LMFDB - Embedded newform 990.2.o.a.329.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [990,2,Mod(329,990)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(990, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([5, 3, 3])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("990.329"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 990 = 2 \cdot 3^{2} \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	990.o (of order $6$, degree $2$, 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:	$7.90518980011$
Analytic rank:	$0$
Dimension:	$144$
Relative dimension:	$72$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			329.3
Character	$\chi$	$=$	990.329
Dual form			990.2.o.a.659.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.866025 + 0.500000i) q^{2} +(-1.67359 - 0.446217i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-0.339852 - 2.21009i) q^{5} +(1.67248 - 0.450358i) q^{6} +(1.06306 + 1.84128i) q^{7} +1.00000i q^{8} +(2.60178 + 1.49356i) q^{9} +(1.39937 + 1.74407i) q^{10} +(2.70959 - 1.91262i) q^{11} +(-1.22323 + 1.22626i) q^{12} +(-2.63748 + 4.56825i) q^{13} +(-1.84128 - 1.06306i) q^{14} +(-0.417409 + 3.85042i) q^{15} +(-0.500000 - 0.866025i) q^{16} -0.850639i q^{17} +(-2.99999 + 0.00742535i) q^{18} -2.62562i q^{19} +(-2.08392 - 0.810725i) q^{20} +(-0.957517 - 3.55589i) q^{21} +(-1.39026 + 3.01117i) q^{22} +(-1.13469 + 1.96534i) q^{23} +(0.446217 - 1.67359i) q^{24} +(-4.76900 + 1.50221i) q^{25} -5.27496i q^{26} +(-3.68785 - 3.66057i) q^{27} +2.12612 q^{28} +(4.51629 + 7.82244i) q^{29} +(-1.56373 - 3.54327i) q^{30} +(-3.51686 + 6.09138i) q^{31} +(0.866025 + 0.500000i) q^{32} +(-5.38818 + 1.99188i) q^{33} +(0.425319 + 0.736675i) q^{34} +(3.70811 - 2.97523i) q^{35} +(2.59436 - 1.50643i) q^{36} -4.77143i q^{37} +(1.31281 + 2.27385i) q^{38} +(6.45248 - 6.46847i) q^{39} +(2.21009 - 0.339852i) q^{40} +(4.60079 - 7.96881i) q^{41} +(2.60718 + 2.60074i) q^{42} +(4.38888 + 7.60176i) q^{43} +(-0.301586 - 3.30288i) q^{44} +(2.41669 - 6.25776i) q^{45} -2.26938i q^{46} +(-0.240394 - 0.416375i) q^{47} +(0.450358 + 1.67248i) q^{48} +(1.23980 - 2.14739i) q^{49} +(3.37897 - 3.68545i) q^{50} +(-0.379569 + 1.42362i) q^{51} +(2.63748 + 4.56825i) q^{52} +9.77771 q^{53} +(5.02406 + 1.32622i) q^{54} +(-5.14793 - 5.33843i) q^{55} +(-1.84128 + 1.06306i) q^{56} +(-1.17160 + 4.39420i) q^{57} +(-7.82244 - 4.51629i) q^{58} +(8.28833 + 4.78527i) q^{59} +(3.12586 + 2.28670i) q^{60} +(5.31642 - 3.06944i) q^{61} -7.03372i q^{62} +(0.0157872 + 6.37835i) q^{63} -1.00000 q^{64} +(10.9926 + 4.27654i) q^{65} +(3.67036 - 4.41910i) q^{66} +(2.27943 + 1.31603i) q^{67} +(-0.736675 - 0.425319i) q^{68} +(2.77597 - 2.78285i) q^{69} +(-1.72370 + 4.43067i) q^{70} +12.5151i q^{71} +(-1.49356 + 2.60178i) q^{72} +6.05548 q^{73} +(2.38572 + 4.13218i) q^{74} +(8.65164 - 0.386061i) q^{75} +(-2.27385 - 1.31281i) q^{76} +(6.40213 + 2.95587i) q^{77} +(-2.35378 + 8.82810i) q^{78} +(-11.3092 + 6.52938i) q^{79} +(-1.74407 + 1.39937i) q^{80} +(4.53853 + 7.77186i) q^{81} +9.20159i q^{82} +(7.73026 - 4.46307i) q^{83} +(-3.55825 - 0.948713i) q^{84} +(-1.87999 + 0.289091i) q^{85} +(-7.60176 - 4.38888i) q^{86} +(-4.06789 - 15.1068i) q^{87} +(1.91262 + 2.70959i) q^{88} -8.26439i q^{89} +(1.03596 + 6.62773i) q^{90} -11.2152 q^{91} +(1.13469 + 1.96534i) q^{92} +(8.60384 - 8.62516i) q^{93} +(0.416375 + 0.240394i) q^{94} +(-5.80286 + 0.892321i) q^{95} +(-1.22626 - 1.22323i) q^{96} +(10.8929 - 6.28902i) q^{97} +2.47959i q^{98} +(9.90638 - 0.929280i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q + 72 q^{4} - 6 q^{5} + 12 q^{9} + 12 q^{11} - 2 q^{15} - 72 q^{16} - 6 q^{20} + 6 q^{25} + 12 q^{31} + 12 q^{45} - 72 q^{49} + 12 q^{55} + 60 q^{59} - 4 q^{60} - 144 q^{64} - 36 q^{66} - 8 q^{69}+ \cdots - 40 q^{99}+O(q^{100}) $ 144 * q + 72 * q^4 - 6 * q^5 + 12 * q^9 + 12 * q^11 - 2 * q^15 - 72 * q^16 - 6 * q^20 + 6 * q^25 + 12 * q^31 + 12 * q^45 - 72 * q^49 + 12 * q^55 + 60 * q^59 - 4 * q^60 - 144 * q^64 - 36 * q^66 - 8 * q^69 + 12 * q^70 + 92 * q^75 - 100 * q^81 + 72 * q^86 - 48 * q^91 - 40 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/990\mathbb{Z}\right)^\times$.

$n$	$397$	$541$	$551$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$3$	−1.67359	−	0.446217i	−0.966245	−	0.257623i
$3$	−1.67359	−	0.446217i	−0.966245	−	0.257623i
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$	−0.339852	−	2.21009i	−0.151986	−	0.988383i
$5$	−0.339852	−	2.21009i	−0.151986	−	0.988383i
$6$	1.67248	−	0.450358i	0.682786	−	0.183858i
$7$	1.06306	+	1.84128i	0.401800	+	0.695938i	0.993943	−	0.109895i	$-0.0350514\pi$
$7$	1.06306	+	1.84128i	0.401800	+	0.695938i	−0.592143	+	0.805833i	$0.701718\pi$
$8$			1.00000i			0.353553i
$9$	2.60178	+	1.49356i	0.867260	+	0.497855i
$10$	1.39937	+	1.74407i	0.442518	+	0.551523i
$11$	2.70959	−	1.91262i	0.816972	−	0.576678i
$11$	2.70959	−	1.91262i	0.816972	−	0.576678i
$12$	−1.22323	+	1.22626i	−0.353116	+	0.353991i
$13$	−2.63748	+	4.56825i	−0.731505	+	1.26700i	0.224734	+	0.974420i	$0.427849\pi$
$13$	−2.63748	+	4.56825i	−0.731505	+	1.26700i	−0.956240	+	0.292584i	$0.905485\pi$
$14$	−1.84128	−	1.06306i	−0.492102	−	0.284115i
$15$	−0.417409	+	3.85042i	−0.107775	+	0.994175i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$		−	0.850639i		−	0.206310i	−0.994665	−	0.103155i	$-0.967106\pi$
$17$		−	0.850639i		−	0.206310i	0.994665	−	0.103155i	$-0.0328938\pi$
$18$	−2.99999	+	0.00742535i	−0.707105	+	0.00175017i
$19$		−	2.62562i		−	0.602358i	−0.953568	−	0.301179i	$-0.902620\pi$
$19$		−	2.62562i		−	0.602358i	0.953568	−	0.301179i	$-0.0973803\pi$
$20$	−2.08392	−	0.810725i	−0.465979	−	0.181284i
$21$	−0.957517	−	3.55589i	−0.208947	−	0.775960i
$22$	−1.39026	+	3.01117i	−0.296405	+	0.641985i
$23$	−1.13469	+	1.96534i	−0.236600	+	0.409803i	−0.959736	−	0.280902i	$-0.909366\pi$
$23$	−1.13469	+	1.96534i	−0.236600	+	0.409803i	0.723137	+	0.690705i	$0.242700\pi$
$24$	0.446217	−	1.67359i	0.0910836	−	0.341619i
$25$	−4.76900	+	1.50221i	−0.953800	+	0.300441i
$26$		−	5.27496i		−	1.03450i
$27$	−3.68785	−	3.66057i	−0.709727	−	0.704477i
$28$	2.12612			0.401800
$29$	4.51629	+	7.82244i	0.838653	+	1.45259i	0.891021	+	0.453962i	$0.149990\pi$
$29$	4.51629	+	7.82244i	0.838653	+	1.45259i	−0.0523679	+	0.998628i	$0.516677\pi$
$30$	−1.56373	−	3.54327i	−0.285496	−	0.646910i
$31$	−3.51686	+	6.09138i	−0.631646	+	1.09404i	0.355569	+	0.934650i	$0.384287\pi$
$31$	−3.51686	+	6.09138i	−0.631646	+	1.09404i	−0.987215	+	0.159393i	$0.949046\pi$
$32$	0.866025	+	0.500000i	0.153093	+	0.0883883i
$33$	−5.38818	+	1.99188i	−0.937961	+	0.346741i
$34$	0.425319	+	0.736675i	0.0729417	+	0.126339i
$35$	3.70811	−	2.97523i	0.626785	−	0.502905i
$36$	2.59436	−	1.50643i	0.432393	−	0.251071i
$37$		−	4.77143i		−	0.784418i	−0.919876	−	0.392209i	$-0.871711\pi$
$37$		−	4.77143i		−	0.784418i	0.919876	−	0.392209i	$-0.128289\pi$
$38$	1.31281	+	2.27385i	0.212966	+	0.368868i
$39$	6.45248	−	6.46847i	1.03322	−	1.03578i
$40$	2.21009	−	0.339852i	0.349446	−	0.0537352i
$41$	4.60079	−	7.96881i	0.718523	−	1.24452i	−0.243061	−	0.970011i	$-0.578152\pi$
$41$	4.60079	−	7.96881i	0.718523	−	1.24452i	0.961585	−	0.274508i	$-0.0885150\pi$
$42$	2.60718	+	2.60074i	0.402297	+	0.401302i
$43$	4.38888	+	7.60176i	0.669297	+	1.15926i	0.978101	+	0.208131i	$0.0667380\pi$
$43$	4.38888	+	7.60176i	0.669297	+	1.15926i	−0.308804	+	0.951126i	$0.599929\pi$
$44$	−0.301586	−	3.30288i	−0.0454658	−	0.497929i
$45$	2.41669	−	6.25776i	0.360260	−	0.932852i
$46$		−	2.26938i		−	0.334602i
$47$	−0.240394	−	0.416375i	−0.0350651	−	0.0607345i	0.847960	−	0.530060i	$-0.177831\pi$
$47$	−0.240394	−	0.416375i	−0.0350651	−	0.0607345i	−0.883025	+	0.469325i	$0.844497\pi$
$48$	0.450358	+	1.67248i	0.0650036	+	0.241401i
$49$	1.23980	−	2.14739i	0.177114	−	0.306770i
$50$	3.37897	−	3.68545i	0.477859	−	0.521201i
$51$	−0.379569	+	1.42362i	−0.0531503	+	0.199346i
$52$	2.63748	+	4.56825i	0.365753	+	0.633502i
$53$	9.77771			1.34307			0.671536	−	0.740972i	$-0.265635\pi$
$53$	9.77771			1.34307			0.671536	+	0.740972i	$0.265635\pi$
$54$	5.02406	+	1.32622i	0.683687	+	0.180476i
$55$	−5.14793	−	5.33843i	−0.694147	−	0.719834i
$56$	−1.84128	+	1.06306i	−0.246051	+	0.142058i
$57$	−1.17160	+	4.39420i	−0.155182	+	0.582026i
$58$	−7.82244	−	4.51629i	−1.02714	−	0.593017i
$59$	8.28833	+	4.78527i	1.07905	+	0.622989i	0.930640	−	0.365937i	$-0.119251\pi$
$59$	8.28833	+	4.78527i	1.07905	+	0.622989i	0.148409	+	0.988926i	$0.452585\pi$
$60$	3.12586	+	2.28670i	0.403547	+	0.295212i
$61$	5.31642	−	3.06944i	0.680698	−	0.393001i	−0.119420	−	0.992844i	$-0.538103\pi$
$61$	5.31642	−	3.06944i	0.680698	−	0.393001i	0.800118	+	0.599843i	$0.204770\pi$
$62$		−	7.03372i		−	0.893283i
$63$	0.0157872	+	6.37835i	0.00198900	+	0.803597i
$64$	−1.00000			−0.125000
$65$	10.9926	+	4.27654i	1.36346	+	0.530440i
$66$	3.67036	−	4.41910i	0.451790	−	0.543954i
$67$	2.27943	+	1.31603i	0.278477	+	0.160779i	0.632734	−	0.774369i	$-0.281933\pi$
$67$	2.27943	+	1.31603i	0.278477	+	0.160779i	−0.354257	+	0.935148i	$0.615266\pi$
$68$	−0.736675	−	0.425319i	−0.0893349	−	0.0515776i
$69$	2.77597	−	2.78285i	0.334188	−	0.335016i
$70$	−1.72370	+	4.43067i	−0.206022	+	0.529567i
$71$			12.5151i			1.48527i	0.669699	+	0.742633i	$0.266423\pi$
$71$			12.5151i			1.48527i	−0.669699	+	0.742633i	$0.733577\pi$
$72$	−1.49356	+	2.60178i	−0.176018	+	0.306623i
$73$	6.05548			0.708740			0.354370	−	0.935105i	$-0.384695\pi$
$73$	6.05548			0.708740			0.354370	+	0.935105i	$0.384695\pi$
$74$	2.38572	+	4.13218i	0.277334	+	0.480356i
$75$	8.65164	−	0.386061i	0.999006	−	0.0445785i
$76$	−2.27385	−	1.31281i	−0.260829	−	0.150590i
$77$	6.40213	+	2.95587i	0.729591	+	0.336853i
$78$	−2.35378	+	8.82810i	−0.266513	+	0.999585i
$79$	−11.3092	+	6.52938i	−1.27239	+	0.734613i	−0.975437	−	0.220281i	$-0.929303\pi$
$79$	−11.3092	+	6.52938i	−1.27239	+	0.734613i	−0.296950	+	0.954893i	$0.595969\pi$
$80$	−1.74407	+	1.39937i	−0.194993	+	0.156454i
$81$	4.53853	+	7.77186i	0.504281	+	0.863540i
$82$			9.20159i			1.01615i
$83$	7.73026	−	4.46307i	0.848506	−	0.489885i	−0.0116406	−	0.999932i	$-0.503705\pi$
$83$	7.73026	−	4.46307i	0.848506	−	0.489885i	0.860146	+	0.510047i	$0.170372\pi$
$84$	−3.55825	−	0.948713i	−0.388237	−	0.103513i
$85$	−1.87999	+	0.289091i	−0.203913	+	0.0313563i
$86$	−7.60176	−	4.38888i	−0.819718	−	0.473265i
$87$	−4.06789	−	15.1068i	−0.436124	−	1.61961i
$88$	1.91262	+	2.70959i	0.203886	+	0.288843i
$89$		−	8.26439i		−	0.876024i	−0.898969	−	0.438012i	$-0.855683\pi$
$89$		−	8.26439i		−	0.876024i	0.898969	−	0.438012i	$-0.144317\pi$
$90$	1.03596	+	6.62773i	0.109200	+	0.698624i
$91$	−11.2152			−1.17567
$92$	1.13469	+	1.96534i	0.118300	+	0.204901i
$93$	8.60384	−	8.62516i	0.892177	−	0.894388i
$94$	0.416375	+	0.240394i	0.0429458	+	0.0247948i
$95$	−5.80286	+	0.892321i	−0.595361	+	0.0915502i
$96$	−1.22626	−	1.22323i	−0.125155	−	0.124845i
$97$	10.8929	−	6.28902i	1.10601	−	0.638554i	0.168215	−	0.985750i	$-0.446200\pi$
$97$	10.8929	−	6.28902i	1.10601	−	0.638554i	0.937792	+	0.347197i	$0.112866\pi$
$98$			2.47959i			0.250477i
$99$	9.90638	−	0.929280i	0.995629	−	0.0933962i
$100$	−1.08355	+	4.88118i	−0.108355	+	0.488118i
$101$	−1.48058	−	2.56444i	−0.147323	−	0.255171i	0.782914	−	0.622130i	$-0.213732\pi$
$101$	−1.48058	−	2.56444i	−0.147323	−	0.255171i	−0.930237	+	0.366958i	$0.880399\pi$
$102$	−0.383092	−	1.42267i	−0.0379317	−	0.140866i
$103$	1.15713	+	0.668067i	0.114015	+	0.0658266i	0.555923	−	0.831234i	$-0.312365\pi$
$103$	1.15713	+	0.668067i	0.114015	+	0.0658266i	−0.441908	+	0.897060i	$0.645698\pi$
$104$	−4.56825	−	2.63748i	−0.447954	−	0.258626i
$105$	−7.53343	+	3.32468i	−0.735188	+	0.324455i
$106$	−8.46774	+	4.88885i	−0.822460	+	0.474847i
$107$		−	5.60586i		−	0.541939i	−0.962588	−	0.270970i	$-0.912656\pi$
$107$		−	5.60586i		−	0.541939i	0.962588	−	0.270970i	$-0.0873443\pi$
$108$	−5.01407	+	1.36349i	−0.482479	+	0.131202i
$109$			15.5011i			1.48474i	0.669991	+	0.742370i	$0.266298\pi$
$109$			15.5011i			1.48474i	−0.669991	+	0.742370i	$0.733702\pi$
$110$	7.12745	+	2.04925i	0.679576	+	0.195388i
$111$	−2.12909	+	7.98540i	−0.202085	+	0.757941i
$112$	1.06306	−	1.84128i	0.100450	−	0.173984i
$113$	−0.672865	+	1.16544i	−0.0632978	+	0.109635i	−0.895938	−	0.444180i	$-0.853495\pi$
$113$	−0.672865	+	1.16544i	−0.0632978	+	0.109635i	0.832640	+	0.553815i	$0.186828\pi$
$114$	−1.18247	−	4.39129i	−0.110748	−	0.411282i
$115$	4.72922	+	1.83985i	0.441002	+	0.171567i
$116$	9.03257			0.838653
$117$	−13.6851	+	7.94634i	−1.26519	+	0.734639i
$118$	−9.57054			−0.881040
$119$	1.56626	−	0.904282i	0.143579	−	0.0828954i
$120$	−3.85042	−	0.417409i	−0.351494	−	0.0381041i
$121$	3.68374	−	10.3648i	0.334886	−	0.942259i
$122$	−3.06944	+	5.31642i	−0.277894	+	0.481326i
$123$	−11.2556	+	11.2835i	−1.01489	+	1.01740i
$124$	3.51686	+	6.09138i	0.315823	+	0.547022i
$125$	4.94076	+	10.0294i	0.441915	+	0.897057i
$126$	−3.20285	−	5.51592i	−0.285333	−	0.491398i
$127$	9.88138			0.876831			0.438415	−	0.898772i	$-0.355540\pi$
$127$	9.88138			0.876831			0.438415	+	0.898772i	$0.355540\pi$
$128$	0.866025	−	0.500000i	0.0765466	−	0.0441942i
$129$	−3.95313	−	14.6806i	−0.348054	−	1.29255i
$130$	−11.6581	+	1.79270i	−1.02249	+	0.157230i
$131$	1.52260	−	2.63722i	0.133030	−	0.230415i	−0.791813	−	0.610764i	$-0.790863\pi$
$131$	1.52260	−	2.63722i	0.133030	−	0.230415i	0.924843	+	0.380348i	$0.124196\pi$
$132$	−0.969073	+	5.66223i	−0.0843470	+	0.492834i
$133$	4.83450	−	2.79120i	0.419204	−	0.242028i
$134$	−2.63206			−0.227376
$135$	−6.83687	+	9.39453i	−0.588424	+	0.808553i
$136$	0.850639			0.0729417
$137$	−7.14317	−	12.3723i	−0.610282	−	1.05704i	−0.991193	−	0.132428i	$-0.957723\pi$
$137$	−7.14317	−	12.3723i	−0.610282	−	1.05704i	0.380910	−	0.924612i	$-0.375611\pi$
$138$	−1.01264	+	3.79801i	−0.0862014	+	0.323308i
$139$	12.1121	+	6.99294i	1.02734	+	0.593133i	0.916221	−	0.400674i	$-0.131224\pi$
$139$	12.1121	+	6.99294i	1.02734	+	0.593133i	0.111116	+	0.993807i	$0.464557\pi$
$140$	−0.722567	−	4.69893i	−0.0610680	−	0.397132i
$141$	0.216527	+	0.804108i	0.0182349	+	0.0677181i
$142$	−6.25754	−	10.8384i	−0.525121	−	0.909536i
$143$	1.59085	+	17.4226i	0.133034	+	1.45695i
$144$	−0.00742535	−	2.99999i	−0.000618780	−	0.249999i
$145$	15.7534	−	12.6399i	1.30825	−	1.04968i
$146$	−5.24420	+	3.02774i	−0.434013	+	0.250577i
$147$	−3.03311	+	3.04063i	−0.250167	+	0.250787i
$148$	−4.13218	−	2.38572i	−0.339663	−	0.196105i
$149$	0.223413	−	0.386962i	0.0183027	−	0.0317011i	−0.856729	−	0.515767i	$-0.827507\pi$
$149$	0.223413	−	0.386962i	0.0183027	−	0.0317011i	0.875032	+	0.484066i	$0.160840\pi$
$150$	−7.29951	+	4.66016i	−0.596003	+	0.380501i
$151$	−13.3077	+	7.68321i	−1.08297	+	0.625251i	−0.931695	−	0.363242i	$-0.881670\pi$
$151$	−13.3077	+	7.68321i	−1.08297	+	0.625251i	−0.151271	+	0.988492i	$0.548337\pi$
$152$	2.62562			0.212966
$153$	1.27048	−	2.21318i	0.102713	−	0.178925i
$154$	−7.02234	+	0.641209i	−0.565877	+	0.0516701i
$155$	14.6577	+	5.70241i	1.17734	+	0.458029i
$156$	−2.37562	−	8.82225i	−0.190202	−	0.706345i
$157$	8.53958	+	4.93033i	0.681532	+	0.393483i	0.800432	−	0.599423i	$-0.204603\pi$
$157$	8.53958	+	4.93033i	0.681532	+	0.393483i	−0.118900	+	0.992906i	$0.537937\pi$
$158$	6.52938	−	11.3092i	0.519449	−	0.899713i
$159$	−16.3638	−	4.36298i	−1.29774	−	0.346007i
$160$	0.810725	−	2.08392i	0.0640935	−	0.164748i
$161$	−4.82499			−0.380263
$162$	−7.81641	−	4.46136i	−0.614115	−	0.350518i
$163$			1.88442i			0.147599i	0.997273	+	0.0737997i	$0.0235125\pi$
$163$			1.88442i			0.147599i	−0.997273	+	0.0737997i	$0.976487\pi$
$164$	−4.60079	−	7.96881i	−0.359262	−	0.622259i
$165$	6.23340	+	11.2314i	0.485270	+	0.874364i
$166$	−4.46307	+	7.73026i	−0.346401	+	0.599984i
$167$	−9.94407	−	5.74121i	−0.769495	−	0.444268i	0.0631993	−	0.998001i	$-0.479870\pi$
$167$	−9.94407	−	5.74121i	−0.769495	−	0.444268i	−0.832695	+	0.553733i	$0.813203\pi$
$168$	3.55589	−	0.957517i	0.274343	−	0.0738740i
$169$	−7.41260	−	12.8390i	−0.570200	−	0.987616i
$170$	1.48357	−	1.19035i	0.113785	−	0.0912960i
$171$	3.92153	−	6.83129i	0.299887	−	0.522402i
$172$	8.77775			0.669297
$173$	−2.69805	+	1.55772i	−0.205129	+	0.118431i	−0.599046	−	0.800715i	$-0.704453\pi$
$173$	−2.69805	+	1.55772i	−0.205129	+	0.118431i	0.393917	+	0.919146i	$0.371120\pi$
$174$	11.0763	+	11.0489i	0.839690	+	0.837615i
$175$	−7.83572	−	7.18412i	−0.592325	−	0.543068i
$176$	−3.01117	−	1.39026i	−0.226976	−	0.104795i
$177$	−11.7360	−	11.7070i	−0.882129	−	0.879949i
$178$	4.13220	+	7.15717i	0.309721	+	0.536453i
$179$		−	4.95206i		−	0.370134i	−0.982726	−	0.185067i	$-0.940750\pi$
$179$		−	4.95206i		−	0.370134i	0.982726	−	0.185067i	$-0.0592503\pi$
$180$	−4.21103	−	5.22180i	−0.313872	−	0.389210i
$181$	23.5835			1.75295			0.876474	−	0.481450i	$-0.159890\pi$
$181$	23.5835			1.75295			0.876474	+	0.481450i	$0.159890\pi$
$182$	9.71267	−	5.60761i	0.719951	−	0.415664i
$183$	−10.2671	+	2.76469i	−0.758968	+	0.204372i
$184$	−1.96534	−	1.13469i	−0.144887	−	0.0836506i
$185$	−10.5453	+	1.62158i	−0.775306	+	0.119221i
$186$	−3.13856	+	11.7715i	−0.230131	+	0.863130i
$187$	−1.62695	−	2.30488i	−0.118974	−	0.168550i
$188$	−0.480789			−0.0350651
$189$	2.81971	−	10.6818i	0.205104	−	0.776984i
$190$	4.57926	−	3.67420i	0.332215	−	0.266555i
$191$	16.2865	−	9.40302i	1.17845	−	0.680379i	0.222795	−	0.974865i	$-0.428482\pi$
$191$	16.2865	−	9.40302i	1.17845	−	0.680379i	0.955656	+	0.294486i	$0.0951486\pi$
$192$	1.67359	+	0.446217i	0.120781	+	0.0322029i
$193$	−6.10832	+	10.5799i	−0.439686	+	0.761559i	−0.997665	−	0.0682963i	$-0.978244\pi$
$193$	−6.10832	+	10.5799i	−0.439686	+	0.761559i	0.557979	+	0.829855i	$0.311577\pi$
$194$	−6.28902	+	10.8929i	−0.451526	+	0.782065i
$195$	−16.4888	−	12.0622i	−1.18079	−	0.863795i
$196$	−1.23980	−	2.14739i	−0.0885569	−	0.153385i
$197$		−	24.7685i		−	1.76468i	−0.470610	−	0.882341i	$-0.655966\pi$
$197$		−	24.7685i		−	1.76468i	0.470610	−	0.882341i	$-0.344034\pi$
$198$	−8.11454	+	5.75797i	−0.576675	+	0.409201i
$199$	−2.38733			−0.169233			−0.0846167	−	0.996414i	$-0.526967\pi$
$199$	−2.38733			−0.169233			−0.0846167	+	0.996414i	$0.526967\pi$
$200$	−1.50221	−	4.76900i	−0.106222	−	0.337219i
$201$	−3.22759	−	3.21961i	−0.227657	−	0.227094i
$202$	2.56444	+	1.48058i	0.180433	+	0.104173i
$203$	−9.60219	+	16.6315i	−0.673941	+	1.16730i
$204$	1.04310	+	1.04053i	0.0730319	+	0.0728513i
$205$	−19.1754	−	7.45996i	−1.33927	−	0.521026i
$206$	−1.33613			−0.0930928
$207$	−5.88759	+	3.41866i	−0.409216	+	0.237613i
$208$	5.27496			0.365753
$209$	−5.02182	−	7.11435i	−0.347367	−	0.492110i
$210$	4.86181	−	6.64597i	0.335497	−	0.458616i
$211$	−2.61561	−	1.51012i	−0.180066	−	0.103961i	0.407258	−	0.913313i	$-0.366485\pi$
$211$	−2.61561	−	1.51012i	−0.180066	−	0.103961i	−0.587324	+	0.809352i	$0.699818\pi$
$212$	4.88885	−	8.46774i	0.335768	−	0.581567i
$213$	5.58444	−	20.9451i	0.382639	−	1.43513i
$214$	2.80293	+	4.85482i	0.191604	+	0.331869i
$215$	15.3090	−	12.2833i	1.04407	−	0.837713i
$216$	3.66057	−	3.68785i	0.249070	−	0.250926i
$217$	−14.9546			−1.01518
$218$	−7.75057	−	13.4244i	−0.524935	−	0.909213i
$219$	−10.1344	−	2.70206i	−0.684817	−	0.182588i
$220$	−7.19718	+	1.78902i	−0.485234	+	0.120616i
$221$	3.88593	+	2.24354i	0.261396	+	0.150917i
$222$	−2.14885	−	7.98011i	−0.144221	−	0.535590i
$223$	−11.1889	+	6.45990i	−0.749263	+	0.432587i	−0.825428	−	0.564508i	$-0.809066\pi$
$223$	−11.1889	+	6.45990i	−0.749263	+	0.432587i	0.0761646	+	0.997095i	$0.475733\pi$
$224$			2.12612i			0.142058i
$225$	−14.6515	−	3.21440i	−0.976769	−	0.214294i
$226$		−	1.34573i		−	0.0895167i
$227$	7.64871	−	4.41599i	0.507663	−	0.293099i	−0.224210	−	0.974541i	$-0.571980\pi$
$227$	7.64871	−	4.41599i	0.507663	−	0.293099i	0.731872	+	0.681442i	$0.238647\pi$
$228$	3.21969	+	3.21173i	0.213229	+	0.212702i
$229$	6.62005	−	11.4663i	0.437465	−	0.757712i	−0.560028	−	0.828473i	$-0.689210\pi$
$229$	6.62005	−	11.4663i	0.437465	−	0.757712i	0.997493	+	0.0707620i	$0.0225431\pi$
$230$	−5.01554	+	0.771254i	−0.330715	+	0.0508550i
$231$	−9.39556	−	7.80364i	−0.618183	−	0.513442i
$232$	−7.82244	+	4.51629i	−0.513568	+	0.296509i
$233$		−	8.87184i		−	0.581214i	−0.956843	−	0.290607i	$-0.906143\pi$
$233$		−	8.87184i		−	0.581214i	0.956843	−	0.290607i	$-0.0938572\pi$
$234$	7.87849	−	13.7243i	0.515033	−	0.897185i
$235$	−0.838528	+	0.672799i	−0.0546996	+	0.0438886i
$236$	8.28833	−	4.78527i	0.539524	−	0.311495i
$237$	21.8405	−	5.88111i	1.41869	−	0.382019i
$238$	−0.904282	+	1.56626i	−0.0586159	+	0.101526i
$239$	−7.75619	+	13.4341i	−0.501706	+	0.868980i	0.498292	+	0.867009i	$0.333961\pi$
$239$	−7.75619	+	13.4341i	−0.501706	+	0.868980i	−0.999998	+	0.00197116i	$0.999373\pi$
$240$	3.54327	−	1.56373i	0.228717	−	0.100938i
$241$	−19.0482	+	10.9975i	−1.22700	+	0.708410i	−0.966402	−	0.257036i	$-0.917254\pi$
$241$	−19.0482	+	10.9975i	−1.22700	+	0.708410i	−0.260601	+	0.965447i	$0.583921\pi$
$242$	1.99221	+	10.8181i	0.128064	+	0.695413i
$243$	−4.12768	−	15.0320i	−0.264791	−	0.964306i
$244$		−	6.13888i		−	0.393001i
$245$	−5.16728	−	2.01027i	−0.330125	−	0.128431i
$246$	4.10590	−	15.3997i	0.261783	−	0.981846i
$247$	11.9945	+	6.92502i	0.763191	+	0.440628i
$248$	−6.09138	−	3.51686i	−0.386803	−	0.223321i
$249$	−14.9287	+	4.01995i	−0.946071	+	0.254754i
$250$	−9.29353	−	6.21533i	−0.587774	−	0.393092i
$251$			18.6317i			1.17602i	0.808854	+	0.588010i	$0.200088\pi$
$251$			18.6317i			1.17602i	−0.808854	+	0.588010i	$0.799912\pi$
$252$	5.53171	+	3.17551i	0.348465	+	0.200038i
$253$	0.684414	+	7.49551i	0.0430288	+	0.471239i
$254$	−8.55753	+	4.94069i	−0.536947	+	0.310007i
$255$	3.27532	+	0.355064i	0.205109	+	0.0222350i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−4.81076	+	8.33248i	−0.300087	+	0.519766i	−0.976155	−	0.217073i	$-0.930349\pi$
$257$	−4.81076	+	8.33248i	−0.300087	+	0.519766i	0.676068	+	0.736839i	$0.263682\pi$
$258$	10.7638	+	10.7372i	0.670125	+	0.668468i
$259$	8.78553	−	5.07233i	0.545906	−	0.315179i
$260$	9.19989	−	7.38160i	0.570553	−	0.457787i
$261$	0.0670700	+	27.0976i	0.00415153	+	1.67730i
$262$			3.04520i			0.188133i
$263$	−10.2301	+	5.90634i	−0.630814	+	0.364201i	−0.781067	−	0.624447i	$-0.785324\pi$
$263$	−10.2301	+	5.90634i	−0.630814	+	0.364201i	0.150253	+	0.988648i	$0.451991\pi$
$264$	−1.99188	−	5.38818i	−0.122591	−	0.331619i
$265$	−3.32297	−	21.6096i	−0.204128	−	1.32747i
$266$	−2.79120	+	4.83450i	−0.171139	+	0.296422i
$267$	−3.68771	+	13.8312i	−0.225684	+	0.846454i
$268$	2.27943	−	1.31603i	0.139239	−	0.0803894i
$269$		−	3.72171i		−	0.226917i	−0.993543	−	0.113458i	$-0.963807\pi$
$269$		−	3.72171i		−	0.226917i	0.993543	−	0.113458i	$-0.0361928\pi$
$270$	1.22363	−	11.5543i	0.0744679	−	0.703175i
$271$			3.69288i			0.224326i	0.993690	+	0.112163i	$0.0357779\pi$
$271$			3.69288i			0.224326i	−0.993690	+	0.112163i	$0.964222\pi$
$272$	−0.736675	+	0.425319i	−0.0446675	+	0.0257888i
$273$	18.7696	+	5.00442i	1.13599	+	0.302881i
$274$	12.3723	+	7.14317i	0.747440	+	0.431535i
$275$	−10.0489	+	13.1917i	−0.605970	+	0.795487i
$276$	−1.02203	−	3.79549i	−0.0615193	−	0.228462i
$277$	12.2738	+	21.2589i	0.737462	+	1.27732i	0.953635	+	0.300967i	$0.0973094\pi$
$277$	12.2738	+	21.2589i	0.737462	+	1.27732i	−0.216172	+	0.976355i	$0.569357\pi$
$278$	−13.9859			−0.838817
$279$	−18.2480	+	10.5958i	−1.09248	+	0.634352i
$280$	2.97523	+	3.70811i	0.177804	+	0.221602i
$281$	11.7870	+	20.4157i	0.703154	+	1.21790i	0.967354	+	0.253430i	$0.0815588\pi$
$281$	11.7870	+	20.4157i	0.703154	+	1.21790i	−0.264200	+	0.964468i	$0.585108\pi$
$282$	−0.589572	−	0.588114i	−0.0351085	−	0.0350217i
$283$	−10.3652	+	17.9530i	−0.616144	+	1.06719i	0.374038	+	0.927413i	$0.377973\pi$
$283$	−10.3652	+	17.9530i	−0.616144	+	1.06719i	−0.990183	+	0.139780i	$0.955360\pi$
$284$	10.8384	+	6.25754i	0.643139	+	0.371317i
$285$	10.1098	+	1.09596i	0.598850	+	0.0649189i
$286$	−10.0890	−	14.2930i	−0.596576	−	0.845161i
$287$	19.5637			1.15481
$288$	1.50643	+	2.59436i	0.0887670	+	0.152874i
$289$	16.2764			0.957436
$290$	−7.32293	+	18.8232i	−0.430017	+	1.10533i
$291$	−21.0365	+	5.66462i	−1.23318	+	0.332066i
$292$	3.02774	−	5.24420i	0.177185	−	0.306893i
$293$	−14.5464	−	8.39838i	−0.849811	−	0.490639i	0.0107762	−	0.999942i	$-0.496570\pi$
$293$	−14.5464	−	8.39838i	−0.849811	−	0.490639i	−0.860587	+	0.509303i	$0.829903\pi$
$294$	1.10644	−	4.14981i	0.0645287	−	0.242022i
$295$	7.75908	−	19.9442i	0.451751	−	1.16120i
$296$	4.77143			0.277334
$297$	−16.9938	−	2.86517i	−0.986083	−	0.166254i
$298$			0.446825i			0.0258839i
$299$	−5.98545	−	10.3671i	−0.346148	−	0.599546i
$300$	3.99148	−	7.68557i	0.230448	−	0.443727i
$301$	−9.33130	+	16.1623i	−0.537847	+	0.931578i
$302$	7.68321	−	13.3077i	0.442119	−	0.765773i
$303$	1.33358	+	4.95247i	0.0766123	+	0.284512i
$304$	−2.27385	+	1.31281i	−0.130414	+	0.0752948i
$305$	−8.59053	−	10.7066i	−0.491892	−	0.613059i
$306$	0.00631629	+	2.55191i	0.000361079	+	0.145883i
$307$	5.35259			0.305488			0.152744	−	0.988266i	$-0.451189\pi$
$307$	5.35259			0.305488			0.152744	+	0.988266i	$0.451189\pi$
$308$	5.76092	−	4.06648i	0.328259	−	0.231709i
$309$	−1.63845	−	1.63440i	−0.0932080	−	0.0929776i
$310$	−15.5451	+	2.39042i	−0.882905	+	0.135767i
$311$	−10.1324	−	5.84994i	−0.574555	−	0.331720i	0.184411	−	0.982849i	$-0.440962\pi$
$311$	−10.1324	−	5.84994i	−0.574555	−	0.331720i	−0.758967	+	0.651129i	$0.774295\pi$
$312$	6.46847	+	6.45248i	0.366205	+	0.365300i
$313$	−22.0355	+	12.7222i	−1.24552	+	0.719101i	−0.970213	−	0.242255i	$-0.922113\pi$
$313$	−22.0355	+	12.7222i	−1.24552	+	0.719101i	−0.275308	+	0.961356i	$0.588780\pi$
$314$	−9.86065			−0.556469
$315$	14.0914	−	2.20258i	0.793959	−	0.124102i
$316$			13.0588i			0.734613i
$317$	−6.34572	−	10.9911i	−0.356411	−	0.617322i	0.630947	−	0.775826i	$-0.282666\pi$
$317$	−6.34572	−	10.9911i	−0.356411	−	0.617322i	−0.987358	+	0.158504i	$0.949333\pi$
$318$	16.3530	−	4.40347i	0.917030	−	0.246934i
$319$	27.1987	+	12.5576i	1.52283	+	0.703092i
$320$	0.339852	+	2.21009i	0.0189983	+	0.123548i
$321$	−2.50143	+	9.38190i	−0.139616	+	0.523646i
$322$	4.17857	−	2.41250i	0.232862	−	0.134443i
$323$	−2.23345			−0.124273
$324$	8.99989	−	0.0445520i	0.499994	−	0.00247511i
$325$	5.71570	−	25.7480i	0.317050	−	1.42824i
$326$	−0.942211	−	1.63196i	−0.0521843	−	0.0903858i
$327$	6.91687	−	25.9425i	0.382504	−	1.43462i
$328$	7.96881	+	4.60079i	0.440004	+	0.254036i
$329$	0.511108	−	0.885265i	0.0281783	−	0.0488063i
$330$	−11.0140	−	6.60999i	−0.606300	−	0.363868i
$331$	−3.21813	−	5.57396i	−0.176884	−	0.306372i	0.763928	−	0.645302i	$-0.223268\pi$
$331$	−3.21813	−	5.57396i	−0.176884	−	0.306372i	−0.940812	+	0.338930i	$0.889935\pi$
$332$		−	8.92613i		−	0.489885i
$333$	7.12644	−	12.4142i	0.390527	−	0.680295i
$334$	11.4824			0.628290
$335$	2.13388	−	5.48501i	0.116586	−	0.299678i
$336$	−2.60074	+	2.60718i	−0.141882	+	0.142233i
$337$	8.23011	−	14.2550i	0.448323	−	0.776517i	−0.549955	−	0.835195i	$-0.685355\pi$
$337$	8.23011	−	14.2550i	0.448323	−	0.776517i	0.998277	+	0.0586773i	$0.0186883\pi$
$338$	12.8390	+	7.41260i	0.698350	+	0.403192i
$339$	1.64614	−	1.65021i	0.0894058	−	0.0896274i
$340$	−0.689634	+	1.77266i	−0.0374007	+	0.0961362i
$341$	2.12127	+	23.2316i	0.114873	+	1.25806i
$342$	0.0194962	+	7.87684i	0.00105423	+	0.425930i
$343$	20.1548			1.08826
$344$	−7.60176	+	4.38888i	−0.409859	+	0.236632i
$345$	−7.09378	−	5.18940i	−0.381916	−	0.279388i
$346$	1.55772	−	2.69805i	0.0837436	−	0.145048i
$347$	19.6808	+	11.3627i	1.05652	+	0.609982i	0.924467	−	0.381261i	$-0.124510\pi$
$347$	19.6808	+	11.3627i	1.05652	+	0.609982i	0.132052	+	0.991243i	$0.457843\pi$
$348$	−15.1168	−	4.03049i	−0.810345	−	0.216057i
$349$	−22.0720	+	12.7433i	−1.18149	+	0.682131i	−0.956358	−	0.292198i	$-0.905613\pi$
$349$	−22.0720	+	12.7433i	−1.18149	+	0.682131i	−0.225128	+	0.974329i	$0.572280\pi$
$350$	10.3780	+	2.30377i	0.554727	+	0.123142i
$351$	26.4490	−	7.19235i	1.41174	−	0.383899i
$352$	3.30288	−	0.301586i	0.176044	−	0.0160746i
$353$	−12.6341	−	21.8829i	−0.672445	−	1.16471i	−0.977209	−	0.212281i	$-0.931911\pi$
$353$	−12.6341	−	21.8829i	−0.672445	−	1.16471i	0.304763	−	0.952428i	$-0.401423\pi$
$354$	16.0171	+	4.27054i	0.851301	+	0.226976i
$355$	27.6595	−	4.25327i	1.46801	−	0.225740i
$356$	−7.15717	−	4.13220i	−0.379329	−	0.219006i
$357$	−3.02478	+	0.814501i	−0.160088	+	0.0431080i
$358$	2.47603	+	4.28861i	0.130862	+	0.226660i
$359$	−36.7591			−1.94007			−0.970036	−	0.242959i	$-0.921882\pi$
$359$	−36.7591			−1.94007			−0.970036	+	0.242959i	$0.921882\pi$
$360$	6.25776	+	2.41669i	0.329813	+	0.127371i
$361$	12.1061			0.637164
$362$	−20.4239	+	11.7917i	−1.07346	+	0.619760i
$363$	−10.7900	+	15.7027i	−0.566330	+	0.824179i
$364$	−5.60761	+	9.71267i	−0.293919	+	0.509082i
$365$	−2.05796	−	13.3832i	−0.107719	−	0.700506i
$366$	7.50925	−	7.52786i	0.392515	−	0.393487i
$367$	5.22004	−	3.01379i	0.272484	−	0.157319i	−0.357532	−	0.933901i	$-0.616382\pi$
$367$	5.22004	−	3.01379i	0.272484	−	0.157319i	0.630016	+	0.776582i	$0.283048\pi$
$368$	2.26938			0.118300
$369$	23.8722	−	13.8615i	1.24274	−	0.721601i
$370$	8.32171	−	6.67698i	0.432625	−	0.347119i
$371$	10.3943	+	18.0035i	0.539646	+	0.934694i
$372$	−3.16769	−	11.7637i	−0.164237	−	0.609921i
$373$	−13.5241	+	23.4245i	−0.700253	+	1.21287i	0.268125	+	0.963384i	$0.413596\pi$
$373$	−13.5241	+	23.4245i	−0.700253	+	1.21287i	−0.968378	+	0.249489i	$0.919737\pi$
$374$	2.56142	+	1.18261i	0.132448	+	0.0611513i
$375$	−3.79350	−	18.9897i	−0.195896	−	0.980625i
$376$	0.416375	−	0.240394i	0.0214729	−	0.0123974i
$377$	−47.6464			−2.45392
$378$	2.89895	+	10.6605i	0.149106	+	0.548319i
$379$	−19.7847			−1.01627			−0.508136	−	0.861277i	$-0.669665\pi$
$379$	−19.7847			−1.01627			−0.508136	+	0.861277i	$0.669665\pi$
$380$	−2.12866	+	5.47158i	−0.109198	+	0.280686i
$381$	−16.5373	−	4.40924i	−0.847234	−	0.225892i
$382$	−9.40302	+	16.2865i	−0.481100	+	0.833290i
$383$	−11.0614	+	19.1589i	−0.565211	+	0.978975i	0.431819	+	0.901960i	$0.357872\pi$
$383$	−11.0614	+	19.1589i	−0.565211	+	0.978975i	−0.997030	+	0.0770142i	$0.975461\pi$
$384$	−1.67248	+	0.450358i	−0.0853482	+	0.0229822i
$385$	4.35696	−	15.1539i	0.222051	−	0.772312i
$386$		−	12.2166i		−	0.621810i
$387$	0.0651779	+	26.3332i	0.00331318	+	1.33859i
$388$		−	12.5780i		−	0.638554i
$389$	0.930800	−	0.537397i	0.0471934	−	0.0272471i	−0.476218	−	0.879327i	$-0.657993\pi$
$389$	0.930800	−	0.537397i	0.0471934	−	0.0272471i	0.523411	+	0.852080i	$0.324659\pi$
$390$	20.3108	+	2.20182i	1.02848	+	0.111493i
$391$	1.67180	+	0.965213i	0.0845465	+	0.0488129i
$392$	2.14739	+	1.23980i	0.108460	+	0.0626192i
$393$	−3.72498	+	3.73421i	−0.187900	+	0.188366i
$394$	12.3843	+	21.4502i	0.623910	+	1.08064i
$395$	18.2740	+	22.7754i	0.919463	+	1.14595i
$396$	4.14841	−	9.04382i	0.208466	−	0.454469i
$397$		−	12.7817i		−	0.641495i	−0.947165	−	0.320748i	$-0.896066\pi$
$397$		−	12.7817i		−	0.641495i	0.947165	−	0.320748i	$-0.103934\pi$
$398$	2.06749	−	1.19367i	0.103634	−	0.0598331i
$399$	−9.33642	+	2.51408i	−0.467406	+	0.125861i
$400$	3.68545	+	3.37897i	0.184272	+	0.168949i
$401$	−5.33315	−	3.07909i	−0.266325	−	0.153763i	0.360892	−	0.932608i	$-0.382472\pi$
$401$	−5.33315	−	3.07909i	−0.266325	−	0.153763i	−0.627216	+	0.778845i	$0.715806\pi$
$402$	4.40498	+	1.17447i	0.219701	+	0.0585773i
$403$	−18.5513	−	32.1318i	−0.924105	−	1.60060i
$404$	−2.96116			−0.147323
$405$	15.6341	−	12.6718i	0.776864	−	0.629669i
$406$		−	19.2044i		−	0.953097i
$407$	−9.12595	−	12.9286i	−0.452357	−	0.640848i
$408$	−1.42362	−	0.379569i	−0.0704796	−	0.0187915i
$409$	23.0316	+	13.2973i	1.13884	+	0.657510i	0.946143	−	0.323749i	$-0.104943\pi$
$409$	23.0316	+	13.2973i	1.13884	+	0.657510i	0.192697	+	0.981258i	$0.438277\pi$
$410$	20.3363	−	3.12717i	1.00434	−	0.154440i
$411$	6.43397	+	23.8936i	0.317364	+	1.17858i
$412$	1.15713	−	0.668067i	0.0570075	−	0.0329133i
$413$			20.3482i			1.00127i
$414$	3.38947	−	5.90444i	0.166583	−	0.290187i
$415$	−12.4909	−	15.5678i	−0.613155	−	0.764193i
$416$	−4.56825	+	2.63748i	−0.223977	+	0.129313i
$417$	−17.1503	−	17.1079i	−0.839854	−	0.837778i
$418$	7.90620	+	3.65030i	0.386705	+	0.178542i
$419$	−0.137055	−	0.0791288i	−0.00669558	−	0.00386570i	0.496648	−	0.867952i	$-0.334564\pi$
$419$	−0.137055	−	0.0791288i	−0.00669558	−	0.00386570i	−0.503344	+	0.864086i	$0.667897\pi$
$420$	−0.887464	+	8.18648i	−0.0433038	+	0.399459i
$421$	−7.78571	−	13.4852i	−0.379452	−	0.657230i	0.611530	−	0.791221i	$-0.290554\pi$
$421$	−7.78571	−	13.4852i	−0.379452	−	0.657230i	−0.990983	+	0.133990i	$0.957221\pi$
$422$	3.02025			0.147023
$423$	−0.00357003	−	1.44236i	−0.000173581	−	0.0701300i
$424$			9.77771i			0.474847i
$425$	1.27783	+	4.05670i	0.0619841	+	0.196779i
$426$	5.63626	+	20.9312i	0.273078	+	1.01412i
$427$	11.3034	+	6.52601i	0.547009	+	0.315816i
$428$	−4.85482	−	2.80293i	−0.234667	−	0.135485i
$429$	5.11182	−	29.8681i	0.246801	−	1.44204i
$430$	−7.11634	+	18.2921i	−0.343181	+	0.882125i
$431$	21.2474			1.02345			0.511726	−	0.859148i	$-0.329006\pi$
$431$	21.2474			1.02345			0.511726	+	0.859148i	$0.329006\pi$
$432$	−1.32622	+	5.02406i	−0.0638078	+	0.241720i
$433$		−	7.46083i		−	0.358544i	−0.983800	−	0.179272i	$-0.942626\pi$
$433$		−	7.46083i		−	0.358544i	0.983800	−	0.179272i	$-0.0573743\pi$
$434$	12.9510	−	7.47728i	0.621669	−	0.358921i
$435$	−32.0048	+	14.1245i	−1.53451	+	0.677216i
$436$	13.4244	+	7.75057i	0.642911	+	0.371185i
$437$	5.16025	+	2.97927i	0.246848	+	0.142518i
$438$	10.1276	−	2.72713i	0.483917	−	0.130307i
$439$	21.3969	−	12.3535i	1.02122	−	0.589601i	0.106762	−	0.994285i	$-0.465952\pi$
$439$	21.3969	−	12.3535i	1.02122	−	0.589601i	0.914457	+	0.404684i	$0.132618\pi$
$440$	5.33843	−	5.14793i	0.254500	−	0.245418i
$441$	6.43295	−	3.73532i	0.306331	−	0.177873i
$442$	−4.48709			−0.213429
$443$	20.0786	+	34.7771i	0.953962	+	1.65231i	0.736726	+	0.676191i	$0.236371\pi$
$443$	20.0786	+	34.7771i	0.953962	+	1.65231i	0.217236	+	0.976119i	$0.430296\pi$
$444$	5.85101	+	5.83655i	0.277677	+	0.276990i
$445$	−18.2651	+	2.80867i	−0.865847	+	0.133144i
$446$	6.45990	−	11.1889i	0.305885	−	0.529809i
$447$	−0.546569	+	0.547923i	−0.0258518	+	0.0259159i
$448$	−1.06306	−	1.84128i	−0.0502250	−	0.0869922i
$449$			38.9543i			1.83837i	0.393829	+	0.919184i	$0.371150\pi$
$449$			38.9543i			1.83837i	−0.393829	+	0.919184i	$0.628850\pi$
$450$	14.2958	−	4.54201i	0.673911	−	0.214113i
$451$	−2.77507	−	30.3918i	−0.130673	−	1.43109i
$452$	0.672865	+	1.16544i	0.0316489	+	0.0548175i
$453$	25.7000	−	6.92039i	1.20749	−	0.325148i
$454$	−4.41599	+	7.64871i	−0.207252	+	0.358972i
$455$	3.81151	+	24.7867i	0.178686	+	1.16202i
$456$	−4.39420	−	1.17160i	−0.205777	−	0.0548650i
$457$	−6.52011	−	11.2932i	−0.304998	−	0.528272i	0.672263	−	0.740312i	$-0.265322\pi$
$457$	−6.52011	−	11.2932i	−0.304998	−	0.528272i	−0.977261	+	0.212041i	$0.931989\pi$
$458$			13.2401i			0.618669i
$459$	−3.11382	+	3.13703i	−0.145341	+	0.146424i
$460$	3.95796	−	3.17570i	0.184541	−	0.148068i
$461$	−17.6968	−	30.6517i	−0.824221	−	1.42759i	−0.902513	−	0.430662i	$-0.858280\pi$
$461$	−17.6968	−	30.6517i	−0.824221	−	1.42759i	0.0782919	−	0.996930i	$-0.475053\pi$
$462$	12.0386	+	2.06037i	0.560087	+	0.0958571i
$463$	11.1320	+	6.42706i	0.517348	+	0.298691i	0.735849	−	0.677146i	$-0.236783\pi$
$463$	11.1320	+	6.42706i	0.517348	+	0.298691i	−0.218501	+	0.975837i	$0.570117\pi$
$464$	4.51629	−	7.82244i	0.209663	−	0.363147i
$465$	−21.9864	−	16.0840i	−1.01960	−	0.745877i
$466$	4.43592	+	7.68324i	0.205490	+	0.355919i
$467$	42.5434			1.96867			0.984337	−	0.176297i	$-0.0564120\pi$
$467$	42.5434			1.96867			0.984337	+	0.176297i	$0.0564120\pi$
$468$	0.0391684	+	15.8248i	0.00181056	+	0.731503i
$469$			5.59609i			0.258404i
$470$	0.389787	−	1.00193i	0.0179796	−	0.0462154i
$471$	−12.0917	−	12.0618i	−0.557157	−	0.555780i
$472$	−4.78527	+	8.28833i	−0.220260	+	0.381501i
$473$	26.4313	+	12.2034i	1.21531	+	0.561111i
$474$	−15.9738	+	16.0134i	−0.733703	+	0.735521i
$475$	3.94422	+	12.5216i	0.180973	+	0.574530i
$476$		−	1.80856i		−	0.0828954i
$477$	25.4395	+	14.6036i	1.16479	+	0.668655i
$478$		−	15.5124i		−	0.709520i
$479$	−15.1857	−	26.3024i	−0.693854	−	1.20179i	−0.970566	−	0.240837i	$-0.922578\pi$
$479$	−15.1857	−	26.3024i	−0.693854	−	1.20179i	0.276712	−	0.960953i	$-0.410755\pi$
$480$	−2.28670	+	3.12586i	−0.104373	+	0.142675i
$481$	21.7971	+	12.5846i	0.993862	+	0.573806i
$482$	10.9975	−	19.0482i	0.500922	−	0.867622i
$483$	8.07504	+	2.15299i	0.367427	+	0.0979646i
$484$	−7.13435	−	8.37264i	−0.324289	−	0.380575i
$485$	−17.6013	−	21.9370i	−0.799233	−	0.996107i
$486$	11.0907	+	10.9543i	0.503084	+	0.496897i
$487$			22.1449i			1.00348i	0.865018	+	0.501740i	$0.167307\pi$
$487$			22.1449i			1.00348i	−0.865018	+	0.501740i	$0.832693\pi$
$488$	3.06944	+	5.31642i	0.138947	+	0.240663i
$489$	0.840861	−	3.15374i	0.0380251	−	0.142617i
$490$	5.48013	−	0.842694i	0.247567	−	0.0380690i
$491$	−18.3433	+	31.7716i	−0.827823	+	1.43383i	0.0719195	+	0.997410i	$0.477088\pi$
$491$	−18.3433	+	31.7716i	−0.827823	+	1.43383i	−0.899743	+	0.436421i	$0.856246\pi$
$492$	4.14401	+	15.3894i	0.186826	+	0.693810i
$493$	6.65407	−	3.84173i	0.299684	−	0.173023i
$494$	−13.8500			−0.623143
$495$	−5.42049	−	21.5782i	−0.243633	−	0.969867i
$496$	7.03372			0.315823
$497$	−23.0437	+	13.3043i	−1.03365	+	0.596780i
$498$	10.9187	−	10.9458i	0.489278	−	0.490491i
$499$	−5.25554	+	9.10287i	−0.235270	+	0.407500i	−0.959351	−	0.282215i	$-0.908931\pi$
$499$	−5.25554	+	9.10287i	−0.235270	+	0.407500i	0.724081	+	0.689715i	$0.242264\pi$
$500$	11.1561	+	0.735873i	0.498916	+	0.0329093i
$501$	14.0804	+	14.0456i	0.629067	+	0.627512i
$502$	−9.31583	−	16.1355i	−0.415786	−	0.720162i
$503$			10.7761i			0.480483i	0.970713	+	0.240242i	$0.0772267\pi$
$503$			10.7761i			0.480483i	−0.970713	+	0.240242i	$0.922773\pi$
$504$	−6.37835	+	0.0157872i	−0.284114	+	0.000703219i
$505$	−5.16447	+	4.14375i	−0.229816	+	0.184394i
$506$	−4.34048	−	6.14910i	−0.192958	−	0.273361i
$507$	6.67665	+	24.7948i	0.296520	+	1.10118i
$508$	4.94069	−	8.55753i	0.219208	−	0.379679i
$509$	12.7453	+	7.35852i	0.564927	+	0.326161i	0.755120	−	0.655586i	$-0.227578\pi$
$509$	12.7453	+	7.35852i	0.564927	+	0.326161i	−0.190194	+	0.981747i	$0.560912\pi$
$510$	−3.01404	+	1.33017i	−0.133464	+	0.0589007i
$511$	6.43735	+	11.1498i	0.284772	+	0.493239i
$512$		−	1.00000i		−	0.0441942i
$513$	−9.61126	+	9.68289i	−0.424347	+	0.427510i
$514$		−	9.62152i		−	0.424387i
$515$	1.08324	−	2.78440i	0.0477331	−	0.122695i
$516$	−14.6903	−	3.91678i	−0.646705	−	0.172427i
$517$	−1.44774	−	0.668422i	−0.0636715	−	0.0293971i
$518$	−5.07233	+	8.78553i	−0.222865	+	0.386014i
$519$	5.21050	−	1.40306i	0.228716	−	0.0615876i
$520$	−4.27654	+	10.9926i	−0.187539	+	0.482057i
$521$			3.15671i			0.138298i	0.997606	+	0.0691490i	$0.0220284\pi$
$521$			3.15671i			0.138298i	−0.997606	+	0.0691490i	$0.977972\pi$
$522$	−13.6069	−	23.4337i	−0.595558	−	1.02567i
$523$	10.3172			0.451138			0.225569	−	0.974227i	$-0.427576\pi$
$523$	10.3172			0.451138			0.225569	+	0.974227i	$0.427576\pi$
$524$	−1.52260	−	2.63722i	−0.0665152	−	0.115208i
$525$	9.90808	+	15.5197i	0.432424	+	0.677334i
$526$	5.90634	−	10.2301i	0.257529	−	0.446053i
$527$	5.18156	+	2.99158i	0.225712	+	0.130315i
$528$	4.41910	+	3.67036i	0.192317	+	0.159732i
$529$	8.92495	+	15.4585i	0.388041	+	0.672107i
$530$	13.6826	+	17.0530i	0.594334	+	0.740735i
$531$	14.4173	+	24.8294i	0.625658	+	1.07750i
$532$		−	5.58240i		−	0.242028i
$533$	24.2690	+	42.0352i	1.05121	+	1.82074i
$534$	−3.72193	−	13.8220i	−0.161064	−	0.598136i
$535$	−12.3895	+	1.90516i	−0.535643	+	0.0823673i
$536$	−1.31603	+	2.27943i	−0.0568439	+	0.0984565i
$537$	−2.20969	+	8.28770i	−0.0953553	+	0.357641i
$538$	1.86085	+	3.22310i	0.0802271	+	0.138957i
$539$	−0.747810	−	8.18981i	−0.0322105	−	0.352760i
$540$	4.71747	+	10.6182i	0.203008	+	0.456933i
$541$		−	34.7034i		−	1.49201i	−0.665938	−	0.746007i	$-0.731969\pi$
$541$		−	34.7034i		−	1.49201i	0.665938	−	0.746007i	$-0.268031\pi$
$542$	−1.84644	−	3.19812i	−0.0793113	−	0.137371i
$543$	−39.4690	−	10.5234i	−1.69378	−	0.451600i
$544$	0.425319	−	0.736675i	0.0182354	−	0.0315847i
$545$	34.2589	−	5.26808i	1.46749	−	0.225660i
$546$	−18.7572	+	5.05086i	−0.802734	+	0.216157i
$547$	−22.1127	−	38.3004i	−0.945473	−	1.63761i	−0.754802	−	0.655953i	$-0.772267\pi$
$547$	−22.1127	−	38.3004i	−0.945473	−	1.63761i	−0.190671	−	0.981654i	$-0.561066\pi$
$548$	−14.2863			−0.610282
$549$	18.4166	−	0.0455833i	0.786000	−	0.00194545i
$550$	2.10675	−	16.4488i	0.0898323	−	0.701377i
$551$	20.5387	−	11.8580i	0.874980	−	0.505170i
$552$	2.78285	+	2.77597i	0.118446	+	0.118153i
$553$	−24.0448	−	13.8823i	−1.02249	−	0.590334i
$554$	−21.2589	−	12.2738i	−0.903203	−	0.521465i
$555$	18.3720	+	1.99164i	0.779850	+	0.0845403i
$556$	12.1121	−	6.99294i	0.513668	−	0.296567i
$557$			18.6694i			0.791049i	0.918455	+	0.395525i	$0.129437\pi$
$557$			18.6694i			0.791049i	−0.918455	+	0.395525i	$0.870563\pi$
$558$	10.5053	−	18.3002i	0.444725	−	0.774709i
$559$	−46.3023			−1.95838
$560$	−4.43067	−	1.72370i	−0.187230	−	0.0728397i
$561$	1.69437	+	4.58339i	0.0715362	+	0.193511i
$562$	−20.4157	−	11.7870i	−0.861184	−	0.497205i
$563$	−31.0205	−	17.9097i	−1.30736	−	0.754805i	−0.325705	−	0.945471i	$-0.605602\pi$
$563$	−31.0205	−	17.9097i	−1.30736	−	0.754805i	−0.981655	+	0.190667i	$0.938935\pi$
$564$	0.804641	+	0.214536i	0.0338815	+	0.00903359i
$565$	2.80440	+	1.09102i	0.117982	+	0.0458995i
$566$		−	20.7303i		−	0.871360i
$567$	−9.48541	+	16.6187i	−0.398350	+	0.697918i
$568$	−12.5151			−0.525121
$569$	−1.31780	−	2.28250i	−0.0552451	−	0.0956873i	0.837080	−	0.547080i	$-0.184261\pi$
$569$	−1.31780	−	2.28250i	−0.0552451	−	0.0956873i	−0.892325	+	0.451393i	$0.850927\pi$
$570$	−9.30328	+	4.10575i	−0.389672	+	0.171971i
$571$	−23.4101	−	13.5158i	−0.979681	−	0.565619i	−0.0775075	−	0.996992i	$-0.524696\pi$
$571$	−23.4101	−	13.5158i	−0.979681	−	0.565619i	−0.902174	+	0.431372i	$0.858029\pi$
$572$	15.8838	+	7.33357i	0.664136	+	0.306632i
$573$	−31.4527	+	8.46945i	−1.31395	+	0.353816i
$574$	−16.9427	+	9.78186i	−0.707174	+	0.408287i
$575$	2.45900	−	11.0773i	0.102547	−	0.461954i
$576$	−2.60178	−	1.49356i	−0.108408	−	0.0622319i
$577$			35.3454i			1.47145i	0.677282	+	0.735724i	$0.263158\pi$
$577$			35.3454i			1.47145i	−0.677282	+	0.735724i	$0.736842\pi$
$578$	−14.0958	+	8.13821i	−0.586307	+	0.338505i
$579$	14.9437	−	14.9808i	0.621040	−	0.622579i
$580$	−3.06973	−	19.9628i	−0.127464	−	0.828910i
$581$	16.4355	+	9.48903i	0.681859	+	0.393671i
$582$	15.3858	−	15.4240i	0.637763	−	0.639343i
$583$	26.4936	−	18.7011i	1.09725	−	0.774519i
$584$			6.05548i			0.250577i
$585$	22.2130	+	27.5448i	0.918396	+	1.13884i
$586$	16.7968			0.693868
$587$	−10.0601	−	17.4246i	−0.415225	−	0.719190i	0.580227	−	0.814455i	$-0.302964\pi$
$587$	−10.0601	−	17.4246i	−0.415225	−	0.719190i	−0.995452	+	0.0952644i	$0.969630\pi$
$588$	1.11670	+	4.14706i	0.0460521	+	0.171022i
$589$	15.9936	+	9.23393i	0.659006	+	0.380478i
$590$	3.25256	+	21.1518i	0.133906	+	0.870804i
$591$	−11.0521	+	41.4522i	−0.454624	+	1.70512i
$592$	−4.13218	+	2.38572i	−0.169832	+	0.0980523i
$593$			32.6723i			1.34169i	0.741597	+	0.670846i	$0.234069\pi$
$593$			32.6723i			1.34169i	−0.741597	+	0.670846i	$0.765931\pi$
$594$	16.1497	−	6.01562i	0.662630	−	0.246824i
$595$	−2.53084	−	3.15426i	−0.103754	−	0.129312i
$596$	−0.223413	−	0.386962i	−0.00915133	−	0.0158506i
$597$	3.99541	+	1.06527i	0.163521	+	0.0435985i
$598$	10.3671	+	5.98545i	0.423943	+	0.244763i
$599$	−31.6551	−	18.2761i	−1.29339	−	0.746740i	−0.314138	−	0.949377i	$-0.601715\pi$
$599$	−31.6551	−	18.2761i	−1.29339	−	0.746740i	−0.979254	+	0.202637i	$0.935049\pi$
$600$	0.386061	+	8.65164i	0.0157609	+	0.353202i
$601$	27.9049	−	16.1109i	1.13827	−	0.657178i	0.192265	−	0.981343i	$-0.438417\pi$
$601$	27.9049	−	16.1109i	1.13827	−	0.657178i	0.946000	+	0.324165i	$0.105083\pi$
$602$		−	18.6626i		−	0.760630i
$603$	3.96501	+	6.82851i	0.161468	+	0.278078i
$604$			15.3664i			0.625251i
$605$	−24.1592	−	4.61890i	−0.982210	−	0.187785i
$606$	−3.63115	−	3.62218i	−0.147506	−	0.147141i
$607$	−5.61178	+	9.71989i	−0.227775	+	0.394518i	−0.957148	−	0.289598i	$-0.906478\pi$
$607$	−5.61178	+	9.71989i	−0.227775	+	0.394518i	0.729373	+	0.684116i	$0.239812\pi$
$608$	1.31281	−	2.27385i	0.0532415	−	0.0922169i
$609$	23.4913	−	23.5495i	0.951917	−	0.954276i
$610$	12.7929	+	4.97694i	0.517971	+	0.201510i
$611$	2.53614			0.102601
$612$	−1.28142	−	2.20686i	−0.0517985	−	0.0892070i
$613$	9.39642			0.379518			0.189759	−	0.981831i	$-0.439229\pi$
$613$	9.39642			0.379518			0.189759	+	0.981831i	$0.439229\pi$
$614$	−4.63548	+	2.67629i	−0.187073	+	0.108006i
$615$	28.7629	+	21.0413i	1.15983	+	0.848466i
$616$	−2.95587	+	6.40213i	−0.119095	+	0.257949i
$617$	6.58534	−	11.4061i	0.265116	−	0.459194i	−0.702478	−	0.711705i	$-0.747923\pi$
$617$	6.58534	−	11.4061i	0.265116	−	0.459194i	0.967594	+	0.252511i	$0.0812565\pi$
$618$	2.23613	+	0.596205i	0.0899505	+	0.0239829i
$619$	−21.9622	−	38.0397i	−0.882736	−	1.52894i	−0.848287	−	0.529538i	$-0.822365\pi$
$619$	−21.9622	−	38.0397i	−0.882736	−	1.52894i	−0.0344497	−	0.999406i	$-0.510968\pi$
$620$	12.2673	−	9.84274i	0.492666	−	0.395294i
$621$	11.3789	−	3.09428i	0.456618	−	0.124169i
$622$	11.6999			0.469122
$623$	15.2170	−	8.78556i	0.609658	−	0.351986i
$624$	−8.82810	−	2.35378i	−0.353407	−	0.0942265i
$625$	20.4868	−	14.3280i	0.819470	−	0.573122i
$626$	12.7222	−	22.0355i	0.508482	−	0.880716i
$627$	5.22991	+	14.1473i	0.208862	+	0.564989i
$628$	8.53958	−	4.93033i	0.340766	−	0.196741i
$629$	−4.05876			−0.161834
$630$	−11.1022	+	8.95318i	−0.442322	+	0.356703i
$631$	4.05490			0.161423			0.0807114	−	0.996738i	$-0.474281\pi$
$631$	4.05490			0.161423			0.0807114	+	0.996738i	$0.474281\pi$
$632$	−6.52938	−	11.3092i	−0.259725	−	0.449856i
$633$	3.70360	+	3.69445i	0.147205	+	0.146841i
$634$	10.9911	+	6.34572i	0.436512	+	0.252021i
$635$	−3.35820	−	21.8387i	−0.133266	−	0.866644i
$636$	−11.9604	+	11.9900i	−0.474259	+	0.475435i
$637$	6.53988	+	11.3274i	0.259119	+	0.448808i
$638$	−29.8335	+	2.72410i	−1.18112	+	0.107848i
$639$	−18.6921	+	32.5615i	−0.739447	+	1.28811i
$640$	−1.39937	−	1.74407i	−0.0553148	−	0.0689404i
$641$	−13.9444	+	8.05080i	−0.550771	+	0.317988i	−0.749433	−	0.662080i	$-0.769674\pi$
$641$	−13.9444	+	8.05080i	−0.550771	+	0.317988i	0.198662	+	0.980068i	$0.436340\pi$
$642$	−2.52465	−	9.37568i	−0.0996398	−	0.370028i
$643$	−21.5384	−	12.4352i	−0.849392	−	0.490397i	0.0110536	−	0.999939i	$-0.496481\pi$
$643$	−21.5384	−	12.4352i	−0.849392	−	0.490397i	−0.860446	+	0.509542i	$0.829815\pi$
$644$	−2.41250	+	4.17857i	−0.0950657	+	0.164659i
$645$	−31.1019	+	13.7260i	−1.22464	+	0.540460i
$646$	1.93423	−	1.11673i	0.0761012	−	0.0439370i
$647$	−17.1494			−0.674214			−0.337107	−	0.941466i	$-0.609448\pi$
$647$	−17.1494			−0.674214			−0.337107	+	0.941466i	$0.609448\pi$
$648$	−7.77186	+	4.53853i	−0.305307	+	0.178290i
$649$	31.6104	−	2.88634i	1.24082	−	0.113299i
$650$	7.92407	+	25.1563i	0.310808	+	0.986711i
$651$	25.0277	+	6.67298i	0.980914	+	0.261535i
$652$	1.63196	+	0.942211i	0.0639124	+	0.0368998i
$653$	13.1635	−	22.7999i	0.515129	−	0.892230i	−0.484717	−	0.874671i	$-0.661077\pi$
$653$	13.1635	−	22.7999i	0.515129	−	0.892230i	0.999846	−	0.0175584i	$-0.00558931\pi$
$654$	6.98106	+	25.9253i	0.272981	+	1.01376i
$655$	−6.34596	−	2.46882i	−0.247957	−	0.0964650i
$656$	−9.20159			−0.359262
$657$	15.7550	+	9.04425i	0.614662	+	0.352850i
$658$			1.02222i			0.0398501i
$659$	−4.99870	−	8.65801i	−0.194722	−	0.337268i	0.752088	−	0.659063i	$-0.229047\pi$
$659$	−4.99870	−	8.65801i	−0.194722	−	0.337268i	−0.946809	+	0.321795i	$0.895714\pi$
$660$	12.8434	+	0.217420i	0.499928	+	0.00846306i
$661$	2.23982	−	3.87949i	0.0871191	−	0.150895i	−0.819173	−	0.573546i	$-0.805567\pi$
$661$	2.23982	−	3.87949i	0.0871191	−	0.150895i	0.906292	+	0.422652i	$0.138901\pi$
$662$	5.57396	+	3.21813i	0.216638	+	0.125076i
$663$	−5.50233	−	5.48873i	−0.213693	−	0.213165i
$664$	4.46307	+	7.73026i	0.173201	+	0.299992i
$665$	−7.81181	−	9.73608i	−0.302929	−	0.377549i
$666$	0.0354296	+	14.3143i	0.00137287	+	0.554666i
$667$	−20.4984			−0.793700
$668$	−9.94407	+	5.74121i	−0.384748	+	0.222134i
$669$	21.6081	−	5.81854i	0.835416	−	0.224958i
$670$	0.894511	+	5.81710i	0.0345580	+	0.224734i
$671$	8.53464	−	18.4852i	0.329476	−	0.713614i
$672$	0.948713	−	3.55825i	0.0365974	−	0.137263i
$673$	−20.2918	−	35.1465i	−0.782193	−	1.35480i	−0.930662	−	0.365881i	$-0.880768\pi$
$673$	−20.2918	−	35.1465i	−0.782193	−	1.35480i	0.148469	−	0.988917i	$-0.452565\pi$
$674$			16.4602i			0.634024i
$675$	23.0863	+	11.9173i	0.888592	+	0.458699i
$676$	−14.8252			−0.570200
$677$	−6.86534	+	3.96371i	−0.263857	+	0.152338i	−0.626093	−	0.779749i	$-0.715347\pi$
$677$	−6.86534	+	3.96371i	−0.263857	+	0.152338i	0.362236	+	0.932086i	$0.382013\pi$
$678$	−0.600488	+	2.25220i	−0.0230616	+	0.0864951i
$679$	23.1597	+	13.3712i	0.888787	+	0.513141i
$680$	−0.289091	−	1.87999i	−0.0110861	−	0.0720943i
$681$	−14.7713	+	3.97755i	−0.566036	+	0.152420i
$682$	−13.4528	−	19.0585i	−0.515136	−	0.729787i
$683$	40.4955			1.54952			0.774759	−	0.632257i	$-0.217871\pi$
$683$	40.4955			1.54952			0.774759	+	0.632257i	$0.217871\pi$
$684$	−3.95530	−	6.81179i	−0.151235	−	0.260455i
$685$	−24.9164	+	19.9918i	−0.952005	+	0.763848i
$686$	−17.4546	+	10.0774i	−0.666418	+	0.384757i
$687$	−16.1957	+	16.2358i	−0.617903	+	0.619434i
$688$	4.38888	−	7.60176i	0.167324	−	0.289814i
$689$	−25.7885	+	44.6670i	−0.982464	+	1.70168i
$690$	8.73809	+	0.947261i	0.332653	+	0.0360616i
$691$	−12.8183	−	22.2019i	−0.487630	−	0.844600i	0.512269	−	0.858825i	$-0.328805\pi$
$691$	−12.8183	−	22.2019i	−0.487630	−	0.844600i	−0.999899	+	0.0142254i	$0.995472\pi$
$692$			3.11544i			0.118431i
$693$	12.2422	+	17.2525i	0.465041	+	0.655369i
$694$	−22.7254			−0.862644
$695$	11.3387	−	29.1454i	0.430101	−	1.10555i
$696$	15.1068	−	4.06789i	0.572620	−	0.154193i
$697$	−6.77858	−	3.91361i	−0.256757	−	0.148239i
$698$	12.7433	−	22.0720i	0.482339	−	0.835436i
$699$	−3.95877	+	14.8478i	−0.149734	+	0.561595i
$700$	−10.1395	+	3.19388i	−0.383237	+	0.120717i
$701$	13.3785			0.505300			0.252650	−	0.967558i	$-0.418698\pi$
$701$	13.3785			0.505300			0.252650	+	0.967558i	$0.418698\pi$
$702$	−19.3094	+	19.4533i	−0.728784	+	0.734216i
$703$	−12.5280			−0.472501
$704$	−2.70959	+	1.91262i	−0.102121	+	0.0720847i
$705$	1.70356	−	0.751821i	0.0641599	−	0.0283152i
$706$	21.8829	+	12.6341i	0.823574	+	0.475491i
$707$	3.14790	−	5.45232i	0.118389	−	0.205056i
$708$	−16.0065	+	4.31017i	−0.601561	+	0.161986i
$709$	16.3310	+	28.2862i	0.613325	+	1.06231i	0.990676	+	0.136239i	$0.0435016\pi$
$709$	16.3310	+	28.2862i	0.613325	+	1.06231i	−0.377351	+	0.926070i	$0.623165\pi$
$710$	−21.8272	+	17.5132i	−0.819158	+	0.657257i
$711$	−39.1762	+	0.0969659i	−1.46922	+	0.00363651i
$712$	8.26439			0.309721
$713$	−7.98110	−	13.8237i	−0.298895	−	0.517701i
$714$	2.21229	−	2.21777i	0.0827927	−	0.0829979i
$715$	37.9648	−	9.43702i	1.41980	−	0.352925i
$716$	−4.28861	−	2.47603i	−0.160273	−	0.0925336i
$717$	18.9752	−	19.0222i	0.708641	−	0.710397i
$718$	31.8343	−	18.3796i	1.18805	−	0.685919i
$719$		−	31.9199i		−	1.19041i	−0.803573	−	0.595206i	$-0.797071\pi$
$719$		−	31.9199i		−	1.19041i	0.803573	−	0.595206i	$-0.202929\pi$
$720$	−6.62773	+	1.03596i	−0.247001	+	0.0386080i
$721$			2.84079i			0.105796i
$722$	−10.4842	+	6.05306i	−0.390182	+	0.225272i
$723$	36.7861	−	9.90561i	1.36809	−	0.368394i
$724$	11.7917	−	20.4239i	0.438237	−	0.759048i
$725$	−33.2891	−	30.5208i	−1.23633	−	1.13351i
$726$	1.49309	−	18.9940i	0.0554136	−	0.704932i
$727$	7.06137	−	4.07688i	0.261892	−	0.151203i	−0.363306	−	0.931670i	$-0.618352\pi$
$727$	7.06137	−	4.07688i	0.261892	−	0.151203i	0.625197	+	0.780467i	$0.285019\pi$
$728$		−	11.2152i		−	0.415664i
$729$	0.200483	+	26.9993i	0.00742529	+	0.999972i
$730$	8.47382	+	10.5612i	0.313630	+	0.390886i
$731$	6.46635	−	3.73335i	0.239167	−	0.138083i
$732$	−2.73927	+	10.2739i	−0.101246	+	0.379736i
$733$	25.0485	−	43.3853i	0.925187	−	1.60247i	0.133927	−	0.990991i	$-0.457241\pi$
$733$	25.0485	−	43.3853i	0.925187	−	1.60247i	0.791260	−	0.611480i	$-0.209426\pi$
$734$	−3.01379	+	5.22004i	−0.111241	+	0.192675i
$735$	7.75087	+	5.67008i	0.285895	+	0.209144i
$736$	−1.96534	+	1.13469i	−0.0724435	+	0.0418253i
$737$	8.69340	−	0.793793i	0.320226	−	0.0292397i
$738$	−13.7432	+	23.9405i	−0.505893	+	0.881263i
$739$			16.7092i			0.614658i	0.951603	+	0.307329i	$0.0994352\pi$
$739$			16.7092i			0.614658i	−0.951603	+	0.307329i	$0.900565\pi$
$740$	−3.86832	+	9.94328i	−0.142202	+	0.365522i
$741$	−16.9837	−	16.9418i	−0.623913	−	0.622371i
$742$	−18.0035	−	10.3943i	−0.660928	−	0.381587i
$743$	7.12955	+	4.11625i	0.261558	+	0.151010i	0.625045	−	0.780589i	$-0.285081\pi$
$743$	7.12955	+	4.11625i	0.261558	+	0.151010i	−0.363487	+	0.931599i	$0.618414\pi$
$744$	8.62516	+	8.60384i	0.316214	+	0.315432i
$745$	−0.931148	−	0.362252i	−0.0341146	−	0.0132719i
$746$		−	27.0482i		−	0.990307i
$747$	26.7783	−	0.0662797i	0.979767	−	0.00242505i
$748$	−2.80956	+	0.256541i	−0.102728	+	0.00938006i
$749$	10.3220	−	5.95938i	0.377156	−	0.217751i
$750$	12.7801	+	14.5488i	0.466664	+	0.531248i
$751$	−1.67986	+	2.90960i	−0.0612990	+	0.106173i	−0.895046	−	0.445973i	$-0.852858\pi$
$751$	−1.67986	+	2.90960i	−0.0612990	+	0.106173i	0.833747	+	0.552146i	$0.186191\pi$
$752$	−0.240394	+	0.416375i	−0.00876628	+	0.0151836i
$753$	8.31376	−	31.1817i	0.302970	−	1.13632i
$754$	41.2630	−	23.8232i	1.50271	−	0.867591i
$755$	21.5032	+	26.8001i	0.782583	+	0.975355i
$756$	−7.84083	−	7.78282i	−0.285168	−	0.283059i
$757$		−	7.65686i		−	0.278293i	−0.990272	−	0.139147i	$-0.955564\pi$
$757$		−	7.65686i		−	0.278293i	0.990272	−	0.139147i	$-0.0444359\pi$
$758$	17.1340	−	9.89235i	0.622337	−	0.359306i
$759$	2.19920	−	12.8498i	0.0798259	−	0.466418i
$760$	−0.892321	−	5.80286i	−0.0323679	−	0.210492i
$761$	8.27969	−	14.3408i	0.300139	−	0.519855i	−0.676029	−	0.736875i	$-0.736300\pi$
$761$	8.27969	−	14.3408i	0.300139	−	0.519855i	0.976167	+	0.217020i	$0.0696338\pi$
$762$	16.5264	−	4.45016i	0.598688	−	0.161212i
$763$	−28.5419	+	16.4787i	−1.03329	+	0.596568i
$764$		−	18.8060i		−	0.680379i
$765$	−5.32310	−	2.05573i	−0.192457	−	0.0743252i
$766$		−	22.1228i		−	0.799329i
$767$	−43.7206	+	25.2421i	−1.57866	+	0.911440i
$768$	1.22323	−	1.22626i	0.0441394	−	0.0442488i
$769$	−15.7217	−	9.07694i	−0.566940	−	0.327323i	0.188987	−	0.981980i	$-0.439480\pi$
$769$	−15.7217	−	9.07694i	−0.566940	−	0.327323i	−0.755926	+	0.654657i	$0.772813\pi$
$770$	3.80369	+	15.3021i	0.137075	+	0.551449i
$771$	11.7693	−	11.7985i	0.423862	−	0.424912i
$772$	6.10832	+	10.5799i	0.219843	+	0.380779i
$773$	29.1490			1.04842			0.524209	−	0.851590i	$-0.324361\pi$
$773$	29.1490			1.04842			0.524209	+	0.851590i	$0.324361\pi$
$774$	−13.2230	−	22.7726i	−0.475292	−	0.818544i
$775$	7.62140	−	34.3328i	0.273769	−	1.23327i
$776$	6.28902	+	10.8929i	0.225763	+	0.391033i
$777$	−16.9667	+	4.56873i	−0.608677	+	0.163902i
$778$	−0.537397	+	0.930800i	−0.0192666	+	0.0333708i
$779$	−20.9231	−	12.0799i	−0.749647	−	0.432809i
$780$	−18.6906	+	8.24859i	−0.669231	+	0.295347i
$781$	23.9366	+	33.9107i	0.856520	+	1.21342i
$782$	−1.93043			−0.0690319
$783$	11.9792	−	45.3801i	0.428101	−	1.62175i
$784$	−2.47959			−0.0885569
$785$	7.99428	−	20.5488i	0.285328	−	0.733419i
$786$	1.35882	−	5.09641i	0.0484676	−	0.181783i
$787$	−8.70436	+	15.0764i	−0.310277	+	0.537415i	−0.978422	−	0.206616i	$-0.933755\pi$
$787$	−8.70436	+	15.0764i	−0.310277	+	0.537415i	0.668145	+	0.744031i	$0.267088\pi$
$788$	−21.4502	−	12.3843i	−0.764130	−	0.441171i
$789$	19.7564	−	5.31994i	0.703348	−	0.189395i
$790$	−27.2134	−	10.5871i	−0.968210	−	0.376671i
$791$	−2.86119			−0.101732
$792$	0.929280	+	9.90638i	0.0330205	+	0.352008i
$793$			32.3823i			1.14993i
$794$	6.39085	+	11.0693i	0.226803	+	0.392834i
$795$	−4.08130	+	37.6483i	−0.144749	+	1.33525i
$796$	−1.19367	+	2.06749i	−0.0423084	+	0.0732802i
$797$	−14.9534	+	25.9001i	−0.529677	+	0.917428i	0.469723	+	0.882814i	$0.344354\pi$
$797$	−14.9534	+	25.9001i	−0.529677	+	0.917428i	−0.999401	+	0.0346145i	$0.988980\pi$
$798$	6.82854	−	6.84547i	0.241728	−	0.242327i
$799$	−0.354185	+	0.204489i	−0.0125302	+	0.00723429i
$800$	−4.88118	−	1.08355i	−0.172576	−	0.0383094i
$801$	12.3434	−	21.5021i	0.436133	−	0.759741i
$802$	6.15819			0.217453
$803$	16.4079	−	11.5818i	0.579020	−	0.408714i
$804$	−4.40206	+	1.18537i	−0.155249	+	0.0418048i
$805$	1.63978	+	10.6637i	0.0577947	+	0.375845i
$806$	32.1318	+	18.5513i	1.13179	+	0.653441i
$807$	−1.66069	+	6.22860i	−0.0584591	+	0.219257i
$808$	2.56444	−	1.48058i	0.0902167	−	0.0520867i
$809$	−52.1806			−1.83457			−0.917286	−	0.398229i	$-0.869625\pi$
$809$	−52.1806			−1.83457			−0.917286	+	0.398229i	$0.869625\pi$
$810$	−7.20360	+	18.7912i	−0.253109	+	0.660255i
$811$		−	17.8096i		−	0.625381i	−0.949855	−	0.312690i	$-0.898770\pi$
$811$		−	17.8096i		−	0.625381i	0.949855	−	0.312690i	$-0.101230\pi$
$812$	9.60219	+	16.6315i	0.336971	+	0.583650i
$813$	1.64782	−	6.18035i	0.0577917	−	0.216754i
$814$	14.3676	+	6.63354i	0.503585	+	0.232505i
$815$	4.16474	−	0.640424i	0.145885	−	0.0224331i
$816$	1.42267	−	0.383092i	0.0498035	−	0.0134109i
$817$	19.9593	−	11.5235i	0.698288	−	0.403157i
$818$	−26.5946			−0.929859
$819$	−29.1796	−	16.7507i	−1.01962	−	0.585316i
$820$	−16.0482	+	12.8764i	−0.560428	+	0.449663i
$821$	−12.5414	−	21.7223i	−0.437697	−	0.758113i	0.559815	−	0.828618i	$-0.310872\pi$
$821$	−12.5414	−	21.7223i	−0.437697	−	0.758113i	−0.997511	+	0.0705051i	$0.977539\pi$
$822$	−17.5188	−	17.4755i	−0.611037	−	0.609527i
$823$	−44.0111	−	25.4098i	−1.53413	−	0.885730i	−0.999165	−	0.0408549i	$-0.986992\pi$
$823$	−44.0111	−	25.4098i	−1.53413	−	0.885730i	−0.534964	−	0.844875i	$-0.679675\pi$
$824$	−0.668067	+	1.15713i	−0.0232732	+	0.0403104i
$825$	22.7040	−	17.5934i	0.790452	−	0.612524i
$826$	−10.1741	−	17.6220i	−0.354002	−	0.613149i
$827$			2.77453i			0.0964799i	0.998836	+	0.0482399i	$0.0153612\pi$
$827$			2.77453i			0.0964799i	−0.998836	+	0.0482399i	$0.984639\pi$
$828$	0.0168510	+	6.80813i	0.000585612	+	0.236599i
$829$	−1.73351			−0.0602072			−0.0301036	−	0.999547i	$-0.509584\pi$
$829$	−1.73351			−0.0602072			−0.0301036	+	0.999547i	$0.509584\pi$
$830$	18.6013	+	7.23664i	0.645662	+	0.251187i
$831$	−11.0552	−	41.0553i	−0.383501	−	1.42419i
$832$	2.63748	−	4.56825i	0.0914382	−	0.158376i
$833$	−1.82665	−	1.05462i	−0.0632898	−	0.0365404i
$834$	23.4066	+	6.24073i	0.810503	+	0.216099i
$835$	−9.30909	+	23.9285i	−0.322154	+	0.828078i
$836$	−8.67212	+	0.791850i	−0.299932	+	0.0273867i
$837$	35.2675	−	9.59039i	1.21902	−	0.331492i
$838$	0.158258			0.00546692
$839$	−2.50245	+	1.44479i	−0.0863942	+	0.0498797i	−0.542575	−	0.840008i	$-0.682550\pi$
$839$	−2.50245	+	1.44479i	−0.0863942	+	0.0498797i	0.456181	+	0.889887i	$0.349217\pi$
$840$	−3.32468	−	7.53343i	−0.114712	−	0.259928i
$841$	−26.2937	+	45.5420i	−0.906678	+	1.57041i
$842$	13.4852	+	7.78571i	0.464732	+	0.268313i
$843$	−10.6167	−	39.4270i	−0.365660	−	1.35794i
$844$	−2.61561	+	1.51012i	−0.0900330	+	0.0519806i
$845$	−25.8562	+	20.7459i	−0.889479	+	0.713680i
$846$	0.724272	+	1.24734i	0.0249010	+	0.0428843i
$847$	23.0006	−	4.23568i	0.790310	−	0.145540i
$848$	−4.88885	−	8.46774i	−0.167884	−	0.290783i
$849$	25.3579	−	25.4207i	0.870281	−	0.872437i
$850$	−3.13499	−	2.87429i	−0.107529	−	0.0985872i
$851$	9.37751	+	5.41411i	0.321457	+	0.185593i
$852$	−15.3467	−	15.3088i	−0.525770	−	0.524471i
$853$	−8.03471	−	13.9165i	−0.275103	−	0.476493i	0.695058	−	0.718954i	$-0.255379\pi$
$853$	−8.03471	−	13.9165i	−0.275103	−	0.476493i	−0.970161	+	0.242461i	$0.922045\pi$
$854$	−13.0520			−0.446631
$855$	−16.4305	−	6.34532i	−0.561911	−	0.217005i
$856$	5.60586			0.191604
$857$	−24.2898	+	14.0237i	−0.829723	+	0.479041i	−0.853758	−	0.520670i	$-0.825682\pi$
$857$	−24.2898	+	14.0237i	−0.829723	+	0.479041i	0.0240350	+	0.999711i	$0.492349\pi$
$858$	10.5071	+	28.4224i	0.358705	+	0.970325i
$859$	−18.2668	+	31.6391i	−0.623256	+	1.07951i	0.365620	+	0.930764i	$0.380857\pi$
$859$	−18.2668	+	31.6391i	−0.623256	+	1.07951i	−0.988875	+	0.148746i	$0.952476\pi$
$860$	−2.98313	−	19.3996i	−0.101724	−	0.661522i
$861$	−32.7416	−	8.72966i	−1.11583	−	0.297506i
$862$	−18.4008	+	10.6237i	−0.626734	+	0.361845i
$863$	5.87019			0.199823			0.0999117	−	0.994996i	$-0.468144\pi$
$863$	5.87019			0.199823			0.0999117	+	0.994996i	$0.468144\pi$
$864$	−1.36349	−	5.01407i	−0.0463868	−	0.170582i
$865$	4.35964	+	5.43354i	0.148232	+	0.184746i
$866$	3.73041	+	6.46127i	0.126765	+	0.219563i
$867$	−27.2400	−	7.26281i	−0.925118	−	0.246658i
$868$	−7.47728	+	12.9510i	−0.253795	+	0.439586i
$869$	−18.1551	+	39.3222i	−0.615869	+	1.33391i
$870$	20.6548	−	28.2346i	0.700262	−	0.957241i
$871$	−12.0239	+	6.94201i	−0.407415	+	0.235221i
$872$	−15.5011			−0.524935
$873$	37.7340	−	0.0933965i	1.27710	−	0.00316099i
$874$	−5.95854			−0.201551
$875$	−13.2146	+	19.7592i	−0.446734	+	0.667983i
$876$	−7.40723	+	7.42559i	−0.250267	+	0.250887i
$877$	3.79422	−	6.57178i	0.128122	−	0.221913i	−0.794827	−	0.606836i	$-0.792439\pi$
$877$	3.79422	−	6.57178i	0.128122	−	0.221913i	0.922949	+	0.384923i	$0.125772\pi$
$878$	−12.3535	+	21.3969i	−0.416911	+	0.722111i
$879$	20.5972	+	20.5463i	0.694726	+	0.693008i
$880$	−2.04925	+	7.12745i	−0.0690802	+	0.240266i
$881$		−	15.9428i		−	0.537125i	−0.963262	−	0.268563i	$-0.913451\pi$
$881$		−	15.9428i		−	0.537125i	0.963262	−	0.268563i	$-0.0865486\pi$
$882$	−3.70343	+	6.45136i	−0.124701	+	0.217229i
$883$		−	21.6305i		−	0.727924i	−0.931414	−	0.363962i	$-0.881424\pi$
$883$		−	21.6305i		−	0.727924i	0.931414	−	0.363962i	$-0.118576\pi$
$884$	3.88593	−	2.24354i	0.130698	−	0.0754585i
$885$	−21.8849	+	29.9162i	−0.735654	+	1.00562i
$886$	−34.7771	−	20.0786i	−1.16836	−	0.674553i
$887$	26.1744	+	15.1118i	0.878852	+	0.507405i	0.870280	−	0.492558i	$-0.163938\pi$
$887$	26.1744	+	15.1118i	0.878852	+	0.507405i	0.00857206	+	0.999963i	$0.497271\pi$
$888$	−7.98540	−	2.12909i	−0.267973	−	0.0714477i
$889$	10.5045	+	18.1944i	0.352310	+	0.610220i
$890$	14.4137	−	11.5649i	0.483147	−	0.387656i
$891$	27.1622	+	12.3780i	0.909967	+	0.414680i
$892$			12.9198i			0.432587i
$893$	−1.09324	+	0.631184i	−0.0365840	+	0.0211218i
$894$	0.199381	−	0.747800i	0.00666829	−	0.0250102i
$895$	−10.9445	+	1.68297i	−0.365834	+	0.0562553i
$896$	1.84128	+	1.06306i	0.0615128	+	0.0355144i
$897$	5.39119	+	20.0211i	0.180007	+	0.668484i
$898$	−19.4772	−	33.7354i	−0.649961	−	1.12577i
$899$	−63.5325			−2.11893
$900$	−10.1095	+	11.0814i	−0.336984	+	0.369380i
$901$		−	8.31730i		−	0.277089i
$902$	17.5992	+	24.9325i	0.585988	+	0.830162i
$903$	22.8286	−	22.8852i	0.759689	−	0.761571i
$904$	−1.16544	−	0.672865i	−0.0387618	−	0.0223792i
$905$	−8.01489	−	52.1217i	−0.266424	−	1.73258i
$906$	−18.7966	+	18.8432i	−0.624477	+	0.626024i
$907$	2.13171	−	1.23075i	0.0707824	−	0.0408662i	−0.464191	−	0.885735i	$-0.653655\pi$
$907$	2.13171	−	1.23075i	0.0707824	−	0.0408662i	0.534974	+	0.844869i	$0.320322\pi$
$908$		−	8.83197i		−	0.293099i
$909$	−0.0219877	−	8.88346i	−0.000729285	−	0.294646i
$910$	−15.6942	−	19.5601i	−0.520258	−	0.648412i
$911$	5.90049	−	3.40665i	0.195492	−	0.112867i	−0.399059	−	0.916925i	$-0.630663\pi$
$911$	5.90049	−	3.40665i	0.195492	−	0.112867i	0.594551	+	0.804058i	$0.297330\pi$
$912$	4.39129	−	1.18247i	0.145410	−	0.0391554i
$913$	12.4097	−	26.8781i	0.410700	−	0.889537i
$914$	11.2932	+	6.52011i	0.373545	+	0.215666i
$915$	9.59952	+	21.7517i	0.317350	+	0.719089i
$916$	−6.62005	−	11.4663i	−0.218732	−	0.378856i
$917$	6.47448			0.213806
$918$	1.12813	−	4.27366i	0.0372340	−	0.141052i
$919$		−	16.5804i		−	0.546939i	−0.961881	−	0.273469i	$-0.911829\pi$
$919$		−	16.5804i		−	0.546939i	0.961881	−	0.273469i	$-0.0881712\pi$
$920$	−1.83985	+	4.72922i	−0.0606580	+	0.155918i
$921$	−8.95802	−	2.38842i	−0.295177	−	0.0787010i
$922$	30.6517	+	17.6968i	1.00946	+	0.582812i
$923$	−57.1720	−	33.0083i	−1.88184	−	1.08648i
$924$	−11.4559	+	4.23498i	−0.376873	+	0.139320i
$925$	7.16767	+	22.7550i	0.235672	+	0.748179i
$926$	−12.8541			−0.422413
$927$	2.01279	+	3.46641i	0.0661086	+	0.113852i
$928$			9.03257i			0.296509i
$929$	25.1586	−	14.5253i	0.825427	−	0.476561i	−0.0268571	−	0.999639i	$-0.508550\pi$
$929$	25.1586	−	14.5253i	0.825427	−	0.476561i	0.852284	+	0.523079i	$0.175217\pi$
$930$	27.0828	+	2.93594i	0.888080	+	0.0962731i
$931$	−5.63823	−	3.25524i	−0.184786	−	0.106686i
$932$	−7.68324	−	4.43592i	−0.251673	−	0.145303i
$933$	14.3471	+	14.3116i	0.469703	+	0.468542i
$934$	−36.8437	+	21.2717i	−1.20556	+	0.696031i
$935$	−4.54107	+	4.37903i	−0.148509	+	0.143210i
$936$	−7.94634	−	13.6851i	−0.259734	−	0.447312i
$937$	−8.96637			−0.292919			−0.146459	−	0.989217i	$-0.546788\pi$
$937$	−8.96637			−0.292919			−0.146459	+	0.989217i	$0.546788\pi$
$938$	−2.79805	−	4.84636i	−0.0913595	−	0.158239i
$939$	42.5552	−	11.4591i	1.38874	−	0.373953i
$940$	0.163397	+	1.06259i	0.00532941	+	0.0346577i
$941$	−6.65048	+	11.5190i	−0.216800	+	0.375508i	−0.953828	−	0.300354i	$-0.902895\pi$
$941$	−6.65048	+	11.5190i	−0.216800	+	0.375508i	0.737028	+	0.675862i	$0.236228\pi$
$942$	16.5027	+	4.39999i	0.537686	+	0.143359i
$943$	10.4410	+	18.0843i	0.340005	+	0.588905i
$944$		−	9.57054i		−	0.311495i
$945$	−24.5660	−	2.60160i	−0.799131	−	0.0846299i
$946$	−28.9919	+	2.64725i	−0.942608	+	0.0860694i
$947$	19.1895	+	33.2372i	0.623575	+	1.08006i	0.988815	+	0.149150i	$0.0476536\pi$
$947$	19.1895	+	33.2372i	0.623575	+	1.08006i	−0.365240	+	0.930913i	$0.619013\pi$
$948$	5.82704	−	21.8550i	0.189253	−	0.709816i
$949$	−15.9712	+	27.6629i	−0.518447	+	0.897977i
$950$	−9.67659	−	8.87190i	−0.313950	−	0.287842i
$951$	5.71569	+	21.2261i	0.185344	+	0.688304i
$952$	0.904282	+	1.56626i	0.0293080	+	0.0507629i
$953$		−	33.6003i		−	1.08842i	−0.838949	−	0.544210i	$-0.816830\pi$
$953$		−	33.6003i		−	1.08842i	0.838949	−	0.544210i	$-0.183170\pi$
$954$	−29.3330	+	0.0726029i	−0.949692	+	0.00235061i
$955$	−26.3165	−	32.7990i	−0.851583	−	1.06135i
$956$	7.75619	+	13.4341i	0.250853	+	0.434490i
$957$	−39.9159	−	33.1528i	−1.29030	−	1.07168i
$958$	26.3024	+	15.1857i	0.849794	+	0.490629i
$959$	15.1873	−	26.3051i	0.490423	−	0.849437i
$960$	0.417409	−	3.85042i	0.0134718	−	0.124272i
$961$	−9.23658	−	15.9982i	−0.297954	−	0.516072i
$962$	−25.1691			−0.811485
$963$	8.37272	−	14.5852i	0.269807	−	0.470002i
$964$			21.9950i			0.708410i
$965$	25.4585	+	9.90433i	0.819538	+	0.318832i
$966$	−8.06969	+	2.17297i	−0.259638	+	0.0699143i
$967$	−17.0724	+	29.5702i	−0.549011	+	0.950914i	0.449332	+	0.893365i	$0.351662\pi$
$967$	−17.0724	+	29.5702i	−0.549011	+	0.950914i	−0.998343	+	0.0575493i	$0.981671\pi$
$968$	10.3648	+	3.68374i	0.333139	+	0.118400i
$969$	3.73788	+	0.996605i	0.120078	+	0.0320156i
$970$	26.2117	+	10.1973i	0.841605	+	0.327417i
$971$			0.123178i			0.00395297i	0.999998	+	0.00197648i	$0.000629135\pi$
$971$			0.123178i			0.00395297i	−0.999998	+	0.00197648i	$0.999371\pi$
$972$	−15.0820	−	3.94134i	−0.483754	−	0.126419i
$973$			29.7357i			0.953283i
$974$	−11.0724	−	19.1780i	−0.354784	−	0.614504i
$975$	−21.0549	+	40.5411i	−0.674297	+	1.29835i
$976$	−5.31642	−	3.06944i	−0.170175	−	0.0982503i
$977$	−4.64314	+	8.04215i	−0.148547	+	0.257291i	−0.930691	−	0.365807i	$-0.880793\pi$
$977$	−4.64314	+	8.04215i	−0.148547	+	0.257291i	0.782144	+	0.623098i	$0.214126\pi$
$978$	0.848664	+	3.15165i	0.0271373	+	0.100779i
$979$	−15.8067	−	22.3931i	−0.505183	−	0.715687i
$980$	−4.32458	+	3.46986i	−0.138144	+	0.110841i
$981$	−23.1519	+	40.3306i	−0.739185	+	1.28766i
$982$		−	36.6867i		−	1.17072i
$983$	−14.0687	−	24.3676i	−0.448721	−	0.777207i	0.549582	−	0.835440i	$-0.314787\pi$
$983$	−14.0687	−	24.3676i	−0.448721	−	0.777207i	−0.998303	+	0.0582323i	$0.981454\pi$
$984$	−11.2835	−	11.2556i	−0.359706	−	0.358817i
$985$	−54.7406	+	8.41761i	−1.74418	+	0.268207i
$986$	−3.84173	+	6.65407i	−0.122346	+	0.211909i
$987$	−1.25040	+	1.25350i	−0.0398008	+	0.0398994i
$988$	11.9945	−	6.92502i	0.381595	−	0.220314i
$989$	−19.9201			−0.633422
$990$	15.4834	+	15.9770i	0.492094	+	0.507783i
$991$	57.5103			1.82687			0.913437	−	0.406980i	$-0.133418\pi$
$991$	57.5103			1.82687			0.913437	+	0.406980i	$0.133418\pi$
$992$	−6.09138	+	3.51686i	−0.193401	+	0.111660i
$993$	2.89862	+	10.7645i	0.0919848	+	0.341600i
$994$	13.3043	−	23.0437i	0.421987	−	0.730903i
$995$	0.811338	+	5.27622i	0.0257212	+	0.167267i
$996$	−3.98299	+	14.9386i	−0.126206	+	0.473349i
$997$	−8.64274	−	14.9697i	−0.273718	−	0.474094i	0.696093	−	0.717952i	$-0.254920\pi$
$997$	−8.64274	−	14.9697i	−0.273718	−	0.474094i	−0.969811	+	0.243858i	$0.921587\pi$
$998$		−	10.5111i		−	0.332723i
$999$	−17.4661	+	17.5963i	−0.552605	+	0.556723i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	990.2.o.a.329.3	✓	144
5.4	even	2	inner	990.2.o.a.329.70	yes	144
9.2	odd	6	inner	990.2.o.a.659.34	yes	144
11.10	odd	2	inner	990.2.o.a.329.39	yes	144
45.29	odd	6	inner	990.2.o.a.659.39	yes	144
55.54	odd	2	inner	990.2.o.a.329.34	yes	144
99.65	even	6	inner	990.2.o.a.659.70	yes	144
495.164	even	6	inner	990.2.o.a.659.3	yes	144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
990.2.o.a.329.3	✓	144	1.1	even	1	trivial
990.2.o.a.329.34	yes	144	55.54	odd	2	inner
990.2.o.a.329.39	yes	144	11.10	odd	2	inner
990.2.o.a.329.70	yes	144	5.4	even	2	inner
990.2.o.a.659.3	yes	144	495.164	even	6	inner
990.2.o.a.659.34	yes	144	9.2	odd	6	inner
990.2.o.a.659.39	yes	144	45.29	odd	6	inner
990.2.o.a.659.70	yes	144	99.65	even	6	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:	\( N \)	\(=\)	\( 990 = 2 \cdot 3^{2} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	990.o (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 + 0.500000i) q^{2} +(-1.67359 - 0.446217i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-0.339852 - 2.21009i) q^{5} +(1.67248 - 0.450358i) q^{6} +(1.06306 + 1.84128i) q^{7} +1.00000i q^{8} +(2.60178 + 1.49356i) q^{9} +(1.39937 + 1.74407i) q^{10} +(2.70959 - 1.91262i) q^{11} +(-1.22323 + 1.22626i) q^{12} +(-2.63748 + 4.56825i) q^{13} +(-1.84128 - 1.06306i) q^{14} +(-0.417409 + 3.85042i) q^{15} +(-0.500000 - 0.866025i) q^{16} -0.850639i q^{17} +(-2.99999 + 0.00742535i) q^{18} -2.62562i q^{19} +(-2.08392 - 0.810725i) q^{20} +(-0.957517 - 3.55589i) q^{21} +(-1.39026 + 3.01117i) q^{22} +(-1.13469 + 1.96534i) q^{23} +(0.446217 - 1.67359i) q^{24} +(-4.76900 + 1.50221i) q^{25} -5.27496i q^{26} +(-3.68785 - 3.66057i) q^{27} +2.12612 q^{28} +(4.51629 + 7.82244i) q^{29} +(-1.56373 - 3.54327i) q^{30} +(-3.51686 + 6.09138i) q^{31} +(0.866025 + 0.500000i) q^{32} +(-5.38818 + 1.99188i) q^{33} +(0.425319 + 0.736675i) q^{34} +(3.70811 - 2.97523i) q^{35} +(2.59436 - 1.50643i) q^{36} -4.77143i q^{37} +(1.31281 + 2.27385i) q^{38} +(6.45248 - 6.46847i) q^{39} +(2.21009 - 0.339852i) q^{40} +(4.60079 - 7.96881i) q^{41} +(2.60718 + 2.60074i) q^{42} +(4.38888 + 7.60176i) q^{43} +(-0.301586 - 3.30288i) q^{44} +(2.41669 - 6.25776i) q^{45} -2.26938i q^{46} +(-0.240394 - 0.416375i) q^{47} +(0.450358 + 1.67248i) q^{48} +(1.23980 - 2.14739i) q^{49} +(3.37897 - 3.68545i) q^{50} +(-0.379569 + 1.42362i) q^{51} +(2.63748 + 4.56825i) q^{52} +9.77771 q^{53} +(5.02406 + 1.32622i) q^{54} +(-5.14793 - 5.33843i) q^{55} +(-1.84128 + 1.06306i) q^{56} +(-1.17160 + 4.39420i) q^{57} +(-7.82244 - 4.51629i) q^{58} +(8.28833 + 4.78527i) q^{59} +(3.12586 + 2.28670i) q^{60} +(5.31642 - 3.06944i) q^{61} -7.03372i q^{62} +(0.0157872 + 6.37835i) q^{63} -1.00000 q^{64} +(10.9926 + 4.27654i) q^{65} +(3.67036 - 4.41910i) q^{66} +(2.27943 + 1.31603i) q^{67} +(-0.736675 - 0.425319i) q^{68} +(2.77597 - 2.78285i) q^{69} +(-1.72370 + 4.43067i) q^{70} +12.5151i q^{71} +(-1.49356 + 2.60178i) q^{72} +6.05548 q^{73} +(2.38572 + 4.13218i) q^{74} +(8.65164 - 0.386061i) q^{75} +(-2.27385 - 1.31281i) q^{76} +(6.40213 + 2.95587i) q^{77} +(-2.35378 + 8.82810i) q^{78} +(-11.3092 + 6.52938i) q^{79} +(-1.74407 + 1.39937i) q^{80} +(4.53853 + 7.77186i) q^{81} +9.20159i q^{82} +(7.73026 - 4.46307i) q^{83} +(-3.55825 - 0.948713i) q^{84} +(-1.87999 + 0.289091i) q^{85} +(-7.60176 - 4.38888i) q^{86} +(-4.06789 - 15.1068i) q^{87} +(1.91262 + 2.70959i) q^{88} -8.26439i q^{89} +(1.03596 + 6.62773i) q^{90} -11.2152 q^{91} +(1.13469 + 1.96534i) q^{92} +(8.60384 - 8.62516i) q^{93} +(0.416375 + 0.240394i) q^{94} +(-5.80286 + 0.892321i) q^{95} +(-1.22626 - 1.22323i) q^{96} +(10.8929 - 6.28902i) q^{97} +2.47959i q^{98} +(9.90638 - 0.929280i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q + 72 q^{4} - 6 q^{5} + 12 q^{9} + 12 q^{11} - 2 q^{15} - 72 q^{16} - 6 q^{20} + 6 q^{25} + 12 q^{31} + 12 q^{45} - 72 q^{49} + 12 q^{55} + 60 q^{59} - 4 q^{60} - 144 q^{64} - 36 q^{66} - 8 q^{69}+ \cdots - 40 q^{99}+O(q^{100}) \) 144 * q + 72 * q^4 - 6 * q^5 + 12 * q^9 + 12 * q^11 - 2 * q^15 - 72 * q^16 - 6 * q^20 + 6 * q^25 + 12 * q^31 + 12 * q^45 - 72 * q^49 + 12 * q^55 + 60 * q^59 - 4 * q^60 - 144 * q^64 - 36 * q^66 - 8 * q^69 + 12 * q^70 + 92 * q^75 - 100 * q^81 + 72 * q^86 - 48 * q^91 - 40 * q^99

Introduction

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