LMFDB - Embedded newform 441.2.w.a.188.1

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			188.1
Character	$\chi$	$=$	441.188
Dual form			441.2.w.a.251.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.13317 + 1.70115i) q^{2} +(1.21148 - 5.30783i) q^{4} +(-1.31998 + 0.635668i) q^{5} +(-0.795783 + 2.52324i) q^{7} +(4.07748 + 8.46697i) q^{8} +(1.73438 - 3.60147i) q^{10} +(2.75661 - 2.19832i) q^{11} +(4.51813 - 3.60309i) q^{13} +(-2.59486 - 6.73625i) q^{14} +(-13.2912 - 6.40071i) q^{16} +(0.0162072 + 0.0710083i) q^{17} +4.52011i q^{19} +(1.77490 + 7.77633i) q^{20} +(-2.14065 + 9.37881i) q^{22} +(1.76402 + 0.402626i) q^{23} +(-1.77918 + 2.23102i) q^{25} +(-3.50857 + 15.3720i) q^{26} +(12.4289 + 7.28073i) q^{28} +(-2.61910 + 0.597792i) q^{29} +7.13274i q^{31} +(20.9170 - 4.77416i) q^{32} +(-0.155368 - 0.123902i) q^{34} +(-0.553525 - 3.83647i) q^{35} +(1.33034 + 5.82860i) q^{37} +(-7.68938 - 9.64217i) q^{38} +(-10.7644 - 8.58430i) q^{40} +(-11.3454 + 5.46367i) q^{41} +(-1.31339 - 0.632493i) q^{43} +(-8.32876 - 17.2949i) q^{44} +(-4.44789 + 2.14199i) q^{46} +(5.84471 + 7.32903i) q^{47} +(-5.73346 - 4.01590i) q^{49} -7.78580i q^{50} +(-13.6510 - 28.3466i) q^{52} +(9.10665 + 2.07853i) q^{53} +(-2.24126 + 4.65403i) q^{55} +(-24.6090 + 3.55058i) q^{56} +(4.57005 - 5.73067i) q^{58} +(0.107203 + 0.0516262i) q^{59} +(3.20130 - 0.730676i) q^{61} +(-12.1339 - 15.2154i) q^{62} +(-18.1023 + 22.6996i) q^{64} +(-3.67347 + 7.62804i) q^{65} +5.78127 q^{67} +0.396535 q^{68} +(7.70718 + 7.24224i) q^{70} +(-0.0872291 - 0.0199095i) q^{71} +(3.43319 + 2.73788i) q^{73} +(-12.7532 - 10.1703i) q^{74} +(23.9920 + 5.47601i) q^{76} +(3.35323 + 8.70497i) q^{77} -2.89253 q^{79} +21.6128 q^{80} +(14.9073 - 30.9552i) q^{82} +(-0.251403 + 0.315250i) q^{83} +(-0.0665309 - 0.0834271i) q^{85} +(3.87765 - 0.885047i) q^{86} +(29.8532 + 14.3765i) q^{88} +(6.88377 - 8.63197i) q^{89} +(5.49600 + 14.2676i) q^{91} +(4.27415 - 8.87536i) q^{92} +(-24.9355 - 5.69137i) q^{94} +(-2.87329 - 5.96645i) q^{95} +14.7498i q^{97} +(19.0621 - 1.18685i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/441\mathbb{Z}\right)^\times$.

$n$	$199$	$344$
$\chi(n)$	$e\left(\frac{5}{14}\right)$	$-1$

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 $

$2$	−2.13317	+	1.70115i	−1.50838	+	1.20289i	−0.589871	+	0.807498i	$0.700821\pi$
$2$	−2.13317	+	1.70115i	−1.50838	+	1.20289i	−0.918511	+	0.395396i	$0.870607\pi$
$3$		0			0
$3$		0			0
$4$	1.21148	−	5.30783i	0.605739	−	2.65392i
$5$	−1.31998	+	0.635668i	−0.590313	+	0.284280i	−0.705097	−	0.709111i	$-0.749097\pi$
$5$	−1.31998	+	0.635668i	−0.590313	+	0.284280i	0.114784	+	0.993390i	$0.463382\pi$
$6$		0			0
$7$	−0.795783	+	2.52324i	−0.300778	+	0.953694i
$7$	−0.795783	+	2.52324i	−0.300778	+	0.953694i
$8$	4.07748	+	8.46697i	1.44161	+	2.99353i
$9$		0			0
$10$	1.73438	−	3.60147i	0.548458	−	1.13889i
$11$	2.75661	−	2.19832i	0.831149	−	0.662819i	−0.112542	−	0.993647i	$-0.535899\pi$
$11$	2.75661	−	2.19832i	0.831149	−	0.662819i	0.943691	+	0.330828i	$0.107328\pi$
$12$		0			0
$13$	4.51813	−	3.60309i	1.25310	−	0.999317i	0.253617	−	0.967305i	$-0.418380\pi$
$13$	4.51813	−	3.60309i	1.25310	−	0.999317i	0.999487	−	0.0320125i	$-0.0101916\pi$
$14$	−2.59486	−	6.73625i	−0.693505	−	1.80034i
$15$		0			0
$16$	−13.2912	−	6.40071i	−3.32280	−	1.60018i
$17$	0.0162072	+	0.0710083i	0.00393082	+	0.0172220i	0.976855	−	0.213901i	$-0.0686171\pi$
$17$	0.0162072	+	0.0710083i	0.00393082	+	0.0172220i	−0.972924	+	0.231123i	$0.925760\pi$
$18$		0			0
$19$			4.52011i			1.03698i	0.855083	+	0.518492i	$0.173506\pi$
$19$			4.52011i			1.03698i	−0.855083	+	0.518492i	$0.826494\pi$
$20$	1.77490	+	7.77633i	0.396879	+	1.73884i
$21$		0			0
$22$	−2.14065	+	9.37881i	−0.456388	+	1.99957i
$23$	1.76402	+	0.402626i	0.367824	+	0.0839533i	0.402438	−	0.915447i	$-0.368163\pi$
$23$	1.76402	+	0.402626i	0.367824	+	0.0839533i	−0.0346140	+	0.999401i	$0.511020\pi$
$24$		0			0
$25$	−1.77918	+	2.23102i	−0.355836	+	0.446204i
$26$	−3.50857	+	15.3720i	−0.688086	+	3.01470i
$27$		0			0
$28$	12.4289	+	7.28073i	2.34883	+	1.37593i
$29$	−2.61910	+	0.597792i	−0.486354	+	0.111007i	−0.458665	−	0.888609i	$-0.651672\pi$
$29$	−2.61910	+	0.597792i	−0.486354	+	0.111007i	−0.0276894	+	0.999617i	$0.508815\pi$
$30$		0			0
$31$			7.13274i			1.28108i	0.767926	+	0.640539i	$0.221289\pi$
$31$			7.13274i			1.28108i	−0.767926	+	0.640539i	$0.778711\pi$
$32$	20.9170	−	4.77416i	3.69763	−	0.843960i
$33$		0			0
$34$	−0.155368	−	0.123902i	−0.0266455	−	0.0212491i
$35$	−0.553525	−	3.83647i	−0.0935629	−	0.648483i
$36$		0			0
$37$	1.33034	+	5.82860i	0.218706	+	0.958216i	0.958435	+	0.285310i	$0.0920967\pi$
$37$	1.33034	+	5.82860i	0.218706	+	0.958216i	−0.739729	+	0.672905i	$0.765046\pi$
$38$	−7.68938	−	9.64217i	−1.24738	−	1.56417i
$39$		0			0
$40$	−10.7644	−	8.58430i	−1.70200	−	1.35730i
$41$	−11.3454	+	5.46367i	−1.77186	+	0.853282i	−0.806984	+	0.590573i	$0.798902\pi$
$41$	−11.3454	+	5.46367i	−1.77186	+	0.853282i	−0.964875	+	0.262709i	$0.915384\pi$
$42$		0			0
$43$	−1.31339	−	0.632493i	−0.200289	−	0.0964543i	0.331050	−	0.943613i	$-0.392597\pi$
$43$	−1.31339	−	0.632493i	−0.200289	−	0.0964543i	−0.531340	+	0.847159i	$0.678311\pi$
$44$	−8.32876	−	17.2949i	−1.25561	−	2.60730i
$45$		0			0
$46$	−4.44789	+	2.14199i	−0.655805	+	0.315819i
$47$	5.84471	+	7.32903i	0.852538	+	1.06905i	0.996834	+	0.0795141i	$0.0253369\pi$
$47$	5.84471	+	7.32903i	0.852538	+	1.06905i	−0.144296	+	0.989535i	$0.546092\pi$
$48$		0			0
$49$	−5.73346	−	4.01590i	−0.819065	−	0.573700i
$50$		−	7.78580i		−	1.10108i
$51$		0			0
$52$	−13.6510	−	28.3466i	−1.89305	−	3.93096i
$53$	9.10665	+	2.07853i	1.25089	+	0.285508i	0.796142	−	0.605110i	$-0.206871\pi$
$53$	9.10665	+	2.07853i	1.25089	+	0.285508i	0.454752	+	0.890618i	$0.349728\pi$
$54$		0			0
$55$	−2.24126	+	4.65403i	−0.302212	+	0.627549i
$56$	−24.6090	+	3.55058i	−3.28851	+	0.474466i
$57$		0			0
$58$	4.57005	−	5.73067i	0.600078	−	0.752474i
$59$	0.107203	+	0.0516262i	0.0139566	+	0.00672116i	0.440849	−	0.897581i	$-0.354677\pi$
$59$	0.107203	+	0.0516262i	0.0139566	+	0.00672116i	−0.426892	+	0.904302i	$0.640392\pi$
$60$		0			0
$61$	3.20130	−	0.730676i	0.409885	−	0.0935535i	−0.0126066	−	0.999921i	$-0.504013\pi$
$61$	3.20130	−	0.730676i	0.409885	−	0.0935535i	0.422491	+	0.906367i	$0.361156\pi$
$62$	−12.1339	−	15.2154i	−1.54100	−	1.93235i
$63$		0			0
$64$	−18.1023	+	22.6996i	−2.26279	+	2.83745i
$65$	−3.67347	+	7.62804i	−0.455638	+	0.946141i
$66$		0			0
$67$	5.78127			0.706294			0.353147	−	0.935568i	$-0.385112\pi$
$67$	5.78127			0.706294			0.353147	+	0.935568i	$0.385112\pi$
$68$	0.396535			0.0480869
$69$		0			0
$70$	7.70718	+	7.24224i	0.921184	+	0.865613i
$71$	−0.0872291	−	0.0199095i	−0.0103522	−	0.00236282i	0.217342	−	0.976096i	$-0.430261\pi$
$71$	−0.0872291	−	0.0199095i	−0.0103522	−	0.00236282i	−0.227694	+	0.973733i	$0.573119\pi$
$72$		0			0
$73$	3.43319	+	2.73788i	0.401824	+	0.320444i	0.803464	−	0.595354i	$-0.202988\pi$
$73$	3.43319	+	2.73788i	0.401824	+	0.320444i	−0.401640	+	0.915798i	$0.631560\pi$
$74$	−12.7532	−	10.1703i	−1.48252	−	1.18227i
$75$		0			0
$76$	23.9920	+	5.47601i	2.75207	+	0.628142i
$77$	3.35323	+	8.70497i	0.382136	+	0.992024i
$78$		0			0
$79$	−2.89253			−0.325435			−0.162718	−	0.986673i	$-0.552026\pi$
$79$	−2.89253			−0.325435			−0.162718	+	0.986673i	$0.552026\pi$
$80$	21.6128			2.41639
$81$		0			0
$82$	14.9073	−	30.9552i	1.64623	−	3.41843i
$83$	−0.251403	+	0.315250i	−0.0275951	+	0.0346032i	−0.795438	−	0.606036i	$-0.792759\pi$
$83$	−0.251403	+	0.315250i	−0.0275951	+	0.0346032i	0.767842	+	0.640639i	$0.221330\pi$
$84$		0			0
$85$	−0.0665309	−	0.0834271i	−0.00721629	−	0.00904894i
$86$	3.87765	−	0.885047i	0.418137	−	0.0954371i
$87$		0			0
$88$	29.8532	+	14.3765i	3.18236	+	1.53254i
$89$	6.88377	−	8.63197i	0.729678	−	0.914987i	−0.269164	−	0.963094i	$-0.586747\pi$
$89$	6.88377	−	8.63197i	0.729678	−	0.914987i	0.998842	+	0.0481072i	$0.0153189\pi$
$90$		0			0
$91$	5.49600	+	14.2676i	0.576137	+	1.49565i
$92$	4.27415	−	8.87536i	0.445611	−	0.925320i
$93$		0			0
$94$	−24.9355	−	5.69137i	−2.57190	−	0.587020i
$95$	−2.87329	−	5.96645i	−0.294793	−	0.612144i
$96$		0			0
$97$			14.7498i			1.49761i	0.662790	+	0.748805i	$0.269372\pi$
$97$			14.7498i			1.49761i	−0.662790	+	0.748805i	$0.730628\pi$
$98$	19.0621	−	1.18685i	1.92556	−	0.119890i
$99$		0			0
$100$	9.68645	+	12.1464i	0.968645	+	1.21464i
$101$	−7.65207	+	3.68504i	−0.761409	+	0.366675i	−0.773951	−	0.633246i	$-0.781722\pi$
$101$	−7.65207	+	3.68504i	−0.761409	+	0.366675i	0.0125414	+	0.999921i	$0.496008\pi$
$102$		0			0
$103$	−1.92234	−	3.99179i	−0.189414	−	0.393322i	0.784537	−	0.620083i	$-0.212901\pi$
$103$	−1.92234	−	3.99179i	−0.189414	−	0.393322i	−0.973951	+	0.226760i	$0.927187\pi$
$104$	48.9299	+	23.5634i	4.79797	+	2.31058i
$105$		0			0
$106$	−22.9619	+	11.0579i	−2.23026	+	1.07404i
$107$	−2.62877	−	2.09637i	−0.254132	−	0.202664i	0.488134	−	0.872769i	$-0.337678\pi$
$107$	−2.62877	−	2.09637i	−0.254132	−	0.202664i	−0.742267	+	0.670105i	$0.766249\pi$
$108$		0			0
$109$	−7.57622	−	9.50028i	−0.725670	−	0.909962i	0.272974	−	0.962022i	$-0.411993\pi$
$109$	−7.57622	−	9.50028i	−0.725670	−	0.909962i	−0.998644	+	0.0520596i	$0.983421\pi$
$110$	−3.13620	−	13.7406i	−0.299025	−	1.31011i
$111$		0			0
$112$	26.7274	−	28.4433i	2.52550	−	2.68764i
$113$	11.1377	+	8.88203i	1.04775	+	0.835551i	0.986695	−	0.162584i	$-0.0519828\pi$
$113$	11.1377	+	8.88203i	1.04775	+	0.835551i	0.0610528	+	0.998135i	$0.480554\pi$
$114$		0			0
$115$	−2.58441	+	0.589874i	−0.240997	+	0.0550060i
$116$			14.6259i			1.35799i
$117$		0			0
$118$	−0.316506	+	0.0722405i	−0.0291368	+	0.00665028i
$119$	−0.192068	−	0.0156126i	−0.0176069	−	0.00143121i
$120$		0			0
$121$	0.318544	−	1.39563i	0.0289585	−	0.126876i
$122$	−5.58594	+	7.00455i	−0.505727	+	0.634162i
$123$		0			0
$124$	37.8594	+	8.64116i	3.39988	+	0.775999i
$125$	2.56033	−	11.2175i	0.229003	−	1.00333i
$126$		0			0
$127$	−4.26155	−	18.6711i	−0.378151	−	1.65679i	−0.703125	−	0.711066i	$-0.748213\pi$
$127$	−4.26155	−	18.6711i	−0.378151	−	1.65679i	0.324974	−	0.945723i	$-0.394644\pi$
$128$		−	36.3073i		−	3.20914i
$129$		0			0
$130$	−5.14028	−	22.5210i	−0.450832	−	1.97523i
$131$	11.8431	+	5.70335i	1.03474	+	0.498304i	0.872585	−	0.488462i	$-0.162442\pi$
$131$	11.8431	+	5.70335i	1.03474	+	0.498304i	0.162153	+	0.986766i	$0.448156\pi$
$132$		0			0
$133$	−11.4053	−	3.59703i	−0.988965	−	0.311902i
$134$	−12.3324	+	9.83479i	−1.06536	+	0.849597i
$135$		0			0
$136$	−0.535141	+	0.426761i	−0.0458880	+	0.0365944i
$137$	−1.52964	+	3.17632i	−0.130686	+	0.271371i	−0.956036	−	0.293249i	$-0.905263\pi$
$137$	−1.52964	+	3.17632i	−0.130686	+	0.271371i	0.825350	+	0.564621i	$0.190978\pi$
$138$		0			0
$139$	4.97429	+	10.3292i	0.421914	+	0.876114i	0.998263	+	0.0589101i	$0.0187625\pi$
$139$	4.97429	+	10.3292i	0.421914	+	0.876114i	−0.576349	+	0.817204i	$0.695523\pi$
$140$	−21.0340	−	1.70979i	−1.77769	−	0.144503i
$141$		0			0
$142$	0.219944	−	0.105919i	0.0184573	−	0.00888855i
$143$	4.53397	−	19.8646i	0.379150	−	1.66116i
$144$		0			0
$145$	3.07716	−	2.45395i	0.255544	−	0.203789i
$146$	−11.9811			−0.991564
$147$		0			0
$148$	32.5489			2.67550
$149$	9.76826	−	7.78993i	0.800247	−	0.638176i	−0.135528	−	0.990774i	$-0.543273\pi$
$149$	9.76826	−	7.78993i	0.800247	−	0.638176i	0.935775	+	0.352598i	$0.114702\pi$
$150$		0			0
$151$	4.64786	−	20.3636i	0.378237	−	1.65717i	−0.324627	−	0.945842i	$-0.605239\pi$
$151$	4.64786	−	20.3636i	0.378237	−	1.65717i	0.702864	−	0.711324i	$-0.251904\pi$
$152$	−38.2716	+	18.4306i	−3.10424	+	1.49492i
$153$		0			0
$154$	−21.9615	−	12.8649i	−1.76971	−	1.03668i
$155$	−4.53406	−	9.41507i	−0.364184	−	0.756236i
$156$		0			0
$157$	−5.01362	+	10.4109i	−0.400131	+	0.830880i	0.599406	+	0.800445i	$0.295403\pi$
$157$	−5.01362	+	10.4109i	−0.400131	+	0.830880i	−0.999537	+	0.0304347i	$0.990311\pi$
$158$	6.17027	−	4.92062i	0.490880	−	0.391464i
$159$		0			0
$160$	−24.5752	+	19.5980i	−1.94284	+	1.54936i
$161$	−2.41970	+	4.13064i	−0.190699	+	0.325540i
$162$		0			0
$163$	8.26562	+	3.98051i	0.647413	+	0.311778i	0.728619	−	0.684920i	$-0.240163\pi$
$163$	8.26562	+	3.98051i	0.647413	+	0.311778i	−0.0812055	+	0.996697i	$0.525877\pi$
$164$	15.2555	+	66.8388i	1.19126	+	5.21923i
$165$		0			0
$166$		−	1.10016i		−	0.0853888i
$167$	4.71322	+	20.6500i	0.364720	+	1.59794i	0.741045	+	0.671456i	$0.234331\pi$
$167$	4.71322	+	20.6500i	0.364720	+	1.59794i	−0.376324	+	0.926488i	$0.622812\pi$
$168$		0			0
$169$	4.53849	−	19.8844i	0.349114	−	1.52957i
$170$	0.283844	+	0.0647855i	0.0217698	+	0.00496882i
$171$		0			0
$172$	−4.94831	+	6.20498i	−0.377305	+	0.473126i
$173$	−1.40176	+	6.14152i	−0.106574	+	0.466931i	0.893274	+	0.449512i	$0.148402\pi$
$173$	−1.40176	+	6.14152i	−0.106574	+	0.466931i	−0.999848	+	0.0174192i	$0.994455\pi$
$174$		0			0
$175$	−4.21355	−	6.26470i	−0.318515	−	0.473567i
$176$	−50.7095	+	11.5741i	−3.82237	+	0.872431i
$177$		0			0
$178$			30.1238i			2.25787i
$179$	10.2984	−	2.35054i	0.769737	−	0.175687i	0.180420	−	0.983590i	$-0.442254\pi$
$179$	10.2984	−	2.35054i	0.769737	−	0.175687i	0.589316	+	0.807902i	$0.299397\pi$
$180$		0			0
$181$	−11.4269	−	9.11265i	−0.849355	−	0.677338i	0.0988136	−	0.995106i	$-0.468495\pi$
$181$	−11.4269	−	9.11265i	−0.849355	−	0.677338i	−0.948168	+	0.317768i	$0.897067\pi$
$182$	−35.9952	−	21.0857i	−2.66814	−	1.56298i
$183$		0			0
$184$	3.78373	+	16.5776i	0.278940	+	1.22212i
$185$	−5.46107	−	6.84797i	−0.401506	−	0.503473i
$186$		0			0
$187$	0.200776	+	0.160114i	0.0146822	+	0.0117087i
$188$	45.9820	−	22.1438i	3.35358	−	1.61500i
$189$		0			0
$190$	16.2790	+	7.83957i	1.18101	+	0.568742i
$191$	1.47744	+	3.06794i	0.106904	+	0.221988i	0.947558	−	0.319585i	$-0.103543\pi$
$191$	1.47744	+	3.06794i	0.106904	+	0.221988i	−0.840654	+	0.541573i	$0.817829\pi$
$192$		0			0
$193$	−24.4304	+	11.7651i	−1.75854	+	0.846867i	−0.784617	+	0.619981i	$0.787140\pi$
$193$	−24.4304	+	11.7651i	−1.75854	+	0.846867i	−0.973921	+	0.226886i	$0.927146\pi$
$194$	−25.0915	−	31.4638i	−1.80147	−	2.25897i
$195$		0			0
$196$	−28.2617	+	25.5671i	−2.01869	+	1.82622i
$197$		−	10.1592i		−	0.723813i	−0.932214	−	0.361906i	$-0.882126\pi$
$197$		−	10.1592i		−	0.723813i	0.932214	−	0.361906i	$-0.117874\pi$
$198$		0			0
$199$	−0.770780	−	1.60054i	−0.0546391	−	0.113459i	0.871862	−	0.489752i	$-0.162913\pi$
$199$	−0.770780	−	1.60054i	−0.0546391	−	0.113459i	−0.926501	+	0.376293i	$0.877199\pi$
$200$	−26.1446	−	5.96732i	−1.84870	−	0.421954i
$201$		0			0
$202$	10.0544	−	20.8781i	0.707424	−	1.46898i
$203$	0.575863	−	7.08432i	0.0404176	−	0.497222i
$204$		0			0
$205$	11.5026	−	14.4239i	0.803380	−	1.00741i
$206$	10.8913	+	5.24498i	0.758834	+	0.365435i
$207$		0			0
$208$	−83.1137	+	18.9702i	−5.76290	+	1.31534i
$209$	9.93666	+	12.4602i	0.687333	+	0.861888i
$210$		0			0
$211$	1.59686	−	2.00239i	0.109932	−	0.137851i	−0.723821	−	0.689987i	$-0.757616\pi$
$211$	1.59686	−	2.00239i	0.109932	−	0.137851i	0.833753	+	0.552137i	$0.186187\pi$
$212$	22.0650	−	45.8185i	1.51543	−	3.14683i
$213$		0			0
$214$	9.17385			0.627112
$215$	2.13570			0.145653
$216$		0			0
$217$	−17.9976	−	5.67612i	−1.22176	−	0.385320i
$218$	32.3228	+	7.37747i	2.18918	+	0.499665i
$219$		0			0
$220$	21.9876	+	17.5345i	1.48240	+	1.18218i
$221$	0.329076	+	0.262429i	0.0221360	+	0.0176529i
$222$		0			0
$223$	9.80139	+	2.23710i	0.656350	+	0.149808i	0.537710	−	0.843130i	$-0.319290\pi$
$223$	9.80139	+	2.23710i	0.656350	+	0.149808i	0.118640	+	0.992937i	$0.462147\pi$
$224$	−4.59903	+	56.5777i	−0.307285	+	3.78025i
$225$		0			0
$226$	−38.8683			−2.58548
$227$	8.61559			0.571837			0.285918	−	0.958254i	$-0.407701\pi$
$227$	8.61559			0.571837			0.285918	+	0.958254i	$0.407701\pi$
$228$		0			0
$229$	−0.485330	+	1.00780i	−0.0320715	+	0.0665971i	−0.916389	−	0.400289i	$-0.868910\pi$
$229$	−0.485330	+	1.00780i	−0.0320715	+	0.0665971i	0.884318	+	0.466886i	$0.154624\pi$
$230$	4.50952	−	5.65476i	0.297349	−	0.372864i
$231$		0			0
$232$	−15.7408	−	19.7383i	−1.03343	−	1.29589i
$233$	−22.2452	+	5.07733i	−1.45733	+	0.332627i	−0.876503	−	0.481397i	$-0.840130\pi$
$233$	−22.2452	+	5.07733i	−1.45733	+	0.332627i	−0.580831	+	0.814024i	$0.697272\pi$
$234$		0			0
$235$	−12.3737	−	5.95887i	−0.807172	−	0.388714i
$236$	0.403898	−	0.506472i	0.0262915	−	0.0329685i
$237$		0			0
$238$	0.436274	−	0.293432i	0.0282795	−	0.0190204i
$239$	6.59530	−	13.6953i	0.426614	−	0.885874i	−0.571264	−	0.820766i	$-0.693547\pi$
$239$	6.59530	−	13.6953i	0.426614	−	0.885874i	0.997878	−	0.0651074i	$-0.0207390\pi$
$240$		0			0
$241$	4.66449	+	1.06464i	0.300466	+	0.0685795i	0.370096	−	0.928993i	$-0.379325\pi$
$241$	4.66449	+	1.06464i	0.300466	+	0.0685795i	−0.0696299	+	0.997573i	$0.522182\pi$
$242$	1.69467	+	3.51902i	0.108937	+	0.226211i
$243$		0			0
$244$		−	17.8772i		−	1.14447i
$245$	10.1208	+	1.65633i	0.646596	+	0.105819i
$246$		0			0
$247$	16.2864	+	20.4224i	1.03628	+	1.29945i
$248$	−60.3927	+	29.0836i	−3.83494	+	1.84681i
$249$		0			0
$250$	13.6211	+	28.2844i	0.861472	+	1.78887i
$251$	−8.64206	−	4.16179i	−0.545482	−	0.262690i	0.140785	−	0.990040i	$-0.455037\pi$
$251$	−8.64206	−	4.16179i	−0.545482	−	0.262690i	−0.686267	+	0.727350i	$0.740752\pi$
$252$		0			0
$253$	5.74782	−	2.76800i	0.361362	−	0.174023i
$254$	40.8529	+	32.5791i	2.56334	+	2.04419i
$255$		0			0
$256$	25.5594	+	32.0504i	1.59746	+	2.00315i
$257$	1.20901	+	5.29704i	0.0754162	+	0.330420i	0.998536	−	0.0540927i	$-0.0172266\pi$
$257$	1.20901	+	5.29704i	0.0754162	+	0.330420i	−0.923120	+	0.384513i	$0.874369\pi$
$258$		0			0
$259$	−15.7656	−	1.28154i	−0.979627	−	0.0796309i
$260$	36.0380	+	28.7394i	2.23498	+	1.78234i
$261$		0			0
$262$	−34.9657	+	7.98068i	−2.16019	+	0.493048i
$263$		−	15.2273i		−	0.938953i	−0.882945	−	0.469476i	$-0.844443\pi$
$263$		−	15.2273i		−	0.938953i	0.882945	−	0.469476i	$-0.155557\pi$
$264$		0			0
$265$	−13.3418	+	3.04519i	−0.819582	+	0.187064i
$266$	30.4486	−	11.7290i	1.86692	−	0.719154i
$267$		0			0
$268$	7.00388	−	30.6860i	0.427830	−	1.87445i
$269$	−2.44899	+	3.07094i	−0.149318	+	0.187238i	−0.850865	−	0.525385i	$-0.823921\pi$
$269$	−2.44899	+	3.07094i	−0.149318	+	0.187238i	0.701547	+	0.712623i	$0.252493\pi$
$270$		0			0
$271$	23.2419	+	5.30480i	1.41184	+	0.322244i	0.859398	−	0.511307i	$-0.170838\pi$
$271$	23.2419	+	5.30480i	1.41184	+	0.322244i	0.552444	+	0.833550i	$0.313695\pi$
$272$	0.239090	−	1.04752i	0.0144970	−	0.0635154i
$273$		0			0
$274$	−2.14042	−	9.37778i	−0.129307	−	0.566533i
$275$			10.0613i			0.606717i
$276$		0			0
$277$	−0.283943	−	1.24404i	−0.0170605	−	0.0747470i	0.965681	−	0.259731i	$-0.0836339\pi$
$277$	−0.283943	−	1.24404i	−0.0170605	−	0.0747470i	−0.982742	+	0.184984i	$0.940777\pi$
$278$	−28.1826	−	13.5720i	−1.69028	−	0.813996i
$279$		0			0
$280$	30.2263	−	20.3298i	1.80637	−	1.21494i
$281$	−3.91830	+	3.12474i	−0.233746	+	0.186406i	−0.733357	−	0.679844i	$-0.762048\pi$
$281$	−3.91830	+	3.12474i	−0.233746	+	0.186406i	0.499611	+	0.866250i	$0.333476\pi$
$282$		0			0
$283$	12.6385	−	10.0788i	0.751279	−	0.599125i	−0.171171	−	0.985241i	$-0.554755\pi$
$283$	12.6385	−	10.0788i	0.751279	−	0.599125i	0.922450	+	0.386116i	$0.126184\pi$
$284$	−0.211352	+	0.438878i	−0.0125415	+	0.0260426i
$285$		0			0
$286$	24.1209	+	50.0877i	1.42630	+	2.96174i
$287$	−4.75764	−	32.9751i	−0.280835	−	1.94646i
$288$		0			0
$289$	15.3117	−	7.37372i	0.900688	−	0.433748i
$290$	−2.38957	+	10.4694i	−0.140321	+	0.614784i
$291$		0			0
$292$	18.6914	−	14.9059i	1.09383	−	0.872303i
$293$	−20.4628			−1.19545			−0.597726	−	0.801701i	$-0.703929\pi$
$293$	−20.4628			−1.19545			−0.597726	+	0.801701i	$0.703929\pi$
$294$		0			0
$295$	−0.174323			−0.0101495
$296$	−43.9262	+	35.0299i	−2.55316	+	2.03607i
$297$		0			0
$298$	−7.58556	+	33.2345i	−0.439420	+	1.92522i
$299$	9.42077	−	4.53681i	0.544817	−	0.262370i
$300$		0			0
$301$	2.64110	−	2.81066i	0.152231	−	0.162004i
$302$	24.7268	+	51.3458i	1.42287	+	2.95462i
$303$		0			0
$304$	28.9319	−	60.0777i	1.65936	−	3.44569i
$305$	−3.76118	+	2.99944i	−0.215365	+	0.171748i
$306$		0			0
$307$	−2.25444	+	1.79785i	−0.128667	+	0.102609i	−0.685709	−	0.727876i	$-0.740508\pi$
$307$	−2.25444	+	1.79785i	−0.128667	+	0.102609i	0.557042	+	0.830485i	$0.311936\pi$
$308$	50.2669	−	7.25249i	2.86422	−	0.413249i
$309$		0			0
$310$	25.6884	+	12.3709i	1.45900	+	0.702618i
$311$	−6.09451	−	26.7018i	−0.345588	−	1.51412i	−0.787078	−	0.616854i	$-0.788407\pi$
$311$	−6.09451	−	26.7018i	−0.345588	−	1.51412i	0.441490	−	0.897266i	$-0.354450\pi$
$312$		0			0
$313$		−	24.6969i		−	1.39595i	−0.716121	−	0.697976i	$-0.754084\pi$
$313$		−	24.6969i		−	1.39595i	0.716121	−	0.697976i	$-0.245916\pi$
$314$	−7.01556	−	30.7372i	−0.395911	−	1.73460i
$315$		0			0
$316$	−3.50424	+	15.3531i	−0.197129	+	0.863678i
$317$	−14.6984	−	3.35481i	−0.825544	−	0.188425i	−0.211180	−	0.977447i	$-0.567731\pi$
$317$	−14.6984	−	3.35481i	−0.825544	−	0.188425i	−0.614365	+	0.789022i	$0.710588\pi$
$318$		0			0
$319$	−5.90569	+	7.40550i	−0.330655	+	0.414628i
$320$	9.46528	−	41.4701i	0.529125	−	2.31825i
$321$		0			0
$322$	−1.86520	−	12.9276i	−0.103943	−	0.720429i
$323$	−0.320965	+	0.0732582i	−0.0178590	+	0.00407620i
$324$		0			0
$325$			16.4906i			0.914733i
$326$	−24.4034	+	5.56993i	−1.35158	+	0.308490i
$327$		0			0
$328$	−92.5216	−	73.7835i	−5.10865	−	4.07401i
$329$	−23.1440	+	8.91526i	−1.27597	+	0.491514i
$330$		0			0
$331$	−3.13342	−	13.7284i	−0.172228	−	0.754582i	−0.985078	−	0.172108i	$-0.944942\pi$
$331$	−3.13342	−	13.7284i	−0.172228	−	0.754582i	0.812850	−	0.582474i	$-0.197915\pi$
$332$	1.36872	+	1.71633i	0.0751185	+	0.0941956i
$333$		0			0
$334$	−45.1828	−	36.0321i	−2.47229	−	1.97159i
$335$	−7.63115	+	3.67497i	−0.416934	+	0.200785i
$336$		0			0
$337$	−1.80007	−	0.866866i	−0.0980558	−	0.0472212i	0.384213	−	0.923245i	$-0.374473\pi$
$337$	−1.80007	−	0.866866i	−0.0980558	−	0.0472212i	−0.482269	+	0.876023i	$0.660187\pi$
$338$	24.1450	+	50.1375i	1.31331	+	2.72712i
$339$		0			0
$340$	−0.523418	+	0.252065i	−0.0283863	+	0.0136701i
$341$	15.6801	+	19.6622i	0.849123	+	1.06477i
$342$		0			0
$343$	14.6957	−	11.2711i	0.793491	−	0.608582i
$344$		−	13.6994i		−	0.738621i
$345$		0			0
$346$	−7.45744	−	15.4855i	−0.400915	−	0.832508i
$347$	20.7078	+	4.72642i	1.11165	+	0.253728i	0.738641	−	0.674099i	$-0.235468\pi$
$347$	20.7078	+	4.72642i	1.11165	+	0.253728i	0.373012	+	0.927826i	$0.378325\pi$
$348$		0			0
$349$	−6.81637	+	14.1543i	−0.364872	+	0.757664i	−0.999890	−	0.0148331i	$-0.995278\pi$
$349$	−6.81637	+	14.1543i	−0.364872	+	0.757664i	0.635018	+	0.772497i	$0.280993\pi$
$350$	19.6454	+	6.19581i	1.05009	+	0.331180i
$351$		0			0
$352$	47.1648	−	59.1427i	2.51389	−	3.15232i
$353$	−13.6112	−	6.55479i	−0.724449	−	0.348876i	0.0350491	−	0.999386i	$-0.488841\pi$
$353$	−13.6112	−	6.55479i	−0.724449	−	0.348876i	−0.759498	+	0.650509i	$0.774556\pi$
$354$		0			0
$355$	0.127796	−	0.0291687i	0.00678273	−	0.00154811i
$356$	−37.4775	−	46.9953i	−1.98631	−	2.49075i
$357$		0			0
$358$	−17.9696	+	22.5332i	−0.949723	+	1.19091i
$359$	−0.547033	+	1.13592i	−0.0288713	+	0.0599518i	−0.914906	−	0.403668i	$-0.867735\pi$
$359$	−0.547033	+	1.13592i	−0.0288713	+	0.0599518i	0.886034	+	0.463619i	$0.153450\pi$
$360$		0			0
$361$	−1.43137			−0.0753354
$362$	39.8775			2.09592
$363$		0			0
$364$	82.3883	−	11.8870i	4.31832	−	0.623046i
$365$	−6.27211	−	1.43157i	−0.328297	−	0.0749318i
$366$		0			0
$367$	6.88746	+	5.49257i	0.359523	+	0.286710i	0.786547	−	0.617530i	$-0.211867\pi$
$367$	6.88746	+	5.49257i	0.359523	+	0.286710i	−0.427024	+	0.904240i	$0.640438\pi$
$368$	−20.8689	−	16.6424i	−1.08786	−	0.867543i
$369$		0			0
$370$	23.2988	+	5.31781i	1.21125	+	0.276460i
$371$	−12.4915	+	21.3242i	−0.648529	+	1.10710i
$372$		0			0
$373$	22.5978			1.17007			0.585036	−	0.811008i	$-0.301081\pi$
$373$	22.5978			1.17007			0.585036	+	0.811008i	$0.301081\pi$
$374$	−0.700667			−0.0362306
$375$		0			0
$376$	−38.2230	+	79.3709i	−1.97120	+	4.09324i
$377$	−9.67953	+	12.1377i	−0.498521	+	0.625126i
$378$		0			0
$379$	0.280801	+	0.352114i	0.0144238	+	0.0180869i	0.788991	−	0.614405i	$-0.210604\pi$
$379$	0.280801	+	0.352114i	0.0144238	+	0.0180869i	−0.774567	+	0.632492i	$0.782032\pi$
$380$	−35.1498	+	8.02272i	−1.80315	+	0.411557i
$381$		0			0
$382$	−8.37066	−	4.03110i	−0.428280	−	0.206249i
$383$	−11.2565	+	14.1152i	−0.575180	+	0.721253i	−0.981282	−	0.192575i	$-0.938316\pi$
$383$	−11.2565	+	14.1152i	−0.575180	+	0.721253i	0.406102	+	0.913828i	$0.366888\pi$
$384$		0			0
$385$	−9.95966	−	9.35884i	−0.507592	−	0.476971i
$386$	32.1001	−	66.6566i	1.63385	−	3.39273i
$387$		0			0
$388$	78.2893	+	17.8690i	3.97453	+	0.907162i
$389$	0.724287	+	1.50400i	0.0367228	+	0.0762557i	0.918523	−	0.395367i	$-0.129383\pi$
$389$	0.724287	+	1.50400i	0.0367228	+	0.0762557i	−0.881800	+	0.471623i	$0.843668\pi$
$390$		0			0
$391$			0.131786i			0.00666468i
$392$	10.6245	−	64.9198i	0.536617	−	3.27894i
$393$		0			0
$394$	17.2823	+	21.6713i	0.870670	+	1.09179i
$395$	3.81808	−	1.83869i	0.192108	−	0.0925145i
$396$		0			0
$397$	−3.34201	−	6.93975i	−0.167731	−	0.348296i	0.800113	−	0.599849i	$-0.204773\pi$
$397$	−3.34201	−	6.93975i	−0.167731	−	0.348296i	−0.967843	+	0.251553i	$0.919059\pi$
$398$	4.36697	+	2.10302i	0.218896	+	0.105415i
$399$		0			0
$400$	37.9275	−	18.2649i	1.89638	−	0.913247i
$401$	−0.0933946	−	0.0744797i	−0.00466390	−	0.00371934i	0.621155	−	0.783688i	$-0.286664\pi$
$401$	−0.0933946	−	0.0744797i	−0.00466390	−	0.00371934i	−0.625819	+	0.779968i	$0.715235\pi$
$402$		0			0
$403$	25.6999	+	32.2267i	1.28020	+	1.60532i
$404$	10.2893	+	45.0803i	0.511911	+	2.24283i
$405$		0			0
$406$	10.8231	+	16.0917i	0.537140	+	0.798618i
$407$	16.4804	+	13.1427i	0.816901	+	0.651457i
$408$		0			0
$409$	−8.45967	+	1.93086i	−0.418304	+	0.0954751i	−0.426492	−	0.904491i	$-0.640251\pi$
$409$	−8.45967	+	1.93086i	−0.418304	+	0.0954751i	0.00818811	+	0.999966i	$0.497394\pi$
$410$			50.3363i			2.48593i
$411$		0			0
$412$	−23.5166	+	5.36752i	−1.15858	+	0.264438i
$413$	−0.215576	+	0.229415i	−0.0106078	+	0.0112888i
$414$		0			0
$415$	0.131453	−	0.575932i	0.00645276	−	0.0282714i
$416$	77.3038	−	96.9360i	3.79013	−	4.75268i
$417$		0			0
$418$	−42.3932	−	9.67598i	−2.07352	−	0.473267i
$419$	−4.97988	+	21.8183i	−0.243283	+	1.06589i	0.694724	+	0.719276i	$0.255527\pi$
$419$	−4.97988	+	21.8183i	−0.243283	+	1.06589i	−0.938007	+	0.346616i	$0.887331\pi$
$420$		0			0
$421$	−3.38186	−	14.8169i	−0.164822	−	0.722131i	−0.988013	−	0.154368i	$-0.950666\pi$
$421$	−3.38186	−	14.8169i	−0.164822	−	0.722131i	0.823192	−	0.567764i	$-0.192191\pi$
$422$			6.98795i			0.340168i
$423$		0			0
$424$	19.5333	+	85.5809i	0.948620	+	4.15618i
$425$	−0.187256	−	0.0901780i	−0.00908327	−	0.00437427i
$426$		0			0
$427$	−0.703872	+	8.65910i	−0.0340628	+	0.419043i
$428$	−14.3119	+	11.4134i	−0.691791	+	0.551685i
$429$		0			0
$430$	−4.55581	+	3.63314i	−0.219701	+	0.175206i
$431$	10.0936	−	20.9597i	0.486193	−	1.00959i	−0.503178	−	0.864183i	$-0.667836\pi$
$431$	10.0936	−	20.9597i	0.486193	−	1.00959i	0.989372	−	0.145408i	$-0.0464496\pi$
$432$		0			0
$433$	4.12640	+	8.56856i	0.198302	+	0.411779i	0.976280	−	0.216513i	$-0.0694685\pi$
$433$	4.12640	+	8.56856i	0.198302	+	0.411779i	−0.777977	+	0.628292i	$0.783754\pi$
$434$	48.0479	−	18.5085i	2.30637	−	0.888435i
$435$		0			0
$436$	−59.6044	+	28.7039i	−2.85453	+	1.37467i
$437$	−1.81991	+	7.97356i	−0.0870583	+	0.381427i
$438$		0			0
$439$	1.45640	−	1.16144i	0.0695101	−	0.0554325i	−0.588118	−	0.808775i	$-0.700131\pi$
$439$	1.45640	−	1.16144i	0.0695101	−	0.0554325i	0.657629	+	0.753342i	$0.271560\pi$
$440$	−48.5443			−2.31426
$441$		0			0
$442$	−1.14841			−0.0546241
$443$	−21.6172	+	17.2392i	−1.02707	+	0.819057i	−0.983667	−	0.180000i	$-0.942390\pi$
$443$	−21.6172	+	17.2392i	−1.02707	+	0.819057i	−0.0433990	+	0.999058i	$0.513819\pi$
$444$		0			0
$445$	−3.59936	+	15.7698i	−0.170626	+	0.747561i
$446$	−24.7137	+	11.9015i	−1.17023	+	0.563552i
$447$		0			0
$448$	−42.8710	−	63.7405i	−2.02546	−	3.01146i
$449$	−1.12501	−	2.33611i	−0.0530926	−	0.110248i	0.872735	−	0.488195i	$-0.162344\pi$
$449$	−1.12501	−	2.33611i	−0.0530926	−	0.110248i	−0.925827	+	0.377947i	$0.876630\pi$
$450$		0			0
$451$	−19.2640	+	40.0021i	−0.907107	+	1.88363i
$452$	60.6374	−	48.3567i	2.85214	−	2.27451i
$453$		0			0
$454$	−18.3785	+	14.6564i	−0.862548	+	0.687859i
$455$	−16.3241	−	15.3393i	−0.765284	−	0.719117i
$456$		0			0
$457$	−17.3537	−	8.35711i	−0.811773	−	0.390929i	−0.0185252	−	0.999828i	$-0.505897\pi$
$457$	−17.3537	−	8.35711i	−0.811773	−	0.390929i	−0.793248	+	0.608899i	$0.791611\pi$
$458$	−0.679121	−	2.97542i	−0.0317333	−	0.139032i
$459$		0			0
$460$			14.4322i			0.672906i
$461$	−2.93845	−	12.8742i	−0.136857	−	0.599610i	−0.996115	−	0.0880666i	$-0.971931\pi$
$461$	−2.93845	−	12.8742i	−0.136857	−	0.599610i	0.859258	−	0.511543i	$-0.170926\pi$
$462$		0			0
$463$	5.06271	−	22.1812i	0.235284	−	1.03085i	−0.709898	−	0.704304i	$-0.751259\pi$
$463$	5.06271	−	22.1812i	0.235284	−	1.03085i	0.945182	−	0.326543i	$-0.105884\pi$
$464$	38.6372	+	8.81870i	1.79369	+	0.409398i
$465$		0			0
$466$	38.8157	−	48.6733i	1.79810	−	2.25475i
$467$	2.10430	−	9.21953i	0.0973753	−	0.426629i	−0.902617	−	0.430444i	$-0.858357\pi$
$467$	2.10430	−	9.21953i	0.0973753	−	0.426629i	0.999993	+	0.00381464i	$0.00121424\pi$
$468$		0			0
$469$	−4.60063	+	14.5875i	−0.212438	+	0.673589i
$470$	36.5322	−	8.33824i	1.68511	−	0.384614i
$471$		0			0
$472$			1.11819i			0.0514689i
$473$	−5.01092	+	1.14371i	−0.230402	+	0.0525878i
$474$		0			0
$475$	−10.0844	−	8.04208i	−0.462706	−	0.368996i
$476$	−0.315556	+	1.00055i	−0.0144635	+	0.0458602i
$477$		0			0
$478$	9.22879	+	40.4340i	0.422115	+	1.84941i
$479$	−17.2516	−	21.6328i	−0.788246	−	0.988429i	−0.999938	−	0.0110924i	$-0.996469\pi$
$479$	−17.2516	−	21.6328i	−0.788246	−	0.988429i	0.211693	−	0.977336i	$-0.432102\pi$
$480$		0			0
$481$	27.0116	+	21.5410i	1.23162	+	0.982187i
$482$	−11.7613	+	5.66393i	−0.535712	+	0.257985i
$483$		0			0
$484$	−7.02187	−	3.38156i	−0.319176	−	0.153707i
$485$	−9.37595	−	19.4694i	−0.425740	−	0.884058i
$486$		0			0
$487$	35.6076	−	17.1477i	1.61353	−	0.777037i	0.613614	−	0.789606i	$-0.289715\pi$
$487$	35.6076	−	17.1477i	1.61353	−	0.777037i	0.999921	+	0.0125691i	$0.00400099\pi$
$488$	19.2399	+	24.1260i	0.870947	+	1.09213i
$489$		0			0
$490$	−24.4071	+	13.6838i	−1.10260	+	0.618171i
$491$		−	8.27699i		−	0.373535i	−0.982404	−	0.186768i	$-0.940199\pi$
$491$		−	8.27699i		−	0.373535i	0.982404	−	0.186768i	$-0.0598012\pi$
$492$		0			0
$493$	−0.0848964	−	0.176289i	−0.00382354	−	0.00793966i
$494$	−69.4832	−	15.8591i	−3.12620	−	0.713534i
$495$		0			0
$496$	45.6546	−	94.8027i	2.04995	−	4.25677i
$497$	0.119652	−	0.204256i	0.00536711	−	0.00916214i
$498$		0			0
$499$	−3.45628	+	4.33403i	−0.154724	+	0.194018i	−0.853152	−	0.521663i	$-0.825312\pi$
$499$	−3.45628	+	4.33403i	−0.154724	+	0.194018i	0.698428	+	0.715681i	$0.253883\pi$
$500$	−56.4390	−	27.1796i	−2.52403	−	1.21551i
$501$		0			0
$502$	25.5148	−	5.82359i	1.13878	−	0.259920i
$503$	−14.2223	−	17.8342i	−0.634141	−	0.795187i	0.356116	−	0.934442i	$-0.384101\pi$
$503$	−14.2223	−	17.8342i	−0.634141	−	0.795187i	−0.990257	+	0.139255i	$0.955529\pi$
$504$		0			0
$505$	7.75810	−	9.72835i	0.345231	−	0.432906i
$506$	−7.55231	+	15.6825i	−0.335741	+	0.697173i
$507$		0			0
$508$	−104.266			−4.62604
$509$	−10.5120			−0.465936			−0.232968	−	0.972484i	$-0.574844\pi$
$509$	−10.5120			−0.465936			−0.232968	+	0.972484i	$0.574844\pi$
$510$		0			0
$511$	−9.64038	+	6.48399i	−0.426465	+	0.286835i
$512$	−38.2512	−	8.73059i	−1.69048	−	0.385841i
$513$		0			0
$514$	−11.5901	−	9.24278i	−0.511217	−	0.407682i
$515$	5.07490	+	4.04710i	0.223627	+	0.178337i
$516$		0			0
$517$	32.2231	+	7.35472i	1.41717	+	0.323460i
$518$	35.8108	−	24.0859i	1.57344	−	1.05827i
$519$		0			0
$520$	−79.5649			−3.48915
$521$	10.3652			0.454108			0.227054	−	0.973882i	$-0.427091\pi$
$521$	10.3652			0.454108			0.227054	+	0.973882i	$0.427091\pi$
$522$		0			0
$523$	−15.5673	+	32.3258i	−0.680710	+	1.41351i	0.218432	+	0.975852i	$0.429906\pi$
$523$	−15.5673	+	32.3258i	−0.680710	+	1.41351i	−0.899142	+	0.437657i	$0.855808\pi$
$524$	44.6201	−	55.9518i	1.94924	−	2.44427i
$525$		0			0
$526$	25.9038	+	32.4824i	1.12946	+	1.41630i
$527$	−0.506484	+	0.115602i	−0.0220628	+	0.00503569i
$528$		0			0
$529$	−17.7726	−	8.55884i	−0.772723	−	0.372124i
$530$	23.2801	−	29.1924i	1.01122	−	1.26804i
$531$		0			0
$532$	−32.9097	+	56.1798i	−1.42682	+	2.43570i
$533$	−31.5741	+	65.5642i	−1.36762	+	2.83990i
$534$		0			0
$535$	4.80251	+	1.09614i	0.207631	+	0.0473904i
$536$	23.5730	+	48.9498i	1.01820	+	2.11431i
$537$		0			0
$538$		−	10.7169i		−	0.462040i
$539$	−24.6332	+	1.53372i	−1.06103	+	0.0660621i
$540$		0			0
$541$	3.39539	+	4.25769i	0.145979	+	0.183052i	0.849445	−	0.527677i	$-0.176937\pi$
$541$	3.39539	+	4.25769i	0.145979	+	0.183052i	−0.703466	+	0.710729i	$0.748365\pi$
$542$	−58.6032	+	28.2218i	−2.51722	+	1.21223i
$543$		0			0
$544$	0.678010	+	1.40790i	0.0290694	+	0.0603633i
$545$	16.0395	+	7.72421i	0.687056	+	0.330869i
$546$		0			0
$547$	−6.43439	+	3.09864i	−0.275115	+	0.132488i	−0.566354	−	0.824162i	$-0.691647\pi$
$547$	−6.43439	+	3.09864i	−0.275115	+	0.132488i	0.291240	+	0.956650i	$0.405932\pi$
$548$	15.0063	+	11.9671i	0.641036	+	0.511209i
$549$		0			0
$550$	−17.1157	−	21.4624i	−0.729816	−	0.915160i
$551$	−2.70208	−	11.8386i	−0.115113	−	0.504341i
$552$		0			0
$553$	2.30183	−	7.29854i	0.0978836	−	0.310366i
$554$	2.72199	+	2.17072i	0.115646	+	0.0922250i
$555$		0			0
$556$	60.8521	−	13.8891i	2.58070	−	0.589029i
$557$		−	38.5139i		−	1.63189i	−0.578131	−	0.815944i	$-0.696218\pi$
$557$		−	38.5139i		−	1.63189i	0.578131	−	0.815944i	$-0.303782\pi$
$558$		0			0
$559$	−8.21298	+	1.87456i	−0.347372	+	0.0792854i
$560$	−17.1991	+	54.5343i	−0.726796	+	2.30450i
$561$		0			0
$562$	3.04276	−	13.3312i	0.128351	−	0.562343i
$563$	−22.1754	+	27.8071i	−0.934582	+	1.17193i	0.0503056	+	0.998734i	$0.483980\pi$
$563$	−22.1754	+	27.8071i	−0.934582	+	1.17193i	−0.984888	+	0.173195i	$0.944591\pi$
$564$		0			0
$565$	−20.3476	−	4.64420i	−0.856028	−	0.195383i
$566$	−9.81443	+	42.9998i	−0.412531	+	1.80742i
$567$		0			0
$568$	−0.187102	−	0.819747i	−0.00785062	−	0.0343958i
$569$		−	17.9670i		−	0.753215i	−0.926373	−	0.376607i	$-0.877091\pi$
$569$		−	17.9670i		−	0.753215i	0.926373	−	0.376607i	$-0.122909\pi$
$570$		0			0
$571$	−1.78530	−	7.82192i	−0.0747125	−	0.327337i	0.923735	−	0.383031i	$-0.125120\pi$
$571$	−1.78530	−	7.82192i	−0.0747125	−	0.327337i	−0.998448	+	0.0556944i	$0.982263\pi$
$572$	−99.9453	−	48.1311i	−4.17892	−	2.01246i
$573$		0			0
$574$	66.2445	+	62.2482i	2.76499	+	2.59819i
$575$	−4.03677	+	3.21922i	−0.168345	+	0.134251i
$576$		0			0
$577$	24.0467	−	19.1766i	1.00108	−	0.798334i	0.0215767	−	0.999767i	$-0.493131\pi$
$577$	24.0467	−	19.1766i	1.00108	−	0.798334i	0.979502	+	0.201433i	$0.0645599\pi$
$578$	−20.1187	+	41.7769i	−0.836827	+	1.73769i
$579$		0			0
$580$	−9.29725	−	19.3059i	−0.386047	−	0.801636i
$581$	−0.595388	−	0.885221i	−0.0247008	−	0.0367252i
$582$		0			0
$583$	29.6728	−	14.2896i	1.22892	−	0.591817i
$584$	−9.18277	+	40.2323i	−0.379986	+	1.66483i
$585$		0			0
$586$	43.6508	−	34.8103i	1.80320	−	1.43800i
$587$	40.1365			1.65661			0.828305	−	0.560277i	$-0.189306\pi$
$587$	40.1365			1.65661			0.828305	+	0.560277i	$0.189306\pi$
$588$		0			0
$589$	−32.2408			−1.32846
$590$	0.371861	−	0.296549i	0.0153093	−	0.0122087i
$591$		0			0
$592$	19.6253	−	85.9842i	0.806596	−	3.53393i
$593$	5.84985	−	2.81714i	0.240224	−	0.115686i	−0.309899	−	0.950770i	$-0.600295\pi$
$593$	5.84985	−	2.81714i	0.240224	−	0.115686i	0.550123	+	0.835084i	$0.314581\pi$
$594$		0			0
$595$	0.263451	−	0.101483i	0.0108004	−	0.00416041i
$596$	−29.5136	−	61.2856i	−1.20892	−	2.51036i
$597$		0			0
$598$	−12.3784	+	25.7039i	−0.506189	+	1.05111i
$599$	17.3733	−	13.8548i	0.709855	−	0.566090i	−0.200613	−	0.979671i	$-0.564293\pi$
$599$	17.3733	−	13.8548i	0.709855	−	0.566090i	0.910468	+	0.413580i	$0.135722\pi$
$600$		0			0
$601$	1.77391	−	1.41465i	0.0723593	−	0.0577046i	−0.586642	−	0.809846i	$-0.699551\pi$
$601$	1.77391	−	1.41465i	0.0723593	−	0.0577046i	0.659001	+	0.752142i	$0.270979\pi$
$602$	−0.852580	+	10.4885i	−0.0347486	+	0.427480i
$603$		0			0
$604$	−102.456	−	49.3401i	−4.16887	−	2.00762i
$605$	0.466688	+	2.04469i	0.0189736	+	0.0831286i
$606$		0			0
$607$		−	11.1437i		−	0.452309i	−0.974091	−	0.226155i	$-0.927385\pi$
$607$		−	11.1437i		−	0.452309i	0.974091	−	0.226155i	$-0.0726154\pi$
$608$	21.5797	+	94.5469i	0.875173	+	3.83438i
$609$		0			0
$610$	2.92075	−	12.7967i	0.118258	−	0.518122i
$611$	52.8143	+	12.0545i	2.13664	+	0.487674i
$612$		0			0
$613$	13.0330	−	16.3429i	0.526399	−	0.660084i	−0.445555	−	0.895255i	$-0.646994\pi$
$613$	13.0330	−	16.3429i	0.526399	−	0.660084i	0.971954	+	0.235171i	$0.0755650\pi$
$614$	1.75069	−	7.67026i	0.0706520	−	0.309547i
$615$		0			0
$616$	−60.0320	+	63.8860i	−2.41876	+	2.57404i
$617$	−38.9482	+	8.88967i	−1.56799	+	0.357884i	−0.916267	−	0.400569i	$-0.868813\pi$
$617$	−38.9482	+	8.88967i	−1.56799	+	0.357884i	−0.651728	+	0.758453i	$0.725955\pi$
$618$		0			0
$619$		−	30.9056i		−	1.24220i	−0.783730	−	0.621101i	$-0.786685\pi$
$619$		−	30.9056i		−	1.24220i	0.783730	−	0.621101i	$-0.213315\pi$
$620$	−55.4665	+	12.6599i	−2.22759	+	0.508433i
$621$		0			0
$622$	58.4244	+	46.5919i	2.34260	+	1.86816i
$623$	16.3025	+	24.2386i	0.653147	+	0.971097i
$624$		0			0
$625$	0.576143	+	2.52425i	0.0230457	+	0.100970i
$626$	42.0131	+	52.6828i	1.67918	+	2.10563i
$627$		0			0
$628$	49.1854	+	39.2241i	1.96271	+	1.56521i
$629$	−0.392318	+	0.188930i	−0.0156427	+	0.00753314i
$630$		0			0
$631$	37.0455	+	17.8402i	1.47476	+	0.710207i	0.986692	−	0.162599i	$-0.0519877\pi$
$631$	37.0455	+	17.8402i	1.47476	+	0.710207i	0.488068	+	0.872806i	$0.337702\pi$
$632$	−11.7942	−	24.4910i	−0.469149	−	0.974199i
$633$		0			0
$634$	37.0613	−	17.8478i	1.47189	−	0.708825i
$635$	17.4938	+	21.9365i	0.694219	+	0.870523i
$636$		0			0
$637$	−40.3742	+	2.51380i	−1.59968	+	0.0996002i
$638$		−	25.8437i		−	1.02316i
$639$		0			0
$640$	23.0794	+	47.9248i	0.912293	+	1.89440i
$641$	9.56366	+	2.18284i	0.377742	+	0.0862171i	0.407176	−	0.913350i	$-0.366513\pi$
$641$	9.56366	+	2.18284i	0.377742	+	0.0862171i	−0.0294344	+	0.999567i	$0.509371\pi$
$642$		0			0
$643$	5.92252	−	12.2982i	0.233561	−	0.484995i	−0.750940	−	0.660370i	$-0.770399\pi$
$643$	5.92252	−	12.2982i	0.233561	−	0.484995i	0.984502	+	0.175375i	$0.0561138\pi$
$644$	18.9933	+	17.8475i	0.748442	+	0.703292i
$645$		0			0
$646$	0.560051	−	0.702282i	0.0220349	−	0.0276309i
$647$	−11.6891	−	5.62917i	−0.459546	−	0.221306i	0.189764	−	0.981830i	$-0.439228\pi$
$647$	−11.6891	−	5.62917i	−0.459546	−	0.221306i	−0.649310	+	0.760524i	$0.724942\pi$
$648$		0			0
$649$	0.409008	−	0.0933534i	0.0160550	−	0.00366444i
$650$	−28.0529	−	35.1773i	−1.10033	−	1.37977i
$651$		0			0
$652$	31.1415	−	39.0502i	1.21960	−	1.52932i
$653$	1.93538	−	4.01886i	0.0757374	−	0.157270i	−0.859662	−	0.510863i	$-0.829326\pi$
$653$	1.93538	−	4.01886i	0.0757374	−	0.157270i	0.935399	+	0.353593i	$0.115040\pi$
$654$		0			0
$655$	−19.2581			−0.752476
$656$	185.766			7.25294
$657$		0			0
$658$	34.2040	−	58.3892i	1.33341	−	2.27625i
$659$	30.2786	+	6.91089i	1.17949	+	0.269210i	0.766935	−	0.641724i	$-0.221781\pi$
$659$	30.2786	+	6.91089i	1.17949	+	0.269210i	0.412551	+	0.910934i	$0.364638\pi$
$660$		0			0
$661$	12.1178	+	9.66364i	0.471329	+	0.375872i	0.830155	−	0.557532i	$-0.188252\pi$
$661$	12.1178	+	9.66364i	0.471329	+	0.375872i	−0.358827	+	0.933404i	$0.616823\pi$
$662$	30.0382	+	23.9547i	1.16747	+	0.931025i
$663$		0			0
$664$	−3.69431	−	0.843201i	−0.143367	−	0.0327225i
$665$	17.3413	−	2.50199i	0.672466	−	0.0970232i
$666$		0			0
$667$	−4.86083			−0.188212
$668$	115.317			4.46174
$669$		0			0
$670$	10.0269	−	20.8211i	0.387373	−	0.804388i
$671$	7.21848	−	9.05168i	0.278666	−	0.349436i
$672$		0			0
$673$	4.35420	+	5.46000i	0.167842	+	0.210467i	0.858638	−	0.512582i	$-0.171311\pi$
$673$	4.35420	+	5.46000i	0.167842	+	0.210467i	−0.690796	+	0.723050i	$0.742740\pi$
$674$	5.31452	−	1.21300i	0.204708	−	0.0467232i
$675$		0			0
$676$	−100.045	−	48.1791i	−3.84788	−	1.85304i
$677$	−16.8312	+	21.1057i	−0.646877	+	0.811158i	−0.991844	−	0.127457i	$-0.959319\pi$
$677$	−16.8312	+	21.1057i	−0.646877	+	0.811158i	0.344967	+	0.938615i	$0.387890\pi$
$678$		0			0
$679$	−37.2171	−	11.7376i	−1.42826	−	0.450448i
$680$	0.435097	−	0.903487i	0.0166852	−	0.0346472i
$681$		0			0
$682$	−66.8966	−	15.2687i	−2.56160	−	0.584669i
$683$	1.44083	+	2.99191i	0.0551318	+	0.114482i	0.926715	−	0.375766i	$-0.122620\pi$
$683$	1.44083	+	2.99191i	0.0551318	+	0.114482i	−0.871583	+	0.490248i	$0.836906\pi$
$684$		0			0
$685$		−	5.16502i		−	0.197345i
$686$	−12.1746	+	49.0427i	−0.464828	+	1.87246i
$687$		0			0
$688$	13.4081	+	16.8132i	0.511178	+	0.640997i
$689$	48.6342	−	23.4210i	1.85281	−	0.892268i
$690$		0			0
$691$	13.0674	+	27.1348i	0.497109	+	1.03226i	0.987037	+	0.160495i	$0.0513090\pi$
$691$	13.0674	+	27.1348i	0.497109	+	1.03226i	−0.489928	+	0.871763i	$0.662977\pi$
$692$	30.9000	+	14.8806i	1.17464	+	0.565677i
$693$		0			0
$694$	−52.2137	+	25.1448i	−1.98200	+	0.954483i
$695$	−13.1319	−	10.4724i	−0.498122	−	0.397239i
$696$		0			0
$697$	−0.571844	−	0.717069i	−0.0216601	−	0.0271609i
$698$	−9.53813	−	41.7893i	−0.361024	−	1.58175i
$699$		0			0
$700$	−38.3566	+	14.7753i	−1.44974	+	0.558454i
$701$	−38.2616	−	30.5126i	−1.44512	−	1.15244i	−0.960693	−	0.277614i	$-0.910457\pi$
$701$	−38.2616	−	30.5126i	−1.44512	−	1.15244i	−0.484427	−	0.874831i	$-0.660972\pi$
$702$		0			0
$703$	−26.3459	+	6.01328i	−0.993654	+	0.226795i
$704$			102.369i			3.85817i
$705$		0			0
$706$	40.1857	−	9.17211i	1.51241	−	0.345197i
$707$	−3.20885	−	22.2405i	−0.120681	−	0.836439i
$708$		0			0
$709$	−4.52772	+	19.8372i	−0.170042	+	0.745003i	0.815938	+	0.578140i	$0.196221\pi$
$709$	−4.52772	+	19.8372i	−0.170042	+	0.745003i	−0.985980	+	0.166864i	$0.946636\pi$
$710$	−0.222991	+	0.279622i	−0.00836872	+	0.0104940i
$711$		0			0
$712$	101.155	+	23.0880i	3.79095	+	0.865259i
$713$	−2.87183	+	12.5823i	−0.107551	+	0.471211i
$714$		0			0
$715$	6.64257	+	29.1030i	0.248418	+	1.08839i
$716$		−	57.5097i		−	2.14924i
$717$		0			0
$718$	−0.765462	−	3.35371i	−0.0285668	−	0.125159i
$719$	17.1150	+	8.24217i	0.638283	+	0.307381i	0.724893	−	0.688861i	$-0.241889\pi$
$719$	17.1150	+	8.24217i	0.638283	+	0.307381i	−0.0866100	+	0.996242i	$0.527603\pi$
$720$		0			0
$721$	11.6020	−	1.67393i	0.432081	−	0.0623405i
$722$	3.05336	−	2.43498i	0.113634	−	0.0906205i
$723$		0			0
$724$	−62.2119	+	49.6123i	−2.31209	+	1.84383i
$725$	3.32616	−	6.90684i	0.123530	−	0.256513i
$726$		0			0
$727$	−3.14524	−	6.53117i	−0.116651	−	0.242228i	0.834466	−	0.551059i	$-0.185776\pi$
$727$	−3.14524	−	6.53117i	−0.116651	−	0.242228i	−0.951117	+	0.308832i	$0.900062\pi$
$728$	−98.3936	+	104.710i	−3.64671	+	3.88082i
$729$		0			0
$730$	15.8148	−	7.61602i	0.585333	−	0.281881i
$731$	0.0236260	−	0.103512i	0.000873839	−	0.00382854i
$732$		0			0
$733$	11.1482	−	8.89042i	0.411770	−	0.328375i	−0.395598	−	0.918424i	$-0.629463\pi$
$733$	11.1482	−	8.89042i	0.411770	−	0.328375i	0.807368	+	0.590048i	$0.200891\pi$
$734$	−24.0358			−0.887179
$735$		0			0
$736$	38.8201			1.43093
$737$	15.9367	−	12.7091i	0.587036	−	0.468145i
$738$		0			0
$739$	−11.0300	+	48.3255i	−0.405744	+	1.77768i	0.197686	+	0.980265i	$0.436657\pi$
$739$	−11.0300	+	48.3255i	−0.405744	+	1.77768i	−0.603430	+	0.797416i	$0.706200\pi$
$740$	−42.9639	+	20.6903i	−1.57938	+	0.760591i
$741$		0			0
$742$	−9.62895	−	66.7381i	−0.353490	−	2.45003i
$743$	−11.8289	−	24.5630i	−0.433962	−	0.901131i	−0.997196	−	0.0748335i	$-0.976157\pi$
$743$	−11.8289	−	24.5630i	−0.433962	−	0.901131i	0.563234	−	0.826297i	$-0.309557\pi$
$744$		0			0
$745$	−7.94209	+	16.4919i	−0.290976	+	0.604217i
$746$	−48.2051	+	38.4423i	−1.76491	+	1.40747i
$747$		0			0
$748$	1.09309	−	0.871712i	0.0399674	−	0.0318730i
$749$	7.38157	−	4.96475i	0.269717	−	0.181408i
$750$		0			0
$751$	20.0306	+	9.64622i	0.730926	+	0.351996i	0.762048	−	0.647520i	$-0.224194\pi$
$751$	20.0306	+	9.64622i	0.730926	+	0.351996i	−0.0311220	+	0.999516i	$0.509908\pi$
$752$	−30.7722	−	134.822i	−1.12215	−	4.91645i
$753$		0			0
$754$		−	42.3582i		−	1.54260i
$755$	6.80942	+	29.8340i	0.247820	+	1.08577i
$756$		0			0
$757$	8.60933	−	37.7200i	0.312912	−	1.37096i	−0.536801	−	0.843709i	$-0.680367\pi$
$757$	8.60933	−	37.7200i	0.312912	−	1.37096i	0.849713	−	0.527246i	$-0.176775\pi$
$758$	−1.19800	−	0.273435i	−0.0435132	−	0.00993159i
$759$		0			0
$760$	38.8020	−	48.6561i	1.40750	−	1.76494i
$761$	0.614011	−	2.69016i	0.0222579	−	0.0975181i	−0.962579	−	0.271002i	$-0.912645\pi$
$761$	0.614011	−	2.69016i	0.0222579	−	0.0975181i	0.984837	+	0.173483i	$0.0555023\pi$
$762$		0			0
$763$	30.0005	−	11.5564i	1.08609	−	0.418371i
$764$	18.0740	−	4.12527i	0.653894	−	0.149247i
$765$		0			0
$766$		−	49.2591i		−	1.77980i
$767$	0.670371	−	0.153008i	0.0242057	−	0.00552479i
$768$		0			0
$769$	−7.05593	−	5.62692i	−0.254443	−	0.202912i	0.487958	−	0.872867i	$-0.337742\pi$
$769$	−7.05593	−	5.62692i	−0.254443	−	0.202912i	−0.742402	+	0.669955i	$0.766313\pi$
$770$	37.1665	+	3.02115i	1.33939	+	0.108875i
$771$		0			0
$772$	32.8501	+	143.926i	1.18230	+	5.18000i
$773$	30.1925	+	37.8602i	1.08595	+	1.36174i	0.927265	+	0.374406i	$0.122153\pi$
$773$	30.1925	+	37.8602i	1.08595	+	1.36174i	0.158683	+	0.987330i	$0.449275\pi$
$774$		0			0
$775$	−15.9133	−	12.6904i	−0.571622	−	0.455853i
$776$	−124.886	+	60.1418i	−4.48314	+	2.15897i
$777$		0			0
$778$	−4.10355	−	1.97617i	−0.147119	−	0.0708490i
$779$	−24.6964	−	51.2826i	−0.884840	−	1.83739i
$780$		0			0
$781$	−0.284224	+	0.136875i	−0.0101703	+	0.00489777i
$782$	−0.224187	−	0.281121i	−0.00801690	−	0.0100529i
$783$		0			0
$784$	50.4999	+	90.0743i	1.80357	+	3.21694i
$785$		−	16.9292i		−	0.604228i
$786$		0			0
$787$	−13.1796	−	27.3678i	−0.469803	−	0.975555i	−0.992409	−	0.122981i	$-0.960755\pi$
$787$	−13.1796	−	27.3678i	−0.469803	−	0.975555i	0.522606	−	0.852574i	$-0.324960\pi$
$788$	−53.9234	−	12.3077i	−1.92094	−	0.438442i
$789$		0			0
$790$	−5.01674	+	10.4174i	−0.178488	+	0.370633i
$791$	−31.2747	+	21.0349i	−1.11200	+	0.747916i
$792$		0			0
$793$	11.8312	−	14.8359i	0.420138	−	0.526837i
$794$	18.9346	+	9.11844i	0.671965	+	0.323601i
$795$		0			0
$796$	−9.42919	+	2.15215i	−0.334209	+	0.0762810i
$797$	24.2001	+	30.3459i	0.857211	+	1.07491i	0.996411	+	0.0846444i	$0.0269754\pi$
$797$	24.2001	+	30.3459i	0.857211	+	1.07491i	−0.139200	+	0.990264i	$0.544453\pi$
$798$		0			0
$799$	−0.425696	+	0.533806i	−0.0150600	+	0.0188847i
$800$	−26.5638	+	55.1602i	−0.939171	+	1.95021i
$801$		0			0
$802$	0.325928			0.0115089
$803$	15.4827			0.546372
$804$		0			0
$805$	0.568235	−	6.99048i	0.0200277	−	0.246382i
$806$	−109.645	−	25.0257i	−3.86207	−	0.881492i
$807$		0			0
$808$	−62.4023	−	49.7642i	−2.19531	−	1.75070i
$809$	3.92906	+	3.13332i	0.138138	+	0.110162i	0.690121	−	0.723694i	$-0.257557\pi$
$809$	3.92906	+	3.13332i	0.138138	+	0.110162i	−0.551983	+	0.833855i	$0.686129\pi$
$810$		0			0
$811$	−17.2672	−	3.94113i	−0.606334	−	0.138392i	−0.0916784	−	0.995789i	$-0.529223\pi$
$811$	−17.2672	−	3.94113i	−0.606334	−	0.138392i	−0.514656	+	0.857397i	$0.672080\pi$
$812$	−36.9047	−	11.6391i	−1.29510	−	0.408452i
$813$		0			0
$814$	−57.5131			−2.01583
$815$	−13.4407			−0.470808
$816$		0			0
$817$	2.85894	−	5.93665i	0.100022	−	0.207697i
$818$	14.7613	−	18.5100i	0.516115	−	0.647188i
$819$		0			0
$820$	−62.6243	−	78.5284i	−2.18693	−	2.74233i
$821$	13.2116	−	3.01546i	0.461088	−	0.105240i	0.0143343	−	0.999897i	$-0.495437\pi$
$821$	13.2116	−	3.01546i	0.461088	−	0.105240i	0.446754	+	0.894657i	$0.352580\pi$
$822$		0			0
$823$	21.2656	+	10.2410i	0.741272	+	0.356978i	0.766106	−	0.642714i	$-0.222192\pi$
$823$	21.2656	+	10.2410i	0.741272	+	0.356978i	−0.0248343	+	0.999692i	$0.507906\pi$
$824$	25.9600	−	32.5529i	0.904361	−	1.13403i
$825$		0			0
$826$	0.0695905	−	0.856109i	0.00242136	−	0.0297878i
$827$	9.12986	−	18.9583i	0.317476	−	0.659246i	−0.679769	−	0.733427i	$-0.737920\pi$
$827$	9.12986	−	18.9583i	0.317476	−	0.659246i	0.997245	+	0.0741803i	$0.0236340\pi$
$828$		0			0
$829$	−11.6767	−	2.66512i	−0.405547	−	0.0925635i	0.0148811	−	0.999889i	$-0.495263\pi$
$829$	−11.6767	−	2.66512i	−0.405547	−	0.0925635i	−0.420428	+	0.907326i	$0.638120\pi$
$830$	0.699335	+	1.45218i	0.0242743	+	0.0504061i
$831$		0			0
$832$			167.784i			5.81687i
$833$	0.192239	−	0.472210i	0.00666069	−	0.0163611i
$834$		0			0
$835$	−19.3479	−	24.2615i	−0.669562	−	0.839604i
$836$	78.1746	−	37.6469i	2.70372	−	1.30205i
$837$		0			0
$838$	−26.4932	−	55.0137i	−0.915192	−	1.90042i
$839$	−29.2161	−	14.0697i	−1.00865	−	0.485741i	−0.144786	−	0.989463i	$-0.546249\pi$
$839$	−29.2161	−	14.0697i	−1.00865	−	0.485741i	−0.863866	+	0.503722i	$0.831964\pi$
$840$		0			0
$841$	−19.6258	+	9.45128i	−0.676751	+	0.325906i
$842$	32.4198	+	25.8540i	1.11726	+	0.890986i
$843$		0			0
$844$	−8.69382	−	10.9017i	−0.299254	−	0.375252i
$845$	6.64918	+	29.1320i	0.228739	+	1.00217i
$846$		0			0
$847$	3.26802	+	1.91438i	0.112290	+	0.0657790i
$848$	−107.734	−	85.9151i	−3.69961	−	2.95034i
$849$		0			0
$850$	0.552857	−	0.126186i	0.0189628	−	0.00432814i
$851$			10.8174i			0.370815i
$852$		0			0
$853$	−13.7231	+	3.13220i	−0.469869	+	0.107245i	−0.450898	−	0.892575i	$-0.648896\pi$
$853$	−13.7231	+	3.13220i	−0.469869	+	0.107245i	−0.0189712	+	0.999820i	$0.506039\pi$
$854$	−13.2289	−	19.6688i	−0.452685	−	0.673051i
$855$		0			0
$856$	7.03118	−	30.8056i	0.240321	−	1.05291i
$857$	20.2084	−	25.3405i	0.690305	−	0.865615i	−0.305953	−	0.952047i	$-0.598975\pi$
$857$	20.2084	−	25.3405i	0.690305	−	0.865615i	0.996258	+	0.0864314i	$0.0275463\pi$
$858$		0			0
$859$	−36.9589	−	8.43563i	−1.26102	−	0.287820i	−0.460789	−	0.887510i	$-0.652434\pi$
$859$	−36.9589	−	8.43563i	−1.26102	−	0.287820i	−0.800233	+	0.599689i	$0.795291\pi$
$860$	2.58735	−	11.3359i	0.0882280	−	0.386552i
$861$		0			0
$862$	14.1240	+	61.8814i	0.481066	+	2.10769i
$863$		−	16.3192i		−	0.555513i	−0.960652	−	0.277756i	$-0.910409\pi$
$863$		−	16.3192i		−	0.555513i	0.960652	−	0.277756i	$-0.0895908\pi$
$864$		0			0
$865$	−2.05367	−	8.99774i	−0.0698270	−	0.305932i
$866$	−23.3787	−	11.2586i	−0.794442	−	0.382583i
$867$		0			0
$868$	−51.9316	+	88.6518i	−1.76267	+	3.00904i
$869$	−7.97358	+	6.35872i	−0.270485	+	0.215705i
$870$		0			0
$871$	26.1205	−	20.8304i	0.885060	−	0.705812i
$872$	49.5467	−	102.885i	1.67786	−	3.48412i
$873$		0			0
$874$	−9.68202	−	20.1049i	−0.327499	−	0.680059i
$875$	26.2670	+	15.3870i	0.887988	+	0.520177i
$876$		0			0
$877$	6.46697	−	3.11433i	0.218374	−	0.105163i	−0.321499	−	0.946910i	$-0.604187\pi$
$877$	6.46697	−	3.11433i	0.218374	−	0.105163i	0.539873	+	0.841747i	$0.318472\pi$
$878$	−1.13097	+	4.95510i	−0.0381684	+	0.167227i
$879$		0			0
$880$	59.5781	−	47.5120i	2.00838	−	1.60163i
$881$	38.2817			1.28974			0.644872	−	0.764291i	$-0.276911\pi$
$881$	38.2817			1.28974			0.644872	+	0.764291i	$0.276911\pi$
$882$		0			0
$883$	−40.4654			−1.36177			−0.680884	−	0.732391i	$-0.738404\pi$
$883$	−40.4654			−1.36177			−0.680884	+	0.732391i	$0.738404\pi$
$884$	1.79160	−	1.42875i	0.0602579	−	0.0480541i
$885$		0			0
$886$	16.7869	−	73.5482i	0.563967	−	2.47090i
$887$	17.2248	−	8.29505i	0.578354	−	0.278520i	−0.121751	−	0.992561i	$-0.538851\pi$
$887$	17.2248	−	8.29505i	0.578354	−	0.278520i	0.700105	+	0.714040i	$0.253137\pi$
$888$		0			0
$889$	50.5028	+	4.10522i	1.69381	+	0.137685i
$890$	−19.1487	−	39.7628i	−0.641867	−	1.33285i
$891$		0			0
$892$	23.7484	−	49.3140i	0.795154	−	1.65115i
$893$	−33.1280	+	26.4187i	−1.10859	+	0.884068i
$894$		0			0
$895$	−12.0995	+	9.64901i	−0.404441	+	0.322531i
$896$	91.6119	+	28.8927i	3.06054	+	0.965238i
$897$		0			0
$898$	6.37392	+	3.06952i	0.212700	+	0.102431i
$899$	−4.26389	−	18.6813i	−0.142209	−	0.623058i
$900$		0			0
$901$			0.680335i			0.0226652i
$902$	−26.9561	−	118.102i	−0.897541	−	3.93238i
$903$		0			0
$904$	−29.7901	+	130.519i	−0.990804	+	4.34100i
$905$	20.8759	+	4.76479i	0.693938	+	0.158387i
$906$		0			0
$907$	−14.0043	+	17.5608i	−0.465005	+	0.583097i	−0.957940	−	0.286969i	$-0.907352\pi$
$907$	−14.0043	+	17.5608i	−0.465005	+	0.583097i	0.492935	+	0.870066i	$0.335924\pi$
$908$	10.4376	−	45.7301i	0.346384	−	1.51761i
$909$		0			0
$910$	60.9165	+	4.95172i	2.01936	+	0.164148i
$911$	29.8696	−	6.81755i	0.989625	−	0.225876i	0.303082	−	0.952964i	$-0.401984\pi$
$911$	29.8696	−	6.81755i	0.989625	−	0.225876i	0.686543	+	0.727089i	$0.259127\pi$
$912$		0			0
$913$			1.42169i			0.0470510i
$914$	51.2352	−	11.6941i	1.69471	−	0.386806i
$915$		0			0
$916$	4.76126	+	3.79697i	0.157316	+	0.125456i
$917$	−23.8155	+	25.3444i	−0.786455	+	0.836945i
$918$		0			0
$919$	−2.15709	−	9.45085i	−0.0711560	−	0.311755i	0.926808	−	0.375536i	$-0.122541\pi$
$919$	−2.15709	−	9.45085i	−0.0711560	−	0.311755i	−0.997964	+	0.0637809i	$0.979684\pi$
$920$	−15.5323	−	19.4769i	−0.512085	−	0.642134i
$921$		0			0
$922$	28.1691	+	22.4641i	0.927700	+	0.739816i
$923$	−0.465848	+	0.224341i	−0.0153336	+	0.00738426i
$924$		0			0
$925$	−15.3706	−	7.40210i	−0.505383	−	0.243380i
$926$	26.9339	+	55.9288i	0.885102	+	1.83793i
$927$		0			0
$928$	−51.9296	+	25.0080i	−1.70467	+	0.820927i
$929$	−31.6092	−	39.6367i	−1.03706	−	1.30044i	−0.952671	−	0.304005i	$-0.901676\pi$
$929$	−31.6092	−	39.6367i	−1.03706	−	1.30044i	−0.0843934	−	0.996433i	$-0.526895\pi$
$930$		0			0
$931$	18.1523	−	25.9158i	0.594918	−	0.849358i
$932$			124.225i			4.06913i
$933$		0			0
$934$	11.1950	+	23.2466i	0.366310	+	0.760651i
$935$	−0.366799	−	0.0837196i	−0.0119956	−	0.00273792i
$936$		0			0
$937$	−19.2346	+	39.9410i	−0.628366	+	1.30482i	0.307193	+	0.951647i	$0.400610\pi$
$937$	−19.2346	+	39.9410i	−0.628366	+	1.30482i	−0.935559	+	0.353169i	$0.885104\pi$
$938$	−15.0016	−	38.9440i	−0.489819	−	1.27157i
$939$		0			0
$940$	−46.6192	+	58.4586i	−1.52055	+	1.90671i
$941$	26.4894	+	12.7566i	0.863531	+	0.415855i	0.812582	−	0.582847i	$-0.198061\pi$
$941$	26.4894	+	12.7566i	0.863531	+	0.415855i	0.0509489	+	0.998701i	$0.483775\pi$
$942$		0			0
$943$	−22.2134	+	5.07006i	−0.723368	+	0.165104i
$944$	−1.09441	−	1.37235i	−0.0356201	−	0.0446662i
$945$		0			0
$946$	8.74354	−	10.9640i	0.284277	−	0.356472i
$947$	−2.71697	+	5.64184i	−0.0882896	+	0.183335i	−0.940438	−	0.339965i	$-0.889585\pi$
$947$	−2.71697	+	5.64184i	−0.0882896	+	0.183335i	0.852149	+	0.523300i	$0.175299\pi$
$948$		0			0
$949$	25.3764			0.823753
$950$	35.1927			1.14180
$951$		0			0
$952$	−0.650963	−	1.68990i	−0.0210978	−	0.0547699i
$953$	32.7472	+	7.47433i	1.06078	+	0.242117i	0.717102	−	0.696968i	$-0.245468\pi$
$953$	32.7472	+	7.47433i	1.06078	+	0.242117i	0.343683	+	0.939086i	$0.388325\pi$
$954$		0			0
$955$	−3.90038	−	3.11045i	−0.126213	−	0.100652i
$956$	−64.7022	−	51.5983i	−2.09262	−	1.66881i
$957$		0			0
$958$	73.6013	+	16.7990i	2.37795	+	0.542751i
$959$	−6.79736	−	6.38730i	−0.219498	−	0.206257i
$960$		0			0
$961$	−19.8760			−0.641161
$962$	−94.2650			−3.03922
$963$		0			0
$964$	11.3019	−	23.4686i	0.364009	−	0.755872i
$965$	24.7689	−	31.0592i	0.797340	−	0.999833i
$966$		0			0
$967$	14.9573	+	18.7559i	0.480994	+	0.603148i	0.961825	−	0.273666i	$-0.0882362\pi$
$967$	14.9573	+	18.7559i	0.480994	+	0.603148i	−0.480830	+	0.876814i	$0.659665\pi$
$968$	13.1156	−	2.99356i	0.421552	−	0.0962166i
$969$		0			0
$970$	53.1208	+	25.5816i	1.70561	+	0.821377i
$971$	11.3142	−	14.1875i	0.363090	−	0.455300i	−0.566410	−	0.824124i	$-0.691668\pi$
$971$	11.3142	−	14.1875i	0.363090	−	0.455300i	0.929499	+	0.368824i	$0.120239\pi$
$972$		0			0
$973$	−30.0216	+	4.33150i	−0.962447	+	0.138862i
$974$	−46.7864	+	97.1529i	−1.49913	+	3.11298i
$975$		0			0
$976$	−47.2260	−	10.7790i	−1.51167	−	0.345028i
$977$	25.0756	+	52.0700i	0.802239	+	1.66587i	0.744583	+	0.667530i	$0.232648\pi$
$977$	25.0756	+	52.0700i	0.802239	+	1.66587i	0.0576562	+	0.998336i	$0.481637\pi$
$978$		0			0
$979$		−	38.9277i		−	1.24414i
$980$	21.0527	−	51.7131i	0.672503	−	1.65191i
$981$		0			0
$982$	14.0804	+	17.6563i	0.449324	+	0.563434i
$983$	−8.47856	+	4.08306i	−0.270424	+	0.130229i	−0.564182	−	0.825650i	$-0.690808\pi$
$983$	−8.47856	+	4.08306i	−0.270424	+	0.130229i	0.293758	+	0.955880i	$0.405094\pi$
$984$		0			0
$985$	6.45788	+	13.4099i	0.205765	+	0.427276i
$986$	0.480993	+	0.231634i	0.0153179	+	0.00737673i
$987$		0			0
$988$	128.130	−	61.7039i	4.07634	−	1.96306i
$989$	−2.06218	−	1.64453i	−0.0655735	−	0.0522932i
$990$		0			0
$991$	−3.54604	−	4.44660i	−0.112644	−	0.141251i	0.722313	−	0.691566i	$-0.243079\pi$
$991$	−3.54604	−	4.44660i	−0.112644	−	0.141251i	−0.834957	+	0.550315i	$0.814508\pi$
$992$	34.0528	+	149.195i	1.08118	+	4.73695i
$993$		0			0
$994$	0.0922321	+	0.639259i	0.00292542	+	0.0202761i
$995$	2.03483	+	1.62272i	0.0645083	+	0.0514437i
$996$		0			0
$997$	−8.69273	+	1.98406i	−0.275302	+	0.0628358i	−0.357943	−	0.933744i	$-0.616522\pi$
$997$	−8.69273	+	1.98406i	−0.275302	+	0.0628358i	0.0826410	+	0.996579i	$0.473665\pi$
$998$		−	15.1249i		−	0.478770i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	441.2.w.a.188.1	✓	120
3.2	odd	2	inner	441.2.w.a.188.20	yes	120
49.6	odd	14	inner	441.2.w.a.251.20	yes	120
147.104	even	14	inner	441.2.w.a.251.1	yes	120

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
441.2.w.a.188.1	✓	120	1.1	even	1	trivial
441.2.w.a.188.20	yes	120	3.2	odd	2	inner
441.2.w.a.251.1	yes	120	147.104	even	14	inner
441.2.w.a.251.20	yes	120	49.6	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)

\(f(q)\)	\(=\)	\(q+(-2.13317 + 1.70115i) q^{2} +(1.21148 - 5.30783i) q^{4} +(-1.31998 + 0.635668i) q^{5} +(-0.795783 + 2.52324i) q^{7} +(4.07748 + 8.46697i) q^{8} +(1.73438 - 3.60147i) q^{10} +(2.75661 - 2.19832i) q^{11} +(4.51813 - 3.60309i) q^{13} +(-2.59486 - 6.73625i) q^{14} +(-13.2912 - 6.40071i) q^{16} +(0.0162072 + 0.0710083i) q^{17} +4.52011i q^{19} +(1.77490 + 7.77633i) q^{20} +(-2.14065 + 9.37881i) q^{22} +(1.76402 + 0.402626i) q^{23} +(-1.77918 + 2.23102i) q^{25} +(-3.50857 + 15.3720i) q^{26} +(12.4289 + 7.28073i) q^{28} +(-2.61910 + 0.597792i) q^{29} +7.13274i q^{31} +(20.9170 - 4.77416i) q^{32} +(-0.155368 - 0.123902i) q^{34} +(-0.553525 - 3.83647i) q^{35} +(1.33034 + 5.82860i) q^{37} +(-7.68938 - 9.64217i) q^{38} +(-10.7644 - 8.58430i) q^{40} +(-11.3454 + 5.46367i) q^{41} +(-1.31339 - 0.632493i) q^{43} +(-8.32876 - 17.2949i) q^{44} +(-4.44789 + 2.14199i) q^{46} +(5.84471 + 7.32903i) q^{47} +(-5.73346 - 4.01590i) q^{49} -7.78580i q^{50} +(-13.6510 - 28.3466i) q^{52} +(9.10665 + 2.07853i) q^{53} +(-2.24126 + 4.65403i) q^{55} +(-24.6090 + 3.55058i) q^{56} +(4.57005 - 5.73067i) q^{58} +(0.107203 + 0.0516262i) q^{59} +(3.20130 - 0.730676i) q^{61} +(-12.1339 - 15.2154i) q^{62} +(-18.1023 + 22.6996i) q^{64} +(-3.67347 + 7.62804i) q^{65} +5.78127 q^{67} +0.396535 q^{68} +(7.70718 + 7.24224i) q^{70} +(-0.0872291 - 0.0199095i) q^{71} +(3.43319 + 2.73788i) q^{73} +(-12.7532 - 10.1703i) q^{74} +(23.9920 + 5.47601i) q^{76} +(3.35323 + 8.70497i) q^{77} -2.89253 q^{79} +21.6128 q^{80} +(14.9073 - 30.9552i) q^{82} +(-0.251403 + 0.315250i) q^{83} +(-0.0665309 - 0.0834271i) q^{85} +(3.87765 - 0.885047i) q^{86} +(29.8532 + 14.3765i) q^{88} +(6.88377 - 8.63197i) q^{89} +(5.49600 + 14.2676i) q^{91} +(4.27415 - 8.87536i) q^{92} +(-24.9355 - 5.69137i) q^{94} +(-2.87329 - 5.96645i) q^{95} +14.7498i q^{97} +(19.0621 - 1.18685i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 120 q + 24 q^{4} - 32 q^{16} - 44 q^{22} - 4 q^{25} - 56 q^{28} + 112 q^{34} - 76 q^{37} + 28 q^{40} + 8 q^{43} - 40 q^{46} - 84 q^{49} - 140 q^{52} + 12 q^{58} - 84 q^{61} + 24 q^{64} + 16 q^{67} + 112 q^{70}+ \cdots - 112 q^{94}+O(q^{100}) \) 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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