LMFDB - Embedded newform 864.2.bi.a.767.23

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [864,2,Mod(95,864)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("864.95"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(864, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([9, 0, 17])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 864 = 2^{5} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	864.bi (of order $18$, degree $6$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$6.89907473464$
Analytic rank:	$0$
Dimension:	$216$
Relative dimension:	$36$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			767.23
Character	$\chi$	$=$	864.767
Dual form			864.2.bi.a.383.23

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.809747 - 1.53111i) q^{3} +(0.571575 - 1.57039i) q^{5} +(-1.77008 - 0.312113i) q^{7} +(-1.68862 - 2.47963i) q^{9} +(6.07031 - 2.20941i) q^{11} +(-0.911289 + 0.764662i) q^{13} +(-1.94161 - 2.14676i) q^{15} +(-1.89816 + 1.09590i) q^{17} +(-0.389926 - 0.225124i) q^{19} +(-1.91120 + 2.45746i) q^{21} +(-1.54739 - 8.77566i) q^{23} +(1.69080 + 1.41875i) q^{25} +(-5.16395 + 0.577594i) q^{27} +(-4.48899 + 5.34977i) q^{29} +(3.78330 - 0.667098i) q^{31} +(1.53255 - 11.0834i) q^{33} +(-1.50187 + 2.60132i) q^{35} +(-3.58021 - 6.20111i) q^{37} +(0.432871 + 2.01447i) q^{39} +(0.682432 + 0.813291i) q^{41} +(-3.59325 - 9.87239i) q^{43} +(-4.85916 + 1.23449i) q^{45} +(-0.778845 + 4.41705i) q^{47} +(-3.54207 - 1.28921i) q^{49} +(0.140922 + 3.79370i) q^{51} +8.34287i q^{53} -10.7956i q^{55} +(-0.660432 + 0.414728i) q^{57} +(12.5693 + 4.57486i) q^{59} +(-0.602055 + 3.41443i) q^{61} +(2.21507 + 4.91619i) q^{63} +(0.679947 + 1.86814i) q^{65} +(3.08006 + 3.67067i) q^{67} +(-14.6895 - 4.73684i) q^{69} +(0.814377 + 1.41054i) q^{71} +(4.49780 - 7.79042i) q^{73} +(3.54138 - 1.43998i) q^{75} +(-11.4345 + 2.01621i) q^{77} +(-0.121747 + 0.145093i) q^{79} +(-3.29713 + 8.37430i) q^{81} +(-0.651774 - 0.546903i) q^{83} +(0.636052 + 3.60723i) q^{85} +(4.55616 + 11.2051i) q^{87} +(8.08976 + 4.67063i) q^{89} +(1.85172 - 1.06909i) q^{91} +(2.04211 - 6.33285i) q^{93} +(-0.576404 + 0.483661i) q^{95} +(1.76799 - 0.643496i) q^{97} +(-15.7290 - 11.3213i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 216 q - 24 q^{29} + 36 q^{33} + 36 q^{41} - 24 q^{45} + 12 q^{57} + 48 q^{65} + 48 q^{69} + 48 q^{77} + 48 q^{81} + 36 q^{89} - 144 q^{93} - 36 q^{97}+O(q^{100}) $ 216 * q - 24 * q^29 + 36 * q^33 + 36 * q^41 - 24 * q^45 + 12 * q^57 + 48 * q^65 + 48 * q^69 + 48 * q^77 + 48 * q^81 + 36 * q^89 - 144 * q^93 - 36 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/864\mathbb{Z}\right)^\times$.

$n$	$325$	$353$	$703$
$\chi(n)$	$1$	$e\left(\frac{13}{18}\right)$	$-1$

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			0
$2$		0			0
$3$	0.809747	−	1.53111i	0.467508	−	0.883989i
$3$	0.809747	−	1.53111i	0.467508	−	0.883989i
$4$		0			0
$5$	0.571575	−	1.57039i	0.255616	−	0.702299i	−0.743809	−	0.668392i	$-0.766983\pi$
$5$	0.571575	−	1.57039i	0.255616	−	0.702299i	0.999425	−	0.0339071i	$-0.0107950\pi$
$6$		0			0
$7$	−1.77008	−	0.312113i	−0.669028	−	0.117968i	−0.171190	−	0.985238i	$-0.554761\pi$
$7$	−1.77008	−	0.312113i	−0.669028	−	0.117968i	−0.497838	+	0.867270i	$0.665872\pi$
$8$		0			0
$9$	−1.68862	−	2.47963i	−0.562873	−	0.826543i
$10$		0			0
$11$	6.07031	−	2.20941i	1.83027	−	0.666162i	0.837450	−	0.546514i	$-0.184046\pi$
$11$	6.07031	−	2.20941i	1.83027	−	0.666162i	0.992816	−	0.119648i	$-0.0381766\pi$
$12$		0			0
$13$	−0.911289	+	0.764662i	−0.252746	+	0.212079i	−0.760354	−	0.649509i	$-0.774974\pi$
$13$	−0.911289	+	0.764662i	−0.252746	+	0.212079i	0.507608	+	0.861588i	$0.330530\pi$
$14$		0			0
$15$	−1.94161	−	2.14676i	−0.501322	−	0.554292i
$16$		0			0
$17$	−1.89816	+	1.09590i	−0.460370	+	0.265795i	−0.712200	−	0.701977i	$-0.752301\pi$
$17$	−1.89816	+	1.09590i	−0.460370	+	0.265795i	0.251830	+	0.967772i	$0.418968\pi$
$18$		0			0
$19$	−0.389926	−	0.225124i	−0.0894552	−	0.0516470i	0.454605	−	0.890693i	$-0.349780\pi$
$19$	−0.389926	−	0.225124i	−0.0894552	−	0.0516470i	−0.544060	+	0.839046i	$0.683114\pi$
$20$		0			0
$21$	−1.91120	+	2.45746i	−0.417058	+	0.536263i
$22$		0			0
$23$	−1.54739	−	8.77566i	−0.322652	−	1.82985i	−0.525684	−	0.850680i	$-0.676190\pi$
$23$	−1.54739	−	8.77566i	−0.322652	−	1.82985i	0.203032	−	0.979172i	$-0.434921\pi$
$24$		0			0
$25$	1.69080	+	1.41875i	0.338160	+	0.283750i
$26$		0			0
$27$	−5.16395	+	0.577594i	−0.993803	+	0.111158i
$28$		0			0
$29$	−4.48899	+	5.34977i	−0.833585	+	0.993428i	0.166388	+	0.986060i	$0.446790\pi$
$29$	−4.48899	+	5.34977i	−0.833585	+	0.993428i	−0.999973	+	0.00736735i	$0.997655\pi$
$30$		0			0
$31$	3.78330	−	0.667098i	0.679501	−	0.119814i	0.176763	−	0.984253i	$-0.443437\pi$
$31$	3.78330	−	0.667098i	0.679501	−	0.119814i	0.502738	+	0.864439i	$0.332326\pi$
$32$		0			0
$33$	1.53255	−	11.0834i	0.266783	−	1.92937i
$34$		0			0
$35$	−1.50187	+	2.60132i	−0.253863	+	0.439703i
$36$		0			0
$37$	−3.58021	−	6.20111i	−0.588584	−	1.01946i	−0.994418	−	0.105510i	$-0.966352\pi$
$37$	−3.58021	−	6.20111i	−0.588584	−	1.01946i	0.405835	−	0.913947i	$-0.366981\pi$
$38$		0			0
$39$	0.432871	+	2.01447i	0.0693149	+	0.322573i
$40$		0			0
$41$	0.682432	+	0.813291i	0.106578	+	0.127015i	0.816696	−	0.577068i	$-0.195803\pi$
$41$	0.682432	+	0.813291i	0.106578	+	0.127015i	−0.710118	+	0.704082i	$0.751359\pi$
$42$		0			0
$43$	−3.59325	−	9.87239i	−0.547966	−	1.50552i	−0.836452	−	0.548041i	$-0.815374\pi$
$43$	−3.59325	−	9.87239i	−0.547966	−	1.50552i	0.288485	−	0.957484i	$-0.406848\pi$
$44$		0			0
$45$	−4.85916	+	1.23449i	−0.724360	+	0.184028i
$46$		0			0
$47$	−0.778845	+	4.41705i	−0.113606	+	0.644293i	0.873825	+	0.486241i	$0.161632\pi$
$47$	−0.778845	+	4.41705i	−0.113606	+	0.644293i	−0.987431	+	0.158052i	$0.949479\pi$
$48$		0			0
$49$	−3.54207	−	1.28921i	−0.506011	−	0.184173i
$50$		0			0
$51$	0.140922	+	3.79370i	0.0197331	+	0.531224i
$52$		0			0
$53$			8.34287i			1.14598i	0.819562	+	0.572990i	$0.194217\pi$
$53$			8.34287i			1.14598i	−0.819562	+	0.572990i	$0.805783\pi$
$54$		0			0
$55$		−	10.7956i		−	1.45568i
$56$		0			0
$57$	−0.660432	+	0.414728i	−0.0874764	+	0.0549321i
$58$		0			0
$59$	12.5693	+	4.57486i	1.63639	+	0.595596i	0.986402	−	0.164352i	$-0.0525533\pi$
$59$	12.5693	+	4.57486i	1.63639	+	0.595596i	0.649984	+	0.759948i	$0.274776\pi$
$60$		0			0
$61$	−0.602055	+	3.41443i	−0.0770853	+	0.437172i	0.921700	+	0.387903i	$0.126800\pi$
$61$	−0.602055	+	3.41443i	−0.0770853	+	0.437172i	−0.998786	+	0.0492695i	$0.984311\pi$
$62$		0			0
$63$	2.21507	+	4.91619i	0.279072	+	0.619381i
$64$		0			0
$65$	0.679947	+	1.86814i	0.0843371	+	0.231714i
$66$		0			0
$67$	3.08006	+	3.67067i	0.376289	+	0.448444i	0.920639	−	0.390414i	$-0.127668\pi$
$67$	3.08006	+	3.67067i	0.376289	+	0.448444i	−0.544350	+	0.838858i	$0.683224\pi$
$68$		0			0
$69$	−14.6895	−	4.73684i	−1.76841	−	0.570249i
$70$		0			0
$71$	0.814377	+	1.41054i	0.0966488	+	0.167401i	0.910296	−	0.413959i	$-0.135854\pi$
$71$	0.814377	+	1.41054i	0.0966488	+	0.167401i	−0.813647	+	0.581360i	$0.802521\pi$
$72$		0			0
$73$	4.49780	−	7.79042i	0.526428	−	0.911800i	−0.473098	−	0.881010i	$-0.656864\pi$
$73$	4.49780	−	7.79042i	0.526428	−	0.911800i	0.999526	−	0.0307901i	$-0.00980235\pi$
$74$		0			0
$75$	3.54138	−	1.43998i	0.408924	−	0.166274i
$76$		0			0
$77$	−11.4345	+	2.01621i	−1.30308	+	0.229769i
$78$		0			0
$79$	−0.121747	+	0.145093i	−0.0136976	+	0.0163242i	−0.772850	−	0.634589i	$-0.781169\pi$
$79$	−0.121747	+	0.145093i	−0.0136976	+	0.0163242i	0.759152	+	0.650913i	$0.225614\pi$
$80$		0			0
$81$	−3.29713	+	8.37430i	−0.366348	+	0.930478i
$82$		0			0
$83$	−0.651774	−	0.546903i	−0.0715414	−	0.0600304i	0.606316	−	0.795224i	$-0.292647\pi$
$83$	−0.651774	−	0.546903i	−0.0715414	−	0.0600304i	−0.677857	+	0.735194i	$0.737091\pi$
$84$		0			0
$85$	0.636052	+	3.60723i	0.0689896	+	0.391259i
$86$		0			0
$87$	4.55616	+	11.2051i	0.488472	+	1.20131i
$88$		0			0
$89$	8.08976	+	4.67063i	0.857513	+	0.495085i	0.863179	−	0.504899i	$-0.168470\pi$
$89$	8.08976	+	4.67063i	0.857513	+	0.495085i	−0.00566567	+	0.999984i	$0.501803\pi$
$90$		0			0
$91$	1.85172	−	1.06909i	0.194113	−	0.112071i
$92$		0			0
$93$	2.04211	−	6.33285i	0.211757	−	0.656686i
$94$		0			0
$95$	−0.576404	+	0.483661i	−0.0591379	+	0.0496225i
$96$		0			0
$97$	1.76799	−	0.643496i	0.179512	−	0.0653371i	−0.250700	−	0.968065i	$-0.580661\pi$
$97$	1.76799	−	0.643496i	0.179512	−	0.0653371i	0.430213	+	0.902728i	$0.358439\pi$
$98$		0			0
$99$	−15.7290	−	11.3213i	−1.58082	−	1.13783i
$100$		0			0
$101$	−12.1644	−	2.14491i	−1.21040	−	0.213426i	−0.468211	−	0.883617i	$-0.655101\pi$
$101$	−12.1644	−	2.14491i	−1.21040	−	0.213426i	−0.742189	+	0.670190i	$0.766212\pi$
$102$		0			0
$103$	3.59764	−	9.88443i	0.354486	−	0.973942i	−0.626425	−	0.779482i	$-0.715482\pi$
$103$	3.59764	−	9.88443i	0.354486	−	0.973942i	0.980910	−	0.194460i	$-0.0622954\pi$
$104$		0			0
$105$	2.76678	+	4.40595i	0.270010	+	0.429977i
$106$		0			0
$107$	7.83849			0.757775			0.378888	−	0.925443i	$-0.376307\pi$
$107$	7.83849			0.757775			0.378888	+	0.925443i	$0.376307\pi$
$108$		0			0
$109$	12.0933			1.15833			0.579164	−	0.815211i	$-0.303379\pi$
$109$	12.0933			1.15833			0.579164	+	0.815211i	$0.303379\pi$
$110$		0			0
$111$	−12.3937	+	0.460381i	−1.17636	+	0.0436975i
$112$		0			0
$113$	3.41089	−	9.37134i	0.320869	−	0.881581i	−0.669461	−	0.742848i	$-0.733475\pi$
$113$	3.41089	−	9.37134i	0.320869	−	0.881581i	0.990330	−	0.138733i	$-0.0443031\pi$
$114$		0			0
$115$	−14.6657	−	2.58595i	−1.36758	−	0.241141i
$116$		0			0
$117$	3.43490	+	0.968437i	0.317557	+	0.0895320i
$118$		0			0
$119$	3.70194	−	1.34739i	0.339356	−	0.123515i
$120$		0			0
$121$	23.5406	−	19.7529i	2.14006	−	1.79572i
$122$		0			0
$123$	1.79784	−	0.386321i	0.162106	−	0.0348334i
$124$		0			0
$125$	10.4308	−	6.02222i	0.932959	−	0.538644i
$126$		0			0
$127$	6.31220	+	3.64435i	0.560117	+	0.323384i	0.753193	−	0.657800i	$-0.228513\pi$
$127$	6.31220	+	3.64435i	0.560117	+	0.323384i	−0.193075	+	0.981184i	$0.561846\pi$
$128$		0			0
$129$	−18.0254	−	2.49246i	−1.58705	−	0.219449i
$130$		0			0
$131$	1.11458	+	6.32111i	0.0973814	+	0.552278i	0.993992	+	0.109457i	$0.0349111\pi$
$131$	1.11458	+	6.32111i	0.0973814	+	0.552278i	−0.896610	+	0.442821i	$0.853978\pi$
$132$		0			0
$133$	0.619937	+	0.520189i	0.0537554	+	0.0451061i
$134$		0			0
$135$	−2.04454	+	8.43955i	−0.175966	+	0.726361i
$136$		0			0
$137$	4.19216	−	4.99602i	0.358160	−	0.426839i	−0.556635	−	0.830757i	$-0.687908\pi$
$137$	4.19216	−	4.99602i	0.358160	−	0.426839i	0.914795	+	0.403919i	$0.132352\pi$
$138$		0			0
$139$	−17.0425	+	3.00505i	−1.44553	+	0.254885i	−0.840712	−	0.541482i	$-0.817863\pi$
$139$	−17.0425	+	3.00505i	−1.44553	+	0.254885i	−0.604813	+	0.796367i	$0.706752\pi$
$140$		0			0
$141$	6.13234	+	4.76919i	0.516436	+	0.401638i
$142$		0			0
$143$	−3.84235	+	6.65515i	−0.321313	+	0.556531i
$144$		0			0
$145$	5.83543	+	10.1073i	0.484606	+	0.839362i
$146$		0			0
$147$	−4.84211	+	4.37938i	−0.399371	+	0.361206i
$148$		0			0
$149$	5.34752	+	6.37292i	0.438086	+	0.522090i	0.939237	−	0.343269i	$-0.111534\pi$
$149$	5.34752	+	6.37292i	0.438086	+	0.522090i	−0.501151	+	0.865360i	$0.667090\pi$
$150$		0			0
$151$	−1.22535	−	3.36663i	−0.0997178	−	0.273973i	0.879795	−	0.475353i	$-0.157680\pi$
$151$	−1.22535	−	3.36663i	−0.0997178	−	0.273973i	−0.979513	+	0.201380i	$0.935457\pi$
$152$		0			0
$153$	5.92269	+	2.85617i	0.478821	+	0.230907i
$154$		0			0
$155$	1.11484	−	6.32255i	0.0895458	−	0.507840i
$156$		0			0
$157$	19.2548	+	7.00816i	1.53670	+	0.559312i	0.965250	−	0.261327i	$-0.0841602\pi$
$157$	19.2548	+	7.00816i	1.53670	+	0.559312i	0.571447	+	0.820639i	$0.306382\pi$
$158$		0			0
$159$	12.7739	+	6.75561i	1.01303	+	0.535755i
$160$		0			0
$161$			16.0166i			1.26228i
$162$		0			0
$163$		−	4.33569i		−	0.339598i	−0.985479	−	0.169799i	$-0.945688\pi$
$163$		−	4.33569i		−	0.339598i	0.985479	−	0.169799i	$-0.0543118\pi$
$164$		0			0
$165$	−16.5293	−	8.74170i	−1.28680	−	0.680540i
$166$		0			0
$167$	15.0532	+	5.47891i	1.16485	+	0.423971i	0.850828	−	0.525444i	$-0.176101\pi$
$167$	15.0532	+	5.47891i	1.16485	+	0.423971i	0.314023	+	0.949415i	$0.398323\pi$
$168$		0			0
$169$	−2.01169	+	11.4088i	−0.154745	+	0.877603i
$170$		0			0
$171$	0.100212	+	1.34702i	0.00766344	+	0.103009i
$172$		0			0
$173$	5.96699	+	16.3942i	0.453662	+	1.24643i	0.930129	+	0.367233i	$0.119695\pi$
$173$	5.96699	+	16.3942i	0.453662	+	1.24643i	−0.476467	+	0.879192i	$0.658083\pi$
$174$		0			0
$175$	−2.55004	−	3.03902i	−0.192765	−	0.229728i
$176$		0			0
$177$	17.1826	−	15.5406i	1.29152	−	1.16810i
$178$		0			0
$179$	9.30716	+	16.1205i	0.695650	+	1.20490i	0.969961	+	0.243260i	$0.0782168\pi$
$179$	9.30716	+	16.1205i	0.695650	+	1.20490i	−0.274311	+	0.961641i	$0.588450\pi$
$180$		0			0
$181$	−5.80023	+	10.0463i	−0.431128	+	0.746736i	−0.996971	−	0.0777776i	$-0.975218\pi$
$181$	−5.80023	+	10.0463i	−0.431128	+	0.746736i	0.565843	+	0.824513i	$0.308551\pi$
$182$		0			0
$183$	4.74036	+	3.68664i	0.350418	+	0.272524i
$184$		0			0
$185$	−11.7845	+	2.07793i	−0.866415	+	0.152772i
$186$		0			0
$187$	−9.10109	+	10.8463i	−0.665538	+	0.793157i
$188$		0			0
$189$	9.32089	+	0.589349i	0.677995	+	0.0428688i
$190$		0			0
$191$	−17.3501	−	14.5585i	−1.25541	−	1.05342i	−0.996155	−	0.0876068i	$-0.972078\pi$
$191$	−17.3501	−	14.5585i	−1.25541	−	1.05342i	−0.259256	−	0.965809i	$-0.583477\pi$
$192$		0			0
$193$	−1.29222	−	7.32852i	−0.0930157	−	0.527519i	−0.995337	−	0.0964550i	$-0.969250\pi$
$193$	−1.29222	−	7.32852i	−0.0930157	−	0.527519i	0.902322	−	0.431063i	$-0.141862\pi$
$194$		0			0
$195$	3.41092	+	0.471645i	0.244261	+	0.0337752i
$196$		0			0
$197$	14.7216	+	8.49954i	1.04887	+	0.605567i	0.922333	−	0.386395i	$-0.126280\pi$
$197$	14.7216	+	8.49954i	1.04887	+	0.605567i	0.126539	+	0.991962i	$0.459613\pi$
$198$		0			0
$199$	16.0104	−	9.24360i	1.13495	−	0.655261i	0.189772	−	0.981828i	$-0.439225\pi$
$199$	16.0104	−	9.24360i	1.13495	−	0.655261i	0.945174	+	0.326567i	$0.105892\pi$
$200$		0			0
$201$	8.11429	−	1.74360i	0.572338	−	0.122984i
$202$		0			0
$203$	9.61562	−	8.06846i	0.674884	−	0.566295i
$204$		0			0
$205$	1.66724	−	0.606827i	0.116445	−	0.0423827i
$206$		0			0
$207$	−19.1475	+	18.6557i	−1.33084	+	1.29666i
$208$		0			0
$209$	−2.86436	−	0.505065i	−0.198132	−	0.0349360i
$210$		0			0
$211$	−1.97577	+	5.42839i	−0.136018	+	0.373706i	−0.988937	−	0.148337i	$-0.952608\pi$
$211$	−1.97577	+	5.42839i	−0.136018	+	0.373706i	0.852919	+	0.522043i	$0.174830\pi$
$212$		0			0
$213$	2.81914	−	0.104721i	0.193164	−	0.00717537i
$214$		0			0
$215$	−17.5573			−1.19740
$216$		0			0
$217$	−6.90496			−0.468739
$218$		0			0
$219$	−8.28594	−	13.1949i	−0.559912	−	0.891630i
$220$		0			0
$221$	0.891775	−	2.45013i	0.0599873	−	0.164814i
$222$		0			0
$223$	−5.42636	−	0.956814i	−0.363376	−	0.0640730i	−0.0110207	−	0.999939i	$-0.503508\pi$
$223$	−5.42636	−	0.956814i	−0.363376	−	0.0640730i	−0.352355	+	0.935866i	$0.614619\pi$
$224$		0			0
$225$	0.662857	−	6.58828i	0.0441905	−	0.439219i
$226$		0			0
$227$	−9.11368	+	3.31711i	−0.604896	+	0.220164i	−0.626269	−	0.779607i	$-0.715419\pi$
$227$	−9.11368	+	3.31711i	−0.604896	+	0.220164i	0.0213722	+	0.999772i	$0.493196\pi$
$228$		0			0
$229$	5.03255	−	4.22281i	0.332560	−	0.279051i	−0.461182	−	0.887306i	$-0.652574\pi$
$229$	5.03255	−	4.22281i	0.332560	−	0.279051i	0.793742	+	0.608254i	$0.208130\pi$
$230$		0			0
$231$	−6.17202	+	19.1402i	−0.406089	+	1.25933i
$232$		0			0
$233$	−14.2815	+	8.24540i	−0.935609	+	0.540174i	−0.888581	−	0.458719i	$-0.848308\pi$
$233$	−14.2815	+	8.24540i	−0.935609	+	0.540174i	−0.0470281	+	0.998894i	$0.514975\pi$
$234$		0			0
$235$	6.49132	+	3.74776i	0.423447	+	0.244477i
$236$		0			0
$237$	0.123569	+	0.303897i	0.00802666	+	0.0197402i
$238$		0			0
$239$	2.37714	+	13.4814i	0.153764	+	0.872040i	0.959907	+	0.280319i	$0.0904401\pi$
$239$	2.37714	+	13.4814i	0.153764	+	0.872040i	−0.806143	+	0.591721i	$0.798449\pi$
$240$		0			0
$241$	5.16159	+	4.33109i	0.332487	+	0.278990i	0.793712	−	0.608293i	$-0.208146\pi$
$241$	5.16159	+	4.33109i	0.332487	+	0.278990i	−0.461225	+	0.887283i	$0.652590\pi$
$242$		0			0
$243$	10.1522	+	11.8294i	0.651262	+	0.758853i
$244$		0			0
$245$	−4.04912	+	4.82555i	−0.258689	+	0.308293i
$246$		0			0
$247$	0.527479	−	0.0930089i	0.0335627	−	0.00591801i
$248$		0			0
$249$	−1.36514	+	0.555086i	−0.0865124	+	0.0351772i
$250$		0			0
$251$	−1.39352	+	2.41364i	−0.0879580	+	0.152348i	−0.906648	−	0.421888i	$-0.861367\pi$
$251$	−1.39352	+	2.41364i	−0.0879580	+	0.152348i	0.818690	+	0.574236i	$0.194701\pi$
$252$		0			0
$253$	−28.7822	−	49.8521i	−1.80952	−	3.13418i
$254$		0			0
$255$	6.03813	+	1.94708i	0.378122	+	0.121931i
$256$		0			0
$257$	−5.30928	−	6.32735i	−0.331184	−	0.394689i	0.574597	−	0.818437i	$-0.305159\pi$
$257$	−5.30928	−	6.32735i	−0.331184	−	0.394689i	−0.905780	+	0.423747i	$0.860714\pi$
$258$		0			0
$259$	4.40182	+	12.0939i	0.273516	+	0.751479i
$260$		0			0
$261$	20.8457	+	2.09731i	1.29031	+	0.129820i
$262$		0			0
$263$	1.60610	−	9.10864i	0.0990363	−	0.561663i	−0.894399	−	0.447269i	$-0.852397\pi$
$263$	1.60610	−	9.10864i	0.0990363	−	0.561663i	0.993436	−	0.114393i	$-0.0364924\pi$
$264$		0			0
$265$	13.1015	+	4.76857i	0.804822	+	0.292931i
$266$		0			0
$267$	13.7019	−	8.60432i	0.838544	−	0.526576i
$268$		0			0
$269$		−	17.1387i		−	1.04496i	−0.852650	−	0.522482i	$-0.825006\pi$
$269$		−	17.1387i		−	1.04496i	0.852650	−	0.522482i	$-0.174994\pi$
$270$		0			0
$271$		−	18.4354i		−	1.11987i	−0.828536	−	0.559936i	$-0.810826\pi$
$271$		−	18.4354i		−	1.11987i	0.828536	−	0.559936i	$-0.189174\pi$
$272$		0			0
$273$	−0.137475	−	3.70088i	−0.00832034	−	0.223988i
$274$		0			0
$275$	13.3983	+	4.87657i	0.807945	+	0.294068i
$276$		0			0
$277$	−0.199280	+	1.13017i	−0.0119736	+	0.0679055i	−0.990209	−	0.139592i	$-0.955421\pi$
$277$	−0.199280	+	1.13017i	−0.0119736	+	0.0679055i	0.978236	+	0.207498i	$0.0665319\pi$
$278$		0			0
$279$	−8.04271	−	8.25471i	−0.481505	−	0.494197i
$280$		0			0
$281$	6.92579	+	19.0285i	0.413158	+	1.13514i	0.955502	+	0.294986i	$0.0953150\pi$
$281$	6.92579	+	19.0285i	0.413158	+	1.13514i	−0.542343	+	0.840157i	$0.682463\pi$
$282$		0			0
$283$	17.0820	+	20.3576i	1.01542	+	1.21013i	0.977519	+	0.210849i	$0.0676230\pi$
$283$	17.0820	+	20.3576i	1.01542	+	1.21013i	0.0379018	+	0.999281i	$0.487933\pi$
$284$		0			0
$285$	0.273798	+	1.27418i	0.0162184	+	0.0754761i
$286$		0			0
$287$	−0.954122	−	1.65259i	−0.0563200	−	0.0975492i
$288$		0			0
$289$	−6.09800	+	10.5621i	−0.358706	+	0.621297i
$290$		0			0
$291$	0.446360	−	3.22806i	0.0261661	−	0.189232i
$292$		0			0
$293$	29.7155	−	5.23964i	1.73600	−	0.306103i	0.785969	−	0.618266i	$-0.212165\pi$
$293$	29.7155	−	5.23964i	1.73600	−	0.306103i	0.950029	+	0.312163i	$0.101053\pi$
$294$		0			0
$295$	14.3686	−	17.1238i	0.836573	−	0.996989i
$296$		0			0
$297$	−30.0706	+	14.9155i	−1.74487	+	0.865483i
$298$		0			0
$299$	8.12053	+	6.81394i	0.469623	+	0.394060i
$300$		0			0
$301$	3.27905	+	18.5964i	0.189001	+	1.07188i
$302$		0			0
$303$	−13.1342	+	16.8882i	−0.754538	+	0.970202i
$304$		0			0
$305$	5.01786	+	2.89706i	0.287322	+	0.165885i
$306$		0			0
$307$	−29.6012	+	17.0902i	−1.68943	+	0.975392i	−0.734476	+	0.678635i	$0.762572\pi$
$307$	−29.6012	+	17.0902i	−1.68943	+	0.975392i	−0.954953	+	0.296757i	$0.904095\pi$
$308$		0			0
$309$	−12.2210	−	13.5123i	−0.695229	−	0.768687i
$310$		0			0
$311$	8.79363	−	7.37873i	0.498641	−	0.418410i	−0.358470	−	0.933541i	$-0.616701\pi$
$311$	8.79363	−	7.37873i	0.498641	−	0.418410i	0.857111	+	0.515132i	$0.172257\pi$
$312$		0			0
$313$	−22.2890	+	8.11254i	−1.25985	+	0.458548i	−0.883719	−	0.468018i	$-0.844968\pi$
$313$	−22.2890	+	8.11254i	−1.25985	+	0.458548i	−0.376131	+	0.926566i	$0.622746\pi$
$314$		0			0
$315$	8.98641	−	0.668549i	0.506327	−	0.0376685i
$316$		0			0
$317$	−28.1842	−	4.96963i	−1.58298	−	0.279122i	−0.688164	−	0.725555i	$-0.741583\pi$
$317$	−28.1842	−	4.96963i	−1.58298	−	0.279122i	−0.894817	+	0.446433i	$0.852694\pi$
$318$		0			0
$319$	−15.4297	+	42.3928i	−0.863898	+	2.37354i
$320$		0			0
$321$	6.34720	−	12.0016i	0.354266	−	0.669865i
$322$		0			0
$323$	0.986855			0.0549101
$324$		0			0
$325$	−2.62567			−0.145646
$326$		0			0
$327$	9.79252	−	18.5162i	0.541527	−	1.02395i
$328$		0			0
$329$	2.75724	−	7.57545i	0.152011	−	0.417648i
$330$		0			0
$331$	4.86633	+	0.858065i	0.267477	+	0.0471635i	0.305778	−	0.952103i	$-0.401083\pi$
$331$	4.86633	+	0.858065i	0.267477	+	0.0471635i	−0.0383008	+	0.999266i	$0.512194\pi$
$332$		0			0
$333$	−9.33085	+	19.3489i	−0.511327	+	1.06031i
$334$		0			0
$335$	7.52487	−	2.73883i	0.411127	−	0.149638i
$336$		0			0
$337$	−12.3480	+	10.3612i	−0.672640	+	0.564412i	−0.913846	−	0.406062i	$-0.866902\pi$
$337$	−12.3480	+	10.3612i	−0.672640	+	0.564412i	0.241205	+	0.970474i	$0.422457\pi$
$338$		0			0
$339$	−11.5866	−	12.8109i	−0.629299	−	0.695791i
$340$		0			0
$341$	21.4919	−	12.4084i	1.16385	−	0.671950i
$342$		0			0
$343$	16.7635	+	9.67839i	0.905142	+	0.522584i
$344$		0			0
$345$	−15.8349	+	20.3608i	−0.852520	+	1.09619i
$346$		0			0
$347$	0.130418	+	0.739634i	0.00700118	+	0.0397057i	0.988108	−	0.153760i	$-0.0491383\pi$
$347$	0.130418	+	0.739634i	0.00700118	+	0.0397057i	−0.981107	+	0.193466i	$0.938027\pi$
$348$		0			0
$349$	20.7774	+	17.4343i	1.11219	+	0.933237i	0.998184	−	0.0602428i	$-0.0191875\pi$
$349$	20.7774	+	17.4343i	1.11219	+	0.933237i	0.114005	+	0.993480i	$0.463632\pi$
$350$		0			0
$351$	4.26419	−	4.47503i	0.227605	−	0.238860i
$352$		0			0
$353$	−3.94779	+	4.70480i	−0.210120	+	0.250411i	−0.860803	−	0.508938i	$-0.830038\pi$
$353$	−3.94779	+	4.70480i	−0.210120	+	0.250411i	0.650683	+	0.759349i	$0.274483\pi$
$354$		0			0
$355$	2.68058	−	0.472658i	0.142270	−	0.0250861i
$356$		0			0
$357$	0.934618	−	6.75913i	0.0494652	−	0.357731i
$358$		0			0
$359$	−10.1221	+	17.5320i	−0.534225	+	0.925305i	0.464976	+	0.885324i	$0.346063\pi$
$359$	−10.1221	+	17.5320i	−0.534225	+	0.925305i	−0.999200	+	0.0399811i	$0.987270\pi$
$360$		0			0
$361$	−9.39864	−	16.2789i	−0.494665	−	0.856785i
$362$		0			0
$363$	−11.1820	−	52.0383i	−0.586904	−	2.73130i
$364$		0			0
$365$	−9.66316	−	11.5161i	−0.505793	−	0.602781i
$366$		0			0
$367$	−12.7400	−	35.0029i	−0.665024	−	1.82714i	−0.552545	−	0.833483i	$-0.686343\pi$
$367$	−12.7400	−	35.0029i	−0.665024	−	1.82714i	−0.112478	−	0.993654i	$-0.535879\pi$
$368$		0			0
$369$	0.864293	−	3.06552i	0.0449933	−	0.159585i
$370$		0			0
$371$	2.60392	−	14.7676i	0.135189	−	0.766693i
$372$		0			0
$373$	−12.7209	−	4.63003i	−0.658664	−	0.239734i	−0.00900450	−	0.999959i	$-0.502866\pi$
$373$	−12.7209	−	4.63003i	−0.658664	−	0.239734i	−0.649659	+	0.760225i	$0.725088\pi$
$374$		0			0
$375$	−0.774400	−	20.8472i	−0.0399899	−	1.07655i
$376$		0			0
$377$		−	8.30775i		−	0.427871i
$378$		0			0
$379$		−	33.1871i		−	1.70471i	−0.522964	−	0.852355i	$-0.675174\pi$
$379$		−	33.1871i		−	1.70471i	0.522964	−	0.852355i	$-0.324826\pi$
$380$		0			0
$381$	10.6912	−	6.71369i	0.547727	−	0.343953i
$382$		0			0
$383$	−17.3496	−	6.31475i	−0.886525	−	0.322669i	−0.141685	−	0.989912i	$-0.545252\pi$
$383$	−17.3496	−	6.31475i	−0.886525	−	0.322669i	−0.744840	+	0.667243i	$0.767474\pi$
$384$		0			0
$385$	−3.36944	+	19.1091i	−0.171723	+	0.973888i
$386$		0			0
$387$	−18.4122	+	25.5806i	−0.935946	+	1.30034i
$388$		0			0
$389$	−4.44341	−	12.2082i	−0.225290	−	0.618979i	0.774620	−	0.632428i	$-0.217941\pi$
$389$	−4.44341	−	12.2082i	−0.225290	−	0.618979i	−0.999910	+	0.0134483i	$0.995719\pi$
$390$		0			0
$391$	12.5544	+	14.9618i	0.634905	+	0.756650i
$392$		0			0
$393$	10.5809	+	3.41195i	0.533734	+	0.172110i
$394$		0			0
$395$	0.158264	+	0.274122i	0.00796314	+	0.0137926i
$396$		0			0
$397$	−1.14814	+	1.98863i	−0.0576234	+	0.0998067i	−0.893398	−	0.449266i	$-0.851686\pi$
$397$	−1.14814	+	1.98863i	−0.0576234	+	0.0998067i	0.835775	+	0.549073i	$0.185019\pi$
$398$		0			0
$399$	1.29846	−	0.527973i	0.0650044	−	0.0264317i
$400$		0			0
$401$	31.9343	−	5.63088i	1.59472	−	0.281193i	0.695448	−	0.718576i	$-0.255206\pi$
$401$	31.9343	−	5.63088i	1.59472	−	0.281193i	0.899275	+	0.437383i	$0.144095\pi$
$402$		0			0
$403$	−2.93758	+	3.50087i	−0.146331	+	0.174391i
$404$		0			0
$405$	11.2664	+	9.96432i	0.559830	+	0.495131i
$406$		0			0
$407$	−35.4338	−	29.7325i	−1.75639	−	1.47378i
$408$		0			0
$409$	−3.53137	−	20.0274i	−0.174615	−	0.990290i	−0.938587	−	0.345042i	$-0.887865\pi$
$409$	−3.53137	−	20.0274i	−0.174615	−	0.990290i	0.763973	−	0.645249i	$-0.223246\pi$
$410$		0			0
$411$	−4.25489	−	10.4642i	−0.209878	−	0.516160i
$412$		0			0
$413$	−20.8208	−	12.0209i	−1.02453	−	0.591511i
$414$		0			0
$415$	−1.23139	+	0.710942i	−0.0604465	+	0.0348988i
$416$		0			0
$417$	−9.19904	+	28.5273i	−0.450479	+	1.39699i
$418$		0			0
$419$	14.4740	−	12.1451i	0.707101	−	0.593328i	−0.216683	−	0.976242i	$-0.569524\pi$
$419$	14.4740	−	12.1451i	0.707101	−	0.593328i	0.923784	+	0.382914i	$0.125079\pi$
$420$		0			0
$421$	14.1732	−	5.15861i	0.690757	−	0.251415i	0.0272979	−	0.999627i	$-0.491310\pi$
$421$	14.1732	−	5.15861i	0.690757	−	0.251415i	0.663459	+	0.748212i	$0.269088\pi$
$422$		0			0
$423$	12.2678	−	5.52746i	0.596482	−	0.268754i
$424$		0			0
$425$	−4.76421	−	0.840058i	−0.231098	−	0.0407488i
$426$		0			0
$427$	2.13137	−	5.85590i	0.103144	−	0.283387i
$428$		0			0
$429$	7.07845	+	11.2721i	0.341751	+	0.544220i
$430$		0			0
$431$	−6.19366			−0.298338			−0.149169	−	0.988812i	$-0.547660\pi$
$431$	−6.19366			−0.298338			−0.149169	+	0.988812i	$0.547660\pi$
$432$		0			0
$433$	−3.19532			−0.153557			−0.0767786	−	0.997048i	$-0.524463\pi$
$433$	−3.19532			−0.153557			−0.0767786	+	0.997048i	$0.524463\pi$
$434$		0			0
$435$	20.2006	−	0.750380i	0.968544	−	0.0359780i
$436$		0			0
$437$	−1.37225	+	3.77022i	−0.0656434	+	0.180354i
$438$		0			0
$439$	−7.52759	−	1.32732i	−0.359272	−	0.0633494i	−0.00890123	−	0.999960i	$-0.502833\pi$
$439$	−7.52759	−	1.32732i	−0.359272	−	0.0633494i	−0.350371	+	0.936611i	$0.613944\pi$
$440$		0			0
$441$	2.78445	+	10.9600i	0.132593	+	0.521906i
$442$		0			0
$443$	−1.59664	+	0.581128i	−0.0758585	+	0.0276102i	−0.379671	−	0.925122i	$-0.623963\pi$
$443$	−1.59664	+	0.581128i	−0.0758585	+	0.0276102i	0.303812	+	0.952732i	$0.401740\pi$
$444$		0			0
$445$	11.9586	−	10.0345i	0.566892	−	0.475679i
$446$		0			0
$447$	14.0878	−	3.02720i	0.666330	−	0.143182i
$448$		0			0
$449$	−6.79214	+	3.92144i	−0.320541	+	0.185064i	−0.651634	−	0.758534i	$-0.725916\pi$
$449$	−6.79214	+	3.92144i	−0.320541	+	0.185064i	0.331093	+	0.943598i	$0.392583\pi$
$450$		0			0
$451$	5.93947	+	3.42915i	0.279679	+	0.161472i
$452$		0			0
$453$	−6.14692	−	0.849965i	−0.288808	−	0.0399348i
$454$		0			0
$455$	−0.620491	−	3.51898i	−0.0290891	−	0.164972i
$456$		0			0
$457$	−24.1977	−	20.3043i	−1.13192	−	0.949794i	−0.132775	−	0.991146i	$-0.542389\pi$
$457$	−24.1977	−	20.3043i	−1.13192	−	0.949794i	−0.999145	+	0.0413525i	$0.986833\pi$
$458$		0			0
$459$	9.16900	−	6.75554i	0.427972	−	0.315322i
$460$		0			0
$461$	−19.7022	+	23.4801i	−0.917621	+	1.09358i	0.0777021	+	0.996977i	$0.475242\pi$
$461$	−19.7022	+	23.4801i	−0.917621	+	1.09358i	−0.995323	+	0.0966015i	$0.969203\pi$
$462$		0			0
$463$	29.1633	−	5.14227i	1.35533	−	0.238981i	0.551667	−	0.834064i	$-0.313992\pi$
$463$	29.1633	−	5.14227i	1.35533	−	0.238981i	0.803664	+	0.595083i	$0.202881\pi$
$464$		0			0
$465$	−8.77781	−	6.82661i	−0.407061	−	0.316576i
$466$		0			0
$467$	−6.70629	+	11.6156i	−0.310330	+	0.537507i	−0.978434	−	0.206561i	$-0.933773\pi$
$467$	−6.70629	+	11.6156i	−0.310330	+	0.537507i	0.668104	+	0.744068i	$0.267106\pi$
$468$		0			0
$469$	−4.30629	−	7.45872i	−0.198846	−	0.344411i
$470$		0			0
$471$	26.3218	−	23.8064i	1.21284	−	1.09694i
$472$		0			0
$473$	−43.6243	−	51.9894i	−2.00585	−	2.39048i
$474$		0			0
$475$	−0.339892	−	0.933847i	−0.0155953	−	0.0428478i
$476$		0			0
$477$	20.6872	−	14.0879i	0.947203	−	0.645042i
$478$		0			0
$479$	−1.03280	+	5.85729i	−0.0471898	+	0.267627i	−0.999269	−	0.0382244i	$-0.987830\pi$
$479$	−1.03280	+	5.85729i	−0.0471898	+	0.267627i	0.952079	+	0.305851i	$0.0989409\pi$
$480$		0			0
$481$	8.00437	+	2.91335i	0.364968	+	0.132837i
$482$		0			0
$483$	24.5232	+	12.9694i	1.11585	+	0.590128i
$484$		0			0
$485$		−	3.14424i		−	0.142773i
$486$		0			0
$487$		−	7.58169i		−	0.343559i	−0.985135	−	0.171780i	$-0.945048\pi$
$487$		−	7.58169i		−	0.343559i	0.985135	−	0.171780i	$-0.0549517\pi$
$488$		0			0
$489$	−6.63844	−	3.51081i	−0.300201	−	0.158765i
$490$		0			0
$491$	−27.5116	−	10.0134i	−1.24158	−	0.451899i	−0.364034	−	0.931386i	$-0.618601\pi$
$491$	−27.5116	−	10.0134i	−1.24158	−	0.451899i	−0.877549	+	0.479487i	$0.840823\pi$
$492$		0			0
$493$	2.65799	−	15.0742i	0.119710	−	0.678907i
$494$		0			0
$495$	−26.7691	+	18.2296i	−1.20318	+	0.819361i
$496$		0			0
$497$	−1.00126	−	2.75095i	−0.0449129	−	0.123397i
$498$		0			0
$499$	−3.52029	−	4.19532i	−0.157590	−	0.187808i	0.681472	−	0.731844i	$-0.261340\pi$
$499$	−3.52029	−	4.19532i	−0.157590	−	0.187808i	−0.839062	+	0.544036i	$0.816896\pi$
$500$		0			0
$501$	20.5781	−	18.6116i	0.919363	−	0.831506i
$502$		0			0
$503$	−2.79350	−	4.83848i	−0.124556	−	0.215737i	0.797003	−	0.603975i	$-0.206417\pi$
$503$	−2.79350	−	4.83848i	−0.124556	−	0.215737i	−0.921559	+	0.388238i	$0.873084\pi$
$504$		0			0
$505$	−10.3212	+	17.8768i	−0.459287	+	0.795508i
$506$		0			0
$507$	15.8393	+	12.3184i	0.703447	+	0.547079i
$508$		0			0
$509$	23.2698	−	4.10310i	1.03142	−	0.181867i	0.367773	−	0.929916i	$-0.380120\pi$
$509$	23.2698	−	4.10310i	1.03142	−	0.181867i	0.663643	+	0.748049i	$0.269009\pi$
$510$		0			0
$511$	−10.3930	+	12.3859i	−0.459758	+	0.547918i
$512$		0			0
$513$	2.14359	+	0.937311i	0.0946418	+	0.0413833i
$514$		0			0
$515$	−13.4661	−	11.2994i	−0.593386	−	0.497910i
$516$		0			0
$517$	5.03125	+	28.5336i	0.221274	+	1.25491i
$518$		0			0
$519$	29.9331	+	4.13899i	1.31392	+	0.181682i
$520$		0			0
$521$	12.6087	+	7.27965i	0.552398	+	0.318927i	0.750089	−	0.661337i	$-0.230011\pi$
$521$	12.6087	+	7.27965i	0.552398	+	0.318927i	−0.197690	+	0.980265i	$0.563344\pi$
$522$		0			0
$523$	27.3579	−	15.7951i	1.19628	−	0.690671i	0.236553	−	0.971618i	$-0.423982\pi$
$523$	27.3579	−	15.7951i	1.19628	−	0.690671i	0.959723	+	0.280948i	$0.0906488\pi$
$524$		0			0
$525$	−6.71797	+	1.44356i	−0.293196	+	0.0630023i
$526$		0			0
$527$	−6.45022	+	5.41238i	−0.280976	+	0.235767i
$528$		0			0
$529$	−53.0049	+	19.2922i	−2.30456	+	0.838792i
$530$		0			0
$531$	−9.88083	−	38.8925i	−0.428792	−	1.68779i
$532$		0			0
$533$	−1.24379	−	0.219313i	−0.0538744	−	0.00949950i
$534$		0			0
$535$	4.48028	−	12.3095i	0.193700	−	0.532185i
$536$		0			0
$537$	32.2187	−	1.19681i	1.39034	−	0.0516462i
$538$		0			0
$539$	−24.3499			−1.04882
$540$		0			0
$541$	−28.5672			−1.22820			−0.614100	−	0.789229i	$-0.710481\pi$
$541$	−28.5672			−1.22820			−0.614100	+	0.789229i	$0.710481\pi$
$542$		0			0
$543$	10.6853	+	17.0158i	0.458550	+	0.730217i
$544$		0			0
$545$	6.91223	−	18.9912i	0.296087	−	0.813493i
$546$		0			0
$547$	−20.1118	−	3.54626i	−0.859920	−	0.151627i	−0.273736	−	0.961805i	$-0.588259\pi$
$547$	−20.1118	−	3.54626i	−0.859920	−	0.151627i	−0.586184	+	0.810178i	$0.699370\pi$
$548$		0			0
$549$	9.48316	−	4.27279i	0.404731	−	0.182358i
$550$		0			0
$551$	2.95474	−	1.07544i	0.125876	−	0.0458151i
$552$		0			0
$553$	0.260788	−	0.218827i	0.0110898	−	0.00930547i
$554$		0			0
$555$	−6.36094	+	19.7260i	−0.270007	+	0.837324i
$556$		0			0
$557$	13.9529	−	8.05574i	0.591205	−	0.341333i	−0.174369	−	0.984680i	$-0.555788\pi$
$557$	13.9529	−	8.05574i	0.591205	−	0.341333i	0.765574	+	0.643348i	$0.222455\pi$
$558$		0			0
$559$	10.8235	+	6.24897i	0.457787	+	0.264303i
$560$		0			0
$561$	9.23727	+	22.7175i	0.389998	+	0.959135i
$562$		0			0
$563$	1.32416	+	7.50966i	0.0558065	+	0.316495i	0.999914	−	0.0131443i	$-0.00418409\pi$
$563$	1.32416	+	7.50966i	0.0558065	+	0.316495i	−0.944107	+	0.329639i	$0.893073\pi$
$564$		0			0
$565$	−12.7671	−	10.7128i	−0.537114	−	0.450693i
$566$		0			0
$567$	8.44992	−	13.7941i	0.354863	−	0.579298i
$568$		0			0
$569$	−8.19563	+	9.76717i	−0.343579	+	0.409461i	−0.909969	−	0.414676i	$-0.863895\pi$
$569$	−8.19563	+	9.76717i	−0.343579	+	0.409461i	0.566390	+	0.824137i	$0.308339\pi$
$570$		0			0
$571$	−24.8917	+	4.38908i	−1.04169	+	0.183677i	−0.668218	−	0.743966i	$-0.732943\pi$
$571$	−24.8917	+	4.38908i	−1.04169	+	0.183677i	−0.373468	+	0.927643i	$0.621832\pi$
$572$		0			0
$573$	−36.3399	+	14.7763i	−1.51812	+	0.617290i
$574$		0			0
$575$	9.83414	−	17.0332i	0.410112	−	0.710335i
$576$		0			0
$577$	−7.44201	−	12.8899i	−0.309815	−	0.536615i	0.668507	−	0.743706i	$-0.266934\pi$
$577$	−7.44201	−	12.8899i	−0.309815	−	0.536615i	−0.978322	+	0.207091i	$0.933600\pi$
$578$		0			0
$579$	−12.2672	−	3.95572i	−0.509806	−	0.164394i
$580$		0			0
$581$	0.982997	+	1.17149i	0.0407816	+	0.0486016i
$582$		0			0
$583$	18.4328	+	50.6437i	0.763409	+	2.09745i
$584$		0			0
$585$	3.48413	−	4.84059i	0.144051	−	0.200134i
$586$		0			0
$587$	−1.14073	+	6.46942i	−0.0470831	+	0.267021i	−0.999257	−	0.0385343i	$-0.987731\pi$
$587$	−1.14073	+	6.46942i	−0.0470831	+	0.267021i	0.952174	+	0.305556i	$0.0988422\pi$
$588$		0			0
$589$	−1.62539	−	0.591593i	−0.0669730	−	0.0243762i
$590$		0			0
$591$	24.9346	−	15.6580i	1.02567	−	0.644084i
$592$		0			0
$593$			14.7990i			0.607720i	0.952717	+	0.303860i	$0.0982756\pi$
$593$			14.7990i			0.607720i	−0.952717	+	0.303860i	$0.901724\pi$
$594$		0			0
$595$		−	6.58362i		−	0.269902i
$596$		0			0
$597$	−1.18864	−	31.9987i	−0.0486477	−	1.30962i
$598$		0			0
$599$	−5.68264	−	2.06831i	−0.232186	−	0.0845089i	0.223307	−	0.974748i	$-0.428315\pi$
$599$	−5.68264	−	2.06831i	−0.232186	−	0.0845089i	−0.455493	+	0.890239i	$0.650537\pi$
$600$		0			0
$601$	−2.62951	+	14.9127i	−0.107260	+	0.608302i	0.883033	+	0.469310i	$0.155497\pi$
$601$	−2.62951	+	14.9127i	−0.107260	+	0.608302i	−0.990294	+	0.138992i	$0.955614\pi$
$602$		0			0
$603$	3.90086	−	13.8358i	0.158855	−	0.563436i
$604$		0			0
$605$	−17.5646	−	48.2582i	−0.714101	−	1.96198i
$606$		0			0
$607$	1.27053	+	1.51416i	0.0515692	+	0.0614577i	0.791212	−	0.611541i	$-0.209450\pi$
$607$	1.27053	+	1.51416i	0.0515692	+	0.0614577i	−0.739643	+	0.672999i	$0.765006\pi$
$608$		0			0
$609$	−4.56751	−	21.2560i	−0.185085	−	0.861337i
$610$		0			0
$611$	−2.66780	−	4.62076i	−0.107928	−	0.186936i
$612$		0			0
$613$	−15.0938	+	26.1432i	−0.609633	+	1.05591i	0.381668	+	0.924299i	$0.375350\pi$
$613$	−15.0938	+	26.1432i	−0.609633	+	1.05591i	−0.991301	+	0.131615i	$0.957984\pi$
$614$		0			0
$615$	0.420925	−	3.04412i	0.0169733	−	0.122751i
$616$		0			0
$617$	−42.6702	+	7.52390i	−1.71784	+	0.302901i	−0.943868	−	0.330323i	$-0.892842\pi$
$617$	−42.6702	+	7.52390i	−1.71784	+	0.302901i	−0.773969	+	0.633224i	$0.781731\pi$
$618$		0			0
$619$	−3.72666	+	4.44126i	−0.149787	+	0.178509i	−0.835721	−	0.549155i	$-0.814950\pi$
$619$	−3.72666	+	4.44126i	−0.149787	+	0.178509i	0.685933	+	0.727664i	$0.259394\pi$
$620$		0			0
$621$	13.0594	+	44.4233i	0.524055	+	1.78265i
$622$		0			0
$623$	−12.8618	−	10.7923i	−0.515296	−	0.432385i
$624$		0			0
$625$	−1.57889	−	8.95432i	−0.0631555	−	0.358173i
$626$		0			0
$627$	−3.09272	+	3.97669i	−0.123511	+	0.158814i
$628$		0			0
$629$	13.5916	+	7.84712i	0.541933	+	0.312885i
$630$		0			0
$631$	−24.2521	+	14.0020i	−0.965462	+	0.557410i	−0.897850	−	0.440302i	$-0.854871\pi$
$631$	−24.2521	+	14.0020i	−0.965462	+	0.557410i	−0.0676120	+	0.997712i	$0.521538\pi$
$632$		0			0
$633$	6.71161	+	7.42076i	0.266763	+	0.294949i
$634$		0			0
$635$	9.33094	−	7.82959i	0.370287	−	0.310708i
$636$		0			0
$637$	4.21366	−	1.53365i	0.166951	−	0.0607653i
$638$		0			0
$639$	2.12245	−	4.40122i	0.0839629	−	0.174110i
$640$		0			0
$641$	36.3599	+	6.41124i	1.43613	+	0.253229i	0.836904	−	0.547350i	$-0.184363\pi$
$641$	36.3599	+	6.41124i	1.43613	+	0.253229i	0.599228	+	0.800579i	$0.295474\pi$
$642$		0			0
$643$	−15.3069	+	42.0554i	−0.603646	+	1.65850i	0.140178	+	0.990126i	$0.455233\pi$
$643$	−15.3069	+	42.0554i	−0.603646	+	1.65850i	−0.743823	+	0.668376i	$0.766990\pi$
$644$		0			0
$645$	−14.2170	+	26.8822i	−0.559793	+	1.05849i
$646$		0			0
$647$	11.3736			0.447144			0.223572	−	0.974687i	$-0.428228\pi$
$647$	11.3736			0.447144			0.223572	+	0.974687i	$0.428228\pi$
$648$		0			0
$649$	86.4073			3.39178
$650$		0			0
$651$	−5.59127	+	10.5723i	−0.219139	+	0.414360i
$652$		0			0
$653$	−2.84613	+	7.81967i	−0.111378	+	0.306007i	−0.982841	−	0.184452i	$-0.940949\pi$
$653$	−2.84613	+	7.81967i	−0.111378	+	0.306007i	0.871464	+	0.490460i	$0.163171\pi$
$654$		0			0
$655$	10.5637	+	1.86266i	0.412756	+	0.0727801i
$656$		0			0
$657$	−26.9124	+	2.00217i	−1.04995	+	0.0781120i
$658$		0			0
$659$	−29.3812	+	10.6939i	−1.14453	+	0.416575i	−0.843547	−	0.537055i	$-0.819537\pi$
$659$	−29.3812	+	10.6939i	−1.14453	+	0.416575i	−0.300983	+	0.953630i	$0.597315\pi$
$660$		0			0
$661$	−31.7234	+	26.6191i	−1.23390	+	1.03536i	−0.235920	+	0.971772i	$0.575810\pi$
$661$	−31.7234	+	26.6191i	−1.23390	+	1.03536i	−0.997976	+	0.0635895i	$0.979745\pi$
$662$		0			0
$663$	−3.02932	−	3.34939i	−0.117649	−	0.130080i
$664$		0			0
$665$	1.17124	−	0.676216i	0.0454187	−	0.0262225i
$666$		0			0
$667$	53.8940	+	31.1157i	2.08678	+	1.20481i
$668$		0			0
$669$	−5.85897	+	7.53360i	−0.226521	+	0.291266i
$670$		0			0
$671$	3.88921	+	22.0568i	0.150141	+	0.851493i
$672$		0			0
$673$	5.52329	+	4.63459i	0.212907	+	0.178650i	0.743004	−	0.669287i	$-0.233400\pi$
$673$	5.52329	+	4.63459i	0.212907	+	0.178650i	−0.530097	+	0.847937i	$0.677845\pi$
$674$		0			0
$675$	−9.55066	−	6.34975i	−0.367605	−	0.244402i
$676$		0			0
$677$	15.0543	−	17.9410i	0.578584	−	0.689530i	−0.394785	−	0.918774i	$-0.629181\pi$
$677$	15.0543	−	17.9410i	0.578584	−	0.689530i	0.973369	+	0.229244i	$0.0736253\pi$
$678$		0			0
$679$	−3.33033	+	0.587227i	−0.127806	+	0.0225357i
$680$		0			0
$681$	−2.30091	+	16.6401i	−0.0881710	+	0.637650i
$682$		0			0
$683$	−0.0848995	+	0.147050i	−0.00324859	+	0.00562672i	−0.867645	−	0.497184i	$-0.834367\pi$
$683$	−0.0848995	+	0.147050i	−0.00324859	+	0.00562672i	0.864397	+	0.502811i	$0.167701\pi$
$684$		0			0
$685$	−5.44956	−	9.43892i	−0.208217	−	0.360643i
$686$		0			0
$687$	−2.39051	−	11.1248i	−0.0912037	−	0.424438i
$688$		0			0
$689$	−6.37948	−	7.60276i	−0.243039	−	0.289642i
$690$		0			0
$691$	−2.67100	−	7.33850i	−0.101609	−	0.279170i	0.878463	−	0.477811i	$-0.158569\pi$
$691$	−2.67100	−	7.33850i	−0.101609	−	0.279170i	−0.980072	+	0.198641i	$0.936347\pi$
$692$		0			0
$693$	24.3080	+	24.9488i	0.923385	+	0.947725i
$694$		0			0
$695$	−5.02196	+	28.4810i	−0.190494	+	1.08034i
$696$		0			0
$697$	−2.18665	−	0.795875i	−0.0828252	−	0.0301459i
$698$		0			0
$699$	1.06028	+	28.5432i	0.0401035	+	1.07960i
$700$		0			0
$701$			3.48510i			0.131630i	0.997832	+	0.0658152i	$0.0209648\pi$
$701$			3.48510i			0.131630i	−0.997832	+	0.0658152i	$0.979035\pi$
$702$		0			0
$703$			3.22397i			0.121594i
$704$		0			0
$705$	10.9946	−	6.90420i	0.414080	−	0.260027i
$706$		0			0
$707$	20.8625	+	7.59332i	0.784614	+	0.285576i
$708$		0			0
$709$	−5.06795	+	28.7418i	−0.190331	+	1.07942i	0.728581	+	0.684959i	$0.240180\pi$
$709$	−5.06795	+	28.7418i	−0.190331	+	1.07942i	−0.918912	+	0.394462i	$0.870931\pi$
$710$		0			0
$711$	0.565361	+	0.0568819i	0.0212027	+	0.00213324i
$712$		0			0
$713$	−11.7085	−	32.1687i	−0.438485	−	1.20473i
$714$		0			0
$715$	8.25498	+	9.83790i	0.308719	+	0.367917i
$716$		0			0
$717$	22.5664	+	7.27687i	0.842759	+	0.271760i
$718$		0			0
$719$	1.85660	+	3.21573i	0.0692396	+	0.119927i	0.898567	−	0.438837i	$-0.144609\pi$
$719$	1.85660	+	3.21573i	0.0692396	+	0.119927i	−0.829327	+	0.558763i	$0.811276\pi$
$720$		0			0
$721$	−9.45317	+	16.3734i	−0.352055	+	0.609776i
$722$		0			0
$723$	10.8110	−	4.39590i	0.402064	−	0.163485i
$724$		0			0
$725$	−15.1800	+	2.67664i	−0.563769	+	0.0994078i
$726$		0			0
$727$	−30.3631	+	36.1853i	−1.12611	+	1.34204i	−0.193517	+	0.981097i	$0.561990\pi$
$727$	−30.3631	+	36.1853i	−1.12611	+	1.34204i	−0.932588	+	0.360943i	$0.882455\pi$
$728$		0			0
$729$	26.3328	−	5.96533i	0.975288	−	0.220938i
$730$		0			0
$731$	17.6397	+	14.8015i	0.652428	+	0.547452i
$732$		0			0
$733$	−6.83812	−	38.7809i	−0.252572	−	1.43241i	−0.802230	−	0.597015i	$-0.796353\pi$
$733$	−6.83812	−	38.7809i	−0.252572	−	1.43241i	0.549658	−	0.835390i	$-0.314758\pi$
$734$		0			0
$735$	4.10971	+	10.1071i	0.151589	+	0.372808i
$736$		0			0
$737$	26.8069	+	15.4770i	0.987446	+	0.570102i
$738$		0			0
$739$	1.71073	−	0.987691i	0.0629303	−	0.0363328i	−0.468205	−	0.883620i	$-0.655099\pi$
$739$	1.71073	−	0.987691i	0.0629303	−	0.0363328i	0.531135	+	0.847287i	$0.321766\pi$
$740$		0			0
$741$	0.284718	−	0.882945i	0.0104594	−	0.0324358i
$742$		0			0
$743$	21.5187	−	18.0563i	0.789443	−	0.662421i	−0.156164	−	0.987731i	$-0.549913\pi$
$743$	21.5187	−	18.0563i	0.789443	−	0.662421i	0.945608	+	0.325310i	$0.105469\pi$
$744$		0			0
$745$	13.0645	−	4.75508i	0.478645	−	0.174213i
$746$		0			0
$747$	−0.255520	+	2.53967i	−0.00934899	+	0.0929216i
$748$		0			0
$749$	−13.8748	−	2.44650i	−0.506973	−	0.0893930i
$750$		0			0
$751$	−9.02069	+	24.7842i	−0.329170	+	0.904387i	0.659153	+	0.752009i	$0.270915\pi$
$751$	−9.02069	+	24.7842i	−0.329170	+	0.904387i	−0.988322	+	0.152377i	$0.951307\pi$
$752$		0			0
$753$	2.56717	+	4.08807i	0.0935527	+	0.148978i
$754$		0			0
$755$	−5.98730			−0.217900
$756$		0			0
$757$	−25.1182			−0.912935			−0.456468	−	0.889740i	$-0.650886\pi$
$757$	−25.1182			−0.912935			−0.456468	+	0.889740i	$0.650886\pi$
$758$		0			0
$759$	−99.6356	+	3.70111i	−3.61654	+	0.134342i
$760$		0			0
$761$	6.11626	−	16.8043i	0.221714	−	0.609155i	−0.778106	−	0.628133i	$-0.783819\pi$
$761$	6.11626	−	16.8043i	0.221714	−	0.609155i	0.999820	+	0.0189785i	$0.00604142\pi$
$762$		0			0
$763$	−21.4061	−	3.77448i	−0.774954	−	0.136645i
$764$		0			0
$765$	7.87055	−	7.66842i	0.284560	−	0.277252i
$766$		0			0
$767$	−14.9525	+	5.44227i	−0.539904	+	0.196509i
$768$		0			0
$769$	18.8921	−	15.8524i	0.681267	−	0.571651i	−0.235109	−	0.971969i	$-0.575545\pi$
$769$	18.8921	−	15.8524i	0.681267	−	0.571651i	0.916376	+	0.400318i	$0.131100\pi$
$770$		0			0
$771$	−13.9871	+	3.00555i	−0.503732	+	0.108242i
$772$		0			0
$773$	35.4233	−	20.4517i	1.27409	−	0.735595i	0.298334	−	0.954462i	$-0.403569\pi$
$773$	35.4233	−	20.4517i	1.27409	−	0.735595i	0.975755	+	0.218866i	$0.0702358\pi$
$774$		0			0
$775$	7.34324	+	4.23962i	0.263777	+	0.152292i
$776$		0			0
$777$	22.0815	+	3.05332i	0.792170	+	0.109537i
$778$		0			0
$779$	−0.0830069	−	0.470756i	−0.00297403	−	0.0168666i
$780$		0			0
$781$	8.05998	+	6.76313i	0.288409	+	0.242004i
$782$		0			0
$783$	20.0909	−	30.2188i	0.717991	−	1.07993i
$784$		0			0
$785$	22.0111	−	26.2318i	0.785609	−	0.936252i
$786$		0			0
$787$	42.4752	−	7.48952i	1.51408	−	0.266973i	0.645975	−	0.763358i	$-0.276451\pi$
$787$	42.4752	−	7.48952i	1.51408	−	0.266973i	0.868102	+	0.496386i	$0.165340\pi$
$788$		0			0
$789$	−12.6458	−	9.83481i	−0.450203	−	0.350129i
$790$		0			0
$791$	−8.96247	+	15.5234i	−0.318669	+	0.551950i
$792$		0			0
$793$	−2.06224	−	3.57190i	−0.0732322	−	0.126842i
$794$		0			0
$795$	17.9102	−	16.1986i	0.635208	−	0.574506i
$796$		0			0
$797$	29.7529	+	35.4582i	1.05390	+	1.25599i	0.965637	+	0.259896i	$0.0836883\pi$
$797$	29.7529	+	35.4582i	1.05390	+	1.25599i	0.0882667	+	0.996097i	$0.471867\pi$
$798$		0			0
$799$	−3.36228	−	9.23778i	−0.118949	−	0.326809i
$800$		0			0
$801$	−2.07910	−	27.9465i	−0.0734613	−	0.987442i
$802$		0			0
$803$	10.0908	−	57.2277i	0.356096	−	2.01952i
$804$		0			0
$805$	25.1523	+	9.15469i	0.886502	+	0.322660i
$806$		0			0
$807$	−26.2413	−	13.8780i	−0.923736	−	0.488529i
$808$		0			0
$809$			24.6327i			0.866039i	0.901385	+	0.433020i	$0.142552\pi$
$809$			24.6327i			0.866039i	−0.901385	+	0.433020i	$0.857448\pi$
$810$		0			0
$811$			7.88512i			0.276884i	0.990371	+	0.138442i	$0.0442095\pi$
$811$			7.88512i			0.276884i	−0.990371	+	0.138442i	$0.955791\pi$
$812$		0			0
$813$	−28.2267	−	14.9280i	−0.989955	−	0.523549i
$814$		0			0
$815$	−6.80872	−	2.47817i	−0.238499	−	0.0868066i
$816$		0			0
$817$	−0.821407	+	4.65843i	−0.0287374	+	0.162978i
$818$		0			0
$819$	−5.77779	−	2.78629i	−0.201892	−	0.0973608i
$820$		0			0
$821$	12.9205	+	35.4989i	0.450929	+	1.23892i	0.932071	+	0.362276i	$0.118000\pi$
$821$	12.9205	+	35.4989i	0.450929	+	1.23892i	−0.481142	+	0.876643i	$0.659778\pi$
$822$		0			0
$823$	−19.6141	−	23.3752i	−0.683706	−	0.814809i	0.306873	−	0.951750i	$-0.400717\pi$
$823$	−19.6141	−	23.3752i	−0.683706	−	0.814809i	−0.990579	+	0.136942i	$0.956273\pi$
$824$		0			0
$825$	18.3158	−	16.5655i	0.637674	−	0.576736i
$826$		0			0
$827$	−10.7624	−	18.6411i	−0.374247	−	0.648214i	0.615967	−	0.787772i	$-0.288765\pi$
$827$	−10.7624	−	18.6411i	−0.374247	−	0.648214i	−0.990214	+	0.139558i	$0.955432\pi$
$828$		0			0
$829$	8.71843	−	15.1008i	0.302804	−	0.524471i	−0.673966	−	0.738762i	$-0.735411\pi$
$829$	8.71843	−	15.1008i	0.302804	−	0.524471i	0.976770	+	0.214291i	$0.0687440\pi$
$830$		0			0
$831$	1.56906	+	1.22027i	0.0544299	+	0.0423308i
$832$		0			0
$833$	8.13625	−	1.43464i	0.281904	−	0.0497074i
$834$		0			0
$835$	17.2081	−	20.5078i	0.595509	−	0.709700i
$836$		0			0
$837$	−19.1515	+	5.63007i	−0.661972	+	0.194604i
$838$		0			0
$839$	38.2029	+	32.0560i	1.31891	+	1.10670i	0.986535	+	0.163549i	$0.0522942\pi$
$839$	38.2029	+	32.0560i	1.31891	+	1.10670i	0.332374	+	0.943148i	$0.392150\pi$
$840$		0			0
$841$	−3.43322	−	19.4707i	−0.118387	−	0.671405i
$842$		0			0
$843$	34.7429	+	4.80407i	1.19661	+	0.165461i
$844$		0			0
$845$	16.7665	+	9.68014i	0.576785	+	0.333007i
$846$		0			0
$847$	−47.8340	+	27.6170i	−1.64360	+	0.948930i
$848$		0			0
$849$	45.0018	−	9.67004i	1.54446	−	0.331875i
$850$		0			0
$851$	−48.8789	+	41.0143i	−1.67555	+	1.40595i
$852$		0			0
$853$	−1.68502	+	0.613298i	−0.0576940	+	0.0209989i	−0.370706	−	0.928750i	$-0.620884\pi$
$853$	−1.68502	+	0.613298i	−0.0576940	+	0.0209989i	0.313012	+	0.949749i	$0.398662\pi$
$854$		0			0
$855$	2.17263	+	0.612551i	0.0743023	+	0.0209488i
$856$		0			0
$857$	9.51511	+	1.67777i	0.325030	+	0.0573116i	0.333782	−	0.942650i	$-0.391675\pi$
$857$	9.51511	+	1.67777i	0.325030	+	0.0573116i	−0.00875246	+	0.999962i	$0.502786\pi$
$858$		0			0
$859$	13.6432	−	37.4844i	0.465500	−	1.27895i	−0.455794	−	0.890085i	$-0.650645\pi$
$859$	13.6432	−	37.4844i	0.465500	−	1.27895i	0.921294	−	0.388866i	$-0.127133\pi$
$860$		0			0
$861$	−3.30290	+	0.122691i	−0.112562	+	0.00418130i
$862$		0			0
$863$	14.6462			0.498564			0.249282	−	0.968431i	$-0.419805\pi$
$863$	14.6462			0.498564			0.249282	+	0.968431i	$0.419805\pi$
$864$		0			0
$865$	29.1558			0.991327
$866$		0			0
$867$	11.2339	+	17.8893i	0.381522	+	0.607553i
$868$		0			0
$869$	−0.418474	+	1.14975i	−0.0141957	+	0.0390025i
$870$		0			0
$871$	−5.61365	−	0.989838i	−0.190211	−	0.0335394i
$872$		0			0
$873$	−4.58109	−	3.29734i	−0.155047	−	0.111598i
$874$		0			0
$875$	−20.3430	+	7.40424i	−0.687718	+	0.250309i
$876$		0			0
$877$	−29.6722	+	24.8980i	−1.00196	+	0.840744i	−0.987255	−	0.159148i	$-0.949125\pi$
$877$	−29.6722	+	24.8980i	−1.00196	+	0.840744i	−0.0147052	+	0.999892i	$0.504681\pi$
$878$		0			0
$879$	16.0395	−	49.7406i	0.541000	−	1.67771i
$880$		0			0
$881$	22.8609	−	13.1987i	0.770203	−	0.444677i	−0.0627438	−	0.998030i	$-0.519985\pi$
$881$	22.8609	−	13.1987i	0.770203	−	0.444677i	0.832947	+	0.553353i	$0.186652\pi$
$882$		0			0
$883$	11.0706	+	6.39159i	0.372554	+	0.215094i	0.674574	−	0.738208i	$-0.264328\pi$
$883$	11.0706	+	6.39159i	0.372554	+	0.215094i	−0.302020	+	0.953302i	$0.597661\pi$
$884$		0			0
$885$	−14.5836	−	35.8660i	−0.490223	−	1.20562i
$886$		0			0
$887$	−5.83595	−	33.0973i	−0.195952	−	1.11130i	−0.911056	−	0.412282i	$-0.864732\pi$
$887$	−5.83595	−	33.0973i	−0.195952	−	1.11130i	0.715104	−	0.699018i	$-0.246379\pi$
$888$		0			0
$889$	−10.0357	−	8.42092i	−0.336585	−	0.282428i
$890$		0			0
$891$	−1.51234	+	58.1193i	−0.0506652	+	1.94707i
$892$		0			0
$893$	1.29808	−	1.54699i	0.0434385	−	0.0517679i
$894$		0			0
$895$	30.6352	−	5.40180i	1.02402	−	0.180562i
$896$		0			0
$897$	17.0085	−	6.91590i	0.567897	−	0.230915i
$898$		0			0
$899$	−13.4144	+	23.2344i	−0.447395	+	0.774911i
$900$		0			0
$901$	−9.14295	−	15.8361i	−0.304596	−	0.527576i
$902$		0			0
$903$	31.1285	+	10.0378i	1.03589	+	0.334037i
$904$		0			0
$905$	12.4613	+	14.8508i	0.414229	+	0.493659i
$906$		0			0
$907$	4.36706	+	11.9984i	0.145006	+	0.398400i	0.990839	−	0.135047i	$-0.0431186\pi$
$907$	4.36706	+	11.9984i	0.145006	+	0.398400i	−0.845833	+	0.533447i	$0.820896\pi$
$908$		0			0
$909$	15.2224	+	33.7851i	0.504896	+	1.12058i
$910$		0			0
$911$	−1.12226	+	6.36463i	−0.0371820	+	0.210870i	−0.997738	−	0.0672153i	$-0.978589\pi$
$911$	−1.12226	+	6.36463i	−0.0371820	+	0.210870i	0.960556	+	0.278085i	$0.0896997\pi$
$912$		0			0
$913$	−5.16480	−	1.87983i	−0.170930	−	0.0622134i
$914$		0			0
$915$	8.49893	−	5.33702i	0.280966	−	0.176437i
$916$		0			0
$917$		−	11.5367i		−	0.380977i
$918$		0			0
$919$		−	50.1534i		−	1.65441i	−0.561903	−	0.827203i	$-0.689931\pi$
$919$		−	50.1534i		−	1.65441i	0.561903	−	0.827203i	$-0.310069\pi$
$920$		0			0
$921$	2.19764	+	59.1616i	0.0724148	+	1.94944i
$922$		0			0
$923$	−1.82072	−	0.662688i	−0.0599298	−	0.0218127i
$924$		0			0
$925$	2.74440	−	15.5643i	0.0902352	−	0.511749i
$926$		0			0
$927$	−30.5848	+	7.77022i	−1.00454	+	0.255208i
$928$		0			0
$929$	16.0919	+	44.2122i	0.527959	+	1.45056i	0.861470	+	0.507809i	$0.169544\pi$
$929$	16.0919	+	44.2122i	0.527959	+	1.45056i	−0.333511	+	0.942746i	$0.608233\pi$
$930$		0			0
$931$	1.09092	+	1.30010i	0.0357533	+	0.0426091i
$932$		0			0
$933$	−4.17706	−	19.4390i	−0.136751	−	0.636403i
$934$		0			0
$935$	11.8309	+	20.4917i	0.386911	+	0.670150i
$936$		0			0
$937$	−14.9922	+	25.9672i	−0.489774	+	0.848313i	−0.999931	−	0.0117685i	$-0.996254\pi$
$937$	−14.9922	+	25.9672i	−0.489774	+	0.848313i	0.510157	+	0.860081i	$0.329587\pi$
$938$		0			0
$939$	−5.62725	+	40.6961i	−0.183638	+	1.32807i
$940$		0			0
$941$	−26.6897	+	4.70611i	−0.870059	+	0.153415i	−0.590817	−	0.806806i	$-0.701194\pi$
$941$	−26.6897	+	4.70611i	−0.870059	+	0.153415i	−0.279242	+	0.960221i	$0.590083\pi$
$942$		0			0
$943$	6.08118	−	7.24727i	0.198031	−	0.236004i
$944$		0			0
$945$	6.25309	−	14.3006i	0.203413	−	0.465197i
$946$		0			0
$947$	18.8480	+	15.8153i	0.612476	+	0.513929i	0.895428	−	0.445205i	$-0.146869\pi$
$947$	18.8480	+	15.8153i	0.612476	+	0.513929i	−0.282952	+	0.959134i	$0.591314\pi$
$948$		0			0
$949$	1.85824	+	10.5386i	0.0603212	+	0.342098i
$950$		0			0
$951$	−30.4311	+	39.1290i	−0.986797	+	1.26885i
$952$		0			0
$953$	−39.8170	−	22.9884i	−1.28980	−	0.744666i	−0.311182	−	0.950350i	$-0.600725\pi$
$953$	−39.8170	−	22.9884i	−1.28980	−	0.744666i	−0.978618	+	0.205684i	$0.934058\pi$
$954$		0			0
$955$	−32.7794	+	18.9252i	−1.06072	+	0.612405i
$956$		0			0
$957$	52.4140	+	57.9521i	1.69430	+	1.87332i
$958$		0			0
$959$	−8.97979	+	7.53494i	−0.289972	+	0.243316i
$960$		0			0
$961$	−15.2621	+	5.55496i	−0.492326	+	0.179192i
$962$		0			0
$963$	−13.2362	−	19.4366i	−0.426531	−	0.626334i
$964$		0			0
$965$	−12.2472	−	2.15952i	−0.394252	−	0.0695173i
$966$		0			0
$967$	−0.232396	+	0.638501i	−0.00747334	+	0.0205328i	−0.943373	−	0.331733i	$-0.892367\pi$
$967$	−0.232396	+	0.638501i	−0.00747334	+	0.0205328i	0.935900	+	0.352266i	$0.114589\pi$
$968$		0			0
$969$	0.799103	−	1.51099i	0.0256709	−	0.0485399i
$970$		0			0
$971$	−33.2286			−1.06636			−0.533178	−	0.846003i	$-0.679003\pi$
$971$	−33.2286			−1.06636			−0.533178	+	0.846003i	$0.679003\pi$
$972$		0			0
$973$	31.1045			0.997165
$974$		0			0
$975$	−2.12613	+	4.02020i	−0.0680906	+	0.128749i
$976$		0			0
$977$	5.51580	−	15.1545i	0.176466	−	0.484836i	−0.819652	−	0.572861i	$-0.805833\pi$
$977$	5.51580	−	15.1545i	0.176466	−	0.484836i	0.996118	+	0.0880250i	$0.0280555\pi$
$978$		0			0
$979$	59.4267	+	10.4785i	1.89928	+	0.334895i
$980$		0			0
$981$	−20.4210	−	29.9869i	−0.651992	−	0.957408i
$982$		0			0
$983$	37.2960	−	13.5746i	1.18956	−	0.432963i	0.329989	−	0.943985i	$-0.392955\pi$
$983$	37.2960	−	13.5746i	1.18956	−	0.432963i	0.859568	+	0.511021i	$0.170733\pi$
$984$		0			0
$985$	21.7621	−	18.2606i	0.693398	−	0.581830i
$986$		0			0
$987$	−9.36621	−	10.3558i	−0.298130	−	0.329630i
$988$		0			0
$989$	−81.0766	+	46.8096i	−2.57809	+	1.48846i
$990$		0			0
$991$	32.3796	+	18.6944i	1.02857	+	0.593846i	0.916575	−	0.399863i	$-0.130942\pi$
$991$	32.3796	+	18.6944i	1.02857	+	0.593846i	0.111996	+	0.993709i	$0.464276\pi$
$992$		0			0
$993$	5.25429	−	6.75608i	0.166740	−	0.214398i
$994$		0			0
$995$	−5.36491	−	30.4259i	−0.170079	−	0.964567i
$996$		0			0
$997$	27.9235	+	23.4306i	0.884346	+	0.742054i	0.967068	−	0.254518i	$-0.0819169\pi$
$997$	27.9235	+	23.4306i	0.884346	+	0.742054i	−0.0827221	+	0.996573i	$0.526361\pi$
$998$		0			0
$999$	22.0698	+	29.9543i	0.698257	+	0.947713i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	864.2.bi.a.767.23	yes	216
4.3	odd	2	inner	864.2.bi.a.767.14	yes	216
27.5	odd	18	inner	864.2.bi.a.383.14	✓	216
108.59	even	18	inner	864.2.bi.a.383.23	yes	216

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
864.2.bi.a.383.14	✓	216	27.5	odd	18	inner
864.2.bi.a.383.23	yes	216	108.59	even	18	inner
864.2.bi.a.767.14	yes	216	4.3	odd	2	inner
864.2.bi.a.767.23	yes	216	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 864 = 2^{5} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	864.bi (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.809747 - 1.53111i) q^{3} +(0.571575 - 1.57039i) q^{5} +(-1.77008 - 0.312113i) q^{7} +(-1.68862 - 2.47963i) q^{9} +(6.07031 - 2.20941i) q^{11} +(-0.911289 + 0.764662i) q^{13} +(-1.94161 - 2.14676i) q^{15} +(-1.89816 + 1.09590i) q^{17} +(-0.389926 - 0.225124i) q^{19} +(-1.91120 + 2.45746i) q^{21} +(-1.54739 - 8.77566i) q^{23} +(1.69080 + 1.41875i) q^{25} +(-5.16395 + 0.577594i) q^{27} +(-4.48899 + 5.34977i) q^{29} +(3.78330 - 0.667098i) q^{31} +(1.53255 - 11.0834i) q^{33} +(-1.50187 + 2.60132i) q^{35} +(-3.58021 - 6.20111i) q^{37} +(0.432871 + 2.01447i) q^{39} +(0.682432 + 0.813291i) q^{41} +(-3.59325 - 9.87239i) q^{43} +(-4.85916 + 1.23449i) q^{45} +(-0.778845 + 4.41705i) q^{47} +(-3.54207 - 1.28921i) q^{49} +(0.140922 + 3.79370i) q^{51} +8.34287i q^{53} -10.7956i q^{55} +(-0.660432 + 0.414728i) q^{57} +(12.5693 + 4.57486i) q^{59} +(-0.602055 + 3.41443i) q^{61} +(2.21507 + 4.91619i) q^{63} +(0.679947 + 1.86814i) q^{65} +(3.08006 + 3.67067i) q^{67} +(-14.6895 - 4.73684i) q^{69} +(0.814377 + 1.41054i) q^{71} +(4.49780 - 7.79042i) q^{73} +(3.54138 - 1.43998i) q^{75} +(-11.4345 + 2.01621i) q^{77} +(-0.121747 + 0.145093i) q^{79} +(-3.29713 + 8.37430i) q^{81} +(-0.651774 - 0.546903i) q^{83} +(0.636052 + 3.60723i) q^{85} +(4.55616 + 11.2051i) q^{87} +(8.08976 + 4.67063i) q^{89} +(1.85172 - 1.06909i) q^{91} +(2.04211 - 6.33285i) q^{93} +(-0.576404 + 0.483661i) q^{95} +(1.76799 - 0.643496i) q^{97} +(-15.7290 - 11.3213i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 216 q - 24 q^{29} + 36 q^{33} + 36 q^{41} - 24 q^{45} + 12 q^{57} + 48 q^{65} + 48 q^{69} + 48 q^{77} + 48 q^{81} + 36 q^{89} - 144 q^{93} - 36 q^{97}+O(q^{100}) \) 216 * q - 24 * q^29 + 36 * q^33 + 36 * q^41 - 24 * q^45 + 12 * q^57 + 48 * q^65 + 48 * q^69 + 48 * q^77 + 48 * q^81 + 36 * q^89 - 144 * q^93 - 36 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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