LMFDB - Embedded newform 864.2.y.c.193.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(864, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 0, 4]))

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

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

chi := DirichletCharacter("864.97");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 864 = 2^{5} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	864.y (of order $9$, degree $6$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$6.89907473464$
Analytic rank:	$0$
Dimension:	$54$
Relative dimension:	$9$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			193.3
Character	$\chi$	$=$	864.193
Dual form			864.2.y.c.385.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.17779 - 1.26996i) q^{3} +(0.191385 - 1.08540i) q^{5} +(-2.62195 + 2.20007i) q^{7} +(-0.225616 + 2.99150i) q^{9} +O(q^{10})$	\(q+(-1.17779 - 1.26996i) q^{3} +(0.191385 - 1.08540i) q^{5} +(-2.62195 + 2.20007i) q^{7} +(-0.225616 + 2.99150i) q^{9} +(0.0811727 + 0.460354i) q^{11} +(3.01725 - 1.09819i) q^{13} +(-1.60382 + 1.03532i) q^{15} +(-0.185192 + 0.320761i) q^{17} +(2.75617 + 4.77383i) q^{19} +(5.88212 + 0.738549i) q^{21} +(-0.107304 - 0.0900389i) q^{23} +(3.55701 + 1.29464i) q^{25} +(4.06483 - 3.23684i) q^{27} +(1.79039 + 0.651649i) q^{29} +(-2.20938 - 1.85389i) q^{31} +(0.489028 - 0.645287i) q^{33} +(1.88615 + 3.26691i) q^{35} +(2.32289 - 4.02336i) q^{37} +(-4.94836 - 2.53836i) q^{39} +(0.00243859 - 0.000887575i) q^{41} +(1.18135 + 6.69975i) q^{43} +(3.20379 + 0.817411i) q^{45} +(6.94945 - 5.83128i) q^{47} +(0.818739 - 4.64330i) q^{49} +(0.625473 - 0.142603i) q^{51} +10.8925 q^{53} +0.515201 q^{55} +(2.81640 - 9.12281i) q^{57} +(1.70529 - 9.67117i) q^{59} +(-8.40201 + 7.05012i) q^{61} +(-5.98998 - 8.33994i) q^{63} +(-0.614516 - 3.48509i) q^{65} +(3.98327 - 1.44979i) q^{67} +(0.0120358 + 0.242320i) q^{69} +(-0.776845 + 1.34554i) q^{71} +(7.58782 + 13.1425i) q^{73} +(-2.54526 - 6.04209i) q^{75} +(-1.22564 - 1.02844i) q^{77} +(-8.87740 - 3.23111i) q^{79} +(-8.89819 - 1.34986i) q^{81} +(16.2493 + 5.91426i) q^{83} +(0.312710 + 0.262395i) q^{85} +(-1.28114 - 3.04124i) q^{87} +(6.38441 + 11.0581i) q^{89} +(-5.49498 + 9.51758i) q^{91} +(0.247815 + 4.98934i) q^{93} +(5.70899 - 2.07790i) q^{95} +(-0.597491 - 3.38854i) q^{97} +(-1.39546 + 0.138965i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 54 q+O(q^{10}) $ 54 * q	$ 54 q + 9 q^{11} + 12 q^{17} - 18 q^{19} + 12 q^{21} + 21 q^{27} + 6 q^{29} - 36 q^{31} - 9 q^{33} - 24 q^{39} + 3 q^{41} + 21 q^{43} + 42 q^{45} - 18 q^{49} - 24 q^{51} + 36 q^{53} + 72 q^{55} + 39 q^{57} - 18 q^{59} - 18 q^{61} + 30 q^{63} + 48 q^{65} + 27 q^{67} + 24 q^{69} + 84 q^{75} + 36 q^{77} - 72 q^{79} + 36 q^{81} - 6 q^{87} + 33 q^{89} - 36 q^{91} + 72 q^{93} - 36 q^{95} + 9 q^{97} - 120 q^{99}+O(q^{100}) $ 54 * q + 9 * q^11 + 12 * q^17 - 18 * q^19 + 12 * q^21 + 21 * q^27 + 6 * q^29 - 36 * q^31 - 9 * q^33 - 24 * q^39 + 3 * q^41 + 21 * q^43 + 42 * q^45 - 18 * q^49 - 24 * q^51 + 36 * q^53 + 72 * q^55 + 39 * q^57 - 18 * q^59 - 18 * q^61 + 30 * q^63 + 48 * q^65 + 27 * q^67 + 24 * q^69 + 84 * q^75 + 36 * q^77 - 72 * q^79 + 36 * q^81 - 6 * q^87 + 33 * q^89 - 36 * q^91 + 72 * q^93 - 36 * q^95 + 9 * q^97 - 120 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−1.17779	−	1.26996i	−0.679998	−	0.733214i
$3$	−1.17779	−	1.26996i	−0.679998	−	0.733214i
$4$		0			0
$5$	0.191385	−	1.08540i	0.0855898	−	0.485404i	−0.911638	−	0.410994i	$-0.865182\pi$
$5$	0.191385	−	1.08540i	0.0855898	−	0.485404i	0.997228	−	0.0744097i	$-0.0237073\pi$
$6$		0			0
$7$	−2.62195	+	2.20007i	−0.991003	+	0.831550i	−0.985713	−	0.168436i	$-0.946128\pi$
$7$	−2.62195	+	2.20007i	−0.991003	+	0.831550i	−0.00529006	+	0.999986i	$0.501684\pi$
$8$		0			0
$9$	−0.225616	+	2.99150i	−0.0752055	+	0.997168i
$10$		0			0
$11$	0.0811727	+	0.460354i	0.0244745	+	0.138802i	0.994597	−	0.103816i	$-0.0331052\pi$
$11$	0.0811727	+	0.460354i	0.0244745	+	0.138802i	−0.970122	+	0.242617i	$0.921994\pi$
$12$		0			0
$13$	3.01725	−	1.09819i	0.836836	−	0.304583i	0.112175	−	0.993689i	$-0.464218\pi$
$13$	3.01725	−	1.09819i	0.836836	−	0.304583i	0.724661	+	0.689105i	$0.241996\pi$
$14$		0			0
$15$	−1.60382	+	1.03532i	−0.414106	+	0.267318i
$16$		0			0
$17$	−0.185192	+	0.320761i	−0.0449156	+	0.0777961i	−0.887609	−	0.460597i	$-0.847635\pi$
$17$	−0.185192	+	0.320761i	−0.0449156	+	0.0777961i	0.842694	+	0.538393i	$0.180969\pi$
$18$		0			0
$19$	2.75617	+	4.77383i	0.632309	+	1.09519i	0.987078	+	0.160238i	$0.0512261\pi$
$19$	2.75617	+	4.77383i	0.632309	+	1.09519i	−0.354769	+	0.934954i	$0.615441\pi$
$20$		0			0
$21$	5.88212	+	0.738549i	1.28358	+	0.161165i
$22$		0			0
$23$	−0.107304	−	0.0900389i	−0.0223745	−	0.0187744i	0.631532	−	0.775350i	$-0.282427\pi$
$23$	−0.107304	−	0.0900389i	−0.0223745	−	0.0187744i	−0.653906	+	0.756576i	$0.726871\pi$
$24$		0			0
$25$	3.55701	+	1.29464i	0.711401	+	0.258929i
$26$		0			0
$27$	4.06483	−	3.23684i	0.782277	−	0.622931i
$28$		0			0
$29$	1.79039	+	0.651649i	0.332467	+	0.121008i	0.502860	−	0.864368i	$-0.332281\pi$
$29$	1.79039	+	0.651649i	0.332467	+	0.121008i	−0.170392	+	0.985376i	$0.554503\pi$
$30$		0			0
$31$	−2.20938	−	1.85389i	−0.396817	−	0.332969i	0.422445	−	0.906389i	$-0.361172\pi$
$31$	−2.20938	−	1.85389i	−0.396817	−	0.332969i	−0.819262	+	0.573420i	$0.805616\pi$
$32$		0			0
$33$	0.489028	−	0.645287i	0.0851288	−	0.112330i
$34$		0			0
$35$	1.88615	+	3.26691i	0.318818	+	0.552209i
$36$		0			0
$37$	2.32289	−	4.02336i	0.381880	−	0.661436i	−0.609451	−	0.792824i	$-0.708610\pi$
$37$	2.32289	−	4.02336i	0.381880	−	0.661436i	0.991331	+	0.131388i	$0.0419434\pi$
$38$		0			0
$39$	−4.94836	−	2.53836i	−0.792371	−	0.406464i
$40$		0			0
$41$	0.00243859		0.000887575i	0.000380844		0.000138616i	−0.341830	−	0.939762i	$-0.611047\pi$
$41$	0.00243859		0.000887575i	0.000380844		0.000138616i	0.342211	+	0.939623i	$0.388824\pi$
$42$		0			0
$43$	1.18135	+	6.69975i	0.180154	+	1.02170i	0.932025	+	0.362393i	$0.118040\pi$
$43$	1.18135	+	6.69975i	0.180154	+	1.02170i	−0.751872	+	0.659310i	$0.770849\pi$
$44$		0			0
$45$	3.20379	+	0.817411i	0.477592	+	0.121852i
$46$		0			0
$47$	6.94945	−	5.83128i	1.01368	−	0.850579i	0.0248605	−	0.999691i	$-0.492086\pi$
$47$	6.94945	−	5.83128i	1.01368	−	0.850579i	0.988820	+	0.149112i	$0.0476414\pi$
$48$		0			0
$49$	0.818739	−	4.64330i	0.116963	−	0.663329i
$50$		0			0
$51$	0.625473	−	0.142603i	0.0875837	−	0.0199684i
$52$		0			0
$53$	10.8925			1.49619			0.748097	−	0.663589i	$-0.230968\pi$
$53$	10.8925			1.49619			0.748097	+	0.663589i	$0.230968\pi$
$54$		0			0
$55$	0.515201			0.0694697
$56$		0			0
$57$	2.81640	−	9.12281i	0.373041	−	1.20835i
$58$		0			0
$59$	1.70529	−	9.67117i	0.222010	−	1.25908i	−0.646310	−	0.763075i	$-0.723689\pi$
$59$	1.70529	−	9.67117i	0.222010	−	1.25908i	0.868320	−	0.496004i	$-0.165200\pi$
$60$		0			0
$61$	−8.40201	+	7.05012i	−1.07577	+	0.902676i	−0.995562	−	0.0941029i	$-0.970002\pi$
$61$	−8.40201	+	7.05012i	−1.07577	+	0.902676i	−0.0802044	+	0.996778i	$0.525557\pi$
$62$		0			0
$63$	−5.98998	−	8.33994i	−0.754666	−	1.05073i
$64$		0			0
$65$	−0.614516	−	3.48509i	−0.0762213	−	0.432273i
$66$		0			0
$67$	3.98327	−	1.44979i	0.486633	−	0.177120i	−0.0870391	−	0.996205i	$-0.527740\pi$
$67$	3.98327	−	1.44979i	0.486633	−	0.177120i	0.573672	+	0.819085i	$0.305518\pi$
$68$		0			0
$69$	0.0120358	+	0.242320i	0.00144894	+	0.0291718i
$70$		0			0
$71$	−0.776845	+	1.34554i	−0.0921946	+	0.159686i	−0.908434	−	0.418028i	$-0.862722\pi$
$71$	−0.776845	+	1.34554i	−0.0921946	+	0.159686i	0.816240	+	0.577713i	$0.196055\pi$
$72$		0			0
$73$	7.58782	+	13.1425i	0.888087	+	1.53821i	0.842134	+	0.539269i	$0.181299\pi$
$73$	7.58782	+	13.1425i	0.888087	+	1.53821i	0.0459537	+	0.998944i	$0.485367\pi$
$74$		0			0
$75$	−2.54526	−	6.04209i	−0.293901	−	0.697680i
$76$		0			0
$77$	−1.22564	−	1.02844i	−0.139675	−	0.117201i
$78$		0			0
$79$	−8.87740	−	3.23111i	−0.998785	−	0.363528i	−0.209669	−	0.977772i	$-0.567239\pi$
$79$	−8.87740	−	3.23111i	−0.998785	−	0.363528i	−0.789116	+	0.614244i	$0.789461\pi$
$80$		0			0
$81$	−8.89819	−	1.34986i	−0.988688	−	0.149985i
$82$		0			0
$83$	16.2493	+	5.91426i	1.78359	+	0.649174i	0.999596	+	0.0284077i	$0.00904366\pi$
$83$	16.2493	+	5.91426i	1.78359	+	0.649174i	0.783995	+	0.620767i	$0.213179\pi$
$84$		0			0
$85$	0.312710	+	0.262395i	0.0339182	+	0.0284608i
$86$		0			0
$87$	−1.28114	−	3.04124i	−0.137352	−	0.326055i
$88$		0			0
$89$	6.38441	+	11.0581i	0.676746	+	1.17216i	0.975955	+	0.217972i	$0.0699440\pi$
$89$	6.38441	+	11.0581i	0.676746	+	1.17216i	−0.299209	+	0.954188i	$0.596723\pi$
$90$		0			0
$91$	−5.49498	+	9.51758i	−0.576030	+	0.997714i
$92$		0			0
$93$	0.247815	+	4.98934i	0.0256972	+	0.517370i
$94$		0			0
$95$	5.70899	−	2.07790i	0.585730	−	0.213188i
$96$		0			0
$97$	−0.597491	−	3.38854i	−0.0606660	−	0.344054i	−0.999999	−	0.00104871i	$-0.999666\pi$
$97$	−0.597491	−	3.38854i	−0.0606660	−	0.344054i	0.939333	−	0.343005i	$-0.111445\pi$
$98$		0			0
$99$	−1.39546	+	0.138965i	−0.140249	+	0.0139665i
$100$		0			0
$101$	2.84018	−	2.38320i	0.282609	−	0.237137i	−0.490453	−	0.871468i	$-0.663169\pi$
$101$	2.84018	−	2.38320i	0.282609	−	0.237137i	0.773062	+	0.634331i	$0.218724\pi$
$102$		0			0
$103$	−2.66196	+	15.0967i	−0.262291	+	1.48752i	0.514350	+	0.857581i	$0.328033\pi$
$103$	−2.66196	+	15.0967i	−0.262291	+	1.48752i	−0.776640	+	0.629944i	$0.783078\pi$
$104$		0			0
$105$	1.92737	−	6.24308i	0.188092	−	0.609263i
$106$		0			0
$107$	9.61957			0.929959			0.464979	−	0.885322i	$-0.346062\pi$
$107$	9.61957			0.929959			0.464979	+	0.885322i	$0.346062\pi$
$108$		0			0
$109$	−16.5616			−1.58632			−0.793159	−	0.609015i	$-0.791565\pi$
$109$	−16.5616			−1.58632			−0.793159	+	0.609015i	$0.791565\pi$
$110$		0			0
$111$	−7.84539	+	1.78869i	−0.744652	+	0.169775i
$112$		0			0
$113$	−2.26702	+	12.8569i	−0.213263	+	1.20948i	0.670631	+	0.741791i	$0.266023\pi$
$113$	−2.26702	+	12.8569i	−0.213263	+	1.20948i	−0.883895	+	0.467686i	$0.845088\pi$
$114$		0			0
$115$	−0.118264	+	0.0992355i	−0.0110282	+	0.00925376i
$116$		0			0
$117$	2.60450	+	9.27390i	0.240786	+	0.857372i
$118$		0			0
$119$	−0.220136	−	1.24845i	−0.0201799	−	0.114446i
$120$		0			0
$121$	10.1313	−	3.68749i	0.921026	−	0.335226i
$122$		0			0
$123$	−0.00399934	−	0.00205155i	−0.000360608	−	0.000184982i
$124$		0			0
$125$	4.84131	−	8.38539i	0.433020	−	0.750012i
$126$		0			0
$127$	1.24368	+	2.15412i	0.110359	+	0.191147i	0.915915	−	0.401372i	$-0.131467\pi$
$127$	1.24368	+	2.15412i	0.110359	+	0.191147i	−0.805556	+	0.592520i	$0.798133\pi$
$128$		0			0
$129$	7.11706	−	9.39118i	0.626622	−	0.826847i
$130$		0			0
$131$	8.70424	+	7.30372i	0.760493	+	0.638129i	0.938255	−	0.345944i	$-0.112441\pi$
$131$	8.70424	+	7.30372i	0.760493	+	0.638129i	−0.177762	+	0.984073i	$0.556886\pi$
$132$		0			0
$133$	−17.7293	−	6.45294i	−1.53733	−	0.559541i
$134$		0			0
$135$	−2.73531	−	5.03143i	−0.235418	−	0.433037i
$136$		0			0
$137$	−19.0988	−	6.95139i	−1.63172	−	0.593897i	−0.646156	−	0.763205i	$-0.723625\pi$
$137$	−19.0988	−	6.95139i	−1.63172	−	0.593897i	−0.985563	+	0.169308i	$0.945847\pi$
$138$		0			0
$139$	−1.28261	−	1.07623i	−0.108789	−	0.0912850i	0.586771	−	0.809753i	$-0.300399\pi$
$139$	−1.28261	−	1.07623i	−0.108789	−	0.0912850i	−0.695560	+	0.718468i	$0.744844\pi$
$140$		0			0
$141$	−15.5905	−	1.95752i	−1.31296	−	0.164853i
$142$		0			0
$143$	0.750475	+	1.29986i	0.0627579	+	0.108700i
$144$		0			0
$145$	1.04995	−	1.81857i	0.0871937	−	0.151024i
$146$		0			0
$147$	−6.86113	+	4.42907i	−0.565896	+	0.365303i
$148$		0			0
$149$	−17.4431	+	6.34876i	−1.42899	+	0.520111i	−0.936642	−	0.350287i	$-0.886084\pi$
$149$	−17.4431	+	6.34876i	−1.42899	+	0.520111i	−0.492350	+	0.870397i	$0.663862\pi$
$150$		0			0
$151$	2.43098	+	13.7868i	0.197830	+	1.12195i	0.908330	+	0.418253i	$0.137358\pi$
$151$	2.43098	+	13.7868i	0.197830	+	1.12195i	−0.710500	+	0.703697i	$0.751531\pi$
$152$		0			0
$153$	−0.917777	−	0.626371i	−0.0741979	−	0.0506391i
$154$		0			0
$155$	−2.43505	+	2.04325i	−0.195588	+	0.164118i
$156$		0			0
$157$	2.56350	−	14.5383i	0.204589	−	1.16028i	−0.693495	−	0.720461i	$-0.743930\pi$
$157$	2.56350	−	14.5383i	0.204589	−	1.16028i	0.898085	−	0.439823i	$-0.144959\pi$
$158$		0			0
$159$	−12.8290	−	13.8330i	−1.01741	−	1.09703i
$160$		0			0
$161$	0.479438			0.0377850
$162$		0			0
$163$	−7.34218			−0.575084			−0.287542	−	0.957768i	$-0.592838\pi$
$163$	−7.34218			−0.575084			−0.287542	+	0.957768i	$0.592838\pi$
$164$		0			0
$165$	−0.606799	−	0.654287i	−0.0472393	−	0.0509362i
$166$		0			0
$167$	−0.437475	+	2.48105i	−0.0338529	+	0.191989i	−0.997044	−	0.0768267i	$-0.975521\pi$
$167$	−0.437475	+	2.48105i	−0.0338529	+	0.191989i	0.963192	+	0.268816i	$0.0866323\pi$
$168$		0			0
$169$	−2.06078	+	1.72920i	−0.158521	+	0.133015i
$170$		0			0
$171$	−14.9028	+	7.16805i	−1.13964	+	0.548154i
$172$		0			0
$173$	−3.07246	−	17.4248i	−0.233595	−	1.32478i	−0.845552	−	0.533893i	$-0.820729\pi$
$173$	−3.07246	−	17.4248i	−0.233595	−	1.32478i	0.611957	−	0.790891i	$-0.290382\pi$
$174$		0			0
$175$	−12.1746	+	4.43119i	−0.920313	+	0.334966i
$176$		0			0
$177$	−14.2905	+	9.22496i	−1.07414	+	0.693391i
$178$		0			0
$179$	8.77136	−	15.1924i	0.655602	−	1.13554i	−0.326140	−	0.945322i	$-0.605748\pi$
$179$	8.77136	−	15.1924i	0.655602	−	1.13554i	0.981742	−	0.190215i	$-0.0609186\pi$
$180$		0			0
$181$	10.4048	+	18.0216i	0.773380	+	1.33953i	0.935701	+	0.352795i	$0.114769\pi$
$181$	10.4048	+	18.0216i	0.773380	+	1.33953i	−0.162321	+	0.986738i	$0.551898\pi$
$182$		0			0
$183$	18.8492	+	2.36668i	1.39337	+	0.174950i
$184$		0			0
$185$	−3.92237	−	3.29126i	−0.288378	−	0.241978i
$186$		0			0
$187$	−0.162696	−	0.0592166i	−0.0118975	−	0.00433034i
$188$		0			0
$189$	−3.53648	+	17.4298i	−0.257241	+	1.26783i
$190$		0			0
$191$	−19.4529	−	7.08028i	−1.40756	−	0.512311i	−0.477150	−	0.878822i	$-0.658330\pi$
$191$	−19.4529	−	7.08028i	−1.40756	−	0.512311i	−0.930414	+	0.366511i	$0.880552\pi$
$192$		0			0
$193$	−1.66437	−	1.39657i	−0.119804	−	0.100527i	0.580918	−	0.813962i	$-0.302694\pi$
$193$	−1.66437	−	1.39657i	−0.119804	−	0.100527i	−0.700721	+	0.713435i	$0.747138\pi$
$194$		0			0
$195$	−3.70217	+	4.88512i	−0.265118	+	0.349831i
$196$		0			0
$197$	−3.43136	−	5.94329i	−0.244474	−	0.423442i	0.717509	−	0.696549i	$-0.245282\pi$
$197$	−3.43136	−	5.94329i	−0.244474	−	0.423442i	−0.961984	+	0.273107i	$0.911949\pi$
$198$		0			0
$199$	1.11328	−	1.92826i	0.0789184	−	0.136691i	−0.823865	−	0.566786i	$-0.808187\pi$
$199$	1.11328	−	1.92826i	0.0789184	−	0.136691i	0.902784	+	0.430095i	$0.141520\pi$
$200$		0			0
$201$	−6.53264	−	3.35105i	−0.460777	−	0.236365i
$202$		0			0
$203$	−6.12799	+	2.23041i	−0.430100	+	0.156544i
$204$		0			0
$205$	−0.000496662	−	0.00281671i	−3.46883e−5	−	0.000196727i
$206$		0			0
$207$	0.293561	−	0.300687i	0.0204039	−	0.0208992i
$208$		0			0
$209$	−1.97392	+	1.65632i	−0.136539	+	0.114570i
$210$		0			0
$211$	−0.300487	+	1.70415i	−0.0206864	+	0.117318i	−0.993402	−	0.114681i	$-0.963416\pi$
$211$	−0.300487	+	1.70415i	−0.0206864	+	0.117318i	0.972716	+	0.231999i	$0.0745266\pi$
$212$		0			0
$213$	2.62374	−	0.598194i	0.179776	−	0.0409876i
$214$		0			0
$215$	7.49798			0.511358
$216$		0			0
$217$	9.87159			0.670127
$218$		0			0
$219$	7.75362	−	25.1154i	0.523941	−	1.69714i
$220$		0			0
$221$	−0.206513	+	1.17119i	−0.0138916	+	0.0787831i
$222$		0			0
$223$	13.9621	−	11.7156i	0.934972	−	0.784534i	−0.0417317	−	0.999129i	$-0.513287\pi$
$223$	13.9621	−	11.7156i	0.934972	−	0.784534i	0.976703	+	0.214595i	$0.0688430\pi$
$224$		0			0
$225$	−4.67545	+	10.3487i	−0.311697	+	0.689914i
$226$		0			0
$227$	0.505142	+	2.86480i	0.0335274	+	0.190143i	0.996972	−	0.0777654i	$-0.0247785\pi$
$227$	0.505142	+	2.86480i	0.0335274	+	0.190143i	−0.963444	+	0.267909i	$0.913667\pi$
$228$		0			0
$229$	−4.14101	+	1.50720i	−0.273645	+	0.0995988i	−0.475198	−	0.879879i	$-0.657624\pi$
$229$	−4.14101	+	1.50720i	−0.273645	+	0.0995988i	0.201553	+	0.979478i	$0.435401\pi$
$230$		0			0
$231$	0.137474	+	2.76780i	0.00904513	+	0.182108i
$232$		0			0
$233$	−6.86339	+	11.8877i	−0.449635	+	0.778791i	−0.998362	−	0.0572104i	$-0.981779\pi$
$233$	−6.86339	+	11.8877i	−0.449635	+	0.778791i	0.548727	+	0.836002i	$0.315113\pi$
$234$		0			0
$235$	−4.99923	−	8.65892i	−0.326114	−	0.564846i
$236$		0			0
$237$	6.35233	+	15.0795i	0.412628	+	0.979522i
$238$		0			0
$239$	18.5330	+	15.5510i	1.19880	+	1.00591i	0.999663	+	0.0259412i	$0.00825828\pi$
$239$	18.5330	+	15.5510i	1.19880	+	1.00591i	0.199137	+	0.979972i	$0.436186\pi$
$240$		0			0
$241$	−19.1724	−	6.97819i	−1.23500	−	0.449505i	−0.359696	−	0.933070i	$-0.617120\pi$
$241$	−19.1724	−	6.97819i	−1.23500	−	0.449505i	−0.875309	+	0.483565i	$0.839342\pi$
$242$		0			0
$243$	8.76593	+	12.8902i	0.562335	+	0.826910i
$244$		0			0
$245$	−4.88313	−	1.77731i	−0.311972	−	0.113548i
$246$		0			0
$247$	13.5587	+	11.3771i	0.862716	+	0.723905i
$248$		0			0
$249$	−11.6274	−	27.6018i	−0.736855	−	1.74919i
$250$		0			0
$251$	−7.76784	−	13.4543i	−0.490302	−	0.849227i	0.509636	−	0.860390i	$-0.329780\pi$
$251$	−7.76784	−	13.4543i	−0.490302	−	0.849227i	−0.999938	+	0.0111628i	$0.996447\pi$
$252$		0			0
$253$	0.0327396	−	0.0567066i	0.00205832	−	0.00356511i
$254$		0			0
$255$	−0.0350751	−	0.706178i	−0.00219649	−	0.0442226i
$256$		0			0
$257$	−22.4742	+	8.17994i	−1.40190	+	0.510251i	−0.928743	−	0.370725i	$-0.879109\pi$
$257$	−22.4742	+	8.17994i	−1.40190	+	0.510251i	−0.473160	+	0.880976i	$0.656887\pi$
$258$		0			0
$259$	2.76120	+	15.6595i	0.171573	+	0.973037i
$260$		0			0
$261$	−2.35335	+	5.20894i	−0.145669	+	0.322425i
$262$		0			0
$263$	4.91903	−	4.12756i	0.303321	−	0.254516i	−0.478404	−	0.878140i	$-0.658785\pi$
$263$	4.91903	−	4.12756i	0.303321	−	0.254516i	0.781725	+	0.623624i	$0.214340\pi$
$264$		0			0
$265$	2.08465	−	11.8226i	0.128059	−	0.726258i
$266$		0			0
$267$	6.52392	−	21.1321i	0.399257	−	1.29327i
$268$		0			0
$269$	21.7739			1.32758			0.663790	−	0.747919i	$-0.268947\pi$
$269$	21.7739			1.32758			0.663790	+	0.747919i	$0.268947\pi$
$270$		0			0
$271$	8.69990			0.528481			0.264241	−	0.964457i	$-0.414879\pi$
$271$	8.69990			0.528481			0.264241	+	0.964457i	$0.414879\pi$
$272$		0			0
$273$	18.5589	−	4.23130i	1.12324	−	0.256090i
$274$		0			0
$275$	−0.307262	+	1.74257i	−0.0185286	+	0.105081i
$276$		0			0
$277$	−7.52847	+	6.31714i	−0.452342	+	0.379560i	−0.840304	−	0.542115i	$-0.817624\pi$
$277$	−7.52847	+	6.31714i	−0.452342	+	0.379560i	0.387962	+	0.921675i	$0.373179\pi$
$278$		0			0
$279$	6.04440	−	6.19111i	0.361869	−	0.370652i
$280$		0			0
$281$	−2.14350	−	12.1564i	−0.127871	−	0.725190i	−0.979561	−	0.201146i	$-0.935534\pi$
$281$	−2.14350	−	12.1564i	−0.127871	−	0.725190i	0.851691	−	0.524045i	$-0.175578\pi$
$282$		0			0
$283$	−3.66683	+	1.33462i	−0.217971	+	0.0793348i	−0.448697	−	0.893684i	$-0.648112\pi$
$283$	−3.66683	+	1.33462i	−0.217971	+	0.0793348i	0.230727	+	0.973019i	$0.425890\pi$
$284$		0			0
$285$	−9.36285	−	4.80287i	−0.554608	−	0.284498i
$286$		0			0
$287$	−0.00444113	+	0.00769226i	−0.000262152	+	0.000454060i
$288$		0			0
$289$	8.43141	+	14.6036i	0.495965	+	0.859037i
$290$		0			0
$291$	−3.59960	+	4.74978i	−0.211013	+	0.278437i
$292$		0			0
$293$	3.05342	+	2.56212i	0.178383	+	0.149681i	0.727607	−	0.685994i	$-0.240632\pi$
$293$	3.05342	+	2.56212i	0.178383	+	0.149681i	−0.549225	+	0.835675i	$0.685077\pi$
$294$		0			0
$295$	−10.1707	−	3.70183i	−0.592160	−	0.215529i
$296$		0			0
$297$	1.82005	+	1.60852i	0.105610	+	0.0933356i
$298$		0			0
$299$	−0.422644	−	0.153830i	−0.0244421	−	0.00889621i
$300$		0			0
$301$	−17.8374	−	14.9673i	−1.02813	−	0.862703i
$302$		0			0
$303$	−6.37171	−	0.800022i	−0.366045	−	0.0459601i
$304$		0			0
$305$	6.04416	+	10.4688i	0.346088	+	0.599441i
$306$		0			0
$307$	−3.29778	+	5.71191i	−0.188214	+	0.325996i	−0.944655	−	0.328066i	$-0.893603\pi$
$307$	−3.29778	+	5.71191i	−0.188214	+	0.325996i	0.756441	+	0.654062i	$0.226937\pi$
$308$		0			0
$309$	22.3075	−	14.4002i	1.26903	−	0.819199i
$310$		0			0
$311$	5.87411	−	2.13800i	0.333090	−	0.121235i	−0.170060	−	0.985434i	$-0.554396\pi$
$311$	5.87411	−	2.13800i	0.333090	−	0.121235i	0.503151	+	0.864199i	$0.332174\pi$
$312$		0			0
$313$	2.75485	+	15.6235i	0.155713	+	0.883095i	0.958131	+	0.286331i	$0.0924358\pi$
$313$	2.75485	+	15.6235i	0.155713	+	0.883095i	−0.802417	+	0.596763i	$0.796453\pi$
$314$		0			0
$315$	−10.1985	+	4.90536i	−0.574622	+	0.276386i
$316$		0			0
$317$	21.9413	−	18.4109i	1.23234	−	1.03406i	0.234261	−	0.972174i	$-0.424733\pi$
$317$	21.9413	−	18.4109i	1.23234	−	1.03406i	0.998083	−	0.0618855i	$-0.0197114\pi$
$318$		0			0
$319$	−0.154658	+	0.877109i	−0.00865919	+	0.0491087i
$320$		0			0
$321$	−11.3298	−	12.2165i	−0.632370	−	0.681859i
$322$		0			0
$323$	−2.04168			−0.113602
$324$		0			0
$325$	12.1542			0.674192
$326$		0			0
$327$	19.5062	+	21.0327i	1.07869	+	1.16311i
$328$		0			0
$329$	−5.39183	+	30.5786i	−0.297261	+	1.68585i
$330$		0			0
$331$	19.6579	−	16.4949i	1.08049	−	0.906642i	0.0845320	−	0.996421i	$-0.473060\pi$
$331$	19.6579	−	16.4949i	1.08049	−	0.906642i	0.995962	+	0.0897789i	$0.0286160\pi$
$332$		0			0
$333$	11.5118	+	7.85666i	0.630843	+	0.430542i
$334$		0			0
$335$	−0.811261	−	4.60089i	−0.0443239	−	0.251373i
$336$		0			0
$337$	10.8396	−	3.94530i	0.590471	−	0.214914i	−0.0294653	−	0.999566i	$-0.509380\pi$
$337$	10.8396	−	3.94530i	0.590471	−	0.214914i	0.619937	+	0.784652i	$0.287158\pi$
$338$		0			0
$339$	18.9979	−	12.2637i	1.03182	−	0.666074i
$340$		0			0
$341$	0.674104	−	1.16758i	0.0365048	−	0.0632282i
$342$		0			0
$343$	−3.91056	−	6.77329i	−0.211151	−	0.365723i
$344$		0			0
$345$	0.265316	+	0.0333127i	0.0142841	+	0.00179349i
$346$		0			0
$347$	−20.6139	−	17.2971i	−1.10661	−	0.928559i	−0.108761	−	0.994068i	$-0.534688\pi$
$347$	−20.6139	−	17.2971i	−1.10661	−	0.928559i	−0.997852	+	0.0655091i	$0.979133\pi$
$348$		0			0
$349$	−18.6059	−	6.77200i	−0.995952	−	0.362497i	−0.207930	−	0.978144i	$-0.566672\pi$
$349$	−18.6059	−	6.77200i	−0.995952	−	0.362497i	−0.788022	+	0.615647i	$0.788895\pi$
$350$		0			0
$351$	8.70996	−	14.2303i	0.464903	−	0.759559i
$352$		0			0
$353$	22.6468	+	8.24277i	1.20537	+	0.438719i	0.865095	−	0.501608i	$-0.167258\pi$
$353$	22.6468	+	8.24277i	1.20537	+	0.438719i	0.340274	+	0.940326i	$0.389480\pi$
$354$		0			0
$355$	1.31176	+	1.10070i	0.0696211	+	0.0584191i
$356$		0			0
$357$	−1.32622	+	1.74998i	−0.0701909	+	0.0926190i
$358$		0			0
$359$	6.30422	+	10.9192i	0.332724	+	0.576295i	0.983045	−	0.183365i	$-0.0586989\pi$
$359$	6.30422	+	10.9192i	0.332724	+	0.576295i	−0.650321	+	0.759660i	$0.725366\pi$
$360$		0			0
$361$	−5.69297	+	9.86052i	−0.299630	+	0.518975i
$362$		0			0
$363$	−16.6155	−	8.52328i	−0.872088	−	0.447356i
$364$		0			0
$365$	15.7170	−	5.72052i	0.822666	−	0.299426i
$366$		0			0
$367$	−1.53647	−	8.71374i	−0.0802030	−	0.454854i	−0.998289	−	0.0584725i	$-0.981377\pi$
$367$	−1.53647	−	8.71374i	−0.0802030	−	0.454854i	0.918086	−	0.396381i	$-0.129734\pi$
$368$		0			0
$369$	0.00210500	+	0.00749531i	0.000109582	+	0.000390190i
$370$		0			0
$371$	−28.5594	+	23.9642i	−1.48273	+	1.24416i
$372$		0			0
$373$	0.480495	−	2.72502i	0.0248791	−	0.141096i	−0.969838	−	0.243750i	$-0.921622\pi$
$373$	0.480495	−	2.72502i	0.0248791	−	0.141096i	0.994717	+	0.102654i	$0.0327334\pi$
$374$		0			0
$375$	−16.3512	+	3.72795i	−0.844372	+	0.192511i
$376$		0			0
$377$	6.11770			0.315078
$378$		0			0
$379$	−21.3071			−1.09447			−0.547235	−	0.836979i	$-0.684320\pi$
$379$	−21.3071			−1.09447			−0.547235	+	0.836979i	$0.684320\pi$
$380$		0			0
$381$	1.27086	−	4.11654i	0.0651080	−	0.210897i
$382$		0			0
$383$	1.58349	−	8.98044i	0.0809127	−	0.458879i	−0.917251	−	0.398309i	$-0.869597\pi$
$383$	1.58349	−	8.98044i	0.0809127	−	0.458879i	0.998164	−	0.0605698i	$-0.0192918\pi$
$384$		0			0
$385$	−1.35083	+	1.13348i	−0.0688447	+	0.0577675i
$386$		0			0
$387$	−20.3089	+	2.02243i	−1.03236	+	0.102806i
$388$		0			0
$389$	−3.35622	−	19.0341i	−0.170167	−	0.965067i	−0.943575	−	0.331158i	$-0.892561\pi$
$389$	−3.35622	−	19.0341i	−0.170167	−	0.965067i	0.773408	−	0.633909i	$-0.218550\pi$
$390$		0			0
$391$	0.0487529	−	0.0177446i	0.00246554	−	0.000897383i
$392$		0			0
$393$	−0.976309	−	19.6563i	−0.0492483	−	0.991530i
$394$		0			0
$395$	−5.20603	+	9.01711i	−0.261944	+	0.453700i
$396$		0			0
$397$	8.65829	+	14.9966i	0.434547	+	0.752658i	0.997259	−	0.0739955i	$-0.0235750\pi$
$397$	8.65829	+	14.9966i	0.434547	+	0.752658i	−0.562711	+	0.826654i	$0.690242\pi$
$398$		0			0
$399$	12.6864	+	30.1158i	0.635116	+	1.50768i
$400$		0			0
$401$	−3.98014	−	3.33974i	−0.198759	−	0.166779i	0.537976	−	0.842960i	$-0.319189\pi$
$401$	−3.98014	−	3.33974i	−0.198759	−	0.166779i	−0.736735	+	0.676182i	$0.763633\pi$
$402$		0			0
$403$	−8.70220	−	3.16734i	−0.433488	−	0.157777i
$404$		0			0
$405$	−3.16812	+	9.39972i	−0.157425	+	0.467076i
$406$		0			0
$407$	2.04072	+	0.742762i	0.101155	+	0.0368173i
$408$		0			0
$409$	9.90532	+	8.31155i	0.489786	+	0.410980i	0.853950	−	0.520355i	$-0.174201\pi$
$409$	9.90532	+	8.31155i	0.489786	+	0.410980i	−0.364163	+	0.931335i	$0.618645\pi$
$410$		0			0
$411$	13.6664	+	32.4421i	0.674112	+	1.60025i
$412$		0			0
$413$	16.8061	+	29.1091i	0.826975	+	1.43236i
$414$		0			0
$415$	9.52918	−	16.5050i	0.467769	−	0.810200i
$416$		0			0
$417$	0.143863	+	2.89644i	0.00704501	+	0.141839i
$418$		0			0
$419$	−30.1726	+	10.9819i	−1.47403	+	0.536502i	−0.949191	−	0.314700i	$-0.898096\pi$
$419$	−30.1726	+	10.9819i	−1.47403	+	0.536502i	−0.524837	+	0.851203i	$0.675874\pi$
$420$		0			0
$421$	−2.08603	−	11.8305i	−0.101667	−	0.576581i	−0.992499	−	0.122250i	$-0.960989\pi$
$421$	−2.08603	−	11.8305i	−0.101667	−	0.576581i	0.890833	−	0.454332i	$-0.150122\pi$
$422$		0			0
$423$	15.8764	+	22.1049i	0.771936	+	1.07478i
$424$		0			0
$425$	−1.07400	+	0.901193i	−0.0520967	+	0.0437143i
$426$		0			0
$427$	6.51882	−	36.9701i	0.315468	−	1.78911i
$428$		0			0
$429$	0.766873	−	2.48404i	0.0370250	−	0.119931i
$430$		0			0
$431$	−35.7747			−1.72321			−0.861603	−	0.507583i	$-0.830539\pi$
$431$	−35.7747			−1.72321			−0.861603	+	0.507583i	$0.830539\pi$
$432$		0			0
$433$	33.4711			1.60852			0.804260	−	0.594278i	$-0.202562\pi$
$433$	33.4711			1.60852			0.804260	+	0.594278i	$0.202562\pi$
$434$		0			0
$435$	−3.54614	+	0.808494i	−0.170024	+	0.0387643i
$436$		0			0
$437$	0.134082	−	0.760415i	0.00641400	−	0.0363756i
$438$		0			0
$439$	11.5002	−	9.64985i	0.548877	−	0.460562i	−0.325684	−	0.945479i	$-0.605594\pi$
$439$	11.5002	−	9.64985i	0.548877	−	0.460562i	0.874560	+	0.484916i	$0.161150\pi$
$440$		0			0
$441$	13.7057	+	3.49687i	0.652654	+	0.166517i
$442$		0			0
$443$	−1.08004	−	6.12523i	−0.0513144	−	0.291019i	0.948341	−	0.317252i	$-0.102760\pi$
$443$	−1.08004	−	6.12523i	−0.0513144	−	0.291019i	−0.999656	+	0.0262329i	$0.991649\pi$
$444$		0			0
$445$	13.2243	−	4.81326i	0.626893	−	0.228171i
$446$		0			0
$447$	28.6070	+	14.6746i	1.35306	+	0.694083i
$448$		0			0
$449$	19.6223	−	33.9868i	0.926034	−	1.60394i	0.136145	−	0.990689i	$-0.456529\pi$
$449$	19.6223	−	33.9868i	0.926034	−	1.60394i	0.789889	−	0.613249i	$-0.210138\pi$
$450$		0			0
$451$	0.000606546		0.00105057i	2.85611e−5		4.94693e-5i
$452$		0			0
$453$	14.6455	−	19.3252i	0.688105	−	0.907975i
$454$		0			0
$455$	9.27869	+	7.78575i	0.434992	+	0.365001i
$456$		0			0
$457$	7.01707	+	2.55401i	0.328245	+	0.119471i	0.500886	−	0.865514i	$-0.333008\pi$
$457$	7.01707	+	2.55401i	0.328245	+	0.119471i	−0.172641	+	0.984985i	$0.555230\pi$
$458$		0			0
$459$	0.285481	+	1.90328i	0.0133251	+	0.0888374i
$460$		0			0
$461$	−22.3242	−	8.12534i	−1.03974	−	0.378435i	−0.234959	−	0.972005i	$-0.575496\pi$
$461$	−22.3242	−	8.12534i	−1.03974	−	0.378435i	−0.804782	+	0.593570i	$0.797718\pi$
$462$		0			0
$463$	2.24046	+	1.87997i	0.104123	+	0.0873694i	0.693363	−	0.720589i	$-0.256128\pi$
$463$	2.24046	+	1.87997i	0.104123	+	0.0873694i	−0.589240	+	0.807958i	$0.700573\pi$
$464$		0			0
$465$	5.46283	+	0.685905i	0.253333	+	0.0318081i
$466$		0			0
$467$	−0.566231	−	0.980742i	−0.0262021	−	0.0453833i	0.852627	−	0.522520i	$-0.175008\pi$
$467$	−0.566231	−	0.980742i	−0.0262021	−	0.0453833i	−0.878829	+	0.477137i	$0.841675\pi$
$468$		0			0
$469$	−7.25426	+	12.5648i	−0.334971	+	0.580186i
$470$		0			0
$471$	−21.4824	+	13.8676i	−0.989857	+	0.638983i
$472$		0			0
$473$	−2.98836	+	1.08767i	−0.137405	+	0.0500113i
$474$		0			0
$475$	3.62331	+	20.5488i	0.166249	+	0.942844i
$476$		0			0
$477$	−2.45752	+	32.5848i	−0.112522	+	1.49196i
$478$		0			0
$479$	17.6751	−	14.8312i	0.807597	−	0.677654i	−0.142436	−	0.989804i	$-0.545494\pi$
$479$	17.6751	−	14.8312i	0.807597	−	0.677654i	0.950033	+	0.312150i	$0.101049\pi$
$480$		0			0
$481$	2.59033	−	14.6905i	0.118109	−	0.669828i
$482$		0			0
$483$	−0.564678	−	0.608869i	−0.0256937	−	0.0277045i
$484$		0			0
$485$	−3.79226			−0.172198
$486$		0			0
$487$	26.7780			1.21343			0.606713	−	0.794921i	$-0.292488\pi$
$487$	26.7780			1.21343			0.606713	+	0.794921i	$0.292488\pi$
$488$		0			0
$489$	8.64756	+	9.32431i	0.391056	+	0.421660i
$490$		0			0
$491$	−1.15676	+	6.56030i	−0.0522038	+	0.296062i	−0.999720	−	0.0236441i	$-0.992473\pi$
$491$	−1.15676	+	6.56030i	−0.0522038	+	0.296062i	0.947517	+	0.319706i	$0.103584\pi$
$492$		0			0
$493$	−0.540590	+	0.453609i	−0.0243469	+	0.0204295i
$494$		0			0
$495$	−0.116238	+	1.54123i	−0.00522450	+	0.0692730i
$496$		0			0
$497$	−0.923431	−	5.23704i	−0.0414216	−	0.234913i
$498$		0			0
$499$	12.9496	−	4.71326i	0.579703	−	0.210994i	−0.0354918	−	0.999370i	$-0.511300\pi$
$499$	12.9496	−	4.71326i	0.579703	−	0.210994i	0.615194	+	0.788375i	$0.289078\pi$
$500$		0			0
$501$	3.66609	−	2.36658i	0.163789	−	0.105731i
$502$		0			0
$503$	−19.1889	+	33.2362i	−0.855592	+	1.48193i	0.0205033	+	0.999790i	$0.493473\pi$
$503$	−19.1889	+	33.2362i	−0.855592	+	1.48193i	−0.876095	+	0.482138i	$0.839860\pi$
$504$		0			0
$505$	−2.04314	−	3.53883i	−0.0909187	−	0.157476i
$506$		0			0
$507$	4.62318	+	0.580479i	0.205323	+	0.0257800i
$508$		0			0
$509$	28.9492	+	24.2912i	1.28315	+	1.07669i	0.992802	+	0.119768i	$0.0382151\pi$
$509$	28.9492	+	24.2912i	1.28315	+	1.07669i	0.290347	+	0.956921i	$0.406229\pi$
$510$		0			0
$511$	−48.8093	−	17.7651i	−2.15920	−	0.785884i
$512$		0			0
$513$	26.6555	+	10.4835i	1.17687	+	0.462859i
$514$		0			0
$515$	15.8765	+	5.77856i	0.699601	+	0.254634i
$516$		0			0
$517$	3.24855	+	2.72586i	0.142871	+	0.119883i
$518$		0			0
$519$	−18.5102	+	24.4247i	−0.812506	+	1.07213i
$520$		0			0
$521$	−4.09467	−	7.09217i	−0.179391	−	0.310714i	0.762281	−	0.647246i	$-0.224079\pi$
$521$	−4.09467	−	7.09217i	−0.179391	−	0.310714i	−0.941672	+	0.336532i	$0.890746\pi$
$522$		0			0
$523$	6.28483	−	10.8856i	0.274816	−	0.475996i	−0.695272	−	0.718746i	$-0.744716\pi$
$523$	6.28483	−	10.8856i	0.274816	−	0.475996i	0.970089	+	0.242750i	$0.0780496\pi$
$524$		0			0
$525$	19.9666	+	10.2423i	0.871413	+	0.447010i
$526$		0			0
$527$	1.00382	−	0.365359i	0.0437270	−	0.0159153i
$528$		0			0
$529$	−3.99050	−	22.6313i	−0.173500	−	0.983968i
$530$		0			0
$531$	28.5466	+	7.28335i	1.23882	+	0.316071i
$532$		0			0
$533$	0.00638313	−	0.00535608i	0.000276484	−	0.000231998i
$534$		0			0
$535$	1.84104	−	10.4410i	0.0795950	−	0.451406i
$536$		0			0
$537$	−29.6247	+	6.75421i	−1.27840	+	0.291466i
$538$		0			0
$539$	2.20402			0.0949338
$540$		0			0
$541$	3.97463			0.170882			0.0854412	−	0.996343i	$-0.472770\pi$
$541$	3.97463			0.170882			0.0854412	+	0.996343i	$0.472770\pi$
$542$		0			0
$543$	10.6321	−	34.4393i	0.456268	−	1.47793i
$544$		0			0
$545$	−3.16964	+	17.9759i	−0.135773	+	0.770005i
$546$		0			0
$547$	17.7725	−	14.9129i	0.759896	−	0.637628i	−0.178204	−	0.983994i	$-0.557029\pi$
$547$	17.7725	−	14.9129i	0.759896	−	0.637628i	0.938100	+	0.346365i	$0.112584\pi$
$548$		0			0
$549$	−19.1948	−	26.7253i	−0.819216	−	1.14061i
$550$		0			0
$551$	1.82376	+	10.3431i	0.0776950	+	0.440630i
$552$		0			0
$553$	30.3847	−	11.0591i	1.29209	−	0.470283i
$554$		0			0
$555$	0.439952	+	8.85769i	0.0186749	+	0.375988i
$556$		0			0
$557$	−3.99853	+	6.92566i	−0.169423	+	0.293449i	−0.938217	−	0.346047i	$-0.887524\pi$
$557$	−3.99853	+	6.92566i	−0.169423	+	0.293449i	0.768794	+	0.639496i	$0.220857\pi$
$558$		0			0
$559$	10.9220	+	18.9175i	0.461953	+	0.800126i
$560$		0			0
$561$	0.116419	+	0.276363i	0.00491522	+	0.0116681i
$562$		0			0
$563$	−34.9637	−	29.3380i	−1.47354	−	1.23645i	−0.912766	−	0.408482i	$-0.866058\pi$
$563$	−34.9637	−	29.3380i	−1.47354	−	1.23645i	−0.560777	−	0.827967i	$-0.689497\pi$
$564$		0			0
$565$	13.5210	+	4.92123i	0.568831	+	0.207038i
$566$		0			0
$567$	26.3004	−	16.0374i	1.10451	−	0.673508i
$568$		0			0
$569$	−14.1425	−	5.14745i	−0.592884	−	0.215792i	0.0281133	−	0.999605i	$-0.491050\pi$
$569$	−14.1425	−	5.14745i	−0.592884	−	0.215792i	−0.620997	+	0.783813i	$0.713272\pi$
$570$		0			0
$571$	−34.2127	−	28.7079i	−1.43176	−	1.20139i	−0.944664	−	0.328039i	$-0.893612\pi$
$571$	−34.2127	−	28.7079i	−1.43176	−	1.20139i	−0.487095	−	0.873349i	$-0.661943\pi$
$572$		0			0
$573$	13.9198	+	33.0436i	0.581507	+	1.38042i
$574$		0			0
$575$	−0.265113	−	0.459190i	−0.0110560	−	0.0191495i
$576$		0			0
$577$	−4.19410	+	7.26439i	−0.174603	+	0.302420i	−0.940024	−	0.341109i	$-0.889197\pi$
$577$	−4.19410	+	7.26439i	−0.174603	+	0.302420i	0.765421	+	0.643530i	$0.222531\pi$
$578$		0			0
$579$	0.186683	+	3.75855i	0.00775830	+	0.156200i
$580$		0			0
$581$	−55.6166	+	20.2428i	−2.30737	+	0.839812i
$582$		0			0
$583$	0.884171	+	5.01438i	0.0366186	+	0.207674i
$584$		0			0
$585$	10.5643	−	1.05203i	0.436781	−	0.0434962i
$586$		0			0
$587$	−0.434808	+	0.364847i	−0.0179465	+	0.0150589i	−0.651717	−	0.758462i	$-0.725951\pi$
$587$	−0.434808	+	0.364847i	−0.0179465	+	0.0150589i	0.633770	+	0.773521i	$0.281506\pi$
$588$		0			0
$589$	2.76073	−	15.6569i	0.113754	−	0.645130i
$590$		0			0
$591$	−3.50634	+	11.3577i	−0.144231	+	0.467191i
$592$		0			0
$593$	40.2329			1.65217			0.826083	−	0.563549i	$-0.190564\pi$
$593$	40.2329			1.65217			0.826083	+	0.563549i	$0.190564\pi$
$594$		0			0
$595$	−1.39720			−0.0572796
$596$		0			0
$597$	−3.76003	+	0.857260i	−0.153888	+	0.0350853i
$598$		0			0
$599$	0.451954	−	2.56316i	0.0184663	−	0.104728i	−0.974181	−	0.225766i	$-0.927511\pi$
$599$	0.451954	−	2.56316i	0.0184663	−	0.104728i	0.992648	+	0.121039i	$0.0386225\pi$
$600$		0			0
$601$	−21.3143	+	17.8848i	−0.869427	+	0.729536i	−0.963977	−	0.265984i	$-0.914303\pi$
$601$	−21.3143	+	17.8848i	−0.869427	+	0.729536i	0.0945507	+	0.995520i	$0.469859\pi$
$602$		0			0
$603$	3.43836	+	12.2431i	0.140021	+	0.498576i
$604$		0			0
$605$	−2.06341	−	11.7022i	−0.0838896	−	0.475761i
$606$		0			0
$607$	13.7189	−	4.99329i	0.556835	−	0.202671i	−0.0482459	−	0.998835i	$-0.515363\pi$
$607$	13.7189	−	4.99329i	0.556835	−	0.202671i	0.605081	+	0.796164i	$0.293141\pi$
$608$		0			0
$609$	10.0500	+	5.15537i	0.407248	+	0.208906i
$610$		0			0
$611$	14.5644	−	25.2263i	0.589212	−	1.02055i
$612$		0			0
$613$	5.30240	+	9.18403i	0.214162	+	0.370939i	0.953013	−	0.302929i	$-0.0979646\pi$
$613$	5.30240	+	9.18403i	0.214162	+	0.370939i	−0.738851	+	0.673869i	$0.764631\pi$
$614$		0			0
$615$	−0.00299215	+	0.00394824i	−0.000120655	+	0.000159208i
$616$		0			0
$617$	−36.4171	−	30.5576i	−1.46610	−	1.23020i	−0.919667	−	0.392700i	$-0.871541\pi$
$617$	−36.4171	−	30.5576i	−1.46610	−	1.23020i	−0.546433	−	0.837503i	$-0.684015\pi$
$618$		0			0
$619$	−9.10175	−	3.31276i	−0.365830	−	0.133151i	0.152563	−	0.988294i	$-0.451247\pi$
$619$	−9.10175	−	3.31276i	−0.365830	−	0.133151i	−0.518393	+	0.855143i	$0.673470\pi$
$620$		0			0
$621$	−0.727615	−	0.0186662i	−0.0291982	−	0.000749050i
$622$		0			0
$623$	−41.0683	−	14.9476i	−1.64537	−	0.598864i
$624$		0			0
$625$	6.32357	+	5.30611i	0.252943	+	0.212244i
$626$		0			0
$627$	4.42833	+	0.556014i	0.176851	+	0.0222051i
$628$		0			0
$629$	0.860358	+	1.49018i	0.0343047	+	0.0594176i
$630$		0			0
$631$	20.8074	−	36.0395i	0.828330	−	1.43471i	−0.0710167	−	0.997475i	$-0.522624\pi$
$631$	20.8074	−	36.0395i	0.828330	−	1.43471i	0.899347	−	0.437235i	$-0.144042\pi$
$632$		0			0
$633$	2.51812	−	1.62552i	0.100086	−	0.0646087i
$634$		0			0
$635$	2.57610	−	0.937623i	0.102229	−	0.0372084i
$636$		0			0
$637$	−2.62889	−	14.9092i	−0.104160	−	0.590722i
$638$		0			0
$639$	−3.84991	−	2.62751i	−0.152300	−	0.103943i
$640$		0			0
$641$	17.9861	−	15.0922i	0.710409	−	0.596104i	−0.214305	−	0.976767i	$-0.568749\pi$
$641$	17.9861	−	15.0922i	0.710409	−	0.596104i	0.924714	+	0.380663i	$0.124304\pi$
$642$		0			0
$643$	8.08736	−	45.8657i	0.318934	−	1.80877i	−0.230325	−	0.973114i	$-0.573979\pi$
$643$	8.08736	−	45.8657i	0.318934	−	1.80877i	0.549259	−	0.835652i	$-0.314910\pi$
$644$		0			0
$645$	−8.83105	−	9.52216i	−0.347722	−	0.374935i
$646$		0			0
$647$	−12.4615			−0.489911			−0.244955	−	0.969534i	$-0.578773\pi$
$647$	−12.4615			−0.489911			−0.244955	+	0.969534i	$0.578773\pi$
$648$		0			0
$649$	4.59058			0.180196
$650$		0			0
$651$	−11.6267	−	12.5366i	−0.455685	−	0.491347i
$652$		0			0
$653$	3.96102	−	22.4640i	0.155007	−	0.879086i	−0.803773	−	0.594936i	$-0.797177\pi$
$653$	3.96102	−	22.4640i	0.155007	−	0.879086i	0.958780	−	0.284150i	$-0.0917115\pi$
$654$		0			0
$655$	9.59329	−	8.04972i	0.374841	−	0.314529i
$656$		0			0
$657$	−41.0278	+	19.7338i	−1.60065	+	0.769890i
$658$		0			0
$659$	3.20506	+	18.1768i	0.124851	+	0.708067i	0.981396	+	0.191994i	$0.0614956\pi$
$659$	3.20506	+	18.1768i	0.124851	+	0.708067i	−0.856545	+	0.516073i	$0.827393\pi$
$660$		0			0
$661$	−3.37935	+	1.22998i	−0.131442	+	0.0478408i	−0.406903	−	0.913471i	$-0.633391\pi$
$661$	−3.37935	+	1.22998i	−0.131442	+	0.0478408i	0.275462	+	0.961312i	$0.411169\pi$
$662$		0			0
$663$	1.73060	−	1.11716i	0.0672111	−	0.0433868i
$664$		0			0
$665$	−10.3971	+	18.0083i	−0.403183	+	0.698333i
$666$		0			0
$667$	−0.133443	−	0.231130i	−0.00516692	−	0.00894938i
$668$		0			0
$669$	−31.3228	−	3.93284i	−1.21101	−	0.152052i
$670$		0			0
$671$	−3.92756	−	3.29562i	−0.151622	−	0.127226i
$672$		0			0
$673$	−13.7612	−	5.00866i	−0.530455	−	0.193070i	0.0628866	−	0.998021i	$-0.479969\pi$
$673$	−13.7612	−	5.00866i	−0.530455	−	0.193070i	−0.593341	+	0.804951i	$0.702192\pi$
$674$		0			0
$675$	18.6492	−	6.25096i	0.717808	−	0.240599i
$676$		0			0
$677$	−6.39065	−	2.32601i	−0.245613	−	0.0893957i	0.216281	−	0.976331i	$-0.430607\pi$
$677$	−6.39065	−	2.32601i	−0.245613	−	0.0893957i	−0.461893	+	0.886936i	$0.652830\pi$
$678$		0			0
$679$	9.02163	+	7.57005i	0.346218	+	0.290512i
$680$		0			0
$681$	3.04324	−	4.01565i	0.116617	−	0.153880i
$682$		0			0
$683$	7.45443	+	12.9114i	0.285236	+	0.494043i	0.972666	−	0.232207i	$-0.0745948\pi$
$683$	7.45443	+	12.9114i	0.285236	+	0.494043i	−0.687431	+	0.726250i	$0.741261\pi$
$684$		0			0
$685$	−11.2002	+	19.3994i	−0.427939	+	0.741211i
$686$		0			0
$687$	6.79133	+	3.48376i	0.259106	+	0.132914i
$688$		0			0
$689$	32.8653	−	11.9620i	1.25207	−	0.455716i
$690$		0			0
$691$	8.66581	+	49.1463i	0.329663	+	1.86961i	0.474644	+	0.880178i	$0.342577\pi$
$691$	8.66581	+	49.1463i	0.329663	+	1.86961i	−0.144981	+	0.989435i	$0.546312\pi$
$692$		0			0
$693$	3.35310	−	3.43448i	0.127374	−	0.130465i
$694$		0			0
$695$	−1.41361	+	1.18616i	−0.0536213	+	0.0449936i
$696$		0			0
$697$	−0.000166907	0	0.000946578i	−6.32206e−6	0	3.58542e-5i
$698$		0			0
$699$	23.1806	−	5.28501i	0.876772	−	0.199898i
$700$		0			0
$701$	1.53268			0.0578886			0.0289443	−	0.999581i	$-0.490785\pi$
$701$	1.53268			0.0578886			0.0289443	+	0.999581i	$0.490785\pi$
$702$		0			0
$703$	25.6091			0.965865
$704$		0			0
$705$	−5.10847	+	16.5472i	−0.192396	+	0.623205i
$706$		0			0
$707$	−2.20360	+	12.4972i	−0.0828748	+	0.470006i
$708$		0			0
$709$	−7.38838	+	6.19959i	−0.277477	+	0.232830i	−0.770896	−	0.636961i	$-0.780191\pi$
$709$	−7.38838	+	6.19959i	−0.277477	+	0.232830i	0.493419	+	0.869791i	$0.335747\pi$
$710$		0			0
$711$	11.6688	−	25.8278i	0.437613	−	0.968617i
$712$		0			0
$713$	0.0701536	+	0.397861i	0.00262727	+	0.0149000i
$714$		0			0
$715$	1.55449	−	0.565789i	0.0581347	−	0.0211593i
$716$		0			0
$717$	−2.07875	−	41.8521i	−0.0776324	−	1.56300i
$718$		0			0
$719$	−16.3486	+	28.3166i	−0.609700	+	1.05603i	0.381590	+	0.924332i	$0.375377\pi$
$719$	−16.3486	+	28.3166i	−0.609700	+	1.05603i	−0.991290	+	0.131699i	$0.957957\pi$
$720$		0			0
$721$	−26.2344	−	45.4393i	−0.977020	−	1.69225i
$722$		0			0
$723$	13.7191	+	32.5671i	0.510217	+	1.21119i
$724$		0			0
$725$	5.52478	+	4.63584i	0.205185	+	0.172171i
$726$		0			0
$727$	−49.0539	−	17.8542i	−1.81931	−	0.662175i	−0.995439	−	0.0953966i	$-0.969588\pi$
$727$	−49.0539	−	17.8542i	−1.81931	−	0.662175i	−0.823871	−	0.566778i	$-0.808190\pi$
$728$		0			0
$729$	6.04571	−	26.3144i	0.223915	−	0.974609i
$730$		0			0
$731$	−2.36780	−	0.861808i	−0.0875762	−	0.0318751i
$732$		0			0
$733$	−9.16043	−	7.68652i	−0.338348	−	0.283908i	0.457743	−	0.889085i	$-0.348658\pi$
$733$	−9.16043	−	7.68652i	−0.338348	−	0.283908i	−0.796091	+	0.605177i	$0.793102\pi$
$734$		0			0
$735$	3.49418	+	8.29470i	0.128885	+	0.305955i
$736$		0			0
$737$	0.990749	+	1.71603i	0.0364947	+	0.0632107i
$738$		0			0
$739$	−11.2526	+	19.4901i	−0.413934	+	0.716955i	−0.995316	−	0.0966761i	$-0.969179\pi$
$739$	−11.2526	+	19.4901i	−0.413934	+	0.716955i	0.581382	+	0.813631i	$0.302512\pi$
$740$		0			0
$741$	−1.52080	−	30.6188i	−0.0558681	−	1.12481i
$742$		0			0
$743$	−22.6713	+	8.25166i	−0.831728	+	0.302724i	−0.722568	−	0.691300i	$-0.757038\pi$
$743$	−22.6713	+	8.25166i	−0.831728	+	0.302724i	−0.109160	+	0.994024i	$0.534816\pi$
$744$		0			0
$745$	3.55258	+	20.1477i	0.130157	+	0.738155i
$746$		0			0
$747$	−21.3586	+	47.2755i	−0.781472	+	1.72972i
$748$		0			0
$749$	−25.2220	+	21.1638i	−0.921591	+	0.773307i
$750$		0			0
$751$	−4.52117	+	25.6408i	−0.164980	+	0.935647i	0.784106	+	0.620628i	$0.213122\pi$
$751$	−4.52117	+	25.6408i	−0.164980	+	0.935647i	−0.949085	+	0.315019i	$0.897989\pi$
$752$		0			0
$753$	−7.93757	+	25.7112i	−0.289261	+	0.936969i
$754$		0			0
$755$	15.4293			0.561531
$756$		0			0
$757$	25.2441			0.917513			0.458757	−	0.888562i	$-0.348295\pi$
$757$	25.2441			0.917513			0.458757	+	0.888562i	$0.348295\pi$
$758$		0			0
$759$	−0.110576	+	0.0252104i	−0.00401364	+	0.000915081i
$760$		0			0
$761$	−3.31921	+	18.8242i	−0.120321	+	0.682376i	0.863656	+	0.504082i	$0.168169\pi$
$761$	−3.31921	+	18.8242i	−0.120321	+	0.682376i	−0.983977	+	0.178294i	$0.942942\pi$
$762$		0			0
$763$	43.4237	−	36.4368i	1.57205	−	1.31910i
$764$		0			0
$765$	−0.855509	+	0.876274i	−0.0309310	+	0.0316817i
$766$		0			0
$767$	−5.47550	−	31.0531i	−0.197709	−	1.12126i
$768$		0			0
$769$	−39.3308	+	14.3152i	−1.41830	+	0.516220i	−0.933555	−	0.358433i	$-0.883311\pi$
$769$	−39.3308	+	14.3152i	−1.41830	+	0.516220i	−0.484748	+	0.874654i	$0.661089\pi$
$770$		0			0
$771$	36.8582	+	18.9072i	1.32741	+	0.680925i
$772$		0			0
$773$	6.11171	−	10.5858i	0.219823	−	0.380745i	−0.734931	−	0.678142i	$-0.762785\pi$
$773$	6.11171	−	10.5858i	0.219823	−	0.380745i	0.954754	+	0.297398i	$0.0961187\pi$
$774$		0			0
$775$	−5.45866	−	9.45468i	−0.196081	−	0.339622i
$776$		0			0
$777$	16.6349	−	21.9503i	0.596775	−	0.787463i
$778$		0			0
$779$	0.0109583	+	0.00919512i	0.000392622	+	0.000329449i
$780$		0			0
$781$	−0.682481	−	0.248403i	−0.0244211	−	0.00888855i
$782$		0			0
$783$	9.38693	−	3.14637i	0.335461	−	0.112442i
$784$		0			0
$785$	−15.2892	−	5.56482i	−0.545696	−	0.198617i
$786$		0			0
$787$	10.9168	+	9.16032i	0.389143	+	0.326530i	0.816279	−	0.577657i	$-0.196033\pi$
$787$	10.9168	+	9.16032i	0.389143	+	0.326530i	−0.427136	+	0.904187i	$0.640477\pi$
$788$		0			0
$789$	−11.0354	−	1.38559i	−0.392872	−	0.0493284i
$790$		0			0
$791$	−22.3422	−	38.6977i	−0.794396	−	1.37593i
$792$		0			0
$793$	−17.6086	+	30.4990i	−0.625300	+	1.08305i
$794$		0			0
$795$	−17.4696	+	11.2772i	−0.619583	+	0.399960i
$796$		0			0
$797$	−5.83172	+	2.12257i	−0.206570	+	0.0751853i	−0.443233	−	0.896406i	$-0.646169\pi$
$797$	−5.83172	+	2.12257i	−0.206570	+	0.0751853i	0.236663	+	0.971592i	$0.423946\pi$
$798$		0			0
$799$	0.583469	+	3.30902i	0.0206417	+	0.117065i
$800$		0			0
$801$	−34.5209	+	16.6041i	−1.21973	+	0.586677i
$802$		0			0
$803$	−5.43427	+	4.55989i	−0.191771	+	0.160915i
$804$		0			0
$805$	0.0917571	−	0.520380i	0.00323401	−	0.0183410i
$806$		0			0
$807$	−25.6451	−	27.6521i	−0.902752	−	0.973400i
$808$		0			0
$809$	−11.7323			−0.412485			−0.206243	−	0.978501i	$-0.566124\pi$
$809$	−11.7323			−0.412485			−0.206243	+	0.978501i	$0.566124\pi$
$810$		0			0
$811$	7.67492			0.269503			0.134752	−	0.990879i	$-0.456976\pi$
$811$	7.67492			0.269503			0.134752	+	0.990879i	$0.456976\pi$
$812$		0			0
$813$	−10.2467	−	11.0486i	−0.359366	−	0.387490i
$814$		0			0
$815$	−1.40518	+	7.96918i	−0.0492214	+	0.279148i
$816$		0			0
$817$	−28.7275	+	24.1052i	−1.00505	+	0.843335i
$818$		0			0
$819$	−27.2321	−	18.5856i	−0.951568	−	0.649433i
$820$		0			0
$821$	5.60542	+	31.7899i	0.195631	+	1.10948i	0.911518	+	0.411260i	$0.134911\pi$
$821$	5.60542	+	31.7899i	0.195631	+	1.10948i	−0.715887	+	0.698216i	$0.753978\pi$
$822$		0			0
$823$	−0.565199	+	0.205716i	−0.0197016	+	0.00717080i	−0.351852	−	0.936056i	$-0.614448\pi$
$823$	−0.565199	+	0.205716i	−0.0197016	+	0.00717080i	0.332151	+	0.943226i	$0.392226\pi$
$824$		0			0
$825$	2.57489	−	1.66217i	0.0896462	−	0.0578694i
$826$		0			0
$827$	−4.24272	+	7.34861i	−0.147534	+	0.255536i	−0.930315	−	0.366760i	$-0.880467\pi$
$827$	−4.24272	+	7.34861i	−0.147534	+	0.255536i	0.782782	+	0.622297i	$0.213800\pi$
$828$		0			0
$829$	−23.6119	−	40.8971i	−0.820076	−	1.42041i	−0.905625	−	0.424080i	$-0.860598\pi$
$829$	−23.6119	−	40.8971i	−0.820076	−	1.42041i	0.0855488	−	0.996334i	$-0.472736\pi$
$830$		0			0
$831$	16.8895	+	2.12062i	0.585891	+	0.0735635i
$832$		0			0
$833$	1.33777	+	1.12252i	0.0463509	+	0.0388930i
$834$		0			0
$835$	2.60919	+	0.949668i	0.0902948	+	0.0328646i
$836$		0			0
$837$	−14.9815	−	0.384336i	−0.517837	−	0.0132846i
$838$		0			0
$839$	24.4594	+	8.90251i	0.844433	+	0.307349i	0.727769	−	0.685823i	$-0.240557\pi$
$839$	24.4594	+	8.90251i	0.844433	+	0.307349i	0.116665	+	0.993171i	$0.462780\pi$
$840$		0			0
$841$	−19.4344	−	16.3074i	−0.670153	−	0.562325i
$842$		0			0
$843$	−12.9136	+	17.0399i	−0.444768	+	0.586884i
$844$		0			0
$845$	1.48246	+	2.56770i	0.0509982	+	0.0883315i
$846$		0			0
$847$	−18.4509	+	31.9580i	−0.633982	+	1.09809i
$848$		0			0
$849$	6.01368	+	3.08484i	0.206389	+	0.105872i
$850$		0			0
$851$	−0.611514	+	0.222573i	−0.0209624	+	0.00762970i
$852$		0			0
$853$	5.43331	+	30.8139i	0.186033	+	1.05505i	0.924621	+	0.380889i	$0.124382\pi$
$853$	5.43331	+	30.8139i	0.186033	+	1.05505i	−0.738588	+	0.674157i	$0.764507\pi$
$854$		0			0
$855$	4.92801	+	17.5473i	0.168534	+	0.600104i
$856$		0			0
$857$	−15.7828	+	13.2433i	−0.539130	+	0.452383i	−0.871240	−	0.490857i	$-0.836684\pi$
$857$	−15.7828	+	13.2433i	−0.539130	+	0.452383i	0.332111	+	0.943240i	$0.392239\pi$
$858$		0			0
$859$	−6.17853	+	35.0402i	−0.210809	+	1.19556i	0.677224	+	0.735776i	$0.263183\pi$
$859$	−6.17853	+	35.0402i	−0.210809	+	1.19556i	−0.888033	+	0.459779i	$0.847929\pi$
$860$		0			0
$861$	0.0149996	−	0.00341980i	0.000511185	−	0.000116547i
$862$		0			0
$863$	−44.8431			−1.52648			−0.763238	−	0.646118i	$-0.776391\pi$
$863$	−44.8431			−1.52648			−0.763238	+	0.646118i	$0.776391\pi$
$864$		0			0
$865$	−19.5008			−0.663048
$866$		0			0
$867$	8.61564	−	27.9076i	0.292603	−	0.947792i
$868$		0			0
$869$	0.766849	−	4.34902i	0.0260136	−	0.147530i
$870$		0			0
$871$	10.4264	−	8.74877i	0.353284	−	0.296441i
$872$		0			0
$873$	10.2716	−	1.02289i	0.347642	−	0.0346195i
$874$		0			0
$875$	5.75483	+	32.6373i	0.194549	+	1.10334i
$876$		0			0
$877$	−3.02554	+	1.10121i	−0.102165	+	0.0371851i	−0.392597	−	0.919711i	$-0.628423\pi$
$877$	−3.02554	+	1.10121i	−0.102165	+	0.0371851i	0.290432	+	0.956896i	$0.406201\pi$
$878$		0			0
$879$	−0.342486	−	6.89537i	−0.0115518	−	0.232575i
$880$		0			0
$881$	−11.6812	+	20.2325i	−0.393550	+	0.681649i	−0.992915	−	0.118827i	$-0.962087\pi$
$881$	−11.6812	+	20.2325i	−0.393550	+	0.681649i	0.599365	+	0.800476i	$0.295420\pi$
$882$		0			0
$883$	−18.6083	−	32.2305i	−0.626218	−	1.08464i	−0.988304	−	0.152496i	$-0.951269\pi$
$883$	−18.6083	−	32.2305i	−0.626218	−	1.08464i	0.362086	−	0.932145i	$-0.382065\pi$
$884$		0			0
$885$	7.27776	+	17.2764i	0.244639	+	0.580739i
$886$		0			0
$887$	−4.84325	−	4.06397i	−0.162620	−	0.136455i	0.557846	−	0.829944i	$-0.311628\pi$
$887$	−4.84325	−	4.06397i	−0.162620	−	0.136455i	−0.720467	+	0.693490i	$0.756072\pi$
$888$		0			0
$889$	−8.00010	−	2.91180i	−0.268315	−	0.0976586i
$890$		0			0
$891$	−0.100876	−	4.20589i	−0.00337947	−	0.140903i
$892$		0			0
$893$	46.9914	+	17.1035i	1.57251	+	0.572346i
$894$		0			0
$895$	−14.8111	−	12.4280i	−0.495081	−	0.415422i
$896$		0			0
$897$	0.302428	+	0.717922i	0.0100978	+	0.0239707i
$898$		0			0
$899$	−2.74757	−	4.75894i	−0.0916367	−	0.158719i
$900$		0			0
$901$	−2.01719	+	3.49388i	−0.0672024	+	0.116398i
$902$		0			0
$903$	2.00073	+	40.2812i	0.0665800	+	1.34048i
$904$		0			0
$905$	21.5519	−	7.84423i	0.716408	−	0.260751i
$906$		0			0
$907$	1.13981	+	6.46421i	0.0378469	+	0.214640i	0.997866	−	0.0652938i	$-0.0207984\pi$
$907$	1.13981	+	6.46421i	0.0378469	+	0.214640i	−0.960019	+	0.279934i	$0.909687\pi$
$908$		0			0
$909$	6.48855	+	9.03410i	0.215212	+	0.299642i
$910$		0			0
$911$	−25.1993	+	21.1448i	−0.834891	+	0.700557i	−0.956408	−	0.292032i	$-0.905668\pi$
$911$	−25.1993	+	21.1448i	−0.834891	+	0.700557i	0.121517	+	0.992589i	$0.461224\pi$
$912$		0			0
$913$	−1.40365	+	7.96050i	−0.0464540	+	0.263454i
$914$		0			0
$915$	6.17623	−	20.0059i	0.204180	−	0.661375i
$916$		0			0
$917$	−38.8908			−1.28429
$918$		0			0
$919$	−30.1720			−0.995284			−0.497642	−	0.867383i	$-0.665801\pi$
$919$	−30.1720			−0.995284			−0.497642	+	0.867383i	$0.665801\pi$
$920$		0			0
$921$	11.1380	−	2.53939i	0.367010	−	0.0836756i
$922$		0			0
$923$	−0.866285	+	4.91295i	−0.0285141	+	0.161712i
$924$		0			0
$925$	13.4713	−	11.3038i	0.442935	−	0.371666i
$926$		0			0
$927$	−44.5613	−	11.3693i	−1.46359	−	0.373418i
$928$		0			0
$929$	0.327907	+	1.85965i	0.0107583	+	0.0610133i	0.989714	−	0.143058i	$-0.0456936\pi$
$929$	0.327907	+	1.85965i	0.0107583	+	0.0610133i	−0.978956	+	0.204071i	$0.934583\pi$
$930$		0			0
$931$	24.4229	−	8.88921i	0.800429	−	0.291332i
$932$		0			0
$933$	−9.63366	−	4.94179i	−0.315392	−	0.161787i
$934$		0			0
$935$	−0.0954110	+	0.165257i	−0.00312027	+	0.00540447i
$936$		0			0
$937$	−5.21901	−	9.03959i	−0.170498	−	0.295311i	0.768096	−	0.640334i	$-0.221204\pi$
$937$	−5.21901	−	9.03959i	−0.170498	−	0.295311i	−0.938594	+	0.345024i	$0.887871\pi$
$938$		0			0
$939$	16.5967	−	21.8998i	0.541613	−	0.714674i
$940$		0			0
$941$	−21.5122	−	18.0508i	−0.701276	−	0.588441i	0.220860	−	0.975306i	$-0.429114\pi$
$941$	−21.5122	−	18.0508i	−0.701276	−	0.588441i	−0.922136	+	0.386865i	$0.873558\pi$
$942$		0			0
$943$	−0.000341588	0	0.000124328i	−1.11236e−5	0	4.04867e-6i
$944$		0			0
$945$	18.2414	+	7.17427i	0.593392	+	0.233379i
$946$		0			0
$947$	−6.84131	−	2.49003i	−0.222313	−	0.0809152i	0.228463	−	0.973553i	$-0.426630\pi$
$947$	−6.84131	−	2.49003i	−0.222313	−	0.0809152i	−0.450775	+	0.892638i	$0.648852\pi$
$948$		0			0
$949$	37.3274	+	31.3214i	1.21170	+	1.01673i
$950$		0			0
$951$	−49.2234	−	6.18041i	−1.59618	−	0.200414i
$952$		0			0
$953$	−12.0274	−	20.8320i	−0.389604	−	0.674815i	0.602792	−	0.797898i	$-0.294055\pi$
$953$	−12.0274	−	20.8320i	−0.389604	−	0.674815i	−0.992396	+	0.123084i	$0.960722\pi$
$954$		0			0
$955$	−11.4079	+	19.7591i	−0.369151	+	0.639388i
$956$		0			0
$957$	1.29605	−	0.836641i	0.0418954	−	0.0270448i
$958$		0			0
$959$	65.3696	−	23.7926i	2.11089	−	0.768302i
$960$		0			0
$961$	−3.93864	−	22.3371i	−0.127053	−	0.720552i
$962$		0			0
$963$	−2.17033	+	28.7770i	−0.0699380	+	0.927325i
$964$		0			0
$965$	−1.83436	+	1.53921i	−0.0590503	+	0.0495491i
$966$		0			0
$967$	−7.65388	+	43.4073i	−0.246132	+	1.39588i	0.571717	+	0.820451i	$0.306278\pi$
$967$	−7.65388	+	43.4073i	−0.246132	+	1.39588i	−0.817849	+	0.575433i	$0.804833\pi$
$968$		0			0
$969$	2.40467	+	2.59286i	0.0772492	+	0.0832947i
$970$		0			0
$971$	35.2279			1.13052			0.565258	−	0.824914i	$-0.308777\pi$
$971$	35.2279			1.13052			0.565258	+	0.824914i	$0.308777\pi$
$972$		0			0
$973$	5.73072			0.183718
$974$		0			0
$975$	−14.3151	−	15.4353i	−0.458449	−	0.494327i
$976$		0			0
$977$	8.77041	−	49.7394i	0.280590	−	1.59131i	−0.440035	−	0.897981i	$-0.645034\pi$
$977$	8.77041	−	49.7394i	0.280590	−	1.59131i	0.720625	−	0.693325i	$-0.243855\pi$
$978$		0			0
$979$	−4.57241	+	3.83671i	−0.146135	+	0.122622i
$980$		0			0
$981$	3.73658	−	49.5442i	0.119300	−	1.58183i
$982$		0			0
$983$	−7.98170	−	45.2665i	−0.254577	−	1.44378i	−0.797157	−	0.603773i	$-0.793663\pi$
$983$	−7.98170	−	45.2665i	−0.254577	−	1.44378i	0.542580	−	0.840004i	$-0.317448\pi$
$984$		0			0
$985$	−7.10753	+	2.58693i	−0.226465	+	0.0824264i
$986$		0			0
$987$	45.1842	−	29.1678i	1.43823	−	0.928420i
$988$		0			0
$989$	0.476475	−	0.825279i	0.0151510	−	0.0262423i
$990$		0			0
$991$	−11.8591	−	20.5406i	−0.376718	−	0.652495i	0.613864	−	0.789411i	$-0.289614\pi$
$991$	−11.8591	−	20.5406i	−0.376718	−	0.652495i	−0.990583	+	0.136917i	$0.956281\pi$
$992$		0			0
$993$	−44.1008	−	5.53722i	−1.39950	−	0.175718i
$994$		0			0
$995$	−1.87986	−	1.57739i	−0.0595956	−	0.0500066i
$996$		0			0
$997$	27.1269	+	9.87338i	0.859117	+	0.312693i	0.733752	−	0.679418i	$-0.237768\pi$
$997$	27.1269	+	9.87338i	0.859117	+	0.312693i	0.125365	+	0.992111i	$0.459990\pi$
$998$		0			0
$999$	−3.58083	−	23.8731i	−0.113292	−	0.755311i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	864.2.y.c.193.3	yes	54
4.3	odd	2		864.2.y.b.193.7	✓	54
27.7	even	9	inner	864.2.y.c.385.3	yes	54
108.7	odd	18		864.2.y.b.385.7	yes	54

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
864.2.y.b.193.7	✓	54	4.3	odd	2
864.2.y.b.385.7	yes	54	108.7	odd	18
864.2.y.c.193.3	yes	54	1.1	even	1	trivial
864.2.y.c.385.3	yes	54	27.7	even	9	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 864 = 2^{5} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	864.y (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.17779 - 1.26996i) q^{3} +(0.191385 - 1.08540i) q^{5} +(-2.62195 + 2.20007i) q^{7} +(-0.225616 + 2.99150i) q^{9} +O(q^{10})\)	\(q+(-1.17779 - 1.26996i) q^{3} +(0.191385 - 1.08540i) q^{5} +(-2.62195 + 2.20007i) q^{7} +(-0.225616 + 2.99150i) q^{9} +(0.0811727 + 0.460354i) q^{11} +(3.01725 - 1.09819i) q^{13} +(-1.60382 + 1.03532i) q^{15} +(-0.185192 + 0.320761i) q^{17} +(2.75617 + 4.77383i) q^{19} +(5.88212 + 0.738549i) q^{21} +(-0.107304 - 0.0900389i) q^{23} +(3.55701 + 1.29464i) q^{25} +(4.06483 - 3.23684i) q^{27} +(1.79039 + 0.651649i) q^{29} +(-2.20938 - 1.85389i) q^{31} +(0.489028 - 0.645287i) q^{33} +(1.88615 + 3.26691i) q^{35} +(2.32289 - 4.02336i) q^{37} +(-4.94836 - 2.53836i) q^{39} +(0.00243859 - 0.000887575i) q^{41} +(1.18135 + 6.69975i) q^{43} +(3.20379 + 0.817411i) q^{45} +(6.94945 - 5.83128i) q^{47} +(0.818739 - 4.64330i) q^{49} +(0.625473 - 0.142603i) q^{51} +10.8925 q^{53} +0.515201 q^{55} +(2.81640 - 9.12281i) q^{57} +(1.70529 - 9.67117i) q^{59} +(-8.40201 + 7.05012i) q^{61} +(-5.98998 - 8.33994i) q^{63} +(-0.614516 - 3.48509i) q^{65} +(3.98327 - 1.44979i) q^{67} +(0.0120358 + 0.242320i) q^{69} +(-0.776845 + 1.34554i) q^{71} +(7.58782 + 13.1425i) q^{73} +(-2.54526 - 6.04209i) q^{75} +(-1.22564 - 1.02844i) q^{77} +(-8.87740 - 3.23111i) q^{79} +(-8.89819 - 1.34986i) q^{81} +(16.2493 + 5.91426i) q^{83} +(0.312710 + 0.262395i) q^{85} +(-1.28114 - 3.04124i) q^{87} +(6.38441 + 11.0581i) q^{89} +(-5.49498 + 9.51758i) q^{91} +(0.247815 + 4.98934i) q^{93} +(5.70899 - 2.07790i) q^{95} +(-0.597491 - 3.38854i) q^{97} +(-1.39546 + 0.138965i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 54 q+O(q^{10}) \) 54 * q	\( 54 q + 9 q^{11} + 12 q^{17} - 18 q^{19} + 12 q^{21} + 21 q^{27} + 6 q^{29} - 36 q^{31} - 9 q^{33} - 24 q^{39} + 3 q^{41} + 21 q^{43} + 42 q^{45} - 18 q^{49} - 24 q^{51} + 36 q^{53} + 72 q^{55} + 39 q^{57} - 18 q^{59} - 18 q^{61} + 30 q^{63} + 48 q^{65} + 27 q^{67} + 24 q^{69} + 84 q^{75} + 36 q^{77} - 72 q^{79} + 36 q^{81} - 6 q^{87} + 33 q^{89} - 36 q^{91} + 72 q^{93} - 36 q^{95} + 9 q^{97} - 120 q^{99}+O(q^{100}) \) 54 * q + 9 * q^11 + 12 * q^17 - 18 * q^19 + 12 * q^21 + 21 * q^27 + 6 * q^29 - 36 * q^31 - 9 * q^33 - 24 * q^39 + 3 * q^41 + 21 * q^43 + 42 * q^45 - 18 * q^49 - 24 * q^51 + 36 * q^53 + 72 * q^55 + 39 * q^57 - 18 * q^59 - 18 * q^61 + 30 * q^63 + 48 * q^65 + 27 * q^67 + 24 * q^69 + 84 * q^75 + 36 * q^77 - 72 * q^79 + 36 * q^81 - 6 * q^87 + 33 * q^89 - 36 * q^91 + 72 * q^93 - 36 * q^95 + 9 * q^97 - 120 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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