LMFDB - Embedded newform 648.2.t.a.613.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [648,2,Mod(37,648)] 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("648.37"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(648, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([0, 9, 14])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 648 = 2^{3} \cdot 3^{4} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	648.t (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:	$5.17430605098$
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			613.6
Character	$\chi$	$=$	648.613
Dual form			648.2.t.a.37.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.21270 - 0.727574i) q^{2} +(0.941271 + 1.76466i) q^{4} +(0.0465753 - 0.127965i) q^{5} +(-0.252128 + 1.42989i) q^{7} +(0.142441 - 2.82484i) q^{8} +(-0.149586 + 0.121295i) q^{10} +(0.771344 + 2.11925i) q^{11} +(0.634290 + 0.755917i) q^{13} +(1.34611 - 1.55058i) q^{14} +(-2.22802 + 3.32204i) q^{16} +(0.439205 + 0.760726i) q^{17} +(-5.20298 - 3.00394i) q^{19} +(0.269654 - 0.0382600i) q^{20} +(0.606505 - 3.13122i) q^{22} +(0.748645 + 4.24578i) q^{23} +(3.81602 + 3.20202i) q^{25} +(-0.219216 - 1.37819i) q^{26} +(-2.76058 + 0.900994i) q^{28} +(0.146501 - 0.174594i) q^{29} +(1.15687 + 6.56095i) q^{31} +(5.11894 - 2.40758i) q^{32} +(0.0208614 - 1.24208i) q^{34} +(0.171232 + 0.0988610i) q^{35} +(-9.25201 + 5.34165i) q^{37} +(4.12405 + 7.42842i) q^{38} +(-0.354845 - 0.149795i) q^{40} +(1.19321 - 1.00123i) q^{41} +(-1.11062 - 3.05141i) q^{43} +(-3.01370 + 3.35595i) q^{44} +(2.18124 - 5.69354i) q^{46} +(-1.36645 + 7.74952i) q^{47} +(4.59683 + 1.67311i) q^{49} +(-2.29797 - 6.65952i) q^{50} +(-0.736895 + 1.83083i) q^{52} -5.08895i q^{53} +0.307115 q^{55} +(4.00329 + 0.915895i) q^{56} +(-0.304692 + 0.105139i) q^{58} +(-3.15956 + 8.68082i) q^{59} +(12.3724 + 2.18158i) q^{61} +(3.37064 - 8.79816i) q^{62} +(-7.95942 - 0.804744i) q^{64} +(0.126273 - 0.0459596i) q^{65} +(5.90023 + 7.03162i) q^{67} +(-0.929007 + 1.49109i) q^{68} +(-0.135724 - 0.244473i) q^{70} +(5.93006 + 10.2712i) q^{71} +(4.88366 - 8.45874i) q^{73} +(15.1063 + 0.253718i) q^{74} +(0.403507 - 12.0090i) q^{76} +(-3.22477 + 0.568614i) q^{77} +(5.49238 + 4.60866i) q^{79} +(0.321333 + 0.439832i) q^{80} +(-2.17548 + 0.346032i) q^{82} +(-0.867764 + 1.03416i) q^{83} +(0.117802 - 0.0207717i) q^{85} +(-0.873278 + 4.50850i) q^{86} +(6.09641 - 1.87706i) q^{88} +(3.19969 - 5.54203i) q^{89} +(-1.24080 + 0.716376i) q^{91} +(-6.78766 + 5.31753i) q^{92} +(7.29544 - 8.40363i) q^{94} +(-0.626728 + 0.525888i) q^{95} +(0.779817 - 0.283830i) q^{97} +(-4.35726 - 5.37352i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 204 q + 6 q^{2} - 6 q^{4} - 12 q^{7} + 3 q^{8} - 3 q^{10} + 21 q^{14} - 6 q^{16} + 6 q^{17} - 15 q^{20} - 6 q^{22} + 12 q^{23} - 12 q^{25} + 30 q^{26} - 12 q^{28} - 12 q^{31} + 36 q^{32} + 42 q^{38} - 21 q^{40}+ \cdots - 54 q^{98}+O(q^{100}) $ 204 * q + 6 * q^2 - 6 * q^4 - 12 * q^7 + 3 * q^8 - 3 * q^10 + 21 * q^14 - 6 * q^16 + 6 * q^17 - 15 * q^20 - 6 * q^22 + 12 * q^23 - 12 * q^25 + 30 * q^26 - 12 * q^28 - 12 * q^31 + 36 * q^32 + 42 * q^38 - 21 * q^40 + 24 * q^41 - 21 * q^44 - 3 * q^46 + 12 * q^47 - 12 * q^49 + 99 * q^50 - 33 * q^52 - 24 * q^55 - 99 * q^56 + 21 * q^58 + 36 * q^62 - 3 * q^64 + 12 * q^65 - 75 * q^68 + 9 * q^70 + 90 * q^71 - 6 * q^73 - 9 * q^74 - 18 * q^76 - 12 * q^79 - 78 * q^80 - 12 * q^82 + 30 * q^86 - 30 * q^88 + 6 * q^89 - 111 * q^92 - 33 * q^94 + 42 * q^95 - 12 * q^97 - 54 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/648\mathbb{Z}\right)^\times$.

$n$	$325$	$487$	$569$
$\chi(n)$	$-1$	$1$	$e\left(\frac{2}{9}\right)$

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 $

$2$	−1.21270	−	0.727574i	−0.857507	−	0.514473i
$2$	−1.21270	−	0.727574i	−0.857507	−	0.514473i
$3$		0			0
$3$		0			0
$4$	0.941271	+	1.76466i	0.470636	+	0.882328i
$5$	0.0465753	−	0.127965i	0.0208291	−	0.0572275i	−0.928842	−	0.370475i	$-0.879195\pi$
$5$	0.0465753	−	0.127965i	0.0208291	−	0.0572275i	0.949671	+	0.313248i	$0.101417\pi$
$6$		0			0
$7$	−0.252128	+	1.42989i	−0.0952954	+	0.540447i	0.899361	+	0.437207i	$0.144032\pi$
$7$	−0.252128	+	1.42989i	−0.0952954	+	0.540447i	−0.994656	+	0.103240i	$0.967079\pi$
$8$	0.142441	−	2.82484i	0.0503604	−	0.998731i
$9$		0			0
$10$	−0.149586	+	0.121295i	−0.0473031	+	0.0383570i
$11$	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	$0.734083\pi$
$14$	1.34611	−	1.55058i	0.359762	−	0.414410i
$15$		0			0
$16$	−2.22802	+	3.32204i	−0.557004	+	0.830510i
$17$	0.439205	+	0.760726i	0.106523	+	0.184503i	0.914359	−	0.404904i	$-0.132695\pi$
$17$	0.439205	+	0.760726i	0.106523	+	0.184503i	−0.807836	+	0.589407i	$0.799362\pi$
$18$		0			0
$19$	−5.20298	−	3.00394i	−1.19364	−	0.689151i	−0.234513	−	0.972113i	$-0.575350\pi$
$19$	−5.20298	−	3.00394i	−1.19364	−	0.689151i	−0.959131	+	0.282962i	$0.908683\pi$
$20$	0.269654	−	0.0382600i	0.0602964	−	0.00855521i
$21$		0			0
$22$	0.606505	−	3.13122i	0.129307	−	0.667579i
$23$	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
$26$	−0.219216	−	1.37819i	−0.0429918	−	0.270286i
$27$		0			0
$28$	−2.76058	+	0.900994i	−0.521701	+	0.170272i
$29$	0.146501	−	0.174594i	0.0272046	−	0.0324212i	−0.752271	−	0.658854i	$-0.771041\pi$
$29$	0.146501	−	0.174594i	0.0272046	−	0.0324212i	0.779475	+	0.626433i	$0.215486\pi$
$30$		0			0
$31$	1.15687	+	6.56095i	0.207781	+	1.17838i	0.893004	+	0.450049i	$0.148593\pi$
$31$	1.15687	+	6.56095i	0.207781	+	1.17838i	−0.685223	+	0.728333i	$0.740295\pi$
$32$	5.11894	−	2.40758i	0.904909	−	0.425604i
$33$		0			0
$34$	0.0208614	−	1.24208i	0.00357770	−	0.213016i
$35$	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	$0.992103\pi$
$38$	4.12405	+	7.42842i	0.669009	+	1.20505i
$39$		0			0
$40$	−0.354845	−	0.149795i	−0.0561060	−	0.0236847i
$41$	1.19321	−	1.00123i	0.186349	−	0.156365i	−0.544841	−	0.838540i	$-0.683410\pi$
$41$	1.19321	−	1.00123i	0.186349	−	0.156365i	0.731190	+	0.682174i	$0.238965\pi$
$42$		0			0
$43$	−1.11062	−	3.05141i	−0.169368	−	0.465335i	0.825749	−	0.564038i	$-0.190753\pi$
$43$	−1.11062	−	3.05141i	−0.169368	−	0.465335i	−0.995117	+	0.0987027i	$0.968531\pi$
$44$	−3.01370	+	3.35595i	−0.454333	+	0.505928i
$45$		0			0
$46$	2.18124	−	5.69354i	0.321606	−	0.839467i
$47$	−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
$50$	−2.29797	−	6.65952i	−0.324982	−	0.941798i
$51$		0			0
$52$	−0.736895	+	1.83083i	−0.102189	+	0.253890i
$53$		−	5.08895i		−	0.699021i	−0.936932	−	0.349510i	$-0.886348\pi$
$53$		−	5.08895i		−	0.699021i	0.936932	−	0.349510i	$-0.113652\pi$
$54$		0			0
$55$	0.307115			0.0414114
$56$	4.00329	+	0.915895i	0.534962	+	0.122392i
$57$		0			0
$58$	−0.304692	+	0.105139i	−0.0400080	+	0.0138054i
$59$	−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	$0.258108\pi$
$62$	3.37064	−	8.79816i	0.428072	−	1.11737i
$63$		0			0
$64$	−7.95942	−	0.804744i	−0.994928	−	0.100593i
$65$	0.126273	−	0.0459596i	0.0156622	−	0.00570059i
$66$		0			0
$67$	5.90023	+	7.03162i	0.720828	+	0.859049i	0.994711	−	0.102714i	$-0.0327526\pi$
$67$	5.90023	+	7.03162i	0.720828	+	0.859049i	−0.273883	+	0.961763i	$0.588308\pi$
$68$	−0.929007	+	1.49109i	−0.112659	+	0.180822i
$69$		0			0
$70$	−0.135724	−	0.244473i	−0.0162222	−	0.0292201i
$71$	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	$-0.0270061\pi$
$74$	15.1063	+	0.253718i	1.75608	+	0.0294941i
$75$		0			0
$76$	0.403507	−	12.0090i	0.0462854	−	1.37752i
$77$	−3.22477	+	0.568614i	−0.367497	+	0.0647996i
$78$		0			0
$79$	5.49238	+	4.60866i	0.617941	+	0.518514i	0.897156	−	0.441714i	$-0.145630\pi$
$79$	5.49238	+	4.60866i	0.617941	+	0.518514i	−0.279214	+	0.960229i	$0.590074\pi$
$80$	0.321333	+	0.439832i	0.0359261	+	0.0491748i
$81$		0			0
$82$	−2.17548	+	0.346032i	−0.240241	+	0.0382129i
$83$	−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
$86$	−0.873278	+	4.50850i	−0.0941680	+	0.486164i
$87$		0			0
$88$	6.09641	−	1.87706i	0.649880	−	0.200095i
$89$	3.19969	−	5.54203i	0.339167	−	0.587454i	−0.645110	−	0.764090i	$-0.723188\pi$
$89$	3.19969	−	5.54203i	0.339167	−	0.587454i	0.984276	+	0.176636i	$0.0565216\pi$
$90$		0			0
$91$	−1.24080	+	0.716376i	−0.130071	+	0.0750966i
$92$	−6.78766	+	5.31753i	−0.707662	+	0.554391i
$93$		0			0
$94$	7.29544	−	8.40363i	0.752467	−	0.866768i
$95$	−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	$0.375475\pi$
$98$	−4.35726	−	5.37352i	−0.440149	−	0.542807i
$99$		0			0
$100$	−2.05855	+	9.74792i	−0.205855	+	0.974792i
$101$	−7.06509	−	1.24577i	−0.703003	−	0.123958i	−0.189291	−	0.981921i	$-0.560619\pi$
$101$	−7.06509	−	1.24577i	−0.703003	−	0.123958i	−0.513712	+	0.857963i	$0.671730\pi$
$102$		0			0
$103$	−7.48465	−	2.72419i	−0.737484	−	0.268422i	−0.0541548	−	0.998533i	$-0.517246\pi$
$103$	−7.48465	−	2.72419i	−0.737484	−	0.268422i	−0.683329	+	0.730110i	$0.739469\pi$
$104$	2.22569	−	1.68409i	0.218247	−	0.165139i
$105$		0			0
$106$	−3.70259	+	6.17136i	−0.359627	+	0.599415i
$107$		−	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	$0.914131\pi$
$110$	−0.372438	−	0.223449i	−0.0355105	−	0.0213050i
$111$		0			0
$112$	−4.18840	−	4.02340i	−0.395767	−	0.380175i
$113$	−11.5278	−	4.19578i	−1.08445	−	0.394706i	−0.262885	−	0.964827i	$-0.584674\pi$
$113$	−11.5278	−	4.19578i	−1.08445	−	0.394706i	−0.821561	+	0.570121i	$0.806896\pi$
$114$		0			0
$115$	0.578178	+	0.101948i	0.0539154	+	0.00950674i
$116$	0.445995	+	0.0941846i	0.0414096	+	0.00874482i
$117$		0			0
$118$	10.1475	−	8.22840i	0.934157	−	0.757486i
$119$	−1.19849	+	0.436214i	−0.109865	+	0.0399877i
$120$		0			0
$121$	4.53023	−	3.80132i	0.411840	−	0.345574i
$122$	−13.4167	−	11.6474i	−1.21469	−	1.05451i
$123$		0			0
$124$	−10.4889	+	8.21712i	−0.941930	+	0.737919i
$125$	1.17714	−	0.679623i	0.105287	−	0.0607873i
$126$		0			0
$127$	−4.15115	+	7.19001i	−0.368355	+	0.638010i	−0.989309	−	0.145838i	$-0.953412\pi$
$127$	−4.15115	+	7.19001i	−0.368355	+	0.638010i	0.620953	+	0.783848i	$0.286746\pi$
$128$	9.06686	+	6.76698i	0.801405	+	0.598122i
$129$		0			0
$130$	−0.186570	−	0.0361379i	−0.0163633	−	0.00316950i
$131$	−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
$134$	−2.03917	−	12.8201i	−0.176157	−	1.10749i
$135$		0			0
$136$	2.21149	−	1.13233i	0.189633	−	0.0970961i
$137$	−6.20446	−	5.20616i	−0.530083	−	0.444792i	0.338047	−	0.941129i	$-0.390234\pi$
$137$	−6.20446	−	5.20616i	−0.530083	−	0.444792i	−0.868130	+	0.496337i	$0.834678\pi$
$138$		0			0
$139$	3.76315	−	0.663545i	0.319186	−	0.0562811i	−0.0117598	−	0.999931i	$-0.503743\pi$
$139$	3.76315	−	0.663545i	0.319186	−	0.0562811i	0.330946	+	0.943650i	$0.392632\pi$
$140$	−0.0132796	+	0.395221i	−0.00112233	+	0.0334023i
$141$		0			0
$142$	0.281666	−	16.7704i	0.0236369	−	1.40734i
$143$	−1.11272	+	1.92729i	−0.0930505	+	0.161168i
$144$		0			0
$145$	−0.0155185	−	0.0268788i	−0.00128874	−	0.00223216i
$146$	−12.0768	+	6.70467i	−0.999480	+	0.554883i
$147$		0			0
$148$	−18.1348	−	11.2987i	−1.49067	−	0.928745i
$149$	14.3501	+	17.1018i	1.17561	+	1.40104i	0.897802	+	0.440400i	$0.145163\pi$
$149$	14.3501	+	17.1018i	1.17561	+	1.40104i	0.277807	+	0.960637i	$0.410392\pi$
$150$		0			0
$151$	−17.9058	+	6.51719i	−1.45716	+	0.530362i	−0.944581	−	0.328280i	$-0.893531\pi$
$151$	−17.9058	+	6.51719i	−1.45716	+	0.530362i	−0.512576	+	0.858642i	$0.671309\pi$
$152$	−9.22676	+	14.2697i	−0.748389	+	1.15742i
$153$		0			0
$154$	4.32438	+	1.65670i	0.348469	+	0.133501i
$155$	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	$-0.000263081\pi$
$158$	−3.30746	−	9.58503i	−0.263127	−	0.762544i
$159$		0			0
$160$	−0.0696688	−	0.767177i	−0.00550780	−	0.0606507i
$161$	−6.25975			−0.493337
$162$		0			0
$163$		−	10.0518i		−	0.787315i	−0.919257	−	0.393657i	$-0.871210\pi$
$163$		−	10.0518i		−	0.787315i	0.919257	−	0.393657i	$-0.128790\pi$
$164$	2.88996	+	1.16319i	0.225668	+	0.0908297i
$165$		0			0
$166$	1.80476	−	0.622761i	0.140077	−	0.0483357i
$167$	−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
$170$	−0.157971	−	0.0605200i	−0.0121158	−	0.00464167i
$171$		0			0
$172$	4.33929	−	4.83207i	0.330868	−	0.368442i
$173$	−6.92421	−	19.0241i	−0.526438	−	1.44638i	−0.863236	−	0.504800i	$-0.831566\pi$
$173$	−6.92421	−	19.0241i	−0.526438	−	1.44638i	0.336798	−	0.941577i	$-0.390656\pi$
$174$		0			0
$175$	−5.54065	+	4.64916i	−0.418834	+	0.351444i
$176$	−8.75880	−	2.15929i	−0.660220	−	0.162763i
$177$		0			0
$178$	−7.91250	+	4.39279i	−0.593067	+	0.329254i
$179$	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	$0.893828\pi$
$182$	2.02593	+	0.0340265i	0.150172	+	0.00252221i
$183$		0			0
$184$	12.1003	−	1.51003i	0.892044	−	0.111321i
$185$	0.252627	+	1.43272i	0.0185735	+	0.105336i
$186$		0			0
$187$	−1.27339	+	1.51757i	−0.0931195	+	0.110976i
$188$	−14.9614	+	4.88309i	−1.09117	+	0.356136i
$189$		0			0
$190$	1.14265	−	0.181751i	0.0828969	−	0.0131856i
$191$	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	$-0.141449\pi$
$194$	−1.15219	−	0.223175i	−0.0827224	−	0.0160230i
$195$		0			0
$196$	1.37440	+	9.68668i	0.0981717	+	0.691906i
$197$	15.7746	+	9.10747i	1.12389	+	0.648881i	0.942392	−	0.334510i	$-0.108571\pi$
$197$	15.7746	+	9.10747i	1.12389	+	0.648881i	0.181502	+	0.983391i	$0.441904\pi$
$198$		0			0
$199$	−8.05228	−	13.9470i	−0.570811	−	0.988674i	−0.996483	−	0.0837964i	$-0.973295\pi$
$199$	−8.05228	−	13.9470i	−0.570811	−	0.988674i	0.425672	−	0.904878i	$-0.360038\pi$
$200$	9.58874	−	10.3235i	0.678026	−	0.729984i
$201$		0			0
$202$	7.66144	+	6.65112i	0.539057	+	0.467971i
$203$	0.212712	+	0.253501i	0.0149295	+	0.0177923i
$204$		0			0
$205$	−0.0725472	−	0.199322i	−0.00506692	−	0.0139212i
$206$	7.09456	+	8.74925i	0.494302	+	0.609589i
$207$		0			0
$208$	−3.92439	+	0.422939i	−0.272108	+	0.0293255i
$209$	2.35282	−	13.3435i	0.162748	−	0.922988i
$210$		0			0
$211$	−6.47874	+	17.8002i	−0.446015	+	1.22542i	0.489461	+	0.872025i	$0.337193\pi$
$211$	−6.47874	+	17.8002i	−0.446015	+	1.22542i	−0.935476	+	0.353390i	$0.885029\pi$
$212$	8.98024	−	4.79008i	0.616765	−	0.328984i
$213$		0			0
$214$	−14.2053	+	23.6770i	−0.971057	+	1.61853i
$215$	−0.442200			−0.0301578
$216$		0			0
$217$	−9.67311			−0.656654
$218$	4.04881	−	6.74842i	0.274220	−	0.457061i
$219$		0			0
$220$	0.289078	+	0.541952i	0.0194897	+	0.0365384i
$221$	−0.296462	+	0.814523i	−0.0199422	+	0.0547908i
$222$		0			0
$223$	2.02862	−	11.5049i	0.135847	−	0.770424i	−0.838420	−	0.545025i	$-0.816520\pi$
$223$	2.02862	−	11.5049i	0.135847	−	0.770424i	0.974267	−	0.225399i	$-0.0723686\pi$
$224$	2.15194	+	7.92654i	0.143783	+	0.529614i
$225$		0			0
$226$	10.9270	+	13.4756i	0.726854	+	0.896381i
$227$	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	$0.910640\pi$
$230$	−0.626980	−	0.544300i	−0.0413418	−	0.0358901i
$231$		0			0
$232$	−0.472331	−	0.438712i	−0.0310100	−	0.0288029i
$233$	0.421533	+	0.730116i	0.0276155	+	0.0478315i	0.879503	−	0.475894i	$-0.157875\pi$
$233$	0.421533	+	0.730116i	0.0276155	+	0.0478315i	−0.851887	+	0.523725i	$0.824542\pi$
$234$		0			0
$235$	0.928021	+	0.535793i	0.0605374	+	0.0349513i
$236$	−18.2927	+	2.59547i	−1.19075	+	0.168951i
$237$		0			0
$238$	1.77078	+	0.342994i	0.114783	+	0.0222330i
$239$	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	$0.629152\pi$
$242$	−8.25955	+	1.31377i	−0.530944	+	0.0844522i
$243$		0			0
$244$	7.79601	+	23.8864i	0.499088	+	1.52917i
$245$	0.428198	−	0.510307i	0.0273566	−	0.0326023i
$246$		0			0
$247$	−1.02947	−	5.83839i	−0.0655033	−	0.371488i
$248$	18.6984	−	2.33343i	1.18735	−	0.148173i
$249$		0			0
$250$	−1.92199	−	0.0322808i	−0.121558	−	0.00204162i
$251$	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
$254$	10.2654	−	5.69903i	0.644106	−	0.357589i
$255$		0			0
$256$	−6.07188	−	14.8031i	−0.379492	−	0.925195i
$257$	12.7573	−	10.7046i	0.795777	−	0.667736i	−0.151391	−	0.988474i	$-0.548375\pi$
$257$	12.7573	−	10.7046i	0.795777	−	0.667736i	0.947168	+	0.320738i	$0.103931\pi$
$258$		0			0
$259$	−5.30528	−	14.5761i	−0.329654	−	0.905717i
$260$	0.199960	+	0.179568i	0.0124010	+	0.0111363i
$261$		0			0
$262$	21.8983	+	8.38939i	1.35288	+	0.518298i
$263$	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
$266$	−11.6616	+	4.02402i	−0.715019	+	0.246728i
$267$		0			0
$268$	−6.85467	+	17.0305i	−0.418716	+	1.04031i
$269$			25.3167i			1.54359i	0.635873	+	0.771793i	$0.280640\pi$
$269$			25.3167i			1.54359i	−0.635873	+	0.771793i	$0.719360\pi$
$270$		0			0
$271$	16.6229			1.00977			0.504884	−	0.863187i	$-0.331535\pi$
$271$	16.6229			1.00977			0.504884	+	0.863187i	$0.331535\pi$
$272$	−3.50572	−	0.235853i	−0.212565	−	0.0143007i
$273$		0			0
$274$	3.73627	+	10.8277i	0.225716	+	0.654126i
$275$	−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	$0.376772\pi$
$278$	−5.04634	−	1.93329i	−0.302659	−	0.115951i
$279$		0			0
$280$	0.303657	−	0.469622i	0.0181470	−	0.0280653i
$281$	15.3990	−	5.60477i	0.918626	−	0.334352i	0.160934	−	0.986965i	$-0.448549\pi$
$281$	15.3990	−	5.60477i	0.918626	−	0.334352i	0.757692	+	0.652613i	$0.226327\pi$
$282$		0			0
$283$	11.8313	+	14.0999i	0.703295	+	0.838154i	0.992895	−	0.118993i	$-0.0379667\pi$
$283$	11.8313	+	14.0999i	0.703295	+	0.838154i	−0.289600	+	0.957148i	$0.593522\pi$
$284$	−12.5433	+	20.1325i	−0.744306	+	1.19464i
$285$		0			0
$286$	2.75164	−	1.52763i	0.162708	−	0.0903309i
$287$	1.13080	+	1.95860i	0.0667490	+	0.115613i
$288$		0			0
$289$	8.11420	−	14.0542i	0.477306	−	0.826718i
$290$	−0.000737097		0.0438866i	−4.32838e−5		0.00257711i
$291$		0			0
$292$	19.5236	+	0.656002i	1.14253	+	0.0383896i
$293$	27.7186	−	4.88753i	1.61934	−	0.285533i	0.710818	−	0.703376i	$-0.248325\pi$
$293$	27.7186	−	4.88753i	1.61934	−	0.285533i	0.908519	+	0.417843i	$0.137214\pi$
$294$		0			0
$295$	0.963681	+	0.808624i	0.0561077	+	0.0470799i
$296$	13.7714	+	26.8963i	0.800449	+	1.56332i
$297$		0			0
$298$	−4.95953	−	31.1801i	−0.287298	−	1.80622i
$299$	−2.73460	+	3.25897i	−0.158146	+	0.188471i
$300$		0			0
$301$	4.64319	−	0.818720i	0.267629	−	0.0471903i
$302$	26.4561	+	5.12445i	1.52238	+	0.294879i
$303$		0			0
$304$	21.5715	−	10.5917i	1.23721	−	0.607473i
$305$	0.855412	−	1.48162i	0.0489808	−	0.0848372i
$306$		0			0
$307$	14.1955	−	8.19580i	0.810182	−	0.467759i	−0.0368369	−	0.999321i	$-0.511728\pi$
$307$	14.1955	−	8.19580i	0.810182	−	0.467759i	0.847019	+	0.531562i	$0.178395\pi$
$308$	−4.03879	−	5.15539i	−0.230132	−	0.293756i
$309$		0			0
$310$	−0.968865	−	0.841101i	−0.0550278	−	0.0477713i
$311$	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	$0.601685\pi$
$314$	−9.43630	+	7.65168i	−0.532521	+	0.431809i
$315$		0			0
$316$	−2.96287	+	14.0302i	−0.166674	+	0.789258i
$317$	−26.6872	−	4.70567i	−1.49890	−	0.264297i	−0.636799	−	0.771030i	$-0.719742\pi$
$317$	−26.6872	−	4.70567i	−1.49890	−	0.264297i	−0.862103	+	0.506733i	$0.830853\pi$
$318$		0			0
$319$	0.483011	+	0.175802i	0.0270434	+	0.00984300i
$320$	−0.473691	+	0.981043i	−0.0264802	+	0.0548420i
$321$		0			0
$322$	7.59118	+	4.55443i	0.423040	+	0.253809i
$323$		−	5.27738i		−	0.293641i
$324$		0			0
$325$			4.91560i			0.272668i
$326$	−7.31340	+	12.1897i	−0.405052	+	0.675128i
$327$		0			0
$328$	−2.65834	−	3.51325i	−0.146782	−	0.193987i
$329$	−10.7364	−	3.90774i	−0.591918	−	0.215441i
$330$		0			0
$331$	−14.1842	−	2.50105i	−0.779633	−	0.137470i	−0.230351	−	0.973108i	$-0.573987\pi$
$331$	−14.1842	−	2.50105i	−0.779633	−	0.137470i	−0.549282	+	0.835637i	$0.685099\pi$
$332$	−2.64174	−	0.557878i	−0.144984	−	0.0306176i
$333$		0			0
$334$	14.1675	+	17.4719i	0.775213	+	0.956018i
$335$	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	$0.420041\pi$
$338$	−11.1496	+	12.8432i	−0.606458	+	0.698580i
$339$		0			0
$340$	0.147539	+	0.188328i	0.00800140	+	0.0102135i
$341$	−13.0120	+	7.51246i	−0.704637	+	0.406822i
$342$		0			0
$343$	−8.63317	+	14.9531i	−0.466147	+	0.807391i
$344$	−8.77793	+	2.70268i	−0.473274	+	0.145719i
$345$		0			0
$346$	−5.44448	+	28.1084i	−0.292697	+	1.51112i
$347$	−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	$0.152516\pi$
$350$	10.1017	−	1.60679i	0.539961	−	0.0858865i
$351$		0			0
$352$	9.05073	+	8.99125i	0.482406	+	0.479235i
$353$	9.20716	+	7.72572i	0.490047	+	0.411199i	0.854043	−	0.520202i	$-0.174143\pi$
$353$	9.20716	+	7.72572i	0.490047	+	0.411199i	−0.363996	+	0.931401i	$0.618588\pi$
$354$		0			0
$355$	1.59054	−	0.280455i	0.0844171	−	0.0148850i
$356$	12.7915	+	0.429801i	0.677951	+	0.0227794i
$357$		0			0
$358$	−31.2406	−	0.524701i	−1.65112	−	0.0277313i
$359$	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
$362$	12.0905	+	21.7780i	0.635464	+	1.14463i
$363$		0			0
$364$	−2.43209	−	1.51528i	−0.127476	−	0.0794223i
$365$	−0.854962	−	1.01890i	−0.0447508	−	0.0533319i
$366$		0			0
$367$	15.1415	−	5.51105i	0.790380	−	0.287675i	0.0848857	−	0.996391i	$-0.472947\pi$
$367$	15.1415	−	5.51105i	0.790380	−	0.287675i	0.705494	+	0.708716i	$0.250725\pi$
$368$	−15.7726	−	6.97264i	−0.822205	−	0.363474i
$369$		0			0
$370$	0.736050	−	1.92126i	0.0382654	−	0.0998816i
$371$	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	$0.964327\pi$
$374$	2.64838	−	0.913864i	0.136944	−	0.0472548i
$375$		0			0
$376$	21.6965	+	4.96384i	1.11891	+	0.255991i
$377$	0.224903			0.0115831
$378$		0			0
$379$		−	12.8581i		−	0.660478i	−0.943897	−	0.330239i	$-0.892871\pi$
$379$		−	12.8581i		−	0.660478i	0.943897	−	0.330239i	$-0.107129\pi$
$380$	−1.51793	−	0.610957i	−0.0778683	−	0.0313414i
$381$		0			0
$382$	−4.33665	−	12.5676i	−0.221882	−	0.643015i
$383$	−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
$386$	−3.74743	+	9.78167i	−0.190739	+	0.497874i
$387$		0			0
$388$	1.23488	+	1.10895i	0.0626916	+	0.0562983i
$389$	−5.45591	−	14.9900i	−0.276625	−	0.760022i	−0.997739	−	0.0672055i	$-0.978592\pi$
$389$	−5.45591	−	14.9900i	−0.276625	−	0.760022i	0.721114	−	0.692817i	$-0.243631\pi$
$390$		0			0
$391$	−2.90106	+	2.43428i	−0.146713	+	0.123107i
$392$	5.38104	−	12.7470i	0.271784	−	0.643820i
$393$		0			0
$394$	−12.5035	−	22.5218i	−0.629916	−	1.13463i
$395$	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	$0.482196\pi$
$398$	−0.382468	+	22.7721i	−0.0191714	+	1.14146i
$399$		0			0
$400$	−19.1394	+	5.54280i	−0.956969	+	0.277140i
$401$	6.01001	+	34.0844i	0.300125	+	1.70210i	0.645607	+	0.763670i	$0.276605\pi$
$401$	6.01001	+	34.0844i	0.300125	+	1.70210i	−0.345481	+	0.938426i	$0.612284\pi$
$402$		0			0
$403$	−4.22574	+	5.03605i	−0.210499	+	0.250863i
$404$	−4.45182	−	13.6401i	−0.221486	−	0.678618i
$405$		0			0
$406$	−0.0735152	−	0.462184i	−0.00364850	−	0.0229378i
$407$	−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	$0.976275\pi$
$410$	−0.0570436	+	0.294501i	−0.00281718	+	0.0145443i
$411$		0			0
$412$	−2.23783	−	15.7720i	−0.110250	−	0.777032i
$413$	−11.6160	−	6.70650i	−0.571586	−	0.330005i
$414$		0			0
$415$	0.0919196	+	0.159209i	0.00451216	+	0.00781529i
$416$	5.06682	+	2.34239i	0.248421	+	0.114845i
$417$		0			0
$418$	−12.5616	+	14.4698i	−0.614410	+	0.707739i
$419$	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	$0.932776\pi$
$422$	20.8077	−	16.8725i	1.01290	−	0.821339i
$423$		0			0
$424$	−14.3755	−	0.724873i	−0.698134	−	0.0352030i
$425$	−0.759843	+	4.30928i	−0.0368578	+	0.209031i
$426$		0			0
$427$	−6.23884	+	17.1411i	−0.301919	+	0.829514i
$428$	34.4536	−	18.3776i	1.66538	−	0.888316i
$429$		0			0
$430$	0.536255	+	0.321733i	0.0258605	+	0.0155154i
$431$	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	$0.815070\pi$
$434$	11.7306	+	7.03791i	0.563085	+	0.337830i
$435$		0			0
$436$	−9.81996	+	5.23799i	−0.470291	+	0.250854i
$437$	8.85888	−	24.3396i	0.423778	−	1.16432i
$438$		0			0
$439$	3.29026	−	18.6600i	0.157036	−	0.890594i	−0.799865	−	0.600180i	$-0.795096\pi$
$439$	3.29026	−	18.6600i	0.157036	−	0.890594i	0.956901	−	0.290414i	$-0.0937931\pi$
$440$	0.0437456	−	0.867550i	0.00208549	−	0.0413588i
$441$		0			0
$442$	0.952145	−	0.772072i	0.0452889	−	0.0367237i
$443$	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
$446$	−10.8308	+	12.4760i	−0.512851	+	0.590754i
$447$		0			0
$448$	3.15749	−	11.1782i	0.149177	−	0.528120i
$449$	−2.07187	−	3.58859i	−0.0977777	−	0.169356i	0.812987	−	0.582282i	$-0.197840\pi$
$449$	−2.07187	−	3.58859i	−0.0977777	−	0.169356i	−0.910765	+	0.412926i	$0.864507\pi$
$450$		0			0
$451$	3.04223	+	1.75643i	0.143253	+	0.0827072i
$452$	−3.44669	−	24.2920i	−0.162119	−	1.14260i
$453$		0			0
$454$	0.487386	−	2.51624i	0.0228742	−	0.118093i
$455$	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	$0.608070\pi$
$458$	2.72563	+	17.1358i	0.127360	+	0.800703i
$459$		0			0
$460$	0.364319	+	1.11625i	0.0169864	+	0.0520452i
$461$	2.36115	−	2.81391i	0.109970	−	0.131057i	−0.708252	−	0.705960i	$-0.750516\pi$
$461$	2.36115	−	2.81391i	0.109970	−	0.131057i	0.818221	+	0.574903i	$0.194960\pi$
$462$		0			0
$463$	−1.02545	−	5.81561i	−0.0476566	−	0.270274i	0.951663	−	0.307143i	$-0.0993729\pi$
$463$	−1.02545	−	5.81561i	−0.0476566	−	0.270274i	−0.999320	+	0.0368684i	$0.988262\pi$
$464$	0.253599	+	0.875681i	0.0117730	+	0.0406525i
$465$		0			0
$466$	0.0200220	−	1.19211i	0.000927501	−	0.0552233i
$467$	−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
$470$	−0.735580	−	1.32496i	−0.0339298	−	0.0611159i
$471$		0			0
$472$	24.0719	+	10.1618i	1.10800	+	0.467733i
$473$	5.61003	−	4.70737i	0.257949	−	0.216445i
$474$		0			0
$475$	−10.2360	−	28.1231i	−0.469659	−	1.29038i
$476$	−1.89787	−	1.70432i	−0.0869888	−	0.0781176i
$477$		0			0
$478$	5.46596	−	14.2674i	0.250007	−	0.652577i
$479$	−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
$482$	−4.12841	−	11.9642i	−0.188044	−	0.544952i
$483$		0			0
$484$	10.9722	+	4.41623i	0.498736	+	0.200738i
$485$		−	0.113009i		−	0.00513145i
$486$		0			0
$487$	16.8387			0.763033			0.381517	−	0.924362i	$-0.375402\pi$
$487$	16.8387			0.763033			0.381517	+	0.924362i	$0.375402\pi$
$488$	7.92494	−	34.6392i	0.358745	−	1.56804i
$489$		0			0
$490$	−0.890561	+	0.307302i	−0.0402314	+	0.0138825i
$491$	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
$494$	−2.99943	+	7.82921i	−0.134951	+	0.352253i
$495$		0			0
$496$	−24.3733	−	10.7747i	−1.09439	−	0.483800i
$497$	−16.1818	+	5.88968i	−0.725851	+	0.264188i
$498$		0			0
$499$	5.09730	+	6.07473i	0.228187	+	0.271942i	0.867974	−	0.496610i	$-0.165422\pi$
$499$	5.09730	+	6.07473i	0.228187	+	0.271942i	−0.639787	+	0.768552i	$0.720978\pi$
$500$	2.30731	+	1.43754i	0.103186	+	0.0642887i
$501$		0			0
$502$	−5.14366	−	9.26499i	−0.229573	−	0.413517i
$503$	−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
$506$	13.7485	+	0.230913i	0.611197	+	0.0102653i
$507$		0			0
$508$	−16.5952	−	0.557607i	−0.736295	−	0.0247398i
$509$	1.32565	−	0.233747i	0.0587583	−	0.0103607i	−0.144192	−	0.989550i	$-0.546058\pi$
$509$	1.32565	−	0.233747i	0.0587583	−	0.0103607i	0.202950	+	0.979189i	$0.434947\pi$
$510$		0			0
$511$	10.8638	+	9.11578i	0.480584	+	0.403258i
$512$	−3.40702	+	22.3694i	−0.150570	+	0.988599i
$513$		0			0
$514$	−23.2591	+	3.69961i	−1.02592	+	0.163183i
$515$	−0.697200	+	0.830890i	−0.0307223	+	0.0366134i
$516$		0			0
$517$	−17.4772	+	3.08170i	−0.768645	+	0.135533i
$518$	−4.17152	+	21.5364i	−0.183286	+	0.946256i
$519$		0			0
$520$	−0.111842	−	0.363247i	−0.00490460	−	0.0159294i
$521$	−13.6363	+	23.6187i	−0.597416	+	1.03475i	0.395785	+	0.918343i	$0.370473\pi$
$521$	−13.6363	+	23.6187i	−0.597416	+	1.03475i	−0.993201	+	0.116412i	$0.962861\pi$
$522$		0			0
$523$	26.9016	−	15.5317i	1.17633	−	0.679152i	0.221164	−	0.975237i	$-0.429014\pi$
$523$	26.9016	−	15.5317i	1.17633	−	0.679152i	0.955162	+	0.296085i	$0.0956811\pi$
$524$	−20.4521	−	26.1064i	−0.893453	−	1.14046i
$525$		0			0
$526$	−17.1449	+	19.7493i	−0.747555	+	0.861109i
$527$	−4.48298	+	3.76167i	−0.195282	+	0.163861i
$528$		0			0
$529$	4.14676	−	1.50930i	0.180294	−	0.0656217i
$530$	0.617266	+	0.761233i	0.0268123	+	0.0330659i
$531$		0			0
$532$	17.0698	+	3.60477i	0.740069	+	0.156287i
$533$	1.51369	+	0.266904i	0.0655651	+	0.0115609i
$534$		0			0
$535$	−2.49841	−	0.909349i	−0.108016	−	0.0393146i
$536$	20.7036	−	15.6656i	0.894260	−	0.676651i
$537$		0			0
$538$	18.4198	−	30.7015i	0.794133	−	1.32364i
$539$			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	$0.856634\pi$
$542$	−20.1585	−	12.0944i	−0.865883	−	0.519498i
$543$		0			0
$544$	4.07977	+	2.83669i	0.174919	+	0.121622i
$545$	0.712098	+	0.259182i	0.0305029	+	0.0111022i
$546$		0			0
$547$	−13.5248	−	2.38478i	−0.578278	−	0.101966i	−0.123144	−	0.992389i	$-0.539298\pi$
$547$	−13.5248	−	2.38478i	−0.578278	−	0.101966i	−0.455134	+	0.890423i	$0.650409\pi$
$548$	3.34700	−	15.8491i	0.142977	−	0.677042i
$549$		0			0
$550$	12.3407	−	10.0068i	0.526208	−	0.426689i
$551$	−1.28671	+	0.468325i	−0.0548158	+	0.0199513i
$552$		0			0
$553$	−7.97465	+	6.69153i	−0.339117	+	0.284553i
$554$	−18.9327	−	16.4360i	−0.804372	−	0.698299i
$555$		0			0
$556$	4.71307	+	6.01609i	0.199879	+	0.255139i
$557$	−8.93296	+	5.15745i	−0.378502	+	0.218528i	−0.677166	−	0.735830i	$-0.736792\pi$
$557$	−8.93296	+	5.15745i	−0.378502	+	0.218528i	0.298665	+	0.954358i	$0.403459\pi$
$558$		0			0
$559$	1.60216	−	2.77502i	0.0677640	−	0.117371i
$560$	−0.709929	+	0.348576i	−0.0300000	+	0.0147300i
$561$		0			0
$562$	−22.7522	−	4.40701i	−0.959743	−	0.185898i
$563$	−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
$566$	−4.08898	−	25.7071i	−0.171873	−	1.08055i
$567$		0			0
$568$	29.8591	−	15.2884i	1.25286	−	0.641488i
$569$	7.37287	+	6.18657i	0.309087	+	0.259355i	0.784114	−	0.620616i	$-0.213118\pi$
$569$	7.37287	+	6.18657i	0.309087	+	0.259355i	−0.475028	+	0.879971i	$0.657562\pi$
$570$		0			0
$571$	6.25643	−	1.10318i	0.261823	−	0.0461665i	−0.0411954	−	0.999151i	$-0.513117\pi$
$571$	6.25643	−	1.10318i	0.261823	−	0.0461665i	0.303019	+	0.952985i	$0.402005\pi$
$572$	−4.44838	−	0.149467i	−0.185996	−	0.00624955i
$573$		0			0
$574$	0.0537108	−	3.19793i	0.00224185	−	0.133479i
$575$	−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	$0.588406\pi$
$578$	−20.0655	+	11.1398i	−0.834617	+	0.463355i
$579$		0			0
$580$	0.0328247	−	0.0526849i	0.00136297	−	0.00218762i
$581$	−1.25995	−	1.50155i	−0.0522714	−	0.0622947i
$582$		0			0
$583$	10.7848	−	3.92533i	0.446659	−	0.162571i
$584$	−23.1990	−	15.0004i	−0.959979	−	0.620722i
$585$		0			0
$586$	−37.1703	−	14.2402i	−1.53549	−	0.588258i
$587$	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
$590$	−0.580319	−	1.68177i	−0.0238914	−	0.0692372i
$591$		0			0
$592$	2.86847	−	42.6368i	0.117893	−	1.75236i
$593$	11.5506			0.474326			0.237163	−	0.971470i	$-0.423782\pi$
$593$	11.5506			0.474326			0.237163	+	0.971470i	$0.423782\pi$
$594$		0			0
$595$			0.173681i			0.00712023i
$596$	−16.6715	+	41.4205i	−0.682890	+	1.69665i
$597$		0			0
$598$	5.68738	−	1.96252i	0.232574	−	0.0802534i
$599$	−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	$0.996075\pi$
$602$	−6.22647	−	2.38541i	−0.253772	−	0.0972220i
$603$		0			0
$604$	−28.3549	−	25.4632i	−1.15374	−	1.03608i
$605$	−0.275437	−	0.756758i	−0.0111981	−	0.0307666i
$606$		0			0
$607$	22.8418	−	19.1665i	0.927119	−	0.777945i	−0.0481792	−	0.998839i	$-0.515342\pi$
$607$	22.8418	−	19.1665i	0.927119	−	0.777945i	0.975298	+	0.220894i	$0.0708974\pi$
$608$	−33.8660	−	2.85041i	−1.37345	−	0.115599i
$609$		0			0
$610$	−2.11534	+	1.17438i	−0.0856477	+	0.0475492i
$611$	−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	$0.651128\pi$
$614$	−23.1780	−	0.389285i	−0.935386	−	0.0157103i
$615$		0			0
$616$	1.14690	+	9.19045i	0.0462101	+	0.370294i
$617$	6.36070	+	36.0733i	0.256072	+	1.45226i	0.793305	+	0.608824i	$0.208359\pi$
$617$	6.36070	+	36.0733i	0.256072	+	1.45226i	−0.537233	+	0.843434i	$0.680530\pi$
$618$		0			0
$619$	−19.5701	+	23.3228i	−0.786590	+	0.937421i	−0.999211	−	0.0397133i	$-0.987356\pi$
$619$	−19.5701	+	23.3228i	−0.786590	+	0.937421i	0.212621	+	0.977135i	$0.431800\pi$
$620$	0.562977	+	1.72492i	0.0226097	+	0.0692745i
$621$		0			0
$622$	−42.9471	+	6.83119i	−1.72202	+	0.273906i
$623$	7.11775	+	5.97250i	0.285167	+	0.239283i
$624$		0			0
$625$	4.29296	+	24.3466i	0.171718	+	0.973864i
$626$	30.4501	+	5.89806i	1.21703	+	0.235734i
$627$		0			0
$628$	17.0105	−	2.41356i	0.678795	−	0.0963114i
$629$	−8.12706	−	4.69216i	−0.324047	−	0.187089i
$630$		0			0
$631$	−19.0463	−	32.9892i	−0.758221	−	1.31328i	−0.943757	−	0.330640i	$-0.892735\pi$
$631$	−19.0463	−	32.9892i	−0.758221	−	1.31328i	0.185536	−	0.982637i	$-0.440598\pi$
$632$	13.8011	−	14.8586i	0.548976	−	0.591045i
$633$		0			0
$634$	28.9398	+	25.1235i	1.14935	+	0.997781i
$635$	0.726725	+	0.866078i	0.0288392	+	0.0343692i
$636$		0			0
$637$	1.65099	+	4.53606i	0.0654147	+	0.179725i
$638$	−0.457837	−	0.564620i	−0.0181260	−	0.0223535i
$639$		0			0
$640$	1.28823	−	0.845063i	0.0509216	−	0.0334041i
$641$	−3.09962	+	17.5788i	−0.122427	+	0.694321i	0.860375	+	0.509661i	$0.170229\pi$
$641$	−3.09962	+	17.5788i	−0.122427	+	0.694321i	−0.982803	+	0.184659i	$0.940882\pi$
$642$		0			0
$643$	3.02218	−	8.30337i	0.119183	−	0.327453i	−0.865728	−	0.500515i	$-0.833144\pi$
$643$	3.02218	−	8.30337i	0.119183	−	0.327453i	0.984911	+	0.173062i	$0.0553662\pi$
$644$	−5.89212	−	11.0463i	−0.232182	−	0.435285i
$645$		0			0
$646$	−3.83969	+	6.39987i	−0.151071	+	0.251800i
$647$	−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
$650$	3.57646	−	5.96114i	0.140280	−	0.233815i
$651$		0			0
$652$	17.7379	−	9.46143i	0.694669	−	0.370538i
$653$	6.26659	−	17.2173i	0.245230	−	0.673765i	−0.754615	−	0.656168i	$-0.772176\pi$
$653$	6.26659	−	17.2173i	0.245230	−	0.673765i	0.999845	−	0.0175970i	$-0.00560160\pi$
$654$		0			0
$655$	−0.392110	+	2.22376i	−0.0153210	+	0.0868897i
$656$	0.667609	+	6.19466i	0.0260657	+	0.241861i
$657$		0			0
$658$	10.1769	+	12.5505i	0.396736	+	0.489268i
$659$	−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	$0.935871\pi$
$662$	15.3814	+	13.3531i	0.597816	+	0.518981i
$663$		0			0
$664$	2.79773	+	2.59860i	0.108573	+	0.100845i
$665$	−0.593945	−	1.02874i	−0.0230322	−	0.0398929i
$666$		0			0
$667$	0.850963	+	0.491304i	0.0329494	+	0.0190234i
$668$	−4.46884	−	31.4960i	−0.172905	−	1.21862i
$669$		0			0
$670$	−1.73549	−	0.336158i	−0.0670479	−	0.0129869i
$671$	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	$0.885980\pi$
$674$	22.1627	−	3.52521i	0.853675	−	0.135786i
$675$		0			0
$676$	22.8655	−	7.46280i	0.879442	−	0.287031i
$677$	−14.0009	+	16.6857i	−0.538100	+	0.641283i	−0.964761	−	0.263129i	$-0.915245\pi$
$677$	−14.0009	+	16.6857i	−0.538100	+	0.641283i	0.426660	+	0.904412i	$0.359690\pi$
$678$		0			0
$679$	0.209232	+	1.18661i	0.00802959	+	0.0455380i
$680$	−0.0418969	−	0.335731i	−0.00160667	−	0.0128747i
$681$		0			0
$682$	21.2454	+	0.356827i	0.813530	+	0.0136636i
$683$	−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
$686$	21.3489	−	11.8523i	0.815105	−	0.452523i
$687$		0			0
$688$	12.6114	+	3.10906i	0.480804	+	0.118532i
$689$	3.84682	−	3.22787i	0.146552	−	0.122972i
$690$		0			0
$691$	10.5292	+	28.9287i	0.400549	+	1.10050i	0.962014	+	0.273000i	$0.0880158\pi$
$691$	10.5292	+	28.9287i	0.400549	+	1.10050i	−0.561465	+	0.827501i	$0.689762\pi$
$692$	27.0534	−	30.1257i	1.02842	−	1.14521i
$693$		0			0
$694$	19.3482	+	7.41246i	0.734449	+	0.281373i
$695$	0.0903596	−	0.512455i	0.00342754	−	0.0194385i
$696$		0			0
$697$	1.28572	+	0.467965i	0.0487003	+	0.0177255i
$698$	−10.8512	+	3.74436i	−0.410723	+	0.141726i
$699$		0			0
$700$	−13.4194	−	5.40122i	−0.507207	−	0.204147i
$701$			41.7650i			1.57744i	0.614751	+	0.788722i	$0.289257\pi$
$701$			41.7650i			1.57744i	−0.614751	+	0.788722i	$0.710743\pi$
$702$		0			0
$703$	64.1840			2.42075
$704$	−4.43400	−	17.4887i	−0.167113	−	0.659132i
$705$		0			0
$706$	−5.54446	−	16.0679i	−0.208668	−	0.604722i
$707$	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	$0.482374\pi$
$710$	−2.13290	−	0.817129i	−0.0800462	−	0.0306663i
$711$		0			0
$712$	−15.1996	−	9.82802i	−0.569628	−	0.368321i
$713$	−26.9903	+	9.82365i	−1.01079	+	0.367899i
$714$		0			0
$715$	0.194800	+	0.232153i	0.00728510	+	0.00868205i
$716$	37.5037	+	23.3662i	1.40158	+	0.873236i
$717$		0			0
$718$	−15.6390	+	8.68230i	−0.583640	+	0.324020i
$719$	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
$722$	0.405981	−	24.1720i	0.0151090	−	0.899590i
$723$		0			0
$724$	1.18297	−	35.2069i	0.0439646	−	1.30845i
$725$	1.11810	−	0.197152i	0.0415253	−	0.00732204i
$726$		0			0
$727$	−13.7551	−	11.5419i	−0.510147	−	0.428065i	0.351034	−	0.936363i	$-0.385830\pi$
$727$	−13.7551	−	11.5419i	−0.510147	−	0.428065i	−0.861181	+	0.508298i	$0.830275\pi$
$728$	1.84691	+	3.60710i	0.0684509	+	0.133688i
$729$		0			0
$730$	0.295482	+	1.85767i	0.0109363	+	0.0687555i
$731$	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	$0.491877\pi$
$734$	−22.3718	−	4.33332i	−0.825757	−	0.159946i
$735$		0			0
$736$	14.0543	+	19.9315i	0.518049	+	0.734684i
$737$	−10.3507	+	17.9279i	−0.381272	+	0.660382i
$738$		0			0
$739$	6.23912	−	3.60216i	0.229510	−	0.132508i	−0.380836	−	0.924643i	$-0.624364\pi$
$739$	6.23912	−	3.60216i	0.229510	−	0.132508i	0.610346	+	0.792135i	$0.291030\pi$
$740$	−2.29047	+	1.79438i	−0.0841992	+	0.0659626i
$741$		0			0
$742$	−7.89083	−	6.85026i	−0.289681	−	0.251481i
$743$	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
$746$	18.8798	−	15.3092i	0.691238	−	0.560509i
$747$		0			0
$748$	−3.87659	−	0.818653i	−0.141742	−	0.0299329i
$749$	27.9175	+	4.92261i	1.02008	+	0.179868i
$750$		0			0
$751$	34.3650	+	12.5079i	1.25400	+	0.456418i	0.881751	−	0.471716i	$-0.156365\pi$
$751$	34.3650	+	12.5079i	1.25400	+	0.456418i	0.372247	+	0.928134i	$0.378587\pi$
$752$	−22.6997	−	21.8055i	−0.827774	−	0.795163i
$753$		0			0
$754$	−0.272739	−	0.163633i	−0.00993257	−	0.00595918i
$755$			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	$-0.230947\pi$
$758$	−9.35525	+	15.5930i	−0.339798	+	0.566365i
$759$		0			0
$760$	1.39628	+	1.84531i	0.0506482	+	0.0669366i
$761$	4.63196	+	1.68589i	0.167908	+	0.0611136i	0.424607	−	0.905378i	$-0.360412\pi$
$761$	4.63196	+	1.68589i	0.167908	+	0.0611136i	−0.256698	+	0.966492i	$0.582635\pi$
$762$		0			0
$763$	−7.95705	−	1.40304i	−0.288065	−	0.0507935i
$764$	−3.88483	+	18.3959i	−0.140548	+	0.665542i
$765$		0			0
$766$	4.39162	+	5.41589i	0.158676	+	0.195684i
$767$	−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	$-0.0660921\pi$
$770$	0.413409	−	0.476207i	0.0148982	−	0.0171613i
$771$		0			0
$772$	11.6614	−	9.13568i	0.419703	−	0.328800i
$773$	−8.17747	+	4.72126i	−0.294123	+	0.169812i	−0.639800	−	0.768542i	$-0.720983\pi$
$773$	−8.17747	+	4.72126i	−0.294123	+	0.169812i	0.345677	+	0.938354i	$0.387649\pi$
$774$		0			0
$775$	−16.5936	+	28.7410i	−0.596061	+	1.03241i
$776$	−0.690697	−	2.24329i	−0.0247946	−	0.0805293i
$777$		0			0
$778$	−4.28996	+	22.1479i	−0.153803	+	0.794040i
$779$	−9.21589	+	1.62501i	−0.330194	+	0.0582220i
$780$		0			0
$781$	−17.1931	+	20.4899i	−0.615216	+	0.733186i
$782$	5.28923	−	0.841308i	0.189143	−	0.0300851i
$783$		0			0
$784$	−15.8000	+	11.5431i	−0.564284	+	0.412255i
$785$	−0.896137	−	0.751949i	−0.0319845	−	0.0268382i
$786$		0			0
$787$	−15.6553	+	2.76045i	−0.558050	+	0.0983993i	−0.445558	−	0.895253i	$-0.646995\pi$
$787$	−15.6553	+	2.76045i	−0.558050	+	0.0983993i	−0.112493	+	0.993653i	$0.535883\pi$
$788$	−1.22337	+	36.4094i	−0.0435807	+	1.29703i
$789$		0			0
$790$	−1.38059	−	0.0231877i	−0.0491192	−	0.000824980i
$791$	8.90599	−	15.4256i	0.316661	−	0.548472i
$792$		0			0
$793$	6.19857	+	10.7362i	0.220118	+	0.381255i
$794$	−14.9802	−	26.9830i	−0.531627	−	0.957591i
$795$		0			0
$796$	17.0322	−	27.3374i	0.603690	−	0.968948i
$797$	−9.18613	−	10.9476i	−0.325389	−	0.387784i	0.578406	−	0.815749i	$-0.303675\pi$
$797$	−9.18613	−	10.9476i	−0.325389	−	0.387784i	−0.903795	+	0.427965i	$0.859231\pi$
$798$		0			0
$799$	−6.49541	+	2.36413i	−0.229791	+	0.0836371i
$800$	27.2431	+	7.20358i	0.963188	+	0.254685i
$801$		0			0
$802$	17.5106	−	45.7068i	0.618322	−	1.61396i
$803$	21.6932	+	3.82509i	0.765536	+	0.134985i
$804$		0			0
$805$	−0.291550	+	0.801026i	−0.0102758	+	0.0282325i
$806$	8.78865	−	3.03266i	0.309567	−	0.106821i
$807$		0			0
$808$	−4.52545	+	19.7803i	−0.159205	+	0.695869i
$809$	−2.71159			−0.0953343			−0.0476672	−	0.998863i	$-0.515179\pi$
$809$	−2.71159			−0.0953343			−0.0476672	+	0.998863i	$0.515179\pi$
$810$		0			0
$811$			38.7762i			1.36162i	0.732462	+	0.680808i	$0.238371\pi$
$811$			38.7762i			1.36162i	−0.732462	+	0.680808i	$0.761629\pi$
$812$	−0.247121	+	0.613977i	−0.00867226	+	0.0215464i
$813$		0			0
$814$	11.1145	+	32.2098i	0.389563	+	1.12895i
$815$	−1.28627	−	0.468164i	−0.0450561	−	0.0163991i
$816$		0			0
$817$	−3.38771	+	19.2126i	−0.118521	+	0.672165i
$818$	−2.04298	+	5.33266i	−0.0714312	+	0.186452i
$819$		0			0
$820$	0.283448	−	0.315637i	0.00989842	−	0.0110225i
$821$	12.6956	+	34.8810i	0.443081	+	1.21736i	0.937455	+	0.348106i	$0.113175\pi$
$821$	12.6956	+	34.8810i	0.443081	+	1.21736i	−0.494374	+	0.869249i	$0.664603\pi$
$822$		0			0
$823$	−16.3072	+	13.6834i	−0.568433	+	0.476972i	−0.881126	−	0.472882i	$-0.843214\pi$
$823$	−16.3072	+	13.6834i	−0.568433	+	0.476972i	0.312692	+	0.949854i	$0.398769\pi$
$824$	−8.76151	+	20.7549i	−0.305222	+	0.723030i
$825$		0			0
$826$	9.20722	+	16.5845i	0.320360	+	0.577047i
$827$	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	$0.538817\pi$
$830$	0.00436601	−	0.259951i	0.000151546	−	0.00902304i
$831$		0			0
$832$	−4.44026	−	6.52710i	−0.153938	−	0.226287i
$833$	0.746175	+	4.23177i	0.0258534	+	0.146622i
$834$		0			0
$835$	−1.39228	+	1.65925i	−0.0481817	+	0.0574207i
$836$	25.7613	−	8.40793i	0.890973	−	0.290794i
$837$		0			0
$838$	−2.41964	−	15.2121i	−0.0835852	−	0.525493i
$839$	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
$842$	−1.51677	+	7.83068i	−0.0522714	+	0.269863i
$843$		0			0
$844$	−37.5094	+	5.32206i	−1.29113	+	0.183193i
$845$	−1.41829	−	0.818851i	−0.0487907	−	0.0281693i
$846$		0			0
$847$	4.29326	+	7.43615i	0.147518	+	0.255509i
$848$	16.9057	+	11.3383i	0.580544	+	0.389358i
$849$		0			0
$850$	4.05678	−	4.67302i	0.139147	−	0.160283i
$851$	−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	$0.755486\pi$
$854$	20.0372	−	16.2477i	0.685660	−	0.555985i
$855$		0			0
$856$	−55.1529	−	2.78105i	−1.88509	−	0.0950542i
$857$	−4.07463	+	23.1084i	−0.139187	+	0.789367i	0.832666	+	0.553776i	$0.186814\pi$
$857$	−4.07463	+	23.1084i	−0.139187	+	0.789367i	−0.971852	+	0.235591i	$0.924297\pi$
$858$		0			0
$859$	11.7827	−	32.3728i	0.402022	−	1.10455i	−0.559264	−	0.828990i	$-0.688916\pi$
$859$	11.7827	−	32.3728i	0.402022	−	1.10455i	0.961285	−	0.275555i	$-0.0888618\pi$
$860$	−0.416230	−	0.780331i	−0.0141933	−	0.0266091i
$861$		0			0
$862$	−14.8716	−	8.92244i	−0.506530	−	0.303900i
$863$	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
$866$	42.1886	+	25.3116i	1.43363	+	0.860124i
$867$		0			0
$868$	−9.10502	−	17.0697i	−0.309045	−	0.579384i
$869$	−5.53038	+	15.1946i	−0.187605	+	0.515442i
$870$		0			0
$871$	−1.57287	+	8.92017i	−0.0532946	+	0.302248i
$872$	15.7197	+	0.792654i	0.532335	+	0.0268427i
$873$		0			0
$874$	−28.4520	+	23.0710i	−0.962403	+	0.780390i
$875$	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	$0.885599\pi$
$878$	−17.5666	+	20.2350i	−0.592845	+	0.682900i
$879$		0			0
$880$	−0.684257	+	1.02025i	−0.0230663	+	0.0343925i
$881$	0.970676	+	1.68126i	0.0327029	+	0.0566431i	0.881914	−	0.471411i	$-0.156255\pi$
$881$	0.970676	+	1.68126i	0.0327029	+	0.0566431i	−0.849211	+	0.528054i	$0.822922\pi$
$882$		0			0
$883$	3.58570	+	2.07021i	0.120669	+	0.0696680i	0.559119	−	0.829087i	$-0.311139\pi$
$883$	3.58570	+	2.07021i	0.120669	+	0.0696680i	−0.438451	+	0.898755i	$0.644473\pi$
$884$	−1.71640	+	0.243534i	−0.0577289	+	0.00819092i
$885$		0			0
$886$	6.74015	−	34.7976i	0.226440	−	1.16905i
$887$	−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
$890$	0.193595	+	1.21712i	0.00648932	+	0.0407978i
$891$		0			0
$892$	22.2116	−	7.24940i	0.743700	−	0.242728i
$893$	30.3887	−	36.2158i	1.01692	−	1.21192i
$894$		0			0
$895$	−0.522445	−	2.96293i	−0.0174634	−	0.0990399i
$896$	−11.9620	+	11.2585i	−0.399624	+	0.376119i
$897$		0			0
$898$	−0.0984100	+	5.85932i	−0.00328398	+	0.195528i
$899$	1.31498	+	0.759206i	0.0438572	+	0.0253209i
$900$		0			0
$901$	3.87129	−	2.23509i	0.128971	−	0.0744617i
$902$	−2.41137	−	4.34347i	−0.0802898	−	0.144622i
$903$		0			0
$904$	−13.4944	+	31.9666i	−0.448818	+	1.06319i
$905$	−1.83739	+	1.54175i	−0.0610768	+	0.0512495i
$906$		0			0
$907$	19.8264	+	54.4726i	0.658325	+	1.80873i	0.584393	+	0.811471i	$0.301333\pi$
$907$	19.8264	+	54.4726i	0.658325	+	1.80873i	0.0739328	+	0.997263i	$0.476445\pi$
$908$	−2.42181	+	2.69683i	−0.0803704	+	0.0894975i
$909$		0			0
$910$	0.0987126	−	0.257663i	0.00327229	−	0.00854144i
$911$	−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
$914$	−6.92245	−	20.0613i	−0.228974	−	0.663568i
$915$		0			0
$916$	9.16220	−	22.7636i	0.302728	−	0.752131i
$917$		−	24.0760i		−	0.795059i
$918$		0			0
$919$	−17.7731			−0.586281			−0.293140	−	0.956069i	$-0.594700\pi$
$919$	−17.7731			−0.586281			−0.293140	+	0.956069i	$0.594700\pi$
$920$	0.370344	−	1.61874i	0.0122099	−	0.0533682i
$921$		0			0
$922$	−4.91069	+	1.69451i	−0.161725	+	0.0558057i
$923$	−4.00277	+	10.9975i	−0.131753	+	0.361988i
$924$		0			0
$925$	−52.4099	−	9.24128i	−1.72323	−	0.303851i
$926$	−2.98773	+	7.79866i	−0.0981828	+	0.256280i
$927$		0			0
$928$	0.329584	−	1.24645i	0.0108191	−	0.0409167i
$929$	53.7456	−	19.5618i	1.76333	−	0.641801i	0.763344	−	0.645993i	$-0.223556\pi$
$929$	53.7456	−	19.5618i	1.76333	−	0.641801i	0.999991	+	0.00419109i	$0.00133407\pi$
$930$		0			0
$931$	−18.8913	−	22.5138i	−0.619137	−	0.737859i
$932$	−0.891627	+	1.43110i	−0.0292062	+	0.0468771i
$933$		0			0
$934$	3.79942	+	6.84369i	0.124321	+	0.223932i
$935$	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	$0.0188399\pi$
$938$	18.8454	+	0.316518i	0.615325	+	0.0103347i
$939$		0			0
$940$	−0.0719709	+	2.14197i	−0.00234743	+	0.0698632i
$941$	−47.0141	+	8.28985i	−1.53261	+	0.270241i	−0.875376	−	0.483442i	$-0.839386\pi$
$941$	−47.0141	+	8.28985i	−1.53261	+	0.270241i	−0.657238	+	0.753683i	$0.728275\pi$
$942$		0			0
$943$	5.14428	+	4.31656i	0.167521	+	0.140567i
$944$	−21.7985	−	29.8372i	−0.709480	−	0.971118i
$945$		0			0
$946$	−10.2282	+	1.62691i	−0.332549	+	0.0528953i
$947$	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
$950$	−8.04851	+	41.5523i	−0.261128	+	1.34813i
$951$		0			0
$952$	1.06152	+	3.44767i	0.0344041	+	0.111740i
$953$	17.4033	−	30.1434i	0.563749	−	0.976442i	−0.433416	−	0.901194i	$-0.642692\pi$
$953$	17.4033	−	30.1434i	0.563749	−	0.976442i	0.997165	−	0.0752476i	$-0.0239747\pi$
$954$		0			0
$955$	1.10867	−	0.640089i	0.0358756	−	0.0207128i
$956$	−17.0092	+	13.3252i	−0.550116	+	0.430967i
$957$		0			0
$958$	7.66301	−	8.82704i	0.247581	−	0.285189i
$959$	9.00855	−	7.55907i	0.290901	−	0.244095i
$960$		0			0
$961$	−12.5773	+	4.57775i	−0.405718	+	0.147669i
$962$	9.39001	+	11.5801i	0.302746	+	0.373357i
$963$		0			0
$964$	−3.69829	+	17.5126i	−0.119114	+	0.564044i
$965$	−0.993327	−	0.175150i	−0.0319763	−	0.00563829i
$966$		0			0
$967$	−7.31794	−	2.66351i	−0.235329	−	0.0856527i	0.221664	−	0.975123i	$-0.428851\pi$
$967$	−7.31794	−	2.66351i	−0.235329	−	0.0856527i	−0.456993	+	0.889470i	$0.651073\pi$
$968$	−10.0928	−	13.3386i	−0.324395	−	0.428720i
$969$		0			0
$970$	−0.0822221	+	0.137045i	−0.00263999	+	0.00440026i
$971$			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
$974$	−20.4202	−	12.2514i	−0.654306	−	0.392560i
$975$		0			0
$976$	−34.8131	+	36.2409i	−1.11434	+	1.16004i
$977$	−42.2729	−	15.3861i	−1.35243	−	0.492244i	−0.438725	−	0.898621i	$-0.644570\pi$
$977$	−42.2729	−	15.3861i	−1.35243	−	0.492244i	−0.913706	+	0.406377i	$0.866792\pi$
$978$		0			0
$979$	14.2130	+	2.50614i	0.454250	+	0.0800965i
$980$	1.30357	+	0.275285i	0.0416409	+	0.00879366i
$981$		0			0
$982$	−36.1289	+	29.2961i	−1.15292	+	0.934876i
$983$	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
$986$	−0.213804	−	0.185609i	−0.00680890	−	0.00591101i
$987$		0			0
$988$	9.33374	−	7.31216i	0.296946	−	0.232631i
$989$	12.1241	−	6.99988i	0.385525	−	0.222583i
$990$		0			0
$991$	−24.4431	+	42.3367i	−0.776462	+	1.34487i	0.157508	+	0.987518i	$0.449654\pi$
$991$	−24.4431	+	42.3367i	−0.776462	+	1.34487i	−0.933969	+	0.357353i	$0.883679\pi$
$992$	21.7180	+	30.7999i	0.689547	+	0.977897i
$993$		0			0
$994$	23.9088	+	4.63103i	0.758340	+	0.146887i
$995$	−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	$0.191993\pi$
$998$	−1.76167	−	11.0755i	−0.0557647	−	0.350588i
$999$		0			0

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
216.2.t.a.157.26	✓	204	27.5	odd	18
216.2.t.a.157.29	yes	204	216.5	odd	18
216.2.t.a.205.26	yes	204	24.5	odd	2
216.2.t.a.205.29	yes	204	3.2	odd	2
648.2.t.a.37.6		204	216.157	even	18	inner
648.2.t.a.37.9		204	27.22	even	9	inner
648.2.t.a.613.6		204	1.1	even	1	trivial
648.2.t.a.613.9		204	8.5	even	2	inner
864.2.bf.a.49.11		204	216.59	even	18
864.2.bf.a.49.24		204	108.59	even	18
864.2.bf.a.529.11		204	12.11	even	2
864.2.bf.a.529.24		204	24.11	even	2

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:	\( N \)	\(=\)	\( 648 = 2^{3} \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	648.t (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.21270 - 0.727574i) q^{2} +(0.941271 + 1.76466i) q^{4} +(0.0465753 - 0.127965i) q^{5} +(-0.252128 + 1.42989i) q^{7} +(0.142441 - 2.82484i) q^{8} +(-0.149586 + 0.121295i) q^{10} +(0.771344 + 2.11925i) q^{11} +(0.634290 + 0.755917i) q^{13} +(1.34611 - 1.55058i) q^{14} +(-2.22802 + 3.32204i) q^{16} +(0.439205 + 0.760726i) q^{17} +(-5.20298 - 3.00394i) q^{19} +(0.269654 - 0.0382600i) q^{20} +(0.606505 - 3.13122i) q^{22} +(0.748645 + 4.24578i) q^{23} +(3.81602 + 3.20202i) q^{25} +(-0.219216 - 1.37819i) q^{26} +(-2.76058 + 0.900994i) q^{28} +(0.146501 - 0.174594i) q^{29} +(1.15687 + 6.56095i) q^{31} +(5.11894 - 2.40758i) q^{32} +(0.0208614 - 1.24208i) q^{34} +(0.171232 + 0.0988610i) q^{35} +(-9.25201 + 5.34165i) q^{37} +(4.12405 + 7.42842i) q^{38} +(-0.354845 - 0.149795i) q^{40} +(1.19321 - 1.00123i) q^{41} +(-1.11062 - 3.05141i) q^{43} +(-3.01370 + 3.35595i) q^{44} +(2.18124 - 5.69354i) q^{46} +(-1.36645 + 7.74952i) q^{47} +(4.59683 + 1.67311i) q^{49} +(-2.29797 - 6.65952i) q^{50} +(-0.736895 + 1.83083i) q^{52} -5.08895i q^{53} +0.307115 q^{55} +(4.00329 + 0.915895i) q^{56} +(-0.304692 + 0.105139i) q^{58} +(-3.15956 + 8.68082i) q^{59} +(12.3724 + 2.18158i) q^{61} +(3.37064 - 8.79816i) q^{62} +(-7.95942 - 0.804744i) q^{64} +(0.126273 - 0.0459596i) q^{65} +(5.90023 + 7.03162i) q^{67} +(-0.929007 + 1.49109i) q^{68} +(-0.135724 - 0.244473i) q^{70} +(5.93006 + 10.2712i) q^{71} +(4.88366 - 8.45874i) q^{73} +(15.1063 + 0.253718i) q^{74} +(0.403507 - 12.0090i) q^{76} +(-3.22477 + 0.568614i) q^{77} +(5.49238 + 4.60866i) q^{79} +(0.321333 + 0.439832i) q^{80} +(-2.17548 + 0.346032i) q^{82} +(-0.867764 + 1.03416i) q^{83} +(0.117802 - 0.0207717i) q^{85} +(-0.873278 + 4.50850i) q^{86} +(6.09641 - 1.87706i) q^{88} +(3.19969 - 5.54203i) q^{89} +(-1.24080 + 0.716376i) q^{91} +(-6.78766 + 5.31753i) q^{92} +(7.29544 - 8.40363i) q^{94} +(-0.626728 + 0.525888i) q^{95} +(0.779817 - 0.283830i) q^{97} +(-4.35726 - 5.37352i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 204 q + 6 q^{2} - 6 q^{4} - 12 q^{7} + 3 q^{8} - 3 q^{10} + 21 q^{14} - 6 q^{16} + 6 q^{17} - 15 q^{20} - 6 q^{22} + 12 q^{23} - 12 q^{25} + 30 q^{26} - 12 q^{28} - 12 q^{31} + 36 q^{32} + 42 q^{38} - 21 q^{40}+ \cdots - 54 q^{98}+O(q^{100}) \) 204 * q + 6 * q^2 - 6 * q^4 - 12 * q^7 + 3 * q^8 - 3 * q^10 + 21 * q^14 - 6 * q^16 + 6 * q^17 - 15 * q^20 - 6 * q^22 + 12 * q^23 - 12 * q^25 + 30 * q^26 - 12 * q^28 - 12 * q^31 + 36 * q^32 + 42 * q^38 - 21 * q^40 + 24 * q^41 - 21 * q^44 - 3 * q^46 + 12 * q^47 - 12 * q^49 + 99 * q^50 - 33 * q^52 - 24 * q^55 - 99 * q^56 + 21 * q^58 + 36 * q^62 - 3 * q^64 + 12 * q^65 - 75 * q^68 + 9 * q^70 + 90 * q^71 - 6 * q^73 - 9 * q^74 - 18 * q^76 - 12 * q^79 - 78 * q^80 - 12 * q^82 + 30 * q^86 - 30 * q^88 + 6 * q^89 - 111 * q^92 - 33 * q^94 + 42 * q^95 - 12 * q^97 - 54 * q^98

Introduction

L-functions

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