LMFDB - Embedded newform 864.2.bf.a.529.11

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [864,2,Mod(49,864)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("864.49"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(864, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([0, 9, 14])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 864 = 2^{5} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	864.bf (of order $18$, degree $6$, not minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$6.89907473464$
Analytic rank:	$0$
Dimension:	$204$
Relative dimension:	$34$ over $\Q(\zeta_{18})$
Twist minimal:	no (minimal twist has level 216)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			529.11
Character	$\chi$	$=$	864.529
Dual form			864.2.bf.a.49.11

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.07385 + 1.35898i) q^{3} +(-0.0465753 + 0.127965i) q^{5} +(0.252128 - 1.42989i) q^{7} +(-0.693675 - 2.91870i) q^{9} +(0.771344 + 2.11925i) q^{11} +(0.634290 + 0.755917i) q^{13} +(-0.123887 - 0.200710i) q^{15} +(-0.439205 - 0.760726i) q^{17} +(5.20298 + 3.00394i) q^{19} +(1.67245 + 1.87813i) q^{21} +(0.748645 + 4.24578i) q^{23} +(3.81602 + 3.20202i) q^{25} +(4.71137 + 2.19157i) q^{27} +(-0.146501 + 0.174594i) q^{29} +(-1.15687 - 6.56095i) q^{31} +(-3.70834 - 1.22752i) q^{33} +(0.171232 + 0.0988610i) q^{35} +(-9.25201 + 5.34165i) q^{37} +(-1.70841 + 0.0502450i) q^{39} +(-1.19321 + 1.00123i) q^{41} +(1.11062 + 3.05141i) q^{43} +(0.405799 + 0.0471736i) q^{45} +(-1.36645 + 7.74952i) q^{47} +(4.59683 + 1.67311i) q^{49} +(1.50546 + 0.220036i) q^{51} +5.08895i q^{53} -0.307115 q^{55} +(-9.66954 + 3.84497i) q^{57} +(-3.15956 + 8.68082i) q^{59} +(12.3724 + 2.18158i) q^{61} +(-4.34831 + 0.255992i) q^{63} +(-0.126273 + 0.0459596i) q^{65} +(-5.90023 - 7.03162i) q^{67} +(-6.57388 - 3.54195i) q^{69} +(5.93006 + 10.2712i) q^{71} +(4.88366 - 8.45874i) q^{73} +(-8.44934 + 1.74741i) q^{75} +(3.22477 - 0.568614i) q^{77} +(-5.49238 - 4.60866i) q^{79} +(-8.03763 + 4.04926i) q^{81} +(-0.867764 + 1.03416i) q^{83} +(0.117802 - 0.0207717i) q^{85} +(-0.0799487 - 0.386581i) q^{87} +(-3.19969 + 5.54203i) q^{89} +(1.24080 - 0.716376i) q^{91} +(10.1585 + 5.47333i) q^{93} +(-0.626728 + 0.525888i) q^{95} +(0.779817 - 0.283830i) q^{97} +(5.65040 - 3.72140i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 204 q + 12 q^{7} - 12 q^{9} + 12 q^{15} - 6 q^{17} + 12 q^{23} - 12 q^{25} + 12 q^{31} + 12 q^{39} - 24 q^{41} + 12 q^{47} - 12 q^{49} + 24 q^{55} - 30 q^{57} + 72 q^{63} - 12 q^{65} + 90 q^{71} - 6 q^{73}+ \cdots - 12 q^{97}+O(q^{100}) $ 204 * q + 12 * q^7 - 12 * q^9 + 12 * q^15 - 6 * q^17 + 12 * q^23 - 12 * q^25 + 12 * q^31 + 12 * q^39 - 24 * q^41 + 12 * q^47 - 12 * q^49 + 24 * q^55 - 30 * q^57 + 72 * q^63 - 12 * q^65 + 90 * q^71 - 6 * q^73 + 12 * q^79 - 12 * q^81 + 48 * q^87 - 6 * q^89 + 42 * q^95 - 12 * q^97

Character values

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

$n$	$325$	$353$	$703$
$\chi(n)$	$-1$	$e\left(\frac{2}{9}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−1.07385	+	1.35898i	−0.619990	+	0.784610i
$3$	−1.07385	+	1.35898i	−0.619990	+	0.784610i
$4$		0			0
$5$	−0.0465753	+	0.127965i	−0.0208291	+	0.0572275i	−0.949671	−	0.313248i	$-0.898583\pi$
$5$	−0.0465753	+	0.127965i	−0.0208291	+	0.0572275i	0.928842	+	0.370475i	$0.120805\pi$
$6$		0			0
$7$	0.252128	−	1.42989i	0.0952954	−	0.540447i	−0.899361	−	0.437207i	$-0.855968\pi$
$7$	0.252128	−	1.42989i	0.0952954	−	0.540447i	0.994656	−	0.103240i	$-0.0329211\pi$
$8$		0			0
$9$	−0.693675	−	2.91870i	−0.231225	−	0.972900i
$10$		0			0
$11$	0.771344	+	2.11925i	0.232569	+	0.638978i	0.999998	−	0.00215610i	$-0.000686309\pi$
$11$	0.771344	+	2.11925i	0.232569	+	0.638978i	−0.767429	+	0.641134i	$0.778464\pi$
$12$		0			0
$13$	0.634290	+	0.755917i	0.175920	+	0.209654i	0.846798	−	0.531914i	$-0.178527\pi$
$13$	0.634290	+	0.755917i	0.175920	+	0.209654i	−0.670878	+	0.741568i	$0.734083\pi$
$14$		0			0
$15$	−0.123887	−	0.200710i	−0.0319874	−	0.0518232i
$16$		0			0
$17$	−0.439205	−	0.760726i	−0.106523	−	0.184503i	0.807836	−	0.589407i	$-0.200638\pi$
$17$	−0.439205	−	0.760726i	−0.106523	−	0.184503i	−0.914359	+	0.404904i	$0.867305\pi$
$18$		0			0
$19$	5.20298	+	3.00394i	1.19364	+	0.689151i	0.959131	−	0.282962i	$-0.0913170\pi$
$19$	5.20298	+	3.00394i	1.19364	+	0.689151i	0.234513	+	0.972113i	$0.424650\pi$
$20$		0			0
$21$	1.67245	+	1.87813i	0.364958	+	0.409842i
$22$		0			0
$23$	0.748645	+	4.24578i	0.156103	+	0.885306i	0.957770	+	0.287535i	$0.0928357\pi$
$23$	0.748645	+	4.24578i	0.156103	+	0.885306i	−0.801667	+	0.597771i	$0.796053\pi$
$24$		0			0
$25$	3.81602	+	3.20202i	0.763203	+	0.640404i
$26$		0			0
$27$	4.71137	+	2.19157i	0.906704	+	0.421767i
$28$		0			0
$29$	−0.146501	+	0.174594i	−0.0272046	+	0.0324212i	−0.779475	−	0.626433i	$-0.784514\pi$
$29$	−0.146501	+	0.174594i	−0.0272046	+	0.0324212i	0.752271	+	0.658854i	$0.228959\pi$
$30$		0			0
$31$	−1.15687	−	6.56095i	−0.207781	−	1.17838i	−0.893004	−	0.450049i	$-0.851407\pi$
$31$	−1.15687	−	6.56095i	−0.207781	−	1.17838i	0.685223	−	0.728333i	$-0.259705\pi$
$32$		0			0
$33$	−3.70834	−	1.22752i	−0.645539	−	0.213684i
$34$		0			0
$35$	0.171232	+	0.0988610i	0.0289435	+	0.0167106i
$36$		0			0
$37$	−9.25201	+	5.34165i	−1.52102	+	0.878162i	−0.521330	+	0.853355i	$0.674564\pi$
$37$	−9.25201	+	5.34165i	−1.52102	+	0.878162i	−0.999692	+	0.0248069i	$0.992103\pi$
$38$		0			0
$39$	−1.70841	+	0.0502450i	−0.273565	+	0.00804563i
$40$		0			0
$41$	−1.19321	+	1.00123i	−0.186349	+	0.156365i	−0.731190	−	0.682174i	$-0.761035\pi$
$41$	−1.19321	+	1.00123i	−0.186349	+	0.156365i	0.544841	+	0.838540i	$0.316590\pi$
$42$		0			0
$43$	1.11062	+	3.05141i	0.169368	+	0.465335i	0.995117	−	0.0987027i	$-0.0314693\pi$
$43$	1.11062	+	3.05141i	0.169368	+	0.465335i	−0.825749	+	0.564038i	$0.809247\pi$
$44$		0			0
$45$	0.405799	+	0.0471736i	0.0604929	+	0.00703222i
$46$		0			0
$47$	−1.36645	+	7.74952i	−0.199317	+	1.13038i	0.706818	+	0.707395i	$0.250130\pi$
$47$	−1.36645	+	7.74952i	−0.199317	+	1.13038i	−0.906135	+	0.422988i	$0.860981\pi$
$48$		0			0
$49$	4.59683	+	1.67311i	0.656691	+	0.239016i
$50$		0			0
$51$	1.50546	+	0.220036i	0.210806	+	0.0308111i
$52$		0			0
$53$			5.08895i			0.699021i	0.936932	+	0.349510i	$0.113652\pi$
$53$			5.08895i			0.699021i	−0.936932	+	0.349510i	$0.886348\pi$
$54$		0			0
$55$	−0.307115			−0.0414114
$56$		0			0
$57$	−9.66954	+	3.84497i	−1.28076	+	0.509279i
$58$		0			0
$59$	−3.15956	+	8.68082i	−0.411340	+	1.13015i	0.545139	+	0.838346i	$0.316477\pi$
$59$	−3.15956	+	8.68082i	−0.411340	+	1.13015i	−0.956479	+	0.291801i	$0.905745\pi$
$60$		0			0
$61$	12.3724	+	2.18158i	1.58412	+	0.279323i	0.895250	−	0.445563i	$-0.146997\pi$
$61$	12.3724	+	2.18158i	1.58412	+	0.279323i	0.688869	+	0.724886i	$0.258108\pi$
$62$		0			0
$63$	−4.34831	+	0.255992i	−0.547836	+	0.0322519i
$64$		0			0
$65$	−0.126273	+	0.0459596i	−0.0156622	+	0.00570059i
$66$		0			0
$67$	−5.90023	−	7.03162i	−0.720828	−	0.859049i	0.273883	−	0.961763i	$-0.411692\pi$
$67$	−5.90023	−	7.03162i	−0.720828	−	0.859049i	−0.994711	+	0.102714i	$0.967247\pi$
$68$		0			0
$69$	−6.57388	−	3.54195i	−0.791402	−	0.426401i
$70$		0			0
$71$	5.93006	+	10.2712i	0.703769	+	1.21896i	0.967134	+	0.254267i	$0.0818341\pi$
$71$	5.93006	+	10.2712i	0.703769	+	1.21896i	−0.263366	+	0.964696i	$0.584833\pi$
$72$		0			0
$73$	4.88366	−	8.45874i	0.571589	−	0.990021i	−0.424814	−	0.905281i	$-0.639661\pi$
$73$	4.88366	−	8.45874i	0.571589	−	0.990021i	0.996403	−	0.0847405i	$-0.0270061\pi$
$74$		0			0
$75$	−8.44934	+	1.74741i	−0.975645	+	0.201773i
$76$		0			0
$77$	3.22477	−	0.568614i	0.367497	−	0.0647996i
$78$		0			0
$79$	−5.49238	−	4.60866i	−0.617941	−	0.518514i	0.279214	−	0.960229i	$-0.409926\pi$
$79$	−5.49238	−	4.60866i	−0.617941	−	0.518514i	−0.897156	+	0.441714i	$0.854370\pi$
$80$		0			0
$81$	−8.03763	+	4.04926i	−0.893070	+	0.449918i
$82$		0			0
$83$	−0.867764	+	1.03416i	−0.0952494	+	0.113514i	−0.811564	−	0.584264i	$-0.801383\pi$
$83$	−0.867764	+	1.03416i	−0.0952494	+	0.113514i	0.716314	+	0.697778i	$0.245828\pi$
$84$		0			0
$85$	0.117802	−	0.0207717i	0.0127774	−	0.00225301i
$86$		0			0
$87$	−0.0799487	−	0.386581i	−0.00857141	−	0.0414458i
$88$		0			0
$89$	−3.19969	+	5.54203i	−0.339167	+	0.587454i	−0.984276	−	0.176636i	$-0.943478\pi$
$89$	−3.19969	+	5.54203i	−0.339167	+	0.587454i	0.645110	+	0.764090i	$0.276812\pi$
$90$		0			0
$91$	1.24080	−	0.716376i	0.130071	−	0.0750966i
$92$		0			0
$93$	10.1585	+	5.47333i	1.05339	+	0.567558i
$94$		0			0
$95$	−0.626728	+	0.525888i	−0.0643010	+	0.0539549i
$96$		0			0
$97$	0.779817	−	0.283830i	0.0791784	−	0.0288186i	−0.302127	−	0.953268i	$-0.597697\pi$
$97$	0.779817	−	0.283830i	0.0791784	−	0.0288186i	0.381306	+	0.924449i	$0.375475\pi$
$98$		0			0
$99$	5.65040	−	3.72140i	0.567886	−	0.374014i
$100$		0			0
$101$	7.06509	+	1.24577i	0.703003	+	0.123958i	0.513712	−	0.857963i	$-0.328270\pi$
$101$	7.06509	+	1.24577i	0.703003	+	0.123958i	0.189291	+	0.981921i	$0.439381\pi$
$102$		0			0
$103$	7.48465	+	2.72419i	0.737484	+	0.268422i	0.683329	−	0.730110i	$-0.260531\pi$
$103$	7.48465	+	2.72419i	0.737484	+	0.268422i	0.0541548	+	0.998533i	$0.482754\pi$
$104$		0			0
$105$	−0.318229	+	0.126540i	−0.0310560	+	0.0123490i
$106$		0			0
$107$		−	19.5243i		−	1.88748i	−0.330687	−	0.943740i	$-0.607280\pi$
$107$		−	19.5243i		−	1.88748i	0.330687	−	0.943740i	$-0.392720\pi$
$108$		0			0
$109$			5.56480i			0.533011i	0.963833	+	0.266506i	$0.0858691\pi$
$109$			5.56480i			0.533011i	−0.963833	+	0.266506i	$0.914131\pi$
$110$		0			0
$111$	2.67609	−	18.3095i	0.254003	−	1.73786i
$112$		0			0
$113$	11.5278	+	4.19578i	1.08445	+	0.394706i	0.821561	−	0.570121i	$-0.193104\pi$
$113$	11.5278	+	4.19578i	1.08445	+	0.394706i	0.262885	+	0.964827i	$0.415326\pi$
$114$		0			0
$115$	−0.578178	−	0.101948i	−0.0539154	−	0.00950674i
$116$		0			0
$117$	1.76631	−	2.37566i	0.163295	−	0.219630i
$118$		0			0
$119$	−1.19849	+	0.436214i	−0.109865	+	0.0399877i
$120$		0			0
$121$	4.53023	−	3.80132i	0.411840	−	0.345574i
$122$		0			0
$123$	−0.0793116	−	2.69673i	−0.00715129	−	0.243156i
$124$		0			0
$125$	−1.17714	+	0.679623i	−0.105287	+	0.0607873i
$126$		0			0
$127$	4.15115	−	7.19001i	0.368355	−	0.638010i	−0.620953	−	0.783848i	$-0.713254\pi$
$127$	4.15115	−	7.19001i	0.368355	−	0.638010i	0.989309	+	0.145838i	$0.0465877\pi$
$128$		0			0
$129$	−5.33946	−	1.76745i	−0.470113	−	0.155615i
$130$		0			0
$131$	−16.3299	+	2.87941i	−1.42675	+	0.251575i	−0.833090	−	0.553138i	$-0.813430\pi$
$131$	−16.3299	+	2.87941i	−1.42675	+	0.251575i	−0.593664	+	0.804713i	$0.702319\pi$
$132$		0			0
$133$	5.60712	−	6.68230i	0.486199	−	0.579429i
$134$		0			0
$135$	−0.499877	+	0.500816i	−0.0430225	+	0.0431034i
$136$		0			0
$137$	6.20446	+	5.20616i	0.530083	+	0.444792i	0.868130	−	0.496337i	$-0.165322\pi$
$137$	6.20446	+	5.20616i	0.530083	+	0.444792i	−0.338047	+	0.941129i	$0.609766\pi$
$138$		0			0
$139$	−3.76315	+	0.663545i	−0.319186	+	0.0562811i	−0.330946	−	0.943650i	$-0.607368\pi$
$139$	−3.76315	+	0.663545i	−0.319186	+	0.0562811i	0.0117598	+	0.999931i	$0.496257\pi$
$140$		0			0
$141$	−9.06410	−	10.1788i	−0.763335	−	0.857212i
$142$		0			0
$143$	−1.11272	+	1.92729i	−0.0930505	+	0.161168i
$144$		0			0
$145$	−0.0155185	−	0.0268788i	−0.00128874	−	0.00223216i
$146$		0			0
$147$	−7.21006	+	4.45035i	−0.594676	+	0.367058i
$148$		0			0
$149$	−14.3501	−	17.1018i	−1.17561	−	1.40104i	−0.897802	−	0.440400i	$-0.854837\pi$
$149$	−14.3501	−	17.1018i	−1.17561	−	1.40104i	−0.277807	−	0.960637i	$-0.589608\pi$
$150$		0			0
$151$	17.9058	−	6.51719i	1.45716	−	0.530362i	0.512576	−	0.858642i	$-0.328691\pi$
$151$	17.9058	−	6.51719i	1.45716	−	0.530362i	0.944581	+	0.328280i	$0.106469\pi$
$152$		0			0
$153$	−1.91566	+	1.80960i	−0.154872	+	0.146298i
$154$		0			0
$155$	0.893452	+	0.157540i	0.0717638	+	0.0126539i
$156$		0			0
$157$	2.93811	−	8.07239i	0.234487	−	0.644247i	−0.765513	−	0.643421i	$-0.777515\pi$
$157$	2.93811	−	8.07239i	0.234487	−	0.644247i	1.00000		0.000826492i	$-0.000263081\pi$
$158$		0			0
$159$	−6.91580	−	5.46479i	−0.548459	−	0.433386i
$160$		0			0
$161$	6.25975			0.493337
$162$		0			0
$163$			10.0518i			0.787315i	0.919257	+	0.393657i	$0.128790\pi$
$163$			10.0518i			0.787315i	−0.919257	+	0.393657i	$0.871210\pi$
$164$		0			0
$165$	0.329797	−	0.417364i	0.0256746	−	0.0324918i
$166$		0			0
$167$	−14.9465	−	5.44008i	−1.15660	−	0.420966i	−0.308715	−	0.951154i	$-0.599899\pi$
$167$	−14.9465	−	5.44008i	−1.15660	−	0.420966i	−0.847880	+	0.530188i	$0.822121\pi$
$168$		0			0
$169$	2.08834	−	11.8436i	0.160641	−	0.911043i
$170$		0			0
$171$	5.15843	−	17.2697i	0.394475	−	1.32065i
$172$		0			0
$173$	6.92421	+	19.0241i	0.526438	+	1.44638i	0.863236	+	0.504800i	$0.168434\pi$
$173$	6.92421	+	19.0241i	0.526438	+	1.44638i	−0.336798	+	0.941577i	$0.609344\pi$
$174$		0			0
$175$	5.54065	−	4.64916i	0.418834	−	0.351444i
$176$		0			0
$177$	−8.40419	−	13.6157i	−0.631698	−	1.02342i
$178$		0			0
$179$	19.1336	−	11.0468i	1.43011	−	0.825676i	0.432984	−	0.901402i	$-0.357461\pi$
$179$	19.1336	−	11.0468i	1.43011	−	0.825676i	0.997129	+	0.0757257i	$0.0241273\pi$
$180$		0			0
$181$	−15.2536	−	8.80669i	−1.13379	−	0.654596i	−0.188907	−	0.981995i	$-0.560494\pi$
$181$	−15.2536	−	8.80669i	−1.13379	−	0.654596i	−0.944886	+	0.327399i	$0.893828\pi$
$182$		0			0
$183$	−16.2508	+	14.4711i	−1.20130	+	1.06974i
$184$		0			0
$185$	−0.252627	−	1.43272i	−0.0185735	−	0.105336i
$186$		0			0
$187$	1.27339	−	1.51757i	0.0931195	−	0.110976i
$188$		0			0
$189$	4.32157	−	6.18419i	0.314348	−	0.449833i
$190$		0			0
$191$	7.20145	+	6.04274i	0.521079	+	0.437237i	0.865008	−	0.501759i	$-0.167313\pi$
$191$	7.20145	+	6.04274i	0.521079	+	0.437237i	−0.343929	+	0.938996i	$0.611758\pi$
$192$		0			0
$193$	−1.28620	−	7.29438i	−0.0925824	−	0.525061i	−0.995461	−	0.0951660i	$-0.969662\pi$
$193$	−1.28620	−	7.29438i	−0.0925824	−	0.525061i	0.902879	−	0.429895i	$-0.141449\pi$
$194$		0			0
$195$	0.0731404	−	0.220957i	0.00523769	−	0.0158230i
$196$		0			0
$197$	−15.7746	−	9.10747i	−1.12389	−	0.648881i	−0.181502	−	0.983391i	$-0.558096\pi$
$197$	−15.7746	−	9.10747i	−1.12389	−	0.648881i	−0.942392	+	0.334510i	$0.891429\pi$
$198$		0			0
$199$	8.05228	+	13.9470i	0.570811	+	0.988674i	0.996483	+	0.0837964i	$0.0267045\pi$
$199$	8.05228	+	13.9470i	0.570811	+	0.988674i	−0.425672	+	0.904878i	$0.639962\pi$
$200$		0			0
$201$	15.8918	−	0.467384i	1.12092	−	0.0329667i
$202$		0			0
$203$	0.212712	+	0.253501i	0.0149295	+	0.0177923i
$204$		0			0
$205$	−0.0725472	−	0.199322i	−0.00506692	−	0.0139212i
$206$		0			0
$207$	11.8728	−	5.13026i	0.825220	−	0.356578i
$208$		0			0
$209$	−2.35282	+	13.3435i	−0.162748	+	0.922988i
$210$		0			0
$211$	6.47874	−	17.8002i	0.446015	−	1.22542i	−0.489461	−	0.872025i	$-0.662807\pi$
$211$	6.47874	−	17.8002i	0.446015	−	1.22542i	0.935476	−	0.353390i	$-0.114971\pi$
$212$		0			0
$213$	−20.3264	−	2.97088i	−1.39274	−	0.203561i
$214$		0			0
$215$	−0.442200			−0.0301578
$216$		0			0
$217$	−9.67311			−0.656654
$218$		0			0
$219$	6.25096	+	15.7203i	0.422401	+	1.06228i
$220$		0			0
$221$	0.296462	−	0.814523i	0.0199422	−	0.0547908i
$222$		0			0
$223$	−2.02862	+	11.5049i	−0.135847	+	0.770424i	0.838420	+	0.545025i	$0.183480\pi$
$223$	−2.02862	+	11.5049i	−0.135847	+	0.770424i	−0.974267	+	0.225399i	$0.927631\pi$
$224$		0			0
$225$	6.69866	−	13.3590i	0.446577	−	0.890598i
$226$		0			0
$227$	0.619851	+	1.70303i	0.0411409	+	0.113034i	0.958562	−	0.284884i	$-0.0919551\pi$
$227$	0.619851	+	1.70303i	0.0411409	+	0.113034i	−0.917421	+	0.397918i	$0.869733\pi$
$228$		0			0
$229$	−7.88646	−	9.39872i	−0.521152	−	0.621085i	0.439701	−	0.898144i	$-0.355085\pi$
$229$	−7.88646	−	9.39872i	−0.521152	−	0.621085i	−0.960853	+	0.277060i	$0.910640\pi$
$230$		0			0
$231$	−2.69020	+	4.99302i	−0.177002	+	0.328517i
$232$		0			0
$233$	−0.421533	−	0.730116i	−0.0276155	−	0.0478315i	0.851887	−	0.523725i	$-0.175458\pi$
$233$	−0.421533	−	0.730116i	−0.0276155	−	0.0478315i	−0.879503	+	0.475894i	$0.842125\pi$
$234$		0			0
$235$	−0.928021	−	0.535793i	−0.0605374	−	0.0349513i
$236$		0			0
$237$	12.1611	−	2.51504i	0.789949	−	0.163369i
$238$		0			0
$239$	1.87603	+	10.6395i	0.121350	+	0.688211i	0.983409	+	0.181402i	$0.0580637\pi$
$239$	1.87603	+	10.6395i	0.121350	+	0.688211i	−0.862059	+	0.506808i	$0.830825\pi$
$240$		0			0
$241$	6.85566	+	5.75258i	0.441612	+	0.370557i	0.836312	−	0.548253i	$-0.184707\pi$
$241$	6.85566	+	5.75258i	0.441612	+	0.370557i	−0.394700	+	0.918810i	$0.629152\pi$
$242$		0			0
$243$	3.12836	−	15.2713i	0.200685	−	0.979656i
$244$		0			0
$245$	−0.428198	+	0.510307i	−0.0273566	+	0.0326023i
$246$		0			0
$247$	1.02947	+	5.83839i	0.0655033	+	0.371488i
$248$		0			0
$249$	−0.473556	−	2.28981i	−0.0300104	−	0.145111i
$250$		0			0
$251$	6.48934	+	3.74662i	0.409603	+	0.236485i	0.690619	−	0.723219i	$-0.257338\pi$
$251$	6.48934	+	3.74662i	0.409603	+	0.236485i	−0.281016	+	0.959703i	$0.590671\pi$
$252$		0			0
$253$	−8.42041	+	4.86153i	−0.529387	+	0.305641i
$254$		0			0
$255$	−0.0982739	+	0.182397i	−0.00615415	+	0.0114221i
$256$		0			0
$257$	−12.7573	+	10.7046i	−0.795777	+	0.667736i	−0.947168	−	0.320738i	$-0.896069\pi$
$257$	−12.7573	+	10.7046i	−0.795777	+	0.667736i	0.151391	+	0.988474i	$0.451625\pi$
$258$		0			0
$259$	5.30528	+	14.5761i	0.329654	+	0.905717i
$260$		0			0
$261$	0.611211	+	0.306483i	0.0378330	+	0.0189708i
$262$		0			0
$263$	3.21128	−	18.2121i	0.198016	−	1.12300i	−0.710042	−	0.704159i	$-0.751324\pi$
$263$	3.21128	−	18.2121i	0.198016	−	1.12300i	0.908058	−	0.418844i	$-0.137565\pi$
$264$		0			0
$265$	−0.651206	−	0.237019i	−0.0400032	−	0.0145600i
$266$		0			0
$267$	−4.09553	−	10.2997i	−0.250642	−	0.630329i
$268$		0			0
$269$		−	25.3167i		−	1.54359i	−0.635873	−	0.771793i	$-0.719360\pi$
$269$		−	25.3167i		−	1.54359i	0.635873	−	0.771793i	$-0.280640\pi$
$270$		0			0
$271$	−16.6229			−1.00977			−0.504884	−	0.863187i	$-0.668465\pi$
$271$	−16.6229			−1.00977			−0.504884	+	0.863187i	$0.668465\pi$
$272$		0			0
$273$	−0.358894	+	2.45551i	−0.0217213	+	0.148614i
$274$		0			0
$275$	−3.84242	+	10.5570i	−0.231707	+	0.636608i
$276$		0			0
$277$	17.4590	+	3.07849i	1.04901	+	0.184969i	0.671475	−	0.741027i	$-0.265661\pi$
$277$	17.4590	+	3.07849i	1.04901	+	0.184969i	0.377534	+	0.925996i	$0.376772\pi$
$278$		0			0
$279$	−18.3470	+	7.92773i	−1.09840	+	0.474621i
$280$		0			0
$281$	−15.3990	+	5.60477i	−0.918626	+	0.334352i	−0.757692	−	0.652613i	$-0.773673\pi$
$281$	−15.3990	+	5.60477i	−0.918626	+	0.334352i	−0.160934	+	0.986965i	$0.551451\pi$
$282$		0			0
$283$	−11.8313	−	14.0999i	−0.703295	−	0.838154i	0.289600	−	0.957148i	$-0.406478\pi$
$283$	−11.8313	−	14.0999i	−0.703295	−	0.838154i	−0.992895	+	0.118993i	$0.962033\pi$
$284$		0			0
$285$	−0.0416579	−	1.41644i	−0.00246760	−	0.0839027i
$286$		0			0
$287$	1.13080	+	1.95860i	0.0667490	+	0.115613i
$288$		0			0
$289$	8.11420	−	14.0542i	0.477306	−	0.826718i
$290$		0			0
$291$	−0.451689	+	1.36455i	−0.0264785	+	0.0799914i
$292$		0			0
$293$	−27.7186	+	4.88753i	−1.61934	+	0.285533i	−0.908519	−	0.417843i	$-0.862786\pi$
$293$	−27.7186	+	4.88753i	−1.61934	+	0.285533i	−0.710818	+	0.703376i	$0.751675\pi$
$294$		0			0
$295$	−0.963681	−	0.808624i	−0.0561077	−	0.0470799i
$296$		0			0
$297$	−1.01039	+	11.6750i	−0.0586286	+	0.677454i
$298$		0			0
$299$	−2.73460	+	3.25897i	−0.158146	+	0.188471i
$300$		0			0
$301$	4.64319	−	0.818720i	0.267629	−	0.0471903i
$302$		0			0
$303$	−9.27986	+	8.26358i	−0.533114	+	0.474730i
$304$		0			0
$305$	−0.855412	+	1.48162i	−0.0489808	+	0.0848372i
$306$		0			0
$307$	−14.1955	+	8.19580i	−0.810182	+	0.467759i	−0.847019	−	0.531562i	$-0.821605\pi$
$307$	−14.1955	+	8.19580i	−0.810182	+	0.467759i	0.0368369	+	0.999321i	$0.488272\pi$
$308$		0			0
$309$	−11.7395	+	7.24613i	−0.667839	+	0.412218i
$310$		0			0
$311$	23.5558	−	19.7657i	1.33573	−	1.12081i	0.353028	−	0.935613i	$-0.385152\pi$
$311$	23.5558	−	19.7657i	1.33573	−	1.12081i	0.982701	−	0.185197i	$-0.0592924\pi$
$312$		0			0
$313$	−20.6090	+	7.50106i	−1.16489	+	0.423985i	−0.850842	−	0.525422i	$-0.823907\pi$
$313$	−20.6090	+	7.50106i	−1.16489	+	0.423985i	−0.314048	+	0.949407i	$0.601685\pi$
$314$		0			0
$315$	0.169766	−	0.568353i	0.00956524	−	0.0320231i
$316$		0			0
$317$	26.6872	+	4.70567i	1.49890	+	0.264297i	0.862103	−	0.506733i	$-0.169147\pi$
$317$	26.6872	+	4.70567i	1.49890	+	0.264297i	0.636799	+	0.771030i	$0.280258\pi$
$318$		0			0
$319$	−0.483011	−	0.175802i	−0.0270434	−	0.00984300i
$320$		0			0
$321$	26.5331	+	20.9662i	1.48094	+	1.17022i
$322$		0			0
$323$		−	5.27738i		−	0.293641i
$324$		0			0
$325$			4.91560i			0.272668i
$326$		0			0
$327$	−7.56248	−	5.97579i	−0.418206	−	0.330462i
$328$		0			0
$329$	10.7364	+	3.90774i	0.591918	+	0.215441i
$330$		0			0
$331$	14.1842	+	2.50105i	0.779633	+	0.137470i	0.549282	−	0.835637i	$-0.314901\pi$
$331$	14.1842	+	2.50105i	0.779633	+	0.137470i	0.230351	+	0.973108i	$0.426013\pi$
$332$		0			0
$333$	22.0086	+	23.2985i	1.20606	+	1.27675i
$334$		0			0
$335$	1.17460	−	0.427521i	0.0641755	−	0.0233580i
$336$		0			0
$337$	−12.1559	+	10.2000i	−0.662174	+	0.555630i	−0.910737	−	0.412986i	$-0.864486\pi$
$337$	−12.1559	+	10.2000i	−0.662174	+	0.555630i	0.248564	+	0.968616i	$0.420041\pi$
$338$		0			0
$339$	−18.0812	+	11.1605i	−0.982036	+	0.606153i
$340$		0			0
$341$	13.0120	−	7.51246i	0.704637	−	0.406822i
$342$		0			0
$343$	8.63317	−	14.9531i	0.466147	−	0.807391i
$344$		0			0
$345$	0.759425	−	0.676257i	0.0408861	−	0.0364085i
$346$		0			0
$347$	−14.4283	+	2.54411i	−0.774554	+	0.136575i	−0.546934	−	0.837175i	$-0.684205\pi$
$347$	−14.4283	+	2.54411i	−0.774554	+	0.136575i	−0.227619	+	0.973750i	$0.573094\pi$
$348$		0			0
$349$	5.21744	−	6.21790i	0.279283	−	0.332837i	−0.608108	−	0.793854i	$-0.708071\pi$
$349$	5.21744	−	6.21790i	0.279283	−	0.332837i	0.887391	+	0.461018i	$0.152516\pi$
$350$		0			0
$351$	1.33173	+	4.95150i	0.0710827	+	0.264291i
$352$		0			0
$353$	−9.20716	−	7.72572i	−0.490047	−	0.411199i	0.363996	−	0.931401i	$-0.381412\pi$
$353$	−9.20716	−	7.72572i	−0.490047	−	0.411199i	−0.854043	+	0.520202i	$0.825857\pi$
$354$		0			0
$355$	−1.59054	+	0.280455i	−0.0844171	+	0.0148850i
$356$		0			0
$357$	0.694194	−	2.09716i	0.0367406	−	0.110993i
$358$		0			0
$359$	6.32415	−	10.9538i	0.333776	−	0.578117i	−0.649473	−	0.760385i	$-0.725010\pi$
$359$	6.32415	−	10.9538i	0.333776	−	0.578117i	0.983249	+	0.182268i	$0.0583438\pi$
$360$		0			0
$361$	8.54731	+	14.8044i	0.449858	+	0.779178i
$362$		0			0
$363$	0.301120	+	10.2386i	0.0158047	+	0.537386i
$364$		0			0
$365$	0.854962	+	1.01890i	0.0447508	+	0.0533319i
$366$		0			0
$367$	−15.1415	+	5.51105i	−0.790380	+	0.287675i	−0.705494	−	0.708716i	$-0.749275\pi$
$367$	−15.1415	+	5.51105i	−0.790380	+	0.287675i	−0.0848857	+	0.996391i	$0.527053\pi$
$368$		0			0
$369$	3.74998	+	2.78811i	0.195216	+	0.145143i
$370$		0			0
$371$	7.27663	+	1.28307i	0.377784	+	0.0666135i
$372$		0			0
$373$	−5.87846	+	16.1509i	−0.304375	+	0.836263i	0.689352	+	0.724427i	$0.257895\pi$
$373$	−5.87846	+	16.1509i	−0.304375	+	0.836263i	−0.993727	+	0.111836i	$0.964327\pi$
$374$		0			0
$375$	0.340482	−	2.32953i	0.0175824	−	0.120297i
$376$		0			0
$377$	−0.224903			−0.0115831
$378$		0			0
$379$			12.8581i			0.660478i	0.943897	+	0.330239i	$0.107129\pi$
$379$			12.8581i			0.660478i	−0.943897	+	0.330239i	$0.892871\pi$
$380$		0			0
$381$	5.31337	+	13.3624i	0.272212	+	0.684575i
$382$		0			0
$383$	−4.63308	−	1.68630i	−0.236740	−	0.0861662i	0.220926	−	0.975291i	$-0.429092\pi$
$383$	−4.63308	−	1.68630i	−0.236740	−	0.0861662i	−0.457666	+	0.889124i	$0.651314\pi$
$384$		0			0
$385$	−0.0774323	+	0.439140i	−0.00394631	+	0.0223807i
$386$		0			0
$387$	8.13574	−	5.35826i	0.413563	−	0.272376i
$388$		0			0
$389$	5.45591	+	14.9900i	0.276625	+	0.760022i	0.997739	+	0.0672055i	$0.0214083\pi$
$389$	5.45591	+	14.9900i	0.276625	+	0.760022i	−0.721114	+	0.692817i	$0.756369\pi$
$390$		0			0
$391$	2.90106	−	2.43428i	0.146713	−	0.123107i
$392$		0			0
$393$	13.6229	−	25.2842i	0.687185	−	1.27542i
$394$		0			0
$395$	0.845555	−	0.488181i	0.0425445	−	0.0245631i
$396$		0			0
$397$	18.8993	+	10.9115i	0.948529	+	0.547633i	0.892624	−	0.450803i	$-0.148862\pi$
$397$	18.8993	+	10.9115i	0.948529	+	0.547633i	0.0559050	+	0.998436i	$0.482196\pi$
$398$		0			0
$399$	3.05992	+	14.7958i	0.153187	+	0.740716i
$400$		0			0
$401$	−6.01001	−	34.0844i	−0.300125	−	1.70210i	−0.645607	−	0.763670i	$-0.723395\pi$
$401$	−6.01001	−	34.0844i	−0.300125	−	1.70210i	0.345481	−	0.938426i	$-0.387716\pi$
$402$		0			0
$403$	4.22574	−	5.03605i	0.210499	−	0.250863i
$404$		0			0
$405$	−0.143807	−	1.21713i	−0.00714581	−	0.0604796i
$406$		0			0
$407$	−18.4568	−	15.4871i	−0.914869	−	0.767667i
$408$		0			0
$409$	−0.701192	−	3.97666i	−0.0346717	−	0.196633i	0.962552	−	0.271097i	$-0.0873865\pi$
$409$	−0.701192	−	3.97666i	−0.0346717	−	0.196633i	−0.997224	+	0.0744641i	$0.976275\pi$
$410$		0			0
$411$	−13.7378	+	2.84111i	−0.677634	+	0.140141i
$412$		0			0
$413$	11.6160	+	6.70650i	0.571586	+	0.330005i
$414$		0			0
$415$	−0.0919196	−	0.159209i	−0.00451216	−	0.00781529i
$416$		0			0
$417$	3.13933	−	5.82661i	0.153733	−	0.285330i
$418$		0			0
$419$	7.00112	+	8.34360i	0.342027	+	0.407612i	0.909449	−	0.415815i	$-0.136504\pi$
$419$	7.00112	+	8.34360i	0.342027	+	0.407612i	−0.567422	+	0.823427i	$0.692059\pi$
$420$		0			0
$421$	−1.92901	−	5.29990i	−0.0940141	−	0.258302i	0.883768	−	0.467925i	$-0.154998\pi$
$421$	−1.92901	−	5.29990i	−0.0940141	−	0.258302i	−0.977782	+	0.209624i	$0.932776\pi$
$422$		0			0
$423$	23.5664	−	1.38739i	1.14584	−	0.0674572i
$424$		0			0
$425$	0.759843	−	4.30928i	0.0368578	−	0.209031i
$426$		0			0
$427$	6.23884	−	17.1411i	0.301919	−	0.829514i
$428$		0			0
$429$	−1.42426	−	3.58180i	−0.0687638	−	0.172931i
$430$		0			0
$431$	12.2633			0.590701			0.295351	−	0.955389i	$-0.404564\pi$
$431$	12.2633			0.590701			0.295351	+	0.955389i	$0.404564\pi$
$432$		0			0
$433$	−34.7890			−1.67185			−0.835927	−	0.548840i	$-0.815070\pi$
$433$	−34.7890			−1.67185			−0.835927	+	0.548840i	$0.815070\pi$
$434$		0			0
$435$	0.0531924	+	0.00777453i	0.00255038	+	0.000372760i
$436$		0			0
$437$	−8.85888	+	24.3396i	−0.423778	+	1.16432i
$438$		0			0
$439$	−3.29026	+	18.6600i	−0.157036	+	0.890594i	0.799865	+	0.600180i	$0.204904\pi$
$439$	−3.29026	+	18.6600i	−0.157036	+	0.890594i	−0.956901	+	0.290414i	$0.906207\pi$
$440$		0			0
$441$	1.69460	−	14.5774i	0.0806953	−	0.694161i
$442$		0			0
$443$	8.57202	+	23.5514i	0.407269	+	1.11896i	0.958620	+	0.284689i	$0.0918904\pi$
$443$	8.57202	+	23.5514i	0.407269	+	1.11896i	−0.551351	+	0.834274i	$0.685887\pi$
$444$		0			0
$445$	−0.560157	−	0.667569i	−0.0265540	−	0.0316458i
$446$		0			0
$447$	38.6511	−	1.13674i	1.82813	−	0.0537659i
$448$		0			0
$449$	2.07187	+	3.58859i	0.0977777	+	0.169356i	0.910765	−	0.412926i	$-0.135493\pi$
$449$	2.07187	+	3.58859i	0.0977777	+	0.169356i	−0.812987	+	0.582282i	$0.802160\pi$
$450$		0			0
$451$	−3.04223	−	1.75643i	−0.143253	−	0.0827072i
$452$		0			0
$453$	−10.3715	+	31.3323i	−0.487296	+	1.47212i
$454$		0			0
$455$	0.0338802	+	0.192144i	0.00158833	+	0.00900785i
$456$		0			0
$457$	11.4954	+	9.64582i	0.537734	+	0.451213i	0.870762	−	0.491704i	$-0.163626\pi$
$457$	11.4954	+	9.64582i	0.537734	+	0.451213i	−0.333028	+	0.942917i	$0.608070\pi$
$458$		0			0
$459$	−0.402079	−	4.54661i	−0.0187674	−	0.212218i
$460$		0			0
$461$	−2.36115	+	2.81391i	−0.109970	+	0.131057i	−0.818221	−	0.574903i	$-0.805040\pi$
$461$	−2.36115	+	2.81391i	−0.109970	+	0.131057i	0.708252	+	0.705960i	$0.249484\pi$
$462$		0			0
$463$	1.02545	+	5.81561i	0.0476566	+	0.270274i	0.999320	−	0.0368684i	$-0.0117382\pi$
$463$	1.02545	+	5.81561i	0.0476566	+	0.270274i	−0.951663	+	0.307143i	$0.900627\pi$
$464$		0			0
$465$	−1.17353	+	1.04501i	−0.0544212	+	0.0484613i
$466$		0			0
$467$	−4.79342	−	2.76748i	−0.221813	−	0.128064i	0.384976	−	0.922926i	$-0.374210\pi$
$467$	−4.79342	−	2.76748i	−0.221813	−	0.128064i	−0.606789	+	0.794863i	$0.707543\pi$
$468$		0			0
$469$	−11.5421	+	6.66381i	−0.532962	+	0.307706i
$470$		0			0
$471$	7.81515	+	12.6614i	0.360103	+	0.583407i
$472$		0			0
$473$	−5.61003	+	4.70737i	−0.257949	+	0.216445i
$474$		0			0
$475$	10.2360	+	28.1231i	0.469659	+	1.29038i
$476$		0			0
$477$	14.8531	−	3.53008i	0.680078	−	0.161631i
$478$		0			0
$479$	−1.43530	+	8.13997i	−0.0655804	+	0.371925i	0.934300	+	0.356487i	$0.116025\pi$
$479$	−1.43530	+	8.13997i	−0.0655804	+	0.371925i	−0.999881	+	0.0154382i	$0.995086\pi$
$480$		0			0
$481$	−9.90631	−	3.60560i	−0.451689	−	0.164401i
$482$		0			0
$483$	−6.72205	+	8.50690i	−0.305864	+	0.387077i
$484$		0			0
$485$			0.113009i			0.00513145i
$486$		0			0
$487$	−16.8387			−0.763033			−0.381517	−	0.924362i	$-0.624598\pi$
$487$	−16.8387			−0.763033			−0.381517	+	0.924362i	$0.624598\pi$
$488$		0			0
$489$	−13.6602	−	10.7941i	−0.617735	−	0.488127i
$490$		0			0
$491$	11.2492	−	30.9069i	0.507669	−	1.39481i	−0.375967	−	0.926633i	$-0.622689\pi$
$491$	11.2492	−	30.9069i	0.507669	−	1.39481i	0.883636	−	0.468175i	$-0.155088\pi$
$492$		0			0
$493$	0.197162	+	0.0347650i	0.00887973	+	0.00156574i
$494$		0			0
$495$	0.213038	+	0.896377i	0.00957534	+	0.0402891i
$496$		0			0
$497$	16.1818	−	5.88968i	0.725851	−	0.264188i
$498$		0			0
$499$	−5.09730	−	6.07473i	−0.228187	−	0.271942i	0.639787	−	0.768552i	$-0.279022\pi$
$499$	−5.09730	−	6.07473i	−0.228187	−	0.271942i	−0.867974	+	0.496610i	$0.834578\pi$
$500$		0			0
$501$	23.4434	−	14.4702i	1.04737	−	0.646481i
$502$		0			0
$503$	−20.9414	−	36.2716i	−0.933731	−	1.61727i	−0.776881	−	0.629647i	$-0.783200\pi$
$503$	−20.9414	−	36.2716i	−0.933731	−	1.61727i	−0.156850	−	0.987622i	$-0.550134\pi$
$504$		0			0
$505$	−0.488473	+	0.846060i	−0.0217368	+	0.0376492i
$506$		0			0
$507$	13.8526	+	15.5563i	0.615217	+	0.690878i
$508$		0			0
$509$	−1.32565	+	0.233747i	−0.0587583	+	0.0103607i	−0.202950	−	0.979189i	$-0.565053\pi$
$509$	−1.32565	+	0.233747i	−0.0587583	+	0.0103607i	0.144192	+	0.989550i	$0.453942\pi$
$510$		0			0
$511$	−10.8638	−	9.11578i	−0.480584	−	0.403258i
$512$		0			0
$513$	17.9298	+	25.5553i	0.791621	+	1.12830i
$514$		0			0
$515$	−0.697200	+	0.830890i	−0.0307223	+	0.0366134i
$516$		0			0
$517$	−17.4772	+	3.08170i	−0.768645	+	0.135533i
$518$		0			0
$519$	−33.2891	−	11.0192i	−1.46123	−	0.483691i
$520$		0			0
$521$	13.6363	−	23.6187i	0.597416	−	1.03475i	−0.395785	−	0.918343i	$-0.629527\pi$
$521$	13.6363	−	23.6187i	0.597416	−	1.03475i	0.993201	−	0.116412i	$-0.0371392\pi$
$522$		0			0
$523$	−26.9016	+	15.5317i	−1.17633	+	0.679152i	−0.955162	−	0.296085i	$-0.904319\pi$
$523$	−26.9016	+	15.5317i	−1.17633	+	0.679152i	−0.221164	+	0.975237i	$0.570986\pi$
$524$		0			0
$525$	0.368281	+	12.5222i	0.0160731	+	0.546513i
$526$		0			0
$527$	−4.48298	+	3.76167i	−0.195282	+	0.163861i
$528$		0			0
$529$	4.14676	−	1.50930i	0.180294	−	0.0656217i
$530$		0			0
$531$	27.5284	+	3.20015i	1.19463	+	0.138875i
$532$		0			0
$533$	−1.51369	−	0.266904i	−0.0655651	−	0.0115609i
$534$		0			0
$535$	2.49841	+	0.909349i	0.108016	+	0.0393146i
$536$		0			0
$537$	−5.53429	+	37.8649i	−0.238822	+	1.63399i
$538$		0			0
$539$			11.0324i			0.475199i
$540$		0			0
$541$			20.2507i			0.870645i	0.900274	+	0.435323i	$0.143366\pi$
$541$			20.2507i			0.870645i	−0.900274	+	0.435323i	$0.856634\pi$
$542$		0			0
$543$	28.3483	−	11.2723i	1.21654	−	0.483742i
$544$		0			0
$545$	−0.712098	−	0.259182i	−0.0305029	−	0.0111022i
$546$		0			0
$547$	13.5248	+	2.38478i	0.578278	+	0.101966i	0.455134	−	0.890423i	$-0.349591\pi$
$547$	13.5248	+	2.38478i	0.578278	+	0.101966i	0.123144	+	0.992389i	$0.460702\pi$
$548$		0			0
$549$	−2.21501	−	37.6245i	−0.0945345	−	1.60578i
$550$		0			0
$551$	−1.28671	+	0.468325i	−0.0548158	+	0.0199513i
$552$		0			0
$553$	−7.97465	+	6.69153i	−0.339117	+	0.284553i
$554$		0			0
$555$	2.21833	+	1.19522i	0.0941628	+	0.0507341i
$556$		0			0
$557$	8.93296	−	5.15745i	0.378502	−	0.218528i	−0.298665	−	0.954358i	$-0.596541\pi$
$557$	8.93296	−	5.15745i	0.378502	−	0.218528i	0.677166	+	0.735830i	$0.263208\pi$
$558$		0			0
$559$	−1.60216	+	2.77502i	−0.0677640	+	0.117371i
$560$		0			0
$561$	0.694914	+	3.36016i	0.0293393	+	0.141866i
$562$		0			0
$563$	−3.14086	+	0.553818i	−0.132371	+	0.0233406i	−0.239441	−	0.970911i	$-0.576964\pi$
$563$	−3.14086	+	0.553818i	−0.132371	+	0.0233406i	0.107070	+	0.994251i	$0.465853\pi$
$564$		0			0
$565$	−1.07382	+	1.27973i	−0.0451761	+	0.0538388i
$566$		0			0
$567$	3.76348	+	12.5139i	0.158051	+	0.525532i
$568$		0			0
$569$	−7.37287	−	6.18657i	−0.309087	−	0.259355i	0.475028	−	0.879971i	$-0.342438\pi$
$569$	−7.37287	−	6.18657i	−0.309087	−	0.259355i	−0.784114	+	0.620616i	$0.786882\pi$
$570$		0			0
$571$	−6.25643	+	1.10318i	−0.261823	+	0.0461665i	−0.303019	−	0.952985i	$-0.597995\pi$
$571$	−6.25643	+	1.10318i	−0.261823	+	0.0461665i	0.0411954	+	0.999151i	$0.486883\pi$
$572$		0			0
$573$	−15.9453	+	3.29764i	−0.666124	+	0.137761i
$574$		0			0
$575$	−10.7382	+	18.5991i	−0.447815	+	0.775638i
$576$		0			0
$577$	16.7124	+	28.9468i	0.695748	+	1.20507i	0.969928	+	0.243393i	$0.0782604\pi$
$577$	16.7124	+	28.9468i	0.695748	+	1.20507i	−0.274179	+	0.961679i	$0.588406\pi$
$578$		0			0
$579$	11.2941	+	6.08518i	0.469368	+	0.252891i
$580$		0			0
$581$	1.25995	+	1.50155i	0.0522714	+	0.0622947i
$582$		0			0
$583$	−10.7848	+	3.92533i	−0.446659	+	0.162571i
$584$		0			0
$585$	0.221735	+	0.336672i	0.00916760	+	0.0139197i
$586$		0			0
$587$	11.4100	+	2.01190i	0.470943	+	0.0830399i	0.404083	−	0.914722i	$-0.367591\pi$
$587$	11.4100	+	2.01190i	0.470943	+	0.0830399i	0.0668600	+	0.997762i	$0.478702\pi$
$588$		0			0
$589$	13.6895	−	37.6117i	0.564067	−	1.54976i
$590$		0			0
$591$	29.3165	−	11.6573i	1.20592	−	0.479519i
$592$		0			0
$593$	−11.5506			−0.474326			−0.237163	−	0.971470i	$-0.576218\pi$
$593$	−11.5506			−0.474326			−0.237163	+	0.971470i	$0.576218\pi$
$594$		0			0
$595$		−	0.173681i		−	0.00712023i
$596$		0			0
$597$	−27.6007	−	4.03408i	−1.12962	−	0.165104i
$598$		0			0
$599$	−27.1047	−	9.86532i	−1.10747	−	0.403086i	−0.277405	−	0.960753i	$-0.589474\pi$
$599$	−27.1047	−	9.86532i	−1.10747	−	0.403086i	−0.830065	+	0.557667i	$0.811697\pi$
$600$		0			0
$601$	−1.58173	+	8.97043i	−0.0645201	+	0.365911i	0.935404	+	0.353581i	$0.115036\pi$
$601$	−1.58173	+	8.97043i	−0.0645201	+	0.365911i	−0.999924	+	0.0123304i	$0.996075\pi$
$602$		0			0
$603$	−16.4304	+	22.0987i	−0.669096	+	0.899927i
$604$		0			0
$605$	0.275437	+	0.756758i	0.0111981	+	0.0307666i
$606$		0			0
$607$	−22.8418	+	19.1665i	−0.927119	+	0.777945i	−0.975298	−	0.220894i	$-0.929103\pi$
$607$	−22.8418	+	19.1665i	−0.927119	+	0.777945i	0.0481792	+	0.998839i	$0.484658\pi$
$608$		0			0
$609$	−0.572925	+	0.0168499i	−0.0232161	+	0.000682792i
$610$		0			0
$611$	−6.72472	+	3.88252i	−0.272053	+	0.157070i
$612$		0			0
$613$	2.09252	+	1.20812i	0.0845161	+	0.0487954i	0.541662	−	0.840596i	$-0.317795\pi$
$613$	2.09252	+	1.20812i	0.0845161	+	0.0487954i	−0.457146	+	0.889391i	$0.651128\pi$
$614$		0			0
$615$	0.348780	+	0.115452i	0.0140642	+	0.00465548i
$616$		0			0
$617$	−6.36070	−	36.0733i	−0.256072	−	1.45226i	−0.793305	−	0.608824i	$-0.791641\pi$
$617$	−6.36070	−	36.0733i	−0.256072	−	1.45226i	0.537233	−	0.843434i	$-0.319470\pi$
$618$		0			0
$619$	19.5701	−	23.3228i	0.786590	−	0.937421i	−0.212621	−	0.977135i	$-0.568200\pi$
$619$	19.5701	−	23.3228i	0.786590	−	0.937421i	0.999211	+	0.0397133i	$0.0126445\pi$
$620$		0			0
$621$	−5.77776	+	21.6442i	−0.231853	+	0.868550i
$622$		0			0
$623$	7.11775	+	5.97250i	0.285167	+	0.239283i
$624$		0			0
$625$	4.29296	+	24.3466i	0.171718	+	0.973864i
$626$		0			0
$627$	−15.6070	−	17.5264i	−0.623284	−	0.699937i
$628$		0			0
$629$	8.12706	+	4.69216i	0.324047	+	0.187089i
$630$		0			0
$631$	19.0463	+	32.9892i	0.758221	+	1.31328i	0.943757	+	0.330640i	$0.107265\pi$
$631$	19.0463	+	32.9892i	0.758221	+	1.31328i	−0.185536	+	0.982637i	$0.559402\pi$
$632$		0			0
$633$	17.2329	+	27.9193i	0.684948	+	1.10969i
$634$		0			0
$635$	0.726725	+	0.866078i	0.0288392	+	0.0343692i
$636$		0			0
$637$	1.65099	+	4.53606i	0.0654147	+	0.179725i
$638$		0			0
$639$	25.8649	−	24.4329i	1.02320	−	0.966551i
$640$		0			0
$641$	3.09962	−	17.5788i	0.122427	−	0.694321i	−0.860375	−	0.509661i	$-0.829771\pi$
$641$	3.09962	−	17.5788i	0.122427	−	0.694321i	0.982803	−	0.184659i	$-0.0591182\pi$
$642$		0			0
$643$	−3.02218	+	8.30337i	−0.119183	+	0.327453i	−0.984911	−	0.173062i	$-0.944634\pi$
$643$	−3.02218	+	8.30337i	−0.119183	+	0.327453i	0.865728	+	0.500515i	$0.166856\pi$
$644$		0			0
$645$	0.474858	−	0.600943i	0.0186975	−	0.0236621i
$646$		0			0
$647$	−20.3838			−0.801371			−0.400686	−	0.916216i	$-0.631228\pi$
$647$	−20.3838			−0.801371			−0.400686	+	0.916216i	$0.631228\pi$
$648$		0			0
$649$	−20.8340			−0.817804
$650$		0			0
$651$	10.3875	−	13.1456i	0.407119	−	0.515217i
$652$		0			0
$653$	−6.26659	+	17.2173i	−0.245230	+	0.673765i	0.754615	+	0.656168i	$0.227824\pi$
$653$	−6.26659	+	17.2173i	−0.245230	+	0.673765i	−0.999845	+	0.0175970i	$0.994398\pi$
$654$		0			0
$655$	0.392110	−	2.22376i	0.0153210	−	0.0868897i
$656$		0			0
$657$	−28.0762	−	8.38632i	−1.09536	−	0.327182i
$658$		0			0
$659$	−1.95819	−	5.38009i	−0.0762803	−	0.209579i	0.895691	−	0.444676i	$-0.146681\pi$
$659$	−1.95819	−	5.38009i	−0.0762803	−	0.209579i	−0.971972	+	0.235098i	$0.924459\pi$
$660$		0			0
$661$	−15.7491	−	18.7691i	−0.612569	−	0.730032i	0.367204	−	0.930140i	$-0.380315\pi$
$661$	−15.7491	−	18.7691i	−0.612569	−	0.730032i	−0.979774	+	0.200109i	$0.935871\pi$
$662$		0			0
$663$	0.788567	+	1.27757i	0.0306254	+	0.0496166i
$664$		0			0
$665$	0.593945	+	1.02874i	0.0230322	+	0.0398929i
$666$		0			0
$667$	−0.850963	−	0.491304i	−0.0329494	−	0.0190234i
$668$		0			0
$669$	−13.4565	−	15.1114i	−0.520259	−	0.584242i
$670$		0			0
$671$	4.92003	+	27.9029i	0.189936	+	1.07718i
$672$		0			0
$673$	−19.5576	−	16.4108i	−0.753889	−	0.632588i	0.182639	−	0.983180i	$-0.441536\pi$
$673$	−19.5576	−	16.4108i	−0.753889	−	0.632588i	−0.936528	+	0.350592i	$0.885980\pi$
$674$		0			0
$675$	10.9612	+	23.4490i	0.421898	+	0.902551i
$676$		0			0
$677$	14.0009	−	16.6857i	0.538100	−	0.641283i	−0.426660	−	0.904412i	$-0.640310\pi$
$677$	14.0009	−	16.6857i	0.538100	−	0.641283i	0.964761	+	0.263129i	$0.0847545\pi$
$678$		0			0
$679$	−0.209232	−	1.18661i	−0.00802959	−	0.0455380i
$680$		0			0
$681$	−2.98001	−	0.986434i	−0.114194	−	0.0378002i
$682$		0			0
$683$	−24.8360	−	14.3391i	−0.950322	−	0.548669i	−0.0571411	−	0.998366i	$-0.518198\pi$
$683$	−24.8360	−	14.3391i	−0.950322	−	0.548669i	−0.893181	+	0.449697i	$0.851532\pi$
$684$		0			0
$685$	−0.955179	+	0.551473i	−0.0364955	+	0.0210707i
$686$		0			0
$687$	21.2416	−	0.624722i	0.810418	−	0.0238346i
$688$		0			0
$689$	−3.84682	+	3.22787i	−0.146552	+	0.122972i
$690$		0			0
$691$	−10.5292	−	28.9287i	−0.400549	−	1.10050i	−0.962014	−	0.273000i	$-0.911984\pi$
$691$	−10.5292	−	28.9287i	−0.400549	−	1.10050i	0.561465	−	0.827501i	$-0.310238\pi$
$692$		0			0
$693$	−3.89656	−	9.01771i	−0.148018	−	0.342555i
$694$		0			0
$695$	0.0903596	−	0.512455i	0.00342754	−	0.0194385i
$696$		0			0
$697$	1.28572	+	0.467965i	0.0487003	+	0.0177255i
$698$		0			0
$699$	1.44488	+	0.211182i	0.0546504	+	0.00798763i
$700$		0			0
$701$		−	41.7650i		−	1.57744i	−0.614751	−	0.788722i	$-0.710743\pi$
$701$		−	41.7650i		−	1.57744i	0.614751	−	0.788722i	$-0.289257\pi$
$702$		0			0
$703$	−64.1840			−2.42075
$704$		0			0
$705$	1.72469	−	0.685802i	0.0649557	−	0.0258288i
$706$		0			0
$707$	3.56262	−	9.78821i	0.133986	−	0.368123i
$708$		0			0
$709$	11.9516	+	2.10739i	0.448852	+	0.0791446i	0.393505	−	0.919323i	$-0.371262\pi$
$709$	11.9516	+	2.10739i	0.448852	+	0.0791446i	0.0553467	+	0.998467i	$0.482374\pi$
$710$		0			0
$711$	−9.64136	+	19.2275i	−0.361579	+	0.721089i
$712$		0			0
$713$	26.9903	−	9.82365i	1.01079	−	0.367899i
$714$		0			0
$715$	−0.194800	−	0.232153i	−0.00728510	−	0.00868205i
$716$		0			0
$717$	−16.4735	−	8.87576i	−0.615213	−	0.331471i
$718$		0			0
$719$	9.22099	+	15.9712i	0.343885	+	0.595626i	0.985151	−	0.171693i	$-0.0549236\pi$
$719$	9.22099	+	15.9712i	0.343885	+	0.595626i	−0.641266	+	0.767319i	$0.721590\pi$
$720$		0			0
$721$	5.78238	−	10.0154i	0.215347	−	0.372992i
$722$		0			0
$723$	−15.1797	+	3.13930i	−0.564537	+	0.116752i
$724$		0			0
$725$	−1.11810	+	0.197152i	−0.0415253	+	0.00732204i
$726$		0			0
$727$	13.7551	+	11.5419i	0.510147	+	0.428065i	0.861181	−	0.508298i	$-0.169725\pi$
$727$	13.7551	+	11.5419i	0.510147	+	0.428065i	−0.351034	+	0.936363i	$0.614170\pi$
$728$		0			0
$729$	17.3941	+	20.6506i	0.644225	+	0.764836i
$730$		0			0
$731$	1.83349	−	2.18507i	0.0678142	−	0.0808178i
$732$		0			0
$733$	−7.91675	+	1.39594i	−0.292412	+	0.0515601i	−0.317930	−	0.948114i	$-0.602988\pi$
$733$	−7.91675	+	1.39594i	−0.292412	+	0.0515601i	0.0255180	+	0.999674i	$0.491877\pi$
$734$		0			0
$735$	−0.233676	−	1.12991i	−0.00861928	−	0.0416773i
$736$		0			0
$737$	10.3507	−	17.9279i	0.381272	−	0.660382i
$738$		0			0
$739$	−6.23912	+	3.60216i	−0.229510	+	0.132508i	−0.610346	−	0.792135i	$-0.708970\pi$
$739$	−6.23912	+	3.60216i	−0.229510	+	0.132508i	0.380836	+	0.924643i	$0.375636\pi$
$740$		0			0
$741$	−9.03977	−	4.87055i	−0.332084	−	0.178924i
$742$		0			0
$743$	28.1102	−	23.5873i	1.03126	−	0.865334i	0.0402635	−	0.999189i	$-0.487180\pi$
$743$	28.1102	−	23.5873i	1.03126	−	0.865334i	0.991001	+	0.133856i	$0.0427358\pi$
$744$		0			0
$745$	2.85679	−	1.03979i	0.104665	−	0.0380949i
$746$		0			0
$747$	3.62035	+	1.81537i	0.132462	+	0.0664210i
$748$		0			0
$749$	−27.9175	−	4.92261i	−1.02008	−	0.179868i
$750$		0			0
$751$	−34.3650	−	12.5079i	−1.25400	−	0.456418i	−0.372247	−	0.928134i	$-0.621413\pi$
$751$	−34.3650	−	12.5079i	−1.25400	−	0.456418i	−0.881751	+	0.471716i	$0.843635\pi$
$752$		0			0
$753$	−12.0602	+	4.79558i	−0.439498	+	0.174761i
$754$		0			0
$755$			2.59486i			0.0944365i
$756$		0			0
$757$		−	36.5128i		−	1.32708i	−0.748140	−	0.663541i	$-0.769053\pi$
$757$		−	36.5128i		−	1.32708i	0.748140	−	0.663541i	$-0.230947\pi$
$758$		0			0
$759$	2.43556	−	16.6638i	0.0884051	−	0.604857i
$760$		0			0
$761$	−4.63196	−	1.68589i	−0.167908	−	0.0611136i	0.256698	−	0.966492i	$-0.417365\pi$
$761$	−4.63196	−	1.68589i	−0.167908	−	0.0611136i	−0.424607	+	0.905378i	$0.639588\pi$
$762$		0			0
$763$	7.95705	+	1.40304i	0.288065	+	0.0507935i
$764$		0			0
$765$	−0.142343	−	0.329420i	−0.00514641	−	0.0119102i
$766$		0			0
$767$	−8.56606	+	3.11779i	−0.309303	+	0.112577i
$768$		0			0
$769$	37.4770	−	31.4469i	1.35145	−	1.13400i	0.372932	−	0.927858i	$-0.378352\pi$
$769$	37.4770	−	31.4469i	1.35145	−	1.13400i	0.978521	−	0.206146i	$-0.0660921\pi$
$770$		0			0
$771$	−0.847962	−	28.8321i	−0.0305386	−	1.03836i
$772$		0			0
$773$	8.17747	−	4.72126i	0.294123	−	0.169812i	−0.345677	−	0.938354i	$-0.612351\pi$
$773$	8.17747	−	4.72126i	0.294123	−	0.169812i	0.639800	+	0.768542i	$0.279017\pi$
$774$		0			0
$775$	16.5936	−	28.7410i	0.596061	−	1.03241i
$776$		0			0
$777$	−25.5058	−	8.44285i	−0.915016	−	0.302886i
$778$		0			0
$779$	−9.21589	+	1.62501i	−0.330194	+	0.0582220i
$780$		0			0
$781$	−17.1931	+	20.4899i	−0.615216	+	0.733186i
$782$		0			0
$783$	−1.07286	+	0.501508i	−0.0383408	+	0.0179224i
$784$		0			0
$785$	0.896137	+	0.751949i	0.0319845	+	0.0268382i
$786$		0			0
$787$	15.6553	−	2.76045i	0.558050	−	0.0983993i	0.112493	−	0.993653i	$-0.464117\pi$
$787$	15.6553	−	2.76045i	0.558050	−	0.0983993i	0.445558	+	0.895253i	$0.353005\pi$
$788$		0			0
$789$	21.3014	+	23.9212i	0.758352	+	0.851616i
$790$		0			0
$791$	8.90599	−	15.4256i	0.316661	−	0.548472i
$792$		0			0
$793$	6.19857	+	10.7362i	0.220118	+	0.381255i
$794$		0			0
$795$	1.02141	−	0.630454i	0.0362255	−	0.0223599i
$796$		0			0
$797$	9.18613	+	10.9476i	0.325389	+	0.387784i	0.903795	−	0.427965i	$-0.140769\pi$
$797$	9.18613	+	10.9476i	0.325389	+	0.387784i	−0.578406	+	0.815749i	$0.696325\pi$
$798$		0			0
$799$	6.49541	−	2.36413i	0.229791	−	0.0836371i
$800$		0			0
$801$	18.3951	+	5.49458i	0.649958	+	0.194141i
$802$		0			0
$803$	21.6932	+	3.82509i	0.765536	+	0.134985i
$804$		0			0
$805$	−0.291550	+	0.801026i	−0.0102758	+	0.0282325i
$806$		0			0
$807$	34.4050	+	27.1865i	1.21111	+	0.957008i
$808$		0			0
$809$	2.71159			0.0953343			0.0476672	−	0.998863i	$-0.484821\pi$
$809$	2.71159			0.0953343			0.0476672	+	0.998863i	$0.484821\pi$
$810$		0			0
$811$		−	38.7762i		−	1.36162i	−0.732462	−	0.680808i	$-0.761629\pi$
$811$		−	38.7762i		−	1.36162i	0.732462	−	0.680808i	$-0.238371\pi$
$812$		0			0
$813$	17.8505	−	22.5902i	0.626046	−	0.792274i
$814$		0			0
$815$	−1.28627	−	0.468164i	−0.0450561	−	0.0163991i
$816$		0			0
$817$	−3.38771	+	19.2126i	−0.118521	+	0.672165i
$818$		0			0
$819$	−2.95160	−	3.12459i	−0.103137	−	0.109182i
$820$		0			0
$821$	−12.6956	−	34.8810i	−0.443081	−	1.21736i	−0.937455	−	0.348106i	$-0.886825\pi$
$821$	−12.6956	−	34.8810i	−0.443081	−	1.21736i	0.494374	−	0.869249i	$-0.335397\pi$
$822$		0			0
$823$	16.3072	−	13.6834i	0.568433	−	0.476972i	−0.312692	−	0.949854i	$-0.601231\pi$
$823$	16.3072	−	13.6834i	0.568433	−	0.476972i	0.881126	+	0.472882i	$0.156786\pi$
$824$		0			0
$825$	−10.2205	−	16.5584i	−0.355833	−	0.576490i
$826$		0			0
$827$	7.73838	−	4.46776i	0.269090	−	0.155359i	−0.359384	−	0.933190i	$-0.617013\pi$
$827$	7.73838	−	4.46776i	0.269090	−	0.155359i	0.628474	+	0.777831i	$0.283680\pi$
$828$		0			0
$829$	19.4960	+	11.2560i	0.677124	+	0.390938i	0.798771	−	0.601636i	$-0.205484\pi$
$829$	19.4960	+	11.2560i	0.677124	+	0.390938i	−0.121647	+	0.992573i	$0.538817\pi$
$830$		0			0
$831$	−22.9320	+	20.4207i	−0.795504	+	0.708385i
$832$		0			0
$833$	−0.746175	−	4.23177i	−0.0258534	−	0.146622i
$834$		0			0
$835$	1.39228	−	1.65925i	0.0481817	−	0.0574207i
$836$		0			0
$837$	8.92830	−	33.4465i	0.308607	−	1.15608i
$838$		0			0
$839$	0.793395	+	0.665737i	0.0273910	+	0.0229838i	0.656380	−	0.754430i	$-0.272087\pi$
$839$	0.793395	+	0.665737i	0.0273910	+	0.0229838i	−0.628989	+	0.777414i	$0.716531\pi$
$840$		0			0
$841$	5.02678	+	28.5083i	0.173337	+	0.983044i
$842$		0			0
$843$	8.91946	−	26.9457i	0.307203	−	0.928058i
$844$		0			0
$845$	1.41829	+	0.818851i	0.0487907	+	0.0281693i
$846$		0			0
$847$	−4.29326	−	7.43615i	−0.147518	−	0.255509i
$848$		0			0
$849$	31.8666	−	0.937207i	1.09366	−	0.0321649i
$850$		0			0
$851$	−29.6060	−	35.2830i	−1.01488	−	1.20949i
$852$		0			0
$853$	8.12987	+	22.3366i	0.278361	+	0.764792i	0.997549	+	0.0699754i	$0.0222921\pi$
$853$	8.12987	+	22.3366i	0.278361	+	0.764792i	−0.719187	+	0.694816i	$0.755486\pi$
$854$		0			0
$855$	1.96965	+	1.46444i	0.0673608	+	0.0500827i
$856$		0			0
$857$	4.07463	−	23.1084i	0.139187	−	0.789367i	−0.832666	−	0.553776i	$-0.813186\pi$
$857$	4.07463	−	23.1084i	0.139187	−	0.789367i	0.971852	−	0.235591i	$-0.0757026\pi$
$858$		0			0
$859$	−11.7827	+	32.3728i	−0.402022	+	1.10455i	0.559264	+	0.828990i	$0.311084\pi$
$859$	−11.7827	+	32.3728i	−0.402022	+	1.10455i	−0.961285	+	0.275555i	$0.911138\pi$
$860$		0			0
$861$	−3.87602	−	0.566515i	−0.132094	−	0.0193068i
$862$		0			0
$863$	26.5038			0.902199			0.451100	−	0.892474i	$-0.351032\pi$
$863$	26.5038			0.902199			0.451100	+	0.892474i	$0.351032\pi$
$864$		0			0
$865$	−2.75691			−0.0937378
$866$		0			0
$867$	10.3860	+	26.1192i	0.352726	+	0.887055i
$868$		0			0
$869$	5.53038	−	15.1946i	0.187605	−	0.515442i
$870$		0			0
$871$	1.57287	−	8.92017i	0.0532946	−	0.302248i
$872$		0			0
$873$	−1.36936	−	2.07917i	−0.0463456	−	0.0703691i
$874$		0			0
$875$	0.674995	+	1.85453i	0.0228190	+	0.0626947i
$876$		0			0
$877$	−12.6506	−	15.0765i	−0.427182	−	0.509096i	0.508925	−	0.860811i	$-0.330043\pi$
$877$	−12.6506	−	15.0765i	−0.427182	−	0.509096i	−0.936107	+	0.351715i	$0.885599\pi$
$878$		0			0
$879$	23.1236	−	42.9176i	0.779941	−	1.44757i
$880$		0			0
$881$	−0.970676	−	1.68126i	−0.0327029	−	0.0566431i	0.849211	−	0.528054i	$-0.177078\pi$
$881$	−0.970676	−	1.68126i	−0.0327029	−	0.0566431i	−0.881914	+	0.471411i	$0.843745\pi$
$882$		0			0
$883$	−3.58570	−	2.07021i	−0.120669	−	0.0696680i	0.438451	−	0.898755i	$-0.355527\pi$
$883$	−3.58570	−	2.07021i	−0.120669	−	0.0696680i	−0.559119	+	0.829087i	$0.688861\pi$
$884$		0			0
$885$	2.13376	−	0.441282i	0.0717256	−	0.0148335i
$886$		0			0
$887$	−4.24470	−	24.0729i	−0.142523	−	0.808289i	−0.969323	−	0.245792i	$-0.920952\pi$
$887$	−4.24470	−	24.0729i	−0.142523	−	0.808289i	0.826799	−	0.562497i	$-0.190159\pi$
$888$		0			0
$889$	−9.23429	−	7.74849i	−0.309708	−	0.259876i
$890$		0			0
$891$	−14.7812	−	13.9104i	−0.495188	−	0.466015i
$892$		0			0
$893$	−30.3887	+	36.2158i	−1.01692	+	1.21192i
$894$		0			0
$895$	0.522445	+	2.96293i	0.0174634	+	0.0990399i
$896$		0			0
$897$	−1.49233	−	7.21593i	−0.0498273	−	0.240933i
$898$		0			0
$899$	1.31498	+	0.759206i	0.0438572	+	0.0253209i
$900$		0			0
$901$	3.87129	−	2.23509i	0.128971	−	0.0744617i
$902$		0			0
$903$	−3.87349	+	7.18921i	−0.128902	+	0.239242i
$904$		0			0
$905$	1.83739	−	1.54175i	0.0610768	−	0.0512495i
$906$		0			0
$907$	−19.8264	−	54.4726i	−0.658325	−	1.80873i	−0.584393	−	0.811471i	$-0.698667\pi$
$907$	−19.8264	−	54.4726i	−0.658325	−	1.80873i	−0.0739328	−	0.997263i	$-0.523555\pi$
$908$		0			0
$909$	−1.26486	−	21.4851i	−0.0419527	−	0.712614i
$910$		0			0
$911$	−1.13796	+	6.45371i	−0.0377024	+	0.213821i	−0.997839	−	0.0657114i	$-0.979068\pi$
$911$	−1.13796	+	6.45371i	−0.0377024	+	0.213821i	0.960136	+	0.279532i	$0.0901794\pi$
$912$		0			0
$913$	−2.86099	−	1.04132i	−0.0946850	−	0.0344625i
$914$		0			0
$915$	−1.09491	−	2.75353i	−0.0361965	−	0.0910290i
$916$		0			0
$917$			24.0760i			0.795059i
$918$		0			0
$919$	17.7731			0.586281			0.293140	−	0.956069i	$-0.405300\pi$
$919$	17.7731			0.586281			0.293140	+	0.956069i	$0.405300\pi$
$920$		0			0
$921$	4.10598	−	28.0926i	0.135297	−	0.925683i
$922$		0			0
$923$	−4.00277	+	10.9975i	−0.131753	+	0.361988i
$924$		0			0
$925$	−52.4099	−	9.24128i	−1.72323	−	0.303851i
$926$		0			0
$927$	2.75918	−	23.7351i	0.0906234	−	0.779564i
$928$		0			0
$929$	−53.7456	+	19.5618i	−1.76333	+	0.641801i	−0.999991	−	0.00419109i	$-0.998666\pi$
$929$	−53.7456	+	19.5618i	−1.76333	+	0.641801i	−0.763344	+	0.645993i	$0.776444\pi$
$930$		0			0
$931$	18.8913	+	22.5138i	0.619137	+	0.737859i
$932$		0			0
$933$	1.56573	+	53.2375i	0.0512597	+	1.74292i
$934$		0			0
$935$	0.134886	+	0.233630i	0.00441126	+	0.00764052i
$936$		0			0
$937$	13.7103	−	23.7470i	0.447897	−	0.775780i	−0.550352	−	0.834933i	$-0.685507\pi$
$937$	13.7103	−	23.7470i	0.447897	−	0.775780i	0.998249	+	0.0591527i	$0.0188399\pi$
$938$		0			0
$939$	11.9372	−	36.0623i	0.389557	−	1.17685i
$940$		0			0
$941$	47.0141	−	8.28985i	1.53261	−	0.270241i	0.657238	−	0.753683i	$-0.271725\pi$
$941$	47.0141	−	8.28985i	1.53261	−	0.270241i	0.875376	+	0.483442i	$0.160614\pi$
$942$		0			0
$943$	−5.14428	−	4.31656i	−0.167521	−	0.140567i
$944$		0			0
$945$	0.590079	+	0.841038i	0.0191953	+	0.0273590i
$946$		0			0
$947$	9.31764	−	11.1043i	0.302783	−	0.360842i	−0.593103	−	0.805126i	$-0.702097\pi$
$947$	9.31764	−	11.1043i	0.302783	−	0.360842i	0.895886	+	0.444284i	$0.146542\pi$
$948$		0			0
$949$	9.49177	−	1.67365i	0.308116	−	0.0543291i
$950$		0			0
$951$	−35.0531	+	31.2143i	−1.13667	+	1.01219i
$952$		0			0
$953$	−17.4033	+	30.1434i	−0.563749	+	0.976442i	0.433416	+	0.901194i	$0.357308\pi$
$953$	−17.4033	+	30.1434i	−0.563749	+	0.976442i	−0.997165	+	0.0752476i	$0.976025\pi$
$954$		0			0
$955$	−1.10867	+	0.640089i	−0.0358756	+	0.0207128i
$956$		0			0
$957$	0.757595	−	0.467619i	0.0244896	−	0.0151160i
$958$		0			0
$959$	9.00855	−	7.55907i	0.290901	−	0.244095i
$960$		0			0
$961$	−12.5773	+	4.57775i	−0.405718	+	0.147669i
$962$		0			0
$963$	−56.9855	+	13.5435i	−1.83633	+	0.436433i
$964$		0			0
$965$	0.993327	+	0.175150i	0.0319763	+	0.00563829i
$966$		0			0
$967$	7.31794	+	2.66351i	0.235329	+	0.0856527i	0.456993	−	0.889470i	$-0.348927\pi$
$967$	7.31794	+	2.66351i	0.235329	+	0.0856527i	−0.221664	+	0.975123i	$0.571149\pi$
$968$		0			0
$969$	7.17188	+	5.66714i	0.230394	+	0.182055i
$970$		0			0
$971$			2.23282i			0.0716547i	0.999358	+	0.0358273i	$0.0114066\pi$
$971$			2.23282i			0.0716547i	−0.999358	+	0.0358273i	$0.988593\pi$
$972$		0			0
$973$			5.54818i			0.177867i
$974$		0			0
$975$	−6.68022	−	5.27864i	−0.213938	−	0.169052i
$976$		0			0
$977$	42.2729	+	15.3861i	1.35243	+	0.492244i	0.913706	−	0.406377i	$-0.133208\pi$
$977$	42.2729	+	15.3861i	1.35243	+	0.492244i	0.438725	+	0.898621i	$0.355430\pi$
$978$		0			0
$979$	−14.2130	−	2.50614i	−0.454250	−	0.0800965i
$980$		0			0
$981$	16.2420	−	3.86016i	0.518567	−	0.123246i
$982$		0			0
$983$	11.4136	−	4.15422i	0.364038	−	0.132499i	−0.153523	−	0.988145i	$-0.549062\pi$
$983$	11.4136	−	4.15422i	0.364038	−	0.132499i	0.517562	+	0.855646i	$0.326840\pi$
$984$		0			0
$985$	1.90014	−	1.59441i	0.0605436	−	0.0508021i
$986$		0			0
$987$	−16.8399	+	10.3943i	−0.536020	+	0.330854i
$988$		0			0
$989$	−12.1241	+	6.99988i	−0.385525	+	0.222583i
$990$		0			0
$991$	24.4431	−	42.3367i	0.776462	−	1.34487i	−0.157508	−	0.987518i	$-0.550346\pi$
$991$	24.4431	−	42.3367i	0.776462	−	1.34487i	0.933969	−	0.357353i	$-0.116321\pi$
$992$		0			0
$993$	−18.6306	+	16.5903i	−0.591225	+	0.526477i
$994$		0			0
$995$	−2.15976	+	0.380823i	−0.0684689	+	0.0120729i
$996$		0			0
$997$	3.84922	−	4.58733i	0.121906	−	0.145282i	−0.701639	−	0.712532i	$-0.747548\pi$
$997$	3.84922	−	4.58733i	0.121906	−	0.145282i	0.823546	+	0.567250i	$0.191993\pi$
$998$		0			0
$999$	−55.2963	+	4.89012i	−1.74950	+	0.154717i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	864.2.bf.a.529.11		204
4.3	odd	2		216.2.t.a.205.29	yes	204
8.3	odd	2		216.2.t.a.205.26	yes	204
8.5	even	2	inner	864.2.bf.a.529.24		204
12.11	even	2		648.2.t.a.613.6		204
24.11	even	2		648.2.t.a.613.9		204
27.22	even	9	inner	864.2.bf.a.49.24		204
108.59	even	18		648.2.t.a.37.9		204
108.103	odd	18		216.2.t.a.157.26	✓	204
216.59	even	18		648.2.t.a.37.6		204
216.157	even	18	inner	864.2.bf.a.49.11		204
216.211	odd	18		216.2.t.a.157.29	yes	204

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
216.2.t.a.157.26	✓	204	108.103	odd	18
216.2.t.a.157.29	yes	204	216.211	odd	18
216.2.t.a.205.26	yes	204	8.3	odd	2
216.2.t.a.205.29	yes	204	4.3	odd	2
648.2.t.a.37.6		204	216.59	even	18
648.2.t.a.37.9		204	108.59	even	18
648.2.t.a.613.6		204	12.11	even	2
648.2.t.a.613.9		204	24.11	even	2
864.2.bf.a.49.11		204	216.157	even	18	inner
864.2.bf.a.49.24		204	27.22	even	9	inner
864.2.bf.a.529.11		204	1.1	even	1	trivial
864.2.bf.a.529.24		204	8.5	even	2	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 864 = 2^{5} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	864.bf (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.07385 + 1.35898i) q^{3} +(-0.0465753 + 0.127965i) q^{5} +(0.252128 - 1.42989i) q^{7} +(-0.693675 - 2.91870i) q^{9} +(0.771344 + 2.11925i) q^{11} +(0.634290 + 0.755917i) q^{13} +(-0.123887 - 0.200710i) q^{15} +(-0.439205 - 0.760726i) q^{17} +(5.20298 + 3.00394i) q^{19} +(1.67245 + 1.87813i) q^{21} +(0.748645 + 4.24578i) q^{23} +(3.81602 + 3.20202i) q^{25} +(4.71137 + 2.19157i) q^{27} +(-0.146501 + 0.174594i) q^{29} +(-1.15687 - 6.56095i) q^{31} +(-3.70834 - 1.22752i) q^{33} +(0.171232 + 0.0988610i) q^{35} +(-9.25201 + 5.34165i) q^{37} +(-1.70841 + 0.0502450i) q^{39} +(-1.19321 + 1.00123i) q^{41} +(1.11062 + 3.05141i) q^{43} +(0.405799 + 0.0471736i) q^{45} +(-1.36645 + 7.74952i) q^{47} +(4.59683 + 1.67311i) q^{49} +(1.50546 + 0.220036i) q^{51} +5.08895i q^{53} -0.307115 q^{55} +(-9.66954 + 3.84497i) q^{57} +(-3.15956 + 8.68082i) q^{59} +(12.3724 + 2.18158i) q^{61} +(-4.34831 + 0.255992i) q^{63} +(-0.126273 + 0.0459596i) q^{65} +(-5.90023 - 7.03162i) q^{67} +(-6.57388 - 3.54195i) q^{69} +(5.93006 + 10.2712i) q^{71} +(4.88366 - 8.45874i) q^{73} +(-8.44934 + 1.74741i) q^{75} +(3.22477 - 0.568614i) q^{77} +(-5.49238 - 4.60866i) q^{79} +(-8.03763 + 4.04926i) q^{81} +(-0.867764 + 1.03416i) q^{83} +(0.117802 - 0.0207717i) q^{85} +(-0.0799487 - 0.386581i) q^{87} +(-3.19969 + 5.54203i) q^{89} +(1.24080 - 0.716376i) q^{91} +(10.1585 + 5.47333i) q^{93} +(-0.626728 + 0.525888i) q^{95} +(0.779817 - 0.283830i) q^{97} +(5.65040 - 3.72140i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 204 q + 12 q^{7} - 12 q^{9} + 12 q^{15} - 6 q^{17} + 12 q^{23} - 12 q^{25} + 12 q^{31} + 12 q^{39} - 24 q^{41} + 12 q^{47} - 12 q^{49} + 24 q^{55} - 30 q^{57} + 72 q^{63} - 12 q^{65} + 90 q^{71} - 6 q^{73}+ \cdots - 12 q^{97}+O(q^{100}) \) 204 * q + 12 * q^7 - 12 * q^9 + 12 * q^15 - 6 * q^17 + 12 * q^23 - 12 * q^25 + 12 * q^31 + 12 * q^39 - 24 * q^41 + 12 * q^47 - 12 * q^49 + 24 * q^55 - 30 * q^57 + 72 * q^63 - 12 * q^65 + 90 * q^71 - 6 * q^73 + 12 * q^79 - 12 * q^81 + 48 * q^87 - 6 * q^89 + 42 * q^95 - 12 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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