LMFDB - Embedded newform 576.2.y.a.527.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [576,2,Mod(47,576)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

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")

//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: f = N[0] # Warning: the index may be different

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			527.8
Character	$\chi$	$=$	576.527
Dual form			576.2.y.a.47.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

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

Display 100 coefficients 10 coefficients

Character values

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

$n$	$65$	$127$	$325$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$	$e\left(\frac{1}{4}\right)$

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
$3$	−0.819834	−	1.52574i	−0.473331	−	0.880884i
$3$	−0.819834	−	1.52574i	−0.473331	−	0.880884i
$4$		0			0
$5$	−0.206232	−	0.769670i	−0.0922300	−	0.344207i	0.904355	−	0.426781i	$-0.140353\pi$
$5$	−0.206232	−	0.769670i	−0.0922300	−	0.344207i	−0.996585	+	0.0825742i	$0.973686\pi$
$6$		0			0
$7$	2.17574	+	3.76849i	0.822352	+	1.42436i	0.903926	+	0.427688i	$0.140672\pi$
$7$	2.17574	+	3.76849i	0.822352	+	1.42436i	−0.0815745	+	0.996667i	$0.525995\pi$
$8$		0			0
$9$	−1.65574	+	2.50170i	−0.551915	+	0.833901i
$10$		0			0
$11$	−1.05570	+	3.93991i	−0.318304	+	1.18793i	0.602570	+	0.798066i	$0.294144\pi$
$11$	−1.05570	+	3.93991i	−0.318304	+	1.18793i	−0.920874	+	0.389861i	$0.872523\pi$
$12$		0			0
$13$	−0.454903	−	1.69772i	−0.126167	−	0.470863i	0.873711	−	0.486445i	$-0.161707\pi$
$13$	−0.454903	−	1.69772i	−0.126167	−	0.470863i	−0.999879	+	0.0155820i	$0.995040\pi$
$14$		0			0
$15$	−1.00524	+	0.945658i	−0.259551	+	0.244168i
$16$		0			0
$17$			6.68683i			1.62180i	0.585188	+	0.810898i	$0.301021\pi$
$17$			6.68683i			1.62180i	−0.585188	+	0.810898i	$0.698979\pi$
$18$		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
$21$	3.96598	−	6.40914i	0.865447	−	1.39859i
$22$		0			0
$23$	−3.88191	−	2.24122i	−0.809433	−	0.467327i	0.0373258	−	0.999303i	$-0.488116\pi$
$23$	−3.88191	−	2.24122i	−0.809433	−	0.467327i	−0.846759	+	0.531977i	$0.821449\pi$
$24$		0			0
$25$	3.78027	−	2.18254i	0.756053	−	0.436508i
$26$		0			0
$27$	5.17437	+	0.475249i	0.995809	+	0.0914618i
$28$		0			0
$29$	−1.06907	+	3.98981i	−0.198520	+	0.740888i	0.792807	+	0.609473i	$0.208619\pi$
$29$	−1.06907	+	3.98981i	−0.198520	+	0.740888i	−0.991327	+	0.131415i	$0.958048\pi$
$30$		0			0
$31$	4.94177	+	2.85313i	0.887568	+	0.512437i	0.873146	−	0.487459i	$-0.162076\pi$
$31$	4.94177	+	2.85313i	0.887568	+	0.512437i	0.0144215	+	0.999896i	$0.495409\pi$
$32$		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	$-0.765008\pi$
$41$	1.36389	−	2.36233i	0.213005	−	0.368935i	0.952653	+	0.304058i	$0.0983418\pi$
$42$		0			0
$43$	8.60436	+	2.30553i	1.31215	+	0.351590i	0.846033	−	0.533131i	$-0.178985\pi$
$43$	8.60436	+	2.30553i	1.31215	+	0.351590i	0.466120	+	0.884722i	$0.345652\pi$
$44$		0			0
$45$	2.26695	+	0.758445i	0.337937	+	0.113062i
$46$		0			0
$47$	−1.23164	−	2.13327i	−0.179654	−	0.311169i	0.762108	−	0.647449i	$-0.224164\pi$
$47$	−1.23164	−	2.13327i	−0.179654	−	0.311169i	−0.941762	+	0.336280i	$0.890831\pi$
$48$		0			0
$49$	−5.96768	+	10.3363i	−0.852525	+	1.47662i
$50$		0			0
$51$	10.2023	−	5.48209i	1.42861	−	0.767647i
$52$		0			0
$53$	1.68291	−	1.68291i	0.231165	−	0.231165i	−0.582014	−	0.813179i	$-0.697735\pi$
$53$	1.68291	−	1.68291i	0.231165	−	0.231165i	0.813179	+	0.582014i	$0.197735\pi$
$54$		0			0
$55$	3.25015			0.438250
$56$		0			0
$57$	0.499978	−	1.66133i	0.0662237	−	0.220048i
$58$		0			0
$59$	1.00516	−	0.269331i	0.130860	−	0.0350640i	−0.192794	−	0.981239i	$-0.561755\pi$
$59$	1.00516	−	0.269331i	0.130860	−	0.0350640i	0.323655	+	0.946175i	$0.395088\pi$
$60$		0			0
$61$	1.97401	+	0.528935i	0.252747	+	0.0677232i	0.382968	−	0.923762i	$-0.374902\pi$
$61$	1.97401	+	0.528935i	0.252747	+	0.0677232i	−0.130221	+	0.991485i	$0.541569\pi$
$62$		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
$67$	−8.01120	+	2.14659i	−0.978723	+	0.262248i	−0.712507	−	0.701665i	$-0.752440\pi$
$67$	−8.01120	+	2.14659i	−0.978723	+	0.262248i	−0.266217	+	0.963913i	$0.585774\pi$
$68$		0			0
$69$	−0.236992	+	7.76019i	−0.0285305	+	0.934217i
$70$		0			0
$71$		−	8.05218i		−	0.955618i	−0.878464	−	0.477809i	$-0.841431\pi$
$71$		−	8.05218i		−	0.955618i	0.878464	−	0.477809i	$-0.158569\pi$
$72$		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
$75$	−6.42917	−	3.97837i	−0.742377	−	0.459383i
$76$		0			0
$77$	−17.1444	+	4.59383i	−1.95379	+	0.523516i
$78$		0			0
$79$	−11.9835	+	6.91865i	−1.34824	+	0.778409i	−0.988001	−	0.154449i	$-0.950640\pi$
$79$	−11.9835	+	6.91865i	−1.34824	+	0.778409i	−0.360243	+	0.932858i	$0.617306\pi$
$80$		0			0
$81$	−3.51702	−	8.28436i	−0.390780	−	0.920484i
$82$		0			0
$83$	−3.05012	−	0.817277i	−0.334794	−	0.0897078i	0.0875058	−	0.996164i	$-0.472110\pi$
$83$	−3.05012	−	0.817277i	−0.334794	−	0.0897078i	−0.422300	+	0.906456i	$0.638777\pi$
$84$		0			0
$85$	5.14666	−	1.37904i	0.558233	−	0.149578i
$86$		0			0
$87$	6.96385	−	1.63987i	0.746603	−	0.175812i
$88$		0			0
$89$	1.71120			0.181386			0.0906932	−	0.995879i	$-0.471092\pi$
$89$	1.71120			0.181386			0.0906932	+	0.995879i	$0.471092\pi$
$90$		0			0
$91$	5.40809	−	5.40809i	0.566922	−	0.566922i
$92$		0			0
$93$	0.301697	−	9.87893i	0.0312845	−	1.02440i
$94$		0			0
$95$	0.399073	−	0.691214i	0.0409440	−	0.0709171i
$96$		0			0
$97$	3.66561	+	6.34903i	0.372187	+	0.644646i	0.989902	−	0.141756i	$-0.0452748\pi$
$97$	3.66561	+	6.34903i	0.372187	+	0.644646i	−0.617715	+	0.786402i	$0.711941\pi$
$98$		0			0
$99$	−8.10851	−	9.16451i	−0.814936	−	0.921068i
$100$		0			0
$101$	−14.0255	−	3.75813i	−1.39559	−	0.373948i	−0.518833	−	0.854876i	$-0.673633\pi$
$101$	−14.0255	−	3.75813i	−1.39559	−	0.373948i	−0.876760	+	0.480928i	$0.840300\pi$
$102$		0			0
$103$	7.43866	−	12.8841i	0.732953	−	1.26951i	−0.222663	−	0.974895i	$-0.571475\pi$
$103$	7.43866	−	12.8841i	0.732953	−	1.26951i	0.955616	−	0.294616i	$-0.0951917\pi$
$104$		0			0
$105$	−5.75084	−	1.73072i	−0.561224	−	0.168901i
$106$		0			0
$107$	0.0974799	+	0.0974799i	0.00942374	+	0.00942374i	0.711803	−	0.702379i	$-0.247879\pi$
$107$	0.0974799	+	0.0974799i	0.00942374	+	0.00942374i	−0.702379	+	0.711803i	$0.747879\pi$
$108$		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	0.799567	−	0.600577i	$-0.205062\pi$
$113$	7.22037	+	4.16868i	0.679235	+	0.392157i	−0.120331	+	0.992734i	$0.538396\pi$
$114$		0			0
$115$	−0.924424	+	3.45000i	−0.0862030	+	0.321714i
$116$		0			0
$117$	5.00039	+	1.67296i	0.462286	+	0.154665i
$118$		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
$123$	−4.72247	−	0.144221i	−0.425811	−	0.0130040i
$124$		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
$131$	5.49193	+	20.4961i	0.479832	+	1.79076i	0.602284	+	0.798282i	$0.294258\pi$
$131$	5.49193	+	20.4961i	0.479832	+	1.79076i	−0.122452	+	0.992474i	$0.539076\pi$
$132$		0			0
$133$	−1.12812	+	4.21019i	−0.0978201	+	0.365070i
$134$		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	$-0.247446\pi$
$137$	−2.93860	−	5.08981i	−0.251062	−	0.434852i	−0.963818	+	0.266560i	$0.914113\pi$
$138$		0			0
$139$	1.86863	+	6.97384i	0.158496	+	0.591513i	0.998781	+	0.0493686i	$0.0157209\pi$
$139$	1.86863	+	6.97384i	0.158496	+	0.591513i	−0.840285	+	0.542145i	$0.817612\pi$
$140$		0			0
$141$	−2.24506	+	3.62809i	−0.189068	+	0.305540i
$142$		0			0
$143$	7.16910			0.599510
$144$		0			0
$145$	3.29131			0.273328
$146$		0			0
$147$	20.6630	+	0.631036i	1.70426	+	0.0520470i
$148$		0			0
$149$	1.16425	+	4.34504i	0.0953792	+	0.355960i	0.997077	−	0.0764076i	$-0.0243450\pi$
$149$	1.16425	+	4.34504i	0.0953792	+	0.355960i	−0.901698	+	0.432367i	$0.857678\pi$
$150$		0			0
$151$	4.23499	+	7.33521i	0.344638	+	0.596931i	0.985288	−	0.170902i	$-0.0546683\pi$
$151$	4.23499	+	7.33521i	0.344638	+	0.596931i	−0.640650	+	0.767833i	$0.721335\pi$
$152$		0			0
$153$	−16.7285	−	11.0717i	−1.35242	−	0.895093i
$154$		0			0
$155$	1.17682	−	4.39194i	0.0945241	−	0.352769i
$156$		0			0
$157$	−4.38117	−	16.3507i	−0.349655	−	1.30493i	−0.887079	−	0.461618i	$-0.847269\pi$
$157$	−4.38117	−	16.3507i	−0.349655	−	1.30493i	0.537423	−	0.843313i	$-0.319398\pi$
$158$		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
$165$	−2.66458	−	4.95887i	−0.207437	−	0.386047i
$166$		0			0
$167$	7.11859	+	4.10992i	0.550853	+	0.318035i	0.749466	−	0.662043i	$-0.230310\pi$
$167$	7.11859	+	4.10992i	0.550853	+	0.318035i	−0.198613	+	0.980078i	$0.563644\pi$
$168$		0			0
$169$	8.58301	−	4.95540i	0.660232	−	0.381185i
$170$		0			0
$171$	−2.94464	+	0.599176i	−0.225183	+	0.0458202i
$172$		0			0
$173$	−2.52258	+	9.41440i	−0.191788	+	0.715764i	0.801287	+	0.598281i	$0.204149\pi$
$173$	−2.52258	+	9.41440i	−0.191788	+	0.715764i	−0.993075	+	0.117483i	$0.962517\pi$
$174$		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	−0.797529	−	0.603281i	$-0.793860\pi$
$179$	−2.59887	+	2.59887i	−0.194248	+	0.194248i	0.603281	+	0.797529i	$0.293860\pi$
$180$		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
$187$	−26.3455	−	7.05926i	−1.92657	−	0.516224i
$188$		0			0
$189$	9.46711	+	20.5336i	0.688631	+	1.49360i
$190$		0			0
$191$	−6.96728	−	12.0677i	−0.504135	−	0.873187i	−0.999989	−	0.00478132i	$-0.998478\pi$
$191$	−6.96728	−	12.0677i	−0.504135	−	0.873187i	0.495854	−	0.868406i	$-0.334855\pi$
$192$		0			0
$193$	−1.34094	+	2.32257i	−0.0965226	+	0.167182i	−0.910243	−	0.414074i	$-0.864105\pi$
$193$	−1.34094	+	2.32257i	−0.0965226	+	0.167182i	0.813720	+	0.581256i	$0.197439\pi$
$194$		0			0
$195$	2.06275	+	1.27643i	0.147716	+	0.0914070i
$196$		0			0
$197$	14.2363	−	14.2363i	1.01430	−	1.01430i	0.0144009	−	0.999896i	$-0.495416\pi$
$197$	14.2363	−	14.2363i	1.01430	−	1.01430i	0.999896	−	0.0144009i	$-0.00458410\pi$
$198$		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
$203$	−17.3615	+	4.65201i	−1.21854	+	0.326507i
$204$		0			0
$205$	−2.09950	−	0.562559i	−0.146635	−	0.0392908i
$206$		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
$211$	−13.2108	+	3.53982i	−0.909469	+	0.243691i	−0.683078	−	0.730345i	$-0.739359\pi$
$211$	−13.2108	+	3.53982i	−0.909469	+	0.243691i	−0.226391	+	0.974037i	$0.572693\pi$
$212$		0			0
$213$	−12.2855	+	6.60145i	−0.841789	+	0.452324i
$214$		0			0
$215$		−	7.09799i		−	0.484079i
$216$		0			0
$217$			24.8307i			1.68562i
$218$		0			0
$219$	14.8473	−	7.97802i	1.00329	−	0.539105i
$220$		0			0
$221$	11.3524	−	3.04186i	0.763643	−	0.204618i
$222$		0			0
$223$	24.3372	−	14.0511i	1.62974	−	0.940931i	0.645570	−	0.763701i	$-0.276620\pi$
$223$	24.3372	−	14.0511i	1.62974	−	0.940931i	0.984169	−	0.177230i	$-0.0567136\pi$
$224$		0			0
$225$	−0.799096	+	13.0708i	−0.0532731	+	0.871388i
$226$		0			0
$227$	−0.489998	−	0.131295i	−0.0325223	−	0.00871433i	0.242521	−	0.970146i	$-0.422026\pi$
$227$	−0.489998	−	0.131295i	−0.0325223	−	0.00871433i	−0.275044	+	0.961432i	$0.588692\pi$
$228$		0			0
$229$	−14.6181	+	3.91690i	−0.965988	+	0.258836i	−0.707133	−	0.707080i	$-0.750012\pi$
$229$	−14.6181	+	3.91690i	−0.965988	+	0.258836i	−0.258855	+	0.965916i	$0.583345\pi$
$230$		0			0
$231$	21.0646	+	22.3917i	1.38595	+	1.47326i
$232$		0			0
$233$	15.4968			1.01523			0.507614	−	0.861584i	$-0.330527\pi$
$233$	15.4968			1.01523			0.507614	+	0.861584i	$0.330527\pi$
$234$		0			0
$235$	−1.38791	+	1.38791i	−0.0905371	+	0.0905371i
$236$		0			0
$237$	20.3805	+	12.6114i	1.32385	+	0.819202i
$238$		0			0
$239$	7.61709	−	13.1932i	0.492709	−	0.853397i	−0.507256	−	0.861796i	$-0.669340\pi$
$239$	7.61709	−	13.1932i	0.492709	−	0.853397i	0.999965	+	0.00839869i	$0.00267342\pi$
$240$		0			0
$241$	−9.10697	−	15.7737i	−0.586632	−	1.01608i	−0.994670	−	0.103111i	$-0.967120\pi$
$241$	−9.10697	−	15.7737i	−0.586632	−	1.01608i	0.408038	−	0.912965i	$-0.366213\pi$
$242$		0			0
$243$	−9.75637	+	12.1578i	−0.625871	+	0.779926i
$244$		0			0
$245$	9.18628	+	2.46146i	0.586890	+	0.157257i
$246$		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	0.634807	−	0.772671i	$-0.281080\pi$
$251$	−2.18418	−	2.18418i	−0.137864	−	0.137864i	−0.772671	+	0.634807i	$0.781080\pi$
$252$		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	0.919926	−	0.392093i	$-0.128249\pi$
$257$	16.6777	+	9.62887i	1.04033	+	0.600633i	0.120400	+	0.992725i	$0.461582\pi$
$258$		0			0
$259$	2.41564	−	9.01529i	0.150101	−	0.560183i
$260$		0			0
$261$	−8.21121	−	9.28058i	−0.508261	−	0.574453i
$262$		0			0
$263$	22.8254	−	13.1782i	1.40747	−	0.812605i	0.412329	−	0.911035i	$-0.364715\pi$
$263$	22.8254	−	13.1782i	1.40747	−	0.812605i	0.995144	+	0.0984300i	$0.0313821\pi$
$264$		0			0
$265$	−1.64235	−	0.948214i	−0.100889	−	0.0582483i
$266$		0			0
$267$	−1.40290	−	2.61083i	−0.0858559	−	0.159781i
$268$		0			0
$269$	−0.605506	−	0.605506i	−0.0369184	−	0.0369184i	0.688407	−	0.725325i	$-0.258310\pi$
$269$	−0.605506	−	0.605506i	−0.0369184	−	0.0369184i	−0.725325	+	0.688407i	$0.758310\pi$
$270$		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
$275$	4.60819	+	17.1980i	0.277884	+	1.03708i
$276$		0			0
$277$	−1.82792	+	6.82191i	−0.109829	+	0.409889i	−0.998848	−	0.0479819i	$-0.984721\pi$
$277$	−1.82792	+	6.82191i	−0.109829	+	0.409889i	0.889019	+	0.457871i	$0.151388\pi$
$278$		0			0
$279$	−15.3200	+	7.63877i	−0.917183	+	0.457321i
$280$		0			0
$281$	−11.8490	−	20.5230i	−0.706849	−	1.22430i	−0.966020	−	0.258467i	$-0.916783\pi$
$281$	−11.8490	−	20.5230i	−0.706849	−	1.22430i	0.259171	−	0.965831i	$-0.416551\pi$
$282$		0			0
$283$	0.194826	+	0.727099i	0.0115812	+	0.0432215i	0.971475	−	0.237143i	$-0.0762112\pi$
$283$	0.194826	+	0.727099i	0.0115812	+	0.0432215i	−0.959893	+	0.280365i	$0.909544\pi$
$284$		0			0
$285$	−1.38178	−	0.0421989i	−0.0818498	−	0.00249965i
$286$		0			0
$287$	11.8699			0.700659
$288$		0			0
$289$	−27.7137			−1.63022
$290$		0			0
$291$	6.68175	−	10.7979i	0.391691	−	0.632985i
$292$		0			0
$293$	5.31070	+	19.8198i	0.310255	+	1.15789i	0.928327	+	0.371765i	$0.121247\pi$
$293$	5.31070	+	19.8198i	0.310255	+	1.15789i	−0.618072	+	0.786121i	$0.712086\pi$
$294$		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
$299$	−2.03907	+	7.60993i	−0.117923	+	0.440093i
$300$		0			0
$301$	10.0325	+	37.4417i	0.578262	+	2.15810i
$302$		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
$309$	−25.7563	−	0.786581i	−1.46522	−	0.0447470i
$310$		0			0
$311$	−0.576605	−	0.332903i	−0.0326963	−	0.0188772i	0.483563	−	0.875310i	$-0.339342\pi$
$311$	−0.576605	−	0.332903i	−0.0326963	−	0.0188772i	−0.516259	+	0.856432i	$0.672676\pi$
$312$		0			0
$313$	14.3283	−	8.27244i	0.809882	−	0.467586i	−0.0370327	−	0.999314i	$-0.511791\pi$
$313$	14.3283	−	8.27244i	0.809882	−	0.467586i	0.846915	+	0.531728i	$0.178457\pi$
$314$		0			0
$315$	2.07411	+	10.1932i	0.116863	+	0.574320i
$316$		0			0
$317$	−1.75927	+	6.56570i	−0.0988107	+	0.368767i	−0.997570	−	0.0696766i	$-0.977803\pi$
$317$	−1.75927	+	6.56570i	−0.0988107	+	0.368767i	0.898759	+	0.438443i	$0.144470\pi$
$318$		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
$331$	−9.39568	−	2.51757i	−0.516434	−	0.138378i	−0.00881711	−	0.999961i	$-0.502807\pi$
$331$	−9.39568	−	2.51757i	−0.516434	−	0.138378i	−0.507616	+	0.861583i	$0.669473\pi$
$332$		0			0
$333$	6.30538	−	1.28302i	0.345532	−	0.0703090i
$334$		0			0
$335$	3.30434	+	5.72328i	0.180535	+	0.312696i
$336$		0			0
$337$	13.5580	−	23.4832i	0.738553	−	1.27921i	−0.214593	−	0.976704i	$-0.568843\pi$
$337$	13.5580	−	23.4832i	0.738553	−	1.27921i	0.953147	−	0.302509i	$-0.0978241\pi$
$338$		0			0
$339$	0.440806	−	14.4340i	0.0239413	−	0.783948i
$340$		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
$347$	30.1679	−	8.08347i	1.61950	−	0.433944i	0.668645	−	0.743582i	$-0.266875\pi$
$347$	30.1679	−	8.08347i	1.61950	−	0.433944i	0.950854	+	0.309638i	$0.100208\pi$
$348$		0			0
$349$	−31.6714	−	8.48634i	−1.69533	−	0.454263i	−0.723576	−	0.690245i	$-0.757503\pi$
$349$	−31.6714	−	8.48634i	−1.69533	−	0.454263i	−0.971757	+	0.235982i	$0.924169\pi$
$350$		0			0
$351$	−1.54700	−	9.00083i	−0.0825726	−	0.480429i
$352$		0			0
$353$	−3.48989	+	2.01489i	−0.185748	+	0.107242i	−0.589990	−	0.807410i	$-0.700869\pi$
$353$	−3.48989	+	2.01489i	−0.185748	+	0.107242i	0.404243	+	0.914652i	$0.367535\pi$
$354$		0			0
$355$	−6.19752	+	1.66062i	−0.328930	+	0.0881366i
$356$		0			0
$357$	42.8569	+	26.5198i	2.26823	+	1.40358i
$358$		0			0
$359$			14.8043i			0.781342i	0.920530	+	0.390671i	$0.127757\pi$
$359$			14.8043i			0.781342i	−0.920530	+	0.390671i	$0.872243\pi$
$360$		0			0
$361$		−	17.9967i		−	0.947193i
$362$		0			0
$363$	−0.298054	+	9.75965i	−0.0156438	+	0.512249i
$364$		0			0
$365$	7.48986	−	2.00690i	0.392037	−	0.105046i
$366$		0			0
$367$	2.66934	−	1.54114i	0.139338	−	0.0804470i	−0.428710	−	0.903442i	$-0.641032\pi$
$367$	2.66934	−	1.54114i	0.139338	−	0.0804470i	0.568049	+	0.822995i	$0.307699\pi$
$368$		0			0
$369$	3.65160	+	7.32348i	0.190094	+	0.381245i
$370$		0			0
$371$	10.0036	+	2.68045i	0.519361	+	0.139162i
$372$		0			0
$373$	28.2816	−	7.57804i	1.46437	−	0.392376i	0.563372	−	0.826204i	$-0.309504\pi$
$373$	28.2816	−	7.57804i	1.46437	−	0.392376i	0.900996	+	0.433828i	$0.142837\pi$
$374$		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
$381$	−7.39721	+	3.97479i	−0.378970	+	0.203635i
$382$		0			0
$383$	−1.66394	+	2.88203i	−0.0850235	+	0.147265i	−0.905401	−	0.424557i	$-0.860430\pi$
$383$	−1.66394	+	2.88203i	−0.0850235	+	0.147265i	0.820378	+	0.571822i	$0.193763\pi$
$384$		0			0
$385$	7.07147	+	12.2481i	0.360396	+	0.624223i
$386$		0			0
$387$	−20.0144	+	17.7082i	−1.01739	+	0.900157i
$388$		0			0
$389$	−6.62255	−	1.77451i	−0.335777	−	0.0899711i	0.0869912	−	0.996209i	$-0.472275\pi$
$389$	−6.62255	−	1.77451i	−0.335777	−	0.0899711i	−0.422768	+	0.906238i	$0.638941\pi$
$390$		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	0.580786	−	0.814056i	$-0.302745\pi$
$401$	3.32787	+	1.92135i	0.166186	+	0.0959474i	−0.414600	+	0.910004i	$0.636079\pi$
$402$		0			0
$403$	2.59579	−	9.68764i	0.129306	−	0.482575i
$404$		0			0
$405$	−5.65090	+	4.41545i	−0.280795	+	0.219405i
$406$		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	$-0.293529\pi$
$409$	4.36888	+	2.52237i	0.216027	+	0.124723i	−0.388082	+	0.921625i	$0.626862\pi$
$410$		0			0
$411$	−5.35654	+	8.65634i	−0.264219	+	0.426986i
$412$		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
$419$	−5.72083	−	21.3504i	−0.279481	−	1.04304i	−0.952779	−	0.303665i	$-0.901790\pi$
$419$	−5.72083	−	21.3504i	−0.279481	−	1.04304i	0.673298	−	0.739371i	$-0.264877\pi$
$420$		0			0
$421$	2.13099	−	7.95298i	0.103858	−	0.387604i	−0.894355	−	0.447358i	$-0.852365\pi$
$421$	2.13099	−	7.95298i	0.103858	−	0.387604i	0.998213	+	0.0597538i	$0.0190316\pi$
$422$		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
$427$	2.30165	+	8.58988i	0.111385	+	0.415693i
$428$		0			0
$429$	−5.87747	−	10.9382i	−0.283767	−	0.528099i
$430$		0			0
$431$	1.08094			0.0520671			0.0260336	−	0.999661i	$-0.491712\pi$
$431$	1.08094			0.0520671			0.0260336	+	0.999661i	$0.491712\pi$
$432$		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
$435$	−2.69833	−	5.02167i	−0.129375	−	0.240771i
$436$		0			0
$437$	−1.16207	−	4.33690i	−0.0555893	−	0.207462i
$438$		0			0
$439$	2.26321	+	3.91999i	0.108017	+	0.187091i	0.914967	−	0.403529i	$-0.132217\pi$
$439$	2.26321	+	3.91999i	0.108017	+	0.187091i	−0.806950	+	0.590620i	$0.798883\pi$
$440$		0			0
$441$	−15.9774	−	32.0437i	−0.760831	−	1.52589i
$442$		0			0
$443$	6.82958	−	25.4883i	0.324483	−	1.21099i	−0.590347	−	0.807149i	$-0.701009\pi$
$443$	6.82958	−	25.4883i	0.324483	−	1.21099i	0.914830	−	0.403838i	$-0.132324\pi$
$444$		0			0
$445$	−0.352904	−	1.31706i	−0.0167293	−	0.0624345i
$446$		0			0
$447$	5.67490	−	5.33856i	0.268414	−	0.252505i
$448$		0			0
$449$		−	5.94688i		−	0.280650i	−0.990105	−	0.140325i	$-0.955185\pi$
$449$		−	5.94688i		−	0.280650i	0.990105	−	0.140325i	$-0.0448148\pi$
$450$		0			0
$451$	7.86752	+	7.86752i	0.370467	+	0.370467i
$452$		0			0
$453$	7.71961	−	12.4751i	0.362699	−	0.586133i
$454$		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	$-0.830544\pi$
$457$	−18.2318	+	10.5261i	−0.852846	+	0.492391i	0.00876413	+	0.999962i	$0.497210\pi$
$458$		0			0
$459$	−3.17791	+	34.6002i	−0.148332	+	1.61500i
$460$		0			0
$461$	10.2518	−	38.2603i	0.477475	−	1.78196i	−0.134314	−	0.990939i	$-0.542883\pi$
$461$	10.2518	−	38.2603i	0.477475	−	1.78196i	0.611788	−	0.791021i	$-0.290450\pi$
$462$		0			0
$463$	−9.98020	−	5.76207i	−0.463819	−	0.267786i	0.249829	−	0.968290i	$-0.419625\pi$
$463$	−9.98020	−	5.76207i	−0.463819	−	0.267786i	−0.713649	+	0.700504i	$0.752959\pi$
$464$		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	$-0.442380\pi$
$467$	25.1476	−	25.1476i	1.16369	−	1.16369i	0.983661	−	0.180032i	$-0.0576202\pi$
$468$		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
$475$	4.22335	+	1.13164i	0.193780	+	0.0519233i
$476$		0			0
$477$	1.42367	+	6.99660i	0.0651853	+	0.320352i
$478$		0			0
$479$	−2.64784	−	4.58619i	−0.120983	−	0.209548i	0.799173	−	0.601101i	$-0.205271\pi$
$479$	−2.64784	−	4.58619i	−0.120983	−	0.209548i	−0.920155	+	0.391553i	$0.871938\pi$
$480$		0			0
$481$	−1.88491	+	3.26477i	−0.0859447	+	0.148861i
$482$		0			0
$483$	−29.7598	+	15.9911i	−1.35412	+	0.727618i
$484$		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
$491$	3.49505	−	0.936497i	0.157730	−	0.0422635i	−0.179090	−	0.983833i	$-0.557315\pi$
$491$	3.49505	−	0.936497i	0.157730	−	0.0422635i	0.336820	+	0.941569i	$0.390649\pi$
$492$		0			0
$493$	−26.6792	−	7.14866i	−1.20157	−	0.321960i
$494$		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
$499$	12.0253	−	3.22216i	0.538325	−	0.144244i	0.0205953	−	0.999788i	$-0.493444\pi$
$499$	12.0253	−	3.22216i	0.538325	−	0.144244i	0.517730	+	0.855544i	$0.326777\pi$
$500$		0			0
$501$	0.434592	−	14.2305i	0.0194162	−	0.635774i
$502$		0			0
$503$		−	16.6233i		−	0.741198i	−0.928793	−	0.370599i	$-0.879152\pi$
$503$		−	16.6233i		−	0.741198i	0.928793	−	0.370599i	$-0.120848\pi$
$504$		0			0
$505$			11.5701i			0.514862i
$506$		0			0
$507$	−14.5973	−	9.03281i	−0.648288	−	0.401161i
$508$		0			0
$509$	15.1091	−	4.04848i	0.669700	−	0.179446i	0.0920802	−	0.995752i	$-0.470648\pi$
$509$	15.1091	−	4.04848i	0.669700	−	0.179446i	0.577620	+	0.816306i	$0.303982\pi$
$510$		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
$515$	−11.4506	−	3.06819i	−0.504575	−	0.135200i
$516$		0			0
$517$	9.70511	−	2.60048i	0.426830	−	0.114369i
$518$		0			0
$519$	16.4320	−	3.86945i	0.721285	−	0.169850i
$520$		0			0
$521$	−40.4461			−1.77198			−0.885988	−	0.463709i	$-0.846518\pi$
$521$	−40.4461			−1.77198			−0.885988	+	0.463709i	$0.846518\pi$
$522$		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
$525$	1.00426	−	32.8842i	0.0438296	−	1.43518i
$526$		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
$531$	−0.990498	+	2.96055i	−0.0429840	+	0.128477i
$532$		0			0
$533$	−4.63102	−	1.24088i	−0.200592	−	0.0537484i
$534$		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
$547$	5.77510	−	21.5530i	0.246926	−	0.921539i	−0.725480	−	0.688243i	$-0.758382\pi$
$547$	5.77510	−	21.5530i	0.246926	−	0.921539i	0.972406	−	0.233296i	$-0.0749511\pi$
$548$		0			0
$549$	−4.59170	+	4.06261i	−0.195969	+	0.173388i
$550$		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
$555$	2.95882	+	0.0903606i	0.125595	+	0.00383559i
$556$		0			0
$557$	−11.6516	−	11.6516i	−0.493695	−	0.493695i	0.415773	−	0.909468i	$-0.363511\pi$
$557$	−11.6516	−	11.6516i	−0.493695	−	0.493695i	−0.909468	+	0.415773i	$0.863511\pi$
$558$		0			0
$559$		−	15.6566i		−	0.662203i
$560$		0			0
$561$	10.8284	+	45.9837i	0.457174	+	1.94143i
$562$		0			0
$563$	1.30826	+	4.88249i	0.0551365	+	0.205772i	0.987999	−	0.154460i	$-0.0493639\pi$
$563$	1.30826	+	4.88249i	0.0551365	+	0.205772i	−0.932862	+	0.360233i	$0.882697\pi$
$564$		0			0
$565$	1.71944	−	6.41702i	0.0723372	−	0.269966i
$566$		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	$-0.129248\pi$
$569$	2.79764	+	4.84565i	0.117283	+	0.203140i	−0.801407	+	0.598119i	$0.795915\pi$
$570$		0			0
$571$	2.31993	+	8.65808i	0.0970859	+	0.362329i	0.997327	−	0.0730613i	$-0.0232769\pi$
$571$	2.31993	+	8.65808i	0.0970859	+	0.362329i	−0.900242	+	0.435391i	$0.856610\pi$
$572$		0			0
$573$	−12.7001	+	20.5237i	−0.530554	+	0.857392i
$574$		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
$579$	4.64297	+	0.141794i	0.192955	+	0.00589274i
$580$		0			0
$581$	−3.55636	−	13.2725i	−0.147543	−	0.550637i
$582$		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
$587$	−1.34545	+	5.02128i	−0.0555325	+	0.207250i	−0.988118	−	0.153700i	$-0.950881\pi$
$587$	−1.34545	+	5.02128i	−0.0555325	+	0.207250i	0.932585	+	0.360950i	$0.117548\pi$
$588$		0			0
$589$	1.47934	+	5.52099i	0.0609553	+	0.227488i
$590$		0			0
$591$	−33.3923	−	10.0495i	−1.37358	−	0.413380i
$592$		0			0
$593$			44.7927i			1.83942i	0.392602	+	0.919708i	$0.371575\pi$
$593$			44.7927i			1.83942i	−0.392602	+	0.919708i	$0.628425\pi$
$594$		0			0
$595$	16.3947	+	16.3947i	0.672116	+	0.672116i
$596$		0			0
$597$	6.47733	+	12.0545i	0.265100	+	0.493358i
$598$		0			0
$599$	27.1165	+	15.6557i	1.10795	+	0.639674i	0.938297	−	0.345830i	$-0.112403\pi$
$599$	27.1165	+	15.6557i	1.10795	+	0.639674i	0.169651	+	0.985504i	$0.445736\pi$
$600$		0			0
$601$	15.4248	−	8.90549i	0.629189	−	0.363262i	−0.151249	−	0.988496i	$-0.548330\pi$
$601$	15.4248	−	8.90549i	0.629189	−	0.363262i	0.780438	+	0.625233i	$0.214996\pi$
$602$		0			0
$603$	7.89436	−	23.5958i	0.321483	−	0.960897i
$604$		0			0
$605$	−1.16261	+	4.33891i	−0.0472667	+	0.176402i
$606$		0			0
$607$	−29.3159	−	16.9255i	−1.18989	−	0.686986i	−0.231612	−	0.972808i	$-0.574400\pi$
$607$	−29.3159	−	16.9255i	−1.18989	−	0.686986i	−0.958283	+	0.285823i	$0.907733\pi$
$608$		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	−0.232932	−	0.972493i	$-0.574832\pi$
$617$	18.0269	−	31.2236i	0.725738	−	1.25701i	0.958670	−	0.284521i	$-0.0918346\pi$
$618$		0			0
$619$	−16.0209	−	4.29280i	−0.643936	−	0.172542i	−0.0779503	−	0.996957i	$-0.524838\pi$
$619$	−16.0209	−	4.29280i	−0.643936	−	0.172542i	−0.565986	+	0.824415i	$0.691504\pi$
$620$		0			0
$621$	−19.0213	−	13.4418i	−0.763298	−	0.539400i
$622$		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
$627$	6.01764	+	3.72372i	0.240322	+	0.148711i
$628$		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
$635$	−3.73158	+	0.999874i	−0.148083	+	0.0396788i
$636$		0			0
$637$	20.2629	+	5.42943i	0.802845	+	0.215122i
$638$		0			0
$639$	20.1441	+	13.3323i	0.796890	+	0.527420i
$640$		0			0
$641$	−40.0952	+	23.1490i	−1.58366	+	0.914329i	−0.589346	+	0.807881i	$0.700615\pi$
$641$	−40.0952	+	23.1490i	−1.58366	+	0.914329i	−0.994318	+	0.106448i	$0.966052\pi$
$642$		0			0
$643$	−10.5870	+	2.83678i	−0.417511	+	0.111872i	−0.461458	−	0.887162i	$-0.652674\pi$
$643$	−10.5870	+	2.83678i	−0.417511	+	0.111872i	0.0439466	+	0.999034i	$0.486007\pi$
$644$		0			0
$645$	−10.8297	+	5.81918i	−0.426418	+	0.229130i
$646$		0			0
$647$		−	10.0479i		−	0.395025i	−0.980300	−	0.197512i	$-0.936714\pi$
$647$		−	10.0479i		−	0.395025i	0.980300	−	0.197512i	$-0.0632863\pi$
$648$		0			0
$649$			4.24456i			0.166614i
$650$		0			0
$651$	37.8851	−	20.3570i	1.48483	−	0.797855i
$652$		0			0
$653$	−25.5935	+	6.85777i	−1.00155	+	0.268365i	−0.722096	−	0.691793i	$-0.756821\pi$
$653$	−25.5935	+	6.85777i	−1.00155	+	0.268365i	−0.279457	+	0.960158i	$0.590154\pi$
$654$		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
$659$	−6.76233	−	1.81196i	−0.263423	−	0.0705840i	0.124690	−	0.992196i	$-0.460206\pi$
$659$	−6.76233	−	1.81196i	−0.263423	−	0.0705840i	−0.388113	+	0.921612i	$0.626873\pi$
$660$		0			0
$661$	20.1902	−	5.40993i	0.785306	−	0.210422i	0.156183	−	0.987728i	$-0.450081\pi$
$661$	20.1902	−	5.40993i	0.785306	−	0.210422i	0.629123	+	0.777306i	$0.283414\pi$
$662$		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
$669$	−41.3907	−	25.6126i	−1.60026	−	0.990240i
$670$		0			0
$671$	−4.16791	+	7.21904i	−0.160901	+	0.278688i
$672$		0			0
$673$	3.86200	+	6.68918i	0.148869	+	0.257849i	0.930810	−	0.365504i	$-0.119103\pi$
$673$	3.86200	+	6.68918i	0.148869	+	0.257849i	−0.781941	+	0.623353i	$0.785770\pi$
$674$		0			0
$675$	20.5978	−	9.49670i	0.792808	−	0.365528i
$676$		0			0
$677$	7.62160	+	2.04220i	0.292922	+	0.0784882i	0.402287	−	0.915513i	$-0.368215\pi$
$677$	7.62160	+	2.04220i	0.292922	+	0.0784882i	−0.109366	+	0.994002i	$0.534882\pi$
$678$		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	0.993666	−	0.112378i	$-0.0358467\pi$
$683$	23.0318	+	23.0318i	0.881288	+	0.881288i	−0.112378	+	0.993666i	$0.535847\pi$
$684$		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
$691$	6.66520	−	24.8749i	0.253556	−	0.946285i	−0.715332	−	0.698785i	$-0.753724\pi$
$691$	6.66520	−	24.8749i	0.253556	−	0.946285i	0.968888	−	0.247500i	$-0.0796089\pi$
$692$		0			0
$693$	16.8944	−	50.4964i	0.641764	−	1.91820i
$694$		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
$699$	−12.7048	−	23.6440i	−0.480540	−	0.894299i
$700$		0			0
$701$	35.0396	+	35.0396i	1.32343	+	1.32343i	0.910983	+	0.412443i	$0.135325\pi$
$701$	35.0396	+	35.0396i	1.32343	+	1.32343i	0.412443	+	0.910983i	$0.364675\pi$
$702$		0			0
$703$		−	2.14843i		−	0.0810295i
$704$		0			0
$705$	3.25543	+	0.979727i	0.122607	+	0.0368987i
$706$		0			0
$707$	−16.3534	−	61.0318i	−0.615034	−	2.29534i
$708$		0			0
$709$	−12.2110	+	45.5722i	−0.458595	+	1.71150i	0.218702	+	0.975792i	$0.429818\pi$
$709$	−12.2110	+	45.5722i	−0.458595	+	1.71150i	−0.677297	+	0.735710i	$0.736849\pi$
$710$		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
$715$	−1.47850	−	5.51784i	−0.0552928	−	0.206356i
$716$		0			0
$717$	−26.3741	−	0.805449i	−0.984959	−	0.0300801i
$718$		0			0
$719$	−26.0582			−0.971806			−0.485903	−	0.874013i	$-0.661509\pi$
$719$	−26.0582			−0.971806			−0.485903	+	0.874013i	$0.661509\pi$
$720$		0			0
$721$	64.7383			2.41098
$722$		0			0
$723$	−16.6004	+	26.8267i	−0.617374	+	0.997695i
$724$		0			0
$725$	4.66655	+	17.4158i	0.173311	+	0.646807i
$726$		0			0
$727$	4.96698	+	8.60307i	0.184215	+	0.319070i	0.943312	−	0.331908i	$-0.107692\pi$
$727$	4.96698	+	8.60307i	0.184215	+	0.319070i	−0.759097	+	0.650978i	$0.774359\pi$
$728$		0			0
$729$	26.5483	+	4.91824i	0.983269	+	0.182157i
$730$		0			0
$731$	−15.4167	+	57.5359i	−0.570207	+	2.12804i
$732$		0			0
$733$	3.40512	+	12.7081i	0.125771	+	0.469384i	0.999866	−	0.0163712i	$-0.00521135\pi$
$733$	3.40512	+	12.7081i	0.125771	+	0.469384i	−0.874095	+	0.485755i	$0.838545\pi$
$734$		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
$741$	−3.04791	−	0.0930813i	−0.111968	−	0.00341943i
$742$		0			0
$743$	8.76936	+	5.06299i	0.321717	+	0.185743i	0.652157	−	0.758084i	$-0.273864\pi$
$743$	8.76936	+	5.06299i	0.321717	+	0.185743i	−0.330441	+	0.943827i	$0.607197\pi$
$744$		0			0
$745$	3.10414	−	1.79218i	0.113727	−	0.0656603i
$746$		0			0
$747$	7.09480	−	6.27728i	0.259585	−	0.229674i
$748$		0			0
$749$	−0.155261	+	0.579443i	−0.00567312	+	0.0211724i
$750$		0			0
$751$	22.6187	+	13.0589i	0.825368	+	0.476526i	0.852264	−	0.523112i	$-0.175229\pi$
$751$	22.6187	+	13.0589i	0.825368	+	0.476526i	−0.0268964	+	0.999638i	$0.508562\pi$
$752$		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	0.0490055	+	0.998799i	$0.484395\pi$
$761$	−23.1857	+	40.1589i	−0.840482	+	1.45576i	−0.889488	+	0.456959i	$0.848939\pi$
$762$		0			0
$763$	52.3487	+	14.0268i	1.89515	+	0.507804i
$764$		0			0
$765$	−5.07159	+	15.1587i	−0.183364	+	0.548065i
$766$		0			0
$767$	−0.914499	−	1.58396i	−0.0330206	−	0.0571934i
$768$		0			0
$769$	−7.38255	+	12.7870i	−0.266222	+	0.461109i	−0.967883	−	0.251401i	$-0.919109\pi$
$769$	−7.38255	+	12.7870i	−0.266222	+	0.461109i	0.701661	+	0.712511i	$0.252442\pi$
$770$		0			0
$771$	1.01818	−	33.3398i	0.0366688	−	1.20071i
$772$		0			0
$773$	22.1409	−	22.1409i	0.796353	−	0.796353i	−0.186165	−	0.982518i	$-0.559606\pi$
$773$	22.1409	−	22.1409i	0.796353	−	0.796353i	0.982518	+	0.186165i	$0.0596060\pi$
$774$		0			0
$775$	24.9083			0.894731
$776$		0			0
$777$	−15.7354	+	3.70541i	−0.564504	+	0.132931i
$778$		0			0
$779$	2.63922	−	0.707177i	0.0945599	−	0.0253372i
$780$		0			0
$781$	31.7248	+	8.50064i	1.13520	+	0.304177i
$782$		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
$787$	4.18136	−	1.12039i	0.149050	−	0.0399377i	−0.183523	−	0.983015i	$-0.558750\pi$
$787$	4.18136	−	1.12039i	0.149050	−	0.0399377i	0.332572	+	0.943078i	$0.392083\pi$
$788$		0			0
$789$	−38.8195	−	24.0215i	−1.38201	−	0.855190i
$790$		0			0
$791$			36.2799i			1.28996i
$792$		0			0
$793$		−	3.59194i		−	0.127553i
$794$		0			0
$795$	−0.100266	+	3.28318i	−0.00355608	+	0.116442i
$796$		0			0
$797$	51.5141	−	13.8032i	1.82472	−	0.488933i	0.827370	−	0.561657i	$-0.189836\pi$
$797$	51.5141	−	13.8032i	1.82472	−	0.488933i	0.997352	+	0.0727237i	$0.0231691\pi$
$798$		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
$803$	−38.3403	−	10.2732i	−1.35300	−	0.362535i
$804$		0			0
$805$	−15.0126	+	4.02261i	−0.529124	+	0.141778i
$806$		0			0
$807$	−0.427428	+	1.42026i	−0.0150462	+	0.0499954i
$808$		0			0
$809$	30.1140			1.05875			0.529375	−	0.848388i	$-0.322426\pi$
$809$	30.1140			1.05875			0.529375	+	0.848388i	$0.322426\pi$
$810$		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
$813$	29.1544	−	15.6657i	1.02249	−	0.549420i
$814$		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
$819$	4.57502	+	22.4839i	0.159864	+	0.785649i
$820$		0			0
$821$	31.8546	+	8.53541i	1.11173	+	0.297888i	0.767533	−	0.641009i	$-0.221484\pi$
$821$	31.8546	+	8.53541i	1.11173	+	0.297888i	0.344199	+	0.938897i	$0.388151\pi$
$822$		0			0
$823$	−4.71220	+	8.16178i	−0.164257	+	0.284502i	−0.936391	−	0.350958i	$-0.885856\pi$
$823$	−4.71220	+	8.16178i	−0.164257	+	0.284502i	0.772134	+	0.635460i	$0.219189\pi$
$824$		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	$0.151735\pi$
$827$	38.7468	+	38.7468i	1.34736	+	1.34736i	0.458841	+	0.888518i	$0.348265\pi$
$828$		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
$835$	1.69520	−	6.32656i	0.0586647	−	0.218940i
$836$		0			0
$837$	24.2146	+	17.1117i	0.836979	+	0.591468i
$838$		0			0
$839$	−25.3695	+	14.6471i	−0.875853	+	0.505674i	−0.869289	−	0.494305i	$-0.835423\pi$
$839$	−25.3695	+	14.6471i	−0.875853	+	0.505674i	−0.00656388	+	0.999978i	$0.502089\pi$
$840$		0			0
$841$	10.3391	+	5.96927i	0.356520	+	0.205837i
$842$		0			0
$843$	−21.5985	+	34.9038i	−0.743892	+	1.20215i
$844$		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
$851$	2.48834	+	9.28662i	0.0852992	+	0.318341i
$852$		0			0
$853$	−10.9035	+	40.6922i	−0.373327	+	1.39328i	0.482447	+	0.875925i	$0.339748\pi$
$853$	−10.9035	+	40.6922i	−0.373327	+	1.39328i	−0.855774	+	0.517350i	$0.826918\pi$
$854$		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	$-0.00520611\pi$
$857$	14.2207	+	24.6310i	0.485769	+	0.841377i	−0.514097	+	0.857732i	$0.671873\pi$
$858$		0			0
$859$	0.896437	+	3.34555i	0.0305860	+	0.114149i	0.979531	−	0.201293i	$-0.0645142\pi$
$859$	0.896437	+	3.34555i	0.0305860	+	0.114149i	−0.948945	+	0.315441i	$0.897848\pi$
$860$		0			0
$861$	−9.73136	−	18.1104i	−0.331644	−	0.617199i
$862$		0			0
$863$	11.1356			0.379062			0.189531	−	0.981875i	$-0.439303\pi$
$863$	11.1356			0.379062			0.189531	+	0.981875i	$0.439303\pi$
$864$		0			0
$865$	7.76622			0.264059
$866$		0			0
$867$	22.7207	+	42.2839i	0.771635	+	1.43604i
$868$		0			0
$869$	−14.6080	−	54.5177i	−0.495541	−	1.84939i
$870$		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
$875$	8.40437	−	31.3655i	0.284119	−	1.06035i
$876$		0			0
$877$	7.32539	+	27.3387i	0.247361	+	0.923163i	0.972182	+	0.234226i	$0.0752557\pi$
$877$	7.32539	+	27.3387i	0.247361	+	0.923163i	−0.724821	+	0.688937i	$0.758078\pi$
$878$		0			0
$879$	25.8859	−	24.3517i	0.873111	−	0.821362i
$880$		0			0
$881$		−	4.86363i		−	0.163860i	−0.996638	−	0.0819299i	$-0.973892\pi$
$881$		−	4.86363i		−	0.163860i	0.996638	−	0.0819299i	$-0.0261084\pi$
$882$		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
$885$	−0.755727	+	1.22128i	−0.0254035	+	0.0410528i
$886$		0			0
$887$	−3.99885	−	2.30874i	−0.134268	−	0.0775199i	0.431361	−	0.902179i	$-0.358033\pi$
$887$	−3.99885	−	2.30874i	−0.134268	−	0.0775199i	−0.565630	+	0.824659i	$0.691367\pi$
$888$		0			0
$889$	18.2707	−	10.5486i	0.612780	−	0.353789i
$890$		0			0
$891$	36.3525	−	5.11099i	1.21785	−	0.171225i
$892$		0			0
$893$	0.638605	−	2.38330i	0.0213701	−	0.0797543i
$894$		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
$907$	−8.35931	−	2.23987i	−0.277566	−	0.0743737i	0.117350	−	0.993091i	$-0.462560\pi$
$907$	−8.35931	−	2.23987i	−0.277566	−	0.0743737i	−0.394917	+	0.918717i	$0.629227\pi$
$908$		0			0
$909$	32.6244	−	28.8652i	1.08208	−	0.957398i
$910$		0			0
$911$	23.9969	+	41.5638i	0.795052	+	1.37707i	0.922806	+	0.385264i	$0.125890\pi$
$911$	23.9969	+	41.5638i	0.795052	+	1.37707i	−0.127755	+	0.991806i	$0.540777\pi$
$912$		0			0
$913$	6.43999	−	11.1544i	0.213133	−	0.369156i
$914$		0			0
$915$	−2.48454	+	1.33504i	−0.0821365	+	0.0441349i
$916$		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
$923$	−13.6703	+	3.66296i	−0.449965	+	0.120568i
$924$		0			0
$925$	−9.04347	−	2.42319i	−0.297347	−	0.0796740i
$926$		0			0
$927$	19.9157	+	39.9421i	0.654119	+	1.31187i
$928$		0			0
$929$	8.80130	−	5.08143i	0.288761	−	0.166716i	−0.348622	−	0.937263i	$-0.613350\pi$
$929$	8.80130	−	5.08143i	0.288761	−	0.166716i	0.637383	+	0.770547i	$0.280017\pi$
$930$		0			0
$931$	−11.5478	+	3.09423i	−0.378465	+	0.101409i
$932$		0			0
$933$	−0.0352020	+	1.15267i	−0.00115246	+	0.0377368i
$934$		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
$939$	−24.3684	−	15.0792i	−0.795232	−	0.492090i
$940$		0			0
$941$	−34.3731	+	9.21025i	−1.12053	+	0.300246i	−0.771099	−	0.636716i	$-0.780293\pi$
$941$	−34.3731	+	9.21025i	−1.12053	+	0.300246i	−0.349433	+	0.936961i	$0.613626\pi$
$942$		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
$947$	10.0399	+	2.69018i	0.326253	+	0.0874191i	0.418228	−	0.908342i	$-0.362651\pi$
$947$	10.0399	+	2.69018i	0.326253	+	0.0874191i	−0.0919752	+	0.995761i	$0.529318\pi$
$948$		0			0
$949$	16.5210	−	4.42678i	0.536293	−	0.143699i
$950$		0			0
$951$	11.4598	−	2.69860i	0.371611	−	0.0875080i
$952$		0			0
$953$	−24.6743			−0.799280			−0.399640	−	0.916672i	$-0.630865\pi$
$953$	−24.6743			−0.799280			−0.399640	+	0.916672i	$0.630865\pi$
$954$		0			0
$955$	−7.85126	+	7.85126i	−0.254061	+	0.254061i
$956$		0			0
$957$	−0.890777	+	29.1681i	−0.0287947	+	0.942871i
$958$		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
$963$	−0.405268	+	0.0824639i	−0.0130596	+	0.00265736i
$964$		0			0
$965$	2.06416	+	0.553089i	0.0664475	+	0.0178046i
$966$		0			0
$967$	−12.5371	+	21.7150i	−0.403167	+	0.698306i	−0.994106	−	0.108410i	$-0.965424\pi$
$967$	−12.5371	+	21.7150i	−0.403167	+	0.698306i	0.590939	+	0.806716i	$0.298757\pi$
$968$		0			0
$969$	11.1090	+	3.34327i	0.356873	+	0.107401i
$970$		0			0
$971$	−18.9203	−	18.9203i	−0.607180	−	0.607180i	0.335028	−	0.942208i	$-0.391254\pi$
$971$	−18.9203	−	18.9203i	−0.607180	−	0.607180i	−0.942208	+	0.335028i	$0.891254\pi$
$972$		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	0.292170	−	0.956366i	$-0.405623\pi$
$977$	−12.1897	−	7.03771i	−0.389982	−	0.225156i	−0.682152	+	0.731210i	$0.738956\pi$
$978$		0			0
$979$	−1.80650	+	6.74196i	−0.0577360	+	0.215474i
$980$		0			0
$981$	7.45005	+	36.6132i	0.237862	+	1.16897i
$982$		0			0
$983$	0.562149	−	0.324557i	0.0179298	−	0.0103518i	−0.491008	−	0.871155i	$-0.663372\pi$
$983$	0.562149	−	0.324557i	0.0179298	−	0.0103518i	0.508938	+	0.860803i	$0.330038\pi$
$984$		0			0
$985$	−13.8933	−	8.02129i	−0.442677	−	0.255579i
$986$		0			0
$987$	−18.5571	−	0.566722i	−0.590678	−	0.0180390i
$988$		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
$995$	1.62940	+	6.08100i	0.0516554	+	0.192781i
$996$		0			0
$997$	−2.07498	+	7.74395i	−0.0657154	+	0.245253i	−0.990968	−	0.134098i	$-0.957186\pi$
$997$	−2.07498	+	7.74395i	−0.0657154	+	0.245253i	0.925253	+	0.379352i	$0.123853\pi$
$998$		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.527.8		88
3.2	odd	2		1728.2.z.a.719.13		88
4.3	odd	2		144.2.u.a.59.20	yes	88
9.2	odd	6	inner	576.2.y.a.335.4		88
9.7	even	3		1728.2.z.a.143.13		88
12.11	even	2		432.2.v.a.395.3		88
16.3	odd	4	inner	576.2.y.a.239.4		88
16.13	even	4		144.2.u.a.131.12	yes	88
36.7	odd	6		432.2.v.a.251.11		88
36.11	even	6		144.2.u.a.11.12	✓	88
48.29	odd	4		432.2.v.a.179.11		88
48.35	even	4		1728.2.z.a.1583.13		88
144.29	odd	12		144.2.u.a.83.20	yes	88
144.61	even	12		432.2.v.a.35.3		88
144.83	even	12	inner	576.2.y.a.47.8		88
144.115	odd	12		1728.2.z.a.1007.13		88

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
144.2.u.a.11.12	✓	88	36.11	even	6
144.2.u.a.59.20	yes	88	4.3	odd	2
144.2.u.a.83.20	yes	88	144.29	odd	12
144.2.u.a.131.12	yes	88	16.13	even	4
432.2.v.a.35.3		88	144.61	even	12
432.2.v.a.179.11		88	48.29	odd	4
432.2.v.a.251.11		88	36.7	odd	6
432.2.v.a.395.3		88	12.11	even	2
576.2.y.a.47.8		88	144.83	even	12	inner
576.2.y.a.239.4		88	16.3	odd	4	inner
576.2.y.a.335.4		88	9.2	odd	6	inner
576.2.y.a.527.8		88	1.1	even	1	trivial
1728.2.z.a.143.13		88	9.7	even	3
1728.2.z.a.719.13		88	3.2	odd	2
1728.2.z.a.1007.13		88	144.115	odd	12
1728.2.z.a.1583.13		88	48.35	even	4

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 $\F_{q}$

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

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

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