LMFDB - Embedded newform 891.2.f.e.487.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [891,2,Mod(82,891)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(891, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([0, 4])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("891.82"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 891 = 3^{4} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	891.f (of order $5$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [36,-1] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$7.11467082010$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$9$ over $\Q(\zeta_{5})$
Twist minimal:	no (minimal twist has level 99)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			487.6
Character	$\chi$	$=$	891.487
Dual form			891.2.f.e.730.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.467460 - 0.339629i) q^{2} +(-0.514863 + 1.58459i) q^{4} +(2.43063 + 1.76596i) q^{5} +(-0.359795 + 1.10733i) q^{7} +(0.654602 + 2.01466i) q^{8} +1.73599 q^{10} +(-3.11301 + 1.14420i) q^{11} +(3.19252 - 2.31950i) q^{13} +(0.207894 + 0.639831i) q^{14} +(-1.70562 - 1.23921i) q^{16} +(-0.254185 - 0.184677i) q^{17} +(1.96794 + 6.05670i) q^{19} +(-4.04976 + 2.94232i) q^{20} +(-1.06660 + 1.59213i) q^{22} +0.0855002 q^{23} +(1.24428 + 3.82951i) q^{25} +(0.704604 - 2.16855i) q^{26} +(-1.56942 - 1.14025i) q^{28} +(2.37938 - 7.32296i) q^{29} +(-5.28194 + 3.83755i) q^{31} -5.45485 q^{32} -0.181543 q^{34} +(-2.83004 + 2.05614i) q^{35} +(-1.92922 + 5.93753i) q^{37} +(2.97697 + 2.16289i) q^{38} +(-1.96670 + 6.05289i) q^{40} +(-1.79510 - 5.52475i) q^{41} -6.78458 q^{43} +(-0.210303 - 5.52194i) q^{44} +(0.0399679 - 0.0290384i) q^{46} +(0.101276 + 0.311695i) q^{47} +(4.56638 + 3.31767i) q^{49} +(1.88227 + 1.36755i) q^{50} +(2.03174 + 6.25305i) q^{52} +(-1.96000 + 1.42402i) q^{53} +(-9.58718 - 2.71632i) q^{55} -2.46642 q^{56} +(-1.37483 - 4.23130i) q^{58} +(0.709513 - 2.18366i) q^{59} +(11.0732 + 8.04513i) q^{61} +(-1.16575 + 3.58780i) q^{62} +(0.861321 - 0.625787i) q^{64} +11.8560 q^{65} +11.6798 q^{67} +(0.423507 - 0.307696i) q^{68} +(-0.624602 + 1.92233i) q^{70} +(7.05272 + 5.12410i) q^{71} +(0.910538 - 2.80235i) q^{73} +(1.11473 + 3.43078i) q^{74} -10.6106 q^{76} +(-0.146963 - 3.85882i) q^{77} +(7.18989 - 5.22376i) q^{79} +(-1.95735 - 6.02412i) q^{80} +(-2.71551 - 1.97293i) q^{82} +(4.01093 + 2.91411i) q^{83} +(-0.291701 - 0.897762i) q^{85} +(-3.17152 + 2.30424i) q^{86} +(-4.34294 - 5.52265i) q^{88} -2.12862 q^{89} +(1.41981 + 4.36973i) q^{91} +(-0.0440209 + 0.135482i) q^{92} +(0.153203 + 0.111309i) q^{94} +(-5.91254 + 18.1969i) q^{95} +(0.0718724 - 0.0522184i) q^{97} +3.26138 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - q^{2} - 11 q^{4} - 8 q^{5} + 2 q^{7} - 3 q^{8} - 4 q^{10} - 2 q^{11} + 11 q^{13} - 10 q^{14} + 9 q^{16} + 10 q^{17} + 4 q^{19} - 45 q^{20} + 16 q^{22} + 20 q^{23} - 11 q^{25} + 6 q^{26} - 27 q^{28}+ \cdots + 164 q^{98}+O(q^{100}) $ 36 * q - q^2 - 11 * q^4 - 8 * q^5 + 2 * q^7 - 3 * q^8 - 4 * q^10 - 2 * q^11 + 11 * q^13 - 10 * q^14 + 9 * q^16 + 10 * q^17 + 4 * q^19 - 45 * q^20 + 16 * q^22 + 20 * q^23 - 11 * q^25 + 6 * q^26 - 27 * q^28 - 23 * q^29 - 3 * q^31 + 18 * q^32 - 8 * q^34 - 9 * q^35 - 21 * q^37 - q^38 + 25 * q^40 + 10 * q^41 + 8 * q^43 - 19 * q^44 - 9 * q^46 - 34 * q^47 - q^49 + 27 * q^52 - 2 * q^53 + 9 * q^55 + 114 * q^56 - q^58 - 16 * q^59 + 3 * q^61 - 92 * q^62 + 13 * q^64 + 84 * q^65 - 10 * q^67 - 23 * q^68 + 46 * q^70 + 24 * q^71 - 20 * q^73 + 68 * q^74 - 16 * q^76 - 26 * q^77 - 19 * q^79 + 28 * q^80 + 47 * q^82 + 7 * q^83 - 25 * q^85 - 77 * q^86 - 18 * q^88 + 28 * q^89 + 10 * q^91 + 50 * q^92 + 63 * q^94 - 77 * q^95 + 33 * q^97 + 164 * q^98

Character values

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

$n$	$244$	$650$
$\chi(n)$	$e\left(\frac{4}{5}\right)$	$1$

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 $

$2$	0.467460	−	0.339629i	0.330544	−	0.240154i	−0.410117	−	0.912033i	$-0.634512\pi$
$2$	0.467460	−	0.339629i	0.330544	−	0.240154i	0.740661	+	0.671878i	$0.234512\pi$
$3$		0			0
$3$		0			0
$4$	−0.514863	+	1.58459i	−0.257432	+	0.792293i
$5$	2.43063	+	1.76596i	1.08701	+	0.789761i	0.978892	−	0.204377i	$-0.0655169\pi$
$5$	2.43063	+	1.76596i	1.08701	+	0.789761i	0.108120	+	0.994138i	$0.465517\pi$
$6$		0			0
$7$	−0.359795	+	1.10733i	−0.135990	+	0.418533i	−0.995743	−	0.0921770i	$-0.970617\pi$
$7$	−0.359795	+	1.10733i	−0.135990	+	0.418533i	0.859753	+	0.510710i	$0.170617\pi$
$8$	0.654602	+	2.01466i	0.231437	+	0.712289i
$9$		0			0
$10$	1.73599			0.548970
$11$	−3.11301	+	1.14420i	−0.938607	+	0.344988i
$11$	−3.11301	+	1.14420i	−0.938607	+	0.344988i
$12$		0			0
$13$	3.19252	−	2.31950i	0.885446	−	0.643314i	−0.0492409	−	0.998787i	$-0.515680\pi$
$13$	3.19252	−	2.31950i	0.885446	−	0.643314i	0.934687	+	0.355473i	$0.115680\pi$
$14$	0.207894	+	0.639831i	0.0555619	+	0.171002i
$15$		0			0
$16$	−1.70562	−	1.23921i	−0.426406	−	0.309802i
$17$	−0.254185	−	0.184677i	−0.0616490	−	0.0447906i	0.556534	−	0.830825i	$-0.312131\pi$
$17$	−0.254185	−	0.184677i	−0.0616490	−	0.0447906i	−0.618183	+	0.786034i	$0.712131\pi$
$18$		0			0
$19$	1.96794	+	6.05670i	0.451477	+	1.38950i	0.875222	+	0.483721i	$0.160715\pi$
$19$	1.96794	+	6.05670i	0.451477	+	1.38950i	−0.423746	+	0.905781i	$0.639285\pi$
$20$	−4.04976	+	2.94232i	−0.905554	+	0.657923i
$21$		0			0
$22$	−1.06660	+	1.59213i	−0.227401	+	0.339444i
$23$	0.0855002			0.0178280			0.00891401	−	0.999960i	$-0.497163\pi$
$23$	0.0855002			0.0178280			0.00891401	+	0.999960i	$0.497163\pi$
$24$		0			0
$25$	1.24428	+	3.82951i	0.248857	+	0.765902i
$26$	0.704604	−	2.16855i	0.138184	−	0.425287i
$27$		0			0
$28$	−1.56942	−	1.14025i	−0.296593	−	0.215487i
$29$	2.37938	−	7.32296i	0.441839	−	1.35984i	−0.444075	−	0.895990i	$-0.646468\pi$
$29$	2.37938	−	7.32296i	0.441839	−	1.35984i	0.885914	−	0.463850i	$-0.153532\pi$
$30$		0			0
$31$	−5.28194	+	3.83755i	−0.948664	+	0.689245i	−0.950491	−	0.310753i	$-0.899419\pi$
$31$	−5.28194	+	3.83755i	−0.948664	+	0.689245i	0.00182628	+	0.999998i	$0.499419\pi$
$32$	−5.45485			−0.964291
$33$		0			0
$34$	−0.181543			−0.0311344
$35$	−2.83004	+	2.05614i	−0.478363	+	0.347551i
$36$		0			0
$37$	−1.92922	+	5.93753i	−0.317162	+	0.976124i	0.657694	+	0.753286i	$0.271532\pi$
$37$	−1.92922	+	5.93753i	−0.317162	+	0.976124i	−0.974855	+	0.222838i	$0.928468\pi$
$38$	2.97697	+	2.16289i	0.482928	+	0.350868i
$39$		0			0
$40$	−1.96670	+	6.05289i	−0.310963	+	0.957046i
$41$	−1.79510	−	5.52475i	−0.280348	−	0.862822i	−0.987755	−	0.156015i	$-0.950135\pi$
$41$	−1.79510	−	5.52475i	−0.280348	−	0.862822i	0.707407	−	0.706807i	$-0.249865\pi$
$42$		0			0
$43$	−6.78458			−1.03464			−0.517320	−	0.855792i	$-0.673070\pi$
$43$	−6.78458			−1.03464			−0.517320	+	0.855792i	$0.673070\pi$
$44$	−0.210303	−	5.52194i	−0.0317043	−	0.832463i
$45$		0			0
$46$	0.0399679	−	0.0290384i	0.00589294	−	0.00428147i
$47$	0.101276	+	0.311695i	0.0147726	+	0.0454654i	0.958171	−	0.286196i	$-0.0923908\pi$
$47$	0.101276	+	0.311695i	0.0147726	+	0.0454654i	−0.943398	+	0.331661i	$0.892391\pi$
$48$		0			0
$49$	4.56638	+	3.31767i	0.652340	+	0.473953i
$50$	1.88227	+	1.36755i	0.266193	+	0.193400i
$51$		0			0
$52$	2.03174	+	6.25305i	0.281752	+	0.867142i
$53$	−1.96000	+	1.42402i	−0.269227	+	0.195605i	−0.714205	−	0.699937i	$-0.753211\pi$
$53$	−1.96000	+	1.42402i	−0.269227	+	0.195605i	0.444978	+	0.895541i	$0.353211\pi$
$54$		0			0
$55$	−9.58718	−	2.71632i	−1.29274	−	0.366269i
$56$	−2.46642			−0.329589
$57$		0			0
$58$	−1.37483	−	4.23130i	−0.180524	−	0.555596i
$59$	0.709513	−	2.18366i	0.0923707	−	0.284288i	−0.894189	−	0.447690i	$-0.852247\pi$
$59$	0.709513	−	2.18366i	0.0923707	−	0.284288i	0.986560	+	0.163402i	$0.0522468\pi$
$60$		0			0
$61$	11.0732	+	8.04513i	1.41778	+	1.03007i	0.992134	+	0.125182i	$0.0399515\pi$
$61$	11.0732	+	8.04513i	1.41778	+	1.03007i	0.425641	+	0.904892i	$0.360049\pi$
$62$	−1.16575	+	3.58780i	−0.148050	+	0.455652i
$63$		0			0
$64$	0.861321	−	0.625787i	0.107665	−	0.0782233i
$65$	11.8560			1.47055
$66$		0			0
$67$	11.6798			1.42691			0.713456	−	0.700700i	$-0.247129\pi$
$67$	11.6798			1.42691			0.713456	+	0.700700i	$0.247129\pi$
$68$	0.423507	−	0.307696i	0.0513578	−	0.0373136i
$69$		0			0
$70$	−0.624602	+	1.92233i	−0.0746542	+	0.229762i
$71$	7.05272	+	5.12410i	0.837004	+	0.608119i	0.921532	−	0.388302i	$-0.126938\pi$
$71$	7.05272	+	5.12410i	0.837004	+	0.608119i	−0.0845279	+	0.996421i	$0.526938\pi$
$72$		0			0
$73$	0.910538	−	2.80235i	0.106570	−	0.327990i	−0.883525	−	0.468383i	$-0.844837\pi$
$73$	0.910538	−	2.80235i	0.106570	−	0.327990i	0.990096	+	0.140393i	$0.0448367\pi$
$74$	1.11473	+	3.43078i	0.129584	+	0.398820i
$75$		0			0
$76$	−10.6106			−1.21712
$77$	−0.146963	−	3.85882i	−0.0167480	−	0.439753i
$78$		0			0
$79$	7.18989	−	5.22376i	0.808926	−	0.587719i	−0.104593	−	0.994515i	$-0.533354\pi$
$79$	7.18989	−	5.22376i	0.808926	−	0.587719i	0.913519	+	0.406796i	$0.133354\pi$
$80$	−1.95735	−	6.02412i	−0.218839	−	0.673517i
$81$		0			0
$82$	−2.71551	−	1.97293i	−0.299878	−	0.217874i
$83$	4.01093	+	2.91411i	0.440257	+	0.319865i	0.785737	−	0.618561i	$-0.212284\pi$
$83$	4.01093	+	2.91411i	0.440257	+	0.319865i	−0.345480	+	0.938426i	$0.612284\pi$
$84$		0			0
$85$	−0.291701	−	0.897762i	−0.0316394	−	0.0973760i
$86$	−3.17152	+	2.30424i	−0.341994	+	0.248473i
$87$		0			0
$88$	−4.34294	−	5.52265i	−0.462959	−	0.588717i
$89$	−2.12862			−0.225634			−0.112817	−	0.993616i	$-0.535987\pi$
$89$	−2.12862			−0.225634			−0.112817	+	0.993616i	$0.535987\pi$
$90$		0			0
$91$	1.41981	+	4.36973i	0.148837	+	0.458072i
$92$	−0.0440209	+	0.135482i	−0.00458950	+	0.0141250i
$93$		0			0
$94$	0.153203	+	0.111309i	0.0158017	+	0.0114806i
$95$	−5.91254	+	18.1969i	−0.606613	+	1.86696i
$96$		0			0
$97$	0.0718724	−	0.0522184i	0.00729754	−	0.00530197i	−0.584131	−	0.811660i	$-0.698564\pi$
$97$	0.0718724	−	0.0522184i	0.00729754	−	0.00530197i	0.591428	+	0.806358i	$0.298564\pi$
$98$	3.26138			0.329449
$99$		0			0
$100$	−6.70883			−0.670883
$101$	−1.66373	+	1.20877i	−0.165547	+	0.120277i	−0.667474	−	0.744633i	$-0.732625\pi$
$101$	−1.66373	+	1.20877i	−0.165547	+	0.120277i	0.501927	+	0.864910i	$0.332625\pi$
$102$		0			0
$103$	−0.932216	+	2.86907i	−0.0918540	+	0.282698i	−0.986421	−	0.164236i	$-0.947484\pi$
$103$	−0.932216	+	2.86907i	−0.0918540	+	0.282698i	0.894567	+	0.446934i	$0.147484\pi$
$104$	6.76283	+	4.91348i	0.663150	+	0.481807i
$105$		0			0
$106$	−0.432581	+	1.33135i	−0.0420160	+	0.129312i
$107$	−3.70600	−	11.4059i	−0.358272	−	1.10265i	−0.954088	−	0.299527i	$-0.903171\pi$
$107$	−3.70600	−	11.4059i	−0.358272	−	1.10265i	0.595815	−	0.803121i	$-0.296829\pi$
$108$		0			0
$109$	5.20013			0.498082			0.249041	−	0.968493i	$-0.419885\pi$
$109$	5.20013			0.498082			0.249041	+	0.968493i	$0.419885\pi$
$110$	−5.40417	+	1.98632i	−0.515267	+	0.189388i
$111$		0			0
$112$	1.98589	−	1.44283i	0.187649	−	0.136335i
$113$	−5.94164	−	18.2865i	−0.558943	−	1.72025i	−0.685298	−	0.728263i	$-0.740328\pi$
$113$	−5.94164	−	18.2865i	−0.558943	−	1.72025i	0.126355	−	0.991985i	$-0.459672\pi$
$114$		0			0
$115$	0.207820	+	0.150990i	0.0193793	+	0.0140799i
$116$	10.3788	+	7.54065i	0.963649	+	0.700132i
$117$		0			0
$118$	−0.409965	−	1.26174i	−0.0377403	−	0.116153i
$119$	0.295953	−	0.215023i	0.0271300	−	0.0197111i
$120$		0			0
$121$	8.38163	−	7.12378i	0.761967	−	0.647616i
$122$	7.90863			0.716014
$123$		0			0
$124$	−3.36146	−	10.3455i	−0.301868	−	0.929054i
$125$	0.903736	−	2.78141i	0.0808326	−	0.248777i
$126$		0			0
$127$	10.6652	+	7.74873i	0.946384	+	0.687588i	0.949949	−	0.312405i	$-0.101135\pi$
$127$	10.6652	+	7.74873i	0.946384	+	0.687588i	−0.00356461	+	0.999994i	$0.501135\pi$
$128$	3.56138	−	10.9608i	0.314785	−	0.968808i
$129$		0			0
$130$	5.54220	−	4.02664i	0.486083	−	0.353160i
$131$	17.9718			1.57020			0.785100	−	0.619369i	$-0.212611\pi$
$131$	17.9718			1.57020			0.785100	+	0.619369i	$0.212611\pi$
$132$		0			0
$133$	−7.41484			−0.642949
$134$	5.45983	−	3.96680i	0.471657	−	0.342679i
$135$		0			0
$136$	0.205670	−	0.632986i	0.0176360	−	0.0542781i
$137$	−13.2693	−	9.64070i	−1.13367	−	0.823661i	−0.147447	−	0.989070i	$-0.547105\pi$
$137$	−13.2693	−	9.64070i	−1.13367	−	0.823661i	−0.986225	+	0.165409i	$0.947105\pi$
$138$		0			0
$139$	−3.67780	+	11.3191i	−0.311947	+	0.960073i	0.665046	+	0.746802i	$0.268412\pi$
$139$	−3.67780	+	11.3191i	−0.311947	+	0.960073i	−0.976993	+	0.213271i	$0.931588\pi$
$140$	−1.80105	−	5.54307i	−0.152217	−	0.468475i
$141$		0			0
$142$	5.03716			0.422709
$143$	−7.28438	+	10.8735i	−0.609150	+	0.909287i
$144$		0			0
$145$	18.7154	−	13.5976i	1.55423	−	1.12922i
$146$	−0.526120	−	1.61923i	−0.0435420	−	0.134008i
$147$		0			0
$148$	−8.41525	−	6.11403i	−0.691729	−	0.502571i
$149$	−3.66623	−	2.66368i	−0.300350	−	0.218217i	0.427395	−	0.904065i	$-0.359431\pi$
$149$	−3.66623	−	2.66368i	−0.300350	−	0.218217i	−0.727745	+	0.685848i	$0.759431\pi$
$150$		0			0
$151$	−0.905687	−	2.78742i	−0.0737037	−	0.226837i	0.907418	−	0.420230i	$-0.138051\pi$
$151$	−0.905687	−	2.78742i	−0.0737037	−	0.226837i	−0.981121	+	0.193393i	$0.938051\pi$
$152$	−10.9140	+	7.92945i	−0.885239	+	0.643164i
$153$		0			0
$154$	−1.37927	−	1.75393i	−0.111144	−	0.141336i
$155$	−19.6154			−1.57555
$156$		0			0
$157$	−5.57888	−	17.1700i	−0.445243	−	1.37032i	−0.882217	−	0.470843i	$-0.843950\pi$
$157$	−5.57888	−	17.1700i	−0.445243	−	1.37032i	0.436974	−	0.899474i	$-0.356050\pi$
$158$	1.58684	−	4.88380i	0.126242	−	0.388534i
$159$		0			0
$160$	−13.2587	−	9.63304i	−1.04820	−	0.761559i
$161$	−0.0307625	+	0.0946773i	−0.00242443	+	0.00746161i
$162$		0			0
$163$	4.71129	−	3.42295i	0.369017	−	0.268106i	−0.387786	−	0.921749i	$-0.626760\pi$
$163$	4.71129	−	3.42295i	0.369017	−	0.268106i	0.756803	+	0.653643i	$0.226760\pi$
$164$	9.67868			0.755778
$165$		0			0
$166$	2.86467			0.222341
$167$	−4.06266	+	2.95170i	−0.314378	+	0.228409i	−0.733773	−	0.679395i	$-0.762242\pi$
$167$	−4.06266	+	2.95170i	−0.314378	+	0.228409i	0.419395	+	0.907804i	$0.362242\pi$
$168$		0			0
$169$	0.794875	−	2.44637i	0.0611442	−	0.188182i
$170$	−0.441265	−	0.320598i	−0.0338435	−	0.0245887i
$171$		0			0
$172$	3.49313	−	10.7508i	0.266349	−	0.819738i
$173$	4.81753	+	14.8268i	0.366270	+	1.12726i	0.949182	+	0.314728i	$0.101913\pi$
$173$	4.81753	+	14.8268i	0.366270	+	1.12726i	−0.582912	+	0.812536i	$0.698087\pi$
$174$		0			0
$175$	−4.68824			−0.354397
$176$	6.72751	+	1.90610i	0.507105	+	0.143677i
$177$		0			0
$178$	−0.995046	+	0.722943i	−0.0745818	+	0.0541869i
$179$	−2.17822	−	6.70387i	−0.162808	−	0.501071i	0.836060	−	0.548638i	$-0.184853\pi$
$179$	−2.17822	−	6.70387i	−0.162808	−	0.501071i	−0.998868	+	0.0475668i	$0.984853\pi$
$180$		0			0
$181$	−2.02068	−	1.46811i	−0.150196	−	0.109124i	0.510149	−	0.860086i	$-0.329590\pi$
$181$	−2.02068	−	1.46811i	−0.150196	−	0.109124i	−0.660345	+	0.750962i	$0.729590\pi$
$182$	2.14779	+	1.56046i	0.159205	+	0.115669i
$183$		0			0
$184$	0.0559686	+	0.172254i	0.00412606	+	0.0126987i
$185$	−15.1747	+	11.0250i	−1.11566	+	0.810577i
$186$		0			0
$187$	1.00259	+	0.284062i	0.0733165	+	0.0207727i
$188$	−0.546051			−0.0398249
$189$		0			0
$190$	3.41633	+	10.5144i	0.247847	+	0.762795i
$191$	3.65350	−	11.2443i	0.264358	−	0.813611i	−0.727483	−	0.686126i	$-0.759310\pi$
$191$	3.65350	−	11.2443i	0.264358	−	0.813611i	0.991841	−	0.127484i	$-0.0406902\pi$
$192$		0			0
$193$	−5.45816	−	3.96559i	−0.392887	−	0.285449i	0.373751	−	0.927529i	$-0.378072\pi$
$193$	−5.45816	−	3.96559i	−0.392887	−	0.285449i	−0.766637	+	0.642080i	$0.778072\pi$
$194$	0.0158626	−	0.0488200i	0.00113887	−	0.00350507i
$195$		0			0
$196$	−7.60820	+	5.52768i	−0.543443	+	0.394834i
$197$	20.6474			1.47107			0.735534	−	0.677488i	$-0.236931\pi$
$197$	20.6474			1.47107			0.735534	+	0.677488i	$0.236931\pi$
$198$		0			0
$199$	−13.2862			−0.941832			−0.470916	−	0.882178i	$-0.656077\pi$
$199$	−13.2862			−0.941832			−0.470916	+	0.882178i	$0.656077\pi$
$200$	−6.90064	+	5.01361i	−0.487949	+	0.354516i
$201$		0			0
$202$	−0.367193	+	1.13010i	−0.0258356	+	0.0795138i
$203$	7.25288	+	5.26953i	0.509053	+	0.369848i
$204$		0			0
$205$	5.39325	−	16.5987i	0.376681	−	1.15931i
$206$	0.538646	+	1.65778i	0.0375292	+	0.115503i
$207$		0			0
$208$	−8.31958			−0.576859
$209$	−13.0563	−	16.6028i	−0.903120	−	1.14844i
$210$		0			0
$211$	6.75126	−	4.90508i	0.464776	−	0.337680i	−0.330626	−	0.943762i	$-0.607260\pi$
$211$	6.75126	−	4.90508i	0.464776	−	0.337680i	0.795402	+	0.606082i	$0.207260\pi$
$212$	−1.24736	−	3.83897i	−0.0856688	−	0.263661i
$213$		0			0
$214$	−5.60618	−	4.07313i	−0.383231	−	0.278433i
$215$	−16.4908	−	11.9813i	−1.12467	−	0.817117i
$216$		0			0
$217$	−2.34904	−	7.22960i	−0.159463	−	0.490778i
$218$	2.43085	−	1.76612i	0.164638	−	0.119616i
$219$		0			0
$220$	9.24034	−	13.7932i	0.622984	−	0.929936i
$221$	−1.23985			−0.0834013
$222$		0			0
$223$	−0.118556	−	0.364878i	−0.00793910	−	0.0244340i	0.947008	−	0.321209i	$-0.104089\pi$
$223$	−0.118556	−	0.364878i	−0.00793910	−	0.0244340i	−0.954948	+	0.296774i	$0.904089\pi$
$224$	1.96263	−	6.04035i	0.131134	−	0.403588i
$225$		0			0
$226$	−8.98811	−	6.53024i	−0.597880	−	0.434385i
$227$	−5.56664	+	17.1324i	−0.369471	+	1.13711i	0.577663	+	0.816276i	$0.303965\pi$
$227$	−5.56664	+	17.1324i	−0.369471	+	1.13711i	−0.947134	+	0.320839i	$0.896035\pi$
$228$		0			0
$229$	−10.8634	+	7.89270i	−0.717872	+	0.521565i	−0.885704	−	0.464251i	$-0.846324\pi$
$229$	−10.8634	+	7.89270i	−0.717872	+	0.521565i	0.167832	+	0.985816i	$0.446324\pi$
$230$	0.148428			0.00978704
$231$		0			0
$232$	16.3108			1.07086
$233$	−2.72611	+	1.98063i	−0.178593	+	0.129756i	−0.673490	−	0.739196i	$-0.735206\pi$
$233$	−2.72611	+	1.98063i	−0.178593	+	0.129756i	0.494897	+	0.868952i	$0.335206\pi$
$234$		0			0
$235$	−0.304276	+	0.936466i	−0.0198488	+	0.0610883i
$236$	3.09489	+	2.24857i	0.201460	+	0.146369i
$237$		0			0
$238$	0.0653183	−	0.201029i	0.00423395	−	0.0130308i
$239$	7.16820	+	22.0615i	0.463673	+	1.42704i	0.860644	+	0.509207i	$0.170061\pi$
$239$	7.16820	+	22.0615i	0.463673	+	1.42704i	−0.396972	+	0.917831i	$0.629939\pi$
$240$		0			0
$241$	15.1641			0.976807			0.488404	−	0.872618i	$-0.337579\pi$
$241$	15.1641			0.976807			0.488404	+	0.872618i	$0.337579\pi$
$242$	1.49863	−	6.17673i	0.0963358	−	0.397055i
$243$		0			0
$244$	−18.4494	+	13.4043i	−1.18110	+	0.858120i
$245$	5.24033	+	16.1281i	0.334792	+	1.03039i
$246$		0			0
$247$	20.3312	+	14.7715i	1.29364	+	0.939887i
$248$	−11.1889	−	8.12923i	−0.710497	−	0.516207i
$249$		0			0
$250$	−0.522189	−	1.60713i	−0.0330262	−	0.101644i
$251$	−0.471095	+	0.342271i	−0.0297353	+	0.0216039i	−0.602554	−	0.798078i	$-0.705850\pi$
$251$	−0.471095	+	0.342271i	−0.0297353	+	0.0216039i	0.572818	+	0.819682i	$0.305850\pi$
$252$		0			0
$253$	−0.266163	+	0.0978289i	−0.0167335	+	0.00615045i
$254$	7.61725			0.477949
$255$		0			0
$256$	−1.39982	−	4.30820i	−0.0874887	−	0.269263i
$257$	3.39036	−	10.4344i	0.211485	−	0.650883i	−0.787900	−	0.615803i	$-0.788832\pi$
$257$	3.39036	−	10.4344i	0.211485	−	0.650883i	0.999385	−	0.0350793i	$-0.0111684\pi$
$258$		0			0
$259$	−5.88071	−	4.27258i	−0.365409	−	0.265485i
$260$	−6.10421	+	18.7868i	−0.378567	+	1.16511i
$261$		0			0
$262$	8.40108	−	6.10374i	0.519020	−	0.377090i
$263$	14.3954			0.887656			0.443828	−	0.896112i	$-0.353620\pi$
$263$	14.3954			0.887656			0.443828	+	0.896112i	$0.353620\pi$
$264$		0			0
$265$	−7.27881			−0.447134
$266$	−3.46614	+	2.51830i	−0.212523	+	0.154407i
$267$		0			0
$268$	−6.01349	+	18.5076i	−0.367333	+	1.13053i
$269$	0.395590	+	0.287413i	0.0241195	+	0.0175239i	0.599780	−	0.800165i	$-0.295255\pi$
$269$	0.395590	+	0.287413i	0.0241195	+	0.0175239i	−0.575660	+	0.817689i	$0.695255\pi$
$270$		0			0
$271$	6.77950	−	20.8652i	0.411825	−	1.26747i	−0.503234	−	0.864150i	$-0.667857\pi$
$271$	6.77950	−	20.8652i	0.411825	−	1.26747i	0.915060	−	0.403318i	$-0.132143\pi$
$272$	0.204692	+	0.629977i	0.0124113	+	0.0381980i
$273$		0			0
$274$	−9.47712			−0.572534
$275$	−8.25517	−	10.4976i	−0.497806	−	0.633029i
$276$		0			0
$277$	−2.32149	+	1.68666i	−0.139485	+	0.101342i	−0.655340	−	0.755334i	$-0.727474\pi$
$277$	−2.32149	+	1.68666i	−0.139485	+	0.101342i	0.515855	+	0.856676i	$0.327474\pi$
$278$	2.12508	+	6.54031i	0.127454	+	0.392262i
$279$		0			0
$280$	−5.99497	−	4.35560i	−0.358268	−	0.260297i
$281$	14.7064	+	10.6848i	0.877308	+	0.637402i	0.932538	−	0.361072i	$-0.117589\pi$
$281$	14.7064	+	10.6848i	0.877308	+	0.637402i	−0.0552299	+	0.998474i	$0.517589\pi$
$282$		0			0
$283$	−6.34632	−	19.5320i	−0.377249	−	1.16105i	−0.941949	−	0.335757i	$-0.891008\pi$
$283$	−6.34632	−	19.5320i	−0.377249	−	1.16105i	0.564699	−	0.825297i	$-0.308992\pi$
$284$	−11.7508	+	8.53744i	−0.697280	+	0.506604i
$285$		0			0
$286$	0.287805	+	7.55691i	0.0170183	+	0.446849i
$287$	6.76362			0.399244
$288$		0			0
$289$	−5.22278	−	16.0741i	−0.307223	−	0.945534i
$290$	4.13058	−	12.7126i	0.242556	−	0.746511i
$291$		0			0
$292$	3.97176	+	2.88565i	0.232430	+	0.168870i
$293$	−0.265775	+	0.817972i	−0.0155268	+	0.0477864i	−0.958520	−	0.285026i	$-0.907998\pi$
$293$	−0.265775	+	0.817972i	−0.0155268	+	0.0477864i	0.942993	+	0.332813i	$0.107998\pi$
$294$		0			0
$295$	5.58081	−	4.05470i	0.324927	−	0.236074i
$296$	−13.2250			−0.768685
$297$		0			0
$298$	−2.61848			−0.151684
$299$	0.272961	−	0.198318i	0.0157857	−	0.0114690i
$300$		0			0
$301$	2.44106	−	7.51280i	0.140700	−	0.433031i
$302$	−1.37006	−	0.995408i	−0.0788382	−	0.0572793i
$303$		0			0
$304$	4.14894	−	12.7691i	0.237958	−	0.732360i
$305$	12.7075	+	39.1095i	0.727627	+	2.23941i
$306$		0			0
$307$	3.48920			0.199139			0.0995696	−	0.995031i	$-0.468253\pi$
$307$	3.48920			0.199139			0.0995696	+	0.995031i	$0.468253\pi$
$308$	6.19029	+	1.75389i	0.352725	+	0.0999370i
$309$		0			0
$310$	−9.16942	+	6.66197i	−0.520788	+	0.378375i
$311$	−3.35138	−	10.3145i	−0.190039	−	0.584881i	0.809959	−	0.586486i	$-0.199489\pi$
$311$	−3.35138	−	10.3145i	−0.190039	−	0.584881i	−0.999999	+	0.00160485i	$0.999489\pi$
$312$		0			0
$313$	22.8799	+	16.6232i	1.29325	+	0.939598i	0.999866	−	0.0163974i	$-0.00521967\pi$
$313$	22.8799	+	16.6232i	1.29325	+	0.939598i	0.293381	+	0.955996i	$0.405220\pi$
$314$	−8.43935	−	6.13155i	−0.476260	−	0.346023i
$315$		0			0
$316$	4.57569	+	14.0825i	0.257403	+	0.792204i
$317$	−0.900053	+	0.653927i	−0.0505520	+	0.0367282i	−0.612774	−	0.790258i	$-0.709947\pi$
$317$	−0.900053	+	0.653927i	−0.0505520	+	0.0367282i	0.562222	+	0.826986i	$0.309947\pi$
$318$		0			0
$319$	0.971887	+	25.5189i	0.0544152	+	1.42878i
$320$	3.19867			0.178811
$321$		0			0
$322$	0.0177750	+	0.0547057i	0.000990559	+	0.00304863i
$323$	0.618308	−	1.90296i	0.0344036	−	0.105883i
$324$		0			0
$325$	12.8550	+	9.33967i	0.713065	+	0.518072i
$326$	1.03980	−	3.20018i	0.0575894	−	0.177242i
$327$		0			0
$328$	9.95541	−	7.23303i	0.549696	−	0.399377i
$329$	−0.381589			−0.0210377
$330$		0			0
$331$	−12.3783			−0.680373			−0.340187	−	0.940358i	$-0.610490\pi$
$331$	−12.3783			−0.680373			−0.340187	+	0.940358i	$0.610490\pi$
$332$	−6.68275	+	4.85530i	−0.366763	+	0.266469i
$333$		0			0
$334$	−0.896648	+	2.75960i	−0.0490624	+	0.150999i
$335$	28.3893	+	20.6260i	1.55107	+	1.12692i
$336$		0			0
$337$	4.16358	−	12.8142i	0.226804	−	0.698032i	−0.771299	−	0.636473i	$-0.780393\pi$
$337$	4.16358	−	12.8142i	0.226804	−	0.698032i	0.998103	−	0.0615594i	$-0.0196074\pi$
$338$	−0.459288	−	1.41354i	−0.0249820	−	0.0768866i
$339$		0			0
$340$	1.57277			0.0852953
$341$	12.0518	−	17.9899i	0.652642	−	0.974208i
$342$		0			0
$343$	−11.9104	+	8.65342i	−0.643102	+	0.467241i
$344$	−4.44120	−	13.6686i	−0.239453	−	0.736962i
$345$		0			0
$346$	7.28763	+	5.29478i	0.391786	+	0.284649i
$347$	7.87915	+	5.72454i	0.422975	+	0.307309i	0.778834	−	0.627230i	$-0.215812\pi$
$347$	7.87915	+	5.72454i	0.422975	+	0.307309i	−0.355859	+	0.934540i	$0.615812\pi$
$348$		0			0
$349$	−1.37210	−	4.22288i	−0.0734466	−	0.226045i	0.907594	−	0.419850i	$-0.137917\pi$
$349$	−1.37210	−	4.22288i	−0.0734466	−	0.226045i	−0.981040	+	0.193804i	$0.937917\pi$
$350$	−2.19156	+	1.59226i	−0.117144	+	0.0851100i
$351$		0			0
$352$	16.9810	−	6.24142i	0.905090	−	0.332669i
$353$	−32.5235			−1.73105			−0.865527	−	0.500863i	$-0.833016\pi$
$353$	−32.5235			−1.73105			−0.865527	+	0.500863i	$0.833016\pi$
$354$		0			0
$355$	8.09363	+	24.9096i	0.429565	+	1.32207i
$356$	1.09595	−	3.37299i	0.0580852	−	0.178768i
$357$		0			0
$358$	−3.29506	−	2.39400i	−0.174149	−	0.126527i
$359$	8.58143	−	26.4109i	0.452911	−	1.39392i	−0.420660	−	0.907218i	$-0.638201\pi$
$359$	8.58143	−	26.4109i	0.452911	−	1.39392i	0.873571	−	0.486697i	$-0.161799\pi$
$360$		0			0
$361$	−17.4395	+	12.6705i	−0.917868	+	0.666870i
$362$	−1.44320			−0.0758529
$363$		0			0
$364$	−7.65523			−0.401243
$365$	7.16201	−	5.20351i	0.374877	−	0.272364i
$366$		0			0
$367$	0.362229	−	1.11483i	0.0189082	−	0.0581934i	−0.941157	−	0.337969i	$-0.890260\pi$
$367$	0.362229	−	1.11483i	0.0189082	−	0.0581934i	0.960065	+	0.279776i	$0.0902601\pi$
$368$	−0.145831	−	0.105952i	−0.00760197	−	0.00552315i
$369$		0			0
$370$	−3.34912	+	10.3075i	−0.174112	+	0.535862i
$371$	−0.871672	−	2.68273i	−0.0452550	−	0.139280i
$372$		0			0
$373$	21.7668			1.12704			0.563520	−	0.826102i	$-0.309447\pi$
$373$	21.7668			1.12704			0.563520	+	0.826102i	$0.309447\pi$
$374$	0.565145	−	0.207721i	0.0292230	−	0.0107410i
$375$		0			0
$376$	−0.561664	+	0.408072i	−0.0289656	+	0.0210447i
$377$	−9.38942	−	28.8977i	−0.483580	−	1.48831i
$378$		0			0
$379$	13.1440	+	9.54967i	0.675161	+	0.490533i	0.871749	−	0.489953i	$-0.162986\pi$
$379$	13.1440	+	9.54967i	0.675161	+	0.490533i	−0.196588	+	0.980486i	$0.562986\pi$
$380$	−25.7904	−	18.7379i	−1.32302	−	0.961232i
$381$		0			0
$382$	−2.11104	−	6.49710i	−0.108010	−	0.332421i
$383$	5.01052	−	3.64036i	0.256026	−	0.186014i	−0.452367	−	0.891832i	$-0.649420\pi$
$383$	5.01052	−	3.64036i	0.256026	−	0.186014i	0.708393	+	0.705818i	$0.249420\pi$
$384$		0			0
$385$	6.45730	−	9.63890i	0.329094	−	0.491244i
$386$	−3.89830			−0.198418
$387$		0			0
$388$	0.0457401	+	0.140773i	0.00232210	+	0.00714669i
$389$	0.223485	−	0.687817i	0.0113312	−	0.0348737i	−0.945231	−	0.326402i	$-0.894164\pi$
$389$	0.223485	−	0.687817i	0.0113312	−	0.0348737i	0.956562	+	0.291528i	$0.0941637\pi$
$390$		0			0
$391$	−0.0217329	−	0.0157899i	−0.00109908	−	0.000798528i
$392$	−3.69481	+	11.3714i	−0.186616	+	0.574345i
$393$		0			0
$394$	9.65184	−	7.01247i	0.486253	−	0.353283i
$395$	26.7009			1.34347
$396$		0			0
$397$	4.08994			0.205268			0.102634	−	0.994719i	$-0.467273\pi$
$397$	4.08994			0.205268			0.102634	+	0.994719i	$0.467273\pi$
$398$	−6.21075	+	4.51238i	−0.311317	+	0.226185i
$399$		0			0
$400$	2.62328	−	8.07363i	0.131164	−	0.403681i
$401$	−4.56793	−	3.31879i	−0.228111	−	0.165733i	0.467859	−	0.883803i	$-0.345026\pi$
$401$	−4.56793	−	3.31879i	−0.228111	−	0.165733i	−0.695970	+	0.718071i	$0.745026\pi$
$402$		0			0
$403$	−7.96148	+	24.5029i	−0.396590	+	1.22058i
$404$	−1.05881	−	3.25868i	−0.0526777	−	0.162125i
$405$		0			0
$406$	5.18012			0.257085
$407$	−0.788016	−	20.6910i	−0.0390605	−	1.02561i
$408$		0			0
$409$	−7.64422	+	5.55385i	−0.377982	+	0.274620i	−0.760513	−	0.649323i	$-0.775053\pi$
$409$	−7.64422	+	5.55385i	−0.377982	+	0.274620i	0.382531	+	0.923943i	$0.375053\pi$
$410$	−3.11629	−	9.59094i	−0.153902	−	0.473663i
$411$		0			0
$412$	−4.06632	−	2.95436i	−0.200333	−	0.145551i
$413$	2.16276	+	1.57134i	0.106422	+	0.0773204i
$414$		0			0
$415$	4.60290	+	14.1663i	0.225948	+	0.695395i
$416$	−17.4147	+	12.6525i	−0.853827	+	0.620342i
$417$		0			0
$418$	−11.7421	−	3.32687i	−0.574324	−	0.162723i
$419$	−0.151564			−0.00740438			−0.00370219	−	0.999993i	$-0.501178\pi$
$419$	−0.151564			−0.00740438			−0.00370219	+	0.999993i	$0.501178\pi$
$420$		0			0
$421$	5.24605	+	16.1457i	0.255677	+	0.786892i	0.993696	+	0.112112i	$0.0357615\pi$
$421$	5.24605	+	16.1457i	0.255677	+	0.786892i	−0.738019	+	0.674780i	$0.764239\pi$
$422$	1.49003	−	4.58585i	0.0725337	−	0.223236i
$423$		0			0
$424$	−4.15194	−	3.01656i	−0.201636	−	0.146497i
$425$	0.390942	−	1.20320i	0.0189635	−	0.0583636i
$426$		0			0
$427$	−12.8927	+	9.36711i	−0.623923	+	0.453306i
$428$	19.9817			0.965852
$429$		0			0
$430$	−11.7780			−0.567986
$431$	−20.5242	+	14.9117i	−0.988618	+	0.718273i	−0.959618	−	0.281307i	$-0.909232\pi$
$431$	−20.5242	+	14.9117i	−0.988618	+	0.718273i	−0.0289998	+	0.999579i	$0.509232\pi$
$432$		0			0
$433$	5.10950	−	15.7254i	0.245547	−	0.755716i	−0.749999	−	0.661439i	$-0.769946\pi$
$433$	5.10950	−	15.7254i	0.245547	−	0.755716i	0.995546	−	0.0942769i	$-0.0300539\pi$
$434$	−3.55347	−	2.58175i	−0.170572	−	0.123928i
$435$		0			0
$436$	−2.67736	+	8.24005i	−0.128222	+	0.394627i
$437$	0.168259	+	0.517849i	0.00804893	+	0.0247721i
$438$		0			0
$439$	−39.2413			−1.87289			−0.936443	−	0.350819i	$-0.885903\pi$
$439$	−39.2413			−1.87289			−0.936443	+	0.350819i	$0.885903\pi$
$440$	−0.803326	−	21.0930i	−0.0382971	−	1.00557i
$441$		0			0
$442$	−0.579580	+	0.421089i	−0.0275678	+	0.0200292i
$443$	−9.94706	−	30.6139i	−0.472599	−	1.45451i	−0.849169	−	0.528122i	$-0.822896\pi$
$443$	−9.94706	−	30.6139i	−0.472599	−	1.45451i	0.376570	−	0.926388i	$-0.377104\pi$
$444$		0			0
$445$	−5.17390	−	3.75906i	−0.245266	−	0.178197i
$446$	−0.179344	−	0.130301i	−0.00849216	−	0.00616992i
$447$		0			0
$448$	0.383056	+	1.17893i	0.0180977	+	0.0556990i
$449$	−20.9085	+	15.1909i	−0.986731	+	0.716902i	−0.959203	−	0.282719i	$-0.908764\pi$
$449$	−20.9085	+	15.1909i	−0.986731	+	0.716902i	−0.0275281	+	0.999621i	$0.508764\pi$
$450$		0			0
$451$	11.9096	+	15.1447i	0.560799	+	0.713134i
$452$	32.0357			1.50683
$453$		0			0
$454$	3.21647	+	9.89928i	0.150957	+	0.464596i
$455$	−4.26572	+	13.1285i	−0.199980	+	0.615476i
$456$		0			0
$457$	10.2877	+	7.47444i	0.481238	+	0.349640i	0.801805	−	0.597586i	$-0.203873\pi$
$457$	10.2877	+	7.47444i	0.481238	+	0.349640i	−0.320567	+	0.947226i	$0.603873\pi$
$458$	−2.39760	+	7.37904i	−0.112032	+	0.344800i
$459$		0			0
$460$	−0.346255	+	0.251569i	−0.0161442	+	0.0117295i
$461$	19.0217			0.885931			0.442965	−	0.896539i	$-0.353927\pi$
$461$	19.0217			0.885931			0.442965	+	0.896539i	$0.353927\pi$
$462$		0			0
$463$	−22.8667			−1.06271			−0.531353	−	0.847150i	$-0.678316\pi$
$463$	−22.8667			−1.06271			−0.531353	+	0.847150i	$0.678316\pi$
$464$	−13.1330	+	9.54168i	−0.609684	+	0.442961i
$465$		0			0
$466$	−0.601664	+	1.85173i	−0.0278716	+	0.0857798i
$467$	12.8819	+	9.35921i	0.596101	+	0.433093i	0.844493	−	0.535567i	$-0.179902\pi$
$467$	12.8819	+	9.35921i	0.596101	+	0.433093i	−0.248392	+	0.968660i	$0.579902\pi$
$468$		0			0
$469$	−4.20232	+	12.9334i	−0.194045	+	0.597210i
$470$	0.175814	+	0.541101i	0.00810971	+	0.0249591i
$471$		0			0
$472$	4.86377			0.223873
$473$	21.1205	−	7.76289i	0.971120	−	0.356938i
$474$		0			0
$475$	−20.7455	+	15.0725i	−0.951870	+	0.691574i
$476$	0.188347	+	0.579671i	0.00863285	+	0.0265692i
$477$		0			0
$478$	10.8436	+	7.87832i	0.495973	+	0.360346i
$479$	−13.2598	−	9.63378i	−0.605854	−	0.440179i	0.242098	−	0.970252i	$-0.422164\pi$
$479$	−13.2598	−	9.63378i	−0.605854	−	0.440179i	−0.847952	+	0.530073i	$0.822164\pi$
$480$		0			0
$481$	7.61303	+	23.4305i	0.347124	+	1.06834i
$482$	7.08862	−	5.15018i	0.322878	−	0.234584i
$483$		0			0
$484$	6.97285	+	16.9492i	0.316948	+	0.770418i
$485$	0.266911			0.0121198
$486$		0			0
$487$	7.04142	+	21.6713i	0.319077	+	0.982019i	0.974044	+	0.226361i	$0.0726828\pi$
$487$	7.04142	+	21.6713i	0.319077	+	0.982019i	−0.654966	+	0.755658i	$0.727317\pi$
$488$	−8.95967	+	27.5750i	−0.405585	+	1.24826i
$489$		0			0
$490$	7.92722	+	5.75946i	0.358115	+	0.260186i
$491$	13.4864	−	41.5070i	0.608634	−	1.87318i	0.139076	−	0.990282i	$-0.455587\pi$
$491$	13.4864	−	41.5070i	0.608634	−	1.87318i	0.469558	−	0.882901i	$-0.344413\pi$
$492$		0			0
$493$	−1.95718	+	1.42198i	−0.0881471	+	0.0640426i
$494$	14.5209			0.653324
$495$		0			0
$496$	13.7645			0.618045
$497$	−8.21163	+	5.96610i	−0.368342	+	0.267616i
$498$		0			0
$499$	−6.21233	+	19.1196i	−0.278102	+	0.855910i	0.710280	+	0.703919i	$0.248568\pi$
$499$	−6.21233	+	19.1196i	−0.278102	+	0.855910i	−0.988382	+	0.151991i	$0.951432\pi$
$500$	3.94209	+	2.86410i	0.176296	+	0.128086i
$501$		0			0
$502$	−0.103973	+	0.319996i	−0.00464054	+	0.0142821i
$503$	3.27815	+	10.0891i	0.146165	+	0.449850i	0.997159	−	0.0753254i	$-0.0239995\pi$
$503$	3.27815	+	10.0891i	0.146165	+	0.449850i	−0.850994	+	0.525176i	$0.824000\pi$
$504$		0			0
$505$	−6.17856			−0.274942
$506$	−0.0911948	+	0.136128i	−0.00405410	+	0.00605162i
$507$		0			0
$508$	−17.7697	+	12.9104i	−0.788401	+	0.572807i
$509$	13.7415	+	42.2919i	0.609080	+	1.87456i	0.465840	+	0.884869i	$0.345752\pi$
$509$	13.7415	+	42.2919i	0.609080	+	1.87456i	0.143240	+	0.989688i	$0.454248\pi$
$510$		0			0
$511$	2.77553	+	2.01654i	0.122782	+	0.0892064i
$512$	16.5301	+	12.0098i	0.730534	+	0.530764i
$513$		0			0
$514$	−1.95899	−	6.02915i	−0.0864073	−	0.265934i
$515$	−7.33253	+	5.32739i	−0.323110	+	0.234753i
$516$		0			0
$517$	−0.671913	−	0.854430i	−0.0295507	−	0.0375778i
$518$	−4.20009			−0.184541
$519$		0			0
$520$	7.76095	+	23.8858i	0.340340	+	1.04746i
$521$	−5.23819	+	16.1215i	−0.229489	+	0.706296i	0.768315	+	0.640071i	$0.221095\pi$
$521$	−5.23819	+	16.1215i	−0.229489	+	0.706296i	−0.997805	+	0.0662243i	$0.978905\pi$
$522$		0			0
$523$	−24.4438	−	17.7595i	−1.06885	−	0.776567i	−0.0931472	−	0.995652i	$-0.529693\pi$
$523$	−24.4438	−	17.7595i	−1.06885	−	0.776567i	−0.975706	+	0.219085i	$0.929693\pi$
$524$	−9.25301	+	28.4778i	−0.404219	+	1.24406i
$525$		0			0
$526$	6.72925	−	4.88909i	0.293409	−	0.213174i
$527$	2.05130			0.0893560
$528$		0			0
$529$	−22.9927			−0.999682
$530$	−3.40255	+	2.47210i	−0.147797	+	0.107381i
$531$		0			0
$532$	3.81763	−	11.7495i	0.165515	−	0.509404i
$533$	−18.5456	−	13.4741i	−0.803298	−	0.583630i
$534$		0			0
$535$	11.1344	−	34.2682i	0.481382	−	1.48154i
$536$	7.64561	+	23.5308i	0.330240	+	1.01637i
$537$		0			0
$538$	0.282536			0.0121810
$539$	−18.0112	−	5.10310i	−0.775799	−	0.219806i
$540$		0			0
$541$	−9.57164	+	6.95421i	−0.411517	+	0.298985i	−0.774216	−	0.632922i	$-0.781855\pi$
$541$	−9.57164	+	6.95421i	−0.411517	+	0.298985i	0.362699	+	0.931906i	$0.381855\pi$
$542$	−3.91728	−	12.0561i	−0.168262	−	0.517856i
$543$		0			0
$544$	1.38654	+	1.00738i	0.0594476	+	0.0431912i
$545$	12.6396	+	9.18321i	0.541421	+	0.393365i
$546$		0			0
$547$	0.786698	+	2.42121i	0.0336368	+	0.103523i	0.966465	−	0.256797i	$-0.0826673\pi$
$547$	0.786698	+	2.42121i	0.0336368	+	0.103523i	−0.932828	+	0.360321i	$0.882667\pi$
$548$	22.1084	−	16.0627i	0.944424	−	0.686164i
$549$		0			0
$550$	−7.42425	−	2.10350i	−0.316571	−	0.0896937i
$551$	49.0355			2.08898
$552$		0			0
$553$	3.19757	+	9.84109i	0.135974	+	0.418486i
$554$	−0.512364	+	1.57690i	−0.0217683	+	0.0669959i
$555$		0			0
$556$	−16.0425	−	11.6556i	−0.680355	−	0.494307i
$557$	−2.98987	+	9.20189i	−0.126685	+	0.389896i	−0.994204	−	0.107507i	$-0.965713\pi$
$557$	−2.98987	+	9.20189i	−0.126685	+	0.389896i	0.867519	+	0.497404i	$0.165713\pi$
$558$		0			0
$559$	−21.6599	+	15.7368i	−0.916117	+	0.665598i
$560$	7.37496			0.311649
$561$		0			0
$562$	10.5035			0.443064
$563$	−19.4061	+	14.0993i	−0.817868	+	0.594216i	−0.916101	−	0.400947i	$-0.868681\pi$
$563$	−19.4061	+	14.0993i	−0.817868	+	0.594216i	0.0982327	+	0.995163i	$0.468681\pi$
$564$		0			0
$565$	17.8512	−	54.9404i	0.751007	−	2.31136i
$566$	−9.60027	−	6.97501i	−0.403530	−	0.293181i
$567$		0			0
$568$	−5.70659	+	17.5631i	−0.239443	+	0.736930i
$569$	11.6249	+	35.7779i	0.487343	+	1.49989i	0.828558	+	0.559903i	$0.189162\pi$
$569$	11.6249	+	35.7779i	0.487343	+	1.49989i	−0.341215	+	0.939985i	$0.610838\pi$
$570$		0			0
$571$	−14.7548			−0.617469			−0.308735	−	0.951148i	$-0.599905\pi$
$571$	−14.7548			−0.617469			−0.308735	+	0.951148i	$0.599905\pi$
$572$	−13.4795	−	17.1411i	−0.563608	−	0.716705i
$573$		0			0
$574$	3.16172	−	2.29712i	0.131968	−	0.0958801i
$575$	0.106386	+	0.327424i	0.00443662	+	0.0136545i
$576$		0			0
$577$	18.0466	+	13.1116i	0.751289	+	0.545843i	0.896226	−	0.443598i	$-0.146298\pi$
$577$	18.0466	+	13.1116i	0.751289	+	0.545843i	−0.144937	+	0.989441i	$0.546298\pi$
$578$	−7.90067	−	5.74017i	−0.328625	−	0.238760i
$579$		0			0
$580$	11.9106	+	36.6571i	0.494562	+	1.52210i
$581$	−4.67001	+	3.39296i	−0.193745	+	0.140764i
$582$		0			0
$583$	4.47213	−	6.67562i	0.185217	−	0.276476i
$584$	6.24181			0.258288
$585$		0			0
$586$	0.153568	+	0.472634i	0.00634384	+	0.0195243i
$587$	0.772594	−	2.37780i	0.0318884	−	0.0981424i	−0.933846	−	0.357677i	$-0.883569\pi$
$587$	0.772594	−	2.37780i	0.0318884	−	0.0981424i	0.965734	+	0.259534i	$0.0835690\pi$
$588$		0			0
$589$	−33.6374	−	24.4390i	−1.38601	−	1.00699i
$590$	1.23171	−	3.79081i	0.0507087	−	0.156065i
$591$		0			0
$592$	10.6484	−	7.73648i	0.437645	−	0.317968i
$593$	10.8953			0.447417			0.223708	−	0.974656i	$-0.428184\pi$
$593$	10.8953			0.447417			0.223708	+	0.974656i	$0.428184\pi$
$594$		0			0
$595$	1.09907			0.0450577
$596$	6.10843	−	4.43804i	0.250211	−	0.181789i
$597$		0			0
$598$	0.0602437	−	0.185411i	0.00246355	−	0.00758203i
$599$	−29.8026	−	21.6529i	−1.21770	−	0.884713i	−0.221796	−	0.975093i	$-0.571192\pi$
$599$	−29.8026	−	21.6529i	−1.21770	−	0.884713i	−0.995907	+	0.0903802i	$0.971192\pi$
$600$		0			0
$601$	−4.77564	+	14.6979i	−0.194802	+	0.599540i	0.805177	+	0.593035i	$0.202070\pi$
$601$	−4.77564	+	14.6979i	−0.194802	+	0.599540i	−0.999979	+	0.00650456i	$0.997930\pi$
$602$	−1.41047	−	4.34099i	−0.0574866	−	0.176925i
$603$		0			0
$604$	4.88321			0.198695
$605$	32.9530	−	2.51367i	1.33973	−	0.102195i
$606$		0			0
$607$	20.6112	−	14.9749i	0.836585	−	0.607814i	−0.0848299	−	0.996395i	$-0.527035\pi$
$607$	20.6112	−	14.9749i	0.836585	−	0.607814i	0.921415	+	0.388581i	$0.127035\pi$
$608$	−10.7348	−	33.0384i	−0.435355	−	1.33988i
$609$		0			0
$610$	19.2230	+	13.9663i	0.778316	+	0.565479i
$611$	1.04630	+	0.760183i	0.0423289	+	0.0307537i
$612$		0			0
$613$	−11.6728	−	35.9252i	−0.471461	−	1.45101i	−0.850672	−	0.525697i	$-0.823805\pi$
$613$	−11.6728	−	35.9252i	−0.471461	−	1.45101i	0.379211	−	0.925310i	$-0.376195\pi$
$614$	1.63106	−	1.18503i	0.0658243	−	0.0478241i
$615$		0			0
$616$	7.67799	−	2.82207i	0.309355	−	0.113704i
$617$	−41.8928			−1.68654			−0.843271	−	0.537489i	$-0.819373\pi$
$617$	−41.8928			−1.68654			−0.843271	+	0.537489i	$0.819373\pi$
$618$		0			0
$619$	−1.85089	−	5.69646i	−0.0743936	−	0.228960i	0.906945	−	0.421250i	$-0.138409\pi$
$619$	−1.85089	−	5.69646i	−0.0743936	−	0.228960i	−0.981338	+	0.192290i	$0.938409\pi$
$620$	10.0993	−	31.0823i	0.405596	−	1.24830i
$621$		0			0
$622$	−5.06974	−	3.68338i	−0.203278	−	0.147690i
$623$	0.765867	−	2.35710i	0.0306838	−	0.0944351i
$624$		0			0
$625$	23.3964	−	16.9985i	0.935856	−	0.679939i
$626$	16.3411			0.653123
$627$		0			0
$628$	30.0798			1.20031
$629$	1.58690	−	1.15295i	0.0632739	−	0.0459712i
$630$		0			0
$631$	−6.64368	+	20.4471i	−0.264481	+	0.813988i	0.727332	+	0.686286i	$0.240760\pi$
$631$	−6.64368	+	20.4471i	−0.264481	+	0.813988i	−0.991813	+	0.127702i	$0.959240\pi$
$632$	15.2306	+	11.0657i	0.605841	+	0.440169i
$633$		0			0
$634$	−0.198646	+	0.611369i	−0.00788923	+	0.0242806i
$635$	12.2393	+	37.6686i	0.485701	+	1.49483i
$636$		0			0
$637$	22.2736			0.882512
$638$	9.12129	+	11.5990i	0.361115	+	0.459208i
$639$		0			0
$640$	28.0127	−	20.3525i	1.10730	−	0.804501i
$641$	−3.96685	−	12.2087i	−0.156681	−	0.482215i	0.841646	−	0.540029i	$-0.181587\pi$
$641$	−3.96685	−	12.2087i	−0.156681	−	0.482215i	−0.998327	+	0.0578142i	$0.981587\pi$
$642$		0			0
$643$	−22.9401	−	16.6670i	−0.904671	−	0.657282i	0.0349907	−	0.999388i	$-0.488860\pi$
$643$	−22.9401	−	16.6670i	−0.904671	−	0.657282i	−0.939661	+	0.342106i	$0.888860\pi$
$644$	−0.134186	−	0.0974917i	−0.00528766	−	0.00384171i
$645$		0			0
$646$	−0.357266	−	1.09955i	−0.0140564	−	0.0432613i
$647$	−14.1536	+	10.2832i	−0.556436	+	0.404274i	−0.830153	−	0.557536i	$-0.811747\pi$
$647$	−14.1536	+	10.2832i	−0.556436	+	0.404274i	0.273717	+	0.961810i	$0.411747\pi$
$648$		0			0
$649$	0.289810	+	7.60956i	0.0113760	+	0.298701i
$650$	9.18120			0.360116
$651$		0			0
$652$	2.99829	+	9.22780i	0.117422	+	0.361389i
$653$	9.05488	−	27.8681i	0.354345	−	1.09056i	−0.602043	−	0.798463i	$-0.705647\pi$
$653$	9.05488	−	27.8681i	0.354345	−	1.09056i	0.956388	−	0.292098i	$-0.0943534\pi$
$654$		0			0
$655$	43.6828	+	31.7374i	1.70683	+	1.24008i
$656$	−3.78455	+	11.6477i	−0.147762	+	0.454764i
$657$		0			0
$658$	−0.178378	+	0.129599i	−0.00695388	+	0.00505229i
$659$	−27.5870			−1.07464			−0.537319	−	0.843379i	$-0.680563\pi$
$659$	−27.5870			−1.07464			−0.537319	+	0.843379i	$0.680563\pi$
$660$		0			0
$661$	29.7552			1.15734			0.578672	−	0.815560i	$-0.303571\pi$
$661$	29.7552			1.15734			0.578672	+	0.815560i	$0.303571\pi$
$662$	−5.78636	+	4.20404i	−0.224893	+	0.163395i
$663$		0			0
$664$	−3.24537	+	9.98823i	−0.125945	+	0.387619i
$665$	−18.0228	−	13.0943i	−0.698893	−	0.507775i
$666$		0			0
$667$	0.203437	−	0.626115i	0.00787711	−	0.0242433i
$668$	−2.58550	−	7.95736i	−0.100036	−	0.307880i
$669$		0			0
$670$	20.2760			0.783332
$671$	−43.6761	−	12.3747i	−1.68610	−	0.477720i
$672$		0			0
$673$	−7.80999	+	5.67429i	−0.301053	+	0.218728i	−0.728048	−	0.685526i	$-0.759572\pi$
$673$	−7.80999	+	5.67429i	−0.301053	+	0.218728i	0.426995	+	0.904254i	$0.359572\pi$
$674$	−2.40577	−	7.40418i	−0.0926666	−	0.285198i
$675$		0			0
$676$	3.46724	+	2.51910i	0.133355	+	0.0968883i
$677$	−0.0793768	−	0.0576706i	−0.00305070	−	0.00221646i	0.586259	−	0.810124i	$-0.300600\pi$
$677$	−0.0793768	−	0.0576706i	−0.00305070	−	0.00221646i	−0.589310	+	0.807907i	$0.700600\pi$
$678$		0			0
$679$	0.0319639	+	0.0983747i	0.00122666	+	0.00377528i
$680$	1.61774	−	1.17535i	0.0620373	−	0.0450727i
$681$		0			0
$682$	−0.476165	−	12.5027i	−0.0182333	−	0.478753i
$683$	−30.5246			−1.16799			−0.583996	−	0.811756i	$-0.698512\pi$
$683$	−30.5246			−1.16799			−0.583996	+	0.811756i	$0.698512\pi$
$684$		0			0
$685$	−15.2277	−	46.8660i	−0.581820	−	1.79066i
$686$	−2.62868	+	8.09025i	−0.100364	+	0.308887i
$687$		0			0
$688$	11.5719	+	8.40751i	0.441176	+	0.320533i
$689$	−2.95431	+	9.09244i	−0.112550	+	0.346395i
$690$		0			0
$691$	−26.5371	+	19.2804i	−1.00952	+	0.733459i	−0.964108	−	0.265509i	$-0.914460\pi$
$691$	−26.5371	+	19.2804i	−1.00952	+	0.733459i	−0.0454115	+	0.998968i	$0.514460\pi$
$692$	−25.9748			−0.987413
$693$		0			0
$694$	5.62741			0.213614
$695$	−28.9284	+	21.0177i	−1.09732	+	0.797248i
$696$		0			0
$697$	−0.564004	+	1.73583i	−0.0213632	+	0.0657491i
$698$	−2.07561	−	1.50802i	−0.0785631	−	0.0570794i
$699$		0			0
$700$	2.41380	−	7.42892i	0.0912331	−	0.280787i
$701$	2.70365	+	8.32098i	0.102115	+	0.314279i	0.989043	−	0.147630i	$-0.0471646\pi$
$701$	2.70365	+	8.32098i	0.102115	+	0.314279i	−0.886927	+	0.461909i	$0.847165\pi$
$702$		0			0
$703$	−39.7584			−1.49952
$704$	−1.96528	+	2.93360i	−0.0740692	+	0.110564i
$705$		0			0
$706$	−15.2034	+	11.0460i	−0.572189	+	0.415720i
$707$	−0.739912	−	2.27721i	−0.0278273	−	0.0856435i
$708$		0			0
$709$	−21.6621	−	15.7385i	−0.813539	−	0.591071i	0.101316	−	0.994854i	$-0.467695\pi$
$709$	−21.6621	−	15.7385i	−0.813539	−	0.591071i	−0.914854	+	0.403784i	$0.867695\pi$
$710$	12.2435	+	8.89542i	0.459490	+	0.333839i
$711$		0			0
$712$	−1.39340	−	4.28845i	−0.0522199	−	0.160716i
$713$	−0.451607	+	0.328111i	−0.0169128	+	0.0122879i
$714$		0			0
$715$	−36.9078	+	13.5656i	−1.38027	+	0.507323i
$716$	11.7443			0.438907
$717$		0			0
$718$	−4.95846	−	15.2606i	−0.185048	−	0.569519i
$719$	4.63672	−	14.2703i	0.172920	−	0.532194i	−0.826612	−	0.562772i	$-0.809735\pi$
$719$	4.63672	−	14.2703i	0.172920	−	0.532194i	0.999532	+	0.0305782i	$0.00973486\pi$
$720$		0			0
$721$	−2.84161	−	2.06455i	−0.105827	−	0.0768879i
$722$	−3.84897	+	11.8459i	−0.143244	+	0.440860i
$723$		0			0
$724$	3.36672	−	2.44607i	0.125123	−	0.0909073i
$725$	31.0040			1.15146
$726$		0			0
$727$	27.5325			1.02112			0.510562	−	0.859841i	$-0.329437\pi$
$727$	27.5325			1.02112			0.510562	+	0.859841i	$0.329437\pi$
$728$	−7.87410	+	5.72087i	−0.291834	+	0.212029i
$729$		0			0
$730$	1.58069	−	4.86486i	0.0585039	−	0.180057i
$731$	1.72454	+	1.25295i	0.0637845	+	0.0463422i
$732$		0			0
$733$	14.7524	−	45.4031i	0.544891	−	1.67700i	−0.176357	−	0.984326i	$-0.556431\pi$
$733$	14.7524	−	45.4031i	0.544891	−	1.67700i	0.721248	−	0.692677i	$-0.243569\pi$
$734$	−0.209300	−	0.644160i	−0.00772541	−	0.0237764i
$735$		0			0
$736$	−0.466391			−0.0171914
$737$	−36.3593	+	13.3640i	−1.33931	+	0.492267i
$738$		0			0
$739$	−1.20421	+	0.874910i	−0.0442976	+	0.0321841i	−0.609714	−	0.792622i	$-0.708716\pi$
$739$	−1.20421	+	0.874910i	−0.0442976	+	0.0321841i	0.565416	+	0.824806i	$0.308716\pi$
$740$	−9.65725	−	29.7220i	−0.355007	−	1.09260i
$741$		0			0
$742$	−1.31861	−	0.958023i	−0.0484076	−	0.0351701i
$743$	−14.6919	−	10.6743i	−0.538993	−	0.391601i	0.284718	−	0.958611i	$-0.408100\pi$
$743$	−14.6919	−	10.6743i	−0.538993	−	0.391601i	−0.823711	+	0.567010i	$0.808100\pi$
$744$		0			0
$745$	−4.20733	−	12.9488i	−0.154145	−	0.474409i
$746$	10.1751	−	7.39264i	0.372537	−	0.270664i
$747$		0			0
$748$	−0.966316	+	1.44243i	−0.0353320	+	0.0527406i
$749$	13.9635			0.510216
$750$		0			0
$751$	−1.35802	−	4.17956i	−0.0495550	−	0.152514i	0.923217	−	0.384279i	$-0.125550\pi$
$751$	−1.35802	−	4.17956i	−0.0495550	−	0.152514i	−0.972772	+	0.231765i	$0.925550\pi$
$752$	0.213517	−	0.657136i	0.00778615	−	0.0239633i
$753$		0			0
$754$	−14.2037	−	10.3196i	−0.517267	−	0.375817i
$755$	2.72107	−	8.37459i	0.0990299	−	0.304783i
$756$		0			0
$757$	11.1369	−	8.09140i	0.404776	−	0.294087i	−0.366708	−	0.930336i	$-0.619515\pi$
$757$	11.1369	−	8.09140i	0.404776	−	0.294087i	0.771483	+	0.636249i	$0.219515\pi$
$758$	9.38763			0.340974
$759$		0			0
$760$	−40.5309			−1.47021
$761$	−25.1654	+	18.2837i	−0.912244	+	0.662784i	−0.941581	−	0.336786i	$-0.890660\pi$
$761$	−25.1654	+	18.2837i	−0.912244	+	0.662784i	0.0293374	+	0.999570i	$0.490660\pi$
$762$		0			0
$763$	−1.87098	+	5.75828i	−0.0677340	+	0.208464i
$764$	15.9365	+	11.5786i	0.576564	+	0.418898i
$765$		0			0
$766$	1.10585	−	3.40344i	0.0399558	−	0.122971i
$767$	−2.79986	−	8.61708i	−0.101097	−	0.311145i
$768$		0			0
$769$	21.9353			0.791009			0.395504	−	0.918464i	$-0.370570\pi$
$769$	21.9353			0.791009			0.395504	+	0.918464i	$0.370570\pi$
$770$	−0.255127	−	6.69888i	−0.00919413	−	0.241411i
$771$		0			0
$772$	9.09402	−	6.60719i	0.327301	−	0.237798i
$773$	3.92965	+	12.0942i	0.141340	+	0.434999i	0.996522	−	0.0833281i	$-0.0265549\pi$
$773$	3.92965	+	12.0942i	0.141340	+	0.434999i	−0.855182	+	0.518327i	$0.826555\pi$
$774$		0			0
$775$	−21.2682	−	15.4522i	−0.763976	−	0.555061i
$776$	0.152250	+	0.110616i	0.00546546	+	0.00397089i
$777$		0			0
$778$	−0.129132	−	0.397429i	−0.00462962	−	0.0142485i
$779$	29.9291	−	21.7448i	1.07232	−	0.779087i
$780$		0			0
$781$	−27.8182	−	7.88168i	−0.995412	−	0.282029i
$782$	−0.0155220			−0.000555064
$783$		0			0
$784$	−3.67724	−	11.3174i	−0.131330	−	0.404193i
$785$	16.7613	−	51.5861i	0.598238	−	1.84119i
$786$		0			0
$787$	13.9650	+	10.1461i	0.497797	+	0.361671i	0.808175	−	0.588942i	$-0.200455\pi$
$787$	13.9650	+	10.1461i	0.497797	+	0.361671i	−0.310378	+	0.950613i	$0.600455\pi$
$788$	−10.6306	+	32.7176i	−0.378700	+	1.16552i
$789$		0			0
$790$	12.4816	−	9.06842i	0.444076	−	0.322640i
$791$	22.3870			0.795991
$792$		0			0
$793$	54.0120			1.91802
$794$	1.91188	−	1.38906i	0.0678501	−	0.0492960i
$795$		0			0
$796$	6.84057	−	21.0531i	0.242457	−	0.746207i
$797$	28.4786	+	20.6909i	1.00876	+	0.732910i	0.963950	−	0.266085i	$-0.0857302\pi$
$797$	28.4786	+	20.6909i	1.00876	+	0.732910i	0.0448149	+	0.998995i	$0.485730\pi$
$798$		0			0
$799$	0.0318199	−	0.0979317i	0.00112571	−	0.00346457i
$800$	−6.78739	−	20.8894i	−0.239970	−	0.738553i
$801$		0			0
$802$	−3.26248			−0.115202
$803$	0.371921	+	9.76556i	0.0131248	+	0.344619i
$804$		0			0
$805$	−0.241968	+	0.175800i	−0.00852827	+	0.00619615i
$806$	4.60024	+	14.1581i	0.162037	+	0.498697i
$807$		0			0
$808$	−3.52434	−	2.56058i	−0.123986	−	0.0900810i
$809$	−15.4367	−	11.2154i	−0.542725	−	0.394313i	0.282371	−	0.959305i	$-0.408879\pi$
$809$	−15.4367	−	11.2154i	−0.542725	−	0.394313i	−0.825096	+	0.564992i	$0.808879\pi$
$810$		0			0
$811$	−9.59769	−	29.5387i	−0.337020	−	1.03724i	−0.965718	−	0.259593i	$-0.916412\pi$
$811$	−9.59769	−	29.5387i	−0.337020	−	1.03724i	0.628698	−	0.777650i	$-0.283588\pi$
$812$	−12.0843	+	8.77973i	−0.424075	+	0.308108i
$813$		0			0
$814$	−7.39563	−	9.40457i	−0.259217	−	0.329630i
$815$	17.4962			0.612865
$816$		0			0
$817$	−13.3517	−	41.0922i	−0.467115	−	1.43763i
$818$	−1.68711	+	5.19240i	−0.0589885	+	0.181548i
$819$		0			0
$820$	23.5253	+	17.0922i	0.821540	+	0.596884i
$821$	−10.5092	+	32.3440i	−0.366774	+	1.12881i	0.582089	+	0.813125i	$0.302236\pi$
$821$	−10.5092	+	32.3440i	−0.366774	+	1.12881i	−0.948863	+	0.315689i	$0.897764\pi$
$822$		0			0
$823$	−12.5851	+	9.14359i	−0.438688	+	0.318726i	−0.785113	−	0.619352i	$-0.787395\pi$
$823$	−12.5851	+	9.14359i	−0.438688	+	0.318726i	0.346425	+	0.938078i	$0.387395\pi$
$824$	−6.39042			−0.222621
$825$		0			0
$826$	1.54467			0.0537461
$827$	12.9667	−	9.42084i	0.450895	−	0.327595i	−0.339054	−	0.940767i	$-0.610107\pi$
$827$	12.9667	−	9.42084i	0.450895	−	0.327595i	0.789949	+	0.613172i	$0.210107\pi$
$828$		0			0
$829$	5.90205	−	18.1646i	0.204987	−	0.630884i	−0.794727	−	0.606967i	$-0.792386\pi$
$829$	5.90205	−	18.1646i	0.204987	−	0.630884i	0.999714	−	0.0239173i	$-0.00761382\pi$
$830$	6.96296	+	5.05888i	0.241688	+	0.175596i
$831$		0			0
$832$	1.29827	−	3.99567i	0.0450095	−	0.138525i
$833$	−0.548012	−	1.68661i	−0.0189875	−	0.0584375i
$834$		0			0
$835$	−15.0874			−0.522122
$836$	33.0308	−	12.1406i	1.14240	−	0.419891i
$837$		0			0
$838$	−0.0708501	+	0.0514756i	−0.00244747	+	0.00177819i
$839$	−0.459793	−	1.41510i	−0.0158738	−	0.0488545i	0.942806	−	0.333342i	$-0.108176\pi$
$839$	−0.459793	−	1.41510i	−0.0158738	−	0.0488545i	−0.958680	+	0.284488i	$0.908176\pi$
$840$		0			0
$841$	−24.5029	−	17.8024i	−0.844927	−	0.613875i
$842$	7.93586	+	5.76574i	0.273488	+	0.198700i
$843$		0			0
$844$	4.29654	+	13.2234i	0.147893	+	0.455168i
$845$	6.25224	−	4.54252i	0.215084	−	0.156267i
$846$		0			0
$847$	4.87274	+	11.8444i	0.167429	+	0.406977i
$848$	5.10768			0.175399
$849$		0			0
$850$	−0.225891	−	0.695221i	−0.00774800	−	0.0238459i
$851$	−0.164949	+	0.507660i	−0.00565437	+	0.0174024i
$852$		0			0
$853$	−30.5825	−	22.2195i	−1.04713	−	0.760781i	−0.0754620	−	0.997149i	$-0.524043\pi$
$853$	−30.5825	−	22.2195i	−1.04713	−	0.760781i	−0.971664	+	0.236367i	$0.924043\pi$
$854$	−2.84548	+	8.75750i	−0.0973704	+	0.299675i
$855$		0			0
$856$	20.5530	−	14.9326i	0.702487	−	0.510387i
$857$	−19.8270			−0.677276			−0.338638	−	0.940917i	$-0.609966\pi$
$857$	−19.8270			−0.677276			−0.338638	+	0.940917i	$0.609966\pi$
$858$		0			0
$859$	−15.7153			−0.536199			−0.268099	−	0.963391i	$-0.586396\pi$
$859$	−15.7153			−0.536199			−0.268099	+	0.963391i	$0.586396\pi$
$860$	27.4759	−	19.9624i	0.936921	−	0.680713i
$861$		0			0
$862$	−4.52979	+	13.9413i	−0.154285	+	0.474842i
$863$	6.57548	+	4.77736i	0.223832	+	0.162623i	0.694050	−	0.719927i	$-0.255825\pi$
$863$	6.57548	+	4.77736i	0.223832	+	0.162623i	−0.470218	+	0.882550i	$0.655825\pi$
$864$		0			0
$865$	−14.4739	+	44.5462i	−0.492128	+	1.51462i
$866$	−2.95233	−	9.08634i	−0.100324	−	0.308766i
$867$		0			0
$868$	12.6654			0.429891
$869$	−16.4052	+	24.4882i	−0.556508	+	0.830707i
$870$		0			0
$871$	37.2879	−	27.0913i	1.26345	−	0.917953i
$872$	3.40401	+	10.4765i	0.115274	+	0.354778i
$873$		0			0
$874$	0.254531	+	0.184928i	0.00860964	+	0.00625527i
$875$	2.75479	+	2.00148i	0.0931290	+	0.0676622i
$876$		0			0
$877$	−0.782904	−	2.40953i	−0.0264368	−	0.0813640i	0.936968	−	0.349416i	$-0.113620\pi$
$877$	−0.782904	−	2.40953i	−0.0264368	−	0.0813640i	−0.963404	+	0.268052i	$0.913620\pi$
$878$	−18.3437	+	13.3275i	−0.619071	+	0.449782i
$879$		0			0
$880$	12.9860	+	16.5135i	0.437759	+	0.556671i
$881$	47.4109			1.59731			0.798657	−	0.601786i	$-0.205544\pi$
$881$	47.4109			1.59731			0.798657	+	0.601786i	$0.205544\pi$
$882$		0			0
$883$	8.19295	+	25.2153i	0.275715	+	0.848563i	0.989029	+	0.147719i	$0.0471930\pi$
$883$	8.19295	+	25.2153i	0.275715	+	0.848563i	−0.713315	+	0.700844i	$0.752807\pi$
$884$	0.638353	−	1.96465i	0.0214701	−	0.0660783i
$885$		0			0
$886$	−15.0472	−	10.9325i	−0.505522	−	0.367283i
$887$	14.7801	−	45.4884i	0.496266	−	1.52735i	−0.318707	−	0.947853i	$-0.603249\pi$
$887$	14.7801	−	45.4884i	0.496266	−	1.52735i	0.814974	−	0.579498i	$-0.196751\pi$
$888$		0			0
$889$	−12.4177	+	9.02200i	−0.416477	+	0.302588i
$890$	−3.69528			−0.123866
$891$		0			0
$892$	0.639221			0.0214027
$893$	−1.68854	+	1.22680i	−0.0565048	+	0.0410531i
$894$		0			0
$895$	6.54430	−	20.1413i	0.218752	−	0.673249i
$896$	10.8559	+	7.88728i	0.362671	+	0.263496i
$897$		0			0
$898$	−4.61459	+	14.2023i	−0.153991	+	0.473935i
$899$	15.5345	+	47.8104i	0.518106	+	1.59457i
$900$		0			0
$901$	0.761187			0.0253588
$902$	10.7108	+	3.03468i	0.356631	+	0.101044i
$903$		0			0
$904$	32.9516	−	23.9407i	1.09595	−	0.796257i
$905$	−2.31891	−	7.13687i	−0.0770832	−	0.237238i
$906$		0			0
$907$	−38.3946	−	27.8953i	−1.27487	−	0.926249i	−0.275487	−	0.961305i	$-0.588839\pi$
$907$	−38.3946	−	27.8953i	−1.27487	−	0.926249i	−0.999385	+	0.0350562i	$0.988839\pi$
$908$	−24.2817	−	17.6417i	−0.805815	−	0.585459i
$909$		0			0
$910$	2.46479	+	7.58583i	0.0817068	+	0.251468i
$911$	−23.0022	+	16.7120i	−0.762095	+	0.553695i	−0.899552	−	0.436813i	$-0.856107\pi$
$911$	−23.0022	+	16.7120i	−0.762095	+	0.553695i	0.137457	+	0.990508i	$0.456107\pi$
$912$		0			0
$913$	−15.8204	−	4.48236i	−0.523578	−	0.148345i
$914$	7.34762			0.243038
$915$		0			0
$916$	−6.91352	−	21.2776i	−0.228429	−	0.703032i
$917$	−6.46615	+	19.9008i	−0.213531	+	0.657181i
$918$		0			0
$919$	−31.0442	−	22.5550i	−1.02406	−	0.744020i	−0.0569449	−	0.998377i	$-0.518136\pi$
$919$	−31.0442	−	22.5550i	−1.02406	−	0.744020i	−0.967110	+	0.254358i	$0.918136\pi$
$920$	−0.168154	+	0.517523i	−0.00554386	+	0.0170622i
$921$		0			0
$922$	8.89190	−	6.46034i	0.292839	−	0.212760i
$923$	34.4013			1.13233
$924$		0			0
$925$	−25.1383			−0.826543
$926$	−10.6893	+	7.76621i	−0.351271	+	0.255214i
$927$		0			0
$928$	−12.9791	+	39.9457i	−0.426061	+	1.31128i
$929$	10.8309	+	7.86907i	0.355349	+	0.258176i	0.751109	−	0.660178i	$-0.229519\pi$
$929$	10.8309	+	7.86907i	0.355349	+	0.258176i	−0.395761	+	0.918354i	$0.629519\pi$
$930$		0			0
$931$	−11.1078	+	34.1862i	−0.364042	+	1.12041i
$932$	−1.73491	−	5.33951i	−0.0568289	−	0.174901i
$933$		0			0
$934$	9.20041			0.301047
$935$	1.93528	+	2.46098i	0.0632905	+	0.0804826i
$936$		0			0
$937$	19.9588	−	14.5010i	0.652027	−	0.473725i	−0.211934	−	0.977284i	$-0.567976\pi$
$937$	19.9588	−	14.5010i	0.652027	−	0.473725i	0.863961	+	0.503559i	$0.167976\pi$
$938$	2.42815	+	7.47309i	0.0792820	+	0.244005i
$939$		0			0
$940$	−1.32725	−	0.964304i	−0.0432901	−	0.0314521i
$941$	6.71670	+	4.87997i	0.218958	+	0.159082i	0.691858	−	0.722034i	$-0.256793\pi$
$941$	6.71670	+	4.87997i	0.218958	+	0.159082i	−0.472899	+	0.881116i	$0.656793\pi$
$942$		0			0
$943$	−0.153481	−	0.472367i	−0.00499804	−	0.0153824i
$944$	−3.91616	+	2.84526i	−0.127460	+	0.0926053i
$945$		0			0
$946$	7.23646	−	10.8020i	0.235278	−	0.351202i
$947$	−37.9496			−1.23320			−0.616598	−	0.787278i	$-0.711490\pi$
$947$	−37.9496			−1.23320			−0.616598	+	0.787278i	$0.711490\pi$
$948$		0			0
$949$	−3.59314	−	11.0585i	−0.116638	−	0.358975i
$950$	−4.57863	+	14.0916i	−0.148550	+	0.457191i
$951$		0			0
$952$	0.626929	+	0.455490i	0.0203189	+	0.0147625i
$953$	15.0400	−	46.2884i	0.487194	−	1.49943i	−0.341583	−	0.939852i	$-0.610963\pi$
$953$	15.0400	−	46.2884i	0.487194	−	1.49943i	0.828778	−	0.559578i	$-0.189037\pi$
$954$		0			0
$955$	28.7373	−	20.8789i	0.929918	−	0.675625i
$956$	−38.6490			−1.25000
$957$		0			0
$958$	−9.47032			−0.305972
$959$	15.4497	−	11.2249i	0.498897	−	0.362470i
$960$		0			0
$961$	3.59254	−	11.0567i	0.115888	−	0.356668i
$962$	11.5165	+	8.36721i	0.371306	+	0.269770i
$963$		0			0
$964$	−7.80746	+	24.0289i	−0.251461	+	0.773918i
$965$	−6.26373	−	19.2778i	−0.201636	−	0.620573i
$966$		0			0
$967$	10.9780			0.353029			0.176515	−	0.984298i	$-0.443518\pi$
$967$	10.9780			0.353029			0.176515	+	0.984298i	$0.443518\pi$
$968$	19.8386	+	12.2229i	0.637637	+	0.392858i
$969$		0			0
$970$	0.124770	−	0.0906508i	0.00400613	−	0.00291062i
$971$	−4.03687	−	12.4242i	−0.129549	−	0.398712i	0.865153	−	0.501508i	$-0.167221\pi$
$971$	−4.03687	−	12.4242i	−0.129549	−	0.398712i	−0.994702	+	0.102796i	$0.967221\pi$
$972$		0			0
$973$	−11.2108	−	8.14510i	−0.359401	−	0.261120i
$974$	10.6518	+	7.73897i	0.341305	+	0.247973i
$975$		0			0
$976$	−8.91708	−	27.4439i	−0.285429	−	0.878459i
$977$	−8.96092	+	6.51049i	−0.286685	+	0.208289i	−0.721828	−	0.692072i	$-0.756698\pi$
$977$	−8.96092	+	6.51049i	−0.286685	+	0.208289i	0.435143	+	0.900361i	$0.356698\pi$
$978$		0			0
$979$	6.62642	−	2.43556i	0.211781	−	0.0778409i
$980$	−28.2544			−0.902554
$981$		0			0
$982$	−7.79262	−	23.9832i	−0.248673	−	0.765336i
$983$	8.16778	−	25.1378i	0.260512	−	0.801772i	−0.732182	−	0.681109i	$-0.761498\pi$
$983$	8.16778	−	25.1378i	0.260512	−	0.801772i	0.992693	−	0.120663i	$-0.0385021\pi$
$984$		0			0
$985$	50.1863	+	36.4625i	1.59907	+	1.16179i
$986$	−0.431959	+	1.32943i	−0.0137564	+	0.0423378i
$987$		0			0
$988$	−33.8745	+	24.6113i	−1.07769	+	0.782989i
$989$	−0.580083			−0.0184456
$990$		0			0
$991$	−18.9911			−0.603272			−0.301636	−	0.953423i	$-0.597533\pi$
$991$	−18.9911			−0.603272			−0.301636	+	0.953423i	$0.597533\pi$
$992$	28.8122	−	20.9333i	0.914788	−	0.664633i
$993$		0			0
$994$	−1.81234	+	5.57782i	−0.0574841	+	0.176918i
$995$	−32.2938	−	23.4628i	−1.02378	−	0.743822i
$996$		0			0
$997$	6.83334	−	21.0309i	0.216414	−	0.666054i	−0.782636	−	0.622480i	$-0.786125\pi$
$997$	6.83334	−	21.0309i	0.216414	−	0.666054i	0.999050	−	0.0435746i	$-0.0138746\pi$
$998$	3.58956	+	11.0475i	0.113625	+	0.349703i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	891.2.f.e.487.6		36
3.2	odd	2		891.2.f.f.487.4		36
9.2	odd	6		99.2.m.b.58.6	yes	72
9.4	even	3		297.2.n.b.289.6		72
9.5	odd	6		99.2.m.b.25.4	yes	72
9.7	even	3		297.2.n.b.91.4		72
11.2	odd	10		9801.2.a.cn.1.11		18
11.4	even	5	inner	891.2.f.e.730.6		36
11.9	even	5		9801.2.a.cp.1.8		18
33.2	even	10		9801.2.a.co.1.8		18
33.20	odd	10		9801.2.a.cm.1.11		18
33.26	odd	10		891.2.f.f.730.4		36
99.2	even	30		1089.2.e.o.364.11		36
99.4	even	15		297.2.n.b.235.4		72
99.20	odd	30		1089.2.e.p.364.8		36
99.59	odd	30		99.2.m.b.70.6	yes	72
99.68	even	30		1089.2.e.o.727.11		36
99.70	even	15		297.2.n.b.37.6		72
99.86	odd	30		1089.2.e.p.727.8		36
99.92	odd	30		99.2.m.b.4.4	✓	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
99.2.m.b.4.4	✓	72	99.92	odd	30
99.2.m.b.25.4	yes	72	9.5	odd	6
99.2.m.b.58.6	yes	72	9.2	odd	6
99.2.m.b.70.6	yes	72	99.59	odd	30
297.2.n.b.37.6		72	99.70	even	15
297.2.n.b.91.4		72	9.7	even	3
297.2.n.b.235.4		72	99.4	even	15
297.2.n.b.289.6		72	9.4	even	3
891.2.f.e.487.6		36	1.1	even	1	trivial
891.2.f.e.730.6		36	11.4	even	5	inner
891.2.f.f.487.4		36	3.2	odd	2
891.2.f.f.730.4		36	33.26	odd	10
1089.2.e.o.364.11		36	99.2	even	30
1089.2.e.o.727.11		36	99.68	even	30
1089.2.e.p.364.8		36	99.20	odd	30
1089.2.e.p.727.8		36	99.86	odd	30
9801.2.a.cm.1.11		18	33.20	odd	10
9801.2.a.cn.1.11		18	11.2	odd	10
9801.2.a.co.1.8		18	33.2	even	10
9801.2.a.cp.1.8		18	11.9	even	5

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.f (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.467460 - 0.339629i) q^{2} +(-0.514863 + 1.58459i) q^{4} +(2.43063 + 1.76596i) q^{5} +(-0.359795 + 1.10733i) q^{7} +(0.654602 + 2.01466i) q^{8} +1.73599 q^{10} +(-3.11301 + 1.14420i) q^{11} +(3.19252 - 2.31950i) q^{13} +(0.207894 + 0.639831i) q^{14} +(-1.70562 - 1.23921i) q^{16} +(-0.254185 - 0.184677i) q^{17} +(1.96794 + 6.05670i) q^{19} +(-4.04976 + 2.94232i) q^{20} +(-1.06660 + 1.59213i) q^{22} +0.0855002 q^{23} +(1.24428 + 3.82951i) q^{25} +(0.704604 - 2.16855i) q^{26} +(-1.56942 - 1.14025i) q^{28} +(2.37938 - 7.32296i) q^{29} +(-5.28194 + 3.83755i) q^{31} -5.45485 q^{32} -0.181543 q^{34} +(-2.83004 + 2.05614i) q^{35} +(-1.92922 + 5.93753i) q^{37} +(2.97697 + 2.16289i) q^{38} +(-1.96670 + 6.05289i) q^{40} +(-1.79510 - 5.52475i) q^{41} -6.78458 q^{43} +(-0.210303 - 5.52194i) q^{44} +(0.0399679 - 0.0290384i) q^{46} +(0.101276 + 0.311695i) q^{47} +(4.56638 + 3.31767i) q^{49} +(1.88227 + 1.36755i) q^{50} +(2.03174 + 6.25305i) q^{52} +(-1.96000 + 1.42402i) q^{53} +(-9.58718 - 2.71632i) q^{55} -2.46642 q^{56} +(-1.37483 - 4.23130i) q^{58} +(0.709513 - 2.18366i) q^{59} +(11.0732 + 8.04513i) q^{61} +(-1.16575 + 3.58780i) q^{62} +(0.861321 - 0.625787i) q^{64} +11.8560 q^{65} +11.6798 q^{67} +(0.423507 - 0.307696i) q^{68} +(-0.624602 + 1.92233i) q^{70} +(7.05272 + 5.12410i) q^{71} +(0.910538 - 2.80235i) q^{73} +(1.11473 + 3.43078i) q^{74} -10.6106 q^{76} +(-0.146963 - 3.85882i) q^{77} +(7.18989 - 5.22376i) q^{79} +(-1.95735 - 6.02412i) q^{80} +(-2.71551 - 1.97293i) q^{82} +(4.01093 + 2.91411i) q^{83} +(-0.291701 - 0.897762i) q^{85} +(-3.17152 + 2.30424i) q^{86} +(-4.34294 - 5.52265i) q^{88} -2.12862 q^{89} +(1.41981 + 4.36973i) q^{91} +(-0.0440209 + 0.135482i) q^{92} +(0.153203 + 0.111309i) q^{94} +(-5.91254 + 18.1969i) q^{95} +(0.0718724 - 0.0522184i) q^{97} +3.26138 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - q^{2} - 11 q^{4} - 8 q^{5} + 2 q^{7} - 3 q^{8} - 4 q^{10} - 2 q^{11} + 11 q^{13} - 10 q^{14} + 9 q^{16} + 10 q^{17} + 4 q^{19} - 45 q^{20} + 16 q^{22} + 20 q^{23} - 11 q^{25} + 6 q^{26} - 27 q^{28}+ \cdots + 164 q^{98}+O(q^{100}) \) 36 * q - q^2 - 11 * q^4 - 8 * q^5 + 2 * q^7 - 3 * q^8 - 4 * q^10 - 2 * q^11 + 11 * q^13 - 10 * q^14 + 9 * q^16 + 10 * q^17 + 4 * q^19 - 45 * q^20 + 16 * q^22 + 20 * q^23 - 11 * q^25 + 6 * q^26 - 27 * q^28 - 23 * q^29 - 3 * q^31 + 18 * q^32 - 8 * q^34 - 9 * q^35 - 21 * q^37 - q^38 + 25 * q^40 + 10 * q^41 + 8 * q^43 - 19 * q^44 - 9 * q^46 - 34 * q^47 - q^49 + 27 * q^52 - 2 * q^53 + 9 * q^55 + 114 * q^56 - q^58 - 16 * q^59 + 3 * q^61 - 92 * q^62 + 13 * q^64 + 84 * q^65 - 10 * q^67 - 23 * q^68 + 46 * q^70 + 24 * q^71 - 20 * q^73 + 68 * q^74 - 16 * q^76 - 26 * q^77 - 19 * q^79 + 28 * q^80 + 47 * q^82 + 7 * q^83 - 25 * q^85 - 77 * q^86 - 18 * q^88 + 28 * q^89 + 10 * q^91 + 50 * q^92 + 63 * q^94 - 77 * q^95 + 33 * q^97 + 164 * q^98

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