LMFDB - Embedded newform 936.2.cw.b.337.26

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [936,2,Mod(25,936)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(936, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 4, 3])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("936.25"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 936 = 2^{3} \cdot 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	936.cw (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [80] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$7.47399762919$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$40$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			337.26
Character	$\chi$	$=$	936.337
Dual form			936.2.cw.b.25.26

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.373720 - 1.69125i) q^{3} +(3.40435 + 1.96550i) q^{5} +(-4.16592 + 2.40520i) q^{7} +(-2.72067 - 1.26411i) q^{9} +(-2.91097 + 1.68065i) q^{11} +(0.448090 + 3.57760i) q^{13} +(4.59643 - 5.02306i) q^{15} -1.07207 q^{17} +6.57228i q^{19} +(2.51090 + 7.94450i) q^{21} +(0.0427423 - 0.0740317i) q^{23} +(5.22640 + 9.05238i) q^{25} +(-3.15470 + 4.12891i) q^{27} +(-0.514326 - 0.890839i) q^{29} +(-6.40180 - 3.69608i) q^{31} +(1.75451 + 5.55127i) q^{33} -18.9097 q^{35} -4.76927i q^{37} +(6.21808 + 0.579189i) q^{39} +(2.17095 + 1.25340i) q^{41} +(1.85904 + 3.21995i) q^{43} +(-6.77749 - 9.65095i) q^{45} +(8.71820 - 5.03346i) q^{47} +(8.06995 - 13.9776i) q^{49} +(-0.400656 + 1.81315i) q^{51} -5.80367 q^{53} -13.2133 q^{55} +(11.1154 + 2.45620i) q^{57} +(10.4025 + 6.00590i) q^{59} +(-2.30828 - 3.99806i) q^{61} +(14.3745 - 1.27755i) q^{63} +(-5.50632 + 13.0601i) q^{65} +(2.45580 + 1.41786i) q^{67} +(-0.109233 - 0.0999551i) q^{69} -1.36430i q^{71} -2.67779i q^{73} +(17.2631 - 5.45609i) q^{75} +(8.08457 - 14.0029i) q^{77} +(0.872958 + 1.51201i) q^{79} +(5.80405 + 6.87845i) q^{81} +(-12.2034 + 7.04566i) q^{83} +(-3.64971 - 2.10716i) q^{85} +(-1.69885 + 0.536931i) q^{87} +9.35462i q^{89} +(-10.4715 - 13.8263i) q^{91} +(-8.64349 + 9.44576i) q^{93} +(-12.9178 + 22.3743i) q^{95} +(6.64133 - 3.83437i) q^{97} +(10.0443 - 0.892695i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q - 6 q^{3} - 6 q^{9} + 6 q^{13} - 4 q^{17} + 10 q^{23} + 44 q^{25} + 6 q^{27} - 52 q^{35} + 40 q^{39} - 26 q^{43} + 48 q^{49} + 36 q^{51} + 60 q^{53} - 16 q^{55} - 10 q^{61} - 26 q^{65} - 38 q^{69}+ \cdots + 8 q^{95}+O(q^{100}) $ 80 * q - 6 * q^3 - 6 * q^9 + 6 * q^13 - 4 * q^17 + 10 * q^23 + 44 * q^25 + 6 * q^27 - 52 * q^35 + 40 * q^39 - 26 * q^43 + 48 * q^49 + 36 * q^51 + 60 * q^53 - 16 * q^55 - 10 * q^61 - 26 * q^65 - 38 * q^69 + 32 * q^75 + 32 * q^77 + 6 * q^79 - 38 * q^81 + 4 * q^87 - 4 * q^91 + 8 * q^95

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/936\mathbb{Z}\right)^\times$.

$n$	$145$	$209$	$469$	$703$
$\chi(n)$	$-1$	$e\left(\frac{1}{3}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.373720	−	1.69125i	0.215768	−	0.976445i
$3$	0.373720	−	1.69125i	0.215768	−	0.976445i
$4$		0			0
$5$	3.40435	+	1.96550i	1.52247	+	0.878999i	0.999647	+	0.0265586i	$0.00845486\pi$
$5$	3.40435	+	1.96550i	1.52247	+	0.878999i	0.522824	+	0.852441i	$0.324878\pi$
$6$		0			0
$7$	−4.16592	+	2.40520i	−1.57457	+	0.909079i	−0.578974	+	0.815346i	$0.696547\pi$
$7$	−4.16592	+	2.40520i	−1.57457	+	0.909079i	−0.995597	+	0.0937328i	$0.970120\pi$
$8$		0			0
$9$	−2.72067	−	1.26411i	−0.906889	−	0.421370i
$10$		0			0
$11$	−2.91097	+	1.68065i	−0.877689	+	0.506734i	−0.869896	−	0.493236i	$-0.835814\pi$
$11$	−2.91097	+	1.68065i	−0.877689	+	0.506734i	−0.00779327	+	0.999970i	$0.502481\pi$
$12$		0			0
$13$	0.448090	+	3.57760i	0.124278	+	0.992247i
$13$	0.448090	+	3.57760i	0.124278	+	0.992247i
$14$		0			0
$15$	4.59643	−	5.02306i	1.18679	−	1.29695i
$16$		0			0
$17$	−1.07207			−0.260016			−0.130008	−	0.991513i	$-0.541500\pi$
$17$	−1.07207			−0.260016			−0.130008	+	0.991513i	$0.541500\pi$
$18$		0			0
$19$			6.57228i			1.50778i	0.656998	+	0.753892i	$0.271826\pi$
$19$			6.57228i			1.50778i	−0.656998	+	0.753892i	$0.728174\pi$
$20$		0			0
$21$	2.51090	+	7.94450i	0.547924	+	1.73363i
$22$		0			0
$23$	0.0427423	−	0.0740317i	0.00891238	−	0.0154367i	−0.861535	−	0.507698i	$-0.830496\pi$
$23$	0.0427423	−	0.0740317i	0.00891238	−	0.0154367i	0.870447	+	0.492262i	$0.163830\pi$
$24$		0			0
$25$	5.22640	+	9.05238i	1.04528	+	1.81048i
$26$		0			0
$27$	−3.15470	+	4.12891i	−0.607122	+	0.794609i
$28$		0			0
$29$	−0.514326	−	0.890839i	−0.0955080	−	0.165425i	0.814313	−	0.580427i	$-0.197114\pi$
$29$	−0.514326	−	0.890839i	−0.0955080	−	0.165425i	−0.909821	+	0.415002i	$0.863781\pi$
$30$		0			0
$31$	−6.40180	−	3.69608i	−1.14980	−	0.663836i	−0.200960	−	0.979600i	$-0.564406\pi$
$31$	−6.40180	−	3.69608i	−1.14980	−	0.663836i	−0.948838	+	0.315764i	$0.897739\pi$
$32$		0			0
$33$	1.75451	+	5.55127i	0.305421	+	0.966352i
$34$		0			0
$35$	−18.9097			−3.19632
$36$		0			0
$37$		−	4.76927i		−	0.784063i	−0.919952	−	0.392031i	$-0.871772\pi$
$37$		−	4.76927i		−	0.784063i	0.919952	−	0.392031i	$-0.128228\pi$
$38$		0			0
$39$	6.21808	+	0.579189i	0.995690	+	0.0927445i
$40$		0			0
$41$	2.17095	+	1.25340i	0.339045	+	0.195748i	0.659850	−	0.751398i	$-0.270620\pi$
$41$	2.17095	+	1.25340i	0.339045	+	0.195748i	−0.320804	+	0.947145i	$0.603953\pi$
$42$		0			0
$43$	1.85904	+	3.21995i	0.283500	+	0.491037i	0.972244	−	0.233967i	$-0.0751709\pi$
$43$	1.85904	+	3.21995i	0.283500	+	0.491037i	−0.688744	+	0.725005i	$0.741838\pi$
$44$		0			0
$45$	−6.77749	−	9.65095i	−1.01033	−	1.43868i
$46$		0			0
$47$	8.71820	−	5.03346i	1.27168	−	0.734205i	0.296377	−	0.955071i	$-0.404222\pi$
$47$	8.71820	−	5.03346i	1.27168	−	0.734205i	0.975304	+	0.220866i	$0.0708883\pi$
$48$		0			0
$49$	8.06995	−	13.9776i	1.15285	−	1.99679i
$50$		0			0
$51$	−0.400656	+	1.81315i	−0.0561030	+	0.253891i
$52$		0			0
$53$	−5.80367			−0.797195			−0.398598	−	0.917126i	$-0.630503\pi$
$53$	−5.80367			−0.797195			−0.398598	+	0.917126i	$0.630503\pi$
$54$		0			0
$55$	−13.2133			−1.78168
$56$		0			0
$57$	11.1154	+	2.45620i	1.47227	+	0.325331i
$58$		0			0
$59$	10.4025	+	6.00590i	1.35429	+	0.781901i	0.988847	−	0.148932i	$-0.0475836\pi$
$59$	10.4025	+	6.00590i	1.35429	+	0.781901i	0.365445	+	0.930833i	$0.380917\pi$
$60$		0			0
$61$	−2.30828	−	3.99806i	−0.295545	−	0.511899i	0.679566	−	0.733614i	$-0.262168\pi$
$61$	−2.30828	−	3.99806i	−0.295545	−	0.511899i	−0.975112	+	0.221715i	$0.928835\pi$
$62$		0			0
$63$	14.3745	−	1.27755i	1.81102	−	0.160956i
$64$		0			0
$65$	−5.50632	+	13.0601i	−0.682975	+	1.61991i
$66$		0			0
$67$	2.45580	+	1.41786i	0.300024	+	0.173219i	0.642454	−	0.766325i	$-0.277916\pi$
$67$	2.45580	+	1.41786i	0.300024	+	0.173219i	−0.342430	+	0.939543i	$0.611250\pi$
$68$		0			0
$69$	−0.109233	−	0.0999551i	−0.0131501	−	0.0120332i
$70$		0			0
$71$		−	1.36430i		−	0.161913i	−0.996718	−	0.0809564i	$-0.974203\pi$
$71$		−	1.36430i		−	0.161913i	0.996718	−	0.0809564i	$-0.0257975\pi$
$72$		0			0
$73$		−	2.67779i		−	0.313412i	−0.987645	−	0.156706i	$-0.949913\pi$
$73$		−	2.67779i		−	0.313412i	0.987645	−	0.156706i	$-0.0500874\pi$
$74$		0			0
$75$	17.2631	−	5.45609i	1.99337	−	0.630015i
$76$		0			0
$77$	8.08457	−	14.0029i	0.921322	−	1.59578i
$78$		0			0
$79$	0.872958	+	1.51201i	0.0982155	+	0.170114i	0.910946	−	0.412525i	$-0.135353\pi$
$79$	0.872958	+	1.51201i	0.0982155	+	0.170114i	−0.812731	+	0.582640i	$0.802020\pi$
$80$		0			0
$81$	5.80405	+	6.87845i	0.644894	+	0.764272i
$82$		0			0
$83$	−12.2034	+	7.04566i	−1.33950	+	0.773362i	−0.986733	−	0.162349i	$-0.948093\pi$
$83$	−12.2034	+	7.04566i	−1.33950	+	0.773362i	−0.352768	+	0.935711i	$0.614760\pi$
$84$		0			0
$85$	−3.64971	−	2.10716i	−0.395867	−	0.228554i
$86$		0			0
$87$	−1.69885	+	0.536931i	−0.182136	+	0.0575650i
$88$		0			0
$89$			9.35462i			0.991587i	0.868440	+	0.495794i	$0.165123\pi$
$89$			9.35462i			0.991587i	−0.868440	+	0.495794i	$0.834877\pi$
$90$		0			0
$91$	−10.4715	−	13.8263i	−1.09772	−	1.44939i
$92$		0			0
$93$	−8.64349	+	9.44576i	−0.896288	+	0.979479i
$94$		0			0
$95$	−12.9178	+	22.3743i	−1.32534	+	2.29556i
$96$		0			0
$97$	6.64133	−	3.83437i	0.674325	−	0.389322i	−0.123388	−	0.992358i	$-0.539376\pi$
$97$	6.64133	−	3.83437i	0.674325	−	0.389322i	0.797713	+	0.603037i	$0.206043\pi$
$98$		0			0
$99$	10.0443	−	0.892695i	1.00949	−	0.0897192i
$100$		0			0
$101$	7.44051	+	12.8873i	0.740358	+	1.28234i	0.952332	+	0.305063i	$0.0986775\pi$
$101$	7.44051	+	12.8873i	0.740358	+	1.28234i	−0.211974	+	0.977275i	$0.567989\pi$
$102$		0			0
$103$	9.46797	−	16.3990i	0.932907	−	1.61584i	0.154582	−	0.987980i	$-0.450597\pi$
$103$	9.46797	−	16.3990i	0.932907	−	1.61584i	0.778325	−	0.627862i	$-0.216070\pi$
$104$		0			0
$105$	−7.06693	+	31.9810i	−0.689662	+	3.12103i
$106$		0			0
$107$	14.6995			1.42105			0.710526	−	0.703671i	$-0.248457\pi$
$107$	14.6995			1.42105			0.710526	+	0.703671i	$0.248457\pi$
$108$		0			0
$109$			4.39621i			0.421081i	0.977585	+	0.210540i	$0.0675224\pi$
$109$			4.39621i			0.421081i	−0.977585	+	0.210540i	$0.932478\pi$
$110$		0			0
$111$	−8.06603	−	1.78237i	−0.765594	−	0.169175i
$112$		0			0
$113$	−1.23196	+	2.13381i	−0.115893	+	0.200732i	−0.918136	−	0.396265i	$-0.870306\pi$
$113$	−1.23196	+	2.13381i	−0.115893	+	0.200732i	0.802244	+	0.596997i	$0.203640\pi$
$114$		0			0
$115$	0.291019	−	0.168020i	0.0271377	−	0.0156679i
$116$		0			0
$117$	3.30338	−	10.2999i	0.305398	−	0.952225i
$118$		0			0
$119$	4.46618	−	2.57855i	0.409414	−	0.236375i
$120$		0			0
$121$	0.149145	−	0.258327i	0.0135587	−	0.0234843i
$122$		0			0
$123$	2.93114	−	3.20320i	0.264292	−	0.288823i
$124$		0			0
$125$			21.4350i			1.91720i
$126$		0			0
$127$	17.2139			1.52749			0.763743	−	0.645520i	$-0.223359\pi$
$127$	17.2139			1.52749			0.763743	+	0.645520i	$0.223359\pi$
$128$		0			0
$129$	6.14050	−	1.94074i	0.540641	−	0.170873i
$130$		0			0
$131$	4.22778	−	7.32272i	0.369382	−	0.639789i	−0.620087	−	0.784533i	$-0.712903\pi$
$131$	4.22778	−	7.32272i	0.369382	−	0.639789i	0.989469	+	0.144744i	$0.0462359\pi$
$132$		0			0
$133$	−15.8076	−	27.3796i	−1.37070	−	2.37411i
$134$		0			0
$135$	−18.8551	+	7.85568i	−1.62279	+	0.676109i
$136$		0			0
$137$	−15.7874	+	9.11483i	−1.34880	+	0.778733i	−0.988080	−	0.153940i	$-0.950804\pi$
$137$	−15.7874	+	9.11483i	−1.34880	+	0.778733i	−0.360724	+	0.932672i	$0.617470\pi$
$138$		0			0
$139$	5.76010	−	9.97679i	0.488565	−	0.846220i	−0.511348	−	0.859374i	$-0.670854\pi$
$139$	5.76010	−	9.97679i	0.488565	−	0.846220i	0.999913	+	0.0131535i	$0.00418701\pi$
$140$		0			0
$141$	−5.25467	−	16.6258i	−0.442523	−	1.40014i
$142$		0			0
$143$	−7.31705	−	9.66119i	−0.611883	−	0.807909i
$144$		0			0
$145$		−	4.04364i		−	0.335806i
$146$		0			0
$147$	−20.6237	−	18.8720i	−1.70101	−	1.55654i
$148$		0			0
$149$	3.77205	+	2.17780i	0.309019	+	0.178412i	0.646487	−	0.762925i	$-0.276237\pi$
$149$	3.77205	+	2.17780i	0.309019	+	0.178412i	−0.337469	+	0.941337i	$0.609571\pi$
$150$		0			0
$151$	3.70820	−	2.14093i	0.301769	−	0.174226i	−0.341468	−	0.939893i	$-0.610924\pi$
$151$	3.70820	−	2.14093i	0.301769	−	0.174226i	0.643237	+	0.765667i	$0.277591\pi$
$152$		0			0
$153$	2.91675	+	1.35522i	0.235806	+	0.109563i
$154$		0			0
$155$	−14.5293	−	25.1655i	−1.16702	−	2.02134i
$156$		0			0
$157$	−0.0630158	+	0.109147i	−0.00502921	+	0.00871085i	−0.868529	−	0.495638i	$-0.834934\pi$
$157$	−0.0630158	+	0.109147i	−0.00502921	+	0.00871085i	0.863500	+	0.504349i	$0.168268\pi$
$158$		0			0
$159$	−2.16895	+	9.81547i	−0.172009	+	0.778417i
$160$		0			0
$161$			0.411214i			0.0324082i
$162$		0			0
$163$			16.6292i			1.30250i	0.758862	+	0.651252i	$0.225756\pi$
$163$			16.6292i			1.30250i	−0.758862	+	0.651252i	$0.774244\pi$
$164$		0			0
$165$	−4.93806	+	22.3469i	−0.384428	+	1.73971i
$166$		0			0
$167$	−1.79761	−	1.03785i	−0.139103	−	0.0803113i	0.428833	−	0.903384i	$-0.358925\pi$
$167$	−1.79761	−	1.03785i	−0.139103	−	0.0803113i	−0.567937	+	0.823072i	$0.692258\pi$
$168$		0			0
$169$	−12.5984	+	3.20617i	−0.969110	+	0.246629i
$170$		0			0
$171$	8.30809	−	17.8810i	0.635336	−	1.36739i
$172$		0			0
$173$	7.17771	+	12.4322i	0.545711	+	0.945200i	0.998562	+	0.0536131i	$0.0170738\pi$
$173$	7.17771	+	12.4322i	0.545711	+	0.945200i	−0.452851	+	0.891586i	$0.649593\pi$
$174$		0			0
$175$	−43.5455	−	25.1410i	−3.29173	−	1.90048i
$176$		0			0
$177$	14.0451	−	15.3487i	1.05570	−	1.15368i
$178$		0			0
$179$	−4.08797			−0.305549			−0.152775	−	0.988261i	$-0.548821\pi$
$179$	−4.08797			−0.305549			−0.152775	+	0.988261i	$0.548821\pi$
$180$		0			0
$181$	−15.9509			−1.18562			−0.592810	−	0.805342i	$-0.701981\pi$
$181$	−15.9509			−1.18562			−0.592810	+	0.805342i	$0.701981\pi$
$182$		0			0
$183$	−7.62438	+	2.40973i	−0.563610	+	0.178132i
$184$		0			0
$185$	9.37400	−	16.2363i	0.689191	−	1.19371i
$186$		0			0
$187$	3.12077	−	1.80178i	0.228213	−	0.131759i
$188$		0			0
$189$	3.21140	−	24.7884i	0.233595	−	1.80309i
$190$		0			0
$191$	−4.96091	−	8.59255i	−0.358959	−	0.621735i	0.628828	−	0.777544i	$-0.283535\pi$
$191$	−4.96091	−	8.59255i	−0.358959	−	0.621735i	−0.987787	+	0.155809i	$0.950202\pi$
$192$		0			0
$193$	−13.2392	−	7.64366i	−0.952979	−	0.550203i	−0.0589743	−	0.998260i	$-0.518783\pi$
$193$	−13.2392	−	7.64366i	−0.952979	−	0.550203i	−0.894005	+	0.448057i	$0.852116\pi$
$194$		0			0
$195$	20.0301	+	14.1934i	1.43439	+	1.01641i
$196$		0			0
$197$			1.23481i			0.0879768i	0.999032	+	0.0439884i	$0.0140065\pi$
$197$			1.23481i			0.0879768i	−0.999032	+	0.0439884i	$0.985994\pi$
$198$		0			0
$199$	−5.64801			−0.400377			−0.200188	−	0.979757i	$-0.564155\pi$
$199$	−5.64801			−0.400377			−0.200188	+	0.979757i	$0.564155\pi$
$200$		0			0
$201$	3.31574	−	3.62350i	0.233874	−	0.255582i
$202$		0			0
$203$	4.28529	+	2.47411i	0.300768	+	0.173649i
$204$		0			0
$205$	4.92711	+	8.53401i	0.344125	+	0.596041i
$206$		0			0
$207$	−0.209872	+	0.147385i	−0.0145871	+	0.0102439i
$208$		0			0
$209$	−11.0457	−	19.1317i	−0.764046	−	1.32337i
$210$		0			0
$211$	−7.62853	+	13.2130i	−0.525170	+	0.909621i	0.474401	+	0.880309i	$0.342665\pi$
$211$	−7.62853	+	13.2130i	−0.525170	+	0.909621i	−0.999570	+	0.0293117i	$0.990668\pi$
$212$		0			0
$213$	−2.30738	−	0.509867i	−0.158099	−	0.0349355i
$214$		0			0
$215$			14.6158i			0.996787i
$216$		0			0
$217$	35.5592			2.41392
$218$		0			0
$219$	−4.52882	−	1.00074i	−0.306029	−	0.0676241i
$220$		0			0
$221$	−0.480385	−	3.83545i	−0.0323142	−	0.258000i
$222$		0			0
$223$	13.9167	−	8.03480i	0.931930	−	0.538050i	0.0445087	−	0.999009i	$-0.485828\pi$
$223$	13.9167	−	8.03480i	0.931930	−	0.538050i	0.887422	+	0.460959i	$0.152494\pi$
$224$		0			0
$225$	−2.77606	−	31.2353i	−0.185071	−	2.08235i
$226$		0			0
$227$	−4.18451	+	2.41593i	−0.277735	+	0.160351i	−0.632398	−	0.774644i	$-0.717929\pi$
$227$	−4.18451	+	2.41593i	−0.277735	+	0.160351i	0.354662	+	0.934994i	$0.384596\pi$
$228$		0			0
$229$	15.6874	+	9.05711i	1.03665	+	0.598510i	0.918883	−	0.394531i	$-0.129093\pi$
$229$	15.6874	+	9.05711i	1.03665	+	0.598510i	0.117768	+	0.993041i	$0.462426\pi$
$230$		0			0
$231$	−20.6610	−	18.9062i	−1.35940	−	1.24394i
$232$		0			0
$233$	−1.37594			−0.0901411			−0.0450705	−	0.998984i	$-0.514351\pi$
$233$	−1.37594			−0.0901411			−0.0450705	+	0.998984i	$0.514351\pi$
$234$		0			0
$235$	39.5731			2.58146
$236$		0			0
$237$	2.88343	−	0.911324i	0.187299	−	0.0591969i
$238$		0			0
$239$	−4.84277	−	2.79597i	−0.313253	−	0.180856i	0.335128	−	0.942172i	$-0.391220\pi$
$239$	−4.84277	−	2.79597i	−0.313253	−	0.180856i	−0.648381	+	0.761316i	$0.724554\pi$
$240$		0			0
$241$	−10.4450	+	6.03041i	−0.672820	+	0.388453i	−0.797144	−	0.603789i	$-0.793657\pi$
$241$	−10.4450	+	6.03041i	−0.672820	+	0.388453i	0.124324	+	0.992242i	$0.460324\pi$
$242$		0			0
$243$	13.8023	−	7.24549i	0.885417	−	0.464798i
$244$		0			0
$245$	54.9458	−	31.7230i	3.51036	−	2.02671i
$246$		0			0
$247$	−23.5130	+	2.94497i	−1.49610	+	0.187384i
$248$		0			0
$249$	7.35531	+	23.2722i	0.466124	+	1.47482i
$250$		0			0
$251$	9.90201			0.625009			0.312505	−	0.949916i	$-0.398832\pi$
$251$	9.90201			0.625009			0.312505	+	0.949916i	$0.398832\pi$
$252$		0			0
$253$			0.287338i			0.0180648i
$254$		0			0
$255$	−4.92772	+	5.38509i	−0.308586	+	0.337228i
$256$		0			0
$257$	−0.0748821	+	0.129700i	−0.00467102	+	0.00809044i	−0.868351	−	0.495949i	$-0.834820\pi$
$257$	−0.0748821	+	0.129700i	−0.00467102	+	0.00809044i	0.863680	+	0.504040i	$0.168154\pi$
$258$		0			0
$259$	11.4710	+	19.8684i	0.712775	+	1.23456i
$260$		0			0
$261$	0.273190	+	3.07384i	0.0169101	+	0.190266i
$262$		0			0
$263$	−3.18077	−	5.50926i	−0.196135	−	0.339716i	0.751137	−	0.660146i	$-0.229506\pi$
$263$	−3.18077	−	5.50926i	−0.196135	−	0.339716i	−0.947272	+	0.320431i	$0.896172\pi$
$264$		0			0
$265$	−19.7577	−	11.4071i	−1.21371	−	0.700734i
$266$		0			0
$267$	15.8210	+	3.49601i	0.968230	+	0.213952i
$268$		0			0
$269$	8.43403			0.514232			0.257116	−	0.966381i	$-0.417228\pi$
$269$	8.43403			0.514232			0.257116	+	0.966381i	$0.417228\pi$
$270$		0			0
$271$			3.97794i			0.241643i	0.992674	+	0.120821i	$0.0385528\pi$
$271$			3.97794i			0.241643i	−0.992674	+	0.120821i	$0.961447\pi$
$272$		0			0
$273$	−27.2971	+	12.5429i	−1.65210	+	0.759128i
$274$		0			0
$275$	−30.4277	−	17.5674i	−1.83486	−	1.05936i
$276$		0			0
$277$	−0.463857	−	0.803425i	−0.0278705	−	0.0482731i	0.851754	−	0.523942i	$-0.175539\pi$
$277$	−0.463857	−	0.803425i	−0.0278705	−	0.0482731i	−0.879624	+	0.475669i	$0.842206\pi$
$278$		0			0
$279$	12.7449	+	18.1484i	0.763018	+	1.08652i
$280$		0			0
$281$	−21.1864	+	12.2320i	−1.26387	+	0.729698i	−0.973822	−	0.227312i	$-0.927006\pi$
$281$	−21.1864	+	12.2320i	−1.26387	+	0.729698i	−0.290053	+	0.957011i	$0.593673\pi$
$282$		0			0
$283$	4.48336	−	7.76541i	0.266508	−	0.461606i	−0.701450	−	0.712719i	$-0.747463\pi$
$283$	4.48336	−	7.76541i	0.266508	−	0.461606i	0.967958	+	0.251114i	$0.0807968\pi$
$284$		0			0
$285$	33.0130	+	30.2091i	1.95552	+	1.78943i
$286$		0			0
$287$	−12.0587			−0.711801
$288$		0			0
$289$	−15.8507			−0.932392
$290$		0			0
$291$	−4.00289	−	12.6651i	−0.234654	−	0.742444i
$292$		0			0
$293$	0.734208	+	0.423895i	0.0428929	+	0.0247642i	0.521293	−	0.853378i	$-0.325450\pi$
$293$	0.734208	+	0.423895i	0.0428929	+	0.0247642i	−0.478400	+	0.878142i	$0.658783\pi$
$294$		0			0
$295$	23.6092	+	40.8923i	1.37458	+	2.38084i
$296$		0			0
$297$	2.24398	−	17.3210i	0.130209	−	1.00507i
$298$		0			0
$299$	0.284008	+	0.119742i	0.0164246	+	0.00692485i
$300$		0			0
$301$	−15.4892	−	8.94270i	−0.892783	−	0.515449i
$302$		0			0
$303$	24.5764	−	7.76751i	1.41188	−	0.446232i
$304$		0			0
$305$		−	18.1477i		−	1.03914i
$306$		0			0
$307$			22.2228i			1.26832i	0.773201	+	0.634162i	$0.218655\pi$
$307$			22.2228i			1.26832i	−0.773201	+	0.634162i	$0.781345\pi$
$308$		0			0
$309$	−24.1965	−	22.1414i	−1.37649	−	1.25958i
$310$		0			0
$311$	−13.5320	+	23.4382i	−0.767331	+	1.32906i	0.171674	+	0.985154i	$0.445082\pi$
$311$	−13.5320	+	23.4382i	−0.767331	+	1.32906i	−0.939005	+	0.343903i	$0.888251\pi$
$312$		0			0
$313$	−10.6275	−	18.4074i	−0.600703	−	1.04045i	−0.992715	−	0.120488i	$-0.961554\pi$
$313$	−10.6275	−	18.4074i	−0.600703	−	1.04045i	0.392012	−	0.919960i	$-0.371779\pi$
$314$		0			0
$315$	51.4469	+	23.9039i	2.89871	+	1.34683i
$316$		0			0
$317$	−9.41447	+	5.43545i	−0.528770	+	0.305285i	−0.740515	−	0.672040i	$-0.765418\pi$
$317$	−9.41447	+	5.43545i	−0.528770	+	0.305285i	0.211746	+	0.977325i	$0.432085\pi$
$318$		0			0
$319$	2.99437	+	1.72880i	0.167653	+	0.0967943i
$320$		0			0
$321$	5.49350	−	24.8605i	0.306617	−	1.38758i
$322$		0			0
$323$		−	7.04597i		−	0.392048i
$324$		0			0
$325$	−30.0439	+	22.7542i	−1.66654	+	1.26218i
$326$		0			0
$327$	7.43510	+	1.64295i	0.411162	+	0.0908556i
$328$		0			0
$329$	−24.2129	+	41.9380i	−1.33490	+	2.31212i
$330$		0			0
$331$	6.42626	−	3.71020i	0.353219	−	0.203931i	−0.312883	−	0.949792i	$-0.601295\pi$
$331$	6.42626	−	3.71020i	0.353219	−	0.203931i	0.666102	+	0.745860i	$0.267961\pi$
$332$		0			0
$333$	−6.02888	+	12.9756i	−0.330381	+	0.711058i
$334$		0			0
$335$	5.57361	+	9.65377i	0.304519	+	0.527442i
$336$		0			0
$337$	10.1784	−	17.6296i	0.554455	−	0.960345i	−0.443490	−	0.896279i	$-0.646260\pi$
$337$	10.1784	−	17.6296i	0.554455	−	0.960345i	0.997946	−	0.0640656i	$-0.0204067\pi$
$338$		0			0
$339$	3.14841	+	2.88100i	0.170998	+	0.156474i
$340$		0			0
$341$	24.8472			1.34555
$342$		0			0
$343$			43.9665i			2.37397i
$344$		0			0
$345$	−0.175404	−	0.554979i	−0.00944345	−	0.0298791i
$346$		0			0
$347$	−4.83922	+	8.38177i	−0.259783	+	0.449957i	−0.966184	−	0.257855i	$-0.916984\pi$
$347$	−4.83922	+	8.38177i	−0.259783	+	0.449957i	0.706401	+	0.707812i	$0.250318\pi$
$348$		0			0
$349$	20.3188	−	11.7311i	1.08764	−	0.627949i	0.154693	−	0.987963i	$-0.450561\pi$
$349$	20.3188	−	11.7311i	1.08764	−	0.627949i	0.932947	+	0.360014i	$0.117228\pi$
$350$		0			0
$351$	−16.1852	−	9.43613i	−0.863900	−	0.503663i
$352$		0			0
$353$	−9.12721	+	5.26960i	−0.485792	+	0.280472i	−0.722827	−	0.691029i	$-0.757158\pi$
$353$	−9.12721	+	5.26960i	−0.485792	+	0.280472i	0.237035	+	0.971501i	$0.423824\pi$
$354$		0			0
$355$	2.68154	−	4.64456i	0.142321	−	0.246508i
$356$		0			0
$357$	−2.69187	−	8.51709i	−0.142469	−	0.450772i
$358$		0			0
$359$		−	33.8494i		−	1.78650i	−0.449557	−	0.893252i	$-0.648418\pi$
$359$		−	33.8494i		−	1.78650i	0.449557	−	0.893252i	$-0.351582\pi$
$360$		0			0
$361$	−24.1949			−1.27341
$362$		0			0
$363$	−0.381158	−	0.348784i	−0.0200056	−	0.0183064i
$364$		0			0
$365$	5.26320	−	9.11613i	0.275489	−	0.477160i
$366$		0			0
$367$	−0.752021	−	1.30254i	−0.0392552	−	0.0679920i	0.845730	−	0.533611i	$-0.179165\pi$
$367$	−0.752021	−	1.30254i	−0.0392552	−	0.0679920i	−0.884985	+	0.465619i	$0.845832\pi$
$368$		0			0
$369$	−4.32199	−	6.15440i	−0.224994	−	0.320385i
$370$		0			0
$371$	24.1776	−	13.9590i	1.25524	−	0.724713i
$372$		0			0
$373$	10.6689	−	18.4790i	0.552414	−	0.956808i	−0.445686	−	0.895189i	$-0.647040\pi$
$373$	10.6689	−	18.4790i	0.552414	−	0.956808i	0.998100	−	0.0616191i	$-0.0196264\pi$
$374$		0			0
$375$	36.2519	+	8.01068i	1.87204	+	0.413670i
$376$		0			0
$377$	2.95660	−	2.23923i	0.152273	−	0.115326i
$378$		0			0
$379$		−	13.1930i		−	0.677681i	−0.940844	−	0.338840i	$-0.889965\pi$
$379$		−	13.1930i		−	0.677681i	0.940844	−	0.338840i	$-0.110035\pi$
$380$		0			0
$381$	6.43318	−	29.1130i	0.329582	−	1.49151i
$382$		0			0
$383$	−6.64542	−	3.83673i	−0.339565	−	0.196048i	0.320515	−	0.947244i	$-0.396144\pi$
$383$	−6.64542	−	3.83673i	−0.339565	−	0.196048i	−0.660080	+	0.751196i	$0.729477\pi$
$384$		0			0
$385$	55.0454	−	31.7805i	2.80537	−	1.61968i
$386$		0			0
$387$	−0.987449	−	11.1104i	−0.0501949	−	0.564775i
$388$		0			0
$389$	−1.23245	−	2.13467i	−0.0624877	−	0.108232i	0.833089	−	0.553139i	$-0.186570\pi$
$389$	−1.23245	−	2.13467i	−0.0624877	−	0.108232i	−0.895577	+	0.444907i	$0.853237\pi$
$390$		0			0
$391$	−0.0458228	+	0.0793675i	−0.00231736	+	0.00401379i
$392$		0			0
$393$	−10.8046	−	9.88688i	−0.545018	−	0.498727i
$394$		0			0
$395$			6.86321i			0.345325i
$396$		0			0
$397$		−	30.6817i		−	1.53987i	−0.638121	−	0.769936i	$-0.720288\pi$
$397$		−	30.6817i		−	1.53987i	0.638121	−	0.769936i	$-0.279712\pi$
$398$		0			0
$399$	−52.2135	+	16.5024i	−2.61394	+	0.826151i
$400$		0			0
$401$	28.8517	+	16.6575i	1.44078	+	0.831837i	0.997902	−	0.0647435i	$-0.0206229\pi$
$401$	28.8517	+	16.6575i	1.44078	+	0.831837i	0.442881	+	0.896580i	$0.353956\pi$
$402$		0			0
$403$	10.3545	−	24.5593i	0.515795	−	1.22338i
$404$		0			0
$405$	6.23940	+	34.8245i	0.310038	+	1.73044i
$406$		0			0
$407$	8.01545	+	13.8832i	0.397311	+	0.688163i
$408$		0			0
$409$	29.0463	+	16.7699i	1.43625	+	0.829219i	0.997587	−	0.0694331i	$-0.0221190\pi$
$409$	29.0463	+	16.7699i	1.43625	+	0.829219i	0.438662	+	0.898652i	$0.355452\pi$
$410$		0			0
$411$	9.51542	+	30.1068i	0.469361	+	1.48506i
$412$		0			0
$413$	−57.7814			−2.84324
$414$		0			0
$415$	−55.3930			−2.71914
$416$		0			0
$417$	−14.7206	−	13.4703i	−0.720871	−	0.659644i
$418$		0			0
$419$	−2.84913	+	4.93483i	−0.139189	+	0.241082i	−0.927190	−	0.374592i	$-0.877783\pi$
$419$	−2.84913	+	4.93483i	−0.139189	+	0.241082i	0.788001	+	0.615674i	$0.211116\pi$
$420$		0			0
$421$	−18.0959	+	10.4477i	−0.881939	+	0.509188i	−0.871297	−	0.490755i	$-0.836721\pi$
$421$	−18.0959	+	10.4477i	−0.881939	+	0.509188i	−0.0106421	+	0.999943i	$0.503388\pi$
$422$		0			0
$423$	−30.0822	+	2.67358i	−1.46265	+	0.129994i
$424$		0			0
$425$	−5.60308	−	9.70482i	−0.271789	−	0.470753i
$426$		0			0
$427$	19.2322	+	11.1037i	0.930714	+	0.537348i
$428$		0			0
$429$	−19.0740	+	8.76440i	−0.920903	+	0.423149i
$430$		0			0
$431$			26.6529i			1.28382i	0.766778	+	0.641912i	$0.221859\pi$
$431$			26.6529i			1.28382i	−0.766778	+	0.641912i	$0.778141\pi$
$432$		0			0
$433$	29.5411			1.41965			0.709827	−	0.704376i	$-0.248773\pi$
$433$	29.5411			1.41965			0.709827	+	0.704376i	$0.248773\pi$
$434$		0			0
$435$	−6.83881	−	1.51119i	−0.327896	−	0.0724560i
$436$		0			0
$437$	0.486557	+	0.280914i	0.0232752	+	0.0134379i
$438$		0			0
$439$	3.60721	+	6.24786i	0.172163	+	0.298194i	0.939176	−	0.343437i	$-0.111591\pi$
$439$	3.60721	+	6.24786i	0.172163	+	0.298194i	−0.767013	+	0.641631i	$0.778258\pi$
$440$		0			0
$441$	−39.6248	+	27.8270i	−1.88690	+	1.32509i
$442$		0			0
$443$	−4.26300	−	7.38373i	−0.202541	−	0.350812i	0.746805	−	0.665043i	$-0.231587\pi$
$443$	−4.26300	−	7.38373i	−0.202541	−	0.350812i	−0.949347	+	0.314231i	$0.898253\pi$
$444$		0			0
$445$	−18.3865	+	31.8464i	−0.871604	+	1.50966i
$446$		0			0
$447$	5.09290	−	5.56561i	0.240886	−	0.263244i
$448$		0			0
$449$			14.0039i			0.660883i	0.943826	+	0.330441i	$0.107198\pi$
$449$			14.0039i			0.660883i	−0.943826	+	0.330441i	$0.892802\pi$
$450$		0			0
$451$	−8.42608			−0.396769
$452$		0			0
$453$	−2.23502	−	7.07161i	−0.105010	−	0.332253i
$454$		0			0
$455$	−8.47323	−	67.6512i	−0.397231	−	3.17154i
$456$		0			0
$457$	29.6357	−	17.1102i	1.38630	−	0.800380i	0.393402	−	0.919366i	$-0.371298\pi$
$457$	29.6357	−	17.1102i	1.38630	−	0.800380i	0.992896	+	0.118987i	$0.0379646\pi$
$458$		0			0
$459$	3.38207	−	4.42649i	0.157861	−	0.206611i
$460$		0			0
$461$	−7.56297	+	4.36648i	−0.352242	+	0.203367i	−0.665672	−	0.746244i	$-0.731855\pi$
$461$	−7.56297	+	4.36648i	−0.352242	+	0.203367i	0.313430	+	0.949611i	$0.398522\pi$
$462$		0			0
$463$	0.0993345	+	0.0573508i	0.00461646	+	0.00266532i	0.502306	−	0.864690i	$-0.332485\pi$
$463$	0.0993345	+	0.0573508i	0.00461646	+	0.00266532i	−0.497690	+	0.867355i	$0.665818\pi$
$464$		0			0
$465$	−47.9911	+	15.1679i	−2.22553	+	0.703393i
$466$		0			0
$467$	42.6123			1.97186			0.985932	−	0.167147i	$-0.0534556\pi$
$467$	42.6123			1.97186			0.985932	+	0.167147i	$0.0534556\pi$
$468$		0			0
$469$	−13.6409			−0.629879
$470$		0			0
$471$	0.161044	+	0.147366i	0.00742052	+	0.00679027i
$472$		0			0
$473$	−10.8232	−	6.24877i	−0.497650	−	0.287319i
$474$		0			0
$475$	−59.4948	+	34.3493i	−2.72981	+	1.57606i
$476$		0			0
$477$	15.7898	+	7.33648i	0.722967	+	0.335914i
$478$		0			0
$479$	−26.1199	+	15.0803i	−1.19345	+	0.689037i	−0.959086	−	0.283113i	$-0.908633\pi$
$479$	−26.1199	+	15.0803i	−1.19345	+	0.689037i	−0.234360	+	0.972150i	$0.575299\pi$
$480$		0			0
$481$	17.0625	−	2.13706i	0.777984	−	0.0974415i
$482$		0			0
$483$	0.695467	+	0.153679i	0.0316448	+	0.00699264i
$484$		0			0
$485$	30.1459			1.36885
$486$		0			0
$487$		−	1.98683i		−	0.0900319i	−0.998986	−	0.0450160i	$-0.985666\pi$
$487$		−	1.98683i		−	0.0900319i	0.998986	−	0.0450160i	$-0.0143339\pi$
$488$		0			0
$489$	28.1242	+	6.21469i	1.27182	+	0.281038i
$490$		0			0
$491$	−9.16415	+	15.8728i	−0.413572	+	0.716328i	−0.995277	−	0.0970714i	$-0.969052\pi$
$491$	−9.16415	+	15.8728i	−0.413572	+	0.716328i	0.581705	+	0.813400i	$0.302386\pi$
$492$		0			0
$493$	0.551396	+	0.955045i	0.0248336	+	0.0430131i
$494$		0			0
$495$	35.9489	+	16.7030i	1.61578	+	0.750745i
$496$		0			0
$497$	3.28141	+	5.68357i	0.147192	+	0.254943i
$498$		0			0
$499$	1.45294	+	0.838857i	0.0650427	+	0.0375524i	0.532169	−	0.846638i	$-0.321377\pi$
$499$	1.45294	+	0.838857i	0.0650427	+	0.0375524i	−0.467126	+	0.884191i	$0.654711\pi$
$500$		0			0
$501$	−2.42707	+	2.65234i	−0.108433	+	0.118498i
$502$		0			0
$503$	3.47253			0.154833			0.0774163	−	0.996999i	$-0.475333\pi$
$503$	3.47253			0.154833			0.0774163	+	0.996999i	$0.475333\pi$
$504$		0			0
$505$			58.4973i			2.60310i
$506$		0			0
$507$	0.714151	+	22.5053i	0.0317166	+	0.999497i
$508$		0			0
$509$	16.0585	+	9.27140i	0.711782	+	0.410948i	0.811720	−	0.584046i	$-0.198531\pi$
$509$	16.0585	+	9.27140i	0.711782	+	0.410948i	−0.0999385	+	0.994994i	$0.531865\pi$
$510$		0			0
$511$	6.44061	+	11.1555i	0.284916	+	0.493489i
$512$		0			0
$513$	−27.1363	−	20.7336i	−1.19810	−	0.915409i
$514$		0			0
$515$	64.4645	−	37.2186i	2.84065	−	1.64005i
$516$		0			0
$517$	−16.9189	+	29.3044i	−0.744093	+	1.28881i
$518$		0			0
$519$	23.7084	−	7.49316i	1.04068	−	0.328913i
$520$		0			0
$521$	25.7368			1.12755			0.563775	−	0.825929i	$-0.309349\pi$
$521$	25.7368			1.12755			0.563775	+	0.825929i	$0.309349\pi$
$522$		0			0
$523$	−6.85993			−0.299964			−0.149982	−	0.988689i	$-0.547922\pi$
$523$	−6.85993			−0.299964			−0.149982	+	0.988689i	$0.547922\pi$
$524$		0			0
$525$	−58.7937	+	64.2508i	−2.56597	+	2.80413i
$526$		0			0
$527$	6.86320	+	3.96247i	0.298966	+	0.172608i
$528$		0			0
$529$	11.4963	+	19.9123i	0.499841	+	0.865750i
$530$		0			0
$531$	−20.7097	−	29.4900i	−0.898722	−	1.27976i
$532$		0			0
$533$	−3.51138	+	8.32842i	−0.152095	+	0.360744i
$534$		0			0
$535$	50.0422	+	28.8919i	2.16351	+	1.24910i
$536$		0			0
$537$	−1.52776	+	6.91379i	−0.0659276	+	0.298352i
$538$		0			0
$539$			54.2509i			2.33675i
$540$		0			0
$541$		−	19.9869i		−	0.859306i	−0.902994	−	0.429653i	$-0.858636\pi$
$541$		−	19.9869i		−	0.859306i	0.902994	−	0.429653i	$-0.141364\pi$
$542$		0			0
$543$	−5.96117	+	26.9770i	−0.255818	+	1.15769i
$544$		0			0
$545$	−8.64077	+	14.9662i	−0.370130	+	0.641084i
$546$		0			0
$547$	−7.24562	−	12.5498i	−0.309800	−	0.536590i	0.668518	−	0.743696i	$-0.266929\pi$
$547$	−7.24562	−	12.5498i	−0.309800	−	0.536590i	−0.978319	+	0.207106i	$0.933596\pi$
$548$		0			0
$549$	1.22607	+	13.7953i	0.0523274	+	0.588770i
$550$		0			0
$551$	5.85485	−	3.38030i	0.249425	−	0.144005i
$552$		0			0
$553$	−7.27336	−	4.19927i	−0.309295	−	0.178571i
$554$		0			0
$555$	−23.9563	−	21.9216i	−1.01689	−	0.930521i
$556$		0			0
$557$		−	12.8651i		−	0.545110i	−0.962140	−	0.272555i	$-0.912131\pi$
$557$		−	12.8651i		−	0.545110i	0.962140	−	0.272555i	$-0.0878687\pi$
$558$		0			0
$559$	−10.6867	+	8.09371i	−0.451998	+	0.342328i
$560$		0			0
$561$	−1.88096	−	5.95137i	−0.0794143	−	0.251267i
$562$		0			0
$563$	−2.23678	+	3.87421i	−0.0942689	+	0.163278i	−0.909303	−	0.416134i	$-0.863385\pi$
$563$	−2.23678	+	3.87421i	−0.0942689	+	0.163278i	0.815034	+	0.579413i	$0.196718\pi$
$564$		0			0
$565$	−8.38802	+	4.84283i	−0.352887	+	0.203739i
$566$		0			0
$567$	−40.7232	−	14.6952i	−1.71022	−	0.617141i
$568$		0			0
$569$	21.7045	+	37.5933i	0.909900	+	1.57599i	0.814202	+	0.580582i	$0.197175\pi$
$569$	21.7045	+	37.5933i	0.909900	+	1.57599i	0.0956977	+	0.995410i	$0.469492\pi$
$570$		0			0
$571$	−9.96107	+	17.2531i	−0.416858	+	0.722019i	−0.995621	−	0.0934764i	$-0.970202\pi$
$571$	−9.96107	+	17.2531i	−0.416858	+	0.722019i	0.578764	+	0.815495i	$0.303535\pi$
$572$		0			0
$573$	−16.3862	+	5.17894i	−0.684542	+	0.216353i
$574$		0			0
$575$	0.893552			0.0372637
$576$		0			0
$577$		−	40.2426i		−	1.67532i	−0.546190	−	0.837661i	$-0.683922\pi$
$577$		−	40.2426i		−	1.67532i	0.546190	−	0.837661i	$-0.316078\pi$
$578$		0			0
$579$	−17.8751	+	19.5343i	−0.742865	+	0.811816i
$580$		0			0
$581$	33.8924	−	58.7034i	1.40609	−	2.43543i
$582$		0			0
$583$	16.8943	−	9.75392i	0.699690	−	0.403966i
$584$		0			0
$585$	31.4903	−	28.5716i	1.30196	−	1.18129i
$586$		0			0
$587$	5.59848	−	3.23229i	0.231074	−	0.133411i	−0.379993	−	0.924989i	$-0.624074\pi$
$587$	5.59848	−	3.23229i	0.231074	−	0.133411i	0.611068	+	0.791578i	$0.290740\pi$
$588$		0			0
$589$	24.2917	−	42.0744i	1.00092	−	1.73365i
$590$		0			0
$591$	2.08838	+	0.461475i	0.0859045	+	0.0189825i
$592$		0			0
$593$		−	20.8574i		−	0.856510i	−0.903658	−	0.428255i	$-0.859129\pi$
$593$		−	20.8574i		−	0.856510i	0.903658	−	0.428255i	$-0.140871\pi$
$594$		0			0
$595$	20.2726			0.831094
$596$		0			0
$597$	−2.11078	+	9.55221i	−0.0863883	+	0.390946i
$598$		0			0
$599$	−3.67196	+	6.36003i	−0.150032	+	0.259864i	−0.931239	−	0.364409i	$-0.881271\pi$
$599$	−3.67196	+	6.36003i	−0.150032	+	0.259864i	0.781207	+	0.624272i	$0.214604\pi$
$600$		0			0
$601$	5.37782	+	9.31465i	0.219366	+	0.379953i	0.954614	−	0.297845i	$-0.0962679\pi$
$601$	5.37782	+	9.31465i	0.219366	+	0.379953i	−0.735248	+	0.677798i	$0.762935\pi$
$602$		0			0
$603$	−4.88909	−	6.96193i	−0.199099	−	0.283512i
$604$		0			0
$605$	1.01549	−	0.586291i	0.0412854	−	0.0238361i
$606$		0			0
$607$	8.29221	−	14.3625i	0.336570	−	0.582957i	−0.647215	−	0.762308i	$-0.724066\pi$
$607$	8.29221	−	14.3625i	0.336570	−	0.582957i	0.983785	+	0.179351i	$0.0573997\pi$
$608$		0			0
$609$	5.78585	−	6.32288i	0.234454	−	0.256216i
$610$		0			0
$611$	21.9142	+	28.9348i	0.886555	+	1.17058i
$612$		0			0
$613$			4.54150i			0.183429i	0.995785	+	0.0917147i	$0.0292348\pi$
$613$			4.54150i			0.183429i	−0.995785	+	0.0917147i	$0.970765\pi$
$614$		0			0
$615$	16.2745	−	5.14366i	0.656252	−	0.207412i
$616$		0			0
$617$	−0.149964	−	0.0865815i	−0.00603731	−	0.00348564i	0.496978	−	0.867763i	$-0.334443\pi$
$617$	−0.149964	−	0.0865815i	−0.00603731	−	0.00348564i	−0.503016	+	0.864277i	$0.667776\pi$
$618$		0			0
$619$	−23.6778	+	13.6704i	−0.951692	+	0.549460i	−0.893606	−	0.448852i	$-0.851833\pi$
$619$	−23.6778	+	13.6704i	−0.951692	+	0.549460i	−0.0580858	+	0.998312i	$0.518500\pi$
$620$		0			0
$621$	0.170831	+	0.410027i	0.00685523	+	0.0164538i
$622$		0			0
$623$	−22.4997	−	38.9706i	−0.901431	−	1.56132i
$624$		0			0
$625$	−15.9985	+	27.7101i	−0.639938	+	1.10841i
$626$		0			0
$627$	−36.4845	+	11.5311i	−1.45705	+	0.460509i
$628$		0			0
$629$			5.11301i			0.203869i
$630$		0			0
$631$			37.8137i			1.50534i	0.658397	+	0.752670i	$0.271235\pi$
$631$			37.8137i			1.50534i	−0.658397	+	0.752670i	$0.728765\pi$
$632$		0			0
$633$	19.4956	+	17.8397i	0.774880	+	0.709066i
$634$		0			0
$635$	58.6021	+	33.8339i	2.32555	+	1.34266i
$636$		0			0
$637$	53.6221	+	22.6078i	2.12459	+	0.895755i
$638$		0			0
$639$	−1.72463	+	3.71181i	−0.0682252	+	0.146837i
$640$		0			0
$641$	−3.77702	−	6.54200i	−0.149184	−	0.258393i	0.781742	−	0.623601i	$-0.214331\pi$
$641$	−3.77702	−	6.54200i	−0.149184	−	0.258393i	−0.930926	+	0.365208i	$0.880998\pi$
$642$		0			0
$643$	24.2155	+	13.9808i	0.954964	+	0.551349i	0.894620	−	0.446829i	$-0.147447\pi$
$643$	24.2155	+	13.9808i	0.954964	+	0.551349i	0.0603447	+	0.998178i	$0.480780\pi$
$644$		0			0
$645$	24.7189	+	5.46221i	0.973307	+	0.215074i
$646$		0			0
$647$	−5.98842			−0.235429			−0.117715	−	0.993047i	$-0.537557\pi$
$647$	−5.98842			−0.235429			−0.117715	+	0.993047i	$0.537557\pi$
$648$		0			0
$649$	−40.3751			−1.58486
$650$		0			0
$651$	13.2892	−	60.1396i	0.520845	−	2.35706i
$652$		0			0
$653$	8.90801	−	15.4291i	0.348597	−	0.603789i	−0.637403	−	0.770531i	$-0.719991\pi$
$653$	8.90801	−	15.4291i	0.348597	−	0.603789i	0.986001	+	0.166742i	$0.0533247\pi$
$654$		0			0
$655$	28.7857	−	16.6194i	1.12475	−	0.649374i
$656$		0			0
$657$	−3.38502	+	7.28537i	−0.132062	+	0.284229i
$658$		0			0
$659$	23.8222	+	41.2613i	0.927982	+	1.60731i	0.786694	+	0.617343i	$0.211791\pi$
$659$	23.8222	+	41.2613i	0.927982	+	1.60731i	0.141288	+	0.989969i	$0.454876\pi$
$660$		0			0
$661$	−4.59633	−	2.65370i	−0.178777	−	0.103217i	0.407941	−	0.913008i	$-0.366247\pi$
$661$	−4.59633	−	2.65370i	−0.178777	−	0.103217i	−0.586718	+	0.809791i	$0.699580\pi$
$662$		0			0
$663$	−6.66624	−	0.620934i	−0.258895	−	0.0241151i
$664$		0			0
$665$		−	124.280i		−	4.81936i
$666$		0			0
$667$	−0.0879339			−0.00340481
$668$		0			0
$669$	−8.38792	−	26.5394i	−0.324296	−	1.02607i
$670$		0			0
$671$	13.4387	+	7.75881i	0.518794	+	0.299526i
$672$		0			0
$673$	13.9628	+	24.1842i	0.538225	+	0.932233i	0.999000	+	0.0447160i	$0.0142383\pi$
$673$	13.9628	+	24.1842i	0.538225	+	0.932233i	−0.460775	+	0.887517i	$0.652428\pi$
$674$		0			0
$675$	−53.8642	−	6.97823i	−2.07323	−	0.268592i
$676$		0			0
$677$	−9.19203	−	15.9211i	−0.353278	−	0.611896i	0.633544	−	0.773707i	$-0.281600\pi$
$677$	−9.19203	−	15.9211i	−0.353278	−	0.611896i	−0.986822	+	0.161811i	$0.948266\pi$
$678$		0			0
$679$	−18.4449	+	31.9474i	−0.707848	+	1.22603i
$680$		0			0
$681$	2.52210	+	7.97993i	0.0966472	+	0.305792i
$682$		0			0
$683$		−	27.5533i		−	1.05430i	−0.849773	−	0.527149i	$-0.823261\pi$
$683$		−	27.5533i		−	1.05430i	0.849773	−	0.527149i	$-0.176739\pi$
$684$		0			0
$685$	−71.6609			−2.73802
$686$		0			0
$687$	21.1805	−	23.1465i	0.808088	−	0.883093i
$688$		0			0
$689$	−2.60056	−	20.7632i	−0.0990736	−	0.791015i
$690$		0			0
$691$	18.0882	−	10.4432i	0.688109	−	0.397280i	−0.114795	−	0.993389i	$-0.536621\pi$
$691$	18.0882	−	10.4432i	0.688109	−	0.397280i	0.802903	+	0.596110i	$0.203288\pi$
$692$		0			0
$693$	−39.6966	+	27.8774i	−1.50795	+	1.05897i
$694$		0			0
$695$	39.2188	−	22.6430i	1.48765	−	0.858897i
$696$		0			0
$697$	−2.32742	−	1.34374i	−0.0881573	−	0.0508976i
$698$		0			0
$699$	−0.514218	+	2.32707i	−0.0194495	+	0.0880178i
$700$		0			0
$701$	39.0518			1.47496			0.737482	−	0.675366i	$-0.236014\pi$
$701$	39.0518			1.47496			0.737482	+	0.675366i	$0.236014\pi$
$702$		0			0
$703$	31.3450			1.18220
$704$		0			0
$705$	14.7893	−	66.9280i	0.556996	−	2.52066i
$706$		0			0
$707$	−61.9932	−	35.7918i	−2.33149	−	1.34609i
$708$		0			0
$709$	2.00983	−	1.16037i	0.0754807	−	0.0435788i	−0.461785	−	0.886992i	$-0.652791\pi$
$709$	2.00983	−	1.16037i	0.0754807	−	0.0435788i	0.537265	+	0.843413i	$0.319457\pi$
$710$		0			0
$711$	−0.463682	−	5.21719i	−0.0173894	−	0.195660i
$712$		0			0
$713$	−0.547255	+	0.315958i	−0.0204949	+	0.0118327i
$714$		0			0
$715$	−5.92072	−	47.2717i	−0.221423	−	1.76786i
$716$		0			0
$717$	−6.53854	+	7.14543i	−0.244186	+	0.266851i
$718$		0			0
$719$	−7.04587			−0.262767			−0.131383	−	0.991332i	$-0.541942\pi$
$719$	−7.04587			−0.262767			−0.131383	+	0.991332i	$0.541942\pi$
$720$		0			0
$721$			91.0893i			3.39234i
$722$		0			0
$723$	6.29544	+	19.9188i	0.234130	+	0.740788i
$724$		0			0
$725$	5.37615	−	9.31176i	0.199665	−	0.345830i
$726$		0			0
$727$	−3.57535	−	6.19269i	−0.132602	−	0.229674i	0.792077	−	0.610422i	$-0.209000\pi$
$727$	−3.57535	−	6.19269i	−0.132602	−	0.229674i	−0.924679	+	0.380748i	$0.875667\pi$
$728$		0			0
$729$	−7.09575	−	26.0509i	−0.262806	−	0.964849i
$730$		0			0
$731$	−1.99302	−	3.45202i	−0.0737147	−	0.127678i
$732$		0			0
$733$	7.90471	+	4.56378i	0.291967	+	0.168567i	0.638829	−	0.769349i	$-0.279419\pi$
$733$	7.90471	+	4.56378i	0.291967	+	0.168567i	−0.346862	+	0.937916i	$0.612753\pi$
$734$		0			0
$735$	−33.1172	−	104.783i	−1.22155	−	3.86497i
$736$		0			0
$737$	−9.53168			−0.351104
$738$		0			0
$739$		−	44.0839i		−	1.62165i	−0.585286	−	0.810827i	$-0.699018\pi$
$739$		−	44.0839i		−	1.62165i	0.585286	−	0.810827i	$-0.300982\pi$
$740$		0			0
$741$	−3.80660	+	40.8670i	−0.139839	+	1.50129i
$742$		0			0
$743$	−22.0405	−	12.7251i	−0.808586	−	0.466838i	0.0378784	−	0.999282i	$-0.487940\pi$
$743$	−22.0405	−	12.7251i	−0.808586	−	0.466838i	−0.846465	+	0.532445i	$0.821273\pi$
$744$		0			0
$745$	8.56093	+	14.8280i	0.313648	+	0.543255i
$746$		0			0
$747$	42.1080	−	3.74239i	1.54065	−	0.136927i
$748$		0			0
$749$	−61.2369	+	35.3551i	−2.23755	+	1.29185i
$750$		0			0
$751$	1.96715	−	3.40721i	0.0717824	−	0.124331i	−0.827900	−	0.560876i	$-0.810465\pi$
$751$	1.96715	−	3.40721i	0.0717824	−	0.124331i	0.899683	+	0.436545i	$0.143798\pi$
$752$		0			0
$753$	3.70058	−	16.7468i	0.134857	−	0.610287i
$754$		0			0
$755$	16.8320			0.612579
$756$		0			0
$757$	33.9336			1.23334			0.616669	−	0.787223i	$-0.288482\pi$
$757$	33.9336			1.23334			0.616669	+	0.787223i	$0.288482\pi$
$758$		0			0
$759$	0.485962	+	0.107384i	0.0176393	+	0.00389780i
$760$		0			0
$761$	9.27065	+	5.35241i	0.336061	+	0.194025i	0.658529	−	0.752556i	$-0.271179\pi$
$761$	9.27065	+	5.35241i	0.336061	+	0.194025i	−0.322468	+	0.946580i	$0.604512\pi$
$762$		0			0
$763$	−10.5738	−	18.3143i	−0.382796	−	0.663022i
$764$		0			0
$765$	7.26596	+	10.3465i	0.262701	+	0.374080i
$766$		0			0
$767$	−16.8254	+	39.9072i	−0.607531	+	1.44097i
$768$		0			0
$769$	11.8513	+	6.84235i	0.427369	+	0.246741i	0.698225	−	0.715878i	$-0.253974\pi$
$769$	11.8513	+	6.84235i	0.427369	+	0.246741i	−0.270856	+	0.962620i	$0.587307\pi$
$770$		0			0
$771$	0.191370	+	0.175116i	0.00689201	+	0.00630664i
$772$		0			0
$773$		−	11.4346i		−	0.411273i	−0.978628	−	0.205637i	$-0.934074\pi$
$773$		−	11.4346i		−	0.411273i	0.978628	−	0.205637i	$-0.0659265\pi$
$774$		0			0
$775$		−	77.2688i		−	2.77558i
$776$		0			0
$777$	37.8894	−	11.9752i	1.35928	−	0.429607i
$778$		0			0
$779$	−8.23769	+	14.2681i	−0.295146	+	0.511207i
$780$		0			0
$781$	2.29291	+	3.97143i	0.0820467	+	0.142109i
$782$		0			0
$783$	5.30074	+	0.686724i	0.189433	+	0.0245415i
$784$		0			0
$785$	−0.429056	+	0.247715i	−0.0153137	+	0.00884134i
$786$		0			0
$787$	−38.5078	−	22.2325i	−1.37265	−	0.792503i	−0.381393	−	0.924413i	$-0.624556\pi$
$787$	−38.5078	−	22.2325i	−1.37265	−	0.792503i	−0.991262	+	0.131910i	$0.957889\pi$
$788$		0			0
$789$	−10.5063	+	3.32057i	−0.374033	+	0.118215i
$790$		0			0
$791$		−	11.8524i		−	0.421423i
$792$		0			0
$793$	13.2691	−	10.0496i	0.471201	−	0.356872i
$794$		0			0
$795$	−26.6762	+	29.1522i	−0.946107	+	1.03392i
$796$		0			0
$797$	4.39354	−	7.60984i	0.155627	−	0.269554i	−0.777660	−	0.628685i	$-0.783593\pi$
$797$	4.39354	−	7.60984i	0.155627	−	0.269554i	0.933287	+	0.359131i	$0.116927\pi$
$798$		0			0
$799$	−9.34656	+	5.39624i	−0.330657	+	0.190905i
$800$		0			0
$801$	11.8253	−	25.4508i	0.417825	−	0.899259i
$802$		0			0
$803$	4.50042	+	7.79495i	0.158816	+	0.275078i
$804$		0			0
$805$	−0.808242	+	1.39992i	−0.0284868	+	0.0493406i
$806$		0			0
$807$	3.15197	−	14.2641i	0.110955	−	0.502119i
$808$		0			0
$809$	−51.4550			−1.80906			−0.904530	−	0.426410i	$-0.859778\pi$
$809$	−51.4550			−1.80906			−0.904530	+	0.426410i	$0.859778\pi$
$810$		0			0
$811$		−	0.149585i		−	0.00525263i	−0.999997	−	0.00262632i	$-0.999164\pi$
$811$		−	0.149585i		−	0.00525263i	0.999997	−	0.00262632i	$-0.000835984\pi$
$812$		0			0
$813$	6.72770	+	1.48664i	0.235951	+	0.0521387i
$814$		0			0
$815$	−32.6848	+	56.6118i	−1.14490	+	1.98302i
$816$		0			0
$817$	−21.1624	+	12.2181i	−0.740378	+	0.427458i
$818$		0			0
$819$	11.0116	+	50.8538i	0.384778	+	1.77698i
$820$		0			0
$821$	3.57618	−	2.06471i	0.124809	−	0.0720588i	−0.436295	−	0.899803i	$-0.643710\pi$
$821$	3.57618	−	2.06471i	0.124809	−	0.0720588i	0.561105	+	0.827745i	$0.310376\pi$
$822$		0			0
$823$	−12.2798	+	21.2693i	−0.428047	+	0.741400i	−0.996700	−	0.0811784i	$-0.974132\pi$
$823$	−12.2798	+	21.2693i	−0.428047	+	0.741400i	0.568652	+	0.822578i	$0.307465\pi$
$824$		0			0
$825$	−41.0824	+	44.8956i	−1.43031	+	1.56306i
$826$		0			0
$827$		−	41.7582i		−	1.45207i	−0.687656	−	0.726037i	$-0.741360\pi$
$827$		−	41.7582i		−	1.45207i	0.687656	−	0.726037i	$-0.258640\pi$
$828$		0			0
$829$	30.9427			1.07468			0.537342	−	0.843365i	$-0.319429\pi$
$829$	30.9427			1.07468			0.537342	+	0.843365i	$0.319429\pi$
$830$		0			0
$831$	−1.53215	+	0.484244i	−0.0531496	+	0.0167982i
$832$		0			0
$833$	−8.65158	+	14.9850i	−0.299759	+	0.519198i
$834$		0			0
$835$	−4.07979	−	7.06641i	−0.141187	−	0.244543i
$836$		0			0
$837$	35.4565	−	14.7724i	1.22556	−	0.510610i
$838$		0			0
$839$	11.2119	−	6.47318i	0.387077	−	0.223479i	−0.293816	−	0.955862i	$-0.594925\pi$
$839$	11.2119	−	6.47318i	0.387077	−	0.223479i	0.680893	+	0.732383i	$0.261592\pi$
$840$		0			0
$841$	13.9709	−	24.1984i	0.481756	−	0.834427i
$842$		0			0
$843$	12.7696	+	40.4029i	0.439807	+	1.39155i
$844$		0			0
$845$	−49.1912	−	13.8473i	−1.69223	−	0.476362i
$846$		0			0
$847$			1.43490i			0.0493036i
$848$		0			0
$849$	−11.4577	−	10.4846i	−0.393228	−	0.359830i
$850$		0			0
$851$	−0.353077	−	0.203849i	−0.0121033	−	0.00698786i
$852$		0			0
$853$	20.6627	−	11.9296i	0.707476	−	0.408462i	−0.102650	−	0.994718i	$-0.532732\pi$
$853$	20.6627	−	11.9296i	0.707476	−	0.408462i	0.810126	+	0.586256i	$0.199399\pi$
$854$		0			0
$855$	63.4287	−	44.5435i	2.16922	−	1.52336i
$856$		0			0
$857$	8.96321	+	15.5247i	0.306177	+	0.530315i	0.977523	−	0.210830i	$-0.0676166\pi$
$857$	8.96321	+	15.5247i	0.306177	+	0.530315i	−0.671345	+	0.741145i	$0.734283\pi$
$858$		0			0
$859$	−7.61224	+	13.1848i	−0.259726	+	0.449859i	−0.966169	−	0.257911i	$-0.916966\pi$
$859$	−7.61224	+	13.1848i	−0.259726	+	0.449859i	0.706442	+	0.707771i	$0.250299\pi$
$860$		0			0
$861$	−4.50658	+	20.3943i	−0.153584	+	0.695035i
$862$		0			0
$863$		−	1.21450i		−	0.0413422i	−0.999786	−	0.0206711i	$-0.993420\pi$
$863$		−	1.21450i		−	0.0413422i	0.999786	−	0.0206711i	$-0.00658029\pi$
$864$		0			0
$865$			56.4312i			1.91872i
$866$		0			0
$867$	−5.92372	+	26.8075i	−0.201180	+	0.910429i
$868$		0			0
$869$	−5.08230	−	2.93427i	−0.172405	−	0.0995382i
$870$		0			0
$871$	−3.97211	+	9.42121i	−0.134590	+	0.319225i
$872$		0			0
$873$	−22.9159	+	2.03667i	−0.775586	+	0.0689309i
$874$		0			0
$875$	−51.5553	−	89.2964i	−1.74289	−	3.01877i
$876$		0			0
$877$	−35.9366	−	20.7480i	−1.21349	−	0.700611i	−0.249975	−	0.968252i	$-0.580422\pi$
$877$	−35.9366	−	20.7480i	−1.21349	−	0.700611i	−0.963519	+	0.267641i	$0.913756\pi$
$878$		0			0
$879$	0.991302	−	1.08331i	0.0334358	−	0.0365392i
$880$		0			0
$881$	−20.3311			−0.684972			−0.342486	−	0.939523i	$-0.611269\pi$
$881$	−20.3311			−0.684972			−0.342486	+	0.939523i	$0.611269\pi$
$882$		0			0
$883$	28.4196			0.956395			0.478197	−	0.878252i	$-0.341290\pi$
$883$	28.4196			0.956395			0.478197	+	0.878252i	$0.341290\pi$
$884$		0			0
$885$	77.9825	−	24.6468i	2.62135	−	0.828493i
$886$		0			0
$887$	5.94448	−	10.2961i	0.199596	−	0.345710i	−0.748802	−	0.662794i	$-0.769370\pi$
$887$	5.94448	−	10.2961i	0.199596	−	0.345710i	0.948397	+	0.317084i	$0.102704\pi$
$888$		0			0
$889$	−71.7118	+	41.4028i	−2.40514	+	1.38861i
$890$		0			0
$891$	−28.4556	−	10.2684i	−0.953299	−	0.344003i
$892$		0			0
$893$	33.0813	+	57.2985i	1.10702	+	1.91742i
$894$		0			0
$895$	−13.9169	−	8.03491i	−0.465190	−	0.268578i
$896$		0			0
$897$	0.308653	−	0.435580i	0.0103056	−	0.0145436i
$898$		0			0
$899$			7.60397i			0.253607i
$900$		0			0
$901$	6.22196			0.207284
$902$		0			0
$903$	−20.9130	+	22.8541i	−0.695941	+	0.760536i
$904$		0			0
$905$	−54.3024	−	31.3515i	−1.80507	−	1.04216i
$906$		0			0
$907$	−7.14235	−	12.3709i	−0.237158	−	0.410770i	0.722740	−	0.691120i	$-0.242883\pi$
$907$	−7.14235	−	12.3709i	−0.237158	−	0.410770i	−0.959898	+	0.280351i	$0.909549\pi$
$908$		0			0
$909$	−3.95211	−	44.4678i	−0.131083	−	1.47490i
$910$		0			0
$911$	23.5622	+	40.8109i	0.780649	+	1.35212i	0.931564	+	0.363578i	$0.118445\pi$
$911$	23.5622	+	40.8109i	0.780649	+	1.35212i	−0.150915	+	0.988547i	$0.548222\pi$
$912$		0			0
$913$	23.6825	−	41.0193i	0.783777	−	1.35754i
$914$		0			0
$915$	−30.6924	−	6.78218i	−1.01466	−	0.224212i
$916$		0			0
$917$			40.6745i			1.34319i
$918$		0			0
$919$	−44.6273			−1.47212			−0.736060	−	0.676916i	$-0.763316\pi$
$919$	−44.6273			−1.47212			−0.736060	+	0.676916i	$0.763316\pi$
$920$		0			0
$921$	37.5844	+	8.30512i	1.23845	+	0.273663i
$922$		0			0
$923$	4.88092	−	0.611329i	0.160658	−	0.0201222i
$924$		0			0
$925$	43.1732	−	24.9261i	1.41953	−	0.819565i
$926$		0			0
$927$	−46.4893	+	32.6476i	−1.52691	+	1.07229i
$928$		0			0
$929$	11.2761	−	6.51027i	0.369958	−	0.213595i	−0.303482	−	0.952837i	$-0.598149\pi$
$929$	11.2761	−	6.51027i	0.369958	−	0.213595i	0.673440	+	0.739242i	$0.264816\pi$
$930$		0			0
$931$	91.8644	+	53.0379i	3.01073	+	1.73825i
$932$		0			0
$933$	34.5827	+	31.6454i	1.13219	+	1.03602i
$934$		0			0
$935$	14.1656			0.463264
$936$		0			0
$937$	−0.395642			−0.0129251			−0.00646253	−	0.999979i	$-0.502057\pi$
$937$	−0.395642			−0.0129251			−0.00646253	+	0.999979i	$0.502057\pi$
$938$		0			0
$939$	−35.1033	+	11.0946i	−1.14555	+	0.362058i
$940$		0			0
$941$	−29.0237	−	16.7568i	−0.946145	−	0.546257i	−0.0542640	−	0.998527i	$-0.517281\pi$
$941$	−29.0237	−	16.7568i	−0.946145	−	0.546257i	−0.891881	+	0.452269i	$0.850615\pi$
$942$		0			0
$943$	0.185583	−	0.107146i	0.00604340	−	0.00348916i
$944$		0			0
$945$	59.6543	−	78.0763i	1.94056	−	2.53982i
$946$		0			0
$947$	22.1028	−	12.7611i	0.718246	−	0.414679i	−0.0958609	−	0.995395i	$-0.530560\pi$
$947$	22.1028	−	12.7611i	0.718246	−	0.414679i	0.814107	+	0.580715i	$0.197227\pi$
$948$		0			0
$949$	9.58006	−	1.19989i	0.310982	−	0.0389501i
$950$		0			0
$951$	5.67433	+	17.9536i	0.184003	+	0.582185i
$952$		0			0
$953$	−13.0504			−0.422743			−0.211372	−	0.977406i	$-0.567793\pi$
$953$	−13.0504			−0.422743			−0.211372	+	0.977406i	$0.567793\pi$
$954$		0			0
$955$		−	39.0027i		−	1.26210i
$956$		0			0
$957$	4.04290	−	4.41815i	0.130688	−	0.142818i
$958$		0			0
$959$	43.8459	−	75.9434i	1.41586	−	2.45234i
$960$		0			0
$961$	11.8220	+	20.4764i	0.381356	+	0.660528i
$962$		0			0
$963$	−39.9924	−	18.5818i	−1.28874	−	0.598789i
$964$		0			0
$965$	−30.0473	−	52.0434i	−0.967256	−	1.67534i
$966$		0			0
$967$	3.09895	+	1.78918i	0.0996555	+	0.0575361i	0.548999	−	0.835823i	$-0.315009\pi$
$967$	3.09895	+	1.78918i	0.0996555	+	0.0575361i	−0.449344	+	0.893359i	$0.648342\pi$
$968$		0			0
$969$	−11.9165	−	2.63322i	−0.382813	−	0.0845913i
$970$		0			0
$971$	−35.7804			−1.14825			−0.574125	−	0.818768i	$-0.694658\pi$
$971$	−35.7804			−1.14825			−0.574125	+	0.818768i	$0.694658\pi$
$972$		0			0
$973$			55.4167i			1.77658i
$974$		0			0
$975$	27.2551	+	59.3155i	0.872862	+	1.89962i
$976$		0			0
$977$	13.0418	+	7.52970i	0.417245	+	0.240896i	0.693898	−	0.720074i	$-0.255892\pi$
$977$	13.0418	+	7.52970i	0.417245	+	0.240896i	−0.276653	+	0.960970i	$0.589225\pi$
$978$		0			0
$979$	−15.7218	−	27.2310i	−0.502471	−	0.870305i
$980$		0			0
$981$	5.55730	−	11.9606i	0.177431	−	0.381873i
$982$		0			0
$983$	−28.4653	+	16.4345i	−0.907903	+	0.524178i	−0.879756	−	0.475425i	$-0.842294\pi$
$983$	−28.4653	+	16.4345i	−0.907903	+	0.524178i	−0.0281475	+	0.999604i	$0.508961\pi$
$984$		0			0
$985$	−2.42703	+	4.20374i	−0.0773316	+	0.133942i
$986$		0			0
$987$	61.8789	+	56.6232i	1.96963	+	1.80234i
$988$		0			0
$989$	0.317838			0.0101066
$990$		0			0
$991$	13.4770			0.428112			0.214056	−	0.976821i	$-0.431333\pi$
$991$	13.4770			0.428112			0.214056	+	0.976821i	$0.431333\pi$
$992$		0			0
$993$	−3.87326	−	12.2550i	−0.122914	−	0.388901i
$994$		0			0
$995$	−19.2278	−	11.1012i	−0.609562	−	0.351931i
$996$		0			0
$997$	−5.73848	−	9.93934i	−0.181740	−	0.314782i	0.760733	−	0.649064i	$-0.224839\pi$
$997$	−5.73848	−	9.93934i	−0.181740	−	0.314782i	−0.942473	+	0.334282i	$0.891506\pi$
$998$		0			0
$999$	19.6919	+	15.0456i	0.623023	+	0.476022i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	936.2.cw.b.337.26	yes	80
3.2	odd	2		2808.2.cw.b.2521.3		80
9.2	odd	6		2808.2.cw.b.1585.38		80
9.7	even	3	inner	936.2.cw.b.25.25	✓	80
13.12	even	2	inner	936.2.cw.b.337.25	yes	80
39.38	odd	2		2808.2.cw.b.2521.38		80
117.25	even	6	inner	936.2.cw.b.25.26	yes	80
117.38	odd	6		2808.2.cw.b.1585.3		80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
936.2.cw.b.25.25	✓	80	9.7	even	3	inner
936.2.cw.b.25.26	yes	80	117.25	even	6	inner
936.2.cw.b.337.25	yes	80	13.12	even	2	inner
936.2.cw.b.337.26	yes	80	1.1	even	1	trivial
2808.2.cw.b.1585.3		80	117.38	odd	6
2808.2.cw.b.1585.38		80	9.2	odd	6
2808.2.cw.b.2521.3		80	3.2	odd	2
2808.2.cw.b.2521.38		80	39.38	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:	\( N \)	\(=\)	\( 936 = 2^{3} \cdot 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	936.cw (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.373720 - 1.69125i) q^{3} +(3.40435 + 1.96550i) q^{5} +(-4.16592 + 2.40520i) q^{7} +(-2.72067 - 1.26411i) q^{9} +(-2.91097 + 1.68065i) q^{11} +(0.448090 + 3.57760i) q^{13} +(4.59643 - 5.02306i) q^{15} -1.07207 q^{17} +6.57228i q^{19} +(2.51090 + 7.94450i) q^{21} +(0.0427423 - 0.0740317i) q^{23} +(5.22640 + 9.05238i) q^{25} +(-3.15470 + 4.12891i) q^{27} +(-0.514326 - 0.890839i) q^{29} +(-6.40180 - 3.69608i) q^{31} +(1.75451 + 5.55127i) q^{33} -18.9097 q^{35} -4.76927i q^{37} +(6.21808 + 0.579189i) q^{39} +(2.17095 + 1.25340i) q^{41} +(1.85904 + 3.21995i) q^{43} +(-6.77749 - 9.65095i) q^{45} +(8.71820 - 5.03346i) q^{47} +(8.06995 - 13.9776i) q^{49} +(-0.400656 + 1.81315i) q^{51} -5.80367 q^{53} -13.2133 q^{55} +(11.1154 + 2.45620i) q^{57} +(10.4025 + 6.00590i) q^{59} +(-2.30828 - 3.99806i) q^{61} +(14.3745 - 1.27755i) q^{63} +(-5.50632 + 13.0601i) q^{65} +(2.45580 + 1.41786i) q^{67} +(-0.109233 - 0.0999551i) q^{69} -1.36430i q^{71} -2.67779i q^{73} +(17.2631 - 5.45609i) q^{75} +(8.08457 - 14.0029i) q^{77} +(0.872958 + 1.51201i) q^{79} +(5.80405 + 6.87845i) q^{81} +(-12.2034 + 7.04566i) q^{83} +(-3.64971 - 2.10716i) q^{85} +(-1.69885 + 0.536931i) q^{87} +9.35462i q^{89} +(-10.4715 - 13.8263i) q^{91} +(-8.64349 + 9.44576i) q^{93} +(-12.9178 + 22.3743i) q^{95} +(6.64133 - 3.83437i) q^{97} +(10.0443 - 0.892695i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q - 6 q^{3} - 6 q^{9} + 6 q^{13} - 4 q^{17} + 10 q^{23} + 44 q^{25} + 6 q^{27} - 52 q^{35} + 40 q^{39} - 26 q^{43} + 48 q^{49} + 36 q^{51} + 60 q^{53} - 16 q^{55} - 10 q^{61} - 26 q^{65} - 38 q^{69}+ \cdots + 8 q^{95}+O(q^{100}) \) 80 * q - 6 * q^3 - 6 * q^9 + 6 * q^13 - 4 * q^17 + 10 * q^23 + 44 * q^25 + 6 * q^27 - 52 * q^35 + 40 * q^39 - 26 * q^43 + 48 * q^49 + 36 * q^51 + 60 * q^53 - 16 * q^55 - 10 * q^61 - 26 * q^65 - 38 * q^69 + 32 * q^75 + 32 * q^77 + 6 * q^79 - 38 * q^81 + 4 * q^87 - 4 * q^91 + 8 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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