+	5.37620i	1.06281	+	0.187403i	0.677604	−	0.735427i	$-0.263018\pi$
$823$	30.4900	+	5.37620i	1.06281	+	0.187403i	0.385209	+	0.922829i	$0.374129\pi$
$824$		0			0
$825$	16.2360	+	21.6609i	0.565264	+	0.754136i
$826$		0			0
$827$	−2.20363	+	3.81679i	−0.0766276	+	0.132723i	−0.901793	−	0.432168i	$-0.857749\pi$
$827$	−2.20363	+	3.81679i	−0.0766276	+	0.132723i	0.825165	+	0.564891i	$0.191082\pi$
$828$		0			0
$829$	−20.7563	−	35.9510i	−0.720896	−	1.24863i	−0.960641	−	0.277792i	$-0.910397\pi$
$829$	−20.7563	−	35.9510i	−0.720896	−	1.24863i	0.239745	−	0.970836i	$-0.422936\pi$
$830$		0			0
$831$	6.91836	+	4.51804i	0.239995	+	0.156729i
$832$		0			0
$833$	6.78961	+	18.6543i	0.235246	+	0.646333i
$834$		0			0
$835$	1.50472	−	0.265322i	0.0520729	−	0.00918186i
$836$		0			0
$837$	−2.82963	+	8.01745i	−0.0978065	+	0.277124i
$838$		0			0
$839$	−1.64766	−	9.34432i	−0.0568834	−	0.322602i	0.943067	−	0.332604i	$-0.107927\pi$
$839$	−1.64766	−	9.34432i	−0.0568834	−	0.322602i	−0.999950	+	0.0100023i	$0.996816\pi$
$840$		0			0
$841$	−26.9709	+	9.81660i	−0.930031	+	0.338503i
$842$		0			0
$843$	1.97686	+	3.90446i	0.0680865	+	0.134477i
$844$		0			0
$845$	34.7197	−	20.0454i	1.19440	−	0.689584i
$846$		0			0
$847$	8.28815	+	4.78516i	0.284784	+	0.164420i
$848$		0			0
$849$	43.1954	+	18.4659i	1.48246	+	0.633748i
$850$		0			0
$851$	−9.06183	+	51.3922i	−0.310636	+	1.76170i
$852$		0			0
$853$	−10.8468	+	9.10150i	−0.371386	+	0.311630i	−0.809309	−	0.587383i	$-0.800158\pi$
$853$	−10.8468	+	9.10150i	−0.371386	+	0.311630i	0.437924	+	0.899012i	$0.355714\pi$
$854$		0			0
$855$	11.5270	−	15.6961i	0.394216	−	0.536795i
$856$		0			0
$857$	−10.9740	+	30.1509i	−0.374866	+	1.02994i	0.598589	+	0.801057i	$0.295728\pi$
$857$	−10.9740	+	30.1509i	−0.374866	+	1.02994i	−0.973455	+	0.228880i	$0.926494\pi$
$858$		0			0
$859$	12.6555	−	15.0823i	0.431801	−	0.514601i	−0.505640	−	0.862745i	$-0.668743\pi$
$859$	12.6555	−	15.0823i	0.431801	−	0.514601i	0.937441	+	0.348144i	$0.113188\pi$
$860$		0			0
$861$	22.1807	−	23.6643i	0.755917	−	0.806476i
$862$		0			0
$863$	−38.5055			−1.31074			−0.655372	−	0.755306i	$-0.727488\pi$
$863$	−38.5055			−1.31074			−0.655372	+	0.755306i	$0.727488\pi$
$864$		0			0
$865$	52.5067			1.78528
$866$		0			0
$867$	−11.2203	−	37.0386i	−0.381061	−	1.25790i
$868$		0			0
$869$	−9.79834	+	11.6772i	−0.332386	+	0.396122i
$870$		0			0
$871$	1.10185	−	3.02731i	0.0373348	−	0.102577i
$872$		0			0
$873$	−1.03877	+	0.253358i	−0.0351572	+	0.00857486i
$874$		0			0
$875$	−6.66925	+	5.59616i	−0.225462	+	0.189185i
$876$		0			0
$877$	−1.82286	+	10.3380i	−0.0615537	+	0.349089i	0.938440	+	0.345443i	$0.112271\pi$
$877$	−1.82286	+	10.3380i	−0.0615537	+	0.349089i	−0.999993	+	0.00364525i	$0.998840\pi$
$878$		0			0
$879$	−2.05159	−	17.0698i	−0.0691986	−	0.575749i
$880$		0			0
$881$	−34.1516	−	19.7174i	−1.15060	−	0.664298i	−0.201565	−	0.979475i	$-0.564603\pi$
$881$	−34.1516	−	19.7174i	−1.15060	−	0.664298i	−0.949033	+	0.315178i	$0.897936\pi$
$882$		0			0
$883$	11.6845	−	6.74603i	0.393213	−	0.227022i	−0.290338	−	0.956924i	$-0.593768\pi$
$883$	11.6845	−	6.74603i	0.393213	−	0.227022i	0.683552	+	0.729902i	$0.260434\pi$
$884$		0			0
$885$	39.4831	+	2.17051i	1.32721	+	0.0729610i
$886$		0			0
$887$	−22.3532	+	8.13590i	−0.750547	+	0.273177i	−0.688836	−	0.724917i	$-0.741878\pi$
$887$	−22.3532	+	8.13590i	−0.750547	+	0.273177i	−0.0617110	+	0.998094i	$0.519656\pi$
$888$		0			0
$889$	−1.32718	−	7.52683i	−0.0445123	−	0.252442i
$890$		0			0
$891$	21.7174	+	4.84895i	0.727561	+	0.162446i
$892$		0			0
$893$	13.1362	−	2.31627i	0.439587	−	0.0775111i
$894$		0			0
$895$	25.9060	+	71.1762i	0.865942	+	2.37916i
$896$		0			0
$897$	0.665427	−	12.1046i	0.0222180	−	0.404160i
$898$		0			0
$899$	0.446739	+	0.773775i	0.0148996	+	0.0258068i
$900$		0			0
$901$	29.4391	−	50.9900i	0.980758	−	1.69872i
$902$		0			0
$903$	−38.8781	+	4.67271i	−1.29378	+	0.155498i
$904$		0			0
$905$	39.2241	+	6.91627i	1.30385	+	0.229905i
$906$		0			0
$907$	−17.8388	−	21.2594i	−0.592327	−	0.705908i	0.383724	−	0.923448i	$-0.374641\pi$
$907$	−17.8388	−	21.2594i	−0.592327	−	0.705908i	−0.976051	+	0.217540i	$0.930197\pi$
$908$		0			0
$909$	−34.9629	+	33.4193i	−1.15964	+	1.10845i
$910$		0			0
$911$	−8.69974	−	3.16645i	−0.288235	−	0.104909i	0.193856	−	0.981030i	$-0.437900\pi$
$911$	−8.69974	−	3.16645i	−0.288235	−	0.104909i	−0.482091	+	0.876121i	$0.660123\pi$
$912$		0			0
$913$	−30.9682	−	25.9854i	−1.02490	−	0.859990i
$914$		0			0
$915$	58.2447	−	17.6444i	1.92551	−	0.583305i
$916$		0			0
$917$			24.6759i			0.814869i
$918$		0			0
$919$			44.0812i			1.45411i	0.686582	+	0.727053i	$0.259110\pi$
$919$			44.0812i			1.45411i	−0.686582	+	0.727053i	$0.740890\pi$
$920$		0			0
$921$	−33.3235	−	31.2344i	−1.09805	−	1.02921i
$922$		0			0
$923$	−3.28997	−	2.76061i	−0.108291	−	0.0908666i
$924$		0			0
$925$	−46.1297	−	16.7898i	−1.51673	−	0.552046i
$926$		0			0
$927$	23.7060	−	10.4096i	0.778608	−	0.341896i
$928$		0			0
$929$	2.50696	+	2.98767i	0.0822505	+	0.0980224i	0.805600	−	0.592459i	$-0.201843\pi$
$929$	2.50696	+	2.98767i	0.0822505	+	0.0980224i	−0.723350	+	0.690482i	$0.757399\pi$
$930$		0			0
$931$	6.01304	+	1.06026i	0.197070	+	0.0347487i
$932$		0			0
$933$	17.8968	−	41.8643i	0.585916	−	1.37057i
$934$		0			0
$935$	26.0907	−	45.1904i	0.853257	−	1.47788i
$936$		0			0
$937$	24.6794	+	42.7459i	0.806240	+	1.39645i	0.915451	+	0.402430i	$0.131834\pi$
$937$	24.6794	+	42.7459i	0.806240	+	1.39645i	−0.109211	+	0.994019i	$0.534832\pi$
$938$		0			0
$939$	−23.0285	+	11.6595i	−0.751508	+	0.380494i
$940$		0			0
$941$	−5.25479	−	14.4374i	−0.171301	−	0.470646i	0.824100	−	0.566445i	$-0.191682\pi$
$941$	−5.25479	−	14.4374i	−0.171301	−	0.470646i	−0.995401	+	0.0957989i	$0.969459\pi$
$942$		0			0
$943$	63.2788	−	11.1578i	2.06064	−	0.363347i
$944$		0			0
$945$	−5.61550	+	33.7753i	−0.182672	+	1.09871i
$946$		0			0
$947$	−6.20628	−	35.1976i	−0.201677	−	1.14377i	−0.902584	−	0.430514i	$-0.858332\pi$
$947$	−6.20628	−	35.1976i	−0.201677	−	1.14377i	0.700907	−	0.713253i	$-0.252779\pi$
$948$		0			0
$949$	−0.650965	+	0.236932i	−0.0211312	+	0.00769114i
$950$		0			0
$951$	−13.0587	+	19.9964i	−0.423457	+	0.648429i
$952$		0			0
$953$	3.93627	−	2.27261i	0.127508	−	0.0736169i	−0.434889	−	0.900484i	$-0.643212\pi$
$953$	3.93627	−	2.27261i	0.127508	−	0.0736169i	0.562397	+	0.826867i	$0.309879\pi$
$954$		0			0
$955$	−15.2333	−	8.79495i	−0.492938	−	0.284598i
$956$		0			0
$957$	1.87116	−	1.40253i	0.0604861	−	0.0453374i
$958$		0			0
$959$	0.591623	−	3.35526i	0.0191045	−	0.108347i
$960$		0			0
$961$	21.6965	−	18.2055i	0.699886	−	0.587274i
$962$		0			0
$963$	22.9686	+	11.3484i	0.740153	+	0.365696i
$964$		0			0
$965$	−5.68300	+	15.6139i	−0.182942	+	0.502629i
$966$		0			0
$967$	−9.50161	+	11.3236i	−0.305551	+	0.364142i	−0.896869	−	0.442297i	$-0.854164\pi$
$967$	−9.50161	+	11.3236i	−0.305551	+	0.364142i	0.591317	+	0.806439i	$0.298608\pi$
$968$		0			0
$969$	−20.4105	−	4.76717i	−0.655680	−	0.153143i
$970$		0			0
$971$	−25.7412			−0.826075			−0.413037	−	0.910714i	$-0.635532\pi$
$971$	−25.7412			−0.826075			−0.413037	+	0.910714i	$0.635532\pi$
$972$		0			0
$973$	25.2332			0.808941
$974$		0			0
$975$	11.1050	+	2.59374i	0.355645	+	0.0830660i
$976$		0			0
$977$	−3.38665	+	4.03605i	−0.108349	+	0.129125i	−0.817493	−	0.575938i	$-0.804637\pi$
$977$	−3.38665	+	4.03605i	−0.108349	+	0.129125i	0.709145	+	0.705063i	$0.249081\pi$
$978$		0			0
$979$	−14.4210	+	39.6214i	−0.460898	+	1.26631i
$980$		0			0
$981$	29.9451	+	14.7953i	0.956073	+	0.472378i
$982$		0			0
$983$	−16.5529	+	13.8896i	−0.527957	+	0.443008i	−0.867395	−	0.497620i	$-0.834207\pi$
$983$	−16.5529	+	13.8896i	−0.527957	+	0.443008i	0.339438	+	0.940628i	$0.389763\pi$
$984$		0			0
$985$	−10.3134	+	58.4902i	−0.328612	+	1.86365i
$986$		0			0
$987$	−18.7657	+	14.0659i	−0.597320	+	0.447722i
$988$		0			0
$989$	−67.1819	−	38.7875i	−2.13626	−	1.23337i
$990$		0			0
$991$	−38.3015	+	22.1134i	−1.21669	+	0.702454i	−0.964208	−	0.265148i	$-0.914579\pi$
$991$	−38.3015	+	22.1134i	−1.21669	+	0.702454i	−0.252479	+	0.967602i	$0.581246\pi$
$992$		0			0
$993$	10.8694	−	16.6440i	0.344930	−	0.528183i
$994$		0			0
$995$	84.8625	−	30.8874i	2.69032	−	0.979198i
$996$		0			0
$997$	2.19158	+	12.4291i	0.0694080	+	0.393632i	0.999644	+	0.0266711i	$0.00849068\pi$
$997$	2.19158	+	12.4291i	0.0694080	+	0.393632i	−0.930236	+	0.366961i	$0.880398\pi$
$998$		0			0
$999$	−37.7824	+	14.1716i	−1.19538	+	0.448370i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	864.2.bi.a.95.4	✓	216
4.3	odd	2	inner	864.2.bi.a.95.33	yes	216
27.2	odd	18	inner	864.2.bi.a.191.33	yes	216
108.83	even	18	inner	864.2.bi.a.191.4	yes	216

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
864.2.bi.a.95.4	✓	216	1.1	even	1	trivial
864.2.bi.a.95.33	yes	216	4.3	odd	2	inner
864.2.bi.a.191.4	yes	216	108.83	even	18	inner
864.2.bi.a.191.33	yes	216	27.2	odd	18	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 864 = 2^{5} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	864.bi (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.68666 - 0.393943i) q^{3} +(2.16279 - 2.57751i) q^{5} +(0.669796 - 1.84025i) q^{7} +(2.68962 + 1.32889i) q^{9} +(1.89402 - 1.58927i) q^{11} +(0.180867 - 1.02575i) q^{13} +(-4.66328 + 3.49537i) q^{15} +(5.43212 + 3.13624i) q^{17} +(1.67078 - 0.964625i) q^{19} +(-1.85467 + 2.84001i) q^{21} +(-6.31451 + 2.29829i) q^{23} +(-1.09767 - 6.22522i) q^{25} +(-4.01296 - 3.30094i) q^{27} +(-0.537761 + 0.0948218i) q^{29} +(-0.559626 - 1.53756i) q^{31} +(-3.82063 + 1.93442i) q^{33} +(-3.29464 - 5.70648i) q^{35} +(3.88295 - 6.72546i) q^{37} +(-0.709147 + 1.65884i) q^{39} +(-9.41682 - 1.66044i) q^{41} +(7.42054 + 8.84345i) q^{43} +(9.24232 - 4.05842i) q^{45} +(6.49706 + 2.36474i) q^{47} +(2.42442 + 2.03433i) q^{49} +(-7.92662 - 7.42970i) q^{51} -9.38676i q^{53} -8.31911i q^{55} +(-3.19804 + 0.968800i) q^{57} +(-5.19772 - 4.36140i) q^{59} +(-9.81295 - 3.57162i) q^{61} +(4.24699 - 4.05948i) q^{63} +(-2.25271 - 2.68467i) q^{65} +(3.04602 + 0.537096i) q^{67} +(11.5558 - 1.38888i) q^{69} +(2.06166 - 3.57091i) q^{71} +(-0.332546 - 0.575987i) q^{73} +(-0.600979 + 10.9322i) q^{75} +(-1.65604 - 4.54995i) q^{77} +(-6.07165 + 1.07060i) q^{79} +(5.46810 + 7.14842i) q^{81} +(-2.83924 - 16.1021i) q^{83} +(19.8322 - 7.21834i) q^{85} +(0.944372 + 0.0519152i) q^{87} +(-14.7688 + 8.52677i) q^{89} +(-1.76649 - 1.01988i) q^{91} +(0.338186 + 2.81379i) q^{93} +(1.12721 - 6.39274i) q^{95} +(-0.273025 + 0.229095i) q^{97} +(7.20615 - 1.75758i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 216 q - 24 q^{29} + 36 q^{33} + 36 q^{41} - 24 q^{45} + 12 q^{57} + 48 q^{65} + 48 q^{69} + 48 q^{77} + 48 q^{81} + 36 q^{89} - 144 q^{93} - 36 q^{97}+O(q^{100}) \) 216 * q - 24 * q^29 + 36 * q^33 + 36 * q^41 - 24 * q^45 + 12 * q^57 + 48 * q^65 + 48 * q^69 + 48 * q^77 + 48 * q^81 + 36 * q^89 - 144 * q^93 - 36 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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