LMFDB - Embedded newform 882.2.l.c.227.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [882,2,Mod(227,882)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(882, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([1, 1]))

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

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

chi := DirichletCharacter("882.227");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 882 = 2 \cdot 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	882.l (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$7.04280545828$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			227.10
Character	$\chi$	$=$	882.227
Dual form			882.2.l.c.509.22

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} +(1.52614 + 0.819074i) q^{3} -1.00000 q^{4} +(1.99341 - 3.45268i) q^{5} +(0.819074 - 1.52614i) q^{6} +1.00000i q^{8} +(1.65823 + 2.50005i) q^{9} +O(q^{10})$	\(q-1.00000i q^{2} +(1.52614 + 0.819074i) q^{3} -1.00000 q^{4} +(1.99341 - 3.45268i) q^{5} +(0.819074 - 1.52614i) q^{6} +1.00000i q^{8} +(1.65823 + 2.50005i) q^{9} +(-3.45268 - 1.99341i) q^{10} +(1.43438 - 0.828141i) q^{11} +(-1.52614 - 0.819074i) q^{12} +(2.60834 - 1.50592i) q^{13} +(5.87023 - 3.63655i) q^{15} +1.00000 q^{16} +(-3.72820 + 6.45743i) q^{17} +(2.50005 - 1.65823i) q^{18} +(3.96054 - 2.28662i) q^{19} +(-1.99341 + 3.45268i) q^{20} +(-0.828141 - 1.43438i) q^{22} +(0.253614 + 0.146424i) q^{23} +(-0.819074 + 1.52614i) q^{24} +(-5.44735 - 9.43509i) q^{25} +(-1.50592 - 2.60834i) q^{26} +(0.482978 + 5.17366i) q^{27} +(-3.18684 - 1.83992i) q^{29} +(-3.63655 - 5.87023i) q^{30} -4.71484i q^{31} -1.00000i q^{32} +(2.86739 - 0.0889974i) q^{33} +(6.45743 + 3.72820i) q^{34} +(-1.65823 - 2.50005i) q^{36} +(-3.00695 - 5.20820i) q^{37} +(-2.28662 - 3.96054i) q^{38} +(5.21416 - 0.161836i) q^{39} +(3.45268 + 1.99341i) q^{40} +(4.88630 + 8.46333i) q^{41} +(-1.29961 + 2.25100i) q^{43} +(-1.43438 + 0.828141i) q^{44} +(11.9374 - 0.741738i) q^{45} +(0.146424 - 0.253614i) q^{46} -13.6124 q^{47} +(1.52614 + 0.819074i) q^{48} +(-9.43509 + 5.44735i) q^{50} +(-10.9789 + 6.80130i) q^{51} +(-2.60834 + 1.50592i) q^{52} +(-0.793421 - 0.458082i) q^{53} +(5.17366 - 0.482978i) q^{54} -6.60330i q^{55} +(7.91727 - 0.245735i) q^{57} +(-1.83992 + 3.18684i) q^{58} +7.06674 q^{59} +(-5.87023 + 3.63655i) q^{60} +6.64659i q^{61} -4.71484 q^{62} -1.00000 q^{64} -12.0077i q^{65} +(-0.0889974 - 2.86739i) q^{66} +4.05676 q^{67} +(3.72820 - 6.45743i) q^{68} +(0.267120 + 0.431193i) q^{69} -13.9437i q^{71} +(-2.50005 + 1.65823i) q^{72} +(3.84574 + 2.22034i) q^{73} +(-5.20820 + 3.00695i) q^{74} +(-0.585407 - 18.8611i) q^{75} +(-3.96054 + 2.28662i) q^{76} +(-0.161836 - 5.21416i) q^{78} +2.84730 q^{79} +(1.99341 - 3.45268i) q^{80} +(-3.50051 + 8.29134i) q^{81} +(8.46333 - 4.88630i) q^{82} +(-2.59432 + 4.49349i) q^{83} +(14.8636 + 25.7446i) q^{85} +(2.25100 + 1.29961i) q^{86} +(-3.35654 - 5.41824i) q^{87} +(0.828141 + 1.43438i) q^{88} +(5.50866 + 9.54128i) q^{89} +(-0.741738 - 11.9374i) q^{90} +(-0.253614 - 0.146424i) q^{92} +(3.86181 - 7.19553i) q^{93} +13.6124i q^{94} -18.2327i q^{95} +(0.819074 - 1.52614i) q^{96} +(2.51510 + 1.45209i) q^{97} +(4.44894 + 2.21278i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 48 q^{4} + 16 q^{9}+O(q^{10}) $ 48 * q - 48 * q^4 + 16 * q^9	$ 48 q - 48 q^{4} + 16 q^{9} - 48 q^{11} + 48 q^{15} + 48 q^{16} + 16 q^{18} - 48 q^{23} - 24 q^{25} - 16 q^{30} - 16 q^{36} + 32 q^{39} + 48 q^{44} - 48 q^{50} - 48 q^{51} + 96 q^{53} - 80 q^{57} - 48 q^{60} - 48 q^{64} - 16 q^{72} + 32 q^{78} - 96 q^{79} + 96 q^{81} + 48 q^{85} - 96 q^{86} + 48 q^{92} + 104 q^{99}+O(q^{100}) $ 48 * q - 48 * q^4 + 16 * q^9 - 48 * q^11 + 48 * q^15 + 48 * q^16 + 16 * q^18 - 48 * q^23 - 24 * q^25 - 16 * q^30 - 16 * q^36 + 32 * q^39 + 48 * q^44 - 48 * q^50 - 48 * q^51 + 96 * q^53 - 80 * q^57 - 48 * q^60 - 48 * q^64 - 16 * q^72 + 32 * q^78 - 96 * q^79 + 96 * q^81 + 48 * q^85 - 96 * q^86 + 48 * q^92 + 104 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/882\mathbb{Z}\right)^\times$.

$n$	$199$	$785$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{6}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		−	1.00000i		−	0.707107i
$2$		−	1.00000i		−	0.707107i
$3$	1.52614	+	0.819074i	0.881120	+	0.472893i
$3$	1.52614	+	0.819074i	0.881120	+	0.472893i
$4$	−1.00000			−0.500000
$5$	1.99341	−	3.45268i	0.891479	−	1.54409i	0.0533767	−	0.998574i	$-0.483002\pi$
$5$	1.99341	−	3.45268i	0.891479	−	1.54409i	0.838102	−	0.545513i	$-0.183665\pi$
$6$	0.819074	−	1.52614i	0.334386	−	0.623046i
$7$		0			0
$7$		0			0
$8$			1.00000i			0.353553i
$9$	1.65823	+	2.50005i	0.552745	+	0.833350i
$10$	−3.45268	−	1.99341i	−1.09183	−	0.630371i
$11$	1.43438	−	0.828141i	0.432483	−	0.249694i	−0.267921	−	0.963441i	$-0.586337\pi$
$11$	1.43438	−	0.828141i	0.432483	−	0.249694i	0.700404	+	0.713747i	$0.253003\pi$
$12$	−1.52614	−	0.819074i	−0.440560	−	0.236446i
$13$	2.60834	−	1.50592i	0.723422	−	0.417668i	−0.0925888	−	0.995704i	$-0.529514\pi$
$13$	2.60834	−	1.50592i	0.723422	−	0.417668i	0.816011	+	0.578036i	$0.196181\pi$
$14$		0			0
$15$	5.87023	−	3.63655i	1.51569	−	0.938952i
$16$	1.00000			0.250000
$17$	−3.72820	+	6.45743i	−0.904221	+	1.56616i	−0.0822619	+	0.996611i	$0.526214\pi$
$17$	−3.72820	+	6.45743i	−0.904221	+	1.56616i	−0.821959	+	0.569546i	$0.807119\pi$
$18$	2.50005	−	1.65823i	0.589268	−	0.390850i
$19$	3.96054	−	2.28662i	0.908610	−	0.524586i	0.0286264	−	0.999590i	$-0.490887\pi$
$19$	3.96054	−	2.28662i	0.908610	−	0.524586i	0.879984	+	0.475004i	$0.157553\pi$
$20$	−1.99341	+	3.45268i	−0.445740	+	0.772044i
$21$		0			0
$22$	−0.828141	−	1.43438i	−0.176560	−	0.305811i
$23$	0.253614	+	0.146424i	0.0528822	+	0.0305316i	0.526208	−	0.850356i	$-0.323613\pi$
$23$	0.253614	+	0.146424i	0.0528822	+	0.0305316i	−0.473326	+	0.880887i	$0.656947\pi$
$24$	−0.819074	+	1.52614i	−0.167193	+	0.311523i
$25$	−5.44735	−	9.43509i	−1.08947	−	1.88702i
$26$	−1.50592	−	2.60834i	−0.295336	−	0.511537i
$27$	0.482978	+	5.17366i	0.0929492	+	0.995671i
$28$		0			0
$29$	−3.18684	−	1.83992i	−0.591781	−	0.341665i	0.174020	−	0.984742i	$-0.444324\pi$
$29$	−3.18684	−	1.83992i	−0.591781	−	0.341665i	−0.765801	+	0.643077i	$0.777657\pi$
$30$	−3.63655	−	5.87023i	−0.663939	−	1.07175i
$31$		−	4.71484i		−	0.846811i	−0.905940	−	0.423405i	$-0.860835\pi$
$31$		−	4.71484i		−	0.846811i	0.905940	−	0.423405i	$-0.139165\pi$
$32$		−	1.00000i		−	0.176777i
$33$	2.86739	−	0.0889974i	0.499148	−	0.0154925i
$34$	6.45743	+	3.72820i	1.10744	+	0.639381i
$35$		0			0
$36$	−1.65823	−	2.50005i	−0.276372	−	0.416675i
$37$	−3.00695	−	5.20820i	−0.494340	−	0.856222i	0.505639	−	0.862745i	$-0.331257\pi$
$37$	−3.00695	−	5.20820i	−0.494340	−	0.856222i	−0.999979	+	0.00652321i	$0.997924\pi$
$38$	−2.28662	−	3.96054i	−0.370939	−	0.642484i
$39$	5.21416	−	0.161836i	0.834934	−	0.0259145i
$40$	3.45268	+	1.99341i	0.545917	+	0.315185i
$41$	4.88630	+	8.46333i	0.763113	+	1.32175i	0.941239	+	0.337742i	$0.109663\pi$
$41$	4.88630	+	8.46333i	0.763113	+	1.32175i	−0.178126	+	0.984008i	$0.557004\pi$
$42$		0			0
$43$	−1.29961	+	2.25100i	−0.198189	+	0.343274i	−0.947941	−	0.318445i	$-0.896839\pi$
$43$	−1.29961	+	2.25100i	−0.198189	+	0.343274i	0.749752	+	0.661719i	$0.230173\pi$
$44$	−1.43438	+	0.828141i	−0.216241	+	0.124847i
$45$	11.9374	−	0.741738i	1.77953	−	0.110572i
$46$	0.146424	−	0.253614i	0.0215891	−	0.0373934i
$47$	−13.6124			−1.98558			−0.992789	−	0.119876i	$-0.961750\pi$
$47$	−13.6124			−1.98558			−0.992789	+	0.119876i	$0.961750\pi$
$48$	1.52614	+	0.819074i	0.220280	+	0.118223i
$49$		0			0
$50$	−9.43509	+	5.44735i	−1.33432	+	0.770372i
$51$	−10.9789	+	6.80130i	−1.53735	+	0.952373i
$52$	−2.60834	+	1.50592i	−0.361711	+	0.208834i
$53$	−0.793421	−	0.458082i	−0.108985	−	0.0629224i	0.444517	−	0.895770i	$-0.353375\pi$
$53$	−0.793421	−	0.458082i	−0.108985	−	0.0629224i	−0.553502	+	0.832848i	$0.686709\pi$
$54$	5.17366	−	0.482978i	0.704046	−	0.0657250i
$55$		−	6.60330i		−	0.890388i
$56$		0			0
$57$	7.91727	−	0.245735i	1.04867	−	0.0325484i
$58$	−1.83992	+	3.18684i	−0.241594	+	0.418452i
$59$	7.06674			0.920011			0.460006	−	0.887916i	$-0.347847\pi$
$59$	7.06674			0.920011			0.460006	+	0.887916i	$0.347847\pi$
$60$	−5.87023	+	3.63655i	−0.757844	+	0.469476i
$61$			6.64659i			0.851008i	0.904957	+	0.425504i	$0.139903\pi$
$61$			6.64659i			0.851008i	−0.904957	+	0.425504i	$0.860097\pi$
$62$	−4.71484			−0.598786
$63$		0			0
$64$	−1.00000			−0.125000
$65$		−	12.0077i		−	1.48937i
$66$	−0.0889974	−	2.86739i	−0.0109548	−	0.352951i
$67$	4.05676			0.495612			0.247806	−	0.968810i	$-0.420290\pi$
$67$	4.05676			0.495612			0.247806	+	0.968810i	$0.420290\pi$
$68$	3.72820	−	6.45743i	0.452111	−	0.783078i
$69$	0.267120	+	0.431193i	0.0321574	+	0.0519096i
$70$		0			0
$71$		−	13.9437i		−	1.65481i	−0.561605	−	0.827406i	$-0.689816\pi$
$71$		−	13.9437i		−	1.65481i	0.561605	−	0.827406i	$-0.310184\pi$
$72$	−2.50005	+	1.65823i	−0.294634	+	0.195425i
$73$	3.84574	+	2.22034i	0.450110	+	0.259871i	0.707877	−	0.706336i	$-0.249653\pi$
$73$	3.84574	+	2.22034i	0.450110	+	0.259871i	−0.257767	+	0.966207i	$0.582987\pi$
$74$	−5.20820	+	3.00695i	−0.605441	+	0.349551i
$75$	−0.585407	−	18.8611i	−0.0675970	−	2.17789i
$76$	−3.96054	+	2.28662i	−0.454305	+	0.262293i
$77$		0			0
$78$	−0.161836	−	5.21416i	−0.0183243	−	0.590387i
$79$	2.84730			0.320346			0.160173	−	0.987089i	$-0.448795\pi$
$79$	2.84730			0.320346			0.160173	+	0.987089i	$0.448795\pi$
$80$	1.99341	−	3.45268i	0.222870	−	0.386022i
$81$	−3.50051	+	8.29134i	−0.388946	+	0.921261i
$82$	8.46333	−	4.88630i	0.934618	−	0.539602i
$83$	−2.59432	+	4.49349i	−0.284763	+	0.493224i	−0.972552	−	0.232687i	$-0.925248\pi$
$83$	−2.59432	+	4.49349i	−0.284763	+	0.493224i	0.687789	+	0.725911i	$0.258582\pi$
$84$		0			0
$85$	14.8636	+	25.7446i	1.61219	+	2.79239i
$86$	2.25100	+	1.29961i	0.242731	+	0.140141i
$87$	−3.35654	−	5.41824i	−0.359859	−	0.580897i
$88$	0.828141	+	1.43438i	0.0882802	+	0.152906i
$89$	5.50866	+	9.54128i	0.583917	+	1.01137i	0.995010	+	0.0997799i	$0.0318139\pi$
$89$	5.50866	+	9.54128i	0.583917	+	1.01137i	−0.411093	+	0.911593i	$0.634853\pi$
$90$	−0.741738	−	11.9374i	−0.0781861	−	1.25832i
$91$		0			0
$92$	−0.253614	−	0.146424i	−0.0264411	−	0.0152658i
$93$	3.86181	−	7.19553i	0.400451	−	0.746142i
$94$			13.6124i			1.40402i
$95$		−	18.2327i		−	1.87063i
$96$	0.819074	−	1.52614i	0.0835964	−	0.155761i
$97$	2.51510	+	1.45209i	0.255369	+	0.147438i	0.622220	−	0.782842i	$-0.286231\pi$
$97$	2.51510	+	1.45209i	0.255369	+	0.147438i	−0.366851	+	0.930280i	$0.619564\pi$
$98$		0			0
$99$	4.44894	+	2.21278i	0.447135	+	0.222393i
$100$	5.44735	+	9.43509i	0.544735	+	0.943509i
$101$	−0.129291	−	0.223938i	−0.0128649	−	0.0222827i	0.859521	−	0.511100i	$-0.170762\pi$
$101$	−0.129291	−	0.223938i	−0.0128649	−	0.0222827i	−0.872386	+	0.488817i	$0.837428\pi$
$102$	6.80130	+	10.9789i	0.673429	+	1.08707i
$103$	−5.89979	−	3.40625i	−0.581324	−	0.335627i	0.180336	−	0.983605i	$-0.442282\pi$
$103$	−5.89979	−	3.40625i	−0.581324	−	0.335627i	−0.761659	+	0.647978i	$0.775615\pi$
$104$	1.50592	+	2.60834i	0.147668	+	0.255768i
$105$		0			0
$106$	−0.458082	+	0.793421i	−0.0444928	+	0.0770639i
$107$	−9.21299	+	5.31912i	−0.890653	+	0.514219i	−0.874156	−	0.485645i	$-0.838585\pi$
$107$	−9.21299	+	5.31912i	−0.890653	+	0.514219i	−0.0164973	+	0.999864i	$0.505251\pi$
$108$	−0.482978	−	5.17366i	−0.0464746	−	0.497835i
$109$	2.25887	−	3.91248i	0.216361	−	0.374748i	−0.737332	−	0.675531i	$-0.763915\pi$
$109$	2.25887	−	3.91248i	0.216361	−	0.374748i	0.953693	+	0.300783i	$0.0972479\pi$
$110$	−6.60330			−0.629600
$111$	−0.323147	−	10.4114i	−0.0306717	−	0.988204i
$112$		0			0
$113$	−1.47530	+	0.851764i	−0.138784	+	0.0801272i	−0.567785	−	0.823177i	$-0.692199\pi$
$113$	−1.47530	+	0.851764i	−0.138784	+	0.0801272i	0.429000	+	0.903304i	$0.358866\pi$
$114$	−0.245735	−	7.91727i	−0.0230152	−	0.741520i
$115$	1.01111	−	0.583767i	0.0942868	−	0.0544365i
$116$	3.18684	+	1.83992i	0.295890	+	0.170832i
$117$	8.09012	+	4.02380i	0.747932	+	0.372000i
$118$		−	7.06674i		−	0.650546i
$119$		0			0
$120$	3.63655	+	5.87023i	0.331970	+	0.535877i
$121$	−4.12836	+	7.15054i	−0.375306	+	0.650049i
$122$	6.64659			0.601754
$123$	0.525114	+	16.9185i	0.0473479	+	1.52549i
$124$			4.71484i			0.423405i
$125$	−23.5011			−2.10200
$126$		0			0
$127$	−4.93203			−0.437647			−0.218823	−	0.975765i	$-0.570222\pi$
$127$	−4.93203			−0.437647			−0.218823	+	0.975765i	$0.570222\pi$
$128$			1.00000i			0.0883883i
$129$	−3.82713	+	2.37087i	−0.336960	+	0.208743i
$130$	−12.0077			−1.05314
$131$	−10.8056	+	18.7158i	−0.944088	+	1.63521i	−0.186520	+	0.982451i	$0.559721\pi$
$131$	−10.8056	+	18.7158i	−0.944088	+	1.63521i	−0.757567	+	0.652757i	$0.773612\pi$
$132$	−2.86739	+	0.0889974i	−0.249574	+	0.00774623i
$133$		0			0
$134$		−	4.05676i		−	0.350451i
$135$	18.8258	+	8.64564i	1.62026	+	0.744098i
$136$	−6.45743	−	3.72820i	−0.553720	−	0.319690i
$137$	5.93663	−	3.42752i	0.507201	−	0.292832i	−0.224482	−	0.974478i	$-0.572069\pi$
$137$	5.93663	−	3.42752i	0.507201	−	0.292832i	0.731682	+	0.681646i	$0.238736\pi$
$138$	0.431193	−	0.267120i	0.0367056	−	0.0227387i
$139$	13.9583	−	8.05882i	1.18393	−	0.683540i	0.227007	−	0.973893i	$-0.427106\pi$
$139$	13.9583	−	8.05882i	1.18393	−	0.683540i	0.956920	+	0.290353i	$0.0937726\pi$
$140$		0			0
$141$	−20.7745	−	11.1496i	−1.74953	−	0.938965i
$142$	−13.9437			−1.17013
$143$	2.49423	−	4.32014i	0.208578	−	0.361268i
$144$	1.65823	+	2.50005i	0.138186	+	0.208338i
$145$	−12.7053	+	7.33543i	−1.05512	+	0.609174i
$146$	2.22034	−	3.84574i	0.183757	−	0.318276i
$147$		0			0
$148$	3.00695	+	5.20820i	0.247170	+	0.428111i
$149$	−1.05460	−	0.608875i	−0.0863964	−	0.0498810i	0.456179	−	0.889888i	$-0.349218\pi$
$149$	−1.05460	−	0.608875i	−0.0863964	−	0.0498810i	−0.542576	+	0.840007i	$0.682551\pi$
$150$	−18.8611	+	0.585407i	−1.54000	+	0.0477983i
$151$	−7.01991	−	12.1588i	−0.571272	−	0.989472i	−0.996436	−	0.0843554i	$-0.973117\pi$
$151$	−7.01991	−	12.1588i	−0.571272	−	0.989472i	0.425164	−	0.905116i	$-0.360216\pi$
$152$	2.28662	+	3.96054i	0.185469	+	0.321242i
$153$	−22.3261	+	1.38725i	−1.80496	+	0.112152i
$154$		0			0
$155$	−16.2789	−	9.39861i	−1.30755	−	0.754914i
$156$	−5.21416	+	0.161836i	−0.417467	+	0.0129573i
$157$			23.5944i			1.88304i	0.336957	+	0.941520i	$0.390602\pi$
$157$			23.5944i			1.88304i	−0.336957	+	0.941520i	$0.609398\pi$
$158$		−	2.84730i		−	0.226519i
$159$	−0.835672	−	1.34897i	−0.0662731	−	0.106980i
$160$	−3.45268	−	1.99341i	−0.272959	−	0.157593i
$161$		0			0
$162$	8.29134	+	3.50051i	0.651430	+	0.275026i
$163$	−0.299613	−	0.518945i	−0.0234675	−	0.0406469i	0.854053	−	0.520186i	$-0.174137\pi$
$163$	−0.299613	−	0.518945i	−0.0234675	−	0.0406469i	−0.877521	+	0.479539i	$0.840804\pi$
$164$	−4.88630	−	8.46333i	−0.381556	−	0.660875i
$165$	5.40859	−	10.0776i	0.421058	−	0.784539i
$166$	4.49349	+	2.59432i	0.348762	+	0.201358i
$167$	2.67267	+	4.62919i	0.206817	+	0.358218i	0.950710	−	0.310081i	$-0.100356\pi$
$167$	2.67267	+	4.62919i	0.206817	+	0.358218i	−0.743893	+	0.668299i	$0.767023\pi$
$168$		0			0
$169$	−1.96439	+	3.40242i	−0.151107	+	0.261725i
$170$	25.7446	−	14.8636i	1.97452	−	1.13999i
$171$	12.2842	+	6.10980i	0.939394	+	0.467228i
$172$	1.29961	−	2.25100i	0.0990947	−	0.171637i
$173$	−12.1235			−0.921734			−0.460867	−	0.887469i	$-0.652461\pi$
$173$	−12.1235			−0.921734			−0.460867	+	0.887469i	$0.652461\pi$
$174$	−5.41824	+	3.35654i	−0.410756	+	0.254459i
$175$		0			0
$176$	1.43438	−	0.828141i	0.108121	−	0.0624235i
$177$	10.7849	+	5.78818i	0.810640	+	0.435067i
$178$	9.54128	−	5.50866i	0.715149	−	0.412891i
$179$	4.81618	+	2.78062i	0.359978	+	0.207833i	0.669071	−	0.743198i	$-0.266692\pi$
$179$	4.81618	+	2.78062i	0.359978	+	0.207833i	−0.309093	+	0.951032i	$0.600025\pi$
$180$	−11.9374	+	0.741738i	−0.889763	+	0.0552859i
$181$			12.5545i			0.933167i	0.884477	+	0.466583i	$0.154515\pi$
$181$			12.5545i			0.933167i	−0.884477	+	0.466583i	$0.845485\pi$
$182$		0			0
$183$	−5.44405	+	10.1437i	−0.402436	+	0.749840i
$184$	−0.146424	+	0.253614i	−0.0107945	+	0.0186967i
$185$	−23.9763			−1.76278
$186$	−7.19553	−	3.86181i	−0.527602	−	0.283161i
$187$			12.3499i			0.903115i
$188$	13.6124			0.992789
$189$		0			0
$190$	−18.2327			−1.32274
$191$			18.9350i			1.37009i	0.728501	+	0.685045i	$0.240217\pi$
$191$			18.9350i			1.37009i	−0.728501	+	0.685045i	$0.759783\pi$
$192$	−1.52614	−	0.819074i	−0.110140	−	0.0591116i
$193$	7.61465			0.548115			0.274057	−	0.961713i	$-0.411634\pi$
$193$	7.61465			0.548115			0.274057	+	0.961713i	$0.411634\pi$
$194$	1.45209	−	2.51510i	0.104254	−	0.180573i
$195$	9.83518	−	18.3255i	0.704312	−	1.31231i
$196$		0			0
$197$			6.04895i			0.430970i	0.976507	+	0.215485i	$0.0691332\pi$
$197$			6.04895i			0.430970i	−0.976507	+	0.215485i	$0.930867\pi$
$198$	2.21278	−	4.44894i	0.157255	−	0.316172i
$199$	−19.8227	−	11.4446i	−1.40519	−	0.811289i	−0.410274	−	0.911962i	$-0.634567\pi$
$199$	−19.8227	−	11.4446i	−1.40519	−	0.811289i	−0.994919	+	0.100674i	$0.967900\pi$
$200$	9.43509	−	5.44735i	0.667162	−	0.385186i
$201$	6.19120	+	3.32279i	0.436694	+	0.234371i
$202$	−0.223938	+	0.129291i	−0.0157562	+	0.00909687i
$203$		0			0
$204$	10.9789	−	6.80130i	0.768676	−	0.476186i
$205$	38.9616			2.72120
$206$	−3.40625	+	5.89979i	−0.237324	+	0.411058i
$207$	0.0544838	+	0.876854i	0.00378689	+	0.0609456i
$208$	2.60834	−	1.50592i	0.180856	−	0.104417i
$209$	3.78729	−	6.55977i	0.261972	−	0.453749i
$210$		0			0
$211$	3.36942	+	5.83601i	0.231961	+	0.401768i	0.958385	−	0.285479i	$-0.0921526\pi$
$211$	3.36942	+	5.83601i	0.231961	+	0.401768i	−0.726424	+	0.687246i	$0.758819\pi$
$212$	0.793421	+	0.458082i	0.0544924	+	0.0314612i
$213$	11.4209	−	21.2801i	0.782548	−	1.45809i
$214$	5.31912	+	9.21299i	0.363608	+	0.629787i
$215$	5.18132	+	8.97432i	0.353363	+	0.612043i
$216$	−5.17366	+	0.482978i	−0.352023	+	0.0328625i
$217$		0			0
$218$	−3.91248	−	2.25887i	−0.264987	−	0.152990i
$219$	4.05053	+	6.53851i	0.273710	+	0.441831i
$220$			6.60330i			0.445194i
$221$			22.4575i			1.51066i
$222$	−10.4114	+	0.323147i	−0.698766	+	0.0216882i
$223$	7.85930	+	4.53757i	0.526298	+	0.303858i	0.739507	−	0.673148i	$-0.235058\pi$
$223$	7.85930	+	4.53757i	0.526298	+	0.303858i	−0.213210	+	0.977006i	$0.568392\pi$
$224$		0			0
$225$	14.5552	−	29.2643i	0.970348	−	1.95095i
$226$	0.851764	+	1.47530i	0.0566585	+	0.0981354i
$227$	0.313680	+	0.543310i	0.0208197	+	0.0360607i	0.876248	−	0.481861i	$-0.160039\pi$
$227$	0.313680	+	0.543310i	0.0208197	+	0.0360607i	−0.855428	+	0.517922i	$0.826706\pi$
$228$	−7.91727	+	0.245735i	−0.524334	+	0.0162742i
$229$	16.0593	+	9.27182i	1.06123	+	0.612699i	0.925771	−	0.378084i	$-0.123417\pi$
$229$	16.0593	+	9.27182i	1.06123	+	0.612699i	0.135455	+	0.990784i	$0.456750\pi$
$230$	−0.583767	−	1.01111i	−0.0384924	−	0.0666708i
$231$		0			0
$232$	1.83992	−	3.18684i	0.120797	−	0.209226i
$233$	−9.02716	+	5.21183i	−0.591389	+	0.341438i	−0.765646	−	0.643262i	$-0.777581\pi$
$233$	−9.02716	+	5.21183i	−0.591389	+	0.341438i	0.174258	+	0.984700i	$0.444247\pi$
$234$	4.02380	−	8.09012i	0.263044	−	0.528868i
$235$	−27.1351	+	46.9994i	−1.77010	+	3.06591i
$236$	−7.06674			−0.460006
$237$	4.34539	+	2.33215i	0.282263	+	0.151489i
$238$		0			0
$239$	5.88865	−	3.39981i	0.380905	−	0.219915i	−0.297307	−	0.954782i	$-0.596089\pi$
$239$	5.88865	−	3.39981i	0.380905	−	0.219915i	0.678212	+	0.734866i	$0.262755\pi$
$240$	5.87023	−	3.63655i	0.378922	−	0.234738i
$241$	16.3106	−	9.41695i	1.05066	−	0.606599i	0.127826	−	0.991797i	$-0.459200\pi$
$241$	16.3106	−	9.41695i	1.05066	−	0.606599i	0.922834	+	0.385197i	$0.125867\pi$
$242$	7.15054	+	4.12836i	0.459654	+	0.265381i
$243$	−12.1335	+	9.78661i	−0.778366	+	0.627811i
$244$		−	6.64659i		−	0.425504i
$245$		0			0
$246$	16.9185	−	0.525114i	1.07868	−	0.0334800i
$247$	6.88694	−	11.9285i	0.438206	−	0.758995i
$248$	4.71484			0.299393
$249$	−7.63980	+	4.73277i	−0.484153	+	0.299927i
$250$			23.5011i			1.48634i
$251$	0.0465190			0.00293625			0.00146813	−	0.999999i	$-0.499533\pi$
$251$	0.0465190			0.00293625			0.00146813	+	0.999999i	$0.499533\pi$
$252$		0			0
$253$	0.485040			0.0304942
$254$			4.93203i			0.309463i
$255$	1.59734	+	51.4644i	0.100029	+	3.22283i
$256$	1.00000			0.0625000
$257$	7.60276	−	13.1684i	0.474247	−	0.821420i	−0.525318	−	0.850906i	$-0.676054\pi$
$257$	7.60276	−	13.1684i	0.474247	−	0.821420i	0.999565	+	0.0294859i	$0.00938701\pi$
$258$	2.37087	+	3.82713i	0.147604	+	0.238267i
$259$		0			0
$260$			12.0077i			0.744685i
$261$	−0.684627	−	11.0183i	−0.0423773	−	0.682014i
$262$	18.7158	+	10.8056i	1.15627	+	0.667571i
$263$	−1.69410	+	0.978086i	−0.104462	+	0.0603114i	−0.551321	−	0.834293i	$-0.685876\pi$
$263$	−1.69410	+	0.978086i	−0.104462	+	0.0603114i	0.446859	+	0.894605i	$0.352543\pi$
$264$	0.0889974	+	2.86739i	0.00547741	+	0.176475i
$265$	−3.16322	+	1.82629i	−0.194315	+	0.112188i
$266$		0			0
$267$	0.591996	+	19.0734i	0.0362296	+	1.16727i
$268$	−4.05676			−0.247806
$269$	2.72936	−	4.72739i	0.166412	−	0.288234i	−0.770744	−	0.637145i	$-0.780115\pi$
$269$	2.72936	−	4.72739i	0.166412	−	0.288234i	0.937156	+	0.348911i	$0.113449\pi$
$270$	8.64564	−	18.8258i	0.526157	−	1.14570i
$271$	12.8145	−	7.39843i	0.778423	−	0.449423i	−0.0574480	−	0.998348i	$-0.518296\pi$
$271$	12.8145	−	7.39843i	0.778423	−	0.449423i	0.835871	+	0.548926i	$0.184963\pi$
$272$	−3.72820	+	6.45743i	−0.226055	+	0.391539i
$273$		0			0
$274$	−3.42752	−	5.93663i	−0.207064	−	0.358645i
$275$	−15.6272	−	9.02236i	−0.942354	−	0.544068i
$276$	−0.267120	−	0.431193i	−0.0160787	−	0.0259548i
$277$	5.23636	+	9.06963i	0.314622	+	0.544941i	0.979357	−	0.202138i	$-0.0647889\pi$
$277$	5.23636	+	9.06963i	0.314622	+	0.544941i	−0.664735	+	0.747079i	$0.731456\pi$
$278$	−8.05882	−	13.9583i	−0.483336	−	0.837163i
$279$	11.7873	−	7.81832i	0.705690	−	0.468070i
$280$		0			0
$281$	1.02488	+	0.591716i	0.0611394	+	0.0352988i	0.530258	−	0.847836i	$-0.322095\pi$
$281$	1.02488	+	0.591716i	0.0611394	+	0.0352988i	−0.469119	+	0.883135i	$0.655428\pi$
$282$	−11.1496	+	20.7745i	−0.663949	+	1.23711i
$283$		−	29.5879i		−	1.75882i	−0.476069	−	0.879408i	$-0.657939\pi$
$283$		−	29.5879i		−	1.75882i	0.476069	−	0.879408i	$-0.342061\pi$
$284$			13.9437i			0.827406i
$285$	14.9339	−	27.8257i	0.884608	−	1.64825i
$286$	−4.32014	−	2.49423i	−0.255455	−	0.147487i
$287$		0			0
$288$	2.50005	−	1.65823i	0.147317	−	0.0977124i
$289$	−19.2989	−	33.4267i	−1.13523	−	1.96628i
$290$	7.33543	+	12.7053i	0.430751	+	0.746083i
$291$	2.64903	+	4.27615i	0.155289	+	0.250673i
$292$	−3.84574	−	2.22034i	−0.225055	−	0.129936i
$293$	−6.64419	−	11.5081i	−0.388158	−	0.672309i	0.604044	−	0.796951i	$-0.293555\pi$
$293$	−6.64419	−	11.5081i	−0.388158	−	0.672309i	−0.992202	+	0.124642i	$0.960222\pi$
$294$		0			0
$295$	14.0869	−	24.3992i	0.820171	−	1.42058i
$296$	5.20820	−	3.00695i	0.302720	−	0.174776i
$297$	4.97730	+	7.02103i	0.288812	+	0.407402i
$298$	−0.608875	+	1.05460i	−0.0352712	+	0.0610915i
$299$	0.882015			0.0510082
$300$	0.585407	+	18.8611i	0.0337985	+	1.08895i
$301$		0			0
$302$	−12.1588	+	7.01991i	−0.699662	+	0.403950i
$303$	−0.0138944	−	0.447661i	−0.000798214	−	0.0257175i
$304$	3.96054	−	2.28662i	0.227153	−	0.131147i
$305$	22.9486	+	13.2494i	1.31403	+	0.758656i
$306$	1.38725	+	22.3261i	0.0793036	+	1.27630i
$307$			3.34549i			0.190937i	0.995432	+	0.0954686i	$0.0304350\pi$
$307$			3.34549i			0.190937i	−0.995432	+	0.0954686i	$0.969565\pi$
$308$		0			0
$309$	−6.21397	−	10.0308i	−0.353500	−	0.570632i
$310$	−9.39861	+	16.2789i	−0.533805	+	0.924577i
$311$	−22.7834			−1.29193			−0.645964	−	0.763368i	$-0.723544\pi$
$311$	−22.7834			−1.29193			−0.645964	+	0.763368i	$0.723544\pi$
$312$	0.161836	+	5.21416i	0.00916217	+	0.295194i
$313$			1.16835i			0.0660393i	0.999455	+	0.0330196i	$0.0105124\pi$
$313$			1.16835i			0.0660393i	−0.999455	+	0.0330196i	$0.989488\pi$
$314$	23.5944			1.33151
$315$		0			0
$316$	−2.84730			−0.160173
$317$			21.8039i			1.22463i	0.790613	+	0.612316i	$0.209762\pi$
$317$			21.8039i			1.22463i	−0.790613	+	0.612316i	$0.790238\pi$
$318$	−1.34897	+	0.835672i	−0.0756465	+	0.0468622i
$319$	−6.09486			−0.341247
$320$	−1.99341	+	3.45268i	−0.111435	+	0.193011i
$321$	−18.4171	+	0.571627i	−1.02794	+	0.0319051i
$322$		0			0
$323$			34.0999i			1.89737i
$324$	3.50051	−	8.29134i	0.194473	−	0.460630i
$325$	−28.4170	−	16.4066i	−1.57629	−	0.910074i
$326$	−0.518945	+	0.299613i	−0.0287417	+	0.0165940i
$327$	6.65198	−	4.12083i	0.367855	−	0.227882i
$328$	−8.46333	+	4.88630i	−0.467309	+	0.269801i
$329$		0			0
$330$	−10.0776	−	5.40859i	−0.554753	−	0.297733i
$331$	−27.8854			−1.53272			−0.766359	−	0.642413i	$-0.777934\pi$
$331$	−27.8854			−1.53272			−0.766359	+	0.642413i	$0.777934\pi$
$332$	2.59432	−	4.49349i	0.142382	−	0.246612i
$333$	8.03452	−	16.1540i	0.440289	−	0.885231i
$334$	4.62919	−	2.67267i	0.253298	−	0.146242i
$335$	8.08678	−	14.0067i	0.441828	−	0.765268i
$336$		0			0
$337$	0.00328349	+	0.00568717i	0.000178863	+	0.000309800i	0.866115	−	0.499845i	$-0.166610\pi$
$337$	0.00328349	+	0.00568717i	0.000178863	+	0.000309800i	−0.865936	+	0.500155i	$0.833276\pi$
$338$	3.40242	+	1.96439i	0.185067	+	0.106849i
$339$	−2.94918	+	0.0915360i	−0.160177	+	0.00497155i
$340$	−14.8636	−	25.7446i	−0.806094	−	1.39620i
$341$	−3.90456	−	6.76289i	−0.211444	−	0.366231i
$342$	6.10980	−	12.2842i	0.330380	−	0.664252i
$343$		0			0
$344$	−2.25100	−	1.29961i	−0.121366	−	0.0700705i
$345$	2.02125	−	0.0627353i	0.108821	−	0.00337756i
$346$			12.1235i			0.651764i
$347$		−	20.4956i		−	1.10026i	−0.835078	−	0.550132i	$-0.814577\pi$
$347$		−	20.4956i		−	1.10026i	0.835078	−	0.550132i	$-0.185423\pi$
$348$	3.35654	+	5.41824i	0.179930	+	0.290448i
$349$	7.24341	+	4.18198i	0.387731	+	0.223856i	0.681176	−	0.732119i	$-0.261469\pi$
$349$	7.24341	+	4.18198i	0.387731	+	0.223856i	−0.293446	+	0.955976i	$0.594802\pi$
$350$		0			0
$351$	9.05090	+	12.7673i	0.483101	+	0.681468i
$352$	−0.828141	−	1.43438i	−0.0441401	−	0.0764529i
$353$	3.07430	+	5.32484i	0.163628	+	0.283413i	0.936167	−	0.351555i	$-0.114347\pi$
$353$	3.07430	+	5.32484i	0.163628	+	0.283413i	−0.772539	+	0.634967i	$0.781014\pi$
$354$	5.78818	−	10.7849i	0.307639	−	0.573209i
$355$	−48.1431	−	27.7955i	−2.55517	−	1.47523i
$356$	−5.50866	−	9.54128i	−0.291958	−	0.505687i
$357$		0			0
$358$	2.78062	−	4.81618i	0.146960	−	0.254543i
$359$	5.02704	−	2.90236i	0.265317	−	0.153181i	−0.361441	−	0.932395i	$-0.617715\pi$
$359$	5.02704	−	2.90236i	0.265317	−	0.153181i	0.626758	+	0.779214i	$0.284382\pi$
$360$	0.741738	+	11.9374i	0.0390930	+	0.629158i
$361$	0.957250	−	1.65801i	0.0503816	−	0.0872634i
$362$	12.5545			0.659849
$363$	−12.1573	+	7.53131i	−0.638093	+	0.395292i
$364$		0			0
$365$	15.3323	−	8.85209i	0.802527	−	0.463339i
$366$	10.1437	+	5.44405i	0.530217	+	0.284565i
$367$	5.16659	−	2.98293i	0.269694	−	0.155708i	−0.359055	−	0.933317i	$-0.616901\pi$
$367$	5.16659	−	2.98293i	0.269694	−	0.155708i	0.628748	+	0.777609i	$0.283568\pi$
$368$	0.253614	+	0.146424i	0.0132206	+	0.00763289i
$369$	−13.0561	+	26.2502i	−0.679674	+	1.36653i
$370$			23.9763i			1.24647i
$371$		0			0
$372$	−3.86181	+	7.19553i	−0.200225	+	0.373071i
$373$	9.43291	−	16.3383i	0.488418	−	0.845964i	−0.511494	−	0.859287i	$-0.670908\pi$
$373$	9.43291	−	16.3383i	0.488418	−	0.845964i	0.999911	+	0.0133229i	$0.00424093\pi$
$374$	12.3499			0.638598
$375$	−35.8661	−	19.2491i	−1.85212	−	0.994022i
$376$		−	13.6124i		−	0.702008i
$377$	−11.0831			−0.570810
$378$		0			0
$379$	−12.5331			−0.643784			−0.321892	−	0.946776i	$-0.604319\pi$
$379$	−12.5331			−0.643784			−0.321892	+	0.946776i	$0.604319\pi$
$380$			18.2327i			0.935316i
$381$	−7.52699	−	4.03970i	−0.385619	−	0.206960i
$382$	18.9350			0.968800
$383$	−0.0844724	+	0.146310i	−0.00431634	+	0.00747612i	−0.868176	−	0.496257i	$-0.834707\pi$
$383$	−0.0844724	+	0.146310i	−0.00431634	+	0.00747612i	0.863859	+	0.503733i	$0.168041\pi$
$384$	−0.819074	+	1.52614i	−0.0417982	+	0.0778807i
$385$		0			0
$386$		−	7.61465i		−	0.387576i
$387$	−7.78268	+	0.483581i	−0.395616	+	0.0245818i
$388$	−2.51510	−	1.45209i	−0.127685	−	0.0737188i
$389$	−7.24937	+	4.18543i	−0.367558	+	0.212210i	−0.672391	−	0.740196i	$-0.734733\pi$
$389$	−7.24937	+	4.18543i	−0.367558	+	0.212210i	0.304833	+	0.952406i	$0.401399\pi$
$390$	−18.3255	−	9.83518i	−0.927945	−	0.498024i
$391$	−1.89105	+	1.09180i	−0.0956344	+	0.0552146i
$392$		0			0
$393$	−31.8205	+	19.7125i	−1.60513	+	0.994362i
$394$	6.04895			0.304741
$395$	5.67582	−	9.83081i	0.285582	−	0.494642i
$396$	−4.44894	−	2.21278i	−0.223568	−	0.111196i
$397$	5.39937	−	3.11733i	0.270987	−	0.156454i	−0.358349	−	0.933588i	$-0.616660\pi$
$397$	5.39937	−	3.11733i	0.270987	−	0.156454i	0.629336	+	0.777133i	$0.283327\pi$
$398$	−11.4446	+	19.8227i	−0.573668	+	0.993622i
$399$		0			0
$400$	−5.44735	−	9.43509i	−0.272368	−	0.471754i
$401$	−28.8079	−	16.6322i	−1.43860	−	0.830573i	−0.440843	−	0.897584i	$-0.645321\pi$
$401$	−28.8079	−	16.6322i	−1.43860	−	0.830573i	−0.997752	+	0.0670106i	$0.978654\pi$
$402$	3.32279	−	6.19120i	0.165726	−	0.308789i
$403$	−7.10019	−	12.2979i	−0.353686	−	0.612602i
$404$	0.129291	+	0.223938i	0.00643246	+	0.0111413i
$405$	21.6494	+	28.6142i	1.07577	+	1.42185i
$406$		0			0
$407$	−8.62625	−	4.98037i	−0.427587	−	0.246868i
$408$	−6.80130	−	10.9789i	−0.336715	−	0.543536i
$409$			20.3147i			1.00450i	0.864723	+	0.502249i	$0.167494\pi$
$409$			20.3147i			1.00450i	−0.864723	+	0.502249i	$0.832506\pi$
$410$		−	38.9616i		−	1.92418i
$411$	11.8675	−	0.368343i	0.585383	−	0.0181690i
$412$	5.89979	+	3.40625i	0.290662	+	0.167814i
$413$		0			0
$414$	0.876854	−	0.0544838i	0.0430950	−	0.00267773i
$415$	10.3431	+	17.9147i	0.507721	+	0.879399i
$416$	−1.50592	−	2.60834i	−0.0738340	−	0.127884i
$417$	27.9031	−	0.866053i	1.36642	−	0.0424108i
$418$	−6.55977	−	3.78729i	−0.320849	−	0.185242i
$419$	15.4796	+	26.8115i	0.756229	+	1.30983i	0.944761	+	0.327759i	$0.106294\pi$
$419$	15.4796	+	26.8115i	0.756229	+	1.30983i	−0.188533	+	0.982067i	$0.560373\pi$
$420$		0			0
$421$	−8.92724	+	15.4624i	−0.435087	+	0.753593i	−0.997303	−	0.0733980i	$-0.976616\pi$
$421$	−8.92724	+	15.4624i	−0.435087	+	0.753593i	0.562216	+	0.826991i	$0.309949\pi$
$422$	5.83601	−	3.36942i	0.284093	−	0.164021i
$423$	−22.5726	−	34.0318i	−1.09752	−	1.65468i
$424$	0.458082	−	0.793421i	0.0222464	−	0.0385319i
$425$	81.2353			3.94049
$426$	−21.2801	−	11.4209i	−1.03102	−	0.553345i
$427$		0			0
$428$	9.21299	−	5.31912i	0.445327	−	0.257110i
$429$	7.34508	−	4.55020i	0.354624	−	0.219686i
$430$	8.97432	−	5.18132i	0.432780	−	0.249866i
$431$	−23.0513	−	13.3087i	−1.11034	−	0.641056i	−0.171423	−	0.985197i	$-0.554837\pi$
$431$	−23.0513	−	13.3087i	−1.11034	−	0.641056i	−0.938918	+	0.344142i	$0.888170\pi$
$432$	0.482978	+	5.17366i	0.0232373	+	0.248918i
$433$		−	12.8312i		−	0.616628i	−0.951285	−	0.308314i	$-0.900235\pi$
$433$		−	12.8312i		−	0.616628i	0.951285	−	0.308314i	$-0.0997648\pi$
$434$		0			0
$435$	−25.3984	+	0.788312i	−1.21776	+	0.0377967i
$436$	−2.25887	+	3.91248i	−0.108180	+	0.187374i
$437$	1.33927			0.0640658
$438$	6.53851	−	4.05053i	0.312422	−	0.193542i
$439$		−	23.4359i		−	1.11853i	−0.828988	−	0.559266i	$-0.811083\pi$
$439$		−	23.4359i		−	1.11853i	0.828988	−	0.559266i	$-0.188917\pi$
$440$	6.60330			0.314800
$441$		0			0
$442$	22.4575			1.06820
$443$		−	18.5863i		−	0.883062i	−0.897246	−	0.441531i	$-0.854436\pi$
$443$		−	18.5863i		−	0.883062i	0.897246	−	0.441531i	$-0.145564\pi$
$444$	0.323147	+	10.4114i	0.0153359	+	0.494102i
$445$	43.9240			2.08220
$446$	4.53757	−	7.85930i	0.214860	−	0.372149i
$447$	−1.11076	−	1.79303i	−0.0525372	−	0.0848074i
$448$		0			0
$449$		−	22.7518i		−	1.07372i	−0.843670	−	0.536862i	$-0.819610\pi$
$449$		−	22.7518i		−	1.07372i	0.843670	−	0.536862i	$-0.180390\pi$
$450$	−29.2643	−	14.5552i	−1.37953	−	0.686140i
$451$	14.0177	+	8.09310i	0.660066	+	0.381089i
$452$	1.47530	−	0.851764i	0.0693922	−	0.0400636i
$453$	−0.754404	−	24.3060i	−0.0354450	−	1.14199i
$454$	0.543310	−	0.313680i	0.0254988	−	0.0147217i
$455$		0			0
$456$	0.245735	+	7.91727i	0.0115076	+	0.370760i
$457$	−26.5061			−1.23990			−0.619952	−	0.784640i	$-0.712848\pi$
$457$	−26.5061			−1.23990			−0.619952	+	0.784640i	$0.712848\pi$
$458$	9.27182	−	16.0593i	0.433244	−	0.750400i
$459$	−35.2092	−	16.1696i	−1.64342	−	0.754734i
$460$	−1.01111	+	0.583767i	−0.0471434	+	0.0272183i
$461$	9.87220	−	17.0992i	0.459794	−	0.796387i	−0.539156	−	0.842206i	$-0.681256\pi$
$461$	9.87220	−	17.0992i	0.459794	−	0.796387i	0.998950	+	0.0458193i	$0.0145898\pi$
$462$		0			0
$463$	−1.87477	−	3.24719i	−0.0871278	−	0.150910i	0.819168	−	0.573553i	$-0.194436\pi$
$463$	−1.87477	−	3.24719i	−0.0871278	−	0.150910i	−0.906296	+	0.422644i	$0.861102\pi$
$464$	−3.18684	−	1.83992i	−0.147945	−	0.0854162i
$465$	−17.1457	−	27.6772i	−0.795115	−	1.28350i
$466$	5.21183	+	9.02716i	0.241433	+	0.418175i
$467$	−9.99748	−	17.3161i	−0.462628	−	0.801296i	0.536463	−	0.843924i	$-0.319760\pi$
$467$	−9.99748	−	17.3161i	−0.462628	−	0.801296i	−0.999091	+	0.0426283i	$0.986427\pi$
$468$	−8.09012	−	4.02380i	−0.373966	−	0.186000i
$469$		0			0
$470$	46.9994	+	27.1351i	2.16792	+	1.25165i
$471$	−19.3256	+	36.0085i	−0.890476	+	1.65918i
$472$			7.06674i			0.325273i
$473$			4.30506i			0.197947i
$474$	2.33215	−	4.34539i	0.107119	−	0.199590i
$475$	−43.1489	−	24.9120i	−1.97981	−	1.14304i
$476$		0			0
$477$	−0.170450	−	2.74320i	−0.00780438	−	0.125603i
$478$	−3.39981	−	5.88865i	−0.155504	−	0.269340i
$479$	5.33187	+	9.23507i	0.243619	+	0.421961i	0.961743	−	0.273955i	$-0.0883319\pi$
$479$	5.33187	+	9.23507i	0.243619	+	0.421961i	−0.718123	+	0.695916i	$0.754999\pi$
$480$	−3.63655	−	5.87023i	−0.165985	−	0.267938i
$481$	−15.6863	−	9.05648i	−0.715233	−	0.412940i
$482$	−9.41695	−	16.3106i	−0.428930	−	0.742929i
$483$		0			0
$484$	4.12836	−	7.15054i	0.187653	−	0.325024i
$485$	10.0272	−	5.78923i	0.455313	−	0.262875i
$486$	9.78661	+	12.1335i	0.443930	+	0.550388i
$487$	8.46164	−	14.6560i	0.383434	−	0.664126i	−0.608117	−	0.793847i	$-0.708075\pi$
$487$	8.46164	−	14.6560i	0.383434	−	0.664126i	0.991551	+	0.129721i	$0.0414082\pi$
$488$	−6.64659			−0.300877
$489$	−0.0321984	−	1.03739i	−0.00145606	−	0.0469124i
$490$		0			0
$491$	20.4285	−	11.7944i	0.921927	−	0.532275i	0.0376778	−	0.999290i	$-0.488004\pi$
$491$	20.4285	−	11.7944i	0.921927	−	0.532275i	0.884249	+	0.467015i	$0.154671\pi$
$492$	−0.525114	−	16.9185i	−0.0236740	−	0.762745i
$493$	23.7623	−	13.7192i	1.07020	−	0.617881i
$494$	−11.9285	−	6.88694i	−0.536690	−	0.309858i
$495$	16.5086	−	10.9498i	0.742005	−	0.492158i
$496$		−	4.71484i		−	0.211703i
$497$		0			0
$498$	4.73277	+	7.63980i	0.212081	+	0.342348i
$499$	3.37814	−	5.85111i	0.151226	−	0.261932i	−0.780452	−	0.625215i	$-0.785011\pi$
$499$	3.37814	−	5.85111i	0.151226	−	0.261932i	0.931679	+	0.363284i	$0.118344\pi$
$500$	23.5011			1.05100
$501$	0.287222	+	9.25393i	0.0128321	+	0.413435i
$502$		−	0.0465190i		−	0.00207625i
$503$	12.7667			0.569240			0.284620	−	0.958640i	$-0.408133\pi$
$503$	12.7667			0.569240			0.284620	+	0.958640i	$0.408133\pi$
$504$		0			0
$505$	−1.03092			−0.0458752
$506$		−	0.485040i		−	0.0215627i
$507$	−5.78478	+	3.58361i	−0.256911	+	0.159154i
$508$	4.93203			0.218823
$509$	2.13873	−	3.70438i	0.0947974	−	0.164194i	−0.814727	−	0.579845i	$-0.803113\pi$
$509$	2.13873	−	3.70438i	0.0947974	−	0.164194i	0.909524	+	0.415651i	$0.136446\pi$
$510$	51.4644	−	1.59734i	2.27888	−	0.0707315i
$511$		0			0
$512$		−	1.00000i		−	0.0441942i
$513$	13.7430	+	19.3861i	0.606770	+	0.855917i
$514$	−13.1684	−	7.60276i	−0.580832	−	0.335343i
$515$	−23.5214	+	13.5801i	−1.03648	+	0.598410i
$516$	3.82713	−	2.37087i	0.168480	−	0.104372i
$517$	−19.5254	+	11.2730i	−0.858728	+	0.495787i
$518$		0			0
$519$	−18.5022	−	9.93006i	−0.812158	−	0.435881i
$520$	12.0077			0.526572
$521$	4.04014	−	6.99773i	0.177002	−	0.306576i	−0.763850	−	0.645393i	$-0.776694\pi$
$521$	4.04014	−	6.99773i	0.177002	−	0.306576i	0.940852	+	0.338817i	$0.110027\pi$
$522$	−11.0183	+	0.684627i	−0.482257	+	0.0299653i
$523$	28.4937	−	16.4508i	1.24594	−	0.719344i	0.275643	−	0.961260i	$-0.411109\pi$
$523$	28.4937	−	16.4508i	1.24594	−	0.719344i	0.970297	+	0.241916i	$0.0777758\pi$
$524$	10.8056	−	18.7158i	0.472044	−	0.817604i
$525$		0			0
$526$	0.978086	+	1.69410i	0.0426466	+	0.0738661i
$527$	30.4458	+	17.5779i	1.32624	+	0.765704i
$528$	2.86739	−	0.0889974i	0.124787	−	0.00387311i
$529$	−11.4571	−	19.8443i	−0.498136	−	0.862796i
$530$	1.82629	+	3.16322i	0.0793289	+	0.137402i
$531$	11.7183	+	17.6672i	0.508531	+	0.766692i
$532$		0			0
$533$	25.4902	+	14.7168i	1.10410	+	0.637455i
$534$	19.0734	−	0.591996i	0.825385	−	0.0256182i
$535$			42.4127i			1.83366i
$536$			4.05676i			0.175225i
$537$	5.07265	+	8.18844i	0.218901	+	0.353357i
$538$	−4.72739	−	2.72936i	−0.203812	−	0.117671i
$539$		0			0
$540$	−18.8258	−	8.64564i	−0.810132	−	0.372049i
$541$	4.39638	+	7.61476i	0.189015	+	0.327384i	0.944922	−	0.327295i	$-0.106137\pi$
$541$	4.39638	+	7.61476i	0.189015	+	0.327384i	−0.755907	+	0.654679i	$0.772804\pi$
$542$	−7.39843	−	12.8145i	−0.317790	−	0.550428i
$543$	−10.2830	+	19.1599i	−0.441288	+	0.822232i
$544$	6.45743	+	3.72820i	0.276860	+	0.159845i
$545$	−9.00571	−	15.5983i	−0.385762	−	0.668160i
$546$		0			0
$547$	15.2530	−	26.4189i	0.652170	−	1.12959i	−0.330425	−	0.943832i	$-0.607192\pi$
$547$	15.2530	−	26.4189i	0.652170	−	1.12959i	0.982595	−	0.185760i	$-0.0594747\pi$
$548$	−5.93663	+	3.42752i	−0.253600	+	0.146416i
$549$	−16.6168	+	11.0216i	−0.709188	+	0.470390i
$550$	−9.02236	+	15.6272i	−0.384715	+	0.666345i
$551$	−16.8288			−0.716931
$552$	−0.431193	+	0.267120i	−0.0183528	+	0.0113694i
$553$		0			0
$554$	9.06963	−	5.23636i	0.385332	−	0.222471i
$555$	−36.5914	−	19.6384i	−1.55322	−	0.833604i
$556$	−13.9583	+	8.05882i	−0.591963	+	0.341770i
$557$	−36.1910	−	20.8949i	−1.53346	−	0.885345i	−0.999199	−	0.0400275i	$-0.987255\pi$
$557$	−36.1910	−	20.8949i	−1.53346	−	0.885345i	−0.534264	−	0.845318i	$-0.679411\pi$
$558$	−7.81832	−	11.7873i	−0.330976	−	0.498998i
$559$			7.82848i			0.331109i
$560$		0			0
$561$	−10.1155	+	18.8477i	−0.427076	+	0.795752i
$562$	0.591716	−	1.02488i	0.0249600	−	0.0432321i
$563$	9.26403			0.390432			0.195216	−	0.980760i	$-0.437459\pi$
$563$	9.26403			0.390432			0.195216	+	0.980760i	$0.437459\pi$
$564$	20.7745	+	11.1496i	0.874766	+	0.469483i
$565$			6.79165i			0.285727i
$566$	−29.5879			−1.24367
$567$		0			0
$568$	13.9437			0.585064
$569$		−	13.2854i		−	0.556955i	−0.960443	−	0.278477i	$-0.910170\pi$
$569$		−	13.2854i		−	0.556955i	0.960443	−	0.278477i	$-0.0898297\pi$
$570$	−27.8257	−	14.9339i	−1.16549	−	0.625512i
$571$	32.4787			1.35919			0.679596	−	0.733587i	$-0.262155\pi$
$571$	32.4787			1.35919			0.679596	+	0.733587i	$0.262155\pi$
$572$	−2.49423	+	4.32014i	−0.104289	+	0.180634i
$573$	−15.5092	+	28.8976i	−0.647905	+	1.20721i
$574$		0			0
$575$		−	3.19050i		−	0.133053i
$576$	−1.65823	−	2.50005i	−0.0690931	−	0.104169i
$577$	−17.5971	−	10.1597i	−0.732575	−	0.422952i	0.0867884	−	0.996227i	$-0.472340\pi$
$577$	−17.5971	−	10.1597i	−0.732575	−	0.422952i	−0.819364	+	0.573274i	$0.805673\pi$
$578$	−33.4267	+	19.2989i	−1.39037	+	0.802730i
$579$	11.6211	+	6.23696i	0.482955	+	0.259199i
$580$	12.7053	−	7.33543i	0.527560	−	0.304587i
$581$		0			0
$582$	4.27615	−	2.64903i	0.177252	−	0.109806i
$583$	−1.51743			−0.0628454
$584$	−2.22034	+	3.84574i	−0.0918783	+	0.159138i
$585$	30.0198	−	19.9116i	1.24117	−	0.823241i
$586$	−11.5081	+	6.64419i	−0.475394	+	0.274469i
$587$	8.67362	−	15.0232i	0.357999	−	0.620072i	−0.629628	−	0.776897i	$-0.716793\pi$
$587$	8.67362	−	15.0232i	0.357999	−	0.620072i	0.987626	+	0.156825i	$0.0501259\pi$
$588$		0			0
$589$	−10.7810	−	18.6733i	−0.444225	−	0.769421i
$590$	−24.3992	−	14.0869i	−1.00450	−	0.579948i
$591$	−4.95454	+	9.23157i	−0.203802	+	0.379736i
$592$	−3.00695	−	5.20820i	−0.123585	−	0.214056i
$593$	14.5697	+	25.2355i	0.598307	+	1.03630i	0.993071	+	0.117515i	$0.0374928\pi$
$593$	14.5697	+	25.2355i	0.598307	+	1.03630i	−0.394765	+	0.918782i	$0.629174\pi$
$594$	7.02103	−	4.97730i	0.288076	−	0.204221i
$595$		0			0
$596$	1.05460	+	0.608875i	0.0431982	+	0.0249405i
$597$	−20.8783	−	33.7024i	−0.854491	−	1.37935i
$598$		−	0.882015i		−	0.0360683i
$599$			36.9120i			1.50818i	0.656768	+	0.754092i	$0.271923\pi$
$599$			36.9120i			1.50818i	−0.656768	+	0.754092i	$0.728077\pi$
$600$	18.8611	−	0.585407i	0.770001	−	0.0238992i
$601$	33.3809	+	19.2725i	1.36164	+	0.786141i	0.989842	−	0.142174i	$-0.0454092\pi$
$601$	33.3809	+	19.2725i	1.36164	+	0.786141i	0.371795	+	0.928315i	$0.378743\pi$
$602$		0			0
$603$	6.72706	+	10.1421i	0.273947	+	0.413019i
$604$	7.01991	+	12.1588i	0.285636	+	0.494736i
$605$	16.4590	+	28.5079i	0.669155	+	1.15901i
$606$	−0.447661	+	0.0138944i	−0.0181850	+	0.000564422i
$607$	−21.2299	−	12.2571i	−0.861696	−	0.497500i	0.00288390	−	0.999996i	$-0.499082\pi$
$607$	−21.2299	−	12.2571i	−0.861696	−	0.497500i	−0.864580	+	0.502495i	$0.832415\pi$
$608$	−2.28662	−	3.96054i	−0.0927346	−	0.160621i
$609$		0			0
$610$	13.2494	−	22.9486i	0.536451	−	0.929160i
$611$	−35.5058	+	20.4993i	−1.43641	+	0.829312i
$612$	22.3261	−	1.38725i	0.902481	−	0.0560761i
$613$	13.1276	−	22.7377i	0.530219	−	0.918367i	−0.469159	−	0.883114i	$-0.655443\pi$
$613$	13.1276	−	22.7377i	0.530219	−	0.918367i	0.999378	−	0.0352531i	$-0.0112237\pi$
$614$	3.34549			0.135013
$615$	59.4610	+	31.9124i	2.39770	+	1.28683i
$616$		0			0
$617$	32.4708	−	18.7470i	1.30723	−	0.754727i	0.325593	−	0.945510i	$-0.394436\pi$
$617$	32.4708	−	18.7470i	1.30723	−	0.754727i	0.981632	+	0.190783i	$0.0611026\pi$
$618$	−10.0308	+	6.21397i	−0.403498	+	0.249962i
$619$	17.1863	−	9.92249i	0.690774	−	0.398819i	−0.113128	−	0.993580i	$-0.536087\pi$
$619$	17.1863	−	9.92249i	0.690774	−	0.398819i	0.803902	+	0.594762i	$0.202754\pi$
$620$	16.2789	+	9.39861i	0.653775	+	0.377457i
$621$	−0.635059	+	1.38283i	−0.0254840	+	0.0554912i
$622$			22.7834i			0.913531i
$623$		0			0
$624$	5.21416	−	0.161836i	0.208733	−	0.00647863i
$625$	−19.6105	+	33.9664i	−0.784421	+	1.35866i
$626$	1.16835			0.0466968
$627$	11.1529	−	6.90909i	0.445404	−	0.275923i
$628$		−	23.5944i		−	0.941520i
$629$	44.8421			1.78797
$630$		0			0
$631$	−26.3099			−1.04738			−0.523691	−	0.851908i	$-0.675445\pi$
$631$	−26.3099			−1.04738			−0.523691	+	0.851908i	$0.675445\pi$
$632$			2.84730i			0.113259i
$633$	0.362100	+	11.6664i	0.0143922	+	0.463698i
$634$	21.8039			0.865945
$635$	−9.83154	+	17.0287i	−0.390153	+	0.675765i
$636$	0.835672	+	1.34897i	0.0331366	+	0.0534901i
$637$		0			0
$638$			6.09486i			0.241298i
$639$	34.8599	−	23.1219i	1.37904	−	0.914689i
$640$	3.45268	+	1.99341i	0.136479	+	0.0787964i
$641$	19.6930	−	11.3697i	0.777826	−	0.449078i	−0.0578333	−	0.998326i	$-0.518419\pi$
$641$	19.6930	−	11.3697i	0.777826	−	0.449078i	0.835659	+	0.549248i	$0.185086\pi$
$642$	0.571627	+	18.4171i	0.0225603	+	0.726865i
$643$	−42.7821	+	24.7003i	−1.68716	+	0.974084i	−0.730488	+	0.682926i	$0.760707\pi$
$643$	−42.7821	+	24.7003i	−1.68716	+	0.974084i	−0.956675	+	0.291158i	$0.905959\pi$
$644$		0			0
$645$	0.556818	+	17.9400i	0.0219247	+	0.706386i
$646$	34.0999			1.34164
$647$	−22.7317	+	39.3724i	−0.893674	+	1.54789i	−0.0582359	+	0.998303i	$0.518548\pi$
$647$	−22.7317	+	39.3724i	−0.893674	+	1.54789i	−0.835438	+	0.549585i	$0.814786\pi$
$648$	−8.29134	−	3.50051i	−0.325715	−	0.137513i
$649$	10.1364	−	5.85226i	0.397889	−	0.229721i
$650$	−16.4066	+	28.4170i	−0.643519	+	1.11461i
$651$		0			0
$652$	0.299613	+	0.518945i	0.0117338	+	0.0203235i
$653$	32.1371	+	18.5543i	1.25762	+	0.726088i	0.972611	−	0.232437i	$-0.0746700\pi$
$653$	32.1371	+	18.5543i	1.25762	+	0.726088i	0.285009	+	0.958525i	$0.408003\pi$
$654$	−4.12083	−	6.65198i	−0.161137	−	0.260113i
$655$	43.0799	+	74.6165i	1.68327	+	2.91551i
$656$	4.88630	+	8.46333i	0.190778	+	0.330437i
$657$	0.826178	+	13.2964i	0.0322323	+	0.518742i
$658$		0			0
$659$	−37.9735	−	21.9240i	−1.47924	−	0.854039i	−0.479515	−	0.877534i	$-0.659187\pi$
$659$	−37.9735	−	21.9240i	−1.47924	−	0.854039i	−0.999724	+	0.0234944i	$0.992521\pi$
$660$	−5.40859	+	10.0776i	−0.210529	+	0.392269i
$661$		−	24.4069i		−	0.949317i	−0.880170	−	0.474659i	$-0.842572\pi$
$661$		−	24.4069i		−	0.949317i	0.880170	−	0.474659i	$-0.157428\pi$
$662$			27.8854i			1.08380i
$663$	−18.3944	+	34.2734i	−0.714379	+	1.33107i
$664$	−4.49349	−	2.59432i	−0.174381	−	0.100679i
$665$		0			0
$666$	−16.1540	−	8.03452i	−0.625953	−	0.311331i
$667$	−0.538818	−	0.933261i	−0.0208631	−	0.0361360i
$668$	−2.67267	−	4.62919i	−0.103409	−	0.179109i
$669$	8.27782	+	13.3623i	0.320039	+	0.516618i
$670$	−14.0067	−	8.08678i	−0.541127	−	0.312420i
$671$	5.50431	+	9.53375i	0.212492	+	0.368046i
$672$		0			0
$673$	−5.68953	+	9.85456i	−0.219315	+	0.379865i	−0.954599	−	0.297894i	$-0.903716\pi$
$673$	−5.68953	+	9.85456i	−0.219315	+	0.379865i	0.735284	+	0.677760i	$0.237049\pi$
$674$	0.00568717	−	0.00328349i	0.000219062	−	0.000126475i
$675$	46.1830	−	32.7397i	1.77758	−	1.26015i
$676$	1.96439	−	3.40242i	0.0755535	−	0.130862i
$677$	−21.9511			−0.843651			−0.421826	−	0.906677i	$-0.638611\pi$
$677$	−21.9511			−0.843651			−0.421826	+	0.906677i	$0.638611\pi$
$678$	0.0915360	+	2.94918i	0.00351542	+	0.113262i
$679$		0			0
$680$	−25.7446	+	14.8636i	−0.987260	+	0.569995i
$681$	0.0337101	+	1.08610i	0.00129177	+	0.0416193i
$682$	−6.76289	+	3.90456i	−0.258964	+	0.149513i
$683$	−8.29828	−	4.79102i	−0.317525	−	0.183323i	0.332764	−	0.943010i	$-0.392019\pi$
$683$	−8.29828	−	4.79102i	−0.317525	−	0.183323i	−0.650289	+	0.759687i	$0.725352\pi$
$684$	−12.2842	−	6.10980i	−0.469697	−	0.233614i
$685$		−	27.3298i		−	1.04422i
$686$		0			0
$687$	16.9145	+	27.3039i	0.645327	+	1.04171i
$688$	−1.29961	+	2.25100i	−0.0495473	+	0.0858185i
$689$	−2.75934			−0.105123
$690$	−0.0627353	−	2.02125i	−0.00238829	−	0.0769478i
$691$		−	0.438731i		−	0.0166901i	−0.999965	−	0.00834506i	$-0.997344\pi$
$691$		−	0.438731i		−	0.0166901i	0.999965	−	0.00834506i	$-0.00265635\pi$
$692$	12.1235			0.460867
$693$		0			0
$694$	−20.4956			−0.778004
$695$		−	64.2581i		−	2.43745i
$696$	5.41824	−	3.35654i	0.205378	−	0.127229i
$697$	−72.8685			−2.76009
$698$	4.18198	−	7.24341i	0.158290	−	0.274167i
$699$	−18.0456	+	0.560097i	−0.682548	+	0.0211848i
$700$		0			0
$701$			29.7259i			1.12273i	0.827568	+	0.561366i	$0.189724\pi$
$701$			29.7259i			1.12273i	−0.827568	+	0.561366i	$0.810276\pi$
$702$	12.7673	−	9.05090i	0.481871	−	0.341604i
$703$	−23.8183	−	13.7515i	−0.898325	−	0.518648i
$704$	−1.43438	+	0.828141i	−0.0540603	+	0.0312118i
$705$	−79.9082	+	49.5022i	−3.00952	+	1.86436i
$706$	5.32484	−	3.07430i	0.200403	−	0.115703i
$707$		0			0
$708$	−10.7849	−	5.78818i	−0.405320	−	0.217533i
$709$	24.4713			0.919038			0.459519	−	0.888168i	$-0.348022\pi$
$709$	24.4713			0.919038			0.459519	+	0.888168i	$0.348022\pi$
$710$	−27.7955	+	48.1431i	−1.04315	+	1.80678i
$711$	4.72149	+	7.11839i	0.177070	+	0.266960i
$712$	−9.54128	+	5.50866i	−0.357575	+	0.206446i
$713$	0.690367	−	1.19575i	0.0258545	−	0.0447812i
$714$		0			0
$715$	−9.94406	−	17.2236i	−0.371887	−	0.644126i
$716$	−4.81618	−	2.78062i	−0.179989	−	0.103917i
$717$	11.7716	−	0.365366i	0.439619	−	0.0136448i
$718$	−2.90236	−	5.02704i	−0.108315	−	0.187608i
$719$	−8.12615	−	14.0749i	−0.303054	−	0.524905i	0.673772	−	0.738939i	$-0.264673\pi$
$719$	−8.12615	−	14.0749i	−0.303054	−	0.524905i	−0.976826	+	0.214034i	$0.931340\pi$
$720$	11.9374	−	0.741738i	0.444882	−	0.0276429i
$721$		0			0
$722$	−1.65801	−	0.957250i	−0.0617046	−	0.0356252i
$723$	32.6056	−	1.01201i	1.21261	−	0.0376369i
$724$		−	12.5545i		−	0.466583i
$725$			40.0908i			1.48894i
$726$	7.53131	+	12.1573i	0.279513	+	0.451200i
$727$	−25.4656	−	14.7026i	−0.944468	−	0.545289i	−0.0531099	−	0.998589i	$-0.516913\pi$
$727$	−25.4656	−	14.7026i	−0.944468	−	0.545289i	−0.891358	+	0.453300i	$0.850247\pi$
$728$		0			0
$729$	−26.5335	+	4.99753i	−0.982721	+	0.185094i
$730$	−8.85209	−	15.3323i	−0.327630	−	0.567473i
$731$	−9.69044	−	16.7843i	−0.358414	−	0.620791i
$732$	5.44405	−	10.1437i	0.201218	−	0.374920i
$733$	31.9175	+	18.4276i	1.17890	+	0.680638i	0.955760	−	0.294149i	$-0.0950361\pi$
$733$	31.9175	+	18.4276i	1.17890	+	0.680638i	0.223139	+	0.974787i	$0.428369\pi$
$734$	−2.98293	−	5.16659i	−0.110102	−	0.190702i
$735$		0			0
$736$	0.146424	−	0.253614i	0.00539727	−	0.00934834i
$737$	5.81895	−	3.35957i	0.214344	−	0.123751i
$738$	26.2502	+	13.0561i	0.966283	+	0.480602i
$739$	21.6130	−	37.4349i	0.795048	−	1.37706i	−0.127761	−	0.991805i	$-0.540779\pi$
$739$	21.6130	−	37.4349i	0.795048	−	1.37706i	0.922809	−	0.385258i	$-0.125888\pi$
$740$	23.9763			0.881388
$741$	20.2808	−	12.5638i	0.745035	−	0.461541i
$742$		0			0
$743$	−28.2201	+	16.2929i	−1.03530	+	0.597729i	−0.918497	−	0.395427i	$-0.870597\pi$
$743$	−28.2201	+	16.2929i	−1.03530	+	0.597729i	−0.116799	+	0.993156i	$0.537263\pi$
$744$	7.19553	+	3.86181i	0.263801	+	0.141581i
$745$	−4.20451	+	2.42747i	−0.154041	+	0.0889357i
$746$	−16.3383	−	9.43291i	−0.598187	−	0.345363i
$747$	−15.5359	+	0.965333i	−0.568430	+	0.0353197i
$748$		−	12.3499i		−	0.451557i
$749$		0			0
$750$	−19.2491	+	35.8661i	−0.702879	+	1.30964i
$751$	17.4592	−	30.2402i	0.637095	−	1.10348i	−0.348972	−	0.937133i	$-0.613469\pi$
$751$	17.4592	−	30.2402i	0.637095	−	1.10348i	0.986067	−	0.166348i	$-0.0531976\pi$
$752$	−13.6124			−0.496394
$753$	0.0709947	+	0.0381025i	0.00258719	+	0.00138853i
$754$			11.0831i			0.403624i
$755$	−55.9741			−2.03711
$756$		0			0
$757$	−26.0470			−0.946693			−0.473346	−	0.880876i	$-0.656954\pi$
$757$	−26.0470			−0.946693			−0.473346	+	0.880876i	$0.656954\pi$
$758$			12.5331i			0.455224i
$759$	0.740241	+	0.397284i	0.0268690	+	0.0144205i
$760$	18.2327			0.661368
$761$	17.1005	−	29.6189i	0.619893	−	1.07369i	−0.369612	−	0.929186i	$-0.620509\pi$
$761$	17.1005	−	29.6189i	0.619893	−	1.07369i	0.989505	−	0.144500i	$-0.0461572\pi$
$762$	−4.03970	+	7.52699i	−0.146343	+	0.272674i
$763$		0			0
$764$		−	18.9350i		−	0.685045i
$765$	−39.7154	+	79.8505i	−1.43591	+	2.88700i
$766$	0.146310	+	0.0844724i	0.00528641	+	0.00305211i
$767$	18.4324	−	10.6420i	0.665556	−	0.384259i
$768$	1.52614	+	0.819074i	0.0550700	+	0.0295558i
$769$	28.9909	−	16.7379i	1.04544	−	0.603585i	0.124071	−	0.992273i	$-0.460405\pi$
$769$	28.9909	−	16.7379i	1.04544	−	0.603585i	0.921369	+	0.388688i	$0.127072\pi$
$770$		0			0
$771$	22.3888	−	13.8696i	0.806312	−	0.499502i
$772$	−7.61465			−0.274057
$773$	5.73718	−	9.93709i	0.206352	−	0.357412i	−0.744211	−	0.667945i	$-0.767174\pi$
$773$	5.73718	−	9.93709i	0.206352	−	0.357412i	0.950563	+	0.310533i	$0.100507\pi$
$774$	0.483581	+	7.78268i	0.0173819	+	0.279743i
$775$	−44.4850	+	25.6834i	−1.59795	+	0.922575i
$776$	−1.45209	+	2.51510i	−0.0521271	+	0.0902867i
$777$		0			0
$778$	4.18543	+	7.24937i	0.150055	+	0.259903i
$779$	38.7048	+	22.3462i	1.38674	+	0.800637i
$780$	−9.83518	+	18.3255i	−0.352156	+	0.656157i
$781$	−11.5473	−	20.0006i	−0.413196	−	0.715677i
$782$	1.09180	+	1.89105i	0.0390426	+	0.0676238i
$783$	7.97995	−	17.3763i	0.285180	−	0.620977i
$784$		0			0
$785$	81.4641	+	47.0333i	2.90758	+	1.67869i
$786$	19.7125	+	31.8205i	0.703120	+	1.13500i
$787$			6.01310i			0.214344i	0.994241	+	0.107172i	$0.0341795\pi$
$787$			6.01310i			0.214344i	−0.994241	+	0.107172i	$0.965820\pi$
$788$		−	6.04895i		−	0.215485i
$789$	−3.38656	+	0.105111i	−0.120565	+	0.00374207i
$790$	−9.83081	−	5.67582i	−0.349765	−	0.201937i
$791$		0			0
$792$	−2.21278	+	4.44894i	−0.0786277	+	0.158086i
$793$	10.0092	+	17.3365i	0.355439	+	0.615638i
$794$	−3.11733	−	5.39937i	−0.110630	−	0.191616i
$795$	−6.32340	+	0.196265i	−0.224268	+	0.00696079i
$796$	19.8227	+	11.4446i	0.702597	+	0.405644i
$797$	−1.19594	−	2.07142i	−0.0423623	−	0.0733736i	0.844067	−	0.536238i	$-0.180155\pi$
$797$	−1.19594	−	2.07142i	−0.0423623	−	0.0733736i	−0.886429	+	0.462864i	$0.846822\pi$
$798$		0			0
$799$	50.7499	−	87.9014i	1.79540	−	3.10973i
$800$	−9.43509	+	5.44735i	−0.333581	+	0.192593i
$801$	−14.7190	+	29.5936i	−0.520072	+	1.04564i
$802$	−16.6322	+	28.8079i	−0.587304	+	1.01724i
$803$	7.35502			0.259553
$804$	−6.19120	−	3.32279i	−0.218347	−	0.117186i
$805$		0			0
$806$	−12.2979	+	7.10019i	−0.433175	+	0.250094i
$807$	8.03748	−	4.97913i	0.282933	−	0.175274i
$808$	0.223938	−	0.129291i	0.00787812	−	0.00454844i
$809$	2.92768	+	1.69030i	0.102932	+	0.0594278i	0.550582	−	0.834781i	$-0.314406\pi$
$809$	2.92768	+	1.69030i	0.102932	+	0.0594278i	−0.447650	+	0.894209i	$0.647739\pi$
$810$	28.6142	−	21.6494i	1.00540	−	0.760684i
$811$		−	38.2801i		−	1.34419i	−0.740463	−	0.672097i	$-0.765394\pi$
$811$		−	38.2801i		−	1.34419i	0.740463	−	0.672097i	$-0.234606\pi$
$812$		0			0
$813$	25.6166	−	0.795083i	0.898413	−	0.0278848i
$814$	−4.98037	+	8.62625i	−0.174562	+	0.302350i
$815$	−2.38901			−0.0836832
$816$	−10.9789	+	6.80130i	−0.384338	+	0.238093i
$817$			11.8869i			0.415870i
$818$	20.3147			0.710287
$819$		0			0
$820$	−38.9616			−1.36060
$821$		−	32.5240i		−	1.13509i	−0.823341	−	0.567547i	$-0.807892\pi$
$821$		−	32.5240i		−	1.13509i	0.823341	−	0.567547i	$-0.192108\pi$
$822$	−0.368343	−	11.8675i	−0.0128474	−	0.413928i
$823$	−0.813298			−0.0283498			−0.0141749	−	0.999900i	$-0.504512\pi$
$823$	−0.813298			−0.0283498			−0.0141749	+	0.999900i	$0.504512\pi$
$824$	3.40625	−	5.89979i	0.118662	−	0.205529i
$825$	−16.4594	−	26.5692i	−0.573041	−	0.925022i
$826$		0			0
$827$			26.0812i			0.906933i	0.891273	+	0.453466i	$0.149813\pi$
$827$			26.0812i			0.906933i	−0.891273	+	0.453466i	$0.850187\pi$
$828$	−0.0544838	−	0.876854i	−0.00189344	−	0.0304728i
$829$	−17.9479	−	10.3622i	−0.623357	−	0.359896i	0.154818	−	0.987943i	$-0.450521\pi$
$829$	−17.9479	−	10.3622i	−0.623357	−	0.359896i	−0.778175	+	0.628047i	$0.783854\pi$
$830$	17.9147	−	10.3431i	0.621829	−	0.359013i
$831$	0.562732	+	18.1305i	0.0195210	+	0.628941i
$832$	−2.60834	+	1.50592i	−0.0904278	+	0.0522085i
$833$		0			0
$834$	−0.866053	−	27.9031i	−0.0299890	−	0.966207i
$835$	21.3109			0.737493
$836$	−3.78729	+	6.55977i	−0.130986	+	0.226875i
$837$	24.3930	−	2.27717i	0.843145	−	0.0787104i
$838$	26.8115	−	15.4796i	0.926187	−	0.534734i
$839$	−6.41783	+	11.1160i	−0.221568	+	0.383767i	−0.955284	−	0.295689i	$-0.904451\pi$
$839$	−6.41783	+	11.1160i	−0.221568	+	0.383767i	0.733716	+	0.679456i	$0.237784\pi$
$840$		0			0
$841$	−7.72938	−	13.3877i	−0.266530	−	0.461644i
$842$	15.4624	+	8.92724i	0.532870	+	0.307653i
$843$	1.07946	+	1.74250i	0.0371786	+	0.0600149i
$844$	−3.36942	−	5.83601i	−0.115980	−	0.200884i
$845$	7.83166	+	13.5648i	0.269417	+	0.466645i
$846$	−34.0318	+	22.5726i	−1.17004	+	0.776062i
$847$		0			0
$848$	−0.793421	−	0.458082i	−0.0272462	−	0.0157306i
$849$	24.2347	−	45.1554i	0.831731	−	1.54973i
$850$		−	81.2353i		−	2.78635i
$851$		−	1.76116i		−	0.0603719i
$852$	−11.4209	+	21.2801i	−0.391274	+	0.729044i
$853$	−30.3664	−	17.5321i	−1.03973	−	0.600287i	−0.119971	−	0.992777i	$-0.538280\pi$
$853$	−30.3664	−	17.5321i	−1.03973	−	0.600287i	−0.919756	+	0.392490i	$0.871614\pi$
$854$		0			0
$855$	45.5826	−	30.2340i	1.55889	−	1.03398i
$856$	−5.31912	−	9.21299i	−0.181804	−	0.314894i
$857$	13.6238	+	23.5972i	0.465382	+	0.806065i	0.999219	−	0.0395226i	$-0.0125837\pi$
$857$	13.6238	+	23.5972i	0.465382	+	0.806065i	−0.533837	+	0.845587i	$0.679250\pi$
$858$	−4.55020	−	7.34508i	−0.155341	−	0.250757i
$859$	6.42983	+	3.71226i	0.219383	+	0.126661i	0.605664	−	0.795720i	$-0.292907\pi$
$859$	6.42983	+	3.71226i	0.219383	+	0.126661i	−0.386282	+	0.922381i	$0.626241\pi$
$860$	−5.18132	−	8.97432i	−0.176682	−	0.306022i
$861$		0			0
$862$	−13.3087	+	23.0513i	−0.453295	+	0.785130i
$863$	−29.0017	+	16.7441i	−0.987228	+	0.569977i	−0.904445	−	0.426591i	$-0.859714\pi$
$863$	−29.0017	+	16.7441i	−0.987228	+	0.569977i	−0.0827837	+	0.996568i	$0.526381\pi$
$864$	5.17366	−	0.482978i	0.176011	−	0.0164313i
$865$	−24.1671	+	41.8587i	−0.821707	+	1.42324i
$866$	−12.8312			−0.436022
$867$	−2.07399	−	66.8213i	−0.0704363	−	2.26937i
$868$		0			0
$869$	4.08411	−	2.35796i	0.138544	−	0.0799885i
$870$	0.788312	+	25.3984i	0.0267263	+	0.861088i
$871$	10.5814	−	6.10917i	0.358537	−	0.207001i
$872$	3.91248	+	2.25887i	0.132493	+	0.0764951i
$873$	0.540317	+	8.69578i	0.0182870	+	0.294308i
$874$		−	1.33927i		−	0.0453013i
$875$		0			0
$876$	−4.05053	−	6.53851i	−0.136855	−	0.220916i
$877$	−9.77904	+	16.9378i	−0.330215	+	0.571948i	−0.982554	−	0.185979i	$-0.940454\pi$
$877$	−9.77904	+	16.9378i	−0.330215	+	0.571948i	0.652339	+	0.757927i	$0.273788\pi$
$878$	−23.4359			−0.790922
$879$	−0.714028	−	23.0051i	−0.0240836	−	0.775942i
$880$		−	6.60330i		−	0.222597i
$881$	−30.1681			−1.01639			−0.508195	−	0.861242i	$-0.669687\pi$
$881$	−30.1681			−1.01639			−0.508195	+	0.861242i	$0.669687\pi$
$882$		0			0
$883$	44.0654			1.48292			0.741459	−	0.670998i	$-0.234134\pi$
$883$	44.0654			1.48292			0.741459	+	0.670998i	$0.234134\pi$
$884$		−	22.4575i		−	0.755328i
$885$	41.4834	−	25.6985i	1.39445	−	0.863846i
$886$	−18.5863			−0.624419
$887$	5.21456	−	9.03188i	0.175088	−	0.303261i	−0.765104	−	0.643907i	$-0.777312\pi$
$887$	5.21456	−	9.03188i	0.175088	−	0.303261i	0.940192	+	0.340646i	$0.110646\pi$
$888$	10.4114	−	0.323147i	0.349383	−	0.0108441i
$889$		0			0
$890$		−	43.9240i		−	1.47234i
$891$	1.84533	+	14.7919i	0.0618208	+	0.495547i
$892$	−7.85930	−	4.53757i	−0.263149	−	0.151929i
$893$	−53.9126	+	31.1264i	−1.80412	+	1.04161i
$894$	−1.79303	+	1.11076i	−0.0599679	+	0.0371494i
$895$	19.2012	−	11.0858i	0.641826	−	0.370558i
$896$		0			0
$897$	1.34608	+	0.722435i	0.0449444	+	0.0241214i
$898$	−22.7518			−0.759237
$899$	−8.67494	+	15.0254i	−0.289326	+	0.501127i
$900$	−14.5552	+	29.2643i	−0.485174	+	0.975475i
$901$	5.91606	−	3.41564i	0.197093	−	0.113791i
$902$	8.09310	−	14.0177i	0.269471	−	0.466737i
$903$		0			0
$904$	−0.851764	−	1.47530i	−0.0283292	−	0.0490677i
$905$	43.3466	+	25.0262i	1.44089	+	0.831899i
$906$	−24.3060	+	0.754404i	−0.807511	+	0.0250634i
$907$	−11.2709	−	19.5218i	−0.374246	−	0.648212i	0.615968	−	0.787771i	$-0.288765\pi$
$907$	−11.2709	−	19.5218i	−0.374246	−	0.648212i	−0.990214	+	0.139559i	$0.955432\pi$
$908$	−0.313680	−	0.543310i	−0.0104098	−	0.0180304i
$909$	0.345463	−	0.694576i	0.0114583	−	0.0230376i
$910$		0			0
$911$	6.57136	+	3.79398i	0.217719	+	0.125700i	0.604894	−	0.796306i	$-0.293216\pi$
$911$	6.57136	+	3.79398i	0.217719	+	0.125700i	−0.387175	+	0.922006i	$0.626549\pi$
$912$	7.91727	−	0.245735i	0.262167	−	0.00813709i
$913$			8.59384i			0.284415i
$914$			26.5061i			0.876744i
$915$	24.1706	+	39.0170i	0.799056	+	1.28986i
$916$	−16.0593	−	9.27182i	−0.530613	−	0.306350i
$917$		0			0
$918$	−16.1696	+	35.2092i	−0.533677	+	1.16208i
$919$	24.5151	+	42.4614i	0.808679	+	1.40067i	0.913779	+	0.406212i	$0.133150\pi$
$919$	24.5151	+	42.4614i	0.808679	+	1.40067i	−0.105100	+	0.994462i	$0.533516\pi$
$920$	0.583767	+	1.01111i	0.0192462	+	0.0333354i
$921$	−2.74021	+	5.10570i	−0.0902928	+	0.168239i
$922$	−17.0992	−	9.87220i	−0.563131	−	0.325124i
$923$	−20.9981	−	36.3698i	−0.691162	−	1.19713i
$924$		0			0
$925$	−32.7599	+	56.7418i	−1.07714	+	1.86566i
$926$	−3.24719	+	1.87477i	−0.106709	+	0.0616086i
$927$	−1.26745	−	20.3981i	−0.0416285	−	0.669963i
$928$	−1.83992	+	3.18684i	−0.0603984	+	0.104613i
$929$	−27.2265			−0.893271			−0.446636	−	0.894716i	$-0.647378\pi$
$929$	−27.2265			−0.893271			−0.446636	+	0.894716i	$0.647378\pi$
$930$	−27.6772	+	17.1457i	−0.907572	+	0.562231i
$931$		0			0
$932$	9.02716	−	5.21183i	0.295694	−	0.170719i
$933$	−34.7708	−	18.6613i	−1.13834	−	0.610943i
$934$	−17.3161	+	9.99748i	−0.566602	+	0.327128i
$935$	42.6403	+	24.6184i	1.39449	+	0.805108i
$936$	−4.02380	+	8.09012i	−0.131522	+	0.264434i
$937$			51.0665i			1.66827i	0.551562	+	0.834134i	$0.314032\pi$
$937$			51.0665i			1.66827i	−0.551562	+	0.834134i	$0.685968\pi$
$938$		0			0
$939$	−0.956968	+	1.78308i	−0.0312295	+	0.0581885i
$940$	27.1351	−	46.9994i	0.885051	−	1.53295i
$941$	46.4303			1.51359			0.756793	−	0.653655i	$-0.226765\pi$
$941$	46.4303			1.51359			0.756793	+	0.653655i	$0.226765\pi$
$942$	36.0085	+	19.3256i	1.17322	+	0.629662i
$943$			2.86189i			0.0931961i
$944$	7.06674			0.230003
$945$		0			0
$946$	4.30506			0.139970
$947$			35.5135i			1.15403i	0.816733	+	0.577016i	$0.195783\pi$
$947$			35.5135i			1.15403i	−0.816733	+	0.577016i	$0.804217\pi$
$948$	−4.34539	−	2.33215i	−0.141132	−	0.0757446i
$949$	13.3746			0.434159
$950$	−24.9120	+	43.1489i	−0.808253	+	1.39994i
$951$	−17.8590	+	33.2760i	−0.579119	+	1.07905i
$952$		0			0
$953$		−	10.1647i		−	0.329268i	−0.986355	−	0.164634i	$-0.947356\pi$
$953$		−	10.1647i		−	0.329268i	0.986355	−	0.164634i	$-0.0526443\pi$
$954$	−2.74320	+	0.170450i	−0.0888144	+	0.00551853i
$955$	65.3766	+	37.7452i	2.11554	+	1.22141i
$956$	−5.88865	+	3.39981i	−0.190452	+	0.109958i
$957$	−9.30164	−	4.99214i	−0.300679	−	0.161373i
$958$	9.23507	−	5.33187i	0.298371	−	0.172265i
$959$		0			0
$960$	−5.87023	+	3.63655i	−0.189461	+	0.117369i
$961$	8.77026			0.282911
$962$	−9.05648	+	15.6863i	−0.291993	+	0.505746i
$963$	−28.5754	−	14.2126i	−0.920829	−	0.457995i
$964$	−16.3106	+	9.41695i	−0.525330	+	0.303300i
$965$	15.1791	−	26.2910i	0.488633	−	0.846337i
$966$		0			0
$967$	15.5961	+	27.0132i	0.501536	+	0.868686i	0.999998	+	0.00177474i	$0.000564917\pi$
$967$	15.5961	+	27.0132i	0.501536	+	0.868686i	−0.498462	+	0.866911i	$0.666102\pi$
$968$	−7.15054	−	4.12836i	−0.229827	−	0.132691i
$969$	−27.9303	+	52.0413i	−0.897252	+	1.67181i
$970$	−5.78923	−	10.0272i	−0.185881	−	0.321955i
$971$	−14.3314	−	24.8228i	−0.459918	−	0.796601i	0.539038	−	0.842281i	$-0.318788\pi$
$971$	−14.3314	−	24.8228i	−0.459918	−	0.796601i	−0.998956	+	0.0456800i	$0.985455\pi$
$972$	12.1335	−	9.78661i	0.389183	−	0.313906i
$973$		0			0
$974$	−14.6560	−	8.46164i	−0.469608	−	0.271128i
$975$	−29.9303	−	48.3145i	−0.958537	−	1.54730i
$976$			6.64659i			0.212752i
$977$		−	29.4022i		−	0.940661i	−0.882490	−	0.470330i	$-0.844135\pi$
$977$		−	29.4022i		−	0.940661i	0.882490	−	0.470330i	$-0.155865\pi$
$978$	−1.03739	+	0.0321984i	−0.0331721	+	0.00102959i
$979$	15.8031	+	9.12390i	0.505068	+	0.291601i
$980$		0			0
$981$	13.5271	−	0.840516i	0.431889	−	0.0268356i
$982$	−11.7944	−	20.4285i	−0.376375	−	0.651901i
$983$	−14.7425	−	25.5348i	−0.470214	−	0.814434i	0.529206	−	0.848493i	$-0.322490\pi$
$983$	−14.7425	−	25.5348i	−0.470214	−	0.814434i	−0.999420	+	0.0340593i	$0.989156\pi$
$984$	−16.9185	+	0.525114i	−0.539342	+	0.0167400i
$985$	20.8851	+	12.0580i	0.665455	+	0.384200i
$986$	−13.7192	−	23.7623i	−0.436908	−	0.756747i
$987$		0			0
$988$	−6.88694	+	11.9285i	−0.219103	+	0.379497i
$989$	−0.659201	+	0.380590i	−0.0209614	+	0.0121021i
$990$	−10.9498	−	16.5086i	−0.348008	−	0.524677i
$991$	6.83215	−	11.8336i	0.217030	−	0.375907i	−0.736868	−	0.676036i	$-0.763696\pi$
$991$	6.83215	−	11.8336i	0.217030	−	0.375907i	0.953899	+	0.300129i	$0.0970296\pi$
$992$	−4.71484			−0.149696
$993$	−42.5571	−	22.8402i	−1.35051	−	0.724811i
$994$		0			0
$995$	−79.0294	+	45.6277i	−2.50540	+	1.44649i
$996$	7.63980	−	4.73277i	0.242076	−	0.149964i
$997$	−29.1701	+	16.8414i	−0.923828	+	0.533372i	−0.884854	−	0.465868i	$-0.845742\pi$
$997$	−29.1701	+	16.8414i	−0.923828	+	0.533372i	−0.0389734	+	0.999240i	$0.512409\pi$
$998$	−5.85111	−	3.37814i	−0.185214	−	0.106933i
$999$	25.4931	−	18.0724i	0.806567	−	0.571785i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	882.2.l.c.227.10		48
3.2	odd	2		2646.2.l.c.521.1		48
7.2	even	3		882.2.t.c.803.3		48
7.3	odd	6		882.2.m.c.587.19	yes	48
7.4	even	3		882.2.m.c.587.18	yes	48
7.5	odd	6		882.2.t.c.803.10		48
7.6	odd	2	inner	882.2.l.c.227.3		48
9.4	even	3		2646.2.t.c.2285.13		48
9.5	odd	6		882.2.t.c.815.10		48
21.2	odd	6		2646.2.t.c.1979.14		48
21.5	even	6		2646.2.t.c.1979.13		48
21.11	odd	6		2646.2.m.c.1763.1		48
21.17	even	6		2646.2.m.c.1763.2		48
21.20	even	2		2646.2.l.c.521.2		48
63.4	even	3		2646.2.m.c.881.2		48
63.5	even	6	inner	882.2.l.c.509.22		48
63.13	odd	6		2646.2.t.c.2285.14		48
63.23	odd	6	inner	882.2.l.c.509.15		48
63.31	odd	6		2646.2.m.c.881.1		48
63.32	odd	6		882.2.m.c.293.19	yes	48
63.40	odd	6		2646.2.l.c.1097.1		48
63.41	even	6		882.2.t.c.815.3		48
63.58	even	3		2646.2.l.c.1097.2		48
63.59	even	6		882.2.m.c.293.18	✓	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
882.2.l.c.227.3		48	7.6	odd	2	inner
882.2.l.c.227.10		48	1.1	even	1	trivial
882.2.l.c.509.15		48	63.23	odd	6	inner
882.2.l.c.509.22		48	63.5	even	6	inner
882.2.m.c.293.18	✓	48	63.59	even	6
882.2.m.c.293.19	yes	48	63.32	odd	6
882.2.m.c.587.18	yes	48	7.4	even	3
882.2.m.c.587.19	yes	48	7.3	odd	6
882.2.t.c.803.3		48	7.2	even	3
882.2.t.c.803.10		48	7.5	odd	6
882.2.t.c.815.3		48	63.41	even	6
882.2.t.c.815.10		48	9.5	odd	6
2646.2.l.c.521.1		48	3.2	odd	2
2646.2.l.c.521.2		48	21.20	even	2
2646.2.l.c.1097.1		48	63.40	odd	6
2646.2.l.c.1097.2		48	63.58	even	3
2646.2.m.c.881.1		48	63.31	odd	6
2646.2.m.c.881.2		48	63.4	even	3
2646.2.m.c.1763.1		48	21.11	odd	6
2646.2.m.c.1763.2		48	21.17	even	6
2646.2.t.c.1979.13		48	21.5	even	6
2646.2.t.c.1979.14		48	21.2	odd	6
2646.2.t.c.2285.13		48	9.4	even	3
2646.2.t.c.2285.14		48	63.13	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 882 = 2 \cdot 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	882.l (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} +(1.52614 + 0.819074i) q^{3} -1.00000 q^{4} +(1.99341 - 3.45268i) q^{5} +(0.819074 - 1.52614i) q^{6} +1.00000i q^{8} +(1.65823 + 2.50005i) q^{9} +O(q^{10})\)	\(q-1.00000i q^{2} +(1.52614 + 0.819074i) q^{3} -1.00000 q^{4} +(1.99341 - 3.45268i) q^{5} +(0.819074 - 1.52614i) q^{6} +1.00000i q^{8} +(1.65823 + 2.50005i) q^{9} +(-3.45268 - 1.99341i) q^{10} +(1.43438 - 0.828141i) q^{11} +(-1.52614 - 0.819074i) q^{12} +(2.60834 - 1.50592i) q^{13} +(5.87023 - 3.63655i) q^{15} +1.00000 q^{16} +(-3.72820 + 6.45743i) q^{17} +(2.50005 - 1.65823i) q^{18} +(3.96054 - 2.28662i) q^{19} +(-1.99341 + 3.45268i) q^{20} +(-0.828141 - 1.43438i) q^{22} +(0.253614 + 0.146424i) q^{23} +(-0.819074 + 1.52614i) q^{24} +(-5.44735 - 9.43509i) q^{25} +(-1.50592 - 2.60834i) q^{26} +(0.482978 + 5.17366i) q^{27} +(-3.18684 - 1.83992i) q^{29} +(-3.63655 - 5.87023i) q^{30} -4.71484i q^{31} -1.00000i q^{32} +(2.86739 - 0.0889974i) q^{33} +(6.45743 + 3.72820i) q^{34} +(-1.65823 - 2.50005i) q^{36} +(-3.00695 - 5.20820i) q^{37} +(-2.28662 - 3.96054i) q^{38} +(5.21416 - 0.161836i) q^{39} +(3.45268 + 1.99341i) q^{40} +(4.88630 + 8.46333i) q^{41} +(-1.29961 + 2.25100i) q^{43} +(-1.43438 + 0.828141i) q^{44} +(11.9374 - 0.741738i) q^{45} +(0.146424 - 0.253614i) q^{46} -13.6124 q^{47} +(1.52614 + 0.819074i) q^{48} +(-9.43509 + 5.44735i) q^{50} +(-10.9789 + 6.80130i) q^{51} +(-2.60834 + 1.50592i) q^{52} +(-0.793421 - 0.458082i) q^{53} +(5.17366 - 0.482978i) q^{54} -6.60330i q^{55} +(7.91727 - 0.245735i) q^{57} +(-1.83992 + 3.18684i) q^{58} +7.06674 q^{59} +(-5.87023 + 3.63655i) q^{60} +6.64659i q^{61} -4.71484 q^{62} -1.00000 q^{64} -12.0077i q^{65} +(-0.0889974 - 2.86739i) q^{66} +4.05676 q^{67} +(3.72820 - 6.45743i) q^{68} +(0.267120 + 0.431193i) q^{69} -13.9437i q^{71} +(-2.50005 + 1.65823i) q^{72} +(3.84574 + 2.22034i) q^{73} +(-5.20820 + 3.00695i) q^{74} +(-0.585407 - 18.8611i) q^{75} +(-3.96054 + 2.28662i) q^{76} +(-0.161836 - 5.21416i) q^{78} +2.84730 q^{79} +(1.99341 - 3.45268i) q^{80} +(-3.50051 + 8.29134i) q^{81} +(8.46333 - 4.88630i) q^{82} +(-2.59432 + 4.49349i) q^{83} +(14.8636 + 25.7446i) q^{85} +(2.25100 + 1.29961i) q^{86} +(-3.35654 - 5.41824i) q^{87} +(0.828141 + 1.43438i) q^{88} +(5.50866 + 9.54128i) q^{89} +(-0.741738 - 11.9374i) q^{90} +(-0.253614 - 0.146424i) q^{92} +(3.86181 - 7.19553i) q^{93} +13.6124i q^{94} -18.2327i q^{95} +(0.819074 - 1.52614i) q^{96} +(2.51510 + 1.45209i) q^{97} +(4.44894 + 2.21278i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 48 q^{4} + 16 q^{9}+O(q^{10}) \) 48 * q - 48 * q^4 + 16 * q^9	\( 48 q - 48 q^{4} + 16 q^{9} - 48 q^{11} + 48 q^{15} + 48 q^{16} + 16 q^{18} - 48 q^{23} - 24 q^{25} - 16 q^{30} - 16 q^{36} + 32 q^{39} + 48 q^{44} - 48 q^{50} - 48 q^{51} + 96 q^{53} - 80 q^{57} - 48 q^{60} - 48 q^{64} - 16 q^{72} + 32 q^{78} - 96 q^{79} + 96 q^{81} + 48 q^{85} - 96 q^{86} + 48 q^{92} + 104 q^{99}+O(q^{100}) \) 48 * q - 48 * q^4 + 16 * q^9 - 48 * q^11 + 48 * q^15 + 48 * q^16 + 16 * q^18 - 48 * q^23 - 24 * q^25 - 16 * q^30 - 16 * q^36 + 32 * q^39 + 48 * q^44 - 48 * q^50 - 48 * q^51 + 96 * q^53 - 80 * q^57 - 48 * q^60 - 48 * q^64 - 16 * q^72 + 32 * q^78 - 96 * q^79 + 96 * q^81 + 48 * q^85 - 96 * q^86 + 48 * q^92 + 104 * q^99

Introduction

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