LMFDB - Embedded newform 512.2.k.a.497.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [512,2,Mod(17,512)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("512.17"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(512, base_ring=CyclotomicField(32)) chi = DirichletCharacter(H, H._module([0, 7])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 512 = 2^{9} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	512.k (of order $32$, degree $16$, not minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$4.08834058349$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$15$ over $\Q(\zeta_{32})$
Twist minimal:	no (minimal twist has level 128)
Sato-Tate group:	$\mathrm{SU}(2)[C_{32}]$

Embedding invariants

Embedding label			497.2
Character	$\chi$	$=$	512.497
Dual form			512.2.k.a.273.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.34878 + 1.25545i) q^{3} +(-2.35055 - 2.86416i) q^{5} +(1.77512 - 1.18610i) q^{7} +(2.27391 - 3.40315i) q^{9} +(-3.00424 + 0.911326i) q^{11} +(4.40033 + 3.61126i) q^{13} +(9.11675 + 3.77628i) q^{15} +(-2.12200 + 0.878960i) q^{17} +(0.222958 + 2.26373i) q^{19} +(-2.68028 + 5.01446i) q^{21} +(-4.14830 + 0.825148i) q^{23} +(-1.70285 + 8.56080i) q^{25} +(-0.285305 + 2.89675i) q^{27} +(-1.05879 + 3.49035i) q^{29} +(0.733820 + 0.733820i) q^{31} +(5.91218 - 5.91218i) q^{33} +(-7.56968 - 2.29624i) q^{35} +(1.40268 + 0.138152i) q^{37} +(-14.8692 - 2.95766i) q^{39} +(1.67780 + 8.43488i) q^{41} +(2.27833 + 1.21779i) q^{43} +(-15.0921 + 1.48644i) q^{45} +(4.22422 + 10.1982i) q^{47} +(-0.934561 + 2.25623i) q^{49} +(3.88062 - 4.72855i) q^{51} +(-0.810406 - 2.67155i) q^{53} +(9.67181 + 6.46250i) q^{55} +(-3.36567 - 5.03709i) q^{57} +(6.48788 - 5.32446i) q^{59} +(4.18727 + 7.83384i) q^{61} -8.73808i q^{63} -21.0917i q^{65} +(-1.02445 - 1.91661i) q^{67} +(8.70752 - 7.14608i) q^{69} +(4.85914 + 7.27222i) q^{71} +(-9.35312 - 6.24955i) q^{73} +(-6.74804 - 22.2453i) q^{75} +(-4.25196 + 5.18103i) q^{77} +(1.50619 - 3.63626i) q^{79} +(1.73229 + 4.18212i) q^{81} +(0.375929 - 0.0370258i) q^{83} +(7.50535 + 4.01169i) q^{85} +(-1.89510 - 9.52732i) q^{87} +(5.47983 + 1.09001i) q^{89} +(12.0944 + 1.19120i) q^{91} +(-2.64486 - 0.802308i) q^{93} +(5.95960 - 5.95960i) q^{95} +(-4.20900 - 4.20900i) q^{97} +(-3.73000 + 12.2962i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q + 16 q^{3} - 16 q^{5} + 16 q^{7} - 16 q^{9} + 16 q^{11} - 16 q^{13} + 16 q^{15} - 16 q^{17} + 16 q^{19} - 16 q^{21} + 16 q^{23} - 16 q^{25} + 16 q^{27} - 16 q^{29} + 16 q^{31} - 16 q^{33} + 16 q^{35}+ \cdots + 16 q^{99}+O(q^{100}) $ 240 * q + 16 * q^3 - 16 * q^5 + 16 * q^7 - 16 * q^9 + 16 * q^11 - 16 * q^13 + 16 * q^15 - 16 * q^17 + 16 * q^19 - 16 * q^21 + 16 * q^23 - 16 * q^25 + 16 * q^27 - 16 * q^29 + 16 * q^31 - 16 * q^33 + 16 * q^35 - 16 * q^37 + 16 * q^39 - 16 * q^41 + 16 * q^43 - 16 * q^45 + 16 * q^47 - 16 * q^49 + 16 * q^51 - 16 * q^53 + 16 * q^55 - 16 * q^57 + 16 * q^59 - 16 * q^61 + 16 * q^67 - 16 * q^69 + 16 * q^71 - 16 * q^73 + 16 * q^75 - 16 * q^77 + 16 * q^79 - 16 * q^81 + 16 * q^83 - 16 * q^85 + 16 * q^87 - 16 * q^89 + 16 * q^91 - 16 * q^93 + 16 * q^95 - 16 * q^97 + 16 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/512\mathbb{Z}\right)^\times$.

$n$	$5$	$511$
$\chi(n)$	$e\left(\frac{9}{32}\right)$	$1$

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 $

$2$		0			0
$2$		0			0
$3$	−2.34878	+	1.25545i	−1.35607	+	0.724835i	−0.979479	−	0.201545i	$-0.935404\pi$
$3$	−2.34878	+	1.25545i	−1.35607	+	0.724835i	−0.376591	+	0.926380i	$0.622904\pi$
$4$		0			0
$5$	−2.35055	−	2.86416i	−1.05120	−	1.28089i	−0.958468	−	0.285200i	$-0.907940\pi$
$5$	−2.35055	−	2.86416i	−1.05120	−	1.28089i	−0.0927320	−	0.995691i	$-0.529560\pi$
$6$		0			0
$7$	1.77512	−	1.18610i	0.670932	−	0.448302i	−0.172879	−	0.984943i	$-0.555307\pi$
$7$	1.77512	−	1.18610i	0.670932	−	0.448302i	0.843811	+	0.536641i	$0.180307\pi$
$8$		0			0
$9$	2.27391	−	3.40315i	0.757971	−	1.13438i
$10$		0			0
$11$	−3.00424	+	0.911326i	−0.905812	+	0.274775i	−0.708621	−	0.705590i	$-0.750682\pi$
$11$	−3.00424	+	0.911326i	−0.905812	+	0.274775i	−0.197192	+	0.980365i	$0.563182\pi$
$12$		0			0
$13$	4.40033	+	3.61126i	1.22043	+	1.00158i	0.999655	+	0.0262590i	$0.00835946\pi$
$13$	4.40033	+	3.61126i	1.22043	+	1.00158i	0.220777	+	0.975324i	$0.429141\pi$
$14$		0			0
$15$	9.11675	+	3.77628i	2.35394	+	0.975032i
$16$		0			0
$17$	−2.12200	+	0.878960i	−0.514660	+	0.213179i	−0.624869	−	0.780729i	$-0.714848\pi$
$17$	−2.12200	+	0.878960i	−0.514660	+	0.213179i	0.110210	+	0.993908i	$0.464848\pi$
$18$		0			0
$19$	0.222958	+	2.26373i	0.0511500	+	0.519334i	0.986286	+	0.165045i	$0.0527771\pi$
$19$	0.222958	+	2.26373i	0.0511500	+	0.519334i	−0.935136	+	0.354289i	$0.884723\pi$
$20$		0			0
$21$	−2.68028	+	5.01446i	−0.584886	+	1.09424i
$22$		0			0
$23$	−4.14830	+	0.825148i	−0.864981	+	0.172055i	−0.607589	−	0.794252i	$-0.707863\pi$
$23$	−4.14830	+	0.825148i	−0.864981	+	0.172055i	−0.257392	+	0.966307i	$0.582863\pi$
$24$		0			0
$25$	−1.70285	+	8.56080i	−0.340570	+	1.71216i
$26$		0			0
$27$	−0.285305	+	2.89675i	−0.0549069	+	0.557480i
$28$		0			0
$29$	−1.05879	+	3.49035i	−0.196612	+	0.648142i	0.802090	+	0.597203i	$0.203721\pi$
$29$	−1.05879	+	3.49035i	−0.196612	+	0.648142i	−0.998702	+	0.0509386i	$0.983779\pi$
$30$		0			0
$31$	0.733820	+	0.733820i	0.131798	+	0.131798i	0.769928	−	0.638130i	$-0.220292\pi$
$31$	0.733820	+	0.733820i	0.131798	+	0.131798i	−0.638130	+	0.769928i	$0.720292\pi$
$32$		0			0
$33$	5.91218	−	5.91218i	1.02918	−	1.02918i
$34$		0			0
$35$	−7.56968	−	2.29624i	−1.27951	−	0.388135i
$36$		0			0
$37$	1.40268	+	0.138152i	0.230600	+	0.0227121i	0.212657	−	0.977127i	$-0.431788\pi$
$37$	1.40268	+	0.138152i	0.230600	+	0.0227121i	0.0179429	+	0.999839i	$0.494288\pi$
$38$		0			0
$39$	−14.8692	−	2.95766i	−2.38097	−	0.473605i
$40$		0			0
$41$	1.67780	+	8.43488i	0.262028	+	1.31731i	0.857730	+	0.514100i	$0.171874\pi$
$41$	1.67780	+	8.43488i	0.262028	+	1.31731i	−0.595702	+	0.803206i	$0.703126\pi$
$42$		0			0
$43$	2.27833	+	1.21779i	0.347442	+	0.185711i	0.635882	−	0.771787i	$-0.280637\pi$
$43$	2.27833	+	1.21779i	0.347442	+	0.185711i	−0.288440	+	0.957498i	$0.593137\pi$
$44$		0			0
$45$	−15.0921	+	1.48644i	−2.24980	+	0.221586i
$46$		0			0
$47$	4.22422	+	10.1982i	0.616166	+	1.48756i	0.856123	+	0.516772i	$0.172867\pi$
$47$	4.22422	+	10.1982i	0.616166	+	1.48756i	−0.239957	+	0.970783i	$0.577133\pi$
$48$		0			0
$49$	−0.934561	+	2.25623i	−0.133509	+	0.322319i
$50$		0			0
$51$	3.88062	−	4.72855i	0.543395	−	0.662129i
$52$		0			0
$53$	−0.810406	−	2.67155i	−0.111318	−	0.366966i	0.883526	−	0.468381i	$-0.155163\pi$
$53$	−0.810406	−	2.67155i	−0.111318	−	0.366966i	−0.994844	+	0.101416i	$0.967663\pi$
$54$		0			0
$55$	9.67181	+	6.46250i	1.30415	+	0.871403i
$56$		0			0
$57$	−3.36567	−	5.03709i	−0.445794	−	0.667179i
$58$		0			0
$59$	6.48788	−	5.32446i	0.844650	−	0.693186i	−0.109021	−	0.994039i	$-0.534771\pi$
$59$	6.48788	−	5.32446i	0.844650	−	0.693186i	0.953670	+	0.300853i	$0.0972715\pi$
$60$		0			0
$61$	4.18727	+	7.83384i	0.536125	+	1.00302i	0.993509	+	0.113751i	$0.0362866\pi$
$61$	4.18727	+	7.83384i	0.536125	+	1.00302i	−0.457384	+	0.889269i	$0.651213\pi$
$62$		0			0
$63$		−	8.73808i		−	1.10089i
$64$		0			0
$65$		−	21.0917i		−	2.61611i
$66$		0			0
$67$	−1.02445	−	1.91661i	−0.125157	−	0.234152i	0.811537	−	0.584300i	$-0.198631\pi$
$67$	−1.02445	−	1.91661i	−0.125157	−	0.234152i	−0.936694	+	0.350149i	$0.886131\pi$
$68$		0			0
$69$	8.70752	−	7.14608i	1.04826	−	0.860287i
$70$		0			0
$71$	4.85914	+	7.27222i	0.576674	+	0.863053i	0.999059	−	0.0433628i	$-0.0138071\pi$
$71$	4.85914	+	7.27222i	0.576674	+	0.863053i	−0.422386	+	0.906416i	$0.638807\pi$
$72$		0			0
$73$	−9.35312	−	6.24955i	−1.09470	−	0.731455i	−0.129137	−	0.991627i	$-0.541221\pi$
$73$	−9.35312	−	6.24955i	−1.09470	−	0.731455i	−0.965562	+	0.260172i	$0.916221\pi$
$74$		0			0
$75$	−6.74804	−	22.2453i	−0.779196	−	2.56867i
$76$		0			0
$77$	−4.25196	+	5.18103i	−0.484556	+	0.590433i
$78$		0			0
$79$	1.50619	−	3.63626i	0.169459	−	0.409111i	−0.816220	−	0.577741i	$-0.803934\pi$
$79$	1.50619	−	3.63626i	0.169459	−	0.409111i	0.985679	+	0.168630i	$0.0539343\pi$
$80$		0			0
$81$	1.73229	+	4.18212i	0.192477	+	0.464680i
$82$		0			0
$83$	0.375929	−	0.0370258i	0.0412636	−	0.00406411i	−0.0773643	−	0.997003i	$-0.524650\pi$
$83$	0.375929	−	0.0370258i	0.0412636	−	0.00406411i	0.118628	+	0.992939i	$0.462150\pi$
$84$		0			0
$85$	7.50535	+	4.01169i	0.814070	+	0.435129i
$86$		0			0
$87$	−1.89510	−	9.52732i	−0.203176	−	1.02144i
$88$		0			0
$89$	5.47983	+	1.09001i	0.580861	+	0.115540i	0.476771	−	0.879028i	$-0.341807\pi$
$89$	5.47983	+	1.09001i	0.580861	+	0.115540i	0.104090	+	0.994568i	$0.466807\pi$
$90$		0			0
$91$	12.0944	+	1.19120i	1.26784	+	0.124871i
$92$		0			0
$93$	−2.64486	−	0.802308i	−0.274259	−	0.0831955i
$94$		0			0
$95$	5.95960	−	5.95960i	0.611442	−	0.611442i
$96$		0			0
$97$	−4.20900	−	4.20900i	−0.427359	−	0.427359i	0.460369	−	0.887728i	$-0.347717\pi$
$97$	−4.20900	−	4.20900i	−0.427359	−	0.427359i	−0.887728	+	0.460369i	$0.847717\pi$
$98$		0			0
$99$	−3.73000	+	12.2962i	−0.374879	+	1.23581i
$100$		0			0
$101$	−1.26435	+	12.8372i	−0.125808	+	1.27735i	0.700306	+	0.713843i	$0.253047\pi$
$101$	−1.26435	+	12.8372i	−0.125808	+	1.27735i	−0.826114	+	0.563503i	$0.809453\pi$
$102$		0			0
$103$	1.03672	−	5.21196i	0.102151	−	0.513550i	−0.895500	−	0.445061i	$-0.853182\pi$
$103$	1.03672	−	5.21196i	0.102151	−	0.513550i	0.997652	−	0.0684892i	$-0.0218179\pi$
$104$		0			0
$105$	20.6624	−	4.11000i	2.01644	−	0.401095i
$106$		0			0
$107$	−7.69560	+	14.3975i	−0.743962	+	1.39185i	0.169749	+	0.985487i	$0.445704\pi$
$107$	−7.69560	+	14.3975i	−0.743962	+	1.39185i	−0.913710	+	0.406367i	$0.866796\pi$
$108$		0			0
$109$	−1.12768	−	11.4495i	−0.108012	−	1.09666i	−0.884503	−	0.466535i	$-0.845502\pi$
$109$	−1.12768	−	11.4495i	−0.108012	−	1.09666i	0.776491	−	0.630129i	$-0.216998\pi$
$110$		0			0
$111$	−3.46805	+	1.43651i	−0.329172	+	0.136348i
$112$		0			0
$113$	−14.2154	−	5.88823i	−1.33728	−	0.553918i	−0.404554	−	0.914514i	$-0.632573\pi$
$113$	−14.2154	−	5.88823i	−1.33728	−	0.553918i	−0.932722	+	0.360596i	$0.882573\pi$
$114$		0			0
$115$	12.1142	+	9.94184i	1.12965	+	0.927081i
$116$		0			0
$117$	22.2956	−	6.76331i	2.06123	−	0.625268i
$118$		0			0
$119$	−2.72427	+	4.07715i	−0.249733	+	0.373752i
$120$		0			0
$121$	−0.951224	+	0.635587i	−0.0864749	+	0.0577807i
$122$		0			0
$123$	−14.5304	−	17.7053i	−1.31016	−	1.59643i
$124$		0			0
$125$	12.1837	−	6.51230i	1.08974	−	0.582478i
$126$		0			0
$127$	−5.24212			−0.465163			−0.232582	−	0.972577i	$-0.574717\pi$
$127$	−5.24212			−0.465163			−0.232582	+	0.972577i	$0.574717\pi$
$128$		0			0
$129$	−6.88017			−0.605765
$130$		0			0
$131$	3.27431	−	1.75016i	0.286078	−	0.152912i	−0.322116	−	0.946700i	$-0.604394\pi$
$131$	3.27431	−	1.75016i	0.286078	−	0.152912i	0.608194	+	0.793788i	$0.291894\pi$
$132$		0			0
$133$	3.08077	+	3.75393i	0.267137	+	0.325507i
$134$		0			0
$135$	8.96738	−	5.99181i	0.771789	−	0.515693i
$136$		0			0
$137$	4.16098	−	6.22734i	0.355496	−	0.532038i	−0.610018	−	0.792388i	$-0.708838\pi$
$137$	4.16098	−	6.22734i	0.355496	−	0.532038i	0.965514	+	0.260350i	$0.0838378\pi$
$138$		0			0
$139$	−5.39432	+	1.63635i	−0.457541	+	0.138793i	−0.510638	−	0.859796i	$-0.670591\pi$
$139$	−5.39432	+	1.63635i	−0.457541	+	0.138793i	0.0530972	+	0.998589i	$0.483091\pi$
$140$		0			0
$141$	−22.7251	−	18.6500i	−1.91380	−	1.57061i
$142$		0			0
$143$	−16.5107	−	6.83895i	−1.38069	−	0.571902i
$144$		0			0
$145$	12.4856	−	5.17173i	1.03688	−	0.429488i
$146$		0			0
$147$	−0.637504	−	6.47269i	−0.0525805	−	0.533858i
$148$		0			0
$149$	4.95792	−	9.27561i	0.406168	−	0.759887i	−0.592798	−	0.805351i	$-0.701977\pi$
$149$	4.95792	−	9.27561i	0.406168	−	0.759887i	0.998966	+	0.0454640i	$0.0144766\pi$
$150$		0			0
$151$	−16.0126	+	3.18511i	−1.30309	+	0.259200i	−0.797366	−	0.603496i	$-0.793774\pi$
$151$	−16.0126	+	3.18511i	−1.30309	+	0.259200i	−0.505722	+	0.862697i	$0.668774\pi$
$152$		0			0
$153$	−1.83400	+	9.22015i	−0.148270	+	0.745405i
$154$		0			0
$155$	0.376893	−	3.82666i	0.0302728	−	0.307365i
$156$		0			0
$157$	−2.96267	+	9.76661i	−0.236447	+	0.779461i	0.755759	+	0.654850i	$0.227268\pi$
$157$	−2.96267	+	9.76661i	−0.236447	+	0.779461i	−0.992206	+	0.124611i	$0.960232\pi$
$158$		0			0
$159$	5.25746	+	5.25746i	0.416944	+	0.416944i
$160$		0			0
$161$	−6.38502	+	6.38502i	−0.503210	+	0.503210i
$162$		0			0
$163$	−15.5566	−	4.71903i	−1.21848	−	0.369623i	−0.385390	−	0.922754i	$-0.625933\pi$
$163$	−15.5566	−	4.71903i	−1.21848	−	0.369623i	−0.833095	+	0.553131i	$0.813433\pi$
$164$		0			0
$165$	−30.8303	−	3.03652i	−2.40014	−	0.236393i
$166$		0			0
$167$	17.4273	+	3.46651i	1.34857	+	0.268246i	0.815956	−	0.578115i	$-0.196211\pi$
$167$	17.4273	+	3.46651i	1.34857	+	0.268246i	0.532610	+	0.846361i	$0.321211\pi$
$168$		0			0
$169$	3.78556	+	19.0313i	0.291197	+	1.46394i
$170$		0			0
$171$	8.21079	+	4.38876i	0.627895	+	0.335617i
$172$		0			0
$173$	−4.62158	+	0.455186i	−0.351372	+	0.0346072i	−0.272164	−	0.962251i	$-0.587739\pi$
$173$	−4.62158	+	0.455186i	−0.351372	+	0.0346072i	−0.0792085	+	0.996858i	$0.525239\pi$
$174$		0			0
$175$	7.13118	+	17.2162i	0.539066	+	1.30142i
$176$		0			0
$177$	−8.55401	+	20.6512i	−0.642959	+	1.55224i
$178$		0			0
$179$	−4.15470	+	5.06252i	−0.310537	+	0.378391i	−0.904769	−	0.425903i	$-0.859956\pi$
$179$	−4.15470	+	5.06252i	−0.310537	+	0.378391i	0.594231	+	0.804294i	$0.297456\pi$
$180$		0			0
$181$	−1.19266	−	3.93167i	−0.0886497	−	0.292239i	0.901394	−	0.433000i	$-0.142545\pi$
$181$	−1.19266	−	3.93167i	−0.0886497	−	0.292239i	−0.990044	+	0.140761i	$0.955045\pi$
$182$		0			0
$183$	−19.6700	−	13.1431i	−1.45405	−	0.971563i
$184$		0			0
$185$	−2.90140	−	4.34225i	−0.213315	−	0.319248i
$186$		0			0
$187$	5.57397	−	4.57444i	0.407609	−	0.334516i
$188$		0			0
$189$	2.92937	+	5.48047i	0.213081	+	0.398646i
$190$		0			0
$191$		−	16.4545i		−	1.19061i	−0.803500	−	0.595304i	$-0.797032\pi$
$191$		−	16.4545i		−	1.19061i	0.803500	−	0.595304i	$-0.202968\pi$
$192$		0			0
$193$			13.0562i			0.939805i	0.882718	+	0.469903i	$0.155711\pi$
$193$			13.0562i			0.939805i	−0.882718	+	0.469903i	$0.844289\pi$
$194$		0			0
$195$	26.4796	+	49.5399i	1.89624	+	3.54762i
$196$		0			0
$197$	11.7091	−	9.60941i	0.834239	−	0.684642i	−0.116988	−	0.993133i	$-0.537324\pi$
$197$	11.7091	−	9.60941i	0.834239	−	0.684642i	0.951227	+	0.308491i	$0.0998239\pi$
$198$		0			0
$199$	3.43353	+	5.13863i	0.243396	+	0.364268i	0.932974	−	0.359943i	$-0.117204\pi$
$199$	3.43353	+	5.13863i	0.243396	+	0.364268i	−0.689578	+	0.724211i	$0.742204\pi$
$200$		0			0
$201$	4.81243	+	3.21556i	0.339442	+	0.226808i
$202$		0			0
$203$	2.26042	+	7.45161i	0.158650	+	0.523000i
$204$		0			0
$205$	20.2151	−	24.6321i	1.41188	−	1.72038i
$206$		0			0
$207$	−6.62477	+	15.9936i	−0.460453	+	1.11163i
$208$		0			0
$209$	−2.73281	−	6.59759i	−0.189032	−	0.456365i
$210$		0			0
$211$	−17.5935	+	1.73281i	−1.21119	+	0.119291i	−0.683373	−	0.730069i	$-0.739488\pi$
$211$	−17.5935	+	1.73281i	−1.21119	+	0.119291i	−0.527813	+	0.849361i	$0.676988\pi$
$212$		0			0
$213$	−20.5430	−	10.9804i	−1.40758	−	0.752368i
$214$		0			0
$215$	−1.86738	−	9.38797i	−0.127355	−	0.640255i
$216$		0			0
$217$	2.17300	+	0.432236i	0.147513	+	0.0293421i
$218$		0			0
$219$	29.8144	+	2.93647i	2.01467	+	0.198428i
$220$		0			0
$221$	−12.5116	−	3.79537i	−0.841624	−	0.255304i
$222$		0			0
$223$	−2.16002	+	2.16002i	−0.144646	+	0.144646i	−0.775721	−	0.631076i	$-0.782614\pi$
$223$	−2.16002	+	2.16002i	−0.144646	+	0.144646i	0.631076	+	0.775721i	$0.282614\pi$
$224$		0			0
$225$	25.2616	+	25.2616i	1.68410	+	1.68410i
$226$		0			0
$227$	0.185477	−	0.611434i	0.0123105	−	0.0405823i	−0.950570	−	0.310511i	$-0.899500\pi$
$227$	0.185477	−	0.611434i	0.0123105	−	0.0405823i	0.962880	+	0.269928i	$0.0870000\pi$
$228$		0			0
$229$	−1.56897	+	15.9300i	−0.103680	+	1.05268i	0.792765	+	0.609528i	$0.208641\pi$
$229$	−1.56897	+	15.9300i	−0.103680	+	1.05268i	−0.896445	+	0.443155i	$0.853859\pi$
$230$		0			0
$231$	3.48241	−	17.5072i	0.229126	−	1.15189i
$232$		0			0
$233$	−16.7807	+	3.33790i	−1.09934	+	0.218673i	−0.711244	−	0.702945i	$-0.751868\pi$
$233$	−16.7807	+	3.33790i	−1.09934	+	0.218673i	−0.388098	+	0.921618i	$0.626868\pi$
$234$		0			0
$235$	19.2799	−	36.0702i	1.25768	−	2.35296i
$236$		0			0
$237$	1.02744	+	10.4317i	0.0667391	+	0.677614i
$238$		0			0
$239$	14.5753	−	6.03728i	0.942796	−	0.390519i	0.142277	−	0.989827i	$-0.454557\pi$
$239$	14.5753	−	6.03728i	0.942796	−	0.390519i	0.800519	+	0.599308i	$0.204557\pi$
$240$		0			0
$241$	23.4975	+	9.73297i	1.51361	+	0.626956i	0.976298	−	0.216430i	$-0.0694415\pi$
$241$	23.4975	+	9.73297i	1.51361	+	0.626956i	0.537307	+	0.843386i	$0.319441\pi$
$242$		0			0
$243$	−16.0694	−	13.1878i	−1.03085	−	0.845997i
$244$		0			0
$245$	8.65894	−	2.62666i	0.553199	−	0.167811i
$246$		0			0
$247$	−7.19381	+	10.7663i	−0.457731	+	0.685044i
$248$		0			0
$249$	−0.836491	+	0.558926i	−0.0530105	+	0.0354205i
$250$		0			0
$251$	15.7570	+	19.1999i	0.994571	+	1.21189i	0.977261	+	0.212038i	$0.0680101\pi$
$251$	15.7570	+	19.1999i	0.994571	+	1.21189i	0.0173097	+	0.999850i	$0.494490\pi$
$252$		0			0
$253$	11.7105	−	6.25940i	0.736234	−	0.393525i
$254$		0			0
$255$	−22.6649			−1.41933
$256$		0			0
$257$	−25.8743			−1.61399			−0.806996	−	0.590556i	$-0.798908\pi$
$257$	−25.8743			−1.61399			−0.806996	+	0.590556i	$0.798908\pi$
$258$		0			0
$259$	2.65380	−	1.41848i	0.164899	−	0.0881402i
$260$		0			0
$261$	9.47060	+	11.5400i	0.586215	+	0.714305i
$262$		0			0
$263$	4.21468	−	2.81616i	0.259889	−	0.173652i	−0.418799	−	0.908079i	$-0.637549\pi$
$263$	4.21468	−	2.81616i	0.259889	−	0.173652i	0.678688	+	0.734427i	$0.262549\pi$
$264$		0			0
$265$	−5.74684	+	8.60075i	−0.353026	+	0.528340i
$266$		0			0
$267$	−14.2394	+	4.31947i	−0.871436	+	0.264347i
$268$		0			0
$269$	20.4268	+	16.7639i	1.24545	+	1.02211i	0.998591	+	0.0530576i	$0.0168967\pi$
$269$	20.4268	+	16.7639i	1.24545	+	1.02211i	0.246854	+	0.969053i	$0.420603\pi$
$270$		0			0
$271$	7.58713	+	3.14269i	0.460885	+	0.190905i	0.601031	−	0.799226i	$-0.294757\pi$
$271$	7.58713	+	3.14269i	0.460885	+	0.190905i	−0.140145	+	0.990131i	$0.544757\pi$
$272$		0			0
$273$	−29.9026	+	12.3861i	−1.80979	+	0.749640i
$274$		0			0
$275$	−2.68591	−	27.2705i	−0.161967	−	1.64448i
$276$		0			0
$277$	8.99602	−	16.8304i	0.540519	−	1.01124i	−0.452329	−	0.891851i	$-0.649407\pi$
$277$	8.99602	−	16.8304i	0.540519	−	1.01124i	0.992848	−	0.119388i	$-0.0380933\pi$
$278$		0			0
$279$	4.16594	−	0.828657i	0.249408	−	0.0496104i
$280$		0			0
$281$	2.19188	−	11.0193i	0.130756	−	0.657357i	−0.858694	−	0.512488i	$-0.828724\pi$
$281$	2.19188	−	11.0193i	0.130756	−	0.657357i	0.989451	−	0.144869i	$-0.0462761\pi$
$282$		0			0
$283$	−2.99934	+	30.4528i	−0.178292	+	1.81023i	0.324567	+	0.945863i	$0.394781\pi$
$283$	−2.99934	+	30.4528i	−0.178292	+	1.81023i	−0.502859	+	0.864368i	$0.667719\pi$
$284$		0			0
$285$	−6.51582	+	21.4798i	−0.385964	+	1.27235i
$286$		0			0
$287$	12.9829	+	12.9829i	0.766355	+	0.766355i
$288$		0			0
$289$	−8.29052	+	8.29052i	−0.487677	+	0.487677i
$290$		0			0
$291$	15.1702	+	4.60183i	0.889293	+	0.269764i
$292$		0			0
$293$	7.03820	+	0.693202i	0.411176	+	0.0404973i	0.301491	−	0.953469i	$-0.402516\pi$
$293$	7.03820	+	0.693202i	0.411176	+	0.0404973i	0.109685	+	0.993966i	$0.465016\pi$
$294$		0			0
$295$	−30.5002	−	6.06687i	−1.77579	−	0.353227i
$296$		0			0
$297$	−1.78276	−	8.96253i	−0.103446	−	0.520059i
$298$		0			0
$299$	−21.2337	−	11.3497i	−1.22798	−	0.656368i
$300$		0			0
$301$	5.48872	−	0.540592i	0.316365	−	0.0311592i
$302$		0			0
$303$	−13.1467	−	31.7390i	−0.755261	−	1.82336i
$304$		0			0
$305$	12.5949	−	30.4069i	0.721184	−	1.74109i
$306$		0			0
$307$	9.52850	−	11.6105i	0.543820	−	0.662647i	−0.426495	−	0.904490i	$-0.640252\pi$
$307$	9.52850	−	11.6105i	0.543820	−	0.662647i	0.970315	+	0.241843i	$0.0777519\pi$
$308$		0			0
$309$	4.10832	+	13.5433i	0.233714	+	0.770452i
$310$		0			0
$311$	2.42437	+	1.61991i	0.137473	+	0.0918568i	0.622405	−	0.782695i	$-0.286156\pi$
$311$	2.42437	+	1.61991i	0.137473	+	0.0918568i	−0.484932	+	0.874552i	$0.661156\pi$
$312$		0			0
$313$	−14.9231	−	22.3340i	−0.843503	−	1.26239i	−0.962985	−	0.269555i	$-0.913123\pi$
$313$	−14.9231	−	22.3340i	−0.843503	−	1.26239i	0.119482	−	0.992836i	$-0.461877\pi$
$314$		0			0
$315$	−25.0272	+	20.5393i	−1.41013	+	1.15726i
$316$		0			0
$317$	−3.12714	−	5.85047i	−0.175638	−	0.328595i	0.778663	−	0.627442i	$-0.215898\pi$
$317$	−3.12714	−	5.85047i	−0.175638	−	0.328595i	−0.954301	+	0.298847i	$0.903398\pi$
$318$		0			0
$319$		−	11.4507i		−	0.641119i
$320$		0			0
$321$		−	43.4779i		−	2.42670i
$322$		0			0
$323$	−2.46284	−	4.60765i	−0.137036	−	0.256376i
$324$		0			0
$325$	−38.4084	+	31.5209i	−2.13051	+	1.74847i
$326$		0			0
$327$	17.0230	+	25.4767i	0.941372	+	1.40886i
$328$		0			0
$329$	19.5945	+	13.0926i	1.08028	+	0.721820i
$330$		0			0
$331$	7.42723	+	24.4843i	0.408238	+	1.34578i	0.884526	+	0.466490i	$0.154482\pi$
$331$	7.42723	+	24.4843i	0.408238	+	1.34578i	−0.476289	+	0.879289i	$0.658018\pi$
$332$		0			0
$333$	3.65974	−	4.45940i	0.200552	−	0.244374i
$334$		0			0
$335$	−3.08146	+	7.43930i	−0.168358	+	0.406452i
$336$		0			0
$337$	6.24956	+	15.0878i	0.340435	+	0.821884i	0.997672	+	0.0681991i	$0.0217253\pi$
$337$	6.24956	+	15.0878i	0.340435	+	0.821884i	−0.657236	+	0.753684i	$0.728275\pi$
$338$		0			0
$339$	40.7814	−	4.01661i	2.21494	−	0.218152i
$340$		0			0
$341$	−2.87332	−	1.53582i	−0.155599	−	0.0831694i
$342$		0			0
$343$	3.93266	+	19.7708i	0.212344	+	1.06752i
$344$		0			0
$345$	−40.9350	−	8.14248i	−2.20387	−	0.438377i
$346$		0			0
$347$	−22.4576	−	2.21188i	−1.20559	−	0.118740i	−0.524804	−	0.851223i	$-0.675861\pi$
$347$	−22.4576	−	2.21188i	−1.20559	−	0.118740i	−0.680785	+	0.732483i	$0.738361\pi$
$348$		0			0
$349$	5.54990	+	1.68354i	0.297079	+	0.0901180i	0.435306	−	0.900283i	$-0.356640\pi$
$349$	5.54990	+	1.68354i	0.297079	+	0.0901180i	−0.138227	+	0.990401i	$0.544140\pi$
$350$		0			0
$351$	−11.7163	+	11.7163i	−0.625372	+	0.625372i
$352$		0			0
$353$	−2.26290	−	2.26290i	−0.120442	−	0.120442i	0.644317	−	0.764759i	$-0.277142\pi$
$353$	−2.26290	−	2.26290i	−0.120442	−	0.120442i	−0.764759	+	0.644317i	$0.777142\pi$
$354$		0			0
$355$	9.40711	−	31.0111i	0.499278	−	1.64590i
$356$		0			0
$357$	1.28005	−	12.9965i	0.0677472	−	0.687849i
$358$		0			0
$359$	−3.26954	+	16.4371i	−0.172560	+	0.867517i	0.793375	+	0.608733i	$0.208322\pi$
$359$	−3.26954	+	16.4371i	−0.172560	+	0.867517i	−0.965935	+	0.258784i	$0.916678\pi$
$360$		0			0
$361$	13.5602	−	2.69729i	0.713693	−	0.141962i
$362$		0			0
$363$	1.43627	−	2.68707i	0.0753846	−	0.141035i
$364$		0			0
$365$	4.08530	+	41.4787i	0.213834	+	2.17110i
$366$		0			0
$367$	2.44587	−	1.01311i	0.127673	−	0.0528840i	−0.317932	−	0.948113i	$-0.602988\pi$
$367$	2.44587	−	1.01311i	0.127673	−	0.0528840i	0.445606	+	0.895229i	$0.352988\pi$
$368$		0			0
$369$	32.5203	+	13.4704i	1.69294	+	0.701239i
$370$		0			0
$371$	−4.60728	−	3.78110i	−0.239198	−	0.196305i
$372$		0			0
$373$	−8.70150	+	2.63957i	−0.450546	+	0.136672i	−0.507400	−	0.861711i	$-0.669393\pi$
$373$	−8.70150	+	2.63957i	−0.450546	+	0.136672i	0.0568534	+	0.998383i	$0.481893\pi$
$374$		0			0
$375$	−20.4409	+	30.5919i	−1.05556	+	1.57976i
$376$		0			0
$377$	−17.2636	+	11.5351i	−0.889119	+	0.594090i
$378$		0			0
$379$	9.32849	+	11.3668i	0.479172	+	0.583873i	0.955350	−	0.295476i	$-0.0954782\pi$
$379$	9.32849	+	11.3668i	0.479172	+	0.583873i	−0.476178	+	0.879349i	$0.657978\pi$
$380$		0			0
$381$	12.3126	−	6.58123i	0.630794	−	0.337166i
$382$		0			0
$383$	−3.03046			−0.154849			−0.0774246	−	0.996998i	$-0.524670\pi$
$383$	−3.03046			−0.154849			−0.0774246	+	0.996998i	$0.524670\pi$
$384$		0			0
$385$	24.8338			1.26565
$386$		0			0
$387$	9.32504	−	4.98434i	0.474019	−	0.253368i
$388$		0			0
$389$	−2.09026	−	2.54698i	−0.105980	−	0.129137i	0.717319	−	0.696745i	$-0.245369\pi$
$389$	−2.09026	−	2.54698i	−0.105980	−	0.129137i	−0.823299	+	0.567608i	$0.807869\pi$
$390$		0			0
$391$	8.07741	−	5.39715i	0.408492	−	0.272946i
$392$		0			0
$393$	−5.49341	+	8.22148i	−0.277106	+	0.414719i
$394$		0			0
$395$	−13.9552	+	4.23327i	−0.702163	+	0.212999i
$396$		0			0
$397$	−18.0553	−	14.8176i	−0.906171	−	0.743675i	0.0609102	−	0.998143i	$-0.480600\pi$
$397$	−18.0553	−	14.8176i	−0.906171	−	0.743675i	−0.967081	+	0.254468i	$0.918100\pi$
$398$		0			0
$399$	−11.9489	−	4.94942i	−0.598195	−	0.247781i
$400$		0			0
$401$	−18.6903	+	7.74178i	−0.933349	+	0.386606i	−0.796948	−	0.604048i	$-0.793554\pi$
$401$	−18.6903	+	7.74178i	−0.933349	+	0.386606i	−0.136401	+	0.990654i	$0.543554\pi$
$402$		0			0
$403$	0.579037	+	5.87906i	0.0288439	+	0.292857i
$404$		0			0
$405$	7.90641	−	14.7918i	0.392872	−	0.735013i
$406$		0			0
$407$	−4.33990	+	0.863261i	−0.215121	+	0.0427902i
$408$		0			0
$409$	−4.61481	+	23.2002i	−0.228188	+	1.14718i	0.681479	+	0.731838i	$0.261337\pi$
$409$	−4.61481	+	23.2002i	−0.228188	+	1.14718i	−0.909666	+	0.415340i	$0.863663\pi$
$410$		0			0
$411$	−1.95511	+	19.8506i	−0.0964385	+	0.979157i
$412$		0			0
$413$	5.20143	−	17.1468i	0.255945	−	0.843739i
$414$		0			0
$415$	−0.989689	−	0.989689i	−0.0485819	−	0.0485819i
$416$		0			0
$417$	10.6157	−	10.6157i	0.519855	−	0.519855i
$418$		0			0
$419$	−33.3546	−	10.1180i	−1.62948	−	0.494297i	−0.662480	−	0.749080i	$-0.730496\pi$
$419$	−33.3546	−	10.1180i	−1.62948	−	0.494297i	−0.966998	+	0.254783i	$0.917996\pi$
$420$		0			0
$421$	−26.9772	−	2.65702i	−1.31479	−	0.129495i	−0.583806	−	0.811893i	$-0.698437\pi$
$421$	−26.9772	−	2.65702i	−1.31479	−	0.129495i	−0.730981	+	0.682398i	$0.760937\pi$
$422$		0			0
$423$	44.3114	+	8.81409i	2.15449	+	0.428556i
$424$		0			0
$425$	−3.91116	−	19.6627i	−0.189719	−	0.953782i
$426$		0			0
$427$	16.7246	+	8.93949i	0.809360	+	0.432612i
$428$		0			0
$429$	47.3660	−	4.66514i	2.28685	−	0.225235i
$430$		0			0
$431$	−9.26076	−	22.3575i	−0.446075	−	1.07692i	−0.973780	−	0.227493i	$-0.926947\pi$
$431$	−9.26076	−	22.3575i	−0.446075	−	1.07692i	0.527705	−	0.849428i	$-0.323053\pi$
$432$		0			0
$433$	13.6385	−	32.9264i	0.655427	−	1.58234i	−0.149365	−	0.988782i	$-0.547723\pi$
$433$	13.6385	−	32.9264i	0.655427	−	1.58234i	0.804792	−	0.593557i	$-0.202277\pi$
$434$		0			0
$435$	−22.8332	+	27.8224i	−1.09477	+	1.33398i
$436$		0			0
$437$	−2.79280	−	9.20664i	−0.133598	−	0.440413i
$438$		0			0
$439$	17.7610	+	11.8675i	0.847687	+	0.566406i	0.901812	−	0.432128i	$-0.142237\pi$
$439$	17.7610	+	11.8675i	0.847687	+	0.566406i	−0.0541255	+	0.998534i	$0.517237\pi$
$440$		0			0
$441$	5.55318	+	8.31092i	0.264437	+	0.395758i
$442$		0			0
$443$	2.16430	−	1.77619i	0.102829	−	0.0843895i	−0.581574	−	0.813493i	$-0.697563\pi$
$443$	2.16430	−	1.77619i	0.102829	−	0.0843895i	0.684403	+	0.729104i	$0.260063\pi$
$444$		0			0
$445$	−9.75869	−	18.2572i	−0.462606	−	0.865475i
$446$		0			0
$447$			28.0108i			1.32487i
$448$		0			0
$449$		−	6.25127i		−	0.295016i	−0.989061	−	0.147508i	$-0.952875\pi$
$449$		−	6.25127i		−	0.295016i	0.989061	−	0.147508i	$-0.0471252\pi$
$450$		0			0
$451$	−12.7274	−	23.8114i	−0.599312	−	1.12123i
$452$		0			0
$453$	33.6114	−	27.5842i	1.57920	−	1.29602i
$454$		0			0
$455$	−25.0168	−	37.4403i	−1.17281	−	1.75523i
$456$		0			0
$457$	−5.13911	−	3.43384i	−0.240397	−	0.160628i	0.429536	−	0.903050i	$-0.358677\pi$
$457$	−5.13911	−	3.43384i	−0.240397	−	0.160628i	−0.669933	+	0.742421i	$0.733677\pi$
$458$		0			0
$459$	−1.94071	−	6.39766i	−0.0905846	−	0.298617i
$460$		0			0
$461$	−4.29080	+	5.22836i	−0.199843	+	0.243509i	−0.863283	−	0.504720i	$-0.831596\pi$
$461$	−4.29080	+	5.22836i	−0.199843	+	0.243509i	0.663440	+	0.748229i	$0.269096\pi$
$462$		0			0
$463$	−3.69113	+	8.91117i	−0.171541	+	0.414137i	−0.986146	−	0.165879i	$-0.946954\pi$
$463$	−3.69113	+	8.91117i	−0.171541	+	0.414137i	0.814605	+	0.580016i	$0.196954\pi$
$464$		0			0
$465$	3.91894	+	9.46116i	0.181737	+	0.438751i
$466$		0			0
$467$	39.4447	−	3.88497i	1.82529	−	0.179775i	0.873558	−	0.486720i	$-0.161807\pi$
$467$	39.4447	−	3.88497i	1.82529	−	0.179775i	0.951727	+	0.306945i	$0.0993068\pi$
$468$		0			0
$469$	−4.09181	−	2.18712i	−0.188942	−	0.100992i
$470$		0			0
$471$	−5.30283	−	26.6591i	−0.244342	−	1.22839i
$472$		0			0
$473$	−7.95444	−	1.58224i	−0.365746	−	0.0727514i
$474$		0			0
$475$	−19.7590	−	1.94609i	−0.906604	−	0.0892927i
$476$		0			0
$477$	−10.9345	−	3.31694i	−0.500655	−	0.151872i
$478$		0			0
$479$	25.7076	−	25.7076i	1.17461	−	1.17461i	0.193512	−	0.981098i	$-0.438012\pi$
$479$	25.7076	−	25.7076i	1.17461	−	1.17461i	0.981098	−	0.193512i	$-0.0619878\pi$
$480$		0			0
$481$	5.67338	+	5.67338i	0.258684	+	0.258684i
$482$		0			0
$483$	6.98095	−	23.0131i	0.317644	−	1.04713i
$484$		0			0
$485$	−2.16176	+	21.9487i	−0.0981604	+	0.996640i
$486$		0			0
$487$	5.68891	−	28.6001i	0.257789	−	1.29599i	−0.607340	−	0.794442i	$-0.707763\pi$
$487$	5.68891	−	28.6001i	0.257789	−	1.29599i	0.865129	−	0.501550i	$-0.167237\pi$
$488$		0			0
$489$	42.4635	−	8.44652i	1.92027	−	0.381965i
$490$		0			0
$491$	0.827745	−	1.54860i	0.0373556	−	0.0698874i	−0.862551	−	0.505970i	$-0.831135\pi$
$491$	0.827745	−	1.54860i	0.0373556	−	0.0698874i	0.899907	+	0.436083i	$0.143635\pi$
$492$		0			0
$493$	−0.821137	−	8.33714i	−0.0369821	−	0.375486i
$494$		0			0
$495$	43.9857	−	18.2195i	1.97701	−	0.818905i
$496$		0			0
$497$	17.2511	+	7.14564i	0.773818	+	0.320526i
$498$		0			0
$499$	−19.7153	−	16.1799i	−0.882577	−	0.724312i	0.0795743	−	0.996829i	$-0.474644\pi$
$499$	−19.7153	−	16.1799i	−0.882577	−	0.724312i	−0.962151	+	0.272517i	$0.912144\pi$
$500$		0			0
$501$	−45.2850	+	13.7370i	−2.02318	+	0.613726i
$502$		0			0
$503$	15.2925	−	22.8869i	0.681861	−	1.02048i	−0.315575	−	0.948901i	$-0.602197\pi$
$503$	15.2925	−	22.8869i	0.681861	−	1.02048i	0.997435	−	0.0715757i	$-0.0228028\pi$
$504$		0			0
$505$	39.7396	−	26.5532i	1.76839	−	1.18160i
$506$		0			0
$507$	−32.7843	−	39.9478i	−1.45600	−	1.77414i
$508$		0			0
$509$	−15.6838	+	8.38317i	−0.695173	+	0.371578i	−0.780827	−	0.624747i	$-0.785202\pi$
$509$	−15.6838	+	8.38317i	−0.695173	+	0.371578i	0.0856542	+	0.996325i	$0.472702\pi$
$510$		0			0
$511$	−24.0155			−1.06238
$512$		0			0
$513$	−6.62106			−0.292327
$514$		0			0
$515$	−17.3648	+	9.28166i	−0.765183	+	0.408999i
$516$		0			0
$517$	−21.9844	−	26.7881i	−0.966874	−	1.17814i
$518$		0			0
$519$	10.2836	−	6.87130i	0.451401	−	0.301617i
$520$		0			0
$521$	8.31872	−	12.4499i	0.364450	−	0.545438i	−0.603247	−	0.797554i	$-0.706127\pi$
$521$	8.31872	−	12.4499i	0.364450	−	0.545438i	0.967697	+	0.252117i	$0.0811267\pi$
$522$		0			0
$523$	6.67447	−	2.02468i	0.291854	−	0.0885330i	−0.140963	−	0.990015i	$-0.545020\pi$
$523$	6.67447	−	2.02468i	0.291854	−	0.0885330i	0.432817	+	0.901482i	$0.357520\pi$
$524$		0			0
$525$	−38.3636	−	31.4842i	−1.67433	−	1.37408i
$526$		0			0
$527$	−2.20216	−	0.912165i	−0.0959276	−	0.0397345i
$528$		0			0
$529$	−4.72170	+	1.95579i	−0.205291	+	0.0850344i
$530$		0			0
$531$	−3.36708	−	34.1866i	−0.146119	−	1.48357i
$532$		0			0
$533$	−23.0776	+	43.1752i	−0.999604	+	1.87013i
$534$		0			0
$535$	59.3255	−	11.8006i	2.56487	−	0.510184i
$536$		0			0
$537$	3.40275	−	17.1068i	0.146840	−	0.738212i
$538$		0			0
$539$	0.751484	−	7.62995i	0.0323687	−	0.328645i
$540$		0			0
$541$	4.97559	−	16.4023i	0.213917	−	0.705190i	−0.782655	−	0.622456i	$-0.786135\pi$
$541$	4.97559	−	16.4023i	0.213917	−	0.705190i	0.996572	−	0.0827339i	$-0.0263652\pi$
$542$		0			0
$543$	7.73732	+	7.73732i	0.332040	+	0.332040i
$544$		0			0
$545$	−30.1425	+	30.1425i	−1.29116	+	1.29116i
$546$		0			0
$547$	26.8558	+	8.14662i	1.14827	+	0.348324i	0.806370	−	0.591412i	$-0.201429\pi$
$547$	26.8558	+	8.14662i	1.14827	+	0.348324i	0.341901	+	0.939736i	$0.388929\pi$
$548$		0			0
$549$	36.1812	+	3.56354i	1.54418	+	0.152088i
$550$		0			0
$551$	−8.13726	−	1.61860i	−0.346659	−	0.0689547i
$552$		0			0
$553$	−1.63929	−	8.24128i	−0.0697098	−	0.350455i
$554$		0			0
$555$	12.2662	+	6.55644i	0.520672	+	0.278305i
$556$		0			0
$557$	12.9648	−	1.27692i	0.549337	−	0.0541050i	0.180458	−	0.983583i	$-0.442242\pi$
$557$	12.9648	−	1.27692i	0.549337	−	0.0541050i	0.368878	+	0.929478i	$0.379742\pi$
$558$		0			0
$559$	5.62764	+	13.5863i	0.238024	+	0.574640i
$560$		0			0
$561$	−7.34906	+	17.7422i	−0.310278	+	0.749076i
$562$		0			0
$563$	−27.7436	+	33.8057i	−1.16925	+	1.42474i	−0.284504	+	0.958675i	$0.591829\pi$
$563$	−27.7436	+	33.8057i	−1.16925	+	1.42474i	−0.884750	+	0.466066i	$0.845671\pi$
$564$		0			0
$565$	16.5493	+	54.5559i	0.696236	+	2.29518i
$566$		0			0
$567$	8.03541	+	5.36909i	0.337456	+	0.225481i
$568$		0			0
$569$	3.71604	+	5.56145i	0.155785	+	0.233148i	0.901149	−	0.433509i	$-0.142725\pi$
$569$	3.71604	+	5.56145i	0.155785	+	0.233148i	−0.745365	+	0.666657i	$0.767725\pi$
$570$		0			0
$571$	15.9215	−	13.0665i	0.666296	−	0.546815i	−0.239306	−	0.970944i	$-0.576920\pi$
$571$	15.9215	−	13.0665i	0.666296	−	0.546815i	0.905602	+	0.424129i	$0.139420\pi$
$572$		0			0
$573$	20.6578	+	38.6481i	0.862994	+	1.61455i
$574$		0			0
$575$		−	36.9179i		−	1.53958i
$576$		0			0
$577$			2.28283i			0.0950356i	0.998870	+	0.0475178i	$0.0151311\pi$
$577$			2.28283i			0.0950356i	−0.998870	+	0.0475178i	$0.984869\pi$
$578$		0			0
$579$	−16.3914	−	30.6662i	−0.681203	−	1.27444i
$580$		0			0
$581$	0.623402	−	0.511613i	0.0258631	−	0.0212253i
$582$		0			0
$583$	4.86931	+	7.28743i	0.201666	+	0.301815i
$584$		0			0
$585$	−71.7783	−	47.9607i	−2.96767	−	1.98293i
$586$		0			0
$587$	−7.20450	−	23.7501i	−0.297362	−	0.980270i	−0.970570	−	0.240818i	$-0.922584\pi$
$587$	−7.20450	−	23.7501i	−0.297362	−	0.980270i	0.673209	−	0.739453i	$-0.264916\pi$
$588$		0			0
$589$	−1.49756	+	1.82478i	−0.0617057	+	0.0751886i
$590$		0			0
$591$	−15.4380	+	37.2706i	−0.635034	+	1.53311i
$592$		0			0
$593$	1.96953	+	4.75487i	0.0808789	+	0.195259i	0.959146	−	0.282911i	$-0.0913002\pi$
$593$	1.96953	+	4.75487i	0.0808789	+	0.195259i	−0.878267	+	0.478170i	$0.841300\pi$
$594$		0			0
$595$	18.0811	−	1.78084i	0.741255	−	0.0730072i
$596$		0			0
$597$	−14.5159	−	7.75891i	−0.594097	−	0.317551i
$598$		0			0
$599$	2.42145	+	12.1734i	0.0989376	+	0.497393i	0.998199	+	0.0599823i	$0.0191044\pi$
$599$	2.42145	+	12.1734i	0.0989376	+	0.497393i	−0.899262	+	0.437411i	$0.855896\pi$
$600$		0			0
$601$	11.6453	+	2.31639i	0.475021	+	0.0944875i	0.426794	−	0.904349i	$-0.359643\pi$
$601$	11.6453	+	2.31639i	0.475021	+	0.0944875i	0.0482267	+	0.998836i	$0.484643\pi$
$602$		0			0
$603$	−8.85204	−	0.871849i	−0.360483	−	0.0355045i
$604$		0			0
$605$	4.05633	+	1.23047i	0.164913	+	0.0500259i
$606$		0			0
$607$	−31.9482	+	31.9482i	−1.29674	+	1.29674i	−0.366202	+	0.930535i	$0.619342\pi$
$607$	−31.9482	+	31.9482i	−1.29674	+	1.29674i	−0.930535	+	0.366202i	$0.880658\pi$
$608$		0			0
$609$	−14.6644	−	14.6644i	−0.594230	−	0.594230i
$610$		0			0
$611$	−18.2403	+	60.1301i	−0.737922	+	2.43260i
$612$		0			0
$613$	0.117361	−	1.19159i	0.00474017	−	0.0481277i	−0.992524	−	0.122052i	$-0.961052\pi$
$613$	0.117361	−	1.19159i	0.00474017	−	0.0481277i	0.997264	+	0.0739246i	$0.0235524\pi$
$614$		0			0
$615$	−16.5564	+	83.2345i	−0.667617	+	3.35634i
$616$		0			0
$617$	1.36091	−	0.270701i	0.0547880	−	0.0108980i	−0.167620	−	0.985852i	$-0.553608\pi$
$617$	1.36091	−	0.270701i	0.0547880	−	0.0108980i	0.222408	+	0.974954i	$0.428608\pi$
$618$		0			0
$619$	−9.74430	+	18.2303i	−0.391656	+	0.732737i	−0.998050	−	0.0624275i	$-0.980116\pi$
$619$	−9.74430	+	18.2303i	−0.391656	+	0.732737i	0.606393	+	0.795165i	$0.292616\pi$
$620$		0			0
$621$	−1.20672	−	12.2520i	−0.0484239	−	0.491656i
$622$		0			0
$623$	11.0202	−	4.56472i	0.441515	−	0.182882i
$624$		0			0
$625$	−6.97013	−	2.88712i	−0.278805	−	0.115485i
$626$		0			0
$627$	14.7017	+	12.0654i	0.587130	+	0.481845i
$628$		0			0
$629$	−3.09792	+	0.939745i	−0.123522	+	0.0374701i
$630$		0			0
$631$	5.39374	−	8.07230i	0.214721	−	0.321353i	−0.708436	−	0.705775i	$-0.750599\pi$
$631$	5.39374	−	8.07230i	0.214721	−	0.321353i	0.923158	+	0.384422i	$0.125599\pi$
$632$		0			0
$633$	39.1478	−	26.1578i	1.55599	−	1.03968i
$634$		0			0
$635$	12.3219	+	15.0143i	0.488980	+	0.595823i
$636$		0			0
$637$	−12.2602	+	6.55322i	−0.485767	+	0.259648i
$638$		0			0
$639$	35.7977			1.41614
$640$		0			0
$641$	45.5260			1.79817			0.899084	−	0.437776i	$-0.144234\pi$
$641$	45.5260			1.79817			0.899084	+	0.437776i	$0.144234\pi$
$642$		0			0
$643$	−8.69364	+	4.64685i	−0.342844	+	0.183254i	−0.633828	−	0.773474i	$-0.718517\pi$
$643$	−8.69364	+	4.64685i	−0.342844	+	0.183254i	0.290984	+	0.956728i	$0.406017\pi$
$644$		0			0
$645$	16.1722	+	19.7059i	0.636780	+	0.775919i
$646$		0			0
$647$	2.48460	−	1.66016i	0.0976798	−	0.0652675i	−0.505771	−	0.862668i	$-0.668792\pi$
$647$	2.48460	−	1.66016i	0.0976798	−	0.0652675i	0.603451	+	0.797400i	$0.293792\pi$
$648$		0			0
$649$	−14.6388	+	21.9085i	−0.574624	+	0.859985i
$650$		0			0
$651$	−5.64655	+	1.71286i	−0.221306	+	0.0671324i
$652$		0			0
$653$	29.1963	+	23.9607i	1.14254	+	0.937656i	0.998650	−	0.0519377i	$-0.0165397\pi$
$653$	29.1963	+	23.9607i	1.14254	+	0.937656i	0.143887	+	0.989594i	$0.454040\pi$
$654$		0			0
$655$	−12.7092	−	5.26432i	−0.496589	−	0.205694i
$656$		0			0
$657$	−42.5363	+	17.6191i	−1.65950	+	0.687388i
$658$		0			0
$659$	0.713561	+	7.24490i	0.0277964	+	0.282221i	0.999028	+	0.0440838i	$0.0140369\pi$
$659$	0.713561	+	7.24490i	0.0277964	+	0.282221i	−0.971231	+	0.238137i	$0.923463\pi$
$660$		0			0
$661$	11.6445	−	21.7854i	0.452920	−	0.847354i	−0.547027	−	0.837115i	$-0.684241\pi$
$661$	11.6445	−	21.7854i	0.452920	−	0.847354i	0.999948	−	0.0102393i	$-0.00325932\pi$
$662$		0			0
$663$	34.1520	−	6.79326i	1.32635	−	0.263828i
$664$		0			0
$665$	3.51034	−	17.6477i	0.136125	−	0.684347i
$666$		0			0
$667$	1.51211	−	15.3527i	0.0585490	−	0.594458i
$668$		0			0
$669$	2.36162	−	7.78522i	0.0913055	−	0.300994i
$670$		0			0
$671$	−19.7188	−	19.7188i	−0.761234	−	0.761234i
$672$		0			0
$673$	25.6942	−	25.6942i	0.990440	−	0.990440i	−0.00951435	−	0.999955i	$-0.503029\pi$
$673$	25.6942	−	25.6942i	0.990440	−	0.990440i	0.999955	+	0.00951435i	$0.00302856\pi$
$674$		0			0
$675$	−24.3127	−	7.37516i	−0.935795	−	0.283870i
$676$		0			0
$677$	7.56047	+	0.744641i	0.290572	+	0.0286189i	0.242253	−	0.970213i	$-0.422114\pi$
$677$	7.56047	+	0.744641i	0.290572	+	0.0286189i	0.0483192	+	0.998832i	$0.484614\pi$
$678$		0			0
$679$	−12.4637	−	2.47919i	−0.478315	−	0.0951427i
$680$		0			0
$681$	0.331981	+	1.66898i	0.0127215	+	0.0639555i
$682$		0			0
$683$	−16.9055	−	9.03616i	−0.646870	−	0.345759i	0.115117	−	0.993352i	$-0.463276\pi$
$683$	−16.9055	−	9.03616i	−0.646870	−	0.345759i	−0.761987	+	0.647593i	$0.775776\pi$
$684$		0			0
$685$	−27.6167	+	2.72001i	−1.05518	+	0.103926i
$686$		0			0
$687$	−16.3141	−	39.3858i	−0.622423	−	1.50266i
$688$		0			0
$689$	6.08160	−	14.6823i	0.231691	−	0.559351i
$690$		0			0
$691$	−10.8155	+	13.1788i	−0.411443	+	0.501344i	−0.936959	−	0.349439i	$-0.886372\pi$
$691$	−10.8155	+	13.1788i	−0.411443	+	0.501344i	0.525516	+	0.850783i	$0.323872\pi$
$692$		0			0
$693$	7.96324	+	26.2513i	0.302498	+	0.997204i
$694$		0			0
$695$	17.3664	+	11.6039i	0.658746	+	0.440160i
$696$		0			0
$697$	−10.9742	−	16.4241i	−0.415678	−	0.622106i
$698$		0			0
$699$	35.2237	−	28.9074i	1.33228	−	1.09338i
$700$		0			0
$701$	13.8768	+	25.9616i	0.524119	+	0.980557i	0.995143	+	0.0984370i	$0.0313843\pi$
$701$	13.8768	+	25.9616i	0.524119	+	0.980557i	−0.471025	+	0.882120i	$0.656116\pi$
$702$		0			0
$703$			3.20610i			0.120920i
$704$		0			0
$705$			108.926i			4.10239i
$706$		0			0
$707$	12.9818	+	24.2871i	0.488229	+	0.913412i
$708$		0			0
$709$	−10.6625	+	8.75053i	−0.400440	+	0.328633i	−0.812964	−	0.582314i	$-0.802147\pi$
$709$	−10.6625	+	8.75053i	−0.400440	+	0.328633i	0.412524	+	0.910947i	$0.364647\pi$
$710$		0			0
$711$	−8.94980	−	13.3943i	−0.335644	−	0.502326i
$712$		0			0
$713$	−3.64961	−	2.43859i	−0.136679	−	0.0913261i
$714$		0			0
$715$	19.2214	+	63.3646i	0.718841	+	2.36970i
$716$		0			0
$717$	−26.6546	+	32.4788i	−0.995436	+	1.21294i
$718$		0			0
$719$	−6.82739	+	16.4828i	−0.254619	+	0.614704i	−0.998566	−	0.0535346i	$-0.982951\pi$
$719$	−6.82739	+	16.4828i	−0.254619	+	0.614704i	0.743947	+	0.668238i	$0.232951\pi$
$720$		0			0
$721$	−4.34158	−	10.4815i	−0.161689	−	0.390352i
$722$		0			0
$723$	−67.4097	+	6.63928i	−2.50699	+	0.246917i
$724$		0			0
$725$	−28.0772	−	15.0076i	−1.04276	−	0.557368i
$726$		0			0
$727$	−1.41470	−	7.11218i	−0.0524683	−	0.263776i	0.945643	−	0.325206i	$-0.105434\pi$
$727$	−1.41470	−	7.11218i	−0.0524683	−	0.263776i	−0.998111	+	0.0614304i	$0.980434\pi$
$728$		0			0
$729$	40.9809	+	8.15161i	1.51781	+	0.301912i
$730$		0			0
$731$	−5.90499	−	0.581591i	−0.218404	−	0.0215109i
$732$		0			0
$733$	14.7665	+	4.47938i	0.545415	+	0.165450i	0.550955	−	0.834535i	$-0.314264\pi$
$733$	14.7665	+	4.47938i	0.545415	+	0.165450i	−0.00554040	+	0.999985i	$0.501764\pi$
$734$		0			0
$735$	−17.0403	+	17.0403i	−0.628542	+	0.628542i
$736$		0			0
$737$	4.82436	+	4.82436i	0.177707	+	0.177707i
$738$		0			0
$739$	−0.853799	+	2.81460i	−0.0314075	+	0.103537i	−0.971243	−	0.238091i	$-0.923478\pi$
$739$	−0.853799	+	2.81460i	−0.0314075	+	0.103537i	0.939835	+	0.341628i	$0.110978\pi$
$740$		0			0
$741$	3.38014	−	34.3192i	0.124173	−	1.26075i
$742$		0			0
$743$	−1.59498	+	8.01851i	−0.0585142	+	0.294171i	−0.998951	−	0.0457987i	$-0.985417\pi$
$743$	−1.59498	+	8.01851i	−0.0585142	+	0.294171i	0.940437	+	0.339969i	$0.110417\pi$
$744$		0			0
$745$	−38.2207	+	7.60256i	−1.40030	+	0.278536i
$746$		0			0
$747$	0.728825	−	1.36354i	0.0266663	−	0.0498892i
$748$		0			0
$749$	3.41617	+	34.6849i	0.124824	+	1.26736i
$750$		0			0
$751$	−45.5276	+	18.8581i	−1.66132	+	0.688143i	−0.998178	−	0.0603455i	$-0.980780\pi$
$751$	−45.5276	+	18.8581i	−1.66132	+	0.688143i	−0.663147	+	0.748489i	$0.730780\pi$
$752$		0			0
$753$	−61.1142	−	25.3143i	−2.22713	−	0.922506i
$754$		0			0
$755$	46.7612	+	38.3759i	1.70181	+	1.39664i
$756$		0			0
$757$	15.1867	−	4.60685i	0.551971	−	0.167439i	−0.00196446	−	0.999998i	$-0.500625\pi$
$757$	15.1867	−	4.60685i	0.551971	−	0.167439i	0.553936	+	0.832559i	$0.313125\pi$
$758$		0			0
$759$	−19.6471	+	29.4039i	−0.713144	+	1.06730i
$760$		0			0
$761$	7.11658	−	4.75515i	0.257976	−	0.172374i	−0.419856	−	0.907591i	$-0.637920\pi$
$761$	7.11658	−	4.75515i	0.257976	−	0.172374i	0.677832	+	0.735217i	$0.262920\pi$
$762$		0			0
$763$	−15.5820	−	18.9867i	−0.564106	−	0.687365i
$764$		0			0
$765$	30.7189	−	16.4196i	1.11064	−	0.593652i
$766$		0			0
$767$	47.7768			1.72512
$768$		0			0
$769$	−52.7650			−1.90276			−0.951378	−	0.308026i	$-0.900332\pi$
$769$	−52.7650			−1.90276			−0.951378	+	0.308026i	$0.900332\pi$
$770$		0			0
$771$	60.7730	−	32.4839i	2.18869	−	1.16988i
$772$		0			0
$773$	−27.0801	−	32.9972i	−0.974003	−	1.18683i	−0.982386	−	0.186861i	$-0.940169\pi$
$773$	−27.0801	−	32.9972i	−0.974003	−	1.18683i	0.00838378	−	0.999965i	$-0.497331\pi$
$774$		0			0
$775$	−7.53167	+	5.03250i	−0.270545	+	0.180773i
$776$		0			0
$777$	−4.45235	+	6.66342i	−0.159727	+	0.239049i
$778$		0			0
$779$	−18.7202	+	5.67870i	−0.670720	+	0.203461i
$780$		0			0
$781$	−21.2254	−	17.4192i	−0.759504	−	0.623309i
$782$		0			0
$783$	−9.80859	−	4.06285i	−0.350530	−	0.145194i
$784$		0			0
$785$	34.9371	−	14.4714i	1.24696	−	0.516506i
$786$		0			0
$787$	−0.162474	−	1.64963i	−0.00579158	−	0.0588029i	0.991855	−	0.127376i	$-0.0406554\pi$
$787$	−0.162474	−	1.64963i	−0.00579158	−	0.0588029i	−0.997646	+	0.0685729i	$0.978155\pi$
$788$		0			0
$789$	−6.36383	+	11.9059i	−0.226558	+	0.423861i
$790$		0			0
$791$	−32.2181	+	6.40858i	−1.14554	+	0.227863i
$792$		0			0
$793$	−9.86463	+	49.5928i	−0.350303	+	1.76109i
$794$		0			0
$795$	2.70026	−	27.4162i	0.0957683	−	0.972351i
$796$		0			0
$797$	12.5311	−	41.3094i	0.443873	−	1.46325i	−0.394876	−	0.918734i	$-0.629213\pi$
$797$	12.5311	−	41.3094i	0.443873	−	1.46325i	0.838749	−	0.544518i	$-0.183287\pi$
$798$		0			0
$799$	−17.9276	−	17.9276i	−0.634232	−	0.634232i
$800$		0			0
$801$	16.1701	−	16.1701i	0.571343	−	0.571343i
$802$		0			0
$803$	33.7944	+	10.2514i	1.19258	+	0.361765i
$804$		0			0
$805$	33.2961	+	3.27938i	1.17353	+	0.115583i
$806$		0			0
$807$	−69.0243	−	13.7298i	−2.42977	−	0.483312i
$808$		0			0
$809$	−2.99285	−	15.0461i	−0.105223	−	0.528992i	−0.997059	−	0.0766334i	$-0.975583\pi$
$809$	−2.99285	−	15.0461i	−0.105223	−	0.528992i	0.891836	−	0.452358i	$-0.149417\pi$
$810$		0			0
$811$	9.70107	+	5.18533i	0.340650	+	0.182081i	0.632847	−	0.774277i	$-0.281886\pi$
$811$	9.70107	+	5.18533i	0.340650	+	0.182081i	−0.292197	+	0.956358i	$0.594386\pi$
$812$		0			0
$813$	−21.7660	+	2.14377i	−0.763367	+	0.0751851i
$814$		0			0
$815$	23.0505	+	55.6488i	0.807424	+	1.94929i
$816$		0			0
$817$	−2.24877	+	5.42902i	−0.0786747	+	0.189937i
$818$		0			0
$819$	31.5555	−	38.4505i	1.10264	−	1.34357i
$820$		0			0
$821$	12.8632	+	42.4044i	0.448930	+	1.47992i	0.831252	+	0.555896i	$0.187625\pi$
$821$	12.8632	+	42.4044i	0.448930	+	1.47992i	−0.382322	+	0.924029i	$0.624875\pi$
$822$		0			0
$823$	−40.6861	−	27.1856i	−1.41823	−	0.947629i	−0.999214	−	0.0396490i	$-0.987376\pi$
$823$	−40.6861	−	27.1856i	−1.41823	−	0.947629i	−0.419013	−	0.907980i	$-0.637624\pi$
$824$		0			0
$825$	40.5454	+	60.6806i	1.41161	+	2.11263i
$826$		0			0
$827$	34.1801	−	28.0509i	1.18856	−	0.975425i	0.188581	−	0.982058i	$-0.439611\pi$
$827$	34.1801	−	28.0509i	1.18856	−	0.975425i	0.999978	+	0.00663288i	$0.00211133\pi$
$828$		0			0
$829$	−25.5280	−	47.7596i	−0.886626	−	1.65876i	−0.743170	−	0.669103i	$-0.766678\pi$
$829$	−25.5280	−	47.7596i	−0.886626	−	1.65876i	−0.143456	−	0.989657i	$-0.545822\pi$
$830$		0			0
$831$			50.8250i			1.76310i
$832$		0			0
$833$		−	5.60916i		−	0.194346i
$834$		0			0
$835$	−31.0352	−	58.0628i	−1.07402	−	2.00935i
$836$		0			0
$837$	−2.33505	+	1.91633i	−0.0807112	+	0.0662380i
$838$		0			0
$839$	21.6160	+	32.3506i	0.746267	+	1.11687i	0.989164	+	0.146816i	$0.0469024\pi$
$839$	21.6160	+	32.3506i	0.746267	+	1.11687i	−0.242897	+	0.970052i	$0.578098\pi$
$840$		0			0
$841$	13.0511	+	8.72047i	0.450038	+	0.300706i
$842$		0			0
$843$	8.68595	+	28.6338i	0.299160	+	0.986199i
$844$		0			0
$845$	45.6105	−	55.5765i	1.56905	−	1.91189i
$846$		0			0
$847$	−0.934667	+	2.25649i	−0.0321156	+	0.0775338i
$848$		0			0
$849$	−31.1872	−	75.2925i	−1.07034	−	2.58403i
$850$		0			0
$851$	−5.93276	+	0.584325i	−0.203372	+	0.0200304i
$852$		0			0
$853$	35.6328	+	19.0461i	1.22004	+	0.652126i	0.950459	−	0.310851i	$-0.100614\pi$
$853$	35.6328	+	19.0461i	1.22004	+	0.652126i	0.269584	+	0.962977i	$0.413114\pi$
$854$		0			0
$855$	−6.72980	−	33.8330i	−0.230154	−	1.15706i
$856$		0			0
$857$	25.4994	+	5.07215i	0.871044	+	0.173261i	0.610323	−	0.792153i	$-0.291040\pi$
$857$	25.4994	+	5.07215i	0.871044	+	0.173261i	0.260721	+	0.965414i	$0.416040\pi$
$858$		0			0
$859$	16.2440	+	1.59989i	0.554236	+	0.0545875i	0.371259	−	0.928530i	$-0.378926\pi$
$859$	16.2440	+	1.59989i	0.554236	+	0.0545875i	0.182978	+	0.983117i	$0.441426\pi$
$860$		0			0
$861$	−46.7933	−	14.1946i	−1.59471	−	0.483750i
$862$		0			0
$863$	10.2495	−	10.2495i	0.348897	−	0.348897i	−0.510802	−	0.859699i	$-0.670651\pi$
$863$	10.2495	−	10.2495i	0.348897	−	0.348897i	0.859699	+	0.510802i	$0.170651\pi$
$864$		0			0
$865$	12.1670	+	12.1670i	0.413691	+	0.413691i
$866$		0			0
$867$	9.06429	−	29.8809i	0.307839	−	1.01481i
$868$		0			0
$869$	−1.21113	+	12.2968i	−0.0410848	+	0.417141i
$870$		0			0
$871$	2.41346	−	12.1333i	0.0817770	−	0.411121i
$872$		0			0
$873$	−23.8947	+	4.75296i	−0.808714	+	0.160863i
$874$		0			0
$875$	13.9032	−	26.0111i	0.470015	−	0.879336i
$876$		0			0
$877$	1.64214	+	16.6729i	0.0554512	+	0.563005i	0.982267	+	0.187489i	$0.0600348\pi$
$877$	1.64214	+	16.6729i	0.0554512	+	0.563005i	−0.926816	+	0.375517i	$0.877465\pi$
$878$		0			0
$879$	−17.4015	+	7.20793i	−0.586937	+	0.243117i
$880$		0			0
$881$	25.2814	+	10.4719i	0.851751	+	0.352807i	0.765476	−	0.643465i	$-0.222504\pi$
$881$	25.2814	+	10.4719i	0.851751	+	0.352807i	0.0862749	+	0.996271i	$0.472504\pi$
$882$		0			0
$883$	16.8236	+	13.8067i	0.566158	+	0.464634i	0.873404	−	0.486996i	$-0.161907\pi$
$883$	16.8236	+	13.8067i	0.566158	+	0.464634i	−0.307246	+	0.951630i	$0.599407\pi$
$884$		0			0
$885$	79.2550	−	24.0418i	2.66413	−	0.808155i
$886$		0			0
$887$	11.4637	−	17.1566i	0.384912	−	0.576062i	−0.587531	−	0.809202i	$-0.699900\pi$
$887$	11.4637	−	17.1566i	0.384912	−	0.576062i	0.972443	+	0.233140i	$0.0748999\pi$
$888$		0			0
$889$	−9.30539	+	6.21767i	−0.312093	+	0.208534i
$890$		0			0
$891$	−9.01548	−	10.9854i	−0.302030	−	0.368025i
$892$		0			0
$893$	−22.1440	+	11.8362i	−0.741022	+	0.396084i
$894$		0			0
$895$	24.2657			0.811114
$896$		0			0
$897$	64.1224			2.14098
$898$		0			0
$899$	−3.33824	+	1.78433i	−0.111337	+	0.0595107i
$900$		0			0
$901$	4.06786	+	4.95671i	0.135520	+	0.165132i
$902$		0			0
$903$	−12.2131	+	8.16055i	−0.406427	+	0.271566i
$904$		0			0
$905$	−8.45753	+	12.6576i	−0.281138	+	0.420752i
$906$		0			0
$907$	−29.8824	+	9.06472i	−0.992228	+	0.300989i	−0.744341	−	0.667800i	$-0.767236\pi$
$907$	−29.8824	+	9.06472i	−0.992228	+	0.300989i	−0.247887	+	0.968789i	$0.579736\pi$
$908$		0			0
$909$	40.8118	+	33.4934i	1.35364	+	1.11091i
$910$		0			0
$911$	23.5842	+	9.76890i	0.781380	+	0.323658i	0.737472	−	0.675378i	$-0.236019\pi$
$911$	23.5842	+	9.76890i	0.781380	+	0.323658i	0.0439074	+	0.999036i	$0.486019\pi$
$912$		0			0
$913$	−1.09564	+	0.453828i	−0.0362603	+	0.0150195i
$914$		0			0
$915$	8.59155	+	87.2315i	0.284028	+	2.88378i
$916$		0			0
$917$	3.73644	−	6.99039i	0.123388	−	0.230843i
$918$		0			0
$919$	50.2229	−	9.98996i	1.65670	−	0.329538i	0.723894	−	0.689912i	$-0.242351\pi$
$919$	50.2229	−	9.98996i	1.65670	−	0.329538i	0.932808	+	0.360373i	$0.117351\pi$
$920$		0			0
$921$	−7.80395	+	39.2331i	−0.257149	+	1.29277i
$922$		0			0
$923$	−4.88003	+	49.5478i	−0.160628	+	1.63089i
$924$		0			0
$925$	−3.57126	+	11.7729i	−0.117422	+	0.387089i
$926$		0			0
$927$	−15.3797	−	15.3797i	−0.505135	−	0.505135i
$928$		0			0
$929$	−5.41129	+	5.41129i	−0.177539	+	0.177539i	−0.790282	−	0.612743i	$-0.790066\pi$
$929$	−5.41129	+	5.41129i	−0.177539	+	0.177539i	0.612743	+	0.790282i	$0.290066\pi$
$930$		0			0
$931$	−5.31585	−	1.61255i	−0.174220	−	0.0528491i
$932$		0			0
$933$	−7.72804	−	0.761145i	−0.253005	−	0.0249188i
$934$		0			0
$935$	−26.2038	−	5.21227i	−0.856957	−	0.170459i
$936$		0			0
$937$	−0.344820	−	1.73353i	−0.0112648	−	0.0566319i	0.974744	−	0.223325i	$-0.0716911\pi$
$937$	−0.344820	−	1.73353i	−0.0112648	−	0.0566319i	−0.986009	+	0.166693i	$0.946691\pi$
$938$		0			0
$939$	63.0903	+	33.7225i	2.05887	+	1.10049i
$940$		0			0
$941$	−57.1654	+	5.63030i	−1.86354	+	0.183543i	−0.966199	−	0.257797i	$-0.917003\pi$
$941$	−57.1654	+	5.63030i	−1.86354	+	0.183543i	−0.897340	+	0.441340i	$0.854503\pi$
$942$		0			0
$943$	−13.9200	−	33.6060i	−0.453299	−	1.09436i
$944$		0			0
$945$	8.81130	−	21.2723i	0.286631	−	0.691990i
$946$		0			0
$947$	−19.3082	+	23.5271i	−0.627433	+	0.764530i	−0.985594	−	0.169131i	$-0.945904\pi$
$947$	−19.3082	+	23.5271i	−0.627433	+	0.764530i	0.358161	+	0.933660i	$0.383404\pi$
$948$		0			0
$949$	−18.5881	−	61.2766i	−0.603394	−	1.98912i
$950$		0			0
$951$	14.6900	+	9.81552i	0.476355	+	0.318290i
$952$		0			0
$953$	25.8785	+	38.7299i	0.838286	+	1.25458i	0.964896	+	0.262631i	$0.0845901\pi$
$953$	25.8785	+	38.7299i	0.838286	+	1.25458i	−0.126611	+	0.991952i	$0.540410\pi$
$954$		0			0
$955$	−47.1284	+	38.6773i	−1.52504	+	1.25157i
$956$		0			0
$957$	14.3758	+	26.8953i	0.464705	+	0.869402i
$958$		0			0
$959$		−	15.9896i		−	0.516331i
$960$		0			0
$961$		−	29.9230i		−	0.965259i
$962$		0			0
$963$	31.4976	+	58.9278i	1.01500	+	1.89892i
$964$		0			0
$965$	37.3950	−	30.6893i	1.20379	−	0.987923i
$966$		0			0
$967$	11.0598	+	16.5521i	0.355659	+	0.532281i	0.965555	−	0.260201i	$-0.0837887\pi$
$967$	11.0598	+	16.5521i	0.355659	+	0.532281i	−0.609896	+	0.792482i	$0.708789\pi$
$968$		0			0
$969$	11.5693	+	7.73039i	0.371661	+	0.248336i
$970$		0			0
$971$	−15.8031	−	52.0957i	−0.507145	−	1.67183i	−0.719383	−	0.694614i	$-0.755575\pi$
$971$	−15.8031	−	52.0957i	−0.507145	−	1.67183i	0.212238	−	0.977218i	$-0.431925\pi$
$972$		0			0
$973$	−7.63470	+	9.30291i	−0.244757	+	0.298238i
$974$		0			0
$975$	50.6399	−	122.256i	1.62178	−	3.91531i
$976$		0			0
$977$	13.4388	+	32.4441i	0.429945	+	1.03798i	0.979305	+	0.202392i	$0.0648716\pi$
$977$	13.4388	+	32.4441i	0.429945	+	1.03798i	−0.549360	+	0.835586i	$0.685128\pi$
$978$		0			0
$979$	−17.4561	+	1.71927i	−0.557898	+	0.0549482i
$980$		0			0
$981$	−41.5286	−	22.1975i	−1.32591	−	0.708712i
$982$		0			0
$983$	−1.32816	−	6.67710i	−0.0423617	−	0.212966i	0.953807	−	0.300420i	$-0.0971269\pi$
$983$	−1.32816	−	6.67710i	−0.0423617	−	0.212966i	−0.996169	+	0.0874539i	$0.972127\pi$
$984$		0			0
$985$	−55.0458	−	10.9493i	−1.75390	−	0.348873i
$986$		0			0
$987$	−62.4604	−	6.15181i	−1.98814	−	0.195814i
$988$		0			0
$989$	−10.4560	−	3.17181i	−0.332483	−	0.100858i
$990$		0			0
$991$	11.4332	−	11.4332i	0.363189	−	0.363189i	−0.501797	−	0.864985i	$-0.667328\pi$
$991$	11.4332	−	11.4332i	0.363189	−	0.363189i	0.864985	+	0.501797i	$0.167328\pi$
$992$		0			0
$993$	−48.1838	−	48.1838i	−1.52907	−	1.52907i
$994$		0			0
$995$	6.64718	−	21.9128i	0.210730	−	0.694683i
$996$		0			0
$997$	−1.43791	+	14.5993i	−0.0455390	+	0.462365i	0.945191	+	0.326519i	$0.105876\pi$
$997$	−1.43791	+	14.5993i	−0.0455390	+	0.462365i	−0.990730	+	0.135847i	$0.956624\pi$
$998$		0			0
$999$	−0.800386	+	4.02381i	−0.0253231	+	0.127308i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	512.2.k.a.497.2		240
4.3	odd	2		128.2.k.a.101.7	✓	240
128.19	odd	32		128.2.k.a.109.7	yes	240
128.109	even	32	inner	512.2.k.a.273.2		240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
128.2.k.a.101.7	✓	240	4.3	odd	2
128.2.k.a.109.7	yes	240	128.19	odd	32
512.2.k.a.273.2		240	128.109	even	32	inner
512.2.k.a.497.2		240	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 512 = 2^{9} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	512.k (of order \(32\), degree \(16\), not minimal)

\(f(q)\)	\(=\)	\(q+(-2.34878 + 1.25545i) q^{3} +(-2.35055 - 2.86416i) q^{5} +(1.77512 - 1.18610i) q^{7} +(2.27391 - 3.40315i) q^{9} +(-3.00424 + 0.911326i) q^{11} +(4.40033 + 3.61126i) q^{13} +(9.11675 + 3.77628i) q^{15} +(-2.12200 + 0.878960i) q^{17} +(0.222958 + 2.26373i) q^{19} +(-2.68028 + 5.01446i) q^{21} +(-4.14830 + 0.825148i) q^{23} +(-1.70285 + 8.56080i) q^{25} +(-0.285305 + 2.89675i) q^{27} +(-1.05879 + 3.49035i) q^{29} +(0.733820 + 0.733820i) q^{31} +(5.91218 - 5.91218i) q^{33} +(-7.56968 - 2.29624i) q^{35} +(1.40268 + 0.138152i) q^{37} +(-14.8692 - 2.95766i) q^{39} +(1.67780 + 8.43488i) q^{41} +(2.27833 + 1.21779i) q^{43} +(-15.0921 + 1.48644i) q^{45} +(4.22422 + 10.1982i) q^{47} +(-0.934561 + 2.25623i) q^{49} +(3.88062 - 4.72855i) q^{51} +(-0.810406 - 2.67155i) q^{53} +(9.67181 + 6.46250i) q^{55} +(-3.36567 - 5.03709i) q^{57} +(6.48788 - 5.32446i) q^{59} +(4.18727 + 7.83384i) q^{61} -8.73808i q^{63} -21.0917i q^{65} +(-1.02445 - 1.91661i) q^{67} +(8.70752 - 7.14608i) q^{69} +(4.85914 + 7.27222i) q^{71} +(-9.35312 - 6.24955i) q^{73} +(-6.74804 - 22.2453i) q^{75} +(-4.25196 + 5.18103i) q^{77} +(1.50619 - 3.63626i) q^{79} +(1.73229 + 4.18212i) q^{81} +(0.375929 - 0.0370258i) q^{83} +(7.50535 + 4.01169i) q^{85} +(-1.89510 - 9.52732i) q^{87} +(5.47983 + 1.09001i) q^{89} +(12.0944 + 1.19120i) q^{91} +(-2.64486 - 0.802308i) q^{93} +(5.95960 - 5.95960i) q^{95} +(-4.20900 - 4.20900i) q^{97} +(-3.73000 + 12.2962i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q + 16 q^{3} - 16 q^{5} + 16 q^{7} - 16 q^{9} + 16 q^{11} - 16 q^{13} + 16 q^{15} - 16 q^{17} + 16 q^{19} - 16 q^{21} + 16 q^{23} - 16 q^{25} + 16 q^{27} - 16 q^{29} + 16 q^{31} - 16 q^{33} + 16 q^{35}+ \cdots + 16 q^{99}+O(q^{100}) \) 240 * q + 16 * q^3 - 16 * q^5 + 16 * q^7 - 16 * q^9 + 16 * q^11 - 16 * q^13 + 16 * q^15 - 16 * q^17 + 16 * q^19 - 16 * q^21 + 16 * q^23 - 16 * q^25 + 16 * q^27 - 16 * q^29 + 16 * q^31 - 16 * q^33 + 16 * q^35 - 16 * q^37 + 16 * q^39 - 16 * q^41 + 16 * q^43 - 16 * q^45 + 16 * q^47 - 16 * q^49 + 16 * q^51 - 16 * q^53 + 16 * q^55 - 16 * q^57 + 16 * q^59 - 16 * q^61 + 16 * q^67 - 16 * q^69 + 16 * q^71 - 16 * q^73 + 16 * q^75 - 16 * q^77 + 16 * q^79 - 16 * q^81 + 16 * q^83 - 16 * q^85 + 16 * q^87 - 16 * q^89 + 16 * q^91 - 16 * q^93 + 16 * q^95 - 16 * q^97 + 16 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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