LMFDB - Embedded newform 819.2.dx.a.503.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [819,2,Mod(503,819)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(819, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 4]))

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

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

chi := DirichletCharacter("819.503");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 819 = 3^{2} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	819.dx (of order $6$, 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:	$6.53974792554$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$36$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			503.14
Character	$\chi$	$=$	819.503
Dual form			819.2.dx.a.692.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.595297 - 0.343695i) q^{2} +(-0.763748 - 1.32285i) q^{4} +2.01783 q^{5} +(1.15619 + 2.37975i) q^{7} +2.42476i q^{8} +O(q^{10})$	\(q+(-0.595297 - 0.343695i) q^{2} +(-0.763748 - 1.32285i) q^{4} +2.01783 q^{5} +(1.15619 + 2.37975i) q^{7} +2.42476i q^{8} +(-1.20121 - 0.693518i) q^{10} +(0.901261 + 0.520343i) q^{11} +(-1.78562 + 3.13234i) q^{13} +(0.129631 - 1.81404i) q^{14} +(-0.694116 + 1.20224i) q^{16} +(2.31510 + 4.00988i) q^{17} +(-4.39603 + 2.53805i) q^{19} +(-1.54111 - 2.66929i) q^{20} +(-0.357679 - 0.619518i) q^{22} +(0.642878 + 0.371166i) q^{23} -0.928355 q^{25} +(2.13954 - 1.25096i) q^{26} +(2.26502 - 3.34700i) q^{28} +(-4.20078 - 2.42532i) q^{29} +8.99744i q^{31} +(5.02623 - 2.90189i) q^{32} -3.18276i q^{34} +(2.33300 + 4.80194i) q^{35} +(-1.60720 + 2.78374i) q^{37} +3.48925 q^{38} +4.89277i q^{40} +(2.61184 - 4.52384i) q^{41} +(-2.97831 - 5.15859i) q^{43} -1.58964i q^{44} +(-0.255135 - 0.441908i) q^{46} +11.6331 q^{47} +(-4.32644 + 5.50290i) q^{49} +(0.552647 + 0.319071i) q^{50} +(5.50738 - 0.0302062i) q^{52} -1.74959i q^{53} +(1.81859 + 1.04997i) q^{55} +(-5.77034 + 2.80349i) q^{56} +(1.66714 + 2.88757i) q^{58} +(4.92676 + 8.53340i) q^{59} +(2.12587 - 1.22737i) q^{61} +(3.09237 - 5.35615i) q^{62} -1.21300 q^{64} +(-3.60309 + 6.32053i) q^{65} +(5.44121 - 9.42445i) q^{67} +(3.53631 - 6.12507i) q^{68} +(0.261575 - 3.66042i) q^{70} +(9.92424 - 5.72976i) q^{71} +5.27545i q^{73} +(1.91352 - 1.10477i) q^{74} +(6.71491 + 3.87685i) q^{76} +(-0.196258 + 2.74640i) q^{77} +9.12427 q^{79} +(-1.40061 + 2.42593i) q^{80} +(-3.10964 + 1.79535i) q^{82} -9.56552 q^{83} +(4.67149 + 8.09126i) q^{85} +4.09453i q^{86} +(-1.26171 + 2.18535i) q^{88} +(-6.32834 + 10.9610i) q^{89} +(-9.51871 - 0.627756i) q^{91} -1.13391i q^{92} +(-6.92513 - 3.99823i) q^{94} +(-8.87044 + 5.12135i) q^{95} +(10.8148 - 6.24396i) q^{97} +(4.46684 - 1.78888i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q + 32 q^{4} - 2 q^{7}+O(q^{10}) $ 72 * q + 32 * q^4 - 2 * q^7	$ 72 q + 32 q^{4} - 2 q^{7} - 24 q^{16} + 24 q^{22} + 56 q^{25} - 8 q^{28} + 16 q^{37} - 4 q^{43} + 32 q^{46} + 26 q^{49} - 40 q^{58} - 64 q^{64} + 60 q^{67} - 40 q^{70} - 72 q^{79} - 80 q^{85} - 24 q^{88} + 2 q^{91}+O(q^{100}) $ 72 * q + 32 * q^4 - 2 * q^7 - 24 * q^16 + 24 * q^22 + 56 * q^25 - 8 * q^28 + 16 * q^37 - 4 * q^43 + 32 * q^46 + 26 * q^49 - 40 * q^58 - 64 * q^64 + 60 * q^67 - 40 * q^70 - 72 * q^79 - 80 * q^85 - 24 * q^88 + 2 * q^91

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/819\mathbb{Z}\right)^\times$.

$n$	$92$	$379$	$703$
$\chi(n)$	$-1$	$e\left(\frac{2}{3}\right)$	$-1$

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 $

$2$	−0.595297	−	0.343695i	−0.420939	−	0.243029i	0.274540	−	0.961576i	$-0.411474\pi$
$2$	−0.595297	−	0.343695i	−0.420939	−	0.243029i	−0.695479	+	0.718547i	$0.744808\pi$
$3$		0			0
$3$		0			0
$4$	−0.763748	−	1.32285i	−0.381874	−	0.661425i
$5$	2.01783			0.902402			0.451201	−	0.892422i	$-0.350996\pi$
$5$	2.01783			0.902402			0.451201	+	0.892422i	$0.350996\pi$
$6$		0			0
$7$	1.15619	+	2.37975i	0.436999	+	0.899462i
$7$	1.15619	+	2.37975i	0.436999	+	0.899462i
$8$			2.42476i			0.857284i
$9$		0			0
$10$	−1.20121	−	0.693518i	−0.379856	−	0.219310i
$11$	0.901261	+	0.520343i	0.271740	+	0.156889i	0.629678	−	0.776856i	$-0.283187\pi$
$11$	0.901261	+	0.520343i	0.271740	+	0.156889i	−0.357938	+	0.933745i	$0.616520\pi$
$12$		0			0
$13$	−1.78562	+	3.13234i	−0.495243	+	0.868755i
$13$	−1.78562	+	3.13234i	−0.495243	+	0.868755i
$14$	0.129631	−	1.81404i	0.0346455	−	0.484822i
$15$		0			0
$16$	−0.694116	+	1.20224i	−0.173529	+	0.300561i
$17$	2.31510	+	4.00988i	0.561495	+	0.972538i	0.997366	+	0.0725290i	$0.0231070\pi$
$17$	2.31510	+	4.00988i	0.561495	+	0.972538i	−0.435871	+	0.900009i	$0.643560\pi$
$18$		0			0
$19$	−4.39603	+	2.53805i	−1.00852	+	0.582268i	−0.910757	−	0.412942i	$-0.864501\pi$
$19$	−4.39603	+	2.53805i	−1.00852	+	0.582268i	−0.0977602	+	0.995210i	$0.531168\pi$
$20$	−1.54111	−	2.66929i	−0.344604	−	0.596871i
$21$		0			0
$22$	−0.357679	−	0.619518i	−0.0762574	−	0.132082i
$23$	0.642878	+	0.371166i	0.134049	+	0.0773934i	0.565525	−	0.824731i	$-0.308674\pi$
$23$	0.642878	+	0.371166i	0.134049	+	0.0773934i	−0.431476	+	0.902125i	$0.642007\pi$
$24$		0			0
$25$	−0.928355			−0.185671
$26$	2.13954	−	1.25096i	0.419599	−	0.245334i
$27$		0			0
$28$	2.26502	−	3.34700i	0.428048	−	0.632523i
$29$	−4.20078	−	2.42532i	−0.780066	−	0.450371i	0.0563878	−	0.998409i	$-0.482042\pi$
$29$	−4.20078	−	2.42532i	−0.780066	−	0.450371i	−0.836454	+	0.548038i	$0.815375\pi$
$30$		0			0
$31$			8.99744i			1.61599i	0.589191	+	0.807994i	$0.299447\pi$
$31$			8.99744i			1.61599i	−0.589191	+	0.807994i	$0.700553\pi$
$32$	5.02623	−	2.90189i	0.888520	−	0.512987i
$33$		0			0
$34$		−	3.18276i		−	0.545838i
$35$	2.33300	+	4.80194i	0.394349	+	0.811676i
$36$		0			0
$37$	−1.60720	+	2.78374i	−0.264221	+	0.457645i	−0.967359	−	0.253409i	$-0.918448\pi$
$37$	−1.60720	+	2.78374i	−0.264221	+	0.457645i	0.703138	+	0.711053i	$0.251782\pi$
$38$	3.48925			0.566032
$39$		0			0
$40$			4.89277i			0.773614i
$41$	2.61184	−	4.52384i	0.407901	−	0.706504i	−0.586754	−	0.809765i	$-0.699594\pi$
$41$	2.61184	−	4.52384i	0.407901	−	0.706504i	0.994654	+	0.103261i	$0.0329277\pi$
$42$		0			0
$43$	−2.97831	−	5.15859i	−0.454189	−	0.786678i	0.544452	−	0.838792i	$-0.316737\pi$
$43$	−2.97831	−	5.15859i	−0.454189	−	0.786678i	−0.998641	+	0.0521137i	$0.983404\pi$
$44$		−	1.58964i		−	0.239648i
$45$		0			0
$46$	−0.255135	−	0.441908i	−0.0376177	−	0.0651557i
$47$	11.6331			1.69686			0.848429	−	0.529309i	$-0.177549\pi$
$47$	11.6331			1.69686			0.848429	+	0.529309i	$0.177549\pi$
$48$		0			0
$49$	−4.32644	+	5.50290i	−0.618063	+	0.786128i
$50$	0.552647	+	0.319071i	0.0781561	+	0.0451234i
$51$		0			0
$52$	5.50738	−	0.0302062i	0.763736	−	0.00418885i
$53$		−	1.74959i		−	0.240325i	−0.992754	−	0.120163i	$-0.961658\pi$
$53$		−	1.74959i		−	0.240325i	0.992754	−	0.120163i	$-0.0383416\pi$
$54$		0			0
$55$	1.81859	+	1.04997i	0.245219	+	0.141577i
$56$	−5.77034	+	2.80349i	−0.771094	+	0.374632i
$57$		0			0
$58$	1.66714	+	2.88757i	0.218906	+	0.379157i
$59$	4.92676	+	8.53340i	0.641410	+	1.11095i	0.985118	+	0.171878i	$0.0549835\pi$
$59$	4.92676	+	8.53340i	0.641410	+	1.11095i	−0.343708	+	0.939076i	$0.611683\pi$
$60$		0			0
$61$	2.12587	−	1.22737i	0.272189	−	0.157149i	−0.357693	−	0.933839i	$-0.616437\pi$
$61$	2.12587	−	1.22737i	0.272189	−	0.157149i	0.629882	+	0.776691i	$0.283103\pi$
$62$	3.09237	−	5.35615i	0.392732	−	0.680232i
$63$		0			0
$64$	−1.21300			−0.151625
$65$	−3.60309	+	6.32053i	−0.446908	+	0.783966i
$66$		0			0
$67$	5.44121	−	9.42445i	0.664749	−	1.15138i	−0.314604	−	0.949223i	$-0.601872\pi$
$67$	5.44121	−	9.42445i	0.664749	−	1.15138i	0.979353	−	0.202156i	$-0.0647949\pi$
$68$	3.53631	−	6.12507i	0.428841	−	0.742774i
$69$		0			0
$70$	0.261575	−	3.66042i	0.0312641	−	0.437504i
$71$	9.92424	−	5.72976i	1.17779	−	0.679998i	0.222288	−	0.974981i	$-0.428648\pi$
$71$	9.92424	−	5.72976i	1.17779	−	0.679998i	0.955502	+	0.294984i	$0.0953142\pi$
$72$		0			0
$73$			5.27545i			0.617444i	0.951152	+	0.308722i	$0.0999013\pi$
$73$			5.27545i			0.617444i	−0.951152	+	0.308722i	$0.900099\pi$
$74$	1.91352	−	1.10477i	0.222442	−	0.128427i
$75$		0			0
$76$	6.71491	+	3.87685i	0.770253	+	0.444706i
$77$	−0.196258	+	2.74640i	−0.0223657	+	0.312981i
$78$		0			0
$79$	9.12427			1.02656			0.513280	−	0.858221i	$-0.328430\pi$
$79$	9.12427			1.02656			0.513280	+	0.858221i	$0.328430\pi$
$80$	−1.40061	+	2.42593i	−0.156593	+	0.271227i
$81$		0			0
$82$	−3.10964	+	1.79535i	−0.343402	+	0.198263i
$83$	−9.56552			−1.04995			−0.524976	−	0.851117i	$-0.675926\pi$
$83$	−9.56552			−1.04995			−0.524976	+	0.851117i	$0.675926\pi$
$84$		0			0
$85$	4.67149	+	8.09126i	0.506694	+	0.877620i
$86$			4.09453i			0.441524i
$87$		0			0
$88$	−1.26171	+	2.18535i	−0.134499	+	0.232959i
$89$	−6.32834	+	10.9610i	−0.670803	+	1.16186i	0.306874	+	0.951750i	$0.400717\pi$
$89$	−6.32834	+	10.9610i	−0.670803	+	1.16186i	−0.977677	+	0.210115i	$0.932616\pi$
$90$		0			0
$91$	−9.51871	−	0.627756i	−0.997832	−	0.0658068i
$92$		−	1.13391i		−	0.118218i
$93$		0			0
$94$	−6.92513	−	3.99823i	−0.714273	−	0.412386i
$95$	−8.87044	+	5.12135i	−0.910088	+	0.525440i
$96$		0			0
$97$	10.8148	−	6.24396i	1.09808	−	0.633978i	0.162365	−	0.986731i	$-0.448088\pi$
$97$	10.8148	−	6.24396i	1.09808	−	0.633978i	0.935716	+	0.352753i	$0.114754\pi$
$98$	4.46684	−	1.78888i	0.451219	−	0.180704i
$99$		0			0
$100$	0.709029	+	1.22807i	0.0709029	+	0.122807i
$101$	−5.49724	+	9.52150i	−0.546996	+	0.947424i	0.451483	+	0.892280i	$0.350895\pi$
$101$	−5.49724	+	9.52150i	−0.546996	+	0.947424i	−0.998478	+	0.0551445i	$0.982438\pi$
$102$		0			0
$103$		−	5.08163i		−	0.500708i	−0.968154	−	0.250354i	$-0.919453\pi$
$103$		−	5.08163i		−	0.500708i	0.968154	−	0.250354i	$-0.0805469\pi$
$104$	−7.59518	−	4.32971i	−0.744769	−	0.424563i
$105$		0			0
$106$	−0.601326	+	1.04153i	−0.0584060	+	0.101162i
$107$	−3.79156	−	2.18906i	−0.366544	−	0.211624i	0.305403	−	0.952223i	$-0.401209\pi$
$107$	−3.79156	−	2.18906i	−0.366544	−	0.211624i	−0.671948	+	0.740599i	$0.734542\pi$
$108$		0			0
$109$	−4.75293			−0.455248			−0.227624	−	0.973749i	$-0.573096\pi$
$109$	−4.75293			−0.455248			−0.227624	+	0.973749i	$0.573096\pi$
$110$	−0.721736	−	1.25008i	−0.0688148	−	0.119191i
$111$		0			0
$112$	−3.66358	−	0.261800i	−0.346175	−	0.0247378i
$113$	6.33230	−	3.65595i	0.595692	−	0.343923i	−0.171653	−	0.985158i	$-0.554911\pi$
$113$	6.33230	−	3.65595i	0.595692	−	0.343923i	0.767345	+	0.641234i	$0.221577\pi$
$114$		0			0
$115$	1.29722	+	0.748950i	0.120966	+	0.0698399i
$116$			7.40934i			0.687940i
$117$		0			0
$118$		−	6.77321i		−	0.623525i
$119$	−6.86581	+	10.1456i	−0.629388	+	0.930042i
$120$		0			0
$121$	−4.95849	−	8.58835i	−0.450771	−	0.780759i
$122$	−1.68736			−0.152767
$123$		0			0
$124$	11.9023	−	6.87177i	1.06885	−	0.617103i
$125$	−11.9624			−1.06995
$126$		0			0
$127$	−0.973844	+	1.68675i	−0.0864146	+	0.149675i	−0.905993	−	0.423292i	$-0.860874\pi$
$127$	−0.973844	+	1.68675i	−0.0864146	+	0.149675i	0.819579	+	0.572967i	$0.194208\pi$
$128$	−9.33036	−	5.38688i	−0.824695	−	0.476138i
$129$		0			0
$130$	4.31724	−	2.52423i	0.378647	−	0.221390i
$131$	1.33631			0.116754			0.0583771	−	0.998295i	$-0.481407\pi$
$131$	1.33631			0.116754			0.0583771	+	0.998295i	$0.481407\pi$
$132$		0			0
$133$	−11.1226	−	7.52698i	−0.964449	−	0.652672i
$134$	−6.47827	+	3.74023i	−0.559637	+	0.323107i
$135$		0			0
$136$	−9.72301	+	5.61358i	−0.833741	+	0.481361i
$137$	8.34737	−	4.81936i	0.713164	−	0.411746i	−0.0990673	−	0.995081i	$-0.531586\pi$
$137$	8.34737	−	4.81936i	0.713164	−	0.411746i	0.812232	+	0.583335i	$0.198253\pi$
$138$		0			0
$139$	13.7300	−	7.92700i	1.16456	−	0.672359i	0.212168	−	0.977233i	$-0.431948\pi$
$139$	13.7300	−	7.92700i	1.16456	−	0.672359i	0.952393	+	0.304874i	$0.0986144\pi$
$140$	4.57042	−	6.75368i	0.386271	−	0.570790i
$141$		0			0
$142$	−7.87716			−0.661036
$143$	−3.23920	+	1.89392i	−0.270876	+	0.158377i
$144$		0			0
$145$	−8.47647	−	4.89389i	−0.703933	−	0.406416i
$146$	1.81314	−	3.14046i	0.150057	−	0.259906i
$147$		0			0
$148$	4.90997			0.403597
$149$	15.3641	−	8.87046i	1.25868	−	0.726697i	0.285859	−	0.958272i	$-0.407721\pi$
$149$	15.3641	−	8.87046i	1.25868	−	0.726697i	0.972817	+	0.231575i	$0.0743879\pi$
$150$		0			0
$151$	−9.49631			−0.772799			−0.386399	−	0.922332i	$-0.626281\pi$
$151$	−9.49631			−0.772799			−0.386399	+	0.922332i	$0.626281\pi$
$152$	−6.15416	−	10.6593i	−0.499169	−	0.864585i
$153$		0			0
$154$	1.06075	−	1.56747i	0.0854780	−	0.126310i
$155$			18.1553i			1.45827i
$156$		0			0
$157$		−	1.33807i		−	0.106790i	−0.998573	−	0.0533949i	$-0.982996\pi$
$157$		−	1.33807i		−	0.106790i	0.998573	−	0.0533949i	$-0.0170042\pi$
$158$	−5.43165	−	3.13597i	−0.432119	−	0.249484i
$159$		0			0
$160$	10.1421	−	5.85553i	0.801802	−	0.462920i
$161$	−0.139993	+	1.95903i	−0.0110330	+	0.154393i
$162$		0			0
$163$	3.15287	+	5.46094i	0.246952	+	0.427734i	0.962679	−	0.270647i	$-0.0872376\pi$
$163$	3.15287	+	5.46094i	0.246952	+	0.427734i	−0.715726	+	0.698381i	$0.753904\pi$
$164$	−7.97914			−0.623066
$165$		0			0
$166$	5.69432	+	3.28762i	0.441965	+	0.255169i
$167$	10.6565	−	18.4576i	0.824623	−	1.42829i	−0.0775845	−	0.996986i	$-0.524721\pi$
$167$	10.6565	−	18.4576i	0.824623	−	1.42829i	0.902207	−	0.431303i	$-0.141946\pi$
$168$		0			0
$169$	−6.62310	−	11.1864i	−0.509469	−	0.860489i
$170$		−	6.42227i		−	0.492565i
$171$		0			0
$172$	−4.54936	+	7.87973i	−0.346886	+	0.600823i
$173$	−6.07966	−	10.5303i	−0.462228	−	0.800602i	0.536844	−	0.843682i	$-0.319616\pi$
$173$	−6.07966	−	10.5303i	−0.462228	−	0.800602i	−0.999072	+	0.0430797i	$0.986283\pi$
$174$		0			0
$175$	−1.07336	−	2.20925i	−0.0811381	−	0.167004i
$176$	−1.25116	+	0.722358i	−0.0943098	+	0.0544498i
$177$		0			0
$178$	7.53449	−	4.35004i	0.564734	−	0.326049i
$179$	1.93993	+	1.12002i	0.144997	+	0.0837141i	0.570743	−	0.821128i	$-0.306655\pi$
$179$	1.93993	+	1.12002i	0.144997	+	0.0837141i	−0.425746	+	0.904843i	$0.639988\pi$
$180$		0			0
$181$			3.29026i			0.244563i	0.992495	+	0.122281i	$0.0390211\pi$
$181$			3.29026i			0.244563i	−0.992495	+	0.122281i	$0.960979\pi$
$182$	5.45071	+	3.64523i	0.404033	+	0.270203i
$183$		0			0
$184$	−0.899989	+	1.55883i	−0.0663481	+	0.114918i
$185$	−3.24305	+	5.61713i	−0.238434	+	0.412979i
$186$		0			0
$187$			4.81860i			0.352371i
$188$	−8.88473	−	15.3888i	−0.647986	−	1.12234i
$189$		0			0
$190$	7.04073			0.510788
$191$	11.1811	−	6.45541i	0.809036	−	0.467097i	−0.0375853	−	0.999293i	$-0.511967\pi$
$191$	11.1811	−	6.45541i	0.809036	−	0.467097i	0.846621	+	0.532197i	$0.178633\pi$
$192$		0			0
$193$	−3.75652	+	6.50649i	−0.270401	+	0.468347i	−0.968964	−	0.247200i	$-0.920489\pi$
$193$	−3.75652	+	6.50649i	−0.270401	+	0.468347i	0.698564	+	0.715548i	$0.253823\pi$
$194$	−8.58406			−0.616300
$195$		0			0
$196$	10.5838	+	1.52041i	0.755987	+	0.108601i
$197$	−21.2270	−	12.2554i	−1.51236	−	0.873163i	−0.999896	−	0.0144555i	$-0.995399\pi$
$197$	−21.2270	−	12.2554i	−1.51236	−	0.873163i	−0.512467	−	0.858707i	$-0.671268\pi$
$198$		0			0
$199$	−12.4831	+	7.20715i	−0.884907	+	0.510901i	−0.872273	−	0.489019i	$-0.837355\pi$
$199$	−12.4831	+	7.20715i	−0.884907	+	0.510901i	−0.0126336	+	0.999920i	$0.504022\pi$
$200$		−	2.25104i		−	0.159173i
$201$		0			0
$202$	6.54498	−	3.77875i	0.460503	−	0.265872i
$203$	0.914760	−	12.8010i	0.0642035	−	0.898451i
$204$		0			0
$205$	5.27025	−	9.12834i	0.368090	−	0.637551i
$206$	−1.74653	+	3.02508i	−0.121686	+	0.210767i
$207$		0			0
$208$	−2.52641	−	4.32096i	−0.175175	−	0.299605i
$209$	−5.28262			−0.365407
$210$		0			0
$211$	−7.97002	+	13.8045i	−0.548678	+	0.950339i	0.449687	+	0.893186i	$0.351536\pi$
$211$	−7.97002	+	13.8045i	−0.548678	+	0.950339i	−0.998365	+	0.0571528i	$0.981798\pi$
$212$	−2.31445	+	1.33625i	−0.158957	+	0.0917739i
$213$		0			0
$214$	1.50474	+	2.60628i	0.102862	+	0.178162i
$215$	−6.00974	−	10.4092i	−0.409861	−	0.709900i
$216$		0			0
$217$	−21.4117	+	10.4028i	−1.45352	+	0.706185i
$218$	2.82941	+	1.63356i	0.191632	+	0.110639i
$219$		0			0
$220$		−	3.20763i		−	0.216259i
$221$	−16.6942	+	0.0915624i	−1.12297	+	0.00615915i
$222$		0			0
$223$	9.99448	+	5.77031i	0.669280	+	0.386409i	0.795804	−	0.605555i	$-0.207049\pi$
$223$	9.99448	+	5.77031i	0.669280	+	0.386409i	−0.126524	+	0.991964i	$0.540382\pi$
$224$	12.7171	+	8.60603i	0.849695	+	0.575014i
$225$		0			0
$226$	−5.02613			−0.334333
$227$	1.74876	+	3.02893i	0.116069	+	0.201037i	0.918207	−	0.396102i	$-0.129637\pi$
$227$	1.74876	+	3.02893i	0.116069	+	0.201037i	−0.802138	+	0.597139i	$0.796304\pi$
$228$		0			0
$229$		−	27.5761i		−	1.82228i	−0.412098	−	0.911140i	$-0.635204\pi$
$229$		−	27.5761i		−	1.82228i	0.412098	−	0.911140i	$-0.364796\pi$
$230$	−0.514821	−	0.891695i	−0.0339463	−	0.0587966i
$231$		0			0
$232$	5.88084	−	10.1859i	0.386096	−	0.668738i
$233$			28.7632i			1.88434i	0.335140	+	0.942168i	$0.391216\pi$
$233$			28.7632i			1.88434i	−0.335140	+	0.942168i	$0.608784\pi$
$234$		0			0
$235$	23.4736			1.53125
$236$	7.52561	−	13.0347i	0.489875	−	0.848489i
$237$		0			0
$238$	7.57417	−	3.67988i	0.490961	−	0.238531i
$239$			24.2756i			1.57026i	0.619334	+	0.785128i	$0.287403\pi$
$239$			24.2756i			1.57026i	−0.619334	+	0.785128i	$0.712597\pi$
$240$		0			0
$241$	−8.04237	+	4.64327i	−0.518055	+	0.299099i	−0.736138	−	0.676831i	$-0.763353\pi$
$241$	−8.04237	+	4.64327i	−0.518055	+	0.299099i	0.218084	+	0.975930i	$0.430019\pi$
$242$			6.81682i			0.438202i
$243$		0			0
$244$	−3.24725	−	1.87480i	−0.207884	−	0.120022i
$245$	−8.73003	+	11.1039i	−0.557741	+	0.709404i
$246$		0			0
$247$	−0.100380	−	18.3018i	−0.00638702	−	1.16452i
$248$	−21.8167			−1.38536
$249$		0			0
$250$	7.12119	+	4.11142i	0.450384	+	0.260029i
$251$	−4.59668	−	7.96169i	−0.290140	−	0.502537i	0.683703	−	0.729761i	$-0.260369\pi$
$251$	−4.59668	−	7.96169i	−0.290140	−	0.502537i	−0.973843	+	0.227223i	$0.927035\pi$
$252$		0			0
$253$	0.386267	+	0.669034i	0.0242844	+	0.0420618i
$254$	1.15945	−	0.669410i	0.0727505	−	0.0420025i
$255$		0			0
$256$	4.91589	+	8.51456i	0.307243	+	0.532160i
$257$	−4.25659	+	7.37263i	−0.265519	+	0.459892i	−0.967699	−	0.252107i	$-0.918877\pi$
$257$	−4.25659	+	7.37263i	−0.265519	+	0.459892i	0.702181	+	0.711999i	$0.252210\pi$
$258$		0			0
$259$	−8.48285	−	0.606186i	−0.527098	−	0.0376666i
$260$	11.1130	−	0.0609511i	0.689197	−	0.00378003i
$261$		0			0
$262$	−0.795503	−	0.459284i	−0.0491463	−	0.0283747i
$263$	8.05580	+	4.65102i	0.496742	+	0.286794i	0.727367	−	0.686249i	$-0.240744\pi$
$263$	8.05580	+	4.65102i	0.496742	+	0.286794i	−0.230625	+	0.973043i	$0.574077\pi$
$264$		0			0
$265$		−	3.53038i		−	0.216870i
$266$	4.03425	+	8.30356i	0.247355	+	0.509124i
$267$		0			0
$268$	−16.6228			−1.01540
$269$	9.65179	+	16.7174i	0.588480	+	1.01928i	0.994432	+	0.105383i	$0.0336068\pi$
$269$	9.65179	+	16.7174i	0.588480	+	1.01928i	−0.405952	+	0.913895i	$0.633060\pi$
$270$		0			0
$271$	−7.71833	−	4.45618i	−0.468855	−	0.270694i	0.246905	−	0.969040i	$-0.420586\pi$
$271$	−7.71833	−	4.45618i	−0.468855	−	0.270694i	−0.715760	+	0.698346i	$0.753920\pi$
$272$	−6.42780			−0.389743
$273$		0			0
$274$	−6.62555			−0.400264
$275$	−0.836690	−	0.483063i	−0.0504543	−	0.0291298i
$276$		0			0
$277$	14.2859	+	24.7439i	0.858355	+	1.48672i	0.873497	+	0.486830i	$0.161847\pi$
$277$	14.2859	+	24.7439i	0.858355	+	1.48672i	−0.0151413	+	0.999885i	$0.504820\pi$
$278$	−10.8979			−0.653611
$279$		0			0
$280$	−11.6436	+	5.65697i	−0.695837	+	0.338069i
$281$		−	31.1628i		−	1.85902i	−0.368801	−	0.929508i	$-0.620232\pi$
$281$		−	31.1628i		−	1.85902i	0.368801	−	0.929508i	$-0.379768\pi$
$282$		0			0
$283$	−12.9844	−	7.49657i	−0.771845	−	0.445625i	0.0616876	−	0.998096i	$-0.480352\pi$
$283$	−12.9844	−	7.49657i	−0.771845	−	0.445625i	−0.833532	+	0.552471i	$0.813685\pi$
$284$	−15.1592	−	8.75218i	−0.899535	−	0.519347i
$285$		0			0
$286$	2.57922	−	0.0141462i	0.152512	−	0.000836483i
$287$	13.7854	+	0.985108i	0.813726	+	0.0581491i
$288$		0			0
$289$	−2.21941	+	3.84413i	−0.130553	+	0.226125i
$290$	3.36401	+	5.82664i	0.197542	+	0.342152i
$291$		0			0
$292$	6.97862	−	4.02911i	0.408393	−	0.235786i
$293$	−6.60454	−	11.4394i	−0.385841	−	0.668296i	0.606044	−	0.795431i	$-0.292755\pi$
$293$	−6.60454	−	11.4394i	−0.385841	−	0.668296i	−0.991885	+	0.127134i	$0.959422\pi$
$294$		0			0
$295$	9.94138	+	17.2190i	0.578809	+	1.00253i
$296$	−6.74992	−	3.89707i	−0.392331	−	0.226513i
$297$		0			0
$298$	−12.1949			−0.706433
$299$	−2.31055	+	1.35095i	−0.133623	+	0.0781274i
$300$		0			0
$301$	8.83267	−	13.0520i	0.509107	−	0.752303i
$302$	5.65312	+	3.26383i	0.325301	+	0.187812i
$303$		0			0
$304$		−	7.04680i		−	0.404162i
$305$	4.28964	−	2.47662i	0.245624	−	0.141811i
$306$		0			0
$307$			17.7238i			1.01155i	0.862666	+	0.505775i	$0.168793\pi$
$307$			17.7238i			1.01155i	−0.862666	+	0.505775i	$0.831207\pi$
$308$	3.78296	−	1.83793i	0.215554	−	0.104726i
$309$		0			0
$310$	6.23989	−	10.8078i	0.354402	−	0.613842i
$311$	25.7336			1.45922			0.729609	−	0.683864i	$-0.239702\pi$
$311$	25.7336			1.45922			0.729609	+	0.683864i	$0.239702\pi$
$312$		0			0
$313$		−	8.72600i		−	0.493222i	−0.969114	−	0.246611i	$-0.920683\pi$
$313$		−	8.72600i		−	0.493222i	0.969114	−	0.246611i	$-0.0793171\pi$
$314$	−0.459889	+	0.796551i	−0.0259530	+	0.0449520i
$315$		0			0
$316$	−6.96864	−	12.0700i	−0.392017	−	0.678993i
$317$			10.0361i			0.563686i	0.959460	+	0.281843i	$0.0909458\pi$
$317$			10.0361i			0.563686i	−0.959460	+	0.281843i	$0.909054\pi$
$318$		0			0
$319$	−2.52400	−	4.37170i	−0.141317	−	0.244768i
$320$	−2.44762			−0.136826
$321$		0			0
$322$	0.756645	−	1.11809i	0.0421662	−	0.0623087i
$323$	−20.3545	−	11.7517i	−1.13256	−	0.653881i
$324$		0			0
$325$	1.65769	−	2.90792i	0.0919522	−	0.161302i
$326$		−	4.33451i		−	0.240066i
$327$		0			0
$328$	10.9692	+	6.33309i	0.605675	+	0.349686i
$329$	13.4501	+	27.6838i	0.741526	+	1.52626i
$330$		0			0
$331$	9.15016	+	15.8485i	0.502938	+	0.871115i	0.999994	+	0.00339618i	$0.00108104\pi$
$331$	9.15016	+	15.8485i	0.502938	+	0.871115i	−0.497056	+	0.867718i	$0.665586\pi$
$332$	7.30564	+	12.6537i	0.400949	+	0.694464i
$333$		0			0
$334$	−12.6875	+	7.32515i	−0.694231	+	0.400814i
$335$	10.9794	−	19.0169i	0.599871	−	1.03901i
$336$		0			0
$337$	−18.9276			−1.03105			−0.515525	−	0.856875i	$-0.672403\pi$
$337$	−18.9276			−1.03105			−0.515525	+	0.856875i	$0.672403\pi$
$338$	0.0980201	+	8.93553i	0.00533159	+	0.486029i
$339$		0			0
$340$	7.13568	−	12.3594i	0.386987	−	0.670280i
$341$	−4.68176	+	8.10904i	−0.253531	+	0.439129i
$342$		0			0
$343$	−18.0977	−	3.93346i	−0.977186	−	0.212387i
$344$	12.5084	−	7.22171i	0.674406	−	0.389369i
$345$		0			0
$346$			8.35819i			0.449339i
$347$	19.2716	−	11.1264i	1.03455	−	0.597299i	0.116266	−	0.993218i	$-0.462907\pi$
$347$	19.2716	−	11.1264i	1.03455	−	0.597299i	0.918285	+	0.395920i	$0.129574\pi$
$348$		0			0
$349$	−1.58994	−	0.917954i	−0.0851077	−	0.0491370i	0.456842	−	0.889548i	$-0.348980\pi$
$349$	−1.58994	−	0.917954i	−0.0851077	−	0.0491370i	−0.541950	+	0.840411i	$0.682314\pi$
$350$	−0.120344	+	1.68407i	−0.00643266	+	0.0900173i
$351$		0			0
$352$	6.03992			0.321929
$353$	−1.25182	+	2.16821i	−0.0666275	+	0.115402i	−0.897415	−	0.441188i	$-0.854557\pi$
$353$	−1.25182	+	2.16821i	−0.0666275	+	0.115402i	0.830787	+	0.556590i	$0.187891\pi$
$354$		0			0
$355$	20.0254	−	11.5617i	1.06284	−	0.613631i
$356$	19.3330			1.02465
$357$		0			0
$358$	−0.769889	−	1.33349i	−0.0406899	−	0.0704769i
$359$		−	19.9661i		−	1.05377i	−0.849937	−	0.526884i	$-0.823360\pi$
$359$		−	19.9661i		−	1.05377i	0.849937	−	0.526884i	$-0.176640\pi$
$360$		0			0
$361$	3.38336	−	5.86015i	0.178072	−	0.308429i
$362$	1.13084	−	1.95868i	0.0594359	−	0.102946i
$363$		0			0
$364$	6.43947	+	13.0713i	0.337520	+	0.685121i
$365$			10.6450i			0.557183i
$366$		0			0
$367$	32.3694	+	18.6885i	1.68967	+	0.975532i	0.954765	+	0.297363i	$0.0961071\pi$
$367$	32.3694	+	18.6885i	1.68967	+	0.975532i	0.734906	+	0.678169i	$0.237226\pi$
$368$	−0.892464	+	0.515264i	−0.0465229	+	0.0268600i
$369$		0			0
$370$	3.86116	−	2.22924i	0.200732	−	0.115893i
$371$	4.16360	−	2.02286i	0.216163	−	0.105022i
$372$		0			0
$373$	2.75134	+	4.76546i	0.142459	+	0.246746i	0.928422	−	0.371527i	$-0.121166\pi$
$373$	2.75134	+	4.76546i	0.142459	+	0.246746i	−0.785963	+	0.618273i	$0.787832\pi$
$374$	1.65613	−	2.86850i	0.0856363	−	0.148326i
$375$		0			0
$376$			28.2075i			1.45469i
$377$	15.0979	−	8.82757i	0.777584	−	0.454643i
$378$		0			0
$379$	5.56789	−	9.64386i	0.286003	−	0.495372i	−0.686849	−	0.726800i	$-0.741007\pi$
$379$	5.56789	−	9.64386i	0.286003	−	0.495372i	0.972852	+	0.231428i	$0.0743399\pi$
$380$	13.5496	+	7.82284i	0.695078	+	0.401303i
$381$		0			0
$382$	−8.87476			−0.454072
$383$	−0.841570	−	1.45764i	−0.0430022	−	0.0744821i	0.843723	−	0.536779i	$-0.180359\pi$
$383$	−0.841570	−	1.45764i	−0.0430022	−	0.0744821i	−0.886725	+	0.462296i	$0.847026\pi$
$384$		0			0
$385$	−0.396016	+	5.54176i	−0.0201828	+	0.282434i
$386$	4.47250	−	2.58220i	0.227644	−	0.131430i
$387$		0			0
$388$	−16.5196	−	9.53761i	−0.838657	−	0.484199i
$389$			34.0819i			1.72802i	0.503473	+	0.864011i	$0.332055\pi$
$389$			34.0819i			1.72802i	−0.503473	+	0.864011i	$0.667945\pi$
$390$		0			0
$391$			3.43715i			0.173824i
$392$	−13.3432	−	10.4906i	−0.673935	−	0.529856i
$393$		0			0
$394$	8.42425	+	14.5912i	0.424408	+	0.735096i
$395$	18.4112			0.926370
$396$		0			0
$397$	−17.1747	+	9.91581i	−0.861973	+	0.497660i	−0.864672	−	0.502336i	$-0.832474\pi$
$397$	−17.1747	+	9.91581i	−0.861973	+	0.497660i	0.00269950	+	0.999996i	$0.499141\pi$
$398$	9.90824			0.496655
$399$		0			0
$400$	0.644386	−	1.11611i	0.0322193	−	0.0558055i
$401$	−6.40638	−	3.69873i	−0.319920	−	0.184706i	0.331437	−	0.943477i	$-0.392467\pi$
$401$	−6.40638	−	3.69873i	−0.319920	−	0.184706i	−0.651357	+	0.758772i	$0.725800\pi$
$402$		0			0
$403$	−28.1830	−	16.0660i	−1.40390	−	0.800306i
$404$	16.7940			0.835533
$405$		0			0
$406$	−4.94418	+	7.30597i	−0.245375	+	0.362589i
$407$	−2.89701	+	1.67259i	−0.143599	+	0.0829071i
$408$		0			0
$409$	−11.2313	+	6.48438i	−0.555351	+	0.320632i	−0.751277	−	0.659987i	$-0.770562\pi$
$409$	−11.2313	+	6.48438i	−0.555351	+	0.320632i	0.195926	+	0.980619i	$0.437229\pi$
$410$	−6.27473	+	3.62272i	−0.309887	+	0.178913i
$411$		0			0
$412$	−6.72223	+	3.88108i	−0.331180	+	0.191207i
$413$	−14.6111	+	21.5907i	−0.718966	+	1.06241i
$414$		0			0
$415$	−19.3016			−0.947478
$416$	0.114770	+	20.9255i	0.00562706	+	1.02596i
$417$		0			0
$418$	3.14473	+	1.81561i	0.153814	+	0.0888044i
$419$	7.25814	−	12.5715i	0.354583	−	0.614157i	−0.632463	−	0.774590i	$-0.717956\pi$
$419$	7.25814	−	12.5715i	0.354583	−	0.614157i	0.987047	+	0.160434i	$0.0512893\pi$
$420$		0			0
$421$	10.4905			0.511273			0.255637	−	0.966773i	$-0.417715\pi$
$421$	10.4905			0.511273			0.255637	+	0.966773i	$0.417715\pi$
$422$	9.48905	−	5.47851i	0.461920	−	0.266690i
$423$		0			0
$424$	4.24235			0.206027
$425$	−2.14924	−	3.72259i	−0.104253	−	0.180572i
$426$		0			0
$427$	5.37874	+	3.63996i	0.260296	+	0.176150i
$428$			6.68756i			0.323255i
$429$		0			0
$430$			8.26207i			0.398432i
$431$	−12.6463	−	7.30133i	−0.609150	−	0.351693i	0.163483	−	0.986546i	$-0.447727\pi$
$431$	−12.6463	−	7.30133i	−0.609150	−	0.351693i	−0.772633	+	0.634854i	$0.781060\pi$
$432$		0			0
$433$	−12.9706	+	7.48858i	−0.623327	+	0.359878i	−0.778163	−	0.628062i	$-0.783848\pi$
$433$	−12.9706	+	7.48858i	−0.623327	+	0.359878i	0.154836	+	0.987940i	$0.450515\pi$
$434$	16.3217	+	1.16635i	0.783466	+	0.0559867i
$435$		0			0
$436$	3.63004	+	6.28742i	0.173847	+	0.301113i
$437$	−3.76814			−0.180255
$438$		0			0
$439$	33.8460	+	19.5410i	1.61538	+	0.932641i	0.988094	+	0.153854i	$0.0491686\pi$
$439$	33.8460	+	19.5410i	1.61538	+	0.932641i	0.627288	+	0.778787i	$0.284165\pi$
$440$	−2.54592	+	4.40966i	−0.121372	+	0.210222i
$441$		0			0
$442$	9.96948	+	5.68320i	0.474200	+	0.270322i
$443$		−	10.9390i		−	0.519727i	−0.965645	−	0.259863i	$-0.916322\pi$
$443$		−	10.9390i		−	0.519727i	0.965645	−	0.259863i	$-0.0836776\pi$
$444$		0			0
$445$	−12.7695	+	22.1175i	−0.605334	+	1.04847i
$446$	−3.96645	−	6.87010i	−0.187817	−	0.325309i
$447$		0			0
$448$	−1.40246	−	2.88663i	−0.0662599	−	0.136381i
$449$	2.34609	−	1.35452i	0.110719	−	0.0639237i	−0.443618	−	0.896216i	$-0.646305\pi$
$449$	2.34609	−	1.35452i	0.110719	−	0.0639237i	0.554337	+	0.832292i	$0.312972\pi$
$450$		0			0
$451$	4.70790	−	2.71811i	0.221686	−	0.127991i
$452$	−9.67255	−	5.58445i	−0.454959	−	0.262670i
$453$		0			0
$454$		−	2.40415i		−	0.112833i
$455$	−19.2072	−	1.26671i	−0.900446	−	0.0593841i
$456$		0			0
$457$	4.93084	−	8.54047i	0.230655	−	0.399506i	−0.727346	−	0.686271i	$-0.759246\pi$
$457$	4.93084	−	8.54047i	0.230655	−	0.399506i	0.958001	+	0.286765i	$0.0925798\pi$
$458$	−9.47776	+	16.4160i	−0.442867	+	0.767067i
$459$		0			0
$460$		−	2.28804i		−	0.106680i
$461$	6.90652	+	11.9624i	0.321669	+	0.557146i	0.980832	−	0.194853i	$-0.0624230\pi$
$461$	6.90652	+	11.9624i	0.321669	+	0.557146i	−0.659164	+	0.751999i	$0.729090\pi$
$462$		0			0
$463$	42.1690			1.95976			0.979880	−	0.199587i	$-0.0639600\pi$
$463$	42.1690			1.95976			0.979880	+	0.199587i	$0.0639600\pi$
$464$	5.83166	−	3.36691i	0.270728	−	0.156305i
$465$		0			0
$466$	9.88575	−	17.1226i	0.457948	−	0.793190i
$467$	17.2719			0.799247			0.399623	−	0.916679i	$-0.369141\pi$
$467$	17.2719			0.799247			0.399623	+	0.916679i	$0.369141\pi$
$468$		0			0
$469$	28.7189	+	2.05226i	1.32612	+	0.0947646i
$470$	−13.9738	−	8.06775i	−0.644561	−	0.372138i
$471$		0			0
$472$	−20.6915	+	11.9462i	−0.952403	+	0.549870i
$473$		−	6.19899i		−	0.285030i
$474$		0			0
$475$	4.08107	−	2.35621i	0.187252	−	0.108110i
$476$	18.6648	+	1.33379i	0.855500	+	0.0611342i
$477$		0			0
$478$	8.34339	−	14.4512i	0.381618	−	0.660981i
$479$	15.6745	−	27.1490i	0.716184	−	1.24047i	−0.246317	−	0.969189i	$-0.579220\pi$
$479$	15.6745	−	27.1490i	0.716184	−	1.24047i	0.962501	−	0.271278i	$-0.0874464\pi$
$480$		0			0
$481$	−5.84979	−	10.0050i	−0.266727	−	0.456189i
$482$	6.38347			0.290759
$483$		0			0
$484$	−7.57406	+	13.1187i	−0.344276	+	0.596303i
$485$	21.8225	−	12.5993i	0.990911	−	0.572103i
$486$		0			0
$487$	1.02001	+	1.76671i	0.0462211	+	0.0800573i	0.888210	−	0.459437i	$-0.151949\pi$
$487$	1.02001	+	1.76671i	0.0462211	+	0.0800573i	−0.841989	+	0.539494i	$0.818615\pi$
$488$	2.97608	+	5.15472i	0.134721	+	0.233343i
$489$		0			0
$490$	9.01333	−	3.60966i	0.407181	−	0.163068i
$491$	23.8672	+	13.7797i	1.07711	+	0.621870i	0.930115	−	0.367267i	$-0.119707\pi$
$491$	23.8672	+	13.7797i	1.07711	+	0.621870i	0.146995	+	0.989137i	$0.453040\pi$
$492$		0			0
$493$		−	22.4595i		−	1.01152i
$494$	−6.23049	+	10.9295i	−0.280323	+	0.491743i
$495$		0			0
$496$	−10.8171	−	6.24527i	−0.485703	−	0.280421i
$497$	25.1097	+	16.9925i	1.12633	+	0.762219i
$498$		0			0
$499$	9.41290			0.421379			0.210690	−	0.977553i	$-0.432429\pi$
$499$	9.41290			0.421379			0.210690	+	0.977553i	$0.432429\pi$
$500$	9.13627	+	15.8245i	0.408587	+	0.707693i
$501$		0			0
$502$			6.31943i			0.282050i
$503$	−17.0006	−	29.4459i	−0.758019	−	1.31293i	−0.943859	−	0.330347i	$-0.892834\pi$
$503$	−17.0006	−	29.4459i	−0.758019	−	1.31293i	0.185841	−	0.982580i	$-0.440499\pi$
$504$		0			0
$505$	−11.0925	+	19.2128i	−0.493610	+	0.854958i
$506$		−	0.531032i		−	0.0236073i
$507$		0			0
$508$	2.97508			0.131998
$509$	−9.38783	+	16.2602i	−0.416108	+	0.720721i	−0.995544	−	0.0942972i	$-0.969940\pi$
$509$	−9.38783	+	16.2602i	−0.416108	+	0.720721i	0.579436	+	0.815018i	$0.303273\pi$
$510$		0			0
$511$	−12.5543	+	6.09942i	−0.555368	+	0.269823i
$512$			14.7893i			0.653600i
$513$		0			0
$514$	5.06787	−	2.92594i	0.223534	−	0.129057i
$515$		−	10.2539i		−	0.451839i
$516$		0			0
$517$	10.4844	+	6.05319i	0.461105	+	0.266219i
$518$	4.84147	+	3.27637i	0.212722	+	0.143956i
$519$		0			0
$520$	−15.3258	−	8.73664i	−0.672081	−	0.383127i
$521$	32.7295			1.43391			0.716953	−	0.697122i	$-0.245536\pi$
$521$	32.7295			1.43391			0.716953	+	0.697122i	$0.245536\pi$
$522$		0			0
$523$	−18.4143	−	10.6315i	−0.805203	−	0.464884i	0.0400843	−	0.999196i	$-0.487237\pi$
$523$	−18.4143	−	10.6315i	−0.805203	−	0.464884i	−0.845287	+	0.534312i	$0.820571\pi$
$524$	−1.02061	−	1.76774i	−0.0445854	−	0.0772241i
$525$		0			0
$526$	−3.19706	−	5.53748i	−0.139399	−	0.241445i
$527$	−36.0786	+	20.8300i	−1.57161	+	0.907369i
$528$		0			0
$529$	−11.2245	−	19.4414i	−0.488021	−	0.845276i
$530$	−1.21338	+	2.10163i	−0.0527056	+	0.0912889i
$531$		0			0
$532$	−1.46223	+	20.4622i	−0.0633959	+	0.887149i
$533$	9.50643	+	16.2590i	0.411769	+	0.704257i
$534$		0			0
$535$	−7.65074	−	4.41716i	−0.330770	−	0.190970i
$536$	22.8521	+	13.1936i	0.987059	+	0.569879i
$537$		0			0
$538$		−	13.2691i		−	0.572071i
$539$	−6.76265	+	2.70831i	−0.291288	+	0.116655i
$540$		0			0
$541$	3.03261			0.130382			0.0651910	−	0.997873i	$-0.479234\pi$
$541$	3.03261			0.130382			0.0651910	+	0.997873i	$0.479234\pi$
$542$	3.06313	+	5.30550i	0.131573	+	0.227891i
$543$		0			0
$544$	23.2725	+	13.4364i	0.997799	+	0.576079i
$545$	−9.59062			−0.410817
$546$		0			0
$547$	−20.7524			−0.887308			−0.443654	−	0.896198i	$-0.646318\pi$
$547$	−20.7524			−0.887308			−0.443654	+	0.896198i	$0.646318\pi$
$548$	−12.7506	−	7.36155i	−0.544678	−	0.314470i
$549$		0			0
$550$	0.332053	+	0.575132i	0.0141588	+	0.0245237i
$551$	24.6223			1.04895
$552$		0			0
$553$	10.5494	+	21.7135i	0.448606	+	0.923352i
$554$		−	19.6399i		−	0.834421i
$555$		0			0
$556$	−20.9725	−	12.1085i	−0.889430	−	0.513513i
$557$	20.3725	+	11.7621i	0.863211	+	0.498375i	0.865086	−	0.501623i	$-0.167264\pi$
$557$	20.3725	+	11.7621i	0.863211	+	0.498375i	−0.00187523	+	0.999998i	$0.500597\pi$
$558$		0			0
$559$	21.4766	−	0.117792i	0.908364	−	0.00498209i
$560$	−7.39248	−	0.528268i	−0.312389	−	0.0223234i
$561$		0			0
$562$	−10.7105	+	18.5511i	−0.451795	+	0.782532i
$563$	−14.1250	−	24.4653i	−0.595299	−	1.03109i	−0.993505	−	0.113792i	$-0.963700\pi$
$563$	−14.1250	−	24.4653i	−0.595299	−	1.03109i	0.398205	−	0.917296i	$-0.369633\pi$
$564$		0			0
$565$	12.7775	−	7.37710i	0.537554	−	0.310357i
$566$	5.15306	+	8.92537i	0.216599	+	0.375161i
$567$		0			0
$568$	13.8933	+	24.0639i	0.582951	+	1.00970i
$569$	−40.7411	−	23.5219i	−1.70796	−	0.986088i	−0.937088	−	0.349092i	$-0.886490\pi$
$569$	−40.7411	−	23.5219i	−1.70796	−	0.986088i	−0.770867	−	0.636996i	$-0.780177\pi$
$570$		0			0
$571$	6.38183			0.267071			0.133536	−	0.991044i	$-0.457367\pi$
$571$	6.38183			0.267071			0.133536	+	0.991044i	$0.457367\pi$
$572$	4.97931	+	2.83851i	0.208195	+	0.118684i
$573$		0			0
$574$	−7.86783	−	5.32440i	−0.328397	−	0.222236i
$575$	−0.596819	−	0.344573i	−0.0248891	−	0.0143697i
$576$		0			0
$577$			5.68163i			0.236529i	0.992982	+	0.118265i	$0.0377331\pi$
$577$			5.68163i			0.236529i	−0.992982	+	0.118265i	$0.962267\pi$
$578$	2.64241	−	1.52560i	0.109910	−	0.0634565i
$579$		0			0
$580$			14.9508i			0.620798i
$581$	−11.0596	−	22.7636i	−0.458828	−	0.944392i
$582$		0			0
$583$	0.910389	−	1.57684i	0.0377045	−	0.0653061i
$584$	−12.7917			−0.529325
$585$		0			0
$586$			9.07978i			0.375082i
$587$	0.374540	−	0.648722i	0.0154589	−	0.0267756i	−0.858192	−	0.513328i	$-0.828412\pi$
$587$	0.374540	−	0.648722i	0.0154589	−	0.0267756i	0.873651	+	0.486552i	$0.161746\pi$
$588$		0			0
$589$	−22.8359	−	39.5530i	−0.940938	−	1.62975i
$590$		−	13.6672i		−	0.562670i
$591$		0			0
$592$	−2.23116	−	3.86448i	−0.0917002	−	0.158829i
$593$	−24.1618			−0.992207			−0.496103	−	0.868263i	$-0.665236\pi$
$593$	−24.1618			−0.992207			−0.496103	+	0.868263i	$0.665236\pi$
$594$		0			0
$595$	−13.8541	+	20.4720i	−0.567961	+	0.839271i
$596$	−23.4686	−	13.5496i	−0.961311	−	0.555013i
$597$		0			0
$598$	1.83978	−	0.0100906i	0.0752342	−	0.000412636i
$599$		−	35.2608i		−	1.44072i	−0.693603	−	0.720358i	$-0.743978\pi$
$599$		−	35.2608i		−	1.44072i	0.693603	−	0.720358i	$-0.256022\pi$
$600$		0			0
$601$	−5.50213	−	3.17666i	−0.224436	−	0.129578i	0.383566	−	0.923513i	$-0.374696\pi$
$601$	−5.50213	−	3.17666i	−0.224436	−	0.129578i	−0.608003	+	0.793935i	$0.708029\pi$
$602$	−9.74396	+	4.73406i	−0.397134	+	0.192946i
$603$		0			0
$604$	7.25278	+	12.5622i	0.295112	+	0.511148i
$605$	−10.0054	−	17.3298i	−0.406777	−	0.704558i
$606$		0			0
$607$	−20.9623	+	12.1026i	−0.850834	+	0.491229i	−0.860932	−	0.508720i	$-0.830119\pi$
$607$	−20.9623	+	12.1026i	−0.850834	+	0.491229i	0.0100980	+	0.999949i	$0.496786\pi$
$608$	−14.7303	+	25.5136i	−0.597392	+	1.03471i
$609$		0			0
$610$	−3.40481			−0.137857
$611$	−20.7723	+	36.4387i	−0.840357	+	1.47415i
$612$		0			0
$613$	18.6617	−	32.3230i	0.753739	−	1.30551i	−0.192260	−	0.981344i	$-0.561582\pi$
$613$	18.6617	−	32.3230i	0.753739	−	1.30551i	0.945999	−	0.324170i	$-0.105085\pi$
$614$	6.09157	−	10.5509i	0.245836	−	0.425800i
$615$		0			0
$616$	−6.65936	−	0.475880i	−0.268313	−	0.0191737i
$617$	35.7790	−	20.6570i	1.44041	−	0.831621i	0.442534	−	0.896752i	$-0.354080\pi$
$617$	35.7790	−	20.6570i	1.44041	−	0.831621i	0.997877	+	0.0651307i	$0.0207464\pi$
$618$		0			0
$619$			29.1307i			1.17086i	0.810722	+	0.585432i	$0.199075\pi$
$619$			29.1307i			1.17086i	−0.810722	+	0.585432i	$0.800925\pi$
$620$	24.0168	−	13.8661i	0.964536	−	0.556875i
$621$		0			0
$622$	−15.3191	−	8.84451i	−0.614241	−	0.354632i
$623$	−33.4013	−	2.38686i	−1.33819	−	0.0956276i
$624$		0			0
$625$	−19.4964			−0.779855
$626$	−2.99908	+	5.19456i	−0.119867	+	0.207616i
$627$		0			0
$628$	−1.77007	+	1.02195i	−0.0706334	+	0.0407802i
$629$	−14.8833			−0.593436
$630$		0			0
$631$	−17.1916	−	29.7767i	−0.684387	−	1.18539i	−0.973629	−	0.228137i	$-0.926737\pi$
$631$	−17.1916	−	29.7767i	−0.684387	−	1.18539i	0.289242	−	0.957256i	$-0.406597\pi$
$632$			22.1242i			0.880054i
$633$		0			0
$634$	3.44937	−	5.97449i	0.136992	−	0.237277i
$635$	−1.96505	+	3.40357i	−0.0779807	+	0.135067i
$636$		0			0
$637$	−9.51155	−	23.3780i	−0.376861	−	0.926270i
$638$			3.46995i			0.137376i
$639$		0			0
$640$	−18.8271	−	10.8698i	−0.744206	−	0.429668i
$641$	−4.91634	+	2.83845i	−0.194184	+	0.112112i	−0.593940	−	0.804510i	$-0.702428\pi$
$641$	−4.91634	+	2.83845i	−0.194184	+	0.112112i	0.399756	+	0.916622i	$0.369095\pi$
$642$		0			0
$643$	0.0260013	−	0.0150119i	0.00102539	−	0.000592011i	−0.499487	−	0.866321i	$-0.666478\pi$
$643$	0.0260013	−	0.0150119i	0.00102539	−	0.000592011i	0.500513	+	0.865729i	$0.333145\pi$
$644$	2.69842	−	1.31101i	0.106333	−	0.0516612i
$645$		0			0
$646$	8.07798	+	13.9915i	0.317824	+	0.550487i
$647$	17.7587	−	30.7590i	0.698168	−	1.20926i	−0.270933	−	0.962598i	$-0.587332\pi$
$647$	17.7587	−	30.7590i	0.698168	−	1.20926i	0.969101	−	0.246665i	$-0.0793346\pi$
$648$		0			0
$649$			10.2544i			0.402522i
$650$	−1.98626	+	1.16134i	−0.0779074	+	0.0455514i
$651$		0			0
$652$	4.81600	−	8.34156i	0.188609	−	0.326681i
$653$	19.8917	+	11.4845i	0.778422	+	0.449422i	0.835871	−	0.548926i	$-0.184963\pi$
$653$	19.8917	+	11.4845i	0.778422	+	0.449422i	−0.0574486	+	0.998348i	$0.518297\pi$
$654$		0			0
$655$	2.69645			0.105359
$656$	3.62584	+	6.28014i	0.141565	+	0.245198i
$657$		0			0
$658$	1.50801	−	21.1028i	0.0587885	−	0.822674i
$659$	−12.6080	+	7.27924i	−0.491138	+	0.283559i	−0.725047	−	0.688700i	$-0.758182\pi$
$659$	−12.6080	+	7.27924i	−0.491138	+	0.283559i	0.233908	+	0.972259i	$0.424848\pi$
$660$		0			0
$661$	−36.8130	−	21.2540i	−1.43186	−	0.826684i	−0.434596	−	0.900626i	$-0.643109\pi$
$661$	−36.8130	−	21.2540i	−1.43186	−	0.826684i	−0.997263	+	0.0739415i	$0.976442\pi$
$662$		−	12.5795i		−	0.488914i
$663$		0			0
$664$		−	23.1941i		−	0.900107i
$665$	−22.4435	−	15.1882i	−0.870321	−	0.588973i
$666$		0			0
$667$	−1.80039	−	3.11837i	−0.0697115	−	0.120744i
$668$	−32.5554			−1.25961
$669$		0			0
$670$	−13.0721	+	7.54715i	−0.505018	+	0.291572i
$671$	2.55461			0.0986198
$672$		0			0
$673$	0.604768	−	1.04749i	0.0233121	−	0.0403777i	−0.854134	−	0.520053i	$-0.825912\pi$
$673$	0.604768	−	1.04749i	0.0233121	−	0.0403777i	0.877446	+	0.479675i	$0.159246\pi$
$674$	11.2675	+	6.50531i	0.434009	+	0.250575i
$675$		0			0
$676$	−9.73949	+	17.3049i	−0.374596	+	0.665574i
$677$	−40.2664			−1.54756			−0.773781	−	0.633453i	$-0.781637\pi$
$677$	−40.2664			−1.54756			−0.773781	+	0.633453i	$0.781637\pi$
$678$		0			0
$679$	27.3631	+	18.5175i	1.05010	+	0.710635i
$680$	−19.6194	+	11.3273i	−0.752369	+	0.434381i
$681$		0			0
$682$	5.57407	−	3.21819i	0.213442	−	0.123231i
$683$	15.8005	−	9.12245i	0.604591	−	0.349061i	−0.166254	−	0.986083i	$-0.553167\pi$
$683$	15.8005	−	9.12245i	0.604591	−	0.349061i	0.770846	+	0.637022i	$0.219834\pi$
$684$		0			0
$685$	16.8436	−	9.72465i	0.643561	−	0.371560i
$686$	9.42161	+	8.56167i	0.359719	+	0.326886i
$687$		0			0
$688$	8.26919			0.315260
$689$	5.48032	+	3.12411i	0.208784	+	0.119019i
$690$		0			0
$691$	34.7342	+	20.0538i	1.32135	+	0.762882i	0.983944	−	0.178478i	$-0.0571173\pi$
$691$	34.7342	+	20.0538i	1.32135	+	0.762882i	0.337406	+	0.941359i	$0.390451\pi$
$692$	−9.28665	+	16.0849i	−0.353025	+	0.611458i
$693$		0			0
$694$	−15.2964			−0.580643
$695$	27.7048	−	15.9953i	1.05090	−	0.606738i
$696$		0			0
$697$	24.1867			0.916137
$698$	0.630992	+	1.09291i	0.0238834	+	0.0413673i
$699$		0			0
$700$	−2.10274	+	3.10720i	−0.0794760	+	0.117441i
$701$			20.7572i			0.783990i	0.919967	+	0.391995i	$0.128215\pi$
$701$			20.7572i			0.783990i	−0.919967	+	0.391995i	$0.871785\pi$
$702$		0			0
$703$		−	16.3165i		−	0.615390i
$704$	−1.09323	−	0.631175i	−0.0412026	−	0.0237883i
$705$		0			0
$706$	1.49041	−	0.860486i	0.0560922	−	0.0323848i
$707$	−29.0147	−	2.07340i	−1.09121	−	0.0779781i
$708$		0			0
$709$	1.55542	+	2.69407i	0.0584152	+	0.101178i	0.893754	−	0.448557i	$-0.148062\pi$
$709$	1.55542	+	2.69407i	0.0584152	+	0.101178i	−0.835339	+	0.549735i	$0.814729\pi$
$710$	−15.8948			−0.596520
$711$		0			0
$712$	−26.5779	−	15.3447i	−0.996048	−	0.575068i
$713$	−3.33954	+	5.78425i	−0.125067	+	0.216622i
$714$		0			0
$715$	−6.53617	+	3.82161i	−0.244439	+	0.142920i
$716$		−	3.42164i		−	0.127873i
$717$		0			0
$718$	−6.86223	+	11.8857i	−0.256096	+	0.443572i
$719$	9.99233	+	17.3072i	0.372651	+	0.645451i	0.989972	−	0.141261i	$-0.0451155\pi$
$719$	9.99233	+	17.3072i	0.372651	+	0.645451i	−0.617321	+	0.786711i	$0.711782\pi$
$720$		0			0
$721$	12.0930	−	5.87533i	0.450367	−	0.218809i
$722$	−4.02821	+	2.32569i	−0.149914	+	0.0865531i
$723$		0			0
$724$	4.35252	−	2.51293i	0.161760	−	0.0933922i
$725$	3.89982	+	2.25156i	0.144836	+	0.0836208i
$726$		0			0
$727$		−	28.8880i		−	1.07140i	−0.844409	−	0.535699i	$-0.820048\pi$
$727$		−	28.8880i		−	1.07140i	0.844409	−	0.535699i	$-0.179952\pi$
$728$	1.52216	−	23.0806i	0.0564151	−	0.855425i
$729$		0			0
$730$	3.65862	−	6.33691i	0.135412	−	0.234540i
$731$	13.7902	−	23.8854i	0.510049	−	0.883432i
$732$		0			0
$733$		−	30.9871i		−	1.14454i	−0.820067	−	0.572268i	$-0.806064\pi$
$733$		−	30.9871i		−	1.14454i	0.820067	−	0.572268i	$-0.193936\pi$
$734$	−12.8463	−	22.2504i	−0.474165	−	0.821278i
$735$		0			0
$736$	4.30833			0.158807
$737$	9.80790	−	5.66259i	0.361279	−	0.208584i
$738$		0			0
$739$	−16.6372	+	28.8164i	−0.612008	+	1.06003i	0.378893	+	0.925440i	$0.376305\pi$
$739$	−16.6372	+	28.8164i	−0.612008	+	1.06003i	−0.990902	+	0.134589i	$0.957029\pi$
$740$	9.90749			0.364206
$741$		0			0
$742$	−3.17383	−	0.226802i	−0.116515	−	0.00832618i
$743$	−8.38644	−	4.84191i	−0.307668	−	0.177632i	0.338214	−	0.941069i	$-0.390177\pi$
$743$	−8.38644	−	4.84191i	−0.307668	−	0.177632i	−0.645883	+	0.763437i	$0.723510\pi$
$744$		0			0
$745$	31.0022	−	17.8991i	1.13583	−	0.655772i
$746$		−	3.78248i		−	0.138487i
$747$		0			0
$748$	6.37428	−	3.68019i	0.233067	−	0.134561i
$749$	0.825649	−	11.5540i	0.0301685	−	0.422172i
$750$		0			0
$751$	−10.0582	+	17.4212i	−0.367027	+	0.635710i	−0.989099	−	0.147250i	$-0.952958\pi$
$751$	−10.0582	+	17.4212i	−0.367027	+	0.635710i	0.622072	+	0.782960i	$0.286291\pi$
$752$	−8.07471	+	13.9858i	−0.294454	+	0.510010i
$753$		0			0
$754$	−12.0218	+	0.0659355i	−0.437806	+	0.00240123i
$755$	−19.1620			−0.697375
$756$		0			0
$757$	4.86466	−	8.42583i	0.176809	−	0.306242i	−0.763977	−	0.645244i	$-0.776756\pi$
$757$	4.86466	−	8.42583i	0.176809	−	0.306242i	0.940786	+	0.339002i	$0.110089\pi$
$758$	−6.62909	+	3.82731i	−0.240779	+	0.139014i
$759$		0			0
$760$	−12.4181	−	21.5087i	−0.450451	−	0.780203i
$761$	5.59635	+	9.69316i	0.202868	+	0.351377i	0.949451	−	0.313915i	$-0.101641\pi$
$761$	5.59635	+	9.69316i	0.202868	+	0.351377i	−0.746584	+	0.665292i	$0.768307\pi$
$762$		0			0
$763$	−5.49530	−	11.3108i	−0.198943	−	0.409479i
$764$	−17.0791	−	9.86060i	−0.617899	−	0.356744i
$765$		0			0
$766$			1.15697i			0.0418032i
$767$	−35.5269	+	0.194854i	−1.28280	+	0.00703576i
$768$		0			0
$769$	−3.49016	−	2.01504i	−0.125858	−	0.0726644i	0.435749	−	0.900068i	$-0.356484\pi$
$769$	−3.49016	−	2.01504i	−0.125858	−	0.0726644i	−0.561607	+	0.827404i	$0.689817\pi$
$770$	2.14042	−	3.16289i	0.0771355	−	0.113983i
$771$		0			0
$772$	11.4761			0.413036
$773$	−26.8907	−	46.5760i	−0.967190	−	1.67522i	−0.703611	−	0.710585i	$-0.748430\pi$
$773$	−26.8907	−	46.5760i	−0.967190	−	1.67522i	−0.263579	−	0.964638i	$-0.584903\pi$
$774$		0			0
$775$		−	8.35282i		−	0.300042i
$776$	15.1401	+	26.2235i	0.543499	+	0.941367i
$777$		0			0
$778$	11.7138	−	20.2889i	0.419959	−	0.727391i
$779$			26.5159i			0.950029i
$780$		0			0
$781$	11.9258			0.426738
$782$	1.18133	−	2.04612i	0.0422443	−	0.0731692i
$783$		0			0
$784$	−3.61278	−	9.02109i	−0.129028	−	0.322182i
$785$		−	2.70001i		−	0.0963673i
$786$		0			0
$787$	21.9883	−	12.6950i	0.783798	−	0.452526i	−0.0539763	−	0.998542i	$-0.517190\pi$
$787$	21.9883	−	12.6950i	0.783798	−	0.452526i	0.837775	+	0.546016i	$0.183856\pi$
$788$			37.4402i			1.33375i
$789$		0			0
$790$	−10.9602	−	6.32785i	−0.389945	−	0.225135i
$791$	16.0216	+	10.8423i	0.569663	+	0.385508i
$792$		0			0
$793$	0.0485425	+	8.85055i	0.00172379	+	0.314292i
$794$	13.6321			0.483784
$795$		0			0
$796$	19.0679	+	11.0089i	0.675845	+	0.390200i
$797$	3.88407	+	6.72740i	0.137581	+	0.238297i	0.926580	−	0.376097i	$-0.122734\pi$
$797$	3.88407	+	6.72740i	0.137581	+	0.238297i	−0.789000	+	0.614394i	$0.789401\pi$
$798$		0			0
$799$	26.9318	+	46.6472i	0.952778	+	1.65026i
$800$	−4.66612	+	2.69399i	−0.164972	+	0.0952468i
$801$		0			0
$802$	2.54247	+	4.40368i	0.0897777	+	0.155499i
$803$	−2.74504	+	4.75455i	−0.0968705	+	0.167785i
$804$		0			0
$805$	−0.282482	+	3.95299i	−0.00995617	+	0.139325i
$806$	11.2555	+	19.2504i	0.396457	+	0.678067i
$807$		0			0
$808$	−23.0874	−	13.3295i	−0.812211	−	0.468930i
$809$	13.1244	+	7.57737i	0.461429	+	0.266406i	0.712645	−	0.701525i	$-0.247497\pi$
$809$	13.1244	+	7.57737i	0.461429	+	0.266406i	−0.251216	+	0.967931i	$0.580830\pi$
$810$		0			0
$811$			25.4887i			0.895028i	0.894277	+	0.447514i	$0.147691\pi$
$811$			25.4887i			0.895028i	−0.894277	+	0.447514i	$0.852309\pi$
$812$	−17.6324	+	8.56661i	−0.618776	+	0.300629i
$813$		0			0
$814$	2.29944			0.0805953
$815$	6.36197	+	11.0193i	0.222850	+	0.385988i
$816$		0			0
$817$	26.1855	+	15.1182i	0.916115	+	0.528919i
$818$	8.91459			0.311691
$819$		0			0
$820$	−16.1006			−0.562256
$821$	−2.83527	−	1.63694i	−0.0989514	−	0.0571296i	0.449708	−	0.893176i	$-0.351528\pi$
$821$	−2.83527	−	1.63694i	−0.0989514	−	0.0571296i	−0.548659	+	0.836046i	$0.684862\pi$
$822$		0			0
$823$	−1.89093	−	3.27519i	−0.0659138	−	0.114166i	0.831185	−	0.555996i	$-0.187663\pi$
$823$	−1.89093	−	3.27519i	−0.0659138	−	0.114166i	−0.897099	+	0.441830i	$0.854330\pi$
$824$	12.3217			0.429248
$825$		0			0
$826$	16.1186	−	7.83113i	0.560837	−	0.272480i
$827$		−	28.5766i		−	0.993706i	−0.867835	−	0.496853i	$-0.834489\pi$
$827$		−	28.5766i		−	0.993706i	0.867835	−	0.496853i	$-0.165511\pi$
$828$		0			0
$829$	31.1205	+	17.9674i	1.08086	+	0.624034i	0.931128	−	0.364693i	$-0.118826\pi$
$829$	31.1205	+	17.9674i	1.08086	+	0.624034i	0.149731	+	0.988727i	$0.452159\pi$
$830$	11.4902	+	6.63386i	0.398830	+	0.230265i
$831$		0			0
$832$	2.16596	−	3.79952i	0.0750910	−	0.131725i
$833$	−32.0821	−	4.60873i	−1.11158	−	0.159683i
$834$		0			0
$835$	21.5030	−	37.2442i	0.744141	−	1.28889i
$836$	4.03459	+	6.98812i	0.139539	+	0.241689i
$837$		0			0
$838$	−8.64150	+	4.98917i	−0.298516	+	0.172348i
$839$	−7.58661	−	13.1404i	−0.261919	−	0.453657i	0.704833	−	0.709373i	$-0.251022\pi$
$839$	−7.58661	−	13.1404i	−0.261919	−	0.453657i	−0.966752	+	0.255717i	$0.917689\pi$
$840$		0			0
$841$	−2.73562	−	4.73823i	−0.0943316	−	0.163387i
$842$	−6.24494	−	3.60552i	−0.215215	−	0.124254i
$843$		0			0
$844$	24.3483			0.838104
$845$	−13.3643	−	22.5722i	−0.459746	−	0.776507i
$846$		0			0
$847$	14.7052	−	21.7297i	0.505276	−	0.746643i
$848$	2.10344	+	1.21442i	0.0722324	+	0.0417034i
$849$		0			0
$850$			2.95473i			0.101346i
$851$	−2.06646	+	1.19307i	−0.0708374	+	0.0408980i
$852$		0			0
$853$		−	46.5366i		−	1.59338i	−0.604386	−	0.796691i	$-0.706582\pi$
$853$		−	46.5366i		−	1.59338i	0.604386	−	0.796691i	$-0.293418\pi$
$854$	−1.95091	−	4.01550i	−0.0667589	−	0.137408i
$855$		0			0
$856$	5.30796	−	9.19365i	0.181422	−	0.314232i
$857$	4.62088			0.157846			0.0789232	−	0.996881i	$-0.474852\pi$
$857$	4.62088			0.157846			0.0789232	+	0.996881i	$0.474852\pi$
$858$		0			0
$859$		−	16.9341i		−	0.577783i	−0.957362	−	0.288892i	$-0.906713\pi$
$859$		−	16.9341i		−	0.577783i	0.957362	−	0.288892i	$-0.0932868\pi$
$860$	−9.17985	+	15.9000i	−0.313030	+	0.542184i
$861$		0			0
$862$	5.01886	+	8.69292i	0.170943	+	0.296082i
$863$		−	25.0855i		−	0.853920i	−0.904270	−	0.426960i	$-0.859584\pi$
$863$		−	25.0855i		−	0.853920i	0.904270	−	0.426960i	$-0.140416\pi$
$864$		0			0
$865$	−12.2677	−	21.2483i	−0.417115	−	0.722465i
$866$	10.2951			0.349843
$867$		0			0
$868$	30.1144	+	20.3793i	1.02215	+	0.691720i
$869$	8.22335	+	4.74775i	0.278958	+	0.161057i
$870$		0			0
$871$	19.8046	+	33.8722i	0.671054	+	1.14772i
$872$		−	11.5247i		−	0.390277i
$873$		0			0
$874$	2.24316	+	1.29509i	0.0758762	+	0.0438071i
$875$	−13.8308	−	28.4676i	−0.467568	−	0.962381i
$876$		0			0
$877$	20.1018	+	34.8173i	0.678789	+	1.17570i	0.975346	+	0.220682i	$0.0708283\pi$
$877$	20.1018	+	34.8173i	0.678789	+	1.17570i	−0.296557	+	0.955015i	$0.595838\pi$
$878$	−13.4323	−	23.2654i	−0.453318	−	0.785169i
$879$		0			0
$880$	−2.52463	+	1.45760i	−0.0851053	+	0.0491356i
$881$	−1.87250	+	3.24326i	−0.0630860	+	0.109268i	−0.895843	−	0.444370i	$-0.853428\pi$
$881$	−1.87250	+	3.24326i	−0.0630860	+	0.109268i	0.832757	+	0.553638i	$0.186761\pi$
$882$		0			0
$883$	−4.08663			−0.137526			−0.0687631	−	0.997633i	$-0.521905\pi$
$883$	−4.08663			−0.137526			−0.0687631	+	0.997633i	$0.521905\pi$
$884$	12.8713	+	22.0140i	0.432908	+	0.740410i
$885$		0			0
$886$	−3.75967	+	6.51195i	−0.126309	+	0.218773i
$887$	−0.121604	+	0.210624i	−0.00408306	+	0.00707208i	−0.868060	−	0.496460i	$-0.834633\pi$
$887$	−0.121604	+	0.210624i	−0.00408306	+	0.00707208i	0.863977	+	0.503532i	$0.167966\pi$
$888$		0			0
$889$	−5.13999	−	0.367305i	−0.172390	−	0.0123190i
$890$	15.2033	−	8.77765i	0.509617	−	0.294227i
$891$		0			0
$892$		−	17.6283i		−	0.590238i
$893$	−51.1393	+	29.5253i	−1.71131	+	0.988026i
$894$		0			0
$895$	3.91445	+	2.26001i	0.130846	+	0.0755437i
$896$	2.03177	−	28.4322i	0.0678768	−	0.949853i
$897$		0			0
$898$	−1.86216			−0.0621412
$899$	21.8217	−	37.7963i	0.727794	−	1.26058i
$900$		0			0
$901$	7.01565	−	4.05049i	0.233725	−	0.134941i
$902$	−3.73680			−0.124422
$903$		0			0
$904$	8.86482	+	15.3543i	0.294840	+	0.510677i
$905$			6.63919i			0.220694i
$906$		0			0
$907$	−3.76108	+	6.51438i	−0.124885	+	0.216307i	−0.921688	−	0.387932i	$-0.873189\pi$
$907$	−3.76108	+	6.51438i	−0.124885	+	0.216307i	0.796803	+	0.604239i	$0.206523\pi$
$908$	2.67122	−	4.62668i	0.0886474	−	0.153542i
$909$		0			0
$910$	10.9986	+	7.35547i	0.364600	+	0.243831i
$911$			9.31296i			0.308552i	0.988028	+	0.154276i	$0.0493045\pi$
$911$			9.31296i			0.308552i	−0.988028	+	0.154276i	$0.950695\pi$
$912$		0			0
$913$	−8.62103	−	4.97735i	−0.285314	−	0.164726i
$914$	−5.87063	+	3.38941i	−0.194183	+	0.112112i
$915$		0			0
$916$	−36.4790	+	21.0612i	−1.20530	+	0.695881i
$917$	1.54503	+	3.18009i	0.0510215	+	0.105016i
$918$		0			0
$919$	−1.94850	−	3.37490i	−0.0642751	−	0.111328i	0.832097	−	0.554630i	$-0.187140\pi$
$919$	−1.94850	−	3.37490i	−0.0642751	−	0.111328i	−0.896372	+	0.443302i	$0.853807\pi$
$920$	−1.81603	+	3.14545i	−0.0598726	+	0.103702i
$921$		0			0
$922$		−	9.49494i		−	0.312699i
$923$	0.226612	+	41.3173i	0.00745903	+	1.35997i
$924$		0			0
$925$	1.49205	−	2.58430i	0.0490582	−	0.0849713i
$926$	−25.1031	−	14.4933i	−0.824939	−	0.476279i
$927$		0			0
$928$	−28.1521			−0.924138
$929$	11.1743	+	19.3545i	0.366617	+	0.635000i	0.989034	−	0.147686i	$-0.0471825\pi$
$929$	11.1743	+	19.3545i	0.366617	+	0.635000i	−0.622417	+	0.782686i	$0.713849\pi$
$930$		0			0
$931$	5.05254	−	35.1716i	0.165590	−	1.15270i
$932$	38.0493	−	21.9678i	1.24635	−	0.719579i
$933$		0			0
$934$	−10.2819	−	5.93625i	−0.336434	−	0.194240i
$935$			9.72312i			0.317980i
$936$		0			0
$937$			54.3887i			1.77680i	0.459070	+	0.888400i	$0.348183\pi$
$937$			54.3887i			1.77680i	−0.459070	+	0.888400i	$0.651817\pi$
$938$	−16.3909	−	11.0923i	−0.535183	−	0.362175i
$939$		0			0
$940$	−17.9279	−	31.0520i	−0.584744	−	1.01281i
$941$	−19.1215			−0.623344			−0.311672	−	0.950190i	$-0.600889\pi$
$941$	−19.1215			−0.623344			−0.311672	+	0.950190i	$0.600889\pi$
$942$		0			0
$943$	3.35819	−	1.93885i	0.109358	−	0.0631376i
$944$	−13.6790			−0.445213
$945$		0			0
$946$	−2.13056	+	3.69024i	−0.0692705	+	0.119980i
$947$	−6.66757	−	3.84952i	−0.216667	−	0.125093i	0.387739	−	0.921769i	$-0.373256\pi$
$947$	−6.66757	−	3.84952i	−0.216667	−	0.125093i	−0.604406	+	0.796677i	$0.706589\pi$
$948$		0			0
$949$	−16.5245	−	9.41996i	−0.536408	−	0.305785i
$950$	−3.23927			−0.105096
$951$		0			0
$952$	−24.6006	−	16.6480i	−0.797310	−	0.539564i
$953$	−13.4575	+	7.76968i	−0.435931	+	0.251685i	−0.701870	−	0.712305i	$-0.747651\pi$
$953$	−13.4575	+	7.76968i	−0.435931	+	0.251685i	0.265939	+	0.963990i	$0.414318\pi$
$954$		0			0
$955$	22.5616	−	13.0259i	0.730075	−	0.421509i
$956$	32.1129	−	18.5404i	1.03861	−	0.599640i
$957$		0			0
$958$	−18.6619	+	10.7745i	−0.602939	+	0.348107i
$959$	21.1200	+	14.2926i	0.682002	+	0.461532i
$960$		0			0
$961$	−49.9539			−1.61142
$962$	0.0436937	+	7.96649i	0.00140874	+	0.256850i
$963$		0			0
$964$	12.2847	+	7.09257i	0.395663	+	0.228436i
$965$	−7.58003	+	13.1290i	−0.244010	+	0.422638i
$966$		0			0
$967$	31.1198			1.00075			0.500373	−	0.865810i	$-0.333196\pi$
$967$	31.1198			1.00075			0.500373	+	0.865810i	$0.333196\pi$
$968$	20.8247	−	12.0232i	0.669332	−	0.386439i
$969$		0			0
$970$	−17.3212			−0.556150
$971$	1.30394	+	2.25849i	0.0418454	+	0.0724784i	0.886190	−	0.463323i	$-0.153343\pi$
$971$	1.30394	+	2.25849i	0.0418454	+	0.0724784i	−0.844344	+	0.535801i	$0.820010\pi$
$972$		0			0
$973$	34.7388	+	23.5088i	1.11367	+	0.753657i
$974$		−	1.40229i		−	0.0449322i
$975$		0			0
$976$			3.40775i			0.109079i
$977$	−24.2102	−	13.9778i	−0.774553	−	0.447188i	0.0599433	−	0.998202i	$-0.480908\pi$
$977$	−24.2102	−	13.9778i	−0.774553	−	0.447188i	−0.834496	+	0.551013i	$0.814241\pi$
$978$		0			0
$979$	−11.4070	+	6.58582i	−0.364569	+	0.210484i
$980$	21.3564	+	3.06793i	0.682204	+	0.0980014i
$981$		0			0
$982$	−9.47204	−	16.4060i	−0.302265	−	0.523538i
$983$	−17.0643			−0.544265			−0.272133	−	0.962260i	$-0.587729\pi$
$983$	−17.0643			−0.544265			−0.272133	+	0.962260i	$0.587729\pi$
$984$		0			0
$985$	−42.8325	−	24.7294i	−1.36476	−	0.787944i
$986$	−7.71921	+	13.3701i	−0.245830	+	0.425790i
$987$		0			0
$988$	−24.1339	+	14.1108i	−0.767802	+	0.448924i
$989$		−	4.42179i		−	0.140605i
$990$		0			0
$991$	−14.0306	+	24.3017i	−0.445696	+	0.771968i	−0.998100	−	0.0616082i	$-0.980377\pi$
$991$	−14.0306	+	24.3017i	−0.445696	+	0.771968i	0.552404	+	0.833576i	$0.313710\pi$
$992$	26.1096	+	45.2232i	0.828981	+	1.43584i
$993$		0			0
$994$	−9.10750	−	18.7457i	−0.288872	−	0.594577i
$995$	−25.1889	+	14.5428i	−0.798541	+	0.461038i
$996$		0			0
$997$	50.2867	−	29.0330i	1.59260	−	0.919485i	0.599735	−	0.800198i	$-0.295272\pi$
$997$	50.2867	−	29.0330i	1.59260	−	0.919485i	0.992860	−	0.119287i	$-0.0380608\pi$
$998$	−5.60347	−	3.23517i	−0.177375	−	0.102407i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	819.2.dx.a.503.14	yes	72
3.2	odd	2	inner	819.2.dx.a.503.23	yes	72
7.6	odd	2	inner	819.2.dx.a.503.13	✓	72
13.3	even	3	inner	819.2.dx.a.692.24	yes	72
21.20	even	2	inner	819.2.dx.a.503.24	yes	72
39.29	odd	6	inner	819.2.dx.a.692.13	yes	72
91.55	odd	6	inner	819.2.dx.a.692.23	yes	72
273.146	even	6	inner	819.2.dx.a.692.14	yes	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
819.2.dx.a.503.13	✓	72	7.6	odd	2	inner
819.2.dx.a.503.14	yes	72	1.1	even	1	trivial
819.2.dx.a.503.23	yes	72	3.2	odd	2	inner
819.2.dx.a.503.24	yes	72	21.20	even	2	inner
819.2.dx.a.692.13	yes	72	39.29	odd	6	inner
819.2.dx.a.692.14	yes	72	273.146	even	6	inner
819.2.dx.a.692.23	yes	72	91.55	odd	6	inner
819.2.dx.a.692.24	yes	72	13.3	even	3	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 819 = 3^{2} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	819.dx (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.595297 - 0.343695i) q^{2} +(-0.763748 - 1.32285i) q^{4} +2.01783 q^{5} +(1.15619 + 2.37975i) q^{7} +2.42476i q^{8} +O(q^{10})\)	\(q+(-0.595297 - 0.343695i) q^{2} +(-0.763748 - 1.32285i) q^{4} +2.01783 q^{5} +(1.15619 + 2.37975i) q^{7} +2.42476i q^{8} +(-1.20121 - 0.693518i) q^{10} +(0.901261 + 0.520343i) q^{11} +(-1.78562 + 3.13234i) q^{13} +(0.129631 - 1.81404i) q^{14} +(-0.694116 + 1.20224i) q^{16} +(2.31510 + 4.00988i) q^{17} +(-4.39603 + 2.53805i) q^{19} +(-1.54111 - 2.66929i) q^{20} +(-0.357679 - 0.619518i) q^{22} +(0.642878 + 0.371166i) q^{23} -0.928355 q^{25} +(2.13954 - 1.25096i) q^{26} +(2.26502 - 3.34700i) q^{28} +(-4.20078 - 2.42532i) q^{29} +8.99744i q^{31} +(5.02623 - 2.90189i) q^{32} -3.18276i q^{34} +(2.33300 + 4.80194i) q^{35} +(-1.60720 + 2.78374i) q^{37} +3.48925 q^{38} +4.89277i q^{40} +(2.61184 - 4.52384i) q^{41} +(-2.97831 - 5.15859i) q^{43} -1.58964i q^{44} +(-0.255135 - 0.441908i) q^{46} +11.6331 q^{47} +(-4.32644 + 5.50290i) q^{49} +(0.552647 + 0.319071i) q^{50} +(5.50738 - 0.0302062i) q^{52} -1.74959i q^{53} +(1.81859 + 1.04997i) q^{55} +(-5.77034 + 2.80349i) q^{56} +(1.66714 + 2.88757i) q^{58} +(4.92676 + 8.53340i) q^{59} +(2.12587 - 1.22737i) q^{61} +(3.09237 - 5.35615i) q^{62} -1.21300 q^{64} +(-3.60309 + 6.32053i) q^{65} +(5.44121 - 9.42445i) q^{67} +(3.53631 - 6.12507i) q^{68} +(0.261575 - 3.66042i) q^{70} +(9.92424 - 5.72976i) q^{71} +5.27545i q^{73} +(1.91352 - 1.10477i) q^{74} +(6.71491 + 3.87685i) q^{76} +(-0.196258 + 2.74640i) q^{77} +9.12427 q^{79} +(-1.40061 + 2.42593i) q^{80} +(-3.10964 + 1.79535i) q^{82} -9.56552 q^{83} +(4.67149 + 8.09126i) q^{85} +4.09453i q^{86} +(-1.26171 + 2.18535i) q^{88} +(-6.32834 + 10.9610i) q^{89} +(-9.51871 - 0.627756i) q^{91} -1.13391i q^{92} +(-6.92513 - 3.99823i) q^{94} +(-8.87044 + 5.12135i) q^{95} +(10.8148 - 6.24396i) q^{97} +(4.46684 - 1.78888i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q + 32 q^{4} - 2 q^{7}+O(q^{10}) \) 72 * q + 32 * q^4 - 2 * q^7	\( 72 q + 32 q^{4} - 2 q^{7} - 24 q^{16} + 24 q^{22} + 56 q^{25} - 8 q^{28} + 16 q^{37} - 4 q^{43} + 32 q^{46} + 26 q^{49} - 40 q^{58} - 64 q^{64} + 60 q^{67} - 40 q^{70} - 72 q^{79} - 80 q^{85} - 24 q^{88} + 2 q^{91}+O(q^{100}) \) 72 * q + 32 * q^4 - 2 * q^7 - 24 * q^16 + 24 * q^22 + 56 * q^25 - 8 * q^28 + 16 * q^37 - 4 * q^43 + 32 * q^46 + 26 * q^49 - 40 * q^58 - 64 * q^64 + 60 * q^67 - 40 * q^70 - 72 * q^79 - 80 * q^85 - 24 * q^88 + 2 * q^91

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