LMFDB - Embedded newform 441.2.w.a.62.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [441,2,Mod(62,441)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(441, base_ring=CyclotomicField(14)) chi = DirichletCharacter(H, H._module([7, 11])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("441.62"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 441 = 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	441.w (of order $14$, degree $6$, 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:	$3.52140272914$
Analytic rank:	$0$
Dimension:	$120$
Relative dimension:	$20$ over $\Q(\zeta_{14})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{14}]$

Embedding invariants

Embedding label			62.4
Character	$\chi$	$=$	441.62
Dual form			441.2.w.a.377.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.08702 + 0.476349i) q^{2} +(2.32682 - 1.12054i) q^{4} +(2.25096 + 2.82261i) q^{5} +(0.212729 - 2.63719i) q^{7} +(-0.975036 + 0.777565i) q^{8} +(-6.04235 - 4.81862i) q^{10} +(2.41874 - 0.552061i) q^{11} +(5.51523 - 1.25882i) q^{13} +(0.812251 + 5.60520i) q^{14} +(-1.55589 + 1.95102i) q^{16} +(-4.22253 - 2.03346i) q^{17} -5.49607i q^{19} +(8.40042 + 4.04543i) q^{20} +(-4.78499 + 2.30433i) q^{22} +(-2.01859 - 4.19164i) q^{23} +(-1.78772 + 7.83253i) q^{25} +(-10.9108 + 5.25436i) q^{26} +(-2.46008 - 6.37463i) q^{28} +(0.799704 - 1.66060i) q^{29} +5.46570i q^{31} +(3.40002 - 7.06021i) q^{32} +(9.78115 + 2.23248i) q^{34} +(7.92260 - 5.33574i) q^{35} +(8.48160 + 4.08452i) q^{37} +(2.61805 + 11.4704i) q^{38} +(-4.38953 - 1.00188i) q^{40} +(1.93756 + 2.42962i) q^{41} +(6.03318 - 7.56536i) q^{43} +(5.00936 - 3.99483i) q^{44} +(6.20952 + 7.78649i) q^{46} +(1.86318 + 8.16313i) q^{47} +(-6.90949 - 1.12201i) q^{49} -17.1983i q^{50} +(11.4224 - 9.10906i) q^{52} +(0.594462 + 1.23441i) q^{53} +(7.00273 + 5.58449i) q^{55} +(1.84316 + 2.73676i) q^{56} +(-0.877974 + 3.84666i) q^{58} +(0.856868 - 1.07448i) q^{59} +(-5.13768 + 10.6685i) q^{61} +(-2.60358 - 11.4070i) q^{62} +(-2.62221 + 11.4886i) q^{64} +(15.9677 + 12.7338i) q^{65} +6.21276 q^{67} -12.1036 q^{68} +(-13.9930 + 14.9097i) q^{70} +(-0.0504417 - 0.104743i) q^{71} +(-2.10438 - 0.480310i) q^{73} +(-19.6470 - 4.48429i) q^{74} +(-6.15856 - 12.7884i) q^{76} +(-0.941351 - 6.49610i) q^{77} -11.3011 q^{79} -9.00923 q^{80} +(-5.20107 - 4.14772i) q^{82} +(-0.130612 + 0.572249i) q^{83} +(-3.76506 - 16.4958i) q^{85} +(-8.98762 + 18.6630i) q^{86} +(-1.92909 + 2.41900i) q^{88} +(1.33313 - 5.84082i) q^{89} +(-2.14648 - 14.8125i) q^{91} +(-9.39377 - 7.49128i) q^{92} +(-7.77701 - 16.1491i) q^{94} +(15.5133 - 12.3714i) q^{95} +6.74458i q^{97} +(14.9547 - 0.949665i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 120 q + 24 q^{4} - 32 q^{16} - 44 q^{22} - 4 q^{25} - 56 q^{28} + 112 q^{34} - 76 q^{37} + 28 q^{40} + 8 q^{43} - 40 q^{46} - 84 q^{49} - 140 q^{52} + 12 q^{58} - 84 q^{61} + 24 q^{64} + 16 q^{67} + 112 q^{70}+ \cdots - 112 q^{94}+O(q^{100}) $ 120 * q + 24 * q^4 - 32 * q^16 - 44 * q^22 - 4 * q^25 - 56 * q^28 + 112 * q^34 - 76 * q^37 + 28 * q^40 + 8 * q^43 - 40 * q^46 - 84 * q^49 - 140 * q^52 + 12 * q^58 - 84 * q^61 + 24 * q^64 + 16 * q^67 + 112 * q^70 - 84 * q^76 - 24 * q^79 + 140 * q^82 - 96 * q^85 - 24 * q^88 - 112 * q^91 - 112 * q^94

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/441\mathbb{Z}\right)^\times$.

$n$	$199$	$344$
$\chi(n)$	$e\left(\frac{11}{14}\right)$	$-1$

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 $

$2$	−2.08702	+	0.476349i	−1.47575	+	0.336830i	−0.883311	−	0.468787i	$-0.844691\pi$
$2$	−2.08702	+	0.476349i	−1.47575	+	0.336830i	−0.592437	+	0.805617i	$0.701834\pi$
$3$		0			0
$3$		0			0
$4$	2.32682	−	1.12054i	1.16341	−	0.560269i
$5$	2.25096	+	2.82261i	1.00666	+	1.26231i	0.964744	+	0.263190i	$0.0847746\pi$
$5$	2.25096	+	2.82261i	1.00666	+	1.26231i	0.0419154	+	0.999121i	$0.486654\pi$
$6$		0			0
$7$	0.212729	−	2.63719i	0.0804041	−	0.996762i
$7$	0.212729	−	2.63719i	0.0804041	−	0.996762i
$8$	−0.975036	+	0.777565i	−0.344727	+	0.274911i
$9$		0			0
$10$	−6.04235	−	4.81862i	−1.91076	−	1.52378i
$11$	2.41874	−	0.552061i	0.729277	−	0.166453i	0.158267	−	0.987396i	$-0.449409\pi$
$11$	2.41874	−	0.552061i	0.729277	−	0.166453i	0.571009	+	0.820944i	$0.306552\pi$
$12$		0			0
$13$	5.51523	−	1.25882i	1.52965	−	0.349133i	0.626832	−	0.779155i	$-0.284351\pi$
$13$	5.51523	−	1.25882i	1.52965	−	0.349133i	0.902818	+	0.430022i	$0.141494\pi$
$14$	0.812251	+	5.60520i	0.217083	+	1.49805i
$15$		0			0
$16$	−1.55589	+	1.95102i	−0.388972	+	0.487756i
$17$	−4.22253	−	2.03346i	−1.02411	−	0.493187i	−0.155060	−	0.987905i	$-0.549557\pi$
$17$	−4.22253	−	2.03346i	−1.02411	−	0.493187i	−0.869053	+	0.494718i	$0.835271\pi$
$18$		0			0
$19$		−	5.49607i		−	1.26089i	−0.776236	−	0.630443i	$-0.782873\pi$
$19$		−	5.49607i		−	1.26089i	0.776236	−	0.630443i	$-0.217127\pi$
$20$	8.40042	+	4.04543i	1.87839	+	0.904586i
$21$		0			0
$22$	−4.78499	+	2.30433i	−1.02016	+	0.491284i
$23$	−2.01859	−	4.19164i	−0.420904	−	0.874016i	−0.998341	−	0.0575810i	$-0.981661\pi$
$23$	−2.01859	−	4.19164i	−0.420904	−	0.874016i	0.577437	−	0.816435i	$-0.304053\pi$
$24$		0			0
$25$	−1.78772	+	7.83253i	−0.357545	+	1.56651i
$26$	−10.9108	+	5.25436i	−2.13978	+	1.03046i
$27$		0			0
$28$	−2.46008	−	6.37463i	−0.464912	−	1.20469i
$29$	0.799704	−	1.66060i	0.148501	−	0.308366i	−0.813427	−	0.581666i	$-0.802401\pi$
$29$	0.799704	−	1.66060i	0.148501	−	0.308366i	0.961929	+	0.273300i	$0.0881152\pi$
$30$		0			0
$31$			5.46570i			0.981668i	0.871253	+	0.490834i	$0.163308\pi$
$31$			5.46570i			0.981668i	−0.871253	+	0.490834i	$0.836692\pi$
$32$	3.40002	−	7.06021i	0.601044	−	1.24808i
$33$		0			0
$34$	9.78115	+	2.23248i	1.67745	+	0.382868i
$35$	7.92260	−	5.33574i	1.33916	−	0.901905i
$36$		0			0
$37$	8.48160	+	4.08452i	1.39437	+	0.671491i	0.972010	−	0.234939i	$-0.0754890\pi$
$37$	8.48160	+	4.08452i	1.39437	+	0.671491i	0.422356	+	0.906430i	$0.361203\pi$
$38$	2.61805	+	11.4704i	0.424704	+	1.86075i
$39$		0			0
$40$	−4.38953	−	1.00188i	−0.694046	−	0.158411i
$41$	1.93756	+	2.42962i	0.302595	+	0.379443i	0.909761	−	0.415133i	$-0.136265\pi$
$41$	1.93756	+	2.42962i	0.302595	+	0.379443i	−0.607165	+	0.794575i	$0.707693\pi$
$42$		0			0
$43$	6.03318	−	7.56536i	0.920051	−	1.15371i	−0.0677061	−	0.997705i	$-0.521568\pi$
$43$	6.03318	−	7.56536i	0.920051	−	1.15371i	0.987757	−	0.156002i	$-0.0498606\pi$
$44$	5.00936	−	3.99483i	0.755190	−	0.602244i
$45$		0			0
$46$	6.20952	+	7.78649i	0.915544	+	1.14806i
$47$	1.86318	+	8.16313i	0.271773	+	1.19072i	0.907919	+	0.419146i	$0.137671\pi$
$47$	1.86318	+	8.16313i	0.271773	+	1.19072i	−0.636146	+	0.771569i	$0.719472\pi$
$48$		0			0
$49$	−6.90949	−	1.12201i	−0.987070	−	0.160288i
$50$		−	17.1983i		−	2.43220i
$51$		0			0
$52$	11.4224	−	9.10906i	1.58400	−	1.26320i
$53$	0.594462	+	1.23441i	0.0816556	+	0.169560i	0.937799	−	0.347179i	$-0.112860\pi$
$53$	0.594462	+	1.23441i	0.0816556	+	0.169560i	−0.856143	+	0.516738i	$0.827146\pi$
$54$		0			0
$55$	7.00273	+	5.58449i	0.944248	+	0.753013i
$56$	1.84316	+	2.73676i	0.246303	+	0.365715i
$57$		0			0
$58$	−0.877974	+	3.84666i	−0.115284	+	0.505091i
$59$	0.856868	−	1.07448i	0.111555	−	0.139885i	−0.722919	−	0.690932i	$-0.757200\pi$
$59$	0.856868	−	1.07448i	0.111555	−	0.139885i	0.834474	+	0.551047i	$0.185772\pi$
$60$		0			0
$61$	−5.13768	+	10.6685i	−0.657813	+	1.36596i	0.258701	+	0.965958i	$0.416706\pi$
$61$	−5.13768	+	10.6685i	−0.657813	+	1.36596i	−0.916513	+	0.400004i	$0.869009\pi$
$62$	−2.60358	−	11.4070i	−0.330655	−	1.44869i
$63$		0			0
$64$	−2.62221	+	11.4886i	−0.327776	+	1.43608i
$65$	15.9677	+	12.7338i	1.98055	+	1.57944i
$66$		0			0
$67$	6.21276			0.759010			0.379505	−	0.925190i	$-0.376094\pi$
$67$	6.21276			0.759010			0.379505	+	0.925190i	$0.376094\pi$
$68$	−12.1036			−1.46778
$69$		0			0
$70$	−13.9930	+	14.9097i	−1.67248	+	1.78206i
$71$	−0.0504417	−	0.104743i	−0.00598632	−	0.0124307i	0.897954	−	0.440089i	$-0.145053\pi$
$71$	−0.0504417	−	0.104743i	−0.00598632	−	0.0124307i	−0.903941	+	0.427658i	$0.859339\pi$
$72$		0			0
$73$	−2.10438	−	0.480310i	−0.246298	−	0.0562160i	0.0975893	−	0.995227i	$-0.468887\pi$
$73$	−2.10438	−	0.480310i	−0.246298	−	0.0562160i	−0.343888	+	0.939011i	$0.611744\pi$
$74$	−19.6470	−	4.48429i	−2.28391	−	0.521288i
$75$		0			0
$76$	−6.15856	−	12.7884i	−0.706435	−	1.46693i
$77$	−0.941351	−	6.49610i	−0.107277	−	0.740299i
$78$		0			0
$79$	−11.3011			−1.27147			−0.635734	−	0.771908i	$-0.719303\pi$
$79$	−11.3011			−1.27147			−0.635734	+	0.771908i	$0.719303\pi$
$80$	−9.00923			−1.00726
$81$		0			0
$82$	−5.20107	−	4.14772i	−0.574362	−	0.458039i
$83$	−0.130612	+	0.572249i	−0.0143365	+	0.0628125i	−0.981590	−	0.190999i	$-0.938827\pi$
$83$	−0.130612	+	0.572249i	−0.0143365	+	0.0628125i	0.967254	+	0.253812i	$0.0816844\pi$
$84$		0			0
$85$	−3.76506	−	16.4958i	−0.408378	−	1.78922i
$86$	−8.98762	+	18.6630i	−0.969160	+	2.01248i
$87$		0			0
$88$	−1.92909	+	2.41900i	−0.205642	+	0.257867i
$89$	1.33313	−	5.84082i	0.141311	−	0.619126i	−0.853820	−	0.520568i	$-0.825720\pi$
$89$	1.33313	−	5.84082i	0.141311	−	0.619126i	0.995131	−	0.0985573i	$-0.0314228\pi$
$90$		0			0
$91$	−2.14648	−	14.8125i	−0.225012	−	1.55277i
$92$	−9.39377	−	7.49128i	−0.979368	−	0.781020i
$93$		0			0
$94$	−7.77701	−	16.1491i	−0.802137	−	1.66566i
$95$	15.5133	−	12.3714i	1.59163	−	1.26928i
$96$		0			0
$97$			6.74458i			0.684808i	0.939553	+	0.342404i	$0.111241\pi$
$97$			6.74458i			0.684808i	−0.939553	+	0.342404i	$0.888759\pi$
$98$	14.9547	−	0.949665i	1.51066	−	0.0959307i
$99$		0			0
$100$	4.61693	+	20.2281i	0.461693	+	2.02281i
$101$	4.27822	+	5.36472i	0.425699	+	0.533810i	0.947712	−	0.319128i	$-0.103390\pi$
$101$	4.27822	+	5.36472i	0.425699	+	0.533810i	−0.522013	+	0.852938i	$0.674819\pi$
$102$		0			0
$103$	−2.19199	+	1.74805i	−0.215983	+	0.172241i	−0.725505	−	0.688217i	$-0.758394\pi$
$103$	−2.19199	+	1.74805i	−0.215983	+	0.172241i	0.509522	+	0.860458i	$0.329822\pi$
$104$	−4.39874	+	5.51584i	−0.431332	+	0.540873i
$105$		0			0
$106$	−1.82867	−	2.29308i	−0.177616	−	0.222723i
$107$	−9.13658	−	2.08536i	−0.883267	−	0.201600i	−0.243252	−	0.969963i	$-0.578214\pi$
$107$	−9.13658	−	2.08536i	−0.883267	−	0.201600i	−0.640014	+	0.768363i	$0.721072\pi$
$108$		0			0
$109$	1.20481	+	5.27862i	0.115400	+	0.505601i	0.999282	+	0.0378903i	$0.0120638\pi$
$109$	1.20481	+	5.27862i	0.115400	+	0.505601i	−0.883882	+	0.467710i	$0.845079\pi$
$110$	−17.2750	−	8.31922i	−1.64711	−	0.793206i
$111$		0			0
$112$	4.81423	+	4.51821i	0.454902	+	0.426931i
$113$	−13.7114	−	3.12954i	−1.28986	−	0.294403i	−0.478056	−	0.878329i	$-0.658659\pi$
$113$	−13.7114	−	3.12954i	−1.28986	−	0.294403i	−0.811807	+	0.583926i	$0.801516\pi$
$114$		0			0
$115$	7.28761	−	15.1329i	0.679573	−	1.41115i
$116$		−	4.76002i		−	0.441957i
$117$		0			0
$118$	−1.27648	+	2.65063i	−0.117509	+	0.244010i
$119$	−6.26087	+	10.7030i	−0.573933	+	0.981143i
$120$		0			0
$121$	−4.36514	+	2.10214i	−0.396831	+	0.191104i
$122$	5.64052	−	24.7127i	0.510669	−	2.23739i
$123$		0			0
$124$	6.12452	+	12.7177i	0.549998	+	1.14208i
$125$	−9.86866	+	4.75249i	−0.882680	+	0.425076i
$126$		0			0
$127$	0.189842	+	0.0914232i	0.0168458	+	0.00811250i	0.442288	−	0.896873i	$-0.354167\pi$
$127$	0.189842	+	0.0914232i	0.0168458	+	0.00811250i	−0.425442	+	0.904986i	$0.639881\pi$
$128$		−	9.55367i		−	0.844433i
$129$		0			0
$130$	−39.3907	−	18.9696i	−3.45480	−	1.66374i
$131$	−3.46562	+	4.34575i	−0.302793	+	0.379690i	−0.909829	−	0.414984i	$-0.863787\pi$
$131$	−3.46562	+	4.34575i	−0.302793	+	0.379690i	0.607036	+	0.794675i	$0.292358\pi$
$132$		0			0
$133$	−14.4942	−	1.16918i	−1.25680	−	0.101380i
$134$	−12.9662	+	2.95945i	−1.12011	+	0.255657i
$135$		0			0
$136$	5.69826	−	1.30059i	0.488622	−	0.111525i
$137$	10.0990	+	8.05366i	0.862814	+	0.688071i	0.951387	−	0.307999i	$-0.0996592\pi$
$137$	10.0990	+	8.05366i	0.862814	+	0.688071i	−0.0885731	+	0.996070i	$0.528231\pi$
$138$		0			0
$139$	9.72014	−	7.75155i	0.824451	−	0.657478i	−0.117557	−	0.993066i	$-0.537506\pi$
$139$	9.72014	−	7.75155i	0.824451	−	0.657478i	0.942009	+	0.335588i	$0.108935\pi$
$140$	12.4556	−	21.2929i	1.05269	−	1.79958i
$141$		0			0
$142$	0.155167	+	0.194574i	0.0130214	+	0.0163283i
$143$	12.6449	−	6.08949i	1.05742	−	0.509228i
$144$		0			0
$145$	6.48734	−	1.48069i	0.538744	−	0.122965i
$146$	4.62068			0.382410
$147$		0			0
$148$	24.3120			1.99844
$149$	−20.2950	+	4.63220i	−1.66263	+	0.379485i	−0.947563	−	0.319569i	$-0.896462\pi$
$149$	−20.2950	+	4.63220i	−1.66263	+	0.379485i	−0.715069	+	0.699054i	$0.753605\pi$
$150$		0			0
$151$	−15.5553	+	7.49106i	−1.26588	+	0.609614i	−0.941722	−	0.336391i	$-0.890794\pi$
$151$	−15.5553	+	7.49106i	−1.26588	+	0.609614i	−0.324153	+	0.946005i	$0.605079\pi$
$152$	4.27355	+	5.35887i	0.346631	+	0.434662i
$153$		0			0
$154$	5.05903	+	13.1091i	0.407668	+	1.05636i
$155$	−15.4275	+	12.3031i	−1.23917	+	0.988205i
$156$		0			0
$157$	−0.179410	−	0.143074i	−0.0143184	−	0.0114186i	0.616304	−	0.787508i	$-0.288629\pi$
$157$	−0.179410	−	0.143074i	−0.0143184	−	0.0114186i	−0.630623	+	0.776089i	$0.717201\pi$
$158$	23.5856	−	5.38325i	1.87637	−	0.428269i
$159$		0			0
$160$	27.5815	−	6.29531i	2.18051	−	0.497688i
$161$	−11.4835	+	4.43170i	−0.905029	+	0.349267i
$162$		0			0
$163$	6.69637	−	8.39698i	0.524500	−	0.657702i	−0.447058	−	0.894505i	$-0.647528\pi$
$163$	6.69637	−	8.39698i	0.524500	−	0.657702i	0.971558	+	0.236803i	$0.0760996\pi$
$164$	7.23082	+	3.48218i	0.564632	+	0.271913i
$165$		0			0
$166$		−	1.25651i		−	0.0975245i
$167$	−2.82756	−	1.36168i	−0.218803	−	0.105370i	0.321271	−	0.946987i	$-0.395890\pi$
$167$	−2.82756	−	1.36168i	−0.218803	−	0.105370i	−0.540075	+	0.841617i	$0.681604\pi$
$168$		0			0
$169$	17.1206	−	8.24483i	1.31697	−	0.634218i
$170$	15.7155	+	32.6336i	1.20533	+	2.50289i
$171$		0			0
$172$	5.56084	−	24.3636i	0.424010	−	1.85771i
$173$	13.4507	−	6.47751i	1.02264	−	0.492476i	0.154076	−	0.988059i	$-0.450760\pi$
$173$	13.4507	−	6.47751i	1.02264	−	0.492476i	0.868560	+	0.495583i	$0.165046\pi$
$174$		0			0
$175$	20.2755	+	6.38077i	1.53269	+	0.482341i
$176$	−2.68620	+	5.57796i	−0.202480	+	0.420455i
$177$		0			0
$178$			12.8250i			0.961272i
$179$	2.70448	−	5.61591i	0.202142	−	0.419753i	−0.775112	−	0.631824i	$-0.782307\pi$
$179$	2.70448	−	5.61591i	0.202142	−	0.419753i	0.977254	+	0.212071i	$0.0680209\pi$
$180$		0			0
$181$	−13.7794	−	3.14506i	−1.02421	−	0.233770i	−0.322758	−	0.946482i	$-0.604610\pi$
$181$	−13.7794	−	3.14506i	−1.02421	−	0.233770i	−0.701457	+	0.712711i	$0.747467\pi$
$182$	11.5357	+	29.8915i	0.855080	+	2.21571i
$183$		0			0
$184$	5.22746	+	2.51741i	0.385374	+	0.185586i
$185$	7.56270	+	33.1344i	0.556021	+	2.43609i
$186$		0			0
$187$	−11.3358	−	2.58732i	−0.828954	−	0.189203i
$188$	13.4824	+	16.9064i	0.983304	+	1.23302i
$189$		0			0
$190$	−26.4835	+	33.2092i	−1.92131	+	2.40925i
$191$	−0.690150	+	0.550376i	−0.0499375	+	0.0398238i	−0.648141	−	0.761521i	$-0.724453\pi$
$191$	−0.690150	+	0.550376i	−0.0499375	+	0.0398238i	0.598203	+	0.801345i	$0.295882\pi$
$192$		0			0
$193$	−1.56777	−	1.96592i	−0.112850	−	0.141510i	0.722198	−	0.691686i	$-0.243132\pi$
$193$	−1.56777	−	1.96592i	−0.112850	−	0.141510i	−0.835048	+	0.550176i	$0.814560\pi$
$194$	−3.21278	−	14.0761i	−0.230664	−	1.01060i
$195$		0			0
$196$	−17.3344	+	5.13162i	−1.23817	+	0.366545i
$197$		−	16.1008i		−	1.14714i	−0.819158	−	0.573568i	$-0.805559\pi$
$197$		−	16.1008i		−	1.14714i	0.819158	−	0.573568i	$-0.194441\pi$
$198$		0			0
$199$	−1.92580	+	1.53577i	−0.136516	+	0.108868i	−0.689367	−	0.724412i	$-0.742111\pi$
$199$	−1.92580	+	1.53577i	−0.136516	+	0.108868i	0.552851	+	0.833280i	$0.313540\pi$
$200$	−4.34721	−	9.02707i	−0.307394	−	0.638310i
$201$		0			0
$202$	−11.4842	−	9.15837i	−0.808027	−	0.644380i
$203$	−4.20920	−	2.46223i	−0.295428	−	0.172814i
$204$		0			0
$205$	−2.49651	+	10.9379i	−0.174364	+	0.763939i
$206$	3.74204	−	4.69237i	0.260721	−	0.326933i
$207$		0			0
$208$	−6.12511	+	12.7189i	−0.424700	+	0.881899i
$209$	−3.03417	−	13.2936i	−0.209878	−	0.919534i
$210$		0			0
$211$	−5.13084	+	22.4797i	−0.353221	+	1.54756i	0.416471	+	0.909149i	$0.363267\pi$
$211$	−5.13084	+	22.4797i	−0.353221	+	1.54756i	−0.769692	+	0.638415i	$0.779590\pi$
$212$	2.76641	+	2.20614i	0.189998	+	0.151518i
$213$		0			0
$214$	20.0616			1.37138
$215$	34.9345			2.38251
$216$		0			0
$217$	14.4141	+	1.16271i	0.978490	+	0.0789301i
$218$	−5.02894	−	10.4427i	−0.340603	−	0.707269i
$219$		0			0
$220$	22.5517	+	5.14729i	1.52044	+	0.347030i
$221$	−25.8480	−	5.89963i	−1.73872	−	0.396852i
$222$		0			0
$223$	−6.87647	−	14.2791i	−0.460482	−	0.956202i	−0.993893	−	0.110345i	$-0.964804\pi$
$223$	−6.87647	−	14.2791i	−0.460482	−	0.956202i	0.533411	−	0.845856i	$-0.320910\pi$
$224$	−17.8958	−	10.4684i	−1.19571	−	0.699449i
$225$		0			0
$226$	30.1068			2.00268
$227$	20.3914			1.35342			0.676711	−	0.736249i	$-0.263405\pi$
$227$	20.3914			1.35342			0.676711	+	0.736249i	$0.263405\pi$
$228$		0			0
$229$	18.2428	+	14.5482i	1.20552	+	0.961371i	0.999851	−	0.0172501i	$-0.00549116\pi$
$229$	18.2428	+	14.5482i	1.20552	+	0.961371i	0.205670	+	0.978621i	$0.434063\pi$
$230$	−8.00088	+	35.0541i	−0.527562	+	2.31140i
$231$		0			0
$232$	0.511487	+	2.24097i	0.0335807	+	0.147127i
$233$	9.92363	−	20.6066i	0.650119	−	1.34999i	−0.271707	−	0.962380i	$-0.587588\pi$
$233$	9.92363	−	20.6066i	0.650119	−	1.34999i	0.921825	−	0.387605i	$-0.126698\pi$
$234$		0			0
$235$	−18.8474	+	23.6339i	−1.22947	+	1.54171i
$236$	0.789784	−	3.46027i	0.0514106	−	0.225245i
$237$		0			0
$238$	7.96821	−	25.3198i	0.516502	−	1.64124i
$239$	19.7044	+	15.7137i	1.27457	+	1.01644i	0.998469	+	0.0553060i	$0.0176134\pi$
$239$	19.7044	+	15.7137i	1.27457	+	1.01644i	0.276100	+	0.961129i	$0.410958\pi$
$240$		0			0
$241$	−8.94537	−	18.5752i	−0.576222	−	1.19654i	−0.961772	−	0.273850i	$-0.911703\pi$
$241$	−8.94537	−	18.5752i	−0.576222	−	1.19654i	0.385551	−	0.922687i	$-0.374012\pi$
$242$	8.10880	−	6.46655i	0.521253	−	0.415686i
$243$		0			0
$244$			30.5807i			1.95773i
$245$	−12.3860	−	22.0284i	−0.791311	−	1.40734i
$246$		0			0
$247$	−6.91854	−	30.3121i	−0.440216	−	1.92871i
$248$	−4.24993	−	5.32925i	−0.269871	−	0.338408i
$249$		0			0
$250$	18.3323	−	14.6195i	1.15943	−	0.924618i
$251$	0.597185	−	0.748847i	0.0376940	−	0.0472668i	−0.762627	−	0.646838i	$-0.776091\pi$
$251$	0.597185	−	0.748847i	0.0376940	−	0.0472668i	0.800321	+	0.599571i	$0.204662\pi$
$252$		0			0
$253$	−7.19646	−	9.02408i	−0.452438	−	0.567339i
$254$	−0.439755	−	0.100371i	−0.0275927	−	0.00629785i
$255$		0			0
$256$	−0.693528	−	3.03854i	−0.0433455	−	0.189909i
$257$	−23.9108	−	11.5148i	−1.49151	−	0.718275i	−0.502291	−	0.864699i	$-0.667509\pi$
$257$	−23.9108	−	11.5148i	−1.49151	−	0.718275i	−0.989222	+	0.146424i	$0.953224\pi$
$258$		0			0
$259$	12.5759	−	21.4986i	0.781430	−	1.33586i
$260$	51.4227	+	11.7369i	3.18910	+	0.727892i
$261$		0			0
$262$	5.16274	−	10.7205i	0.318955	−	0.662317i
$263$			13.2563i			0.817419i	0.912665	+	0.408709i	$0.134021\pi$
$263$			13.2563i			0.817419i	−0.912665	+	0.408709i	$0.865979\pi$
$264$		0			0
$265$	−2.14616	+	4.45655i	−0.131838	+	0.273764i
$266$	30.8066	−	4.46419i	1.88887	−	0.273717i
$267$		0			0
$268$	14.4560	−	6.96164i	0.883040	−	0.425250i
$269$	−1.28551	+	5.63220i	−0.0783791	+	0.343401i	−0.998879	−	0.0473422i	$-0.984925\pi$
$269$	−1.28551	+	5.63220i	−0.0783791	+	0.343401i	0.920500	+	0.390743i	$0.127782\pi$
$270$		0			0
$271$	1.41890	+	2.94639i	0.0861923	+	0.178980i	0.939610	−	0.342248i	$-0.111188\pi$
$271$	1.41890	+	2.94639i	0.0861923	+	0.178980i	−0.853417	+	0.521228i	$0.825474\pi$
$272$	10.5371	−	5.07441i	0.638907	−	0.307681i
$273$		0			0
$274$	−24.9132	−	11.9975i	−1.50506	−	0.724798i
$275$			19.9318i			1.20193i
$276$		0			0
$277$	7.22028	+	3.47711i	0.433825	+	0.208919i	0.638034	−	0.770008i	$-0.279748\pi$
$277$	7.22028	+	3.47711i	0.433825	+	0.208919i	−0.204209	+	0.978927i	$0.565462\pi$
$278$	−16.5937	+	20.8079i	−0.995225	+	1.24797i
$279$		0			0
$280$	−3.57593	+	11.3629i	−0.213703	+	0.679062i
$281$	−17.5801	+	4.01254i	−1.04874	+	0.239368i	−0.711964	−	0.702216i	$-0.752194\pi$
$281$	−17.5801	+	4.01254i	−1.04874	+	0.239368i	−0.336777	+	0.941584i	$0.609337\pi$
$282$		0			0
$283$	−16.0873	+	3.67181i	−0.956288	+	0.218266i	−0.672065	−	0.740492i	$-0.734593\pi$
$283$	−16.0873	+	3.67181i	−0.956288	+	0.218266i	−0.284223	+	0.958758i	$0.591735\pi$
$284$	−0.234737	−	0.187197i	−0.0139291	−	0.0111081i
$285$		0			0
$286$	−23.4896	+	18.7323i	−1.38897	+	1.10767i
$287$	6.81953	−	4.59284i	0.402544	−	0.271107i
$288$		0			0
$289$	3.09543	+	3.88155i	0.182084	+	0.228327i
$290$	−12.8339	+	6.18048i	−0.753633	+	0.362930i
$291$		0			0
$292$	−5.43471	+	1.24044i	−0.318042	+	0.0725911i
$293$	0.0380752			0.00222437			0.00111219	−	0.999999i	$-0.499646\pi$
$293$	0.0380752			0.00222437			0.00111219	+	0.999999i	$0.499646\pi$
$294$		0			0
$295$	4.96161			0.288876
$296$	−11.4458	+	2.61244i	−0.665276	+	0.151845i
$297$		0			0
$298$	40.1496	−	19.3350i	2.32580	−	1.12005i
$299$	−16.4095	−	20.5768i	−0.948984	−	1.18999i
$300$		0			0
$301$	−18.6678	−	17.5200i	−1.07600	−	1.00983i
$302$	28.8960	−	23.0438i	1.66278	−	1.32602i
$303$		0			0
$304$	10.7230	+	8.55129i	0.615005	+	0.490450i
$305$	−41.6778	+	9.51268i	−2.38646	+	0.544694i
$306$		0			0
$307$	4.80078	−	1.09575i	0.273995	−	0.0625375i	−0.0833157	−	0.996523i	$-0.526551\pi$
$307$	4.80078	−	1.09575i	0.273995	−	0.0625375i	0.357310	+	0.933986i	$0.383694\pi$
$308$	−9.46947	−	14.0604i	−0.539573	−	0.801167i
$309$		0			0
$310$	26.3371	−	33.0257i	1.49585	−	1.87573i
$311$	28.4804	+	13.7154i	1.61498	+	0.777731i	0.999942	−	0.0107695i	$-0.00342812\pi$
$311$	28.4804	+	13.7154i	1.61498	+	0.777731i	0.615034	+	0.788501i	$0.289142\pi$
$312$		0			0
$313$			1.29521i			0.0732094i	0.999330	+	0.0366047i	$0.0116542\pi$
$313$			1.29521i			0.0732094i	−0.999330	+	0.0366047i	$0.988346\pi$
$314$	0.442585	+	0.213138i	0.0249765	+	0.0120281i
$315$		0			0
$316$	−26.2955	+	12.6633i	−1.47924	+	0.712364i
$317$	−14.1606	−	29.4047i	−0.795337	−	1.65153i	−0.758020	−	0.652231i	$-0.773833\pi$
$317$	−14.1606	−	29.4047i	−0.795337	−	1.65153i	−0.0373165	−	0.999303i	$-0.511881\pi$
$318$		0			0
$319$	1.01752	−	4.45805i	0.0569702	−	0.249603i
$320$	−38.3305	+	18.4590i	−2.14274	+	1.03189i
$321$		0			0
$322$	21.8554	−	14.7192i	1.21795	−	0.820271i
$323$	−11.1761	+	23.2073i	−0.621852	+	1.29129i
$324$		0			0
$325$			45.4487i			2.52104i
$326$	−9.97558	+	20.7145i	−0.552496	+	1.14727i
$327$		0			0
$328$	−3.77837	−	0.862389i	−0.208626	−	0.0476174i
$329$	21.9240	−	3.17702i	1.20871	−	0.175155i
$330$		0			0
$331$	−28.6576	−	13.8008i	−1.57517	−	0.758560i	−0.576865	−	0.816839i	$-0.695724\pi$
$331$	−28.6576	−	13.8008i	−1.57517	−	0.758560i	−0.998300	+	0.0582797i	$0.981438\pi$
$332$	0.337316	+	1.47788i	0.0185126	+	0.0811090i
$333$		0			0
$334$	6.54983	+	1.49496i	0.358391	+	0.0818003i
$335$	13.9847	+	17.5362i	0.764065	+	0.958107i
$336$		0			0
$337$	−8.66974	+	10.8715i	−0.472271	+	0.592209i	−0.959725	−	0.280940i	$-0.909354\pi$
$337$	−8.66974	+	10.8715i	−0.472271	+	0.592209i	0.487455	+	0.873148i	$0.337925\pi$
$338$	−31.8036	+	25.3625i	−1.72989	+	1.37954i
$339$		0			0
$340$	−27.2448	−	34.1639i	−1.47756	−	1.85280i
$341$	3.01740	+	13.2201i	0.163401	+	0.715907i
$342$		0			0
$343$	−4.42881	+	17.9829i	−0.239133	+	0.970987i
$344$			12.0677i			0.650646i
$345$		0			0
$346$	−24.9863	+	19.9259i	−1.34327	+	1.07122i
$347$	6.34306	+	13.1715i	0.340513	+	0.707083i	0.998962	−	0.0455420i	$-0.0145015\pi$
$347$	6.34306	+	13.1715i	0.340513	+	0.707083i	−0.658449	+	0.752625i	$0.728787\pi$
$348$		0			0
$349$	19.8349	+	15.8178i	1.06174	+	0.846709i	0.988593	−	0.150612i	$-0.0481245\pi$
$349$	19.8349	+	15.8178i	1.06174	+	0.846709i	0.0731466	+	0.997321i	$0.476696\pi$
$350$	−45.3550	−	3.65857i	−2.42433	−	0.195559i
$351$		0			0
$352$	4.32608	−	18.9538i	0.230581	−	1.01024i
$353$	−14.7630	+	18.5122i	−0.785755	+	0.985306i	0.214209	+	0.976788i	$0.431283\pi$
$353$	−14.7630	+	18.5122i	−0.785755	+	0.985306i	−0.999964	+	0.00851784i	$0.997289\pi$
$354$		0			0
$355$	0.182107	−	0.378150i	0.00966526	−	0.0200701i
$356$	−3.44291	−	15.0844i	−0.182474	−	0.799470i
$357$		0			0
$358$	−2.96918	+	13.0088i	−0.156926	+	0.687537i
$359$	−20.1008	−	16.0298i	−1.06088	−	0.846023i	−0.0723992	−	0.997376i	$-0.523066\pi$
$359$	−20.1008	−	16.0298i	−1.06088	−	0.846023i	−0.988480	+	0.151353i	$0.951637\pi$
$360$		0			0
$361$	−11.2068			−0.589833
$362$	30.2561			1.59022
$363$		0			0
$364$	−21.5924	−	32.0608i	−1.13175	−	1.68044i
$365$	−3.38113	−	7.02099i	−0.176977	−	0.367496i
$366$		0			0
$367$	9.93071	+	2.26662i	0.518379	+	0.118317i	0.473702	−	0.880685i	$-0.342917\pi$
$367$	9.93071	+	2.26662i	0.518379	+	0.118317i	0.0446763	+	0.999002i	$0.485774\pi$
$368$	11.3187	+	2.58341i	0.590027	+	0.134670i
$369$		0			0
$370$	−31.5671	−	65.5497i	−1.64109	−	3.40777i
$371$	3.38183	−	1.30511i	0.175576	−	0.0677580i
$372$		0			0
$373$	−24.3982			−1.26329			−0.631645	−	0.775257i	$-0.717620\pi$
$373$	−24.3982			−1.26329			−0.631645	+	0.775257i	$0.717620\pi$
$374$	24.8905			1.28706
$375$		0			0
$376$	−8.16403	−	6.51060i	−0.421028	−	0.335759i
$377$	2.32016	−	10.1653i	0.119494	−	0.523539i
$378$		0			0
$379$	−2.74465	−	12.0251i	−0.140983	−	0.617687i	−0.995208	−	0.0977830i	$-0.968825\pi$
$379$	−2.74465	−	12.0251i	−0.140983	−	0.617687i	0.854225	−	0.519904i	$-0.174032\pi$
$380$	22.2340	−	46.1693i	1.14058	−	2.36844i
$381$		0			0
$382$	1.17819	−	1.47740i	0.0602813	−	0.0755904i
$383$	−0.625679	+	2.74128i	−0.0319707	+	0.140073i	−0.988394	−	0.151910i	$-0.951458\pi$
$383$	−0.625679	+	2.74128i	−0.0319707	+	0.140073i	0.956424	+	0.291982i	$0.0943149\pi$
$384$		0			0
$385$	16.2170	−	17.2795i	0.826496	−	0.880646i
$386$	4.20843	+	3.35611i	0.214203	+	0.170821i
$387$		0			0
$388$	7.55756	+	15.6934i	0.383677	+	0.796713i
$389$	3.60389	−	2.87401i	0.182724	−	0.145718i	−0.527856	−	0.849334i	$-0.677004\pi$
$389$	3.60389	−	2.87401i	0.182724	−	0.145718i	0.710580	+	0.703616i	$0.248432\pi$
$390$		0			0
$391$			21.8040i			1.10268i
$392$	7.60944	−	4.27858i	0.384335	−	0.216101i
$393$		0			0
$394$	7.66962	+	33.6028i	0.386390	+	1.69288i
$395$	−25.4382	−	31.8985i	−1.27994	−	1.60499i
$396$		0			0
$397$	3.62178	−	2.88827i	0.181772	−	0.144958i	−0.528377	−	0.849010i	$-0.677199\pi$
$397$	3.62178	−	2.88827i	0.181772	−	0.144958i	0.710149	+	0.704052i	$0.248628\pi$
$398$	3.28762	−	4.12255i	0.164794	−	0.206645i
$399$		0			0
$400$	−12.5000	−	15.6745i	−0.624998	−	0.783723i
$401$	−11.6033	−	2.64838i	−0.579442	−	0.132254i	−0.0772524	−	0.997012i	$-0.524615\pi$
$401$	−11.6033	−	2.64838i	−0.579442	−	0.132254i	−0.502189	+	0.864758i	$0.667472\pi$
$402$		0			0
$403$	6.88030	+	30.1446i	0.342732	+	1.50161i
$404$	15.9660	+	7.68883i	0.794339	+	0.382534i
$405$		0			0
$406$	9.95757	+	3.13368i	0.494186	+	0.155522i
$407$	22.7697	+	5.19703i	1.12865	+	0.257607i
$408$		0			0
$409$	−0.0113431	+	0.0235542i	−0.000560882	+	0.00116468i	−0.901249	−	0.433301i	$-0.857349\pi$
$409$	−0.0113431	+	0.0235542i	−0.000560882	+	0.00116468i	0.900688	+	0.434466i	$0.143063\pi$
$410$		−	24.0170i		−	1.18611i
$411$		0			0
$412$	−3.14160	+	6.52360i	−0.154776	+	0.321395i
$413$	−2.65132	−	2.48829i	−0.130463	−	0.122441i
$414$		0			0
$415$	−1.90924	+	0.919442i	−0.0937210	+	0.0451336i
$416$	9.86438	−	43.2187i	0.483641	−	2.11897i
$417$		0			0
$418$	12.6648	+	26.2986i	0.619454	+	1.28631i
$419$	−19.8521	+	9.56027i	−0.969838	+	0.467050i	−0.850598	−	0.525816i	$-0.823760\pi$
$419$	−19.8521	+	9.56027i	−0.969838	+	0.467050i	−0.119240	+	0.992865i	$0.538046\pi$
$420$		0			0
$421$	17.1780	+	8.27249i	0.837205	+	0.403177i	0.802812	−	0.596232i	$-0.203336\pi$
$421$	17.1780	+	8.27249i	0.837205	+	0.403177i	0.0343926	+	0.999408i	$0.489050\pi$
$422$		−	49.3597i		−	2.40279i
$423$		0			0
$424$	−1.53946	−	0.741364i	−0.0747627	−	0.0360038i
$425$	23.4759	−	29.4378i	1.13875	−	1.42794i
$426$		0			0
$427$	27.0419	+	15.8185i	1.30865	+	0.765512i
$428$	−23.5959	+	5.38561i	−1.14055	+	0.260323i
$429$		0			0
$430$	−72.9092	+	16.6410i	−3.51599	+	0.802502i
$431$	−12.7747	−	10.1875i	−0.615337	−	0.490715i	0.265515	−	0.964107i	$-0.414458\pi$
$431$	−12.7747	−	10.1875i	−0.615337	−	0.490715i	−0.880852	+	0.473392i	$0.843030\pi$
$432$		0			0
$433$	−4.91646	+	3.92075i	−0.236270	+	0.188419i	−0.734466	−	0.678645i	$-0.762567\pi$
$433$	−4.91646	+	3.92075i	−0.236270	+	0.188419i	0.498196	+	0.867064i	$0.333996\pi$
$434$	−30.6363	+	4.43952i	−1.47059	+	0.213104i
$435$		0			0
$436$	8.71828	+	10.9324i	0.417530	+	0.523566i
$437$	−23.0375	+	11.0943i	−1.10203	+	0.530712i
$438$		0			0
$439$	−5.76219	+	1.31518i	−0.275014	+	0.0627703i	−0.357804	−	0.933797i	$-0.616474\pi$
$439$	−5.76219	+	1.31518i	−0.275014	+	0.0627703i	0.0827892	+	0.996567i	$0.473617\pi$
$440$	−11.1702			−0.532519
$441$		0			0
$442$	56.7556			2.69959
$443$	3.00551	−	0.685988i	0.142796	−	0.0325923i	−0.150525	−	0.988606i	$-0.548097\pi$
$443$	3.00551	−	0.685988i	0.142796	−	0.0325923i	0.293321	+	0.956014i	$0.405239\pi$
$444$		0			0
$445$	19.4872	−	9.38454i	0.923782	−	0.444870i
$446$	21.1532	+	26.5253i	1.00163	+	1.25601i
$447$		0			0
$448$	29.7399	+	9.35922i	1.40508	+	0.442182i
$449$	−28.2620	+	22.5382i	−1.33377	+	1.06364i	−0.341452	+	0.939899i	$0.610919\pi$
$449$	−28.2620	+	22.5382i	−1.33377	+	1.06364i	−0.992314	+	0.123744i	$0.960510\pi$
$450$		0			0
$451$	6.02773	+	4.80696i	0.283835	+	0.226351i
$452$	−35.4108	+	8.08229i	−1.66558	+	0.380159i
$453$		0			0
$454$	−42.5572	+	9.71341i	−1.99731	+	0.455873i
$455$	36.9783	−	39.4010i	1.73357	−	1.84715i
$456$		0			0
$457$	−11.3269	+	14.2035i	−0.529849	+	0.664410i	−0.972668	−	0.232201i	$-0.925407\pi$
$457$	−11.3269	+	14.2035i	−0.529849	+	0.664410i	0.442819	+	0.896611i	$0.353979\pi$
$458$	−45.0033	−	21.6724i	−2.10286	−	1.01269i
$459$		0			0
$460$		−	43.3776i		−	2.02249i
$461$	20.5242	+	9.88391i	0.955905	+	0.460340i	0.845753	−	0.533575i	$-0.179152\pi$
$461$	20.5242	+	9.88391i	0.955905	+	0.460340i	0.110153	+	0.993915i	$0.464866\pi$
$462$		0			0
$463$	−35.5308	+	17.1107i	−1.65126	+	0.795204i	−0.651940	+	0.758270i	$0.726045\pi$
$463$	−35.5308	+	17.1107i	−1.65126	+	0.795204i	−0.999318	+	0.0369334i	$0.988241\pi$
$464$	1.99562	+	4.14396i	0.0926446	+	0.192378i
$465$		0			0
$466$	−10.8949	+	47.7336i	−0.504696	+	2.21122i
$467$	13.4779	−	6.49063i	0.623685	−	0.300351i	−0.0952234	−	0.995456i	$-0.530357\pi$
$467$	13.4779	−	6.49063i	0.623685	−	0.300351i	0.718908	+	0.695105i	$0.244642\pi$
$468$		0			0
$469$	1.32164	−	16.3842i	0.0610275	−	0.756553i
$470$	28.0770	−	58.3025i	1.29510	−	2.68929i
$471$		0			0
$472$			1.71393i			0.0788898i
$473$	10.4161	−	21.6293i	0.478934	−	0.994516i
$474$		0			0
$475$	43.0482	+	9.82547i	1.97519	+	0.450823i
$476$	−2.57480	+	31.9195i	−0.118016	+	1.46303i
$477$		0			0
$478$	−48.6087	−	23.4087i	−2.22331	−	1.07069i
$479$	−5.93866	−	26.0189i	−0.271344	−	1.18884i	−0.908428	−	0.418042i	$-0.862717\pi$
$479$	−5.93866	−	26.0189i	−0.271344	−	1.18884i	0.637084	−	0.770795i	$-0.280141\pi$
$480$		0			0
$481$	51.9196	+	11.8503i	2.36733	+	0.540328i
$482$	27.5175	+	34.5059i	1.25339	+	1.57170i
$483$		0			0
$484$	−7.80137	+	9.78261i	−0.354608	+	0.444664i
$485$	−19.0373	+	15.1818i	−0.864441	+	0.689369i
$486$		0			0
$487$	−11.1767	−	14.0151i	−0.506463	−	0.635084i	0.461211	−	0.887291i	$-0.347415\pi$
$487$	−11.1767	−	14.0151i	−0.506463	−	0.635084i	−0.967673	+	0.252206i	$0.918844\pi$
$488$	−3.28603	−	14.3971i	−0.148752	−	0.651724i
$489$		0			0
$490$	36.3431	+	40.0738i	1.64181	+	1.81035i
$491$		−	26.9866i		−	1.21789i	−0.793213	−	0.608944i	$-0.791593\pi$
$491$		−	26.9866i		−	1.21789i	0.793213	−	0.608944i	$-0.208407\pi$
$492$		0			0
$493$	−6.75354	+	5.38577i	−0.304164	+	0.242563i
$494$	28.8783	+	59.9665i	1.29930	+	2.69802i
$495$		0			0
$496$	−10.6637	−	8.50402i	−0.478814	−	0.381842i
$497$	−0.286958	+	0.110742i	−0.0128718	+	0.00496746i
$498$		0			0
$499$	0.493922	−	2.16401i	0.0221110	−	0.0968746i	−0.962668	−	0.270683i	$-0.912750\pi$
$499$	0.493922	−	2.16401i	0.0221110	−	0.0968746i	0.984779	+	0.173809i	$0.0556075\pi$
$500$	−17.6372	+	22.1164i	−0.788761	+	0.989076i
$501$		0			0
$502$	−0.889627	+	1.84733i	−0.0397060	+	0.0824504i
$503$	−7.52668	−	32.9765i	−0.335598	−	1.47035i	−0.808113	−	0.589028i	$-0.799511\pi$
$503$	−7.52668	−	32.9765i	−0.335598	−	1.47035i	0.472515	−	0.881323i	$-0.343346\pi$
$504$		0			0
$505$	−5.51243	+	24.1515i	−0.245300	+	1.07473i
$506$	19.3178	+	15.4054i	0.858781	+	0.684855i
$507$		0			0
$508$	0.544172			0.0241437
$509$	33.9677			1.50559			0.752795	−	0.658255i	$-0.228705\pi$
$509$	33.9677			1.50559			0.752795	+	0.658255i	$0.228705\pi$
$510$		0			0
$511$	−1.71433	+	5.44745i	−0.0758374	+	0.240981i
$512$	11.1852	+	23.2263i	0.494320	+	1.02647i
$513$		0			0
$514$	55.3874	+	12.6418i	2.44303	+	0.557607i
$515$	−9.86814	−	2.25234i	−0.434842	−	0.0992499i
$516$		0			0
$517$	9.01309	+	18.7159i	0.396395	+	0.823123i
$518$	−16.0054	+	50.8587i	−0.703236	+	2.23460i
$519$		0			0
$520$	−25.4705			−1.11695
$521$	41.3605			1.81204			0.906019	−	0.423236i	$-0.139106\pi$
$521$	41.3605			1.81204			0.906019	+	0.423236i	$0.139106\pi$
$522$		0			0
$523$	17.2140	+	13.7277i	0.752716	+	0.600271i	0.922854	−	0.385150i	$-0.125850\pi$
$523$	17.2140	+	13.7277i	0.752716	+	0.600271i	−0.170139	+	0.985420i	$0.554422\pi$
$524$	−3.19430	+	13.9951i	−0.139544	+	0.611381i
$525$		0			0
$526$	−6.31463	−	27.6662i	−0.275331	−	1.20630i
$527$	11.1143	−	23.0790i	0.484146	−	1.00534i
$528$		0			0
$529$	0.845143	−	1.05978i	0.0367454	−	0.0460772i
$530$	2.35621	−	10.3232i	0.102347	−	0.448413i
$531$		0			0
$532$	−35.0354	+	13.5208i	−1.51898	+	0.586201i
$533$	13.7445	+	10.9609i	0.595341	+	0.474768i
$534$		0			0
$535$	−14.6799	−	30.4831i	−0.634667	−	1.31790i
$536$	−6.05767	+	4.83083i	−0.261651	+	0.208660i
$537$		0			0
$538$		−	12.3669i		−	0.533174i
$539$	−17.3317	+	1.10061i	−0.746528	+	0.0474064i
$540$		0			0
$541$	2.31388	+	10.1378i	0.0994816	+	0.435857i	0.999999	+	0.00103828i	$0.000330494\pi$
$541$	2.31388	+	10.1378i	0.0994816	+	0.435857i	−0.900518	+	0.434819i	$0.856812\pi$
$542$	−4.36480	−	5.47328i	−0.187484	−	0.235098i
$543$		0			0
$544$	−28.7133	+	22.8981i	−1.23107	+	0.981748i
$545$	−12.1875	+	15.2827i	−0.522057	+	0.654638i
$546$		0			0
$547$	−24.6968	−	30.9688i	−1.05596	−	1.32413i	−0.943828	−	0.330438i	$-0.892804\pi$
$547$	−24.6968	−	30.9688i	−1.05596	−	1.32413i	−0.112132	−	0.993693i	$-0.535768\pi$
$548$	32.5229	+	7.42315i	1.38931	+	0.317101i
$549$		0			0
$550$	−9.49449	−	41.5981i	−0.404846	−	1.77375i
$551$	−9.12680	−	4.39523i	−0.388815	−	0.187243i
$552$		0			0
$553$	−2.40407	+	29.8030i	−0.102231	+	1.26735i
$554$	−16.7252	−	3.81742i	−0.710587	−	0.162187i
$555$		0			0
$556$	13.9311	−	28.9282i	0.590811	−	1.22683i
$557$			14.9986i			0.635511i	0.948173	+	0.317755i	$0.102929\pi$
$557$			14.9986i			0.635511i	−0.948173	+	0.317755i	$0.897071\pi$
$558$		0			0
$559$	23.7510	−	49.3194i	1.00456	−	2.08599i
$560$	−1.91653	+	23.7590i	−0.0809881	+	1.00400i
$561$		0			0
$562$	34.7787	−	16.7485i	1.46705	−	0.706495i
$563$	−4.42643	+	19.3935i	−0.186552	+	0.817337i	0.791865	+	0.610696i	$0.209110\pi$
$563$	−4.42643	+	19.3935i	−0.186552	+	0.817337i	−0.978417	+	0.206641i	$0.933747\pi$
$564$		0			0
$565$	−22.0304	−	45.7465i	−0.926825	−	1.92457i
$566$	31.8254	−	15.3263i	1.33772	−	0.644213i
$567$		0			0
$568$	0.130627	+	0.0629067i	0.00548099	+	0.00263951i
$569$			6.21580i			0.260580i	0.991476	+	0.130290i	$0.0415908\pi$
$569$			6.21580i			0.260580i	−0.991476	+	0.130290i	$0.958409\pi$
$570$		0			0
$571$	11.8217	+	5.69303i	0.494723	+	0.238246i	0.664572	−	0.747224i	$-0.268614\pi$
$571$	11.8217	+	5.69303i	0.494723	+	0.238246i	−0.169849	+	0.985470i	$0.554328\pi$
$572$	22.5990	−	28.3383i	0.944913	−	1.18488i
$573$		0			0
$574$	−12.0447	+	12.8338i	−0.502737	+	0.535674i
$575$	36.4398	−	8.31715i	1.51964	−	0.346849i
$576$		0			0
$577$	14.5003	−	3.30960i	0.603656	−	0.137781i	0.0902394	−	0.995920i	$-0.471237\pi$
$577$	14.5003	−	3.30960i	0.603656	−	0.137781i	0.513416	+	0.858140i	$0.328380\pi$
$578$	−8.30922	−	6.62638i	−0.345618	−	0.275621i
$579$		0			0
$580$	13.4357	−	10.7146i	0.557887	−	0.444900i
$581$	1.48134	+	0.466183i	0.0614564	+	0.0193405i
$582$		0			0
$583$	2.11932	+	2.65754i	0.0877732	+	0.110064i
$584$	2.42531	−	1.16797i	0.100360	−	0.0483309i
$585$		0			0
$586$	−0.0794638	+	0.0181371i	−0.00328262	+	0.000749236i
$587$	−31.7302			−1.30965			−0.654823	−	0.755782i	$-0.727257\pi$
$587$	−31.7302			−1.30965			−0.654823	+	0.755782i	$0.727257\pi$
$588$		0			0
$589$	30.0399			1.23777
$590$	−10.3550	+	2.36346i	−0.426309	+	0.0973022i
$591$		0			0
$592$	−21.1654	+	10.1927i	−0.869894	+	0.418919i
$593$	0.0568661	+	0.0713078i	0.00233521	+	0.00292826i	0.782998	−	0.622025i	$-0.213690\pi$
$593$	0.0568661	+	0.0713078i	0.00233521	+	0.00292826i	−0.780663	+	0.624953i	$0.785118\pi$
$594$		0			0
$595$	−44.3034	+	6.42002i	−1.81626	+	0.263195i
$596$	−42.0323	+	33.5196i	−1.72171	+	1.37302i
$597$		0			0
$598$	44.0487	+	35.1277i	1.80128	+	1.43648i
$599$	12.4813	−	2.84878i	0.509973	−	0.116398i	0.0402109	−	0.999191i	$-0.487197\pi$
$599$	12.4813	−	2.84878i	0.509973	−	0.116398i	0.469762	+	0.882793i	$0.344340\pi$
$600$		0			0
$601$	−11.5018	+	2.62520i	−0.469167	+	0.107084i	−0.450567	−	0.892743i	$-0.648778\pi$
$601$	−11.5018	+	2.62520i	−0.469167	+	0.107084i	−0.0186002	+	0.999827i	$0.505921\pi$
$602$	47.3058	+	27.6722i	1.92804	+	1.12783i
$603$		0			0
$604$	−27.8005	+	34.8607i	−1.13119	+	1.41846i
$605$	−15.7593	−	7.58927i	−0.640706	−	0.308548i
$606$		0			0
$607$		−	10.4717i		−	0.425032i	−0.977158	−	0.212516i	$-0.931834\pi$
$607$		−	10.4717i		−	0.425032i	0.977158	−	0.212516i	$-0.0681657\pi$
$608$	−38.8034	−	18.6867i	−1.57369	−	0.757848i
$609$		0			0
$610$	82.4511	−	39.7064i	3.33835	−	1.60766i
$611$	20.5518	+	42.6762i	0.831435	+	1.72649i
$612$		0			0
$613$	6.03873	−	26.4574i	0.243902	−	1.06860i	−0.693528	−	0.720430i	$-0.743945\pi$
$613$	6.03873	−	26.4574i	0.243902	−	1.06860i	0.937430	−	0.348174i	$-0.113198\pi$
$614$	−9.49737	+	4.57369i	−0.383283	+	0.184579i
$615$		0			0
$616$	5.96899	+	5.60196i	0.240497	+	0.225710i
$617$	−6.61067	+	13.7272i	−0.266136	+	0.552636i	−0.990618	−	0.136657i	$-0.956364\pi$
$617$	−6.61067	+	13.7272i	−0.266136	+	0.552636i	0.724483	+	0.689293i	$0.242079\pi$
$618$		0			0
$619$			29.2828i			1.17697i	0.808507	+	0.588487i	$0.200276\pi$
$619$			29.2828i			1.17697i	−0.808507	+	0.588487i	$0.799724\pi$
$620$	−22.1111	+	45.9141i	−0.888003	+	1.84396i
$621$		0			0
$622$	−65.9726	−	15.0578i	−2.64526	−	0.603764i
$623$	−15.1197	−	4.75822i	−0.605759	−	0.190634i
$624$		0			0
$625$	0.563350	+	0.271295i	0.0225340	+	0.0108518i
$626$	−0.616971	−	2.70313i	−0.0246591	−	0.108039i
$627$		0			0
$628$	−0.577774	−	0.131873i	−0.0230557	−	0.00526231i
$629$	−27.5080	−	34.4940i	−1.09682	−	1.37537i
$630$		0			0
$631$	23.9307	−	30.0082i	0.952668	−	1.19461i	−0.0281348	−	0.999604i	$-0.508957\pi$
$631$	23.9307	−	30.0082i	0.952668	−	1.19461i	0.980803	−	0.195003i	$-0.0624718\pi$
$632$	11.0189	−	8.78731i	0.438310	−	0.349540i
$633$		0			0
$634$	43.5604	+	54.6230i	1.73000	+	2.16936i
$635$	0.169275	+	0.741641i	0.00671747	+	0.0294311i
$636$		0			0
$637$	−39.5199	+	2.50961i	−1.56583	+	0.0994345i
$638$			9.78874i			0.387540i
$639$		0			0
$640$	26.9663	−	21.5049i	1.06594	−	0.850057i
$641$	−1.21207	−	2.51690i	−0.0478740	−	0.0994115i	0.875660	−	0.482929i	$-0.160427\pi$
$641$	−1.21207	−	2.51690i	−0.0478740	−	0.0994115i	−0.923534	+	0.383517i	$0.874713\pi$
$642$		0			0
$643$	13.9597	+	11.1325i	0.550518	+	0.439023i	0.858829	−	0.512262i	$-0.171192\pi$
$643$	13.9597	+	11.1325i	0.550518	+	0.439023i	−0.308311	+	0.951285i	$0.599764\pi$
$644$	−21.7542	+	23.1795i	−0.857237	+	0.913400i
$645$		0			0
$646$	12.2699	−	53.7579i	0.482753	−	2.11508i
$647$	−9.51744	+	11.9345i	−0.374169	+	0.469193i	−0.932889	−	0.360163i	$-0.882721\pi$
$647$	−9.51744	+	11.9345i	−0.374169	+	0.469193i	0.558720	+	0.829356i	$0.311293\pi$
$648$		0			0
$649$	1.47936	−	3.07192i	0.0580700	−	0.120584i
$650$	−21.6494	−	94.8524i	−0.849161	−	3.72042i
$651$		0			0
$652$	6.17211	−	27.0418i	0.241719	−	1.05904i
$653$	11.1937	+	8.92667i	0.438043	+	0.349328i	0.817546	−	0.575863i	$-0.195334\pi$
$653$	11.1937	+	8.92667i	0.438043	+	0.349328i	−0.379503	+	0.925190i	$0.623905\pi$
$654$		0			0
$655$	−20.0674			−0.784096
$656$	−7.75487			−0.302777
$657$		0			0
$658$	−44.2426	+	17.0740i	−1.72476	+	0.665615i
$659$	11.8488	+	24.6043i	0.461565	+	0.958449i	0.993730	+	0.111808i	$0.0356643\pi$
$659$	11.8488	+	24.6043i	0.461565	+	0.958449i	−0.532165	+	0.846641i	$0.678621\pi$
$660$		0			0
$661$	−25.1228	−	5.73412i	−0.977165	−	0.223032i	−0.296021	−	0.955181i	$-0.595660\pi$
$661$	−25.1228	−	5.73412i	−0.977165	−	0.223032i	−0.681144	+	0.732150i	$0.738517\pi$
$662$	66.3831	+	15.1515i	2.58005	+	0.588880i
$663$		0			0
$664$	−0.317609	−	0.659523i	−0.0123256	−	0.0255945i
$665$	−29.3256	−	43.5432i	−1.13720	−	1.68853i
$666$		0			0
$667$	−8.57491			−0.332022
$668$	−8.10505			−0.313594
$669$		0			0
$670$	−37.5397	−	29.9369i	−1.45029	−	1.15656i
$671$	−6.53703	+	28.6406i	−0.252359	+	1.10566i
$672$		0			0
$673$	−0.469412	−	2.05663i	−0.0180945	−	0.0792772i	0.965075	−	0.261976i	$-0.0843740\pi$
$673$	−0.469412	−	2.05663i	−0.0180945	−	0.0792772i	−0.983169	+	0.182698i	$0.941517\pi$
$674$	12.9153	−	26.8189i	0.497479	−	1.03303i
$675$		0			0
$676$	30.5978	−	38.3685i	1.17684	−	1.47571i
$677$	−8.99912	+	39.4277i	−0.345864	+	1.51533i	0.440605	+	0.897701i	$0.354764\pi$
$677$	−8.99912	+	39.4277i	−0.345864	+	1.51533i	−0.786469	+	0.617630i	$0.788093\pi$
$678$		0			0
$679$	17.7867	+	1.43477i	0.682591	+	0.0550614i
$680$	16.4976	+	13.1564i	0.632655	+	0.504525i
$681$		0			0
$682$	−12.5948	−	26.1533i	−0.482278	−	1.00146i
$683$	−15.0885	+	12.0327i	−0.577344	+	0.460417i	−0.868106	−	0.496379i	$-0.834663\pi$
$683$	−15.0885	+	12.0327i	−0.577344	+	0.460417i	0.290762	+	0.956795i	$0.406091\pi$
$684$		0			0
$685$			46.6340i			1.78179i
$686$	0.676870	−	39.6405i	0.0258430	−	1.51348i
$687$		0			0
$688$	5.37325	+	23.5417i	0.204853	+	0.897521i
$689$	4.83249	+	6.05976i	0.184103	+	0.230858i
$690$		0			0
$691$	9.95908	−	7.94210i	0.378861	−	0.302132i	−0.415481	−	0.909602i	$-0.636387\pi$
$691$	9.95908	−	7.94210i	0.378861	−	0.302132i	0.794343	+	0.607470i	$0.207815\pi$
$692$	24.0390	−	30.1440i	0.913827	−	1.14590i
$693$		0			0
$694$	−19.5124	−	24.4677i	−0.740679	−	0.928782i
$695$	43.7593	+	9.98777i	1.65988	+	0.378858i
$696$		0			0
$697$	−3.24085	−	14.1991i	−0.122756	−	0.537828i
$698$	−48.9308	−	23.5638i	−1.85206	−	0.891904i
$699$		0			0
$700$	54.3274	−	7.87260i	2.05338	−	0.297556i
$701$	−1.92525	−	0.439425i	−0.0727156	−	0.0165969i	0.186008	−	0.982548i	$-0.440445\pi$
$701$	−1.92525	−	0.439425i	−0.0727156	−	0.0165969i	−0.258724	+	0.965951i	$0.583302\pi$
$702$		0			0
$703$	22.4488	−	46.6155i	0.846674	−	1.75814i
$704$			29.2356i			1.10186i
$705$		0			0
$706$	21.9924	−	45.6678i	0.827696	−	1.71873i
$707$	15.0579	−	10.1412i	0.566309	−	0.381400i
$708$		0			0
$709$	0.809818	−	0.389988i	0.0304133	−	0.0146463i	−0.418615	−	0.908164i	$-0.637484\pi$
$709$	0.809818	−	0.389988i	0.0304133	−	0.0146463i	0.449029	+	0.893517i	$0.351770\pi$
$710$	−0.199931	+	0.875955i	−0.00750327	+	0.0328740i
$711$		0			0
$712$	3.24177	+	6.73160i	0.121490	+	0.252277i
$713$	22.9102	−	11.0330i	0.857994	−	0.413188i
$714$		0			0
$715$	45.6515	+	21.9846i	1.70727	+	0.822178i
$716$		−	16.0977i		−	0.601598i
$717$		0			0
$718$	49.5866	+	23.8797i	1.85056	+	0.891181i
$719$	3.94929	−	4.95225i	0.147284	−	0.184688i	−0.702717	−	0.711469i	$-0.748030\pi$
$719$	3.94929	−	4.95225i	0.147284	−	0.184688i	0.850001	+	0.526782i	$0.176601\pi$
$720$		0			0
$721$	4.14363	+	6.15253i	0.154317	+	0.229132i
$722$	23.3889	−	5.33837i	0.870445	−	0.198673i
$723$		0			0
$724$	−35.5864	+	8.12235i	−1.32256	+	0.301865i
$725$	11.5771	+	9.23241i	0.429962	+	0.342883i
$726$		0			0
$727$	−38.3357	+	30.5717i	−1.42179	+	1.13384i	−0.451395	+	0.892324i	$0.649073\pi$
$727$	−38.3357	+	30.5717i	−1.42179	+	1.13384i	−0.970397	+	0.241516i	$0.922355\pi$
$728$	13.6106	+	12.7737i	0.504441	+	0.473423i
$729$		0			0
$730$	10.4010	+	13.0424i	0.384956	+	0.482720i
$731$	−40.8591	+	19.6767i	−1.51123	+	0.727770i
$732$		0			0
$733$	−14.0006	+	3.19555i	−0.517125	+	0.118030i	−0.473115	−	0.881001i	$-0.656870\pi$
$733$	−14.0006	+	3.19555i	−0.517125	+	0.118030i	−0.0440098	+	0.999031i	$0.514013\pi$
$734$	−21.8053			−0.804849
$735$		0			0
$736$	−36.4570			−1.34382
$737$	15.0270	−	3.42982i	0.553528	−	0.126339i
$738$		0			0
$739$	−10.5426	+	5.07703i	−0.387814	+	0.186762i	−0.617623	−	0.786474i	$-0.711904\pi$
$739$	−10.5426	+	5.07703i	−0.387814	+	0.186762i	0.229809	+	0.973236i	$0.426190\pi$
$740$	54.7253	+	68.6234i	2.01174	+	2.52265i
$741$		0			0
$742$	−6.43628	+	4.33473i	−0.236283	+	0.159133i
$743$	−8.35021	+	6.65907i	−0.306340	+	0.244298i	−0.764577	−	0.644532i	$-0.777052\pi$
$743$	−8.35021	+	6.65907i	−0.306340	+	0.244298i	0.458238	+	0.888830i	$0.348481\pi$
$744$		0			0
$745$	−58.7581	−	46.8581i	−2.15273	−	1.71675i
$746$	50.9196	−	11.6221i	1.86430	−	0.425514i
$747$		0			0
$748$	−29.2755	+	6.68194i	−1.07042	+	0.244316i
$749$	−7.44311	+	23.6512i	−0.271965	+	0.864197i
$750$		0			0
$751$	2.94786	−	3.69650i	0.107569	−	0.134887i	−0.725133	−	0.688609i	$-0.758222\pi$
$751$	2.94786	−	3.69650i	0.107569	−	0.134887i	0.832702	+	0.553722i	$0.186793\pi$
$752$	−18.8254	−	9.06582i	−0.686491	−	0.330597i
$753$		0			0
$754$			22.3204i			0.812861i
$755$	−56.1588	−	27.0446i	−2.04383	−	0.984255i
$756$		0			0
$757$	44.5744	−	21.4659i	1.62008	−	0.780191i	0.620093	−	0.784528i	$-0.287095\pi$
$757$	44.5744	−	21.4659i	1.62008	−	0.780191i	0.999991	+	0.00433706i	$0.00138053\pi$
$758$	11.4563	+	23.7892i	0.416111	+	0.864063i
$759$		0			0
$760$	−5.50642	+	24.1252i	−0.199739	+	0.875112i
$761$	−10.6689	+	5.13787i	−0.386747	+	0.186248i	−0.617146	−	0.786849i	$-0.711711\pi$
$761$	−10.6689	+	5.13787i	−0.386747	+	0.186248i	0.230399	+	0.973096i	$0.425997\pi$
$762$		0			0
$763$	14.1770	−	2.05439i	0.513242	−	0.0743740i
$764$	−0.989138	+	2.05397i	−0.0357857	+	0.0743099i
$765$		0			0
$766$		−	6.01916i		−	0.217481i
$767$	3.37326	−	7.00464i	0.121801	−	0.252923i
$768$		0			0
$769$	−26.2882	−	6.00010i	−0.947975	−	0.216369i	−0.279535	−	0.960135i	$-0.590180\pi$
$769$	−26.2882	−	6.00010i	−0.947975	−	0.216369i	−0.668440	+	0.743766i	$0.733038\pi$
$770$	−25.6142	+	43.7877i	−0.923073	+	1.57800i
$771$		0			0
$772$	−5.85079	−	2.81759i	−0.210575	−	0.101407i
$773$	3.88268	+	17.0112i	0.139650	+	0.611849i	0.995511	+	0.0946425i	$0.0301708\pi$
$773$	3.88268	+	17.0112i	0.139650	+	0.611849i	−0.855861	+	0.517206i	$0.826972\pi$
$774$		0			0
$775$	−42.8102	−	9.77116i	−1.53779	−	0.350990i
$776$	−5.24435	−	6.57620i	−0.188261	−	0.236072i
$777$		0			0
$778$	−6.15237	+	7.71483i	−0.220573	+	0.276590i
$779$	13.3534	−	10.6489i	0.478434	−	0.381538i
$780$		0			0
$781$	−0.179830	−	0.225499i	−0.00643481	−	0.00806900i
$782$	−10.3863	−	45.5055i	−0.371414	−	1.62727i
$783$		0			0
$784$	12.9395	−	11.7349i	0.462124	−	0.419102i
$785$		−	0.828458i		−	0.0295689i
$786$		0			0
$787$	33.9371	−	27.0639i	1.20973	−	0.964725i	0.209812	−	0.977742i	$-0.432715\pi$
$787$	33.9371	−	27.0639i	1.20973	−	0.964725i	0.999915	+	0.0130164i	$0.00414335\pi$
$788$	−18.0416	−	37.4637i	−0.642705	−	1.33459i
$789$		0			0
$790$	68.2850	+	54.4555i	2.42947	+	1.93744i
$791$	−11.1700	+	35.4938i	−0.397160	+	1.26202i
$792$		0			0
$793$	−14.9058	+	65.3067i	−0.529321	+	2.31911i
$794$	−6.18292	+	7.75313i	−0.219423	+	0.275148i
$795$		0			0
$796$	−2.76010	+	5.73140i	−0.0978290	+	0.203144i
$797$	7.70022	+	33.7369i	0.272756	+	1.19502i	0.906745	+	0.421679i	$0.138559\pi$
$797$	7.70022	+	33.7369i	0.272756	+	1.19502i	−0.633989	+	0.773342i	$0.718584\pi$
$798$		0			0
$799$	8.73208	−	38.2578i	0.308919	−	1.35346i
$800$	49.2210	+	39.2525i	1.74023	+	1.38778i
$801$		0			0
$802$	25.4779			0.899657
$803$	−5.35509			−0.188977
$804$		0			0
$805$	−38.3579	−	22.4380i	−1.35194	−	0.790835i
$806$	−28.7187	−	59.6350i	−1.01157	−	2.10055i
$807$		0			0
$808$	−8.34283	−	1.90420i	−0.293500	−	0.0669894i
$809$	−10.1621	−	2.31944i	−0.357281	−	0.0815471i	0.0401130	−	0.999195i	$-0.487228\pi$
$809$	−10.1621	−	2.31944i	−0.357281	−	0.0815471i	−0.397394	+	0.917648i	$0.630085\pi$
$810$		0			0
$811$	1.64622	+	3.41841i	0.0578065	+	0.120036i	0.927871	−	0.372902i	$-0.121637\pi$
$811$	1.64622	+	3.41841i	0.0578065	+	0.120036i	−0.870064	+	0.492938i	$0.835923\pi$
$812$	−12.5531	−	1.01260i	−0.440526	−	0.0355352i
$813$		0			0
$814$	−49.9964			−1.75237
$815$	38.7747			1.35822
$816$		0			0
$817$	−41.5798	−	33.1588i	−1.45469	−	1.16008i
$818$	0.0124533	−	0.0545616i	0.000435420	−	0.00190770i
$819$		0			0
$820$	6.44744	+	28.2481i	0.225154	+	0.986465i
$821$	−12.3918	+	25.7317i	−0.432475	+	0.898044i	0.564867	+	0.825182i	$0.308928\pi$
$821$	−12.3918	+	25.7317i	−0.432475	+	0.898044i	−0.997342	+	0.0728619i	$0.976787\pi$
$822$		0			0
$823$	−16.8334	+	21.1084i	−0.586776	+	0.735794i	−0.983252	−	0.182251i	$-0.941662\pi$
$823$	−16.8334	+	21.1084i	−0.586776	+	0.735794i	0.396476	+	0.918045i	$0.370233\pi$
$824$	0.778042	−	3.40882i	0.0271044	−	0.118752i
$825$		0			0
$826$	6.71866	+	3.93017i	0.233772	+	0.136748i
$827$	31.6716	+	25.2573i	1.10133	+	0.878281i	0.993265	−	0.115863i	$-0.0369634\pi$
$827$	31.6716	+	25.2573i	1.10133	+	0.878281i	0.108064	+	0.994144i	$0.465535\pi$
$828$		0			0
$829$	18.5911	+	38.6048i	0.645696	+	1.34080i	0.924768	+	0.380531i	$0.124259\pi$
$829$	18.5911	+	38.6048i	0.645696	+	1.34080i	−0.279072	+	0.960270i	$0.590027\pi$
$830$	3.54666	−	2.82836i	0.123106	−	0.0981739i
$831$		0			0
$832$			66.6634i			2.31114i
$833$	26.8939	+	18.7879i	0.931820	+	0.650963i
$834$		0			0
$835$	−2.52122	−	11.0462i	−0.0872506	−	0.382270i
$836$	−21.9559	−	27.5318i	−0.759360	−	0.952208i
$837$		0			0
$838$	36.8778	−	29.4090i	1.27392	−	1.01592i
$839$	10.3305	−	12.9541i	0.356649	−	0.447224i	−0.570847	−	0.821056i	$-0.693385\pi$
$839$	10.3305	−	12.9541i	0.356649	−	0.447224i	0.927496	+	0.373833i	$0.121957\pi$
$840$		0			0
$841$	15.9631	+	20.0171i	0.550453	+	0.690246i
$842$	−39.7915	−	9.08215i	−1.37131	−	0.312992i
$843$		0			0
$844$	13.2508	+	58.0554i	0.456111	+	1.99835i
$845$	61.8097	+	29.7660i	2.12632	+	1.02398i
$846$		0			0
$847$	4.61514	+	11.9589i	0.158578	+	0.410912i
$848$	−3.33329	−	0.760801i	−0.114466	−	0.0261260i
$849$		0			0
$850$	−34.9720	+	72.6201i	−1.19953	+	2.49085i
$851$		−	43.7967i		−	1.50133i
$852$		0			0
$853$	7.53422	−	15.6450i	0.257967	−	0.535674i	−0.731254	−	0.682105i	$-0.761065\pi$
$853$	7.53422	−	15.6450i	0.257967	−	0.535674i	0.989221	+	0.146432i	$0.0467788\pi$
$854$	−63.9722	−	20.1322i	−2.18908	−	0.688911i
$855$		0			0
$856$	10.5300	−	5.07098i	0.359908	−	0.173323i
$857$	2.92698	−	12.8239i	0.0999836	−	0.438057i	−0.900014	−	0.435861i	$-0.856444\pi$
$857$	2.92698	−	12.8239i	0.0999836	−	0.438057i	0.999998	−	0.00219585i	$-0.000698960\pi$
$858$		0			0
$859$	−15.0195	−	31.1883i	−0.512459	−	1.06413i	−0.983313	−	0.181920i	$-0.941769\pi$
$859$	−15.0195	−	31.1883i	−0.512459	−	1.06413i	0.470855	−	0.882211i	$-0.343946\pi$
$860$	81.2864	−	39.1455i	2.77184	−	1.33485i
$861$		0			0
$862$	31.5140	+	15.1763i	1.07337	+	0.516908i
$863$		−	19.3005i		−	0.656997i	−0.944505	−	0.328498i	$-0.893457\pi$
$863$		−	19.3005i		−	0.656997i	0.944505	−	0.328498i	$-0.106543\pi$
$864$		0			0
$865$	48.5604	+	23.3855i	1.65110	+	0.795130i
$866$	8.39312	−	10.5246i	0.285210	−	0.357642i
$867$		0			0
$868$	34.8418	−	13.4461i	1.18261	−	0.456389i
$869$	−27.3343	+	6.23887i	−0.927252	+	0.211639i
$870$		0			0
$871$	34.2648	−	7.82072i	1.16102	−	0.264995i
$872$	−5.27921	−	4.21003i	−0.178777	−	0.142570i
$873$		0			0
$874$	42.7951	−	34.1280i	1.44757	−	1.15440i
$875$	10.4339	+	27.0365i	0.352729	+	0.914000i
$876$		0			0
$877$	−4.48317	−	5.62172i	−0.151386	−	0.189832i	0.700356	−	0.713794i	$-0.253025\pi$
$877$	−4.48317	−	5.62172i	−0.151386	−	0.189832i	−0.851742	+	0.523962i	$0.824453\pi$
$878$	11.3993	−	5.48964i	0.384709	−	0.185266i
$879$		0			0
$880$	−21.7910	+	4.97364i	−0.734573	+	0.167661i
$881$	44.6956			1.50583			0.752916	−	0.658117i	$-0.228647\pi$
$881$	44.6956			1.50583			0.752916	+	0.658117i	$0.228647\pi$
$882$		0			0
$883$	−8.25940			−0.277951			−0.138975	−	0.990296i	$-0.544381\pi$
$883$	−8.25940			−0.277951			−0.138975	+	0.990296i	$0.544381\pi$
$884$	−66.7543	+	15.2362i	−2.24519	+	0.512450i
$885$		0			0
$886$	−5.94580	+	2.86335i	−0.199753	+	0.0961960i
$887$	4.54928	+	5.70461i	0.152750	+	0.191542i	0.852318	−	0.523023i	$-0.175196\pi$
$887$	4.54928	+	5.70461i	0.152750	+	0.191542i	−0.699569	+	0.714565i	$0.746624\pi$
$888$		0			0
$889$	0.281485	−	0.481201i	0.00944070	−	0.0161390i
$890$	−36.1999	+	28.8685i	−1.21342	+	0.967673i
$891$		0			0
$892$	−32.0006	−	25.5196i	−1.07146	−	0.854461i
$893$	44.8652	−	10.2402i	1.50136	−	0.342675i
$894$		0			0
$895$	21.9392	−	5.00748i	0.733347	−	0.167382i
$896$	−25.1948	−	2.03235i	−0.841699	−	0.0678959i
$897$		0			0
$898$	48.2474	−	60.5003i	1.61004	−	2.01892i
$899$	9.07635	+	4.37094i	0.302713	+	0.145779i
$900$		0			0
$901$		−	6.42116i		−	0.213920i
$902$	−14.8698	−	7.16092i	−0.495111	−	0.238433i
$903$		0			0
$904$	15.8026	−	7.61011i	0.525585	−	0.253109i
$905$	−22.1396	−	45.9733i	−0.735945	−	1.52821i
$906$		0			0
$907$	8.61261	−	37.7343i	0.285977	−	1.25295i	−0.604015	−	0.796973i	$-0.706433\pi$
$907$	8.61261	−	37.7343i	0.285977	−	1.25295i	0.889993	−	0.455975i	$-0.150709\pi$
$908$	47.4470	−	22.8493i	1.57459	−	0.758280i
$909$		0			0
$910$	−58.4059	+	99.8453i	−1.93614	+	3.30984i
$911$	−16.1611	+	33.5589i	−0.535442	+	1.11186i	0.441284	+	0.897367i	$0.354523\pi$
$911$	−16.1611	+	33.5589i	−0.535442	+	1.11186i	−0.976726	+	0.214490i	$0.931191\pi$
$912$		0			0
$913$			1.45623i			0.0481941i
$914$	16.8737	−	35.0385i	0.558131	−	1.15897i
$915$		0			0
$916$	58.7496	+	13.4092i	1.94114	+	0.443053i
$917$	10.7233	+	10.0640i	0.354115	+	0.332341i
$918$		0			0
$919$	2.90009	+	1.39661i	0.0956651	+	0.0460699i	0.481104	−	0.876663i	$-0.340236\pi$
$919$	2.90009	+	1.39661i	0.0956651	+	0.0460699i	−0.385439	+	0.922733i	$0.625950\pi$
$920$	4.66112	+	20.4217i	0.153673	+	0.673283i
$921$		0			0
$922$	−47.5426	−	10.8513i	−1.56573	−	0.357368i
$923$	−0.410050	−	0.514186i	−0.0134970	−	0.0169246i
$924$		0			0
$925$	−47.1549	+	59.1304i	−1.55044	+	1.94420i
$926$	66.0030	−	52.6356i	2.16899	−	1.72971i
$927$		0			0
$928$	−9.00520	−	11.2922i	−0.295610	−	0.370683i
$929$	−3.46567	−	15.1841i	−0.113705	−	0.498173i	−0.999424	−	0.0339509i	$-0.989191\pi$
$929$	−3.46567	−	15.1841i	−0.113705	−	0.498173i	0.885719	−	0.464222i	$-0.153666\pi$
$930$		0			0
$931$	−6.16667	+	37.9751i	−0.202104	+	1.24458i
$932$		−	59.0677i		−	1.93483i
$933$		0			0
$934$	−25.0370	+	19.9663i	−0.819234	+	0.653318i
$935$	−18.2134	−	37.8204i	−0.595641	−	1.23686i
$936$		0			0
$937$	3.38495	+	2.69941i	0.110582	+	0.0881859i	0.677220	−	0.735781i	$-0.263185\pi$
$937$	3.38495	+	2.69941i	0.110582	+	0.0881859i	−0.566638	+	0.823967i	$0.691756\pi$
$938$	5.04632	+	34.8238i	0.164768	+	1.13704i
$939$		0			0
$940$	−17.3719	+	76.1111i	−0.566608	+	2.48247i
$941$	19.0408	−	23.8764i	0.620712	−	0.778348i	−0.367732	−	0.929932i	$-0.619866\pi$
$941$	19.0408	−	23.8764i	0.620712	−	0.778348i	0.988444	+	0.151583i	$0.0484372\pi$
$942$		0			0
$943$	6.27295	−	13.0259i	0.204275	−	0.424182i
$944$	0.763141	+	3.34354i	0.0248381	+	0.108823i
$945$		0			0
$946$	−11.4356	+	50.1026i	−0.371803	+	1.62898i
$947$	−19.2341	−	15.3387i	−0.625025	−	0.498441i	0.259002	−	0.965877i	$-0.416606\pi$
$947$	−19.2341	−	15.3387i	−0.625025	−	0.498441i	−0.884027	+	0.467436i	$0.845178\pi$
$948$		0			0
$949$	−12.2107			−0.396377
$950$	−94.5229			−3.06673
$951$		0			0
$952$	−2.21771	−	15.3040i	−0.0718765	−	0.496007i
$953$	−13.7853	−	28.6255i	−0.446550	−	0.927271i	−0.995795	−	0.0916093i	$-0.970799\pi$
$953$	−13.7853	−	28.6255i	−0.446550	−	0.927271i	0.549245	−	0.835661i	$-0.314915\pi$
$954$		0			0
$955$	−3.10700	−	0.709152i	−0.100540	−	0.0229476i
$956$	63.4563	+	14.4835i	2.05232	+	0.468429i
$957$		0			0
$958$	24.7882	+	51.4733i	0.800871	+	1.66303i
$959$	23.3874	−	24.9196i	0.755217	−	0.804696i
$960$		0			0
$961$	1.12617			0.0363282
$962$	−114.002			−3.67558
$963$		0			0
$964$	−41.6285	−	33.1976i	−1.34076	−	1.06922i
$965$	2.02004	−	8.85039i	0.0650275	−	0.284904i
$966$		0			0
$967$	−4.02816	−	17.6485i	−0.129537	−	0.567538i	−0.997485	−	0.0708827i	$-0.977418\pi$
$967$	−4.02816	−	17.6485i	−0.129537	−	0.567538i	0.867948	−	0.496655i	$-0.165439\pi$
$968$	2.62162	−	5.44384i	0.0842620	−	0.174972i
$969$		0			0
$970$	32.4995	−	40.7531i	1.04350	−	1.30850i
$971$	−7.29986	+	31.9828i	−0.234264	+	1.02638i	0.711797	+	0.702386i	$0.247882\pi$
$971$	−7.29986	+	31.9828i	−0.234264	+	1.02638i	−0.946060	+	0.323991i	$0.894975\pi$
$972$		0			0
$973$	−18.3745	−	27.2828i	−0.589060	−	0.874646i
$974$	30.0020	+	23.9258i	0.961327	+	0.766633i
$975$		0			0
$976$	−12.8208	−	26.6228i	−0.410385	−	0.852174i
$977$	−41.0200	+	32.7124i	−1.31235	+	1.04656i	−0.317180	+	0.948365i	$0.602736\pi$
$977$	−41.0200	+	32.7124i	−1.31235	+	1.04656i	−0.995167	+	0.0981960i	$0.968693\pi$
$978$		0			0
$979$		−	14.8634i		−	0.475036i
$980$	−53.5036	−	37.3773i	−1.70911	−	1.19397i
$981$		0			0
$982$	12.8551	+	56.3217i	0.410221	+	1.79730i
$983$	−1.40419	−	1.76080i	−0.0447868	−	0.0561609i	0.758934	−	0.651168i	$-0.225721\pi$
$983$	−1.40419	−	1.76080i	−0.0447868	−	0.0561609i	−0.803720	+	0.595007i	$0.797149\pi$
$984$		0			0
$985$	45.4464	−	36.2423i	1.44804	−	1.15478i
$986$	11.5293	−	14.4573i	0.367168	−	0.460414i
$987$		0			0
$988$	−50.0641	−	62.7784i	−1.59275	−	1.99725i
$989$	−43.8897	−	10.0175i	−1.39561	−	0.318539i
$990$		0			0
$991$	−0.272429	−	1.19359i	−0.00865398	−	0.0379156i	0.970417	−	0.241437i	$-0.0776186\pi$
$991$	−0.272429	−	1.19359i	−0.00865398	−	0.0379156i	−0.979071	+	0.203521i	$0.934761\pi$
$992$	38.5889	+	18.5835i	1.22520	+	0.590025i
$993$		0			0
$994$	0.546135	−	0.367813i	0.0173224	−	0.0116663i
$995$	−8.66979	−	1.97882i	−0.274851	−	0.0627329i
$996$		0			0
$997$	−0.829695	+	1.72288i	−0.0262767	+	0.0545642i	−0.913694	−	0.406403i	$-0.866783\pi$
$997$	−0.829695	+	1.72288i	−0.0262767	+	0.0545642i	0.887417	+	0.460967i	$0.152497\pi$
$998$			4.75163i			0.150410i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	441.2.w.a.62.4	✓	120
3.2	odd	2	inner	441.2.w.a.62.17	yes	120
49.34	odd	14	inner	441.2.w.a.377.17	yes	120
147.83	even	14	inner	441.2.w.a.377.4	yes	120

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
441.2.w.a.62.4	✓	120	1.1	even	1	trivial
441.2.w.a.62.17	yes	120	3.2	odd	2	inner
441.2.w.a.377.4	yes	120	147.83	even	14	inner
441.2.w.a.377.17	yes	120	49.34	odd	14	inner

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:	\( N \)	\(=\)	\( 441 = 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	441.w (of order \(14\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.08702 + 0.476349i) q^{2} +(2.32682 - 1.12054i) q^{4} +(2.25096 + 2.82261i) q^{5} +(0.212729 - 2.63719i) q^{7} +(-0.975036 + 0.777565i) q^{8} +(-6.04235 - 4.81862i) q^{10} +(2.41874 - 0.552061i) q^{11} +(5.51523 - 1.25882i) q^{13} +(0.812251 + 5.60520i) q^{14} +(-1.55589 + 1.95102i) q^{16} +(-4.22253 - 2.03346i) q^{17} -5.49607i q^{19} +(8.40042 + 4.04543i) q^{20} +(-4.78499 + 2.30433i) q^{22} +(-2.01859 - 4.19164i) q^{23} +(-1.78772 + 7.83253i) q^{25} +(-10.9108 + 5.25436i) q^{26} +(-2.46008 - 6.37463i) q^{28} +(0.799704 - 1.66060i) q^{29} +5.46570i q^{31} +(3.40002 - 7.06021i) q^{32} +(9.78115 + 2.23248i) q^{34} +(7.92260 - 5.33574i) q^{35} +(8.48160 + 4.08452i) q^{37} +(2.61805 + 11.4704i) q^{38} +(-4.38953 - 1.00188i) q^{40} +(1.93756 + 2.42962i) q^{41} +(6.03318 - 7.56536i) q^{43} +(5.00936 - 3.99483i) q^{44} +(6.20952 + 7.78649i) q^{46} +(1.86318 + 8.16313i) q^{47} +(-6.90949 - 1.12201i) q^{49} -17.1983i q^{50} +(11.4224 - 9.10906i) q^{52} +(0.594462 + 1.23441i) q^{53} +(7.00273 + 5.58449i) q^{55} +(1.84316 + 2.73676i) q^{56} +(-0.877974 + 3.84666i) q^{58} +(0.856868 - 1.07448i) q^{59} +(-5.13768 + 10.6685i) q^{61} +(-2.60358 - 11.4070i) q^{62} +(-2.62221 + 11.4886i) q^{64} +(15.9677 + 12.7338i) q^{65} +6.21276 q^{67} -12.1036 q^{68} +(-13.9930 + 14.9097i) q^{70} +(-0.0504417 - 0.104743i) q^{71} +(-2.10438 - 0.480310i) q^{73} +(-19.6470 - 4.48429i) q^{74} +(-6.15856 - 12.7884i) q^{76} +(-0.941351 - 6.49610i) q^{77} -11.3011 q^{79} -9.00923 q^{80} +(-5.20107 - 4.14772i) q^{82} +(-0.130612 + 0.572249i) q^{83} +(-3.76506 - 16.4958i) q^{85} +(-8.98762 + 18.6630i) q^{86} +(-1.92909 + 2.41900i) q^{88} +(1.33313 - 5.84082i) q^{89} +(-2.14648 - 14.8125i) q^{91} +(-9.39377 - 7.49128i) q^{92} +(-7.77701 - 16.1491i) q^{94} +(15.5133 - 12.3714i) q^{95} +6.74458i q^{97} +(14.9547 - 0.949665i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 120 q + 24 q^{4} - 32 q^{16} - 44 q^{22} - 4 q^{25} - 56 q^{28} + 112 q^{34} - 76 q^{37} + 28 q^{40} + 8 q^{43} - 40 q^{46} - 84 q^{49} - 140 q^{52} + 12 q^{58} - 84 q^{61} + 24 q^{64} + 16 q^{67} + 112 q^{70}+ \cdots - 112 q^{94}+O(q^{100}) \) 120 * q + 24 * q^4 - 32 * q^16 - 44 * q^22 - 4 * q^25 - 56 * q^28 + 112 * q^34 - 76 * q^37 + 28 * q^40 + 8 * q^43 - 40 * q^46 - 84 * q^49 - 140 * q^52 + 12 * q^58 - 84 * q^61 + 24 * q^64 + 16 * q^67 + 112 * q^70 - 84 * q^76 - 24 * q^79 + 140 * q^82 - 96 * q^85 - 24 * q^88 - 112 * q^91 - 112 * q^94

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