LMFDB - Embedded newform 666.2.bs.b.557.4

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			557.4
Character	$\chi$	$=$	666.557
Dual form			666.2.bs.b.611.4

$q$-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 $\left(\mathbb{Z}/666\mathbb{Z}\right)^\times$.

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

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	0.958897	−	0.283754i	$-0.0915800\pi$
$5$	3.03635	+	1.41587i	1.35790	+	0.633197i	0.398999	+	0.916951i	$0.369358\pi$
$6$		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	0.797766	−	0.602967i	$-0.206015\pi$
$11$	−0.408947	−	0.708318i	−0.123302	−	0.213566i	−0.921068	+	0.389402i	$0.872682\pi$
$12$		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	−0.714631	−	0.699502i	$-0.753405\pi$
$17$	0.771448	−	1.10174i	0.187104	−	0.267212i	0.901735	+	0.432290i	$0.142294\pi$
$18$		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	−0.726766	−	0.686885i	$-0.758978\pi$
$23$	−4.85685	+	1.30139i	−1.01272	+	0.271358i	−0.285956	+	0.958243i	$0.592311\pi$
$24$		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	0.536844	−	0.843682i	$-0.319616\pi$
$29$	3.12298	+	0.836800i	0.579923	+	0.155390i	0.0430794	+	0.999072i	$0.486283\pi$
$30$		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	$-0.852720\pi$
$41$	0.631977	−	3.58412i	0.0986982	−	0.559745i	0.993551	−	0.113384i	$-0.0361691\pi$
$42$		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	0.683820	−	0.729651i	$-0.260317\pi$
$47$	2.69999	+	1.55884i	0.393834	+	0.227380i	−0.289986	+	0.957031i	$0.593651\pi$
$48$		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	−0.773503	−	0.633793i	$-0.781497\pi$
$53$	1.64843	−	4.52901i	0.226429	−	0.622108i	0.999932	+	0.0116849i	$0.00371952\pi$
$54$		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	$-0.974217\pi$
$59$	−3.21090	−	6.88580i	−0.418024	−	0.896454i	0.578698	−	0.815542i	$-0.303561\pi$
$60$		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	$-0.537702\pi$
$71$	7.41721	−	8.83948i	0.880260	−	1.04905i	0.998427	−	0.0560597i	$-0.0178537\pi$
$72$		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	−0.634354	−	0.773042i	$-0.718734\pi$
$83$	−8.80119	+	1.55189i	−0.966057	+	0.170342i	−0.331702	+	0.943384i	$0.607623\pi$
$84$		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	−0.193854	−	0.981030i	$-0.562099\pi$
$89$	4.08541	−	1.90506i	0.433052	−	0.201936i	0.626906	+	0.779095i	$0.284321\pi$
$90$		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	−0.855344	−	0.518060i	$-0.826654\pi$
$101$	0.210861	−	0.365223i	0.0209815	−	0.0363410i	0.876326	+	0.481719i	$0.159988\pi$
$102$		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	0.848882	−	0.528582i	$-0.177276\pi$
$107$	15.1622	+	2.67351i	1.46579	+	0.258458i	0.616903	+	0.787039i	$0.288387\pi$
$108$		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	$-0.941564\pi$
$113$	0.178190	−	2.03672i	0.0167627	−	0.191599i	0.999959	−	0.00904765i	$-0.00287999\pi$
$114$		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	−0.0292006	−	0.999574i	$-0.509296\pi$
$131$	−11.1992	−	7.84177i	−0.978480	−	0.685139i	−0.949279	+	0.314435i	$0.898185\pi$
$132$		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	$-0.325811\pi$
$137$	17.7917	−	10.2720i	1.52004	−	0.877598i	0.999721	−	0.0236291i	$-0.00752207\pi$
$138$		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	$-0.707265\pi$
$149$		−	19.4180i		−	1.59078i	0.606095	−	0.795392i	$-0.292735\pi$
$150$		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	$0.0861362\pi$
$167$	0.789044	+	9.01881i	0.0610581	+	0.697897i	−0.902551	+	0.430582i	$0.858308\pi$
$168$		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	−0.913038	−	0.407875i	$-0.866270\pi$
$173$	−8.81124	+	7.39351i	−0.669906	+	0.562118i	0.243131	+	0.969993i	$0.421825\pi$
$174$		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	−0.0874747	−	0.996167i	$-0.527880\pi$
$179$	12.1575	−	12.1575i	0.908692	−	0.908692i	0.996167	+	0.0874747i	$0.0278797\pi$
$180$		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	0.728561	−	0.684981i	$-0.240189\pi$
$191$	0.602298	+	0.602298i	0.0435807	+	0.0435807i	−0.684981	+	0.728561i	$0.740189\pi$
$192$		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	0.996158	−	0.0875797i	$-0.0279133\pi$
$197$	10.3433	+	12.3266i	0.736927	+	0.878236i	−0.259230	+	0.965816i	$0.583469\pi$
$198$		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	0.819800	−	0.572650i	$-0.194085\pi$
$227$	13.6816	+	6.37985i	0.908082	+	0.423446i	0.0882819	+	0.996096i	$0.471862\pi$
$228$		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	$-0.936320\pi$
$233$	−10.1069	−	17.5057i	−0.662128	−	1.14684i	0.317928	−	0.948115i	$-0.397013\pi$
$234$		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	$0.474422\pi$
$239$	−13.6639	+	19.5141i	−0.883846	+	1.26226i	−0.964114	+	0.265489i	$0.914467\pi$
$240$		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	−0.698879	−	0.715240i	$-0.746317\pi$
$251$	−26.3270	−	7.05430i	−1.66175	−	0.445264i	−0.962867	+	0.269976i	$0.912984\pi$
$252$		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	−0.264898	−	0.964276i	$-0.585338\pi$
$257$	−11.1131	−	0.972272i	−0.693217	−	0.0606486i	−0.428319	+	0.903628i	$0.640894\pi$
$258$		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	$-0.837174\pi$
$263$	1.86233	−	10.5618i	0.114836	−	0.651269i	0.986831	−	0.161754i	$-0.0517151\pi$
$264$		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	0.0586788	−	0.998277i	$-0.481311\pi$
$269$	−12.7358	−	7.35301i	−0.776515	−	0.448321i	−0.835194	+	0.549956i	$0.814645\pi$
$270$		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	0.981209	−	0.192946i	$-0.0618044\pi$
$281$	3.39778	+	7.28656i	0.202695	+	0.434680i	−0.778515	+	0.627626i	$0.784027\pi$
$282$		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	$-0.444380\pi$
$293$	19.0596	−	22.7143i	1.11347	−	1.32698i	0.939623	−	0.342210i	$-0.111176\pi$
$294$		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	−0.899548	−	0.436822i	$-0.856104\pi$
$311$	−20.1595	+	9.40054i	−1.14314	+	0.533056i	−0.243594	+	0.969877i	$0.578326\pi$
$312$		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	0.211074	−	0.977470i	$-0.432304\pi$
$317$	−4.54976	−	1.65598i	−0.255540	−	0.0930088i	−0.466614	+	0.884461i	$0.654526\pi$
$318$		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	0.898742	−	0.438478i	$-0.144482\pi$
$347$	−1.84100	−	6.87072i	−0.0988302	−	0.368840i	−0.997572	+	0.0696382i	$0.977816\pi$
$348$		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	0.962866	−	0.269979i	$-0.0870167\pi$
$353$	19.5114	+	13.6621i	1.03849	+	0.727158i	0.0756226	+	0.997137i	$0.475906\pi$
$354$		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	−0.947320	−	0.320289i	$-0.896220\pi$
$359$	−21.6682	+	12.5101i	−1.14360	+	0.660259i	−0.196281	+	0.980548i	$0.562887\pi$
$360$		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	−0.999684	−	0.0251179i	$-0.992004\pi$
$383$	−25.7936	+	18.0609i	−1.31799	+	0.922869i	−0.318309	+	0.947987i	$0.603115\pi$
$384$		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	$0.191151\pi$
$389$	2.18251	+	24.9462i	0.110658	+	1.26482i	−0.714385	+	0.699752i	$0.753294\pi$
$390$		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	−0.770195	−	0.637809i	$-0.779841\pi$
$401$	−2.65103	+	2.65103i	−0.132386	+	0.132386i	0.637809	+	0.770195i	$0.279841\pi$
$402$		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	0.473508	−	0.880790i	$-0.342988\pi$
$419$	−9.74603	−	11.6149i	−0.476124	−	0.567423i	−0.949632	+	0.313367i	$0.898543\pi$
$420$		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	0.471791	−	0.881710i	$-0.343608\pi$
$431$	−10.7562	−	15.3614i	−0.518108	−	0.739935i	−0.989899	+	0.141776i	$0.954719\pi$
$432$		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	$-0.152734\pi$
$443$	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	0.818979	−	0.573823i	$-0.194540\pi$
$449$	19.1943	+	8.95045i	0.905835	+	0.422398i	0.0868558	+	0.996221i	$0.472318\pi$
$450$		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	−0.900481	−	0.434894i	$-0.856786\pi$
$461$	−3.94703	+	5.63695i	−0.183832	+	0.262539i	0.716650	+	0.697433i	$0.245675\pi$
$462$		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	0.562120	−	0.827056i	$-0.309986\pi$
$467$	31.6040	−	8.46826i	1.46246	−	0.391864i	0.900338	+	0.435191i	$0.143319\pi$
$468$		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	−0.200937	−	0.979604i	$-0.564399\pi$
$479$	−12.4516	−	1.08937i	−0.568928	−	0.0497748i	−0.367991	+	0.929829i	$0.619954\pi$
$480$		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	0.987311	−	0.158797i	$-0.0507615\pi$
$491$	29.7687	+	17.1870i	1.34344	+	0.775638i	0.356134	+	0.934435i	$0.384095\pi$
$492$		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	0.873656	−	0.486544i	$-0.161743\pi$
$503$	−1.35987	−	2.91624i	−0.0606334	−	0.130029i	−0.934290	+	0.356515i	$0.883965\pi$
$504$		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	$-0.965252\pi$
$509$	−2.19317	−	12.4381i	−0.0972105	−	0.551308i	0.896837	−	0.442361i	$-0.145859\pi$
$510$		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	−0.0809762	−	0.996716i	$-0.525804\pi$
$521$	−24.5741	−	20.6201i	−1.07661	−	0.903384i	−0.995635	+	0.0933320i	$0.970248\pi$
$522$		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	$0.230422\pi$
$557$	−2.44565	+	27.9540i	−0.103626	+	1.18445i	−0.852859	+	0.522141i	$0.825133\pi$
$558$		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	−0.993492	−	0.113898i	$-0.963666\pi$
$563$	−1.80695	+	6.74362i	−0.0761538	+	0.284210i	0.917339	+	0.398108i	$0.130333\pi$
$564$		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	$-0.801846\pi$
$569$	−9.55065	−	35.6435i	−0.400384	−	1.49425i	0.412028	−	0.911171i	$-0.364820\pi$
$570$		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	−0.937628	−	0.347639i	$-0.886983\pi$
$587$	−1.66266	+	3.56560i	−0.0686255	+	0.147168i	0.869003	+	0.494807i	$0.164761\pi$
$588$		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	$0.452013\pi$
$593$			48.1508i			1.97732i	−0.150186	+	0.988658i	$0.547987\pi$
$594$		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	$-0.838552\pi$
$599$	−12.6466	−	34.7463i	−0.516726	−	1.41969i	0.357380	−	0.933959i	$-0.383670\pi$
$600$		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	−0.516540	−	0.856263i	$-0.672780\pi$
$617$	5.88742	−	4.94013i	0.237018	−	0.198882i	0.753558	+	0.657381i	$0.228336\pi$
$618$		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	0.948522	−	0.316712i	$-0.102579\pi$
$641$	11.9478	+	14.2389i	0.471912	+	0.562402i	−0.476610	+	0.879115i	$0.658135\pi$
$642$		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	0.448078	−	0.893994i	$-0.352109\pi$
$647$	26.5704	−	2.32461i	1.04459	−	0.0913897i	0.596511	+	0.802605i	$0.296553\pi$
$648$		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	0.729369	−	0.684121i	$-0.239814\pi$
$653$	−4.16408	−	5.94692i	−0.162953	−	0.232721i	−0.892322	+	0.451400i	$0.850925\pi$
$654$		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	−0.884151	−	0.467200i	$-0.845263\pi$
$659$	−32.3747	+	11.7834i	−1.26114	+	0.459018i	−0.376989	+	0.926218i	$0.623040\pi$
$660$		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	$0.135142\pi$
$677$	21.1366	+	36.6096i	0.812344	+	1.40702i	−0.0988759	+	0.995100i	$0.531525\pi$
$678$		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	−0.907966	−	0.419044i	$-0.862365\pi$
$683$	−5.32225	+	7.60097i	−0.203650	+	0.290843i	0.704315	+	0.709887i	$0.251254\pi$
$684$		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	−0.247446	−	0.968902i	$-0.579591\pi$
$701$	−17.4580	−	1.52738i	−0.659381	−	0.0576884i	−0.411935	+	0.911213i	$0.635147\pi$
$702$		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	−0.941266	−	0.337666i	$-0.890363\pi$
$719$	−0.0849192	+	0.233314i	−0.00316695	+	0.00870113i	0.938099	+	0.346367i	$0.112585\pi$
$720$		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	0.788037	−	0.615628i	$-0.211098\pi$
$743$	8.68448	+	7.28714i	0.318603	+	0.267339i	−0.469434	+	0.882967i	$0.655542\pi$
$744$		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	−0.610319	−	0.792156i	$-0.708959\pi$
$761$	−43.7804	−	15.9348i	−1.58704	−	0.577635i	−0.976719	+	0.214521i	$0.931181\pi$
$762$		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	0.520250	−	0.854014i	$-0.325839\pi$
$773$	19.9357	+	3.51520i	0.717036	+	0.126433i	0.196786	+	0.980447i	$0.436950\pi$
$774$		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
$785$	3.65062	−	13.6243i	0.130296	−	0.486271i
$786$		0			0
$787$	23.5128	−	40.7254i	0.838141	−	1.45170i	−0.0533066	−	0.998578i	$-0.516976\pi$
$787$	23.5128	−	40.7254i	0.838141	−	1.45170i	0.891447	−	0.453124i	$-0.149691\pi$
$788$	−8.04563	−	13.9354i	−0.286614	−	0.496430i
$789$		0			0
$790$	16.7461	+	23.9159i	0.595798	+	0.850888i
$791$	0.918140	+	3.42654i	0.0326453	+	0.121834i
$792$		0			0
$793$	−73.5417	−	26.7670i	−2.61154	−	0.950524i
$794$	2.39729	−	3.42369i	0.0850768	−	0.121502i
$795$		0			0
$796$	−1.05132	+	0.0919787i	−0.0372631	+	0.00326010i
$797$	20.0847	+	14.0634i	0.711436	+	0.498153i	0.872391	−	0.488809i	$-0.162569\pi$
$797$	20.0847	+	14.0634i	0.711436	+	0.498153i	−0.160955	+	0.986962i	$0.551457\pi$
$798$		0			0
$799$	3.80035	−	1.77213i	0.134447	−	0.0626935i
$800$	−6.01202	+	1.61092i	−0.212557	+	0.0569545i
$801$		0			0
$802$	−2.40989	−	2.87199i	−0.0850960	−	0.101414i
$803$	4.81085	−	2.77754i	0.169771	−	0.0980174i
$804$		0			0
$805$	28.7847	−	5.07553i	1.01453	−	0.178889i
$806$	−50.2633	−	13.4680i	−1.77045	−	0.474390i
$807$		0			0
$808$	−0.298203	−	0.298203i	−0.0104907	−	0.0104907i
$809$	7.26412	−	15.5780i	0.255393	−	0.547692i	−0.736249	−	0.676711i	$-0.763405\pi$
$809$	7.26412	−	15.5780i	0.255393	−	0.547692i	0.991642	+	0.129018i	$0.0411826\pi$
$810$		0			0
$811$	22.7118	+	19.0574i	0.797519	+	0.669197i	0.947594	−	0.319477i	$-0.103507\pi$
$811$	22.7118	+	19.0574i	0.797519	+	0.669197i	−0.150075	+	0.988675i	$0.547952\pi$
$812$	5.58849	+	0.488929i	0.196118	+	0.0171581i
$813$		0			0
$814$	1.53966	−	4.73082i	0.0539650	−	0.165815i
$815$		−	69.7488i		−	2.44320i
$816$		0			0
$817$	11.0370	−	13.1534i	0.386135	−	0.460178i
$818$	−0.0721556	+	0.409215i	−0.00252286	+	0.0143079i
$819$		0			0
$820$	−8.62167	+	8.62167i	−0.301082	+	0.301082i
$821$	−14.2508	−	39.1536i	−0.497355	−	1.36647i	−0.893822	−	0.448423i	$-0.851986\pi$
$821$	−14.2508	−	39.1536i	−0.497355	−	1.36647i	0.396467	−	0.918049i	$-0.370236\pi$
$822$		0			0
$823$	−6.05186	−	34.3218i	−0.210954	−	1.19638i	−0.887790	−	0.460248i	$-0.847760\pi$
$823$	−6.05186	−	34.3218i	−0.210954	−	1.19638i	0.676836	−	0.736134i	$-0.263351\pi$
$824$	−5.35456	−	3.09146i	−0.186535	−	0.107696i
$825$		0			0
$826$	−10.0985	+	8.47365i	−0.351372	+	0.294836i
$827$	−43.6790	+	30.5844i	−1.51887	+	1.06352i	−0.544447	+	0.838795i	$0.683260\pi$
$827$	−43.6790	+	30.5844i	−1.51887	+	1.06352i	−0.974422	+	0.224728i	$0.927851\pi$
$828$		0			0
$829$	5.45646	+	11.7014i	0.189511	+	0.406407i	0.977989	−	0.208655i	$-0.0669087\pi$
$829$	5.45646	+	11.7014i	0.189511	+	0.406407i	−0.788479	+	0.615062i	$0.789131\pi$
$830$	10.2404	−	28.1353i	0.355450	−	0.976591i
$831$		0			0
$832$	−0.580952	−	6.64032i	−0.0201409	−	0.230212i
$833$	0.467651	+	5.34528i	0.0162032	+	0.185203i
$834$		0			0
$835$	−10.3737	+	28.5014i	−0.358996	+	0.986333i
$836$	−0.568582	−	1.21933i	−0.0196648	−	0.0421714i
$837$		0			0
$838$	12.4201	−	8.69664i	0.429045	−	0.300420i
$839$	15.2962	−	12.8350i	0.528083	−	0.443114i	−0.339356	−	0.940658i	$-0.610209\pi$
$839$	15.2962	−	12.8350i	0.528083	−	0.443114i	0.867439	+	0.497544i	$0.165765\pi$
$840$		0			0
$841$	−16.0620	−	9.27338i	−0.553861	−	0.319772i
$842$	1.15046	+	6.52456i	0.0396473	+	0.224851i
$843$		0			0
$844$	1.38735	+	3.81171i	0.0477546	+	0.131205i
$845$	−74.4601	+	74.4601i	−2.56150	+	2.56150i
$846$		0			0
$847$	−3.11271	+	17.6531i	−0.106954	+	0.606567i
$848$	3.09803	−	3.69208i	0.106387	−	0.126787i
$849$		0			0
$850$			8.37128i			0.287133i
$851$	−14.3719	+	26.9982i	−0.492662	+	0.925487i
$852$		0			0
$853$	15.8877	+	1.38999i	0.543983	+	0.0475923i	0.355836	−	0.934549i	$-0.384196\pi$
$853$	15.8877	+	1.38999i	0.543983	+	0.0475923i	0.188147	+	0.982141i	$0.439752\pi$
$854$	15.6057	+	13.0947i	0.534015	+	0.448091i
$855$		0			0
$856$	6.50667	−	13.9536i	0.222394	−	0.476925i
$857$	−22.4900	−	22.4900i	−0.768243	−	0.768243i	0.209554	−	0.977797i	$-0.432799\pi$
$857$	−22.4900	−	22.4900i	−0.768243	−	0.768243i	−0.977797	+	0.209554i	$0.932799\pi$
$858$		0			0
$859$	40.3104	+	10.8011i	1.37537	+	0.368530i	0.869438	−	0.494042i	$-0.164481\pi$
$859$	40.3104	+	10.8011i	1.37537	+	0.368530i	0.505935	+	0.862572i	$0.331148\pi$
$860$	34.4400	−	6.07270i	1.17439	−	0.207077i
$861$		0			0
$862$	16.2405	−	9.37643i	0.553152	−	0.319362i
$863$	7.60959	+	9.06876i	0.259034	+	0.308704i	0.879850	−	0.475252i	$-0.157643\pi$
$863$	7.60959	+	9.06876i	0.259034	+	0.308704i	−0.620816	+	0.783956i	$0.713199\pi$
$864$		0			0
$865$	−37.2223	+	9.97367i	−1.26559	+	0.339115i
$866$	15.4286	−	7.19446i	0.524284	−	0.244478i
$867$		0			0
$868$	11.0956	+	7.76923i	0.376610	+	0.263705i
$869$	−7.10047	+	0.621211i	−0.240867	+	0.0210731i
$870$		0			0
$871$	−22.3409	+	31.9061i	−0.756991	+	1.08110i
$872$	−9.82921	−	3.57754i	−0.332859	−	0.121151i
$873$		0			0
$874$	2.14069	+	7.98917i	0.0724100	+	0.270238i
$875$	−4.08140	−	5.82884i	−0.137976	−	0.197051i
$876$		0			0
$877$	−12.3356	−	21.3658i	−0.416542	−	0.721472i	0.579047	−	0.815294i	$-0.303425\pi$
$877$	−12.3356	−	21.3658i	−0.416542	−	0.721472i	−0.995589	+	0.0938220i	$0.970092\pi$
$878$	3.18311	−	5.51331i	0.107425	−	0.186065i
$879$		0			0
$880$	0.709201	−	2.64677i	0.0239072	−	0.0892228i
$881$	−19.0880	+	6.94746i	−0.643091	+	0.234066i	−0.642919	−	0.765934i	$-0.722277\pi$
$881$	−19.0880	+	6.94746i	−0.643091	+	0.234066i	−0.000171879		1.00000i	$0.500055\pi$
$882$		0			0
$883$	43.5791	+	20.3212i	1.46655	+	0.683864i	0.981648	−	0.190703i	$-0.0610767\pi$
$883$	43.5791	+	20.3212i	1.46655	+	0.683864i	0.484904	+	0.874567i	$0.338855\pi$
$884$	−8.82900	−	1.55679i	−0.296951	−	0.0523605i
$885$		0			0
$886$	−3.25453	+	37.1994i	−0.109338	+	1.24974i
$887$	−21.0719			−0.707526			−0.353763	−	0.935335i	$-0.615098\pi$
$887$	−21.0719			−0.707526			−0.353763	+	0.935335i	$0.615098\pi$
$888$		0			0
$889$	−26.0035			−0.872128
$890$	−1.31623	+	15.0446i	−0.0441201	+	0.504295i
$891$		0			0
$892$	−10.6428	−	1.87661i	−0.356347	−	0.0628336i
$893$	−4.64788	−	2.16734i	−0.155535	−	0.0725274i
$894$		0			0
$895$	54.1277	−	19.7009i	1.80929	−	0.658528i
$896$	−0.449077	+	1.67598i	−0.0150026	+	0.0559905i
$897$		0			0
$898$	−10.5893	+	18.3412i	−0.353369	+	0.612053i
$899$	12.6200	+	21.8584i	0.420899	+	0.729019i
$900$		0			0
$901$	−3.71813	−	5.31004i	−0.123869	−	0.176903i
$902$	−0.770415	−	2.87523i	−0.0256520	−	0.0957346i
$903$		0			0
$904$	−1.92121	−	0.699262i	−0.0638983	−	0.0232571i
$905$	−36.8432	+	52.6175i	−1.22471	+	1.74907i
$906$		0			0
$907$	−29.4839	+	2.57951i	−0.978997	+	0.0856511i	−0.565407	−	0.824812i	$-0.691281\pi$
$907$	−29.4839	+	2.57951i	−0.978997	+	0.0856511i	−0.413590	+	0.910463i	$0.635725\pi$
$908$	−12.3659	−	8.65872i	−0.410378	−	0.287350i
$909$		0			0
$910$	35.1173	−	16.3754i	1.16413	−	0.542841i
$911$	38.9347	−	10.4325i	1.28996	−	0.345645i	0.452317	−	0.891857i	$-0.350598\pi$
$911$	38.9347	−	10.4325i	1.28996	−	0.345645i	0.837646	+	0.546213i	$0.183931\pi$
$912$		0			0
$913$	4.69846	+	5.59940i	0.155496	+	0.185313i
$914$	3.30448	−	1.90784i	0.109302	−	0.0631058i
$915$		0			0
$916$	14.9124	−	2.62946i	0.492720	−	0.0868798i
$917$	22.9135	+	6.13965i	0.756670	+	0.202749i
$918$		0			0
$919$	28.9146	+	28.9146i	0.953805	+	0.953805i	0.998979	−	0.0451741i	$-0.0143843\pi$
$919$	28.9146	+	28.9146i	0.953805	+	0.953805i	−0.0451741	+	0.998979i	$0.514384\pi$
$920$	−7.11926	+	15.2673i	−0.234715	+	0.503348i
$921$		0			0
$922$	−5.27149	−	4.42331i	−0.173607	−	0.145674i
$923$	76.6234	+	6.70368i	2.52209	+	0.220654i
$924$		0			0
$925$	37.8069	+	1.99964i	1.24308	+	0.0657478i
$926$		−	3.22906i		−	0.106113i
$927$		0			0
$928$	−2.07823	+	2.47674i	−0.0682212	+	0.0813028i
$929$	0.899532	−	5.10150i	0.0295127	−	0.167375i	−0.966489	−	0.256707i	$-0.917362\pi$
$929$	0.899532	−	5.10150i	0.0295127	−	0.167375i	0.996002	+	0.0893326i	$0.0284734\pi$
$930$		0			0
$931$	4.64027	−	4.64027i	0.152079	−	0.152079i
$932$	6.91355	+	18.9948i	0.226461	+	0.622196i
$933$		0			0
$934$	5.68157	+	32.2218i	0.185907	+	1.05433i
$935$	−3.19168	−	1.84272i	−0.104379	−	0.0602633i
$936$		0			0
$937$	10.5487	−	8.85138i	0.344610	−	0.289162i	−0.454012	−	0.890996i	$-0.650008\pi$
$937$	10.5487	−	8.85138i	0.344610	−	0.289162i	0.798621	+	0.601834i	$0.205563\pi$
$938$	8.30526	−	5.81540i	0.271176	−	0.189880i
$939$		0			0
$940$	−4.41424	−	9.46637i	−0.143977	−	0.308759i
$941$	−8.72276	+	23.9656i	−0.284354	+	0.781256i	0.712476	+	0.701696i	$0.247574\pi$
$941$	−8.72276	+	23.9656i	−0.284354	+	0.781256i	−0.996830	+	0.0795597i	$0.974649\pi$
$942$		0			0
$943$	1.59491	+	18.2300i	0.0519376	+	0.593649i
$944$	−0.662178	−	7.56873i	−0.0215520	−	0.246341i
$945$		0			0
$946$	−2.92001	+	8.02267i	−0.0949378	+	0.260839i
$947$	5.94520	+	12.7495i	0.193193	+	0.414304i	0.978913	−	0.204279i	$-0.0654850\pi$
$947$	5.94520	+	12.7495i	0.193193	+	0.414304i	−0.785720	+	0.618583i	$0.787707\pi$
$948$		0			0
$949$	−37.0854	+	25.9675i	−1.20384	+	0.842939i
$950$	7.84293	−	6.58100i	0.254458	−	0.213516i
$951$		0			0
$952$	2.02102	+	1.16684i	0.0655016	+	0.0378174i
$953$	−2.19265	−	12.4351i	−0.0710270	−	0.402814i	−0.999506	−	0.0314291i	$-0.989994\pi$
$953$	−2.19265	−	12.4351i	−0.0710270	−	0.402814i	0.928479	−	0.371385i	$-0.121117\pi$
$954$		0			0
$955$	0.976008	+	2.68156i	0.0315829	+	0.0867733i
$956$	16.8449	−	16.8449i	0.544804	−	0.544804i
$957$		0			0
$958$	2.17046	−	12.3093i	0.0701243	−	0.397695i
$959$	−22.9128	+	27.3064i	−0.739893	+	0.881770i
$960$		0			0
$961$			29.9431i			0.965906i
$962$	−9.13985	+	39.5022i	−0.294680	+	1.27360i
$963$		0			0
$964$	8.22920	+	0.719962i	0.265045	+	0.0231884i
$965$	−31.3459	−	26.3023i	−1.00906	−	0.846701i
$966$		0			0
$967$	6.65539	−	14.2725i	0.214023	−	0.458974i	−0.769761	−	0.638332i	$-0.779625\pi$
$967$	6.65539	−	14.2725i	0.214023	−	0.458974i	0.983784	+	0.179359i	$0.0574023\pi$
$968$	−7.30515	−	7.30515i	−0.234797	−	0.234797i
$969$		0			0
$970$	28.9453	+	7.75587i	0.929377	+	0.249026i
$971$	52.3094	−	9.22356i	1.67869	−	0.295998i	0.748515	−	0.663118i	$-0.230767\pi$
$971$	52.3094	−	9.22356i	1.67869	−	0.295998i	0.930174	+	0.367120i	$0.119656\pi$
$972$		0			0
$973$	−18.6110	+	10.7451i	−0.596641	+	0.344471i
$974$	17.8871	+	21.3170i	0.573140	+	0.683042i
$975$		0			0
$976$	−11.3409	+	3.03878i	−0.363013	+	0.0972691i
$977$	2.85269	−	1.33023i	0.0912656	−	0.0425578i	−0.376449	−	0.926437i	$-0.622855\pi$
$977$	2.85269	−	1.33023i	0.0912656	−	0.0425578i	0.467715	+	0.883879i	$0.345077\pi$
$978$		0			0
$979$	−3.02010	−	2.11470i	−0.0965228	−	0.0675860i
$980$	13.3147	−	1.16488i	0.425322	−	0.0372108i
$981$		0			0
$982$	−19.7161	+	28.1575i	−0.629166	+	0.898543i
$983$	−50.2414	−	18.2864i	−1.60245	−	0.583244i	−0.622524	−	0.782601i	$-0.713893\pi$
$983$	−50.2414	−	18.2864i	−1.60245	−	0.583244i	−0.979927	+	0.199356i	$0.936115\pi$
$984$		0			0
$985$	13.9528	+	52.0727i	0.444574	+	1.65917i
$986$	2.49421	+	3.56210i	0.0794317	+	0.113440i
$987$		0			0
$988$	5.48229	+	9.49561i	0.174415	+	0.302096i
$989$	26.2432	−	45.4545i	0.834484	−	1.44537i
$990$		0			0
$991$	−12.9112	+	48.1852i	−0.410138	+	1.53065i	0.384242	+	0.923232i	$0.374463\pi$
$991$	−12.9112	+	48.1852i	−0.410138	+	1.53065i	−0.794380	+	0.607422i	$0.792204\pi$
$992$	−7.33581	+	2.67002i	−0.232912	+	0.0847731i
$993$		0			0
$994$	−18.1457	−	8.46147i	−0.575546	−	0.268381i
$995$	3.48192	+	0.613956i	0.110384	+	0.0194637i
$996$		0			0
$997$	−2.75910	+	31.5366i	−0.0873815	+	0.998776i	0.818293	+	0.574802i	$0.194921\pi$
$997$	−2.75910	+	31.5366i	−0.0873815	+	0.998776i	−0.905674	+	0.423974i	$0.860635\pi$
$998$	20.1063			0.636455
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	666.2.bs.b.557.4	✓	96
3.2	odd	2	inner	666.2.bs.b.557.5	yes	96
37.19	odd	36	inner	666.2.bs.b.611.5	yes	96
111.56	even	36	inner	666.2.bs.b.611.4	yes	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
666.2.bs.b.557.4	✓	96	1.1	even	1	trivial
666.2.bs.b.557.5	yes	96	3.2	odd	2	inner
666.2.bs.b.611.4	yes	96	111.56	even	36	inner
666.2.bs.b.611.5	yes	96	37.19	odd	36	inner

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

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Representations

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Database

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