LMFDB - Embedded newform 216.2.t.a.157.29

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [216,2,Mod(13,216)] 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("216.13"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(216, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([0, 9, 8])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 216 = 2^{3} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	216.t (of order $18$, degree $6$, 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:	$1.72476868366$
Analytic rank:	$0$
Dimension:	$204$
Relative dimension:	$34$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			157.29
Character	$\chi$	$=$	216.157
Dual form			216.2.t.a.205.29

$q$-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} +(1.07385 + 1.35898i) q^{3} +(0.941271 - 1.76466i) q^{4} +(-0.0465753 - 0.127965i) q^{5} +(2.29102 + 0.866728i) q^{6} +(-0.252128 - 1.42989i) q^{7} +(-0.142441 - 2.82484i) q^{8} +(-0.693675 + 2.91870i) q^{9} +(-0.149586 - 0.121295i) q^{10} +(-0.771344 + 2.11925i) q^{11} +(3.40893 - 0.615810i) q^{12} +(0.634290 - 0.755917i) q^{13} +(-1.34611 - 1.55058i) q^{14} +(0.123887 - 0.200710i) q^{15} +(-2.22802 - 3.32204i) q^{16} +(-0.439205 + 0.760726i) q^{17} +(1.28235 + 4.04420i) q^{18} +(-5.20298 + 3.00394i) q^{19} +(-0.269654 - 0.0382600i) q^{20} +(1.67245 - 1.87813i) q^{21} +(0.606505 + 3.13122i) q^{22} +(-0.748645 + 4.24578i) q^{23} +(3.68595 - 3.22704i) q^{24} +(3.81602 - 3.20202i) q^{25} +(0.219216 - 1.37819i) q^{26} +(-4.71137 + 2.19157i) q^{27} +(-2.76058 - 0.900994i) q^{28} +(-0.146501 - 0.174594i) q^{29} +(0.00420544 - 0.333538i) q^{30} +(1.15687 - 6.56095i) q^{31} +(-5.11894 - 2.40758i) q^{32} +(-3.70834 + 1.22752i) q^{33} +(0.0208614 + 1.24208i) q^{34} +(-0.171232 + 0.0988610i) q^{35} +(4.49757 + 3.97139i) q^{36} +(-9.25201 - 5.34165i) q^{37} +(-4.12405 + 7.42842i) q^{38} +(1.70841 + 0.0502450i) q^{39} +(-0.354845 + 0.149795i) q^{40} +(-1.19321 - 1.00123i) q^{41} +(0.661694 - 3.49443i) q^{42} +(-1.11062 + 3.05141i) q^{43} +(3.01370 + 3.35595i) q^{44} +(0.405799 - 0.0471736i) q^{45} +(2.18124 + 5.69354i) q^{46} +(1.36645 + 7.74952i) q^{47} +(2.12203 - 6.59522i) q^{48} +(4.59683 - 1.67311i) q^{49} +(2.29797 - 6.65952i) q^{50} +(-1.50546 + 0.220036i) q^{51} +(-0.736895 - 1.83083i) q^{52} -5.08895i q^{53} +(-4.11894 + 6.08558i) q^{54} +0.307115 q^{55} +(-4.00329 + 0.915895i) q^{56} +(-9.66954 - 3.84497i) q^{57} +(-0.304692 - 0.105139i) q^{58} +(3.15956 + 8.68082i) q^{59} +(-0.237574 - 0.407541i) q^{60} +(12.3724 - 2.18158i) q^{61} +(-3.37064 - 8.79816i) q^{62} +(4.34831 + 0.255992i) q^{63} +(-7.95942 + 0.804744i) q^{64} +(-0.126273 - 0.0459596i) q^{65} +(-3.60398 + 4.18671i) q^{66} +(5.90023 - 7.03162i) q^{67} +(0.929007 + 1.49109i) q^{68} +(-6.57388 + 3.54195i) q^{69} +(-0.135724 + 0.244473i) q^{70} +(-5.93006 + 10.2712i) q^{71} +(8.34367 + 1.54378i) q^{72} +(4.88366 + 8.45874i) q^{73} +(-15.1063 + 0.253718i) q^{74} +(8.44934 + 1.74741i) q^{75} +(0.403507 + 12.0090i) q^{76} +(3.22477 + 0.568614i) q^{77} +(2.10835 - 1.18207i) q^{78} +(5.49238 - 4.60866i) q^{79} +(-0.321333 + 0.439832i) q^{80} +(-8.03763 - 4.04926i) q^{81} +(-2.17548 - 0.346032i) q^{82} +(0.867764 + 1.03416i) q^{83} +(-1.74003 - 4.71912i) q^{84} +(0.117802 + 0.0207717i) q^{85} +(0.873278 + 4.50850i) q^{86} +(0.0799487 - 0.386581i) q^{87} +(6.09641 + 1.87706i) q^{88} +(-3.19969 - 5.54203i) q^{89} +(0.457789 - 0.352456i) q^{90} +(-1.24080 - 0.716376i) q^{91} +(6.78766 + 5.31753i) q^{92} +(10.1585 - 5.47333i) q^{93} +(7.29544 + 8.40363i) q^{94} +(0.626728 + 0.525888i) q^{95} +(-2.22513 - 9.54195i) q^{96} +(0.779817 + 0.283830i) q^{97} +(4.35726 - 5.37352i) q^{98} +(-5.65040 - 3.72140i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 204 q - 6 q^{2} - 6 q^{4} - 6 q^{6} - 12 q^{7} - 3 q^{8} - 12 q^{9} - 3 q^{10} + 3 q^{12} - 21 q^{14} - 12 q^{15} - 6 q^{16} - 6 q^{17} - 27 q^{18} + 15 q^{20} - 6 q^{22} - 12 q^{23} - 12 q^{25} - 30 q^{26}+ \cdots + 54 q^{98}+O(q^{100}) $ 204 * q - 6 * q^2 - 6 * q^4 - 6 * q^6 - 12 * q^7 - 3 * q^8 - 12 * q^9 - 3 * q^10 + 3 * q^12 - 21 * q^14 - 12 * q^15 - 6 * q^16 - 6 * q^17 - 27 * q^18 + 15 * q^20 - 6 * q^22 - 12 * q^23 - 12 * q^25 - 30 * q^26 - 12 * q^28 - 39 * q^30 - 12 * q^31 - 36 * q^32 - 36 * q^36 - 42 * q^38 - 12 * q^39 - 21 * q^40 - 24 * q^41 - 66 * q^42 + 21 * q^44 - 3 * q^46 - 12 * q^47 + 51 * q^48 - 12 * q^49 - 99 * q^50 - 33 * q^52 - 90 * q^54 - 24 * q^55 + 99 * q^56 - 30 * q^57 + 21 * q^58 + 102 * q^60 - 36 * q^62 - 72 * q^63 - 3 * q^64 - 12 * q^65 - 9 * q^66 + 75 * q^68 + 9 * q^70 - 90 * q^71 + 60 * q^72 - 6 * q^73 + 9 * q^74 - 18 * q^76 + 12 * q^78 - 12 * q^79 + 78 * q^80 - 12 * q^81 - 12 * q^82 + 102 * q^84 - 30 * q^86 - 48 * q^87 - 30 * q^88 - 6 * q^89 + 6 * q^90 + 111 * q^92 - 33 * q^94 - 42 * q^95 + 126 * q^96 - 12 * q^97 + 54 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/216\mathbb{Z}\right)^\times$.

$n$	$55$	$109$	$137$
$\chi(n)$	$1$	$-1$	$e\left(\frac{7}{9}\right)$

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 $

$2$	1.21270	−	0.727574i	0.857507	−	0.514473i
$2$	1.21270	−	0.727574i	0.857507	−	0.514473i
$3$	1.07385	+	1.35898i	0.619990	+	0.784610i
$3$	1.07385	+	1.35898i	0.619990	+	0.784610i
$4$	0.941271	−	1.76466i	0.470636	−	0.882328i
$5$	−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	$0.898583\pi$
$6$	2.29102	+	0.866728i	0.935306	+	0.353840i
$7$	−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	$-0.144032\pi$
$8$	−0.142441	−	2.82484i	−0.0503604	−	0.998731i
$9$	−0.693675	+	2.91870i	−0.231225	+	0.972900i
$10$	−0.149586	−	0.121295i	−0.0473031	−	0.0383570i
$11$	−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	$0.221536\pi$
$12$	3.40893	−	0.615810i	0.984072	−	0.177769i
$13$	0.634290	−	0.755917i	0.175920	−	0.209654i	−0.670878	−	0.741568i	$-0.734083\pi$
$13$	0.634290	−	0.755917i	0.175920	−	0.209654i	0.846798	+	0.531914i	$0.178527\pi$
$14$	−1.34611	−	1.55058i	−0.359762	−	0.414410i
$15$	0.123887	−	0.200710i	0.0319874	−	0.0518232i
$16$	−2.22802	−	3.32204i	−0.557004	−	0.830510i
$17$	−0.439205	+	0.760726i	−0.106523	+	0.184503i	−0.914359	−	0.404904i	$-0.867305\pi$
$17$	−0.439205	+	0.760726i	−0.106523	+	0.184503i	0.807836	+	0.589407i	$0.200638\pi$
$18$	1.28235	+	4.04420i	0.302254	+	0.953227i
$19$	−5.20298	+	3.00394i	−1.19364	+	0.689151i	−0.959131	−	0.282962i	$-0.908683\pi$
$19$	−5.20298	+	3.00394i	−1.19364	+	0.689151i	−0.234513	+	0.972113i	$0.575350\pi$
$20$	−0.269654	−	0.0382600i	−0.0602964	−	0.00855521i
$21$	1.67245	−	1.87813i	0.364958	−	0.409842i
$22$	0.606505	+	3.13122i	0.129307	+	0.667579i
$23$	−0.748645	+	4.24578i	−0.156103	+	0.885306i	0.801667	+	0.597771i	$0.203947\pi$
$23$	−0.748645	+	4.24578i	−0.156103	+	0.885306i	−0.957770	+	0.287535i	$0.907164\pi$
$24$	3.68595	−	3.22704i	0.752391	−	0.658716i
$25$	3.81602	−	3.20202i	0.763203	−	0.640404i
$26$	0.219216	−	1.37819i	0.0429918	−	0.270286i
$27$	−4.71137	+	2.19157i	−0.906704	+	0.421767i
$28$	−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	$0.784514\pi$
$30$	0.00420544	−	0.333538i	0.000767805	−	0.0608954i
$31$	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	$-0.148593\pi$
$32$	−5.11894	−	2.40758i	−0.904909	−	0.425604i
$33$	−3.70834	+	1.22752i	−0.645539	+	0.213684i
$34$	0.0208614	+	1.24208i	0.00357770	+	0.213016i
$35$	−0.171232	+	0.0988610i	−0.0289435	+	0.0167106i
$36$	4.49757	+	3.97139i	0.749594	+	0.661898i
$37$	−9.25201	−	5.34165i	−1.52102	−	0.878162i	−0.999692	−	0.0248069i	$-0.992103\pi$
$37$	−9.25201	−	5.34165i	−1.52102	−	0.878162i	−0.521330	−	0.853355i	$-0.674564\pi$
$38$	−4.12405	+	7.42842i	−0.669009	+	1.20505i
$39$	1.70841	+	0.0502450i	0.273565	+	0.00804563i
$40$	−0.354845	+	0.149795i	−0.0561060	+	0.0236847i
$41$	−1.19321	−	1.00123i	−0.186349	−	0.156365i	0.544841	−	0.838540i	$-0.316590\pi$
$41$	−1.19321	−	1.00123i	−0.186349	−	0.156365i	−0.731190	+	0.682174i	$0.761035\pi$
$42$	0.661694	−	3.49443i	0.102102	−	0.539203i
$43$	−1.11062	+	3.05141i	−0.169368	+	0.465335i	−0.995117	−	0.0987027i	$-0.968531\pi$
$43$	−1.11062	+	3.05141i	−0.169368	+	0.465335i	0.825749	+	0.564038i	$0.190753\pi$
$44$	3.01370	+	3.35595i	0.454333	+	0.505928i
$45$	0.405799	−	0.0471736i	0.0604929	−	0.00703222i
$46$	2.18124	+	5.69354i	0.321606	+	0.839467i
$47$	1.36645	+	7.74952i	0.199317	+	1.13038i	0.906135	+	0.422988i	$0.139019\pi$
$47$	1.36645	+	7.74952i	0.199317	+	1.13038i	−0.706818	+	0.707395i	$0.749870\pi$
$48$	2.12203	−	6.59522i	0.306289	−	0.951939i
$49$	4.59683	−	1.67311i	0.656691	−	0.239016i
$50$	2.29797	−	6.65952i	0.324982	−	0.941798i
$51$	−1.50546	+	0.220036i	−0.210806	+	0.0308111i
$52$	−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	$-0.113652\pi$
$54$	−4.11894	+	6.08558i	−0.560517	+	0.828143i
$55$	0.307115			0.0414114
$56$	−4.00329	+	0.915895i	−0.534962	+	0.122392i
$57$	−9.66954	−	3.84497i	−1.28076	−	0.509279i
$58$	−0.304692	−	0.105139i	−0.0400080	−	0.0138054i
$59$	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	$0.683523\pi$
$60$	−0.237574	−	0.407541i	−0.0306706	−	0.0526133i
$61$	12.3724	−	2.18158i	1.58412	−	0.279323i	0.688869	−	0.724886i	$-0.258108\pi$
$61$	12.3724	−	2.18158i	1.58412	−	0.279323i	0.895250	+	0.445563i	$0.146997\pi$
$62$	−3.37064	−	8.79816i	−0.428072	−	1.11737i
$63$	4.34831	+	0.255992i	0.547836	+	0.0322519i
$64$	−7.95942	+	0.804744i	−0.994928	+	0.100593i
$65$	−0.126273	−	0.0459596i	−0.0156622	−	0.00570059i
$66$	−3.60398	+	4.18671i	−0.443619	+	0.515348i
$67$	5.90023	−	7.03162i	0.720828	−	0.859049i	−0.273883	−	0.961763i	$-0.588308\pi$
$67$	5.90023	−	7.03162i	0.720828	−	0.859049i	0.994711	+	0.102714i	$0.0327526\pi$
$68$	0.929007	+	1.49109i	0.112659	+	0.180822i
$69$	−6.57388	+	3.54195i	−0.791402	+	0.426401i
$70$	−0.135724	+	0.244473i	−0.0162222	+	0.0292201i
$71$	−5.93006	+	10.2712i	−0.703769	+	1.21896i	0.263366	+	0.964696i	$0.415167\pi$
$71$	−5.93006	+	10.2712i	−0.703769	+	1.21896i	−0.967134	+	0.254267i	$0.918166\pi$
$72$	8.34367	+	1.54378i	0.983310	+	0.181936i
$73$	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	$0.639661\pi$
$74$	−15.1063	+	0.253718i	−1.75608	+	0.0294941i
$75$	8.44934	+	1.74741i	0.975645	+	0.201773i
$76$	0.403507	+	12.0090i	0.0462854	+	1.37752i
$77$	3.22477	+	0.568614i	0.367497	+	0.0647996i
$78$	2.10835	−	1.18207i	0.238723	−	0.133843i
$79$	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
$81$	−8.03763	−	4.04926i	−0.893070	−	0.449918i
$82$	−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	$0.754172\pi$
$84$	−1.74003	−	4.71912i	−0.189852	−	0.514899i
$85$	0.117802	+	0.0207717i	0.0127774	+	0.00225301i
$86$	0.873278	+	4.50850i	0.0941680	+	0.486164i
$87$	0.0799487	−	0.386581i	0.00857141	−	0.0414458i
$88$	6.09641	+	1.87706i	0.649880	+	0.200095i
$89$	−3.19969	−	5.54203i	−0.339167	−	0.587454i	0.645110	−	0.764090i	$-0.276812\pi$
$89$	−3.19969	−	5.54203i	−0.339167	−	0.587454i	−0.984276	+	0.176636i	$0.943478\pi$
$90$	0.457789	−	0.352456i	0.0482552	−	0.0371521i
$91$	−1.24080	−	0.716376i	−0.130071	−	0.0750966i
$92$	6.78766	+	5.31753i	0.707662	+	0.554391i
$93$	10.1585	−	5.47333i	1.05339	−	0.567558i
$94$	7.29544	+	8.40363i	0.752467	+	0.866768i
$95$	0.626728	+	0.525888i	0.0643010	+	0.0539549i
$96$	−2.22513	−	9.54195i	−0.227102	−	0.973871i
$97$	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	$0.597697\pi$
$98$	4.35726	−	5.37352i	0.440149	−	0.542807i
$99$	−5.65040	−	3.72140i	−0.567886	−	0.374014i
$100$	−2.05855	−	9.74792i	−0.205855	−	0.974792i
$101$	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	$0.328270\pi$
$102$	−1.66557	+	1.36217i	−0.164916	+	0.134875i
$103$	−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	$0.517246\pi$
$104$	−2.22569	−	1.68409i	−0.218247	−	0.165139i
$105$	−0.318229	−	0.126540i	−0.0310560	−	0.0123490i
$106$	−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	$-0.392720\pi$
$108$	−0.567321	+	10.3768i	−0.0545905	+	0.998509i
$109$		−	5.56480i		−	0.533011i	−0.963833	−	0.266506i	$-0.914131\pi$
$109$		−	5.56480i		−	0.533011i	0.963833	−	0.266506i	$-0.0858691\pi$
$110$	0.372438	−	0.223449i	0.0355105	−	0.0213050i
$111$	−2.67609	−	18.3095i	−0.254003	−	1.73786i
$112$	−4.18840	+	4.02340i	−0.395767	+	0.380175i
$113$	11.5278	−	4.19578i	1.08445	−	0.394706i	0.262885	−	0.964827i	$-0.415326\pi$
$113$	11.5278	−	4.19578i	1.08445	−	0.394706i	0.821561	+	0.570121i	$0.193104\pi$
$114$	−14.5237	+	2.37253i	−1.36027	+	0.222208i
$115$	0.578178	−	0.101948i	0.0539154	−	0.00950674i
$116$	−0.445995	+	0.0941846i	−0.0414096	+	0.00874482i
$117$	1.76631	+	2.37566i	0.163295	+	0.219630i
$118$	10.1475	+	8.22840i	0.934157	+	0.757486i
$119$	1.19849	+	0.436214i	0.109865	+	0.0399877i
$120$	−0.584621	−	0.321371i	−0.0533684	−	0.0293370i
$121$	4.53023	+	3.80132i	0.411840	+	0.345574i
$122$	13.4167	−	11.6474i	1.21469	−	1.05451i
$123$	0.0793116	−	2.69673i	0.00715129	−	0.243156i
$124$	−10.4889	−	8.21712i	−0.941930	−	0.737919i
$125$	−1.17714	−	0.679623i	−0.105287	−	0.0607873i
$126$	5.45944	−	2.85328i	0.486366	−	0.254190i
$127$	−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	$0.953412\pi$
$128$	−9.06686	+	6.76698i	−0.801405	+	0.598122i
$129$	−5.33946	+	1.76745i	−0.470113	+	0.155615i
$130$	−0.186570	+	0.0361379i	−0.0163633	+	0.00316950i
$131$	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	$0.297681\pi$
$132$	−1.32440	+	7.69937i	−0.115274	+	0.670144i
$133$	5.60712	+	6.68230i	0.486199	+	0.579429i
$134$	2.03917	−	12.8201i	0.176157	−	1.10749i
$135$	0.499877	+	0.500816i	0.0430225	+	0.0431034i
$136$	2.21149	+	1.13233i	0.189633	+	0.0970961i
$137$	6.20446	−	5.20616i	0.530083	−	0.444792i	−0.338047	−	0.941129i	$-0.609766\pi$
$137$	6.20446	−	5.20616i	0.530083	−	0.444792i	0.868130	+	0.496337i	$0.165322\pi$
$138$	−5.39510	+	9.07830i	−0.459261	+	0.772796i
$139$	3.76315	+	0.663545i	0.319186	+	0.0562811i	0.330946	−	0.943650i	$-0.392632\pi$
$139$	3.76315	+	0.663545i	0.319186	+	0.0562811i	−0.0117598	+	0.999931i	$0.503743\pi$
$140$	0.0132796	+	0.395221i	0.00112233	+	0.0334023i
$141$	−9.06410	+	10.1788i	−0.763335	+	0.857212i
$142$	0.281666	+	16.7704i	0.0236369	+	1.40734i
$143$	1.11272	+	1.92729i	0.0930505	+	0.161168i
$144$	11.2416	−	4.19850i	0.936796	−	0.349875i
$145$	−0.0155185	+	0.0268788i	−0.00128874	+	0.00223216i
$146$	12.0768	+	6.70467i	0.999480	+	0.554883i
$147$	7.21006	+	4.45035i	0.594676	+	0.367058i
$148$	−18.1348	+	11.2987i	−1.49067	+	0.928745i
$149$	−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	$0.854837\pi$
$150$	11.5179	−	4.02845i	0.940429	−	0.328921i
$151$	−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	$0.893531\pi$
$152$	9.22676	+	14.2697i	0.748389	+	1.15742i
$153$	−1.91566	−	1.80960i	−0.154872	−	0.146298i
$154$	4.32438	−	1.65670i	0.348469	−	0.133501i
$155$	−0.893452	+	0.157540i	−0.0717638	+	0.0126539i
$156$	1.69675	−	2.96747i	0.135848	−	0.237588i
$157$	2.93811	+	8.07239i	0.234487	+	0.644247i	1.00000		0.000826492i	$0.000263081\pi$
$157$	2.93811	+	8.07239i	0.234487	+	0.644247i	−0.765513	+	0.643421i	$0.777515\pi$
$158$	3.30746	−	9.58503i	0.263127	−	0.762544i
$159$	6.91580	−	5.46479i	0.548459	−	0.433386i
$160$	−0.0696688	+	0.767177i	−0.00550780	+	0.0606507i
$161$	6.25975			0.493337
$162$	−12.6934	+	0.937447i	−0.997284	+	0.0736528i
$163$			10.0518i			0.787315i	0.919257	+	0.393657i	$0.128790\pi$
$163$			10.0518i			0.787315i	−0.919257	+	0.393657i	$0.871210\pi$
$164$	−2.88996	+	1.16319i	−0.225668	+	0.0908297i
$165$	0.329797	+	0.417364i	0.0256746	+	0.0324918i
$166$	1.80476	+	0.622761i	0.140077	+	0.0483357i
$167$	14.9465	−	5.44008i	1.15660	−	0.420966i	0.308715	−	0.951154i	$-0.400101\pi$
$167$	14.9465	−	5.44008i	1.15660	−	0.420966i	0.847880	+	0.530188i	$0.177879\pi$
$168$	−5.54364	−	4.45687i	−0.427701	−	0.343855i
$169$	2.08834	+	11.8436i	0.160641	+	0.911043i
$170$	0.157971	−	0.0605200i	0.0121158	−	0.00464167i
$171$	−5.15843	−	17.2697i	−0.394475	−	1.32065i
$172$	4.33929	+	4.83207i	0.330868	+	0.368442i
$173$	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	$-0.168434\pi$
$174$	−0.184313	−	0.526975i	−0.0139727	−	0.0399498i
$175$	−5.54065	−	4.64916i	−0.418834	−	0.351444i
$176$	8.75880	−	2.15929i	0.660220	−	0.162763i
$177$	−8.40419	+	13.6157i	−0.631698	+	1.02342i
$178$	−7.91250	−	4.39279i	−0.593067	−	0.329254i
$179$	−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	$0.975873\pi$
$180$	0.298721	−	0.760498i	0.0222654	−	0.0566842i
$181$	−15.2536	+	8.80669i	−1.13379	+	0.654596i	−0.944886	−	0.327399i	$-0.893828\pi$
$181$	−15.2536	+	8.80669i	−1.13379	+	0.654596i	−0.188907	+	0.981995i	$0.560494\pi$
$182$	−2.02593	+	0.0340265i	−0.150172	+	0.00252221i
$183$	16.2508	+	14.4711i	1.20130	+	1.06974i
$184$	12.1003	+	1.51003i	0.892044	+	0.111321i
$185$	−0.252627	+	1.43272i	−0.0185735	+	0.105336i
$186$	8.33698	−	14.0286i	0.611297	−	1.02863i
$187$	−1.27339	−	1.51757i	−0.0931195	−	0.110976i
$188$	14.9614	+	4.88309i	1.09117	+	0.356136i
$189$	4.32157	+	6.18419i	0.314348	+	0.449833i
$190$	1.14265	+	0.181751i	0.0828969	+	0.0131856i
$191$	−7.20145	+	6.04274i	−0.521079	+	0.437237i	−0.865008	−	0.501759i	$-0.832687\pi$
$191$	−7.20145	+	6.04274i	−0.521079	+	0.437237i	0.343929	+	0.938996i	$0.388242\pi$
$192$	−9.64089	−	9.95255i	−0.695771	−	0.718263i
$193$	−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	$0.969662\pi$
$194$	1.15219	−	0.223175i	0.0827224	−	0.0160230i
$195$	−0.0731404	−	0.220957i	−0.00523769	−	0.0158230i
$196$	1.37440	−	9.68668i	0.0981717	−	0.691906i
$197$	−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	$0.558096\pi$
$198$	−9.55982	−	0.401842i	−0.679387	−	0.0285577i
$199$	−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	$0.973295\pi$
$200$	−9.58874	−	10.3235i	−0.678026	−	0.729984i
$201$	15.8918	+	0.467384i	1.12092	+	0.0329667i
$202$	7.66144	−	6.65112i	0.539057	−	0.467971i
$203$	−0.212712	+	0.253501i	−0.0149295	+	0.0177923i
$204$	−1.02876	+	2.86372i	−0.0720273	+	0.200501i
$205$	−0.0725472	+	0.199322i	−0.00506692	+	0.0139212i
$206$	−7.09456	+	8.74925i	−0.494302	+	0.609589i
$207$	−11.8728	−	5.13026i	−0.825220	−	0.356578i
$208$	−3.92439	−	0.422939i	−0.272108	−	0.0293255i
$209$	−2.35282	−	13.3435i	−0.162748	−	0.922988i
$210$	−0.477983	+	0.0780810i	−0.0329839	+	0.00538810i
$211$	−6.47874	−	17.8002i	−0.446015	−	1.22542i	−0.935476	−	0.353390i	$-0.885029\pi$
$211$	−6.47874	−	17.8002i	−0.446015	−	1.22542i	0.489461	−	0.872025i	$-0.337193\pi$
$212$	−8.98024	−	4.79008i	−0.616765	−	0.328984i
$213$	−20.3264	+	2.97088i	−1.39274	+	0.203561i
$214$	−14.2053	−	23.6770i	−0.971057	−	1.61853i
$215$	0.442200			0.0301578
$216$	6.86191	+	12.9967i	0.466894	+	0.884313i
$217$	−9.67311			−0.656654
$218$	−4.04881	−	6.74842i	−0.274220	−	0.457061i
$219$	−6.25096	+	15.7203i	−0.422401	+	1.06228i
$220$	0.289078	−	0.541952i	0.0194897	−	0.0365384i
$221$	0.296462	+	0.814523i	0.0199422	+	0.0547908i
$222$	−16.5668	−	20.2568i	−1.11189	−	1.35955i
$223$	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	$0.816520\pi$
$224$	−2.15194	+	7.92654i	−0.143783	+	0.529614i
$225$	6.69866	+	13.3590i	0.446577	+	0.890598i
$226$	10.9270	−	13.4756i	0.726854	−	0.896381i
$227$	−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	$0.130267\pi$
$228$	−15.8867	+	13.4443i	−1.05212	+	0.890367i
$229$	−7.88646	+	9.39872i	−0.521152	+	0.621085i	−0.960853	−	0.277060i	$-0.910640\pi$
$229$	−7.88646	+	9.39872i	−0.521152	+	0.621085i	0.439701	+	0.898144i	$0.355085\pi$
$230$	0.626980	−	0.544300i	0.0413418	−	0.0358901i
$231$	2.69020	+	4.99302i	0.177002	+	0.328517i
$232$	−0.472331	+	0.438712i	−0.0310100	+	0.0288029i
$233$	−0.421533	+	0.730116i	−0.0276155	+	0.0478315i	−0.879503	−	0.475894i	$-0.842125\pi$
$233$	−0.421533	+	0.730116i	−0.0276155	+	0.0478315i	0.851887	+	0.523725i	$0.175458\pi$
$234$	3.87047	+	1.59584i	0.253020	+	0.104323i
$235$	0.928021	−	0.535793i	0.0605374	−	0.0349513i
$236$	18.2927	+	2.59547i	1.19075	+	0.168951i
$237$	12.1611	+	2.51504i	0.789949	+	0.163369i
$238$	1.77078	−	0.342994i	0.114783	−	0.0222330i
$239$	−1.87603	+	10.6395i	−0.121350	+	0.688211i	0.862059	+	0.506808i	$0.169175\pi$
$239$	−1.87603	+	10.6395i	−0.121350	+	0.688211i	−0.983409	+	0.181402i	$0.941936\pi$
$240$	−0.942790	+	0.0356297i	−0.0608568	+	0.00229989i
$241$	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
$243$	−3.12836	−	15.2713i	−0.200685	−	0.979656i
$244$	7.79601	−	23.8864i	0.499088	−	1.52917i
$245$	−0.428198	−	0.510307i	−0.0273566	−	0.0326023i
$246$	−1.86589	−	3.32802i	−0.118965	−	0.212187i
$247$	−1.02947	+	5.83839i	−0.0655033	+	0.371488i
$248$	−18.6984	−	2.33343i	−1.18735	−	0.148173i
$249$	−0.473556	+	2.28981i	−0.0300104	+	0.145111i
$250$	−1.92199	+	0.0322808i	−0.121558	+	0.00204162i
$251$	−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	$0.409329\pi$
$252$	4.54468	−	7.43232i	0.286288	−	0.468192i
$253$	−8.42041	−	4.86153i	−0.529387	−	0.305641i
$254$	−10.2654	−	5.69903i	−0.644106	−	0.357589i
$255$	0.0982739	+	0.182397i	0.00615415	+	0.0114221i
$256$	−6.07188	+	14.8031i	−0.379492	+	0.925195i
$257$	−12.7573	−	10.7046i	−0.795777	−	0.667736i	0.151391	−	0.988474i	$-0.451625\pi$
$257$	−12.7573	−	10.7046i	−0.795777	−	0.667736i	−0.947168	+	0.320738i	$0.896069\pi$
$258$	−5.18920	+	6.02824i	−0.323066	+	0.375302i
$259$	−5.30528	+	14.5761i	−0.329654	+	0.905717i
$260$	−0.199960	+	0.179568i	−0.0124010	+	0.0111363i
$261$	0.611211	−	0.306483i	0.0378330	−	0.0189708i
$262$	21.8983	−	8.38939i	1.35288	−	0.518298i
$263$	−3.21128	−	18.2121i	−0.198016	−	1.12300i	−0.908058	−	0.418844i	$-0.862435\pi$
$263$	−3.21128	−	18.2121i	−0.198016	−	1.12300i	0.710042	−	0.704159i	$-0.248676\pi$
$264$	3.99577	+	10.3006i	0.245923	+	0.633959i
$265$	−0.651206	+	0.237019i	−0.0400032	+	0.0145600i
$266$	11.6616	+	4.02402i	0.715019	+	0.246728i
$267$	4.09553	−	10.2997i	0.250642	−	0.630329i
$268$	−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	$0.719360\pi$
$270$	0.970580	+	0.243641i	0.0590676	+	0.0148275i
$271$	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
$273$	−0.358894	−	2.45551i	−0.0217213	−	0.148614i
$274$	3.73627	−	10.8277i	0.225716	−	0.654126i
$275$	3.84242	+	10.5570i	0.231707	+	0.636608i
$276$	0.0625161	+	14.9346i	0.00376303	+	0.898955i
$277$	17.4590	−	3.07849i	1.04901	−	0.184969i	0.377534	−	0.925996i	$-0.376772\pi$
$277$	17.4590	−	3.07849i	1.04901	−	0.184969i	0.671475	+	0.741027i	$0.265661\pi$
$278$	5.04634	−	1.93329i	0.302659	−	0.115951i
$279$	18.3470	+	7.92773i	1.09840	+	0.474621i
$280$	0.303657	+	0.469622i	0.0181470	+	0.0280653i
$281$	−15.3990	−	5.60477i	−0.918626	−	0.334352i	−0.160934	−	0.986965i	$-0.551451\pi$
$281$	−15.3990	−	5.60477i	−0.918626	−	0.334352i	−0.757692	+	0.652613i	$0.773673\pi$
$282$	−3.58616	+	18.9387i	−0.213553	+	1.12778i
$283$	11.8313	−	14.0999i	0.703295	−	0.838154i	−0.289600	−	0.957148i	$-0.593522\pi$
$283$	11.8313	−	14.0999i	0.703295	−	0.838154i	0.992895	+	0.118993i	$0.0379667\pi$
$284$	12.5433	+	20.1325i	0.744306	+	1.19464i
$285$	−0.0416579	+	1.41644i	−0.00246760	+	0.0839027i
$286$	2.75164	+	1.52763i	0.162708	+	0.0903309i
$287$	−1.13080	+	1.95860i	−0.0667490	+	0.115613i
$288$	10.5779	−	13.2706i	0.623308	−	0.781976i
$289$	8.11420	+	14.0542i	0.477306	+	0.826718i
$290$	0.000737097		0.0438866i	4.32838e−5		0.00257711i
$291$	0.451689	+	1.36455i	0.0264785	+	0.0799914i
$292$	19.5236	−	0.656002i	1.14253	−	0.0383896i
$293$	−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	$0.862786\pi$
$294$	11.9816	+	0.151071i	0.698780	+	0.00881063i
$295$	0.963681	−	0.808624i	0.0561077	−	0.0470799i
$296$	−13.7714	+	26.8963i	−0.800449	+	1.56332i
$297$	−1.01039	−	11.6750i	−0.0586286	−	0.677454i
$298$	−4.95953	+	31.1801i	−0.287298	+	1.80622i
$299$	2.73460	+	3.25897i	0.158146	+	0.188471i
$300$	11.0367	−	13.2654i	0.637203	−	0.765877i
$301$	4.64319	+	0.818720i	0.267629	+	0.0471903i
$302$	−26.4561	+	5.12445i	−1.52238	+	0.294879i
$303$	9.27986	+	8.26358i	0.533114	+	0.474730i
$304$	21.5715	+	10.5917i	1.23721	+	0.607473i
$305$	−0.855412	−	1.48162i	−0.0489808	−	0.0848372i
$306$	−3.63974	−	0.800715i	−0.208070	−	0.0457738i
$307$	14.1955	+	8.19580i	0.810182	+	0.467759i	0.847019	−	0.531562i	$-0.178395\pi$
$307$	14.1955	+	8.19580i	0.810182	+	0.467759i	−0.0368369	+	0.999321i	$0.511728\pi$
$308$	4.03879	−	5.15539i	0.230132	−	0.293756i
$309$	−11.7395	−	7.24613i	−0.667839	−	0.412218i
$310$	−0.968865	+	0.841101i	−0.0550278	+	0.0477713i
$311$	−23.5558	−	19.7657i	−1.33573	−	1.12081i	−0.982701	−	0.185197i	$-0.940708\pi$
$311$	−23.5558	−	19.7657i	−1.33573	−	1.12081i	−0.353028	−	0.935613i	$-0.614848\pi$
$312$	−0.101414	−	4.83315i	−0.00574142	−	0.273623i
$313$	−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	$0.823907\pi$
$314$	9.43630	+	7.65168i	0.532521	+	0.431809i
$315$	−0.169766	−	0.568353i	−0.00956524	−	0.0320231i
$316$	−2.96287	−	14.0302i	−0.166674	−	0.789258i
$317$	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	$0.169147\pi$
$318$	4.41073	−	11.6589i	0.247342	−	0.653798i
$319$	0.483011	−	0.175802i	0.0270434	−	0.00984300i
$320$	0.473691	+	0.981043i	0.0264802	+	0.0548420i
$321$	26.5331	−	20.9662i	1.48094	−	1.17022i
$322$	7.59118	−	4.55443i	0.423040	−	0.253809i
$323$		−	5.27738i		−	0.293641i
$324$	−14.7111	+	10.3722i	−0.817285	+	0.576233i
$325$		−	4.91560i		−	0.272668i
$326$	7.31340	+	12.1897i	0.405052	+	0.675128i
$327$	7.56248	−	5.97579i	0.418206	−	0.330462i
$328$	−2.65834	+	3.51325i	−0.146782	+	0.193987i
$329$	10.7364	−	3.90774i	0.591918	−	0.215441i
$330$	0.703607	+	0.266185i	0.0387323	+	0.0146530i
$331$	−14.1842	+	2.50105i	−0.779633	+	0.137470i	−0.549282	−	0.835637i	$-0.685099\pi$
$331$	−14.1842	+	2.50105i	−0.779633	+	0.137470i	−0.230351	+	0.973108i	$0.573987\pi$
$332$	2.64174	−	0.557878i	0.144984	−	0.0306176i
$333$	22.0086	−	23.2985i	1.20606	−	1.27675i
$334$	14.1675	−	17.4719i	0.775213	−	0.956018i
$335$	−1.17460	−	0.427521i	−0.0641755	−	0.0233580i
$336$	−9.96546	−	1.37143i	−0.543661	−	0.0748176i
$337$	−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	$0.864486\pi$
$338$	11.1496	+	12.8432i	0.606458	+	0.698580i
$339$	18.0812	+	11.1605i	0.982036	+	0.606153i
$340$	0.147539	−	0.188328i	0.00800140	−	0.0102135i
$341$	13.0120	+	7.51246i	0.704637	+	0.406822i
$342$	−18.8206	−	17.1898i	−1.01770	−	0.929516i
$343$	−8.63317	−	14.9531i	−0.466147	−	0.807391i
$344$	8.77793	+	2.70268i	0.473274	+	0.145719i
$345$	0.759425	+	0.676257i	0.0408861	+	0.0364085i
$346$	−5.44448	−	28.1084i	−0.292697	−	1.51112i
$347$	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	$0.426906\pi$
$348$	−0.606929	−	0.504960i	−0.0325348	−	0.0270687i
$349$	5.21744	+	6.21790i	0.279283	+	0.332837i	0.887391	−	0.461018i	$-0.152516\pi$
$349$	5.21744	+	6.21790i	0.279283	+	0.332837i	−0.608108	+	0.793854i	$0.708071\pi$
$350$	−10.1017	−	1.60679i	−0.539961	−	0.0858865i
$351$	−1.33173	+	4.95150i	−0.0710827	+	0.264291i
$352$	9.05073	−	8.99125i	0.482406	−	0.479235i
$353$	−9.20716	+	7.72572i	−0.490047	+	0.411199i	−0.854043	−	0.520202i	$-0.825857\pi$
$353$	−9.20716	+	7.72572i	−0.490047	+	0.411199i	0.363996	+	0.931401i	$0.381412\pi$
$354$	−0.285287	+	22.6264i	−0.0151629	+	1.20258i
$355$	1.59054	+	0.280455i	0.0844171	+	0.0148850i
$356$	−12.7915	+	0.429801i	−0.677951	+	0.0227794i
$357$	0.694194	+	2.09716i	0.0367406	+	0.110993i
$358$	−31.2406	+	0.524701i	−1.65112	+	0.0277313i
$359$	−6.32415	−	10.9538i	−0.333776	−	0.578117i	0.649473	−	0.760385i	$-0.274990\pi$
$359$	−6.32415	−	10.9538i	−0.333776	−	0.578117i	−0.983249	+	0.182268i	$0.941656\pi$
$360$	−0.191060	−	1.13960i	−0.0100697	−	0.0600620i
$361$	8.54731	−	14.8044i	0.449858	−	0.779178i
$362$	−12.0905	+	21.7780i	−0.635464	+	1.14463i
$363$	−0.301120	+	10.2386i	−0.0158047	+	0.537386i
$364$	−2.43209	+	1.51528i	−0.127476	+	0.0794223i
$365$	0.854962	−	1.01890i	0.0447508	−	0.0533319i
$366$	30.2362	+	5.72542i	1.58047	+	0.299273i
$367$	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	$0.472947\pi$
$368$	15.7726	−	6.97264i	0.822205	−	0.363474i
$369$	3.74998	−	2.78811i	0.195216	−	0.145143i
$370$	0.736050	+	1.92126i	0.0382654	+	0.0998816i
$371$	−7.27663	+	1.28307i	−0.377784	+	0.0666135i
$372$	−0.0966055	−	23.0782i	−0.00500876	−	1.19655i
$373$	−5.87846	−	16.1509i	−0.304375	−	0.836263i	−0.993727	−	0.111836i	$-0.964327\pi$
$373$	−5.87846	−	16.1509i	−0.304375	−	0.836263i	0.689352	−	0.724427i	$-0.257895\pi$
$374$	−2.64838	−	0.913864i	−0.136944	−	0.0472548i
$375$	−0.340482	−	2.32953i	−0.0175824	−	0.120297i
$376$	21.6965	−	4.96384i	1.11891	−	0.255991i
$377$	−0.224903			−0.0115831
$378$	9.74021	+	4.35529i	0.500982	+	0.224012i
$379$			12.8581i			0.660478i	0.943897	+	0.330239i	$0.107129\pi$
$379$			12.8581i			0.660478i	−0.943897	+	0.330239i	$0.892871\pi$
$380$	1.51793	−	0.610957i	0.0778683	−	0.0313414i
$381$	5.31337	−	13.3624i	0.272212	−	0.684575i
$382$	−4.33665	+	12.5676i	−0.221882	+	0.643015i
$383$	4.63308	−	1.68630i	0.236740	−	0.0861662i	−0.220926	−	0.975291i	$-0.570908\pi$
$383$	4.63308	−	1.68630i	0.236740	−	0.0861662i	0.457666	+	0.889124i	$0.348686\pi$
$384$	−18.9327	−	5.05497i	−0.966156	−	0.257960i
$385$	−0.0774323	−	0.439140i	−0.00394631	−	0.0223807i
$386$	3.74743	+	9.78167i	0.190739	+	0.497874i
$387$	−8.13574	−	5.35826i	−0.413563	−	0.272376i
$388$	1.23488	−	1.10895i	0.0626916	−	0.0562983i
$389$	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	$-0.0214083\pi$
$390$	−0.249460	−	0.214739i	−0.0126319	−	0.0108737i
$391$	−2.90106	−	2.43428i	−0.146713	−	0.123107i
$392$	−5.38104	−	12.7470i	−0.271784	−	0.643820i
$393$	13.6229	+	25.2842i	0.687185	+	1.27542i
$394$	−12.5035	+	22.5218i	−0.629916	+	1.13463i
$395$	−0.845555	−	0.488181i	−0.0425445	−	0.0245631i
$396$	−11.8855	+	6.46817i	−0.597271	+	0.325038i
$397$	18.8993	−	10.9115i	0.948529	−	0.547633i	0.0559050	−	0.998436i	$-0.482196\pi$
$397$	18.8993	−	10.9115i	0.948529	−	0.547633i	0.892624	+	0.450803i	$0.148862\pi$
$398$	0.382468	+	22.7721i	0.0191714	+	1.14146i
$399$	−3.05992	+	14.7958i	−0.153187	+	0.740716i
$400$	−19.1394	−	5.54280i	−0.956969	−	0.277140i
$401$	−6.01001	+	34.0844i	−0.300125	+	1.70210i	0.345481	+	0.938426i	$0.387716\pi$
$401$	−6.01001	+	34.0844i	−0.300125	+	1.70210i	−0.645607	+	0.763670i	$0.723395\pi$
$402$	19.6121	−	10.9957i	0.978161	−	0.548416i
$403$	−4.22574	−	5.03605i	−0.210499	−	0.250863i
$404$	4.45182	−	13.6401i	0.221486	−	0.678618i
$405$	−0.143807	+	1.21713i	−0.00714581	+	0.0604796i
$406$	−0.0735152	+	0.462184i	−0.00364850	+	0.0229378i
$407$	18.4568	−	15.4871i	0.914869	−	0.767667i
$408$	0.836003	+	4.22133i	0.0413883	+	0.208987i
$409$	−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	$0.0873865\pi$
$410$	0.0570436	+	0.294501i	0.00281718	+	0.0145443i
$411$	13.7378	+	2.84111i	0.677634	+	0.140141i
$412$	−2.23783	+	15.7720i	−0.110250	+	0.777032i
$413$	11.6160	−	6.70650i	0.571586	−	0.330005i
$414$	−18.1308	+	2.41692i	−0.891081	+	0.118785i
$415$	0.0919196	−	0.159209i	0.00451216	−	0.00781529i
$416$	−5.06682	+	2.34239i	−0.248421	+	0.114845i
$417$	3.13933	+	5.82661i	0.153733	+	0.285330i
$418$	−12.5616	−	14.4698i	−0.614410	−	0.707739i
$419$	−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	$0.307941\pi$
$420$	−0.522839	+	0.442456i	−0.0255119	+	0.0215897i
$421$	−1.92901	+	5.29990i	−0.0940141	+	0.258302i	−0.977782	−	0.209624i	$-0.932776\pi$
$421$	−1.92901	+	5.29990i	−0.0940141	+	0.258302i	0.883768	+	0.467925i	$0.154998\pi$
$422$	−20.8077	−	16.8725i	−1.01290	−	0.821339i
$423$	−23.5664	−	1.38739i	−1.14584	−	0.0674572i
$424$	−14.3755	+	0.724873i	−0.698134	+	0.0352030i
$425$	0.759843	+	4.30928i	0.0368578	+	0.209031i
$426$	−22.4882	+	18.3917i	−1.08956	+	0.891082i
$427$	−6.23884	−	17.1411i	−0.301919	−	0.829514i
$428$	−34.4536	−	18.3776i	−1.66538	−	0.888316i
$429$	−1.42426	+	3.58180i	−0.0687638	+	0.172931i
$430$	0.536255	−	0.321733i	0.0258605	−	0.0155154i
$431$	−12.2633			−0.590701			−0.295351	−	0.955389i	$-0.595436\pi$
$431$	−12.2633			−0.590701			−0.295351	+	0.955389i	$0.595436\pi$
$432$	17.7775	+	10.7685i	0.855320	+	0.518100i
$433$	−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
$435$	−0.0531924	+	0.00777453i	−0.00255038	+	0.000372760i
$436$	−9.81996	−	5.23799i	−0.470291	−	0.250854i
$437$	−8.85888	−	24.3396i	−0.423778	−	1.16432i
$438$	3.85714	+	23.6120i	0.184301	+	1.12822i
$439$	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	$0.795096\pi$
$440$	−0.0437456	−	0.867550i	−0.00208549	−	0.0413588i
$441$	1.69460	+	14.5774i	0.0806953	+	0.694161i
$442$	0.952145	+	0.772072i	0.0452889	+	0.0367237i
$443$	−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	$0.908110\pi$
$444$	−34.8289	−	12.5118i	−1.65291	−	0.593785i
$445$	−0.560157	+	0.667569i	−0.0265540	+	0.0316458i
$446$	10.8308	+	12.4760i	0.512851	+	0.590754i
$447$	−38.6511	−	1.13674i	−1.82813	−	0.0537659i
$448$	3.15749	+	11.1782i	0.149177	+	0.528120i
$449$	2.07187	−	3.58859i	0.0977777	−	0.169356i	−0.812987	−	0.582282i	$-0.802160\pi$
$449$	2.07187	−	3.58859i	0.0977777	−	0.169356i	0.910765	+	0.412926i	$0.135493\pi$
$450$	17.8431	+	11.3266i	0.841131	+	0.533942i
$451$	3.04223	−	1.75643i	0.143253	−	0.0827072i
$452$	3.44669	−	24.2920i	0.162119	−	1.14260i
$453$	−10.3715	−	31.3323i	−0.487296	−	1.47212i
$454$	0.487386	+	2.51624i	0.0228742	+	0.118093i
$455$	−0.0338802	+	0.192144i	−0.00158833	+	0.00900785i
$456$	−9.48408	+	27.8626i	−0.444133	+	1.30478i
$457$	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
$459$	0.402079	−	4.54661i	0.0187674	−	0.212218i
$460$	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	$0.805040\pi$
$462$	6.89519	+	4.09771i	0.320793	+	0.190643i
$463$	−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	$0.0993729\pi$
$464$	−0.253599	+	0.875681i	−0.0117730	+	0.0406525i
$465$	−1.17353	−	1.04501i	−0.0544212	−	0.0484613i
$466$	0.0200220	+	1.19211i	0.000927501	+	0.0552233i
$467$	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	$0.292457\pi$
$468$	5.85480	−	0.880777i	0.270638	−	0.0407139i
$469$	−11.5421	−	6.66381i	−0.532962	−	0.307706i
$470$	0.735580	−	1.32496i	0.0339298	−	0.0611159i
$471$	−7.81515	+	12.6614i	−0.360103	+	0.583407i
$472$	24.0719	−	10.1618i	1.10800	−	0.467733i
$473$	−5.61003	−	4.70737i	−0.257949	−	0.216445i
$474$	16.5776	−	5.79813i	0.761436	−	0.266317i
$475$	−10.2360	+	28.1231i	−0.469659	+	1.29038i
$476$	1.89787	−	1.70432i	0.0869888	−	0.0781176i
$477$	14.8531	+	3.53008i	0.680078	+	0.161631i
$478$	5.46596	+	14.2674i	0.250007	+	0.652577i
$479$	1.43530	+	8.13997i	0.0655804	+	0.371925i	0.999881	+	0.0154382i	$0.00491432\pi$
$479$	1.43530	+	8.13997i	0.0655804	+	0.371925i	−0.934300	+	0.356487i	$0.883975\pi$
$480$	−1.11740	+	0.729158i	−0.0510019	+	0.0332813i
$481$	−9.90631	+	3.60560i	−0.451689	+	0.164401i
$482$	4.12841	−	11.9642i	0.188044	−	0.544952i
$483$	6.72205	+	8.50690i	0.305864	+	0.387077i
$484$	10.9722	−	4.41623i	0.498736	−	0.200738i
$485$		−	0.113009i		−	0.00513145i
$486$	−14.9048	−	16.2434i	−0.676095	−	0.736815i
$487$	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
$489$	−13.6602	+	10.7941i	−0.617735	+	0.488127i
$490$	−0.890561	−	0.307302i	−0.0402314	−	0.0138825i
$491$	−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	$-0.377311\pi$
$492$	−4.68415	−	2.67831i	−0.211178	−	0.120748i
$493$	0.197162	−	0.0347650i	0.00887973	−	0.00156574i
$494$	2.99943	+	7.82921i	0.134951	+	0.352253i
$495$	−0.213038	+	0.896377i	−0.00957534	+	0.0402891i
$496$	−24.3733	+	10.7747i	−1.09439	+	0.483800i
$497$	16.1818	+	5.88968i	0.725851	+	0.264188i
$498$	1.09173	+	3.12140i	0.0489216	+	0.139873i
$499$	5.09730	−	6.07473i	0.228187	−	0.271942i	−0.639787	−	0.768552i	$-0.720978\pi$
$499$	5.09730	−	6.07473i	0.228187	−	0.271942i	0.867974	+	0.496610i	$0.165422\pi$
$500$	−2.30731	+	1.43754i	−0.103186	+	0.0642887i
$501$	23.4434	+	14.4702i	1.04737	+	0.646481i
$502$	−5.14366	+	9.26499i	−0.229573	+	0.413517i
$503$	20.9414	−	36.2716i	0.933731	−	1.61727i	0.156850	−	0.987622i	$-0.449866\pi$
$503$	20.9414	−	36.2716i	0.933731	−	1.61727i	0.776881	−	0.629647i	$-0.216800\pi$
$504$	0.103759	−	12.3197i	0.00462178	−	0.548765i
$505$	−0.488473	−	0.846060i	−0.0217368	−	0.0376492i
$506$	−13.7485	+	0.230913i	−0.611197	+	0.0102653i
$507$	−13.8526	+	15.5563i	−0.615217	+	0.690878i
$508$	−16.5952	+	0.557607i	−0.736295	+	0.0247398i
$509$	−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	$0.565053\pi$
$510$	0.251884	+	0.149691i	0.0111536	+	0.00662842i
$511$	10.8638	−	9.11578i	0.480584	−	0.403258i
$512$	3.40702	+	22.3694i	0.150570	+	0.988599i
$513$	17.9298	−	25.5553i	0.791621	−	1.12830i
$514$	−23.2591	−	3.69961i	−1.02592	−	0.163183i
$515$	0.697200	+	0.830890i	0.0307223	+	0.0366134i
$516$	−1.90694	+	11.0860i	−0.0839484	+	0.488032i
$517$	−17.4772	−	3.08170i	−0.768645	−	0.135533i
$518$	4.17152	+	21.5364i	0.183286	+	0.946256i
$519$	33.2891	−	11.0192i	1.46123	−	0.483691i
$520$	−0.111842	+	0.363247i	−0.00490460	+	0.0159294i
$521$	13.6363	+	23.6187i	0.597416	+	1.03475i	0.993201	+	0.116412i	$0.0371392\pi$
$521$	13.6363	+	23.6187i	0.597416	+	1.03475i	−0.395785	+	0.918343i	$0.629527\pi$
$522$	0.518225	−	0.816372i	0.0226821	−	0.0357316i
$523$	26.9016	+	15.5317i	1.17633	+	0.679152i	0.955162	−	0.296085i	$-0.0956811\pi$
$523$	26.9016	+	15.5317i	1.17633	+	0.679152i	0.221164	+	0.975237i	$0.429014\pi$
$524$	20.4521	−	26.1064i	0.893453	−	1.14046i
$525$	0.368281	−	12.5222i	0.0160731	−	0.546513i
$526$	−17.1449	−	19.7493i	−0.747555	−	0.861109i
$527$	4.48298	+	3.76167i	0.195282	+	0.163861i
$528$	12.3401	+	9.58431i	0.537035	+	0.417103i
$529$	4.14676	+	1.50930i	0.180294	+	0.0656217i
$530$	−0.617266	+	0.761233i	−0.0268123	+	0.0330659i
$531$	−27.5284	+	3.20015i	−1.19463	+	0.138875i
$532$	17.0698	−	3.60477i	0.740069	−	0.156287i
$533$	−1.51369	+	0.266904i	−0.0655651	+	0.0115609i
$534$	−2.52713	−	15.4702i	−0.109360	−	0.669460i
$535$	−2.49841	+	0.909349i	−0.108016	+	0.0393146i
$536$	−20.7036	−	15.6656i	−0.894260	−	0.676651i
$537$	−5.53429	−	37.8649i	−0.238822	−	1.63399i
$538$	18.4198	+	30.7015i	0.794133	+	1.32364i
$539$			11.0324i			0.475199i
$540$	1.35429	−	0.410706i	0.0582793	−	0.0176740i
$541$		−	20.2507i		−	0.870645i	−0.900274	−	0.435323i	$-0.856634\pi$
$541$		−	20.2507i		−	0.870645i	0.900274	−	0.435323i	$-0.143366\pi$
$542$	20.1585	−	12.0944i	0.865883	−	0.519498i
$543$	−28.3483	−	11.2723i	−1.21654	−	0.483742i
$544$	4.07977	−	2.83669i	0.174919	−	0.121622i
$545$	−0.712098	+	0.259182i	−0.0305029	+	0.0111022i
$546$	−2.22180	−	2.71667i	−0.0950841	−	0.116263i
$547$	−13.5248	+	2.38478i	−0.578278	+	0.101966i	−0.455134	−	0.890423i	$-0.650409\pi$
$547$	−13.5248	+	2.38478i	−0.578278	+	0.101966i	−0.123144	+	0.992389i	$0.539298\pi$
$548$	−3.34700	−	15.8491i	−0.142977	−	0.677042i
$549$	−2.21501	+	37.6245i	−0.0945345	+	1.60578i
$550$	12.3407	+	10.0068i	0.526208	+	0.426689i
$551$	1.28671	+	0.468325i	0.0548158	+	0.0199513i
$552$	10.9418	+	18.0656i	0.465715	+	0.768924i
$553$	−7.97465	−	6.69153i	−0.339117	−	0.284553i
$554$	18.9327	−	16.4360i	0.804372	−	0.698299i
$555$	−2.21833	+	1.19522i	−0.0941628	+	0.0507341i
$556$	4.71307	−	6.01609i	0.199879	−	0.255139i
$557$	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	$0.596541\pi$
$558$	28.0173	−	3.73484i	1.18607	−	0.158108i
$559$	1.60216	+	2.77502i	0.0677640	+	0.117371i
$560$	0.709929	+	0.348576i	0.0300000	+	0.0147300i
$561$	0.694914	−	3.36016i	0.0293393	−	0.141866i
$562$	−22.7522	+	4.40701i	−0.959743	+	0.185898i
$563$	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	$0.534147\pi$
$564$	9.43035	+	25.5761i	0.397090	+	1.07695i
$565$	−1.07382	−	1.27973i	−0.0451761	−	0.0538388i
$566$	4.08898	−	25.7071i	0.171873	−	1.08055i
$567$	−3.76348	+	12.5139i	−0.158051	+	0.525532i
$568$	29.8591	+	15.2884i	1.25286	+	0.641488i
$569$	−7.37287	+	6.18657i	−0.309087	+	0.259355i	−0.784114	−	0.620616i	$-0.786882\pi$
$569$	−7.37287	+	6.18657i	−0.309087	+	0.259355i	0.475028	+	0.879971i	$0.342438\pi$
$570$	0.980047	+	1.74802i	0.0410497	+	0.0732166i
$571$	6.25643	+	1.10318i	0.261823	+	0.0461665i	0.303019	−	0.952985i	$-0.402005\pi$
$571$	6.25643	+	1.10318i	0.261823	+	0.0461665i	−0.0411954	+	0.999151i	$0.513117\pi$
$572$	4.44838	−	0.149467i	0.185996	−	0.00624955i
$573$	−15.9453	−	3.29764i	−0.666124	−	0.137761i
$574$	0.0537108	+	3.19793i	0.00224185	+	0.133479i
$575$	10.7382	+	18.5991i	0.447815	+	0.775638i
$576$	3.17244	−	23.7894i	0.132185	−	0.991225i
$577$	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	$-0.0782604\pi$
$578$	20.0655	+	11.1398i	0.834617	+	0.463355i
$579$	−11.2941	+	6.08518i	−0.469368	+	0.252891i
$580$	0.0328247	+	0.0526849i	0.00136297	+	0.00218762i
$581$	1.25995	−	1.50155i	0.0522714	−	0.0622947i
$582$	1.54057	+	1.32615i	0.0638589	+	0.0549707i
$583$	10.7848	+	3.92533i	0.446659	+	0.162571i
$584$	23.1990	−	15.0004i	0.959979	−	0.620722i
$585$	0.221735	−	0.336672i	0.00916760	−	0.0139197i
$586$	−37.1703	+	14.2402i	−1.53549	+	0.588258i
$587$	−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	$0.521298\pi$
$588$	14.6400	−	8.53429i	0.603741	−	0.351948i
$589$	13.6895	+	37.6117i	0.564067	+	1.54976i
$590$	0.580319	−	1.68177i	0.0238914	−	0.0692372i
$591$	−29.3165	−	11.6573i	−1.20592	−	0.479519i
$592$	2.86847	+	42.6368i	0.117893	+	1.75236i
$593$	−11.5506			−0.474326			−0.237163	−	0.971470i	$-0.576218\pi$
$593$	−11.5506			−0.474326			−0.237163	+	0.971470i	$0.576218\pi$
$594$	−9.71975	−	13.4232i	−0.398806	−	0.550759i
$595$		−	0.173681i		−	0.00712023i
$596$	16.6715	+	41.4205i	0.682890	+	1.69665i
$597$	−27.6007	+	4.03408i	−1.12962	+	0.165104i
$598$	5.68738	+	1.96252i	0.232574	+	0.0802534i
$599$	27.1047	−	9.86532i	1.10747	−	0.403086i	0.277405	−	0.960753i	$-0.410526\pi$
$599$	27.1047	−	9.86532i	1.10747	−	0.403086i	0.830065	+	0.557667i	$0.188303\pi$
$600$	3.73261	−	24.1169i	0.152383	−	0.984569i
$601$	−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	$-0.115036\pi$
$602$	6.22647	−	2.38541i	0.253772	−	0.0972220i
$603$	16.4304	+	22.0987i	0.669096	+	0.899927i
$604$	−28.3549	+	25.4632i	−1.15374	+	1.03608i
$605$	0.275437	−	0.756758i	0.0111981	−	0.0307666i
$606$	17.2660	+	3.26944i	0.701384	+	0.132812i
$607$	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	$0.515342\pi$
$608$	33.8660	−	2.85041i	1.37345	−	0.115599i
$609$	−0.572925	−	0.0168499i	−0.0232161	−	0.000682792i
$610$	−2.11534	−	1.17438i	−0.0856477	−	0.0475492i
$611$	6.72472	+	3.88252i	0.272053	+	0.157070i
$612$	−4.99649	+	1.67716i	−0.201971	+	0.0677952i
$613$	2.09252	−	1.20812i	0.0845161	−	0.0487954i	−0.457146	−	0.889391i	$-0.651128\pi$
$613$	2.09252	−	1.20812i	0.0845161	−	0.0487954i	0.541662	+	0.840596i	$0.317795\pi$
$614$	23.1780	−	0.389285i	0.935386	−	0.0157103i
$615$	−0.348780	+	0.115452i	−0.0140642	+	0.00465548i
$616$	1.14690	−	9.19045i	0.0462101	−	0.370294i
$617$	−6.36070	+	36.0733i	−0.256072	+	1.45226i	0.537233	+	0.843434i	$0.319470\pi$
$617$	−6.36070	+	36.0733i	−0.256072	+	1.45226i	−0.793305	+	0.608824i	$0.791641\pi$
$618$	−19.5086	−	0.245976i	−0.784752	−	0.00989461i
$619$	−19.5701	−	23.3228i	−0.786590	−	0.937421i	0.212621	−	0.977135i	$-0.431800\pi$
$619$	−19.5701	−	23.3228i	−0.786590	−	0.937421i	−0.999211	+	0.0397133i	$0.987356\pi$
$620$	−0.562977	+	1.72492i	−0.0226097	+	0.0692745i
$621$	−5.77776	−	21.6442i	−0.231853	−	0.868550i
$622$	−42.9471	−	6.83119i	−1.72202	−	0.273906i
$623$	−7.11775	+	5.97250i	−0.285167	+	0.239283i
$624$	−3.63946	−	5.78736i	−0.145695	−	0.231680i
$625$	4.29296	−	24.3466i	0.171718	−	0.973864i
$626$	−30.4501	+	5.89806i	−1.21703	+	0.235734i
$627$	15.6070	−	17.5264i	0.623284	−	0.699937i
$628$	17.0105	+	2.41356i	0.678795	+	0.0963114i
$629$	8.12706	−	4.69216i	0.324047	−	0.187089i
$630$	−0.619394	−	0.565723i	−0.0246773	−	0.0225390i
$631$	−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	$0.892735\pi$
$632$	−13.8011	−	14.8586i	−0.548976	−	0.591045i
$633$	17.2329	−	27.9193i	0.684948	−	1.10969i
$634$	28.9398	−	25.1235i	1.14935	−	0.997781i
$635$	−0.726725	+	0.866078i	−0.0288392	+	0.0343692i
$636$	−3.13383	−	17.3479i	−0.124264	−	0.687887i
$637$	1.65099	−	4.53606i	0.0654147	−	0.179725i
$638$	0.457837	−	0.564620i	0.0181260	−	0.0223535i
$639$	−25.8649	−	24.4329i	−1.02320	−	0.966551i
$640$	1.28823	+	0.845063i	0.0509216	+	0.0334041i
$641$	3.09962	+	17.5788i	0.122427	+	0.694321i	0.982803	+	0.184659i	$0.0591182\pi$
$641$	3.09962	+	17.5788i	0.122427	+	0.694321i	−0.860375	+	0.509661i	$0.829771\pi$
$642$	16.9222	−	44.7305i	0.667867	−	1.76537i
$643$	3.02218	+	8.30337i	0.119183	+	0.327453i	0.984911	−	0.173062i	$-0.0553662\pi$
$643$	3.02218	+	8.30337i	0.119183	+	0.327453i	−0.865728	+	0.500515i	$0.833144\pi$
$644$	5.89212	−	11.0463i	0.232182	−	0.435285i
$645$	0.474858	+	0.600943i	0.0186975	+	0.0236621i
$646$	−3.83969	−	6.39987i	−0.151071	−	0.251800i
$647$	20.3838			0.801371			0.400686	−	0.916216i	$-0.368772\pi$
$647$	20.3838			0.801371			0.400686	+	0.916216i	$0.368772\pi$
$648$	−10.2936	+	23.2818i	−0.404371	+	0.914595i
$649$	−20.8340			−0.817804
$650$	−3.57646	−	5.96114i	−0.140280	−	0.233815i
$651$	−10.3875	−	13.1456i	−0.407119	−	0.515217i
$652$	17.7379	+	9.46143i	0.694669	+	0.370538i
$653$	−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	$-0.227824\pi$
$654$	4.82317	−	12.7491i	0.188601	−	0.498529i
$655$	−0.392110	−	2.22376i	−0.0153210	−	0.0868897i
$656$	−0.667609	+	6.19466i	−0.0260657	+	0.241861i
$657$	−28.0762	+	8.38632i	−1.09536	+	0.327182i
$658$	10.1769	−	12.5505i	0.396736	−	0.489268i
$659$	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	$0.0755410\pi$
$660$	1.04693	−	0.189124i	0.0407518	−	0.00736166i
$661$	−15.7491	+	18.7691i	−0.612569	+	0.730032i	−0.979774	−	0.200109i	$-0.935871\pi$
$661$	−15.7491	+	18.7691i	−0.612569	+	0.730032i	0.367204	+	0.930140i	$0.380315\pi$
$662$	−15.3814	+	13.3531i	−0.597816	+	0.518981i
$663$	−0.788567	+	1.27757i	−0.0306254	+	0.0496166i
$664$	2.79773	−	2.59860i	0.108573	−	0.100845i
$665$	0.593945	−	1.02874i	0.0230322	−	0.0398929i
$666$	9.73836	−	44.2669i	0.377354	−	1.71531i
$667$	0.850963	−	0.491304i	0.0329494	−	0.0190234i
$668$	4.46884	−	31.4960i	0.172905	−	1.21862i
$669$	−13.4565	+	15.1114i	−0.520259	+	0.584242i
$670$	−1.73549	+	0.336158i	−0.0670479	+	0.0129869i
$671$	−4.92003	+	27.9029i	−0.189936	+	1.07718i
$672$	−13.0829	+	5.58749i	−0.504684	+	0.215542i
$673$	−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
$675$	−10.9612	+	23.4490i	−0.421898	+	0.902551i
$676$	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	$0.640310\pi$
$678$	30.0471	+	0.378851i	1.15395	+	0.0145497i
$679$	0.209232	−	1.18661i	0.00802959	−	0.0455380i
$680$	0.0418969	−	0.335731i	0.00160667	−	0.0128747i
$681$	−2.98001	+	0.986434i	−0.114194	+	0.0378002i
$682$	21.2454	−	0.356827i	0.813530	−	0.0136636i
$683$	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	$0.148468\pi$
$684$	−35.3305	−	7.15261i	−1.35090	−	0.273487i
$685$	−0.955179	−	0.551473i	−0.0364955	−	0.0210707i
$686$	−21.3489	−	11.8523i	−0.815105	−	0.452523i
$687$	−21.2416	−	0.624722i	−0.810418	−	0.0238346i
$688$	12.6114	−	3.10906i	0.480804	−	0.118532i
$689$	−3.84682	−	3.22787i	−0.146552	−	0.122972i
$690$	1.41298	+	0.267557i	0.0537912	+	0.0101857i
$691$	10.5292	−	28.9287i	0.400549	−	1.10050i	−0.561465	−	0.827501i	$-0.689762\pi$
$691$	10.5292	−	28.9287i	0.400549	−	1.10050i	0.962014	−	0.273000i	$-0.0880158\pi$
$692$	−27.0534	−	30.1257i	−1.02842	−	1.14521i
$693$	−3.89656	+	9.01771i	−0.148018	+	0.342555i
$694$	19.3482	−	7.41246i	0.734449	−	0.281373i
$695$	−0.0903596	−	0.512455i	−0.00342754	−	0.0194385i
$696$	−1.10342	−	0.170777i	−0.0418249	−	0.00647330i
$697$	1.28572	−	0.467965i	0.0487003	−	0.0177255i
$698$	10.8512	+	3.74436i	0.410723	+	0.141726i
$699$	−1.44488	+	0.211182i	−0.0546504	+	0.00798763i
$700$	−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	$0.710743\pi$
$702$	1.98759	+	6.97360i	0.0750168	+	0.263202i
$703$	64.1840			2.42075
$704$	4.43400	−	17.4887i	0.167113	−	0.659132i
$705$	1.72469	+	0.685802i	0.0649557	+	0.0258288i
$706$	−5.54446	+	16.0679i	−0.208668	+	0.604722i
$707$	−3.56262	−	9.78821i	−0.133986	−	0.368123i
$708$	16.1165	+	27.6466i	0.605693	+	1.03902i
$709$	11.9516	−	2.10739i	0.448852	−	0.0791446i	0.0553467	−	0.998467i	$-0.482374\pi$
$709$	11.9516	−	2.10739i	0.448852	−	0.0791446i	0.393505	+	0.919323i	$0.371262\pi$
$710$	2.13290	−	0.817129i	0.0800462	−	0.0306663i
$711$	9.64136	+	19.2275i	0.361579	+	0.721089i
$712$	−15.1996	+	9.82802i	−0.569628	+	0.368321i
$713$	26.9903	+	9.82365i	1.01079	+	0.367899i
$714$	2.36769	+	2.03814i	0.0886084	+	0.0762755i
$715$	0.194800	−	0.232153i	0.00728510	−	0.00868205i
$716$	−37.5037	+	23.3662i	−1.40158	+	0.873236i
$717$	−16.4735	+	8.87576i	−0.615213	+	0.331471i
$718$	−15.6390	−	8.68230i	−0.583640	−	0.324020i
$719$	−9.22099	+	15.9712i	−0.343885	+	0.595626i	−0.985151	−	0.171693i	$-0.945076\pi$
$719$	−9.22099	+	15.9712i	−0.343885	+	0.595626i	0.641266	+	0.767319i	$0.278410\pi$
$720$	−1.06084	−	1.24298i	−0.0395351	−	0.0463230i
$721$	5.78238	+	10.0154i	0.215347	+	0.372992i
$722$	−0.405981	−	24.1720i	−0.0151090	−	0.899590i
$723$	15.1797	+	3.13930i	0.564537	+	0.116752i
$724$	1.18297	+	35.2069i	0.0439646	+	1.30845i
$725$	−1.11810	−	0.197152i	−0.0415253	−	0.00732204i
$726$	7.08416	+	12.6354i	0.262918	+	0.468943i
$727$	−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
$729$	17.3941	−	20.6506i	0.644225	−	0.764836i
$730$	0.295482	−	1.85767i	0.0109363	−	0.0687555i
$731$	−1.83349	−	2.18507i	−0.0678142	−	0.0808178i
$732$	40.8330	−	15.0559i	1.50923	−	0.556481i
$733$	−7.91675	−	1.39594i	−0.292412	−	0.0515601i	0.0255180	−	0.999674i	$-0.491877\pi$
$733$	−7.91675	−	1.39594i	−0.292412	−	0.0515601i	−0.317930	+	0.948114i	$0.602988\pi$
$734$	22.3718	−	4.33332i	0.825757	−	0.159946i
$735$	0.233676	−	1.12991i	0.00861928	−	0.0416773i
$736$	14.0543	−	19.9315i	0.518049	−	0.734684i
$737$	10.3507	+	17.9279i	0.381272	+	0.660382i
$738$	2.51904	−	6.10953i	0.0927270	−	0.224895i
$739$	6.23912	+	3.60216i	0.229510	+	0.132508i	0.610346	−	0.792135i	$-0.291030\pi$
$739$	6.23912	+	3.60216i	0.229510	+	0.132508i	−0.380836	+	0.924643i	$0.624364\pi$
$740$	2.29047	+	1.79438i	0.0841992	+	0.0659626i
$741$	−9.03977	+	4.87055i	−0.332084	+	0.178924i
$742$	−7.89083	+	6.85026i	−0.289681	+	0.251481i
$743$	−28.1102	−	23.5873i	−1.03126	−	0.865334i	−0.0402635	−	0.999189i	$-0.512820\pi$
$743$	−28.1102	−	23.5873i	−1.03126	−	0.865334i	−0.991001	+	0.133856i	$0.957264\pi$
$744$	−16.9083	−	27.9166i	−0.619887	−	1.02347i
$745$	2.85679	+	1.03979i	0.104665	+	0.0380949i
$746$	−18.8798	−	15.3092i	−0.691238	−	0.560509i
$747$	−3.62035	+	1.81537i	−0.132462	+	0.0664210i
$748$	−3.87659	+	0.818653i	−0.141742	+	0.0299329i
$749$	−27.9175	+	4.92261i	−1.02008	+	0.179868i
$750$	−2.10781	−	2.57729i	−0.0769663	−	0.0941094i
$751$	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	$0.156365\pi$
$752$	22.6997	−	21.8055i	0.827774	−	0.795163i
$753$	−12.0602	−	4.79558i	−0.439498	−	0.174761i
$754$	−0.272739	+	0.163633i	−0.00993257	+	0.00595918i
$755$			2.59486i			0.0944365i
$756$	14.9807	−	1.80508i	0.544844	−	0.0656500i
$757$			36.5128i			1.32708i	0.748140	+	0.663541i	$0.230947\pi$
$757$			36.5128i			1.32708i	−0.748140	+	0.663541i	$0.769053\pi$
$758$	9.35525	+	15.5930i	0.339798	+	0.566365i
$759$	−2.43556	−	16.6638i	−0.0884051	−	0.604857i
$760$	1.39628	−	1.84531i	0.0506482	−	0.0669366i
$761$	−4.63196	+	1.68589i	−0.167908	+	0.0611136i	−0.424607	−	0.905378i	$-0.639588\pi$
$761$	−4.63196	+	1.68589i	−0.167908	+	0.0611136i	0.256698	+	0.966492i	$0.417365\pi$
$762$	−3.27860	−	20.0704i	−0.118771	−	0.727073i
$763$	−7.95705	+	1.40304i	−0.288065	+	0.0507935i
$764$	3.88483	+	18.3959i	0.140548	+	0.665542i
$765$	−0.142343	+	0.329420i	−0.00514641	+	0.0119102i
$766$	4.39162	−	5.41589i	0.158676	−	0.195684i
$767$	8.56606	+	3.11779i	0.309303	+	0.112577i
$768$	−26.6375	+	7.64480i	−0.961198	+	0.275858i
$769$	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	$0.378352\pi$
$770$	−0.413409	−	0.476207i	−0.0148982	−	0.0171613i
$771$	0.847962	−	28.8321i	0.0305386	−	1.03836i
$772$	11.6614	+	9.13568i	0.419703	+	0.328800i
$773$	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	$0.612351\pi$
$774$	−13.7647	−	0.578593i	−0.494763	−	0.0207971i
$775$	−16.5936	−	28.7410i	−0.596061	−	1.03241i
$776$	0.690697	−	2.24329i	0.0247946	−	0.0805293i
$777$	−25.5058	+	8.44285i	−0.915016	+	0.302886i
$778$	−4.28996	−	22.1479i	−0.153803	−	0.794040i
$779$	9.21589	+	1.62501i	0.330194	+	0.0582220i
$780$	−0.458758	−	0.0789127i	−0.0164262	−	0.00282553i
$781$	−17.1931	−	20.4899i	−0.615216	−	0.733186i
$782$	−5.28923	−	0.841308i	−0.189143	−	0.0300851i
$783$	1.07286	+	0.501508i	0.0383408	+	0.0179224i
$784$	−15.8000	−	11.5431i	−0.564284	−	0.412255i
$785$	0.896137	−	0.751949i	0.0319845	−	0.0268382i
$786$	34.9166	+	20.7504i	1.24543	+	0.740143i
$787$	−15.6553	−	2.76045i	−0.558050	−	0.0983993i	−0.112493	−	0.993653i	$-0.535883\pi$
$787$	−15.6553	−	2.76045i	−0.558050	−	0.0983993i	−0.445558	+	0.895253i	$0.646995\pi$
$788$	1.22337	+	36.4094i	0.0435807	+	1.29703i
$789$	21.3014	−	23.9212i	0.758352	−	0.851616i
$790$	−1.38059	+	0.0231877i	−0.0491192	+	0.000824980i
$791$	−8.90599	−	15.4256i	−0.316661	−	0.548472i
$792$	−9.70749	+	16.4915i	−0.344941	+	0.586001i
$793$	6.19857	−	10.7362i	0.220118	−	0.381255i
$794$	14.9802	−	26.9830i	0.531627	−	0.957591i
$795$	−1.02141	−	0.630454i	−0.0362255	−	0.0223599i
$796$	17.0322	+	27.3374i	0.603690	+	0.968948i
$797$	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	$0.140769\pi$
$798$	7.05429	+	20.1691i	0.249719	+	0.713980i
$799$	−6.49541	−	2.36413i	−0.229791	−	0.0836371i
$800$	−27.2431	+	7.20358i	−0.963188	+	0.254685i
$801$	18.3951	−	5.49458i	0.649958	−	0.194141i
$802$	17.5106	+	45.7068i	0.618322	+	1.61396i
$803$	−21.6932	+	3.82509i	−0.765536	+	0.134985i
$804$	15.7833	−	27.6037i	0.556634	−	0.973507i
$805$	−0.291550	−	0.801026i	−0.0102758	−	0.0282325i
$806$	−8.78865	−	3.03266i	−0.309567	−	0.106821i
$807$	−34.4050	+	27.1865i	−1.21111	+	0.957008i
$808$	−4.52545	−	19.7803i	−0.159205	−	0.695869i
$809$	2.71159			0.0953343			0.0476672	−	0.998863i	$-0.484821\pi$
$809$	2.71159			0.0953343			0.0476672	+	0.998863i	$0.484821\pi$
$810$	0.711157	+	1.58064i	0.0249875	+	0.0555380i
$811$		−	38.7762i		−	1.36162i	−0.732462	−	0.680808i	$-0.761629\pi$
$811$		−	38.7762i		−	1.36162i	0.732462	−	0.680808i	$-0.238371\pi$
$812$	0.247121	+	0.613977i	0.00867226	+	0.0215464i
$813$	17.8505	+	22.5902i	0.626046	+	0.792274i
$814$	11.1145	−	32.2098i	0.389563	−	1.12895i
$815$	1.28627	−	0.468164i	0.0450561	−	0.0163991i
$816$	4.08515	+	4.51094i	0.143009	+	0.157914i
$817$	−3.38771	−	19.2126i	−0.118521	−	0.672165i
$818$	2.04298	+	5.33266i	0.0714312	+	0.186452i
$819$	2.95160	−	3.12459i	0.103137	−	0.109182i
$820$	0.283448	+	0.315637i	0.00989842	+	0.0110225i
$821$	−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	$0.886825\pi$
$822$	18.7269	−	6.54985i	0.653175	−	0.228452i
$823$	−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	$0.843214\pi$
$824$	8.76151	+	20.7549i	0.305222	+	0.723030i
$825$	−10.2205	+	16.5584i	−0.355833	+	0.576490i
$826$	9.20722	−	16.5845i	0.320360	−	0.577047i
$827$	−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	$0.716320\pi$
$828$	−20.2287	+	16.1225i	−0.702996	+	0.560296i
$829$	19.4960	−	11.2560i	0.677124	−	0.390938i	−0.121647	−	0.992573i	$-0.538817\pi$
$829$	19.4960	−	11.2560i	0.677124	−	0.390938i	0.798771	+	0.601636i	$0.205484\pi$
$830$	−0.00436601	−	0.259951i	−0.000151546	−	0.00902304i
$831$	22.9320	+	20.4207i	0.795504	+	0.708385i
$832$	−4.44026	+	6.52710i	−0.153938	+	0.226287i
$833$	−0.746175	+	4.23177i	−0.0258534	+	0.146622i
$834$	8.04635	+	4.78182i	0.278622	+	0.165581i
$835$	−1.39228	−	1.65925i	−0.0481817	−	0.0574207i
$836$	−25.7613	−	8.40793i	−0.890973	−	0.290794i
$837$	8.92830	+	33.4465i	0.308607	+	1.15608i
$838$	−2.41964	+	15.2121i	−0.0835852	+	0.525493i
$839$	−0.793395	+	0.665737i	−0.0273910	+	0.0229838i	−0.656380	−	0.754430i	$-0.727913\pi$
$839$	−0.793395	+	0.665737i	−0.0273910	+	0.0229838i	0.628989	+	0.777414i	$0.283469\pi$
$840$	−0.312125	+	0.916970i	−0.0107693	+	0.0316385i
$841$	5.02678	−	28.5083i	0.173337	−	0.983044i
$842$	1.51677	+	7.83068i	0.0522714	+	0.269863i
$843$	−8.91946	−	26.9457i	−0.307203	−	0.928058i
$844$	−37.5094	−	5.32206i	−1.29113	−	0.183193i
$845$	1.41829	−	0.818851i	0.0487907	−	0.0281693i
$846$	−29.5883	+	15.4638i	−1.01727	+	0.531657i
$847$	4.29326	−	7.43615i	0.147518	−	0.255509i
$848$	−16.9057	+	11.3383i	−0.580544	+	0.389358i
$849$	31.8666	+	0.937207i	1.09366	+	0.0321649i
$850$	4.05678	+	4.67302i	0.139147	+	0.160283i
$851$	29.6060	−	35.2830i	1.01488	−	1.20949i
$852$	−13.8900	+	38.6654i	−0.475865	+	1.32466i
$853$	8.12987	−	22.3366i	0.278361	−	0.764792i	−0.719187	−	0.694816i	$-0.755486\pi$
$853$	8.12987	−	22.3366i	0.278361	−	0.764792i	0.997549	−	0.0699754i	$-0.0222921\pi$
$854$	−20.0372	−	16.2477i	−0.685660	−	0.555985i
$855$	−1.96965	+	1.46444i	−0.0673608	+	0.0500827i
$856$	−55.1529	+	2.78105i	−1.88509	+	0.0950542i
$857$	4.07463	+	23.1084i	0.139187	+	0.789367i	0.971852	+	0.235591i	$0.0757026\pi$
$857$	4.07463	+	23.1084i	0.139187	+	0.789367i	−0.832666	+	0.553776i	$0.813186\pi$
$858$	0.878834	+	5.37990i	0.0300029	+	0.183667i
$859$	11.7827	+	32.3728i	0.402022	+	1.10455i	0.961285	+	0.275555i	$0.0888618\pi$
$859$	11.7827	+	32.3728i	0.402022	+	1.10455i	−0.559264	+	0.828990i	$0.688916\pi$
$860$	0.416230	−	0.780331i	0.0141933	−	0.0266091i
$861$	−3.87602	+	0.566515i	−0.132094	+	0.0193068i
$862$	−14.8716	+	8.92244i	−0.506530	+	0.303900i
$863$	−26.5038			−0.902199			−0.451100	−	0.892474i	$-0.648968\pi$
$863$	−26.5038			−0.902199			−0.451100	+	0.892474i	$0.648968\pi$
$864$	29.3936	+	0.124511i	0.999991	+	0.00423595i
$865$	−2.75691			−0.0937378
$866$	−42.1886	+	25.3116i	−1.43363	+	0.860124i
$867$	−10.3860	+	26.1192i	−0.352726	+	0.887055i
$868$	−9.10502	+	17.0697i	−0.309045	+	0.579384i
$869$	5.53038	+	15.1946i	0.187605	+	0.515442i
$870$	−0.0588497	+	0.0481295i	−0.00199519	+	0.00163174i
$871$	−1.57287	−	8.92017i	−0.0532946	−	0.302248i
$872$	−15.7197	+	0.792654i	−0.532335	+	0.0268427i
$873$	−1.36936	+	2.07917i	−0.0463456	+	0.0703691i
$874$	−28.4520	−	23.0710i	−0.962403	−	0.780390i
$875$	−0.674995	+	1.85453i	−0.0228190	+	0.0626947i
$876$	21.8570	+	25.8278i	0.738480	+	0.872641i
$877$	−12.6506	+	15.0765i	−0.427182	+	0.509096i	−0.936107	−	0.351715i	$-0.885599\pi$
$877$	−12.6506	+	15.0765i	−0.427182	+	0.509096i	0.508925	+	0.860811i	$0.330043\pi$
$878$	17.5666	+	20.2350i	0.592845	+	0.682900i
$879$	−23.1236	−	42.9176i	−0.779941	−	1.44757i
$880$	−0.684257	−	1.02025i	−0.0230663	−	0.0343925i
$881$	−0.970676	+	1.68126i	−0.0327029	+	0.0566431i	−0.881914	−	0.471411i	$-0.843745\pi$
$881$	−0.970676	+	1.68126i	−0.0327029	+	0.0566431i	0.849211	+	0.528054i	$0.177078\pi$
$882$	12.6612	+	16.4450i	0.426324	+	0.553732i
$883$	3.58570	−	2.07021i	0.120669	−	0.0696680i	−0.438451	−	0.898755i	$-0.644473\pi$
$883$	3.58570	−	2.07021i	0.120669	−	0.0696680i	0.559119	+	0.829087i	$0.311139\pi$
$884$	1.71640	+	0.243534i	0.0577289	+	0.00819092i
$885$	2.13376	+	0.441282i	0.0717256	+	0.0148335i
$886$	6.74015	+	34.7976i	0.226440	+	1.16905i
$887$	4.24470	−	24.0729i	0.142523	−	0.808289i	−0.826799	−	0.562497i	$-0.809841\pi$
$887$	4.24470	−	24.0729i	0.142523	−	0.808289i	0.969323	−	0.245792i	$-0.0790481\pi$
$888$	−51.3402	+	10.1675i	−1.72286	+	0.341200i
$889$	−9.23429	+	7.74849i	−0.309708	+	0.259876i
$890$	−0.193595	+	1.21712i	−0.00648932	+	0.0407978i
$891$	14.7812	−	13.9104i	0.495188	−	0.466015i
$892$	22.2116	+	7.24940i	0.743700	+	0.242728i
$893$	−30.3887	−	36.2158i	−1.01692	−	1.21192i
$894$	−47.6991	+	26.7430i	−1.59530	+	0.894420i
$895$	−0.522445	+	2.96293i	−0.0174634	+	0.0990399i
$896$	11.9620	+	11.2585i	0.399624	+	0.376119i
$897$	−1.49233	+	7.21593i	−0.0498273	+	0.240933i
$898$	−0.0984100	−	5.85932i	−0.00328398	−	0.195528i
$899$	−1.31498	+	0.759206i	−0.0438572	+	0.0253209i
$900$	29.8792	+	0.753590i	0.995974	+	0.0251197i
$901$	3.87129	+	2.23509i	0.128971	+	0.0744617i
$902$	2.41137	−	4.34347i	0.0802898	−	0.144622i
$903$	3.87349	+	7.18921i	0.128902	+	0.239242i
$904$	−13.4944	−	31.9666i	−0.448818	−	1.06319i
$905$	1.83739	+	1.54175i	0.0610768	+	0.0512495i
$906$	−35.3741	−	30.4505i	−1.17522	−	1.01165i
$907$	19.8264	−	54.4726i	0.658325	−	1.80873i	0.0739328	−	0.997263i	$-0.476445\pi$
$907$	19.8264	−	54.4726i	0.658325	−	1.80873i	0.584393	−	0.811471i	$-0.301333\pi$
$908$	2.42181	+	2.69683i	0.0803704	+	0.0894975i
$909$	−1.26486	+	21.4851i	−0.0419527	+	0.712614i
$910$	0.0987126	+	0.257663i	0.00327229	+	0.00854144i
$911$	1.13796	+	6.45371i	0.0377024	+	0.213821i	0.997839	−	0.0657114i	$-0.0209317\pi$
$911$	1.13796	+	6.45371i	0.0377024	+	0.213821i	−0.960136	+	0.279532i	$0.909821\pi$
$912$	8.77078	+	40.6893i	0.290429	+	1.34736i
$913$	−2.86099	+	1.04132i	−0.0946850	+	0.0344625i
$914$	6.92245	−	20.0613i	0.228974	−	0.663568i
$915$	1.09491	−	2.75353i	0.0361965	−	0.0910290i
$916$	9.16220	+	22.7636i	0.302728	+	0.752131i
$917$		−	24.0760i		−	0.795059i
$918$	−2.82040	−	5.80620i	−0.0930869	−	0.191633i
$919$	−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
$921$	4.10598	+	28.0926i	0.135297	+	0.925683i
$922$	−4.91069	−	1.69451i	−0.161725	−	0.0558057i
$923$	4.00277	+	10.9975i	0.131753	+	0.361988i
$924$	11.3432	−	0.0474825i	0.373163	−	0.00156206i
$925$	−52.4099	+	9.24128i	−1.72323	+	0.303851i
$926$	2.98773	+	7.79866i	0.0981828	+	0.256280i
$927$	−2.75918	−	23.7351i	−0.0906234	−	0.779564i
$928$	0.329584	+	1.24645i	0.0108191	+	0.0409167i
$929$	−53.7456	−	19.5618i	−1.76333	−	0.641801i	−0.763344	−	0.645993i	$-0.776444\pi$
$929$	−53.7456	−	19.5618i	−1.76333	−	0.641801i	−0.999991	+	0.00419109i	$0.998666\pi$
$930$	−2.18346	−	0.413453i	−0.0715985	−	0.0135577i
$931$	−18.8913	+	22.5138i	−0.619137	+	0.737859i
$932$	0.891627	+	1.43110i	0.0292062	+	0.0468771i
$933$	1.56573	−	53.2375i	0.0512597	−	1.74292i
$934$	3.79942	−	6.84369i	0.124321	−	0.223932i
$935$	−0.134886	+	0.233630i	−0.00441126	+	0.00764052i
$936$	6.45927	−	5.32792i	0.211128	−	0.174148i
$937$	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	$0.685507\pi$
$938$	−18.8454	+	0.316518i	−0.615325	+	0.0103347i
$939$	−11.9372	−	36.0623i	−0.389557	−	1.17685i
$940$	−0.0719709	−	2.14197i	−0.00234743	−	0.0698632i
$941$	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	$0.271725\pi$
$942$	−0.265292	+	21.0406i	−0.00864368	+	0.685539i
$943$	5.14428	−	4.31656i	0.167521	−	0.140567i
$944$	21.7985	−	29.8372i	0.709480	−	0.971118i
$945$	0.590079	−	0.841038i	0.0191953	−	0.0273590i
$946$	−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	$0.853458\pi$
$948$	15.8851	−	19.0928i	0.515923	−	0.620107i
$949$	9.49177	+	1.67365i	0.308116	+	0.0543291i
$950$	8.04851	+	41.5523i	0.261128	+	1.34813i
$951$	35.0531	+	31.2143i	1.13667	+	1.01219i
$952$	1.06152	−	3.44767i	0.0344041	−	0.111740i
$953$	−17.4033	−	30.1434i	−0.563749	−	0.976442i	−0.997165	−	0.0752476i	$-0.976025\pi$
$953$	−17.4033	−	30.1434i	−0.563749	−	0.976442i	0.433416	−	0.901194i	$-0.357308\pi$
$954$	20.5807	−	6.52583i	0.666326	−	0.211282i
$955$	1.10867	+	0.640089i	0.0358756	+	0.0207128i
$956$	17.0092	+	13.3252i	0.550116	+	0.430967i
$957$	0.757595	+	0.467619i	0.0244896	+	0.0151160i
$958$	7.66301	+	8.82704i	0.247581	+	0.285189i
$959$	−9.00855	−	7.55907i	−0.290901	−	0.244095i
$960$	−0.824547	+	1.69724i	−0.0266121	+	0.0547781i
$961$	−12.5773	−	4.57775i	−0.405718	−	0.147669i
$962$	−9.39001	+	11.5801i	−0.302746	+	0.373357i
$963$	56.9855	+	13.5435i	1.83633	+	0.436433i
$964$	−3.69829	−	17.5126i	−0.119114	−	0.564044i
$965$	0.993327	−	0.175150i	0.0319763	−	0.00563829i
$966$	14.3412	+	5.42550i	0.461421	+	0.174563i
$967$	−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	$0.428851\pi$
$968$	10.0928	−	13.3386i	0.324395	−	0.428720i
$969$	7.17188	−	5.66714i	0.230394	−	0.182055i
$970$	−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	$0.988593\pi$
$972$	−29.8933	−	8.85397i	−0.958827	−	0.283991i
$973$		−	5.54818i		−	0.177867i
$974$	20.4202	−	12.2514i	0.654306	−	0.392560i
$975$	6.68022	−	5.27864i	0.213938	−	0.169052i
$976$	−34.8131	−	36.2409i	−1.11434	−	1.16004i
$977$	42.2729	−	15.3861i	1.35243	−	0.492244i	0.438725	−	0.898621i	$-0.355430\pi$
$977$	42.2729	−	15.3861i	1.35243	−	0.492244i	0.913706	+	0.406377i	$0.133208\pi$
$978$	−8.71214	+	23.0288i	−0.278584	+	0.736380i
$979$	14.2130	−	2.50614i	0.454250	−	0.0800965i
$980$	−1.30357	+	0.275285i	−0.0416409	+	0.00879366i
$981$	16.2420	+	3.86016i	0.518567	+	0.123246i
$982$	−36.1289	−	29.2961i	−1.15292	−	0.934876i
$983$	−11.4136	−	4.15422i	−0.364038	−	0.132499i	0.153523	−	0.988145i	$-0.450938\pi$
$983$	−11.4136	−	4.15422i	−0.364038	−	0.132499i	−0.517562	+	0.855646i	$0.673160\pi$
$984$	−7.62913	+	0.160082i	−0.243208	+	0.00510321i
$985$	1.90014	+	1.59441i	0.0605436	+	0.0508021i
$986$	0.213804	−	0.185609i	0.00680890	−	0.00591101i
$987$	16.8399	+	10.3943i	0.536020	+	0.330854i
$988$	9.33374	+	7.31216i	0.296946	+	0.232631i
$989$	−12.1241	−	6.99988i	−0.385525	−	0.222583i
$990$	0.393830	+	1.24203i	0.0125167	+	0.0394745i
$991$	−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	$-0.449654\pi$
$992$	−21.7180	+	30.7999i	−0.689547	+	0.977897i
$993$	−18.6306	−	16.5903i	−0.591225	−	0.526477i
$994$	23.9088	−	4.63103i	0.758340	−	0.146887i
$995$	2.15976	+	0.380823i	0.0684689	+	0.0120729i
$996$	3.59499	+	2.99100i	0.113912	+	0.0947734i
$997$	3.84922	+	4.58733i	0.121906	+	0.145282i	0.823546	−	0.567250i	$-0.191993\pi$
$997$	3.84922	+	4.58733i	0.121906	+	0.145282i	−0.701639	+	0.712532i	$0.747548\pi$
$998$	1.76167	−	11.0755i	0.0557647	−	0.350588i
$999$	55.2963	+	4.89012i	1.74950	+	0.154717i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	216.2.t.a.157.29	yes	204
3.2	odd	2		648.2.t.a.37.6		204
4.3	odd	2		864.2.bf.a.49.11		204
8.3	odd	2		864.2.bf.a.49.24		204
8.5	even	2	inner	216.2.t.a.157.26	✓	204
24.5	odd	2		648.2.t.a.37.9		204
27.11	odd	18		648.2.t.a.613.9		204
27.16	even	9	inner	216.2.t.a.205.26	yes	204
108.43	odd	18		864.2.bf.a.529.24		204
216.43	odd	18		864.2.bf.a.529.11		204
216.173	odd	18		648.2.t.a.613.6		204
216.205	even	18	inner	216.2.t.a.205.29	yes	204

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
216.2.t.a.157.26	✓	204	8.5	even	2	inner
216.2.t.a.157.29	yes	204	1.1	even	1	trivial
216.2.t.a.205.26	yes	204	27.16	even	9	inner
216.2.t.a.205.29	yes	204	216.205	even	18	inner
648.2.t.a.37.6		204	3.2	odd	2
648.2.t.a.37.9		204	24.5	odd	2
648.2.t.a.613.6		204	216.173	odd	18
648.2.t.a.613.9		204	27.11	odd	18
864.2.bf.a.49.11		204	4.3	odd	2
864.2.bf.a.49.24		204	8.3	odd	2
864.2.bf.a.529.11		204	216.43	odd	18
864.2.bf.a.529.24		204	108.43	odd	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:	\( N \)	\(=\)	\( 216 = 2^{3} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	216.t (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(1.21270 - 0.727574i) q^{2} +(1.07385 + 1.35898i) q^{3} +(0.941271 - 1.76466i) q^{4} +(-0.0465753 - 0.127965i) q^{5} +(2.29102 + 0.866728i) q^{6} +(-0.252128 - 1.42989i) q^{7} +(-0.142441 - 2.82484i) q^{8} +(-0.693675 + 2.91870i) q^{9} +(-0.149586 - 0.121295i) q^{10} +(-0.771344 + 2.11925i) q^{11} +(3.40893 - 0.615810i) q^{12} +(0.634290 - 0.755917i) q^{13} +(-1.34611 - 1.55058i) q^{14} +(0.123887 - 0.200710i) q^{15} +(-2.22802 - 3.32204i) q^{16} +(-0.439205 + 0.760726i) q^{17} +(1.28235 + 4.04420i) q^{18} +(-5.20298 + 3.00394i) q^{19} +(-0.269654 - 0.0382600i) q^{20} +(1.67245 - 1.87813i) q^{21} +(0.606505 + 3.13122i) q^{22} +(-0.748645 + 4.24578i) q^{23} +(3.68595 - 3.22704i) q^{24} +(3.81602 - 3.20202i) q^{25} +(0.219216 - 1.37819i) q^{26} +(-4.71137 + 2.19157i) q^{27} +(-2.76058 - 0.900994i) q^{28} +(-0.146501 - 0.174594i) q^{29} +(0.00420544 - 0.333538i) q^{30} +(1.15687 - 6.56095i) q^{31} +(-5.11894 - 2.40758i) q^{32} +(-3.70834 + 1.22752i) q^{33} +(0.0208614 + 1.24208i) q^{34} +(-0.171232 + 0.0988610i) q^{35} +(4.49757 + 3.97139i) q^{36} +(-9.25201 - 5.34165i) q^{37} +(-4.12405 + 7.42842i) q^{38} +(1.70841 + 0.0502450i) q^{39} +(-0.354845 + 0.149795i) q^{40} +(-1.19321 - 1.00123i) q^{41} +(0.661694 - 3.49443i) q^{42} +(-1.11062 + 3.05141i) q^{43} +(3.01370 + 3.35595i) q^{44} +(0.405799 - 0.0471736i) q^{45} +(2.18124 + 5.69354i) q^{46} +(1.36645 + 7.74952i) q^{47} +(2.12203 - 6.59522i) q^{48} +(4.59683 - 1.67311i) q^{49} +(2.29797 - 6.65952i) q^{50} +(-1.50546 + 0.220036i) q^{51} +(-0.736895 - 1.83083i) q^{52} -5.08895i q^{53} +(-4.11894 + 6.08558i) q^{54} +0.307115 q^{55} +(-4.00329 + 0.915895i) q^{56} +(-9.66954 - 3.84497i) q^{57} +(-0.304692 - 0.105139i) q^{58} +(3.15956 + 8.68082i) q^{59} +(-0.237574 - 0.407541i) q^{60} +(12.3724 - 2.18158i) q^{61} +(-3.37064 - 8.79816i) q^{62} +(4.34831 + 0.255992i) q^{63} +(-7.95942 + 0.804744i) q^{64} +(-0.126273 - 0.0459596i) q^{65} +(-3.60398 + 4.18671i) q^{66} +(5.90023 - 7.03162i) q^{67} +(0.929007 + 1.49109i) q^{68} +(-6.57388 + 3.54195i) q^{69} +(-0.135724 + 0.244473i) q^{70} +(-5.93006 + 10.2712i) q^{71} +(8.34367 + 1.54378i) q^{72} +(4.88366 + 8.45874i) q^{73} +(-15.1063 + 0.253718i) q^{74} +(8.44934 + 1.74741i) q^{75} +(0.403507 + 12.0090i) q^{76} +(3.22477 + 0.568614i) q^{77} +(2.10835 - 1.18207i) q^{78} +(5.49238 - 4.60866i) q^{79} +(-0.321333 + 0.439832i) q^{80} +(-8.03763 - 4.04926i) q^{81} +(-2.17548 - 0.346032i) q^{82} +(0.867764 + 1.03416i) q^{83} +(-1.74003 - 4.71912i) q^{84} +(0.117802 + 0.0207717i) q^{85} +(0.873278 + 4.50850i) q^{86} +(0.0799487 - 0.386581i) q^{87} +(6.09641 + 1.87706i) q^{88} +(-3.19969 - 5.54203i) q^{89} +(0.457789 - 0.352456i) q^{90} +(-1.24080 - 0.716376i) q^{91} +(6.78766 + 5.31753i) q^{92} +(10.1585 - 5.47333i) q^{93} +(7.29544 + 8.40363i) q^{94} +(0.626728 + 0.525888i) q^{95} +(-2.22513 - 9.54195i) q^{96} +(0.779817 + 0.283830i) q^{97} +(4.35726 - 5.37352i) q^{98} +(-5.65040 - 3.72140i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 204 q - 6 q^{2} - 6 q^{4} - 6 q^{6} - 12 q^{7} - 3 q^{8} - 12 q^{9} - 3 q^{10} + 3 q^{12} - 21 q^{14} - 12 q^{15} - 6 q^{16} - 6 q^{17} - 27 q^{18} + 15 q^{20} - 6 q^{22} - 12 q^{23} - 12 q^{25} - 30 q^{26}+ \cdots + 54 q^{98}+O(q^{100}) \) 204 * q - 6 * q^2 - 6 * q^4 - 6 * q^6 - 12 * q^7 - 3 * q^8 - 12 * q^9 - 3 * q^10 + 3 * q^12 - 21 * q^14 - 12 * q^15 - 6 * q^16 - 6 * q^17 - 27 * q^18 + 15 * q^20 - 6 * q^22 - 12 * q^23 - 12 * q^25 - 30 * q^26 - 12 * q^28 - 39 * q^30 - 12 * q^31 - 36 * q^32 - 36 * q^36 - 42 * q^38 - 12 * q^39 - 21 * q^40 - 24 * q^41 - 66 * q^42 + 21 * q^44 - 3 * q^46 - 12 * q^47 + 51 * q^48 - 12 * q^49 - 99 * q^50 - 33 * q^52 - 90 * q^54 - 24 * q^55 + 99 * q^56 - 30 * q^57 + 21 * q^58 + 102 * q^60 - 36 * q^62 - 72 * q^63 - 3 * q^64 - 12 * q^65 - 9 * q^66 + 75 * q^68 + 9 * q^70 - 90 * q^71 + 60 * q^72 - 6 * q^73 + 9 * q^74 - 18 * q^76 + 12 * q^78 - 12 * q^79 + 78 * q^80 - 12 * q^81 - 12 * q^82 + 102 * q^84 - 30 * q^86 - 48 * q^87 - 30 * q^88 - 6 * q^89 + 6 * q^90 + 111 * q^92 - 33 * q^94 - 42 * q^95 + 126 * q^96 - 12 * q^97 + 54 * q^98

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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