LMFDB - Embedded newform 891.2.n.f.136.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [891,2,Mod(136,891)] 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("891.136"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(891, base_ring=CyclotomicField(30)) chi = DirichletCharacter(H, H._module([20, 6])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 891 = 3^{4} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	891.n (of order $15$, degree $8$, not minimal)

Newform invariants

comment:select newform

sage:traces = [32,-2,0,4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(4)] == traces)

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

Self dual:	no
Analytic conductor:	$7.11467082010$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$4$ over $\Q(\zeta_{15})$
Twist minimal:	no (minimal twist has level 297)
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			136.3
Character	$\chi$	$=$	891.136
Dual form			891.2.n.f.190.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.330935 - 0.147342i) q^{2} +(-1.25045 + 1.38877i) q^{4} +(-2.45353 - 1.09238i) q^{5} +(2.43963 + 0.518560i) q^{7} +(-0.433081 + 1.33288i) q^{8} -0.972914 q^{10} +(-2.12100 - 2.54978i) q^{11} +(-0.399048 + 3.79669i) q^{13} +(0.883767 - 0.187850i) q^{14} +(-0.337612 - 3.21216i) q^{16} +(-0.909782 + 0.660995i) q^{17} +(2.09612 - 6.45120i) q^{19} +(4.58509 - 2.04141i) q^{20} +(-1.07760 - 0.531300i) q^{22} +(-3.37470 - 5.84515i) q^{23} +(1.48086 + 1.64467i) q^{25} +(0.427353 + 1.31526i) q^{26} +(-3.77080 + 2.73965i) q^{28} +(7.26230 + 1.54365i) q^{29} +(0.700806 - 6.66772i) q^{31} +(-1.98649 - 3.44070i) q^{32} +(-0.203687 + 0.352796i) q^{34} +(-5.41925 - 3.93732i) q^{35} +(-0.0589927 - 0.181561i) q^{37} +(-0.256851 - 2.44378i) q^{38} +(2.51860 - 2.79719i) q^{40} +(-0.622411 + 0.132298i) q^{41} +(-2.36375 + 4.09413i) q^{43} +(6.19326 + 0.242800i) q^{44} +(-1.97805 - 1.43713i) q^{46} +(-7.55641 - 8.39225i) q^{47} +(-0.711915 - 0.316965i) q^{49} +(0.732399 + 0.326085i) q^{50} +(-4.77374 - 5.30177i) q^{52} +(-4.45732 - 3.23843i) q^{53} +(2.41860 + 8.57290i) q^{55} +(-1.74774 + 3.02717i) q^{56} +(2.63080 - 0.559193i) q^{58} +(5.64028 - 6.26417i) q^{59} +(-0.179980 - 1.71240i) q^{61} +(-0.750514 - 2.30984i) q^{62} +(4.06165 + 2.95096i) q^{64} +(5.12652 - 8.87939i) q^{65} +(-2.25335 - 3.90292i) q^{67} +(0.219670 - 2.09002i) q^{68} +(-2.37355 - 0.504514i) q^{70} +(9.95124 - 7.23000i) q^{71} +(-0.658284 - 2.02599i) q^{73} +(-0.0462743 - 0.0513928i) q^{74} +(6.33812 + 10.9779i) q^{76} +(-3.85224 - 7.32038i) q^{77} +(-10.5808 + 4.71086i) q^{79} +(-2.68057 + 8.24994i) q^{80} +(-0.186485 + 0.135489i) q^{82} +(0.0855484 + 0.813939i) q^{83} +(2.95424 - 0.627943i) q^{85} +(-0.179010 + 1.70317i) q^{86} +(4.31712 - 1.72279i) q^{88} -1.42041 q^{89} +(-2.94234 + 9.05560i) q^{91} +(12.3375 + 2.62241i) q^{92} +(-3.73721 - 1.66392i) q^{94} +(-12.1901 + 13.5385i) q^{95} +(9.20051 - 4.09633i) q^{97} -0.282300 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 2 q^{2} + 4 q^{4} - q^{5} + 2 q^{7} + 12 q^{10} - 13 q^{11} + 2 q^{13} + 22 q^{14} + 24 q^{16} - 4 q^{17} - 4 q^{19} - 15 q^{22} - 14 q^{23} + 19 q^{25} + 42 q^{26} + 30 q^{28} - q^{29} - 14 q^{31}+ \cdots + 52 q^{98}+O(q^{100}) $ 32 * q - 2 * q^2 + 4 * q^4 - q^5 + 2 * q^7 + 12 * q^10 - 13 * q^11 + 2 * q^13 + 22 * q^14 + 24 * q^16 - 4 * q^17 - 4 * q^19 - 15 * q^22 - 14 * q^23 + 19 * q^25 + 42 * q^26 + 30 * q^28 - q^29 - 14 * q^31 + 48 * q^32 - 10 * q^34 - 36 * q^35 + 18 * q^37 - 11 * q^38 - 33 * q^40 - 25 * q^41 - 14 * q^43 + 28 * q^44 + 8 * q^46 + 28 * q^47 + 4 * q^49 + 63 * q^50 - 10 * q^52 + 2 * q^53 - 80 * q^55 - 96 * q^56 + 20 * q^58 - 41 * q^59 - 10 * q^62 - 184 * q^64 + 60 * q^65 + 48 * q^67 - 25 * q^68 + 31 * q^70 + 6 * q^71 - 26 * q^73 - 29 * q^74 + 58 * q^76 + 2 * q^77 - 166 * q^80 + 82 * q^82 + 14 * q^83 + 10 * q^85 + 56 * q^86 - 86 * q^88 + 164 * q^89 + 28 * q^91 - 74 * q^92 + 2 * q^94 + 56 * q^95 - 12 * q^97 + 52 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/891\mathbb{Z}\right)^\times$.

$n$	$244$	$650$
$\chi(n)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	0.330935	−	0.147342i	0.234007	−	0.104187i	−0.286384	−	0.958115i	$-0.592453\pi$
$2$	0.330935	−	0.147342i	0.234007	−	0.104187i	0.520390	+	0.853929i	$0.325786\pi$
$3$		0			0
$3$		0			0
$4$	−1.25045	+	1.38877i	−0.625226	+	0.694384i
$5$	−2.45353	−	1.09238i	−1.09725	−	0.488528i	−0.223404	−	0.974726i	$-0.571717\pi$
$5$	−2.45353	−	1.09238i	−1.09725	−	0.488528i	−0.873849	+	0.486198i	$0.838384\pi$
$6$		0			0
$7$	2.43963	+	0.518560i	0.922094	+	0.195997i	0.644414	−	0.764676i	$-0.277101\pi$
$7$	2.43963	+	0.518560i	0.922094	+	0.195997i	0.277680	+	0.960674i	$0.410435\pi$
$8$	−0.433081	+	1.33288i	−0.153117	+	0.471246i
$9$		0			0
$10$	−0.972914			−0.307663
$11$	−2.12100	−	2.54978i	−0.639505	−	0.768787i
$11$	−2.12100	−	2.54978i	−0.639505	−	0.768787i
$12$		0			0
$13$	−0.399048	+	3.79669i	−0.110676	+	1.05301i	0.788383	+	0.615185i	$0.210919\pi$
$13$	−0.399048	+	3.79669i	−0.110676	+	1.05301i	−0.899059	+	0.437828i	$0.855748\pi$
$14$	0.883767	−	0.187850i	0.236197	−	0.0502051i
$15$		0			0
$16$	−0.337612	−	3.21216i	−0.0844029	−	0.803040i
$17$	−0.909782	+	0.660995i	−0.220654	+	0.160315i	−0.692621	−	0.721301i	$-0.743544\pi$
$17$	−0.909782	+	0.660995i	−0.220654	+	0.160315i	0.471967	+	0.881616i	$0.343544\pi$
$18$		0			0
$19$	2.09612	−	6.45120i	0.480883	−	1.48001i	−0.356973	−	0.934115i	$-0.616191\pi$
$19$	2.09612	−	6.45120i	0.480883	−	1.48001i	0.837856	−	0.545891i	$-0.183809\pi$
$20$	4.58509	−	2.04141i	1.02526	−	0.456474i
$21$		0			0
$22$	−1.07760	−	0.531300i	−0.229746	−	0.113273i
$23$	−3.37470	−	5.84515i	−0.703674	−	1.21880i	−0.967168	−	0.254138i	$-0.918208\pi$
$23$	−3.37470	−	5.84515i	−0.703674	−	1.21880i	0.263494	−	0.964661i	$-0.415125\pi$
$24$		0			0
$25$	1.48086	+	1.64467i	0.296173	+	0.328933i
$26$	0.427353	+	1.31526i	0.0838108	+	0.257943i
$27$		0			0
$28$	−3.77080	+	2.73965i	−0.712615	+	0.517745i
$29$	7.26230	+	1.54365i	1.34857	+	0.286648i	0.824904	−	0.565273i	$-0.191229\pi$
$29$	7.26230	+	1.54365i	1.34857	+	0.286648i	0.523670	+	0.851921i	$0.324562\pi$
$30$		0			0
$31$	0.700806	−	6.66772i	0.125868	−	1.19756i	−0.731129	−	0.682239i	$-0.761006\pi$
$31$	0.700806	−	6.66772i	0.125868	−	1.19756i	0.856998	−	0.515320i	$-0.172327\pi$
$32$	−1.98649	−	3.44070i	−0.351165	−	0.608236i
$33$		0			0
$34$	−0.203687	+	0.352796i	−0.0349320	+	0.0605040i
$35$	−5.41925	−	3.93732i	−0.916020	−	0.665528i
$36$		0			0
$37$	−0.0589927	−	0.181561i	−0.00969834	−	0.0298484i	0.946090	−	0.323903i	$-0.104995\pi$
$37$	−0.0589927	−	0.181561i	−0.00969834	−	0.0298484i	−0.955789	+	0.294055i	$0.904995\pi$
$38$	−0.256851	−	2.44378i	−0.0416668	−	0.396433i
$39$		0			0
$40$	2.51860	−	2.79719i	0.398225	−	0.442274i
$41$	−0.622411	+	0.132298i	−0.0972043	+	0.0206614i	−0.256257	−	0.966609i	$-0.582489\pi$
$41$	−0.622411	+	0.132298i	−0.0972043	+	0.0206614i	0.159053	+	0.987270i	$0.449156\pi$
$42$		0			0
$43$	−2.36375	+	4.09413i	−0.360468	+	0.624349i	−0.988038	−	0.154212i	$-0.950716\pi$
$43$	−2.36375	+	4.09413i	−0.360468	+	0.624349i	0.627570	+	0.778560i	$0.284050\pi$
$44$	6.19326	+	0.242800i	0.933669	+	0.0366035i
$45$		0			0
$46$	−1.97805	−	1.43713i	−0.291647	−	0.211894i
$47$	−7.55641	−	8.39225i	−1.10222	−	1.22413i	−0.972579	−	0.232573i	$-0.925285\pi$
$47$	−7.55641	−	8.39225i	−1.10222	−	1.22413i	−0.129637	−	0.991562i	$-0.541381\pi$
$48$		0			0
$49$	−0.711915	−	0.316965i	−0.101702	−	0.0452807i
$50$	0.732399	+	0.326085i	0.103577	+	0.0461154i
$51$		0			0
$52$	−4.77374	−	5.30177i	−0.661998	−	0.735223i
$53$	−4.45732	−	3.23843i	−0.612259	−	0.444833i	0.237950	−	0.971277i	$-0.423525\pi$
$53$	−4.45732	−	3.23843i	−0.612259	−	0.444833i	−0.850209	+	0.526445i	$0.823525\pi$
$54$		0			0
$55$	2.41860	+	8.57290i	0.326125	+	1.15597i
$56$	−1.74774	+	3.02717i	−0.233551	+	0.404523i
$57$		0			0
$58$	2.63080	−	0.559193i	0.345440	−	0.0734256i
$59$	5.64028	−	6.26417i	0.734302	−	0.815525i	−0.254133	−	0.967169i	$-0.581790\pi$
$59$	5.64028	−	6.26417i	0.734302	−	0.815525i	0.988435	+	0.151644i	$0.0484567\pi$
$60$		0			0
$61$	−0.179980	−	1.71240i	−0.0230441	−	0.219250i	−0.999984	−	0.00573345i	$-0.998175\pi$
$61$	−0.179980	−	1.71240i	−0.0230441	−	0.219250i	0.976939	−	0.213516i	$-0.0684917\pi$
$62$	−0.750514	−	2.30984i	−0.0953154	−	0.293351i
$63$		0			0
$64$	4.06165	+	2.95096i	0.507706	+	0.368870i
$65$	5.12652	−	8.87939i	0.635866	−	1.10135i
$66$		0			0
$67$	−2.25335	−	3.90292i	−0.275291	−	0.476817i	0.694918	−	0.719089i	$-0.255441\pi$
$67$	−2.25335	−	3.90292i	−0.275291	−	0.476817i	−0.970208	+	0.242272i	$0.922107\pi$
$68$	0.219670	−	2.09002i	0.0266389	−	0.253452i
$69$		0			0
$70$	−2.37355	−	0.504514i	−0.283694	−	0.0603010i
$71$	9.95124	−	7.23000i	1.18099	−	0.858043i	0.188711	−	0.982033i	$-0.439569\pi$
$71$	9.95124	−	7.23000i	1.18099	−	0.858043i	0.992284	+	0.123990i	$0.0395689\pi$
$72$		0			0
$73$	−0.658284	−	2.02599i	−0.0770463	−	0.237124i	0.905114	−	0.425168i	$-0.139785\pi$
$73$	−0.658284	−	2.02599i	−0.0770463	−	0.237124i	−0.982161	+	0.188044i	$0.939785\pi$
$74$	−0.0462743	−	0.0513928i	−0.00537928	−	0.00597429i
$75$		0			0
$76$	6.33812	+	10.9779i	0.727032	+	1.25926i
$77$	−3.85224	−	7.32038i	−0.439004	−	0.834235i
$78$		0			0
$79$	−10.5808	+	4.71086i	−1.19043	+	0.530013i	−0.903769	−	0.428020i	$-0.859211\pi$
$79$	−10.5808	+	4.71086i	−1.19043	+	0.530013i	−0.286659	+	0.958033i	$0.592545\pi$
$80$	−2.68057	+	8.24994i	−0.299696	+	0.922371i
$81$		0			0
$82$	−0.186485	+	0.135489i	−0.0205938	+	0.0149623i
$83$	0.0855484	+	0.813939i	0.00939016	+	0.0893414i	0.998213	−	0.0597523i	$-0.0190311\pi$
$83$	0.0855484	+	0.813939i	0.00939016	+	0.0893414i	−0.988823	+	0.149094i	$0.952364\pi$
$84$		0			0
$85$	2.95424	−	0.627943i	0.320432	−	0.0681099i
$86$	−0.179010	+	1.70317i	−0.0193032	+	0.183658i
$87$		0			0
$88$	4.31712	−	1.72279i	0.460207	−	0.183650i
$89$	−1.42041			−0.150564			−0.0752818	−	0.997162i	$-0.523986\pi$
$89$	−1.42041			−0.150564			−0.0752818	+	0.997162i	$0.523986\pi$
$90$		0			0
$91$	−2.94234	+	9.05560i	−0.308441	+	0.949285i
$92$	12.3375	+	2.62241i	1.28627	+	0.273405i
$93$		0			0
$94$	−3.73721	−	1.66392i	−0.385464	−	0.171620i
$95$	−12.1901	+	13.5385i	−1.25068	+	1.38902i
$96$		0			0
$97$	9.20051	−	4.09633i	0.934170	−	0.415919i	0.117532	−	0.993069i	$-0.462502\pi$
$97$	9.20051	−	4.09633i	0.934170	−	0.415919i	0.816638	+	0.577150i	$0.195835\pi$
$98$	−0.282300			−0.0285166
$99$		0			0
$100$	−4.13581			−0.413581
$101$	−17.4889	+	7.78658i	−1.74021	+	0.774794i	−0.746178	+	0.665746i	$0.768113\pi$
$101$	−17.4889	+	7.78658i	−1.74021	+	0.774794i	−0.994037	+	0.109048i	$0.965220\pi$
$102$		0			0
$103$	−2.07866	+	2.30858i	−0.204816	+	0.227472i	−0.836798	−	0.547512i	$-0.815575\pi$
$103$	−2.07866	+	2.30858i	−0.204816	+	0.227472i	0.631982	+	0.774983i	$0.282242\pi$
$104$	−4.88773	−	2.17616i	−0.479282	−	0.213390i
$105$		0			0
$106$	−1.95224	−	0.414962i	−0.189618	−	0.0403046i
$107$	−3.05389	+	9.39890i	−0.295231	+	0.908626i	0.687913	+	0.725793i	$0.258527\pi$
$107$	−3.05389	+	9.39890i	−0.295231	+	0.908626i	−0.983144	+	0.182833i	$0.941473\pi$
$108$		0			0
$109$	18.0851			1.73224			0.866121	−	0.499834i	$-0.166606\pi$
$109$	18.0851			1.73224			0.866121	+	0.499834i	$0.166606\pi$
$110$	2.06355	+	2.48072i	0.196752	+	0.236527i
$111$		0			0
$112$	0.842049	−	8.01156i	0.0795662	−	0.757021i
$113$	4.96890	−	1.05617i	0.467435	−	0.0993564i	0.0318282	−	0.999493i	$-0.489867\pi$
$113$	4.96890	−	1.05617i	0.467435	−	0.0993564i	0.435607	+	0.900137i	$0.356534\pi$
$114$		0			0
$115$	1.89479	+	18.0277i	0.176690	+	1.68110i
$116$	−11.2249	+	8.15539i	−1.04221	+	0.757209i
$117$		0			0
$118$	0.943595	−	2.90409i	0.0868650	−	0.267343i
$119$	−2.56230	+	1.14081i	−0.234886	+	0.104578i
$120$		0			0
$121$	−2.00273	+	10.8161i	−0.182066	+	0.983286i
$122$	−0.311870	−	0.540174i	−0.0282354	−	0.0489051i
$123$		0			0
$124$	8.38360	+	9.31093i	0.752869	+	0.836146i
$125$	2.31293	+	7.11847i	0.206875	+	0.636695i
$126$		0			0
$127$	−0.674959	+	0.490387i	−0.0598930	+	0.0435148i	−0.617329	−	0.786705i	$-0.711785\pi$
$127$	−0.674959	+	0.490387i	−0.0598930	+	0.0435148i	0.557436	+	0.830220i	$0.311785\pi$
$128$	9.55127	+	2.03019i	0.844221	+	0.179445i
$129$		0			0
$130$	0.388240	−	3.69386i	0.0340509	−	0.323973i
$131$	9.87633	+	17.1063i	0.862899	+	1.49459i	0.869118	+	0.494605i	$0.164687\pi$
$131$	9.87633	+	17.1063i	0.862899	+	1.49459i	−0.00621860	+	0.999981i	$0.501979\pi$
$132$		0			0
$133$	8.45910	−	14.6516i	0.733497	−	1.27045i
$134$	−1.32078	−	0.959601i	−0.114098	−	0.0828969i
$135$		0			0
$136$	−0.487022	−	1.49890i	−0.0417618	−	0.128529i
$137$	0.414245	+	3.94128i	0.0353913	+	0.336726i	0.997863	+	0.0653432i	$0.0208142\pi$
$137$	0.414245	+	3.94128i	0.0353913	+	0.336726i	−0.962472	+	0.271383i	$0.912519\pi$
$138$		0			0
$139$	−2.27822	+	2.53022i	−0.193236	+	0.214610i	−0.831975	−	0.554813i	$-0.812790\pi$
$139$	−2.27822	+	2.53022i	−0.193236	+	0.214610i	0.638739	+	0.769424i	$0.279456\pi$
$140$	12.2445	−	2.60266i	1.03485	−	0.219965i
$141$		0			0
$142$	2.22794	−	3.85890i	0.186964	−	0.323832i
$143$	10.5271	−	7.03530i	0.880321	−	0.588321i
$144$		0			0
$145$	−16.1320	−	11.7206i	−1.33969	−	0.973343i
$146$	−0.516363	−	0.573479i	−0.0427345	−	0.0474614i
$147$		0			0
$148$	0.325913	+	0.145106i	0.0267899	+	0.0119276i
$149$	4.70840	+	2.09632i	0.385728	+	0.171737i	0.590433	−	0.807087i	$-0.298957\pi$
$149$	4.70840	+	2.09632i	0.385728	+	0.171737i	−0.204705	+	0.978824i	$0.565624\pi$
$150$		0			0
$151$	−9.19736	−	10.2147i	−0.748470	−	0.831261i	0.241813	−	0.970323i	$-0.422258\pi$
$151$	−9.19736	−	10.2147i	−0.748470	−	0.831261i	−0.990284	+	0.139062i	$0.955591\pi$
$152$	7.69091	+	5.58778i	0.623816	+	0.453229i
$153$		0			0
$154$	−2.35344	−	1.85498i	−0.189646	−	0.149478i
$155$	−9.00316	+	15.5939i	−0.723151	+	1.25253i
$156$		0			0
$157$	−16.2708	+	3.45846i	−1.29855	+	0.276015i	−0.804778	−	0.593576i	$-0.797716\pi$
$157$	−16.2708	+	3.45846i	−1.29855	+	0.276015i	−0.493772	+	0.869591i	$0.664382\pi$
$158$	−2.80744	+	3.11798i	−0.223348	+	0.248053i
$159$		0			0
$160$	1.11535	+	10.6119i	0.0881765	+	0.838943i
$161$	−5.20197	−	16.0100i	−0.409973	−	1.26177i
$162$		0			0
$163$	−18.4445	−	13.4007i	−1.44469	−	1.04963i	−0.987037	−	0.160492i	$-0.948692\pi$
$163$	−18.4445	−	13.4007i	−1.44469	−	1.04963i	−0.457648	−	0.889134i	$-0.651308\pi$
$164$	0.594565	−	1.02982i	0.0464277	−	0.0804152i
$165$		0			0
$166$	0.148238	+	0.256756i	0.0115055	+	0.0199282i
$167$	−1.31701	+	12.5305i	−0.101913	+	0.969641i	0.817388	+	0.576087i	$0.195421\pi$
$167$	−1.31701	+	12.5305i	−0.101913	+	0.969641i	−0.919302	+	0.393554i	$0.871245\pi$
$168$		0			0
$169$	−1.53972	−	0.327277i	−0.118440	−	0.0251752i
$170$	0.885140	−	0.643092i	0.0678871	−	0.0493229i
$171$		0			0
$172$	−2.73004	−	8.40221i	−0.208164	−	0.640662i
$173$	−4.80433	−	5.33575i	−0.365267	−	0.405670i	0.532295	−	0.846559i	$-0.321330\pi$
$173$	−4.80433	−	5.33575i	−0.365267	−	0.405670i	−0.897561	+	0.440889i	$0.854663\pi$
$174$		0			0
$175$	2.75991	+	4.78030i	0.208629	+	0.361357i
$176$	−7.47422	+	7.67382i	−0.563390	+	0.578436i
$177$		0			0
$178$	−0.470065	+	0.209287i	−0.0352329	+	0.0156867i
$179$	2.78001	−	8.55598i	0.207788	−	0.639504i	−0.791800	−	0.610781i	$-0.790856\pi$
$179$	2.78001	−	8.55598i	0.207788	−	0.639504i	0.999587	−	0.0287236i	$-0.00914427\pi$
$180$		0			0
$181$	−1.51882	+	1.10349i	−0.112893	+	0.0820215i	−0.642799	−	0.766035i	$-0.722227\pi$
$181$	−1.51882	+	1.10349i	−0.112893	+	0.0820215i	0.529906	+	0.848056i	$0.322227\pi$
$182$	0.360545	+	3.43035i	0.0267253	+	0.254275i
$183$		0			0
$184$	9.25244	−	1.96667i	0.682099	−	0.144985i
$185$	−0.0535935	+	0.509908i	−0.00394027	+	0.0374892i
$186$		0			0
$187$	3.61504	+	0.917771i	0.264358	+	0.0671141i
$188$	21.1038			1.53915
$189$		0			0
$190$	−2.03935	+	6.27646i	−0.147950	+	0.455343i
$191$	−6.26510	−	1.33169i	−0.453327	−	0.0963576i	−0.0244108	−	0.999702i	$-0.507771\pi$
$191$	−6.26510	−	1.33169i	−0.453327	−	0.0963576i	−0.428916	+	0.903344i	$0.641104\pi$
$192$		0			0
$193$	2.57473	+	1.14634i	0.185333	+	0.0825156i	0.497305	−	0.867576i	$-0.334323\pi$
$193$	2.57473	+	1.14634i	0.185333	+	0.0825156i	−0.311972	+	0.950091i	$0.600990\pi$
$194$	2.44121	−	2.71124i	0.175269	−	0.194656i
$195$		0			0
$196$	1.33041	−	0.592336i	0.0950291	−	0.0423097i
$197$	−25.7193			−1.83243			−0.916213	−	0.400692i	$-0.868770\pi$
$197$	−25.7193			−1.83243			−0.916213	+	0.400692i	$0.868770\pi$
$198$		0			0
$199$	13.3474			0.946174			0.473087	−	0.881016i	$-0.343140\pi$
$199$	13.3474			0.946174			0.473087	+	0.881016i	$0.343140\pi$
$200$	−2.83348	+	1.26155i	−0.200358	+	0.0892049i
$201$		0			0
$202$	−4.64042	+	5.15371i	−0.326499	+	0.362614i
$203$	16.9169	+	7.53187i	1.18733	+	0.528634i
$204$		0			0
$205$	1.67162	+	0.355315i	0.116751	+	0.0248163i
$206$	−0.347751	+	1.07027i	−0.0242289	+	0.0745690i
$207$		0			0
$208$	12.3303			0.854953
$209$	−20.8950	+	8.33834i	−1.44534	+	0.576775i
$210$		0			0
$211$	1.64442	−	15.6456i	0.113206	−	1.07709i	−0.779486	−	0.626420i	$-0.784520\pi$
$211$	1.64442	−	15.6456i	0.113206	−	1.07709i	0.892692	−	0.450667i	$-0.148814\pi$
$212$	10.0711	−	2.14068i	0.691685	−	0.147022i
$213$		0			0
$214$	0.374213	+	3.56040i	0.0255807	+	0.243384i
$215$	10.2719	−	7.46296i	0.700536	−	0.508969i
$216$		0			0
$217$	5.16732	−	15.9034i	0.350781	−	1.07959i
$218$	5.98502	−	2.66470i	0.405356	−	0.180476i
$219$		0			0
$220$	−14.9301	−	7.36113i	−1.00659	−	0.496287i
$221$	−2.14655	−	3.71793i	−0.144392	−	0.250095i
$222$		0			0
$223$	−12.6350	−	14.0325i	−0.846099	−	0.939688i	0.152720	−	0.988269i	$-0.451197\pi$
$223$	−12.6350	−	14.0325i	−0.846099	−	0.939688i	−0.998819	+	0.0485812i	$0.984530\pi$
$224$	−3.06210	−	9.42417i	−0.204595	−	0.629679i
$225$		0			0
$226$	1.48877	−	1.08165i	0.0990314	−	0.0719505i
$227$	−1.05585	−	0.224429i	−0.0700794	−	0.0148958i	0.172739	−	0.984968i	$-0.444738\pi$
$227$	−1.05585	−	0.224429i	−0.0700794	−	0.0148958i	−0.242818	+	0.970072i	$0.578072\pi$
$228$		0			0
$229$	1.28178	−	12.1953i	0.0847024	−	0.805889i	−0.866885	−	0.498509i	$-0.833881\pi$
$229$	1.28178	−	12.1953i	0.0847024	−	0.805889i	0.951587	−	0.307380i	$-0.0994523\pi$
$230$	3.28330	+	5.68684i	0.216494	+	0.374979i
$231$		0			0
$232$	−5.20267	+	9.01128i	−0.341572	+	0.591620i
$233$	12.1863	+	8.85388i	0.798353	+	0.580037i	0.910430	−	0.413662i	$-0.135751\pi$
$233$	12.1863	+	8.85388i	0.798353	+	0.580037i	−0.112078	+	0.993699i	$0.535751\pi$
$234$		0			0
$235$	9.37235	+	28.8451i	0.611385	+	1.88165i
$236$	1.64657	+	15.6661i	0.107183	+	1.01978i
$237$		0			0
$238$	−0.679867	+	0.755068i	−0.0440692	+	0.0489438i
$239$	14.0790	−	2.99259i	0.910696	−	0.193574i	0.271339	−	0.962484i	$-0.412534\pi$
$239$	14.0790	−	2.99259i	0.910696	−	0.193574i	0.639358	+	0.768910i	$0.279200\pi$
$240$		0			0
$241$	6.01413	−	10.4168i	0.387404	−	0.671004i	−0.604695	−	0.796457i	$-0.706705\pi$
$241$	6.01413	−	10.4168i	0.387404	−	0.671004i	0.992100	+	0.125453i	$0.0400384\pi$
$242$	0.930898	+	3.87453i	0.0598404	+	0.249064i
$243$		0			0
$244$	2.60318	+	1.89132i	0.166651	+	0.121079i
$245$	1.40046	+	1.55537i	0.0894721	+	0.0993688i
$246$		0			0
$247$	23.6568	+	10.5327i	1.50524	+	0.670178i
$248$	8.58380	+	3.82176i	0.545072	+	0.242682i
$249$		0			0
$250$	1.81428	+	2.01496i	0.114745	+	0.127437i
$251$	−11.5075	−	8.36069i	−0.726347	−	0.527722i	0.162058	−	0.986781i	$-0.448187\pi$
$251$	−11.5075	−	8.36069i	−0.726347	−	0.527722i	−0.888406	+	0.459059i	$0.848187\pi$
$252$		0			0
$253$	−7.74611	+	21.0023i	−0.486994	+	1.32040i
$254$	−0.151113	+	0.261736i	−0.00948170	+	0.0164228i
$255$		0			0
$256$	−6.36155	+	1.35219i	−0.397597	+	0.0845118i
$257$	−7.27168	+	8.07601i	−0.453595	+	0.503768i	−0.925953	−	0.377639i	$-0.876736\pi$
$257$	−7.27168	+	8.07601i	−0.453595	+	0.503768i	0.472358	+	0.881407i	$0.343403\pi$
$258$		0			0
$259$	−0.0497703	−	0.473533i	−0.00309258	−	0.0294239i
$260$	5.92095	+	18.2228i	0.367202	+	1.13013i
$261$		0			0
$262$	5.78891	+	4.20589i	0.357640	+	0.259841i
$263$	1.29031	−	2.23489i	0.0795640	−	0.137809i	−0.823498	−	0.567319i	$-0.807981\pi$
$263$	1.29031	−	2.23489i	0.0795640	−	0.137809i	0.903062	+	0.429510i	$0.141314\pi$
$264$		0			0
$265$	7.39856	+	12.8147i	0.454490	+	0.787200i
$266$	0.640622	−	6.09511i	0.0392791	−	0.373715i
$267$		0			0
$268$	8.23796	+	1.75103i	0.503213	+	0.106961i
$269$	4.58187	−	3.32892i	0.279361	−	0.202968i	−0.439277	−	0.898351i	$-0.644765\pi$
$269$	4.58187	−	3.32892i	0.279361	−	0.202968i	0.718639	+	0.695383i	$0.244765\pi$
$270$		0			0
$271$	0.742616	+	2.28554i	0.0451107	+	0.138836i	0.971075	−	0.238775i	$-0.0767457\pi$
$271$	0.742616	+	2.28554i	0.0451107	+	0.138836i	−0.925964	+	0.377611i	$0.876746\pi$
$272$	2.43037	+	2.69920i	0.147363	+	0.163663i
$273$		0			0
$274$	0.717804	+	1.24327i	0.0433641	+	0.0751088i
$275$	1.05262	−	7.26421i	0.0634755	−	0.438048i
$276$		0			0
$277$	2.38442	−	1.06161i	0.143266	−	0.0637860i	−0.333851	−	0.942626i	$-0.608348\pi$
$277$	2.38442	−	1.06161i	0.143266	−	0.0637860i	0.477117	+	0.878840i	$0.341682\pi$
$278$	−0.381136	+	1.17302i	−0.0228590	+	0.0703529i
$279$		0			0
$280$	7.59496	−	5.51806i	0.453886	−	0.329767i
$281$	0.925910	+	8.80945i	0.0552352	+	0.525528i	0.986799	+	0.161950i	$0.0517783\pi$
$281$	0.925910	+	8.80945i	0.0552352	+	0.525528i	−0.931564	+	0.363578i	$0.881555\pi$
$282$		0			0
$283$	13.2156	−	2.80905i	0.785583	−	0.166981i	0.202380	−	0.979307i	$-0.435132\pi$
$283$	13.2156	−	2.80905i	0.785583	−	0.166981i	0.583203	+	0.812326i	$0.301799\pi$
$284$	−2.40276	+	22.8607i	−0.142578	+	1.35654i
$285$		0			0
$286$	2.44720	−	3.87931i	0.144706	−	0.229389i
$287$	−1.58706			−0.0936811
$288$		0			0
$289$	−4.86250	+	14.9652i	−0.286029	+	0.880308i
$290$	−7.06559	−	1.50184i	−0.414906	−	0.0881910i
$291$		0			0
$292$	3.63678	+	1.61920i	0.212827	+	0.0947565i
$293$	−11.8559	+	13.1673i	−0.692630	+	0.769244i	−0.982185	−	0.187918i	$-0.939826\pi$
$293$	−11.8559	+	13.1673i	−0.692630	+	0.769244i	0.289555	+	0.957162i	$0.406493\pi$
$294$		0			0
$295$	−20.6815	+	9.20799i	−1.20412	+	0.536110i
$296$	0.267548			0.0155509
$297$		0			0
$298$	1.86705			0.108156
$299$	23.5389	−	10.4802i	1.36129	−	0.606086i
$300$		0			0
$301$	−7.88972	+	8.76242i	−0.454756	+	0.505058i
$302$	−4.54879	−	2.02525i	−0.261753	−	0.116540i
$303$		0			0
$304$	−21.4300	−	4.55508i	−1.22909	−	0.261252i
$305$	−1.42901	+	4.39803i	−0.0818246	+	0.251830i
$306$		0			0
$307$	11.3039			0.645145			0.322573	−	0.946545i	$-0.395452\pi$
$307$	11.3039			0.645145			0.322573	+	0.946545i	$0.395452\pi$
$308$	14.9834	+	3.80392i	0.853757	+	0.216748i
$309$		0			0
$310$	−0.681824	+	6.48713i	−0.0387250	+	0.368444i
$311$	−6.46082	+	1.37329i	−0.366359	+	0.0778721i	−0.387413	−	0.921906i	$-0.626631\pi$
$311$	−6.46082	+	1.37329i	−0.366359	+	0.0778721i	0.0210536	+	0.999778i	$0.493298\pi$
$312$		0			0
$313$	−3.27168	−	31.1279i	−0.184926	−	1.75945i	−0.556310	−	0.830975i	$-0.687783\pi$
$313$	−3.27168	−	31.1279i	−0.184926	−	1.75945i	0.371384	−	0.928479i	$-0.378883\pi$
$314$	−4.87500	+	3.54190i	−0.275112	+	0.199881i
$315$		0			0
$316$	6.68845	−	20.5849i	0.376254	−	1.15799i
$317$	−11.7357	+	5.22507i	−0.659143	+	0.293469i	−0.708918	−	0.705291i	$-0.750816\pi$
$317$	−11.7357	+	5.22507i	−0.659143	+	0.293469i	0.0497751	+	0.998760i	$0.484150\pi$
$318$		0			0
$319$	−11.4674	−	21.7913i	−0.642049	−	1.22008i
$320$	−6.74181	−	11.6772i	−0.376879	−	0.652773i
$321$		0			0
$322$	−4.08046	−	4.53181i	−0.227395	−	0.252548i
$323$	2.35720	+	7.25471i	0.131158	+	0.403663i
$324$		0			0
$325$	−6.83523	+	4.96608i	−0.379150	+	0.275469i
$326$	−8.07843	−	1.71712i	−0.447423	−	0.0951027i
$327$		0			0
$328$	0.0932167	−	0.886898i	0.00514703	−	0.0489707i
$329$	−14.0830	−	24.3924i	−0.776420	−	1.34480i
$330$		0			0
$331$	−9.58347	+	16.5991i	−0.526755	+	0.912367i	0.472759	+	0.881192i	$0.343258\pi$
$331$	−9.58347	+	16.5991i	−0.526755	+	0.912367i	−0.999514	+	0.0311751i	$0.990075\pi$
$332$	−1.23735	−	0.898985i	−0.0679082	−	0.0493382i
$333$		0			0
$334$	1.41043	+	4.34085i	0.0771751	+	0.237521i
$335$	1.26519	+	12.0375i	0.0691246	+	0.657676i
$336$		0			0
$337$	21.8806	−	24.3009i	1.19191	−	1.32375i	0.258047	−	0.966132i	$-0.416921\pi$
$337$	21.8806	−	24.3009i	1.19191	−	1.32375i	0.933866	−	0.357622i	$-0.116412\pi$
$338$	−0.557769	+	0.118557i	−0.0303386	+	0.00644867i
$339$		0			0
$340$	−2.82207	+	4.88796i	−0.153048	+	0.265087i
$341$	−18.4876	+	12.3553i	−1.00116	+	0.669079i
$342$		0			0
$343$	−15.6970	−	11.4046i	−0.847560	−	0.615788i
$344$	−4.43331	−	4.92369i	−0.239028	−	0.265467i
$345$		0			0
$346$	−2.37610	−	1.05791i	−0.127740	−	0.0568736i
$347$	−10.0313	−	4.46622i	−0.538508	−	0.239759i	0.119415	−	0.992844i	$-0.461898\pi$
$347$	−10.0313	−	4.46622i	−0.538508	−	0.239759i	−0.657923	+	0.753085i	$0.728565\pi$
$348$		0			0
$349$	15.8586	+	17.6128i	0.848892	+	0.942790i	0.998947	−	0.0458881i	$-0.0146118\pi$
$349$	15.8586	+	17.6128i	0.848892	+	0.942790i	−0.150055	+	0.988678i	$0.547945\pi$
$350$	1.61769	+	1.17532i	0.0864691	+	0.0628235i
$351$		0			0
$352$	−4.55968	+	12.3628i	−0.243032	+	0.658942i
$353$	14.7938	−	25.6236i	0.787394	−	1.36381i	−0.140165	−	0.990128i	$-0.544763\pi$
$353$	14.7938	−	25.6236i	0.787394	−	1.36381i	0.927559	−	0.373678i	$-0.121903\pi$
$354$		0			0
$355$	−32.3136	+	6.86847i	−1.71503	+	0.364540i
$356$	1.77616	−	1.97263i	0.0941363	−	0.104549i
$357$		0			0
$358$	−0.340652	−	3.24109i	−0.0180040	−	0.171297i
$359$	−8.83869	−	27.2027i	−0.466488	−	1.43570i	−0.857102	−	0.515148i	$-0.827737\pi$
$359$	−8.83869	−	27.2027i	−0.466488	−	1.43570i	0.390614	−	0.920555i	$-0.372263\pi$
$360$		0			0
$361$	−21.8529	−	15.8771i	−1.15015	−	0.835635i
$362$	−0.340041	+	0.588968i	−0.0178722	+	0.0309555i
$363$		0			0
$364$	−8.89687	−	15.4098i	−0.466323	−	0.807695i
$365$	−0.598035	+	5.68992i	−0.0313026	+	0.297824i
$366$		0			0
$367$	3.50166	+	0.744300i	0.182785	+	0.0388522i	0.298395	−	0.954443i	$-0.403549\pi$
$367$	3.50166	+	0.744300i	0.182785	+	0.0388522i	−0.115610	+	0.993295i	$0.536882\pi$
$368$	−17.6362	+	12.8135i	−0.919352	+	0.667948i
$369$		0			0
$370$	0.0573948	+	0.176643i	0.00298382	+	0.00918324i
$371$	−9.19489	−	10.2120i	−0.477375	−	0.530179i
$372$		0			0
$373$	18.4968	+	32.0373i	0.957726	+	1.65883i	0.728004	+	0.685573i	$0.240448\pi$
$373$	18.4968	+	32.0373i	0.957726	+	1.65883i	0.229722	+	0.973256i	$0.426218\pi$
$374$	1.33157	−	0.228924i	0.0688538	−	0.0118374i
$375$		0			0
$376$	14.4584	−	6.43731i	0.745637	−	0.331979i
$377$	−8.75877	+	26.9567i	−0.451100	+	1.38834i
$378$		0			0
$379$	19.4747	−	14.1492i	1.00035	−	0.726796i	0.0381863	−	0.999271i	$-0.487842\pi$
$379$	19.4747	−	14.1492i	1.00035	−	0.726796i	0.962163	+	0.272474i	$0.0878420\pi$
$380$	−3.55866	−	33.8584i	−0.182555	−	1.73690i
$381$		0			0
$382$	−2.26956	+	0.482409i	−0.116121	+	0.0246822i
$383$	3.66049	−	34.8273i	0.187043	−	1.77959i	−0.350706	−	0.936486i	$-0.614058\pi$
$383$	3.66049	−	34.8273i	0.187043	−	1.77959i	0.537749	−	0.843105i	$-0.319275\pi$
$384$		0			0
$385$	1.45494	+	22.1689i	0.0741508	+	1.12983i
$386$	1.02097			0.0519662
$387$		0			0
$388$	−5.81594	+	17.8996i	−0.295260	+	0.908716i
$389$	−4.01974	−	0.854423i	−0.203809	−	0.0433210i	0.104876	−	0.994485i	$-0.466556\pi$
$389$	−4.01974	−	0.854423i	−0.203809	−	0.0433210i	−0.308685	+	0.951164i	$0.599889\pi$
$390$		0			0
$391$	6.93386	+	3.08715i	0.350660	+	0.156124i
$392$	0.730795	−	0.811630i	0.0369107	−	0.0409935i
$393$		0			0
$394$	−8.51143	+	3.78953i	−0.428800	+	0.190914i
$395$	31.1063			1.56513
$396$		0			0
$397$	−23.0629			−1.15749			−0.578747	−	0.815507i	$-0.696458\pi$
$397$	−23.0629			−1.15749			−0.578747	+	0.815507i	$0.696458\pi$
$398$	4.41714	−	1.96664i	0.221411	−	0.0985786i
$399$		0			0
$400$	4.78297	−	5.31203i	0.239149	−	0.265601i
$401$	−3.42617	−	1.52543i	−0.171095	−	0.0761763i	0.319402	−	0.947619i	$-0.396518\pi$
$401$	−3.42617	−	1.52543i	−0.171095	−	0.0761763i	−0.490497	+	0.871443i	$0.663185\pi$
$402$		0			0
$403$	25.0356	+	5.32149i	1.24711	+	0.265082i
$404$	11.0553	−	34.0248i	0.550024	−	1.69280i
$405$		0			0
$406$	6.70815			0.332920
$407$	−0.337816	+	0.535508i	−0.0167449	+	0.0265442i
$408$		0			0
$409$	2.86874	−	27.2942i	0.141850	−	1.34961i	−0.659630	−	0.751590i	$-0.729287\pi$
$409$	2.86874	−	27.2942i	0.141850	−	1.34961i	0.801480	−	0.598022i	$-0.204046\pi$
$410$	0.605553	−	0.128714i	0.0299061	−	0.00635674i
$411$		0			0
$412$	−0.606825	−	5.77355i	−0.0298961	−	0.284442i
$413$	17.0086	−	12.3574i	0.836937	−	0.608070i
$414$		0			0
$415$	0.679237	−	2.09048i	0.0333424	−	0.102617i
$416$	13.8560	−	6.16909i	0.679347	−	0.302465i
$417$		0			0
$418$	−5.68631	+	5.83816i	−0.278126	+	0.285554i
$419$	10.7023	+	18.5369i	0.522840	+	0.905586i	0.999647	+	0.0265777i	$0.00846093\pi$
$419$	10.7023	+	18.5369i	0.522840	+	0.905586i	−0.476806	+	0.879008i	$0.658206\pi$
$420$		0			0
$421$	7.30873	+	8.11716i	0.356206	+	0.395606i	0.894439	−	0.447189i	$-0.147575\pi$
$421$	7.30873	+	8.11716i	0.356206	+	0.395606i	−0.538234	+	0.842796i	$0.680908\pi$
$422$	−1.76106	−	5.41997i	−0.0857269	−	0.263840i
$423$		0			0
$424$	6.24683	−	4.53859i	0.303373	−	0.220413i
$425$	−2.43438	−	0.517443i	−0.118085	−	0.0250997i
$426$		0			0
$427$	0.448895	−	4.27095i	0.0217235	−	0.206686i
$428$	−9.23416	−	15.9940i	−0.446350	−	0.773101i
$429$		0			0
$430$	2.29972	−	3.98324i	0.110902	−	0.192089i
$431$	9.56381	+	6.94852i	0.460673	+	0.334698i	0.793795	−	0.608185i	$-0.208102\pi$
$431$	9.56381	+	6.94852i	0.460673	+	0.334698i	−0.333122	+	0.942884i	$0.608102\pi$
$432$		0			0
$433$	−7.50566	−	23.1000i	−0.360699	−	1.11012i	−0.952631	−	0.304129i	$-0.901635\pi$
$433$	−7.50566	−	23.1000i	−0.360699	−	1.11012i	0.591932	−	0.805988i	$-0.298365\pi$
$434$	−0.633186	−	6.02436i	−0.0303939	−	0.289178i
$435$		0			0
$436$	−22.6146	+	25.1161i	−1.08304	+	1.20284i
$437$	−44.7820	+	9.51872i	−2.14222	+	0.455342i
$438$		0			0
$439$	9.28957	−	16.0900i	0.443367	−	0.767934i	−0.554570	−	0.832137i	$-0.687117\pi$
$439$	9.28957	−	16.0900i	0.443367	−	0.767934i	0.997937	+	0.0642030i	$0.0204505\pi$
$440$	−12.4741	−	0.489035i	−0.594681	−	0.0233139i
$441$		0			0
$442$	−1.25818	−	0.914119i	−0.0598453	−	0.0434802i
$443$	13.2128	+	14.6743i	0.627761	+	0.697199i	0.970190	−	0.242345i	$-0.0779165\pi$
$443$	13.2128	+	14.6743i	0.627761	+	0.697199i	−0.342430	+	0.939543i	$0.611250\pi$
$444$		0			0
$445$	3.48503	+	1.55164i	0.165206	+	0.0735546i
$446$	−6.24894	−	2.78221i	−0.295896	−	0.131741i
$447$		0			0
$448$	8.37869	+	9.30547i	0.395856	+	0.439642i
$449$	−1.68475	−	1.22404i	−0.0795083	−	0.0577662i	0.547321	−	0.836923i	$-0.315648\pi$
$449$	−1.68475	−	1.22404i	−0.0795083	−	0.0577662i	−0.626829	+	0.779157i	$0.715648\pi$
$450$		0			0
$451$	1.65746	+	1.30641i	0.0780468	+	0.0615163i
$452$	−4.74660	+	8.22135i	−0.223261	+	0.386700i
$453$		0			0
$454$	−0.382487	+	0.0813001i	−0.0179510	+	0.00381560i
$455$	17.1113	−	19.0040i	0.802191	−	0.890923i
$456$		0			0
$457$	0.866319	+	8.24248i	0.0405247	+	0.385567i	0.995920	+	0.0902376i	$0.0287626\pi$
$457$	0.866319	+	8.24248i	0.0405247	+	0.385567i	−0.955396	+	0.295329i	$0.904571\pi$
$458$	−1.37270	−	4.22472i	−0.0641418	−	0.197408i
$459$		0			0
$460$	−27.4057	−	19.9114i	−1.27780	−	0.928374i
$461$	3.27711	−	5.67613i	0.152630	−	0.264364i	−0.779563	−	0.626324i	$-0.784559\pi$
$461$	3.27711	−	5.67613i	0.152630	−	0.264364i	0.932194	+	0.361960i	$0.117892\pi$
$462$		0			0
$463$	−0.136703	−	0.236776i	−0.00635310	−	0.0110039i	0.862831	−	0.505492i	$-0.168689\pi$
$463$	−0.136703	−	0.236776i	−0.00635310	−	0.0110039i	−0.869184	+	0.494488i	$0.835356\pi$
$464$	2.50661	−	23.8488i	0.116366	−	1.10715i
$465$		0			0
$466$	5.33744	+	1.13451i	0.247252	+	0.0525550i
$467$	−6.19971	+	4.50435i	−0.286888	+	0.208437i	−0.721916	−	0.691980i	$-0.756738\pi$
$467$	−6.19971	+	4.50435i	−0.286888	+	0.208437i	0.435028	+	0.900417i	$0.356738\pi$
$468$		0			0
$469$	−3.47345	−	10.6902i	−0.160389	−	0.493627i
$470$	7.35174	+	8.16494i	0.339111	+	0.376620i
$471$		0			0
$472$	5.90672	+	10.2307i	0.271879	+	0.470908i
$473$	15.4526	−	2.65661i	0.710512	−	0.122151i
$474$		0			0
$475$	13.7141	−	6.10593i	0.629248	−	0.280159i
$476$	1.61971	−	4.98497i	0.0742395	−	0.228486i
$477$		0			0
$478$	4.21831	−	3.06478i	0.192941	−	0.140180i
$479$	−2.42582	−	23.0802i	−0.110839	−	1.05456i	−0.898657	−	0.438652i	$-0.855456\pi$
$479$	−2.42582	−	23.0802i	−0.110839	−	1.05456i	0.787818	−	0.615908i	$-0.211211\pi$
$480$		0			0
$481$	0.712872	−	0.151526i	0.0325041	−	0.00690897i
$482$	0.455460	−	4.33342i	0.0207457	−	0.197382i
$483$		0			0
$484$	−12.5168	−	16.3064i	−0.568946	−	0.741200i
$485$	−27.0485			−1.22821
$486$		0			0
$487$	−7.44592	+	22.9162i	−0.337407	+	1.03843i	0.628117	+	0.778119i	$0.283826\pi$
$487$	−7.44592	+	22.9162i	−0.337407	+	1.03843i	−0.965524	+	0.260313i	$0.916174\pi$
$488$	2.36037	+	0.501713i	0.106849	+	0.0227115i
$489$		0			0
$490$	0.692633	+	0.308380i	0.0312900	+	0.0139312i
$491$	23.5319	−	26.1348i	1.06198	−	1.17945i	0.0787837	−	0.996892i	$-0.474896\pi$
$491$	23.5319	−	26.1348i	1.06198	−	1.17945i	0.983196	−	0.182556i	$-0.0584370\pi$
$492$		0			0
$493$	−7.62745	+	3.39596i	−0.343523	+	0.152946i
$494$	9.38077			0.422061
$495$		0			0
$496$	−21.6544			−0.972311
$497$	28.0266	−	12.4782i	1.25716	−	0.559725i
$498$		0			0
$499$	−15.2234	+	16.9074i	−0.681495	+	0.756877i	−0.980317	−	0.197432i	$-0.936740\pi$
$499$	−15.2234	+	16.9074i	−0.681495	+	0.756877i	0.298821	+	0.954309i	$0.403407\pi$
$500$	−12.7781	−	5.68918i	−0.571455	−	0.254428i
$501$		0			0
$502$	−5.04012	−	1.07131i	−0.224952	−	0.0478150i
$503$	1.55585	−	4.78840i	0.0693718	−	0.213504i	−0.910360	−	0.413816i	$-0.864196\pi$
$503$	1.55585	−	4.78840i	0.0693718	−	0.213504i	0.979732	+	0.200312i	$0.0641956\pi$
$504$		0			0
$505$	51.4156			2.28796
$506$	0.531059	+	8.09173i	0.0236085	+	0.359721i
$507$		0			0
$508$	0.162971	−	1.55057i	0.00723068	−	0.0687953i
$509$	9.10275	−	1.93485i	0.403472	−	0.0857606i	−0.00170572	−	0.999999i	$-0.500543\pi$
$509$	9.10275	−	1.93485i	0.403472	−	0.0857606i	0.405178	+	0.914238i	$0.367210\pi$
$510$		0			0
$511$	−0.555374	−	5.28403i	−0.0245683	−	0.233752i
$512$	−17.7056	+	12.8639i	−0.782483	+	0.568507i
$513$		0			0
$514$	−1.21652	+	3.74406i	−0.0536584	+	0.165144i
$515$	7.62191	−	3.39349i	0.335862	−	0.149535i
$516$		0			0
$517$	−5.37122	+	37.0671i	−0.236226	+	1.63021i
$518$	−0.0862420	−	0.149376i	−0.00378926	−	0.00656319i
$519$		0			0
$520$	9.61501	+	10.6786i	0.421646	+	0.468285i
$521$	−3.41257	−	10.5028i	−0.149507	−	0.460136i	0.848056	−	0.529907i	$-0.177773\pi$
$521$	−3.41257	−	10.5028i	−0.149507	−	0.460136i	−0.997563	+	0.0697708i	$0.977773\pi$
$522$		0			0
$523$	15.7075	−	11.4122i	0.686841	−	0.499019i	−0.188779	−	0.982020i	$-0.560453\pi$
$523$	15.7075	−	11.4122i	0.686841	−	0.499019i	0.875620	+	0.483001i	$0.160453\pi$
$524$	−36.1066	−	7.67469i	−1.57732	−	0.335271i
$525$		0			0
$526$	0.0977175	−	0.929720i	0.00426069	−	0.0405377i
$527$	3.76975	+	6.52940i	0.164213	+	0.284425i
$528$		0			0
$529$	−11.2772	+	19.5327i	−0.490314	+	0.849249i
$530$	4.33659	+	3.15071i	0.188369	+	0.136858i
$531$		0			0
$532$	9.76996	+	30.0688i	0.423581	+	1.30365i
$533$	−0.253921	−	2.41590i	−0.0109985	−	0.104644i
$534$		0			0
$535$	17.7600	−	19.7245i	0.767832	−	0.852764i
$536$	6.17802	−	1.31318i	0.266850	−	0.0567207i
$537$		0			0
$538$	1.02581	−	1.77676i	0.0442259	−	0.0766016i
$539$	0.701781	+	2.48751i	0.0302278	+	0.107145i
$540$		0			0
$541$	17.0772	+	12.4073i	0.734205	+	0.533431i	0.890891	−	0.454217i	$-0.150081\pi$
$541$	17.0772	+	12.4073i	0.734205	+	0.533431i	−0.156686	+	0.987649i	$0.550081\pi$
$542$	0.582513	+	0.646946i	0.0250211	+	0.0277887i
$543$		0			0
$544$	4.08156	+	1.81723i	0.174996	+	0.0779130i
$545$	−44.3725	−	19.7559i	−1.90071	−	0.846250i
$546$		0			0
$547$	−9.39733	−	10.4368i	−0.401801	−	0.446245i	0.507958	−	0.861382i	$-0.330400\pi$
$547$	−9.39733	−	10.4368i	−0.401801	−	0.446245i	−0.909759	+	0.415137i	$0.863734\pi$
$548$	−5.99151	−	4.35309i	−0.255945	−	0.185955i
$549$		0			0
$550$	−0.721973	−	2.55908i	−0.0307850	−	0.109120i
$551$	25.1810	−	43.6148i	1.07275	−	1.85805i
$552$		0			0
$553$	−28.2560	+	6.00600i	−1.20157	+	0.255401i
$554$	0.632668	−	0.702649i	0.0268795	−	0.0298527i
$555$		0			0
$556$	−0.665083	−	6.32784i	−0.0282058	−	0.268360i
$557$	12.8094	+	39.4233i	0.542752	+	1.67042i	0.726276	+	0.687403i	$0.241249\pi$
$557$	12.8094	+	39.4233i	0.542752	+	1.67042i	−0.183524	+	0.983015i	$0.558751\pi$
$558$		0			0
$559$	−14.6009	−	10.6082i	−0.617552	−	0.448678i
$560$	−10.8177	+	18.7368i	−0.457131	+	0.791773i
$561$		0			0
$562$	1.60442	+	2.77893i	0.0676783	+	0.117222i
$563$	−0.778683	+	7.40867i	−0.0328176	+	0.312238i	0.965783	+	0.259352i	$0.0835088\pi$
$563$	−0.778683	+	7.40867i	−0.0328176	+	0.312238i	−0.998601	+	0.0528866i	$0.983158\pi$
$564$		0			0
$565$	−13.3451	−	2.83659i	−0.561433	−	0.119336i
$566$	3.95961	−	2.87682i	0.166435	−	0.120922i
$567$		0			0
$568$	5.32707	+	16.3950i	0.223519	+	0.687920i
$569$	16.3418	+	18.1495i	0.685086	+	0.760865i	0.980928	−	0.194372i	$-0.0622669\pi$
$569$	16.3418	+	18.1495i	0.685086	+	0.760865i	−0.295842	+	0.955237i	$0.595600\pi$
$570$		0			0
$571$	6.40805	+	11.0991i	0.268169	+	0.464482i	0.968389	−	0.249445i	$-0.0802482\pi$
$571$	6.40805	+	11.0991i	0.268169	+	0.464482i	−0.700220	+	0.713927i	$0.746915\pi$
$572$	−3.39325	+	23.4170i	−0.141879	+	0.979114i
$573$		0			0
$574$	−0.525214	+	0.233840i	−0.0219220	+	0.00976031i
$575$	4.61585	−	14.2061i	0.192494	−	0.592437i
$576$		0			0
$577$	11.7428	−	8.53166i	0.488860	−	0.355178i	−0.315886	−	0.948797i	$-0.602302\pi$
$577$	11.7428	−	8.53166i	0.488860	−	0.355178i	0.804746	+	0.593620i	$0.202302\pi$
$578$	0.595834	+	5.66898i	0.0247834	+	0.235798i
$579$		0			0
$580$	36.4495	−	7.74758i	1.51348	−	0.321701i
$581$	−0.213369	+	2.03007i	−0.00885205	+	0.0842216i
$582$		0			0
$583$	1.19669	+	18.2339i	0.0495617	+	0.755170i
$584$	2.98550			0.123541
$585$		0			0
$586$	−1.98344	+	6.10441i	−0.0819353	+	0.252171i
$587$	−21.9256	−	4.66043i	−0.904966	−	0.192357i	−0.268155	−	0.963376i	$-0.586414\pi$
$587$	−21.9256	−	4.66043i	−0.904966	−	0.192357i	−0.636812	+	0.771019i	$0.719747\pi$
$588$		0			0
$589$	−41.5458	−	18.4974i	−1.71187	−	0.762172i
$590$	−5.48751	+	6.09450i	−0.225917	+	0.250907i
$591$		0			0
$592$	−0.563286	+	0.250791i	−0.0231509	+	0.0103074i
$593$	−18.2533			−0.749572			−0.374786	−	0.927111i	$-0.622284\pi$
$593$	−18.2533			−0.749572			−0.374786	+	0.927111i	$0.622284\pi$
$594$		0			0
$595$	7.53288			0.308818
$596$	−8.79894	+	3.91754i	−0.360418	+	0.160469i
$597$		0			0
$598$	6.24569	−	6.93654i	0.255405	−	0.283656i
$599$	24.1386	+	10.7472i	0.986276	+	0.439118i	0.835524	−	0.549453i	$-0.185164\pi$
$599$	24.1386	+	10.7472i	0.986276	+	0.439118i	0.150751	+	0.988572i	$0.451831\pi$
$600$		0			0
$601$	−13.5233	−	2.87446i	−0.551625	−	0.117252i	−0.0763376	−	0.997082i	$-0.524323\pi$
$601$	−13.5233	−	2.87446i	−0.551625	−	0.117252i	−0.475288	+	0.879830i	$0.657656\pi$
$602$	−1.31992	+	4.06228i	−0.0537958	+	0.165566i
$603$		0			0
$604$	25.6867			1.04518
$605$	16.7291	−	24.3500i	0.680136	−	0.989969i
$606$		0			0
$607$	1.52423	−	14.5021i	0.0618668	−	0.588623i	−0.919043	−	0.394158i	$-0.871036\pi$
$607$	1.52423	−	14.5021i	0.0618668	−	0.588623i	0.980909	−	0.194465i	$-0.0622971\pi$
$608$	−26.3606	+	5.60312i	−1.06906	+	0.227236i
$609$		0			0
$610$	0.175105	+	1.66602i	0.00708980	+	0.0674550i
$611$	34.8782	−	25.3405i	1.41102	−	1.02517i
$612$		0			0
$613$	−9.31252	+	28.6610i	−0.376129	+	1.15761i	0.566585	+	0.824004i	$0.308264\pi$
$613$	−9.31252	+	28.6610i	−0.376129	+	1.15761i	−0.942714	+	0.333603i	$0.891736\pi$
$614$	3.74085	−	1.66553i	0.150968	−	0.0672154i
$615$		0			0
$616$	11.4256	−	1.96428i	0.460349	−	0.0791432i
$617$	−9.84784	−	17.0570i	−0.396459	−	0.686687i	0.596827	−	0.802370i	$-0.296428\pi$
$617$	−9.84784	−	17.0570i	−0.396459	−	0.686687i	−0.993286	+	0.115683i	$0.963094\pi$
$618$		0			0
$619$	0.865258	+	0.960967i	0.0347777	+	0.0386245i	0.760283	−	0.649592i	$-0.225060\pi$
$619$	0.865258	+	0.960967i	0.0347777	+	0.0386245i	−0.725505	+	0.688217i	$0.758394\pi$
$620$	−10.3983	−	32.0028i	−0.417607	−	1.28526i
$621$		0			0
$622$	−1.93577	+	1.40642i	−0.0776173	+	0.0563923i
$623$	−3.46529	−	0.736570i	−0.138834	−	0.0295100i
$624$		0			0
$625$	3.25791	−	30.9970i	0.130316	−	1.23988i
$626$	−5.66916	−	9.81928i	−0.226585	−	0.392457i
$627$		0			0
$628$	15.5428	−	26.9210i	0.620227	−	1.07426i
$629$	0.173681	+	0.126187i	0.00692513	+	0.00503140i
$630$		0			0
$631$	13.6277	+	41.9417i	0.542509	+	1.66967i	0.726839	+	0.686808i	$0.240988\pi$
$631$	13.6277	+	41.9417i	0.542509	+	1.66967i	−0.184330	+	0.982864i	$0.559012\pi$
$632$	−1.69671	−	16.1431i	−0.0674915	−	0.642138i
$633$		0			0
$634$	−3.11389	+	3.45832i	−0.123668	+	0.137348i
$635$	2.19172	−	0.465865i	0.0869759	−	0.0184873i
$636$		0			0
$637$	1.48751	−	2.57644i	0.0589372	−	0.102082i
$638$	−7.00573	−	5.52190i	−0.277360	−	0.218614i
$639$		0			0
$640$	−21.2166	−	15.4148i	−0.838660	−	0.609322i
$641$	18.0626	+	20.0605i	0.713429	+	0.792343i	0.985453	−	0.169947i	$-0.0543597\pi$
$641$	18.0626	+	20.0605i	0.713429	+	0.792343i	−0.272024	+	0.962290i	$0.587693\pi$
$642$		0			0
$643$	−9.27843	−	4.13102i	−0.365905	−	0.162912i	0.215544	−	0.976494i	$-0.430848\pi$
$643$	−9.27843	−	4.13102i	−0.365905	−	0.162912i	−0.581449	+	0.813583i	$0.697514\pi$
$644$	28.7390	+	12.7954i	1.13248	+	0.504211i
$645$		0			0
$646$	1.84900	+	2.05353i	0.0727481	+	0.0807949i
$647$	27.2093	+	19.7687i	1.06971	+	0.777189i	0.975860	−	0.218397i	$-0.0700828\pi$
$647$	27.2093	+	19.7687i	1.06971	+	0.777189i	0.0938493	+	0.995586i	$0.470083\pi$
$648$		0			0
$649$	−27.9353	−	1.09517i	−1.09656	−	0.0429893i
$650$	−1.53031	+	2.65057i	−0.0600236	+	0.103964i
$651$		0			0
$652$	41.6745	−	8.85818i	1.63210	−	0.346913i
$653$	−7.57971	+	8.41812i	−0.296617	+	0.329426i	−0.872970	−	0.487775i	$-0.837809\pi$
$653$	−7.57971	+	8.41812i	−0.296617	+	0.329426i	0.576353	+	0.817201i	$0.304475\pi$
$654$		0			0
$655$	−5.54526	−	52.7596i	−0.216671	−	2.06149i
$656$	0.635094	+	1.95462i	0.0247963	+	0.0763150i
$657$		0			0
$658$	−8.25459	−	5.99731i	−0.321797	−	0.233800i
$659$	−16.1903	+	28.0424i	−0.630684	+	1.09238i	0.356729	+	0.934208i	$0.383892\pi$
$659$	−16.1903	+	28.0424i	−0.630684	+	1.09238i	−0.987412	+	0.158168i	$0.949441\pi$
$660$		0			0
$661$	−1.57119	−	2.72139i	−0.0611123	−	0.105850i	0.833851	−	0.551990i	$-0.186131\pi$
$661$	−1.57119	−	2.72139i	−0.0611123	−	0.105850i	−0.894963	+	0.446141i	$0.852798\pi$
$662$	−0.725773	+	6.90527i	−0.0282080	+	0.268381i
$663$		0			0
$664$	−1.12194	−	0.238475i	−0.0435396	−	0.00925462i
$665$	−36.7598	+	26.7076i	−1.42548	+	1.03567i
$666$		0			0
$667$	−15.4852	−	47.6586i	−0.599590	−	1.84535i
$668$	−15.7551	−	17.4979i	−0.609585	−	0.677012i
$669$		0			0
$670$	2.19232	+	3.79721i	0.0846966	+	0.146699i
$671$	−3.98449	+	4.09090i	−0.153820	+	0.157927i
$672$		0			0
$673$	−35.3255	+	15.7279i	−1.36170	+	0.606267i	−0.952040	−	0.305972i	$-0.901018\pi$
$673$	−35.3255	+	15.7279i	−1.36170	+	0.606267i	−0.409658	+	0.912239i	$0.634352\pi$
$674$	3.66053	−	11.2660i	0.140998	−	0.433949i
$675$		0			0
$676$	2.37986	−	1.72907i	0.0915329	−	0.0665025i
$677$	4.77915	+	45.4706i	0.183678	+	1.74758i	0.566778	+	0.823870i	$0.308190\pi$
$677$	4.77915	+	45.4706i	0.183678	+	1.74758i	−0.383101	+	0.923707i	$0.625144\pi$
$678$		0			0
$679$	24.5700	−	5.22252i	0.942912	−	0.200422i
$680$	−0.442448	+	4.20961i	−0.0169671	+	0.161431i
$681$		0			0
$682$	−4.29775	+	6.81282i	−0.164569	+	0.260876i
$683$	−11.3550			−0.434485			−0.217243	−	0.976118i	$-0.569706\pi$
$683$	−11.3550			−0.434485			−0.217243	+	0.976118i	$0.569706\pi$
$684$		0			0
$685$	3.28902	−	10.1226i	0.125667	−	0.386763i
$686$	−6.87508	−	1.46134i	−0.262492	−	0.0557943i
$687$		0			0
$688$	13.9490	+	6.21050i	0.531801	+	0.236773i
$689$	14.0740	−	15.6308i	0.536177	−	0.595485i
$690$		0			0
$691$	7.96598	−	3.54668i	0.303040	−	0.134922i	−0.249583	−	0.968353i	$-0.580294\pi$
$691$	7.96598	−	3.54668i	0.303040	−	0.134922i	0.552623	+	0.833431i	$0.313627\pi$
$692$	13.4177			0.510065
$693$		0			0
$694$	−3.97778			−0.150994
$695$	8.35365	−	3.71929i	0.316872	−	0.141081i
$696$		0			0
$697$	0.478810	−	0.531772i	0.0181362	−	0.0201423i
$698$	7.84327	+	3.49205i	0.296872	+	0.132176i
$699$		0			0
$700$	−10.0899	−	2.14467i	−0.381361	−	0.0810607i
$701$	−12.5650	+	38.6712i	−0.474575	+	1.46059i	0.371954	+	0.928251i	$0.378688\pi$
$701$	−12.5650	+	38.6712i	−0.474575	+	1.46059i	−0.846530	+	0.532342i	$0.821312\pi$
$702$		0			0
$703$	−1.29494			−0.0488396
$704$	−1.09046	−	16.6153i	−0.0410982	−	0.626212i
$705$		0			0
$706$	1.12036	−	10.6595i	0.0421653	−	0.401176i
$707$	−46.7044	+	9.92733i	−1.75650	+	0.373356i
$708$		0			0
$709$	1.75005	+	16.6506i	0.0657244	+	0.625326i	0.976957	+	0.213434i	$0.0684650\pi$
$709$	1.75005	+	16.6506i	0.0657244	+	0.625326i	−0.911233	+	0.411891i	$0.864868\pi$
$710$	−9.68171	+	7.03417i	−0.363348	+	0.263988i
$711$		0			0
$712$	0.615154	−	1.89325i	0.0230539	−	0.0709525i
$713$	−41.3389	+	18.4053i	−1.54815	+	0.689282i
$714$		0			0
$715$	−33.5138	+	5.76169i	−1.25335	+	0.215475i
$716$	8.40601	+	14.5596i	0.314147	+	0.544119i
$717$		0			0
$718$	−6.93313	−	7.70002i	−0.258742	−	0.287362i
$719$	5.99373	+	18.4468i	0.223528	+	0.687949i	0.998438	+	0.0558770i	$0.0177955\pi$
$719$	5.99373	+	18.4468i	0.223528	+	0.687949i	−0.774909	+	0.632072i	$0.782205\pi$
$720$		0			0
$721$	−6.26830	+	4.55419i	−0.233444	+	0.169607i
$722$	−9.57126	−	2.03443i	−0.356205	−	0.0757138i
$723$		0			0
$724$	0.366724	−	3.48914i	0.0136292	−	0.129673i
$725$	8.21569	+	14.2300i	0.305123	+	0.528488i
$726$		0			0
$727$	−2.89216	+	5.00937i	−0.107264	+	0.185787i	−0.914661	−	0.404222i	$-0.867542\pi$
$727$	−2.89216	+	5.00937i	−0.107264	+	0.185787i	0.807397	+	0.590009i	$0.200876\pi$
$728$	−10.7958	−	7.84361i	−0.400119	−	0.290704i
$729$		0			0
$730$	0.640454	+	1.97111i	0.0237043	+	0.0729542i
$731$	−0.555706	−	5.28719i	−0.0205535	−	0.195554i
$732$		0			0
$733$	15.1974	−	16.8785i	0.561330	−	0.623420i	−0.393947	−	0.919133i	$-0.628891\pi$
$733$	15.1974	−	16.8785i	0.561330	−	0.623420i	0.955277	+	0.295713i	$0.0955572\pi$
$734$	1.26849	−	0.269626i	0.0468208	−	0.00995207i
$735$		0			0
$736$	−13.4076	+	23.2227i	−0.494212	+	0.856000i
$737$	−5.17222	+	14.0236i	−0.190521	+	0.516567i
$738$		0			0
$739$	9.31755	+	6.76960i	0.342752	+	0.249024i	0.745822	−	0.666145i	$-0.232057\pi$
$739$	9.31755	+	6.76960i	0.342752	+	0.249024i	−0.403070	+	0.915169i	$0.632057\pi$
$740$	−0.641128	−	0.712044i	−0.0235683	−	0.0261753i
$741$		0			0
$742$	−4.54757	−	2.02471i	−0.166946	−	0.0743293i
$743$	39.2878	+	17.4921i	1.44133	+	0.641721i	0.970631	−	0.240573i	$-0.0773354\pi$
$743$	39.2878	+	17.4921i	1.44133	+	0.641721i	0.470698	+	0.882294i	$0.344002\pi$
$744$		0			0
$745$	−9.26224	−	10.2868i	−0.339342	−	0.376878i
$746$	10.8417	+	7.87694i	0.396942	+	0.288395i
$747$		0			0
$748$	−5.79500	+	3.87282i	−0.211886	+	0.141604i
$749$	−12.3243	+	21.3462i	−0.450319	+	0.779975i
$750$		0			0
$751$	−3.52024	+	0.748251i	−0.128455	+	0.0273041i	−0.271691	−	0.962385i	$-0.587583\pi$
$751$	−3.52024	+	0.748251i	−0.128455	+	0.0273041i	0.143235	+	0.989689i	$0.454249\pi$
$752$	−24.4061	+	27.1057i	−0.889999	+	0.988444i
$753$		0			0
$754$	1.07327	+	10.2115i	0.0390861	+	0.371880i
$755$	11.4076	+	35.1091i	0.415167	+	1.27775i
$756$		0			0
$757$	12.2911	+	8.93000i	0.446727	+	0.324566i	0.788302	−	0.615288i	$-0.210960\pi$
$757$	12.2911	+	8.93000i	0.446727	+	0.324566i	−0.341575	+	0.939855i	$0.610960\pi$
$758$	4.36010	−	7.55192i	0.158366	−	0.274298i
$759$		0			0
$760$	−12.7659	−	22.1112i	−0.463068	−	0.802058i
$761$	1.70539	−	16.2257i	0.0618205	−	0.588183i	−0.919134	−	0.393945i	$-0.871110\pi$
$761$	1.70539	−	16.2257i	0.0618205	−	0.588183i	0.980954	−	0.194238i	$-0.0622233\pi$
$762$		0			0
$763$	44.1211	+	9.37823i	1.59729	+	0.339515i
$764$	9.68362	−	7.03556i	0.350341	−	0.254538i
$765$		0			0
$766$	−3.92013	−	12.0649i	−0.141640	−	0.435923i
$767$	21.5324	+	23.9141i	0.777489	+	0.863489i
$768$		0			0
$769$	−3.33336	−	5.77355i	−0.120204	−	0.208200i	0.799644	−	0.600474i	$-0.205022\pi$
$769$	−3.33336	−	5.77355i	−0.120204	−	0.208200i	−0.919848	+	0.392275i	$0.871688\pi$
$770$	3.74790	+	7.12211i	0.135065	+	0.256663i
$771$		0			0
$772$	−4.81158	+	2.14225i	−0.173173	+	0.0771014i
$773$	15.7232	−	48.3910i	0.565524	−	1.74050i	−0.100865	−	0.994900i	$-0.532161\pi$
$773$	15.7232	−	48.3910i	0.565524	−	1.74050i	0.666389	−	0.745604i	$-0.267839\pi$
$774$		0			0
$775$	12.0040	−	8.72140i	0.431196	−	0.313282i
$776$	1.47537	+	14.0373i	0.0529629	+	0.503908i
$777$		0			0
$778$	−1.45617	+	0.309518i	−0.0522062	+	0.0110968i
$779$	−0.451171	+	4.29261i	−0.0161649	+	0.153799i
$780$		0			0
$781$	−39.5415	−	10.0386i	−1.41490	−	0.359210i
$782$	2.74953			0.0983229
$783$		0			0
$784$	−0.777792	+	2.39380i	−0.0277783	+	0.0854928i
$785$	43.6988	+	9.28848i	1.55968	+	0.331520i
$786$		0			0
$787$	−27.7299	−	12.3462i	−0.988465	−	0.440093i	−0.152159	−	0.988356i	$-0.548623\pi$
$787$	−27.7299	−	12.3462i	−0.988465	−	0.440093i	−0.836306	+	0.548263i	$0.815289\pi$
$788$	32.1608	−	35.7182i	1.14568	−	1.27241i
$789$		0			0
$790$	10.2942	−	4.58326i	0.366250	−	0.163065i
$791$	12.6700			0.450493
$792$		0			0
$793$	6.57326			0.233423
$794$	−7.63233	+	3.39813i	−0.270861	+	0.120595i
$795$		0			0
$796$	−16.6903	+	18.5365i	−0.591573	+	0.657008i
$797$	3.62872	+	1.61561i	0.128536	+	0.0572279i	0.469997	−	0.882668i	$-0.344255\pi$
$797$	3.62872	+	1.61561i	0.128536	+	0.0572279i	−0.341461	+	0.939896i	$0.610922\pi$
$798$		0			0
$799$	12.4219	+	2.64036i	0.439456	+	0.0934092i
$800$	2.71709	−	8.36233i	0.0960635	−	0.295653i
$801$		0			0
$802$	−1.35860			−0.0479738
$803$	−3.76960	+	5.97560i	−0.133026	+	0.210874i
$804$		0			0
$805$	−4.72587	+	44.9636i	−0.166565	+	1.58476i
$806$	9.06926	−	1.92773i	0.319451	−	0.0679014i
$807$		0			0
$808$	−2.80449	−	26.6830i	−0.0986617	−	0.938703i
$809$	4.26011	−	3.09515i	0.149778	−	0.108820i	−0.510373	−	0.859953i	$-0.670493\pi$
$809$	4.26011	−	3.09515i	0.149778	−	0.108820i	0.660150	+	0.751133i	$0.270493\pi$
$810$		0			0
$811$	11.6366	−	35.8137i	0.408615	−	1.25759i	−0.509223	−	0.860635i	$-0.670067\pi$
$811$	11.6366	−	35.8137i	0.408615	−	1.25759i	0.917838	−	0.396954i	$-0.129933\pi$
$812$	−31.6138	+	14.0754i	−1.10943	+	0.493948i
$813$		0			0
$814$	−0.0328925	+	0.226993i	−0.00115288	+	0.00795611i
$815$	30.6155	+	53.0275i	1.07241	+	1.85747i
$816$		0			0
$817$	21.4573	+	23.8308i	0.750697	+	0.833733i
$818$	−3.07222	−	9.45531i	−0.107418	−	0.330597i
$819$		0			0
$820$	−2.58374	+	1.87719i	−0.0902280	+	0.0655545i
$821$	2.05555	+	0.436921i	0.0717392	+	0.0152486i	0.243641	−	0.969865i	$-0.421658\pi$
$821$	2.05555	+	0.436921i	0.0717392	+	0.0152486i	−0.171902	+	0.985114i	$0.554991\pi$
$822$		0			0
$823$	0.695103	−	6.61346i	0.0242298	−	0.230531i	−0.975705	−	0.219089i	$-0.929691\pi$
$823$	0.695103	−	6.61346i	0.0242298	−	0.230531i	0.999935	−	0.0114413i	$-0.00364197\pi$
$824$	−2.17685	−	3.77042i	−0.0758342	−	0.131349i
$825$		0			0
$826$	3.80797	−	6.59559i	0.132496	−	0.229490i
$827$	−17.8702	−	12.9834i	−0.621407	−	0.451479i	0.232006	−	0.972714i	$-0.425471\pi$
$827$	−17.8702	−	12.9834i	−0.621407	−	0.451479i	−0.853413	+	0.521236i	$0.825471\pi$
$828$		0			0
$829$	1.19544	+	3.67920i	0.0415195	+	0.127784i	0.969668	−	0.244427i	$-0.0785998\pi$
$829$	1.19544	+	3.67920i	0.0415195	+	0.127784i	−0.928148	+	0.372211i	$0.878600\pi$
$830$	−0.0832313	−	0.791893i	−0.00288900	−	0.0274870i
$831$		0			0
$832$	−12.8247	+	14.2433i	−0.444616	+	0.493796i
$833$	0.857200	−	0.182203i	0.0297002	−	0.00631298i
$834$		0			0
$835$	16.9195	−	29.3054i	0.585522	−	1.01415i
$836$	14.5482	−	39.4450i	0.503159	−	1.36423i
$837$		0			0
$838$	6.27302	+	4.55762i	0.216698	+	0.157440i
$839$	15.6831	+	17.4178i	0.541439	+	0.601329i	0.950326	−	0.311256i	$-0.100750\pi$
$839$	15.6831	+	17.4178i	0.541439	+	0.601329i	−0.408887	+	0.912585i	$0.634083\pi$
$840$		0			0
$841$	23.8653	+	10.6255i	0.822941	+	0.366397i
$842$	3.61472	+	1.60938i	0.124571	+	0.0554627i
$843$		0			0
$844$	19.6718	+	21.8478i	0.677132	+	0.752032i
$845$	3.42023	+	2.48494i	0.117660	+	0.0854847i
$846$		0			0
$847$	−10.4947	+	25.3489i	−0.360604	+	0.870998i
$848$	−8.89751	+	15.4109i	−0.305542	+	0.529214i
$849$		0			0
$850$	−0.881863	+	0.187446i	−0.0302477	+	0.00642934i
$851$	−0.862168	+	0.957535i	−0.0295548	+	0.0328239i
$852$		0			0
$853$	2.19431	+	20.8775i	0.0751319	+	0.714832i	0.965643	+	0.259871i	$0.0836801\pi$
$853$	2.19431	+	20.8775i	0.0751319	+	0.714832i	−0.890511	+	0.454961i	$0.849653\pi$
$854$	−0.480735	−	1.47955i	−0.0164504	−	0.0506291i
$855$		0			0
$856$	−11.2051	−	8.14097i	−0.382982	−	0.278252i
$857$	14.1590	−	24.5241i	0.483662	−	0.837728i	−0.516162	−	0.856491i	$-0.672640\pi$
$857$	14.1590	−	24.5241i	0.483662	−	0.837728i	0.999824	+	0.0187634i	$0.00597292\pi$
$858$		0			0
$859$	27.8536	+	48.2438i	0.950351	+	1.64606i	0.744665	+	0.667439i	$0.232609\pi$
$859$	27.8536	+	48.2438i	0.950351	+	1.64606i	0.205687	+	0.978618i	$0.434057\pi$
$860$	−2.48018	+	23.5973i	−0.0845734	+	0.804662i
$861$		0			0
$862$	4.18881	+	0.890360i	0.142672	+	0.0303258i
$863$	24.8932	−	18.0860i	0.847375	−	0.615654i	−0.0770462	−	0.997028i	$-0.524549\pi$
$863$	24.8932	−	18.0860i	0.847375	−	0.615654i	0.924421	+	0.381374i	$0.124549\pi$
$864$		0			0
$865$	5.95890	+	18.3396i	0.202609	+	0.623565i
$866$	−5.88749	−	6.53872i	−0.200065	−	0.222195i
$867$		0			0
$868$	15.6246	+	27.0626i	0.530334	+	0.918566i
$869$	34.4534	+	16.9869i	1.16875	+	0.576239i
$870$		0			0
$871$	15.7174	−	6.99783i	0.532563	−	0.237112i
$872$	−7.83232	+	24.1054i	−0.265236	+	0.816312i
$873$		0			0
$874$	−13.4175	+	9.74835i	−0.453852	+	0.329743i
$875$	1.95135	+	18.5658i	0.0659676	+	0.627640i
$876$		0			0
$877$	−30.3158	+	6.44382i	−1.02369	+	0.217592i	−0.689020	−	0.724743i	$-0.741959\pi$
$877$	−30.3158	+	6.44382i	−1.02369	+	0.217592i	−0.334672	+	0.942335i	$0.608625\pi$
$878$	0.703515	−	6.69350i	0.0237425	−	0.225895i
$879$		0			0
$880$	26.7210	−	10.6633i	0.900764	−	0.359458i
$881$	−29.9198			−1.00802			−0.504012	−	0.863697i	$-0.668143\pi$
$881$	−29.9198			−1.00802			−0.504012	+	0.863697i	$0.668143\pi$
$882$		0			0
$883$	4.39514	−	13.5269i	0.147908	−	0.455215i	−0.849465	−	0.527645i	$-0.823075\pi$
$883$	4.39514	−	13.5269i	0.147908	−	0.455215i	0.997374	+	0.0724296i	$0.0230753\pi$
$884$	7.84750	+	1.66804i	0.263940	+	0.0561022i
$885$		0			0
$886$	6.53474	+	2.90945i	0.219539	+	0.0977450i
$887$	1.76034	−	1.95505i	0.0591064	−	0.0656443i	−0.712866	−	0.701300i	$-0.752603\pi$
$887$	1.76034	−	1.95505i	0.0591064	−	0.0656443i	0.771973	+	0.635656i	$0.219270\pi$
$888$		0			0
$889$	−1.90095	+	0.846356i	−0.0637557	+	0.0283859i
$890$	1.38194			0.0463228
$891$		0			0
$892$	35.2874			1.18151
$893$	−69.9792	+	31.1567i	−2.34176	+	1.04262i
$894$		0			0
$895$	−16.1672	+	17.9555i	−0.540411	+	0.600188i
$896$	22.2488	+	9.90582i	0.743281	+	0.330930i
$897$		0			0
$898$	−0.737897	−	0.156845i	−0.0246239	−	0.00523398i
$899$	15.3821	−	47.3412i	0.513021	−	1.57892i
$900$		0			0
$901$	6.19577			0.206411
$902$	0.741002	+	0.188123i	0.0246727	+	0.00626380i
$903$		0			0
$904$	−0.744179	+	7.08039i	−0.0247510	+	0.235490i
$905$	4.93190	−	1.04831i	0.163942	−	0.0348469i
$906$		0			0
$907$	1.06227	+	10.1068i	0.0352720	+	0.335591i	0.997901	+	0.0647656i	$0.0206300\pi$
$907$	1.06227	+	10.1068i	0.0352720	+	0.335591i	−0.962628	+	0.270825i	$0.912703\pi$
$908$	1.63197	−	1.18570i	0.0541589	−	0.0393488i
$909$		0			0
$910$	2.86265	−	8.81033i	0.0948959	−	0.292060i
$911$	5.38285	−	2.39660i	0.178342	−	0.0794029i	−0.315623	−	0.948885i	$-0.602214\pi$
$911$	5.38285	−	2.39660i	0.178342	−	0.0794029i	0.493965	+	0.869482i	$0.335547\pi$
$912$		0			0
$913$	1.89391	−	1.94449i	0.0626794	−	0.0643533i
$914$	1.50116	+	2.60008i	0.0496539	+	0.0860031i
$915$		0			0
$916$	15.3337	+	17.0298i	0.506638	+	0.562679i
$917$	15.2240	+	46.8546i	0.502740	+	1.54727i
$918$		0			0
$919$	−26.1285	+	18.9835i	−0.861899	+	0.626206i	−0.928401	−	0.371580i	$-0.878816\pi$
$919$	−26.1285	+	18.9835i	−0.861899	+	0.626206i	0.0665018	+	0.997786i	$0.478816\pi$
$920$	−24.8495	−	5.28192i	−0.819264	−	0.174140i
$921$		0			0
$922$	0.248182	−	2.36129i	0.00817342	−	0.0777649i
$923$	23.4791	+	40.6669i	0.772823	+	1.33857i
$924$		0			0
$925$	0.211247	−	0.365890i	0.00694575	−	0.0120304i
$926$	−0.0801267	−	0.0582155i	−0.00263313	−	0.00191308i
$927$		0			0
$928$	−9.11525	−	28.0539i	−0.299223	−	0.920913i
$929$	−5.10969	−	48.6154i	−0.167643	−	1.59502i	−0.678003	−	0.735059i	$-0.737154\pi$
$929$	−5.10969	−	48.6154i	−0.167643	−	1.59502i	0.510360	−	0.859961i	$-0.329512\pi$
$930$		0			0
$931$	−3.53707	+	3.92831i	−0.115923	+	0.128745i
$932$	−27.5344	+	5.85262i	−0.901920	+	0.191709i
$933$		0			0
$934$	−1.38802	+	2.40413i	−0.0454175	+	0.0786655i
$935$	−7.86705	−	6.20078i	−0.257280	−	0.202787i
$936$		0			0
$937$	−36.4628	−	26.4917i	−1.19119	−	0.865447i	−0.197797	−	0.980243i	$-0.563379\pi$
$937$	−36.4628	−	26.4917i	−1.19119	−	0.865447i	−0.993389	+	0.114796i	$0.963379\pi$
$938$	−2.72460	−	3.02598i	−0.0889614	−	0.0988016i
$939$		0			0
$940$	−51.7789	−	23.0534i	−1.68884	−	0.751920i
$941$	−15.0315	−	6.69245i	−0.490012	−	0.218168i	0.146830	−	0.989162i	$-0.453093\pi$
$941$	−15.0315	−	6.69245i	−0.490012	−	0.218168i	−0.636842	+	0.770994i	$0.719760\pi$
$942$		0			0
$943$	2.87375	+	3.19162i	0.0935822	+	0.103934i
$944$	−22.0257	−	16.0026i	−0.716877	−	0.520841i
$945$		0			0
$946$	4.72239	−	3.15599i	0.153538	−	0.102610i
$947$	3.50636	−	6.07320i	0.113942	−	0.197352i	−0.803415	−	0.595420i	$-0.796986\pi$
$947$	3.50636	−	6.07320i	0.113942	−	0.197352i	0.917356	+	0.398067i	$0.130319\pi$
$948$		0			0
$949$	7.95474	−	1.69083i	0.258222	−	0.0548868i
$950$	3.63883	−	4.04134i	0.118059	−	0.131118i
$951$		0			0
$952$	−0.410885	−	3.90931i	−0.0133169	−	0.126702i
$953$	3.34588	+	10.2976i	0.108384	+	0.333571i	0.990510	−	0.137443i	$-0.0438883\pi$
$953$	3.34588	+	10.2976i	0.108384	+	0.333571i	−0.882126	+	0.471014i	$0.843888\pi$
$954$		0			0
$955$	13.9169	+	10.1112i	0.450341	+	0.327192i
$956$	−13.4491	+	23.2946i	−0.434976	+	0.753401i
$957$		0			0
$958$	−4.20347	−	7.28062i	−0.135808	−	0.235226i
$959$	−1.03318	+	9.83008i	−0.0333632	+	0.317430i
$960$		0			0
$961$	−13.6448	−	2.90030i	−0.440156	−	0.0935581i
$962$	0.213588	−	0.155181i	0.00688637	−	0.00500324i
$963$		0			0
$964$	6.94611	+	21.3779i	0.223719	+	0.688537i
$965$	−5.06493	−	5.62518i	−0.163046	−	0.181081i
$966$		0			0
$967$	−2.94103	−	5.09401i	−0.0945771	−	0.163812i	0.814855	−	0.579665i	$-0.196817\pi$
$967$	−2.94103	−	5.09401i	−0.0945771	−	0.163812i	−0.909432	+	0.415853i	$0.863483\pi$
$968$	−13.5493	−	7.35367i	−0.435492	−	0.236356i
$969$		0			0
$970$	−8.95130	+	3.98538i	−0.287409	+	0.127963i
$971$	5.64280	−	17.3667i	0.181086	−	0.557325i	−0.818773	−	0.574117i	$-0.805345\pi$
$971$	5.64280	−	17.3667i	0.181086	−	0.557325i	0.999859	+	0.0167920i	$0.00534530\pi$
$972$		0			0
$973$	−6.87009	+	4.99141i	−0.220245	+	0.160017i
$974$	0.912397	+	8.68088i	0.0292351	+	0.278153i
$975$		0			0
$976$	−5.43973	+	1.15625i	−0.174121	+	0.0370106i
$977$	0.175438	−	1.66919i	0.00561277	−	0.0534020i	−0.991357	−	0.131192i	$-0.958120\pi$
$977$	0.175438	−	1.66919i	0.00561277	−	0.0534020i	0.996970	+	0.0777898i	$0.0247863\pi$
$978$		0			0
$979$	3.01270	+	3.62174i	0.0962862	+	0.115751i
$980$	−3.91125			−0.124940
$981$		0			0
$982$	3.93678	−	12.1162i	0.125628	−	0.386643i
$983$	−10.9739	−	2.33258i	−0.350014	−	0.0743977i	0.0295501	−	0.999563i	$-0.490593\pi$
$983$	−10.9739	−	2.33258i	−0.350014	−	0.0743977i	−0.379564	+	0.925166i	$0.623926\pi$
$984$		0			0
$985$	63.1032	+	28.0953i	2.01063	+	0.895192i
$986$	−2.02383	+	2.24769i	−0.0644518	+	0.0715809i
$987$		0			0
$988$	−44.2091	+	19.6832i	−1.40648	+	0.626205i
$989$	31.9077			1.01461
$990$		0			0
$991$	−7.78978			−0.247451			−0.123725	−	0.992317i	$-0.539484\pi$
$991$	−7.78978			−0.247451			−0.123725	+	0.992317i	$0.539484\pi$
$992$	−24.3338	+	10.8341i	−0.772599	+	0.343983i
$993$		0			0
$994$	7.43642	−	8.25898i	0.235869	−	0.261959i
$995$	−32.7483	−	14.5805i	−1.03819	−	0.462233i
$996$		0			0
$997$	42.3765	+	9.00741i	1.34208	+	0.285268i	0.822310	−	0.569040i	$-0.192685\pi$
$997$	42.3765	+	9.00741i	1.34208	+	0.285268i	0.519768	+	0.854307i	$0.326018\pi$
$998$	−2.54682	+	7.83830i	−0.0806181	+	0.248117i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	891.2.n.f.136.3		32
3.2	odd	2		891.2.n.i.136.2		32
9.2	odd	6		297.2.f.a.136.3	✓	16
9.4	even	3	inner	891.2.n.f.433.2		32
9.5	odd	6		891.2.n.i.433.3		32
9.7	even	3		297.2.f.d.136.2	yes	16
11.3	even	5	inner	891.2.n.f.784.2		32
33.14	odd	10		891.2.n.i.784.3		32
99.14	odd	30		891.2.n.i.190.2		32
99.16	even	15		3267.2.a.be.1.6		8
99.25	even	15		297.2.f.d.190.2	yes	16
99.38	odd	30		3267.2.a.bm.1.3		8
99.47	odd	30		297.2.f.a.190.3	yes	16
99.58	even	15	inner	891.2.n.f.190.3		32
99.61	odd	30		3267.2.a.bl.1.3		8
99.83	even	30		3267.2.a.bf.1.6		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
297.2.f.a.136.3	✓	16	9.2	odd	6
297.2.f.a.190.3	yes	16	99.47	odd	30
297.2.f.d.136.2	yes	16	9.7	even	3
297.2.f.d.190.2	yes	16	99.25	even	15
891.2.n.f.136.3		32	1.1	even	1	trivial
891.2.n.f.190.3		32	99.58	even	15	inner
891.2.n.f.433.2		32	9.4	even	3	inner
891.2.n.f.784.2		32	11.3	even	5	inner
891.2.n.i.136.2		32	3.2	odd	2
891.2.n.i.190.2		32	99.14	odd	30
891.2.n.i.433.3		32	9.5	odd	6
891.2.n.i.784.3		32	33.14	odd	10
3267.2.a.be.1.6		8	99.16	even	15
3267.2.a.bf.1.6		8	99.83	even	30
3267.2.a.bl.1.3		8	99.61	odd	30
3267.2.a.bm.1.3		8	99.38	odd	30

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:	\( N \)	\(=\)	\( 891 = 3^{4} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	891.n (of order \(15\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.330935 - 0.147342i) q^{2} +(-1.25045 + 1.38877i) q^{4} +(-2.45353 - 1.09238i) q^{5} +(2.43963 + 0.518560i) q^{7} +(-0.433081 + 1.33288i) q^{8} -0.972914 q^{10} +(-2.12100 - 2.54978i) q^{11} +(-0.399048 + 3.79669i) q^{13} +(0.883767 - 0.187850i) q^{14} +(-0.337612 - 3.21216i) q^{16} +(-0.909782 + 0.660995i) q^{17} +(2.09612 - 6.45120i) q^{19} +(4.58509 - 2.04141i) q^{20} +(-1.07760 - 0.531300i) q^{22} +(-3.37470 - 5.84515i) q^{23} +(1.48086 + 1.64467i) q^{25} +(0.427353 + 1.31526i) q^{26} +(-3.77080 + 2.73965i) q^{28} +(7.26230 + 1.54365i) q^{29} +(0.700806 - 6.66772i) q^{31} +(-1.98649 - 3.44070i) q^{32} +(-0.203687 + 0.352796i) q^{34} +(-5.41925 - 3.93732i) q^{35} +(-0.0589927 - 0.181561i) q^{37} +(-0.256851 - 2.44378i) q^{38} +(2.51860 - 2.79719i) q^{40} +(-0.622411 + 0.132298i) q^{41} +(-2.36375 + 4.09413i) q^{43} +(6.19326 + 0.242800i) q^{44} +(-1.97805 - 1.43713i) q^{46} +(-7.55641 - 8.39225i) q^{47} +(-0.711915 - 0.316965i) q^{49} +(0.732399 + 0.326085i) q^{50} +(-4.77374 - 5.30177i) q^{52} +(-4.45732 - 3.23843i) q^{53} +(2.41860 + 8.57290i) q^{55} +(-1.74774 + 3.02717i) q^{56} +(2.63080 - 0.559193i) q^{58} +(5.64028 - 6.26417i) q^{59} +(-0.179980 - 1.71240i) q^{61} +(-0.750514 - 2.30984i) q^{62} +(4.06165 + 2.95096i) q^{64} +(5.12652 - 8.87939i) q^{65} +(-2.25335 - 3.90292i) q^{67} +(0.219670 - 2.09002i) q^{68} +(-2.37355 - 0.504514i) q^{70} +(9.95124 - 7.23000i) q^{71} +(-0.658284 - 2.02599i) q^{73} +(-0.0462743 - 0.0513928i) q^{74} +(6.33812 + 10.9779i) q^{76} +(-3.85224 - 7.32038i) q^{77} +(-10.5808 + 4.71086i) q^{79} +(-2.68057 + 8.24994i) q^{80} +(-0.186485 + 0.135489i) q^{82} +(0.0855484 + 0.813939i) q^{83} +(2.95424 - 0.627943i) q^{85} +(-0.179010 + 1.70317i) q^{86} +(4.31712 - 1.72279i) q^{88} -1.42041 q^{89} +(-2.94234 + 9.05560i) q^{91} +(12.3375 + 2.62241i) q^{92} +(-3.73721 - 1.66392i) q^{94} +(-12.1901 + 13.5385i) q^{95} +(9.20051 - 4.09633i) q^{97} -0.282300 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 2 q^{2} + 4 q^{4} - q^{5} + 2 q^{7} + 12 q^{10} - 13 q^{11} + 2 q^{13} + 22 q^{14} + 24 q^{16} - 4 q^{17} - 4 q^{19} - 15 q^{22} - 14 q^{23} + 19 q^{25} + 42 q^{26} + 30 q^{28} - q^{29} - 14 q^{31}+ \cdots + 52 q^{98}+O(q^{100}) \) 32 * q - 2 * q^2 + 4 * q^4 - q^5 + 2 * q^7 + 12 * q^10 - 13 * q^11 + 2 * q^13 + 22 * q^14 + 24 * q^16 - 4 * q^17 - 4 * q^19 - 15 * q^22 - 14 * q^23 + 19 * q^25 + 42 * q^26 + 30 * q^28 - q^29 - 14 * q^31 + 48 * q^32 - 10 * q^34 - 36 * q^35 + 18 * q^37 - 11 * q^38 - 33 * q^40 - 25 * q^41 - 14 * q^43 + 28 * q^44 + 8 * q^46 + 28 * q^47 + 4 * q^49 + 63 * q^50 - 10 * q^52 + 2 * q^53 - 80 * q^55 - 96 * q^56 + 20 * q^58 - 41 * q^59 - 10 * q^62 - 184 * q^64 + 60 * q^65 + 48 * q^67 - 25 * q^68 + 31 * q^70 + 6 * q^71 - 26 * q^73 - 29 * q^74 + 58 * q^76 + 2 * q^77 - 166 * q^80 + 82 * q^82 + 14 * q^83 + 10 * q^85 + 56 * q^86 - 86 * q^88 + 164 * q^89 + 28 * q^91 - 74 * q^92 + 2 * q^94 + 56 * q^95 - 12 * q^97 + 52 * q^98

Introduction

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