LMFDB - Embedded newform 648.2.l.f.539.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [648,2,Mod(107,648)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(648, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 1]))

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

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

chi := DirichletCharacter("648.107");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 648 = 2^{3} \cdot 3^{4} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	648.l (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$5.17430605098$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	16.0.534694406811304329216.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 2x^{14} - 2x^{12} + 4x^{10} + 4x^{8} + 16x^{6} - 32x^{4} - 128x^{2} + 256 $ x^16 - 2x^14 - 2x^12 + 4x^10 + 4x^8 + 16x^6 - 32x^4 - 128*x^2 + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{4}\cdot 3^{4} $
Twist minimal:	no (minimal twist has level 216)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			539.6
Root			$0.841995 + 1.13624i$ of defining polynomial
Character	$\chi$	$=$	648.539
Dual form			648.2.l.f.107.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.841995 - 1.13624i) q^{2} +(-0.582088 - 1.91342i) q^{4} +(1.53819 - 2.66422i) q^{5} +(3.45632 - 1.99551i) q^{7} +(-2.66422 - 0.949697i) q^{8} +O(q^{10})$	\(q+(0.841995 - 1.13624i) q^{2} +(-0.582088 - 1.91342i) q^{4} +(1.53819 - 2.66422i) q^{5} +(3.45632 - 1.99551i) q^{7} +(-2.66422 - 0.949697i) q^{8} +(-1.73205 - 3.99102i) q^{10} +(-1.64492 + 0.949697i) q^{11} +(-0.926118 - 0.534695i) q^{13} +(0.642827 - 5.60742i) q^{14} +(-3.32235 + 2.22756i) q^{16} +7.08863i q^{17} +3.73205 q^{19} +(-5.99313 - 1.39239i) q^{20} +(-0.305932 + 2.66867i) q^{22} +(-0.412157 + 0.713876i) q^{23} +(-2.23205 - 3.86603i) q^{25} +(-1.38733 + 0.602084i) q^{26} +(-5.83013 - 5.45183i) q^{28} +(-2.25207 - 3.90069i) q^{29} +(5.06040 + 2.92163i) q^{31} +(-0.266355 + 5.65058i) q^{32} +(8.05440 + 5.96859i) q^{34} -12.2779i q^{35} +6.91264i q^{37} +(3.14237 - 4.24051i) q^{38} +(-6.62828 + 5.63726i) q^{40} +(-3.28985 - 1.89939i) q^{41} +(-1.00000 - 1.73205i) q^{43} +(2.77466 + 2.59462i) q^{44} +(0.464102 + 1.06939i) q^{46} +(-3.48853 - 6.04232i) q^{47} +(4.46410 - 7.73205i) q^{49} +(-6.27211 - 0.719026i) q^{50} +(-0.484012 + 2.08329i) q^{52} -10.6569 q^{53} +5.84325i q^{55} +(-11.1035 + 2.03402i) q^{56} +(-6.32835 - 0.725474i) q^{58} +(1.64492 + 0.949697i) q^{59} +(-0.926118 + 0.534695i) q^{61} +(7.58051 - 3.28985i) q^{62} +(6.19615 + 5.06040i) q^{64} +(-2.84909 + 1.64492i) q^{65} +(4.59808 - 7.96410i) q^{67} +(13.5635 - 4.12621i) q^{68} +(-13.9506 - 10.3379i) q^{70} +10.6569 q^{71} +5.92820 q^{73} +(7.85443 + 5.82041i) q^{74} +(-2.17238 - 7.14098i) q^{76} +(-3.79025 + 6.56491i) q^{77} +(-5.30856 + 3.06490i) q^{79} +(0.824313 + 12.2779i) q^{80} +(-4.92820 + 2.13878i) q^{82} +(8.98803 - 5.18924i) q^{83} +(18.8857 + 10.9037i) q^{85} +(-2.81002 - 0.322137i) q^{86} +(5.28436 - 0.968024i) q^{88} +13.6683i q^{89} -4.26795 q^{91} +(1.60586 + 0.373089i) q^{92} +(-9.80286 - 1.12379i) q^{94} +(5.74060 - 9.94301i) q^{95} +(5.69615 + 9.86603i) q^{97} +(-5.02672 - 11.5826i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 4 q^{4}+O(q^{10}) $ 16 * q + 4 * q^4	$ 16 q + 4 q^{4} + 16 q^{16} + 32 q^{19} + 8 q^{22} - 8 q^{25} - 24 q^{28} + 32 q^{34} - 24 q^{40} - 16 q^{43} - 48 q^{46} + 16 q^{49} - 36 q^{52} - 48 q^{58} + 16 q^{64} + 32 q^{67} - 72 q^{70} - 16 q^{73} + 20 q^{76} + 32 q^{82} + 56 q^{88} - 96 q^{91} + 24 q^{94} + 8 q^{97}+O(q^{100}) $ 16 * q + 4 * q^4 + 16 * q^16 + 32 * q^19 + 8 * q^22 - 8 * q^25 - 24 * q^28 + 32 * q^34 - 24 * q^40 - 16 * q^43 - 48 * q^46 + 16 * q^49 - 36 * q^52 - 48 * q^58 + 16 * q^64 + 32 * q^67 - 72 * q^70 - 16 * q^73 + 20 * q^76 + 32 * q^82 + 56 * q^88 - 96 * q^91 + 24 * q^94 + 8 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/648\mathbb{Z}\right)^\times$.

$n$	$325$	$487$	$569$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{5}{6}\right)$

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 $

$2$	0.841995	−	1.13624i	0.595380	−	0.803444i
$2$	0.841995	−	1.13624i	0.595380	−	0.803444i
$3$		0			0
$3$		0			0
$4$	−0.582088	−	1.91342i	−0.291044	−	0.956710i
$5$	1.53819	−	2.66422i	0.687899	−	1.19148i	−0.284617	−	0.958641i	$-0.591867\pi$
$5$	1.53819	−	2.66422i	0.687899	−	1.19148i	0.972516	−	0.232835i	$-0.0748002\pi$
$6$		0			0
$7$	3.45632	−	1.99551i	1.30637	−	0.754231i	0.324879	−	0.945756i	$-0.394677\pi$
$7$	3.45632	−	1.99551i	1.30637	−	0.754231i	0.981488	+	0.191525i	$0.0613432\pi$
$8$	−2.66422	−	0.949697i	−0.941945	−	0.335768i
$9$		0			0
$10$	−1.73205	−	3.99102i	−0.547723	−	1.26207i
$11$	−1.64492	+	0.949697i	−0.495963	+	0.286344i	−0.727045	−	0.686590i	$-0.759107\pi$
$11$	−1.64492	+	0.949697i	−0.495963	+	0.286344i	0.231082	+	0.972934i	$0.425773\pi$
$12$		0			0
$13$	−0.926118	−	0.534695i	−0.256859	−	0.148298i	0.366042	−	0.930598i	$-0.380713\pi$
$13$	−0.926118	−	0.534695i	−0.256859	−	0.148298i	−0.622901	+	0.782301i	$0.714046\pi$
$14$	0.642827	−	5.60742i	0.171803	−	1.49865i
$15$		0			0
$16$	−3.32235	+	2.22756i	−0.830587	+	0.556890i
$17$			7.08863i			1.71925i	0.510929	+	0.859623i	$0.329302\pi$
$17$			7.08863i			1.71925i	−0.510929	+	0.859623i	$0.670698\pi$
$18$		0			0
$19$	3.73205			0.856191			0.428096	−	0.903733i	$-0.359185\pi$
$19$	3.73205			0.856191			0.428096	+	0.903733i	$0.359185\pi$
$20$	−5.99313	−	1.39239i	−1.34011	−	0.311347i
$21$		0			0
$22$	−0.305932	+	2.66867i	−0.0652250	+	0.568962i
$23$	−0.412157	+	0.713876i	−0.0859406	+	0.148853i	−0.905792	−	0.423723i	$-0.860723\pi$
$23$	−0.412157	+	0.713876i	−0.0859406	+	0.148853i	0.819851	+	0.572577i	$0.194056\pi$
$24$		0			0
$25$	−2.23205	−	3.86603i	−0.446410	−	0.773205i
$26$	−1.38733	+	0.602084i	−0.272078	+	0.118078i
$27$		0			0
$28$	−5.83013	−	5.45183i	−1.10179	−	1.03030i
$29$	−2.25207	−	3.90069i	−0.418198	−	0.724340i	0.577560	−	0.816348i	$-0.304005\pi$
$29$	−2.25207	−	3.90069i	−0.418198	−	0.724340i	−0.995758	+	0.0920079i	$0.970672\pi$
$30$		0			0
$31$	5.06040	+	2.92163i	0.908876	+	0.524740i	0.880069	−	0.474845i	$-0.157496\pi$
$31$	5.06040	+	2.92163i	0.908876	+	0.524740i	0.0288063	+	0.999585i	$0.490829\pi$
$32$	−0.266355	+	5.65058i	−0.0470854	+	0.998891i
$33$		0			0
$34$	8.05440	+	5.96859i	1.38132	+	1.02361i
$35$		−	12.2779i		−	2.07534i
$36$		0			0
$37$			6.91264i			1.13643i	0.822880	+	0.568216i	$0.192366\pi$
$37$			6.91264i			1.13643i	−0.822880	+	0.568216i	$0.807634\pi$
$38$	3.14237	−	4.24051i	0.509759	−	0.687902i
$39$		0			0
$40$	−6.62828	+	5.63726i	−1.04802	+	0.891330i
$41$	−3.28985	−	1.89939i	−0.513788	−	0.296635i	0.220602	−	0.975364i	$-0.429198\pi$
$41$	−3.28985	−	1.89939i	−0.513788	−	0.296635i	−0.734389	+	0.678729i	$0.762531\pi$
$42$		0			0
$43$	−1.00000	−	1.73205i	−0.152499	−	0.264135i	0.779647	−	0.626219i	$-0.215399\pi$
$43$	−1.00000	−	1.73205i	−0.152499	−	0.264135i	−0.932145	+	0.362084i	$0.882065\pi$
$44$	2.77466	+	2.59462i	0.418296	+	0.391154i
$45$		0			0
$46$	0.464102	+	1.06939i	0.0684280	+	0.157673i
$47$	−3.48853	−	6.04232i	−0.508855	−	0.881363i	−0.999947	−	0.0102553i	$-0.996736\pi$
$47$	−3.48853	−	6.04232i	−0.508855	−	0.881363i	0.491092	−	0.871108i	$-0.336598\pi$
$48$		0			0
$49$	4.46410	−	7.73205i	0.637729	−	1.10458i
$50$	−6.27211	−	0.719026i	−0.887011	−	0.101686i
$51$		0			0
$52$	−0.484012	+	2.08329i	−0.0671204	+	0.288901i
$53$	−10.6569			−1.46384			−0.731918	−	0.681393i	$-0.761375\pi$
$53$	−10.6569			−1.46384			−0.731918	+	0.681393i	$0.761375\pi$
$54$		0			0
$55$			5.84325i			0.787904i
$56$	−11.1035	+	2.03402i	−1.48377	+	0.271807i
$57$		0			0
$58$	−6.32835	−	0.725474i	−0.830954	−	0.0952593i
$59$	1.64492	+	0.949697i	0.214151	+	0.123640i	0.603239	−	0.797561i	$-0.293877\pi$
$59$	1.64492	+	0.949697i	0.214151	+	0.123640i	−0.389088	+	0.921201i	$0.627210\pi$
$60$		0			0
$61$	−0.926118	+	0.534695i	−0.118577	+	0.0684606i	−0.558116	−	0.829763i	$-0.688475\pi$
$61$	−0.926118	+	0.534695i	−0.118577	+	0.0684606i	0.439538	+	0.898224i	$0.355142\pi$
$62$	7.58051	−	3.28985i	0.962725	−	0.417811i
$63$		0			0
$64$	6.19615	+	5.06040i	0.774519	+	0.632551i
$65$	−2.84909	+	1.64492i	−0.353386	+	0.204028i
$66$		0			0
$67$	4.59808	−	7.96410i	0.561744	−	0.972970i	−0.435600	−	0.900140i	$-0.643464\pi$
$67$	4.59808	−	7.96410i	0.561744	−	0.972970i	0.997344	−	0.0728295i	$-0.0232029\pi$
$68$	13.5635	−	4.12621i	1.64482	−	0.500377i
$69$		0			0
$70$	−13.9506	−	10.3379i	−1.66742	−	1.23562i
$71$	10.6569			1.26474			0.632370	−	0.774667i	$-0.282082\pi$
$71$	10.6569			1.26474			0.632370	+	0.774667i	$0.282082\pi$
$72$		0			0
$73$	5.92820			0.693844			0.346922	−	0.937894i	$-0.387227\pi$
$73$	5.92820			0.693844			0.346922	+	0.937894i	$0.387227\pi$
$74$	7.85443	+	5.82041i	0.913059	+	0.676609i
$75$		0			0
$76$	−2.17238	−	7.14098i	−0.249190	−	0.819126i
$77$	−3.79025	+	6.56491i	−0.431940	+	0.748141i
$78$		0			0
$79$	−5.30856	+	3.06490i	−0.597259	+	0.344828i	−0.767963	−	0.640495i	$-0.778729\pi$
$79$	−5.30856	+	3.06490i	−0.597259	+	0.344828i	0.170703	+	0.985322i	$0.445396\pi$
$80$	0.824313	+	12.2779i	0.0921610	+	1.37271i
$81$		0			0
$82$	−4.92820	+	2.13878i	−0.544229	+	0.236189i
$83$	8.98803	−	5.18924i	0.986564	−	0.569593i	0.0823186	−	0.996606i	$-0.473768\pi$
$83$	8.98803	−	5.18924i	0.986564	−	0.569593i	0.904245	+	0.427013i	$0.140434\pi$
$84$		0			0
$85$	18.8857	+	10.9037i	2.04844	+	1.18267i
$86$	−2.81002	−	0.322137i	−0.303013	−	0.0347369i
$87$		0			0
$88$	5.28436	−	0.968024i	0.563315	−	0.103192i
$89$			13.6683i			1.44884i	0.689359	+	0.724420i	$0.257892\pi$
$89$			13.6683i			1.44884i	−0.689359	+	0.724420i	$0.742108\pi$
$90$		0			0
$91$	−4.26795			−0.447403
$92$	1.60586	+	0.373089i	0.167422	+	0.0388972i
$93$		0			0
$94$	−9.80286	−	1.12379i	−1.01109	−	0.115910i
$95$	5.74060	−	9.94301i	0.588973	−	1.02013i
$96$		0			0
$97$	5.69615	+	9.86603i	0.578357	+	1.00174i	0.995668	+	0.0929795i	$0.0296391\pi$
$97$	5.69615	+	9.86603i	0.578357	+	1.00174i	−0.417311	+	0.908764i	$0.637028\pi$
$98$	−5.02672	−	11.5826i	−0.507776	−	1.17002i
$99$		0			0
$100$	−6.09808	+	6.52122i	−0.609808	+	0.652122i
$101$	3.07638	+	5.32844i	0.306111	+	0.530200i	0.977508	−	0.210898i	$-0.0676388\pi$
$101$	3.07638	+	5.32844i	0.306111	+	0.530200i	−0.671397	+	0.741098i	$0.734305\pi$
$102$		0			0
$103$	3.45632	+	1.99551i	0.340561	+	0.196623i	0.660520	−	0.750808i	$-0.270336\pi$
$103$	3.45632	+	1.99551i	0.340561	+	0.196623i	−0.319959	+	0.947431i	$0.603669\pi$
$104$	1.95959	+	2.30408i	0.192153	+	0.225933i
$105$		0			0
$106$	−8.97305	+	12.1088i	−0.871539	+	1.17611i
$107$		−	8.47908i		−	0.819704i	−0.912152	−	0.409852i	$-0.865580\pi$
$107$		−	8.47908i		−	0.819704i	0.912152	−	0.409852i	$-0.134420\pi$
$108$		0			0
$109$		−	10.1208i		−	0.969398i	−0.874681	−	0.484699i	$-0.838929\pi$
$109$		−	10.1208i		−	0.969398i	0.874681	−	0.484699i	$-0.161071\pi$
$110$	6.63934	+	4.91999i	0.633037	+	0.469103i
$111$		0			0
$112$	−7.03798	+	14.3289i	−0.665027	+	1.35396i
$113$	9.42878	+	5.44371i	0.886985	+	0.512101i	0.872955	−	0.487800i	$-0.162201\pi$
$113$	9.42878	+	5.44371i	0.886985	+	0.512101i	0.0140300	+	0.999902i	$0.495534\pi$
$114$		0			0
$115$	1.26795	+	2.19615i	0.118237	+	0.204792i
$116$	−6.15276	+	6.57969i	−0.571269	+	0.610909i
$117$		0			0
$118$	2.46410	−	1.06939i	0.226839	−	0.0984453i
$119$	14.1454	+	24.5006i	1.29671	+	2.24597i
$120$		0			0
$121$	−3.69615	+	6.40192i	−0.336014	+	0.581993i
$122$	−0.172245	+	1.50250i	−0.0155943	+	0.136030i
$123$		0			0
$124$	2.64469	−	11.3833i	0.237500	−	1.02225i
$125$	1.64863			0.147458
$126$		0			0
$127$		0			0		1.00000			$0$
$127$		0			0		−1.00000			$\pi$
$128$	10.9670	−	2.77949i	0.969352	−	0.245674i
$129$		0			0
$130$	−0.529891	+	4.62227i	−0.0464745	+	0.405400i
$131$	−8.98803	−	5.18924i	−0.785287	−	0.453386i	0.0530134	−	0.998594i	$-0.483117\pi$
$131$	−8.98803	−	5.18924i	−0.785287	−	0.453386i	−0.838301	+	0.545208i	$0.816451\pi$
$132$		0			0
$133$	12.8992	−	7.44734i	1.11850	−	0.645766i
$134$	−5.17758	−	11.9303i	−0.447275	−	1.03062i
$135$		0			0
$136$	6.73205	−	18.8857i	0.577269	−	1.61943i
$137$	−15.1270	+	8.73356i	−1.29238	+	0.746158i	−0.979076	−	0.203494i	$-0.934770\pi$
$137$	−15.1270	+	8.73356i	−1.29238	+	0.746158i	−0.313307	+	0.949652i	$0.601437\pi$
$138$		0			0
$139$	1.59808	−	2.76795i	0.135547	−	0.234774i	−0.790259	−	0.612773i	$-0.790054\pi$
$139$	1.59808	−	2.76795i	0.135547	−	0.234774i	0.925806	+	0.377998i	$0.123387\pi$
$140$	−23.4927	+	7.14681i	−1.98550	+	0.604015i
$141$		0			0
$142$	8.97305	−	12.1088i	0.753001	−	1.01615i
$143$	2.03119			0.169857
$144$		0			0
$145$	−13.8564			−1.15071
$146$	4.99152	−	6.73587i	0.413101	−	0.557465i
$147$		0			0
$148$	13.2268	−	4.02377i	1.08723	−	0.330752i
$149$	−3.07638	+	5.32844i	−0.252027	+	0.436523i	−0.964084	−	0.265599i	$-0.914430\pi$
$149$	−3.07638	+	5.32844i	−0.252027	+	0.436523i	0.712057	+	0.702122i	$0.247764\pi$
$150$		0			0
$151$	−8.51673	+	4.91713i	−0.693081	+	0.400151i	−0.804765	−	0.593593i	$-0.797709\pi$
$151$	−8.51673	+	4.91713i	−0.693081	+	0.400151i	0.111684	+	0.993744i	$0.464376\pi$
$152$	−9.94301	−	3.54432i	−0.806485	−	0.287482i
$153$		0			0
$154$	4.26795	+	9.83427i	0.343921	+	0.792468i
$155$	15.5677	−	8.98803i	1.25043	−	0.721936i
$156$		0			0
$157$	−18.8857	−	10.9037i	−1.50724	−	0.870207i	−0.999965	−	0.00842371i	$-0.997319\pi$
$157$	−18.8857	−	10.9037i	−1.50724	−	0.870207i	−0.507277	−	0.861783i	$-0.669348\pi$
$158$	−0.987317	+	8.61243i	−0.0785467	+	0.685168i
$159$		0			0
$160$	14.6447	+	9.40129i	1.15776	+	0.743237i
$161$			3.28985i			0.259276i
$162$		0			0
$163$	8.80385			0.689571			0.344785	−	0.938682i	$-0.387952\pi$
$163$	8.80385			0.689571			0.344785	+	0.938682i	$0.387952\pi$
$164$	−1.71935	+	7.40047i	−0.134259	+	0.577880i
$165$		0			0
$166$	1.67165	−	14.5819i	0.129745	−	1.13177i
$167$	−11.0690	+	19.1721i	−0.856548	+	1.48359i	0.0186530	+	0.999826i	$0.494062\pi$
$167$	−11.0690	+	19.1721i	−0.856548	+	1.48359i	−0.875201	+	0.483759i	$0.839271\pi$
$168$		0			0
$169$	−5.92820	−	10.2679i	−0.456016	−	0.789842i
$170$	28.2908	−	12.2779i	2.16981	−	0.941670i
$171$		0			0
$172$	−2.73205	+	2.92163i	−0.208317	+	0.222772i
$173$	−0.824313	−	1.42775i	−0.0626714	−	0.108550i	0.832987	−	0.553292i	$-0.186629\pi$
$173$	−0.824313	−	1.42775i	−0.0626714	−	0.108550i	−0.895659	+	0.444742i	$0.853295\pi$
$174$		0			0
$175$	−15.4294	−	8.90815i	−1.16635	−	0.673393i
$176$	3.34950	−	6.81938i	0.252478	−	0.514030i
$177$		0			0
$178$	15.5305	+	11.5087i	1.16406	+	0.862611i
$179$			3.79879i			0.283935i	0.989871	+	0.141967i	$0.0453428\pi$
$179$			3.79879i			0.283935i	−0.989871	+	0.141967i	$0.954657\pi$
$180$		0			0
$181$			3.20817i			0.238461i	0.992867	+	0.119231i	$0.0380428\pi$
$181$			3.20817i			0.238461i	−0.992867	+	0.119231i	$0.961957\pi$
$182$	−3.59359	+	4.84942i	−0.266375	+	0.359463i
$183$		0			0
$184$	1.77604	−	1.51050i	0.130932	−	0.111356i
$185$	18.4168	+	10.6329i	1.35403	+	0.781750i
$186$		0			0
$187$	−6.73205	−	11.6603i	−0.492296	−	0.852682i
$188$	−9.53085	+	10.1922i	−0.695109	+	0.743342i
$189$		0			0
$190$	−6.46410	−	14.8947i	−0.468955	−	1.08057i
$191$	−3.48853	−	6.04232i	−0.252421	−	0.437207i	0.711770	−	0.702412i	$-0.247894\pi$
$191$	−3.48853	−	6.04232i	−0.252421	−	0.437207i	−0.964192	+	0.265205i	$0.914560\pi$
$192$		0			0
$193$	2.69615	−	4.66987i	0.194073	−	0.336145i	−0.752523	−	0.658566i	$-0.771163\pi$
$193$	2.69615	−	4.66987i	0.194073	−	0.336145i	0.946596	+	0.322421i	$0.104497\pi$
$194$	16.0063	+	1.83494i	1.14919	+	0.131741i
$195$		0			0
$196$	−17.3932	−	4.04096i	−1.24237	−	0.288640i
$197$	17.0305			1.21337			0.606687	−	0.794941i	$-0.292498\pi$
$197$	17.0305			1.21337			0.606687	+	0.794941i	$0.292498\pi$
$198$		0			0
$199$		−	15.6775i		−	1.11135i	−0.831400	−	0.555675i	$-0.812460\pi$
$199$		−	15.6775i		−	1.11135i	0.831400	−	0.555675i	$-0.187540\pi$
$200$	2.27513	+	12.4197i	0.160876	+	0.878207i
$201$		0			0
$202$	8.64469	+	0.991015i	0.608238	+	0.0697276i
$203$	−15.5677	−	8.98803i	−1.09264	−	0.630836i
$204$		0			0
$205$	−10.1208	+	5.84325i	−0.706868	+	0.408110i
$206$	5.17758	−	2.24701i	0.360739	−	0.156556i
$207$		0			0
$208$	4.26795	−	0.286542i	0.295929	−	0.0198681i
$209$	−6.13894	+	3.54432i	−0.424639	+	0.245165i
$210$		0			0
$211$	−10.5263	+	18.2321i	−0.724659	+	1.25515i	0.234455	+	0.972127i	$0.424669\pi$
$211$	−10.5263	+	18.2321i	−0.724659	+	1.25515i	−0.959114	+	0.283019i	$0.908664\pi$
$212$	6.20325	+	20.3911i	0.426041	+	1.40047i
$213$		0			0
$214$	−9.63429	−	7.13935i	−0.658586	−	0.488036i
$215$	−6.15276			−0.419614
$216$		0			0
$217$	23.3205			1.58310
$218$	−11.4997	−	8.52167i	−0.778857	−	0.577160i
$219$		0			0
$220$	11.1806	−	3.40129i	0.753795	−	0.229315i
$221$	3.79025	−	6.56491i	0.254960	−	0.441604i
$222$		0			0
$223$	22.5902	−	13.0424i	1.51275	−	0.873386i	0.512860	−	0.858472i	$-0.328586\pi$
$223$	22.5902	−	13.0424i	1.51275	−	0.873386i	0.999889	−	0.0149140i	$-0.00474744\pi$
$224$	10.3552	+	20.0617i	0.691884	+	1.34043i
$225$		0			0
$226$	14.1244	−	6.12979i	0.939538	−	0.407748i
$227$	3.28985	−	1.89939i	0.218355	−	0.126067i	−0.386833	−	0.922150i	$-0.626431\pi$
$227$	3.28985	−	1.89939i	0.218355	−	0.126067i	0.605188	+	0.796082i	$0.293098\pi$
$228$		0			0
$229$	−10.1208	−	5.84325i	−0.668802	−	0.386133i	0.126821	−	0.991926i	$-0.459523\pi$
$229$	−10.1208	−	5.84325i	−0.668802	−	0.386133i	−0.795623	+	0.605793i	$0.792856\pi$
$230$	3.56297	+	0.408453i	0.234935	+	0.0269326i
$231$		0			0
$232$	2.29553	+	12.5311i	0.150709	+	0.822706i
$233$		−	14.1773i		−	0.928784i	−0.885630	−	0.464392i	$-0.846273\pi$
$233$		−	14.1773i		−	0.928784i	0.885630	−	0.464392i	$-0.153727\pi$
$234$		0			0
$235$	−21.4641			−1.40016
$236$	0.859677	−	3.70023i	0.0559602	−	0.240865i
$237$		0			0
$238$	39.7490	+	4.55676i	2.57654	+	0.295371i
$239$	6.15276	−	10.6569i	0.397989	−	0.689337i	−0.595489	−	0.803363i	$-0.703042\pi$
$239$	6.15276	−	10.6569i	0.397989	−	0.689337i	0.993478	+	0.114027i	$0.0363750\pi$
$240$		0			0
$241$	2.69615	+	4.66987i	0.173674	+	0.300813i	0.939702	−	0.341995i	$-0.111103\pi$
$241$	2.69615	+	4.66987i	0.173674	+	0.300813i	−0.766027	+	0.642808i	$0.777769\pi$
$242$	4.16199	+	9.59011i	0.267543	+	0.616476i
$243$		0			0
$244$	1.56218	+	1.46081i	0.100008	+	0.0935190i
$245$	−13.7333	−	23.7867i	−0.877386	−	1.51968i
$246$		0			0
$247$	−3.45632	−	1.99551i	−0.219920	−	0.126971i
$248$	−10.7074	−	12.5897i	−0.679919	−	0.799447i
$249$		0			0
$250$	1.38814	−	1.87324i	0.0877934	−	0.118474i
$251$		−	14.1773i		−	0.894861i	−0.894319	−	0.447431i	$-0.852339\pi$
$251$		−	14.1773i		−	0.894861i	0.894319	−	0.447431i	$-0.147661\pi$
$252$		0			0
$253$		−	1.56569i		−	0.0984344i
$254$		0			0
$255$		0			0
$256$	6.07597	−	14.8014i	0.379748	−	0.925090i
$257$	−3.28985	−	1.89939i	−0.205215	−	0.118481i	0.393871	−	0.919166i	$-0.371136\pi$
$257$	−3.28985	−	1.89939i	−0.205215	−	0.118481i	−0.599086	+	0.800685i	$0.704469\pi$
$258$		0			0
$259$	13.7942	+	23.8923i	0.857132	+	1.48460i
$260$	4.80585	+	4.49401i	0.298046	+	0.278707i
$261$		0			0
$262$	−13.4641	+	5.84325i	−0.831815	+	0.360997i
$263$	1.64863	+	2.85550i	0.101659	+	0.176078i	0.912368	−	0.409371i	$-0.134252\pi$
$263$	1.64863	+	2.85550i	0.101659	+	0.176078i	−0.810710	+	0.585449i	$0.800918\pi$
$264$		0			0
$265$	−16.3923	+	28.3923i	−1.00697	+	1.74413i
$266$	2.39906	−	20.9272i	0.147096	−	1.28313i
$267$		0			0
$268$	−17.9152	−	4.16224i	−1.09434	−	0.254249i
$269$	−19.8860			−1.21247			−0.606236	−	0.795285i	$-0.707321\pi$
$269$	−19.8860			−1.21247			−0.606236	+	0.795285i	$0.707321\pi$
$270$		0			0
$271$			11.9730i			0.727311i	0.931534	+	0.363655i	$0.118471\pi$
$271$			11.9730i			0.727311i	−0.931534	+	0.363655i	$0.881529\pi$
$272$	−15.7903	−	23.5509i	−0.957430	−	1.42798i
$273$		0			0
$274$	−2.81340	+	24.5415i	−0.169964	+	1.48261i
$275$	7.34310	+	4.23954i	0.442806	+	0.255654i
$276$		0			0
$277$	−18.8857	+	10.9037i	−1.13473	+	0.655137i	−0.945120	−	0.326722i	$-0.894056\pi$
$277$	−18.8857	+	10.9037i	−1.13473	+	0.655137i	−0.189611	+	0.981859i	$0.560723\pi$
$278$	−1.79949	−	4.14640i	−0.107926	−	0.248685i
$279$		0			0
$280$	−11.6603	+	32.7110i	−0.696833	+	1.95485i
$281$	8.98803	−	5.18924i	0.536181	−	0.309564i	−0.207349	−	0.978267i	$-0.566484\pi$
$281$	8.98803	−	5.18924i	0.536181	−	0.309564i	0.743530	+	0.668703i	$0.233150\pi$
$282$		0			0
$283$	−13.9282	+	24.1244i	−0.827946	+	1.43404i	0.0717013	+	0.997426i	$0.477157\pi$
$283$	−13.9282	+	24.1244i	−0.827946	+	1.43404i	−0.899647	+	0.436618i	$0.856176\pi$
$284$	−6.20325	−	20.3911i	−0.368095	−	1.20999i
$285$		0			0
$286$	1.71025	−	2.30792i	0.101129	−	0.136470i
$287$	−15.1610			−0.894926
$288$		0			0
$289$	−33.2487			−1.95581
$290$	−11.6670	+	15.7442i	−0.685111	+	0.924532i
$291$		0			0
$292$	−3.45074	−	11.3431i	−0.201939	−	0.663807i
$293$	−3.79025	+	6.56491i	−0.221429	+	0.383526i	−0.955242	−	0.295825i	$-0.904405\pi$
$293$	−3.79025	+	6.56491i	−0.221429	+	0.383526i	0.733813	+	0.679351i	$0.237739\pi$
$294$		0			0
$295$	5.06040	−	2.92163i	0.294628	−	0.170104i
$296$	6.56491	−	18.4168i	0.381578	−	1.07046i
$297$		0			0
$298$	3.46410	+	7.98203i	0.200670	+	0.462387i
$299$	0.763411	−	0.440756i	0.0441492	−	0.0254896i
$300$		0			0
$301$	−6.91264	−	3.99102i	−0.398438	−	0.230038i
$302$	−1.58399	+	13.8173i	−0.0911484	+	0.795094i
$303$		0			0
$304$	−12.3992	+	8.31336i	−0.711141	+	0.476804i
$305$			3.28985i			0.188376i
$306$		0			0
$307$	20.9282			1.19444			0.597218	−	0.802079i	$-0.296273\pi$
$307$	20.9282			1.19444			0.597218	+	0.802079i	$0.296273\pi$
$308$	14.7677	+	3.43098i	0.841467	+	0.195499i
$309$		0			0
$310$	2.89538	−	25.2566i	0.164446	−	1.43448i
$311$	10.2447	−	17.7444i	0.580925	−	1.00619i	−0.414445	−	0.910075i	$-0.636024\pi$
$311$	10.2447	−	17.7444i	0.580925	−	1.00619i	0.995370	−	0.0961176i	$-0.0306425\pi$
$312$		0			0
$313$	−4.69615	−	8.13397i	−0.265442	−	0.459759i	0.702237	−	0.711943i	$-0.252185\pi$
$313$	−4.69615	−	8.13397i	−0.265442	−	0.459759i	−0.967679	+	0.252184i	$0.918851\pi$
$314$	−28.2908	+	12.2779i	−1.59654	+	0.692880i
$315$		0			0
$316$	8.95448	+	8.37345i	0.503729	+	0.471044i
$317$	8.40482	+	14.5576i	0.472062	+	0.817635i	0.999489	−	0.0319652i	$-0.0101766\pi$
$317$	8.40482	+	14.5576i	0.472062	+	0.817635i	−0.527427	+	0.849600i	$0.676843\pi$
$318$		0			0
$319$	7.40895	+	4.27756i	0.414821	+	0.239497i
$320$	23.0129	−	8.72406i	1.28646	−	0.487690i
$321$		0			0
$322$	3.73806	+	2.77003i	0.208314	+	0.154368i
$323$			26.4551i			1.47200i
$324$		0			0
$325$			4.77386i			0.264806i
$326$	7.41280	−	10.0033i	0.410557	−	0.554031i
$327$		0			0
$328$	6.96103	+	8.18476i	0.384359	+	0.451928i
$329$	−24.1150	−	13.9228i	−1.32950	−	0.767589i
$330$		0			0
$331$	−0.937822	−	1.62436i	−0.0515474	−	0.0892827i	0.839100	−	0.543977i	$-0.183082\pi$
$331$	−0.937822	−	1.62436i	−0.0515474	−	0.0892827i	−0.890648	+	0.454694i	$0.849749\pi$
$332$	−15.1610	−	14.1773i	−0.832069	−	0.778079i
$333$		0			0
$334$	12.4641	+	28.7200i	0.682005	+	1.57149i
$335$	−14.1454	−	24.5006i	−0.772847	−	1.33861i
$336$		0			0
$337$	5.69615	−	9.86603i	0.310289	−	0.537437i	−0.668136	−	0.744039i	$-0.732907\pi$
$337$	5.69615	−	9.86603i	0.310289	−	0.537437i	0.978425	+	0.206603i	$0.0662408\pi$
$338$	−16.6584	−	1.90969i	−0.906097	−	0.103874i
$339$		0			0
$340$	9.87013	−	42.4831i	0.535283	−	2.30397i
$341$	−11.0986			−0.601025
$342$		0			0
$343$		−	7.69549i		−	0.415517i
$344$	1.01930	+	5.56426i	0.0549569	+	0.300005i
$345$		0			0
$346$	−2.31634	−	0.265542i	−0.124527	−	0.0142756i
$347$	6.57969	+	3.79879i	0.353216	+	0.203930i	0.666101	−	0.745862i	$-0.267962\pi$
$347$	6.57969	+	3.79879i	0.353216	+	0.203930i	−0.312885	+	0.949791i	$0.601295\pi$
$348$		0			0
$349$	2.28205	−	1.31754i	0.122155	−	0.0705264i	−0.437677	−	0.899132i	$-0.644199\pi$
$349$	2.28205	−	1.31754i	0.122155	−	0.0705264i	0.559833	+	0.828606i	$0.310865\pi$
$350$	−23.1133	+	10.0309i	−1.23546	+	0.536172i
$351$		0			0
$352$	−4.92820	−	9.54773i	−0.262674	−	0.508895i
$353$	−6.57969	+	3.79879i	−0.350202	+	0.202189i	−0.664774	−	0.747044i	$-0.731472\pi$
$353$	−6.57969	+	3.79879i	−0.350202	+	0.202189i	0.314572	+	0.949233i	$0.398139\pi$
$354$		0			0
$355$	16.3923	−	28.3923i	0.870013	−	1.50691i
$356$	26.1532	−	7.95617i	1.38612	−	0.421676i
$357$		0			0
$358$	4.31634	+	3.19856i	0.228126	+	0.169049i
$359$	23.7867			1.25541			0.627707	−	0.778449i	$-0.283993\pi$
$359$	23.7867			1.25541			0.627707	+	0.778449i	$0.283993\pi$
$360$		0			0
$361$	−5.07180			−0.266937
$362$	3.64525	+	2.70126i	0.191590	+	0.141975i
$363$		0			0
$364$	2.48432	+	8.16638i	0.130214	+	0.428034i
$365$	9.11870	−	15.7940i	0.477294	−	0.826698i
$366$		0			0
$367$	−32.4628	+	18.7424i	−1.69455	+	0.978346i	−0.743785	+	0.668419i	$0.766971\pi$
$367$	−32.4628	+	18.7424i	−1.69455	+	0.978346i	−0.950760	+	0.309927i	$0.899695\pi$
$368$	−0.220874	−	3.28985i	−0.0115139	−	0.171495i
$369$		0			0
$370$	27.5885	−	11.9730i	1.43426	−	0.622449i
$371$	−36.8336	+	21.2659i	−1.91231	+	1.10407i
$372$		0			0
$373$	−16.1073	−	9.29957i	−0.834006	−	0.481514i	0.0212163	−	0.999775i	$-0.493246\pi$
$373$	−16.1073	−	9.29957i	−0.834006	−	0.481514i	−0.855222	+	0.518261i	$0.826579\pi$
$374$	−18.9172	−	2.16864i	−0.978186	−	0.112138i
$375$		0			0
$376$	3.55586	+	19.4111i	0.183379	+	1.00105i
$377$			4.81667i			0.248071i
$378$		0			0
$379$	−26.2679			−1.34929			−0.674647	−	0.738141i	$-0.735704\pi$
$379$	−26.2679			−1.34929			−0.674647	+	0.738141i	$0.735704\pi$
$380$	−22.3667	−	5.19646i	−1.14739	−	0.266573i
$381$		0			0
$382$	−9.80286	−	1.12379i	−0.501558	−	0.0574979i
$383$	0.824313	−	1.42775i	0.0421204	−	0.0729547i	−0.844197	−	0.536034i	$-0.819922\pi$
$383$	0.824313	−	1.42775i	0.0421204	−	0.0729547i	0.886317	+	0.463079i	$0.153255\pi$
$384$		0			0
$385$	11.6603	+	20.1962i	0.594262	+	1.02929i
$386$	−3.03596	−	6.99549i	−0.154526	−	0.356061i
$387$		0			0
$388$	15.5622	−	16.6420i	0.790050	−	0.844871i
$389$	7.69095	+	13.3211i	0.389946	+	0.675407i	0.992442	−	0.122715i	$-0.0391602\pi$
$389$	7.69095	+	13.3211i	0.389946	+	0.675407i	−0.602496	+	0.798122i	$0.705827\pi$
$390$		0			0
$391$	−5.06040	−	2.92163i	−0.255916	−	0.147753i
$392$	−19.2365	+	16.3604i	−0.971588	+	0.826323i
$393$		0			0
$394$	14.3396	−	19.3508i	0.722419	−	0.974878i
$395$			18.8576i			0.948827i
$396$		0			0
$397$		−	10.1208i		−	0.507949i	−0.967211	−	0.253974i	$-0.918262\pi$
$397$		−	10.1208i		−	0.507949i	0.967211	−	0.253974i	$-0.0817379\pi$
$398$	−17.8134	−	13.2004i	−0.892907	−	0.661676i
$399$		0			0
$400$	16.0274	+	7.87225i	0.801372	+	0.393613i
$401$	−13.1594	−	7.59757i	−0.657148	−	0.379405i	0.134041	−	0.990976i	$-0.457205\pi$
$401$	−13.1594	−	7.59757i	−0.657148	−	0.379405i	−0.791190	+	0.611571i	$0.790538\pi$
$402$		0			0
$403$	−3.12436	−	5.41154i	−0.155635	−	0.269568i
$404$	8.40482	−	8.98803i	0.418155	−	0.447171i
$405$		0			0
$406$	−23.3205	+	10.1208i	−1.15738	+	0.502287i
$407$	−6.56491	−	11.3708i	−0.325411	−	0.563628i
$408$		0			0
$409$	4.30385	−	7.45448i	0.212812	−	0.368600i	−0.739782	−	0.672847i	$-0.765071\pi$
$409$	4.30385	−	7.45448i	0.212812	−	0.368600i	0.952593	+	0.304246i	$0.0984046\pi$
$410$	−1.88233	+	16.4197i	−0.0929615	+	0.810910i
$411$		0			0
$412$	1.80636	−	7.77495i	0.0889929	−	0.383044i
$413$	7.58051			0.373012
$414$		0			0
$415$		−	31.9281i		−	1.56729i
$416$	3.26801	−	5.09069i	0.160227	−	0.249591i
$417$		0			0
$418$	−1.14176	+	9.95961i	−0.0558451	+	0.487140i
$419$	22.9108	+	13.2276i	1.11927	+	0.646209i	0.941214	−	0.337812i	$-0.109687\pi$
$419$	22.9108	+	13.2276i	1.11927	+	0.646209i	0.178053	+	0.984021i	$0.443020\pi$
$420$		0			0
$421$	−4.13429	+	2.38693i	−0.201493	+	0.116332i	−0.597352	−	0.801979i	$-0.703780\pi$
$421$	−4.13429	+	2.38693i	−0.201493	+	0.116332i	0.395859	+	0.918311i	$0.370447\pi$
$422$	11.8529	+	27.3117i	0.576992	+	1.32951i
$423$		0			0
$424$	28.3923	+	10.1208i	1.37885	+	0.491510i
$425$	27.4048	−	15.8222i	1.32933	−	0.767489i
$426$		0			0
$427$	−2.13397	+	3.69615i	−0.103270	+	0.178869i
$428$	−16.2240	+	4.93558i	−0.784219	+	0.238570i
$429$		0			0
$430$	−5.18059	+	6.99102i	−0.249830	+	0.337137i
$431$	−0.382565			−0.0184275			−0.00921375	−	0.999958i	$-0.502933\pi$
$431$	−0.382565			−0.0184275			−0.00921375	+	0.999958i	$0.502933\pi$
$432$		0			0
$433$	4.53590			0.217981			0.108991	−	0.994043i	$-0.465238\pi$
$433$	4.53590			0.217981			0.108991	+	0.994043i	$0.465238\pi$
$434$	19.6358	−	26.4977i	0.942546	−	1.27193i
$435$		0			0
$436$	−19.3654	+	5.89121i	−0.927432	+	0.282138i
$437$	−1.53819	+	2.66422i	−0.0735816	+	0.127447i
$438$		0			0
$439$	−12.4694	+	7.19918i	−0.595130	+	0.343598i	−0.767123	−	0.641500i	$-0.778313\pi$
$439$	−12.4694	+	7.19918i	−0.595130	+	0.343598i	0.171994	+	0.985098i	$0.444979\pi$
$440$	5.54932	−	15.5677i	0.264553	−	0.742162i
$441$		0			0
$442$	−4.26795	−	9.83427i	−0.203006	−	0.467768i
$443$	−23.6742	+	13.6683i	−1.12480	+	0.649402i	−0.942621	−	0.333864i	$-0.891647\pi$
$443$	−23.6742	+	13.6683i	−1.12480	+	0.649402i	−0.182176	+	0.983266i	$0.558314\pi$
$444$		0			0
$445$	36.4154	+	21.0245i	1.72626	+	0.996655i
$446$	4.20145	−	36.6495i	0.198944	−	1.73541i
$447$		0			0
$448$	31.5140	+	5.12591i	1.48889	+	0.242177i
$449$		−	24.0468i		−	1.13484i	−0.823429	−	0.567419i	$-0.807942\pi$
$449$		−	24.0468i		−	1.13484i	0.823429	−	0.567419i	$-0.192058\pi$
$450$		0			0
$451$	7.21539			0.339759
$452$	4.92771	−	21.2099i	0.231780	−	0.997631i
$453$		0			0
$454$	0.611865	−	5.33734i	0.0287162	−	0.250494i
$455$	−6.56491	+	11.3708i	−0.307768	+	0.533070i
$456$		0			0
$457$	−3.19615	−	5.53590i	−0.149510	−	0.258958i	0.781537	−	0.623859i	$-0.214436\pi$
$457$	−3.19615	−	5.53590i	−0.149510	−	0.258958i	−0.931046	+	0.364901i	$0.881103\pi$
$458$	−15.1610	+	6.57969i	−0.708428	+	0.307449i
$459$		0			0
$460$	3.46410	−	3.70447i	0.161515	−	0.172722i
$461$	−2.96594	−	5.13716i	−0.138138	−	0.239261i	0.788654	−	0.614837i	$-0.210778\pi$
$461$	−2.96594	−	5.13716i	−0.138138	−	0.239261i	−0.926792	+	0.375576i	$0.877445\pi$
$462$		0			0
$463$	−2.10039	−	1.21266i	−0.0976134	−	0.0563571i	0.450399	−	0.892828i	$-0.351282\pi$
$463$	−2.10039	−	1.21266i	−0.0976134	−	0.0563571i	−0.548012	+	0.836470i	$0.684615\pi$
$464$	16.1712	+	7.94284i	0.750727	+	0.368737i
$465$		0			0
$466$	−16.1088	−	11.9372i	−0.746225	−	0.552980i
$467$		−	19.8754i		−	0.919726i	−0.887990	−	0.459863i	$-0.847899\pi$
$467$		−	19.8754i		−	0.919726i	0.887990	−	0.459863i	$-0.152101\pi$
$468$		0			0
$469$		−	36.7020i		−	1.69474i
$470$	−18.0727	+	24.3884i	−0.833630	+	1.12495i
$471$		0			0
$472$	−3.48052	−	4.09238i	−0.160204	−	0.188367i
$473$	3.28985	+	1.89939i	0.151267	+	0.0873342i
$474$		0			0
$475$	−8.33013	−	14.4282i	−0.382212	−	0.662011i
$476$	38.6460	−	41.3276i	1.77134	−	1.89425i
$477$		0			0
$478$	−6.92820	−	15.9641i	−0.316889	−	0.730179i
$479$	3.07638	+	5.32844i	0.140563	+	0.243463i	0.927709	−	0.373304i	$-0.121775\pi$
$479$	3.07638	+	5.32844i	0.140563	+	0.243463i	−0.787146	+	0.616767i	$0.788442\pi$
$480$		0			0
$481$	3.69615	−	6.40192i	0.168530	−	0.291903i
$482$	7.57625	+	0.868531i	0.345089	+	0.0395605i
$483$		0			0
$484$	14.4011	+	3.34580i	0.654593	+	0.152082i
$485$	35.0470			1.59140
$486$		0			0
$487$			33.2073i			1.50477i	0.658726	+	0.752383i	$0.271096\pi$
$487$			33.2073i			1.50477i	−0.658726	+	0.752383i	$0.728904\pi$
$488$	2.97518	−	0.545014i	0.134680	−	0.0246716i
$489$		0			0
$490$	−38.5908	−	4.42399i	−1.74335	−	0.199856i
$491$	28.6090	+	16.5174i	1.29111	+	0.745420i	0.978850	−	0.204578i	$-0.0655821\pi$
$491$	28.6090	+	16.5174i	1.29111	+	0.745420i	0.312256	+	0.949998i	$0.398915\pi$
$492$		0			0
$493$	27.6506	−	15.9641i	1.24532	−	0.718985i
$494$	−5.17758	+	2.24701i	−0.232950	+	0.101098i
$495$		0			0
$496$	−23.3205	+	1.56569i	−1.04712	+	0.0703018i
$497$	36.8336	−	21.2659i	1.65221	−	0.953906i
$498$		0			0
$499$	2.80385	−	4.85641i	0.125517	−	0.217403i	−0.796418	−	0.604747i	$-0.793274\pi$
$499$	2.80385	−	4.85641i	0.125517	−	0.217403i	0.921935	+	0.387344i	$0.126608\pi$
$500$	−0.959646	−	3.15451i	−0.0429167	−	0.141074i
$501$		0			0
$502$	−16.1088	−	11.9372i	−0.718971	−	0.532783i
$503$	−29.4977			−1.31524			−0.657619	−	0.753351i	$-0.728436\pi$
$503$	−29.4977			−1.31524			−0.657619	+	0.753351i	$0.728436\pi$
$504$		0			0
$505$	18.9282			0.842294
$506$	−1.77901	−	1.31831i	−0.0790865	−	0.0586059i
$507$		0			0
$508$		0			0
$509$	0.110437	−	0.191282i	0.00489503	−	0.00847845i	−0.863568	−	0.504233i	$-0.831775\pi$
$509$	0.110437	−	0.191282i	0.00489503	−	0.00847845i	0.868463	+	0.495755i	$0.165109\pi$
$510$		0			0
$511$	20.4898	−	11.8298i	0.906414	−	0.523318i
$512$	−11.7021	−	19.3665i	−0.517163	−	0.855887i
$513$		0			0
$514$	−4.92820	+	2.13878i	−0.217374	+	0.0943375i
$515$	10.6329	−	6.13894i	0.468544	−	0.270514i
$516$		0			0
$517$	11.4767	+	6.62610i	0.504746	+	0.291416i
$518$	38.7621	+	4.44363i	1.70311	+	0.195242i
$519$		0			0
$520$	9.15278	−	1.67667i	0.401376	−	0.0735267i
$521$			7.08863i			0.310559i	0.987871	+	0.155279i	$0.0496278\pi$
$521$			7.08863i			0.310559i	−0.987871	+	0.155279i	$0.950372\pi$
$522$		0			0
$523$	−37.5885			−1.64363			−0.821814	−	0.569756i	$-0.807038\pi$
$523$	−37.5885			−1.64363			−0.821814	+	0.569756i	$0.807038\pi$
$524$	−4.69736	+	20.2185i	−0.205205	+	0.883247i
$525$		0			0
$526$	4.63268	+	0.531084i	0.201994	+	0.0231563i
$527$	−20.7103	+	35.8713i	−0.902156	+	1.56258i
$528$		0			0
$529$	11.1603	+	19.3301i	0.485228	+	0.840440i
$530$	18.4583	+	42.5318i	0.801776	+	1.84746i
$531$		0			0
$532$	−21.7583	−	20.3465i	−0.943343	−	0.882133i
$533$	2.03119	+	3.51813i	0.0879806	+	0.152387i
$534$		0			0
$535$	−22.5902	−	13.0424i	−0.976658	−	0.563874i
$536$	−19.8138	+	16.8514i	−0.855825	+	0.727868i
$537$		0			0
$538$	−16.7439	+	22.5953i	−0.721882	+	0.974153i
$539$			16.9582i			0.730440i
$540$		0			0
$541$			34.5632i			1.48599i	0.669298	+	0.742994i	$0.266595\pi$
$541$			34.5632i			1.48599i	−0.669298	+	0.742994i	$0.733405\pi$
$542$	13.6043	+	10.0812i	0.584353	+	0.433027i
$543$		0			0
$544$	−40.0549	−	1.88809i	−1.71734	−	0.0809514i
$545$	−26.9641	−	15.5677i	−1.15501	−	0.666848i
$546$		0			0
$547$	15.7942	+	27.3564i	0.675312	+	1.16968i	0.976377	+	0.216072i	$0.0693245\pi$
$547$	15.7942	+	27.3564i	0.675312	+	1.16968i	−0.301065	+	0.953604i	$0.597342\pi$
$548$	25.5162	+	23.8605i	1.09000	+	1.01927i
$549$		0			0
$550$	11.0000	−	4.77386i	0.469042	−	0.203558i
$551$	−8.40482	−	14.5576i	−0.358057	−	0.620174i
$552$		0			0
$553$	−12.2321	+	21.1865i	−0.520160	+	0.900943i
$554$	−3.51247	+	30.6395i	−0.149231	+	1.30175i
$555$		0			0
$556$	−6.22647	−	1.44660i	−0.264061	−	0.0613494i
$557$	14.9401			0.633034			0.316517	−	0.948587i	$-0.397487\pi$
$557$	14.9401			0.633034			0.316517	+	0.948587i	$0.397487\pi$
$558$		0			0
$559$			2.13878i			0.0904607i
$560$	27.3497	+	40.7913i	1.15573	+	1.72375i
$561$		0			0
$562$	1.67165	−	14.5819i	0.0705141	−	0.615099i
$563$	−30.2539	−	17.4671i	−1.27505	−	0.736151i	−0.299117	−	0.954217i	$-0.596692\pi$
$563$	−30.2539	−	17.4671i	−1.27505	−	0.736151i	−0.975934	+	0.218066i	$0.930025\pi$
$564$		0			0
$565$	29.0065	−	16.7469i	1.22031	−	0.704548i
$566$	15.6836	+	36.1384i	0.659231	+	1.51901i
$567$		0			0
$568$	−28.3923	−	10.1208i	−1.19131	−	0.424660i
$569$	−5.25742	+	3.03538i	−0.220403	+	0.127250i	−0.606137	−	0.795360i	$-0.707282\pi$
$569$	−5.25742	+	3.03538i	−0.220403	+	0.127250i	0.385734	+	0.922610i	$0.373948\pi$
$570$		0			0
$571$	1.59808	−	2.76795i	0.0668774	−	0.115835i	−0.830648	−	0.556798i	$-0.812030\pi$
$571$	1.59808	−	2.76795i	0.0668774	−	0.115835i	0.897525	+	0.440963i	$0.145363\pi$
$572$	−1.18233	−	3.88652i	−0.0494358	−	0.162504i
$573$		0			0
$574$	−12.7655	+	17.2266i	−0.532822	+	0.719023i
$575$	3.67982			0.153459
$576$		0			0
$577$	11.9282			0.496578			0.248289	−	0.968686i	$-0.420132\pi$
$577$	11.9282			0.496578			0.248289	+	0.968686i	$0.420132\pi$
$578$	−27.9953	+	37.7786i	−1.16445	+	1.57138i
$579$		0			0
$580$	8.06565	+	26.5131i	0.334908	+	1.10090i
$581$	20.7103	−	35.8713i	0.859209	−	1.48819i
$582$		0			0
$583$	17.5298	−	10.1208i	0.726008	−	0.419161i
$584$	−15.7940	−	5.62999i	−0.653562	−	0.232971i
$585$		0			0
$586$	4.26795	+	9.83427i	0.176307	+	0.406250i
$587$	−28.6090	+	16.5174i	−1.18082	+	0.681747i	−0.956204	−	0.292701i	$-0.905446\pi$
$587$	−28.6090	+	16.5174i	−1.18082	+	0.681747i	−0.224616	+	0.974447i	$0.572113\pi$
$588$		0			0
$589$	18.8857	+	10.9037i	0.778171	+	0.449277i
$590$	0.941164	−	8.20984i	0.0387471	−	0.337994i
$591$		0			0
$592$	−15.3983	−	22.9662i	−0.632867	−	0.943904i
$593$		−	38.7330i		−	1.59057i	−0.606233	−	0.795287i	$-0.707320\pi$
$593$		−	38.7330i		−	1.59057i	0.606233	−	0.795287i	$-0.292680\pi$
$594$		0			0
$595$	87.0333			3.56802
$596$	11.9863	+	2.78478i	0.490977	+	0.114069i
$597$		0			0
$598$	0.141984	−	1.23853i	0.00580615	−	0.0506474i
$599$	−11.2603	+	19.5035i	−0.460084	+	0.796890i	−0.998965	−	0.0454928i	$-0.985514\pi$
$599$	−11.2603	+	19.5035i	−0.460084	+	0.796890i	0.538880	+	0.842382i	$0.318848\pi$
$600$		0			0
$601$	−15.1962	−	26.3205i	−0.619864	−	1.07364i	−0.989510	−	0.144463i	$-0.953854\pi$
$601$	−15.1962	−	26.3205i	−0.619864	−	1.07364i	0.369646	−	0.929173i	$-0.379479\pi$
$602$	−10.3552	+	4.49401i	−0.422045	+	0.183162i
$603$		0			0
$604$	14.3660	+	13.4339i	0.584545	+	0.546616i
$605$	11.3708	+	19.6947i	0.462287	+	0.800705i
$606$		0			0
$607$	30.6106	+	17.6730i	1.24245	+	0.717326i	0.969591	−	0.244729i	$-0.0786992\pi$
$607$	30.6106	+	17.6730i	1.24245	+	0.717326i	0.272854	+	0.962056i	$0.412032\pi$
$608$	−0.994051	+	21.0883i	−0.0403141	+	0.855242i
$609$		0			0
$610$	3.73806	+	2.77003i	0.151350	+	0.112155i
$611$			7.46120i			0.301848i
$612$		0			0
$613$		−	6.91264i		−	0.279199i	−0.990208	−	0.139599i	$-0.955418\pi$
$613$		−	6.91264i		−	0.279199i	0.990208	−	0.139599i	$-0.0445815\pi$
$614$	17.6214	−	23.7795i	0.711144	−	0.959662i
$615$		0			0
$616$	16.3328	−	13.8908i	0.658065	−	0.559676i
$617$	24.9965	+	14.4317i	1.00632	+	0.581000i	0.910112	−	0.414361i	$-0.135995\pi$
$617$	24.9965	+	14.4317i	1.00632	+	0.581000i	0.0962087	+	0.995361i	$0.469328\pi$
$618$		0			0
$619$	−18.5981	−	32.2128i	−0.747520	−	1.29474i	−0.949008	−	0.315251i	$-0.897911\pi$
$619$	−18.5981	−	32.2128i	−0.747520	−	1.29474i	0.201488	−	0.979491i	$-0.435422\pi$
$620$	−26.2597	−	24.5557i	−1.05461	−	0.986182i
$621$		0			0
$622$	−11.5359	−	26.5812i	−0.462547	−	1.06581i
$623$	27.2752	+	47.2421i	1.09276	+	1.89272i
$624$		0			0
$625$	13.6962	−	23.7224i	0.547846	−	0.948897i
$626$	−13.1963	−	1.51280i	−0.527430	−	0.0604638i
$627$		0			0
$628$	−9.87013	+	42.4831i	−0.393861	+	1.69526i
$629$	−49.0012			−1.95380
$630$		0			0
$631$			22.0939i			0.879542i	0.898110	+	0.439771i	$0.144940\pi$
$631$			22.0939i			0.879542i	−0.898110	+	0.439771i	$0.855060\pi$
$632$	17.0539	−	3.12405i	0.678368	−	0.124268i
$633$		0			0
$634$	23.6177	+	2.70750i	0.937980	+	0.107529i
$635$		0			0
$636$		0			0
$637$	−8.26857	+	4.77386i	−0.327613	+	0.189147i
$638$	11.0986	−	4.81667i	0.439399	−	0.190694i
$639$		0			0
$640$	9.46410	−	33.4938i	0.374101	−	1.32396i
$641$	30.2539	−	17.4671i	1.19496	−	0.689909i	0.235531	−	0.971867i	$-0.424317\pi$
$641$	30.2539	−	17.4671i	1.19496	−	0.689909i	0.959427	+	0.281957i	$0.0909837\pi$
$642$		0			0
$643$	9.39230	−	16.2679i	0.370396	−	0.641545i	−0.619230	−	0.785210i	$-0.712555\pi$
$643$	9.39230	−	16.2679i	0.370396	−	0.641545i	0.989626	+	0.143664i	$0.0458885\pi$
$644$	6.29485	−	1.91498i	0.248052	−	0.0754608i
$645$		0			0
$646$	30.0594	+	22.2751i	1.18267	+	0.876402i
$647$	−39.7720			−1.56360			−0.781800	−	0.623529i	$-0.785698\pi$
$647$	−39.7720			−1.56360			−0.781800	+	0.623529i	$0.785698\pi$
$648$		0			0
$649$	−3.60770			−0.141614
$650$	5.42426	+	4.01957i	0.212757	+	0.157660i
$651$		0			0
$652$	−5.12462	−	16.8455i	−0.200696	−	0.659719i
$653$	−16.2062	+	28.0700i	−0.634198	+	1.09846i	0.352487	+	0.935817i	$0.385336\pi$
$653$	−16.2062	+	28.0700i	−0.634198	+	1.09846i	−0.986685	+	0.162646i	$0.947997\pi$
$654$		0			0
$655$	−27.6506	+	15.9641i	−1.08040	+	0.623767i
$656$	15.1610	−	1.01788i	0.591938	−	0.0397416i
$657$		0			0
$658$	−36.1244	+	15.6775i	−1.40827	+	0.611173i
$659$	18.8576	−	10.8874i	0.734586	−	0.424114i	−0.0855113	−	0.996337i	$-0.527252\pi$
$659$	18.8576	−	10.8874i	0.734586	−	0.424114i	0.820098	+	0.572224i	$0.193919\pi$
$660$		0			0
$661$	−39.1938	−	22.6285i	−1.52446	−	0.880149i	−0.999580	−	0.0289735i	$-0.990776\pi$
$661$	−39.1938	−	22.6285i	−1.52446	−	0.880149i	−0.524882	−	0.851175i	$-0.675891\pi$
$662$	−2.63530	−	0.302107i	−0.102424	−	0.0117417i
$663$		0			0
$664$	−28.8743	+	5.28938i	−1.12054	+	0.205268i
$665$		−	45.8216i		−	1.77689i
$666$		0			0
$667$	3.71281			0.143761
$668$	43.1275	+	10.0198i	1.66865	+	0.387679i
$669$		0			0
$670$	−39.7490	−	4.55676i	−1.53564	−	0.176043i
$671$	1.01560	−	1.75906i	0.0392066	−	0.0679079i
$672$		0			0
$673$	−17.6244	−	30.5263i	−0.679369	−	1.17670i	−0.975171	−	0.221452i	$-0.928920\pi$
$673$	−17.6244	−	30.5263i	−0.679369	−	1.17670i	0.295802	−	0.955249i	$-0.404413\pi$
$674$	−6.41405	−	14.7793i	−0.247060	−	0.569279i
$675$		0			0
$676$	−16.1962	+	17.3200i	−0.622929	+	0.666154i
$677$	22.2485	+	38.5356i	0.855080	+	1.48104i	0.876571	+	0.481273i	$0.159826\pi$
$677$	22.2485	+	38.5356i	0.855080	+	1.48104i	−0.0214905	+	0.999769i	$0.506841\pi$
$678$		0			0
$679$	39.3755	+	22.7334i	1.51109	+	0.872429i
$680$	−39.9605	−	46.9854i	−1.53241	−	1.80181i
$681$		0			0
$682$	−9.34500	+	12.6107i	−0.357838	+	0.482890i
$683$			39.7509i			1.52103i	0.649323	+	0.760513i	$0.275052\pi$
$683$			39.7509i			1.52103i	−0.649323	+	0.760513i	$0.724948\pi$
$684$		0			0
$685$			53.7354i			2.05313i
$686$	−8.74393	−	6.47956i	−0.333845	−	0.247391i
$687$		0			0
$688$	7.18059	+	3.52691i	0.273757	+	0.134462i
$689$	9.86954	+	5.69818i	0.375999	+	0.217083i
$690$		0			0
$691$	−1.92820	−	3.33975i	−0.0733523	−	0.127050i	0.827016	−	0.562178i	$-0.190036\pi$
$691$	−1.92820	−	3.33975i	−0.0733523	−	0.127050i	−0.900369	+	0.435128i	$0.856703\pi$
$692$	−2.25207	+	2.40833i	−0.0856107	+	0.0915511i
$693$		0			0
$694$	9.85641	−	4.27756i	0.374144	−	0.162374i
$695$	−4.91629	−	8.51526i	−0.186485	−	0.323002i
$696$		0			0
$697$	13.4641	−	23.3205i	0.509989	−	0.883327i
$698$	0.424429	−	3.70232i	0.0160649	−	0.140135i
$699$		0			0
$700$	−8.06377	+	34.7082i	−0.304782	+	1.31185i
$701$	51.8567			1.95860			0.979300	−	0.202415i	$-0.0648790\pi$
$701$	51.8567			1.95860			0.979300	+	0.202415i	$0.0648790\pi$
$702$		0			0
$703$			25.7983i			0.973002i
$704$	−14.9980	−	2.43951i	−0.565260	−	0.0919425i
$705$		0			0
$706$	−1.22373	+	10.6747i	−0.0460557	+	0.401747i
$707$	21.2659	+	12.2779i	0.799786	+	0.461757i
$708$		0			0
$709$	−30.4289	+	17.5681i	−1.14278	+	0.659786i	−0.947118	−	0.320885i	$-0.896020\pi$
$709$	−30.4289	+	17.5681i	−1.14278	+	0.659786i	−0.195664	+	0.980671i	$0.562686\pi$
$710$	−18.4583	−	42.5318i	−0.692726	−	1.59619i
$711$		0			0
$712$	12.9808	−	36.4154i	0.486475	−	1.36473i
$713$	−4.17136	+	2.40833i	−0.156219	+	0.0901928i
$714$		0			0
$715$	3.12436	−	5.41154i	0.116844	−	0.202380i
$716$	7.26867	−	2.21123i	0.271643	−	0.0826375i
$717$		0			0
$718$	20.0283	−	27.0274i	0.747449	−	1.00866i
$719$	7.80138			0.290942			0.145471	−	0.989362i	$-0.453530\pi$
$719$	7.80138			0.290942			0.145471	+	0.989362i	$0.453530\pi$
$720$		0			0
$721$	15.9282			0.593197
$722$	−4.27043	+	5.76278i	−0.158929	+	0.214469i
$723$		0			0
$724$	6.13857	−	1.86744i	0.228138	−	0.0694028i
$725$	−10.0534	+	17.4131i	−0.373376	+	0.646706i
$726$		0			0
$727$	22.5902	−	13.0424i	0.837823	−	0.483717i	−0.0187009	−	0.999825i	$-0.505953\pi$
$727$	22.5902	−	13.0424i	0.837823	−	0.483717i	0.856524	+	0.516108i	$0.172620\pi$
$728$	11.3708	+	4.05326i	0.421428	+	0.150224i
$729$		0			0
$730$	−10.2679	−	23.6595i	−0.380034	−	0.875679i
$731$	12.2779	−	7.08863i	0.454113	−	0.262183i
$732$		0			0
$733$	11.4767	+	6.62610i	0.423903	+	0.244741i	0.696746	−	0.717318i	$-0.254631\pi$
$733$	11.4767	+	6.62610i	0.423903	+	0.244741i	−0.272843	+	0.962059i	$0.587964\pi$
$734$	−6.03763	+	52.6666i	−0.222853	+	1.94396i
$735$		0			0
$736$	−3.92403	−	2.51907i	−0.144642	−	0.0928541i
$737$			17.4671i			0.643409i
$738$		0			0
$739$	−20.6410			−0.759292			−0.379646	−	0.925132i	$-0.623954\pi$
$739$	−20.6410			−0.759292			−0.379646	+	0.925132i	$0.623954\pi$
$740$	9.62508	−	41.4284i	0.353825	−	1.52294i
$741$		0			0
$742$	−6.85053	+	59.7577i	−0.251491	+	2.19377i
$743$	25.8475	−	44.7692i	0.948253	−	1.64242i	0.199148	−	0.979969i	$-0.436182\pi$
$743$	25.8475	−	44.7692i	0.948253	−	1.64242i	0.749104	−	0.662452i	$-0.230484\pi$
$744$		0			0
$745$	9.46410	+	16.3923i	0.346738	+	0.600568i
$746$	−24.1289	+	10.4716i	−0.883420	+	0.383393i
$747$		0			0
$748$	−18.3923	+	19.6685i	−0.672489	+	0.719153i
$749$	−16.9201	−	29.3064i	−0.618246	−	1.07083i
$750$		0			0
$751$	−17.2816	−	9.97754i	−0.630615	−	0.364086i	0.150375	−	0.988629i	$-0.451952\pi$
$751$	−17.2816	−	9.97754i	−0.630615	−	0.364086i	−0.780990	+	0.624543i	$0.785285\pi$
$752$	25.0497	+	12.3038i	0.913470	+	0.448672i
$753$		0			0
$754$	5.47290	+	4.05561i	0.199311	+	0.147697i
$755$			30.2539i			1.10105i
$756$		0			0
$757$			52.0930i			1.89335i	0.322189	+	0.946675i	$0.395581\pi$
$757$			52.0930i			1.89335i	−0.322189	+	0.946675i	$0.604419\pi$
$758$	−22.1175	+	29.8467i	−0.803343	+	1.08408i
$759$		0			0
$760$	−24.7371	+	21.0386i	−0.897308	+	0.763149i
$761$	−37.2744	−	21.5204i	−1.35119	−	0.780113i	−0.362778	−	0.931876i	$-0.618172\pi$
$761$	−37.2744	−	21.5204i	−1.35119	−	0.780113i	−0.988417	+	0.151763i	$0.951505\pi$
$762$		0			0
$763$	−20.1962	−	34.9808i	−0.731150	−	1.26639i
$764$	−9.53085	+	10.1922i	−0.344814	+	0.368741i
$765$		0			0
$766$	−0.928203	−	2.13878i	−0.0335373	−	0.0772772i
$767$	−1.01560	−	1.75906i	−0.0366710	−	0.0635161i
$768$		0			0
$769$	−2.03590	+	3.52628i	−0.0734164	+	0.127161i	−0.900397	−	0.435070i	$-0.856724\pi$
$769$	−2.03590	+	3.52628i	−0.0734164	+	0.127161i	0.826980	+	0.562231i	$0.190057\pi$
$770$	32.7656	+	3.75620i	1.18079	+	0.135364i
$771$		0			0
$772$	−10.5048	−	2.44059i	−0.378077	−	0.0878388i
$773$	44.7179			1.60839			0.804196	−	0.594364i	$-0.202596\pi$
$773$	44.7179			1.60839			0.804196	+	0.594364i	$0.202596\pi$
$774$		0			0
$775$		−	26.0849i		−	0.936996i
$776$	−5.80608	−	31.6949i	−0.208426	−	1.13778i
$777$		0			0
$778$	21.6117	+	2.47754i	0.774818	+	0.0888241i
$779$	−12.2779	−	7.08863i	−0.439900	−	0.253977i
$780$		0			0
$781$	−17.5298	+	10.1208i	−0.627264	+	0.362151i
$782$	−7.58051	+	3.28985i	−0.271078	+	0.117645i
$783$		0			0
$784$	2.39230	+	35.6326i	0.0854395	+	1.27259i
$785$	−58.0995	+	33.5438i	−2.07366	+	1.19723i
$786$		0			0
$787$	−3.72243	+	6.44744i	−0.132690	+	0.229826i	−0.924713	−	0.380666i	$-0.875695\pi$
$787$	−3.72243	+	6.44744i	−0.132690	+	0.229826i	0.792022	+	0.610492i	$0.209028\pi$
$788$	−9.91327	−	32.5865i	−0.353146	−	1.16085i
$789$		0			0
$790$	21.4267	+	15.8780i	0.762329	+	0.564913i
$791$	43.4519			1.54497
$792$		0			0
$793$	1.14359			0.0406102
$794$	−11.4997	−	8.52167i	−0.408108	−	0.302423i
$795$		0			0
$796$	−29.9977	+	9.12570i	−1.06324	+	0.323452i
$797$	−13.7333	+	23.7867i	−0.486457	+	0.842569i	−0.999879	−	0.0155679i	$-0.995044\pi$
$797$	−13.7333	+	23.7867i	−0.486457	+	0.842569i	0.513422	+	0.858136i	$0.328378\pi$
$798$		0			0
$799$	42.8318	−	24.7289i	1.51528	−	0.874847i
$800$	22.4398	−	11.5826i	0.793367	−	0.409508i
$801$		0			0
$802$	−19.7128	+	8.55511i	−0.696084	+	0.302092i
$803$	−9.75144	+	5.62999i	−0.344121	+	0.198678i
$804$		0			0
$805$	8.76488	+	5.06040i	0.308921	+	0.178356i
$806$	−8.77951	−	1.00647i	−0.309245	−	0.0354514i
$807$		0			0
$808$	−3.13575	−	17.1178i	−0.110315	−	0.602201i
$809$		−	14.1773i		−	0.498446i	−0.968446	−	0.249223i	$-0.919825\pi$
$809$		−	14.1773i		−	0.498446i	0.968446	−	0.249223i	$-0.0801752\pi$
$810$		0			0
$811$	−27.0718			−0.950619			−0.475310	−	0.879819i	$-0.657664\pi$
$811$	−27.0718			−0.950619			−0.475310	+	0.879819i	$0.657664\pi$
$812$	−8.13607	+	35.0194i	−0.285520	+	1.22894i
$813$		0			0
$814$	−18.4476	−	2.11480i	−0.646586	−	0.0741238i
$815$	13.5420	−	23.4554i	0.474355	−	0.821607i
$816$		0			0
$817$	−3.73205	−	6.46410i	−0.130568	−	0.226150i
$818$	−4.84627	−	11.1668i	−0.169446	−	0.390440i
$819$		0			0
$820$	17.0718	+	15.9641i	0.596173	+	0.557489i
$821$	−5.43888	−	9.42042i	−0.189818	−	0.328775i	0.755371	−	0.655297i	$-0.227457\pi$
$821$	−5.43888	−	9.42042i	−0.189818	−	0.328775i	−0.945190	+	0.326522i	$0.894123\pi$
$822$		0			0
$823$	20.9861	+	12.1163i	0.731529	+	0.422348i	0.818981	−	0.573820i	$-0.194539\pi$
$823$	20.9861	+	12.1163i	0.731529	+	0.422348i	−0.0874525	+	0.996169i	$0.527873\pi$
$824$	−7.31328	−	8.59893i	−0.254770	−	0.299558i
$825$		0			0
$826$	6.38275	−	8.61329i	0.222084	−	0.299695i
$827$			40.6324i			1.41293i	0.707749	+	0.706464i	$0.249711\pi$
$827$			40.6324i			1.41293i	−0.707749	+	0.706464i	$0.750289\pi$
$828$		0			0
$829$		−	34.5632i		−	1.20043i	−0.799839	−	0.600215i	$-0.795082\pi$
$829$		−	34.5632i		−	1.20043i	0.799839	−	0.600215i	$-0.204918\pi$
$830$	−36.2781	−	26.8833i	−1.25923	−	0.933134i
$831$		0			0
$832$	−3.03260	−	7.99958i	−0.105136	−	0.277336i
$833$	54.8097	+	31.6444i	1.89904	+	1.09641i
$834$		0			0
$835$	34.0526	+	58.9808i	1.17844	+	2.04111i
$836$	10.3552	+	9.68325i	0.358141	+	0.334902i
$837$		0			0
$838$	34.3205	−	14.8947i	1.18558	−	0.514528i
$839$	−12.5264	−	21.6963i	−0.432459	−	0.749041i	0.564626	−	0.825347i	$-0.309021\pi$
$839$	−12.5264	−	21.6963i	−0.432459	−	0.749041i	−0.997084	+	0.0763065i	$0.975687\pi$
$840$		0			0
$841$	4.35641	−	7.54552i	0.150221	−	0.260190i
$842$	−0.768919	+	6.70733i	−0.0264987	+	0.231150i
$843$		0			0
$844$	41.0128	+	9.52852i	1.41172	+	0.327985i
$845$	−36.4748			−1.25477
$846$		0			0
$847$			29.5028i			1.01373i
$848$	35.4059	−	23.7388i	1.21584	−	0.815195i
$849$		0			0
$850$	5.09691	−	44.4607i	0.174823	−	1.52499i
$851$	−4.93477	−	2.84909i	−0.169162	−	0.0976655i
$852$		0			0
$853$	−12.8992	+	7.44734i	−0.441659	+	0.254992i	−0.704301	−	0.709901i	$-0.748739\pi$
$853$	−12.8992	+	7.44734i	−0.441659	+	0.254992i	0.262642	+	0.964893i	$0.415406\pi$
$854$	2.40292	+	5.53685i	0.0822264	+	0.189467i
$855$		0			0
$856$	−8.05256	+	22.5902i	−0.275231	+	0.772116i
$857$	−0.881512	+	0.508941i	−0.0301119	+	0.0173851i	−0.514980	−	0.857202i	$-0.672201\pi$
$857$	−0.881512	+	0.508941i	−0.0301119	+	0.0173851i	0.484869	+	0.874587i	$0.338867\pi$
$858$		0			0
$859$	−5.79423	+	10.0359i	−0.197697	+	0.342420i	−0.947781	−	0.318921i	$-0.896679\pi$
$859$	−5.79423	+	10.0359i	−0.197697	+	0.342420i	0.750085	+	0.661342i	$0.230013\pi$
$860$	3.58145	+	11.7728i	0.122126	+	0.401449i
$861$		0			0
$862$	−0.322118	+	0.434686i	−0.0109714	+	0.0148055i
$863$	15.9853			0.544147			0.272073	−	0.962276i	$-0.412291\pi$
$863$	15.9853			0.544147			0.272073	+	0.962276i	$0.412291\pi$
$864$		0			0
$865$	−5.07180			−0.172446
$866$	3.81920	−	5.15387i	0.129782	−	0.175136i
$867$		0			0
$868$	−13.5746	−	44.6219i	−0.460752	−	1.51457i
$869$	5.82145	−	10.0830i	0.197479	−	0.342044i
$870$		0			0
$871$	−8.51673	+	4.91713i	−0.288578	+	0.166611i
$872$	−9.61170	+	26.9641i	−0.325493	+	0.913119i
$873$		0			0
$874$	1.73205	+	3.99102i	0.0585875	+	0.134998i
$875$	5.69818	−	3.28985i	0.192634	−	0.111217i
$876$		0			0
$877$	16.6036	+	9.58611i	0.560665	+	0.323700i	0.753412	−	0.657548i	$-0.228406\pi$
$877$	16.6036	+	9.58611i	0.560665	+	0.323700i	−0.192747	+	0.981248i	$0.561740\pi$
$878$	−2.31912	+	20.2299i	−0.0782666	+	0.682725i
$879$		0			0
$880$	−13.0162	−	19.4133i	−0.438776	−	0.654422i
$881$		−	6.07075i		−	0.204529i	−0.994757	−	0.102264i	$-0.967391\pi$
$881$		−	6.07075i		−	0.204529i	0.994757	−	0.102264i	$-0.0326088\pi$
$882$		0			0
$883$	44.1244			1.48490			0.742451	−	0.669900i	$-0.233663\pi$
$883$	44.1244			1.48490			0.742451	+	0.669900i	$0.233663\pi$
$884$	−14.7677	−	3.43098i	−0.496691	−	0.115397i
$885$		0			0
$886$	−4.40307	+	38.4083i	−0.147924	+	1.29035i
$887$	12.9090	−	22.3590i	0.433440	−	0.750740i	−0.563727	−	0.825961i	$-0.690633\pi$
$887$	12.9090	−	22.3590i	0.433440	−	0.750740i	0.997167	+	0.0752210i	$0.0239662\pi$
$888$		0			0
$889$		0			0
$890$	54.5505	−	23.6742i	1.82854	−	0.793562i
$891$		0			0
$892$	−38.1051	−	35.6326i	−1.27585	−	1.19307i
$893$	−13.0194	−	22.5502i	−0.435677	−	0.754615i
$894$		0			0
$895$	10.1208	+	5.84325i	0.338301	+	0.195318i
$896$	32.3589	−	31.4915i	1.08103	−	1.05206i
$897$		0			0
$898$	−27.3230	−	20.2473i	−0.911779	−	0.675661i
$899$		−	26.3188i		−	0.877780i
$900$		0			0
$901$		−	75.5427i		−	2.51669i
$902$	6.07532	−	8.19842i	0.202286	−	0.272978i
$903$		0			0
$904$	−19.9505	−	23.4577i	−0.663543	−	0.780193i
$905$	8.54727	+	4.93477i	0.284121	+	0.164037i
$906$		0			0
$907$	23.1865	+	40.1603i	0.769896	+	1.33350i	0.937619	+	0.347665i	$0.113025\pi$
$907$	23.1865	+	40.1603i	0.769896	+	1.33350i	−0.167723	+	0.985834i	$0.553641\pi$
$908$	−5.54932	−	5.18924i	−0.184161	−	0.172211i
$909$		0			0
$910$	7.39230	+	17.0335i	0.245053	+	0.564653i
$911$	0.220874	+	0.382565i	0.00731788	+	0.0126749i	0.869661	−	0.493649i	$-0.164337\pi$
$911$	0.220874	+	0.382565i	0.00731788	+	0.0126749i	−0.862343	+	0.506324i	$0.831004\pi$
$912$		0			0
$913$	−9.85641	+	17.0718i	−0.326199	+	0.564994i
$914$	−8.98126	−	1.02960i	−0.297074	−	0.0340561i
$915$		0			0
$916$	−5.28938	+	22.7666i	−0.174766	+	0.752231i
$917$	−41.4207			−1.36783
$918$		0			0
$919$		−	58.0130i		−	1.91367i	−0.290628	−	0.956836i	$-0.593864\pi$
$919$		−	58.0130i		−	1.91367i	0.290628	−	0.956836i	$-0.406136\pi$
$920$	−1.29242	−	7.05520i	−0.0426098	−	0.232603i
$921$		0			0
$922$	−8.33436	−	0.955439i	−0.274478	−	0.0314657i
$923$	−9.86954	−	5.69818i	−0.324860	−	0.187558i
$924$		0			0
$925$	26.7244	−	15.4294i	0.878694	−	0.507314i
$926$	−3.14639	+	1.36549i	−0.103397	+	0.0448729i
$927$		0			0
$928$	22.6410	−	11.6865i	0.743228	−	0.383628i
$929$	−17.9761	+	10.3785i	−0.589775	+	0.340507i	−0.765009	−	0.644020i	$-0.777265\pi$
$929$	−17.9761	+	10.3785i	−0.589775	+	0.340507i	0.175233	+	0.984527i	$0.443932\pi$
$930$		0			0
$931$	16.6603	−	28.8564i	0.546018	−	0.945731i
$932$	−27.1271	+	8.25242i	−0.888576	+	0.270317i
$933$		0			0
$934$	−22.5833	−	16.7350i	−0.738948	−	0.547587i
$935$	−41.4207			−1.35460
$936$		0			0
$937$	−23.3923			−0.764193			−0.382097	−	0.924122i	$-0.624798\pi$
$937$	−23.3923			−0.764193			−0.382097	+	0.924122i	$0.624798\pi$
$938$	−41.7023	−	30.9029i	−1.36163	−	1.00902i
$939$		0			0
$940$	12.4940	+	41.0698i	0.407510	+	1.33955i
$941$	9.33957	−	16.1766i	0.304461	−	0.527342i	−0.672680	−	0.739934i	$-0.734857\pi$
$941$	9.33957	−	16.1766i	0.304461	−	0.527342i	0.977141	+	0.212591i	$0.0681902\pi$
$942$		0			0
$943$	2.71186	−	1.56569i	0.0883104	−	0.0509860i
$944$	−7.58051	+	0.508941i	−0.246725	+	0.0165646i
$945$		0			0
$946$	4.92820	−	2.13878i	0.160230	−	0.0695377i
$947$	25.3192	−	14.6180i	0.822762	−	0.475022i	−0.0286060	−	0.999591i	$-0.509107\pi$
$947$	25.3192	−	14.6180i	0.822762	−	0.475022i	0.851368	+	0.524569i	$0.175773\pi$
$948$		0			0
$949$	−5.49022	−	3.16978i	−0.178220	−	0.102895i
$950$	−23.4078	−	2.68344i	−0.759451	−	0.0870624i
$951$		0			0
$952$	−14.4184	−	78.7088i	−0.467303	−	2.55097i
$953$		−	15.7041i		−	0.508705i	−0.967112	−	0.254353i	$-0.918138\pi$
$953$		−	15.7041i		−	0.508705i	0.967112	−	0.254353i	$-0.0818624\pi$
$954$		0			0
$955$	−21.4641			−0.694562
$956$	−23.9725	−	5.56955i	−0.775327	−	0.180132i
$957$		0			0
$958$	8.64469	+	0.991015i	0.279297	+	0.0320183i
$959$	−34.8558	+	60.3719i	−1.12555	+	1.94951i
$960$		0			0
$961$	1.57180	+	2.72243i	0.0507031	+	0.0878204i
$962$	−4.16199	−	9.59011i	−0.134188	−	0.309198i
$963$		0			0
$964$	7.36603	−	7.87715i	0.237244	−	0.253706i
$965$	−8.29438	−	14.3663i	−0.267006	−	0.462467i
$966$		0			0
$967$	−8.51673	−	4.91713i	−0.273879	−	0.158124i	0.356770	−	0.934192i	$-0.383878\pi$
$967$	−8.51673	−	4.91713i	−0.273879	−	0.158124i	−0.630649	+	0.776068i	$0.717211\pi$
$968$	15.9273	−	13.5459i	0.511921	−	0.435382i
$969$		0			0
$970$	29.5094	−	39.8219i	0.947491	−	1.27860i
$971$		−	55.8275i		−	1.79159i	−0.444466	−	0.895796i	$-0.646607\pi$
$971$		−	55.8275i		−	1.79159i	0.444466	−	0.895796i	$-0.353393\pi$
$972$		0			0
$973$		−	12.7559i		−	0.408935i
$974$	37.7315	+	27.9604i	1.20899	+	0.895908i
$975$		0			0
$976$	1.88582	−	3.83942i	0.0603637	−	0.122897i
$977$	−20.3844	−	11.7689i	−0.652154	−	0.376521i	0.137127	−	0.990554i	$-0.456213\pi$
$977$	−20.3844	−	11.7689i	−0.652154	−	0.376521i	−0.789281	+	0.614032i	$0.789547\pi$
$978$		0			0
$979$	−12.9808	−	22.4833i	−0.414867	−	0.718571i
$980$	−37.5200	+	40.1235i	−1.19853	+	1.28170i
$981$		0			0
$982$	42.8564	−	18.5991i	1.36760	−	0.593523i
$983$	−27.6578	−	47.9047i	−0.882147	−	1.52792i	−0.848949	−	0.528475i	$-0.822764\pi$
$983$	−27.6578	−	47.9047i	−0.882147	−	1.52792i	−0.0331982	−	0.999449i	$-0.510569\pi$
$984$		0			0
$985$	26.1962	−	45.3731i	0.834679	−	1.44571i
$986$	5.14262	−	44.8594i	0.163774	−	1.42861i
$987$		0			0
$988$	−1.80636	+	7.77495i	−0.0574679	+	0.247354i
$989$	1.64863			0.0524233
$990$		0			0
$991$		−	25.7983i		−	0.819511i	−0.912195	−	0.409755i	$-0.865614\pi$
$991$		−	25.7983i		−	0.819511i	0.912195	−	0.409755i	$-0.134386\pi$
$992$	−17.8567	+	27.8160i	−0.566952	+	0.883160i
$993$		0			0
$994$	6.85053	−	59.7577i	0.217286	−	1.89540i
$995$	−41.7684	−	24.1150i	−1.32415	−	0.764497i
$996$		0			0
$997$	−1.35593	+	0.782847i	−0.0429428	+	0.0247930i	−0.521318	−	0.853363i	$-0.674559\pi$
$997$	−1.35593	+	0.782847i	−0.0429428	+	0.0247930i	0.478375	+	0.878156i	$0.341226\pi$
$998$	−3.15722	−	7.27492i	−0.0999402	−	0.230284i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	648.2.l.f.539.6		16
3.2	odd	2	inner	648.2.l.f.539.3		16
4.3	odd	2		2592.2.p.f.2159.7		16
8.3	odd	2	inner	648.2.l.f.539.8		16
8.5	even	2		2592.2.p.f.2159.2		16
9.2	odd	6	inner	648.2.l.f.107.8		16
9.4	even	3		216.2.f.a.107.6	yes	8
9.5	odd	6		216.2.f.a.107.3	✓	8
9.7	even	3	inner	648.2.l.f.107.1		16
12.11	even	2		2592.2.p.f.2159.1		16
24.5	odd	2		2592.2.p.f.2159.8		16
24.11	even	2	inner	648.2.l.f.539.1		16
36.7	odd	6		2592.2.p.f.431.8		16
36.11	even	6		2592.2.p.f.431.2		16
36.23	even	6		864.2.f.a.431.7		8
36.31	odd	6		864.2.f.a.431.1		8
72.5	odd	6		864.2.f.a.431.2		8
72.11	even	6	inner	648.2.l.f.107.6		16
72.13	even	6		864.2.f.a.431.8		8
72.29	odd	6		2592.2.p.f.431.7		16
72.43	odd	6	inner	648.2.l.f.107.3		16
72.59	even	6		216.2.f.a.107.5	yes	8
72.61	even	6		2592.2.p.f.431.1		16
72.67	odd	6		216.2.f.a.107.4	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
216.2.f.a.107.3	✓	8	9.5	odd	6
216.2.f.a.107.4	yes	8	72.67	odd	6
216.2.f.a.107.5	yes	8	72.59	even	6
216.2.f.a.107.6	yes	8	9.4	even	3
648.2.l.f.107.1		16	9.7	even	3	inner
648.2.l.f.107.3		16	72.43	odd	6	inner
648.2.l.f.107.6		16	72.11	even	6	inner
648.2.l.f.107.8		16	9.2	odd	6	inner
648.2.l.f.539.1		16	24.11	even	2	inner
648.2.l.f.539.3		16	3.2	odd	2	inner
648.2.l.f.539.6		16	1.1	even	1	trivial
648.2.l.f.539.8		16	8.3	odd	2	inner
864.2.f.a.431.1		8	36.31	odd	6
864.2.f.a.431.2		8	72.5	odd	6
864.2.f.a.431.7		8	36.23	even	6
864.2.f.a.431.8		8	72.13	even	6
2592.2.p.f.431.1		16	72.61	even	6
2592.2.p.f.431.2		16	36.11	even	6
2592.2.p.f.431.7		16	72.29	odd	6
2592.2.p.f.431.8		16	36.7	odd	6
2592.2.p.f.2159.1		16	12.11	even	2
2592.2.p.f.2159.2		16	8.5	even	2
2592.2.p.f.2159.7		16	4.3	odd	2
2592.2.p.f.2159.8		16	24.5	odd	2

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:	\( N \)	\(=\)	\( 648 = 2^{3} \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	648.l (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.841995 - 1.13624i) q^{2} +(-0.582088 - 1.91342i) q^{4} +(1.53819 - 2.66422i) q^{5} +(3.45632 - 1.99551i) q^{7} +(-2.66422 - 0.949697i) q^{8} +O(q^{10})\)	\(q+(0.841995 - 1.13624i) q^{2} +(-0.582088 - 1.91342i) q^{4} +(1.53819 - 2.66422i) q^{5} +(3.45632 - 1.99551i) q^{7} +(-2.66422 - 0.949697i) q^{8} +(-1.73205 - 3.99102i) q^{10} +(-1.64492 + 0.949697i) q^{11} +(-0.926118 - 0.534695i) q^{13} +(0.642827 - 5.60742i) q^{14} +(-3.32235 + 2.22756i) q^{16} +7.08863i q^{17} +3.73205 q^{19} +(-5.99313 - 1.39239i) q^{20} +(-0.305932 + 2.66867i) q^{22} +(-0.412157 + 0.713876i) q^{23} +(-2.23205 - 3.86603i) q^{25} +(-1.38733 + 0.602084i) q^{26} +(-5.83013 - 5.45183i) q^{28} +(-2.25207 - 3.90069i) q^{29} +(5.06040 + 2.92163i) q^{31} +(-0.266355 + 5.65058i) q^{32} +(8.05440 + 5.96859i) q^{34} -12.2779i q^{35} +6.91264i q^{37} +(3.14237 - 4.24051i) q^{38} +(-6.62828 + 5.63726i) q^{40} +(-3.28985 - 1.89939i) q^{41} +(-1.00000 - 1.73205i) q^{43} +(2.77466 + 2.59462i) q^{44} +(0.464102 + 1.06939i) q^{46} +(-3.48853 - 6.04232i) q^{47} +(4.46410 - 7.73205i) q^{49} +(-6.27211 - 0.719026i) q^{50} +(-0.484012 + 2.08329i) q^{52} -10.6569 q^{53} +5.84325i q^{55} +(-11.1035 + 2.03402i) q^{56} +(-6.32835 - 0.725474i) q^{58} +(1.64492 + 0.949697i) q^{59} +(-0.926118 + 0.534695i) q^{61} +(7.58051 - 3.28985i) q^{62} +(6.19615 + 5.06040i) q^{64} +(-2.84909 + 1.64492i) q^{65} +(4.59808 - 7.96410i) q^{67} +(13.5635 - 4.12621i) q^{68} +(-13.9506 - 10.3379i) q^{70} +10.6569 q^{71} +5.92820 q^{73} +(7.85443 + 5.82041i) q^{74} +(-2.17238 - 7.14098i) q^{76} +(-3.79025 + 6.56491i) q^{77} +(-5.30856 + 3.06490i) q^{79} +(0.824313 + 12.2779i) q^{80} +(-4.92820 + 2.13878i) q^{82} +(8.98803 - 5.18924i) q^{83} +(18.8857 + 10.9037i) q^{85} +(-2.81002 - 0.322137i) q^{86} +(5.28436 - 0.968024i) q^{88} +13.6683i q^{89} -4.26795 q^{91} +(1.60586 + 0.373089i) q^{92} +(-9.80286 - 1.12379i) q^{94} +(5.74060 - 9.94301i) q^{95} +(5.69615 + 9.86603i) q^{97} +(-5.02672 - 11.5826i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 4 q^{4}+O(q^{10}) \) 16 * q + 4 * q^4	\( 16 q + 4 q^{4} + 16 q^{16} + 32 q^{19} + 8 q^{22} - 8 q^{25} - 24 q^{28} + 32 q^{34} - 24 q^{40} - 16 q^{43} - 48 q^{46} + 16 q^{49} - 36 q^{52} - 48 q^{58} + 16 q^{64} + 32 q^{67} - 72 q^{70} - 16 q^{73} + 20 q^{76} + 32 q^{82} + 56 q^{88} - 96 q^{91} + 24 q^{94} + 8 q^{97}+O(q^{100}) \) 16 * q + 4 * q^4 + 16 * q^16 + 32 * q^19 + 8 * q^22 - 8 * q^25 - 24 * q^28 + 32 * q^34 - 24 * q^40 - 16 * q^43 - 48 * q^46 + 16 * q^49 - 36 * q^52 - 48 * q^58 + 16 * q^64 + 32 * q^67 - 72 * q^70 - 16 * q^73 + 20 * q^76 + 32 * q^82 + 56 * q^88 - 96 * q^91 + 24 * q^94 + 8 * q^97

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