LMFDB - Embedded newform 468.2.k.a.445.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [468,2,Mod(61,468)] 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("468.61"); 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, 4])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 468 = 2^{2} \cdot 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	468.k (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			445.1
Character	$\chi$	$=$	468.445
Dual form			468.2.k.a.61.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.72988 + 0.0866924i) q^{3} +(0.826802 - 1.43206i) q^{5} -3.50986 q^{7} +(2.98497 - 0.299935i) q^{9} +(-2.50348 + 4.33615i) q^{11} +(3.08461 + 1.86687i) q^{13} +(-1.30612 + 2.54897i) q^{15} +(-0.982875 + 1.70239i) q^{17} +(0.724325 - 1.25457i) q^{19} +(6.07163 - 0.304278i) q^{21} +6.38468 q^{23} +(1.13280 + 1.96206i) q^{25} +(-5.13764 + 0.777625i) q^{27} +(-4.80530 + 8.32302i) q^{29} +(-4.78740 + 8.29202i) q^{31} +(3.95481 - 7.71806i) q^{33} +(-2.90196 + 5.02634i) q^{35} +(0.862266 + 1.49349i) q^{37} +(-5.49784 - 2.96205i) q^{39} -10.7593 q^{41} +12.2696 q^{43} +(2.03845 - 4.52265i) q^{45} +(-0.870397 - 1.50757i) q^{47} +5.31910 q^{49} +(1.55267 - 3.03014i) q^{51} -7.82781 q^{53} +(4.13976 + 7.17028i) q^{55} +(-1.14423 + 2.23305i) q^{57} +(-1.48418 - 2.57067i) q^{59} +4.77997 q^{61} +(-10.4768 + 1.05273i) q^{63} +(5.22383 - 2.87382i) q^{65} +12.5004 q^{67} +(-11.0447 + 0.553503i) q^{69} +(-3.50147 + 6.06472i) q^{71} +2.22966 q^{73} +(-2.12970 - 3.29593i) q^{75} +(8.78686 - 15.2193i) q^{77} +(-8.49580 - 14.7152i) q^{79} +(8.82008 - 1.79059i) q^{81} +(-2.22230 - 3.84913i) q^{83} +(1.62529 + 2.81508i) q^{85} +(7.59105 - 14.8144i) q^{87} +(-2.12011 - 3.67214i) q^{89} +(-10.8265 - 6.55245i) q^{91} +(7.56277 - 14.7592i) q^{93} +(-1.19775 - 2.07456i) q^{95} +4.77804 q^{97} +(-6.17224 + 13.6942i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q - 4 q^{7} - 2 q^{9} - 4 q^{11} + q^{13} - 4 q^{15} - 8 q^{17} - q^{19} + 14 q^{21} + 8 q^{23} - 14 q^{25} - 13 q^{29} + 2 q^{31} - 25 q^{33} + 3 q^{35} - q^{37} - 3 q^{39} - 8 q^{41} - 4 q^{43}+ \cdots - 29 q^{99}+O(q^{100}) $ 28 * q - 4 * q^7 - 2 * q^9 - 4 * q^11 + q^13 - 4 * q^15 - 8 * q^17 - q^19 + 14 * q^21 + 8 * q^23 - 14 * q^25 - 13 * q^29 + 2 * q^31 - 25 * q^33 + 3 * q^35 - q^37 - 3 * q^39 - 8 * q^41 - 4 * q^43 - 38 * q^45 + 11 * q^47 + 24 * q^49 + 5 * q^51 + 52 * q^53 - q^57 - 8 * q^59 + 14 * q^61 - 21 * q^63 + 38 * q^65 + 14 * q^67 - 21 * q^69 - 12 * q^71 + 14 * q^73 - 14 * q^75 - 28 * q^77 + 5 * q^79 + 10 * q^81 + 9 * q^83 + 18 * q^85 + 18 * q^87 - 11 * q^89 - q^91 - 9 * q^93 + 28 * q^95 + 50 * q^97 - 29 * q^99

Character values

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

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

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
$3$	−1.72988	+	0.0866924i	−0.998747	+	0.0500519i
$3$	−1.72988	+	0.0866924i	−0.998747	+	0.0500519i
$4$		0			0
$5$	0.826802	−	1.43206i	0.369757	−	0.640438i	−0.619770	−	0.784783i	$-0.712774\pi$
$5$	0.826802	−	1.43206i	0.369757	−	0.640438i	0.989527	+	0.144345i	$0.0461076\pi$
$6$		0			0
$7$	−3.50986			−1.32660			−0.663301	−	0.748353i	$-0.730845\pi$
$7$	−3.50986			−1.32660			−0.663301	+	0.748353i	$0.730845\pi$
$8$		0			0
$9$	2.98497	−	0.299935i	0.994990	−	0.0999783i
$10$		0			0
$11$	−2.50348	+	4.33615i	−0.754827	+	1.30740i	0.190633	+	0.981661i	$0.438946\pi$
$11$	−2.50348	+	4.33615i	−0.754827	+	1.30740i	−0.945460	+	0.325738i	$0.894387\pi$
$12$		0			0
$13$	3.08461	+	1.86687i	0.855516	+	0.517777i
$13$	3.08461	+	1.86687i	0.855516	+	0.517777i
$14$		0			0
$15$	−1.30612	+	2.54897i	−0.337238	+	0.658142i
$16$		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
$23$	6.38468			1.33130			0.665649	−	0.746265i	$-0.268155\pi$
$23$	6.38468			1.33130			0.665649	+	0.746265i	$0.268155\pi$
$24$		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
$29$	−4.80530	+	8.32302i	−0.892322	+	1.54555i	−0.0552368	+	0.998473i	$0.517591\pi$
$29$	−4.80530	+	8.32302i	−0.892322	+	1.54555i	−0.837085	+	0.547073i	$0.815742\pi$
$30$		0			0
$31$	−4.78740	+	8.29202i	−0.859842	+	1.48929i	0.0122364	+	0.999925i	$0.496105\pi$
$31$	−4.78740	+	8.29202i	−0.859842	+	1.48929i	−0.872079	+	0.489365i	$0.837228\pi$
$32$		0			0
$33$	3.95481	−	7.71806i	0.688443	−	1.34354i
$34$		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
$39$	−5.49784	−	2.96205i	−0.880359	−	0.474308i
$40$		0			0
$41$	−10.7593			−1.68032			−0.840159	−	0.542340i	$-0.817539\pi$
$41$	−10.7593			−1.68032			−0.840159	+	0.542340i	$0.817539\pi$
$42$		0			0
$43$	12.2696			1.87110			0.935551	−	0.353193i	$-0.114904\pi$
$43$	12.2696			1.87110			0.935551	+	0.353193i	$0.114904\pi$
$44$		0			0
$45$	2.03845	−	4.52265i	0.303874	−	0.674197i
$46$		0			0
$47$	−0.870397	−	1.50757i	−0.126960	−	0.219902i	0.795537	−	0.605905i	$-0.207189\pi$
$47$	−0.870397	−	1.50757i	−0.126960	−	0.219902i	−0.922498	+	0.386003i	$0.873855\pi$
$48$		0			0
$49$	5.31910			0.759872
$50$		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
$59$	−1.48418	−	2.57067i	−0.193224	−	0.334673i	0.753093	−	0.657914i	$-0.228561\pi$
$59$	−1.48418	−	2.57067i	−0.193224	−	0.334673i	−0.946317	+	0.323241i	$0.895228\pi$
$60$		0			0
$61$	4.77997			0.612013			0.306006	−	0.952029i	$-0.401007\pi$
$61$	4.77997			0.612013			0.306006	+	0.952029i	$0.401007\pi$
$62$		0			0
$63$	−10.4768	+	1.05273i	−1.31995	+	0.132631i
$64$		0			0
$65$	5.22383	−	2.87382i	0.647937	−	0.356453i
$66$		0			0
$67$	12.5004			1.52717			0.763584	−	0.645709i	$-0.223438\pi$
$67$	12.5004			1.52717			0.763584	+	0.645709i	$0.223438\pi$
$68$		0			0
$69$	−11.0447	+	0.553503i	−1.32963	+	0.0666340i
$70$		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
$75$	−2.12970	−	3.29593i	−0.245917	−	0.380581i
$76$		0			0
$77$	8.78686	−	15.2193i	1.00136	−	1.73440i
$78$		0			0
$79$	−8.49580	−	14.7152i	−0.955852	−	1.65558i	−0.732406	−	0.680869i	$-0.761602\pi$
$79$	−8.49580	−	14.7152i	−0.955852	−	1.65558i	−0.223447	−	0.974716i	$-0.571731\pi$
$80$		0			0
$81$	8.82008	−	1.79059i	0.980009	−	0.198955i
$82$		0			0
$83$	−2.22230	−	3.84913i	−0.243929	−	0.422497i	0.717901	−	0.696145i	$-0.245103\pi$
$83$	−2.22230	−	3.84913i	−0.243929	−	0.422497i	−0.961830	+	0.273648i	$0.911770\pi$
$84$		0			0
$85$	1.62529	+	2.81508i	0.176287	+	0.305338i
$86$		0			0
$87$	7.59105	−	14.8144i	0.813846	−	1.58827i
$88$		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
$93$	7.56277	−	14.7592i	0.784223	−	1.53046i
$94$		0			0
$95$	−1.19775	−	2.07456i	−0.122886	−	0.212845i
$96$		0			0
$97$	4.77804			0.485137			0.242568	−	0.970134i	$-0.422010\pi$
$97$	4.77804			0.485137			0.242568	+	0.970134i	$0.422010\pi$
$98$		0			0
$99$	−6.17224	+	13.6942i	−0.620334	+	1.37632i
$100$		0			0
$101$	−2.32194	+	4.02172i	−0.231042	+	0.400176i	−0.958115	−	0.286384i	$-0.907547\pi$
$101$	−2.32194	+	4.02172i	−0.231042	+	0.400176i	0.727073	+	0.686560i	$0.240880\pi$
$102$		0			0
$103$	−3.47526	+	6.01933i	−0.342428	+	0.593102i	−0.984883	−	0.173221i	$-0.944583\pi$
$103$	−3.47526	+	6.01933i	−0.342428	+	0.593102i	0.642455	+	0.766323i	$0.277916\pi$
$104$		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
$111$	−1.62109	−	2.50880i	−0.153867	−	0.238125i
$112$		0			0
$113$	−4.57209	−	7.91910i	−0.430106	−	0.744966i	0.566776	−	0.823872i	$-0.308191\pi$
$113$	−4.57209	−	7.91910i	−0.430106	−	0.744966i	−0.996882	+	0.0789062i	$0.974857\pi$
$114$		0			0
$115$	5.27886	−	9.14326i	0.492257	−	0.852614i
$116$		0			0
$117$	9.76739	+	4.64737i	0.902996	+	0.429650i
$118$		0			0
$119$	3.44975	−	5.97515i	0.316238	−	0.547741i
$120$		0			0
$121$	−7.03482	−	12.1847i	−0.639529	−	1.10770i
$122$		0			0
$123$	18.6123	−	0.932749i	1.67821	−	0.0841031i
$124$		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	−0.953750	−	0.300600i	$-0.902813\pi$
$131$	−2.47850	+	4.29289i	−0.216547	+	0.375071i	0.737203	+	0.675672i	$0.236146\pi$
$132$		0			0
$133$	−2.54228	+	4.40336i	−0.220444	+	0.381819i
$134$		0			0
$135$	−3.13420	+	8.00036i	−0.269749	+	0.688561i
$136$		0			0
$137$	0.0122966			0.00105057			0.000525285	−	1.00000i	$-0.499833\pi$
$137$	0.0122966			0.00105057			0.000525285		1.00000i	$0.499833\pi$
$138$		0			0
$139$	0.524409	+	0.908303i	0.0444798	+	0.0770412i	0.887408	−	0.460985i	$-0.152504\pi$
$139$	0.524409	+	0.908303i	0.0444798	+	0.0770412i	−0.842928	+	0.538026i	$0.819170\pi$
$140$		0			0
$141$	1.63638	+	2.53246i	0.137808	+	0.213272i
$142$		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
$147$	−9.20141	+	0.461126i	−0.758920	+	0.0380330i
$148$		0			0
$149$	8.47773	+	14.6839i	0.694523	+	1.20295i	0.970341	+	0.241739i	$0.0777178\pi$
$149$	8.47773	+	14.6839i	0.694523	+	1.20295i	−0.275818	+	0.961210i	$0.588949\pi$
$150$		0			0
$151$	4.12187	+	7.13929i	0.335433	+	0.580987i	0.983568	−	0.180538i	$-0.0577840\pi$
$151$	4.12187	+	7.13929i	0.335433	+	0.580987i	−0.648135	+	0.761526i	$0.724451\pi$
$152$		0			0
$153$	−2.42325	+	5.37638i	−0.195908	+	0.434654i
$154$		0			0
$155$	7.91646	+	13.7117i	0.635865	+	1.10135i
$156$		0			0
$157$	0.660501	−	1.14402i	0.0527137	−	0.0913028i	−0.838464	−	0.544956i	$-0.816546\pi$
$157$	0.660501	−	1.14402i	0.0527137	−	0.0913028i	0.891178	+	0.453653i	$0.149880\pi$
$158$		0			0
$159$	13.5412	−	0.678612i	1.07388	−	0.0538174i
$160$		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
$165$	−7.78290	−	12.0448i	−0.605898	−	0.937689i
$166$		0			0
$167$	−10.0132			−0.774844			−0.387422	−	0.921902i	$-0.626634\pi$
$167$	−10.0132			−0.774844			−0.387422	+	0.921902i	$0.626634\pi$
$168$		0			0
$169$	6.02958	+	11.5171i	0.463814	+	0.885933i
$170$		0			0
$171$	1.78580	−	3.96210i	0.136564	−	0.302989i
$172$		0			0
$173$	8.40854			0.639290			0.319645	−	0.947537i	$-0.396436\pi$
$173$	8.40854			0.639290			0.319645	+	0.947537i	$0.396436\pi$
$174$		0			0
$175$	−3.97596	−	6.88657i	−0.300554	−	0.520575i
$176$		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
$185$	2.85169			0.209661
$186$		0			0
$187$	−4.92121	−	8.52379i	−0.359875	−	0.623321i
$188$		0			0
$189$	18.0324	−	2.72935i	1.31166	−	0.198531i
$190$		0			0
$191$	1.45538			0.105308			0.0526540	−	0.998613i	$-0.483232\pi$
$191$	1.45538			0.105308			0.0526540	+	0.998613i	$0.483232\pi$
$192$		0			0
$193$	−10.3243			−0.743160			−0.371580	−	0.928401i	$-0.621184\pi$
$193$	−10.3243			−0.743160			−0.371580	+	0.928401i	$0.621184\pi$
$194$		0			0
$195$	−8.78747	+	5.42422i	−0.629284	+	0.388437i
$196$		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
$201$	−21.6242	+	1.08369i	−1.52525	+	0.0764376i
$202$		0			0
$203$	16.8659	−	29.2126i	1.18376	−	2.05032i
$204$		0			0
$205$	−8.89580	+	15.4080i	−0.621310	+	1.07614i
$206$		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
$211$	17.3073			1.19149			0.595743	−	0.803175i	$-0.296858\pi$
$211$	17.3073			1.19149			0.595743	+	0.803175i	$0.296858\pi$
$212$		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
$219$	−3.85704	+	0.193294i	−0.260635	+	0.0130616i
$220$		0			0
$221$	−6.20992	+	3.41630i	−0.417725	+	0.229805i
$222$		0			0
$223$	−11.3230	+	19.6120i	−0.758242	+	1.31331i	0.185505	+	0.982643i	$0.440608\pi$
$223$	−11.3230	+	19.6120i	−0.758242	+	1.31331i	−0.943746	+	0.330670i	$0.892725\pi$
$224$		0			0
$225$	3.96986	+	5.51693i	0.264657	+	0.367796i
$226$		0			0
$227$	15.5160			1.02983			0.514917	−	0.857240i	$-0.327823\pi$
$227$	15.5160			1.02983			0.514917	+	0.857240i	$0.327823\pi$
$228$		0			0
$229$	3.33988	−	5.78483i	0.220705	−	0.382273i	−0.734317	−	0.678807i	$-0.762497\pi$
$229$	3.33988	−	5.78483i	0.220705	−	0.382273i	0.955022	+	0.296534i	$0.0958308\pi$
$230$		0			0
$231$	−13.8808	+	27.0893i	−0.913290	+	1.78234i
$232$		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
$237$	15.9724	+	24.7189i	1.03752	+	1.60567i
$238$		0			0
$239$	4.26040	−	7.37923i	0.275582	−	0.477323i	−0.694700	−	0.719300i	$-0.744463\pi$
$239$	4.26040	−	7.37923i	0.275582	−	0.477323i	0.970282	+	0.241977i	$0.0777960\pi$
$240$		0			0
$241$	−18.3375			−1.18122			−0.590612	−	0.806956i	$-0.701114\pi$
$241$	−18.3375			−1.18122			−0.590612	+	0.806956i	$0.701114\pi$
$242$		0			0
$243$	−15.1024	+	3.86214i	−0.968822	+	0.247757i
$244$		0			0
$245$	4.39784	−	7.61729i	0.280968	−	0.486651i
$246$		0			0
$247$	4.57638	−	2.51763i	0.291188	−	0.160193i
$248$		0			0
$249$	4.17800	+	6.46588i	0.264770	+	0.409758i
$250$		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
$257$	5.60911			0.349887			0.174943	−	0.984578i	$-0.444026\pi$
$257$	5.60911			0.349887			0.174943	+	0.984578i	$0.444026\pi$
$258$		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
$263$	−11.1528	+	19.3172i	−0.687710	+	1.19115i	0.284867	+	0.958567i	$0.408051\pi$
$263$	−11.1528	+	19.3172i	−0.687710	+	1.19115i	−0.972577	+	0.232581i	$0.925283\pi$
$264$		0			0
$265$	−6.47205	+	11.2099i	−0.397575	+	0.688619i
$266$		0			0
$267$	3.98589	+	6.16857i	0.243932	+	0.377510i
$268$		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
$273$	19.2966	+	10.3964i	1.16789	+	0.629218i
$274$		0			0
$275$	−11.3437			−0.684054
$276$		0			0
$277$	0.220883			0.0132716			0.00663580	−	0.999978i	$-0.497888\pi$
$277$	0.220883			0.0132716			0.00663580	+	0.999978i	$0.497888\pi$
$278$		0			0
$279$	−11.8032	+	26.1873i	−0.706637	+	1.56779i
$280$		0			0
$281$	9.42986	+	16.3330i	0.562538	+	0.974345i	0.997274	+	0.0737867i	$0.0235084\pi$
$281$	9.42986	+	16.3330i	0.562538	+	0.974345i	−0.434736	+	0.900558i	$0.643158\pi$
$282$		0			0
$283$	1.47869			0.0878991			0.0439495	−	0.999034i	$-0.486006\pi$
$283$	1.47869			0.0878991			0.0439495	+	0.999034i	$0.486006\pi$
$284$		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
$293$	−4.65804	−	8.06795i	−0.272125	−	0.471335i	0.697281	−	0.716798i	$-0.254393\pi$
$293$	−4.65804	−	8.06795i	−0.272125	−	0.471335i	−0.969406	+	0.245463i	$0.921060\pi$
$294$		0			0
$295$	−4.90848			−0.285783
$296$		0			0
$297$	9.49006	−	24.2243i	0.550669	−	1.40564i
$298$		0			0
$299$	19.6942	+	11.9194i	1.13895	+	0.689315i
$300$		0			0
$301$	−43.0647			−2.48221
$302$		0			0
$303$	3.66803	−	7.15839i	0.210723	−	0.411239i
$304$		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
$309$	5.48996	−	10.7140i	0.312313	−	0.609498i
$310$		0			0
$311$	4.23963	−	7.34325i	0.240407	−	0.416398i	−0.720423	−	0.693535i	$-0.756052\pi$
$311$	4.23963	−	7.34325i	0.240407	−	0.416398i	0.960830	+	0.277137i	$0.0893857\pi$
$312$		0			0
$313$	0.215576	+	0.373388i	0.0121851	+	0.0211052i	0.872054	−	0.489410i	$-0.162788\pi$
$313$	0.215576	+	0.373388i	0.0121851	+	0.0211052i	−0.859869	+	0.510515i	$0.829455\pi$
$314$		0			0
$315$	−7.15468	+	15.8739i	−0.403120	+	0.894390i
$316$		0			0
$317$	2.95969	+	5.12633i	0.166233	+	0.287923i	0.937092	−	0.349082i	$-0.113506\pi$
$317$	2.95969	+	5.12633i	0.166233	+	0.287923i	−0.770860	+	0.637005i	$0.780173\pi$
$318$		0			0
$319$	−24.0599	−	41.6730i	−1.34710	−	2.33324i
$320$		0			0
$321$	−7.62046	−	11.7934i	−0.425333	−	0.658246i
$322$		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
$327$	16.5641	−	0.830103i	0.915994	−	0.0459048i
$328$		0			0
$329$	3.05497	+	5.29137i	0.168426	+	0.291722i
$330$		0			0
$331$	13.0612			0.717908			0.358954	−	0.933355i	$-0.383134\pi$
$331$	13.0612			0.717908			0.358954	+	0.933355i	$0.383134\pi$
$332$		0			0
$333$	3.02179	+	4.19939i	0.165593	+	0.230125i
$334$		0			0
$335$	10.3354	−	17.9014i	0.564681	−	0.978056i
$336$		0			0
$337$	11.3051	−	19.5811i	0.615831	−	1.06665i	−0.374408	−	0.927264i	$-0.622154\pi$
$337$	11.3051	−	19.5811i	0.615831	−	1.06665i	0.990238	−	0.139386i	$-0.0445128\pi$
$338$		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
$345$	−8.33915	+	16.2744i	−0.448965	+	0.876183i
$346$		0			0
$347$	15.9399	+	27.6087i	0.855699	+	1.48211i	0.875995	+	0.482320i	$0.160206\pi$
$347$	15.9399	+	27.6087i	0.855699	+	1.48211i	−0.0202963	+	0.999794i	$0.506461\pi$
$348$		0			0
$349$	5.20670	−	9.01828i	0.278708	−	0.482737i	−0.692356	−	0.721556i	$-0.743427\pi$
$349$	5.20670	−	9.01828i	0.278708	−	0.482737i	0.971064	+	0.238819i	$0.0767603\pi$
$350$		0			0
$351$	−17.2993	−	7.19264i	−0.923369	−	0.383915i
$352$		0			0
$353$	7.36243	−	12.7521i	0.391863	−	0.678726i	−0.600832	−	0.799375i	$-0.705164\pi$
$353$	7.36243	−	12.7521i	0.391863	−	0.678726i	0.992695	+	0.120649i	$0.0384974\pi$
$354$		0			0
$355$	5.79003	+	10.0286i	0.307303	+	0.532265i
$356$		0			0
$357$	−5.44966	+	10.6354i	−0.288426	+	0.562882i
$358$		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
$367$	6.55553	−	11.3545i	0.342196	−	0.592701i	−0.642644	−	0.766165i	$-0.722163\pi$
$367$	6.55553	−	11.3545i	0.342196	−	0.592701i	0.984840	+	0.173464i	$0.0554960\pi$
$368$		0			0
$369$	−32.1161	+	3.22709i	−1.67190	+	0.167995i
$370$		0			0
$371$	27.4745			1.42641
$372$		0			0
$373$	11.5830	+	20.0623i	0.599744	+	1.03879i	0.992859	+	0.119297i	$0.0380642\pi$
$373$	11.5830	+	20.0623i	0.599744	+	1.03879i	−0.393115	+	0.919489i	$0.628602\pi$
$374$		0			0
$375$	−20.7835	+	1.04156i	−1.07325	+	0.0537858i
$376$		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
$381$	9.26595	+	14.3400i	0.474709	+	0.734660i
$382$		0			0
$383$	−18.3035	−	31.7027i	−0.935267	−	1.61993i	−0.774156	−	0.632994i	$-0.781826\pi$
$383$	−18.3035	−	31.7027i	−0.935267	−	1.61993i	−0.161111	−	0.986936i	$-0.551508\pi$
$384$		0			0
$385$	−14.5300	−	25.1667i	−0.740516	−	1.28261i
$386$		0			0
$387$	36.6245	−	3.68009i	1.86173	−	0.187069i
$388$		0			0
$389$	−2.76801	−	4.79433i	−0.140344	−	0.243082i	0.787282	−	0.616592i	$-0.211487\pi$
$389$	−2.76801	−	4.79433i	−0.140344	−	0.243082i	−0.927626	+	0.373510i	$0.878154\pi$
$390$		0			0
$391$	−6.27534	+	10.8692i	−0.317358	+	0.549680i
$392$		0			0
$393$	3.91535	−	7.64104i	0.197503	−	0.385440i
$394$		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
$399$	4.01610	−	7.83768i	0.201057	−	0.392375i
$400$		0			0
$401$	24.3613			1.21655			0.608273	−	0.793728i	$-0.291863\pi$
$401$	24.3613			1.21655			0.608273	+	0.793728i	$0.291863\pi$
$402$		0			0
$403$	−30.2474	+	16.6402i	−1.50673	+	0.828905i
$404$		0			0
$405$	4.72821	−	14.1114i	0.234947	−	0.701199i
$406$		0			0
$407$	−8.63466			−0.428004
$408$		0			0
$409$	−5.62960	−	9.75076i	−0.278366	−	0.482144i	0.692613	−	0.721310i	$-0.256459\pi$
$409$	−5.62960	−	9.75076i	−0.278366	−	0.482144i	−0.970979	+	0.239166i	$0.923126\pi$
$410$		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
$419$	38.4548			1.87864			0.939319	−	0.343046i	$-0.111459\pi$
$419$	38.4548			1.87864			0.939319	+	0.343046i	$0.111459\pi$
$420$		0			0
$421$	11.2699	+	19.5201i	0.549263	+	0.951351i	0.998325	+	0.0578506i	$0.0184247\pi$
$421$	11.2699	+	19.5201i	0.549263	+	0.951351i	−0.449063	+	0.893500i	$0.648242\pi$
$422$		0			0
$423$	−3.05028	−	4.23899i	−0.148310	−	0.206107i
$424$		0			0
$425$	−4.45360			−0.216031
$426$		0			0
$427$	−16.7770			−0.811897
$428$		0			0
$429$	26.6076	−	16.4240i	1.28463	−	0.792960i
$430$		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
$435$	−14.9389	−	23.1194i	−0.716264	−	1.10849i
$436$		0			0
$437$	4.62459	−	8.01002i	0.221224	−	0.383171i
$438$		0			0
$439$	16.2116	−	28.0793i	0.773737	−	1.34015i	−0.161764	−	0.986829i	$-0.551718\pi$
$439$	16.2116	−	28.0793i	0.773737	−	1.34015i	0.935501	−	0.353323i	$-0.114948\pi$
$440$		0			0
$441$	15.8774	−	1.59539i	0.756065	−	0.0759707i
$442$		0			0
$443$	−6.55432	−	11.3524i	−0.311405	−	0.539370i	0.667262	−	0.744823i	$-0.267466\pi$
$443$	−6.55432	−	11.3524i	−0.311405	−	0.539370i	−0.978667	+	0.205454i	$0.934133\pi$
$444$		0			0
$445$	−7.01165			−0.332384
$446$		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
$453$	−7.74926	−	11.9928i	−0.364092	−	0.563470i
$454$		0			0
$455$	−18.3349	+	10.0867i	−0.859554	+	0.472871i
$456$		0			0
$457$	−8.55281	+	14.8139i	−0.400083	+	0.692965i	−0.993736	−	0.111757i	$-0.964352\pi$
$457$	−8.55281	+	14.8139i	−0.400083	+	0.692965i	0.593652	+	0.804722i	$0.297686\pi$
$458$		0			0
$459$	3.72583	−	9.51056i	0.173907	−	0.443915i
$460$		0			0
$461$	−33.1328			−1.54315			−0.771575	−	0.636138i	$-0.780531\pi$
$461$	−33.1328			−1.54315			−0.771575	+	0.636138i	$0.780531\pi$
$462$		0			0
$463$	9.37793	−	16.2430i	0.435829	−	0.754878i	−0.561534	−	0.827454i	$-0.689789\pi$
$463$	9.37793	−	16.2430i	0.435829	−	0.754878i	0.997363	+	0.0725756i	$0.0231219\pi$
$464$		0			0
$465$	−14.8832	−	23.0333i	−0.690193	−	1.06814i
$466$		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
$471$	−1.04341	+	2.03628i	−0.0480778	+	0.0938268i
$472$		0			0
$473$	−30.7168	+	53.2030i	−1.41236	+	2.44628i
$474$		0			0
$475$	3.28206			0.150591
$476$		0			0
$477$	−23.3658	+	2.34783i	−1.06984	+	0.107500i
$478$		0			0
$479$	8.19158	−	14.1882i	0.374283	−	0.648277i	−0.615937	−	0.787796i	$-0.711222\pi$
$479$	8.19158	−	14.1882i	0.374283	−	0.648277i	0.990219	+	0.139519i	$0.0445556\pi$
$480$		0			0
$481$	−0.128400	+	6.21656i	−0.00585454	+	0.283451i
$482$		0			0
$483$	38.7654	−	1.94272i	1.76389	−	0.0883967i
$484$		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
$491$	13.7085			0.618657			0.309328	−	0.950955i	$-0.399896\pi$
$491$	13.7085			0.618657			0.309328	+	0.950955i	$0.399896\pi$
$492$		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
$497$	12.2896	−	21.2863i	0.551266	−	0.954821i
$498$		0			0
$499$	2.76875	−	4.79561i	0.123946	−	0.214681i	−0.797374	−	0.603485i	$-0.793778\pi$
$499$	2.76875	−	4.79561i	0.123946	−	0.214681i	0.921320	+	0.388804i	$0.127112\pi$
$500$		0			0
$501$	17.3216	−	0.868068i	0.773873	−	0.0387824i
$502$		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
$507$	−11.4289	−	19.4005i	−0.507575	−	0.861607i
$508$		0			0
$509$	−22.7496			−1.00836			−0.504180	−	0.863599i	$-0.668205\pi$
$509$	−22.7496			−1.00836			−0.504180	+	0.863599i	$0.668205\pi$
$510$		0			0
$511$	−7.82578			−0.346192
$512$		0			0
$513$	−2.74574	+	7.00877i	−0.121227	+	0.309445i
$514$		0			0
$515$	5.74671	+	9.95359i	0.253230	+	0.438607i
$516$		0			0
$517$	8.71609			0.383333
$518$		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
$527$	−9.41083	−	16.3000i	−0.409942	−	0.710041i
$528$		0			0
$529$	17.7641			0.772354
$530$		0			0
$531$	−5.20126	−	7.22822i	−0.225715	−	0.313678i
$532$		0			0
$533$	−33.1882	−	20.0862i	−1.43754	−	0.870030i
$534$		0			0
$535$	13.4053			0.579562
$536$		0			0
$537$	−7.72106	−	11.9491i	−0.333188	−	0.515643i
$538$		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
$543$	−18.9730	+	0.950826i	−0.814209	+	0.0408038i
$544$		0			0
$545$	−7.91684	+	13.7124i	−0.339120	+	0.587374i
$546$		0			0
$547$	−2.55758	−	4.42986i	−0.109354	−	0.189407i	0.806155	−	0.591705i	$-0.201545\pi$
$547$	−2.55758	−	4.42986i	−0.109354	−	0.189407i	−0.915509	+	0.402298i	$0.868212\pi$
$548$		0			0
$549$	14.2681	−	1.43368i	0.608946	−	0.0611880i
$550$		0			0
$551$	6.96120	+	12.0572i	0.296557	+	0.513652i
$552$		0			0
$553$	29.8191	+	51.6481i	1.26804	+	2.19630i
$554$		0			0
$555$	−4.93308	+	0.247220i	−0.209398	+	0.0104939i
$556$		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
$561$	9.25206	+	14.3185i	0.390622	+	0.604528i
$562$		0			0
$563$	−16.0330	−	27.7699i	−0.675710	−	1.17036i	−0.976261	−	0.216598i	$-0.930504\pi$
$563$	−16.0330	−	27.7699i	−0.675710	−	1.17036i	0.300551	−	0.953766i	$-0.402829\pi$
$564$		0			0
$565$	−15.1209			−0.636139
$566$		0			0
$567$	−30.9572	+	6.28473i	−1.30008	+	0.263934i
$568$		0			0
$569$	−20.4237	+	35.3749i	−0.856206	+	1.48299i	0.0193165	+	0.999813i	$0.493851\pi$
$569$	−20.4237	+	35.3749i	−0.856206	+	1.48299i	−0.875522	+	0.483178i	$0.839482\pi$
$570$		0			0
$571$	0.269451	−	0.466702i	0.0112762	−	0.0195309i	−0.860332	−	0.509734i	$-0.829744\pi$
$571$	0.269451	−	0.466702i	0.0112762	−	0.0195309i	0.871608	+	0.490203i	$0.163077\pi$
$572$		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
$579$	17.8598	−	0.895039i	0.742228	−	0.0371965i
$580$		0			0
$581$	7.79995	+	13.5099i	0.323596	+	0.560485i
$582$		0			0
$583$	19.5968	−	33.9426i	0.811615	−	1.40576i
$584$		0			0
$585$	14.7310	−	10.1451i	0.609053	−	0.419447i
$586$		0			0
$587$	19.4497	−	33.6879i	0.802776	−	1.39045i	−0.115007	−	0.993365i	$-0.536689\pi$
$587$	19.4497	−	33.6879i	0.802776	−	1.39045i	0.917783	−	0.397083i	$-0.129978\pi$
$588$		0			0
$589$	6.93527	+	12.0122i	0.285763	+	0.494956i
$590$		0			0
$591$	9.51289	+	14.7222i	0.391308	+	0.605589i
$592$		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	−0.697367	−	0.716714i	$-0.745645\pi$
$599$	6.65728	−	11.5307i	0.272009	−	0.471133i	0.969376	+	0.245581i	$0.0789786\pi$
$600$		0			0
$601$	−15.7116	+	27.2132i	−0.640888	+	1.11005i	0.344347	+	0.938842i	$0.388100\pi$
$601$	−15.7116	+	27.2132i	−0.640888	+	1.11005i	−0.985235	+	0.171208i	$0.945233\pi$
$602$		0			0
$603$	37.3133	−	3.74931i	1.51952	−	0.152684i
$604$		0			0
$605$	−23.2656			−0.945881
$606$		0			0
$607$	12.0979	+	20.9542i	0.491038	+	0.850503i	0.999947	−	0.0103174i	$-0.00328420\pi$
$607$	12.0979	+	20.9542i	0.491038	+	0.850503i	−0.508909	+	0.860821i	$0.669951\pi$
$608$		0			0
$609$	−26.6435	+	51.9965i	−1.07965	+	2.10700i
$610$		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
$615$	14.0529	−	27.4251i	0.566668	−	1.10589i
$616$		0			0
$617$	8.24120	+	14.2742i	0.331778	+	0.574657i	0.982861	−	0.184350i	$-0.0590181\pi$
$617$	8.24120	+	14.2742i	0.331778	+	0.574657i	−0.651082	+	0.759007i	$0.725685\pi$
$618$		0			0
$619$	6.79563	+	11.7704i	0.273139	+	0.473091i	0.969664	−	0.244442i	$-0.0786046\pi$
$619$	6.79563	+	11.7704i	0.273139	+	0.473091i	−0.696525	+	0.717533i	$0.745271\pi$
$620$		0			0
$621$	−32.8022	+	4.96489i	−1.31631	+	0.199234i
$622$		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
$627$	−6.81826	−	10.5520i	−0.272295	−	0.421405i
$628$		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
$633$	−29.9396	+	1.50041i	−1.18999	+	0.0596361i
$634$		0			0
$635$	−16.2999			−0.646842
$636$		0			0
$637$	16.4073	+	9.93008i	0.650083	+	0.393444i
$638$		0			0
$639$	−8.63275	+	19.1532i	−0.341506	+	0.757689i
$640$		0			0
$641$	8.04947			0.317935			0.158967	−	0.987284i	$-0.449184\pi$
$641$	8.04947			0.317935			0.158967	+	0.987284i	$0.449184\pi$
$642$		0			0
$643$	11.4136	+	19.7690i	0.450110	+	0.779613i	0.998392	−	0.0566799i	$-0.0180514\pi$
$643$	11.4136	+	19.7690i	0.450110	+	0.779613i	−0.548282	+	0.836293i	$0.684718\pi$
$644$		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
$653$	16.2617			0.636370			0.318185	−	0.948029i	$-0.396927\pi$
$653$	16.2617			0.636370			0.318185	+	0.948029i	$0.396927\pi$
$654$		0			0
$655$	4.09845	+	7.09873i	0.160140	+	0.277370i
$656$		0			0
$657$	6.65546	−	0.668752i	0.259654	−	0.0260905i
$658$		0			0
$659$	−27.2808			−1.06271			−0.531355	−	0.847149i	$-0.678317\pi$
$659$	−27.2808			−1.06271			−0.531355	+	0.847149i	$0.678317\pi$
$660$		0			0
$661$	0.558818			0.0217355			0.0108678	−	0.999941i	$-0.496541\pi$
$661$	0.558818			0.0217355			0.0108678	+	0.999941i	$0.496541\pi$
$662$		0			0
$663$	10.4463	−	6.44814i	0.405699	−	0.250425i
$664$		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
$669$	17.8872	−	34.9079i	0.691558	−	1.34962i
$670$		0			0
$671$	−11.9666	+	20.7267i	−0.461964	+	0.800145i
$672$		0			0
$673$	8.56550	−	14.8359i	0.330176	−	0.571881i	−0.652370	−	0.757900i	$-0.726225\pi$
$673$	8.56550	−	14.8359i	0.330176	−	0.571881i	0.982546	+	0.186019i	$0.0595586\pi$
$674$		0			0
$675$	−7.34565	−	9.19948i	−0.282734	−	0.354088i
$676$		0			0
$677$	−21.0208	−	36.4091i	−0.807896	−	1.39932i	−0.914319	−	0.404996i	$-0.867273\pi$
$677$	−21.0208	−	36.4091i	−0.807896	−	1.39932i	0.106423	−	0.994321i	$-0.466060\pi$
$678$		0			0
$679$	−16.7702			−0.643583
$680$		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
$687$	−5.27608	+	10.2966i	−0.201295	+	0.392840i
$688$		0			0
$689$	−24.1457	−	14.6135i	−0.919878	−	0.556730i
$690$		0			0
$691$	−11.8805	+	20.5777i	−0.451957	+	0.782812i	−0.998508	−	0.0546138i	$-0.982607\pi$
$691$	−11.8805	+	20.5777i	−0.451957	+	0.782812i	0.546551	+	0.837426i	$0.315941\pi$
$692$		0			0
$693$	21.6637	−	48.0646i	0.822936	−	1.82582i
$694$		0			0
$695$	1.73433			0.0657868
$696$		0			0
$697$	10.5750	−	18.3165i	0.400558	−	0.693787i
$698$		0			0
$699$	25.9904	−	1.30250i	0.983048	−	0.0492651i
$700$		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
$705$	4.97960	−	0.249551i	0.187543	−	0.00939865i
$706$		0			0
$707$	8.14969	−	14.1157i	0.306501	−	0.530875i
$708$		0			0
$709$	11.0151			0.413682			0.206841	−	0.978375i	$-0.433682\pi$
$709$	11.0151			0.413682			0.206841	+	0.978375i	$0.433682\pi$
$710$		0			0
$711$	−29.7733	−	41.3761i	−1.11659	−	1.55173i
$712$		0			0
$713$	−30.5660	+	52.9419i	−1.14471	+	1.98269i
$714$		0			0
$715$	−0.616452	+	29.8459i	−0.0230540	+	1.11617i
$716$		0			0
$717$	−6.73026	+	13.1345i	−0.251346	+	0.490518i
$718$		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
$725$	−21.7737			−0.808656
$726$		0			0
$727$	20.2911	+	35.1452i	0.752556	+	1.30346i	0.946580	+	0.322468i	$0.104512\pi$
$727$	20.2911	+	35.1452i	0.752556	+	1.30346i	−0.194025	+	0.980997i	$0.562154\pi$
$728$		0			0
$729$	25.7906	−	7.99031i	0.955207	−	0.295937i
$730$		0			0
$731$	−12.0595	+	20.8877i	−0.446037	+	0.772559i
$732$		0			0
$733$	18.4885	−	32.0230i	0.682888	−	1.18280i	−0.291207	−	0.956660i	$-0.594057\pi$
$733$	18.4885	−	32.0230i	0.682888	−	1.18280i	0.974095	−	0.226137i	$-0.0726098\pi$
$734$		0			0
$735$	−6.94738	+	13.5583i	−0.256258	+	0.500104i
$736$		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
$741$	−7.69832	+	4.75193i	−0.282805	+	0.174566i
$742$		0			0
$743$	−44.2428			−1.62311			−0.811555	−	0.584276i	$-0.801379\pi$
$743$	−44.2428			−1.62311			−0.811555	+	0.584276i	$0.801379\pi$
$744$		0			0
$745$	28.0376			1.02722
$746$		0			0
$747$	−7.78797	−	10.8230i	−0.284947	−	0.395992i
$748$		0			0
$749$	−14.2267	−	24.6414i	−0.519833	−	0.900378i
$750$		0			0
$751$	−10.2828			−0.375225			−0.187613	−	0.982243i	$-0.560075\pi$
$751$	−10.2828			−0.375225			−0.187613	+	0.982243i	$0.560075\pi$
$752$		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
$761$	8.08162	+	13.9978i	0.292958	+	0.507419i	0.974508	−	0.224353i	$-0.0720269\pi$
$761$	8.08162	+	13.9978i	0.292958	+	0.507419i	−0.681549	+	0.731772i	$0.738694\pi$
$762$		0			0
$763$	33.6078			1.21668
$764$		0			0
$765$	5.69577	+	7.91544i	0.205931	+	0.286183i
$766$		0			0
$767$	0.221009	−	10.7003i	0.00798018	−	0.386365i
$768$		0			0
$769$	13.3575			0.481684			0.240842	−	0.970564i	$-0.422576\pi$
$769$	13.3575			0.481684			0.240842	+	0.970564i	$0.422576\pi$
$770$		0			0
$771$	−9.70309	+	0.486268i	−0.349448	+	0.0175125i
$772$		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
$777$	5.68980	+	8.80555i	0.204120	+	0.315897i
$778$		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
$783$	18.2157	−	46.4974i	0.650975	−	1.66168i
$784$		0			0
$785$	−1.09221	−	1.89176i	−0.0389825	−	0.0675197i
$786$		0			0
$787$	−19.4001	−	33.6020i	−0.691540	−	1.19778i	−0.971333	−	0.237722i	$-0.923599\pi$
$787$	−19.4001	−	33.6020i	−0.691540	−	1.19778i	0.279793	−	0.960060i	$-0.409734\pi$
$788$		0			0
$789$	17.6183	−	34.3833i	0.627229	−	1.22408i
$790$		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
$795$	10.2240	−	19.9529i	0.362610	−	0.707656i
$796$		0			0
$797$	25.4413	+	44.0656i	0.901177	+	1.56088i	0.825969	+	0.563716i	$0.190629\pi$
$797$	25.4413	+	44.0656i	0.901177	+	1.56088i	0.0752076	+	0.997168i	$0.476038\pi$
$798$		0			0
$799$	3.42197			0.121060
$800$		0			0
$801$	−7.42988	−	10.3253i	−0.262522	−	0.364828i
$802$		0			0
$803$	−5.58190	+	9.66814i	−0.196981	+	0.341181i
$804$		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
$813$	25.5523	+	39.5448i	0.896159	+	1.38690i
$814$		0			0
$815$	7.66430	+	13.2750i	0.268469	+	0.465002i
$816$		0			0
$817$	8.88720	−	15.3931i	0.310924	−	0.538536i
$818$		0			0
$819$	−34.2822	−	16.3116i	−1.19792	−	0.569974i
$820$		0			0
$821$	−11.8122	+	20.4593i	−0.412249	+	0.714036i	−0.995135	−	0.0985177i	$-0.968590\pi$
$821$	−11.8122	+	20.4593i	−0.412249	+	0.714036i	0.582886	+	0.812554i	$0.301923\pi$
$822$		0			0
$823$	12.4584	+	21.5785i	0.434271	+	0.752180i	0.997236	−	0.0743011i	$-0.0236726\pi$
$823$	12.4584	+	21.5785i	0.434271	+	0.752180i	−0.562965	+	0.826481i	$0.690339\pi$
$824$		0			0
$825$	19.6233	−	0.983417i	0.683196	−	0.0342382i
$826$		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
$835$	−8.27893	+	14.3395i	−0.286504	+	0.496240i
$836$		0			0
$837$	18.1478	−	46.3242i	0.627281	−	1.60120i
$838$		0			0
$839$	−43.0248			−1.48538			−0.742690	−	0.669635i	$-0.766451\pi$
$839$	−43.0248			−1.48538			−0.742690	+	0.669635i	$0.766451\pi$
$840$		0			0
$841$	−31.6818	−	54.8745i	−1.09248	−	1.89222i
$842$		0			0
$843$	−17.7285	−	27.4366i	−0.610601	−	0.944967i
$844$		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
$849$	−2.55796	+	0.128191i	−0.0877889	+	0.00439951i
$850$		0			0
$851$	5.50529	+	9.53545i	0.188719	+	0.326871i
$852$		0			0
$853$	−4.75065	−	8.22837i	−0.162659	−	0.281734i	0.773162	−	0.634208i	$-0.218674\pi$
$853$	−4.75065	−	8.22837i	−0.162659	−	0.281734i	−0.935822	+	0.352474i	$0.885340\pi$
$854$		0			0
$855$	−4.19747	−	5.83325i	−0.143550	−	0.199493i
$856$		0			0
$857$	−12.3253	−	21.3480i	−0.421024	−	0.729234i	0.575016	−	0.818142i	$-0.304996\pi$
$857$	−12.3253	−	21.3480i	−0.421024	−	0.729234i	−0.996040	+	0.0889077i	$0.971662\pi$
$858$		0			0
$859$	4.10381	−	7.10801i	0.140020	−	0.242522i	−0.787484	−	0.616335i	$-0.788617\pi$
$859$	4.10381	−	7.10801i	0.140020	−	0.242522i	0.927504	+	0.373813i	$0.121950\pi$
$860$		0			0
$861$	−65.3265	+	3.27382i	−2.22632	+	0.111571i
$862$		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
$867$	−12.3479	−	19.1097i	−0.419357	−	0.648998i
$868$		0			0
$869$	85.0762			2.88601
$870$		0			0
$871$	38.5588	+	23.3366i	1.30652	+	0.790732i
$872$		0			0
$873$	14.2623	−	1.43310i	0.482706	−	0.0485031i
$874$		0			0
$875$	−42.1689			−1.42557
$876$		0			0
$877$	11.9207	+	20.6473i	0.402534	+	0.697209i	0.994031	−	0.109098i	$-0.0347962\pi$
$877$	11.9207	+	20.6473i	0.402534	+	0.697209i	−0.591497	+	0.806307i	$0.701463\pi$
$878$		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
$887$	−13.1345			−0.441014			−0.220507	−	0.975385i	$-0.570771\pi$
$887$	−13.1345			−0.441014			−0.220507	+	0.975385i	$0.570771\pi$
$888$		0			0
$889$	17.2987	+	29.9622i	0.580180	+	1.00490i
$890$		0			0
$891$	−14.3166	+	42.7279i	−0.479624	+	1.43144i
$892$		0			0
$893$	−2.52180			−0.0843889
$894$		0			0
$895$	13.5823			0.454005
$896$		0			0
$897$	−35.1020	−	18.9117i	−1.17202	−	0.631445i
$898$		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
$903$	74.4967	−	3.73338i	2.47909	−	0.124239i
$904$		0			0
$905$	9.06820	−	15.7066i	0.301437	−	0.522105i
$906$		0			0
$907$	17.3953	−	30.1296i	0.577603	−	1.00044i	−0.418151	−	0.908378i	$-0.637322\pi$
$907$	17.3953	−	30.1296i	0.577603	−	1.00044i	0.995753	−	0.0920599i	$-0.0293451\pi$
$908$		0			0
$909$	−5.72467	+	12.7012i	−0.189875	+	0.421271i
$910$		0			0
$911$	−14.7500	−	25.5478i	−0.488690	−	0.846435i	0.511226	−	0.859446i	$-0.329192\pi$
$911$	−14.7500	−	25.5478i	−0.488690	−	0.846435i	−0.999915	+	0.0130113i	$0.995858\pi$
$912$		0			0
$913$	22.2539			0.736496
$914$		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
$921$	5.76484	−	0.288903i	0.189958	−	0.00951969i
$922$		0			0
$923$	−22.1227	+	12.1705i	−0.728177	+	0.400596i
$924$		0			0
$925$	−1.95355	+	3.38364i	−0.0642322	+	0.111253i
$926$		0			0
$927$	−8.56814	+	19.0099i	−0.281415	+	0.624366i
$928$		0			0
$929$	43.3703			1.42293			0.711466	−	0.702720i	$-0.248031\pi$
$929$	43.3703			1.42293			0.711466	+	0.702720i	$0.248031\pi$
$930$		0			0
$931$	3.85276	−	6.67318i	0.126269	−	0.218705i
$932$		0			0
$933$	−6.69744	+	13.0705i	−0.219264	+	0.427908i
$934$		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
$939$	−0.405290	−	0.627228i	−0.0132261	−	0.0204688i
$940$		0			0
$941$	1.29883	−	2.24964i	0.0423407	−	0.0733362i	−0.844078	−	0.536220i	$-0.819852\pi$
$941$	1.29883	−	2.24964i	0.0423407	−	0.0733362i	0.886419	+	0.462884i	$0.153185\pi$
$942$		0			0
$943$	−68.6946			−2.23700
$944$		0			0
$945$	11.0006	−	28.0801i	0.357849	−	0.913446i
$946$		0			0
$947$	6.13201	−	10.6209i	0.199263	−	0.345134i	−0.749026	−	0.662540i	$-0.769478\pi$
$947$	6.13201	−	10.6209i	0.199263	−	0.345134i	0.948290	+	0.317406i	$0.102812\pi$
$948$		0			0
$949$	6.87761	+	4.16248i	0.223257	+	0.135120i
$950$		0			0
$951$	−5.56431	−	8.61135i	−0.180435	−	0.279242i
$952$		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
$959$	−0.0431594			−0.00139369
$960$		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
$965$	−8.53615	+	14.7851i	−0.274789	+	0.475948i
$966$		0			0
$967$	−1.72209	+	2.98275i	−0.0553787	+	0.0959187i	−0.892386	−	0.451273i	$-0.850970\pi$
$967$	−1.72209	+	2.98275i	−0.0553787	+	0.0959187i	0.837007	+	0.547192i	$0.184303\pi$
$968$		0			0
$969$	−2.67687	−	4.14274i	−0.0859936	−	0.133084i
$970$		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
$975$	−0.416210	−	14.1425i	−0.0133294	−	0.452923i
$976$		0			0
$977$	−18.0223			−0.576585			−0.288293	−	0.957542i	$-0.593088\pi$
$977$	−18.0223			−0.576585			−0.288293	+	0.957542i	$0.593088\pi$
$978$		0			0
$979$	21.2306			0.678534
$980$		0			0
$981$	−28.5819	+	2.87196i	−0.912549	+	0.0916945i
$982$		0			0
$983$	18.6651	+	32.3288i	0.595323	+	1.03113i	0.993501	+	0.113821i	$0.0363091\pi$
$983$	18.6651	+	32.3288i	0.595323	+	1.03113i	−0.398178	+	0.917308i	$0.630358\pi$
$984$		0			0
$985$	−16.7343			−0.533199
$986$		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
$995$	−5.68199	−	9.84150i	−0.180131	−	0.311997i
$996$		0			0
$997$	40.5279			1.28353			0.641766	−	0.766901i	$-0.278202\pi$
$997$	40.5279			1.28353			0.641766	+	0.766901i	$0.278202\pi$
$998$		0			0
$999$	−5.59138	−	7.00248i	−0.176904	−	0.221549i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
468.2.j.a.133.10	✓	28	9.7	even	3
468.2.j.a.373.10	yes	28	13.9	even	3
468.2.k.a.61.1	yes	28	117.61	even	3	inner
468.2.k.a.445.1	yes	28	1.1	even	1	trivial
1404.2.j.a.289.5		28	9.2	odd	6
1404.2.j.a.685.5		28	39.35	odd	6
1404.2.k.a.1153.5		28	117.74	odd	6
1404.2.k.a.1225.5		28	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-1.72988 + 0.0866924i) q^{3} +(0.826802 - 1.43206i) q^{5} -3.50986 q^{7} +(2.98497 - 0.299935i) q^{9} +(-2.50348 + 4.33615i) q^{11} +(3.08461 + 1.86687i) q^{13} +(-1.30612 + 2.54897i) q^{15} +(-0.982875 + 1.70239i) q^{17} +(0.724325 - 1.25457i) q^{19} +(6.07163 - 0.304278i) q^{21} +6.38468 q^{23} +(1.13280 + 1.96206i) q^{25} +(-5.13764 + 0.777625i) q^{27} +(-4.80530 + 8.32302i) q^{29} +(-4.78740 + 8.29202i) q^{31} +(3.95481 - 7.71806i) q^{33} +(-2.90196 + 5.02634i) q^{35} +(0.862266 + 1.49349i) q^{37} +(-5.49784 - 2.96205i) q^{39} -10.7593 q^{41} +12.2696 q^{43} +(2.03845 - 4.52265i) q^{45} +(-0.870397 - 1.50757i) q^{47} +5.31910 q^{49} +(1.55267 - 3.03014i) q^{51} -7.82781 q^{53} +(4.13976 + 7.17028i) q^{55} +(-1.14423 + 2.23305i) q^{57} +(-1.48418 - 2.57067i) q^{59} +4.77997 q^{61} +(-10.4768 + 1.05273i) q^{63} +(5.22383 - 2.87382i) q^{65} +12.5004 q^{67} +(-11.0447 + 0.553503i) q^{69} +(-3.50147 + 6.06472i) q^{71} +2.22966 q^{73} +(-2.12970 - 3.29593i) q^{75} +(8.78686 - 15.2193i) q^{77} +(-8.49580 - 14.7152i) q^{79} +(8.82008 - 1.79059i) q^{81} +(-2.22230 - 3.84913i) q^{83} +(1.62529 + 2.81508i) q^{85} +(7.59105 - 14.8144i) q^{87} +(-2.12011 - 3.67214i) q^{89} +(-10.8265 - 6.55245i) q^{91} +(7.56277 - 14.7592i) q^{93} +(-1.19775 - 2.07456i) q^{95} +4.77804 q^{97} +(-6.17224 + 13.6942i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - 4 q^{7} - 2 q^{9} - 4 q^{11} + q^{13} - 4 q^{15} - 8 q^{17} - q^{19} + 14 q^{21} + 8 q^{23} - 14 q^{25} - 13 q^{29} + 2 q^{31} - 25 q^{33} + 3 q^{35} - q^{37} - 3 q^{39} - 8 q^{41} - 4 q^{43}+ \cdots - 29 q^{99}+O(q^{100}) \) 28 * q - 4 * q^7 - 2 * q^9 - 4 * q^11 + q^13 - 4 * q^15 - 8 * q^17 - q^19 + 14 * q^21 + 8 * q^23 - 14 * q^25 - 13 * q^29 + 2 * q^31 - 25 * q^33 + 3 * q^35 - q^37 - 3 * q^39 - 8 * q^41 - 4 * q^43 - 38 * q^45 + 11 * q^47 + 24 * q^49 + 5 * q^51 + 52 * q^53 - q^57 - 8 * q^59 + 14 * q^61 - 21 * q^63 + 38 * q^65 + 14 * q^67 - 21 * q^69 - 12 * q^71 + 14 * q^73 - 14 * q^75 - 28 * q^77 + 5 * q^79 + 10 * q^81 + 9 * q^83 + 18 * q^85 + 18 * q^87 - 11 * q^89 - q^91 - 9 * q^93 + 28 * q^95 + 50 * q^97 - 29 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more