LMFDB - Embedded newform 640.2.bm.a.101.8

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [640,2,Mod(21,640)] 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("640.21"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(640, base_ring=CyclotomicField(32)) chi = DirichletCharacter(H, H._module([0, 13, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 640 = 2^{7} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	640.bm (of order $32$, degree $16$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$5.11042572936$
Analytic rank:	$0$
Dimension:	$1024$
Relative dimension:	$64$ over $\Q(\zeta_{32})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{32}]$

Embedding invariants

Embedding label			101.8
Character	$\chi$	$=$	640.101
Dual form			640.2.bm.a.621.8

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.31296 + 0.525486i) q^{2} +(0.559854 - 0.299248i) q^{3} +(1.44773 - 1.37988i) q^{4} +(-0.634393 - 0.773010i) q^{5} +(-0.577815 + 0.687096i) q^{6} +(0.496210 - 0.331557i) q^{7} +(-1.17570 + 2.57249i) q^{8} +(-1.44282 + 2.15934i) q^{9} +(1.23914 + 0.681567i) q^{10} +(-3.63933 + 1.10398i) q^{11} +(0.397589 - 1.20576i) q^{12} +(-1.80404 - 1.48054i) q^{13} +(-0.477276 + 0.696073i) q^{14} +(-0.586489 - 0.242932i) q^{15} +(0.191840 - 3.99540i) q^{16} +(-2.07829 + 0.860858i) q^{17} +(0.759668 - 3.59331i) q^{18} +(-0.0393542 - 0.399570i) q^{19} +(-1.98509 - 0.243721i) q^{20} +(0.178587 - 0.334113i) q^{21} +(4.19818 - 3.36190i) q^{22} +(-3.83145 + 0.762123i) q^{23} +(0.111593 + 1.79205i) q^{24} +(-0.195090 + 0.980785i) q^{25} +(3.14664 + 0.995890i) q^{26} +(-0.348260 + 3.53594i) q^{27} +(0.260868 - 1.16472i) q^{28} +(-1.37475 + 4.53194i) q^{29} +(0.897695 + 0.0107680i) q^{30} +(3.97644 + 3.97644i) q^{31} +(1.84765 + 5.34661i) q^{32} +(-1.70713 + 1.70713i) q^{33} +(2.27635 - 2.22239i) q^{34} +(-0.571089 - 0.173238i) q^{35} +(0.890819 + 5.11707i) q^{36} +(-4.54118 - 0.447267i) q^{37} +(0.261639 + 0.503940i) q^{38} +(-1.45305 - 0.289029i) q^{39} +(2.73442 - 0.723144i) q^{40} +(0.363685 + 1.82837i) q^{41} +(-0.0589062 + 0.532523i) q^{42} +(-2.61710 - 1.39887i) q^{43} +(-3.74541 + 6.62012i) q^{44} +(2.58451 - 0.254552i) q^{45} +(4.63006 - 3.01401i) q^{46} +(0.0931769 + 0.224949i) q^{47} +(-1.08821 - 2.29425i) q^{48} +(-2.54249 + 6.13811i) q^{49} +(-0.259243 - 1.39025i) q^{50} +(-0.905931 + 1.10388i) q^{51} +(-4.65474 + 0.345949i) q^{52} +(-3.81768 - 12.5852i) q^{53} +(-1.40084 - 4.82556i) q^{54} +(3.16216 + 2.11289i) q^{55} +(0.269534 + 1.66631i) q^{56} +(-0.141603 - 0.211924i) q^{57} +(-0.576480 - 6.67267i) q^{58} +(-3.21145 + 2.63557i) q^{59} +(-1.18430 + 0.457588i) q^{60} +(1.83544 + 3.43387i) q^{61} +(-7.31046 - 3.13134i) q^{62} +1.54986i q^{63} +(-5.23545 - 6.04897i) q^{64} +2.33379i q^{65} +(1.34432 - 3.13847i) q^{66} +(-1.38568 - 2.59243i) q^{67} +(-1.82092 + 4.11410i) q^{68} +(-1.91699 + 1.57323i) q^{69} +(0.840852 - 0.0726447i) q^{70} +(7.78645 + 11.6532i) q^{71} +(-3.85856 - 6.25039i) q^{72} +(-13.4068 - 8.95813i) q^{73} +(6.19742 - 1.79908i) q^{74} +(0.184276 + 0.607477i) q^{75} +(-0.608335 - 0.524165i) q^{76} +(-1.43984 + 1.75445i) q^{77} +(2.05968 - 0.384072i) q^{78} +(3.10829 - 7.50408i) q^{79} +(-3.21019 + 2.38636i) q^{80} +(-2.11835 - 5.11416i) q^{81} +(-1.43828 - 2.20946i) q^{82} +(0.942875 - 0.0928651i) q^{83} +(-0.202492 - 0.730136i) q^{84} +(1.98391 + 1.06042i) q^{85} +(4.17124 + 0.461411i) q^{86} +(0.586516 + 2.94861i) q^{87} +(1.43879 - 10.6601i) q^{88} +(-10.0120 - 1.99150i) q^{89} +(-3.25959 + 1.69234i) q^{90} +(-1.38607 - 0.136516i) q^{91} +(-4.49526 + 6.39030i) q^{92} +(3.41616 + 1.03628i) q^{93} +(-0.240545 - 0.246386i) q^{94} +(-0.283906 + 0.283906i) q^{95} +(2.63437 + 2.44041i) q^{96} +(2.72152 + 2.72152i) q^{97} +(0.112696 - 9.39514i) q^{98} +(2.86705 - 9.45140i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 1024 q - 192 q^{52} - 128 q^{54} - 32 q^{56} - 288 q^{58} - 192 q^{62} - 192 q^{64} - 192 q^{66} - 192 q^{68} - 288 q^{72} - 32 q^{74} - 128 q^{76} - 192 q^{78}+O(q^{100}) $ 1024 * q - 192 * q^52 - 128 * q^54 - 32 * q^56 - 288 * q^58 - 192 * q^62 - 192 * q^64 - 192 * q^66 - 192 * q^68 - 288 * q^72 - 32 * q^74 - 128 * q^76 - 192 * q^78

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/640\mathbb{Z}\right)^\times$.

$n$	$257$	$261$	$511$
$\chi(n)$	$1$	$e\left(\frac{9}{32}\right)$	$1$

Coefficient data

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

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

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

$2$	−1.31296	+	0.525486i	−0.928403	+	0.371575i
$2$	−1.31296	+	0.525486i	−0.928403	+	0.371575i
$3$	0.559854	−	0.299248i	0.323232	−	0.172771i	−0.301798	−	0.953372i	$-0.597587\pi$
$3$	0.559854	−	0.299248i	0.323232	−	0.172771i	0.625030	+	0.780601i	$0.285087\pi$
$4$	1.44773	−	1.37988i	0.723865	−	0.689942i
$5$	−0.634393	−	0.773010i	−0.283709	−	0.345701i
$5$	−0.634393	−	0.773010i	−0.283709	−	0.345701i
$6$	−0.577815	+	0.687096i	−0.235892	+	0.280506i
$7$	0.496210	−	0.331557i	0.187550	−	0.125317i	−0.458251	−	0.888823i	$-0.651524\pi$
$7$	0.496210	−	0.331557i	0.187550	−	0.125317i	0.645800	+	0.763506i	$0.276524\pi$
$8$	−1.17570	+	2.57249i	−0.415673	+	0.909514i
$9$	−1.44282	+	2.15934i	−0.480941	+	0.719779i
$10$	1.23914	+	0.681567i	0.391850	+	0.215530i
$11$	−3.63933	+	1.10398i	−1.09730	+	0.332862i	−0.786486	−	0.617608i	$-0.788102\pi$
$11$	−3.63933	+	1.10398i	−1.09730	+	0.332862i	−0.310815	+	0.950471i	$0.600602\pi$
$12$	0.397589	−	1.20576i	0.114774	−	0.348074i
$13$	−1.80404	−	1.48054i	−0.500351	−	0.410628i	0.350075	−	0.936722i	$-0.386156\pi$
$13$	−1.80404	−	1.48054i	−0.500351	−	0.410628i	−0.850426	+	0.526094i	$0.823656\pi$
$14$	−0.477276	+	0.696073i	−0.127557	+	0.186033i
$15$	−0.586489	−	0.242932i	−0.151431	−	0.0627247i
$16$	0.191840	−	3.99540i	0.0479599	−	0.998849i
$17$	−2.07829	+	0.860858i	−0.504061	+	0.208789i	−0.620199	−	0.784444i	$-0.712948\pi$
$17$	−2.07829	+	0.860858i	−0.504061	+	0.208789i	0.116139	+	0.993233i	$0.462948\pi$
$18$	0.759668	−	3.59331i	0.179056	−	0.846951i
$19$	−0.0393542	−	0.399570i	−0.00902848	−	0.0916677i	0.989614	−	0.143747i	$-0.0459151\pi$
$19$	−0.0393542	−	0.399570i	−0.00902848	−	0.0916677i	−0.998643	+	0.0520793i	$0.983415\pi$
$20$	−1.98509	−	0.243721i	−0.443881	−	0.0544976i
$21$	0.178587	−	0.334113i	0.0389710	−	0.0729095i
$22$	4.19818	−	3.36190i	0.895054	−	0.716760i
$23$	−3.83145	+	0.762123i	−0.798913	+	0.158914i	−0.577633	−	0.816297i	$-0.696023\pi$
$23$	−3.83145	+	0.762123i	−0.798913	+	0.158914i	−0.221280	+	0.975210i	$0.571023\pi$
$24$	0.111593	+	1.79205i	0.0227789	+	0.365800i
$25$	−0.195090	+	0.980785i	−0.0390181	+	0.196157i
$26$	3.14664	+	0.995890i	0.617106	+	0.195310i
$27$	−0.348260	+	3.53594i	−0.0670226	+	0.680492i
$28$	0.260868	−	1.16472i	0.0492993	−	0.220111i
$29$	−1.37475	+	4.53194i	−0.255284	+	0.841560i	0.731822	+	0.681496i	$0.238670\pi$
$29$	−1.37475	+	4.53194i	−0.255284	+	0.841560i	−0.987107	+	0.160064i	$0.948830\pi$
$30$	0.897695	+	0.0107680i	0.163896	+	0.00196595i
$31$	3.97644	+	3.97644i	0.714189	+	0.714189i	0.967409	−	0.253220i	$-0.0814896\pi$
$31$	3.97644	+	3.97644i	0.714189	+	0.714189i	−0.253220	+	0.967409i	$0.581490\pi$
$32$	1.84765	+	5.34661i	0.326621	+	0.945155i
$33$	−1.70713	+	1.70713i	−0.297173	+	0.297173i
$34$	2.27635	−	2.22239i	0.390391	−	0.381136i
$35$	−0.571089	−	0.173238i	−0.0965317	−	0.0292826i
$36$	0.890819	+	5.11707i	0.148470	+	0.852844i
$37$	−4.54118	−	0.447267i	−0.746565	−	0.0735302i	−0.282422	−	0.959290i	$-0.591138\pi$
$37$	−4.54118	−	0.447267i	−0.746565	−	0.0735302i	−0.464143	+	0.885760i	$0.653638\pi$
$38$	0.261639	+	0.503940i	0.0424435	+	0.0817498i
$39$	−1.45305	−	0.289029i	−0.232674	−	0.0462817i
$40$	2.73442	−	0.723144i	0.432350	−	0.114339i
$41$	0.363685	+	1.82837i	0.0567980	+	0.285543i	0.998737	−	0.0502408i	$-0.0159989\pi$
$41$	0.363685	+	1.82837i	0.0567980	+	0.285543i	−0.941939	+	0.335784i	$0.890999\pi$
$42$	−0.0589062	+	0.532523i	−0.00908942	+	0.0821701i
$43$	−2.61710	−	1.39887i	−0.399105	−	0.213326i	0.259619	−	0.965711i	$-0.416403\pi$
$43$	−2.61710	−	1.39887i	−0.399105	−	0.213326i	−0.658723	+	0.752385i	$0.728903\pi$
$44$	−3.74541	+	6.62012i	−0.564641	+	0.998021i
$45$	2.58451	−	0.254552i	0.385276	−	0.0379464i
$46$	4.63006	−	3.01401i	0.682665	−	0.444392i
$47$	0.0931769	+	0.224949i	0.0135912	+	0.0328122i	0.930529	−	0.366217i	$-0.119347\pi$
$47$	0.0931769	+	0.224949i	0.0135912	+	0.0328122i	−0.916938	+	0.399029i	$0.869347\pi$
$48$	−1.08821	−	2.29425i	−0.157070	−	0.331146i
$49$	−2.54249	+	6.13811i	−0.363213	+	0.876873i
$50$	−0.259243	−	1.39025i	−0.0366625	−	0.196611i
$51$	−0.905931	+	1.10388i	−0.126856	+	0.154574i
$52$	−4.65474	+	0.345949i	−0.645496	+	0.0479745i
$53$	−3.81768	−	12.5852i	−0.524399	−	1.72871i	−0.672839	−	0.739789i	$-0.734925\pi$
$53$	−3.81768	−	12.5852i	−0.524399	−	1.72871i	0.148440	−	0.988921i	$-0.452575\pi$
$54$	−1.40084	−	4.82556i	−0.190630	−	0.656675i
$55$	3.16216	+	2.11289i	0.426385	+	0.284901i
$56$	0.269534	+	1.66631i	0.0360180	+	0.222670i
$57$	−0.141603	−	0.211924i	−0.0187558	−	0.0280701i
$58$	−0.576480	−	6.67267i	−0.0756955	−	0.876164i
$59$	−3.21145	+	2.63557i	−0.418095	+	0.343122i	−0.819803	−	0.572646i	$-0.805917\pi$
$59$	−3.21145	+	2.63557i	−0.418095	+	0.343122i	0.401707	+	0.915768i	$0.368417\pi$
$60$	−1.18430	+	0.457588i	−0.152892	+	0.0590743i
$61$	1.83544	+	3.43387i	0.235004	+	0.439662i	0.971586	−	0.236686i	$-0.0760614\pi$
$61$	1.83544	+	3.43387i	0.235004	+	0.439662i	−0.736582	+	0.676348i	$0.763561\pi$
$62$	−7.31046	−	3.13134i	−0.928430	−	0.397681i
$63$			1.54986i			0.195265i
$64$	−5.23545	−	6.04897i	−0.654432	−	0.756121i
$65$			2.33379i			0.289471i
$66$	1.34432	−	3.13847i	0.165475	−	0.386319i
$67$	−1.38568	−	2.59243i	−0.169288	−	0.316716i	0.782943	−	0.622093i	$-0.213717\pi$
$67$	−1.38568	−	2.59243i	−0.169288	−	0.316716i	−0.952231	+	0.305377i	$0.901217\pi$
$68$	−1.82092	+	4.11410i	−0.220819	+	0.498907i
$69$	−1.91699	+	1.57323i	−0.230778	+	0.189395i
$70$	0.840852	−	0.0726447i	0.100501	−	0.00868270i
$71$	7.78645	+	11.6532i	0.924081	+	1.38299i	0.923754	+	0.382985i	$0.125104\pi$
$71$	7.78645	+	11.6532i	0.924081	+	1.38299i	0.000326750		1.00000i	$0.499896\pi$
$72$	−3.85856	−	6.25039i	−0.454735	−	0.736616i
$73$	−13.4068	−	8.95813i	−1.56915	−	1.04847i	−0.968518	−	0.248942i	$-0.919917\pi$
$73$	−13.4068	−	8.95813i	−1.56915	−	1.04847i	−0.600628	−	0.799528i	$-0.705083\pi$
$74$	6.19742	−	1.79908i	0.720435	−	0.209139i
$75$	0.184276	+	0.607477i	0.0212784	+	0.0701454i
$76$	−0.608335	−	0.524165i	−0.0697808	−	0.0601259i
$77$	−1.43984	+	1.75445i	−0.164085	+	0.199938i
$78$	2.05968	−	0.384072i	0.233212	−	0.0434876i
$79$	3.10829	−	7.50408i	0.349710	−	0.844275i	−0.646944	−	0.762538i	$-0.723953\pi$
$79$	3.10829	−	7.50408i	0.349710	−	0.844275i	0.996654	−	0.0817372i	$-0.0260468\pi$
$80$	−3.21019	+	2.38636i	−0.358910	+	0.266803i
$81$	−2.11835	−	5.11416i	−0.235373	−	0.568240i
$82$	−1.43828	−	2.20946i	−0.158832	−	0.243994i
$83$	0.942875	−	0.0928651i	0.103494	−	0.0101933i	−0.0461376	−	0.998935i	$-0.514691\pi$
$83$	0.942875	−	0.0928651i	0.103494	−	0.0101933i	0.149632	+	0.988742i	$0.452191\pi$
$84$	−0.202492	−	0.730136i	−0.0220937	−	0.0796643i
$85$	1.98391	+	1.06042i	0.215185	+	0.115019i
$86$	4.17124	+	0.461411i	0.449797	+	0.0497552i
$87$	0.586516	+	2.94861i	0.0628811	+	0.316125i
$88$	1.43879	−	10.6601i	0.153375	−	1.13637i
$89$	−10.0120	−	1.99150i	−1.06127	−	0.211099i	−0.366561	−	0.930394i	$-0.619465\pi$
$89$	−10.0120	−	1.99150i	−1.06127	−	0.211099i	−0.694705	+	0.719295i	$0.744465\pi$
$90$	−3.25959	+	1.69234i	−0.343591	+	0.178388i
$91$	−1.38607	−	0.136516i	−0.145299	−	0.0143107i
$92$	−4.49526	+	6.39030i	−0.468663	+	0.666235i
$93$	3.41616	+	1.03628i	0.354240	+	0.107457i
$94$	−0.240545	−	0.246386i	−0.0248103	−	0.0254127i
$95$	−0.283906	+	0.283906i	−0.0291281	+	0.0291281i
$96$	2.63437	+	2.44041i	0.268870	+	0.249074i
$97$	2.72152	+	2.72152i	0.276328	+	0.276328i	0.831641	−	0.555313i	$-0.187402\pi$
$97$	2.72152	+	2.72152i	0.276328	+	0.276328i	−0.555313	+	0.831641i	$0.687402\pi$
$98$	0.112696	−	9.39514i	0.0113840	−	0.949053i
$99$	2.86705	−	9.45140i	0.288150	−	0.949902i
$100$	1.07093	+	1.68911i	0.107093	+	0.168911i
$101$	−0.821028	+	8.33603i	−0.0816953	+	0.829466i	0.863801	+	0.503833i	$0.168077\pi$
$101$	−0.821028	+	8.33603i	−0.0816953	+	0.829466i	−0.945496	+	0.325633i	$0.894423\pi$
$102$	0.609378	−	1.92541i	0.0603374	−	0.190644i
$103$	−2.11387	+	10.6272i	−0.208286	+	1.04713i	0.725207	+	0.688531i	$0.241744\pi$
$103$	−2.11387	+	10.6272i	−0.208286	+	1.04713i	−0.933493	+	0.358595i	$0.883256\pi$
$104$	5.92969	−	2.90022i	0.581454	−	0.284390i
$105$	−0.371568	+	0.0739094i	−0.0362613	+	0.00721282i
$106$	11.6258	+	14.5177i	1.12920	+	1.41009i
$107$	−0.510452	+	0.954988i	−0.0493472	+	0.0923222i	−0.905386	−	0.424589i	$-0.860418\pi$
$107$	−0.510452	+	0.954988i	−0.0493472	+	0.0923222i	0.856039	+	0.516912i	$0.172918\pi$
$108$	4.37500	+	5.59964i	0.420985	+	0.538826i
$109$	−0.519574	−	5.27533i	−0.0497662	−	0.505285i	−0.987465	−	0.157836i	$-0.949548\pi$
$109$	−0.519574	−	5.27533i	−0.0497662	−	0.505285i	0.937699	−	0.347448i	$-0.112952\pi$
$110$	−5.26208	−	1.11247i	−0.501719	−	0.106069i
$111$	−2.67624	+	1.10853i	−0.254017	+	0.105217i
$112$	−1.22951	−	2.04616i	−0.116178	−	0.193344i
$113$	−13.2716	−	5.49729i	−1.24849	−	0.517142i	−0.342133	−	0.939652i	$-0.611149\pi$
$113$	−13.2716	−	5.49729i	−1.24849	−	0.517142i	−0.906358	+	0.422510i	$0.861149\pi$
$114$	0.297283	+	0.203838i	0.0278431	+	0.0190911i
$115$	3.01978	+	2.47827i	0.281595	+	0.231099i
$116$	4.26329	+	8.45801i	0.395836	+	0.785307i
$117$	5.79990	−	1.75938i	0.536201	−	0.162655i
$118$	2.83155	−	5.14797i	0.260666	−	0.473909i
$119$	−0.745848	+	1.11624i	−0.0683717	+	0.102326i
$120$	1.31448	−	1.22313i	0.119995	−	0.111656i
$121$	2.87982	−	1.92423i	0.261801	−	0.174930i
$122$	−4.21431	−	3.54404i	−0.381546	−	0.320862i
$123$	0.750746	+	0.914786i	0.0676925	+	0.0824835i
$124$	11.2438	+	0.269781i	1.00973	+	0.0242271i
$125$	0.881921	−	0.471397i	0.0788814	−	0.0421630i
$126$	−0.814432	−	2.03491i	−0.0725553	−	0.181284i
$127$	20.1863			1.79124			0.895621	−	0.444818i	$-0.146732\pi$
$127$	20.1863			1.79124			0.895621	+	0.444818i	$0.146732\pi$
$128$	10.0526	+	5.19090i	0.888532	+	0.458815i
$129$	−1.88381			−0.165860
$130$	−1.22637	−	3.06417i	−0.107560	−	0.268745i
$131$	4.38543	−	2.34406i	0.383157	−	0.204802i	−0.268562	−	0.963263i	$-0.586548\pi$
$131$	4.38543	−	2.34406i	0.383157	−	0.204802i	0.651719	+	0.758461i	$0.274048\pi$
$132$	−0.115820	+	4.82711i	−0.0100809	+	0.420146i
$133$	−0.152008	−	0.185223i	−0.0131808	−	0.0160608i
$134$	3.18163	+	2.67560i	0.274851	+	0.231137i
$135$	2.95425	−	1.97397i	0.254262	−	0.169892i
$136$	0.228902	−	6.35851i	0.0196282	−	0.545238i
$137$	−2.50354	+	3.74682i	−0.213892	+	0.320112i	−0.922865	−	0.385124i	$-0.874159\pi$
$137$	−2.50354	+	3.74682i	−0.213892	+	0.320112i	0.708973	+	0.705236i	$0.249159\pi$
$138$	1.69022	−	3.07294i	0.143881	−	0.261586i
$139$	−9.97339	+	3.02539i	−0.845932	+	0.256611i	−0.683356	−	0.730085i	$-0.739480\pi$
$139$	−9.97339	+	3.02539i	−0.845932	+	0.256611i	−0.162576	+	0.986696i	$0.551980\pi$
$140$	−1.06583	+	0.537235i	−0.0900792	+	0.0454047i
$141$	0.119481	+	0.0980555i	0.0100621	+	0.00825776i
$142$	−16.3469	−	11.2086i	−1.37180	−	0.940603i
$143$	8.19999	+	3.39655i	0.685718	+	0.284034i
$144$	8.35062	+	6.17890i	0.695885	+	0.514908i
$145$	4.37537	−	1.81234i	0.363354	−	0.150506i
$146$	22.3100	+	4.71659i	1.84639	+	0.390348i
$147$	0.413396	+	4.19728i	0.0340963	+	0.346186i
$148$	−7.19157	+	5.61878i	−0.591144	+	0.461861i
$149$	−0.979610	+	1.83272i	−0.0802527	+	0.150142i	−0.918847	−	0.394615i	$-0.870878\pi$
$149$	−0.979610	+	1.83272i	−0.0802527	+	0.150142i	0.838594	+	0.544757i	$0.183378\pi$
$150$	−0.561168	−	0.700758i	−0.0458192	−	0.0572167i
$151$	21.6874	−	4.31390i	1.76490	−	0.351060i	0.797306	−	0.603575i	$-0.206258\pi$
$151$	21.6874	−	4.31390i	1.76490	−	0.351060i	0.967593	+	0.252515i	$0.0812576\pi$
$152$	1.07416	+	0.368537i	0.0871260	+	0.0298923i
$153$	1.13973	−	5.72981i	0.0921417	−	0.463228i
$154$	0.968515	−	3.06014i	0.0780452	−	0.246593i
$155$	0.551202	−	5.59645i	0.0442736	−	0.449518i
$156$	−2.50245	+	1.58660i	−0.200356	+	0.127030i
$157$	5.12090	−	16.8813i	0.408692	−	1.34728i	−0.475320	−	0.879813i	$-0.657668\pi$
$157$	5.12090	−	16.8813i	0.408692	−	1.34728i	0.884012	−	0.467464i	$-0.154832\pi$
$158$	−0.137775	+	11.4859i	−0.0109608	+	0.913771i
$159$	−5.90344	−	5.90344i	−0.468173	−	0.468173i
$160$	2.96085	−	4.82010i	0.234076	−	0.381063i
$161$	−1.64852	+	1.64852i	−0.129921	+	0.129921i
$162$	5.46873	+	5.60152i	0.429664	+	0.440097i
$163$	7.34442	+	2.22790i	0.575259	+	0.174503i	0.564491	−	0.825439i	$-0.309072\pi$
$163$	7.34442	+	2.22790i	0.575259	+	0.174503i	0.0107679	+	0.999942i	$0.496572\pi$
$164$	3.04945	+	2.14514i	0.238122	+	0.167507i
$165$	2.40262	+	0.236638i	0.187044	+	0.0184222i
$166$	−1.18916	+	0.617395i	−0.0922965	+	0.0479192i
$167$	5.23139	+	1.04059i	0.404817	+	0.0805231i	0.393299	−	0.919411i	$-0.371334\pi$
$167$	5.23139	+	1.04059i	0.404817	+	0.0805231i	0.0115179	+	0.999934i	$0.496334\pi$
$168$	0.649540	+	0.852233i	0.0501131	+	0.0657512i
$169$	−1.47360	−	7.40830i	−0.113354	−	0.569869i
$170$	−3.16203	−	0.349775i	−0.242517	−	0.0268265i
$171$	0.919589	+	0.491530i	0.0703227	+	0.0375883i
$172$	−5.71914	+	1.58611i	−0.436080	+	0.120940i
$173$	10.7971	−	1.06343i	0.820891	−	0.0808507i	0.321153	−	0.947027i	$-0.395930\pi$
$173$	10.7971	−	1.06343i	0.820891	−	0.0808507i	0.499738	+	0.866177i	$0.333430\pi$
$174$	−2.31953	−	3.56321i	−0.175843	−	0.270126i
$175$	0.228380	+	0.551359i	0.0172639	+	0.0416788i
$176$	3.71267	+	14.7524i	0.279853	+	1.11200i
$177$	−1.00925	+	2.43655i	−0.0758602	+	0.183143i
$178$	14.1918	−	2.64638i	1.06372	−	0.198355i
$179$	13.8331	−	16.8557i	1.03393	−	1.25985i	0.0689276	−	0.997622i	$-0.478042\pi$
$179$	13.8331	−	16.8557i	1.03393	−	1.25985i	0.965006	−	0.262230i	$-0.0844578\pi$
$180$	3.39042	−	3.93484i	0.252707	−	0.293286i
$181$	−3.86835	−	12.7522i	−0.287532	−	0.947867i	−0.975104	−	0.221750i	$-0.928823\pi$
$181$	−3.86835	−	12.7522i	−0.287532	−	0.947867i	0.687571	−	0.726117i	$-0.258677\pi$
$182$	1.89159	−	0.549119i	0.140214	−	0.0407034i
$183$	2.05516	+	1.37321i	0.151922	+	0.101511i
$184$	2.54408	−	10.7524i	0.187552	−	0.792678i
$185$	2.53515	+	3.79412i	0.186388	+	0.278949i
$186$	−5.02984	+	0.434549i	−0.368806	+	0.0318627i
$187$	6.61324	−	5.42735i	0.483608	−	0.396887i
$188$	0.445298	+	0.197092i	0.0324767	+	0.0143744i
$189$	0.999556	+	1.87004i	0.0727070	+	0.136025i
$190$	0.223569	−	0.521946i	0.0162194	−	0.0378659i
$191$			2.99215i			0.216504i	0.994123	+	0.108252i	$0.0345253\pi$
$191$			2.99215i			0.216504i	−0.994123	+	0.108252i	$0.965475\pi$
$192$	−4.74123	−	1.81984i	−0.342169	−	0.131336i
$193$			16.3698i			1.17832i	0.808015	+	0.589162i	$0.200542\pi$
$193$			16.3698i			1.17832i	−0.808015	+	0.589162i	$0.799458\pi$
$194$	−5.00336	−	2.14313i	−0.359221	−	0.153867i
$195$	0.698381	+	1.30658i	0.0500121	+	0.0935661i
$196$	4.78905	+	12.3947i	0.342075	+	0.885333i
$197$	−5.22201	+	4.28559i	−0.372052	+	0.305336i	−0.801776	−	0.597625i	$-0.796111\pi$
$197$	−5.22201	+	4.28559i	−0.372052	+	0.305336i	0.429723	+	0.902961i	$0.358611\pi$
$198$	1.20225	+	13.9159i	0.0854405	+	0.988961i
$199$	7.21133	+	10.7925i	0.511198	+	0.765061i	0.993848	−	0.110752i	$-0.0353258\pi$
$199$	7.21133	+	10.7925i	0.511198	+	0.765061i	−0.482650	+	0.875813i	$0.660326\pi$
$200$	−2.29370	−	1.65498i	−0.162189	−	0.117025i
$201$	−1.55156	−	1.03672i	−0.109439	−	0.0731246i
$202$	−3.30249	−	11.3763i	−0.232362	−	0.800435i
$203$	0.820432	+	2.70460i	0.0575830	+	0.189826i
$204$	0.211684	+	2.84820i	0.0148208	+	0.199414i
$205$	1.18263	−	1.44104i	0.0825983	−	0.100646i
$206$	−2.80899	−	15.0638i	−0.195712	−	1.04955i
$207$	3.88243	−	9.37301i	0.269847	−	0.651469i
$208$	−6.26143	+	6.92384i	−0.434152	+	0.480082i
$209$	0.584341	+	1.41072i	0.0404197	+	0.0975818i
$210$	0.449015	−	0.292294i	0.0309850	−	0.0201702i
$211$	4.29808	−	0.423324i	0.295892	−	0.0291428i	0.0510180	−	0.998698i	$-0.483753\pi$
$211$	4.29808	−	0.423324i	0.295892	−	0.0291428i	0.244874	+	0.969555i	$0.421253\pi$
$212$	−22.8931	−	12.9520i	−1.57230	−	0.889548i
$213$	7.84648	+	4.19403i	0.537632	+	0.287370i
$214$	0.168370	−	1.52210i	0.0115095	−	0.104048i
$215$	0.578931	+	2.91048i	0.0394828	+	0.198493i
$216$	−8.68674	−	5.05311i	−0.591058	−	0.343820i
$217$	3.29156	+	0.654733i	0.223446	+	0.0444461i
$218$	3.45429	+	6.65327i	0.233954	+	0.450616i
$219$	−10.1866	−	1.00329i	−0.688343	−	0.0677959i
$220$	7.49348	−	1.30452i	0.505211	−	0.0879510i
$221$	5.02386	+	1.52397i	0.337942	+	0.102513i
$222$	2.93128	−	2.86179i	0.196734	−	0.192071i
$223$	−18.3951	+	18.3951i	−1.23183	+	1.23183i	−0.268569	+	0.963261i	$0.586551\pi$
$223$	−18.3951	+	18.3951i	−1.23183	+	1.23183i	−0.963261	+	0.268569i	$0.913449\pi$
$224$	2.68953	+	2.04044i	0.179702	+	0.136333i
$225$	−1.83637	−	1.83637i	−0.122424	−	0.122424i
$226$	20.3139	+	0.243668i	1.35126	+	0.0162086i
$227$	2.14550	−	7.07277i	0.142402	−	0.469436i	−0.856507	−	0.516135i	$-0.827370\pi$
$227$	2.14550	−	7.07277i	0.142402	−	0.469436i	0.998909	+	0.0466992i	$0.0148702\pi$
$228$	−0.497434	−	0.111413i	−0.0329434	−	0.00737850i
$229$	0.0204345	−	0.207475i	0.00135035	−	0.0137103i	−0.994486	−	0.104870i	$-0.966557\pi$
$229$	0.0204345	−	0.207475i	0.00135035	−	0.0137103i	0.995836	+	0.0911597i	$0.0290574\pi$
$230$	−5.26714	−	1.66701i	−0.347305	−	0.109920i
$231$	−0.281085	+	1.41311i	−0.0184940	+	0.0929756i
$232$	−10.0421	−	8.86474i	−0.659296	−	0.581999i
$233$	3.09068	−	0.614774i	0.202477	−	0.0402752i	−0.0928097	−	0.995684i	$-0.529585\pi$
$233$	3.09068	−	0.614774i	0.202477	−	0.0402752i	0.295287	+	0.955409i	$0.404585\pi$
$234$	−6.69051	+	5.35776i	−0.437372	+	0.350248i
$235$	0.114777	−	0.214733i	0.00748723	−	0.0140076i
$236$	−1.01253	+	8.24702i	−0.0659101	+	0.536835i
$237$	−0.505393	−	5.13134i	−0.0328288	−	0.333316i
$238$	0.392700	−	1.85751i	0.0254550	−	0.120405i
$239$	−13.9745	+	5.78844i	−0.903937	+	0.374423i	−0.785733	−	0.618566i	$-0.787714\pi$
$239$	−13.9745	+	5.78844i	−0.903937	+	0.374423i	−0.118205	+	0.992989i	$0.537714\pi$
$240$	−1.08312	+	2.29665i	−0.0699152	+	0.148248i
$241$	2.62563	+	1.08757i	0.169132	+	0.0700567i	0.465643	−	0.884973i	$-0.345823\pi$
$241$	2.62563	+	1.08757i	0.169132	+	0.0700567i	−0.296511	+	0.955029i	$0.595823\pi$
$242$	−2.76993	+	4.03974i	−0.178058	+	0.259684i
$243$	−10.9560	−	8.99136i	−0.702828	−	0.576796i
$244$	7.39557	+	2.43862i	0.473453	+	0.156116i
$245$	6.35776	−	1.92861i	0.406183	−	0.123214i
$246$	−1.46641	−	0.806572i	−0.0934947	−	0.0514251i
$247$	−0.520582	+	0.779107i	−0.0331239	+	0.0495734i
$248$	−14.9045	+	5.55426i	−0.946434	+	0.352696i
$249$	0.500082	−	0.334144i	0.0316914	−	0.0211755i
$250$	−0.910215	+	1.08236i	−0.0575671	+	0.0684546i
$251$	−6.72648	−	8.19623i	−0.424571	−	0.517342i	0.516161	−	0.856492i	$-0.327361\pi$
$251$	−6.72648	−	8.19623i	−0.424571	−	0.517342i	−0.940732	+	0.339150i	$0.889861\pi$
$252$	2.13863	+	2.24378i	0.134721	+	0.141345i
$253$	13.1026	−	7.00346i	0.823751	−	0.440304i
$254$	−26.5038	+	10.6076i	−1.66299	+	0.665580i
$255$	1.42803			0.0894266
$256$	−15.9264	−	1.53295i	−0.995400	−	0.0958094i
$257$	2.39667			0.149500			0.0747502	−	0.997202i	$-0.476184\pi$
$257$	2.39667			0.149500			0.0747502	+	0.997202i	$0.476184\pi$
$258$	2.47336	−	0.989913i	0.153985	−	0.0616293i
$259$	−2.40167	+	1.28372i	−0.149233	+	0.0797665i
$260$	3.22036	+	3.37869i	0.199718	+	0.209538i
$261$	−7.80247	−	9.50734i	−0.482961	−	0.588489i
$262$	−4.52613	+	5.38215i	−0.279625	+	0.332510i
$263$	7.01229	−	4.68546i	0.432396	−	0.288918i	−0.320262	−	0.947329i	$-0.603771\pi$
$263$	7.01229	−	4.68546i	0.432396	−	0.288918i	0.752659	+	0.658411i	$0.228771\pi$
$264$	−2.38451	−	6.39866i	−0.146756	−	0.393810i
$265$	−7.30658	+	10.9351i	−0.448840	+	0.671736i
$266$	0.296913	+	0.163312i	0.0182049	+	0.0100133i
$267$	−6.20119	+	1.88111i	−0.379506	+	0.115122i
$268$	−5.58335	−	1.84106i	−0.341057	−	0.112460i
$269$	−16.2470	−	13.3335i	−0.990594	−	0.812960i	−0.00823563	−	0.999966i	$-0.502622\pi$
$269$	−16.2470	−	13.3335i	−0.990594	−	0.812960i	−0.982359	+	0.187006i	$0.940122\pi$
$270$	−2.84152	+	4.14416i	−0.172930	+	0.252206i
$271$	−8.74499	−	3.62229i	−0.531220	−	0.220039i	0.100917	−	0.994895i	$-0.467822\pi$
$271$	−8.74499	−	3.62229i	−0.531220	−	0.220039i	−0.632138	+	0.774856i	$0.717822\pi$
$272$	3.04077	+	8.46876i	0.184374	+	0.513494i
$273$	−0.816847	+	0.338349i	−0.0494378	+	0.0204778i
$274$	1.31815	−	6.23500i	0.0796325	−	0.376670i
$275$	−0.372768	−	3.78478i	−0.0224788	−	0.228231i
$276$	−0.604403	+	4.92284i	−0.0363808	+	0.296320i
$277$	7.41147	−	13.8659i	0.445312	−	0.833120i	−0.554688	−	0.832059i	$-0.687162\pi$
$277$	7.41147	−	13.8659i	0.445312	−	0.833120i	0.999999	−	0.00106114i	$-0.000337770\pi$
$278$	11.5049	−	9.21310i	0.690016	−	0.552565i
$279$	−14.3238	+	2.84917i	−0.857541	+	0.170576i
$280$	1.11708	−	1.26545i	0.0667586	−	0.0756250i
$281$	−3.27924	+	16.4858i	−0.195623	+	0.983463i	0.750799	+	0.660531i	$0.229669\pi$
$281$	−3.27924	+	16.4858i	−0.195623	+	0.983463i	−0.946422	+	0.322932i	$0.895331\pi$
$282$	−0.208400	−	0.0659574i	−0.0124101	−	0.00392771i
$283$	0.0364592	−	0.370176i	0.00216727	−	0.0220047i	−0.994040	−	0.109013i	$-0.965231\pi$
$283$	0.0364592	−	0.370176i	0.00216727	−	0.0220047i	0.996208	+	0.0870088i	$0.0277308\pi$
$284$	27.3528	+	6.12634i	1.62309	+	0.363532i
$285$	−0.0739875	+	0.243904i	−0.00438264	+	0.0144476i
$286$	−12.5511	−	0.150552i	−0.742162	−	0.00890235i
$287$	0.786672	+	0.786672i	0.0464358	+	0.0464358i
$288$	−14.2110	−	3.72452i	−0.837389	−	0.219469i
$289$	−8.44258	+	8.44258i	−0.496622	+	0.496622i
$290$	−4.79233	+	4.67872i	−0.281415	+	0.274744i
$291$	2.33806	+	0.709243i	0.137060	+	0.0415766i
$292$	−31.7706	+	5.53087i	−1.85923	+	0.323670i
$293$	−16.6860	−	1.64343i	−0.974807	−	0.0960101i	−0.401947	−	0.915663i	$-0.631666\pi$
$293$	−16.6860	−	1.64343i	−0.974807	−	0.0960101i	−0.572860	+	0.819653i	$0.694166\pi$
$294$	−2.74838	−	5.29363i	−0.160289	−	0.308731i
$295$	4.07465	+	0.810498i	0.237235	+	0.0471890i
$296$	6.48966	−	11.1563i	0.377204	−	0.648447i
$297$	−2.63617	−	13.2529i	−0.152966	−	0.769014i
$298$	0.323120	−	2.92106i	0.0187178	−	0.169212i
$299$	8.04045	+	4.29771i	0.464991	+	0.248543i
$300$	1.10503	+	0.625182i	0.0637989	+	0.0360949i
$301$	−1.76244	+	0.173585i	−0.101585	+	0.0100053i
$302$	−26.2079	+	17.0604i	−1.50809	+	0.981717i
$303$	2.03489	+	4.91265i	0.116901	+	0.282224i
$304$	−1.60399	+	0.0805824i	−0.0919952	+	0.00462172i
$305$	1.49003	−	3.59724i	0.0853186	−	0.205977i
$306$	1.51451	+	8.12192i	0.0865790	+	0.464299i
$307$	−9.23874	+	11.2574i	−0.527282	+	0.642496i	−0.966738	−	0.255769i	$-0.917671\pi$
$307$	−9.23874	+	11.2574i	−0.527282	+	0.642496i	0.439455	+	0.898264i	$0.355171\pi$
$308$	0.336440	+	4.52679i	0.0191705	+	0.257938i
$309$	1.99670	+	6.58223i	0.113588	+	0.374450i
$310$	2.21715	+	7.63757i	0.125926	+	0.433785i
$311$	0.549698	+	0.367296i	0.0311705	+	0.0208275i	0.571058	−	0.820910i	$-0.306533\pi$
$311$	0.549698	+	0.367296i	0.0311705	+	0.0208275i	−0.539887	+	0.841737i	$0.681533\pi$
$312$	2.45188	−	3.39815i	0.138810	−	0.192382i
$313$	−16.2968	−	24.3898i	−0.921148	−	1.37860i	−0.925558	−	0.378605i	$-0.876404\pi$
$313$	−16.2968	−	24.3898i	−0.921148	−	1.37860i	0.00441047	−	0.999990i	$-0.498596\pi$
$314$	2.14737	+	24.8555i	0.121183	+	1.40268i
$315$	1.19806	−	0.983223i	0.0675031	−	0.0553984i
$316$	−5.85480	−	15.1530i	−0.329358	−	0.852420i
$317$	−1.17709	−	2.20217i	−0.0661118	−	0.123686i	0.846694	−	0.532080i	$-0.178589\pi$
$317$	−1.17709	−	2.20217i	−0.0661118	−	0.123686i	−0.912806	+	0.408393i	$0.866089\pi$
$318$	10.8532	+	4.64881i	0.608615	+	0.260692i
$319$		−	18.0109i		−	1.00842i
$320$	−1.35458	+	7.88449i	−0.0757233	+	0.440756i
$321$			0.687406i			0.0383672i
$322$	1.29817	−	3.03071i	0.0723439	−	0.168895i
$323$	0.425763	+	0.796546i	0.0236901	+	0.0443210i
$324$	−10.1237	−	4.48083i	−0.562430	−	0.248935i
$325$	1.80404	−	1.48054i	0.100070	−	0.0821255i
$326$	−10.8137	+	0.934237i	−0.598913	+	0.0517426i
$327$	−1.86952	−	2.79793i	−0.103385	−	0.154726i
$328$	−5.13105	−	1.21404i	−0.283315	−	0.0670339i
$329$	0.120819	+	0.0807284i	0.00666095	+	0.00445070i
$330$	−3.27890	+	0.951849i	−0.180497	+	0.0523975i
$331$	6.04061	+	19.9132i	0.332022	+	1.09453i	0.951018	+	0.309135i	$0.100040\pi$
$331$	6.04061	+	19.9132i	0.332022	+	1.09453i	−0.618996	+	0.785394i	$0.712460\pi$
$332$	1.23688	−	1.43550i	0.0678828	−	0.0787834i
$333$	7.51792	−	9.16061i	0.411979	−	0.501998i
$334$	−7.41542	+	1.38277i	−0.405754	+	0.0756619i
$335$	−1.12491	+	2.71577i	−0.0614603	+	0.148378i
$336$	−1.30066	−	0.777624i	−0.0709566	−	0.0424228i
$337$	7.04272	+	17.0026i	0.383642	+	0.926193i	0.991255	+	0.131960i	$0.0421270\pi$
$337$	7.04272	+	17.0026i	0.383642	+	0.926193i	−0.607613	+	0.794233i	$0.707873\pi$
$338$	5.82774	+	8.95245i	0.316987	+	0.486949i
$339$	−9.07524	+	0.893833i	−0.492899	+	0.0485463i
$340$	4.33542	−	1.20236i	0.235121	−	0.0652072i
$341$	−18.8615	−	10.0817i	−1.02141	−	0.545953i
$342$	−1.46568	−	0.162129i	−0.0792547	−	0.00876693i
$343$	1.58852	+	7.98601i	0.0857718	+	0.431204i
$344$	6.67552	−	5.08783i	0.359920	−	0.274317i
$345$	2.43225	+	0.483804i	0.130948	+	0.0260472i
$346$	−13.6174	+	7.06998i	−0.732076	+	0.380084i
$347$	5.32661	+	0.524625i	0.285947	+	0.0281634i	0.239974	−	0.970779i	$-0.422861\pi$
$347$	5.32661	+	0.524625i	0.285947	+	0.0281634i	0.0459734	+	0.998943i	$0.485361\pi$
$348$	4.91786	+	3.45947i	0.263625	+	0.185447i
$349$	31.5752	+	9.57822i	1.69018	+	0.512710i	0.981278	−	0.192597i	$-0.0616911\pi$
$349$	31.5752	+	9.57822i	1.69018	+	0.512710i	0.708902	+	0.705307i	$0.249191\pi$
$350$	−0.589586	−	0.603902i	−0.0315147	−	0.0322799i
$351$	5.86337	−	5.86337i	0.312964	−	0.312964i
$352$	−12.6268	−	17.4183i	−0.673008	−	0.928400i
$353$	−0.542673	−	0.542673i	−0.0288836	−	0.0288836i	0.692517	−	0.721401i	$-0.256502\pi$
$353$	−0.542673	−	0.542673i	−0.0288836	−	0.0288836i	−0.721401	+	0.692517i	$0.756502\pi$
$354$	0.0447353	−	3.72945i	0.00237765	−	0.198218i
$355$	4.06841	−	13.4117i	0.215929	−	0.711821i
$356$	−17.2426	+	10.9322i	−0.913858	+	0.579405i
$357$	−0.0835330	+	0.848125i	−0.00442103	+	0.0448875i
$358$	−9.30488	+	29.3999i	−0.491778	+	1.55383i
$359$	−0.577870	+	2.90515i	−0.0304988	+	0.153328i	−0.993034	−	0.117829i	$-0.962406\pi$
$359$	−0.577870	+	2.90515i	−0.0304988	+	0.153328i	0.962535	+	0.271157i	$0.0874064\pi$
$360$	−2.38378	+	6.94791i	−0.125636	+	0.366187i
$361$	18.4768	−	3.67527i	0.972464	−	0.193435i
$362$	11.7801	+	14.7104i	0.619149	+	0.773163i
$363$	1.03645	−	1.93907i	0.0543997	−	0.101775i
$364$	−2.19502	+	1.71497i	−0.115051	+	0.0898890i
$365$	1.58045	+	16.0466i	0.0827245	+	0.839916i
$366$	−3.41995	−	0.723017i	−0.178763	−	0.0377927i
$367$	−19.9762	+	8.27439i	−1.04275	+	0.431920i	−0.837297	−	0.546748i	$-0.815866\pi$
$367$	−19.9762	+	8.27439i	−1.04275	+	0.431920i	−0.205449	+	0.978668i	$0.565866\pi$
$368$	2.30996	+	15.4544i	0.120415	+	0.805615i
$369$	−4.47280	−	1.85269i	−0.232844	−	0.0964473i
$370$	−5.32231	−	3.64934i	−0.276694	−	0.189720i
$371$	−6.06708	−	4.97913i	−0.314987	−	0.258503i
$372$	6.37563	−	3.21365i	0.330561	−	0.166620i
$373$	0.252650	−	0.0766406i	0.0130817	−	0.00396830i	−0.283737	−	0.958902i	$-0.591574\pi$
$373$	0.252650	−	0.0766406i	0.0130817	−	0.00396830i	0.296819	+	0.954934i	$0.404074\pi$
$374$	−5.83093	+	10.6011i	−0.301510	+	0.548167i
$375$	0.352682	−	0.527827i	0.0182124	−	0.0272568i
$376$	−0.688228	−	0.0247757i	−0.0354926	−	0.00127771i
$377$	9.18981	−	6.14044i	0.473299	−	0.316249i
$378$	−2.29506	−	1.93003i	−0.118045	−	0.0992702i
$379$	−17.1361	−	20.8804i	−0.880224	−	1.07256i	−0.996845	−	0.0793790i	$-0.974706\pi$
$379$	−17.1361	−	20.8804i	−0.880224	−	1.07256i	0.116621	−	0.993176i	$-0.462794\pi$
$380$	−0.0192616	+	0.802776i	−0.000988100	+	0.0411815i
$381$	11.3014	−	6.04070i	0.578986	−	0.309475i
$382$	−1.57233	−	3.92857i	−0.0804474	−	0.201003i
$383$	25.3745			1.29658			0.648289	−	0.761395i	$-0.275485\pi$
$383$	25.3745			1.29658			0.648289	+	0.761395i	$0.275485\pi$
$384$	7.18135	−	0.102074i	0.366472	−	0.00520893i
$385$	2.26964			0.115671
$386$	−8.60210	−	21.4929i	−0.437835	−	1.09396i
$387$	6.79666	−	3.63289i	0.345494	−	0.184670i
$388$	7.69540	+	0.184641i	0.390675	+	0.00937375i
$389$	3.12227	+	3.80450i	0.158305	+	0.192896i	0.846123	−	0.532988i	$-0.178931\pi$
$389$	3.12227	+	3.80450i	0.158305	+	0.192896i	−0.687817	+	0.725884i	$0.741431\pi$
$390$	−1.60354	−	1.34850i	−0.0811982	−	0.0682838i
$391$	7.30680	−	4.88225i	0.369521	−	0.246906i
$392$	−12.8011	−	13.7571i	−0.646551	−	0.694840i
$393$	1.75375	−	2.62467i	0.0884648	−	0.132397i
$394$	4.60427	−	8.37090i	0.231960	−	0.421720i
$395$	−7.77261	+	2.35780i	−0.391082	+	0.118634i
$396$	−8.89113	−	17.6393i	−0.446796	−	0.886407i
$397$	12.3023	+	10.0963i	0.617437	+	0.506717i	0.890323	−	0.455329i	$-0.150478\pi$
$397$	12.3023	+	10.0963i	0.617437	+	0.506717i	−0.272887	+	0.962046i	$0.587978\pi$
$398$	−15.1395	−	10.3807i	−0.758875	−	0.520337i
$399$	−0.140530	−	0.0582094i	−0.00703530	−	0.00291412i
$400$	3.88120	+	0.967617i	0.194060	+	0.0483808i
$401$	8.97579	−	3.71790i	0.448230	−	0.185663i	−0.147138	−	0.989116i	$-0.547006\pi$
$401$	8.97579	−	3.71790i	0.448230	−	0.185663i	0.595368	+	0.803453i	$0.297006\pi$
$402$	2.58192	+	0.545849i	0.128774	+	0.0272244i
$403$	−1.28639	−	13.0609i	−0.0640796	−	0.650611i
$404$	10.3141	+	13.2012i	0.513147	+	0.656786i
$405$	−2.60943	+	4.88190i	−0.129664	+	0.242583i
$406$	−2.49842	−	3.11991i	−0.123995	−	0.154838i
$407$	17.0206	−	3.38562i	0.843682	−	0.167819i
$408$	−1.77462	−	3.62834i	−0.0878569	−	0.179629i
$409$	−3.43717	+	17.2798i	−0.169957	+	0.854432i	0.797873	+	0.602826i	$0.205959\pi$
$409$	−3.43717	+	17.2798i	−0.169957	+	0.854432i	−0.967830	+	0.251606i	$0.919041\pi$
$410$	−0.795499	+	2.51348i	−0.0392869	+	0.124132i
$411$	−0.280390	+	2.84685i	−0.0138306	+	0.140425i
$412$	11.6039	+	18.3022i	0.571685	+	0.901682i
$413$	−0.719713	+	2.37258i	−0.0354148	+	0.116747i
$414$	−0.172089	+	14.3465i	−0.00845771	+	0.705094i
$415$	−0.669939	−	0.669939i	−0.0328860	−	0.0328860i
$416$	4.58262	−	12.3810i	0.224682	−	0.607029i
$417$	−4.67830	+	4.67830i	−0.229097	+	0.229097i
$418$	−1.50853	−	1.54516i	−0.0737847	−	0.0755763i
$419$	−1.02720	−	0.311599i	−0.0501821	−	0.0152226i	0.265094	−	0.964223i	$-0.414597\pi$
$419$	−1.02720	−	0.311599i	−0.0501821	−	0.0152226i	−0.315276	+	0.949000i	$0.602097\pi$
$420$	−0.435943	+	0.619721i	−0.0212718	+	0.0302393i
$421$	−13.9044	−	1.36946i	−0.677660	−	0.0667436i	−0.246669	−	0.969100i	$-0.579336\pi$
$421$	−13.9044	−	1.36946i	−0.677660	−	0.0667436i	−0.430991	+	0.902356i	$0.641836\pi$
$422$	−5.42076	+	2.81439i	−0.263878	+	0.137002i
$423$	−0.620178	−	0.123361i	−0.0301541	−	0.00599802i
$424$	36.8638	+	4.97548i	1.79026	+	0.241631i
$425$	−0.438862	−	2.20631i	−0.0212879	−	0.107022i
$426$	−12.5060	−	1.38338i	−0.605919	−	0.0670251i
$427$	2.04929	+	1.09537i	0.0991720	+	0.0530086i
$428$	0.578777	+	2.08693i	0.0279763	+	0.100876i
$429$	5.60721	−	0.552262i	0.270719	−	0.0266635i
$430$	−2.28953	−	3.51713i	−0.110411	−	0.169611i
$431$	−12.0234	−	29.0271i	−0.579147	−	1.39819i	−0.893579	−	0.448905i	$-0.851814\pi$
$431$	−12.0234	−	29.0271i	−0.579147	−	1.39819i	0.314432	−	0.949280i	$-0.398186\pi$
$432$	14.0607	+	2.06977i	0.676495	+	0.0995818i
$433$	−6.52660	+	15.7566i	−0.313649	+	0.757215i	0.685915	+	0.727681i	$0.259402\pi$
$433$	−6.52660	+	15.7566i	−0.313649	+	0.757215i	−0.999564	+	0.0295331i	$0.990598\pi$
$434$	−4.66574	+	0.870032i	−0.223963	+	0.0417629i
$435$	1.90723	−	2.32396i	0.0914446	−	0.111426i
$436$	−8.03154	−	6.92029i	−0.384641	−	0.331422i
$437$	0.455305	+	1.50094i	0.0217802	+	0.0717997i
$438$	13.9018	−	4.03561i	0.664251	−	0.192829i
$439$	−16.8865	−	11.2832i	−0.805947	−	0.538516i	0.0829879	−	0.996551i	$-0.473554\pi$
$439$	−16.8865	−	11.2832i	−0.805947	−	0.538516i	−0.888935	+	0.458034i	$0.848554\pi$
$440$	−9.15314	+	5.65051i	−0.436359	+	0.269377i
$441$	−9.58590	−	14.3463i	−0.456471	−	0.683158i
$442$	−7.39696	+	0.639054i	−0.351837	+	0.0303967i
$443$	4.03201	−	3.30898i	0.191566	−	0.157215i	−0.533721	−	0.845661i	$-0.679207\pi$
$443$	4.03201	−	3.30898i	0.191566	−	0.157215i	0.725288	+	0.688446i	$0.241707\pi$
$444$	−2.34482	+	5.29776i	−0.111280	+	0.251421i
$445$	4.81207	+	9.00274i	0.228114	+	0.426771i
$446$	14.4857	−	33.8185i	0.685918	−	1.60135i
$447$			1.31920i			0.0623961i
$448$	−4.60346	−	1.26571i	−0.217493	−	0.0597991i
$449$			39.5223i			1.86517i	0.360944	+	0.932587i	$0.382454\pi$
$449$			39.5223i			1.86517i	−0.360944	+	0.932587i	$0.617546\pi$
$450$	3.37606	+	1.44609i	0.159149	+	0.0681694i
$451$	−3.34205	−	6.25254i	−0.157371	−	0.294420i
$452$	−26.7994	+	10.3547i	−1.26054	+	0.487046i
$453$	10.8509	−	8.90508i	0.509819	−	0.418397i
$454$	0.899682	+	10.4137i	0.0422242	+	0.488739i
$455$	0.773783	+	1.15805i	0.0362755	+	0.0542902i
$456$	0.711657	−	0.115114i	0.0333264	−	0.00539071i
$457$	4.62431	+	3.08987i	0.216316	+	0.144538i	0.659008	−	0.752136i	$-0.270976\pi$
$457$	4.62431	+	3.08987i	0.216316	+	0.144538i	−0.442692	+	0.896674i	$0.645976\pi$
$458$	0.0821954	+	0.283144i	0.00384074	+	0.0132305i
$459$	−2.32016	−	7.64853i	−0.108296	−	0.357003i
$460$	7.79154	−	0.579083i	0.363282	−	0.0269999i
$461$	−10.9728	+	13.3703i	−0.511052	+	0.622719i	−0.963057	−	0.269296i	$-0.913209\pi$
$461$	−10.9728	+	13.3703i	−0.511052	+	0.622719i	0.452005	+	0.892015i	$0.350709\pi$
$462$	−0.373515	−	2.00306i	−0.0173775	−	0.0931908i
$463$	−11.5159	+	27.8017i	−0.535187	+	1.29206i	0.392861	+	0.919598i	$0.371485\pi$
$463$	−11.5159	+	27.8017i	−0.535187	+	1.29206i	−0.928049	+	0.372459i	$0.878515\pi$
$464$	17.8432	+	6.36207i	0.828348	+	0.295352i
$465$	−1.36613	−	3.29814i	−0.0633530	−	0.152948i
$466$	−3.73488	+	2.43128i	−0.173015	+	0.112627i
$467$	3.72328	−	0.366711i	0.172293	−	0.0169694i	−0.0115028	−	0.999934i	$-0.503662\pi$
$467$	3.72328	−	0.366711i	0.172293	−	0.0169694i	0.183796	+	0.982964i	$0.441162\pi$
$468$	5.96894	−	10.5503i	0.275914	−	0.487687i
$469$	−1.54713	−	0.826958i	−0.0714398	−	0.0381854i
$470$	−0.0378587	+	0.342249i	−0.00174629	+	0.0157868i
$471$	−2.18475	−	10.9835i	−0.100668	−	0.506093i
$472$	−3.00428	−	11.3601i	−0.138283	−	0.522890i
$473$	11.0688	+	2.20173i	0.508946	+	0.101236i
$474$	3.36001	+	6.47167i	0.154330	+	0.297253i
$475$	0.399570	+	0.0393542i	0.0183335	+	0.00180570i
$476$	0.460496	+	2.64520i	0.0211068	+	0.121242i
$477$	32.6839	+	9.91457i	1.49650	+	0.453957i
$478$	15.3063	−	14.9434i	0.700092	−	0.683496i
$479$	26.4422	−	26.4422i	1.20818	−	1.20818i	0.236559	−	0.971617i	$-0.423980\pi$
$479$	26.4422	−	26.4422i	1.20818	−	1.20818i	0.971617	−	0.236559i	$-0.0760196\pi$
$480$	0.215236	−	3.58458i	0.00982412	−	0.163613i
$481$	7.53028	+	7.53028i	0.343351	+	0.343351i
$482$	−4.01886	−	0.0482068i	−0.183054	−	0.00219576i
$483$	−0.429613	+	1.41624i	−0.0195481	+	0.0644414i
$484$	1.51398	−	6.75958i	0.0688171	−	0.307253i
$485$	0.377249	−	3.83027i	0.0171300	−	0.173924i
$486$	19.1096	+	6.04807i	0.866831	+	0.274346i
$487$	−1.72875	+	8.69102i	−0.0783372	+	0.393828i	0.921646	+	0.388032i	$0.126845\pi$
$487$	−1.72875	+	8.69102i	−0.0783372	+	0.393828i	−0.999983	+	0.00579606i	$0.998155\pi$
$488$	−10.9915	+	0.684458i	−0.497564	+	0.0309840i
$489$	4.77850	−	0.950502i	0.216091	−	0.0429832i
$490$	−7.33404	+	5.87310i	−0.331318	+	0.265320i
$491$	−11.9312	+	22.3217i	−0.538447	+	1.00736i	0.454717	+	0.890636i	$0.349740\pi$
$491$	−11.9312	+	22.3217i	−0.538447	+	1.00736i	−0.993164	+	0.116727i	$0.962760\pi$
$492$	2.34918	+	0.288421i	0.105909	+	0.0130030i
$493$	−1.04422	−	10.6022i	−0.0470294	−	0.477498i
$494$	0.274095	−	1.29649i	0.0123321	−	0.0583321i
$495$	−9.12487	+	3.77965i	−0.410132	+	0.169882i
$496$	16.6503	−	15.1246i	0.747620	−	0.679115i
$497$	7.72743	+	3.20081i	0.346622	+	0.143576i
$498$	−0.481000	+	0.701505i	−0.0215541	+	0.0314352i
$499$	−27.8858	−	22.8853i	−1.24834	−	1.02449i	−0.998418	−	0.0562206i	$-0.982095\pi$
$499$	−27.8858	−	22.8853i	−1.24834	−	1.02449i	−0.249922	−	0.968266i	$-0.580405\pi$
$500$	0.626310	−	1.89940i	0.0280094	−	0.0849439i
$501$	3.24021	−	0.982907i	0.144762	−	0.0439130i
$502$	13.1386	+	7.22666i	0.586404	+	0.322542i
$503$	−17.0999	+	25.5918i	−0.762447	+	1.14108i	0.223611	+	0.974678i	$0.428215\pi$
$503$	−17.0999	+	25.5918i	−0.762447	+	1.14108i	−0.986058	+	0.166404i	$0.946785\pi$
$504$	−3.98702	−	1.82218i	−0.177596	−	0.0811662i
$505$	6.96470	−	4.65366i	0.309925	−	0.207085i
$506$	−13.5229	+	16.0805i	−0.601167	+	0.714864i
$507$	−3.04192	−	3.70659i	−0.135097	−	0.164616i
$508$	29.2243	−	27.8547i	1.29662	−	1.23585i
$509$	−5.65648	+	3.02345i	−0.250719	+	0.134012i	−0.591970	−	0.805960i	$-0.701650\pi$
$509$	−5.65648	+	3.02345i	−0.250719	+	0.134012i	0.341251	+	0.939972i	$0.389150\pi$
$510$	−1.87494	+	0.750409i	−0.0830239	+	0.0332286i
$511$	−9.62272			−0.425684
$512$	21.7163	−	6.35639i	0.959732	−	0.280916i
$513$	1.42656			0.0629843
$514$	−3.14674	+	1.25942i	−0.138797	+	0.0555506i
$515$	9.55593	−	5.10775i	0.421085	−	0.225074i
$516$	−2.72724	+	2.59943i	−0.120060	+	0.114434i
$517$	−0.587441	−	0.715799i	−0.0258356	−	0.0314808i
$518$	2.47872	−	2.94752i	0.108909	−	0.129507i
$519$	5.72659	−	3.82639i	0.251369	−	0.167960i
$520$	−6.00365	−	2.74384i	−0.263278	−	0.120325i
$521$	−1.01090	+	1.51292i	−0.0442883	+	0.0662822i	−0.852953	−	0.521988i	$-0.825191\pi$
$521$	−1.01090	+	1.51292i	−0.0442883	+	0.0662822i	0.808665	+	0.588270i	$0.200191\pi$
$522$	15.2403	+	8.38267i	0.667050	+	0.366899i
$523$	−35.7502	+	10.8447i	−1.56325	+	0.474206i	−0.949097	−	0.314984i	$-0.898001\pi$
$523$	−35.7502	+	10.8447i	−1.56325	+	0.474206i	−0.614150	+	0.789190i	$0.710501\pi$
$524$	3.11439	−	9.44496i	0.136053	−	0.412605i
$525$	0.292853	+	0.240338i	0.0127811	+	0.0104892i
$526$	−6.74471	+	9.83668i	−0.294083	+	0.428900i
$527$	−11.6874	−	4.84106i	−0.509109	−	0.210880i
$528$	6.49317	+	7.14816i	0.282579	+	0.311084i
$529$	−7.15005	+	2.96165i	−0.310872	+	0.128767i
$530$	3.84703	−	18.1968i	0.167104	−	0.790419i
$531$	−1.05753	−	10.7373i	−0.0458929	−	0.465958i
$532$	−0.475653	−	0.0583984i	−0.0206222	−	0.00253189i
$533$	2.05086	−	3.83690i	0.0888328	−	0.166195i
$534$	7.15342	−	5.72846i	0.309559	−	0.247895i
$535$	1.06204	−	0.211254i	0.0459161	−	0.00913329i
$536$	8.29817	−	0.516738i	0.358426	−	0.0223197i
$537$	2.70048	−	13.5762i	0.116534	−	0.585858i
$538$	28.3382	+	8.96885i	1.22175	+	0.386675i
$539$	2.47662	−	25.1455i	0.106675	−	1.08309i
$540$	1.55311	−	6.93430i	0.0668352	−	0.298405i
$541$	−6.88850	+	22.7083i	−0.296160	+	0.976308i	0.674988	+	0.737829i	$0.264149\pi$
$541$	−6.88850	+	22.7083i	−0.296160	+	0.976308i	−0.971148	+	0.238479i	$0.923351\pi$
$542$	13.3853	+	0.160559i	0.574947	+	0.00689658i
$543$	−5.98180	−	5.98180i	−0.256704	−	0.256704i
$544$	−8.44262	−	9.52126i	−0.361975	−	0.408221i
$545$	−3.74827	+	3.74827i	−0.160558	+	0.160558i
$546$	0.894690	−	0.873480i	0.0382892	−	0.0373815i
$547$	39.8718	+	12.0950i	1.70480	+	0.517144i	0.984329	−	0.176344i	$-0.0564271\pi$
$547$	39.8718	+	12.0950i	1.70480	+	0.517144i	0.720468	+	0.693488i	$0.243927\pi$
$548$	1.54572	+	8.87897i	0.0660299	+	0.379291i
$549$	−10.0631	−	0.991130i	−0.429483	−	0.0423004i
$550$	2.47828	+	4.77338i	0.105674	+	0.203538i
$551$	1.86493	+	0.370958i	0.0794487	+	0.0158033i
$552$	−1.79332	−	6.78109i	−0.0763289	−	0.288622i
$553$	−0.945664	−	4.75418i	−0.0402137	−	0.202168i
$554$	−2.44464	+	22.1000i	−0.103863	+	0.938938i
$555$	2.55470	+	1.36551i	0.108441	+	0.0579629i
$556$	−10.2641	+	18.1421i	−0.435294	+	0.769395i
$557$	28.5046	−	2.80746i	1.20778	−	0.118956i	0.525982	−	0.850496i	$-0.323698\pi$
$557$	28.5046	−	2.80746i	1.20778	−	0.118956i	0.681799	+	0.731540i	$0.261198\pi$
$558$	17.3093	−	11.2678i	0.732763	−	0.477004i
$559$	2.65028	+	6.39835i	0.112095	+	0.270621i
$560$	−0.801712	+	2.24850i	−0.0338785	+	0.0950163i
$561$	2.07832	−	5.01752i	0.0877469	−	0.211840i
$562$	−4.35757	−	23.3684i	−0.183813	−	0.985738i
$563$	20.7516	−	25.2859i	0.874577	−	1.06568i	−0.122738	−	0.992439i	$-0.539167\pi$
$563$	20.7516	−	25.2859i	0.874577	−	1.06568i	0.997315	−	0.0732360i	$-0.0233326\pi$
$564$	0.308281	−	0.0229121i	0.0129810	−	0.000964773i
$565$	4.16998	+	13.7466i	0.175432	+	0.578322i
$566$	0.146653	+	0.505185i	0.00616428	+	0.0212345i
$567$	−2.74678	−	1.83534i	−0.115354	−	0.0770771i
$568$	−39.1324	+	6.32986i	−1.64196	+	0.265595i
$569$	14.1521	+	21.1802i	0.593288	+	0.887918i	0.999667	−	0.0257863i	$-0.00820893\pi$
$569$	14.1521	+	21.1802i	0.593288	+	0.887918i	−0.406380	+	0.913704i	$0.633209\pi$
$570$	−0.0310255	−	0.359116i	−0.00129952	−	0.0150417i
$571$	−26.5409	+	21.7816i	−1.11070	+	0.911531i	−0.996637	−	0.0819418i	$-0.973888\pi$
$571$	−26.5409	+	21.7816i	−1.11070	+	0.911531i	−0.114067	+	0.993473i	$0.536388\pi$
$572$	16.5582	−	6.39776i	0.692334	−	0.267504i
$573$	0.895394	+	1.67516i	0.0374056	+	0.0699810i
$574$	−1.44625	−	0.619484i	−0.0603655	−	0.0258568i
$575$		−	3.90651i		−	0.162913i
$576$	20.6156	−	2.57752i	0.858984	−	0.107397i
$577$			41.6273i			1.73297i	0.499207	+	0.866483i	$0.333625\pi$
$577$			41.6273i			1.73297i	−0.499207	+	0.866483i	$0.666375\pi$
$578$	6.64832	−	15.5212i	0.276534	−	0.645598i
$579$	4.89863	+	9.16469i	0.203580	+	0.380872i
$580$	3.83353	−	8.66127i	0.159179	−	0.359640i
$581$	0.437074	−	0.358697i	0.0181329	−	0.0148813i
$582$	−3.44248	+	0.297410i	−0.142695	+	0.0123280i
$583$	27.7876	+	41.5871i	1.15085	+	1.72236i
$584$	38.8071	−	23.9568i	1.60585	−	0.991340i
$585$	−5.03943	−	3.36724i	−0.208355	−	0.139218i
$586$	22.7717	−	6.61051i	0.940689	−	0.273077i
$587$	2.19428	+	7.23356i	0.0905675	+	0.298561i	0.990509	−	0.137450i	$-0.0438908\pi$
$587$	2.19428	+	7.23356i	0.0905675	+	0.298561i	−0.899941	+	0.436011i	$0.856391\pi$
$588$	6.39025	+	5.50609i	0.263529	+	0.227067i
$589$	1.43238	−	1.74536i	0.0590200	−	0.0719161i
$590$	−5.77575	+	1.07702i	−0.237784	+	0.0443401i
$591$	−1.64111	+	3.96198i	−0.0675061	+	0.162974i
$592$	−2.65819	+	18.0580i	−0.109251	+	0.742179i
$593$	−16.5013	−	39.8377i	−0.677627	−	1.63594i	−0.768326	−	0.640059i	$-0.778910\pi$
$593$	−16.5013	−	39.8377i	−0.677627	−	1.63594i	0.0906984	−	0.995878i	$-0.471090\pi$
$594$	10.4254	+	16.0153i	0.427760	+	0.657116i
$595$	1.33603	−	0.131587i	0.0547717	−	0.00539454i
$596$	1.11073	+	4.00503i	0.0454974	+	0.164052i
$597$	7.26693	+	3.88426i	0.297416	+	0.158972i
$598$	−12.8152	−	1.41758i	−0.524051	−	0.0579691i
$599$	−5.16412	−	25.9618i	−0.211000	−	1.06077i	−0.930504	−	0.366281i	$-0.880631\pi$
$599$	−5.16412	−	25.9618i	−0.211000	−	1.06077i	0.719504	−	0.694488i	$-0.244369\pi$
$600$	−1.77938	−	0.240162i	−0.0726431	−	0.00980458i
$601$	32.1093	+	6.38693i	1.30977	+	0.260528i	0.800112	−	0.599851i	$-0.204774\pi$
$601$	32.1093	+	6.38693i	1.30977	+	0.260528i	0.509654	+	0.860380i	$0.329774\pi$
$602$	2.22280	−	1.15405i	0.0905944	−	0.0470355i
$603$	7.59723	+	0.748262i	0.309383	+	0.0304716i
$604$	25.4449	−	36.1715i	1.03534	−	1.47180i
$605$	−3.31439	−	1.00541i	−0.134749	−	0.0408756i
$606$	−5.25326	−	5.38081i	−0.213399	−	0.218581i
$607$	13.1655	−	13.1655i	0.534369	−	0.534369i	−0.387500	−	0.921870i	$-0.626661\pi$
$607$	13.1655	−	13.1655i	0.534369	−	0.534369i	0.921870	+	0.387500i	$0.126661\pi$
$608$	2.06363	−	0.948676i	0.0836913	−	0.0384739i
$609$	1.26867	+	1.26867i	0.0514091	+	0.0514091i
$610$	−0.0660455	+	5.50602i	−0.00267410	+	0.222932i
$611$	0.164950	−	0.543769i	0.00667318	−	0.0219985i
$612$	−6.25645	−	9.86791i	−0.252902	−	0.398886i
$613$	0.154725	−	1.57095i	0.00624928	−	0.0634500i	−0.991554	−	0.129692i	$-0.958601\pi$
$613$	0.154725	−	1.57095i	0.00624928	−	0.0634500i	0.997804	+	0.0662423i	$0.0211010\pi$
$614$	6.21447	−	19.6354i	0.250796	−	0.792420i
$615$	0.230871	−	1.16067i	0.00930963	−	0.0468027i
$616$	−2.82050	−	5.76670i	−0.113641	−	0.232347i
$617$	−30.4293	+	6.05276i	−1.22504	+	0.243675i	−0.764886	−	0.644165i	$-0.777205\pi$
$617$	−30.4293	+	6.05276i	−1.22504	+	0.243675i	−0.460151	+	0.887841i	$0.652205\pi$
$618$	−6.08045	−	7.59297i	−0.244592	−	0.305434i
$619$	−17.5994	+	32.9261i	−0.707379	+	1.32341i	0.229346	+	0.973345i	$0.426341\pi$
$619$	−17.5994	+	32.9261i	−0.707379	+	1.32341i	−0.936724	+	0.350068i	$0.886159\pi$
$620$	−6.92446	−	8.86274i	−0.278093	−	0.355936i
$621$	−1.36048	−	13.8132i	−0.0545942	−	0.554305i
$622$	−0.914740	−	0.193387i	−0.0366777	−	0.00775411i
$623$	−5.62833	+	2.33133i	−0.225494	+	0.0934028i
$624$	−1.43354	+	5.75006i	−0.0573875	+	0.230186i
$625$	−0.923880	−	0.382683i	−0.0369552	−	0.0153073i
$626$	34.2135	+	23.4592i	1.36745	+	0.937617i
$627$	0.749302	+	0.614936i	0.0299242	+	0.0245582i
$628$	−15.8806	−	31.5058i	−0.633705	−	1.25722i
$629$	9.82294	−	2.97976i	0.391666	−	0.118811i
$630$	−1.05634	+	1.92050i	−0.0420855	+	0.0765144i
$631$	−6.98480	+	10.4535i	−0.278061	+	0.416147i	−0.944044	−	0.329820i	$-0.893012\pi$
$631$	−6.98480	+	10.4535i	−0.278061	+	0.416147i	0.665983	+	0.745966i	$0.268012\pi$
$632$	15.6498	+	16.8186i	0.622515	+	0.669009i
$633$	2.27962	−	1.52319i	0.0906067	−	0.0605414i
$634$	2.70268	+	2.27282i	0.107337	+	0.0902654i
$635$	−12.8060	−	15.6042i	−0.508192	−	0.619234i
$636$	−16.6926	−	0.400519i	−0.661907	−	0.0158816i
$637$	13.6745	−	7.30916i	0.541802	−	0.289599i
$638$	9.46449	+	23.6476i	0.374703	+	0.936219i
$639$	−36.3978			−1.43987
$640$	−2.36468	−	11.0638i	−0.0934720	−	0.437336i
$641$	−28.8148			−1.13812			−0.569059	−	0.822297i	$-0.692692\pi$
$641$	−28.8148			−1.13812			−0.569059	+	0.822297i	$0.692692\pi$
$642$	−0.361222	−	0.902536i	−0.0142563	−	0.0356203i
$643$	−27.8073	+	14.8633i	−1.09661	+	0.586153i	−0.917524	−	0.397680i	$-0.869815\pi$
$643$	−27.8073	+	14.8633i	−1.09661	+	0.586153i	−0.179090	+	0.983833i	$0.557315\pi$
$644$	−0.111844	+	4.66137i	−0.00440726	+	0.183684i
$645$	1.19507	+	1.45620i	0.0470560	+	0.0573379i
$646$	−0.977584	−	0.822101i	−0.0384625	−	0.0323451i
$647$	−21.4480	+	14.3311i	−0.843209	+	0.563414i	−0.900457	−	0.434946i	$-0.856768\pi$
$647$	−21.4480	+	14.3311i	−0.843209	+	0.563414i	0.0572477	+	0.998360i	$0.481768\pi$
$648$	15.6467	+	0.563269i	0.614660	+	0.0221273i
$649$	8.77793	−	13.1371i	0.344564	−	0.515676i
$650$	−1.59063	+	2.89189i	−0.0623897	+	0.113429i
$651$	2.03872	−	0.618440i	0.0799038	−	0.0242386i
$652$	13.7070	−	6.90904i	0.536807	−	0.270579i
$653$	19.8126	+	16.2598i	0.775326	+	0.636293i	0.936514	−	0.350630i	$-0.114033\pi$
$653$	19.8126	+	16.2598i	0.775326	+	0.636293i	−0.161188	+	0.986924i	$0.551533\pi$
$654$	3.92488	+	2.69117i	0.153475	+	0.105233i
$655$	−4.59408	−	1.90293i	−0.179505	−	0.0743536i
$656$	7.37482	−	1.10231i	0.287938	−	0.0430380i
$657$	38.6873	−	16.0248i	1.50933	−	0.625187i
$658$	−0.201052	−	0.0425047i	−0.00783781	−	0.00165701i
$659$	1.03436	+	10.5021i	0.0402931	+	0.409103i	0.994083	+	0.108627i	$0.0346454\pi$
$659$	1.03436	+	10.5021i	0.0402931	+	0.409103i	−0.953790	+	0.300476i	$0.902855\pi$
$660$	3.80488	−	2.97275i	0.148105	−	0.115714i
$661$	12.8392	−	24.0205i	0.499388	−	0.934290i	−0.498344	−	0.866980i	$-0.666058\pi$
$661$	12.8392	−	24.0205i	0.499388	−	0.934290i	0.997732	−	0.0673105i	$-0.0214418\pi$
$662$	−18.3952	−	22.9710i	−0.714950	−	0.892794i
$663$	3.26868	−	0.650180i	0.126945	−	0.0252509i
$664$	−0.869644	+	2.53472i	−0.0337487	+	0.0983663i
$665$	−0.0467460	+	0.235008i	−0.00181273	+	0.00911322i
$666$	−5.05696	+	15.9781i	−0.195953	+	0.619138i
$667$	1.81339	−	18.4116i	0.0702146	−	0.712901i
$668$	9.00953	−	5.71222i	0.348589	−	0.221013i
$669$	−4.79388	+	15.8033i	−0.185342	+	0.610991i
$670$	0.0498617	−	4.15682i	0.00192632	−	0.160592i
$671$	−10.4707	−	10.4707i	−0.404217	−	0.404217i
$672$	2.11634	+	0.337513i	0.0816396	+	0.0130198i
$673$	−16.5863	+	16.5863i	−0.639354	+	0.639354i	−0.950396	−	0.311042i	$-0.899322\pi$
$673$	−16.5863	+	16.5863i	−0.639354	+	0.639354i	0.311042	+	0.950396i	$0.399322\pi$
$674$	−18.1815	−	18.6229i	−0.700324	−	0.717329i
$675$	−3.40006	−	1.03140i	−0.130868	−	0.0396984i
$676$	−12.3560	−	8.69181i	−0.475230	−	0.334301i
$677$	−45.9429	−	4.52498i	−1.76573	−	0.173909i	−0.837629	−	0.546239i	$-0.816059\pi$
$677$	−45.9429	−	4.52498i	−1.76573	−	0.173909i	−0.928101	+	0.372330i	$0.878559\pi$
$678$	11.4457	−	5.94248i	0.439571	−	0.228219i
$679$	2.25278	+	0.448106i	0.0864539	+	0.0171967i
$680$	−5.06041	+	3.85685i	−0.194058	+	0.147904i
$681$	−0.915345	−	4.60175i	−0.0350761	−	0.176340i
$682$	30.0622	+	3.32539i	1.15114	+	0.127336i
$683$	−0.683563	−	0.365372i	−0.0261558	−	0.0139806i	0.458267	−	0.888815i	$-0.348470\pi$
$683$	−0.683563	−	0.365372i	−0.0261558	−	0.0139806i	−0.484423	+	0.874834i	$0.660970\pi$
$684$	2.00957	−	0.557323i	0.0768378	−	0.0213098i
$685$	4.48456	−	0.441690i	0.171346	−	0.0168761i
$686$	−6.28220	−	9.65057i	−0.239855	−	0.368461i
$687$	−0.0506461	−	0.122271i	−0.00193227	−	0.00466491i
$688$	−6.09111	+	10.1880i	−0.232221	+	0.388414i
$689$	−11.7456	+	28.3564i	−0.447473	+	1.08029i
$690$	−3.44768	+	0.642897i	−0.131251	+	0.0244747i
$691$	−25.2210	+	30.7319i	−0.959453	+	1.16910i	0.0260874	+	0.999660i	$0.491695\pi$
$691$	−25.2210	+	30.7319i	−0.959453	+	1.16910i	−0.985541	+	0.169438i	$0.945805\pi$
$692$	14.1639	−	16.4384i	0.538432	−	0.624892i
$693$	−1.71102	−	5.64047i	−0.0649962	−	0.214264i
$694$	−7.26931	+	2.11025i	−0.275939	+	0.0801038i
$695$	8.66571	+	5.79024i	0.328709	+	0.219636i
$696$	−8.27486	−	1.95788i	−0.313658	−	0.0742133i
$697$	−2.32981	−	3.48680i	−0.0882478	−	0.132072i
$698$	−46.4901	+	4.01648i	−1.75968	+	0.152026i
$699$	1.54636	−	1.26906i	0.0584886	−	0.0480004i
$700$	1.09144	+	0.483080i	0.0412527	+	0.0182587i
$701$	−12.8040	−	23.9546i	−0.483600	−	0.904751i	−0.998861	−	0.0477181i	$-0.984805\pi$
$701$	−12.8040	−	23.9546i	−0.483600	−	0.904751i	0.515261	−	0.857033i	$-0.327695\pi$
$702$	−4.61725	+	10.7795i	−0.174267	+	0.406846i
$703$			1.83212i			0.0690998i
$704$	25.7315	+	16.2344i	0.969793	+	0.611856i
$705$		−	0.154566i		−	0.00582128i
$706$	0.997676	+	0.427341i	0.0375480	+	0.0160832i
$707$	2.35647	+	4.40864i	0.0886241	+	0.165804i
$708$	1.90104	+	4.92013i	0.0714453	+	0.184910i
$709$	−31.9529	+	26.2231i	−1.20002	+	0.984828i	−0.200029	+	0.979790i	$0.564104\pi$
$709$	−31.9529	+	26.2231i	−1.20002	+	0.984828i	−0.999987	+	0.00503812i	$0.998396\pi$
$710$	1.70602	+	19.7470i	0.0640259	+	0.741091i
$711$	11.7191	+	17.5389i	0.439502	+	0.657761i
$712$	16.8942	−	23.4143i	0.633137	−	0.877488i
$713$	−18.2660	−	12.2050i	−0.684069	−	0.457080i
$714$	−0.336002	−	1.15745i	−0.0125746	−	0.0433165i
$715$	−2.57645	−	8.49343i	−0.0963539	−	0.317636i
$716$	−3.23230	−	43.4905i	−0.120797	−	1.62532i
$717$	−6.09152	+	7.42253i	−0.227492	+	0.277200i
$718$	−0.767894	−	4.11801i	−0.0286576	−	0.153683i
$719$	12.6418	−	30.5201i	0.471461	−	1.13821i	−0.492057	−	0.870563i	$-0.663755\pi$
$719$	12.6418	−	30.5201i	0.471461	−	1.13821i	0.963518	−	0.267645i	$-0.0862453\pi$
$720$	−0.521225	−	10.3750i	−0.0194249	−	0.386652i
$721$	2.47458	+	5.97417i	0.0921583	+	0.222490i
$722$	−22.3280	+	14.5348i	−0.830963	+	0.540929i
$723$	1.79543	−	0.176834i	0.0667726	−	0.00657653i
$724$	−23.1970	−	13.1239i	−0.862108	−	0.487747i
$725$	−4.17666	−	2.23247i	−0.155117	−	0.0829119i
$726$	−0.341869	+	3.09056i	−0.0126880	+	0.114701i
$727$	−3.52763	−	17.7346i	−0.130832	−	0.657739i	−0.989421	−	0.145074i	$-0.953658\pi$
$727$	−3.52763	−	17.7346i	−0.130832	−	0.657739i	0.858588	−	0.512666i	$-0.171342\pi$
$728$	1.98079	−	3.40515i	0.0734128	−	0.126203i
$729$	7.46307	+	1.48450i	0.276410	+	0.0549814i
$730$	−10.5073	−	20.2380i	−0.388893	−	0.749042i
$731$	6.64334	+	0.654312i	0.245713	+	0.0242006i
$732$	4.87019	−	0.847840i	0.180007	−	0.0313371i
$733$	8.96172	+	2.71851i	0.331009	+	0.100410i	0.451415	−	0.892314i	$-0.350920\pi$
$733$	8.96172	+	2.71851i	0.331009	+	0.100410i	−0.120406	+	0.992725i	$0.538420\pi$
$734$	21.8798	−	21.3611i	0.807599	−	0.788454i
$735$	2.98229	−	2.98229i	0.110003	−	0.110003i
$736$	−11.1539	−	19.0771i	−0.411140	−	0.703192i
$737$	7.90496	+	7.90496i	0.291183	+	0.291183i
$738$	6.84617	+	0.0821208i	0.252011	+	0.00302291i
$739$	3.95701	−	13.0445i	0.145561	−	0.479850i	−0.853595	−	0.520938i	$-0.825582\pi$
$739$	3.95701	−	13.0445i	0.145561	−	0.479850i	0.999156	+	0.0410878i	$0.0130823\pi$
$740$	8.90566	+	1.99465i	0.327379	+	0.0733246i
$741$	−0.0583039	+	0.591969i	−0.00214185	+	0.0217465i
$742$	10.5823	+	3.34923i	0.388488	+	0.122954i
$743$	−2.82582	+	14.2064i	−0.103669	+	0.521181i	0.893698	+	0.448669i	$0.148102\pi$
$743$	−2.82582	+	14.2064i	−0.103669	+	0.521181i	−0.997368	+	0.0725124i	$0.976898\pi$
$744$	−6.68222	+	7.56970i	−0.244982	+	0.277519i
$745$	2.03817	−	0.405417i	0.0746728	−	0.0148533i
$746$	−0.291446	+	0.233390i	−0.0106706	+	0.00854502i
$747$	−1.15988	+	2.16997i	−0.0424376	+	0.0793952i
$748$	2.08507	−	16.9828i	0.0762378	−	0.620954i
$749$	0.0633417	+	0.643119i	0.00231445	+	0.0234991i
$750$	−0.185693	+	0.878345i	−0.00678054	+	0.0320726i
$751$	−23.3358	+	9.66599i	−0.851534	+	0.352717i	−0.765391	−	0.643566i	$-0.777454\pi$
$751$	−23.3358	+	9.66599i	−0.851534	+	0.352717i	−0.0861432	+	0.996283i	$0.527454\pi$
$752$	0.916635	−	0.329124i	0.0334262	−	0.0120019i
$753$	−6.21855	−	2.57581i	−0.226617	−	0.0938677i
$754$	−8.83915	+	12.8913i	−0.321903	+	0.469472i
$755$	−17.0931	−	14.0279i	−0.622080	−	0.510528i
$756$	4.02752	+	1.32804i	0.146480	+	0.0483002i
$757$	−44.5024	+	13.4996i	−1.61747	+	0.490653i	−0.963911	−	0.266226i	$-0.914223\pi$
$757$	−44.5024	+	13.4996i	−1.61747	+	0.490653i	−0.653556	+	0.756879i	$0.726723\pi$
$758$	33.4714	+	18.4104i	1.21574	+	0.668695i
$759$	5.23975	−	7.84183i	0.190191	−	0.284640i
$760$	−0.396558	−	1.06413i	−0.0143847	−	0.0386002i
$761$	36.1025	−	24.1229i	1.30871	−	0.874454i	0.311587	−	0.950217i	$-0.399139\pi$
$761$	36.1025	−	24.1229i	1.30871	−	0.874454i	0.997126	+	0.0757632i	$0.0241393\pi$
$762$	−11.6639	+	13.8699i	−0.422540	+	0.502454i
$763$	−2.00689	−	2.44540i	−0.0726543	−	0.0885295i
$764$	4.12881	+	4.33182i	0.149375	+	0.156720i
$765$	−5.15224	+	2.75393i	−0.186280	+	0.0995685i
$766$	−33.3157	+	13.3339i	−1.20375	+	0.481775i
$767$	9.69565			0.350090
$768$	−9.37519	+	3.90772i	−0.338298	+	0.141008i
$769$	45.7074			1.64825			0.824126	−	0.566406i	$-0.191667\pi$
$769$	45.7074			1.64825			0.824126	+	0.566406i	$0.191667\pi$
$770$	−2.97994	+	1.19266i	−0.107390	+	0.0429806i
$771$	1.34179	−	0.717200i	0.0483233	−	0.0258293i
$772$	22.5884	+	23.6990i	0.812975	+	0.852947i
$773$	21.7367	+	26.4863i	0.781816	+	0.952645i	0.999728	−	0.0233231i	$-0.00742464\pi$
$773$	21.7367	+	26.4863i	0.781816	+	0.952645i	−0.217912	+	0.975968i	$0.569925\pi$
$774$	−7.01471	+	8.34139i	−0.252139	+	0.299825i
$775$	−4.67579	+	3.12427i	−0.167959	+	0.112227i
$776$	−10.2008	+	3.80140i	−0.366187	+	0.136462i
$777$	−0.960435	+	1.43739i	−0.0344554	+	0.0515662i
$778$	−6.09862	−	3.35444i	−0.218646	−	0.120263i
$779$	0.716248	−	0.217272i	0.0256623	−	0.00778456i
$780$	2.81400	+	0.927888i	0.100757	+	0.0332237i
$781$	−41.2024	−	33.8140i	−1.47434	−	1.20996i
$782$	−7.02799	+	10.2498i	−0.251320	+	0.366533i
$783$	−15.5459	−	6.43932i	−0.555565	−	0.230123i
$784$	24.0364	+	11.3358i	0.858445	+	0.404850i
$785$	−16.2981	+	6.75090i	−0.581704	+	0.240950i
$786$	−0.923374	+	4.36765i	−0.0329356	+	0.155789i
$787$	4.21242	+	42.7694i	0.150156	+	1.52456i	0.714859	+	0.699269i	$0.246491\pi$
$787$	4.21242	+	42.7694i	0.150156	+	1.52456i	−0.564702	+	0.825295i	$0.691009\pi$
$788$	−1.64643	+	13.4101i	−0.0586518	+	0.477716i
$789$	2.52374	−	4.72159i	0.0898476	−	0.168093i
$790$	8.96614	−	7.18009i	0.319001	−	0.255456i
$791$	−8.40819	+	1.67249i	−0.298961	+	0.0594670i
$792$	20.9429	+	18.4875i	0.744173	+	0.656925i
$793$	1.77276	−	8.91229i	0.0629527	−	0.316485i
$794$	−21.4579	−	6.79129i	−0.761513	−	0.241014i
$795$	−0.818318	+	8.30852i	−0.0290228	+	0.294673i
$796$	25.3325	+	5.67384i	0.897886	+	0.201104i
$797$	−5.08948	+	16.7778i	−0.180279	+	0.594299i	0.819496	+	0.573084i	$0.194253\pi$
$797$	−5.08948	+	16.7778i	−0.180279	+	0.594299i	−0.999775	+	0.0212145i	$0.993247\pi$
$798$	0.215098	+	0.00258014i	0.00761440	+	9.13359e-5i
$799$	−0.387298	−	0.387298i	−0.0137016	−	0.0137016i
$800$	−5.60433	+	0.769074i	−0.198143	+	0.0271909i
$801$	18.7458	−	18.7458i	0.662351	−	0.662351i
$802$	−9.83116	+	9.59810i	−0.347150	+	0.338921i
$803$	58.6814	+	17.8008i	2.07082	+	0.628177i
$804$	−3.67679	+	0.640085i	−0.129670	+	0.0225740i
$805$	2.32013	+	0.228513i	0.0817738	+	0.00805402i
$806$	8.55231	+	16.4725i	0.301242	+	0.580219i
$807$	−13.0860	−	2.60296i	−0.460647	−	0.0916285i
$808$	−20.4791	−	11.9128i	−0.720453	−	0.419090i
$809$	−2.68337	−	13.4902i	−0.0943422	−	0.474290i	−0.998855	−	0.0478435i	$-0.984765\pi$
$809$	−2.68337	−	13.4902i	−0.0943422	−	0.474290i	0.904513	−	0.426447i	$-0.140235\pi$
$810$	0.860708	−	7.78095i	0.0302422	−	0.273395i
$811$	−13.2148	−	7.06346i	−0.464034	−	0.248032i	0.222774	−	0.974870i	$-0.428489\pi$
$811$	−13.2148	−	7.06346i	−0.464034	−	0.248032i	−0.686808	+	0.726839i	$0.740989\pi$
$812$	4.91980	+	2.78343i	0.172651	+	0.0976792i
$813$	−5.97988	+	0.588967i	−0.209724	+	0.0206560i
$814$	−20.5683	+	13.3893i	−0.720919	+	0.469294i
$815$	−2.93706	−	7.09068i	−0.102881	−	0.248376i
$816$	4.23665	+	3.83132i	0.148312	+	0.134123i
$817$	−0.455953	+	1.10077i	−0.0159518	+	0.0385110i
$818$	−4.56743	−	24.4939i	−0.159697	−	0.856409i
$819$	2.29463	−	2.79602i	0.0801810	−	0.0977008i
$820$	−0.276338	−	3.71812i	−0.00965014	−	0.129842i
$821$	4.04386	+	13.3308i	0.141132	+	0.465248i	0.998801	−	0.0489529i	$-0.0155884\pi$
$821$	4.04386	+	13.3308i	0.141132	+	0.465248i	−0.857670	+	0.514201i	$0.828088\pi$
$822$	−1.12784	−	3.88514i	−0.0393379	−	0.135510i
$823$	−21.9581	−	14.6719i	−0.765410	−	0.511431i	0.110517	−	0.993874i	$-0.464749\pi$
$823$	−21.9581	−	14.6719i	−0.765410	−	0.511431i	−0.875927	+	0.482444i	$0.839749\pi$
$824$	−24.8530	−	17.9323i	−0.865796	−	0.624701i
$825$	−1.34128	−	2.00737i	−0.0466975	−	0.0698878i
$826$	−0.301801	−	3.49330i	−0.0105010	−	0.121547i
$827$	−15.9575	+	13.0960i	−0.554898	+	0.455393i	−0.869572	−	0.493807i	$-0.835605\pi$
$827$	−15.9575	+	13.0960i	−0.554898	+	0.455393i	0.314674	+	0.949200i	$0.398105\pi$
$828$	−7.31296	−	18.9269i	−0.254143	−	0.657754i
$829$	2.88704	+	5.40128i	0.100271	+	0.187594i	0.927055	−	0.374926i	$-0.122332\pi$
$829$	2.88704	+	5.40128i	0.100271	+	0.187594i	−0.826784	+	0.562520i	$0.809832\pi$
$830$	1.23165	+	0.527560i	0.0427511	+	0.0183119i
$831$		−	9.98073i		−	0.346228i
$832$	0.489243	+	18.6639i	0.0169614	+	0.647054i
$833$		−	14.9455i		−	0.517832i
$834$	3.68404	−	8.60080i	0.127568	−	0.297821i
$835$	−2.51437	−	4.70406i	−0.0870135	−	0.162791i
$836$	2.79260	+	1.23602i	0.0965842	+	0.0427487i
$837$	−15.4453	+	12.6756i	−0.533867	+	0.438133i
$838$	1.51242	−	0.130664i	0.0522456	−	0.00451371i
$839$	5.84617	+	8.74942i	0.201832	+	0.302063i	0.918554	−	0.395296i	$-0.129358\pi$
$839$	5.84617	+	8.74942i	0.201832	+	0.302063i	−0.716721	+	0.697360i	$0.754358\pi$
$840$	0.246721	−	1.04275i	0.00851269	−	0.0359783i
$841$	5.46409	+	3.65099i	0.188417	+	0.125896i
$842$	18.9756	−	5.50852i	0.653941	−	0.189836i
$843$	3.09746	+	10.2110i	0.106682	+	0.351684i
$844$	5.63832	−	6.54371i	0.194079	−	0.225244i
$845$	−4.79185	+	5.83889i	−0.164845	+	0.200864i
$846$	0.879094	−	0.163927i	0.0302239	−	0.00563592i
$847$	0.791001	−	1.90965i	0.0271791	−	0.0656162i
$848$	−51.0153	+	12.8388i	−1.75187	+	0.440886i
$849$	−0.0903627	−	0.218155i	−0.00310124	−	0.00748706i
$850$	1.73559	+	2.66618i	0.0595303	+	0.0914491i
$851$	17.7402	−	1.74725i	0.608125	−	0.0598951i
$852$	17.1469	−	4.75541i	0.587442	−	0.162918i
$853$	7.13628	+	3.81442i	0.244342	+	0.130603i	0.589023	−	0.808117i	$-0.299513\pi$
$853$	7.13628	+	3.81442i	0.244342	+	0.130603i	−0.344681	+	0.938720i	$0.612013\pi$
$854$	−3.26623	−	0.361302i	−0.111768	−	0.0123635i
$855$	−0.203423	−	1.02268i	−0.00695691	−	0.0349748i
$856$	−1.85656	−	2.43592i	−0.0634560	−	0.0832579i
$857$	29.1527	+	5.79883i	0.995836	+	0.198084i	0.665998	−	0.745953i	$-0.268006\pi$
$857$	29.1527	+	5.79883i	0.995836	+	0.198084i	0.329838	+	0.944037i	$0.393006\pi$
$858$	−7.07184	+	3.67161i	−0.241429	+	0.125347i
$859$	44.6577	+	4.39840i	1.52370	+	0.150071i	0.824914	−	0.565259i	$-0.191224\pi$
$859$	44.6577	+	4.39840i	1.52370	+	0.150071i	0.698787	+	0.715330i	$0.253724\pi$
$860$	4.85427	+	3.41473i	0.165529	+	0.116441i
$861$	0.675831	+	0.205011i	0.0230323	+	0.00698676i
$862$	31.0396	+	31.7933i	1.05721	+	1.08288i
$863$	11.3420	−	11.3420i	0.386086	−	0.386086i	−0.487203	−	0.873289i	$-0.661983\pi$
$863$	11.3420	−	11.3420i	0.386086	−	0.386086i	0.873289	+	0.487203i	$0.161983\pi$
$864$	−19.5487	+	4.67116i	−0.665062	+	0.158916i
$865$	−7.67167	−	7.67167i	−0.260845	−	0.260845i
$866$	0.289292	−	24.1174i	0.00983055	−	0.819544i
$867$	−2.20019	+	7.25304i	−0.0747222	+	0.246326i
$868$	5.66875	−	3.59410i	0.192410	−	0.121992i
$869$	−3.02776	+	30.7413i	−0.102710	+	1.04283i
$870$	−1.28290	+	4.05349i	−0.0434945	+	0.137426i
$871$	−1.33836	+	6.72841i	−0.0453487	+	0.227984i
$872$	14.1816	+	4.86561i	0.480250	+	0.164770i
$873$	−9.80335	+	1.95001i	−0.331793	+	0.0659977i
$874$	−1.38652	−	1.73142i	−0.0468998	−	0.0585661i
$875$	0.281323	−	0.526319i	0.00951047	−	0.0177928i
$876$	−16.1318	+	12.6038i	−0.545043	+	0.425842i
$877$	0.0493137	+	0.500691i	0.00166521	+	0.0169071i	0.995981	−	0.0895600i	$-0.0285461\pi$
$877$	0.0493137	+	0.500691i	0.00166521	+	0.0169071i	−0.994316	+	0.106467i	$0.966046\pi$
$878$	28.1004	+	5.94076i	0.948342	+	0.200491i
$879$	−9.83352	+	4.07318i	−0.331676	+	0.137385i
$880$	9.04844	−	12.2287i	0.305023	−	0.412231i
$881$	−22.0728	−	9.14283i	−0.743650	−	0.308030i	−0.0215022	−	0.999769i	$-0.506845\pi$
$881$	−22.0728	−	9.14283i	−0.743650	−	0.308030i	−0.722148	+	0.691739i	$0.756845\pi$
$882$	20.1247	+	13.7989i	0.677633	+	0.464632i
$883$	−22.0722	−	18.1142i	−0.742790	−	0.609592i	0.184981	−	0.982742i	$-0.440778\pi$
$883$	−22.0722	−	18.1142i	−0.742790	−	0.609592i	−0.927771	+	0.373150i	$0.878278\pi$
$884$	9.37610	−	4.72605i	0.315352	−	0.158954i
$885$	2.52375	−	0.765570i	0.0848348	−	0.0257344i
$886$	−3.55504	+	6.46333i	−0.119434	+	0.217140i
$887$	8.78945	−	13.1543i	0.295121	−	0.441679i	−0.654045	−	0.756455i	$-0.726929\pi$
$887$	8.78945	−	13.1543i	0.295121	−	0.441679i	0.949166	+	0.314776i	$0.101929\pi$
$888$	0.294759	−	8.18792i	0.00989146	−	0.274769i
$889$	10.0166	−	6.69290i	0.335947	−	0.224473i
$890$	−11.0489	−	9.29157i	−0.370359	−	0.311454i
$891$	13.3553	+	16.2735i	0.447420	+	0.545183i
$892$	−1.24802	+	52.0143i	−0.0417867	+	1.74157i
$893$	0.0862160	−	0.0460834i	0.00288511	−	0.00154212i
$894$	−0.693222	−	1.73206i	−0.0231848	−	0.0579287i
$895$	−21.8052			−0.728868
$896$	6.70928	−	0.757230i	0.224141	−	0.0252973i
$897$	5.78756			0.193241
$898$	−20.7684	−	51.8913i	−0.693052	−	1.73163i
$899$	−23.4876	+	12.5544i	−0.783354	+	0.418711i
$900$	−5.19253	−	0.124588i	−0.173084	−	0.00415294i
$901$	18.7683	+	22.8693i	0.625264	+	0.761886i
$902$	7.67360	+	6.45313i	0.255503	+	0.214866i
$903$	−0.934764	+	0.624589i	−0.0311070	+	0.0207850i
$904$	29.7452	−	27.6780i	0.989312	−	0.920558i
$905$	−7.40356	+	11.0802i	−0.246103	+	0.368319i
$906$	−9.56727	+	17.3940i	−0.317851	+	0.577877i
$907$	25.4244	−	7.71241i	0.844203	−	0.256086i	0.161583	−	0.986859i	$-0.448340\pi$
$907$	25.4244	−	7.71241i	0.844203	−	0.256086i	0.682621	+	0.730773i	$0.260840\pi$
$908$	−6.65349	−	13.2000i	−0.220804	−	0.438057i
$909$	−16.8157	−	13.8003i	−0.557742	−	0.457727i
$910$	−1.62448	−	1.11386i	−0.0538512	−	0.0369241i
$911$	−16.2706	−	6.73949i	−0.539068	−	0.223289i	0.0965016	−	0.995333i	$-0.469235\pi$
$911$	−16.2706	−	6.73949i	−0.539068	−	0.223289i	−0.635570	+	0.772044i	$0.719235\pi$
$912$	−0.873887	+	0.525106i	−0.0289373	+	0.0173880i
$913$	−3.32892	+	1.37888i	−0.110171	+	0.0456343i
$914$	−7.69522	−	1.62686i	−0.254535	−	0.0538118i
$915$	−0.242271	−	2.45982i	−0.00800922	−	0.0813190i
$916$	−0.256708	−	0.328565i	−0.00848186	−	0.0108561i
$917$	1.39891	−	2.61717i	0.0461960	−	0.0864266i
$918$	7.06547	+	8.82301i	0.233195	+	0.291203i
$919$	2.88593	−	0.574047i	0.0951980	−	0.0189361i	−0.147261	−	0.989098i	$-0.547046\pi$
$919$	2.88593	−	0.574047i	0.0951980	−	0.0189361i	0.242459	+	0.970162i	$0.422046\pi$
$920$	−9.92568	+	4.85465i	−0.327240	+	0.160053i
$921$	−1.80358	+	9.06719i	−0.0594299	+	0.298774i
$922$	7.38087	−	23.3208i	0.243076	−	0.768028i
$923$	3.20600	−	32.5511i	0.105527	−	1.07143i
$924$	1.54299	+	2.43366i	0.0507606	+	0.0800616i
$925$	1.32461	−	4.36666i	0.0435530	−	0.143575i
$926$	0.510441	−	42.5540i	0.0167741	−	1.39841i
$927$	−19.8977	−	19.8977i	−0.653526	−	0.653526i
$928$	−26.7705	+	1.02318i	−0.878786	+	0.0335877i
$929$	15.5939	−	15.5939i	0.511618	−	0.511618i	−0.403404	−	0.915022i	$-0.632173\pi$
$929$	15.5939	−	15.5939i	0.511618	−	0.511618i	0.915022	+	0.403404i	$0.132173\pi$
$930$	3.52681	+	3.61244i	0.115649	+	0.118457i
$931$	2.55267	+	0.774342i	0.0836602	+	0.0253780i
$932$	3.62615	−	5.15481i	0.118778	−	0.168851i
$933$	0.417663	+	0.0411362i	0.0136737	+	0.00134674i
$934$	−4.69582	+	2.43801i	−0.153652	+	0.0797741i
$935$	−8.39079	−	1.66903i	−0.274408	−	0.0545832i
$936$	−2.29295	+	16.9887i	−0.0749475	+	0.555293i
$937$	−0.623823	−	3.13617i	−0.0203794	−	0.102454i	0.969257	−	0.246051i	$-0.0791331\pi$
$937$	−0.623823	−	3.13617i	−0.0203794	−	0.102454i	−0.989636	+	0.143597i	$0.954133\pi$
$938$	2.46587	+	0.272768i	0.0805136	+	0.00890620i
$939$	−16.4224	−	8.77797i	−0.535926	−	0.286458i
$940$	−0.130140	−	0.469254i	−0.00424471	−	0.0153054i
$941$	−38.2760	+	3.76985i	−1.24776	+	0.122894i	−0.700246	−	0.713902i	$-0.746926\pi$
$941$	−38.2760	+	3.76985i	−1.24776	+	0.122894i	−0.547515	+	0.836796i	$0.684426\pi$
$942$	8.64017	+	13.2728i	0.281512	+	0.432452i
$943$	−2.78688	−	6.72812i	−0.0907533	−	0.219098i
$944$	9.91407	+	13.3366i	0.322675	+	0.434070i
$945$	0.811447	−	1.95901i	0.0263964	−	0.0637265i
$946$	−15.6899	+	2.92574i	−0.510124	+	0.0951239i
$947$	−30.2693	+	36.8833i	−0.983621	+	1.19855i	−0.00353080	+	0.999994i	$0.501124\pi$
$947$	−30.2693	+	36.8833i	−0.983621	+	1.19855i	−0.980090	+	0.198552i	$0.936376\pi$
$948$	−7.81232	−	6.73140i	−0.253732	−	0.218626i
$949$	10.9236	+	36.0101i	0.354593	+	1.16894i
$950$	−0.545300	+	0.158298i	−0.0176919	+	0.00513586i
$951$	−1.31799	−	0.880655i	−0.0427388	−	0.0285572i
$952$	−1.99463	−	3.23105i	−0.0646462	−	0.104719i
$953$	−15.3540	−	22.9790i	−0.497366	−	0.744361i	0.494838	−	0.868985i	$-0.335228\pi$
$953$	−15.3540	−	22.9790i	−0.497366	−	0.744361i	−0.992204	+	0.124624i	$0.960228\pi$
$954$	−48.1227	+	4.15752i	−1.55803	+	0.134605i
$955$	2.31296	−	1.89820i	0.0748456	−	0.0614242i
$956$	−12.2440	+	27.6633i	−0.395998	+	0.894696i
$957$	−5.38974	−	10.0835i	−0.174225	−	0.325953i
$958$	−20.8226	+	48.6126i	−0.672747	+	1.57060i
$959$			2.68927i			0.0868412i
$960$	1.60105	+	4.81952i	0.0516737	+	0.155549i
$961$			0.624083i			0.0201317i
$962$	−13.8440	−	5.92990i	−0.446349	−	0.191188i
$963$	−1.32565	−	2.48012i	−0.0427185	−	0.0799207i
$964$	5.30193	−	2.04856i	0.170764	−	0.0659796i
$965$	12.6540	−	10.3849i	0.407347	−	0.334301i
$966$	−0.180152	−	2.08523i	−0.00579628	−	0.0670911i
$967$	15.4094	+	23.0618i	0.495532	+	0.741617i	0.991972	−	0.126454i	$-0.0403597\pi$
$967$	15.4094	+	23.0618i	0.495532	+	0.741617i	−0.496440	+	0.868071i	$0.665360\pi$
$968$	1.56427	+	9.67063i	0.0502776	+	0.310826i
$969$	0.476730	+	0.318541i	0.0153148	+	0.0102330i
$970$	1.51744	+	5.22724i	0.0487221	+	0.167836i
$971$	16.9441	+	55.8573i	0.543763	+	1.79255i	0.607186	+	0.794560i	$0.292298\pi$
$971$	16.9441	+	55.8573i	0.543763	+	1.79255i	−0.0634229	+	0.997987i	$0.520202\pi$
$972$	−28.2684	+	2.10096i	−0.906708	+	0.0673884i
$973$	−3.94581	+	4.80798i	−0.126497	+	0.154137i
$974$	−2.29723	−	12.3194i	−0.0736079	−	0.394739i
$975$	0.566951	−	1.36874i	0.0181570	−	0.0438348i
$976$	14.0718	−	6.67457i	0.450427	−	0.213648i
$977$	−18.1580	−	43.8372i	−0.580925	−	1.40248i	−0.891975	−	0.452084i	$-0.850681\pi$
$977$	−18.1580	−	43.8372i	−0.580925	−	1.40248i	0.311050	−	0.950394i	$-0.399319\pi$
$978$	−5.77450	+	3.75900i	−0.184648	+	0.120200i
$979$	38.6354	−	3.80526i	1.23479	−	0.121617i
$980$	6.54307	−	11.5651i	0.209011	−	0.369433i
$981$	12.1409	+	6.48943i	0.387628	+	0.207192i
$982$	3.93544	−	35.5771i	0.125585	−	1.13531i
$983$	−3.31858	−	16.6836i	−0.105846	−	0.532125i	−0.996931	−	0.0782878i	$-0.975055\pi$
$983$	−3.31858	−	16.6836i	−0.105846	−	0.532125i	0.891085	−	0.453837i	$-0.149945\pi$
$984$	−3.23593	+	0.855774i	−0.103158	+	0.0272811i
$985$	6.62561	+	1.31792i	0.211109	+	0.0419923i
$986$	6.94231	+	13.3715i	0.221088	+	0.425835i
$987$	0.0917986	+	0.00904138i	0.00292198	+	0.000287790i
$988$	0.321415	+	1.84628i	0.0102256	+	0.0587380i
$989$	11.0934	+	3.36515i	0.352750	+	0.107006i
$990$	9.99444	−	9.75751i	0.317644	−	0.310114i
$991$	23.3349	−	23.3349i	0.741257	−	0.741257i	−0.231563	−	0.972820i	$-0.574384\pi$
$991$	23.3349	−	23.3349i	0.741257	−	0.741257i	0.972820	+	0.231563i	$0.0743839\pi$
$992$	−13.9134	+	28.6075i	−0.441750	+	0.908289i
$993$	9.34085	+	9.34085i	0.296423	+	0.296423i
$994$	−11.8278	−	0.141876i	−0.375154	−	0.00450003i
$995$	3.76791	−	12.4211i	0.119451	−	0.393777i
$996$	0.262903	−	1.17381i	0.00833041	−	0.0371935i
$997$	0.0725655	−	0.736770i	0.00229817	−	0.0233337i	−0.993967	−	0.109677i	$-0.965018\pi$
$997$	0.0725655	−	0.736770i	0.00229817	−	0.0233337i	0.996265	+	0.0863435i	$0.0275183\pi$
$998$	48.6389	+	15.3939i	1.53964	+	0.487285i
$999$	3.16302	−	15.9016i	0.100073	−	0.503103i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	640.2.bm.a.101.8	✓	1024
128.109	even	32	inner	640.2.bm.a.621.8	yes	1024

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
640.2.bm.a.101.8	✓	1024	1.1	even	1	trivial
640.2.bm.a.621.8	yes	1024	128.109	even	32	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 640 = 2^{7} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	640.bm (of order \(32\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.31296 + 0.525486i) q^{2} +(0.559854 - 0.299248i) q^{3} +(1.44773 - 1.37988i) q^{4} +(-0.634393 - 0.773010i) q^{5} +(-0.577815 + 0.687096i) q^{6} +(0.496210 - 0.331557i) q^{7} +(-1.17570 + 2.57249i) q^{8} +(-1.44282 + 2.15934i) q^{9} +(1.23914 + 0.681567i) q^{10} +(-3.63933 + 1.10398i) q^{11} +(0.397589 - 1.20576i) q^{12} +(-1.80404 - 1.48054i) q^{13} +(-0.477276 + 0.696073i) q^{14} +(-0.586489 - 0.242932i) q^{15} +(0.191840 - 3.99540i) q^{16} +(-2.07829 + 0.860858i) q^{17} +(0.759668 - 3.59331i) q^{18} +(-0.0393542 - 0.399570i) q^{19} +(-1.98509 - 0.243721i) q^{20} +(0.178587 - 0.334113i) q^{21} +(4.19818 - 3.36190i) q^{22} +(-3.83145 + 0.762123i) q^{23} +(0.111593 + 1.79205i) q^{24} +(-0.195090 + 0.980785i) q^{25} +(3.14664 + 0.995890i) q^{26} +(-0.348260 + 3.53594i) q^{27} +(0.260868 - 1.16472i) q^{28} +(-1.37475 + 4.53194i) q^{29} +(0.897695 + 0.0107680i) q^{30} +(3.97644 + 3.97644i) q^{31} +(1.84765 + 5.34661i) q^{32} +(-1.70713 + 1.70713i) q^{33} +(2.27635 - 2.22239i) q^{34} +(-0.571089 - 0.173238i) q^{35} +(0.890819 + 5.11707i) q^{36} +(-4.54118 - 0.447267i) q^{37} +(0.261639 + 0.503940i) q^{38} +(-1.45305 - 0.289029i) q^{39} +(2.73442 - 0.723144i) q^{40} +(0.363685 + 1.82837i) q^{41} +(-0.0589062 + 0.532523i) q^{42} +(-2.61710 - 1.39887i) q^{43} +(-3.74541 + 6.62012i) q^{44} +(2.58451 - 0.254552i) q^{45} +(4.63006 - 3.01401i) q^{46} +(0.0931769 + 0.224949i) q^{47} +(-1.08821 - 2.29425i) q^{48} +(-2.54249 + 6.13811i) q^{49} +(-0.259243 - 1.39025i) q^{50} +(-0.905931 + 1.10388i) q^{51} +(-4.65474 + 0.345949i) q^{52} +(-3.81768 - 12.5852i) q^{53} +(-1.40084 - 4.82556i) q^{54} +(3.16216 + 2.11289i) q^{55} +(0.269534 + 1.66631i) q^{56} +(-0.141603 - 0.211924i) q^{57} +(-0.576480 - 6.67267i) q^{58} +(-3.21145 + 2.63557i) q^{59} +(-1.18430 + 0.457588i) q^{60} +(1.83544 + 3.43387i) q^{61} +(-7.31046 - 3.13134i) q^{62} +1.54986i q^{63} +(-5.23545 - 6.04897i) q^{64} +2.33379i q^{65} +(1.34432 - 3.13847i) q^{66} +(-1.38568 - 2.59243i) q^{67} +(-1.82092 + 4.11410i) q^{68} +(-1.91699 + 1.57323i) q^{69} +(0.840852 - 0.0726447i) q^{70} +(7.78645 + 11.6532i) q^{71} +(-3.85856 - 6.25039i) q^{72} +(-13.4068 - 8.95813i) q^{73} +(6.19742 - 1.79908i) q^{74} +(0.184276 + 0.607477i) q^{75} +(-0.608335 - 0.524165i) q^{76} +(-1.43984 + 1.75445i) q^{77} +(2.05968 - 0.384072i) q^{78} +(3.10829 - 7.50408i) q^{79} +(-3.21019 + 2.38636i) q^{80} +(-2.11835 - 5.11416i) q^{81} +(-1.43828 - 2.20946i) q^{82} +(0.942875 - 0.0928651i) q^{83} +(-0.202492 - 0.730136i) q^{84} +(1.98391 + 1.06042i) q^{85} +(4.17124 + 0.461411i) q^{86} +(0.586516 + 2.94861i) q^{87} +(1.43879 - 10.6601i) q^{88} +(-10.0120 - 1.99150i) q^{89} +(-3.25959 + 1.69234i) q^{90} +(-1.38607 - 0.136516i) q^{91} +(-4.49526 + 6.39030i) q^{92} +(3.41616 + 1.03628i) q^{93} +(-0.240545 - 0.246386i) q^{94} +(-0.283906 + 0.283906i) q^{95} +(2.63437 + 2.44041i) q^{96} +(2.72152 + 2.72152i) q^{97} +(0.112696 - 9.39514i) q^{98} +(2.86705 - 9.45140i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 1024 q - 192 q^{52} - 128 q^{54} - 32 q^{56} - 288 q^{58} - 192 q^{62} - 192 q^{64} - 192 q^{66} - 192 q^{68} - 288 q^{72} - 32 q^{74} - 128 q^{76} - 192 q^{78}+O(q^{100}) \) 1024 * q - 192 * q^52 - 128 * q^54 - 32 * q^56 - 288 * q^58 - 192 * q^62 - 192 * q^64 - 192 * q^66 - 192 * q^68 - 288 * q^72 - 32 * q^74 - 128 * q^76 - 192 * q^78

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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