LMFDB - Embedded newform 576.2.y.a.335.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [576,2,Mod(47,576)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(576, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([6, 9, 2])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("576.47"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 576 = 2^{6} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	576.y (of order $12$, degree $4$, not minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$4.59938315643$
Analytic rank:	$0$
Dimension:	$88$
Relative dimension:	$22$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 144)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			335.4
Character	$\chi$	$=$	576.335
Dual form			576.2.y.a.239.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.52574 - 0.819834i) q^{3} +(-0.769670 - 0.206232i) q^{5} +(2.17574 - 3.76849i) q^{7} +(1.65574 + 2.50170i) q^{9} +(-3.93991 + 1.05570i) q^{11} +(1.69772 + 0.454903i) q^{13} +(1.00524 + 0.945658i) q^{15} -6.68683i q^{17} +(0.708282 + 0.708282i) q^{19} +(-6.40914 + 3.96598i) q^{21} +(-3.88191 + 2.24122i) q^{23} +(-3.78027 - 2.18254i) q^{25} +(-0.475249 - 5.17437i) q^{27} +(-3.98981 + 1.06907i) q^{29} +(-4.94177 + 2.85313i) q^{31} +(6.87676 + 1.61936i) q^{33} +(-2.45179 + 2.45179i) q^{35} +(-1.51665 - 1.51665i) q^{37} +(-2.21733 - 2.08591i) q^{39} +(-1.36389 - 2.36233i) q^{41} +(-2.30553 - 8.60436i) q^{43} +(-0.758445 - 2.26695i) q^{45} +(1.23164 - 2.13327i) q^{47} +(-5.96768 - 10.3363i) q^{49} +(-5.48209 + 10.2023i) q^{51} +(-1.68291 + 1.68291i) q^{53} +3.25015 q^{55} +(-0.499978 - 1.66133i) q^{57} +(0.269331 - 1.00516i) q^{59} +(-0.528935 - 1.97401i) q^{61} +(13.0301 - 0.796606i) q^{63} +(-1.21287 - 0.700250i) q^{65} +(2.14659 - 8.01120i) q^{67} +(7.76019 - 0.236992i) q^{69} +8.05218i q^{71} +9.73126i q^{73} +(3.97837 + 6.42917i) q^{75} +(-4.59383 + 17.1444i) q^{77} +(11.9835 + 6.91865i) q^{79} +(-3.51702 + 8.28436i) q^{81} +(-0.817277 - 3.05012i) q^{83} +(-1.37904 + 5.14666i) q^{85} +(6.96385 + 1.63987i) q^{87} -1.71120 q^{89} +(5.40809 - 5.40809i) q^{91} +(9.87893 - 0.301697i) q^{93} +(-0.399073 - 0.691214i) q^{95} +(3.66561 - 6.34903i) q^{97} +(-9.16451 - 8.10851i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 88 q + 4 q^{3} - 6 q^{5} + 4 q^{7} + 6 q^{11} - 2 q^{13} + 8 q^{19} + 2 q^{21} + 12 q^{23} + 16 q^{27} - 6 q^{29} - 8 q^{33} - 8 q^{37} + 32 q^{39} + 2 q^{43} + 6 q^{45} - 24 q^{49} + 12 q^{51} + 16 q^{55}+ \cdots - 46 q^{99}+O(q^{100}) $ 88 * q + 4 * q^3 - 6 * q^5 + 4 * q^7 + 6 * q^11 - 2 * q^13 + 8 * q^19 + 2 * q^21 + 12 * q^23 + 16 * q^27 - 6 * q^29 - 8 * q^33 - 8 * q^37 + 32 * q^39 + 2 * q^43 + 6 * q^45 - 24 * q^49 + 12 * q^51 + 16 * q^55 + 42 * q^59 - 2 * q^61 - 12 * q^65 + 2 * q^67 - 10 * q^69 + 56 * q^75 - 6 * q^77 - 8 * q^81 - 54 * q^83 + 8 * q^85 - 48 * q^87 - 20 * q^91 - 34 * q^93 - 4 * q^97 - 46 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/576\mathbb{Z}\right)^\times$.

$n$	$65$	$127$	$325$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$-1$	$e\left(\frac{1}{4}\right)$

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
$3$	−1.52574	−	0.819834i	−0.880884	−	0.473331i
$3$	−1.52574	−	0.819834i	−0.880884	−	0.473331i
$4$		0			0
$5$	−0.769670	−	0.206232i	−0.344207	−	0.0922300i	0.0825742	−	0.996585i	$-0.473686\pi$
$5$	−0.769670	−	0.206232i	−0.344207	−	0.0922300i	−0.426781	+	0.904355i	$0.640353\pi$
$6$		0			0
$7$	2.17574	−	3.76849i	0.822352	−	1.42436i	−0.0815745	−	0.996667i	$-0.525995\pi$
$7$	2.17574	−	3.76849i	0.822352	−	1.42436i	0.903926	−	0.427688i	$-0.140672\pi$
$8$		0			0
$9$	1.65574	+	2.50170i	0.551915	+	0.833901i
$10$		0			0
$11$	−3.93991	+	1.05570i	−1.18793	+	0.318304i	−0.798066	−	0.602570i	$-0.794144\pi$
$11$	−3.93991	+	1.05570i	−1.18793	+	0.318304i	−0.389861	+	0.920874i	$0.627477\pi$
$12$		0			0
$13$	1.69772	+	0.454903i	0.470863	+	0.126167i	0.486445	−	0.873711i	$-0.338293\pi$
$13$	1.69772	+	0.454903i	0.470863	+	0.126167i	−0.0155820	+	0.999879i	$0.504960\pi$
$14$		0			0
$15$	1.00524	+	0.945658i	0.259551	+	0.244168i
$16$		0			0
$17$		−	6.68683i		−	1.62180i	−0.585188	−	0.810898i	$-0.698979\pi$
$17$		−	6.68683i		−	1.62180i	0.585188	−	0.810898i	$-0.301021\pi$
$18$		0			0
$19$	0.708282	+	0.708282i	0.162491	+	0.162491i	0.783669	−	0.621178i	$-0.213346\pi$
$19$	0.708282	+	0.708282i	0.162491	+	0.162491i	−0.621178	+	0.783669i	$0.713346\pi$
$20$		0			0
$21$	−6.40914	+	3.96598i	−1.39859	+	0.865447i
$22$		0			0
$23$	−3.88191	+	2.24122i	−0.809433	+	0.467327i	−0.846759	−	0.531977i	$-0.821449\pi$
$23$	−3.88191	+	2.24122i	−0.809433	+	0.467327i	0.0373258	+	0.999303i	$0.488116\pi$
$24$		0			0
$25$	−3.78027	−	2.18254i	−0.756053	−	0.436508i
$26$		0			0
$27$	−0.475249	−	5.17437i	−0.0914618	−	0.995809i
$28$		0			0
$29$	−3.98981	+	1.06907i	−0.740888	+	0.198520i	−0.609473	−	0.792807i	$-0.708619\pi$
$29$	−3.98981	+	1.06907i	−0.740888	+	0.198520i	−0.131415	+	0.991327i	$0.541952\pi$
$30$		0			0
$31$	−4.94177	+	2.85313i	−0.887568	+	0.512437i	−0.873146	−	0.487459i	$-0.837924\pi$
$31$	−4.94177	+	2.85313i	−0.887568	+	0.512437i	−0.0144215	+	0.999896i	$0.504591\pi$
$32$		0			0
$33$	6.87676	+	1.61936i	1.19709	+	0.281894i
$34$		0			0
$35$	−2.45179	+	2.45179i	−0.414427	+	0.414427i
$36$		0			0
$37$	−1.51665	−	1.51665i	−0.249335	−	0.249335i	0.571363	−	0.820698i	$-0.306415\pi$
$37$	−1.51665	−	1.51665i	−0.249335	−	0.249335i	−0.820698	+	0.571363i	$0.806415\pi$
$38$		0			0
$39$	−2.21733	−	2.08591i	−0.355057	−	0.334013i
$40$		0			0
$41$	−1.36389	−	2.36233i	−0.213005	−	0.368935i	0.739649	−	0.672993i	$-0.234992\pi$
$41$	−1.36389	−	2.36233i	−0.213005	−	0.368935i	−0.952653	+	0.304058i	$0.901658\pi$
$42$		0			0
$43$	−2.30553	−	8.60436i	−0.351590	−	1.31215i	−0.884722	−	0.466120i	$-0.845652\pi$
$43$	−2.30553	−	8.60436i	−0.351590	−	1.31215i	0.533131	−	0.846033i	$-0.321015\pi$
$44$		0			0
$45$	−0.758445	−	2.26695i	−0.113062	−	0.337937i
$46$		0			0
$47$	1.23164	−	2.13327i	0.179654	−	0.311169i	−0.762108	−	0.647449i	$-0.775836\pi$
$47$	1.23164	−	2.13327i	0.179654	−	0.311169i	0.941762	+	0.336280i	$0.109169\pi$
$48$		0			0
$49$	−5.96768	−	10.3363i	−0.852525	−	1.47662i
$50$		0			0
$51$	−5.48209	+	10.2023i	−0.767647	+	1.42861i
$52$		0			0
$53$	−1.68291	+	1.68291i	−0.231165	+	0.231165i	−0.813179	−	0.582014i	$-0.802265\pi$
$53$	−1.68291	+	1.68291i	−0.231165	+	0.231165i	0.582014	+	0.813179i	$0.302265\pi$
$54$		0			0
$55$	3.25015			0.438250
$56$		0			0
$57$	−0.499978	−	1.66133i	−0.0662237	−	0.220048i
$58$		0			0
$59$	0.269331	−	1.00516i	0.0350640	−	0.130860i	−0.946175	−	0.323655i	$-0.895088\pi$
$59$	0.269331	−	1.00516i	0.0350640	−	0.130860i	0.981239	+	0.192794i	$0.0617550\pi$
$60$		0			0
$61$	−0.528935	−	1.97401i	−0.0677232	−	0.252747i	0.923762	−	0.382968i	$-0.125098\pi$
$61$	−0.528935	−	1.97401i	−0.0677232	−	0.252747i	−0.991485	+	0.130221i	$0.958431\pi$
$62$		0			0
$63$	13.0301	−	0.796606i	1.64164	−	0.100363i
$64$		0			0
$65$	−1.21287	−	0.700250i	−0.150438	−	0.0868553i
$66$		0			0
$67$	2.14659	−	8.01120i	0.262248	−	0.978723i	−0.701665	−	0.712507i	$-0.747560\pi$
$67$	2.14659	−	8.01120i	0.262248	−	0.978723i	0.963913	−	0.266217i	$-0.0857736\pi$
$68$		0			0
$69$	7.76019	−	0.236992i	0.934217	−	0.0285305i
$70$		0			0
$71$			8.05218i			0.955618i	0.878464	+	0.477809i	$0.158569\pi$
$71$			8.05218i			0.955618i	−0.878464	+	0.477809i	$0.841431\pi$
$72$		0			0
$73$			9.73126i			1.13896i	0.822006	+	0.569479i	$0.192855\pi$
$73$			9.73126i			1.13896i	−0.822006	+	0.569479i	$0.807145\pi$
$74$		0			0
$75$	3.97837	+	6.42917i	0.459383	+	0.742377i
$76$		0			0
$77$	−4.59383	+	17.1444i	−0.523516	+	1.95379i
$78$		0			0
$79$	11.9835	+	6.91865i	1.34824	+	0.778409i	0.988001	−	0.154449i	$-0.0493604\pi$
$79$	11.9835	+	6.91865i	1.34824	+	0.778409i	0.360243	+	0.932858i	$0.382694\pi$
$80$		0			0
$81$	−3.51702	+	8.28436i	−0.390780	+	0.920484i
$82$		0			0
$83$	−0.817277	−	3.05012i	−0.0897078	−	0.334794i	0.906456	−	0.422300i	$-0.138777\pi$
$83$	−0.817277	−	3.05012i	−0.0897078	−	0.334794i	−0.996164	+	0.0875058i	$0.972110\pi$
$84$		0			0
$85$	−1.37904	+	5.14666i	−0.149578	+	0.558233i
$86$		0			0
$87$	6.96385	+	1.63987i	0.746603	+	0.175812i
$88$		0			0
$89$	−1.71120			−0.181386			−0.0906932	−	0.995879i	$-0.528908\pi$
$89$	−1.71120			−0.181386			−0.0906932	+	0.995879i	$0.528908\pi$
$90$		0			0
$91$	5.40809	−	5.40809i	0.566922	−	0.566922i
$92$		0			0
$93$	9.87893	−	0.301697i	1.02440	−	0.0312845i
$94$		0			0
$95$	−0.399073	−	0.691214i	−0.0409440	−	0.0709171i
$96$		0			0
$97$	3.66561	−	6.34903i	0.372187	−	0.644646i	−0.617715	−	0.786402i	$-0.711941\pi$
$97$	3.66561	−	6.34903i	0.372187	−	0.644646i	0.989902	+	0.141756i	$0.0452748\pi$
$98$		0			0
$99$	−9.16451	−	8.10851i	−0.921068	−	0.814936i
$100$		0			0
$101$	−3.75813	−	14.0255i	−0.373948	−	1.39559i	−0.854876	−	0.518833i	$-0.826367\pi$
$101$	−3.75813	−	14.0255i	−0.373948	−	1.39559i	0.480928	−	0.876760i	$-0.340300\pi$
$102$		0			0
$103$	7.43866	+	12.8841i	0.732953	+	1.26951i	0.955616	+	0.294616i	$0.0951917\pi$
$103$	7.43866	+	12.8841i	0.732953	+	1.26951i	−0.222663	+	0.974895i	$0.571475\pi$
$104$		0			0
$105$	5.75084	−	1.73072i	0.561224	−	0.168901i
$106$		0			0
$107$	−0.0974799	−	0.0974799i	−0.00942374	−	0.00942374i	0.702379	−	0.711803i	$-0.252121\pi$
$107$	−0.0974799	−	0.0974799i	−0.00942374	−	0.00942374i	−0.711803	+	0.702379i	$0.752121\pi$
$108$		0			0
$109$	8.80665	−	8.80665i	0.843524	−	0.843524i	−0.145791	−	0.989315i	$-0.546573\pi$
$109$	8.80665	−	8.80665i	0.843524	−	0.843524i	0.989315	+	0.145791i	$0.0465728\pi$
$110$		0			0
$111$	1.07060	+	3.55740i	0.101617	+	0.337654i
$112$		0			0
$113$	7.22037	−	4.16868i	0.679235	−	0.392157i	−0.120331	−	0.992734i	$-0.538396\pi$
$113$	7.22037	−	4.16868i	0.679235	−	0.392157i	0.799567	+	0.600577i	$0.205062\pi$
$114$		0			0
$115$	3.45000	−	0.924424i	0.321714	−	0.0862030i
$116$		0			0
$117$	1.67296	+	5.00039i	0.154665	+	0.462286i
$118$		0			0
$119$	−25.1993	−	14.5488i	−2.31001	−	1.33369i
$120$		0			0
$121$	4.88210	−	2.81868i	0.443827	−	0.256244i
$122$		0			0
$123$	0.144221	+	4.72247i	0.0130040	+	0.425811i
$124$		0			0
$125$	5.27664	+	5.27664i	0.471957	+	0.471957i
$126$		0			0
$127$		−	4.84829i		−	0.430216i	−0.976590	−	0.215108i	$-0.930990\pi$
$127$		−	4.84829i		−	0.430216i	0.976590	−	0.215108i	$-0.0690103\pi$
$128$		0			0
$129$	−3.53651	+	15.0181i	−0.311373	+	1.32227i
$130$		0			0
$131$	20.4961	+	5.49193i	1.79076	+	0.479832i	0.992474	−	0.122452i	$-0.0390758\pi$
$131$	20.4961	+	5.49193i	1.79076	+	0.479832i	0.798282	+	0.602284i	$0.205742\pi$
$132$		0			0
$133$	4.21019	−	1.12812i	0.365070	−	0.0978201i
$134$		0			0
$135$	−0.701338	+	4.08057i	−0.0603616	+	0.351200i
$136$		0			0
$137$	2.93860	−	5.08981i	0.251062	−	0.434852i	−0.712757	−	0.701411i	$-0.752554\pi$
$137$	2.93860	−	5.08981i	0.251062	−	0.434852i	0.963818	+	0.266560i	$0.0858869\pi$
$138$		0			0
$139$	−6.97384	−	1.86863i	−0.591513	−	0.158496i	−0.0493686	−	0.998781i	$-0.515721\pi$
$139$	−6.97384	−	1.86863i	−0.591513	−	0.158496i	−0.542145	+	0.840285i	$0.682388\pi$
$140$		0			0
$141$	−3.62809	+	2.24506i	−0.305540	+	0.189068i
$142$		0			0
$143$	−7.16910			−0.599510
$144$		0			0
$145$	3.29131			0.273328
$146$		0			0
$147$	0.631036	+	20.6630i	0.0520470	+	1.70426i
$148$		0			0
$149$	4.34504	+	1.16425i	0.355960	+	0.0953792i	0.432367	−	0.901698i	$-0.357678\pi$
$149$	4.34504	+	1.16425i	0.355960	+	0.0953792i	−0.0764076	+	0.997077i	$0.524345\pi$
$150$		0			0
$151$	4.23499	−	7.33521i	0.344638	−	0.596931i	−0.640650	−	0.767833i	$-0.721335\pi$
$151$	4.23499	−	7.33521i	0.344638	−	0.596931i	0.985288	+	0.170902i	$0.0546683\pi$
$152$		0			0
$153$	16.7285	−	11.0717i	1.35242	−	0.895093i
$154$		0			0
$155$	4.39194	−	1.17682i	0.352769	−	0.0945241i
$156$		0			0
$157$	16.3507	+	4.38117i	1.30493	+	0.349655i	0.843313	−	0.537423i	$-0.180602\pi$
$157$	16.3507	+	4.38117i	1.30493	+	0.349655i	0.461618	+	0.887079i	$0.347269\pi$
$158$		0			0
$159$	3.94738	−	1.18797i	0.313048	−	0.0942121i
$160$		0			0
$161$			19.5052i			1.53723i
$162$		0			0
$163$	−13.6982	−	13.6982i	−1.07293	−	1.07293i	−0.997123	−	0.0758059i	$-0.975847\pi$
$163$	−13.6982	−	13.6982i	−1.07293	−	1.07293i	−0.0758059	−	0.997123i	$-0.524153\pi$
$164$		0			0
$165$	−4.95887	−	2.66458i	−0.386047	−	0.207437i
$166$		0			0
$167$	7.11859	−	4.10992i	0.550853	−	0.318035i	−0.198613	−	0.980078i	$-0.563644\pi$
$167$	7.11859	−	4.10992i	0.550853	−	0.318035i	0.749466	+	0.662043i	$0.230310\pi$
$168$		0			0
$169$	−8.58301	−	4.95540i	−0.660232	−	0.381185i
$170$		0			0
$171$	−0.599176	+	2.94464i	−0.0458202	+	0.225183i
$172$		0			0
$173$	−9.41440	+	2.52258i	−0.715764	+	0.191788i	−0.598281	−	0.801287i	$-0.704149\pi$
$173$	−9.41440	+	2.52258i	−0.715764	+	0.191788i	−0.117483	+	0.993075i	$0.537483\pi$
$174$		0			0
$175$	−16.4497	+	9.49727i	−1.24348	+	0.717926i
$176$		0			0
$177$	−1.23499	+	1.31280i	−0.0928277	+	0.0986761i
$178$		0			0
$179$	2.59887	−	2.59887i	0.194248	−	0.194248i	−0.603281	−	0.797529i	$-0.706140\pi$
$179$	2.59887	−	2.59887i	0.194248	−	0.194248i	0.797529	+	0.603281i	$0.206140\pi$
$180$		0			0
$181$	6.92926	+	6.92926i	0.515048	+	0.515048i	0.916069	−	0.401021i	$-0.131345\pi$
$181$	6.92926	+	6.92926i	0.515048	+	0.515048i	−0.401021	+	0.916069i	$0.631345\pi$
$182$		0			0
$183$	−0.811348	+	3.44546i	−0.0599765	+	0.254696i
$184$		0			0
$185$	0.854536	+	1.48010i	0.0628267	+	0.108819i
$186$		0			0
$187$	7.05926	+	26.3455i	0.516224	+	1.92657i
$188$		0			0
$189$	−20.5336	−	9.46711i	−1.49360	−	0.688631i
$190$		0			0
$191$	6.96728	−	12.0677i	0.504135	−	0.873187i	−0.495854	−	0.868406i	$-0.665145\pi$
$191$	6.96728	−	12.0677i	0.504135	−	0.873187i	0.999989	−	0.00478132i	$-0.00152195\pi$
$192$		0			0
$193$	−1.34094	−	2.32257i	−0.0965226	−	0.167182i	0.813720	−	0.581256i	$-0.197439\pi$
$193$	−1.34094	−	2.32257i	−0.0965226	−	0.167182i	−0.910243	+	0.414074i	$0.864105\pi$
$194$		0			0
$195$	1.27643	+	2.06275i	0.0914070	+	0.147716i
$196$		0			0
$197$	−14.2363	+	14.2363i	−1.01430	+	1.01430i	−0.0144009	+	0.999896i	$0.504584\pi$
$197$	−14.2363	+	14.2363i	−1.01430	+	1.01430i	−0.999896	+	0.0144009i	$0.995416\pi$
$198$		0			0
$199$	−7.90078			−0.560072			−0.280036	−	0.959990i	$-0.590346\pi$
$199$	−7.90078			−0.560072			−0.280036	+	0.959990i	$0.590346\pi$
$200$		0			0
$201$	−9.84299	+	10.4631i	−0.694271	+	0.738012i
$202$		0			0
$203$	−4.65201	+	17.3615i	−0.326507	+	1.21854i
$204$		0			0
$205$	0.562559	+	2.09950i	0.0392908	+	0.146635i
$206$		0			0
$207$	−12.0343	−	6.00048i	−0.836442	−	0.417062i
$208$		0			0
$209$	−3.53830	−	2.04284i	−0.244749	−	0.141306i
$210$		0			0
$211$	3.53982	−	13.2108i	0.243691	−	0.909469i	−0.730345	−	0.683078i	$-0.760641\pi$
$211$	3.53982	−	13.2108i	0.243691	−	0.909469i	0.974037	−	0.226391i	$-0.0726926\pi$
$212$		0			0
$213$	6.60145	−	12.2855i	0.452324	−	0.841789i
$214$		0			0
$215$			7.09799i			0.484079i
$216$		0			0
$217$			24.8307i			1.68562i
$218$		0			0
$219$	7.97802	−	14.8473i	0.539105	−	1.00329i
$220$		0			0
$221$	3.04186	−	11.3524i	0.204618	−	0.763643i
$222$		0			0
$223$	−24.3372	−	14.0511i	−1.62974	−	0.940931i	−0.984169	−	0.177230i	$-0.943286\pi$
$223$	−24.3372	−	14.0511i	−1.62974	−	0.940931i	−0.645570	−	0.763701i	$-0.723380\pi$
$224$		0			0
$225$	−0.799096	−	13.0708i	−0.0532731	−	0.871388i
$226$		0			0
$227$	−0.131295	−	0.489998i	−0.00871433	−	0.0325223i	0.961432	−	0.275044i	$-0.0886923\pi$
$227$	−0.131295	−	0.489998i	−0.00871433	−	0.0325223i	−0.970146	+	0.242521i	$0.922026\pi$
$228$		0			0
$229$	3.91690	−	14.6181i	0.258836	−	0.965988i	−0.707080	−	0.707133i	$-0.749988\pi$
$229$	3.91690	−	14.6181i	0.258836	−	0.965988i	0.965916	−	0.258855i	$-0.0833452\pi$
$230$		0			0
$231$	21.0646	−	22.3917i	1.38595	−	1.47326i
$232$		0			0
$233$	−15.4968			−1.01523			−0.507614	−	0.861584i	$-0.669473\pi$
$233$	−15.4968			−1.01523			−0.507614	+	0.861584i	$0.669473\pi$
$234$		0			0
$235$	−1.38791	+	1.38791i	−0.0905371	+	0.0905371i
$236$		0			0
$237$	−12.6114	−	20.3805i	−0.819202	−	1.32385i
$238$		0			0
$239$	−7.61709	−	13.1932i	−0.492709	−	0.853397i	0.507256	−	0.861796i	$-0.330660\pi$
$239$	−7.61709	−	13.1932i	−0.492709	−	0.853397i	−0.999965	+	0.00839869i	$0.997327\pi$
$240$		0			0
$241$	−9.10697	+	15.7737i	−0.586632	+	1.01608i	0.408038	+	0.912965i	$0.366213\pi$
$241$	−9.10697	+	15.7737i	−0.586632	+	1.01608i	−0.994670	+	0.103111i	$0.967120\pi$
$242$		0			0
$243$	12.1578	−	9.75637i	0.779926	−	0.625871i
$244$		0			0
$245$	2.46146	+	9.18628i	0.157257	+	0.586890i
$246$		0			0
$247$	0.880265	+	1.52466i	0.0560099	+	0.0970121i
$248$		0			0
$249$	−1.25364	+	5.32371i	−0.0794463	+	0.337376i
$250$		0			0
$251$	2.18418	+	2.18418i	0.137864	+	0.137864i	0.772671	−	0.634807i	$-0.218920\pi$
$251$	2.18418	+	2.18418i	0.137864	+	0.137864i	−0.634807	+	0.772671i	$0.718920\pi$
$252$		0			0
$253$	12.9283	−	12.9283i	0.812796	−	0.812796i
$254$		0			0
$255$	6.32346	−	6.72185i	0.395990	−	0.420939i
$256$		0			0
$257$	16.6777	−	9.62887i	1.04033	−	0.600633i	0.120400	−	0.992725i	$-0.461582\pi$
$257$	16.6777	−	9.62887i	1.04033	−	0.600633i	0.919926	+	0.392093i	$0.128249\pi$
$258$		0			0
$259$	−9.01529	+	2.41564i	−0.560183	+	0.150101i
$260$		0			0
$261$	−9.28058	−	8.21121i	−0.574453	−	0.508261i
$262$		0			0
$263$	22.8254	+	13.1782i	1.40747	+	0.812605i	0.995144	−	0.0984300i	$-0.0313821\pi$
$263$	22.8254	+	13.1782i	1.40747	+	0.812605i	0.412329	+	0.911035i	$0.364715\pi$
$264$		0			0
$265$	1.64235	−	0.948214i	0.100889	−	0.0582483i
$266$		0			0
$267$	2.61083	+	1.40290i	0.159781	+	0.0858559i
$268$		0			0
$269$	0.605506	+	0.605506i	0.0369184	+	0.0369184i	0.725325	−	0.688407i	$-0.241690\pi$
$269$	0.605506	+	0.605506i	0.0369184	+	0.0369184i	−0.688407	+	0.725325i	$0.741690\pi$
$270$		0			0
$271$			19.1084i			1.16075i	0.814349	+	0.580376i	$0.197094\pi$
$271$			19.1084i			1.16075i	−0.814349	+	0.580376i	$0.802906\pi$
$272$		0			0
$273$	−12.6851	+	3.81759i	−0.767735	+	0.231051i
$274$		0			0
$275$	17.1980	+	4.60819i	1.03708	+	0.277884i
$276$		0			0
$277$	6.82191	−	1.82792i	0.409889	−	0.109829i	−0.0479819	−	0.998848i	$-0.515279\pi$
$277$	6.82191	−	1.82792i	0.409889	−	0.109829i	0.457871	+	0.889019i	$0.348612\pi$
$278$		0			0
$279$	−15.3200	−	7.63877i	−0.917183	−	0.457321i
$280$		0			0
$281$	11.8490	−	20.5230i	0.706849	−	1.22430i	−0.259171	−	0.965831i	$-0.583449\pi$
$281$	11.8490	−	20.5230i	0.706849	−	1.22430i	0.966020	−	0.258467i	$-0.0832174\pi$
$282$		0			0
$283$	−0.727099	−	0.194826i	−0.0432215	−	0.0115812i	0.237143	−	0.971475i	$-0.423789\pi$
$283$	−0.727099	−	0.194826i	−0.0432215	−	0.0115812i	−0.280365	+	0.959893i	$0.590456\pi$
$284$		0			0
$285$	0.0421989	+	1.38178i	0.00249965	+	0.0818498i
$286$		0			0
$287$	−11.8699			−0.700659
$288$		0			0
$289$	−27.7137			−1.63022
$290$		0			0
$291$	−10.7979	+	6.68175i	−0.632985	+	0.391691i
$292$		0			0
$293$	19.8198	+	5.31070i	1.15789	+	0.310255i	0.786121	−	0.618072i	$-0.212086\pi$
$293$	19.8198	+	5.31070i	1.15789	+	0.310255i	0.371765	+	0.928327i	$0.378753\pi$
$294$		0			0
$295$	−0.414592	+	0.718095i	−0.0241385	+	0.0418091i
$296$		0			0
$297$	7.33500	+	19.8848i	0.425620	+	1.15384i
$298$		0			0
$299$	−7.60993	+	2.03907i	−0.440093	+	0.117923i
$300$		0			0
$301$	−37.4417	−	10.0325i	−2.15810	−	0.578262i
$302$		0			0
$303$	−5.76469	+	24.4803i	−0.331173	+	1.40636i
$304$		0			0
$305$			1.62842i			0.0932432i
$306$		0			0
$307$	15.3450	+	15.3450i	0.875783	+	0.875783i	0.993095	−	0.117312i	$-0.0374277\pi$
$307$	15.3450	+	15.3450i	0.875783	+	0.875783i	−0.117312	+	0.993095i	$0.537428\pi$
$308$		0			0
$309$	−0.786581	−	25.7563i	−0.0447470	−	1.46522i
$310$		0			0
$311$	−0.576605	+	0.332903i	−0.0326963	+	0.0188772i	−0.516259	−	0.856432i	$-0.672676\pi$
$311$	−0.576605	+	0.332903i	−0.0326963	+	0.0188772i	0.483563	+	0.875310i	$0.339342\pi$
$312$		0			0
$313$	−14.3283	−	8.27244i	−0.809882	−	0.467586i	0.0370327	−	0.999314i	$-0.488209\pi$
$313$	−14.3283	−	8.27244i	−0.809882	−	0.467586i	−0.846915	+	0.531728i	$0.821543\pi$
$314$		0			0
$315$	−10.1932	−	2.07411i	−0.574320	−	0.116863i
$316$		0			0
$317$	−6.56570	+	1.75927i	−0.368767	+	0.0988107i	−0.438443	−	0.898759i	$-0.644470\pi$
$317$	−6.56570	+	1.75927i	−0.368767	+	0.0988107i	0.0696766	+	0.997570i	$0.477803\pi$
$318$		0			0
$319$	14.5909	−	8.42404i	0.816931	−	0.471656i
$320$		0			0
$321$	0.0688113	+	0.228646i	0.00384067	+	0.0127618i
$322$		0			0
$323$	4.73616	−	4.73616i	0.263527	−	0.263527i
$324$		0			0
$325$	−5.42499	−	5.42499i	−0.300924	−	0.300924i
$326$		0			0
$327$	−20.6566	+	6.21664i	−1.14231	+	0.343781i
$328$		0			0
$329$	−5.35946	−	9.28286i	−0.295477	−	0.511781i
$330$		0			0
$331$	2.51757	+	9.39568i	0.138378	+	0.516434i	0.999961	+	0.00881711i	$0.00280661\pi$
$331$	2.51757	+	9.39568i	0.138378	+	0.516434i	−0.861583	+	0.507616i	$0.830527\pi$
$332$		0			0
$333$	1.28302	−	6.30538i	0.0703090	−	0.345532i
$334$		0			0
$335$	−3.30434	+	5.72328i	−0.180535	+	0.312696i
$336$		0			0
$337$	13.5580	+	23.4832i	0.738553	+	1.27921i	0.953147	+	0.302509i	$0.0978241\pi$
$337$	13.5580	+	23.4832i	0.738553	+	1.27921i	−0.214593	+	0.976704i	$0.568843\pi$
$338$		0			0
$339$	−14.4340	+	0.440806i	−0.783948	+	0.0239413i
$340$		0			0
$341$	16.4581	−	16.4581i	0.891254	−	0.891254i
$342$		0			0
$343$	−21.4761			−1.15960
$344$		0			0
$345$	−6.02166	−	1.41800i	−0.324195	−	0.0763425i
$346$		0			0
$347$	8.08347	−	30.1679i	0.433944	−	1.61950i	−0.309638	−	0.950854i	$-0.600208\pi$
$347$	8.08347	−	30.1679i	0.433944	−	1.61950i	0.743582	−	0.668645i	$-0.233125\pi$
$348$		0			0
$349$	8.48634	+	31.6714i	0.454263	+	1.69533i	0.690245	+	0.723576i	$0.257503\pi$
$349$	8.48634	+	31.6714i	0.454263	+	1.69533i	−0.235982	+	0.971757i	$0.575831\pi$
$350$		0			0
$351$	1.54700	−	9.00083i	0.0825726	−	0.480429i
$352$		0			0
$353$	−3.48989	−	2.01489i	−0.185748	−	0.107242i	0.404243	−	0.914652i	$-0.367535\pi$
$353$	−3.48989	−	2.01489i	−0.185748	−	0.107242i	−0.589990	+	0.807410i	$0.700869\pi$
$354$		0			0
$355$	1.66062	−	6.19752i	0.0881366	−	0.328930i
$356$		0			0
$357$	26.5198	+	42.8569i	1.40358	+	2.26823i
$358$		0			0
$359$		−	14.8043i		−	0.781342i	−0.920530	−	0.390671i	$-0.872243\pi$
$359$		−	14.8043i		−	0.781342i	0.920530	−	0.390671i	$-0.127757\pi$
$360$		0			0
$361$		−	17.9967i		−	0.947193i
$362$		0			0
$363$	−9.75965	+	0.298054i	−0.512249	+	0.0156438i
$364$		0			0
$365$	2.00690	−	7.48986i	0.105046	−	0.392037i
$366$		0			0
$367$	−2.66934	−	1.54114i	−0.139338	−	0.0804470i	0.428710	−	0.903442i	$-0.358968\pi$
$367$	−2.66934	−	1.54114i	−0.139338	−	0.0804470i	−0.568049	+	0.822995i	$0.692301\pi$
$368$		0			0
$369$	3.65160	−	7.32348i	0.190094	−	0.381245i
$370$		0			0
$371$	2.68045	+	10.0036i	0.139162	+	0.519361i
$372$		0			0
$373$	−7.57804	+	28.2816i	−0.392376	+	1.46437i	0.433828	+	0.900996i	$0.357163\pi$
$373$	−7.57804	+	28.2816i	−0.392376	+	1.46437i	−0.826204	+	0.563372i	$0.809504\pi$
$374$		0			0
$375$	−3.72479	−	12.3767i	−0.192347	−	0.639131i
$376$		0			0
$377$	−7.25990			−0.373904
$378$		0			0
$379$	13.0654	−	13.0654i	0.671124	−	0.671124i	−0.286851	−	0.957975i	$-0.592608\pi$
$379$	13.0654	−	13.0654i	0.671124	−	0.671124i	0.957975	+	0.286851i	$0.0926085\pi$
$380$		0			0
$381$	−3.97479	+	7.39721i	−0.203635	+	0.378970i
$382$		0			0
$383$	1.66394	+	2.88203i	0.0850235	+	0.147265i	0.905401	−	0.424557i	$-0.139570\pi$
$383$	1.66394	+	2.88203i	0.0850235	+	0.147265i	−0.820378	+	0.571822i	$0.806237\pi$
$384$		0			0
$385$	7.07147	−	12.2481i	0.360396	−	0.624223i
$386$		0			0
$387$	17.7082	−	20.0144i	0.900157	−	1.01739i
$388$		0			0
$389$	−1.77451	−	6.62255i	−0.0899711	−	0.335777i	0.906238	−	0.422768i	$-0.138941\pi$
$389$	−1.77451	−	6.62255i	−0.0899711	−	0.335777i	−0.996209	+	0.0869912i	$0.972275\pi$
$390$		0			0
$391$	14.9867	+	25.9577i	0.757908	+	1.31274i
$392$		0			0
$393$	−26.7693	−	25.1827i	−1.35033	−	1.27030i
$394$		0			0
$395$	−7.79645	−	7.79645i	−0.392282	−	0.392282i
$396$		0			0
$397$	2.33820	−	2.33820i	0.117351	−	0.117351i	−0.645993	−	0.763344i	$-0.723556\pi$
$397$	2.33820	−	2.33820i	0.117351	−	0.117351i	0.763344	+	0.645993i	$0.223556\pi$
$398$		0			0
$399$	−7.34851	−	1.73045i	−0.367886	−	0.0866307i
$400$		0			0
$401$	3.32787	−	1.92135i	0.166186	−	0.0959474i	−0.414600	−	0.910004i	$-0.636079\pi$
$401$	3.32787	−	1.92135i	0.166186	−	0.0959474i	0.580786	+	0.814056i	$0.302745\pi$
$402$		0			0
$403$	−9.68764	+	2.59579i	−0.482575	+	0.129306i
$404$		0			0
$405$	4.41545	−	5.65090i	0.219405	−	0.280795i
$406$		0			0
$407$	7.57656	+	4.37433i	0.375556	+	0.216828i
$408$		0			0
$409$	−4.36888	+	2.52237i	−0.216027	+	0.124723i	−0.604109	−	0.796901i	$-0.706471\pi$
$409$	−4.36888	+	2.52237i	−0.216027	+	0.124723i	0.388082	+	0.921625i	$0.373138\pi$
$410$		0			0
$411$	−8.65634	+	5.35654i	−0.426986	+	0.264219i
$412$		0			0
$413$	−3.20193	−	3.20193i	−0.157557	−	0.157557i
$414$		0			0
$415$			2.51613i			0.123512i
$416$		0			0
$417$	9.10827	+	8.56844i	0.446034	+	0.419598i
$418$		0			0
$419$	−21.3504	−	5.72083i	−1.04304	−	0.279481i	−0.303665	−	0.952779i	$-0.598210\pi$
$419$	−21.3504	−	5.72083i	−1.04304	−	0.279481i	−0.739371	+	0.673298i	$0.764877\pi$
$420$		0			0
$421$	−7.95298	+	2.13099i	−0.387604	+	0.103858i	−0.447358	−	0.894355i	$-0.647635\pi$
$421$	−7.95298	+	2.13099i	−0.387604	+	0.103858i	0.0597538	+	0.998213i	$0.480968\pi$
$422$		0			0
$423$	7.37608	−	0.450943i	0.358637	−	0.0219256i
$424$		0			0
$425$	−14.5943	+	25.2780i	−0.707926	+	1.22616i
$426$		0			0
$427$	−8.58988	−	2.30165i	−0.415693	−	0.111385i
$428$		0			0
$429$	10.9382	+	5.87747i	0.528099	+	0.283767i
$430$		0			0
$431$	−1.08094			−0.0520671			−0.0260336	−	0.999661i	$-0.508288\pi$
$431$	−1.08094			−0.0520671			−0.0260336	+	0.999661i	$0.508288\pi$
$432$		0			0
$433$	−15.5307			−0.746359			−0.373179	−	0.927759i	$-0.621732\pi$
$433$	−15.5307			−0.746359			−0.373179	+	0.927759i	$0.621732\pi$
$434$		0			0
$435$	−5.02167	−	2.69833i	−0.240771	−	0.129375i
$436$		0			0
$437$	−4.33690	−	1.16207i	−0.207462	−	0.0555893i
$438$		0			0
$439$	2.26321	−	3.91999i	0.108017	−	0.187091i	−0.806950	−	0.590620i	$-0.798883\pi$
$439$	2.26321	−	3.91999i	0.108017	−	0.187091i	0.914967	+	0.403529i	$0.132217\pi$
$440$		0			0
$441$	15.9774	−	32.0437i	0.760831	−	1.52589i
$442$		0			0
$443$	25.4883	−	6.82958i	1.21099	−	0.324483i	0.403838	−	0.914830i	$-0.367676\pi$
$443$	25.4883	−	6.82958i	1.21099	−	0.324483i	0.807149	+	0.590347i	$0.201009\pi$
$444$		0			0
$445$	1.31706	+	0.352904i	0.0624345	+	0.0167293i
$446$		0			0
$447$	−5.67490	−	5.33856i	−0.268414	−	0.252505i
$448$		0			0
$449$			5.94688i			0.280650i	0.990105	+	0.140325i	$0.0448148\pi$
$449$			5.94688i			0.280650i	−0.990105	+	0.140325i	$0.955185\pi$
$450$		0			0
$451$	7.86752	+	7.86752i	0.370467	+	0.370467i
$452$		0			0
$453$	−12.4751	+	7.71961i	−0.586133	+	0.362699i
$454$		0			0
$455$	−5.27777	+	3.04712i	−0.247426	+	0.142851i
$456$		0			0
$457$	18.2318	+	10.5261i	0.852846	+	0.492391i	0.861610	−	0.507571i	$-0.169456\pi$
$457$	18.2318	+	10.5261i	0.852846	+	0.492391i	−0.00876413	+	0.999962i	$0.502790\pi$
$458$		0			0
$459$	−34.6002	+	3.17791i	−1.61500	+	0.148332i
$460$		0			0
$461$	38.2603	−	10.2518i	1.78196	−	0.477475i	0.791021	−	0.611788i	$-0.209550\pi$
$461$	38.2603	−	10.2518i	1.78196	−	0.477475i	0.990939	+	0.134314i	$0.0428829\pi$
$462$		0			0
$463$	9.98020	−	5.76207i	0.463819	−	0.267786i	−0.249829	−	0.968290i	$-0.580375\pi$
$463$	9.98020	−	5.76207i	0.463819	−	0.267786i	0.713649	+	0.700504i	$0.247041\pi$
$464$		0			0
$465$	−7.66573	−	1.80515i	−0.355490	−	0.0837118i
$466$		0			0
$467$	−25.1476	+	25.1476i	−1.16369	+	1.16369i	−0.180032	+	0.983661i	$0.557620\pi$
$467$	−25.1476	+	25.1476i	−1.16369	+	1.16369i	−0.983661	+	0.180032i	$0.942380\pi$
$468$		0			0
$469$	−25.5197	−	25.5197i	−1.17839	−	1.17839i
$470$		0			0
$471$	−21.3551	−	20.0894i	−0.983990	−	0.925671i
$472$		0			0
$473$	18.1672	+	31.4664i	0.835327	+	1.44683i
$474$		0			0
$475$	−1.13164	−	4.22335i	−0.0519233	−	0.193780i
$476$		0			0
$477$	−6.99660	−	1.42367i	−0.320352	−	0.0651853i
$478$		0			0
$479$	2.64784	−	4.58619i	0.120983	−	0.209548i	−0.799173	−	0.601101i	$-0.794729\pi$
$479$	2.64784	−	4.58619i	0.120983	−	0.209548i	0.920155	+	0.391553i	$0.128062\pi$
$480$		0			0
$481$	−1.88491	−	3.26477i	−0.0859447	−	0.148861i
$482$		0			0
$483$	15.9911	−	29.7598i	0.727618	−	1.35412i
$484$		0			0
$485$	−4.13069	+	4.13069i	−0.187565	+	0.187565i
$486$		0			0
$487$	−1.85543			−0.0840775			−0.0420387	−	0.999116i	$-0.513385\pi$
$487$	−1.85543			−0.0840775			−0.0420387	+	0.999116i	$0.513385\pi$
$488$		0			0
$489$	9.66962	+	32.1302i	0.437275	+	1.45298i
$490$		0			0
$491$	0.936497	−	3.49505i	0.0422635	−	0.157730i	−0.941569	−	0.336820i	$-0.890649\pi$
$491$	0.936497	−	3.49505i	0.0422635	−	0.157730i	0.983833	+	0.179090i	$0.0573154\pi$
$492$		0			0
$493$	7.14866	+	26.6792i	0.321960	+	1.20157i
$494$		0			0
$495$	5.38141	+	8.13090i	0.241877	+	0.365457i
$496$		0			0
$497$	30.3446	+	17.5194i	1.36114	+	0.785854i
$498$		0			0
$499$	−3.22216	+	12.0253i	−0.144244	+	0.538325i	0.855544	+	0.517730i	$0.173223\pi$
$499$	−3.22216	+	12.0253i	−0.144244	+	0.538325i	−0.999788	+	0.0205953i	$0.993444\pi$
$500$		0			0
$501$	−14.2305	+	0.434592i	−0.635774	+	0.0194162i
$502$		0			0
$503$			16.6233i			0.741198i	0.928793	+	0.370599i	$0.120848\pi$
$503$			16.6233i			0.741198i	−0.928793	+	0.370599i	$0.879152\pi$
$504$		0			0
$505$			11.5701i			0.514862i
$506$		0			0
$507$	9.03281	+	14.5973i	0.401161	+	0.648288i
$508$		0			0
$509$	4.04848	−	15.1091i	0.179446	−	0.669700i	−0.816306	−	0.577620i	$-0.803982\pi$
$509$	4.04848	−	15.1091i	0.179446	−	0.669700i	0.995752	−	0.0920802i	$-0.0293516\pi$
$510$		0			0
$511$	36.6722	+	21.1727i	1.62228	+	0.936624i
$512$		0			0
$513$	3.32830	−	4.00153i	0.146948	−	0.176672i
$514$		0			0
$515$	−3.06819	−	11.4506i	−0.135200	−	0.504575i
$516$		0			0
$517$	−2.60048	+	9.70511i	−0.114369	+	0.426830i
$518$		0			0
$519$	16.4320	+	3.86945i	0.721285	+	0.169850i
$520$		0			0
$521$	40.4461			1.77198			0.885988	−	0.463709i	$-0.153482\pi$
$521$	40.4461			1.77198			0.885988	+	0.463709i	$0.153482\pi$
$522$		0			0
$523$	−7.69126	+	7.69126i	−0.336315	+	0.336315i	−0.854979	−	0.518663i	$-0.826430\pi$
$523$	−7.69126	+	7.69126i	−0.336315	+	0.336315i	0.518663	+	0.854979i	$0.326430\pi$
$524$		0			0
$525$	32.8842	−	1.00426i	1.43518	−	0.0438296i
$526$		0			0
$527$	19.0784	+	33.0448i	0.831069	+	1.43945i
$528$		0			0
$529$	−1.45387	+	2.51818i	−0.0632119	+	0.109486i
$530$		0			0
$531$	2.96055	−	0.990498i	0.128477	−	0.0429840i
$532$		0			0
$533$	−1.24088	−	4.63102i	−0.0537484	−	0.200592i
$534$		0			0
$535$	0.0549239	+	0.0951309i	0.00237457	+	0.00411287i
$536$		0			0
$537$	−6.09583	+	1.83455i	−0.263054	+	0.0791666i
$538$		0			0
$539$	34.4241	+	34.4241i	1.48275	+	1.48275i
$540$		0			0
$541$	−17.0176	+	17.0176i	−0.731643	+	0.731643i	−0.970945	−	0.239302i	$-0.923081\pi$
$541$	−17.0176	+	17.0176i	−0.731643	+	0.731643i	0.239302	+	0.970945i	$0.423081\pi$
$542$		0			0
$543$	−4.89138	−	16.2531i	−0.209909	−	0.697486i
$544$		0			0
$545$	−8.59443	+	4.96200i	−0.368145	+	0.212549i
$546$		0			0
$547$	−21.5530	+	5.77510i	−0.921539	+	0.246926i	−0.688243	−	0.725480i	$-0.741618\pi$
$547$	−21.5530	+	5.77510i	−0.921539	+	0.246926i	−0.233296	+	0.972406i	$0.574951\pi$
$548$		0			0
$549$	4.06261	−	4.59170i	0.173388	−	0.195969i
$550$		0			0
$551$	−3.58311	−	2.06871i	−0.152645	−	0.0881299i
$552$		0			0
$553$	52.1457	−	30.1064i	2.21746	−	1.28025i
$554$		0			0
$555$	−0.0903606	−	2.95882i	−0.00383559	−	0.125595i
$556$		0			0
$557$	11.6516	+	11.6516i	0.493695	+	0.493695i	0.909468	−	0.415773i	$-0.136489\pi$
$557$	11.6516	+	11.6516i	0.493695	+	0.493695i	−0.415773	+	0.909468i	$0.636489\pi$
$558$		0			0
$559$		−	15.6566i		−	0.662203i
$560$		0			0
$561$	10.8284	−	45.9837i	0.457174	−	1.94143i
$562$		0			0
$563$	4.88249	+	1.30826i	0.205772	+	0.0551365i	0.360233	−	0.932862i	$-0.382697\pi$
$563$	4.88249	+	1.30826i	0.205772	+	0.0551365i	−0.154460	+	0.987999i	$0.549364\pi$
$564$		0			0
$565$	−6.41702	+	1.71944i	−0.269966	+	0.0723372i
$566$		0			0
$567$	23.5674	+	31.2785i	0.989737	+	1.31357i
$568$		0			0
$569$	−2.79764	+	4.84565i	−0.117283	+	0.203140i	−0.918690	−	0.394979i	$-0.870752\pi$
$569$	−2.79764	+	4.84565i	−0.117283	+	0.203140i	0.801407	+	0.598119i	$0.204085\pi$
$570$		0			0
$571$	−8.65808	−	2.31993i	−0.362329	−	0.0970859i	0.0730613	−	0.997327i	$-0.476723\pi$
$571$	−8.65808	−	2.31993i	−0.362329	−	0.0970859i	−0.435391	+	0.900242i	$0.643390\pi$
$572$		0			0
$573$	−20.5237	+	12.7001i	−0.857392	+	0.530554i
$574$		0			0
$575$	19.5662			0.815966
$576$		0			0
$577$	16.6893			0.694785			0.347393	−	0.937720i	$-0.387067\pi$
$577$	16.6893			0.694785			0.347393	+	0.937720i	$0.387067\pi$
$578$		0			0
$579$	0.141794	+	4.64297i	0.00589274	+	0.192955i
$580$		0			0
$581$	−13.2725	−	3.55636i	−0.550637	−	0.147543i
$582$		0			0
$583$	4.85387	−	8.40714i	0.201027	−	0.348188i
$584$		0			0
$585$	−0.256384	−	4.19367i	−0.0106002	−	0.173387i
$586$		0			0
$587$	−5.02128	+	1.34545i	−0.207250	+	0.0555325i	−0.360950	−	0.932585i	$-0.617548\pi$
$587$	−5.02128	+	1.34545i	−0.207250	+	0.0555325i	0.153700	+	0.988118i	$0.450881\pi$
$588$		0			0
$589$	−5.52099	−	1.47934i	−0.227488	−	0.0609553i
$590$		0			0
$591$	33.3923	−	10.0495i	1.37358	−	0.413380i
$592$		0			0
$593$		−	44.7927i		−	1.83942i	−0.392602	−	0.919708i	$-0.628425\pi$
$593$		−	44.7927i		−	1.83942i	0.392602	−	0.919708i	$-0.371575\pi$
$594$		0			0
$595$	16.3947	+	16.3947i	0.672116	+	0.672116i
$596$		0			0
$597$	12.0545	+	6.47733i	0.493358	+	0.265100i
$598$		0			0
$599$	27.1165	−	15.6557i	1.10795	−	0.639674i	0.169651	−	0.985504i	$-0.445736\pi$
$599$	27.1165	−	15.6557i	1.10795	−	0.639674i	0.938297	+	0.345830i	$0.112403\pi$
$600$		0			0
$601$	−15.4248	−	8.90549i	−0.629189	−	0.363262i	0.151249	−	0.988496i	$-0.451670\pi$
$601$	−15.4248	−	8.90549i	−0.629189	−	0.363262i	−0.780438	+	0.625233i	$0.785004\pi$
$602$		0			0
$603$	23.5958	−	7.89436i	0.960897	−	0.321483i
$604$		0			0
$605$	−4.33891	+	1.16261i	−0.176402	+	0.0472667i
$606$		0			0
$607$	29.3159	−	16.9255i	1.18989	−	0.686986i	0.231612	−	0.972808i	$-0.425600\pi$
$607$	29.3159	−	16.9255i	1.18989	−	0.686986i	0.958283	+	0.285823i	$0.0922668\pi$
$608$		0			0
$609$	21.3313	−	22.6753i	0.864389	−	0.918848i
$610$		0			0
$611$	3.06141	−	3.06141i	0.123852	−	0.123852i
$612$		0			0
$613$	−11.3734	−	11.3734i	−0.459367	−	0.459367i	0.439081	−	0.898448i	$-0.355304\pi$
$613$	−11.3734	−	11.3734i	−0.459367	−	0.459367i	−0.898448	+	0.439081i	$0.855304\pi$
$614$		0			0
$615$	0.862923	−	3.66448i	0.0347964	−	0.147766i
$616$		0			0
$617$	−18.0269	−	31.2236i	−0.725738	−	1.25701i	−0.958670	−	0.284521i	$-0.908165\pi$
$617$	−18.0269	−	31.2236i	−0.725738	−	1.25701i	0.232932	−	0.972493i	$-0.425168\pi$
$618$		0			0
$619$	4.29280	+	16.0209i	0.172542	+	0.643936i	0.996957	+	0.0779503i	$0.0248375\pi$
$619$	4.29280	+	16.0209i	0.172542	+	0.643936i	−0.824415	+	0.565986i	$0.808496\pi$
$620$		0			0
$621$	13.4418	+	19.0213i	0.539400	+	0.763298i
$622$		0			0
$623$	−3.72312	+	6.44863i	−0.149163	+	0.258359i
$624$		0			0
$625$	7.93964	+	13.7519i	0.317585	+	0.550074i
$626$		0			0
$627$	3.72372	+	6.01764i	0.148711	+	0.240322i
$628$		0			0
$629$	−10.1416	+	10.1416i	−0.404371	+	0.404371i
$630$		0			0
$631$	−24.4330			−0.972664			−0.486332	−	0.873774i	$-0.661665\pi$
$631$	−24.4330			−0.972664			−0.486332	+	0.873774i	$0.661665\pi$
$632$		0			0
$633$	−16.2315	+	17.2541i	−0.645144	+	0.685790i
$634$		0			0
$635$	−0.999874	+	3.73158i	−0.0396788	+	0.148083i
$636$		0			0
$637$	−5.42943	−	20.2629i	−0.215122	−	0.802845i
$638$		0			0
$639$	−20.1441	+	13.3323i	−0.796890	+	0.527420i
$640$		0			0
$641$	−40.0952	−	23.1490i	−1.58366	−	0.914329i	−0.994318	−	0.106448i	$-0.966052\pi$
$641$	−40.0952	−	23.1490i	−1.58366	−	0.914329i	−0.589346	−	0.807881i	$-0.700615\pi$
$642$		0			0
$643$	2.83678	−	10.5870i	0.111872	−	0.417511i	−0.887162	−	0.461458i	$-0.847326\pi$
$643$	2.83678	−	10.5870i	0.111872	−	0.417511i	0.999034	+	0.0439466i	$0.0139932\pi$
$644$		0			0
$645$	5.81918	−	10.8297i	0.229130	−	0.426418i
$646$		0			0
$647$			10.0479i			0.395025i	0.980300	+	0.197512i	$0.0632863\pi$
$647$			10.0479i			0.395025i	−0.980300	+	0.197512i	$0.936714\pi$
$648$		0			0
$649$			4.24456i			0.166614i
$650$		0			0
$651$	20.3570	−	37.8851i	0.797855	−	1.48483i
$652$		0			0
$653$	−6.85777	+	25.5935i	−0.268365	+	1.00155i	0.691793	+	0.722096i	$0.256821\pi$
$653$	−6.85777	+	25.5935i	−0.268365	+	1.00155i	−0.960158	+	0.279457i	$0.909846\pi$
$654$		0			0
$655$	−14.6427	−	8.45394i	−0.572136	−	0.330323i
$656$		0			0
$657$	−24.3447	+	16.1125i	−0.949778	+	0.628608i
$658$		0			0
$659$	−1.81196	−	6.76233i	−0.0705840	−	0.263423i	0.921612	−	0.388113i	$-0.126873\pi$
$659$	−1.81196	−	6.76233i	−0.0705840	−	0.263423i	−0.992196	+	0.124690i	$0.960206\pi$
$660$		0			0
$661$	−5.40993	+	20.1902i	−0.210422	+	0.785306i	0.777306	+	0.629123i	$0.216586\pi$
$661$	−5.40993	+	20.1902i	−0.210422	+	0.785306i	−0.987728	+	0.156183i	$0.950081\pi$
$662$		0			0
$663$	−13.9481	+	14.8269i	−0.541701	+	0.575830i
$664$		0			0
$665$	−3.47311			−0.134681
$666$		0			0
$667$	13.0920	−	13.0920i	0.506926	−	0.506926i
$668$		0			0
$669$	25.6126	+	41.3907i	0.990240	+	1.60026i
$670$		0			0
$671$	4.16791	+	7.21904i	0.160901	+	0.278688i
$672$		0			0
$673$	3.86200	−	6.68918i	0.148869	−	0.257849i	−0.781941	−	0.623353i	$-0.785770\pi$
$673$	3.86200	−	6.68918i	0.148869	−	0.257849i	0.930810	+	0.365504i	$0.119103\pi$
$674$		0			0
$675$	−9.49670	+	20.5978i	−0.365528	+	0.792808i
$676$		0			0
$677$	2.04220	+	7.62160i	0.0784882	+	0.292922i	0.994002	−	0.109366i	$-0.0348819\pi$
$677$	2.04220	+	7.62160i	0.0784882	+	0.292922i	−0.915513	+	0.402287i	$0.868215\pi$
$678$		0			0
$679$	−15.9508	−	27.6277i	−0.612137	−	1.06025i
$680$		0			0
$681$	−0.201396	+	0.855248i	−0.00771752	+	0.0327732i
$682$		0			0
$683$	−23.0318	−	23.0318i	−0.881288	−	0.881288i	0.112378	−	0.993666i	$-0.464153\pi$
$683$	−23.0318	−	23.0318i	−0.881288	−	0.881288i	−0.993666	+	0.112378i	$0.964153\pi$
$684$		0			0
$685$	−3.31144	+	3.31144i	−0.126524	+	0.126524i
$686$		0			0
$687$	−17.9605	+	19.0921i	−0.685237	+	0.728409i
$688$		0			0
$689$	−3.62267	+	2.09155i	−0.138013	+	0.0796816i
$690$		0			0
$691$	−24.8749	+	6.66520i	−0.946285	+	0.253556i	−0.698785	−	0.715332i	$-0.746276\pi$
$691$	−24.8749	+	6.66520i	−0.946285	+	0.253556i	−0.247500	+	0.968888i	$0.579609\pi$
$692$		0			0
$693$	−50.4964	+	16.8944i	−1.91820	+	0.641764i
$694$		0			0
$695$	4.98218	+	2.87646i	0.188985	+	0.109111i
$696$		0			0
$697$	−15.7965	+	9.12014i	−0.598337	+	0.345450i
$698$		0			0
$699$	23.6440	+	12.7048i	0.894299	+	0.480540i
$700$		0			0
$701$	−35.0396	−	35.0396i	−1.32343	−	1.32343i	−0.910983	−	0.412443i	$-0.864675\pi$
$701$	−35.0396	−	35.0396i	−1.32343	−	1.32343i	−0.412443	−	0.910983i	$-0.635325\pi$
$702$		0			0
$703$		−	2.14843i		−	0.0810295i
$704$		0			0
$705$	3.25543	−	0.979727i	0.122607	−	0.0368987i
$706$		0			0
$707$	−61.0318	−	16.3534i	−2.29534	−	0.615034i
$708$		0			0
$709$	45.5722	−	12.2110i	1.71150	−	0.458595i	0.735710	−	0.677297i	$-0.236849\pi$
$709$	45.5722	−	12.2110i	1.71150	−	0.458595i	0.975792	+	0.218702i	$0.0701821\pi$
$710$		0			0
$711$	2.53314	+	41.4345i	0.0950000	+	1.55392i
$712$		0			0
$713$	12.7890	−	22.1512i	0.478951	−	0.829568i
$714$		0			0
$715$	5.51784	+	1.47850i	0.206356	+	0.0552928i
$716$		0			0
$717$	0.805449	+	26.3741i	0.0300801	+	0.984959i
$718$		0			0
$719$	26.0582			0.971806			0.485903	−	0.874013i	$-0.338491\pi$
$719$	26.0582			0.971806			0.485903	+	0.874013i	$0.338491\pi$
$720$		0			0
$721$	64.7383			2.41098
$722$		0			0
$723$	26.8267	−	16.6004i	0.997695	−	0.617374i
$724$		0			0
$725$	17.4158	+	4.66655i	0.646807	+	0.173311i
$726$		0			0
$727$	4.96698	−	8.60307i	0.184215	−	0.319070i	−0.759097	−	0.650978i	$-0.774359\pi$
$727$	4.96698	−	8.60307i	0.184215	−	0.319070i	0.943312	+	0.331908i	$0.107692\pi$
$728$		0			0
$729$	−26.5483	+	4.91824i	−0.983269	+	0.182157i
$730$		0			0
$731$	−57.5359	+	15.4167i	−2.12804	+	0.570207i
$732$		0			0
$733$	−12.7081	−	3.40512i	−0.469384	−	0.125771i	0.0163712	−	0.999866i	$-0.494789\pi$
$733$	−12.7081	−	3.40512i	−0.469384	−	0.125771i	−0.485755	+	0.874095i	$0.661455\pi$
$734$		0			0
$735$	3.77569	−	16.0338i	0.139269	−	0.591417i
$736$		0			0
$737$			33.8295i			1.24613i
$738$		0			0
$739$	32.6637	+	32.6637i	1.20155	+	1.20155i	0.973694	+	0.227861i	$0.0731732\pi$
$739$	32.6637	+	32.6637i	1.20155	+	1.20155i	0.227861	+	0.973694i	$0.426827\pi$
$740$		0			0
$741$	−0.0930813	−	3.04791i	−0.00341943	−	0.111968i
$742$		0			0
$743$	8.76936	−	5.06299i	0.321717	−	0.185743i	−0.330441	−	0.943827i	$-0.607197\pi$
$743$	8.76936	−	5.06299i	0.321717	−	0.185743i	0.652157	+	0.758084i	$0.273864\pi$
$744$		0			0
$745$	−3.10414	−	1.79218i	−0.113727	−	0.0656603i
$746$		0			0
$747$	6.27728	−	7.09480i	0.229674	−	0.259585i
$748$		0			0
$749$	−0.579443	+	0.155261i	−0.0211724	+	0.00567312i
$750$		0			0
$751$	−22.6187	+	13.0589i	−0.825368	+	0.476526i	−0.852264	−	0.523112i	$-0.824771\pi$
$751$	−22.6187	+	13.0589i	−0.825368	+	0.476526i	0.0268964	+	0.999638i	$0.491438\pi$
$752$		0			0
$753$	−1.54182	−	5.12315i	−0.0561870	−	0.186698i
$754$		0			0
$755$	−4.77230	+	4.77230i	−0.173682	+	0.173682i
$756$		0			0
$757$	2.39808	+	2.39808i	0.0871596	+	0.0871596i	0.749342	−	0.662183i	$-0.230370\pi$
$757$	2.39808	+	2.39808i	0.0871596	+	0.0871596i	−0.662183	+	0.749342i	$0.730370\pi$
$758$		0			0
$759$	−30.3243	+	9.12612i	−1.10070	+	0.331257i
$760$		0			0
$761$	23.1857	+	40.1589i	0.840482	+	1.45576i	0.889488	+	0.456959i	$0.151061\pi$
$761$	23.1857	+	40.1589i	0.840482	+	1.45576i	−0.0490055	+	0.998799i	$0.515605\pi$
$762$		0			0
$763$	−14.0268	−	52.3487i	−0.507804	−	1.89515i
$764$		0			0
$765$	−15.1587	+	5.07159i	−0.548065	+	0.183364i
$766$		0			0
$767$	0.914499	−	1.58396i	0.0330206	−	0.0571934i
$768$		0			0
$769$	−7.38255	−	12.7870i	−0.266222	−	0.461109i	0.701661	−	0.712511i	$-0.252442\pi$
$769$	−7.38255	−	12.7870i	−0.266222	−	0.461109i	−0.967883	+	0.251401i	$0.919109\pi$
$770$		0			0
$771$	−33.3398	+	1.01818i	−1.20071	+	0.0366688i
$772$		0			0
$773$	−22.1409	+	22.1409i	−0.796353	+	0.796353i	−0.982518	−	0.186165i	$-0.940394\pi$
$773$	−22.1409	+	22.1409i	−0.796353	+	0.796353i	0.186165	+	0.982518i	$0.440394\pi$
$774$		0			0
$775$	24.9083			0.894731
$776$		0			0
$777$	15.7354	+	3.70541i	0.564504	+	0.132931i
$778$		0			0
$779$	0.707177	−	2.63922i	0.0253372	−	0.0945599i
$780$		0			0
$781$	−8.50064	−	31.7248i	−0.304177	−	1.13520i
$782$		0			0
$783$	7.42790	+	20.1367i	0.265451	+	0.719626i
$784$		0			0
$785$	−11.6811	−	6.74410i	−0.416917	−	0.240707i
$786$		0			0
$787$	−1.12039	+	4.18136i	−0.0399377	+	0.149050i	−0.983015	−	0.183523i	$-0.941250\pi$
$787$	−1.12039	+	4.18136i	−0.0399377	+	0.149050i	0.943078	+	0.332572i	$0.107917\pi$
$788$		0			0
$789$	−24.0215	−	38.8195i	−0.855190	−	1.38201i
$790$		0			0
$791$		−	36.2799i		−	1.28996i
$792$		0			0
$793$		−	3.59194i		−	0.127553i
$794$		0			0
$795$	−3.28318	+	0.100266i	−0.116442	+	0.00355608i
$796$		0			0
$797$	13.8032	−	51.5141i	0.488933	−	1.82472i	−0.0727237	−	0.997352i	$-0.523169\pi$
$797$	13.8032	−	51.5141i	0.488933	−	1.82472i	0.561657	−	0.827370i	$-0.310164\pi$
$798$		0			0
$799$	−14.2648	−	8.23579i	−0.504652	−	0.291361i
$800$		0			0
$801$	−2.83330	−	4.28090i	−0.100110	−	0.151258i
$802$		0			0
$803$	−10.2732	−	38.3403i	−0.362535	−	1.35300i
$804$		0			0
$805$	4.02261	−	15.0126i	0.141778	−	0.529124i
$806$		0			0
$807$	−0.427428	−	1.42026i	−0.0150462	−	0.0499954i
$808$		0			0
$809$	−30.1140			−1.05875			−0.529375	−	0.848388i	$-0.677574\pi$
$809$	−30.1140			−1.05875			−0.529375	+	0.848388i	$0.677574\pi$
$810$		0			0
$811$	−20.5672	+	20.5672i	−0.722214	+	0.722214i	−0.969056	−	0.246842i	$-0.920607\pi$
$811$	−20.5672	+	20.5672i	−0.722214	+	0.722214i	0.246842	+	0.969056i	$0.420607\pi$
$812$		0			0
$813$	15.6657	−	29.1544i	0.549420	−	1.02249i
$814$		0			0
$815$	7.71810	+	13.3681i	0.270353	+	0.468265i
$816$		0			0
$817$	4.46135	−	7.72728i	0.156083	−	0.270343i
$818$		0			0
$819$	22.4839	+	4.57502i	0.785649	+	0.159864i
$820$		0			0
$821$	8.53541	+	31.8546i	0.297888	+	1.11173i	0.938897	+	0.344199i	$0.111849\pi$
$821$	8.53541	+	31.8546i	0.297888	+	1.11173i	−0.641009	+	0.767533i	$0.721484\pi$
$822$		0			0
$823$	−4.71220	−	8.16178i	−0.164257	−	0.284502i	0.772134	−	0.635460i	$-0.219189\pi$
$823$	−4.71220	−	8.16178i	−0.164257	−	0.284502i	−0.936391	+	0.350958i	$0.885856\pi$
$824$		0			0
$825$	−22.4617	−	21.1304i	−0.782015	−	0.735666i
$826$		0			0
$827$	−38.7468	−	38.7468i	−1.34736	−	1.34736i	−0.888518	−	0.458841i	$-0.848265\pi$
$827$	−38.7468	−	38.7468i	−1.34736	−	1.34736i	−0.458841	−	0.888518i	$-0.651735\pi$
$828$		0			0
$829$	11.0569	−	11.0569i	0.384021	−	0.384021i	−0.488528	−	0.872548i	$-0.662466\pi$
$829$	11.0569	−	11.0569i	0.384021	−	0.384021i	0.872548	+	0.488528i	$0.162466\pi$
$830$		0			0
$831$	−11.9070	−	2.80390i	−0.413050	−	0.0972662i
$832$		0			0
$833$	−69.1173	+	39.9049i	−2.39477	+	1.38262i
$834$		0			0
$835$	−6.32656	+	1.69520i	−0.218940	+	0.0586647i
$836$		0			0
$837$	17.1117	+	24.2146i	0.591468	+	0.836979i
$838$		0			0
$839$	−25.3695	−	14.6471i	−0.875853	−	0.505674i	−0.00656388	−	0.999978i	$-0.502089\pi$
$839$	−25.3695	−	14.6471i	−0.875853	−	0.505674i	−0.869289	+	0.494305i	$0.835423\pi$
$840$		0			0
$841$	−10.3391	+	5.96927i	−0.356520	+	0.205837i
$842$		0			0
$843$	−34.9038	+	21.5985i	−1.20215	+	0.743892i
$844$		0			0
$845$	5.58412	+	5.58412i	0.192100	+	0.192100i
$846$		0			0
$847$		−	24.5309i		−	0.842891i
$848$		0			0
$849$	0.949637	+	0.893353i	0.0325914	+	0.0306598i
$850$		0			0
$851$	9.28662	+	2.48834i	0.318341	+	0.0852992i
$852$		0			0
$853$	40.6922	−	10.9035i	1.39328	−	0.373327i	0.517350	−	0.855774i	$-0.326918\pi$
$853$	40.6922	−	10.9035i	1.39328	−	0.373327i	0.875925	+	0.482447i	$0.160252\pi$
$854$		0			0
$855$	1.06845	−	2.14283i	0.0365402	−	0.0732834i
$856$		0			0
$857$	−14.2207	+	24.6310i	−0.485769	+	0.841377i	−0.999866	−	0.0163548i	$-0.994794\pi$
$857$	−14.2207	+	24.6310i	−0.485769	+	0.841377i	0.514097	+	0.857732i	$0.328127\pi$
$858$		0			0
$859$	−3.34555	−	0.896437i	−0.114149	−	0.0305860i	0.201293	−	0.979531i	$-0.435486\pi$
$859$	−3.34555	−	0.896437i	−0.114149	−	0.0305860i	−0.315441	+	0.948945i	$0.602152\pi$
$860$		0			0
$861$	18.1104	+	9.73136i	0.617199	+	0.331644i
$862$		0			0
$863$	−11.1356			−0.379062			−0.189531	−	0.981875i	$-0.560697\pi$
$863$	−11.1356			−0.379062			−0.189531	+	0.981875i	$0.560697\pi$
$864$		0			0
$865$	7.76622			0.264059
$866$		0			0
$867$	42.2839	+	22.7207i	1.43604	+	0.771635i
$868$		0			0
$869$	−54.5177	−	14.6080i	−1.84939	−	0.495541i
$870$		0			0
$871$	7.28863	−	12.6243i	0.246966	−	0.427757i
$872$		0			0
$873$	21.9527	−	1.34210i	0.742986	−	0.0454231i
$874$		0			0
$875$	31.3655	−	8.40437i	1.06035	−	0.284119i
$876$		0			0
$877$	−27.3387	−	7.32539i	−0.923163	−	0.247361i	−0.234226	−	0.972182i	$-0.575256\pi$
$877$	−27.3387	−	7.32539i	−0.923163	−	0.247361i	−0.688937	+	0.724821i	$0.741922\pi$
$878$		0			0
$879$	−25.8859	−	24.3517i	−0.873111	−	0.821362i
$880$		0			0
$881$			4.86363i			0.163860i	0.996638	+	0.0819299i	$0.0261084\pi$
$881$			4.86363i			0.163860i	−0.996638	+	0.0819299i	$0.973892\pi$
$882$		0			0
$883$	−8.56478	−	8.56478i	−0.288228	−	0.288228i	0.548151	−	0.836379i	$-0.315332\pi$
$883$	−8.56478	−	8.56478i	−0.288228	−	0.288228i	−0.836379	+	0.548151i	$0.815332\pi$
$884$		0			0
$885$	1.22128	−	0.755727i	0.0410528	−	0.0254035i
$886$		0			0
$887$	−3.99885	+	2.30874i	−0.134268	+	0.0775199i	−0.565630	−	0.824659i	$-0.691367\pi$
$887$	−3.99885	+	2.30874i	−0.134268	+	0.0775199i	0.431361	+	0.902179i	$0.358033\pi$
$888$		0			0
$889$	−18.2707	−	10.5486i	−0.612780	−	0.353789i
$890$		0			0
$891$	5.11099	−	36.3525i	0.171225	−	1.21785i
$892$		0			0
$893$	2.38330	−	0.638605i	0.0797543	−	0.0213701i
$894$		0			0
$895$	−2.53624	+	1.46430i	−0.0847772	+	0.0489461i
$896$		0			0
$897$	13.2824	+	3.12779i	0.443488	+	0.104434i
$898$		0			0
$899$	16.6665	−	16.6665i	0.555859	−	0.555859i
$900$		0			0
$901$	11.2533	+	11.2533i	0.374903	+	0.374903i
$902$		0			0
$903$	48.9012	+	46.0029i	1.62733	+	1.53088i
$904$		0			0
$905$	−3.90421	−	6.76228i	−0.129780	−	0.224786i
$906$		0			0
$907$	2.23987	+	8.35931i	0.0743737	+	0.277566i	0.993091	−	0.117350i	$-0.0374401\pi$
$907$	2.23987	+	8.35931i	0.0743737	+	0.277566i	−0.918717	+	0.394917i	$0.870773\pi$
$908$		0			0
$909$	28.8652	−	32.6244i	0.957398	−	1.08208i
$910$		0			0
$911$	−23.9969	+	41.5638i	−0.795052	+	1.37707i	0.127755	+	0.991806i	$0.459223\pi$
$911$	−23.9969	+	41.5638i	−0.795052	+	1.37707i	−0.922806	+	0.385264i	$0.874110\pi$
$912$		0			0
$913$	6.43999	+	11.1544i	0.213133	+	0.369156i
$914$		0			0
$915$	1.33504	−	2.48454i	0.0441349	−	0.0821365i
$916$		0			0
$917$	65.2905	−	65.2905i	2.15608	−	2.15608i
$918$		0			0
$919$	−51.8939			−1.71182			−0.855910	−	0.517124i	$-0.827003\pi$
$919$	−51.8939			−1.71182			−0.855910	+	0.517124i	$0.827003\pi$
$920$		0			0
$921$	−10.8320	−	35.9927i	−0.356928	−	1.18600i
$922$		0			0
$923$	−3.66296	+	13.6703i	−0.120568	+	0.449965i
$924$		0			0
$925$	2.42319	+	9.04347i	0.0796740	+	0.297347i
$926$		0			0
$927$	−19.9157	+	39.9421i	−0.654119	+	1.31187i
$928$		0			0
$929$	8.80130	+	5.08143i	0.288761	+	0.166716i	0.637383	−	0.770547i	$-0.280017\pi$
$929$	8.80130	+	5.08143i	0.288761	+	0.166716i	−0.348622	+	0.937263i	$0.613350\pi$
$930$		0			0
$931$	3.09423	−	11.5478i	0.101409	−	0.378465i
$932$		0			0
$933$	1.15267	−	0.0352020i	0.0377368	−	0.00115246i
$934$		0			0
$935$		−	21.7332i		−	0.710751i
$936$		0			0
$937$		−	37.8157i		−	1.23539i	−0.786420	−	0.617693i	$-0.788068\pi$
$937$		−	37.8157i		−	1.23539i	0.786420	−	0.617693i	$-0.211932\pi$
$938$		0			0
$939$	15.0792	+	24.3684i	0.492090	+	0.795232i
$940$		0			0
$941$	−9.21025	+	34.3731i	−0.300246	+	1.12053i	0.636716	+	0.771099i	$0.280293\pi$
$941$	−9.21025	+	34.3731i	−0.300246	+	1.12053i	−0.936961	+	0.349433i	$0.886374\pi$
$942$		0			0
$943$	10.5890	+	6.11357i	0.344826	+	0.199085i
$944$		0			0
$945$	13.8517	+	11.5212i	0.450595	+	0.374786i
$946$		0			0
$947$	2.69018	+	10.0399i	0.0874191	+	0.326253i	0.995761	−	0.0919752i	$-0.0293181\pi$
$947$	2.69018	+	10.0399i	0.0874191	+	0.326253i	−0.908342	+	0.418228i	$0.862651\pi$
$948$		0			0
$949$	−4.42678	+	16.5210i	−0.143699	+	0.536293i
$950$		0			0
$951$	11.4598	+	2.69860i	0.371611	+	0.0875080i
$952$		0			0
$953$	24.6743			0.799280			0.399640	−	0.916672i	$-0.369135\pi$
$953$	24.6743			0.799280			0.399640	+	0.916672i	$0.369135\pi$
$954$		0			0
$955$	−7.85126	+	7.85126i	−0.254061	+	0.254061i
$956$		0			0
$957$	−29.1681	+	0.890777i	−0.942871	+	0.0287947i
$958$		0			0
$959$	−12.7873	−	22.1482i	−0.412922	−	0.715203i
$960$		0			0
$961$	0.780708	−	1.35223i	0.0251841	−	0.0436202i
$962$		0			0
$963$	0.0824639	−	0.405268i	0.00265736	−	0.0130596i
$964$		0			0
$965$	0.553089	+	2.06416i	0.0178046	+	0.0664475i
$966$		0			0
$967$	−12.5371	−	21.7150i	−0.403167	−	0.698306i	0.590939	−	0.806716i	$-0.298757\pi$
$967$	−12.5371	−	21.7150i	−0.403167	−	0.698306i	−0.994106	+	0.108410i	$0.965424\pi$
$968$		0			0
$969$	−11.1090	+	3.34327i	−0.356873	+	0.107401i
$970$		0			0
$971$	18.9203	+	18.9203i	0.607180	+	0.607180i	0.942208	−	0.335028i	$-0.108746\pi$
$971$	18.9203	+	18.9203i	0.607180	+	0.607180i	−0.335028	+	0.942208i	$0.608746\pi$
$972$		0			0
$973$	−22.2152	+	22.2152i	−0.712186	+	0.712186i
$974$		0			0
$975$	3.82952	+	12.7247i	0.122643	+	0.407517i
$976$		0			0
$977$	−12.1897	+	7.03771i	−0.389982	+	0.225156i	−0.682152	−	0.731210i	$-0.738956\pi$
$977$	−12.1897	+	7.03771i	−0.389982	+	0.225156i	0.292170	+	0.956366i	$0.405623\pi$
$978$		0			0
$979$	6.74196	−	1.80650i	0.215474	−	0.0577360i
$980$		0			0
$981$	36.6132	+	7.45005i	1.16897	+	0.237862i
$982$		0			0
$983$	0.562149	+	0.324557i	0.0179298	+	0.0103518i	0.508938	−	0.860803i	$-0.330038\pi$
$983$	0.562149	+	0.324557i	0.0179298	+	0.0103518i	−0.491008	+	0.871155i	$0.663372\pi$
$984$		0			0
$985$	13.8933	−	8.02129i	0.442677	−	0.255579i
$986$		0			0
$987$	0.566722	+	18.5571i	0.0180390	+	0.590678i
$988$		0			0
$989$	28.2341	+	28.2341i	0.897792	+	0.897792i
$990$		0			0
$991$		−	36.5529i		−	1.16114i	−0.814210	−	0.580571i	$-0.802829\pi$
$991$		−	36.5529i		−	1.16114i	0.814210	−	0.580571i	$-0.197171\pi$
$992$		0			0
$993$	3.86176	−	16.3993i	0.122549	−	0.520417i
$994$		0			0
$995$	6.08100	+	1.62940i	0.192781	+	0.0516554i
$996$		0			0
$997$	7.74395	−	2.07498i	0.245253	−	0.0657154i	−0.134098	−	0.990968i	$-0.542814\pi$
$997$	7.74395	−	2.07498i	0.245253	−	0.0657154i	0.379352	+	0.925253i	$0.376147\pi$
$998$		0			0
$999$	−7.12691	+	8.56848i	−0.225485	+	0.271095i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	576.2.y.a.335.4		88
3.2	odd	2		1728.2.z.a.143.13		88
4.3	odd	2		144.2.u.a.11.12	✓	88
9.4	even	3		1728.2.z.a.719.13		88
9.5	odd	6	inner	576.2.y.a.527.8		88
12.11	even	2		432.2.v.a.251.11		88
16.3	odd	4	inner	576.2.y.a.47.8		88
16.13	even	4		144.2.u.a.83.20	yes	88
36.23	even	6		144.2.u.a.59.20	yes	88
36.31	odd	6		432.2.v.a.395.3		88
48.29	odd	4		432.2.v.a.35.3		88
48.35	even	4		1728.2.z.a.1007.13		88
144.13	even	12		432.2.v.a.179.11		88
144.67	odd	12		1728.2.z.a.1583.13		88
144.77	odd	12		144.2.u.a.131.12	yes	88
144.131	even	12	inner	576.2.y.a.239.4		88

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
144.2.u.a.11.12	✓	88	4.3	odd	2
144.2.u.a.59.20	yes	88	36.23	even	6
144.2.u.a.83.20	yes	88	16.13	even	4
144.2.u.a.131.12	yes	88	144.77	odd	12
432.2.v.a.35.3		88	48.29	odd	4
432.2.v.a.179.11		88	144.13	even	12
432.2.v.a.251.11		88	12.11	even	2
432.2.v.a.395.3		88	36.31	odd	6
576.2.y.a.47.8		88	16.3	odd	4	inner
576.2.y.a.239.4		88	144.131	even	12	inner
576.2.y.a.335.4		88	1.1	even	1	trivial
576.2.y.a.527.8		88	9.5	odd	6	inner
1728.2.z.a.143.13		88	3.2	odd	2
1728.2.z.a.719.13		88	9.4	even	3
1728.2.z.a.1007.13		88	48.35	even	4
1728.2.z.a.1583.13		88	144.67	odd	12

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:	\( N \)	\(=\)	\( 576 = 2^{6} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	576.y (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.52574 - 0.819834i) q^{3} +(-0.769670 - 0.206232i) q^{5} +(2.17574 - 3.76849i) q^{7} +(1.65574 + 2.50170i) q^{9} +(-3.93991 + 1.05570i) q^{11} +(1.69772 + 0.454903i) q^{13} +(1.00524 + 0.945658i) q^{15} -6.68683i q^{17} +(0.708282 + 0.708282i) q^{19} +(-6.40914 + 3.96598i) q^{21} +(-3.88191 + 2.24122i) q^{23} +(-3.78027 - 2.18254i) q^{25} +(-0.475249 - 5.17437i) q^{27} +(-3.98981 + 1.06907i) q^{29} +(-4.94177 + 2.85313i) q^{31} +(6.87676 + 1.61936i) q^{33} +(-2.45179 + 2.45179i) q^{35} +(-1.51665 - 1.51665i) q^{37} +(-2.21733 - 2.08591i) q^{39} +(-1.36389 - 2.36233i) q^{41} +(-2.30553 - 8.60436i) q^{43} +(-0.758445 - 2.26695i) q^{45} +(1.23164 - 2.13327i) q^{47} +(-5.96768 - 10.3363i) q^{49} +(-5.48209 + 10.2023i) q^{51} +(-1.68291 + 1.68291i) q^{53} +3.25015 q^{55} +(-0.499978 - 1.66133i) q^{57} +(0.269331 - 1.00516i) q^{59} +(-0.528935 - 1.97401i) q^{61} +(13.0301 - 0.796606i) q^{63} +(-1.21287 - 0.700250i) q^{65} +(2.14659 - 8.01120i) q^{67} +(7.76019 - 0.236992i) q^{69} +8.05218i q^{71} +9.73126i q^{73} +(3.97837 + 6.42917i) q^{75} +(-4.59383 + 17.1444i) q^{77} +(11.9835 + 6.91865i) q^{79} +(-3.51702 + 8.28436i) q^{81} +(-0.817277 - 3.05012i) q^{83} +(-1.37904 + 5.14666i) q^{85} +(6.96385 + 1.63987i) q^{87} -1.71120 q^{89} +(5.40809 - 5.40809i) q^{91} +(9.87893 - 0.301697i) q^{93} +(-0.399073 - 0.691214i) q^{95} +(3.66561 - 6.34903i) q^{97} +(-9.16451 - 8.10851i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 88 q + 4 q^{3} - 6 q^{5} + 4 q^{7} + 6 q^{11} - 2 q^{13} + 8 q^{19} + 2 q^{21} + 12 q^{23} + 16 q^{27} - 6 q^{29} - 8 q^{33} - 8 q^{37} + 32 q^{39} + 2 q^{43} + 6 q^{45} - 24 q^{49} + 12 q^{51} + 16 q^{55}+ \cdots - 46 q^{99}+O(q^{100}) \) 88 * q + 4 * q^3 - 6 * q^5 + 4 * q^7 + 6 * q^11 - 2 * q^13 + 8 * q^19 + 2 * q^21 + 12 * q^23 + 16 * q^27 - 6 * q^29 - 8 * q^33 - 8 * q^37 + 32 * q^39 + 2 * q^43 + 6 * q^45 - 24 * q^49 + 12 * q^51 + 16 * q^55 + 42 * q^59 - 2 * q^61 - 12 * q^65 + 2 * q^67 - 10 * q^69 + 56 * q^75 - 6 * q^77 - 8 * q^81 - 54 * q^83 + 8 * q^85 - 48 * q^87 - 20 * q^91 - 34 * q^93 - 4 * q^97 - 46 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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