LMFDB - Embedded newform 648.2.l.g.107.3

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:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			107.3
Character	$\chi$	$=$	648.107
Dual form			648.2.l.g.539.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.31951 - 0.508820i) q^{2} +(1.48220 + 1.34278i) q^{4} +(-1.95986 - 3.39458i) q^{5} +(-3.00711 - 1.73615i) q^{7} +(-1.27255 - 2.52599i) q^{8} +O(q^{10})$	\(q+(-1.31951 - 0.508820i) q^{2} +(1.48220 + 1.34278i) q^{4} +(-1.95986 - 3.39458i) q^{5} +(-3.00711 - 1.73615i) q^{7} +(-1.27255 - 2.52599i) q^{8} +(0.858824 + 5.47639i) q^{10} +(-1.93759 - 1.11867i) q^{11} +(-3.12401 + 1.80365i) q^{13} +(3.08451 + 3.82094i) q^{14} +(0.393860 + 3.98056i) q^{16} +2.82210i q^{17} +5.58120 q^{19} +(1.65327 - 7.66313i) q^{20} +(1.98747 + 2.46198i) q^{22} +(3.08676 + 5.34643i) q^{23} +(-5.18212 + 8.97569i) q^{25} +(5.03989 - 0.790370i) q^{26} +(-2.12587 - 6.61123i) q^{28} +(1.29632 - 2.24529i) q^{29} +(3.82670 - 2.20935i) q^{31} +(1.50569 - 5.45279i) q^{32} +(1.43594 - 3.72379i) q^{34} +13.6105i q^{35} +0.789564i q^{37} +(-7.36444 - 2.83983i) q^{38} +(-6.08066 + 9.27035i) q^{40} +(-5.21055 + 3.00831i) q^{41} +(1.01109 - 1.75125i) q^{43} +(-1.36977 - 4.25986i) q^{44} +(-1.35264 - 8.62526i) q^{46} +(-1.33927 + 2.31968i) q^{47} +(2.52846 + 4.37942i) q^{49} +(11.4049 - 9.20673i) q^{50} +(-7.05233 - 1.52150i) q^{52} -8.31448 q^{53} +8.76974i q^{55} +(-0.558827 + 9.80526i) q^{56} +(-2.85295 + 2.30308i) q^{58} +(1.05095 - 0.606768i) q^{59} +(-1.02208 - 0.590096i) q^{61} +(-6.17352 + 0.968150i) q^{62} +(-4.76126 + 6.42888i) q^{64} +(12.2453 + 7.06980i) q^{65} +(-4.10141 - 7.10386i) q^{67} +(-3.78947 + 4.18293i) q^{68} +(6.92529 - 17.9591i) q^{70} -8.04637 q^{71} -5.18358 q^{73} +(0.401746 - 1.04184i) q^{74} +(8.27248 + 7.49435i) q^{76} +(3.88436 + 6.72791i) q^{77} +(11.7143 + 6.76323i) q^{79} +(12.7404 - 9.13834i) q^{80} +(8.40606 - 1.31826i) q^{82} +(2.25256 + 1.30051i) q^{83} +(9.57985 - 5.53093i) q^{85} +(-2.22521 + 1.79633i) q^{86} +(-0.360073 + 6.31789i) q^{88} +1.32088i q^{89} +12.5256 q^{91} +(-2.60389 + 12.0694i) q^{92} +(2.94747 - 2.37939i) q^{94} +(-10.9384 - 18.9458i) q^{95} +(-7.60966 + 13.1803i) q^{97} +(-1.10799 - 7.06521i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q+O(q^{10}) $ 48 * q	$ 48 q - 12 q^{16} + 12 q^{22} - 24 q^{25} + 24 q^{28} + 24 q^{34} + 24 q^{40} - 24 q^{46} + 24 q^{49} + 12 q^{58} + 48 q^{64} - 48 q^{67} + 36 q^{70} + 60 q^{76} - 72 q^{82} + 60 q^{88} - 48 q^{94}+O(q^{100}) $ 48 * q - 12 * q^16 + 12 * q^22 - 24 * q^25 + 24 * q^28 + 24 * q^34 + 24 * q^40 - 24 * q^46 + 24 * q^49 + 12 * q^58 + 48 * q^64 - 48 * q^67 + 36 * q^70 + 60 * q^76 - 72 * q^82 + 60 * q^88 - 48 * q^94

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	−1.31951	−	0.508820i	−0.933033	−	0.359790i
$2$	−1.31951	−	0.508820i	−0.933033	−	0.359790i
$3$		0			0
$3$		0			0
$4$	1.48220	+	1.34278i	0.741102	+	0.671392i
$5$	−1.95986	−	3.39458i	−0.876477	−	1.51810i	−0.855181	−	0.518329i	$-0.826554\pi$
$5$	−1.95986	−	3.39458i	−0.876477	−	1.51810i	−0.0212956	−	0.999773i	$-0.506779\pi$
$6$		0			0
$7$	−3.00711	−	1.73615i	−1.13658	−	0.656204i	−0.190998	−	0.981590i	$-0.561172\pi$
$7$	−3.00711	−	1.73615i	−1.13658	−	0.656204i	−0.945581	+	0.325386i	$0.894506\pi$
$8$	−1.27255	−	2.52599i	−0.449913	−	0.893072i
$9$		0			0
$10$	0.858824	+	5.47639i	0.271584	+	1.73179i
$11$	−1.93759	−	1.11867i	−0.584205	−	0.337291i	0.178598	−	0.983922i	$-0.442844\pi$
$11$	−1.93759	−	1.11867i	−0.584205	−	0.337291i	−0.762803	+	0.646631i	$0.776177\pi$
$12$		0			0
$13$	−3.12401	+	1.80365i	−0.866444	+	0.500242i	−0.866165	−	0.499758i	$-0.833422\pi$
$13$	−3.12401	+	1.80365i	−0.866444	+	0.500242i	−0.000279232		1.00000i	$0.500089\pi$
$14$	3.08451	+	3.82094i	0.824371	+	1.02119i
$15$		0			0
$16$	0.393860	+	3.98056i	0.0984651	+	0.995141i
$17$			2.82210i			0.684460i	0.939616	+	0.342230i	$0.111182\pi$
$17$			2.82210i			0.684460i	−0.939616	+	0.342230i	$0.888818\pi$
$18$		0			0
$19$	5.58120			1.28042			0.640208	−	0.768202i	$-0.278848\pi$
$19$	5.58120			1.28042			0.640208	+	0.768202i	$0.278848\pi$
$20$	1.65327	−	7.66313i	0.369683	−	1.71353i
$21$		0			0
$22$	1.98747	+	2.46198i	0.423729	+	0.524895i
$23$	3.08676	+	5.34643i	0.643634	+	1.11481i	0.984615	+	0.174737i	$0.0559075\pi$
$23$	3.08676	+	5.34643i	0.643634	+	1.11481i	−0.340981	+	0.940070i	$0.610759\pi$
$24$		0			0
$25$	−5.18212	+	8.97569i	−1.03642	+	1.79514i
$26$	5.03989	−	0.790370i	0.988403	−	0.155004i
$27$		0			0
$28$	−2.12587	−	6.61123i	−0.401751	−	1.24941i
$29$	1.29632	−	2.24529i	0.240720	−	0.416939i	−0.720200	−	0.693767i	$-0.755950\pi$
$29$	1.29632	−	2.24529i	0.240720	−	0.416939i	0.960920	+	0.276828i	$0.0892831\pi$
$30$		0			0
$31$	3.82670	−	2.20935i	0.687296	−	0.396810i	−0.115302	−	0.993330i	$-0.536784\pi$
$31$	3.82670	−	2.20935i	0.687296	−	0.396810i	0.802598	+	0.596520i	$0.203450\pi$
$32$	1.50569	−	5.45279i	0.266170	−	0.963926i
$33$		0			0
$34$	1.43594	−	3.72379i	0.246262	−	0.638624i
$35$			13.6105i			2.30059i
$36$		0			0
$37$			0.789564i			0.129803i	0.997892	+	0.0649017i	$0.0206734\pi$
$37$			0.789564i			0.129803i	−0.997892	+	0.0649017i	$0.979327\pi$
$38$	−7.36444	−	2.83983i	−1.19467	−	0.460681i
$39$		0			0
$40$	−6.08066	+	9.27035i	−0.961437	+	1.46577i
$41$	−5.21055	+	3.00831i	−0.813752	+	0.469820i	−0.848257	−	0.529585i	$-0.822348\pi$
$41$	−5.21055	+	3.00831i	−0.813752	+	0.469820i	0.0345054	+	0.999405i	$0.489014\pi$
$42$		0			0
$43$	1.01109	−	1.75125i	0.154189	−	0.267063i	−0.778574	−	0.627552i	$-0.784057\pi$
$43$	1.01109	−	1.75125i	0.154189	−	0.267063i	0.932763	+	0.360489i	$0.117390\pi$
$44$	−1.36977	−	4.25986i	−0.206501	−	0.642198i
$45$		0			0
$46$	−1.35264	−	8.62526i	−0.199436	−	1.27173i
$47$	−1.33927	+	2.31968i	−0.195352	+	0.338360i	−0.947016	−	0.321187i	$-0.895918\pi$
$47$	−1.33927	+	2.31968i	−0.195352	+	0.338360i	0.751664	+	0.659547i	$0.229252\pi$
$48$		0			0
$49$	2.52846	+	4.37942i	0.361208	+	0.625631i
$50$	11.4049	−	9.20673i	1.61289	−	1.30203i
$51$		0			0
$52$	−7.05233	−	1.52150i	−0.977982	−	0.210994i
$53$	−8.31448			−1.14208			−0.571041	−	0.820922i	$-0.693460\pi$
$53$	−8.31448			−1.14208			−0.571041	+	0.820922i	$0.693460\pi$
$54$		0			0
$55$			8.76974i			1.18251i
$56$	−0.558827	+	9.80526i	−0.0746764	+	1.31028i
$57$		0			0
$58$	−2.85295	+	2.30308i	−0.374610	+	0.302410i
$59$	1.05095	−	0.606768i	0.136822	−	0.0789945i	−0.430026	−	0.902816i	$-0.641496\pi$
$59$	1.05095	−	0.606768i	0.136822	−	0.0789945i	0.566849	+	0.823822i	$0.308162\pi$
$60$		0			0
$61$	−1.02208	−	0.590096i	−0.130863	−	0.0755540i	0.433139	−	0.901327i	$-0.357406\pi$
$61$	−1.02208	−	0.590096i	−0.130863	−	0.0755540i	−0.564003	+	0.825773i	$0.690739\pi$
$62$	−6.17352	+	0.968150i	−0.784038	+	0.122955i
$63$		0			0
$64$	−4.76126	+	6.42888i	−0.595157	+	0.803610i
$65$	12.2453	+	7.06980i	1.51884	+	0.876901i
$66$		0			0
$67$	−4.10141	−	7.10386i	−0.501067	−	0.867874i	−0.999999	−	0.00123290i	$-0.999608\pi$
$67$	−4.10141	−	7.10386i	−0.501067	−	0.867874i	0.498932	−	0.866641i	$-0.333726\pi$
$68$	−3.78947	+	4.18293i	−0.459541	+	0.507255i
$69$		0			0
$70$	6.92529	−	17.9591i	0.827730	−	2.14653i
$71$	−8.04637			−0.954929			−0.477465	−	0.878651i	$-0.658444\pi$
$71$	−8.04637			−0.954929			−0.477465	+	0.878651i	$0.658444\pi$
$72$		0			0
$73$	−5.18358			−0.606692			−0.303346	−	0.952881i	$-0.598104\pi$
$73$	−5.18358			−0.606692			−0.303346	+	0.952881i	$0.598104\pi$
$74$	0.401746	−	1.04184i	0.0467020	−	0.121111i
$75$		0			0
$76$	8.27248	+	7.49435i	0.948919	+	0.859661i
$77$	3.88436	+	6.72791i	0.442664	+	0.766716i
$78$		0			0
$79$	11.7143	+	6.76323i	1.31796	+	0.760923i	0.983400	−	0.181452i	$-0.0580798\pi$
$79$	11.7143	+	6.76323i	1.31796	+	0.760923i	0.334558	+	0.942375i	$0.391413\pi$
$80$	12.7404	−	9.13834i	1.42442	−	1.02170i
$81$		0			0
$82$	8.40606	−	1.31826i	0.928294	−	0.145578i
$83$	2.25256	+	1.30051i	0.247250	+	0.142750i	0.618504	−	0.785781i	$-0.287739\pi$
$83$	2.25256	+	1.30051i	0.247250	+	0.142750i	−0.371254	+	0.928531i	$0.621072\pi$
$84$		0			0
$85$	9.57985	−	5.53093i	1.03908	−	0.599913i
$86$	−2.22521	+	1.79633i	−0.239950	+	0.193703i
$87$		0			0
$88$	−0.360073	+	6.31789i	−0.0383839	+	0.673489i
$89$			1.32088i			0.140013i	0.997547	+	0.0700067i	$0.0223021\pi$
$89$			1.32088i			0.140013i	−0.997547	+	0.0700067i	$0.977698\pi$
$90$		0			0
$91$	12.5256			1.31304
$92$	−2.60389	+	12.0694i	−0.271474	+	1.25832i
$93$		0			0
$94$	2.94747	−	2.37939i	0.304009	−	0.245415i
$95$	−10.9384	−	18.9458i	−1.12225	−	1.94380i
$96$		0			0
$97$	−7.60966	+	13.1803i	−0.772644	+	1.33826i	0.163465	+	0.986549i	$0.447733\pi$
$97$	−7.60966	+	13.1803i	−0.772644	+	1.33826i	−0.936109	+	0.351710i	$0.885600\pi$
$98$	−1.10799	−	7.06521i	−0.111924	−	0.713694i
$99$		0			0
$100$	−19.7334	+	6.34534i	−1.97334	+	0.634534i
$101$	−6.44640	+	11.1655i	−0.641441	+	1.11101i	0.343670	+	0.939090i	$0.388330\pi$
$101$	−6.44640	+	11.1655i	−0.641441	+	1.11101i	−0.985111	+	0.171918i	$0.945003\pi$
$102$		0			0
$103$	−14.8436	+	8.56996i	−1.46258	+	0.844423i	−0.999130	−	0.0416977i	$-0.986723\pi$
$103$	−14.8436	+	8.56996i	−1.46258	+	0.844423i	−0.463454	+	0.886121i	$0.653390\pi$
$104$	8.53144	+	5.59599i	0.836577	+	0.548732i
$105$		0			0
$106$	10.9710	+	4.23057i	1.06560	+	0.410910i
$107$			7.36254i			0.711763i	0.934531	+	0.355882i	$0.115819\pi$
$107$			7.36254i			0.711763i	−0.934531	+	0.355882i	$0.884181\pi$
$108$		0			0
$109$		−	6.93497i		−	0.664250i	−0.943235	−	0.332125i	$-0.892234\pi$
$109$		−	6.93497i		−	0.664250i	0.943235	−	0.332125i	$-0.107766\pi$
$110$	4.46222	−	11.5717i	0.425456	−	1.10332i
$111$		0			0
$112$	5.72649	−	12.6538i	0.541102	−	1.19567i
$113$	−16.1204	+	9.30714i	−1.51648	+	0.875542i	−0.516670	+	0.856185i	$0.672829\pi$
$113$	−16.1204	+	9.30714i	−1.51648	+	0.875542i	−0.999813	+	0.0193570i	$0.993838\pi$
$114$		0			0
$115$	12.0993	−	20.9565i	1.12826	−	1.95421i
$116$	4.93634	−	1.58730i	0.458328	−	0.147377i
$117$		0			0
$118$	−1.69548	+	0.265890i	−0.156081	+	0.0244771i
$119$	4.89960	−	8.48636i	0.449146	−	0.777943i
$120$		0			0
$121$	−2.99716	−	5.19124i	−0.272469	−	0.471931i
$122$	1.04839	+	1.29869i	0.0949164	+	0.117578i
$123$		0			0
$124$	8.63863	+	1.86373i	0.775772	+	0.167368i
$125$	21.0263			1.88065
$126$		0			0
$127$		−	17.5635i		−	1.55850i	−0.626710	−	0.779252i	$-0.715599\pi$
$127$		−	17.5635i		−	1.55850i	0.626710	−	0.779252i	$-0.284401\pi$
$128$	9.55366	−	6.06033i	0.844432	−	0.535663i
$129$		0			0
$130$	−12.5605	−	15.5593i	−1.10162	−	1.36464i
$131$	9.58873	−	5.53606i	0.837771	−	0.483687i	−0.0187348	−	0.999824i	$-0.505964\pi$
$131$	9.58873	−	5.53606i	0.837771	−	0.483687i	0.856506	+	0.516137i	$0.172630\pi$
$132$		0			0
$133$	−16.7833	−	9.68983i	−1.45529	−	0.840214i
$134$	1.79727	+	11.4605i	0.155260	+	0.990034i
$135$		0			0
$136$	7.12860	−	3.59125i	0.611272	−	0.307947i
$137$	3.86569	+	2.23186i	0.330268	+	0.190680i	0.655960	−	0.754796i	$-0.272264\pi$
$137$	3.86569	+	2.23186i	0.330268	+	0.190680i	−0.325692	+	0.945476i	$0.605597\pi$
$138$		0			0
$139$	−11.3087	−	19.5872i	−0.959187	−	1.66136i	−0.724481	−	0.689295i	$-0.757921\pi$
$139$	−11.3087	−	19.5872i	−0.959187	−	1.66136i	−0.234706	−	0.972066i	$-0.575413\pi$
$140$	−18.2759	+	20.1735i	−1.54460	+	1.70497i
$141$		0			0
$142$	10.6173	+	4.09416i	0.890981	+	0.343574i
$143$	8.07073			0.674908
$144$		0			0
$145$	−10.1624			−0.843942
$146$	6.83977	+	2.63751i	0.566063	+	0.218282i
$147$		0			0
$148$	−1.06021	+	1.17029i	−0.0871490	+	0.0961976i
$149$	−0.810568	−	1.40395i	−0.0664043	−	0.115016i	0.830912	−	0.556404i	$-0.187819\pi$
$149$	−0.810568	−	1.40395i	−0.0664043	−	0.115016i	−0.897316	+	0.441389i	$0.854486\pi$
$150$		0			0
$151$	−10.2559	−	5.92125i	−0.834613	−	0.481864i	0.0208164	−	0.999783i	$-0.493373\pi$
$151$	−10.2559	−	5.92125i	−0.834613	−	0.481864i	−0.855430	+	0.517919i	$0.826707\pi$
$152$	−7.10234	−	14.0981i	−0.576076	−	1.14350i
$153$		0			0
$154$	−1.70215	−	10.8540i	−0.137163	−	0.874638i
$155$	−14.9996	−	8.66003i	−1.20480	−	0.695590i
$156$		0			0
$157$	−0.617113	+	0.356290i	−0.0492510	+	0.0284351i	−0.524423	−	0.851458i	$-0.675719\pi$
$157$	−0.617113	+	0.356290i	−0.0492510	+	0.0284351i	0.475172	+	0.879893i	$0.342386\pi$
$158$	−12.0158	−	14.8846i	−0.955926	−	1.18415i
$159$		0			0
$160$	−21.4609	+	5.57553i	−1.69663	+	0.440785i
$161$		−	21.4364i		−	1.68942i
$162$		0			0
$163$	−5.44787			−0.426710			−0.213355	−	0.976975i	$-0.568439\pi$
$163$	−5.44787			−0.426710			−0.213355	+	0.976975i	$0.568439\pi$
$164$	−11.7626	−	2.53771i	−0.918506	−	0.198162i
$165$		0			0
$166$	−2.31054	−	2.86218i	−0.179333	−	0.222149i
$167$	4.89960	+	8.48636i	0.379142	+	0.656694i	0.990938	−	0.134322i	$-0.0428857\pi$
$167$	4.89960	+	8.48636i	0.379142	+	0.656694i	−0.611795	+	0.791016i	$0.709552\pi$
$168$		0			0
$169$	0.00628838	−	0.0108918i	0.000483722	−	0.000837830i
$170$	−15.4549	+	2.42369i	−1.18534	+	0.185888i
$171$		0			0
$172$	3.85019	−	1.23804i	0.293574	−	0.0943999i
$173$	−0.785920	+	1.36125i	−0.0597524	+	0.103494i	−0.894354	−	0.447360i	$-0.852364\pi$
$173$	−0.785920	+	1.36125i	−0.0597524	+	0.103494i	0.834602	+	0.550854i	$0.185698\pi$
$174$		0			0
$175$	31.1663	−	17.9939i	2.35595	−	1.36021i
$176$	3.68979	−	8.15330i	0.278128	−	0.614578i
$177$		0			0
$178$	0.672092	−	1.74292i	0.0503754	−	0.130637i
$179$		−	12.8514i		−	0.960561i	−0.877115	−	0.480281i	$-0.840535\pi$
$179$		−	12.8514i		−	0.960561i	0.877115	−	0.480281i	$-0.159465\pi$
$180$		0			0
$181$			19.0571i			1.41650i	0.705961	+	0.708251i	$0.250515\pi$
$181$			19.0571i			1.41650i	−0.705961	+	0.708251i	$0.749485\pi$
$182$	−16.5277	−	6.37329i	−1.22511	−	0.472420i
$183$		0			0
$184$	9.57698	−	14.6007i	0.706024	−	1.07638i
$185$	2.68024	−	1.54744i	0.197055	−	0.113770i
$186$		0			0
$187$	3.15699	−	5.46807i	0.230862	−	0.399865i
$188$	−5.09990	+	1.63989i	−0.371948	+	0.119601i
$189$		0			0
$190$	4.79327	+	30.5649i	0.347740	+	2.21741i
$191$	−3.57251	+	6.18777i	−0.258498	+	0.447731i	−0.965840	−	0.259140i	$-0.916561\pi$
$191$	−3.57251	+	6.18777i	−0.258498	+	0.447731i	0.707342	+	0.706872i	$0.249894\pi$
$192$		0			0
$193$	0.500000	+	0.866025i	0.0359908	+	0.0623379i	0.883460	−	0.468507i	$-0.155208\pi$
$193$	0.500000	+	0.866025i	0.0359908	+	0.0623379i	−0.847469	+	0.530845i	$0.821875\pi$
$194$	16.7474	−	13.5196i	1.20239	−	0.970650i
$195$		0			0
$196$	−2.13292	+	9.88637i	−0.152352	+	0.706169i
$197$	−6.80640			−0.484936			−0.242468	−	0.970159i	$-0.577957\pi$
$197$	−6.80640			−0.484936			−0.242468	+	0.970159i	$0.577957\pi$
$198$		0			0
$199$			5.29743i			0.375525i	0.982214	+	0.187762i	$0.0601235\pi$
$199$			5.29743i			0.375525i	−0.982214	+	0.187762i	$0.939876\pi$
$200$	29.2670	+	1.66800i	2.06949	+	0.117946i
$201$		0			0
$202$	14.1873	−	11.4529i	0.998216	−	0.805824i
$203$	−7.79632	+	4.50121i	−0.547195	+	0.315923i
$204$		0			0
$205$	20.4239	+	11.7918i	1.42647	+	0.823572i
$206$	23.9468	−	3.75541i	1.66845	−	0.261652i
$207$		0			0
$208$	−8.40995	−	11.7249i	−0.583125	−	0.812977i
$209$	−10.8141	−	6.24351i	−0.748026	−	0.431873i
$210$		0			0
$211$	10.0771	+	17.4540i	0.693735	+	1.20158i	0.970605	+	0.240677i	$0.0773694\pi$
$211$	10.0771	+	17.4540i	0.693735	+	1.20158i	−0.276870	+	0.960907i	$0.589297\pi$
$212$	−12.3238	−	11.1646i	−0.846399	−	0.766785i
$213$		0			0
$214$	3.74621	−	9.71493i	0.256085	−	0.664099i
$215$	−7.92635			−0.540573
$216$		0			0
$217$	−15.3431			−1.04155
$218$	−3.52865	+	9.15075i	−0.238990	+	0.619767i
$219$		0			0
$220$	−11.7759	+	12.9985i	−0.793929	+	0.876362i
$221$	−5.09007	−	8.81627i	−0.342395	−	0.593046i
$222$		0			0
$223$	11.0755	+	6.39444i	0.741670	+	0.428203i	0.822676	−	0.568510i	$-0.192480\pi$
$223$	11.0755	+	6.39444i	0.741670	+	0.428203i	−0.0810063	+	0.996714i	$0.525813\pi$
$224$	−13.9946	+	13.7830i	−0.935056	+	0.920916i
$225$		0			0
$226$	26.0067	−	4.07845i	1.72994	−	0.271294i
$227$	6.20659	+	3.58338i	0.411946	+	0.237837i	0.691626	−	0.722256i	$-0.256895\pi$
$227$	6.20659	+	3.58338i	0.411946	+	0.237837i	−0.279680	+	0.960093i	$0.590228\pi$
$228$		0			0
$229$	−15.4318	+	8.90955i	−1.01976	+	0.588759i	−0.914035	−	0.405636i	$-0.867050\pi$
$229$	−15.4318	+	8.90955i	−1.01976	+	0.588759i	−0.105727	+	0.994395i	$0.533717\pi$
$230$	−26.6282	+	21.4960i	−1.75581	+	1.41740i
$231$		0			0
$232$	−7.32119	−	0.417254i	−0.480660	−	0.0273941i
$233$		−	16.0956i		−	1.05446i	−0.849724	−	0.527228i	$-0.823231\pi$
$233$		−	16.0956i		−	1.05446i	0.849724	−	0.527228i	$-0.176769\pi$
$234$		0			0
$235$	10.4991			0.684887
$236$	2.37249	+	0.511849i	0.154436	+	0.0333185i
$237$		0			0
$238$	−10.7831	+	8.70480i	−0.698964	+	0.564249i
$239$	12.5390	+	21.7181i	0.811078	+	1.40483i	0.912110	+	0.409946i	$0.134452\pi$
$239$	12.5390	+	21.7181i	0.811078	+	1.40483i	−0.101032	+	0.994883i	$0.532214\pi$
$240$		0			0
$241$	0.899088	−	1.55727i	0.0579153	−	0.100312i	−0.835614	−	0.549317i	$-0.814888\pi$
$241$	0.899088	−	1.55727i	0.0579153	−	0.100312i	0.893529	+	0.449005i	$0.148221\pi$
$242$	1.31338	+	8.37490i	0.0844270	+	0.538359i
$243$		0			0
$244$	−0.722554	−	2.24707i	−0.0462568	−	0.143854i
$245$	9.91086	−	17.1661i	0.633182	−	1.09670i
$246$		0			0
$247$	−17.4357	+	10.0665i	−1.10941	+	0.640518i
$248$	−10.4504	−	6.85472i	−0.663604	−	0.435275i
$249$		0			0
$250$	−27.7444	−	10.6986i	−1.75471	−	0.676639i
$251$		−	12.0475i		−	0.760429i	−0.924898	−	0.380214i	$-0.875850\pi$
$251$		−	12.0475i		−	0.760429i	0.924898	−	0.380214i	$-0.124150\pi$
$252$		0			0
$253$		−	13.8122i		−	0.868368i
$254$	−8.93664	+	23.1751i	−0.560734	+	1.45414i
$255$		0			0
$256$	−15.6897	+	3.13557i	−0.980609	+	0.195973i
$257$	19.6731	−	11.3583i	1.22717	−	0.708509i	0.260735	−	0.965410i	$-0.416035\pi$
$257$	19.6731	−	11.3583i	1.22717	−	0.708509i	0.966438	+	0.256902i	$0.0827017\pi$
$258$		0			0
$259$	1.37080	−	2.37430i	0.0851776	−	0.147532i
$260$	8.65675	+	26.9216i	0.536869	+	1.66961i
$261$		0			0
$262$	−15.4693	+	2.42593i	−0.955694	+	0.149875i
$263$	6.63638	−	11.4945i	0.409217	−	0.708784i	−0.585586	−	0.810611i	$-0.699135\pi$
$263$	6.63638	−	11.4945i	0.409217	−	0.708784i	0.994802	+	0.101827i	$0.0324687\pi$
$264$		0			0
$265$	16.2952	+	28.2242i	1.00101	+	1.73380i
$266$	17.2153	+	21.3255i	1.05554	+	1.30755i
$267$		0			0
$268$	3.45981	−	16.0367i	0.211342	−	0.979596i
$269$	−4.87238			−0.297074			−0.148537	−	0.988907i	$-0.547456\pi$
$269$	−4.87238			−0.297074			−0.148537	+	0.988907i	$0.547456\pi$
$270$		0			0
$271$			13.4828i			0.819021i	0.912305	+	0.409511i	$0.134301\pi$
$271$			13.4828i			0.819021i	−0.912305	+	0.409511i	$0.865699\pi$
$272$	−11.2335	+	1.11151i	−0.681134	+	0.0673954i
$273$		0			0
$274$	−3.96520	−	4.91189i	−0.239546	−	0.296738i
$275$	20.0816	−	11.5941i	1.21097	−	0.699153i
$276$		0			0
$277$	22.4970	+	12.9887i	1.35171	+	0.780413i	0.988490	−	0.151289i	$-0.0483424\pi$
$277$	22.4970	+	12.9887i	1.35171	+	0.780413i	0.363225	+	0.931702i	$0.381676\pi$
$278$	4.95552	+	31.5995i	0.297212	+	1.89521i
$279$		0			0
$280$	34.3800	−	17.3200i	2.05460	−	1.03507i
$281$	13.8005	+	7.96775i	0.823272	+	0.475316i	0.851543	−	0.524284i	$-0.175667\pi$
$281$	13.8005	+	7.96775i	0.823272	+	0.475316i	−0.0282717	+	0.999600i	$0.509000\pi$
$282$		0			0
$283$	5.07775	+	8.79492i	0.301841	+	0.522804i	0.976553	−	0.215277i	$-0.0690655\pi$
$283$	5.07775	+	8.79492i	0.301841	+	0.522804i	−0.674712	+	0.738081i	$0.735732\pi$
$284$	−11.9264	−	10.8045i	−0.707700	−	0.641132i
$285$		0			0
$286$	−10.6494	−	4.10655i	−0.629712	−	0.242825i
$287$	20.8916			1.23319
$288$		0			0
$289$	9.03575			0.531515
$290$	13.4094	+	5.17084i	0.787426	+	0.303642i
$291$		0			0
$292$	−7.68312	−	6.96042i	−0.449621	−	0.407328i
$293$	−6.92756	−	11.9989i	−0.404712	−	0.700983i	0.589575	−	0.807713i	$-0.299295\pi$
$293$	−6.92756	−	11.9989i	−0.404712	−	0.700983i	−0.994288	+	0.106731i	$0.965962\pi$
$294$		0			0
$295$	−4.11945	−	2.37836i	−0.239843	−	0.138474i
$296$	1.99443	−	1.00476i	0.115924	−	0.0584002i
$297$		0			0
$298$	0.355196	+	2.26495i	0.0205760	+	0.131205i
$299$	−19.2861	−	11.1349i	−1.11535	−	0.643946i
$300$		0			0
$301$	−6.08088	+	3.51080i	−0.350496	+	0.202359i
$302$	10.5199	+	13.0315i	0.605352	+	0.749881i
$303$		0			0
$304$	2.19821	+	22.2163i	0.126076	+	1.27419i
$305$			4.62603i			0.264885i
$306$		0			0
$307$	−32.6798			−1.86513			−0.932567	−	0.360996i	$-0.882437\pi$
$307$	−32.6798			−1.86513			−0.932567	+	0.360996i	$0.882437\pi$
$308$	−3.27671	+	15.1880i	−0.186708	+	0.865416i
$309$		0			0
$310$	15.3857	+	19.0591i	0.873850	+	1.08248i
$311$	7.91164	+	13.7034i	0.448628	+	0.777046i	0.998297	−	0.0583363i	$-0.0185796\pi$
$311$	7.91164	+	13.7034i	0.448628	+	0.777046i	−0.549669	+	0.835382i	$0.685246\pi$
$312$		0			0
$313$	0.549292	−	0.951402i	0.0310478	−	0.0537764i	−0.850084	−	0.526647i	$-0.823449\pi$
$313$	0.549292	−	0.951402i	0.0310478	−	0.0537764i	0.881132	+	0.472871i	$0.156782\pi$
$314$	0.995574	−	0.156129i	0.0561835	−	0.00881085i
$315$		0			0
$316$	8.28137	+	25.7542i	0.465863	+	1.44879i
$317$	7.19696	−	12.4655i	0.404222	−	0.700132i	−0.590009	−	0.807397i	$-0.700876\pi$
$317$	7.19696	−	12.4655i	0.404222	−	0.700132i	0.994231	+	0.107264i	$0.0342092\pi$
$318$		0			0
$319$	−5.02346	+	2.90030i	−0.281260	+	0.162385i
$320$	31.1547	+	3.56275i	1.74160	+	0.199164i
$321$		0			0
$322$	−10.9073	+	28.2855i	−0.607837	+	1.57629i
$323$			15.7507i			0.876393i
$324$		0			0
$325$		−	37.3868i		−	2.07385i
$326$	7.18851	+	2.77199i	0.398135	+	0.153526i
$327$		0			0
$328$	14.2296	+	9.33359i	0.785700	+	0.515361i
$329$	8.05464	−	4.65035i	0.444067	−	0.256382i
$330$		0			0
$331$	−2.15383	+	3.73055i	−0.118385	+	0.205049i	−0.919128	−	0.393959i	$-0.871105\pi$
$331$	−2.15383	+	3.73055i	−0.118385	+	0.205049i	0.800743	+	0.599009i	$0.204438\pi$
$332$	1.59244	+	4.95232i	0.0873964	+	0.271794i
$333$		0			0
$334$	−2.14704	−	13.6908i	−0.117481	−	0.749129i
$335$	−16.0764	+	27.8451i	−0.878348	+	1.52134i
$336$		0			0
$337$	−1.97288	−	3.41713i	−0.107470	−	0.186143i	0.807275	−	0.590176i	$-0.200941\pi$
$337$	−1.97288	−	3.41713i	−0.107470	−	0.186143i	−0.914744	+	0.404033i	$0.867608\pi$
$338$	−0.0138395	+	0.0111722i	−0.000752771	+	0.000607685i
$339$		0			0
$340$	21.6261	+	4.66570i	1.17284	+	0.253033i
$341$	−9.88610			−0.535362
$342$		0			0
$343$			6.74698i			0.364303i
$344$	−5.71030	−	0.325445i	−0.307878	−	0.0175468i
$345$		0			0
$346$	1.72966	−	1.39629i	0.0929871	−	0.0750652i
$347$	11.1611	−	6.44386i	0.599159	−	0.345925i	−0.169552	−	0.985521i	$-0.554232\pi$
$347$	11.1611	−	6.44386i	0.599159	−	0.345925i	0.768711	+	0.639597i	$0.220899\pi$
$348$		0			0
$349$	−27.1725	−	15.6881i	−1.45451	−	0.839762i	−0.455778	−	0.890093i	$-0.650639\pi$
$349$	−27.1725	−	15.6881i	−1.45451	−	0.839762i	−0.998733	+	0.0503310i	$0.983972\pi$
$350$	−50.2799	+	7.88504i	−2.68757	+	0.421473i
$351$		0			0
$352$	−9.01726	+	8.88090i	−0.480622	+	0.473354i
$353$	−26.9440	−	15.5561i	−1.43408	−	0.827969i	−0.436655	−	0.899629i	$-0.643837\pi$
$353$	−26.9440	−	15.5561i	−1.43408	−	0.827969i	−0.997429	+	0.0716597i	$0.977170\pi$
$354$		0			0
$355$	15.7698	+	27.3141i	0.836973	+	1.44968i
$356$	−1.77366	+	1.95782i	−0.0940038	+	0.103764i
$357$		0			0
$358$	−6.53907	+	16.9576i	−0.345600	+	0.896236i
$359$	−4.32503			−0.228266			−0.114133	−	0.993465i	$-0.536409\pi$
$359$	−4.32503			−0.228266			−0.114133	+	0.993465i	$0.536409\pi$
$360$		0			0
$361$	12.1498			0.639465
$362$	9.69662	−	25.1460i	0.509643	−	1.32164i
$363$		0			0
$364$	18.5656	+	16.8192i	0.973099	+	0.881567i
$365$	10.1591	+	17.5961i	0.531751	+	0.921020i
$366$		0			0
$367$	−17.4987	−	10.1029i	−0.913426	−	0.527367i	−0.0318943	−	0.999491i	$-0.510154\pi$
$367$	−17.4987	−	10.1029i	−0.913426	−	0.527367i	−0.881532	+	0.472124i	$0.843487\pi$
$368$	−20.0660	+	14.3928i	−1.04601	+	0.750276i
$369$		0			0
$370$	−4.32396	+	0.678096i	−0.224792	+	0.0352525i
$371$	25.0025	+	14.4352i	1.29807	+	0.749439i
$372$		0			0
$373$	8.23323	−	4.75346i	0.426301	−	0.246125i	−0.271469	−	0.962447i	$-0.587509\pi$
$373$	8.23323	−	4.75346i	0.426301	−	0.246125i	0.697769	+	0.716322i	$0.254176\pi$
$374$	−6.94794	+	5.60883i	−0.359270	+	0.290026i
$375$		0			0
$376$	7.56377	+	0.431079i	0.390072	+	0.0222312i
$377$			9.35239i			0.481673i
$378$		0			0
$379$	−6.44297			−0.330953			−0.165477	−	0.986214i	$-0.552916\pi$
$379$	−6.44297			−0.330953			−0.165477	+	0.986214i	$0.552916\pi$
$380$	9.22725	−	42.7695i	0.473348	−	2.19403i
$381$		0			0
$382$	7.86242	−	6.34705i	0.402276	−	0.324743i
$383$	−10.5127	−	18.2084i	−0.537171	−	0.930408i	−0.999055	−	0.0434675i	$-0.986160\pi$
$383$	−10.5127	−	18.2084i	−0.537171	−	0.930408i	0.461883	−	0.886941i	$-0.347174\pi$
$384$		0			0
$385$	15.2256	−	26.3715i	0.775969	−	1.34402i
$386$	−0.219103	−	1.39714i	−0.0111521	−	0.0711124i
$387$		0			0
$388$	−28.9774	+	9.31780i	−1.47110	+	0.473039i
$389$	−8.89336	+	15.4038i	−0.450911	+	0.781001i	−0.998443	−	0.0557836i	$-0.982234\pi$
$389$	−8.89336	+	15.4038i	−0.450911	+	0.781001i	0.547531	+	0.836785i	$0.315568\pi$
$390$		0			0
$391$	−15.0882	+	8.71115i	−0.763041	+	0.440542i
$392$	7.84479	−	11.9599i	0.396222	−	0.604065i
$393$		0			0
$394$	8.98111	+	3.46323i	0.452462	+	0.174475i
$395$		−	53.0200i		−	2.66773i
$396$		0			0
$397$			21.5182i			1.07997i	0.841675	+	0.539984i	$0.181570\pi$
$397$			21.5182i			1.07997i	−0.841675	+	0.539984i	$0.818430\pi$
$398$	2.69544	−	6.99000i	0.135110	−	0.350377i
$399$		0			0
$400$	−37.7693	−	17.0926i	−1.88847	−	0.854628i
$401$	16.3567	−	9.44352i	0.816812	−	0.471587i	−0.0325036	−	0.999472i	$-0.510348\pi$
$401$	16.3567	−	9.44352i	0.816812	−	0.471587i	0.849316	+	0.527885i	$0.177015\pi$
$402$		0			0
$403$	−7.96977	+	13.8040i	−0.397002	+	0.687628i
$404$	−24.5477	+	7.89342i	−1.22130	+	0.392712i
$405$		0			0
$406$	12.5776	−	1.97246i	0.624217	−	0.0978915i
$407$	0.883259	−	1.52985i	0.0437815	−	0.0758319i
$408$		0			0
$409$	−4.68840	−	8.12055i	−0.231827	−	0.401536i	0.726519	−	0.687146i	$-0.241137\pi$
$409$	−4.68840	−	8.12055i	−0.231827	−	0.401536i	−0.958346	+	0.285611i	$0.907804\pi$
$410$	−20.9497	−	25.9514i	−1.03463	−	1.28165i
$411$		0			0
$412$	−33.5089	−	7.22933i	−1.65086	−	0.356164i
$413$	−4.21377			−0.207346
$414$		0			0
$415$		−	10.1953i		−	0.500468i
$416$	5.13113	+	19.7503i	0.251574	+	0.968338i
$417$		0			0
$418$	11.0924	+	13.7408i	0.542549	+	0.672084i
$419$	−21.5767	+	12.4573i	−1.05409	+	0.608581i	−0.923792	−	0.382894i	$-0.874927\pi$
$419$	−21.5767	+	12.4573i	−1.05409	+	0.608581i	−0.130300	+	0.991475i	$0.541594\pi$
$420$		0			0
$421$	−25.1079	−	14.4960i	−1.22368	−	0.706493i	−0.257981	−	0.966150i	$-0.583057\pi$
$421$	−25.1079	−	14.4960i	−1.22368	−	0.706493i	−0.965701	+	0.259657i	$0.916391\pi$
$422$	−4.41584	−	28.1581i	−0.214960	−	1.37072i
$423$		0			0
$424$	10.5806	+	21.0023i	0.513837	+	1.01996i
$425$	−25.3303	−	14.6245i	−1.22870	−	0.709390i
$426$		0			0
$427$	2.04899	+	3.54896i	0.0991578	+	0.171746i
$428$	−9.88630	+	10.9128i	−0.477872	+	0.527489i
$429$		0			0
$430$	10.4589	+	4.03308i	0.504372	+	0.194493i
$431$	9.81289			0.472670			0.236335	−	0.971672i	$-0.424054\pi$
$431$	9.81289			0.472670			0.236335	+	0.971672i	$0.424054\pi$
$432$		0			0
$433$	−2.07517			−0.0997261			−0.0498631	−	0.998756i	$-0.515878\pi$
$433$	−2.07517			−0.0997261			−0.0498631	+	0.998756i	$0.515878\pi$
$434$	20.2453	+	7.80686i	0.971805	+	0.374741i
$435$		0			0
$436$	9.31217	−	10.2790i	0.445972	−	0.492277i
$437$	17.2278	+	29.8395i	0.824120	+	1.42742i
$438$		0			0
$439$	6.42920	+	3.71190i	0.306849	+	0.177159i	0.645516	−	0.763747i	$-0.276643\pi$
$439$	6.42920	+	3.71190i	0.306849	+	0.177159i	−0.338667	+	0.940906i	$0.609976\pi$
$440$	22.1523	−	11.1599i	1.05607	−	0.532027i
$441$		0			0
$442$	2.23050	+	14.2231i	0.106094	+	0.676522i
$443$	−33.0596	−	19.0869i	−1.57071	−	0.906848i	−0.996082	−	0.0884308i	$-0.971815\pi$
$443$	−33.0596	−	19.0869i	−1.57071	−	0.906848i	−0.574624	−	0.818417i	$-0.694852\pi$
$444$		0			0
$445$	4.48384	−	2.58875i	0.212555	−	0.122718i
$446$	−11.3606	−	14.0729i	−0.537939	−	0.666373i
$447$		0			0
$448$	25.4791	−	11.0660i	1.20378	−	0.522821i
$449$			26.3232i			1.24227i	0.783704	+	0.621135i	$0.213328\pi$
$449$			26.3232i			1.24227i	−0.783704	+	0.621135i	$0.786672\pi$
$450$		0			0
$451$	13.4612			0.633864
$452$	−36.3913	−	7.85119i	−1.71170	−	0.369289i
$453$		0			0
$454$	−6.36636	−	7.88633i	−0.298788	−	0.370124i
$455$	−24.5485	−	42.5193i	−1.15085	−	1.99333i
$456$		0			0
$457$	15.6550	−	27.1153i	0.732310	−	1.26840i	−0.223583	−	0.974685i	$-0.571775\pi$
$457$	15.6550	−	27.1153i	0.732310	−	1.26840i	0.955893	−	0.293714i	$-0.0948913\pi$
$458$	24.8957	−	3.90422i	1.16330	−	0.182432i
$459$		0			0
$460$	46.0737	−	14.8152i	2.14820	−	0.690760i
$461$	−8.12726	+	14.0768i	−0.378524	+	0.655623i	−0.990848	−	0.134984i	$-0.956902\pi$
$461$	−8.12726	+	14.0768i	−0.378524	+	0.655623i	0.612323	+	0.790607i	$0.290235\pi$
$462$		0			0
$463$	−1.51695	+	0.875811i	−0.0704986	+	0.0407024i	−0.534835	−	0.844957i	$-0.679626\pi$
$463$	−1.51695	+	0.875811i	−0.0704986	+	0.0407024i	0.464336	+	0.885659i	$0.346293\pi$
$464$	9.44807	+	4.27574i	0.438616	+	0.198496i
$465$		0			0
$466$	−8.18974	+	21.2382i	−0.379383	+	0.983842i
$467$			28.2590i			1.30767i	0.756638	+	0.653834i	$0.226841\pi$
$467$			28.2590i			1.30767i	−0.756638	+	0.653834i	$0.773159\pi$
$468$		0			0
$469$			28.4827i			1.31521i
$470$	−13.8537	−	5.34216i	−0.639022	−	0.246415i
$471$		0			0
$472$	−2.87008	−	1.88256i	−0.132106	−	0.0866517i
$473$	−3.91814	+	2.26214i	−0.180156	+	0.104013i
$474$		0			0
$475$	−28.9224	+	50.0951i	−1.32705	+	2.29852i
$476$	18.6576	−	5.99941i	0.855168	−	0.274982i
$477$		0			0
$478$	−5.49465	−	35.0373i	−0.251320	−	1.60257i
$479$	19.4966	−	33.7691i	0.890823	−	1.54295i	0.0519326	−	0.998651i	$-0.483462\pi$
$479$	19.4966	−	33.7691i	0.890823	−	1.54295i	0.838890	−	0.544300i	$-0.183205\pi$
$480$		0			0
$481$	−1.42409	−	2.46660i	−0.0649331	−	0.112467i
$482$	−1.97872	+	1.59735i	−0.0901283	+	0.0727573i
$483$		0			0
$484$	2.52831	−	11.7190i	0.114923	−	0.532683i
$485$	59.6555			2.70882
$486$		0			0
$487$		−	32.4478i		−	1.47035i	−0.677876	−	0.735176i	$-0.737100\pi$
$487$		−	32.4478i		−	1.47035i	0.677876	−	0.735176i	$-0.262900\pi$
$488$	−0.189938	+	3.33268i	−0.00859809	+	0.150863i
$489$		0			0
$490$	−21.8119	+	17.6080i	−0.985362	+	0.795448i
$491$	−20.1605	+	11.6397i	−0.909830	+	0.525291i	−0.880376	−	0.474276i	$-0.842710\pi$
$491$	−20.1605	+	11.6397i	−0.909830	+	0.525291i	−0.0294535	+	0.999566i	$0.509377\pi$
$492$		0			0
$493$	6.33642	+	3.65834i	0.285378	+	0.164763i
$494$	28.1286	−	4.41121i	1.26557	−	0.198470i
$495$		0			0
$496$	10.3016	+	14.3622i	0.462557	+	0.644884i
$497$	24.1963	+	13.9697i	1.08535	+	0.626629i
$498$		0			0
$499$	−12.7382	−	22.0632i	−0.570240	−	0.987685i	−0.996541	−	0.0831033i	$-0.973517\pi$
$499$	−12.7382	−	22.0632i	−0.570240	−	0.987685i	0.426301	−	0.904581i	$-0.359816\pi$
$500$	31.1653	+	28.2338i	1.39375	+	1.26265i
$501$		0			0
$502$	−6.12999	+	15.8967i	−0.273595	+	0.709505i
$503$	−3.28606			−0.146518			−0.0732591	−	0.997313i	$-0.523340\pi$
$503$	−3.28606			−0.146518			−0.0732591	+	0.997313i	$0.523340\pi$
$504$		0			0
$505$	50.5362			2.24883
$506$	−7.02795	+	18.2254i	−0.312430	+	0.810217i
$507$		0			0
$508$	23.5839	−	26.0326i	1.04637	−	1.15501i
$509$	−3.64555	−	6.31428i	−0.161586	−	0.279875i	0.773852	−	0.633367i	$-0.218328\pi$
$509$	−3.64555	−	6.31428i	−0.161586	−	0.279875i	−0.935438	+	0.353492i	$0.884994\pi$
$510$		0			0
$511$	15.5876	+	8.99948i	0.689553	+	0.398114i
$512$	22.2982	+	3.84585i	0.985450	+	0.169964i
$513$		0			0
$514$	−31.7381	+	4.97726i	−1.39991	+	0.219538i
$515$	58.1828	+	33.5919i	2.56384	+	1.48023i
$516$		0			0
$517$	5.18990	−	2.99639i	0.228252	−	0.131781i
$518$	−3.01688	+	2.43542i	−0.132554	+	0.107006i
$519$		0			0
$520$	2.27560	−	39.9280i	0.0997918	−	1.75096i
$521$		−	12.6094i		−	0.552430i	−0.961096	−	0.276215i	$-0.910920\pi$
$521$		−	12.6094i		−	0.552430i	0.961096	−	0.276215i	$-0.0890801\pi$
$522$		0			0
$523$	−2.17065			−0.0949159			−0.0474579	−	0.998873i	$-0.515112\pi$
$523$	−2.17065			−0.0949159			−0.0474579	+	0.998873i	$0.515112\pi$
$524$	21.6462	+	4.67003i	0.945618	+	0.204011i
$525$		0			0
$526$	−14.6054	+	11.7904i	−0.636826	+	0.514087i
$527$	6.23500	+	10.7993i	0.271601	+	0.470426i
$528$		0			0
$529$	−7.55620	+	13.0877i	−0.328530	+	0.569031i
$530$	−7.14067	−	45.5334i	−0.310171	−	1.97784i
$531$		0			0
$532$	−11.8649	−	36.8986i	−0.514408	−	1.59976i
$533$	10.8519	−	18.7960i	0.470047	−	0.814145i
$534$		0			0
$535$	24.9927	−	14.4296i	1.08053	−	0.623844i
$536$	−12.7250	+	19.4001i	−0.549638	+	0.837957i
$537$		0			0
$538$	6.42914	+	2.47916i	0.277180	+	0.106884i
$539$		−	11.3140i		−	0.487330i
$540$		0			0
$541$			35.1130i			1.50963i	0.655941	+	0.754813i	$0.272272\pi$
$541$			35.1130i			1.50963i	−0.655941	+	0.754813i	$0.727728\pi$
$542$	6.86031	−	17.7907i	0.294676	−	0.764174i
$543$		0			0
$544$	15.3883	+	4.24920i	0.659769	+	0.182183i
$545$	−23.5413	+	13.5916i	−1.00840	+	0.582199i
$546$		0			0
$547$	1.98825	−	3.44374i	0.0850112	−	0.147244i	−0.820385	−	0.571812i	$-0.806241\pi$
$547$	1.98825	−	3.44374i	0.0850112	−	0.147244i	0.905396	+	0.424568i	$0.139574\pi$
$548$	2.73284	+	8.49886i	0.116741	+	0.363053i
$549$		0			0
$550$	−32.3972	+	5.08062i	−1.38142	+	0.216638i
$551$	7.23501	−	12.5314i	0.308222	−	0.533856i
$552$		0			0
$553$	−23.4840	−	40.6755i	−0.998642	−	1.72970i
$554$	−23.0761	−	28.5856i	−0.980410	−	1.21448i
$555$		0			0
$556$	9.53960	−	44.2173i	0.404569	−	1.87523i
$557$	−44.8573			−1.90067			−0.950333	−	0.311236i	$-0.899257\pi$
$557$	−44.8573			−1.90067			−0.950333	+	0.311236i	$0.899257\pi$
$558$		0			0
$559$			7.29457i			0.308527i
$560$	−54.1774	+	5.36063i	−2.28941	+	0.226528i
$561$		0			0
$562$	−14.1558	−	17.5355i	−0.597126	−	0.739691i
$563$	−7.07017	+	4.08196i	−0.297972	+	0.172034i	−0.641531	−	0.767097i	$-0.721701\pi$
$563$	−7.07017	+	4.08196i	−0.297972	+	0.172034i	0.343559	+	0.939131i	$0.388367\pi$
$564$		0			0
$565$	63.1876	+	36.4814i	2.65832	+	1.53478i
$566$	−2.22510	−	14.1886i	−0.0935280	−	0.596393i
$567$		0			0
$568$	10.2394	+	20.3251i	0.429635	+	0.852821i
$569$	−23.4933	−	13.5638i	−0.984889	−	0.568626i	−0.0811464	−	0.996702i	$-0.525858\pi$
$569$	−23.4933	−	13.5638i	−0.984889	−	0.568626i	−0.903743	+	0.428076i	$0.859191\pi$
$570$		0			0
$571$	−10.4444	−	18.0902i	−0.437083	−	0.757051i	0.560380	−	0.828236i	$-0.310655\pi$
$571$	−10.4444	−	18.0902i	−0.437083	−	0.757051i	−0.997463	+	0.0711851i	$0.977322\pi$
$572$	11.9625	+	10.8373i	0.500176	+	0.453128i
$573$		0			0
$574$	−27.5666	−	10.6301i	−1.15061	−	0.443690i
$575$	−63.9838			−2.66831
$576$		0			0
$577$	−24.2888			−1.01116			−0.505578	−	0.862781i	$-0.668721\pi$
$577$	−24.2888			−1.01116			−0.505578	+	0.862781i	$0.668721\pi$
$578$	−11.9227	−	4.59757i	−0.495921	−	0.191234i
$579$		0			0
$580$	−15.0628	−	13.6459i	−0.625447	−	0.566616i
$581$	−4.51578	−	7.82157i	−0.187346	−	0.324493i
$582$		0			0
$583$	16.1101	+	9.30114i	0.667210	+	0.385214i
$584$	6.59634	+	13.0937i	0.272958	+	0.541820i
$585$		0			0
$586$	3.03570	+	19.3575i	0.125404	+	0.799652i
$587$	17.0442	+	9.84047i	0.703489	+	0.406160i	0.808646	−	0.588296i	$-0.200201\pi$
$587$	17.0442	+	9.84047i	0.703489	+	0.406160i	−0.105156	+	0.994456i	$0.533534\pi$
$588$		0			0
$589$	21.3576	−	12.3308i	0.880024	−	0.508082i
$590$	4.22548	+	5.23433i	0.173960	+	0.215494i
$591$		0			0
$592$	−3.14291	+	0.310978i	−0.129173	+	0.0127811i
$593$			12.8901i			0.529332i	0.964340	+	0.264666i	$0.0852617\pi$
$593$			12.8901i			0.529332i	−0.964340	+	0.264666i	$0.914738\pi$
$594$		0			0
$595$	−38.4102			−1.57466
$596$	0.683768	−	3.16935i	0.0280082	−	0.129822i
$597$		0			0
$598$	19.7826	+	24.5057i	0.808970	+	1.00211i
$599$	2.00875	+	3.47926i	0.0820754	+	0.142159i	0.904141	−	0.427234i	$-0.140512\pi$
$599$	2.00875	+	3.47926i	0.0820754	+	0.142159i	−0.822066	+	0.569392i	$0.807179\pi$
$600$		0			0
$601$	12.2222	−	21.1694i	0.498552	−	0.863518i	−0.501446	−	0.865189i	$-0.667199\pi$
$601$	12.2222	−	21.1694i	0.498552	−	0.863518i	0.999999	+	0.00167083i	$0.000531843\pi$
$602$	9.81014	−	1.53845i	0.399831	−	0.0627027i
$603$		0			0
$604$	−7.25038	−	22.5480i	−0.295014	−	0.917463i
$605$	−11.7481	+	20.3482i	−0.477626	+	0.827273i
$606$		0			0
$607$	−19.0749	+	11.0129i	−0.774227	+	0.447000i	−0.834380	−	0.551189i	$-0.814174\pi$
$607$	−19.0749	+	11.0129i	−0.774227	+	0.447000i	0.0601534	+	0.998189i	$0.480841\pi$
$608$	8.40355	−	30.4331i	0.340809	−	1.23423i
$609$		0			0
$610$	2.35381	−	6.10408i	0.0953032	−	0.247147i
$611$		−	9.66227i		−	0.390893i
$612$		0			0
$613$		−	16.3463i		−	0.660222i	−0.943942	−	0.330111i	$-0.892914\pi$
$613$		−	16.3463i		−	0.660222i	0.943942	−	0.330111i	$-0.107086\pi$
$614$	43.1213	+	16.6281i	1.74023	+	0.671057i
$615$		0			0
$616$	12.0516	−	18.3734i	0.485573	−	0.740286i
$617$	9.05798	−	5.22962i	0.364660	−	0.210537i	−0.306463	−	0.951883i	$-0.599146\pi$
$617$	9.05798	−	5.22962i	0.364660	−	0.210537i	0.671123	+	0.741346i	$0.265812\pi$
$618$		0			0
$619$	−16.6472	+	28.8338i	−0.669107	+	1.15893i	0.309047	+	0.951047i	$0.399990\pi$
$619$	−16.6472	+	28.8338i	−0.669107	+	1.15893i	−0.978154	+	0.207881i	$0.933343\pi$
$620$	−10.6039	−	32.9772i	−0.425864	−	1.32440i
$621$		0			0
$622$	−3.46693	−	22.1073i	−0.139011	−	0.886422i
$623$	2.29326	−	3.97204i	0.0918774	−	0.159136i
$624$		0			0
$625$	−15.2981	−	26.4970i	−0.611923	−	1.05988i
$626$	−1.20889	+	0.975892i	−0.0483169	+	0.0390045i
$627$		0			0
$628$	−1.39311	−	0.300555i	−0.0555911	−	0.0119934i
$629$	−2.22823			−0.0888453
$630$		0			0
$631$		−	8.54812i		−	0.340295i	−0.985419	−	0.170148i	$-0.945576\pi$
$631$		−	8.54812i		−	0.340295i	0.985419	−	0.170148i	$-0.0544245\pi$
$632$	2.17693	−	38.1966i	0.0865935	−	1.51938i
$633$		0			0
$634$	−15.8391	+	12.7864i	−0.629053	+	0.507812i
$635$	−59.6206	+	34.4219i	−2.36597	+	1.36599i
$636$		0			0
$637$	−15.7979	−	9.12090i	−0.625934	−	0.361383i
$638$	8.10423	−	1.27093i	0.320849	−	0.0503165i
$639$		0			0
$640$	−39.2961	−	20.5532i	−1.55332	−	0.812438i
$641$	12.1917	+	7.03889i	0.481544	+	0.278020i	0.721060	−	0.692873i	$-0.243655\pi$
$641$	12.1917	+	7.03889i	0.481544	+	0.278020i	−0.239516	+	0.970892i	$0.576989\pi$
$642$		0			0
$643$	14.7787	+	25.5974i	0.582815	+	1.00946i	0.995144	+	0.0984299i	$0.0313820\pi$
$643$	14.7787	+	25.5974i	0.582815	+	1.00946i	−0.412329	+	0.911035i	$0.635285\pi$
$644$	28.7844	−	31.7731i	1.13427	−	1.25203i
$645$		0			0
$646$	8.01428	−	20.7832i	0.315318	−	0.817704i
$647$	17.5491			0.689925			0.344963	−	0.938616i	$-0.387892\pi$
$647$	17.5491			0.689925			0.344963	+	0.938616i	$0.387892\pi$
$648$		0			0
$649$	−2.71509			−0.106577
$650$	−19.0232	+	49.3322i	−0.746150	+	1.93497i
$651$		0			0
$652$	−8.07486	−	7.31532i	−0.316236	−	0.286490i
$653$	−15.8564	−	27.4641i	−0.620509	−	1.07475i	−0.989391	−	0.145277i	$-0.953593\pi$
$653$	−15.8564	−	27.4641i	−0.620509	−	1.07475i	0.368882	−	0.929476i	$-0.379741\pi$
$654$		0			0
$655$	−37.5852	−	21.6998i	−1.46857	−	0.847882i
$656$	−14.0270	−	19.5561i	−0.547663	−	0.763536i
$657$		0			0
$658$	−12.9944	+	2.03781i	−0.506573	+	0.0794422i
$659$	15.8810	+	9.16890i	0.618636	+	0.357170i	0.776338	−	0.630317i	$-0.217075\pi$
$659$	15.8810	+	9.16890i	0.618636	+	0.357170i	−0.157702	+	0.987487i	$0.550408\pi$
$660$		0			0
$661$	11.4984	−	6.63860i	0.447236	−	0.258212i	−0.259426	−	0.965763i	$-0.583534\pi$
$661$	11.4984	−	6.63860i	0.447236	−	0.258212i	0.706662	+	0.707551i	$0.250200\pi$
$662$	4.74017	−	3.82657i	0.184232	−	0.148724i
$663$		0			0
$664$	0.418605	−	7.34490i	0.0162450	−	0.285037i
$665$			75.9629i			2.94571i
$666$		0			0
$667$	16.0057			0.619743
$668$	−4.13314	+	19.1576i	−0.159916	+	0.741231i
$669$		0			0
$670$	35.3811	−	28.5619i	1.36689	−	1.10344i
$671$	1.32024	+	2.28673i	0.0509674	+	0.0882781i
$672$		0			0
$673$	16.0826	−	27.8558i	0.619937	−	1.07376i	−0.369560	−	0.929207i	$-0.620492\pi$
$673$	16.0826	−	27.8558i	0.619937	−	1.07376i	0.989497	−	0.144555i	$-0.0461751\pi$
$674$	0.864528	+	5.51277i	0.0333004	+	0.212344i
$675$		0			0
$676$	0.0239460	−	0.00769993i	0.000921000	−	0.000296151i
$677$	−10.4767	+	18.1461i	−0.402651	+	0.697413i	−0.994045	−	0.108970i	$-0.965245\pi$
$677$	−10.4767	+	18.1461i	−0.402651	+	0.697413i	0.591394	+	0.806383i	$0.298578\pi$
$678$		0			0
$679$	45.7661	−	26.4231i	1.75634	−	1.01402i
$680$	−26.1619	−	17.1602i	−1.00326	−	0.658065i
$681$		0			0
$682$	13.0448	+	5.03025i	0.499511	+	0.192618i
$683$			3.04131i			0.116373i	0.998306	+	0.0581863i	$0.0185318\pi$
$683$			3.04131i			0.116373i	−0.998306	+	0.0581863i	$0.981468\pi$
$684$		0			0
$685$		−	17.4965i		−	0.668508i
$686$	3.43300	−	8.90269i	0.131072	−	0.339906i
$687$		0			0
$688$	7.36919	+	3.33494i	0.280948	+	0.127143i
$689$	25.9745	−	14.9964i	0.989550	−	0.571317i
$690$		0			0
$691$	0.513536	−	0.889471i	0.0195358	−	0.0338371i	−0.856092	−	0.516823i	$-0.827114\pi$
$691$	0.513536	−	0.889471i	0.0195358	−	0.0338371i	0.875628	+	0.482986i	$0.160448\pi$
$692$	−2.99276	+	0.962334i	−0.113768	+	0.0365825i
$693$		0			0
$694$	−18.0059	+	2.82374i	−0.683495	+	0.107188i
$695$	−44.3268	+	76.7762i	−1.68141	+	2.91229i
$696$		0			0
$697$	−8.48976	−	14.7047i	−0.321573	−	0.556980i
$698$	27.8720	+	34.5264i	1.05497	+	1.30684i
$699$		0			0
$700$	70.3568	+	15.1790i	2.65924	+	0.573714i
$701$	−19.6972			−0.743953			−0.371977	−	0.928242i	$-0.621320\pi$
$701$	−19.6972			−0.743953			−0.371977	+	0.928242i	$0.621320\pi$
$702$		0			0
$703$			4.40671i			0.166202i
$704$	16.4171	−	7.13026i	0.618744	−	0.268732i
$705$		0			0
$706$	27.6376	+	34.2361i	1.04015	+	1.28849i
$707$	38.7700	−	22.3839i	1.45810	−	0.841833i
$708$		0			0
$709$	−38.0410	−	21.9630i	−1.42866	−	0.824837i	−0.431645	−	0.902043i	$-0.642067\pi$
$709$	−38.0410	−	21.9630i	−1.42866	−	0.824837i	−0.997015	+	0.0772060i	$0.975400\pi$
$710$	−6.91042	−	44.0651i	−0.259343	−	1.65373i
$711$		0			0
$712$	3.33654	−	1.68088i	0.125042	−	0.0629938i
$713$	23.6242	+	13.6395i	0.884734	+	0.510802i
$714$		0			0
$715$	−15.8175	−	27.3967i	−0.591542	−	1.02458i
$716$	17.2567	−	19.0485i	0.644913	−	0.711874i
$717$		0			0
$718$	5.70691	+	2.20066i	0.212980	+	0.0821279i
$719$	32.2200			1.20160			0.600802	−	0.799398i	$-0.294848\pi$
$719$	32.2200			1.20160			0.600802	+	0.799398i	$0.294848\pi$
$720$		0			0
$721$	59.5151			2.21646
$722$	−16.0318	−	6.18208i	−0.596642	−	0.230073i
$723$		0			0
$724$	−25.5896	+	28.2465i	−0.951028	+	1.04977i
$725$	13.4353	+	23.2707i	0.498976	+	0.864251i
$726$		0			0
$727$	−18.6265	−	10.7540i	−0.690820	−	0.398845i	0.113099	−	0.993584i	$-0.463922\pi$
$727$	−18.6265	−	10.7540i	−0.690820	−	0.398845i	−0.803919	+	0.594739i	$0.797256\pi$
$728$	−15.9394	−	31.6396i	−0.590755	−	1.17264i
$729$		0			0
$730$	−4.45178	−	28.3873i	−0.164768	−	1.05066i
$731$	4.94221	+	2.85338i	0.182794	+	0.105536i
$732$		0			0
$733$	−11.7946	+	6.80963i	−0.435644	+	0.251519i	−0.701748	−	0.712425i	$-0.747597\pi$
$733$	−11.7946	+	6.80963i	−0.435644	+	0.251519i	0.266104	+	0.963944i	$0.414264\pi$
$734$	17.9492	+	22.2346i	0.662516	+	0.820693i
$735$		0			0
$736$	33.8006	−	8.78141i	1.24591	−	0.323687i
$737$			18.3525i			0.676022i
$738$		0			0
$739$	−35.1234			−1.29204			−0.646018	−	0.763322i	$-0.723567\pi$
$739$	−35.1234			−1.29204			−0.646018	+	0.763322i	$0.723567\pi$
$740$	6.05053	+	1.30536i	0.222422	+	0.0479861i
$741$		0			0
$742$	−25.6461	−	31.7692i	−0.941498	−	1.16628i
$743$	8.64518	+	14.9739i	0.317161	+	0.549339i	0.979895	−	0.199516i	$-0.0639371\pi$
$743$	8.64518	+	14.9739i	0.317161	+	0.549339i	−0.662733	+	0.748855i	$0.730604\pi$
$744$		0			0
$745$	−3.17720	+	5.50308i	−0.116404	+	0.201617i
$746$	−13.2825	+	2.08300i	−0.486306	+	0.0762639i
$747$		0			0
$748$	12.0218	−	3.86564i	0.439559	−	0.141342i
$749$	12.7825	−	22.1399i	0.467062	−	0.808976i
$750$		0			0
$751$	−30.6773	+	17.7116i	−1.11943	+	0.646304i	−0.941256	−	0.337695i	$-0.890353\pi$
$751$	−30.6773	+	17.7116i	−1.11943	+	0.646304i	−0.178175	+	0.983999i	$0.557019\pi$
$752$	−9.76111	−	4.41741i	−0.355951	−	0.161086i
$753$		0			0
$754$	4.75868	−	12.3406i	0.173301	−	0.449417i
$755$			46.4193i			1.68937i
$756$		0			0
$757$		−	13.5075i		−	0.490939i	−0.969404	−	0.245470i	$-0.921058\pi$
$757$		−	13.5075i		−	0.490939i	0.969404	−	0.245470i	$-0.0789422\pi$
$758$	8.50155	+	3.27831i	0.308790	+	0.119074i
$759$		0			0
$760$	−33.9374	+	51.7397i	−1.23104	+	1.87680i
$761$	−37.6951	+	21.7633i	−1.36645	+	0.788917i	−0.990472	−	0.137713i	$-0.956025\pi$
$761$	−37.6951	+	21.7633i	−1.36645	+	0.788917i	−0.375973	+	0.926631i	$0.622691\pi$
$762$		0			0
$763$	−12.0402	+	20.8542i	−0.435884	+	0.754972i
$764$	−13.6040	+	4.37443i	−0.492177	+	0.158261i
$765$		0			0
$766$	4.60671	+	29.3752i	0.166447	+	1.06137i
$767$	−2.18879	+	3.79110i	−0.0790327	+	0.136889i
$768$		0			0
$769$	4.95747	+	8.58658i	0.178771	+	0.309640i	0.941460	−	0.337125i	$-0.109455\pi$
$769$	4.95747	+	8.58658i	0.178771	+	0.309640i	−0.762689	+	0.646765i	$0.776121\pi$
$770$	−33.5087	+	27.0504i	−1.20757	+	0.974827i
$771$		0			0
$772$	−0.421783	+	1.95502i	−0.0151803	+	0.0703627i
$773$	−5.07749			−0.182625			−0.0913123	−	0.995822i	$-0.529106\pi$
$773$	−5.07749			−0.182625			−0.0913123	+	0.995822i	$0.529106\pi$
$774$		0			0
$775$			45.7964i			1.64505i
$776$	42.9770	+	2.44937i	1.54278	+	0.0879273i
$777$		0			0
$778$	19.5726	−	15.8003i	0.701712	−	0.566467i
$779$	−29.0812	+	16.7900i	−1.04194	+	0.601565i
$780$		0			0
$781$	15.5906	+	9.00122i	0.557875	+	0.322089i
$782$	24.3414	−	3.81728i	0.870445	−	0.136506i
$783$		0			0
$784$	−16.4367	+	11.7896i	−0.587025	+	0.421056i
$785$	2.41891	+	1.39656i	0.0863347	+	0.0498454i
$786$		0			0
$787$	15.3686	+	26.6193i	0.547833	+	0.948875i	0.998423	+	0.0561434i	$0.0178804\pi$
$787$	15.3686	+	26.6193i	0.547833	+	0.948875i	−0.450590	+	0.892731i	$0.648786\pi$
$788$	−10.0885	−	9.13953i	−0.359387	−	0.325582i
$789$		0			0
$790$	−26.9776	+	69.9603i	−0.959821	+	2.48908i
$791$	64.6345			2.29814
$792$		0			0
$793$	4.25730			0.151181
$794$	10.9489	−	28.3935i	0.388562	−	1.00765i
$795$		0			0
$796$	−7.11331	+	7.85188i	−0.252124	+	0.278302i
$797$	−21.0052	−	36.3822i	−0.744044	−	1.28872i	−0.950640	−	0.310296i	$-0.899572\pi$
$797$	−21.0052	−	36.3822i	−0.744044	−	1.28872i	0.206596	−	0.978426i	$-0.433761\pi$
$798$		0			0
$799$	−6.54637	−	3.77955i	−0.231594	−	0.133711i
$800$	41.1399	+	41.7716i	1.45451	+	1.47685i
$801$		0			0
$802$	−26.3878	+	4.13821i	−0.931785	+	0.146125i
$803$	10.0436	+	5.79870i	0.354432	+	0.204632i
$804$		0			0
$805$	−72.7675	+	42.0123i	−2.56472	+	1.48074i
$806$	17.5399	−	14.1594i	0.617818	−	0.498742i
$807$		0			0
$808$	36.4073	+	2.07495i	1.28080	+	0.0729964i
$809$		−	35.6802i		−	1.25445i	−0.778838	−	0.627225i	$-0.784191\pi$
$809$		−	35.6802i		−	1.25445i	0.778838	−	0.627225i	$-0.215809\pi$
$810$		0			0
$811$	31.2629			1.09779			0.548894	−	0.835892i	$-0.315049\pi$
$811$	31.2629			1.09779			0.548894	+	0.835892i	$0.315049\pi$
$812$	−17.5999	−	3.79707i	−0.617635	−	0.133251i
$813$		0			0
$814$	−1.94389	+	1.56923i	−0.0681332	+	0.0550015i
$815$	10.6771	+	18.4932i	0.374002	+	0.647790i
$816$		0			0
$817$	5.64307	−	9.77409i	0.197426	−	0.341952i
$818$	2.05449	+	13.1007i	0.0718335	+	0.458055i
$819$		0			0
$820$	14.4386	+	44.9027i	0.504219	+	1.56807i
$821$	25.2740	−	43.7759i	0.882070	−	1.52779i	0.0330343	−	0.999454i	$-0.489483\pi$
$821$	25.2740	−	43.7759i	0.882070	−	1.52779i	0.849036	−	0.528336i	$-0.177184\pi$
$822$		0			0
$823$	22.0294	−	12.7187i	0.767897	−	0.443345i	−0.0642272	−	0.997935i	$-0.520458\pi$
$823$	22.0294	−	12.7187i	0.767897	−	0.443345i	0.832124	+	0.554590i	$0.187125\pi$
$824$	40.5368	+	26.5891i	1.41217	+	0.926277i
$825$		0			0
$826$	5.56010	+	2.14405i	0.193461	+	0.0746011i
$827$			7.65569i			0.266214i	0.991102	+	0.133107i	$0.0424955\pi$
$827$			7.65569i			0.266214i	−0.991102	+	0.133107i	$0.957505\pi$
$828$		0			0
$829$		−	44.3468i		−	1.54023i	−0.637906	−	0.770114i	$-0.720199\pi$
$829$		−	44.3468i		−	1.54023i	0.637906	−	0.770114i	$-0.279801\pi$
$830$	−5.18758	+	13.4528i	−0.180063	+	0.466953i
$831$		0			0
$832$	3.27878	−	28.6715i	0.113671	−	0.994005i
$833$	−12.3592	+	7.13557i	−0.428220	+	0.247233i
$834$		0			0
$835$	19.2051	−	33.2642i	0.664619	−	1.15115i
$836$	−7.64499	−	23.7751i	−0.264407	−	0.822281i
$837$		0			0
$838$	34.8092	−	5.45888i	1.20246	−	0.188574i
$839$	−11.4867	+	19.8955i	−0.396564	+	0.686869i	−0.993299	−	0.115569i	$-0.963131\pi$
$839$	−11.4867	+	19.8955i	−0.396564	+	0.686869i	0.596735	+	0.802438i	$0.296464\pi$
$840$		0			0
$841$	11.1391	+	19.2935i	0.384108	+	0.665294i
$842$	25.7542	+	31.9030i	0.887547	+	1.09945i
$843$		0			0
$844$	−8.50069	+	39.4018i	−0.292606	+	1.35626i
$845$	−0.0492974			−0.00169588
$846$		0			0
$847$			20.8141i			0.715183i
$848$	−3.27474	−	33.0963i	−0.112455	−	1.13653i
$849$		0			0
$850$	25.9823	+	32.1856i	0.891186	+	1.10396i
$851$	−4.22134	+	2.43719i	−0.144706	+	0.0835460i
$852$		0			0
$853$	9.04208	+	5.22045i	0.309595	+	0.178745i	0.646745	−	0.762706i	$-0.276130\pi$
$853$	9.04208	+	5.22045i	0.309595	+	0.178745i	−0.337150	+	0.941451i	$0.609463\pi$
$854$	−0.897882	−	5.72545i	−0.0307249	−	0.195921i
$855$		0			0
$856$	18.5977	−	9.36917i	0.635656	−	0.320232i
$857$	9.72768	+	5.61628i	0.332291	+	0.191848i	0.656858	−	0.754014i	$-0.271885\pi$
$857$	9.72768	+	5.61628i	0.332291	+	0.191848i	−0.324567	+	0.945863i	$0.605218\pi$
$858$		0			0
$859$	−12.7809	−	22.1371i	−0.436078	−	0.755308i	0.561305	−	0.827609i	$-0.310299\pi$
$859$	−12.7809	−	22.1371i	−0.436078	−	0.755308i	−0.997383	+	0.0723003i	$0.976966\pi$
$860$	−11.7485	−	10.6434i	−0.400619	−	0.362936i
$861$		0			0
$862$	−12.9482	−	4.99300i	−0.441017	−	0.170062i
$863$	−34.5634			−1.17655			−0.588277	−	0.808660i	$-0.700193\pi$
$863$	−34.5634			−1.17655			−0.588277	+	0.808660i	$0.700193\pi$
$864$		0			0
$865$	6.16117			0.209486
$866$	2.73820	+	1.05589i	0.0930478	+	0.0358805i
$867$		0			0
$868$	−22.7416	−	20.6024i	−0.771899	−	0.699292i
$869$	−15.1316	−	26.2087i	−0.513305	−	0.889071i
$870$		0			0
$871$	25.6257	+	14.7950i	0.868294	+	0.501310i
$872$	−17.5177	+	8.82507i	−0.593223	+	0.298854i
$873$		0			0
$874$	−7.54935	−	48.1393i	−0.255361	−	1.62834i
$875$	−63.2283	−	36.5049i	−2.13751	−	1.23409i
$876$		0			0
$877$	47.5137	−	27.4320i	1.60442	−	0.926314i	0.613835	−	0.789434i	$-0.289626\pi$
$877$	47.5137	−	27.4320i	1.60442	−	0.926314i	0.990588	−	0.136880i	$-0.0437075\pi$
$878$	−6.59469	−	8.16919i	−0.222560	−	0.275697i
$879$		0			0
$880$	−34.9085	+	3.45405i	−1.17676	+	0.116436i
$881$			10.8673i			0.366130i	0.983101	+	0.183065i	$0.0586018\pi$
$881$			10.8673i			0.366130i	−0.983101	+	0.183065i	$0.941398\pi$
$882$		0			0
$883$	25.0646			0.843491			0.421745	−	0.906714i	$-0.361418\pi$
$883$	25.0646			0.843491			0.421745	+	0.906714i	$0.361418\pi$
$884$	4.29382	−	19.9024i	0.144417	−	0.669390i
$885$		0			0
$886$	33.9105	+	42.0067i	1.13925	+	1.41124i
$887$	−8.62211	−	14.9339i	−0.289502	−	0.501432i	0.684189	−	0.729305i	$-0.260156\pi$
$887$	−8.62211	−	14.9339i	−0.289502	−	0.501432i	−0.973691	+	0.227872i	$0.926823\pi$
$888$		0			0
$889$	−30.4929	+	52.8152i	−1.02270	+	1.77136i
$890$	−7.23367	+	1.13441i	−0.242473	+	0.0380254i
$891$		0			0
$892$	7.82979	+	24.3499i	0.262161	+	0.815294i
$893$	−7.47472	+	12.9466i	−0.250132	+	0.433242i
$894$		0			0
$895$	−43.6252	+	25.1870i	−1.45823	+	0.841910i
$896$	−39.2505	+	1.63745i	−1.31127	+	0.0547035i
$897$		0			0
$898$	13.3938	−	34.7337i	0.446956	−	1.15908i
$899$		−	11.4561i		−	0.382081i
$900$		0			0
$901$		−	23.4643i		−	0.781709i
$902$	−17.7622	−	6.84934i	−0.591416	−	0.228058i
$903$		0			0
$904$	44.0237	+	28.8763i	1.46421	+	0.960411i
$905$	64.6908	−	37.3492i	2.15039	−	1.24153i
$906$		0			0
$907$	−19.1384	+	33.1487i	−0.635481	+	1.10068i	0.350933	+	0.936401i	$0.385865\pi$
$907$	−19.1384	+	33.1487i	−0.635481	+	1.10068i	−0.986413	+	0.164284i	$0.947469\pi$
$908$	4.38773	+	13.6454i	0.145612	+	0.452839i
$909$		0			0
$910$	10.7573	+	68.5953i	0.356601	+	2.27391i
$911$	10.7303	−	18.5854i	0.355511	−	0.615762i	−0.631695	−	0.775217i	$-0.717640\pi$
$911$	10.7303	−	18.5854i	0.355511	−	0.615762i	0.987205	+	0.159455i	$0.0509737\pi$
$912$		0			0
$913$	−2.90969	−	5.03972i	−0.0962965	−	0.166791i
$914$	−34.4537	+	27.8132i	−1.13963	+	0.919980i
$915$		0			0
$916$	−34.8367	−	7.51579i	−1.15104	−	0.248329i
$917$	−38.4458			−1.26959
$918$		0			0
$919$		−	24.2130i		−	0.798712i	−0.916796	−	0.399356i	$-0.869234\pi$
$919$		−	24.2130i		−	0.798712i	0.916796	−	0.399356i	$-0.130766\pi$
$920$	−68.3328	−	3.89447i	−2.25287	−	0.128397i
$921$		0			0
$922$	17.8866	−	14.4392i	0.589062	−	0.475529i
$923$	25.1369	−	14.5128i	0.827393	−	0.477695i
$924$		0			0
$925$	−7.08688	−	4.09161i	−0.233015	−	0.134531i
$926$	2.44726	−	0.383786i	0.0804219	−	0.0126120i
$927$		0			0
$928$	−10.2912	−	10.4492i	−0.337826	−	0.343013i
$929$	−49.4714	−	28.5623i	−1.62310	−	0.937099i	−0.986083	−	0.166251i	$-0.946834\pi$
$929$	−49.4714	−	28.5623i	−1.62310	−	0.937099i	−0.637020	−	0.770848i	$-0.719833\pi$
$930$		0			0
$931$	14.1118	+	24.4424i	0.462497	+	0.801068i
$932$	21.6129	−	23.8569i	0.707953	−	0.781459i
$933$		0			0
$934$	14.3787	−	37.2879i	0.470486	−	1.22010i
$935$	−24.7491			−0.809382
$936$		0			0
$937$	−52.3140			−1.70902			−0.854512	−	0.519431i	$-0.826144\pi$
$937$	−52.3140			−1.70902			−0.854512	+	0.519431i	$0.826144\pi$
$938$	14.4926	−	37.5832i	0.473200	−	1.22714i
$939$		0			0
$940$	15.5618	+	14.0981i	0.507571	+	0.459828i
$941$	10.7295	+	18.5840i	0.349772	+	0.605822i	0.986209	−	0.165506i	$-0.0529258\pi$
$941$	10.7295	+	18.5840i	0.349772	+	0.605822i	−0.636437	+	0.771329i	$0.719592\pi$
$942$		0			0
$943$	−32.1675	−	18.5719i	−1.04752	−	0.604784i
$944$	2.82921	+	3.94440i	0.0920828	+	0.128379i
$945$		0			0
$946$	6.32103	−	0.991283i	0.205515	−	0.0322294i
$947$	42.1119	+	24.3133i	1.36845	+	0.790077i	0.990731	−	0.135842i	$-0.0433739\pi$
$947$	42.1119	+	24.3133i	1.36845	+	0.790077i	0.377723	+	0.925919i	$0.376707\pi$
$948$		0			0
$949$	16.1935	−	9.34934i	0.525664	−	0.303493i
$950$	63.6528	−	51.3846i	2.06517	−	1.66714i
$951$		0			0
$952$	−27.6714	−	1.57707i	−0.896836	−	0.0511130i
$953$		−	12.7176i		−	0.411962i	−0.978556	−	0.205981i	$-0.933962\pi$
$953$		−	12.7176i		−	0.411962i	0.978556	−	0.205981i	$-0.0660385\pi$
$954$		0			0
$955$	28.0065			0.906269
$956$	−10.5774	+	49.0278i	−0.342099	+	1.58567i
$957$		0			0
$958$	−42.9084	+	34.6384i	−1.38631	+	1.11912i
$959$	−7.74969	−	13.4229i	−0.250251	−	0.433447i
$960$		0			0
$961$	−5.73757	+	9.93777i	−0.185083	+	0.320573i
$962$	0.624047	+	3.97931i	0.0201201	+	0.128298i
$963$		0			0
$964$	3.42370	−	1.10091i	0.110270	−	0.0354578i
$965$	1.95986	−	3.39458i	0.0630902	−	0.109275i
$966$		0			0
$967$	33.0397	−	19.0755i	1.06248	−	0.613426i	0.136366	−	0.990658i	$-0.456458\pi$
$967$	33.0397	−	19.0755i	1.06248	−	0.613426i	0.926119	+	0.377233i	$0.123124\pi$
$968$	−9.29899	+	14.1769i	−0.298881	+	0.455663i
$969$		0			0
$970$	−78.7160	−	30.3539i	−2.52742	−	0.974606i
$971$		−	3.75217i		−	0.120413i	−0.998186	−	0.0602065i	$-0.980824\pi$
$971$		−	3.75217i		−	0.120413i	0.998186	−	0.0602065i	$-0.0191759\pi$
$972$		0			0
$973$			78.5342i			2.51769i
$974$	−16.5101	+	42.8152i	−0.529018	+	1.37189i
$975$		0			0
$976$	1.94636	−	4.30085i	0.0623014	−	0.137667i
$977$	−12.3310	+	7.11929i	−0.394502	+	0.227766i	−0.684109	−	0.729380i	$-0.739809\pi$
$977$	−12.3310	+	7.11929i	−0.394502	+	0.227766i	0.289607	+	0.957146i	$0.406475\pi$
$978$		0			0
$979$	1.47763	−	2.55933i	0.0472252	−	0.0817965i
$980$	37.7403	−	12.1355i	1.20557	−	0.387656i
$981$		0			0
$982$	32.5244	−	5.10057i	1.03790	−	0.162766i
$983$	30.9711	−	53.6436i	0.987825	−	1.71096i	0.359187	−	0.933266i	$-0.383054\pi$
$983$	30.9711	−	53.6436i	0.987825	−	1.71096i	0.628638	−	0.777698i	$-0.283613\pi$
$984$		0			0
$985$	13.3396	+	23.1049i	0.425035	+	0.736183i
$986$	−6.49953	−	8.05130i	−0.206987	−	0.256406i
$987$		0			0
$988$	−39.3605	−	8.49178i	−1.25222	−	0.270159i
$989$	12.4839			0.396965
$990$		0			0
$991$			28.6375i			0.909700i	0.890568	+	0.454850i	$0.150307\pi$
$991$			28.6375i			0.909700i	−0.890568	+	0.454850i	$0.849693\pi$
$992$	−6.28529	−	24.1928i	−0.199558	−	0.768121i
$993$		0			0
$994$	−24.8191	−	30.7448i	−0.787215	−	0.975164i
$995$	17.9826	−	10.3822i	0.570085	−	0.329139i
$996$		0			0
$997$	−1.71576	−	0.990596i	−0.0543387	−	0.0313725i	0.472585	−	0.881285i	$-0.343321\pi$
$997$	−1.71576	−	0.990596i	−0.0543387	−	0.0313725i	−0.526923	+	0.849913i	$0.676654\pi$
$998$	5.58196	+	35.5940i	0.176694	+	1.12671i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	648.2.l.g.107.3		48
3.2	odd	2	inner	648.2.l.g.107.22		48
4.3	odd	2		2592.2.p.g.431.2		48
8.3	odd	2	inner	648.2.l.g.107.5		48
8.5	even	2		2592.2.p.g.431.23		48
9.2	odd	6		648.2.f.c.323.11	✓	24
9.4	even	3	inner	648.2.l.g.539.20		48
9.5	odd	6	inner	648.2.l.g.539.5		48
9.7	even	3		648.2.f.c.323.14	yes	24
12.11	even	2		2592.2.p.g.431.24		48
24.5	odd	2		2592.2.p.g.431.1		48
24.11	even	2	inner	648.2.l.g.107.20		48
36.7	odd	6		2592.2.f.c.1295.23		24
36.11	even	6		2592.2.f.c.1295.1		24
36.23	even	6		2592.2.p.g.2159.23		48
36.31	odd	6		2592.2.p.g.2159.1		48
72.5	odd	6		2592.2.p.g.2159.2		48
72.11	even	6		648.2.f.c.323.13	yes	24
72.13	even	6		2592.2.p.g.2159.24		48
72.29	odd	6		2592.2.f.c.1295.24		24
72.43	odd	6		648.2.f.c.323.12	yes	24
72.59	even	6	inner	648.2.l.g.539.3		48
72.61	even	6		2592.2.f.c.1295.2		24
72.67	odd	6	inner	648.2.l.g.539.22		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
648.2.f.c.323.11	✓	24	9.2	odd	6
648.2.f.c.323.12	yes	24	72.43	odd	6
648.2.f.c.323.13	yes	24	72.11	even	6
648.2.f.c.323.14	yes	24	9.7	even	3
648.2.l.g.107.3		48	1.1	even	1	trivial
648.2.l.g.107.5		48	8.3	odd	2	inner
648.2.l.g.107.20		48	24.11	even	2	inner
648.2.l.g.107.22		48	3.2	odd	2	inner
648.2.l.g.539.3		48	72.59	even	6	inner
648.2.l.g.539.5		48	9.5	odd	6	inner
648.2.l.g.539.20		48	9.4	even	3	inner
648.2.l.g.539.22		48	72.67	odd	6	inner
2592.2.f.c.1295.1		24	36.11	even	6
2592.2.f.c.1295.2		24	72.61	even	6
2592.2.f.c.1295.23		24	36.7	odd	6
2592.2.f.c.1295.24		24	72.29	odd	6
2592.2.p.g.431.1		48	24.5	odd	2
2592.2.p.g.431.2		48	4.3	odd	2
2592.2.p.g.431.23		48	8.5	even	2
2592.2.p.g.431.24		48	12.11	even	2
2592.2.p.g.2159.1		48	36.31	odd	6
2592.2.p.g.2159.2		48	72.5	odd	6
2592.2.p.g.2159.23		48	36.23	even	6
2592.2.p.g.2159.24		48	72.13	even	6

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)

\(f(q)\)	\(=\)	\(q+(-1.31951 - 0.508820i) q^{2} +(1.48220 + 1.34278i) q^{4} +(-1.95986 - 3.39458i) q^{5} +(-3.00711 - 1.73615i) q^{7} +(-1.27255 - 2.52599i) q^{8} +O(q^{10})\)	\(q+(-1.31951 - 0.508820i) q^{2} +(1.48220 + 1.34278i) q^{4} +(-1.95986 - 3.39458i) q^{5} +(-3.00711 - 1.73615i) q^{7} +(-1.27255 - 2.52599i) q^{8} +(0.858824 + 5.47639i) q^{10} +(-1.93759 - 1.11867i) q^{11} +(-3.12401 + 1.80365i) q^{13} +(3.08451 + 3.82094i) q^{14} +(0.393860 + 3.98056i) q^{16} +2.82210i q^{17} +5.58120 q^{19} +(1.65327 - 7.66313i) q^{20} +(1.98747 + 2.46198i) q^{22} +(3.08676 + 5.34643i) q^{23} +(-5.18212 + 8.97569i) q^{25} +(5.03989 - 0.790370i) q^{26} +(-2.12587 - 6.61123i) q^{28} +(1.29632 - 2.24529i) q^{29} +(3.82670 - 2.20935i) q^{31} +(1.50569 - 5.45279i) q^{32} +(1.43594 - 3.72379i) q^{34} +13.6105i q^{35} +0.789564i q^{37} +(-7.36444 - 2.83983i) q^{38} +(-6.08066 + 9.27035i) q^{40} +(-5.21055 + 3.00831i) q^{41} +(1.01109 - 1.75125i) q^{43} +(-1.36977 - 4.25986i) q^{44} +(-1.35264 - 8.62526i) q^{46} +(-1.33927 + 2.31968i) q^{47} +(2.52846 + 4.37942i) q^{49} +(11.4049 - 9.20673i) q^{50} +(-7.05233 - 1.52150i) q^{52} -8.31448 q^{53} +8.76974i q^{55} +(-0.558827 + 9.80526i) q^{56} +(-2.85295 + 2.30308i) q^{58} +(1.05095 - 0.606768i) q^{59} +(-1.02208 - 0.590096i) q^{61} +(-6.17352 + 0.968150i) q^{62} +(-4.76126 + 6.42888i) q^{64} +(12.2453 + 7.06980i) q^{65} +(-4.10141 - 7.10386i) q^{67} +(-3.78947 + 4.18293i) q^{68} +(6.92529 - 17.9591i) q^{70} -8.04637 q^{71} -5.18358 q^{73} +(0.401746 - 1.04184i) q^{74} +(8.27248 + 7.49435i) q^{76} +(3.88436 + 6.72791i) q^{77} +(11.7143 + 6.76323i) q^{79} +(12.7404 - 9.13834i) q^{80} +(8.40606 - 1.31826i) q^{82} +(2.25256 + 1.30051i) q^{83} +(9.57985 - 5.53093i) q^{85} +(-2.22521 + 1.79633i) q^{86} +(-0.360073 + 6.31789i) q^{88} +1.32088i q^{89} +12.5256 q^{91} +(-2.60389 + 12.0694i) q^{92} +(2.94747 - 2.37939i) q^{94} +(-10.9384 - 18.9458i) q^{95} +(-7.60966 + 13.1803i) q^{97} +(-1.10799 - 7.06521i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q+O(q^{10}) \) 48 * q	\( 48 q - 12 q^{16} + 12 q^{22} - 24 q^{25} + 24 q^{28} + 24 q^{34} + 24 q^{40} - 24 q^{46} + 24 q^{49} + 12 q^{58} + 48 q^{64} - 48 q^{67} + 36 q^{70} + 60 q^{76} - 72 q^{82} + 60 q^{88} - 48 q^{94}+O(q^{100}) \) 48 * q - 12 * q^16 + 12 * q^22 - 24 * q^25 + 24 * q^28 + 24 * q^34 + 24 * q^40 - 24 * q^46 + 24 * q^49 + 12 * q^58 + 48 * q^64 - 48 * q^67 + 36 * q^70 + 60 * q^76 - 72 * q^82 + 60 * q^88 - 48 * q^94

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