LMFDB - Embedded newform 468.2.j.a.133.10

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [468,2,Mod(133,468)] 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("468.133"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(468, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 4, 2])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 468 = 2^{2} \cdot 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	468.j (of order $3$, degree $2$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$3.73699881460$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$14$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			133.10
Character	$\chi$	$=$	468.133
Dual form			468.2.j.a.373.10

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.940018 - 1.45477i) q^{3} +(0.826802 + 1.43206i) q^{5} +(1.75493 + 3.03963i) q^{7} +(-1.23273 - 2.73503i) q^{9} +5.00696 q^{11} +(-3.15906 + 1.73791i) q^{13} +(2.86054 + 0.143355i) q^{15} +(-0.982875 + 1.70239i) q^{17} +(0.724325 - 1.25457i) q^{19} +(6.07163 + 0.304278i) q^{21} +(-3.19234 + 5.52930i) q^{23} +(1.13280 - 1.96206i) q^{25} +(-5.13764 - 0.777625i) q^{27} +9.61060 q^{29} +(-4.78740 - 8.29202i) q^{31} +(4.70663 - 7.28399i) q^{33} +(-2.90196 + 5.02634i) q^{35} +(0.862266 + 1.49349i) q^{37} +(-0.441306 + 6.22939i) q^{39} +(5.37964 - 9.31782i) q^{41} +(-6.13481 - 10.6258i) q^{43} +(2.89750 - 4.02668i) q^{45} +(-0.870397 + 1.50757i) q^{47} +(-2.65955 + 4.60648i) q^{49} +(1.55267 + 3.03014i) q^{51} -7.82781 q^{53} +(4.13976 + 7.17028i) q^{55} +(-1.14423 - 2.23305i) q^{57} +2.96836 q^{59} +(-2.38999 - 4.13958i) q^{61} +(6.15010 - 8.54683i) q^{63} +(-5.10071 - 3.08706i) q^{65} +(-6.25020 + 10.8257i) q^{67} +(5.04302 + 9.84177i) q^{69} +(-3.50147 + 6.06472i) q^{71} +2.22966 q^{73} +(-1.78951 - 3.49234i) q^{75} +(8.78686 + 15.2193i) q^{77} +(-8.49580 + 14.7152i) q^{79} +(-5.96074 + 6.74312i) q^{81} +(-2.22230 + 3.84913i) q^{83} -3.25057 q^{85} +(9.03413 - 13.9812i) q^{87} +(-2.12011 - 3.67214i) q^{89} +(-10.8265 - 6.55245i) q^{91} +(-16.5633 - 0.830062i) q^{93} +2.39549 q^{95} +(-2.38902 - 4.13790i) q^{97} +(-6.17224 - 13.6942i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q + 2 q^{7} - 2 q^{9} + 8 q^{11} + q^{13} - 10 q^{15} - 8 q^{17} - q^{19} + 14 q^{21} - 4 q^{23} - 14 q^{25} + 26 q^{29} + 2 q^{31} + 8 q^{33} + 3 q^{35} - q^{37} - 12 q^{39} + 4 q^{41} + 2 q^{43}+ \cdots - 29 q^{99}+O(q^{100}) $ 28 * q + 2 * q^7 - 2 * q^9 + 8 * q^11 + q^13 - 10 * q^15 - 8 * q^17 - q^19 + 14 * q^21 - 4 * q^23 - 14 * q^25 + 26 * q^29 + 2 * q^31 + 8 * q^33 + 3 * q^35 - q^37 - 12 * q^39 + 4 * q^41 + 2 * q^43 + q^45 + 11 * q^47 - 12 * q^49 + 5 * q^51 + 52 * q^53 - q^57 + 16 * q^59 - 7 * q^61 - 24 * q^63 - 31 * q^65 - 7 * q^67 + 24 * q^69 - 12 * q^71 + 14 * q^73 + 16 * q^75 - 28 * q^77 + 5 * q^79 - 50 * q^81 + 9 * q^83 - 36 * q^85 - 21 * q^87 - 11 * q^89 - q^91 - 33 * q^93 - 56 * q^95 - 25 * q^97 - 29 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/468\mathbb{Z}\right)^\times$.

$n$	$145$	$209$	$235$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$	$1$

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			0
$2$		0			0
$3$	0.940018	−	1.45477i	0.542720	−	0.839914i
$3$	0.940018	−	1.45477i	0.542720	−	0.839914i
$4$		0			0
$5$	0.826802	+	1.43206i	0.369757	+	0.640438i	0.989527	−	0.144345i	$-0.0461076\pi$
$5$	0.826802	+	1.43206i	0.369757	+	0.640438i	−0.619770	+	0.784783i	$0.712774\pi$
$6$		0			0
$7$	1.75493	+	3.03963i	0.663301	+	1.14887i	0.979743	+	0.200259i	$0.0641784\pi$
$7$	1.75493	+	3.03963i	0.663301	+	1.14887i	−0.316442	+	0.948612i	$0.602488\pi$
$8$		0			0
$9$	−1.23273	−	2.73503i	−0.410911	−	0.911675i
$10$		0			0
$11$	5.00696			1.50965			0.754827	−	0.655924i	$-0.227721\pi$
$11$	5.00696			1.50965			0.754827	+	0.655924i	$0.227721\pi$
$12$		0			0
$13$	−3.15906	+	1.73791i	−0.876166	+	0.482010i
$13$	−3.15906	+	1.73791i	−0.876166	+	0.482010i
$14$		0			0
$15$	2.86054	+	0.143355i	0.738587	+	0.0370141i
$16$		0			0
$17$	−0.982875	+	1.70239i	−0.238382	+	0.412890i	−0.960250	−	0.279141i	$-0.909950\pi$
$17$	−0.982875	+	1.70239i	−0.238382	+	0.412890i	0.721868	+	0.692031i	$0.243284\pi$
$18$		0			0
$19$	0.724325	−	1.25457i	0.166172	−	0.287818i	−0.770899	−	0.636957i	$-0.780193\pi$
$19$	0.724325	−	1.25457i	0.166172	−	0.287818i	0.937071	+	0.349140i	$0.113526\pi$
$20$		0			0
$21$	6.07163	+	0.304278i	1.32494	+	0.0663989i
$22$		0			0
$23$	−3.19234	+	5.52930i	−0.665649	+	1.15294i	0.313460	+	0.949601i	$0.398512\pi$
$23$	−3.19234	+	5.52930i	−0.665649	+	1.15294i	−0.979109	+	0.203336i	$0.934821\pi$
$24$		0			0
$25$	1.13280	−	1.96206i	0.226560	−	0.392413i
$26$		0			0
$27$	−5.13764	−	0.777625i	−0.988738	−	0.149654i
$28$		0			0
$29$	9.61060			1.78464			0.892322	−	0.451400i	$-0.149075\pi$
$29$	9.61060			1.78464			0.892322	+	0.451400i	$0.149075\pi$
$30$		0			0
$31$	−4.78740	−	8.29202i	−0.859842	−	1.48929i	−0.872079	−	0.489365i	$-0.837228\pi$
$31$	−4.78740	−	8.29202i	−0.859842	−	1.48929i	0.0122364	−	0.999925i	$-0.496105\pi$
$32$		0			0
$33$	4.70663	−	7.28399i	0.819319	−	1.26798i
$34$		0			0
$35$	−2.90196	+	5.02634i	−0.490520	+	0.849606i
$36$		0			0
$37$	0.862266	+	1.49349i	0.141756	+	0.245528i	0.928158	−	0.372187i	$-0.121392\pi$
$37$	0.862266	+	1.49349i	0.141756	+	0.245528i	−0.786402	+	0.617715i	$0.788059\pi$
$38$		0			0
$39$	−0.441306	+	6.22939i	−0.0706654	+	0.997500i
$40$		0			0
$41$	5.37964	−	9.31782i	0.840159	−	1.45520i	−0.0496002	−	0.998769i	$-0.515795\pi$
$41$	5.37964	−	9.31782i	0.840159	−	1.45520i	0.889760	−	0.456430i	$-0.150872\pi$
$42$		0			0
$43$	−6.13481	−	10.6258i	−0.935551	−	1.62042i	−0.773649	−	0.633614i	$-0.781571\pi$
$43$	−6.13481	−	10.6258i	−0.935551	−	1.62042i	−0.161901	−	0.986807i	$-0.551763\pi$
$44$		0			0
$45$	2.89750	−	4.02668i	0.431934	−	0.600261i
$46$		0			0
$47$	−0.870397	+	1.50757i	−0.126960	+	0.219902i	−0.922498	−	0.386003i	$-0.873855\pi$
$47$	−0.870397	+	1.50757i	−0.126960	+	0.219902i	0.795537	+	0.605905i	$0.207189\pi$
$48$		0			0
$49$	−2.65955	+	4.60648i	−0.379936	+	0.658069i
$50$		0			0
$51$	1.55267	+	3.03014i	0.217417	+	0.424304i
$52$		0			0
$53$	−7.82781			−1.07523			−0.537616	−	0.843190i	$-0.680675\pi$
$53$	−7.82781			−1.07523			−0.537616	+	0.843190i	$0.680675\pi$
$54$		0			0
$55$	4.13976	+	7.17028i	0.558205	+	0.966840i
$56$		0			0
$57$	−1.14423	−	2.23305i	−0.151558	−	0.295774i
$58$		0			0
$59$	2.96836			0.386447			0.193224	−	0.981155i	$-0.438106\pi$
$59$	2.96836			0.386447			0.193224	+	0.981155i	$0.438106\pi$
$60$		0			0
$61$	−2.38999	−	4.13958i	−0.306006	−	0.530019i	0.671478	−	0.741024i	$-0.265660\pi$
$61$	−2.38999	−	4.13958i	−0.306006	−	0.530019i	−0.977485	+	0.211005i	$0.932326\pi$
$62$		0			0
$63$	6.15010	−	8.54683i	0.774840	−	1.07680i
$64$		0			0
$65$	−5.10071	−	3.08706i	−0.632666	−	0.382903i
$66$		0			0
$67$	−6.25020	+	10.8257i	−0.763584	+	1.32257i	0.177408	+	0.984137i	$0.443229\pi$
$67$	−6.25020	+	10.8257i	−0.763584	+	1.32257i	−0.940992	+	0.338429i	$0.890105\pi$
$68$		0			0
$69$	5.04302	+	9.84177i	0.607108	+	1.18481i
$70$		0			0
$71$	−3.50147	+	6.06472i	−0.415547	+	0.719749i	−0.995486	−	0.0949111i	$-0.969743\pi$
$71$	−3.50147	+	6.06472i	−0.415547	+	0.719749i	0.579938	+	0.814660i	$0.303077\pi$
$72$		0			0
$73$	2.22966			0.260962			0.130481	−	0.991451i	$-0.458348\pi$
$73$	2.22966			0.260962			0.130481	+	0.991451i	$0.458348\pi$
$74$		0			0
$75$	−1.78951	−	3.49234i	−0.206635	−	0.403261i
$76$		0			0
$77$	8.78686	+	15.2193i	1.00136	+	1.73440i
$78$		0			0
$79$	−8.49580	+	14.7152i	−0.955852	+	1.65558i	−0.223447	+	0.974716i	$0.571731\pi$
$79$	−8.49580	+	14.7152i	−0.955852	+	1.65558i	−0.732406	+	0.680869i	$0.761602\pi$
$80$		0			0
$81$	−5.96074	+	6.74312i	−0.662304	+	0.749235i
$82$		0			0
$83$	−2.22230	+	3.84913i	−0.243929	+	0.422497i	−0.961830	−	0.273648i	$-0.911770\pi$
$83$	−2.22230	+	3.84913i	−0.243929	+	0.422497i	0.717901	+	0.696145i	$0.245103\pi$
$84$		0			0
$85$	−3.25057			−0.352574
$86$		0			0
$87$	9.03413	−	13.9812i	0.968561	−	1.49895i
$88$		0			0
$89$	−2.12011	−	3.67214i	−0.224732	−	0.389246i	0.731507	−	0.681834i	$-0.238817\pi$
$89$	−2.12011	−	3.67214i	−0.224732	−	0.389246i	−0.956239	+	0.292587i	$0.905484\pi$
$90$		0			0
$91$	−10.8265	−	6.55245i	−1.13493	−	0.686884i
$92$		0			0
$93$	−16.5633	−	0.830062i	−1.71753	−	0.0860735i
$94$		0			0
$95$	2.39549			0.245772
$96$		0			0
$97$	−2.38902	−	4.13790i	−0.242568	−	0.420141i	0.718877	−	0.695137i	$-0.244657\pi$
$97$	−2.38902	−	4.13790i	−0.242568	−	0.420141i	−0.961445	+	0.274997i	$0.911323\pi$
$98$		0			0
$99$	−6.17224	−	13.6942i	−0.620334	−	1.37632i
$100$		0			0
$101$	4.64389			0.462084			0.231042	−	0.972944i	$-0.425787\pi$
$101$	4.64389			0.462084			0.231042	+	0.972944i	$0.425787\pi$
$102$		0			0
$103$	−3.47526	−	6.01933i	−0.342428	−	0.593102i	0.642455	−	0.766323i	$-0.277916\pi$
$103$	−3.47526	−	6.01933i	−0.342428	−	0.593102i	−0.984883	+	0.173221i	$0.944583\pi$
$104$		0			0
$105$	4.58429	+	8.94654i	0.447381	+	0.873092i
$106$		0			0
$107$	4.05336	+	7.02063i	0.391853	+	0.678710i	0.992694	−	0.120659i	$-0.0385007\pi$
$107$	4.05336	+	7.02063i	0.391853	+	0.678710i	−0.600841	+	0.799369i	$0.705167\pi$
$108$		0			0
$109$	−9.57526			−0.917144			−0.458572	−	0.888657i	$-0.651639\pi$
$109$	−9.57526			−0.917144			−0.458572	+	0.888657i	$0.651639\pi$
$110$		0			0
$111$	2.98323	+	0.149504i	0.283156	+	0.0141903i
$112$		0			0
$113$	9.14418			0.860213			0.430106	−	0.902778i	$-0.358476\pi$
$113$	9.14418			0.860213			0.430106	+	0.902778i	$0.358476\pi$
$114$		0			0
$115$	−10.5577			−0.984513
$116$		0			0
$117$	8.64751	+	6.49773i	0.799463	+	0.600716i
$118$		0			0
$119$	−6.89950			−0.632476
$120$		0			0
$121$	14.0696			1.27906
$122$		0			0
$123$	−8.49836	−	16.5851i	−0.766271	−	1.49543i
$124$		0			0
$125$	12.0144			1.07460
$126$		0			0
$127$	−4.92860	−	8.53659i	−0.437343	−	0.757500i	0.560141	−	0.828397i	$-0.310747\pi$
$127$	−4.92860	−	8.53659i	−0.437343	−	0.757500i	−0.997484	+	0.0708976i	$0.977414\pi$
$128$		0			0
$129$	−21.2250	−	1.06368i	−1.86876	−	0.0936521i
$130$		0			0
$131$	−2.47850	−	4.29289i	−0.216547	−	0.375071i	0.737203	−	0.675672i	$-0.236146\pi$
$131$	−2.47850	−	4.29289i	−0.216547	−	0.375071i	−0.953750	+	0.300600i	$0.902813\pi$
$132$		0			0
$133$	5.08456			0.440887
$134$		0			0
$135$	−3.13420	−	8.00036i	−0.269749	−	0.688561i
$136$		0			0
$137$	−0.00614831	−	0.0106492i	−0.000525285	−	0.000909821i	0.865763	−	0.500455i	$-0.166834\pi$
$137$	−0.00614831	−	0.0106492i	−0.000525285	−	0.000909821i	−0.866288	+	0.499545i	$0.833501\pi$
$138$		0			0
$139$	−1.04882			−0.0889596			−0.0444798	−	0.999010i	$-0.514163\pi$
$139$	−1.04882			−0.0889596			−0.0444798	+	0.999010i	$0.514163\pi$
$140$		0			0
$141$	1.37499	+	2.68338i	0.115795	+	0.225981i
$142$		0			0
$143$	−15.8173	+	8.70165i	−1.32271	+	0.727668i
$144$		0			0
$145$	7.94606	+	13.7630i	0.659884	+	1.14295i
$146$		0			0
$147$	4.20136	+	8.19922i	0.346522	+	0.676260i
$148$		0			0
$149$	−16.9555			−1.38905			−0.694523	−	0.719471i	$-0.744384\pi$
$149$	−16.9555			−1.38905			−0.694523	+	0.719471i	$0.744384\pi$
$150$		0			0
$151$	4.12187	−	7.13929i	0.335433	−	0.580987i	−0.648135	−	0.761526i	$-0.724451\pi$
$151$	4.12187	−	7.13929i	0.335433	−	0.580987i	0.983568	+	0.180538i	$0.0577840\pi$
$152$		0			0
$153$	5.86770	+	0.589597i	0.474376	+	0.0476661i
$154$		0			0
$155$	7.91646	−	13.7117i	0.635865	−	1.10135i
$156$		0			0
$157$	0.660501	+	1.14402i	0.0527137	+	0.0913028i	0.891178	−	0.453653i	$-0.149880\pi$
$157$	0.660501	+	1.14402i	0.0527137	+	0.0913028i	−0.838464	+	0.544956i	$0.816546\pi$
$158$		0			0
$159$	−7.35828	+	11.3877i	−0.583550	+	0.903103i
$160$		0			0
$161$	−22.4093			−1.76610
$162$		0			0
$163$	−4.63491	+	8.02790i	−0.363034	+	0.628794i	−0.988459	−	0.151491i	$-0.951593\pi$
$163$	−4.63491	+	8.02790i	−0.363034	+	0.628794i	0.625424	+	0.780285i	$0.284926\pi$
$164$		0			0
$165$	14.3226	+	0.717772i	1.11501	+	0.0558784i
$166$		0			0
$167$	5.00660	−	8.67168i	0.387422	−	0.671035i	−0.604680	−	0.796469i	$-0.706699\pi$
$167$	5.00660	−	8.67168i	0.387422	−	0.671035i	0.992102	+	0.125434i	$0.0400322\pi$
$168$		0			0
$169$	6.95933	−	10.9803i	0.535333	−	0.844641i
$170$		0			0
$171$	−4.32418	−	0.434501i	−0.330678	−	0.0332271i
$172$		0			0
$173$	−4.20427	−	7.28201i	−0.319645	−	0.553641i	0.660769	−	0.750589i	$-0.270230\pi$
$173$	−4.20427	−	7.28201i	−0.319645	−	0.553641i	−0.980414	+	0.196948i	$0.936897\pi$
$174$		0			0
$175$	7.95192			0.601109
$176$		0			0
$177$	2.79031	−	4.31829i	0.209732	−	0.324582i
$178$		0			0
$179$	4.10687	+	7.11330i	0.306962	+	0.531673i	0.977696	−	0.210024i	$-0.0673543\pi$
$179$	4.10687	+	7.11330i	0.306962	+	0.531673i	−0.670735	+	0.741698i	$0.734021\pi$
$180$		0			0
$181$	10.9678			0.815231			0.407615	−	0.913154i	$-0.366360\pi$
$181$	10.9678			0.815231			0.407615	+	0.913154i	$0.366360\pi$
$182$		0			0
$183$	−8.26878	−	0.414387i	−0.611246	−	0.0306324i
$184$		0			0
$185$	−1.42585	+	2.46964i	−0.104830	+	0.181571i
$186$		0			0
$187$	−4.92121	+	8.52379i	−0.359875	+	0.623321i
$188$		0			0
$189$	−6.65250	−	16.9812i	−0.483898	−	1.23520i
$190$		0			0
$191$	−0.727692	−	1.26040i	−0.0526540	−	0.0911993i	0.838497	−	0.544906i	$-0.183435\pi$
$191$	−0.727692	−	1.26040i	−0.0526540	−	0.0911993i	−0.891151	+	0.453707i	$0.850101\pi$
$192$		0			0
$193$	5.16215	−	8.94111i	0.371580	−	0.643595i	−0.618229	−	0.785998i	$-0.712150\pi$
$193$	5.16215	−	8.94111i	0.371580	−	0.643595i	0.989809	+	0.142403i	$0.0454828\pi$
$194$		0			0
$195$	−9.28574	+	4.51849i	−0.664966	+	0.323576i
$196$		0			0
$197$	−5.05995	−	8.76409i	−0.360507	−	0.624416i	0.627538	−	0.778586i	$-0.284063\pi$
$197$	−5.05995	−	8.76409i	−0.360507	−	0.624416i	−0.988044	+	0.154170i	$0.950730\pi$
$198$		0			0
$199$	3.43613	−	5.95155i	0.243581	−	0.421894i	−0.718151	−	0.695887i	$-0.755011\pi$
$199$	3.43613	−	5.95155i	0.243581	−	0.421894i	0.961732	+	0.273993i	$0.0883446\pi$
$200$		0			0
$201$	9.87360	+	19.2690i	0.696430	+	1.35913i
$202$		0			0
$203$	16.8659	+	29.2126i	1.18376	+	2.05032i
$204$		0			0
$205$	17.7916			1.24262
$206$		0			0
$207$	19.0581	+	1.91499i	1.32463	+	0.133101i
$208$		0			0
$209$	3.62667	−	6.28157i	0.250862	−	0.434505i
$210$		0			0
$211$	−8.65367	+	14.9886i	−0.595743	+	1.03186i	0.397698	+	0.917516i	$0.369809\pi$
$211$	−8.65367	+	14.9886i	−0.595743	+	1.03186i	−0.993442	+	0.114341i	$0.963524\pi$
$212$		0			0
$213$	5.53135	+	10.7948i	0.379002	+	0.739646i
$214$		0			0
$215$	10.1446	−	17.5709i	0.691853	−	1.19832i
$216$		0			0
$217$	16.8031	−	29.1038i	1.14067	−	1.97570i
$218$		0			0
$219$	2.09592	−	3.24365i	0.141629	−	0.219185i
$220$		0			0
$221$	0.146360	−	7.08610i	0.00984524	−	0.476663i
$222$		0			0
$223$	22.6459			1.51648			0.758242	−	0.651973i	$-0.226059\pi$
$223$	22.6459			1.51648			0.758242	+	0.651973i	$0.226059\pi$
$224$		0			0
$225$	−6.76273	−	0.679531i	−0.450849	−	0.0453021i
$226$		0			0
$227$	−7.75800	−	13.4373i	−0.514917	−	0.891862i	−0.999850	−	0.0173110i	$-0.994489\pi$
$227$	−7.75800	−	13.4373i	−0.514917	−	0.891862i	0.484933	−	0.874551i	$-0.338844\pi$
$228$		0			0
$229$	3.33988	+	5.78483i	0.220705	+	0.382273i	0.955022	−	0.296534i	$-0.0958308\pi$
$229$	3.33988	+	5.78483i	0.220705	+	0.382273i	−0.734317	+	0.678807i	$0.762497\pi$
$230$		0			0
$231$	30.4004	+	1.52351i	2.00020	+	0.100239i
$232$		0			0
$233$	−15.0244			−0.984281			−0.492141	−	0.870516i	$-0.663785\pi$
$233$	−15.0244			−0.984281			−0.492141	+	0.870516i	$0.663785\pi$
$234$		0			0
$235$	−2.87858			−0.187778
$236$		0			0
$237$	13.4210	+	26.1920i	0.871789	+	1.70135i
$238$		0			0
$239$	4.26040	+	7.37923i	0.275582	+	0.477323i	0.970282	−	0.241977i	$-0.0777960\pi$
$239$	4.26040	+	7.37923i	0.275582	+	0.477323i	−0.694700	+	0.719300i	$0.744463\pi$
$240$		0			0
$241$	9.16876	+	15.8808i	0.590612	+	1.02297i	0.994150	+	0.108007i	$0.0344469\pi$
$241$	9.16876	+	15.8808i	0.590612	+	1.02297i	−0.403538	+	0.914963i	$0.632220\pi$
$242$		0			0
$243$	4.20651	+	15.0102i	0.269848	+	0.962903i
$244$		0			0
$245$	−8.79569			−0.561936
$246$		0			0
$247$	−0.107859	+	5.22207i	−0.00686293	+	0.332272i
$248$		0			0
$249$	3.51062	+	6.85119i	0.222476	+	0.434176i
$250$		0			0
$251$	−5.78538	+	10.0206i	−0.365170	+	0.632493i	−0.988803	−	0.149224i	$-0.952323\pi$
$251$	−5.78538	+	10.0206i	−0.365170	+	0.632493i	0.623633	+	0.781717i	$0.285656\pi$
$252$		0			0
$253$	−15.9839	+	27.6850i	−1.00490	+	1.74054i
$254$		0			0
$255$	−3.05559	+	4.72884i	−0.191349	+	0.296132i
$256$		0			0
$257$	−2.80456	+	4.85764i	−0.174943	+	0.303011i	−0.940142	−	0.340784i	$-0.889308\pi$
$257$	−2.80456	+	4.85764i	−0.174943	+	0.303011i	0.765198	+	0.643795i	$0.222641\pi$
$258$		0			0
$259$	−3.02643	+	5.24193i	−0.188053	+	0.325718i
$260$		0			0
$261$	−11.8473	−	26.2852i	−0.733330	−	1.62702i
$262$		0			0
$263$	22.3056			1.37542			0.687710	−	0.725986i	$-0.258616\pi$
$263$	22.3056			1.37542			0.687710	+	0.725986i	$0.258616\pi$
$264$		0			0
$265$	−6.47205	−	11.2099i	−0.397575	−	0.688619i
$266$		0			0
$267$	−7.33508	−	0.367595i	−0.448900	−	0.0224965i
$268$		0			0
$269$	6.49509	−	11.2498i	0.396013	−	0.685914i	−0.597217	−	0.802080i	$-0.703727\pi$
$269$	6.49509	−	11.2498i	0.396013	−	0.685914i	0.993230	+	0.116165i	$0.0370603\pi$
$270$		0			0
$271$	−13.5914	−	23.5410i	−0.825619	−	1.43001i	−0.901445	−	0.432893i	$-0.857493\pi$
$271$	−13.5914	−	23.5410i	−0.825619	−	1.43001i	0.0758262	−	0.997121i	$-0.475841\pi$
$272$		0			0
$273$	−19.7095	+	9.59073i	−1.19287	+	0.580457i
$274$		0			0
$275$	5.67187	−	9.82397i	0.342027	−	0.592408i
$276$		0			0
$277$	−0.110442	−	0.191291i	−0.00663580	−	0.0114935i	0.862688	−	0.505736i	$-0.168779\pi$
$277$	−0.110442	−	0.191291i	−0.00663580	−	0.0114935i	−0.869324	+	0.494242i	$0.835446\pi$
$278$		0			0
$279$	−16.7773	+	23.3155i	−1.00443	+	1.39586i
$280$		0			0
$281$	9.42986	−	16.3330i	0.562538	−	0.974345i	−0.434736	−	0.900558i	$-0.643158\pi$
$281$	9.42986	−	16.3330i	0.562538	−	0.974345i	0.997274	−	0.0737867i	$-0.0235084\pi$
$282$		0			0
$283$	−0.739346	+	1.28058i	−0.0439495	+	0.0761228i	−0.887163	−	0.461455i	$-0.847327\pi$
$283$	−0.739346	+	1.28058i	−0.0439495	+	0.0761228i	0.843214	+	0.537578i	$0.180661\pi$
$284$		0			0
$285$	2.25181	−	3.48490i	0.133386	−	0.206428i
$286$		0			0
$287$	37.7636			2.22911
$288$		0			0
$289$	6.56791	+	11.3760i	0.386348	+	0.669174i
$290$		0			0
$291$	−8.26544	−	0.414220i	−0.484528	−	0.0242820i
$292$		0			0
$293$	9.31607			0.544251			0.272125	−	0.962262i	$-0.412273\pi$
$293$	9.31607			0.544251			0.272125	+	0.962262i	$0.412273\pi$
$294$		0			0
$295$	2.45424	+	4.25087i	0.142891	+	0.247495i
$296$		0			0
$297$	−25.7239	−	3.89354i	−1.49265	−	0.225926i
$298$		0			0
$299$	0.475372	−	23.0154i	0.0274915	−	1.33101i
$300$		0			0
$301$	21.5323	−	37.2951i	1.24110	−	2.14965i
$302$		0			0
$303$	4.36534	−	6.75580i	0.250782	−	0.388111i
$304$		0			0
$305$	3.95209	−	6.84522i	0.226296	−	0.391956i
$306$		0			0
$307$	−3.33251			−0.190196			−0.0950982	−	0.995468i	$-0.530317\pi$
$307$	−3.33251			−0.190196			−0.0950982	+	0.995468i	$0.530317\pi$
$308$		0			0
$309$	−12.0236	−	0.602558i	−0.683997	−	0.0342783i
$310$		0			0
$311$	4.23963	+	7.34325i	0.240407	+	0.416398i	0.960830	−	0.277137i	$-0.0893857\pi$
$311$	4.23963	+	7.34325i	0.240407	+	0.416398i	−0.720423	+	0.693535i	$0.756052\pi$
$312$		0			0
$313$	0.215576	−	0.373388i	0.0121851	−	0.0211052i	−0.859869	−	0.510515i	$-0.829455\pi$
$313$	0.215576	−	0.373388i	0.0121851	−	0.0211052i	0.872054	+	0.489410i	$0.162788\pi$
$314$		0			0
$315$	17.3245	+	1.74080i	0.976125	+	0.0980827i
$316$		0			0
$317$	2.95969	−	5.12633i	0.166233	−	0.287923i	−0.770860	−	0.637005i	$-0.780173\pi$
$317$	2.95969	−	5.12633i	0.166233	−	0.287923i	0.937092	+	0.349082i	$0.113506\pi$
$318$		0			0
$319$	48.1199			2.69420
$320$		0			0
$321$	14.0237	+	0.702791i	0.782724	+	0.0392260i
$322$		0			0
$323$	1.42384	+	2.46617i	0.0792247	+	0.137221i
$324$		0			0
$325$	−0.168685	+	8.16698i	−0.00935697	+	0.453023i
$326$		0			0
$327$	−9.00092	+	13.9298i	−0.497752	+	0.770322i
$328$		0			0
$329$	−6.10994			−0.336852
$330$		0			0
$331$	−6.53059	−	11.3113i	−0.358954	−	0.621726i	0.628833	−	0.777541i	$-0.283533\pi$
$331$	−6.53059	−	11.3113i	−0.358954	−	0.621726i	−0.987786	+	0.155815i	$0.950200\pi$
$332$		0			0
$333$	3.02179	−	4.19939i	0.165593	−	0.230125i
$334$		0			0
$335$	−20.6707			−1.12936
$336$		0			0
$337$	11.3051	+	19.5811i	0.615831	+	1.06665i	0.990238	+	0.139386i	$0.0445128\pi$
$337$	11.3051	+	19.5811i	0.615831	+	1.06665i	−0.374408	+	0.927264i	$0.622154\pi$
$338$		0			0
$339$	8.59570	−	13.3027i	0.466854	−	0.722505i
$340$		0			0
$341$	−23.9703	−	41.5178i	−1.29807	−	2.24831i
$342$		0			0
$343$	5.89970			0.318554
$344$		0			0
$345$	−9.92445	+	15.3591i	−0.534315	+	0.826906i
$346$		0			0
$347$	−31.8798			−1.71140			−0.855699	−	0.517474i	$-0.826872\pi$
$347$	−31.8798			−1.71140			−0.855699	+	0.517474i	$0.826872\pi$
$348$		0			0
$349$	−10.4134			−0.557417			−0.278708	−	0.960376i	$-0.589906\pi$
$349$	−10.4134			−0.557417			−0.278708	+	0.960376i	$0.589906\pi$
$350$		0			0
$351$	17.5815	−	6.47219i	0.938434	−	0.345460i
$352$		0			0
$353$	−14.7249			−0.783726			−0.391863	−	0.920024i	$-0.628169\pi$
$353$	−14.7249			−0.783726			−0.391863	+	0.920024i	$0.628169\pi$
$354$		0			0
$355$	−11.5801			−0.614606
$356$		0			0
$357$	−6.48566	+	10.0372i	−0.343257	+	0.531226i
$358$		0			0
$359$	−9.70132			−0.512016			−0.256008	−	0.966675i	$-0.582407\pi$
$359$	−9.70132			−0.512016			−0.256008	+	0.966675i	$0.582407\pi$
$360$		0			0
$361$	8.45071	+	14.6371i	0.444774	+	0.770371i
$362$		0			0
$363$	13.2257	−	20.4681i	0.694169	−	1.07430i
$364$		0			0
$365$	1.84348	+	3.19301i	0.0964924	+	0.167130i
$366$		0			0
$367$	−13.1111			−0.684392			−0.342196	−	0.939629i	$-0.611171\pi$
$367$	−13.1111			−0.684392			−0.342196	+	0.939629i	$0.611171\pi$
$368$		0			0
$369$	−32.1161	−	3.22709i	−1.67190	−	0.167995i
$370$		0			0
$371$	−13.7373	−	23.7936i	−0.713203	−	1.23530i
$372$		0			0
$373$	−23.1660			−1.19949			−0.599744	−	0.800192i	$-0.704731\pi$
$373$	−23.1660			−1.19949			−0.599744	+	0.800192i	$0.704731\pi$
$374$		0			0
$375$	11.2938	−	17.4783i	0.583207	−	0.902573i
$376$		0			0
$377$	−30.3605	+	16.7024i	−1.56364	+	0.860216i
$378$		0			0
$379$	5.97448	+	10.3481i	0.306888	+	0.531546i	0.977680	−	0.210100i	$-0.0673789\pi$
$379$	5.97448	+	10.3481i	0.306888	+	0.531546i	−0.670792	+	0.741646i	$0.734046\pi$
$380$		0			0
$381$	−17.0518	−	0.854545i	−0.873589	−	0.0437796i
$382$		0			0
$383$	36.6071			1.87053			0.935267	−	0.353942i	$-0.115159\pi$
$383$	36.6071			1.87053			0.935267	+	0.353942i	$0.115159\pi$
$384$		0			0
$385$	−14.5300	+	25.1667i	−0.740516	+	1.28261i
$386$		0			0
$387$	−21.4993	+	29.8777i	−1.09287	+	1.51877i
$388$		0			0
$389$	−2.76801	+	4.79433i	−0.140344	+	0.243082i	−0.927626	−	0.373510i	$-0.878154\pi$
$389$	−2.76801	+	4.79433i	−0.140344	+	0.243082i	0.787282	+	0.616592i	$0.211487\pi$
$390$		0			0
$391$	−6.27534	−	10.8692i	−0.317358	−	0.549680i
$392$		0			0
$393$	−8.57501	−	0.429734i	−0.432552	−	0.0216772i
$394$		0			0
$395$	−28.0974			−1.41373
$396$		0			0
$397$	1.77564	−	3.07551i	0.0891171	−	0.154355i	−0.818021	−	0.575188i	$-0.804929\pi$
$397$	1.77564	−	3.07551i	0.0891171	−	0.154355i	0.907138	+	0.420833i	$0.138262\pi$
$398$		0			0
$399$	4.77958	−	7.39688i	0.239278	−	0.370307i
$400$		0			0
$401$	−12.1807	+	21.0975i	−0.608273	+	1.05356i	0.383252	+	0.923644i	$0.374804\pi$
$401$	−12.1807	+	21.0975i	−0.608273	+	1.05356i	−0.991525	+	0.129916i	$0.958529\pi$
$402$		0			0
$403$	29.5345	+	17.8749i	1.47122	+	0.890413i
$404$		0			0
$405$	−14.5849	−	2.96093i	−0.724730	−	0.147130i
$406$		0			0
$407$	4.31733	+	7.47783i	0.214002	+	0.370662i
$408$		0			0
$409$	11.2592			0.556732			0.278366	−	0.960475i	$-0.410207\pi$
$409$	11.2592			0.556732			0.278366	+	0.960475i	$0.410207\pi$
$410$		0			0
$411$	−0.0212717	−	0.00106602i	−0.00104925	−	5.25830e-5i
$412$		0			0
$413$	5.20926	+	9.02269i	0.256331	+	0.443978i
$414$		0			0
$415$	−7.34959			−0.360777
$416$		0			0
$417$	−0.985907	+	1.52579i	−0.0482801	+	0.0747184i
$418$		0			0
$419$	−19.2274	+	33.3028i	−0.939319	+	1.62695i	−0.172573	+	0.984997i	$0.555208\pi$
$419$	−19.2274	+	33.3028i	−0.939319	+	1.62695i	−0.766746	+	0.641951i	$0.778125\pi$
$420$		0			0
$421$	11.2699	−	19.5201i	0.549263	−	0.951351i	−0.449063	−	0.893500i	$-0.648242\pi$
$421$	11.2699	−	19.5201i	0.549263	−	0.951351i	0.998325	−	0.0578506i	$-0.0184247\pi$
$422$		0			0
$423$	5.19622	+	0.522125i	0.252649	+	0.0253866i
$424$		0			0
$425$	2.22680	+	3.85693i	0.108016	+	0.187088i
$426$		0			0
$427$	8.38851	−	14.5293i	0.405949	−	0.703124i
$428$		0			0
$429$	−2.20960	+	31.1903i	−0.106680	+	1.50588i
$430$		0			0
$431$	5.97132	+	10.3426i	0.287629	+	0.498187i	0.973243	−	0.229777i	$-0.0737998\pi$
$431$	5.97132	+	10.3426i	0.287629	+	0.498187i	−0.685615	+	0.727965i	$0.740466\pi$
$432$		0			0
$433$	12.5066	−	21.6620i	0.601028	−	1.04101i	−0.391638	−	0.920120i	$-0.628091\pi$
$433$	12.5066	−	21.6620i	0.601028	−	1.04101i	0.992666	−	0.120892i	$-0.0385754\pi$
$434$		0			0
$435$	27.4915	+	1.37773i	1.31811	+	0.0660569i
$436$		0			0
$437$	4.62459	+	8.01002i	0.221224	+	0.383171i
$438$		0			0
$439$	−32.4232			−1.54747			−0.773737	−	0.633506i	$-0.781615\pi$
$439$	−32.4232			−1.54747			−0.773737	+	0.633506i	$0.781615\pi$
$440$		0			0
$441$	15.8774	+	1.59539i	0.756065	+	0.0759707i
$442$		0			0
$443$	−6.55432	+	11.3524i	−0.311405	+	0.539370i	−0.978667	−	0.205454i	$-0.934133\pi$
$443$	−6.55432	+	11.3524i	−0.311405	+	0.539370i	0.667262	+	0.744823i	$0.267466\pi$
$444$		0			0
$445$	3.50583	−	6.07227i	0.166192	−	0.287853i
$446$		0			0
$447$	−15.9384	+	24.6664i	−0.753862	+	1.16668i
$448$		0			0
$449$	15.6886	−	27.1735i	0.740392	−	1.28240i	−0.211925	−	0.977286i	$-0.567973\pi$
$449$	15.6886	−	27.1735i	0.740392	−	1.28240i	0.952317	−	0.305111i	$-0.0986934\pi$
$450$		0			0
$451$	26.9357	−	46.6539i	1.26835	−	2.19685i
$452$		0			0
$453$	−6.51142	−	12.7074i	−0.305933	−	0.597048i
$454$		0			0
$455$	0.432131	−	20.9218i	0.0202586	−	0.980831i
$456$		0			0
$457$	17.1056			0.800167			0.400083	−	0.916479i	$-0.368981\pi$
$457$	17.1056			0.800167			0.400083	+	0.916479i	$0.368981\pi$
$458$		0			0
$459$	6.37347	−	7.98195i	0.297488	−	0.372565i
$460$		0			0
$461$	16.5664	+	28.6939i	0.771575	+	1.33641i	0.936699	+	0.350135i	$0.113864\pi$
$461$	16.5664	+	28.6939i	0.771575	+	1.33641i	−0.165124	+	0.986273i	$0.552802\pi$
$462$		0			0
$463$	9.37793	+	16.2430i	0.435829	+	0.754878i	0.997363	−	0.0725756i	$-0.0231219\pi$
$463$	9.37793	+	16.2430i	0.435829	+	0.754878i	−0.561534	+	0.827454i	$0.689789\pi$
$464$		0			0
$465$	−12.5058	−	24.4059i	−0.579944	−	1.13180i
$466$		0			0
$467$	11.3134			0.523523			0.261762	−	0.965133i	$-0.415697\pi$
$467$	11.3134			0.523523			0.261762	+	0.965133i	$0.415697\pi$
$468$		0			0
$469$	−43.8747			−2.02594
$470$		0			0
$471$	2.28517	+	0.114521i	0.105295	+	0.00527684i
$472$		0			0
$473$	−30.7168	−	53.2030i	−1.41236	−	2.44628i
$474$		0			0
$475$	−1.64103	−	2.84235i	−0.0752956	−	0.130416i
$476$		0			0
$477$	9.64960	+	21.4093i	0.441825	+	0.980263i
$478$		0			0
$479$	−16.3832			−0.748565			−0.374283	−	0.927315i	$-0.622111\pi$
$479$	−16.3832			−0.748565			−0.374283	+	0.927315i	$0.622111\pi$
$480$		0			0
$481$	−5.31950	−	3.21948i	−0.242548	−	0.146796i
$482$		0			0
$483$	−21.0652	+	32.6005i	−0.958498	+	1.48337i
$484$		0			0
$485$	3.95049	−	6.84245i	0.179383	−	0.310700i
$486$		0			0
$487$	−1.01175	+	1.75240i	−0.0458467	+	0.0794089i	−0.888038	−	0.459770i	$-0.847932\pi$
$487$	−1.01175	+	1.75240i	−0.0458467	+	0.0794089i	0.842191	+	0.539179i	$0.181265\pi$
$488$		0			0
$489$	7.32188	+	14.2891i	0.331107	+	0.646176i
$490$		0			0
$491$	−6.85426	+	11.8719i	−0.309328	+	0.535773i	−0.978216	−	0.207591i	$-0.933438\pi$
$491$	−6.85426	+	11.8719i	−0.309328	+	0.535773i	0.668887	+	0.743364i	$0.266771\pi$
$492$		0			0
$493$	−9.44602	+	16.3610i	−0.425427	+	0.736861i
$494$		0			0
$495$	14.5077	−	20.1614i	0.652071	−	0.906187i
$496$		0			0
$497$	−24.5793			−1.10253
$498$		0			0
$499$	2.76875	+	4.79561i	0.123946	+	0.214681i	0.921320	−	0.388804i	$-0.127112\pi$
$499$	2.76875	+	4.79561i	0.123946	+	0.214681i	−0.797374	+	0.603485i	$0.793778\pi$
$500$		0			0
$501$	−7.90905	−	15.4350i	−0.353350	−	0.689585i
$502$		0			0
$503$	−5.37660	+	9.31254i	−0.239731	+	0.415226i	−0.960637	−	0.277807i	$-0.910392\pi$
$503$	−5.37660	+	9.31254i	−0.239731	+	0.415226i	0.720906	+	0.693033i	$0.243726\pi$
$504$		0			0
$505$	3.83957	+	6.65033i	0.170859	+	0.295936i
$506$		0			0
$507$	−9.43201	−	20.4460i	−0.418890	−	0.908037i
$508$		0			0
$509$	11.3748	−	19.7018i	0.504180	−	0.873265i	−0.495808	−	0.868432i	$-0.665128\pi$
$509$	11.3748	−	19.7018i	0.504180	−	0.873265i	0.999988	−	0.00483331i	$-0.00153850\pi$
$510$		0			0
$511$	3.91289	+	6.77733i	0.173096	+	0.299811i
$512$		0			0
$513$	−4.69690	+	5.88226i	−0.207373	+	0.259708i
$514$		0			0
$515$	5.74671	−	9.95359i	0.253230	−	0.438607i
$516$		0			0
$517$	−4.35804	+	7.54835i	−0.191667	+	0.331976i
$518$		0			0
$519$	−14.5458	−	0.728957i	−0.638488	−	0.0319976i
$520$		0			0
$521$	36.8064			1.61252			0.806259	−	0.591563i	$-0.201489\pi$
$521$	36.8064			1.61252			0.806259	+	0.591563i	$0.201489\pi$
$522$		0			0
$523$	−0.646458	−	1.11970i	−0.0282677	−	0.0489610i	0.851546	−	0.524281i	$-0.175666\pi$
$523$	−0.646458	−	1.11970i	−0.0282677	−	0.0489610i	−0.879813	+	0.475320i	$0.842332\pi$
$524$		0			0
$525$	7.47495	−	11.5682i	0.326233	−	0.504880i
$526$		0			0
$527$	18.8217			0.819884
$528$		0			0
$529$	−8.88207	−	15.3842i	−0.386177	−	0.668878i
$530$		0			0
$531$	−3.65919	−	8.11853i	−0.158795	−	0.352314i
$532$		0			0
$533$	−0.801084	+	38.7849i	−0.0346988	+	1.67996i
$534$		0			0
$535$	−6.70265	+	11.6093i	−0.289781	+	0.501915i
$536$		0			0
$537$	14.2088	+	0.712068i	0.613154	+	0.0307280i
$538$		0			0
$539$	−13.3163	+	23.0645i	−0.573572	+	0.993456i
$540$		0			0
$541$	−30.2710			−1.30145			−0.650725	−	0.759313i	$-0.725535\pi$
$541$	−30.2710			−1.30145			−0.650725	+	0.759313i	$0.725535\pi$
$542$		0			0
$543$	10.3099	−	15.9557i	0.442442	−	0.684724i
$544$		0			0
$545$	−7.91684	−	13.7124i	−0.339120	−	0.587374i
$546$		0			0
$547$	−2.55758	+	4.42986i	−0.109354	+	0.189407i	−0.915509	−	0.402298i	$-0.868212\pi$
$547$	−2.55758	+	4.42986i	−0.109354	+	0.189407i	0.806155	+	0.591705i	$0.201545\pi$
$548$		0			0
$549$	−8.37564	+	11.6397i	−0.357464	+	0.496769i
$550$		0			0
$551$	6.96120	−	12.0572i	0.296557	−	0.513652i
$552$		0			0
$553$	−59.6381			−2.53607
$554$		0			0
$555$	2.25244	+	4.39579i	0.0956109	+	0.186591i
$556$		0			0
$557$	−0.372512	−	0.645209i	−0.0157838	−	0.0273384i	0.858026	−	0.513607i	$-0.171691\pi$
$557$	−0.372512	−	0.645209i	−0.0157838	−	0.0273384i	−0.873809	+	0.486269i	$0.838358\pi$
$558$		0			0
$559$	37.8470	+	22.9058i	1.60076	+	0.968813i
$560$		0			0
$561$	7.77416	+	15.1718i	0.328225	+	0.640553i
$562$		0			0
$563$	32.0660			1.35142			0.675710	−	0.737168i	$-0.263837\pi$
$563$	32.0660			1.35142			0.675710	+	0.737168i	$0.263837\pi$
$564$		0			0
$565$	7.56043	+	13.0950i	0.318070	+	0.550913i
$566$		0			0
$567$	−30.9572	−	6.28473i	−1.30008	−	0.263934i
$568$		0			0
$569$	40.8474			1.71241			0.856206	−	0.516635i	$-0.172816\pi$
$569$	40.8474			1.71241			0.856206	+	0.516635i	$0.172816\pi$
$570$		0			0
$571$	0.269451	+	0.466702i	0.0112762	+	0.0195309i	0.871608	−	0.490203i	$-0.163077\pi$
$571$	0.269451	+	0.466702i	0.0112762	+	0.0195309i	−0.860332	+	0.509734i	$0.829744\pi$
$572$		0			0
$573$	−2.51764	−	0.126171i	−0.105176	−	0.00527086i
$574$		0			0
$575$	7.23255	+	12.5272i	0.301618	+	0.522418i
$576$		0			0
$577$	15.0441			0.626294			0.313147	−	0.949705i	$-0.398617\pi$
$577$	15.0441			0.626294			0.313147	+	0.949705i	$0.398617\pi$
$578$		0			0
$579$	−8.15478	−	15.9146i	−0.338901	−	0.661387i
$580$		0			0
$581$	−15.5999			−0.647193
$582$		0			0
$583$	−39.1935			−1.62323
$584$		0			0
$585$	−2.15538	+	17.7561i	−0.0891141	+	0.734125i
$586$		0			0
$587$	−38.8994			−1.60555			−0.802776	−	0.596281i	$-0.796644\pi$
$587$	−38.8994			−1.60555			−0.802776	+	0.596281i	$0.796644\pi$
$588$		0			0
$589$	−13.8705			−0.571526
$590$		0			0
$591$	−17.5062	−	0.877319i	−0.720109	−	0.0360881i
$592$		0			0
$593$	32.3325			1.32774			0.663868	−	0.747850i	$-0.268914\pi$
$593$	32.3325			1.32774			0.663868	+	0.747850i	$0.268914\pi$
$594$		0			0
$595$	−5.70452	−	9.88052i	−0.233863	−	0.405062i
$596$		0			0
$597$	−5.42814	−	10.5934i	−0.222159	−	0.433557i
$598$		0			0
$599$	6.65728	+	11.5307i	0.272009	+	0.471133i	0.969376	−	0.245581i	$-0.0789786\pi$
$599$	6.65728	+	11.5307i	0.272009	+	0.471133i	−0.697367	+	0.716714i	$0.745645\pi$
$600$		0			0
$601$	31.4231			1.28178			0.640888	−	0.767634i	$-0.278566\pi$
$601$	31.4231			1.28178			0.640888	+	0.767634i	$0.278566\pi$
$602$		0			0
$603$	37.3133	+	3.74931i	1.51952	+	0.152684i
$604$		0			0
$605$	11.6328	+	20.1486i	0.472940	+	0.819157i
$606$		0			0
$607$	−24.1958			−0.982076			−0.491038	−	0.871138i	$-0.663382\pi$
$607$	−24.1958			−0.982076			−0.491038	+	0.871138i	$0.663382\pi$
$608$		0			0
$609$	58.3520	+	2.92429i	2.36454	+	0.118498i
$610$		0			0
$611$	0.129611	−	6.27519i	0.00524350	−	0.253867i
$612$		0			0
$613$	−7.56923	−	13.1103i	−0.305718	−	0.529520i	0.671703	−	0.740821i	$-0.265563\pi$
$613$	−7.56923	−	13.1103i	−0.305718	−	0.529520i	−0.977421	+	0.211301i	$0.932230\pi$
$614$		0			0
$615$	16.7244	−	25.8827i	0.674394	−	1.04369i
$616$		0			0
$617$	−16.4824			−0.663556			−0.331778	−	0.943357i	$-0.607649\pi$
$617$	−16.4824			−0.663556			−0.331778	+	0.943357i	$0.607649\pi$
$618$		0			0
$619$	6.79563	−	11.7704i	0.273139	−	0.473091i	−0.696525	−	0.717533i	$-0.745271\pi$
$619$	6.79563	−	11.7704i	0.273139	−	0.473091i	0.969664	+	0.244442i	$0.0786046\pi$
$620$		0			0
$621$	20.7008	−	25.9251i	0.830695	−	1.04034i
$622$		0			0
$623$	7.44130	−	12.8887i	0.298129	−	0.516375i
$624$		0			0
$625$	4.26955	+	7.39507i	0.170782	+	0.295803i
$626$		0			0
$627$	−5.72913	−	11.1808i	−0.228800	−	0.446517i
$628$		0			0
$629$	−3.39000			−0.135168
$630$		0			0
$631$	−5.94680	+	10.3002i	−0.236738	+	0.410043i	−0.959776	−	0.280765i	$-0.909412\pi$
$631$	−5.94680	+	10.3002i	−0.236738	+	0.410043i	0.723038	+	0.690808i	$0.242745\pi$
$632$		0			0
$633$	13.6704	+	26.6787i	0.543350	+	1.06038i
$634$		0			0
$635$	8.14995	−	14.1161i	0.323421	−	0.560182i
$636$		0			0
$637$	0.396034	−	19.1742i	0.0156915	−	0.759710i
$638$		0			0
$639$	20.9035	+	2.10042i	0.826931	+	0.0830915i
$640$		0			0
$641$	−4.02473	−	6.97104i	−0.158967	−	0.275340i	0.775529	−	0.631312i	$-0.217483\pi$
$641$	−4.02473	−	6.97104i	−0.158967	−	0.275340i	−0.934497	+	0.355972i	$0.884150\pi$
$642$		0			0
$643$	−22.8273			−0.900220			−0.450110	−	0.892973i	$-0.648615\pi$
$643$	−22.8273			−0.900220			−0.450110	+	0.892973i	$0.648615\pi$
$644$		0			0
$645$	−16.0256	−	31.2750i	−0.631007	−	1.23145i
$646$		0			0
$647$	3.91414	+	6.77949i	0.153881	+	0.266529i	0.932651	−	0.360780i	$-0.117490\pi$
$647$	3.91414	+	6.77949i	0.153881	+	0.266529i	−0.778770	+	0.627309i	$0.784156\pi$
$648$		0			0
$649$	14.8624			0.583402
$650$		0			0
$651$	−26.5443	−	51.8028i	−1.04035	−	2.03031i
$652$		0			0
$653$	−8.13086	+	14.0831i	−0.318185	+	0.551113i	−0.980109	−	0.198458i	$-0.936407\pi$
$653$	−8.13086	+	14.0831i	−0.318185	+	0.551113i	0.661924	+	0.749571i	$0.269740\pi$
$654$		0			0
$655$	4.09845	−	7.09873i	0.160140	−	0.277370i
$656$		0			0
$657$	−2.74857	−	6.09817i	−0.107232	−	0.237912i
$658$		0			0
$659$	13.6404	+	23.6259i	0.531355	+	0.920334i	0.999330	+	0.0365923i	$0.0116503\pi$
$659$	13.6404	+	23.6259i	0.531355	+	0.920334i	−0.467975	+	0.883742i	$0.655016\pi$
$660$		0			0
$661$	−0.279409	+	0.483951i	−0.0108678	+	0.0188235i	−0.871408	−	0.490559i	$-0.836793\pi$
$661$	−0.279409	+	0.483951i	−0.0108678	+	0.0188235i	0.860540	+	0.509382i	$0.170126\pi$
$662$		0			0
$663$	−10.1711	−	6.87398i	−0.395012	−	0.266963i
$664$		0			0
$665$	4.20392	+	7.28141i	0.163021	+	0.282361i
$666$		0			0
$667$	−30.6803	+	53.1398i	−1.18795	+	2.05758i
$668$		0			0
$669$	21.2876	−	32.9447i	0.823025	−	1.27372i
$670$		0			0
$671$	−11.9666	−	20.7267i	−0.461964	−	0.800145i
$672$		0			0
$673$	−17.1310			−0.660352			−0.330176	−	0.943919i	$-0.607108\pi$
$673$	−17.1310			−0.660352			−0.330176	+	0.943919i	$0.607108\pi$
$674$		0			0
$675$	−7.34565	+	9.19948i	−0.282734	+	0.354088i
$676$		0			0
$677$	−21.0208	+	36.4091i	−0.807896	+	1.39932i	0.106423	+	0.994321i	$0.466060\pi$
$677$	−21.0208	+	36.4091i	−0.807896	+	1.39932i	−0.914319	+	0.404996i	$0.867273\pi$
$678$		0			0
$679$	8.38512	−	14.5235i	0.321791	−	0.557359i
$680$		0			0
$681$	−26.8408	−	1.34512i	−1.02854	−	0.0515451i
$682$		0			0
$683$	10.4554	−	18.1093i	0.400065	−	0.692933i	−0.593668	−	0.804710i	$-0.702321\pi$
$683$	10.4554	−	18.1093i	0.400065	−	0.692933i	0.993733	+	0.111777i	$0.0356542\pi$
$684$		0			0
$685$	0.0101669	−	0.0176095i	0.000388456	−	0.000672825i
$686$		0			0
$687$	11.5552	+	0.579084i	0.440857	+	0.0220934i
$688$		0			0
$689$	24.7285	−	13.6040i	0.942082	−	0.518273i
$690$		0			0
$691$	23.7611			0.903914			0.451957	−	0.892040i	$-0.350726\pi$
$691$	23.7611			0.903914			0.451957	+	0.892040i	$0.350726\pi$
$692$		0			0
$693$	30.7933	−	42.7936i	1.16974	−	1.62559i
$694$		0			0
$695$	−0.867164	−	1.50197i	−0.0328934	−	0.0569731i
$696$		0			0
$697$	10.5750	+	18.3165i	0.400558	+	0.693787i
$698$		0			0
$699$	−14.1232	+	21.8571i	−0.534189	+	0.826712i
$700$		0			0
$701$	30.8413			1.16486			0.582429	−	0.812881i	$-0.302102\pi$
$701$	30.8413			1.16486			0.582429	+	0.812881i	$0.302102\pi$
$702$		0			0
$703$	2.49824			0.0942231
$704$		0			0
$705$	−2.70592	+	4.18769i	−0.101911	+	0.157717i
$706$		0			0
$707$	8.14969	+	14.1157i	0.306501	+	0.530875i
$708$		0			0
$709$	−5.50757	−	9.53938i	−0.206841	−	0.358259i	0.743877	−	0.668317i	$-0.232985\pi$
$709$	−5.50757	−	9.53938i	−0.206841	−	0.358259i	−0.950718	+	0.310058i	$0.899652\pi$
$710$		0			0
$711$	50.7194	+	5.09637i	1.90213	+	0.191129i
$712$		0			0
$713$	61.1320			2.28941
$714$		0			0
$715$	−25.5391	−	15.4568i	−0.955107	−	0.578052i
$716$		0			0
$717$	14.7400	+	0.738689i	0.550474	+	0.0275868i
$718$		0			0
$719$	−18.1480	+	31.4332i	−0.676805	+	1.17226i	0.299133	+	0.954212i	$0.403303\pi$
$719$	−18.1480	+	31.4332i	−0.676805	+	1.17226i	−0.975938	+	0.218049i	$0.930031\pi$
$720$		0			0
$721$	12.1977	−	21.1270i	0.454265	−	0.786811i
$722$		0			0
$723$	31.7217	+	1.58972i	1.17974	+	0.0591225i
$724$		0			0
$725$	10.8869	−	18.8566i	0.404328	−	0.700317i
$726$		0			0
$727$	20.2911	−	35.1452i	0.752556	−	1.30346i	−0.194025	−	0.980997i	$-0.562154\pi$
$727$	20.2911	−	35.1452i	0.752556	−	1.30346i	0.946580	−	0.322468i	$-0.104512\pi$
$728$		0			0
$729$	25.7906	+	7.99031i	0.955207	+	0.295937i
$730$		0			0
$731$	24.1190			0.892074
$732$		0			0
$733$	18.4885	+	32.0230i	0.682888	+	1.18280i	0.974095	+	0.226137i	$0.0726098\pi$
$733$	18.4885	+	32.0230i	0.682888	+	1.18280i	−0.291207	+	0.956660i	$0.594057\pi$
$734$		0			0
$735$	−8.26810	+	12.7957i	−0.304974	+	0.471978i
$736$		0			0
$737$	−31.2945	+	54.2037i	−1.15275	+	1.99662i
$738$		0			0
$739$	10.1289	+	17.5438i	0.372598	+	0.645359i	0.989964	−	0.141317i	$-0.0451337\pi$
$739$	10.1289	+	17.5438i	0.372598	+	0.645359i	−0.617366	+	0.786676i	$0.711800\pi$
$740$		0			0
$741$	7.49554	+	5.06575i	0.275356	+	0.186095i
$742$		0			0
$743$	22.1214	−	38.3154i	0.811555	−	1.40565i	−0.100220	−	0.994965i	$-0.531955\pi$
$743$	22.1214	−	38.3154i	0.811555	−	1.40565i	0.911775	−	0.410689i	$-0.134712\pi$
$744$		0			0
$745$	−14.0188	−	24.2813i	−0.513609	−	0.889597i
$746$		0			0
$747$	13.2670	+	1.33309i	0.485413	+	0.0487752i
$748$		0			0
$749$	−14.2267	+	24.6414i	−0.519833	+	0.900378i
$750$		0			0
$751$	5.14141	−	8.90518i	0.187613	−	0.324955i	−0.756841	−	0.653599i	$-0.773258\pi$
$751$	5.14141	−	8.90518i	0.187613	−	0.324955i	0.944454	+	0.328644i	$0.106592\pi$
$752$		0			0
$753$	9.13931	+	17.8359i	0.333055	+	0.649978i
$754$		0			0
$755$	13.6319			0.496115
$756$		0			0
$757$	−1.24016	−	2.14801i	−0.0450743	−	0.0780709i	0.842608	−	0.538527i	$-0.181019\pi$
$757$	−1.24016	−	2.14801i	−0.0450743	−	0.0780709i	−0.887682	+	0.460456i	$0.847686\pi$
$758$		0			0
$759$	25.2502	+	49.2773i	0.916523	+	1.78865i
$760$		0			0
$761$	−16.1632			−0.585917			−0.292958	−	0.956125i	$-0.594640\pi$
$761$	−16.1632			−0.585917			−0.292958	+	0.956125i	$0.594640\pi$
$762$		0			0
$763$	−16.8039	−	29.1052i	−0.608342	−	1.05368i
$764$		0			0
$765$	4.00709	+	8.89040i	0.144877	+	0.321433i
$766$		0			0
$767$	−9.37722	+	5.15874i	−0.338592	+	0.186271i
$768$		0			0
$769$	−6.67875	+	11.5679i	−0.240842	+	0.417151i	−0.960954	−	0.276707i	$-0.910757\pi$
$769$	−6.67875	+	11.5679i	−0.240842	+	0.417151i	0.720112	+	0.693857i	$0.244090\pi$
$770$		0			0
$771$	4.43043	+	8.64626i	0.159558	+	0.311387i
$772$		0			0
$773$	−0.835057	+	1.44636i	−0.0300349	+	0.0520220i	−0.880652	−	0.473763i	$-0.842895\pi$
$773$	−0.835057	+	1.44636i	−0.0300349	+	0.0520220i	0.850617	+	0.525785i	$0.176229\pi$
$774$		0			0
$775$	−21.6926			−0.779222
$776$		0			0
$777$	4.78093	+	9.33028i	0.171515	+	0.334722i
$778$		0			0
$779$	−7.79323	−	13.4983i	−0.279221	−	0.483626i
$780$		0			0
$781$	−17.5317	+	30.3658i	−0.627333	+	1.08657i
$782$		0			0
$783$	−49.3758	−	7.47345i	−1.76455	−	0.267079i
$784$		0			0
$785$	−1.09221	+	1.89176i	−0.0389825	+	0.0675197i
$786$		0			0
$787$	38.8003			1.38308			0.691540	−	0.722338i	$-0.256933\pi$
$787$	38.8003			1.38308			0.691540	+	0.722338i	$0.256933\pi$
$788$		0			0
$789$	20.9676	−	32.4495i	0.746467	−	1.15523i
$790$		0			0
$791$	16.0474	+	27.7949i	0.570580	+	0.988273i
$792$		0			0
$793$	14.7443	+	8.92359i	0.523587	+	0.316886i
$794$		0			0
$795$	−22.3917	−	1.12215i	−0.794153	−	0.0397987i
$796$		0			0
$797$	−50.8826			−1.80235			−0.901177	−	0.433452i	$-0.857295\pi$
$797$	−50.8826			−1.80235			−0.901177	+	0.433452i	$0.857295\pi$
$798$		0			0
$799$	−1.71098	−	2.96351i	−0.0605302	−	0.104841i
$800$		0			0
$801$	−7.42988	+	10.3253i	−0.262522	+	0.364828i
$802$		0			0
$803$	11.1638			0.393962
$804$		0			0
$805$	−18.5281	−	32.0916i	−0.653029	−	1.13108i
$806$		0			0
$807$	−10.2605	−	20.0239i	−0.361185	−	0.704876i
$808$		0			0
$809$	4.23379	+	7.33314i	0.148852	+	0.257820i	0.930804	−	0.365520i	$-0.119109\pi$
$809$	4.23379	+	7.33314i	0.148852	+	0.257820i	−0.781951	+	0.623340i	$0.785775\pi$
$810$		0			0
$811$	4.41113			0.154896			0.0774479	−	0.996996i	$-0.475323\pi$
$811$	4.41113			0.154896			0.0774479	+	0.996996i	$0.475323\pi$
$812$		0			0
$813$	−47.0230	−	2.35654i	−1.64917	−	0.0826476i
$814$		0			0
$815$	−15.3286			−0.536938
$816$		0			0
$817$	−17.7744			−0.621848
$818$		0			0
$819$	−4.57491	+	37.6883i	−0.159860	+	1.31693i
$820$		0			0
$821$	23.6244			0.824498			0.412249	−	0.911071i	$-0.364743\pi$
$821$	23.6244			0.824498			0.412249	+	0.911071i	$0.364743\pi$
$822$		0			0
$823$	−24.9167			−0.868543			−0.434271	−	0.900782i	$-0.642994\pi$
$823$	−24.9167			−0.868543			−0.434271	+	0.900782i	$0.642994\pi$
$824$		0			0
$825$	−8.95999	−	17.4860i	−0.311947	−	0.608784i
$826$		0			0
$827$	3.01028			0.104678			0.0523389	−	0.998629i	$-0.483332\pi$
$827$	3.01028			0.104678			0.0523389	+	0.998629i	$0.483332\pi$
$828$		0			0
$829$	−3.60061	−	6.23644i	−0.125054	−	0.216601i	0.796700	−	0.604375i	$-0.206577\pi$
$829$	−3.60061	−	6.23644i	−0.125054	−	0.216601i	−0.921754	+	0.387775i	$0.873244\pi$
$830$		0			0
$831$	−0.382102	−	0.0191489i	−0.0132550	−	0.000664268i
$832$		0			0
$833$	−5.22801	−	9.05519i	−0.181140	−	0.313744i
$834$		0			0
$835$	16.5579			0.573008
$836$		0			0
$837$	18.1478	+	46.3242i	0.627281	+	1.60120i
$838$		0			0
$839$	21.5124	+	37.2606i	0.742690	+	1.28638i	0.951266	+	0.308371i	$0.0997839\pi$
$839$	21.5124	+	37.2606i	0.742690	+	1.28638i	−0.208576	+	0.978006i	$0.566883\pi$
$840$		0			0
$841$	63.3636			2.18495
$842$		0			0
$843$	−14.8966	−	29.0716i	−0.513065	−	1.00128i
$844$		0			0
$845$	21.4785	+	0.887635i	0.738883	+	0.0305356i
$846$		0			0
$847$	24.6912	+	42.7664i	0.848400	+	1.46947i
$848$		0			0
$849$	1.16796	+	2.27935i	0.0400844	+	0.0782272i
$850$		0			0
$851$	−11.0106			−0.377438
$852$		0			0
$853$	−4.75065	+	8.22837i	−0.162659	+	0.281734i	−0.935822	−	0.352474i	$-0.885340\pi$
$853$	−4.75065	+	8.22837i	−0.162659	+	0.281734i	0.773162	+	0.634208i	$0.218674\pi$
$854$		0			0
$855$	−2.95300	−	6.55174i	−0.100991	−	0.224065i
$856$		0			0
$857$	−12.3253	+	21.3480i	−0.421024	+	0.729234i	−0.996040	−	0.0889077i	$-0.971662\pi$
$857$	−12.3253	+	21.3480i	−0.421024	+	0.729234i	0.575016	+	0.818142i	$0.304996\pi$
$858$		0			0
$859$	4.10381	+	7.10801i	0.140020	+	0.242522i	0.927504	−	0.373813i	$-0.121950\pi$
$859$	4.10381	+	7.10801i	0.140020	+	0.242522i	−0.787484	+	0.616335i	$0.788617\pi$
$860$		0			0
$861$	35.4984	−	54.9375i	1.20978	−	1.87226i
$862$		0			0
$863$	16.3550			0.556731			0.278366	−	0.960475i	$-0.410207\pi$
$863$	16.3550			0.556731			0.278366	+	0.960475i	$0.410207\pi$
$864$		0			0
$865$	6.95220	−	12.0416i	0.236382	−	0.409425i
$866$		0			0
$867$	22.7234	+	1.13878i	0.771727	+	0.0386749i
$868$		0			0
$869$	−42.5381	+	73.6782i	−1.44301	+	2.49936i
$870$		0			0
$871$	0.930719	−	45.0612i	0.0315362	−	1.52684i
$872$		0			0
$873$	−8.37225	+	11.6350i	−0.283358	+	0.393784i
$874$		0			0
$875$	21.0844	+	36.5193i	0.712784	+	1.23458i
$876$		0			0
$877$	−23.8414			−0.805068			−0.402534	−	0.915405i	$-0.631870\pi$
$877$	−23.8414			−0.805068			−0.402534	+	0.915405i	$0.631870\pi$
$878$		0			0
$879$	8.75727	−	13.5528i	0.295375	−	0.457124i
$880$		0			0
$881$	−16.2280	−	28.1076i	−0.546734	−	0.946971i	−0.998496	−	0.0548320i	$-0.982538\pi$
$881$	−16.2280	−	28.1076i	−0.546734	−	0.946971i	0.451762	−	0.892139i	$-0.350796\pi$
$882$		0			0
$883$	−46.3015			−1.55817			−0.779084	−	0.626920i	$-0.784315\pi$
$883$	−46.3015			−1.55817			−0.779084	+	0.626920i	$0.784315\pi$
$884$		0			0
$885$	8.49109	+	0.425528i	0.285425	+	0.0143040i
$886$		0			0
$887$	6.56726	−	11.3748i	0.220507	−	0.381929i	−0.734455	−	0.678657i	$-0.762562\pi$
$887$	6.56726	−	11.3748i	0.220507	−	0.381929i	0.954962	+	0.296728i	$0.0958955\pi$
$888$		0			0
$889$	17.2987	−	29.9622i	0.580180	−	1.00490i
$890$		0			0
$891$	−29.8452	+	33.7625i	−0.999851	+	1.13109i
$892$		0			0
$893$	1.26090	+	2.18395i	0.0421945	+	0.0730830i
$894$		0			0
$895$	−6.79113	+	11.7626i	−0.227002	+	0.393180i
$896$		0			0
$897$	−33.0353	−	22.3264i	−1.10302	−	0.745458i
$898$		0			0
$899$	−46.0098	−	79.6913i	−1.53451	−	2.65785i
$900$		0			0
$901$	7.69376	−	13.3260i	0.256316	−	0.443953i
$902$		0			0
$903$	−34.0151	−	66.3827i	−1.13195	−	2.20908i
$904$		0			0
$905$	9.06820	+	15.7066i	0.301437	+	0.522105i
$906$		0			0
$907$	−34.7907			−1.15521			−0.577603	−	0.816318i	$-0.696012\pi$
$907$	−34.7907			−1.15521			−0.577603	+	0.816318i	$0.696012\pi$
$908$		0			0
$909$	−5.72467	−	12.7012i	−0.189875	−	0.421271i
$910$		0			0
$911$	−14.7500	+	25.5478i	−0.488690	+	0.846435i	−0.999915	−	0.0130113i	$-0.995858\pi$
$911$	−14.7500	+	25.5478i	−0.488690	+	0.846435i	0.511226	+	0.859446i	$0.329192\pi$
$912$		0			0
$913$	−11.1269	+	19.2724i	−0.368248	+	0.637824i
$914$		0			0
$915$	−6.24321	−	12.1840i	−0.206394	−	0.402791i
$916$		0			0
$917$	8.69918	−	15.0674i	0.287272	−	0.497570i
$918$		0			0
$919$	−10.4757	+	18.1445i	−0.345562	+	0.598530i	−0.985456	−	0.169933i	$-0.945645\pi$
$919$	−10.4757	+	18.1445i	−0.345562	+	0.598530i	0.639894	+	0.768463i	$0.278978\pi$
$920$		0			0
$921$	−3.13262	+	4.84805i	−0.103223	+	0.159749i
$922$		0			0
$923$	0.521404	−	25.2440i	0.0171622	−	0.830918i
$924$		0			0
$925$	3.90709			0.128464
$926$		0			0
$927$	−12.1790	+	16.9252i	−0.400009	+	0.555895i
$928$		0			0
$929$	−21.6851	−	37.5598i	−0.711466	−	1.23230i	−0.964307	−	0.264788i	$-0.914698\pi$
$929$	−21.6851	−	37.5598i	−0.711466	−	1.23230i	0.252841	−	0.967508i	$-0.418635\pi$
$930$		0			0
$931$	3.85276	+	6.67318i	0.126269	+	0.218705i
$932$		0			0
$933$	14.6681	+	0.735087i	0.480212	+	0.0240657i
$934$		0			0
$935$	−16.2755			−0.532265
$936$		0			0
$937$	−19.9060			−0.650300			−0.325150	−	0.945663i	$-0.605415\pi$
$937$	−19.9060			−0.650300			−0.325150	+	0.945663i	$0.605415\pi$
$938$		0			0
$939$	−0.340550	−	0.664606i	−0.0111134	−	0.0216886i
$940$		0			0
$941$	1.29883	+	2.24964i	0.0423407	+	0.0733362i	0.886419	−	0.462884i	$-0.153185\pi$
$941$	1.29883	+	2.24964i	0.0423407	+	0.0733362i	−0.844078	+	0.536220i	$0.819852\pi$
$942$		0			0
$943$	34.3473	+	59.4913i	1.11850	+	1.93730i
$944$		0			0
$945$	18.8178	−	23.5668i	0.612143	−	0.766630i
$946$		0			0
$947$	−12.2640			−0.398527			−0.199263	−	0.979946i	$-0.563855\pi$
$947$	−12.2640			−0.398527			−0.199263	+	0.979946i	$0.563855\pi$
$948$		0			0
$949$	−7.04362	+	3.87495i	−0.228646	+	0.125786i
$950$		0			0
$951$	−4.67549	−	9.12451i	−0.151613	−	0.295883i
$952$		0			0
$953$	16.3572	−	28.3315i	0.529862	−	0.917747i	−0.469532	−	0.882916i	$-0.655577\pi$
$953$	16.3572	−	28.3315i	0.529862	−	0.917747i	0.999393	−	0.0348314i	$-0.0110894\pi$
$954$		0			0
$955$	1.20331	−	2.08420i	0.0389383	−	0.0674432i
$956$		0			0
$957$	45.2335	−	70.0035i	1.46219	−	2.26289i
$958$		0			0
$959$	0.0215797	−	0.0373771i	0.000696844	−	0.00120697i
$960$		0			0
$961$	−30.3384	+	52.5476i	−0.978658	+	1.69508i
$962$		0			0
$963$	14.2049	−	19.7406i	0.457746	−	0.636132i
$964$		0			0
$965$	17.0723			0.549577
$966$		0			0
$967$	−1.72209	−	2.98275i	−0.0553787	−	0.0959187i	0.837007	−	0.547192i	$-0.184303\pi$
$967$	−1.72209	−	2.98275i	−0.0553787	−	0.0959187i	−0.892386	+	0.451273i	$0.850970\pi$
$968$		0			0
$969$	4.92615	+	0.246873i	0.158251	+	0.00793069i
$970$		0			0
$971$	−26.3611	+	45.6588i	−0.845969	+	1.46526i	0.0388082	+	0.999247i	$0.487644\pi$
$971$	−26.3611	+	45.6588i	−0.845969	+	1.46526i	−0.884777	+	0.466014i	$0.845689\pi$
$972$		0			0
$973$	−1.84060	−	3.18801i	−0.0590070	−	0.102203i
$974$		0			0
$975$	11.7225	+	7.92251i	0.375422	+	0.253723i
$976$		0			0
$977$	9.01116	−	15.6078i	0.288293	−	0.499337i	−0.685110	−	0.728440i	$-0.740246\pi$
$977$	9.01116	−	15.6078i	0.288293	−	0.499337i	0.973402	+	0.229103i	$0.0735791\pi$
$978$		0			0
$979$	−10.6153	−	18.3863i	−0.339267	−	0.587628i
$980$		0			0
$981$	11.8037	+	26.1886i	0.376865	+	0.836138i
$982$		0			0
$983$	18.6651	−	32.3288i	0.595323	−	1.03113i	−0.398178	−	0.917308i	$-0.630358\pi$
$983$	18.6651	−	32.3288i	0.595323	−	1.03113i	0.993501	−	0.113821i	$-0.0363091\pi$
$984$		0			0
$985$	8.36715	−	14.4923i	0.266600	−	0.461764i
$986$		0			0
$987$	−5.74345	+	8.88858i	−0.182816	+	0.282927i
$988$		0			0
$989$	78.3377			2.49099
$990$		0			0
$991$	−11.9106	−	20.6298i	−0.378353	−	0.655326i	0.612470	−	0.790494i	$-0.290176\pi$
$991$	−11.9106	−	20.6298i	−0.378353	−	0.655326i	−0.990823	+	0.135168i	$0.956843\pi$
$992$		0			0
$993$	−22.5943	−	1.13231i	−0.717008	−	0.0359326i
$994$		0			0
$995$	11.3640			0.360263
$996$		0			0
$997$	−20.2639	−	35.0982i	−0.641766	−	1.11157i	−0.985038	−	0.172335i	$-0.944869\pi$
$997$	−20.2639	−	35.0982i	−0.641766	−	1.11157i	0.343273	−	0.939236i	$-0.388464\pi$
$998$		0			0
$999$	−3.26863	−	8.34352i	−0.103415	−	0.263977i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	468.2.j.a.133.10	✓	28
3.2	odd	2		1404.2.j.a.289.5		28
9.4	even	3		468.2.k.a.445.1	yes	28
9.5	odd	6		1404.2.k.a.1225.5		28
13.9	even	3		468.2.k.a.61.1	yes	28
39.35	odd	6		1404.2.k.a.1153.5		28
117.22	even	3	inner	468.2.j.a.373.10	yes	28
117.113	odd	6		1404.2.j.a.685.5		28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
468.2.j.a.133.10	✓	28	1.1	even	1	trivial
468.2.j.a.373.10	yes	28	117.22	even	3	inner
468.2.k.a.61.1	yes	28	13.9	even	3
468.2.k.a.445.1	yes	28	9.4	even	3
1404.2.j.a.289.5		28	3.2	odd	2
1404.2.j.a.685.5		28	117.113	odd	6
1404.2.k.a.1153.5		28	39.35	odd	6
1404.2.k.a.1225.5		28	9.5	odd	6

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:	\( N \)	\(=\)	\( 468 = 2^{2} \cdot 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	468.j (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.940018 - 1.45477i) q^{3} +(0.826802 + 1.43206i) q^{5} +(1.75493 + 3.03963i) q^{7} +(-1.23273 - 2.73503i) q^{9} +5.00696 q^{11} +(-3.15906 + 1.73791i) q^{13} +(2.86054 + 0.143355i) q^{15} +(-0.982875 + 1.70239i) q^{17} +(0.724325 - 1.25457i) q^{19} +(6.07163 + 0.304278i) q^{21} +(-3.19234 + 5.52930i) q^{23} +(1.13280 - 1.96206i) q^{25} +(-5.13764 - 0.777625i) q^{27} +9.61060 q^{29} +(-4.78740 - 8.29202i) q^{31} +(4.70663 - 7.28399i) q^{33} +(-2.90196 + 5.02634i) q^{35} +(0.862266 + 1.49349i) q^{37} +(-0.441306 + 6.22939i) q^{39} +(5.37964 - 9.31782i) q^{41} +(-6.13481 - 10.6258i) q^{43} +(2.89750 - 4.02668i) q^{45} +(-0.870397 + 1.50757i) q^{47} +(-2.65955 + 4.60648i) q^{49} +(1.55267 + 3.03014i) q^{51} -7.82781 q^{53} +(4.13976 + 7.17028i) q^{55} +(-1.14423 - 2.23305i) q^{57} +2.96836 q^{59} +(-2.38999 - 4.13958i) q^{61} +(6.15010 - 8.54683i) q^{63} +(-5.10071 - 3.08706i) q^{65} +(-6.25020 + 10.8257i) q^{67} +(5.04302 + 9.84177i) q^{69} +(-3.50147 + 6.06472i) q^{71} +2.22966 q^{73} +(-1.78951 - 3.49234i) q^{75} +(8.78686 + 15.2193i) q^{77} +(-8.49580 + 14.7152i) q^{79} +(-5.96074 + 6.74312i) q^{81} +(-2.22230 + 3.84913i) q^{83} -3.25057 q^{85} +(9.03413 - 13.9812i) q^{87} +(-2.12011 - 3.67214i) q^{89} +(-10.8265 - 6.55245i) q^{91} +(-16.5633 - 0.830062i) q^{93} +2.39549 q^{95} +(-2.38902 - 4.13790i) q^{97} +(-6.17224 - 13.6942i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + 2 q^{7} - 2 q^{9} + 8 q^{11} + q^{13} - 10 q^{15} - 8 q^{17} - q^{19} + 14 q^{21} - 4 q^{23} - 14 q^{25} + 26 q^{29} + 2 q^{31} + 8 q^{33} + 3 q^{35} - q^{37} - 12 q^{39} + 4 q^{41} + 2 q^{43}+ \cdots - 29 q^{99}+O(q^{100}) \) 28 * q + 2 * q^7 - 2 * q^9 + 8 * q^11 + q^13 - 10 * q^15 - 8 * q^17 - q^19 + 14 * q^21 - 4 * q^23 - 14 * q^25 + 26 * q^29 + 2 * q^31 + 8 * q^33 + 3 * q^35 - q^37 - 12 * q^39 + 4 * q^41 + 2 * q^43 + q^45 + 11 * q^47 - 12 * q^49 + 5 * q^51 + 52 * q^53 - q^57 + 16 * q^59 - 7 * q^61 - 24 * q^63 - 31 * q^65 - 7 * q^67 + 24 * q^69 - 12 * q^71 + 14 * q^73 + 16 * q^75 - 28 * q^77 + 5 * q^79 - 50 * q^81 + 9 * q^83 - 36 * q^85 - 21 * q^87 - 11 * q^89 - q^91 - 33 * q^93 - 56 * q^95 - 25 * q^97 - 29 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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