LMFDB - Embedded newform 1008.2.cz.g.367.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1008,2,Mod(367,1008)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1008, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 0, 4, 1])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1008.367"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 1008 = 2^{4} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1008.cz (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [24,0,-3,0,-3,0,4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$8.04892052375$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			367.1
Character	$\chi$	$=$	1008.367
Dual form			1008.2.cz.g.607.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.72726 + 0.128734i) q^{3} +(2.43562 + 1.40621i) q^{5} +(-0.717569 + 2.54659i) q^{7} +(2.96686 - 0.444713i) q^{9} +(2.29039 - 1.32236i) q^{11} +(4.59264 - 2.65156i) q^{13} +(-4.38797 - 2.11534i) q^{15} +(-2.35660 - 1.36058i) q^{17} +(0.274171 + 0.474878i) q^{19} +(0.911596 - 4.49099i) q^{21} +(1.98081 + 1.14362i) q^{23} +(1.45483 + 2.51983i) q^{25} +(-5.06728 + 1.15007i) q^{27} +(-3.72965 + 6.45995i) q^{29} +2.76772 q^{31} +(-3.78587 + 2.57891i) q^{33} +(-5.32874 + 5.19346i) q^{35} +(1.81274 + 3.13976i) q^{37} +(-7.59134 + 5.17117i) q^{39} +(7.12184 - 4.11180i) q^{41} +(-3.93586 - 2.27237i) q^{43} +(7.85149 + 3.08886i) q^{45} +11.2264 q^{47} +(-5.97019 - 3.65470i) q^{49} +(4.24562 + 2.04671i) q^{51} +(-2.53317 + 4.38758i) q^{53} +7.43804 q^{55} +(-0.534697 - 0.784943i) q^{57} +3.35948 q^{59} +14.4210i q^{61} +(-0.996422 + 7.87446i) q^{63} +14.9146 q^{65} +10.8513i q^{67} +(-3.56860 - 1.72034i) q^{69} -12.7616i q^{71} +(4.29405 + 2.47917i) q^{73} +(-2.83725 - 4.16512i) q^{75} +(1.72399 + 6.78157i) q^{77} -5.61310i q^{79} +(8.60446 - 2.63880i) q^{81} +(-0.719239 + 1.24576i) q^{83} +(-3.82652 - 6.62773i) q^{85} +(5.61047 - 11.6381i) q^{87} +(3.24680 - 1.87454i) q^{89} +(3.45690 + 13.5982i) q^{91} +(-4.78058 + 0.356299i) q^{93} +1.54216i q^{95} +(-15.7452 - 9.09049i) q^{97} +(6.20720 - 4.94182i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 3 q^{3} - 3 q^{5} + 4 q^{7} + 17 q^{9} - 9 q^{11} - 3 q^{13} - 6 q^{15} - 3 q^{17} - 4 q^{19} + 13 q^{21} - 6 q^{23} + 15 q^{25} + 9 q^{27} + 18 q^{29} + 34 q^{31} - 21 q^{33} - 42 q^{35} - 3 q^{37}+ \cdots + 30 q^{99}+O(q^{100}) $ 24 * q - 3 * q^3 - 3 * q^5 + 4 * q^7 + 17 * q^9 - 9 * q^11 - 3 * q^13 - 6 * q^15 - 3 * q^17 - 4 * q^19 + 13 * q^21 - 6 * q^23 + 15 * q^25 + 9 * q^27 + 18 * q^29 + 34 * q^31 - 21 * q^33 - 42 * q^35 - 3 * q^37 + 27 * q^39 + 36 * q^41 + 24 * q^43 + 21 * q^45 - 42 * q^47 + 30 * q^49 - 6 * q^51 - 12 * q^53 - 30 * q^55 - 13 * q^57 - 12 * q^59 - 3 * q^63 + 6 * q^69 + 48 * q^73 + 36 * q^75 - 48 * q^77 - 31 * q^81 - 48 * q^83 - 21 * q^85 + 15 * q^87 + 39 * q^89 + 9 * q^91 + 10 * q^93 + 3 * q^97 + 30 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1008\mathbb{Z}\right)^\times$.

$n$	$127$	$577$	$757$	$785$
$\chi(n)$	$-1$	$e\left(\frac{1}{6}\right)$	$1$	$e\left(\frac{2}{3}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	−1.72726	+	0.128734i	−0.997234	+	0.0743244i
$3$	−1.72726	+	0.128734i	−0.997234	+	0.0743244i
$4$		0			0
$5$	2.43562	+	1.40621i	1.08924	+	0.628874i	0.933374	−	0.358904i	$-0.116849\pi$
$5$	2.43562	+	1.40621i	1.08924	+	0.628874i	0.155867	+	0.987778i	$0.450183\pi$
$6$		0			0
$7$	−0.717569	+	2.54659i	−0.271215	+	0.962519i
$7$	−0.717569	+	2.54659i	−0.271215	+	0.962519i
$8$		0			0
$9$	2.96686	−	0.444713i	0.988952	−	0.148238i
$10$		0			0
$11$	2.29039	−	1.32236i	0.690580	−	0.398706i	−0.113249	−	0.993567i	$-0.536126\pi$
$11$	2.29039	−	1.32236i	0.690580	−	0.398706i	0.803829	+	0.594860i	$0.202793\pi$
$12$		0			0
$13$	4.59264	−	2.65156i	1.27377	−	0.735411i	0.298074	−	0.954543i	$-0.403656\pi$
$13$	4.59264	−	2.65156i	1.27377	−	0.735411i	0.975695	+	0.219131i	$0.0703223\pi$
$14$		0			0
$15$	−4.38797	−	2.11534i	−1.13297	−	0.546177i
$16$		0			0
$17$	−2.35660	−	1.36058i	−0.571560	−	0.329990i	0.186212	−	0.982510i	$-0.440379\pi$
$17$	−2.35660	−	1.36058i	−0.571560	−	0.329990i	−0.757772	+	0.652519i	$0.773712\pi$
$18$		0			0
$19$	0.274171	+	0.474878i	0.0628991	+	0.108944i	0.895760	−	0.444538i	$-0.146632\pi$
$19$	0.274171	+	0.474878i	0.0628991	+	0.108944i	−0.832861	+	0.553482i	$0.813299\pi$
$20$		0			0
$21$	0.911596	−	4.49099i	0.198927	−	0.980014i
$22$		0			0
$23$	1.98081	+	1.14362i	0.413028	+	0.238462i	0.692090	−	0.721811i	$-0.256690\pi$
$23$	1.98081	+	1.14362i	0.413028	+	0.238462i	−0.279062	+	0.960273i	$0.590023\pi$
$24$		0			0
$25$	1.45483	+	2.51983i	0.290965	+	0.503966i
$26$		0			0
$27$	−5.06728	+	1.15007i	−0.975199	+	0.221331i
$28$		0			0
$29$	−3.72965	+	6.45995i	−0.692579	+	1.19958i	0.278410	+	0.960462i	$0.410192\pi$
$29$	−3.72965	+	6.45995i	−0.692579	+	1.19958i	−0.970990	+	0.239121i	$0.923141\pi$
$30$		0			0
$31$	2.76772			0.497098			0.248549	−	0.968619i	$-0.420046\pi$
$31$	2.76772			0.497098			0.248549	+	0.968619i	$0.420046\pi$
$32$		0			0
$33$	−3.78587	+	2.57891i	−0.659036	+	0.448931i
$34$		0			0
$35$	−5.32874	+	5.19346i	−0.900722	+	0.877855i
$36$		0			0
$37$	1.81274	+	3.13976i	0.298013	+	0.516174i	0.975681	−	0.219194i	$-0.0703427\pi$
$37$	1.81274	+	3.13976i	0.298013	+	0.516174i	−0.677668	+	0.735368i	$0.737009\pi$
$38$		0			0
$39$	−7.59134	+	5.17117i	−1.21559	+	0.828049i
$40$		0			0
$41$	7.12184	−	4.11180i	1.11224	−	0.642155i	0.172835	−	0.984951i	$-0.444707\pi$
$41$	7.12184	−	4.11180i	1.11224	−	0.642155i	0.939410	+	0.342796i	$0.111374\pi$
$42$		0			0
$43$	−3.93586	−	2.27237i	−0.600213	−	0.346533i	0.168912	−	0.985631i	$-0.445975\pi$
$43$	−3.93586	−	2.27237i	−0.600213	−	0.346533i	−0.769125	+	0.639098i	$0.779308\pi$
$44$		0			0
$45$	7.85149	+	3.08886i	1.17043	+	0.460459i
$46$		0			0
$47$	11.2264			1.63754			0.818768	−	0.574124i	$-0.194657\pi$
$47$	11.2264			1.63754			0.818768	+	0.574124i	$0.194657\pi$
$48$		0			0
$49$	−5.97019	−	3.65470i	−0.852884	−	0.522100i
$50$		0			0
$51$	4.24562	+	2.04671i	0.594505	+	0.286597i
$52$		0			0
$53$	−2.53317	+	4.38758i	−0.347957	+	0.602680i	−0.985886	−	0.167415i	$-0.946458\pi$
$53$	−2.53317	+	4.38758i	−0.347957	+	0.602680i	0.637929	+	0.770095i	$0.279791\pi$
$54$		0			0
$55$	7.43804			1.00294
$56$		0			0
$57$	−0.534697	−	0.784943i	−0.0708224	−	0.103968i
$58$		0			0
$59$	3.35948			0.437367			0.218684	−	0.975796i	$-0.429824\pi$
$59$	3.35948			0.437367			0.218684	+	0.975796i	$0.429824\pi$
$60$		0			0
$61$			14.4210i			1.84642i	0.384294	+	0.923211i	$0.374445\pi$
$61$			14.4210i			1.84642i	−0.384294	+	0.923211i	$0.625555\pi$
$62$		0			0
$63$	−0.996422	+	7.87446i	−0.125537	+	0.992089i
$64$		0			0
$65$	14.9146			1.84992
$66$		0			0
$67$			10.8513i			1.32570i	0.748752	+	0.662851i	$0.230654\pi$
$67$			10.8513i			1.32570i	−0.748752	+	0.662851i	$0.769346\pi$
$68$		0			0
$69$	−3.56860	−	1.72034i	−0.429609	−	0.207104i
$70$		0			0
$71$		−	12.7616i		−	1.51453i	−0.653109	−	0.757263i	$-0.726536\pi$
$71$		−	12.7616i		−	1.51453i	0.653109	−	0.757263i	$-0.273464\pi$
$72$		0			0
$73$	4.29405	+	2.47917i	0.502581	+	0.290165i	0.729779	−	0.683684i	$-0.239623\pi$
$73$	4.29405	+	2.47917i	0.502581	+	0.290165i	−0.227198	+	0.973849i	$0.572956\pi$
$74$		0			0
$75$	−2.83725	−	4.16512i	−0.327617	−	0.480947i
$76$		0			0
$77$	1.72399	+	6.78157i	0.196467	+	0.772831i
$78$		0			0
$79$		−	5.61310i		−	0.631523i	−0.948839	−	0.315761i	$-0.897740\pi$
$79$		−	5.61310i		−	0.631523i	0.948839	−	0.315761i	$-0.102260\pi$
$80$		0			0
$81$	8.60446	−	2.63880i	0.956051	−	0.293200i
$82$		0			0
$83$	−0.719239	+	1.24576i	−0.0789467	+	0.136740i	−0.902796	−	0.430070i	$-0.858489\pi$
$83$	−0.719239	+	1.24576i	−0.0789467	+	0.136740i	0.823849	+	0.566809i	$0.191822\pi$
$84$		0			0
$85$	−3.82652	−	6.62773i	−0.415044	−	0.718878i
$86$		0			0
$87$	5.61047	−	11.6381i	0.601506	−	1.24774i
$88$		0			0
$89$	3.24680	−	1.87454i	0.344160	−	0.198701i	−0.317950	−	0.948107i	$-0.602994\pi$
$89$	3.24680	−	1.87454i	0.344160	−	0.198701i	0.662110	+	0.749407i	$0.269661\pi$
$90$		0			0
$91$	3.45690	+	13.5982i	0.362381	+	1.42548i
$92$		0			0
$93$	−4.78058	+	0.356299i	−0.495723	+	0.0369465i
$94$		0			0
$95$			1.54216i			0.158223i
$96$		0			0
$97$	−15.7452	−	9.09049i	−1.59868	−	0.922999i	−0.991742	−	0.128251i	$-0.959064\pi$
$97$	−15.7452	−	9.09049i	−1.59868	−	0.922999i	−0.606939	−	0.794748i	$-0.707603\pi$
$98$		0			0
$99$	6.20720	−	4.94182i	0.623847	−	0.496671i
$100$		0			0
$101$	2.36076	−	1.36298i	0.234904	−	0.135622i	−0.377928	−	0.925835i	$-0.623363\pi$
$101$	2.36076	−	1.36298i	0.234904	−	0.135622i	0.612832	+	0.790213i	$0.290030\pi$
$102$		0			0
$103$	−7.63868	+	13.2306i	−0.752661	+	1.30365i	0.193867	+	0.981028i	$0.437897\pi$
$103$	−7.63868	+	13.2306i	−0.752661	+	1.30365i	−0.946529	+	0.322620i	$0.895436\pi$
$104$		0			0
$105$	8.53555	−	9.65645i	0.832985	−	0.942373i
$106$		0			0
$107$	−3.60969	+	2.08406i	−0.348962	+	0.201473i	−0.664228	−	0.747530i	$-0.731240\pi$
$107$	−3.60969	+	2.08406i	−0.348962	+	0.201473i	0.315266	+	0.949003i	$0.397906\pi$
$108$		0			0
$109$	−3.62697	+	6.28209i	−0.347400	+	0.601715i	−0.985787	−	0.168001i	$-0.946269\pi$
$109$	−3.62697	+	6.28209i	−0.347400	+	0.601715i	0.638387	+	0.769716i	$0.279602\pi$
$110$		0			0
$111$	−3.53527	−	5.18983i	−0.335553	−	0.492597i
$112$		0			0
$113$	8.08514	+	14.0039i	0.760586	+	1.31737i	0.942549	+	0.334068i	$0.108421\pi$
$113$	8.08514	+	14.0039i	0.760586	+	1.31737i	−0.181963	+	0.983305i	$0.558245\pi$
$114$		0			0
$115$	3.21634	+	5.57086i	0.299925	+	0.519485i
$116$		0			0
$117$	12.4465	−	9.90921i	1.15068	−	0.916107i
$118$		0			0
$119$	5.15586	−	5.02497i	0.472637	−	0.460638i
$120$		0			0
$121$	−2.00273	+	3.46883i	−0.182066	+	0.315348i
$122$		0			0
$123$	−11.7719	+	8.01896i	−1.06144	+	0.723045i
$124$		0			0
$125$		−	5.87892i		−	0.525826i
$126$		0			0
$127$			22.0446i			1.95614i	0.208270	+	0.978071i	$0.433217\pi$
$127$			22.0446i			1.95614i	−0.208270	+	0.978071i	$0.566783\pi$
$128$		0			0
$129$	7.09078	+	3.41830i	0.624309	+	0.300964i
$130$		0			0
$131$	5.74098	−	9.94366i	0.501591	−	0.868782i	−0.498407	−	0.866943i	$-0.666081\pi$
$131$	5.74098	−	9.94366i	0.501591	−	0.868782i	0.999998	−	0.00183866i	$-0.000585263\pi$
$132$		0			0
$133$	−1.40605	+	0.357442i	−0.121920	+	0.0309942i
$134$		0			0
$135$	−13.9592	−	4.32451i	−1.20142	−	0.372194i
$136$		0			0
$137$	−0.234259	−	0.405749i	−0.0200141	−	0.0346655i	0.855845	−	0.517233i	$-0.173038\pi$
$137$	−0.234259	−	0.405749i	−0.0200141	−	0.0346655i	−0.875859	+	0.482567i	$0.839704\pi$
$138$		0			0
$139$	−1.46737	−	2.54156i	−0.124461	−	0.215572i	0.797061	−	0.603899i	$-0.206387\pi$
$139$	−1.46737	−	2.54156i	−0.124461	−	0.215572i	−0.921522	+	0.388326i	$0.873053\pi$
$140$		0			0
$141$	−19.3909	+	1.44521i	−1.63301	+	0.121709i
$142$		0			0
$143$	7.01264	−	12.1462i	0.586426	−	1.01572i
$144$		0			0
$145$	−18.1680	+	10.4893i	−1.50877	+	0.871091i
$146$		0			0
$147$	10.7826	+	5.54405i	0.889330	+	0.457266i
$148$		0			0
$149$	−0.0215175	+	0.0372695i	−0.00176279	+	0.00305323i	−0.866905	−	0.498473i	$-0.833894\pi$
$149$	−0.0215175	+	0.0372695i	−0.00176279	+	0.00305323i	0.865143	+	0.501526i	$0.167228\pi$
$150$		0			0
$151$	7.73688	−	4.46689i	0.629618	−	0.363510i	−0.150986	−	0.988536i	$-0.548245\pi$
$151$	7.73688	−	4.46689i	0.629618	−	0.363510i	0.780604	+	0.625026i	$0.214911\pi$
$152$		0			0
$153$	−7.59676	−	2.98864i	−0.614162	−	0.241618i
$154$		0			0
$155$	6.74112	+	3.89199i	0.541460	+	0.312612i
$156$		0			0
$157$		−	6.85048i		−	0.546728i	−0.961911	−	0.273364i	$-0.911864\pi$
$157$		−	6.85048i		−	0.546728i	0.961911	−	0.273364i	$-0.0881363\pi$
$158$		0			0
$159$	3.81061	−	7.90459i	0.302201	−	0.626875i
$160$		0			0
$161$	−4.33370	+	4.22368i	−0.341544	+	0.332873i
$162$		0			0
$163$	−11.9751	+	6.91382i	−0.937961	+	0.541532i	−0.889320	−	0.457285i	$-0.848822\pi$
$163$	−11.9751	+	6.91382i	−0.937961	+	0.541532i	−0.0486402	+	0.998816i	$0.515489\pi$
$164$		0			0
$165$	−12.8474	+	0.957525i	−1.00017	+	0.0745433i
$166$		0			0
$167$	−11.0194	−	19.0862i	−0.852710	−	1.47694i	−0.878754	−	0.477276i	$-0.841624\pi$
$167$	−11.0194	−	19.0862i	−0.852710	−	1.47694i	0.0260438	−	0.999661i	$-0.491709\pi$
$168$		0			0
$169$	7.56157	−	13.0970i	0.581660	−	1.00746i
$170$		0			0
$171$	1.02461	+	1.28697i	0.0783539	+	0.0984168i
$172$		0			0
$173$		−	13.6309i		−	1.03634i	−0.855279	−	0.518168i	$-0.826614\pi$
$173$		−	13.6309i		−	1.03634i	0.855279	−	0.518168i	$-0.173386\pi$
$174$		0			0
$175$	−7.46090	+	1.89669i	−0.563991	+	0.143376i
$176$		0			0
$177$	−5.80270	+	0.432478i	−0.436157	+	0.0325070i
$178$		0			0
$179$	−0.827409	−	0.477705i	−0.0618434	−	0.0357053i	0.468759	−	0.883326i	$-0.344701\pi$
$179$	−0.827409	−	0.477705i	−0.0618434	−	0.0357053i	−0.530603	+	0.847621i	$0.678034\pi$
$180$		0			0
$181$		−	17.0078i		−	1.26418i	−0.774896	−	0.632089i	$-0.782198\pi$
$181$		−	17.0078i		−	1.26418i	0.774896	−	0.632089i	$-0.217802\pi$
$182$		0			0
$183$	−1.85647	−	24.9088i	−0.137234	−	1.84131i
$184$		0			0
$185$			10.1964i			0.749651i
$186$		0			0
$187$	−7.19672			−0.526277
$188$		0			0
$189$	0.707373	−	13.7295i	0.0514538	−	0.998675i
$190$		0			0
$191$		−	6.56323i		−	0.474898i	−0.971400	−	0.237449i	$-0.923689\pi$
$191$		−	6.56323i		−	0.474898i	0.971400	−	0.237449i	$-0.0763113\pi$
$192$		0			0
$193$	−22.2982			−1.60506			−0.802531	−	0.596611i	$-0.796514\pi$
$193$	−22.2982			−1.60506			−0.802531	+	0.596611i	$0.796514\pi$
$194$		0			0
$195$	−25.7613	+	1.92001i	−1.84481	+	0.137495i
$196$		0			0
$197$	−17.0488			−1.21467			−0.607337	−	0.794444i	$-0.707762\pi$
$197$	−17.0488			−1.21467			−0.607337	+	0.794444i	$0.707762\pi$
$198$		0			0
$199$	9.52787	−	16.5028i	0.675413	−	1.16985i	−0.300935	−	0.953645i	$-0.597299\pi$
$199$	9.52787	−	16.5028i	0.675413	−	1.16985i	0.976348	−	0.216205i	$-0.0693679\pi$
$200$		0			0
$201$	−1.39693	−	18.7431i	−0.0985320	−	1.32203i
$202$		0			0
$203$	−13.7745	−	14.1333i	−0.966783	−	0.991966i
$204$		0			0
$205$	23.1281			1.61534
$206$		0			0
$207$	6.38537	+	2.51207i	0.443814	+	0.174601i
$208$		0			0
$209$	1.25592	+	0.725105i	0.0868737	+	0.0501566i
$210$		0			0
$211$	9.26806	−	5.35092i	0.638040	−	0.368372i	−0.145819	−	0.989311i	$-0.546582\pi$
$211$	9.26806	−	5.35092i	0.638040	−	0.368372i	0.783859	+	0.620939i	$0.213248\pi$
$212$		0			0
$213$	1.64285	+	22.0427i	0.112566	+	1.51034i
$214$		0			0
$215$	−6.39084	−	11.0693i	−0.435851	−	0.754917i
$216$		0			0
$217$	−1.98603	+	7.04824i	−0.134821	+	0.478466i
$218$		0			0
$219$	−7.73609	−	3.72938i	−0.522757	−	0.252008i
$220$		0			0
$221$	−14.4307			−0.970714
$222$		0			0
$223$	9.37765	−	16.2426i	0.627974	−	1.08768i	−0.359984	−	0.932959i	$-0.617218\pi$
$223$	9.37765	−	16.2426i	0.627974	−	1.08768i	0.987958	−	0.154724i	$-0.0494489\pi$
$224$		0			0
$225$	5.43686	+	6.82900i	0.362457	+	0.455266i
$226$		0			0
$227$	11.0322	+	19.1084i	0.732235	+	1.26827i	0.955926	+	0.293608i	$0.0948561\pi$
$227$	11.0322	+	19.1084i	0.732235	+	1.26827i	−0.223691	+	0.974660i	$0.571811\pi$
$228$		0			0
$229$	3.77115	+	2.17728i	0.249205	+	0.143878i	0.619400	−	0.785076i	$-0.287376\pi$
$229$	3.77115	+	2.17728i	0.249205	+	0.143878i	−0.370195	+	0.928954i	$0.620709\pi$
$230$		0			0
$231$	−3.85079	−	11.4916i	−0.253363	−	0.756091i
$232$		0			0
$233$	−11.9938	−	20.7738i	−0.785738	−	1.36094i	−0.928557	−	0.371189i	$-0.878950\pi$
$233$	−11.9938	−	20.7738i	−0.785738	−	1.36094i	0.142820	−	0.989749i	$-0.454383\pi$
$234$		0			0
$235$	27.3432	+	15.7866i	1.78367	+	1.02980i
$236$		0			0
$237$	0.722594	+	9.69528i	0.0469375	+	0.629776i
$238$		0			0
$239$	−5.03528	+	2.90712i	−0.325705	+	0.188046i	−0.653933	−	0.756553i	$-0.726882\pi$
$239$	−5.03528	+	2.90712i	−0.325705	+	0.188046i	0.328227	+	0.944599i	$0.393549\pi$
$240$		0			0
$241$	−19.7657	+	11.4117i	−1.27322	+	0.735094i	−0.975593	−	0.219589i	$-0.929528\pi$
$241$	−19.7657	+	11.4117i	−1.27322	+	0.735094i	−0.297627	+	0.954682i	$0.596195\pi$
$242$		0			0
$243$	−14.5224	+	5.66557i	−0.931615	+	0.363447i
$244$		0			0
$245$	−9.40185	−	17.2968i	−0.600662	−	1.10505i
$246$		0			0
$247$	2.51834	+	1.45396i	0.160238	+	0.0925135i
$248$		0			0
$249$	1.08194	−	2.24434i	0.0685653	−	0.142229i
$250$		0			0
$251$	11.8200			0.746073			0.373036	−	0.927817i	$-0.378317\pi$
$251$	11.8200			0.746073			0.373036	+	0.927817i	$0.378317\pi$
$252$		0			0
$253$	6.04912			0.380305
$254$		0			0
$255$	7.46261	+	10.9552i	0.467327	+	0.686042i
$256$		0			0
$257$	13.8901	+	8.01947i	0.866443	+	0.500241i	0.866165	−	0.499759i	$-0.166578\pi$
$257$	13.8901	+	8.01947i	0.866443	+	0.500241i	0.000278427		1.00000i	$0.499911\pi$
$258$		0			0
$259$	−9.29644	+	2.36331i	−0.577653	+	0.146849i
$260$		0			0
$261$	−8.19252	+	20.8244i	−0.507104	+	1.28900i
$262$		0			0
$263$	26.0915	−	15.0639i	1.60887	−	0.928880i	0.619244	−	0.785199i	$-0.287439\pi$
$263$	26.0915	−	15.0639i	1.60887	−	0.928880i	0.989624	−	0.143682i	$-0.0458942\pi$
$264$		0			0
$265$	−12.3397	+	7.12431i	−0.758019	+	0.437643i
$266$		0			0
$267$	−5.36675	+	3.65579i	−0.328440	+	0.223731i
$268$		0			0
$269$	2.95818	+	1.70791i	0.180363	+	0.104133i	0.587463	−	0.809251i	$-0.300127\pi$
$269$	2.95818	+	1.70791i	0.180363	+	0.104133i	−0.407100	+	0.913384i	$0.633460\pi$
$270$		0			0
$271$	−13.6039	−	23.5627i	−0.826381	−	1.43133i	−0.900859	−	0.434111i	$-0.857063\pi$
$271$	−13.6039	−	23.5627i	−0.826381	−	1.43133i	0.0744785	−	0.997223i	$-0.476271\pi$
$272$		0			0
$273$	−7.72151	−	23.0427i	−0.467327	−	1.39461i
$274$		0			0
$275$	6.66425	+	3.84761i	0.401869	+	0.232019i
$276$		0			0
$277$	−2.99541	−	5.18820i	−0.179977	−	0.311729i	0.761896	−	0.647700i	$-0.224269\pi$
$277$	−2.99541	−	5.18820i	−0.179977	−	0.311729i	−0.941872	+	0.335971i	$0.890936\pi$
$278$		0			0
$279$	8.21143	−	1.23084i	0.491606	−	0.0736886i
$280$		0			0
$281$	2.69154	−	4.66188i	0.160564	−	0.278105i	−0.774507	−	0.632565i	$-0.782002\pi$
$281$	2.69154	−	4.66188i	0.160564	−	0.278105i	0.935071	+	0.354460i	$0.115335\pi$
$282$		0			0
$283$	−3.48890			−0.207393			−0.103697	−	0.994609i	$-0.533067\pi$
$283$	−3.48890			−0.207393			−0.103697	+	0.994609i	$0.533067\pi$
$284$		0			0
$285$	−0.198528	−	2.66372i	−0.0117598	−	0.157785i
$286$		0			0
$287$	5.36063	+	21.0869i	0.316428	+	1.24472i
$288$		0			0
$289$	−4.79762	−	8.30973i	−0.282213	−	0.488807i
$290$		0			0
$291$	28.3663	+	13.6747i	1.66286	+	0.801625i
$292$		0			0
$293$	26.2148	−	15.1351i	1.53149	−	0.884205i	0.532194	−	0.846622i	$-0.321368\pi$
$293$	26.2148	−	15.1351i	1.53149	−	0.884205i	0.999294	−	0.0375823i	$-0.0119656\pi$
$294$		0			0
$295$	8.18241	+	4.72412i	0.476399	+	0.275049i
$296$		0			0
$297$	−10.0853	+	9.33488i	−0.585206	+	0.541665i
$298$		0			0
$299$	12.1296			0.701470
$300$		0			0
$301$	8.61103	−	8.39242i	0.496332	−	0.483731i
$302$		0			0
$303$	−3.90218	+	2.65814i	−0.224174	+	0.152706i
$304$		0			0
$305$	−20.2789	+	35.1241i	−1.16117	+	2.01120i
$306$		0			0
$307$	−15.5495			−0.887456			−0.443728	−	0.896162i	$-0.646344\pi$
$307$	−15.5495			−0.887456			−0.443728	+	0.896162i	$0.646344\pi$
$308$		0			0
$309$	11.4908	−	23.8360i	0.653687	−	1.35598i
$310$		0			0
$311$	18.7047			1.06065			0.530323	−	0.847796i	$-0.322071\pi$
$311$	18.7047			1.06065			0.530323	+	0.847796i	$0.322071\pi$
$312$		0			0
$313$		−	14.7439i		−	0.833372i	−0.909050	−	0.416686i	$-0.863191\pi$
$313$		−	14.7439i		−	0.833372i	0.909050	−	0.416686i	$-0.136809\pi$
$314$		0			0
$315$	−13.5000	+	17.7780i	−0.760640	+	1.00168i
$316$		0			0
$317$	−29.4472			−1.65392			−0.826960	−	0.562261i	$-0.809932\pi$
$317$	−29.4472			−1.65392			−0.826960	+	0.562261i	$0.809932\pi$
$318$		0			0
$319$			19.7278i			1.10454i
$320$		0			0
$321$	5.96659	−	4.06440i	0.333023	−	0.226853i
$322$		0			0
$323$		−	1.49213i		−	0.0830244i
$324$		0			0
$325$	13.3630	+	7.71512i	0.741245	+	0.427958i
$326$		0			0
$327$	5.45600	−	11.3177i	0.301717	−	0.625871i
$328$		0			0
$329$	−8.05570	+	28.5889i	−0.444125	+	1.57616i
$330$		0			0
$331$			26.1343i			1.43647i	0.695800	+	0.718236i	$0.255050\pi$
$331$			26.1343i			1.43647i	−0.695800	+	0.718236i	$0.744950\pi$
$332$		0			0
$333$	6.77444	+	8.50907i	0.371237	+	0.466294i
$334$		0			0
$335$	−15.2592	+	26.4297i	−0.833699	+	1.44401i
$336$		0			0
$337$	13.7702	+	23.8507i	0.750110	+	1.29923i	0.947769	+	0.318958i	$0.103333\pi$
$337$	13.7702	+	23.8507i	0.750110	+	1.29923i	−0.197659	+	0.980271i	$0.563334\pi$
$338$		0			0
$339$	−15.7679	−	23.1475i	−0.856395	−	1.25720i
$340$		0			0
$341$	6.33918	−	3.65992i	0.343286	−	0.198196i
$342$		0			0
$343$	13.5910	−	12.5811i	0.733846	−	0.679316i
$344$		0			0
$345$	−6.27261	−	9.20827i	−0.337706	−	0.495757i
$346$		0			0
$347$			11.9584i			0.641962i	0.947086	+	0.320981i	$0.104013\pi$
$347$			11.9584i			0.641962i	−0.947086	+	0.320981i	$0.895987\pi$
$348$		0			0
$349$	2.51240	+	1.45053i	0.134485	+	0.0776452i	0.565733	−	0.824588i	$-0.308593\pi$
$349$	2.51240	+	1.45053i	0.134485	+	0.0776452i	−0.431248	+	0.902234i	$0.641927\pi$
$350$		0			0
$351$	−20.2227	+	18.7181i	−1.07941	+	0.999097i
$352$		0			0
$353$	23.9384	−	13.8208i	1.27411	−	0.735610i	0.298354	−	0.954455i	$-0.403563\pi$
$353$	23.9384	−	13.8208i	1.27411	−	0.735610i	0.975759	+	0.218846i	$0.0702292\pi$
$354$		0			0
$355$	17.9455	−	31.0825i	0.952447	−	1.64969i
$356$		0			0
$357$	−8.25864	+	9.34317i	−0.437093	+	0.494493i
$358$		0			0
$359$	2.49496	−	1.44047i	0.131679	−	0.0760249i	−0.432713	−	0.901532i	$-0.642444\pi$
$359$	2.49496	−	1.44047i	0.131679	−	0.0760249i	0.564392	+	0.825507i	$0.309110\pi$
$360$		0			0
$361$	9.34966	−	16.1941i	0.492087	−	0.852320i
$362$		0			0
$363$	3.01268	−	6.24939i	0.158125	−	0.328008i
$364$		0			0
$365$	6.97245	+	12.0766i	0.364954	+	0.632120i
$366$		0			0
$367$	0.682581	+	1.18227i	0.0356304	+	0.0617137i	0.883291	−	0.468826i	$-0.155323\pi$
$367$	0.682581	+	1.18227i	0.0356304	+	0.0617137i	−0.847660	+	0.530539i	$0.821989\pi$
$368$		0			0
$369$	19.3009	−	15.3663i	1.00476	−	0.799937i
$370$		0			0
$371$	−9.35561	−	9.59931i	−0.485719	−	0.498371i
$372$		0			0
$373$	−4.76730	+	8.25721i	−0.246841	+	0.427542i	−0.962648	−	0.270757i	$-0.912726\pi$
$373$	−4.76730	+	8.25721i	−0.246841	+	0.427542i	0.715806	+	0.698299i	$0.246059\pi$
$374$		0			0
$375$	0.756815	+	10.1544i	0.0390817	+	0.524372i
$376$		0			0
$377$			39.5577i			2.03732i
$378$		0			0
$379$		−	5.58137i		−	0.286696i	−0.989672	−	0.143348i	$-0.954213\pi$
$379$		−	5.58137i		−	0.286696i	0.989672	−	0.143348i	$-0.0457867\pi$
$380$		0			0
$381$	−2.83788	−	38.0768i	−0.145389	−	1.95073i
$382$		0			0
$383$	−16.5981	+	28.7488i	−0.848124	+	1.46899i	0.0347558	+	0.999396i	$0.488935\pi$
$383$	−16.5981	+	28.7488i	−0.848124	+	1.46899i	−0.882880	+	0.469599i	$0.844399\pi$
$384$		0			0
$385$	−5.33730	+	18.9416i	−0.272014	+	0.965353i
$386$		0			0
$387$	−12.6877	−	4.99146i	−0.644951	−	0.253730i
$388$		0			0
$389$	0.338305	+	0.585961i	0.0171527	+	0.0297094i	0.874474	−	0.485072i	$-0.161207\pi$
$389$	0.338305	+	0.585961i	0.0171527	+	0.0297094i	−0.857322	+	0.514781i	$0.827873\pi$
$390$		0			0
$391$	−3.11199	−	5.39013i	−0.157380	−	0.272590i
$392$		0			0
$393$	−8.63608	+	17.9144i	−0.435632	+	0.903659i
$394$		0			0
$395$	7.89316	−	13.6714i	0.397148	−	0.687881i
$396$		0			0
$397$	−20.5945	+	11.8902i	−1.03361	+	0.596754i	−0.918016	−	0.396543i	$-0.870210\pi$
$397$	−20.5945	+	11.8902i	−1.03361	+	0.596754i	−0.115592	+	0.993297i	$0.536877\pi$
$398$		0			0
$399$	2.38261	−	0.798402i	0.119279	−	0.0399701i
$400$		0			0
$401$	17.7910	−	30.8149i	0.888440	−	1.53882i	0.0467213	−	0.998908i	$-0.485123\pi$
$401$	17.7910	−	30.8149i	0.888440	−	1.53882i	0.841719	−	0.539916i	$-0.181544\pi$
$402$		0			0
$403$	12.7112	−	7.33879i	0.633188	−	0.365571i
$404$		0			0
$405$	24.6679	+	5.67253i	1.22576	+	0.281870i
$406$		0			0
$407$	8.30379	+	4.79420i	0.411604	+	0.237640i
$408$		0			0
$409$			13.0895i			0.647235i	0.946188	+	0.323617i	$0.104899\pi$
$409$			13.0895i			0.647235i	−0.946188	+	0.323617i	$0.895101\pi$
$410$		0			0
$411$	0.456861	+	0.670678i	0.0225353	+	0.0330821i
$412$		0			0
$413$	−2.41066	+	8.55520i	−0.118621	+	0.420974i
$414$		0			0
$415$	−3.50358	+	2.02280i	−0.171984	+	0.0992951i
$416$		0			0
$417$	2.86172	+	4.20104i	0.140139	+	0.205726i
$418$		0			0
$419$	−10.5482	−	18.2700i	−0.515313	−	0.892548i	−0.999842	−	0.0177728i	$-0.994342\pi$
$419$	−10.5482	−	18.2700i	−0.515313	−	0.892548i	0.484529	−	0.874775i	$-0.338991\pi$
$420$		0			0
$421$	14.0124	−	24.2702i	0.682924	−	1.18286i	−0.291161	−	0.956674i	$-0.594041\pi$
$421$	14.0124	−	24.2702i	0.682924	−	1.18286i	0.974084	−	0.226185i	$-0.0726253\pi$
$422$		0			0
$423$	33.3071	−	4.99252i	1.61944	−	0.242745i
$424$		0			0
$425$		−	7.91765i		−	0.384062i
$426$		0			0
$427$	−36.7243	−	10.3481i	−1.77722	−	0.500778i
$428$		0			0
$429$	−10.5490	+	21.8825i	−0.509312	+	1.05650i
$430$		0			0
$431$	−9.70704	−	5.60436i	−0.467572	−	0.269953i	0.247651	−	0.968849i	$-0.420341\pi$
$431$	−9.70704	−	5.60436i	−0.467572	−	0.269953i	−0.715223	+	0.698897i	$0.753675\pi$
$432$		0			0
$433$		−	5.09237i		−	0.244724i	−0.992486	−	0.122362i	$-0.960953\pi$
$433$		−	5.09237i		−	0.244724i	0.992486	−	0.122362i	$-0.0390468\pi$
$434$		0			0
$435$	30.0306	−	20.4566i	1.43986	−	0.980820i
$436$		0			0
$437$			1.25419i			0.0599962i
$438$		0			0
$439$	−12.7128			−0.606747			−0.303374	−	0.952872i	$-0.598113\pi$
$439$	−12.7128			−0.606747			−0.303374	+	0.952872i	$0.598113\pi$
$440$		0			0
$441$	−19.3380	−	8.18794i	−0.920856	−	0.389902i
$442$		0			0
$443$			12.8916i			0.612498i	0.951951	+	0.306249i	$0.0990740\pi$
$443$			12.8916i			0.612498i	−0.951951	+	0.306249i	$0.900926\pi$
$444$		0			0
$445$	10.5439			0.499831
$446$		0			0
$447$	0.0323686	−	0.0671441i	0.00153098	−	0.00317581i
$448$		0			0
$449$	−10.8543			−0.512245			−0.256122	−	0.966644i	$-0.582445\pi$
$449$	−10.8543			−0.512245			−0.256122	+	0.966644i	$0.582445\pi$
$450$		0			0
$451$	10.8745	−	18.8353i	0.512062	−	0.886918i
$452$		0			0
$453$	−12.7886	+	8.71148i	−0.600859	+	0.409301i
$454$		0			0
$455$	−10.7022	+	37.9812i	−0.501728	+	1.78059i
$456$		0			0
$457$	17.0059			0.795503			0.397751	−	0.917493i	$-0.369791\pi$
$457$	17.0059			0.795503			0.397751	+	0.917493i	$0.369791\pi$
$458$		0			0
$459$	13.5063	+	4.18421i	0.630421	+	0.195302i
$460$		0			0
$461$	−6.55493	−	3.78449i	−0.305294	−	0.176261i	0.339525	−	0.940597i	$-0.389734\pi$
$461$	−6.55493	−	3.78449i	−0.305294	−	0.176261i	−0.644819	+	0.764336i	$0.723067\pi$
$462$		0			0
$463$	3.62448	−	2.09260i	0.168444	−	0.0972512i	−0.413408	−	0.910546i	$-0.635662\pi$
$463$	3.62448	−	2.09260i	0.168444	−	0.0972512i	0.581852	+	0.813295i	$0.302328\pi$
$464$		0			0
$465$	−12.1447	−	5.85466i	−0.563197	−	0.271503i
$466$		0			0
$467$	−4.17316	−	7.22813i	−0.193111	−	0.334478i	0.753169	−	0.657827i	$-0.228524\pi$
$467$	−4.17316	−	7.22813i	−0.193111	−	0.334478i	−0.946280	+	0.323350i	$0.895191\pi$
$468$		0			0
$469$	−27.6338	−	7.78657i	−1.27601	−	0.359551i
$470$		0			0
$471$	0.881887	+	11.8326i	0.0406352	+	0.545216i
$472$		0			0
$473$	−12.0196			−0.552660
$474$		0			0
$475$	−0.797742	+	1.38173i	−0.0366029	+	0.0633981i
$476$		0			0
$477$	−5.56433	+	14.1438i	−0.254773	+	0.647602i
$478$		0			0
$479$	−13.4529	−	23.3011i	−0.614677	−	1.06465i	−0.990441	−	0.137937i	$-0.955953\pi$
$479$	−13.4529	−	23.3011i	−0.614677	−	1.06465i	0.375764	−	0.926716i	$-0.377380\pi$
$480$		0			0
$481$	16.6506	+	9.61321i	0.759200	+	0.438325i
$482$		0			0
$483$	6.94170	−	7.85329i	0.315858	−	0.357337i
$484$		0			0
$485$	−25.5662	−	44.2819i	−1.16090	−	2.01074i
$486$		0			0
$487$	−26.8047	−	15.4757i	−1.21464	−	0.701270i	−0.250870	−	0.968021i	$-0.580717\pi$
$487$	−26.8047	−	15.4757i	−1.21464	−	0.701270i	−0.963766	+	0.266751i	$0.914050\pi$
$488$		0			0
$489$	19.7940	−	13.4836i	0.895117	−	0.609747i
$490$		0			0
$491$	−9.30274	+	5.37094i	−0.419827	+	0.242387i	−0.695003	−	0.719007i	$-0.744597\pi$
$491$	−9.30274	+	5.37094i	−0.419827	+	0.242387i	0.275176	+	0.961394i	$0.411264\pi$
$492$		0			0
$493$	17.5786	−	10.1490i	0.791701	−	0.457089i
$494$		0			0
$495$	22.0676	−	3.30779i	0.991864	−	0.148674i
$496$		0			0
$497$	32.4986	+	9.15734i	1.45776	+	0.410763i
$498$		0			0
$499$	−2.01094	−	1.16102i	−0.0900220	−	0.0519742i	0.454313	−	0.890842i	$-0.349885\pi$
$499$	−2.01094	−	1.16102i	−0.0900220	−	0.0519742i	−0.544335	+	0.838868i	$0.683218\pi$
$500$		0			0
$501$	21.4905	+	31.5483i	0.960124	+	1.40947i
$502$		0			0
$503$	−37.1284			−1.65547			−0.827736	−	0.561117i	$-0.810372\pi$
$503$	−37.1284			−1.65547			−0.827736	+	0.561117i	$0.810372\pi$
$504$		0			0
$505$	7.66654			0.341156
$506$		0			0
$507$	−11.3748	+	23.5954i	−0.505172	+	1.04791i
$508$		0			0
$509$	36.2251	+	20.9146i	1.60565	+	0.927023i	0.990328	+	0.138747i	$0.0443076\pi$
$509$	36.2251	+	20.9146i	1.60565	+	0.927023i	0.615323	+	0.788275i	$0.289026\pi$
$510$		0			0
$511$	−9.39469	+	9.15619i	−0.415597	+	0.405046i
$512$		0			0
$513$	−1.93544	−	2.09103i	−0.0854519	−	0.0923210i
$514$		0			0
$515$	−37.2098	+	21.4831i	−1.63966	+	0.946658i
$516$		0			0
$517$	25.7128	−	14.8453i	1.13085	−	0.652896i
$518$		0			0
$519$	1.75475	+	23.5441i	0.0770251	+	1.03347i
$520$		0			0
$521$	−5.56496	−	3.21293i	−0.243805	−	0.140761i	0.373119	−	0.927783i	$-0.378288\pi$
$521$	−5.56496	−	3.21293i	−0.243805	−	0.140761i	−0.616924	+	0.787022i	$0.711622\pi$
$522$		0			0
$523$	−1.15469	−	1.99999i	−0.0504912	−	0.0874533i	0.839675	−	0.543089i	$-0.182745\pi$
$523$	−1.15469	−	1.99999i	−0.0504912	−	0.0874533i	−0.890166	+	0.455636i	$0.849412\pi$
$524$		0			0
$525$	12.6428	−	4.23654i	0.551775	−	0.184898i
$526$		0			0
$527$	−6.52242	−	3.76572i	−0.284121	−	0.164037i
$528$		0			0
$529$	−8.88425	−	15.3880i	−0.386272	−	0.669042i
$530$		0			0
$531$	9.96709	−	1.49400i	0.432535	−	0.0648343i
$532$		0			0
$533$	21.8054	−	37.7680i	0.944496	−	1.63591i
$534$		0			0
$535$	−11.7224			−0.506806
$536$		0			0
$537$	1.49065	+	0.718605i	0.0643261	+	0.0310101i
$538$		0			0
$539$	−18.5069	−	0.475960i	−0.797149	−	0.0205011i
$540$		0			0
$541$	−0.713219	−	1.23533i	−0.0306637	−	0.0531111i	0.850286	−	0.526320i	$-0.176429\pi$
$541$	−0.713219	−	1.23533i	−0.0306637	−	0.0531111i	−0.880950	+	0.473209i	$0.843095\pi$
$542$		0			0
$543$	2.18947	+	29.3768i	0.0939593	+	1.26068i
$544$		0			0
$545$	−17.6678	+	10.2005i	−0.756806	+	0.436942i
$546$		0			0
$547$	3.62835	+	2.09483i	0.155137	+	0.0895685i	0.575559	−	0.817760i	$-0.304785\pi$
$547$	3.62835	+	2.09483i	0.155137	+	0.0895685i	−0.420422	+	0.907329i	$0.638118\pi$
$548$		0			0
$549$	6.41321	+	42.7851i	0.273709	+	1.82602i
$550$		0			0
$551$	−4.09025			−0.174251
$552$		0			0
$553$	14.2942	+	4.02778i	0.607852	+	0.171279i
$554$		0			0
$555$	−1.31261	−	17.6118i	−0.0557174	−	0.747578i
$556$		0			0
$557$	8.75539	−	15.1648i	0.370978	−	0.642552i	−0.618739	−	0.785597i	$-0.712356\pi$
$557$	8.75539	−	15.1648i	0.370978	−	0.642552i	0.989716	+	0.143045i	$0.0456893\pi$
$558$		0			0
$559$	−24.1013			−1.01938
$560$		0			0
$561$	12.4306	−	0.926461i	0.524821	−	0.0391152i
$562$		0			0
$563$	−4.72155			−0.198989			−0.0994947	−	0.995038i	$-0.531723\pi$
$563$	−4.72155			−0.198989			−0.0994947	+	0.995038i	$0.531723\pi$
$564$		0			0
$565$			45.4774i			1.91325i
$566$		0			0
$567$	0.545634	+	23.8055i	0.0229145	+	0.999737i
$568$		0			0
$569$	23.7443			0.995411			0.497705	−	0.867346i	$-0.334176\pi$
$569$	23.7443			0.995411			0.497705	+	0.867346i	$0.334176\pi$
$570$		0			0
$571$			29.6501i			1.24082i	0.784278	+	0.620409i	$0.213034\pi$
$571$			29.6501i			1.24082i	−0.784278	+	0.620409i	$0.786966\pi$
$572$		0			0
$573$	0.844908	+	11.3364i	0.0352965	+	0.473585i
$574$		0			0
$575$			6.65509i			0.277536i
$576$		0			0
$577$	13.4530	+	7.76707i	0.560054	+	0.323347i	0.753167	−	0.657829i	$-0.228525\pi$
$577$	13.4530	+	7.76707i	0.560054	+	0.323347i	−0.193113	+	0.981176i	$0.561858\pi$
$578$		0			0
$579$	38.5148	−	2.87053i	1.60062	−	0.119295i
$580$		0			0
$581$	−2.65633	−	2.72552i	−0.110203	−	0.113074i
$582$		0			0
$583$			13.3990i			0.554931i
$584$		0			0
$585$	44.2494	−	6.63270i	1.82949	−	0.274228i
$586$		0			0
$587$	−0.553171	+	0.958120i	−0.0228318	+	0.0395458i	−0.877216	−	0.480097i	$-0.840602\pi$
$587$	−0.553171	+	0.958120i	−0.0228318	+	0.0395458i	0.854384	+	0.519643i	$0.173935\pi$
$588$		0			0
$589$	0.758829	+	1.31433i	0.0312670	+	0.0541561i
$590$		0			0
$591$	29.4477	−	2.19475i	1.21131	−	0.0902800i
$592$		0			0
$593$	14.2753	−	8.24185i	0.586216	−	0.338452i	−0.177384	−	0.984142i	$-0.556763\pi$
$593$	14.2753	−	8.24185i	0.586216	−	0.338452i	0.763600	+	0.645690i	$0.223430\pi$
$594$		0			0
$595$	19.6239	−	4.98871i	0.804500	−	0.204517i
$596$		0			0
$597$	−14.3327	+	29.7311i	−0.586596	+	1.21681i
$598$		0			0
$599$			20.5047i			0.837801i	0.908032	+	0.418900i	$0.137584\pi$
$599$			20.5047i			0.837801i	−0.908032	+	0.418900i	$0.862416\pi$
$600$		0			0
$601$	15.8353	+	9.14249i	0.645934	+	0.372930i	0.786897	−	0.617085i	$-0.211686\pi$
$601$	15.8353	+	9.14249i	0.645934	+	0.372930i	−0.140963	+	0.990015i	$0.545020\pi$
$602$		0			0
$603$	4.82573	+	32.1943i	0.196519	+	1.31105i
$604$		0			0
$605$	−9.75577	+	5.63250i	−0.396629	+	0.228994i
$606$		0			0
$607$	−0.148266	+	0.256804i	−0.00601794	+	0.0104234i	−0.869019	−	0.494779i	$-0.835249\pi$
$607$	−0.148266	+	0.256804i	−0.00601794	+	0.0104234i	0.863001	+	0.505203i	$0.168582\pi$
$608$		0			0
$609$	25.6116	+	22.6387i	1.03784	+	0.917367i
$610$		0			0
$611$	51.5588	−	29.7675i	2.08584	−	1.20426i
$612$		0			0
$613$	14.4270	−	24.9882i	0.582700	−	1.00927i	−0.412458	−	0.910976i	$-0.635330\pi$
$613$	14.4270	−	24.9882i	0.582700	−	1.00927i	0.995158	−	0.0982888i	$-0.0313369\pi$
$614$		0			0
$615$	−39.9483	+	2.97737i	−1.61087	+	0.120059i
$616$		0			0
$617$	−13.6978	−	23.7253i	−0.551454	−	0.955146i	−0.998170	−	0.0604700i	$-0.980740\pi$
$617$	−13.6978	−	23.7253i	−0.551454	−	0.955146i	0.446716	−	0.894676i	$-0.352593\pi$
$618$		0			0
$619$	2.51347	+	4.35345i	0.101025	+	0.174980i	0.912107	−	0.409952i	$-0.134455\pi$
$619$	2.51347	+	4.35345i	0.101025	+	0.174980i	−0.811082	+	0.584932i	$0.801121\pi$
$620$		0			0
$621$	−11.3526	−	3.51699i	−0.455563	−	0.141132i
$622$		0			0
$623$	2.44387	+	9.61335i	0.0979117	+	0.385151i
$624$		0			0
$625$	15.5411	−	26.9180i	0.621644	−	1.07672i
$626$		0			0
$627$	−2.26264	−	1.09077i	−0.0903613	−	0.0435610i
$628$		0			0
$629$		−	9.86556i		−	0.393366i
$630$		0			0
$631$			7.26095i			0.289054i	0.989501	+	0.144527i	$0.0461660\pi$
$631$			7.26095i			0.289054i	−0.989501	+	0.144527i	$0.953834\pi$
$632$		0			0
$633$	−15.3195	+	10.4355i	−0.608896	+	0.414775i
$634$		0			0
$635$	−30.9992	+	53.6923i	−1.23017	+	2.13071i
$636$		0			0
$637$	−37.1096	−	0.954384i	−1.47034	−	0.0378141i
$638$		0			0
$639$	−5.67526	−	37.8619i	−0.224510	−	1.49779i
$640$		0			0
$641$	−13.2794	−	23.0007i	−0.524507	−	0.908472i	−0.999593	−	0.0285328i	$-0.990916\pi$
$641$	−13.2794	−	23.0007i	−0.524507	−	0.908472i	0.475086	−	0.879939i	$-0.342417\pi$
$642$		0			0
$643$	−0.856940	−	1.48426i	−0.0337944	−	0.0585337i	0.848634	−	0.528981i	$-0.177426\pi$
$643$	−0.856940	−	1.48426i	−0.0337944	−	0.0585337i	−0.882428	+	0.470448i	$0.844092\pi$
$644$		0			0
$645$	12.4636	+	18.2968i	0.490755	+	0.720434i
$646$		0			0
$647$	13.8968	−	24.0699i	0.546339	−	0.946287i	−0.452182	−	0.891926i	$-0.649354\pi$
$647$	13.8968	−	24.0699i	0.546339	−	0.946287i	0.998521	−	0.0543614i	$-0.0173123\pi$
$648$		0			0
$649$	7.69453	−	4.44244i	0.302037	−	0.174381i
$650$		0			0
$651$	2.52305	−	12.4298i	0.0988860	−	0.487163i
$652$		0			0
$653$	−7.65604	+	13.2607i	−0.299604	+	0.518929i	−0.976045	−	0.217567i	$-0.930188\pi$
$653$	−7.65604	+	13.2607i	−0.299604	+	0.518929i	0.676441	+	0.736497i	$0.263521\pi$
$654$		0			0
$655$	27.9657	−	16.1460i	1.09271	−	0.630876i
$656$		0			0
$657$	13.8423	+	5.44572i	0.540041	+	0.212458i
$658$		0			0
$659$	−41.7362	−	24.0964i	−1.62581	−	0.938663i	−0.985324	−	0.170694i	$-0.945399\pi$
$659$	−41.7362	−	24.0964i	−1.62581	−	0.938663i	−0.640488	−	0.767968i	$-0.721268\pi$
$660$		0			0
$661$		−	17.5852i		−	0.683987i	−0.939702	−	0.341993i	$-0.888898\pi$
$661$		−	17.5852i		−	0.683987i	0.939702	−	0.341993i	$-0.111102\pi$
$662$		0			0
$663$	24.9256	−	1.85772i	0.968029	−	0.0721477i
$664$		0			0
$665$	−3.92725	−	1.10661i	−0.152292	−	0.0429124i
$666$		0			0
$667$	−14.7755	+	8.53064i	−0.572110	+	0.330308i
$668$		0			0
$669$	−14.1067	+	29.2624i	−0.545396	+	1.13135i
$670$		0			0
$671$	19.0698	+	33.0298i	0.736180	+	1.27510i
$672$		0			0
$673$	−7.47021	+	12.9388i	−0.287955	+	0.498753i	−0.973322	−	0.229445i	$-0.926309\pi$
$673$	−7.47021	+	12.9388i	−0.287955	+	0.498753i	0.685366	+	0.728199i	$0.259642\pi$
$674$		0			0
$675$	−10.2700	−	11.0955i	−0.395292	−	0.427068i
$676$		0			0
$677$			1.54926i			0.0595427i	0.999557	+	0.0297714i	$0.00947792\pi$
$677$			1.54926i			0.0595427i	−0.999557	+	0.0297714i	$0.990522\pi$
$678$		0			0
$679$	34.4479	−	33.5734i	1.32199	−	1.28843i
$680$		0			0
$681$	−21.5154	−	31.5849i	−0.824473	−	1.21034i
$682$		0			0
$683$	−5.97005	−	3.44681i	−0.228438	−	0.131889i	0.381413	−	0.924405i	$-0.375437\pi$
$683$	−5.97005	−	3.44681i	−0.228438	−	0.131889i	−0.609851	+	0.792516i	$0.708771\pi$
$684$		0			0
$685$		−	1.31767i		−	0.0503455i
$686$		0			0
$687$	−6.79405	−	3.27525i	−0.259209	−	0.124958i
$688$		0			0
$689$			26.8674i			1.02357i
$690$		0			0
$691$	−39.3194			−1.49578			−0.747890	−	0.663822i	$-0.768933\pi$
$691$	−39.3194			−1.49578			−0.747890	+	0.663822i	$0.768933\pi$
$692$		0			0
$693$	8.13067	+	19.3532i	0.308859	+	0.735169i
$694$		0			0
$695$		−	8.25370i		−	0.313081i
$696$		0			0
$697$	−22.3778			−0.847619
$698$		0			0
$699$	23.3906	+	34.3378i	0.884715	+	1.29877i
$700$		0			0
$701$	−21.0215			−0.793970			−0.396985	−	0.917825i	$-0.629943\pi$
$701$	−21.0215			−0.793970			−0.396985	+	0.917825i	$0.629943\pi$
$702$		0			0
$703$	−0.994003	+	1.72166i	−0.0374895	+	0.0649338i
$704$		0			0
$705$	−49.2611	−	23.7476i	−1.85528	−	0.894385i
$706$		0			0
$707$	1.77695	+	6.98990i	0.0668290	+	0.262882i
$708$		0			0
$709$	38.0038			1.42726			0.713630	−	0.700522i	$-0.247050\pi$
$709$	38.0038			1.42726			0.713630	+	0.700522i	$0.247050\pi$
$710$		0			0
$711$	−2.49622	−	16.6532i	−0.0936154	−	0.624545i
$712$		0			0
$713$	5.48234	+	3.16523i	0.205315	+	0.118539i
$714$		0			0
$715$	34.1602	−	19.7224i	1.27752	−	0.737577i
$716$		0			0
$717$	8.32300	−	5.66956i	0.310828	−	0.211734i
$718$		0			0
$719$	3.72516	+	6.45216i	0.138925	+	0.240625i	0.927090	−	0.374839i	$-0.122302\pi$
$719$	3.72516	+	6.45216i	0.138925	+	0.240625i	−0.788165	+	0.615464i	$0.788969\pi$
$720$		0			0
$721$	−28.2115	−	28.9464i	−1.05065	−	1.07802i
$722$		0			0
$723$	32.6714	−	22.2555i	1.21506	−	0.827692i
$724$		0			0
$725$	−21.7040			−0.806066
$726$		0			0
$727$	−9.88775	+	17.1261i	−0.366716	+	0.635171i	−0.989050	−	0.147581i	$-0.952851\pi$
$727$	−9.88775	+	17.1261i	−0.366716	+	0.635171i	0.622334	+	0.782752i	$0.286185\pi$
$728$		0			0
$729$	24.3547	−	11.6554i	0.902025	−	0.431683i
$730$		0			0
$731$	6.18350	+	10.7101i	0.228705	+	0.396129i
$732$		0			0
$733$	28.4508	+	16.4261i	1.05085	+	0.606711i	0.922888	−	0.385068i	$-0.125822\pi$
$733$	28.4508	+	16.4261i	1.05085	+	0.606711i	0.127966	+	0.991779i	$0.459155\pi$
$734$		0			0
$735$	18.4661	+	28.6657i	0.681133	+	1.05735i
$736$		0			0
$737$	14.3494	+	24.8538i	0.528566	+	0.915502i
$738$		0			0
$739$	−22.2229	−	12.8304i	−0.817484	−	0.471975i	0.0320642	−	0.999486i	$-0.489792\pi$
$739$	−22.2229	−	12.8304i	−0.817484	−	0.471975i	−0.849548	+	0.527511i	$0.823125\pi$
$740$		0			0
$741$	−4.53700	−	2.18718i	−0.166671	−	0.0803480i
$742$		0			0
$743$	38.0089	−	21.9445i	1.39441	−	0.805064i	0.400612	−	0.916248i	$-0.368798\pi$
$743$	38.0089	−	21.9445i	1.39441	−	0.805064i	0.993800	+	0.111184i	$0.0354643\pi$
$744$		0			0
$745$	−0.104817	+	0.0605162i	−0.00384020	+	0.00221714i
$746$		0			0
$747$	−1.57987	+	4.01584i	−0.0578045	+	0.146932i
$748$		0			0
$749$	−2.71703	−	10.6878i	−0.0992780	−	0.390525i
$750$		0			0
$751$	7.84327	+	4.52831i	0.286205	+	0.165241i	0.636229	−	0.771500i	$-0.280493\pi$
$751$	7.84327	+	4.52831i	0.286205	+	0.165241i	−0.350024	+	0.936741i	$0.613827\pi$
$752$		0			0
$753$	−20.4162	+	1.52163i	−0.744009	+	0.0554514i
$754$		0			0
$755$	25.1255			0.914409
$756$		0			0
$757$	26.8619			0.976314			0.488157	−	0.872756i	$-0.337669\pi$
$757$	26.8619			0.976314			0.488157	+	0.872756i	$0.337669\pi$
$758$		0			0
$759$	−10.4484	+	0.778726i	−0.379253	+	0.0282660i
$760$		0			0
$761$	−10.5578	−	6.09556i	−0.382721	−	0.220964i	0.296281	−	0.955101i	$-0.404254\pi$
$761$	−10.5578	−	6.09556i	−0.382721	−	0.220964i	−0.679001	+	0.734137i	$0.737587\pi$
$762$		0			0
$763$	−13.3953	−	13.7442i	−0.484942	−	0.497574i
$764$		0			0
$765$	−14.3002	−	17.9618i	−0.517024	−	0.649410i
$766$		0			0
$767$	15.4289	−	8.90787i	0.557105	−	0.321645i
$768$		0			0
$769$	−21.7503	+	12.5575i	−0.784335	+	0.452836i	−0.837964	−	0.545725i	$-0.816254\pi$
$769$	−21.7503	+	12.5575i	−0.784335	+	0.452836i	0.0536296	+	0.998561i	$0.482921\pi$
$770$		0			0
$771$	−25.0243	−	12.0636i	−0.901227	−	0.434460i
$772$		0			0
$773$	−37.6545	−	21.7398i	−1.35434	−	0.781928i	−0.365484	−	0.930817i	$-0.619097\pi$
$773$	−37.6545	−	21.7398i	−1.35434	−	0.781928i	−0.988854	+	0.148890i	$0.952430\pi$
$774$		0			0
$775$	4.02655	+	6.97420i	0.144638	+	0.250521i
$776$		0			0
$777$	15.7531	−	5.27882i	0.565141	−	0.189376i
$778$		0			0
$779$	3.90520	+	2.25467i	0.139918	+	0.0807819i
$780$		0			0
$781$	−16.8755	−	29.2292i	−0.603852	−	1.04590i
$782$		0			0
$783$	11.4698	−	37.0238i	0.409898	−	1.32312i
$784$		0			0
$785$	9.63318	−	16.6852i	0.343823	−	0.595519i
$786$		0			0
$787$	24.3945			0.869570			0.434785	−	0.900534i	$-0.356824\pi$
$787$	24.3945			0.869570			0.434785	+	0.900534i	$0.356824\pi$
$788$		0			0
$789$	−43.1275	+	29.3781i	−1.53538	+	1.04589i
$790$		0			0
$791$	−41.4637	+	10.5408i	−1.47428	+	0.374786i
$792$		0			0
$793$	38.2382	+	66.2306i	1.35788	+	2.35192i
$794$		0			0
$795$	20.3967	−	13.8941i	0.723395	−	0.492772i
$796$		0			0
$797$	−44.9314	+	25.9412i	−1.59155	+	0.918883i	−0.598510	+	0.801115i	$0.704240\pi$
$797$	−44.9314	+	25.9412i	−1.59155	+	0.918883i	−0.993041	+	0.117768i	$0.962426\pi$
$798$		0			0
$799$	−26.4561	−	15.2744i	−0.935950	−	0.540371i
$800$		0			0
$801$	8.79914	−	7.00538i	0.310902	−	0.247523i
$802$		0			0
$803$	13.1134			0.462763
$804$		0			0
$805$	−16.4946	+	4.19320i	−0.581359	+	0.147791i
$806$		0			0
$807$	−5.32941	−	2.56918i	−0.187604	−	0.0904395i
$808$		0			0
$809$	−20.4027	+	35.3386i	−0.717322	+	1.24244i	0.244735	+	0.969590i	$0.421299\pi$
$809$	−20.4027	+	35.3386i	−0.717322	+	1.24244i	−0.962057	+	0.272848i	$0.912034\pi$
$810$		0			0
$811$	−11.1712			−0.392275			−0.196137	−	0.980576i	$-0.562840\pi$
$811$	−11.1712			−0.392275			−0.196137	+	0.980576i	$0.562840\pi$
$812$		0			0
$813$	26.5309	+	38.9477i	0.930478	+	1.36595i
$814$		0			0
$815$	−38.8890			−1.36222
$816$		0			0
$817$		−	2.49207i		−	0.0871865i
$818$		0			0
$819$	16.3034	+	38.8067i	0.569688	+	1.35601i
$820$		0			0
$821$	−2.72262			−0.0950202			−0.0475101	−	0.998871i	$-0.515129\pi$
$821$	−2.72262			−0.0950202			−0.0475101	+	0.998871i	$0.515129\pi$
$822$		0			0
$823$		−	43.9095i		−	1.53059i	−0.643681	−	0.765294i	$-0.722593\pi$
$823$		−	43.9095i		−	1.53059i	0.643681	−	0.765294i	$-0.277407\pi$
$824$		0			0
$825$	−12.0062	−	5.78790i	−0.418002	−	0.201509i
$826$		0			0
$827$			16.2663i			0.565635i	0.959174	+	0.282818i	$0.0912691\pi$
$827$			16.2663i			0.565635i	−0.959174	+	0.282818i	$0.908731\pi$
$828$		0			0
$829$	10.7476	+	6.20515i	0.373281	+	0.215514i	0.674891	−	0.737918i	$-0.264191\pi$
$829$	10.7476	+	6.20515i	0.373281	+	0.215514i	−0.301610	+	0.953431i	$0.597524\pi$
$830$		0			0
$831$	5.84175	+	8.57577i	0.202648	+	0.297490i
$832$		0			0
$833$	9.09683	+	16.7356i	0.315187	+	0.579855i
$834$		0			0
$835$		−	61.9824i		−	2.14499i
$836$		0			0
$837$	−14.0248	+	3.18307i	−0.484769	+	0.110023i
$838$		0			0
$839$	−0.102613	+	0.177730i	−0.00354258	+	0.00613593i	−0.867791	−	0.496929i	$-0.834461\pi$
$839$	−0.102613	+	0.177730i	−0.00354258	+	0.00613593i	0.864249	+	0.503065i	$0.167794\pi$
$840$		0			0
$841$	−13.3206	−	23.0720i	−0.459333	−	0.795588i
$842$		0			0
$843$	−4.04885	+	8.39878i	−0.139450	+	0.289269i
$844$		0			0
$845$	36.8342	−	21.2662i	1.26714	−	0.731581i
$846$		0			0
$847$	−7.39658	−	7.58925i	−0.254149	−	0.260770i
$848$		0			0
$849$	6.02623	−	0.449138i	0.206820	−	0.0154144i
$850$		0			0
$851$			8.29238i			0.284259i
$852$		0			0
$853$	12.9524	+	7.47805i	0.443480	+	0.256044i	0.705073	−	0.709135i	$-0.250914\pi$
$853$	12.9524	+	7.47805i	0.443480	+	0.256044i	−0.261592	+	0.965178i	$0.584248\pi$
$854$		0			0
$855$	0.685820	+	4.57537i	0.0234545	+	0.156474i
$856$		0			0
$857$	−29.1218	+	16.8135i	−0.994783	+	0.574338i	−0.906701	−	0.421775i	$-0.861407\pi$
$857$	−29.1218	+	16.8135i	−0.994783	+	0.574338i	−0.0880827	+	0.996113i	$0.528074\pi$
$858$		0			0
$859$	8.44207	−	14.6221i	0.288040	−	0.498899i	−0.685302	−	0.728259i	$-0.740330\pi$
$859$	8.44207	−	14.6221i	0.288040	−	0.498899i	0.973342	+	0.229360i	$0.0736632\pi$
$860$		0			0
$861$	−11.9738	−	35.7324i	−0.408066	−	1.21776i
$862$		0			0
$863$	−25.5168	+	14.7321i	−0.868602	+	0.501487i	−0.866883	−	0.498511i	$-0.833880\pi$
$863$	−25.5168	+	14.7321i	−0.868602	+	0.501487i	−0.00171845	+	0.999999i	$0.500547\pi$
$864$		0			0
$865$	19.1678	−	33.1996i	0.651725	−	1.12882i
$866$		0			0
$867$	9.35648	+	13.7354i	0.317763	+	0.466480i
$868$		0			0
$869$	−7.42253	−	12.8562i	−0.251792	−	0.436117i
$870$		0			0
$871$	28.7730	+	49.8363i	0.974936	+	1.68864i
$872$		0			0
$873$	−50.7563	−	19.9681i	−1.71784	−	0.675817i
$874$		0			0
$875$	14.9712	+	4.21853i	0.506118	+	0.142612i
$876$		0			0
$877$	−17.3493	+	30.0498i	−0.585844	+	1.01471i	0.408926	+	0.912567i	$0.365903\pi$
$877$	−17.3493	+	30.0498i	−0.585844	+	1.01471i	−0.994770	+	0.102143i	$0.967430\pi$
$878$		0			0
$879$	−43.3315	+	29.5171i	−1.46153	+	0.995586i
$880$		0			0
$881$		−	1.50899i		−	0.0508393i	−0.999677	−	0.0254196i	$-0.991908\pi$
$881$		−	1.50899i		−	0.0508393i	0.999677	−	0.0254196i	$-0.00809220\pi$
$882$		0			0
$883$		−	36.2503i		−	1.21992i	−0.792432	−	0.609960i	$-0.791185\pi$
$883$		−	36.2503i		−	1.21992i	0.792432	−	0.609960i	$-0.208815\pi$
$884$		0			0
$885$	−14.7413	−	7.10643i	−0.495524	−	0.238880i
$886$		0			0
$887$	−16.5409	+	28.6496i	−0.555387	+	0.961959i	0.442486	+	0.896775i	$0.354097\pi$
$887$	−16.5409	+	28.6496i	−0.555387	+	0.961959i	−0.997873	+	0.0651837i	$0.979237\pi$
$888$		0			0
$889$	−56.1385	−	15.8185i	−1.88282	−	0.530536i
$890$		0			0
$891$	16.2182	−	17.4221i	0.543329	−	0.583662i
$892$		0			0
$893$	3.07795	+	5.33116i	0.103000	+	0.178401i
$894$		0			0
$895$	−1.34350	−	2.32701i	−0.0449083	−	0.0777834i
$896$		0			0
$897$	−20.9509	+	1.56148i	−0.699530	+	0.0521364i
$898$		0			0
$899$	−10.3226	+	17.8794i	−0.344280	+	0.596310i
$900$		0			0
$901$	11.9393	−	6.89317i	0.397757	−	0.229645i
$902$		0			0
$903$	−13.7931	+	15.6044i	−0.459006	+	0.519283i
$904$		0			0
$905$	23.9164	−	41.4244i	0.795008	−	1.37700i
$906$		0			0
$907$	29.9958	−	17.3181i	0.995993	−	0.575037i	0.0889325	−	0.996038i	$-0.471654\pi$
$907$	29.9958	−	17.3181i	0.995993	−	0.575037i	0.907060	+	0.421001i	$0.138321\pi$
$908$		0			0
$909$	6.39788	−	5.09363i	0.212204	−	0.168945i
$910$		0			0
$911$	−5.24077	−	3.02576i	−0.173634	−	0.100248i	0.410664	−	0.911787i	$-0.365297\pi$
$911$	−5.24077	−	3.02576i	−0.173634	−	0.100248i	−0.584298	+	0.811539i	$0.698630\pi$
$912$		0			0
$913$			3.80437i			0.125906i
$914$		0			0
$915$	30.5053	−	63.2790i	1.00847	−	2.09194i
$916$		0			0
$917$	21.2028	+	21.7551i	0.700179	+	0.718418i
$918$		0			0
$919$	−17.5675	+	10.1426i	−0.579499	+	0.334574i	−0.760934	−	0.648829i	$-0.775259\pi$
$919$	−17.5675	+	10.1426i	−0.579499	+	0.334574i	0.181435	+	0.983403i	$0.441926\pi$
$920$		0			0
$921$	26.8580	−	2.00174i	0.885001	−	0.0659596i
$922$		0			0
$923$	−33.8383	−	58.6096i	−1.11380	−	1.92916i
$924$		0			0
$925$	−5.27445	+	9.13562i	−0.173423	+	0.300377i
$926$		0			0
$927$	−16.7790	+	42.6502i	−0.551096	+	1.40082i
$928$		0			0
$929$		−	5.32035i		−	0.174555i	−0.996184	−	0.0872775i	$-0.972183\pi$
$929$		−	5.32035i		−	0.174555i	0.996184	−	0.0872775i	$-0.0278167\pi$
$930$		0			0
$931$	0.0986831	−	3.83712i	0.00323421	−	0.125757i
$932$		0			0
$933$	−32.3079	+	2.40793i	−1.05771	+	0.0788319i
$934$		0			0
$935$	−17.5285	−	10.1201i	−0.573243	−	0.330962i
$936$		0			0
$937$		−	12.6595i		−	0.413566i	−0.978387	−	0.206783i	$-0.933701\pi$
$937$		−	12.6595i		−	0.413566i	0.978387	−	0.206783i	$-0.0662995\pi$
$938$		0			0
$939$	1.89803	+	25.4665i	0.0619399	+	0.831067i
$940$		0			0
$941$		−	36.1276i		−	1.17772i	−0.808233	−	0.588862i	$-0.799576\pi$
$941$		−	36.1276i		−	1.17772i	0.808233	−	0.588862i	$-0.200424\pi$
$942$		0			0
$943$	18.8094			0.612518
$944$		0			0
$945$	21.0294	−	32.4452i	0.684087	−	1.05544i
$946$		0			0
$947$			14.7825i			0.480367i	0.970728	+	0.240183i	$0.0772076\pi$
$947$			14.7825i			0.480367i	−0.970728	+	0.240183i	$0.922792\pi$
$948$		0			0
$949$	26.2947			0.853562
$950$		0			0
$951$	50.8630	−	3.79085i	1.64934	−	0.122927i
$952$		0			0
$953$	−38.7897			−1.25652			−0.628260	−	0.778003i	$-0.716233\pi$
$953$	−38.7897			−1.25652			−0.628260	+	0.778003i	$0.716233\pi$
$954$		0			0
$955$	9.22924	−	15.9855i	0.298651	−	0.517279i
$956$		0			0
$957$	−2.53963	−	34.0750i	−0.0820945	−	1.10149i
$958$		0			0
$959$	1.20137	−	0.305409i	0.0387943	−	0.00986216i
$960$		0			0
$961$	−23.3397			−0.752894
$962$		0			0
$963$	−9.78263	+	7.78837i	−0.315241	+	0.250977i
$964$		0			0
$965$	−54.3100	−	31.3559i	−1.74830	−	1.00938i
$966$		0			0
$967$	−11.6680	+	6.73651i	−0.375217	+	0.216632i	−0.675735	−	0.737144i	$-0.736174\pi$
$967$	−11.6680	+	6.73651i	−0.375217	+	0.216632i	0.300518	+	0.953776i	$0.402840\pi$
$968$		0			0
$969$	0.192087	+	2.57730i	0.00617074	+	0.0827947i
$970$		0			0
$971$	24.9384	+	43.1946i	0.800312	+	1.38618i	0.919411	+	0.393299i	$0.128666\pi$
$971$	24.9384	+	43.1946i	0.800312	+	1.38618i	−0.119098	+	0.992882i	$0.538000\pi$
$972$		0			0
$973$	7.52524	−	1.91304i	0.241248	−	0.0613293i
$974$		0			0
$975$	−24.0746	−	11.6058i	−0.771003	−	0.371682i
$976$		0			0
$977$	−1.24236			−0.0397466			−0.0198733	−	0.999803i	$-0.506326\pi$
$977$	−1.24236			−0.0397466			−0.0198733	+	0.999803i	$0.506326\pi$
$978$		0			0
$979$	4.95763	−	8.58687i	0.158447	−	0.274437i
$980$		0			0
$981$	−7.96695	+	20.2510i	−0.254365	+	0.646565i
$982$		0			0
$983$	11.2694	+	19.5192i	0.359439	+	0.622567i	0.987867	−	0.155301i	$-0.0496346\pi$
$983$	11.2694	+	19.5192i	0.359439	+	0.622567i	−0.628428	+	0.777868i	$0.716301\pi$
$984$		0			0
$985$	−41.5243	−	23.9741i	−1.32307	−	0.763877i
$986$		0			0
$987$	10.2339	−	50.4176i	0.325750	−	1.60481i
$988$		0			0
$989$	−5.19747	−	9.00228i	−0.165270	−	0.286256i
$990$		0			0
$991$	−7.51321	−	4.33776i	−0.238665	−	0.137793i	0.375898	−	0.926661i	$-0.377334\pi$
$991$	−7.51321	−	4.33776i	−0.238665	−	0.137793i	−0.614563	+	0.788868i	$0.710668\pi$
$992$		0			0
$993$	−3.36437	−	45.1408i	−0.106765	−	1.43250i
$994$		0			0
$995$	46.4125	−	26.7963i	1.47138	−	0.849499i
$996$		0			0
$997$	7.45870	−	4.30628i	0.236219	−	0.136381i	−0.377219	−	0.926124i	$-0.623119\pi$
$997$	7.45870	−	4.30628i	0.236219	−	0.136381i	0.613438	+	0.789743i	$0.289786\pi$
$998$		0			0
$999$	−12.7966	−	13.8253i	−0.404867	−	0.437413i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1008.2.cz.g.367.1	yes	24
3.2	odd	2		3024.2.cz.h.2719.3		24
4.3	odd	2		1008.2.cz.h.367.12	yes	24
7.5	odd	6		1008.2.bf.g.943.5	yes	24
9.4	even	3		1008.2.bf.h.31.8	yes	24
9.5	odd	6		3024.2.bf.g.1711.10		24
12.11	even	2		3024.2.cz.g.2719.3		24
21.5	even	6		3024.2.bf.h.2287.3		24
28.19	even	6		1008.2.bf.h.943.8	yes	24
36.23	even	6		3024.2.bf.h.1711.10		24
36.31	odd	6		1008.2.bf.g.31.5	✓	24
63.5	even	6		3024.2.cz.g.1279.3		24
63.40	odd	6		1008.2.cz.h.607.12	yes	24
84.47	odd	6		3024.2.bf.g.2287.3		24
252.103	even	6	inner	1008.2.cz.g.607.1	yes	24
252.131	odd	6		3024.2.cz.h.1279.3		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1008.2.bf.g.31.5	✓	24	36.31	odd	6
1008.2.bf.g.943.5	yes	24	7.5	odd	6
1008.2.bf.h.31.8	yes	24	9.4	even	3
1008.2.bf.h.943.8	yes	24	28.19	even	6
1008.2.cz.g.367.1	yes	24	1.1	even	1	trivial
1008.2.cz.g.607.1	yes	24	252.103	even	6	inner
1008.2.cz.h.367.12	yes	24	4.3	odd	2
1008.2.cz.h.607.12	yes	24	63.40	odd	6
3024.2.bf.g.1711.10		24	9.5	odd	6
3024.2.bf.g.2287.3		24	84.47	odd	6
3024.2.bf.h.1711.10		24	36.23	even	6
3024.2.bf.h.2287.3		24	21.5	even	6
3024.2.cz.g.1279.3		24	63.5	even	6
3024.2.cz.g.2719.3		24	12.11	even	2
3024.2.cz.h.1279.3		24	252.131	odd	6
3024.2.cz.h.2719.3		24	3.2	odd	2

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:	\( N \)	\(=\)	\( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1008.cz (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.72726 + 0.128734i) q^{3} +(2.43562 + 1.40621i) q^{5} +(-0.717569 + 2.54659i) q^{7} +(2.96686 - 0.444713i) q^{9} +(2.29039 - 1.32236i) q^{11} +(4.59264 - 2.65156i) q^{13} +(-4.38797 - 2.11534i) q^{15} +(-2.35660 - 1.36058i) q^{17} +(0.274171 + 0.474878i) q^{19} +(0.911596 - 4.49099i) q^{21} +(1.98081 + 1.14362i) q^{23} +(1.45483 + 2.51983i) q^{25} +(-5.06728 + 1.15007i) q^{27} +(-3.72965 + 6.45995i) q^{29} +2.76772 q^{31} +(-3.78587 + 2.57891i) q^{33} +(-5.32874 + 5.19346i) q^{35} +(1.81274 + 3.13976i) q^{37} +(-7.59134 + 5.17117i) q^{39} +(7.12184 - 4.11180i) q^{41} +(-3.93586 - 2.27237i) q^{43} +(7.85149 + 3.08886i) q^{45} +11.2264 q^{47} +(-5.97019 - 3.65470i) q^{49} +(4.24562 + 2.04671i) q^{51} +(-2.53317 + 4.38758i) q^{53} +7.43804 q^{55} +(-0.534697 - 0.784943i) q^{57} +3.35948 q^{59} +14.4210i q^{61} +(-0.996422 + 7.87446i) q^{63} +14.9146 q^{65} +10.8513i q^{67} +(-3.56860 - 1.72034i) q^{69} -12.7616i q^{71} +(4.29405 + 2.47917i) q^{73} +(-2.83725 - 4.16512i) q^{75} +(1.72399 + 6.78157i) q^{77} -5.61310i q^{79} +(8.60446 - 2.63880i) q^{81} +(-0.719239 + 1.24576i) q^{83} +(-3.82652 - 6.62773i) q^{85} +(5.61047 - 11.6381i) q^{87} +(3.24680 - 1.87454i) q^{89} +(3.45690 + 13.5982i) q^{91} +(-4.78058 + 0.356299i) q^{93} +1.54216i q^{95} +(-15.7452 - 9.09049i) q^{97} +(6.20720 - 4.94182i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 3 q^{3} - 3 q^{5} + 4 q^{7} + 17 q^{9} - 9 q^{11} - 3 q^{13} - 6 q^{15} - 3 q^{17} - 4 q^{19} + 13 q^{21} - 6 q^{23} + 15 q^{25} + 9 q^{27} + 18 q^{29} + 34 q^{31} - 21 q^{33} - 42 q^{35} - 3 q^{37}+ \cdots + 30 q^{99}+O(q^{100}) \) 24 * q - 3 * q^3 - 3 * q^5 + 4 * q^7 + 17 * q^9 - 9 * q^11 - 3 * q^13 - 6 * q^15 - 3 * q^17 - 4 * q^19 + 13 * q^21 - 6 * q^23 + 15 * q^25 + 9 * q^27 + 18 * q^29 + 34 * q^31 - 21 * q^33 - 42 * q^35 - 3 * q^37 + 27 * q^39 + 36 * q^41 + 24 * q^43 + 21 * q^45 - 42 * q^47 + 30 * q^49 - 6 * q^51 - 12 * q^53 - 30 * q^55 - 13 * q^57 - 12 * q^59 - 3 * q^63 + 6 * q^69 + 48 * q^73 + 36 * q^75 - 48 * q^77 - 31 * q^81 - 48 * q^83 - 21 * q^85 + 15 * q^87 + 39 * q^89 + 9 * q^91 + 10 * q^93 + 3 * q^97 + 30 * q^99

Introduction

L-functions

Modular forms

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Database

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