LMFDB - Embedded newform 864.2.y.b.193.7

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			193.7
Character	$\chi$	$=$	864.193
Dual form			864.2.y.b.385.7

$q$-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	0.00529006	−	0.999986i	$-0.498316\pi$
$7$	2.62195	−	2.20007i	0.991003	−	0.831550i	0.985713	+	0.168436i	$0.0538717\pi$
$8$		0			0
$9$	−0.225616	+	2.99150i	−0.0752055	+	0.997168i
$10$		0			0
$11$	−0.0811727	−	0.460354i	−0.0244745	−	0.138802i	0.970122	−	0.242617i	$-0.0780059\pi$
$11$	−0.0811727	−	0.460354i	−0.0244745	−	0.138802i	−0.994597	+	0.103816i	$0.966895\pi$
$12$		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	$-0.948774\pi$
$19$	−2.75617	−	4.77383i	−0.632309	−	1.09519i	0.354769	−	0.934954i	$-0.384559\pi$
$20$		0			0
$21$	5.88212	+	0.738549i	1.28358	+	0.161165i
$22$		0			0
$23$	0.107304	+	0.0900389i	0.0223745	+	0.0187744i	0.653906	−	0.756576i	$-0.273129\pi$
$23$	0.107304	+	0.0900389i	0.0223745	+	0.0187744i	−0.631532	+	0.775350i	$0.717573\pi$
$24$		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	0.819262	−	0.573420i	$-0.194384\pi$
$31$	2.20938	+	1.85389i	0.396817	+	0.332969i	−0.422445	+	0.906389i	$0.638828\pi$
$32$		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	$-0.881960\pi$
$43$	−1.18135	−	6.69975i	−0.180154	−	1.02170i	0.751872	−	0.659310i	$-0.229151\pi$
$44$		0			0
$45$	3.20379	+	0.817411i	0.477592	+	0.121852i
$46$		0			0
$47$	−6.94945	+	5.83128i	−1.01368	+	0.850579i	−0.988820	−	0.149112i	$-0.952359\pi$
$47$	−6.94945	+	5.83128i	−1.01368	+	0.850579i	−0.0248605	+	0.999691i	$0.507914\pi$
$48$		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	$0.276311\pi$
$59$	−1.70529	+	9.67117i	−0.222010	+	1.25908i	−0.868320	+	0.496004i	$0.834800\pi$
$60$		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	−0.573672	−	0.819085i	$-0.694482\pi$
$67$	−3.98327	+	1.44979i	−0.486633	+	0.177120i	0.0870391	+	0.996205i	$0.472260\pi$
$68$		0			0
$69$	0.0120358	+	0.242320i	0.00144894	+	0.0291718i
$70$		0			0
$71$	0.776845	−	1.34554i	0.0921946	−	0.159686i	−0.816240	−	0.577713i	$-0.803945\pi$
$71$	0.776845	−	1.34554i	0.0921946	−	0.159686i	0.908434	+	0.418028i	$0.137278\pi$
$72$		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	0.789116	−	0.614244i	$-0.210539\pi$
$79$	8.87740	+	3.23111i	0.998785	+	0.363528i	0.209669	+	0.977772i	$0.432761\pi$
$80$		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	$-0.990956\pi$
$83$	−16.2493	−	5.91426i	−1.78359	−	0.649174i	−0.783995	−	0.620767i	$-0.786821\pi$
$84$		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	$-0.671967\pi$
$103$	2.66196	−	15.0967i	0.262291	−	1.48752i	0.776640	−	0.629944i	$-0.216922\pi$
$104$		0			0
$105$	1.92737	−	6.24308i	0.188092	−	0.609263i
$106$		0			0
$107$	−9.61957			−0.929959			−0.464979	−	0.885322i	$-0.653938\pi$
$107$	−9.61957			−0.929959			−0.464979	+	0.885322i	$0.653938\pi$
$108$		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	0.805556	−	0.592520i	$-0.201867\pi$
$127$	−1.24368	−	2.15412i	−0.110359	−	0.191147i	−0.915915	+	0.401372i	$0.868533\pi$
$128$		0			0
$129$	7.11706	−	9.39118i	0.626622	−	0.826847i
$130$		0			0
$131$	−8.70424	−	7.30372i	−0.760493	−	0.638129i	0.177762	−	0.984073i	$-0.443114\pi$
$131$	−8.70424	−	7.30372i	−0.760493	−	0.638129i	−0.938255	+	0.345944i	$0.887559\pi$
$132$		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	0.695560	−	0.718468i	$-0.255156\pi$
$139$	1.28261	+	1.07623i	0.108789	+	0.0912850i	−0.586771	+	0.809753i	$0.699601\pi$
$140$		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	$-0.862642\pi$
$151$	−2.43098	−	13.7868i	−0.197830	−	1.12195i	0.710500	−	0.703697i	$-0.248469\pi$
$152$		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	$-0.407162\pi$
$163$	7.34218			0.575084			0.287542	+	0.957768i	$0.407162\pi$
$164$		0			0
$165$	−0.606799	−	0.654287i	−0.0472393	−	0.0509362i
$166$		0			0
$167$	0.437475	−	2.48105i	0.0338529	−	0.191989i	−0.963192	−	0.268816i	$-0.913368\pi$
$167$	0.437475	−	2.48105i	0.0338529	−	0.191989i	0.997044	+	0.0768267i	$0.0244788\pi$
$168$		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	$0.394252\pi$
$179$	−8.77136	+	15.1924i	−0.655602	+	1.13554i	−0.981742	+	0.190215i	$0.939081\pi$
$180$		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	0.930414	−	0.366511i	$-0.119448\pi$
$191$	19.4529	+	7.08028i	1.40756	+	0.512311i	0.477150	+	0.878822i	$0.341670\pi$
$192$		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	−0.902784	−	0.430095i	$-0.858480\pi$
$199$	−1.11328	+	1.92826i	−0.0789184	+	0.136691i	0.823865	+	0.566786i	$0.191813\pi$
$200$		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	−0.972716	−	0.231999i	$-0.925473\pi$
$211$	0.300487	−	1.70415i	0.0206864	−	0.117318i	0.993402	+	0.114681i	$0.0365845\pi$
$212$		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	−0.976703	−	0.214595i	$-0.931157\pi$
$223$	−13.9621	+	11.7156i	−0.934972	+	0.784534i	0.0417317	+	0.999129i	$0.486713\pi$
$224$		0			0
$225$	−4.67545	+	10.3487i	−0.311697	+	0.689914i
$226$		0			0
$227$	−0.505142	−	2.86480i	−0.0335274	−	0.190143i	0.963444	−	0.267909i	$-0.0863326\pi$
$227$	−0.505142	−	2.86480i	−0.0335274	−	0.190143i	−0.996972	+	0.0777654i	$0.975221\pi$
$228$		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	$-0.991742\pi$
$239$	−18.5330	−	15.5510i	−1.19880	−	1.00591i	−0.199137	−	0.979972i	$-0.563814\pi$
$240$		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	0.999938	−	0.0111628i	$-0.00355330\pi$
$251$	7.76784	+	13.4543i	0.490302	+	0.849227i	−0.509636	+	0.860390i	$0.670220\pi$
$252$		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	−0.781725	−	0.623624i	$-0.785660\pi$
$263$	−4.91903	+	4.12756i	−0.303321	+	0.254516i	0.478404	+	0.878140i	$0.341215\pi$
$264$		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	$-0.585121\pi$
$271$	−8.69990			−0.528481			−0.264241	+	0.964457i	$0.585121\pi$
$272$		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	−0.230727	−	0.973019i	$-0.574110\pi$
$283$	3.66683	−	1.33462i	0.217971	−	0.0793348i	0.448697	+	0.893684i	$0.351888\pi$
$284$		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	−0.756441	−	0.654062i	$-0.773063\pi$
$307$	3.29778	−	5.71191i	0.188214	−	0.325996i	0.944655	+	0.328066i	$0.106397\pi$
$308$		0			0
$309$	22.3075	−	14.4002i	1.26903	−	0.819199i
$310$		0			0
$311$	−5.87411	+	2.13800i	−0.333090	+	0.121235i	−0.503151	−	0.864199i	$-0.667826\pi$
$311$	−5.87411	+	2.13800i	−0.333090	+	0.121235i	0.170060	+	0.985434i	$0.445604\pi$
$312$		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	−0.995962	−	0.0897789i	$-0.971384\pi$
$331$	−19.6579	+	16.4949i	−1.08049	+	0.906642i	−0.0845320	+	0.996421i	$0.526940\pi$
$332$		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	0.997852	−	0.0655091i	$-0.0208672\pi$
$347$	20.6139	+	17.2971i	1.10661	+	0.928559i	0.108761	+	0.994068i	$0.465312\pi$
$348$		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	0.650321	−	0.759660i	$-0.274634\pi$
$359$	−6.30422	−	10.9192i	−0.332724	−	0.576295i	−0.983045	+	0.183365i	$0.941301\pi$
$360$		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	$0.0186230\pi$
$367$	1.53647	+	8.71374i	0.0802030	+	0.454854i	−0.918086	+	0.396381i	$0.870266\pi$
$368$		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	$-0.315680\pi$
$379$	21.3071			1.09447			0.547235	+	0.836979i	$0.315680\pi$
$380$		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	$0.130403\pi$
$383$	−1.58349	+	8.98044i	−0.0809127	+	0.458879i	−0.998164	+	0.0605698i	$0.980708\pi$
$384$		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	0.524837	−	0.851203i	$-0.324126\pi$
$419$	30.1726	−	10.9819i	1.47403	−	0.536502i	0.949191	+	0.314700i	$0.101904\pi$
$420$		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	$-0.169461\pi$
$431$	35.7747			1.72321			0.861603	+	0.507583i	$0.169461\pi$
$432$		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	−0.874560	−	0.484916i	$-0.838850\pi$
$439$	−11.5002	+	9.64985i	−0.548877	+	0.460562i	0.325684	+	0.945479i	$0.394406\pi$
$440$		0			0
$441$	13.7057	+	3.49687i	0.652654	+	0.166517i
$442$		0			0
$443$	1.08004	+	6.12523i	0.0513144	+	0.291019i	0.999656	−	0.0262329i	$-0.00835116\pi$
$443$	1.08004	+	6.12523i	0.0513144	+	0.291019i	−0.948341	+	0.317252i	$0.897240\pi$
$444$		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	0.589240	−	0.807958i	$-0.299427\pi$
$463$	−2.24046	−	1.87997i	−0.104123	−	0.0873694i	−0.693363	+	0.720589i	$0.743872\pi$
$464$		0			0
$465$	5.46283	+	0.685905i	0.253333	+	0.0318081i
$466$		0			0
$467$	0.566231	+	0.980742i	0.0262021	+	0.0453833i	0.878829	−	0.477137i	$-0.158325\pi$
$467$	0.566231	+	0.980742i	0.0262021	+	0.0453833i	−0.852627	+	0.522520i	$0.824992\pi$
$468$		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	−0.950033	−	0.312150i	$-0.898951\pi$
$479$	−17.6751	+	14.8312i	−0.807597	+	0.677654i	0.142436	+	0.989804i	$0.454506\pi$
$480$		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	$-0.707512\pi$
$487$	−26.7780			−1.21343			−0.606713	+	0.794921i	$0.707512\pi$
$488$		0			0
$489$	8.64756	+	9.32431i	0.391056	+	0.421660i
$490$		0			0
$491$	1.15676	−	6.56030i	0.0522038	−	0.296062i	−0.947517	−	0.319706i	$-0.896416\pi$
$491$	1.15676	−	6.56030i	0.0522038	−	0.296062i	0.999720	+	0.0236441i	$0.00752684\pi$
$492$		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	−0.615194	−	0.788375i	$-0.710922\pi$
$499$	−12.9496	+	4.71326i	−0.579703	+	0.210994i	0.0354918	+	0.999370i	$0.488700\pi$
$500$		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	$-0.506527\pi$
$503$	19.1889	−	33.2362i	0.855592	−	1.48193i	0.876095	−	0.482138i	$-0.160140\pi$
$504$		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	−0.970089	−	0.242750i	$-0.921950\pi$
$523$	−6.28483	+	10.8856i	−0.274816	+	0.475996i	0.695272	+	0.718746i	$0.255284\pi$
$524$		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	−0.938100	−	0.346365i	$-0.887416\pi$
$547$	−17.7725	+	14.9129i	−0.759896	+	0.637628i	0.178204	+	0.983994i	$0.442971\pi$
$548$		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	$0.133942\pi$
$563$	34.9637	+	29.3380i	1.47354	+	1.23645i	0.560777	+	0.827967i	$0.310503\pi$
$564$		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	$0.106388\pi$
$571$	34.2127	+	28.7079i	1.43176	+	1.20139i	0.487095	+	0.873349i	$0.338057\pi$
$572$		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	−0.633770	−	0.773521i	$-0.718494\pi$
$587$	0.434808	−	0.364847i	0.0179465	−	0.0150589i	0.651717	+	0.758462i	$0.274049\pi$
$588$		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	−0.992648	−	0.121039i	$-0.961378\pi$
$599$	−0.451954	+	2.56316i	−0.0184663	+	0.104728i	0.974181	+	0.225766i	$0.0724886\pi$
$600$		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	−0.605081	−	0.796164i	$-0.706859\pi$
$607$	−13.7189	+	4.99329i	−0.556835	+	0.202671i	0.0482459	+	0.998835i	$0.484637\pi$
$608$		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	0.518393	−	0.855143i	$-0.326530\pi$
$619$	9.10175	+	3.31276i	0.365830	+	0.133151i	−0.152563	+	0.988294i	$0.548753\pi$
$620$		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	$0.477376\pi$
$631$	−20.8074	+	36.0395i	−0.828330	+	1.43471i	−0.899347	+	0.437235i	$0.855958\pi$
$632$		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	$0.426021\pi$
$643$	−8.08736	+	45.8657i	−0.318934	+	1.80877i	−0.549259	+	0.835652i	$0.685090\pi$
$644$		0			0
$645$	−8.83105	−	9.52216i	−0.347722	−	0.374935i
$646$		0			0
$647$	12.4615			0.489911			0.244955	−	0.969534i	$-0.421227\pi$
$647$	12.4615			0.489911			0.244955	+	0.969534i	$0.421227\pi$
$648$		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	$-0.938504\pi$
$659$	−3.20506	−	18.1768i	−0.124851	−	0.708067i	0.856545	−	0.516073i	$-0.172607\pi$
$660$		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	0.687431	−	0.726250i	$-0.258739\pi$
$683$	−7.45443	−	12.9114i	−0.285236	−	0.494043i	−0.972666	+	0.232207i	$0.925405\pi$
$684$		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	$-0.657423\pi$
$691$	−8.66581	−	49.1463i	−0.329663	−	1.86961i	0.144981	−	0.989435i	$-0.453688\pi$
$692$		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	$-0.624623\pi$
$719$	16.3486	−	28.3166i	0.609700	−	1.05603i	0.991290	−	0.131699i	$-0.0420433\pi$
$720$		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	$0.0304119\pi$
$727$	49.0539	+	17.8542i	1.81931	+	0.662175i	0.823871	+	0.566778i	$0.191810\pi$
$728$		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	−0.581382	−	0.813631i	$-0.697488\pi$
$739$	11.2526	−	19.4901i	0.413934	−	0.716955i	0.995316	+	0.0966761i	$0.0308211\pi$
$740$		0			0
$741$	−1.52080	−	30.6188i	−0.0558681	−	1.12481i
$742$		0			0
$743$	22.6713	−	8.25166i	0.831728	−	0.302724i	0.109160	−	0.994024i	$-0.465184\pi$
$743$	22.6713	−	8.25166i	0.831728	−	0.302724i	0.722568	+	0.691300i	$0.242962\pi$
$744$		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	$-0.786878\pi$
$751$	4.52117	−	25.6408i	0.164980	−	0.935647i	0.949085	−	0.315019i	$-0.102011\pi$
$752$		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	0.427136	−	0.904187i	$-0.359523\pi$
$787$	−10.9168	−	9.16032i	−0.389143	−	0.326530i	−0.816279	+	0.577657i	$0.803967\pi$
$788$		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	$-0.543024\pi$
$811$	−7.67492			−0.269503			−0.134752	+	0.990879i	$0.543024\pi$
$812$		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	−0.332151	−	0.943226i	$-0.607774\pi$
$823$	0.565199	−	0.205716i	0.0197016	−	0.00717080i	0.351852	+	0.936056i	$0.385552\pi$
$824$		0			0
$825$	2.57489	−	1.66217i	0.0896462	−	0.0578694i
$826$		0			0
$827$	4.24272	−	7.34861i	0.147534	−	0.255536i	−0.782782	−	0.622297i	$-0.786200\pi$
$827$	4.24272	−	7.34861i	0.147534	−	0.255536i	0.930315	+	0.366760i	$0.119533\pi$
$828$		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	−0.116665	−	0.993171i	$-0.537220\pi$
$839$	−24.4594	−	8.90251i	−0.844433	−	0.307349i	−0.727769	+	0.685823i	$0.759443\pi$
$840$		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	$-0.736817\pi$
$859$	6.17853	−	35.0402i	0.210809	−	1.19556i	0.888033	−	0.459779i	$-0.152071\pi$
$860$		0			0
$861$	0.0149996	−	0.00341980i	0.000511185	−	0.000116547i
$862$		0			0
$863$	44.8431			1.52648			0.763238	−	0.646118i	$-0.223609\pi$
$863$	44.8431			1.52648			0.763238	+	0.646118i	$0.223609\pi$
$864$		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	$0.0487313\pi$
$883$	18.6083	+	32.2305i	0.626218	+	1.08464i	−0.362086	+	0.932145i	$0.617935\pi$
$884$		0			0
$885$	7.27776	+	17.2764i	0.244639	+	0.580739i
$886$		0			0
$887$	4.84325	+	4.06397i	0.162620	+	0.136455i	0.720467	−	0.693490i	$-0.243928\pi$
$887$	4.84325	+	4.06397i	0.162620	+	0.136455i	−0.557846	+	0.829944i	$0.688372\pi$
$888$		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	0.960019	−	0.279934i	$-0.0903127\pi$
$907$	−1.13981	−	6.46421i	−0.0378469	−	0.214640i	−0.997866	+	0.0652938i	$0.979202\pi$
$908$		0			0
$909$	6.48855	+	9.03410i	0.215212	+	0.299642i
$910$		0			0
$911$	25.1993	−	21.1448i	0.834891	−	0.700557i	−0.121517	−	0.992589i	$-0.538776\pi$
$911$	25.1993	−	21.1448i	0.834891	−	0.700557i	0.956408	+	0.292032i	$0.0943315\pi$
$912$		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	$-0.334199\pi$
$919$	30.1720			0.995284			0.497642	+	0.867383i	$0.334199\pi$
$920$		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	0.450775	−	0.892638i	$-0.351148\pi$
$947$	6.84131	+	2.49003i	0.222313	+	0.0809152i	−0.228463	+	0.973553i	$0.573370\pi$
$948$		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	$-0.693722\pi$
$967$	7.65388	−	43.4073i	0.246132	−	1.39588i	0.817849	−	0.575433i	$-0.195167\pi$
$968$		0			0
$969$	2.40467	+	2.59286i	0.0772492	+	0.0832947i
$970$		0			0
$971$	−35.2279			−1.13052			−0.565258	−	0.824914i	$-0.691223\pi$
$971$	−35.2279			−1.13052			−0.565258	+	0.824914i	$0.691223\pi$
$972$		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	$0.206337\pi$
$983$	7.98170	+	45.2665i	0.254577	+	1.44378i	−0.542580	+	0.840004i	$0.682552\pi$
$984$		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	0.990583	−	0.136917i	$-0.0437192\pi$
$991$	11.8591	+	20.5406i	0.376718	+	0.652495i	−0.613864	+	0.789411i	$0.710386\pi$
$992$		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.b.193.7	✓	54
4.3	odd	2		864.2.y.c.193.3	yes	54
27.7	even	9	inner	864.2.y.b.385.7	yes	54
108.7	odd	18		864.2.y.c.385.3	yes	54

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

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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