LMFDB - Embedded newform 468.2.k.a.61.11

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [468,2,Mod(61,468)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("468.61"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(468, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 4, 4])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 468 = 2^{2} \cdot 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	468.k (of order $3$, degree $2$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$3.73699881460$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$14$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			61.11
Character	$\chi$	$=$	468.61
Dual form			468.2.k.a.445.11

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.20815 - 1.24112i) q^{3} +(1.66845 + 2.88984i) q^{5} -0.0102323 q^{7} +(-0.0807596 - 2.99891i) q^{9} +(-0.798063 - 1.38229i) q^{11} +(3.42617 - 1.12309i) q^{13} +(5.60238 + 1.42061i) q^{15} +(2.62956 + 4.55453i) q^{17} +(0.538519 + 0.932743i) q^{19} +(-0.0123622 + 0.0126995i) q^{21} -2.42269 q^{23} +(-3.06747 + 5.31301i) q^{25} +(-3.81958 - 3.52290i) q^{27} +(2.23251 + 3.86681i) q^{29} +(-1.47581 - 2.55618i) q^{31} +(-2.67976 - 0.679513i) q^{33} +(-0.0170722 - 0.0295698i) q^{35} +(4.21638 - 7.30299i) q^{37} +(2.74544 - 5.60915i) q^{39} +6.41407 q^{41} -10.4798 q^{43} +(8.53165 - 5.23693i) q^{45} +(4.91647 - 8.51558i) q^{47} -6.99990 q^{49} +(8.82961 + 2.23894i) q^{51} -5.27921 q^{53} +(2.66306 - 4.61256i) q^{55} +(1.80826 + 0.458524i) q^{57} +(-5.53108 + 9.58012i) q^{59} -10.8830 q^{61} +(0.000826358 + 0.0306858i) q^{63} +(8.96196 + 8.02729i) q^{65} -3.39007 q^{67} +(-2.92697 + 3.00685i) q^{69} +(1.93480 + 3.35118i) q^{71} -11.6238 q^{73} +(2.88813 + 10.2260i) q^{75} +(0.00816604 + 0.0141440i) q^{77} +(0.0422648 - 0.0732048i) q^{79} +(-8.98696 + 0.484382i) q^{81} +(7.14463 - 12.3749i) q^{83} +(-8.77459 + 15.1980i) q^{85} +(7.49638 + 1.90087i) q^{87} +(-1.47575 + 2.55607i) q^{89} +(-0.0350577 + 0.0114918i) q^{91} +(-4.95552 - 1.25658i) q^{93} +(-1.79699 + 3.11247i) q^{95} +7.56780 q^{97} +(-4.08090 + 2.50495i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q - 4 q^{7} - 2 q^{9} - 4 q^{11} + q^{13} - 4 q^{15} - 8 q^{17} - q^{19} + 14 q^{21} + 8 q^{23} - 14 q^{25} - 13 q^{29} + 2 q^{31} - 25 q^{33} + 3 q^{35} - q^{37} - 3 q^{39} - 8 q^{41} - 4 q^{43}+ \cdots - 29 q^{99}+O(q^{100}) $ 28 * q - 4 * q^7 - 2 * q^9 - 4 * q^11 + q^13 - 4 * q^15 - 8 * q^17 - q^19 + 14 * q^21 + 8 * q^23 - 14 * q^25 - 13 * q^29 + 2 * q^31 - 25 * q^33 + 3 * q^35 - q^37 - 3 * q^39 - 8 * q^41 - 4 * q^43 - 38 * q^45 + 11 * q^47 + 24 * q^49 + 5 * q^51 + 52 * q^53 - q^57 - 8 * q^59 + 14 * q^61 - 21 * q^63 + 38 * q^65 + 14 * q^67 - 21 * q^69 - 12 * q^71 + 14 * q^73 - 14 * q^75 - 28 * q^77 + 5 * q^79 + 10 * q^81 + 9 * q^83 + 18 * q^85 + 18 * q^87 - 11 * q^89 - q^91 - 9 * q^93 + 28 * q^95 + 50 * q^97 - 29 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/468\mathbb{Z}\right)^\times$.

$n$	$145$	$209$	$235$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	1.20815	−	1.24112i	0.697524	−	0.716561i
$3$	1.20815	−	1.24112i	0.697524	−	0.716561i
$4$		0			0
$5$	1.66845	+	2.88984i	0.746155	+	1.29238i	0.949653	+	0.313303i	$0.101435\pi$
$5$	1.66845	+	2.88984i	0.746155	+	1.29238i	−0.203499	+	0.979075i	$0.565231\pi$
$6$		0			0
$7$	−0.0102323			−0.00386746			−0.00193373	−	0.999998i	$-0.500616\pi$
$7$	−0.0102323			−0.00386746			−0.00193373	+	0.999998i	$0.500616\pi$
$8$		0			0
$9$	−0.0807596	−	2.99891i	−0.0269199	−	0.999638i
$10$		0			0
$11$	−0.798063	−	1.38229i	−0.240625	−	0.416775i	0.720267	−	0.693696i	$-0.244019\pi$
$11$	−0.798063	−	1.38229i	−0.240625	−	0.416775i	−0.960892	+	0.276922i	$0.910686\pi$
$12$		0			0
$13$	3.42617	−	1.12309i	0.950250	−	0.311489i
$13$	3.42617	−	1.12309i	0.950250	−	0.311489i
$14$		0			0
$15$	5.60238	+	1.42061i	1.44653	+	0.366799i
$16$		0			0
$17$	2.62956	+	4.55453i	0.637761	+	1.10464i	0.985923	+	0.167201i	$0.0534728\pi$
$17$	2.62956	+	4.55453i	0.637761	+	1.10464i	−0.348161	+	0.937435i	$0.613194\pi$
$18$		0			0
$19$	0.538519	+	0.932743i	0.123545	+	0.213986i	0.921163	−	0.389177i	$-0.127240\pi$
$19$	0.538519	+	0.932743i	0.123545	+	0.213986i	−0.797618	+	0.603162i	$0.793907\pi$
$20$		0			0
$21$	−0.0123622	+	0.0126995i	−0.00269764	+	0.00277127i
$22$		0			0
$23$	−2.42269			−0.505166			−0.252583	−	0.967575i	$-0.581280\pi$
$23$	−2.42269			−0.505166			−0.252583	+	0.967575i	$0.581280\pi$
$24$		0			0
$25$	−3.06747	+	5.31301i	−0.613494	+	1.06260i
$26$		0			0
$27$	−3.81958	−	3.52290i	−0.735079	−	0.677982i
$28$		0			0
$29$	2.23251	+	3.86681i	0.414566	+	0.718049i	0.995383	−	0.0959849i	$-0.0306001\pi$
$29$	2.23251	+	3.86681i	0.414566	+	0.718049i	−0.580817	+	0.814034i	$0.697267\pi$
$30$		0			0
$31$	−1.47581	−	2.55618i	−0.265063	−	0.459103i	0.702517	−	0.711667i	$-0.252060\pi$
$31$	−1.47581	−	2.55618i	−0.265063	−	0.459103i	−0.967580	+	0.252564i	$0.918726\pi$
$32$		0			0
$33$	−2.67976	−	0.679513i	−0.466486	−	0.118288i
$34$		0			0
$35$	−0.0170722	−	0.0295698i	−0.00288572	−	0.00499821i
$36$		0			0
$37$	4.21638	−	7.30299i	0.693169	−	1.20060i	−0.277625	−	0.960689i	$-0.589547\pi$
$37$	4.21638	−	7.30299i	0.693169	−	1.20060i	0.970794	−	0.239914i	$-0.0771193\pi$
$38$		0			0
$39$	2.74544	−	5.60915i	0.439622	−	0.898183i
$40$		0			0
$41$	6.41407			1.00171			0.500855	−	0.865531i	$-0.333019\pi$
$41$	6.41407			1.00171			0.500855	+	0.865531i	$0.333019\pi$
$42$		0			0
$43$	−10.4798			−1.59816			−0.799080	−	0.601224i	$-0.794680\pi$
$43$	−10.4798			−1.59816			−0.799080	+	0.601224i	$0.794680\pi$
$44$		0			0
$45$	8.53165	−	5.23693i	1.27182	−	0.780675i
$46$		0			0
$47$	4.91647	−	8.51558i	0.717141	−	1.24213i	−0.244987	−	0.969526i	$-0.578784\pi$
$47$	4.91647	−	8.51558i	0.717141	−	1.24213i	0.962128	−	0.272599i	$-0.0878831\pi$
$48$		0			0
$49$	−6.99990			−0.999985
$50$		0			0
$51$	8.82961	+	2.23894i	1.23639	+	0.313515i
$52$		0			0
$53$	−5.27921			−0.725156			−0.362578	−	0.931953i	$-0.618103\pi$
$53$	−5.27921			−0.725156			−0.362578	+	0.931953i	$0.618103\pi$
$54$		0			0
$55$	2.66306	−	4.61256i	0.359087	−	0.621957i
$56$		0			0
$57$	1.80826	+	0.458524i	0.239509	+	0.0607329i
$58$		0			0
$59$	−5.53108	+	9.58012i	−0.720086	+	1.24723i	0.240879	+	0.970555i	$0.422564\pi$
$59$	−5.53108	+	9.58012i	−0.720086	+	1.24723i	−0.960965	+	0.276670i	$0.910769\pi$
$60$		0			0
$61$	−10.8830			−1.39343			−0.696715	−	0.717348i	$-0.745356\pi$
$61$	−10.8830			−1.39343			−0.696715	+	0.717348i	$0.745356\pi$
$62$		0			0
$63$	0.000826358		0.0306858i	0.000104111		0.00386605i
$64$		0			0
$65$	8.96196	+	8.02729i	1.11159	+	0.995663i
$66$		0			0
$67$	−3.39007			−0.414163			−0.207081	−	0.978324i	$-0.566396\pi$
$67$	−3.39007			−0.414163			−0.207081	+	0.978324i	$0.566396\pi$
$68$		0			0
$69$	−2.92697	+	3.00685i	−0.352366	+	0.361983i
$70$		0			0
$71$	1.93480	+	3.35118i	0.229619	+	0.397712i	0.957695	−	0.287784i	$-0.0929187\pi$
$71$	1.93480	+	3.35118i	0.229619	+	0.397712i	−0.728076	+	0.685496i	$0.759585\pi$
$72$		0			0
$73$	−11.6238			−1.36046			−0.680232	−	0.732997i	$-0.738121\pi$
$73$	−11.6238			−1.36046			−0.680232	+	0.732997i	$0.738121\pi$
$74$		0			0
$75$	2.88813	+	10.2260i	0.333493	+	1.18080i
$76$		0			0
$77$	0.00816604	+	0.0141440i	0.000930607	+	0.00161186i
$78$		0			0
$79$	0.0422648	−	0.0732048i	0.00475516	−	0.00823619i	−0.863638	−	0.504112i	$-0.831820\pi$
$79$	0.0422648	−	0.0732048i	0.00475516	−	0.00823619i	0.868393	+	0.495876i	$0.165153\pi$
$80$		0			0
$81$	−8.98696	+	0.484382i	−0.998551	+	0.0538202i
$82$		0			0
$83$	7.14463	−	12.3749i	0.784225	−	1.35832i	−0.145235	−	0.989397i	$-0.546394\pi$
$83$	7.14463	−	12.3749i	0.784225	−	1.35832i	0.929461	−	0.368921i	$-0.120273\pi$
$84$		0			0
$85$	−8.77459	+	15.1980i	−0.951737	+	1.64846i
$86$		0			0
$87$	7.49638	+	1.90087i	0.803696	+	0.203795i
$88$		0			0
$89$	−1.47575	+	2.55607i	−0.156429	+	0.270942i	−0.933578	−	0.358373i	$-0.883331\pi$
$89$	−1.47575	+	2.55607i	−0.156429	+	0.270942i	0.777150	+	0.629316i	$0.216665\pi$
$90$		0			0
$91$	−0.0350577	+	0.0114918i	−0.00367505	+	0.00120467i
$92$		0			0
$93$	−4.95552	−	1.25658i	−0.513864	−	0.130301i
$94$		0			0
$95$	−1.79699	+	3.11247i	−0.184367	+	0.319333i
$96$		0			0
$97$	7.56780			0.768394			0.384197	−	0.923251i	$-0.374478\pi$
$97$	7.56780			0.768394			0.384197	+	0.923251i	$0.374478\pi$
$98$		0			0
$99$	−4.08090	+	2.50495i	−0.410146	+	0.251757i
$100$		0			0
$101$	−3.70513	−	6.41747i	−0.368674	−	0.638562i	0.620685	−	0.784060i	$-0.286855\pi$
$101$	−3.70513	−	6.41747i	−0.368674	−	0.638562i	−0.989358	+	0.145498i	$0.953521\pi$
$102$		0			0
$103$	1.73997	+	3.01372i	0.171445	+	0.296951i	0.938925	−	0.344122i	$-0.111823\pi$
$103$	1.73997	+	3.01372i	0.171445	+	0.296951i	−0.767481	+	0.641072i	$0.778490\pi$
$104$		0			0
$105$	−0.0573254	−	0.0145361i	−0.00559439	−	0.00141858i
$106$		0			0
$107$	−7.67101	+	13.2866i	−0.741584	+	1.28446i	0.210190	+	0.977661i	$0.432592\pi$
$107$	−7.67101	+	13.2866i	−0.741584	+	1.28446i	−0.951774	+	0.306801i	$0.900742\pi$
$108$		0			0
$109$	−1.79923			−0.172335			−0.0861674	−	0.996281i	$-0.527462\pi$
$109$	−1.79923			−0.172335			−0.0861674	+	0.996281i	$0.527462\pi$
$110$		0			0
$111$	−3.96988	−	14.0561i	−0.376804	−	1.33415i
$112$		0			0
$113$	−8.12251	+	14.0686i	−0.764102	+	1.32346i	0.176619	+	0.984279i	$0.443484\pi$
$113$	−8.12251	+	14.0686i	−0.764102	+	1.32346i	−0.940720	+	0.339184i	$0.889849\pi$
$114$		0			0
$115$	−4.04215	−	7.00120i	−0.376932	−	0.652866i
$116$		0			0
$117$	−3.64474	−	10.1841i	−0.336956	−	0.941520i
$118$		0			0
$119$	−0.0269065	−	0.0466034i	−0.00246651	−	0.00427213i
$120$		0			0
$121$	4.22619	−	7.31998i	0.384199	−	0.665452i
$122$		0			0
$123$	7.74914	−	7.96063i	0.698716	−	0.717786i
$124$		0			0
$125$	−3.78718			−0.338736
$126$		0			0
$127$	0.649469	−	1.12491i	0.0576311	−	0.0998200i	−0.835770	−	0.549079i	$-0.814979\pi$
$127$	0.649469	−	1.12491i	0.0576311	−	0.0998200i	0.893402	+	0.449259i	$0.148312\pi$
$128$		0			0
$129$	−12.6612	+	13.0067i	−1.11476	+	1.14518i
$130$		0			0
$131$	1.60383	+	2.77792i	0.140127	+	0.242708i	0.927544	−	0.373713i	$-0.121915\pi$
$131$	1.60383	+	2.77792i	0.140127	+	0.242708i	−0.787417	+	0.616421i	$0.788582\pi$
$132$		0			0
$133$	−0.00551030	−	0.00954413i	−0.000477804	−	0.000827581i
$134$		0			0
$135$	3.80783	−	16.9158i	0.327726	−	1.45588i
$136$		0			0
$137$	−14.7995			−1.26440			−0.632201	−	0.774804i	$-0.717848\pi$
$137$	−14.7995			−1.26440			−0.632201	+	0.774804i	$0.717848\pi$
$138$		0			0
$139$	7.40470	−	12.8253i	0.628058	−	1.08783i	−0.359883	−	0.932998i	$-0.617183\pi$
$139$	7.40470	−	12.8253i	0.628058	−	1.08783i	0.987941	−	0.154831i	$-0.0494834\pi$
$140$		0			0
$141$	−4.62904	−	16.3900i	−0.389835	−	1.38029i
$142$		0			0
$143$	−4.28673	−	3.83966i	−0.358475	−	0.321088i
$144$		0			0
$145$	−7.44966	+	12.9032i	−0.618661	+	1.07155i
$146$		0			0
$147$	−8.45691	+	8.68771i	−0.697514	+	0.716550i
$148$		0			0
$149$	0.731623	−	1.26721i	0.0599369	−	0.103814i	−0.834500	−	0.551008i	$-0.814243\pi$
$149$	0.731623	−	1.26721i	0.0599369	−	0.103814i	0.894437	+	0.447194i	$0.147577\pi$
$150$		0			0
$151$	5.34215	−	9.25288i	0.434738	−	0.752989i	−0.562536	−	0.826773i	$-0.690174\pi$
$151$	5.34215	−	9.25288i	0.434738	−	0.752989i	0.997274	+	0.0737841i	$0.0235076\pi$
$152$		0			0
$153$	13.4463	−	8.25364i	1.08707	−	0.667267i
$154$		0			0
$155$	4.92464	−	8.52972i	0.395556	−	0.685124i
$156$		0			0
$157$	5.41225	+	9.37430i	0.431945	+	0.748150i	0.997041	−	0.0768749i	$-0.0244942\pi$
$157$	5.41225	+	9.37430i	0.431945	+	0.748150i	−0.565096	+	0.825025i	$0.691161\pi$
$158$		0			0
$159$	−6.37807	+	6.55214i	−0.505814	+	0.519619i
$160$		0			0
$161$	0.0247898			0.00195371
$162$		0			0
$163$	8.68816	+	15.0483i	0.680509	+	1.17868i	0.974826	+	0.222968i	$0.0715746\pi$
$163$	8.68816	+	15.0483i	0.680509	+	1.17868i	−0.294317	+	0.955708i	$0.595092\pi$
$164$		0			0
$165$	−2.50737	−	8.87783i	−0.195198	−	0.691138i
$166$		0			0
$167$	−8.34269			−0.645577			−0.322788	−	0.946471i	$-0.604620\pi$
$167$	−8.34269			−0.645577			−0.322788	+	0.946471i	$0.604620\pi$
$168$		0			0
$169$	10.4773	−	7.69579i	0.805950	−	0.591984i
$170$		0			0
$171$	2.75372	−	1.69030i	0.210583	−	0.129260i
$172$		0			0
$173$	11.6480			0.885581			0.442790	−	0.896625i	$-0.353989\pi$
$173$	11.6480			0.885581			0.442790	+	0.896625i	$0.353989\pi$
$174$		0			0
$175$	0.0313873	−	0.0543645i	0.00237266	−	0.00410957i
$176$		0			0
$177$	5.20772	+	18.4389i	0.391436	+	1.38596i
$178$		0			0
$179$	−4.03526	+	6.98927i	−0.301609	+	0.522403i	−0.976501	−	0.215514i	$-0.930857\pi$
$179$	−4.03526	+	6.98927i	−0.301609	+	0.522403i	0.674891	+	0.737917i	$0.264191\pi$
$180$		0			0
$181$	−14.6028			−1.08542			−0.542710	−	0.839920i	$-0.682602\pi$
$181$	−14.6028			−1.08542			−0.542710	+	0.839920i	$0.682602\pi$
$182$		0			0
$183$	−13.1483	+	13.5072i	−0.971951	+	0.998478i
$184$		0			0
$185$	28.1393			2.06884
$186$		0			0
$187$	4.19711	−	7.26960i	0.306923	−	0.531606i
$188$		0			0
$189$	0.0390832	+	0.0360474i	0.00284288	+	0.00262206i
$190$		0			0
$191$	−12.3672			−0.894857			−0.447429	−	0.894320i	$-0.647660\pi$
$191$	−12.3672			−0.894857			−0.447429	+	0.894320i	$0.647660\pi$
$192$		0			0
$193$	−17.9223			−1.29007			−0.645037	−	0.764151i	$-0.723158\pi$
$193$	−17.9223			−1.29007			−0.645037	+	0.764151i	$0.723158\pi$
$194$		0			0
$195$	20.7902	−	1.42472i	1.48882	−	0.102026i
$196$		0			0
$197$	1.59771	−	2.76731i	0.113832	−	0.197163i	−0.803480	−	0.595331i	$-0.797021\pi$
$197$	1.59771	−	2.76731i	0.113832	−	0.197163i	0.917312	+	0.398169i	$0.130354\pi$
$198$		0			0
$199$	−12.4051	−	21.4862i	−0.879371	−	1.52312i	−0.852032	−	0.523490i	$-0.824630\pi$
$199$	−12.4051	−	21.4862i	−0.879371	−	1.52312i	−0.0273392	−	0.999626i	$-0.508703\pi$
$200$		0			0
$201$	−4.09570	+	4.20748i	−0.288888	+	0.296773i
$202$		0			0
$203$	−0.0228437	−	0.0395665i	−0.00160332	−	0.00277702i
$204$		0			0
$205$	10.7016	+	18.5357i	0.747430	+	1.29459i
$206$		0			0
$207$	0.195656	+	7.26544i	0.0135990	+	0.504983i
$208$		0			0
$209$	0.859545	−	1.48877i	0.0594559	−	0.102981i
$210$		0			0
$211$	24.1866			1.66507			0.832537	−	0.553969i	$-0.186887\pi$
$211$	24.1866			1.66507			0.832537	+	0.553969i	$0.186887\pi$
$212$		0			0
$213$	6.49674	+	1.64739i	0.445149	+	0.112877i
$214$		0			0
$215$	−17.4851	−	30.2851i	−1.19248	−	2.06543i
$216$		0			0
$217$	0.0151010	+	0.0261556i	0.00102512	+	0.00177556i
$218$		0			0
$219$	−14.0433	+	14.4266i	−0.948957	+	0.974856i
$220$		0			0
$221$	14.1245	+	12.6514i	0.950114	+	0.851024i
$222$		0			0
$223$	4.03403	+	6.98714i	0.270138	+	0.467893i	0.968897	−	0.247464i	$-0.0795972\pi$
$223$	4.03403	+	6.98714i	0.270138	+	0.467893i	−0.698759	+	0.715357i	$0.746264\pi$
$224$		0			0
$225$	16.1810	+	8.76999i	1.07873	+	0.584666i
$226$		0			0
$227$	17.3794			1.15351			0.576757	−	0.816916i	$-0.304318\pi$
$227$	17.3794			1.15351			0.576757	+	0.816916i	$0.304318\pi$
$228$		0			0
$229$	13.3449	+	23.1141i	0.881857	+	1.52742i	0.849274	+	0.527952i	$0.177040\pi$
$229$	13.3449	+	23.1141i	0.881857	+	1.52742i	0.0325830	+	0.999469i	$0.489627\pi$
$230$		0			0
$231$	0.0274202	+	0.00695299i	0.00180412	+	0.000457473i
$232$		0			0
$233$	4.21829			0.276349			0.138175	−	0.990408i	$-0.455876\pi$
$233$	4.21829			0.276349			0.138175	+	0.990408i	$0.455876\pi$
$234$		0			0
$235$	32.8116			2.14039
$236$		0			0
$237$	−0.0397939	−	0.140898i	−0.00258489	−	0.00915231i
$238$		0			0
$239$	−3.80822	−	6.59604i	−0.246333	−	0.426662i	0.716172	−	0.697924i	$-0.245893\pi$
$239$	−3.80822	−	6.59604i	−0.246333	−	0.426662i	−0.962506	+	0.271262i	$0.912559\pi$
$240$		0			0
$241$	2.42805			0.156404			0.0782021	−	0.996938i	$-0.475082\pi$
$241$	2.42805			0.156404			0.0782021	+	0.996938i	$0.475082\pi$
$242$		0			0
$243$	−10.2564	+	11.7391i	−0.657948	+	0.753064i
$244$		0			0
$245$	−11.6790	−	20.2286i	−0.746144	−	1.29236i
$246$		0			0
$247$	2.89261	+	2.59094i	0.184053	+	0.164857i
$248$		0			0
$249$	−6.72693	−	23.8180i	−0.426302	−	1.50941i
$250$		0			0
$251$	−6.94330	−	12.0262i	−0.438257	−	0.759084i	0.559298	−	0.828967i	$-0.311071\pi$
$251$	−6.94330	−	12.0262i	−0.438257	−	0.759084i	−0.997555	+	0.0698827i	$0.977738\pi$
$252$		0			0
$253$	1.93346	+	3.34885i	0.121556	+	0.210541i
$254$		0			0
$255$	8.26159	+	29.2518i	0.517361	+	1.83182i
$256$		0			0
$257$	16.3511			1.01995			0.509977	−	0.860188i	$-0.329654\pi$
$257$	16.3511			1.01995			0.509977	+	0.860188i	$0.329654\pi$
$258$		0			0
$259$	−0.0431434	+	0.0747265i	−0.00268080	+	0.00464328i
$260$		0			0
$261$	11.4159	−	7.00737i	0.706629	−	0.433746i
$262$		0			0
$263$	13.0566	+	22.6146i	0.805102	+	1.39448i	0.916222	+	0.400671i	$0.131223\pi$
$263$	13.0566	+	22.6146i	0.805102	+	1.39448i	−0.111119	+	0.993807i	$0.535444\pi$
$264$		0			0
$265$	−8.80812	−	15.2561i	−0.541078	−	0.937175i
$266$		0			0
$267$	1.38947	+	4.91968i	0.0850340	+	0.301080i
$268$		0			0
$269$	−5.60821	−	9.71370i	−0.341938	−	0.592255i	0.642854	−	0.765988i	$-0.277750\pi$
$269$	−5.60821	−	9.71370i	−0.341938	−	0.592255i	−0.984793	+	0.173734i	$0.944417\pi$
$270$		0			0
$271$	10.8606	−	18.8111i	0.659735	−	1.14269i	−0.320949	−	0.947096i	$-0.604002\pi$
$271$	10.8606	−	18.8111i	0.659735	−	1.14269i	0.980684	−	0.195598i	$-0.0626648\pi$
$272$		0			0
$273$	−0.0280922	+	0.0573947i	−0.00170022	+	0.00347368i
$274$		0			0
$275$	9.79213			0.590488
$276$		0			0
$277$	18.8036			1.12980			0.564899	−	0.825160i	$-0.308915\pi$
$277$	18.8036			1.12980			0.564899	+	0.825160i	$0.308915\pi$
$278$		0			0
$279$	−7.54657	+	4.63226i	−0.451801	+	0.277326i
$280$		0			0
$281$	7.54698	−	13.0718i	0.450215	−	0.779796i	−0.548184	−	0.836358i	$-0.684681\pi$
$281$	7.54698	−	13.0718i	0.450215	−	0.779796i	0.998399	+	0.0565622i	$0.0180139\pi$
$282$		0			0
$283$	12.4437			0.739702			0.369851	−	0.929091i	$-0.379409\pi$
$283$	12.4437			0.739702			0.369851	+	0.929091i	$0.379409\pi$
$284$		0			0
$285$	1.69193	+	5.99061i	0.100221	+	0.354853i
$286$		0			0
$287$	−0.0656308			−0.00387406
$288$		0			0
$289$	−5.32915	+	9.23036i	−0.313479	+	0.542962i
$290$		0			0
$291$	9.14302	−	9.39256i	0.535974	−	0.550601i
$292$		0			0
$293$	16.0902	−	27.8691i	0.940001	−	1.62813i	0.174537	−	0.984651i	$-0.444157\pi$
$293$	16.0902	−	27.8691i	0.940001	−	1.62813i	0.765464	−	0.643479i	$-0.222509\pi$
$294$		0			0
$295$	−36.9134			−2.14918
$296$		0			0
$297$	−1.82138	+	8.09125i	−0.105687	+	0.469502i
$298$		0			0
$299$	−8.30057	+	2.72090i	−0.480034	+	0.157354i
$300$		0			0
$301$	0.107233			0.00618081
$302$		0			0
$303$	−12.4412	−	3.15474i	−0.714728	−	0.181235i
$304$		0			0
$305$	−18.1578	−	31.4503i	−1.03971	−	1.80084i
$306$		0			0
$307$	−16.1883			−0.923916			−0.461958	−	0.886902i	$-0.652853\pi$
$307$	−16.1883			−0.923916			−0.461958	+	0.886902i	$0.652853\pi$
$308$		0			0
$309$	5.84253	+	1.48150i	0.332370	+	0.0842798i
$310$		0			0
$311$	0.376469	+	0.652063i	0.0213476	+	0.0369751i	0.876502	−	0.481398i	$-0.159871\pi$
$311$	0.376469	+	0.652063i	0.0213476	+	0.0369751i	−0.855154	+	0.518374i	$0.826538\pi$
$312$		0			0
$313$	9.45372	−	16.3743i	0.534356	−	0.925532i	−0.464838	−	0.885396i	$-0.653888\pi$
$313$	9.45372	−	16.3743i	0.534356	−	0.925532i	0.999194	−	0.0401361i	$-0.0127792\pi$
$314$		0			0
$315$	−0.0872986	+	0.0535859i	−0.00491872	+	0.00301923i
$316$		0			0
$317$	1.61800	−	2.80247i	0.0908762	−	0.157402i	−0.817004	−	0.576632i	$-0.804367\pi$
$317$	1.61800	−	2.80247i	0.0908762	−	0.157402i	0.907880	+	0.419230i	$0.137700\pi$
$318$		0			0
$319$	3.56336	−	6.17192i	0.199510	−	0.345561i
$320$		0			0
$321$	7.22253	+	25.5728i	0.403122	+	1.42733i
$322$		0			0
$323$	−2.83214	+	4.90540i	−0.157584	+	0.272944i
$324$		0			0
$325$	−4.54270	+	21.6483i	−0.251984	+	1.20083i
$326$		0			0
$327$	−2.17373	+	2.23306i	−0.120208	+	0.123488i
$328$		0			0
$329$	−0.0503069	+	0.0871342i	−0.00277351	+	0.00480386i
$330$		0			0
$331$	25.1091			1.38012			0.690060	−	0.723752i	$-0.257584\pi$
$331$	25.1091			1.38012			0.690060	+	0.723752i	$0.257584\pi$
$332$		0			0
$333$	−22.2415	−	12.0548i	−1.21883	−	0.660598i
$334$		0			0
$335$	−5.65617	−	9.79677i	−0.309029	−	0.535255i
$336$		0			0
$337$	−18.1685	−	31.4687i	−0.989699	−	1.71421i	−0.618835	−	0.785521i	$-0.712395\pi$
$337$	−18.1685	−	31.4687i	−0.989699	−	1.71421i	−0.370863	−	0.928687i	$-0.620938\pi$
$338$		0			0
$339$	7.64764	+	27.0780i	0.415363	+	1.47067i
$340$		0			0
$341$	−2.35558	+	4.07998i	−0.127562	+	0.220943i
$342$		0			0
$343$	0.143251			0.00773485
$344$		0			0
$345$	−13.5728	−	3.44170i	−0.730738	−	0.185295i
$346$		0			0
$347$	−15.4139	+	26.6977i	−0.827464	+	1.43321i	0.0725576	+	0.997364i	$0.476884\pi$
$347$	−15.4139	+	26.6977i	−0.827464	+	1.43321i	−0.900022	+	0.435845i	$0.856449\pi$
$348$		0			0
$349$	6.13548	+	10.6270i	0.328425	+	0.568848i	0.982199	−	0.187841i	$-0.0601490\pi$
$349$	6.13548	+	10.6270i	0.328425	+	0.568848i	−0.653775	+	0.756689i	$0.726816\pi$
$350$		0			0
$351$	−17.0431	−	7.78033i	−0.909692	−	0.415283i
$352$		0			0
$353$	5.56638	+	9.64125i	0.296268	+	0.513152i	0.975279	−	0.220976i	$-0.0709244\pi$
$353$	5.56638	+	9.64125i	0.296268	+	0.513152i	−0.679011	+	0.734128i	$0.737591\pi$
$354$		0			0
$355$	−6.45626	+	11.1826i	−0.342662	+	0.593509i
$356$		0			0
$357$	−0.0903474	−	0.0229096i	−0.00478169	−	0.00121250i
$358$		0			0
$359$	−20.5430			−1.08422			−0.542110	−	0.840307i	$-0.682374\pi$
$359$	−20.5430			−1.08422			−0.542110	+	0.840307i	$0.682374\pi$
$360$		0			0
$361$	8.91999	−	15.4499i	0.469473	−	0.813152i
$362$		0			0
$363$	−3.97911	−	14.0888i	−0.208849	−	0.739471i
$364$		0			0
$365$	−19.3938	−	33.5910i	−1.01512	−	1.75823i
$366$		0			0
$367$	13.0356	+	22.5782i	0.680451	+	1.17857i	0.974843	+	0.222891i	$0.0715492\pi$
$367$	13.0356	+	22.5782i	0.680451	+	1.17857i	−0.294393	+	0.955684i	$0.595117\pi$
$368$		0			0
$369$	−0.517997	−	19.2352i	−0.0269659	−	1.00135i
$370$		0			0
$371$	0.0540186			0.00280451
$372$		0			0
$373$	4.61039	−	7.98543i	0.238717	−	0.413470i	−0.721629	−	0.692280i	$-0.756606\pi$
$373$	4.61039	−	7.98543i	0.238717	−	0.413470i	0.960346	+	0.278810i	$0.0899398\pi$
$374$		0			0
$375$	−4.57547	+	4.70035i	−0.236276	+	0.242725i
$376$		0			0
$377$	11.9917	+	10.7411i	0.617605	+	0.553194i
$378$		0			0
$379$	−18.1438	+	31.4259i	−0.931982	+	1.61424i	−0.152054	+	0.988372i	$0.548589\pi$
$379$	−18.1438	+	31.4259i	−0.931982	+	1.61424i	−0.779929	+	0.625869i	$0.784745\pi$
$380$		0			0
$381$	−0.611499	−	2.16513i	−0.0313280	−	0.110923i
$382$		0			0
$383$	−15.8019	+	27.3696i	−0.807437	+	1.39852i	0.107196	+	0.994238i	$0.465813\pi$
$383$	−15.8019	+	27.3696i	−0.807437	+	1.39852i	−0.914633	+	0.404285i	$0.867521\pi$
$384$		0			0
$385$	−0.0272493	+	0.0471972i	−0.00138875	+	0.00240539i
$386$		0			0
$387$	0.846347	+	31.4281i	0.0430223	+	1.59758i
$388$		0			0
$389$	−4.02494	+	6.97141i	−0.204073	+	0.353464i	−0.949837	−	0.312746i	$-0.898751\pi$
$389$	−4.02494	+	6.97141i	−0.204073	+	0.353464i	0.745764	+	0.666210i	$0.232085\pi$
$390$		0			0
$391$	−6.37061	−	11.0342i	−0.322176	−	0.558024i
$392$		0			0
$393$	5.38540	+	1.36559i	0.271657	+	0.0688847i
$394$		0			0
$395$	0.282067			0.0141924
$396$		0			0
$397$	17.3633	+	30.0740i	0.871437	+	1.50937i	0.860511	+	0.509433i	$0.170145\pi$
$397$	17.3633	+	30.0740i	0.871437	+	1.50937i	0.0109262	+	0.999940i	$0.496522\pi$
$398$		0			0
$399$	−0.0185027	−	0.00469176i	−0.000926292	−	0.000234882i
$400$		0			0
$401$	−6.71575			−0.335369			−0.167684	−	0.985841i	$-0.553629\pi$
$401$	−6.71575			−0.335369			−0.167684	+	0.985841i	$0.553629\pi$
$402$		0			0
$403$	−7.92720	−	7.10045i	−0.394882	−	0.353699i
$404$		0			0
$405$	−16.3941	−	25.1627i	−0.814629	−	1.25035i
$406$		0			0
$407$	−13.4598			−0.667175
$408$		0			0
$409$	−2.03024	+	3.51648i	−0.100389	+	0.173879i	−0.911845	−	0.410535i	$-0.865342\pi$
$409$	−2.03024	+	3.51648i	−0.100389	+	0.173879i	0.811456	+	0.584414i	$0.198675\pi$
$410$		0			0
$411$	−17.8799	+	18.3679i	−0.881952	+	0.906022i
$412$		0			0
$413$	0.0565958	−	0.0980269i	0.00278490	−	0.00482359i
$414$		0			0
$415$	47.6819			2.34061
$416$		0			0
$417$	−6.97179	−	24.6850i	−0.341410	−	1.20883i
$418$		0			0
$419$	11.5848			0.565955			0.282978	−	0.959126i	$-0.408678\pi$
$419$	11.5848			0.565955			0.282978	+	0.959126i	$0.408678\pi$
$420$		0			0
$421$	10.3527	−	17.9315i	0.504562	−	0.873927i	−0.495424	−	0.868651i	$-0.664987\pi$
$421$	10.3527	−	17.9315i	0.504562	−	0.873927i	0.999986	−	0.00527578i	$-0.00167934\pi$
$422$		0			0
$423$	−25.9345	−	14.0564i	−1.26098	−	0.683443i
$424$		0			0
$425$	−32.2643			−1.56505
$426$		0			0
$427$	0.111359			0.00538903
$428$		0			0
$429$	−9.94448	+	0.681478i	−0.480124	+	0.0329021i
$430$		0			0
$431$	14.2615	−	24.7017i	0.686954	−	1.18984i	−0.285864	−	0.958270i	$-0.592281\pi$
$431$	14.2615	−	24.7017i	0.686954	−	1.18984i	0.972818	−	0.231570i	$-0.0743861\pi$
$432$		0			0
$433$	0.406291	+	0.703716i	0.0195251	+	0.0338184i	0.875623	−	0.482995i	$-0.160451\pi$
$433$	0.406291	+	0.703716i	0.0195251	+	0.0338184i	−0.856098	+	0.516814i	$0.827118\pi$
$434$		0			0
$435$	7.01413	+	24.8349i	0.336302	+	1.19074i
$436$		0			0
$437$	−1.30467	−	2.25975i	−0.0624107	−	0.108098i
$438$		0			0
$439$	1.54559	+	2.67704i	0.0737670	+	0.127768i	0.900549	−	0.434754i	$-0.143165\pi$
$439$	1.54559	+	2.67704i	0.0737670	+	0.127768i	−0.826782	+	0.562522i	$0.809831\pi$
$440$		0			0
$441$	0.565309	+	20.9921i	0.0269195	+	0.999623i
$442$		0			0
$443$	12.8847	−	22.3169i	0.612170	−	1.06031i	−0.378704	−	0.925518i	$-0.623630\pi$
$443$	12.8847	−	22.3169i	0.612170	−	1.06031i	0.990874	−	0.134791i	$-0.0430364\pi$
$444$		0			0
$445$	−9.84885			−0.466880
$446$		0			0
$447$	−0.688850	−	2.43901i	−0.0325815	−	0.115361i
$448$		0			0
$449$	14.5947	+	25.2788i	0.688767	+	1.19298i	0.972237	+	0.233998i	$0.0751809\pi$
$449$	14.5947	+	25.2788i	0.688767	+	1.19298i	−0.283470	+	0.958981i	$0.591486\pi$
$450$		0			0
$451$	−5.11883	−	8.86607i	−0.241036	−	0.417487i
$452$		0			0
$453$	−5.02983	−	17.8091i	−0.236322	−	0.836744i
$454$		0			0
$455$	−0.0917017	−	0.0821379i	−0.00429904	−	0.00385068i
$456$		0			0
$457$	8.31447	+	14.4011i	0.388935	+	0.673654i	0.992306	−	0.123806i	$-0.0395099\pi$
$457$	8.31447	+	14.4011i	0.388935	+	0.673654i	−0.603372	+	0.797460i	$0.706177\pi$
$458$		0			0
$459$	6.00132	−	26.6600i	0.280118	−	1.24438i
$460$		0			0
$461$	−8.55288			−0.398347			−0.199174	−	0.979964i	$-0.563826\pi$
$461$	−8.55288			−0.398347			−0.199174	+	0.979964i	$0.563826\pi$
$462$		0			0
$463$	7.03741	+	12.1891i	0.327056	+	0.566478i	0.981926	−	0.189264i	$-0.0606101\pi$
$463$	7.03741	+	12.1891i	0.327056	+	0.566478i	−0.654870	+	0.755741i	$0.727277\pi$
$464$		0			0
$465$	−4.63673	−	16.4172i	−0.215023	−	0.761331i
$466$		0			0
$467$	−28.4099			−1.31466			−0.657328	−	0.753605i	$-0.728313\pi$
$467$	−28.4099			−1.31466			−0.657328	+	0.753605i	$0.728313\pi$
$468$		0			0
$469$	0.0346883			0.00160176
$470$		0			0
$471$	18.1734	+	4.60827i	0.837387	+	0.212338i
$472$		0			0
$473$	8.36357	+	14.4861i	0.384557	+	0.666073i
$474$		0			0
$475$	−6.60756			−0.303176
$476$		0			0
$477$	0.426347	+	15.8319i	0.0195211	+	0.724893i
$478$		0			0
$479$	−7.37328	−	12.7709i	−0.336894	−	0.583517i	0.646953	−	0.762530i	$-0.276043\pi$
$479$	−7.37328	−	12.7709i	−0.336894	−	0.583517i	−0.983847	+	0.179013i	$0.942710\pi$
$480$		0			0
$481$	6.24416	−	29.7567i	0.284709	−	1.35679i
$482$		0			0
$483$	0.0299497	−	0.0307671i	0.00136276	−	0.00139995i
$484$		0			0
$485$	12.6265	+	21.8698i	0.573341	+	0.993056i
$486$		0			0
$487$	−10.8985	−	18.8767i	−0.493856	−	0.855384i	0.506119	−	0.862464i	$-0.331080\pi$
$487$	−10.8985	−	18.8767i	−0.493856	−	0.855384i	−0.999975	+	0.00707973i	$0.997746\pi$
$488$		0			0
$489$	29.1734	+	7.39755i	1.31927	+	0.334529i
$490$		0			0
$491$	−25.9667			−1.17186			−0.585931	−	0.810361i	$-0.699271\pi$
$491$	−25.9667			−1.17186			−0.585931	+	0.810361i	$0.699271\pi$
$492$		0			0
$493$	−11.7410	+	20.3360i	−0.528788	+	0.915889i
$494$		0			0
$495$	−14.0477	−	7.61378i	−0.631398	−	0.342214i
$496$		0			0
$497$	−0.0197975	−	0.0342903i	−0.000888041	−	0.00153813i
$498$		0			0
$499$	−1.53590	−	2.66026i	−0.0687564	−	0.119090i	0.829598	−	0.558362i	$-0.188570\pi$
$499$	−1.53590	−	2.66026i	−0.0687564	−	0.119090i	−0.898354	+	0.439272i	$0.855236\pi$
$500$		0			0
$501$	−10.0792	+	10.3543i	−0.450305	+	0.462595i
$502$		0			0
$503$	11.2760	+	19.5306i	0.502771	+	0.870824i	0.999995	+	0.00320229i	$0.00101932\pi$
$503$	11.2760	+	19.5306i	0.502771	+	0.870824i	−0.497224	+	0.867622i	$0.665647\pi$
$504$		0			0
$505$	12.3637	−	21.4145i	0.550175	−	0.952932i
$506$		0			0
$507$	3.10678	−	22.3013i	0.137977	−	0.990435i
$508$		0			0
$509$	11.1485			0.494149			0.247075	−	0.968996i	$-0.420531\pi$
$509$	11.1485			0.494149			0.247075	+	0.968996i	$0.420531\pi$
$510$		0			0
$511$	0.118939			0.00526154
$512$		0			0
$513$	1.22904	−	5.45983i	0.0542634	−	0.241058i
$514$		0			0
$515$	−5.80612	+	10.0565i	−0.255848	+	0.443142i
$516$		0			0
$517$	−15.6946			−0.690249
$518$		0			0
$519$	14.0725	−	14.4566i	0.617714	−	0.634573i
$520$		0			0
$521$	−3.23730			−0.141829			−0.0709144	−	0.997482i	$-0.522592\pi$
$521$	−3.23730			−0.141829			−0.0709144	+	0.997482i	$0.522592\pi$
$522$		0			0
$523$	−9.74636	+	16.8812i	−0.426178	+	0.738163i	−0.996530	−	0.0832382i	$-0.973474\pi$
$523$	−9.74636	+	16.8812i	−0.426178	+	0.738163i	0.570351	+	0.821401i	$0.306807\pi$
$524$		0			0
$525$	−0.0295523	−	0.104636i	−0.00128977	−	0.00456668i
$526$		0			0
$527$	7.76146	−	13.4432i	0.338094	−	0.585597i
$528$		0			0
$529$	−17.1306			−0.744807
$530$		0			0
$531$	29.1766	+	15.8136i	1.26616	+	0.686250i
$532$		0			0
$533$	21.9757	−	7.20356i	0.951874	−	0.312021i
$534$		0			0
$535$	−51.1948			−2.21335
$536$		0			0
$537$	3.79934	+	13.4523i	0.163954	+	0.580510i
$538$		0			0
$539$	5.58636	+	9.67585i	0.240621	+	0.416769i
$540$		0			0
$541$	39.6790			1.70593			0.852966	−	0.521967i	$-0.174801\pi$
$541$	39.6790			1.70593			0.852966	+	0.521967i	$0.174801\pi$
$542$		0			0
$543$	−17.6424	+	18.1239i	−0.757107	+	0.777770i
$544$		0			0
$545$	−3.00193	−	5.19949i	−0.128588	−	0.222722i
$546$		0			0
$547$	2.31210	−	4.00468i	0.0988583	−	0.171228i	−0.812354	−	0.583165i	$-0.801814\pi$
$547$	2.31210	−	4.00468i	0.0988583	−	0.171228i	0.911212	+	0.411937i	$0.135148\pi$
$548$		0			0
$549$	0.878909	+	32.6373i	0.0375109	+	1.39292i
$550$		0			0
$551$	−2.40450	+	4.16471i	−0.102435	+	0.177423i
$552$		0			0
$553$	−0.000432467	0	0.000749056i	−1.83904e−5	0	3.18531e-5i
$554$		0			0
$555$	33.9965	−	34.9243i	1.44307	−	1.48245i
$556$		0			0
$557$	−6.99536	+	12.1163i	−0.296403	+	0.513385i	−0.975310	−	0.220839i	$-0.929120\pi$
$557$	−6.99536	+	12.1163i	−0.296403	+	0.513385i	0.678907	+	0.734224i	$0.262454\pi$
$558$		0			0
$559$	−35.9058	+	11.7698i	−1.51865	+	0.497809i
$560$		0			0
$561$	−3.95173	−	13.9919i	−0.166842	−	0.590737i
$562$		0			0
$563$	−3.11628	+	5.39756i	−0.131336	+	0.227480i	−0.924192	−	0.381929i	$-0.875260\pi$
$563$	−3.11628	+	5.39756i	−0.131336	+	0.227480i	0.792856	+	0.609409i	$0.208593\pi$
$564$		0			0
$565$	−54.2081			−2.28055
$566$		0			0
$567$	0.0919575	−	0.00495635i	0.00386185	−	0.000208147i
$568$		0			0
$569$	14.9219	+	25.8455i	0.625558	+	1.08350i	0.988433	+	0.151660i	$0.0484619\pi$
$569$	14.9219	+	25.8455i	0.625558	+	1.08350i	−0.362875	+	0.931838i	$0.618205\pi$
$570$		0			0
$571$	17.0296	+	29.4962i	0.712668	+	1.23438i	0.963852	+	0.266438i	$0.0858469\pi$
$571$	17.0296	+	29.4962i	0.712668	+	1.23438i	−0.251184	+	0.967939i	$0.580820\pi$
$572$		0			0
$573$	−14.9414	+	15.3492i	−0.624185	+	0.641220i
$574$		0			0
$575$	7.43153	−	12.8718i	0.309916	−	0.536791i
$576$		0			0
$577$	−27.1865			−1.13179			−0.565895	−	0.824477i	$-0.691469\pi$
$577$	−27.1865			−1.13179			−0.565895	+	0.824477i	$0.691469\pi$
$578$		0			0
$579$	−21.6528	+	22.2437i	−0.899858	+	0.924417i
$580$		0			0
$581$	−0.0731062	+	0.126624i	−0.00303296	+	0.00525324i
$582$		0			0
$583$	4.21315	+	7.29738i	0.174491	+	0.302227i
$584$		0			0
$585$	23.3494	−	27.5244i	0.965379	−	1.13799i
$586$		0			0
$587$	19.0165	+	32.9376i	0.784895	+	1.35948i	0.929062	+	0.369925i	$0.120617\pi$
$587$	19.0165	+	32.9376i	0.784895	+	1.35948i	−0.144166	+	0.989553i	$0.546050\pi$
$588$		0			0
$589$	1.58950	−	2.75310i	0.0654944	−	0.113440i
$590$		0			0
$591$	−1.50430	−	5.32626i	−0.0618786	−	0.219093i
$592$		0			0
$593$	−16.5666			−0.680308			−0.340154	−	0.940370i	$-0.610479\pi$
$593$	−16.5666			−0.680308			−0.340154	+	0.940370i	$0.610479\pi$
$594$		0			0
$595$	0.0897844	−	0.155511i	0.00368080	−	0.00637534i
$596$		0			0
$597$	−41.6541	−	10.5623i	−1.70479	−	0.432287i
$598$		0			0
$599$	−24.1602	−	41.8467i	−0.987158	−	1.70981i	−0.631923	−	0.775031i	$-0.717734\pi$
$599$	−24.1602	−	41.8467i	−0.987158	−	1.70981i	−0.355236	−	0.934777i	$-0.615599\pi$
$600$		0			0
$601$	−2.54011	−	4.39959i	−0.103613	−	0.179463i	0.809558	−	0.587040i	$-0.199707\pi$
$601$	−2.54011	−	4.39959i	−0.103613	−	0.179463i	−0.913171	+	0.407577i	$0.866374\pi$
$602$		0			0
$603$	0.273780	+	10.1665i	0.0111492	+	0.414013i
$604$		0			0
$605$	28.2048			1.14669
$606$		0			0
$607$	15.8874	−	27.5177i	0.644848	−	1.11691i	−0.339489	−	0.940610i	$-0.610254\pi$
$607$	15.8874	−	27.5177i	0.644848	−	1.11691i	0.984337	−	0.176299i	$-0.0564126\pi$
$608$		0			0
$609$	−0.0767054	−	0.0194503i	−0.00310826	−	0.000788168i
$610$		0			0
$611$	7.28095	−	34.6975i	0.294556	−	1.40371i
$612$		0			0
$613$	10.5861	−	18.3357i	0.427570	−	0.740573i	−0.569087	−	0.822278i	$-0.692703\pi$
$613$	10.5861	−	18.3357i	0.427570	−	0.740573i	0.996657	+	0.0817046i	$0.0260364\pi$
$614$		0			0
$615$	35.9341	+	9.11188i	1.44900	+	0.367426i
$616$		0			0
$617$	6.76704	−	11.7209i	0.272431	−	0.471864i	−0.697053	−	0.717020i	$-0.745506\pi$
$617$	6.76704	−	11.7209i	0.272431	−	0.471864i	0.969484	+	0.245156i	$0.0788391\pi$
$618$		0			0
$619$	6.51136	−	11.2780i	0.261714	−	0.453301i	−0.704984	−	0.709223i	$-0.749046\pi$
$619$	6.51136	−	11.2780i	0.261714	−	0.453301i	0.966697	+	0.255922i	$0.0823791\pi$
$620$		0			0
$621$	9.25367	+	8.53489i	0.371337	+	0.342494i
$622$		0			0
$623$	0.0151003	−	0.0261545i	0.000604981	−	0.00104786i
$624$		0			0
$625$	9.01861	+	15.6207i	0.360745	+	0.624828i
$626$		0			0
$627$	−0.809292	−	2.86546i	−0.0323200	−	0.114435i
$628$		0			0
$629$	44.3489			1.76831
$630$		0			0
$631$	−19.6481	−	34.0315i	−0.782179	−	1.35477i	−0.930670	−	0.365860i	$-0.880775\pi$
$631$	−19.6481	−	34.0315i	−0.782179	−	1.35477i	0.148491	−	0.988914i	$-0.452558\pi$
$632$		0			0
$633$	29.2210	−	30.0185i	1.16143	−	1.19313i
$634$		0			0
$635$	4.33443			0.172007
$636$		0			0
$637$	−23.9829	+	7.86150i	−0.950236	+	0.311484i
$638$		0			0
$639$	9.89364	−	6.07295i	0.391386	−	0.240242i
$640$		0			0
$641$	−49.4497			−1.95314			−0.976572	−	0.215190i	$-0.930963\pi$
$641$	−49.4497			−1.95314			−0.976572	+	0.215190i	$0.930963\pi$
$642$		0			0
$643$	−16.6129	+	28.7744i	−0.655150	+	1.13475i	0.326706	+	0.945126i	$0.394061\pi$
$643$	−16.6129	+	28.7744i	−0.655150	+	1.13475i	−0.981856	+	0.189627i	$0.939272\pi$
$644$		0			0
$645$	−58.7121	−	14.8877i	−2.31179	−	0.586204i
$646$		0			0
$647$	3.14446	−	5.44637i	0.123622	−	0.214119i	−0.797572	−	0.603224i	$-0.793882\pi$
$647$	3.14446	−	5.44637i	0.123622	−	0.214119i	0.921193	+	0.389105i	$0.127216\pi$
$648$		0			0
$649$	17.6566			0.693083
$650$		0			0
$651$	0.0507065	+	0.0128578i	0.00198734	+	0.000503935i
$652$		0			0
$653$	21.3932			0.837181			0.418591	−	0.908175i	$-0.362524\pi$
$653$	21.3932			0.837181			0.418591	+	0.908175i	$0.362524\pi$
$654$		0			0
$655$	−5.35184	+	9.26965i	−0.209113	+	0.362195i
$656$		0			0
$657$	0.938734	+	34.8588i	0.0366235	+	1.35997i
$658$		0			0
$659$	6.23848			0.243017			0.121508	−	0.992590i	$-0.461227\pi$
$659$	6.23848			0.243017			0.121508	+	0.992590i	$0.461227\pi$
$660$		0			0
$661$	23.5869			0.917425			0.458712	−	0.888585i	$-0.348311\pi$
$661$	23.5869			0.917425			0.458712	+	0.888585i	$0.348311\pi$
$662$		0			0
$663$	32.7663	−	2.24542i	1.27254	−	0.0872048i
$664$		0			0
$665$	0.0183874	−	0.0318478i	0.000713031	−	0.00123501i
$666$		0			0
$667$	−5.40868	−	9.36810i	−0.209425	−	0.362734i
$668$		0			0
$669$	13.5456	+	3.43478i	0.523702	+	0.132796i
$670$		0			0
$671$	8.68535	+	15.0435i	0.335294	+	0.580746i
$672$		0			0
$673$	−21.7158	−	37.6129i	−0.837082	−	1.44987i	−0.892324	−	0.451396i	$-0.850926\pi$
$673$	−21.7158	−	37.6129i	−0.837082	−	1.44987i	0.0552411	−	0.998473i	$-0.482407\pi$
$674$		0			0
$675$	30.4336	−	9.48711i	1.17139	−	0.365159i
$676$		0			0
$677$	−6.42619	+	11.1305i	−0.246979	+	0.427779i	−0.962686	−	0.270621i	$-0.912771\pi$
$677$	−6.42619	+	11.1305i	−0.246979	+	0.427779i	0.715707	+	0.698400i	$0.246104\pi$
$678$		0			0
$679$	−0.0774362			−0.00297173
$680$		0			0
$681$	20.9969	−	21.5700i	0.804604	−	0.826564i
$682$		0			0
$683$	18.6982	+	32.3862i	0.715467	+	1.23922i	0.962779	+	0.270289i	$0.0871191\pi$
$683$	18.6982	+	32.3862i	0.715467	+	1.23922i	−0.247313	+	0.968936i	$0.579548\pi$
$684$		0			0
$685$	−24.6922	−	42.7681i	−0.943440	−	1.63409i
$686$		0			0
$687$	44.8100	+	11.3626i	1.70961	+	0.433509i
$688$		0			0
$689$	−18.0875	+	5.92902i	−0.689079	+	0.225878i
$690$		0			0
$691$	−4.02691	−	6.97482i	−0.153191	−	0.265335i	0.779208	−	0.626766i	$-0.215622\pi$
$691$	−4.02691	−	6.97482i	−0.153191	−	0.265335i	−0.932399	+	0.361431i	$0.882288\pi$
$692$		0			0
$693$	0.0417571	−	0.0256315i	0.00158622	−	0.000973660i
$694$		0			0
$695$	49.4176			1.87451
$696$		0			0
$697$	16.8662	+	29.2130i	0.638851	+	1.10652i
$698$		0			0
$699$	5.09632	−	5.23541i	0.192760	−	0.198021i
$700$		0			0
$701$	25.2004			0.951805			0.475903	−	0.879498i	$-0.342121\pi$
$701$	25.2004			0.951805			0.475903	+	0.879498i	$0.342121\pi$
$702$		0			0
$703$	9.08241			0.342550
$704$		0			0
$705$	39.6413	−	40.7232i	1.49298	−	1.53372i
$706$		0			0
$707$	0.0379121	+	0.0656656i	0.00142583	+	0.00246961i
$708$		0			0
$709$	−3.34357			−0.125570			−0.0627852	−	0.998027i	$-0.519998\pi$
$709$	−3.34357			−0.125570			−0.0627852	+	0.998027i	$0.519998\pi$
$710$		0			0
$711$	−0.222948	−	0.120837i	−0.00836121	−	0.00453172i
$712$		0			0
$713$	3.57543	+	6.19283i	0.133901	+	0.231923i
$714$		0			0
$715$	3.94380	−	18.7943i	0.147490	−	0.702866i
$716$		0			0
$717$	−12.7874	−	3.24252i	−0.477553	−	0.121094i
$718$		0			0
$719$	8.68263	+	15.0388i	0.323807	+	0.560851i	0.981270	−	0.192636i	$-0.0617037\pi$
$719$	8.68263	+	15.0388i	0.323807	+	0.560851i	−0.657463	+	0.753487i	$0.728370\pi$
$720$		0			0
$721$	−0.0178040	−	0.0308374i	−0.000663054	−	0.00114844i
$722$		0			0
$723$	2.93344	−	3.01350i	0.109096	−	0.112073i
$724$		0			0
$725$	−27.3926			−1.01733
$726$		0			0
$727$	−6.14162	+	10.6376i	−0.227780	+	0.394527i	−0.957150	−	0.289593i	$-0.906480\pi$
$727$	−6.14162	+	10.6376i	−0.227780	+	0.394527i	0.729370	+	0.684120i	$0.239813\pi$
$728$		0			0
$729$	2.17840	+	26.9120i	0.0806815	+	0.996740i
$730$		0			0
$731$	−27.5573	−	47.7307i	−1.01925	−	1.76538i
$732$		0			0
$733$	16.5584	+	28.6799i	0.611597	+	1.05932i	0.990971	+	0.134074i	$0.0428061\pi$
$733$	16.5584	+	28.6799i	0.611597	+	1.05932i	−0.379374	+	0.925243i	$0.623861\pi$
$734$		0			0
$735$	−39.2161	−	9.94411i	−1.44651	−	0.366794i
$736$		0			0
$737$	2.70549	+	4.68604i	0.0996579	+	0.172613i
$738$		0			0
$739$	4.40386	−	7.62771i	0.161999	−	0.280590i	−0.773587	−	0.633690i	$-0.781539\pi$
$739$	4.40386	−	7.62771i	0.161999	−	0.280590i	0.935585	+	0.353101i	$0.114873\pi$
$740$		0			0
$741$	6.71037	−	0.459850i	0.246511	−	0.0168930i
$742$		0			0
$743$	36.6179			1.34338			0.671691	−	0.740832i	$-0.265568\pi$
$743$	36.6179			1.34338			0.671691	+	0.740832i	$0.265568\pi$
$744$		0			0
$745$	4.88271			0.178889
$746$		0			0
$747$	−37.6882	−	20.4267i	−1.37894	−	0.747376i
$748$		0			0
$749$	0.0784922	−	0.135953i	0.00286804	−	0.00496760i
$750$		0			0
$751$	13.6627			0.498558			0.249279	−	0.968432i	$-0.419806\pi$
$751$	13.6627			0.498558			0.249279	+	0.968432i	$0.419806\pi$
$752$		0			0
$753$	−23.3144	−	5.91189i	−0.849625	−	0.215441i
$754$		0			0
$755$	35.6525			1.29753
$756$		0			0
$757$	−27.4148	+	47.4837i	−0.996406	+	1.72583i	−0.424848	+	0.905265i	$0.639672\pi$
$757$	−27.4148	+	47.4837i	−0.996406	+	1.72583i	−0.571559	+	0.820561i	$0.693661\pi$
$758$		0			0
$759$	6.49224	+	1.64625i	0.235653	+	0.0597551i
$760$		0			0
$761$	7.08893	−	12.2784i	0.256974	−	0.445091i	−0.708456	−	0.705755i	$-0.750608\pi$
$761$	7.08893	−	12.2784i	0.256974	−	0.445091i	0.965430	+	0.260663i	$0.0839413\pi$
$762$		0			0
$763$	0.0184103			0.000666497
$764$		0			0
$765$	46.2862	+	25.0868i	1.67348	+	0.907016i
$766$		0			0
$767$	−8.19114	+	39.0351i	−0.295765	+	1.40947i
$768$		0			0
$769$	20.8197			0.750777			0.375388	−	0.926868i	$-0.377509\pi$
$769$	20.8197			0.750777			0.375388	+	0.926868i	$0.377509\pi$
$770$		0			0
$771$	19.7546	−	20.2937i	0.711443	−	0.730860i
$772$		0			0
$773$	12.2988	+	21.3022i	0.442359	+	0.766188i	0.997864	−	0.0653251i	$-0.0208084\pi$
$773$	12.2988	+	21.3022i	0.442359	+	0.766188i	−0.555505	+	0.831513i	$0.687475\pi$
$774$		0			0
$775$	18.1080			0.650459
$776$		0			0
$777$	0.0406211	+	0.143827i	0.00145727	+	0.00515976i
$778$		0			0
$779$	3.45410	+	5.98267i	0.123756	+	0.214352i
$780$		0			0
$781$	3.08819	−	5.34890i	0.110504	−	0.191399i
$782$		0			0
$783$	5.09515	−	22.6345i	0.182086	−	0.808891i
$784$		0			0
$785$	−18.0602	+	31.2811i	−0.644595	+	1.11647i
$786$		0			0
$787$	−8.15152	+	14.1189i	−0.290570	+	0.503283i	−0.973945	−	0.226785i	$-0.927178\pi$
$787$	−8.15152	+	14.1189i	−0.290570	+	0.503283i	0.683374	+	0.730068i	$0.260512\pi$
$788$		0			0
$789$	43.8417	+	11.1170i	1.56081	+	0.395777i
$790$		0			0
$791$	0.0831122	−	0.143955i	0.00295513	−	0.00511843i
$792$		0			0
$793$	−37.2872	+	12.2226i	−1.32411	+	0.434037i
$794$		0			0
$795$	−29.5762	−	7.49969i	−1.04896	−	0.265987i
$796$		0			0
$797$	−16.7580	+	29.0256i	−0.593597	+	1.02814i	0.400146	+	0.916452i	$0.368959\pi$
$797$	−16.7580	+	29.0256i	−0.593597	+	1.02814i	−0.993743	+	0.111689i	$0.964374\pi$
$798$		0			0
$799$	51.7126			1.82946
$800$		0			0
$801$	7.78460	+	4.21920i	0.275055	+	0.149078i
$802$		0			0
$803$	9.27654	+	16.0674i	0.327362	+	0.567007i
$804$		0			0
$805$	0.0413606	+	0.0716386i	0.00145777	+	0.00252493i
$806$		0			0
$807$	−18.8314	−	4.77512i	−0.662897	−	0.168092i
$808$		0			0
$809$	−6.27596	+	10.8703i	−0.220651	+	0.382179i	−0.955006	−	0.296587i	$-0.904152\pi$
$809$	−6.27596	+	10.8703i	−0.220651	+	0.382179i	0.734355	+	0.678766i	$0.237485\pi$
$810$		0			0
$811$	−31.5098			−1.10646			−0.553230	−	0.833029i	$-0.686605\pi$
$811$	−31.5098			−1.10646			−0.553230	+	0.833029i	$0.686605\pi$
$812$		0			0
$813$	−10.2257	−	36.2059i	−0.358629	−	1.26980i
$814$		0			0
$815$	−28.9916	+	50.2149i	−1.01553	+	1.75895i
$816$		0			0
$817$	−5.64360	−	9.77500i	−0.197444	−	0.341984i
$818$		0			0
$819$	0.0372942	+	0.104207i	0.00130316	+	0.00364129i
$820$		0			0
$821$	3.70635	+	6.41958i	0.129352	+	0.224045i	0.923426	−	0.383777i	$-0.125377\pi$
$821$	3.70635	+	6.41958i	0.129352	+	0.224045i	−0.794073	+	0.607822i	$0.792043\pi$
$822$		0			0
$823$	−22.4892	+	38.9524i	−0.783922	+	1.35779i	0.145718	+	0.989326i	$0.453451\pi$
$823$	−22.4892	+	38.9524i	−0.783922	+	1.35779i	−0.929641	+	0.368467i	$0.879883\pi$
$824$		0			0
$825$	11.8303	−	12.1532i	0.411880	−	0.423121i
$826$		0			0
$827$	−17.6384			−0.613346			−0.306673	−	0.951815i	$-0.599216\pi$
$827$	−17.6384			−0.613346			−0.306673	+	0.951815i	$0.599216\pi$
$828$		0			0
$829$	20.2587	−	35.0891i	0.703613	−	1.21869i	−0.263576	−	0.964639i	$-0.584902\pi$
$829$	20.2587	−	35.0891i	0.703613	−	1.21869i	0.967190	−	0.254056i	$-0.0817646\pi$
$830$		0			0
$831$	22.7175	−	23.3375i	0.788062	−	0.809570i
$832$		0			0
$833$	−18.4066	−	31.8812i	−0.637752	−	1.10462i
$834$		0			0
$835$	−13.9194	−	24.1091i	−0.481700	−	0.834329i
$836$		0			0
$837$	−3.36817	+	14.9627i	−0.116421	+	0.517185i
$838$		0			0
$839$	21.2322			0.733018			0.366509	−	0.930414i	$-0.380553\pi$
$839$	21.2322			0.733018			0.366509	+	0.930414i	$0.380553\pi$
$840$		0			0
$841$	4.53183	−	7.84936i	0.156270	−	0.270668i
$842$		0			0
$843$	−7.10576	−	25.1593i	−0.244735	−	0.866533i
$844$		0			0
$845$	39.7206	+	17.4378i	1.36643	+	0.599880i
$846$		0			0
$847$	−0.0432438	+	0.0749004i	−0.00148587	+	0.00257361i
$848$		0			0
$849$	15.0338	−	15.4441i	0.515960	−	0.530042i
$850$		0			0
$851$	−10.2150	+	17.6929i	−0.350165	+	0.606504i
$852$		0			0
$853$	16.8214	−	29.1355i	0.575954	−	0.997582i	−0.419983	−	0.907532i	$-0.637964\pi$
$853$	16.8214	−	29.1355i	0.575954	−	0.997582i	0.995937	−	0.0900501i	$-0.0287027\pi$
$854$		0			0
$855$	9.47916	+	5.13765i	0.324181	+	0.175704i
$856$		0			0
$857$	−20.1528	+	34.9056i	−0.688406	+	1.19235i	0.283948	+	0.958840i	$0.408356\pi$
$857$	−20.1528	+	34.9056i	−0.688406	+	1.19235i	−0.972354	+	0.233514i	$0.924978\pi$
$858$		0			0
$859$	7.34388	+	12.7200i	0.250570	+	0.434000i	0.963683	−	0.267049i	$-0.0860486\pi$
$859$	7.34388	+	12.7200i	0.250570	+	0.434000i	−0.713113	+	0.701049i	$0.752715\pi$
$860$		0			0
$861$	−0.0792917	+	0.0814557i	−0.00270225	+	0.00277600i
$862$		0			0
$863$	−14.9208			−0.507909			−0.253954	−	0.967216i	$-0.581731\pi$
$863$	−14.9208			−0.507909			−0.253954	+	0.967216i	$0.581731\pi$
$864$		0			0
$865$	19.4341	+	33.6609i	0.660780	+	1.14450i
$866$		0			0
$867$	5.01759	+	17.7657i	0.170406	+	0.603356i
$868$		0			0
$869$	−0.134920			−0.00457685
$870$		0			0
$871$	−11.6150	+	3.80734i	−0.393558	+	0.129007i
$872$		0			0
$873$	−0.611173	−	22.6952i	−0.0206851	−	0.768116i
$874$		0			0
$875$	0.0387517			0.00131004
$876$		0			0
$877$	23.8711	−	41.3459i	0.806069	−	1.39615i	−0.109498	−	0.993987i	$-0.534924\pi$
$877$	23.8711	−	41.3459i	0.806069	−	1.39615i	0.915567	−	0.402165i	$-0.131742\pi$
$878$		0			0
$879$	−15.1495	−	53.6399i	−0.510981	−	1.80923i
$880$		0			0
$881$	−8.65508	+	14.9910i	−0.291597	+	0.505061i	−0.974188	−	0.225740i	$-0.927520\pi$
$881$	−8.65508	+	14.9910i	−0.291597	+	0.505061i	0.682590	+	0.730801i	$0.260853\pi$
$882$		0			0
$883$	10.2700			0.345614			0.172807	−	0.984956i	$-0.444716\pi$
$883$	10.2700			0.345614			0.172807	+	0.984956i	$0.444716\pi$
$884$		0			0
$885$	−44.5968	+	45.8140i	−1.49911	+	1.54002i
$886$		0			0
$887$	−43.1760			−1.44971			−0.724853	−	0.688903i	$-0.758092\pi$
$887$	−43.1760			−1.44971			−0.724853	+	0.688903i	$0.758092\pi$
$888$		0			0
$889$	−0.00664558	+	0.0115105i	−0.000222886	+	0.000386049i
$890$		0			0
$891$	7.84171	+	12.0360i	0.262707	+	0.403220i
$892$		0			0
$893$	10.5905			0.354396
$894$		0			0
$895$	−26.9306			−0.900189
$896$		0			0
$897$	−6.65135	+	13.5892i	−0.222082	+	0.453732i
$898$		0			0
$899$	6.58951	−	11.4134i	0.219772	−	0.380657i
$900$		0			0
$901$	−13.8820	−	24.0443i	−0.462476	−	0.801033i
$902$		0			0
$903$	0.129553	−	0.133089i	0.00431127	−	0.00442893i
$904$		0			0
$905$	−24.3642	−	42.2000i	−0.809892	−	1.40277i
$906$		0			0
$907$	9.76654	+	16.9162i	0.324293	+	0.561692i	0.981369	−	0.192133i	$-0.0615404\pi$
$907$	9.76654	+	16.9162i	0.324293	+	0.561692i	−0.657076	+	0.753824i	$0.728207\pi$
$908$		0			0
$909$	−18.9462	+	11.6296i	−0.628406	+	0.385730i
$910$		0			0
$911$	−0.757377	+	1.31182i	−0.0250930	+	0.0434624i	−0.878299	−	0.478111i	$-0.841322\pi$
$911$	−0.757377	+	1.31182i	−0.0250930	+	0.0434624i	0.853206	+	0.521574i	$0.174655\pi$
$912$		0			0
$913$	−22.8075			−0.754817
$914$		0			0
$915$	−60.9709	−	15.4605i	−2.01564	−	0.511109i
$916$		0			0
$917$	−0.0164109	−	0.0284246i	−0.000541937	−	0.000938662i
$918$		0			0
$919$	6.40403	+	11.0921i	0.211249	+	0.365895i	0.952106	−	0.305769i	$-0.0989134\pi$
$919$	6.40403	+	11.0921i	0.211249	+	0.365895i	−0.740856	+	0.671663i	$0.765580\pi$
$920$		0			0
$921$	−19.5579	+	20.0916i	−0.644454	+	0.662042i
$922$		0			0
$923$	10.3926	+	9.30877i	0.342078	+	0.306402i
$924$		0			0
$925$	25.8672	+	44.8034i	0.850509	+	1.47313i
$926$		0			0
$927$	8.89737	−	5.46141i	0.292228	−	0.179376i
$928$		0			0
$929$	−42.9072			−1.40774			−0.703870	−	0.710329i	$-0.748546\pi$
$929$	−42.9072			−1.40774			−0.703870	+	0.710329i	$0.748546\pi$
$930$		0			0
$931$	−3.76958	−	6.52910i	−0.123543	−	0.213983i
$932$		0			0
$933$	1.26412	+	0.320545i	0.0413854	+	0.0104942i
$934$		0			0
$935$	28.0107			0.916047
$936$		0			0
$937$	−19.8226			−0.647576			−0.323788	−	0.946130i	$-0.604957\pi$
$937$	−19.8226			−0.647576			−0.323788	+	0.946130i	$0.604957\pi$
$938$		0			0
$939$	−8.90102	−	31.5158i	−0.290474	−	1.02848i
$940$		0			0
$941$	−0.755494	−	1.30855i	−0.0246284	−	0.0426576i	0.853449	−	0.521177i	$-0.174507\pi$
$941$	−0.755494	−	1.30855i	−0.0246284	−	0.0426576i	−0.878077	+	0.478520i	$0.841174\pi$
$942$		0			0
$943$	−15.5393			−0.506030
$944$		0			0
$945$	−0.0389630	+	0.173088i	−0.00126747	+	0.00563055i
$946$		0			0
$947$	−14.4986	−	25.1123i	−0.471141	−	0.816041i	0.528314	−	0.849049i	$-0.322824\pi$
$947$	−14.4986	−	25.1123i	−0.471141	−	0.816041i	−0.999455	+	0.0330085i	$0.989491\pi$
$948$		0			0
$949$	−39.8252	+	13.0546i	−1.29278	+	0.423769i
$950$		0			0
$951$	−1.52341	−	5.39393i	−0.0493999	−	0.174910i
$952$		0			0
$953$	−4.62180	−	8.00519i	−0.149715	−	0.259313i	0.781407	−	0.624021i	$-0.214502\pi$
$953$	−4.62180	−	8.00519i	−0.149715	−	0.259313i	−0.931122	+	0.364708i	$0.881169\pi$
$954$		0			0
$955$	−20.6340	−	35.7392i	−0.667702	−	1.15649i
$956$		0			0
$957$	−3.35503	−	11.8792i	−0.108453	−	0.383998i
$958$		0			0
$959$	0.151433			0.00489002
$960$		0			0
$961$	11.1440	−	19.3019i	0.359483	−	0.622643i
$962$		0			0
$963$	40.4648	+	21.9317i	1.30396	+	0.706738i
$964$		0			0
$965$	−29.9025	−	51.7926i	−0.962595	−	1.66726i
$966$		0			0
$967$	8.55097	+	14.8107i	0.274981	+	0.476281i	0.970130	−	0.242585i	$-0.0779952\pi$
$967$	8.55097	+	14.8107i	0.274981	+	0.476281i	−0.695150	+	0.718865i	$0.744662\pi$
$968$		0			0
$969$	2.66656	+	9.44147i	0.0856622	+	0.303304i
$970$		0			0
$971$	10.4610	+	18.1189i	0.335709	+	0.581465i	0.983621	−	0.180251i	$-0.0576909\pi$
$971$	10.4610	+	18.1189i	0.335709	+	0.581465i	−0.647912	+	0.761715i	$0.724358\pi$
$972$		0			0
$973$	−0.0757673	+	0.131233i	−0.00242899	+	0.00420713i
$974$		0			0
$975$	21.3799	+	31.7924i	0.684706	+	1.01817i
$976$		0			0
$977$	17.1338			0.548158			0.274079	−	0.961707i	$-0.411627\pi$
$977$	17.1338			0.548158			0.274079	+	0.961707i	$0.411627\pi$
$978$		0			0
$979$	4.71095			0.150563
$980$		0			0
$981$	0.145305	+	5.39573i	0.00463923	+	0.172272i
$982$		0			0
$983$	12.5557	−	21.7471i	0.400465	−	0.693625i	−0.593317	−	0.804969i	$-0.702182\pi$
$983$	12.5557	−	21.7471i	0.400465	−	0.693625i	0.993782	+	0.111344i	$0.0355154\pi$
$984$		0			0
$985$	10.6628			0.339745
$986$		0			0
$987$	0.0473658	+	0.167708i	0.00150767	+	0.00533820i
$988$		0			0
$989$	25.3894			0.807337
$990$		0			0
$991$	−10.7270	+	18.5797i	−0.340754	+	0.590204i	−0.984573	−	0.174974i	$-0.944016\pi$
$991$	−10.7270	+	18.5797i	−0.340754	+	0.590204i	0.643819	+	0.765178i	$0.277349\pi$
$992$		0			0
$993$	30.3355	−	31.1634i	0.962667	−	0.988940i
$994$		0			0
$995$	41.3945	−	71.6974i	1.31229	−	2.27296i
$996$		0			0
$997$	−34.2908			−1.08600			−0.543000	−	0.839733i	$-0.682712\pi$
$997$	−34.2908			−1.08600			−0.543000	+	0.839733i	$0.682712\pi$
$998$		0			0
$999$	−41.8325	+	13.0405i	−1.32352	+	0.412582i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	468.2.k.a.61.11	yes	28
3.2	odd	2		1404.2.k.a.1153.2		28
9.4	even	3		468.2.j.a.373.8	yes	28
9.5	odd	6		1404.2.j.a.685.2		28
13.3	even	3		468.2.j.a.133.8	✓	28
39.29	odd	6		1404.2.j.a.289.2		28
117.68	odd	6		1404.2.k.a.1225.2		28
117.94	even	3	inner	468.2.k.a.445.11	yes	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
468.2.j.a.133.8	✓	28	13.3	even	3
468.2.j.a.373.8	yes	28	9.4	even	3
468.2.k.a.61.11	yes	28	1.1	even	1	trivial
468.2.k.a.445.11	yes	28	117.94	even	3	inner
1404.2.j.a.289.2		28	39.29	odd	6
1404.2.j.a.685.2		28	9.5	odd	6
1404.2.k.a.1153.2		28	3.2	odd	2
1404.2.k.a.1225.2		28	117.68	odd	6

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:	\( N \)	\(=\)	\( 468 = 2^{2} \cdot 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	468.k (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.20815 - 1.24112i) q^{3} +(1.66845 + 2.88984i) q^{5} -0.0102323 q^{7} +(-0.0807596 - 2.99891i) q^{9} +(-0.798063 - 1.38229i) q^{11} +(3.42617 - 1.12309i) q^{13} +(5.60238 + 1.42061i) q^{15} +(2.62956 + 4.55453i) q^{17} +(0.538519 + 0.932743i) q^{19} +(-0.0123622 + 0.0126995i) q^{21} -2.42269 q^{23} +(-3.06747 + 5.31301i) q^{25} +(-3.81958 - 3.52290i) q^{27} +(2.23251 + 3.86681i) q^{29} +(-1.47581 - 2.55618i) q^{31} +(-2.67976 - 0.679513i) q^{33} +(-0.0170722 - 0.0295698i) q^{35} +(4.21638 - 7.30299i) q^{37} +(2.74544 - 5.60915i) q^{39} +6.41407 q^{41} -10.4798 q^{43} +(8.53165 - 5.23693i) q^{45} +(4.91647 - 8.51558i) q^{47} -6.99990 q^{49} +(8.82961 + 2.23894i) q^{51} -5.27921 q^{53} +(2.66306 - 4.61256i) q^{55} +(1.80826 + 0.458524i) q^{57} +(-5.53108 + 9.58012i) q^{59} -10.8830 q^{61} +(0.000826358 + 0.0306858i) q^{63} +(8.96196 + 8.02729i) q^{65} -3.39007 q^{67} +(-2.92697 + 3.00685i) q^{69} +(1.93480 + 3.35118i) q^{71} -11.6238 q^{73} +(2.88813 + 10.2260i) q^{75} +(0.00816604 + 0.0141440i) q^{77} +(0.0422648 - 0.0732048i) q^{79} +(-8.98696 + 0.484382i) q^{81} +(7.14463 - 12.3749i) q^{83} +(-8.77459 + 15.1980i) q^{85} +(7.49638 + 1.90087i) q^{87} +(-1.47575 + 2.55607i) q^{89} +(-0.0350577 + 0.0114918i) q^{91} +(-4.95552 - 1.25658i) q^{93} +(-1.79699 + 3.11247i) q^{95} +7.56780 q^{97} +(-4.08090 + 2.50495i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - 4 q^{7} - 2 q^{9} - 4 q^{11} + q^{13} - 4 q^{15} - 8 q^{17} - q^{19} + 14 q^{21} + 8 q^{23} - 14 q^{25} - 13 q^{29} + 2 q^{31} - 25 q^{33} + 3 q^{35} - q^{37} - 3 q^{39} - 8 q^{41} - 4 q^{43}+ \cdots - 29 q^{99}+O(q^{100}) \) 28 * q - 4 * q^7 - 2 * q^9 - 4 * q^11 + q^13 - 4 * q^15 - 8 * q^17 - q^19 + 14 * q^21 + 8 * q^23 - 14 * q^25 - 13 * q^29 + 2 * q^31 - 25 * q^33 + 3 * q^35 - q^37 - 3 * q^39 - 8 * q^41 - 4 * q^43 - 38 * q^45 + 11 * q^47 + 24 * q^49 + 5 * q^51 + 52 * q^53 - q^57 - 8 * q^59 + 14 * q^61 - 21 * q^63 + 38 * q^65 + 14 * q^67 - 21 * q^69 - 12 * q^71 + 14 * q^73 - 14 * q^75 - 28 * q^77 + 5 * q^79 + 10 * q^81 + 9 * q^83 + 18 * q^85 + 18 * q^87 - 11 * q^89 - q^91 - 9 * q^93 + 28 * q^95 + 50 * q^97 - 29 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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