LMFDB - Embedded newform 864.2.bi.a.767.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [864,2,Mod(95,864)]

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

lf = mfeigenbasis(mf)

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")

//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);

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

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			767.16
Character	$\chi$	$=$	864.767
Dual form			864.2.bi.a.383.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.203793 - 1.72002i) q^{3} +(-0.448183 + 1.23137i) q^{5} +(4.76300 + 0.839845i) q^{7} +(-2.91694 + 0.701056i) q^{9} +O(q^{10})$	\(q+(-0.203793 - 1.72002i) q^{3} +(-0.448183 + 1.23137i) q^{5} +(4.76300 + 0.839845i) q^{7} +(-2.91694 + 0.701056i) q^{9} +(-0.844448 + 0.307354i) q^{11} +(1.35620 - 1.13799i) q^{13} +(2.20932 + 0.519938i) q^{15} +(0.708938 - 0.409306i) q^{17} +(2.14516 + 1.23851i) q^{19} +(0.473885 - 8.36361i) q^{21} +(1.28676 + 7.29760i) q^{23} +(2.51481 + 2.11018i) q^{25} +(1.80028 + 4.87432i) q^{27} +(-0.109778 + 0.130828i) q^{29} +(5.33772 - 0.941183i) q^{31} +(0.700747 + 1.38983i) q^{33} +(-3.16886 + 5.48862i) q^{35} +(-3.80198 - 6.58521i) q^{37} +(-2.23375 - 2.10078i) q^{39} +(-2.45413 - 2.92471i) q^{41} +(0.555775 + 1.52698i) q^{43} +(0.444061 - 3.90604i) q^{45} +(1.91737 - 10.8739i) q^{47} +(15.4030 + 5.60623i) q^{49} +(-0.848491 - 1.13597i) q^{51} -8.64685i q^{53} -1.17758i q^{55} +(1.69309 - 3.94212i) q^{57} +(10.7491 + 3.91234i) q^{59} +(-0.757897 + 4.29825i) q^{61} +(-14.4821 + 0.889352i) q^{63} +(0.793460 + 2.18001i) q^{65} +(-9.78772 - 11.6645i) q^{67} +(12.2898 - 3.70046i) q^{69} +(3.05643 + 5.29388i) q^{71} +(-1.18611 + 2.05440i) q^{73} +(3.11705 - 4.75557i) q^{75} +(-4.28024 + 0.754721i) q^{77} +(8.52050 - 10.1543i) q^{79} +(8.01704 - 4.08987i) q^{81} +(7.00731 + 5.87983i) q^{83} +(0.186274 + 1.05641i) q^{85} +(0.247398 + 0.162158i) q^{87} +(-5.24813 - 3.03001i) q^{89} +(7.41532 - 4.28124i) q^{91} +(-2.70664 - 8.98917i) q^{93} +(-2.48649 + 2.08641i) q^{95} +(-9.41639 + 3.42728i) q^{97} +(2.24773 - 1.48854i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 216 q+O(q^{10}) $ 216 * 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

Display 100 coefficients 10 coefficients

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
$3$	−0.203793	−	1.72002i	−0.117660	−	0.993054i
$3$	−0.203793	−	1.72002i	−0.117660	−	0.993054i
$4$		0			0
$5$	−0.448183	+	1.23137i	−0.200433	+	0.550686i	−0.998664	−	0.0516651i	$-0.983547\pi$
$5$	−0.448183	+	1.23137i	−0.200433	+	0.550686i	0.798231	+	0.602351i	$0.205769\pi$
$6$		0			0
$7$	4.76300	+	0.839845i	1.80024	+	0.317432i	0.970571	−	0.240816i	$-0.0774151\pi$
$7$	4.76300	+	0.839845i	1.80024	+	0.317432i	0.829674	+	0.558248i	$0.188526\pi$
$8$		0			0
$9$	−2.91694	+	0.701056i	−0.972312	+	0.233685i
$10$		0			0
$11$	−0.844448	+	0.307354i	−0.254611	+	0.0926707i	−0.466172	−	0.884694i	$-0.654367\pi$
$11$	−0.844448	+	0.307354i	−0.254611	+	0.0926707i	0.211562	+	0.977365i	$0.432145\pi$
$12$		0			0
$13$	1.35620	−	1.13799i	0.376142	−	0.315621i	−0.435043	−	0.900410i	$-0.643267\pi$
$13$	1.35620	−	1.13799i	0.376142	−	0.315621i	0.811186	+	0.584789i	$0.198823\pi$
$14$		0			0
$15$	2.20932	+	0.519938i	0.570444	+	0.134248i
$16$		0			0
$17$	0.708938	−	0.409306i	0.171943	−	0.0992712i	−0.411559	−	0.911383i	$-0.635016\pi$
$17$	0.708938	−	0.409306i	0.171943	−	0.0992712i	0.583502	+	0.812112i	$0.301682\pi$
$18$		0			0
$19$	2.14516	+	1.23851i	0.492134	+	0.284134i	0.725459	−	0.688265i	$-0.241627\pi$
$19$	2.14516	+	1.23851i	0.492134	+	0.284134i	−0.233325	+	0.972399i	$0.574961\pi$
$20$		0			0
$21$	0.473885	−	8.36361i	0.103410	−	1.82509i
$22$		0			0
$23$	1.28676	+	7.29760i	0.268309	+	1.52165i	0.759445	+	0.650572i	$0.225471\pi$
$23$	1.28676	+	7.29760i	0.268309	+	1.52165i	−0.491136	+	0.871083i	$0.663418\pi$
$24$		0			0
$25$	2.51481	+	2.11018i	0.502963	+	0.422036i
$26$		0			0
$27$	1.80028	+	4.87432i	0.346464	+	0.938063i
$28$		0			0
$29$	−0.109778	+	0.130828i	−0.0203852	+	0.0242941i	−0.776141	−	0.630560i	$-0.782825\pi$
$29$	−0.109778	+	0.130828i	−0.0203852	+	0.0242941i	0.755756	+	0.654854i	$0.227270\pi$
$30$		0			0
$31$	5.33772	−	0.941183i	0.958682	−	0.169042i	0.327651	−	0.944799i	$-0.393743\pi$
$31$	5.33772	−	0.941183i	0.958682	−	0.169042i	0.631031	+	0.775757i	$0.282632\pi$
$32$		0			0
$33$	0.700747	+	1.38983i	0.121984	+	0.241939i
$34$		0			0
$35$	−3.16886	+	5.48862i	−0.535634	+	0.927746i
$36$		0			0
$37$	−3.80198	−	6.58521i	−0.625041	−	1.08260i	−0.988533	−	0.151005i	$-0.951749\pi$
$37$	−3.80198	−	6.58521i	−0.625041	−	1.08260i	0.363492	−	0.931597i	$-0.381584\pi$
$38$		0			0
$39$	−2.23375	−	2.10078i	−0.357686	−	0.336394i
$40$		0			0
$41$	−2.45413	−	2.92471i	−0.383270	−	0.456763i	0.539573	−	0.841939i	$-0.318586\pi$
$41$	−2.45413	−	2.92471i	−0.383270	−	0.456763i	−0.922844	+	0.385175i	$0.874141\pi$
$42$		0			0
$43$	0.555775	+	1.52698i	0.0847549	+	0.232862i	0.974829	−	0.222954i	$-0.0715698\pi$
$43$	0.555775	+	1.52698i	0.0847549	+	0.232862i	−0.890074	+	0.455816i	$0.849348\pi$
$44$		0			0
$45$	0.444061	−	3.90604i	0.0661966	−	0.582277i
$46$		0			0
$47$	1.91737	−	10.8739i	0.279676	−	1.58612i	−0.444027	−	0.896013i	$-0.646451\pi$
$47$	1.91737	−	10.8739i	0.279676	−	1.58612i	0.723704	−	0.690111i	$-0.242438\pi$
$48$		0			0
$49$	15.4030	+	5.60623i	2.20043	+	0.800890i
$50$		0			0
$51$	−0.848491	−	1.13597i	−0.118812	−	0.159068i
$52$		0			0
$53$		−	8.64685i		−	1.18774i	−0.804563	−	0.593868i	$-0.797600\pi$
$53$		−	8.64685i		−	1.18774i	0.804563	−	0.593868i	$-0.202400\pi$
$54$		0			0
$55$		−	1.17758i		−	0.158785i
$56$		0			0
$57$	1.69309	−	3.94212i	0.224256	−	0.522147i
$58$		0			0
$59$	10.7491	+	3.91234i	1.39941	+	0.509344i	0.928003	−	0.372572i	$-0.121524\pi$
$59$	10.7491	+	3.91234i	1.39941	+	0.509344i	0.471407	+	0.881916i	$0.343746\pi$
$60$		0			0
$61$	−0.757897	+	4.29825i	−0.0970387	+	0.550334i	0.897065	+	0.441899i	$0.145695\pi$
$61$	−0.757897	+	4.29825i	−0.0970387	+	0.550334i	−0.994104	+	0.108435i	$0.965416\pi$
$62$		0			0
$63$	−14.4821	+	0.889352i	−1.82458	+	0.112048i
$64$		0			0
$65$	0.793460	+	2.18001i	0.0984166	+	0.270397i
$66$		0			0
$67$	−9.78772	−	11.6645i	−1.19576	−	1.42505i	−0.879183	−	0.476484i	$-0.841911\pi$
$67$	−9.78772	−	11.6645i	−1.19576	−	1.42505i	−0.316577	−	0.948567i	$-0.602534\pi$
$68$		0			0
$69$	12.2898	−	3.70046i	1.47952	−	0.445483i
$70$		0			0
$71$	3.05643	+	5.29388i	0.362731	+	0.628268i	0.988409	−	0.151813i	$-0.0485111\pi$
$71$	3.05643	+	5.29388i	0.362731	+	0.628268i	−0.625678	+	0.780081i	$0.715178\pi$
$72$		0			0
$73$	−1.18611	+	2.05440i	−0.138824	+	0.240449i	−0.927052	−	0.374934i	$-0.877665\pi$
$73$	−1.18611	+	2.05440i	−0.138824	+	0.240449i	0.788228	+	0.615383i	$0.210999\pi$
$74$		0			0
$75$	3.11705	−	4.75557i	0.359926	−	0.549126i
$76$		0			0
$77$	−4.28024	+	0.754721i	−0.487778	+	0.0860085i
$78$		0			0
$79$	8.52050	−	10.1543i	0.958631	−	1.14245i	−0.0311010	−	0.999516i	$-0.509901\pi$
$79$	8.52050	−	10.1543i	0.958631	−	1.14245i	0.989732	−	0.142936i	$-0.0456542\pi$
$80$		0			0
$81$	8.01704	−	4.08987i	0.890782	−	0.454430i
$82$		0			0
$83$	7.00731	+	5.87983i	0.769152	+	0.645395i	0.940492	−	0.339817i	$-0.110365\pi$
$83$	7.00731	+	5.87983i	0.769152	+	0.645395i	−0.171340	+	0.985212i	$0.554810\pi$
$84$		0			0
$85$	0.186274	+	1.05641i	0.0202042	+	0.114584i
$86$		0			0
$87$	0.247398	+	0.162158i	0.0265239	+	0.0173852i
$88$		0			0
$89$	−5.24813	−	3.03001i	−0.556300	−	0.321180i	0.195359	−	0.980732i	$-0.437413\pi$
$89$	−5.24813	−	3.03001i	−0.556300	−	0.321180i	−0.751659	+	0.659552i	$0.770746\pi$
$90$		0			0
$91$	7.41532	−	4.28124i	0.777337	−	0.448795i
$92$		0			0
$93$	−2.70664	−	8.98917i	−0.280666	−	0.932134i
$94$		0			0
$95$	−2.48649	+	2.08641i	−0.255109	+	0.214062i
$96$		0			0
$97$	−9.41639	+	3.42728i	−0.956089	+	0.347988i	−0.772500	−	0.635015i	$-0.780994\pi$
$97$	−9.41639	+	3.42728i	−0.956089	+	0.347988i	−0.183589	+	0.983003i	$0.558772\pi$
$98$		0			0
$99$	2.24773	−	1.48854i	0.225905	−	0.149604i
$100$		0			0
$101$	−13.1787	−	2.32376i	−1.31133	−	0.231223i	−0.526097	−	0.850425i	$-0.676345\pi$
$101$	−13.1787	−	2.32376i	−1.31133	−	0.231223i	−0.785232	+	0.619202i	$0.787456\pi$
$102$		0			0
$103$	−4.72126	+	12.9715i	−0.465199	+	1.27812i	0.456328	+	0.889811i	$0.349164\pi$
$103$	−4.72126	+	12.9715i	−0.465199	+	1.27812i	−0.921528	+	0.388313i	$0.873058\pi$
$104$		0			0
$105$	10.0863	+	4.33195i	0.984325	+	0.422755i
$106$		0			0
$107$	−9.79480			−0.946899			−0.473450	−	0.880821i	$-0.656991\pi$
$107$	−9.79480			−0.946899			−0.473450	+	0.880821i	$0.656991\pi$
$108$		0			0
$109$	−1.54270			−0.147763			−0.0738817	−	0.997267i	$-0.523539\pi$
$109$	−1.54270			−0.147763			−0.0738817	+	0.997267i	$0.523539\pi$
$110$		0			0
$111$	−10.5519	+	7.88149i	−1.00154	+	0.748078i
$112$		0			0
$113$	1.10758	−	3.04304i	0.104192	−	0.286265i	−0.876632	−	0.481162i	$-0.840215\pi$
$113$	1.10758	−	3.04304i	0.104192	−	0.286265i	0.980824	+	0.194897i	$0.0624371\pi$
$114$		0			0
$115$	−9.56276	−	1.68617i	−0.891732	−	0.157236i
$116$		0			0
$117$	−3.15816	+	4.27021i	−0.291972	+	0.394781i
$118$		0			0
$119$	3.72043	−	1.35412i	0.341051	−	0.124132i
$120$		0			0
$121$	−7.80786	+	6.55157i	−0.709806	+	0.595598i
$122$		0			0
$123$	−4.53043	+	4.81718i	−0.408495	+	0.434351i
$124$		0			0
$125$	−9.39970	+	5.42692i	−0.840735	+	0.485399i
$126$		0			0
$127$	8.45326	+	4.88049i	0.750105	+	0.433074i	0.825732	−	0.564063i	$-0.190762\pi$
$127$	8.45326	+	4.88049i	0.750105	+	0.433074i	−0.0756266	+	0.997136i	$0.524096\pi$
$128$		0			0
$129$	2.51317	−	1.26713i	0.221272	−	0.111565i
$130$		0			0
$131$	2.47229	+	14.0210i	0.216005	+	1.22502i	0.879154	+	0.476537i	$0.158108\pi$
$131$	2.47229	+	14.0210i	0.216005	+	1.22502i	−0.663150	+	0.748487i	$0.730781\pi$
$132$		0			0
$133$	9.17726	+	7.70063i	0.795769	+	0.667729i
$134$		0			0
$135$	−6.80895	+	0.0322290i	−0.586021	+	0.00277383i
$136$		0			0
$137$	−14.3330	+	17.0814i	−1.22455	+	1.45936i	−0.379063	+	0.925371i	$0.623753\pi$
$137$	−14.3330	+	17.0814i	−1.22455	+	1.45936i	−0.845489	+	0.533993i	$0.820691\pi$
$138$		0			0
$139$	6.09071	−	1.07396i	0.516607	−	0.0910918i	0.0907348	−	0.995875i	$-0.471078\pi$
$139$	6.09071	−	1.07396i	0.516607	−	0.0910918i	0.425872	+	0.904783i	$0.359967\pi$
$140$		0			0
$141$	−19.0941	−	1.08188i	−1.60801	−	0.0911107i
$142$		0			0
$143$	−0.795476	+	1.37781i	−0.0665211	+	0.115218i
$144$		0			0
$145$	−0.111897	−	0.193812i	−0.00929257	−	0.0160952i
$146$		0			0
$147$	6.50380	−	27.6359i	0.536425	−	2.27937i
$148$		0			0
$149$	2.52223	+	3.00588i	0.206629	+	0.246251i	0.859399	−	0.511305i	$-0.170838\pi$
$149$	2.52223	+	3.00588i	0.206629	+	0.246251i	−0.652770	+	0.757556i	$0.726393\pi$
$150$		0			0
$151$	−2.82037	−	7.74890i	−0.229518	−	0.630596i	0.770458	−	0.637491i	$-0.220028\pi$
$151$	−2.82037	−	7.74890i	−0.229518	−	0.630596i	−0.999976	+	0.00689453i	$0.997805\pi$
$152$		0			0
$153$	−1.78098	+	1.69092i	−0.143984	+	0.136703i
$154$		0			0
$155$	−1.23333	+	6.99454i	−0.0990631	+	0.561815i
$156$		0			0
$157$	18.3520	+	6.67960i	1.46465	+	0.533090i	0.946643	−	0.322285i	$-0.104451\pi$
$157$	18.3520	+	6.67960i	1.46465	+	0.533090i	0.518010	+	0.855375i	$0.326673\pi$
$158$		0			0
$159$	−14.8727	+	1.76217i	−1.17949	+	0.139749i
$160$		0			0
$161$			35.8391i			2.82452i
$162$		0			0
$163$		−	18.2255i		−	1.42754i	−0.700383	−	0.713768i	$-0.746987\pi$
$163$		−	18.2255i		−	1.42754i	0.700383	−	0.713768i	$-0.253013\pi$
$164$		0			0
$165$	−2.02546	+	0.239982i	−0.157682	+	0.0186826i
$166$		0			0
$167$	−1.66120	−	0.604627i	−0.128547	−	0.0467874i	0.276945	−	0.960886i	$-0.410678\pi$
$167$	−1.66120	−	0.604627i	−0.128547	−	0.0467874i	−0.405493	+	0.914098i	$0.632900\pi$
$168$		0			0
$169$	−1.71316	+	9.71582i	−0.131782	+	0.747371i
$170$		0			0
$171$	−7.12557	−	2.10878i	−0.544906	−	0.161262i
$172$		0			0
$173$	−7.50479	−	20.6192i	−0.570579	−	1.56765i	−0.803593	−	0.595179i	$-0.797081\pi$
$173$	−7.50479	−	20.6192i	−0.570579	−	1.56765i	0.233014	−	0.972473i	$-0.425141\pi$
$174$		0			0
$175$	10.2058	+	12.1628i	0.771488	+	0.919424i
$176$		0			0
$177$	4.53872	−	19.2859i	0.341151	−	1.44962i
$178$		0			0
$179$	2.39241	+	4.14377i	0.178817	+	0.309720i	0.941476	−	0.337081i	$-0.109440\pi$
$179$	2.39241	+	4.14377i	0.178817	+	0.309720i	−0.762659	+	0.646801i	$0.776106\pi$
$180$		0			0
$181$	3.55343	−	6.15472i	0.264124	−	0.457477i	−0.703209	−	0.710983i	$-0.748250\pi$
$181$	3.55343	−	6.15472i	0.264124	−	0.457477i	0.967334	+	0.253506i	$0.0815837\pi$
$182$		0			0
$183$	7.54752	+	0.427646i	0.557929	+	0.0316125i
$184$		0			0
$185$	9.81283	−	1.73027i	0.721453	−	0.127212i
$186$		0			0
$187$	−0.472860	+	0.563532i	−0.0345789	+	0.0412096i
$188$		0			0
$189$	4.48106	+	24.7283i	0.325949	+	1.79872i
$190$		0			0
$191$	−16.4820	−	13.8300i	−1.19259	−	1.00071i	−0.999811	−	0.0194643i	$-0.993804\pi$
$191$	−16.4820	−	13.8300i	−1.19259	−	1.00071i	−0.192784	−	0.981241i	$-0.561752\pi$
$192$		0			0
$193$	−0.928856	−	5.26781i	−0.0668605	−	0.379185i	−0.999816	−	0.0191926i	$-0.993890\pi$
$193$	−0.928856	−	5.26781i	−0.0668605	−	0.379185i	0.932955	−	0.359992i	$-0.117221\pi$
$194$		0			0
$195$	3.58797	−	1.80904i	0.256940	−	0.129548i
$196$		0			0
$197$	18.5003	+	10.6811i	1.31809	+	0.761000i	0.983421	−	0.181336i	$-0.0580422\pi$
$197$	18.5003	+	10.6811i	1.31809	+	0.761000i	0.334669	+	0.942336i	$0.391375\pi$
$198$		0			0
$199$	9.39493	−	5.42417i	0.665989	−	0.384509i	−0.128566	−	0.991701i	$-0.541037\pi$
$199$	9.39493	−	5.42417i	0.665989	−	0.384509i	0.794555	+	0.607192i	$0.207704\pi$
$200$		0			0
$201$	−18.0686	+	19.2122i	−1.27446	+	1.35513i
$202$		0			0
$203$	−0.632746	+	0.530937i	−0.0444101	+	0.0372645i
$204$		0			0
$205$	4.70131	−	1.71114i	0.328353	−	0.119511i
$206$		0			0
$207$	−8.86943	−	20.3845i	−0.616468	−	1.41682i
$208$		0			0
$209$	−2.19214	−	0.386533i	−0.151633	−	0.0267371i
$210$		0			0
$211$	−7.71029	+	21.1839i	−0.530799	+	1.45836i	0.327324	+	0.944912i	$0.393853\pi$
$211$	−7.71029	+	21.1839i	−0.530799	+	1.45836i	−0.858123	+	0.513445i	$0.828369\pi$
$212$		0			0
$213$	8.48271	−	6.33597i	0.581226	−	0.434133i
$214$		0			0
$215$	−2.12937			−0.145222
$216$		0			0
$217$	26.2140			1.77952
$218$		0			0
$219$	3.77533	+	1.62146i	0.255113	+	0.109568i
$220$		0			0
$221$	0.495678	−	1.36186i	0.0333429	−	0.0916089i
$222$		0			0
$223$	−8.12659	−	1.43294i	−0.544197	−	0.0959566i	−0.105210	−	0.994450i	$-0.533551\pi$
$223$	−8.12659	−	1.43294i	−0.544197	−	0.0959566i	−0.438987	+	0.898493i	$0.644663\pi$
$224$		0			0
$225$	−8.81490	−	4.39223i	−0.587660	−	0.292816i
$226$		0			0
$227$	−16.6850	+	6.07283i	−1.10742	+	0.403068i	−0.830047	−	0.557694i	$-0.811686\pi$
$227$	−16.6850	+	6.07283i	−1.10742	+	0.403068i	−0.277374	+	0.960762i	$0.589464\pi$
$228$		0			0
$229$	−19.1253	+	16.0480i	−1.26383	+	1.06048i	−0.268570	+	0.963260i	$0.586551\pi$
$229$	−19.1253	+	16.0480i	−1.26383	+	1.06048i	−0.995263	+	0.0972213i	$0.969005\pi$
$230$		0			0
$231$	2.17042	+	7.20828i	0.142803	+	0.474270i
$232$		0			0
$233$	1.13467	−	0.655101i	0.0743346	−	0.0429171i	−0.462372	−	0.886686i	$-0.653002\pi$
$233$	1.13467	−	0.655101i	0.0743346	−	0.0429171i	0.536707	+	0.843769i	$0.319668\pi$
$234$		0			0
$235$	12.5305	+	7.23449i	0.817400	+	0.471926i
$236$		0			0
$237$	−19.2021	−	12.5860i	−1.24731	−	0.817552i
$238$		0			0
$239$	−2.48029	−	14.0664i	−0.160436	−	0.909880i	−0.953646	−	0.300931i	$-0.902703\pi$
$239$	−2.48029	−	14.0664i	−0.160436	−	0.909880i	0.793209	−	0.608949i	$-0.208409\pi$
$240$		0			0
$241$	−22.1586	−	18.5933i	−1.42736	−	1.19770i	−0.947251	−	0.320492i	$-0.896152\pi$
$241$	−22.1586	−	18.5933i	−1.42736	−	1.19770i	−0.480111	−	0.877208i	$-0.659404\pi$
$242$		0			0
$243$	−8.66847	−	12.9560i	−0.556083	−	0.831127i
$244$		0			0
$245$	−13.8067	+	16.4542i	−0.882078	+	1.05122i
$246$		0			0
$247$	4.31868	−	0.761500i	0.274791	−	0.0484531i
$248$		0			0
$249$	8.68539	−	13.2510i	0.550414	−	0.839747i
$250$		0			0
$251$	−10.3158	+	17.8675i	−0.651128	+	1.12779i	0.331721	+	0.943378i	$0.392371\pi$
$251$	−10.3158	+	17.8675i	−0.651128	+	1.12779i	−0.982849	+	0.184410i	$0.940963\pi$
$252$		0			0
$253$	−3.32955	−	5.76695i	−0.209327	−	0.362565i
$254$		0			0
$255$	1.77909	−	0.535683i	0.111411	−	0.0335458i
$256$		0			0
$257$	−10.4205	−	12.4187i	−0.650014	−	0.774657i	0.335902	−	0.941897i	$-0.390959\pi$
$257$	−10.4205	−	12.4187i	−0.650014	−	0.774657i	−0.985916	+	0.167240i	$0.946514\pi$
$258$		0			0
$259$	−12.5782	−	34.5585i	−0.781574	−	2.14736i
$260$		0			0
$261$	0.228497	−	0.458577i	0.0141436	−	0.0283852i
$262$		0			0
$263$	−0.177029	+	1.00398i	−0.0109161	+	0.0619080i	−0.989779	−	0.142608i	$-0.954451\pi$
$263$	−0.177029	+	1.00398i	−0.0109161	+	0.0619080i	0.978863	+	0.204516i	$0.0655622\pi$
$264$		0			0
$265$	10.6475	+	3.87537i	0.654070	+	0.238062i
$266$		0			0
$267$	−4.14214	+	9.64438i	−0.253495	+	0.590226i
$268$		0			0
$269$			5.87390i			0.358138i	0.983837	+	0.179069i	$0.0573086\pi$
$269$			5.87390i			0.358138i	−0.983837	+	0.179069i	$0.942691\pi$
$270$		0			0
$271$		−	16.4894i		−	1.00166i	−0.865547	−	0.500828i	$-0.833029\pi$
$271$		−	16.4894i		−	1.00166i	0.865547	−	0.500828i	$-0.166971\pi$
$272$		0			0
$273$	−8.87500	−	11.8820i	−0.537139	−	0.719132i
$274$		0			0
$275$	−2.77220	−	1.00900i	−0.167170	−	0.0608449i
$276$		0			0
$277$	−1.59003	+	9.01750i	−0.0955355	+	0.541809i	0.899046	+	0.437853i	$0.144261\pi$
$277$	−1.59003	+	9.01750i	−0.0955355	+	0.541809i	−0.994582	+	0.103956i	$0.966850\pi$
$278$		0			0
$279$	−14.9100	+	6.48741i	−0.892636	+	0.388391i
$280$		0			0
$281$	−5.53194	−	15.1989i	−0.330008	−	0.906689i	−0.988108	−	0.153759i	$-0.950862\pi$
$281$	−5.53194	−	15.1989i	−0.330008	−	0.906689i	0.658101	−	0.752930i	$-0.271360\pi$
$282$		0			0
$283$	−3.90907	−	4.65865i	−0.232370	−	0.276928i	0.637242	−	0.770664i	$-0.280075\pi$
$283$	−3.90907	−	4.65865i	−0.232370	−	0.276928i	−0.869612	+	0.493736i	$0.835631\pi$
$284$		0			0
$285$	4.09540	+	3.85162i	0.242591	+	0.228150i
$286$		0			0
$287$	−9.23269	−	15.9915i	−0.544989	−	0.943948i
$288$		0			0
$289$	−8.16494	+	14.1421i	−0.480290	+	0.831887i
$290$		0			0
$291$	7.81399	+	15.4979i	0.458064	+	0.908504i
$292$		0			0
$293$	20.8773	−	3.68123i	1.21966	−	0.215060i	0.473483	−	0.880803i	$-0.342997\pi$
$293$	20.8773	−	3.68123i	1.21966	−	0.215060i	0.746181	+	0.665743i	$0.231885\pi$
$294$		0			0
$295$	−9.63510	+	11.4827i	−0.560977	+	0.668546i
$296$		0			0
$297$	−3.01838	−	3.56279i	−0.175144	−	0.206734i
$298$		0			0
$299$	10.0497	+	8.43269i	0.581188	+	0.487675i
$300$		0			0
$301$	1.36473	+	7.73976i	0.0786617	+	0.446113i
$302$		0			0
$303$	−1.31119	+	23.1412i	−0.0753258	+	1.32943i
$304$		0			0
$305$	−4.95306	−	2.85965i	−0.283612	−	0.163743i
$306$		0			0
$307$	−10.3867	+	5.99675i	−0.592799	+	0.342252i	−0.766203	−	0.642598i	$-0.777856\pi$
$307$	−10.3867	+	5.99675i	−0.592799	+	0.342252i	0.173405	+	0.984851i	$0.444523\pi$
$308$		0			0
$309$	23.2735	+	5.47715i	1.32398	+	0.311584i
$310$		0			0
$311$	19.8986	−	16.6969i	1.12835	−	0.946795i	0.129351	−	0.991599i	$-0.458711\pi$
$311$	19.8986	−	16.6969i	1.12835	−	0.946795i	0.998996	+	0.0448035i	$0.0142662\pi$
$312$		0			0
$313$	−13.1404	+	4.78272i	−0.742740	+	0.270335i	−0.685548	−	0.728028i	$-0.740437\pi$
$313$	−13.1404	+	4.78272i	−0.742740	+	0.270335i	−0.0571926	+	0.998363i	$0.518215\pi$
$314$		0			0
$315$	5.39553	−	18.2315i	0.304003	−	1.02723i
$316$		0			0
$317$	−8.05088	−	1.41959i	−0.452182	−	0.0797320i	−0.0570812	−	0.998370i	$-0.518179\pi$
$317$	−8.05088	−	1.41959i	−0.452182	−	0.0797320i	−0.395101	+	0.918638i	$0.629290\pi$
$318$		0			0
$319$	0.0524910	−	0.144218i	0.00293893	−	0.00807466i
$320$		0			0
$321$	1.99611	+	16.8473i	0.111412	+	0.940322i
$322$		0			0
$323$	2.02772			0.112825
$324$		0			0
$325$	5.81195			0.322389
$326$		0			0
$327$	0.314390	+	2.65347i	0.0173858	+	0.146737i
$328$		0			0
$329$	18.2648	−	50.1822i	1.00697	−	2.76663i
$330$		0			0
$331$	−22.5186	−	3.97063i	−1.23773	−	0.218246i	−0.483789	−	0.875184i	$-0.660740\pi$
$331$	−22.5186	−	3.97063i	−1.23773	−	0.218246i	−0.753944	+	0.656939i	$0.771851\pi$
$332$		0			0
$333$	15.7067	+	16.5433i	0.860723	+	0.906565i
$334$		0			0
$335$	18.7501	−	6.82447i	1.02443	−	0.372861i
$336$		0			0
$337$	23.0001	−	19.2994i	1.25289	−	1.05130i	0.256492	−	0.966546i	$-0.417433\pi$
$337$	23.0001	−	19.2994i	1.25289	−	1.05130i	0.996402	−	0.0847566i	$-0.0270113\pi$
$338$		0			0
$339$	−5.45981	−	1.28490i	−0.296536	−	0.0697864i
$340$		0			0
$341$	−4.21815	+	2.43535i	−0.228426	+	0.131882i
$342$		0			0
$343$	39.3365	+	22.7109i	2.12397	+	1.22627i
$344$		0			0
$345$	−0.951428	+	16.7918i	−0.0512232	+	0.904039i
$346$		0			0
$347$	0.389040	+	2.20636i	0.0208848	+	0.118443i	0.993468	−	0.114112i	$-0.0364023\pi$
$347$	0.389040	+	2.20636i	0.0208848	+	0.118443i	−0.972583	+	0.232556i	$0.925291\pi$
$348$		0			0
$349$	2.18159	+	1.83057i	0.116778	+	0.0979880i	0.699306	−	0.714822i	$-0.253492\pi$
$349$	2.18159	+	1.83057i	0.116778	+	0.0979880i	−0.582529	+	0.812810i	$0.697937\pi$
$350$		0			0
$351$	7.98846	+	4.56186i	0.426392	+	0.243494i
$352$		0			0
$353$	8.76320	−	10.4436i	0.466418	−	0.555855i	−0.480640	−	0.876918i	$-0.659596\pi$
$353$	8.76320	−	10.4436i	0.466418	−	0.555855i	0.947058	+	0.321063i	$0.104040\pi$
$354$		0			0
$355$	−7.88858	+	1.39097i	−0.418682	+	0.0738250i
$356$		0			0
$357$	−3.08732	−	6.12325i	−0.163398	−	0.324077i
$358$		0			0
$359$	0.410795	−	0.711518i	0.0216809	−	0.0375525i	−0.854981	−	0.518659i	$-0.826432\pi$
$359$	0.410795	−	0.711518i	0.0216809	−	0.0375525i	0.876662	+	0.481106i	$0.159765\pi$
$360$		0			0
$361$	−6.43218	−	11.1409i	−0.338536	−	0.586361i
$362$		0			0
$363$	12.8600	+	12.0945i	0.674976	+	0.634797i
$364$		0			0
$365$	−1.99814	−	2.38129i	−0.104587	−	0.124642i
$366$		0			0
$367$	0.168731	+	0.463584i	0.00880768	+	0.0241989i	0.944019	−	0.329892i	$-0.107012\pi$
$367$	0.168731	+	0.463584i	0.00880768	+	0.0241989i	−0.935211	+	0.354091i	$0.884790\pi$
$368$		0			0
$369$	9.20892	+	6.81073i	0.479397	+	0.354552i
$370$		0			0
$371$	7.26201	−	41.1849i	0.377025	−	2.13822i
$372$		0			0
$373$	−11.2429	−	4.09207i	−0.582134	−	0.211880i	0.0341322	−	0.999417i	$-0.489133\pi$
$373$	−11.2429	−	4.09207i	−0.582134	−	0.211880i	−0.616266	+	0.787538i	$0.711356\pi$
$374$		0			0
$375$	11.2500	+	15.0617i	0.580948	+	0.777783i
$376$		0			0
$377$			0.302355i			0.0155720i
$378$		0			0
$379$		−	5.12124i		−	0.263060i	−0.991312	−	0.131530i	$-0.958011\pi$
$379$		−	5.12124i		−	0.263060i	0.991312	−	0.131530i	$-0.0419890\pi$
$380$		0			0
$381$	6.67183	−	15.5344i	0.341808	−	0.795851i
$382$		0			0
$383$	21.6665	+	7.88596i	1.10711	+	0.402954i	0.829931	−	0.557866i	$-0.188380\pi$
$383$	21.6665	+	7.88596i	1.10711	+	0.402954i	0.277175	+	0.960819i	$0.410602\pi$
$384$		0			0
$385$	0.988985	−	5.60882i	0.0504034	−	0.285852i
$386$		0			0
$387$	−2.69166	−	4.06447i	−0.136825	−	0.206609i
$388$		0			0
$389$	0.636088	+	1.74764i	0.0322510	+	0.0886088i	0.954773	−	0.297335i	$-0.0960980\pi$
$389$	0.636088	+	1.74764i	0.0322510	+	0.0886088i	−0.922522	+	0.385944i	$0.873876\pi$
$390$		0			0
$391$	3.89918	+	4.64687i	0.197190	+	0.235002i
$392$		0			0
$393$	23.6126	−	7.10977i	1.19110	−	0.358641i
$394$		0			0
$395$	8.68502	+	15.0429i	0.436991	+	0.756890i
$396$		0			0
$397$	0.623914	−	1.08065i	0.0313134	−	0.0542363i	−0.849944	−	0.526873i	$-0.823364\pi$
$397$	0.623914	−	1.08065i	0.0313134	−	0.0542363i	0.881257	+	0.472637i	$0.156698\pi$
$398$		0			0
$399$	11.3750	−	17.3544i	0.569461	−	0.868806i
$400$		0			0
$401$	−4.78102	+	0.843022i	−0.238753	+	0.0420985i	−0.291744	−	0.956496i	$-0.594236\pi$
$401$	−4.78102	+	0.843022i	−0.238753	+	0.0420985i	0.0529914	+	0.998595i	$0.483124\pi$
$402$		0			0
$403$	6.16796	−	7.35069i	0.307248	−	0.366164i
$404$		0			0
$405$	1.44305	+	11.7050i	0.0717058	+	0.581625i
$406$		0			0
$407$	5.23456	+	4.39232i	0.259468	+	0.217719i
$408$		0			0
$409$	−1.14231	−	6.47835i	−0.0564835	−	0.320334i	0.943454	−	0.331503i	$-0.107556\pi$
$409$	−1.14231	−	6.47835i	−0.0564835	−	0.320334i	−0.999938	+	0.0111692i	$0.996445\pi$
$410$		0			0
$411$	32.3013	+	21.1720i	1.59331	+	1.04434i
$412$		0			0
$413$	47.9121	+	27.6620i	2.35760	+	1.36116i
$414$		0			0
$415$	−10.3808	+	5.99336i	−0.509574	+	0.294203i
$416$		0			0
$417$	−3.08847	−	10.2573i	−0.151243	−	0.502301i
$418$		0			0
$419$	−7.70073	+	6.46168i	−0.376205	+	0.315674i	−0.811211	−	0.584754i	$-0.801191\pi$
$419$	−7.70073	+	6.46168i	−0.376205	+	0.315674i	0.435005	+	0.900428i	$0.356747\pi$
$420$		0			0
$421$	−16.6228	+	6.05019i	−0.810143	+	0.294868i	−0.713683	−	0.700469i	$-0.752974\pi$
$421$	−16.6228	+	6.05019i	−0.810143	+	0.294868i	−0.0964603	+	0.995337i	$0.530752\pi$
$422$		0			0
$423$	2.03039	+	33.0627i	0.0987208	+	1.60756i
$424$		0			0
$425$	2.64656	+	0.466659i	0.128377	+	0.0226363i
$426$		0			0
$427$	−7.21972	+	19.8360i	−0.349387	+	0.959933i
$428$		0			0
$429$	2.53196	+	1.08745i	0.122244	+	0.0525025i
$430$		0			0
$431$	−21.3681			−1.02927			−0.514633	−	0.857410i	$-0.672072\pi$
$431$	−21.3681			−1.02927			−0.514633	+	0.857410i	$0.672072\pi$
$432$		0			0
$433$	−4.46822			−0.214729			−0.107364	−	0.994220i	$-0.534241\pi$
$433$	−4.46822			−0.214729			−0.107364	+	0.994220i	$0.534241\pi$
$434$		0			0
$435$	−0.310556	+	0.231963i	−0.0148900	+	0.0111218i
$436$		0			0
$437$	−6.27783	+	17.2482i	−0.300310	+	0.825094i
$438$		0			0
$439$	4.51694	+	0.796458i	0.215582	+	0.0380129i	0.280396	−	0.959884i	$-0.409534\pi$
$439$	4.51694	+	0.796458i	0.215582	+	0.0380129i	−0.0648140	+	0.997897i	$0.520645\pi$
$440$		0			0
$441$	−48.8598	−	5.55466i	−2.32666	−	0.264508i
$442$		0			0
$443$	1.50013	−	0.546001i	0.0712732	−	0.0259413i	−0.306138	−	0.951987i	$-0.599037\pi$
$443$	1.50013	−	0.546001i	0.0712732	−	0.0259413i	0.377411	+	0.926046i	$0.376815\pi$
$444$		0			0
$445$	6.08319	−	5.10440i	0.288371	−	0.241972i
$446$		0			0
$447$	4.65616	−	4.95087i	0.220229	−	0.234168i
$448$		0			0
$449$	6.59416	−	3.80714i	0.311198	−	0.179670i	−0.336265	−	0.941768i	$-0.609164\pi$
$449$	6.59416	−	3.80714i	0.311198	−	0.179670i	0.647462	+	0.762097i	$0.275830\pi$
$450$		0			0
$451$	2.97130	+	1.71548i	0.139913	+	0.0807789i
$452$		0			0
$453$	−12.7535	+	6.43026i	−0.599211	+	0.302120i
$454$		0			0
$455$	1.94838	+	11.0498i	0.0913413	+	0.518022i
$456$		0			0
$457$	1.24164	+	1.04186i	0.0580816	+	0.0487362i	0.671366	−	0.741126i	$-0.265708\pi$
$457$	1.24164	+	1.04186i	0.0580816	+	0.0487362i	−0.613285	+	0.789862i	$0.710152\pi$
$458$		0			0
$459$	3.27137	+	2.71873i	0.152695	+	0.126899i
$460$		0			0
$461$	11.2418	−	13.3974i	0.523582	−	0.623980i	−0.437842	−	0.899052i	$-0.644257\pi$
$461$	11.2418	−	13.3974i	0.523582	−	0.623980i	0.961424	+	0.275072i	$0.0887016\pi$
$462$		0			0
$463$	−24.0486	+	4.24041i	−1.11763	+	0.197069i	−0.701801	−	0.712373i	$-0.747620\pi$
$463$	−24.0486	+	4.24041i	−1.11763	+	0.197069i	−0.415831	+	0.909442i	$0.636509\pi$
$464$		0			0
$465$	12.2821	+	0.695908i	0.569568	+	0.0322719i
$466$		0			0
$467$	4.27236	−	7.39995i	0.197701	−	0.342429i	−0.750081	−	0.661346i	$-0.769986\pi$
$467$	4.27236	−	7.39995i	0.197701	−	0.342429i	0.947783	+	0.318917i	$0.103319\pi$
$468$		0			0
$469$	−36.8225	−	63.7784i	−1.70030	−	2.94501i
$470$		0			0
$471$	7.74902	−	32.9271i	0.357056	−	1.51720i
$472$		0			0
$473$	−0.938646	−	1.11863i	−0.0431590	−	0.0514349i
$474$		0			0
$475$	2.78121	+	7.64130i	0.127610	+	0.350607i
$476$		0			0
$477$	6.06192	+	25.2223i	0.277556	+	1.15485i
$478$		0			0
$479$	0.322833	−	1.83088i	0.0147506	−	0.0836548i	−0.976544	−	0.215319i	$-0.930921\pi$
$479$	0.322833	−	1.83088i	0.0147506	−	0.0836548i	0.991294	+	0.131664i	$0.0420320\pi$
$480$		0			0
$481$	−12.6501	−	4.60427i	−0.576797	−	0.209937i
$482$		0			0
$483$	61.6440	−	7.30376i	2.80490	−	0.332333i
$484$		0			0
$485$		−	13.1311i		−	0.596254i
$486$		0			0
$487$			13.1247i			0.594739i	0.954763	+	0.297369i	$0.0961093\pi$
$487$			13.1247i			0.594739i	−0.954763	+	0.297369i	$0.903891\pi$
$488$		0			0
$489$	−31.3483	+	3.71424i	−1.41762	+	0.167964i
$490$		0			0
$491$	39.1970	+	14.2665i	1.76893	+	0.643839i	0.999990	+	0.00452408i	$0.00144006\pi$
$491$	39.1970	+	14.2665i	1.76893	+	0.643839i	0.768945	+	0.639315i	$0.220782\pi$
$492$		0			0
$493$	−0.0242770	+	0.137682i	−0.00109338	+	0.00620086i
$494$		0			0
$495$	0.825549	+	3.43493i	0.0371057	+	0.154389i
$496$		0			0
$497$	10.1117	+	27.7817i	0.453572	+	1.24618i
$498$		0			0
$499$	18.6441	+	22.2192i	0.834624	+	0.994666i	0.999964	+	0.00842976i	$0.00268331\pi$
$499$	18.6441	+	22.2192i	0.834624	+	0.994666i	−0.165340	+	0.986237i	$0.552872\pi$
$500$		0			0
$501$	−0.701430	+	2.98051i	−0.0313376	+	0.133160i
$502$		0			0
$503$	−12.9793	−	22.4809i	−0.578720	−	1.00237i	−0.995627	−	0.0934227i	$-0.970219\pi$
$503$	−12.9793	−	22.4809i	−0.578720	−	1.00237i	0.416907	−	0.908949i	$-0.363114\pi$
$504$		0			0
$505$	8.76787	−	15.1864i	0.390165	−	0.675786i
$506$		0			0
$507$	17.0605	+	0.966657i	0.757685	+	0.0429307i
$508$		0			0
$509$	−11.0255	+	1.94409i	−0.488695	+	0.0861701i	−0.412566	−	0.910928i	$-0.635367\pi$
$509$	−11.0255	+	1.94409i	−0.488695	+	0.0861701i	−0.0761292	+	0.997098i	$0.524256\pi$
$510$		0			0
$511$	−7.37482	+	8.78896i	−0.326243	+	0.388801i
$512$		0			0
$513$	−2.17500	+	12.6859i	−0.0960286	+	0.560095i
$514$		0			0
$515$	−13.8568	−	11.6272i	−0.610604	−	0.512358i
$516$		0			0
$517$	1.72303	+	9.77177i	0.0757786	+	0.429762i
$518$		0			0
$519$	−33.9361	+	17.1104i	−1.48963	+	0.751065i
$520$		0			0
$521$	−27.1483	−	15.6741i	−1.18939	−	0.686695i	−0.231222	−	0.972901i	$-0.574272\pi$
$521$	−27.1483	−	15.6741i	−1.18939	−	0.686695i	−0.958168	+	0.286206i	$0.907606\pi$
$522$		0			0
$523$	−28.5486	+	16.4825i	−1.24834	+	0.720731i	−0.970779	−	0.239977i	$-0.922860\pi$
$523$	−28.5486	+	16.4825i	−1.24834	+	0.720731i	−0.277563	+	0.960707i	$0.589527\pi$
$524$		0			0
$525$	18.8404	−	20.0329i	0.822264	−	0.874309i
$526$		0			0
$527$	3.39888	−	2.85200i	0.148058	−	0.124235i
$528$		0			0
$529$	−29.9862	+	10.9141i	−1.30375	+	0.474526i
$530$		0			0
$531$	−34.0971	−	3.87636i	−1.47969	−	0.168220i
$532$		0			0
$533$	−6.65657	−	1.17373i	−0.288328	−	0.0508400i
$534$		0			0
$535$	4.38986	−	12.0610i	0.189790	−	0.521444i
$536$		0			0
$537$	6.63982	−	4.95946i	0.286529	−	0.214017i
$538$		0			0
$539$	−14.7301			−0.634471
$540$		0			0
$541$	20.7542			0.892293			0.446146	−	0.894960i	$-0.352796\pi$
$541$	20.7542			0.892293			0.446146	+	0.894960i	$0.352796\pi$
$542$		0			0
$543$	−11.3104	−	4.85768i	−0.485376	−	0.208463i
$544$		0			0
$545$	0.691410	−	1.89963i	0.0296167	−	0.0813713i
$546$		0			0
$547$	24.7674	+	4.36716i	1.05898	+	0.186726i	0.675902	−	0.736991i	$-0.263754\pi$
$547$	24.7674	+	4.36716i	1.05898	+	0.186726i	0.383074	+	0.923718i	$0.374865\pi$
$548$		0			0
$549$	−0.802572	−	13.0690i	−0.0342529	−	0.557773i
$550$		0			0
$551$	−0.397523	+	0.144686i	−0.0169350	+	0.00616385i
$552$		0			0
$553$	49.1112	−	41.2092i	2.08842	−	1.75239i
$554$		0			0
$555$	−4.97588	−	16.5256i	−0.211214	−	0.701474i
$556$		0			0
$557$	31.7257	−	18.3168i	1.34426	−	0.776110i	0.356832	−	0.934169i	$-0.383857\pi$
$557$	31.7257	−	18.3168i	1.34426	−	0.776110i	0.987430	+	0.158059i	$0.0505236\pi$
$558$		0			0
$559$	2.49142	+	1.43842i	0.105376	+	0.0608389i
$560$		0			0
$561$	1.06565	+	0.698484i	0.0449919	+	0.0294900i
$562$		0			0
$563$	1.25844	+	7.13697i	0.0530369	+	0.300787i	0.999775	−	0.0212177i	$-0.00675430\pi$
$563$	1.25844	+	7.13697i	0.0530369	+	0.300787i	−0.946738	+	0.322005i	$0.895643\pi$
$564$		0			0
$565$	3.25072	+	2.72768i	0.136759	+	0.114754i
$566$		0			0
$567$	41.6200	−	12.7470i	1.74788	−	0.535323i
$568$		0			0
$569$	20.9212	−	24.9329i	0.877063	−	1.04524i	−0.121549	−	0.992585i	$-0.538786\pi$
$569$	20.9212	−	24.9329i	0.877063	−	1.04524i	0.998613	−	0.0526578i	$-0.0167693\pi$
$570$		0			0
$571$	−9.12840	+	1.60958i	−0.382012	+	0.0673589i	−0.361357	−	0.932428i	$-0.617686\pi$
$571$	−9.12840	+	1.60958i	−0.382012	+	0.0673589i	−0.0206550	+	0.999787i	$0.506575\pi$
$572$		0			0
$573$	−20.4290	+	31.1678i	−0.853434	+	1.30205i
$574$		0			0
$575$	−12.1633	+	21.0674i	−0.507243	+	0.878571i
$576$		0			0
$577$	−14.2229	−	24.6348i	−0.592107	−	1.02556i	−0.993948	−	0.109850i	$-0.964963\pi$
$577$	−14.2229	−	24.6348i	−0.592107	−	1.02556i	0.401841	−	0.915709i	$-0.368370\pi$
$578$		0			0
$579$	−8.87144	+	2.67119i	−0.368684	+	0.111011i
$580$		0			0
$581$	28.4377	+	33.8907i	1.17979	+	1.40602i
$582$		0			0
$583$	2.65764	+	7.30181i	0.110068	+	0.302410i
$584$		0			0
$585$	−3.84278	−	5.80270i	−0.158880	−	0.239912i
$586$		0			0
$587$	8.04410	−	45.6204i	0.332016	−	1.88295i	−0.122899	−	0.992419i	$-0.539219\pi$
$587$	8.04410	−	45.6204i	0.332016	−	1.88295i	0.454915	−	0.890535i	$-0.349670\pi$
$588$		0			0
$589$	12.6159	+	4.59183i	0.519831	+	0.189203i
$590$		0			0
$591$	14.6015	−	33.9976i	0.600627	−	1.39847i
$592$		0			0
$593$			38.4802i			1.58019i	0.612983	+	0.790096i	$0.289969\pi$
$593$			38.4802i			1.58019i	−0.612983	+	0.790096i	$0.710031\pi$
$594$		0			0
$595$			5.18812i			0.212692i
$596$		0			0
$597$	−11.2443	−	15.0541i	−0.460198	−	0.616122i
$598$		0			0
$599$	−0.703679	−	0.256118i	−0.0287515	−	0.0104647i	0.327604	−	0.944815i	$-0.393759\pi$
$599$	−0.703679	−	0.256118i	−0.0287515	−	0.0104647i	−0.356356	+	0.934350i	$0.615981\pi$
$600$		0			0
$601$	−2.54887	+	14.4554i	−0.103971	+	0.589646i	0.887656	+	0.460507i	$0.152332\pi$
$601$	−2.54887	+	14.4554i	−0.103971	+	0.589646i	−0.991626	+	0.129139i	$0.958779\pi$
$602$		0			0
$603$	36.7276	+	27.1630i	1.49567	+	1.10616i
$604$		0			0
$605$	−4.56808	−	12.5507i	−0.185719	−	0.510258i
$606$		0			0
$607$	−0.585828	−	0.698163i	−0.0237780	−	0.0283376i	0.754024	−	0.656846i	$-0.228110\pi$
$607$	−0.585828	−	0.698163i	−0.0237780	−	0.0283376i	−0.777802	+	0.628509i	$0.783666\pi$
$608$		0			0
$609$	1.04217	+	0.980135i	0.0422309	+	0.0397171i
$610$		0			0
$611$	−9.77405	−	16.9292i	−0.395416	−	0.684880i
$612$		0			0
$613$	8.09558	−	14.0220i	0.326977	−	0.566341i	−0.654933	−	0.755687i	$-0.727303\pi$
$613$	8.09558	−	14.0220i	0.326977	−	0.566341i	0.981911	+	0.189345i	$0.0606366\pi$
$614$		0			0
$615$	−3.90128	−	7.73762i	−0.157315	−	0.312011i
$616$		0			0
$617$	31.4959	−	5.55358i	1.26798	−	0.223579i	0.501110	−	0.865384i	$-0.332925\pi$
$617$	31.4959	−	5.55358i	1.26798	−	0.223579i	0.766868	+	0.641805i	$0.221814\pi$
$618$		0			0
$619$	−1.71534	+	2.04426i	−0.0689454	+	0.0821659i	−0.799415	−	0.600780i	$-0.794857\pi$
$619$	−1.71534	+	2.04426i	−0.0689454	+	0.0821659i	0.730469	+	0.682946i	$0.239301\pi$
$620$		0			0
$621$	−33.2543	+	19.4098i	−1.33445	+	0.778889i
$622$		0			0
$623$	−22.4521	−	18.8395i	−0.899524	−	0.754791i
$624$		0			0
$625$	0.380536	+	2.15813i	0.0152214	+	0.0863251i
$626$		0			0
$627$	−0.218103	+	3.84930i	−0.00871018	+	0.153726i
$628$		0			0
$629$	−5.39073	−	3.11234i	−0.214943	−	0.124097i
$630$		0			0
$631$	5.07657	−	2.93096i	0.202095	−	0.116680i	−0.395537	−	0.918450i	$-0.629442\pi$
$631$	5.07657	−	2.93096i	0.202095	−	0.116680i	0.597632	+	0.801770i	$0.296108\pi$
$632$		0			0
$633$	38.0080	+	8.94474i	1.51068	+	0.355521i
$634$		0			0
$635$	−9.79830	+	8.22175i	−0.388834	+	0.326270i
$636$		0			0
$637$	27.2694	−	9.92523i	1.08045	−	0.393252i
$638$		0			0
$639$	−12.6267	−	13.2992i	−0.499505	−	0.526108i
$640$		0			0
$641$	39.1324	+	6.90010i	1.54564	+	0.272538i	0.880450	−	0.474139i	$-0.157240\pi$
$641$	39.1324	+	6.90010i	1.54564	+	0.272538i	0.665188	+	0.746676i	$0.268352\pi$
$642$		0			0
$643$	3.14851	−	8.65047i	0.124165	−	0.341141i	−0.862000	−	0.506909i	$-0.830788\pi$
$643$	3.14851	−	8.65047i	0.124165	−	0.341141i	0.986165	+	0.165768i	$0.0530102\pi$
$644$		0			0
$645$	0.433950	+	3.66255i	0.0170868	+	0.144213i
$646$		0			0
$647$	−33.6328			−1.32224			−0.661122	−	0.750279i	$-0.729919\pi$
$647$	−33.6328			−1.32224			−0.661122	+	0.750279i	$0.729919\pi$
$648$		0			0
$649$	−10.2795			−0.403506
$650$		0			0
$651$	−5.34222	−	45.0886i	−0.209378	−	1.76716i
$652$		0			0
$653$	7.02522	−	19.3016i	0.274918	−	0.755331i	−0.723001	−	0.690847i	$-0.757238\pi$
$653$	7.02522	−	19.3016i	0.274918	−	0.755331i	0.997919	−	0.0644840i	$-0.0205402\pi$
$654$		0			0
$655$	−18.3732	−	3.23968i	−0.717899	−	0.126585i
$656$		0			0
$657$	2.01956	−	6.82409i	0.0787904	−	0.266233i
$658$		0			0
$659$	20.2055	−	7.35420i	0.787094	−	0.286479i	0.0829665	−	0.996552i	$-0.473561\pi$
$659$	20.2055	−	7.35420i	0.787094	−	0.286479i	0.704128	+	0.710074i	$0.251338\pi$
$660$		0			0
$661$	−5.31450	+	4.45939i	−0.206710	+	0.173450i	−0.740265	−	0.672315i	$-0.765300\pi$
$661$	−5.31450	+	4.45939i	−0.206710	+	0.173450i	0.533555	+	0.845765i	$0.320856\pi$
$662$		0			0
$663$	−2.44345	−	0.575038i	−0.0948957	−	0.0223326i
$664$		0			0
$665$	−13.5954	+	7.84932i	−0.527208	+	0.304384i
$666$		0			0
$667$	−1.09599	−	0.632769i	−0.0424368	−	0.0245009i
$668$		0			0
$669$	−0.808540	+	14.2699i	−0.0312599	+	0.551707i
$670$		0			0
$671$	−0.681078	−	3.86259i	−0.0262927	−	0.149114i
$672$		0			0
$673$	−34.7433	−	29.1531i	−1.33926	−	1.12377i	−0.981816	−	0.189833i	$-0.939205\pi$
$673$	−34.7433	−	29.1531i	−1.33926	−	1.12377i	−0.357440	−	0.933936i	$-0.616350\pi$
$674$		0			0
$675$	−5.75832	+	16.0569i	−0.221638	+	0.618031i
$676$		0			0
$677$	−17.9845	+	21.4331i	−0.691201	+	0.823741i	−0.991500	−	0.130104i	$-0.958469\pi$
$677$	−17.9845	+	21.4331i	−0.691201	+	0.823741i	0.300300	+	0.953845i	$0.402913\pi$
$678$		0			0
$679$	−47.7286	+	8.41585i	−1.83166	+	0.322971i
$680$		0			0
$681$	13.8457	+	27.4609i	0.530567	+	1.05230i
$682$		0			0
$683$	5.84178	−	10.1183i	0.223529	−	0.387164i	−0.732348	−	0.680931i	$-0.761575\pi$
$683$	5.84178	−	10.1183i	0.223529	−	0.387164i	0.955877	+	0.293766i	$0.0949088\pi$
$684$		0			0
$685$	−14.6098	−	25.3049i	−0.558211	−	0.966849i
$686$		0			0
$687$	31.5005	+	29.6254i	1.20182	+	1.13028i
$688$		0			0
$689$	−9.84000	−	11.7269i	−0.374874	−	0.446758i
$690$		0			0
$691$	−1.10341	−	3.03159i	−0.0419756	−	0.115327i	0.916934	−	0.399039i	$-0.130656\pi$
$691$	−1.10341	−	3.03159i	−0.0419756	−	0.115327i	−0.958910	+	0.283712i	$0.908434\pi$
$692$		0			0
$693$	11.9561	−	5.20216i	0.454174	−	0.197614i
$694$		0			0
$695$	−1.40731	+	7.98125i	−0.0533823	+	0.302746i
$696$		0			0
$697$	−2.93693	−	1.06895i	−0.111244	−	0.0404895i
$698$		0			0
$699$	−1.35802	−	1.81815i	−0.0513652	−	0.0687687i
$700$		0			0
$701$		−	47.5367i		−	1.79544i	−0.440569	−	0.897719i	$-0.645223\pi$
$701$		−	47.5367i		−	1.79544i	0.440569	−	0.897719i	$-0.354777\pi$
$702$		0			0
$703$		−	18.8351i		−	0.710381i
$704$		0			0
$705$	9.88984	−	23.0271i	0.372473	−	0.867249i
$706$		0			0
$707$	−60.8185	−	22.1361i	−2.28732	−	0.832515i
$708$		0			0
$709$	−3.66040	+	20.7591i	−0.137469	+	0.779626i	0.835639	+	0.549279i	$0.185097\pi$
$709$	−3.66040	+	20.7591i	−0.137469	+	0.779626i	−0.973108	+	0.230348i	$0.926014\pi$
$710$		0			0
$711$	−17.7350	+	35.5929i	−0.665115	+	1.33484i
$712$		0			0
$713$	13.7368	+	37.7414i	0.514446	+	1.41343i
$714$		0			0
$715$	−1.34007	−	1.59704i	−0.0501158	−	0.0597257i
$716$		0			0
$717$	−23.6890	+	7.13278i	−0.884683	+	0.266378i
$718$		0			0
$719$	13.9679	+	24.1931i	0.520915	+	0.902251i	0.999704	+	0.0243210i	$0.00774238\pi$
$719$	13.9679	+	24.1931i	0.520915	+	0.902251i	−0.478789	+	0.877930i	$0.658924\pi$
$720$		0			0
$721$	−33.3814	+	57.8184i	−1.24319	+	2.15327i
$722$		0			0
$723$	−27.4651	+	41.9025i	−1.02144	+	1.55837i
$724$		0			0
$725$	−0.552141	+	0.0973573i	−0.0205060	+	0.00361576i
$726$		0			0
$727$	1.13886	−	1.35724i	0.0422380	−	0.0503372i	−0.744512	−	0.667609i	$-0.767318\pi$
$727$	1.13886	−	1.35724i	0.0422380	−	0.0503372i	0.786750	+	0.617272i	$0.211762\pi$
$728$		0			0
$729$	−20.5180	+	17.5503i	−0.759925	+	0.650011i
$730$		0			0
$731$	1.01901	+	0.855052i	0.0376895	+	0.0316252i
$732$		0			0
$733$	7.32246	+	41.5277i	0.270461	+	1.53386i	0.753020	+	0.657998i	$0.228597\pi$
$733$	7.32246	+	41.5277i	0.270461	+	1.53386i	−0.482558	+	0.875864i	$0.660292\pi$
$734$		0			0
$735$	31.1152	+	20.3946i	1.14770	+	0.752264i
$736$		0			0
$737$	11.8504	+	6.84181i	0.436514	+	0.252021i
$738$		0			0
$739$	−18.4096	+	10.6288i	−0.677208	+	0.390986i	−0.798802	−	0.601594i	$-0.794533\pi$
$739$	−18.4096	+	10.6288i	−0.677208	+	0.390986i	0.121595	+	0.992580i	$0.461199\pi$
$740$		0			0
$741$	−2.18991	−	7.27303i	−0.0804484	−	0.267181i
$742$		0			0
$743$	10.2817	−	8.62740i	0.377200	−	0.316509i	−0.434402	−	0.900719i	$-0.643040\pi$
$743$	10.2817	−	8.62740i	0.377200	−	0.316509i	0.811602	+	0.584211i	$0.198596\pi$
$744$		0			0
$745$	−4.83178	+	1.75862i	−0.177023	+	0.0644310i
$746$		0			0
$747$	−24.5620	−	12.2386i	−0.898675	−	0.447786i
$748$		0			0
$749$	−46.6526	−	8.22612i	−1.70465	−	0.300576i
$750$		0			0
$751$	4.29807	−	11.8089i	0.156839	−	0.430911i	−0.836240	−	0.548364i	$-0.815251\pi$
$751$	4.29807	−	11.8089i	0.156839	−	0.430911i	0.993078	+	0.117453i	$0.0374730\pi$
$752$		0			0
$753$	32.8348	+	14.1021i	1.19657	+	0.513910i
$754$		0			0
$755$	10.8058			0.393264
$756$		0			0
$757$	−4.78739			−0.174001			−0.0870003	−	0.996208i	$-0.527728\pi$
$757$	−4.78739			−0.174001			−0.0870003	+	0.996208i	$0.527728\pi$
$758$		0			0
$759$	−9.24073	+	6.90216i	−0.335417	+	0.250532i
$760$		0			0
$761$	−9.75276	+	26.7955i	−0.353537	+	0.971336i	0.627687	+	0.778466i	$0.284002\pi$
$761$	−9.75276	+	26.7955i	−0.353537	+	0.971336i	−0.981224	+	0.192870i	$0.938220\pi$
$762$		0			0
$763$	−7.34786	−	1.29563i	−0.266010	−	0.0469048i
$764$		0			0
$765$	−1.28395	−	2.95089i	−0.0464213	−	0.106690i
$766$		0			0
$767$	19.0301	−	6.92639i	0.687137	−	0.250097i
$768$		0			0
$769$	0.580256	−	0.486892i	0.0209246	−	0.0175578i	−0.632265	−	0.774752i	$-0.717875\pi$
$769$	0.580256	−	0.486892i	0.0209246	−	0.0175578i	0.653190	+	0.757194i	$0.273430\pi$
$770$		0			0
$771$	−19.2368	+	20.4543i	−0.692795	+	0.736645i
$772$		0			0
$773$	29.8026	−	17.2065i	1.07192	−	0.618875i	0.143217	−	0.989691i	$-0.454255\pi$
$773$	29.8026	−	17.2065i	1.07192	−	0.618875i	0.928706	+	0.370816i	$0.120922\pi$
$774$		0			0
$775$	15.4094	+	8.89664i	0.553523	+	0.319577i
$776$		0			0
$777$	−56.8779	+	28.6776i	−2.04048	+	1.02880i
$778$		0			0
$779$	−1.64221	−	9.31345i	−0.0588384	−	0.333689i
$780$		0			0
$781$	−4.20809	−	3.53101i	−0.150577	−	0.126349i
$782$		0			0
$783$	−0.835328	−	0.299564i	−0.0298522	−	0.0107056i
$784$		0			0
$785$	−16.4501	+	19.6045i	−0.587131	+	0.699715i
$786$		0			0
$787$	−25.6026	+	4.51442i	−0.912633	+	0.160922i	−0.610199	−	0.792248i	$-0.708910\pi$
$787$	−25.6026	+	4.51442i	−0.912633	+	0.160922i	−0.302434	+	0.953170i	$0.597799\pi$
$788$		0			0
$789$	1.76294	+	0.0998890i	0.0627624	+	0.00355614i
$790$		0			0
$791$	7.83107	−	13.5638i	0.278441	−	0.482274i
$792$		0			0
$793$	3.86349	+	6.69176i	0.137197	+	0.237631i
$794$		0			0
$795$	4.49583	−	19.1037i	0.159451	−	0.677537i
$796$		0			0
$797$	−16.5285	−	19.6979i	−0.585469	−	0.697735i	0.389259	−	0.921128i	$-0.372731\pi$
$797$	−16.5285	−	19.6979i	−0.585469	−	0.697735i	−0.974728	+	0.223393i	$0.928287\pi$
$798$		0			0
$799$	−3.09146	−	8.49373i	−0.109368	−	0.300486i
$800$		0			0
$801$	17.4327	+	5.15911i	0.615953	+	0.182288i
$802$		0			0
$803$	0.370179	−	2.09939i	0.0130633	−	0.0740859i
$804$		0			0
$805$	−44.1313	−	16.0625i	−1.55542	−	0.566128i
$806$		0			0
$807$	10.1032	−	1.19706i	0.355651	−	0.0421385i
$808$		0			0
$809$		−	31.7597i		−	1.11661i	−0.829636	−	0.558305i	$-0.811452\pi$
$809$		−	31.7597i		−	1.11661i	0.829636	−	0.558305i	$-0.188548\pi$
$810$		0			0
$811$		−	34.9131i		−	1.22596i	−0.790097	−	0.612982i	$-0.789970\pi$
$811$		−	34.9131i		−	1.22596i	0.790097	−	0.612982i	$-0.210030\pi$
$812$		0			0
$813$	−28.3620	+	3.36041i	−0.994699	+	0.117855i
$814$		0			0
$815$	22.4424	+	8.16838i	0.786124	+	0.286126i
$816$		0			0
$817$	−0.698952	+	3.96395i	−0.0244532	+	0.138681i
$818$		0			0
$819$	−18.6286	+	17.6866i	−0.650937	+	0.618021i
$820$		0			0
$821$	−8.51832	−	23.4039i	−0.297291	−	0.816802i	−0.994950	−	0.100371i	$-0.967997\pi$
$821$	−8.51832	−	23.4039i	−0.297291	−	0.816802i	0.697659	−	0.716430i	$-0.254225\pi$
$822$		0			0
$823$	−0.911545	−	1.08634i	−0.0317745	−	0.0378673i	0.749923	−	0.661525i	$-0.230090\pi$
$823$	−0.911545	−	1.08634i	−0.0317745	−	0.0378673i	−0.781698	+	0.623658i	$0.785646\pi$
$824$		0			0
$825$	−1.17054	+	4.97387i	−0.0407531	+	0.173168i
$826$		0			0
$827$	−9.70930	−	16.8170i	−0.337625	−	0.584785i	0.646360	−	0.763033i	$-0.276290\pi$
$827$	−9.70930	−	16.8170i	−0.337625	−	0.584785i	−0.983986	+	0.178248i	$0.942957\pi$
$828$		0			0
$829$	−14.5122	+	25.1358i	−0.504029	+	0.873003i	0.495960	+	0.868345i	$0.334816\pi$
$829$	−14.5122	+	25.1358i	−0.504029	+	0.873003i	−0.999989	+	0.00465817i	$0.998517\pi$
$830$		0			0
$831$	15.8343	+	0.897179i	0.549286	+	0.0311228i
$832$		0			0
$833$	13.2144	−	2.33006i	0.457853	−	0.0807318i
$834$		0			0
$835$	1.48904	−	1.77457i	0.0515304	−	0.0614115i
$836$		0			0
$837$	14.1970	+	24.3233i	0.490721	+	0.840738i
$838$		0			0
$839$	−14.8247	−	12.4394i	−0.511806	−	0.429457i	0.349958	−	0.936765i	$-0.386196\pi$
$839$	−14.8247	−	12.4394i	−0.511806	−	0.429457i	−0.861764	+	0.507309i	$0.830640\pi$
$840$		0			0
$841$	5.03073	+	28.5307i	0.173474	+	0.983817i
$842$		0			0
$843$	−25.0150	+	12.6125i	−0.861562	+	0.434396i
$844$		0			0
$845$	−11.1960	−	6.46400i	−0.385153	−	0.222368i
$846$		0			0
$847$	−42.6912	+	24.6478i	−1.46689	+	0.846907i
$848$		0			0
$849$	−7.21633	+	7.67308i	−0.247664	+	0.263339i
$850$		0			0
$851$	43.1640	−	36.2189i	1.47964	−	1.24157i
$852$		0			0
$853$	9.02903	−	3.28630i	0.309148	−	0.112521i	−0.182787	−	0.983153i	$-0.558512\pi$
$853$	9.02903	−	3.28630i	0.309148	−	0.112521i	0.491935	+	0.870632i	$0.336290\pi$
$854$		0			0
$855$	5.79025	−	7.82911i	0.198022	−	0.267750i
$856$		0			0
$857$	−6.92312	−	1.22073i	−0.236489	−	0.0416995i	0.0541472	−	0.998533i	$-0.482756\pi$
$857$	−6.92312	−	1.22073i	−0.236489	−	0.0416995i	−0.290637	+	0.956833i	$0.593867\pi$
$858$		0			0
$859$	8.26389	−	22.7048i	0.281960	−	0.774679i	−0.715168	−	0.698952i	$-0.753650\pi$
$859$	8.26389	−	22.7048i	0.281960	−	0.774679i	0.997129	−	0.0757272i	$-0.0241278\pi$
$860$		0			0
$861$	−25.6241	+	19.1394i	−0.873268	+	0.652268i
$862$		0			0
$863$	47.9943			1.63374			0.816872	−	0.576818i	$-0.195706\pi$
$863$	47.9943			1.63374			0.816872	+	0.576818i	$0.195706\pi$
$864$		0			0
$865$	28.7535			0.977648
$866$		0			0
$867$	25.9886	+	11.1618i	0.882620	+	0.379075i
$868$		0			0
$869$	−4.07414	+	11.1936i	−0.138206	+	0.379717i
$870$		0			0
$871$	−26.5482	−	4.68117i	−0.899552	−	0.158615i
$872$		0			0
$873$	25.0643	−	16.5986i	0.848298	−	0.561777i
$874$		0			0
$875$	−49.3286	+	17.9541i	−1.66761	+	0.606960i
$876$		0			0
$877$	−9.68250	+	8.12459i	−0.326955	+	0.274348i	−0.791458	−	0.611224i	$-0.790678\pi$
$877$	−9.68250	+	8.12459i	−0.326955	+	0.274348i	0.464503	+	0.885572i	$0.346233\pi$
$878$		0			0
$879$	−10.5864	−	35.1591i	−0.357071	−	1.18589i
$880$		0			0
$881$	−37.8501	+	21.8527i	−1.27520	+	0.736238i	−0.975962	−	0.217941i	$-0.930066\pi$
$881$	−37.8501	+	21.8527i	−1.27520	+	0.736238i	−0.299239	+	0.954178i	$0.596733\pi$
$882$		0			0
$883$	27.7005	+	15.9929i	0.932196	+	0.538203i	0.887505	−	0.460797i	$-0.152437\pi$
$883$	27.7005	+	15.9929i	0.932196	+	0.538203i	0.0446903	+	0.999001i	$0.485770\pi$
$884$		0			0
$885$	21.7140	+	14.2325i	0.729907	+	0.478419i
$886$		0			0
$887$	−1.94356	−	11.0225i	−0.0652585	−	0.370099i	−0.999895	−	0.0144946i	$-0.995386\pi$
$887$	−1.94356	−	11.0225i	−0.0652585	−	0.370099i	0.934636	−	0.355605i	$-0.115725\pi$
$888$		0			0
$889$	36.1640	+	30.3452i	1.21290	+	1.01775i
$890$		0			0
$891$	−5.51294	+	5.91775i	−0.184690	+	0.198252i
$892$		0			0
$893$	17.5805	−	20.9517i	0.588310	−	0.701120i
$894$		0			0
$895$	−6.17476	+	1.08878i	−0.206400	+	0.0363938i
$896$		0			0
$897$	12.4563	−	19.0042i	0.415905	−	0.634531i
$898$		0			0
$899$	−0.462829	+	0.801643i	−0.0154362	+	0.0267363i
$900$		0			0
$901$	−3.53920	−	6.13008i	−0.117908	−	0.204223i
$902$		0			0
$903$	13.0344	−	3.92467i	0.433759	−	0.130605i
$904$		0			0
$905$	5.98617	+	7.13404i	0.198987	+	0.237143i
$906$		0			0
$907$	9.11867	+	25.0534i	0.302781	+	0.831883i	0.994014	+	0.109251i	$0.0348454\pi$
$907$	9.11867	+	25.0534i	0.302781	+	0.831883i	−0.691234	+	0.722631i	$0.742932\pi$
$908$		0			0
$909$	40.0705	−	2.46074i	1.32905	−	0.0816175i
$910$		0			0
$911$	−4.68320	+	26.5597i	−0.155161	+	0.879963i	0.803477	+	0.595336i	$0.202981\pi$
$911$	−4.68320	+	26.5597i	−0.155161	+	0.879963i	−0.958638	+	0.284628i	$0.908130\pi$
$912$		0			0
$913$	−7.72450	−	2.81149i	−0.255644	−	0.0930466i
$914$		0			0
$915$	−3.90926	+	9.10214i	−0.129236	+	0.300908i
$916$		0			0
$917$			68.8586i			2.27391i
$918$		0			0
$919$		−	50.9517i		−	1.68074i	−0.542013	−	0.840370i	$-0.682338\pi$
$919$		−	50.9517i		−	1.68074i	0.542013	−	0.840370i	$-0.317662\pi$
$920$		0			0
$921$	12.4313	+	16.6432i	0.409624	+	0.548412i
$922$		0			0
$923$	10.1695	+	3.70140i	0.334733	+	0.121833i
$924$		0			0
$925$	4.33472	−	24.5834i	0.142525	−	0.808298i
$926$		0			0
$927$	4.67783	−	41.1470i	0.153640	−	1.35145i
$928$		0			0
$929$	−1.42239	−	3.90799i	−0.0466672	−	0.128217i	0.914170	−	0.405332i	$-0.132844\pi$
$929$	−1.42239	−	3.90799i	−0.0466672	−	0.128217i	−0.960837	+	0.277115i	$0.910622\pi$
$930$		0			0
$931$	26.0985	+	31.1030i	0.855345	+	1.01936i
$932$		0			0
$933$	−32.7742	−	30.8233i	−1.07298	−	1.00911i
$934$		0			0
$935$	−0.481990	−	0.834832i	−0.0157628	−	0.0273019i
$936$		0			0
$937$	−26.0895	+	45.1883i	−0.852306	+	1.47624i	0.0268167	+	0.999640i	$0.491463\pi$
$937$	−26.0895	+	45.1883i	−0.852306	+	1.47624i	−0.879122	+	0.476596i	$0.841870\pi$
$938$		0			0
$939$	10.9043	+	21.6271i	0.355848	+	0.705773i
$940$		0			0
$941$	−0.0645744	+	0.0113862i	−0.00210507	+	0.000371180i	−0.174701	−	0.984622i	$-0.555896\pi$
$941$	−0.0645744	+	0.0113862i	−0.00210507	+	0.000371180i	0.172596	+	0.984993i	$0.444785\pi$
$942$		0			0
$943$	18.1855	−	21.6726i	0.592201	−	0.705758i
$944$		0			0
$945$	−32.4581	−	5.56496i	−1.05586	−	0.181028i
$946$		0			0
$947$	−2.62754	−	2.20476i	−0.0853835	−	0.0716452i	0.599097	−	0.800677i	$-0.295526\pi$
$947$	−2.62754	−	2.20476i	−0.0853835	−	0.0716452i	−0.684480	+	0.729031i	$0.739971\pi$
$948$		0			0
$949$	0.729281	+	4.13596i	0.0236735	+	0.134259i
$950$		0			0
$951$	−0.801007	+	14.1370i	−0.0259744	+	0.458423i
$952$		0			0
$953$	22.3251	+	12.8894i	0.723180	+	0.417528i	0.815922	−	0.578162i	$-0.196230\pi$
$953$	22.3251	+	12.8894i	0.723180	+	0.417528i	−0.0927418	+	0.995690i	$0.529563\pi$
$954$		0			0
$955$	24.4168	−	14.0971i	0.790111	−	0.456171i
$956$		0			0
$957$	−0.258755	−	0.0608951i	−0.00836436	−	0.00196846i
$958$		0			0
$959$	−82.6139	+	69.3213i	−2.66774	+	2.23850i
$960$		0			0
$961$	−1.52508	+	0.555085i	−0.0491962	+	0.0179060i
$962$		0			0
$963$	28.5708	−	6.86670i	0.920682	−	0.221276i
$964$		0			0
$965$	6.90293	+	1.21717i	0.222213	+	0.0391822i
$966$		0			0
$967$	7.26651	−	19.9646i	0.233675	−	0.642017i	−0.766325	−	0.642454i	$-0.777917\pi$
$967$	7.26651	−	19.9646i	0.233675	−	0.642017i	1.00000		0.000436043i	$0.000138797\pi$
$968$		0			0
$969$	−0.413234	−	3.48772i	−0.0132750	−	0.112042i
$970$		0			0
$971$	−6.72838			−0.215924			−0.107962	−	0.994155i	$-0.534432\pi$
$971$	−6.72838			−0.215924			−0.107962	+	0.994155i	$0.534432\pi$
$972$		0			0
$973$	29.9120			0.958935
$974$		0			0
$975$	−1.18443	−	9.99667i	−0.0379322	−	0.320150i
$976$		0			0
$977$	9.20736	−	25.2970i	0.294569	−	0.809323i	−0.700814	−	0.713344i	$-0.747180\pi$
$977$	9.20736	−	25.2970i	0.294569	−	0.809323i	0.995383	−	0.0959788i	$-0.0305981\pi$
$978$		0			0
$979$	5.36306	+	0.945652i	0.171404	+	0.0302232i
$980$		0			0
$981$	4.49995	−	1.08152i	0.143672	−	0.0345301i
$982$		0			0
$983$	44.4703	−	16.1859i	1.41838	−	0.516249i	0.484805	−	0.874623i	$-0.338891\pi$
$983$	44.4703	−	16.1859i	1.41838	−	0.516249i	0.933578	+	0.358373i	$0.116669\pi$
$984$		0			0
$985$	−21.4440	+	17.9936i	−0.683261	+	0.573324i
$986$		0			0
$987$	−90.0366	−	21.1891i	−2.86590	−	0.674456i
$988$		0			0
$989$	−10.4281	+	6.02068i	−0.331595	+	0.191447i
$990$		0			0
$991$	−34.3612	−	19.8384i	−1.09152	−	0.630189i	−0.157538	−	0.987513i	$-0.550356\pi$
$991$	−34.3612	−	19.8384i	−1.09152	−	0.630189i	−0.933980	+	0.357324i	$0.883689\pi$
$992$		0			0
$993$	−2.24044	+	39.5416i	−0.0710983	+	1.25481i
$994$		0			0
$995$	2.46852	+	13.9997i	0.0782573	+	0.443819i
$996$		0			0
$997$	10.3628	+	8.69542i	0.328193	+	0.275387i	0.791963	−	0.610569i	$-0.209059\pi$
$997$	10.3628	+	8.69542i	0.328193	+	0.275387i	−0.463770	+	0.885956i	$0.653504\pi$
$998$		0			0
$999$	25.2538	−	30.3873i	0.798995	−	0.961411i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	864.2.bi.a.767.16	yes	216
4.3	odd	2	inner	864.2.bi.a.767.21	yes	216
27.5	odd	18	inner	864.2.bi.a.383.21	yes	216
108.59	even	18	inner	864.2.bi.a.383.16	✓	216

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
864.2.bi.a.383.16	✓	216	108.59	even	18	inner
864.2.bi.a.383.21	yes	216	27.5	odd	18	inner
864.2.bi.a.767.16	yes	216	1.1	even	1	trivial
864.2.bi.a.767.21	yes	216	4.3	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-0.203793 - 1.72002i) q^{3} +(-0.448183 + 1.23137i) q^{5} +(4.76300 + 0.839845i) q^{7} +(-2.91694 + 0.701056i) q^{9} +O(q^{10})\)	\(q+(-0.203793 - 1.72002i) q^{3} +(-0.448183 + 1.23137i) q^{5} +(4.76300 + 0.839845i) q^{7} +(-2.91694 + 0.701056i) q^{9} +(-0.844448 + 0.307354i) q^{11} +(1.35620 - 1.13799i) q^{13} +(2.20932 + 0.519938i) q^{15} +(0.708938 - 0.409306i) q^{17} +(2.14516 + 1.23851i) q^{19} +(0.473885 - 8.36361i) q^{21} +(1.28676 + 7.29760i) q^{23} +(2.51481 + 2.11018i) q^{25} +(1.80028 + 4.87432i) q^{27} +(-0.109778 + 0.130828i) q^{29} +(5.33772 - 0.941183i) q^{31} +(0.700747 + 1.38983i) q^{33} +(-3.16886 + 5.48862i) q^{35} +(-3.80198 - 6.58521i) q^{37} +(-2.23375 - 2.10078i) q^{39} +(-2.45413 - 2.92471i) q^{41} +(0.555775 + 1.52698i) q^{43} +(0.444061 - 3.90604i) q^{45} +(1.91737 - 10.8739i) q^{47} +(15.4030 + 5.60623i) q^{49} +(-0.848491 - 1.13597i) q^{51} -8.64685i q^{53} -1.17758i q^{55} +(1.69309 - 3.94212i) q^{57} +(10.7491 + 3.91234i) q^{59} +(-0.757897 + 4.29825i) q^{61} +(-14.4821 + 0.889352i) q^{63} +(0.793460 + 2.18001i) q^{65} +(-9.78772 - 11.6645i) q^{67} +(12.2898 - 3.70046i) q^{69} +(3.05643 + 5.29388i) q^{71} +(-1.18611 + 2.05440i) q^{73} +(3.11705 - 4.75557i) q^{75} +(-4.28024 + 0.754721i) q^{77} +(8.52050 - 10.1543i) q^{79} +(8.01704 - 4.08987i) q^{81} +(7.00731 + 5.87983i) q^{83} +(0.186274 + 1.05641i) q^{85} +(0.247398 + 0.162158i) q^{87} +(-5.24813 - 3.03001i) q^{89} +(7.41532 - 4.28124i) q^{91} +(-2.70664 - 8.98917i) q^{93} +(-2.48649 + 2.08641i) q^{95} +(-9.41639 + 3.42728i) q^{97} +(2.24773 - 1.48854i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 216 q+O(q^{10}) \) 216 * 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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