LMFDB - Embedded newform 2646.2.l.c.521.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2646,2,Mod(521,2646)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2646, 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("2646.521");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2646 = 2 \cdot 3^{3} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2646.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:	$21.1284163748$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 882)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			521.2
Character	$\chi$	$=$	2646.521
Dual form			2646.2.l.c.1097.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000i q^{2} -1.00000 q^{4} +(1.99341 - 3.45268i) q^{5} -1.00000i q^{8} +O(q^{10})$	\(q+1.00000i q^{2} -1.00000 q^{4} +(1.99341 - 3.45268i) q^{5} -1.00000i q^{8} +(3.45268 + 1.99341i) q^{10} +(-1.43438 + 0.828141i) q^{11} +(-2.60834 + 1.50592i) q^{13} +1.00000 q^{16} +(-3.72820 + 6.45743i) q^{17} +(-3.96054 + 2.28662i) q^{19} +(-1.99341 + 3.45268i) q^{20} +(-0.828141 - 1.43438i) q^{22} +(-0.253614 - 0.146424i) q^{23} +(-5.44735 - 9.43509i) q^{25} +(-1.50592 - 2.60834i) q^{26} +(3.18684 + 1.83992i) q^{29} +4.71484i q^{31} +1.00000i q^{32} +(-6.45743 - 3.72820i) q^{34} +(-3.00695 - 5.20820i) q^{37} +(-2.28662 - 3.96054i) q^{38} +(-3.45268 - 1.99341i) q^{40} +(4.88630 + 8.46333i) q^{41} +(-1.29961 + 2.25100i) q^{43} +(1.43438 - 0.828141i) q^{44} +(0.146424 - 0.253614i) q^{46} -13.6124 q^{47} +(9.43509 - 5.44735i) q^{50} +(2.60834 - 1.50592i) q^{52} +(0.793421 + 0.458082i) q^{53} +6.60330i q^{55} +(-1.83992 + 3.18684i) q^{58} +7.06674 q^{59} -6.64659i q^{61} -4.71484 q^{62} -1.00000 q^{64} +12.0077i q^{65} +4.05676 q^{67} +(3.72820 - 6.45743i) q^{68} +13.9437i q^{71} +(-3.84574 - 2.22034i) q^{73} +(5.20820 - 3.00695i) q^{74} +(3.96054 - 2.28662i) q^{76} +2.84730 q^{79} +(1.99341 - 3.45268i) q^{80} +(-8.46333 + 4.88630i) q^{82} +(-2.59432 + 4.49349i) q^{83} +(14.8636 + 25.7446i) q^{85} +(-2.25100 - 1.29961i) q^{86} +(0.828141 + 1.43438i) q^{88} +(5.50866 + 9.54128i) q^{89} +(0.253614 + 0.146424i) q^{92} -13.6124i q^{94} +18.2327i q^{95} +(-2.51510 - 1.45209i) q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 48 q^{4}+O(q^{10}) $ 48 * q - 48 * q^4	$ 48 q - 48 q^{4} + 48 q^{11} + 48 q^{16} + 48 q^{23} - 24 q^{25} - 48 q^{44} + 48 q^{50} - 96 q^{53} - 48 q^{64} - 96 q^{79} + 48 q^{85} + 96 q^{86} - 48 q^{92}+O(q^{100}) $ 48 * q - 48 * q^4 + 48 * q^11 + 48 * q^16 + 48 * q^23 - 24 * q^25 - 48 * q^44 + 48 * q^50 - 96 * q^53 - 48 * q^64 - 96 * q^79 + 48 * q^85 + 96 * q^86 - 48 * q^92

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2646\mathbb{Z}\right)^\times$.

$n$	$785$	$1081$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{6}\right)$

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
$3$		0			0
$3$		0			0
$4$	−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			0
$7$		0			0
$7$		0			0
$8$		−	1.00000i		−	0.353553i
$9$		0			0
$10$	3.45268	+	1.99341i	1.09183	+	0.630371i
$11$	−1.43438	+	0.828141i	−0.432483	+	0.249694i	−0.700404	−	0.713747i	$-0.746997\pi$
$11$	−1.43438	+	0.828141i	−0.432483	+	0.249694i	0.267921	+	0.963441i	$0.413663\pi$
$12$		0			0
$13$	−2.60834	+	1.50592i	−0.723422	+	0.417668i	−0.816011	−	0.578036i	$-0.803819\pi$
$13$	−2.60834	+	1.50592i	−0.723422	+	0.417668i	0.0925888	+	0.995704i	$0.470486\pi$
$14$		0			0
$15$		0			0
$16$	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	$0.807119\pi$
$18$		0			0
$19$	−3.96054	+	2.28662i	−0.908610	+	0.524586i	−0.879984	−	0.475004i	$-0.842447\pi$
$19$	−3.96054	+	2.28662i	−0.908610	+	0.524586i	−0.0286264	+	0.999590i	$0.509113\pi$
$20$	−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	0.473326	−	0.880887i	$-0.343053\pi$
$23$	−0.253614	−	0.146424i	−0.0528822	−	0.0305316i	−0.526208	+	0.850356i	$0.676387\pi$
$24$		0			0
$25$	−5.44735	−	9.43509i	−1.08947	−	1.88702i
$26$	−1.50592	−	2.60834i	−0.295336	−	0.511537i
$27$		0			0
$28$		0			0
$29$	3.18684	+	1.83992i	0.591781	+	0.341665i	0.765801	−	0.643077i	$-0.222343\pi$
$29$	3.18684	+	1.83992i	0.591781	+	0.341665i	−0.174020	+	0.984742i	$0.555676\pi$
$30$		0			0
$31$			4.71484i			0.846811i	0.905940	+	0.423405i	$0.139165\pi$
$31$			4.71484i			0.846811i	−0.905940	+	0.423405i	$0.860835\pi$
$32$			1.00000i			0.176777i
$33$		0			0
$34$	−6.45743	−	3.72820i	−1.10744	−	0.639381i
$35$		0			0
$36$		0			0
$37$	−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
$39$		0			0
$40$	−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
$45$		0			0
$46$	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	$0.961750\pi$
$48$		0			0
$49$		0			0
$50$	9.43509	−	5.44735i	1.33432	−	0.770372i
$51$		0			0
$52$	2.60834	−	1.50592i	0.361711	−	0.208834i
$53$	0.793421	+	0.458082i	0.108985	+	0.0629224i	0.553502	−	0.832848i	$-0.313291\pi$
$53$	0.793421	+	0.458082i	0.108985	+	0.0629224i	−0.444517	+	0.895770i	$0.646625\pi$
$54$		0			0
$55$			6.60330i			0.890388i
$56$		0			0
$57$		0			0
$58$	−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	$0.347847\pi$
$60$		0			0
$61$		−	6.64659i		−	0.851008i	−0.904957	−	0.425504i	$-0.860097\pi$
$61$		−	6.64659i		−	0.851008i	0.904957	−	0.425504i	$-0.139903\pi$
$62$	−4.71484			−0.598786
$63$		0			0
$64$	−1.00000			−0.125000
$65$			12.0077i			1.48937i
$66$		0			0
$67$	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			0
$70$		0			0
$71$			13.9437i			1.65481i	0.561605	+	0.827406i	$0.310184\pi$
$71$			13.9437i			1.65481i	−0.561605	+	0.827406i	$0.689816\pi$
$72$		0			0
$73$	−3.84574	−	2.22034i	−0.450110	−	0.259871i	0.257767	−	0.966207i	$-0.417013\pi$
$73$	−3.84574	−	2.22034i	−0.450110	−	0.259871i	−0.707877	+	0.706336i	$0.750347\pi$
$74$	5.20820	−	3.00695i	0.605441	−	0.349551i
$75$		0			0
$76$	3.96054	−	2.28662i	0.454305	−	0.262293i
$77$		0			0
$78$		0			0
$79$	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
$81$		0			0
$82$	−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
$87$		0			0
$88$	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			0
$91$		0			0
$92$	0.253614	+	0.146424i	0.0264411	+	0.0152658i
$93$		0			0
$94$		−	13.6124i		−	1.40402i
$95$			18.2327i			1.87063i
$96$		0			0
$97$	−2.51510	−	1.45209i	−0.255369	−	0.147438i	0.366851	−	0.930280i	$-0.380436\pi$
$97$	−2.51510	−	1.45209i	−0.255369	−	0.147438i	−0.622220	+	0.782842i	$0.713769\pi$
$98$		0			0
$99$		0			0
$100$	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	$0.837428\pi$
$102$		0			0
$103$	5.89979	+	3.40625i	0.581324	+	0.335627i	0.761659	−	0.647978i	$-0.224385\pi$
$103$	5.89979	+	3.40625i	0.581324	+	0.335627i	−0.180336	+	0.983605i	$0.557718\pi$
$104$	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	0.0164973	−	0.999864i	$-0.494749\pi$
$107$	9.21299	−	5.31912i	0.890653	−	0.514219i	0.874156	+	0.485645i	$0.161415\pi$
$108$		0			0
$109$	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			0
$112$		0			0
$113$	1.47530	−	0.851764i	0.138784	−	0.0801272i	−0.429000	−	0.903304i	$-0.641134\pi$
$113$	1.47530	−	0.851764i	0.138784	−	0.0801272i	0.567785	+	0.823177i	$0.307801\pi$
$114$		0			0
$115$	−1.01111	+	0.583767i	−0.0942868	+	0.0544365i
$116$	−3.18684	−	1.83992i	−0.295890	−	0.170832i
$117$		0			0
$118$			7.06674i			0.650546i
$119$		0			0
$120$		0			0
$121$	−4.12836	+	7.15054i	−0.375306	+	0.650049i
$122$	6.64659			0.601754
$123$		0			0
$124$		−	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
$129$		0			0
$130$	−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	$0.773612\pi$
$132$		0			0
$133$		0			0
$134$			4.05676i			0.350451i
$135$		0			0
$136$	6.45743	+	3.72820i	0.553720	+	0.319690i
$137$	−5.93663	+	3.42752i	−0.507201	+	0.292832i	−0.731682	−	0.681646i	$-0.761264\pi$
$137$	−5.93663	+	3.42752i	−0.507201	+	0.292832i	0.224482	+	0.974478i	$0.427931\pi$
$138$		0			0
$139$	−13.9583	+	8.05882i	−1.18393	+	0.683540i	−0.956920	−	0.290353i	$-0.906227\pi$
$139$	−13.9583	+	8.05882i	−1.18393	+	0.683540i	−0.227007	+	0.973893i	$0.572894\pi$
$140$		0			0
$141$		0			0
$142$	−13.9437			−1.17013
$143$	2.49423	−	4.32014i	0.208578	−	0.361268i
$144$		0			0
$145$	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	0.542576	−	0.840007i	$-0.317449\pi$
$149$	1.05460	+	0.608875i	0.0863964	+	0.0498810i	−0.456179	+	0.889888i	$0.650782\pi$
$150$		0			0
$151$	−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
$153$		0			0
$154$		0			0
$155$	16.2789	+	9.39861i	1.30755	+	0.754914i
$156$		0			0
$157$		−	23.5944i		−	1.88304i	−0.336957	−	0.941520i	$-0.609398\pi$
$157$		−	23.5944i		−	1.88304i	0.336957	−	0.941520i	$-0.390602\pi$
$158$			2.84730i			0.226519i
$159$		0			0
$160$	3.45268	+	1.99341i	0.272959	+	0.157593i
$161$		0			0
$162$		0			0
$163$	−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
$165$		0			0
$166$	−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
$171$		0			0
$172$	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	$0.652461\pi$
$174$		0			0
$175$		0			0
$176$	−1.43438	+	0.828141i	−0.108121	+	0.0624235i
$177$		0			0
$178$	−9.54128	+	5.50866i	−0.715149	+	0.412891i
$179$	−4.81618	−	2.78062i	−0.359978	−	0.207833i	0.309093	−	0.951032i	$-0.399975\pi$
$179$	−4.81618	−	2.78062i	−0.359978	−	0.207833i	−0.669071	+	0.743198i	$0.733308\pi$
$180$		0			0
$181$		−	12.5545i		−	0.933167i	−0.884477	−	0.466583i	$-0.845485\pi$
$181$		−	12.5545i		−	0.933167i	0.884477	−	0.466583i	$-0.154515\pi$
$182$		0			0
$183$		0			0
$184$	−0.146424	+	0.253614i	−0.0107945	+	0.0186967i
$185$	−23.9763			−1.76278
$186$		0			0
$187$		−	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	$-0.759783\pi$
$191$		−	18.9350i		−	1.37009i	0.728501	−	0.685045i	$-0.240217\pi$
$192$		0			0
$193$	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
$195$		0			0
$196$		0			0
$197$		−	6.04895i		−	0.430970i	−0.976507	−	0.215485i	$-0.930867\pi$
$197$		−	6.04895i		−	0.430970i	0.976507	−	0.215485i	$-0.0691332\pi$
$198$		0			0
$199$	19.8227	+	11.4446i	1.40519	+	0.811289i	0.994919	−	0.100674i	$-0.0320998\pi$
$199$	19.8227	+	11.4446i	1.40519	+	0.811289i	0.410274	+	0.911962i	$0.365433\pi$
$200$	−9.43509	+	5.44735i	−0.667162	+	0.385186i
$201$		0			0
$202$	0.223938	−	0.129291i	0.0157562	−	0.00909687i
$203$		0			0
$204$		0			0
$205$	38.9616			2.72120
$206$	−3.40625	+	5.89979i	−0.237324	+	0.411058i
$207$		0			0
$208$	−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
$213$		0			0
$214$	5.31912	+	9.21299i	0.363608	+	0.629787i
$215$	5.18132	+	8.97432i	0.353363	+	0.612043i
$216$		0			0
$217$		0			0
$218$	3.91248	+	2.25887i	0.264987	+	0.152990i
$219$		0			0
$220$		−	6.60330i		−	0.445194i
$221$		−	22.4575i		−	1.51066i
$222$		0			0
$223$	−7.85930	−	4.53757i	−0.526298	−	0.303858i	0.213210	−	0.977006i	$-0.431608\pi$
$223$	−7.85930	−	4.53757i	−0.526298	−	0.303858i	−0.739507	+	0.673148i	$0.764942\pi$
$224$		0			0
$225$		0			0
$226$	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	$0.826706\pi$
$228$		0			0
$229$	−16.0593	−	9.27182i	−1.06123	−	0.612699i	−0.135455	−	0.990784i	$-0.543250\pi$
$229$	−16.0593	−	9.27182i	−1.06123	−	0.612699i	−0.925771	+	0.378084i	$0.876583\pi$
$230$	−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	−0.174258	−	0.984700i	$-0.555753\pi$
$233$	9.02716	−	5.21183i	0.591389	−	0.341438i	0.765646	+	0.643262i	$0.222419\pi$
$234$		0			0
$235$	−27.1351	+	46.9994i	−1.77010	+	3.06591i
$236$	−7.06674			−0.460006
$237$		0			0
$238$		0			0
$239$	−5.88865	+	3.39981i	−0.380905	+	0.219915i	−0.678212	−	0.734866i	$-0.737245\pi$
$239$	−5.88865	+	3.39981i	−0.380905	+	0.219915i	0.297307	+	0.954782i	$0.403911\pi$
$240$		0			0
$241$	−16.3106	+	9.41695i	−1.05066	+	0.606599i	−0.922834	−	0.385197i	$-0.874133\pi$
$241$	−16.3106	+	9.41695i	−1.05066	+	0.606599i	−0.127826	+	0.991797i	$0.540800\pi$
$242$	−7.15054	−	4.12836i	−0.459654	−	0.265381i
$243$		0			0
$244$			6.64659i			0.425504i
$245$		0			0
$246$		0			0
$247$	6.88694	−	11.9285i	0.438206	−	0.758995i
$248$	4.71484			0.299393
$249$		0			0
$250$		−	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
$255$		0			0
$256$	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	$0.00938701\pi$
$258$		0			0
$259$		0			0
$260$		−	12.0077i		−	0.744685i
$261$		0			0
$262$	−18.7158	−	10.8056i	−1.15627	−	0.667571i
$263$	1.69410	−	0.978086i	0.104462	−	0.0603114i	−0.446859	−	0.894605i	$-0.647457\pi$
$263$	1.69410	−	0.978086i	0.104462	−	0.0603114i	0.551321	+	0.834293i	$0.314124\pi$
$264$		0			0
$265$	3.16322	−	1.82629i	0.194315	−	0.112188i
$266$		0			0
$267$		0			0
$268$	−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	$0.113449\pi$
$270$		0			0
$271$	−12.8145	+	7.39843i	−0.778423	+	0.449423i	−0.835871	−	0.548926i	$-0.815037\pi$
$271$	−12.8145	+	7.39843i	−0.778423	+	0.449423i	0.0574480	+	0.998348i	$0.481704\pi$
$272$	−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			0
$277$	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
$279$		0			0
$280$		0			0
$281$	−1.02488	−	0.591716i	−0.0611394	−	0.0352988i	0.469119	−	0.883135i	$-0.344572\pi$
$281$	−1.02488	−	0.591716i	−0.0611394	−	0.0352988i	−0.530258	+	0.847836i	$0.677905\pi$
$282$		0			0
$283$			29.5879i			1.75882i	0.476069	+	0.879408i	$0.342061\pi$
$283$			29.5879i			1.75882i	−0.476069	+	0.879408i	$0.657939\pi$
$284$		−	13.9437i		−	0.827406i
$285$		0			0
$286$	4.32014	+	2.49423i	0.255455	+	0.147487i
$287$		0			0
$288$		0			0
$289$	−19.2989	−	33.4267i	−1.13523	−	1.96628i
$290$	7.33543	+	12.7053i	0.430751	+	0.746083i
$291$		0			0
$292$	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
$297$		0			0
$298$	−0.608875	+	1.05460i	−0.0352712	+	0.0610915i
$299$	0.882015			0.0510082
$300$		0			0
$301$		0			0
$302$	12.1588	−	7.01991i	0.699662	−	0.403950i
$303$		0			0
$304$	−3.96054	+	2.28662i	−0.227153	+	0.131147i
$305$	−22.9486	−	13.2494i	−1.31403	−	0.758656i
$306$		0			0
$307$		−	3.34549i		−	0.190937i	−0.995432	−	0.0954686i	$-0.969565\pi$
$307$		−	3.34549i		−	0.190937i	0.995432	−	0.0954686i	$-0.0304350\pi$
$308$		0			0
$309$		0			0
$310$	−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			0
$313$		−	1.16835i		−	0.0660393i	−0.999455	−	0.0330196i	$-0.989488\pi$
$313$		−	1.16835i		−	0.0660393i	0.999455	−	0.0330196i	$-0.0105124\pi$
$314$	23.5944			1.33151
$315$		0			0
$316$	−2.84730			−0.160173
$317$		−	21.8039i		−	1.22463i	−0.790613	−	0.612316i	$-0.790238\pi$
$317$		−	21.8039i		−	1.22463i	0.790613	−	0.612316i	$-0.209762\pi$
$318$		0			0
$319$	−6.09486			−0.341247
$320$	−1.99341	+	3.45268i	−0.111435	+	0.193011i
$321$		0			0
$322$		0			0
$323$		−	34.0999i		−	1.89737i
$324$		0			0
$325$	28.4170	+	16.4066i	1.57629	+	0.910074i
$326$	0.518945	−	0.299613i	0.0287417	−	0.0165940i
$327$		0			0
$328$	8.46333	−	4.88630i	0.467309	−	0.269801i
$329$		0			0
$330$		0			0
$331$	−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
$333$		0			0
$334$	−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
$339$		0			0
$340$	−14.8636	−	25.7446i	−0.806094	−	1.39620i
$341$	−3.90456	−	6.76289i	−0.211444	−	0.366231i
$342$		0			0
$343$		0			0
$344$	2.25100	+	1.29961i	0.121366	+	0.0700705i
$345$		0			0
$346$		−	12.1235i		−	0.651764i
$347$			20.4956i			1.10026i	0.835078	+	0.550132i	$0.185423\pi$
$347$			20.4956i			1.10026i	−0.835078	+	0.550132i	$0.814577\pi$
$348$		0			0
$349$	−7.24341	−	4.18198i	−0.387731	−	0.223856i	0.293446	−	0.955976i	$-0.405198\pi$
$349$	−7.24341	−	4.18198i	−0.387731	−	0.223856i	−0.681176	+	0.732119i	$0.738531\pi$
$350$		0			0
$351$		0			0
$352$	−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	$0.781014\pi$
$354$		0			0
$355$	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	−0.626758	−	0.779214i	$-0.715618\pi$
$359$	−5.02704	+	2.90236i	−0.265317	+	0.153181i	0.361441	+	0.932395i	$0.382285\pi$
$360$		0			0
$361$	0.957250	−	1.65801i	0.0503816	−	0.0872634i
$362$	12.5545			0.659849
$363$		0			0
$364$		0			0
$365$	−15.3323	+	8.85209i	−0.802527	+	0.463339i
$366$		0			0
$367$	−5.16659	+	2.98293i	−0.269694	+	0.155708i	−0.628748	−	0.777609i	$-0.716432\pi$
$367$	−5.16659	+	2.98293i	−0.269694	+	0.155708i	0.359055	+	0.933317i	$0.383099\pi$
$368$	−0.253614	−	0.146424i	−0.0132206	−	0.00763289i
$369$		0			0
$370$		−	23.9763i		−	1.24647i
$371$		0			0
$372$		0			0
$373$	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
$375$		0			0
$376$			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
$381$		0			0
$382$	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			0
$385$		0			0
$386$			7.61465i			0.387576i
$387$		0			0
$388$	2.51510	+	1.45209i	0.127685	+	0.0737188i
$389$	7.24937	−	4.18543i	0.367558	−	0.212210i	−0.304833	−	0.952406i	$-0.598601\pi$
$389$	7.24937	−	4.18543i	0.367558	−	0.212210i	0.672391	+	0.740196i	$0.265267\pi$
$390$		0			0
$391$	1.89105	−	1.09180i	0.0956344	−	0.0552146i
$392$		0			0
$393$		0			0
$394$	6.04895			0.304741
$395$	5.67582	−	9.83081i	0.285582	−	0.494642i
$396$		0			0
$397$	−5.39937	+	3.11733i	−0.270987	+	0.156454i	−0.629336	−	0.777133i	$-0.716673\pi$
$397$	−5.39937	+	3.11733i	−0.270987	+	0.156454i	0.358349	+	0.933588i	$0.383340\pi$
$398$	−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	0.997752	−	0.0670106i	$-0.0213461\pi$
$401$	28.8079	+	16.6322i	1.43860	+	0.830573i	0.440843	+	0.897584i	$0.354679\pi$
$402$		0			0
$403$	−7.10019	−	12.2979i	−0.353686	−	0.612602i
$404$	0.129291	+	0.223938i	0.00643246	+	0.0111413i
$405$		0			0
$406$		0			0
$407$	8.62625	+	4.98037i	0.427587	+	0.246868i
$408$		0			0
$409$		−	20.3147i		−	1.00450i	−0.864723	−	0.502249i	$-0.832506\pi$
$409$		−	20.3147i		−	1.00450i	0.864723	−	0.502249i	$-0.167494\pi$
$410$			38.9616i			1.92418i
$411$		0			0
$412$	−5.89979	−	3.40625i	−0.290662	−	0.167814i
$413$		0			0
$414$		0			0
$415$	10.3431	+	17.9147i	0.507721	+	0.879399i
$416$	−1.50592	−	2.60834i	−0.0738340	−	0.127884i
$417$		0			0
$418$	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
$423$		0			0
$424$	0.458082	−	0.793421i	0.0222464	−	0.0385319i
$425$	81.2353			3.94049
$426$		0			0
$427$		0			0
$428$	−9.21299	+	5.31912i	−0.445327	+	0.257110i
$429$		0			0
$430$	−8.97432	+	5.18132i	−0.432780	+	0.249866i
$431$	23.0513	+	13.3087i	1.11034	+	0.641056i	0.938918	−	0.344142i	$-0.111830\pi$
$431$	23.0513	+	13.3087i	1.11034	+	0.641056i	0.171423	+	0.985197i	$0.445163\pi$
$432$		0			0
$433$			12.8312i			0.616628i	0.951285	+	0.308314i	$0.0997648\pi$
$433$			12.8312i			0.616628i	−0.951285	+	0.308314i	$0.900235\pi$
$434$		0			0
$435$		0			0
$436$	−2.25887	+	3.91248i	−0.108180	+	0.187374i
$437$	1.33927			0.0640658
$438$		0			0
$439$			23.4359i			1.11853i	0.828988	+	0.559266i	$0.188917\pi$
$439$			23.4359i			1.11853i	−0.828988	+	0.559266i	$0.811083\pi$
$440$	6.60330			0.314800
$441$		0			0
$442$	22.4575			1.06820
$443$			18.5863i			0.883062i	0.897246	+	0.441531i	$0.145564\pi$
$443$			18.5863i			0.883062i	−0.897246	+	0.441531i	$0.854436\pi$
$444$		0			0
$445$	43.9240			2.08220
$446$	4.53757	−	7.85930i	0.214860	−	0.372149i
$447$		0			0
$448$		0			0
$449$			22.7518i			1.07372i	0.843670	+	0.536862i	$0.180390\pi$
$449$			22.7518i			1.07372i	−0.843670	+	0.536862i	$0.819610\pi$
$450$		0			0
$451$	−14.0177	−	8.09310i	−0.660066	−	0.381089i
$452$	−1.47530	+	0.851764i	−0.0693922	+	0.0400636i
$453$		0			0
$454$	−0.543310	+	0.313680i	−0.0254988	+	0.0147217i
$455$		0			0
$456$		0			0
$457$	−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
$459$		0			0
$460$	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
$465$		0			0
$466$	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	$0.986427\pi$
$468$		0			0
$469$		0			0
$470$	−46.9994	−	27.1351i	−2.16792	−	1.25165i
$471$		0			0
$472$		−	7.06674i		−	0.325273i
$473$		−	4.30506i		−	0.197947i
$474$		0			0
$475$	43.1489	+	24.9120i	1.97981	+	1.14304i
$476$		0			0
$477$		0			0
$478$	−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	$0.754999\pi$
$480$		0			0
$481$	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
$486$		0			0
$487$	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			0
$490$		0			0
$491$	−20.4285	+	11.7944i	−0.921927	+	0.532275i	−0.884249	−	0.467015i	$-0.845329\pi$
$491$	−20.4285	+	11.7944i	−0.921927	+	0.532275i	−0.0376778	+	0.999290i	$0.511996\pi$
$492$		0			0
$493$	−23.7623	+	13.7192i	−1.07020	+	0.617881i
$494$	11.9285	+	6.88694i	0.536690	+	0.309858i
$495$		0			0
$496$			4.71484i			0.211703i
$497$		0			0
$498$		0			0
$499$	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			0
$502$			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
$507$		0			0
$508$	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	$0.136446\pi$
$510$		0			0
$511$		0			0
$512$			1.00000i			0.0441942i
$513$		0			0
$514$	13.1684	+	7.60276i	0.580832	+	0.335343i
$515$	23.5214	−	13.5801i	1.03648	−	0.598410i
$516$		0			0
$517$	19.5254	−	11.2730i	0.858728	−	0.495787i
$518$		0			0
$519$		0			0
$520$	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	$0.110027\pi$
$522$		0			0
$523$	−28.4937	+	16.4508i	−1.24594	+	0.719344i	−0.970297	−	0.241916i	$-0.922224\pi$
$523$	−28.4937	+	16.4508i	−1.24594	+	0.719344i	−0.275643	+	0.961260i	$0.588891\pi$
$524$	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
$528$		0			0
$529$	−11.4571	−	19.8443i	−0.498136	−	0.862796i
$530$	1.82629	+	3.16322i	0.0793289	+	0.137402i
$531$		0			0
$532$		0			0
$533$	−25.4902	−	14.7168i	−1.10410	−	0.637455i
$534$		0			0
$535$		−	42.4127i		−	1.83366i
$536$		−	4.05676i		−	0.175225i
$537$		0			0
$538$	4.72739	+	2.72936i	0.203812	+	0.117671i
$539$		0			0
$540$		0			0
$541$	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
$543$		0			0
$544$	−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
$549$		0			0
$550$	−9.02236	+	15.6272i	−0.384715	+	0.666345i
$551$	−16.8288			−0.716931
$552$		0			0
$553$		0			0
$554$	−9.06963	+	5.23636i	−0.385332	+	0.222471i
$555$		0			0
$556$	13.9583	−	8.05882i	0.591963	−	0.341770i
$557$	36.1910	+	20.8949i	1.53346	+	0.885345i	0.999199	+	0.0400275i	$0.0127445\pi$
$557$	36.1910	+	20.8949i	1.53346	+	0.885345i	0.534264	+	0.845318i	$0.320589\pi$
$558$		0			0
$559$		−	7.82848i		−	0.331109i
$560$		0			0
$561$		0			0
$562$	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	$0.437459\pi$
$564$		0			0
$565$		−	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	$0.0898297\pi$
$569$			13.2854i			0.556955i	−0.960443	+	0.278477i	$0.910170\pi$
$570$		0			0
$571$	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
$573$		0			0
$574$		0			0
$575$			3.19050i			0.133053i
$576$		0			0
$577$	17.5971	+	10.1597i	0.732575	+	0.422952i	0.819364	−	0.573274i	$-0.194327\pi$
$577$	17.5971	+	10.1597i	0.732575	+	0.422952i	−0.0867884	+	0.996227i	$0.527660\pi$
$578$	33.4267	−	19.2989i	1.39037	−	0.802730i
$579$		0			0
$580$	−12.7053	+	7.33543i	−0.527560	+	0.304587i
$581$		0			0
$582$		0			0
$583$	−1.51743			−0.0628454
$584$	−2.22034	+	3.84574i	−0.0918783	+	0.159138i
$585$		0			0
$586$	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
$591$		0			0
$592$	−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	$0.629174\pi$
$594$		0			0
$595$		0			0
$596$	−1.05460	−	0.608875i	−0.0431982	−	0.0249405i
$597$		0			0
$598$			0.882015i			0.0360683i
$599$		−	36.9120i		−	1.50818i	−0.656768	−	0.754092i	$-0.728077\pi$
$599$		−	36.9120i		−	1.50818i	0.656768	−	0.754092i	$-0.271923\pi$
$600$		0			0
$601$	−33.3809	−	19.2725i	−1.36164	−	0.786141i	−0.371795	−	0.928315i	$-0.621257\pi$
$601$	−33.3809	−	19.2725i	−1.36164	−	0.786141i	−0.989842	+	0.142174i	$0.954591\pi$
$602$		0			0
$603$		0			0
$604$	7.01991	+	12.1588i	0.285636	+	0.494736i
$605$	16.4590	+	28.5079i	0.669155	+	1.15901i
$606$		0			0
$607$	21.2299	+	12.2571i	0.861696	+	0.497500i	0.864580	−	0.502495i	$-0.167585\pi$
$607$	21.2299	+	12.2571i	0.861696	+	0.497500i	−0.00288390	+	0.999996i	$0.500918\pi$
$608$	−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
$612$		0			0
$613$	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
$615$		0			0
$616$		0			0
$617$	−32.4708	+	18.7470i	−1.30723	+	0.754727i	−0.981632	−	0.190783i	$-0.938897\pi$
$617$	−32.4708	+	18.7470i	−1.30723	+	0.754727i	−0.325593	+	0.945510i	$0.605564\pi$
$618$		0			0
$619$	−17.1863	+	9.92249i	−0.690774	+	0.398819i	−0.803902	−	0.594762i	$-0.797246\pi$
$619$	−17.1863	+	9.92249i	−0.690774	+	0.398819i	0.113128	+	0.993580i	$0.463913\pi$
$620$	−16.2789	−	9.39861i	−0.653775	−	0.377457i
$621$		0			0
$622$		−	22.7834i		−	0.913531i
$623$		0			0
$624$		0			0
$625$	−19.6105	+	33.9664i	−0.784421	+	1.35866i
$626$	1.16835			0.0466968
$627$		0			0
$628$			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			0
$634$	21.8039			0.865945
$635$	−9.83154	+	17.0287i	−0.390153	+	0.675765i
$636$		0			0
$637$		0			0
$638$		−	6.09486i		−	0.241298i
$639$		0			0
$640$	−3.45268	−	1.99341i	−0.136479	−	0.0787964i
$641$	−19.6930	+	11.3697i	−0.777826	+	0.449078i	−0.835659	−	0.549248i	$-0.814914\pi$
$641$	−19.6930	+	11.3697i	−0.777826	+	0.449078i	0.0578333	+	0.998326i	$0.481581\pi$
$642$		0			0
$643$	42.7821	−	24.7003i	1.68716	−	0.974084i	0.730488	−	0.682926i	$-0.239293\pi$
$643$	42.7821	−	24.7003i	1.68716	−	0.974084i	0.956675	−	0.291158i	$-0.0940406\pi$
$644$		0			0
$645$		0			0
$646$	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	$0.814786\pi$
$648$		0			0
$649$	−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	−0.285009	−	0.958525i	$-0.591997\pi$
$653$	−32.1371	−	18.5543i	−1.25762	−	0.726088i	−0.972611	+	0.232437i	$0.925330\pi$
$654$		0			0
$655$	43.0799	+	74.6165i	1.68327	+	2.91551i
$656$	4.88630	+	8.46333i	0.190778	+	0.330437i
$657$		0			0
$658$		0			0
$659$	37.9735	+	21.9240i	1.47924	+	0.854039i	0.999724	−	0.0234944i	$-0.00747920\pi$
$659$	37.9735	+	21.9240i	1.47924	+	0.854039i	0.479515	+	0.877534i	$0.340813\pi$
$660$		0			0
$661$			24.4069i			0.949317i	0.880170	+	0.474659i	$0.157428\pi$
$661$			24.4069i			0.949317i	−0.880170	+	0.474659i	$0.842572\pi$
$662$		−	27.8854i		−	1.08380i
$663$		0			0
$664$	4.49349	+	2.59432i	0.174381	+	0.100679i
$665$		0			0
$666$		0			0
$667$	−0.538818	−	0.933261i	−0.0208631	−	0.0361360i
$668$	−2.67267	−	4.62919i	−0.103409	−	0.179109i
$669$		0			0
$670$	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
$675$		0			0
$676$	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			0
$679$		0			0
$680$	25.7446	−	14.8636i	0.987260	−	0.569995i
$681$		0			0
$682$	6.76289	−	3.90456i	0.258964	−	0.149513i
$683$	8.29828	+	4.79102i	0.317525	+	0.183323i	0.650289	−	0.759687i	$-0.274648\pi$
$683$	8.29828	+	4.79102i	0.317525	+	0.183323i	−0.332764	+	0.943010i	$0.607981\pi$
$684$		0			0
$685$			27.3298i			1.04422i
$686$		0			0
$687$		0			0
$688$	−1.29961	+	2.25100i	−0.0495473	+	0.0858185i
$689$	−2.75934			−0.105123
$690$		0			0
$691$			0.438731i			0.0166901i	0.999965	+	0.00834506i	$0.00265635\pi$
$691$			0.438731i			0.0166901i	−0.999965	+	0.00834506i	$0.997344\pi$
$692$	12.1235			0.460867
$693$		0			0
$694$	−20.4956			−0.778004
$695$			64.2581i			2.43745i
$696$		0			0
$697$	−72.8685			−2.76009
$698$	4.18198	−	7.24341i	0.158290	−	0.274167i
$699$		0			0
$700$		0			0
$701$		−	29.7259i		−	1.12273i	−0.827568	−	0.561366i	$-0.810276\pi$
$701$		−	29.7259i		−	1.12273i	0.827568	−	0.561366i	$-0.189724\pi$
$702$		0			0
$703$	23.8183	+	13.7515i	0.898325	+	0.518648i
$704$	1.43438	−	0.828141i	0.0540603	−	0.0312118i
$705$		0			0
$706$	−5.32484	+	3.07430i	−0.200403	+	0.115703i
$707$		0			0
$708$		0			0
$709$	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
$711$		0			0
$712$	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
$717$		0			0
$718$	−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	$0.931340\pi$
$720$		0			0
$721$		0			0
$722$	1.65801	+	0.957250i	0.0617046	+	0.0356252i
$723$		0			0
$724$			12.5545i			0.466583i
$725$		−	40.0908i		−	1.48894i
$726$		0			0
$727$	25.4656	+	14.7026i	0.944468	+	0.545289i	0.891358	−	0.453300i	$-0.149753\pi$
$727$	25.4656	+	14.7026i	0.944468	+	0.545289i	0.0531099	+	0.998589i	$0.483087\pi$
$728$		0			0
$729$		0			0
$730$	−8.85209	−	15.3323i	−0.327630	−	0.567473i
$731$	−9.69044	−	16.7843i	−0.358414	−	0.620791i
$732$		0			0
$733$	−31.9175	−	18.4276i	−1.17890	−	0.680638i	−0.223139	−	0.974787i	$-0.571631\pi$
$733$	−31.9175	−	18.4276i	−1.17890	−	0.680638i	−0.955760	+	0.294149i	$0.904964\pi$
$734$	−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
$738$		0			0
$739$	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
$741$		0			0
$742$		0			0
$743$	28.2201	−	16.2929i	1.03530	−	0.597729i	0.116799	−	0.993156i	$-0.462737\pi$
$743$	28.2201	−	16.2929i	1.03530	−	0.597729i	0.918497	+	0.395427i	$0.129403\pi$
$744$		0			0
$745$	4.20451	−	2.42747i	0.154041	−	0.0889357i
$746$	16.3383	+	9.43291i	0.598187	+	0.345363i
$747$		0			0
$748$			12.3499i			0.451557i
$749$		0			0
$750$		0			0
$751$	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			0
$754$		−	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			0
$760$	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	$-0.0461572\pi$
$762$		0			0
$763$		0			0
$764$			18.9350i			0.685045i
$765$		0			0
$766$	−0.146310	−	0.0844724i	−0.00528641	−	0.00305211i
$767$	−18.4324	+	10.6420i	−0.665556	+	0.384259i
$768$		0			0
$769$	−28.9909	+	16.7379i	−1.04544	+	0.603585i	−0.921369	−	0.388688i	$-0.872928\pi$
$769$	−28.9909	+	16.7379i	−1.04544	+	0.603585i	−0.124071	+	0.992273i	$0.539595\pi$
$770$		0			0
$771$		0			0
$772$	−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			0
$775$	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
$780$		0			0
$781$	−11.5473	−	20.0006i	−0.413196	−	0.715677i
$782$	1.09180	+	1.89105i	0.0390426	+	0.0676238i
$783$		0			0
$784$		0			0
$785$	−81.4641	−	47.0333i	−2.90758	−	1.67869i
$786$		0			0
$787$		−	6.01310i		−	0.214344i	−0.994241	−	0.107172i	$-0.965820\pi$
$787$		−	6.01310i		−	0.214344i	0.994241	−	0.107172i	$-0.0341795\pi$
$788$			6.04895i			0.215485i
$789$		0			0
$790$	9.83081	+	5.67582i	0.349765	+	0.201937i
$791$		0			0
$792$		0			0
$793$	10.0092	+	17.3365i	0.355439	+	0.615638i
$794$	−3.11733	−	5.39937i	−0.110630	−	0.191616i
$795$		0			0
$796$	−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
$801$		0			0
$802$	−16.6322	+	28.8079i	−0.587304	+	1.01724i
$803$	7.35502			0.259553
$804$		0			0
$805$		0			0
$806$	12.2979	−	7.10019i	0.433175	−	0.250094i
$807$		0			0
$808$	−0.223938	+	0.129291i	−0.00787812	+	0.00454844i
$809$	−2.92768	−	1.69030i	−0.102932	−	0.0594278i	0.447650	−	0.894209i	$-0.352261\pi$
$809$	−2.92768	−	1.69030i	−0.102932	−	0.0594278i	−0.550582	+	0.834781i	$0.685594\pi$
$810$		0			0
$811$			38.2801i			1.34419i	0.740463	+	0.672097i	$0.234606\pi$
$811$			38.2801i			1.34419i	−0.740463	+	0.672097i	$0.765394\pi$
$812$		0			0
$813$		0			0
$814$	−4.98037	+	8.62625i	−0.174562	+	0.302350i
$815$	−2.38901			−0.0836832
$816$		0			0
$817$		−	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	$0.192108\pi$
$821$			32.5240i			1.13509i	−0.823341	+	0.567547i	$0.807892\pi$
$822$		0			0
$823$	−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
$825$		0			0
$826$		0			0
$827$		−	26.0812i		−	0.906933i	−0.891273	−	0.453466i	$-0.850187\pi$
$827$		−	26.0812i		−	0.906933i	0.891273	−	0.453466i	$-0.149813\pi$
$828$		0			0
$829$	17.9479	+	10.3622i	0.623357	+	0.359896i	0.778175	−	0.628047i	$-0.216146\pi$
$829$	17.9479	+	10.3622i	0.623357	+	0.359896i	−0.154818	+	0.987943i	$0.549479\pi$
$830$	−17.9147	+	10.3431i	−0.621829	+	0.359013i
$831$		0			0
$832$	2.60834	−	1.50592i	0.0904278	−	0.0522085i
$833$		0			0
$834$		0			0
$835$	21.3109			0.737493
$836$	−3.78729	+	6.55977i	−0.130986	+	0.226875i
$837$		0			0
$838$	−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
$843$		0			0
$844$	−3.36942	−	5.83601i	−0.115980	−	0.200884i
$845$	7.83166	+	13.5648i	0.269417	+	0.466645i
$846$		0			0
$847$		0			0
$848$	0.793421	+	0.458082i	0.0272462	+	0.0157306i
$849$		0			0
$850$			81.2353i			2.78635i
$851$			1.76116i			0.0603719i
$852$		0			0
$853$	30.3664	+	17.5321i	1.03973	+	0.600287i	0.919756	−	0.392490i	$-0.128386\pi$
$853$	30.3664	+	17.5321i	1.03973	+	0.600287i	0.119971	+	0.992777i	$0.461720\pi$
$854$		0			0
$855$		0			0
$856$	−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	$0.679250\pi$
$858$		0			0
$859$	−6.42983	−	3.71226i	−0.219383	−	0.126661i	0.386282	−	0.922381i	$-0.373759\pi$
$859$	−6.42983	−	3.71226i	−0.219383	−	0.126661i	−0.605664	+	0.795720i	$0.707093\pi$
$860$	−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	0.0827837	−	0.996568i	$-0.473619\pi$
$863$	29.0017	−	16.7441i	0.987228	−	0.569977i	0.904445	+	0.426591i	$0.140286\pi$
$864$		0			0
$865$	−24.1671	+	41.8587i	−0.821707	+	1.42324i
$866$	−12.8312			−0.436022
$867$		0			0
$868$		0			0
$869$	−4.08411	+	2.35796i	−0.138544	+	0.0799885i
$870$		0			0
$871$	−10.5814	+	6.10917i	−0.358537	+	0.207001i
$872$	−3.91248	−	2.25887i	−0.132493	−	0.0764951i
$873$		0			0
$874$			1.33927i			0.0453013i
$875$		0			0
$876$		0			0
$877$	−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			0
$880$			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
$885$		0			0
$886$	−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	$0.110646\pi$
$888$		0			0
$889$		0			0
$890$			43.9240i			1.47234i
$891$		0			0
$892$	7.85930	+	4.53757i	0.263149	+	0.151929i
$893$	53.9126	−	31.1264i	1.80412	−	1.04161i
$894$		0			0
$895$	−19.2012	+	11.0858i	−0.641826	+	0.370558i
$896$		0			0
$897$		0			0
$898$	−22.7518			−0.759237
$899$	−8.67494	+	15.0254i	−0.289326	+	0.501127i
$900$		0			0
$901$	−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
$906$		0			0
$907$	−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			0
$910$		0			0
$911$	−6.57136	−	3.79398i	−0.217719	−	0.125700i	0.387175	−	0.922006i	$-0.373451\pi$
$911$	−6.57136	−	3.79398i	−0.217719	−	0.125700i	−0.604894	+	0.796306i	$0.706784\pi$
$912$		0			0
$913$		−	8.59384i		−	0.284415i
$914$		−	26.5061i		−	0.876744i
$915$		0			0
$916$	16.0593	+	9.27182i	0.530613	+	0.306350i
$917$		0			0
$918$		0			0
$919$	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
$921$		0			0
$922$	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
$927$		0			0
$928$	−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	$0.647378\pi$
$930$		0			0
$931$		0			0
$932$	−9.02716	+	5.21183i	−0.295694	+	0.170719i
$933$		0			0
$934$	17.3161	−	9.99748i	0.566602	−	0.327128i
$935$	−42.6403	−	24.6184i	−1.39449	−	0.805108i
$936$		0			0
$937$		−	51.0665i		−	1.66827i	−0.551562	−	0.834134i	$-0.685968\pi$
$937$		−	51.0665i		−	1.66827i	0.551562	−	0.834134i	$-0.314032\pi$
$938$		0			0
$939$		0			0
$940$	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	$0.226765\pi$
$942$		0			0
$943$		−	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	$-0.804217\pi$
$947$		−	35.5135i		−	1.15403i	0.816733	−	0.577016i	$-0.195783\pi$
$948$		0			0
$949$	13.3746			0.434159
$950$	−24.9120	+	43.1489i	−0.808253	+	1.39994i
$951$		0			0
$952$		0			0
$953$			10.1647i			0.329268i	0.986355	+	0.164634i	$0.0526443\pi$
$953$			10.1647i			0.329268i	−0.986355	+	0.164634i	$0.947356\pi$
$954$		0			0
$955$	−65.3766	−	37.7452i	−2.11554	−	1.22141i
$956$	5.88865	−	3.39981i	0.190452	−	0.109958i
$957$		0			0
$958$	−9.23507	+	5.33187i	−0.298371	+	0.172265i
$959$		0			0
$960$		0			0
$961$	8.77026			0.282911
$962$	−9.05648	+	15.6863i	−0.291993	+	0.505746i
$963$		0			0
$964$	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
$969$		0			0
$970$	−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	$0.985455\pi$
$972$		0			0
$973$		0			0
$974$	14.6560	+	8.46164i	0.469608	+	0.271128i
$975$		0			0
$976$		−	6.64659i		−	0.212752i
$977$			29.4022i			0.940661i	0.882490	+	0.470330i	$0.155865\pi$
$977$			29.4022i			0.940661i	−0.882490	+	0.470330i	$0.844135\pi$
$978$		0			0
$979$	−15.8031	−	9.12390i	−0.505068	−	0.291601i
$980$		0			0
$981$		0			0
$982$	−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	$0.989156\pi$
$984$		0			0
$985$	−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
$990$		0			0
$991$	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
$993$		0			0
$994$		0			0
$995$	79.0294	−	45.6277i	2.50540	−	1.44649i
$996$		0			0
$997$	29.1701	−	16.8414i	0.923828	−	0.533372i	0.0389734	−	0.999240i	$-0.487591\pi$
$997$	29.1701	−	16.8414i	0.923828	−	0.533372i	0.884854	+	0.465868i	$0.154258\pi$
$998$	5.85111	+	3.37814i	0.185214	+	0.106933i
$999$		0			0

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
882.2.l.c.227.3		48	3.2	odd	2
882.2.l.c.227.10		48	21.20	even	2
882.2.l.c.509.15		48	63.40	odd	6
882.2.l.c.509.22		48	63.58	even	3
882.2.m.c.293.18	✓	48	63.4	even	3
882.2.m.c.293.19	yes	48	63.31	odd	6
882.2.m.c.587.18	yes	48	21.17	even	6
882.2.m.c.587.19	yes	48	21.11	odd	6
882.2.t.c.803.3		48	21.5	even	6
882.2.t.c.803.10		48	21.2	odd	6
882.2.t.c.815.3		48	9.4	even	3
882.2.t.c.815.10		48	63.13	odd	6
2646.2.l.c.521.1		48	7.6	odd	2	inner
2646.2.l.c.521.2		48	1.1	even	1	trivial
2646.2.l.c.1097.1		48	63.23	odd	6	inner
2646.2.l.c.1097.2		48	63.5	even	6	inner
2646.2.m.c.881.1		48	63.32	odd	6
2646.2.m.c.881.2		48	63.59	even	6
2646.2.m.c.1763.1		48	7.3	odd	6
2646.2.m.c.1763.2		48	7.4	even	3
2646.2.t.c.1979.13		48	7.2	even	3
2646.2.t.c.1979.14		48	7.5	odd	6
2646.2.t.c.2285.13		48	63.41	even	6
2646.2.t.c.2285.14		48	9.5	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:	\( N \)	\(=\)	\( 2646 = 2 \cdot 3^{3} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2646.l (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} -1.00000 q^{4} +(1.99341 - 3.45268i) q^{5} -1.00000i q^{8} +O(q^{10})\)	\(q+1.00000i q^{2} -1.00000 q^{4} +(1.99341 - 3.45268i) q^{5} -1.00000i q^{8} +(3.45268 + 1.99341i) q^{10} +(-1.43438 + 0.828141i) q^{11} +(-2.60834 + 1.50592i) q^{13} +1.00000 q^{16} +(-3.72820 + 6.45743i) q^{17} +(-3.96054 + 2.28662i) q^{19} +(-1.99341 + 3.45268i) q^{20} +(-0.828141 - 1.43438i) q^{22} +(-0.253614 - 0.146424i) q^{23} +(-5.44735 - 9.43509i) q^{25} +(-1.50592 - 2.60834i) q^{26} +(3.18684 + 1.83992i) q^{29} +4.71484i q^{31} +1.00000i q^{32} +(-6.45743 - 3.72820i) q^{34} +(-3.00695 - 5.20820i) q^{37} +(-2.28662 - 3.96054i) q^{38} +(-3.45268 - 1.99341i) q^{40} +(4.88630 + 8.46333i) q^{41} +(-1.29961 + 2.25100i) q^{43} +(1.43438 - 0.828141i) q^{44} +(0.146424 - 0.253614i) q^{46} -13.6124 q^{47} +(9.43509 - 5.44735i) q^{50} +(2.60834 - 1.50592i) q^{52} +(0.793421 + 0.458082i) q^{53} +6.60330i q^{55} +(-1.83992 + 3.18684i) q^{58} +7.06674 q^{59} -6.64659i q^{61} -4.71484 q^{62} -1.00000 q^{64} +12.0077i q^{65} +4.05676 q^{67} +(3.72820 - 6.45743i) q^{68} +13.9437i q^{71} +(-3.84574 - 2.22034i) q^{73} +(5.20820 - 3.00695i) q^{74} +(3.96054 - 2.28662i) q^{76} +2.84730 q^{79} +(1.99341 - 3.45268i) q^{80} +(-8.46333 + 4.88630i) q^{82} +(-2.59432 + 4.49349i) q^{83} +(14.8636 + 25.7446i) q^{85} +(-2.25100 - 1.29961i) q^{86} +(0.828141 + 1.43438i) q^{88} +(5.50866 + 9.54128i) q^{89} +(0.253614 + 0.146424i) q^{92} -13.6124i q^{94} +18.2327i q^{95} +(-2.51510 - 1.45209i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 48 q^{4}+O(q^{10}) \) 48 * q - 48 * q^4	\( 48 q - 48 q^{4} + 48 q^{11} + 48 q^{16} + 48 q^{23} - 24 q^{25} - 48 q^{44} + 48 q^{50} - 96 q^{53} - 48 q^{64} - 96 q^{79} + 48 q^{85} + 96 q^{86} - 48 q^{92}+O(q^{100}) \) 48 * q - 48 * q^4 + 48 * q^11 + 48 * q^16 + 48 * q^23 - 24 * q^25 - 48 * q^44 + 48 * q^50 - 96 * q^53 - 48 * q^64 - 96 * q^79 + 48 * q^85 + 96 * q^86 - 48 * q^92

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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