LMFDB - Embedded newform 666.2.bs.b.557.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [666,2,Mod(17,666)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(666, base_ring=CyclotomicField(36))

chi = DirichletCharacter(H, H._module([18, 7]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("666.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 666 = 2 \cdot 3^{2} \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	666.bs (of order $36$, degree $12$, 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:	$5.31803677462$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$8$ over $\Q(\zeta_{36})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label			557.5
Character	$\chi$	$=$	666.557
Dual form			666.2.bs.b.611.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.0871557 - 0.996195i) q^{2} +(-0.984808 - 0.173648i) q^{4} +(-3.03635 - 1.41587i) q^{5} +(-1.63046 + 0.593439i) q^{7} +(-0.258819 + 0.965926i) q^{8} +O(q^{10})$	\(q+(0.0871557 - 0.996195i) q^{2} +(-0.984808 - 0.173648i) q^{4} +(-3.03635 - 1.41587i) q^{5} +(-1.63046 + 0.593439i) q^{7} +(-0.258819 + 0.965926i) q^{8} +(-1.67512 + 2.90139i) q^{10} +(0.408947 + 0.708318i) q^{11} +(3.82328 + 5.46021i) q^{13} +(0.449077 + 1.67598i) q^{14} +(0.939693 + 0.342020i) q^{16} +(-0.771448 + 1.10174i) q^{17} +(-1.63867 + 0.143365i) q^{19} +(2.74436 + 1.92162i) q^{20} +(0.741264 - 0.345657i) q^{22} +(4.85685 - 1.30139i) q^{23} +(4.00077 + 4.76794i) q^{25} +(5.77265 - 3.33284i) q^{26} +(1.70874 - 0.301297i) q^{28} +(-3.12298 - 0.836800i) q^{29} +(5.52010 + 5.52010i) q^{31} +(0.422618 - 0.906308i) q^{32} +(1.03031 + 0.864536i) q^{34} +(5.79088 + 0.506636i) q^{35} +(4.15058 - 4.44665i) q^{37} +1.64493i q^{38} +(2.15349 - 2.56643i) q^{40} +(-0.631977 + 3.58412i) q^{41} +(-7.38109 + 7.38109i) q^{43} +(-0.279736 - 0.768570i) q^{44} +(-0.873134 - 4.95179i) q^{46} +(-2.69999 - 1.55884i) q^{47} +(-3.05608 + 2.56435i) q^{49} +(5.09848 - 3.57000i) q^{50} +(-2.81704 - 6.04116i) q^{52} +(-1.64843 + 4.52901i) q^{53} +(-0.238819 - 2.72972i) q^{55} +(-0.151224 - 1.72850i) q^{56} +(-1.10580 + 3.03817i) q^{58} +(3.21090 + 6.88580i) q^{59} +(-9.61763 + 6.73434i) q^{61} +(5.98021 - 5.01799i) q^{62} +(-0.866025 - 0.500000i) q^{64} +(-3.87785 - 21.9924i) q^{65} +(1.99855 + 5.49098i) q^{67} +(0.951044 - 0.951044i) q^{68} +(1.00942 - 5.72469i) q^{70} +(-7.41721 + 8.83948i) q^{71} +6.79194i q^{73} +(-4.06798 - 4.52233i) q^{74} +(1.63867 + 0.143365i) q^{76} +(-1.08712 - 0.912199i) q^{77} +(3.68293 - 7.89808i) q^{79} +(-2.36898 - 2.36898i) q^{80} +(3.51540 + 0.941948i) q^{82} +(8.80119 - 1.55189i) q^{83} +(3.90231 - 2.25300i) q^{85} +(6.70970 + 7.99631i) q^{86} +(-0.790026 + 0.211687i) q^{88} +(-4.08541 + 1.90506i) q^{89} +(-9.47401 - 6.63377i) q^{91} +(-5.00904 + 0.438235i) q^{92} +(-1.78823 + 2.55386i) q^{94} +(5.17856 + 1.88484i) q^{95} +(-2.31502 - 8.63977i) q^{97} +(2.28824 + 3.26795i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q+O(q^{10}) $ 96 * q	$ 96 q - 12 q^{13} + 24 q^{19} + 12 q^{22} + 48 q^{31} + 72 q^{34} + 24 q^{37} + 72 q^{43} + 60 q^{46} + 12 q^{52} - 60 q^{55} + 12 q^{58} - 120 q^{61} + 36 q^{67} + 12 q^{70} - 24 q^{76} + 60 q^{79} + 96 q^{82} - 108 q^{85} - 24 q^{88} + 216 q^{91} - 60 q^{94} + 24 q^{97}+O(q^{100}) $ 96 * q - 12 * q^13 + 24 * q^19 + 12 * q^22 + 48 * q^31 + 72 * q^34 + 24 * q^37 + 72 * q^43 + 60 * q^46 + 12 * q^52 - 60 * q^55 + 12 * q^58 - 120 * q^61 + 36 * q^67 + 12 * q^70 - 24 * q^76 + 60 * q^79 + 96 * q^82 - 108 * q^85 - 24 * q^88 + 216 * q^91 - 60 * q^94 + 24 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/666\mathbb{Z}\right)^\times$.

$n$	$371$	$631$
$\chi(n)$	$-1$	$e\left(\frac{1}{36}\right)$

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 $

$2$	0.0871557	−	0.996195i	0.0616284	−	0.704416i
$2$	0.0871557	−	0.996195i	0.0616284	−	0.704416i
$3$		0			0
$3$		0			0
$4$	−0.984808	−	0.173648i	−0.492404	−	0.0868241i
$5$	−3.03635	−	1.41587i	−1.35790	−	0.633197i	−0.398999	−	0.916951i	$-0.630642\pi$
$5$	−3.03635	−	1.41587i	−1.35790	−	0.633197i	−0.958897	+	0.283754i	$0.908420\pi$
$6$		0			0
$7$	−1.63046	+	0.593439i	−0.616256	+	0.224299i	−0.631238	−	0.775589i	$-0.717453\pi$
$7$	−1.63046	+	0.593439i	−0.616256	+	0.224299i	0.0149822	+	0.999888i	$0.495231\pi$
$8$	−0.258819	+	0.965926i	−0.0915064	+	0.341506i
$9$		0			0
$10$	−1.67512	+	2.90139i	−0.529719	+	0.917501i
$11$	0.408947	+	0.708318i	0.123302	+	0.213566i	0.921068	−	0.389402i	$-0.127318\pi$
$11$	0.408947	+	0.708318i	0.123302	+	0.213566i	−0.797766	+	0.602967i	$0.793985\pi$
$12$		0			0
$13$	3.82328	+	5.46021i	1.06039	+	1.51439i	0.842710	+	0.538368i	$0.180959\pi$
$13$	3.82328	+	5.46021i	1.06039	+	1.51439i	0.217677	+	0.976021i	$0.430152\pi$
$14$	0.449077	+	1.67598i	0.120021	+	0.447924i
$15$		0			0
$16$	0.939693	+	0.342020i	0.234923	+	0.0855050i
$17$	−0.771448	+	1.10174i	−0.187104	+	0.267212i	−0.901735	−	0.432290i	$-0.857706\pi$
$17$	−0.771448	+	1.10174i	−0.187104	+	0.267212i	0.714631	+	0.699502i	$0.246595\pi$
$18$		0			0
$19$	−1.63867	+	0.143365i	−0.375937	+	0.0328902i	−0.273559	−	0.961855i	$-0.588201\pi$
$19$	−1.63867	+	0.143365i	−0.375937	+	0.0328902i	−0.102378	+	0.994746i	$0.532645\pi$
$20$	2.74436	+	1.92162i	0.613656	+	0.429687i
$21$		0			0
$22$	0.741264	−	0.345657i	0.158038	−	0.0736944i
$23$	4.85685	−	1.30139i	1.01272	−	0.271358i	0.285956	−	0.958243i	$-0.407689\pi$
$23$	4.85685	−	1.30139i	1.01272	−	0.271358i	0.726766	+	0.686885i	$0.241022\pi$
$24$		0			0
$25$	4.00077	+	4.76794i	0.800155	+	0.953588i
$26$	5.77265	−	3.33284i	1.13211	−	0.653624i
$27$		0			0
$28$	1.70874	−	0.301297i	0.322922	−	0.0569398i
$29$	−3.12298	−	0.836800i	−0.579923	−	0.155390i	−0.0430794	−	0.999072i	$-0.513717\pi$
$29$	−3.12298	−	0.836800i	−0.579923	−	0.155390i	−0.536844	+	0.843682i	$0.680384\pi$
$30$		0			0
$31$	5.52010	+	5.52010i	0.991440	+	0.991440i	0.999964	−	0.00852369i	$-0.00271321\pi$
$31$	5.52010	+	5.52010i	0.991440	+	0.991440i	−0.00852369	+	0.999964i	$0.502713\pi$
$32$	0.422618	−	0.906308i	0.0747091	−	0.160214i
$33$		0			0
$34$	1.03031	+	0.864536i	0.176697	+	0.148267i
$35$	5.79088	+	0.506636i	0.978837	+	0.0856372i
$36$		0			0
$37$	4.15058	−	4.44665i	0.682351	−	0.731025i
$37$	4.15058	−	4.44665i	0.682351	−	0.731025i
$38$			1.64493i			0.266843i
$39$		0			0
$40$	2.15349	−	2.56643i	0.340497	−	0.405789i
$41$	−0.631977	+	3.58412i	−0.0986982	+	0.559745i	0.894853	+	0.446361i	$0.147280\pi$
$41$	−0.631977	+	3.58412i	−0.0986982	+	0.559745i	−0.993551	+	0.113384i	$0.963831\pi$
$42$		0			0
$43$	−7.38109	+	7.38109i	−1.12561	+	1.12561i	−0.134723	+	0.990883i	$0.543014\pi$
$43$	−7.38109	+	7.38109i	−1.12561	+	1.12561i	−0.990883	+	0.134723i	$0.956986\pi$
$44$	−0.279736	−	0.768570i	−0.0421719	−	0.115866i
$45$		0			0
$46$	−0.873134	−	4.95179i	−0.128737	−	0.730101i
$47$	−2.69999	−	1.55884i	−0.393834	−	0.227380i	0.289986	−	0.957031i	$-0.406349\pi$
$47$	−2.69999	−	1.55884i	−0.393834	−	0.227380i	−0.683820	+	0.729651i	$0.739683\pi$
$48$		0			0
$49$	−3.05608	+	2.56435i	−0.436583	+	0.366336i
$50$	5.09848	−	3.57000i	0.721035	−	0.504874i
$51$		0			0
$52$	−2.81704	−	6.04116i	−0.390653	−	0.837758i
$53$	−1.64843	+	4.52901i	−0.226429	+	0.622108i	−0.999932	−	0.0116849i	$-0.996280\pi$
$53$	−1.64843	+	4.52901i	−0.226429	+	0.622108i	0.773503	+	0.633793i	$0.218503\pi$
$54$		0			0
$55$	−0.238819	−	2.72972i	−0.0322024	−	0.368075i
$56$	−0.151224	−	1.72850i	−0.0202081	−	0.230980i
$57$		0			0
$58$	−1.10580	+	3.03817i	−0.145199	+	0.398931i
$59$	3.21090	+	6.88580i	0.418024	+	0.896454i	0.996721	+	0.0809123i	$0.0257834\pi$
$59$	3.21090	+	6.88580i	0.418024	+	0.896454i	−0.578698	+	0.815542i	$0.696439\pi$
$60$		0			0
$61$	−9.61763	+	6.73434i	−1.23141	+	0.862243i	−0.994023	−	0.109171i	$-0.965180\pi$
$61$	−9.61763	+	6.73434i	−1.23141	+	0.862243i	−0.237388	+	0.971415i	$0.576291\pi$
$62$	5.98021	−	5.01799i	0.759487	−	0.637285i
$63$		0			0
$64$	−0.866025	−	0.500000i	−0.108253	−	0.0625000i
$65$	−3.87785	−	21.9924i	−0.480988	−	2.72782i
$66$		0			0
$67$	1.99855	+	5.49098i	0.244162	+	0.670830i	0.999873	+	0.0159247i	$0.00506921\pi$
$67$	1.99855	+	5.49098i	0.244162	+	0.670830i	−0.755711	+	0.654905i	$0.772709\pi$
$68$	0.951044	−	0.951044i	0.115331	−	0.115331i
$69$		0			0
$70$	1.00942	−	5.72469i	0.120648	−	0.684231i
$71$	−7.41721	+	8.83948i	−0.880260	+	1.04905i	0.118167	+	0.992994i	$0.462298\pi$
$71$	−7.41721	+	8.83948i	−0.880260	+	1.04905i	−0.998427	+	0.0560597i	$0.982146\pi$
$72$		0			0
$73$			6.79194i			0.794936i	0.917616	+	0.397468i	$0.130111\pi$
$73$			6.79194i			0.794936i	−0.917616	+	0.397468i	$0.869889\pi$
$74$	−4.06798	−	4.52233i	−0.472894	−	0.525711i
$75$		0			0
$76$	1.63867	+	0.143365i	0.187968	+	0.0164451i
$77$	−1.08712	−	0.912199i	−0.123888	−	0.103955i
$78$		0			0
$79$	3.68293	−	7.89808i	0.414363	−	0.888603i	−0.582749	−	0.812652i	$-0.698023\pi$
$79$	3.68293	−	7.89808i	0.414363	−	0.888603i	0.997112	−	0.0759511i	$-0.0241993\pi$
$80$	−2.36898	−	2.36898i	−0.264860	−	0.264860i
$81$		0			0
$82$	3.51540	+	0.941948i	0.388211	+	0.104021i
$83$	8.80119	−	1.55189i	0.966057	−	0.170342i	0.331702	−	0.943384i	$-0.392377\pi$
$83$	8.80119	−	1.55189i	0.966057	−	0.170342i	0.634354	+	0.773042i	$0.281266\pi$
$84$		0			0
$85$	3.90231	−	2.25300i	0.423265	−	0.244372i
$86$	6.70970	+	7.99631i	0.723526	+	0.862264i
$87$		0			0
$88$	−0.790026	+	0.211687i	−0.0842170	+	0.0225659i
$89$	−4.08541	+	1.90506i	−0.433052	+	0.201936i	−0.626906	−	0.779095i	$-0.715679\pi$
$89$	−4.08541	+	1.90506i	−0.433052	+	0.201936i	0.193854	+	0.981030i	$0.437901\pi$
$90$		0			0
$91$	−9.47401	−	6.63377i	−0.993146	−	0.695408i
$92$	−5.00904	+	0.438235i	−0.522229	+	0.0456891i
$93$		0			0
$94$	−1.78823	+	2.55386i	−0.184442	+	0.263410i
$95$	5.17856	+	1.88484i	0.531309	+	0.193381i
$96$		0			0
$97$	−2.31502	−	8.63977i	−0.235055	−	0.877236i	−0.978124	−	0.208022i	$-0.933298\pi$
$97$	−2.31502	−	8.63977i	−0.235055	−	0.877236i	0.743070	−	0.669214i	$-0.233369\pi$
$98$	2.28824	+	3.26795i	0.231147	+	0.330113i
$99$		0			0
$100$	−3.11205	−	5.39023i	−0.311205	−	0.539023i
$101$	−0.210861	+	0.365223i	−0.0209815	+	0.0363410i	−0.876326	−	0.481719i	$-0.840012\pi$
$101$	−0.210861	+	0.365223i	−0.0209815	+	0.0363410i	0.855344	+	0.518060i	$0.173346\pi$
$102$		0			0
$103$	1.60026	−	5.97223i	0.157678	−	0.588462i	−0.841183	−	0.540750i	$-0.818140\pi$
$103$	1.60026	−	5.97223i	0.157678	−	0.588462i	0.998861	−	0.0477116i	$-0.0151929\pi$
$104$	−6.26369	+	2.27980i	−0.614206	+	0.223553i
$105$		0			0
$106$	4.36811	+	2.03688i	0.424268	+	0.197839i
$107$	−15.1622	−	2.67351i	−1.46579	−	0.258458i	−0.616903	−	0.787039i	$-0.711613\pi$
$107$	−15.1622	−	2.67351i	−1.46579	−	0.258458i	−0.848882	+	0.528582i	$0.822724\pi$
$108$		0			0
$109$	0.911651	−	10.4202i	0.0873204	−	0.998076i	−0.818526	−	0.574470i	$-0.805208\pi$
$109$	0.911651	−	10.4202i	0.0873204	−	0.998076i	0.905846	−	0.423607i	$-0.139236\pi$
$110$	−2.74014			−0.261262
$111$		0			0
$112$	−1.73510			−0.163952
$113$	−0.178190	+	2.03672i	−0.0167627	+	0.191599i	0.983196	+	0.182551i	$0.0584355\pi$
$113$	−0.178190	+	2.03672i	−0.0167627	+	0.191599i	−0.999959	+	0.00904765i	$0.997120\pi$
$114$		0			0
$115$	−16.5897	−	2.92521i	−1.54699	−	0.272777i
$116$	2.93023	+	1.36639i	0.272065	+	0.126866i
$117$		0			0
$118$	7.13944	−	2.59854i	0.657239	−	0.239215i
$119$	0.603999	−	2.25416i	0.0553685	−	0.206638i
$120$		0			0
$121$	5.16552	−	8.94695i	0.469593	−	0.813359i
$122$	5.87048	+	10.1680i	0.531488	+	0.920564i
$123$		0			0
$124$	−4.47769	−	6.39480i	−0.402108	−	0.574270i
$125$	−1.06142	−	3.96129i	−0.0949367	−	0.354309i
$126$		0			0
$127$	14.0829	+	5.12576i	1.24966	+	0.454838i	0.880285	−	0.474445i	$-0.157351\pi$
$127$	14.0829	+	5.12576i	1.24966	+	0.454838i	0.369371	+	0.929282i	$0.379573\pi$
$128$	−0.573576	+	0.819152i	−0.0506975	+	0.0724035i
$129$		0			0
$130$	−22.2466	+	1.94633i	−1.95116	+	0.170704i
$131$	11.1992	+	7.84177i	0.978480	+	0.685139i	0.949279	−	0.314435i	$-0.101815\pi$
$131$	11.1992	+	7.84177i	0.978480	+	0.685139i	0.0292006	+	0.999574i	$0.490704\pi$
$132$		0			0
$133$	2.58671	−	1.20620i	0.224296	−	0.104591i
$134$	5.64427	−	1.51238i	0.487591	−	0.130650i
$135$		0			0
$136$	−0.864536	−	1.03031i	−0.0741333	−	0.0883487i
$137$	−17.7917	+	10.2720i	−1.52004	+	0.877598i	−0.520324	+	0.853969i	$0.674189\pi$
$137$	−17.7917	+	10.2720i	−1.52004	+	0.877598i	−0.999721	+	0.0236291i	$0.992478\pi$
$138$		0			0
$139$	12.1974	−	2.15072i	1.03457	−	0.182422i	0.369519	−	0.929223i	$-0.379523\pi$
$139$	12.1974	−	2.15072i	1.03457	−	0.182422i	0.665047	+	0.746801i	$0.268411\pi$
$140$	−5.61493	−	1.50452i	−0.474548	−	0.127155i
$141$		0			0
$142$	8.15939	+	8.15939i	0.684721	+	0.684721i
$143$	−2.30404	+	4.94103i	−0.192674	+	0.413190i
$144$		0			0
$145$	8.29765	+	6.96256i	0.689083	+	0.578209i
$146$	6.76609	+	0.591956i	0.559966	+	0.0489906i
$147$		0			0
$148$	−4.85967	+	3.65836i	−0.399463	+	0.300715i
$149$			19.4180i			1.59078i	0.606095	+	0.795392i	$0.292735\pi$
$149$			19.4180i			1.59078i	−0.606095	+	0.795392i	$0.707265\pi$
$150$		0			0
$151$	12.6426	−	15.0668i	1.02884	−	1.22612i	0.0550915	−	0.998481i	$-0.482455\pi$
$151$	12.6426	−	15.0668i	1.02884	−	1.22612i	0.973746	−	0.227639i	$-0.0731006\pi$
$152$	0.285639	−	1.61994i	0.0231684	−	0.131395i
$153$		0			0
$154$	−1.00348	+	1.00348i	−0.0808624	+	0.0808624i
$155$	−8.94519	−	24.5767i	−0.718495	−	1.97405i
$156$		0			0
$157$	−0.731079	−	4.14615i	−0.0583465	−	0.330899i	0.941637	−	0.336630i	$-0.109287\pi$
$157$	−0.731079	−	4.14615i	−0.0583465	−	0.330899i	−0.999984	+	0.00573047i	$0.998176\pi$
$158$	−7.54704	−	4.35728i	−0.600410	−	0.346647i
$159$		0			0
$160$	−2.56643	+	2.15349i	−0.202894	+	0.170248i
$161$	−7.14660	+	5.00411i	−0.563231	+	0.394379i
$162$		0			0
$163$	−8.79852	−	18.8685i	−0.689153	−	1.47789i	−0.869316	−	0.494257i	$-0.835440\pi$
$163$	−8.79852	−	18.8685i	−0.689153	−	1.47789i	0.180163	−	0.983637i	$-0.442337\pi$
$164$	1.24475	−	3.41993i	0.0971987	−	0.267051i
$165$		0			0
$166$	−0.778908	−	8.90296i	−0.0604550	−	0.691004i
$167$	−0.789044	−	9.01881i	−0.0610581	−	0.697897i	−0.963609	−	0.267314i	$-0.913864\pi$
$167$	−0.789044	−	9.01881i	−0.0610581	−	0.697897i	0.902551	−	0.430582i	$-0.141692\pi$
$168$		0			0
$169$	−10.7501	+	29.5358i	−0.826934	+	2.27198i
$170$	−1.90432	−	4.08382i	−0.146055	−	0.313215i
$171$		0			0
$172$	8.55067	−	5.98724i	0.651983	−	0.456523i
$173$	8.81124	−	7.39351i	0.669906	−	0.562118i	−0.243131	−	0.969993i	$-0.578175\pi$
$173$	8.81124	−	7.39351i	0.669906	−	0.562118i	0.913038	+	0.407875i	$0.133730\pi$
$174$		0			0
$175$	−9.35259	−	5.39972i	−0.706989	−	0.408180i
$176$	0.142026	+	0.805469i	0.0107056	+	0.0607145i
$177$		0			0
$178$	1.54174	+	4.23590i	0.115558	+	0.317494i
$179$	−12.1575	+	12.1575i	−0.908692	+	0.908692i	−0.996167	−	0.0874747i	$-0.972120\pi$
$179$	−12.1575	+	12.1575i	−0.908692	+	0.908692i	0.0874747	+	0.996167i	$0.472120\pi$
$180$		0			0
$181$	−3.32936	+	18.8817i	−0.247469	+	1.40347i	0.567219	+	0.823567i	$0.308019\pi$
$181$	−3.32936	+	18.8817i	−0.247469	+	1.40347i	−0.814688	+	0.579900i	$0.803092\pi$
$182$	−7.43424	+	8.85978i	−0.551063	+	0.656731i
$183$		0			0
$184$			5.02818i			0.370682i
$185$	−18.8985	+	7.62489i	−1.38944	+	0.560593i
$186$		0			0
$187$	−1.09587	−	0.0958758i	−0.0801376	−	0.00701113i
$188$	2.38828	+	2.00401i	0.174184	+	0.146157i
$189$		0			0
$190$	2.32901	−	4.99458i	0.168964	−	0.362345i
$191$	−0.602298	−	0.602298i	−0.0435807	−	0.0435807i	0.684981	−	0.728561i	$-0.259811\pi$
$191$	−0.602298	−	0.602298i	−0.0435807	−	0.0435807i	−0.728561	+	0.684981i	$0.759811\pi$
$192$		0			0
$193$	−11.7976	−	3.16116i	−0.849211	−	0.227545i	−0.192134	−	0.981369i	$-0.561541\pi$
$193$	−11.7976	−	3.16116i	−0.849211	−	0.227545i	−0.657077	+	0.753823i	$0.728207\pi$
$194$	−8.80866	+	1.55320i	−0.632425	+	0.111514i
$195$		0			0
$196$	3.45495	−	1.99471i	0.246782	−	0.142480i
$197$	−10.3433	−	12.3266i	−0.736927	−	0.878236i	0.259230	−	0.965816i	$-0.416531\pi$
$197$	−10.3433	−	12.3266i	−0.736927	−	0.878236i	−0.996158	+	0.0875797i	$0.972087\pi$
$198$		0			0
$199$	1.01938	−	0.273141i	0.0722617	−	0.0193625i	−0.222507	−	0.974931i	$-0.571424\pi$
$199$	1.01938	−	0.273141i	0.0722617	−	0.0193625i	0.294769	+	0.955569i	$0.404757\pi$
$200$	−5.64095	+	2.63042i	−0.398875	+	0.185999i
$201$		0			0
$202$	0.345455	+	0.241890i	0.0243061	+	0.0170193i
$203$	5.58849	−	0.488929i	0.392235	−	0.0343161i
$204$		0			0
$205$	6.99355	−	9.98783i	0.488451	−	0.697580i
$206$	−5.81004	−	2.11468i	−0.404804	−	0.147337i
$207$		0			0
$208$	1.72521	+	6.43855i	0.119621	+	0.446433i
$209$	−0.771678	−	1.10207i	−0.0533781	−	0.0762318i
$210$		0			0
$211$	−2.02817	−	3.51289i	−0.139625	−	0.241838i	0.787730	−	0.616021i	$-0.211256\pi$
$211$	−2.02817	−	3.51289i	−0.139625	−	0.241838i	−0.927355	+	0.374183i	$0.877923\pi$
$212$	2.40984	−	4.17396i	0.165508	−	0.286669i
$213$		0			0
$214$	−3.98480	+	14.8715i	−0.272396	+	1.01659i
$215$	32.8622	−	11.9609i	2.24119	−	0.815725i
$216$		0			0
$217$	−12.2762	−	5.72447i	−0.833360	−	0.388602i
$218$	−10.3011	−	1.81636i	−0.697680	−	0.123020i
$219$		0			0
$220$	−0.238819	+	2.72972i	−0.0161012	+	0.184037i
$221$	−8.96520			−0.603065
$222$		0			0
$223$	10.8070			0.723688			0.361844	−	0.932239i	$-0.382147\pi$
$223$	10.8070			0.723688			0.361844	+	0.932239i	$0.382147\pi$
$224$	−0.151224	+	1.72850i	−0.0101041	+	0.115490i
$225$		0			0
$226$	2.01344	+	0.355024i	0.133932	+	0.0236159i
$227$	−13.6816	−	6.37985i	−0.908082	−	0.423446i	−0.0882819	−	0.996096i	$-0.528138\pi$
$227$	−13.6816	−	6.37985i	−0.908082	−	0.423446i	−0.819800	+	0.572650i	$0.805915\pi$
$228$		0			0
$229$	−14.2293	+	5.17903i	−0.940296	+	0.342240i	−0.766283	−	0.642504i	$-0.777896\pi$
$229$	−14.2293	+	5.17903i	−0.940296	+	0.342240i	−0.174013	+	0.984743i	$0.555674\pi$
$230$	−4.35996	+	16.2716i	−0.287487	+	1.07292i
$231$		0			0
$232$	1.61657	−	2.79999i	0.106133	−	0.183828i
$233$	10.1069	+	17.5057i	0.662128	+	1.14684i	0.980056	+	0.198724i	$0.0636797\pi$
$233$	10.1069	+	17.5057i	0.662128	+	1.14684i	−0.317928	+	0.948115i	$0.602987\pi$
$234$		0			0
$235$	5.99100	+	8.55603i	0.390810	+	0.558134i
$236$	−1.96641	−	7.33875i	−0.128003	−	0.477712i
$237$		0			0
$238$	−2.19294	−	0.798163i	−0.142147	−	0.0517372i
$239$	13.6639	−	19.5141i	0.883846	−	1.26226i	−0.0802681	−	0.996773i	$-0.525578\pi$
$239$	13.6639	−	19.5141i	0.883846	−	1.26226i	0.964114	−	0.265489i	$-0.0855335\pi$
$240$		0			0
$241$	−8.22920	+	0.719962i	−0.530090	+	0.0463768i	−0.349059	−	0.937101i	$-0.613499\pi$
$241$	−8.22920	+	0.719962i	−0.530090	+	0.0463768i	−0.181030	+	0.983477i	$0.557943\pi$
$242$	−8.46270	−	5.92565i	−0.544003	−	0.380915i
$243$		0			0
$244$	10.6409	−	4.96194i	0.681215	−	0.317656i
$245$	12.9101	−	3.45925i	0.824797	−	0.221004i
$246$		0			0
$247$	−7.04790	−	8.39936i	−0.448447	−	0.534438i
$248$	−6.76072	+	3.90330i	−0.429306	+	0.247860i
$249$		0			0
$250$	−4.03873	+	0.712136i	−0.255431	+	0.0450395i
$251$	26.3270	+	7.05430i	1.66175	+	0.445264i	0.962867	−	0.269976i	$-0.0870158\pi$
$251$	26.3270	+	7.05430i	1.66175	+	0.445264i	0.698879	+	0.715240i	$0.253683\pi$
$252$		0			0
$253$	2.90799	+	2.90799i	0.182824	+	0.182824i
$254$	6.33366	−	13.5826i	0.397409	−	0.852247i
$255$		0			0
$256$	0.766044	+	0.642788i	0.0478778	+	0.0401742i
$257$	11.1131	+	0.972272i	0.693217	+	0.0606486i	0.428319	−	0.903628i	$-0.359106\pi$
$257$	11.1131	+	0.972272i	0.693217	+	0.0606486i	0.264898	+	0.964276i	$0.414662\pi$
$258$		0			0
$259$	−4.12854	+	9.71321i	−0.256535	+	0.603549i
$260$			22.3316i			1.38495i
$261$		0			0
$262$	8.78801	−	10.4731i	0.542925	−	0.647033i
$263$	−1.86233	+	10.5618i	−0.114836	+	0.651269i	0.871995	+	0.489515i	$0.162826\pi$
$263$	−1.86233	+	10.5618i	−0.114836	+	0.651269i	−0.986831	+	0.161754i	$0.948285\pi$
$264$		0			0
$265$	11.4177	−	11.4177i	0.701383	−	0.701383i
$266$	−0.976166	−	2.68199i	−0.0598526	−	0.164444i
$267$		0			0
$268$	−1.01469	−	5.75460i	−0.0619822	−	0.351518i
$269$	12.7358	+	7.35301i	0.776515	+	0.448321i	0.835194	−	0.549956i	$-0.185355\pi$
$269$	12.7358	+	7.35301i	0.776515	+	0.448321i	−0.0586788	+	0.998277i	$0.518689\pi$
$270$		0			0
$271$	15.0829	−	12.6560i	0.916218	−	0.768798i	−0.0570735	−	0.998370i	$-0.518177\pi$
$271$	15.0829	−	12.6560i	0.916218	−	0.768798i	0.973292	+	0.229572i	$0.0737325\pi$
$272$	−1.10174	+	0.771448i	−0.0668029	+	0.0467759i
$273$		0			0
$274$	8.68229	+	18.6192i	0.524516	+	1.12483i
$275$	−1.74111	+	4.78365i	−0.104993	+	0.288465i
$276$		0			0
$277$	−0.361843	−	4.13588i	−0.0217410	−	0.248501i	−0.999286	−	0.0377754i	$-0.987973\pi$
$277$	−0.361843	−	4.13588i	−0.0217410	−	0.248501i	0.977545	−	0.210726i	$-0.0675827\pi$
$278$	−1.07947	−	12.3384i	−0.0647422	−	0.740007i
$279$		0			0
$280$	−1.98816	+	5.46243i	−0.118815	+	0.326443i
$281$	−3.39778	−	7.28656i	−0.202695	−	0.434680i	0.778515	−	0.627626i	$-0.215973\pi$
$281$	−3.39778	−	7.28656i	−0.202695	−	0.434680i	−0.981209	+	0.192946i	$0.938196\pi$
$282$		0			0
$283$	−17.3177	+	12.1260i	−1.02943	+	0.720817i	−0.960918	−	0.276833i	$-0.910715\pi$
$283$	−17.3177	+	12.1260i	−1.02943	+	0.720817i	−0.0685151	+	0.997650i	$0.521826\pi$
$284$	8.83948	−	7.41721i	0.524527	−	0.440130i
$285$		0			0
$286$	4.72142	+	2.72591i	0.279183	+	0.161187i
$287$	−1.09654	−	6.21880i	−0.0647269	−	0.367084i
$288$		0			0
$289$	5.19564	+	14.2749i	0.305626	+	0.839700i
$290$	7.65925	−	7.65925i	0.449767	−	0.449767i
$291$		0			0
$292$	1.17941	−	6.68875i	0.0690196	−	0.391430i
$293$	−19.0596	+	22.7143i	−1.11347	+	1.32698i	−0.173848	+	0.984773i	$0.555620\pi$
$293$	−19.0596	+	22.7143i	−1.11347	+	1.32698i	−0.939623	+	0.342210i	$0.888824\pi$
$294$		0			0
$295$		−	25.4539i		−	1.48198i
$296$	3.22089	+	5.16003i	0.187210	+	0.299921i
$297$		0			0
$298$	19.3441	+	1.69239i	1.12057	+	0.0980375i
$299$	25.6749	+	21.5438i	1.48482	+	1.24591i
$300$		0			0
$301$	7.65435	−	16.4148i	0.441190	−	0.946134i
$302$	−13.9076	−	13.9076i	−0.800293	−	0.800293i
$303$		0			0
$304$	−1.58888	−	0.425739i	−0.0911286	−	0.0244178i
$305$	38.7374	−	6.83045i	2.21810	−	0.391111i
$306$		0			0
$307$	−0.876906	+	0.506282i	−0.0500476	+	0.0288950i	−0.524815	−	0.851216i	$-0.675866\pi$
$307$	−0.876906	+	0.506282i	−0.0500476	+	0.0288950i	0.474767	+	0.880111i	$0.342532\pi$
$308$	0.912199	+	1.08712i	0.0519773	+	0.0619442i
$309$		0			0
$310$	−25.2628	+	6.76915i	−1.43483	+	0.384462i
$311$	20.1595	−	9.40054i	1.14314	−	0.533056i	0.243594	−	0.969877i	$-0.421674\pi$
$311$	20.1595	−	9.40054i	1.14314	−	0.533056i	0.899548	+	0.436822i	$0.143896\pi$
$312$		0			0
$313$	0.248543	+	0.174032i	0.0140485	+	0.00983686i	0.580580	−	0.814203i	$-0.302826\pi$
$313$	0.248543	+	0.174032i	0.0140485	+	0.00983686i	−0.566531	+	0.824040i	$0.691715\pi$
$314$	−4.19410	+	0.366936i	−0.236686	+	0.0207074i
$315$		0			0
$316$	−4.99847	+	7.13855i	−0.281186	+	0.401575i
$317$	4.54976	+	1.65598i	0.255540	+	0.0930088i	0.466614	−	0.884461i	$-0.345474\pi$
$317$	4.54976	+	1.65598i	0.255540	+	0.0930088i	−0.211074	+	0.977470i	$0.567696\pi$
$318$		0			0
$319$	−0.684415	−	2.55427i	−0.0383199	−	0.143012i
$320$	1.92162	+	2.74436i	0.107422	+	0.153414i
$321$		0			0
$322$	4.36220	+	7.55554i	0.243096	+	0.421054i
$323$	1.10620	−	1.91599i	0.0615505	−	0.106609i
$324$		0			0
$325$	−10.7379	+	40.0742i	−0.595629	+	2.22292i
$326$	−19.5635	+	7.12054i	−1.08352	+	0.394370i
$327$		0			0
$328$	−3.29842	−	1.53808i	−0.182125	−	0.0849263i
$329$	5.32731	+	0.939349i	0.293704	+	0.0517880i
$330$		0			0
$331$	−0.0646081	+	0.738474i	−0.00355118	+	0.0405902i	−0.997764	−	0.0668426i	$-0.978707\pi$
$331$	−0.0646081	+	0.738474i	−0.00355118	+	0.0405902i	0.994212	+	0.107433i	$0.0342630\pi$
$332$	−8.93697			−0.490480
$333$		0			0
$334$	−9.05326			−0.495373
$335$	1.70622	−	19.5022i	0.0932209	−	1.06552i
$336$		0			0
$337$	8.58179	+	1.51320i	0.467480	+	0.0824294i	0.402426	−	0.915452i	$-0.368167\pi$
$337$	8.58179	+	1.51320i	0.467480	+	0.0824294i	0.0650538	+	0.997882i	$0.479278\pi$
$338$	28.4864	+	13.2834i	1.54946	+	0.722524i
$339$		0			0
$340$	−4.23426	+	1.54114i	−0.229635	+	0.0835802i
$341$	−1.65255	+	6.16742i	−0.0894909	+	0.333984i
$342$		0			0
$343$	9.53388	−	16.5132i	0.514781	−	0.891627i
$344$	−5.21922	−	9.03996i	−0.281402	−	0.487402i
$345$		0			0
$346$	−6.59742	−	9.42210i	−0.354680	−	0.506535i
$347$	1.84100	+	6.87072i	0.0988302	+	0.368840i	0.997572	−	0.0696382i	$-0.0221845\pi$
$347$	1.84100	+	6.87072i	0.0988302	+	0.368840i	−0.898742	+	0.438478i	$0.855518\pi$
$348$		0			0
$349$	19.7211	+	7.17791i	1.05565	+	0.384225i	0.810792	−	0.585335i	$-0.199037\pi$
$349$	19.7211	+	7.17791i	1.05565	+	0.384225i	0.244857	+	0.969559i	$0.421259\pi$
$350$	−6.19430	+	8.84638i	−0.331099	+	0.472859i
$351$		0			0
$352$	0.814782	−	0.0712842i	0.0434280	−	0.00379946i
$353$	−19.5114	−	13.6621i	−1.03849	−	0.727158i	−0.0756226	−	0.997137i	$-0.524094\pi$
$353$	−19.5114	−	13.6621i	−1.03849	−	0.727158i	−0.962866	+	0.269979i	$0.912983\pi$
$354$		0			0
$355$	35.0368	−	16.3379i	1.85956	−	0.867127i
$356$	4.35415	−	1.16669i	0.230769	−	0.0618345i
$357$		0			0
$358$	11.0516	+	13.1708i	0.584096	+	0.696099i
$359$	21.6682	−	12.5101i	1.14360	−	0.660259i	0.196281	−	0.980548i	$-0.437113\pi$
$359$	21.6682	−	12.5101i	1.14360	−	0.660259i	0.947320	+	0.320289i	$0.103780\pi$
$360$		0			0
$361$	−16.0467	+	2.82946i	−0.844561	+	0.148919i
$362$	18.5197	+	4.96234i	0.973374	+	0.260815i
$363$		0			0
$364$	8.17813	+	8.17813i	0.428651	+	0.428651i
$365$	9.61651	−	20.6227i	0.503351	−	1.07944i
$366$		0			0
$367$	4.09410	+	3.43536i	0.213710	+	0.179324i	0.743359	−	0.668893i	$-0.233232\pi$
$367$	4.09410	+	3.43536i	0.213710	+	0.179324i	−0.529648	+	0.848217i	$0.677676\pi$
$368$	5.00904	+	0.438235i	0.261114	+	0.0228446i
$369$		0			0
$370$	5.94877	+	19.4911i	0.309262	+	1.01330i
$371$		−	8.36262i		−	0.434165i
$372$		0			0
$373$	−18.0104	+	21.4640i	−0.932544	+	1.11136i	0.0610250	+	0.998136i	$0.480563\pi$
$373$	−18.0104	+	21.4640i	−0.932544	+	1.11136i	−0.993569	+	0.113227i	$0.963881\pi$
$374$	−0.191022	+	1.08334i	−0.00987751	+	0.0560181i
$375$		0			0
$376$	2.20453	−	2.20453i	0.113690	−	0.113690i
$377$	−7.37092	−	20.2514i	−0.379622	−	1.04300i
$378$		0			0
$379$	3.89565	+	22.0933i	0.200106	+	1.13486i	0.904957	+	0.425503i	$0.139903\pi$
$379$	3.89565	+	22.0933i	0.200106	+	1.13486i	−0.704851	+	0.709355i	$0.748986\pi$
$380$	−4.77259	−	2.75545i	−0.244829	−	0.141352i
$381$		0			0
$382$	−0.652499	+	0.547512i	−0.0333848	+	0.0280131i
$383$	25.7936	−	18.0609i	1.31799	−	0.922869i	0.318309	−	0.947987i	$-0.396885\pi$
$383$	25.7936	−	18.0609i	1.31799	−	0.922869i	0.999684	+	0.0251179i	$0.00799611\pi$
$384$		0			0
$385$	2.00931	+	4.30897i	0.102404	+	0.219605i
$386$	−4.17736	+	11.4772i	−0.212622	+	0.584174i
$387$		0			0
$388$	0.779569	+	8.91051i	0.0395766	+	0.452363i
$389$	−2.18251	−	24.9462i	−0.110658	−	1.26482i	−0.825043	−	0.565070i	$-0.808849\pi$
$389$	−2.18251	−	24.9462i	−0.110658	−	1.26482i	0.714385	−	0.699752i	$-0.246706\pi$
$390$		0			0
$391$	−2.31301	+	6.35495i	−0.116974	+	0.321383i
$392$	−1.68600	−	3.61565i	−0.0851561	−	0.182618i
$393$		0			0
$394$	−13.1812	+	9.22957i	−0.664059	+	0.464979i
$395$	−22.3653	+	18.7667i	−1.12532	+	0.944258i
$396$		0			0
$397$	−3.61960	−	2.08978i	−0.181662	−	0.104883i	0.406411	−	0.913690i	$-0.366780\pi$
$397$	−3.61960	−	2.08978i	−0.181662	−	0.104883i	−0.588074	+	0.808807i	$0.700113\pi$
$398$	−0.183257	−	1.03930i	−0.00918586	−	0.0520956i
$399$		0			0
$400$	2.12877	+	5.84874i	0.106438	+	0.292437i
$401$	2.65103	−	2.65103i	0.132386	−	0.132386i	−0.637809	−	0.770195i	$-0.720159\pi$
$401$	2.65103	−	2.65103i	0.132386	−	0.132386i	0.770195	+	0.637809i	$0.220159\pi$
$402$		0			0
$403$	−9.03602	+	51.2458i	−0.450116	+	2.55274i
$404$	0.271078	−	0.323058i	0.0134866	−	0.0160728i
$405$		0			0
$406$		−	5.60984i		−	0.278411i
$407$	4.84701	+	1.12148i	0.240257	+	0.0555897i
$408$		0			0
$409$	0.413946	+	0.0362156i	0.0204683	+	0.00179075i	0.0973853	−	0.995247i	$-0.468952\pi$
$409$	0.413946	+	0.0362156i	0.0204683	+	0.00179075i	−0.0769170	+	0.997038i	$0.524508\pi$
$410$	−9.34029	−	7.83744i	−0.461284	−	0.387063i
$411$		0			0
$412$	−2.61301	+	5.60362i	−0.128734	+	0.276071i
$413$	−9.32155	−	9.32155i	−0.458683	−	0.458683i
$414$		0			0
$415$	−28.9208	−	7.74929i	−1.41966	−	0.380398i
$416$	6.56442	−	1.15748i	0.321847	−	0.0567503i
$417$		0			0
$418$	−1.16513	+	0.672690i	−0.0569885	+	0.0329023i
$419$	9.74603	+	11.6149i	0.476124	+	0.567423i	0.949632	−	0.313367i	$-0.101457\pi$
$419$	9.74603	+	11.6149i	0.476124	+	0.567423i	−0.473508	+	0.880790i	$0.657012\pi$
$420$		0			0
$421$	6.39946	−	1.71473i	0.311891	−	0.0835708i	−0.0994784	−	0.995040i	$-0.531717\pi$
$421$	6.39946	−	1.71473i	0.311891	−	0.0835708i	0.411369	+	0.911469i	$0.365051\pi$
$422$	−3.67629	+	1.71428i	−0.178959	+	0.0834500i
$423$		0			0
$424$	−3.94805	−	2.76445i	−0.191734	−	0.134254i
$425$	−8.33943	+	0.729605i	−0.404522	+	0.0353911i
$426$		0			0
$427$	11.6847	−	16.6875i	0.565465	−	0.807567i
$428$	14.4676	+	5.26578i	0.699318	+	0.254531i
$429$		0			0
$430$	−9.05123	−	33.7797i	−0.436489	−	1.62900i
$431$	10.7562	+	15.3614i	0.518108	+	0.739935i	0.989899	−	0.141776i	$-0.0452812\pi$
$431$	10.7562	+	15.3614i	0.518108	+	0.739935i	−0.471791	+	0.881710i	$0.656392\pi$
$432$		0			0
$433$	−8.51178	−	14.7428i	−0.409050	−	0.708495i	0.585734	−	0.810504i	$-0.300806\pi$
$433$	−8.51178	−	14.7428i	−0.409050	−	0.708495i	−0.994784	+	0.102008i	$0.967473\pi$
$434$	−6.77262	+	11.7305i	−0.325096	+	0.563083i
$435$		0			0
$436$	−2.70725	+	10.1036i	−0.129654	+	0.483875i
$437$	−7.77220	+	2.82885i	−0.371795	+	0.135322i
$438$		0			0
$439$	−5.76976	−	2.69048i	−0.275375	−	0.128410i	0.280025	−	0.959993i	$-0.409657\pi$
$439$	−5.76976	−	2.69048i	−0.275375	−	0.128410i	−0.555400	+	0.831583i	$0.687435\pi$
$440$	2.69851	+	0.475821i	0.128647	+	0.0226839i
$441$		0			0
$442$	−0.781369	+	8.93109i	−0.0371659	+	0.424808i
$443$	−37.3415			−1.77415			−0.887075	−	0.461626i	$-0.847266\pi$
$443$	−37.3415			−1.77415			−0.887075	+	0.461626i	$0.847266\pi$
$444$		0			0
$445$	15.1020			0.715905
$446$	0.941890	−	10.7658i	0.0445998	−	0.509778i
$447$		0			0
$448$	1.70874	+	0.301297i	0.0807304	+	0.0142349i
$449$	−19.1943	−	8.95045i	−0.905835	−	0.422398i	−0.0868558	−	0.996221i	$-0.527682\pi$
$449$	−19.1943	−	8.95045i	−0.905835	−	0.422398i	−0.818979	+	0.573823i	$0.805460\pi$
$450$		0			0
$451$	−2.79714	+	1.01808i	−0.131712	+	0.0479393i
$452$	0.529157	−	1.97484i	0.0248894	−	0.0928886i
$453$		0			0
$454$	−7.54801	+	13.0735i	−0.354245	+	0.613571i
$455$	19.3738	+	33.5564i	0.908258	+	1.57315i
$456$		0			0
$457$	−2.18859	−	3.12562i	−0.102378	−	0.146211i	0.764695	−	0.644393i	$-0.222890\pi$
$457$	−2.18859	−	3.12562i	−0.102378	−	0.146211i	−0.867072	+	0.498182i	$0.834001\pi$
$458$	3.91916	+	14.6265i	0.183130	+	0.683451i
$459$		0			0
$460$	15.8297	+	5.76153i	0.738063	+	0.268633i
$461$	3.94703	−	5.63695i	0.183832	−	0.262539i	−0.716650	−	0.697433i	$-0.754325\pi$
$461$	3.94703	−	5.63695i	0.183832	−	0.262539i	0.900481	+	0.434894i	$0.143214\pi$
$462$		0			0
$463$	−3.21677	+	0.281431i	−0.149496	+	0.0130792i	−0.161658	−	0.986847i	$-0.551684\pi$
$463$	−3.21677	+	0.281431i	−0.149496	+	0.0130792i	0.0121620	+	0.999926i	$0.496129\pi$
$464$	−2.64844	−	1.85446i	−0.122951	−	0.0860910i
$465$		0			0
$466$	18.3200	−	8.54275i	0.848657	−	0.395735i
$467$	−31.6040	+	8.46826i	−1.46246	+	0.391864i	−0.900338	−	0.435191i	$-0.856681\pi$
$467$	−31.6040	+	8.46826i	−1.46246	+	0.391864i	−0.562120	+	0.827056i	$0.690014\pi$
$468$		0			0
$469$	−6.51712	−	7.76681i	−0.300933	−	0.358638i
$470$	9.04562	−	5.22249i	0.417243	−	0.240896i
$471$		0			0
$472$	−7.48221	+	1.31932i	−0.344397	+	0.0607264i
$473$	−8.24664	−	2.20968i	−0.379181	−	0.101601i
$474$		0			0
$475$	−7.23951	−	7.23951i	−0.332171	−	0.332171i
$476$	−0.986253	+	2.11503i	−0.0452048	+	0.0969421i
$477$		0			0
$478$	−18.2490	−	15.3127i	−0.834688	−	0.700386i
$479$	12.4516	+	1.08937i	0.568928	+	0.0497748i	0.367991	−	0.929829i	$-0.380046\pi$
$479$	12.4516	+	1.08937i	0.568928	+	0.0497748i	0.200937	+	0.979604i	$0.435601\pi$
$480$		0			0
$481$	40.1484	+	5.66222i	1.83061	+	0.258175i
$482$			8.26064i			0.376262i
$483$		0			0
$484$	−6.64067	+	7.91404i	−0.301849	+	0.359729i
$485$	−5.20361	+	29.5111i	−0.236284	+	1.34003i
$486$		0			0
$487$	19.6770	−	19.6770i	0.891648	−	0.891648i	−0.103030	−	0.994678i	$-0.532854\pi$
$487$	19.6770	−	19.6770i	0.891648	−	0.891648i	0.994678	+	0.103030i	$0.0328538\pi$
$488$	−4.01564	−	11.0329i	−0.181780	−	0.499435i
$489$		0			0
$490$	−2.32090	−	13.1625i	−0.104848	−	0.594620i
$491$	−29.7687	−	17.1870i	−1.34344	−	0.775638i	−0.356134	−	0.934435i	$-0.615905\pi$
$491$	−29.7687	−	17.1870i	−1.34344	−	0.775638i	−0.987311	+	0.158797i	$0.949239\pi$
$492$		0			0
$493$	3.33116	−	2.79517i	0.150028	−	0.125888i
$494$	−8.98166	+	6.28903i	−0.404104	+	0.282957i
$495$		0			0
$496$	3.29921	+	7.07519i	0.148139	+	0.317685i
$497$	6.84777	−	18.8141i	0.307164	−	0.843927i
$498$		0			0
$499$	−1.75238	−	20.0298i	−0.0784475	−	0.896659i	−0.928833	−	0.370499i	$-0.879187\pi$
$499$	−1.75238	−	20.0298i	−0.0784475	−	0.896659i	0.850386	−	0.526160i	$-0.176369\pi$
$500$	0.357428	+	4.08542i	0.0159847	+	0.182706i
$501$		0			0
$502$	9.32201	−	25.6120i	0.416062	−	1.14312i
$503$	1.35987	+	2.91624i	0.0606334	+	0.130029i	0.934290	−	0.356515i	$-0.116035\pi$
$503$	1.35987	+	2.91624i	0.0606334	+	0.130029i	−0.873656	+	0.486544i	$0.838257\pi$
$504$		0			0
$505$	1.15736	−	0.810390i	0.0515017	−	0.0360619i
$506$	3.15037	−	2.64348i	0.140051	−	0.117517i
$507$		0			0
$508$	−12.9789	−	7.49336i	−0.575845	−	0.332464i
$509$	2.19317	+	12.4381i	0.0972105	+	0.551308i	0.994048	+	0.108947i	$0.0347479\pi$
$509$	2.19317	+	12.4381i	0.0972105	+	0.551308i	−0.896837	+	0.442361i	$0.854141\pi$
$510$		0			0
$511$	−4.03060	−	11.0740i	−0.178303	−	0.489884i
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$		0			0
$514$	1.93714	−	10.9861i	0.0854438	−	0.484576i
$515$	−13.3149	+	15.8680i	−0.586722	+	0.699229i
$516$		0			0
$517$		−	2.54994i		−	0.112146i
$518$	9.31642	+	4.95939i	0.409340	+	0.217903i
$519$		0			0
$520$	22.2466	+	1.94633i	0.975580	+	0.0853522i
$521$	24.5741	+	20.6201i	1.07661	+	0.903384i	0.995635	−	0.0933320i	$-0.0297518\pi$
$521$	24.5741	+	20.6201i	1.07661	+	0.903384i	0.0809762	+	0.996716i	$0.474196\pi$
$522$		0			0
$523$	−6.24419	+	13.3907i	−0.273039	+	0.585535i	−0.994238	−	0.107193i	$-0.965814\pi$
$523$	−6.24419	+	13.3907i	−0.273039	+	0.585535i	0.721199	+	0.692728i	$0.243591\pi$
$524$	−9.66736	−	9.66736i	−0.422321	−	0.422321i
$525$		0			0
$526$	10.3593	+	2.77577i	0.451687	+	0.121029i
$527$	−10.3402	+	1.82326i	−0.450426	+	0.0794223i
$528$		0			0
$529$	1.97676	−	1.14128i	0.0859461	−	0.0496210i
$530$	−10.3791	−	12.3694i	−0.450841	−	0.537291i
$531$		0			0
$532$	−2.75687	+	0.738700i	−0.119525	+	0.0320267i
$533$	−21.9862	+	10.2524i	−0.952330	+	0.444079i
$534$		0			0
$535$	42.2524	+	29.5854i	1.82673	+	1.27909i
$536$	−5.82114	+	0.509284i	−0.251435	+	0.0219977i
$537$		0			0
$538$	8.43503	−	12.0465i	0.363660	−	0.519360i
$539$	−3.06615	−	1.11599i	−0.132069	−	0.0480690i
$540$		0			0
$541$	−7.38298	−	27.5537i	−0.317419	−	1.18462i	−0.921716	−	0.387865i	$-0.873213\pi$
$541$	−7.38298	−	27.5537i	−0.317419	−	1.18462i	0.604297	−	0.796759i	$-0.293454\pi$
$542$	−11.2933	−	16.1285i	−0.485089	−	0.692779i
$543$		0			0
$544$	0.672489	+	1.16479i	0.0288327	+	0.0499398i
$545$	−17.5218	+	30.3486i	−0.750551	+	1.29999i
$546$		0			0
$547$	−8.29393	+	30.9534i	−0.354623	+	1.32347i	0.526335	+	0.850277i	$0.323566\pi$
$547$	−8.29393	+	30.9534i	−0.354623	+	1.32347i	−0.880958	+	0.473194i	$0.843101\pi$
$548$	19.3051	−	7.02648i	0.824673	−	0.300156i
$549$		0			0
$550$	4.61370	+	2.15141i	0.196729	+	0.0917362i
$551$	5.23751	+	0.923514i	0.223125	+	0.0393430i
$552$		0			0
$553$	−1.31785	+	15.0631i	−0.0560407	+	0.640548i
$554$	−4.15168			−0.176388
$555$		0			0
$556$	−12.3855			−0.525263
$557$	2.44565	−	27.9540i	0.103626	−	1.18445i	−0.749233	−	0.662306i	$-0.769578\pi$
$557$	2.44565	−	27.9540i	0.103626	−	1.18445i	0.852859	−	0.522141i	$-0.174867\pi$
$558$		0			0
$559$	−68.5223	−	12.0823i	−2.89818	−	0.511028i
$560$	5.26837	+	2.45668i	0.222629	+	0.103814i
$561$		0			0
$562$	−7.55497	+	2.74978i	−0.318687	+	0.115993i
$563$	1.80695	−	6.74362i	0.0761538	−	0.284210i	−0.917339	−	0.398108i	$-0.869667\pi$
$563$	1.80695	−	6.74362i	0.0761538	−	0.284210i	0.993492	+	0.113898i	$0.0363337\pi$
$564$		0			0
$565$	3.42479	−	5.93191i	0.144082	−	0.249557i
$566$	10.5705	+	18.3087i	0.444313	+	0.769572i
$567$		0			0
$568$	−6.61857	−	9.45230i	−0.277709	−	0.396610i
$569$	9.55065	+	35.6435i	0.400384	+	1.49425i	0.812413	+	0.583083i	$0.198154\pi$
$569$	9.55065	+	35.6435i	0.400384	+	1.49425i	−0.412028	+	0.911171i	$0.635180\pi$
$570$		0			0
$571$	14.9607	+	5.44523i	0.626084	+	0.227876i	0.635526	−	0.772079i	$-0.280783\pi$
$571$	14.9607	+	5.44523i	0.626084	+	0.227876i	−0.00944192	+	0.999955i	$0.503006\pi$
$572$	3.12704	−	4.46587i	0.130748	−	0.186728i
$573$		0			0
$574$	−6.29071	+	0.550366i	−0.262569	+	0.0229718i
$575$	25.6361	+	17.9506i	1.06910	+	0.748591i
$576$		0			0
$577$	23.2050	−	10.8207i	0.966035	−	0.450470i	0.125421	−	0.992104i	$-0.459972\pi$
$577$	23.2050	−	10.8207i	0.966035	−	0.450470i	0.840614	+	0.541634i	$0.182194\pi$
$578$	14.6734	−	3.93173i	0.610333	−	0.163538i
$579$		0			0
$580$	−6.96256	−	8.29765i	−0.289105	−	0.344541i
$581$	−13.4291	+	7.75327i	−0.557131	+	0.321660i
$582$		0			0
$583$	−3.88210	+	0.684519i	−0.160780	+	0.0283499i
$584$	−6.56051	−	1.75788i	−0.271476	−	0.0727417i
$585$		0			0
$586$	20.9667	+	20.9667i	0.866127	+	0.866127i
$587$	1.66266	−	3.56560i	0.0686255	−	0.147168i	−0.869003	−	0.494807i	$-0.835239\pi$
$587$	1.66266	−	3.56560i	0.0686255	−	0.147168i	0.937628	+	0.347639i	$0.113017\pi$
$588$		0			0
$589$	−9.83702	−	8.25424i	−0.405328	−	0.340110i
$590$	−25.3570	−	2.21845i	−1.04393	−	0.0913323i
$591$		0			0
$592$	5.42111	−	2.75890i	0.222806	−	0.113390i
$593$		−	48.1508i		−	1.97732i	−0.150186	−	0.988658i	$-0.547987\pi$
$593$		−	48.1508i		−	1.97732i	0.150186	−	0.988658i	$-0.452013\pi$
$594$		0			0
$595$	−5.02555	+	5.98921i	−0.206027	+	0.245534i
$596$	3.37190	−	19.1230i	0.138118	−	0.783308i
$597$		0			0
$598$	23.6996	−	23.6996i	0.969147	−	0.969147i
$599$	12.6466	+	34.7463i	0.516726	+	1.41969i	0.874106	+	0.485734i	$0.161448\pi$
$599$	12.6466	+	34.7463i	0.516726	+	1.41969i	−0.357380	+	0.933959i	$0.616330\pi$
$600$		0			0
$601$	1.37685	+	7.80848i	0.0561627	+	0.318514i	0.999927	−	0.0121053i	$-0.00385335\pi$
$601$	1.37685	+	7.80848i	0.0561627	+	0.318514i	−0.943764	+	0.330620i	$0.892742\pi$
$602$	−15.6852	−	9.05587i	−0.639282	−	0.369090i
$603$		0			0
$604$	−15.0668	+	12.6426i	−0.613060	+	0.514419i
$605$	−28.3521	+	19.8523i	−1.15268	+	0.807112i
$606$		0			0
$607$	7.35163	+	15.7656i	0.298394	+	0.639907i	0.997149	−	0.0754532i	$-0.0240404\pi$
$607$	7.35163	+	15.7656i	0.298394	+	0.639907i	−0.698756	+	0.715360i	$0.746263\pi$
$608$	−0.562599	+	1.54573i	−0.0228164	+	0.0626876i
$609$		0			0
$610$	−3.42827	−	39.1853i	−0.138807	−	1.58657i
$611$	−1.81123	−	20.7024i	−0.0732744	−	0.837530i
$612$		0			0
$613$	−11.8053	+	32.4349i	−0.476812	+	1.31003i	0.435372	+	0.900251i	$0.356617\pi$
$613$	−11.8053	+	32.4349i	−0.476812	+	1.31003i	−0.912184	+	0.409781i	$0.865605\pi$
$614$	0.427928	+	0.917694i	0.0172698	+	0.0370351i
$615$		0			0
$616$	1.16248	−	0.813979i	0.0468378	−	0.0327962i
$617$	−5.88742	+	4.94013i	−0.237018	+	0.198882i	−0.753558	−	0.657381i	$-0.771664\pi$
$617$	−5.88742	+	4.94013i	−0.237018	+	0.198882i	0.516540	+	0.856263i	$0.327220\pi$
$618$		0			0
$619$	−28.1737	−	16.2661i	−1.13240	−	0.653790i	−0.187860	−	0.982196i	$-0.560155\pi$
$619$	−28.1737	−	16.2661i	−1.13240	−	0.653790i	−0.944537	+	0.328406i	$0.893489\pi$
$620$	4.54159	+	25.7567i	0.182395	+	1.03441i
$621$		0			0
$622$	−7.60775	−	20.9021i	−0.305043	−	0.838099i
$623$	5.53056	−	5.53056i	0.221577	−	0.221577i
$624$		0			0
$625$	3.01819	−	17.1170i	0.120728	−	0.684681i
$626$	0.195032	−	0.232430i	0.00779503	−	0.00928975i
$627$		0			0
$628$			4.21012i			0.168002i
$629$	1.69711	+	8.00323i	0.0676681	+	0.319110i
$630$		0			0
$631$	−45.5685	−	3.98673i	−1.81405	−	0.158709i	−0.870986	−	0.491308i	$-0.836519\pi$
$631$	−45.5685	−	3.98673i	−1.81405	−	0.158709i	−0.943068	+	0.332599i	$0.892074\pi$
$632$	6.67574	+	5.60161i	0.265547	+	0.222820i
$633$		0			0
$634$	2.04621	−	4.38811i	0.0812654	−	0.174274i
$635$	−35.5032	−	35.5032i	−1.40890	−	1.40890i
$636$		0			0
$637$	−25.6861	−	6.88258i	−1.01772	−	0.272698i
$638$	−2.60420	+	0.459191i	−0.103101	+	0.0181795i
$639$		0			0
$640$	2.90139	−	1.67512i	0.114688	−	0.0662149i
$641$	−11.9478	−	14.2389i	−0.471912	−	0.562402i	0.476610	−	0.879115i	$-0.341865\pi$
$641$	−11.9478	−	14.2389i	−0.471912	−	0.562402i	−0.948522	+	0.316712i	$0.897421\pi$
$642$		0			0
$643$	−3.08212	+	0.825851i	−0.121547	+	0.0325684i	−0.319080	−	0.947728i	$-0.603374\pi$
$643$	−3.08212	+	0.825851i	−0.121547	+	0.0325684i	0.197533	+	0.980296i	$0.436707\pi$
$644$	7.90698	−	3.68709i	0.311579	−	0.145292i
$645$		0			0
$646$	−1.81229	−	1.26898i	−0.0713036	−	0.0499273i
$647$	−26.5704	+	2.32461i	−1.04459	+	0.0913897i	−0.596511	−	0.802605i	$-0.703447\pi$
$647$	−26.5704	+	2.32461i	−1.04459	+	0.0913897i	−0.448078	+	0.893994i	$0.647891\pi$
$648$		0			0
$649$	−3.56424	+	5.09027i	−0.139909	+	0.199810i
$650$	38.9859	+	14.1897i	1.52915	+	0.556565i
$651$		0			0
$652$	5.38837	+	20.1097i	0.211025	+	0.787556i
$653$	4.16408	+	5.94692i	0.162953	+	0.232721i	0.892322	−	0.451400i	$-0.149075\pi$
$653$	4.16408	+	5.94692i	0.162953	+	0.232721i	−0.729369	+	0.684121i	$0.760186\pi$
$654$		0			0
$655$	−22.9018	−	39.6670i	−0.894846	−	1.54992i
$656$	−1.81970	+	3.15182i	−0.0710475	+	0.123058i
$657$		0			0
$658$	1.40008	−	5.22517i	0.0545808	−	0.203698i
$659$	32.3747	−	11.7834i	1.26114	−	0.459018i	0.376989	−	0.926218i	$-0.376960\pi$
$659$	32.3747	−	11.7834i	1.26114	−	0.459018i	0.884151	+	0.467200i	$0.154737\pi$
$660$		0			0
$661$	−33.1559	−	15.4608i	−1.28961	−	0.601357i	−0.347825	−	0.937560i	$-0.613080\pi$
$661$	−33.1559	−	15.4608i	−1.28961	−	0.601357i	−0.941790	+	0.336203i	$0.890857\pi$
$662$	0.730033	+	0.128724i	0.0283735	+	0.00500302i
$663$		0			0
$664$	−0.778908	+	8.90296i	−0.0302275	+	0.345502i
$665$	−9.56198			−0.370798
$666$		0			0
$667$	−16.2568			−0.629467
$668$	−0.789044	+	9.01881i	−0.0305290	+	0.348948i
$669$		0			0
$670$	−19.2793	−	3.39946i	−0.744824	−	0.131333i
$671$	−8.70315	−	4.05835i	−0.335981	−	0.156671i
$672$		0			0
$673$	37.0570	−	13.4876i	1.42844	−	0.519910i	0.491957	−	0.870619i	$-0.336282\pi$
$673$	37.0570	−	13.4876i	1.42844	−	0.519910i	0.936485	+	0.350709i	$0.114059\pi$
$674$	2.25540	−	8.41725i	0.0868746	−	0.324220i
$675$		0			0
$676$	15.7157	−	27.2203i	0.604448	−	1.04694i
$677$	−21.1366	−	36.6096i	−0.812344	−	1.40702i	−0.911220	−	0.411921i	$-0.864858\pi$
$677$	−21.1366	−	36.6096i	−0.812344	−	1.40702i	0.0988759	−	0.995100i	$-0.468475\pi$
$678$		0			0
$679$	8.90173	+	12.7130i	0.341617	+	0.487880i
$680$	1.16624	+	4.35246i	0.0447232	+	0.166909i
$681$		0			0
$682$	5.99992	+	2.18379i	0.229749	+	0.0836217i
$683$	5.32225	−	7.60097i	0.203650	−	0.290843i	−0.704315	−	0.709887i	$-0.748746\pi$
$683$	5.32225	−	7.60097i	0.203650	−	0.290843i	0.907966	+	0.419044i	$0.137635\pi$
$684$		0			0
$685$	68.5656	−	5.99871i	2.61976	−	0.229199i
$686$	−15.6194	−	10.9368i	−0.596351	−	0.417570i
$687$		0			0
$688$	−9.46044	+	4.41148i	−0.360676	+	0.168186i
$689$	−31.0317	+	8.31493i	−1.18221	+	0.316773i
$690$		0			0
$691$	8.66544	+	10.3271i	0.329649	+	0.392860i	0.905256	−	0.424866i	$-0.139679\pi$
$691$	8.66544	+	10.3271i	0.329649	+	0.392860i	−0.575608	+	0.817726i	$0.695234\pi$
$692$	−9.96125	+	5.75113i	−0.378670	+	0.218625i
$693$		0			0
$694$	7.00503	−	1.23518i	0.265907	−	0.0468866i
$695$	−40.0806	−	10.7396i	−1.52034	−	0.407374i
$696$		0			0
$697$	−3.46124	−	3.46124i	−0.131104	−	0.131104i
$698$	8.86941	−	19.0205i	0.335712	−	0.719937i
$699$		0			0
$700$	8.27285	+	6.94174i	0.312684	+	0.262373i
$701$	17.4580	+	1.52738i	0.659381	+	0.0576884i	0.411935	−	0.911213i	$-0.364853\pi$
$701$	17.4580	+	1.52738i	0.659381	+	0.0576884i	0.247446	+	0.968902i	$0.420409\pi$
$702$		0			0
$703$	−6.16394	+	7.88165i	−0.232477	+	0.297262i
$704$		−	0.817895i		−	0.0308256i
$705$		0			0
$706$	−15.3106	+	18.2465i	−0.576222	+	0.686715i
$707$	0.127064	−	0.720615i	0.00477873	−	0.0271015i
$708$		0			0
$709$	11.5743	−	11.5743i	0.434682	−	0.434682i	−0.455536	−	0.890217i	$-0.650552\pi$
$709$	11.5743	−	11.5743i	0.434682	−	0.434682i	0.890217	+	0.455536i	$0.150552\pi$
$710$	−13.2221	−	36.3274i	−0.496216	−	1.36334i
$711$		0			0
$712$	−0.782762	−	4.43926i	−0.0293352	−	0.166368i
$713$	33.9941	+	19.6265i	1.27309	+	0.735018i
$714$		0			0
$715$	13.9917	−	11.7405i	0.523261	−	0.439068i
$716$	14.0839	−	9.86165i	0.526340	−	0.368547i
$717$		0			0
$718$	−10.5740	−	22.6760i	−0.394618	−	0.846262i
$719$	0.0849192	−	0.233314i	0.00316695	−	0.00870113i	−0.938099	−	0.346367i	$-0.887415\pi$
$719$	0.0849192	−	0.233314i	0.00316695	−	0.00870113i	0.941266	+	0.337666i	$0.109637\pi$
$720$		0			0
$721$	0.935004	+	10.6871i	0.0348214	+	0.398010i
$722$	1.42013	+	16.2322i	0.0528519	+	0.604100i
$723$		0			0
$724$	6.55755	−	18.0167i	0.243710	−	0.669586i
$725$	−8.50453	−	18.2380i	−0.315850	−	0.677343i
$726$		0			0
$727$	22.6187	−	15.8378i	0.838882	−	0.587392i	−0.0732381	−	0.997314i	$-0.523333\pi$
$727$	22.6187	−	15.8378i	0.838882	−	0.587392i	0.912120	+	0.409923i	$0.134444\pi$
$728$	8.85978	−	7.43424i	0.328365	−	0.275531i
$729$		0			0
$730$	−19.7061	−	11.3773i	−0.729354	−	0.421093i
$731$	−2.43793	−	13.8262i	−0.0901701	−	0.511380i
$732$		0			0
$733$	17.1150	+	47.0230i	0.632156	+	1.73683i	0.675069	+	0.737754i	$0.264114\pi$
$733$	17.1150	+	47.0230i	0.632156	+	1.73683i	−0.0429139	+	0.999079i	$0.513664\pi$
$734$	3.77911	−	3.77911i	0.139489	−	0.139489i
$735$		0			0
$736$	0.873134	−	4.95179i	0.0321841	−	0.182525i
$737$	−3.07205	+	3.66113i	−0.113161	+	0.134860i
$738$		0			0
$739$			9.81171i			0.360930i	0.983581	+	0.180465i	$0.0577602\pi$
$739$			9.81171i			0.360930i	−0.983581	+	0.180465i	$0.942240\pi$
$740$	19.9354	−	4.22737i	0.732841	−	0.155401i
$741$		0			0
$742$	−8.33079	−	0.728850i	−0.305833	−	0.0267569i
$743$	−8.68448	−	7.28714i	−0.318603	−	0.267339i	0.469434	−	0.882967i	$-0.344458\pi$
$743$	−8.68448	−	7.28714i	−0.318603	−	0.267339i	−0.788037	+	0.615628i	$0.788902\pi$
$744$		0			0
$745$	27.4934	−	58.9598i	1.00728	−	2.16012i
$746$	19.8126	+	19.8126i	0.725391	+	0.725391i
$747$		0			0
$748$	1.06257	+	0.284714i	0.0388513	+	0.0104102i
$749$	26.3079	−	4.63880i	0.961271	−	0.169498i
$750$		0			0
$751$	9.74676	−	5.62729i	0.355664	−	0.205343i	−0.311513	−	0.950242i	$-0.600836\pi$
$751$	9.74676	−	5.62729i	0.355664	−	0.205343i	0.667177	+	0.744899i	$0.267502\pi$
$752$	−2.00401	−	2.38828i	−0.0730787	−	0.0870918i
$753$		0			0
$754$	−20.8168	+	5.57784i	−0.758103	+	0.203133i
$755$	−59.7199	+	27.8478i	−2.17343	+	1.01349i
$756$		0			0
$757$	−36.7598	−	25.7395i	−1.33606	−	0.935519i	−0.336079	−	0.941834i	$-0.609101\pi$
$757$	−36.7598	−	25.7395i	−1.33606	−	0.935519i	−0.999980	+	0.00631526i	$0.997990\pi$
$758$	22.3488	−	1.95527i	0.811744	−	0.0710184i
$759$		0			0
$760$	−3.16093	+	4.51427i	−0.114659	+	0.163750i
$761$	43.7804	+	15.9348i	1.58704	+	0.577635i	0.976719	−	0.214521i	$-0.0688190\pi$
$761$	43.7804	+	15.9348i	1.58704	+	0.577635i	0.610319	+	0.792156i	$0.291041\pi$
$762$		0			0
$763$	4.69736	+	17.5308i	0.170056	+	0.634657i
$764$	0.488559	+	0.697735i	0.0176755	+	0.0252432i
$765$		0			0
$766$	−15.7441	−	27.2696i	−0.568858	−	0.985291i
$767$	−25.3217	+	43.8585i	−0.914314	+	1.58364i
$768$		0			0
$769$	−6.23702	+	23.2769i	−0.224913	+	0.839385i	0.757527	+	0.652804i	$0.226407\pi$
$769$	−6.23702	+	23.2769i	−0.224913	+	0.839385i	−0.982439	+	0.186581i	$0.940259\pi$
$770$	4.46770	−	1.62611i	0.161005	−	0.0586009i
$771$		0			0
$772$	11.0695	+	5.16177i	0.398398	+	0.185776i
$773$	−19.9357	−	3.51520i	−0.717036	−	0.126433i	−0.196786	−	0.980447i	$-0.563050\pi$
$773$	−19.9357	−	3.51520i	−0.717036	−	0.126433i	−0.520250	+	0.854014i	$0.674161\pi$
$774$		0			0
$775$	−4.23482	+	48.4042i	−0.152119	+	1.73873i
$776$	8.94455			0.321091
$777$		0			0
$778$	−25.0415			−0.897781
$779$	0.521764	−	5.96379i	0.0186941	−	0.213675i
$780$		0			0
$781$	−9.29441	−	1.63885i	−0.332580	−	0.0586428i
$782$	6.12917	+	2.85808i	0.219179	+	0.102205i
$783$		0			0
$784$	−3.74884	+	1.36446i	−0.133887	+	0.0487309i

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:	\( N \)	\(=\)	\( 666 = 2 \cdot 3^{2} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	666.bs (of order \(36\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(0.0871557 - 0.996195i) q^{2} +(-0.984808 - 0.173648i) q^{4} +(-3.03635 - 1.41587i) q^{5} +(-1.63046 + 0.593439i) q^{7} +(-0.258819 + 0.965926i) q^{8} +O(q^{10})\)	\(q+(0.0871557 - 0.996195i) q^{2} +(-0.984808 - 0.173648i) q^{4} +(-3.03635 - 1.41587i) q^{5} +(-1.63046 + 0.593439i) q^{7} +(-0.258819 + 0.965926i) q^{8} +(-1.67512 + 2.90139i) q^{10} +(0.408947 + 0.708318i) q^{11} +(3.82328 + 5.46021i) q^{13} +(0.449077 + 1.67598i) q^{14} +(0.939693 + 0.342020i) q^{16} +(-0.771448 + 1.10174i) q^{17} +(-1.63867 + 0.143365i) q^{19} +(2.74436 + 1.92162i) q^{20} +(0.741264 - 0.345657i) q^{22} +(4.85685 - 1.30139i) q^{23} +(4.00077 + 4.76794i) q^{25} +(5.77265 - 3.33284i) q^{26} +(1.70874 - 0.301297i) q^{28} +(-3.12298 - 0.836800i) q^{29} +(5.52010 + 5.52010i) q^{31} +(0.422618 - 0.906308i) q^{32} +(1.03031 + 0.864536i) q^{34} +(5.79088 + 0.506636i) q^{35} +(4.15058 - 4.44665i) q^{37} +1.64493i q^{38} +(2.15349 - 2.56643i) q^{40} +(-0.631977 + 3.58412i) q^{41} +(-7.38109 + 7.38109i) q^{43} +(-0.279736 - 0.768570i) q^{44} +(-0.873134 - 4.95179i) q^{46} +(-2.69999 - 1.55884i) q^{47} +(-3.05608 + 2.56435i) q^{49} +(5.09848 - 3.57000i) q^{50} +(-2.81704 - 6.04116i) q^{52} +(-1.64843 + 4.52901i) q^{53} +(-0.238819 - 2.72972i) q^{55} +(-0.151224 - 1.72850i) q^{56} +(-1.10580 + 3.03817i) q^{58} +(3.21090 + 6.88580i) q^{59} +(-9.61763 + 6.73434i) q^{61} +(5.98021 - 5.01799i) q^{62} +(-0.866025 - 0.500000i) q^{64} +(-3.87785 - 21.9924i) q^{65} +(1.99855 + 5.49098i) q^{67} +(0.951044 - 0.951044i) q^{68} +(1.00942 - 5.72469i) q^{70} +(-7.41721 + 8.83948i) q^{71} +6.79194i q^{73} +(-4.06798 - 4.52233i) q^{74} +(1.63867 + 0.143365i) q^{76} +(-1.08712 - 0.912199i) q^{77} +(3.68293 - 7.89808i) q^{79} +(-2.36898 - 2.36898i) q^{80} +(3.51540 + 0.941948i) q^{82} +(8.80119 - 1.55189i) q^{83} +(3.90231 - 2.25300i) q^{85} +(6.70970 + 7.99631i) q^{86} +(-0.790026 + 0.211687i) q^{88} +(-4.08541 + 1.90506i) q^{89} +(-9.47401 - 6.63377i) q^{91} +(-5.00904 + 0.438235i) q^{92} +(-1.78823 + 2.55386i) q^{94} +(5.17856 + 1.88484i) q^{95} +(-2.31502 - 8.63977i) q^{97} +(2.28824 + 3.26795i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q+O(q^{10}) \) 96 * q	\( 96 q - 12 q^{13} + 24 q^{19} + 12 q^{22} + 48 q^{31} + 72 q^{34} + 24 q^{37} + 72 q^{43} + 60 q^{46} + 12 q^{52} - 60 q^{55} + 12 q^{58} - 120 q^{61} + 36 q^{67} + 12 q^{70} - 24 q^{76} + 60 q^{79} + 96 q^{82} - 108 q^{85} - 24 q^{88} + 216 q^{91} - 60 q^{94} + 24 q^{97}+O(q^{100}) \) 96 * q - 12 * q^13 + 24 * q^19 + 12 * q^22 + 48 * q^31 + 72 * q^34 + 24 * q^37 + 72 * q^43 + 60 * q^46 + 12 * q^52 - 60 * q^55 + 12 * q^58 - 120 * q^61 + 36 * q^67 + 12 * q^70 - 24 * q^76 + 60 * q^79 + 96 * q^82 - 108 * q^85 - 24 * q^88 + 216 * q^91 - 60 * q^94 + 24 * q^97

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