LMFDB - Embedded newform 891.2.f.f.487.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [891,2,Mod(82,891)]

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

lf = mfeigenbasis(mf)

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")

//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: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$7.11467082010$
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			487.4
Character	$\chi$	$=$	891.487
Dual form			891.2.f.f.730.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.467460 + 0.339629i) q^{2} +(-0.514863 + 1.58459i) q^{4} +(-2.43063 - 1.76596i) q^{5} +(-0.359795 + 1.10733i) q^{7} +(-0.654602 - 2.01466i) q^{8} +1.73599 q^{10} +(3.11301 - 1.14420i) q^{11} +(3.19252 - 2.31950i) q^{13} +(-0.207894 - 0.639831i) q^{14} +(-1.70562 - 1.23921i) q^{16} +(0.254185 + 0.184677i) q^{17} +(1.96794 + 6.05670i) q^{19} +(4.04976 - 2.94232i) q^{20} +(-1.06660 + 1.59213i) q^{22} -0.0855002 q^{23} +(1.24428 + 3.82951i) q^{25} +(-0.704604 + 2.16855i) q^{26} +(-1.56942 - 1.14025i) q^{28} +(-2.37938 + 7.32296i) q^{29} +(-5.28194 + 3.83755i) q^{31} +5.45485 q^{32} -0.181543 q^{34} +(2.83004 - 2.05614i) q^{35} +(-1.92922 + 5.93753i) q^{37} +(-2.97697 - 2.16289i) q^{38} +(-1.96670 + 6.05289i) q^{40} +(1.79510 + 5.52475i) q^{41} -6.78458 q^{43} +(0.210303 + 5.52194i) q^{44} +(0.0399679 - 0.0290384i) q^{46} +(-0.101276 - 0.311695i) q^{47} +(4.56638 + 3.31767i) q^{49} +(-1.88227 - 1.36755i) q^{50} +(2.03174 + 6.25305i) q^{52} +(1.96000 - 1.42402i) q^{53} +(-9.58718 - 2.71632i) q^{55} +2.46642 q^{56} +(-1.37483 - 4.23130i) q^{58} +(-0.709513 + 2.18366i) q^{59} +(11.0732 + 8.04513i) q^{61} +(1.16575 - 3.58780i) q^{62} +(0.861321 - 0.625787i) q^{64} -11.8560 q^{65} +11.6798 q^{67} +(-0.423507 + 0.307696i) q^{68} +(-0.624602 + 1.92233i) q^{70} +(-7.05272 - 5.12410i) q^{71} +(0.910538 - 2.80235i) q^{73} +(-1.11473 - 3.43078i) q^{74} -10.6106 q^{76} +(0.146963 + 3.85882i) q^{77} +(7.18989 - 5.22376i) q^{79} +(1.95735 + 6.02412i) q^{80} +(-2.71551 - 1.97293i) q^{82} +(-4.01093 - 2.91411i) q^{83} +(-0.291701 - 0.897762i) q^{85} +(3.17152 - 2.30424i) q^{86} +(-4.34294 - 5.52265i) q^{88} +2.12862 q^{89} +(1.41981 + 4.36973i) q^{91} +(0.0440209 - 0.135482i) q^{92} +(0.153203 + 0.111309i) q^{94} +(5.91254 - 18.1969i) q^{95} +(0.0718724 - 0.0522184i) q^{97} -3.26138 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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	−0.740661	−	0.671878i	$-0.765488\pi$
$2$	−0.467460	+	0.339629i	−0.330544	+	0.240154i	0.410117	+	0.912033i	$0.365488\pi$
$3$		0			0
$3$		0			0
$4$	−0.514863	+	1.58459i	−0.257432	+	0.792293i
$5$	−2.43063	−	1.76596i	−1.08701	−	0.789761i	−0.108120	−	0.994138i	$-0.534483\pi$
$5$	−2.43063	−	1.76596i	−1.08701	−	0.789761i	−0.978892	+	0.204377i	$0.934483\pi$
$6$		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	0.618183	−	0.786034i	$-0.287869\pi$
$17$	0.254185	+	0.184677i	0.0616490	+	0.0447906i	−0.556534	+	0.830825i	$0.687869\pi$
$18$		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	$-0.502837\pi$
$23$	−0.0855002			−0.0178280			−0.00891401	+	0.999960i	$0.502837\pi$
$24$		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	$0.353532\pi$
$29$	−2.37938	+	7.32296i	−0.441839	+	1.35984i	−0.885914	+	0.463850i	$0.846468\pi$
$30$		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	$0.0498649\pi$
$41$	1.79510	+	5.52475i	0.280348	+	0.862822i	−0.707407	+	0.706807i	$0.750135\pi$
$42$		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	0.943398	−	0.331661i	$-0.107609\pi$
$47$	−0.101276	−	0.311695i	−0.0147726	−	0.0454654i	−0.958171	+	0.286196i	$0.907609\pi$
$48$		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	−0.444978	−	0.895541i	$-0.646789\pi$
$53$	1.96000	−	1.42402i	0.269227	−	0.195605i	0.714205	+	0.699937i	$0.246789\pi$
$54$		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	−0.986560	−	0.163402i	$-0.947753\pi$
$59$	−0.709513	+	2.18366i	−0.0923707	+	0.284288i	0.894189	+	0.447690i	$0.147753\pi$
$60$		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	0.0845279	−	0.996421i	$-0.473062\pi$
$71$	−7.05272	−	5.12410i	−0.837004	−	0.608119i	−0.921532	+	0.388302i	$0.873062\pi$
$72$		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	0.345480	−	0.938426i	$-0.387716\pi$
$83$	−4.01093	−	2.91411i	−0.440257	−	0.319865i	−0.785737	+	0.618561i	$0.787716\pi$
$84$		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	$-0.464013\pi$
$89$	2.12862			0.225634			0.112817	+	0.993616i	$0.464013\pi$
$90$		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	−0.501927	−	0.864910i	$-0.667375\pi$
$101$	1.66373	−	1.20877i	0.165547	−	0.120277i	0.667474	+	0.744633i	$0.267375\pi$
$102$		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	$0.0968290\pi$
$107$	3.70600	+	11.4059i	0.358272	+	1.10265i	−0.595815	+	0.803121i	$0.703171\pi$
$108$		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	$0.259672\pi$
$113$	5.94164	+	18.2865i	0.558943	+	1.72025i	−0.126355	+	0.991985i	$0.540328\pi$
$114$		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	$-0.787389\pi$
$131$	−17.9718			−1.57020			−0.785100	+	0.619369i	$0.787389\pi$
$132$		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	0.986225	−	0.165409i	$-0.0528945\pi$
$137$	13.2693	+	9.64070i	1.13367	+	0.823661i	0.147447	+	0.989070i	$0.452895\pi$
$138$		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	0.727745	−	0.685848i	$-0.240569\pi$
$149$	3.66623	+	2.66368i	0.300350	+	0.218217i	−0.427395	+	0.904065i	$0.640569\pi$
$150$		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	−0.419395	−	0.907804i	$-0.637758\pi$
$167$	4.06266	−	2.95170i	0.314378	−	0.228409i	0.733773	+	0.679395i	$0.237758\pi$
$168$		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	$-0.898087\pi$
$173$	−4.81753	−	14.8268i	−0.366270	−	1.12726i	0.582912	−	0.812536i	$-0.301913\pi$
$174$		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	0.998868	−	0.0475668i	$-0.0151467\pi$
$179$	2.17822	+	6.70387i	0.162808	+	0.501071i	−0.836060	+	0.548638i	$0.815147\pi$
$180$		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	$0.240690\pi$
$191$	−3.65350	+	11.2443i	−0.264358	+	0.813611i	−0.991841	+	0.127484i	$0.959310\pi$
$192$		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	$-0.763069\pi$
$197$	−20.6474			−1.47107			−0.735534	+	0.677488i	$0.763069\pi$
$198$		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	$-0.696035\pi$
$227$	5.56664	−	17.1324i	0.369471	−	1.13711i	0.947134	−	0.320839i	$-0.103965\pi$
$228$		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	−0.494897	−	0.868952i	$-0.664794\pi$
$233$	2.72611	−	1.98063i	0.178593	−	0.129756i	0.673490	+	0.739196i	$0.264794\pi$
$234$		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	$-0.829939\pi$
$239$	−7.16820	−	22.0615i	−0.463673	−	1.42704i	0.396972	−	0.917831i	$-0.370061\pi$
$240$		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	−0.572818	−	0.819682i	$-0.694150\pi$
$251$	0.471095	−	0.342271i	0.0297353	−	0.0216039i	0.602554	+	0.798078i	$0.294150\pi$
$252$		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	$0.211168\pi$
$257$	−3.39036	+	10.4344i	−0.211485	+	0.650883i	−0.999385	+	0.0350793i	$0.988832\pi$
$258$		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	$-0.646380\pi$
$263$	−14.3954			−0.887656			−0.443828	+	0.896112i	$0.646380\pi$
$264$		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	0.575660	−	0.817689i	$-0.304745\pi$
$269$	−0.395590	−	0.287413i	−0.0241195	−	0.0175239i	−0.599780	+	0.800165i	$0.704745\pi$
$270$		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	0.0552299	−	0.998474i	$-0.482411\pi$
$281$	−14.7064	−	10.6848i	−0.877308	−	0.637402i	−0.932538	+	0.361072i	$0.882411\pi$
$282$		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	−0.942993	−	0.332813i	$-0.892002\pi$
$293$	0.265775	−	0.817972i	0.0155268	−	0.0477864i	0.958520	+	0.285026i	$0.0920023\pi$
$294$		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	0.999999	−	0.00160485i	$-0.000510839\pi$
$311$	3.35138	+	10.3145i	0.190039	+	0.584881i	−0.809959	+	0.586486i	$0.800511\pi$
$312$		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	−0.562222	−	0.826986i	$-0.690053\pi$
$317$	0.900053	−	0.653927i	0.0505520	−	0.0367282i	0.612774	+	0.790258i	$0.290053\pi$
$318$		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	0.355859	−	0.934540i	$-0.384188\pi$
$347$	−7.87915	−	5.72454i	−0.422975	−	0.307309i	−0.778834	+	0.627230i	$0.784188\pi$
$348$		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	$-0.166984\pi$
$353$	32.5235			1.73105			0.865527	+	0.500863i	$0.166984\pi$
$354$		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	$0.361799\pi$
$359$	−8.58143	+	26.4109i	−0.452911	+	1.39392i	−0.873571	+	0.486697i	$0.838201\pi$
$360$		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	−0.708393	−	0.705818i	$-0.750580\pi$
$383$	−5.01052	+	3.64036i	−0.256026	+	0.186014i	0.452367	+	0.891832i	$0.350580\pi$
$384$		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	−0.956562	−	0.291528i	$-0.905836\pi$
$389$	−0.223485	+	0.687817i	−0.0113312	+	0.0348737i	0.945231	+	0.326402i	$0.105836\pi$
$390$		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	0.695970	−	0.718071i	$-0.254974\pi$
$401$	4.56793	+	3.31879i	0.228111	+	0.165733i	−0.467859	+	0.883803i	$0.654974\pi$
$402$		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	$-0.498822\pi$
$419$	0.151564			0.00740438			0.00370219	+	0.999993i	$0.498822\pi$
$420$		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	0.0289998	−	0.999579i	$-0.490768\pi$
$431$	20.5242	−	14.9117i	0.988618	−	0.718273i	0.959618	+	0.281307i	$0.0907678\pi$
$432$		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	$0.177104\pi$
$443$	9.94706	+	30.6139i	0.472599	+	1.45451i	−0.376570	+	0.926388i	$0.622896\pi$
$444$		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	0.0275281	−	0.999621i	$-0.491236\pi$
$449$	20.9085	−	15.1909i	0.986731	−	0.716902i	0.959203	+	0.282719i	$0.0912364\pi$
$450$		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	$-0.646073\pi$
$461$	−19.0217			−0.885931			−0.442965	+	0.896539i	$0.646073\pi$
$462$		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	0.248392	−	0.968660i	$-0.420098\pi$
$467$	−12.8819	−	9.35921i	−0.596101	−	0.433093i	−0.844493	+	0.535567i	$0.820098\pi$
$468$		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	0.847952	−	0.530073i	$-0.177836\pi$
$479$	13.2598	+	9.63378i	0.605854	+	0.440179i	−0.242098	+	0.970252i	$0.577836\pi$
$480$		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	$0.544413\pi$
$491$	−13.4864	+	41.5070i	−0.608634	+	1.87318i	−0.469558	+	0.882901i	$0.655587\pi$
$492$		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	0.850994	−	0.525176i	$-0.176000\pi$
$503$	−3.27815	−	10.0891i	−0.146165	−	0.449850i	−0.997159	+	0.0753254i	$0.976000\pi$
$504$		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	$-0.654248\pi$
$509$	−13.7415	−	42.2919i	−0.609080	−	1.87456i	−0.143240	−	0.989688i	$-0.545752\pi$
$510$		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	$-0.778905\pi$
$521$	5.23819	−	16.1215i	0.229489	−	0.706296i	0.997805	−	0.0662243i	$-0.0210953\pi$
$522$		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	−0.867519	−	0.497404i	$-0.834287\pi$
$557$	2.98987	−	9.20189i	0.126685	−	0.389896i	0.994204	+	0.107507i	$0.0342868\pi$
$558$		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	−0.0982327	−	0.995163i	$-0.531319\pi$
$563$	19.4061	−	14.0993i	0.817868	−	0.594216i	0.916101	+	0.400947i	$0.131319\pi$
$564$		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	$-0.810838\pi$
$569$	−11.6249	−	35.7779i	−0.487343	−	1.49989i	0.341215	−	0.939985i	$-0.389162\pi$
$570$		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	−0.965734	−	0.259534i	$-0.916431\pi$
$587$	−0.772594	+	2.37780i	−0.0318884	+	0.0981424i	0.933846	+	0.357677i	$0.116431\pi$
$588$		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	$-0.571816\pi$
$593$	−10.8953			−0.447417			−0.223708	+	0.974656i	$0.571816\pi$
$594$		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	0.995907	−	0.0903802i	$-0.0288082\pi$
$599$	29.8026	+	21.6529i	1.21770	+	0.884713i	0.221796	+	0.975093i	$0.428808\pi$
$600$		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	$-0.180627\pi$
$617$	41.8928			1.68654			0.843271	+	0.537489i	$0.180627\pi$
$618$		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	0.998327	−	0.0578142i	$-0.0184131\pi$
$641$	3.96685	+	12.2087i	0.156681	+	0.482215i	−0.841646	+	0.540029i	$0.818413\pi$
$642$		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	−0.273717	−	0.961810i	$-0.588253\pi$
$647$	14.1536	−	10.2832i	0.556436	−	0.404274i	0.830153	+	0.557536i	$0.188253\pi$
$648$		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	$0.294353\pi$
$653$	−9.05488	+	27.8681i	−0.354345	+	1.09056i	−0.956388	+	0.292098i	$0.905647\pi$
$654$		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	$-0.319437\pi$
$659$	27.5870			1.07464			0.537319	+	0.843379i	$0.319437\pi$
$660$		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	0.589310	−	0.807907i	$-0.299400\pi$
$677$	0.0793768	+	0.0576706i	0.00305070	+	0.00221646i	−0.586259	+	0.810124i	$0.699400\pi$
$678$		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	$-0.301488\pi$
$683$	30.5246			1.16799			0.583996	+	0.811756i	$0.301488\pi$
$684$		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	0.886927	−	0.461909i	$-0.152835\pi$
$701$	−2.70365	−	8.32098i	−0.102115	−	0.314279i	−0.989043	+	0.147630i	$0.952835\pi$
$702$		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	−0.999532	−	0.0305782i	$-0.990265\pi$
$719$	−4.63672	+	14.2703i	−0.172920	+	0.532194i	0.826612	+	0.562772i	$0.190265\pi$
$720$		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	0.823711	−	0.567010i	$-0.191900\pi$
$743$	14.6919	+	10.6743i	0.538993	+	0.391601i	−0.284718	+	0.958611i	$0.591900\pi$
$744$		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	−0.0293374	−	0.999570i	$-0.509340\pi$
$761$	25.1654	−	18.2837i	0.912244	−	0.662784i	0.941581	+	0.336786i	$0.109340\pi$
$762$		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	0.855182	−	0.518327i	$-0.173445\pi$
$773$	−3.92965	−	12.0942i	−0.141340	−	0.434999i	−0.996522	+	0.0833281i	$0.973445\pi$
$774$		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	−0.0448149	−	0.998995i	$-0.514270\pi$
$797$	−28.4786	−	20.6909i	−1.00876	−	0.732910i	−0.963950	+	0.266085i	$0.914270\pi$
$798$		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	0.825096	−	0.564992i	$-0.191121\pi$
$809$	15.4367	+	11.2154i	0.542725	+	0.394313i	−0.282371	+	0.959305i	$0.591121\pi$
$810$		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	$-0.697764\pi$
$821$	10.5092	−	32.3440i	0.366774	−	1.12881i	0.948863	−	0.315689i	$-0.102236\pi$
$822$		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	−0.789949	−	0.613172i	$-0.789893\pi$
$827$	−12.9667	+	9.42084i	−0.450895	+	0.327595i	0.339054	+	0.940767i	$0.389893\pi$
$828$		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	0.958680	−	0.284488i	$-0.0918235\pi$
$839$	0.459793	+	1.41510i	0.0158738	+	0.0488545i	−0.942806	+	0.333342i	$0.891824\pi$
$840$		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	$-0.390034\pi$
$857$	19.8270			0.677276			0.338638	+	0.940917i	$0.390034\pi$
$858$		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	0.470218	−	0.882550i	$-0.344175\pi$
$863$	−6.57548	−	4.77736i	−0.223832	−	0.162623i	−0.694050	+	0.719927i	$0.744175\pi$
$864$		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	$-0.794456\pi$
$881$	−47.4109			−1.59731			−0.798657	+	0.601786i	$0.794456\pi$
$882$		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	$0.396751\pi$
$887$	−14.7801	+	45.4884i	−0.496266	+	1.52735i	−0.814974	+	0.579498i	$0.803249\pi$
$888$		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	−0.137457	−	0.990508i	$-0.543893\pi$
$911$	23.0022	−	16.7120i	0.762095	−	0.553695i	0.899552	+	0.436813i	$0.143893\pi$
$912$		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	0.395761	−	0.918354i	$-0.370481\pi$
$929$	−10.8309	−	7.86907i	−0.355349	−	0.258176i	−0.751109	+	0.660178i	$0.770481\pi$
$930$		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	0.472899	−	0.881116i	$-0.343207\pi$
$941$	−6.71670	−	4.87997i	−0.218958	−	0.159082i	−0.691858	+	0.722034i	$0.743207\pi$
$942$		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	$-0.288510\pi$
$947$	37.9496			1.23320			0.616598	+	0.787278i	$0.288510\pi$
$948$		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	$0.389037\pi$
$953$	−15.0400	+	46.2884i	−0.487194	+	1.49943i	−0.828778	+	0.559578i	$0.810963\pi$
$954$		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	0.994702	−	0.102796i	$-0.0327789\pi$
$971$	4.03687	+	12.4242i	0.129549	+	0.398712i	−0.865153	+	0.501508i	$0.832779\pi$
$972$		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	−0.435143	−	0.900361i	$-0.643302\pi$
$977$	8.96092	−	6.51049i	0.286685	−	0.208289i	0.721828	+	0.692072i	$0.243302\pi$
$978$		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	$0.238502\pi$
$983$	−8.16778	+	25.1378i	−0.260512	+	0.801772i	−0.992693	+	0.120663i	$0.961498\pi$
$984$		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.f.487.4		36
3.2	odd	2		891.2.f.e.487.6		36
9.2	odd	6		297.2.n.b.91.4		72
9.4	even	3		99.2.m.b.25.4	yes	72
9.5	odd	6		297.2.n.b.289.6		72
9.7	even	3		99.2.m.b.58.6	yes	72
11.2	odd	10		9801.2.a.co.1.8		18
11.4	even	5	inner	891.2.f.f.730.4		36
11.9	even	5		9801.2.a.cm.1.11		18
33.2	even	10		9801.2.a.cn.1.11		18
33.20	odd	10		9801.2.a.cp.1.8		18
33.26	odd	10		891.2.f.e.730.6		36
99.4	even	15		99.2.m.b.70.6	yes	72
99.13	odd	30		1089.2.e.o.727.11		36
99.31	even	15		1089.2.e.p.727.8		36
99.59	odd	30		297.2.n.b.235.4		72
99.70	even	15		99.2.m.b.4.4	✓	72
99.79	odd	30		1089.2.e.o.364.11		36
99.92	odd	30		297.2.n.b.37.6		72
99.97	even	15		1089.2.e.p.364.8		36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
99.2.m.b.4.4	✓	72	99.70	even	15
99.2.m.b.25.4	yes	72	9.4	even	3
99.2.m.b.58.6	yes	72	9.7	even	3
99.2.m.b.70.6	yes	72	99.4	even	15
297.2.n.b.37.6		72	99.92	odd	30
297.2.n.b.91.4		72	9.2	odd	6
297.2.n.b.235.4		72	99.59	odd	30
297.2.n.b.289.6		72	9.5	odd	6
891.2.f.e.487.6		36	3.2	odd	2
891.2.f.e.730.6		36	33.26	odd	10
891.2.f.f.487.4		36	1.1	even	1	trivial
891.2.f.f.730.4		36	11.4	even	5	inner
1089.2.e.o.364.11		36	99.79	odd	30
1089.2.e.o.727.11		36	99.13	odd	30
1089.2.e.p.364.8		36	99.97	even	15
1089.2.e.p.727.8		36	99.31	even	15
9801.2.a.cm.1.11		18	11.9	even	5
9801.2.a.cn.1.11		18	33.2	even	10
9801.2.a.co.1.8		18	11.2	odd	10
9801.2.a.cp.1.8		18	33.20	odd	10

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 891 = 3^{4} \cdot 11 \)
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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