LMFDB - Embedded newform 666.2.bs.b.611.4

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			611.4
Character	$\chi$	$=$	666.611
Dual form			666.2.bs.b.557.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.0871557 - 0.996195i) q^{2} +(-0.984808 + 0.173648i) q^{4} +(3.03635 - 1.41587i) q^{5} +(-1.63046 - 0.593439i) q^{7} +(0.258819 + 0.965926i) q^{8} +O(q^{10})$	\(q+(-0.0871557 - 0.996195i) q^{2} +(-0.984808 + 0.173648i) q^{4} +(3.03635 - 1.41587i) q^{5} +(-1.63046 - 0.593439i) q^{7} +(0.258819 + 0.965926i) q^{8} +(-1.67512 - 2.90139i) q^{10} +(-0.408947 + 0.708318i) q^{11} +(3.82328 - 5.46021i) q^{13} +(-0.449077 + 1.67598i) q^{14} +(0.939693 - 0.342020i) q^{16} +(0.771448 + 1.10174i) q^{17} +(-1.63867 - 0.143365i) q^{19} +(-2.74436 + 1.92162i) q^{20} +(0.741264 + 0.345657i) q^{22} +(-4.85685 - 1.30139i) q^{23} +(4.00077 - 4.76794i) q^{25} +(-5.77265 - 3.33284i) q^{26} +(1.70874 + 0.301297i) q^{28} +(3.12298 - 0.836800i) q^{29} +(5.52010 - 5.52010i) q^{31} +(-0.422618 - 0.906308i) q^{32} +(1.03031 - 0.864536i) q^{34} +(-5.79088 + 0.506636i) q^{35} +(4.15058 + 4.44665i) q^{37} +1.64493i q^{38} +(2.15349 + 2.56643i) q^{40} +(0.631977 + 3.58412i) q^{41} +(-7.38109 - 7.38109i) q^{43} +(0.279736 - 0.768570i) q^{44} +(-0.873134 + 4.95179i) q^{46} +(2.69999 - 1.55884i) q^{47} +(-3.05608 - 2.56435i) q^{49} +(-5.09848 - 3.57000i) q^{50} +(-2.81704 + 6.04116i) q^{52} +(1.64843 + 4.52901i) q^{53} +(-0.238819 + 2.72972i) q^{55} +(0.151224 - 1.72850i) q^{56} +(-1.10580 - 3.03817i) q^{58} +(-3.21090 + 6.88580i) q^{59} +(-9.61763 - 6.73434i) q^{61} +(-5.98021 - 5.01799i) q^{62} +(-0.866025 + 0.500000i) q^{64} +(3.87785 - 21.9924i) q^{65} +(1.99855 - 5.49098i) q^{67} +(-0.951044 - 0.951044i) q^{68} +(1.00942 + 5.72469i) q^{70} +(7.41721 + 8.83948i) q^{71} -6.79194i q^{73} +(4.06798 - 4.52233i) q^{74} +(1.63867 - 0.143365i) q^{76} +(1.08712 - 0.912199i) q^{77} +(3.68293 + 7.89808i) q^{79} +(2.36898 - 2.36898i) q^{80} +(3.51540 - 0.941948i) q^{82} +(-8.80119 - 1.55189i) q^{83} +(3.90231 + 2.25300i) q^{85} +(-6.70970 + 7.99631i) q^{86} +(-0.790026 - 0.211687i) q^{88} +(4.08541 + 1.90506i) q^{89} +(-9.47401 + 6.63377i) q^{91} +(5.00904 + 0.438235i) q^{92} +(-1.78823 - 2.55386i) q^{94} +(-5.17856 + 1.88484i) q^{95} +(-2.31502 + 8.63977i) q^{97} +(-2.28824 + 3.26795i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/666\mathbb{Z}\right)^\times$.

$n$	$371$	$631$
$\chi(n)$	$-1$	$e\left(\frac{35}{36}\right)$

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	$-0.369358\pi$
$5$	3.03635	−	1.41587i	1.35790	−	0.633197i	0.958897	+	0.283754i	$0.0915800\pi$
$6$		0			0
$7$	−1.63046	−	0.593439i	−0.616256	−	0.224299i	0.0149822	−	0.999888i	$-0.495231\pi$
$7$	−1.63046	−	0.593439i	−0.616256	−	0.224299i	−0.631238	+	0.775589i	$0.717453\pi$
$8$	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	$-0.872682\pi$
$11$	−0.408947	+	0.708318i	−0.123302	+	0.213566i	0.797766	+	0.602967i	$0.206015\pi$
$12$		0			0
$13$	3.82328	−	5.46021i	1.06039	−	1.51439i	0.217677	−	0.976021i	$-0.430152\pi$
$13$	3.82328	−	5.46021i	1.06039	−	1.51439i	0.842710	−	0.538368i	$-0.180959\pi$
$14$	−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	$-0.142294\pi$
$17$	0.771448	+	1.10174i	0.187104	+	0.267212i	−0.714631	+	0.699502i	$0.753405\pi$
$18$		0			0
$19$	−1.63867	−	0.143365i	−0.375937	−	0.0328902i	−0.102378	−	0.994746i	$-0.532645\pi$
$19$	−1.63867	−	0.143365i	−0.375937	−	0.0328902i	−0.273559	+	0.961855i	$0.588201\pi$
$20$	−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	$-0.592311\pi$
$23$	−4.85685	−	1.30139i	−1.01272	−	0.271358i	−0.726766	+	0.686885i	$0.758978\pi$
$24$		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	$-0.486283\pi$
$29$	3.12298	−	0.836800i	0.579923	−	0.155390i	0.536844	+	0.843682i	$0.319616\pi$
$30$		0			0
$31$	5.52010	−	5.52010i	0.991440	−	0.991440i	−0.00852369	−	0.999964i	$-0.502713\pi$
$31$	5.52010	−	5.52010i	0.991440	−	0.991440i	0.999964	+	0.00852369i	$0.00271321\pi$
$32$	−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	0.993551	+	0.113384i	$0.0361691\pi$
$41$	0.631977	+	3.58412i	0.0986982	+	0.559745i	−0.894853	+	0.446361i	$0.852720\pi$
$42$		0			0
$43$	−7.38109	−	7.38109i	−1.12561	−	1.12561i	−0.990883	−	0.134723i	$-0.956986\pi$
$43$	−7.38109	−	7.38109i	−1.12561	−	1.12561i	−0.134723	−	0.990883i	$-0.543014\pi$
$44$	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	$-0.593651\pi$
$47$	2.69999	−	1.55884i	0.393834	−	0.227380i	0.683820	+	0.729651i	$0.260317\pi$
$48$		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	$-0.00371952\pi$
$53$	1.64843	+	4.52901i	0.226429	+	0.622108i	−0.773503	+	0.633793i	$0.781497\pi$
$54$		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	0.578698	+	0.815542i	$0.303561\pi$
$59$	−3.21090	+	6.88580i	−0.418024	+	0.896454i	−0.996721	+	0.0809123i	$0.974217\pi$
$60$		0			0
$61$	−9.61763	−	6.73434i	−1.23141	−	0.862243i	−0.237388	−	0.971415i	$-0.576291\pi$
$61$	−9.61763	−	6.73434i	−1.23141	−	0.862243i	−0.994023	+	0.109171i	$0.965180\pi$
$62$	−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	−0.755711	−	0.654905i	$-0.772709\pi$
$67$	1.99855	−	5.49098i	0.244162	−	0.670830i	0.999873	−	0.0159247i	$-0.00506921\pi$
$68$	−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	0.998427	+	0.0560597i	$0.0178537\pi$
$71$	7.41721	+	8.83948i	0.880260	+	1.04905i	−0.118167	+	0.992994i	$0.537702\pi$
$72$		0			0
$73$		−	6.79194i		−	0.794936i	−0.917616	−	0.397468i	$-0.869889\pi$
$73$		−	6.79194i		−	0.794936i	0.917616	−	0.397468i	$-0.130111\pi$
$74$	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	0.997112	+	0.0759511i	$0.0241993\pi$
$79$	3.68293	+	7.89808i	0.414363	+	0.888603i	−0.582749	+	0.812652i	$0.698023\pi$
$80$	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	$-0.607623\pi$
$83$	−8.80119	−	1.55189i	−0.966057	−	0.170342i	−0.634354	+	0.773042i	$0.718734\pi$
$84$		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	$-0.284321\pi$
$89$	4.08541	+	1.90506i	0.433052	+	0.201936i	−0.193854	+	0.981030i	$0.562099\pi$
$90$		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	0.743070	+	0.669214i	$0.233369\pi$
$97$	−2.31502	+	8.63977i	−0.235055	+	0.877236i	−0.978124	+	0.208022i	$0.933298\pi$
$98$	−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	$-0.159988\pi$
$101$	0.210861	+	0.365223i	0.0209815	+	0.0363410i	−0.855344	+	0.518060i	$0.826654\pi$
$102$		0			0
$103$	1.60026	+	5.97223i	0.157678	+	0.588462i	0.998861	+	0.0477116i	$0.0151929\pi$
$103$	1.60026	+	5.97223i	0.157678	+	0.588462i	−0.841183	+	0.540750i	$0.818140\pi$
$104$	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	$-0.288387\pi$
$107$	15.1622	−	2.67351i	1.46579	−	0.258458i	0.848882	+	0.528582i	$0.177276\pi$
$108$		0			0
$109$	0.911651	+	10.4202i	0.0873204	+	0.998076i	0.905846	+	0.423607i	$0.139236\pi$
$109$	0.911651	+	10.4202i	0.0873204	+	0.998076i	−0.818526	+	0.574470i	$0.805208\pi$
$110$	2.74014			0.261262
$111$		0			0
$112$	−1.73510			−0.163952
$113$	0.178190	+	2.03672i	0.0167627	+	0.191599i	0.999959	+	0.00904765i	$0.00287999\pi$
$113$	0.178190	+	2.03672i	0.0167627	+	0.191599i	−0.983196	+	0.182551i	$0.941564\pi$
$114$		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	0.369371	−	0.929282i	$-0.379573\pi$
$127$	14.0829	−	5.12576i	1.24966	−	0.454838i	0.880285	+	0.474445i	$0.157351\pi$
$128$	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	$-0.898185\pi$
$131$	−11.1992	+	7.84177i	−0.978480	+	0.685139i	−0.0292006	+	0.999574i	$0.509296\pi$
$132$		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	0.999721	+	0.0236291i	$0.00752207\pi$
$137$	17.7917	+	10.2720i	1.52004	+	0.877598i	0.520324	+	0.853969i	$0.325811\pi$
$138$		0			0
$139$	12.1974	+	2.15072i	1.03457	+	0.182422i	0.665047	−	0.746801i	$-0.268411\pi$
$139$	12.1974	+	2.15072i	1.03457	+	0.182422i	0.369519	+	0.929223i	$0.379523\pi$
$140$	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	0.973746	+	0.227639i	$0.0731006\pi$
$151$	12.6426	+	15.0668i	1.02884	+	1.22612i	0.0550915	+	0.998481i	$0.482455\pi$
$152$	−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	−0.999984	−	0.00573047i	$-0.998176\pi$
$157$	−0.731079	+	4.14615i	−0.0583465	+	0.330899i	0.941637	+	0.336630i	$0.109287\pi$
$158$	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	0.180163	+	0.983637i	$0.442337\pi$
$163$	−8.79852	+	18.8685i	−0.689153	+	1.47789i	−0.869316	+	0.494257i	$0.835440\pi$
$164$	−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	−0.902551	−	0.430582i	$-0.858308\pi$
$167$	0.789044	−	9.01881i	0.0610581	−	0.697897i	0.963609	−	0.267314i	$-0.0861362\pi$
$168$		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	$-0.421825\pi$
$173$	−8.81124	−	7.39351i	−0.669906	−	0.562118i	−0.913038	+	0.407875i	$0.866270\pi$
$174$		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	$-0.0278797\pi$
$179$	12.1575	+	12.1575i	0.908692	+	0.908692i	−0.0874747	+	0.996167i	$0.527880\pi$
$180$		0			0
$181$	−3.32936	−	18.8817i	−0.247469	−	1.40347i	−0.814688	−	0.579900i	$-0.803092\pi$
$181$	−3.32936	−	18.8817i	−0.247469	−	1.40347i	0.567219	−	0.823567i	$-0.308019\pi$
$182$	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	$-0.740189\pi$
$191$	0.602298	−	0.602298i	0.0435807	−	0.0435807i	0.728561	+	0.684981i	$0.240189\pi$
$192$		0			0
$193$	−11.7976	+	3.16116i	−0.849211	+	0.227545i	−0.657077	−	0.753823i	$-0.728207\pi$
$193$	−11.7976	+	3.16116i	−0.849211	+	0.227545i	−0.192134	+	0.981369i	$0.561541\pi$
$194$	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	$-0.583469\pi$
$197$	10.3433	−	12.3266i	0.736927	−	0.878236i	0.996158	+	0.0875797i	$0.0279133\pi$
$198$		0			0
$199$	1.01938	+	0.273141i	0.0722617	+	0.0193625i	0.294769	−	0.955569i	$-0.404757\pi$
$199$	1.01938	+	0.273141i	0.0722617	+	0.0193625i	−0.222507	+	0.974931i	$0.571424\pi$
$200$	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	−0.927355	−	0.374183i	$-0.877923\pi$
$211$	−2.02817	+	3.51289i	−0.139625	+	0.241838i	0.787730	+	0.616021i	$0.211256\pi$
$212$	−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	$-0.471862\pi$
$227$	13.6816	−	6.37985i	0.908082	−	0.423446i	0.819800	+	0.572650i	$0.194085\pi$
$228$		0			0
$229$	−14.2293	−	5.17903i	−0.940296	−	0.342240i	−0.174013	−	0.984743i	$-0.555674\pi$
$229$	−14.2293	−	5.17903i	−0.940296	−	0.342240i	−0.766283	+	0.642504i	$0.777896\pi$
$230$	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	0.317928	+	0.948115i	$0.397013\pi$
$233$	−10.1069	+	17.5057i	−0.662128	+	1.14684i	−0.980056	+	0.198724i	$0.936320\pi$
$234$		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	−0.964114	−	0.265489i	$-0.914467\pi$
$239$	−13.6639	−	19.5141i	−0.883846	−	1.26226i	0.0802681	−	0.996773i	$-0.474422\pi$
$240$		0			0
$241$	−8.22920	−	0.719962i	−0.530090	−	0.0463768i	−0.181030	−	0.983477i	$-0.557943\pi$
$241$	−8.22920	−	0.719962i	−0.530090	−	0.0463768i	−0.349059	+	0.937101i	$0.613499\pi$
$242$	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	$-0.912984\pi$
$251$	−26.3270	+	7.05430i	−1.66175	+	0.445264i	−0.698879	+	0.715240i	$0.746317\pi$
$252$		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	$-0.640894\pi$
$257$	−11.1131	+	0.972272i	−0.693217	+	0.0606486i	−0.264898	+	0.964276i	$0.585338\pi$
$258$		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	0.986831	+	0.161754i	$0.0517151\pi$
$263$	1.86233	+	10.5618i	0.114836	+	0.651269i	−0.871995	+	0.489515i	$0.837174\pi$
$264$		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	$-0.814645\pi$
$269$	−12.7358	+	7.35301i	−0.776515	+	0.448321i	0.0586788	+	0.998277i	$0.481311\pi$
$270$		0			0
$271$	15.0829	+	12.6560i	0.916218	+	0.768798i	0.973292	−	0.229572i	$-0.0737325\pi$
$271$	15.0829	+	12.6560i	0.916218	+	0.768798i	−0.0570735	+	0.998370i	$0.518177\pi$
$272$	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	0.977545	+	0.210726i	$0.0675827\pi$
$277$	−0.361843	+	4.13588i	−0.0217410	+	0.248501i	−0.999286	+	0.0377754i	$0.987973\pi$
$278$	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	$-0.784027\pi$
$281$	3.39778	−	7.28656i	0.202695	−	0.434680i	0.981209	+	0.192946i	$0.0618044\pi$
$282$		0			0
$283$	−17.3177	−	12.1260i	−1.02943	−	0.720817i	−0.0685151	−	0.997650i	$-0.521826\pi$
$283$	−17.3177	−	12.1260i	−1.02943	−	0.720817i	−0.960918	+	0.276833i	$0.910715\pi$
$284$	−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	0.939623	+	0.342210i	$0.111176\pi$
$293$	19.0596	+	22.7143i	1.11347	+	1.32698i	0.173848	+	0.984773i	$0.444380\pi$
$294$		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	0.474767	−	0.880111i	$-0.342532\pi$
$307$	−0.876906	−	0.506282i	−0.0500476	−	0.0288950i	−0.524815	+	0.851216i	$0.675866\pi$
$308$	−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	$-0.578326\pi$
$311$	−20.1595	−	9.40054i	−1.14314	−	0.533056i	−0.899548	+	0.436822i	$0.856104\pi$
$312$		0			0
$313$	0.248543	−	0.174032i	0.0140485	−	0.00983686i	−0.566531	−	0.824040i	$-0.691715\pi$
$313$	0.248543	−	0.174032i	0.0140485	−	0.00983686i	0.580580	+	0.814203i	$0.302826\pi$
$314$	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	$-0.654526\pi$
$317$	−4.54976	+	1.65598i	−0.255540	+	0.0930088i	0.211074	+	0.977470i	$0.432304\pi$
$318$		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	0.994212	−	0.107433i	$-0.0342630\pi$
$331$	−0.0646081	−	0.738474i	−0.00355118	−	0.0405902i	−0.997764	+	0.0668426i	$0.978707\pi$
$332$	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	0.0650538	−	0.997882i	$-0.479278\pi$
$337$	8.58179	−	1.51320i	0.467480	−	0.0824294i	0.402426	+	0.915452i	$0.368167\pi$
$338$	−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	$-0.977816\pi$
$347$	−1.84100	+	6.87072i	−0.0988302	+	0.368840i	0.898742	+	0.438478i	$0.144482\pi$
$348$		0			0
$349$	19.7211	−	7.17791i	1.05565	−	0.384225i	0.244857	−	0.969559i	$-0.421259\pi$
$349$	19.7211	−	7.17791i	1.05565	−	0.384225i	0.810792	+	0.585335i	$0.199037\pi$
$350$	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	$-0.475906\pi$
$353$	19.5114	−	13.6621i	1.03849	−	0.727158i	0.962866	+	0.269979i	$0.0870167\pi$
$354$		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	$-0.562887\pi$
$359$	−21.6682	−	12.5101i	−1.14360	−	0.660259i	−0.947320	+	0.320289i	$0.896220\pi$
$360$		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	−0.529648	−	0.848217i	$-0.677676\pi$
$367$	4.09410	−	3.43536i	0.213710	−	0.179324i	0.743359	+	0.668893i	$0.233232\pi$
$368$	−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	−0.993569	−	0.113227i	$-0.963881\pi$
$373$	−18.0104	−	21.4640i	−0.932544	−	1.11136i	0.0610250	−	0.998136i	$-0.480563\pi$
$374$	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	−0.704851	−	0.709355i	$-0.748986\pi$
$379$	3.89565	−	22.0933i	0.200106	−	1.13486i	0.904957	−	0.425503i	$-0.139903\pi$
$380$	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	$-0.603115\pi$
$383$	−25.7936	−	18.0609i	−1.31799	−	0.922869i	−0.999684	+	0.0251179i	$0.992004\pi$
$384$		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	−0.714385	−	0.699752i	$-0.753294\pi$
$389$	2.18251	−	24.9462i	0.110658	−	1.26482i	0.825043	−	0.565070i	$-0.191151\pi$
$390$		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	−0.588074	−	0.808807i	$-0.700113\pi$
$397$	−3.61960	+	2.08978i	−0.181662	+	0.104883i	0.406411	+	0.913690i	$0.366780\pi$
$398$	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	$-0.279841\pi$
$401$	−2.65103	−	2.65103i	−0.132386	−	0.132386i	−0.770195	+	0.637809i	$0.779841\pi$
$402$		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	−0.0769170	−	0.997038i	$-0.524508\pi$
$409$	0.413946	−	0.0362156i	0.0204683	−	0.00179075i	0.0973853	+	0.995247i	$0.468952\pi$
$410$	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	$-0.898543\pi$
$419$	−9.74603	+	11.6149i	−0.476124	+	0.567423i	0.473508	+	0.880790i	$0.342988\pi$
$420$		0			0
$421$	6.39946	+	1.71473i	0.311891	+	0.0835708i	0.411369	−	0.911469i	$-0.365051\pi$
$421$	6.39946	+	1.71473i	0.311891	+	0.0835708i	−0.0994784	+	0.995040i	$0.531717\pi$
$422$	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	$-0.954719\pi$
$431$	−10.7562	+	15.3614i	−0.518108	+	0.739935i	0.471791	+	0.881710i	$0.343608\pi$
$432$		0			0
$433$	−8.51178	+	14.7428i	−0.409050	+	0.708495i	−0.994784	−	0.102008i	$-0.967473\pi$
$433$	−8.51178	+	14.7428i	−0.409050	+	0.708495i	0.585734	+	0.810504i	$0.300806\pi$
$434$	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	−0.555400	−	0.831583i	$-0.687435\pi$
$439$	−5.76976	+	2.69048i	−0.275375	+	0.128410i	0.280025	+	0.959993i	$0.409657\pi$
$440$	−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	$-0.152734\pi$
$443$	37.3415			1.77415			0.887075	+	0.461626i	$0.152734\pi$
$444$		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	$-0.472318\pi$
$449$	19.1943	−	8.95045i	0.905835	−	0.422398i	0.818979	+	0.573823i	$0.194540\pi$
$450$		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	−0.867072	−	0.498182i	$-0.834001\pi$
$457$	−2.18859	+	3.12562i	−0.102378	+	0.146211i	0.764695	+	0.644393i	$0.222890\pi$
$458$	−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	$-0.245675\pi$
$461$	−3.94703	−	5.63695i	−0.183832	−	0.262539i	−0.900481	+	0.434894i	$0.856786\pi$
$462$		0			0
$463$	−3.21677	−	0.281431i	−0.149496	−	0.0130792i	0.0121620	−	0.999926i	$-0.496129\pi$
$463$	−3.21677	−	0.281431i	−0.149496	−	0.0130792i	−0.161658	+	0.986847i	$0.551684\pi$
$464$	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	$-0.143319\pi$
$467$	31.6040	+	8.46826i	1.46246	+	0.391864i	0.562120	+	0.827056i	$0.309986\pi$
$468$		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	$-0.619954\pi$
$479$	−12.4516	+	1.08937i	−0.568928	+	0.0497748i	−0.200937	+	0.979604i	$0.564399\pi$
$480$		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	0.994678	−	0.103030i	$-0.0328538\pi$
$487$	19.6770	+	19.6770i	0.891648	+	0.891648i	−0.103030	+	0.994678i	$0.532854\pi$
$488$	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	$-0.384095\pi$
$491$	29.7687	−	17.1870i	1.34344	−	0.775638i	0.987311	+	0.158797i	$0.0507615\pi$
$492$		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	0.850386	+	0.526160i	$0.176369\pi$
$499$	−1.75238	+	20.0298i	−0.0784475	+	0.896659i	−0.928833	+	0.370499i	$0.879187\pi$
$500$	−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	$-0.883965\pi$
$503$	−1.35987	+	2.91624i	−0.0606334	+	0.130029i	0.873656	+	0.486544i	$0.161743\pi$
$504$		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	0.896837	+	0.442361i	$0.145859\pi$
$509$	−2.19317	+	12.4381i	−0.0972105	+	0.551308i	−0.994048	+	0.108947i	$0.965252\pi$
$510$		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	$-0.970248\pi$
$521$	−24.5741	+	20.6201i	−1.07661	+	0.903384i	−0.0809762	+	0.996716i	$0.525804\pi$
$522$		0			0
$523$	−6.24419	−	13.3907i	−0.273039	−	0.585535i	0.721199	−	0.692728i	$-0.243591\pi$
$523$	−6.24419	−	13.3907i	−0.273039	−	0.585535i	−0.994238	+	0.107193i	$0.965814\pi$
$524$	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	0.604297	+	0.796759i	$0.293454\pi$
$541$	−7.38298	+	27.5537i	−0.317419	+	1.18462i	−0.921716	+	0.387865i	$0.873213\pi$
$542$	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	−0.880958	−	0.473194i	$-0.843101\pi$
$547$	−8.29393	−	30.9534i	−0.354623	−	1.32347i	0.526335	−	0.850277i	$-0.323566\pi$
$548$	−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	−0.852859	−	0.522141i	$-0.825133\pi$
$557$	−2.44565	−	27.9540i	−0.103626	−	1.18445i	0.749233	−	0.662306i	$-0.230422\pi$
$558$		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	$-0.130333\pi$
$563$	−1.80695	−	6.74362i	−0.0761538	−	0.284210i	−0.993492	+	0.113898i	$0.963666\pi$
$564$		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	0.412028	+	0.911171i	$0.364820\pi$
$569$	−9.55065	+	35.6435i	−0.400384	+	1.49425i	−0.812413	+	0.583083i	$0.801846\pi$
$570$		0			0
$571$	14.9607	−	5.44523i	0.626084	−	0.227876i	−0.00944192	−	0.999955i	$-0.503006\pi$
$571$	14.9607	−	5.44523i	0.626084	−	0.227876i	0.635526	+	0.772079i	$0.280783\pi$
$572$	−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	0.840614	−	0.541634i	$-0.182194\pi$
$577$	23.2050	+	10.8207i	0.966035	+	0.450470i	0.125421	+	0.992104i	$0.459972\pi$
$578$	−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	$-0.164761\pi$
$587$	−1.66266	−	3.56560i	−0.0686255	−	0.147168i	−0.937628	+	0.347639i	$0.886983\pi$
$588$		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	0.357380	+	0.933959i	$0.383670\pi$
$599$	−12.6466	+	34.7463i	−0.516726	+	1.41969i	−0.874106	+	0.485734i	$0.838552\pi$
$600$		0			0
$601$	1.37685	−	7.80848i	0.0561627	−	0.318514i	−0.943764	−	0.330620i	$-0.892742\pi$
$601$	1.37685	−	7.80848i	0.0561627	−	0.318514i	0.999927	+	0.0121053i	$0.00385335\pi$
$602$	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	−0.698756	−	0.715360i	$-0.746263\pi$
$607$	7.35163	−	15.7656i	0.298394	−	0.639907i	0.997149	+	0.0754532i	$0.0240404\pi$
$608$	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	−0.912184	−	0.409781i	$-0.865605\pi$
$613$	−11.8053	−	32.4349i	−0.476812	−	1.31003i	0.435372	−	0.900251i	$-0.356617\pi$
$614$	−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	$-0.228336\pi$
$617$	5.88742	+	4.94013i	0.237018	+	0.198882i	−0.516540	+	0.856263i	$0.672780\pi$
$618$		0			0
$619$	−28.1737	+	16.2661i	−1.13240	+	0.653790i	−0.944537	−	0.328406i	$-0.893489\pi$
$619$	−28.1737	+	16.2661i	−1.13240	+	0.653790i	−0.187860	+	0.982196i	$0.560155\pi$
$620$	−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	−0.943068	−	0.332599i	$-0.892074\pi$
$631$	−45.5685	+	3.98673i	−1.81405	+	0.158709i	−0.870986	+	0.491308i	$0.836519\pi$
$632$	−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	$-0.658135\pi$
$641$	11.9478	−	14.2389i	0.471912	−	0.562402i	0.948522	+	0.316712i	$0.102579\pi$
$642$		0			0
$643$	−3.08212	−	0.825851i	−0.121547	−	0.0325684i	0.197533	−	0.980296i	$-0.436707\pi$
$643$	−3.08212	−	0.825851i	−0.121547	−	0.0325684i	−0.319080	+	0.947728i	$0.603374\pi$
$644$	−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	$-0.296553\pi$
$647$	26.5704	+	2.32461i	1.04459	+	0.0913897i	0.448078	+	0.893994i	$0.352109\pi$
$648$		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	$-0.850925\pi$
$653$	−4.16408	+	5.94692i	−0.162953	+	0.232721i	0.729369	+	0.684121i	$0.239814\pi$
$654$		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	$-0.623040\pi$
$659$	−32.3747	−	11.7834i	−1.26114	−	0.459018i	−0.884151	+	0.467200i	$0.845263\pi$
$660$		0			0
$661$	−33.1559	+	15.4608i	−1.28961	+	0.601357i	−0.941790	−	0.336203i	$-0.890857\pi$
$661$	−33.1559	+	15.4608i	−1.28961	+	0.601357i	−0.347825	+	0.937560i	$0.613080\pi$
$662$	−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	0.936485	−	0.350709i	$-0.114059\pi$
$673$	37.0570	+	13.4876i	1.42844	+	0.519910i	0.491957	+	0.870619i	$0.336282\pi$
$674$	−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	−0.0988759	−	0.995100i	$-0.531525\pi$
$677$	21.1366	−	36.6096i	0.812344	−	1.40702i	0.911220	−	0.411921i	$-0.135142\pi$
$678$		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	$-0.251254\pi$
$683$	−5.32225	−	7.60097i	−0.203650	−	0.290843i	−0.907966	+	0.419044i	$0.862365\pi$
$684$		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	−0.575608	−	0.817726i	$-0.695234\pi$
$691$	8.66544	−	10.3271i	0.329649	−	0.392860i	0.905256	+	0.424866i	$0.139679\pi$
$692$	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	$-0.635147\pi$
$701$	−17.4580	+	1.52738i	−0.659381	+	0.0576884i	−0.247446	+	0.968902i	$0.579591\pi$
$702$		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	0.890217	−	0.455536i	$-0.150552\pi$
$709$	11.5743	+	11.5743i	0.434682	+	0.434682i	−0.455536	+	0.890217i	$0.650552\pi$
$710$	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	$-0.112585\pi$
$719$	−0.0849192	−	0.233314i	−0.00316695	−	0.00870113i	−0.941266	+	0.337666i	$0.890363\pi$
$720$		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	0.912120	−	0.409923i	$-0.134444\pi$
$727$	22.6187	+	15.8378i	0.838882	+	0.587392i	−0.0732381	+	0.997314i	$0.523333\pi$
$728$	−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	−0.0429139	−	0.999079i	$-0.513664\pi$
$733$	17.1150	−	47.0230i	0.632156	−	1.73683i	0.675069	−	0.737754i	$-0.264114\pi$
$734$	−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	$-0.942240\pi$
$739$		−	9.81171i		−	0.360930i	0.983581	−	0.180465i	$-0.0577602\pi$
$740$	−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	$-0.655542\pi$
$743$	8.68448	−	7.28714i	0.318603	−	0.267339i	0.788037	+	0.615628i	$0.211098\pi$
$744$		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	0.667177	−	0.744899i	$-0.267502\pi$
$751$	9.74676	+	5.62729i	0.355664	+	0.205343i	−0.311513	+	0.950242i	$0.600836\pi$
$752$	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	−0.999980	−	0.00631526i	$-0.997990\pi$
$757$	−36.7598	+	25.7395i	−1.33606	+	0.935519i	−0.336079	+	0.941834i	$0.609101\pi$
$758$	−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	$-0.931181\pi$
$761$	−43.7804	+	15.9348i	−1.58704	+	0.577635i	−0.610319	+	0.792156i	$0.708959\pi$
$762$		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	−0.982439	−	0.186581i	$-0.940259\pi$
$769$	−6.23702	−	23.2769i	−0.224913	−	0.839385i	0.757527	−	0.652804i	$-0.226407\pi$
$770$	−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	$-0.436950\pi$
$773$	19.9357	−	3.51520i	0.717036	−	0.126433i	0.520250	+	0.854014i	$0.325839\pi$
$774$		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

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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more