LMFDB - Embedded newform 441.2.w.a.377.4

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)

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);

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")

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			377.4
Character	$\chi$	$=$	441.377
Dual form			441.2.w.a.62.4

$q$-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 $\left(\mathbb{Z}/441\mathbb{Z}\right)^\times$.

$n$	$199$	$344$
$\chi(n)$	$e\left(\frac{3}{14}\right)$	$-1$

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	−0.592437	−	0.805617i	$-0.701834\pi$
$2$	−2.08702	−	0.476349i	−1.47575	−	0.336830i	−0.883311	+	0.468787i	$0.844691\pi$
$3$		0			0
$3$		0			0
$4$	2.32682	+	1.12054i	1.16341	+	0.560269i
$5$	2.25096	−	2.82261i	1.00666	−	1.26231i	0.0419154	−	0.999121i	$-0.486654\pi$
$5$	2.25096	−	2.82261i	1.00666	−	1.26231i	0.964744	−	0.263190i	$-0.0847746\pi$
$6$		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	0.571009	−	0.820944i	$-0.306552\pi$
$11$	2.41874	+	0.552061i	0.729277	+	0.166453i	0.158267	+	0.987396i	$0.449409\pi$
$12$		0			0
$13$	5.51523	+	1.25882i	1.52965	+	0.349133i	0.902818	−	0.430022i	$-0.141494\pi$
$13$	5.51523	+	1.25882i	1.52965	+	0.349133i	0.626832	+	0.779155i	$0.284351\pi$
$14$	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	−0.869053	−	0.494718i	$-0.835271\pi$
$17$	−4.22253	+	2.03346i	−1.02411	+	0.493187i	−0.155060	+	0.987905i	$0.549557\pi$
$18$		0			0
$19$			5.49607i			1.26089i	0.776236	+	0.630443i	$0.217127\pi$
$19$			5.49607i			1.26089i	−0.776236	+	0.630443i	$0.782873\pi$
$20$	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	0.577437	+	0.816435i	$0.304053\pi$
$23$	−2.01859	+	4.19164i	−0.420904	+	0.874016i	−0.998341	+	0.0575810i	$0.981661\pi$
$24$		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	0.961929	−	0.273300i	$-0.0881152\pi$
$29$	0.799704	+	1.66060i	0.148501	+	0.308366i	−0.813427	+	0.581666i	$0.802401\pi$
$30$		0			0
$31$		−	5.46570i		−	0.981668i	−0.871253	−	0.490834i	$-0.836692\pi$
$31$		−	5.46570i		−	0.981668i	0.871253	−	0.490834i	$-0.163308\pi$
$32$	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	0.422356	−	0.906430i	$-0.361203\pi$
$37$	8.48160	−	4.08452i	1.39437	−	0.671491i	0.972010	+	0.234939i	$0.0754890\pi$
$38$	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	−0.607165	−	0.794575i	$-0.707693\pi$
$41$	1.93756	−	2.42962i	0.302595	−	0.379443i	0.909761	+	0.415133i	$0.136265\pi$
$42$		0			0
$43$	6.03318	+	7.56536i	0.920051	+	1.15371i	0.987757	+	0.156002i	$0.0498606\pi$
$43$	6.03318	+	7.56536i	0.920051	+	1.15371i	−0.0677061	+	0.997705i	$0.521568\pi$
$44$	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	−0.636146	−	0.771569i	$-0.719472\pi$
$47$	1.86318	−	8.16313i	0.271773	−	1.19072i	0.907919	−	0.419146i	$-0.137671\pi$
$48$		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	−0.856143	−	0.516738i	$-0.827146\pi$
$53$	0.594462	−	1.23441i	0.0816556	−	0.169560i	0.937799	+	0.347179i	$0.112860\pi$
$54$		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	0.834474	−	0.551047i	$-0.185772\pi$
$59$	0.856868	+	1.07448i	0.111555	+	0.139885i	−0.722919	+	0.690932i	$0.757200\pi$
$60$		0			0
$61$	−5.13768	−	10.6685i	−0.657813	−	1.36596i	−0.916513	−	0.400004i	$-0.869009\pi$
$61$	−5.13768	−	10.6685i	−0.657813	−	1.36596i	0.258701	−	0.965958i	$-0.416706\pi$
$62$	−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	−0.903941	−	0.427658i	$-0.859339\pi$
$71$	−0.0504417	+	0.104743i	−0.00598632	+	0.0124307i	0.897954	+	0.440089i	$0.145053\pi$
$72$		0			0
$73$	−2.10438	+	0.480310i	−0.246298	+	0.0562160i	−0.343888	−	0.939011i	$-0.611744\pi$
$73$	−2.10438	+	0.480310i	−0.246298	+	0.0562160i	0.0975893	+	0.995227i	$0.468887\pi$
$74$	−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	0.967254	−	0.253812i	$-0.0816844\pi$
$83$	−0.130612	−	0.572249i	−0.0143365	−	0.0628125i	−0.981590	+	0.190999i	$0.938827\pi$
$84$		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	0.995131	+	0.0985573i	$0.0314228\pi$
$89$	1.33313	+	5.84082i	0.141311	+	0.619126i	−0.853820	+	0.520568i	$0.825720\pi$
$90$		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	$-0.888759\pi$
$97$		−	6.74458i		−	0.684808i	0.939553	−	0.342404i	$-0.111241\pi$
$98$	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	−0.522013	−	0.852938i	$-0.674819\pi$
$101$	4.27822	−	5.36472i	0.425699	−	0.533810i	0.947712	+	0.319128i	$0.103390\pi$
$102$		0			0
$103$	−2.19199	−	1.74805i	−0.215983	−	0.172241i	0.509522	−	0.860458i	$-0.329822\pi$
$103$	−2.19199	−	1.74805i	−0.215983	−	0.172241i	−0.725505	+	0.688217i	$0.758394\pi$
$104$	−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	−0.640014	−	0.768363i	$-0.721072\pi$
$107$	−9.13658	+	2.08536i	−0.883267	+	0.201600i	−0.243252	+	0.969963i	$0.578214\pi$
$108$		0			0
$109$	1.20481	−	5.27862i	0.115400	−	0.505601i	−0.883882	−	0.467710i	$-0.845079\pi$
$109$	1.20481	−	5.27862i	0.115400	−	0.505601i	0.999282	−	0.0378903i	$-0.0120638\pi$
$110$	−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	−0.811807	−	0.583926i	$-0.801516\pi$
$113$	−13.7114	+	3.12954i	−1.28986	+	0.294403i	−0.478056	+	0.878329i	$0.658659\pi$
$114$		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	−0.425442	−	0.904986i	$-0.639881\pi$
$127$	0.189842	−	0.0914232i	0.0168458	−	0.00811250i	0.442288	+	0.896873i	$0.354167\pi$
$128$			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	0.607036	−	0.794675i	$-0.292358\pi$
$131$	−3.46562	−	4.34575i	−0.302793	−	0.379690i	−0.909829	+	0.414984i	$0.863787\pi$
$132$		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	−0.0885731	−	0.996070i	$-0.528231\pi$
$137$	10.0990	−	8.05366i	0.862814	−	0.688071i	0.951387	+	0.307999i	$0.0996592\pi$
$138$		0			0
$139$	9.72014	+	7.75155i	0.824451	+	0.657478i	0.942009	−	0.335588i	$-0.108935\pi$
$139$	9.72014	+	7.75155i	0.824451	+	0.657478i	−0.117557	+	0.993066i	$0.537506\pi$
$140$	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	−0.715069	−	0.699054i	$-0.753605\pi$
$149$	−20.2950	−	4.63220i	−1.66263	−	0.379485i	−0.947563	+	0.319569i	$0.896462\pi$
$150$		0			0
$151$	−15.5553	−	7.49106i	−1.26588	−	0.609614i	−0.324153	−	0.946005i	$-0.605079\pi$
$151$	−15.5553	−	7.49106i	−1.26588	−	0.609614i	−0.941722	+	0.336391i	$0.890794\pi$
$152$	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	−0.630623	−	0.776089i	$-0.717201\pi$
$157$	−0.179410	+	0.143074i	−0.0143184	+	0.0114186i	0.616304	+	0.787508i	$0.288629\pi$
$158$	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	0.971558	−	0.236803i	$-0.0760996\pi$
$163$	6.69637	+	8.39698i	0.524500	+	0.657702i	−0.447058	+	0.894505i	$0.647528\pi$
$164$	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	−0.540075	−	0.841617i	$-0.681604\pi$
$167$	−2.82756	+	1.36168i	−0.218803	+	0.105370i	0.321271	+	0.946987i	$0.395890\pi$
$168$		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	0.868560	−	0.495583i	$-0.165046\pi$
$173$	13.4507	+	6.47751i	1.02264	+	0.492476i	0.154076	+	0.988059i	$0.450760\pi$
$174$		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	0.977254	−	0.212071i	$-0.0680209\pi$
$179$	2.70448	+	5.61591i	0.202142	+	0.419753i	−0.775112	+	0.631824i	$0.782307\pi$
$180$		0			0
$181$	−13.7794	+	3.14506i	−1.02421	+	0.233770i	−0.701457	−	0.712711i	$-0.747467\pi$
$181$	−13.7794	+	3.14506i	−1.02421	+	0.233770i	−0.322758	+	0.946482i	$0.604610\pi$
$182$	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	0.598203	−	0.801345i	$-0.295882\pi$
$191$	−0.690150	−	0.550376i	−0.0499375	−	0.0398238i	−0.648141	+	0.761521i	$0.724453\pi$
$192$		0			0
$193$	−1.56777	+	1.96592i	−0.112850	+	0.141510i	−0.835048	−	0.550176i	$-0.814560\pi$
$193$	−1.56777	+	1.96592i	−0.112850	+	0.141510i	0.722198	+	0.691686i	$0.243132\pi$
$194$	−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	$0.194441\pi$
$197$			16.1008i			1.14714i	−0.819158	+	0.573568i	$0.805559\pi$
$198$		0			0
$199$	−1.92580	−	1.53577i	−0.136516	−	0.108868i	0.552851	−	0.833280i	$-0.313540\pi$
$199$	−1.92580	−	1.53577i	−0.136516	−	0.108868i	−0.689367	+	0.724412i	$0.742111\pi$
$200$	−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	−0.769692	−	0.638415i	$-0.779590\pi$
$211$	−5.13084	−	22.4797i	−0.353221	−	1.54756i	0.416471	−	0.909149i	$-0.363267\pi$
$212$	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	0.533411	+	0.845856i	$0.320910\pi$
$223$	−6.87647	+	14.2791i	−0.460482	+	0.956202i	−0.993893	+	0.110345i	$0.964804\pi$
$224$	−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	0.205670	−	0.978621i	$-0.434063\pi$
$229$	18.2428	−	14.5482i	1.20552	−	0.961371i	0.999851	+	0.0172501i	$0.00549116\pi$
$230$	−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	0.921825	+	0.387605i	$0.126698\pi$
$233$	9.92363	+	20.6066i	0.650119	+	1.34999i	−0.271707	+	0.962380i	$0.587588\pi$
$234$		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	0.276100	−	0.961129i	$-0.410958\pi$
$239$	19.7044	−	15.7137i	1.27457	−	1.01644i	0.998469	−	0.0553060i	$-0.0176134\pi$
$240$		0			0
$241$	−8.94537	+	18.5752i	−0.576222	+	1.19654i	0.385551	+	0.922687i	$0.374012\pi$
$241$	−8.94537	+	18.5752i	−0.576222	+	1.19654i	−0.961772	+	0.273850i	$0.911703\pi$
$242$	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	0.800321	−	0.599571i	$-0.204662\pi$
$251$	0.597185	+	0.748847i	0.0376940	+	0.0472668i	−0.762627	+	0.646838i	$0.776091\pi$
$252$		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	−0.989222	−	0.146424i	$-0.953224\pi$
$257$	−23.9108	+	11.5148i	−1.49151	+	0.718275i	−0.502291	+	0.864699i	$0.667509\pi$
$258$		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	$-0.865979\pi$
$263$		−	13.2563i		−	0.817419i	0.912665	−	0.408709i	$-0.134021\pi$
$264$		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	0.920500	−	0.390743i	$-0.127782\pi$
$269$	−1.28551	−	5.63220i	−0.0783791	−	0.343401i	−0.998879	+	0.0473422i	$0.984925\pi$
$270$		0			0
$271$	1.41890	−	2.94639i	0.0861923	−	0.178980i	−0.853417	−	0.521228i	$-0.825474\pi$
$271$	1.41890	−	2.94639i	0.0861923	−	0.178980i	0.939610	+	0.342248i	$0.111188\pi$
$272$	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	−0.204209	−	0.978927i	$-0.565462\pi$
$277$	7.22028	−	3.47711i	0.433825	−	0.208919i	0.638034	+	0.770008i	$0.279748\pi$
$278$	−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	−0.336777	−	0.941584i	$-0.609337\pi$
$281$	−17.5801	−	4.01254i	−1.04874	−	0.239368i	−0.711964	+	0.702216i	$0.752194\pi$
$282$		0			0
$283$	−16.0873	−	3.67181i	−0.956288	−	0.218266i	−0.284223	−	0.958758i	$-0.591735\pi$
$283$	−16.0873	−	3.67181i	−0.956288	−	0.218266i	−0.672065	+	0.740492i	$0.734593\pi$
$284$	−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	0.357310	−	0.933986i	$-0.383694\pi$
$307$	4.80078	+	1.09575i	0.273995	+	0.0625375i	−0.0833157	+	0.996523i	$0.526551\pi$
$308$	−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	0.615034	−	0.788501i	$-0.289142\pi$
$311$	28.4804	−	13.7154i	1.61498	−	0.777731i	0.999942	+	0.0107695i	$0.00342812\pi$
$312$		0			0
$313$		−	1.29521i		−	0.0732094i	−0.999330	−	0.0366047i	$-0.988346\pi$
$313$		−	1.29521i		−	0.0732094i	0.999330	−	0.0366047i	$-0.0116542\pi$
$314$	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	−0.0373165	+	0.999303i	$0.511881\pi$
$317$	−14.1606	+	29.4047i	−0.795337	+	1.65153i	−0.758020	+	0.652231i	$0.773833\pi$
$318$		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	−0.998300	−	0.0582797i	$-0.981438\pi$
$331$	−28.6576	+	13.8008i	−1.57517	+	0.758560i	−0.576865	+	0.816839i	$0.695724\pi$
$332$	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	0.487455	−	0.873148i	$-0.337925\pi$
$337$	−8.66974	−	10.8715i	−0.472271	−	0.592209i	−0.959725	+	0.280940i	$0.909354\pi$
$338$	−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	−0.658449	−	0.752625i	$-0.728787\pi$
$347$	6.34306	−	13.1715i	0.340513	−	0.707083i	0.998962	+	0.0455420i	$0.0145015\pi$
$348$		0			0
$349$	19.8349	−	15.8178i	1.06174	−	0.846709i	0.0731466	−	0.997321i	$-0.476696\pi$
$349$	19.8349	−	15.8178i	1.06174	−	0.846709i	0.988593	+	0.150612i	$0.0481245\pi$
$350$	−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	−0.999964	−	0.00851784i	$-0.997289\pi$
$353$	−14.7630	−	18.5122i	−0.785755	−	0.985306i	0.214209	−	0.976788i	$-0.431283\pi$
$354$		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	−0.988480	−	0.151353i	$-0.951637\pi$
$359$	−20.1008	+	16.0298i	−1.06088	+	0.846023i	−0.0723992	+	0.997376i	$0.523066\pi$
$360$		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	0.0446763	−	0.999002i	$-0.485774\pi$
$367$	9.93071	−	2.26662i	0.518379	−	0.118317i	0.473702	+	0.880685i	$0.342917\pi$
$368$	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	0.854225	+	0.519904i	$0.174032\pi$
$379$	−2.74465	+	12.0251i	−0.140983	+	0.617687i	−0.995208	+	0.0977830i	$0.968825\pi$
$380$	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	0.956424	−	0.291982i	$-0.0943149\pi$
$383$	−0.625679	−	2.74128i	−0.0319707	−	0.140073i	−0.988394	+	0.151910i	$0.951458\pi$
$384$		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	0.710580	−	0.703616i	$-0.248432\pi$
$389$	3.60389	+	2.87401i	0.182724	+	0.145718i	−0.527856	+	0.849334i	$0.677004\pi$
$390$		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	0.710149	−	0.704052i	$-0.248628\pi$
$397$	3.62178	+	2.88827i	0.181772	+	0.144958i	−0.528377	+	0.849010i	$0.677199\pi$
$398$	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	−0.502189	−	0.864758i	$-0.667472\pi$
$401$	−11.6033	+	2.64838i	−0.579442	+	0.132254i	−0.0772524	+	0.997012i	$0.524615\pi$
$402$		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	0.900688	−	0.434466i	$-0.143063\pi$
$409$	−0.0113431	−	0.0235542i	−0.000560882	−	0.00116468i	−0.901249	+	0.433301i	$0.857349\pi$
$410$			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	−0.119240	−	0.992865i	$-0.538046\pi$
$419$	−19.8521	−	9.56027i	−0.969838	−	0.467050i	−0.850598	+	0.525816i	$0.823760\pi$
$420$		0			0
$421$	17.1780	−	8.27249i	0.837205	−	0.403177i	0.0343926	−	0.999408i	$-0.489050\pi$
$421$	17.1780	−	8.27249i	0.837205	−	0.403177i	0.802812	+	0.596232i	$0.203336\pi$
$422$			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	−0.880852	−	0.473392i	$-0.843030\pi$
$431$	−12.7747	+	10.1875i	−0.615337	+	0.490715i	0.265515	+	0.964107i	$0.414458\pi$
$432$		0			0
$433$	−4.91646	−	3.92075i	−0.236270	−	0.188419i	0.498196	−	0.867064i	$-0.333996\pi$
$433$	−4.91646	−	3.92075i	−0.236270	−	0.188419i	−0.734466	+	0.678645i	$0.762567\pi$
$434$	−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	0.0827892	−	0.996567i	$-0.473617\pi$
$439$	−5.76219	−	1.31518i	−0.275014	−	0.0627703i	−0.357804	+	0.933797i	$0.616474\pi$
$440$	−11.1702			−0.532519
$441$		0			0
$442$	56.7556			2.69959
$443$	3.00551	+	0.685988i	0.142796	+	0.0325923i	0.293321	−	0.956014i	$-0.405239\pi$
$443$	3.00551	+	0.685988i	0.142796	+	0.0325923i	−0.150525	+	0.988606i	$0.548097\pi$
$444$		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	−0.992314	−	0.123744i	$-0.960510\pi$
$449$	−28.2620	−	22.5382i	−1.33377	−	1.06364i	−0.341452	−	0.939899i	$-0.610919\pi$
$450$		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	0.442819	−	0.896611i	$-0.353979\pi$
$457$	−11.3269	−	14.2035i	−0.529849	−	0.664410i	−0.972668	+	0.232201i	$0.925407\pi$
$458$	−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	0.110153	−	0.993915i	$-0.464866\pi$
$461$	20.5242	−	9.88391i	0.955905	−	0.460340i	0.845753	+	0.533575i	$0.179152\pi$
$462$		0			0
$463$	−35.5308	−	17.1107i	−1.65126	−	0.795204i	−0.999318	−	0.0369334i	$-0.988241\pi$
$463$	−35.5308	−	17.1107i	−1.65126	−	0.795204i	−0.651940	−	0.758270i	$-0.726045\pi$
$464$	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	0.718908	−	0.695105i	$-0.244642\pi$
$467$	13.4779	+	6.49063i	0.623685	+	0.300351i	−0.0952234	+	0.995456i	$0.530357\pi$
$468$		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	0.637084	+	0.770795i	$0.280141\pi$
$479$	−5.93866	+	26.0189i	−0.271344	+	1.18884i	−0.908428	+	0.418042i	$0.862717\pi$
$480$		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	−0.967673	−	0.252206i	$-0.918844\pi$
$487$	−11.1767	+	14.0151i	−0.506463	+	0.635084i	0.461211	+	0.887291i	$0.347415\pi$
$488$	−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	$0.208407\pi$
$491$			26.9866i			1.21789i	−0.793213	+	0.608944i	$0.791593\pi$
$492$		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	0.984779	−	0.173809i	$-0.0556075\pi$
$499$	0.493922	+	2.16401i	0.0221110	+	0.0968746i	−0.962668	+	0.270683i	$0.912750\pi$
$500$	−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	0.472515	+	0.881323i	$0.343346\pi$
$503$	−7.52668	+	32.9765i	−0.335598	+	1.47035i	−0.808113	+	0.589028i	$0.799511\pi$
$504$		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	−0.170139	−	0.985420i	$-0.554422\pi$
$523$	17.2140	−	13.7277i	0.752716	−	0.600271i	0.922854	+	0.385150i	$0.125850\pi$
$524$	−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	−0.900518	−	0.434819i	$-0.856812\pi$
$541$	2.31388	−	10.1378i	0.0994816	−	0.435857i	0.999999	−	0.00103828i	$-0.000330494\pi$
$542$	−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	−0.112132	+	0.993693i	$0.535768\pi$
$547$	−24.6968	+	30.9688i	−1.05596	+	1.32413i	−0.943828	+	0.330438i	$0.892804\pi$
$548$	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	$-0.897071\pi$
$557$		−	14.9986i		−	0.635511i	0.948173	−	0.317755i	$-0.102929\pi$
$558$		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	−0.978417	−	0.206641i	$-0.933747\pi$
$563$	−4.42643	−	19.3935i	−0.186552	−	0.817337i	0.791865	−	0.610696i	$-0.209110\pi$
$564$		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	$-0.958409\pi$
$569$		−	6.21580i		−	0.260580i	0.991476	−	0.130290i	$-0.0415908\pi$
$570$		0			0
$571$	11.8217	−	5.69303i	0.494723	−	0.238246i	−0.169849	−	0.985470i	$-0.554328\pi$
$571$	11.8217	−	5.69303i	0.494723	−	0.238246i	0.664572	+	0.747224i	$0.268614\pi$
$572$	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	0.513416	−	0.858140i	$-0.328380\pi$
$577$	14.5003	+	3.30960i	0.603656	+	0.137781i	0.0902394	+	0.995920i	$0.471237\pi$
$578$	−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	−0.780663	−	0.624953i	$-0.785118\pi$
$593$	0.0568661	−	0.0713078i	0.00233521	−	0.00292826i	0.782998	+	0.622025i	$0.213690\pi$
$594$		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	0.469762	−	0.882793i	$-0.344340\pi$
$599$	12.4813	+	2.84878i	0.509973	+	0.116398i	0.0402109	+	0.999191i	$0.487197\pi$
$600$		0			0
$601$	−11.5018	−	2.62520i	−0.469167	−	0.107084i	−0.0186002	−	0.999827i	$-0.505921\pi$
$601$	−11.5018	−	2.62520i	−0.469167	−	0.107084i	−0.450567	+	0.892743i	$0.648778\pi$
$602$	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	$0.0681657\pi$
$607$			10.4717i			0.425032i	−0.977158	+	0.212516i	$0.931834\pi$
$608$	−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	0.937430	+	0.348174i	$0.113198\pi$
$613$	6.03873	+	26.4574i	0.243902	+	1.06860i	−0.693528	+	0.720430i	$0.743945\pi$
$614$	−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	0.724483	−	0.689293i	$-0.242079\pi$
$617$	−6.61067	−	13.7272i	−0.266136	−	0.552636i	−0.990618	+	0.136657i	$0.956364\pi$
$618$		0			0
$619$		−	29.2828i		−	1.17697i	−0.808507	−	0.588487i	$-0.799724\pi$
$619$		−	29.2828i		−	1.17697i	0.808507	−	0.588487i	$-0.200276\pi$
$620$	−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	0.980803	+	0.195003i	$0.0624718\pi$
$631$	23.9307	+	30.0082i	0.952668	+	1.19461i	−0.0281348	+	0.999604i	$0.508957\pi$
$632$	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	−0.923534	−	0.383517i	$-0.874713\pi$
$641$	−1.21207	+	2.51690i	−0.0478740	+	0.0994115i	0.875660	+	0.482929i	$0.160427\pi$
$642$		0			0
$643$	13.9597	−	11.1325i	0.550518	−	0.439023i	−0.308311	−	0.951285i	$-0.599764\pi$
$643$	13.9597	−	11.1325i	0.550518	−	0.439023i	0.858829	+	0.512262i	$0.171192\pi$
$644$	−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	0.558720	−	0.829356i	$-0.311293\pi$
$647$	−9.51744	−	11.9345i	−0.374169	−	0.469193i	−0.932889	+	0.360163i	$0.882721\pi$
$648$		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	−0.379503	−	0.925190i	$-0.623905\pi$
$653$	11.1937	−	8.92667i	0.438043	−	0.349328i	0.817546	+	0.575863i	$0.195334\pi$
$654$		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	−0.532165	−	0.846641i	$-0.678621\pi$
$659$	11.8488	−	24.6043i	0.461565	−	0.958449i	0.993730	−	0.111808i	$-0.0356643\pi$
$660$		0			0
$661$	−25.1228	+	5.73412i	−0.977165	+	0.223032i	−0.681144	−	0.732150i	$-0.738517\pi$
$661$	−25.1228	+	5.73412i	−0.977165	+	0.223032i	−0.296021	+	0.955181i	$0.595660\pi$
$662$	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	−0.983169	−	0.182698i	$-0.941517\pi$
$673$	−0.469412	+	2.05663i	−0.0180945	+	0.0792772i	0.965075	+	0.261976i	$0.0843740\pi$
$674$	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	−0.786469	−	0.617630i	$-0.788093\pi$
$677$	−8.99912	−	39.4277i	−0.345864	−	1.51533i	0.440605	−	0.897701i	$-0.354764\pi$
$678$		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	0.290762	−	0.956795i	$-0.406091\pi$
$683$	−15.0885	−	12.0327i	−0.577344	−	0.460417i	−0.868106	+	0.496379i	$0.834663\pi$
$684$		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	0.794343	−	0.607470i	$-0.207815\pi$
$691$	9.95908	+	7.94210i	0.378861	+	0.302132i	−0.415481	+	0.909602i	$0.636387\pi$
$692$	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	−0.258724	−	0.965951i	$-0.583302\pi$
$701$	−1.92525	+	0.439425i	−0.0727156	+	0.0165969i	0.186008	+	0.982548i	$0.440445\pi$
$702$		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	0.449029	−	0.893517i	$-0.351770\pi$
$709$	0.809818	+	0.389988i	0.0304133	+	0.0146463i	−0.418615	+	0.908164i	$0.637484\pi$
$710$	−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	0.850001	−	0.526782i	$-0.176601\pi$
$719$	3.94929	+	4.95225i	0.147284	+	0.184688i	−0.702717	+	0.711469i	$0.748030\pi$
$720$		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	−0.970397	−	0.241516i	$-0.922355\pi$
$727$	−38.3357	−	30.5717i	−1.42179	−	1.13384i	−0.451395	−	0.892324i	$-0.649073\pi$
$728$	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	−0.0440098	−	0.999031i	$-0.514013\pi$
$733$	−14.0006	−	3.19555i	−0.517125	−	0.118030i	−0.473115	+	0.881001i	$0.656870\pi$
$734$	−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	0.229809	−	0.973236i	$-0.426190\pi$
$739$	−10.5426	−	5.07703i	−0.387814	−	0.186762i	−0.617623	+	0.786474i	$0.711904\pi$
$740$	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	0.458238	−	0.888830i	$-0.348481\pi$
$743$	−8.35021	−	6.65907i	−0.306340	−	0.244298i	−0.764577	+	0.644532i	$0.777052\pi$
$744$		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	0.832702	−	0.553722i	$-0.186793\pi$
$751$	2.94786	+	3.69650i	0.107569	+	0.134887i	−0.725133	+	0.688609i	$0.758222\pi$
$752$	−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	0.999991	−	0.00433706i	$-0.00138053\pi$
$757$	44.5744	+	21.4659i	1.62008	+	0.780191i	0.620093	+	0.784528i	$0.287095\pi$
$758$	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	0.230399	−	0.973096i	$-0.425997\pi$
$761$	−10.6689	−	5.13787i	−0.386747	−	0.186248i	−0.617146	+	0.786849i	$0.711711\pi$
$762$		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	−0.668440	−	0.743766i	$-0.733038\pi$
$769$	−26.2882	+	6.00010i	−0.947975	+	0.216369i	−0.279535	+	0.960135i	$0.590180\pi$
$770$	−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	−0.855861	−	0.517206i	$-0.826972\pi$
$773$	3.88268	−	17.0112i	0.139650	−	0.611849i	0.995511	−	0.0946425i	$-0.0301708\pi$
$774$		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	0.999915	−	0.0130164i	$-0.00414335\pi$
$787$	33.9371	+	27.0639i	1.20973	+	0.964725i	0.209812	+	0.977742i	$0.432715\pi$
$788$	−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	−0.633989	−	0.773342i	$-0.718584\pi$
$797$	7.70022	−	33.7369i	0.272756	−	1.19502i	0.906745	−	0.421679i	$-0.138559\pi$
$798$		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	−0.397394	−	0.917648i	$-0.630085\pi$
$809$	−10.1621	+	2.31944i	−0.357281	+	0.0815471i	0.0401130	+	0.999195i	$0.487228\pi$
$810$		0			0
$811$	1.64622	−	3.41841i	0.0578065	−	0.120036i	−0.870064	−	0.492938i	$-0.835923\pi$
$811$	1.64622	−	3.41841i	0.0578065	−	0.120036i	0.927871	+	0.372902i	$0.121637\pi$
$812$	−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	−0.997342	−	0.0728619i	$-0.976787\pi$
$821$	−12.3918	−	25.7317i	−0.432475	−	0.898044i	0.564867	−	0.825182i	$-0.308928\pi$
$822$		0			0
$823$	−16.8334	−	21.1084i	−0.586776	−	0.735794i	0.396476	−	0.918045i	$-0.370233\pi$
$823$	−16.8334	−	21.1084i	−0.586776	−	0.735794i	−0.983252	+	0.182251i	$0.941662\pi$
$824$	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	0.108064	−	0.994144i	$-0.465535\pi$
$827$	31.6716	−	25.2573i	1.10133	−	0.878281i	0.993265	+	0.115863i	$0.0369634\pi$
$828$		0			0
$829$	18.5911	−	38.6048i	0.645696	−	1.34080i	−0.279072	−	0.960270i	$-0.590027\pi$
$829$	18.5911	−	38.6048i	0.645696	−	1.34080i	0.924768	−	0.380531i	$-0.124259\pi$
$830$	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	0.927496	−	0.373833i	$-0.121957\pi$
$839$	10.3305	+	12.9541i	0.356649	+	0.447224i	−0.570847	+	0.821056i	$0.693385\pi$
$840$		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	0.989221	−	0.146432i	$-0.0467788\pi$
$853$	7.53422	+	15.6450i	0.257967	+	0.535674i	−0.731254	+	0.682105i	$0.761065\pi$
$854$	−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	0.999998	+	0.00219585i	$0.000698960\pi$
$857$	2.92698	+	12.8239i	0.0999836	+	0.438057i	−0.900014	+	0.435861i	$0.856444\pi$
$858$		0			0
$859$	−15.0195	+	31.1883i	−0.512459	+	1.06413i	0.470855	+	0.882211i	$0.343946\pi$
$859$	−15.0195	+	31.1883i	−0.512459	+	1.06413i	−0.983313	+	0.181920i	$0.941769\pi$
$860$	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	$0.106543\pi$
$863$			19.3005i			0.656997i	−0.944505	+	0.328498i	$0.893457\pi$
$864$		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	−0.851742	−	0.523962i	$-0.824453\pi$
$877$	−4.48317	+	5.62172i	−0.151386	+	0.189832i	0.700356	+	0.713794i	$0.253025\pi$
$878$	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	−0.699569	−	0.714565i	$-0.746624\pi$
$887$	4.54928	−	5.70461i	0.152750	−	0.191542i	0.852318	+	0.523023i	$0.175196\pi$
$888$		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	0.889993	+	0.455975i	$0.150709\pi$
$907$	8.61261	+	37.7343i	0.285977	+	1.25295i	−0.604015	+	0.796973i	$0.706433\pi$
$908$	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	−0.976726	−	0.214490i	$-0.931191\pi$
$911$	−16.1611	−	33.5589i	−0.535442	−	1.11186i	0.441284	−	0.897367i	$-0.354523\pi$
$912$		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	−0.385439	−	0.922733i	$-0.625950\pi$
$919$	2.90009	−	1.39661i	0.0956651	−	0.0460699i	0.481104	+	0.876663i	$0.340236\pi$
$920$	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	0.885719	+	0.464222i	$0.153666\pi$
$929$	−3.46567	+	15.1841i	−0.113705	+	0.498173i	−0.999424	+	0.0339509i	$0.989191\pi$
$930$		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	−0.566638	−	0.823967i	$-0.691756\pi$
$937$	3.38495	−	2.69941i	0.110582	−	0.0881859i	0.677220	+	0.735781i	$0.263185\pi$
$938$	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	0.988444	−	0.151583i	$-0.0484372\pi$
$941$	19.0408	+	23.8764i	0.620712	+	0.778348i	−0.367732	+	0.929932i	$0.619866\pi$
$942$		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	−0.884027	−	0.467436i	$-0.845178\pi$
$947$	−19.2341	+	15.3387i	−0.625025	+	0.498441i	0.259002	+	0.965877i	$0.416606\pi$
$948$		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	0.549245	+	0.835661i	$0.314915\pi$
$953$	−13.7853	+	28.6255i	−0.446550	+	0.927271i	−0.995795	+	0.0916093i	$0.970799\pi$
$954$		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	0.867948	+	0.496655i	$0.165439\pi$
$967$	−4.02816	+	17.6485i	−0.129537	+	0.567538i	−0.997485	+	0.0708827i	$0.977418\pi$
$968$	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	−0.946060	−	0.323991i	$-0.894975\pi$
$971$	−7.29986	−	31.9828i	−0.234264	−	1.02638i	0.711797	−	0.702386i	$-0.247882\pi$
$972$		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	−0.995167	−	0.0981960i	$-0.968693\pi$
$977$	−41.0200	−	32.7124i	−1.31235	−	1.04656i	−0.317180	−	0.948365i	$-0.602736\pi$
$978$		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	−0.803720	−	0.595007i	$-0.797149\pi$
$983$	−1.40419	+	1.76080i	−0.0447868	+	0.0561609i	0.758934	+	0.651168i	$0.225721\pi$
$984$		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	−0.979071	−	0.203521i	$-0.934761\pi$
$991$	−0.272429	+	1.19359i	−0.00865398	+	0.0379156i	0.970417	+	0.241437i	$0.0776186\pi$
$992$	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	0.887417	−	0.460967i	$-0.152497\pi$
$997$	−0.829695	−	1.72288i	−0.0262767	−	0.0545642i	−0.913694	+	0.406403i	$0.866783\pi$
$998$		−	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.377.4	yes	120
3.2	odd	2	inner	441.2.w.a.377.17	yes	120
49.13	odd	14	inner	441.2.w.a.62.17	yes	120
147.62	even	14	inner	441.2.w.a.62.4	✓	120

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
441.2.w.a.62.4	✓	120	147.62	even	14	inner
441.2.w.a.62.17	yes	120	49.13	odd	14	inner
441.2.w.a.377.4	yes	120	1.1	even	1	trivial
441.2.w.a.377.17	yes	120	3.2	odd	2	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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