LMFDB - Embedded newform 648.2.t.a.37.9

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			37.9
Character	$\chi$	$=$	648.37
Dual form			648.2.t.a.613.9

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.927104 + 1.06793i) q^{2} +(-0.280958 - 1.98017i) q^{4} +(-0.0465753 - 0.127965i) q^{5} +(-0.252128 - 1.42989i) q^{7} +(2.37516 + 1.53578i) q^{8} +(0.179838 + 0.0688972i) q^{10} +(-0.771344 + 2.11925i) q^{11} +(-0.634290 + 0.755917i) q^{13} +(1.76077 + 1.05640i) q^{14} +(-3.84213 + 1.11269i) q^{16} +(0.439205 - 0.760726i) q^{17} +(5.20298 - 3.00394i) q^{19} +(-0.240306 + 0.128180i) q^{20} +(-1.54810 - 2.78851i) q^{22} +(0.748645 - 4.24578i) q^{23} +(3.81602 - 3.20202i) q^{25} +(-0.219216 - 1.37819i) q^{26} +(-2.76058 + 0.900994i) q^{28} +(-0.146501 - 0.174594i) q^{29} +(1.15687 - 6.56095i) q^{31} +(2.37377 - 5.13471i) q^{32} +(0.405215 + 1.17431i) q^{34} +(-0.171232 + 0.0988610i) q^{35} +(9.25201 + 5.34165i) q^{37} +(-1.61569 + 8.34139i) q^{38} +(0.0859012 - 0.375466i) q^{40} +(1.19321 + 1.00123i) q^{41} +(1.11062 - 3.05141i) q^{43} +(4.41319 + 0.931971i) q^{44} +(3.84013 + 4.73578i) q^{46} +(-1.36645 - 7.74952i) q^{47} +(4.59683 - 1.67311i) q^{49} +(-0.118305 + 7.04385i) q^{50} +(1.67505 + 1.04362i) q^{52} -5.08895i q^{53} +0.307115 q^{55} +(1.59714 - 3.78343i) q^{56} +(0.322276 + 0.00541278i) q^{58} +(3.15956 + 8.68082i) q^{59} +(-12.3724 + 2.18158i) q^{61} +(5.93411 + 7.31814i) q^{62} +(3.28278 + 7.29543i) q^{64} +(0.126273 + 0.0459596i) q^{65} +(-5.90023 + 7.03162i) q^{67} +(-1.62976 - 0.655968i) q^{68} +(0.0531732 - 0.274519i) q^{70} +(5.93006 - 10.2712i) q^{71} +(4.88366 + 8.45874i) q^{73} +(-14.2821 + 4.92826i) q^{74} +(-7.41012 - 9.45878i) q^{76} +(3.22477 + 0.568614i) q^{77} +(5.49238 - 4.60866i) q^{79} +(0.321333 + 0.439832i) q^{80} +(-2.17548 + 0.346032i) q^{82} +(0.867764 + 1.03416i) q^{83} +(-0.117802 - 0.0207717i) q^{85} +(2.22904 + 4.01504i) q^{86} +(-5.08676 + 3.84895i) q^{88} +(3.19969 + 5.54203i) q^{89} +(1.24080 + 0.716376i) q^{91} +(-8.61769 - 0.289558i) q^{92} +(9.54280 + 5.72533i) q^{94} +(-0.626728 - 0.525888i) q^{95} +(0.779817 + 0.283830i) q^{97} +(-2.47497 + 6.46025i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/648\mathbb{Z}\right)^\times$.

$n$	$325$	$487$	$569$
$\chi(n)$	$-1$	$1$	$e\left(\frac{7}{9}\right)$

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 $

$2$	−0.927104	+	1.06793i	−0.655561	+	0.755142i
$2$	−0.927104	+	1.06793i	−0.655561	+	0.755142i
$3$		0			0
$3$		0			0
$4$	−0.280958	−	1.98017i	−0.140479	−	0.990084i
$5$	−0.0465753	−	0.127965i	−0.0208291	−	0.0572275i	0.928842	−	0.370475i	$-0.120805\pi$
$5$	−0.0465753	−	0.127965i	−0.0208291	−	0.0572275i	−0.949671	+	0.313248i	$0.898583\pi$
$6$		0			0
$7$	−0.252128	−	1.42989i	−0.0952954	−	0.540447i	−0.994656	−	0.103240i	$-0.967079\pi$
$7$	−0.252128	−	1.42989i	−0.0952954	−	0.540447i	0.899361	−	0.437207i	$-0.144032\pi$
$8$	2.37516	+	1.53578i	0.839746	+	0.542979i
$9$		0			0
$10$	0.179838	+	0.0688972i	0.0568697	+	0.0217872i
$11$	−0.771344	+	2.11925i	−0.232569	+	0.638978i	−0.999998	−	0.00215610i	$-0.999314\pi$
$11$	−0.771344	+	2.11925i	−0.232569	+	0.638978i	0.767429	+	0.641134i	$0.221536\pi$
$12$		0			0
$13$	−0.634290	+	0.755917i	−0.175920	+	0.209654i	−0.846798	−	0.531914i	$-0.821473\pi$
$13$	−0.634290	+	0.755917i	−0.175920	+	0.209654i	0.670878	+	0.741568i	$0.265917\pi$
$14$	1.76077	+	1.05640i	0.470586	+	0.282335i
$15$		0			0
$16$	−3.84213	+	1.11269i	−0.960531	+	0.278172i
$17$	0.439205	−	0.760726i	0.106523	−	0.184503i	−0.807836	−	0.589407i	$-0.799362\pi$
$17$	0.439205	−	0.760726i	0.106523	−	0.184503i	0.914359	+	0.404904i	$0.132695\pi$
$18$		0			0
$19$	5.20298	−	3.00394i	1.19364	−	0.689151i	0.234513	−	0.972113i	$-0.424650\pi$
$19$	5.20298	−	3.00394i	1.19364	−	0.689151i	0.959131	+	0.282962i	$0.0913170\pi$
$20$	−0.240306	+	0.128180i	−0.0537340	+	0.0286618i
$21$		0			0
$22$	−1.54810	−	2.78851i	−0.330056	−	0.594512i
$23$	0.748645	−	4.24578i	0.156103	−	0.885306i	−0.801667	−	0.597771i	$-0.796053\pi$
$23$	0.748645	−	4.24578i	0.156103	−	0.885306i	0.957770	−	0.287535i	$-0.0928357\pi$
$24$		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	$-0.228959\pi$
$29$	−0.146501	−	0.174594i	−0.0272046	−	0.0324212i	−0.779475	+	0.626433i	$0.784514\pi$
$30$		0			0
$31$	1.15687	−	6.56095i	0.207781	−	1.17838i	−0.685223	−	0.728333i	$-0.740295\pi$
$31$	1.15687	−	6.56095i	0.207781	−	1.17838i	0.893004	−	0.450049i	$-0.148593\pi$
$32$	2.37377	−	5.13471i	0.419628	−	0.907696i
$33$		0			0
$34$	0.405215	+	1.17431i	0.0694937	+	0.201393i
$35$	−0.171232	+	0.0988610i	−0.0289435	+	0.0167106i
$36$		0			0
$37$	9.25201	+	5.34165i	1.52102	+	0.878162i	0.999692	+	0.0248069i	$0.00789709\pi$
$37$	9.25201	+	5.34165i	1.52102	+	0.878162i	0.521330	+	0.853355i	$0.325436\pi$
$38$	−1.61569	+	8.34139i	−0.262100	+	1.35315i
$39$		0			0
$40$	0.0859012	−	0.375466i	0.0135822	−	0.0593664i
$41$	1.19321	+	1.00123i	0.186349	+	0.156365i	0.731190	−	0.682174i	$-0.238965\pi$
$41$	1.19321	+	1.00123i	0.186349	+	0.156365i	−0.544841	+	0.838540i	$0.683410\pi$
$42$		0			0
$43$	1.11062	−	3.05141i	0.169368	−	0.465335i	−0.825749	−	0.564038i	$-0.809247\pi$
$43$	1.11062	−	3.05141i	0.169368	−	0.465335i	0.995117	+	0.0987027i	$0.0314693\pi$
$44$	4.41319	+	0.931971i	0.665313	+	0.140500i
$45$		0			0
$46$	3.84013	+	4.73578i	0.566197	+	0.698253i
$47$	−1.36645	−	7.74952i	−0.199317	−	1.13038i	−0.906135	−	0.422988i	$-0.860981\pi$
$47$	−1.36645	−	7.74952i	−0.199317	−	1.13038i	0.706818	−	0.707395i	$-0.250130\pi$
$48$		0			0
$49$	4.59683	−	1.67311i	0.656691	−	0.239016i
$50$	−0.118305	+	7.04385i	−0.0167308	+	0.996151i
$51$		0			0
$52$	1.67505	+	1.04362i	0.232288	+	0.144724i
$53$		−	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
$56$	1.59714	−	3.78343i	0.213427	−	0.505582i
$57$		0			0
$58$	0.322276	+	0.00541278i	0.0423169	+	0.000710733i
$59$	3.15956	+	8.68082i	0.411340	+	1.13015i	0.956479	+	0.291801i	$0.0942546\pi$
$59$	3.15956	+	8.68082i	0.411340	+	1.13015i	−0.545139	+	0.838346i	$0.683523\pi$
$60$		0			0
$61$	−12.3724	+	2.18158i	−1.58412	+	0.279323i	−0.895250	−	0.445563i	$-0.853003\pi$
$61$	−12.3724	+	2.18158i	−1.58412	+	0.279323i	−0.688869	+	0.724886i	$0.741892\pi$
$62$	5.93411	+	7.31814i	0.753633	+	0.929405i
$63$		0			0
$64$	3.28278	+	7.29543i	0.410348	+	0.911929i
$65$	0.126273	+	0.0459596i	0.0156622	+	0.00570059i
$66$		0			0
$67$	−5.90023	+	7.03162i	−0.720828	+	0.859049i	−0.994711	−	0.102714i	$-0.967247\pi$
$67$	−5.90023	+	7.03162i	−0.720828	+	0.859049i	0.273883	+	0.961763i	$0.411692\pi$
$68$	−1.62976	−	0.655968i	−0.197638	−	0.0795478i
$69$		0			0
$70$	0.0531732	−	0.274519i	0.00635542	−	0.0328113i
$71$	5.93006	−	10.2712i	0.703769	−	1.21896i	−0.263366	−	0.964696i	$-0.584833\pi$
$71$	5.93006	−	10.2712i	0.703769	−	1.21896i	0.967134	−	0.254267i	$-0.0818341\pi$
$72$		0			0
$73$	4.88366	+	8.45874i	0.571589	+	0.990021i	0.996403	+	0.0847405i	$0.0270061\pi$
$73$	4.88366	+	8.45874i	0.571589	+	0.990021i	−0.424814	+	0.905281i	$0.639661\pi$
$74$	−14.2821	+	4.92826i	−1.66026	+	0.572898i
$75$		0			0
$76$	−7.41012	−	9.45878i	−0.849999	−	1.08500i
$77$	3.22477	+	0.568614i	0.367497	+	0.0647996i
$78$		0			0
$79$	5.49238	−	4.60866i	0.617941	−	0.518514i	−0.279214	−	0.960229i	$-0.590074\pi$
$79$	5.49238	−	4.60866i	0.617941	−	0.518514i	0.897156	+	0.441714i	$0.145630\pi$
$80$	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	$-0.198617\pi$
$83$	0.867764	+	1.03416i	0.0952494	+	0.113514i	−0.716314	+	0.697778i	$0.754172\pi$
$84$		0			0
$85$	−0.117802	−	0.0207717i	−0.0127774	−	0.00225301i
$86$	2.22904	+	4.01504i	0.240363	+	0.432953i
$87$		0			0
$88$	−5.08676	+	3.84895i	−0.542251	+	0.410300i
$89$	3.19969	+	5.54203i	0.339167	+	0.587454i	0.984276	−	0.176636i	$-0.0565216\pi$
$89$	3.19969	+	5.54203i	0.339167	+	0.587454i	−0.645110	+	0.764090i	$0.723188\pi$
$90$		0			0
$91$	1.24080	+	0.716376i	0.130071	+	0.0750966i
$92$	−8.61769	−	0.289558i	−0.898456	−	0.0301885i
$93$		0			0
$94$	9.54280	+	5.72533i	0.984264	+	0.590523i
$95$	−0.626728	−	0.525888i	−0.0643010	−	0.0539549i
$96$		0			0
$97$	0.779817	+	0.283830i	0.0791784	+	0.0288186i	0.381306	−	0.924449i	$-0.375475\pi$
$97$	0.779817	+	0.283830i	0.0791784	+	0.0288186i	−0.302127	+	0.953268i	$0.597697\pi$
$98$	−2.47497	+	6.46025i	−0.250010	+	0.652584i
$99$		0			0
$100$	−7.41267	−	6.65672i	−0.741267	−	0.665672i
$101$	7.06509	−	1.24577i	0.703003	−	0.123958i	0.189291	−	0.981921i	$-0.439381\pi$
$101$	7.06509	−	1.24577i	0.703003	−	0.123958i	0.513712	+	0.857963i	$0.328270\pi$
$102$		0			0
$103$	−7.48465	+	2.72419i	−0.737484	+	0.268422i	−0.683329	−	0.730110i	$-0.739469\pi$
$103$	−7.48465	+	2.72419i	−0.737484	+	0.268422i	−0.0541548	+	0.998533i	$0.517246\pi$
$104$	−2.66746	+	0.821298i	−0.261566	+	0.0805349i
$105$		0			0
$106$	5.43465	+	4.71798i	0.527860	+	0.458251i
$107$		−	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	$0.914131\pi$
$110$	−0.284727	+	0.327978i	−0.0271477	+	0.0312715i
$111$		0			0
$112$	2.55973	+	5.21327i	0.241871	+	0.492608i
$113$	−11.5278	+	4.19578i	−1.08445	+	0.394706i	−0.821561	−	0.570121i	$-0.806896\pi$
$113$	−11.5278	+	4.19578i	−1.08445	+	0.394706i	−0.262885	+	0.964827i	$0.584674\pi$
$114$		0			0
$115$	−0.578178	+	0.101948i	−0.0539154	+	0.00950674i
$116$	−0.304564	+	0.339151i	−0.0282780	+	0.0314894i
$117$		0			0
$118$	−12.1998	−	4.67383i	−1.12308	−	0.430261i
$119$	−1.19849	−	0.436214i	−0.109865	−	0.0399877i
$120$		0			0
$121$	4.53023	+	3.80132i	0.411840	+	0.345574i
$122$	9.14068	−	15.2354i	0.827558	−	1.37935i
$123$		0			0
$124$	−13.3168	−	0.447451i	−1.19589	−	0.0401823i
$125$	−1.17714	−	0.679623i	−0.105287	−	0.0607873i
$126$		0			0
$127$	−4.15115	−	7.19001i	−0.368355	−	0.638010i	0.620953	−	0.783848i	$-0.286746\pi$
$127$	−4.15115	−	7.19001i	−0.368355	−	0.638010i	−0.989309	+	0.145838i	$0.953412\pi$
$128$	−10.8345	−	3.25783i	−0.957644	−	0.287955i
$129$		0			0
$130$	−0.166150	+	0.0922416i	−0.0145723	+	0.00809013i
$131$	16.3299	+	2.87941i	1.42675	+	0.251575i	0.833090	−	0.553138i	$-0.186570\pi$
$131$	16.3299	+	2.87941i	1.42675	+	0.251575i	0.593664	+	0.804713i	$0.297681\pi$
$132$		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	−0.868130	−	0.496337i	$-0.834678\pi$
$137$	−6.20446	+	5.20616i	−0.530083	+	0.444792i	0.338047	+	0.941129i	$0.390234\pi$
$138$		0			0
$139$	−3.76315	−	0.663545i	−0.319186	−	0.0562811i	0.0117598	−	0.999931i	$-0.496257\pi$
$139$	−3.76315	−	0.663545i	−0.319186	−	0.0562811i	−0.330946	+	0.943650i	$0.607368\pi$
$140$	0.243870	+	0.311293i	0.0206108	+	0.0263090i
$141$		0			0
$142$	5.47113	+	15.8553i	0.459127	+	1.33055i
$143$	−1.11272	−	1.92729i	−0.0930505	−	0.161168i
$144$		0			0
$145$	−0.0155185	+	0.0268788i	−0.00128874	+	0.00223216i
$146$	−13.5610	−	2.62672i	−1.12232	−	0.217389i
$147$		0			0
$148$	7.97794	−	19.8213i	0.655783	−	1.62930i
$149$	−14.3501	+	17.1018i	−1.17561	+	1.40104i	−0.277807	+	0.960637i	$0.589608\pi$
$149$	−14.3501	+	17.1018i	−1.17561	+	1.40104i	−0.897802	+	0.440400i	$0.854837\pi$
$150$		0			0
$151$	−17.9058	−	6.51719i	−1.45716	−	0.530362i	−0.512576	−	0.858642i	$-0.671309\pi$
$151$	−17.9058	−	6.51719i	−1.45716	−	0.530362i	−0.944581	+	0.328280i	$0.893531\pi$
$152$	16.9713	+	0.855766i	1.37655	+	0.0694118i
$153$		0			0
$154$	−3.59694	+	2.91667i	−0.289850	+	0.235032i
$155$	−0.893452	+	0.157540i	−0.0717638	+	0.0126539i
$156$		0			0
$157$	−2.93811	−	8.07239i	−0.234487	−	0.644247i	−1.00000		0.000826492i	$-0.999737\pi$
$157$	−2.93811	−	8.07239i	−0.234487	−	0.644247i	0.765513	−	0.643421i	$-0.222485\pi$
$158$	−0.170276	+	10.1382i	−0.0135464	+	0.806552i
$159$		0			0
$160$	−0.767620	−	0.0646086i	−0.0606857	−	0.00510776i
$161$	−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	$-0.128790\pi$
$164$	1.64735	−	2.64407i	0.128637	−	0.206467i
$165$		0			0
$166$	−1.90892	−	0.0320612i	−0.148161	−	0.00248843i
$167$	−14.9465	+	5.44008i	−1.15660	+	0.420966i	−0.847880	−	0.530188i	$-0.822121\pi$
$167$	−14.9465	+	5.44008i	−1.15660	+	0.420966i	−0.308715	+	0.951154i	$0.599899\pi$
$168$		0			0
$169$	2.08834	+	11.8436i	0.160641	+	0.911043i
$170$	0.131398	−	0.106547i	0.0100777	−	0.00817179i
$171$		0			0
$172$	−6.35434	−	1.34190i	−0.484514	−	0.102319i
$173$	6.92421	−	19.0241i	0.526438	−	1.44638i	−0.336798	−	0.941577i	$-0.609344\pi$
$173$	6.92421	−	19.0241i	0.526438	−	1.44638i	0.863236	−	0.504800i	$-0.168434\pi$
$174$		0			0
$175$	−5.54065	−	4.64916i	−0.418834	−	0.351444i
$176$	0.605538	−	9.00069i	0.0456441	−	0.678453i
$177$		0			0
$178$	−8.88495	−	1.72098i	−0.665956	−	0.128993i
$179$	−19.1336	−	11.0468i	−1.43011	−	0.825676i	−0.432984	−	0.901402i	$-0.642539\pi$
$179$	−19.1336	−	11.0468i	−1.43011	−	0.825676i	−0.997129	+	0.0757257i	$0.975873\pi$
$180$		0			0
$181$	15.2536	−	8.80669i	1.13379	−	0.654596i	0.188907	−	0.981995i	$-0.439506\pi$
$181$	15.2536	−	8.80669i	1.13379	−	0.654596i	0.944886	+	0.327399i	$0.106172\pi$
$182$	−1.91539	+	0.660935i	−0.141978	+	0.0489918i
$183$		0			0
$184$	8.29872	−	8.93466i	0.611790	−	0.658672i
$185$	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	−0.343929	−	0.938996i	$-0.611758\pi$
$191$	7.20145	−	6.04274i	0.521079	−	0.437237i	0.865008	+	0.501759i	$0.167313\pi$
$192$		0			0
$193$	−1.28620	+	7.29438i	−0.0925824	+	0.525061i	0.902879	+	0.429895i	$0.141449\pi$
$193$	−1.28620	+	7.29438i	−0.0925824	+	0.525061i	−0.995461	+	0.0951660i	$0.969662\pi$
$194$	−1.02608	+	0.569652i	−0.0736684	+	0.0408986i
$195$		0			0
$196$	−4.60456	−	8.63243i	−0.328897	−	0.616602i
$197$	−15.7746	+	9.10747i	−1.12389	+	0.648881i	−0.942392	−	0.334510i	$-0.891429\pi$
$197$	−15.7746	+	9.10747i	−1.12389	+	0.648881i	−0.181502	+	0.983391i	$0.558096\pi$
$198$		0			0
$199$	−8.05228	+	13.9470i	−0.570811	+	0.988674i	0.425672	+	0.904878i	$0.360038\pi$
$199$	−8.05228	+	13.9470i	−0.570811	+	0.988674i	−0.996483	+	0.0837964i	$0.973295\pi$
$200$	13.9812	−	1.74476i	0.988623	−	0.123373i
$201$		0			0
$202$	−5.21968	+	8.70000i	−0.367255	+	0.612130i
$203$	−0.212712	+	0.253501i	−0.0149295	+	0.0177923i
$204$		0			0
$205$	0.0725472	−	0.199322i	0.00506692	−	0.0139212i
$206$	4.02979	−	10.5187i	0.280769	−	0.732872i
$207$		0			0
$208$	1.59592	−	3.61009i	0.110657	−	0.250315i
$209$	2.35282	+	13.3435i	0.162748	+	0.922988i
$210$		0			0
$211$	6.47874	+	17.8002i	0.446015	+	1.22542i	0.935476	+	0.353390i	$0.114971\pi$
$211$	6.47874	+	17.8002i	0.446015	+	1.22542i	−0.489461	+	0.872025i	$0.662807\pi$
$212$	−10.0770	+	1.42978i	−0.692089	+	0.0981977i
$213$		0			0
$214$	20.8506	+	18.1010i	1.42532	+	1.23736i
$215$	−0.442200			−0.0301578
$216$		0			0
$217$	−9.67311			−0.656654
$218$	−5.94283	−	5.15915i	−0.402499	−	0.349422i
$219$		0			0
$220$	−0.0862864	−	0.608139i	−0.00581742	−	0.0410007i
$221$	0.296462	+	0.814523i	0.0199422	+	0.0547908i
$222$		0			0
$223$	2.02862	+	11.5049i	0.135847	+	0.770424i	0.974267	+	0.225399i	$0.0723686\pi$
$223$	2.02862	+	11.5049i	0.135847	+	0.770424i	−0.838420	+	0.545025i	$0.816520\pi$
$224$	−7.94055	−	2.09963i	−0.530551	−	0.140287i
$225$		0			0
$226$	6.20667	−	16.2009i	0.412862	−	1.07766i
$227$	−0.619851	+	1.70303i	−0.0411409	+	0.113034i	−0.958562	−	0.284884i	$-0.908045\pi$
$227$	−0.619851	+	1.70303i	−0.0411409	+	0.113034i	0.917421	+	0.397918i	$0.130267\pi$
$228$		0			0
$229$	7.88646	−	9.39872i	0.521152	−	0.621085i	−0.439701	−	0.898144i	$-0.644915\pi$
$229$	7.88646	−	9.39872i	0.521152	−	0.621085i	0.960853	+	0.277060i	$0.0893599\pi$
$230$	0.427157	−	0.711972i	0.0281659	−	0.0469460i
$231$		0			0
$232$	−0.0798278	−	0.639681i	−0.00524095	−	0.0419971i
$233$	0.421533	−	0.730116i	0.0276155	−	0.0478315i	−0.851887	−	0.523725i	$-0.824542\pi$
$233$	0.421533	−	0.730116i	0.0276155	−	0.0478315i	0.879503	+	0.475894i	$0.157875\pi$
$234$		0			0
$235$	−0.928021	+	0.535793i	−0.0605374	+	0.0349513i
$236$	16.3018	−	8.69541i	1.06116	−	0.566023i
$237$		0			0
$238$	1.57697	−	0.875489i	0.102220	−	0.0567495i
$239$	1.87603	−	10.6395i	0.121350	−	0.688211i	−0.862059	−	0.506808i	$-0.830825\pi$
$239$	1.87603	−	10.6395i	0.121350	−	0.688211i	0.983409	−	0.181402i	$-0.0580637\pi$
$240$		0			0
$241$	6.85566	−	5.75258i	0.441612	−	0.370557i	−0.394700	−	0.918810i	$-0.629152\pi$
$241$	6.85566	−	5.75258i	0.441612	−	0.370557i	0.836312	+	0.548253i	$0.184707\pi$
$242$	−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
$248$	12.8239	−	13.8066i	0.814319	−	0.876721i
$249$		0			0
$250$	1.81712	−	0.627026i	0.114925	−	0.0396566i
$251$	−6.48934	+	3.74662i	−0.409603	+	0.236485i	−0.690619	−	0.723219i	$-0.742662\pi$
$251$	−6.48934	+	3.74662i	−0.409603	+	0.236485i	0.281016	+	0.959703i	$0.409329\pi$
$252$		0			0
$253$	8.42041	+	4.86153i	0.529387	+	0.305641i
$254$	11.5270	+	2.23273i	0.723267	+	0.140094i
$255$		0			0
$256$	13.5239	−	8.55017i	0.845241	−	0.534385i
$257$	12.7573	+	10.7046i	0.795777	+	0.667736i	0.947168	−	0.320738i	$-0.103931\pi$
$257$	12.7573	+	10.7046i	0.795777	+	0.667736i	−0.151391	+	0.988474i	$0.548375\pi$
$258$		0			0
$259$	5.30528	−	14.5761i	0.329654	−	0.905717i
$260$	0.0555303	−	0.262954i	0.00344384	−	0.0163077i
$261$		0			0
$262$	−18.2146	+	14.7698i	−1.12530	+	0.912479i
$263$	3.21128	+	18.2121i	0.198016	+	1.12300i	0.908058	+	0.418844i	$0.137565\pi$
$263$	3.21128	+	18.2121i	0.198016	+	1.12300i	−0.710042	+	0.704159i	$0.751324\pi$
$264$		0			0
$265$	−0.651206	+	0.237019i	−0.0400032	+	0.0145600i
$266$	12.3346	+	0.207166i	0.756284	+	0.0127022i
$267$		0			0
$268$	15.5815	+	9.70785i	0.951792	+	0.593002i
$269$			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	$0.331535\pi$
$272$	−0.841031	+	3.41150i	−0.0509950	+	0.206853i
$273$		0			0
$274$	0.192352	−	11.4526i	0.0116204	−	0.691876i
$275$	3.84242	+	10.5570i	0.231707	+	0.636608i
$276$		0			0
$277$	−17.4590	+	3.07849i	−1.04901	+	0.184969i	−0.671475	−	0.741027i	$-0.734339\pi$
$277$	−17.4590	+	3.07849i	−1.04901	+	0.184969i	−0.377534	+	0.925996i	$0.623228\pi$
$278$	4.19745	−	3.40361i	0.251746	−	0.204135i
$279$		0			0
$280$	−0.558533	−	0.0281637i	−0.0333787	−	0.00168310i
$281$	15.3990	+	5.60477i	0.918626	+	0.334352i	0.757692	−	0.652613i	$-0.226327\pi$
$281$	15.3990	+	5.60477i	0.918626	+	0.334352i	0.160934	+	0.986965i	$0.448549\pi$
$282$		0			0
$283$	−11.8313	+	14.0999i	−0.703295	+	0.838154i	−0.992895	−	0.118993i	$-0.962033\pi$
$283$	−11.8313	+	14.0999i	−0.703295	+	0.838154i	0.289600	+	0.957148i	$0.406478\pi$
$284$	−22.0047	−	8.85674i	−1.30574	−	0.525551i
$285$		0			0
$286$	3.08983	+	0.598487i	0.182705	+	0.0353893i
$287$	1.13080	−	1.95860i	0.0667490	−	0.115613i
$288$		0			0
$289$	8.11420	+	14.0542i	0.477306	+	0.826718i
$290$	−0.0143175	−	0.0414921i	−0.000840751	−	0.00243650i
$291$		0			0
$292$	15.3776	−	12.0470i	0.899908	−	0.704998i
$293$	−27.7186	−	4.88753i	−1.61934	−	0.285533i	−0.710818	−	0.703376i	$-0.751675\pi$
$293$	−27.7186	−	4.88753i	−1.61934	−	0.285533i	−0.908519	+	0.417843i	$0.862786\pi$
$294$		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
$302$	23.5605	−	13.0801i	1.35575	−	0.752676i
$303$		0			0
$304$	−16.6480	+	17.3308i	−0.954831	+	0.993989i
$305$	0.855412	+	1.48162i	0.0489808	+	0.0848372i
$306$		0			0
$307$	−14.1955	−	8.19580i	−0.810182	−	0.467759i	0.0368369	−	0.999321i	$-0.488272\pi$
$307$	−14.1955	−	8.19580i	−0.810182	−	0.467759i	−0.847019	+	0.531562i	$0.821605\pi$
$308$	0.219926	−	6.54534i	0.0125315	−	0.372956i
$309$		0			0
$310$	0.660081	−	1.10020i	0.0374901	−	0.0624872i
$311$	23.5558	+	19.7657i	1.33573	+	1.12081i	0.982701	+	0.185197i	$0.0592924\pi$
$311$	23.5558	+	19.7657i	1.33573	+	1.12081i	0.353028	+	0.935613i	$0.385152\pi$
$312$		0			0
$313$	−20.6090	−	7.50106i	−1.16489	−	0.423985i	−0.314048	−	0.949407i	$-0.601685\pi$
$313$	−20.6090	−	7.50106i	−1.16489	−	0.423985i	−0.850842	+	0.525422i	$0.823907\pi$
$314$	11.3447	+	4.34624i	0.640218	+	0.245273i
$315$		0			0
$316$	−10.6690	−	9.58100i	−0.600180	−	0.538973i
$317$	26.6872	−	4.70567i	1.49890	−	0.264297i	0.636799	−	0.771030i	$-0.280258\pi$
$317$	26.6872	−	4.70567i	1.49890	−	0.264297i	0.862103	+	0.506733i	$0.169147\pi$
$318$		0			0
$319$	0.483011	−	0.175802i	0.0270434	−	0.00984300i
$320$	0.780661	−	0.759867i	0.0436403	−	0.0424779i
$321$		0			0
$322$	5.80343	−	6.68498i	0.323413	−	0.372540i
$323$		−	5.27738i		−	0.293641i
$324$		0			0
$325$			4.91560i			0.272668i
$326$	10.7346	+	9.31902i	0.594534	+	0.516133i
$327$		0			0
$328$	1.29642	+	4.21058i	0.0715827	+	0.232491i
$329$	−10.7364	+	3.90774i	−0.591918	+	0.215441i
$330$		0			0
$331$	14.1842	−	2.50105i	0.779633	−	0.137470i	0.230351	−	0.973108i	$-0.426013\pi$
$331$	14.1842	−	2.50105i	0.779633	−	0.137470i	0.549282	+	0.835637i	$0.314901\pi$
$332$	1.80401	−	2.00887i	0.0990077	−	0.110251i
$333$		0			0
$334$	8.04732	−	21.0054i	0.440330	−	1.14936i
$335$	1.17460	+	0.427521i	0.0641755	+	0.0233580i
$336$		0			0
$337$	−12.1559	−	10.2000i	−0.662174	−	0.555630i	0.248564	−	0.968616i	$-0.420041\pi$
$337$	−12.1559	−	10.2000i	−0.662174	−	0.555630i	−0.910737	+	0.412986i	$0.864486\pi$
$338$	−14.5842	−	8.75000i	−0.793277	−	0.475937i
$339$		0			0
$340$	−0.00803399	+	0.239104i	−0.000435704	+	0.0129672i
$341$	13.0120	+	7.51246i	0.704637	+	0.406822i
$342$		0			0
$343$	−8.63317	−	14.9531i	−0.466147	−	0.807391i
$344$	7.32419	−	5.54192i	0.394894	−	0.298800i
$345$		0			0
$346$	13.8970	+	25.0319i	0.747107	+	1.34572i
$347$	14.4283	+	2.54411i	0.774554	+	0.136575i	0.546934	−	0.837175i	$-0.315795\pi$
$347$	14.4283	+	2.54411i	0.774554	+	0.136575i	0.227619	+	0.973750i	$0.426906\pi$
$348$		0			0
$349$	−5.21744	−	6.21790i	−0.279283	−	0.332837i	0.608108	−	0.793854i	$-0.291929\pi$
$349$	−5.21744	−	6.21790i	−0.279283	−	0.332837i	−0.887391	+	0.461018i	$0.847484\pi$
$350$	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	−0.363996	−	0.931401i	$-0.618588\pi$
$353$	9.20716	−	7.72572i	0.490047	−	0.411199i	0.854043	+	0.520202i	$0.174143\pi$
$354$		0			0
$355$	−1.59054	−	0.280455i	−0.0844171	−	0.0148850i
$356$	10.0752	−	7.89300i	0.533983	−	0.418328i
$357$		0			0
$358$	29.5361	−	10.1919i	1.56103	−	0.538657i
$359$	6.32415	+	10.9538i	0.333776	+	0.578117i	0.983249	−	0.182268i	$-0.0583438\pi$
$359$	6.32415	+	10.9538i	0.333776	+	0.578117i	−0.649473	+	0.760385i	$0.725010\pi$
$360$		0			0
$361$	8.54731	−	14.8044i	0.449858	−	0.779178i
$362$	−4.73675	+	24.4545i	−0.248958	+	1.28530i
$363$		0			0
$364$	1.06993	−	2.65826i	0.0560797	−	0.139331i
$365$	0.854962	−	1.01890i	0.0447508	−	0.0533319i
$366$		0			0
$367$	15.1415	+	5.51105i	0.790380	+	0.287675i	0.705494	−	0.708716i	$-0.250725\pi$
$367$	15.1415	+	5.51105i	0.790380	+	0.287675i	0.0848857	+	0.996391i	$0.472947\pi$
$368$	1.84783	+	17.1458i	0.0963250	+	0.893788i
$369$		0			0
$370$	1.29584	+	1.59807i	0.0673673	+	0.0830796i
$371$	−7.27663	+	1.28307i	−0.377784	+	0.0666135i
$372$		0			0
$373$	5.87846	+	16.1509i	0.304375	+	0.836263i	0.993727	+	0.111836i	$0.0356733\pi$
$373$	5.87846	+	16.1509i	0.304375	+	0.836263i	−0.689352	+	0.724427i	$0.742105\pi$
$374$	−2.80122	−	0.0470479i	−0.144848	−	0.00243279i
$375$		0			0
$376$	8.65599	−	20.5049i	0.446398	−	1.05746i
$377$	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	$-0.107129\pi$
$380$	−0.865261	+	1.38878i	−0.0443870	+	0.0712429i
$381$		0			0
$382$	−0.223261	+	13.2929i	−0.0114230	+	0.680124i
$383$	−4.63308	+	1.68630i	−0.236740	+	0.0861662i	−0.457666	−	0.889124i	$-0.651314\pi$
$383$	−4.63308	+	1.68630i	−0.236740	+	0.0861662i	0.220926	+	0.975291i	$0.429092\pi$
$384$		0			0
$385$	−0.0774323	−	0.439140i	−0.00394631	−	0.0223807i
$386$	−6.59746	−	8.13621i	−0.335802	−	0.414122i
$387$		0			0
$388$	0.342936	−	1.62391i	0.0174099	−	0.0824417i
$389$	5.45591	−	14.9900i	0.276625	−	0.760022i	−0.721114	−	0.692817i	$-0.756369\pi$
$389$	5.45591	−	14.9900i	0.276625	−	0.760022i	0.997739	−	0.0672055i	$-0.0214083\pi$
$390$		0			0
$391$	−2.90106	−	2.43428i	−0.146713	−	0.123107i
$392$	13.4877	+	3.08580i	0.681234	+	0.155856i
$393$		0			0
$394$	4.89853	−	25.2898i	0.246784	−	1.27408i
$395$	−0.845555	−	0.488181i	−0.0425445	−	0.0245631i
$396$		0			0
$397$	−18.8993	+	10.9115i	−0.948529	+	0.547633i	−0.892624	−	0.450803i	$-0.851138\pi$
$397$	−18.8993	+	10.9115i	−0.948529	+	0.547633i	−0.0559050	+	0.998436i	$0.517804\pi$
$398$	−7.42911	−	21.5296i	−0.372388	−	1.07918i
$399$		0			0
$400$	−11.0988	+	16.5486i	−0.554938	+	0.827429i
$401$	6.01001	−	34.0844i	0.300125	−	1.70210i	−0.345481	−	0.938426i	$-0.612284\pi$
$401$	6.01001	−	34.0844i	0.300125	−	1.70210i	0.645607	−	0.763670i	$-0.276605\pi$
$402$		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	−0.997224	−	0.0744641i	$-0.976275\pi$
$409$	−0.701192	+	3.97666i	−0.0346717	+	0.196633i	0.962552	+	0.271097i	$0.0873865\pi$
$410$	0.145603	+	0.262267i	0.00719084	+	0.0129525i
$411$		0			0
$412$	7.49722	+	14.0555i	0.369361	+	0.692463i
$413$	11.6160	−	6.70650i	0.571586	−	0.330005i
$414$		0			0
$415$	0.0919196	−	0.159209i	0.00451216	−	0.00781529i
$416$	2.37575	+	5.05127i	0.116481	+	0.247659i
$417$		0			0
$418$	−16.4312	−	9.85815i	−0.803678	−	0.482178i
$419$	−7.00112	+	8.34360i	−0.342027	+	0.407612i	−0.909449	−	0.415815i	$-0.863496\pi$
$419$	−7.00112	+	8.34360i	−0.342027	+	0.407612i	0.567422	+	0.823427i	$0.307941\pi$
$420$		0			0
$421$	1.92901	−	5.29990i	0.0940141	−	0.258302i	−0.883768	−	0.467925i	$-0.845002\pi$
$421$	1.92901	−	5.29990i	0.0940141	−	0.258302i	0.977782	+	0.209624i	$0.0672239\pi$
$422$	−25.0158	−	9.58376i	−1.21775	−	0.466530i
$423$		0			0
$424$	7.81549	−	12.0871i	0.379554	−	0.587000i
$425$	−0.759843	−	4.30928i	−0.0368578	−	0.209031i
$426$		0			0
$427$	6.23884	+	17.1411i	0.301919	+	0.829514i
$428$	−38.6613	+	5.48549i	−1.86876	+	0.265151i
$429$		0			0
$430$	0.409965	−	0.472240i	0.0197703	−	0.0227734i
$431$	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	$0.815070\pi$
$434$	8.96798	−	10.3302i	0.430477	−	0.495867i
$435$		0			0
$436$	11.0192	−	1.56347i	0.527726	−	0.0748769i
$437$	−8.85888	−	24.3396i	−0.423778	−	1.16432i
$438$		0			0
$439$	3.29026	+	18.6600i	0.157036	+	0.890594i	0.956901	+	0.290414i	$0.0937931\pi$
$439$	3.29026	+	18.6600i	0.157036	+	0.890594i	−0.799865	+	0.600180i	$0.795096\pi$
$440$	0.729447	+	0.471660i	0.0347750	+	0.0224855i
$441$		0			0
$442$	−1.14471	−	0.438546i	−0.0544481	−	0.0208595i
$443$	−8.57202	+	23.5514i	−0.407269	+	1.11896i	0.551351	+	0.834274i	$0.314113\pi$
$443$	−8.57202	+	23.5514i	−0.407269	+	1.11896i	−0.958620	+	0.284689i	$0.908110\pi$
$444$		0			0
$445$	0.560157	−	0.667569i	0.0265540	−	0.0316458i
$446$	−14.1672	−	8.49979i	−0.670835	−	0.402477i
$447$		0			0
$448$	9.60398	−	6.53340i	0.453745	−	0.308674i
$449$	−2.07187	+	3.58859i	−0.0977777	+	0.169356i	−0.910765	−	0.412926i	$-0.864507\pi$
$449$	−2.07187	+	3.58859i	−0.0977777	+	0.169356i	0.812987	+	0.582282i	$0.197840\pi$
$450$		0			0
$451$	−3.04223	+	1.75643i	−0.143253	+	0.0827072i
$452$	11.5472	+	21.6482i	0.543134	+	1.01824i
$453$		0			0
$454$	−1.24405	−	2.24084i	−0.0583862	−	0.105168i
$455$	0.0338802	−	0.192144i	0.00158833	−	0.00900785i
$456$		0			0
$457$	11.4954	−	9.64582i	0.537734	−	0.451213i	−0.333028	−	0.942917i	$-0.608070\pi$
$457$	11.4954	−	9.64582i	0.537734	−	0.451213i	0.870762	+	0.491704i	$0.163626\pi$
$458$	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	$-0.249484\pi$
$461$	−2.36115	−	2.81391i	−0.109970	−	0.131057i	−0.818221	+	0.574903i	$0.805040\pi$
$462$		0			0
$463$	−1.02545	+	5.81561i	−0.0476566	+	0.270274i	−0.999320	−	0.0368684i	$-0.988262\pi$
$463$	−1.02545	+	5.81561i	−0.0476566	+	0.270274i	0.951663	+	0.307143i	$0.0993729\pi$
$464$	0.757145	+	0.507800i	0.0351496	+	0.0235740i
$465$		0			0
$466$	0.388910	+	1.12706i	0.0180159	+	0.0522101i
$467$	4.79342	−	2.76748i	0.221813	−	0.128064i	−0.384976	−	0.922926i	$-0.625790\pi$
$467$	4.79342	−	2.76748i	0.221813	−	0.128064i	0.606789	+	0.794863i	$0.292457\pi$
$468$		0			0
$469$	11.5421	+	6.66381i	0.532962	+	0.307706i
$470$	0.288181	−	1.48780i	0.0132928	−	0.0686271i
$471$		0			0
$472$	−5.82734	+	25.4707i	−0.268225	+	1.17239i
$473$	5.61003	+	4.70737i	0.257949	+	0.216445i
$474$		0			0
$475$	10.2360	−	28.1231i	0.469659	−	1.29038i
$476$	−0.527052	+	2.49577i	−0.0241574	+	0.114393i
$477$		0			0
$478$	9.62297	+	11.8674i	0.440144	+	0.542801i
$479$	−1.43530	−	8.13997i	−0.0655804	−	0.371925i	−0.999881	−	0.0154382i	$-0.995086\pi$
$479$	−1.43530	−	8.13997i	−0.0655804	−	0.371925i	0.934300	−	0.356487i	$-0.116025\pi$
$480$		0			0
$481$	−9.90631	+	3.60560i	−0.451689	+	0.164401i
$482$	−0.212540	+	12.6546i	−0.00968095	+	0.576402i
$483$		0			0
$484$	6.25444	−	10.0386i	0.284293	−	0.456301i
$485$		−	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	$0.375402\pi$
$488$	−32.7368	−	13.8196i	−1.48192	−	0.625583i
$489$		0			0
$490$	0.941957	+	0.0158206i	0.0425533	+	0.000714702i
$491$	−11.2492	−	30.9069i	−0.507669	−	1.39481i	−0.883636	−	0.468175i	$-0.844912\pi$
$491$	−11.2492	−	30.9069i	−0.507669	−	1.39481i	0.375967	−	0.926633i	$-0.377311\pi$
$492$		0			0
$493$	−0.197162	+	0.0347650i	−0.00887973	+	0.00156574i
$494$	−5.28058	−	6.51219i	−0.237585	−	0.292997i
$495$		0			0
$496$	2.85544	+	26.4952i	0.128213	+	1.18967i
$497$	−16.1818	−	5.88968i	−0.725851	−	0.264188i
$498$		0			0
$499$	−5.09730	+	6.07473i	−0.228187	+	0.271942i	−0.867974	−	0.496610i	$-0.834578\pi$
$499$	−5.09730	+	6.07473i	−0.228187	+	0.271942i	0.639787	+	0.768552i	$0.279022\pi$
$500$	−1.01504	+	2.52188i	−0.0453940	+	0.112782i
$501$		0			0
$502$	2.01515	−	10.4037i	0.0899406	−	0.464339i
$503$	−20.9414	+	36.2716i	−0.933731	+	1.61727i	−0.156850	+	0.987622i	$0.550134\pi$
$503$	−20.9414	+	36.2716i	−0.933731	+	1.61727i	−0.776881	+	0.629647i	$0.783200\pi$
$504$		0			0
$505$	−0.488473	−	0.846060i	−0.0217368	−	0.0376492i
$506$	−12.9984	+	4.48529i	−0.577848	+	0.199395i
$507$		0			0
$508$	−13.0711	+	10.2401i	−0.579937	+	0.454329i
$509$	−1.32565	−	0.233747i	−0.0587583	−	0.0103607i	0.144192	−	0.989550i	$-0.453942\pi$
$509$	−1.32565	−	0.233747i	−0.0587583	−	0.0103607i	−0.202950	+	0.979189i	$0.565053\pi$
$510$		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
$518$	10.6478	+	19.1793i	0.467836	+	0.842688i
$519$		0			0
$520$	0.229335	+	0.303088i	0.0100570	+	0.0132913i
$521$	−13.6363	−	23.6187i	−0.597416	−	1.03475i	−0.993201	−	0.116412i	$-0.962861\pi$
$521$	−13.6363	−	23.6187i	−0.597416	−	1.03475i	0.395785	−	0.918343i	$-0.370473\pi$
$522$		0			0
$523$	−26.9016	−	15.5317i	−1.17633	−	0.679152i	−0.221164	−	0.975237i	$-0.570986\pi$
$523$	−26.9016	−	15.5317i	−1.17633	−	0.679152i	−0.955162	+	0.296085i	$0.904319\pi$
$524$	1.11369	−	33.1450i	0.0486516	−	1.44795i
$525$		0			0
$526$	−22.4264	−	13.4550i	−0.977839	−	0.586667i
$527$	−4.48298	−	3.76167i	−0.195282	−	0.163861i
$528$		0			0
$529$	4.14676	+	1.50930i	0.180294	+	0.0656217i
$530$	0.350614	−	0.915185i	0.0152297	−	0.0397531i
$531$		0			0
$532$	−11.6567	+	12.9805i	−0.505383	+	0.562775i
$533$	−1.51369	+	0.266904i	−0.0655651	+	0.0115609i
$534$		0			0
$535$	−2.49841	+	0.909349i	−0.108016	+	0.0393146i
$536$	−24.8130	+	7.63980i	−1.07176	+	0.329989i
$537$		0			0
$538$	−27.0365	−	23.4712i	−1.16563	−	1.01192i
$539$			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	$0.856634\pi$
$542$	−15.4111	+	17.7521i	−0.661965	+	0.762518i
$543$		0			0
$544$	−2.86353	−	4.06098i	−0.122773	−	0.174113i
$545$	0.712098	−	0.259182i	0.0305029	−	0.0111022i
$546$		0			0
$547$	13.5248	−	2.38478i	0.578278	−	0.101966i	0.123144	−	0.992389i	$-0.460702\pi$
$547$	13.5248	−	2.38478i	0.578278	−	0.101966i	0.455134	+	0.890423i	$0.349591\pi$
$548$	12.0523	+	10.8232i	0.514847	+	0.462342i
$549$		0			0
$550$	−14.8364	−	5.68395i	−0.632628	−	0.242364i
$551$	−1.28671	−	0.468325i	−0.0548158	−	0.0199513i
$552$		0			0
$553$	−7.97465	−	6.69153i	−0.339117	−	0.284553i
$554$	12.8987	−	21.4991i	0.548013	−	0.913410i
$555$		0			0
$556$	−0.256643	+	7.63809i	−0.0108841	+	0.323927i
$557$	8.93296	+	5.15745i	0.378502	+	0.218528i	0.677166	−	0.735830i	$-0.263208\pi$
$557$	8.93296	+	5.15745i	0.378502	+	0.218528i	−0.298665	+	0.954358i	$0.596541\pi$
$558$		0			0
$559$	1.60216	+	2.77502i	0.0677640	+	0.117371i
$560$	0.547895	−	0.570364i	0.0231528	−	0.0241023i
$561$		0			0
$562$	−20.2620	+	11.2489i	−0.854699	+	0.474505i
$563$	3.14086	+	0.553818i	0.132371	+	0.0233406i	0.239441	−	0.970911i	$-0.423036\pi$
$563$	3.14086	+	0.553818i	0.132371	+	0.0233406i	−0.107070	+	0.994251i	$0.534147\pi$
$564$		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	−0.475028	−	0.879971i	$-0.657562\pi$
$569$	7.37287	−	6.18657i	0.309087	−	0.259355i	0.784114	+	0.620616i	$0.213118\pi$
$570$		0			0
$571$	−6.25643	−	1.10318i	−0.261823	−	0.0461665i	0.0411954	−	0.999151i	$-0.486883\pi$
$571$	−6.25643	−	1.10318i	−0.261823	−	0.0461665i	−0.303019	+	0.952985i	$0.597995\pi$
$572$	−3.50373	+	2.74487i	−0.146498	+	0.114769i
$573$		0			0
$574$	1.04329	+	3.02344i	0.0435459	+	0.126196i
$575$	−10.7382	−	18.5991i	−0.447815	−	0.775638i
$576$		0			0
$577$	16.7124	−	28.9468i	0.695748	−	1.20507i	−0.274179	−	0.961679i	$-0.588406\pi$
$577$	16.7124	−	28.9468i	0.695748	−	1.20507i	0.969928	−	0.243393i	$-0.0782604\pi$
$578$	−22.5316	−	4.36429i	−0.937193	−	0.181531i
$579$		0			0
$580$	0.0575845	+	0.0231773i	0.00239107	+	0.000962387i
$581$	1.25995	−	1.50155i	0.0522714	−	0.0622947i
$582$		0			0
$583$	10.7848	+	3.92533i	0.446659	+	0.162571i
$584$	−1.39126	+	27.5911i	−0.0575709	+	1.14173i
$585$		0			0
$586$	30.9176	−	25.0703i	1.27719	−	1.03565i
$587$	−11.4100	+	2.01190i	−0.470943	+	0.0830399i	−0.404083	−	0.914722i	$-0.632409\pi$
$587$	−11.4100	+	2.01190i	−0.470943	+	0.0830399i	−0.0668600	+	0.997762i	$0.521298\pi$
$588$		0			0
$589$	−13.6895	−	37.6117i	−0.564067	−	1.54976i
$590$	−0.0298762	+	1.77882i	−0.00122998	+	0.0732330i
$591$		0			0
$592$	−41.4910	−	10.2287i	−1.70527	−	0.420397i
$593$	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
$596$	37.8963	+	23.6108i	1.55229	+	0.967135i
$597$		0			0
$598$	−6.01561	−	0.101035i	−0.245997	−	0.00413163i
$599$	−27.1047	+	9.86532i	−1.10747	+	0.403086i	−0.830065	−	0.557667i	$-0.811697\pi$
$599$	−27.1047	+	9.86532i	−1.10747	+	0.403086i	−0.277405	+	0.960753i	$0.589474\pi$
$600$		0			0
$601$	−1.58173	−	8.97043i	−0.0645201	−	0.365911i	−0.999924	−	0.0123304i	$-0.996075\pi$
$601$	−1.58173	−	8.97043i	−0.0645201	−	0.365911i	0.935404	−	0.353581i	$-0.115036\pi$
$602$	5.17906	−	4.19958i	0.211083	−	0.171162i
$603$		0			0
$604$	−7.87435	+	37.2876i	−0.320403	+	1.51721i
$605$	0.275437	−	0.756758i	0.0111981	−	0.0307666i
$606$		0			0
$607$	22.8418	+	19.1665i	0.927119	+	0.777945i	0.975298	−	0.220894i	$-0.0708974\pi$
$607$	22.8418	+	19.1665i	0.927119	+	0.777945i	−0.0481792	+	0.998839i	$0.515342\pi$
$608$	−3.07366	−	33.8464i	−0.124653	−	1.37265i
$609$		0			0
$610$	−2.37532	−	0.460091i	−0.0961740	−	0.0186285i
$611$	6.72472	+	3.88252i	0.272053	+	0.157070i
$612$		0			0
$613$	−2.09252	+	1.20812i	−0.0845161	+	0.0487954i	−0.541662	−	0.840596i	$-0.682205\pi$
$613$	−2.09252	+	1.20812i	−0.0845161	+	0.0487954i	0.457146	+	0.889391i	$0.348872\pi$
$614$	21.9133	−	7.56152i	0.884349	−	0.305158i
$615$		0			0
$616$	6.78609	+	6.30308i	0.273419	+	0.253958i
$617$	6.36070	−	36.0733i	0.256072	−	1.45226i	−0.537233	−	0.843434i	$-0.680530\pi$
$617$	6.36070	−	36.0733i	0.256072	−	1.45226i	0.793305	−	0.608824i	$-0.208359\pi$
$618$		0			0
$619$	19.5701	+	23.3228i	0.786590	+	0.937421i	0.999211	−	0.0397133i	$-0.0126445\pi$
$619$	19.5701	+	23.3228i	0.786590	+	0.937421i	−0.212621	+	0.977135i	$0.568200\pi$
$620$	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
$626$	27.1173	−	15.0548i	1.08383	−	0.601709i
$627$		0			0
$628$	−15.1592	+	8.08595i	−0.604918	+	0.322665i
$629$	8.12706	−	4.69216i	0.324047	−	0.187089i
$630$		0			0
$631$	−19.0463	+	32.9892i	−0.758221	+	1.31328i	0.185536	+	0.982637i	$0.440598\pi$
$631$	−19.0463	+	32.9892i	−0.758221	+	1.31328i	−0.943757	+	0.330640i	$0.892735\pi$
$632$	20.1232	−	2.51123i	0.800457	−	0.0998914i
$633$		0			0
$634$	−19.7165	+	32.8628i	−0.783041	+	1.30515i
$635$	−0.726725	+	0.866078i	−0.0288392	+	0.0343692i
$636$		0			0
$637$	−1.65099	+	4.53606i	−0.0654147	+	0.179725i
$638$	−0.260057	+	0.678809i	−0.0102958	+	0.0268743i
$639$		0			0
$640$	0.0877331	+	1.53817i	0.00346796	+	0.0608014i
$641$	−3.09962	−	17.5788i	−0.122427	−	0.694321i	−0.982803	−	0.184659i	$-0.940882\pi$
$641$	−3.09962	−	17.5788i	−0.122427	−	0.694321i	0.860375	−	0.509661i	$-0.170229\pi$
$642$		0			0
$643$	−3.02218	−	8.30337i	−0.119183	−	0.327453i	0.865728	−	0.500515i	$-0.166856\pi$
$643$	−3.02218	−	8.30337i	−0.119183	−	0.327453i	−0.984911	+	0.173062i	$0.944634\pi$
$644$	1.75873	+	12.3953i	0.0693035	+	0.488445i
$645$		0			0
$646$	5.63589	+	4.89268i	0.221741	+	0.192500i
$647$	−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
$650$	−5.24953	−	4.55727i	−0.205903	−	0.178751i
$651$		0			0
$652$	−19.9042	+	2.82412i	−0.779507	+	0.110601i
$653$	−6.26659	−	17.2173i	−0.245230	−	0.673765i	−0.999845	−	0.0175970i	$-0.994398\pi$
$653$	−6.26659	−	17.2173i	−0.245230	−	0.673765i	0.754615	−	0.656168i	$-0.227824\pi$
$654$		0			0
$655$	−0.392110	−	2.22376i	−0.0153210	−	0.0868897i
$656$	−5.69853	−	2.51916i	−0.222490	−	0.0983567i
$657$		0			0
$658$	5.78058	−	15.0887i	0.225350	−	0.588217i
$659$	1.95819	−	5.38009i	0.0762803	−	0.209579i	−0.895691	−	0.444676i	$-0.853319\pi$
$659$	1.95819	−	5.38009i	0.0762803	−	0.209579i	0.971972	+	0.235098i	$0.0755410\pi$
$660$		0			0
$661$	15.7491	−	18.7691i	0.612569	−	0.730032i	−0.367204	−	0.930140i	$-0.619685\pi$
$661$	15.7491	−	18.7691i	0.612569	−	0.730032i	0.979774	+	0.200109i	$0.0641295\pi$
$662$	−10.4792	+	17.4665i	−0.407287	+	0.678854i
$663$		0			0
$664$	0.472840	+	3.78899i	0.0183497	+	0.147041i
$665$	−0.593945	+	1.02874i	−0.0230322	+	0.0398929i
$666$		0			0
$667$	−0.850963	+	0.491304i	−0.0329494	+	0.0190234i
$668$	14.9716	+	28.0681i	0.579269	+	1.08599i
$669$		0			0
$670$	−1.54554	+	0.858041i	−0.0597095	+	0.0331490i
$671$	4.92003	−	27.9029i	0.189936	−	1.07718i
$672$		0			0
$673$	−19.5576	+	16.4108i	−0.753889	+	0.632588i	−0.936528	−	0.350592i	$-0.885980\pi$
$673$	−19.5576	+	16.4108i	−0.753889	+	0.632588i	0.182639	+	0.983180i	$0.441536\pi$
$674$	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	$-0.0847545\pi$
$677$	14.0009	+	16.6857i	0.538100	+	0.641283i	−0.426660	+	0.904412i	$0.640310\pi$
$678$		0			0
$679$	0.209232	−	1.18661i	0.00802959	−	0.0455380i
$680$	−0.247898	−	0.230254i	−0.00950647	−	0.00882983i
$681$		0			0
$682$	−20.0862	+	6.93106i	−0.769142	+	0.265404i
$683$	24.8360	−	14.3391i	0.950322	−	0.548669i	0.0571411	−	0.998366i	$-0.481802\pi$
$683$	24.8360	−	14.3391i	0.950322	−	0.548669i	0.893181	+	0.449697i	$0.148468\pi$
$684$		0			0
$685$	0.955179	+	0.551473i	0.0364955	+	0.0210707i
$686$	23.9727	+	4.64342i	0.915283	+	0.177287i
$687$		0			0
$688$	−0.871885	+	12.9597i	−0.0332403	+	0.494083i
$689$	3.84682	+	3.22787i	0.146552	+	0.122972i
$690$		0			0
$691$	−10.5292	+	28.9287i	−0.400549	+	1.10050i	0.561465	+	0.827501i	$0.310238\pi$
$691$	−10.5292	+	28.9287i	−0.400549	+	1.10050i	−0.962014	+	0.273000i	$0.911984\pi$
$692$	−39.6163	−	8.36612i	−1.50599	−	0.318032i
$693$		0			0
$694$	−16.0935	+	13.0498i	−0.610901	+	0.495365i
$695$	0.0903596	+	0.512455i	0.00342754	+	0.0194385i
$696$		0			0
$697$	1.28572	−	0.467965i	0.0487003	−	0.0177255i
$698$	11.4774	+	0.192768i	0.434426	+	0.00729639i
$699$		0			0
$700$	−7.64943	+	12.2776i	−0.289121	+	0.464051i
$701$			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
$704$	−17.9930	+	1.32975i	−0.678137	+	0.0501168i
$705$		0			0
$706$	−0.285442	+	16.9952i	−0.0107427	+	0.639621i
$707$	−3.56262	−	9.78821i	−0.133986	−	0.368123i
$708$		0			0
$709$	−11.9516	+	2.10739i	−0.448852	+	0.0791446i	−0.393505	−	0.919323i	$-0.628738\pi$
$709$	−11.9516	+	2.10739i	−0.448852	+	0.0791446i	−0.0553467	+	0.998467i	$0.517626\pi$
$710$	1.77410	−	1.43858i	0.0665809	−	0.0539889i
$711$		0			0
$712$	−0.911532	+	18.0772i	−0.0341611	+	0.677472i
$713$	−26.9903	−	9.82365i	−1.01079	−	0.367899i
$714$		0			0
$715$	−0.194800	+	0.232153i	−0.00728510	+	0.00868205i
$716$	−16.4988	+	40.9914i	−0.616588	+	1.53192i
$717$		0			0
$718$	−17.5610	−	3.40150i	−0.655371	−	0.126943i
$719$	9.22099	−	15.9712i	0.343885	−	0.595626i	−0.641266	−	0.767319i	$-0.721590\pi$
$719$	9.22099	−	15.9712i	0.343885	−	0.595626i	0.985151	+	0.171693i	$0.0549236\pi$
$720$		0			0
$721$	5.78238	+	10.0154i	0.215347	+	0.372992i
$722$	7.88583	+	22.8531i	0.293480	+	0.850506i
$723$		0			0
$724$	−21.7243	−	27.7304i	−0.807379	−	1.03059i
$725$	−1.11810	−	0.197152i	−0.0415253	−	0.00732204i
$726$		0			0
$727$	−13.7551	+	11.5419i	−0.510147	+	0.428065i	−0.861181	−	0.508298i	$-0.830275\pi$
$727$	−13.7551	+	11.5419i	−0.510147	+	0.428065i	0.351034	+	0.936363i	$0.385830\pi$
$728$	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	$-0.397012\pi$
$733$	7.91675	+	1.39594i	0.292412	+	0.0515601i	−0.0255180	+	0.999674i	$0.508123\pi$
$734$	−19.9232	+	11.0608i	−0.735377	+	0.408260i
$735$		0			0
$736$	−20.0237	−	13.9226i	−0.738084	−	0.513194i
$737$	−10.3507	−	17.9279i	−0.381272	−	0.660382i
$738$		0			0
$739$	−6.23912	−	3.60216i	−0.229510	−	0.132508i	0.380836	−	0.924643i	$-0.375636\pi$
$739$	−6.23912	−	3.60216i	−0.229510	−	0.132508i	−0.610346	+	0.792135i	$0.708970\pi$
$740$	−2.90800	−	0.0977101i	−0.106900	−	0.00359190i
$741$		0			0
$742$	5.37596	−	8.96048i	0.197358	−	0.328950i
$743$	28.1102	+	23.5873i	1.03126	+	0.865334i	0.991001	−	0.133856i	$-0.0427358\pi$
$743$	28.1102	+	23.5873i	1.03126	+	0.865334i	0.0402635	+	0.999189i	$0.487180\pi$
$744$		0			0
$745$	2.85679	+	1.03979i	0.104665	+	0.0380949i
$746$	−22.6980	−	8.69579i	−0.831034	−	0.318375i
$747$		0			0
$748$	2.64727	−	2.94790i	0.0967937	−	0.107786i
$749$	−27.9175	+	4.92261i	−1.02008	+	0.179868i
$750$		0			0
$751$	34.3650	−	12.5079i	1.25400	−	0.456418i	0.372247	−	0.928134i	$-0.378587\pi$
$751$	34.3650	−	12.5079i	1.25400	−	0.456418i	0.881751	+	0.471716i	$0.156365\pi$
$752$	13.8729	+	28.2542i	0.505891	+	1.03032i
$753$		0			0
$754$	−0.208508	+	0.240181i	−0.00759342	+	0.00874687i
$755$			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	$-0.230947\pi$
$758$	13.7316	+	11.9208i	0.498755	+	0.432984i
$759$		0			0
$760$	−0.680935	−	2.21158i	−0.0247001	−	0.0802225i
$761$	4.63196	−	1.68589i	0.167908	−	0.0611136i	−0.256698	−	0.966492i	$-0.582635\pi$
$761$	4.63196	−	1.68589i	0.167908	−	0.0611136i	0.424607	+	0.905378i	$0.360412\pi$
$762$		0			0
$763$	7.95705	−	1.40304i	0.288065	−	0.0507935i
$764$	−13.9889	−	12.5623i	−0.506102	−	0.454489i
$765$		0			0
$766$	2.49449	−	6.51120i	0.0901296	−	0.235259i
$767$	−8.56606	−	3.11779i	−0.309303	−	0.112577i
$768$		0			0
$769$	37.4770	+	31.4469i	1.35145	+	1.13400i	0.978521	+	0.206146i	$0.0660921\pi$
$769$	37.4770	+	31.4469i	1.35145	+	1.13400i	0.372932	+	0.927858i	$0.378352\pi$
$770$	0.540760	+	0.324436i	0.0194876	+	0.0116919i
$771$		0			0
$772$	14.8055	+	0.497469i	0.532860	+	0.0179043i
$773$	8.17747	+	4.72126i	0.294123	+	0.169812i	0.639800	−	0.768542i	$-0.279017\pi$
$773$	8.17747	+	4.72126i	0.294123	+	0.169812i	−0.345677	+	0.938354i	$0.612351\pi$
$774$		0			0
$775$	−16.5936	−	28.7410i	−0.596061	−	1.03241i
$776$	1.41629	+	1.87177i	0.0508419	+	0.0671925i
$777$		0			0
$778$	10.9501	+	19.7238i	0.392580	+	0.707133i
$779$	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	$-0.353005\pi$
$787$	15.6553	+	2.76045i	0.558050	+	0.0983993i	0.112493	+	0.993653i	$0.464117\pi$
$788$	22.4663	+	28.6775i	0.800330	+	1.02160i
$789$		0			0
$790$	1.30526	−	0.450401i	0.0464391	−	0.0160245i
$791$	8.90599	+	15.4256i	0.316661	+	0.548472i
$792$		0			0
$793$	6.19857	−	10.7362i	0.220118	−	0.381255i
$794$	5.86885	−	30.2993i	0.208278	−	1.07528i
$795$		0			0
$796$	29.8797	+	12.0264i	1.05906	+	0.426263i
$797$	9.18613	−	10.9476i	0.325389	−	0.387784i	−0.578406	−	0.815749i	$-0.696325\pi$
$797$	9.18613	−	10.9476i	0.325389	−	0.387784i	0.903795	+	0.427965i	$0.140769\pi$
$798$		0			0
$799$	−6.49541	−	2.36413i	−0.229791	−	0.0836371i
$800$	−7.38306	−	27.1950i	−0.261031	−	0.961488i
$801$		0			0
$802$	30.8280	+	38.0181i	1.08857	+	1.34247i
$803$	−21.6932	+	3.82509i	−0.765536	+	0.134985i
$804$		0			0
$805$	0.291550	+	0.801026i	0.0102758	+	0.0282325i
$806$	−9.29586	−	0.156128i	−0.327433	−	0.00549939i
$807$		0			0
$808$	18.6940	+	7.89151i	0.657651	+	0.277622i
$809$	−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	$0.761629\pi$
$812$	0.561737	+	0.349983i	0.0197131	+	0.0122820i
$813$		0			0
$814$	0.572201	−	34.0687i	0.0200556	−	1.19411i
$815$	−1.28627	+	0.468164i	−0.0450561	+	0.0163991i
$816$		0			0
$817$	−3.38771	−	19.2126i	−0.118521	−	0.672165i
$818$	−3.59672	−	4.43560i	−0.125757	−	0.155087i
$819$		0			0
$820$	−0.415073	−	0.0876546i	−0.0144950	−	0.00306103i
$821$	−12.6956	+	34.8810i	−0.443081	+	1.21736i	0.494374	+	0.869249i	$0.335397\pi$
$821$	−12.6956	+	34.8810i	−0.443081	+	1.21736i	−0.937455	+	0.348106i	$0.886825\pi$
$822$		0			0
$823$	−16.3072	−	13.6834i	−0.568433	−	0.476972i	0.312692	−	0.949854i	$-0.398769\pi$
$823$	−16.3072	−	13.6834i	−0.568433	−	0.476972i	−0.881126	+	0.472882i	$0.843214\pi$
$824$	−21.9610	−	5.02436i	−0.765047	−	0.175032i
$825$		0			0
$826$	−3.60715	+	18.6227i	−0.125509	+	0.647967i
$827$	−7.73838	−	4.46776i	−0.269090	−	0.155359i	0.359384	−	0.933190i	$-0.382987\pi$
$827$	−7.73838	−	4.46776i	−0.269090	−	0.155359i	−0.628474	+	0.777831i	$0.716320\pi$
$828$		0			0
$829$	−19.4960	+	11.2560i	−0.677124	+	0.390938i	−0.798771	−	0.601636i	$-0.794516\pi$
$829$	−19.4960	+	11.2560i	−0.677124	+	0.390938i	0.121647	+	0.992573i	$0.461183\pi$
$830$	0.0848059	+	0.245768i	0.00294365	+	0.00853072i
$831$		0			0
$832$	−7.59698	−	2.14591i	−0.263378	−	0.0743960i
$833$	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	−0.628989	−	0.777414i	$-0.716531\pi$
$839$	0.793395	−	0.665737i	0.0273910	−	0.0229838i	0.656380	+	0.754430i	$0.272087\pi$
$840$		0			0
$841$	5.02678	−	28.5083i	0.173337	−	0.983044i
$842$	3.87155	+	6.97361i	0.133422	+	0.240326i
$843$		0			0
$844$	33.4271	−	17.8301i	1.15061	−	0.613737i
$845$	1.41829	−	0.818851i	0.0487907	−	0.0281693i
$846$		0			0
$847$	4.29326	−	7.43615i	0.147518	−	0.255509i
$848$	5.66241	+	19.5524i	0.194448	+	0.671431i
$849$		0			0
$850$	5.30648	+	3.18369i	0.182011	+	0.109200i
$851$	29.6060	−	35.2830i	1.01488	−	1.20949i
$852$		0			0
$853$	−8.12987	+	22.3366i	−0.278361	+	0.764792i	0.719187	+	0.694816i	$0.244514\pi$
$853$	−8.12987	+	22.3366i	−0.278361	+	0.764792i	−0.997549	+	0.0699754i	$0.977708\pi$
$854$	−24.0895	−	9.22889i	−0.824327	−	0.315806i
$855$		0			0
$856$	29.9849	−	46.3733i	1.02486	−	1.58501i
$857$	−4.07463	−	23.1084i	−0.139187	−	0.789367i	−0.971852	−	0.235591i	$-0.924297\pi$
$857$	−4.07463	−	23.1084i	−0.139187	−	0.789367i	0.832666	−	0.553776i	$-0.186814\pi$
$858$		0			0
$859$	−11.7827	−	32.3728i	−0.402022	−	1.10455i	−0.961285	−	0.275555i	$-0.911138\pi$
$859$	−11.7827	−	32.3728i	−0.402022	−	1.10455i	0.559264	−	0.828990i	$-0.311084\pi$
$860$	0.124240	+	0.875630i	0.00423653	+	0.0298587i
$861$		0			0
$862$	−11.3693	+	13.0963i	−0.387241	+	0.446063i
$863$	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
$866$	32.2530	−	37.1523i	1.09600	−	1.26249i
$867$		0			0
$868$	2.71774	+	19.1544i	0.0922460	+	0.650142i
$869$	5.53038	+	15.1946i	0.187605	+	0.515442i
$870$		0			0
$871$	−1.57287	−	8.92017i	−0.0532946	−	0.302248i
$872$	−8.54629	+	13.2173i	−0.289414	+	0.447594i
$873$		0			0
$874$	34.2061	+	13.1046i	1.15704	+	0.443270i
$875$	−0.674995	+	1.85453i	−0.0228190	+	0.0626947i
$876$		0			0
$877$	12.6506	−	15.0765i	0.427182	−	0.509096i	−0.508925	−	0.860811i	$-0.669957\pi$
$877$	12.6506	−	15.0765i	0.427182	−	0.509096i	0.936107	+	0.351715i	$0.114401\pi$
$878$	−22.9780	−	13.7860i	−0.775471	−	0.465255i
$879$		0			0
$880$	−1.17997	+	0.341723i	−0.0397769	+	0.0115195i
$881$	0.970676	−	1.68126i	0.0327029	−	0.0566431i	−0.849211	−	0.528054i	$-0.822922\pi$
$881$	0.970676	−	1.68126i	0.0327029	−	0.0566431i	0.881914	+	0.471411i	$0.156255\pi$
$882$		0			0
$883$	−3.58570	+	2.07021i	−0.120669	+	0.0696680i	−0.559119	−	0.829087i	$-0.688861\pi$
$883$	−3.58570	+	2.07021i	−0.120669	+	0.0696680i	0.438451	+	0.898755i	$0.355527\pi$
$884$	1.52960	−	0.815891i	0.0514460	−	0.0274414i
$885$		0			0
$886$	−17.2042	−	30.9890i	−0.577986	−	1.04109i
$887$	−4.24470	+	24.0729i	−0.142523	+	0.808289i	0.826799	+	0.562497i	$0.190159\pi$
$887$	−4.24470	+	24.0729i	−0.142523	+	0.808289i	−0.969323	+	0.245792i	$0.920952\pi$
$888$		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
$896$	−1.92666	+	16.3135i	−0.0643651	+	0.544997i
$897$		0			0
$898$	−1.91153	−	5.53961i	−0.0637885	−	0.184859i
$899$	−1.31498	+	0.759206i	−0.0438572	+	0.0253209i
$900$		0			0
$901$	−3.87129	−	2.23509i	−0.128971	−	0.0744617i
$902$	0.944712	−	4.87729i	0.0314555	−	0.162396i
$903$		0			0
$904$	−33.8242	−	7.73849i	−1.12498	−	0.257378i
$905$	−1.83739	−	1.54175i	−0.0610768	−	0.0512495i
$906$		0			0
$907$	−19.8264	+	54.4726i	−0.658325	+	1.80873i	−0.0739328	+	0.997263i	$0.523555\pi$
$907$	−19.8264	+	54.4726i	−0.658325	+	1.80873i	−0.584393	+	0.811471i	$0.698667\pi$
$908$	3.54643	+	0.748929i	0.117692	+	0.0248541i
$909$		0			0
$910$	0.173786	+	0.214319i	0.00576096	+	0.00710461i
$911$	−1.13796	−	6.45371i	−0.0377024	−	0.213821i	0.960136	−	0.279532i	$-0.0901794\pi$
$911$	−1.13796	−	6.45371i	−0.0377024	−	0.213821i	−0.997839	+	0.0657114i	$0.979068\pi$
$912$		0			0
$913$	−2.86099	+	1.04132i	−0.0946850	+	0.0344625i
$914$	−0.356384	+	21.2190i	−0.0117881	+	0.701863i
$915$		0			0
$916$	−20.8268	−	12.9759i	−0.688137	−	0.428735i
$917$		−	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	$0.594700\pi$
$920$	−1.52984	−	0.645808i	−0.0504372	−	0.0212917i
$921$		0			0
$922$	5.19410	+	0.0872373i	0.171058	+	0.00287301i
$923$	4.00277	+	10.9975i	0.131753	+	0.361988i
$924$		0			0
$925$	52.4099	−	9.24128i	1.72323	−	0.303851i
$926$	−5.25998	−	6.48678i	−0.172854	−	0.213169i
$927$		0			0
$928$	−1.24425	+	0.337796i	−0.0408444	+	0.0110887i
$929$	53.7456	+	19.5618i	1.76333	+	0.641801i	0.999991	−	0.00419109i	$-0.00133407\pi$
$929$	53.7456	+	19.5618i	1.76333	+	0.641801i	0.763344	+	0.645993i	$0.223556\pi$
$930$		0			0
$931$	18.8913	−	22.5138i	0.619137	−	0.737859i
$932$	−1.56418	−	0.629573i	−0.0512366	−	0.0206224i
$933$		0			0
$934$	−1.48851	+	7.68479i	−0.0487056	+	0.251454i
$935$	0.134886	−	0.233630i	0.00441126	−	0.00764052i
$936$		0			0
$937$	13.7103	+	23.7470i	0.447897	+	0.775780i	0.998249	−	0.0591527i	$-0.0188399\pi$
$937$	13.7103	+	23.7470i	0.447897	+	0.775780i	−0.550352	+	0.834933i	$0.685507\pi$
$938$	−17.8172	+	6.14809i	−0.581751	+	0.200742i
$939$		0			0
$940$	1.32170	+	1.68710i	0.0431090	+	0.0550272i
$941$	47.0141	+	8.28985i	1.53261	+	0.270241i	0.875376	−	0.483442i	$-0.160614\pi$
$941$	47.0141	+	8.28985i	1.53261	+	0.270241i	0.657238	+	0.753683i	$0.271725\pi$
$942$		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	$-0.297903\pi$
$947$	−9.31764	−	11.1043i	−0.302783	−	0.360842i	−0.895886	+	0.444284i	$0.853458\pi$
$948$		0			0
$949$	−9.49177	−	1.67365i	−0.308116	−	0.0543291i
$950$	20.5438	+	37.0044i	0.666528	+	1.20058i
$951$		0			0
$952$	−2.17668	−	2.87669i	−0.0705465	−	0.0932341i
$953$	17.4033	+	30.1434i	0.563749	+	0.976442i	0.997165	+	0.0752476i	$0.0239747\pi$
$953$	17.4033	+	30.1434i	0.563749	+	0.976442i	−0.433416	+	0.901194i	$0.642692\pi$
$954$		0			0
$955$	−1.10867	−	0.640089i	−0.0358756	−	0.0207128i
$956$	−21.5950	−	0.725602i	−0.698433	−	0.0234677i
$957$		0			0
$958$	10.0236	+	6.01380i	0.323848	+	0.194297i
$959$	9.00855	+	7.55907i	0.290901	+	0.244095i
$960$		0			0
$961$	−12.5773	−	4.57775i	−0.405718	−	0.147669i
$962$	5.33364	−	13.9220i	0.171963	−	0.448864i
$963$		0			0
$964$	−13.3172	−	11.9591i	−0.428919	−	0.385178i
$965$	0.993327	−	0.175150i	0.0319763	−	0.00563829i
$966$		0			0
$967$	−7.31794	+	2.66351i	−0.235329	+	0.0856527i	−0.456993	−	0.889470i	$-0.651073\pi$
$967$	−7.31794	+	2.66351i	−0.235329	+	0.0856527i	0.221664	+	0.975123i	$0.428851\pi$
$968$	4.92206	+	15.9862i	0.158201	+	0.513815i
$969$		0			0
$970$	0.120685	+	0.104771i	0.00387498	+	0.00336398i
$971$			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
$974$	−15.6112	+	17.9826i	−0.500215	+	0.576199i
$975$		0			0
$976$	45.1088	−	22.1485i	1.44390	−	0.708956i
$977$	−42.2729	+	15.3861i	−1.35243	+	0.492244i	−0.913706	−	0.406377i	$-0.866792\pi$
$977$	−42.2729	+	15.3861i	−1.35243	+	0.492244i	−0.438725	+	0.898621i	$0.644570\pi$
$978$		0			0
$979$	−14.2130	+	2.50614i	−0.454250	+	0.0800965i
$980$	−0.890187	+	0.991279i	−0.0284360	+	0.0316652i
$981$		0			0
$982$	43.4356	+	16.6405i	1.38609	+	0.531020i
$983$	11.4136	+	4.15422i	0.364038	+	0.132499i	0.517562	−	0.855646i	$-0.326840\pi$
$983$	11.4136	+	4.15422i	0.364038	+	0.132499i	−0.153523	+	0.988145i	$0.549062\pi$
$984$		0			0
$985$	1.90014	+	1.59441i	0.0605436	+	0.0508021i
$986$	0.145663	−	0.242786i	0.00463885	−	0.00773189i
$987$		0			0
$988$	11.8502	+	0.398173i	0.377006	+	0.0126676i
$989$	−12.1241	−	6.99988i	−0.385525	−	0.222583i
$990$		0			0
$991$	−24.4431	−	42.3367i	−0.776462	−	1.34487i	−0.933969	−	0.357353i	$-0.883679\pi$
$991$	−24.4431	−	42.3367i	−0.776462	−	1.34487i	0.157508	−	0.987518i	$-0.449654\pi$
$992$	−30.9424	−	21.5144i	−0.982422	−	0.683083i
$993$		0			0
$994$	21.2919	−	11.8207i	0.675339	−	0.374929i
$995$	2.15976	+	0.380823i	0.0684689	+	0.0120729i
$996$		0			0
$997$	−3.84922	−	4.58733i	−0.121906	−	0.145282i	0.701639	−	0.712532i	$-0.252452\pi$
$997$	−3.84922	−	4.58733i	−0.121906	−	0.145282i	−0.823546	+	0.567250i	$0.808007\pi$
$998$	−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.37.9		204
3.2	odd	2		216.2.t.a.157.26	✓	204
8.5	even	2	inner	648.2.t.a.37.6		204
12.11	even	2		864.2.bf.a.49.24		204
24.5	odd	2		216.2.t.a.157.29	yes	204
24.11	even	2		864.2.bf.a.49.11		204
27.11	odd	18		216.2.t.a.205.29	yes	204
27.16	even	9	inner	648.2.t.a.613.6		204
108.11	even	18		864.2.bf.a.529.11		204
216.11	even	18		864.2.bf.a.529.24		204
216.173	odd	18		216.2.t.a.205.26	yes	204
216.205	even	18	inner	648.2.t.a.613.9		204

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
216.2.t.a.157.26	✓	204	3.2	odd	2
216.2.t.a.157.29	yes	204	24.5	odd	2
216.2.t.a.205.26	yes	204	216.173	odd	18
216.2.t.a.205.29	yes	204	27.11	odd	18
648.2.t.a.37.6		204	8.5	even	2	inner
648.2.t.a.37.9		204	1.1	even	1	trivial
648.2.t.a.613.6		204	27.16	even	9	inner
648.2.t.a.613.9		204	216.205	even	18	inner
864.2.bf.a.49.11		204	24.11	even	2
864.2.bf.a.49.24		204	12.11	even	2
864.2.bf.a.529.11		204	108.11	even	18
864.2.bf.a.529.24		204	216.11	even	18

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
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)

\(f(q)\)	\(=\)	\(q+(-0.927104 + 1.06793i) q^{2} +(-0.280958 - 1.98017i) q^{4} +(-0.0465753 - 0.127965i) q^{5} +(-0.252128 - 1.42989i) q^{7} +(2.37516 + 1.53578i) q^{8} +(0.179838 + 0.0688972i) q^{10} +(-0.771344 + 2.11925i) q^{11} +(-0.634290 + 0.755917i) q^{13} +(1.76077 + 1.05640i) q^{14} +(-3.84213 + 1.11269i) q^{16} +(0.439205 - 0.760726i) q^{17} +(5.20298 - 3.00394i) q^{19} +(-0.240306 + 0.128180i) q^{20} +(-1.54810 - 2.78851i) q^{22} +(0.748645 - 4.24578i) q^{23} +(3.81602 - 3.20202i) q^{25} +(-0.219216 - 1.37819i) q^{26} +(-2.76058 + 0.900994i) q^{28} +(-0.146501 - 0.174594i) q^{29} +(1.15687 - 6.56095i) q^{31} +(2.37377 - 5.13471i) q^{32} +(0.405215 + 1.17431i) q^{34} +(-0.171232 + 0.0988610i) q^{35} +(9.25201 + 5.34165i) q^{37} +(-1.61569 + 8.34139i) q^{38} +(0.0859012 - 0.375466i) q^{40} +(1.19321 + 1.00123i) q^{41} +(1.11062 - 3.05141i) q^{43} +(4.41319 + 0.931971i) q^{44} +(3.84013 + 4.73578i) q^{46} +(-1.36645 - 7.74952i) q^{47} +(4.59683 - 1.67311i) q^{49} +(-0.118305 + 7.04385i) q^{50} +(1.67505 + 1.04362i) q^{52} -5.08895i q^{53} +0.307115 q^{55} +(1.59714 - 3.78343i) q^{56} +(0.322276 + 0.00541278i) q^{58} +(3.15956 + 8.68082i) q^{59} +(-12.3724 + 2.18158i) q^{61} +(5.93411 + 7.31814i) q^{62} +(3.28278 + 7.29543i) q^{64} +(0.126273 + 0.0459596i) q^{65} +(-5.90023 + 7.03162i) q^{67} +(-1.62976 - 0.655968i) q^{68} +(0.0531732 - 0.274519i) q^{70} +(5.93006 - 10.2712i) q^{71} +(4.88366 + 8.45874i) q^{73} +(-14.2821 + 4.92826i) q^{74} +(-7.41012 - 9.45878i) q^{76} +(3.22477 + 0.568614i) q^{77} +(5.49238 - 4.60866i) q^{79} +(0.321333 + 0.439832i) q^{80} +(-2.17548 + 0.346032i) q^{82} +(0.867764 + 1.03416i) q^{83} +(-0.117802 - 0.0207717i) q^{85} +(2.22904 + 4.01504i) q^{86} +(-5.08676 + 3.84895i) q^{88} +(3.19969 + 5.54203i) q^{89} +(1.24080 + 0.716376i) q^{91} +(-8.61769 - 0.289558i) q^{92} +(9.54280 + 5.72533i) q^{94} +(-0.626728 - 0.525888i) q^{95} +(0.779817 + 0.283830i) q^{97} +(-2.47497 + 6.46025i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 204 q + 6 q^{2} - 6 q^{4} - 12 q^{7} + 3 q^{8} - 3 q^{10} + 21 q^{14} - 6 q^{16} + 6 q^{17} - 15 q^{20} - 6 q^{22} + 12 q^{23} - 12 q^{25} + 30 q^{26} - 12 q^{28} - 12 q^{31} + 36 q^{32} + 42 q^{38} - 21 q^{40}+ \cdots - 54 q^{98}+O(q^{100}) \) 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

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more