LMFDB - Embedded newform 864.2.bi.a.95.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [864,2,Mod(95,864)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

chi = DirichletCharacter(H, H._module([9, 0, 17]))

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

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

chi := DirichletCharacter("864.95");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$6.89907473464$
Analytic rank:	$0$
Dimension:	$216$
Relative dimension:	$36$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			95.12
Character	$\chi$	$=$	864.95
Dual form			864.2.bi.a.191.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.948095 - 1.44952i) q^{3} +(0.639391 - 0.761997i) q^{5} +(1.09080 - 2.99694i) q^{7} +(-1.20223 + 2.74857i) q^{9} +O(q^{10})$	\(q+(-0.948095 - 1.44952i) q^{3} +(0.639391 - 0.761997i) q^{5} +(1.09080 - 2.99694i) q^{7} +(-1.20223 + 2.74857i) q^{9} +(3.13020 - 2.62655i) q^{11} +(0.0936778 - 0.531273i) q^{13} +(-1.71073 - 0.204367i) q^{15} +(-3.62860 - 2.09497i) q^{17} +(1.81639 - 1.04869i) q^{19} +(-5.37831 + 1.26025i) q^{21} +(-0.324292 + 0.118033i) q^{23} +(0.696423 + 3.94961i) q^{25} +(5.12395 - 0.863242i) q^{27} +(5.07035 - 0.894039i) q^{29} +(0.748585 + 2.05672i) q^{31} +(-6.77496 - 2.04708i) q^{33} +(-1.58621 - 2.74740i) q^{35} +(0.779711 - 1.35050i) q^{37} +(-0.858908 + 0.367909i) q^{39} +(-10.6914 - 1.88519i) q^{41} +(-7.54575 - 8.99267i) q^{43} +(1.32570 + 2.67351i) q^{45} +(-7.77604 - 2.83025i) q^{47} +(-2.42950 - 2.03859i) q^{49} +(0.403546 + 7.24597i) q^{51} +1.35172i q^{53} -4.06459i q^{55} +(-3.24221 - 1.63864i) q^{57} +(-7.48289 - 6.27889i) q^{59} +(6.13900 + 2.23441i) q^{61} +(6.92591 + 6.60115i) q^{63} +(-0.344932 - 0.411074i) q^{65} +(0.348168 + 0.0613915i) q^{67} +(0.478551 + 0.358163i) q^{69} +(-4.98682 + 8.63743i) q^{71} +(1.02639 + 1.77776i) q^{73} +(5.06478 - 4.75409i) q^{75} +(-4.45719 - 12.2460i) q^{77} +(15.1479 - 2.67098i) q^{79} +(-6.10927 - 6.60884i) q^{81} +(0.957481 + 5.43015i) q^{83} +(-3.91646 + 1.42547i) q^{85} +(-6.10310 - 6.50195i) q^{87} +(-0.959546 + 0.553994i) q^{89} +(-1.49001 - 0.860258i) q^{91} +(2.27153 - 3.03506i) q^{93} +(0.362282 - 2.05461i) q^{95} +(-13.2583 + 11.1251i) q^{97} +(3.45602 + 11.7613i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 216 q+O(q^{10}) $ 216 * q	$ 216 q - 24 q^{29} + 36 q^{33} + 36 q^{41} - 24 q^{45} + 12 q^{57} + 48 q^{65} + 48 q^{69} + 48 q^{77} + 48 q^{81} + 36 q^{89} - 144 q^{93} - 36 q^{97}+O(q^{100}) $ 216 * q - 24 * q^29 + 36 * q^33 + 36 * q^41 - 24 * q^45 + 12 * q^57 + 48 * q^65 + 48 * q^69 + 48 * q^77 + 48 * q^81 + 36 * q^89 - 144 * q^93 - 36 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$325$	$353$	$703$
$\chi(n)$	$1$	$e\left(\frac{17}{18}\right)$	$-1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.948095	−	1.44952i	−0.547383	−	0.836882i
$3$	−0.948095	−	1.44952i	−0.547383	−	0.836882i
$4$		0			0
$5$	0.639391	−	0.761997i	0.285944	−	0.340775i	−0.603883	−	0.797073i	$-0.706380\pi$
$5$	0.639391	−	0.761997i	0.285944	−	0.340775i	0.889827	+	0.456298i	$0.150825\pi$
$6$		0			0
$7$	1.09080	−	2.99694i	0.412282	−	1.13274i	−0.543692	−	0.839285i	$-0.682974\pi$
$7$	1.09080	−	2.99694i	0.412282	−	1.13274i	0.955974	−	0.293452i	$-0.0948039\pi$
$8$		0			0
$9$	−1.20223	+	2.74857i	−0.400744	+	0.916190i
$10$		0			0
$11$	3.13020	−	2.62655i	0.943790	−	0.791933i	−0.0344512	−	0.999406i	$-0.510968\pi$
$11$	3.13020	−	2.62655i	0.943790	−	0.791933i	0.978241	+	0.207473i	$0.0665239\pi$
$12$		0			0
$13$	0.0936778	−	0.531273i	0.0259816	−	0.147349i	−0.969057	−	0.246836i	$-0.920609\pi$
$13$	0.0936778	−	0.531273i	0.0259816	−	0.147349i	0.995039	+	0.0994872i	$0.0317202\pi$
$14$		0			0
$15$	−1.71073	−	0.204367i	−0.441710	−	0.0527673i
$16$		0			0
$17$	−3.62860	−	2.09497i	−0.880065	−	0.508106i	−0.00938501	−	0.999956i	$-0.502987\pi$
$17$	−3.62860	−	2.09497i	−0.880065	−	0.508106i	−0.870680	+	0.491850i	$0.836321\pi$
$18$		0			0
$19$	1.81639	−	1.04869i	0.416708	−	0.240586i	−0.276960	−	0.960881i	$-0.589327\pi$
$19$	1.81639	−	1.04869i	0.416708	−	0.240586i	0.693668	+	0.720295i	$0.255994\pi$
$20$		0			0
$21$	−5.37831	+	1.26025i	−1.17364	+	0.275009i
$22$		0			0
$23$	−0.324292	+	0.118033i	−0.0676196	+	0.0246115i	−0.375609	−	0.926778i	$-0.622566\pi$
$23$	−0.324292	+	0.118033i	−0.0676196	+	0.0246115i	0.307989	+	0.951390i	$0.400344\pi$
$24$		0			0
$25$	0.696423	+	3.94961i	0.139285	+	0.789922i
$26$		0			0
$27$	5.12395	−	0.863242i	0.986104	−	0.166131i
$28$		0			0
$29$	5.07035	−	0.894039i	0.941539	−	0.166019i	0.318247	−	0.948008i	$-0.396906\pi$
$29$	5.07035	−	0.894039i	0.941539	−	0.166019i	0.623292	+	0.781989i	$0.285795\pi$
$30$		0			0
$31$	0.748585	+	2.05672i	0.134450	+	0.369398i	0.988587	−	0.150650i	$-0.0481365\pi$
$31$	0.748585	+	2.05672i	0.134450	+	0.369398i	−0.854137	+	0.520047i	$0.825914\pi$
$32$		0			0
$33$	−6.77496	−	2.04708i	−1.17937	−	0.356350i
$34$		0			0
$35$	−1.58621	−	2.74740i	−0.268119	−	0.464395i
$36$		0			0
$37$	0.779711	−	1.35050i	0.128184	−	0.222021i	−0.794789	−	0.606886i	$-0.792419\pi$
$37$	0.779711	−	1.35050i	0.128184	−	0.222021i	0.922973	+	0.384865i	$0.125752\pi$
$38$		0			0
$39$	−0.858908	+	0.367909i	−0.137535	+	0.0589127i
$40$		0			0
$41$	−10.6914	−	1.88519i	−1.66972	−	0.294417i	−0.742756	−	0.669562i	$-0.766482\pi$
$41$	−10.6914	−	1.88519i	−1.66972	−	0.294417i	−0.926966	+	0.375145i	$0.877593\pi$
$42$		0			0
$43$	−7.54575	−	8.99267i	−1.15072	−	1.37137i	−0.916914	−	0.399085i	$-0.869328\pi$
$43$	−7.54575	−	8.99267i	−1.15072	−	1.37137i	−0.233802	−	0.972284i	$-0.575117\pi$
$44$		0			0
$45$	1.32570	+	2.67351i	0.197624	+	0.398543i
$46$		0			0
$47$	−7.77604	−	2.83025i	−1.13425	−	0.412834i	−0.294418	−	0.955677i	$-0.595126\pi$
$47$	−7.77604	−	2.83025i	−1.13425	−	0.412834i	−0.839834	+	0.542843i	$0.817348\pi$
$48$		0			0
$49$	−2.42950	−	2.03859i	−0.347071	−	0.291227i
$50$		0			0
$51$	0.403546	+	7.24597i	0.0565077	+	1.01464i
$52$		0			0
$53$			1.35172i			0.185673i	0.995681	+	0.0928364i	$0.0295934\pi$
$53$			1.35172i			0.185673i	−0.995681	+	0.0928364i	$0.970407\pi$
$54$		0			0
$55$		−	4.06459i		−	0.548069i
$56$		0			0
$57$	−3.24221	−	1.63864i	−0.429441	−	0.217043i
$58$		0			0
$59$	−7.48289	−	6.27889i	−0.974190	−	0.817442i	0.00901309	−	0.999959i	$-0.497131\pi$
$59$	−7.48289	−	6.27889i	−0.974190	−	0.817442i	−0.983203	+	0.182517i	$0.941575\pi$
$60$		0			0
$61$	6.13900	+	2.23441i	0.786018	+	0.286087i	0.703680	−	0.710517i	$-0.251539\pi$
$61$	6.13900	+	2.23441i	0.786018	+	0.286087i	0.0823382	+	0.996604i	$0.473761\pi$
$62$		0			0
$63$	6.92591	+	6.60115i	0.872582	+	0.831667i
$64$		0			0
$65$	−0.344932	−	0.411074i	−0.0427835	−	0.0509874i
$66$		0			0
$67$	0.348168	+	0.0613915i	0.0425355	+	0.00750016i	0.194875	−	0.980828i	$-0.437570\pi$
$67$	0.348168	+	0.0613915i	0.0425355	+	0.00750016i	−0.152340	+	0.988328i	$0.548681\pi$
$68$		0			0
$69$	0.478551	+	0.358163i	0.0576108	+	0.0431178i
$70$		0			0
$71$	−4.98682	+	8.63743i	−0.591827	+	1.02507i	0.402160	+	0.915570i	$0.368260\pi$
$71$	−4.98682	+	8.63743i	−0.591827	+	1.02507i	−0.993986	+	0.109504i	$0.965074\pi$
$72$		0			0
$73$	1.02639	+	1.77776i	0.120130	+	0.208071i	0.919819	−	0.392343i	$-0.128335\pi$
$73$	1.02639	+	1.77776i	0.120130	+	0.208071i	−0.799689	+	0.600415i	$0.795002\pi$
$74$		0			0
$75$	5.06478	−	4.75409i	0.584830	−	0.548955i
$76$		0			0
$77$	−4.45719	−	12.2460i	−0.507944	−	1.39557i
$78$		0			0
$79$	15.1479	−	2.67098i	1.70427	−	0.300509i	0.765089	−	0.643925i	$-0.222695\pi$
$79$	15.1479	−	2.67098i	1.70427	−	0.300509i	0.939184	+	0.343415i	$0.111584\pi$
$80$		0			0
$81$	−6.10927	−	6.60884i	−0.678808	−	0.734316i
$82$		0			0
$83$	0.957481	+	5.43015i	0.105097	+	0.596036i	0.991181	+	0.132512i	$0.0423042\pi$
$83$	0.957481	+	5.43015i	0.105097	+	0.596036i	−0.886084	+	0.463524i	$0.846585\pi$
$84$		0			0
$85$	−3.91646	+	1.42547i	−0.424799	+	0.154614i
$86$		0			0
$87$	−6.10310	−	6.50195i	−0.654321	−	0.697082i
$88$		0			0
$89$	−0.959546	+	0.553994i	−0.101712	+	0.0587233i	−0.549993	−	0.835169i	$-0.685370\pi$
$89$	−0.959546	+	0.553994i	−0.101712	+	0.0587233i	0.448281	+	0.893893i	$0.352036\pi$
$90$		0			0
$91$	−1.49001	−	0.860258i	−0.156196	−	0.0901796i
$92$		0			0
$93$	2.27153	−	3.03506i	0.235547	−	0.314721i
$94$		0			0
$95$	0.362282	−	2.05461i	0.0371694	−	0.210798i
$96$		0			0
$97$	−13.2583	+	11.1251i	−1.34618	+	1.12958i	−0.366188	+	0.930541i	$0.619337\pi$
$97$	−13.2583	+	11.1251i	−1.34618	+	1.12958i	−0.979992	+	0.199038i	$0.936218\pi$
$98$		0			0
$99$	3.45602	+	11.7613i	0.347343	+	1.18205i
$100$		0			0
$101$	1.43768	−	3.94998i	0.143054	−	0.393038i	−0.847387	−	0.530976i	$-0.821825\pi$
$101$	1.43768	−	3.94998i	0.143054	−	0.393038i	0.990441	+	0.137938i	$0.0440476\pi$
$102$		0			0
$103$	12.4917	−	14.8870i	1.23084	−	1.46686i	0.394280	−	0.918990i	$-0.370994\pi$
$103$	12.4917	−	14.8870i	1.23084	−	1.46686i	0.836563	−	0.547871i	$-0.184562\pi$
$104$		0			0
$105$	−2.47854	+	4.90405i	−0.241881	+	0.478586i
$106$		0			0
$107$	−10.0006			−0.966799			−0.483399	−	0.875400i	$-0.660598\pi$
$107$	−10.0006			−0.966799			−0.483399	+	0.875400i	$0.660598\pi$
$108$		0			0
$109$	16.7896			1.60816			0.804078	−	0.594523i	$-0.202659\pi$
$109$	16.7896			1.60816			0.804078	+	0.594523i	$0.202659\pi$
$110$		0			0
$111$	−2.69682	+	0.150192i	−0.255971	+	0.0142556i
$112$		0			0
$113$	6.00421	−	7.15554i	0.564829	−	0.673137i	−0.405732	−	0.913992i	$-0.632983\pi$
$113$	6.00421	−	7.15554i	0.564829	−	0.673137i	0.970561	+	0.240855i	$0.0774279\pi$
$114$		0			0
$115$	−0.117409	+	0.322579i	−0.0109485	+	0.0300806i
$116$		0			0
$117$	1.34762	+	0.896194i	0.124587	+	0.0828532i
$118$		0			0
$119$	−10.2366	+	8.58951i	−0.938385	+	0.787399i
$120$		0			0
$121$	0.989251	−	5.61032i	0.0899319	−	0.510029i
$122$		0			0
$123$	7.40387	+	17.2848i	0.667585	+	1.55852i
$124$		0			0
$125$	7.76212	+	4.48146i	0.694265	+	0.400834i
$126$		0			0
$127$	−4.69208	+	2.70897i	−0.416355	+	0.240382i	−0.693516	−	0.720441i	$-0.743940\pi$
$127$	−4.69208	+	2.70897i	−0.416355	+	0.240382i	0.277162	+	0.960823i	$0.410606\pi$
$128$		0			0
$129$	−5.88100	+	19.4636i	−0.517793	+	1.71368i
$130$		0			0
$131$	3.55492	−	1.29389i	0.310595	−	0.113047i	−0.182020	−	0.983295i	$-0.558263\pi$
$131$	3.55492	−	1.29389i	0.310595	−	0.113047i	0.492615	+	0.870248i	$0.336041\pi$
$132$		0			0
$133$	−1.16156	−	6.58751i	−0.100720	−	0.571210i
$134$		0			0
$135$	2.61842	−	4.45638i	0.225357	−	0.383544i
$136$		0			0
$137$	17.0978	−	3.01480i	1.46076	−	0.257571i	0.613899	−	0.789385i	$-0.289600\pi$
$137$	17.0978	−	3.01480i	1.46076	−	0.257571i	0.846862	+	0.531813i	$0.178489\pi$
$138$		0			0
$139$	1.41729	+	3.89397i	0.120213	+	0.330282i	0.985174	−	0.171556i	$-0.0548795\pi$
$139$	1.41729	+	3.89397i	0.120213	+	0.330282i	−0.864962	+	0.501838i	$0.832657\pi$
$140$		0			0
$141$	3.26992	+	13.9549i	0.275377	+	1.17521i
$142$		0			0
$143$	−1.10218	−	1.90904i	−0.0921693	−	0.159642i
$144$		0			0
$145$	2.56068	−	4.43523i	0.212653	−	0.368326i
$146$		0			0
$147$	−0.651589	+	5.45439i	−0.0537422	+	0.449871i
$148$		0			0
$149$	3.25027	+	0.573110i	0.266272	+	0.0469510i	0.305190	−	0.952291i	$-0.401280\pi$
$149$	3.25027	+	0.573110i	0.266272	+	0.0469510i	−0.0389179	+	0.999242i	$0.512391\pi$
$150$		0			0
$151$	−6.57177	−	7.83193i	−0.534803	−	0.637353i	0.429211	−	0.903204i	$-0.358792\pi$
$151$	−6.57177	−	7.83193i	−0.534803	−	0.637353i	−0.964014	+	0.265851i	$0.914347\pi$
$152$		0			0
$153$	10.1206	−	7.45482i	0.818202	−	0.602686i
$154$		0			0
$155$	2.04585	+	0.744629i	0.164327	+	0.0598101i
$156$		0			0
$157$	16.6304	+	13.9546i	1.32725	+	1.11370i	0.984711	+	0.174194i	$0.0557320\pi$
$157$	16.6304	+	13.9546i	1.32725	+	1.11370i	0.342541	+	0.939503i	$0.388712\pi$
$158$		0			0
$159$	1.95935	−	1.28156i	0.155386	−	0.101634i
$160$		0			0
$161$			1.10063i			0.0867422i
$162$		0			0
$163$			10.8159i			0.847163i	0.905858	+	0.423581i	$0.139227\pi$
$163$			10.8159i			0.847163i	−0.905858	+	0.423581i	$0.860773\pi$
$164$		0			0
$165$	−5.89171	+	3.85362i	−0.458669	+	0.300004i
$166$		0			0
$167$	−0.410460	−	0.344417i	−0.0317623	−	0.0266518i	0.626768	−	0.779206i	$-0.284377\pi$
$167$	−0.410460	−	0.344417i	−0.0317623	−	0.0266518i	−0.658531	+	0.752554i	$0.728822\pi$
$168$		0			0
$169$	11.9425	+	4.34672i	0.918656	+	0.334363i
$170$		0			0
$171$	0.698683	+	6.25324i	0.0534296	+	0.478197i
$172$		0			0
$173$	−12.2679	−	14.6203i	−0.932709	−	1.11156i	−0.993548	−	0.113412i	$-0.963822\pi$
$173$	−12.2679	−	14.6203i	−0.932709	−	1.11156i	0.0608393	−	0.998148i	$-0.480622\pi$
$174$		0			0
$175$	12.5964	+	2.22109i	0.952198	+	0.167898i
$176$		0			0
$177$	−2.00691	+	16.7996i	−0.150848	+	1.26274i
$178$		0			0
$179$	3.37173	−	5.84000i	0.252015	−	0.436502i	−0.712066	−	0.702113i	$-0.752240\pi$
$179$	3.37173	−	5.84000i	0.252015	−	0.436502i	0.964080	+	0.265611i	$0.0855736\pi$
$180$		0			0
$181$	11.3233	+	19.6125i	0.841651	+	1.45778i	0.888498	+	0.458881i	$0.151749\pi$
$181$	11.3233	+	19.6125i	0.841651	+	1.45778i	−0.0468467	+	0.998902i	$0.514917\pi$
$182$		0			0
$183$	−2.58152	−	11.0170i	−0.190831	−	0.814404i
$184$		0			0
$185$	−0.530535	−	1.45763i	−0.0390057	−	0.107167i
$186$		0			0
$187$	−16.8608	+	2.97301i	−1.23298	+	0.217408i
$188$		0			0
$189$	3.00210	−	16.2978i	0.218371	−	1.18549i
$190$		0			0
$191$	4.43163	+	25.1330i	0.320662	+	1.81856i	0.538555	+	0.842591i	$0.318971\pi$
$191$	4.43163	+	25.1330i	0.320662	+	1.81856i	−0.217893	+	0.975973i	$0.569918\pi$
$192$		0			0
$193$	19.4228	−	7.06933i	1.39809	−	0.508861i	0.470476	−	0.882413i	$-0.344082\pi$
$193$	19.4228	−	7.06933i	1.39809	−	0.508861i	0.927609	+	0.373552i	$0.121860\pi$
$194$		0			0
$195$	−0.268833	+	0.889723i	−0.0192515	+	0.0637144i
$196$		0			0
$197$	5.32408	−	3.07386i	0.379325	−	0.219003i	−0.298200	−	0.954504i	$-0.596386\pi$
$197$	5.32408	−	3.07386i	0.379325	−	0.219003i	0.677525	+	0.735500i	$0.263053\pi$
$198$		0			0
$199$	13.7114	+	7.91626i	0.971973	+	0.561169i	0.899837	−	0.436226i	$-0.143685\pi$
$199$	13.7114	+	7.91626i	0.971973	+	0.561169i	0.0721361	+	0.997395i	$0.477018\pi$
$200$		0			0
$201$	−0.241108	−	0.562883i	−0.0170065	−	0.0397027i
$202$		0			0
$203$	2.85134	−	16.1707i	0.200125	−	1.13496i
$204$		0			0
$205$	−8.27252	+	6.94147i	−0.577778	+	0.484813i
$206$		0			0
$207$	0.0654534	−	1.03324i	0.00454933	−	0.0718154i
$208$		0			0
$209$	2.93121	−	8.05344i	0.202756	−	0.557068i
$210$		0			0
$211$	7.22652	−	8.61223i	0.497494	−	0.592891i	−0.457613	−	0.889152i	$-0.651295\pi$
$211$	7.22652	−	8.61223i	0.497494	−	0.592891i	0.955107	+	0.296261i	$0.0957398\pi$
$212$		0			0
$213$	17.2481	−	0.960590i	1.18182	−	0.0658185i
$214$		0			0
$215$	−11.6771			−0.796369
$216$		0			0
$217$	6.98042			0.473862
$218$		0			0
$219$	1.60379	−	3.17327i	0.108374	−	0.214429i
$220$		0			0
$221$	−1.45292	+	1.73153i	−0.0977342	+	0.116475i
$222$		0			0
$223$	−3.92359	+	10.7800i	−0.262743	+	0.721880i	0.736237	+	0.676724i	$0.236601\pi$
$223$	−3.92359	+	10.7800i	−0.262743	+	0.721880i	−0.998980	+	0.0451561i	$0.985621\pi$
$224$		0			0
$225$	−11.6930	−	2.83418i	−0.779536	−	0.188946i
$226$		0			0
$227$	−2.95295	+	2.47782i	−0.195994	+	0.164459i	−0.735503	−	0.677521i	$-0.763054\pi$
$227$	−2.95295	+	2.47782i	−0.195994	+	0.164459i	0.539509	+	0.841980i	$0.318610\pi$
$228$		0			0
$229$	4.70689	−	26.6941i	0.311040	−	1.76400i	−0.282574	−	0.959246i	$-0.591188\pi$
$229$	4.70689	−	26.6941i	0.311040	−	1.76400i	0.593614	−	0.804750i	$-0.297701\pi$
$230$		0			0
$231$	−13.5251	+	18.0712i	−0.889884	+	1.18900i
$232$		0			0
$233$	−10.9088	−	6.29821i	−0.714660	−	0.412609i	0.0981239	−	0.995174i	$-0.468716\pi$
$233$	−10.9088	−	6.29821i	−0.714660	−	0.412609i	−0.812784	+	0.582565i	$0.802049\pi$
$234$		0			0
$235$	−7.12857	+	4.11568i	−0.465017	+	0.268477i
$236$		0			0
$237$	−18.2333	−	19.4249i	−1.18438	−	1.26178i
$238$		0			0
$239$	3.85552	−	1.40330i	0.249393	−	0.0907717i	−0.214299	−	0.976768i	$-0.568747\pi$
$239$	3.85552	−	1.40330i	0.249393	−	0.0907717i	0.463692	+	0.885996i	$0.346524\pi$
$240$		0			0
$241$	0.831303	+	4.71455i	0.0535489	+	0.303691i	0.999805	−	0.0197261i	$-0.00627941\pi$
$241$	0.831303	+	4.71455i	0.0535489	+	0.303691i	−0.946256	+	0.323417i	$0.895168\pi$
$242$		0			0
$243$	−3.78749	+	15.1213i	−0.242968	+	0.970034i
$244$		0			0
$245$	−3.10680	+	0.547812i	−0.198486	+	0.0349985i
$246$		0			0
$247$	−0.386987	−	1.06324i	−0.0246234	−	0.0676522i
$248$		0			0
$249$	6.96334	−	6.53618i	0.441284	−	0.414214i
$250$		0			0
$251$	−11.8554	−	20.5341i	−0.748305	−	1.29610i	−0.948635	−	0.316373i	$-0.897535\pi$
$251$	−11.8554	−	20.5341i	−0.748305	−	1.29610i	0.200330	−	0.979728i	$-0.435798\pi$
$252$		0			0
$253$	−0.705080	+	1.22123i	−0.0443280	+	0.0767784i
$254$		0			0
$255$	5.77943	+	4.32551i	0.361922	+	0.270874i
$256$		0			0
$257$	−3.51180	−	0.619224i	−0.219060	−	0.0386262i	0.0630409	−	0.998011i	$-0.479920\pi$
$257$	−3.51180	−	0.619224i	−0.219060	−	0.0386262i	−0.282101	+	0.959385i	$0.591031\pi$
$258$		0			0
$259$	−3.19686	−	3.80987i	−0.198643	−	0.236734i
$260$		0			0
$261$	−3.63841	+	15.0110i	−0.225212	+	0.929160i
$262$		0			0
$263$	20.6235	+	7.50634i	1.27170	+	0.462861i	0.887679	−	0.460463i	$-0.152317\pi$
$263$	20.6235	+	7.50634i	1.27170	+	0.462861i	0.384021	+	0.923324i	$0.374539\pi$
$264$		0			0
$265$	1.03000	+	0.864277i	0.0632727	+	0.0530921i
$266$		0			0
$267$	1.71277	+	0.865645i	0.104820	+	0.0529766i
$268$		0			0
$269$			32.3498i			1.97240i	0.165559	+	0.986200i	$0.447057\pi$
$269$			32.3498i			1.97240i	−0.165559	+	0.986200i	$0.552943\pi$
$270$		0			0
$271$			17.6632i			1.07296i	0.843912	+	0.536482i	$0.180247\pi$
$271$			17.6632i			1.07296i	−0.843912	+	0.536482i	$0.819753\pi$
$272$		0			0
$273$	0.165708	+	2.97541i	0.0100291	+	0.180080i
$274$		0			0
$275$	12.5538	+	10.5339i	0.757021	+	0.635216i
$276$		0			0
$277$	−13.4802	−	4.90639i	−0.809946	−	0.294796i	−0.0963446	−	0.995348i	$-0.530715\pi$
$277$	−13.4802	−	4.90639i	−0.809946	−	0.294796i	−0.713602	+	0.700552i	$0.752937\pi$
$278$		0			0
$279$	−6.55301	−	0.415117i	−0.392319	−	0.0248524i
$280$		0			0
$281$	8.74805	+	10.4255i	0.521865	+	0.621935i	0.961021	−	0.276476i	$-0.0891668\pi$
$281$	8.74805	+	10.4255i	0.521865	+	0.621935i	−0.439156	+	0.898411i	$0.644722\pi$
$282$		0			0
$283$	−11.3496	−	2.00123i	−0.674661	−	0.118961i	−0.174187	−	0.984713i	$-0.555730\pi$
$283$	−11.3496	−	2.00123i	−0.674661	−	0.118961i	−0.500474	+	0.865752i	$0.666841\pi$
$284$		0			0
$285$	−3.32167	+	1.42282i	−0.196759	+	0.0842808i
$286$		0			0
$287$	−17.3120	+	29.9852i	−1.02189	+	1.76997i
$288$		0			0
$289$	0.277826	+	0.481208i	0.0163427	+	0.0283063i
$290$		0			0
$291$	28.6962	+	8.67064i	1.68220	+	0.508282i
$292$		0			0
$293$	−5.12897	−	14.0917i	−0.299637	−	0.823247i	−0.994560	−	0.104163i	$-0.966784\pi$
$293$	−5.12897	−	14.0917i	−0.299637	−	0.823247i	0.694923	−	0.719084i	$-0.255439\pi$
$294$		0			0
$295$	−9.56899	+	1.68727i	−0.557128	+	0.0982367i
$296$		0			0
$297$	13.7716	−	16.1604i	0.799110	−	0.937721i
$298$		0			0
$299$	0.0323287	+	0.183345i	0.00186962	+	0.0106031i
$300$		0			0
$301$	−35.1814	+	12.8050i	−2.02782	+	0.738066i
$302$		0			0
$303$	−7.08864	+	1.66101i	−0.407232	+	0.0954227i
$304$		0			0
$305$	5.62783	−	3.24923i	0.322249	−	0.186050i
$306$		0			0
$307$	−7.31569	−	4.22372i	−0.417529	−	0.241060i	0.276491	−	0.961017i	$-0.410828\pi$
$307$	−7.31569	−	4.22372i	−0.417529	−	0.241060i	−0.694019	+	0.719956i	$0.744162\pi$
$308$		0			0
$309$	−33.4224	−	3.99269i	−1.90133	−	0.227136i
$310$		0			0
$311$	0.0607317	−	0.344426i	0.00344378	−	0.0195306i	−0.983037	−	0.183405i	$-0.941288\pi$
$311$	0.0607317	−	0.344426i	0.00344378	−	0.0195306i	0.986481	+	0.163874i	$0.0523992\pi$
$312$		0			0
$313$	−3.15937	+	2.65102i	−0.178578	+	0.149845i	−0.727695	−	0.685901i	$-0.759408\pi$
$313$	−3.15937	+	2.65102i	−0.178578	+	0.149845i	0.549117	+	0.835745i	$0.314964\pi$
$314$		0			0
$315$	9.45842	−	1.05680i	0.532921	−	0.0595440i
$316$		0			0
$317$	3.53067	−	9.70042i	0.198302	−	0.544830i	−0.800189	−	0.599748i	$-0.795267\pi$
$317$	3.53067	−	9.70042i	0.198302	−	0.544830i	0.998491	+	0.0549179i	$0.0174897\pi$
$318$		0			0
$319$	13.5229	−	16.1160i	0.757139	−	0.902323i
$320$		0			0
$321$	9.48156	+	14.4962i	0.529209	+	0.809097i
$322$		0			0
$323$	−8.78792			−0.488973
$324$		0			0
$325$	2.16356			0.120013
$326$		0			0
$327$	−15.9182	−	24.3370i	−0.880277	−	1.34584i
$328$		0			0
$329$	−16.9642	+	20.2171i	−0.935264	+	1.11460i
$330$		0			0
$331$	5.47116	−	15.0319i	0.300722	−	0.826227i	−0.693653	−	0.720309i	$-0.744000\pi$
$331$	5.47116	−	15.0319i	0.300722	−	0.826227i	0.994375	−	0.105918i	$-0.0337780\pi$
$332$		0			0
$333$	2.77455	+	3.76670i	0.152044	+	0.206414i
$334$		0			0
$335$	0.269396	−	0.226050i	0.0147187	−	0.0123504i
$336$		0			0
$337$	5.14158	−	29.1594i	0.280080	−	1.58841i	−0.442269	−	0.896883i	$-0.645826\pi$
$337$	5.14158	−	29.1594i	0.280080	−	1.58841i	0.722349	−	0.691529i	$-0.243063\pi$
$338$		0			0
$339$	−16.0647	−	1.91911i	−0.872514	−	0.104232i
$340$		0			0
$341$	7.74529	+	4.47174i	0.419431	+	0.242159i
$342$		0			0
$343$	10.5743	−	6.10510i	0.570961	−	0.329644i
$344$		0			0
$345$	0.578900	−	0.135648i	0.0311669	−	0.00730305i
$346$		0			0
$347$	16.6872	−	6.07363i	0.895813	−	0.326049i	0.147240	−	0.989101i	$-0.452961\pi$
$347$	16.6872	−	6.07363i	0.895813	−	0.326049i	0.748574	+	0.663051i	$0.230739\pi$
$348$		0			0
$349$	−2.10158	−	11.9186i	−0.112495	−	0.637990i	−0.987960	−	0.154709i	$-0.950556\pi$
$349$	−2.10158	−	11.9186i	−0.112495	−	0.637990i	0.875465	−	0.483281i	$-0.160555\pi$
$350$		0			0
$351$	0.0213826	−	2.80308i	0.00114132	−	0.149617i
$352$		0			0
$353$	17.3649	−	3.06190i	0.924239	−	0.162968i	0.308777	−	0.951135i	$-0.400080\pi$
$353$	17.3649	−	3.06190i	0.924239	−	0.162968i	0.615462	+	0.788166i	$0.288969\pi$
$354$		0			0
$355$	3.39316	+	9.32263i	0.180090	+	0.494794i
$356$		0			0
$357$	22.1559	+	6.69448i	1.17262	+	0.354309i
$358$		0			0
$359$	−14.3226	−	24.8074i	−0.755917	−	1.30929i	−0.944917	−	0.327310i	$-0.893858\pi$
$359$	−14.3226	−	24.8074i	−0.755917	−	1.30929i	0.189000	−	0.981977i	$-0.439475\pi$
$360$		0			0
$361$	−7.30049	+	12.6448i	−0.384236	+	0.665517i
$362$		0			0
$363$	−9.07019	+	3.88518i	−0.476062	+	0.203919i
$364$		0			0
$365$	2.01092	+	0.354579i	0.105256	+	0.0185595i
$366$		0			0
$367$	−15.6407	−	18.6399i	−0.816439	−	0.972994i	0.183511	−	0.983018i	$-0.441254\pi$
$367$	−15.6407	−	18.6399i	−0.816439	−	0.972994i	−0.999950	+	0.0100239i	$0.996809\pi$
$368$		0			0
$369$	18.0352	−	27.1197i	0.938873	−	1.41180i
$370$		0			0
$371$	4.05102	+	1.47445i	0.210318	+	0.0765496i
$372$		0			0
$373$	−26.5304	−	22.2617i	−1.37369	−	1.15267i	−0.971480	−	0.237121i	$-0.923796\pi$
$373$	−26.5304	−	22.2617i	−1.37369	−	1.15267i	−0.402214	−	0.915546i	$-0.631759\pi$
$374$		0			0
$375$	−0.863245	−	15.5002i	−0.0445778	−	0.800428i
$376$		0			0
$377$		−	2.77749i		−	0.143048i
$378$		0			0
$379$			6.23721i			0.320384i	0.987086	+	0.160192i	$0.0512114\pi$
$379$			6.23721i			0.320384i	−0.987086	+	0.160192i	$0.948789\pi$
$380$		0			0
$381$	8.37525	+	4.23291i	0.429077	+	0.216859i
$382$		0			0
$383$	8.53869	+	7.16481i	0.436307	+	0.366105i	0.834325	−	0.551273i	$-0.185858\pi$
$383$	8.53869	+	7.16481i	0.436307	+	0.366105i	−0.398018	+	0.917377i	$0.630302\pi$
$384$		0			0
$385$	−12.1813	−	4.43364i	−0.620818	−	0.225959i
$386$		0			0
$387$	33.7887	−	9.92873i	1.71758	−	0.504706i
$388$		0			0
$389$	14.0325	+	16.7233i	0.711476	+	0.847904i	0.993773	−	0.111423i	$-0.0355408\pi$
$389$	14.0325	+	16.7233i	0.711476	+	0.847904i	−0.282297	+	0.959327i	$0.591096\pi$
$390$		0			0
$391$	1.42400	+	0.251090i	0.0720149	+	0.0126982i
$392$		0			0
$393$	−5.24592	−	3.92621i	−0.264622	−	0.198051i
$394$		0			0
$395$	7.65016	−	13.2505i	0.384921	−	0.666703i
$396$		0			0
$397$	3.36647	+	5.83090i	0.168958	+	0.292644i	0.938054	−	0.346489i	$-0.112626\pi$
$397$	3.36647	+	5.83090i	0.168958	+	0.292644i	−0.769096	+	0.639134i	$0.779293\pi$
$398$		0			0
$399$	−8.44748	+	7.92929i	−0.422903	+	0.396961i
$400$		0			0
$401$	7.17243	+	19.7061i	0.358174	+	0.984075i	0.979663	+	0.200652i	$0.0643060\pi$
$401$	7.17243	+	19.7061i	0.358174	+	0.984075i	−0.621488	+	0.783423i	$0.713472\pi$
$402$		0			0
$403$	1.16281	−	0.205034i	0.0579235	−	0.0102135i
$404$		0			0
$405$	−8.94213	+	0.429614i	−0.444338	+	0.0213477i
$406$		0			0
$407$	−1.10650	−	6.27527i	−0.0548472	−	0.311054i
$408$		0			0
$409$	−12.1954	+	4.43875i	−0.603022	+	0.219482i	−0.625447	−	0.780267i	$-0.715083\pi$
$409$	−12.1954	+	4.43875i	−0.603022	+	0.219482i	0.0224254	+	0.999749i	$0.492861\pi$
$410$		0			0
$411$	−20.5803	−	21.9253i	−1.01515	−	1.08149i
$412$		0			0
$413$	−26.9798	+	15.5768i	−1.32759	+	0.766483i
$414$		0			0
$415$	4.74996	+	2.74239i	0.233166	+	0.134619i
$416$		0			0
$417$	4.30067	−	5.74624i	0.210605	−	0.281395i
$418$		0			0
$419$	3.88733	−	22.0461i	0.189908	−	1.07702i	−0.729576	−	0.683899i	$-0.760283\pi$
$419$	3.88733	−	22.0461i	0.189908	−	1.07702i	0.919485	−	0.393125i	$-0.128606\pi$
$420$		0			0
$421$	4.37134	−	3.66799i	0.213046	−	0.178767i	−0.530020	−	0.847985i	$-0.677815\pi$
$421$	4.37134	−	3.66799i	0.213046	−	0.178767i	0.743066	+	0.669219i	$0.233371\pi$
$422$		0			0
$423$	17.1277	−	17.9704i	0.832779	−	0.873749i
$424$		0			0
$425$	5.74729	−	15.7905i	0.278784	−	0.765954i
$426$		0			0
$427$	13.3928	−	15.9609i	0.648123	−	0.772403i
$428$		0			0
$429$	−1.72222	+	3.40759i	−0.0831496	+	0.164520i
$430$		0			0
$431$	2.80858			0.135285			0.0676423	−	0.997710i	$-0.478452\pi$
$431$	2.80858			0.135285			0.0676423	+	0.997710i	$0.478452\pi$
$432$		0			0
$433$	−3.44197			−0.165411			−0.0827054	−	0.996574i	$-0.526356\pi$
$433$	−3.44197			−0.165411			−0.0827054	+	0.996574i	$0.526356\pi$
$434$		0			0
$435$	−8.85673	+	0.493253i	−0.424648	+	0.0236497i
$436$		0			0
$437$	−0.465261	+	0.554476i	−0.0222564	+	0.0265242i
$438$		0			0
$439$	5.76570	−	15.8411i	0.275182	−	0.756056i	−0.722709	−	0.691152i	$-0.757104\pi$
$439$	5.76570	−	15.8411i	0.275182	−	0.756056i	0.997891	−	0.0649044i	$-0.0206742\pi$
$440$		0			0
$441$	8.52403	−	4.22679i	0.405906	−	0.201276i
$442$		0			0
$443$	6.07589	−	5.09828i	0.288674	−	0.242226i	−0.486937	−	0.873437i	$-0.661886\pi$
$443$	6.07589	−	5.09828i	0.288674	−	0.242226i	0.775612	+	0.631210i	$0.217442\pi$
$444$		0			0
$445$	−0.191384	+	1.08539i	−0.00907245	+	0.0514524i
$446$		0			0
$447$	−2.25083	−	5.25470i	−0.106460	−	0.248539i
$448$		0			0
$449$	11.0454	+	6.37705i	0.521264	+	0.300952i	0.737452	−	0.675400i	$-0.236029\pi$
$449$	11.0454	+	6.37705i	0.521264	+	0.300952i	−0.216188	+	0.976352i	$0.569362\pi$
$450$		0			0
$451$	−38.4178	+	22.1806i	−1.80903	+	1.04444i
$452$		0			0
$453$	−5.12190	+	16.9513i	−0.240648	+	0.796443i
$454$		0			0
$455$	−1.60821	+	0.585342i	−0.0753942	+	0.0274412i
$456$		0			0
$457$	6.82552	+	38.7095i	0.319284	+	1.81075i	0.547122	+	0.837053i	$0.315723\pi$
$457$	6.82552	+	38.7095i	0.319284	+	1.81075i	−0.227838	+	0.973699i	$0.573166\pi$
$458$		0			0
$459$	−20.4012	−	7.60217i	−0.952247	−	0.354839i
$460$		0			0
$461$	−36.4213	+	6.42206i	−1.69631	+	0.299105i	−0.936403	−	0.350926i	$-0.885867\pi$
$461$	−36.4213	+	6.42206i	−1.69631	+	0.299105i	−0.759908	+	0.650031i	$0.774756\pi$
$462$		0			0
$463$	8.88724	+	24.4175i	0.413025	+	1.13478i	0.955574	+	0.294753i	$0.0952372\pi$
$463$	8.88724	+	24.4175i	0.413025	+	1.13478i	−0.542549	+	0.840024i	$0.682541\pi$
$464$		0			0
$465$	−0.860305	−	3.67149i	−0.0398957	−	0.170261i
$466$		0			0
$467$	18.9292	+	32.7863i	0.875937	+	1.51717i	0.855761	+	0.517371i	$0.173089\pi$
$467$	18.9292	+	32.7863i	0.875937	+	1.51717i	0.0201762	+	0.999796i	$0.493577\pi$
$468$		0			0
$469$	0.563767	−	0.976474i	0.0260324	−	0.0450894i
$470$		0			0
$471$	4.46027	−	37.3364i	0.205518	−	1.72037i
$472$		0			0
$473$	−47.2393	−	8.32957i	−2.17207	−	0.382994i
$474$		0			0
$475$	5.40690	+	6.44369i	0.248085	+	0.295657i
$476$		0			0
$477$	−3.71529	−	1.62508i	−0.170112	−	0.0744073i
$478$		0			0
$479$	22.2128	+	8.08481i	1.01493	+	0.369404i	0.795324	−	0.606184i	$-0.207301\pi$
$479$	22.2128	+	8.08481i	1.01493	+	0.369404i	0.219606	+	0.975589i	$0.429523\pi$
$480$		0			0
$481$	−0.644442	−	0.540751i	−0.0293840	−	0.0246561i
$482$		0			0
$483$	1.59539	−	1.04351i	0.0725930	−	0.0474812i
$484$		0			0
$485$			17.2161i			0.781741i
$486$		0			0
$487$			13.1794i			0.597216i	0.954376	+	0.298608i	$0.0965223\pi$
$487$			13.1794i			0.597216i	−0.954376	+	0.298608i	$0.903478\pi$
$488$		0			0
$489$	15.6778	−	10.2545i	0.708976	−	0.463722i
$490$		0			0
$491$	−1.42772	−	1.19800i	−0.0644320	−	0.0540648i	0.610003	−	0.792399i	$-0.291168\pi$
$491$	−1.42772	−	1.19800i	−0.0644320	−	0.0540648i	−0.674435	+	0.738334i	$0.735613\pi$
$492$		0			0
$493$	−20.2712	−	7.37813i	−0.912971	−	0.332294i
$494$		0			0
$495$	11.1718	+	4.88658i	0.502135	+	0.219635i
$496$		0			0
$497$	20.4462	+	24.3669i	0.917139	+	1.09300i
$498$		0			0
$499$	−11.6383	−	2.05215i	−0.521003	−	0.0918669i	−0.0930387	−	0.995662i	$-0.529658\pi$
$499$	−11.6383	−	2.05215i	−0.521003	−	0.0918669i	−0.427964	+	0.903796i	$0.640769\pi$
$500$		0			0
$501$	−0.110085	+	0.921510i	−0.00491823	+	0.0411700i
$502$		0			0
$503$	10.9176	−	18.9099i	0.486793	−	0.843150i	−0.513092	−	0.858334i	$-0.671500\pi$
$503$	10.9176	−	18.9099i	0.486793	−	0.843150i	0.999885	+	0.0151838i	$0.00483333\pi$
$504$		0			0
$505$	−2.09064	−	3.62109i	−0.0930321	−	0.161136i
$506$		0			0
$507$	−5.02197	−	21.4321i	−0.223034	−	0.951832i
$508$		0			0
$509$	−14.9773	−	41.1498i	−0.663858	−	1.82393i	−0.558509	−	0.829499i	$-0.688626\pi$
$509$	−14.9773	−	41.1498i	−0.663858	−	1.82393i	−0.105349	−	0.994435i	$-0.533596\pi$
$510$		0			0
$511$	6.44743	−	1.13686i	0.285218	−	0.0502916i
$512$		0			0
$513$	8.40179	−	6.94142i	0.370948	−	0.306471i
$514$		0			0
$515$	−3.35678	−	19.0373i	−0.147917	−	0.838882i
$516$		0			0
$517$	−31.7743	+	11.5649i	−1.39743	+	0.508624i
$518$		0			0
$519$	−9.56132	+	31.6440i	−0.419695	+	1.38902i
$520$		0			0
$521$	−22.1325	+	12.7782i	−0.969642	+	0.559823i	−0.899127	−	0.437687i	$-0.855798\pi$
$521$	−22.1325	+	12.7782i	−0.969642	+	0.559823i	−0.0705152	+	0.997511i	$0.522464\pi$
$522$		0			0
$523$	−6.53074	−	3.77053i	−0.285570	−	0.164874i	0.350373	−	0.936610i	$-0.386055\pi$
$523$	−6.53074	−	3.77053i	−0.285570	−	0.164874i	−0.635942	+	0.771737i	$0.719388\pi$
$524$		0			0
$525$	−8.72307	−	20.3646i	−0.380706	−	0.888783i
$526$		0			0
$527$	1.59246	−	9.03128i	0.0693686	−	0.393409i
$528$		0			0
$529$	−17.5278	+	14.7076i	−0.762078	+	0.639459i
$530$		0			0
$531$	26.2541	−	13.0186i	1.13933	−	0.564958i
$532$		0			0
$533$	−2.00310	+	5.50348i	−0.0867640	+	0.238382i
$534$		0			0
$535$	−6.39432	+	7.62046i	−0.276451	+	0.329461i
$536$		0			0
$537$	−11.6619	+	0.649481i	−0.503249	+	0.0280272i
$538$		0			0
$539$	−12.9593			−0.558195
$540$		0			0
$541$	19.3240			0.830803			0.415401	−	0.909638i	$-0.363641\pi$
$541$	19.3240			0.830803			0.415401	+	0.909638i	$0.363641\pi$
$542$		0			0
$543$	17.6932	−	35.0078i	0.759287	−	1.50233i
$544$		0			0
$545$	10.7352	−	12.7937i	0.459843	−	0.548020i
$546$		0			0
$547$	−10.7459	+	29.5242i	−0.459463	+	1.26236i	0.466423	+	0.884562i	$0.345542\pi$
$547$	−10.7459	+	29.5242i	−0.459463	+	1.26236i	−0.925886	+	0.377802i	$0.876680\pi$
$548$		0			0
$549$	−13.5219	+	14.1872i	−0.577102	+	0.605494i
$550$		0			0
$551$	8.27214	−	6.94115i	0.352405	−	0.295703i
$552$		0			0
$553$	8.51851	−	48.3109i	0.362244	−	2.05439i
$554$		0			0
$555$	−1.60988	+	2.15100i	−0.0683354	+	0.0913048i
$556$		0			0
$557$	−1.51498	−	0.874672i	−0.0641916	−	0.0370610i	0.467561	−	0.883961i	$-0.345133\pi$
$557$	−1.51498	−	0.874672i	−0.0641916	−	0.0370610i	−0.531752	+	0.846900i	$0.678466\pi$
$558$		0			0
$559$	−5.48444	+	3.16644i	−0.231967	+	0.133926i
$560$		0			0
$561$	20.2951	+	21.6214i	0.856858	+	0.912855i
$562$		0			0
$563$	19.5609	−	7.11960i	0.824395	−	0.300055i	0.104839	−	0.994489i	$-0.466567\pi$
$563$	19.5609	−	7.11960i	0.824395	−	0.300055i	0.719557	+	0.694434i	$0.244345\pi$
$564$		0			0
$565$	−1.61346	−	9.15038i	−0.0678787	−	0.384959i
$566$		0			0
$567$	−26.4703	+	11.1002i	−1.11165	+	0.466166i
$568$		0			0
$569$	11.5633	−	2.03892i	0.484759	−	0.0854762i	0.0740730	−	0.997253i	$-0.476400\pi$
$569$	11.5633	−	2.03892i	0.484759	−	0.0854762i	0.410686	+	0.911777i	$0.365289\pi$
$570$		0			0
$571$	9.65982	+	26.5401i	0.404251	+	1.11067i	0.960166	+	0.279431i	$0.0901458\pi$
$571$	9.65982	+	26.5401i	0.404251	+	1.11067i	−0.555915	+	0.831239i	$0.687632\pi$
$572$		0			0
$573$	32.2293	−	30.2523i	1.34640	−	1.26381i
$574$		0			0
$575$	−0.692028	−	1.19863i	−0.0288596	−	0.0499862i
$576$		0			0
$577$	13.7542	−	23.8230i	0.572596	−	0.991765i	−0.423702	−	0.905801i	$-0.639270\pi$
$577$	13.7542	−	23.8230i	0.572596	−	0.991765i	0.996298	−	0.0859637i	$-0.0273969\pi$
$578$		0			0
$579$	−28.6618	−	21.4514i	−1.19114	−	0.891491i
$580$		0			0
$581$	17.3182	+	3.05367i	0.718482	+	0.126688i
$582$		0			0
$583$	3.55035	+	4.23114i	0.147040	+	0.175236i
$584$		0			0
$585$	1.54455	−	0.453863i	0.0638594	−	0.0187649i
$586$		0			0
$587$	20.2703	+	7.37777i	0.836643	+	0.304513i	0.724582	−	0.689188i	$-0.242033\pi$
$587$	20.2703	+	7.37777i	0.836643	+	0.304513i	0.112061	+	0.993701i	$0.464255\pi$
$588$		0			0
$589$	3.51659	+	2.95077i	0.144898	+	0.121584i
$590$		0			0
$591$	−9.50336	−	4.80306i	−0.390916	−	0.197572i
$592$		0			0
$593$			13.5049i			0.554580i	0.960786	+	0.277290i	$0.0894363\pi$
$593$			13.5049i			0.554580i	−0.960786	+	0.277290i	$0.910564\pi$
$594$		0			0
$595$			13.2923i			0.544931i
$596$		0			0
$597$	−1.52488	−	27.3803i	−0.0624090	−	1.12060i
$598$		0			0
$599$	−18.5591	−	15.5729i	−0.758303	−	0.636292i	0.179381	−	0.983780i	$-0.442590\pi$
$599$	−18.5591	−	15.5729i	−0.758303	−	0.636292i	−0.937685	+	0.347488i	$0.887035\pi$
$600$		0			0
$601$	−1.66286	−	0.605230i	−0.0678293	−	0.0246878i	0.307883	−	0.951424i	$-0.400380\pi$
$601$	−1.66286	−	0.605230i	−0.0678293	−	0.0246878i	−0.375712	+	0.926736i	$0.622602\pi$
$602$		0			0
$603$	−0.587318	+	0.883158i	−0.0239174	+	0.0359650i
$604$		0			0
$605$	−3.64253	−	4.34100i	−0.148090	−	0.176487i
$606$		0			0
$607$	−17.8306	−	3.14401i	−0.723720	−	0.127611i	−0.200359	−	0.979723i	$-0.564211\pi$
$607$	−17.8306	−	3.14401i	−0.723720	−	0.127611i	−0.523361	+	0.852111i	$0.675322\pi$
$608$		0			0
$609$	−26.1432	+	11.1983i	−1.05938	+	0.453778i
$610$		0			0
$611$	−2.23208	+	3.86607i	−0.0903002	+	0.156404i
$612$		0			0
$613$	−1.85926	−	3.22034i	−0.0750949	−	0.130068i	0.826033	−	0.563622i	$-0.190593\pi$
$613$	−1.85926	−	3.22034i	−0.0750949	−	0.130068i	−0.901128	+	0.433554i	$0.857259\pi$
$614$		0			0
$615$	17.9049	+	5.41004i	0.721997	+	0.218154i
$616$		0			0
$617$	4.69845	+	12.9089i	0.189153	+	0.519693i	0.997628	−	0.0688376i	$-0.0219290\pi$
$617$	4.69845	+	12.9089i	0.189153	+	0.519693i	−0.808475	+	0.588530i	$0.799707\pi$
$618$		0			0
$619$	−21.2614	+	3.74896i	−0.854568	+	0.150683i	−0.583736	−	0.811943i	$-0.698410\pi$
$619$	−21.2614	+	3.74896i	−0.854568	+	0.150683i	−0.270832	+	0.962627i	$0.587299\pi$
$620$		0			0
$621$	−1.55977	+	0.884736i	−0.0625912	+	0.0355032i
$622$		0			0
$623$	0.613617	+	3.48000i	0.0245841	+	0.139423i
$624$		0			0
$625$	−10.4655	+	3.80912i	−0.418619	+	0.152365i
$626$		0			0
$627$	−14.4527	+	3.38656i	−0.577185	+	0.135246i
$628$		0			0
$629$	−5.65852	+	3.26695i	−0.225620	+	0.130262i
$630$		0			0
$631$	−23.5804	−	13.6141i	−0.938719	−	0.541970i	−0.0491606	−	0.998791i	$-0.515655\pi$
$631$	−23.5804	−	13.6141i	−0.938719	−	0.541970i	−0.889559	+	0.456821i	$0.848988\pi$
$632$		0			0
$633$	−19.3351	−	2.30979i	−0.768500	−	0.0918061i
$634$		0			0
$635$	−0.935845	+	5.30744i	−0.0371379	+	0.210619i
$636$		0			0
$637$	−1.31064	+	1.09976i	−0.0519294	+	0.0435740i
$638$		0			0
$639$	−17.7453	−	24.0908i	−0.701991	−	0.953018i
$640$		0			0
$641$	5.24940	−	14.4226i	0.207339	−	0.569659i	−0.791816	−	0.610759i	$-0.790864\pi$
$641$	5.24940	−	14.4226i	0.207339	−	0.569659i	0.999155	+	0.0411007i	$0.0130865\pi$
$642$		0			0
$643$	12.0733	−	14.3884i	0.476125	−	0.567424i	−0.473507	−	0.880790i	$-0.657012\pi$
$643$	12.0733	−	14.3884i	0.476125	−	0.567424i	0.949632	+	0.313366i	$0.101457\pi$
$644$		0			0
$645$	11.0710	+	16.9262i	0.435919	+	0.666467i
$646$		0			0
$647$	36.1679			1.42191			0.710954	−	0.703239i	$-0.248264\pi$
$647$	36.1679			1.42191			0.710954	+	0.703239i	$0.248264\pi$
$648$		0			0
$649$	−39.9147			−1.56679
$650$		0			0
$651$	−6.61810	−	10.1183i	−0.259384	−	0.396567i
$652$		0			0
$653$	5.48542	−	6.53727i	0.214661	−	0.255823i	−0.647959	−	0.761675i	$-0.724377\pi$
$653$	5.48542	−	6.53727i	0.214661	−	0.255823i	0.862620	+	0.505852i	$0.168822\pi$
$654$		0			0
$655$	1.28705	−	3.53614i	0.0502892	−	0.138168i
$656$		0			0
$657$	−6.12027	+	0.683826i	−0.238774	+	0.0266786i
$658$		0			0
$659$	−18.5696	+	15.5818i	−0.723370	+	0.606980i	−0.928315	−	0.371794i	$-0.878743\pi$
$659$	−18.5696	+	15.5818i	−0.723370	+	0.606980i	0.204945	+	0.978774i	$0.434298\pi$
$660$		0			0
$661$	−2.11748	+	12.0088i	−0.0823604	+	0.467089i	0.915535	+	0.402239i	$0.131768\pi$
$661$	−2.11748	+	12.0088i	−0.0823604	+	0.467089i	−0.997895	+	0.0648497i	$0.979343\pi$
$662$		0			0
$663$	3.88740	+	0.464394i	0.150974	+	0.0180356i
$664$		0			0
$665$	−5.76235	−	3.32689i	−0.223454	−	0.129011i
$666$		0			0
$667$	−1.53875	+	0.888397i	−0.0595806	+	0.0343989i
$668$		0			0
$669$	19.3457	−	4.53310i	0.747949	−	0.175260i
$670$		0			0
$671$	25.0850	−	9.13021i	0.968397	−	0.352468i
$672$		0			0
$673$	0.200195	+	1.13536i	0.00771695	+	0.0437650i	0.988423	−	0.151723i	$-0.0484821\pi$
$673$	0.200195	+	1.13536i	0.00771695	+	0.0437650i	−0.980706	+	0.195488i	$0.937371\pi$
$674$		0			0
$675$	6.97790	+	19.6364i	0.268580	+	0.755806i
$676$		0			0
$677$	30.3913	−	5.35881i	1.16803	−	0.205956i	0.444198	−	0.895929i	$-0.353489\pi$
$677$	30.3913	−	5.35881i	1.16803	−	0.205956i	0.723835	+	0.689973i	$0.242378\pi$
$678$		0			0
$679$	18.8790	+	51.8696i	0.724509	+	1.99057i
$680$		0			0
$681$	6.39134	+	1.93116i	0.244917	+	0.0740023i
$682$		0			0
$683$	18.6387	+	32.2832i	0.713191	+	1.23528i	0.963653	+	0.267157i	$0.0860842\pi$
$683$	18.6387	+	32.2832i	0.713191	+	1.23528i	−0.250462	+	0.968126i	$0.580583\pi$
$684$		0			0
$685$	8.63489	−	14.9561i	0.329922	−	0.571442i
$686$		0			0
$687$	−43.1563	+	18.4858i	−1.64651	+	0.705277i
$688$		0			0
$689$	0.718132	+	0.126626i	0.0273586	+	0.00482407i
$690$		0			0
$691$	6.53280	+	7.78548i	0.248519	+	0.296174i	0.875854	−	0.482576i	$-0.160299\pi$
$691$	6.53280	+	7.78548i	0.248519	+	0.296174i	−0.627335	+	0.778750i	$0.715854\pi$
$692$		0			0
$693$	39.0177	+	2.47167i	1.48216	+	0.0938912i
$694$		0			0
$695$	3.87339	+	1.40980i	0.146926	+	0.0534767i
$696$		0			0
$697$	34.8455	+	29.2389i	1.31987	+	1.10750i
$698$		0			0
$699$	1.21320	+	21.7839i	0.0458873	+	0.823942i
$700$		0			0
$701$			39.2641i			1.48298i	0.670962	+	0.741492i	$0.265882\pi$
$701$			39.2641i			1.48298i	−0.670962	+	0.741492i	$0.734118\pi$
$702$		0			0
$703$		−	3.27070i		−	0.123357i
$704$		0			0
$705$	12.7243	+	6.43097i	0.479226	+	0.242204i
$706$		0			0
$707$	−10.2696	−	8.61726i	−0.386230	−	0.324085i
$708$		0			0
$709$	−24.9160	−	9.06870i	−0.935742	−	0.340582i	−0.171259	−	0.985226i	$-0.554783\pi$
$709$	−24.9160	−	9.06870i	−0.935742	−	0.340582i	−0.764483	+	0.644644i	$0.777006\pi$
$710$		0			0
$711$	−10.8699	+	44.8462i	−0.407654	+	1.68186i
$712$		0			0
$713$	−0.485521	−	0.578621i	−0.0181829	−	0.0216695i
$714$		0			0
$715$	−2.15941	−	0.380762i	−0.0807573	−	0.0142397i
$716$		0			0
$717$	−5.68951	−	4.25821i	−0.212479	−	0.159026i
$718$		0			0
$719$	−5.99328	+	10.3807i	−0.223512	+	0.387133i	−0.955872	−	0.293784i	$-0.905085\pi$
$719$	−5.99328	+	10.3807i	−0.223512	+	0.387133i	0.732360	+	0.680917i	$0.238419\pi$
$720$		0			0
$721$	−30.9896	−	53.6756i	−1.15411	−	1.99898i
$722$		0			0
$723$	6.04570	−	5.67484i	0.224842	−	0.211049i
$724$		0			0
$725$	7.06221	+	19.4033i	0.262284	+	0.720619i
$726$		0			0
$727$	−45.4417	+	8.01260i	−1.68534	+	0.297171i	−0.932537	−	0.361076i	$-0.882410\pi$
$727$	−45.4417	+	8.01260i	−1.68534	+	0.297171i	−0.752803	+	0.658246i	$0.771299\pi$
$728$		0			0
$729$	25.5096	−	8.84641i	0.944801	−	0.327645i
$730$		0			0
$731$	8.54109	+	48.4389i	0.315904	+	1.79158i
$732$		0			0
$733$	−3.58949	+	1.30647i	−0.132581	+	0.0482555i	−0.407458	−	0.913224i	$-0.633585\pi$
$733$	−3.58949	+	1.30647i	−0.132581	+	0.0482555i	0.274878	+	0.961479i	$0.411363\pi$
$734$		0			0
$735$	3.73961	+	3.98400i	0.137937	+	0.146952i
$736$		0			0
$737$	1.25108	−	0.722313i	0.0460842	−	0.0266067i
$738$		0			0
$739$	33.4832	+	19.3315i	1.23170	+	0.711122i	0.967384	−	0.253315i	$-0.0815208\pi$
$739$	33.4832	+	19.3315i	1.23170	+	0.711122i	0.264315	+	0.964436i	$0.414854\pi$
$740$		0			0
$741$	−1.17429	+	1.56900i	−0.0431385	+	0.0576385i
$742$		0			0
$743$	−5.78818	+	32.8264i	−0.212348	+	1.20428i	0.673102	+	0.739549i	$0.264961\pi$
$743$	−5.78818	+	32.8264i	−0.212348	+	1.20428i	−0.885450	+	0.464735i	$0.846150\pi$
$744$		0			0
$745$	2.51490	−	2.11025i	0.0921388	−	0.0773136i
$746$		0			0
$747$	−16.0763	−	3.89659i	−0.588199	−	0.142569i
$748$		0			0
$749$	−10.9087	+	29.9713i	−0.398594	+	1.09513i
$750$		0			0
$751$	13.7510	−	16.3878i	0.501781	−	0.598000i	−0.454392	−	0.890802i	$-0.650143\pi$
$751$	13.7510	−	16.3878i	0.501781	−	0.598000i	0.956173	+	0.292802i	$0.0945878\pi$
$752$		0			0
$753$	−18.5246	+	36.6529i	−0.675075	+	1.33571i
$754$		0			0
$755$	−10.1698			−0.370118
$756$		0			0
$757$	40.3960			1.46822			0.734110	−	0.679031i	$-0.237600\pi$
$757$	40.3960			1.46822			0.734110	+	0.679031i	$0.237600\pi$
$758$		0			0
$759$	2.43869	−	0.135817i	0.0885189	−	0.00492983i
$760$		0			0
$761$	−22.3492	+	26.6348i	−0.810159	+	0.965509i	−0.999867	−	0.0163311i	$-0.994801\pi$
$761$	−22.3492	+	26.6348i	−0.810159	+	0.965509i	0.189708	+	0.981841i	$0.439246\pi$
$762$		0			0
$763$	18.3141	−	50.3176i	0.663015	−	1.82162i
$764$		0			0
$765$	0.790477	−	12.4784i	0.0285797	−	0.451158i
$766$		0			0
$767$	−4.03679	+	3.38727i	−0.145760	+	0.122307i
$768$		0			0
$769$	2.46457	−	13.9772i	0.0888745	−	0.504032i	−0.907579	−	0.419882i	$-0.862071\pi$
$769$	2.46457	−	13.9772i	0.0888745	−	0.504032i	0.996453	−	0.0841501i	$-0.0268175\pi$
$770$		0			0
$771$	2.43194	+	5.67751i	0.0875840	+	0.204471i
$772$		0			0
$773$	37.2161	+	21.4867i	1.33857	+	0.772824i	0.986596	−	0.163185i	$-0.0521767\pi$
$773$	37.2161	+	21.4867i	1.33857	+	0.772824i	0.351976	+	0.936009i	$0.385510\pi$
$774$		0			0
$775$	−7.60191	+	4.38897i	−0.273069	+	0.157656i
$776$		0			0
$777$	−2.49156	+	8.24603i	−0.0893843	+	0.295825i
$778$		0			0
$779$	−21.3968	+	7.78779i	−0.766619	+	0.279027i
$780$		0			0
$781$	7.07687	+	40.1349i	0.253230	+	1.43614i
$782$		0			0
$783$	25.2084	−	8.95794i	0.900875	−	0.320131i
$784$		0			0
$785$	21.2667	−	3.74989i	0.759041	−	0.133839i
$786$		0			0
$787$	−3.47322	−	9.54261i	−0.123807	−	0.340157i	0.862269	−	0.506450i	$-0.169043\pi$
$787$	−3.47322	−	9.54261i	−0.123807	−	0.340157i	−0.986076	+	0.166293i	$0.946820\pi$
$788$		0			0
$789$	−8.67243	−	37.0110i	−0.308747	−	1.31763i
$790$		0			0
$791$	−14.8954	−	25.7995i	−0.529618	−	0.917325i
$792$		0			0
$793$	1.76217	−	3.05217i	0.0625765	−	0.108386i
$794$		0			0
$795$	0.276246	−	2.31243i	0.00979745	−	0.0820135i
$796$		0			0
$797$	−0.873477	−	0.154018i	−0.0309401	−	0.00545558i	0.158157	−	0.987414i	$-0.449445\pi$
$797$	−0.873477	−	0.154018i	−0.0309401	−	0.00545558i	−0.189097	+	0.981958i	$0.560556\pi$
$798$		0			0
$799$	22.2868	+	26.5604i	0.788452	+	0.939640i
$800$		0			0
$801$	−0.369095	−	3.30341i	−0.0130413	−	0.116720i
$802$		0			0
$803$	7.88219	+	2.86888i	0.278156	+	0.101241i
$804$		0			0
$805$	0.838680	+	0.703736i	0.0295596	+	0.0248034i
$806$		0			0
$807$	46.8917	−	30.6706i	1.65067	−	1.07966i
$808$		0			0
$809$		−	34.1167i		−	1.19948i	−0.800195	−	0.599740i	$-0.795271\pi$
$809$		−	34.1167i		−	1.19948i	0.800195	−	0.599740i	$-0.204729\pi$
$810$		0			0
$811$		−	7.65168i		−	0.268687i	−0.990935	−	0.134343i	$-0.957107\pi$
$811$		−	7.65168i		−	0.268687i	0.990935	−	0.134343i	$-0.0428925\pi$
$812$		0			0
$813$	25.6032	−	16.7464i	0.897945	−	0.587322i
$814$		0			0
$815$	8.24164	+	6.91556i	0.288692	+	0.242241i
$816$		0			0
$817$	−23.1365	−	8.42101i	−0.809445	−	0.294614i
$818$		0			0
$819$	4.15582	−	3.06117i	0.145216	−	0.106966i
$820$		0			0
$821$	−8.60560	−	10.2558i	−0.300337	−	0.357928i	0.594678	−	0.803964i	$-0.297280\pi$
$821$	−8.60560	−	10.2558i	−0.300337	−	0.357928i	−0.895015	+	0.446036i	$0.852835\pi$
$822$		0			0
$823$	−39.5457	−	6.97297i	−1.37848	−	0.243062i	−0.565206	−	0.824950i	$-0.691203\pi$
$823$	−39.5457	−	6.97297i	−1.37848	−	0.243062i	−0.813269	+	0.581887i	$0.802314\pi$
$824$		0			0
$825$	3.36691	−	28.1841i	0.117221	−	0.981244i
$826$		0			0
$827$	7.92209	−	13.7215i	0.275478	−	0.477142i	−0.694778	−	0.719225i	$-0.744497\pi$
$827$	7.92209	−	13.7215i	0.275478	−	0.477142i	0.970256	+	0.242083i	$0.0778306\pi$
$828$		0			0
$829$	20.7345	+	35.9131i	0.720138	+	1.24732i	0.960944	+	0.276742i	$0.0892547\pi$
$829$	20.7345	+	35.9131i	0.720138	+	1.24732i	−0.240807	+	0.970573i	$0.577412\pi$
$830$		0			0
$831$	5.66858	+	24.1916i	0.196641	+	0.839196i
$832$		0			0
$833$	4.54488	+	12.4870i	0.157471	+	0.432648i
$834$		0			0
$835$	−0.524888	+	0.0925520i	−0.0181645	+	0.00320289i
$836$		0			0
$837$	5.61116	+	9.89231i	0.193950	+	0.341928i
$838$		0			0
$839$	−0.0366578	−	0.207897i	−0.00126557	−	0.00717740i	0.984168	−	0.177236i	$-0.0567155\pi$
$839$	−0.0366578	−	0.207897i	−0.00126557	−	0.00717740i	−0.985434	+	0.170058i	$0.945604\pi$
$840$		0			0
$841$	−2.34199	+	0.852415i	−0.0807583	+	0.0293936i
$842$		0			0
$843$	6.81805	−	22.5649i	0.234826	−	0.777176i
$844$		0			0
$845$	10.9481	−	6.32091i	0.376627	−	0.217446i
$846$		0			0
$847$	−15.7347	−	9.08445i	−0.540652	−	0.312145i
$848$		0			0
$849$	7.85963	+	18.3488i	0.269742	+	0.629729i
$850$		0			0
$851$	−0.0934512	+	0.529988i	−0.00320346	+	0.0181677i
$852$		0			0
$853$	25.8429	−	21.6847i	0.884843	−	0.742471i	−0.0823260	−	0.996605i	$-0.526235\pi$
$853$	25.8429	−	21.6847i	0.884843	−	0.742471i	0.967169	+	0.254134i	$0.0817904\pi$
$854$		0			0
$855$	5.21168	+	3.46587i	0.178236	+	0.118530i
$856$		0			0
$857$	−15.0626	+	41.3843i	−0.514530	+	1.41366i	0.361939	+	0.932202i	$0.382115\pi$
$857$	−15.0626	+	41.3843i	−0.514530	+	1.41366i	−0.876469	+	0.481458i	$0.840107\pi$
$858$		0			0
$859$	0.702158	−	0.836800i	0.0239573	−	0.0285512i	−0.753933	−	0.656952i	$-0.771846\pi$
$859$	0.702158	−	0.836800i	0.0239573	−	0.0285512i	0.777890	+	0.628400i	$0.216290\pi$
$860$		0			0
$861$	59.8777	−	3.33473i	2.04063	−	0.113647i
$862$		0			0
$863$	27.9682			0.952049			0.476024	−	0.879432i	$-0.342077\pi$
$863$	27.9682			0.952049			0.476024	+	0.879432i	$0.342077\pi$
$864$		0			0
$865$	−18.9846			−0.645495
$866$		0			0
$867$	0.434117	−	0.858945i	0.0147434	−	0.0291713i
$868$		0			0
$869$	40.4004	−	48.1474i	1.37049	−	1.63329i
$870$		0			0
$871$	0.0652313	−	0.179222i	0.00221028	−	0.00607269i
$872$		0			0
$873$	−14.6384	−	49.8164i	−0.495435	−	1.68603i
$874$		0			0
$875$	21.8976	−	18.3742i	0.740273	−	0.621163i
$876$		0			0
$877$	4.54524	−	25.7773i	0.153482	−	0.870438i	−0.806679	−	0.590990i	$-0.798737\pi$
$877$	4.54524	−	25.7773i	0.153482	−	0.870438i	0.960161	−	0.279448i	$-0.0901516\pi$
$878$		0			0
$879$	−15.5635	+	20.7948i	−0.524945	+	0.701393i
$880$		0			0
$881$	0.0929680	+	0.0536751i	0.00313217	+	0.00180836i	0.501565	−	0.865120i	$-0.332758\pi$
$881$	0.0929680	+	0.0536751i	0.00313217	+	0.00180836i	−0.498433	+	0.866928i	$0.666091\pi$
$882$		0			0
$883$	25.8385	−	14.9179i	0.869535	−	0.502026i	0.00234156	−	0.999997i	$-0.499255\pi$
$883$	25.8385	−	14.9179i	0.869535	−	0.502026i	0.867194	+	0.497971i	$0.165921\pi$
$884$		0			0
$885$	11.5180	+	12.2708i	0.387175	+	0.412478i
$886$		0			0
$887$	−5.01473	+	1.82521i	−0.168378	+	0.0612847i	−0.424834	−	0.905271i	$-0.639667\pi$
$887$	−5.01473	+	1.82521i	−0.168378	+	0.0612847i	0.256456	+	0.966556i	$0.417445\pi$
$888$		0			0
$889$	3.00052	+	17.0168i	0.100634	+	0.570725i
$890$		0			0
$891$	−36.4816	−	4.64067i	−1.22218	−	0.155468i
$892$		0			0
$893$	−17.0924	+	3.01384i	−0.571974	+	0.100854i
$894$		0			0
$895$	−2.29421	−	6.30329i	−0.0766870	−	0.210696i
$896$		0			0
$897$	0.235112	−	0.220690i	0.00785016	−	0.00736861i
$898$		0			0
$899$	5.63437	+	9.75902i	0.187917	+	0.325482i
$900$		0			0
$901$	2.83181	−	4.90484i	0.0943414	−	0.163404i
$902$		0			0
$903$	51.9164	+	38.8559i	1.72767	+	1.29304i
$904$		0			0
$905$	22.1846	+	3.91175i	0.737442	+	0.130031i
$906$		0			0
$907$	9.85143	+	11.7405i	0.327111	+	0.389836i	0.904387	−	0.426713i	$-0.140329\pi$
$907$	9.85143	+	11.7405i	0.327111	+	0.389836i	−0.577276	+	0.816549i	$0.695884\pi$
$908$		0			0
$909$	9.12838	+	8.70035i	0.302769	+	0.288572i
$910$		0			0
$911$	−48.5187	−	17.6594i	−1.60750	−	0.585081i	−0.626555	−	0.779377i	$-0.715536\pi$
$911$	−48.5187	−	17.6594i	−1.60750	−	0.585081i	−0.980943	+	0.194296i	$0.937758\pi$
$912$		0			0
$913$	17.2596	+	14.4826i	0.571210	+	0.479303i
$914$		0			0
$915$	−10.0456	−	5.07709i	−0.332096	−	0.167844i
$916$		0			0
$917$		−	12.0653i		−	0.398430i
$918$		0			0
$919$			5.59132i			0.184441i	0.995739	+	0.0922204i	$0.0293964\pi$
$919$			5.59132i			0.184441i	−0.995739	+	0.0922204i	$0.970604\pi$
$920$		0			0
$921$	0.813596	+	14.6087i	0.0268089	+	0.481375i
$922$		0			0
$923$	4.12168	+	3.45850i	0.135667	+	0.113838i
$924$		0			0
$925$	5.87695	+	2.13904i	0.193233	+	0.0703311i
$926$		0			0
$927$	25.9001	+	52.2319i	0.850671	+	1.71552i
$928$		0			0
$929$	6.56442	+	7.82317i	0.215372	+	0.256670i	0.862904	−	0.505368i	$-0.168643\pi$
$929$	6.56442	+	7.82317i	0.215372	+	0.256670i	−0.647532	+	0.762038i	$0.724199\pi$
$930$		0			0
$931$	−6.55076	−	1.15508i	−0.214693	−	0.0378561i
$932$		0			0
$933$	−0.556833	+	0.238517i	−0.0182299	+	0.00780869i
$934$		0			0
$935$	−8.51521	+	14.7488i	−0.278477	+	0.482336i
$936$		0			0
$937$	20.8340	+	36.0855i	0.680616	+	1.17886i	0.974793	+	0.223110i	$0.0716210\pi$
$937$	20.8340	+	36.0855i	0.680616	+	1.17886i	−0.294178	+	0.955751i	$0.595046\pi$
$938$		0			0
$939$	6.83810	+	2.06615i	0.223153	+	0.0674263i
$940$		0			0
$941$	12.2176	+	33.5676i	0.398283	+	1.09427i	0.963120	+	0.269071i	$0.0867166\pi$
$941$	12.2176	+	33.5676i	0.398283	+	1.09427i	−0.564837	+	0.825202i	$0.691061\pi$
$942$		0			0
$943$	3.68967	−	0.650588i	0.120152	−	0.0211861i
$944$		0			0
$945$	−10.4993	−	12.7082i	−0.341543	−	0.413399i
$946$		0			0
$947$	−5.34207	−	30.2964i	−0.173594	−	0.984499i	−0.939754	−	0.341850i	$-0.888946\pi$
$947$	−5.34207	−	30.2964i	−0.173594	−	0.984499i	0.766161	−	0.642649i	$-0.222165\pi$
$948$		0			0
$949$	1.04063	−	0.378758i	0.0337802	−	0.0122950i
$950$		0			0
$951$	−17.4084	+	4.07914i	−0.564506	+	0.132275i
$952$		0			0
$953$	19.2865	−	11.1351i	0.624751	−	0.360700i	−0.153965	−	0.988076i	$-0.549204\pi$
$953$	19.2865	−	11.1351i	0.624751	−	0.360700i	0.778716	+	0.627376i	$0.215871\pi$
$954$		0			0
$955$	21.9848	+	12.6930i	0.711413	+	0.410734i
$956$		0			0
$957$	−36.1816	−	4.32230i	−1.16958	−	0.139720i
$958$		0			0
$959$	9.61502	−	54.5295i	0.310485	−	1.76085i
$960$		0			0
$961$	20.0777	−	16.8472i	0.647666	−	0.543457i
$962$		0			0
$963$	12.0231	−	27.4875i	0.387439	−	0.885771i
$964$		0			0
$965$	7.03197	−	19.3202i	0.226367	−	0.621939i
$966$		0			0
$967$	−7.30702	+	8.70816i	−0.234978	+	0.280036i	−0.870628	−	0.491941i	$-0.836287\pi$
$967$	−7.30702	+	8.70816i	−0.234978	+	0.280036i	0.635651	+	0.771977i	$0.280732\pi$
$968$		0			0
$969$	8.33178	+	12.7383i	0.267655	+	0.409213i
$970$		0			0
$971$	−44.4515			−1.42652			−0.713258	−	0.700902i	$-0.752781\pi$
$971$	−44.4515			−1.42652			−0.713258	+	0.700902i	$0.752781\pi$
$972$		0			0
$973$	13.2160			0.423684
$974$		0			0
$975$	−2.05126	−	3.13613i	−0.0656930	−	0.100437i
$976$		0			0
$977$	−34.7566	+	41.4213i	−1.11196	+	1.32518i	−0.171539	+	0.985177i	$0.554874\pi$
$977$	−34.7566	+	41.4213i	−1.11196	+	1.32518i	−0.940423	+	0.340007i	$0.889570\pi$
$978$		0			0
$979$	−1.54848	+	4.25440i	−0.0494895	+	0.135971i
$980$		0			0
$981$	−20.1851	+	46.1475i	−0.644459	+	1.47338i
$982$		0			0
$983$	−5.19470	+	4.35887i	−0.165685	+	0.139026i	−0.721860	−	0.692039i	$-0.756713\pi$
$983$	−5.19470	+	4.35887i	−0.165685	+	0.139026i	0.556175	+	0.831065i	$0.312268\pi$
$984$		0			0
$985$	1.06190	−	6.02233i	0.0338349	−	0.191887i
$986$		0			0
$987$	45.3888	+	5.42221i	1.44474	+	0.172591i
$988$		0			0
$989$	3.50846	+	2.02561i	0.111562	+	0.0644106i
$990$		0			0
$991$	−30.9811	+	17.8869i	−0.984146	+	0.568197i	−0.903519	−	0.428547i	$-0.859026\pi$
$991$	−30.9811	+	17.8869i	−0.984146	+	0.568197i	−0.0806269	+	0.996744i	$0.525692\pi$
$992$		0			0
$993$	−26.9762	+	6.32108i	−0.856065	+	0.200594i
$994$		0			0
$995$	14.7991	−	5.38643i	0.469163	−	0.170761i
$996$		0			0
$997$	−9.82244	−	55.7058i	−0.311080	−	1.76422i	−0.593407	−	0.804903i	$-0.702217\pi$
$997$	−9.82244	−	55.7058i	−0.311080	−	1.76422i	0.282327	−	0.959318i	$-0.408894\pi$
$998$		0			0
$999$	2.82939	−	7.59296i	0.0895179	−	0.240231i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	864.2.bi.a.95.12	✓	216
4.3	odd	2	inner	864.2.bi.a.95.25	yes	216
27.2	odd	18	inner	864.2.bi.a.191.25	yes	216
108.83	even	18	inner	864.2.bi.a.191.12	yes	216

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
864.2.bi.a.95.12	✓	216	1.1	even	1	trivial
864.2.bi.a.95.25	yes	216	4.3	odd	2	inner
864.2.bi.a.191.12	yes	216	108.83	even	18	inner
864.2.bi.a.191.25	yes	216	27.2	odd	18	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.bi (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.948095 - 1.44952i) q^{3} +(0.639391 - 0.761997i) q^{5} +(1.09080 - 2.99694i) q^{7} +(-1.20223 + 2.74857i) q^{9} +O(q^{10})\)	\(q+(-0.948095 - 1.44952i) q^{3} +(0.639391 - 0.761997i) q^{5} +(1.09080 - 2.99694i) q^{7} +(-1.20223 + 2.74857i) q^{9} +(3.13020 - 2.62655i) q^{11} +(0.0936778 - 0.531273i) q^{13} +(-1.71073 - 0.204367i) q^{15} +(-3.62860 - 2.09497i) q^{17} +(1.81639 - 1.04869i) q^{19} +(-5.37831 + 1.26025i) q^{21} +(-0.324292 + 0.118033i) q^{23} +(0.696423 + 3.94961i) q^{25} +(5.12395 - 0.863242i) q^{27} +(5.07035 - 0.894039i) q^{29} +(0.748585 + 2.05672i) q^{31} +(-6.77496 - 2.04708i) q^{33} +(-1.58621 - 2.74740i) q^{35} +(0.779711 - 1.35050i) q^{37} +(-0.858908 + 0.367909i) q^{39} +(-10.6914 - 1.88519i) q^{41} +(-7.54575 - 8.99267i) q^{43} +(1.32570 + 2.67351i) q^{45} +(-7.77604 - 2.83025i) q^{47} +(-2.42950 - 2.03859i) q^{49} +(0.403546 + 7.24597i) q^{51} +1.35172i q^{53} -4.06459i q^{55} +(-3.24221 - 1.63864i) q^{57} +(-7.48289 - 6.27889i) q^{59} +(6.13900 + 2.23441i) q^{61} +(6.92591 + 6.60115i) q^{63} +(-0.344932 - 0.411074i) q^{65} +(0.348168 + 0.0613915i) q^{67} +(0.478551 + 0.358163i) q^{69} +(-4.98682 + 8.63743i) q^{71} +(1.02639 + 1.77776i) q^{73} +(5.06478 - 4.75409i) q^{75} +(-4.45719 - 12.2460i) q^{77} +(15.1479 - 2.67098i) q^{79} +(-6.10927 - 6.60884i) q^{81} +(0.957481 + 5.43015i) q^{83} +(-3.91646 + 1.42547i) q^{85} +(-6.10310 - 6.50195i) q^{87} +(-0.959546 + 0.553994i) q^{89} +(-1.49001 - 0.860258i) q^{91} +(2.27153 - 3.03506i) q^{93} +(0.362282 - 2.05461i) q^{95} +(-13.2583 + 11.1251i) q^{97} +(3.45602 + 11.7613i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 216 q+O(q^{10}) \) 216 * q	\( 216 q - 24 q^{29} + 36 q^{33} + 36 q^{41} - 24 q^{45} + 12 q^{57} + 48 q^{65} + 48 q^{69} + 48 q^{77} + 48 q^{81} + 36 q^{89} - 144 q^{93} - 36 q^{97}+O(q^{100}) \) 216 * q - 24 * q^29 + 36 * q^33 + 36 * q^41 - 24 * q^45 + 12 * q^57 + 48 * q^65 + 48 * q^69 + 48 * q^77 + 48 * q^81 + 36 * q^89 - 144 * q^93 - 36 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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