LMFDB - Embedded newform 441.2.w.a.251.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [441,2,Mod(62,441)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

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")

//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: f = N[0] # Warning: the index may be different

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			251.1
Character	$\chi$	$=$	441.251
Dual form			441.2.w.a.188.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

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

Display 100 coefficients 10 coefficients

Character values

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

$n$	$199$	$344$
$\chi(n)$	$e\left(\frac{9}{14}\right)$	$-1$

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	−0.918511	−	0.395396i	$-0.870607\pi$
$2$	−2.13317	−	1.70115i	−1.50838	−	1.20289i	−0.589871	−	0.807498i	$-0.700821\pi$
$3$		0			0
$3$		0			0
$4$	1.21148	+	5.30783i	0.605739	+	2.65392i
$5$	−1.31998	−	0.635668i	−0.590313	−	0.284280i	0.114784	−	0.993390i	$-0.463382\pi$
$5$	−1.31998	−	0.635668i	−0.590313	−	0.284280i	−0.705097	+	0.709111i	$0.749097\pi$
$6$		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	0.943691	−	0.330828i	$-0.107328\pi$
$11$	2.75661	+	2.19832i	0.831149	+	0.662819i	−0.112542	+	0.993647i	$0.535899\pi$
$12$		0			0
$13$	4.51813	+	3.60309i	1.25310	+	0.999317i	0.999487	+	0.0320125i	$0.0101916\pi$
$13$	4.51813	+	3.60309i	1.25310	+	0.999317i	0.253617	+	0.967305i	$0.418380\pi$
$14$	−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	−0.972924	−	0.231123i	$-0.925760\pi$
$17$	0.0162072	−	0.0710083i	0.00393082	−	0.0172220i	0.976855	+	0.213901i	$0.0686171\pi$
$18$		0			0
$19$		−	4.52011i		−	1.03698i	−0.855083	−	0.518492i	$-0.826494\pi$
$19$		−	4.52011i		−	1.03698i	0.855083	−	0.518492i	$-0.173506\pi$
$20$	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	−0.0346140	−	0.999401i	$-0.511020\pi$
$23$	1.76402	−	0.402626i	0.367824	−	0.0839533i	0.402438	+	0.915447i	$0.368163\pi$
$24$		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	−0.0276894	−	0.999617i	$-0.508815\pi$
$29$	−2.61910	−	0.597792i	−0.486354	−	0.111007i	−0.458665	+	0.888609i	$0.651672\pi$
$30$		0			0
$31$		−	7.13274i		−	1.28108i	−0.767926	−	0.640539i	$-0.778711\pi$
$31$		−	7.13274i		−	1.28108i	0.767926	−	0.640539i	$-0.221289\pi$
$32$	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	−0.739729	−	0.672905i	$-0.765046\pi$
$37$	1.33034	−	5.82860i	0.218706	−	0.958216i	0.958435	−	0.285310i	$-0.0920967\pi$
$38$	−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	−0.964875	−	0.262709i	$-0.915384\pi$
$41$	−11.3454	−	5.46367i	−1.77186	−	0.853282i	−0.806984	−	0.590573i	$-0.798902\pi$
$42$		0			0
$43$	−1.31339	+	0.632493i	−0.200289	+	0.0964543i	−0.531340	−	0.847159i	$-0.678311\pi$
$43$	−1.31339	+	0.632493i	−0.200289	+	0.0964543i	0.331050	+	0.943613i	$0.392597\pi$
$44$	−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	−0.144296	−	0.989535i	$-0.546092\pi$
$47$	5.84471	−	7.32903i	0.852538	−	1.06905i	0.996834	−	0.0795141i	$-0.0253369\pi$
$48$		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	0.454752	−	0.890618i	$-0.349728\pi$
$53$	9.10665	−	2.07853i	1.25089	−	0.285508i	0.796142	+	0.605110i	$0.206871\pi$
$54$		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	−0.426892	−	0.904302i	$-0.640392\pi$
$59$	0.107203	−	0.0516262i	0.0139566	−	0.00672116i	0.440849	+	0.897581i	$0.354677\pi$
$60$		0			0
$61$	3.20130	+	0.730676i	0.409885	+	0.0935535i	0.422491	−	0.906367i	$-0.361156\pi$
$61$	3.20130	+	0.730676i	0.409885	+	0.0935535i	−0.0126066	+	0.999921i	$0.504013\pi$
$62$	−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	−0.227694	−	0.973733i	$-0.573119\pi$
$71$	−0.0872291	+	0.0199095i	−0.0103522	+	0.00236282i	0.217342	+	0.976096i	$0.430261\pi$
$72$		0			0
$73$	3.43319	−	2.73788i	0.401824	−	0.320444i	−0.401640	−	0.915798i	$-0.631560\pi$
$73$	3.43319	−	2.73788i	0.401824	−	0.320444i	0.803464	+	0.595354i	$0.202988\pi$
$74$	−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	0.767842	−	0.640639i	$-0.221330\pi$
$83$	−0.251403	−	0.315250i	−0.0275951	−	0.0346032i	−0.795438	+	0.606036i	$0.792759\pi$
$84$		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	0.998842	−	0.0481072i	$-0.0153189\pi$
$89$	6.88377	+	8.63197i	0.729678	+	0.914987i	−0.269164	+	0.963094i	$0.586747\pi$
$90$		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	$-0.730628\pi$
$97$		−	14.7498i		−	1.49761i	0.662790	−	0.748805i	$-0.269372\pi$
$98$	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	0.0125414	−	0.999921i	$-0.496008\pi$
$101$	−7.65207	−	3.68504i	−0.761409	−	0.366675i	−0.773951	+	0.633246i	$0.781722\pi$
$102$		0			0
$103$	−1.92234	+	3.99179i	−0.189414	+	0.393322i	−0.973951	−	0.226760i	$-0.927187\pi$
$103$	−1.92234	+	3.99179i	−0.189414	+	0.393322i	0.784537	+	0.620083i	$0.212901\pi$
$104$	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	−0.742267	−	0.670105i	$-0.766249\pi$
$107$	−2.62877	+	2.09637i	−0.254132	+	0.202664i	0.488134	+	0.872769i	$0.337678\pi$
$108$		0			0
$109$	−7.57622	+	9.50028i	−0.725670	+	0.909962i	−0.998644	−	0.0520596i	$-0.983421\pi$
$109$	−7.57622	+	9.50028i	−0.725670	+	0.909962i	0.272974	+	0.962022i	$0.411993\pi$
$110$	−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	0.0610528	−	0.998135i	$-0.480554\pi$
$113$	11.1377	−	8.88203i	1.04775	−	0.835551i	0.986695	+	0.162584i	$0.0519828\pi$
$114$		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	0.324974	+	0.945723i	$0.394644\pi$
$127$	−4.26155	+	18.6711i	−0.378151	+	1.65679i	−0.703125	+	0.711066i	$0.748213\pi$
$128$			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	0.162153	−	0.986766i	$-0.448156\pi$
$131$	11.8431	−	5.70335i	1.03474	−	0.498304i	0.872585	+	0.488462i	$0.162442\pi$
$132$		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	0.825350	−	0.564621i	$-0.190978\pi$
$137$	−1.52964	−	3.17632i	−0.130686	−	0.271371i	−0.956036	+	0.293249i	$0.905263\pi$
$138$		0			0
$139$	4.97429	−	10.3292i	0.421914	−	0.876114i	−0.576349	−	0.817204i	$-0.695523\pi$
$139$	4.97429	−	10.3292i	0.421914	−	0.876114i	0.998263	−	0.0589101i	$-0.0187625\pi$
$140$	−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	0.935775	−	0.352598i	$-0.114702\pi$
$149$	9.76826	+	7.78993i	0.800247	+	0.638176i	−0.135528	+	0.990774i	$0.543273\pi$
$150$		0			0
$151$	4.64786	+	20.3636i	0.378237	+	1.65717i	0.702864	+	0.711324i	$0.251904\pi$
$151$	4.64786	+	20.3636i	0.378237	+	1.65717i	−0.324627	+	0.945842i	$0.605239\pi$
$152$	−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	−0.999537	−	0.0304347i	$-0.990311\pi$
$157$	−5.01362	−	10.4109i	−0.400131	−	0.830880i	0.599406	−	0.800445i	$-0.295403\pi$
$158$	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	−0.0812055	−	0.996697i	$-0.525877\pi$
$163$	8.26562	−	3.98051i	0.647413	−	0.311778i	0.728619	+	0.684920i	$0.240163\pi$
$164$	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	−0.376324	−	0.926488i	$-0.622812\pi$
$167$	4.71322	−	20.6500i	0.364720	−	1.59794i	0.741045	−	0.671456i	$-0.234331\pi$
$168$		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	−0.999848	−	0.0174192i	$-0.994455\pi$
$173$	−1.40176	−	6.14152i	−0.106574	−	0.466931i	0.893274	−	0.449512i	$-0.148402\pi$
$174$		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	0.589316	−	0.807902i	$-0.299397\pi$
$179$	10.2984	+	2.35054i	0.769737	+	0.175687i	0.180420	+	0.983590i	$0.442254\pi$
$180$		0			0
$181$	−11.4269	+	9.11265i	−0.849355	+	0.677338i	−0.948168	−	0.317768i	$-0.897067\pi$
$181$	−11.4269	+	9.11265i	−0.849355	+	0.677338i	0.0988136	+	0.995106i	$0.468495\pi$
$182$	−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	−0.840654	−	0.541573i	$-0.817829\pi$
$191$	1.47744	−	3.06794i	0.106904	−	0.221988i	0.947558	+	0.319585i	$0.103543\pi$
$192$		0			0
$193$	−24.4304	−	11.7651i	−1.75854	−	0.846867i	−0.973921	−	0.226886i	$-0.927146\pi$
$193$	−24.4304	−	11.7651i	−1.75854	−	0.846867i	−0.784617	−	0.619981i	$-0.787140\pi$
$194$	−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	$0.117874\pi$
$197$			10.1592i			0.723813i	−0.932214	+	0.361906i	$0.882126\pi$
$198$		0			0
$199$	−0.770780	+	1.60054i	−0.0546391	+	0.113459i	−0.926501	−	0.376293i	$-0.877199\pi$
$199$	−0.770780	+	1.60054i	−0.0546391	+	0.113459i	0.871862	+	0.489752i	$0.162913\pi$
$200$	−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	0.833753	−	0.552137i	$-0.186187\pi$
$211$	1.59686	+	2.00239i	0.109932	+	0.137851i	−0.723821	+	0.689987i	$0.757616\pi$
$212$	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	0.118640	−	0.992937i	$-0.462147\pi$
$223$	9.80139	−	2.23710i	0.656350	−	0.149808i	0.537710	+	0.843130i	$0.319290\pi$
$224$	−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	0.884318	−	0.466886i	$-0.154624\pi$
$229$	−0.485330	−	1.00780i	−0.0320715	−	0.0665971i	−0.916389	+	0.400289i	$0.868910\pi$
$230$	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	−0.580831	−	0.814024i	$-0.697272\pi$
$233$	−22.2452	−	5.07733i	−1.45733	−	0.332627i	−0.876503	+	0.481397i	$0.840130\pi$
$234$		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	0.997878	+	0.0651074i	$0.0207390\pi$
$239$	6.59530	+	13.6953i	0.426614	+	0.885874i	−0.571264	+	0.820766i	$0.693547\pi$
$240$		0			0
$241$	4.66449	−	1.06464i	0.300466	−	0.0685795i	−0.0696299	−	0.997573i	$-0.522182\pi$
$241$	4.66449	−	1.06464i	0.300466	−	0.0685795i	0.370096	+	0.928993i	$0.379325\pi$
$242$	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	−0.686267	−	0.727350i	$-0.740752\pi$
$251$	−8.64206	+	4.16179i	−0.545482	+	0.262690i	0.140785	+	0.990040i	$0.455037\pi$
$252$		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	−0.923120	−	0.384513i	$-0.874369\pi$
$257$	1.20901	−	5.29704i	0.0754162	−	0.330420i	0.998536	+	0.0540927i	$0.0172266\pi$
$258$		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	$0.155557\pi$
$263$			15.2273i			0.938953i	−0.882945	+	0.469476i	$0.844443\pi$
$264$		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	0.701547	−	0.712623i	$-0.252493\pi$
$269$	−2.44899	−	3.07094i	−0.149318	−	0.187238i	−0.850865	+	0.525385i	$0.823921\pi$
$270$		0			0
$271$	23.2419	−	5.30480i	1.41184	−	0.322244i	0.552444	−	0.833550i	$-0.313695\pi$
$271$	23.2419	−	5.30480i	1.41184	−	0.322244i	0.859398	+	0.511307i	$0.170838\pi$
$272$	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	−0.982742	−	0.184984i	$-0.940777\pi$
$277$	−0.283943	+	1.24404i	−0.0170605	+	0.0747470i	0.965681	+	0.259731i	$0.0836339\pi$
$278$	−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	0.499611	−	0.866250i	$-0.333476\pi$
$281$	−3.91830	−	3.12474i	−0.233746	−	0.186406i	−0.733357	+	0.679844i	$0.762048\pi$
$282$		0			0
$283$	12.6385	+	10.0788i	0.751279	+	0.599125i	0.922450	−	0.386116i	$-0.126184\pi$
$283$	12.6385	+	10.0788i	0.751279	+	0.599125i	−0.171171	+	0.985241i	$0.554755\pi$
$284$	−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	0.557042	−	0.830485i	$-0.311936\pi$
$307$	−2.25444	−	1.79785i	−0.128667	−	0.102609i	−0.685709	+	0.727876i	$0.740508\pi$
$308$	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	0.441490	+	0.897266i	$0.354450\pi$
$311$	−6.09451	+	26.7018i	−0.345588	+	1.51412i	−0.787078	+	0.616854i	$0.788407\pi$
$312$		0			0
$313$			24.6969i			1.39595i	0.716121	+	0.697976i	$0.245916\pi$
$313$			24.6969i			1.39595i	−0.716121	+	0.697976i	$0.754084\pi$
$314$	−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	−0.614365	−	0.789022i	$-0.710588\pi$
$317$	−14.6984	+	3.35481i	−0.825544	+	0.188425i	−0.211180	+	0.977447i	$0.567731\pi$
$318$		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	0.812850	+	0.582474i	$0.197915\pi$
$331$	−3.13342	+	13.7284i	−0.172228	+	0.754582i	−0.985078	+	0.172108i	$0.944942\pi$
$332$	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	−0.482269	−	0.876023i	$-0.660187\pi$
$337$	−1.80007	+	0.866866i	−0.0980558	+	0.0472212i	0.384213	+	0.923245i	$0.374473\pi$
$338$	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	0.373012	−	0.927826i	$-0.378325\pi$
$347$	20.7078	−	4.72642i	1.11165	−	0.253728i	0.738641	+	0.674099i	$0.235468\pi$
$348$		0			0
$349$	−6.81637	−	14.1543i	−0.364872	−	0.757664i	0.635018	−	0.772497i	$-0.280993\pi$
$349$	−6.81637	−	14.1543i	−0.364872	−	0.757664i	−0.999890	+	0.0148331i	$0.995278\pi$
$350$	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	−0.759498	−	0.650509i	$-0.774556\pi$
$353$	−13.6112	+	6.55479i	−0.724449	+	0.348876i	0.0350491	+	0.999386i	$0.488841\pi$
$354$		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	0.886034	−	0.463619i	$-0.153450\pi$
$359$	−0.547033	−	1.13592i	−0.0288713	−	0.0599518i	−0.914906	+	0.403668i	$0.867735\pi$
$360$		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	−0.427024	−	0.904240i	$-0.640438\pi$
$367$	6.88746	−	5.49257i	0.359523	−	0.286710i	0.786547	+	0.617530i	$0.211867\pi$
$368$	−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	−0.774567	−	0.632492i	$-0.782032\pi$
$379$	0.280801	−	0.352114i	0.0144238	−	0.0180869i	0.788991	+	0.614405i	$0.210604\pi$
$380$	−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	0.406102	−	0.913828i	$-0.366888\pi$
$383$	−11.2565	−	14.1152i	−0.575180	−	0.721253i	−0.981282	+	0.192575i	$0.938316\pi$
$384$		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	−0.881800	−	0.471623i	$-0.843668\pi$
$389$	0.724287	−	1.50400i	0.0367228	−	0.0762557i	0.918523	+	0.395367i	$0.129383\pi$
$390$		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	−0.967843	−	0.251553i	$-0.919059\pi$
$397$	−3.34201	+	6.93975i	−0.167731	+	0.348296i	0.800113	+	0.599849i	$0.204773\pi$
$398$	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	−0.625819	−	0.779968i	$-0.715235\pi$
$401$	−0.0933946	+	0.0744797i	−0.00466390	+	0.00371934i	0.621155	+	0.783688i	$0.286664\pi$
$402$		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	0.00818811	−	0.999966i	$-0.497394\pi$
$409$	−8.45967	−	1.93086i	−0.418304	−	0.0954751i	−0.426492	+	0.904491i	$0.640251\pi$
$410$		−	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	−0.938007	−	0.346616i	$-0.887331\pi$
$419$	−4.97988	−	21.8183i	−0.243283	−	1.06589i	0.694724	−	0.719276i	$-0.255527\pi$
$420$		0			0
$421$	−3.38186	+	14.8169i	−0.164822	+	0.722131i	0.823192	+	0.567764i	$0.192191\pi$
$421$	−3.38186	+	14.8169i	−0.164822	+	0.722131i	−0.988013	+	0.154368i	$0.950666\pi$
$422$		−	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	0.989372	+	0.145408i	$0.0464496\pi$
$431$	10.0936	+	20.9597i	0.486193	+	1.00959i	−0.503178	+	0.864183i	$0.667836\pi$
$432$		0			0
$433$	4.12640	−	8.56856i	0.198302	−	0.411779i	−0.777977	−	0.628292i	$-0.783754\pi$
$433$	4.12640	−	8.56856i	0.198302	−	0.411779i	0.976280	+	0.216513i	$0.0694685\pi$
$434$	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	0.657629	−	0.753342i	$-0.271560\pi$
$439$	1.45640	+	1.16144i	0.0695101	+	0.0554325i	−0.588118	+	0.808775i	$0.700131\pi$
$440$	−48.5443			−2.31426
$441$		0			0
$442$	−1.14841			−0.0546241
$443$	−21.6172	−	17.2392i	−1.02707	−	0.819057i	−0.0433990	−	0.999058i	$-0.513819\pi$
$443$	−21.6172	−	17.2392i	−1.02707	−	0.819057i	−0.983667	+	0.180000i	$0.942390\pi$
$444$		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	−0.925827	−	0.377947i	$-0.876630\pi$
$449$	−1.12501	+	2.33611i	−0.0530926	+	0.110248i	0.872735	+	0.488195i	$0.162344\pi$
$450$		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	−0.793248	−	0.608899i	$-0.791611\pi$
$457$	−17.3537	+	8.35711i	−0.811773	+	0.390929i	−0.0185252	+	0.999828i	$0.505897\pi$
$458$	−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	0.859258	+	0.511543i	$0.170926\pi$
$461$	−2.93845	+	12.8742i	−0.136857	+	0.599610i	−0.996115	+	0.0880666i	$0.971931\pi$
$462$		0			0
$463$	5.06271	+	22.1812i	0.235284	+	1.03085i	0.945182	+	0.326543i	$0.105884\pi$
$463$	5.06271	+	22.1812i	0.235284	+	1.03085i	−0.709898	+	0.704304i	$0.751259\pi$
$464$	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	0.999993	−	0.00381464i	$-0.00121424\pi$
$467$	2.10430	+	9.21953i	0.0973753	+	0.426629i	−0.902617	+	0.430444i	$0.858357\pi$
$468$		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	0.211693	+	0.977336i	$0.432102\pi$
$479$	−17.2516	+	21.6328i	−0.788246	+	0.988429i	−0.999938	+	0.0110924i	$0.996469\pi$
$480$		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	0.999921	−	0.0125691i	$-0.00400099\pi$
$487$	35.6076	+	17.1477i	1.61353	+	0.777037i	0.613614	+	0.789606i	$0.289715\pi$
$488$	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	$0.0598012\pi$
$491$			8.27699i			0.373535i	−0.982404	+	0.186768i	$0.940199\pi$
$492$		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	0.698428	−	0.715681i	$-0.253883\pi$
$499$	−3.45628	−	4.33403i	−0.154724	−	0.194018i	−0.853152	+	0.521663i	$0.825312\pi$
$500$	−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	−0.990257	−	0.139255i	$-0.955529\pi$
$503$	−14.2223	+	17.8342i	−0.634141	+	0.795187i	0.356116	+	0.934442i	$0.384101\pi$
$504$		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	−0.899142	−	0.437657i	$-0.855808\pi$
$523$	−15.5673	−	32.3258i	−0.680710	−	1.41351i	0.218432	−	0.975852i	$-0.429906\pi$
$524$	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	−0.703466	−	0.710729i	$-0.748365\pi$
$541$	3.39539	−	4.25769i	0.145979	−	0.183052i	0.849445	+	0.527677i	$0.176937\pi$
$542$	−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	0.291240	−	0.956650i	$-0.405932\pi$
$547$	−6.43439	−	3.09864i	−0.275115	−	0.132488i	−0.566354	+	0.824162i	$0.691647\pi$
$548$	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	$0.303782\pi$
$557$			38.5139i			1.63189i	−0.578131	+	0.815944i	$0.696218\pi$
$558$		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	−0.984888	−	0.173195i	$-0.944591\pi$
$563$	−22.1754	−	27.8071i	−0.934582	−	1.17193i	0.0503056	−	0.998734i	$-0.483980\pi$
$564$		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	$0.122909\pi$
$569$			17.9670i			0.753215i	−0.926373	+	0.376607i	$0.877091\pi$
$570$		0			0
$571$	−1.78530	+	7.82192i	−0.0747125	+	0.327337i	−0.998448	−	0.0556944i	$-0.982263\pi$
$571$	−1.78530	+	7.82192i	−0.0747125	+	0.327337i	0.923735	+	0.383031i	$0.125120\pi$
$572$	−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	0.979502	−	0.201433i	$-0.0645599\pi$
$577$	24.0467	+	19.1766i	1.00108	+	0.798334i	0.0215767	+	0.999767i	$0.493131\pi$
$578$	−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	0.550123	−	0.835084i	$-0.314581\pi$
$593$	5.84985	+	2.81714i	0.240224	+	0.115686i	−0.309899	+	0.950770i	$0.600295\pi$
$594$		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	0.910468	−	0.413580i	$-0.135722\pi$
$599$	17.3733	+	13.8548i	0.709855	+	0.566090i	−0.200613	+	0.979671i	$0.564293\pi$
$600$		0			0
$601$	1.77391	+	1.41465i	0.0723593	+	0.0577046i	0.659001	−	0.752142i	$-0.270979\pi$
$601$	1.77391	+	1.41465i	0.0723593	+	0.0577046i	−0.586642	+	0.809846i	$0.699551\pi$
$602$	−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	$0.0726154\pi$
$607$			11.1437i			0.452309i	−0.974091	+	0.226155i	$0.927385\pi$
$608$	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	0.971954	−	0.235171i	$-0.0755650\pi$
$613$	13.0330	+	16.3429i	0.526399	+	0.660084i	−0.445555	+	0.895255i	$0.646994\pi$
$614$	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	−0.651728	−	0.758453i	$-0.725955\pi$
$617$	−38.9482	−	8.88967i	−1.56799	−	0.357884i	−0.916267	+	0.400569i	$0.868813\pi$
$618$		0			0
$619$			30.9056i			1.24220i	0.783730	+	0.621101i	$0.213315\pi$
$619$			30.9056i			1.24220i	−0.783730	+	0.621101i	$0.786685\pi$
$620$	−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	0.488068	−	0.872806i	$-0.337702\pi$
$631$	37.0455	−	17.8402i	1.47476	−	0.710207i	0.986692	+	0.162599i	$0.0519877\pi$
$632$	−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	−0.0294344	−	0.999567i	$-0.509371\pi$
$641$	9.56366	−	2.18284i	0.377742	−	0.0862171i	0.407176	+	0.913350i	$0.366513\pi$
$642$		0			0
$643$	5.92252	+	12.2982i	0.233561	+	0.484995i	0.984502	−	0.175375i	$-0.0561138\pi$
$643$	5.92252	+	12.2982i	0.233561	+	0.484995i	−0.750940	+	0.660370i	$0.770399\pi$
$644$	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	−0.649310	−	0.760524i	$-0.724942\pi$
$647$	−11.6891	+	5.62917i	−0.459546	+	0.221306i	0.189764	+	0.981830i	$0.439228\pi$
$648$		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	0.935399	−	0.353593i	$-0.115040\pi$
$653$	1.93538	+	4.01886i	0.0757374	+	0.157270i	−0.859662	+	0.510863i	$0.829326\pi$
$654$		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	0.412551	−	0.910934i	$-0.364638\pi$
$659$	30.2786	−	6.91089i	1.17949	−	0.269210i	0.766935	+	0.641724i	$0.221781\pi$
$660$		0			0
$661$	12.1178	−	9.66364i	0.471329	−	0.375872i	−0.358827	−	0.933404i	$-0.616823\pi$
$661$	12.1178	−	9.66364i	0.471329	−	0.375872i	0.830155	+	0.557532i	$0.188252\pi$
$662$	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	−0.690796	−	0.723050i	$-0.742740\pi$
$673$	4.35420	−	5.46000i	0.167842	−	0.210467i	0.858638	+	0.512582i	$0.171311\pi$
$674$	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	0.344967	−	0.938615i	$-0.387890\pi$
$677$	−16.8312	−	21.1057i	−0.646877	−	0.811158i	−0.991844	+	0.127457i	$0.959319\pi$
$678$		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	−0.871583	−	0.490248i	$-0.836906\pi$
$683$	1.44083	−	2.99191i	0.0551318	−	0.114482i	0.926715	+	0.375766i	$0.122620\pi$
$684$		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	−0.489928	−	0.871763i	$-0.662977\pi$
$691$	13.0674	−	27.1348i	0.497109	−	1.03226i	0.987037	−	0.160495i	$-0.0513090\pi$
$692$	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	−0.484427	+	0.874831i	$0.660972\pi$
$701$	−38.2616	+	30.5126i	−1.44512	+	1.15244i	−0.960693	+	0.277614i	$0.910457\pi$
$702$		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	−0.985980	−	0.166864i	$-0.946636\pi$
$709$	−4.52772	−	19.8372i	−0.170042	−	0.745003i	0.815938	−	0.578140i	$-0.196221\pi$
$710$	−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	−0.0866100	−	0.996242i	$-0.527603\pi$
$719$	17.1150	−	8.24217i	0.638283	−	0.307381i	0.724893	+	0.688861i	$0.241889\pi$
$720$		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	−0.951117	−	0.308832i	$-0.900062\pi$
$727$	−3.14524	+	6.53117i	−0.116651	+	0.242228i	0.834466	+	0.551059i	$0.185776\pi$
$728$	−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	0.807368	−	0.590048i	$-0.200891\pi$
$733$	11.1482	+	8.89042i	0.411770	+	0.328375i	−0.395598	+	0.918424i	$0.629463\pi$
$734$	−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	−0.603430	−	0.797416i	$-0.706200\pi$
$739$	−11.0300	−	48.3255i	−0.405744	−	1.77768i	0.197686	−	0.980265i	$-0.436657\pi$
$740$	−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	0.563234	+	0.826297i	$0.309557\pi$
$743$	−11.8289	+	24.5630i	−0.433962	+	0.901131i	−0.997196	+	0.0748335i	$0.976157\pi$
$744$		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	−0.0311220	−	0.999516i	$-0.509908\pi$
$751$	20.0306	−	9.64622i	0.730926	−	0.351996i	0.762048	+	0.647520i	$0.224194\pi$
$752$	−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	0.849713	+	0.527246i	$0.176775\pi$
$757$	8.60933	+	37.7200i	0.312912	+	1.37096i	−0.536801	+	0.843709i	$0.680367\pi$
$758$	−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	0.984837	−	0.173483i	$-0.0555023\pi$
$761$	0.614011	+	2.69016i	0.0222579	+	0.0975181i	−0.962579	+	0.271002i	$0.912645\pi$
$762$		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	−0.742402	−	0.669955i	$-0.766313\pi$
$769$	−7.05593	+	5.62692i	−0.254443	+	0.202912i	0.487958	+	0.872867i	$0.337742\pi$
$770$	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	0.158683	−	0.987330i	$-0.449275\pi$
$773$	30.1925	−	37.8602i	1.08595	−	1.36174i	0.927265	−	0.374406i	$-0.122153\pi$
$774$		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	−

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 $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(-2.13317 - 1.70115i) q^{2} +(1.21148 + 5.30783i) q^{4} +(-1.31998 - 0.635668i) q^{5} +(-0.795783 - 2.52324i) q^{7} +(4.07748 - 8.46697i) q^{8} +O(q^{10})\)	\(q+(-2.13317 - 1.70115i) q^{2} +(1.21148 + 5.30783i) q^{4} +(-1.31998 - 0.635668i) q^{5} +(-0.795783 - 2.52324i) q^{7} +(4.07748 - 8.46697i) q^{8} +(1.73438 + 3.60147i) q^{10} +(2.75661 + 2.19832i) q^{11} +(4.51813 + 3.60309i) q^{13} +(-2.59486 + 6.73625i) q^{14} +(-13.2912 + 6.40071i) q^{16} +(0.0162072 - 0.0710083i) q^{17} -4.52011i q^{19} +(1.77490 - 7.77633i) q^{20} +(-2.14065 - 9.37881i) q^{22} +(1.76402 - 0.402626i) q^{23} +(-1.77918 - 2.23102i) q^{25} +(-3.50857 - 15.3720i) q^{26} +(12.4289 - 7.28073i) q^{28} +(-2.61910 - 0.597792i) q^{29} -7.13274i q^{31} +(20.9170 + 4.77416i) q^{32} +(-0.155368 + 0.123902i) q^{34} +(-0.553525 + 3.83647i) q^{35} +(1.33034 - 5.82860i) q^{37} +(-7.68938 + 9.64217i) q^{38} +(-10.7644 + 8.58430i) q^{40} +(-11.3454 - 5.46367i) q^{41} +(-1.31339 + 0.632493i) q^{43} +(-8.32876 + 17.2949i) q^{44} +(-4.44789 - 2.14199i) q^{46} +(5.84471 - 7.32903i) q^{47} +(-5.73346 + 4.01590i) q^{49} +7.78580i q^{50} +(-13.6510 + 28.3466i) q^{52} +(9.10665 - 2.07853i) q^{53} +(-2.24126 - 4.65403i) q^{55} +(-24.6090 - 3.55058i) q^{56} +(4.57005 + 5.73067i) q^{58} +(0.107203 - 0.0516262i) q^{59} +(3.20130 + 0.730676i) q^{61} +(-12.1339 + 15.2154i) q^{62} +(-18.1023 - 22.6996i) q^{64} +(-3.67347 - 7.62804i) q^{65} +5.78127 q^{67} +0.396535 q^{68} +(7.70718 - 7.24224i) q^{70} +(-0.0872291 + 0.0199095i) q^{71} +(3.43319 - 2.73788i) q^{73} +(-12.7532 + 10.1703i) q^{74} +(23.9920 - 5.47601i) q^{76} +(3.35323 - 8.70497i) q^{77} -2.89253 q^{79} +21.6128 q^{80} +(14.9073 + 30.9552i) q^{82} +(-0.251403 - 0.315250i) q^{83} +(-0.0665309 + 0.0834271i) q^{85} +(3.87765 + 0.885047i) q^{86} +(29.8532 - 14.3765i) q^{88} +(6.88377 + 8.63197i) q^{89} +(5.49600 - 14.2676i) q^{91} +(4.27415 + 8.87536i) q^{92} +(-24.9355 + 5.69137i) q^{94} +(-2.87329 + 5.96645i) q^{95} -14.7498i q^{97} +(19.0621 + 1.18685i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 120 q + 24 q^{4}+O(q^{10}) \) 120 * q + 24 * q^4	\( 120 q + 24 q^{4} - 32 q^{16} - 44 q^{22} - 4 q^{25} - 56 q^{28} + 112 q^{34} - 76 q^{37} + 28 q^{40} + 8 q^{43} - 40 q^{46} - 84 q^{49} - 140 q^{52} + 12 q^{58} - 84 q^{61} + 24 q^{64} + 16 q^{67} + 112 q^{70} - 84 q^{76} - 24 q^{79} + 140 q^{82} - 96 q^{85} - 24 q^{88} - 112 q^{91} - 112 q^{94}+O(q^{100}) \) 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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