LMFDB - Embedded newform 1008.2.cx.i.895.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1008,2,Mod(223,1008)] 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("1008.223"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1008, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 0, 4, 3])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 1008 = 2^{4} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1008.cx (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [24,0,0,0,0,0,-6,0,20,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(11)] == traces)

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

Self dual:	no
Analytic conductor:	$8.04892052375$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			895.5
Character	$\chi$	$=$	1008.895
Dual form			1008.2.cx.i.223.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.11570 + 1.32484i) q^{3} +(-0.263424 - 0.152088i) q^{5} +(-2.20588 + 1.46085i) q^{7} +(-0.510411 - 2.95626i) q^{9} +(-0.437319 + 0.252486i) q^{11} +(4.11032 + 2.37309i) q^{13} +(0.495396 - 0.179310i) q^{15} +4.53143i q^{17} -4.38692 q^{19} +(0.525718 - 4.55232i) q^{21} +(-2.76828 - 1.59826i) q^{23} +(-2.45374 - 4.25000i) q^{25} +(4.48605 + 2.62210i) q^{27} +(-4.86854 - 8.43256i) q^{29} +(-1.83961 + 3.18629i) q^{31} +(0.153414 - 0.861079i) q^{33} +(0.803260 - 0.0493346i) q^{35} -3.70424 q^{37} +(-7.72987 + 2.79785i) q^{39} +(-7.01616 - 4.05078i) q^{41} +(3.99621 - 2.30721i) q^{43} +(-0.315157 + 0.856378i) q^{45} +(-3.23026 - 5.59497i) q^{47} +(2.73184 - 6.44492i) q^{49} +(-6.00342 - 5.05573i) q^{51} +6.52863 q^{53} +0.153601 q^{55} +(4.89450 - 5.81197i) q^{57} +(6.40501 - 11.0938i) q^{59} +(2.16357 - 1.24914i) q^{61} +(5.44456 + 5.77553i) q^{63} +(-0.721838 - 1.25026i) q^{65} +(-6.03544 - 3.48457i) q^{67} +(5.20602 - 1.88434i) q^{69} +10.1334i q^{71} +7.13486i q^{73} +(8.36822 + 1.49093i) q^{75} +(0.595831 - 1.19581i) q^{77} +(-5.96149 + 3.44187i) q^{79} +(-8.47896 + 3.01781i) q^{81} +(-3.66905 - 6.35498i) q^{83} +(0.689176 - 1.19369i) q^{85} +(16.6036 + 2.95819i) q^{87} -11.8721i q^{89} +(-12.5336 + 0.769788i) q^{91} +(-2.16888 - 5.99215i) q^{93} +(1.15562 + 0.667198i) q^{95} +(-10.9944 + 6.34762i) q^{97} +(0.969628 + 1.16396i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 6 q^{7} + 20 q^{9} + 24 q^{15} + 10 q^{21} + 18 q^{23} + 24 q^{25} - 6 q^{29} - 12 q^{37} - 12 q^{39} + 42 q^{43} + 12 q^{49} - 42 q^{51} + 96 q^{53} - 22 q^{57} + 18 q^{63} + 42 q^{65} + 36 q^{67}+ \cdots + 12 q^{99}+O(q^{100}) $ 24 * q - 6 * q^7 + 20 * q^9 + 24 * q^15 + 10 * q^21 + 18 * q^23 + 24 * q^25 - 6 * q^29 - 12 * q^37 - 12 * q^39 + 42 * q^43 + 12 * q^49 - 42 * q^51 + 96 * q^53 - 22 * q^57 + 18 * q^63 + 42 * q^65 + 36 * q^67 - 18 * q^77 - 60 * q^79 - 64 * q^81 - 6 * q^85 + 82 * q^93 - 126 * q^95 + 12 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1008\mathbb{Z}\right)^\times$.

$n$	$127$	$577$	$757$	$785$
$\chi(n)$	$-1$	$-1$	$1$	$e\left(\frac{1}{3}\right)$

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
$3$	−1.11570	+	1.32484i	−0.644152	+	0.764898i
$3$	−1.11570	+	1.32484i	−0.644152	+	0.764898i
$4$		0			0
$5$	−0.263424	−	0.152088i	−0.117807	−	0.0680158i	0.439939	−	0.898028i	$-0.355000\pi$
$5$	−0.263424	−	0.152088i	−0.117807	−	0.0680158i	−0.557746	+	0.830012i	$0.688334\pi$
$6$		0			0
$7$	−2.20588	+	1.46085i	−0.833745	+	0.552149i
$7$	−2.20588	+	1.46085i	−0.833745	+	0.552149i
$8$		0			0
$9$	−0.510411	−	2.95626i	−0.170137	−	0.985420i
$10$		0			0
$11$	−0.437319	+	0.252486i	−0.131857	+	0.0761275i	−0.564477	−	0.825449i	$-0.690922\pi$
$11$	−0.437319	+	0.252486i	−0.131857	+	0.0761275i	0.432621	+	0.901576i	$0.357589\pi$
$12$		0			0
$13$	4.11032	+	2.37309i	1.14000	+	0.658177i	0.946430	−	0.322910i	$-0.104661\pi$
$13$	4.11032	+	2.37309i	1.14000	+	0.658177i	0.193567	+	0.981087i	$0.437994\pi$
$14$		0			0
$15$	0.495396	−	0.179310i	0.127911	−	0.0462977i
$16$		0			0
$17$			4.53143i			1.09903i	0.835483	+	0.549516i	$0.185188\pi$
$17$			4.53143i			1.09903i	−0.835483	+	0.549516i	$0.814812\pi$
$18$		0			0
$19$	−4.38692			−1.00643			−0.503214	−	0.864162i	$-0.667849\pi$
$19$	−4.38692			−1.00643			−0.503214	+	0.864162i	$0.667849\pi$
$20$		0			0
$21$	0.525718	−	4.55232i	0.114721	−	0.993398i
$22$		0			0
$23$	−2.76828	−	1.59826i	−0.577225	−	0.333261i	0.182805	−	0.983149i	$-0.441482\pi$
$23$	−2.76828	−	1.59826i	−0.577225	−	0.333261i	−0.760030	+	0.649888i	$0.774816\pi$
$24$		0			0
$25$	−2.45374	−	4.25000i	−0.490748	−	0.850000i
$26$		0			0
$27$	4.48605	+	2.62210i	0.863340	+	0.504623i
$28$		0			0
$29$	−4.86854	−	8.43256i	−0.904065	−	1.56589i	−0.822168	−	0.569246i	$-0.807235\pi$
$29$	−4.86854	−	8.43256i	−0.904065	−	1.56589i	−0.0818973	−	0.996641i	$-0.526098\pi$
$30$		0			0
$31$	−1.83961	+	3.18629i	−0.330403	+	0.572275i	−0.982591	−	0.185782i	$-0.940518\pi$
$31$	−1.83961	+	3.18629i	−0.330403	+	0.572275i	0.652188	+	0.758058i	$0.273851\pi$
$32$		0			0
$33$	0.153414	−	0.861079i	0.0267060	−	0.149895i
$34$		0			0
$35$	0.803260	−	0.0493346i	0.135776	−	0.00833907i
$36$		0			0
$37$	−3.70424			−0.608973			−0.304487	−	0.952517i	$-0.598485\pi$
$37$	−3.70424			−0.608973			−0.304487	+	0.952517i	$0.598485\pi$
$38$		0			0
$39$	−7.72987	+	2.79785i	−1.23777	+	0.448015i
$40$		0			0
$41$	−7.01616	−	4.05078i	−1.09574	−	0.632626i	−0.160641	−	0.987013i	$-0.551356\pi$
$41$	−7.01616	−	4.05078i	−1.09574	−	0.632626i	−0.935099	+	0.354387i	$0.884690\pi$
$42$		0			0
$43$	3.99621	−	2.30721i	0.609417	−	0.351847i	−0.163320	−	0.986573i	$-0.552220\pi$
$43$	3.99621	−	2.30721i	0.609417	−	0.351847i	0.772737	+	0.634726i	$0.218887\pi$
$44$		0			0
$45$	−0.315157	+	0.856378i	−0.0469809	+	0.127661i
$46$		0			0
$47$	−3.23026	−	5.59497i	−0.471181	−	0.816110i	0.528275	−	0.849073i	$-0.322839\pi$
$47$	−3.23026	−	5.59497i	−0.471181	−	0.816110i	−0.999457	+	0.0329634i	$0.989506\pi$
$48$		0			0
$49$	2.73184	−	6.44492i	0.390263	−	0.920704i
$50$		0			0
$51$	−6.00342	−	5.05573i	−0.840648	−	0.707944i
$52$		0			0
$53$	6.52863			0.896776			0.448388	−	0.893839i	$-0.351998\pi$
$53$	6.52863			0.896776			0.448388	+	0.893839i	$0.351998\pi$
$54$		0			0
$55$	0.153601			0.0207115
$56$		0			0
$57$	4.89450	−	5.81197i	0.648293	−	0.769815i
$58$		0			0
$59$	6.40501	−	11.0938i	0.833861	−	1.44429i	−0.0610931	−	0.998132i	$-0.519459\pi$
$59$	6.40501	−	11.0938i	0.833861	−	1.44429i	0.894954	−	0.446158i	$-0.147208\pi$
$60$		0			0
$61$	2.16357	−	1.24914i	0.277017	−	0.159936i	−0.355055	−	0.934845i	$-0.615538\pi$
$61$	2.16357	−	1.24914i	0.277017	−	0.159936i	0.632072	+	0.774910i	$0.282205\pi$
$62$		0			0
$63$	5.44456	+	5.77553i	0.685950	+	0.727649i
$64$		0			0
$65$	−0.721838	−	1.25026i	−0.0895329	−	0.155076i
$66$		0			0
$67$	−6.03544	−	3.48457i	−0.737347	−	0.425707i	0.0837570	−	0.996486i	$-0.473308\pi$
$67$	−6.03544	−	3.48457i	−0.737347	−	0.425707i	−0.821104	+	0.570779i	$0.806641\pi$
$68$		0			0
$69$	5.20602	−	1.88434i	0.626731	−	0.226848i
$70$		0			0
$71$			10.1334i			1.20261i	0.799019	+	0.601306i	$0.205353\pi$
$71$			10.1334i			1.20261i	−0.799019	+	0.601306i	$0.794647\pi$
$72$		0			0
$73$			7.13486i			0.835072i	0.908660	+	0.417536i	$0.137106\pi$
$73$			7.13486i			0.835072i	−0.908660	+	0.417536i	$0.862894\pi$
$74$		0			0
$75$	8.36822	+	1.49093i	0.966279	+	0.172157i
$76$		0			0
$77$	0.595831	−	1.19581i	0.0679012	−	0.136276i
$78$		0			0
$79$	−5.96149	+	3.44187i	−0.670720	+	0.387240i	−0.796349	−	0.604837i	$-0.793238\pi$
$79$	−5.96149	+	3.44187i	−0.670720	+	0.387240i	0.125630	+	0.992077i	$0.459905\pi$
$80$		0			0
$81$	−8.47896	+	3.01781i	−0.942107	+	0.335313i
$82$		0			0
$83$	−3.66905	−	6.35498i	−0.402731	−	0.697550i	0.591324	−	0.806434i	$-0.298606\pi$
$83$	−3.66905	−	6.35498i	−0.402731	−	0.697550i	−0.994054	+	0.108884i	$0.965272\pi$
$84$		0			0
$85$	0.689176	−	1.19369i	0.0747516	−	0.129474i
$86$		0			0
$87$	16.6036	+	2.95819i	1.78010	+	0.317151i
$88$		0			0
$89$		−	11.8721i		−	1.25844i	−0.777226	−	0.629221i	$-0.783374\pi$
$89$		−	11.8721i		−	1.25844i	0.777226	−	0.629221i	$-0.216626\pi$
$90$		0			0
$91$	−12.5336	+	0.769788i	−1.31388	+	0.0806958i
$92$		0			0
$93$	−2.16888	−	5.99215i	−0.224902	−	0.621357i
$94$		0			0
$95$	1.15562	+	0.667198i	0.118564	+	0.0684531i
$96$		0			0
$97$	−10.9944	+	6.34762i	−1.11631	+	0.644503i	−0.940457	−	0.339913i	$-0.889602\pi$
$97$	−10.9944	+	6.34762i	−1.11631	+	0.644503i	−0.175855	+	0.984416i	$0.556269\pi$
$98$		0			0
$99$	0.969628	+	1.16396i	0.0974513	+	0.116982i
$100$		0			0
$101$	−7.37796	+	4.25966i	−0.734134	+	0.423852i	−0.819933	−	0.572460i	$-0.805989\pi$
$101$	−7.37796	+	4.25966i	−0.734134	+	0.423852i	0.0857986	+	0.996313i	$0.472656\pi$
$102$		0			0
$103$	−5.50115	+	9.52828i	−0.542045	+	0.938849i	0.456742	+	0.889599i	$0.349016\pi$
$103$	−5.50115	+	9.52828i	−0.542045	+	0.938849i	−0.998786	+	0.0492499i	$0.984317\pi$
$104$		0			0
$105$	−0.830840	+	1.11924i	−0.0810817	+	0.109226i
$106$		0			0
$107$		−	12.8308i		−	1.24040i	−0.784445	−	0.620198i	$-0.787052\pi$
$107$		−	12.8308i		−	1.24040i	0.784445	−	0.620198i	$-0.212948\pi$
$108$		0			0
$109$	3.17561			0.304169			0.152084	−	0.988368i	$-0.451401\pi$
$109$	3.17561			0.304169			0.152084	+	0.988368i	$0.451401\pi$
$110$		0			0
$111$	4.13283	−	4.90753i	0.392271	−	0.465802i
$112$		0			0
$113$	−2.65916	+	4.60580i	−0.250152	+	0.433277i	−0.963568	−	0.267465i	$-0.913814\pi$
$113$	−2.65916	+	4.60580i	−0.250152	+	0.433277i	0.713415	+	0.700742i	$0.247147\pi$
$114$		0			0
$115$	0.486154	+	0.842043i	0.0453341	+	0.0785209i
$116$		0			0
$117$	4.91753	−	13.3624i	0.454626	−	1.23536i
$118$		0			0
$119$	−6.61973	−	9.99580i	−0.606830	−	0.916313i
$120$		0			0
$121$	−5.37250	+	9.30544i	−0.488409	+	0.845950i
$122$		0			0
$123$	13.1946	−	4.77583i	1.18972	−	0.430622i
$124$		0			0
$125$			3.01362i			0.269546i
$126$		0			0
$127$			9.70351i			0.861047i	0.902579	+	0.430523i	$0.141671\pi$
$127$			9.70351i			0.861047i	−0.902579	+	0.430523i	$0.858329\pi$
$128$		0			0
$129$	−1.40190	+	7.86852i	−0.123430	+	0.692784i
$130$		0			0
$131$	3.44590	−	5.96848i	0.301070	−	0.521468i	−0.675309	−	0.737535i	$-0.735990\pi$
$131$	3.44590	−	5.96848i	0.301070	−	0.521468i	0.976379	+	0.216067i	$0.0693230\pi$
$132$		0			0
$133$	9.67703	−	6.40863i	0.839105	−	0.555699i
$134$		0			0
$135$	−0.782943	−	1.37300i	−0.0673850	−	0.118169i
$136$		0			0
$137$	−3.70803	−	6.42249i	−0.316798	−	0.548710i	0.663020	−	0.748602i	$-0.269274\pi$
$137$	−3.70803	−	6.42249i	−0.316798	−	0.548710i	−0.979818	+	0.199891i	$0.935941\pi$
$138$		0			0
$139$	−8.55841	+	14.8236i	−0.725915	+	1.25732i	0.232681	+	0.972553i	$0.425250\pi$
$139$	−8.55841	+	14.8236i	−0.725915	+	1.25732i	−0.958596	+	0.284769i	$0.908083\pi$
$140$		0			0
$141$	11.0165	+	1.96275i	0.927753	+	0.165293i
$142$		0			0
$143$	−2.39669			−0.200422
$144$		0			0
$145$			2.96179i			0.245963i
$146$		0			0
$147$	5.49058	+	10.8099i	0.452856	+	0.891584i
$148$		0			0
$149$	−8.24061	+	14.2732i	−0.675097	+	1.16930i	0.301343	+	0.953516i	$0.402565\pi$
$149$	−8.24061	+	14.2732i	−0.675097	+	1.16930i	−0.976440	+	0.215787i	$0.930768\pi$
$150$		0			0
$151$	5.27913	−	3.04790i	0.429609	−	0.248035i	−0.269571	−	0.962981i	$-0.586882\pi$
$151$	5.27913	−	3.04790i	0.429609	−	0.248035i	0.699180	+	0.714946i	$0.253549\pi$
$152$		0			0
$153$	13.3961	−	2.31289i	1.08301	−	0.186986i
$154$		0			0
$155$	0.969194	−	0.559565i	0.0778476	−	0.0449453i
$156$		0			0
$157$	9.90234	+	5.71712i	0.790293	+	0.456276i	0.840066	−	0.542485i	$-0.182516\pi$
$157$	9.90234	+	5.71712i	0.790293	+	0.456276i	−0.0497728	+	0.998761i	$0.515850\pi$
$158$		0			0
$159$	−7.28401	+	8.64939i	−0.577660	+	0.685942i
$160$		0			0
$161$	8.44132	−	0.518448i	0.665269	−	0.0408594i
$162$		0			0
$163$		−	21.3884i		−	1.67527i	−0.546230	−	0.837635i	$-0.683938\pi$
$163$		−	21.3884i		−	1.67527i	0.546230	−	0.837635i	$-0.316062\pi$
$164$		0			0
$165$	−0.171373	+	0.203497i	−0.0133414	+	0.0158422i
$166$		0			0
$167$	3.05790	−	5.29644i	0.236627	−	0.409850i	−0.723117	−	0.690725i	$-0.757291\pi$
$167$	3.05790	−	5.29644i	0.236627	−	0.409850i	0.959744	+	0.280875i	$0.0906246\pi$
$168$		0			0
$169$	4.76313	+	8.24999i	0.366395	+	0.634614i
$170$		0			0
$171$	2.23913	+	12.9689i	0.171231	+	0.991755i
$172$		0			0
$173$	−14.7638	+	8.52391i	−1.12247	+	0.648061i	−0.942031	−	0.335524i	$-0.891086\pi$
$173$	−14.7638	+	8.52391i	−1.12247	+	0.648061i	−0.180443	+	0.983585i	$0.557753\pi$
$174$		0			0
$175$	11.6213	+	5.79046i	0.878485	+	0.437718i
$176$		0			0
$177$	7.55144	+	20.8630i	0.567601	+	1.56816i
$178$		0			0
$179$		−	13.3401i		−	0.997083i	−0.866866	−	0.498541i	$-0.833869\pi$
$179$		−	13.3401i		−	0.997083i	0.866866	−	0.498541i	$-0.166131\pi$
$180$		0			0
$181$			18.7431i			1.39316i	0.717478	+	0.696581i	$0.245296\pi$
$181$			18.7431i			1.39316i	−0.717478	+	0.696581i	$0.754704\pi$
$182$		0			0
$183$	−0.758994	+	4.26006i	−0.0561064	+	0.314912i
$184$		0			0
$185$	0.975786	+	0.563370i	0.0717412	+	0.0414198i
$186$		0			0
$187$	−1.14412	−	1.98168i	−0.0836666	−	0.144915i
$188$		0			0
$189$	−13.7262	+	0.769393i	−0.998433	+	0.0559651i
$190$		0			0
$191$	−10.4812	+	6.05130i	−0.758389	+	0.437856i	−0.828717	−	0.559668i	$-0.810929\pi$
$191$	−10.4812	+	6.05130i	−0.758389	+	0.437856i	0.0703277	+	0.997524i	$0.477595\pi$
$192$		0			0
$193$	−3.76431	+	6.51998i	−0.270961	+	0.469318i	−0.969108	−	0.246636i	$-0.920675\pi$
$193$	−3.76431	+	6.51998i	−0.270961	+	0.469318i	0.698147	+	0.715954i	$0.254008\pi$
$194$		0			0
$195$	2.46175	+	0.438599i	0.176290	+	0.0314087i
$196$		0			0
$197$	20.2028			1.43939			0.719695	−	0.694290i	$-0.244282\pi$
$197$	20.2028			1.43939			0.719695	+	0.694290i	$0.244282\pi$
$198$		0			0
$199$	−22.8387			−1.61900			−0.809498	−	0.587123i	$-0.800260\pi$
$199$	−22.8387			−1.61900			−0.809498	+	0.587123i	$0.800260\pi$
$200$		0			0
$201$	11.3503	−	4.10827i	0.800586	−	0.289775i
$202$		0			0
$203$	23.0581	+	11.4890i	1.61836	+	0.806372i
$204$		0			0
$205$	1.23215	+	2.13415i	0.0860571	+	0.149055i
$206$		0			0
$207$	−3.31193	+	8.99952i	−0.230195	+	0.625510i
$208$		0			0
$209$	1.91849	−	1.10764i	0.132704	−	0.0766169i
$210$		0			0
$211$	12.0100	+	6.93397i	0.826802	+	0.477354i	0.852756	−	0.522309i	$-0.174929\pi$
$211$	12.0100	+	6.93397i	0.826802	+	0.477354i	−0.0259543	+	0.999663i	$0.508262\pi$
$212$		0			0
$213$	−13.4251	−	11.3059i	−0.919874	−	0.774664i
$214$		0			0
$215$	−1.40360			−0.0957246
$216$		0			0
$217$	−0.596736	−	9.71598i	−0.0405091	−	0.659564i
$218$		0			0
$219$	−9.45256	−	7.96039i	−0.638745	−	0.537913i
$220$		0			0
$221$	−10.7535	+	18.6256i	−0.723358	+	1.25289i
$222$		0			0
$223$	0.736818	+	1.27621i	0.0493410	+	0.0854611i	0.889641	−	0.456660i	$-0.150955\pi$
$223$	0.736818	+	1.27621i	0.0493410	+	0.0854611i	−0.840300	+	0.542122i	$0.817621\pi$
$224$		0			0
$225$	−11.3117	+	9.42314i	−0.754113	+	0.628209i
$226$		0			0
$227$	3.97759	+	6.88940i	0.264002	+	0.457265i	0.967302	−	0.253628i	$-0.0816240\pi$
$227$	3.97759	+	6.88940i	0.264002	+	0.457265i	−0.703299	+	0.710894i	$0.748291\pi$
$228$		0			0
$229$	10.4194	+	6.01565i	0.688534	+	0.397525i	0.803063	−	0.595895i	$-0.203202\pi$
$229$	10.4194	+	6.01565i	0.688534	+	0.397525i	−0.114528	+	0.993420i	$0.536536\pi$
$230$		0			0
$231$	0.919493	+	2.12355i	0.0604982	+	0.139720i
$232$		0			0
$233$	−0.753935			−0.0493919			−0.0246960	−	0.999695i	$-0.507862\pi$
$233$	−0.753935			−0.0493919			−0.0246960	+	0.999695i	$0.507862\pi$
$234$		0			0
$235$			1.96513i			0.128191i
$236$		0			0
$237$	2.09133	−	11.7381i	0.135846	−	0.762473i
$238$		0			0
$239$	17.2884	+	9.98149i	1.11830	+	0.645649i	0.940965	−	0.338503i	$-0.109920\pi$
$239$	17.2884	+	9.98149i	1.11830	+	0.645649i	0.177331	+	0.984151i	$0.443254\pi$
$240$		0			0
$241$	8.36779	−	4.83114i	0.539017	−	0.311201i	−0.205664	−	0.978623i	$-0.565935\pi$
$241$	8.36779	−	4.83114i	0.539017	−	0.311201i	0.744680	+	0.667421i	$0.232602\pi$
$242$		0			0
$243$	5.46188	−	14.6003i	0.350380	−	0.936608i
$244$		0			0
$245$	−1.69983	+	1.28227i	−0.108598	+	0.0819211i
$246$		0			0
$247$	−18.0316	−	10.4106i	−1.14732	−	0.662408i
$248$		0			0
$249$	12.5129	+	2.22937i	0.792974	+	0.141280i
$250$		0			0
$251$	−10.7572			−0.678988			−0.339494	−	0.940608i	$-0.610256\pi$
$251$	−10.7572			−0.678988			−0.339494	+	0.940608i	$0.610256\pi$
$252$		0			0
$253$	1.61416			0.101481
$254$		0			0
$255$	0.812531	+	2.24485i	0.0508827	+	0.140578i
$256$		0			0
$257$	−4.58326	−	2.64615i	−0.285896	−	0.165062i	0.350194	−	0.936677i	$-0.386116\pi$
$257$	−4.58326	−	2.64615i	−0.285896	−	0.165062i	−0.636090	+	0.771615i	$0.719449\pi$
$258$		0			0
$259$	8.17112	−	5.41133i	0.507728	−	0.336244i
$260$		0			0
$261$	−22.4439	+	18.6967i	−1.38924	+	1.15730i
$262$		0			0
$263$	−4.44999	+	2.56921i	−0.274398	+	0.158424i	−0.630885	−	0.775877i	$-0.717308\pi$
$263$	−4.44999	+	2.56921i	−0.274398	+	0.158424i	0.356486	+	0.934301i	$0.383975\pi$
$264$		0			0
$265$	−1.71980	−	0.992926i	−0.105646	−	0.0609949i
$266$		0			0
$267$	15.7287	+	13.2458i	0.962580	+	0.810628i
$268$		0			0
$269$			25.3041i			1.54282i	0.636339	+	0.771410i	$0.280448\pi$
$269$			25.3041i			1.54282i	−0.636339	+	0.771410i	$0.719552\pi$
$270$		0			0
$271$	1.08622			0.0659832			0.0329916	−	0.999456i	$-0.489497\pi$
$271$	1.08622			0.0659832			0.0329916	+	0.999456i	$0.489497\pi$
$272$		0			0
$273$	12.9639	−	17.4639i	0.784614	−	1.05696i
$274$		0			0
$275$	2.14613	+	1.23907i	0.129417	+	0.0747188i
$276$		0			0
$277$	8.84602	+	15.3218i	0.531506	+	0.920595i	0.999324	+	0.0367702i	$0.0117069\pi$
$277$	8.84602	+	15.3218i	0.531506	+	0.920595i	−0.467818	+	0.883825i	$0.654960\pi$
$278$		0			0
$279$	10.3585	+	3.81204i	0.620146	+	0.228221i
$280$		0			0
$281$	4.17929	+	7.23874i	0.249315	+	0.431827i	0.963336	−	0.268298i	$-0.0864611\pi$
$281$	4.17929	+	7.23874i	0.249315	+	0.431827i	−0.714021	+	0.700125i	$0.753128\pi$
$282$		0			0
$283$	3.68489	−	6.38242i	0.219044	−	0.379396i	−0.735472	−	0.677555i	$-0.763039\pi$
$283$	3.68489	−	6.38242i	0.219044	−	0.379396i	0.954516	+	0.298160i	$0.0963728\pi$
$284$		0			0
$285$	−2.17326	+	0.786619i	−0.128733	+	0.0465953i
$286$		0			0
$287$	21.3944	−	1.31400i	1.26287	−	0.0775630i
$288$		0			0
$289$	−3.53384			−0.207873
$290$		0			0
$291$	3.85690	−	21.6479i	0.226095	−	1.26902i
$292$		0			0
$293$	−27.5794	−	15.9230i	−1.61120	−	0.930229i	−0.989092	−	0.147300i	$-0.952942\pi$
$293$	−27.5794	−	15.9230i	−1.61120	−	0.930229i	−0.622112	−	0.782928i	$-0.713725\pi$
$294$		0			0
$295$	−3.37447	+	1.94825i	−0.196469	+	0.113432i
$296$		0			0
$297$	−2.62388	−	0.0140288i	−0.152253	−	0.000814032i
$298$		0			0
$299$	−7.58566	−	13.1387i	−0.438690	−	0.759833i
$300$		0			0
$301$	−5.44469	+	10.9273i	−0.313827	+	0.629840i
$302$		0			0
$303$	2.58823	−	14.5271i	0.148690	−	0.834563i
$304$		0			0
$305$	−0.759916			−0.0435126
$306$		0			0
$307$	15.6701			0.894342			0.447171	−	0.894448i	$-0.352431\pi$
$307$	15.6701			0.894342			0.447171	+	0.894448i	$0.352431\pi$
$308$		0			0
$309$	−6.48580	−	17.9189i	−0.368964	−	1.01937i
$310$		0			0
$311$	11.4295	−	19.7965i	0.648110	−	1.12256i	−0.335464	−	0.942053i	$-0.608893\pi$
$311$	11.4295	−	19.7965i	0.648110	−	1.12256i	0.983574	−	0.180506i	$-0.0577735\pi$
$312$		0			0
$313$	−16.9021	+	9.75842i	−0.955362	+	0.551579i	−0.894743	−	0.446582i	$-0.852641\pi$
$313$	−16.9021	+	9.75842i	−0.955362	+	0.551579i	−0.0606196	+	0.998161i	$0.519308\pi$
$314$		0			0
$315$	−0.555839	−	2.34947i	−0.0313180	−	0.132377i
$316$		0			0
$317$	−5.39581	−	9.34581i	−0.303059	−	0.524913i	0.673768	−	0.738943i	$-0.264675\pi$
$317$	−5.39581	−	9.34581i	−0.303059	−	0.524913i	−0.976827	+	0.214029i	$0.931341\pi$
$318$		0			0
$319$	4.25821	+	2.45848i	0.238414	+	0.137648i
$320$		0			0
$321$	16.9987	+	14.3153i	0.948776	+	0.799003i
$322$		0			0
$323$		−	19.8790i		−	1.10610i
$324$		0			0
$325$		−	23.2918i		−	1.29200i
$326$		0			0
$327$	−3.54304	+	4.20718i	−0.195931	+	0.232658i
$328$		0			0
$329$	15.2990	+	7.62293i	0.843459	+	0.420265i
$330$		0			0
$331$	6.82866	−	3.94253i	0.375337	−	0.216701i	−0.300450	−	0.953797i	$-0.597137\pi$
$331$	6.82866	−	3.94253i	0.375337	−	0.216701i	0.675788	+	0.737096i	$0.263804\pi$
$332$		0			0
$333$	1.89068	+	10.9507i	0.103609	+	0.600095i
$334$		0			0
$335$	1.05992	+	1.83584i	0.0579097	+	0.100303i
$336$		0			0
$337$	8.80232	−	15.2461i	0.479493	−	0.830506i	−0.520230	−	0.854026i	$-0.674154\pi$
$337$	8.80232	−	15.2461i	0.479493	−	0.830506i	0.999723	+	0.0235197i	$0.00748726\pi$
$338$		0			0
$339$	−3.13512	−	8.66166i	−0.170276	−	0.470437i
$340$		0			0
$341$		−	1.85790i		−	0.100611i
$342$		0			0
$343$	3.38894	+	18.2076i	0.182986	+	0.983116i
$344$		0			0
$345$	−1.65798	−	0.295394i	−0.0892625	−	0.0159035i
$346$		0			0
$347$	−10.3211	−	5.95887i	−0.554064	−	0.319889i	0.196696	−	0.980465i	$-0.436979\pi$
$347$	−10.3211	−	5.95887i	−0.554064	−	0.319889i	−0.750759	+	0.660576i	$0.770312\pi$
$348$		0			0
$349$	−6.44783	+	3.72265i	−0.345144	+	0.199269i	−0.662545	−	0.749023i	$-0.730523\pi$
$349$	−6.44783	+	3.72265i	−0.345144	+	0.199269i	0.317400	+	0.948292i	$0.397190\pi$
$350$		0			0
$351$	12.2166	+	21.4235i	0.652073	+	1.14350i
$352$		0			0
$353$	22.6054	−	13.0512i	1.20316	−	0.694647i	0.241906	−	0.970300i	$-0.422227\pi$
$353$	22.6054	−	13.0512i	1.20316	−	0.694647i	0.961257	+	0.275653i	$0.0888940\pi$
$354$		0			0
$355$	1.54117	−	2.66938i	0.0817966	−	0.141676i
$356$		0			0
$357$	20.6285	+	2.38225i	1.09178	+	0.126082i
$358$		0			0
$359$		−	29.3206i		−	1.54748i	−0.633502	−	0.773741i	$-0.718383\pi$
$359$		−	29.3206i		−	1.54748i	0.633502	−	0.773741i	$-0.281617\pi$
$360$		0			0
$361$	0.245065			0.0128981
$362$		0			0
$363$	−6.33412	−	17.4998i	−0.332455	−	0.918503i
$364$		0			0
$365$	1.08513	−	1.87949i	0.0567981	−	0.0983772i
$366$		0			0
$367$	−0.989656	−	1.71414i	−0.0516596	−	0.0894771i	0.839039	−	0.544071i	$-0.183118\pi$
$367$	−0.989656	−	1.71414i	−0.0516596	−	0.0894771i	−0.890699	+	0.454594i	$0.849784\pi$
$368$		0			0
$369$	−8.39405	+	22.8092i	−0.436977	+	1.18740i
$370$		0			0
$371$	−14.4014	+	9.53734i	−0.747683	+	0.495154i
$372$		0			0
$373$	2.72184	−	4.71436i	0.140931	−	0.244100i	−0.786916	−	0.617060i	$-0.788324\pi$
$373$	2.72184	−	4.71436i	0.140931	−	0.244100i	0.927848	+	0.372959i	$0.121657\pi$
$374$		0			0
$375$	−3.99256	−	3.36230i	−0.206175	−	0.173629i
$376$		0			0
$377$		−	46.2140i		−	2.38014i
$378$		0			0
$379$			5.40049i			0.277404i	0.990334	+	0.138702i	$0.0442931\pi$
$379$			5.40049i			0.277404i	−0.990334	+	0.138702i	$0.955707\pi$
$380$		0			0
$381$	−12.8556	−	10.8262i	−0.658613	−	0.554645i
$382$		0			0
$383$	−14.2110	+	24.6142i	−0.726149	+	1.25773i	0.232350	+	0.972632i	$0.425359\pi$
$383$	−14.2110	+	24.6142i	−0.726149	+	1.25773i	−0.958499	+	0.285095i	$0.907975\pi$
$384$		0			0
$385$	−0.338825	+	0.224387i	−0.0172681	+	0.0114358i
$386$		0			0
$387$	−8.86044	−	10.6362i	−0.450401	−	0.540670i
$388$		0			0
$389$	−13.3498	−	23.1225i	−0.676862	−	1.17236i	−0.975921	−	0.218124i	$-0.930006\pi$
$389$	−13.3498	−	23.1225i	−0.676862	−	1.17236i	0.299060	−	0.954234i	$-0.403327\pi$
$390$		0			0
$391$	7.24242	−	12.5442i	0.366265	−	0.634390i
$392$		0			0
$393$	4.06268	+	11.2243i	0.204935	+	0.566192i
$394$		0			0
$395$	2.09387			0.105354
$396$		0			0
$397$			3.70933i			0.186166i	0.995658	+	0.0930829i	$0.0296722\pi$
$397$			3.70933i			0.186166i	−0.995658	+	0.0930829i	$0.970328\pi$
$398$		0			0
$399$	−2.30628	+	19.9707i	−0.115459	+	0.999784i
$400$		0			0
$401$	−9.74810	+	16.8842i	−0.486797	+	0.843157i	−0.999885	−	0.0151789i	$-0.995168\pi$
$401$	−9.74810	+	16.8842i	−0.486797	+	0.843157i	0.513088	+	0.858336i	$0.328502\pi$
$402$		0			0
$403$	−15.1227	+	8.73112i	−0.753317	+	0.434928i
$404$		0			0
$405$	2.69254	+	0.494583i	0.133793	+	0.0245760i
$406$		0			0
$407$	1.61994	−	0.935270i	0.0802972	−	0.0463596i
$408$		0			0
$409$	−29.8309	−	17.2229i	−1.47504	−	0.851616i	−0.475438	−	0.879749i	$-0.657711\pi$
$409$	−29.8309	−	17.2229i	−1.47504	−	0.851616i	−0.999604	+	0.0281328i	$0.991044\pi$
$410$		0			0
$411$	12.6458	+	2.25305i	0.623773	+	0.111135i
$412$		0			0
$413$	2.07767	+	33.8284i	0.102235	+	1.66459i
$414$		0			0
$415$			2.23207i			0.109568i
$416$		0			0
$417$	−10.0903	−	27.8773i	−0.494123	−	1.36516i
$418$		0			0
$419$	−19.7174	+	34.1516i	−0.963259	+	1.66841i	−0.249036	+	0.968494i	$0.580114\pi$
$419$	−19.7174	+	34.1516i	−0.963259	+	1.66841i	−0.714222	+	0.699919i	$0.753219\pi$
$420$		0			0
$421$	−16.8161	−	29.1263i	−0.819567	−	1.41953i	−0.906002	−	0.423274i	$-0.860881\pi$
$421$	−16.8161	−	29.1263i	−0.819567	−	1.41953i	0.0864352	−	0.996257i	$-0.472452\pi$
$422$		0			0
$423$	−14.8914	+	12.4052i	−0.724046	+	0.603162i
$424$		0			0
$425$	19.2586	−	11.1189i	0.934178	−	0.539348i
$426$		0			0
$427$	−2.94778	+	5.91610i	−0.142653	+	0.286300i
$428$		0			0
$429$	2.67400	−	3.17524i	0.129102	−	0.153302i
$430$		0			0
$431$			27.3561i			1.31770i	0.752276	+	0.658848i	$0.228956\pi$
$431$			27.3561i			1.31770i	−0.752276	+	0.658848i	$0.771044\pi$
$432$		0			0
$433$			22.7292i			1.09229i	0.837689	+	0.546147i	$0.183906\pi$
$433$			22.7292i			1.09229i	−0.837689	+	0.546147i	$0.816094\pi$
$434$		0			0
$435$	−3.92390	−	3.30447i	−0.188136	−	0.158437i
$436$		0			0
$437$	12.1442	+	7.01146i	0.580936	+	0.335404i
$438$		0			0
$439$	1.84811	+	3.20101i	0.0882053	+	0.152776i	0.906753	−	0.421663i	$-0.138554\pi$
$439$	1.84811	+	3.20101i	0.0882053	+	0.152776i	−0.818547	+	0.574439i	$0.805220\pi$
$440$		0			0
$441$	−20.4472	−	4.78647i	−0.973678	−	0.227927i
$442$		0			0
$443$	−21.1702	+	12.2226i	−1.00582	+	0.580713i	−0.909966	−	0.414682i	$-0.863893\pi$
$443$	−21.1702	+	12.2226i	−1.00582	+	0.580713i	−0.0958579	+	0.995395i	$0.530559\pi$
$444$		0			0
$445$	−1.80561	+	3.12740i	−0.0855940	+	0.148253i
$446$		0			0
$447$	−9.71560	−	26.8421i	−0.459532	−	1.26959i
$448$		0			0
$449$	27.6399			1.30441			0.652204	−	0.758043i	$-0.273844\pi$
$449$	27.6399			1.30441			0.652204	+	0.758043i	$0.273844\pi$
$450$		0			0
$451$	4.09107			0.192641
$452$		0			0
$453$	−1.85195	+	10.3946i	−0.0870122	+	0.488379i
$454$		0			0
$455$	3.41873	+	1.70343i	0.160273	+	0.0798580i
$456$		0			0
$457$	−5.54654	−	9.60690i	−0.259456	−	0.449392i	0.706640	−	0.707573i	$-0.250210\pi$
$457$	−5.54654	−	9.60690i	−0.259456	−	0.449392i	−0.966096	+	0.258182i	$0.916877\pi$
$458$		0			0
$459$	−11.8818	+	20.3282i	−0.554597	+	0.948839i
$460$		0			0
$461$	−3.24445	+	1.87318i	−0.151109	+	0.0872428i	−0.573648	−	0.819102i	$-0.694472\pi$
$461$	−3.24445	+	1.87318i	−0.151109	+	0.0872428i	0.422539	+	0.906345i	$0.361139\pi$
$462$		0			0
$463$	3.52542	+	2.03540i	0.163840	+	0.0945931i	0.579678	−	0.814846i	$-0.303178\pi$
$463$	3.52542	+	2.03540i	0.163840	+	0.0945931i	−0.415838	+	0.909439i	$0.636512\pi$
$464$		0			0
$465$	−0.339999	+	1.90834i	−0.0157671	+	0.0884970i
$466$		0			0
$467$	15.3831			0.711843			0.355922	−	0.934516i	$-0.384167\pi$
$467$	15.3831			0.711843			0.355922	+	0.934516i	$0.384167\pi$
$468$		0			0
$469$	18.4039	−	1.13033i	0.849814	−	0.0521938i
$470$		0			0
$471$	−18.6224	+	6.74042i	−0.858073	+	0.310582i
$472$		0			0
$473$	−1.16508	+	2.01798i	−0.0535705	+	0.0927868i
$474$		0			0
$475$	10.7644	+	18.6444i	0.493902	+	0.855464i
$476$		0			0
$477$	−3.33228	−	19.3003i	−0.152575	−	0.883701i
$478$		0			0
$479$	−2.93712	−	5.08724i	−0.134200	−	0.232442i	0.791091	−	0.611698i	$-0.209513\pi$
$479$	−2.93712	−	5.08724i	−0.134200	−	0.232442i	−0.925292	+	0.379256i	$0.876180\pi$
$480$		0			0
$481$	−15.2256	−	8.79050i	−0.694227	−	0.400812i
$482$		0			0
$483$	−8.73114	+	11.7618i	−0.397281	+	0.535182i
$484$		0			0
$485$	3.86159			0.175346
$486$		0			0
$487$		−	31.9979i		−	1.44996i	−0.688769	−	0.724981i	$-0.741849\pi$
$487$		−	31.9979i		−	1.44996i	0.688769	−	0.724981i	$-0.258151\pi$
$488$		0			0
$489$	28.3363	+	23.8631i	1.28141	+	1.07913i
$490$		0			0
$491$	25.3831	+	14.6549i	1.14552	+	0.661367i	0.947792	−	0.318890i	$-0.103310\pi$
$491$	25.3831	+	14.6549i	1.14552	+	0.661367i	0.197729	+	0.980257i	$0.436643\pi$
$492$		0			0
$493$	38.2115	−	22.0614i	1.72096	−	0.993597i
$494$		0			0
$495$	−0.0783994	−	0.454084i	−0.00352379	−	0.0204095i
$496$		0			0
$497$	−14.8033	−	22.3531i	−0.664021	−	1.00267i
$498$		0			0
$499$	−27.0620	−	15.6242i	−1.21146	−	0.699437i	−0.248383	−	0.968662i	$-0.579899\pi$
$499$	−27.0620	−	15.6242i	−1.21146	−	0.699437i	−0.963077	+	0.269225i	$0.913233\pi$
$500$		0			0
$501$	3.60523	+	9.96048i	0.161070	+	0.445002i
$502$		0			0
$503$	−27.9078			−1.24435			−0.622175	−	0.782878i	$-0.713751\pi$
$503$	−27.9078			−1.24435			−0.622175	+	0.782878i	$0.713751\pi$
$504$		0			0
$505$	2.59138			0.115315
$506$		0			0
$507$	−16.2442	−	2.89415i	−0.721429	−	0.128534i
$508$		0			0
$509$	15.8612	+	9.15745i	0.703034	+	0.405897i	0.808477	−	0.588528i	$-0.200293\pi$
$509$	15.8612	+	9.15745i	0.703034	+	0.405897i	−0.105442	+	0.994425i	$0.533626\pi$
$510$		0			0
$511$	−10.4230	−	15.7387i	−0.461084	−	0.696238i
$512$		0			0
$513$	−19.6799	−	11.5029i	−0.868890	−	0.507867i
$514$		0			0
$515$	2.89827	−	1.67332i	0.127713	−	0.0737353i
$516$		0			0
$517$	2.82531	+	1.63119i	0.124257	+	0.0717397i
$518$		0			0
$519$	5.17925	−	29.0699i	0.227344	−	1.27603i
$520$		0			0
$521$		−	5.07663i		−	0.222411i	−0.993797	−	0.111206i	$-0.964529\pi$
$521$		−	5.07663i		−	0.222411i	0.993797	−	0.111206i	$-0.0354712\pi$
$522$		0			0
$523$	33.2565			1.45421			0.727104	−	0.686528i	$-0.240866\pi$
$523$	33.2565			1.45421			0.727104	+	0.686528i	$0.240866\pi$
$524$		0			0
$525$	−20.6373	+	8.93590i	−0.900687	+	0.389995i
$526$		0			0
$527$	−14.4385	−	8.33605i	−0.628949	−	0.363124i
$528$		0			0
$529$	−6.39110	−	11.0697i	−0.277874	−	0.481292i
$530$		0			0
$531$	−36.0654	−	13.2725i	−1.56510	−	0.575977i
$532$		0			0
$533$	−19.2258	−	33.3000i	−0.832760	−	1.44238i
$534$		0			0
$535$	−1.95140	+	3.37993i	−0.0843665	+	0.146127i
$536$		0			0
$537$	17.6735	+	14.8835i	0.762666	+	0.642273i
$538$		0			0
$539$	0.432570	+	3.50824i	0.0186321	+	0.151111i
$540$		0			0
$541$	−15.9402			−0.685321			−0.342661	−	0.939459i	$-0.611328\pi$
$541$	−15.9402			−0.685321			−0.342661	+	0.939459i	$0.611328\pi$
$542$		0			0
$543$	−24.8316	−	20.9117i	−1.06563	−	0.897407i
$544$		0			0
$545$	−0.836533	−	0.482973i	−0.0358331	−	0.0206883i
$546$		0			0
$547$	−7.68696	+	4.43807i	−0.328670	+	0.189758i	−0.655251	−	0.755412i	$-0.727437\pi$
$547$	−7.68696	+	4.43807i	−0.328670	+	0.189758i	0.326580	+	0.945169i	$0.394104\pi$
$548$		0			0
$549$	−4.79709	−	5.75851i	−0.204735	−	0.245767i
$550$		0			0
$551$	21.3579	+	36.9929i	0.909877	+	1.57595i
$552$		0			0
$553$	8.12230	−	16.3012i	0.345395	−	0.693197i
$554$		0			0
$555$	−1.83506	+	0.664207i	−0.0778941	+	0.0281940i
$556$		0			0
$557$	34.7304			1.47157			0.735786	−	0.677214i	$-0.236813\pi$
$557$	34.7304			1.47157			0.735786	+	0.677214i	$0.236813\pi$
$558$		0			0
$559$	21.9009			0.926311
$560$		0			0
$561$	3.90192	+	0.695186i	0.164739	+	0.0293508i
$562$		0			0
$563$	−16.0862	+	27.8622i	−0.677953	+	1.17425i	0.297643	+	0.954677i	$0.403800\pi$
$563$	−16.0862	+	27.8622i	−0.677953	+	1.17425i	−0.975596	+	0.219572i	$0.929534\pi$
$564$		0			0
$565$	1.40097	−	0.808852i	0.0589393	−	0.0340286i
$566$		0			0
$567$	14.2950	−	19.0434i	0.600335	−	0.799749i
$568$		0			0
$569$	0.136604	+	0.236606i	0.00572675	+	0.00991903i	0.868875	−	0.495032i	$-0.164844\pi$
$569$	0.136604	+	0.236606i	0.00572675	+	0.00991903i	−0.863148	+	0.504951i	$0.831510\pi$
$570$		0			0
$571$	12.4639	+	7.19606i	0.521599	+	0.301146i	0.737589	−	0.675250i	$-0.235964\pi$
$571$	12.4639	+	7.19606i	0.521599	+	0.301146i	−0.215989	+	0.976396i	$0.569298\pi$
$572$		0			0
$573$	3.67685	−	20.6373i	0.153603	−	0.862136i
$574$		0			0
$575$			15.6869i			0.654189i
$576$		0			0
$577$		−	42.6896i		−	1.77719i	−0.458693	−	0.888595i	$-0.651682\pi$
$577$		−	42.6896i		−	1.77719i	0.458693	−	0.888595i	$-0.348318\pi$
$578$		0			0
$579$	−4.43808	−	12.2615i	−0.184440	−	0.509570i
$580$		0			0
$581$	17.3772	+	8.65842i	0.720926	+	0.359212i
$582$		0			0
$583$	−2.85509	+	1.64839i	−0.118246	+	0.0682693i
$584$		0			0
$585$	−3.32766	+	2.77209i	−0.137582	+	0.114612i
$586$		0			0
$587$	12.7821	+	22.1393i	0.527575	+	0.913786i	0.999483	+	0.0321388i	$0.0102319\pi$
$587$	12.7821	+	22.1393i	0.527575	+	0.913786i	−0.471909	+	0.881647i	$0.656435\pi$
$588$		0			0
$589$	8.07021	−	13.9780i	0.332527	−	0.575954i
$590$		0			0
$591$	−22.5403	+	26.7655i	−0.927186	+	1.10099i
$592$		0			0
$593$			17.4510i			0.716626i	0.933602	+	0.358313i	$0.116648\pi$
$593$			17.4510i			0.716626i	−0.933602	+	0.358313i	$0.883352\pi$
$594$		0			0
$595$	0.223556	+	3.63992i	0.00916491	+	0.149222i
$596$		0			0
$597$	25.4813	−	30.2577i	1.04288	−	1.23837i
$598$		0			0
$599$	−20.2258	−	11.6774i	−0.826403	−	0.477124i	0.0262162	−	0.999656i	$-0.491654\pi$
$599$	−20.2258	−	11.6774i	−0.826403	−	0.477124i	−0.852620	+	0.522532i	$0.824987\pi$
$600$		0			0
$601$	−41.6504	+	24.0469i	−1.69896	+	0.980892i	−0.752202	+	0.658933i	$0.771008\pi$
$601$	−41.6504	+	24.0469i	−1.69896	+	0.980892i	−0.946753	+	0.321959i	$0.895659\pi$
$602$		0			0
$603$	−7.22073	+	19.6209i	−0.294051	+	0.799025i
$604$		0			0
$605$	2.83049	−	1.63419i	0.115076	−	0.0664391i
$606$		0			0
$607$	12.7020	−	22.0005i	0.515559	−	0.892975i	−0.484278	−	0.874914i	$-0.660918\pi$
$607$	12.7020	−	22.0005i	0.515559	−	0.892975i	0.999837	−	0.0180603i	$-0.00574910\pi$
$608$		0			0
$609$	−40.9472	+	17.7300i	−1.65926	+	0.718456i
$610$		0			0
$611$		−	30.6628i		−	1.24048i
$612$		0			0
$613$	−27.0827			−1.09386			−0.546929	−	0.837179i	$-0.684203\pi$
$613$	−27.0827			−1.09386			−0.546929	+	0.837179i	$0.684203\pi$
$614$		0			0
$615$	−4.20212	−	0.748672i	−0.169446	−	0.0301894i
$616$		0			0
$617$	−7.71009	+	13.3543i	−0.310397	+	0.537623i	−0.978448	−	0.206492i	$-0.933795\pi$
$617$	−7.71009	+	13.3543i	−0.310397	+	0.537623i	0.668052	+	0.744115i	$0.267129\pi$
$618$		0			0
$619$	−20.7162	−	35.8815i	−0.832654	−	1.44220i	−0.895927	−	0.444202i	$-0.853487\pi$
$619$	−20.7162	−	35.8815i	−0.832654	−	1.44220i	0.0632732	−	0.997996i	$-0.479846\pi$
$620$		0			0
$621$	−8.22780	−	14.4286i	−0.330170	−	0.578999i
$622$		0			0
$623$	17.3434	+	26.1885i	0.694848	+	1.04922i
$624$		0			0
$625$	−11.8104	+	20.4561i	−0.472414	+	0.818246i
$626$		0			0
$627$	−0.673016	+	3.77748i	−0.0268777	+	0.150858i
$628$		0			0
$629$		−	16.7855i		−	0.669281i
$630$		0			0
$631$		−	1.25386i		−	0.0499155i	−0.999689	−	0.0249577i	$-0.992055\pi$
$631$		−	1.25386i		−	0.0499155i	0.999689	−	0.0249577i	$-0.00794512\pi$
$632$		0			0
$633$	−22.5860	+	8.17508i	−0.897713	+	0.324930i
$634$		0			0
$635$	1.47579	−	2.55614i	0.0585648	−	0.101437i
$636$		0			0
$637$	26.5231	−	20.0078i	1.05088	−	0.792737i
$638$		0			0
$639$	29.9569	−	5.17219i	1.18508	−	0.204608i
$640$		0			0
$641$	−13.7743	−	23.8578i	−0.544052	−	0.942326i	−0.998666	−	0.0516376i	$-0.983556\pi$
$641$	−13.7743	−	23.8578i	−0.544052	−	0.942326i	0.454613	−	0.890689i	$-0.349777\pi$
$642$		0			0
$643$	18.6020	−	32.2196i	0.733591	−	1.27062i	−0.221748	−	0.975104i	$-0.571176\pi$
$643$	18.6020	−	32.2196i	0.733591	−	1.27062i	0.955339	−	0.295512i	$-0.0954904\pi$
$644$		0			0
$645$	1.56600	−	1.85955i	0.0616612	−	0.0732196i
$646$		0			0
$647$	13.0336			0.512403			0.256201	−	0.966623i	$-0.417529\pi$
$647$	13.0336			0.512403			0.256201	+	0.966623i	$0.417529\pi$
$648$		0			0
$649$			6.46871i			0.253919i
$650$		0			0
$651$	13.5379	+	10.0496i	0.530593	+	0.393874i
$652$		0			0
$653$	3.89056	−	6.73864i	0.152249	−	0.263704i	−0.779805	−	0.626023i	$-0.784682\pi$
$653$	3.89056	−	6.73864i	0.152249	−	0.263704i	0.932054	+	0.362319i	$0.118015\pi$
$654$		0			0
$655$	−1.81547	+	1.04816i	−0.0709362	+	0.0409550i
$656$		0			0
$657$	21.0925	−	3.64171i	0.822897	−	0.142077i
$658$		0			0
$659$	−36.1876	+	20.8929i	−1.40967	+	0.813873i	−0.995356	−	0.0962621i	$-0.969311\pi$
$659$	−36.1876	+	20.8929i	−1.40967	+	0.813873i	−0.414313	+	0.910135i	$0.635978\pi$
$660$		0			0
$661$	19.3416	+	11.1669i	0.752303	+	0.434342i	0.826525	−	0.562899i	$-0.190314\pi$
$661$	19.3416	+	11.1669i	0.752303	+	0.434342i	−0.0742225	+	0.997242i	$0.523648\pi$
$662$		0			0
$663$	−12.6783	−	35.0273i	−0.492383	−	1.36035i
$664$		0			0
$665$	−3.52384	+	0.216427i	−0.136649	+	0.00839268i
$666$		0			0
$667$			31.1249i			1.20516i
$668$		0			0
$669$	−2.51284	−	0.447701i	−0.0971520	−	0.0173091i
$670$		0			0
$671$	−0.630781	+	1.09254i	−0.0243510	+	0.0421772i
$672$		0			0
$673$	12.9074	+	22.3563i	0.497544	+	0.861771i	0.999996	−	0.00283382i	$-0.000902033\pi$
$673$	12.9074	+	22.3563i	0.497544	+	0.861771i	−0.502452	+	0.864605i	$0.667569\pi$
$674$		0			0
$675$	0.136336	−	25.4996i	0.00524757	−	0.981481i
$676$		0			0
$677$	−9.62411	+	5.55648i	−0.369885	+	0.213553i	−0.673408	−	0.739271i	$-0.735170\pi$
$677$	−9.62411	+	5.55648i	−0.369885	+	0.213553i	0.303523	+	0.952824i	$0.401837\pi$
$678$		0			0
$679$	14.9794	−	30.0633i	0.574858	−	1.15372i
$680$		0			0
$681$	−13.5652	−	2.41684i	−0.519819	−	0.0926136i
$682$		0			0
$683$			7.40166i			0.283217i	0.989923	+	0.141608i	$0.0452273\pi$
$683$			7.40166i			0.283217i	−0.989923	+	0.141608i	$0.954773\pi$
$684$		0			0
$685$			2.25578i			0.0861891i
$686$		0			0
$687$	−19.5948	+	7.09239i	−0.747587	+	0.270591i
$688$		0			0
$689$	26.8347	+	15.4930i	1.02232	+	0.590237i
$690$		0			0
$691$	1.63144	+	2.82574i	0.0620630	+	0.107496i	0.895387	−	0.445288i	$-0.146899\pi$
$691$	1.63144	+	2.82574i	0.0620630	+	0.107496i	−0.833324	+	0.552784i	$0.813565\pi$
$692$		0			0
$693$	−3.83925	−	1.15108i	−0.145841	−	0.0437257i
$694$		0			0
$695$	4.50899	−	2.60326i	0.171036	−	0.0987474i
$696$		0			0
$697$	18.3558	−	31.7932i	0.695277	−	1.20425i
$698$		0			0
$699$	0.841168	−	0.998845i	0.0318159	−	0.0377798i
$700$		0			0
$701$	−24.7327			−0.934142			−0.467071	−	0.884220i	$-0.654691\pi$
$701$	−24.7327			−0.934142			−0.467071	+	0.884220i	$0.654691\pi$
$702$		0			0
$703$	16.2502			0.612888
$704$		0			0
$705$	−2.60349	−	2.19251i	−0.0980531	−	0.0825745i
$706$		0			0
$707$	10.0522	−	20.1744i	0.378051	−	0.758737i
$708$		0			0
$709$	10.1878	+	17.6458i	0.382612	+	0.662703i	0.991435	−	0.130603i	$-0.0416913\pi$
$709$	10.1878	+	17.6458i	0.382612	+	0.662703i	−0.608823	+	0.793306i	$0.708358\pi$
$710$		0			0
$711$	13.2179	+	15.8670i	0.495709	+	0.595057i
$712$		0			0
$713$	10.1851	−	5.88036i	0.381434	−	0.220221i
$714$		0			0
$715$	0.631347	+	0.364508i	0.0236110	+	0.0136318i
$716$		0			0
$717$	−32.5127	+	11.7681i	−1.21421	+	0.439486i
$718$		0			0
$719$	−22.9742			−0.856793			−0.428396	−	0.903591i	$-0.640921\pi$
$719$	−22.9742			−0.856793			−0.428396	+	0.903591i	$0.640921\pi$
$720$		0			0
$721$	−1.78448	−	29.0546i	−0.0664573	−	1.08205i
$722$		0			0
$723$	−2.93547	+	16.4761i	−0.109171	+	0.612754i
$724$		0			0
$725$	−23.8922	+	41.3826i	−0.887336	+	1.53691i
$726$		0			0
$727$	25.3044	+	43.8285i	0.938489	+	1.62551i	0.768291	+	0.640100i	$0.221107\pi$
$727$	25.3044	+	43.8285i	0.938489	+	1.62551i	0.170197	+	0.985410i	$0.445560\pi$
$728$		0			0
$729$	13.2492	+	23.5257i	0.490711	+	0.871322i
$730$		0			0
$731$	10.4550	+	18.1086i	0.386691	+	0.669769i
$732$		0			0
$733$	−0.788561	−	0.455276i	−0.0291262	−	0.0168160i	0.485366	−	0.874311i	$-0.338686\pi$
$733$	−0.788561	−	0.455276i	−0.0291262	−	0.0168160i	−0.514492	+	0.857495i	$0.672020\pi$
$734$		0			0
$735$	0.197701	−	3.68263i	0.00729233	−	0.135836i
$736$		0			0
$737$	3.51922			0.129632
$738$		0			0
$739$			11.5676i			0.425521i	0.977104	+	0.212761i	$0.0682455\pi$
$739$			11.5676i			0.425521i	−0.977104	+	0.212761i	$0.931755\pi$
$740$		0			0
$741$	33.9103	−	12.2739i	1.24573	−	0.450895i
$742$		0			0
$743$	−36.1075	−	20.8467i	−1.32466	−	0.764790i	−0.340188	−	0.940357i	$-0.610491\pi$
$743$	−36.1075	−	20.8467i	−1.32466	−	0.764790i	−0.984467	+	0.175567i	$0.943824\pi$
$744$		0			0
$745$	4.34155	−	2.50660i	0.159062	−	0.0918346i
$746$		0			0
$747$	−16.9143	+	14.0903i	−0.618860	+	0.515538i
$748$		0			0
$749$	18.7438	+	28.3031i	0.684883	+	1.03417i
$750$		0			0
$751$	17.1295	+	9.88969i	0.625063	+	0.360880i	0.778837	−	0.627226i	$-0.215810\pi$
$751$	17.1295	+	9.88969i	0.625063	+	0.360880i	−0.153775	+	0.988106i	$0.549143\pi$
$752$		0			0
$753$	12.0018	−	14.2516i	0.437372	−	0.519357i
$754$		0			0
$755$	−1.85420			−0.0674812
$756$		0			0
$757$	25.5667			0.929236			0.464618	−	0.885511i	$-0.346192\pi$
$757$	25.5667			0.929236			0.464618	+	0.885511i	$0.346192\pi$
$758$		0			0
$759$	−1.80093	+	2.13851i	−0.0653694	+	0.0776229i
$760$		0			0
$761$	−35.2307	−	20.3405i	−1.27711	−	0.737342i	−0.300797	−	0.953688i	$-0.597253\pi$
$761$	−35.2307	−	20.3405i	−1.27711	−	0.737342i	−0.976317	+	0.216347i	$0.930586\pi$
$762$		0			0
$763$	−7.00503	+	4.63909i	−0.253599	+	0.167946i
$764$		0			0
$765$	−3.88061	−	1.42811i	−0.140304	−	0.0516335i
$766$		0			0
$767$	52.6532	−	30.3994i	1.90120	−	1.09766i
$768$		0			0
$769$	−38.0816	−	21.9864i	−1.37326	−	0.792851i	−0.381921	−	0.924195i	$-0.624737\pi$
$769$	−38.0816	−	21.9864i	−1.37326	−	0.792851i	−0.991337	+	0.131344i	$0.958071\pi$
$770$		0			0
$771$	8.61929	−	3.11978i	0.310416	−	0.112356i
$772$		0			0
$773$			16.8373i			0.605596i	0.953055	+	0.302798i	$0.0979208\pi$
$773$			16.8373i			0.605596i	−0.953055	+	0.302798i	$0.902079\pi$
$774$		0			0
$775$	18.0557			0.648579
$776$		0			0
$777$	−1.94738	+	16.8629i	−0.0698620	+	0.604952i
$778$		0			0
$779$	30.7793	+	17.7705i	1.10278	+	0.636693i
$780$		0			0
$781$	−2.55854	−	4.43152i	−0.0915518	−	0.158572i
$782$		0			0
$783$	0.270508	−	50.5946i	0.00966717	−	1.80810i
$784$		0			0
$785$	−1.73901	−	3.01205i	−0.0620679	−	0.107505i
$786$		0			0
$787$	10.5794	−	18.3240i	0.377115	−	0.653182i	−0.613526	−	0.789674i	$-0.710250\pi$
$787$	10.5794	−	18.3240i	0.377115	−	0.653182i	0.990641	+	0.136492i	$0.0435829\pi$
$788$		0			0
$789$	1.56108	−	8.76201i	0.0555761	−	0.311936i
$790$		0			0
$791$	−0.862583	−	14.0445i	−0.0306699	−	0.499364i
$792$		0			0
$793$	11.8573			0.421064
$794$		0			0
$795$	3.23425	−	1.17065i	0.114707	−	0.0415186i
$796$		0			0
$797$	−7.19124	−	4.15186i	−0.254727	−	0.147066i	0.367200	−	0.930142i	$-0.380316\pi$
$797$	−7.19124	−	4.15186i	−0.254727	−	0.147066i	−0.621927	+	0.783076i	$0.713650\pi$
$798$		0			0
$799$	25.3532	−	14.6377i	0.896931	−	0.517844i
$800$		0			0
$801$	−35.0971	+	6.05966i	−1.24010	+	0.214108i
$802$		0			0
$803$	−1.80146	−	3.12021i	−0.0635720	−	0.110110i
$804$		0			0
$805$	−2.30250	−	1.14725i	−0.0811523	−	0.0404353i
$806$		0			0
$807$	−33.5239	−	28.2319i	−1.18010	−	0.993810i
$808$		0			0
$809$	40.9535			1.43985			0.719925	−	0.694052i	$-0.244176\pi$
$809$	40.9535			1.43985			0.719925	+	0.694052i	$0.244176\pi$
$810$		0			0
$811$	4.74782			0.166718			0.0833592	−	0.996520i	$-0.473435\pi$
$811$	4.74782			0.166718			0.0833592	+	0.996520i	$0.473435\pi$
$812$		0			0
$813$	−1.21190	+	1.43907i	−0.0425032	+	0.0504704i
$814$		0			0
$815$	−3.25292	+	5.63422i	−0.113945	+	0.197358i
$816$		0			0
$817$	−17.5311	+	10.1216i	−0.613334	+	0.354109i
$818$		0			0
$819$	8.67298	+	36.6597i	0.303059	+	1.28099i
$820$		0			0
$821$	2.73543	+	4.73790i	0.0954671	+	0.165354i	0.909803	−	0.415039i	$-0.136232\pi$
$821$	2.73543	+	4.73790i	0.0954671	+	0.165354i	−0.814336	+	0.580393i	$0.802899\pi$
$822$		0			0
$823$	−14.7561	−	8.51945i	−0.514366	−	0.296969i	0.220260	−	0.975441i	$-0.429309\pi$
$823$	−14.7561	−	8.51945i	−0.514366	−	0.296969i	−0.734627	+	0.678472i	$0.762643\pi$
$824$		0			0
$825$	−4.03602	+	1.46085i	−0.140516	+	0.0508603i
$826$		0			0
$827$			26.6988i			0.928408i	0.885728	+	0.464204i	$0.153659\pi$
$827$			26.6988i			0.928408i	−0.885728	+	0.464204i	$0.846341\pi$
$828$		0			0
$829$		−	44.8881i		−	1.55903i	−0.626385	−	0.779514i	$-0.715466\pi$
$829$		−	44.8881i		−	1.55903i	0.626385	−	0.779514i	$-0.284534\pi$
$830$		0			0
$831$	−30.1684	−	5.37496i	−1.04653	−	0.186455i
$832$		0			0
$833$	29.2047	+	12.3791i	1.01188	+	0.428912i
$834$		0			0
$835$	−1.61105	+	0.930139i	−0.0557526	+	0.0321888i
$836$		0			0
$837$	−16.6073	+	9.47023i	−0.574034	+	0.327339i
$838$		0			0
$839$	7.36959	+	12.7645i	0.254427	+	0.440680i	0.964740	−	0.263206i	$-0.0847799\pi$
$839$	7.36959	+	12.7645i	0.254427	+	0.440680i	−0.710313	+	0.703886i	$0.751447\pi$
$840$		0			0
$841$	−32.9053	+	56.9937i	−1.13467	+	1.96530i
$842$		0			0
$843$	−14.2530	−	2.53939i	−0.490901	−	0.0874614i
$844$		0			0
$845$		−	2.89766i		−	0.0996826i
$846$		0			0
$847$	−1.74274	−	28.3751i	−0.0598813	−	0.974981i
$848$		0			0
$849$	4.34445	+	12.0028i	0.149101	+	0.411935i
$850$		0			0
$851$	10.2544	+	5.92035i	0.351515	+	0.202947i
$852$		0			0
$853$	−16.9795	+	9.80312i	−0.581367	+	0.335652i	−0.761676	−	0.647958i	$-0.775623\pi$
$853$	−16.9795	+	9.80312i	−0.581367	+	0.335652i	0.180309	+	0.983610i	$0.442290\pi$
$854$		0			0
$855$	1.38257	−	3.75686i	0.0472829	−	0.128482i
$856$		0			0
$857$	2.10408	−	1.21479i	0.0718739	−	0.0414964i	−0.463632	−	0.886028i	$-0.653454\pi$
$857$	2.10408	−	1.21479i	0.0718739	−	0.0414964i	0.535506	+	0.844531i	$0.320121\pi$
$858$		0			0
$859$	1.95139	−	3.37990i	0.0665804	−	0.115321i	−0.830814	−	0.556551i	$-0.812124\pi$
$859$	1.95139	−	3.37990i	0.0665804	−	0.115321i	0.897394	+	0.441230i	$0.145458\pi$
$860$		0			0
$861$	−22.1290	+	29.8102i	−0.754154	+	1.01593i
$862$		0			0
$863$			16.0577i			0.546610i	0.961927	+	0.273305i	$0.0881169\pi$
$863$			16.0577i			0.546610i	−0.961927	+	0.273305i	$0.911883\pi$
$864$		0			0
$865$	5.18554			0.176314
$866$		0			0
$867$	3.94272	−	4.68178i	0.133902	−	0.159001i
$868$		0			0
$869$	1.73805	−	3.01039i	0.0589593	−	0.102120i
$870$		0			0
$871$	−16.5384	−	28.6453i	−0.560382	−	0.970610i
$872$		0			0
$873$	24.3769	+	29.2624i	0.825032	+	0.990383i
$874$		0			0
$875$	−4.40244	−	6.64769i	−0.148830	−	0.224733i
$876$		0			0
$877$	4.93618	−	8.54972i	0.166683	−	0.288703i	−0.770569	−	0.637357i	$-0.780028\pi$
$877$	4.93618	−	8.54972i	0.166683	−	0.288703i	0.937252	+	0.348654i	$0.113361\pi$
$878$		0			0
$879$	51.8658	−	18.7730i	1.74939	−	0.633197i
$880$		0			0
$881$		−	53.8542i		−	1.81439i	−0.420706	−	0.907197i	$-0.638217\pi$
$881$		−	53.8542i		−	1.81439i	0.420706	−	0.907197i	$-0.361783\pi$
$882$		0			0
$883$		−	5.54895i		−	0.186737i	−0.995632	−	0.0933685i	$-0.970237\pi$
$883$		−	5.54895i		−	0.186737i	0.995632	−	0.0933685i	$-0.0297635\pi$
$884$		0			0
$885$	1.18378	−	6.64431i	0.0397925	−	0.223346i
$886$		0			0
$887$	−15.6555	+	27.1160i	−0.525659	+	0.910467i	0.473895	+	0.880582i	$0.342848\pi$
$887$	−15.6555	+	27.1160i	−0.525659	+	0.910467i	−0.999553	+	0.0298859i	$0.990486\pi$
$888$		0			0
$889$	−14.1754	−	21.4048i	−0.475426	−	0.717894i
$890$		0			0
$891$	2.94606	−	3.46057i	0.0986966	−	0.115934i
$892$		0			0
$893$	14.1709	+	24.5447i	0.474210	+	0.821356i
$894$		0			0
$895$	−2.02886	+	3.51409i	−0.0678174	+	0.117463i
$896$		0			0
$897$	25.8701	+	4.60915i	0.863778	+	0.153895i
$898$		0			0
$899$	35.8248			1.19482
$900$		0			0
$901$			29.5840i			0.985586i
$902$		0			0
$903$	−8.40230	−	19.4050i	−0.279611	−	0.645758i
$904$		0			0
$905$	2.85060	−	4.93738i	0.0947570	−	0.164124i
$906$		0			0
$907$	18.0671	−	10.4310i	0.599907	−	0.346357i	−0.169098	−	0.985599i	$-0.554085\pi$
$907$	18.0671	−	10.4310i	0.599907	−	0.346357i	0.769005	+	0.639243i	$0.220752\pi$
$908$		0			0
$909$	16.3585	+	19.6370i	0.542576	+	0.651318i
$910$		0			0
$911$	39.2773	−	22.6768i	1.30132	−	0.751315i	0.320686	−	0.947185i	$-0.396086\pi$
$911$	39.2773	−	22.6768i	1.30132	−	0.751315i	0.980630	+	0.195870i	$0.0627532\pi$
$912$		0			0
$913$	3.20909	+	1.85277i	0.106205	+	0.0613178i
$914$		0			0
$915$	0.847841	−	1.00677i	0.0280288	−	0.0332827i
$916$		0			0
$917$	1.11779	+	18.1997i	0.0369126	+	0.601007i
$918$		0			0
$919$		−	41.0838i		−	1.35523i	−0.735418	−	0.677614i	$-0.763014\pi$
$919$		−	41.0838i		−	1.35523i	0.735418	−	0.677614i	$-0.236986\pi$
$920$		0			0
$921$	−17.4832	+	20.7605i	−0.576092	+	0.684080i
$922$		0			0
$923$	−24.0474	+	41.6514i	−0.791531	+	1.37097i
$924$		0			0
$925$	9.08923	+	15.7430i	0.298852	+	0.517627i
$926$		0			0
$927$	30.9759	+	11.3995i	1.01738	+	0.374409i
$928$		0			0
$929$	47.4341	−	27.3861i	1.55626	−	0.898508i	0.558651	−	0.829403i	$-0.311319\pi$
$929$	47.4341	−	27.3861i	1.55626	−	0.898508i	0.997609	−	0.0691051i	$-0.0220144\pi$
$930$		0			0
$931$	−11.9844	+	28.2734i	−0.392772	+	0.926622i
$932$		0			0
$933$	13.4753	+	37.2294i	0.441162	+	1.21884i
$934$		0			0
$935$			0.696030i			0.0227626i
$936$		0			0
$937$			49.8542i			1.62867i	0.580398	+	0.814333i	$0.302897\pi$
$937$			49.8542i			1.62867i	−0.580398	+	0.814333i	$0.697103\pi$
$938$		0			0
$939$	5.92935	−	33.2801i	0.193497	−	1.08605i
$940$		0			0
$941$	40.4860	+	23.3746i	1.31981	+	0.761990i	0.983697	−	0.179833i	$-0.0575557\pi$
$941$	40.4860	+	23.3746i	1.31981	+	0.761990i	0.336109	+	0.941823i	$0.390889\pi$
$942$		0			0
$943$	12.9484	+	22.4274i	0.421659	+	0.730335i
$944$		0			0
$945$	3.73282	+	1.88491i	0.121429	+	0.0613161i
$946$		0			0
$947$	−32.2031	+	18.5925i	−1.04646	+	0.604174i	−0.921656	−	0.388008i	$-0.873163\pi$
$947$	−32.2031	+	18.5925i	−1.04646	+	0.604174i	−0.124803	+	0.992181i	$0.539830\pi$
$948$		0			0
$949$	−16.9317	+	29.3265i	−0.549626	+	0.951979i
$950$		0			0
$951$	18.4018	+	3.27857i	0.596721	+	0.106315i
$952$		0			0
$953$	−4.40328			−0.142636			−0.0713180	−	0.997454i	$-0.522721\pi$
$953$	−4.40328			−0.142636			−0.0713180	+	0.997454i	$0.522721\pi$
$954$		0			0
$955$	3.68132			0.119125
$956$		0			0
$957$	−8.00800	+	2.89852i	−0.258862	+	0.0936959i
$958$		0			0
$959$	17.5618	+	8.75039i	0.567099	+	0.282565i
$960$		0			0
$961$	8.73168	+	15.1237i	0.281667	+	0.487862i
$962$		0			0
$963$	−37.9311	+	6.54895i	−1.22231	+	0.211037i
$964$		0			0
$965$	1.98322	−	1.14501i	0.0638422	−	0.0368593i
$966$		0			0
$967$	5.78787	+	3.34163i	0.186125	+	0.107460i	0.590167	−	0.807281i	$-0.299062\pi$
$967$	5.78787	+	3.34163i	0.186125	+	0.107460i	−0.404042	+	0.914740i	$0.632395\pi$
$968$		0			0
$969$	26.3365	+	22.1791i	0.846052	+	0.712495i
$970$		0			0
$971$	−9.90431			−0.317844			−0.158922	−	0.987291i	$-0.550802\pi$
$971$	−9.90431			−0.317844			−0.158922	+	0.987291i	$0.550802\pi$
$972$		0			0
$973$	−2.77620	−	45.2017i	−0.0890007	−	1.44910i
$974$		0			0
$975$	30.8579	+	25.9867i	0.988245	+	0.832242i
$976$		0			0
$977$	−5.26197	+	9.11399i	−0.168345	+	0.291582i	−0.937838	−	0.347073i	$-0.887176\pi$
$977$	−5.26197	+	9.11399i	−0.168345	+	0.291582i	0.769493	+	0.638655i	$0.220509\pi$
$978$		0			0
$979$	2.99755	+	5.19191i	0.0958021	+	0.165934i
$980$		0			0
$981$	−1.62087	−	9.38794i	−0.0517503	−	0.299734i
$982$		0			0
$983$	−16.3117	−	28.2526i	−0.520261	−	0.901119i	−0.999723	−	0.0235560i	$-0.992501\pi$
$983$	−16.3117	−	28.2526i	−0.520261	−	0.901119i	0.479461	−	0.877563i	$-0.340832\pi$
$984$		0			0
$985$	−5.32191	−	3.07260i	−0.169570	−	0.0979013i
$986$		0			0
$987$	−27.1683	+	11.7638i	−0.864776	+	0.374445i
$988$		0			0
$989$	−14.7502			−0.469028
$990$		0			0
$991$			51.9373i			1.64984i	0.565248	+	0.824921i	$0.308780\pi$
$991$			51.9373i			1.64984i	−0.565248	+	0.824921i	$0.691220\pi$
$992$		0			0
$993$	−2.39554	+	13.4456i	−0.0760200	+	0.426683i
$994$		0			0
$995$	6.01628	+	3.47350i	0.190729	+	0.110117i
$996$		0			0
$997$	−23.7739	+	13.7259i	−0.752927	+	0.434703i	−0.826751	−	0.562568i	$-0.809813\pi$
$997$	−23.7739	+	13.7259i	−0.752927	+	0.434703i	0.0738233	+	0.997271i	$0.476480\pi$
$998$		0			0
$999$	−16.6174	−	9.71288i	−0.525751	−	0.307302i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1008.2.cx.i.895.5	yes	24
3.2	odd	2		3024.2.cx.i.2575.7		24
4.3	odd	2		1008.2.cx.j.895.8	yes	24
7.6	odd	2	inner	1008.2.cx.i.895.8	yes	24
9.2	odd	6		3024.2.cx.j.559.6		24
9.7	even	3		1008.2.cx.j.223.5	yes	24
12.11	even	2		3024.2.cx.j.2575.7		24
21.20	even	2		3024.2.cx.i.2575.6		24
28.27	even	2		1008.2.cx.j.895.5	yes	24
36.7	odd	6	inner	1008.2.cx.i.223.8	yes	24
36.11	even	6		3024.2.cx.i.559.6		24
63.20	even	6		3024.2.cx.j.559.7		24
63.34	odd	6		1008.2.cx.j.223.8	yes	24
84.83	odd	2		3024.2.cx.j.2575.6		24
252.83	odd	6		3024.2.cx.i.559.7		24
252.223	even	6	inner	1008.2.cx.i.223.5	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1008.2.cx.i.223.5	✓	24	252.223	even	6	inner
1008.2.cx.i.223.8	yes	24	36.7	odd	6	inner
1008.2.cx.i.895.5	yes	24	1.1	even	1	trivial
1008.2.cx.i.895.8	yes	24	7.6	odd	2	inner
1008.2.cx.j.223.5	yes	24	9.7	even	3
1008.2.cx.j.223.8	yes	24	63.34	odd	6
1008.2.cx.j.895.5	yes	24	28.27	even	2
1008.2.cx.j.895.8	yes	24	4.3	odd	2
3024.2.cx.i.559.6		24	36.11	even	6
3024.2.cx.i.559.7		24	252.83	odd	6
3024.2.cx.i.2575.6		24	21.20	even	2
3024.2.cx.i.2575.7		24	3.2	odd	2
3024.2.cx.j.559.6		24	9.2	odd	6
3024.2.cx.j.559.7		24	63.20	even	6
3024.2.cx.j.2575.6		24	84.83	odd	2
3024.2.cx.j.2575.7		24	12.11	even	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:	\( N \)	\(=\)	\( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1008.cx (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.11570 + 1.32484i) q^{3} +(-0.263424 - 0.152088i) q^{5} +(-2.20588 + 1.46085i) q^{7} +(-0.510411 - 2.95626i) q^{9} +(-0.437319 + 0.252486i) q^{11} +(4.11032 + 2.37309i) q^{13} +(0.495396 - 0.179310i) q^{15} +4.53143i q^{17} -4.38692 q^{19} +(0.525718 - 4.55232i) q^{21} +(-2.76828 - 1.59826i) q^{23} +(-2.45374 - 4.25000i) q^{25} +(4.48605 + 2.62210i) q^{27} +(-4.86854 - 8.43256i) q^{29} +(-1.83961 + 3.18629i) q^{31} +(0.153414 - 0.861079i) q^{33} +(0.803260 - 0.0493346i) q^{35} -3.70424 q^{37} +(-7.72987 + 2.79785i) q^{39} +(-7.01616 - 4.05078i) q^{41} +(3.99621 - 2.30721i) q^{43} +(-0.315157 + 0.856378i) q^{45} +(-3.23026 - 5.59497i) q^{47} +(2.73184 - 6.44492i) q^{49} +(-6.00342 - 5.05573i) q^{51} +6.52863 q^{53} +0.153601 q^{55} +(4.89450 - 5.81197i) q^{57} +(6.40501 - 11.0938i) q^{59} +(2.16357 - 1.24914i) q^{61} +(5.44456 + 5.77553i) q^{63} +(-0.721838 - 1.25026i) q^{65} +(-6.03544 - 3.48457i) q^{67} +(5.20602 - 1.88434i) q^{69} +10.1334i q^{71} +7.13486i q^{73} +(8.36822 + 1.49093i) q^{75} +(0.595831 - 1.19581i) q^{77} +(-5.96149 + 3.44187i) q^{79} +(-8.47896 + 3.01781i) q^{81} +(-3.66905 - 6.35498i) q^{83} +(0.689176 - 1.19369i) q^{85} +(16.6036 + 2.95819i) q^{87} -11.8721i q^{89} +(-12.5336 + 0.769788i) q^{91} +(-2.16888 - 5.99215i) q^{93} +(1.15562 + 0.667198i) q^{95} +(-10.9944 + 6.34762i) q^{97} +(0.969628 + 1.16396i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 6 q^{7} + 20 q^{9} + 24 q^{15} + 10 q^{21} + 18 q^{23} + 24 q^{25} - 6 q^{29} - 12 q^{37} - 12 q^{39} + 42 q^{43} + 12 q^{49} - 42 q^{51} + 96 q^{53} - 22 q^{57} + 18 q^{63} + 42 q^{65} + 36 q^{67}+ \cdots + 12 q^{99}+O(q^{100}) \) 24 * q - 6 * q^7 + 20 * q^9 + 24 * q^15 + 10 * q^21 + 18 * q^23 + 24 * q^25 - 6 * q^29 - 12 * q^37 - 12 * q^39 + 42 * q^43 + 12 * q^49 - 42 * q^51 + 96 * q^53 - 22 * q^57 + 18 * q^63 + 42 * q^65 + 36 * q^67 - 18 * q^77 - 60 * q^79 - 64 * q^81 - 6 * q^85 + 82 * q^93 - 126 * q^95 + 12 * q^99

Introduction

L-functions

Modular forms

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Database

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