LMFDB - Embedded newform 864.2.v.a.109.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [864,2,Mod(109,864)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(864, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([0, 7, 0]))

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

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

chi := DirichletCharacter("864.109");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 864 = 2^{5} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	864.v (of order $8$, degree $4$, 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:	$128$
Relative dimension:	$32$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			109.20
Character	$\chi$	$=$	864.109
Dual form			864.2.v.a.325.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.567462 + 1.29537i) q^{2} +(-1.35597 + 1.47015i) q^{4} +(-2.16011 + 0.894745i) q^{5} +(1.46314 - 1.46314i) q^{7} +(-2.67385 - 0.922239i) q^{8} +O(q^{10})$	\(q+(0.567462 + 1.29537i) q^{2} +(-1.35597 + 1.47015i) q^{4} +(-2.16011 + 0.894745i) q^{5} +(1.46314 - 1.46314i) q^{7} +(-2.67385 - 0.922239i) q^{8} +(-2.38480 - 2.29041i) q^{10} +(-2.39513 - 5.78235i) q^{11} +(0.0552727 + 0.0228947i) q^{13} +(2.72558 + 1.06503i) q^{14} +(-0.322664 - 3.98696i) q^{16} +3.26457i q^{17} +(-0.456261 - 0.188990i) q^{19} +(1.61364 - 4.38892i) q^{20} +(6.13115 - 6.38384i) q^{22} +(-6.25659 - 6.25659i) q^{23} +(0.329954 - 0.329954i) q^{25} +(0.00170799 + 0.0845906i) q^{26} +(0.167050 + 4.13501i) q^{28} +(3.28735 - 7.93636i) q^{29} +6.60653 q^{31} +(4.98150 - 2.68042i) q^{32} +(-4.22883 + 1.85252i) q^{34} +(-1.85140 + 4.46967i) q^{35} +(-0.590451 + 0.244573i) q^{37} +(-0.0140990 - 0.698273i) q^{38} +(6.60097 - 0.400280i) q^{40} +(-1.11963 - 1.11963i) q^{41} +(-3.75382 - 9.06253i) q^{43} +(11.7486 + 4.31953i) q^{44} +(4.55424 - 11.6550i) q^{46} +12.0850i q^{47} +2.71846i q^{49} +(0.614649 + 0.240177i) q^{50} +(-0.108607 + 0.0502144i) q^{52} +(0.152093 + 0.367185i) q^{53} +(10.3475 + 10.3475i) q^{55} +(-5.26157 + 2.56285i) q^{56} +(12.1460 - 0.245242i) q^{58} +(-4.24644 + 1.75893i) q^{59} +(0.578617 - 1.39691i) q^{61} +(3.74895 + 8.55791i) q^{62} +(6.29895 + 4.93186i) q^{64} -0.139880 q^{65} +(3.44098 - 8.30727i) q^{67} +(-4.79940 - 4.42667i) q^{68} +(-6.84048 + 0.138117i) q^{70} +(2.39497 - 2.39497i) q^{71} +(-9.83836 - 9.83836i) q^{73} +(-0.651871 - 0.626068i) q^{74} +(0.896522 - 0.414506i) q^{76} +(-11.9648 - 4.95597i) q^{77} -3.62239i q^{79} +(4.26431 + 8.32356i) q^{80} +(0.814992 - 2.08569i) q^{82} +(-9.86593 - 4.08660i) q^{83} +(-2.92096 - 7.05182i) q^{85} +(9.60920 - 10.0052i) q^{86} +(1.07150 + 17.6700i) q^{88} +(-6.31778 + 6.31778i) q^{89} +(0.114370 - 0.0473735i) q^{91} +(17.6819 - 0.714329i) q^{92} +(-15.6546 + 6.85778i) q^{94} +1.15467 q^{95} -4.47320 q^{97} +(-3.52141 + 1.54262i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 128 q+O(q^{10}) $ 128 * q	$ 128 q - 8 q^{10} - 32 q^{16} + 32 q^{22} + 64 q^{40} + 64 q^{46} + 88 q^{52} - 64 q^{55} + 64 q^{58} - 32 q^{61} - 96 q^{64} + 64 q^{67} + 48 q^{70} + 32 q^{76} + 40 q^{82} + 40 q^{88} - 48 q^{91} + 24 q^{94}+O(q^{100}) $ 128 * q - 8 * q^10 - 32 * q^16 + 32 * q^22 + 64 * q^40 + 64 * q^46 + 88 * q^52 - 64 * q^55 + 64 * q^58 - 32 * q^61 - 96 * q^64 + 64 * q^67 + 48 * q^70 + 32 * q^76 + 40 * q^82 + 40 * q^88 - 48 * q^91 + 24 * q^94

Display 100 coefficients 10 coefficients

Character values

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

$n$	$325$	$353$	$703$
$\chi(n)$	$e\left(\frac{7}{8}\right)$	$1$	$1$

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 $

$2$	0.567462	+	1.29537i	0.401256	+	0.915966i
$2$	0.567462	+	1.29537i	0.401256	+	0.915966i
$3$		0			0
$3$		0			0
$4$	−1.35597	+	1.47015i	−0.677987	+	0.735073i
$5$	−2.16011	+	0.894745i	−0.966029	+	0.400142i	−0.809232	−	0.587489i	$-0.800117\pi$
$5$	−2.16011	+	0.894745i	−0.966029	+	0.400142i	−0.156796	+	0.987631i	$0.550117\pi$
$6$		0			0
$7$	1.46314	−	1.46314i	0.553014	−	0.553014i	−0.374295	−	0.927309i	$-0.622115\pi$
$7$	1.46314	−	1.46314i	0.553014	−	0.553014i	0.927309	+	0.374295i	$0.122115\pi$
$8$	−2.67385	−	0.922239i	−0.945349	−	0.326061i
$9$		0			0
$10$	−2.38480	−	2.29041i	−0.754141	−	0.724290i
$11$	−2.39513	−	5.78235i	−0.722158	−	1.74344i	−0.667108	−	0.744961i	$-0.732468\pi$
$11$	−2.39513	−	5.78235i	−0.722158	−	1.74344i	−0.0550506	−	0.998484i	$-0.517532\pi$
$12$		0			0
$13$	0.0552727	+	0.0228947i	0.0153299	+	0.00634985i	0.390335	−	0.920673i	$-0.372359\pi$
$13$	0.0552727	+	0.0228947i	0.0153299	+	0.00634985i	−0.375005	+	0.927023i	$0.622359\pi$
$14$	2.72558	+	1.06503i	0.728442	+	0.284642i
$15$		0			0
$16$	−0.322664	−	3.98696i	−0.0806661	−	0.996741i
$17$			3.26457i			0.791775i	0.918299	+	0.395887i	$0.129563\pi$
$17$			3.26457i			0.791775i	−0.918299	+	0.395887i	$0.870437\pi$
$18$		0			0
$19$	−0.456261	−	0.188990i	−0.104674	−	0.0433572i	0.329732	−	0.944075i	$-0.393042\pi$
$19$	−0.456261	−	0.188990i	−0.104674	−	0.0433572i	−0.434406	+	0.900717i	$0.643042\pi$
$20$	1.61364	−	4.38892i	0.360821	−	0.981393i
$21$		0			0
$22$	6.13115	−	6.38384i	1.30717	−	1.36104i
$23$	−6.25659	−	6.25659i	−1.30459	−	1.30459i	−0.925262	−	0.379328i	$-0.876155\pi$
$23$	−6.25659	−	6.25659i	−1.30459	−	1.30459i	−0.379328	−	0.925262i	$-0.623845\pi$
$24$		0			0
$25$	0.329954	−	0.329954i	0.0659908	−	0.0659908i
$26$	0.00170799	+	0.0845906i	0.000334964	+	0.0165896i
$27$		0			0
$28$	0.167050	+	4.13501i	0.0315694	+	0.781443i
$29$	3.28735	−	7.93636i	0.610445	−	1.47374i	−0.252068	−	0.967710i	$-0.581111\pi$
$29$	3.28735	−	7.93636i	0.610445	−	1.47374i	0.862513	−	0.506035i	$-0.168889\pi$
$30$		0			0
$31$	6.60653			1.18657			0.593284	−	0.804994i	$-0.297831\pi$
$31$	6.60653			1.18657			0.593284	+	0.804994i	$0.297831\pi$
$32$	4.98150	−	2.68042i	0.880613	−	0.473836i
$33$		0			0
$34$	−4.22883	+	1.85252i	−0.725239	+	0.317704i
$35$	−1.85140	+	4.46967i	−0.312943	+	0.755512i
$36$		0			0
$37$	−0.590451	+	0.244573i	−0.0970696	+	0.0402076i	−0.430690	−	0.902500i	$-0.641730\pi$
$37$	−0.590451	+	0.244573i	−0.0970696	+	0.0402076i	0.333620	+	0.942708i	$0.391730\pi$
$38$	−0.0140990	−	0.698273i	−0.00228715	−	0.113275i
$39$		0			0
$40$	6.60097	−	0.400280i	1.04370	−	0.0632898i
$41$	−1.11963	−	1.11963i	−0.174857	−	0.174857i	0.614252	−	0.789110i	$-0.289458\pi$
$41$	−1.11963	−	1.11963i	−0.174857	−	0.174857i	−0.789110	+	0.614252i	$0.789458\pi$
$42$		0			0
$43$	−3.75382	−	9.06253i	−0.572453	−	1.38202i	−0.899461	−	0.437002i	$-0.856040\pi$
$43$	−3.75382	−	9.06253i	−0.572453	−	1.38202i	0.327008	−	0.945022i	$-0.393960\pi$
$44$	11.7486	+	4.31953i	1.77117	+	0.651194i
$45$		0			0
$46$	4.55424	−	11.6550i	0.671486	−	1.71843i
$47$			12.0850i			1.76278i	0.472389	+	0.881390i	$0.343392\pi$
$47$			12.0850i			1.76278i	−0.472389	+	0.881390i	$0.656608\pi$
$48$		0			0
$49$			2.71846i			0.388351i
$50$	0.614649	+	0.240177i	0.0869245	+	0.0339661i
$51$		0			0
$52$	−0.108607	+	0.0502144i	−0.0150611	+	0.00696348i
$53$	0.152093	+	0.367185i	0.0208916	+	0.0504367i	0.933981	−	0.357322i	$-0.116310\pi$
$53$	0.152093	+	0.367185i	0.0208916	+	0.0504367i	−0.913090	+	0.407759i	$0.866310\pi$
$54$		0			0
$55$	10.3475	+	10.3475i	1.39525	+	1.39525i
$56$	−5.26157	+	2.56285i	−0.703107	+	0.342475i
$57$		0			0
$58$	12.1460	−	0.245242i	1.59484	−	0.0322018i
$59$	−4.24644	+	1.75893i	−0.552840	+	0.228994i	−0.641573	−	0.767062i	$-0.721718\pi$
$59$	−4.24644	+	1.75893i	−0.552840	+	0.228994i	0.0887336	+	0.996055i	$0.471718\pi$
$60$		0			0
$61$	0.578617	−	1.39691i	0.0740844	−	0.178855i	−0.882499	−	0.470314i	$-0.844141\pi$
$61$	0.578617	−	1.39691i	0.0740844	−	0.178855i	0.956583	+	0.291459i	$0.0941406\pi$
$62$	3.74895	+	8.55791i	0.476117	+	1.08686i
$63$		0			0
$64$	6.29895	+	4.93186i	0.787369	+	0.616482i
$65$	−0.139880			−0.0173500
$66$		0			0
$67$	3.44098	−	8.30727i	0.420383	−	1.01489i	−0.561852	−	0.827238i	$-0.689911\pi$
$67$	3.44098	−	8.30727i	0.420383	−	1.01489i	0.982235	−	0.187657i	$-0.0600892\pi$
$68$	−4.79940	−	4.42667i	−0.582012	−	0.536813i
$69$		0			0
$70$	−6.84048	+	0.138117i	−0.817593	+	0.0165082i
$71$	2.39497	−	2.39497i	0.284231	−	0.284231i	−0.550563	−	0.834794i	$-0.685587\pi$
$71$	2.39497	−	2.39497i	0.284231	−	0.284231i	0.834794	+	0.550563i	$0.185587\pi$
$72$		0			0
$73$	−9.83836	−	9.83836i	−1.15149	−	1.15149i	−0.986253	−	0.165240i	$-0.947160\pi$
$73$	−9.83836	−	9.83836i	−1.15149	−	1.15149i	−0.165240	−	0.986253i	$-0.552840\pi$
$74$	−0.651871	−	0.626068i	−0.0757785	−	0.0727790i
$75$		0			0
$76$	0.896522	−	0.414506i	0.102838	−	0.0475471i
$77$	−11.9648	−	4.95597i	−1.36351	−	0.564786i
$78$		0			0
$79$		−	3.62239i		−	0.407550i	−0.979018	−	0.203775i	$-0.934679\pi$
$79$		−	3.62239i		−	0.407550i	0.979018	−	0.203775i	$-0.0653212\pi$
$80$	4.26431	+	8.32356i	0.476764	+	0.930603i
$81$		0			0
$82$	0.814992	−	2.08569i	0.0900008	−	0.230326i
$83$	−9.86593	−	4.08660i	−1.08293	−	0.448563i	−0.231392	−	0.972861i	$-0.574328\pi$
$83$	−9.86593	−	4.08660i	−1.08293	−	0.448563i	−0.851535	+	0.524298i	$0.824328\pi$
$84$		0			0
$85$	−2.92096	−	7.05182i	−0.316822	−	0.764877i
$86$	9.60920	−	10.0052i	1.03619	−	1.07889i
$87$		0			0
$88$	1.07150	+	17.6700i	0.114222	+	1.88363i
$89$	−6.31778	+	6.31778i	−0.669684	+	0.669684i	−0.957643	−	0.287959i	$-0.907023\pi$
$89$	−6.31778	+	6.31778i	−0.669684	+	0.669684i	0.287959	+	0.957643i	$0.407023\pi$
$90$		0			0
$91$	0.114370	−	0.0473735i	0.0119892	−	0.00496609i
$92$	17.6819	−	0.714329i	1.84347	−	0.0744739i
$93$		0			0
$94$	−15.6546	+	6.85778i	−1.61465	+	0.707326i
$95$	1.15467			0.118467
$96$		0			0
$97$	−4.47320			−0.454185			−0.227093	−	0.973873i	$-0.572922\pi$
$97$	−4.47320			−0.454185			−0.227093	+	0.973873i	$0.572922\pi$
$98$	−3.52141	+	1.54262i	−0.355716	+	0.155828i
$99$		0			0
$100$	0.0376715	+	0.932490i	0.00376715	+	0.0932490i
$101$	1.15367	−	0.477866i	0.114794	−	0.0475494i	−0.324547	−	0.945870i	$-0.605212\pi$
$101$	1.15367	−	0.477866i	0.114794	−	0.0475494i	0.439341	+	0.898320i	$0.355212\pi$
$102$		0			0
$103$	6.51916	−	6.51916i	0.642352	−	0.642352i	−0.308781	−	0.951133i	$-0.599921\pi$
$103$	6.51916	−	6.51916i	0.642352	−	0.642352i	0.951133	+	0.308781i	$0.0999210\pi$
$104$	−0.126677	−	0.112192i	−0.0124217	−	0.0110013i
$105$		0			0
$106$	−0.389334	+	0.405380i	−0.0378154	+	0.0393740i
$107$	0.262336	+	0.633334i	0.0253609	+	0.0612267i	0.936053	−	0.351860i	$-0.114451\pi$
$107$	0.262336	+	0.633334i	0.0253609	+	0.0612267i	−0.910692	+	0.413087i	$0.864451\pi$
$108$		0			0
$109$	−10.6809	−	4.42416i	−1.02304	−	0.423758i	−0.192846	−	0.981229i	$-0.561772\pi$
$109$	−10.6809	−	4.42416i	−1.02304	−	0.423758i	−0.830196	+	0.557471i	$0.811772\pi$
$110$	−7.53202	+	19.2756i	−0.718150	+	1.83786i
$111$		0			0
$112$	−6.30558	−	5.36138i	−0.595821	−	0.506602i
$113$			12.3132i			1.15833i	0.815210	+	0.579166i	$0.196622\pi$
$113$			12.3132i			1.15833i	−0.815210	+	0.579166i	$0.803378\pi$
$114$		0			0
$115$	19.1130	+	7.91685i	1.78229	+	0.738250i
$116$	7.21005	+	15.5944i	0.669437	+	1.44790i
$117$		0			0
$118$	−4.68817	−	4.50259i	−0.431581	−	0.414497i
$119$	4.77652	+	4.77652i	0.437862	+	0.437862i
$120$		0			0
$121$	−19.9208	+	19.9208i	−1.81098	+	1.81098i
$122$	2.13786	−	0.0431659i	0.193552	−	0.00390805i
$123$		0			0
$124$	−8.95828	+	9.71256i	−0.804478	+	0.872214i
$125$	4.05621	−	9.79257i	0.362799	−	0.875874i
$126$		0			0
$127$	−14.9033			−1.32245			−0.661226	−	0.750186i	$-0.729964\pi$
$127$	−14.9033			−1.32245			−0.661226	+	0.750186i	$0.729964\pi$
$128$	−2.81418	+	10.9581i	−0.248741	+	0.968570i
$129$		0			0
$130$	−0.0793765	−	0.181196i	−0.00696178	−	0.0158920i
$131$	3.60890	−	8.71265i	0.315311	−	0.761227i	−0.684180	−	0.729313i	$-0.739840\pi$
$131$	3.60890	−	8.71265i	0.315311	−	0.761227i	0.999491	−	0.0319142i	$-0.0101603\pi$
$132$		0			0
$133$	−0.944091	+	0.391055i	−0.0818631	+	0.0339088i
$134$	12.7136	−	0.256703i	1.09829	−	0.0221758i
$135$		0			0
$136$	3.01072	−	8.72897i	0.258167	−	0.748503i
$137$	−3.61267	−	3.61267i	−0.308651	−	0.308651i	0.535735	−	0.844386i	$-0.320035\pi$
$137$	−3.61267	−	3.61267i	−0.308651	−	0.308651i	−0.844386	+	0.535735i	$0.820035\pi$
$138$		0			0
$139$	5.59533	+	13.5083i	0.474590	+	1.14576i	0.962113	+	0.272651i	$0.0879006\pi$
$139$	5.59533	+	13.5083i	0.474590	+	1.14576i	−0.487523	+	0.873110i	$0.662099\pi$
$140$	−4.06062	−	8.78258i	−0.343185	−	0.742264i
$141$		0			0
$142$	4.46143	+	1.74332i	0.374395	+	0.146296i
$143$		−	0.374442i		−	0.0313124i
$144$		0			0
$145$			20.0847i			1.66794i
$146$	7.16144	−	18.3272i	0.592685	−	1.51677i
$147$		0			0
$148$	0.441079	−	1.19969i	0.0362565	−	0.0986135i
$149$	1.25331	+	3.02575i	0.102675	+	0.247879i	0.966866	−	0.255285i	$-0.0821692\pi$
$149$	1.25331	+	3.02575i	0.102675	+	0.247879i	−0.864191	+	0.503164i	$0.832169\pi$
$150$		0			0
$151$	−0.224843	−	0.224843i	−0.0182974	−	0.0182974i	0.697899	−	0.716196i	$-0.254118\pi$
$151$	−0.224843	−	0.224843i	−0.0182974	−	0.0182974i	−0.716196	+	0.697899i	$0.754118\pi$
$152$	1.04568	+	0.926112i	0.0848159	+	0.0751176i
$153$		0			0
$154$	−0.369724	−	18.3112i	−0.0297932	−	1.47556i
$155$	−14.2708	+	5.91116i	−1.14626	+	0.474796i
$156$		0			0
$157$	−0.194373	+	0.469257i	−0.0155126	+	0.0374508i	−0.931446	−	0.363879i	$-0.881452\pi$
$157$	−0.194373	+	0.469257i	−0.0155126	+	0.0374508i	0.915933	+	0.401330i	$0.131452\pi$
$158$	4.69234	−	2.05556i	0.373302	−	0.163532i
$159$		0			0
$160$	−8.36228	+	10.2472i	−0.661096	+	0.810109i
$161$	−18.3085			−1.44291
$162$		0			0
$163$	−8.75493	+	21.1363i	−0.685739	+	1.65552i	0.0674553	+	0.997722i	$0.478512\pi$
$163$	−8.75493	+	21.1363i	−0.685739	+	1.65552i	−0.753194	+	0.657798i	$0.771488\pi$
$164$	3.16422	−	0.127831i	0.247084	−	0.00998191i
$165$		0			0
$166$	−0.304868	−	15.0990i	−0.0236623	−	1.17191i
$167$	14.8393	−	14.8393i	1.14830	−	1.14830i	0.161412	−	0.986887i	$-0.448395\pi$
$167$	14.8393	−	14.8393i	1.14830	−	1.14830i	0.986887	−	0.161412i	$-0.0516048\pi$
$168$		0			0
$169$	−9.18986	−	9.18986i	−0.706912	−	0.706912i
$170$	7.47719	−	7.78536i	0.573474	−	0.597110i
$171$		0			0
$172$	18.4133	+	6.76989i	1.40400	+	0.516200i
$173$	−14.0446	−	5.81747i	−1.06779	−	0.442294i	−0.221581	−	0.975142i	$-0.571122\pi$
$173$	−14.0446	−	5.81747i	−1.06779	−	0.442294i	−0.846211	+	0.532848i	$0.821122\pi$
$174$		0			0
$175$		−	0.965536i		−	0.0729877i
$176$	−22.2812	+	11.4151i	−1.67951	+	0.860442i
$177$		0			0
$178$	−11.7690	−	4.59878i	−0.882122	−	0.344693i
$179$	3.27556	+	1.35678i	0.244827	+	0.101411i	0.501723	−	0.865028i	$-0.332700\pi$
$179$	3.27556	+	1.35678i	0.244827	+	0.101411i	−0.256896	+	0.966439i	$0.582700\pi$
$180$		0			0
$181$	2.13658	+	5.15816i	0.158811	+	0.383403i	0.983177	−	0.182653i	$-0.0584686\pi$
$181$	2.13658	+	5.15816i	0.158811	+	0.383403i	−0.824367	+	0.566056i	$0.808469\pi$
$182$	0.126267	+	0.121269i	0.00935951	+	0.00898903i
$183$		0			0
$184$	10.9591	+	22.4993i	0.807917	+	1.65867i
$185$	1.05661	−	1.05661i	0.0776833	−	0.0776833i
$186$		0			0
$187$	18.8769	−	7.81907i	1.38042	−	0.571787i
$188$	−17.7668	−	16.3870i	−1.29577	−	1.19514i
$189$		0			0
$190$	0.655231	+	1.49573i	0.0475355	+	0.108511i
$191$	16.0419			1.16075			0.580375	−	0.814350i	$-0.302906\pi$
$191$	16.0419			1.16075			0.580375	+	0.814350i	$0.302906\pi$
$192$		0			0
$193$	4.08991			0.294398			0.147199	−	0.989107i	$-0.452974\pi$
$193$	4.08991			0.294398			0.147199	+	0.989107i	$0.452974\pi$
$194$	−2.53837	−	5.79446i	−0.182244	−	0.416018i
$195$		0			0
$196$	−3.99653	−	3.68616i	−0.285466	−	0.263297i
$197$	11.7515	−	4.86763i	0.837259	−	0.346804i	0.0774867	−	0.996993i	$-0.475310\pi$
$197$	11.7515	−	4.86763i	0.837259	−	0.346804i	0.759772	+	0.650189i	$0.225310\pi$
$198$		0			0
$199$	5.00147	−	5.00147i	0.354544	−	0.354544i	−0.507253	−	0.861797i	$-0.669339\pi$
$199$	5.00147	−	5.00147i	0.354544	−	0.354544i	0.861797	+	0.507253i	$0.169339\pi$
$200$	−1.18654	+	0.577951i	−0.0839013	+	0.0408673i
$201$		0			0
$202$	1.27368	+	1.22326i	0.0896156	+	0.0860683i
$203$	−6.80214	−	16.4218i	−0.477417	−	1.15259i
$204$		0			0
$205$	3.42031	+	1.41674i	0.238885	+	0.0989493i
$206$	12.1441	+	4.74536i	0.846120	+	0.330625i
$207$		0			0
$208$	0.0734459	−	0.227758i	0.00509256	−	0.0157922i
$209$			3.09092i			0.213803i
$210$		0			0
$211$	8.45453	+	3.50198i	0.582034	+	0.241086i	0.654219	−	0.756305i	$-0.272997\pi$
$211$	8.45453	+	3.50198i	0.582034	+	0.241086i	−0.0721855	+	0.997391i	$0.522997\pi$
$212$	−0.746050	−	0.274294i	−0.0512389	−	0.0188386i
$213$		0			0
$214$	−0.671538	+	0.699215i	−0.0459054	+	0.0477973i
$215$	16.2173	+	16.2173i	1.10601	+	1.10601i
$216$		0			0
$217$	9.66626	−	9.66626i	0.656188	−	0.656188i
$218$	−0.330050	−	16.3462i	−0.0223538	−	1.10711i
$219$		0			0
$220$	−29.2432	+	1.18139i	−1.97158	+	0.0796494i
$221$	−0.0747414	+	0.180442i	−0.00502765	+	0.0121378i
$222$		0			0
$223$	16.0650			1.07579			0.537896	−	0.843011i	$-0.319219\pi$
$223$	16.0650			1.07579			0.537896	+	0.843011i	$0.319219\pi$
$224$	3.36680	−	11.2104i	0.224954	−	0.749029i
$225$		0			0
$226$	−15.9502	+	6.98729i	−1.06099	+	0.464787i
$227$	−4.12630	+	9.96177i	−0.273872	+	0.661186i	−0.999642	−	0.0267514i	$-0.991484\pi$
$227$	−4.12630	+	9.96177i	−0.273872	+	0.661186i	0.725770	+	0.687938i	$0.241484\pi$
$228$		0			0
$229$	−3.28112	+	1.35908i	−0.216822	+	0.0898108i	−0.488451	−	0.872591i	$-0.662438\pi$
$229$	−3.28112	+	1.35908i	−0.216822	+	0.0898108i	0.271628	+	0.962402i	$0.412438\pi$
$230$	0.590611	+	29.2509i	0.0389437	+	1.92875i
$231$		0			0
$232$	−16.1091	+	18.1889i	−1.05761	+	1.19416i
$233$	17.4031	+	17.4031i	1.14011	+	1.14011i	0.988429	+	0.151684i	$0.0484697\pi$
$233$	17.4031	+	17.4031i	1.14011	+	1.14011i	0.151684	+	0.988429i	$0.451530\pi$
$234$		0			0
$235$	−10.8130	−	26.1049i	−0.705363	−	1.70290i
$236$	3.17218	−	8.62797i	0.206491	−	0.561633i
$237$		0			0
$238$	−3.47687	+	8.89785i	−0.225372	+	0.576762i
$239$		−	13.3610i		−	0.864251i	−0.901814	−	0.432125i	$-0.857764\pi$
$239$		−	13.3610i		−	0.864251i	0.901814	−	0.432125i	$-0.142236\pi$
$240$		0			0
$241$		−	4.39060i		−	0.282823i	−0.989951	−	0.141412i	$-0.954836\pi$
$241$		−	4.39060i		−	0.282823i	0.989951	−	0.141412i	$-0.0451641\pi$
$242$	−37.1091	−	14.5005i	−2.38546	−	0.932130i
$243$		0			0
$244$	1.26907	+	2.74482i	0.0812437	+	0.175719i
$245$	−2.43233	−	5.87215i	−0.155396	−	0.375158i
$246$		0			0
$247$	−0.0208920	−	0.0208920i	−0.00132932	−	0.00132932i
$248$	−17.6649	−	6.09280i	−1.12172	−	0.386893i
$249$		0			0
$250$	14.9868	−	0.302601i	0.947846	−	0.0191381i
$251$	−18.1050	+	7.49935i	−1.14278	+	0.473355i	−0.872106	−	0.489317i	$-0.837246\pi$
$251$	−18.1050	+	7.49935i	−1.14278	+	0.473355i	−0.270673	+	0.962671i	$0.587246\pi$
$252$		0			0
$253$	−21.1925	+	51.1632i	−1.33236	+	3.21660i
$254$	−8.45704	−	19.3053i	−0.530642	−	1.21132i
$255$		0			0
$256$	−15.7918	+	2.57290i	−0.986986	+	0.160806i
$257$	−24.9051			−1.55354			−0.776769	−	0.629786i	$-0.783143\pi$
$257$	−24.9051			−1.55354			−0.776769	+	0.629786i	$0.783143\pi$
$258$		0			0
$259$	−0.506068	+	1.22176i	−0.0314455	+	0.0759162i
$260$	0.189674	−	0.205644i	0.0117631	−	0.0127535i
$261$		0			0
$262$	13.3340	−	0.269230i	0.823779	−	0.0166331i
$263$	0.341086	−	0.341086i	0.0210323	−	0.0210323i	−0.696512	−	0.717545i	$-0.745266\pi$
$263$	0.341086	−	0.341086i	0.0210323	−	0.0210323i	0.717545	+	0.696512i	$0.245266\pi$
$264$		0			0
$265$	−0.657074	−	0.657074i	−0.0403637	−	0.0403637i
$266$	−1.04230	−	1.00104i	−0.0639074	−	0.0613777i
$267$		0			0
$268$	7.54702	+	16.3232i	0.461008	+	0.997098i
$269$	19.0868	+	7.90603i	1.16375	+	0.482039i	0.879120	−	0.476600i	$-0.158131\pi$
$269$	19.0868	+	7.90603i	1.16375	+	0.482039i	0.284625	+	0.958639i	$0.408131\pi$
$270$		0			0
$271$			13.2155i			0.802784i	0.915906	+	0.401392i	$0.131474\pi$
$271$			13.2155i			0.802784i	−0.915906	+	0.401392i	$0.868526\pi$
$272$	13.0157	−	1.05336i	0.789194	−	0.0638693i
$273$		0			0
$274$	2.62970	−	6.72980i	0.158866	−	0.406562i
$275$	−2.69819	−	1.11763i	−0.162707	−	0.0673955i
$276$		0			0
$277$	−9.53617	−	23.0223i	−0.572973	−	1.38328i	−0.899013	−	0.437922i	$-0.855714\pi$
$277$	−9.53617	−	23.0223i	−0.572973	−	1.38328i	0.326040	−	0.945356i	$-0.394286\pi$
$278$	−14.3232	+	14.9135i	−0.859047	+	0.894452i
$279$		0			0
$280$	9.07246	−	10.2438i	0.542183	−	0.612183i
$281$	11.1422	−	11.1422i	0.664686	−	0.664686i	−0.291795	−	0.956481i	$-0.594253\pi$
$281$	11.1422	−	11.1422i	0.664686	−	0.664686i	0.956481	+	0.291795i	$0.0942526\pi$
$282$		0			0
$283$	−10.4532	+	4.32986i	−0.621379	+	0.257384i	−0.671085	−	0.741380i	$-0.734172\pi$
$283$	−10.4532	+	4.32986i	−0.621379	+	0.257384i	0.0497061	+	0.998764i	$0.484172\pi$
$284$	0.273439	+	6.76848i	0.0162256	+	0.401635i
$285$		0			0
$286$	0.485042	−	0.212482i	0.0286811	−	0.0125643i
$287$	−3.27635			−0.193397
$288$		0			0
$289$	6.34258			0.373093
$290$	−26.0172	+	11.3973i	−1.52778	+	0.669272i
$291$		0			0
$292$	27.8044	−	1.12327i	1.62713	−	0.0657342i
$293$	21.1780	−	8.77221i	1.23723	−	0.512478i	0.334383	−	0.942437i	$-0.391472\pi$
$293$	21.1780	−	8.77221i	1.23723	−	0.512478i	0.902848	+	0.429959i	$0.141472\pi$
$294$		0			0
$295$	7.59897	−	7.59897i	0.442429	−	0.442429i
$296$	1.80433	−	0.109414i	0.104875	−	0.00635956i
$297$		0			0
$298$	−3.20827	+	3.34049i	−0.185850	+	0.193510i
$299$	−0.202576	−	0.489062i	−0.0117153	−	0.0282832i
$300$		0			0
$301$	−18.7521	−	7.76737i	−1.08085	−	0.447704i
$302$	0.163665	−	0.418844i	0.00941787	−	0.0241018i
$303$		0			0
$304$	−0.606276	+	1.88008i	−0.0347723	+	0.107830i
$305$			3.53518i			0.202424i
$306$		0			0
$307$	−4.30394	−	1.78275i	−0.245639	−	0.101747i	0.256468	−	0.966553i	$-0.417441\pi$
$307$	−4.30394	−	1.78275i	−0.245639	−	0.101747i	−0.502106	+	0.864806i	$0.667441\pi$
$308$	23.5100	−	10.8698i	1.33960	−	0.619365i
$309$		0			0
$310$	−15.7553	−	15.1316i	−0.894839	−	0.859419i
$311$	13.1986	+	13.1986i	0.748421	+	0.748421i	0.974183	−	0.225761i	$-0.0724869\pi$
$311$	13.1986	+	13.1986i	0.748421	+	0.748421i	−0.225761	+	0.974183i	$0.572487\pi$
$312$		0			0
$313$	13.2136	−	13.2136i	0.746877	−	0.746877i	−0.227014	−	0.973891i	$-0.572896\pi$
$313$	13.2136	−	13.2136i	0.746877	−	0.746877i	0.973891	+	0.227014i	$0.0728964\pi$
$314$	−0.718161	+	0.0145005i	−0.0405282	+	0.000818312i
$315$		0			0
$316$	5.32544	+	4.91187i	0.299579	+	0.276314i
$317$	3.77929	−	9.12400i	0.212266	−	0.512455i	−0.781505	−	0.623899i	$-0.785548\pi$
$317$	3.77929	−	9.12400i	0.212266	−	0.512455i	0.993771	+	0.111444i	$0.0355476\pi$
$318$		0			0
$319$	−53.7644			−3.01023
$320$	−18.0192	−	5.01739i	−1.00730	−	0.280480i
$321$		0			0
$322$	−10.3894	−	23.7163i	−0.578977	−	1.32166i
$323$	0.616970	−	1.48950i	0.0343291	−	0.0828779i
$324$		0			0
$325$	0.0257917	−	0.0106833i	0.00143066	−	0.000592600i
$326$	−32.3474	+	0.653133i	−1.79156	+	0.0361737i
$327$		0			0
$328$	1.96116	+	4.02630i	0.108287	+	0.222315i
$329$	17.6820	+	17.6820i	0.974843	+	0.974843i
$330$		0			0
$331$	−2.86478	−	6.91618i	−0.157462	−	0.380148i	0.825385	−	0.564571i	$-0.190958\pi$
$331$	−2.86478	−	6.91618i	−0.157462	−	0.380148i	−0.982847	+	0.184423i	$0.940958\pi$
$332$	19.3859	−	8.96304i	1.06394	−	0.491911i
$333$		0			0
$334$	27.6431	+	10.8017i	1.51256	+	0.591041i
$335$			21.0234i			1.14863i
$336$		0			0
$337$		−	12.2162i		−	0.665461i	−0.943022	−	0.332730i	$-0.892030\pi$
$337$		−	12.2162i		−	0.665461i	0.943022	−	0.332730i	$-0.107970\pi$
$338$	6.68939	−	17.1192i	0.363855	−	0.931160i
$339$		0			0
$340$	14.3280	+	5.26785i	0.777042	+	0.285689i
$341$	−15.8235	−	38.2013i	−0.856889	−	2.06871i
$342$		0			0
$343$	14.2194	+	14.2194i	0.767778	+	0.767778i
$344$	1.67934	+	27.6938i	0.0905438	+	1.49315i
$345$		0			0
$346$	−0.433993	−	21.4942i	−0.0233316	−	1.15553i
$347$	−13.7143	+	5.68066i	−0.736223	+	0.304954i	−0.719106	−	0.694900i	$-0.755449\pi$
$347$	−13.7143	+	5.68066i	−0.736223	+	0.304954i	−0.0171166	+	0.999854i	$0.505449\pi$
$348$		0			0
$349$	−7.44624	+	17.9768i	−0.398588	+	0.962277i	0.589413	+	0.807832i	$0.299359\pi$
$349$	−7.44624	+	17.9768i	−0.398588	+	0.962277i	−0.988001	+	0.154445i	$0.950641\pi$
$350$	1.25073	−	0.547905i	0.0668542	−	0.0292867i
$351$		0			0
$352$	−27.4305	−	22.3848i	−1.46205	−	1.19312i
$353$	26.6175			1.41671			0.708354	−	0.705858i	$-0.249438\pi$
$353$	26.6175			1.41671			0.708354	+	0.705858i	$0.249438\pi$
$354$		0			0
$355$	−3.03050	+	7.31628i	−0.160842	+	0.388308i
$356$	−0.721315	−	17.8548i	−0.0382296	−	0.946304i
$357$		0			0
$358$	0.101218	+	5.01299i	0.00534955	+	0.264945i
$359$	−6.75743	+	6.75743i	−0.356643	+	0.356643i	−0.862574	−	0.505931i	$-0.831149\pi$
$359$	−6.75743	+	6.75743i	−0.356643	+	0.356643i	0.505931	+	0.862574i	$0.331149\pi$
$360$		0			0
$361$	−13.2626	−	13.2626i	−0.698030	−	0.698030i
$362$	−5.46930	+	5.69472i	−0.287460	+	0.299308i
$363$		0			0
$364$	−0.0854365	+	0.232378i	−0.00447809	+	0.0121799i
$365$	30.0547	+	12.4491i	1.57314	+	0.651615i
$366$		0			0
$367$		−	11.9220i		−	0.622322i	−0.950357	−	0.311161i	$-0.899282\pi$
$367$		−	11.9220i		−	0.622322i	0.950357	−	0.311161i	$-0.100718\pi$
$368$	−22.9260	+	26.9636i	−1.19510	+	1.40557i
$369$		0			0
$370$	1.96828	+	0.769115i	0.102326	+	0.0399844i
$371$	0.759775	+	0.314709i	0.0394455	+	0.0163389i
$372$		0			0
$373$	7.22670	+	17.4468i	0.374184	+	0.903361i	0.993031	+	0.117849i	$0.0376000\pi$
$373$	7.22670	+	17.4468i	0.374184	+	0.903361i	−0.618847	+	0.785511i	$0.712400\pi$
$374$	20.8405	+	20.0156i	1.07764	+	1.03498i
$375$		0			0
$376$	11.1453	−	32.3135i	0.574774	−	1.66644i
$377$	0.363401	−	0.363401i	0.0187161	−	0.0187161i
$378$		0			0
$379$	21.2575	−	8.80513i	1.09192	−	0.452289i	0.237246	−	0.971450i	$-0.423755\pi$
$379$	21.2575	−	8.80513i	1.09192	−	0.452289i	0.854677	+	0.519160i	$0.173755\pi$
$380$	−1.56570	+	1.69754i	−0.0803189	+	0.0870817i
$381$		0			0
$382$	9.10314	+	20.7802i	0.465757	+	1.06321i
$383$	32.8281			1.67744			0.838719	−	0.544564i	$-0.183305\pi$
$383$	32.8281			1.67744			0.838719	+	0.544564i	$0.183305\pi$
$384$		0			0
$385$	30.2795			1.54319
$386$	2.32086	+	5.29795i	0.118129	+	0.269658i
$387$		0			0
$388$	6.06555	−	6.57627i	0.307932	−	0.333859i
$389$	−0.635526	+	0.263244i	−0.0322225	+	0.0133470i	−0.398736	−	0.917066i	$-0.630551\pi$
$389$	−0.635526	+	0.263244i	−0.0322225	+	0.0133470i	0.366514	+	0.930413i	$0.380551\pi$
$390$		0			0
$391$	20.4251	−	20.4251i	1.03294	−	1.03294i
$392$	2.50707	−	7.26875i	0.126626	−	0.367127i
$393$		0			0
$394$	12.9739	+	12.4604i	0.653616	+	0.627744i
$395$	3.24111	+	7.82474i	0.163078	+	0.393705i
$396$		0			0
$397$	−6.42539	−	2.66148i	−0.322481	−	0.133576i	0.215570	−	0.976488i	$-0.430839\pi$
$397$	−6.42539	−	2.66148i	−0.322481	−	0.133576i	−0.538051	+	0.842912i	$0.680839\pi$
$398$	9.31689	+	3.64062i	0.467014	+	0.182488i
$399$		0			0
$400$	−1.42198	−	1.20905i	−0.0710990	−	0.0604525i
$401$			37.6097i			1.87814i	0.343730	+	0.939069i	$0.388310\pi$
$401$			37.6097i			1.87814i	−0.343730	+	0.939069i	$0.611690\pi$
$402$		0			0
$403$	0.365161	+	0.151255i	0.0181900	+	0.00753453i
$404$	−0.861814	+	2.34404i	−0.0428769	+	0.116620i
$405$		0			0
$406$	17.4124	−	18.1301i	0.864163	−	0.899779i
$407$	2.82841	+	2.82841i	0.140199	+	0.140199i
$408$		0			0
$409$	−6.67172	+	6.67172i	−0.329895	+	0.329895i	−0.852547	−	0.522651i	$-0.824943\pi$
$409$	−6.67172	+	6.67172i	−0.329895	+	0.329895i	0.522651	+	0.852547i	$0.324943\pi$
$410$	0.105691	+	5.23452i	0.00521971	+	0.258514i
$411$		0			0
$412$	0.744307	+	18.4239i	0.0366694	+	0.907683i
$413$	−3.63957	+	8.78669i	−0.179091	+	0.432365i
$414$		0			0
$415$	24.9679			1.22563
$416$	0.336709	−	0.0341040i	0.0165085	−	0.00167209i
$417$		0			0
$418$	−4.00389	+	1.75398i	−0.195837	+	0.0857898i
$419$	9.24059	−	22.3088i	0.451432	−	1.08985i	−0.520346	−	0.853956i	$-0.674197\pi$
$419$	9.24059	−	22.3088i	0.451432	−	1.08985i	0.971778	−	0.235898i	$-0.0758031\pi$
$420$		0			0
$421$	25.9531	−	10.7501i	1.26488	−	0.523929i	0.353474	−	0.935444i	$-0.385000\pi$
$421$	25.9531	−	10.7501i	1.26488	−	0.523929i	0.911403	+	0.411515i	$0.135000\pi$
$422$	0.261254	+	12.9390i	0.0127176	+	0.629860i
$423$		0			0
$424$	−0.0680414	−	1.12206i	−0.00330438	−	0.0544922i
$425$	1.07716	+	1.07716i	0.0522498	+	0.0522498i
$426$		0			0
$427$	−1.19727	−	2.89046i	−0.0579399	−	0.139879i
$428$	−1.28681	−	0.473113i	−0.0622005	−	0.0228688i
$429$		0			0
$430$	−11.8047	+	30.2101i	−0.569275	+	1.45686i
$431$		−	34.3112i		−	1.65271i	−0.563148	−	0.826356i	$-0.690410\pi$
$431$		−	34.3112i		−	1.65271i	0.563148	−	0.826356i	$-0.309590\pi$
$432$		0			0
$433$		−	21.0166i		−	1.00999i	−0.863121	−	0.504997i	$-0.831494\pi$
$433$		−	21.0166i		−	1.00999i	0.863121	−	0.504997i	$-0.168506\pi$
$434$	18.0066	+	7.03617i	0.864346	+	0.337747i
$435$		0			0
$436$	20.9872	−	9.70340i	1.00510	−	0.464708i
$437$	1.67221	+	4.03707i	0.0799927	+	0.193119i
$438$		0			0
$439$	−8.73217	−	8.73217i	−0.416764	−	0.416764i	0.467323	−	0.884087i	$-0.345219\pi$
$439$	−8.73217	−	8.73217i	−0.416764	−	0.416764i	−0.884087	+	0.467323i	$0.845219\pi$
$440$	−18.1247	−	37.2104i	−0.864062	−	1.77394i
$441$		0			0
$442$	−0.276152	+	0.00557584i	−0.0131352	+	0.000265216i
$443$	20.3275	−	8.41993i	0.965789	−	0.400043i	0.156646	−	0.987655i	$-0.449932\pi$
$443$	20.3275	−	8.41993i	0.965789	−	0.400043i	0.809143	+	0.587612i	$0.199932\pi$
$444$		0			0
$445$	7.99427	−	19.2999i	0.378965	−	0.914902i
$446$	9.11627	+	20.8102i	0.431668	+	0.985389i
$447$		0			0
$448$	16.4322	−	2.00024i	0.776349	−	0.0945024i
$449$	24.6957			1.16546			0.582730	−	0.812666i	$-0.301984\pi$
$449$	24.6957			1.16546			0.582730	+	0.812666i	$0.301984\pi$
$450$		0			0
$451$	−3.79244	+	9.15577i	−0.178579	+	0.431128i
$452$	−18.1023	−	16.6964i	−0.851459	−	0.785334i
$453$		0			0
$454$	−15.2457	+	0.307829i	−0.715517	+	0.0144471i
$455$	−0.204664	+	0.204664i	−0.00959477	+	0.00959477i
$456$		0			0
$457$	−9.41902	−	9.41902i	−0.440603	−	0.440603i	0.451612	−	0.892215i	$-0.350849\pi$
$457$	−9.41902	−	9.41902i	−0.440603	−	0.440603i	−0.892215	+	0.451612i	$0.850849\pi$
$458$	−3.62243	−	3.47904i	−0.169265	−	0.162565i
$459$		0			0
$460$	−37.5556	+	17.3638i	−1.75104	+	0.809592i
$461$	9.14047	+	3.78611i	0.425714	+	0.176337i	0.585245	−	0.810856i	$-0.300998\pi$
$461$	9.14047	+	3.78611i	0.425714	+	0.176337i	−0.159531	+	0.987193i	$0.550998\pi$
$462$		0			0
$463$			20.9637i			0.974264i	0.873328	+	0.487132i	$0.161957\pi$
$463$			20.9637i			0.974264i	−0.873328	+	0.487132i	$0.838043\pi$
$464$	−32.7027	−	10.5458i	−1.51818	−	0.489574i
$465$		0			0
$466$	−12.6679	+	32.4190i	−0.586828	+	1.50178i
$467$	−16.0094	−	6.63133i	−0.740829	−	0.306861i	−0.0198354	−	0.999803i	$-0.506314\pi$
$467$	−16.0094	−	6.63133i	−0.740829	−	0.306861i	−0.720993	+	0.692942i	$0.756314\pi$
$468$		0			0
$469$	−7.12005	−	17.1893i	−0.328773	−	0.793729i
$470$	27.6796	−	28.8204i	1.27676	−	1.32939i
$471$		0			0
$472$	12.9765	−	0.786890i	0.597292	−	0.0362195i
$473$	−43.4119	+	43.4119i	−1.99608	+	1.99608i
$474$		0			0
$475$	−0.212903	+	0.0881874i	−0.00976867	+	0.00404632i
$476$	−13.4990	+	0.545345i	−0.618726	+	0.0249958i
$477$		0			0
$478$	17.3074	−	7.58185i	0.791624	−	0.346786i
$479$	11.4416			0.522780			0.261390	−	0.965233i	$-0.415819\pi$
$479$	11.4416			0.522780			0.261390	+	0.965233i	$0.415819\pi$
$480$		0			0
$481$	−0.0382353			−0.00174338
$482$	5.68746	−	2.49150i	0.259057	−	0.113485i
$483$		0			0
$484$	−2.27440	−	56.2986i	−0.103382	−	2.55903i
$485$	9.66259	−	4.00238i	0.438756	−	0.181739i
$486$		0			0
$487$	6.40830	−	6.40830i	0.290388	−	0.290388i	−0.546846	−	0.837234i	$-0.684172\pi$
$487$	6.40830	−	6.40830i	0.290388	−	0.290388i	0.837234	+	0.546846i	$0.184172\pi$
$488$	−2.83542	+	3.20149i	−0.128353	+	0.144925i
$489$		0			0
$490$	6.22637	−	6.48299i	0.281279	−	0.292871i
$491$	−1.87362	−	4.52331i	−0.0845552	−	0.204134i	0.875947	−	0.482408i	$-0.160238\pi$
$491$	−1.87362	−	4.52331i	−0.0845552	−	0.204134i	−0.960502	+	0.278274i	$0.910238\pi$
$492$		0			0
$493$	25.9088	+	10.7318i	1.16687	+	0.483335i
$494$	0.0152075	−	0.0389182i	0.000684216	−	0.00175101i
$495$		0			0
$496$	−2.13169	−	26.3400i	−0.0957157	−	1.18270i
$497$		−	7.00834i		−	0.314367i
$498$		0			0
$499$	27.7568	+	11.4973i	1.24257	+	0.514688i	0.904516	−	0.426440i	$-0.140232\pi$
$499$	27.7568	+	11.4973i	1.24257	+	0.514688i	0.338051	+	0.941128i	$0.390232\pi$
$500$	8.89639	+	19.2417i	0.397859	+	0.860515i
$501$		0			0
$502$	−19.9883	−	19.1971i	−0.892124	−	0.856811i
$503$	8.03823	+	8.03823i	0.358407	+	0.358407i	0.863225	−	0.504819i	$-0.168441\pi$
$503$	8.03823	+	8.03823i	0.358407	+	0.358407i	−0.504819	+	0.863225i	$0.668441\pi$
$504$		0			0
$505$	−2.06448	+	2.06448i	−0.0918682	+	0.0918682i
$506$	−78.3012	+	1.58100i	−3.48092	+	0.0702838i
$507$		0			0
$508$	20.2085	−	21.9100i	0.896606	−	0.972100i
$509$	−3.62960	+	8.76263i	−0.160879	+	0.388397i	−0.983678	−	0.179935i	$-0.942411\pi$
$509$	−3.62960	+	8.76263i	−0.160879	+	0.388397i	0.822799	+	0.568332i	$0.192411\pi$
$510$		0			0
$511$	−28.7898			−1.27358
$512$	−12.2941	−	18.9962i	−0.543327	−	0.839521i
$513$		0			0
$514$	−14.1327	−	32.2614i	−0.623366	−	1.42299i
$515$	−8.24909	+	19.9151i	−0.363498	+	0.877563i
$516$		0			0
$517$	69.8798	−	28.9452i	3.07331	−	1.27301i
$518$	−1.86980	+	0.0377535i	−0.0821544	+	0.00165880i
$519$		0			0
$520$	0.374018	+	0.129003i	0.0164018	+	0.00565714i
$521$	−6.13944	−	6.13944i	−0.268974	−	0.268974i	0.559713	−	0.828687i	$-0.310911\pi$
$521$	−6.13944	−	6.13944i	−0.268974	−	0.268974i	−0.828687	+	0.559713i	$0.810911\pi$
$522$		0			0
$523$	−6.64181	−	16.0347i	−0.290426	−	0.701150i	0.709568	−	0.704637i	$-0.248890\pi$
$523$	−6.64181	−	16.0347i	−0.290426	−	0.701150i	−0.999994	+	0.00348661i	$0.998890\pi$
$524$	7.91530	+	17.1197i	0.345781	+	0.747879i
$525$		0			0
$526$	0.635386	+	0.248280i	0.0277041	+	0.0108255i
$527$			21.5675i			0.939494i
$528$		0			0
$529$			55.2899i			2.40391i
$530$	0.478290	−	1.22402i	0.0207756	−	0.0531680i
$531$		0			0
$532$	0.705255	−	1.91821i	0.0305767	−	0.0831651i
$533$	−0.0362515	−	0.0875188i	−0.00157023	−	0.00379086i
$534$		0			0
$535$	−1.13334	−	1.13334i	−0.0489988	−	0.0489988i
$536$	−16.8620	+	19.0390i	−0.728326	+	0.822359i
$537$		0			0
$538$	0.589803	+	29.2109i	0.0254282	+	1.25937i
$539$	15.7191	−	6.51105i	0.677068	−	0.280451i
$540$		0			0
$541$	−4.68635	+	11.3138i	−0.201482	+	0.486420i	−0.992033	−	0.125975i	$-0.959794\pi$
$541$	−4.68635	+	11.3138i	−0.201482	+	0.486420i	0.790552	+	0.612396i	$0.209794\pi$
$542$	−17.1190	+	7.49929i	−0.735323	+	0.322122i
$543$		0			0
$544$	8.75042	+	16.2625i	0.375171	+	0.697247i
$545$	27.0303			1.15785
$546$		0			0
$547$	−12.1142	+	29.2461i	−0.517964	+	1.25048i	0.421188	+	0.906973i	$0.361613\pi$
$547$	−12.1142	+	29.2461i	−0.517964	+	1.25048i	−0.939152	+	0.343502i	$0.888387\pi$
$548$	10.2098	−	0.412466i	0.436143	−	0.0176197i
$549$		0			0
$550$	−0.0833770	−	4.12937i	−0.00355521	−	0.176077i
$551$	−2.99978	+	2.99978i	−0.127795	+	0.127795i
$552$		0			0
$553$	−5.30005	−	5.30005i	−0.225381	−	0.225381i
$554$	24.4111	−	25.4172i	1.03713	−	1.07987i
$555$		0			0
$556$	−27.4464	−	10.0910i	−1.16398	−	0.427953i
$557$	−24.2696	−	10.0528i	−1.02833	−	0.425950i	−0.196223	−	0.980559i	$-0.562868\pi$
$557$	−24.2696	−	10.0528i	−1.02833	−	0.425950i	−0.832111	+	0.554609i	$0.812868\pi$
$558$		0			0
$559$		−	0.586854i		−	0.0248213i
$560$	18.4178	+	5.93925i	0.778293	+	0.250979i
$561$		0			0
$562$	20.7560	+	8.11049i	0.875538	+	0.342120i
$563$	−18.4201	−	7.62986i	−0.776315	−	0.321560i	−0.0408878	−	0.999164i	$-0.513019\pi$
$563$	−18.4201	−	7.62986i	−0.776315	−	0.321560i	−0.735428	+	0.677603i	$0.763019\pi$
$564$		0			0
$565$	−11.0172	−	26.5979i	−0.463497	−	1.11898i
$566$	−11.5406	−	11.0838i	−0.485087	−	0.465885i
$567$		0			0
$568$	−8.61253	+	4.19506i	−0.361374	+	0.176021i
$569$	−25.2695	+	25.2695i	−1.05935	+	1.05935i	−0.0612266	+	0.998124i	$0.519501\pi$
$569$	−25.2695	+	25.2695i	−1.05935	+	1.05935i	−0.998124	+	0.0612266i	$0.980499\pi$
$570$		0			0
$571$	36.0258	−	14.9224i	1.50763	−	0.624482i	0.532565	−	0.846389i	$-0.321228\pi$
$571$	36.0258	−	14.9224i	1.50763	−	0.624482i	0.975068	+	0.221907i	$0.0712281\pi$
$572$	0.550485	+	0.507734i	0.0230169	+	0.0212294i
$573$		0			0
$574$	−1.85920	−	4.24409i	−0.0776017	−	0.177145i
$575$	−4.12878			−0.172182
$576$		0			0
$577$	29.5817			1.23150			0.615752	−	0.787940i	$-0.288852\pi$
$577$	29.5817			1.23150			0.615752	+	0.787940i	$0.288852\pi$
$578$	3.59917	+	8.21600i	0.149706	+	0.341741i
$579$		0			0
$580$	−29.5275	−	27.2344i	−1.22606	−	1.13085i
$581$	−20.4145	+	8.45595i	−0.846935	+	0.350812i
$582$		0			0
$583$	1.75891	−	1.75891i	0.0728466	−	0.0728466i
$584$	17.2330	+	35.3796i	0.713106	+	1.46402i
$585$		0			0
$586$	23.3810	+	22.4555i	0.965859	+	0.927627i
$587$	13.5028	+	32.5986i	0.557319	+	1.34549i	0.911881	+	0.410455i	$0.134630\pi$
$587$	13.5028	+	32.5986i	0.557319	+	1.34549i	−0.354561	+	0.935033i	$0.615370\pi$
$588$		0			0
$589$	−3.01430	−	1.24857i	−0.124202	−	0.0514462i
$590$	14.1556	+	5.53137i	0.582777	+	0.227723i
$591$		0			0
$592$	1.16562	+	2.27519i	0.0479068	+	0.0935099i
$593$		−	34.7178i		−	1.42569i	−0.701323	−	0.712844i	$-0.747407\pi$
$593$		−	34.7178i		−	1.42569i	0.701323	−	0.712844i	$-0.252593\pi$
$594$		0			0
$595$	−14.5915	−	6.04401i	−0.598195	−	0.247780i
$596$	−6.14775	−	2.26030i	−0.251822	−	0.0925853i
$597$		0			0
$598$	0.518563	−	0.539935i	0.0212056	−	0.0220796i
$599$	−0.840657	−	0.840657i	−0.0343483	−	0.0343483i	0.689724	−	0.724072i	$-0.257732\pi$
$599$	−0.840657	−	0.840657i	−0.0343483	−	0.0343483i	−0.724072	+	0.689724i	$0.757732\pi$
$600$		0			0
$601$	−0.647523	+	0.647523i	−0.0264130	+	0.0264130i	−0.720190	−	0.693777i	$-0.755945\pi$
$601$	−0.647523	+	0.647523i	−0.0264130	+	0.0264130i	0.693777	+	0.720190i	$0.255945\pi$
$602$	−0.579459	−	28.6986i	−0.0236170	−	1.16967i
$603$		0			0
$604$	0.635432	−	0.0256708i	0.0258554	−	0.00104453i
$605$	25.2070	−	60.8550i	1.02481	−	2.47411i
$606$		0			0
$607$	−46.7752			−1.89855			−0.949273	−	0.314452i	$-0.898179\pi$
$607$	−46.7752			−1.89855			−0.949273	+	0.314452i	$0.898179\pi$
$608$	−2.77944	+	0.281520i	−0.112721	+	0.0114171i
$609$		0			0
$610$	−4.57937	+	2.00608i	−0.185413	+	0.0812237i
$611$	−0.276683	+	0.667972i	−0.0111934	+	0.0270233i
$612$		0			0
$613$	−15.0801	+	6.24640i	−0.609081	+	0.252290i	−0.665836	−	0.746099i	$-0.731925\pi$
$613$	−15.0801	+	6.24640i	−0.609081	+	0.252290i	0.0567545	+	0.998388i	$0.481925\pi$
$614$	−0.132996	−	6.58684i	−0.00536729	−	0.265823i
$615$		0			0
$616$	27.4214	+	24.2859i	1.10484	+	0.978508i
$617$	−0.207739	−	0.207739i	−0.00836324	−	0.00836324i	0.702913	−	0.711276i	$-0.251882\pi$
$617$	−0.207739	−	0.207739i	−0.00836324	−	0.00836324i	−0.711276	+	0.702913i	$0.751882\pi$
$618$		0			0
$619$	−12.5663	−	30.3378i	−0.505083	−	1.21938i	−0.946683	−	0.322166i	$-0.895589\pi$
$619$	−12.5663	−	30.3378i	−0.505083	−	1.21938i	0.441600	−	0.897212i	$-0.354411\pi$
$620$	10.6606	−	28.9955i	0.428139	−	1.16449i
$621$		0			0
$622$	−9.60736	+	24.5867i	−0.385220	+	0.985837i
$623$			18.4876i			0.740689i
$624$		0			0
$625$			27.1154i			1.08462i
$626$	24.6147	+	9.61832i	0.983803	+	0.384425i
$627$		0			0
$628$	−0.426312	−	0.922057i	−0.0170117	−	0.0367941i
$629$	−0.798426	−	1.92757i	−0.0318353	−	0.0768573i
$630$		0			0
$631$	−1.04178	−	1.04178i	−0.0414728	−	0.0414728i	0.686066	−	0.727539i	$-0.259336\pi$
$631$	−1.04178	−	1.04178i	−0.0414728	−	0.0414728i	−0.727539	+	0.686066i	$0.759336\pi$
$632$	−3.34071	+	9.68572i	−0.132886	+	0.385277i
$633$		0			0
$634$	13.9636	−	0.281941i	0.554564	−	0.0111973i
$635$	32.1927	−	13.3346i	1.27753	−	0.529169i
$636$		0			0
$637$	−0.0622383	+	0.150257i	−0.00246597	+	0.00595338i
$638$	−30.5092	−	69.6449i	−1.20787	−	2.75727i
$639$		0			0
$640$	−3.72580	−	26.1887i	−0.147275	−	1.03520i
$641$	27.9724			1.10484			0.552421	−	0.833565i	$-0.313704\pi$
$641$	27.9724			1.10484			0.552421	+	0.833565i	$0.313704\pi$
$642$		0			0
$643$	−17.1230	+	41.3386i	−0.675266	+	1.63024i	0.0972657	+	0.995258i	$0.468990\pi$
$643$	−17.1230	+	41.3386i	−0.675266	+	1.63024i	−0.772531	+	0.634977i	$0.781010\pi$
$644$	24.8259	−	26.9162i	0.978277	−	1.06065i
$645$		0			0
$646$	2.27956	−	0.0460270i	0.0896881	−	0.00181091i
$647$	12.5087	−	12.5087i	0.491766	−	0.491766i	−0.417096	−	0.908862i	$-0.636952\pi$
$647$	12.5087	−	12.5087i	0.491766	−	0.491766i	0.908862	+	0.417096i	$0.136952\pi$
$648$		0			0
$649$	20.3416	+	20.3416i	0.798476	+	0.798476i
$650$	0.0284746	+	0.0273474i	0.00111686	+	0.00107266i
$651$		0			0
$652$	−19.2020	−	41.5313i	−0.752007	−	1.62649i
$653$	−37.1822	−	15.4014i	−1.45505	−	0.602703i	−0.491658	−	0.870789i	$-0.663609\pi$
$653$	−37.1822	−	15.4014i	−1.45505	−	0.602703i	−0.963395	+	0.268086i	$0.913609\pi$
$654$		0			0
$655$			22.0493i			0.861537i
$656$	−4.10267	+	4.82520i	−0.160182	+	0.188392i
$657$		0			0
$658$	−12.8709	+	32.9387i	−0.501761	+	1.28408i
$659$	−34.3332	−	14.2213i	−1.33743	−	0.553982i	−0.404665	−	0.914465i	$-0.632612\pi$
$659$	−34.3332	−	14.2213i	−1.33743	−	0.553982i	−0.932766	+	0.360483i	$0.882612\pi$
$660$		0			0
$661$	−12.1157	−	29.2500i	−0.471248	−	1.13769i	−0.963612	−	0.267304i	$-0.913867\pi$
$661$	−12.1157	−	29.2500i	−0.471248	−	1.13769i	0.492365	−	0.870389i	$-0.336133\pi$
$662$	7.33338	−	7.63562i	0.285020	−	0.296767i
$663$		0			0
$664$	22.6112	+	20.0257i	0.877485	+	0.777149i
$665$	1.68944	−	1.68944i	0.0655138	−	0.0655138i
$666$		0			0
$667$	−70.2222	+	29.0870i	−2.71901	+	1.12625i
$668$	1.69423	+	41.9377i	0.0655519	+	1.62262i
$669$		0			0
$670$	−27.2331	+	11.9300i	−1.05211	+	0.460895i
$671$	−9.46327			−0.365325
$672$		0			0
$673$	−20.3366			−0.783917			−0.391958	−	0.919983i	$-0.628202\pi$
$673$	−20.3366			−0.783917			−0.391958	+	0.919983i	$0.628202\pi$
$674$	15.8246	−	6.93224i	0.609539	−	0.267020i
$675$		0			0
$676$	25.9717	−	1.04923i	0.998910	−	0.0403548i
$677$	1.06604	−	0.441568i	0.0409712	−	0.0169708i	−0.362104	−	0.932138i	$-0.617941\pi$
$677$	1.06604	−	0.441568i	0.0409712	−	0.0169708i	0.403075	+	0.915167i	$0.367941\pi$
$678$		0			0
$679$	−6.54491	+	6.54491i	−0.251171	+	0.251171i
$680$	1.30674	+	21.5493i	0.0501112	+	0.826379i
$681$		0			0
$682$	40.5056	−	42.1750i	1.55104	−	1.61497i
$683$	−9.86389	−	23.8135i	−0.377431	−	0.911200i	−0.992446	−	0.122684i	$-0.960850\pi$
$683$	−9.86389	−	23.8135i	−0.377431	−	0.911200i	0.615014	−	0.788516i	$-0.289150\pi$
$684$		0			0
$685$	11.0362	+	4.57133i	0.421670	+	0.174662i
$686$	−10.3505	+	26.4884i	−0.395183	+	1.01133i
$687$		0			0
$688$	−34.9208	+	17.8905i	−1.33134	+	0.682070i
$689$			0.0237774i			0.000905848i
$690$		0			0
$691$	−25.2626	−	10.4641i	−0.961035	−	0.398074i	−0.153667	−	0.988123i	$-0.549108\pi$
$691$	−25.2626	−	10.4641i	−0.961035	−	0.398074i	−0.807367	+	0.590049i	$0.799108\pi$
$692$	27.5967	−	12.7593i	1.04907	−	0.485036i
$693$		0			0
$694$	−15.1409	−	14.5416i	−0.574741	−	0.551991i
$695$	−24.1730	−	24.1730i	−0.916935	−	0.916935i
$696$		0			0
$697$	3.65512	−	3.65512i	0.138447	−	0.138447i
$698$	−27.5121	+	0.555503i	−1.04135	+	0.0210261i
$699$		0			0
$700$	1.41948	+	1.30924i	0.0536513	+	0.0494847i
$701$	1.87688	−	4.53118i	0.0708887	−	0.171140i	−0.884464	−	0.466609i	$-0.845476\pi$
$701$	1.87688	−	4.53118i	0.0708887	−	0.171140i	0.955353	+	0.295468i	$0.0954757\pi$
$702$		0			0
$703$	0.315622			0.0119039
$704$	13.4310	−	48.2352i	0.506198	−	1.81793i
$705$		0			0
$706$	15.1044	+	34.4796i	0.568462	+	1.29766i
$707$	0.988794	−	2.38716i	0.0371874	−	0.0897784i
$708$		0			0
$709$	23.6589	−	9.79984i	0.888529	−	0.368041i	0.108730	−	0.994071i	$-0.465322\pi$
$709$	23.6589	−	9.79984i	0.888529	−	0.368041i	0.779798	+	0.626031i	$0.215322\pi$
$710$	−11.1970	+	0.226081i	−0.420215	+	0.00848465i
$711$		0			0
$712$	22.7193	−	11.0663i	0.851442	−	0.414727i
$713$	−41.3344	−	41.3344i	−1.54798	−	1.54798i
$714$		0			0
$715$	0.335030	+	0.808835i	0.0125294	+	0.0302487i
$716$	−6.43625	+	2.97579i	−0.240534	+	0.111211i
$717$		0			0
$718$	−12.5880	−	4.91880i	−0.469778	−	0.183568i
$719$			7.42466i			0.276893i	0.990370	+	0.138447i	$0.0442109\pi$
$719$			7.42466i			0.276893i	−0.990370	+	0.138447i	$0.955789\pi$
$720$		0			0
$721$		−	19.0769i		−	0.710460i
$722$	9.65396	−	24.7060i	0.359283	−	0.919460i
$723$		0			0
$724$	−10.4804	−	3.85325i	−0.389501	−	0.143205i
$725$	−1.53396	−	3.70331i	−0.0569698	−	0.137537i
$726$		0			0
$727$	12.2805	+	12.2805i	0.455457	+	0.455457i	0.897161	−	0.441704i	$-0.145626\pi$
$727$	12.2805	+	12.2805i	0.455457	+	0.455457i	−0.441704	+	0.897161i	$0.645626\pi$
$728$	−0.349497	+	0.0211933i	−0.0129532	+	0.000785478i
$729$		0			0
$730$	0.928723	+	45.9964i	0.0343736	+	1.70240i
$731$	29.5853	−	12.2546i	1.09425	−	0.453254i
$732$		0			0
$733$	−13.1888	+	31.8405i	−0.487138	+	1.17606i	0.469016	+	0.883190i	$0.344609\pi$
$733$	−13.1888	+	31.8405i	−0.487138	+	1.17606i	−0.956154	+	0.292865i	$0.905391\pi$
$734$	15.4434	−	6.76526i	0.570026	−	0.249710i
$735$		0			0
$736$	−47.9375	−	14.3969i	−1.76700	−	0.530678i
$737$	−56.2772			−2.07300
$738$		0			0
$739$	15.3244	−	36.9964i	0.563717	−	1.36093i	−0.343056	−	0.939315i	$-0.611462\pi$
$739$	15.3244	−	36.9964i	0.563717	−	1.36093i	0.906773	−	0.421619i	$-0.138538\pi$
$740$	0.120635	+	2.98610i	0.00443463	+	0.109771i
$741$		0			0
$742$	0.0234778	+	1.16278i	0.000861899	+	0.0426868i
$743$	−6.80014	+	6.80014i	−0.249473	+	0.249473i	−0.820754	−	0.571281i	$-0.806446\pi$
$743$	−6.80014	+	6.80014i	−0.249473	+	0.249473i	0.571281	+	0.820754i	$0.306446\pi$
$744$		0			0
$745$	−5.41455	−	5.41455i	−0.198374	−	0.198374i
$746$	−18.4992	+	19.2616i	−0.677304	+	0.705219i
$747$		0			0
$748$	−14.1014	+	38.3543i	−0.515599	+	1.40237i
$749$	1.31049	+	0.542822i	0.0478842	+	0.0198343i
$750$		0			0
$751$		−	44.2155i		−	1.61345i	−0.590930	−	0.806723i	$-0.701239\pi$
$751$		−	44.2155i		−	1.61345i	0.590930	−	0.806723i	$-0.298761\pi$
$752$	48.1825	−	3.89940i	1.75704	−	0.142197i
$753$		0			0
$754$	0.676956	+	0.264523i	0.0246533	+	0.00963338i
$755$	0.686860	+	0.284507i	0.0249974	+	0.0103543i
$756$		0			0
$757$	14.0190	+	33.8448i	0.509529	+	1.23011i	0.944155	+	0.329500i	$0.106880\pi$
$757$	14.0190	+	33.8448i	0.509529	+	1.23011i	−0.434627	+	0.900611i	$0.643120\pi$
$758$	23.4687	+	22.5398i	0.852422	+	0.818681i
$759$		0			0
$760$	−3.08742	−	1.06488i	−0.111992	−	0.0386274i
$761$	27.3391	−	27.3391i	0.991041	−	0.991041i	−0.00891938	−	0.999960i	$-0.502839\pi$
$761$	27.3391	−	27.3391i	0.991041	−	0.991041i	0.999960	+	0.00891938i	$0.00283916\pi$
$762$		0			0
$763$	−22.1007	+	9.15443i	−0.800100	+	0.331412i
$764$	−21.7524	+	23.5839i	−0.786973	+	0.853236i
$765$		0			0
$766$	18.6287	+	42.5246i	0.673082	+	1.53648i
$767$	−0.274983			−0.00992906
$768$		0			0
$769$	41.0566			1.48054			0.740269	−	0.672311i	$-0.234698\pi$
$769$	41.0566			1.48054			0.740269	+	0.672311i	$0.234698\pi$
$770$	17.1825	+	39.2232i	0.619213	+	1.41351i
$771$		0			0
$772$	−5.54581	+	6.01276i	−0.199598	+	0.216404i
$773$	−27.0461	+	11.2029i	−0.972781	+	0.402939i	−0.811747	−	0.584010i	$-0.801483\pi$
$773$	−27.0461	+	11.2029i	−0.972781	+	0.402939i	−0.161034	+	0.986949i	$0.551483\pi$
$774$		0			0
$775$	2.17985	−	2.17985i	0.0783025	−	0.0783025i
$776$	11.9607	+	4.12537i	0.429363	+	0.148092i
$777$		0			0
$778$	−0.701635	−	0.673862i	−0.0251548	−	0.0241591i
$779$	0.299246	+	0.722444i	0.0107216	+	0.0258842i
$780$		0			0
$781$	−19.5848	−	8.11230i	−0.700800	−	0.290281i
$782$	38.0485	+	14.8676i	1.36061	+	0.531665i
$783$		0			0
$784$	10.8384	−	0.877149i	0.387085	−	0.0313268i
$785$		−	1.18756i		−	0.0423858i
$786$		0			0
$787$	−10.4486	−	4.32794i	−0.372452	−	0.154275i	0.188603	−	0.982053i	$-0.439604\pi$
$787$	−10.4486	−	4.32794i	−0.372452	−	0.154275i	−0.561054	+	0.827779i	$0.689604\pi$
$788$	−8.77860	+	23.8768i	−0.312725	+	0.850576i
$789$		0			0
$790$	−8.29674	+	8.63868i	−0.295185	+	0.307351i
$791$	18.0160	+	18.0160i	0.640574	+	0.640574i
$792$		0			0
$793$	0.0639635	−	0.0639635i	0.00227141	−	0.00227141i
$794$	−0.198551	−	9.83356i	−0.00704632	−	0.348980i
$795$		0			0
$796$	0.571028	+	14.1347i	0.0202395	+	0.500993i
$797$	−13.3448	+	32.2171i	−0.472696	+	1.14119i	0.490271	+	0.871570i	$0.336898\pi$
$797$	−13.3448	+	32.2171i	−0.472696	+	1.14119i	−0.962967	+	0.269619i	$0.913102\pi$
$798$		0			0
$799$	−39.4524			−1.39572
$800$	0.759251	−	2.52808i	0.0268436	−	0.0893812i
$801$		0			0
$802$	−48.7185	+	21.3420i	−1.72031	+	0.753614i
$803$	−33.3247	+	80.4530i	−1.17600	+	2.83913i
$804$		0			0
$805$	39.5483	−	16.3815i	1.39390	−	0.577370i
$806$	0.0112839	+	0.558850i	0.000397457	+	0.0196847i
$807$		0			0
$808$	−3.52545	+	0.213781i	−0.124025	+	0.00752080i
$809$	2.75554	+	2.75554i	0.0968795	+	0.0968795i	0.753885	−	0.657006i	$-0.228177\pi$
$809$	2.75554	+	2.75554i	0.0968795	+	0.0968795i	−0.657006	+	0.753885i	$0.728177\pi$
$810$		0			0
$811$	−18.4234	−	44.4780i	−0.646933	−	1.56183i	−0.817148	−	0.576427i	$-0.804446\pi$
$811$	−18.4234	−	44.4780i	−0.646933	−	1.56183i	0.170215	−	0.985407i	$-0.445554\pi$
$812$	33.3660	+	12.2674i	1.17092	+	0.430502i
$813$		0			0
$814$	−2.05883	+	5.26886i	−0.0721620	+	0.184674i
$815$		−	53.4900i		−	1.87367i
$816$		0			0
$817$			4.84432i			0.169481i
$818$	−12.4283	−	4.85641i	−0.434545	−	0.169800i
$819$		0			0
$820$	−6.72067	+	3.10730i	−0.234696	+	0.108511i
$821$	6.71325	+	16.2072i	0.234294	+	0.565636i	0.996674	−	0.0814939i	$-0.0259691\pi$
$821$	6.71325	+	16.2072i	0.234294	+	0.565636i	−0.762380	+	0.647130i	$0.775969\pi$
$822$		0			0
$823$	3.56436	+	3.56436i	0.124246	+	0.124246i	0.766496	−	0.642250i	$-0.221999\pi$
$823$	3.56436	+	3.56436i	0.124246	+	0.124246i	−0.642250	+	0.766496i	$0.721999\pi$
$824$	−23.4435	+	11.4190i	−0.816693	+	0.397801i
$825$		0			0
$826$	−13.4473	+	0.271518i	−0.467893	+	0.00944732i
$827$	−47.5146	+	19.6812i	−1.65225	+	0.684382i	−0.997446	−	0.0714207i	$-0.977247\pi$
$827$	−47.5146	+	19.6812i	−1.65225	+	0.684382i	−0.654799	+	0.755803i	$0.727247\pi$
$828$		0			0
$829$	10.4074	−	25.1257i	0.361463	−	0.872650i	−0.633623	−	0.773642i	$-0.718433\pi$
$829$	10.4074	−	25.1257i	0.361463	−	0.872650i	0.995087	−	0.0990081i	$-0.0315670\pi$
$830$	14.1683	+	32.3427i	0.491790	+	1.12263i
$831$		0			0
$832$	0.235247	+	0.416810i	0.00815571	+	0.0144503i
$833$	−8.87459			−0.307486
$834$		0			0
$835$	−18.7771	+	45.3318i	−0.649807	+	1.56877i
$836$	−4.54411	−	4.19121i	−0.157161	−	0.144956i
$837$		0			0
$838$	34.1418	−	0.689364i	1.17941	−	0.0238137i
$839$	−15.1006	+	15.1006i	−0.521330	+	0.521330i	−0.917973	−	0.396643i	$-0.870175\pi$
$839$	−15.1006	+	15.1006i	−0.521330	+	0.521330i	0.396643	+	0.917973i	$0.370175\pi$
$840$		0			0
$841$	−31.6730	−	31.6730i	−1.09217	−	1.09217i
$842$	28.6528	+	27.5186i	0.987441	+	0.948355i
$843$		0			0
$844$	−16.6126	+	7.68080i	−0.571828	+	0.264384i
$845$	28.0736	+	11.6285i	0.965763	+	0.400032i
$846$		0			0
$847$			58.2937i			2.00299i
$848$	1.41488	−	0.724867i	0.0485871	−	0.0248920i
$849$		0			0
$850$	−0.784074	+	2.00657i	−0.0268935	+	0.0688246i
$851$	5.22441	+	2.16402i	0.179090	+	0.0741817i
$852$		0			0
$853$	3.55795	+	8.58965i	0.121822	+	0.294104i	0.973012	−	0.230753i	$-0.0741188\pi$
$853$	3.55795	+	8.58965i	0.121822	+	0.294104i	−0.851191	+	0.524857i	$0.824119\pi$
$854$	3.06482	−	3.19113i	0.104876	−	0.109198i
$855$		0			0
$856$	−0.117360	−	1.93538i	−0.00401129	−	0.0661498i
$857$	−16.1608	+	16.1608i	−0.552042	+	0.552042i	−0.927030	−	0.374988i	$-0.877647\pi$
$857$	−16.1608	+	16.1608i	−0.552042	+	0.552042i	0.374988	+	0.927030i	$0.377647\pi$
$858$		0			0
$859$	19.7234	−	8.16969i	0.672953	−	0.278746i	−0.0199246	−	0.999801i	$-0.506343\pi$
$859$	19.7234	−	8.16969i	0.672953	−	0.278746i	0.692878	+	0.721055i	$0.256343\pi$
$860$	−45.8321	+	1.85156i	−1.56286	+	0.0631378i
$861$		0			0
$862$	44.4457	−	19.4703i	1.51383	−	0.663160i
$863$	7.49235			0.255042			0.127521	−	0.991836i	$-0.459298\pi$
$863$	7.49235			0.255042			0.127521	+	0.991836i	$0.459298\pi$
$864$		0			0
$865$	35.5430			1.20850
$866$	27.2243	−	11.9261i	0.925120	−	0.405266i
$867$		0			0
$868$	1.10362	+	27.3180i	0.0374592	+	0.927234i
$869$	−20.9459	+	8.67608i	−0.710541	+	0.294316i
$870$		0			0
$871$	0.380385	−	0.380385i	0.0128889	−	0.0128889i
$872$	24.4789	+	21.6799i	0.828960	+	0.734173i
$873$		0			0
$874$	−4.28060	+	4.45702i	−0.144793	+	0.150761i
$875$	−8.39307	−	20.2627i	−0.283738	−	0.685003i
$876$		0			0
$877$	36.4548	+	15.1001i	1.23099	+	0.509893i	0.900888	−	0.434052i	$-0.142916\pi$
$877$	36.4548	+	15.1001i	1.23099	+	0.509893i	0.330103	+	0.943945i	$0.392916\pi$
$878$	6.35623	−	16.2666i	0.214512	−	0.548970i
$879$		0			0
$880$	37.9162	−	44.5937i	1.27816	−	1.50325i
$881$			22.3181i			0.751915i	0.926637	+	0.375958i	$0.122686\pi$
$881$			22.3181i			0.751915i	−0.926637	+	0.375958i	$0.877314\pi$
$882$		0			0
$883$	−15.5754	−	6.45156i	−0.524155	−	0.217112i	0.104886	−	0.994484i	$-0.466552\pi$
$883$	−15.5754	−	6.45156i	−0.524155	−	0.217112i	−0.629041	+	0.777372i	$0.716552\pi$
$884$	−0.163928	−	0.354555i	−0.00551351	−	0.0119250i
$885$		0			0
$886$	22.4420	+	21.5537i	0.753954	+	0.724110i
$887$	−12.3188	−	12.3188i	−0.413624	−	0.413624i	0.469375	−	0.882999i	$-0.344479\pi$
$887$	−12.3188	−	12.3188i	−0.413624	−	0.413624i	−0.882999	+	0.469375i	$0.844479\pi$
$888$		0			0
$889$	−21.8056	+	21.8056i	−0.731335	+	0.731335i
$890$	29.5370	−	0.596387i	0.990081	−	0.0199909i
$891$		0			0
$892$	−21.7837	+	23.6179i	−0.729374	+	0.790787i
$893$	2.28394	−	5.51393i	0.0764293	−	0.184517i
$894$		0			0
$895$	−8.28953			−0.277088
$896$	11.9157	+	20.1508i	0.398076	+	0.673190i
$897$		0			0
$898$	14.0138	+	31.9901i	0.467648	+	1.06752i
$899$	21.7179	−	52.4318i	0.724334	−	1.74870i
$900$		0			0
$901$	−1.19870	+	0.496518i	−0.0399345	+	0.0165414i
$902$	−14.0122	+	0.282923i	−0.466555	+	0.00942030i
$903$		0			0
$904$	11.3558	−	32.9237i	0.377687	−	1.09503i
$905$	−9.23047	−	9.23047i	−0.306831	−	0.306831i
$906$		0			0
$907$	−3.49309	−	8.43307i	−0.115986	−	0.280015i	0.855216	−	0.518271i	$-0.173424\pi$
$907$	−3.49309	−	8.43307i	−0.115986	−	0.280015i	−0.971202	+	0.238256i	$0.923424\pi$
$908$	−9.05011	−	19.5742i	−0.300338	−	0.649592i
$909$		0			0
$910$	−0.381254	−	0.148977i	−0.0126384	−	0.00493853i
$911$		−	14.1627i		−	0.469232i	−0.972088	−	0.234616i	$-0.924617\pi$
$911$		−	14.1627i		−	0.469232i	0.972088	−	0.234616i	$-0.0753833\pi$
$912$		0			0
$913$			66.8362i			2.21196i
$914$	6.85620	−	17.5461i	0.226783	−	0.580372i
$915$		0			0
$916$	2.45106	−	6.66661i	0.0809854	−	0.220271i
$917$	−7.46749	−	18.0281i	−0.246598	−	0.595341i
$918$		0			0
$919$	17.1001	+	17.1001i	0.564082	+	0.564082i	0.930464	−	0.366383i	$-0.119404\pi$
$919$	17.1001	+	17.1001i	0.564082	+	0.564082i	−0.366383	+	0.930464i	$0.619404\pi$
$920$	−43.8040	−	38.7952i	−1.44417	−	1.27904i
$921$		0			0
$922$	0.282450	+	13.9888i	0.00930200	+	0.460696i
$923$	0.187209	−	0.0775444i	0.00616205	−	0.00255240i
$924$		0			0
$925$	−0.114124	+	0.275520i	−0.00375237	+	0.00905903i
$926$	−27.1557	+	11.8961i	−0.892392	+	0.390929i
$927$		0			0
$928$	−4.89684	−	48.3464i	−0.160747	−	1.58705i
$929$	0.261586			0.00858236			0.00429118	−	0.999991i	$-0.498634\pi$
$929$	0.261586			0.00858236			0.00429118	+	0.999991i	$0.498634\pi$
$930$		0			0
$931$	0.513760	−	1.24033i	0.0168378	−	0.0406501i
$932$	−49.1832	+	1.98695i	−1.61105	+	0.0650846i
$933$		0			0
$934$	−0.494709	−	24.5012i	−0.0161874	−	0.801704i
$935$	−33.7800	+	33.7800i	−1.10472	+	1.10472i
$936$		0			0
$937$	−21.0093	−	21.0093i	−0.686345	−	0.686345i	0.275077	−	0.961422i	$-0.411297\pi$
$937$	−21.0093	−	21.0093i	−0.686345	−	0.686345i	−0.961422	+	0.275077i	$0.911297\pi$
$938$	18.2262	−	18.9774i	0.595106	−	0.619633i
$939$		0			0
$940$	53.0402	+	19.5009i	1.72998	+	0.636049i
$941$	45.9724	+	19.0424i	1.49866	+	0.620765i	0.973181	−	0.230042i	$-0.0738865\pi$
$941$	45.9724	+	19.0424i	1.49866	+	0.620765i	0.525478	+	0.850807i	$0.323886\pi$
$942$		0			0
$943$			14.0102i			0.456234i
$944$	8.38299	+	16.3629i	0.272843	+	0.532566i
$945$		0			0
$946$	−80.8690	−	31.5999i	−2.62928	−	1.02740i
$947$	7.49492	+	3.10450i	0.243552	+	0.100883i	0.501121	−	0.865377i	$-0.332921\pi$
$947$	7.49492	+	3.10450i	0.243552	+	0.100883i	−0.257569	+	0.966260i	$0.582921\pi$
$948$		0			0
$949$	−0.318547	−	0.769040i	−0.0103405	−	0.0249641i
$950$	−0.235050	−	0.225746i	−0.00762602	−	0.00732416i
$951$		0			0
$952$	−8.36659	−	17.1768i	−0.271163	−	0.556703i
$953$	25.1462	−	25.1462i	0.814565	−	0.814565i	−0.170750	−	0.985314i	$-0.554619\pi$
$953$	25.1462	−	25.1462i	0.814565	−	0.814565i	0.985314	+	0.170750i	$0.0546190\pi$
$954$		0			0
$955$	−34.6521	+	14.3534i	−1.12132	+	0.464465i
$956$	19.6426	+	18.1172i	0.635288	+	0.585951i
$957$		0			0
$958$	6.49267	+	14.8211i	0.209769	+	0.478849i
$959$	−10.5717			−0.341377
$960$		0			0
$961$	12.6462			0.407942
$962$	−0.0216971	−	0.0495289i	−0.000699541	−	0.00159688i
$963$		0			0
$964$	6.45482	+	5.95354i	0.207896	+	0.191751i
$965$	−8.83463	+	3.65942i	−0.284397	+	0.117801i
$966$		0			0
$967$	−22.5199	+	22.5199i	−0.724191	+	0.724191i	−0.969456	−	0.245265i	$-0.921125\pi$
$967$	−22.5199	+	22.5199i	−0.724191	+	0.724191i	0.245265	+	0.969456i	$0.421125\pi$
$968$	71.6369	−	34.8935i	2.30250	−	1.12152i
$969$		0			0
$970$	10.6677	+	10.2455i	0.342520	+	0.328962i
$971$	0.448715	+	1.08329i	0.0143999	+	0.0347645i	0.930916	−	0.365233i	$-0.119011\pi$
$971$	0.448715	+	1.08329i	0.0143999	+	0.0347645i	−0.916516	+	0.399998i	$0.869011\pi$
$972$		0			0
$973$	27.9513	+	11.5778i	0.896077	+	0.371167i
$974$	11.9376	+	4.66467i	0.382505	+	0.149466i
$975$		0			0
$976$	−5.75611	−	1.85620i	−0.184249	−	0.0594154i
$977$		−	11.9638i		−	0.382756i	−0.981516	−	0.191378i	$-0.938704\pi$
$977$		−	11.9638i		−	0.382756i	0.981516	−	0.191378i	$-0.0612957\pi$
$978$		0			0
$979$	51.6635	+	21.3997i	1.65117	+	0.683939i
$980$	11.9311	+	4.38662i	0.381125	+	0.140125i
$981$		0			0
$982$	4.79616	−	4.99384i	0.153052	−	0.159360i
$983$	−33.2465	−	33.2465i	−1.06040	−	1.06040i	−0.998055	−	0.0623428i	$-0.980143\pi$
$983$	−33.2465	−	33.2465i	−1.06040	−	1.06040i	−0.0623428	−	0.998055i	$-0.519857\pi$
$984$		0			0
$985$	−21.0292	+	21.0292i	−0.670045	+	0.670045i
$986$	0.800609	+	39.6514i	0.0254966	+	1.26276i
$987$		0			0
$988$	0.0590432	−	0.00238528i	0.00187841	−	7.58858e-5i
$989$	−33.2144	+	80.1867i	−1.05616	+	2.54979i
$990$		0			0
$991$	0.0761252			0.00241820			0.00120910	−	0.999999i	$-0.499615\pi$
$991$	0.0761252			0.00241820			0.00120910	+	0.999999i	$0.499615\pi$
$992$	32.9104	−	17.7083i	1.04491	−	0.562238i
$993$		0			0
$994$	9.07841	−	3.97696i	0.287950	−	0.126142i
$995$	−6.32866	+	15.2787i	−0.200632	+	0.484368i
$996$		0			0
$997$	−50.5849	+	20.9529i	−1.60204	+	0.663586i	−0.991702	−	0.128556i	$-0.958966\pi$
$997$	−50.5849	+	20.9529i	−1.60204	+	0.663586i	−0.610336	+	0.792142i	$0.708966\pi$
$998$	0.857716	+	42.4797i	0.0271505	+	1.34467i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	864.2.v.a.109.20	yes	128
3.2	odd	2	inner	864.2.v.a.109.13	✓	128
32.5	even	8	inner	864.2.v.a.325.20	yes	128
96.5	odd	8	inner	864.2.v.a.325.13	yes	128

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
864.2.v.a.109.13	✓	128	3.2	odd	2	inner
864.2.v.a.109.20	yes	128	1.1	even	1	trivial
864.2.v.a.325.13	yes	128	96.5	odd	8	inner
864.2.v.a.325.20	yes	128	32.5	even	8	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.v (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.567462 + 1.29537i) q^{2} +(-1.35597 + 1.47015i) q^{4} +(-2.16011 + 0.894745i) q^{5} +(1.46314 - 1.46314i) q^{7} +(-2.67385 - 0.922239i) q^{8} +O(q^{10})\)	\(q+(0.567462 + 1.29537i) q^{2} +(-1.35597 + 1.47015i) q^{4} +(-2.16011 + 0.894745i) q^{5} +(1.46314 - 1.46314i) q^{7} +(-2.67385 - 0.922239i) q^{8} +(-2.38480 - 2.29041i) q^{10} +(-2.39513 - 5.78235i) q^{11} +(0.0552727 + 0.0228947i) q^{13} +(2.72558 + 1.06503i) q^{14} +(-0.322664 - 3.98696i) q^{16} +3.26457i q^{17} +(-0.456261 - 0.188990i) q^{19} +(1.61364 - 4.38892i) q^{20} +(6.13115 - 6.38384i) q^{22} +(-6.25659 - 6.25659i) q^{23} +(0.329954 - 0.329954i) q^{25} +(0.00170799 + 0.0845906i) q^{26} +(0.167050 + 4.13501i) q^{28} +(3.28735 - 7.93636i) q^{29} +6.60653 q^{31} +(4.98150 - 2.68042i) q^{32} +(-4.22883 + 1.85252i) q^{34} +(-1.85140 + 4.46967i) q^{35} +(-0.590451 + 0.244573i) q^{37} +(-0.0140990 - 0.698273i) q^{38} +(6.60097 - 0.400280i) q^{40} +(-1.11963 - 1.11963i) q^{41} +(-3.75382 - 9.06253i) q^{43} +(11.7486 + 4.31953i) q^{44} +(4.55424 - 11.6550i) q^{46} +12.0850i q^{47} +2.71846i q^{49} +(0.614649 + 0.240177i) q^{50} +(-0.108607 + 0.0502144i) q^{52} +(0.152093 + 0.367185i) q^{53} +(10.3475 + 10.3475i) q^{55} +(-5.26157 + 2.56285i) q^{56} +(12.1460 - 0.245242i) q^{58} +(-4.24644 + 1.75893i) q^{59} +(0.578617 - 1.39691i) q^{61} +(3.74895 + 8.55791i) q^{62} +(6.29895 + 4.93186i) q^{64} -0.139880 q^{65} +(3.44098 - 8.30727i) q^{67} +(-4.79940 - 4.42667i) q^{68} +(-6.84048 + 0.138117i) q^{70} +(2.39497 - 2.39497i) q^{71} +(-9.83836 - 9.83836i) q^{73} +(-0.651871 - 0.626068i) q^{74} +(0.896522 - 0.414506i) q^{76} +(-11.9648 - 4.95597i) q^{77} -3.62239i q^{79} +(4.26431 + 8.32356i) q^{80} +(0.814992 - 2.08569i) q^{82} +(-9.86593 - 4.08660i) q^{83} +(-2.92096 - 7.05182i) q^{85} +(9.60920 - 10.0052i) q^{86} +(1.07150 + 17.6700i) q^{88} +(-6.31778 + 6.31778i) q^{89} +(0.114370 - 0.0473735i) q^{91} +(17.6819 - 0.714329i) q^{92} +(-15.6546 + 6.85778i) q^{94} +1.15467 q^{95} -4.47320 q^{97} +(-3.52141 + 1.54262i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 128 q+O(q^{10}) \) 128 * q	\( 128 q - 8 q^{10} - 32 q^{16} + 32 q^{22} + 64 q^{40} + 64 q^{46} + 88 q^{52} - 64 q^{55} + 64 q^{58} - 32 q^{61} - 96 q^{64} + 64 q^{67} + 48 q^{70} + 32 q^{76} + 40 q^{82} + 40 q^{88} - 48 q^{91} + 24 q^{94}+O(q^{100}) \) 128 * q - 8 * q^10 - 32 * q^16 + 32 * q^22 + 64 * q^40 + 64 * q^46 + 88 * q^52 - 64 * q^55 + 64 * q^58 - 32 * q^61 - 96 * q^64 + 64 * q^67 + 48 * q^70 + 32 * q^76 + 40 * q^82 + 40 * q^88 - 48 * q^91 + 24 * q^94

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