LMFDB - Embedded newform 864.2.bi.a.767.28

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			767.28
Character	$\chi$	$=$	864.767
Dual form			864.2.bi.a.383.28

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.30774 - 1.13570i) q^{3} +(-0.759337 + 2.08626i) q^{5} +(1.09449 + 0.192988i) q^{7} +(0.420385 - 2.97040i) q^{9} +O(q^{10})$	\(q+(1.30774 - 1.13570i) q^{3} +(-0.759337 + 2.08626i) q^{5} +(1.09449 + 0.192988i) q^{7} +(0.420385 - 2.97040i) q^{9} +(1.84085 - 0.670015i) q^{11} +(-2.48264 + 2.08318i) q^{13} +(1.37634 + 3.59067i) q^{15} +(3.10139 - 1.79059i) q^{17} +(6.22628 + 3.59475i) q^{19} +(1.65049 - 0.990631i) q^{21} +(-0.119240 - 0.676242i) q^{23} +(0.0543297 + 0.0455881i) q^{25} +(-2.82372 - 4.36195i) q^{27} +(5.21402 - 6.21382i) q^{29} +(2.39541 - 0.422376i) q^{31} +(1.64643 - 2.96686i) q^{33} +(-1.23371 + 2.13685i) q^{35} +(3.40506 + 5.89774i) q^{37} +(-0.880793 + 5.54380i) q^{39} +(-4.84322 - 5.77192i) q^{41} +(3.11336 + 8.55390i) q^{43} +(5.87782 + 3.13257i) q^{45} +(-1.60128 + 9.08128i) q^{47} +(-5.41718 - 1.97169i) q^{49} +(2.02225 - 5.86386i) q^{51} -0.398168i q^{53} +4.34926i q^{55} +(12.2249 - 2.37017i) q^{57} +(-6.64567 - 2.41883i) q^{59} +(0.285667 - 1.62010i) q^{61} +(1.03336 - 3.16995i) q^{63} +(-2.46090 - 6.76128i) q^{65} +(1.00291 + 1.19522i) q^{67} +(-0.923941 - 0.748931i) q^{69} +(-1.82788 - 3.16598i) q^{71} +(5.80701 - 10.0580i) q^{73} +(0.122824 - 0.00208463i) q^{75} +(2.14410 - 0.378063i) q^{77} +(3.03105 - 3.61226i) q^{79} +(-8.64655 - 2.49742i) q^{81} +(6.03298 + 5.06227i) q^{83} +(1.38063 + 7.82996i) q^{85} +(-0.238424 - 14.0476i) q^{87} +(-7.16383 - 4.13604i) q^{89} +(-3.11926 + 1.80091i) q^{91} +(2.65289 - 3.27282i) q^{93} +(-12.2274 + 10.2600i) q^{95} +(-11.6474 + 4.23932i) q^{97} +(-1.21635 - 5.74973i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	1.30774	−	1.13570i	0.755026	−	0.655695i
$3$	1.30774	−	1.13570i	0.755026	−	0.655695i
$4$		0			0
$5$	−0.759337	+	2.08626i	−0.339586	+	0.933004i	0.645926	+	0.763400i	$0.276471\pi$
$5$	−0.759337	+	2.08626i	−0.339586	+	0.933004i	−0.985512	+	0.169605i	$0.945751\pi$
$6$		0			0
$7$	1.09449	+	0.192988i	0.413679	+	0.0729427i	0.376614	−	0.926370i	$-0.377088\pi$
$7$	1.09449	+	0.192988i	0.413679	+	0.0729427i	0.0370645	+	0.999313i	$0.488199\pi$
$8$		0			0
$9$	0.420385	−	2.97040i	0.140128	−	0.990133i
$10$		0			0
$11$	1.84085	−	0.670015i	0.555038	−	0.202017i	−0.0492457	−	0.998787i	$-0.515682\pi$
$11$	1.84085	−	0.670015i	0.555038	−	0.202017i	0.604283	+	0.796770i	$0.293460\pi$
$12$		0			0
$13$	−2.48264	+	2.08318i	−0.688561	+	0.577771i	−0.918494	−	0.395435i	$-0.870594\pi$
$13$	−2.48264	+	2.08318i	−0.688561	+	0.577771i	0.229933	+	0.973206i	$0.426149\pi$
$14$		0			0
$15$	1.37634	+	3.59067i	0.355370	+	0.927107i
$16$		0			0
$17$	3.10139	−	1.79059i	0.752197	−	0.434281i	−0.0742905	−	0.997237i	$-0.523669\pi$
$17$	3.10139	−	1.79059i	0.752197	−	0.434281i	0.826487	+	0.562956i	$0.190336\pi$
$18$		0			0
$19$	6.22628	+	3.59475i	1.42841	+	0.824692i	0.996995	−	0.0774633i	$-0.0246821\pi$
$19$	6.22628	+	3.59475i	1.42841	+	0.824692i	0.431412	+	0.902155i	$0.358015\pi$
$20$		0			0
$21$	1.65049	−	0.990631i	0.360166	−	0.216173i
$22$		0			0
$23$	−0.119240	−	0.676242i	−0.0248632	−	0.141006i	0.969849	−	0.243706i	$-0.0783631\pi$
$23$	−0.119240	−	0.676242i	−0.0248632	−	0.141006i	−0.994712	+	0.102700i	$0.967252\pi$
$24$		0			0
$25$	0.0543297	+	0.0455881i	0.0108659	+	0.00911761i
$26$		0			0
$27$	−2.82372	−	4.36195i	−0.543425	−	0.839458i
$28$		0			0
$29$	5.21402	−	6.21382i	0.968218	−	1.15388i	−0.0198410	−	0.999803i	$-0.506316\pi$
$29$	5.21402	−	6.21382i	0.968218	−	1.15388i	0.988059	−	0.154074i	$-0.0492396\pi$
$30$		0			0
$31$	2.39541	−	0.422376i	0.430229	−	0.0758609i	0.0456593	−	0.998957i	$-0.485461\pi$
$31$	2.39541	−	0.422376i	0.430229	−	0.0758609i	0.384569	+	0.923096i	$0.374350\pi$
$32$		0			0
$33$	1.64643	−	2.96686i	0.286606	−	0.516464i
$34$		0			0
$35$	−1.23371	+	2.13685i	−0.208535	+	0.361194i
$36$		0			0
$37$	3.40506	+	5.89774i	0.559789	+	0.969583i	0.997514	+	0.0704736i	$0.0224511\pi$
$37$	3.40506	+	5.89774i	0.559789	+	0.969583i	−0.437725	+	0.899109i	$0.644216\pi$
$38$		0			0
$39$	−0.880793	+	5.54380i	−0.141040	+	0.887718i
$40$		0			0
$41$	−4.84322	−	5.77192i	−0.756383	−	0.901423i	0.241230	−	0.970468i	$-0.422449\pi$
$41$	−4.84322	−	5.77192i	−0.756383	−	0.901423i	−0.997614	+	0.0690454i	$0.978005\pi$
$42$		0			0
$43$	3.11336	+	8.55390i	0.474784	+	1.30446i	0.913868	+	0.406011i	$0.133081\pi$
$43$	3.11336	+	8.55390i	0.474784	+	1.30446i	−0.439084	+	0.898446i	$0.644697\pi$
$44$		0			0
$45$	5.87782	+	3.13257i	0.876213	+	0.466976i
$46$		0			0
$47$	−1.60128	+	9.08128i	−0.233570	+	1.32464i	0.612034	+	0.790831i	$0.290351\pi$
$47$	−1.60128	+	9.08128i	−0.233570	+	1.32464i	−0.845604	+	0.533810i	$0.820760\pi$
$48$		0			0
$49$	−5.41718	−	1.97169i	−0.773883	−	0.281670i
$50$		0			0
$51$	2.02225	−	5.86386i	0.283172	−	0.821105i
$52$		0			0
$53$		−	0.398168i		−	0.0546926i	−0.999626	−	0.0273463i	$-0.991294\pi$
$53$		−	0.398168i		−	0.0546926i	0.999626	−	0.0273463i	$-0.00870569\pi$
$54$		0			0
$55$			4.34926i			0.586455i
$56$		0			0
$57$	12.2249	−	2.37017i	1.61923	−	0.313936i
$58$		0			0
$59$	−6.64567	−	2.41883i	−0.865193	−	0.314904i	−0.128974	−	0.991648i	$-0.541168\pi$
$59$	−6.64567	−	2.41883i	−0.865193	−	0.314904i	−0.736219	+	0.676744i	$0.763391\pi$
$60$		0			0
$61$	0.285667	−	1.62010i	0.0365759	−	0.207432i	−0.961043	−	0.276399i	$-0.910859\pi$
$61$	0.285667	−	1.62010i	0.0365759	−	0.207432i	0.997619	+	0.0689663i	$0.0219701\pi$
$62$		0			0
$63$	1.03336	−	3.16995i	0.130191	−	0.399376i
$64$		0			0
$65$	−2.46090	−	6.76128i	−0.305238	−	0.838633i
$66$		0			0
$67$	1.00291	+	1.19522i	0.122525	+	0.146019i	0.823820	−	0.566852i	$-0.191839\pi$
$67$	1.00291	+	1.19522i	0.122525	+	0.146019i	−0.701295	+	0.712871i	$0.747394\pi$
$68$		0			0
$69$	−0.923941	−	0.748931i	−0.111229	−	0.0901607i
$70$		0			0
$71$	−1.82788	−	3.16598i	−0.216929	−	0.375732i	0.736938	−	0.675960i	$-0.236271\pi$
$71$	−1.82788	−	3.16598i	−0.216929	−	0.375732i	−0.953868	+	0.300228i	$0.902937\pi$
$72$		0			0
$73$	5.80701	−	10.0580i	0.679659	−	1.17720i	−0.295424	−	0.955366i	$-0.595461\pi$
$73$	5.80701	−	10.0580i	0.679659	−	1.17720i	0.975084	−	0.221838i	$-0.0712057\pi$
$74$		0			0
$75$	0.122824	−	0.00208463i	0.0141824	−	0.000240712i
$76$		0			0
$77$	2.14410	−	0.378063i	0.244343	−	0.0430843i
$78$		0			0
$79$	3.03105	−	3.61226i	0.341019	−	0.406411i	−0.568091	−	0.822965i	$-0.692318\pi$
$79$	3.03105	−	3.61226i	0.341019	−	0.406411i	0.909111	+	0.416554i	$0.136762\pi$
$80$		0			0
$81$	−8.64655	−	2.49742i	−0.960728	−	0.277492i
$82$		0			0
$83$	6.03298	+	5.06227i	0.662206	+	0.555657i	0.910747	−	0.412965i	$-0.135507\pi$
$83$	6.03298	+	5.06227i	0.662206	+	0.555657i	−0.248541	+	0.968621i	$0.579951\pi$
$84$		0			0
$85$	1.38063	+	7.82996i	0.149751	+	0.849278i
$86$		0			0
$87$	−0.238424	−	14.0476i	−0.0255617	−	1.50606i
$88$		0			0
$89$	−7.16383	−	4.13604i	−0.759364	−	0.438419i	0.0697032	−	0.997568i	$-0.477795\pi$
$89$	−7.16383	−	4.13604i	−0.759364	−	0.438419i	−0.829067	+	0.559149i	$0.811128\pi$
$90$		0			0
$91$	−3.11926	+	1.80091i	−0.326987	+	0.188786i
$92$		0			0
$93$	2.65289	−	3.27282i	0.275092	−	0.339376i
$94$		0			0
$95$	−12.2274	+	10.2600i	−1.25451	+	1.05266i
$96$		0			0
$97$	−11.6474	+	4.23932i	−1.18262	+	0.430438i	−0.857126	−	0.515106i	$-0.827752\pi$
$97$	−11.6474	+	4.23932i	−1.18262	+	0.430438i	−0.325493	+	0.945544i	$0.605530\pi$
$98$		0			0
$99$	−1.21635	−	5.74973i	−0.122247	−	0.577870i
$100$		0			0
$101$	−14.3246	−	2.52581i	−1.42535	−	0.251327i	−0.592830	−	0.805327i	$-0.701990\pi$
$101$	−14.3246	−	2.52581i	−1.42535	−	0.251327i	−0.832516	+	0.554000i	$0.813101\pi$
$102$		0			0
$103$	6.05926	−	16.6477i	0.597036	−	1.64034i	−0.160111	−	0.987099i	$-0.551185\pi$
$103$	6.05926	−	16.6477i	0.597036	−	1.64034i	0.757147	−	0.653245i	$-0.226593\pi$
$104$		0			0
$105$	0.813437	+	4.19558i	0.0793833	+	0.409446i
$106$		0			0
$107$	−1.75066			−0.169243			−0.0846214	−	0.996413i	$-0.526968\pi$
$107$	−1.75066			−0.169243			−0.0846214	+	0.996413i	$0.526968\pi$
$108$		0			0
$109$	−4.63294			−0.443755			−0.221877	−	0.975075i	$-0.571218\pi$
$109$	−4.63294			−0.443755			−0.221877	+	0.975075i	$0.571218\pi$
$110$		0			0
$111$	11.1510	+	3.84561i	1.05841	+	0.365009i
$112$		0			0
$113$	0.0295145	−	0.0810904i	0.00277649	−	0.00762834i	−0.938297	−	0.345831i	$-0.887597\pi$
$113$	0.0295145	−	0.0810904i	0.00277649	−	0.00762834i	0.941073	+	0.338203i	$0.109819\pi$
$114$		0			0
$115$	1.50136	+	0.264730i	0.140003	+	0.0246862i
$116$		0			0
$117$	5.14422	+	8.25018i	0.475584	+	0.762729i
$118$		0			0
$119$	3.74000	−	1.36125i	0.342845	−	0.124786i
$120$		0			0
$121$	−5.48668	+	4.60387i	−0.498789	+	0.418533i
$122$		0			0
$123$	−12.8888	−	2.04776i	−1.16215	−	0.184641i
$124$		0			0
$125$	−9.74991	+	5.62911i	−0.872058	+	0.503483i
$126$		0			0
$127$	−2.28611	−	1.31989i	−0.202860	−	0.117121i	0.395129	−	0.918626i	$-0.370700\pi$
$127$	−2.28611	−	1.31989i	−0.202860	−	0.117121i	−0.597989	+	0.801505i	$0.704033\pi$
$128$		0			0
$129$	13.7861	+	7.65047i	1.21380	+	0.673586i
$130$		0			0
$131$	1.29087	+	7.32090i	0.112784	+	0.639630i	0.987824	+	0.155579i	$0.0497242\pi$
$131$	1.29087	+	7.32090i	0.112784	+	0.639630i	−0.875039	+	0.484052i	$0.839165\pi$
$132$		0			0
$133$	6.12087	+	5.13602i	0.530747	+	0.445349i
$134$		0			0
$135$	11.2443	−	2.57882i	0.967757	−	0.221950i
$136$		0			0
$137$	7.70520	−	9.18270i	0.658300	−	0.784531i	−0.328841	−	0.944385i	$-0.606658\pi$
$137$	7.70520	−	9.18270i	0.658300	−	0.784531i	0.987141	+	0.159854i	$0.0511025\pi$
$138$		0			0
$139$	0.837753	−	0.147718i	0.0710573	−	0.0125293i	−0.138006	−	0.990431i	$-0.544069\pi$
$139$	0.837753	−	0.147718i	0.0710573	−	0.0125293i	0.209064	+	0.977902i	$0.432958\pi$
$140$		0			0
$141$	8.21953	+	13.6946i	0.692209	+	1.15329i
$142$		0			0
$143$	−3.17441	+	5.49824i	−0.265458	+	0.459786i
$144$		0			0
$145$	9.00446	+	15.5962i	0.747780	+	1.29519i
$146$		0			0
$147$	−9.32353	+	3.57381i	−0.768992	+	0.294763i
$148$		0			0
$149$	10.2538	+	12.2201i	0.840028	+	1.00111i	0.999902	+	0.0139688i	$0.00444656\pi$
$149$	10.2538	+	12.2201i	0.840028	+	1.00111i	−0.159875	+	0.987137i	$0.551109\pi$
$150$		0			0
$151$	−1.48818	−	4.08874i	−0.121106	−	0.332737i	0.864295	−	0.502985i	$-0.167765\pi$
$151$	−1.48818	−	4.08874i	−0.121106	−	0.332737i	−0.985401	+	0.170249i	$0.945543\pi$
$152$		0			0
$153$	−4.01498	−	9.96509i	−0.324592	−	0.805630i
$154$		0			0
$155$	−0.937738	+	5.31818i	−0.0753210	+	0.427166i
$156$		0			0
$157$	−12.5468	−	4.56667i	−1.00134	−	0.364460i	−0.211242	−	0.977434i	$-0.567751\pi$
$157$	−12.5468	−	4.56667i	−1.00134	−	0.364460i	−0.790103	+	0.612974i	$0.789973\pi$
$158$		0			0
$159$	−0.452199	−	0.520702i	−0.0358617	−	0.0412944i
$160$		0			0
$161$		−	0.763153i		−	0.0601449i
$162$		0			0
$163$			23.7645i			1.86138i	0.365810	+	0.930690i	$0.380792\pi$
$163$			23.7645i			1.86138i	−0.365810	+	0.930690i	$0.619208\pi$
$164$		0			0
$165$	4.93945	+	5.68772i	0.384535	+	0.442788i
$166$		0			0
$167$	−19.9959	−	7.27791i	−1.54733	−	0.563181i	−0.579539	−	0.814944i	$-0.696767\pi$
$167$	−19.9959	−	7.27791i	−1.54733	−	0.563181i	−0.967789	+	0.251763i	$0.918990\pi$
$168$		0			0
$169$	−0.433571	+	2.45890i	−0.0333516	+	0.189146i
$170$		0			0
$171$	13.2953	−	16.9834i	1.01672	−	1.29875i
$172$		0			0
$173$	−0.440440	−	1.21010i	−0.0334860	−	0.0920021i	0.921823	−	0.387611i	$-0.126700\pi$
$173$	−0.440440	−	1.21010i	−0.0334860	−	0.0920021i	−0.955309	+	0.295609i	$0.904477\pi$
$174$		0			0
$175$	0.0506655	+	0.0603807i	0.00382995	+	0.00456435i
$176$		0			0
$177$	−11.4379	+	4.38426i	−0.859724	+	0.329541i
$178$		0			0
$179$	−5.08184	−	8.80200i	−0.379834	−	0.657892i	0.611204	−	0.791473i	$-0.290686\pi$
$179$	−5.08184	−	8.80200i	−0.379834	−	0.657892i	−0.991038	+	0.133581i	$0.957352\pi$
$180$		0			0
$181$	−9.03527	+	15.6495i	−0.671586	+	1.16322i	0.305868	+	0.952074i	$0.401053\pi$
$181$	−9.03527	+	15.6495i	−0.671586	+	1.16322i	−0.977454	+	0.211148i	$0.932280\pi$
$182$		0			0
$183$	−1.46636	−	2.44310i	−0.108397	−	0.180600i
$184$		0			0
$185$	−14.8898	+	2.62548i	−1.09472	+	0.193029i
$186$		0			0
$187$	4.50947	−	5.37418i	0.329765	−	0.392999i
$188$		0			0
$189$	−2.24873	−	5.31906i	−0.163571	−	0.386905i
$190$		0			0
$191$	−11.9854	−	10.0570i	−0.867236	−	0.727697i	0.0962785	−	0.995354i	$-0.469306\pi$
$191$	−11.9854	−	10.0570i	−0.867236	−	0.727697i	−0.963514	+	0.267657i	$0.913750\pi$
$192$		0			0
$193$	1.69429	+	9.60879i	0.121958	+	0.691656i	0.983068	+	0.183238i	$0.0586581\pi$
$193$	1.69429	+	9.60879i	0.121958	+	0.691656i	−0.861111	+	0.508417i	$0.830231\pi$
$194$		0			0
$195$	−10.8970	−	6.04718i	−0.780350	−	0.433047i
$196$		0			0
$197$	−17.3732	−	10.0304i	−1.23779	−	0.714636i	−0.269145	−	0.963100i	$-0.586741\pi$
$197$	−17.3732	−	10.0304i	−1.23779	−	0.714636i	−0.968641	+	0.248463i	$0.920074\pi$
$198$		0			0
$199$	11.2096	−	6.47187i	0.794628	−	0.458779i	−0.0469614	−	0.998897i	$-0.514954\pi$
$199$	11.2096	−	6.47187i	0.794628	−	0.458779i	0.841589	+	0.540118i	$0.181620\pi$
$200$		0			0
$201$	2.66895	+	0.424041i	0.188253	+	0.0299095i
$202$		0			0
$203$	6.90589	−	5.79473i	0.484698	−	0.406710i
$204$		0			0
$205$	15.7194	−	5.72138i	1.09789	−	0.399599i
$206$		0			0
$207$	−2.05884	+	0.0699075i	−0.143099	+	0.00485890i
$208$		0			0
$209$	13.8702	+	2.44569i	0.959422	+	0.169172i
$210$		0			0
$211$	−5.25220	+	14.4303i	−0.361576	+	0.993422i	0.616896	+	0.787045i	$0.288390\pi$
$211$	−5.25220	+	14.4303i	−0.361576	+	0.993422i	−0.978472	+	0.206378i	$0.933832\pi$
$212$		0			0
$213$	−5.98598	−	2.06437i	−0.410153	−	0.141448i
$214$		0			0
$215$	−20.2098			−1.37829
$216$		0			0
$217$	2.70327			0.183510
$218$		0			0
$219$	−3.82880	−	19.7483i	−0.258726	−	1.33447i
$220$		0			0
$221$	−3.96951	+	10.9061i	−0.267018	+	0.733626i
$222$		0			0
$223$	22.1128	+	3.89908i	1.48078	+	0.261102i	0.854890	−	0.518809i	$-0.173624\pi$
$223$	22.1128	+	3.89908i	1.48078	+	0.261102i	0.625891	+	0.779910i	$0.284735\pi$
$224$		0			0
$225$	0.158254	−	0.142216i	0.0105503	−	0.00948110i
$226$		0			0
$227$	15.9082	−	5.79010i	1.05586	−	0.384303i	0.244990	−	0.969525i	$-0.421215\pi$
$227$	15.9082	−	5.79010i	1.05586	−	0.384303i	0.810873	+	0.585223i	$0.198993\pi$
$228$		0			0
$229$	−17.6703	+	14.8271i	−1.16769	+	0.979805i	−0.999982	−	0.00603288i	$-0.998080\pi$
$229$	−17.6703	+	14.8271i	−1.16769	+	0.979805i	−0.167704	+	0.985837i	$0.553635\pi$
$230$		0			0
$231$	2.37457	−	2.92946i	0.156235	−	0.192744i
$232$		0			0
$233$	−16.9121	+	9.76420i	−1.10795	+	0.639674i	−0.938297	−	0.345830i	$-0.887597\pi$
$233$	−16.9121	+	9.76420i	−1.10795	+	0.639674i	−0.169651	+	0.985504i	$0.554264\pi$
$234$		0			0
$235$	−17.7300	−	10.2364i	−1.15658	−	0.667751i
$236$		0			0
$237$	−0.138602	−	8.16626i	−0.00900318	−	0.530456i
$238$		0			0
$239$	1.35790	+	7.70104i	0.0878353	+	0.498139i	0.996709	+	0.0810667i	$0.0258327\pi$
$239$	1.35790	+	7.70104i	0.0878353	+	0.498139i	−0.908873	+	0.417072i	$0.863056\pi$
$240$		0			0
$241$	−14.4411	−	12.1175i	−0.930234	−	0.780559i	0.0456256	−	0.998959i	$-0.485472\pi$
$241$	−14.4411	−	12.1175i	−0.930234	−	0.780559i	−0.975859	+	0.218400i	$0.929916\pi$
$242$		0			0
$243$	−14.1438	+	6.55387i	−0.907324	+	0.420431i
$244$		0			0
$245$	8.22693	−	9.80448i	0.525599	−	0.626385i
$246$		0			0
$247$	−22.9462	+	4.04603i	−1.46003	+	0.257442i
$248$		0			0
$249$	13.6388	−	0.231485i	0.864324	−	0.0146698i
$250$		0			0
$251$	14.4214	−	24.9787i	0.910274	−	1.57664i	0.0965958	−	0.995324i	$-0.469205\pi$
$251$	14.4214	−	24.9787i	0.910274	−	1.57664i	0.813678	−	0.581316i	$-0.197462\pi$
$252$		0			0
$253$	−0.672595	−	1.16497i	−0.0422857	−	0.0732409i
$254$		0			0
$255$	10.6980	+	8.67160i	0.669933	+	0.543036i
$256$		0			0
$257$	0.0390252	+	0.0465084i	0.00243432	+	0.00290111i	0.767260	−	0.641336i	$-0.221619\pi$
$257$	0.0390252	+	0.0465084i	0.00243432	+	0.00290111i	−0.764826	+	0.644237i	$0.777175\pi$
$258$		0			0
$259$	2.58862	+	7.11216i	0.160849	+	0.441928i
$260$		0			0
$261$	−16.2656	−	18.0999i	−1.00682	−	1.12036i
$262$		0			0
$263$	−3.32372	+	18.8498i	−0.204950	+	1.16233i	0.692570	+	0.721351i	$0.256479\pi$
$263$	−3.32372	+	18.8498i	−0.204950	+	1.16233i	−0.897519	+	0.440975i	$0.854633\pi$
$264$		0			0
$265$	0.830683	+	0.302344i	0.0510285	+	0.0185728i
$266$		0			0
$267$	−14.0657	+	2.72706i	−0.860809	+	0.166893i
$268$		0			0
$269$		−	25.5653i		−	1.55874i	−0.626563	−	0.779371i	$-0.715539\pi$
$269$		−	25.5653i		−	1.55874i	0.626563	−	0.779371i	$-0.284461\pi$
$270$		0			0
$271$			15.6152i			0.948557i	0.880375	+	0.474278i	$0.157291\pi$
$271$			15.6152i			0.948557i	−0.880375	+	0.474278i	$0.842709\pi$
$272$		0			0
$273$	−2.03391	+	5.89766i	−0.123098	+	0.356942i
$274$		0			0
$275$	0.130558	+	0.0475191i	0.00787292	+	0.00286551i
$276$		0			0
$277$	4.72241	−	26.7821i	0.283742	−	1.60918i	−0.426002	−	0.904722i	$-0.640078\pi$
$277$	4.72241	−	26.7821i	0.283742	−	1.60918i	0.709744	−	0.704459i	$-0.248810\pi$
$278$		0			0
$279$	−0.247629	−	7.29289i	−0.0148252	−	0.436614i
$280$		0			0
$281$	6.11174	+	16.7919i	0.364596	+	1.00172i	0.977384	+	0.211471i	$0.0678255\pi$
$281$	6.11174	+	16.7919i	0.364596	+	1.00172i	−0.612788	+	0.790247i	$0.709952\pi$
$282$		0			0
$283$	−18.3072	−	21.8177i	−1.08825	−	1.29693i	−0.951948	−	0.306259i	$-0.900923\pi$
$283$	−18.3072	−	21.8177i	−1.08825	−	1.29693i	−0.136302	−	0.990667i	$-0.543522\pi$
$284$		0			0
$285$	−4.33805	+	27.3041i	−0.256964	+	1.61736i
$286$		0			0
$287$	−4.18695	−	7.25200i	−0.247148	−	0.428072i
$288$		0			0
$289$	−2.08760	+	3.61584i	−0.122800	+	0.212696i
$290$		0			0
$291$	−10.4173	+	18.7719i	−0.610672	+	1.10043i
$292$		0			0
$293$	26.2942	−	4.63637i	1.53612	−	0.270860i	0.659376	−	0.751814i	$-0.270821\pi$
$293$	26.2942	−	4.63637i	1.53612	−	0.270860i	0.876746	+	0.480954i	$0.159710\pi$
$294$		0			0
$295$	10.0926	−	12.0279i	0.587614	−	0.700292i
$296$		0			0
$297$	−8.12062	−	6.13777i	−0.471206	−	0.356150i
$298$		0			0
$299$	1.70477	+	1.43047i	0.0985891	+	0.0827261i
$300$		0			0
$301$	1.75675	+	9.96301i	0.101257	+	0.574258i
$302$		0			0
$303$	−21.6014	+	12.9652i	−1.24097	+	0.744834i
$304$		0			0
$305$	3.16303	+	1.82618i	0.181115	+	0.104567i
$306$		0			0
$307$	1.14270	−	0.659738i	0.0652173	−	0.0376532i	−0.467037	−	0.884238i	$-0.654678\pi$
$307$	1.14270	−	0.659738i	0.0652173	−	0.0376532i	0.532254	+	0.846585i	$0.321345\pi$
$308$		0			0
$309$	−10.9828	−	28.6524i	−0.624787	−	1.62998i
$310$		0			0
$311$	−15.7035	+	13.1768i	−0.890465	+	0.747189i	−0.968303	−	0.249777i	$-0.919643\pi$
$311$	−15.7035	+	13.1768i	−0.890465	+	0.747189i	0.0778385	+	0.996966i	$0.475198\pi$
$312$		0			0
$313$	−3.04672	+	1.10892i	−0.172211	+	0.0626796i	−0.426687	−	0.904399i	$-0.640319\pi$
$313$	−3.04672	+	1.10892i	−0.172211	+	0.0626796i	0.254476	+	0.967079i	$0.418097\pi$
$314$		0			0
$315$	5.82867	+	4.56292i	0.328408	+	0.257091i
$316$		0			0
$317$	−8.17032	−	1.44065i	−0.458891	−	0.0809148i	−0.0605759	−	0.998164i	$-0.519294\pi$
$317$	−8.17032	−	1.44065i	−0.458891	−	0.0809148i	−0.398315	+	0.917249i	$0.630405\pi$
$318$		0			0
$319$	5.43487	−	14.9322i	0.304294	−	0.836042i
$320$		0			0
$321$	−2.28942	+	1.98822i	−0.127783	+	0.110972i
$322$		0			0
$323$	25.7468			1.43259
$324$		0			0
$325$	−0.229850			−0.0127498
$326$		0			0
$327$	−6.05869	+	5.26161i	−0.335046	+	0.290968i
$328$		0			0
$329$	−3.50516	+	9.63036i	−0.193246	+	0.530939i
$330$		0			0
$331$	29.4969	+	5.20110i	1.62130	+	0.285878i	0.909249	−	0.416254i	$-0.136657\pi$
$331$	29.4969	+	5.20110i	1.62130	+	0.285878i	0.712047	+	0.702132i	$0.247768\pi$
$332$		0			0
$333$	18.9501	−	7.63507i	1.03846	−	0.418399i
$334$		0			0
$335$	−3.25508	+	1.18475i	−0.177844	+	0.0647300i
$336$		0			0
$337$	4.00756	−	3.36274i	0.218306	−	0.183180i	−0.527076	−	0.849818i	$-0.676712\pi$
$337$	4.00756	−	3.36274i	0.218306	−	0.183180i	0.745382	+	0.666638i	$0.232267\pi$
$338$		0			0
$339$	−0.0534967	−	0.139565i	−0.00290554	−	0.00758013i
$340$		0			0
$341$	4.12660	−	2.38249i	0.223468	−	0.129019i
$342$		0			0
$343$	−12.2859	−	7.09327i	−0.663376	−	0.383000i
$344$		0			0
$345$	2.26405	−	1.35889i	0.121892	−	0.0731602i
$346$		0			0
$347$	−1.31120	−	7.43617i	−0.0703888	−	0.399195i	−0.999563	−	0.0295531i	$-0.990592\pi$
$347$	−1.31120	−	7.43617i	−0.0703888	−	0.399195i	0.929174	−	0.369642i	$-0.120520\pi$
$348$		0			0
$349$	−23.0744	−	19.3617i	−1.23514	−	1.03641i	−0.997888	−	0.0649621i	$-0.979307\pi$
$349$	−23.0744	−	19.3617i	−1.23514	−	1.03641i	−0.237257	−	0.971447i	$-0.576248\pi$
$350$		0			0
$351$	16.0970	+	4.94684i	0.859196	+	0.264043i
$352$		0			0
$353$	20.7547	−	24.7345i	1.10466	−	1.31649i	0.160491	−	0.987037i	$-0.448692\pi$
$353$	20.7547	−	24.7345i	1.10466	−	1.31649i	0.944173	−	0.329450i	$-0.106863\pi$
$354$		0			0
$355$	7.99303	−	1.40939i	0.424226	−	0.0748025i
$356$		0			0
$357$	3.34500	−	6.02767i	0.177036	−	0.319018i
$358$		0			0
$359$	12.3446	−	21.3815i	0.651523	−	1.12847i	−0.331230	−	0.943550i	$-0.607464\pi$
$359$	12.3446	−	21.3815i	0.651523	−	1.12847i	0.982753	−	0.184922i	$-0.0592031\pi$
$360$		0			0
$361$	16.3444	+	28.3094i	0.860232	+	1.48997i
$362$		0			0
$363$	−1.94657	+	12.2519i	−0.102168	+	0.643057i
$364$		0			0
$365$	16.5742	+	19.7524i	0.867534	+	1.03389i
$366$		0			0
$367$	−1.50702	−	4.14051i	−0.0786660	−	0.216133i	0.894125	−	0.447817i	$-0.147799\pi$
$367$	−1.50702	−	4.14051i	−0.0786660	−	0.216133i	−0.972791	+	0.231684i	$0.925576\pi$
$368$		0			0
$369$	−19.1809	+	11.9599i	−0.998519	+	0.622605i
$370$		0			0
$371$	0.0768419	−	0.435792i	0.00398943	−	0.0226252i
$372$		0			0
$373$	14.7746	+	5.37751i	0.764999	+	0.278437i	0.694903	−	0.719103i	$-0.255447\pi$
$373$	14.7746	+	5.37751i	0.764999	+	0.278437i	0.0700960	+	0.997540i	$0.477669\pi$
$374$		0			0
$375$	−6.35741	+	18.4344i	−0.328295	+	0.951947i
$376$		0			0
$377$			26.2884i			1.35392i
$378$		0			0
$379$			29.5536i			1.51807i	0.651051	+	0.759034i	$0.274329\pi$
$379$			29.5536i			1.51807i	−0.651051	+	0.759034i	$0.725671\pi$
$380$		0			0
$381$	−4.48864	+	0.870256i	−0.229960	+	0.0445846i
$382$		0			0
$383$	24.1726	+	8.79812i	1.23516	+	0.449563i	0.875363	−	0.483466i	$-0.160622\pi$
$383$	24.1726	+	8.79812i	1.23516	+	0.449563i	0.359801	+	0.933029i	$0.382845\pi$
$384$		0			0
$385$	−0.839357	+	4.76023i	−0.0427776	+	0.242604i
$386$		0			0
$387$	26.7173	−	5.65200i	1.35812	−	0.287308i
$388$		0			0
$389$	0.0463695	+	0.127399i	0.00235103	+	0.00645940i	0.940863	−	0.338788i	$-0.110017\pi$
$389$	0.0463695	+	0.127399i	0.00235103	+	0.00645940i	−0.938512	+	0.345248i	$0.887795\pi$
$390$		0			0
$391$	−1.58068	−	1.88378i	−0.0799383	−	0.0952667i
$392$		0			0
$393$	10.0025	+	8.10782i	0.504557	+	0.408985i
$394$		0			0
$395$	5.23453	+	9.06648i	0.263378	+	0.456184i
$396$		0			0
$397$	16.7413	−	28.9968i	0.840221	−	1.45531i	−0.0494869	−	0.998775i	$-0.515759\pi$
$397$	16.7413	−	28.9968i	0.840221	−	1.45531i	0.889708	−	0.456530i	$-0.150908\pi$
$398$		0			0
$399$	13.8375	−	0.234857i	0.692741	−	0.0117576i
$400$		0			0
$401$	10.0840	−	1.77808i	0.503570	−	0.0887930i	0.0839082	−	0.996473i	$-0.473260\pi$
$401$	10.0840	−	1.77808i	0.503570	−	0.0887930i	0.419662	+	0.907681i	$0.362149\pi$
$402$		0			0
$403$	−5.06706	+	6.03869i	−0.252408	+	0.300809i
$404$		0			0
$405$	11.7759	−	16.1426i	0.585150	−	0.802131i
$406$		0			0
$407$	10.2198	+	8.57542i	0.506576	+	0.425068i
$408$		0			0
$409$	−4.75855	−	26.9871i	−0.235295	−	1.33443i	−0.841991	−	0.539492i	$-0.818616\pi$
$409$	−4.75855	−	26.9871i	−0.235295	−	1.33443i	0.606696	−	0.794934i	$-0.292495\pi$
$410$		0			0
$411$	−0.352339	−	20.7594i	−0.0173796	−	1.02398i
$412$		0			0
$413$	−6.80683	−	3.92992i	−0.334942	−	0.193379i
$414$		0			0
$415$	−15.1423	+	8.74241i	−0.743306	+	0.429148i
$416$		0			0
$417$	0.927803	−	1.14461i	0.0454347	−	0.0560519i
$418$		0			0
$419$	−22.1246	+	18.5647i	−1.08086	+	0.906946i	−0.995992	−	0.0894467i	$-0.971490\pi$
$419$	−22.1246	+	18.5647i	−1.08086	+	0.906946i	−0.0848644	+	0.996393i	$0.527046\pi$
$420$		0			0
$421$	16.2961	−	5.93128i	0.794221	−	0.289073i	0.0871315	−	0.996197i	$-0.472230\pi$
$421$	16.2961	−	5.93128i	0.794221	−	0.289073i	0.707090	+	0.707124i	$0.250008\pi$
$422$		0			0
$423$	26.3019	+	8.57407i	1.27884	+	0.416885i
$424$		0			0
$425$	0.250127	+	0.0441041i	0.0121329	+	0.00213936i
$426$		0			0
$427$	0.625320	−	1.71805i	0.0302614	−	0.0831425i
$428$		0			0
$429$	2.09302	+	10.7955i	0.101052	+	0.521209i
$430$		0			0
$431$	25.0204			1.20519			0.602595	−	0.798047i	$-0.294133\pi$
$431$	25.0204			1.20519			0.602595	+	0.798047i	$0.294133\pi$
$432$		0			0
$433$	25.1327			1.20780			0.603899	−	0.797061i	$-0.293613\pi$
$433$	25.1327			1.20780			0.603899	+	0.797061i	$0.293613\pi$
$434$		0			0
$435$	29.4881	+	10.1695i	1.41384	+	0.487589i
$436$		0			0
$437$	1.68850	−	4.63911i	0.0807718	−	0.221919i
$438$		0			0
$439$	−4.24549	−	0.748594i	−0.202626	−	0.0357284i	0.0714139	−	0.997447i	$-0.477249\pi$
$439$	−4.24549	−	0.748594i	−0.202626	−	0.0357284i	−0.274040	+	0.961718i	$0.588360\pi$
$440$		0			0
$441$	−8.13402	+	15.2623i	−0.387334	+	0.726777i
$442$		0			0
$443$	−4.33583	+	1.57811i	−0.206001	+	0.0749784i	−0.442960	−	0.896541i	$-0.646072\pi$
$443$	−4.33583	+	1.57811i	−0.206001	+	0.0749784i	0.236959	+	0.971520i	$0.423849\pi$
$444$		0			0
$445$	14.0686	−	11.8050i	0.666916	−	0.559609i
$446$		0			0
$447$	27.2877	+	4.33544i	1.29066	+	0.205059i
$448$		0			0
$449$	−8.54006	+	4.93060i	−0.403030	+	0.232690i	−0.687791	−	0.725909i	$-0.741419\pi$
$449$	−8.54006	+	4.93060i	−0.403030	+	0.232690i	0.284760	+	0.958599i	$0.408086\pi$
$450$		0			0
$451$	−12.7829	−	7.38022i	−0.601924	−	0.347521i
$452$		0			0
$453$	−6.58972	−	3.65690i	−0.309612	−	0.171816i
$454$		0			0
$455$	−1.38859	−	7.87509i	−0.0650981	−	0.369190i
$456$		0			0
$457$	−5.03988	−	4.22896i	−0.235755	−	0.197822i	0.517254	−	0.855832i	$-0.326954\pi$
$457$	−5.03988	−	4.22896i	−0.235755	−	0.197822i	−0.753010	+	0.658010i	$0.771399\pi$
$458$		0			0
$459$	−16.5679	−	8.47198i	−0.773323	−	0.395438i
$460$		0			0
$461$	−21.2453	+	25.3192i	−0.989493	+	1.17923i	−0.00568889	+	0.999984i	$0.501811\pi$
$461$	−21.2453	+	25.3192i	−0.989493	+	1.17923i	−0.983804	+	0.179248i	$0.942634\pi$
$462$		0			0
$463$	−5.50204	+	0.970158i	−0.255701	+	0.0450871i	−0.300029	−	0.953930i	$-0.596996\pi$
$463$	−5.50204	+	0.970158i	−0.255701	+	0.0450871i	0.0443279	+	0.999017i	$0.485885\pi$
$464$		0			0
$465$	4.81352	+	8.01980i	0.223222	+	0.371909i
$466$		0			0
$467$	9.98757	−	17.2990i	0.462170	−	0.800501i	−0.536899	−	0.843646i	$-0.680404\pi$
$467$	9.98757	−	17.2990i	0.462170	−	0.800501i	0.999069	+	0.0431451i	$0.0137378\pi$
$468$		0			0
$469$	0.867011	+	1.50171i	0.0400348	+	0.0693424i
$470$		0			0
$471$	−21.5944	+	8.27735i	−0.995016	+	0.381400i
$472$		0			0
$473$	11.4625	+	13.6605i	0.527045	+	0.628108i
$474$		0			0
$475$	0.174395	+	0.479146i	0.00800178	+	0.0219847i
$476$		0			0
$477$	−1.18272	−	0.167384i	−0.0541530	−	0.00766399i
$478$		0			0
$479$	−2.52065	+	14.2953i	−0.115171	+	0.653169i	0.871494	+	0.490406i	$0.163152\pi$
$479$	−2.52065	+	14.2953i	−0.115171	+	0.653169i	−0.986665	+	0.162762i	$0.947960\pi$
$480$		0			0
$481$	−20.7396	−	7.54861i	−0.945646	−	0.344187i
$482$		0			0
$483$	−0.866710	−	0.998008i	−0.0394367	−	0.0454109i
$484$		0			0
$485$		−	27.5187i		−	1.24956i
$486$		0			0
$487$		−	15.7036i		−	0.711597i	−0.934563	−	0.355799i	$-0.884209\pi$
$487$		−	15.7036i		−	0.711597i	0.934563	−	0.355799i	$-0.115791\pi$
$488$		0			0
$489$	26.9893	+	31.0779i	1.22050	+	1.40539i
$490$		0			0
$491$	11.7019	+	4.25915i	0.528101	+	0.192213i	0.592290	−	0.805725i	$-0.298224\pi$
$491$	11.7019	+	4.25915i	0.528101	+	0.192213i	−0.0641894	+	0.997938i	$0.520446\pi$
$492$		0			0
$493$	5.04429	−	28.6076i	0.227183	−	1.28842i
$494$		0			0
$495$	12.9191	+	1.82837i	0.580668	+	0.0821790i
$496$		0			0
$497$	−1.38960	−	3.81789i	−0.0623321	−	0.171256i
$498$		0			0
$499$	−0.603763	−	0.719537i	−0.0270282	−	0.0322109i	0.752361	−	0.658751i	$-0.228915\pi$
$499$	−0.603763	−	0.719537i	−0.0270282	−	0.0322109i	−0.779389	+	0.626540i	$0.784470\pi$
$500$		0			0
$501$	−34.4150	+	13.1916i	−1.53755	+	0.589359i
$502$		0			0
$503$	−5.87081	−	10.1685i	−0.261766	−	0.453393i	0.704945	−	0.709262i	$-0.250972\pi$
$503$	−5.87081	−	10.1685i	−0.261766	−	0.453393i	−0.966711	+	0.255869i	$0.917638\pi$
$504$		0			0
$505$	16.1467	−	27.9668i	0.718517	−	1.24451i
$506$		0			0
$507$	2.22557	+	3.70802i	0.0988409	+	0.164679i
$508$		0			0
$509$	−9.57823	+	1.68890i	−0.424548	+	0.0748592i	−0.381840	−	0.924228i	$-0.624709\pi$
$509$	−9.57823	+	1.68890i	−0.424548	+	0.0748592i	−0.0427076	+	0.999088i	$0.513598\pi$
$510$		0			0
$511$	8.29681	−	9.88775i	0.367029	−	0.437408i
$512$		0			0
$513$	−1.90116	−	37.3093i	−0.0839383	−	1.64725i
$514$		0			0
$515$	30.1304	+	25.2824i	1.32770	+	1.11407i
$516$		0			0
$517$	3.13689	+	17.7902i	0.137960	+	0.782411i
$518$		0			0
$519$	−1.95029	−	1.08229i	−0.0856081	−	0.0475074i
$520$		0			0
$521$	−10.9472	−	6.32035i	−0.479604	−	0.276900i	0.240647	−	0.970613i	$-0.422640\pi$
$521$	−10.9472	−	6.32035i	−0.479604	−	0.276900i	−0.720252	+	0.693713i	$0.755974\pi$
$522$		0			0
$523$	5.34646	−	3.08678i	0.233784	−	0.134976i	−0.378532	−	0.925588i	$-0.623571\pi$
$523$	5.34646	−	3.08678i	0.233784	−	0.134976i	0.612317	+	0.790613i	$0.290238\pi$
$524$		0			0
$525$	0.134832	+	0.0214219i	0.00588453	+	0.000934929i
$526$		0			0
$527$	6.67279	−	5.59914i	0.290671	−	0.243902i
$528$		0			0
$529$	21.1698	−	7.70519i	0.920428	−	0.335008i
$530$		0			0
$531$	−9.97863	+	18.7235i	−0.433035	+	0.812529i
$532$		0			0
$533$	24.0479	+	4.24030i	1.04163	+	0.183668i
$534$		0			0
$535$	1.32934	−	3.65234i	0.0574724	−	0.157904i
$536$		0			0
$537$	−16.6421	−	5.73933i	−0.718161	−	0.247670i
$538$		0			0
$539$	−11.2933			−0.486436
$540$		0			0
$541$	−41.9992			−1.80569			−0.902843	−	0.429970i	$-0.858524\pi$
$541$	−41.9992			−1.80569			−0.902843	+	0.429970i	$0.858524\pi$
$542$		0			0
$543$	5.95733	+	30.7269i	0.255653	+	1.31862i
$544$		0			0
$545$	3.51796	−	9.66551i	0.150693	−	0.414025i
$546$		0			0
$547$	−12.8165	−	2.25990i	−0.547995	−	0.0966263i	−0.107206	−	0.994237i	$-0.534190\pi$
$547$	−12.8165	−	2.25990i	−0.547995	−	0.0966263i	−0.440789	+	0.897611i	$0.645301\pi$
$548$		0			0
$549$	−4.69225	−	1.52961i	−0.200260	−	0.0652822i
$550$		0			0
$551$	54.8011	−	19.9460i	2.33460	−	0.849726i
$552$		0			0
$553$	4.01458	−	3.36863i	0.170717	−	0.143249i
$554$		0			0
$555$	−16.4903	+	20.3438i	−0.699975	+	0.863545i
$556$		0			0
$557$	−0.710695	+	0.410320i	−0.0301131	+	0.0173858i	−0.514981	−	0.857202i	$-0.672201\pi$
$557$	−0.710695	+	0.410320i	−0.0301131	+	0.0173858i	0.484868	+	0.874587i	$0.338868\pi$
$558$		0			0
$559$	−25.5487	−	14.7506i	−1.08060	−	0.623882i
$560$		0			0
$561$	−0.206207	−	12.1494i	−0.00870606	−	0.512950i
$562$		0			0
$563$	3.27754	+	18.5879i	0.138132	+	0.783385i	0.972627	+	0.232370i	$0.0746481\pi$
$563$	3.27754	+	18.5879i	0.138132	+	0.783385i	−0.834496	+	0.551015i	$0.814241\pi$
$564$		0			0
$565$	0.146764	+	0.123150i	0.00617442	+	0.00518095i
$566$		0			0
$567$	−8.98160	−	4.40209i	−0.377192	−	0.184871i
$568$		0			0
$569$	8.60251	−	10.2521i	0.360636	−	0.429789i	−0.554967	−	0.831872i	$-0.687269\pi$
$569$	8.60251	−	10.2521i	0.360636	−	0.429789i	0.915603	+	0.402083i	$0.131714\pi$
$570$		0			0
$571$	−14.1345	+	2.49230i	−0.591512	+	0.104300i	−0.461388	−	0.887198i	$-0.652649\pi$
$571$	−14.1345	+	2.49230i	−0.591512	+	0.104300i	−0.130124	+	0.991498i	$0.541537\pi$
$572$		0			0
$573$	−27.0955	+	0.459880i	−1.13193	+	0.0192118i
$574$		0			0
$575$	0.0243503	−	0.0421759i	0.00101548	−	0.00175886i
$576$		0			0
$577$	18.2624	+	31.6315i	0.760275	+	1.31683i	0.942709	+	0.333617i	$0.108269\pi$
$577$	18.2624	+	31.6315i	0.760275	+	1.31683i	−0.182434	+	0.983218i	$0.558398\pi$
$578$		0			0
$579$	13.1284	+	10.6416i	0.545596	+	0.442251i
$580$		0			0
$581$	5.62609	+	6.70491i	0.233409	+	0.278167i
$582$		0			0
$583$	−0.266779	−	0.732969i	−0.0110489	−	0.0303565i
$584$		0			0
$585$	−21.1182	+	4.46753i	−0.873131	+	0.184710i
$586$		0			0
$587$	7.07473	−	40.1228i	0.292005	−	1.65604i	−0.387126	−	0.922027i	$-0.626532\pi$
$587$	7.07473	−	40.1228i	0.292005	−	1.65604i	0.679131	−	0.734017i	$-0.262357\pi$
$588$		0			0
$589$	16.4328	+	5.98107i	0.677104	+	0.246446i
$590$		0			0
$591$	−34.1111	+	6.61346i	−1.40314	+	0.272041i
$592$		0			0
$593$			38.9773i			1.60061i	0.599596	+	0.800303i	$0.295328\pi$
$593$			38.9773i			1.60061i	−0.599596	+	0.800303i	$0.704672\pi$
$594$		0			0
$595$			8.83627i			0.362252i
$596$		0			0
$597$	7.30920	−	21.1943i	0.299146	−	0.867423i
$598$		0			0
$599$	−13.3729	−	4.86735i	−0.546404	−	0.198875i	0.0540442	−	0.998539i	$-0.482789\pi$
$599$	−13.3729	−	4.86735i	−0.546404	−	0.198875i	−0.600448	+	0.799664i	$0.705011\pi$
$600$		0			0
$601$	5.05604	−	28.6743i	0.206240	−	1.16965i	−0.689236	−	0.724537i	$-0.742054\pi$
$601$	5.05604	−	28.6743i	0.206240	−	1.16965i	0.895476	−	0.445110i	$-0.146835\pi$
$602$		0			0
$603$	3.97189	−	2.47659i	0.161748	−	0.100854i
$604$		0			0
$605$	−5.43863	−	14.9425i	−0.221112	−	0.607500i
$606$		0			0
$607$	−12.3207	−	14.6832i	−0.500080	−	0.595973i	0.455671	−	0.890148i	$-0.349399\pi$
$607$	−12.3207	−	14.6832i	−0.500080	−	0.595973i	−0.955751	+	0.294176i	$0.904955\pi$
$608$		0			0
$609$	2.45007	−	15.4210i	0.0992820	−	0.624891i
$610$		0			0
$611$	−14.9426	−	25.8813i	−0.604513	−	1.04705i
$612$		0			0
$613$	24.2789	−	42.0523i	0.980615	−	1.69847i	0.320614	−	0.947210i	$-0.396111\pi$
$613$	24.2789	−	42.0523i	0.980615	−	1.69847i	0.660001	−	0.751265i	$-0.270556\pi$
$614$		0			0
$615$	14.0591	−	25.3345i	0.566919	−	1.02159i
$616$		0			0
$617$	−1.98179	+	0.349444i	−0.0797840	+	0.0140681i	−0.213398	−	0.976965i	$-0.568453\pi$
$617$	−1.98179	+	0.349444i	−0.0797840	+	0.0140681i	0.133614	+	0.991033i	$0.457342\pi$
$618$		0			0
$619$	−10.6027	+	12.6358i	−0.426157	+	0.507874i	−0.935809	−	0.352506i	$-0.885329\pi$
$619$	−10.6027	+	12.6358i	−0.426157	+	0.507874i	0.509653	+	0.860380i	$0.329774\pi$
$620$		0			0
$621$	−2.61303	+	2.42963i	−0.104857	+	0.0974979i
$622$		0			0
$623$	−7.04254	−	5.90939i	−0.282153	−	0.236755i
$624$		0			0
$625$	−4.27875	−	24.2660i	−0.171150	−	0.970641i
$626$		0			0
$627$	20.9162	−	12.5540i	0.835314	−	0.501359i
$628$		0			0
$629$	21.1208	+	12.1941i	0.842142	+	0.486211i
$630$		0			0
$631$	26.3628	−	15.2206i	1.04949	−	0.605922i	0.126982	−	0.991905i	$-0.459471\pi$
$631$	26.3628	−	15.2206i	1.04949	−	0.605922i	0.922506	+	0.385983i	$0.126138\pi$
$632$		0			0
$633$	9.51991	+	24.8360i	0.378383	+	0.987143i
$634$		0			0
$635$	4.48956	−	3.76719i	0.178163	−	0.149496i
$636$		0			0
$637$	17.5563	−	6.38998i	0.695607	−	0.253180i
$638$		0			0
$639$	−10.1726	+	4.09860i	−0.402423	+	0.162138i
$640$		0			0
$641$	23.6619	+	4.17224i	0.934590	+	0.164793i	0.620149	−	0.784484i	$-0.287072\pi$
$641$	23.6619	+	4.17224i	0.934590	+	0.164793i	0.314441	+	0.949277i	$0.398183\pi$
$642$		0			0
$643$	−4.91291	+	13.4981i	−0.193746	+	0.532313i	−0.998085	−	0.0618578i	$-0.980297\pi$
$643$	−4.91291	+	13.4981i	−0.193746	+	0.532313i	0.804339	+	0.594171i	$0.202520\pi$
$644$		0			0
$645$	−26.4292	+	22.9522i	−1.04065	+	0.903740i
$646$		0			0
$647$	−8.01172			−0.314973			−0.157487	−	0.987521i	$-0.550339\pi$
$647$	−8.01172			−0.314973			−0.157487	+	0.987521i	$0.550339\pi$
$648$		0			0
$649$	−13.8543			−0.543831
$650$		0			0
$651$	3.53518	−	3.07010i	0.138555	−	0.120327i
$652$		0			0
$653$	−10.7005	+	29.3993i	−0.418742	+	1.15048i	0.533676	+	0.845689i	$0.320810\pi$
$653$	−10.7005	+	29.3993i	−0.418742	+	1.15048i	−0.952418	+	0.304795i	$0.901412\pi$
$654$		0			0
$655$	−16.2535	−	2.86593i	−0.635077	−	0.111981i
$656$		0			0
$657$	−27.4352	−	21.4774i	−1.07035	−	0.837913i
$658$		0			0
$659$	−33.0904	+	12.0439i	−1.28902	+	0.469165i	−0.893405	−	0.449251i	$-0.851691\pi$
$659$	−33.0904	+	12.0439i	−1.28902	+	0.469165i	−0.395615	+	0.918416i	$0.629469\pi$
$660$		0			0
$661$	−23.6535	+	19.8476i	−0.920014	+	0.771983i	−0.973998	−	0.226559i	$-0.927253\pi$
$661$	−23.6535	+	19.8476i	−0.920014	+	0.771983i	0.0539838	+	0.998542i	$0.482808\pi$
$662$		0			0
$663$	7.19497	+	18.7706i	0.279429	+	0.728989i
$664$		0			0
$665$	−15.3629	+	8.86976i	−0.595747	+	0.343955i
$666$		0			0
$667$	−4.82376	−	2.78500i	−0.186777	−	0.107836i
$668$		0			0
$669$	33.3460	−	20.0144i	1.28923	−	0.773802i
$670$		0			0
$671$	−0.559620	−	3.17376i	−0.0216039	−	0.122522i
$672$		0			0
$673$	19.9697	+	16.7566i	0.769776	+	0.645919i	0.940652	−	0.339374i	$-0.110215\pi$
$673$	19.9697	+	16.7566i	0.769776	+	0.645919i	−0.170875	+	0.985293i	$0.554660\pi$
$674$		0			0
$675$	0.0454410	−	0.365711i	0.00174903	−	0.0140762i
$676$		0			0
$677$	−5.05253	+	6.02137i	−0.194185	+	0.231420i	−0.854347	−	0.519702i	$-0.826043\pi$
$677$	−5.05253	+	6.02137i	−0.194185	+	0.231420i	0.660163	+	0.751123i	$0.270487\pi$
$678$		0			0
$679$	−13.5662	+	2.39208i	−0.520622	+	0.0917997i
$680$		0			0
$681$	14.2280	−	25.6388i	0.545219	−	0.982482i
$682$		0			0
$683$	−19.0403	+	32.9788i	−0.728558	+	1.26190i	0.228935	+	0.973442i	$0.426476\pi$
$683$	−19.0403	+	32.9788i	−0.728558	+	1.26190i	−0.957493	+	0.288457i	$0.906858\pi$
$684$		0			0
$685$	13.3067	+	23.0478i	0.508422	+	0.880612i
$686$		0			0
$687$	−6.26907	+	39.4582i	−0.239180	+	1.50542i
$688$		0			0
$689$	0.829458	+	0.988510i	0.0315998	+	0.0376592i
$690$		0			0
$691$	−15.2477	−	41.8928i	−0.580051	−	1.59368i	−0.788093	−	0.615556i	$-0.788931\pi$
$691$	−15.2477	−	41.8928i	−0.580051	−	1.59368i	0.208042	−	0.978120i	$-0.433291\pi$
$692$		0			0
$693$	−0.221649	−	6.52777i	−0.00841977	−	0.247969i
$694$		0			0
$695$	−0.327958	+	1.85994i	−0.0124401	+	0.0705515i
$696$		0			0
$697$	−25.3558	−	9.22876i	−0.960420	−	0.349564i
$698$		0			0
$699$	−11.0275	+	31.9761i	−0.417099	+	1.20945i
$700$		0			0
$701$			18.7875i			0.709593i	0.934943	+	0.354797i	$0.115450\pi$
$701$			18.7875i			0.709593i	−0.934943	+	0.354797i	$0.884550\pi$
$702$		0			0
$703$			48.9613i			1.84661i
$704$		0			0
$705$	−34.8118	+	6.74930i	−1.31109	+	0.254193i
$706$		0			0
$707$	−15.1907	−	5.52895i	−0.571303	−	0.207937i
$708$		0			0
$709$	−0.412286	+	2.33819i	−0.0154837	+	0.0878126i	−0.991570	−	0.129569i	$-0.958641\pi$
$709$	−0.412286	+	2.33819i	−0.0154837	+	0.0878126i	0.976087	+	0.217382i	$0.0697517\pi$
$710$		0			0
$711$	−9.45565	−	10.5220i	−0.354615	−	0.394604i
$712$		0			0
$713$	−0.571256	−	1.56951i	−0.0213937	−	0.0587787i
$714$		0			0
$715$	−9.06032	−	10.7977i	−0.338837	−	0.403810i
$716$		0			0
$717$	10.5218	+	8.52882i	0.392945	+	0.318515i
$718$		0			0
$719$	2.83629	+	4.91260i	0.105776	+	0.183209i	0.914055	−	0.405591i	$-0.132934\pi$
$719$	2.83629	+	4.91260i	0.105776	+	0.183209i	−0.808279	+	0.588799i	$0.799601\pi$
$720$		0			0
$721$	9.84461	−	17.0514i	0.366632	−	0.635026i
$722$		0			0
$723$	−32.6471	+	0.554104i	−1.21416	+	0.0206074i
$724$		0			0
$725$	0.566552	−	0.0998984i	0.0210412	−	0.00371013i
$726$		0			0
$727$	−19.1496	+	22.8216i	−0.710218	+	0.846405i	−0.993642	−	0.112590i	$-0.964085\pi$
$727$	−19.1496	+	22.8216i	−0.710218	+	0.846405i	0.283424	+	0.958995i	$0.408530\pi$
$728$		0			0
$729$	−11.0532	+	24.6338i	−0.409379	+	0.912364i
$730$		0			0
$731$	24.9722	+	20.9542i	0.923631	+	0.775019i
$732$		0			0
$733$	2.25772	+	12.8042i	0.0833909	+	0.472933i	0.997692	+	0.0678987i	$0.0216295\pi$
$733$	2.25772	+	12.8042i	0.0833909	+	0.472933i	−0.914301	+	0.405035i	$0.867259\pi$
$734$		0			0
$735$	−0.376197	−	22.1650i	−0.0138762	−	0.817570i
$736$		0			0
$737$	2.64702	+	1.52826i	0.0975042	+	0.0562941i
$738$		0			0
$739$	−4.38752	+	2.53314i	−0.161398	+	0.0931830i	−0.578523	−	0.815666i	$-0.696371\pi$
$739$	−4.38752	+	2.53314i	−0.161398	+	0.0931830i	0.417126	+	0.908849i	$0.363037\pi$
$740$		0			0
$741$	−25.4126	+	31.3510i	−0.933556	+	1.15171i
$742$		0			0
$743$	26.5734	−	22.2977i	0.974882	−	0.818023i	−0.00842733	−	0.999964i	$-0.502683\pi$
$743$	26.5734	−	22.2977i	0.974882	−	0.818023i	0.983309	+	0.181941i	$0.0582381\pi$
$744$		0			0
$745$	−33.2804	+	12.1131i	−1.21930	+	0.443788i
$746$		0			0
$747$	17.5732	−	15.7923i	0.642968	−	0.577809i
$748$		0			0
$749$	−1.91608	−	0.337857i	−0.0700122	−	0.0123450i
$750$		0			0
$751$	5.47262	−	15.0359i	0.199699	−	0.548668i	−0.798907	−	0.601455i	$-0.794588\pi$
$751$	5.47262	−	15.0359i	0.199699	−	0.548668i	0.998606	+	0.0527866i	$0.0168103\pi$
$752$		0			0
$753$	−9.50865	−	49.0441i	−0.346515	−	1.78727i
$754$		0			0
$755$	9.66020			0.351571
$756$		0			0
$757$	−30.5182			−1.10920			−0.554602	−	0.832116i	$-0.687130\pi$
$757$	−30.5182			−1.10920			−0.554602	+	0.832116i	$0.687130\pi$
$758$		0			0
$759$	−2.20263	−	0.759616i	−0.0799505	−	0.0275723i
$760$		0			0
$761$	−3.97746	+	10.9280i	−0.144183	+	0.396139i	−0.990672	−	0.136266i	$-0.956490\pi$
$761$	−3.97746	+	10.9280i	−0.144183	+	0.396139i	0.846489	+	0.532406i	$0.178712\pi$
$762$		0			0
$763$	−5.07071	−	0.894103i	−0.183572	−	0.0323687i
$764$		0			0
$765$	23.8385	−	0.809433i	0.861883	−	0.0292651i
$766$		0			0
$767$	21.5377	−	7.83908i	0.777681	−	0.283053i
$768$		0			0
$769$	−20.3136	+	17.0451i	−0.732526	+	0.614663i	−0.930819	−	0.365480i	$-0.880905\pi$
$769$	−20.3136	+	17.0451i	−0.732526	+	0.614663i	0.198293	+	0.980143i	$0.436460\pi$
$770$		0			0
$771$	0.103854	+	0.0165003i	0.00374022	+	0.000594243i
$772$		0			0
$773$	31.4782	−	18.1739i	1.13219	−	0.653671i	0.187707	−	0.982225i	$-0.439895\pi$
$773$	31.4782	−	18.1739i	1.13219	−	0.653671i	0.944485	+	0.328554i	$0.106561\pi$
$774$		0			0
$775$	0.149397	+	0.0862546i	0.00536651	+	0.00309836i
$776$		0			0
$777$	11.4625	+	6.36100i	0.411215	+	0.228200i
$778$		0			0
$779$	−9.40665	−	53.3478i	−0.337028	−	1.91138i
$780$		0			0
$781$	−5.48610	−	4.60339i	−0.196308	−	0.164722i
$782$		0			0
$783$	−41.8273	−	5.19720i	−1.49479	−	0.185733i
$784$		0			0
$785$	19.0545	−	22.7083i	0.680085	−	0.810494i
$786$		0			0
$787$	44.7921	−	7.89805i	1.59667	−	0.281535i	0.696656	−	0.717406i	$-0.254670\pi$
$787$	44.7921	−	7.89805i	1.59667	−	0.281535i	0.900009	+	0.435870i	$0.143559\pi$
$788$		0			0
$789$	17.0610	+	28.4254i	0.607389	+	1.01197i
$790$		0			0
$791$	0.0479528	−	0.0830568i	0.00170501	−	0.00295316i
$792$		0			0
$793$	2.66575	+	4.61722i	0.0946637	+	0.163962i
$794$		0			0
$795$	1.42969	−	0.548016i	0.0507059	−	0.0194361i
$796$		0			0
$797$	13.4563	+	16.0365i	0.476645	+	0.568043i	0.949769	−	0.312953i	$-0.101318\pi$
$797$	13.4563	+	16.0365i	0.476645	+	0.568043i	−0.473124	+	0.880996i	$0.656874\pi$
$798$		0			0
$799$	11.2946	+	31.0318i	0.399576	+	1.09783i
$800$		0			0
$801$	−15.2973	+	19.5407i	−0.540502	+	0.690437i
$802$		0			0
$803$	3.95081	−	22.4061i	0.139421	−	0.790695i
$804$		0			0
$805$	1.59214	+	0.579490i	0.0561154	+	0.0204243i
$806$		0			0
$807$	−29.0344	−	33.4328i	−1.02206	−	1.17689i
$808$		0			0
$809$		−	0.636338i		−	0.0223725i	−0.999937	−	0.0111862i	$-0.996439\pi$
$809$		−	0.636338i		−	0.0223725i	0.999937	−	0.0111862i	$-0.00356076\pi$
$810$		0			0
$811$		−	23.6017i		−	0.828768i	−0.910102	−	0.414384i	$-0.863997\pi$
$811$		−	23.6017i		−	0.828768i	0.910102	−	0.414384i	$-0.136003\pi$
$812$		0			0
$813$	17.7342	+	20.4207i	0.621964	+	0.716185i
$814$		0			0
$815$	−49.5789	−	18.0453i	−1.73667	−	0.632098i
$816$		0			0
$817$	−11.3644	+	64.4508i	−0.397590	+	2.25485i
$818$		0			0
$819$	4.03812	+	10.0225i	0.141103	+	0.350215i
$820$		0			0
$821$	7.97255	+	21.9044i	0.278244	+	0.764469i	0.997562	+	0.0697878i	$0.0222322\pi$
$821$	7.97255	+	21.9044i	0.278244	+	0.764469i	−0.719318	+	0.694681i	$0.755546\pi$
$822$		0			0
$823$	−9.38307	−	11.1823i	−0.327073	−	0.389791i	0.577301	−	0.816532i	$-0.304106\pi$
$823$	−9.38307	−	11.1823i	−0.327073	−	0.389791i	−0.904374	+	0.426741i	$0.859662\pi$
$824$		0			0
$825$	0.224703	−	0.0861311i	0.00782316	−	0.00299870i
$826$		0			0
$827$	0.575505	+	0.996803i	0.0200123	+	0.0346623i	0.875858	−	0.482569i	$-0.160296\pi$
$827$	0.575505	+	0.996803i	0.0200123	+	0.0346623i	−0.855846	+	0.517231i	$0.826963\pi$
$828$		0			0
$829$	2.64001	−	4.57263i	0.0916912	−	0.158814i	−0.816532	−	0.577301i	$-0.804106\pi$
$829$	2.64001	−	4.57263i	0.0916912	−	0.158814i	0.908223	+	0.418487i	$0.137439\pi$
$830$		0			0
$831$	−24.2407	−	40.3874i	−0.840899	−	1.40102i
$832$		0			0
$833$	−20.3313	+	3.58495i	−0.704436	+	0.124211i
$834$		0			0
$835$	30.3672	−	36.1903i	1.05090	−	1.25242i
$836$		0			0
$837$	−8.60635	−	9.25600i	−0.297479	−	0.319934i
$838$		0			0
$839$	3.44214	+	2.88830i	0.118836	+	0.0997151i	0.700269	−	0.713879i	$-0.253063\pi$
$839$	3.44214	+	2.88830i	0.118836	+	0.0997151i	−0.581433	+	0.813594i	$0.697508\pi$
$840$		0			0
$841$	−6.38982	−	36.2385i	−0.220339	−	1.24960i
$842$		0			0
$843$	27.0630	+	15.0184i	0.932101	+	0.517260i
$844$		0			0
$845$	−4.80068	−	2.77168i	−0.165149	−	0.0953485i
$846$		0			0
$847$	−6.89361	+	3.98003i	−0.236867	+	0.136755i
$848$		0			0
$849$	−48.7194	−	7.74049i	−1.67205	−	0.265653i
$850$		0			0
$851$	3.58228	−	3.00589i	0.122799	−	0.103041i
$852$		0			0
$853$	−22.8883	+	8.33065i	−0.783679	+	0.285236i	−0.702706	−	0.711480i	$-0.748025\pi$
$853$	−22.8883	+	8.33065i	−0.783679	+	0.285236i	−0.0809734	+	0.996716i	$0.525803\pi$
$854$		0			0
$855$	25.3362	+	40.6335i	0.866479	+	1.38964i
$856$		0			0
$857$	−3.20938	−	0.565900i	−0.109630	−	0.0193308i	0.118564	−	0.992946i	$-0.462171\pi$
$857$	−3.20938	−	0.565900i	−0.109630	−	0.0193308i	−0.228194	+	0.973616i	$0.573282\pi$
$858$		0			0
$859$	10.4359	−	28.6725i	0.356070	−	0.978294i	−0.624310	−	0.781177i	$-0.714620\pi$
$859$	10.4359	−	28.6725i	0.356070	−	0.978294i	0.980380	−	0.197117i	$-0.0631580\pi$
$860$		0			0
$861$	−13.7115	−	4.72866i	−0.467288	−	0.161152i
$862$		0			0
$863$	35.4682			1.20735			0.603676	−	0.797230i	$-0.293702\pi$
$863$	35.4682			1.20735			0.603676	+	0.797230i	$0.293702\pi$
$864$		0			0
$865$	2.85902			0.0972097
$866$		0			0
$867$	1.37644	+	7.09947i	0.0467465	+	0.241111i
$868$		0			0
$869$	3.15944	−	8.68048i	0.107177	−	0.294465i
$870$		0			0
$871$	−4.97972	−	0.878060i	−0.168731	−	0.0297519i
$872$		0			0
$873$	7.69607	+	36.3797i	0.260473	+	1.23127i
$874$		0			0
$875$	−11.7575	+	4.27939i	−0.397477	+	0.144670i
$876$		0			0
$877$	−19.1892	+	16.1017i	−0.647974	+	0.543714i	−0.906455	−	0.422302i	$-0.861222\pi$
$877$	−19.1892	+	16.1017i	−0.647974	+	0.543714i	0.258482	+	0.966016i	$0.416778\pi$
$878$		0			0
$879$	29.1205	−	35.9254i	0.982210	−	1.21173i
$880$		0			0
$881$	7.94239	−	4.58554i	0.267586	−	0.154491i	−0.360204	−	0.932873i	$-0.617293\pi$
$881$	7.94239	−	4.58554i	0.267586	−	0.154491i	0.627790	+	0.778383i	$0.283960\pi$
$882$		0			0
$883$	−10.8537	−	6.26639i	−0.365256	−	0.210881i	0.306128	−	0.951990i	$-0.400967\pi$
$883$	−10.8537	−	6.26639i	−0.365256	−	0.210881i	−0.671384	+	0.741110i	$0.734300\pi$
$884$		0			0
$885$	−0.461510	−	27.1916i	−0.0155135	−	0.914034i
$886$		0			0
$887$	1.64470	+	9.32755i	0.0552236	+	0.313189i	0.999890	−	0.0148446i	$-0.00472535\pi$
$887$	1.64470	+	9.32755i	0.0552236	+	0.313189i	−0.944666	+	0.328033i	$0.893614\pi$
$888$		0			0
$889$	−2.24741	−	1.88580i	−0.0753756	−	0.0632476i
$890$		0			0
$891$	−17.5903	+	1.19593i	−0.589298	+	0.0400653i
$892$		0			0
$893$	−42.6149	+	50.7865i	−1.42605	+	1.69950i
$894$		0			0
$895$	22.2221	−	3.91835i	0.742803	−	0.130976i
$896$		0			0
$897$	3.85397	−	0.0654117i	0.128680	−	0.00218403i
$898$		0			0
$899$	9.86514	−	17.0869i	0.329021	−	0.569881i
$900$		0			0
$901$	−0.712955	−	1.23487i	−0.0237520	−	0.0411396i
$902$		0			0
$903$	13.6123	+	11.0339i	0.452990	+	0.367186i
$904$		0			0
$905$	−25.7882	−	30.7332i	−0.857230	−	1.02161i
$906$		0			0
$907$	3.37587	+	9.27512i	0.112094	+	0.307975i	0.983037	−	0.183409i	$-0.0587133\pi$
$907$	3.37587	+	9.27512i	0.112094	+	0.307975i	−0.870943	+	0.491384i	$0.836491\pi$
$908$		0			0
$909$	−13.5245	+	41.4879i	−0.448579	+	1.37607i
$910$		0			0
$911$	−0.0737890	+	0.418478i	−0.00244474	+	0.0138648i	−0.986006	−	0.166711i	$-0.946685\pi$
$911$	−0.0737890	+	0.418478i	−0.00244474	+	0.0138648i	0.983561	+	0.180576i	$0.0577963\pi$
$912$		0			0
$913$	14.4976	+	5.27670i	0.479801	+	0.174633i
$914$		0			0
$915$	6.21042	−	1.20407i	0.205310	−	0.0398055i
$916$		0			0
$917$			8.26179i			0.272828i
$918$		0			0
$919$			36.5918i			1.20705i	0.797343	+	0.603526i	$0.206238\pi$
$919$			36.5918i			1.20705i	−0.797343	+	0.603526i	$0.793762\pi$
$920$		0			0
$921$	0.745095	−	2.16053i	0.0245517	−	0.0711918i
$922$		0			0
$923$	11.1333	+	4.05218i	0.366456	+	0.133379i
$924$		0			0
$925$	−0.0838704	+	0.475653i	−0.00275764	+	0.0156394i
$926$		0			0
$927$	−46.9030	−	24.9969i	−1.54050	−	0.821004i
$928$		0			0
$929$	−12.5437	−	34.4636i	−0.411546	−	1.13071i	−0.956369	−	0.292163i	$-0.905625\pi$
$929$	−12.5437	−	34.4636i	−0.411546	−	1.13071i	0.544822	−	0.838552i	$-0.316597\pi$
$930$		0			0
$931$	−26.6412	−	31.7497i	−0.873129	−	1.04055i
$932$		0			0
$933$	−5.57130	+	35.0663i	−0.182396	+	1.14802i
$934$		0			0
$935$	7.78773	+	13.4887i	0.254686	+	0.441129i
$936$		0			0
$937$	10.6627	−	18.4684i	0.348336	−	0.603335i	−0.637618	−	0.770352i	$-0.720080\pi$
$937$	10.6627	−	18.4684i	0.348336	−	0.603335i	0.985954	+	0.167017i	$0.0534136\pi$
$938$		0			0
$939$	−2.72494	+	4.91033i	−0.0889250	+	0.160243i
$940$		0			0
$941$	−7.15449	+	1.26153i	−0.233230	+	0.0411247i	−0.289041	−	0.957317i	$-0.593336\pi$
$941$	−7.15449	+	1.26153i	−0.233230	+	0.0411247i	0.0558116	+	0.998441i	$0.482225\pi$
$942$		0			0
$943$	−3.32571	+	3.96343i	−0.108300	+	0.129067i
$944$		0			0
$945$	12.8045	−	0.652476i	0.416530	−	0.0212250i
$946$		0			0
$947$	−16.8337	−	14.1251i	−0.547021	−	0.459005i	0.326910	−	0.945056i	$-0.393993\pi$
$947$	−16.8337	−	14.1251i	−0.547021	−	0.459005i	−0.873931	+	0.486050i	$0.838437\pi$
$948$		0			0
$949$	6.53601	+	37.0676i	0.212168	+	1.20326i
$950$		0			0
$951$	−12.3208	+	7.39501i	−0.399530	+	0.239799i
$952$		0			0
$953$	31.4933	+	18.1827i	1.02017	+	0.588995i	0.914153	−	0.405370i	$-0.132857\pi$
$953$	31.4933	+	18.1827i	1.02017	+	0.588995i	0.106016	+	0.994364i	$0.466191\pi$
$954$		0			0
$955$	30.0825	−	17.3681i	0.973445	−	0.562019i
$956$		0			0
$957$	−9.85102	−	25.6998i	−0.318438	−	0.830758i
$958$		0			0
$959$	10.2054	−	8.56337i	0.329550	−	0.276526i
$960$		0			0
$961$	−23.5709	+	8.57910i	−0.760351	+	0.276745i
$962$		0			0
$963$	−0.735952	+	5.20016i	−0.0237157	+	0.167573i
$964$		0			0
$965$	−21.3330	−	3.76158i	−0.686733	−	0.121089i
$966$		0			0
$967$	−13.6545	+	37.5155i	−0.439099	+	1.20642i	0.500980	+	0.865459i	$0.332973\pi$
$967$	−13.6545	+	37.5155i	−0.439099	+	1.20642i	−0.940079	+	0.340957i	$0.889249\pi$
$968$		0			0
$969$	33.6702	−	29.2406i	1.08164	−	0.939343i
$970$		0			0
$971$	−41.6947			−1.33805			−0.669023	−	0.743242i	$-0.733287\pi$
$971$	−41.6947			−1.33805			−0.669023	+	0.743242i	$0.733287\pi$
$972$		0			0
$973$	0.945421			0.0303088
$974$		0			0
$975$	−0.300584	+	0.261039i	−0.00962640	+	0.00835995i
$976$		0			0
$977$	1.09675	−	3.01330i	0.0350882	−	0.0964041i	−0.920911	−	0.389772i	$-0.872554\pi$
$977$	1.09675	−	3.01330i	0.0350882	−	0.0964041i	0.956000	+	0.293368i	$0.0947761\pi$
$978$		0			0
$979$	−15.9587	−	2.81396i	−0.510044	−	0.0899345i
$980$		0			0
$981$	−1.94762	+	13.7617i	−0.0621826	+	0.439376i
$982$		0			0
$983$	−26.1055	+	9.50161i	−0.832635	+	0.303054i	−0.722940	−	0.690911i	$-0.757210\pi$
$983$	−26.1055	+	9.50161i	−0.832635	+	0.303054i	−0.109695	+	0.993965i	$0.534987\pi$
$984$		0			0
$985$	34.1181	−	28.6285i	1.08709	−	0.912180i
$986$		0			0
$987$	6.35331	+	16.5748i	0.202228	+	0.527583i
$988$		0			0
$989$	5.41327	−	3.12535i	0.172132	−	0.0993804i
$990$		0			0
$991$	−10.6621	−	6.15575i	−0.338692	−	0.195544i	0.321001	−	0.947079i	$-0.395981\pi$
$991$	−10.6621	−	6.15575i	−0.338692	−	0.195544i	−0.659693	+	0.751535i	$0.729314\pi$
$992$		0			0
$993$	44.4812	−	26.6978i	1.41157	−	0.847230i
$994$		0			0
$995$	4.99014	+	28.3005i	0.158198	+	0.897186i
$996$		0			0
$997$	46.5106	+	39.0271i	1.47301	+	1.23600i	0.913286	+	0.407318i	$0.133536\pi$
$997$	46.5106	+	39.0271i	1.47301	+	1.23600i	0.559721	+	0.828681i	$0.310908\pi$
$998$		0			0
$999$	16.1107	−	31.5063i	0.509721	−	0.996814i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	864.2.bi.a.767.28	yes	216
4.3	odd	2	inner	864.2.bi.a.767.9	yes	216
27.5	odd	18	inner	864.2.bi.a.383.9	✓	216
108.59	even	18	inner	864.2.bi.a.383.28	yes	216

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
864.2.bi.a.383.9	✓	216	27.5	odd	18	inner
864.2.bi.a.383.28	yes	216	108.59	even	18	inner
864.2.bi.a.767.9	yes	216	4.3	odd	2	inner
864.2.bi.a.767.28	yes	216	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(1.30774 - 1.13570i) q^{3} +(-0.759337 + 2.08626i) q^{5} +(1.09449 + 0.192988i) q^{7} +(0.420385 - 2.97040i) q^{9} +O(q^{10})\)	\(q+(1.30774 - 1.13570i) q^{3} +(-0.759337 + 2.08626i) q^{5} +(1.09449 + 0.192988i) q^{7} +(0.420385 - 2.97040i) q^{9} +(1.84085 - 0.670015i) q^{11} +(-2.48264 + 2.08318i) q^{13} +(1.37634 + 3.59067i) q^{15} +(3.10139 - 1.79059i) q^{17} +(6.22628 + 3.59475i) q^{19} +(1.65049 - 0.990631i) q^{21} +(-0.119240 - 0.676242i) q^{23} +(0.0543297 + 0.0455881i) q^{25} +(-2.82372 - 4.36195i) q^{27} +(5.21402 - 6.21382i) q^{29} +(2.39541 - 0.422376i) q^{31} +(1.64643 - 2.96686i) q^{33} +(-1.23371 + 2.13685i) q^{35} +(3.40506 + 5.89774i) q^{37} +(-0.880793 + 5.54380i) q^{39} +(-4.84322 - 5.77192i) q^{41} +(3.11336 + 8.55390i) q^{43} +(5.87782 + 3.13257i) q^{45} +(-1.60128 + 9.08128i) q^{47} +(-5.41718 - 1.97169i) q^{49} +(2.02225 - 5.86386i) q^{51} -0.398168i q^{53} +4.34926i q^{55} +(12.2249 - 2.37017i) q^{57} +(-6.64567 - 2.41883i) q^{59} +(0.285667 - 1.62010i) q^{61} +(1.03336 - 3.16995i) q^{63} +(-2.46090 - 6.76128i) q^{65} +(1.00291 + 1.19522i) q^{67} +(-0.923941 - 0.748931i) q^{69} +(-1.82788 - 3.16598i) q^{71} +(5.80701 - 10.0580i) q^{73} +(0.122824 - 0.00208463i) q^{75} +(2.14410 - 0.378063i) q^{77} +(3.03105 - 3.61226i) q^{79} +(-8.64655 - 2.49742i) q^{81} +(6.03298 + 5.06227i) q^{83} +(1.38063 + 7.82996i) q^{85} +(-0.238424 - 14.0476i) q^{87} +(-7.16383 - 4.13604i) q^{89} +(-3.11926 + 1.80091i) q^{91} +(2.65289 - 3.27282i) q^{93} +(-12.2274 + 10.2600i) q^{95} +(-11.6474 + 4.23932i) q^{97} +(-1.21635 - 5.74973i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 216 q+O(q^{10}) \) 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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