LMFDB - Embedded newform 666.2.be.d.467.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [666,2,Mod(125,666)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(666, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 11]))

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

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

chi := DirichletCharacter("666.125");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 666 = 2 \cdot 3^{2} \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	666.be (of order $12$, degree $4$, 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:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{12})$
Coefficient field:	16.0.6040479020157644046336.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 7x^{12} - 32x^{8} - 567x^{4} + 6561 $ x^16 - 7x^12 - 32x^8 - 567*x^4 + 6561
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			467.3
Root			$0.0537601 - 1.73122i$ of defining polynomial
Character	$\chi$	$=$	666.467
Dual form			666.2.be.d.251.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.965926 - 0.258819i) q^{2} +(0.866025 - 0.500000i) q^{4} +(-0.765290 - 0.205059i) q^{5} +(-0.896143 - 1.55217i) q^{7} +(0.707107 - 0.707107i) q^{8} -0.792287 q^{10} +4.98417 q^{11} +(0.0278283 - 0.103857i) q^{13} +(-1.26734 - 1.26734i) q^{14} +(0.500000 - 0.866025i) q^{16} +(0.912166 + 3.40425i) q^{17} +(2.21397 - 8.26264i) q^{19} +(-0.765290 + 0.205059i) q^{20} +(4.81433 - 1.29000i) q^{22} +(5.99711 - 5.99711i) q^{23} +(-3.78651 - 2.18614i) q^{25} -0.107520i q^{26} +(-1.55217 - 0.896143i) q^{28} +(-4.02266 - 4.02266i) q^{29} +(-6.76493 + 6.76493i) q^{31} +(0.258819 - 0.965926i) q^{32} +(1.76217 + 3.05217i) q^{34} +(0.367525 + 1.37162i) q^{35} +(4.26613 - 4.33591i) q^{37} -8.55412i q^{38} +(-0.686141 + 0.396143i) q^{40} +(4.52147 + 7.83142i) q^{41} +(2.24060 + 2.24060i) q^{43} +(4.31641 - 2.49208i) q^{44} +(4.24060 - 7.34493i) q^{46} +8.63283i q^{47} +(1.89385 - 3.28025i) q^{49} +(-4.22330 - 1.13163i) q^{50} +(-0.0278283 - 0.103857i) q^{52} +(0.970349 + 0.560232i) q^{53} +(-3.81433 - 1.02205i) q^{55} +(-1.73122 - 0.463878i) q^{56} +(-4.92674 - 2.84445i) q^{58} +(3.06049 + 11.4219i) q^{59} +(-2.05217 - 0.549876i) q^{61} +(-4.78353 + 8.28532i) q^{62} -1.00000i q^{64} +(-0.0425934 + 0.0737740i) q^{65} +(-12.9290 + 7.46458i) q^{67} +(2.49208 + 2.49208i) q^{68} +(0.710003 + 1.22976i) q^{70} +(-5.01144 + 2.89335i) q^{71} +2.90818i q^{73} +(2.99855 - 5.29232i) q^{74} +(-2.21397 - 8.26264i) q^{76} +(-4.46653 - 7.73625i) q^{77} +(-0.0278283 + 0.103857i) q^{79} +(-0.560232 + 0.560232i) q^{80} +(6.39433 + 6.39433i) q^{82} +(3.41423 + 1.97121i) q^{83} -2.79229i q^{85} +(2.74416 + 1.58434i) q^{86} +(3.52434 - 3.52434i) q^{88} +(5.75830 - 1.54293i) q^{89} +(-0.186141 + 0.0498762i) q^{91} +(2.19509 - 8.19220i) q^{92} +(2.23434 + 8.33867i) q^{94} +(-3.38866 + 5.86933i) q^{95} +(-0.841688 - 0.841688i) q^{97} +(0.980331 - 3.65864i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 8 q^{7} + 4 q^{13} + 8 q^{16} + 16 q^{19} + 20 q^{22} + 12 q^{28} - 12 q^{31} + 8 q^{34} + 12 q^{37} + 12 q^{40} - 20 q^{43} + 12 q^{46} + 20 q^{49} - 4 q^{52} - 4 q^{55} + 4 q^{61} - 132 q^{67}+ \cdots - 40 q^{97}+O(q^{100}) $ 16 * q - 8 * q^7 + 4 * q^13 + 8 * q^16 + 16 * q^19 + 20 * q^22 + 12 * q^28 - 12 * q^31 + 8 * q^34 + 12 * q^37 + 12 * q^40 - 20 * q^43 + 12 * q^46 + 20 * q^49 - 4 * q^52 - 4 * q^55 + 4 * q^61 - 132 * q^67 + 28 * q^70 - 16 * q^76 - 4 * q^79 + 12 * q^82 + 16 * q^88 + 20 * q^91 + 12 * q^94 - 40 * q^97

Character values

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

$n$	$371$	$631$
$\chi(n)$	$-1$	$e\left(\frac{5}{12}\right)$

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 $

$2$	0.965926	−	0.258819i	0.683013	−	0.183013i
$2$	0.965926	−	0.258819i	0.683013	−	0.183013i
$3$		0			0
$3$		0			0
$4$	0.866025	−	0.500000i	0.433013	−	0.250000i
$5$	−0.765290	−	0.205059i	−0.342248	−	0.0917052i	0.0836009	−	0.996499i	$-0.473358\pi$
$5$	−0.765290	−	0.205059i	−0.342248	−	0.0917052i	−0.425849	+	0.904794i	$0.640025\pi$
$6$		0			0
$7$	−0.896143	−	1.55217i	−0.338710	−	0.586664i	0.645480	−	0.763777i	$-0.276657\pi$
$7$	−0.896143	−	1.55217i	−0.338710	−	0.586664i	−0.984190	+	0.177114i	$0.943324\pi$
$8$	0.707107	−	0.707107i	0.250000	−	0.250000i
$9$		0			0
$10$	−0.792287			−0.250543
$11$	4.98417			1.50278			0.751391	−	0.659857i	$-0.229383\pi$
$11$	4.98417			1.50278			0.751391	+	0.659857i	$0.229383\pi$
$12$		0			0
$13$	0.0278283	−	0.103857i	0.00771817	−	0.0288046i	−0.961959	−	0.273193i	$-0.911920\pi$
$13$	0.0278283	−	0.103857i	0.00771817	−	0.0288046i	0.969678	+	0.244388i	$0.0785870\pi$
$14$	−1.26734	−	1.26734i	−0.338710	−	0.338710i
$15$		0			0
$16$	0.500000	−	0.866025i	0.125000	−	0.216506i
$17$	0.912166	+	3.40425i	0.221233	+	0.825652i	0.983879	+	0.178836i	$0.0572331\pi$
$17$	0.912166	+	3.40425i	0.221233	+	0.825652i	−0.762646	+	0.646816i	$0.776100\pi$
$18$		0			0
$19$	2.21397	−	8.26264i	0.507919	−	1.89558i	0.0676637	−	0.997708i	$-0.478446\pi$
$19$	2.21397	−	8.26264i	0.507919	−	1.89558i	0.440256	−	0.897872i	$-0.354888\pi$
$20$	−0.765290	+	0.205059i	−0.171124	+	0.0458526i
$21$		0			0
$22$	4.81433	−	1.29000i	1.02642	−	0.275028i
$23$	5.99711	−	5.99711i	1.25048	−	1.25048i	0.294980	−	0.955503i	$-0.404687\pi$
$23$	5.99711	−	5.99711i	1.25048	−	1.25048i	0.955503	−	0.294980i	$-0.0953131\pi$
$24$		0			0
$25$	−3.78651	−	2.18614i	−0.757301	−	0.437228i
$26$		−	0.107520i		−	0.0210864i
$27$		0			0
$28$	−1.55217	−	0.896143i	−0.293332	−	0.169355i
$29$	−4.02266	−	4.02266i	−0.746990	−	0.746990i	0.226923	−	0.973913i	$-0.427133\pi$
$29$	−4.02266	−	4.02266i	−0.746990	−	0.746990i	−0.973913	+	0.226923i	$0.927133\pi$
$30$		0			0
$31$	−6.76493	+	6.76493i	−1.21502	+	1.21502i	−0.245663	+	0.969355i	$0.579006\pi$
$31$	−6.76493	+	6.76493i	−1.21502	+	1.21502i	−0.969355	+	0.245663i	$0.920994\pi$
$32$	0.258819	−	0.965926i	0.0457532	−	0.170753i
$33$		0			0
$34$	1.76217	+	3.05217i	0.302209	+	0.523442i
$35$	0.367525	+	1.37162i	0.0621230	+	0.231846i
$36$		0			0
$37$	4.26613	−	4.33591i	0.701348	−	0.712819i
$37$	4.26613	−	4.33591i	0.701348	−	0.712819i
$38$		−	8.55412i		−	1.38766i
$39$		0			0
$40$	−0.686141	+	0.396143i	−0.108488	+	0.0626358i
$41$	4.52147	+	7.83142i	0.706136	+	1.22306i	0.966280	+	0.257493i	$0.0828964\pi$
$41$	4.52147	+	7.83142i	0.706136	+	1.22306i	−0.260145	+	0.965570i	$0.583770\pi$
$42$		0			0
$43$	2.24060	+	2.24060i	0.341688	+	0.341688i	0.857002	−	0.515314i	$-0.172325\pi$
$43$	2.24060	+	2.24060i	0.341688	+	0.341688i	−0.515314	+	0.857002i	$0.672325\pi$
$44$	4.31641	−	2.49208i	0.650724	−	0.375696i
$45$		0			0
$46$	4.24060	−	7.34493i	0.625242	−	1.08295i
$47$			8.63283i			1.25923i	0.776908	+	0.629614i	$0.216787\pi$
$47$			8.63283i			1.25923i	−0.776908	+	0.629614i	$0.783213\pi$
$48$		0			0
$49$	1.89385	−	3.28025i	0.270551	−	0.468607i
$50$	−4.22330	−	1.13163i	−0.597265	−	0.160037i
$51$		0			0
$52$	−0.0278283	−	0.103857i	−0.00385909	−	0.0144023i
$53$	0.970349	+	0.560232i	0.133288	+	0.0769537i	0.565161	−	0.824980i	$-0.308814\pi$
$53$	0.970349	+	0.560232i	0.133288	+	0.0769537i	−0.431873	+	0.901934i	$0.642147\pi$
$54$		0			0
$55$	−3.81433	−	1.02205i	−0.514325	−	0.137813i
$56$	−1.73122	−	0.463878i	−0.231344	−	0.0619883i
$57$		0			0
$58$	−4.92674	−	2.84445i	−0.646912	−	0.373495i
$59$	3.06049	+	11.4219i	0.398442	+	1.48700i	0.815838	+	0.578280i	$0.196276\pi$
$59$	3.06049	+	11.4219i	0.398442	+	1.48700i	−0.417396	+	0.908725i	$0.637057\pi$
$60$		0			0
$61$	−2.05217	−	0.549876i	−0.262753	−	0.0704044i	0.125037	−	0.992152i	$-0.460095\pi$
$61$	−2.05217	−	0.549876i	−0.262753	−	0.0704044i	−0.387790	+	0.921748i	$0.626762\pi$
$62$	−4.78353	+	8.28532i	−0.607509	+	1.05224i
$63$		0			0
$64$		−	1.00000i		−	0.125000i
$65$	−0.0425934	+	0.0737740i	−0.00528306	+	0.00915053i
$66$		0			0
$67$	−12.9290	+	7.46458i	−1.57953	+	0.911943i	−0.584608	+	0.811316i	$0.698752\pi$
$67$	−12.9290	+	7.46458i	−1.57953	+	0.911943i	−0.994924	+	0.100627i	$0.967915\pi$
$68$	2.49208	+	2.49208i	0.302209	+	0.302209i
$69$		0			0
$70$	0.710003	+	1.22976i	0.0848616	+	0.146985i
$71$	−5.01144	+	2.89335i	−0.594748	+	0.343378i	−0.766973	−	0.641680i	$-0.778238\pi$
$71$	−5.01144	+	2.89335i	−0.594748	+	0.343378i	0.172225	+	0.985058i	$0.444905\pi$
$72$		0			0
$73$			2.90818i			0.340377i	0.985412	+	0.170188i	$0.0544376\pi$
$73$			2.90818i			0.340377i	−0.985412	+	0.170188i	$0.945562\pi$
$74$	2.99855	−	5.29232i	0.348575	−	0.615220i
$75$		0			0
$76$	−2.21397	−	8.26264i	−0.253960	−	0.947790i
$77$	−4.46653	−	7.73625i	−0.509008	−	0.881628i
$78$		0			0
$79$	−0.0278283	+	0.103857i	−0.00313092	+	0.0116848i	−0.967474	−	0.252972i	$-0.918592\pi$
$79$	−0.0278283	+	0.103857i	−0.00313092	+	0.0116848i	0.964343	+	0.264657i	$0.0852586\pi$
$80$	−0.560232	+	0.560232i	−0.0626358	+	0.0626358i
$81$		0			0
$82$	6.39433	+	6.39433i	0.706136	+	0.706136i
$83$	3.41423	+	1.97121i	0.374760	+	0.216368i	0.675536	−	0.737327i	$-0.263912\pi$
$83$	3.41423	+	1.97121i	0.374760	+	0.216368i	−0.300776	+	0.953695i	$0.597246\pi$
$84$		0			0
$85$		−	2.79229i		−	0.302866i
$86$	2.74416	+	1.58434i	0.295910	+	0.170844i
$87$		0			0
$88$	3.52434	−	3.52434i	0.375696	−	0.375696i
$89$	5.75830	−	1.54293i	0.610379	−	0.163551i	0.0596287	−	0.998221i	$-0.481008\pi$
$89$	5.75830	−	1.54293i	0.610379	−	0.163551i	0.550750	+	0.834670i	$0.314342\pi$
$90$		0			0
$91$	−0.186141	+	0.0498762i	−0.0195128	+	0.00522845i
$92$	2.19509	−	8.19220i	0.228854	−	0.854096i
$93$		0			0
$94$	2.23434	+	8.33867i	0.230455	+	0.860068i
$95$	−3.38866	+	5.86933i	−0.347669	+	0.602180i
$96$		0			0
$97$	−0.841688	−	0.841688i	−0.0854604	−	0.0854604i	0.663084	−	0.748545i	$-0.269247\pi$
$97$	−0.841688	−	0.841688i	−0.0854604	−	0.0854604i	−0.748545	+	0.663084i	$0.769247\pi$
$98$	0.980331	−	3.65864i	0.0990284	−	0.369579i
$99$		0			0
$100$	−4.37228			−0.437228
$101$	−3.67984			−0.366158			−0.183079	−	0.983098i	$-0.558606\pi$
$101$	−3.67984			−0.366158			−0.183079	+	0.983098i	$0.558606\pi$
$102$		0			0
$103$	4.16915	−	4.16915i	0.410798	−	0.410798i	−0.471218	−	0.882017i	$-0.656186\pi$
$103$	4.16915	−	4.16915i	0.410798	−	0.410798i	0.882017	+	0.471218i	$0.156186\pi$
$104$	−0.0537601	−	0.0931152i	−0.00527161	−	0.00913070i
$105$		0			0
$106$	1.08228	+	0.289997i	0.105121	+	0.0281670i
$107$	−6.57967	+	3.79878i	−0.636081	+	0.367242i	−0.783103	−	0.621892i	$-0.786364\pi$
$107$	−6.57967	+	3.79878i	−0.636081	+	0.367242i	0.147022	+	0.989133i	$0.453031\pi$
$108$		0			0
$109$	−1.29854	+	0.347944i	−0.124378	+	0.0333269i	−0.320471	−	0.947258i	$-0.603841\pi$
$109$	−1.29854	+	0.347944i	−0.124378	+	0.0333269i	0.196093	+	0.980585i	$0.437175\pi$
$110$	−3.94889			−0.376512
$111$		0			0
$112$	−1.79229			−0.169355
$113$	−18.8250	+	5.04416i	−1.77091	+	0.474514i	−0.988879	−	0.148723i	$-0.952484\pi$
$113$	−18.8250	+	5.04416i	−1.77091	+	0.474514i	−0.782033	+	0.623237i	$0.785817\pi$
$114$		0			0
$115$	−5.81929	+	3.35977i	−0.542652	+	0.313300i
$116$	−5.49506	−	1.47240i	−0.510204	−	0.136709i
$117$		0			0
$118$	5.91241	+	10.2406i	0.544282	+	0.942723i
$119$	4.46653	−	4.46653i	0.409446	−	0.409446i
$120$		0			0
$121$	13.8419			1.25836
$122$	−2.12456			−0.192349
$123$		0			0
$124$	−2.47614	+	9.24107i	−0.222364	+	0.829873i
$125$	5.25065	+	5.25065i	0.469632	+	0.469632i
$126$		0			0
$127$	−4.78193	+	8.28254i	−0.424327	+	0.734957i	−0.996357	−	0.0852761i	$-0.972823\pi$
$127$	−4.78193	+	8.28254i	−0.424327	+	0.734957i	0.572030	+	0.820233i	$0.306156\pi$
$128$	−0.258819	−	0.965926i	−0.0228766	−	0.0853766i
$129$		0			0
$130$	−0.0220480	+	0.0822842i	−0.00193374	+	0.00721680i
$131$	8.80388	−	2.35899i	0.769198	−	0.206106i	0.147181	−	0.989110i	$-0.452980\pi$
$131$	8.80388	−	2.35899i	0.769198	−	0.206106i	0.622017	+	0.783004i	$0.286313\pi$
$132$		0			0
$133$	−14.8090	+	3.96807i	−1.28411	+	0.344075i
$134$	−10.5565	+	10.5565i	−0.911943	+	0.911943i
$135$		0			0
$136$	3.05217	+	1.76217i	0.261721	+	0.151105i
$137$		−	17.3708i		−	1.48409i	−0.670351	−	0.742044i	$-0.733856\pi$
$137$		−	17.3708i		−	1.48409i	0.670351	−	0.742044i	$-0.266144\pi$
$138$		0			0
$139$	15.9125	+	9.18709i	1.34968	+	0.779239i	0.988204	−	0.153142i	$-0.0489392\pi$
$139$	15.9125	+	9.18709i	1.34968	+	0.779239i	0.361477	+	0.932381i	$0.382273\pi$
$140$	1.00410	+	1.00410i	0.0848616	+	0.0848616i
$141$		0			0
$142$	−4.09182	+	4.09182i	−0.343378	+	0.343378i
$143$	0.138701	−	0.517638i	0.0115987	−	0.0432871i
$144$		0			0
$145$	2.25362	+	3.90339i	0.187153	+	0.324159i
$146$	0.752692	+	2.80909i	0.0622933	+	0.232482i
$147$		0			0
$148$	1.52663	−	5.88807i	0.125488	−	0.483997i
$149$		−	1.20618i		−	0.0988143i	−0.998779	−	0.0494072i	$-0.984267\pi$
$149$		−	1.20618i		−	0.0988143i	0.998779	−	0.0494072i	$-0.0157332\pi$
$150$		0			0
$151$	6.05904	−	3.49819i	0.493077	−	0.284678i	−0.232773	−	0.972531i	$-0.574780\pi$
$151$	6.05904	−	3.49819i	0.493077	−	0.284678i	0.725850	+	0.687853i	$0.241447\pi$
$152$	−4.27706	−	7.40808i	−0.346915	−	0.600875i
$153$		0			0
$154$	−6.31662	−	6.31662i	−0.509008	−	0.509008i
$155$	6.56435	−	3.78993i	0.527261	−	0.304414i
$156$		0			0
$157$	−8.71820	+	15.1004i	−0.695788	+	1.20514i	0.274126	+	0.961694i	$0.411611\pi$
$157$	−8.71820	+	15.1004i	−0.695788	+	1.20514i	−0.969914	+	0.243447i	$0.921722\pi$
$158$			0.107520i			0.00855385i
$159$		0			0
$160$	−0.396143	+	0.686141i	−0.0313179	+	0.0542442i
$161$	−14.6828	−	3.93424i	−1.15717	−	0.310061i
$162$		0			0
$163$	3.72217	+	13.8913i	0.291543	+	1.08805i	0.943925	+	0.330161i	$0.107103\pi$
$163$	3.72217	+	13.8913i	0.291543	+	1.08805i	−0.652382	+	0.757890i	$0.726230\pi$
$164$	7.83142	+	4.52147i	0.611531	+	0.353068i
$165$		0			0
$166$	3.80808	+	1.02037i	0.295564	+	0.0791962i
$167$	−14.5054	−	3.88671i	−1.12246	−	0.300763i	−0.350582	−	0.936532i	$-0.614016\pi$
$167$	−14.5054	−	3.88671i	−1.12246	−	0.300763i	−0.771879	+	0.635769i	$0.780683\pi$
$168$		0			0
$169$	11.2483	+	6.49422i	0.865255	+	0.499555i
$170$	−0.722697	−	2.69714i	−0.0554283	−	0.206861i
$171$		0			0
$172$	3.06071	+	0.820115i	0.233377	+	0.0625332i
$173$	−0.921013	+	1.59524i	−0.0700233	+	0.121284i	−0.898911	−	0.438131i	$-0.855641\pi$
$173$	−0.921013	+	1.59524i	−0.0700233	+	0.121284i	0.828888	+	0.559415i	$0.188974\pi$
$174$		0			0
$175$			7.83638i			0.592375i
$176$	2.49208	−	4.31641i	0.187848	−	0.325362i
$177$		0			0
$178$	5.16275	−	2.98072i	0.386965	−	0.223414i
$179$	−3.22506	−	3.22506i	−0.241052	−	0.241052i	0.576233	−	0.817285i	$-0.304522\pi$
$179$	−3.22506	−	3.22506i	−0.241052	−	0.241052i	−0.817285	+	0.576233i	$0.804522\pi$
$180$		0			0
$181$	−11.2596	−	19.5023i	−0.836922	−	1.44959i	−0.892456	−	0.451134i	$-0.851020\pi$
$181$	−11.2596	−	19.5023i	−0.836922	−	1.44959i	0.0555345	−	0.998457i	$-0.482314\pi$
$182$	−0.166889	+	0.0963535i	−0.0123706	+	0.00714220i
$183$		0			0
$184$		−	8.48119i		−	0.625242i
$185$	−4.15395	+	2.44342i	−0.305404	+	0.179644i
$186$		0			0
$187$	4.54639	+	16.9673i	0.332465	+	1.24077i
$188$	4.31641	+	7.47625i	0.314807	+	0.545262i
$189$		0			0
$190$	−1.75410	+	6.54639i	−0.127256	+	0.474925i
$191$	−1.17684	+	1.17684i	−0.0851531	+	0.0851531i	−0.748400	−	0.663247i	$-0.769178\pi$
$191$	−1.17684	+	1.17684i	−0.0851531	+	0.0851531i	0.663247	+	0.748400i	$0.269178\pi$
$192$		0			0
$193$	8.26264	+	8.26264i	0.594758	+	0.594758i	0.938913	−	0.344155i	$-0.111834\pi$
$193$	8.26264	+	8.26264i	0.594758	+	0.594758i	−0.344155	+	0.938913i	$0.611834\pi$
$194$	−1.03085	−	0.595163i	−0.0740109	−	0.0427302i
$195$		0			0
$196$		−	3.78771i		−	0.270551i
$197$	−9.14410	−	5.27935i	−0.651490	−	0.376138i	0.137537	−	0.990497i	$-0.456081\pi$
$197$	−9.14410	−	5.27935i	−0.651490	−	0.376138i	−0.789027	+	0.614359i	$0.789415\pi$
$198$		0			0
$199$	16.6329	−	16.6329i	1.17908	−	1.17908i	0.199095	−	0.979980i	$-0.436200\pi$
$199$	16.6329	−	16.6329i	1.17908	−	1.17908i	0.979980	−	0.199095i	$-0.0638002\pi$
$200$	−4.22330	+	1.13163i	−0.298632	+	0.0800183i
$201$		0			0
$202$	−3.55446	+	0.952414i	−0.250091	+	0.0670116i
$203$	−2.63896	+	9.84873i	−0.185219	+	0.691245i
$204$		0			0
$205$	−1.85434	−	6.92048i	−0.129513	−	0.483347i
$206$	2.94803	−	5.10614i	0.205399	−	0.355762i
$207$		0			0
$208$	−0.0760282	−	0.0760282i	−0.00527161	−	0.00527161i
$209$	11.0348	−	41.1824i	0.763292	−	2.84865i
$210$		0			0
$211$	−23.4651			−1.61540			−0.807700	−	0.589593i	$-0.799288\pi$
$211$	−23.4651			−1.61540			−0.807700	+	0.589593i	$0.799288\pi$
$212$	1.12046			0.0769537
$213$		0			0
$214$	−5.37228	+	5.37228i	−0.367242	+	0.367242i
$215$	−1.25525	−	2.17416i	−0.0856075	−	0.148277i
$216$		0			0
$217$	16.5627	+	4.43795i	1.12435	+	0.301268i
$218$	−1.16424	+	0.672175i	−0.0788524	+	0.0455255i
$219$		0			0
$220$	−3.81433	+	1.02205i	−0.257162	+	0.0689065i
$221$	0.378937			0.0254901
$222$		0			0
$223$	−20.1248			−1.34765			−0.673827	−	0.738889i	$-0.735351\pi$
$223$	−20.1248			−1.34765			−0.673827	+	0.738889i	$0.735351\pi$
$224$	−1.73122	+	0.463878i	−0.115672	+	0.0309942i
$225$		0			0
$226$	−16.8781	+	9.74456i	−1.12271	+	0.648199i
$227$	26.7043	+	7.15539i	1.77242	+	0.474920i	0.989169	−	0.146780i	$-0.0468911\pi$
$227$	26.7043	+	7.15539i	1.77242	+	0.474920i	0.783255	+	0.621700i	$0.213558\pi$
$228$		0			0
$229$	3.12737	+	5.41676i	0.206662	+	0.357950i	0.950661	−	0.310231i	$-0.100406\pi$
$229$	3.12737	+	5.41676i	0.206662	+	0.357950i	−0.743999	+	0.668181i	$0.767073\pi$
$230$	−4.75143	+	4.75143i	−0.313300	+	0.313300i
$231$		0			0
$232$	−5.68891			−0.373495
$233$	−4.12762			−0.270409			−0.135205	−	0.990818i	$-0.543169\pi$
$233$	−4.12762			−0.270409			−0.135205	+	0.990818i	$0.543169\pi$
$234$		0			0
$235$	1.77024	−	6.60662i	0.115478	−	0.430968i
$236$	8.36141	+	8.36141i	0.544282	+	0.544282i
$237$		0			0
$238$	3.15831	−	5.47036i	0.204723	−	0.354591i
$239$	7.24419	+	27.0357i	0.468588	+	1.74879i	0.644713	+	0.764425i	$0.276977\pi$
$239$	7.24419	+	27.0357i	0.468588	+	1.74879i	−0.176125	+	0.984368i	$0.556356\pi$
$240$		0			0
$241$	3.35143	−	12.5077i	0.215885	−	0.805693i	−0.769968	−	0.638082i	$-0.779728\pi$
$241$	3.35143	−	12.5077i	0.215885	−	0.805693i	0.985853	−	0.167611i	$-0.0536053\pi$
$242$	13.3703	−	3.58255i	0.859473	−	0.230295i
$243$		0			0
$244$	−2.05217	+	0.549876i	−0.131376	+	0.0352022i
$245$	−2.12199	+	2.12199i	−0.135569	+	0.135569i
$246$		0			0
$247$	−0.796518	−	0.459870i	−0.0506813	−	0.0292608i
$248$			9.56706i			0.607509i
$249$		0			0
$250$	6.43070	+	3.71277i	0.406713	+	0.234816i
$251$	8.30142	+	8.30142i	0.523981	+	0.523981i	0.918771	−	0.394790i	$-0.129183\pi$
$251$	8.30142	+	8.30142i	0.523981	+	0.523981i	−0.394790	+	0.918771i	$0.629183\pi$
$252$		0			0
$253$	29.8906	−	29.8906i	1.87921	−	1.87921i
$254$	−2.47531	+	9.23797i	−0.155315	+	0.579642i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	4.70514	+	17.5598i	0.293498	+	1.09535i	0.942403	+	0.334481i	$0.108561\pi$
$257$	4.70514	+	17.5598i	0.293498	+	1.09535i	−0.648904	+	0.760870i	$0.724772\pi$
$258$		0			0
$259$	−10.5531	−	2.73615i	−0.655739	−	0.170016i
$260$			0.0851868i			0.00528306i
$261$		0			0
$262$	7.89334	−	4.55722i	0.487652	−	0.281546i
$263$	−9.28386	−	16.0801i	−0.572467	−	0.991542i	−0.996312	−	0.0858072i	$-0.972653\pi$
$263$	−9.28386	−	16.0801i	−0.572467	−	0.991542i	0.423845	−	0.905735i	$-0.360680\pi$
$264$		0			0
$265$	−0.627719	−	0.627719i	−0.0385605	−	0.0385605i
$266$	−13.2774	+	7.66572i	−0.814090	+	0.470015i
$267$		0			0
$268$	−7.46458	+	12.9290i	−0.455972	+	0.789766i
$269$		−	4.56704i		−	0.278457i	−0.990260	−	0.139229i	$-0.955538\pi$
$269$		−	4.56704i		−	0.278457i	0.990260	−	0.139229i	$-0.0444623\pi$
$270$		0			0
$271$	2.34773	−	4.06639i	0.142615	−	0.247016i	−0.785866	−	0.618397i	$-0.787782\pi$
$271$	2.34773	−	4.06639i	0.142615	−	0.247016i	0.928480	+	0.371381i	$0.121116\pi$
$272$	3.40425	+	0.912166i	0.206413	+	0.0553082i
$273$		0			0
$274$	−4.49590	−	16.7789i	−0.271607	−	1.01365i
$275$	−18.8726	−	10.8961i	−1.13806	−	0.657059i
$276$		0			0
$277$	18.4300	+	4.93830i	1.10735	+	0.296714i	0.765754	−	0.643133i	$-0.222366\pi$
$277$	18.4300	+	4.93830i	1.10735	+	0.296714i	0.341596	+	0.939847i	$0.389033\pi$
$278$	17.7481	+	4.75559i	1.06446	+	0.285221i
$279$		0			0
$280$	1.22976	+	0.710003i	0.0734923	+	0.0424308i
$281$	−6.10881	−	22.7984i	−0.364421	−	1.36004i	−0.868204	−	0.496207i	$-0.834726\pi$
$281$	−6.10881	−	22.7984i	−0.364421	−	1.36004i	0.503783	−	0.863830i	$-0.331941\pi$
$282$		0			0
$283$	−6.37604	−	1.70845i	−0.379016	−	0.101557i	0.0642809	−	0.997932i	$-0.479525\pi$
$283$	−6.37604	−	1.70845i	−0.379016	−	0.101557i	−0.443297	+	0.896375i	$0.646191\pi$
$284$	−2.89335	+	5.01144i	−0.171689	+	0.297374i
$285$		0			0
$286$		−	0.535898i		−	0.0316883i
$287$	8.10378	−	14.0362i	0.478351	−	0.828528i
$288$		0			0
$289$	3.96557	−	2.28952i	0.233269	−	0.134678i
$290$	3.18710	+	3.18710i	0.187153	+	0.187153i
$291$		0			0
$292$	1.45409	+	2.51856i	0.0850942	+	0.147387i
$293$	−0.583026	+	0.336610i	−0.0340608	+	0.0196650i	−0.516934	−	0.856025i	$-0.672927\pi$
$293$	−0.583026	+	0.336610i	−0.0340608	+	0.0196650i	0.482873	+	0.875690i	$0.339593\pi$
$294$		0			0
$295$		−	9.36865i		−	0.545464i
$296$	−0.0493365	−	6.08256i	−0.00286762	−	0.353542i
$297$		0			0
$298$	−0.312183	−	1.16508i	−0.0180843	−	0.0674915i
$299$	−0.455950	−	0.789728i	−0.0263682	−	0.0456711i
$300$		0			0
$301$	1.46988	−	5.48567i	0.0847226	−	0.316189i
$302$	4.94718	−	4.94718i	0.284678	−	0.284678i
$303$		0			0
$304$	−6.04868	−	6.04868i	−0.346915	−	0.346915i
$305$	1.45775	+	0.841630i	0.0834703	+	0.0481916i
$306$		0			0
$307$			5.44263i			0.310627i	0.987865	+	0.155314i	$0.0496388\pi$
$307$			5.44263i			0.310627i	−0.987865	+	0.155314i	$0.950361\pi$
$308$	−7.73625	−	4.46653i	−0.440814	−	0.254504i
$309$		0			0
$310$	5.35977	−	5.35977i	0.304414	−	0.304414i
$311$	−10.4362	+	2.79638i	−0.591784	+	0.158568i	−0.542269	−	0.840205i	$-0.682434\pi$
$311$	−10.4362	+	2.79638i	−0.591784	+	0.158568i	−0.0495157	+	0.998773i	$0.515768\pi$
$312$		0			0
$313$	−3.13623	+	0.840349i	−0.177270	+	0.0474993i	−0.346362	−	0.938101i	$-0.612583\pi$
$313$	−3.13623	+	0.840349i	−0.177270	+	0.0474993i	0.169092	+	0.985600i	$0.445916\pi$
$314$	−4.51287	+	16.8423i	−0.254676	+	0.950464i
$315$		0			0
$316$	0.0278283	+	0.103857i	0.00156546	+	0.00584238i
$317$	5.83841	−	10.1124i	0.327918	−	0.567971i	−0.654181	−	0.756338i	$-0.726986\pi$
$317$	5.83841	−	10.1124i	0.327918	−	0.567971i	0.982099	+	0.188368i	$0.0603197\pi$
$318$		0			0
$319$	−20.0496	−	20.0496i	−1.12256	−	1.12256i
$320$	−0.205059	+	0.765290i	−0.0114631	+	0.0427810i
$321$		0			0
$322$	−15.2007			−0.847104
$323$	30.1476			1.67746
$324$		0			0
$325$	−0.332417	+	0.332417i	−0.0184392	+	0.0184392i
$326$	7.19067	+	12.4546i	0.398255	+	0.689797i
$327$		0			0
$328$	8.73482	+	2.34049i	0.482300	+	0.129232i
$329$	13.3996	−	7.73625i	0.738743	−	0.426513i
$330$		0			0
$331$	22.2516	−	5.96229i	1.22306	−	0.327717i	0.411184	−	0.911552i	$-0.365115\pi$
$331$	22.2516	−	5.96229i	1.22306	−	0.327717i	0.811872	+	0.583835i	$0.198449\pi$
$332$	3.94241			0.216368
$333$		0			0
$334$	−15.0171			−0.821699
$335$	11.4251	−	3.06136i	0.624222	−	0.167260i
$336$		0			0
$337$	0.497068	−	0.286982i	0.0270770	−	0.0156329i	−0.486400	−	0.873736i	$-0.661690\pi$
$337$	0.497068	−	0.286982i	0.0270770	−	0.0156329i	0.513477	+	0.858103i	$0.328357\pi$
$338$	12.5459	+	3.36166i	0.682405	+	0.182850i
$339$		0			0
$340$	−1.39614	−	2.41819i	−0.0757165	−	0.131145i
$341$	−33.7176	+	33.7176i	−1.82591	+	1.82591i
$342$		0			0
$343$	−19.3347			−1.04397
$344$	3.16868			0.170844
$345$		0			0
$346$	−0.476751	+	1.77926i	−0.0256303	+	0.0956536i
$347$	8.37128	+	8.37128i	0.449394	+	0.449394i	0.895153	−	0.445759i	$-0.147066\pi$
$347$	8.37128	+	8.37128i	0.449394	+	0.449394i	−0.445759	+	0.895153i	$0.647066\pi$
$348$		0			0
$349$	5.94253	−	10.2928i	0.318096	−	0.550959i	−0.661995	−	0.749509i	$-0.730290\pi$
$349$	5.94253	−	10.2928i	0.318096	−	0.550959i	0.980091	+	0.198550i	$0.0636231\pi$
$350$	2.02821	+	7.56936i	0.108412	+	0.404600i
$351$		0			0
$352$	1.29000	−	4.81433i	0.0687571	−	0.256605i
$353$	−20.0086	+	5.36130i	−1.06495	+	0.285353i	−0.748417	−	0.663228i	$-0.769186\pi$
$353$	−20.0086	+	5.36130i	−1.06495	+	0.285353i	−0.316535	+	0.948581i	$0.602519\pi$
$354$		0			0
$355$	4.42851	−	1.18662i	0.235041	−	0.0629791i
$356$	4.21537	−	4.21537i	0.223414	−	0.223414i
$357$		0			0
$358$	−3.94987	−	2.28046i	−0.208757	−	0.120526i
$359$			14.1435i			0.746464i	0.927738	+	0.373232i	$0.121751\pi$
$359$			14.1435i			0.746464i	−0.927738	+	0.373232i	$0.878249\pi$
$360$		0			0
$361$	−46.9152	−	27.0865i	−2.46922	−	1.42560i
$362$	−15.9235	−	15.9235i	−0.836922	−	0.836922i
$363$		0			0
$364$	−0.136264	+	0.136264i	−0.00714220	+	0.00714220i
$365$	0.596348	−	2.22560i	0.0312143	−	0.116493i
$366$		0			0
$367$	5.73783	+	9.93821i	0.299512	+	0.518771i	0.976024	−	0.217661i	$-0.0698427\pi$
$367$	5.73783	+	9.93821i	0.299512	+	0.518771i	−0.676512	+	0.736432i	$0.736509\pi$
$368$	−2.19509	−	8.19220i	−0.114427	−	0.427048i
$369$		0			0
$370$	−3.38000	+	3.43528i	−0.175718	+	0.178592i
$371$		−	2.00819i		−	0.104260i
$372$		0			0
$373$	−12.4379	+	7.18105i	−0.644012	+	0.371820i	−0.786158	−	0.618025i	$-0.787933\pi$
$373$	−12.4379	+	7.18105i	−0.644012	+	0.371820i	0.142146	+	0.989846i	$0.454600\pi$
$374$	8.78294	+	15.2125i	0.454155	+	0.786620i
$375$		0			0
$376$	6.10433	+	6.10433i	0.314807	+	0.314807i
$377$	−0.529724	+	0.305836i	−0.0272822	+	0.0157514i
$378$		0			0
$379$	9.82685	−	17.0206i	0.504771	−	0.874289i	−0.495214	−	0.868771i	$-0.664910\pi$
$379$	9.82685	−	17.0206i	0.504771	−	0.874289i	0.999985	−	0.00551811i	$-0.00175648\pi$
$380$			6.77732i			0.347669i
$381$		0			0
$382$	−0.832151	+	1.44133i	−0.0425766	+	0.0737448i
$383$	−6.70238	−	1.79590i	−0.342476	−	0.0917660i	0.0834818	−	0.996509i	$-0.473396\pi$
$383$	−6.70238	−	1.79590i	−0.342476	−	0.0917660i	−0.425957	+	0.904743i	$0.640063\pi$
$384$		0			0
$385$	1.83180	+	6.83638i	0.0933573	+	0.348414i
$386$	10.1196	+	5.84257i	0.515076	+	0.297379i
$387$		0			0
$388$	−1.14977	−	0.308079i	−0.0583706	−	0.0156403i
$389$	14.8872	+	3.98900i	0.754809	+	0.202251i	0.615650	−	0.788020i	$-0.288893\pi$
$389$	14.8872	+	3.98900i	0.754809	+	0.202251i	0.139159	+	0.990270i	$0.455560\pi$
$390$		0			0
$391$	25.8860	+	14.9453i	1.30911	+	0.755816i
$392$	−0.980331	−	3.65864i	−0.0495142	−	0.184789i
$393$		0			0
$394$	−10.1989	−	2.73279i	−0.513814	−	0.137676i
$395$	0.0425934	−	0.0737740i	0.00214311	−	0.00371197i
$396$		0			0
$397$			15.0940i			0.757546i	0.925490	+	0.378773i	$0.123654\pi$
$397$			15.0940i			0.757546i	−0.925490	+	0.378773i	$0.876346\pi$
$398$	11.7612	−	20.3711i	0.589538	−	1.02111i
$399$		0			0
$400$	−3.78651	+	2.18614i	−0.189325	+	0.109307i
$401$	11.2363	+	11.2363i	0.561116	+	0.561116i	0.929624	−	0.368508i	$-0.120131\pi$
$401$	11.2363	+	11.2363i	0.561116	+	0.561116i	−0.368508	+	0.929624i	$0.620131\pi$
$402$		0			0
$403$	0.514326	+	0.890839i	0.0256204	+	0.0443758i
$404$	−3.18684	+	1.83992i	−0.158551	+	0.0915395i
$405$		0			0
$406$			10.1962i			0.506027i
$407$	21.2631	−	21.6109i	1.05397	−	1.07121i
$408$		0			0
$409$	−5.55070	−	20.7155i	−0.274464	−	1.02432i	−0.956199	−	0.292716i	$-0.905441\pi$
$409$	−5.55070	−	20.7155i	−0.274464	−	1.02432i	0.681735	−	0.731599i	$-0.261226\pi$
$410$	−3.58230	−	6.20473i	−0.176917	−	0.306430i
$411$		0			0
$412$	1.52601	−	5.69516i	0.0751813	−	0.280580i
$413$	14.9861	−	14.9861i	0.737415	−	0.737415i
$414$		0			0
$415$	−2.20866	−	2.20866i	−0.108419	−	0.108419i
$416$	−0.0931152	−	0.0537601i	−0.00456535	−	0.00263580i
$417$		0			0
$418$		−	42.6352i		−	2.08535i
$419$	16.1336	+	9.31474i	0.788178	+	0.455055i	0.839321	−	0.543637i	$-0.182953\pi$
$419$	16.1336	+	9.31474i	0.788178	+	0.455055i	−0.0511427	+	0.998691i	$0.516286\pi$
$420$		0			0
$421$	18.9146	−	18.9146i	0.921842	−	0.921842i	−0.0753175	−	0.997160i	$-0.523997\pi$
$421$	18.9146	−	18.9146i	0.921842	−	0.921842i	0.997160	+	0.0753175i	$0.0239970\pi$
$422$	−22.6655	+	6.07320i	−1.10334	+	0.295639i
$423$		0			0
$424$	1.08228	−	0.289997i	0.0525604	−	0.0140835i
$425$	3.98825	−	14.8843i	0.193458	−	0.721996i
$426$		0			0
$427$	0.985536	+	3.67807i	0.0476934	+	0.177994i
$428$	−3.79878	+	6.57967i	−0.183621	+	0.318041i
$429$		0			0
$430$	−1.77520	−	1.77520i	−0.0856075	−	0.0856075i
$431$	−0.477908	+	1.78358i	−0.0230200	+	0.0859118i	−0.976480	−	0.215607i	$-0.930827\pi$
$431$	−0.477908	+	1.78358i	−0.0230200	+	0.0859118i	0.953460	+	0.301519i	$0.0974936\pi$
$432$		0			0
$433$	−23.4164			−1.12532			−0.562660	−	0.826689i	$-0.690222\pi$
$433$	−23.4164			−1.12532			−0.562660	+	0.826689i	$0.690222\pi$
$434$	17.1469			0.823079
$435$		0			0
$436$	−0.950599	+	0.950599i	−0.0455255	+	0.0455255i
$437$	−36.2746	−	62.8294i	−1.73525	−	3.00554i
$438$		0			0
$439$	13.0416	+	3.49449i	0.622441	+	0.166783i	0.556237	−	0.831023i	$-0.312245\pi$
$439$	13.0416	+	3.49449i	0.622441	+	0.166783i	0.0662040	+	0.997806i	$0.478911\pi$
$440$	−3.41984	+	1.97445i	−0.163034	+	0.0941280i
$441$		0			0
$442$	0.366025	−	0.0980762i	0.0174101	−	0.00466501i
$443$	12.3490			0.586718			0.293359	−	0.956002i	$-0.405227\pi$
$443$	12.3490			0.586718			0.293359	+	0.956002i	$0.405227\pi$
$444$		0			0
$445$	−4.72317			−0.223900
$446$	−19.4390	+	5.20868i	−0.920465	+	0.246638i
$447$		0			0
$448$	−1.55217	+	0.896143i	−0.0733330	+	0.0423388i
$449$	−8.02367	−	2.14994i	−0.378660	−	0.101462i	0.0644684	−	0.997920i	$-0.479465\pi$
$449$	−8.02367	−	2.14994i	−0.378660	−	0.101462i	−0.443129	+	0.896458i	$0.646132\pi$
$450$		0			0
$451$	22.5358	+	39.0331i	1.06117	+	1.83800i
$452$	−13.7809	+	13.7809i	−0.648199	+	0.648199i
$453$		0			0
$454$	27.6463			1.29750
$455$	0.152679			0.00715771
$456$		0			0
$457$	6.24444	−	23.3045i	0.292102	−	1.09014i	−0.651389	−	0.758744i	$-0.725813\pi$
$457$	6.24444	−	23.3045i	0.292102	−	1.09014i	0.943491	−	0.331397i	$-0.107520\pi$
$458$	4.42277	+	4.42277i	0.206662	+	0.206662i
$459$		0			0
$460$	−3.35977	+	5.81929i	−0.156650	+	0.271326i
$461$	7.27574	+	27.1534i	0.338865	+	1.26466i	0.899618	+	0.436678i	$0.143845\pi$
$461$	7.27574	+	27.1534i	0.338865	+	1.26466i	−0.560753	+	0.827983i	$0.689488\pi$
$462$		0			0
$463$	5.06434	−	18.9004i	0.235360	−	0.878375i	−0.742626	−	0.669706i	$-0.766420\pi$
$463$	5.06434	−	18.9004i	0.235360	−	0.878375i	0.977986	−	0.208669i	$-0.0669131\pi$
$464$	−5.49506	+	1.47240i	−0.255102	+	0.0683543i
$465$		0			0
$466$	−3.98697	+	1.06831i	−0.184693	+	0.0494883i
$467$	7.16747	−	7.16747i	0.331671	−	0.331671i	−0.521550	−	0.853221i	$-0.674646\pi$
$467$	7.16747	−	7.16747i	0.331671	−	0.331671i	0.853221	+	0.521550i	$0.174646\pi$
$468$		0			0
$469$	23.1725	+	13.3787i	1.07001	+	0.617769i
$470$		−	6.83968i		−	0.315491i
$471$		0			0
$472$	10.2406	+	5.91241i	0.471362	+	0.272141i
$473$	11.1675	+	11.1675i	0.513482	+	0.513482i
$474$		0			0
$475$	−26.4465	+	26.4465i	−1.21345	+	1.21345i
$476$	1.63486	−	6.10139i	0.0749338	−	0.279657i
$477$		0			0
$478$	13.9947	+	24.2395i	0.640102	+	1.10869i
$479$	−4.30956	−	16.0835i	−0.196909	−	0.734874i	−0.991764	−	0.128075i	$-0.959120\pi$
$479$	−4.30956	−	16.0835i	−0.196909	−	0.734874i	0.794855	−	0.606799i	$-0.207547\pi$
$480$		0			0
$481$	−0.331593	−	0.563727i	−0.0151193	−	0.0257037i
$482$		−	12.9489i		−	0.589808i
$483$		0			0
$484$	11.9874	−	6.92096i	0.544884	−	0.314589i
$485$	0.471540	+	0.816731i	0.0214115	+	0.0370858i
$486$		0			0
$487$	−2.35061	−	2.35061i	−0.106516	−	0.106516i	0.651840	−	0.758356i	$-0.273997\pi$
$487$	−2.35061	−	2.35061i	−0.106516	−	0.106516i	−0.758356	+	0.651840i	$0.773997\pi$
$488$	−1.83992	+	1.06228i	−0.0832893	+	0.0480871i
$489$		0			0
$490$	−1.50048	+	2.59890i	−0.0677846	+	0.117406i
$491$			21.6729i			0.978086i	0.872260	+	0.489043i	$0.162654\pi$
$491$			21.6729i			0.978086i	−0.872260	+	0.489043i	$0.837346\pi$
$492$		0			0
$493$	10.0248	−	17.3635i	0.451495	−	0.782012i
$494$	−0.888401	−	0.238046i	−0.0399710	−	0.0107102i
$495$		0			0
$496$	2.47614	+	9.24107i	0.111182	+	0.414936i
$497$	8.98193	+	5.18572i	0.402895	+	0.232611i
$498$		0			0
$499$	−12.7053	−	3.40437i	−0.568766	−	0.152400i	−0.0370355	−	0.999314i	$-0.511791\pi$
$499$	−12.7053	−	3.40437i	−0.568766	−	0.152400i	−0.531731	+	0.846914i	$0.678458\pi$
$500$	7.17252	+	1.92187i	0.320765	+	0.0859487i
$501$		0			0
$502$	10.1671	+	5.86999i	0.453781	+	0.261991i
$503$	5.22764	+	19.5098i	0.233089	+	0.869900i	0.979001	+	0.203855i	$0.0653473\pi$
$503$	5.22764	+	19.5098i	0.233089	+	0.869900i	−0.745912	+	0.666045i	$0.767986\pi$
$504$		0			0
$505$	2.81615	+	0.754585i	0.125317	+	0.0335786i
$506$	21.1358	−	36.6083i	0.939603	−	1.62744i
$507$		0			0
$508$			9.56385i			0.424327i
$509$	−12.2010	+	21.1327i	−0.540799	+	0.936691i	0.458060	+	0.888921i	$0.348545\pi$
$509$	−12.2010	+	21.1327i	−0.540799	+	0.936691i	−0.998858	+	0.0477694i	$0.984789\pi$
$510$		0			0
$511$	4.51398	−	2.60615i	0.199687	−	0.115289i
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$		0			0
$514$	9.08963	+	15.7437i	0.400926	+	0.694425i
$515$	−4.04553	+	2.33569i	−0.178267	+	0.102923i
$516$		0			0
$517$			43.0275i			1.89235i
$518$	−10.9017	+	0.0884251i	−0.478993	+	0.00388518i
$519$		0			0
$520$	0.0220480	+	0.0822842i	0.000966868	+	0.00360840i
$521$	−4.59382	−	7.95672i	−0.201259	−	0.348590i	0.747676	−	0.664064i	$-0.231170\pi$
$521$	−4.59382	−	7.95672i	−0.201259	−	0.348590i	−0.948934	+	0.315474i	$0.897837\pi$
$522$		0			0
$523$	4.67977	−	17.4652i	0.204632	−	0.763698i	−0.784929	−	0.619586i	$-0.787301\pi$
$523$	4.67977	−	17.4652i	0.204632	−	0.763698i	0.989561	−	0.144112i	$-0.0460326\pi$
$524$	6.44488	−	6.44488i	0.281546	−	0.281546i
$525$		0			0
$526$	−13.1294	−	13.1294i	−0.572467	−	0.572467i
$527$	−29.2003	−	16.8588i	−1.27198	−	0.734380i
$528$		0			0
$529$		−	48.9306i		−	2.12742i
$530$	−0.768795	−	0.443864i	−0.0333943	−	0.0192802i
$531$		0			0
$532$	−10.8410	+	10.8410i	−0.470015	+	0.470015i
$533$	0.939169	−	0.251650i	0.0406799	−	0.0109002i
$534$		0			0
$535$	5.81433	−	1.55795i	0.251376	−	0.0673559i
$536$	−3.86395	+	14.4205i	−0.166897	+	0.622869i
$537$		0			0
$538$	−1.18204	−	4.41142i	−0.0509612	−	0.190190i
$539$	9.43928	−	16.3493i	0.406579	−	0.704215i
$540$		0			0
$541$	−2.60437	−	2.60437i	−0.111971	−	0.111971i	0.648902	−	0.760872i	$-0.275229\pi$
$541$	−2.60437	−	2.60437i	−0.111971	−	0.111971i	−0.760872	+	0.648902i	$0.775229\pi$
$542$	1.21528	−	4.53547i	0.0522006	−	0.194815i
$543$		0			0
$544$	3.52434			0.151105
$545$	1.06511			0.0456244
$546$		0			0
$547$	−26.6204	+	26.6204i	−1.13821	+	1.13821i	−0.149434	+	0.988772i	$0.547745\pi$
$547$	−26.6204	+	26.6204i	−1.13821	+	1.13821i	−0.988772	+	0.149434i	$0.952255\pi$
$548$	−8.68540	−	15.0436i	−0.371022	−	0.642629i
$549$		0			0
$550$	−21.0496	−	5.64023i	−0.897559	−	0.240500i
$551$	−42.1439	+	24.3318i	−1.79539	+	1.03657i
$552$		0			0
$553$	0.186141	−	0.0498762i	0.00791551	−	0.00212095i
$554$	19.0801			0.810637
$555$		0			0
$556$	18.3742			0.779239
$557$	22.5007	−	6.02905i	0.953386	−	0.255459i	0.251587	−	0.967835i	$-0.419047\pi$
$557$	22.5007	−	6.02905i	0.953386	−	0.255459i	0.701798	+	0.712376i	$0.252381\pi$
$558$		0			0
$559$	0.295052	−	0.170349i	0.0124794	−	0.00720498i
$560$	1.37162	+	0.367525i	0.0579615	+	0.0155307i
$561$		0			0
$562$	−11.8013	−	20.4405i	−0.497808	−	0.862229i
$563$	−2.51051	+	2.51051i	−0.105805	+	0.105805i	−0.758028	−	0.652222i	$-0.773837\pi$
$563$	−2.51051	+	2.51051i	−0.105805	+	0.105805i	0.652222	+	0.758028i	$0.273837\pi$
$564$		0			0
$565$	15.4410			0.649607
$566$	−6.60096			−0.277459
$567$		0			0
$568$	−1.49771	+	5.58953i	−0.0628425	+	0.234531i
$569$	−14.5450	−	14.5450i	−0.609760	−	0.609760i	0.333123	−	0.942883i	$-0.391898\pi$
$569$	−14.5450	−	14.5450i	−0.609760	−	0.609760i	−0.942883	+	0.333123i	$0.891898\pi$
$570$		0			0
$571$	−15.7795	+	27.3309i	−0.660353	+	1.14376i	0.320170	+	0.947360i	$0.396260\pi$
$571$	−15.7795	+	27.3309i	−0.660353	+	1.14376i	−0.980523	+	0.196404i	$0.937074\pi$
$572$	−0.138701	−	0.517638i	−0.00579937	−	0.0216435i
$573$		0			0
$574$	4.19482	−	15.6553i	0.175089	−	0.653439i
$575$	−35.8186	+	9.59757i	−1.49374	+	0.400246i
$576$		0			0
$577$	−32.2224	+	8.63397i	−1.34144	+	0.359437i	−0.856967	−	0.515371i	$-0.827654\pi$
$577$	−32.2224	+	8.63397i	−1.34144	+	0.359437i	−0.484470	+	0.874808i	$0.660988\pi$
$578$	3.23787	−	3.23787i	0.134678	−	0.134678i
$579$		0			0
$580$	3.90339	+	2.25362i	0.162079	+	0.0935766i
$581$		−	7.06594i		−	0.293144i
$582$		0			0
$583$	4.83638	+	2.79229i	0.200303	+	0.115645i
$584$	2.05639	+	2.05639i	0.0850942	+	0.0850942i
$585$		0			0
$586$	−0.476039	+	0.476039i	−0.0196650	+	0.0196650i
$587$	−3.35254	+	12.5119i	−0.138374	+	0.516420i	0.861587	+	0.507610i	$0.169471\pi$
$587$	−3.35254	+	12.5119i	−0.138374	+	0.516420i	−0.999961	+	0.00880962i	$0.997196\pi$
$588$		0			0
$589$	40.9189	+	70.8736i	1.68603	+	2.92030i
$590$	−2.42479	−	9.04942i	−0.0998269	−	0.372559i
$591$		0			0
$592$	−1.62194	−	5.86253i	−0.0666613	−	0.240949i
$593$		−	3.82605i		−	0.157117i	−0.996910	−	0.0785584i	$-0.974968\pi$
$593$		−	3.82605i		−	0.157117i	0.996910	−	0.0785584i	$-0.0250317\pi$
$594$		0			0
$595$	−4.33409	+	2.50229i	−0.177680	+	0.102584i
$596$	−0.603091	−	1.04458i	−0.0247036	−	0.0427879i
$597$		0			0
$598$	−0.644810	−	0.644810i	−0.0263682	−	0.0263682i
$599$	21.0110	−	12.1307i	0.858486	−	0.495647i	−0.00501889	−	0.999987i	$-0.501598\pi$
$599$	21.0110	−	12.1307i	0.858486	−	0.495647i	0.863505	+	0.504340i	$0.168264\pi$
$600$		0			0
$601$	−15.3406	+	26.5707i	−0.625757	+	1.08384i	0.362637	+	0.931930i	$0.381876\pi$
$601$	−15.3406	+	26.5707i	−0.625757	+	1.08384i	−0.988394	+	0.151912i	$0.951457\pi$
$602$		−	5.67919i		−	0.231466i
$603$		0			0
$604$	3.49819	−	6.05904i	0.142339	−	0.246539i
$605$	−10.5931	−	2.83841i	−0.430670	−	0.115398i
$606$		0			0
$607$	3.36991	+	12.5767i	0.136780	+	0.510471i	0.999984	+	0.00561578i	$0.00178757\pi$
$607$	3.36991	+	12.5767i	0.136780	+	0.510471i	−0.863204	+	0.504856i	$0.831546\pi$
$608$	−7.40808	−	4.27706i	−0.300437	−	0.173458i
$609$		0			0
$610$	1.62590	+	0.435660i	0.0658309	+	0.0176393i
$611$	0.896575	+	0.240237i	0.0362716	+	0.00971894i
$612$		0			0
$613$	2.61099	+	1.50746i	0.105457	+	0.0608856i	0.551801	−	0.833976i	$-0.313941\pi$
$613$	2.61099	+	1.50746i	0.105457	+	0.0608856i	−0.446344	+	0.894862i	$0.647274\pi$
$614$	1.40866	+	5.25718i	0.0568487	+	0.212162i
$615$		0			0
$616$	−8.62867	−	2.31205i	−0.347659	−	0.0931550i
$617$	−18.8360	+	32.6249i	−0.758308	+	1.31343i	0.185405	+	0.982662i	$0.440640\pi$
$617$	−18.8360	+	32.6249i	−0.758308	+	1.31343i	−0.943713	+	0.330765i	$0.892693\pi$
$618$		0			0
$619$		−	22.5053i		−	0.904563i	−0.891875	−	0.452281i	$-0.850610\pi$
$619$		−	22.5053i		−	0.904563i	0.891875	−	0.452281i	$-0.149390\pi$
$620$	3.78993	−	6.56435i	0.152207	−	0.263631i
$621$		0			0
$622$	−9.35687	+	5.40219i	−0.375176	+	0.216608i
$623$	−7.55515	−	7.55515i	−0.302691	−	0.302691i
$624$		0			0
$625$	7.98913	+	13.8376i	0.319565	+	0.553503i
$626$	−2.81186	+	1.62343i	−0.112385	+	0.0648853i
$627$		0			0
$628$			17.4364i			0.695788i
$629$	18.6519	+	10.5679i	0.743701	+	0.421371i
$630$		0			0
$631$	0.374964	+	1.39938i	0.0149271	+	0.0557086i	0.972988	−	0.230857i	$-0.0741530\pi$
$631$	0.374964	+	1.39938i	0.0149271	+	0.0557086i	−0.958061	+	0.286566i	$0.907486\pi$
$632$	0.0537601	+	0.0931152i	0.00213846	+	0.00370392i
$633$		0			0
$634$	3.02219	−	11.2790i	0.120026	−	0.447944i
$635$	5.35797	−	5.35797i	0.212625	−	0.212625i
$636$		0			0
$637$	−0.287973	−	0.287973i	−0.0114099	−	0.0114099i
$638$	−24.5557	−	14.1772i	−0.972169	−	0.561282i
$639$		0			0
$640$			0.792287i			0.0313179i
$641$	9.43096	+	5.44497i	0.372500	+	0.215063i	0.674550	−	0.738229i	$-0.264338\pi$
$641$	9.43096	+	5.44497i	0.372500	+	0.215063i	−0.302050	+	0.953292i	$0.597671\pi$
$642$		0			0
$643$	17.0252	−	17.0252i	0.671409	−	0.671409i	−0.286632	−	0.958041i	$-0.592536\pi$
$643$	17.0252	−	17.0252i	0.671409	−	0.671409i	0.958041	+	0.286632i	$0.0925357\pi$
$644$	−14.6828	+	3.93424i	−0.578583	+	0.155031i
$645$		0			0
$646$	29.1204	−	7.80277i	1.14572	−	0.306996i
$647$	−4.01905	+	14.9993i	−0.158005	+	0.589683i	0.840824	+	0.541308i	$0.182071\pi$
$647$	−4.01905	+	14.9993i	−0.158005	+	0.589683i	−0.998829	+	0.0483749i	$0.984596\pi$
$648$		0			0
$649$	15.2540	+	56.9287i	0.598771	+	2.23465i
$650$	−0.235054	+	0.407126i	−0.00921958	+	0.0159688i
$651$		0			0
$652$	10.1691	+	10.1691i	0.398255	+	0.398255i
$653$	0.221964	−	0.828380i	0.00868611	−	0.0324170i	−0.961447	−	0.274991i	$-0.911325\pi$
$653$	0.221964	−	0.828380i	0.00868611	−	0.0324170i	0.970133	+	0.242574i	$0.0779918\pi$
$654$		0			0
$655$	−7.22125			−0.282158
$656$	9.04295			0.353068
$657$		0			0
$658$	10.9407	−	10.9407i	0.426513	−	0.426513i
$659$	−2.26089	−	3.91597i	−0.0880717	−	0.152545i	0.818624	−	0.574329i	$-0.194737\pi$
$659$	−2.26089	−	3.91597i	−0.0880717	−	0.152545i	−0.906696	+	0.421785i	$0.861404\pi$
$660$		0			0
$661$	−47.2167	−	12.6517i	−1.83652	−	0.492093i	−0.837957	−	0.545736i	$-0.816250\pi$
$661$	−47.2167	−	12.6517i	−1.83652	−	0.492093i	−0.998560	+	0.0536429i	$0.982917\pi$
$662$	19.9502	−	11.5183i	0.775387	−	0.447670i
$663$		0			0
$664$	3.80808	−	1.02037i	0.147782	−	0.0395981i
$665$	12.1469			0.471036
$666$		0			0
$667$	−48.2487			−1.86820
$668$	−14.5054	+	3.88671i	−0.561231	+	0.150381i
$669$		0			0
$670$	10.2435	−	5.91409i	0.395741	−	0.228481i
$671$	−10.2283	−	2.74067i	−0.394861	−	0.105803i
$672$		0			0
$673$	12.7612	+	22.1031i	0.491909	+	0.852012i	0.999957	−	0.00931715i	$-0.00296578\pi$
$673$	12.7612	+	22.1031i	0.491909	+	0.852012i	−0.508047	+	0.861329i	$0.669632\pi$
$674$	0.405854	−	0.405854i	0.0156329	−	0.0156329i
$675$		0			0
$676$	12.9884			0.499555
$677$	−12.0765			−0.464139			−0.232070	−	0.972699i	$-0.574550\pi$
$677$	−12.0765			−0.464139			−0.232070	+	0.972699i	$0.574550\pi$
$678$		0			0
$679$	−0.552166	+	2.06071i	−0.0211902	+	0.0790829i
$680$	−1.97445	−	1.97445i	−0.0757165	−	0.0757165i
$681$		0			0
$682$	−23.8419	+	41.2954i	−0.912954	+	1.58128i
$683$	8.08028	+	30.1560i	0.309183	+	1.15389i	0.929284	+	0.369366i	$0.120425\pi$
$683$	8.08028	+	30.1560i	0.309183	+	1.15389i	−0.620101	+	0.784522i	$0.712908\pi$
$684$		0			0
$685$	−3.56204	+	13.2937i	−0.136099	+	0.507927i
$686$	−18.6759	+	5.00418i	−0.713047	+	0.191060i
$687$		0			0
$688$	3.06071	−	0.820115i	0.116689	−	0.0312666i
$689$	0.0851868	−	0.0851868i	0.00324536	−	0.00324536i
$690$		0			0
$691$	8.41072	+	4.85593i	0.319959	+	0.184728i	0.651374	−	0.758757i	$-0.274193\pi$
$691$	8.41072	+	4.85593i	0.319959	+	0.184728i	−0.331415	+	0.943485i	$0.607526\pi$
$692$			1.84203i			0.0700233i
$693$		0			0
$694$	10.2527	+	5.91939i	0.389187	+	0.224697i
$695$	−10.2938	−	10.2938i	−0.390466	−	0.390466i
$696$		0			0
$697$	−22.5358	+	22.5358i	−0.853603	+	0.853603i
$698$	3.07608	−	11.4801i	0.116431	−	0.434528i
$699$		0			0
$700$	3.91819	+	6.78651i	0.148094	+	0.256506i
$701$	2.50113	+	9.33433i	0.0944662	+	0.352553i	0.996938	−	0.0781963i	$-0.0249161\pi$
$701$	2.50113	+	9.33433i	0.0944662	+	0.352553i	−0.902472	+	0.430749i	$0.858249\pi$
$702$		0			0
$703$	−26.3810	−	44.8491i	−0.994977	−	1.69152i
$704$		−	4.98417i		−	0.187848i
$705$		0			0
$706$	−17.9392	+	10.3572i	−0.675153	+	0.389800i
$707$	3.29767	+	5.71173i	0.124022	+	0.214812i
$708$		0			0
$709$	−22.0107	−	22.0107i	−0.826630	−	0.826630i	0.160419	−	0.987049i	$-0.448715\pi$
$709$	−22.0107	−	22.0107i	−0.826630	−	0.826630i	−0.987049	+	0.160419i	$0.948715\pi$
$710$	3.97050	−	2.29237i	0.149010	−	0.0860310i
$711$		0			0
$712$	2.98072	−	5.16275i	0.111707	−	0.193482i
$713$			81.1401i			3.03872i
$714$		0			0
$715$	−0.212293	+	0.367702i	−0.00793930	+	0.0137513i
$716$	−4.40551	−	1.18045i	−0.164642	−	0.0441156i
$717$		0			0
$718$	3.66060	+	13.6616i	0.136612	+	0.509845i
$719$	−41.0502	−	23.7004i	−1.53091	−	0.883874i	−0.999320	−	0.0368750i	$-0.988260\pi$
$719$	−41.0502	−	23.7004i	−1.53091	−	0.883874i	−0.531595	−	0.846999i	$-0.678407\pi$
$720$		0			0
$721$	−10.2074	−	2.73506i	−0.380142	−	0.101859i
$722$	−52.3271	−	14.0210i	−1.94741	−	0.521807i
$723$		0			0
$724$	−19.5023	−	11.2596i	−0.724795	−	0.418461i
$725$	6.43773	+	24.0260i	0.239091	+	0.892302i
$726$		0			0
$727$	−10.1143	−	2.71013i	−0.375120	−	0.100513i	0.0663327	−	0.997798i	$-0.478870\pi$
$727$	−10.1143	−	2.71013i	−0.375120	−	0.100513i	−0.441453	+	0.897284i	$0.645537\pi$
$728$	−0.0963535	+	0.166889i	−0.00357110	+	0.00618532i
$729$		0			0
$730$		−	2.30411i		−	0.0852790i
$731$	−5.58375	+	9.67134i	−0.206523	+	0.357708i
$732$		0			0
$733$	20.0631	−	11.5834i	0.741048	−	0.427844i	−0.0814022	−	0.996681i	$-0.525940\pi$
$733$	20.0631	−	11.5834i	0.741048	−	0.427844i	0.822450	+	0.568837i	$0.192606\pi$
$734$	8.11452	+	8.11452i	0.299512	+	0.299512i
$735$		0			0
$736$	−4.24060	−	7.34493i	−0.156310	−	0.270738i
$737$	−64.4404	+	37.2047i	−2.37369	+	1.37045i
$738$		0			0
$739$			31.6978i			1.16602i	0.812464	+	0.583011i	$0.198126\pi$
$739$			31.6978i			1.16602i	−0.812464	+	0.583011i	$0.801874\pi$
$740$	−2.37572	+	4.19304i	−0.0873330	+	0.154139i
$741$		0			0
$742$	−0.519758	−	1.93976i	−0.0190809	−	0.0712110i
$743$	7.17719	+	12.4313i	0.263305	+	0.456058i	0.967118	−	0.254327i	$-0.0818540\pi$
$743$	7.17719	+	12.4313i	0.263305	+	0.456058i	−0.703813	+	0.710385i	$0.748521\pi$
$744$		0			0
$745$	−0.247339	+	0.923080i	−0.00906178	+	0.0338190i
$746$	−10.1555	+	10.1555i	−0.371820	+	0.371820i
$747$		0			0
$748$	12.4210	+	12.4210i	0.454155	+	0.454155i
$749$	11.7927	+	6.80850i	0.430895	+	0.248777i
$750$		0			0
$751$		−	31.5531i		−	1.15139i	−0.817665	−	0.575694i	$-0.804732\pi$
$751$		−	31.5531i		−	1.15139i	0.817665	−	0.575694i	$-0.195268\pi$
$752$	7.47625	+	4.31641i	0.272631	+	0.157403i
$753$		0			0
$754$	−0.432518	+	0.432518i	−0.0157514	+	0.0157514i
$755$	−5.35426	+	1.43467i	−0.194861	+	0.0522129i
$756$		0			0
$757$	2.75841	−	0.739115i	0.100256	−	0.0268636i	−0.208342	−	0.978056i	$-0.566807\pi$
$757$	2.75841	−	0.739115i	0.100256	−	0.0268636i	0.308598	+	0.951192i	$0.400140\pi$
$758$	5.08675	−	18.9840i	0.184759	−	0.689530i
$759$		0			0
$760$	1.75410	+	6.54639i	0.0636279	+	0.237462i
$761$	13.9132	−	24.0984i	0.504354	−	0.873567i	−0.495633	−	0.868532i	$-0.665064\pi$
$761$	13.9132	−	24.0984i	0.504354	−	0.873567i	0.999987	−	0.00503492i	$-0.00160267\pi$
$762$		0			0
$763$	1.70375	+	1.70375i	0.0616798	+	0.0616798i
$764$	−0.430753	+	1.60759i	−0.0155841	+	0.0581607i
$765$		0			0
$766$	−6.93881			−0.250709
$767$	1.27141			0.0459078
$768$		0			0
$769$	6.45747	−	6.45747i	0.232862	−	0.232862i	−0.581024	−	0.813886i	$-0.697348\pi$
$769$	6.45747	−	6.45747i	0.232862	−	0.232862i	0.813886	+	0.581024i	$0.197348\pi$
$770$	3.53877	+	6.12933i	0.127528	+	0.220886i
$771$		0			0
$772$	11.2870	+	3.02434i	0.406227	+	0.108848i
$773$	11.2931	−	6.52009i	0.406186	−	0.234511i	−0.282964	−	0.959131i	$-0.591318\pi$
$773$	11.2931	−	6.52009i	0.406186	−	0.234511i	0.689149	+	0.724619i	$0.257984\pi$
$774$		0			0
$775$	40.4046	−	10.8264i	1.45137	−	0.388895i
$776$	−1.19033			−0.0427302
$777$		0			0
$778$	15.4123			0.552559
$779$	74.7187	−	20.0208i	2.67707	−	0.717320i
$780$		0			0
$781$	−24.9778	+	14.4210i	−0.893777	+	0.516022i
$782$	28.8721	+	7.73625i	1.03246	+	0.276648i
$783$		0			0
$784$	−1.89385	−	3.28025i	−0.0676376	−	0.117152i
$785$	9.76842	−	9.76842i	0.348650	−	0.348650i
$786$		0			0
$787$	12.3019			0.438514			0.219257	−	0.975667i	$-0.429637\pi$
$787$	12.3019			0.438514			0.219257	+	0.975667i	$0.429637\pi$
$788$	−10.5587			−0.376138
$789$		0			0
$790$	0.0220480	−	0.0822842i	0.000784432	−	0.00292754i
$791$	24.6993	+	24.6993i	0.878207	+	0.878207i
$792$		0			0
$793$	−0.114216	+	0.197829i	−0.00405594	+	0.00702510i
$794$	3.90661	+	14.5797i	0.138641	+	0.517414i
$795$		0			0
$796$	6.08806	−	22.7210i	0.215786	−	0.805323i
$797$	16.1588	−	4.32974i	0.572375	−	0.153367i	0.0389893	−	0.999240i	$-0.487586\pi$
$797$	16.1588	−	4.32974i	0.572375	−	0.153367i	0.533386	+	0.845872i	$0.320920\pi$
$798$		0			0
$799$	−29.3883	+	7.87457i	−1.03968	+	0.278582i
$800$	−3.09167	+	3.09167i	−0.109307	+	0.109307i
$801$		0			0
$802$	13.7617	+	7.94529i	0.485941	+	0.280558i
$803$			14.4949i			0.511512i
$804$		0			0
$805$	10.4298	+	6.02167i	0.367604	+	0.212236i
$806$	0.727367	+	0.727367i	0.0256204	+	0.0256204i
$807$		0			0
$808$	−2.60204	+	2.60204i	−0.0915395	+	0.0915395i
$809$	8.46249	−	31.5825i	0.297525	−	1.11038i	−0.641666	−	0.766985i	$-0.721756\pi$
$809$	8.46249	−	31.5825i	0.297525	−	1.11038i	0.939191	−	0.343395i	$-0.111577\pi$
$810$		0			0
$811$	−13.1780	−	22.8250i	−0.462743	−	0.801495i	0.536353	−	0.843994i	$-0.319801\pi$
$811$	−13.1780	−	22.8250i	−0.462743	−	0.801495i	−0.999097	+	0.0424987i	$0.986468\pi$
$812$	2.63896	+	9.84873i	0.0926093	+	0.345623i
$813$		0			0
$814$	14.9453	−	26.3778i	0.523832	−	0.924542i
$815$		−	11.3942i		−	0.399120i
$816$		0			0
$817$	23.4739	−	13.5526i	0.821247	−	0.474147i
$818$	−10.7231	−	18.5730i	−0.374925	−	0.649390i
$819$		0			0
$820$	−5.06614	−	5.06614i	−0.176917	−	0.176917i
$821$	16.7391	−	9.66433i	0.584199	−	0.337288i	−0.178601	−	0.983922i	$-0.557157\pi$
$821$	16.7391	−	9.66433i	0.584199	−	0.337288i	0.762800	+	0.646634i	$0.223824\pi$
$822$		0			0
$823$	−14.8848	+	25.7812i	−0.518852	+	0.898678i	0.480908	+	0.876771i	$0.340307\pi$
$823$	−14.8848	+	25.7812i	−0.518852	+	0.898678i	−0.999760	+	0.0219068i	$0.993026\pi$
$824$		−	5.89607i		−	0.205399i
$825$		0			0
$826$	10.5967	−	18.3541i	0.368708	−	0.638620i
$827$	−17.7198	−	4.74800i	−0.616177	−	0.165104i	−0.0627876	−	0.998027i	$-0.519999\pi$
$827$	−17.7198	−	4.74800i	−0.616177	−	0.165104i	−0.553389	+	0.832923i	$0.686666\pi$
$828$		0			0
$829$	−10.3968	−	38.8015i	−0.361097	−	1.34763i	−0.872636	−	0.488372i	$-0.837591\pi$
$829$	−10.3968	−	38.8015i	−0.361097	−	1.34763i	0.511539	−	0.859260i	$-0.329076\pi$
$830$	−2.70505	−	1.56176i	−0.0938937	−	0.0542095i
$831$		0			0
$832$	−0.103857	−	0.0278283i	−0.00360058	−	0.000964772i
$833$	12.8943	+	3.45502i	0.446761	+	0.119709i
$834$		0			0
$835$	10.3038	+	5.94892i	0.356579	+	0.205871i
$836$	−11.0348	−	41.1824i	−0.381646	−	1.42432i
$837$		0			0
$838$	17.9947	+	4.82166i	0.621616	+	0.166562i
$839$	−8.50761	+	14.7356i	−0.293715	+	0.508730i	−0.974685	−	0.223581i	$-0.928225\pi$
$839$	−8.50761	+	14.7356i	−0.293715	+	0.508730i	0.680970	+	0.732312i	$0.261558\pi$
$840$		0			0
$841$			3.36365i			0.115988i
$842$	13.3747	−	23.1656i	0.460921	−	0.798339i
$843$		0			0
$844$	−20.3213	+	11.7325i	−0.699489	+	0.403850i
$845$	−7.27653	−	7.27653i	−0.250320	−	0.250320i
$846$		0			0
$847$	−12.4043	−	21.4849i	−0.426218	−	0.738232i
$848$	0.970349	−	0.560232i	0.0333219	−	0.0192384i
$849$		0			0
$850$		−	15.4094i		−	0.528538i
$851$	−0.418432	−	51.5874i	−0.0143437	−	1.76839i
$852$		0			0
$853$	−6.77831	−	25.2970i	−0.232085	−	0.866153i	−0.979441	−	0.201729i	$-0.935344\pi$
$853$	−6.77831	−	25.2970i	−0.232085	−	0.866153i	0.747356	−	0.664423i	$-0.231323\pi$
$854$	1.90391	+	3.29767i	0.0651504	+	0.112844i
$855$		0			0
$856$	−1.96639	+	7.33867i	−0.0672099	+	0.250831i
$857$	−19.9710	+	19.9710i	−0.682197	+	0.682197i	−0.960495	−	0.278298i	$-0.910230\pi$
$857$	−19.9710	+	19.9710i	−0.682197	+	0.682197i	0.278298	+	0.960495i	$0.410230\pi$
$858$		0			0
$859$	7.23411	+	7.23411i	0.246825	+	0.246825i	0.819666	−	0.572841i	$-0.194159\pi$
$859$	7.23411	+	7.23411i	0.246825	+	0.246825i	−0.572841	+	0.819666i	$0.694159\pi$
$860$	−2.17416	−	1.25525i	−0.0741383	−	0.0428038i
$861$		0			0
$862$			1.84649i			0.0628918i
$863$	−47.0658	−	27.1735i	−1.60214	−	0.924996i	−0.991059	−	0.133427i	$-0.957402\pi$
$863$	−47.0658	−	27.1735i	−1.60214	−	0.924996i	−0.611081	−	0.791568i	$-0.709265\pi$
$864$		0			0
$865$	1.03196	−	1.03196i	0.0350877	−	0.0350877i
$866$	−22.6185	+	6.06060i	−0.768607	+	0.205948i
$867$		0			0
$868$	16.5627	−	4.43795i	0.562173	−	0.150634i
$869$	−0.138701	+	0.517638i	−0.00470510	+	0.0175597i
$870$		0			0
$871$	0.415452	+	1.55049i	0.0140771	+	0.0525363i
$872$	−0.672175	+	1.16424i	−0.0227627	+	0.0394262i
$873$		0			0
$874$	−51.3000	−	51.3000i	−1.73525	−	1.73525i
$875$	3.44454	−	12.8552i	0.116447	−	0.434585i
$876$		0			0
$877$	−35.8379			−1.21016			−0.605079	−	0.796165i	$-0.706859\pi$
$877$	−35.8379			−1.21016			−0.605079	+	0.796165i	$0.706859\pi$
$878$	13.5017			0.455659
$879$		0			0
$880$	−2.79229	+	2.79229i	−0.0941280	+	0.0941280i
$881$	14.6808	+	25.4279i	0.494609	+	0.856688i	0.999981	−	0.00621358i	$-0.00197786\pi$
$881$	14.6808	+	25.4279i	0.494609	+	0.856688i	−0.505371	+	0.862902i	$0.668645\pi$
$882$		0			0
$883$	40.8471	+	10.9449i	1.37461	+	0.368327i	0.869162	−	0.494528i	$-0.164659\pi$
$883$	40.8471	+	10.9449i	1.37461	+	0.368327i	0.505452	+	0.862854i	$0.331326\pi$
$884$	0.328169	−	0.189469i	0.0110375	−	0.00637252i
$885$		0			0
$886$	11.9282	−	3.19615i	0.400736	−	0.107377i
$887$	−29.9674			−1.00621			−0.503103	−	0.864227i	$-0.667808\pi$
$887$	−29.9674			−1.00621			−0.503103	+	0.864227i	$0.667808\pi$
$888$		0			0
$889$	17.1412			0.574896
$890$	−4.56223	+	1.22245i	−0.152926	+	0.0409765i
$891$		0			0
$892$	−17.4286	+	10.0624i	−0.583552	+	0.336914i
$893$	71.3300	+	19.1128i	2.38697	+	0.639586i
$894$		0			0
$895$	1.80678	+	3.12943i	0.0603940	+	0.104605i
$896$	−1.26734	+	1.26734i	−0.0423388	+	0.0423388i
$897$		0			0
$898$	−8.30671			−0.277199
$899$	54.4261			1.81521
$900$		0			0
$901$	−1.02205	+	3.81433i	−0.0340494	+	0.127074i
$902$	31.8704	+	31.8704i	1.06117	+	1.06117i
$903$		0			0
$904$	−9.74456	+	16.8781i	−0.324099	+	0.561357i
$905$	4.61778	+	17.2338i	0.153500	+	0.572870i
$906$		0			0
$907$	3.76598	−	14.0548i	0.125047	−	0.466683i	−0.874794	−	0.484495i	$-0.839003\pi$
$907$	3.76598	−	14.0548i	0.125047	−	0.466683i	0.999841	+	0.0178120i	$0.00567003\pi$
$908$	26.7043	−	7.15539i	0.886212	−	0.237460i
$909$		0			0
$910$	0.147477	−	0.0395163i	0.00488881	−	0.00130995i
$911$	−3.47075	+	3.47075i	−0.114991	+	0.114991i	−0.762261	−	0.647270i	$-0.775911\pi$
$911$	−3.47075	+	3.47075i	−0.114991	+	0.114991i	0.647270	+	0.762261i	$0.275911\pi$
$912$		0			0
$913$	17.0171	+	9.82482i	0.563184	+	0.325154i
$914$		−	24.1266i		−	0.798038i
$915$		0			0
$916$	5.41676	+	3.12737i	0.178975	+	0.103331i
$917$	−11.5511	−	11.5511i	−0.381450	−	0.381450i
$918$		0			0
$919$	22.0066	−	22.0066i	0.725932	−	0.725932i	−0.243875	−	0.969807i	$-0.578419\pi$
$919$	22.0066	−	22.0066i	0.725932	−	0.725932i	0.969807	+	0.243875i	$0.0784186\pi$
$920$	−1.73914	+	6.49058i	−0.0573379	+	0.213988i
$921$		0			0
$922$	14.0557	+	24.3451i	0.462898	+	0.801764i
$923$	0.161034	+	0.600987i	0.00530050	+	0.0197817i
$924$		0			0
$925$	−25.6327	+	7.09157i	−0.842796	+	0.233169i
$926$		−	19.5671i		−	0.643015i
$927$		0			0
$928$	−4.92674	+	2.84445i	−0.161728	+	0.0933737i
$929$	8.13078	+	14.0829i	0.266762	+	0.462046i	0.968024	−	0.250858i	$-0.0807128\pi$
$929$	8.13078	+	14.0829i	0.266762	+	0.462046i	−0.701262	+	0.712904i	$0.747379\pi$
$930$		0			0
$931$	−22.9106	−	22.9106i	−0.750865	−	0.750865i
$932$	−3.57462	+	2.06381i	−0.117091	+	0.0676023i
$933$		0			0
$934$	5.06817	−	8.77833i	0.165836	−	0.287236i
$935$		−	13.9172i		−	0.455142i
$936$		0			0
$937$	−8.09651	+	14.0236i	−0.264501	+	0.458130i	−0.967433	−	0.253128i	$-0.918541\pi$
$937$	−8.09651	+	14.0236i	−0.264501	+	0.458130i	0.702931	+	0.711258i	$0.251874\pi$
$938$	25.8456	+	6.92531i	0.843889	+	0.226119i
$939$		0			0
$940$	−1.77024	−	6.60662i	−0.0577388	−	0.215484i
$941$	−28.5919	−	16.5075i	−0.932068	−	0.538130i	−0.0446030	−	0.999005i	$-0.514202\pi$
$941$	−28.5919	−	16.5075i	−0.932068	−	0.538130i	−0.887465	+	0.460875i	$0.847536\pi$
$942$		0			0
$943$	74.0817	+	19.8501i	2.41243	+	0.646409i
$944$	11.4219	+	3.06049i	0.371751	+	0.0996104i
$945$		0			0
$946$	13.6773	+	7.89662i	0.444689	+	0.256741i
$947$	−5.47080	−	20.4173i	−0.177777	−	0.663474i	−0.996062	−	0.0886605i	$-0.971741\pi$
$947$	−5.47080	−	20.4173i	−0.177777	−	0.663474i	0.818285	−	0.574813i	$-0.194925\pi$
$948$		0			0
$949$	0.302033	+	0.0809296i	0.00980442	+	0.00262709i
$950$	−18.7005	+	32.3902i	−0.606725	+	1.05088i
$951$		0			0
$952$		−	6.31662i		−	0.204723i
$953$	8.15315	−	14.1217i	0.264106	−	0.457446i	−0.703223	−	0.710970i	$-0.748256\pi$
$953$	8.15315	−	14.1217i	0.264106	−	0.457446i	0.967329	+	0.253524i	$0.0815897\pi$
$954$		0			0
$955$	1.14195	−	0.659303i	0.0369525	−	0.0213345i
$956$	19.7915	+	19.7915i	0.640102	+	0.640102i
$957$		0			0
$958$	−8.32544	−	14.4201i	−0.268983	−	0.465892i
$959$	−26.9624	+	15.5667i	−0.870661	+	0.502676i
$960$		0			0
$961$		−	60.5287i		−	1.95254i
$962$	−0.466197	−	0.458696i	−0.0150308	−	0.0147889i
$963$		0			0
$964$	−3.35143	−	12.5077i	−0.107942	−	0.402847i
$965$	−4.62899	−	8.01765i	−0.149013	−	0.258097i
$966$		0			0
$967$	7.10431	−	26.5136i	0.228459	−	0.852621i	−0.752530	−	0.658558i	$-0.771167\pi$
$967$	7.10431	−	26.5136i	0.228459	−	0.852621i	0.980989	−	0.194063i	$-0.0621666\pi$
$968$	9.78771	−	9.78771i	0.314589	−	0.314589i
$969$		0			0
$970$	0.666858	+	0.666858i	0.0214115	+	0.0214115i
$971$	7.18762	+	4.14977i	0.230662	+	0.133173i	0.610877	−	0.791725i	$-0.290817\pi$
$971$	7.18762	+	4.14977i	0.230662	+	0.133173i	−0.380216	+	0.924898i	$0.624150\pi$
$972$		0			0
$973$		−	32.9318i		−	1.05575i
$974$	−2.87890	−	1.66213i	−0.0922458	−	0.0532582i
$975$		0			0
$976$	−1.50229	+	1.50229i	−0.0480871	+	0.0480871i
$977$	7.66321	−	2.05335i	0.245168	−	0.0656925i	−0.134142	−	0.990962i	$-0.542828\pi$
$977$	7.66321	−	2.05335i	0.245168	−	0.0656925i	0.379310	+	0.925270i	$0.376161\pi$
$978$		0			0
$979$	28.7003	−	7.69023i	0.917267	−	0.245781i
$980$	−0.776703	+	2.89870i	−0.0248109	+	0.0925955i
$981$		0			0
$982$	5.60937	+	20.9345i	0.179002	+	0.668045i
$983$	−10.1378	+	17.5593i	−0.323347	+	0.560053i	−0.981176	−	0.193114i	$-0.938141\pi$
$983$	−10.1378	+	17.5593i	−0.323347	+	0.560053i	0.657830	+	0.753167i	$0.271475\pi$
$984$		0			0
$985$	5.91531	+	5.91531i	0.188478	+	0.188478i
$986$	5.18923	−	19.3665i	0.165259	−	0.616753i
$987$		0			0
$988$	−0.919740			−0.0292608
$989$	26.8742			0.854550
$990$		0			0
$991$	−4.99520	+	4.99520i	−0.158678	+	0.158678i	−0.781981	−	0.623303i	$-0.785790\pi$
$991$	−4.99520	+	4.99520i	−0.158678	+	0.158678i	0.623303	+	0.781981i	$0.285790\pi$
$992$	4.78353	+	8.28532i	0.151877	+	0.263059i
$993$		0			0
$994$	10.0180	+	2.68433i	0.317753	+	0.0851417i
$995$	−16.1397	+	9.31828i	−0.511664	+	0.295409i
$996$		0			0
$997$	−53.8898	+	14.4397i	−1.70671	+	0.457311i	−0.974614	−	0.223894i	$-0.928123\pi$
$997$	−53.8898	+	14.4397i	−1.70671	+	0.457311i	−0.732093	+	0.681205i	$0.761456\pi$
$998$	−13.1535			−0.416366
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	666.2.be.d.467.3	yes	16
3.2	odd	2	inner	666.2.be.d.467.2	yes	16
37.29	odd	12	inner	666.2.be.d.251.2	✓	16
111.29	even	12	inner	666.2.be.d.251.3	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
666.2.be.d.251.2	✓	16	37.29	odd	12	inner
666.2.be.d.251.3	yes	16	111.29	even	12	inner
666.2.be.d.467.2	yes	16	3.2	odd	2	inner
666.2.be.d.467.3	yes	16	1.1	even	1	trivial

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.be (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.965926 - 0.258819i) q^{2} +(0.866025 - 0.500000i) q^{4} +(-0.765290 - 0.205059i) q^{5} +(-0.896143 - 1.55217i) q^{7} +(0.707107 - 0.707107i) q^{8} -0.792287 q^{10} +4.98417 q^{11} +(0.0278283 - 0.103857i) q^{13} +(-1.26734 - 1.26734i) q^{14} +(0.500000 - 0.866025i) q^{16} +(0.912166 + 3.40425i) q^{17} +(2.21397 - 8.26264i) q^{19} +(-0.765290 + 0.205059i) q^{20} +(4.81433 - 1.29000i) q^{22} +(5.99711 - 5.99711i) q^{23} +(-3.78651 - 2.18614i) q^{25} -0.107520i q^{26} +(-1.55217 - 0.896143i) q^{28} +(-4.02266 - 4.02266i) q^{29} +(-6.76493 + 6.76493i) q^{31} +(0.258819 - 0.965926i) q^{32} +(1.76217 + 3.05217i) q^{34} +(0.367525 + 1.37162i) q^{35} +(4.26613 - 4.33591i) q^{37} -8.55412i q^{38} +(-0.686141 + 0.396143i) q^{40} +(4.52147 + 7.83142i) q^{41} +(2.24060 + 2.24060i) q^{43} +(4.31641 - 2.49208i) q^{44} +(4.24060 - 7.34493i) q^{46} +8.63283i q^{47} +(1.89385 - 3.28025i) q^{49} +(-4.22330 - 1.13163i) q^{50} +(-0.0278283 - 0.103857i) q^{52} +(0.970349 + 0.560232i) q^{53} +(-3.81433 - 1.02205i) q^{55} +(-1.73122 - 0.463878i) q^{56} +(-4.92674 - 2.84445i) q^{58} +(3.06049 + 11.4219i) q^{59} +(-2.05217 - 0.549876i) q^{61} +(-4.78353 + 8.28532i) q^{62} -1.00000i q^{64} +(-0.0425934 + 0.0737740i) q^{65} +(-12.9290 + 7.46458i) q^{67} +(2.49208 + 2.49208i) q^{68} +(0.710003 + 1.22976i) q^{70} +(-5.01144 + 2.89335i) q^{71} +2.90818i q^{73} +(2.99855 - 5.29232i) q^{74} +(-2.21397 - 8.26264i) q^{76} +(-4.46653 - 7.73625i) q^{77} +(-0.0278283 + 0.103857i) q^{79} +(-0.560232 + 0.560232i) q^{80} +(6.39433 + 6.39433i) q^{82} +(3.41423 + 1.97121i) q^{83} -2.79229i q^{85} +(2.74416 + 1.58434i) q^{86} +(3.52434 - 3.52434i) q^{88} +(5.75830 - 1.54293i) q^{89} +(-0.186141 + 0.0498762i) q^{91} +(2.19509 - 8.19220i) q^{92} +(2.23434 + 8.33867i) q^{94} +(-3.38866 + 5.86933i) q^{95} +(-0.841688 - 0.841688i) q^{97} +(0.980331 - 3.65864i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 8 q^{7} + 4 q^{13} + 8 q^{16} + 16 q^{19} + 20 q^{22} + 12 q^{28} - 12 q^{31} + 8 q^{34} + 12 q^{37} + 12 q^{40} - 20 q^{43} + 12 q^{46} + 20 q^{49} - 4 q^{52} - 4 q^{55} + 4 q^{61} - 132 q^{67}+ \cdots - 40 q^{97}+O(q^{100}) \) 16 * q - 8 * q^7 + 4 * q^13 + 8 * q^16 + 16 * q^19 + 20 * q^22 + 12 * q^28 - 12 * q^31 + 8 * q^34 + 12 * q^37 + 12 * q^40 - 20 * q^43 + 12 * q^46 + 20 * q^49 - 4 * q^52 - 4 * q^55 + 4 * q^61 - 132 * q^67 + 28 * q^70 - 16 * q^76 - 4 * q^79 + 12 * q^82 + 16 * q^88 + 20 * q^91 + 12 * q^94 - 40 * q^97

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