LMFDB - Embedded newform 216.2.t.a.157.26

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			157.26
Character	$\chi$	$=$	216.157
Dual form			216.2.t.a.205.26

$q$-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} +(-1.07385 - 1.35898i) q^{3} +(-0.280958 - 1.98017i) q^{4} +(0.0465753 + 0.127965i) q^{5} +(-2.44688 - 0.113116i) q^{6} +(-0.252128 - 1.42989i) q^{7} +(-2.37516 - 1.53578i) q^{8} +(-0.693675 + 2.91870i) q^{9} +(0.179838 + 0.0688972i) q^{10} +(0.771344 - 2.11925i) q^{11} +(-2.38931 + 2.50823i) q^{12} +(-0.634290 + 0.755917i) q^{13} +(-1.76077 - 1.05640i) q^{14} +(0.123887 - 0.200710i) q^{15} +(-3.84213 + 1.11269i) q^{16} +(-0.439205 + 0.760726i) q^{17} +(2.47387 + 3.44674i) q^{18} +(5.20298 - 3.00394i) q^{19} +(0.240306 - 0.128180i) q^{20} +(-1.67245 + 1.87813i) q^{21} +(-1.54810 - 2.78851i) q^{22} +(-0.748645 + 4.24578i) q^{23} +(0.463481 + 4.87701i) 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} +(-0.0994893 - 0.318382i) q^{30} +(1.15687 - 6.56095i) q^{31} +(-2.37377 + 5.13471i) q^{32} +(-3.70834 + 1.22752i) q^{33} +(0.405215 + 1.17431i) q^{34} +(0.171232 - 0.0988610i) q^{35} +(5.97441 + 0.553560i) q^{36} +(9.25201 + 5.34165i) q^{37} +(1.61569 - 8.34139i) q^{38} +(1.70841 + 0.0502450i) q^{39} +(0.0859012 - 0.375466i) q^{40} +(-1.19321 - 1.00123i) q^{41} +(0.455183 + 3.52728i) q^{42} +(1.11062 - 3.05141i) q^{43} +(-4.41319 - 0.931971i) q^{44} +(-0.405799 + 0.0471736i) q^{45} +(3.84013 + 4.73578i) q^{46} +(1.36645 + 7.74952i) q^{47} +(5.63801 + 4.02652i) q^{48} +(4.59683 - 1.67311i) q^{49} +(0.118305 - 7.04385i) q^{50} +(1.50546 - 0.220036i) q^{51} +(1.67505 + 1.04362i) q^{52} +5.08895i q^{53} +(2.02749 - 7.06324i) q^{54} +0.307115 q^{55} +(-1.59714 + 3.78343i) q^{56} +(-9.66954 - 3.84497i) q^{57} +(0.322276 + 0.00541278i) q^{58} +(-3.15956 - 8.68082i) q^{59} +(-0.432247 - 0.188925i) q^{60} +(-12.3724 + 2.18158i) q^{61} +(-5.93411 - 7.31814i) q^{62} +(4.34831 + 0.255992i) q^{63} +(3.28278 + 7.29543i) q^{64} +(-0.126273 - 0.0459596i) q^{65} +(-2.12711 + 5.09830i) q^{66} +(-5.90023 + 7.03162i) q^{67} +(1.62976 + 0.655968i) q^{68} +(6.57388 - 3.54195i) q^{69} +(0.0531732 - 0.274519i) q^{70} +(-5.93006 + 10.2712i) q^{71} +(6.13006 - 5.86706i) q^{72} +(4.88366 + 8.45874i) q^{73} +(14.2821 - 4.92826i) q^{74} +(-8.44934 - 1.74741i) q^{75} +(-7.41012 - 9.45878i) q^{76} +(-3.22477 - 0.568614i) q^{77} +(1.63754 - 1.77789i) 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} +(4.18890 + 2.78405i) q^{84} +(-0.117802 - 0.0207717i) q^{85} +(-2.22904 - 4.01504i) q^{86} +(0.0799487 - 0.386581i) q^{87} +(-5.08676 + 3.84895i) q^{88} +(-3.19969 - 5.54203i) q^{89} +(-0.325839 + 0.477100i) q^{90} +(1.24080 + 0.716376i) q^{91} +(8.61769 + 0.289558i) q^{92} +(-10.1585 + 5.47333i) q^{93} +(9.54280 + 5.72533i) q^{94} +(0.626728 + 0.525888i) q^{95} +(9.52707 - 2.28800i) q^{96} +(0.779817 + 0.283830i) q^{97} +(2.47497 - 6.46025i) 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 $

$2$	0.927104	−	1.06793i	0.655561	−	0.755142i
$2$	0.927104	−	1.06793i	0.655561	−	0.755142i
$3$	−1.07385	−	1.35898i	−0.619990	−	0.784610i
$3$	−1.07385	−	1.35898i	−0.619990	−	0.784610i
$4$	−0.280958	−	1.98017i	−0.140479	−	0.990084i
$5$	0.0465753	+	0.127965i	0.0208291	+	0.0572275i	0.949671	−	0.313248i	$-0.101417\pi$
$5$	0.0465753	+	0.127965i	0.0208291	+	0.0572275i	−0.928842	+	0.370475i	$0.879195\pi$
$6$	−2.44688	−	0.113116i	−0.998933	−	0.0461793i
$7$	−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
$9$	−0.693675	+	2.91870i	−0.231225	+	0.972900i
$10$	0.179838	+	0.0688972i	0.0568697	+	0.0217872i
$11$	0.771344	−	2.11925i	0.232569	−	0.638978i	−0.767429	−	0.641134i	$-0.778464\pi$
$11$	0.771344	−	2.11925i	0.232569	−	0.638978i	0.999998	+	0.00215610i	$0.000686309\pi$
$12$	−2.38931	+	2.50823i	−0.689734	+	0.724063i
$13$	−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
$15$	0.123887	−	0.200710i	0.0319874	−	0.0518232i
$16$	−3.84213	+	1.11269i	−0.960531	+	0.278172i
$17$	−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	$0.200638\pi$
$18$	2.47387	+	3.44674i	0.583096	+	0.812403i
$19$	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
$21$	−1.67245	+	1.87813i	−0.364958	+	0.409842i
$22$	−1.54810	−	2.78851i	−0.330056	−	0.594512i
$23$	−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	$0.907164\pi$
$24$	0.463481	+	4.87701i	0.0946077	+	0.995515i
$25$	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	0.779475	−	0.626433i	$-0.215486\pi$
$29$	0.146501	+	0.174594i	0.0272046	+	0.0324212i	−0.752271	+	0.658854i	$0.771041\pi$
$30$	−0.0994893	−	0.318382i	−0.0181642	−	0.0581284i
$31$	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
$33$	−3.70834	+	1.22752i	−0.645539	+	0.213684i
$34$	0.405215	+	1.17431i	0.0694937	+	0.201393i
$35$	0.171232	−	0.0988610i	0.0289435	−	0.0167106i
$36$	5.97441	+	0.553560i	0.995735	+	0.0922600i
$37$	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
$39$	1.70841	+	0.0502450i	0.273565	+	0.00804563i
$40$	0.0859012	−	0.375466i	0.0135822	−	0.0593664i
$41$	−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	$0.761035\pi$
$42$	0.455183	+	3.52728i	0.0702363	+	0.544271i
$43$	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
$45$	−0.405799	+	0.0471736i	−0.0604929	+	0.00703222i
$46$	3.84013	+	4.73578i	0.566197	+	0.698253i
$47$	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	$0.749870\pi$
$48$	5.63801	+	4.02652i	0.813776	+	0.581179i
$49$	4.59683	−	1.67311i	0.656691	−	0.239016i
$50$	0.118305	−	7.04385i	0.0167308	−	0.996151i
$51$	1.50546	−	0.220036i	0.210806	−	0.0308111i
$52$	1.67505	+	1.04362i	0.232288	+	0.144724i
$53$			5.08895i			0.699021i	0.936932	+	0.349510i	$0.113652\pi$
$53$			5.08895i			0.699021i	−0.936932	+	0.349510i	$0.886348\pi$
$54$	2.02749	−	7.06324i	0.275906	−	0.961185i
$55$	0.307115			0.0414114
$56$	−1.59714	+	3.78343i	−0.213427	+	0.505582i
$57$	−9.66954	−	3.84497i	−1.28076	−	0.509279i
$58$	0.322276	+	0.00541278i	0.0423169	+	0.000710733i
$59$	−3.15956	−	8.68082i	−0.411340	−	1.13015i	−0.956479	−	0.291801i	$-0.905745\pi$
$59$	−3.15956	−	8.68082i	−0.411340	−	1.13015i	0.545139	−	0.838346i	$-0.316477\pi$
$60$	−0.432247	−	0.188925i	−0.0558029	−	0.0243902i
$61$	−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
$63$	4.34831	+	0.255992i	0.547836	+	0.0322519i
$64$	3.28278	+	7.29543i	0.410348	+	0.911929i
$65$	−0.126273	−	0.0459596i	−0.0156622	−	0.00570059i
$66$	−2.12711	+	5.09830i	−0.261829	+	0.627557i
$67$	−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
$69$	6.57388	−	3.54195i	0.791402	−	0.426401i
$70$	0.0531732	−	0.274519i	0.00635542	−	0.0328113i
$71$	−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	$0.918166\pi$
$72$	6.13006	−	5.86706i	0.722435	−	0.691439i
$73$	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
$75$	−8.44934	−	1.74741i	−0.975645	−	0.201773i
$76$	−7.41012	−	9.45878i	−0.849999	−	1.08500i
$77$	−3.22477	−	0.568614i	−0.367497	−	0.0647996i
$78$	1.63754	−	1.77789i	0.185414	−	0.201306i
$79$	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	0.716314	−	0.697778i	$-0.245828\pi$
$83$	−0.867764	−	1.03416i	−0.0952494	−	0.113514i	−0.811564	+	0.584264i	$0.801383\pi$
$84$	4.18890	+	2.78405i	0.457046	+	0.303765i
$85$	−0.117802	−	0.0207717i	−0.0127774	−	0.00225301i
$86$	−2.22904	−	4.01504i	−0.240363	−	0.432953i
$87$	0.0799487	−	0.386581i	0.00857141	−	0.0414458i
$88$	−5.08676	+	3.84895i	−0.542251	+	0.410300i
$89$	−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	$0.943478\pi$
$90$	−0.325839	+	0.477100i	−0.0343465	+	0.0502908i
$91$	1.24080	+	0.716376i	0.130071	+	0.0750966i
$92$	8.61769	+	0.289558i	0.898456	+	0.0301885i
$93$	−10.1585	+	5.47333i	−1.05339	+	0.567558i
$94$	9.54280	+	5.72533i	0.984264	+	0.590523i
$95$	0.626728	+	0.525888i	0.0643010	+	0.0539549i
$96$	9.52707	−	2.28800i	0.972352	−	0.233518i
$97$	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
$99$	5.65040	+	3.72140i	0.567886	+	0.374014i
$100$	−7.41267	−	6.65672i	−0.741267	−	0.665672i
$101$	−7.06509	+	1.24577i	−0.703003	+	0.123958i	−0.513712	−	0.857963i	$-0.671730\pi$
$101$	−7.06509	+	1.24577i	−0.703003	+	0.123958i	−0.189291	+	0.981921i	$0.560619\pi$
$102$	1.16073	−	1.81172i	0.114929	−	0.179387i
$103$	−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
$105$	−0.318229	−	0.126540i	−0.0310560	−	0.0123490i
$106$	5.43465	+	4.71798i	0.527860	+	0.458251i
$107$			19.5243i			1.88748i	0.330687	+	0.943740i	$0.392720\pi$
$107$			19.5243i			1.88748i	−0.330687	+	0.943740i	$0.607280\pi$
$108$	−5.66336	−	8.71357i	−0.544958	−	0.838464i
$109$			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
$111$	−2.67609	−	18.3095i	−0.254003	−	1.73786i
$112$	2.55973	+	5.21327i	0.241871	+	0.492608i
$113$	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	$0.193104\pi$
$114$	−13.0708	+	6.76173i	−1.22420	+	0.633294i
$115$	−0.578178	+	0.101948i	−0.0539154	+	0.00950674i
$116$	0.304564	−	0.339151i	0.0282780	−	0.0314894i
$117$	−1.76631	−	2.37566i	−0.163295	−	0.219630i
$118$	−12.1998	−	4.67383i	−1.12308	−	0.430261i
$119$	1.19849	+	0.436214i	0.109865	+	0.0399877i
$120$	−0.602498	+	0.286457i	−0.0550003	+	0.0261499i
$121$	4.53023	+	3.80132i	0.411840	+	0.345574i
$122$	−9.14068	+	15.2354i	−0.827558	+	1.37935i
$123$	−0.0793116	+	2.69673i	−0.00715129	+	0.243156i
$124$	−13.3168	−	0.447451i	−1.19589	−	0.0401823i
$125$	1.17714	+	0.679623i	0.105287	+	0.0607873i
$126$	4.30472	−	4.40637i	0.383495	−	0.392551i
$127$	−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
$129$	−5.33946	+	1.76745i	−0.470113	+	0.155615i
$130$	−0.166150	+	0.0922416i	−0.0145723	+	0.00809013i
$131$	−16.3299	−	2.87941i	−1.42675	−	0.251575i	−0.593664	−	0.804713i	$-0.702319\pi$
$131$	−16.3299	−	2.87941i	−1.42675	−	0.251575i	−0.833090	+	0.553138i	$0.813430\pi$
$132$	3.47259	+	6.99825i	0.302250	+	0.609120i
$133$	−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	$0.165322\pi$
$138$	2.31211	−	10.3042i	0.196820	−	0.877153i
$139$	−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
$141$	9.06410	−	10.1788i	0.763335	−	0.857212i
$142$	5.47113	+	15.8553i	0.459127	+	1.33055i
$143$	1.11272	+	1.92729i	0.0930505	+	0.161168i
$144$	−0.582416	−	11.9859i	−0.0485346	−	0.998821i
$145$	−0.0155185	+	0.0268788i	−0.00128874	+	0.00223216i
$146$	13.5610	+	2.62672i	1.12232	+	0.217389i
$147$	−7.21006	−	4.45035i	−0.594676	−	0.367058i
$148$	7.97794	−	19.8213i	0.655783	−	1.62930i
$149$	14.3501	−	17.1018i	1.17561	−	1.40104i	0.277807	−	0.960637i	$-0.410392\pi$
$149$	14.3501	−	17.1018i	1.17561	−	1.40104i	0.897802	−	0.440400i	$-0.145163\pi$
$150$	−9.69952	+	7.40329i	−0.791962	+	0.604476i
$151$	−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
$153$	−1.91566	−	1.80960i	−0.154872	−	0.146298i
$154$	−3.59694	+	2.91667i	−0.289850	+	0.235032i
$155$	0.893452	−	0.157540i	0.0717638	−	0.0126539i
$156$	−0.380499	−	3.39706i	−0.0304643	−	0.271983i
$157$	−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
$159$	6.91580	−	5.46479i	0.548459	−	0.433386i
$160$	−0.767620	−	0.0646086i	−0.0606857	−	0.00510776i
$161$	6.25975			0.493337
$162$	−11.7760	+	4.82956i	−0.925214	+	0.379446i
$163$		−	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
$165$	−0.329797	−	0.417364i	−0.0256746	−	0.0324918i
$166$	−1.90892	−	0.0320612i	−0.148161	−	0.00248843i
$167$	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	$0.177879\pi$
$168$	6.85672	−	1.89236i	0.529007	−	0.145998i
$169$	2.08834	+	11.8436i	0.160641	+	0.911043i
$170$	−0.131398	+	0.106547i	−0.0100777	+	0.00817179i
$171$	5.15843	+	17.2697i	0.394475	+	1.32065i
$172$	−6.35434	−	1.34190i	−0.484514	−	0.102319i
$173$	−6.92421	+	19.0241i	−0.526438	+	1.44638i	0.336798	+	0.941577i	$0.390656\pi$
$173$	−6.92421	+	19.0241i	−0.526438	+	1.44638i	−0.863236	+	0.504800i	$0.831566\pi$
$174$	−0.338722	−	0.443781i	−0.0256784	−	0.0336429i
$175$	−5.54065	−	4.64916i	−0.418834	−	0.351444i
$176$	−0.605538	+	9.00069i	−0.0456441	+	0.678453i
$177$	−8.40419	+	13.6157i	−0.631698	+	1.02342i
$178$	−8.88495	−	1.72098i	−0.665956	−	0.128993i
$179$	19.1336	+	11.0468i	1.43011	+	0.825676i	0.997129	−	0.0757257i	$-0.0241273\pi$
$179$	19.1336	+	11.0468i	1.43011	+	0.825676i	0.432984	+	0.901402i	$0.357461\pi$
$180$	0.207424	+	0.790296i	0.0154605	+	0.0589052i
$181$	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
$183$	16.2508	+	14.4711i	1.20130	+	1.06974i
$184$	8.29872	−	8.93466i	0.611790	−	0.658672i
$185$	−0.252627	+	1.43272i	−0.0185735	+	0.105336i
$186$	−3.57287	+	15.9230i	−0.261976	+	1.16753i
$187$	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	$0.388242\pi$
$192$	6.38915	−	12.2955i	0.461097	−	0.887350i
$193$	−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
$195$	0.0731404	+	0.220957i	0.00523769	+	0.0158230i
$196$	−4.60456	−	8.63243i	−0.328897	−	0.616602i
$197$	15.7746	−	9.10747i	1.12389	−	0.648881i	0.181502	−	0.983391i	$-0.441904\pi$
$197$	15.7746	−	9.10747i	1.12389	−	0.648881i	0.942392	+	0.334510i	$0.108571\pi$
$198$	9.21270	−	2.58412i	0.654718	−	0.183646i
$199$	−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
$201$	15.8918	+	0.467384i	1.12092	+	0.0329667i
$202$	−5.21968	+	8.70000i	−0.367255	+	0.612130i
$203$	0.212712	−	0.253501i	0.0149295	−	0.0177923i
$204$	−0.858677	−	2.91923i	−0.0601194	−	0.204387i
$205$	0.0725472	−	0.199322i	0.00506692	−	0.0139212i
$206$	−4.02979	+	10.5187i	−0.280769	+	0.732872i
$207$	−11.8728	−	5.13026i	−0.825220	−	0.356578i
$208$	1.59592	−	3.61009i	0.110657	−	0.250315i
$209$	−2.35282	−	13.3435i	−0.162748	−	0.922988i
$210$	−0.430167	+	0.222532i	−0.0296843	+	0.0153561i
$211$	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
$213$	20.3264	−	2.97088i	1.39274	−	0.203561i
$214$	20.8506	+	18.1010i	1.42532	+	1.23736i
$215$	0.442200			0.0301578
$216$	−14.5560	−	2.03029i	−0.990412	−	0.138144i
$217$	−9.67311			−0.656654
$218$	5.94283	+	5.15915i	0.402499	+	0.349422i
$219$	6.25096	−	15.7203i	0.422401	−	1.06228i
$220$	−0.0862864	−	0.608139i	−0.00581742	−	0.0410007i
$221$	−0.296462	−	0.814523i	−0.0199422	−	0.0547908i
$222$	−22.0343	−	14.1169i	−1.47885	−	0.947465i
$223$	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
$225$	6.69866	+	13.3590i	0.446577	+	0.890598i
$226$	6.20667	−	16.2009i	0.412862	−	1.07766i
$227$	0.619851	−	1.70303i	0.0411409	−	0.113034i	−0.917421	−	0.397918i	$-0.869733\pi$
$227$	0.619851	−	1.70303i	0.0411409	−	0.113034i	0.958562	+	0.284884i	$0.0919551\pi$
$228$	−4.89695	+	20.2276i	−0.324308	+	1.33960i
$229$	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
$231$	2.69020	+	4.99302i	0.177002	+	0.328517i
$232$	−0.0798278	−	0.639681i	−0.00524095	−	0.0419971i
$233$	−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	$0.175458\pi$
$234$	−4.17459	−	0.316192i	−0.272902	−	0.0206701i
$235$	−0.928021	+	0.535793i	−0.0605374	+	0.0349513i
$236$	−16.3018	+	8.69541i	−1.06116	+	0.566023i
$237$	−12.1611	−	2.51504i	−0.789949	−	0.163369i
$238$	1.57697	−	0.875489i	0.102220	−	0.0567495i
$239$	−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	$0.941936\pi$
$240$	−0.252661	+	0.909002i	−0.0163092	+	0.0586758i
$241$	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
$246$	2.80640	+	2.58485i	0.178929	+	0.164804i
$247$	−1.02947	+	5.83839i	−0.0655033	+	0.371488i
$248$	−12.8239	+	13.8066i	−0.814319	+	0.876721i
$249$	−0.473556	+	2.28981i	−0.0300104	+	0.145111i
$250$	1.81712	−	0.627026i	0.114925	−	0.0396566i
$251$	6.48934	−	3.74662i	0.409603	−	0.236485i	−0.281016	−	0.959703i	$-0.590671\pi$
$251$	6.48934	−	3.74662i	0.409603	−	0.236485i	0.690619	+	0.723219i	$0.257338\pi$
$252$	−0.714786	−	8.68231i	−0.0450273	−	0.546934i
$253$	8.42041	+	4.86153i	0.529387	+	0.305641i
$254$	−11.5270	−	2.23273i	−0.723267	−	0.140094i
$255$	0.0982739	+	0.182397i	0.00615415	+	0.0114221i
$256$	13.5239	−	8.55017i	0.845241	−	0.534385i
$257$	−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	$0.896069\pi$
$258$	−3.06272	+	7.34079i	−0.190676	+	0.457018i
$259$	5.30528	−	14.5761i	0.329654	−	0.905717i
$260$	−0.0555303	+	0.262954i	−0.00344384	+	0.0163077i
$261$	−0.611211	+	0.306483i	−0.0378330	+	0.0189708i
$262$	−18.2146	+	14.7698i	−1.12530	+	0.912479i
$263$	−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	$-0.248676\pi$
$264$	10.6931	+	2.77962i	0.658115	+	0.171074i
$265$	−0.651206	+	0.237019i	−0.0400032	+	0.0145600i
$266$	−12.3346	−	0.207166i	−0.756284	−	0.0127022i
$267$	−4.09553	+	10.2997i	−0.250642	+	0.630329i
$268$	15.5815	+	9.70785i	0.951792	+	0.593002i
$269$		−	25.3167i		−	1.54359i	−0.635873	−	0.771793i	$-0.719360\pi$
$269$		−	25.3167i		−	1.54359i	0.635873	−	0.771793i	$-0.280640\pi$
$270$	0.998275	−	0.0695258i	0.0607531	−	0.00423120i
$271$	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
$273$	−0.358894	−	2.45551i	−0.0217213	−	0.148614i
$274$	0.192352	−	11.4526i	0.0116204	−	0.691876i
$275$	−3.84242	−	10.5570i	−0.231707	−	0.636608i
$276$	−8.86064	−	12.0222i	−0.533348	−	0.723654i
$277$	−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
$279$	18.3470	+	7.92773i	1.09840	+	0.474621i
$280$	−0.558533	−	0.0281637i	−0.0333787	−	0.00168310i
$281$	−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	$0.773673\pi$
$282$	−2.46694	−	19.1167i	−0.146904	−	1.13838i
$283$	−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
$285$	0.0416579	−	1.41644i	0.00246760	−	0.0839027i
$286$	3.08983	+	0.598487i	0.182705	+	0.0353893i
$287$	−1.13080	+	1.95860i	−0.0667490	+	0.115613i
$288$	−13.3400	−	10.4902i	−0.786070	−	0.618138i
$289$	8.11420	+	14.0542i	0.477306	+	0.826718i
$290$	0.0143175	+	0.0414921i	0.000840751	+	0.00243650i
$291$	−0.451689	−	1.36455i	−0.0264785	−	0.0799914i
$292$	15.3776	−	12.0470i	0.899908	−	0.704998i
$293$	27.7186	+	4.88753i	1.61934	+	0.285533i	0.908519	−	0.417843i	$-0.137214\pi$
$293$	27.7186	+	4.88753i	1.61934	+	0.285533i	0.710818	+	0.703376i	$0.248325\pi$
$294$	−11.4371	+	3.57392i	−0.667028	+	0.208435i
$295$	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
$300$	−1.08625	+	17.2220i	−0.0627145	+	0.994315i
$301$	−4.64319	−	0.818720i	−0.267629	−	0.0471903i
$302$	−23.5605	+	13.0801i	−1.35575	+	0.752676i
$303$	9.27986	+	8.26358i	0.533114	+	0.474730i
$304$	−16.6480	+	17.3308i	−0.954831	+	0.993989i
$305$	−0.855412	−	1.48162i	−0.0489808	−	0.0848372i
$306$	−3.70855	+	0.368109i	−0.212004	+	0.0210434i
$307$	−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
$309$	11.7395	+	7.24613i	0.667839	+	0.412218i
$310$	0.660081	−	1.10020i	0.0374901	−	0.0624872i
$311$	−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	$-0.614848\pi$
$312$	−3.98059	−	2.74308i	−0.225357	−	0.155296i
$313$	−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
$315$	0.169766	+	0.568353i	0.00956524	+	0.0320231i
$316$	−10.6690	−	9.58100i	−0.600180	−	0.538973i
$317$	−26.6872	+	4.70567i	−1.49890	+	0.264297i	−0.862103	−	0.506733i	$-0.830853\pi$
$317$	−26.6872	+	4.70567i	−1.49890	+	0.264297i	−0.636799	+	0.771030i	$0.719742\pi$
$318$	0.575640	−	12.4520i	0.0322803	−	0.698275i
$319$	0.483011	−	0.175802i	0.0270434	−	0.00984300i
$320$	−0.780661	+	0.759867i	−0.0436403	+	0.0424779i
$321$	26.5331	−	20.9662i	1.48094	−	1.17022i
$322$	5.80343	−	6.68498i	0.323413	−	0.372540i
$323$			5.27738i			0.293641i
$324$	−5.75997	+	17.0535i	−0.319999	+	0.947418i
$325$			4.91560i			0.272668i
$326$	−10.7346	−	9.31902i	−0.594534	−	0.516133i
$327$	7.56248	−	5.97579i	0.418206	−	0.330462i
$328$	1.29642	+	4.21058i	0.0715827	+	0.232491i
$329$	10.7364	−	3.90774i	0.591918	−	0.215441i
$330$	−0.751472	−	0.0347395i	−0.0413672	−	0.00191235i
$331$	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
$333$	−22.0086	+	23.2985i	−1.20606	+	1.27675i
$334$	8.04732	−	21.0054i	0.440330	−	1.14936i
$335$	−1.17460	−	0.427521i	−0.0641755	−	0.0233580i
$336$	4.33598	−	9.07692i	0.236547	−	0.495187i
$337$	−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
$339$	−18.0812	−	11.1605i	−0.982036	−	0.606153i
$340$	−0.00803399	+	0.239104i	−0.000435704	+	0.0129672i
$341$	−13.0120	−	7.51246i	−0.704637	−	0.406822i
$342$	23.2253	+	10.5019i	1.25588	+	0.567880i
$343$	−8.63317	−	14.9531i	−0.466147	−	0.807391i
$344$	−7.32419	+	5.54192i	−0.394894	+	0.298800i
$345$	0.759425	+	0.676257i	0.0408861	+	0.0364085i
$346$	13.8970	+	25.0319i	0.747107	+	1.34572i
$347$	−14.4283	−	2.54411i	−0.774554	−	0.136575i	−0.227619	−	0.973750i	$-0.573094\pi$
$347$	−14.4283	−	2.54411i	−0.774554	−	0.136575i	−0.546934	+	0.837175i	$0.684205\pi$
$348$	−0.787958	−	0.0496989i	−0.0422390	−	0.00266414i
$349$	−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
$351$	−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	$0.381412\pi$
$354$	6.74912	+	21.5983i	0.358712	+	1.14794i
$355$	−1.59054	−	0.280455i	−0.0844171	−	0.0148850i
$356$	−10.0752	+	7.89300i	−0.533983	+	0.418328i
$357$	−0.694194	−	2.09716i	−0.0367406	−	0.110993i
$358$	29.5361	−	10.1919i	1.56103	−	0.538657i
$359$	−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	$0.941656\pi$
$360$	1.03629	+	0.511171i	0.0546170	+	0.0269411i
$361$	8.54731	−	14.8044i	0.449858	−	0.779178i
$362$	4.73675	−	24.4545i	0.248958	−	1.28530i
$363$	0.301120	−	10.2386i	0.0158047	−	0.537386i
$364$	1.06993	−	2.65826i	0.0560797	−	0.139331i
$365$	−0.854962	+	1.01890i	−0.0447508	+	0.0533319i
$366$	30.5204	−	3.93855i	1.59533	−	0.205871i
$367$	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
$369$	3.74998	−	2.78811i	0.195216	−	0.145143i
$370$	1.29584	+	1.59807i	0.0673673	+	0.0830796i
$371$	7.27663	−	1.28307i	0.377784	−	0.0666135i
$372$	13.6922	+	18.5778i	0.709910	+	0.963216i
$373$	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
$375$	−0.340482	−	2.32953i	−0.0175824	−	0.120297i
$376$	8.65599	−	20.5049i	0.446398	−	1.05746i
$377$	−0.224903			−0.0115831
$378$	−10.6108	−	1.11824i	−0.545762	−	0.0575162i
$379$		−	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
$381$	−5.31337	+	13.3624i	−0.272212	+	0.684575i
$382$	−0.223261	+	13.2929i	−0.0114230	+	0.680124i
$383$	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	$0.348686\pi$
$384$	−7.20734	−	18.2224i	−0.367798	−	0.929906i
$385$	−0.0774323	−	0.439140i	−0.00394631	−	0.0223807i
$386$	6.59746	+	8.13621i	0.335802	+	0.414122i
$387$	8.13574	+	5.35826i	0.413563	+	0.272376i
$388$	0.342936	−	1.62391i	0.0174099	−	0.0824417i
$389$	−5.45591	+	14.9900i	−0.276625	+	0.760022i	0.721114	+	0.692817i	$0.243631\pi$
$389$	−5.45591	+	14.9900i	−0.276625	+	0.760022i	−0.997739	+	0.0672055i	$0.978592\pi$
$390$	0.303776	+	0.126741i	0.0153823	+	0.00641778i
$391$	−2.90106	−	2.43428i	−0.146713	−	0.123107i
$392$	−13.4877	−	3.08580i	−0.681234	−	0.155856i
$393$	13.6229	+	25.2842i	0.687185	+	1.27542i
$394$	4.89853	−	25.2898i	0.246784	−	1.27408i
$395$	0.845555	+	0.488181i	0.0425445	+	0.0245631i
$396$	5.78146	−	12.2343i	0.290529	−	0.614796i
$397$	−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
$399$	−3.05992	+	14.7958i	−0.153187	+	0.740716i
$400$	−11.0988	+	16.5486i	−0.554938	+	0.827429i
$401$	−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	$0.723395\pi$
$402$	15.2325	−	16.5381i	0.759729	−	0.824845i
$403$	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
$408$	−3.91363	−	1.78942i	−0.193753	−	0.0885897i
$409$	−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
$411$	−13.7378	−	2.84111i	−0.677634	−	0.140141i
$412$	7.49722	+	14.0555i	0.369361	+	0.692463i
$413$	−11.6160	+	6.70650i	−0.571586	+	0.330005i
$414$	−16.4861	+	7.92310i	−0.810249	+	0.389399i
$415$	0.0919196	−	0.159209i	0.00451216	−	0.00781529i
$416$	−2.37575	−	5.05127i	−0.116481	−	0.247659i
$417$	3.13933	+	5.82661i	0.153733	+	0.285330i
$418$	−16.4312	−	9.85815i	−0.803678	−	0.482178i
$419$	7.00112	−	8.34360i	0.342027	−	0.407612i	−0.567422	−	0.823427i	$-0.692059\pi$
$419$	7.00112	−	8.34360i	0.342027	−	0.407612i	0.909449	+	0.415815i	$0.136504\pi$
$420$	−0.161161	+	0.665699i	−0.00786384	+	0.0324828i
$421$	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
$423$	−23.5664	−	1.38739i	−1.14584	−	0.0674572i
$424$	7.81549	−	12.0871i	0.379554	−	0.587000i
$425$	0.759843	+	4.30928i	0.0368578	+	0.209031i
$426$	15.6720	−	24.4615i	0.759309	−	1.18516i
$427$	6.23884	+	17.1411i	0.301919	+	0.829514i
$428$	38.6613	−	5.48549i	1.86876	−	0.265151i
$429$	1.42426	−	3.58180i	0.0687638	−	0.172931i
$430$	0.409965	−	0.472240i	0.0197703	−	0.0227734i
$431$	−12.2633			−0.590701			−0.295351	−	0.955389i	$-0.595436\pi$
$431$	−12.2633			−0.590701			−0.295351	+	0.955389i	$0.595436\pi$
$432$	−15.6632	+	13.6626i	−0.753594	+	0.657340i
$433$	−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
$435$	0.0531924	−	0.00777453i	0.00255038	−	0.000372760i
$436$	11.0192	−	1.56347i	0.527726	−	0.0748769i
$437$	8.85888	+	24.3396i	0.423778	+	1.16432i
$438$	−10.9929	−	21.2499i	−0.525261	−	1.01536i
$439$	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
$441$	1.69460	+	14.5774i	0.0806953	+	0.694161i
$442$	−1.14471	−	0.438546i	−0.0544481	−	0.0208595i
$443$	8.57202	−	23.5514i	0.407269	−	1.11896i	−0.551351	−	0.834274i	$-0.685887\pi$
$443$	8.57202	−	23.5514i	0.407269	−	1.11896i	0.958620	−	0.284689i	$-0.0918904\pi$
$444$	−35.5040	+	10.4433i	−1.68495	+	0.495617i
$445$	0.560157	−	0.667569i	0.0265540	−	0.0316458i
$446$	14.1672	+	8.49979i	0.670835	+	0.402477i
$447$	−38.6511	−	1.13674i	−1.82813	−	0.0537659i
$448$	9.60398	−	6.53340i	0.453745	−	0.308674i
$449$	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	$0.135493\pi$
$450$	20.4768	+	5.23144i	0.965287	+	0.246612i
$451$	−3.04223	+	1.75643i	−0.143253	+	0.0827072i
$452$	−11.5472	−	21.6482i	−0.543134	−	1.01824i
$453$	10.3715	+	31.3323i	0.487296	+	1.47212i
$454$	−1.24405	−	2.24084i	−0.0583862	−	0.105168i
$455$	−0.0338802	+	0.192144i	−0.00158833	+	0.00900785i
$456$	17.0617	+	23.9827i	0.798988	+	1.12309i
$457$	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	0.818221	−	0.574903i	$-0.194960\pi$
$461$	2.36115	+	2.81391i	0.109970	+	0.131057i	−0.708252	+	0.705960i	$0.750516\pi$
$462$	7.82630	+	1.75610i	0.364112	+	0.0817012i
$463$	−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
$465$	−1.17353	−	1.04501i	−0.0544212	−	0.0484613i
$466$	0.388910	+	1.12706i	0.0180159	+	0.0522101i
$467$	−4.79342	+	2.76748i	−0.221813	+	0.128064i	−0.606789	−	0.794863i	$-0.707543\pi$
$467$	−4.79342	+	2.76748i	−0.221813	+	0.128064i	0.384976	+	0.922926i	$0.374210\pi$
$468$	−4.20795	+	4.16504i	−0.194513	+	0.192529i
$469$	11.5421	+	6.66381i	0.532962	+	0.307706i
$470$	−0.288181	+	1.48780i	−0.0132928	+	0.0686271i
$471$	−7.81515	+	12.6614i	−0.360103	+	0.583407i
$472$	−5.82734	+	25.4707i	−0.268225	+	1.17239i
$473$	−5.61003	−	4.70737i	−0.257949	−	0.216445i
$474$	−13.9605	+	10.6555i	−0.641227	+	0.489425i
$475$	10.2360	−	28.1231i	0.469659	−	1.29038i
$476$	0.527052	−	2.49577i	0.0241574	−	0.114393i
$477$	−14.8531	−	3.53008i	−0.680078	−	0.161631i
$478$	9.62297	+	11.8674i	0.440144	+	0.542801i
$479$	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	$0.883975\pi$
$480$	0.736510	+	1.11256i	0.0336169	+	0.0507813i
$481$	−9.90631	+	3.60560i	−0.451689	+	0.164401i
$482$	0.212540	−	12.6546i	0.00968095	−	0.576402i
$483$	−6.72205	−	8.50690i	−0.305864	−	0.387077i
$484$	6.25444	−	10.0386i	0.284293	−	0.456301i
$485$			0.113009i			0.00513145i
$486$	19.2091	+	10.8172i	0.871340	+	0.490679i
$487$	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
$489$	−13.6602	+	10.7941i	−0.617735	+	0.488127i
$490$	0.941957	+	0.0158206i	0.0425533	+	0.000714702i
$491$	11.2492	+	30.9069i	0.507669	+	1.39481i	0.883636	+	0.468175i	$0.155088\pi$
$491$	11.2492	+	30.9069i	0.507669	+	1.39481i	−0.375967	+	0.926633i	$0.622689\pi$
$492$	5.36226	−	0.600617i	0.241749	−	0.0270779i
$493$	−0.197162	+	0.0347650i	−0.00887973	+	0.00156574i
$494$	5.28058	+	6.51219i	0.237585	+	0.292997i
$495$	−0.213038	+	0.896377i	−0.00957534	+	0.0402891i
$496$	2.85544	+	26.4952i	0.128213	+	1.18967i
$497$	16.1818	+	5.88968i	0.725851	+	0.264188i
$498$	2.00633	+	2.62862i	0.0899058	+	0.117791i
$499$	−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
$501$	−23.4434	−	14.4702i	−1.04737	−	0.646481i
$502$	2.01515	−	10.4037i	0.0899406	−	0.464339i
$503$	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	$-0.216800\pi$
$504$	−9.93480	−	7.28606i	−0.442531	−	0.324547i
$505$	−0.488473	−	0.846060i	−0.0217368	−	0.0376492i
$506$	12.9984	−	4.48529i	0.577848	−	0.199395i
$507$	13.8526	−	15.5563i	0.615217	−	0.690878i
$508$	−13.0711	+	10.2401i	−0.579937	+	0.454329i
$509$	1.32565	+	0.233747i	0.0587583	+	0.0103607i	0.202950	−	0.979189i	$-0.434947\pi$
$509$	1.32565	+	0.233747i	0.0587583	+	0.0103607i	−0.144192	+	0.989550i	$0.546058\pi$
$510$	0.285898	+	0.0641510i	0.0126598	+	0.00284066i
$511$	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
$516$	5.00001	+	10.0764i	0.220113	+	0.443591i
$517$	17.4772	+	3.08170i	0.768645	+	0.135533i
$518$	−10.6478	−	19.1793i	−0.467836	−	0.842688i
$519$	33.2891	−	11.0192i	1.46123	−	0.483691i
$520$	0.229335	+	0.303088i	0.0100570	+	0.0132913i
$521$	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	$0.629527\pi$
$522$	−0.239353	+	0.936873i	−0.0104762	+	0.0410058i
$523$	−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
$525$	−0.368281	+	12.5222i	−0.0160731	+	0.546513i
$526$	−22.4264	−	13.4550i	−0.977839	−	0.586667i
$527$	4.48298	+	3.76167i	0.195282	+	0.163861i
$528$	12.8821	−	8.84252i	0.560620	−	0.384821i
$529$	4.14676	+	1.50930i	0.180294	+	0.0656217i
$530$	−0.350614	+	0.915185i	−0.0152297	+	0.0397531i
$531$	27.5284	−	3.20015i	1.19463	−	0.138875i
$532$	−11.6567	+	12.9805i	−0.505383	+	0.562775i
$533$	1.51369	−	0.266904i	0.0655651	−	0.0115609i
$534$	7.20236	+	13.9226i	0.311677	+	0.602490i
$535$	−2.49841	+	0.909349i	−0.108016	+	0.0393146i
$536$	24.8130	−	7.63980i	1.07176	−	0.329989i
$537$	−5.53429	−	37.8649i	−0.238822	−	1.63399i
$538$	−27.0365	−	23.4712i	−1.16563	−	1.01192i
$539$		−	11.0324i		−	0.475199i
$540$	0.851256	−	1.13055i	0.0366322	−	0.0486510i
$541$			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
$543$	−28.3483	−	11.2723i	−1.21654	−	0.483742i
$544$	−2.86353	−	4.06098i	−0.122773	−	0.174113i
$545$	−0.712098	+	0.259182i	−0.0305029	+	0.0111022i
$546$	−2.95505	−	1.89324i	−0.126465	−	0.0810231i
$547$	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
$549$	2.21501	−	37.6245i	0.0945345	−	1.60578i
$550$	−14.8364	−	5.68395i	−0.632628	−	0.242364i
$551$	1.28671	+	0.468325i	0.0548158	+	0.0199513i
$552$	−21.0537	−	1.68331i	−0.896104	−	0.0716464i
$553$	−7.97465	−	6.69153i	−0.339117	−	0.284553i
$554$	−12.8987	+	21.4991i	−0.548013	+	0.913410i
$555$	2.21833	−	1.19522i	0.0941628	−	0.0507341i
$556$	−0.256643	+	7.63809i	−0.0108841	+	0.323927i
$557$	−8.93296	−	5.15745i	−0.378502	−	0.218528i	0.298665	−	0.954358i	$-0.403459\pi$
$557$	−8.93296	−	5.15745i	−0.378502	−	0.218528i	−0.677166	+	0.735830i	$0.736792\pi$
$558$	25.4758	−	12.2435i	1.07848	−	0.518308i
$559$	1.60216	+	2.77502i	0.0677640	+	0.117371i
$560$	−0.547895	+	0.570364i	−0.0231528	+	0.0241023i
$561$	0.694914	−	3.36016i	0.0293393	−	0.141866i
$562$	−20.2620	+	11.2489i	−0.854699	+	0.474505i
$563$	−3.14086	−	0.553818i	−0.132371	−	0.0233406i	0.107070	−	0.994251i	$-0.465853\pi$
$563$	−3.14086	−	0.553818i	−0.132371	−	0.0233406i	−0.239441	+	0.970911i	$0.576964\pi$
$564$	−22.7024	−	15.0886i	−0.955944	−	0.635345i
$565$	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	$0.342438\pi$
$570$	−1.47404	−	1.35767i	−0.0617408	−	0.0568667i
$571$	−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
$573$	15.9453	+	3.29764i	0.666124	+	0.137761i
$574$	1.04329	+	3.02344i	0.0435459	+	0.126196i
$575$	10.7382	+	18.5991i	0.447815	+	0.775638i
$576$	−23.5704	+	4.52080i	−0.982099	+	0.188367i
$577$	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
$579$	11.2941	−	6.08518i	0.469368	−	0.252891i
$580$	0.0575845	+	0.0231773i	0.00239107	+	0.000962387i
$581$	−1.25995	+	1.50155i	−0.0522714	+	0.0622947i
$582$	−1.87601	−	0.782707i	−0.0777631	−	0.0324443i
$583$	10.7848	+	3.92533i	0.446659	+	0.162571i
$584$	1.39126	−	27.5911i	0.0575709	−	1.14173i
$585$	0.221735	−	0.336672i	0.00916760	−	0.0139197i
$586$	30.9176	−	25.0703i	1.27719	−	1.03565i
$587$	11.4100	−	2.01190i	0.470943	−	0.0830399i	0.0668600	−	0.997762i	$-0.478702\pi$
$587$	11.4100	−	2.01190i	0.470943	−	0.0830399i	0.404083	+	0.914722i	$0.367591\pi$
$588$	−6.78671	+	15.5275i	−0.279879	+	0.640343i
$589$	−13.6895	−	37.6117i	−0.564067	−	1.54976i
$590$	0.0298762	−	1.77882i	0.00122998	−	0.0732330i
$591$	−29.3165	−	11.6573i	−1.20592	−	0.479519i
$592$	−41.4910	−	10.2287i	−1.70527	−	0.420397i
$593$	−11.5506			−0.474326			−0.237163	−	0.971470i	$-0.576218\pi$
$593$	−11.5506			−0.474326			−0.237163	+	0.971470i	$0.576218\pi$
$594$	−13.4049	−	9.74494i	−0.550009	−	0.399840i
$595$			0.173681i			0.00712023i
$596$	−37.8963	−	23.6108i	−1.55229	−	0.967135i
$597$	27.6007	−	4.03408i	1.12962	−	0.165104i
$598$	−6.01561	−	0.101035i	−0.245997	−	0.00413163i
$599$	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	$0.188303\pi$
$600$	17.3849	+	17.1267i	0.709736	+	0.699193i
$601$	−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
$603$	−16.4304	−	22.0987i	−0.669096	−	0.899927i
$604$	−7.87435	+	37.2876i	−0.320403	+	1.51721i
$605$	−0.275437	+	0.756758i	−0.0111981	+	0.0307666i
$606$	17.4283	−	2.24906i	0.707978	−	0.0913620i
$607$	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
$609$	−0.572925	−	0.0168499i	−0.0232161	−	0.000682792i
$610$	−2.37532	−	0.460091i	−0.0961740	−	0.0186285i
$611$	−6.72472	−	3.88252i	−0.272053	−	0.157070i
$612$	−3.04510	+	4.30176i	−0.123091	+	0.173888i
$613$	−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
$615$	−0.348780	+	0.115452i	−0.0140642	+	0.00465548i
$616$	6.78609	+	6.30308i	0.273419	+	0.253958i
$617$	−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	$0.791641\pi$
$618$	18.6222	−	5.81912i	0.749093	−	0.234079i
$619$	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
$621$	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
$624$	−6.61985	+	1.70788i	−0.265006	+	0.0683700i
$625$	4.29296	−	24.3466i	0.171718	−	0.973864i
$626$	−27.1173	+	15.0548i	−1.08383	+	0.601709i
$627$	−15.6070	+	17.5264i	−0.623284	+	0.699937i
$628$	−15.1592	+	8.08595i	−0.604918	+	0.322665i
$629$	−8.12706	+	4.69216i	−0.324047	+	0.187089i
$630$	0.764354	+	0.345624i	0.0304526	+	0.0137700i
$631$	−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
$633$	17.2329	−	27.9193i	0.684948	−	1.10969i
$634$	−19.7165	+	32.8628i	−0.783041	+	1.30515i
$635$	0.726725	−	0.866078i	0.0288392	−	0.0343692i
$636$	−12.7642	−	12.1591i	−0.506135	−	0.482138i
$637$	−1.65099	+	4.53606i	−0.0654147	+	0.179725i
$638$	0.260057	−	0.678809i	0.0102958	−	0.0268743i
$639$	−25.8649	−	24.4329i	−1.02320	−	0.966551i
$640$	0.0877331	+	1.53817i	0.00346796	+	0.0608014i
$641$	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	$0.829771\pi$
$642$	2.20850	−	47.7734i	0.0871625	−	1.88547i
$643$	−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
$645$	−0.474858	−	0.600943i	−0.0186975	−	0.0236621i
$646$	5.63589	+	4.89268i	0.221741	+	0.192500i
$647$	20.3838			0.801371			0.400686	−	0.916216i	$-0.368772\pi$
$647$	20.3838			0.801371			0.400686	+	0.916216i	$0.368772\pi$
$648$	12.8719	+	21.9616i	0.505657	+	0.862735i
$649$	−20.8340			−0.817804
$650$	5.24953	+	4.55727i	0.205903	+	0.178751i
$651$	10.3875	+	13.1456i	0.407119	+	0.515217i
$652$	−19.9042	+	2.82412i	−0.779507	+	0.110601i
$653$	6.26659	+	17.2173i	0.245230	+	0.673765i	0.999845	+	0.0175970i	$0.00560160\pi$
$653$	6.26659	+	17.2173i	0.245230	+	0.673765i	−0.754615	+	0.656168i	$0.772176\pi$
$654$	0.629466	−	13.6164i	0.0246141	−	0.532443i
$655$	−0.392110	−	2.22376i	−0.0153210	−	0.0868897i
$656$	5.69853	+	2.51916i	0.222490	+	0.0983567i
$657$	−28.0762	+	8.38632i	−1.09536	+	0.327182i
$658$	5.78058	−	15.0887i	0.225350	−	0.588217i
$659$	−1.95819	+	5.38009i	−0.0762803	+	0.209579i	−0.971972	−	0.235098i	$-0.924459\pi$
$659$	−1.95819	+	5.38009i	−0.0762803	+	0.209579i	0.895691	+	0.444676i	$0.146681\pi$
$660$	−0.733792	+	0.770314i	−0.0285628	+	0.0299844i
$661$	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
$663$	−0.788567	+	1.27757i	−0.0306254	+	0.0496166i
$664$	0.472840	+	3.78899i	0.0183497	+	0.147041i
$665$	0.593945	−	1.02874i	0.0230322	−	0.0398929i
$666$	4.47698	+	45.1038i	0.173479	+	1.74774i
$667$	−0.850963	+	0.491304i	−0.0329494	+	0.0190234i
$668$	−14.9716	−	28.0681i	−0.579269	−	1.08599i
$669$	13.4565	−	15.1114i	0.520259	−	0.584242i
$670$	−1.54554	+	0.858041i	−0.0597095	+	0.0331490i
$671$	−4.92003	+	27.9029i	−0.189936	+	1.07718i
$672$	−5.67363	−	13.0458i	−0.218865	−	0.503252i
$673$	−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	0.426660	−	0.904412i	$-0.359690\pi$
$677$	−14.0009	−	16.6857i	−0.538100	−	0.641283i	−0.964761	+	0.263129i	$0.915245\pi$
$678$	−28.6818	+	8.96259i	−1.10152	+	0.344206i
$679$	0.209232	−	1.18661i	0.00802959	−	0.0455380i
$680$	0.247898	+	0.230254i	0.00950647	+	0.00882983i
$681$	−2.98001	+	0.986434i	−0.114194	+	0.0378002i
$682$	−20.0862	+	6.93106i	−0.769142	+	0.265404i
$683$	−24.8360	+	14.3391i	−0.950322	+	0.548669i	−0.893181	−	0.449697i	$-0.851532\pi$
$683$	−24.8360	+	14.3391i	−0.950322	+	0.548669i	−0.0571411	+	0.998366i	$0.518198\pi$
$684$	32.7476	−	15.0666i	1.25213	−	0.576086i
$685$	0.955179	+	0.551473i	0.0364955	+	0.0210707i
$686$	−23.9727	−	4.64342i	−0.915283	−	0.177287i
$687$	−21.2416	−	0.624722i	−0.810418	−	0.0238346i
$688$	−0.871885	+	12.9597i	−0.0332403	+	0.494083i
$689$	−3.84682	−	3.22787i	−0.146552	−	0.122972i
$690$	1.42626	−	0.184054i	0.0542969	−	0.00700682i
$691$	−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
$693$	3.89656	−	9.01771i	0.148018	−	0.342555i
$694$	−16.0935	+	13.0498i	−0.610901	+	0.495365i
$695$	−0.0903596	−	0.512455i	−0.00342754	−	0.0194385i
$696$	−0.783593	+	0.795409i	−0.0297020	+	0.0301499i
$697$	1.28572	−	0.467965i	0.0487003	−	0.0177255i
$698$	−11.4774	−	0.192768i	−0.434426	−	0.00729639i
$699$	1.44488	−	0.211182i	0.0546504	−	0.00798763i
$700$	−7.64943	+	12.2776i	−0.289121	+	0.464051i
$701$		−	41.7650i		−	1.57744i	−0.614751	−	0.788722i	$-0.710743\pi$
$701$		−	41.7650i		−	1.57744i	0.614751	−	0.788722i	$-0.289257\pi$
$702$	4.05321	+	6.01275i	0.152978	+	0.226937i
$703$	64.1840			2.42075
$704$	17.9930	−	1.32975i	0.678137	−	0.0501168i
$705$	1.72469	+	0.685802i	0.0649557	+	0.0258288i
$706$	−0.285442	+	16.9952i	−0.0107427	+	0.639621i
$707$	3.56262	+	9.78821i	0.133986	+	0.368123i
$708$	29.3227	+	12.8163i	1.10201	+	0.481665i
$709$	−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
$711$	9.64136	+	19.2275i	0.361579	+	0.721089i
$712$	−0.911532	+	18.0772i	−0.0341611	+	0.677472i
$713$	26.9903	+	9.82365i	1.01079	+	0.367899i
$714$	−2.88321	−	1.20293i	−0.107901	−	0.0450185i
$715$	−0.194800	+	0.232153i	−0.00728510	+	0.00868205i
$716$	16.4988	−	40.9914i	0.616588	−	1.53192i
$717$	16.4735	−	8.87576i	0.615213	−	0.331471i
$718$	−17.5610	−	3.40150i	−0.655371	−	0.126943i
$719$	−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	$0.278410\pi$
$720$	1.50664	−	0.632774i	0.0561492	−	0.0235821i
$721$	5.78238	+	10.0154i	0.215347	+	0.372992i
$722$	−7.88583	−	22.8531i	−0.293480	−	0.850506i
$723$	−15.1797	−	3.13930i	−0.564537	−	0.116752i
$724$	−21.7243	−	27.7304i	−0.807379	−	1.03059i
$725$	1.11810	+	0.197152i	0.0415253	+	0.00732204i
$726$	−10.6549	−	9.81380i	−0.395442	−	0.364224i
$727$	−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
$732$	24.0895	−	36.2452i	0.890373	−	1.33966i
$733$	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
$735$	0.233676	−	1.12991i	0.00861928	−	0.0416773i
$736$	−20.0237	−	13.9226i	−0.738084	−	0.513194i
$737$	10.3507	+	17.9279i	0.381272	+	0.660382i
$738$	0.499108	−	6.58960i	0.0183724	−	0.242566i
$739$	−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
$741$	9.03977	−	4.87055i	0.332084	−	0.178924i
$742$	5.37596	−	8.96048i	0.197358	−	0.328950i
$743$	−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	$0.957264\pi$
$744$	32.5340	+	2.60120i	1.19275	+	0.0953645i
$745$	2.85679	+	1.03979i	0.104665	+	0.0380949i
$746$	22.6980	+	8.69579i	0.831034	+	0.318375i
$747$	3.62035	−	1.81537i	0.132462	−	0.0664210i
$748$	2.64727	−	2.94790i	0.0967937	−	0.107786i
$749$	27.9175	−	4.92261i	1.02008	−	0.179868i
$750$	−2.80344	−	1.79611i	−0.102367	−	0.0655846i
$751$	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
$753$	−12.0602	−	4.79558i	−0.439498	−	0.174761i
$754$	−0.208508	+	0.240181i	−0.00759342	+	0.00874687i
$755$		−	2.59486i		−	0.0944365i
$756$	−11.0315	+	10.2949i	−0.401213	+	0.374423i
$757$		−	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
$759$	−2.43556	−	16.6638i	−0.0884051	−	0.604857i
$760$	−0.680935	−	2.21158i	−0.0247001	−	0.0802225i
$761$	−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	$0.417365\pi$
$762$	9.34405	+	18.0626i	0.338499	+	0.654340i
$763$	7.95705	−	1.40304i	0.288065	−	0.0507935i
$764$	13.9889	+	12.5623i	0.506102	+	0.454489i
$765$	0.142343	−	0.329420i	0.00514641	−	0.0119102i
$766$	2.49449	−	6.51120i	0.0901296	−	0.235259i
$767$	8.56606	+	3.11779i	0.309303	+	0.112577i
$768$	−26.1422	−	9.19707i	−0.943325	−	0.331871i
$769$	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
$771$	−0.847962	+	28.8321i	−0.0305386	+	1.03836i
$772$	14.8055	+	0.497469i	0.532860	+	0.0179043i
$773$	−8.17747	−	4.72126i	−0.294123	−	0.169812i	0.345677	−	0.938354i	$-0.387649\pi$
$773$	−8.17747	−	4.72126i	−0.294123	−	0.169812i	−0.639800	+	0.768542i	$0.720983\pi$
$774$	13.2649	−	3.72076i	0.476798	−	0.133740i
$775$	−16.5936	−	28.7410i	−0.596061	−	1.03241i
$776$	−1.41629	−	1.87177i	−0.0508419	−	0.0671925i
$777$	−25.5058	+	8.44285i	−0.915016	+	0.302886i
$778$	10.9501	+	19.7238i	0.392580	+	0.707133i
$779$	−9.21589	−	1.62501i	−0.330194	−	0.0582220i
$780$	0.416982	−	0.206910i	0.0149304	−	0.00740856i
$781$	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
$786$	39.6316	+	8.89273i	1.41361	+	0.317193i
$787$	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
$789$	−21.3014	+	23.9212i	−0.758352	+	0.851616i
$790$	1.30526	−	0.450401i	0.0464391	−	0.0160245i
$791$	−8.90599	−	15.4256i	−0.316661	−	0.548472i
$792$	−7.70538	−	17.5167i	−0.273799	−	0.622427i
$793$	6.19857	−	10.7362i	0.220118	−	0.381255i
$794$	−5.86885	+	30.2993i	−0.208278	+	1.07528i
$795$	1.02141	+	0.630454i	0.0362255	+	0.0223599i
$796$	29.8797	+	12.0264i	1.05906	+	0.426263i
$797$	−9.18613	+	10.9476i	−0.325389	+	0.387784i	−0.903795	−	0.427965i	$-0.859231\pi$
$797$	−9.18613	+	10.9476i	−0.325389	+	0.387784i	0.578406	+	0.815749i	$0.303675\pi$
$798$	12.9640	+	16.9850i	0.458922	+	0.601263i
$799$	−6.49541	−	2.36413i	−0.229791	−	0.0836371i
$800$	7.38306	+	27.1950i	0.261031	+	0.961488i
$801$	18.3951	−	5.49458i	0.649958	−	0.194141i
$802$	30.8280	+	38.0181i	1.08857	+	1.34247i
$803$	21.6932	−	3.82509i	0.765536	−	0.134985i
$804$	−3.53944	−	31.5998i	−0.124826	−	1.11444i
$805$	0.291550	+	0.801026i	0.0102758	+	0.0282325i
$806$	9.29586	+	0.156128i	0.327433	+	0.00549939i
$807$	−34.4050	+	27.1865i	−1.21111	+	0.957008i
$808$	18.6940	+	7.89151i	0.657651	+	0.277622i
$809$	2.71159			0.0953343			0.0476672	−	0.998863i	$-0.484821\pi$
$809$	2.71159			0.0953343			0.0476672	+	0.998863i	$0.484821\pi$
$810$	−1.16649	−	1.28198i	−0.0409862	−	0.0450442i
$811$			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
$813$	−17.8505	−	22.5902i	−0.626046	−	0.792274i
$814$	0.572201	−	34.0687i	0.0200556	−	1.19411i
$815$	1.28627	−	0.468164i	0.0450561	−	0.0163991i
$816$	−5.53932	+	2.52051i	−0.193915	+	0.0882354i
$817$	−3.38771	−	19.2126i	−0.118521	−	0.672165i
$818$	3.59672	+	4.43560i	0.125757	+	0.155087i
$819$	−2.95160	+	3.12459i	−0.103137	+	0.109182i
$820$	−0.415073	−	0.0876546i	−0.0144950	−	0.00306103i
$821$	12.6956	−	34.8810i	0.443081	−	1.21736i	−0.494374	−	0.869249i	$-0.664603\pi$
$821$	12.6956	−	34.8810i	0.443081	−	1.21736i	0.937455	−	0.348106i	$-0.113175\pi$
$822$	−15.7704	+	12.0370i	−0.550058	+	0.419839i
$823$	−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
$825$	−10.2205	+	16.5584i	−0.355833	+	0.576490i
$826$	−3.60715	+	18.6227i	−0.125509	+	0.647967i
$827$	7.73838	+	4.46776i	0.269090	+	0.155359i	0.628474	−	0.777831i	$-0.283680\pi$
$827$	7.73838	+	4.46776i	0.269090	+	0.155359i	−0.359384	+	0.933190i	$0.617013\pi$
$828$	−6.82301	+	24.9516i	−0.237116	+	0.867128i
$829$	−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
$831$	22.9320	+	20.4207i	0.795504	+	0.708385i
$832$	−7.59698	−	2.14591i	−0.263378	−	0.0743960i
$833$	−0.746175	+	4.23177i	−0.0258534	+	0.146622i
$834$	9.13290	+	2.04928i	0.316247	+	0.0709609i
$835$	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	$0.283469\pi$
$840$	0.561509	+	0.789281i	0.0193739	+	0.0272328i
$841$	5.02678	−	28.5083i	0.173337	−	0.983044i
$842$	−3.87155	−	6.97361i	−0.133422	−	0.240326i
$843$	8.91946	+	26.9457i	0.307203	+	0.928058i
$844$	33.4271	−	17.8301i	1.15061	−	0.613737i
$845$	−1.41829	+	0.818851i	−0.0487907	+	0.0281693i
$846$	−23.3301	+	23.8811i	−0.802106	+	0.821048i
$847$	4.29326	−	7.43615i	0.147518	−	0.255509i
$848$	−5.66241	−	19.5524i	−0.194448	−	0.671431i
$849$	31.8666	+	0.937207i	1.09366	+	0.0321649i
$850$	5.30648	+	3.18369i	0.182011	+	0.109200i
$851$	−29.6060	+	35.2830i	−1.01488	+	1.20949i
$852$	−11.5937	−	39.4149i	−0.397193	−	1.35033i
$853$	−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
$855$	−1.96965	+	1.46444i	−0.0673608	+	0.0500827i
$856$	29.9849	−	46.3733i	1.02486	−	1.58501i
$857$	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	$0.813186\pi$
$858$	−2.50469	−	4.84171i	−0.0855086	−	0.165293i
$859$	−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
$861$	3.87602	−	0.566515i	0.132094	−	0.0193068i
$862$	−11.3693	+	13.0963i	−0.387241	+	0.446063i
$863$	−26.5038			−0.902199			−0.451100	−	0.892474i	$-0.648968\pi$
$863$	−26.5038			−0.902199			−0.451100	+	0.892474i	$0.648968\pi$
$864$	0.0693110	+	29.3938i	0.00235801	+	0.999997i
$865$	−2.75691			−0.0937378
$866$	−32.2530	+	37.1523i	−1.09600	+	1.26249i
$867$	10.3860	−	26.1192i	0.352726	−	0.887055i
$868$	2.71774	+	19.1544i	0.0922460	+	0.650142i
$869$	−5.53038	−	15.1946i	−0.187605	−	0.515442i
$870$	0.0410122	−	0.0640136i	0.00139044	−	0.00217027i
$871$	−1.57287	−	8.92017i	−0.0532946	−	0.302248i
$872$	8.54629	−	13.2173i	0.289414	−	0.447594i
$873$	−1.36936	+	2.07917i	−0.0463456	+	0.0703691i
$874$	34.2061	+	13.1046i	1.15704	+	0.443270i
$875$	0.674995	−	1.85453i	0.0228190	−	0.0626947i
$876$	−32.8850	−	7.96122i	−1.11108	−	0.268985i
$877$	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
$879$	−23.1236	−	42.9176i	−0.779941	−	1.44757i
$880$	−1.17997	+	0.341723i	−0.0397769	+	0.0115195i
$881$	−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	$0.177078\pi$
$882$	17.1387	+	11.7050i	0.577091	+	0.394129i
$883$	−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
$885$	−2.13376	−	0.441282i	−0.0717256	−	0.0148335i
$886$	−17.2042	−	30.9890i	−0.577986	−	1.04109i
$887$	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	$-0.0790481\pi$
$888$	−21.7631	+	47.5979i	−0.730323	+	1.59728i
$889$	−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
$894$	−37.0475	+	40.2228i	−1.23905	+	1.34525i
$895$	−0.522445	+	2.96293i	−0.0174634	+	0.0990399i
$896$	1.92666	−	16.3135i	0.0643651	−	0.544997i
$897$	−1.49233	+	7.21593i	−0.0498273	+	0.240933i
$898$	−1.91153	−	5.53961i	−0.0637885	−	0.184859i
$899$	1.31498	−	0.759206i	0.0438572	−	0.0253209i
$900$	24.5710	−	17.0178i	0.819032	−	0.567259i
$901$	−3.87129	−	2.23509i	−0.128971	−	0.0744617i
$902$	−0.944712	+	4.87729i	−0.0314555	+	0.162396i
$903$	3.87349	+	7.18921i	0.128902	+	0.239242i
$904$	−33.8242	−	7.73849i	−1.12498	−	0.257378i
$905$	1.83739	+	1.54175i	0.0610768	+	0.0512495i
$906$	43.0762	+	17.9722i	1.43111	+	0.597086i
$907$	−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
$909$	1.26486	−	21.4851i	0.0419527	−	0.712614i
$910$	0.173786	+	0.214319i	0.00576096	+	0.00710461i
$911$	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	$0.909821\pi$
$912$	41.4298	+	4.01367i	1.37188	+	0.132906i
$913$	−2.86099	+	1.04132i	−0.0946850	+	0.0344625i
$914$	0.356384	−	21.2190i	0.0117881	−	0.701863i
$915$	−1.09491	+	2.75353i	−0.0361965	+	0.0910290i
$916$	−20.8268	−	12.9759i	−0.688137	−	0.428735i
$917$			24.0760i			0.795059i
$918$	4.48270	+	4.64457i	0.147951	+	0.153294i
$919$	−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
$921$	4.10598	+	28.0926i	0.135297	+	0.925683i
$922$	5.19410	+	0.0872373i	0.171058	+	0.00287301i
$923$	−4.00277	−	10.9975i	−0.131753	−	0.361988i
$924$	9.13119	−	6.72987i	0.300394	−	0.221396i
$925$	52.4099	−	9.24128i	1.72323	−	0.303851i
$926$	5.25998	+	6.48678i	0.172854	+	0.213169i
$927$	−2.75918	−	23.7351i	−0.0906234	−	0.779564i
$928$	−1.24425	+	0.337796i	−0.0408444	+	0.0110887i
$929$	−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	$0.998666\pi$
$930$	−2.20399	+	0.284417i	−0.0722716	+	0.00932639i
$931$	18.8913	−	22.5138i	0.619137	−	0.737859i
$932$	1.56418	+	0.629573i	0.0512366	+	0.0206224i
$933$	−1.56573	+	53.2375i	−0.0512597	+	1.74292i
$934$	−1.48851	+	7.68479i	−0.0487056	+	0.251454i
$935$	−0.134886	+	0.233630i	−0.00441126	+	0.00764052i
$936$	0.546773	+	8.35523i	0.0178718	+	0.273099i
$937$	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
$939$	11.9372	+	36.0623i	0.389557	+	1.17685i
$940$	1.32170	+	1.68710i	0.0431090	+	0.0550272i
$941$	−47.0141	−	8.28985i	−1.53261	−	0.270241i	−0.657238	−	0.753683i	$-0.728275\pi$
$941$	−47.0141	−	8.28985i	−1.53261	−	0.270241i	−0.875376	+	0.483442i	$0.839386\pi$
$942$	6.27608	+	20.0845i	0.204486	+	0.654388i
$943$	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	0.895886	−	0.444284i	$-0.146542\pi$
$947$	9.31764	+	11.1043i	0.302783	+	0.360842i	−0.593103	+	0.805126i	$0.702097\pi$
$948$	−1.56343	+	24.7877i	−0.0507779	+	0.805066i
$949$	−9.49177	−	1.67365i	−0.308116	−	0.0543291i
$950$	−20.5438	−	37.0044i	−0.666528	−	1.20058i
$951$	35.0531	+	31.2143i	1.13667	+	1.01219i
$952$	−2.17668	−	2.87669i	−0.0705465	−	0.0932341i
$953$	−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	$-0.357308\pi$
$954$	−17.5403	+	12.5894i	−0.567887	+	0.407596i
$955$	−1.10867	−	0.640089i	−0.0358756	−	0.0207128i
$956$	21.5950	+	0.725602i	0.698433	+	0.0234677i
$957$	−0.757595	−	0.467619i	−0.0244896	−	0.0151160i
$958$	10.0236	+	6.01380i	0.323848	+	0.194297i
$959$	−9.00855	−	7.55907i	−0.290901	−	0.244095i
$960$	1.87096	+	0.244919i	0.0603851	+	0.00790473i
$961$	−12.5773	−	4.57775i	−0.405718	−	0.147669i
$962$	−5.33364	+	13.9220i	−0.171963	+	0.448864i
$963$	−56.9855	−	13.5435i	−1.83633	−	0.436433i
$964$	−13.3172	−	11.9591i	−0.428919	−	0.385178i
$965$	−0.993327	+	0.175150i	−0.0319763	+	0.00563829i
$966$	−15.3168	−	0.708075i	−0.492811	−	0.0227820i
$967$	−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
$969$	7.17188	−	5.66714i	0.230394	−	0.182055i
$970$	0.120685	+	0.104771i	0.00387498	+	0.00336398i
$971$		−	2.23282i		−	0.0716547i	−0.999358	−	0.0358273i	$-0.988593\pi$
$971$		−	2.23282i		−	0.0716547i	0.999358	−	0.0358273i	$-0.0114066\pi$
$972$	29.3608	−	10.4853i	0.941749	−	0.336316i
$973$			5.54818i			0.177867i
$974$	15.6112	−	17.9826i	0.500215	−	0.576199i
$975$	6.68022	−	5.27864i	0.213938	−	0.169052i
$976$	45.1088	−	22.1485i	1.44390	−	0.708956i
$977$	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	$0.133208\pi$
$978$	−1.13701	+	24.5954i	−0.0363576	+	0.786475i
$979$	−14.2130	+	2.50614i	−0.454250	+	0.0800965i
$980$	0.890187	−	0.991279i	0.0284360	−	0.0316652i
$981$	−16.2420	−	3.86016i	−0.518567	−	0.123246i
$982$	43.4356	+	16.6405i	1.38609	+	0.531020i
$983$	−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	$0.673160\pi$
$984$	4.32995	−	6.28337i	0.138034	−	0.200306i
$985$	1.90014	+	1.59441i	0.0605436	+	0.0508021i
$986$	−0.145663	+	0.242786i	−0.00463885	+	0.00773189i
$987$	−16.8399	−	10.3943i	−0.536020	−	0.330854i
$988$	11.8502	+	0.398173i	0.377006	+	0.0126676i
$989$	12.1241	+	6.99988i	0.385525	+	0.222583i
$990$	0.759761	+	1.05854i	0.0241468	+	0.0336427i
$991$	−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
$993$	−18.6306	−	16.5903i	−0.591225	−	0.526477i
$994$	21.2919	−	11.8207i	0.675339	−	0.374929i
$995$	−2.15976	−	0.380823i	−0.0684689	−	0.0120729i
$996$	4.66727	+	0.294379i	0.147888	+	0.00932774i
$997$	−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
$999$	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.157.26	✓	204
3.2	odd	2		648.2.t.a.37.9		204
4.3	odd	2		864.2.bf.a.49.24		204
8.3	odd	2		864.2.bf.a.49.11		204
8.5	even	2	inner	216.2.t.a.157.29	yes	204
24.5	odd	2		648.2.t.a.37.6		204
27.11	odd	18		648.2.t.a.613.6		204
27.16	even	9	inner	216.2.t.a.205.29	yes	204
108.43	odd	18		864.2.bf.a.529.11		204
216.43	odd	18		864.2.bf.a.529.24		204
216.173	odd	18		648.2.t.a.613.9		204
216.205	even	18	inner	216.2.t.a.205.26	yes	204

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
216.2.t.a.157.26	✓	204	1.1	even	1	trivial
216.2.t.a.157.29	yes	204	8.5	even	2	inner
216.2.t.a.205.26	yes	204	216.205	even	18	inner
216.2.t.a.205.29	yes	204	27.16	even	9	inner
648.2.t.a.37.6		204	24.5	odd	2
648.2.t.a.37.9		204	3.2	odd	2
648.2.t.a.613.6		204	27.11	odd	18
648.2.t.a.613.9		204	216.173	odd	18
864.2.bf.a.49.11		204	8.3	odd	2
864.2.bf.a.49.24		204	4.3	odd	2
864.2.bf.a.529.11		204	108.43	odd	18
864.2.bf.a.529.24		204	216.43	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+(0.927104 - 1.06793i) q^{2} +(-1.07385 - 1.35898i) q^{3} +(-0.280958 - 1.98017i) q^{4} +(0.0465753 + 0.127965i) q^{5} +(-2.44688 - 0.113116i) q^{6} +(-0.252128 - 1.42989i) q^{7} +(-2.37516 - 1.53578i) q^{8} +(-0.693675 + 2.91870i) q^{9} +(0.179838 + 0.0688972i) q^{10} +(0.771344 - 2.11925i) q^{11} +(-2.38931 + 2.50823i) q^{12} +(-0.634290 + 0.755917i) q^{13} +(-1.76077 - 1.05640i) q^{14} +(0.123887 - 0.200710i) q^{15} +(-3.84213 + 1.11269i) q^{16} +(-0.439205 + 0.760726i) q^{17} +(2.47387 + 3.44674i) q^{18} +(5.20298 - 3.00394i) q^{19} +(0.240306 - 0.128180i) q^{20} +(-1.67245 + 1.87813i) q^{21} +(-1.54810 - 2.78851i) q^{22} +(-0.748645 + 4.24578i) q^{23} +(0.463481 + 4.87701i) 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} +(-0.0994893 - 0.318382i) q^{30} +(1.15687 - 6.56095i) q^{31} +(-2.37377 + 5.13471i) q^{32} +(-3.70834 + 1.22752i) q^{33} +(0.405215 + 1.17431i) q^{34} +(0.171232 - 0.0988610i) q^{35} +(5.97441 + 0.553560i) q^{36} +(9.25201 + 5.34165i) q^{37} +(1.61569 - 8.34139i) q^{38} +(1.70841 + 0.0502450i) q^{39} +(0.0859012 - 0.375466i) q^{40} +(-1.19321 - 1.00123i) q^{41} +(0.455183 + 3.52728i) q^{42} +(1.11062 - 3.05141i) q^{43} +(-4.41319 - 0.931971i) q^{44} +(-0.405799 + 0.0471736i) q^{45} +(3.84013 + 4.73578i) q^{46} +(1.36645 + 7.74952i) q^{47} +(5.63801 + 4.02652i) q^{48} +(4.59683 - 1.67311i) q^{49} +(0.118305 - 7.04385i) q^{50} +(1.50546 - 0.220036i) q^{51} +(1.67505 + 1.04362i) q^{52} +5.08895i q^{53} +(2.02749 - 7.06324i) q^{54} +0.307115 q^{55} +(-1.59714 + 3.78343i) q^{56} +(-9.66954 - 3.84497i) q^{57} +(0.322276 + 0.00541278i) q^{58} +(-3.15956 - 8.68082i) q^{59} +(-0.432247 - 0.188925i) q^{60} +(-12.3724 + 2.18158i) q^{61} +(-5.93411 - 7.31814i) q^{62} +(4.34831 + 0.255992i) q^{63} +(3.28278 + 7.29543i) q^{64} +(-0.126273 - 0.0459596i) q^{65} +(-2.12711 + 5.09830i) q^{66} +(-5.90023 + 7.03162i) q^{67} +(1.62976 + 0.655968i) q^{68} +(6.57388 - 3.54195i) q^{69} +(0.0531732 - 0.274519i) q^{70} +(-5.93006 + 10.2712i) q^{71} +(6.13006 - 5.86706i) q^{72} +(4.88366 + 8.45874i) q^{73} +(14.2821 - 4.92826i) q^{74} +(-8.44934 - 1.74741i) q^{75} +(-7.41012 - 9.45878i) q^{76} +(-3.22477 - 0.568614i) q^{77} +(1.63754 - 1.77789i) 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} +(4.18890 + 2.78405i) q^{84} +(-0.117802 - 0.0207717i) q^{85} +(-2.22904 - 4.01504i) q^{86} +(0.0799487 - 0.386581i) q^{87} +(-5.08676 + 3.84895i) q^{88} +(-3.19969 - 5.54203i) q^{89} +(-0.325839 + 0.477100i) q^{90} +(1.24080 + 0.716376i) q^{91} +(8.61769 + 0.289558i) q^{92} +(-10.1585 + 5.47333i) q^{93} +(9.54280 + 5.72533i) q^{94} +(0.626728 + 0.525888i) q^{95} +(9.52707 - 2.28800i) q^{96} +(0.779817 + 0.283830i) q^{97} +(2.47497 - 6.46025i) 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

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more