LMFDB - Embedded newform 864.2.y.d.97.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [864,2,Mod(97,864)]

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([0, 0, 4]))

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

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

chi := DirichletCharacter("864.97");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 864 = 2^{5} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	864.y (of order $9$, 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:	$60$
Relative dimension:	$10$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			97.1
Character	$\chi$	$=$	864.97
Dual form			864.2.y.d.481.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.71652 + 0.231448i) q^{3} +(-3.16823 - 1.15314i) q^{5} +(0.327751 - 1.85877i) q^{7} +(2.89286 - 0.794570i) q^{9} +O(q^{10})$	\(q+(-1.71652 + 0.231448i) q^{3} +(-3.16823 - 1.15314i) q^{5} +(0.327751 - 1.85877i) q^{7} +(2.89286 - 0.794570i) q^{9} +(-1.02523 + 0.373154i) q^{11} +(3.24237 - 2.72067i) q^{13} +(5.70522 + 1.24611i) q^{15} +(-2.38359 - 4.12849i) q^{17} +(-3.92301 + 6.79485i) q^{19} +(-0.132382 + 3.26647i) q^{21} +(-0.662754 - 3.75866i) q^{23} +(4.87773 + 4.09290i) q^{25} +(-4.78175 + 2.03344i) q^{27} +(0.559333 + 0.469337i) q^{29} +(1.03858 + 5.89007i) q^{31} +(1.67346 - 0.877813i) q^{33} +(-3.18182 + 5.51107i) q^{35} +(0.515042 + 0.892080i) q^{37} +(-4.93589 + 5.42052i) q^{39} +(-5.42160 + 4.54926i) q^{41} +(-8.06987 + 2.93719i) q^{43} +(-10.0815 - 0.818501i) q^{45} +(-2.24919 + 12.7558i) q^{47} +(3.23024 + 1.17571i) q^{49} +(5.04700 + 6.53495i) q^{51} -1.32343 q^{53} +3.67847 q^{55} +(5.16125 - 12.5714i) q^{57} +(0.0466975 + 0.0169965i) q^{59} +(-0.338763 + 1.92122i) q^{61} +(-0.528783 - 5.63759i) q^{63} +(-13.4099 + 4.88080i) q^{65} +(10.4938 - 8.80533i) q^{67} +(2.00756 + 6.29842i) q^{69} +(0.558990 + 0.968200i) q^{71} +(-2.47817 + 4.29232i) q^{73} +(-9.32000 - 5.89659i) q^{75} +(0.357586 + 2.02797i) q^{77} +(-9.50049 - 7.97186i) q^{79} +(7.73732 - 4.59716i) q^{81} +(2.45089 + 2.05654i) q^{83} +(2.79101 + 15.8286i) q^{85} +(-1.06873 - 0.676167i) q^{87} +(-6.29772 + 10.9080i) q^{89} +(-3.99441 - 6.91852i) q^{91} +(-3.14598 - 9.87003i) q^{93} +(20.2644 - 17.0039i) q^{95} +(-12.1809 + 4.43349i) q^{97} +(-2.66936 + 1.89410i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 60 q + 12 q^{9}+O(q^{10}) $ 60 * q + 12 * q^9	$ 60 q + 12 q^{9} - 12 q^{17} + 24 q^{21} - 24 q^{25} + 6 q^{29} - 12 q^{33} - 30 q^{37} - 30 q^{41} - 90 q^{45} + 42 q^{49} - 36 q^{53} - 60 q^{57} + 48 q^{61} + 12 q^{65} + 78 q^{69} - 48 q^{73} - 12 q^{77} + 12 q^{81} - 102 q^{85} - 12 q^{89} - 36 q^{93} + 12 q^{97}+O(q^{100}) $ 60 * q + 12 * q^9 - 12 * q^17 + 24 * q^21 - 24 * q^25 + 6 * q^29 - 12 * q^33 - 30 * q^37 - 30 * q^41 - 90 * q^45 + 42 * q^49 - 36 * q^53 - 60 * q^57 + 48 * q^61 + 12 * q^65 + 78 * q^69 - 48 * q^73 - 12 * q^77 + 12 * q^81 - 102 * q^85 - 12 * q^89 - 36 * q^93 + 12 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$325$	$353$	$703$
$\chi(n)$	$1$	$e\left(\frac{2}{9}\right)$	$1$

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
$3$	−1.71652	+	0.231448i	−0.991032	+	0.133627i
$3$	−1.71652	+	0.231448i	−0.991032	+	0.133627i
$4$		0			0
$5$	−3.16823	−	1.15314i	−1.41688	−	0.515701i	−0.483736	−	0.875214i	$-0.660720\pi$
$5$	−3.16823	−	1.15314i	−1.41688	−	0.515701i	−0.933140	+	0.359513i	$0.882943\pi$
$6$		0			0
$7$	0.327751	−	1.85877i	0.123878	−	0.702549i	−0.858089	−	0.513500i	$-0.828348\pi$
$7$	0.327751	−	1.85877i	0.123878	−	0.702549i	0.981968	−	0.189049i	$-0.0605404\pi$
$8$		0			0
$9$	2.89286	−	0.794570i	0.964288	−	0.264857i
$10$		0			0
$11$	−1.02523	+	0.373154i	−0.309119	+	0.112510i	−0.491921	−	0.870640i	$-0.663705\pi$
$11$	−1.02523	+	0.373154i	−0.309119	+	0.112510i	0.182803	+	0.983150i	$0.441483\pi$
$12$		0			0
$13$	3.24237	−	2.72067i	0.899271	−	0.754578i	−0.0707769	−	0.997492i	$-0.522548\pi$
$13$	3.24237	−	2.72067i	0.899271	−	0.754578i	0.970048	+	0.242914i	$0.0781034\pi$
$14$		0			0
$15$	5.70522	+	1.24611i	1.47308	+	0.321743i
$16$		0			0
$17$	−2.38359	−	4.12849i	−0.578104	−	1.00131i	−0.995697	−	0.0926717i	$-0.970459\pi$
$17$	−2.38359	−	4.12849i	−0.578104	−	1.00131i	0.417592	−	0.908635i	$-0.362874\pi$
$18$		0			0
$19$	−3.92301	+	6.79485i	−0.900000	+	1.55884i	−0.0725073	+	0.997368i	$0.523100\pi$
$19$	−3.92301	+	6.79485i	−0.900000	+	1.55884i	−0.827492	+	0.561477i	$0.810233\pi$
$20$		0			0
$21$	−0.132382	+	3.26647i	−0.0288881	+	0.712802i
$22$		0			0
$23$	−0.662754	−	3.75866i	−0.138194	−	0.783736i	−0.972582	−	0.232559i	$-0.925290\pi$
$23$	−0.662754	−	3.75866i	−0.138194	−	0.783736i	0.834389	−	0.551177i	$-0.185821\pi$
$24$		0			0
$25$	4.87773	+	4.09290i	0.975546	+	0.818580i
$26$		0			0
$27$	−4.78175	+	2.03344i	−0.920248	+	0.391336i
$28$		0			0
$29$	0.559333	+	0.469337i	0.103866	+	0.0871536i	0.693242	−	0.720705i	$-0.256182\pi$
$29$	0.559333	+	0.469337i	0.103866	+	0.0871536i	−0.589376	+	0.807859i	$0.700626\pi$
$30$		0			0
$31$	1.03858	+	5.89007i	0.186534	+	1.05789i	0.923968	+	0.382469i	$0.124926\pi$
$31$	1.03858	+	5.89007i	0.186534	+	1.05789i	−0.737434	+	0.675419i	$0.763963\pi$
$32$		0			0
$33$	1.67346	−	0.877813i	0.291312	−	0.152808i
$34$		0			0
$35$	−3.18182	+	5.51107i	−0.537825	+	0.931541i
$36$		0			0
$37$	0.515042	+	0.892080i	0.0846725	+	0.146657i	0.905252	−	0.424876i	$-0.139682\pi$
$37$	0.515042	+	0.892080i	0.0846725	+	0.146657i	−0.820579	+	0.571533i	$0.806349\pi$
$38$		0			0
$39$	−4.93589	+	5.42052i	−0.790374	+	0.867977i
$40$		0			0
$41$	−5.42160	+	4.54926i	−0.846712	+	0.710476i	−0.959063	−	0.283193i	$-0.908606\pi$
$41$	−5.42160	+	4.54926i	−0.846712	+	0.710476i	0.112351	+	0.993669i	$0.464162\pi$
$42$		0			0
$43$	−8.06987	+	2.93719i	−1.23064	+	0.447918i	−0.873818	−	0.486253i	$-0.838363\pi$
$43$	−8.06987	+	2.93719i	−1.23064	+	0.447918i	−0.356826	+	0.934171i	$0.616141\pi$
$44$		0			0
$45$	−10.0815	−	0.818501i	−1.50286	−	0.122015i
$46$		0			0
$47$	−2.24919	+	12.7558i	−0.328079	+	1.86063i	0.159014	+	0.987276i	$0.449169\pi$
$47$	−2.24919	+	12.7558i	−0.328079	+	1.86063i	−0.487093	+	0.873350i	$0.661943\pi$
$48$		0			0
$49$	3.23024	+	1.17571i	0.461463	+	0.167959i
$50$		0			0
$51$	5.04700	+	6.53495i	0.706721	+	0.915076i
$52$		0			0
$53$	−1.32343			−0.181787			−0.0908935	−	0.995861i	$-0.528972\pi$
$53$	−1.32343			−0.181787			−0.0908935	+	0.995861i	$0.528972\pi$
$54$		0			0
$55$	3.67847			0.496005
$56$		0			0
$57$	5.16125	−	12.5714i	0.683625	−	1.66513i
$58$		0			0
$59$	0.0466975	+	0.0169965i	0.00607950	+	0.00221276i	0.345058	−	0.938581i	$-0.387859\pi$
$59$	0.0466975	+	0.0169965i	0.00607950	+	0.00221276i	−0.338979	+	0.940794i	$0.610081\pi$
$60$		0			0
$61$	−0.338763	+	1.92122i	−0.0433742	+	0.245987i	−0.998784	−	0.0492950i	$-0.984303\pi$
$61$	−0.338763	+	1.92122i	−0.0433742	+	0.245987i	0.955410	+	0.295282i	$0.0954137\pi$
$62$		0			0
$63$	−0.528783	−	5.63759i	−0.0666204	−	0.710270i
$64$		0			0
$65$	−13.4099	+	4.88080i	−1.66329	+	0.605389i
$66$		0			0
$67$	10.4938	−	8.80533i	1.28202	−	1.07574i	0.289057	−	0.957312i	$-0.406658\pi$
$67$	10.4938	−	8.80533i	1.28202	−	1.07574i	0.992962	−	0.118430i	$-0.0377862\pi$
$68$		0			0
$69$	2.00756	+	6.29842i	0.241682	+	0.758240i
$70$		0			0
$71$	0.558990	+	0.968200i	0.0663399	+	0.114904i	0.897288	−	0.441446i	$-0.145534\pi$
$71$	0.558990	+	0.968200i	0.0663399	+	0.114904i	−0.830948	+	0.556351i	$0.812201\pi$
$72$		0			0
$73$	−2.47817	+	4.29232i	−0.290048	+	0.502378i	−0.973821	−	0.227317i	$-0.927005\pi$
$73$	−2.47817	+	4.29232i	−0.290048	+	0.502378i	0.683773	+	0.729695i	$0.260338\pi$
$74$		0			0
$75$	−9.32000	−	5.89659i	−1.07618	−	0.680880i
$76$		0			0
$77$	0.357586	+	2.02797i	0.0407507	+	0.231109i
$78$		0			0
$79$	−9.50049	−	7.97186i	−1.06889	−	0.896904i	−0.0739374	−	0.997263i	$-0.523557\pi$
$79$	−9.50049	−	7.97186i	−1.06889	−	0.896904i	−0.994951	+	0.100359i	$0.968001\pi$
$80$		0			0
$81$	7.73732	−	4.59716i	0.859702	−	0.510796i
$82$		0			0
$83$	2.45089	+	2.05654i	0.269020	+	0.225735i	0.767311	−	0.641275i	$-0.221594\pi$
$83$	2.45089	+	2.05654i	0.269020	+	0.225735i	−0.498291	+	0.867010i	$0.666039\pi$
$84$		0			0
$85$	2.79101	+	15.8286i	0.302728	+	1.71686i
$86$		0			0
$87$	−1.06873	−	0.676167i	−0.114580	−	0.0724928i
$88$		0			0
$89$	−6.29772	+	10.9080i	−0.667557	+	1.15624i	0.311029	+	0.950400i	$0.399326\pi$
$89$	−6.29772	+	10.9080i	−0.667557	+	1.15624i	−0.978585	+	0.205841i	$0.934007\pi$
$90$		0			0
$91$	−3.99441	−	6.91852i	−0.418728	−	0.725258i
$92$		0			0
$93$	−3.14598	−	9.87003i	−0.326223	−	1.02347i
$94$		0			0
$95$	20.2644	−	17.0039i	2.07909	−	1.74456i
$96$		0			0
$97$	−12.1809	+	4.43349i	−1.23679	+	0.450153i	−0.875916	−	0.482464i	$-0.839742\pi$
$97$	−12.1809	+	4.43349i	−1.23679	+	0.450153i	−0.360869	+	0.932616i	$0.617520\pi$
$98$		0			0
$99$	−2.66936	+	1.89410i	−0.268280	+	0.190364i
$100$		0			0
$101$	2.42146	−	13.7328i	0.240944	−	1.36646i	−0.588782	−	0.808292i	$-0.700392\pi$
$101$	2.42146	−	13.7328i	0.240944	−	1.36646i	0.829726	−	0.558170i	$-0.188496\pi$
$102$		0			0
$103$	16.0090	+	5.82681i	1.57742	+	0.574133i	0.974640	−	0.223777i	$-0.0718386\pi$
$103$	16.0090	+	5.82681i	1.57742	+	0.574133i	0.602777	+	0.797910i	$0.294061\pi$
$104$		0			0
$105$	4.18612	−	10.1963i	0.408523	−	0.995054i
$106$		0			0
$107$	−13.4865			−1.30379			−0.651895	−	0.758309i	$-0.726026\pi$
$107$	−13.4865			−1.30379			−0.651895	+	0.758309i	$0.726026\pi$
$108$		0			0
$109$	10.8589			1.04009			0.520047	−	0.854138i	$-0.325914\pi$
$109$	10.8589			1.04009			0.520047	+	0.854138i	$0.325914\pi$
$110$		0			0
$111$	−1.09055	−	1.41206i	−0.103510	−	0.134027i
$112$		0			0
$113$	0.250185	+	0.0910600i	0.0235355	+	0.00856620i	0.353761	−	0.935336i	$-0.384903\pi$
$113$	0.250185	+	0.0910600i	0.0235355	+	0.00856620i	−0.330226	+	0.943902i	$0.607125\pi$
$114$		0			0
$115$	−2.23451	+	12.6726i	−0.208370	+	1.18172i
$116$		0			0
$117$	7.21796	−	10.4468i	0.667301	−	0.965808i
$118$		0			0
$119$	−8.45514	+	3.07742i	−0.775081	+	0.282107i
$120$		0			0
$121$	−7.51463	+	6.30553i	−0.683149	+	0.573230i
$122$		0			0
$123$	8.25335	−	9.06371i	0.744180	−	0.817247i
$124$		0			0
$125$	−2.30517	−	3.99268i	−0.206181	−	0.357116i
$126$		0			0
$127$	3.91894	−	6.78780i	0.347750	−	0.602320i	−0.638100	−	0.769954i	$-0.720279\pi$
$127$	3.91894	−	6.78780i	0.347750	−	0.602320i	0.985849	+	0.167634i	$0.0536126\pi$
$128$		0			0
$129$	13.1723	−	6.90950i	1.15975	−	0.608348i
$130$		0			0
$131$	−0.636455	−	3.60951i	−0.0556073	−	0.315365i	0.944299	−	0.329090i	$-0.106742\pi$
$131$	−0.636455	−	3.60951i	−0.0556073	−	0.315365i	−0.999906	+	0.0137255i	$0.995631\pi$
$132$		0			0
$133$	11.3443	+	9.51899i	0.983675	+	0.825401i
$134$		0			0
$135$	17.4945	−	0.928377i	1.50569	−	0.0799020i
$136$		0			0
$137$	17.3105	+	14.5253i	1.47894	+	1.24098i	0.907308	+	0.420467i	$0.138134\pi$
$137$	17.3105	+	14.5253i	1.47894	+	1.24098i	0.571631	+	0.820511i	$0.306311\pi$
$138$		0			0
$139$	0.0488813	+	0.277220i	0.00414606	+	0.0235135i	0.986811	−	0.161879i	$-0.0517555\pi$
$139$	0.0488813	+	0.277220i	0.00414606	+	0.0235135i	−0.982665	+	0.185393i	$0.940644\pi$
$140$		0			0
$141$	0.908470	−	22.4161i	0.0765070	−	1.88778i
$142$		0			0
$143$	−2.30895	+	3.99922i	−0.193084	+	0.334431i
$144$		0			0
$145$	−1.23089	−	2.13196i	−0.102220	−	0.177049i
$146$		0			0
$147$	−5.81688	−	1.27050i	−0.479768	−	0.104789i
$148$		0			0
$149$	1.79297	−	1.50448i	0.146885	−	0.123252i	−0.566384	−	0.824142i	$-0.691658\pi$
$149$	1.79297	−	1.50448i	0.146885	−	0.123252i	0.713269	+	0.700890i	$0.247214\pi$
$150$		0			0
$151$	−8.94857	+	3.25701i	−0.728225	+	0.265052i	−0.679413	−	0.733756i	$-0.737766\pi$
$151$	−8.94857	+	3.25701i	−0.728225	+	0.265052i	−0.0488114	+	0.998808i	$0.515543\pi$
$152$		0			0
$153$	−10.1758	−	10.0492i	−0.822662	−	0.812433i
$154$		0			0
$155$	3.50163	−	19.8587i	0.281258	−	1.59509i
$156$		0			0
$157$	8.39637	+	3.05603i	0.670103	+	0.243898i	0.654592	−	0.755982i	$-0.272840\pi$
$157$	8.39637	+	3.05603i	0.670103	+	0.243898i	0.0155110	+	0.999880i	$0.495063\pi$
$158$		0			0
$159$	2.27169	−	0.306306i	0.180157	−	0.0242916i
$160$		0			0
$161$	−7.20371			−0.567732
$162$		0			0
$163$	−5.40976			−0.423725			−0.211862	−	0.977300i	$-0.567953\pi$
$163$	−5.40976			−0.423725			−0.211862	+	0.977300i	$0.567953\pi$
$164$		0			0
$165$	−6.31415	+	0.851375i	−0.491556	+	0.0662795i
$166$		0			0
$167$	7.93902	+	2.88957i	0.614340	+	0.223601i	0.630401	−	0.776270i	$-0.282890\pi$
$167$	7.93902	+	2.88957i	0.614340	+	0.223601i	−0.0160614	+	0.999871i	$0.505113\pi$
$168$		0			0
$169$	0.853478	−	4.84032i	0.0656522	−	0.372332i
$170$		0			0
$171$	−5.94974	+	22.7737i	−0.454988	+	1.74155i
$172$		0			0
$173$	−20.1789	+	7.34451i	−1.53417	+	0.558393i	−0.964639	−	0.263576i	$-0.915098\pi$
$173$	−20.1789	+	7.34451i	−1.53417	+	0.558393i	−0.569532	+	0.821969i	$0.692876\pi$
$174$		0			0
$175$	9.20644	−	7.72512i	0.695942	−	0.583964i
$176$		0			0
$177$	−0.0840909	−	0.0183667i	−0.00632066	−	0.00138053i
$178$		0			0
$179$	9.62464	+	16.6704i	0.719380	+	1.24600i	0.961246	+	0.275692i	$0.0889071\pi$
$179$	9.62464	+	16.6704i	0.719380	+	1.24600i	−0.241866	+	0.970310i	$0.577760\pi$
$180$		0			0
$181$	−9.90487	+	17.1557i	−0.736224	+	1.27518i	0.217961	+	0.975957i	$0.430059\pi$
$181$	−9.90487	+	17.1557i	−0.736224	+	1.27518i	−0.954184	+	0.299219i	$0.903274\pi$
$182$		0			0
$183$	0.136830	−	3.37622i	0.0101147	−	0.249577i
$184$		0			0
$185$	−0.603079	−	3.42023i	−0.0443393	−	0.251460i
$186$		0			0
$187$	3.98429	+	3.34321i	0.291360	+	0.244480i
$188$		0			0
$189$	2.21248	+	9.55463i	0.160934	+	0.694997i
$190$		0			0
$191$	−17.8237	−	14.9559i	−1.28968	−	1.08217i	−0.991831	−	0.127555i	$-0.959287\pi$
$191$	−17.8237	−	14.9559i	−1.28968	−	1.08217i	−0.297847	−	0.954614i	$-0.596269\pi$
$192$		0			0
$193$	−4.01131	−	22.7493i	−0.288740	−	1.63753i	−0.691611	−	0.722270i	$-0.743099\pi$
$193$	−4.01131	−	22.7493i	−0.288740	−	1.63753i	0.402871	−	0.915257i	$-0.368012\pi$
$194$		0			0
$195$	21.8886	−	11.4817i	1.56748	−	0.822219i
$196$		0			0
$197$	4.15123	−	7.19013i	0.295763	−	0.512276i	−0.679399	−	0.733769i	$-0.737760\pi$
$197$	4.15123	−	7.19013i	0.295763	−	0.512276i	0.975162	+	0.221493i	$0.0710929\pi$
$198$		0			0
$199$	−6.19584	−	10.7315i	−0.439211	−	0.760737i	0.558417	−	0.829560i	$-0.311409\pi$
$199$	−6.19584	−	10.7315i	−0.439211	−	0.760737i	−0.997629	+	0.0688236i	$0.978075\pi$
$200$		0			0
$201$	−15.9748	+	17.5433i	−1.12677	+	1.23741i
$202$		0			0
$203$	1.05571	−	0.885847i	0.0740964	−	0.0621743i
$204$		0			0
$205$	22.4228	−	8.16124i	1.56608	−	0.570006i
$206$		0			0
$207$	−4.90378	−	10.3467i	−0.340836	−	0.719145i
$208$		0			0
$209$	1.48647	−	8.43017i	0.102821	−	0.583127i
$210$		0			0
$211$	−4.40724	−	1.60410i	−0.303407	−	0.110431i	0.185830	−	0.982582i	$-0.440502\pi$
$211$	−4.40724	−	1.60410i	−0.303407	−	0.110431i	−0.489237	+	0.872151i	$0.662725\pi$
$212$		0			0
$213$	−1.18360	−	1.53255i	−0.0810993	−	0.105009i
$214$		0			0
$215$	28.9542			1.97466
$216$		0			0
$217$	11.2887			0.766326
$218$		0			0
$219$	3.26038	−	7.94141i	0.220316	−	0.536631i
$220$		0			0
$221$	−18.9607	−	6.90114i	−1.27544	−	0.464221i
$222$		0			0
$223$	0.680072	−	3.85688i	0.0455410	−	0.258276i	−0.953534	−	0.301287i	$-0.902584\pi$
$223$	0.680072	−	3.85688i	0.0455410	−	0.258276i	0.999075	+	0.0430109i	$0.0136950\pi$
$224$		0			0
$225$	17.3627	+	7.96451i	1.15751	+	0.530967i
$226$		0			0
$227$	−5.34972	+	1.94714i	−0.355073	+	0.129236i	−0.513397	−	0.858151i	$-0.671613\pi$
$227$	−5.34972	+	1.94714i	−0.355073	+	0.129236i	0.158324	+	0.987387i	$0.449391\pi$
$228$		0			0
$229$	2.70843	−	2.27264i	0.178978	−	0.150180i	−0.548898	−	0.835890i	$-0.684952\pi$
$229$	2.70843	−	2.27264i	0.178978	−	0.150180i	0.727875	+	0.685709i	$0.240508\pi$
$230$		0			0
$231$	−1.08317	−	3.39828i	−0.0712675	−	0.223591i
$232$		0			0
$233$	8.67482	+	15.0252i	0.568306	+	0.984336i	0.996734	+	0.0807594i	$0.0257345\pi$
$233$	8.67482	+	15.0252i	0.568306	+	0.984336i	−0.428427	+	0.903576i	$0.640932\pi$
$234$		0			0
$235$	21.8352	−	37.8197i	1.42437	−	2.46709i
$236$		0			0
$237$	18.1528	+	11.4850i	1.17915	+	0.746028i
$238$		0			0
$239$	−3.71081	−	21.0451i	−0.240033	−	1.36129i	−0.831752	−	0.555148i	$-0.812662\pi$
$239$	−3.71081	−	21.0451i	−0.240033	−	1.36129i	0.591719	−	0.806144i	$-0.298449\pi$
$240$		0			0
$241$	−8.78491	−	7.37141i	−0.565886	−	0.474835i	0.314392	−	0.949293i	$-0.398199\pi$
$241$	−8.78491	−	7.37141i	−0.565886	−	0.474835i	−0.880278	+	0.474459i	$0.842644\pi$
$242$		0			0
$243$	−12.2172	+	9.68190i	−0.783736	+	0.621094i
$244$		0			0
$245$	−8.87839	−	7.44985i	−0.567220	−	0.475954i
$246$		0			0
$247$	5.76670	+	32.7046i	0.366926	+	2.08094i
$248$		0			0
$249$	−4.68298	−	2.96283i	−0.296772	−	0.187762i
$250$		0			0
$251$	4.78819	−	8.29338i	0.302228	−	0.523474i	−0.674413	−	0.738355i	$-0.735603\pi$
$251$	4.78819	−	8.29338i	0.302228	−	0.523474i	0.976640	+	0.214881i	$0.0689364\pi$
$252$		0			0
$253$	2.08203	+	3.60619i	0.130896	+	0.226719i
$254$		0			0
$255$	−8.45433	−	26.5241i	−0.529431	−	1.66101i
$256$		0			0
$257$	−5.95295	+	4.99512i	−0.371335	+	0.311587i	−0.809289	−	0.587410i	$-0.800148\pi$
$257$	−5.95295	+	4.99512i	−0.371335	+	0.311587i	0.437954	+	0.898997i	$0.355703\pi$
$258$		0			0
$259$	1.82698	−	0.664965i	0.113523	−	0.0413189i
$260$		0			0
$261$	1.99100	+	0.913297i	0.123240	+	0.0565317i
$262$		0			0
$263$	0.0921302	−	0.522496i	0.00568099	−	0.0322185i	−0.981835	−	0.189734i	$-0.939237\pi$
$263$	0.0921302	−	0.522496i	0.00568099	−	0.0322185i	0.987516	+	0.157516i	$0.0503485\pi$
$264$		0			0
$265$	4.19293	+	1.52610i	0.257570	+	0.0937477i
$266$		0			0
$267$	8.28551	−	20.1813i	0.507065	−	1.23508i
$268$		0			0
$269$	−14.1627			−0.863517			−0.431759	−	0.901989i	$-0.642107\pi$
$269$	−14.1627			−0.863517			−0.431759	+	0.901989i	$0.642107\pi$
$270$		0			0
$271$	−20.2700			−1.23131			−0.615657	−	0.788014i	$-0.711109\pi$
$271$	−20.2700			−1.23131			−0.615657	+	0.788014i	$0.711109\pi$
$272$		0			0
$273$	8.45775	+	10.9513i	0.511886	+	0.662800i
$274$		0			0
$275$	−6.52808	−	2.37603i	−0.393658	−	0.143280i
$276$		0			0
$277$	−2.20863	+	12.5258i	−0.132704	+	0.752602i	0.843727	+	0.536772i	$0.180357\pi$
$277$	−2.20863	+	12.5258i	−0.132704	+	0.752602i	−0.976431	+	0.215829i	$0.930755\pi$
$278$		0			0
$279$	7.68454	+	16.2139i	0.460061	+	0.970703i
$280$		0			0
$281$	−22.0550	+	8.02738i	−1.31569	+	0.478873i	−0.902076	−	0.431577i	$-0.857957\pi$
$281$	−22.0550	+	8.02738i	−1.31569	+	0.478873i	−0.413618	+	0.910451i	$0.635735\pi$
$282$		0			0
$283$	−1.02118	+	0.856871i	−0.0607028	+	0.0509357i	−0.672634	−	0.739975i	$-0.734837\pi$
$283$	−1.02118	+	0.856871i	−0.0607028	+	0.0509357i	0.611931	+	0.790911i	$0.290393\pi$
$284$		0			0
$285$	−30.8487	+	33.8776i	−1.82732	+	2.00674i
$286$		0			0
$287$	6.67910	+	11.5685i	0.394255	+	0.682869i
$288$		0			0
$289$	−2.86296	+	4.95879i	−0.168409	+	0.291694i
$290$		0			0
$291$	19.8826	−	10.4294i	1.16554	−	0.611383i
$292$		0			0
$293$	−2.09870	−	11.9023i	−0.122607	−	0.695341i	−0.982700	−	0.185204i	$-0.940706\pi$
$293$	−2.09870	−	11.9023i	−0.122607	−	0.695341i	0.860093	−	0.510138i	$-0.170406\pi$
$294$		0			0
$295$	−0.128349	−	0.107698i	−0.00747278	−	0.00627040i
$296$		0			0
$297$	4.14361	−	3.86907i	0.240437	−	0.224506i
$298$		0			0
$299$	−12.3750	−	10.3838i	−0.715663	−	0.600513i
$300$		0			0
$301$	2.81466	+	15.9627i	0.162234	+	0.920075i
$302$		0			0
$303$	−0.978049	+	24.1330i	−0.0561875	+	1.38640i
$304$		0			0
$305$	3.28872	−	5.69623i	0.188312	−	0.326165i
$306$		0			0
$307$	−3.50253	−	6.06655i	−0.199900	−	0.346236i	0.748596	−	0.663026i	$-0.230728\pi$
$307$	−3.50253	−	6.06655i	−0.199900	−	0.346236i	−0.948496	+	0.316790i	$0.897395\pi$
$308$		0			0
$309$	−28.8284	−	6.29656i	−1.63999	−	0.358199i
$310$		0			0
$311$	−13.3819	+	11.2288i	−0.758820	+	0.636725i	−0.937819	−	0.347124i	$-0.887158\pi$
$311$	−13.3819	+	11.2288i	−0.758820	+	0.636725i	0.179000	+	0.983849i	$0.442714\pi$
$312$		0			0
$313$	13.2884	−	4.83657i	0.751103	−	0.273379i	0.0620330	−	0.998074i	$-0.480242\pi$
$313$	13.2884	−	4.83657i	0.751103	−	0.273379i	0.689070	+	0.724695i	$0.258019\pi$
$314$		0			0
$315$	−4.82563	+	18.4709i	−0.271894	+	1.04072i
$316$		0			0
$317$	1.26823	−	7.19249i	0.0712309	−	0.403971i	−0.928256	−	0.371942i	$-0.878692\pi$
$317$	1.26823	−	7.19249i	0.0712309	−	0.403971i	0.999487	−	0.0320287i	$-0.0101968\pi$
$318$		0			0
$319$	−0.748581	−	0.272461i	−0.0419125	−	0.0152549i
$320$		0			0
$321$	23.1498	−	3.12143i	1.29210	−	0.174221i
$322$		0			0
$323$	37.4033			2.08117
$324$		0			0
$325$	26.9508			1.49496
$326$		0			0
$327$	−18.6395	+	2.51327i	−1.03077	+	0.138984i
$328$		0			0
$329$	22.9730	+	8.36147i	1.26654	+	0.460983i
$330$		0			0
$331$	−5.94572	+	33.7198i	−0.326806	+	1.85341i	0.169860	+	0.985468i	$0.445668\pi$
$331$	−5.94572	+	33.7198i	−0.326806	+	1.85341i	−0.496666	+	0.867942i	$0.665443\pi$
$332$		0			0
$333$	2.19877	+	2.17143i	0.120492	+	0.118993i
$334$		0			0
$335$	−43.4005	+	15.7965i	−2.37122	+	0.863055i
$336$		0			0
$337$	−12.9455	+	10.8625i	−0.705184	+	0.591719i	−0.923243	−	0.384216i	$-0.874472\pi$
$337$	−12.9455	+	10.8625i	−0.705184	+	0.591719i	0.218060	+	0.975935i	$0.430027\pi$
$338$		0			0
$339$	−0.450523	−	0.0984011i	−0.0244691	−	0.00534441i
$340$		0			0
$341$	−3.26268	−	5.65113i	−0.176684	−	0.306026i
$342$		0			0
$343$	9.85015	−	17.0610i	0.531858	−	0.921205i
$344$		0			0
$345$	0.902541	−	22.2698i	0.0485912	−	1.19897i
$346$		0			0
$347$	−0.0862504	−	0.489150i	−0.00463016	−	0.0262590i	0.982405	−	0.186762i	$-0.0597994\pi$
$347$	−0.0862504	−	0.489150i	−0.00463016	−	0.0262590i	−0.987035	+	0.160503i	$0.948688\pi$
$348$		0			0
$349$	−11.3724	−	9.54261i	−0.608753	−	0.510804i	0.285493	−	0.958381i	$-0.407843\pi$
$349$	−11.3724	−	9.54261i	−0.608753	−	0.510804i	−0.894246	+	0.447577i	$0.852287\pi$
$350$		0			0
$351$	−9.97186	+	19.6027i	−0.532259	+	1.04632i
$352$		0			0
$353$	4.24329	+	3.56054i	0.225847	+	0.189508i	0.748689	−	0.662921i	$-0.230684\pi$
$353$	4.24329	+	3.56054i	0.225847	+	0.189508i	−0.522842	+	0.852430i	$0.675128\pi$
$354$		0			0
$355$	−0.654539	−	3.71208i	−0.0347393	−	0.197016i
$356$		0			0
$357$	13.8011	−	7.23937i	0.730433	−	0.383148i
$358$		0			0
$359$	−8.71630	+	15.0971i	−0.460029	+	0.796793i	−0.998962	−	0.0455557i	$-0.985494\pi$
$359$	−8.71630	+	15.0971i	−0.460029	+	0.796793i	0.538933	+	0.842348i	$0.318827\pi$
$360$		0			0
$361$	−21.2800	−	36.8580i	−1.12000	−	1.93989i
$362$		0			0
$363$	11.4396	−	12.5628i	0.600423	−	0.659376i
$364$		0			0
$365$	12.8011	−	10.7414i	0.670039	−	0.562230i
$366$		0			0
$367$	−10.1558	+	3.69639i	−0.530126	+	0.192950i	−0.593195	−	0.805059i	$-0.702134\pi$
$367$	−10.1558	+	3.69639i	−0.530126	+	0.192950i	0.0630685	+	0.998009i	$0.479911\pi$
$368$		0			0
$369$	−12.0692	+	17.4682i	−0.628300	+	0.909360i
$370$		0			0
$371$	−0.433756	+	2.45995i	−0.0225195	+	0.127714i
$372$		0			0
$373$	−25.0766	−	9.12715i	−1.29842	−	0.472586i	−0.401938	−	0.915667i	$-0.631663\pi$
$373$	−25.0766	−	9.12715i	−1.29842	−	0.472586i	−0.896482	+	0.443081i	$0.853885\pi$
$374$		0			0
$375$	4.88097	+	6.31998i	0.252052	+	0.326362i
$376$		0			0
$377$	3.09047			0.159167
$378$		0			0
$379$	27.3254			1.40361			0.701807	−	0.712367i	$-0.252377\pi$
$379$	27.3254			1.40361			0.701807	+	0.712367i	$0.252377\pi$
$380$		0			0
$381$	−5.15590	+	12.5584i	−0.264145	+	0.643387i
$382$		0			0
$383$	8.41613	+	3.06322i	0.430044	+	0.156523i	0.547968	−	0.836499i	$-0.315402\pi$
$383$	8.41613	+	3.06322i	0.430044	+	0.156523i	−0.117924	+	0.993023i	$0.537624\pi$
$384$		0			0
$385$	1.20562	−	6.83743i	0.0614442	−	0.348468i
$386$		0			0
$387$	−21.0112	+	14.9090i	−1.06806	+	0.757866i
$388$		0			0
$389$	30.2818	−	11.0217i	1.53535	−	0.558821i	0.570423	−	0.821351i	$-0.306779\pi$
$389$	30.2818	−	11.0217i	1.53535	−	0.558821i	0.964924	+	0.262530i	$0.0845569\pi$
$390$		0			0
$391$	−13.9379	+	11.6953i	−0.704869	+	0.591455i
$392$		0			0
$393$	1.92790	+	6.04849i	0.0972497	+	0.305106i
$394$		0			0
$395$	20.9071	+	36.2121i	1.05195	+	1.82203i
$396$		0			0
$397$	3.91266	−	6.77693i	0.196371	−	0.340124i	−0.750978	−	0.660327i	$-0.770418\pi$
$397$	3.91266	−	6.77693i	0.196371	−	0.340124i	0.947349	+	0.320203i	$0.103751\pi$
$398$		0			0
$399$	−21.6758	−	13.7139i	−1.08515	−	0.686553i
$400$		0			0
$401$	3.99691	+	22.6676i	0.199596	+	1.13197i	0.905719	+	0.423878i	$0.139331\pi$
$401$	3.99691	+	22.6676i	0.199596	+	1.13197i	−0.706123	+	0.708089i	$0.749557\pi$
$402$		0			0
$403$	19.3924	+	16.2721i	0.966003	+	0.810573i
$404$		0			0
$405$	−29.8148	+	5.64265i	−1.48151	+	0.280386i
$406$		0			0
$407$	−0.860920	−	0.722398i	−0.0426742	−	0.0358079i
$408$		0			0
$409$	−0.444963	−	2.52351i	−0.0220020	−	0.124780i	0.971828	−	0.235689i	$-0.0757347\pi$
$409$	−0.444963	−	2.52351i	−0.0220020	−	0.124780i	−0.993831	+	0.110910i	$0.964624\pi$
$410$		0			0
$411$	−33.0757	−	20.9264i	−1.63150	−	1.03222i
$412$		0			0
$413$	0.0468978	−	0.0812293i	0.00230769	−	0.00399703i
$414$		0			0
$415$	−5.39350	−	9.34182i	−0.264757	−	0.458572i
$416$		0			0
$417$	−0.148068	−	0.464539i	−0.00725090	−	0.0227486i
$418$		0			0
$419$	13.2085	−	11.0833i	0.645279	−	0.541454i	−0.260355	−	0.965513i	$-0.583840\pi$
$419$	13.2085	−	11.0833i	0.645279	−	0.541454i	0.905634	+	0.424059i	$0.139395\pi$
$420$		0			0
$421$	−32.3577	+	11.7772i	−1.57702	+	0.573988i	−0.974553	−	0.224158i	$-0.928037\pi$
$421$	−32.3577	+	11.7772i	−1.57702	+	0.573988i	−0.602465	+	0.798145i	$0.705815\pi$
$422$		0			0
$423$	3.62877	+	38.6880i	0.176437	+	1.88107i
$424$		0			0
$425$	5.27102	−	29.8934i	0.255682	−	1.45004i
$426$		0			0
$427$	3.46008	+	1.25937i	0.167445	+	0.0609450i
$428$		0			0
$429$	3.03774	−	7.39913i	0.146663	−	0.357233i
$430$		0			0
$431$	−17.0041			−0.819056			−0.409528	−	0.912297i	$-0.634307\pi$
$431$	−17.0041			−0.819056			−0.409528	+	0.912297i	$0.634307\pi$
$432$		0			0
$433$	0.814729			0.0391534			0.0195767	−	0.999808i	$-0.493768\pi$
$433$	0.814729			0.0391534			0.0195767	+	0.999808i	$0.493768\pi$
$434$		0			0
$435$	2.60627	+	3.37465i	0.124961	+	0.161802i
$436$		0			0
$437$	28.1395	+	10.2420i	1.34610	+	0.489939i
$438$		0			0
$439$	−0.788389	+	4.47118i	−0.0376277	+	0.213398i	−0.997824	−	0.0659272i	$-0.978999\pi$
$439$	−0.788389	+	4.47118i	−0.0376277	+	0.213398i	0.960197	+	0.279325i	$0.0901106\pi$
$440$		0			0
$441$	10.2788	+	0.834521i	0.489468	+	0.0397391i
$442$		0			0
$443$	14.7185	−	5.35709i	0.699296	−	0.254523i	0.0321856	−	0.999482i	$-0.489753\pi$
$443$	14.7185	−	5.35709i	0.699296	−	0.254523i	0.667110	+	0.744959i	$0.267531\pi$
$444$		0			0
$445$	32.5310	−	27.2968i	1.54212	−	1.29399i
$446$		0			0
$447$	−2.72945	+	2.99744i	−0.129098	+	0.141774i
$448$		0			0
$449$	11.1555	+	19.3219i	0.526461	+	0.911857i	0.999525	+	0.0308287i	$0.00981462\pi$
$449$	11.1555	+	19.3219i	0.526461	+	0.911857i	−0.473064	+	0.881028i	$0.656852\pi$
$450$		0			0
$451$	3.86082	−	6.68714i	0.181799	−	0.314885i
$452$		0			0
$453$	14.6066	−	7.66185i	0.686276	−	0.359985i
$454$		0			0
$455$	4.67718	+	26.5256i	0.219269	+	1.24354i
$456$		0			0
$457$	−25.3140	−	21.2410i	−1.18414	−	0.993610i	−0.999943	−	0.0107208i	$-0.996587\pi$
$457$	−25.3140	−	21.2410i	−1.18414	−	0.993610i	−0.184196	−	0.982890i	$-0.558968\pi$
$458$		0			0
$459$	19.7927	+	14.8945i	0.923846	+	0.695217i
$460$		0			0
$461$	21.5501	+	18.0827i	1.00369	+	0.842196i	0.987491	−	0.157673i	$-0.0503991\pi$
$461$	21.5501	+	18.0827i	1.00369	+	0.842196i	0.0161987	+	0.999869i	$0.494844\pi$
$462$		0			0
$463$	−1.11579	−	6.32794i	−0.0518550	−	0.294084i	0.947841	−	0.318744i	$-0.103261\pi$
$463$	−1.11579	−	6.32794i	−0.0518550	−	0.294084i	−0.999696	+	0.0246595i	$0.992150\pi$
$464$		0			0
$465$	−1.41434	+	34.8983i	−0.0655884	+	1.61837i
$466$		0			0
$467$	−16.6727	+	28.8779i	−0.771520	+	1.33631i	0.165210	+	0.986258i	$0.447170\pi$
$467$	−16.6727	+	28.8779i	−0.771520	+	1.33631i	−0.936730	+	0.350054i	$0.886163\pi$
$468$		0			0
$469$	−12.9277	−	22.3915i	−0.596947	−	1.03394i
$470$		0			0
$471$	−15.1198	−	3.30240i	−0.696685	−	0.152167i
$472$		0			0
$473$	7.17746	−	6.02260i	0.330020	−	0.276920i
$474$		0			0
$475$	−46.9460	+	17.0869i	−2.15403	+	0.784003i
$476$		0			0
$477$	−3.82850	+	1.05156i	−0.175295	+	0.0481475i
$478$		0			0
$479$	−1.72050	+	9.75741i	−0.0786114	+	0.445828i	0.919942	+	0.392055i	$0.128236\pi$
$479$	−1.72050	+	9.75741i	−0.0786114	+	0.445828i	−0.998553	+	0.0537726i	$0.982875\pi$
$480$		0			0
$481$	4.09701	+	1.49119i	0.186808	+	0.0679924i
$482$		0			0
$483$	12.3653	−	1.66729i	0.562640	−	0.0758641i
$484$		0			0
$485$	43.7044			1.98452
$486$		0			0
$487$	−26.1120			−1.18325			−0.591624	−	0.806214i	$-0.701513\pi$
$487$	−26.1120			−1.18325			−0.591624	+	0.806214i	$0.701513\pi$
$488$		0			0
$489$	9.28594	−	1.25208i	0.419925	−	0.0566209i
$490$		0			0
$491$	−10.2428	−	3.72809i	−0.462253	−	0.168246i	0.100387	−	0.994949i	$-0.467992\pi$
$491$	−10.2428	−	3.72809i	−0.462253	−	0.168246i	−0.562640	+	0.826702i	$0.690214\pi$
$492$		0			0
$493$	0.604432	−	3.42791i	0.0272223	−	0.154385i
$494$		0			0
$495$	10.6413	−	2.92280i	0.478291	−	0.131370i
$496$		0			0
$497$	1.98287	−	0.721706i	0.0889439	−	0.0323729i
$498$		0			0
$499$	−16.0558	+	13.4724i	−0.718756	+	0.603108i	−0.927041	−	0.374960i	$-0.877656\pi$
$499$	−16.0558	+	13.4724i	−0.718756	+	0.603108i	0.208285	+	0.978068i	$0.433212\pi$
$500$		0			0
$501$	−14.2962	−	3.12252i	−0.638709	−	0.139504i
$502$		0			0
$503$	−18.5254	−	32.0870i	−0.826007	−	1.43069i	−0.901147	−	0.433514i	$-0.857274\pi$
$503$	−18.5254	−	32.0870i	−0.826007	−	1.43069i	0.0751396	−	0.997173i	$-0.476060\pi$
$504$		0			0
$505$	−23.5076	+	40.7163i	−1.04607	+	1.81185i
$506$		0			0
$507$	−0.344728	+	8.50602i	−0.0153099	+	0.377766i
$508$		0			0
$509$	0.00382077	+	0.0216686i	0.000169352	+	0.000960446i	0.984892	−	0.173168i	$-0.0554003\pi$
$509$	0.00382077	+	0.0216686i	0.000169352	+	0.000960446i	−0.984723	+	0.174128i	$0.944289\pi$
$510$		0			0
$511$	7.16622	+	6.01317i	0.317015	+	0.266007i
$512$		0			0
$513$	4.94191	−	40.4685i	0.218191	−	1.78673i
$514$		0			0
$515$	−44.0012	−	36.9214i	−1.93892	−	1.62695i
$516$		0			0
$517$	−2.45393	−	13.9170i	−0.107924	−	0.612067i
$518$		0			0
$519$	32.9375	−	17.2773i	1.44580	−	0.758391i
$520$		0			0
$521$	9.70395	−	16.8077i	0.425138	−	0.736360i	−0.571295	−	0.820744i	$-0.693559\pi$
$521$	9.70395	−	16.8077i	0.425138	−	0.736360i	0.996433	+	0.0843841i	$0.0268923\pi$
$522$		0			0
$523$	−11.2440	−	19.4751i	−0.491664	−	0.851587i	0.508290	−	0.861186i	$-0.330278\pi$
$523$	−11.2440	−	19.4751i	−0.491664	−	0.851587i	−0.999954	+	0.00959924i	$0.996944\pi$
$524$		0			0
$525$	−14.0151	+	15.3911i	−0.611667	+	0.671724i
$526$		0			0
$527$	21.8416	−	18.3272i	0.951433	−	0.798347i
$528$		0			0
$529$	7.92462	−	2.88433i	0.344549	−	0.125405i
$530$		0			0
$531$	0.148594	+	0.0120641i	0.00644845	+	0.000523539i
$532$		0			0
$533$	−5.20178	+	29.5008i	−0.225314	+	1.27782i
$534$		0			0
$535$	42.7284	+	15.5519i	1.84731	+	0.672365i
$536$		0			0
$537$	−20.3792	−	26.3874i	−0.879427	−	1.13870i
$538$		0			0
$539$	−3.75047			−0.161544
$540$		0			0
$541$	−2.71855			−0.116880			−0.0584398	−	0.998291i	$-0.518613\pi$
$541$	−2.71855			−0.116880			−0.0584398	+	0.998291i	$0.518613\pi$
$542$		0			0
$543$	13.0312	−	31.7406i	0.559223	−	1.36212i
$544$		0			0
$545$	−34.4035	−	12.5219i	−1.47368	−	0.536377i
$546$		0			0
$547$	−1.96058	+	11.1190i	−0.0838284	+	0.475415i	0.913775	+	0.406221i	$0.133154\pi$
$547$	−1.96058	+	11.1190i	−0.0838284	+	0.475415i	−0.997603	+	0.0691936i	$0.977957\pi$
$548$		0			0
$549$	0.546549	+	5.82700i	0.0233261	+	0.248690i
$550$		0			0
$551$	−5.38334	+	1.95938i	−0.229338	+	0.0834722i
$552$		0			0
$553$	−17.9317	+	15.0464i	−0.762531	+	0.639840i
$554$		0			0
$555$	1.82680	+	5.73130i	0.0775434	+	0.243280i
$556$		0			0
$557$	−0.362190	−	0.627331i	−0.0153465	−	0.0265809i	0.858250	−	0.513232i	$-0.171552\pi$
$557$	−0.362190	−	0.627331i	−0.0153465	−	0.0265809i	−0.873597	+	0.486651i	$0.838218\pi$
$558$		0			0
$559$	−18.1744	+	31.4789i	−0.768694	+	1.33142i
$560$		0			0
$561$	−7.61288	−	4.81653i	−0.321416	−	0.203354i
$562$		0			0
$563$	−5.78818	−	32.8264i	−0.243943	−	1.38347i	−0.822935	−	0.568135i	$-0.807665\pi$
$563$	−5.78818	−	32.8264i	−0.243943	−	1.38347i	0.578993	−	0.815333i	$-0.303446\pi$
$564$		0			0
$565$	−0.687640	−	0.576998i	−0.0289292	−	0.0242745i
$566$		0			0
$567$	−6.00916	−	15.8886i	−0.252361	−	0.667259i
$568$		0			0
$569$	24.4874	+	20.5474i	1.02657	+	0.861390i	0.990438	−	0.137957i	$-0.0440535\pi$
$569$	24.4874	+	20.5474i	1.02657	+	0.861390i	0.0361270	+	0.999347i	$0.488498\pi$
$570$		0			0
$571$	−0.970647	−	5.50481i	−0.0406203	−	0.230369i	0.957738	−	0.287641i	$-0.0928710\pi$
$571$	−0.970647	−	5.50481i	−0.0406203	−	0.230369i	−0.998359	+	0.0572717i	$0.981760\pi$
$572$		0			0
$573$	34.0562	+	21.5467i	1.42272	+	0.900128i
$574$		0			0
$575$	12.1511	−	21.0463i	0.506736	−	0.877693i
$576$		0			0
$577$	−12.5549	−	21.7457i	−0.522667	−	0.905285i	−0.999652	−	0.0263741i	$-0.991604\pi$
$577$	−12.5549	−	21.7457i	−0.522667	−	0.905285i	0.476985	−	0.878911i	$-0.341729\pi$
$578$		0			0
$579$	12.1508	+	38.1211i	0.504968	+	1.58426i
$580$		0			0
$581$	4.62592	−	3.88161i	0.191915	−	0.161036i
$582$		0			0
$583$	1.35682	−	0.493843i	0.0561938	−	0.0204529i
$584$		0			0
$585$	−34.9148	+	24.7746i	−1.44355	+	1.02430i
$586$		0			0
$587$	−0.822653	+	4.66550i	−0.0339545	+	0.192566i	−0.997067	−	0.0765334i	$-0.975615\pi$
$587$	−0.822653	+	4.66550i	−0.0339545	+	0.192566i	0.963112	+	0.269099i	$0.0867259\pi$
$588$		0			0
$589$	−44.0965	−	16.0498i	−1.81696	−	0.661321i
$590$		0			0
$591$	−5.46151	+	13.3028i	−0.224656	+	0.547203i
$592$		0			0
$593$	10.0515			0.412764			0.206382	−	0.978472i	$-0.433831\pi$
$593$	10.0515			0.412764			0.206382	+	0.978472i	$0.433831\pi$
$594$		0			0
$595$	30.3365			1.24368
$596$		0			0
$597$	13.1191	+	16.9868i	0.536927	+	0.695224i
$598$		0			0
$599$	38.2358	+	13.9167i	1.56227	+	0.568621i	0.971256	−	0.238037i	$-0.0765040\pi$
$599$	38.2358	+	13.9167i	1.56227	+	0.568621i	0.591018	+	0.806658i	$0.298726\pi$
$600$		0			0
$601$	−7.72510	+	43.8112i	−0.315114	+	1.78710i	0.256468	+	0.966553i	$0.417441\pi$
$601$	−7.72510	+	43.8112i	−0.315114	+	1.78710i	−0.571582	+	0.820545i	$0.693670\pi$
$602$		0			0
$603$	23.3606	−	33.8107i	0.951318	−	1.37688i
$604$		0			0
$605$	31.0793	−	11.3119i	1.26355	−	0.459895i
$606$		0			0
$607$	19.0122	−	15.9531i	0.771681	−	0.647518i	−0.169458	−	0.985537i	$-0.554202\pi$
$607$	19.0122	−	15.9531i	0.771681	−	0.647518i	0.941139	+	0.338020i	$0.109757\pi$
$608$		0			0
$609$	−1.60712	+	1.76491i	−0.0651237	+	0.0715179i
$610$		0			0
$611$	27.4116	+	47.4783i	1.10896	+	1.92077i
$612$		0			0
$613$	−19.6560	+	34.0452i	−0.793898	+	1.37507i	0.129639	+	0.991561i	$0.458618\pi$
$613$	−19.6560	+	34.0452i	−0.793898	+	1.37507i	−0.923537	+	0.383510i	$0.874715\pi$
$614$		0			0
$615$	−36.6003	+	19.1986i	−1.47587	+	0.774164i
$616$		0			0
$617$	−1.22534	−	6.94924i	−0.0493303	−	0.279766i	0.950157	−	0.311770i	$-0.100922\pi$
$617$	−1.22534	−	6.94924i	−0.0493303	−	0.279766i	−0.999488	+	0.0320045i	$0.989811\pi$
$618$		0			0
$619$	−33.4867	−	28.0987i	−1.34594	−	1.12938i	−0.980056	−	0.198723i	$-0.936321\pi$
$619$	−33.4867	−	28.0987i	−1.34594	−	1.12938i	−0.365889	−	0.930659i	$-0.619235\pi$
$620$		0			0
$621$	10.8121	+	16.6253i	0.433876	+	0.667151i
$622$		0			0
$623$	18.2113	+	15.2811i	0.729621	+	0.612225i
$624$		0			0
$625$	−2.82926	−	16.0455i	−0.113170	−	0.641821i
$626$		0			0
$627$	−0.600397	+	14.8146i	−0.0239776	+	0.591637i
$628$		0			0
$629$	2.45530	−	4.25270i	0.0978990	−	0.169566i
$630$		0			0
$631$	−19.9652	−	34.5807i	−0.794801	−	1.37664i	−0.922965	−	0.384883i	$-0.874242\pi$
$631$	−19.9652	−	34.5807i	−0.794801	−	1.37664i	0.128164	−	0.991753i	$-0.459091\pi$
$632$		0			0
$633$	7.93636	+	1.73342i	0.315442	+	0.0688974i
$634$		0			0
$635$	−20.2434	+	16.9862i	−0.803335	+	0.674078i
$636$		0			0
$637$	13.6724	−	4.97633i	0.541718	−	0.197169i
$638$		0			0
$639$	2.38638	+	2.35671i	0.0944039	+	0.0932301i
$640$		0			0
$641$	−3.06777	+	17.3982i	−0.121170	+	0.687187i	0.862340	+	0.506330i	$0.168998\pi$
$641$	−3.06777	+	17.3982i	−0.121170	+	0.687187i	−0.983509	+	0.180857i	$0.942113\pi$
$642$		0			0
$643$	32.8189	+	11.9451i	1.29425	+	0.471069i	0.895121	−	0.445824i	$-0.147089\pi$
$643$	32.8189	+	11.9451i	1.29425	+	0.471069i	0.399132	+	0.916893i	$0.369312\pi$
$644$		0			0
$645$	−49.7004	+	6.70140i	−1.95695	+	0.263868i
$646$		0			0
$647$	−36.6275			−1.43997			−0.719987	−	0.693987i	$-0.755852\pi$
$647$	−36.6275			−1.43997			−0.719987	+	0.693987i	$0.755852\pi$
$648$		0			0
$649$	−0.0542181			−0.00212825
$650$		0			0
$651$	−19.3772	+	2.61275i	−0.759453	+	0.102402i
$652$		0			0
$653$	17.3365	+	6.30996i	0.678429	+	0.246928i	0.658173	−	0.752867i	$-0.271330\pi$
$653$	17.3365	+	6.30996i	0.678429	+	0.246928i	0.0202561	+	0.999795i	$0.493552\pi$
$654$		0			0
$655$	−2.14585	+	12.1697i	−0.0838451	+	0.475509i
$656$		0			0
$657$	−3.75847	+	14.3862i	−0.146632	+	0.561258i
$658$		0			0
$659$	4.16632	−	1.51641i	0.162297	−	0.0590711i	−0.259594	−	0.965718i	$-0.583589\pi$
$659$	4.16632	−	1.51641i	0.162297	−	0.0590711i	0.421891	+	0.906647i	$0.361367\pi$
$660$		0			0
$661$	5.97642	−	5.01482i	0.232456	−	0.195054i	−0.519118	−	0.854703i	$-0.673739\pi$
$661$	5.97642	−	5.01482i	0.232456	−	0.195054i	0.751574	+	0.659649i	$0.229295\pi$
$662$		0			0
$663$	34.1437	+	7.45750i	1.32603	+	0.289625i
$664$		0			0
$665$	−24.9646	−	43.2399i	−0.968085	−	1.67677i
$666$		0			0
$667$	1.39338	−	2.41340i	0.0539518	−	0.0934473i
$668$		0			0
$669$	−0.274687	+	6.77780i	−0.0106200	+	0.262045i
$670$		0			0
$671$	−0.369600	−	2.09611i	−0.0142683	−	0.0809193i
$672$		0			0
$673$	19.9667	+	16.7541i	0.769661	+	0.645822i	0.940622	−	0.339456i	$-0.110243\pi$
$673$	19.9667	+	16.7541i	0.769661	+	0.645822i	−0.170961	+	0.985278i	$0.554687\pi$
$674$		0			0
$675$	−31.6467	−	9.65265i	−1.21808	−	0.371531i
$676$		0			0
$677$	−20.4049	−	17.1217i	−0.784222	−	0.658041i	0.160086	−	0.987103i	$-0.448823\pi$
$677$	−20.4049	−	17.1217i	−0.784222	−	0.658041i	−0.944308	+	0.329062i	$0.893267\pi$
$678$		0			0
$679$	4.24853	+	24.0946i	0.163044	+	0.924666i
$680$		0			0
$681$	8.73222	−	4.58048i	0.334619	−	0.175524i
$682$		0			0
$683$	−1.63151	+	2.82586i	−0.0624281	+	0.108129i	−0.895550	−	0.444960i	$-0.853218\pi$
$683$	−1.63151	+	2.82586i	−0.0624281	+	0.108129i	0.833122	+	0.553089i	$0.186551\pi$
$684$		0			0
$685$	−38.0941	−	65.9809i	−1.45550	−	2.52100i
$686$		0			0
$687$	−4.12306	+	4.52788i	−0.157305	+	0.172750i
$688$		0			0
$689$	−4.29105	+	3.60062i	−0.163476	+	0.137173i
$690$		0			0
$691$	5.30016	−	1.92910i	0.201628	−	0.0733865i	−0.239232	−	0.970962i	$-0.576896\pi$
$691$	5.30016	−	1.92910i	0.201628	−	0.0733865i	0.440860	+	0.897576i	$0.354674\pi$
$692$		0			0
$693$	2.64581	+	5.58252i	0.100506	+	0.212062i
$694$		0			0
$695$	0.164806	−	0.934663i	0.00625146	−	0.0354538i
$696$		0			0
$697$	31.7044	+	11.5395i	1.20089	+	0.437089i
$698$		0			0
$699$	−18.3680	−	23.7833i	−0.694743	−	0.899567i
$700$		0			0
$701$	−16.5696			−0.625824			−0.312912	−	0.949782i	$-0.601305\pi$
$701$	−16.5696			−0.625824			−0.312912	+	0.949782i	$0.601305\pi$
$702$		0			0
$703$	−8.08206			−0.304821
$704$		0			0
$705$	−28.7272	+	69.9719i	−1.08193	+	2.63530i
$706$		0			0
$707$	−24.7324	−	9.00187i	−0.930159	−	0.338550i
$708$		0			0
$709$	7.39869	−	41.9601i	0.277864	−	1.57584i	−0.451852	−	0.892093i	$-0.649236\pi$
$709$	7.39869	−	41.9601i	0.277864	−	1.57584i	0.729716	−	0.683751i	$-0.239652\pi$
$710$		0			0
$711$	−33.8178	−	15.5127i	−1.26827	−	0.581771i
$712$		0			0
$713$	21.4505	−	7.80733i	0.803326	−	0.292387i
$714$		0			0
$715$	11.9269	−	10.0079i	0.446042	−	0.374274i
$716$		0			0
$717$	11.2405	+	35.2654i	0.419785	+	1.31701i
$718$		0			0
$719$	−7.89094	−	13.6675i	−0.294282	−	0.509712i	0.680535	−	0.732715i	$-0.261747\pi$
$719$	−7.89094	−	13.6675i	−0.294282	−	0.509712i	−0.974818	+	0.223003i	$0.928414\pi$
$720$		0			0
$721$	16.0777	−	27.8474i	0.598765	−	1.03709i
$722$		0			0
$723$	16.7855	+	10.6199i	0.624261	+	0.394959i
$724$		0			0
$725$	0.807329	+	4.57859i	0.0299835	+	0.170045i
$726$		0			0
$727$	−24.1307	−	20.2480i	−0.894957	−	0.750958i	0.0742408	−	0.997240i	$-0.476347\pi$
$727$	−24.1307	−	20.2480i	−0.894957	−	0.750958i	−0.969198	+	0.246282i	$0.920791\pi$
$728$		0			0
$729$	18.7302	−	19.4468i	0.693712	−	0.720252i
$730$		0			0
$731$	31.3614	+	26.3153i	1.15994	+	0.973308i
$732$		0			0
$733$	1.57724	+	8.94496i	0.0582566	+	0.330390i	0.999982	−	0.00599283i	$-0.00190759\pi$
$733$	1.57724	+	8.94496i	0.0582566	+	0.330390i	−0.941725	+	0.336383i	$0.890796\pi$
$734$		0			0
$735$	16.9642	+	10.7329i	0.625733	+	0.395890i
$736$		0			0
$737$	−7.47281	+	12.9433i	−0.275265	+	0.476772i
$738$		0			0
$739$	6.54893	+	11.3431i	0.240906	+	0.417262i	0.960973	−	0.276643i	$-0.0892220\pi$
$739$	6.54893	+	11.3431i	0.240906	+	0.417262i	−0.720066	+	0.693905i	$0.755889\pi$
$740$		0			0
$741$	−17.4681	−	54.8033i	−0.641705	−	2.01325i
$742$		0			0
$743$	26.8337	−	22.5162i	0.984434	−	0.826038i	−0.000318629	−	1.00000i	$-0.500101\pi$
$743$	26.8337	−	22.5162i	0.984434	−	0.826038i	0.984752	+	0.173962i	$0.0556570\pi$
$744$		0			0
$745$	−7.41540	+	2.69899i	−0.271679	+	0.0988832i
$746$		0			0
$747$	8.72415	+	4.00189i	0.319200	+	0.146421i
$748$		0			0
$749$	−4.42022	+	25.0683i	−0.161511	+	0.915976i
$750$		0			0
$751$	15.2812	+	5.56189i	0.557618	+	0.202956i	0.605428	−	0.795900i	$-0.293002\pi$
$751$	15.2812	+	5.56189i	0.557618	+	0.202956i	−0.0478100	+	0.998856i	$0.515224\pi$
$752$		0			0
$753$	−6.29952	+	15.3440i	−0.229567	+	0.559165i
$754$		0			0
$755$	32.1069			1.16849
$756$		0			0
$757$	33.2298			1.20776			0.603878	−	0.797077i	$-0.293621\pi$
$757$	33.2298			1.20776			0.603878	+	0.797077i	$0.293621\pi$
$758$		0			0
$759$	−4.40849	−	5.70820i	−0.160018	−	0.207195i
$760$		0			0
$761$	3.83379	+	1.39538i	0.138975	+	0.0505827i	0.410571	−	0.911829i	$-0.365329\pi$
$761$	3.83379	+	1.39538i	0.138975	+	0.0505827i	−0.271596	+	0.962411i	$0.587552\pi$
$762$		0			0
$763$	3.55902	−	20.1842i	0.128845	−	0.730717i
$764$		0			0
$765$	20.6510	+	43.5724i	0.746637	+	1.57536i
$766$		0			0
$767$	0.197652	−	0.0719396i	0.00713681	−	0.00259759i
$768$		0			0
$769$	24.9486	−	20.9343i	0.899669	−	0.754912i	−0.0704570	−	0.997515i	$-0.522446\pi$
$769$	24.9486	−	20.9343i	0.899669	−	0.754912i	0.970126	+	0.242603i	$0.0780013\pi$
$770$		0			0
$771$	9.06224	−	9.95201i	0.326369	−	0.358413i
$772$		0			0
$773$	−1.51250	−	2.61972i	−0.0544007	−	0.0942248i	0.837543	−	0.546372i	$-0.183991\pi$
$773$	−1.51250	−	2.61972i	−0.0544007	−	0.0942248i	−0.891943	+	0.452147i	$0.850658\pi$
$774$		0			0
$775$	−19.0416	+	32.9810i	−0.683993	+	1.18471i
$776$		0			0
$777$	−2.98213	+	1.56427i	−0.106983	+	0.0561181i
$778$		0			0
$779$	−9.64257	−	54.6857i	−0.345481	−	1.95932i
$780$		0			0
$781$	−0.934381	−	0.784039i	−0.0334348	−	0.0280551i
$782$		0			0
$783$	−3.62896	−	1.10688i	−0.129688	−	0.0395566i
$784$		0			0
$785$	−23.0776	−	19.3644i	−0.823675	−	0.691145i
$786$		0			0
$787$	−3.29832	−	18.7057i	−0.117572	−	0.666786i	−0.985444	−	0.169998i	$-0.945624\pi$
$787$	−3.29832	−	18.7057i	−0.117572	−	0.666786i	0.867872	−	0.496788i	$-0.165487\pi$
$788$		0			0
$789$	−0.0372122	+	0.918198i	−0.00132479	+	0.0326887i
$790$		0			0
$791$	0.251258	−	0.435192i	0.00893371	−	0.0154736i
$792$		0			0
$793$	4.12861	+	7.15097i	0.146611	+	0.253938i
$794$		0			0
$795$	−7.55045	−	1.64913i	−0.267787	−	0.0584888i
$796$		0			0
$797$	−26.1488	+	21.9415i	−0.926239	+	0.777207i	−0.975138	−	0.221597i	$-0.928873\pi$
$797$	−26.1488	+	21.9415i	−0.926239	+	0.777207i	0.0488991	+	0.998804i	$0.484429\pi$
$798$		0			0
$799$	58.0234	−	21.1188i	2.05272	−	0.747129i
$800$		0			0
$801$	−9.55129	+	36.5592i	−0.337478	+	1.29176i
$802$		0			0
$803$	0.939005	−	5.32536i	0.0331368	−	0.187928i
$804$		0			0
$805$	22.8230	+	8.30690i	0.804406	+	0.292780i
$806$		0			0
$807$	24.3106	−	3.27794i	0.855773	−	0.115389i
$808$		0			0
$809$	37.1827			1.30728			0.653638	−	0.756808i	$-0.273242\pi$
$809$	37.1827			1.30728			0.653638	+	0.756808i	$0.273242\pi$
$810$		0			0
$811$	32.1690			1.12961			0.564804	−	0.825225i	$-0.308952\pi$
$811$	32.1690			1.12961			0.564804	+	0.825225i	$0.308952\pi$
$812$		0			0
$813$	34.7938	−	4.69146i	1.22027	−	0.164537i
$814$		0			0
$815$	17.1394	+	6.23821i	0.600365	+	0.218515i
$816$		0			0
$817$	11.7004	−	66.3562i	0.409345	−	2.32151i
$818$		0			0
$819$	−17.0525	−	16.8405i	−0.595863	−	0.588454i
$820$		0			0
$821$	25.7808	−	9.38344i	0.899756	−	0.327484i	0.149601	−	0.988746i	$-0.452201\pi$
$821$	25.7808	−	9.38344i	0.899756	−	0.327484i	0.750155	+	0.661262i	$0.229979\pi$
$822$		0			0
$823$	28.8334	−	24.1941i	1.00507	−	0.843354i	0.0173916	−	0.999849i	$-0.494464\pi$
$823$	28.8334	−	24.1941i	1.00507	−	0.843354i	0.987679	+	0.156494i	$0.0500193\pi$
$824$		0			0
$825$	11.7555	+	2.56758i	0.409274	+	0.0893916i
$826$		0			0
$827$	−22.9973	−	39.8326i	−0.799696	−	1.38511i	−0.919814	−	0.392355i	$-0.871661\pi$
$827$	−22.9973	−	39.8326i	−0.799696	−	1.38511i	0.120118	−	0.992760i	$-0.461673\pi$
$828$		0			0
$829$	−2.55472	+	4.42490i	−0.0887291	+	0.153683i	−0.906974	−	0.421186i	$-0.861614\pi$
$829$	−2.55472	+	4.42490i	−0.0887291	+	0.153683i	0.818245	+	0.574870i	$0.194947\pi$
$830$		0			0
$831$	0.892087	−	22.0119i	0.0309462	−	0.763585i
$832$		0			0
$833$	−2.84564	−	16.1384i	−0.0985957	−	0.559164i
$834$		0			0
$835$	−21.8206	−	18.3096i	−0.755132	−	0.633631i
$836$		0			0
$837$	−16.9433	−	26.0529i	−0.585647	−	0.900521i
$838$		0			0
$839$	8.82167	+	7.40226i	0.304558	+	0.255555i	0.782238	−	0.622979i	$-0.214078\pi$
$839$	8.82167	+	7.40226i	0.304558	+	0.255555i	−0.477680	+	0.878534i	$0.658522\pi$
$840$		0			0
$841$	−4.94322	−	28.0344i	−0.170456	−	0.966703i
$842$		0			0
$843$	35.9999	−	18.8837i	1.23990	−	0.650390i
$844$		0			0
$845$	−8.28559	+	14.3511i	−0.285033	+	0.493691i
$846$		0			0
$847$	9.25759	+	16.0346i	0.318095	+	0.550956i
$848$		0			0
$849$	1.55455	−	1.70718i	0.0533520	−	0.0585904i
$850$		0			0
$851$	3.01168	−	2.52710i	0.103239	−	0.0866279i
$852$		0			0
$853$	−25.3880	+	9.24047i	−0.869268	+	0.316388i	−0.737871	−	0.674942i	$-0.764169\pi$
$853$	−25.3880	+	9.24047i	−0.869268	+	0.316388i	−0.131397	+	0.991330i	$0.541946\pi$
$854$		0			0
$855$	45.1114	−	65.2913i	1.54278	−	2.23292i
$856$		0			0
$857$	5.30574	−	30.0903i	0.181240	−	1.02787i	−0.749451	−	0.662060i	$-0.769682\pi$
$857$	5.30574	−	30.0903i	0.181240	−	1.02787i	0.930691	−	0.365806i	$-0.119207\pi$
$858$		0			0
$859$	−36.1286	−	13.1497i	−1.23269	−	0.448663i	−0.358173	−	0.933655i	$-0.616600\pi$
$859$	−36.1286	−	13.1497i	−1.23269	−	0.448663i	−0.874519	+	0.484992i	$0.838822\pi$
$860$		0			0
$861$	−14.1423	−	18.3117i	−0.481969	−	0.624062i
$862$		0			0
$863$	−10.9738			−0.373552			−0.186776	−	0.982402i	$-0.559804\pi$
$863$	−10.9738			−0.373552			−0.186776	+	0.982402i	$0.559804\pi$
$864$		0			0
$865$	72.4006			2.46169
$866$		0			0
$867$	3.76662	−	9.17448i	0.127921	−	0.311582i
$868$		0			0
$869$	12.7149	+	4.62785i	0.431324	+	0.156989i
$870$		0			0
$871$	10.0683	−	57.1002i	0.341152	−	1.93477i
$872$		0			0
$873$	−31.7150	+	22.5041i	−1.07339	+	0.761648i
$874$		0			0
$875$	−8.17700	+	2.97618i	−0.276433	+	0.100613i
$876$		0			0
$877$	−36.7424	+	30.8306i	−1.24070	+	1.04107i	−0.243235	+	0.969967i	$0.578209\pi$
$877$	−36.7424	+	30.8306i	−1.24070	+	1.04107i	−0.997469	+	0.0711065i	$0.977347\pi$
$878$		0			0
$879$	6.35723	+	19.9448i	0.214424	+	0.672722i
$880$		0			0
$881$	3.10886	+	5.38470i	0.104740	+	0.181415i	0.913632	−	0.406542i	$-0.133266\pi$
$881$	3.10886	+	5.38470i	0.104740	+	0.181415i	−0.808892	+	0.587957i	$0.799932\pi$
$882$		0			0
$883$	5.77731	−	10.0066i	0.194422	−	0.336748i	−0.752289	−	0.658833i	$-0.771050\pi$
$883$	5.77731	−	10.0066i	0.194422	−	0.336748i	0.946711	+	0.322085i	$0.104384\pi$
$884$		0			0
$885$	0.245240	+	0.155159i	0.00824365	+	0.00521561i
$886$		0			0
$887$	−0.450206	−	2.55324i	−0.0151164	−	0.0857295i	0.976316	−	0.216348i	$-0.0694147\pi$
$887$	−0.450206	−	2.55324i	−0.0151164	−	0.0857295i	−0.991433	+	0.130619i	$0.958304\pi$
$888$		0			0
$889$	−11.3325	−	9.50912i	−0.380081	−	0.318926i
$890$		0			0
$891$	−6.21709	+	7.60036i	−0.208280	+	0.254622i
$892$		0			0
$893$	−77.8502	−	65.3241i	−2.60516	−	2.18599i
$894$		0			0
$895$	−11.2698	−	63.9142i	−0.376708	−	2.13641i
$896$		0			0
$897$	23.6452	+	14.9599i	0.789489	+	0.499495i
$898$		0			0
$899$	−2.18351	+	3.78196i	−0.0728242	+	0.126135i
$900$		0			0
$901$	3.15451	+	5.46377i	0.105092	+	0.182025i
$902$		0			0
$903$	−8.52595	−	26.7488i	−0.283726	−	0.890145i
$904$		0			0
$905$	51.1639	−	42.9316i	1.70075	−	1.42710i
$906$		0			0
$907$	−37.0665	+	13.4911i	−1.23077	+	0.447965i	−0.873863	−	0.486173i	$-0.838392\pi$
$907$	−37.0665	+	13.4911i	−1.23077	+	0.447965i	−0.356911	+	0.934138i	$0.616170\pi$
$908$		0			0
$909$	−3.90670	−	41.6511i	−0.129577	−	1.38148i
$910$		0			0
$911$	−3.70931	+	21.0365i	−0.122895	+	0.696972i	0.859641	+	0.510899i	$0.170687\pi$
$911$	−3.70931	+	21.0365i	−0.122895	+	0.696972i	−0.982536	+	0.186073i	$0.940424\pi$
$912$		0			0
$913$	−3.28013	−	1.19387i	−0.108557	−	0.0395114i
$914$		0			0
$915$	−4.32676	+	10.5388i	−0.143038	+	0.348404i
$916$		0			0
$917$	−6.91786			−0.228448
$918$		0			0
$919$	−15.6987			−0.517852			−0.258926	−	0.965897i	$-0.583369\pi$
$919$	−15.6987			−0.517852			−0.258926	+	0.965897i	$0.583369\pi$
$920$		0			0
$921$	7.41624	+	9.60269i	0.244373	+	0.316419i
$922$		0			0
$923$	4.44660	+	1.61843i	0.146362	+	0.0532713i
$924$		0			0
$925$	−1.13896	+	6.45934i	−0.0374486	+	0.212382i
$926$		0			0
$927$	50.9418	+	4.13588i	1.67315	+	0.135840i
$928$		0			0
$929$	2.56209	−	0.932525i	0.0840595	−	0.0305951i	−0.299648	−	0.954050i	$-0.596869\pi$
$929$	2.56209	−	0.932525i	0.0840595	−	0.0305951i	0.383708	+	0.923455i	$0.374647\pi$
$930$		0			0
$931$	−20.6610	+	17.3367i	−0.677139	+	0.568187i
$932$		0			0
$933$	20.3714	−	22.3716i	0.666931	−	0.732414i
$934$		0			0
$935$	−8.76794	−	15.1865i	−0.286742	−	0.496652i
$936$		0			0
$937$	−29.2489	+	50.6605i	−0.955519	+	1.65501i	−0.222342	+	0.974969i	$0.571370\pi$
$937$	−29.2489	+	50.6605i	−0.955519	+	1.65501i	−0.733177	+	0.680038i	$0.761963\pi$
$938$		0			0
$939$	−21.6903	+	11.3776i	−0.707836	+	0.371295i
$940$		0			0
$941$	−3.06649	−	17.3909i	−0.0999647	−	0.566928i	−0.993113	−	0.117165i	$-0.962619\pi$
$941$	−3.06649	−	17.3909i	−0.0999647	−	0.566928i	0.893148	−	0.449763i	$-0.148492\pi$
$942$		0			0
$943$	20.6923	+	17.3629i	0.673835	+	0.565415i
$944$		0			0
$945$	4.00821	−	32.8226i	0.130387	−	1.06772i
$946$		0			0
$947$	11.9547	+	10.0312i	0.388475	+	0.325969i	0.816019	−	0.578025i	$-0.196177\pi$
$947$	11.9547	+	10.0312i	0.388475	+	0.325969i	−0.427544	+	0.903995i	$0.640621\pi$
$948$		0			0
$949$	3.64284	+	20.6596i	0.118252	+	0.670638i
$950$		0			0
$951$	−0.512250	+	12.6396i	−0.0166108	+	0.409866i
$952$		0			0
$953$	−4.96502	+	8.59968i	−0.160833	+	0.278571i	−0.935168	−	0.354205i	$-0.884751\pi$
$953$	−4.96502	+	8.59968i	−0.160833	+	0.278571i	0.774335	+	0.632776i	$0.218085\pi$
$954$		0			0
$955$	39.2234	+	67.9369i	1.26924	+	2.19839i
$956$		0			0
$957$	1.34801	+	0.294426i	0.0435751	+	0.00951746i
$958$		0			0
$959$	32.6727	−	27.4156i	1.05506	−	0.885297i
$960$		0			0
$961$	−4.48381	+	1.63197i	−0.144639	+	0.0526443i
$962$		0			0
$963$	−39.0146	+	10.7160i	−1.25723	+	0.345317i
$964$		0			0
$965$	−13.5244	+	76.7005i	−0.435365	+	2.46908i
$966$		0			0
$967$	32.0278	+	11.6572i	1.02995	+	0.374870i	0.801060	−	0.598584i	$-0.204270\pi$
$967$	32.0278	+	11.6572i	1.02995	+	0.374870i	0.228886	+	0.973453i	$0.426492\pi$
$968$		0			0
$969$	−64.2034	+	8.65693i	−2.06251	+	0.278101i
$970$		0			0
$971$	−36.4399			−1.16941			−0.584705	−	0.811246i	$-0.698790\pi$
$971$	−36.4399			−1.16941			−0.584705	+	0.811246i	$0.698790\pi$
$972$		0			0
$973$	0.531308			0.0170330
$974$		0			0
$975$	−46.2615	+	6.23772i	−1.48156	+	0.199767i
$976$		0			0
$977$	10.5261	+	3.83119i	0.336760	+	0.122571i	0.504865	−	0.863199i	$-0.331542\pi$
$977$	10.5261	+	3.83119i	0.336760	+	0.122571i	−0.168105	+	0.985769i	$0.553765\pi$
$978$		0			0
$979$	2.38627	−	13.5332i	0.0762655	−	0.432523i
$980$		0			0
$981$	31.4133	−	8.62816i	1.00295	−	0.275476i
$982$		0			0
$983$	36.5258	−	13.2943i	1.16499	−	0.424022i	0.314113	−	0.949386i	$-0.398293\pi$
$983$	36.5258	−	13.2943i	1.16499	−	0.424022i	0.850878	+	0.525363i	$0.176071\pi$
$984$		0			0
$985$	−21.4433	+	17.9931i	−0.683240	+	0.573306i
$986$		0			0
$987$	−41.3687	−	9.03556i	−1.31678	−	0.287605i
$988$		0			0
$989$	16.3883	+	28.3853i	0.521116	+	0.902600i
$990$		0			0
$991$	−5.27130	+	9.13016i	−0.167448	+	0.290029i	−0.937522	−	0.347926i	$-0.886886\pi$
$991$	−5.27130	+	9.13016i	−0.167448	+	0.290029i	0.770074	+	0.637955i	$0.220219\pi$
$992$		0			0
$993$	2.40153	−	59.2568i	0.0762102	−	1.88046i
$994$		0			0
$995$	7.25490	+	41.1446i	0.229996	+	1.30437i
$996$		0			0
$997$	15.2344	+	12.7832i	0.482477	+	0.404846i	0.851321	−	0.524645i	$-0.175802\pi$
$997$	15.2344	+	12.7832i	0.482477	+	0.404846i	−0.368844	+	0.929491i	$0.620246\pi$
$998$		0			0
$999$	−4.27679	−	3.21839i	−0.135312	−	0.101825i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	864.2.y.d.97.1	✓	60
4.3	odd	2	inner	864.2.y.d.97.10	yes	60
27.22	even	9	inner	864.2.y.d.481.1	yes	60
108.103	odd	18	inner	864.2.y.d.481.10	yes	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
864.2.y.d.97.1	✓	60	1.1	even	1	trivial
864.2.y.d.97.10	yes	60	4.3	odd	2	inner
864.2.y.d.481.1	yes	60	27.22	even	9	inner
864.2.y.d.481.10	yes	60	108.103	odd	18	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.y (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.71652 + 0.231448i) q^{3} +(-3.16823 - 1.15314i) q^{5} +(0.327751 - 1.85877i) q^{7} +(2.89286 - 0.794570i) q^{9} +O(q^{10})\)	\(q+(-1.71652 + 0.231448i) q^{3} +(-3.16823 - 1.15314i) q^{5} +(0.327751 - 1.85877i) q^{7} +(2.89286 - 0.794570i) q^{9} +(-1.02523 + 0.373154i) q^{11} +(3.24237 - 2.72067i) q^{13} +(5.70522 + 1.24611i) q^{15} +(-2.38359 - 4.12849i) q^{17} +(-3.92301 + 6.79485i) q^{19} +(-0.132382 + 3.26647i) q^{21} +(-0.662754 - 3.75866i) q^{23} +(4.87773 + 4.09290i) q^{25} +(-4.78175 + 2.03344i) q^{27} +(0.559333 + 0.469337i) q^{29} +(1.03858 + 5.89007i) q^{31} +(1.67346 - 0.877813i) q^{33} +(-3.18182 + 5.51107i) q^{35} +(0.515042 + 0.892080i) q^{37} +(-4.93589 + 5.42052i) q^{39} +(-5.42160 + 4.54926i) q^{41} +(-8.06987 + 2.93719i) q^{43} +(-10.0815 - 0.818501i) q^{45} +(-2.24919 + 12.7558i) q^{47} +(3.23024 + 1.17571i) q^{49} +(5.04700 + 6.53495i) q^{51} -1.32343 q^{53} +3.67847 q^{55} +(5.16125 - 12.5714i) q^{57} +(0.0466975 + 0.0169965i) q^{59} +(-0.338763 + 1.92122i) q^{61} +(-0.528783 - 5.63759i) q^{63} +(-13.4099 + 4.88080i) q^{65} +(10.4938 - 8.80533i) q^{67} +(2.00756 + 6.29842i) q^{69} +(0.558990 + 0.968200i) q^{71} +(-2.47817 + 4.29232i) q^{73} +(-9.32000 - 5.89659i) q^{75} +(0.357586 + 2.02797i) q^{77} +(-9.50049 - 7.97186i) q^{79} +(7.73732 - 4.59716i) q^{81} +(2.45089 + 2.05654i) q^{83} +(2.79101 + 15.8286i) q^{85} +(-1.06873 - 0.676167i) q^{87} +(-6.29772 + 10.9080i) q^{89} +(-3.99441 - 6.91852i) q^{91} +(-3.14598 - 9.87003i) q^{93} +(20.2644 - 17.0039i) q^{95} +(-12.1809 + 4.43349i) q^{97} +(-2.66936 + 1.89410i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q + 12 q^{9}+O(q^{10}) \) 60 * q + 12 * q^9	\( 60 q + 12 q^{9} - 12 q^{17} + 24 q^{21} - 24 q^{25} + 6 q^{29} - 12 q^{33} - 30 q^{37} - 30 q^{41} - 90 q^{45} + 42 q^{49} - 36 q^{53} - 60 q^{57} + 48 q^{61} + 12 q^{65} + 78 q^{69} - 48 q^{73} - 12 q^{77} + 12 q^{81} - 102 q^{85} - 12 q^{89} - 36 q^{93} + 12 q^{97}+O(q^{100}) \) 60 * q + 12 * q^9 - 12 * q^17 + 24 * q^21 - 24 * q^25 + 6 * q^29 - 12 * q^33 - 30 * q^37 - 30 * q^41 - 90 * q^45 + 42 * q^49 - 36 * q^53 - 60 * q^57 + 48 * q^61 + 12 * q^65 + 78 * q^69 - 48 * q^73 - 12 * q^77 + 12 * q^81 - 102 * q^85 - 12 * q^89 - 36 * q^93 + 12 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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