LMFDB - Embedded newform 720.2.u.a.179.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [720,2,Mod(179,720)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(720, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 3, 2, 2]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("720.179");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 720 = 2^{4} \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	720.u (of order $4$, degree $2$, 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:	$5.74922894553$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$48$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			179.20
Character	$\chi$	$=$	720.179
Dual form			720.2.u.a.539.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.581659 + 1.28906i) q^{2} +(-1.32335 - 1.49958i) q^{4} +(0.0342493 + 2.23581i) q^{5} -4.97879i q^{7} +(2.70279 - 0.833625i) q^{8} +(-2.90201 - 1.25633i) q^{10} +(0.299629 - 0.299629i) q^{11} +(-3.41391 + 3.41391i) q^{13} +(6.41795 + 2.89596i) q^{14} +(-0.497509 + 3.96894i) q^{16} -5.22586 q^{17} +(-3.58000 + 3.58000i) q^{19} +(3.30746 - 3.01011i) q^{20} +(0.211957 + 0.560520i) q^{22} -6.15703 q^{23} +(-4.99765 + 0.153150i) q^{25} +(-2.41500 - 6.38646i) q^{26} +(-7.46612 + 6.58866i) q^{28} +(-3.26048 + 3.26048i) q^{29} -7.77031i q^{31} +(-4.82682 - 2.94989i) q^{32} +(3.03966 - 6.73644i) q^{34} +(11.1316 - 0.170520i) q^{35} +(2.27648 + 2.27648i) q^{37} +(-2.53249 - 6.69716i) q^{38} +(1.95639 + 6.01436i) q^{40} +7.32246 q^{41} +(1.76594 - 1.76594i) q^{43} +(-0.845831 - 0.0528060i) q^{44} +(3.58129 - 7.93678i) q^{46} +1.69344i q^{47} -17.7884 q^{49} +(2.70951 - 6.53135i) q^{50} +(9.63723 + 0.601662i) q^{52} +(2.95155 - 2.95155i) q^{53} +(0.680173 + 0.659649i) q^{55} +(-4.15045 - 13.4566i) q^{56} +(-2.30646 - 6.09944i) q^{58} +(-4.14389 + 4.14389i) q^{59} +(-9.38240 - 9.38240i) q^{61} +(10.0164 + 4.51967i) q^{62} +(6.61014 - 4.50623i) q^{64} +(-7.74976 - 7.51592i) q^{65} +(-0.0409648 - 0.0409648i) q^{67} +(6.91562 + 7.83661i) q^{68} +(-6.25499 + 14.4485i) q^{70} +4.96779i q^{71} +3.87421 q^{73} +(-4.25865 + 1.61038i) q^{74} +(10.1061 + 0.630932i) q^{76} +(-1.49179 - 1.49179i) q^{77} -0.521248i q^{79} +(-8.89082 - 0.976399i) q^{80} +(-4.25917 + 9.43908i) q^{82} +(-9.49013 + 9.49013i) q^{83} +(-0.178982 - 11.6840i) q^{85} +(1.24923 + 3.30358i) q^{86} +(0.560055 - 1.05961i) q^{88} +3.52625 q^{89} +(16.9971 + 16.9971i) q^{91} +(8.14788 + 9.23299i) q^{92} +(-2.18294 - 0.985002i) q^{94} +(-8.12679 - 7.88156i) q^{95} -3.30729i q^{97} +(10.3467 - 22.9302i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q - 8 q^{16} - 16 q^{19} + 72 q^{34} + 8 q^{40} + 8 q^{46} - 96 q^{49} + 64 q^{55} - 32 q^{61} + 48 q^{64} + 24 q^{70} + 40 q^{76} - 88 q^{94}+O(q^{100}) $ 96 * q - 8 * q^16 - 16 * q^19 + 72 * q^34 + 8 * q^40 + 8 * q^46 - 96 * q^49 + 64 * q^55 - 32 * q^61 + 48 * q^64 + 24 * q^70 + 40 * q^76 - 88 * q^94

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/720\mathbb{Z}\right)^\times$.

$n$	$181$	$271$	$577$	$641$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$-1$	$-1$	$-1$

Coefficient data

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

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

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

$2$	−0.581659	+	1.28906i	−0.411295	+	0.911502i
$2$	−0.581659	+	1.28906i	−0.411295	+	0.911502i
$3$		0			0
$3$		0			0
$4$	−1.32335	−	1.49958i	−0.661673	−	0.749792i
$5$	0.0342493	+	2.23581i	0.0153168	+	0.999883i
$5$	0.0342493	+	2.23581i	0.0153168	+	0.999883i
$6$		0			0
$7$		−	4.97879i		−	1.88181i	−0.338676	−	0.940903i	$-0.609979\pi$
$7$		−	4.97879i		−	1.88181i	0.338676	−	0.940903i	$-0.390021\pi$
$8$	2.70279	−	0.833625i	0.955580	−	0.294731i
$9$		0			0
$10$	−2.90201	−	1.25633i	−0.917695	−	0.397285i
$11$	0.299629	−	0.299629i	0.0903414	−	0.0903414i	−0.660492	−	0.750833i	$-0.729652\pi$
$11$	0.299629	−	0.299629i	0.0903414	−	0.0903414i	0.750833	+	0.660492i	$0.229652\pi$
$12$		0			0
$13$	−3.41391	+	3.41391i	−0.946848	+	0.946848i	−0.998657	−	0.0518087i	$-0.983501\pi$
$13$	−3.41391	+	3.41391i	−0.946848	+	0.946848i	0.0518087	+	0.998657i	$0.483501\pi$
$14$	6.41795	+	2.89596i	1.71527	+	0.773977i
$15$		0			0
$16$	−0.497509	+	3.96894i	−0.124377	+	0.992235i
$17$	−5.22586			−1.26746			−0.633728	−	0.773556i	$-0.718476\pi$
$17$	−5.22586			−1.26746			−0.633728	+	0.773556i	$0.718476\pi$
$18$		0			0
$19$	−3.58000	+	3.58000i	−0.821307	+	0.821307i	−0.986296	−	0.164988i	$-0.947241\pi$
$19$	−3.58000	+	3.58000i	−0.821307	+	0.821307i	0.164988	+	0.986296i	$0.447241\pi$
$20$	3.30746	−	3.01011i	0.739570	−	0.673080i
$21$		0			0
$22$	0.211957	+	0.560520i	0.0451895	+	0.119503i
$23$	−6.15703			−1.28383			−0.641915	−	0.766776i	$-0.721860\pi$
$23$	−6.15703			−1.28383			−0.641915	+	0.766776i	$0.721860\pi$
$24$		0			0
$25$	−4.99765	+	0.153150i	−0.999531	+	0.0306300i
$26$	−2.41500	−	6.38646i	−0.473621	−	1.25249i
$27$		0			0
$28$	−7.46612	+	6.58866i	−1.41096	+	1.24514i
$29$	−3.26048	+	3.26048i	−0.605456	+	0.605456i	−0.941755	−	0.336299i	$-0.890825\pi$
$29$	−3.26048	+	3.26048i	−0.605456	+	0.605456i	0.336299	+	0.941755i	$0.390825\pi$
$30$		0			0
$31$		−	7.77031i		−	1.39559i	−0.716298	−	0.697795i	$-0.754165\pi$
$31$		−	7.77031i		−	1.39559i	0.716298	−	0.697795i	$-0.245835\pi$
$32$	−4.82682	−	2.94989i	−0.853269	−	0.521471i
$33$		0			0
$34$	3.03966	−	6.73644i	0.521298	−	1.15529i
$35$	11.1316	−	0.170520i	1.88159	−	0.0288232i
$36$		0			0
$37$	2.27648	+	2.27648i	0.374251	+	0.374251i	0.869023	−	0.494772i	$-0.164748\pi$
$37$	2.27648	+	2.27648i	0.374251	+	0.374251i	−0.494772	+	0.869023i	$0.664748\pi$
$38$	−2.53249	−	6.69716i	−0.410824	−	1.08642i
$39$		0			0
$40$	1.95639	+	6.01436i	0.309333	+	0.950954i
$41$	7.32246			1.14358			0.571788	−	0.820401i	$-0.306250\pi$
$41$	7.32246			1.14358			0.571788	+	0.820401i	$0.306250\pi$
$42$		0			0
$43$	1.76594	−	1.76594i	0.269304	−	0.269304i	−0.559516	−	0.828820i	$-0.689013\pi$
$43$	1.76594	−	1.76594i	0.269304	−	0.269304i	0.828820	+	0.559516i	$0.189013\pi$
$44$	−0.845831	−	0.0528060i	−0.127514	−	0.00796081i
$45$		0			0
$46$	3.58129	−	7.93678i	0.528032	−	1.17021i
$47$			1.69344i			0.247013i	0.992344	+	0.123507i	$0.0394140\pi$
$47$			1.69344i			0.247013i	−0.992344	+	0.123507i	$0.960586\pi$
$48$		0			0
$49$	−17.7884			−2.54119
$50$	2.70951	−	6.53135i	0.383183	−	0.923673i
$51$		0			0
$52$	9.63723	+	0.601662i	1.33644	+	0.0834355i
$53$	2.95155	−	2.95155i	0.405427	−	0.405427i	−0.474714	−	0.880140i	$-0.657448\pi$
$53$	2.95155	−	2.95155i	0.405427	−	0.405427i	0.880140	+	0.474714i	$0.157448\pi$
$54$		0			0
$55$	0.680173	+	0.659649i	0.0917145	+	0.0889471i
$56$	−4.15045	−	13.4566i	−0.554627	−	1.79822i
$57$		0			0
$58$	−2.30646	−	6.09944i	−0.302854	−	0.800895i
$59$	−4.14389	+	4.14389i	−0.539489	+	0.539489i	−0.923379	−	0.383890i	$-0.874584\pi$
$59$	−4.14389	+	4.14389i	−0.539489	+	0.539489i	0.383890	+	0.923379i	$0.374584\pi$
$60$		0			0
$61$	−9.38240	−	9.38240i	−1.20129	−	1.20129i	−0.973773	−	0.227520i	$-0.926938\pi$
$61$	−9.38240	−	9.38240i	−1.20129	−	1.20129i	−0.227520	−	0.973773i	$-0.573062\pi$
$62$	10.0164	+	4.51967i	1.27208	+	0.573999i
$63$		0			0
$64$	6.61014	−	4.50623i	0.826267	−	0.563278i
$65$	−7.74976	−	7.51592i	−0.961240	−	0.932235i
$66$		0			0
$67$	−0.0409648	−	0.0409648i	−0.00500465	−	0.00500465i	0.704600	−	0.709605i	$-0.251126\pi$
$67$	−0.0409648	−	0.0409648i	−0.00500465	−	0.00500465i	−0.709605	+	0.704600i	$0.751126\pi$
$68$	6.91562	+	7.83661i	0.838642	+	0.950329i
$69$		0			0
$70$	−6.25499	+	14.4485i	−0.747614	+	1.72692i
$71$			4.96779i			0.589568i	0.955564	+	0.294784i	$0.0952477\pi$
$71$			4.96779i			0.589568i	−0.955564	+	0.294784i	$0.904752\pi$
$72$		0			0
$73$	3.87421			0.453442			0.226721	−	0.973960i	$-0.427199\pi$
$73$	3.87421			0.453442			0.226721	+	0.973960i	$0.427199\pi$
$74$	−4.25865	+	1.61038i	−0.495058	+	0.187203i
$75$		0			0
$76$	10.1061	+	0.630932i	1.15925	+	0.0723729i
$77$	−1.49179	−	1.49179i	−0.170005	−	0.170005i
$78$		0			0
$79$		−	0.521248i		−	0.0586450i	−0.999570	−	0.0293225i	$-0.990665\pi$
$79$		−	0.521248i		−	0.0586450i	0.999570	−	0.0293225i	$-0.00933498\pi$
$80$	−8.89082	−	0.976399i	−0.994024	−	0.109165i
$81$		0			0
$82$	−4.25917	+	9.43908i	−0.470347	+	1.04237i
$83$	−9.49013	+	9.49013i	−1.04168	+	1.04168i	−0.0425846	+	0.999093i	$0.513559\pi$
$83$	−9.49013	+	9.49013i	−1.04168	+	1.04168i	−0.999093	+	0.0425846i	$0.986441\pi$
$84$		0			0
$85$	−0.178982	−	11.6840i	−0.0194133	−	1.26731i
$86$	1.24923	+	3.30358i	0.134708	+	0.356234i
$87$		0			0
$88$	0.560055	−	1.05961i	0.0597020	−	0.112955i
$89$	3.52625			0.373782			0.186891	−	0.982381i	$-0.440159\pi$
$89$	3.52625			0.373782			0.186891	+	0.982381i	$0.440159\pi$
$90$		0			0
$91$	16.9971	+	16.9971i	1.78178	+	1.78178i
$92$	8.14788	+	9.23299i	0.849476	+	0.962606i
$93$		0			0
$94$	−2.18294	−	0.985002i	−0.225153	−	0.101595i
$95$	−8.12679	−	7.88156i	−0.833791	−	0.808631i
$96$		0			0
$97$		−	3.30729i		−	0.335805i	−0.985804	−	0.167902i	$-0.946301\pi$
$97$		−	3.30729i		−	0.335805i	0.985804	−	0.167902i	$-0.0536993\pi$
$98$	10.3467	−	22.9302i	1.04518	−	2.31630i
$99$		0			0
$100$	6.84329	+	7.29174i	0.684329	+	0.729174i
$101$	−7.55836	−	7.55836i	−0.752085	−	0.752085i	0.222783	−	0.974868i	$-0.428486\pi$
$101$	−7.55836	−	7.55836i	−0.752085	−	0.752085i	−0.974868	+	0.222783i	$0.928486\pi$
$102$		0			0
$103$		−	13.0592i		−	1.28676i	−0.765546	−	0.643381i	$-0.777531\pi$
$103$		−	13.0592i		−	1.28676i	0.765546	−	0.643381i	$-0.222469\pi$
$104$	−6.38116	+	12.0730i	−0.625724	+	1.18386i
$105$		0			0
$106$	2.08793	+	5.52152i	0.202797	+	0.536297i
$107$	7.46283	+	7.46283i	0.721459	+	0.721459i	0.968902	−	0.247443i	$-0.0795904\pi$
$107$	7.46283	+	7.46283i	0.721459	+	0.721459i	−0.247443	+	0.968902i	$0.579590\pi$
$108$		0			0
$109$	3.43459	+	3.43459i	0.328974	+	0.328974i	0.852196	−	0.523222i	$-0.175270\pi$
$109$	3.43459	+	3.43459i	0.328974	+	0.328974i	−0.523222	+	0.852196i	$0.675270\pi$
$110$	−1.24596	+	0.493093i	−0.118797	+	0.0470146i
$111$		0			0
$112$	19.7605	+	2.47699i	1.86719	+	0.234054i
$113$	−5.42433			−0.510278			−0.255139	−	0.966904i	$-0.582121\pi$
$113$	−5.42433			−0.510278			−0.255139	+	0.966904i	$0.582121\pi$
$114$		0			0
$115$	−0.210874	−	13.7659i	−0.0196641	−	1.28368i
$116$	9.20411	+	0.574621i	0.854580	+	0.0533523i
$117$		0			0
$118$	−2.93139	−	7.75205i	−0.269856	−	0.713634i
$119$			26.0184i			2.38511i
$120$		0			0
$121$			10.8204i			0.983677i
$122$	17.5518	−	6.63712i	1.58907	−	0.600896i
$123$		0			0
$124$	−11.6522	+	10.2828i	−1.04640	+	0.923424i
$125$	−0.513580	−	11.1685i	−0.0459359	−	0.998944i
$126$		0			0
$127$	9.57690			0.849813			0.424906	−	0.905237i	$-0.360307\pi$
$127$	9.57690			0.849813			0.424906	+	0.905237i	$0.360307\pi$
$128$	1.96395	+	11.1419i	0.173590	+	0.984818i
$129$		0			0
$130$	14.1962	−	5.61821i	1.24509	−	0.492749i
$131$	−12.5044	−	12.5044i	−1.09252	−	1.09252i	−0.995259	−	0.0972558i	$-0.968994\pi$
$131$	−12.5044	−	12.5044i	−1.09252	−	1.09252i	−0.0972558	−	0.995259i	$-0.531006\pi$
$132$		0			0
$133$	17.8241	+	17.8241i	1.54554	+	1.54554i
$134$	0.0766335	−	0.0289785i	0.00662013	−	0.00250336i
$135$		0			0
$136$	−14.1244	+	4.35640i	−1.21116	+	0.373559i
$137$			3.21459i			0.274641i	0.990527	+	0.137320i	$0.0438490\pi$
$137$			3.21459i			0.274641i	−0.990527	+	0.137320i	$0.956151\pi$
$138$		0			0
$139$	−0.728605	−	0.728605i	−0.0617994	−	0.0617994i	0.675532	−	0.737331i	$-0.263914\pi$
$139$	−0.728605	−	0.728605i	−0.0617994	−	0.0617994i	−0.737331	+	0.675532i	$0.763914\pi$
$140$	−14.9867	−	16.4671i	−1.26661	−	1.39173i
$141$		0			0
$142$	−6.40377	−	2.88956i	−0.537392	−	0.242486i
$143$			2.04581i			0.171079i
$144$		0			0
$145$	−7.40147	−	7.17813i	−0.614658	−	0.596111i
$146$	−2.25347	+	4.99409i	−0.186498	+	0.413314i
$147$		0			0
$148$	0.401203	−	6.42634i	0.0329787	−	0.528242i
$149$	−3.90021	−	3.90021i	−0.319518	−	0.319518i	0.529064	−	0.848582i	$-0.322543\pi$
$149$	−3.90021	−	3.90021i	−0.319518	−	0.319518i	−0.848582	+	0.529064i	$0.822543\pi$
$150$		0			0
$151$	2.48795			0.202467			0.101233	−	0.994863i	$-0.467721\pi$
$151$	2.48795			0.202467			0.101233	+	0.994863i	$0.467721\pi$
$152$	−6.69160	+	12.6603i	−0.542760	+	1.02689i
$153$		0			0
$154$	2.79071	−	1.05529i	0.224882	−	0.0850378i
$155$	17.3729	−	0.266128i	1.39543	−	0.0213759i
$156$		0			0
$157$	6.88372	−	6.88372i	0.549380	−	0.549380i	−0.376881	−	0.926262i	$-0.623003\pi$
$157$	6.88372	−	6.88372i	0.549380	−	0.549380i	0.926262	+	0.376881i	$0.123003\pi$
$158$	0.671920	+	0.303189i	0.0534551	+	0.0241204i
$159$		0			0
$160$	6.43006	−	10.8929i	0.508341	−	0.861156i
$161$			30.6546i			2.41592i
$162$		0			0
$163$	−0.954196	−	0.954196i	−0.0747384	−	0.0747384i	0.668749	−	0.743488i	$-0.266830\pi$
$163$	−0.954196	−	0.954196i	−0.0747384	−	0.0747384i	−0.743488	+	0.668749i	$0.766830\pi$
$164$	−9.69015	−	10.9806i	−0.756674	−	0.857445i
$165$		0			0
$166$	−6.71332	−	17.7534i	−0.521055	−	1.37793i
$167$	9.73397			0.753237			0.376619	−	0.926368i	$-0.377087\pi$
$167$	9.73397			0.753237			0.376619	+	0.926368i	$0.377087\pi$
$168$		0			0
$169$		−	10.3096i		−	0.793044i
$170$	15.1655	+	6.56538i	1.16314	+	0.503542i
$171$		0			0
$172$	−4.98514	−	0.311227i	−0.380113	−	0.0237308i
$173$	−7.85395	−	7.85395i	−0.597125	−	0.597125i	0.342421	−	0.939546i	$-0.388753\pi$
$173$	−7.85395	−	7.85395i	−0.597125	−	0.597125i	−0.939546	+	0.342421i	$0.888753\pi$
$174$		0			0
$175$	0.762501	+	24.8823i	0.0576396	+	1.88092i
$176$	1.04014	+	1.33828i	0.0784035	+	0.100876i
$177$		0			0
$178$	−2.05107	+	4.54554i	−0.153734	+	0.340703i
$179$	9.13459	+	9.13459i	0.682751	+	0.682751i	0.960619	−	0.277868i	$-0.0896278\pi$
$179$	9.13459	+	9.13459i	0.682751	+	0.682751i	−0.277868	+	0.960619i	$0.589628\pi$
$180$		0			0
$181$	−15.9005	+	15.9005i	−1.18188	+	1.18188i	−0.202621	+	0.979257i	$0.564946\pi$
$181$	−15.9005	+	15.9005i	−1.18188	+	1.18188i	−0.979257	+	0.202621i	$0.935054\pi$
$182$	−31.7969	+	12.0238i	−2.35694	+	0.891262i
$183$		0			0
$184$	−16.6412	+	5.13266i	−1.22680	+	0.378384i
$185$	−5.01180	+	5.16773i	−0.368475	+	0.379939i
$186$		0			0
$187$	−1.56582	+	1.56582i	−0.114504	+	0.114504i
$188$	2.53945	−	2.24100i	0.185209	−	0.163442i
$189$		0			0
$190$	14.8868	−	5.89153i	1.08000	−	0.427417i
$191$	2.16753			0.156837			0.0784183	−	0.996921i	$-0.475013\pi$
$191$	2.16753			0.156837			0.0784183	+	0.996921i	$0.475013\pi$
$192$		0			0
$193$			23.0521i			1.65932i	0.558265	+	0.829662i	$0.311467\pi$
$193$			23.0521i			1.65932i	−0.558265	+	0.829662i	$0.688533\pi$
$194$	4.26329	+	1.92371i	0.306087	+	0.138115i
$195$		0			0
$196$	23.5402	+	26.6751i	1.68144	+	1.90537i
$197$	1.52767	−	1.52767i	0.108842	−	0.108842i	−0.650588	−	0.759431i	$-0.725478\pi$
$197$	1.52767	−	1.52767i	0.108842	−	0.108842i	0.759431	+	0.650588i	$0.225478\pi$
$198$		0			0
$199$	−3.12757			−0.221708			−0.110854	−	0.993837i	$-0.535359\pi$
$199$	−3.12757			−0.221708			−0.110854	+	0.993837i	$0.535359\pi$
$200$	−13.3799	+	4.58010i	−0.946104	+	0.323862i
$201$		0			0
$202$	14.1396	−	5.34678i	0.994855	−	0.376198i
$203$	16.2332	+	16.2332i	1.13935	+	1.13935i
$204$		0			0
$205$	0.250789	+	16.3716i	0.0175159	+	1.14344i
$206$	16.8341	+	7.59600i	1.17289	+	0.529239i
$207$		0			0
$208$	−11.8512	−	15.2481i	−0.821730	−	1.05726i
$209$			2.14534i			0.148396i
$210$		0			0
$211$	2.66344	−	2.66344i	0.183359	−	0.183359i	−0.609459	−	0.792818i	$-0.708613\pi$
$211$	2.66344	−	2.66344i	0.183359	−	0.183359i	0.792818	+	0.609459i	$0.208613\pi$
$212$	−8.33202	−	0.520176i	−0.572246	−	0.0357259i
$213$		0			0
$214$	−13.9608	+	5.27921i	−0.954344	+	0.360879i
$215$	4.00879	+	3.88782i	0.273397	+	0.265147i
$216$		0			0
$217$	−38.6868			−2.62623
$218$	−6.42515	+	2.42963i	−0.435166	+	0.164555i
$219$		0			0
$220$	0.0890949	−	1.89292i	0.00600677	−	0.127621i
$221$	17.8406	−	17.8406i	1.20009	−	1.20009i
$222$		0			0
$223$	22.8494			1.53011			0.765053	−	0.643967i	$-0.222713\pi$
$223$	22.8494			1.53011			0.765053	+	0.643967i	$0.222713\pi$
$224$	−14.6869	+	24.0317i	−0.981307	+	1.60569i
$225$		0			0
$226$	3.15511	−	6.99228i	0.209875	−	0.465119i
$227$	2.89777	−	2.89777i	0.192332	−	0.192332i	−0.604371	−	0.796703i	$-0.706576\pi$
$227$	2.89777	−	2.89777i	0.192332	−	0.192332i	0.796703	+	0.604371i	$0.206576\pi$
$228$		0			0
$229$	13.7901	−	13.7901i	0.911276	−	0.911276i	−0.0850965	−	0.996373i	$-0.527120\pi$
$229$	13.7901	−	13.7901i	0.911276	−	0.911276i	0.996373	+	0.0850965i	$0.0271199\pi$
$230$	17.8677	+	7.73524i	1.17816	+	0.510047i
$231$		0			0
$232$	−6.09437	+	11.5304i	−0.400115	+	0.757008i
$233$			27.8531i			1.82472i	0.409388	+	0.912360i	$0.365742\pi$
$233$			27.8531i			1.82472i	−0.409388	+	0.912360i	$0.634258\pi$
$234$		0			0
$235$	−3.78619	+	0.0579991i	−0.246984	+	0.00378344i
$236$	11.6979	+	0.730312i	0.761470	+	0.0475393i
$237$		0			0
$238$	−33.5393	−	15.1339i	−2.17403	−	0.980982i
$239$	−22.7939			−1.47441			−0.737207	−	0.675667i	$-0.763856\pi$
$239$	−22.7939			−1.47441			−0.737207	+	0.675667i	$0.763856\pi$
$240$		0			0
$241$	4.33189			0.279042			0.139521	−	0.990219i	$-0.455444\pi$
$241$	4.33189			0.279042			0.139521	+	0.990219i	$0.455444\pi$
$242$	−13.9482	−	6.29381i	−0.896624	−	0.404581i
$243$		0			0
$244$	−1.65354	+	26.4859i	−0.105857	+	1.69558i
$245$	−0.609240	−	39.7713i	−0.0389229	−	2.54090i
$246$		0			0
$247$		−	24.4436i		−	1.55531i
$248$	−6.47753	−	21.0015i	−0.411324	−	1.33360i
$249$		0			0
$250$	14.6956	+	5.83424i	0.929433	+	0.368990i
$251$	4.97266	−	4.97266i	0.313872	−	0.313872i	−0.532536	−	0.846407i	$-0.678761\pi$
$251$	4.97266	−	4.97266i	0.313872	−	0.313872i	0.846407	+	0.532536i	$0.178761\pi$
$252$		0			0
$253$	−1.84482	+	1.84482i	−0.115983	+	0.115983i
$254$	−5.57049	+	12.3452i	−0.349524	+	0.774606i
$255$		0			0
$256$	−15.5050	−	3.94916i	−0.969061	−	0.246823i
$257$	−8.06975			−0.503377			−0.251689	−	0.967808i	$-0.580986\pi$
$257$	−8.06975			−0.503377			−0.251689	+	0.967808i	$0.580986\pi$
$258$		0			0
$259$	11.3341	−	11.3341i	0.704267	−	0.704267i
$260$	−1.01513	+	21.5676i	−0.0629557	+	1.33757i
$261$		0			0
$262$	23.3922	−	8.84562i	1.44518	−	0.546484i
$263$	−17.5377			−1.08142			−0.540710	−	0.841209i	$-0.681845\pi$
$263$	−17.5377			−1.08142			−0.540710	+	0.841209i	$0.681845\pi$
$264$		0			0
$265$	6.70018	+	6.49800i	0.411589	+	0.399169i
$266$	−33.3438	+	12.6087i	−2.04444	+	0.773091i
$267$		0			0
$268$	−0.00721956	+	0.115641i	−0.000441005	+	0.00706388i
$269$	−1.87139	+	1.87139i	−0.114101	+	0.114101i	−0.761852	−	0.647751i	$-0.775710\pi$
$269$	−1.87139	+	1.87139i	−0.114101	+	0.114101i	0.647751	+	0.761852i	$0.275710\pi$
$270$		0			0
$271$		−	22.9224i		−	1.39244i	−0.717831	−	0.696218i	$-0.754865\pi$
$271$		−	22.9224i		−	1.39244i	0.717831	−	0.696218i	$-0.245135\pi$
$272$	2.59991	−	20.7411i	0.157643	−	1.25761i
$273$		0			0
$274$	−4.14379	−	1.86979i	−0.250336	−	0.112958i
$275$	−1.45155	+	1.54333i	−0.0875319	+	0.0930662i
$276$		0			0
$277$	13.2521	+	13.2521i	0.796239	+	0.796239i	0.982500	−	0.186261i	$-0.0596372\pi$
$277$	13.2521	+	13.2521i	0.796239	+	0.796239i	−0.186261	+	0.982500i	$0.559637\pi$
$278$	1.36301	−	0.515415i	0.0817481	−	0.0309126i
$279$		0			0
$280$	29.9442	−	9.74047i	1.78951	−	0.582104i
$281$	12.2485			0.730684			0.365342	−	0.930873i	$-0.380952\pi$
$281$	12.2485			0.730684			0.365342	+	0.930873i	$0.380952\pi$
$282$		0			0
$283$	−2.62423	+	2.62423i	−0.155994	+	0.155994i	−0.780789	−	0.624795i	$-0.785183\pi$
$283$	−2.62423	+	2.62423i	−0.155994	+	0.155994i	0.624795	+	0.780789i	$0.285183\pi$
$284$	7.44962	−	6.57410i	0.442053	−	0.390101i
$285$		0			0
$286$	−2.63717	−	1.18996i	−0.155939	−	0.0703640i
$287$		−	36.4570i		−	2.15199i
$288$		0			0
$289$	10.3096			0.606445
$290$	13.5582	−	5.36571i	0.796163	−	0.315085i
$291$		0			0
$292$	−5.12693	−	5.80971i	−0.300031	−	0.339988i
$293$	3.96865	−	3.96865i	0.231851	−	0.231851i	−0.581614	−	0.813465i	$-0.697578\pi$
$293$	3.96865	−	3.96865i	0.231851	−	0.231851i	0.813465	+	0.581614i	$0.197578\pi$
$294$		0			0
$295$	−9.40686	−	9.12301i	−0.547689	−	0.531162i
$296$	8.05057	+	4.25511i	0.467930	+	0.247323i
$297$		0			0
$298$	7.29619	−	2.75901i	0.422657	−	0.159825i
$299$	21.0196	−	21.0196i	1.21559	−	1.21559i
$300$		0			0
$301$	−8.79226	−	8.79226i	−0.506778	−	0.506778i
$302$	−1.44714	+	3.20712i	−0.0832734	+	0.184549i
$303$		0			0
$304$	−12.4277	−	15.9899i	−0.712778	−	0.917082i
$305$	20.6559	−	21.2986i	1.18275	−	1.21955i
$306$		0			0
$307$	5.66311	+	5.66311i	0.323211	+	0.323211i	0.849997	−	0.526787i	$-0.176603\pi$
$307$	5.66311	+	5.66311i	0.323211	+	0.323211i	−0.526787	+	0.849997i	$0.676603\pi$
$308$	−0.262910	+	4.21121i	−0.0149807	+	0.239956i
$309$		0			0
$310$	−9.76205	+	22.5495i	−0.554447	+	1.28073i
$311$		−	29.5732i		−	1.67694i	−0.544947	−	0.838470i	$-0.683450\pi$
$311$		−	29.5732i		−	1.67694i	0.544947	−	0.838470i	$-0.316550\pi$
$312$		0			0
$313$	12.2408			0.691891			0.345945	−	0.938255i	$-0.387558\pi$
$313$	12.2408			0.691891			0.345945	+	0.938255i	$0.387558\pi$
$314$	4.86954	+	12.8775i	0.274804	+	0.726719i
$315$		0			0
$316$	−0.781656	+	0.689792i	−0.0439716	+	0.0388038i
$317$	12.0077	+	12.0077i	0.674419	+	0.674419i	0.958732	−	0.284312i	$-0.0917653\pi$
$317$	12.0077	+	12.0077i	0.674419	+	0.674419i	−0.284312	+	0.958732i	$0.591765\pi$
$318$		0			0
$319$			1.95387i			0.109395i
$320$	10.3014	+	14.6246i	0.575868	+	0.817543i
$321$		0			0
$322$	−39.5155	−	17.8305i	−2.20212	−	0.993655i
$323$	18.7085	−	18.7085i	1.04097	−	1.04097i
$324$		0			0
$325$	16.5387	−	17.5844i	0.917402	−	0.975406i
$326$	1.78503	−	0.674998i	0.0988637	−	0.0373847i
$327$		0			0
$328$	19.7911	−	6.10419i	1.09278	−	0.337047i
$329$	8.43126			0.464831
$330$		0			0
$331$	6.22467	+	6.22467i	0.342139	+	0.342139i	0.857171	−	0.515032i	$-0.172220\pi$
$331$	6.22467	+	6.22467i	0.342139	+	0.342139i	−0.515032	+	0.857171i	$0.672220\pi$
$332$	26.7900	+	1.67253i	1.47029	+	0.0917917i
$333$		0			0
$334$	−5.66185	+	12.5477i	−0.309803	+	0.686578i
$335$	0.0901863	−	0.0929923i	0.00492740	−	0.00508071i
$336$		0			0
$337$		−	2.44733i		−	0.133315i	−0.997776	−	0.0666574i	$-0.978767\pi$
$337$		−	2.44733i		−	0.133315i	0.997776	−	0.0666574i	$-0.0212335\pi$
$338$	13.2896	+	5.99665i	0.722861	+	0.326175i
$339$		0			0
$340$	−17.2843	+	15.7304i	−0.937372	+	0.853099i
$341$	−2.32821	−	2.32821i	−0.126080	−	0.126080i
$342$		0			0
$343$			53.7130i			2.90023i
$344$	3.30084	−	6.24511i	0.177969	−	0.336714i
$345$		0			0
$346$	14.6925	−	5.55589i	0.789875	−	0.298687i
$347$	−7.80648	−	7.80648i	−0.419074	−	0.419074i	0.465811	−	0.884884i	$-0.345763\pi$
$347$	−7.80648	−	7.80648i	−0.419074	−	0.419074i	−0.884884	+	0.465811i	$0.845763\pi$
$348$		0			0
$349$	−18.4011	−	18.4011i	−0.984990	−	0.984990i	0.0148993	−	0.999889i	$-0.495257\pi$
$349$	−18.4011	−	18.4011i	−0.984990	−	0.984990i	−0.999889	+	0.0148993i	$0.995257\pi$
$350$	−32.5182	−	13.4901i	−1.73817	−	0.721075i
$351$		0			0
$352$	−2.33012	+	0.562382i	−0.124196	+	0.0299751i
$353$	−23.6781			−1.26026			−0.630128	−	0.776491i	$-0.716998\pi$
$353$	−23.6781			−1.26026			−0.630128	+	0.776491i	$0.716998\pi$
$354$		0			0
$355$	−11.1070	+	0.170143i	−0.589499	+	0.00903028i
$356$	−4.66645	−	5.28791i	−0.247321	−	0.280259i
$357$		0			0
$358$	−17.0882	+	6.46181i	−0.903141	+	0.341517i
$359$			0.461358i			0.0243495i	0.999926	+	0.0121748i	$0.00387544\pi$
$359$			0.461358i			0.0243495i	−0.999926	+	0.0121748i	$0.996125\pi$
$360$		0			0
$361$		−	6.63274i		−	0.349092i
$362$	−11.2481	−	29.7454i	−0.591185	−	1.56339i
$363$		0			0
$364$	2.99555	−	47.9818i	0.157009	−	2.51493i
$365$	0.132689	+	8.66199i	0.00694528	+	0.453389i
$366$		0			0
$367$	−20.2030			−1.05459			−0.527294	−	0.849683i	$-0.676793\pi$
$367$	−20.2030			−1.05459			−0.527294	+	0.849683i	$0.676793\pi$
$368$	3.06318	−	24.4369i	0.159679	−	1.27386i
$369$		0			0
$370$	−3.74636	−	9.46636i	−0.194764	−	0.492133i
$371$	−14.6952	−	14.6952i	−0.762934	−	0.762934i
$372$		0			0
$373$	−5.66776	−	5.66776i	−0.293465	−	0.293465i	0.544982	−	0.838448i	$-0.316536\pi$
$373$	−5.66776	−	5.66776i	−0.293465	−	0.293465i	−0.838448	+	0.544982i	$0.816536\pi$
$374$	−1.10766	−	2.92920i	−0.0572757	−	0.151465i
$375$		0			0
$376$	1.41169	+	4.57700i	0.0728024	+	0.236041i
$377$		−	22.2620i		−	1.14655i
$378$		0			0
$379$	6.20237	+	6.20237i	0.318594	+	0.318594i	0.848227	−	0.529633i	$-0.177670\pi$
$379$	6.20237	+	6.20237i	0.318594	+	0.318594i	−0.529633	+	0.848227i	$0.677670\pi$
$380$	−1.06452	+	22.6168i	−0.0546085	+	1.16022i
$381$		0			0
$382$	−1.26076	+	2.79407i	−0.0645061	+	0.142957i
$383$			4.89671i			0.250210i	0.992143	+	0.125105i	$0.0399268\pi$
$383$			4.89671i			0.250210i	−0.992143	+	0.125105i	$0.960073\pi$
$384$		0			0
$385$	3.28425	−	3.38644i	0.167381	−	0.172589i
$386$	−29.7155	−	13.4084i	−1.51248	−	0.682472i
$387$		0			0
$388$	−4.95956	+	4.37669i	−0.251784	+	0.222193i
$389$	−13.7639	−	13.7639i	−0.697860	−	0.697860i	0.266089	−	0.963949i	$-0.414269\pi$
$389$	−13.7639	−	13.7639i	−0.697860	−	0.697860i	−0.963949	+	0.266089i	$0.914269\pi$
$390$		0			0
$391$	32.1758			1.62720
$392$	−48.0782	+	14.8288i	−2.42831	+	0.748969i
$393$		0			0
$394$	1.08068	+	2.85784i	0.0544437	+	0.143976i
$395$	1.16541	−	0.0178524i	0.0586381	−	0.000898253i
$396$		0			0
$397$	−16.2544	+	16.2544i	−0.815787	+	0.815787i	−0.985495	−	0.169707i	$-0.945718\pi$
$397$	−16.2544	+	16.2544i	−0.815787	+	0.815787i	0.169707	+	0.985495i	$0.445718\pi$
$398$	1.81918	−	4.03162i	0.0911872	−	0.202087i
$399$		0			0
$400$	1.87853	−	19.9116i	0.0939267	−	0.995579i
$401$			10.0348i			0.501116i	0.968102	+	0.250558i	$0.0806140\pi$
$401$			10.0348i			0.501116i	−0.968102	+	0.250558i	$0.919386\pi$
$402$		0			0
$403$	26.5272	+	26.5272i	1.32141	+	1.32141i
$404$	−1.33207	+	21.3367i	−0.0662731	+	1.06154i
$405$		0			0
$406$	−30.3678	+	11.4834i	−1.50713	+	0.569912i
$407$	1.36420			0.0676207
$408$		0			0
$409$			33.3911i			1.65108i	0.564341	+	0.825542i	$0.309130\pi$
$409$			33.3911i			1.65108i	−0.564341	+	0.825542i	$0.690870\pi$
$410$	−21.2498	−	9.19940i	−1.04945	−	0.454326i
$411$		0			0
$412$	−19.5834	+	17.2819i	−0.964804	+	0.851416i
$413$	20.6316	+	20.6316i	1.01521	+	1.01521i
$414$		0			0
$415$	−21.5431	−	20.8931i	−1.05751	−	1.02560i
$416$	26.5490	−	6.40768i	1.30167	−	0.314162i
$417$		0			0
$418$	−2.76547	−	1.24785i	−0.135263	−	0.0610346i
$419$	12.9105	+	12.9105i	0.630718	+	0.630718i	0.948248	−	0.317530i	$-0.102853\pi$
$419$	12.9105	+	12.9105i	0.630718	+	0.630718i	−0.317530	+	0.948248i	$0.602853\pi$
$420$		0			0
$421$	0.923750	−	0.923750i	0.0450208	−	0.0450208i	−0.684238	−	0.729259i	$-0.739865\pi$
$421$	0.923750	−	0.923750i	0.0450208	−	0.0450208i	0.729259	+	0.684238i	$0.239865\pi$
$422$	1.88412	+	4.98255i	0.0917175	+	0.242547i
$423$		0			0
$424$	5.51693	−	10.4379i	0.267926	−	0.506910i
$425$	26.1170	−	0.800339i	1.26686	−	0.0388221i
$426$		0			0
$427$	−46.7130	+	46.7130i	−2.26060	+	2.26060i
$428$	1.31524	−	21.0671i	0.0635743	−	1.01831i
$429$		0			0
$430$	−7.34338	+	2.90618i	−0.354129	+	0.140148i
$431$	−23.5531			−1.13451			−0.567255	−	0.823542i	$-0.691995\pi$
$431$	−23.5531			−1.13451			−0.567255	+	0.823542i	$0.691995\pi$
$432$		0			0
$433$		−	38.5735i		−	1.85373i	−0.375400	−	0.926863i	$-0.622495\pi$
$433$		−	38.5735i		−	1.85373i	0.375400	−	0.926863i	$-0.377505\pi$
$434$	22.5025	−	49.8695i	1.08015	−	2.39381i
$435$		0			0
$436$	0.605306	−	9.69561i	0.0289889	−	0.464336i
$437$	22.0421	−	22.0421i	1.05442	−	1.05442i
$438$		0			0
$439$	−30.3538			−1.44871			−0.724355	−	0.689427i	$-0.757862\pi$
$439$	−30.3538			−1.44871			−0.724355	+	0.689427i	$0.757862\pi$
$440$	2.38827	+	1.21588i	0.113856	+	0.0579649i
$441$		0			0
$442$	12.6204	+	33.3747i	0.600294	+	1.58747i
$443$	4.74763	+	4.74763i	0.225567	+	0.225567i	0.810838	−	0.585271i	$-0.199012\pi$
$443$	4.74763	+	4.74763i	0.225567	+	0.225567i	−0.585271	+	0.810838i	$0.699012\pi$
$444$		0			0
$445$	0.120772	+	7.88401i	0.00572513	+	0.373738i
$446$	−13.2905	+	29.4542i	−0.629325	+	1.39470i
$447$		0			0
$448$	−22.4356	−	32.9105i	−1.05998	−	1.55487i
$449$		−	10.1268i		−	0.477914i	−0.971030	−	0.238957i	$-0.923194\pi$
$449$		−	10.1268i		−	0.477914i	0.971030	−	0.238957i	$-0.0768055\pi$
$450$		0			0
$451$	2.19402	−	2.19402i	0.103312	−	0.103312i
$452$	7.17826	+	8.13424i	0.337637	+	0.382602i
$453$		0			0
$454$	2.04988	+	5.42091i	0.0962058	+	0.254416i
$455$	−37.4202	+	38.5845i	−1.75428	+	1.80887i
$456$		0			0
$457$	1.44447			0.0675695			0.0337847	−	0.999429i	$-0.489244\pi$
$457$	1.44447			0.0675695			0.0337847	+	0.999429i	$0.489244\pi$
$458$	9.75513	+	25.7974i	0.455827	+	1.20543i
$459$		0			0
$460$	−20.3641	+	18.5333i	−0.949482	+	0.864120i
$461$	−26.8623	+	26.8623i	−1.25110	+	1.25110i	−0.295878	+	0.955226i	$0.595612\pi$
$461$	−26.8623	+	26.8623i	−1.25110	+	1.25110i	−0.955226	+	0.295878i	$0.904388\pi$
$462$		0			0
$463$	20.2597			0.941547			0.470774	−	0.882254i	$-0.343975\pi$
$463$	20.2597			0.941547			0.470774	+	0.882254i	$0.343975\pi$
$464$	−11.3185	−	14.5628i	−0.525450	−	0.676059i
$465$		0			0
$466$	−35.9044	−	16.2010i	−1.66324	−	0.750498i
$467$	−9.09888	+	9.09888i	−0.421046	+	0.421046i	−0.885564	−	0.464518i	$-0.846228\pi$
$467$	−9.09888	+	9.09888i	−0.421046	+	0.421046i	0.464518	+	0.885564i	$0.346228\pi$
$468$		0			0
$469$	−0.203955	+	0.203955i	−0.00941777	+	0.00941777i
$470$	2.12751	−	4.91436i	0.0981346	−	0.226683i
$471$		0			0
$472$	−7.74561	+	14.6545i	−0.356521	+	0.674529i
$473$		−	1.05825i		−	0.0486586i
$474$		0			0
$475$	17.3433	−	18.4399i	0.795765	−	0.846079i
$476$	39.0169	−	34.4314i	1.78833	−	1.57816i
$477$		0			0
$478$	13.2583	−	29.3827i	0.606419	−	1.34393i
$479$	4.60465			0.210392			0.105196	−	0.994452i	$-0.466453\pi$
$479$	4.60465			0.210392			0.105196	+	0.994452i	$0.466453\pi$
$480$		0			0
$481$	−15.5434			−0.708718
$482$	−2.51968	+	5.58406i	−0.114768	+	0.254347i
$483$		0			0
$484$	16.2262	−	14.3192i	0.737553	−	0.650873i
$485$	7.39446	−	0.113273i	0.335765	−	0.00514344i
$486$		0			0
$487$		−	32.2084i		−	1.45950i	−0.683713	−	0.729751i	$-0.739636\pi$
$487$		−	32.2084i		−	1.45950i	0.683713	−	0.729751i	$-0.260364\pi$
$488$	−33.1801	−	17.5372i	−1.50199	−	0.793874i
$489$		0			0
$490$	51.6219	+	22.3480i	2.33204	+	1.00958i
$491$	17.4179	−	17.4179i	0.786059	−	0.786059i	−0.194786	−	0.980846i	$-0.562401\pi$
$491$	17.4179	−	17.4179i	0.786059	−	0.786059i	0.980846	+	0.194786i	$0.0624014\pi$
$492$		0			0
$493$	17.0388	−	17.0388i	0.767389	−	0.767389i
$494$	31.5092	+	14.2178i	1.41767	+	0.639690i
$495$		0			0
$496$	30.8399	+	3.86580i	1.38475	+	0.173579i
$497$	24.7336			1.10945
$498$		0			0
$499$	−15.6000	+	15.6000i	−0.698354	+	0.698354i	−0.964055	−	0.265701i	$-0.914396\pi$
$499$	−15.6000	+	15.6000i	−0.698354	+	0.698354i	0.265701	+	0.964055i	$0.414396\pi$
$500$	−16.0685	+	15.5500i	−0.718606	+	0.695417i
$501$		0			0
$502$	3.51766	+	9.30245i	0.157001	+	0.415189i
$503$	2.39149			0.106631			0.0533157	−	0.998578i	$-0.483021\pi$
$503$	2.39149			0.106631			0.0533157	+	0.998578i	$0.483021\pi$
$504$		0			0
$505$	16.6401	−	17.1579i	0.740477	−	0.763516i
$506$	−1.30503	−	3.45114i	−0.0580156	−	0.153422i
$507$		0			0
$508$	−12.6736	−	14.3614i	−0.562298	−	0.637183i
$509$	1.78164	−	1.78164i	0.0789700	−	0.0789700i	−0.666518	−	0.745489i	$-0.732216\pi$
$509$	1.78164	−	1.78164i	0.0789700	−	0.0789700i	0.745489	+	0.666518i	$0.232216\pi$
$510$		0			0
$511$		−	19.2889i		−	0.853291i
$512$	14.1093	−	17.6898i	0.623549	−	0.781784i
$513$		0			0
$514$	4.69384	−	10.4024i	0.207036	−	0.458829i
$515$	29.1979	−	0.447269i	1.28661	−	0.0197090i
$516$		0			0
$517$	0.507402	+	0.507402i	0.0223155	+	0.0223155i
$518$	8.01776	+	21.2029i	0.352280	+	0.931603i
$519$		0			0
$520$	−27.2114	−	13.8535i	−1.19330	−	0.607518i
$521$	6.52761			0.285980			0.142990	−	0.989724i	$-0.454328\pi$
$521$	6.52761			0.285980			0.142990	+	0.989724i	$0.454328\pi$
$522$		0			0
$523$	−8.63265	+	8.63265i	−0.377479	+	0.377479i	−0.870192	−	0.492713i	$-0.836005\pi$
$523$	−8.63265	+	8.63265i	−0.377479	+	0.377479i	0.492713	+	0.870192i	$0.336005\pi$
$524$	−2.20376	+	35.2991i	−0.0962715	+	1.54205i
$525$		0			0
$526$	10.2010	−	22.6071i	0.444783	−	0.985718i
$527$			40.6065i			1.76885i
$528$		0			0
$529$	14.9090			0.648219
$530$	−12.2735	+	4.85731i	−0.533128	+	0.210988i
$531$		0			0
$532$	3.14128	−	50.3161i	0.136192	−	2.18148i
$533$	−24.9982	+	24.9982i	−1.08279	+	1.08279i
$534$		0			0
$535$	−16.4298	+	16.9410i	−0.710324	+	0.732425i
$536$	−0.144868	−	0.0765699i	−0.00625736	−	0.00330732i
$537$		0			0
$538$	−1.32382	−	3.50085i	−0.0570741	−	0.150932i
$539$	−5.32990	+	5.32990i	−0.229575	+	0.229575i
$540$		0			0
$541$	28.4777	+	28.4777i	1.22435	+	1.22435i	0.966070	+	0.258280i	$0.0831557\pi$
$541$	28.4777	+	28.4777i	1.22435	+	1.22435i	0.258280	+	0.966070i	$0.416844\pi$
$542$	29.5483	+	13.3330i	1.26921	+	0.572701i
$543$		0			0
$544$	25.2243	+	15.4157i	1.08148	+	0.660942i
$545$	−7.56144	+	7.79671i	−0.323897	+	0.333974i
$546$		0			0
$547$	7.40756	+	7.40756i	0.316724	+	0.316724i	0.847508	−	0.530783i	$-0.178102\pi$
$547$	7.40756	+	7.40756i	0.316724	+	0.316724i	−0.530783	+	0.847508i	$0.678102\pi$
$548$	4.82055	−	4.25401i	0.205924	−	0.181722i
$549$		0			0
$550$	−1.14513	−	2.76883i	−0.0488286	−	0.118063i
$551$		−	23.3450i		−	0.994531i
$552$		0			0
$553$	−2.59519			−0.110359
$554$	−24.7909	+	9.37451i	−1.05326	+	0.398285i
$555$		0			0
$556$	−0.128408	+	2.05680i	−0.00544571	+	0.0872278i
$557$	1.55719	+	1.55719i	0.0659803	+	0.0659803i	0.739327	−	0.673347i	$-0.235144\pi$
$557$	1.55719	+	1.55719i	0.0659803	+	0.0659803i	−0.673347	+	0.739327i	$0.735144\pi$
$558$		0			0
$559$			12.0575i			0.509980i
$560$	−4.86129	+	44.2655i	−0.205427	+	1.87056i
$561$		0			0
$562$	−7.12444	+	15.7890i	−0.300526	+	0.666020i
$563$	−14.0768	+	14.0768i	−0.593265	+	0.593265i	−0.938512	−	0.345247i	$-0.887795\pi$
$563$	−14.0768	+	14.0768i	−0.593265	+	0.593265i	0.345247	+	0.938512i	$0.387795\pi$
$564$		0			0
$565$	−0.185780	−	12.1277i	−0.00781581	−	0.510218i
$566$	−1.85638	−	4.90920i	−0.0780296	−	0.206349i
$567$		0			0
$568$	4.14127	+	13.4269i	0.173764	+	0.563379i
$569$	−19.8358			−0.831559			−0.415779	−	0.909466i	$-0.636491\pi$
$569$	−19.8358			−0.831559			−0.415779	+	0.909466i	$0.636491\pi$
$570$		0			0
$571$	−14.2584	−	14.2584i	−0.596696	−	0.596696i	0.342736	−	0.939432i	$-0.388646\pi$
$571$	−14.2584	−	14.2584i	−0.596696	−	0.596696i	−0.939432	+	0.342736i	$0.888646\pi$
$572$	3.06787	−	2.70732i	0.128274	−	0.113199i
$573$		0			0
$574$	46.9952	+	21.2055i	1.96154	+	0.885101i
$575$	30.7707	−	0.942948i	1.28323	−	0.0393236i
$576$		0			0
$577$		−	16.0197i		−	0.666908i	−0.942766	−	0.333454i	$-0.891786\pi$
$577$		−	16.0197i		−	0.666908i	0.942766	−	0.333454i	$-0.108214\pi$
$578$	−5.99665	+	13.2896i	−0.249428	+	0.552776i
$579$		0			0
$580$	−0.969507	+	20.5983i	−0.0402566	+	0.855297i
$581$	47.2494	+	47.2494i	1.96023	+	1.96023i
$582$		0			0
$583$		−	1.76874i		−	0.0732536i
$584$	10.4712	−	3.22964i	0.433301	−	0.133644i
$585$		0			0
$586$	2.80743	+	7.42423i	0.115974	+	0.306692i
$587$	−6.80793	−	6.80793i	−0.280993	−	0.280993i	0.552512	−	0.833505i	$-0.313669\pi$
$587$	−6.80793	−	6.80793i	−0.280993	−	0.280993i	−0.833505	+	0.552512i	$0.813669\pi$
$588$		0			0
$589$	27.8177	+	27.8177i	1.14621	+	1.14621i
$590$	17.2317	−	6.81952i	0.709417	−	0.280755i
$591$		0			0
$592$	−10.1678	+	7.90264i	−0.417893	+	0.324797i
$593$	−27.4172			−1.12589			−0.562944	−	0.826495i	$-0.690331\pi$
$593$	−27.4172			−1.12589			−0.562944	+	0.826495i	$0.690331\pi$
$594$		0			0
$595$	−58.1722	+	0.891115i	−2.38483	+	0.0365321i
$596$	−0.687367	+	11.0100i	−0.0281556	+	0.450988i
$597$		0			0
$598$	14.8692	+	39.3216i	0.608048	+	1.60798i
$599$		−	39.5624i		−	1.61647i	−0.588857	−	0.808237i	$-0.700422\pi$
$599$		−	39.5624i		−	1.61647i	0.588857	−	0.808237i	$-0.299578\pi$
$600$		0			0
$601$			20.5453i			0.838061i	0.907972	+	0.419030i	$0.137630\pi$
$601$			20.5453i			0.838061i	−0.907972	+	0.419030i	$0.862370\pi$
$602$	16.4478	−	6.21965i	0.670364	−	0.253494i
$603$		0			0
$604$	−3.29242	−	3.73089i	−0.133967	−	0.151808i
$605$	−24.1924	+	0.370593i	−0.983561	+	0.0150668i
$606$		0			0
$607$	−19.1918			−0.778971			−0.389485	−	0.921033i	$-0.627347\pi$
$607$	−19.1918			−0.778971			−0.389485	+	0.921033i	$0.627347\pi$
$608$	27.8406	−	6.71941i	1.12908	−	0.272508i
$609$		0			0
$610$	15.4404	+	39.0152i	0.625165	+	1.57968i
$611$	−5.78124	−	5.78124i	−0.233884	−	0.233884i
$612$		0			0
$613$	3.14030	+	3.14030i	0.126836	+	0.126836i	0.767675	−	0.640839i	$-0.221414\pi$
$613$	3.14030	+	3.14030i	0.126836	+	0.126836i	−0.640839	+	0.767675i	$0.721414\pi$
$614$	−10.5941	+	4.00608i	−0.427542	+	0.161672i
$615$		0			0
$616$	−5.27558	−	2.78840i	−0.212559	−	0.112348i
$617$		−	26.9611i		−	1.08541i	−0.839922	−	0.542707i	$-0.817399\pi$
$617$		−	26.9611i		−	1.08541i	0.839922	−	0.542707i	$-0.182601\pi$
$618$		0			0
$619$	−10.1272	−	10.1272i	−0.407046	−	0.407046i	0.473661	−	0.880707i	$-0.342932\pi$
$619$	−10.1272	−	10.1272i	−0.407046	−	0.407046i	−0.880707	+	0.473661i	$0.842932\pi$
$620$	−23.3895	−	25.7000i	−0.939343	−	1.03214i
$621$		0			0
$622$	38.1216	+	17.2015i	1.52854	+	0.689717i
$623$		−	17.5565i		−	0.703385i
$624$		0			0
$625$	24.9531	−	1.53078i	0.998124	−	0.0612312i
$626$	−7.11997	+	15.7791i	−0.284571	+	0.630660i
$627$		0			0
$628$	−19.4323	−	1.21317i	−0.775432	−	0.0484109i
$629$	−11.8966	−	11.8966i	−0.474347	−	0.474347i
$630$		0			0
$631$	−24.9414			−0.992900			−0.496450	−	0.868065i	$-0.665363\pi$
$631$	−24.9414			−0.992900			−0.496450	+	0.868065i	$0.665363\pi$
$632$	−0.434526	−	1.40882i	−0.0172845	−	0.0560400i
$633$		0			0
$634$	−22.4630	+	8.49425i	−0.892120	+	0.337350i
$635$	0.328003	+	21.4121i	0.0130164	+	0.849713i
$636$		0			0
$637$	60.7278	−	60.7278i	2.40612	−	2.40612i
$638$	−2.51865	−	1.13648i	−0.0997142	−	0.0449938i
$639$		0			0
$640$	−24.8440	+	4.77261i	−0.982044	+	0.188654i
$641$			20.1001i			0.793908i	0.917839	+	0.396954i	$0.129933\pi$
$641$			20.1001i			0.793908i	−0.917839	+	0.396954i	$0.870067\pi$
$642$		0			0
$643$	−6.20809	−	6.20809i	−0.244823	−	0.244823i	0.574019	−	0.818842i	$-0.305384\pi$
$643$	−6.20809	−	6.20809i	−0.244823	−	0.244823i	−0.818842	+	0.574019i	$0.805384\pi$
$644$	45.9691	−	40.5666i	1.81144	−	1.59855i
$645$		0			0
$646$	13.2344	+	34.9984i	0.520702	+	1.37699i
$647$	3.57164			0.140416			0.0702078	−	0.997532i	$-0.477634\pi$
$647$	3.57164			0.140416			0.0702078	+	0.997532i	$0.477634\pi$
$648$		0			0
$649$			2.48326i			0.0974763i
$650$	13.0474	+	31.5475i	0.511762	+	1.23739i
$651$		0			0
$652$	−0.168166	+	2.69363i	−0.00658588	+	0.105491i
$653$	−27.2873	−	27.2873i	−1.06783	−	1.06783i	−0.997525	−	0.0703096i	$-0.977601\pi$
$653$	−27.2873	−	27.2873i	−1.06783	−	1.06783i	−0.0703096	−	0.997525i	$-0.522399\pi$
$654$		0			0
$655$	27.5292	−	28.3857i	1.07565	−	1.10912i
$656$	−3.64299	+	29.0624i	−0.142235	+	1.13470i
$657$		0			0
$658$	−4.90412	+	10.8684i	−0.191182	+	0.423694i
$659$	−32.0510	−	32.0510i	−1.24853	−	1.24853i	−0.956370	−	0.292159i	$-0.905626\pi$
$659$	−32.0510	−	32.0510i	−1.24853	−	1.24853i	−0.292159	−	0.956370i	$-0.594374\pi$
$660$		0			0
$661$	11.8765	−	11.8765i	0.461942	−	0.461942i	−0.437350	−	0.899291i	$-0.644083\pi$
$661$	11.8765	−	11.8765i	0.461942	−	0.461942i	0.899291	+	0.437350i	$0.144083\pi$
$662$	−11.6446	+	4.40334i	−0.452580	+	0.171140i
$663$		0			0
$664$	−17.7386	+	33.5610i	−0.688392	+	1.30242i
$665$	−39.2407	+	40.4616i	−1.52169	+	1.56903i
$666$		0			0
$667$	20.0749	−	20.0749i	0.777302	−	0.777302i
$668$	−12.8814	−	14.5969i	−0.498397	−	0.564772i
$669$		0			0
$670$	0.0674150	+	0.170345i	0.00260447	+	0.00658101i
$671$	−5.62247			−0.217053
$672$		0			0
$673$			4.29764i			0.165662i	0.996564	+	0.0828309i	$0.0263961\pi$
$673$			4.29764i			0.165662i	−0.996564	+	0.0828309i	$0.973604\pi$
$674$	3.15476	+	1.42351i	0.121517	+	0.0548317i
$675$		0			0
$676$	−15.4601	+	13.6431i	−0.594618	+	0.524736i
$677$	−22.4731	+	22.4731i	−0.863711	+	0.863711i	−0.991767	−	0.128056i	$-0.959126\pi$
$677$	−22.4731	+	22.4731i	−0.863711	+	0.863711i	0.128056	+	0.991767i	$0.459126\pi$
$678$		0			0
$679$	−16.4663			−0.631919
$680$	−10.2238	−	31.4302i	−0.392066	−	1.20529i
$681$		0			0
$682$	4.35542	−	1.64698i	0.166778	−	0.0630659i
$683$	−6.83685	−	6.83685i	−0.261605	−	0.261605i	0.564101	−	0.825706i	$-0.309223\pi$
$683$	−6.83685	−	6.83685i	−0.261605	−	0.261605i	−0.825706	+	0.564101i	$0.809223\pi$
$684$		0			0
$685$	−7.18720	+	0.110098i	−0.274609	+	0.00420661i
$686$	−69.2392	−	31.2426i	−2.64356	−	1.19285i
$687$		0			0
$688$	6.13035	+	7.88750i	0.233717	+	0.300708i
$689$			20.1527i			0.767755i
$690$		0			0
$691$	8.12866	−	8.12866i	0.309229	−	0.309229i	−0.535381	−	0.844610i	$-0.679832\pi$
$691$	8.12866	−	8.12866i	0.309229	−	0.309229i	0.844610	+	0.535381i	$0.179832\pi$
$692$	−1.38417	+	22.1712i	−0.0526182	+	0.842821i
$693$		0			0
$694$	14.6037	−	5.52231i	0.554349	−	0.209624i
$695$	1.60406	−	1.65397i	0.0608456	−	0.0627388i
$696$		0			0
$697$	−38.2661			−1.44943
$698$	34.4233	−	13.0170i	1.30294	−	0.492699i
$699$		0			0
$700$	36.3040	−	34.0713i	1.37216	−	1.28777i
$701$	−32.3973	+	32.3973i	−1.22363	+	1.22363i	−0.257298	+	0.966332i	$0.582832\pi$
$701$	−32.3973	+	32.3973i	−1.22363	+	1.22363i	−0.966332	+	0.257298i	$0.917168\pi$
$702$		0			0
$703$	−16.2996			−0.614750
$704$	0.630392	−	3.33078i	0.0237588	−	0.125533i
$705$		0			0
$706$	13.7726	−	30.5224i	0.518337	−	1.14873i
$707$	−37.6315	+	37.6315i	−1.41528	+	1.41528i
$708$		0			0
$709$	11.9419	−	11.9419i	0.448488	−	0.448488i	−0.446364	−	0.894852i	$-0.647281\pi$
$709$	11.9419	−	11.9419i	0.448488	−	0.448488i	0.894852	+	0.446364i	$0.147281\pi$
$710$	6.24116	−	14.4166i	0.234227	−	0.541044i
$711$		0			0
$712$	9.53071	−	2.93957i	0.357178	−	0.110165i
$713$			47.8421i			1.79170i
$714$		0			0
$715$	−4.57403	+	0.0700677i	−0.171059	+	0.00262038i
$716$	1.60986	−	25.7863i	0.0601634	−	0.963680i
$717$		0			0
$718$	−0.594717	−	0.268353i	−0.0221947	−	0.0100148i
$719$	50.1912			1.87182			0.935908	−	0.352243i	$-0.114581\pi$
$719$	50.1912			1.87182			0.935908	+	0.352243i	$0.114581\pi$
$720$		0			0
$721$	−65.0191			−2.42144
$722$	8.55000	+	3.85799i	0.318198	+	0.143580i
$723$		0			0
$724$	44.8862	+	2.80229i	1.66818	+	0.104146i
$725$	15.7954	−	16.7941i	0.586627	−	0.623717i
$726$		0			0
$727$		−	8.79380i		−	0.326144i	−0.986614	−	0.163072i	$-0.947860\pi$
$727$		−	8.79380i		−	0.326144i	0.986614	−	0.163072i	$-0.0521403\pi$
$728$	60.1089	+	31.7704i	2.22779	+	1.17749i
$729$		0			0
$730$	−11.2430	−	4.86728i	−0.416122	−	0.180146i
$731$	−9.22857	+	9.22857i	−0.341331	+	0.341331i
$732$		0			0
$733$	−23.9818	+	23.9818i	−0.885787	+	0.885787i	−0.994115	−	0.108328i	$-0.965450\pi$
$733$	−23.9818	+	23.9818i	−0.885787	+	0.885787i	0.108328	+	0.994115i	$0.465450\pi$
$734$	11.7513	−	26.0429i	0.433747	−	0.961260i
$735$		0			0
$736$	29.7189	+	18.1625i	1.09545	+	0.669480i
$737$	−0.0245484			−0.000904253
$738$		0			0
$739$	−4.55372	+	4.55372i	−0.167511	+	0.167511i	−0.785884	−	0.618373i	$-0.787792\pi$
$739$	−4.55372	+	4.55372i	−0.167511	+	0.167511i	0.618373	+	0.785884i	$0.287792\pi$
$740$	14.3818	+	0.676913i	0.528685	+	0.0248838i
$741$		0			0
$742$	27.4905	−	10.3954i	1.00921	−	0.381626i
$743$	−5.94900			−0.218248			−0.109124	−	0.994028i	$-0.534805\pi$
$743$	−5.94900			−0.218248			−0.109124	+	0.994028i	$0.534805\pi$
$744$		0			0
$745$	8.58653	−	8.85369i	0.314586	−	0.324374i
$746$	10.6028	−	4.00937i	0.388195	−	0.146794i
$747$		0			0
$748$	4.42019	+	0.275957i	0.161618	+	0.0100900i
$749$	37.1559	−	37.1559i	1.35765	−	1.35765i
$750$		0			0
$751$			40.6618i			1.48377i	0.670528	+	0.741884i	$0.266068\pi$
$751$			40.6618i			1.48377i	−0.670528	+	0.741884i	$0.733932\pi$
$752$	−6.72115	−	0.842499i	−0.245095	−	0.0307228i
$753$		0			0
$754$	28.6970	+	12.9489i	1.04508	+	0.471570i
$755$	0.0852107	+	5.56257i	0.00310113	+	0.202443i
$756$		0			0
$757$	13.2358	+	13.2358i	0.481064	+	0.481064i	0.905471	−	0.424407i	$-0.139518\pi$
$757$	13.2358	+	13.2358i	0.481064	+	0.481064i	−0.424407	+	0.905471i	$0.639518\pi$
$758$	−11.6029	+	4.38756i	−0.421436	+	0.159363i
$759$		0			0
$760$	−28.5353	−	14.5275i	−1.03508	−	0.526968i
$761$	3.22651			0.116961			0.0584805	−	0.998289i	$-0.481374\pi$
$761$	3.22651			0.116961			0.0584805	+	0.998289i	$0.481374\pi$
$762$		0			0
$763$	17.1001	−	17.1001i	0.619065	−	0.619065i
$764$	−2.86839	−	3.25039i	−0.103775	−	0.117595i
$765$		0			0
$766$	−6.31215	−	2.84821i	−0.228067	−	0.102910i
$767$		−	28.2937i		−	1.02163i
$768$		0			0
$769$	33.3777			1.20363			0.601815	−	0.798635i	$-0.294444\pi$
$769$	33.3777			1.20363			0.601815	+	0.798635i	$0.294444\pi$
$770$	2.45501	+	6.20335i	0.0884723	+	0.223553i
$771$		0			0
$772$	34.5685	−	30.5059i	1.24415	−	1.09793i
$773$	22.5192	−	22.5192i	0.809958	−	0.809958i	−0.174669	−	0.984627i	$-0.555886\pi$
$773$	22.5192	−	22.5192i	0.809958	−	0.809958i	0.984627	+	0.174669i	$0.0558857\pi$
$774$		0			0
$775$	1.19002	+	38.8333i	0.0427468	+	1.39493i
$776$	−2.75704	−	8.93891i	−0.0989720	−	0.320888i
$777$		0			0
$778$	25.7485	−	9.73662i	0.923127	−	0.349075i
$779$	−26.2144	+	26.2144i	−0.939227	+	0.939227i
$780$		0			0
$781$	1.48849	+	1.48849i	0.0532624	+	0.0532624i
$782$	−18.7153	+	41.4764i	−0.669258	+	1.48319i
$783$		0			0
$784$	8.84986	−	70.6009i	0.316066	−	2.52146i
$785$	15.6264	+	15.1549i	0.557731	+	0.540901i
$786$		0			0
$787$	23.0883	+	23.0883i	0.823007	+	0.823007i	0.986538	−	0.163531i	$-0.0522883\pi$
$787$	23.0883	+	23.0883i	0.823007	+	0.823007i	−0.163531	+	0.986538i	$0.552288\pi$
$788$	−4.31251	−	0.269234i	−0.153627	−	0.00959108i
$789$		0			0
$790$	−0.654858	+	1.51267i	−0.0232988	+	0.0538183i
$791$			27.0066i			0.960244i
$792$		0			0
$793$	64.0614			2.27489
$794$	−11.4984	−	30.4075i	−0.408063	−	1.07912i
$795$		0			0
$796$	4.13886	+	4.69006i	0.146698	+	0.166235i
$797$	14.3550	+	14.3550i	0.508481	+	0.508481i	0.914060	−	0.405579i	$-0.132930\pi$
$797$	14.3550	+	14.3550i	0.508481	+	0.508481i	−0.405579	+	0.914060i	$0.632930\pi$
$798$		0			0
$799$		−	8.84965i		−	0.313078i
$800$	24.5745	+	14.0033i	0.868841	+	0.495091i
$801$		0			0
$802$	−12.9355	−	5.83685i	−0.456768	−	0.206106i
$803$	1.16083	−	1.16083i	0.0409646	−	0.0409646i
$804$		0			0
$805$	−68.5377	+	1.04990i	−2.41563	+	0.0370041i
$806$	−49.6248	+	18.7653i	−1.74796	+	0.660980i
$807$		0			0
$808$	−26.7295	−	14.1278i	−0.940340	−	0.497014i
$809$	−26.4918			−0.931404			−0.465702	−	0.884942i	$-0.654198\pi$
$809$	−26.4918			−0.931404			−0.465702	+	0.884942i	$0.654198\pi$
$810$		0			0
$811$	−15.3655	−	15.3655i	−0.539554	−	0.539554i	0.383844	−	0.923398i	$-0.374600\pi$
$811$	−15.3655	−	15.3655i	−0.539554	−	0.539554i	−0.923398	+	0.383844i	$0.874600\pi$
$812$	2.86092	−	45.8253i	0.100399	−	1.60815i
$813$		0			0
$814$	−0.793497	+	1.75853i	−0.0278120	+	0.0616364i
$815$	2.10072	−	2.16608i	0.0735849	−	0.0758744i
$816$		0			0
$817$			12.6441i			0.442362i
$818$	−43.0431	−	19.4222i	−1.50497	−	0.679082i
$819$		0			0
$820$	24.2187	−	22.0414i	0.845754	−	0.769718i
$821$	38.5448	+	38.5448i	1.34522	+	1.34522i	0.890772	+	0.454450i	$0.150164\pi$
$821$	38.5448	+	38.5448i	1.34522	+	1.34522i	0.454450	+	0.890772i	$0.349836\pi$
$822$		0			0
$823$			15.7862i			0.550272i	0.961405	+	0.275136i	$0.0887229\pi$
$823$			15.7862i			0.550272i	−0.961405	+	0.275136i	$0.911277\pi$
$824$	−10.8865	−	35.2963i	−0.379249	−	1.22960i
$825$		0			0
$826$	−38.5958	+	14.5948i	−1.34292	+	0.507817i
$827$	−38.2660	−	38.2660i	−1.33064	−	1.33064i	−0.904799	−	0.425840i	$-0.859979\pi$
$827$	−38.2660	−	38.2660i	−1.33064	−	1.33064i	−0.425840	−	0.904799i	$-0.640021\pi$
$828$		0			0
$829$	17.1402	+	17.1402i	0.595303	+	0.595303i	0.939059	−	0.343756i	$-0.111699\pi$
$829$	17.1402	+	17.1402i	0.595303	+	0.595303i	−0.343756	+	0.939059i	$0.611699\pi$
$830$	39.4631	−	15.6177i	1.36979	−	0.542099i
$831$		0			0
$832$	−7.18257	+	37.9503i	−0.249011	+	1.31569i
$833$	92.9594			3.22085
$834$		0			0
$835$	0.333382	+	21.7633i	0.0115372	+	0.753149i
$836$	3.21712	−	2.83903i	0.111266	−	0.0981897i
$837$		0			0
$838$	−24.1519	+	9.13288i	−0.834312	+	0.315490i
$839$			49.2982i			1.70196i	0.525197	+	0.850981i	$0.323992\pi$
$839$			49.2982i			1.70196i	−0.525197	+	0.850981i	$0.676008\pi$
$840$		0			0
$841$			7.73855i			0.266847i
$842$	0.653461	+	1.72807i	0.0225197	+	0.0595534i
$843$		0			0
$844$	−7.51871	−	0.469400i	−0.258805	−	0.0161574i
$845$	23.0502	−	0.353096i	0.792951	−	0.0121469i
$846$		0			0
$847$	53.8727			1.85109
$848$	10.2461	+	13.1829i	0.351853	+	0.452704i
$849$		0			0
$850$	−14.1595	+	34.1319i	−0.485667	+	1.17071i
$851$	−14.0164	−	14.0164i	−0.480474	−	0.480474i
$852$		0			0
$853$	−36.9286	−	36.9286i	−1.26441	−	1.26441i	−0.948933	−	0.315477i	$-0.897835\pi$
$853$	−36.9286	−	36.9286i	−1.26441	−	1.26441i	−0.315477	−	0.948933i	$-0.602165\pi$
$854$	−33.0448	−	87.3869i	−1.13077	−	2.99032i
$855$		0			0
$856$	26.3917	+	13.9493i	0.902048	+	0.476776i
$857$		−	2.74943i		−	0.0939189i	−0.998897	−	0.0469594i	$-0.985047\pi$
$857$		−	2.74943i		−	0.0939189i	0.998897	−	0.0469594i	$-0.0149532\pi$
$858$		0			0
$859$	14.1089	+	14.1089i	0.481390	+	0.481390i	0.905575	−	0.424186i	$-0.139440\pi$
$859$	14.1089	+	14.1089i	0.481390	+	0.481390i	−0.424186	+	0.905575i	$0.639440\pi$
$860$	0.525105	−	11.1565i	0.0179059	−	0.380432i
$861$		0			0
$862$	13.6998	−	30.3613i	0.466618	−	1.03411i
$863$		−	3.40986i		−	0.116073i	−0.998314	−	0.0580364i	$-0.981516\pi$
$863$		−	3.40986i		−	0.116073i	0.998314	−	0.0580364i	$-0.0184840\pi$
$864$		0			0
$865$	17.2909	−	17.8289i	0.587909	−	0.606201i
$866$	49.7236	+	22.4366i	1.68968	+	0.762428i
$867$		0			0
$868$	51.1960	+	58.0141i	1.73771	+	1.96913i
$869$	−0.156181	−	0.156181i	−0.00529807	−	0.00529807i
$870$		0			0
$871$	0.279700			0.00947728
$872$	12.1461	+	6.41981i	0.411320	+	0.217402i
$873$		0			0
$874$	15.5926	+	41.2346i	0.527428	+	1.39478i
$875$	−55.6058	+	2.55700i	−1.87982	+	0.0864425i
$876$		0			0
$877$	31.8968	−	31.8968i	1.07708	−	1.07708i	0.0803069	−	0.996770i	$-0.474410\pi$
$877$	31.8968	−	31.8968i	1.07708	−	1.07708i	0.996770	−	0.0803069i	$-0.0255900\pi$
$878$	17.6556	−	39.1279i	0.595847	−	1.32050i
$879$		0			0
$880$	−2.95650	+	2.37139i	−0.0996636	+	0.0799394i
$881$			7.77943i			0.262096i	0.991376	+	0.131048i	$0.0418342\pi$
$881$			7.77943i			0.262096i	−0.991376	+	0.131048i	$0.958166\pi$
$882$		0			0
$883$	−29.0951	−	29.0951i	−0.979129	−	0.979129i	0.0206577	−	0.999787i	$-0.493424\pi$
$883$	−29.0951	−	29.0951i	−0.979129	−	0.979129i	−0.999787	+	0.0206577i	$0.993424\pi$
$884$	−50.3628	−	3.14420i	−1.69388	−	0.105751i
$885$		0			0
$886$	−8.88148	+	3.35848i	−0.298379	+	0.112830i
$887$	20.4586			0.686933			0.343467	−	0.939165i	$-0.388399\pi$
$887$	20.4586			0.686933			0.343467	+	0.939165i	$0.388399\pi$
$888$		0			0
$889$		−	47.6814i		−	1.59918i
$890$	−10.2332	−	4.43012i	−0.343018	−	0.148498i
$891$		0			0
$892$	−30.2376	−	34.2646i	−1.01243	−	1.14726i
$893$	−6.06250	−	6.06250i	−0.202874	−	0.202874i
$894$		0			0
$895$	−20.1103	+	20.7360i	−0.672213	+	0.693128i
$896$	55.4734	−	9.77808i	1.85324	−	0.326663i
$897$		0			0
$898$	13.0541	+	5.89035i	0.435620	+	0.196564i
$899$	25.3349	+	25.3349i	0.844968	+	0.844968i
$900$		0			0
$901$	−15.4244	+	15.4244i	−0.513861	+	0.513861i
$902$	1.55205	+	4.10439i	0.0516776	+	0.136661i
$903$		0			0
$904$	−14.6608	+	4.52186i	−0.487611	+	0.150395i
$905$	−36.0951	−	35.0060i	−1.19984	−	1.16364i
$906$		0			0
$907$	−24.1511	+	24.1511i	−0.801925	+	0.801925i	−0.983396	−	0.181471i	$-0.941914\pi$
$907$	−24.1511	+	24.1511i	−0.801925	+	0.801925i	0.181471	+	0.983396i	$0.441914\pi$
$908$	−8.18021	−	0.510698i	−0.271470	−	0.0169481i
$909$		0			0
$910$	−27.9719	−	70.6798i	−0.927258	−	2.34301i
$911$	−29.3578			−0.972668			−0.486334	−	0.873773i	$-0.661666\pi$
$911$	−29.3578			−0.972668			−0.486334	+	0.873773i	$0.661666\pi$
$912$		0			0
$913$			5.68703i			0.188213i
$914$	−0.840189	+	1.86201i	−0.0277910	+	0.0615897i
$915$		0			0
$916$	−38.9285	−	2.43035i	−1.28623	−	0.0803009i
$917$	−62.2568	+	62.2568i	−2.05590	+	2.05590i
$918$		0			0
$919$	42.3082			1.39562			0.697809	−	0.716284i	$-0.254159\pi$
$919$	42.3082			1.39562			0.697809	+	0.716284i	$0.254159\pi$
$920$	−12.0456	−	37.0306i	−0.397131	−	1.22086i
$921$		0			0
$922$	−19.0024	−	50.2518i	−0.625811	−	1.65496i
$923$	−16.9596	−	16.9596i	−0.558231	−	0.558231i
$924$		0			0
$925$	−11.7257	−	11.0284i	−0.385539	−	0.362612i
$926$	−11.7842	+	26.1159i	−0.387253	+	0.858223i
$927$		0			0
$928$	25.3558	−	6.11970i	0.832344	−	0.200889i
$929$		−	27.8428i		−	0.913494i	−0.889597	−	0.456747i	$-0.849014\pi$
$929$		−	27.8428i		−	0.913494i	0.889597	−	0.456747i	$-0.150986\pi$
$930$		0			0
$931$	63.6822	−	63.6822i	2.08710	−	2.08710i
$932$	41.7682	−	36.8594i	1.36816	−	1.20737i
$933$		0			0
$934$	−6.43655	−	17.0214i	−0.210610	−	0.556958i
$935$	−3.55449	−	3.44723i	−0.116244	−	0.112737i
$936$		0			0
$937$	−29.0721			−0.949745			−0.474873	−	0.880054i	$-0.657506\pi$
$937$	−29.0721			−0.949745			−0.474873	+	0.880054i	$0.657506\pi$
$938$	−0.144278	−	0.381542i	−0.00471084	−	0.0124578i
$939$		0			0
$940$	5.09742	+	5.60097i	0.166260	+	0.182683i
$941$	−3.40692	+	3.40692i	−0.111062	+	0.111062i	−0.760454	−	0.649392i	$-0.775024\pi$
$941$	−3.40692	+	3.40692i	−0.111062	+	0.111062i	0.649392	+	0.760454i	$0.275024\pi$
$942$		0			0
$943$	−45.0846			−1.46816
$944$	−14.3852	−	18.5085i	−0.468200	−	0.602400i
$945$		0			0
$946$	1.36415	+	0.615543i	0.0443524	+	0.0200130i
$947$	9.01416	−	9.01416i	0.292921	−	0.292921i	−0.545312	−	0.838233i	$-0.683589\pi$
$947$	9.01416	−	9.01416i	0.292921	−	0.292921i	0.838233	+	0.545312i	$0.183589\pi$
$948$		0			0
$949$	−13.2262	+	13.2262i	−0.429341	+	0.429341i
$950$	13.6822	+	33.0822i	0.443909	+	1.07333i
$951$		0			0
$952$	21.6896	+	70.3224i	0.702965	+	2.27916i
$953$		−	35.7289i		−	1.15737i	−0.815550	−	0.578687i	$-0.803565\pi$
$953$		−	35.7289i		−	1.15737i	0.815550	−	0.578687i	$-0.196435\pi$
$954$		0			0
$955$	0.0742364	+	4.84617i	0.00240223	+	0.156818i
$956$	30.1642	+	34.1814i	0.975581	+	1.10550i
$957$		0			0
$958$	−2.67834	+	5.93567i	−0.0865331	+	0.191773i
$959$	16.0048			0.516821
$960$		0			0
$961$	−29.3778			−0.947671
$962$	9.04095	−	20.0363i	0.291492	−	0.645998i
$963$		0			0
$964$	−5.73259	−	6.49604i	−0.184634	−	0.209223i
$965$	−51.5400	+	0.789519i	−1.65913	+	0.0254155i
$966$		0			0
$967$			0.997773i			0.0320862i	0.999871	+	0.0160431i	$0.00510690\pi$
$967$			0.997773i			0.0320862i	−0.999871	+	0.0160431i	$0.994893\pi$
$968$	9.02020	+	29.2454i	0.289920	+	0.939982i
$969$		0			0
$970$	−4.15504	+	9.59778i	−0.133410	+	0.308166i
$971$	42.0632	−	42.0632i	1.34987	−	1.34987i	0.464075	−	0.885796i	$-0.346387\pi$
$971$	42.0632	−	42.0632i	1.34987	−	1.34987i	0.885796	−	0.464075i	$-0.153613\pi$
$972$		0			0
$973$	−3.62757	+	3.62757i	−0.116295	+	0.116295i
$974$	41.5185	+	18.7343i	1.33034	+	0.600285i
$975$		0			0
$976$	41.9060	−	32.5704i	1.34138	−	1.04255i
$977$	−16.7515			−0.535927			−0.267963	−	0.963429i	$-0.586351\pi$
$977$	−16.7515			−0.535927			−0.267963	+	0.963429i	$0.586351\pi$
$978$		0			0
$979$	1.05657	−	1.05657i	0.0337680	−	0.0337680i
$980$	−58.8342	+	53.5448i	−1.87939	+	1.71043i
$981$		0			0
$982$	12.3214	+	32.5840i	0.393193	+	1.03980i
$983$	−40.1381			−1.28021			−0.640103	−	0.768289i	$-0.721108\pi$
$983$	−40.1381			−1.28021			−0.640103	+	0.768289i	$0.721108\pi$
$984$		0			0
$985$	3.46790	+	3.36326i	0.110497	+	0.107162i
$986$	12.0532	+	31.8748i	0.383854	+	1.01510i
$987$		0			0
$988$	−36.6552	+	32.3473i	−1.16616	+	1.02911i
$989$	−10.8730	+	10.8730i	−0.345740	+	0.345740i
$990$		0			0
$991$			52.3742i			1.66372i	0.554984	+	0.831861i	$0.312724\pi$
$991$			52.3742i			1.66372i	−0.554984	+	0.831861i	$0.687276\pi$
$992$	−22.9215	+	37.5059i	−0.727760	+	1.19081i
$993$		0			0
$994$	−14.3865	+	31.8830i	−0.456312	+	1.01127i
$995$	−0.107117	−	6.99264i	−0.00339585	−	0.221682i
$996$		0			0
$997$	7.28564	+	7.28564i	0.230738	+	0.230738i	0.813001	−	0.582262i	$-0.197832\pi$
$997$	7.28564	+	7.28564i	0.230738	+	0.230738i	−0.582262	+	0.813001i	$0.697832\pi$
$998$	−11.0355	−	29.1833i	−0.349322	−	0.923781i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	720.2.u.a.179.20	yes	96
3.2	odd	2	inner	720.2.u.a.179.29	yes	96
4.3	odd	2		2880.2.u.a.2159.25		96
5.4	even	2	inner	720.2.u.a.179.30	yes	96
12.11	even	2		2880.2.u.a.2159.24		96
15.14	odd	2	inner	720.2.u.a.179.19	✓	96
16.5	even	4		2880.2.u.a.719.1		96
16.11	odd	4	inner	720.2.u.a.539.19	yes	96
20.19	odd	2		2880.2.u.a.2159.48		96
48.5	odd	4		2880.2.u.a.719.48		96
48.11	even	4	inner	720.2.u.a.539.30	yes	96
60.59	even	2		2880.2.u.a.2159.1		96
80.59	odd	4	inner	720.2.u.a.539.29	yes	96
80.69	even	4		2880.2.u.a.719.24		96
240.59	even	4	inner	720.2.u.a.539.20	yes	96
240.149	odd	4		2880.2.u.a.719.25		96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
720.2.u.a.179.19	✓	96	15.14	odd	2	inner
720.2.u.a.179.20	yes	96	1.1	even	1	trivial
720.2.u.a.179.29	yes	96	3.2	odd	2	inner
720.2.u.a.179.30	yes	96	5.4	even	2	inner
720.2.u.a.539.19	yes	96	16.11	odd	4	inner
720.2.u.a.539.20	yes	96	240.59	even	4	inner
720.2.u.a.539.29	yes	96	80.59	odd	4	inner
720.2.u.a.539.30	yes	96	48.11	even	4	inner
2880.2.u.a.719.1		96	16.5	even	4
2880.2.u.a.719.24		96	80.69	even	4
2880.2.u.a.719.25		96	240.149	odd	4
2880.2.u.a.719.48		96	48.5	odd	4
2880.2.u.a.2159.1		96	60.59	even	2
2880.2.u.a.2159.24		96	12.11	even	2
2880.2.u.a.2159.25		96	4.3	odd	2
2880.2.u.a.2159.48		96	20.19	odd	2

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:	\( N \)	\(=\)	\( 720 = 2^{4} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	720.u (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.581659 + 1.28906i) q^{2} +(-1.32335 - 1.49958i) q^{4} +(0.0342493 + 2.23581i) q^{5} -4.97879i q^{7} +(2.70279 - 0.833625i) q^{8} +(-2.90201 - 1.25633i) q^{10} +(0.299629 - 0.299629i) q^{11} +(-3.41391 + 3.41391i) q^{13} +(6.41795 + 2.89596i) q^{14} +(-0.497509 + 3.96894i) q^{16} -5.22586 q^{17} +(-3.58000 + 3.58000i) q^{19} +(3.30746 - 3.01011i) q^{20} +(0.211957 + 0.560520i) q^{22} -6.15703 q^{23} +(-4.99765 + 0.153150i) q^{25} +(-2.41500 - 6.38646i) q^{26} +(-7.46612 + 6.58866i) q^{28} +(-3.26048 + 3.26048i) q^{29} -7.77031i q^{31} +(-4.82682 - 2.94989i) q^{32} +(3.03966 - 6.73644i) q^{34} +(11.1316 - 0.170520i) q^{35} +(2.27648 + 2.27648i) q^{37} +(-2.53249 - 6.69716i) q^{38} +(1.95639 + 6.01436i) q^{40} +7.32246 q^{41} +(1.76594 - 1.76594i) q^{43} +(-0.845831 - 0.0528060i) q^{44} +(3.58129 - 7.93678i) q^{46} +1.69344i q^{47} -17.7884 q^{49} +(2.70951 - 6.53135i) q^{50} +(9.63723 + 0.601662i) q^{52} +(2.95155 - 2.95155i) q^{53} +(0.680173 + 0.659649i) q^{55} +(-4.15045 - 13.4566i) q^{56} +(-2.30646 - 6.09944i) q^{58} +(-4.14389 + 4.14389i) q^{59} +(-9.38240 - 9.38240i) q^{61} +(10.0164 + 4.51967i) q^{62} +(6.61014 - 4.50623i) q^{64} +(-7.74976 - 7.51592i) q^{65} +(-0.0409648 - 0.0409648i) q^{67} +(6.91562 + 7.83661i) q^{68} +(-6.25499 + 14.4485i) q^{70} +4.96779i q^{71} +3.87421 q^{73} +(-4.25865 + 1.61038i) q^{74} +(10.1061 + 0.630932i) q^{76} +(-1.49179 - 1.49179i) q^{77} -0.521248i q^{79} +(-8.89082 - 0.976399i) q^{80} +(-4.25917 + 9.43908i) q^{82} +(-9.49013 + 9.49013i) q^{83} +(-0.178982 - 11.6840i) q^{85} +(1.24923 + 3.30358i) q^{86} +(0.560055 - 1.05961i) q^{88} +3.52625 q^{89} +(16.9971 + 16.9971i) q^{91} +(8.14788 + 9.23299i) q^{92} +(-2.18294 - 0.985002i) q^{94} +(-8.12679 - 7.88156i) q^{95} -3.30729i q^{97} +(10.3467 - 22.9302i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q - 8 q^{16} - 16 q^{19} + 72 q^{34} + 8 q^{40} + 8 q^{46} - 96 q^{49} + 64 q^{55} - 32 q^{61} + 48 q^{64} + 24 q^{70} + 40 q^{76} - 88 q^{94}+O(q^{100}) \) 96 * q - 8 * q^16 - 16 * q^19 + 72 * q^34 + 8 * q^40 + 8 * q^46 - 96 * q^49 + 64 * q^55 - 32 * q^61 + 48 * q^64 + 24 * q^70 + 40 * q^76 - 88 * q^94

Introduction

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