LMFDB - Embedded newform 990.2.o.a.659.14

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			659.14
Character	$\chi$	$=$	990.659
Dual form			990.2.o.a.329.14

$q$-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} +(-0.690097 - 1.58864i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-1.04557 - 1.97656i) q^{5} +(-0.196677 + 1.72085i) q^{6} +(0.998734 - 1.72986i) q^{7} -1.00000i q^{8} +(-2.04753 + 2.19263i) q^{9} +(-0.0827910 + 2.23453i) q^{10} +(0.989910 - 3.16545i) q^{11} +(1.03075 - 1.39196i) q^{12} +(-0.497691 - 0.862025i) q^{13} +(-1.72986 + 0.998734i) q^{14} +(-2.41849 + 3.02505i) q^{15} +(-0.500000 + 0.866025i) q^{16} -0.515407i q^{17} +(2.86953 - 0.875104i) q^{18} -3.42216i q^{19} +(1.18897 - 1.89377i) q^{20} +(-3.43734 - 0.392856i) q^{21} +(-2.44001 + 2.24641i) q^{22} +(-2.97205 - 5.14774i) q^{23} +(-1.58864 + 0.690097i) q^{24} +(-2.81357 + 4.13326i) q^{25} +0.995381i q^{26} +(4.89628 + 1.73966i) q^{27} +1.99747 q^{28} +(2.19758 - 3.80632i) q^{29} +(3.60700 - 1.41052i) q^{30} +(0.0604533 + 0.104708i) q^{31} +(0.866025 - 0.500000i) q^{32} +(-5.71188 + 0.611860i) q^{33} +(-0.257703 + 0.446355i) q^{34} +(-4.46341 - 0.165372i) q^{35} +(-2.92264 - 0.676902i) q^{36} +7.46673i q^{37} +(-1.71108 + 2.96367i) q^{38} +(-1.02599 + 1.38553i) q^{39} +(-1.97656 + 1.04557i) q^{40} +(-2.08885 - 3.61799i) q^{41} +(2.78040 + 2.05889i) q^{42} +(0.0818843 - 0.141828i) q^{43} +(3.23632 - 0.725438i) q^{44} +(6.47469 + 1.75453i) q^{45} +5.94409i q^{46} +(-0.478067 + 0.828036i) q^{47} +(1.72085 + 0.196677i) q^{48} +(1.50506 + 2.60684i) q^{49} +(4.50325 - 2.17272i) q^{50} +(-0.818794 + 0.355681i) q^{51} +(0.497691 - 0.862025i) q^{52} -1.55175 q^{53} +(-3.37047 - 3.95473i) q^{54} +(-7.29172 + 1.35308i) q^{55} +(-1.72986 - 0.998734i) q^{56} +(-5.43656 + 2.36162i) q^{57} +(-3.80632 + 2.19758i) q^{58} +(-3.95204 + 2.28171i) q^{59} +(-3.82901 - 0.581952i) q^{60} +(5.10478 + 2.94725i) q^{61} -0.120907i q^{62} +(1.74799 + 5.73179i) q^{63} -1.00000 q^{64} +(-1.18347 + 1.88502i) q^{65} +(5.25257 + 2.32606i) q^{66} +(-0.990408 + 0.571812i) q^{67} +(0.446355 - 0.257703i) q^{68} +(-6.12688 + 8.27394i) q^{69} +(3.78274 + 2.37492i) q^{70} -0.982823i q^{71} +(2.19263 + 2.04753i) q^{72} -10.8871 q^{73} +(3.73336 - 6.46637i) q^{74} +(8.50788 + 1.61740i) q^{75} +(2.96367 - 1.71108i) q^{76} +(-4.48712 - 4.87385i) q^{77} +(1.58130 - 0.686909i) q^{78} +(6.91684 + 3.99344i) q^{79} +(2.23453 + 0.0827910i) q^{80} +(-0.615219 - 8.97895i) q^{81} +4.17769i q^{82} +(10.9902 + 6.34519i) q^{83} +(-1.37845 - 3.17325i) q^{84} +(-1.01873 + 0.538893i) q^{85} +(-0.141828 + 0.0818843i) q^{86} +(-7.56340 - 0.864426i) q^{87} +(-3.16545 - 0.989910i) q^{88} +9.77063i q^{89} +(-4.72998 - 4.75681i) q^{90} -1.98824 q^{91} +(2.97205 - 5.14774i) q^{92} +(0.124625 - 0.168297i) q^{93} +(0.828036 - 0.478067i) q^{94} +(-6.76409 + 3.57810i) q^{95} +(-1.39196 - 1.03075i) q^{96} +(-0.229422 - 0.132457i) q^{97} -3.01012i q^{98} +(4.91378 + 8.65187i) 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 $\left(\mathbb{Z}/990\mathbb{Z}\right)^\times$.

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

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
$3$	−0.690097	−	1.58864i	−0.398428	−	0.917200i
$3$	−0.690097	−	1.58864i	−0.398428	−	0.917200i
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$	−1.04557	−	1.97656i	−0.467592	−	0.883944i
$5$	−1.04557	−	1.97656i	−0.467592	−	0.883944i
$6$	−0.196677	+	1.72085i	−0.0802930	+	0.702533i
$7$	0.998734	−	1.72986i	0.377486	−	0.653825i	−0.613210	−	0.789920i	$-0.710122\pi$
$7$	0.998734	−	1.72986i	0.377486	−	0.653825i	0.990696	+	0.136095i	$0.0434553\pi$
$8$		−	1.00000i		−	0.353553i
$9$	−2.04753	+	2.19263i	−0.682511	+	0.730875i
$10$	−0.0827910	+	2.23453i	−0.0261808	+	0.706622i
$11$	0.989910	−	3.16545i	0.298469	−	0.954419i
$11$	0.989910	−	3.16545i	0.298469	−	0.954419i
$12$	1.03075	−	1.39196i	0.297552	−	0.401824i
$13$	−0.497691	−	0.862025i	−0.138035	−	0.239083i	0.788718	−	0.614755i	$-0.210745\pi$
$13$	−0.497691	−	0.862025i	−0.138035	−	0.239083i	−0.926753	+	0.375672i	$0.877412\pi$
$14$	−1.72986	+	0.998734i	−0.462324	+	0.266923i
$15$	−2.41849	+	3.02505i	−0.624452	+	0.781063i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$		−	0.515407i		−	0.125005i	−0.998045	−	0.0625023i	$-0.980092\pi$
$17$		−	0.515407i		−	0.125005i	0.998045	−	0.0625023i	$-0.0199081\pi$
$18$	2.86953	−	0.875104i	0.676354	−	0.206264i
$19$		−	3.42216i		−	0.785096i	−0.919731	−	0.392548i	$-0.871594\pi$
$19$		−	3.42216i		−	0.785096i	0.919731	−	0.392548i	$-0.128406\pi$
$20$	1.18897	−	1.89377i	0.265861	−	0.423459i
$21$	−3.43734	−	0.392856i	−0.750089	−	0.0857282i
$22$	−2.44001	+	2.24641i	−0.520212	+	0.478935i
$23$	−2.97205	−	5.14774i	−0.619715	−	1.07338i	−0.989538	−	0.144275i	$-0.953915\pi$
$23$	−2.97205	−	5.14774i	−0.619715	−	1.07338i	0.369823	−	0.929102i	$-0.379418\pi$
$24$	−1.58864	+	0.690097i	−0.324279	+	0.140865i
$25$	−2.81357	+	4.13326i	−0.562715	+	0.826651i
$26$			0.995381i			0.195210i
$27$	4.89628	+	1.73966i	0.942290	+	0.334798i
$28$	1.99747			0.377486
$29$	2.19758	−	3.80632i	0.408080	−	0.706815i	−0.586595	−	0.809881i	$-0.699532\pi$
$29$	2.19758	−	3.80632i	0.408080	−	0.706815i	0.994675	+	0.103065i	$0.0328651\pi$
$30$	3.60700	−	1.41052i	0.658545	−	0.257525i
$31$	0.0604533	+	0.104708i	0.0108577	+	0.0188062i	0.871403	−	0.490567i	$-0.163210\pi$
$31$	0.0604533	+	0.104708i	0.0108577	+	0.0188062i	−0.860545	+	0.509374i	$0.829877\pi$
$32$	0.866025	−	0.500000i	0.153093	−	0.0883883i
$33$	−5.71188	+	0.611860i	−0.994311	+	0.106511i
$34$	−0.257703	+	0.446355i	−0.0441958	+	0.0765493i
$35$	−4.46341	−	0.165372i	−0.754454	−	0.0279530i
$36$	−2.92264	−	0.676902i	−0.487106	−	0.112817i
$37$			7.46673i			1.22752i	0.789492	+	0.613761i	$0.210344\pi$
$37$			7.46673i			1.22752i	−0.789492	+	0.613761i	$0.789656\pi$
$38$	−1.71108	+	2.96367i	−0.277573	+	0.480771i
$39$	−1.02599	+	1.38553i	−0.164290	+	0.221862i
$40$	−1.97656	+	1.04557i	−0.312521	+	0.165319i
$41$	−2.08885	−	3.61799i	−0.326223	−	0.565035i	0.655536	−	0.755164i	$-0.272443\pi$
$41$	−2.08885	−	3.61799i	−0.326223	−	0.565035i	−0.981759	+	0.190129i	$0.939109\pi$
$42$	2.78040	+	2.05889i	0.429024	+	0.317694i
$43$	0.0818843	−	0.141828i	0.0124872	−	0.0216285i	−0.859714	−	0.510775i	$-0.829358\pi$
$43$	0.0818843	−	0.141828i	0.0124872	−	0.0216285i	0.872201	+	0.489147i	$0.162692\pi$
$44$	3.23632	−	0.725438i	0.487893	−	0.109364i
$45$	6.47469	+	1.75453i	0.965190	+	0.261550i
$46$			5.94409i			0.876409i
$47$	−0.478067	+	0.828036i	−0.0697332	+	0.120781i	−0.898784	−	0.438392i	$-0.855548\pi$
$47$	−0.478067	+	0.828036i	−0.0697332	+	0.120781i	0.829051	+	0.559174i	$0.188881\pi$
$48$	1.72085	+	0.196677i	0.248383	+	0.0283879i
$49$	1.50506	+	2.60684i	0.215009	+	0.372406i
$50$	4.50325	−	2.17272i	0.636856	−	0.307269i
$51$	−0.818794	+	0.355681i	−0.114654	+	0.0498053i
$52$	0.497691	−	0.862025i	0.0690173	−	0.119541i
$53$	−1.55175			−0.213149			−0.106575	−	0.994305i	$-0.533988\pi$
$53$	−1.55175			−0.213149			−0.106575	+	0.994305i	$0.533988\pi$
$54$	−3.37047	−	3.95473i	−0.458663	−	0.538171i
$55$	−7.29172	+	1.35308i	−0.983215	+	0.182449i
$56$	−1.72986	−	0.998734i	−0.231162	−	0.133461i
$57$	−5.43656	+	2.36162i	−0.720090	+	0.312804i
$58$	−3.80632	+	2.19758i	−0.499794	+	0.288556i
$59$	−3.95204	+	2.28171i	−0.514512	+	0.297054i	−0.734687	−	0.678407i	$-0.762671\pi$
$59$	−3.95204	+	2.28171i	−0.514512	+	0.297054i	0.220174	+	0.975461i	$0.429337\pi$
$60$	−3.82901	−	0.581952i	−0.494323	−	0.0751297i
$61$	5.10478	+	2.94725i	0.653600	+	0.377356i	0.789834	−	0.613321i	$-0.210167\pi$
$61$	5.10478	+	2.94725i	0.653600	+	0.377356i	−0.136234	+	0.990677i	$0.543500\pi$
$62$		−	0.120907i		−	0.0153552i
$63$	1.74799	+	5.73179i	0.220226	+	0.722138i
$64$	−1.00000			−0.125000
$65$	−1.18347	+	1.88502i	−0.146792	+	0.233808i
$66$	5.25257	+	2.32606i	0.646546	+	0.286318i
$67$	−0.990408	+	0.571812i	−0.120998	+	0.0698580i	−0.559277	−	0.828981i	$-0.688921\pi$
$67$	−0.990408	+	0.571812i	−0.120998	+	0.0698580i	0.438280	+	0.898839i	$0.355588\pi$
$68$	0.446355	−	0.257703i	0.0541286	−	0.0312511i
$69$	−6.12688	+	8.27394i	−0.737590	+	0.996065i
$70$	3.78274	+	2.37492i	0.452124	+	0.283858i
$71$		−	0.982823i		−	0.116640i	−0.998298	−	0.0583198i	$-0.981426\pi$
$71$		−	0.982823i		−	0.116640i	0.998298	−	0.0583198i	$-0.0185743\pi$
$72$	2.19263	+	2.04753i	0.258403	+	0.241304i
$73$	−10.8871			−1.27424			−0.637119	−	0.770766i	$-0.719874\pi$
$73$	−10.8871			−1.27424			−0.637119	+	0.770766i	$0.719874\pi$
$74$	3.73336	−	6.46637i	0.433995	−	0.751701i
$75$	8.50788	+	1.61740i	0.982405	+	0.186761i
$76$	2.96367	−	1.71108i	0.339957	−	0.196274i
$77$	−4.48712	−	4.87385i	−0.511355	−	0.555426i
$78$	1.58130	−	0.686909i	0.179047	−	0.0777772i
$79$	6.91684	+	3.99344i	0.778206	+	0.449297i	0.835794	−	0.549043i	$-0.185008\pi$
$79$	6.91684	+	3.99344i	0.778206	+	0.449297i	−0.0575884	+	0.998340i	$0.518341\pi$
$80$	2.23453	+	0.0827910i	0.249829	+	0.00925631i
$81$	−0.615219	−	8.97895i	−0.0683576	−	0.997661i
$82$			4.17769i			0.461349i
$83$	10.9902	+	6.34519i	1.20633	+	0.696475i	0.961956	−	0.273206i	$-0.0880839\pi$
$83$	10.9902	+	6.34519i	1.20633	+	0.696475i	0.244375	+	0.969681i	$0.421417\pi$
$84$	−1.37845	−	3.17325i	−0.150401	−	0.346230i
$85$	−1.01873	+	0.538893i	−0.110497	+	0.0584512i
$86$	−0.141828	+	0.0818843i	−0.0152937	+	0.00882981i
$87$	−7.56340	−	0.864426i	−0.810881	−	0.0926762i
$88$	−3.16545	−	0.989910i	−0.337438	−	0.105525i
$89$			9.77063i			1.03568i	0.855476	+	0.517842i	$0.173265\pi$
$89$			9.77063i			1.03568i	−0.855476	+	0.517842i	$0.826735\pi$
$90$	−4.72998	−	4.75681i	−0.498584	−	0.501412i
$91$	−1.98824			−0.208424
$92$	2.97205	−	5.14774i	0.309857	−	0.536689i
$93$	0.124625	−	0.168297i	0.0129230	−	0.0174516i
$94$	0.828036	−	0.478067i	0.0854054	−	0.0493088i
$95$	−6.76409	+	3.57810i	−0.693981	+	0.367105i
$96$	−1.39196	−	1.03075i	−0.142066	−	0.105201i
$97$	−0.229422	−	0.132457i	−0.0232943	−	0.0134490i	0.488308	−	0.872672i	$-0.337614\pi$
$97$	−0.229422	−	0.132457i	−0.0232943	−	0.0134490i	−0.511602	+	0.859223i	$0.670948\pi$
$98$		−	3.01012i		−	0.304068i
$99$	4.91378	+	8.65187i	0.493853	+	0.869545i
$100$	−4.98629	−	0.369999i	−0.498629	−	0.0369999i
$101$	−6.03924	+	10.4603i	−0.600927	+	1.04084i	0.391754	+	0.920070i	$0.371868\pi$
$101$	−6.03924	+	10.4603i	−0.600927	+	1.04084i	−0.992681	+	0.120766i	$0.961465\pi$
$102$	0.886937	+	0.101369i	0.0878198	+	0.0100370i
$103$	−16.2386	+	9.37534i	−1.60003	+	0.923780i	−0.608555	+	0.793512i	$0.708250\pi$
$103$	−16.2386	+	9.37534i	−1.60003	+	0.923780i	−0.991479	+	0.130268i	$0.958416\pi$
$104$	−0.862025	+	0.497691i	−0.0845285	+	0.0488026i
$105$	2.81747	+	7.20486i	0.274957	+	0.703123i
$106$	1.34386	+	0.775876i	0.130527	+	0.0753597i
$107$			0.527090i			0.0509557i	0.999675	+	0.0254779i	$0.00811073\pi$
$107$			0.527090i			0.0509557i	−0.999675	+	0.0254779i	$0.991889\pi$
$108$	0.941550	+	5.11014i	0.0906007	+	0.491723i
$109$		−	3.51771i		−	0.336936i	−0.985707	−	0.168468i	$-0.946118\pi$
$109$		−	3.51771i		−	0.336936i	0.985707	−	0.168468i	$-0.0538819\pi$
$110$	6.99135	+	2.47406i	0.666599	+	0.235892i
$111$	11.8619	−	5.15276i	1.12588	−	0.489079i
$112$	0.998734	+	1.72986i	0.0943715	+	0.163456i
$113$	−8.86031	−	15.3465i	−0.833508	−	1.44368i	−0.895240	−	0.445585i	$-0.852996\pi$
$113$	−8.86031	−	15.3465i	−0.833508	−	1.44368i	0.0617322	−	0.998093i	$-0.480338\pi$
$114$	5.88901	+	0.673059i	0.551556	+	0.0630378i
$115$	−7.06733	+	11.2567i	−0.659032	+	1.04970i
$116$	4.39516			0.408080
$117$	2.90914	+	0.673776i	0.268950	+	0.0622906i
$118$	4.56343			0.420098
$119$	−0.891581	−	0.514754i	−0.0817311	−	0.0471875i
$120$	3.02505	+	2.41849i	0.276148	+	0.220777i
$121$	−9.04016	−	6.26702i	−0.821832	−	0.569729i
$122$	−2.94725	−	5.10478i	−0.266831	−	0.462165i
$123$	−4.30616	+	5.81518i	−0.388274	+	0.524337i
$124$	−0.0604533	+	0.104708i	−0.00542887	+	0.00940308i
$125$	11.1114	+	1.23959i	0.993835	+	0.110873i
$126$	1.35209	−	5.83787i	0.120454	−	0.520079i
$127$	20.0737			1.78125			0.890625	−	0.454738i	$-0.150267\pi$
$127$	20.0737			1.78125			0.890625	+	0.454738i	$0.150267\pi$
$128$	0.866025	+	0.500000i	0.0765466	+	0.0441942i
$129$	−0.281821	−	0.0322095i	−0.0248129	−	0.00283589i
$130$	1.96743	−	1.04074i	0.172555	−	0.0912789i
$131$	−4.78632	−	8.29015i	−0.418183	−	0.724314i	0.577574	−	0.816338i	$-0.303999\pi$
$131$	−4.78632	−	8.29015i	−0.418183	−	0.724314i	−0.995757	+	0.0920246i	$0.970666\pi$
$132$	−3.38583	−	4.64071i	−0.294699	−	0.403922i
$133$	−5.91984	−	3.41782i	−0.513315	−	0.296363i
$134$	1.14362			0.0987941
$135$	−1.68085	−	11.4967i	−0.144665	−	0.989481i
$136$	−0.515407			−0.0441958
$137$	5.39400	−	9.34267i	0.460840	−	0.798199i	−0.538163	−	0.842841i	$-0.680881\pi$
$137$	5.39400	−	9.34267i	0.460840	−	0.798199i	0.999003	+	0.0446423i	$0.0142148\pi$
$138$	9.44301	−	4.10200i	0.803842	−	0.349186i
$139$	10.5408	−	6.08571i	0.894056	−	0.516183i	0.0187887	−	0.999823i	$-0.494019\pi$
$139$	10.5408	−	6.08571i	0.894056	−	0.516183i	0.875267	+	0.483640i	$0.160686\pi$
$140$	−2.08849	−	3.94811i	−0.176510	−	0.333677i
$141$	1.64536	+	0.188049i	0.138564	+	0.0158366i
$142$	−0.491411	+	0.851149i	−0.0412383	+	0.0714269i
$143$	−3.22137	+	0.722088i	−0.269384	+	0.0603840i
$144$	−0.875104	−	2.86953i	−0.0729253	−	0.239127i
$145$	−9.82113	−	0.363879i	−0.815600	−	0.0302185i
$146$	9.42850	+	5.44355i	0.780308	+	0.450511i
$147$	3.10269	−	4.18997i	0.255905	−	0.345583i
$148$	−6.46637	+	3.73336i	−0.531533	+	0.306881i
$149$	5.64515	+	9.77769i	0.462469	+	0.801019i	0.999083	−	0.0428081i	$-0.0136304\pi$
$149$	5.64515	+	9.77769i	0.462469	+	0.801019i	−0.536615	+	0.843827i	$0.680297\pi$
$150$	−6.55934	−	5.65465i	−0.535568	−	0.461700i
$151$	−9.75999	−	5.63493i	−0.794256	−	0.458564i	0.0472024	−	0.998885i	$-0.484969\pi$
$151$	−9.75999	−	5.63493i	−0.794256	−	0.458564i	−0.841459	+	0.540321i	$0.818303\pi$
$152$	−3.42216			−0.277573
$153$	1.13009	+	1.05531i	0.0913627	+	0.0853170i
$154$	1.44904	+	6.46444i	0.116767	+	0.520919i
$155$	0.143754	−	0.228969i	0.0115466	−	0.0183913i
$156$	−1.71290	−	0.195769i	−0.137142	−	0.0156740i
$157$	−5.46901	+	3.15753i	−0.436474	+	0.251999i	−0.702101	−	0.712077i	$-0.747755\pi$
$157$	−5.46901	+	3.15753i	−0.436474	+	0.251999i	0.265627	+	0.964076i	$0.414421\pi$
$158$	−3.99344	−	6.91684i	−0.317701	−	0.550274i
$159$	1.07086	+	2.46517i	0.0849246	+	0.195501i
$160$	−1.89377	−	1.18897i	−0.149716	−	0.0939961i
$161$	−11.8731			−0.935735
$162$	−3.95668	+	8.08361i	−0.310866	+	0.635108i
$163$			5.78806i			0.453356i	0.973970	+	0.226678i	$0.0727864\pi$
$163$			5.78806i			0.453356i	−0.973970	+	0.226678i	$0.927214\pi$
$164$	2.08885	−	3.61799i	0.163112	−	0.282517i
$165$	7.18154	+	10.6501i	0.559082	+	0.829112i
$166$	−6.34519	−	10.9902i	−0.492482	−	0.853004i
$167$	−13.5845	+	7.84301i	−1.05120	+	0.606910i	−0.922985	−	0.384836i	$-0.874258\pi$
$167$	−13.5845	+	7.84301i	−1.05120	+	0.606910i	−0.128215	+	0.991746i	$0.540925\pi$
$168$	−0.392856	+	3.43734i	−0.0303095	+	0.265196i
$169$	6.00461	−	10.4003i	0.461893	−	0.800022i
$170$	1.15169	+	0.0426710i	0.0883309	+	0.00327272i
$171$	7.50351	+	7.00697i	0.573807	+	0.535837i
$172$	0.163769			0.0124872
$173$	−9.26010	−	5.34632i	−0.704033	−	0.406473i	0.104815	−	0.994492i	$-0.466575\pi$
$173$	−9.26010	−	5.34632i	−0.704033	−	0.406473i	−0.808848	+	0.588018i	$0.799908\pi$
$174$	6.11788	+	4.53031i	0.463795	+	0.343442i
$175$	4.33993	+	8.99511i	0.328068	+	0.679966i
$176$	2.24641	+	2.44001i	0.169329	+	0.183923i
$177$	6.35211	+	4.70376i	0.477454	+	0.353556i
$178$	4.88531	−	8.46161i	0.366170	−	0.634224i
$179$		−	14.8155i		−	1.10736i	−0.832730	−	0.553679i	$-0.813223\pi$
$179$		−	14.8155i		−	1.10736i	0.832730	−	0.553679i	$-0.186777\pi$
$180$	1.71788	+	6.48451i	0.128043	+	0.483327i
$181$	7.70901			0.573006			0.286503	−	0.958079i	$-0.407507\pi$
$181$	7.70901			0.573006			0.286503	+	0.958079i	$0.407507\pi$
$182$	1.72187	+	0.994121i	0.127633	+	0.0736892i
$183$	1.15931	−	10.1435i	0.0856987	−	0.749831i
$184$	−5.14774	+	2.97205i	−0.379496	+	0.219102i
$185$	14.7584	−	7.80697i	1.08506	−	0.573980i
$186$	−0.192077	+	0.0834373i	−0.0140838	+	0.00611792i
$187$	−1.63150	−	0.510206i	−0.119307	−	0.0373100i
$188$	−0.956133			−0.0697332
$189$	7.89945	−	6.73241i	0.574601	−	0.489711i
$190$	7.64692	+	0.283324i	0.554766	+	0.0205545i
$191$	3.16360	+	1.82651i	0.228910	+	0.132161i	0.610069	−	0.792348i	$-0.291142\pi$
$191$	3.16360	+	1.82651i	0.228910	+	0.132161i	−0.381159	+	0.924510i	$0.624475\pi$
$192$	0.690097	+	1.58864i	0.0498034	+	0.114650i
$193$	−9.26150	−	16.0414i	−0.666657	−	1.15468i	−0.978833	−	0.204660i	$-0.934391\pi$
$193$	−9.26150	−	16.0414i	−0.666657	−	1.15468i	0.312176	−	0.950024i	$-0.398942\pi$
$194$	0.132457	+	0.229422i	0.00950986	+	0.0164716i
$195$	3.81133	+	0.579264i	0.272935	+	0.0414820i
$196$	−1.50506	+	2.60684i	−0.107504	+	0.186203i
$197$		−	8.63325i		−	0.615094i	−0.951533	−	0.307547i	$-0.900492\pi$
$197$		−	8.63325i		−	0.615094i	0.951533	−	0.307547i	$-0.0995081\pi$
$198$	0.0704773	−	9.94962i	0.00500860	−	0.707089i
$199$	23.4446			1.66194			0.830972	−	0.556314i	$-0.187785\pi$
$199$	23.4446			1.66194			0.830972	+	0.556314i	$0.187785\pi$
$200$	4.13326	+	2.81357i	0.292265	+	0.198950i
$201$	1.59188	+	1.17879i	0.112282	+	0.0831456i
$202$	10.4603	−	6.03924i	0.735982	−	0.424919i
$203$	−4.38959	−	7.60300i	−0.308089	−	0.533626i
$204$	−0.717426	−	0.531256i	−0.0502298	−	0.0371954i
$205$	−4.96714	+	7.91158i	−0.346920	+	0.552569i
$206$	18.7507			1.30642
$207$	17.3724	+	4.02357i	1.20747	+	0.279658i
$208$	0.995381			0.0690173
$209$	−10.8327	−	3.38762i	−0.749311	−	0.234327i
$210$	1.16243	−	7.64833i	0.0802154	−	0.527785i
$211$	15.4846	−	8.94005i	1.06600	−	0.615458i	0.138918	−	0.990304i	$-0.455638\pi$
$211$	15.4846	−	8.94005i	1.06600	−	0.615458i	0.927087	+	0.374846i	$0.122304\pi$
$212$	−0.775876	−	1.34386i	−0.0532874	−	0.0922964i
$213$	−1.56135	+	0.678243i	−0.106982	+	0.0464724i
$214$	0.263545	−	0.456473i	0.0180156	−	0.0312039i
$215$	−0.365946	−	0.0135586i	−0.0249573	−	0.000924686i
$216$	1.73966	−	4.89628i	0.118369	−	0.333150i
$217$	0.241507			0.0163946
$218$	−1.75886	+	3.04643i	−0.119125	+	0.206330i
$219$	7.51315	+	17.2956i	0.507691	+	1.16873i
$220$	−4.81766	−	5.63827i	−0.324807	−	0.380132i
$221$	−0.444294	+	0.256513i	−0.0298864	+	0.0172549i
$222$	−12.8491	−	1.46853i	−0.862375	−	0.0985615i
$223$	−14.0114	−	8.08949i	−0.938273	−	0.541712i	−0.0488548	−	0.998806i	$-0.515557\pi$
$223$	−14.0114	−	8.08949i	−0.938273	−	0.541712i	−0.889419	+	0.457093i	$0.848890\pi$
$224$		−	1.99747i		−	0.133461i
$225$	−3.30180	−	14.6321i	−0.220120	−	0.975473i
$226$			17.7206i			1.17876i
$227$	20.1345	+	11.6247i	1.33637	+	0.771555i	0.986268	−	0.165155i	$-0.0528125\pi$
$227$	20.1345	+	11.6247i	1.33637	+	0.771555i	0.350105	+	0.936710i	$0.386146\pi$
$228$	−4.76350	−	3.52739i	−0.315471	−	0.233607i
$229$	−10.9630	−	18.9885i	−0.724456	−	1.25480i	−0.959197	−	0.282737i	$-0.908758\pi$
$229$	−10.9630	−	18.9885i	−0.724456	−	1.25480i	0.234741	−	0.972058i	$-0.424576\pi$
$230$	11.7489	−	6.21496i	0.774697	−	0.409802i
$231$	−4.64622	+	10.4918i	−0.305699	+	0.690312i
$232$	−3.80632	−	2.19758i	−0.249897	−	0.144278i
$233$		−	30.4209i		−	1.99294i	−0.0839648	−	0.996469i	$-0.526758\pi$
$233$		−	30.4209i		−	1.99294i	0.0839648	−	0.996469i	$-0.473242\pi$
$234$	−2.18250	−	2.03808i	−0.142674	−	0.133233i
$235$	2.13651	+	0.0791592i	0.139371	+	0.00516378i
$236$	−3.95204	−	2.28171i	−0.257256	−	0.148527i
$237$	1.57084	−	13.7442i	0.102037	−	0.892782i
$238$	0.514754	+	0.891581i	0.0333666	+	0.0577926i
$239$	−8.20840	−	14.2174i	−0.530957	−	0.919645i	−0.999347	−	0.0361231i	$-0.988499\pi$
$239$	−8.20840	−	14.2174i	−0.530957	−	0.919645i	0.468390	−	0.883522i	$-0.344834\pi$
$240$	−1.41052	−	3.60700i	−0.0910487	−	0.232831i
$241$	−24.8491	−	14.3466i	−1.60067	−	0.924148i	−0.991353	−	0.131222i	$-0.958110\pi$
$241$	−24.8491	−	14.3466i	−1.60067	−	0.924148i	−0.609318	−	0.792926i	$-0.708557\pi$
$242$	4.69549	+	9.94748i	0.301838	+	0.639448i
$243$	−13.8397	+	7.17370i	−0.887819	+	0.460193i
$244$			5.89449i			0.377356i
$245$	3.57893	−	5.70047i	0.228650	−	0.364190i
$246$	6.63684	−	2.88301i	0.423149	−	0.183814i
$247$	−2.94998	+	1.70317i	−0.187703	+	0.108370i
$248$	0.104708	−	0.0604533i	0.00664898	−	0.00383879i
$249$	2.49591	−	21.8382i	0.158172	−	1.38394i
$250$	−9.00296	−	6.62922i	−0.569397	−	0.419269i
$251$			2.54515i			0.160648i	0.996769	+	0.0803242i	$0.0255955\pi$
$251$			2.54515i			0.160648i	−0.996769	+	0.0803242i	$0.974404\pi$
$252$	−4.08988	+	4.37970i	−0.257638	+	0.275895i
$253$	−19.2370	+	4.31207i	−1.20942	+	0.271098i
$254$	−17.3843	−	10.0368i	−1.09079	−	0.629767i
$255$	1.55913	+	1.24651i	0.0976365	+	0.0780593i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	7.03142	+	12.1788i	0.438608	+	0.759691i	0.997582	−	0.0694939i	$-0.0221384\pi$
$257$	7.03142	+	12.1788i	0.438608	+	0.759691i	−0.558975	+	0.829185i	$0.688805\pi$
$258$	0.227959	+	0.168805i	0.0141921	+	0.0105093i
$259$	12.9164	+	7.45727i	0.802585	+	0.463372i
$260$	−2.22421	−	0.0824086i	−0.137940	−	0.00511076i
$261$	3.84622	+	12.6120i	0.238075	+	0.780665i
$262$			9.57264i			0.591400i
$263$	9.44160	+	5.45111i	0.582194	+	0.336130i	0.762005	−	0.647571i	$-0.224215\pi$
$263$	9.44160	+	5.45111i	0.582194	+	0.336130i	−0.179811	+	0.983701i	$0.557549\pi$
$264$	0.611860	+	5.71188i	0.0376574	+	0.351542i
$265$	1.62246	+	3.06713i	0.0996670	+	0.188412i
$266$	3.41782	+	5.91984i	0.209560	+	0.362969i
$267$	15.5220	−	6.74268i	0.949929	−	0.412645i
$268$	−0.990408	−	0.571812i	−0.0604988	−	0.0349290i
$269$		−	15.1823i		−	0.925678i	−0.886442	−	0.462839i	$-0.846831\pi$
$269$		−	15.1823i		−	0.925678i	0.886442	−	0.462839i	$-0.153169\pi$
$270$	−4.29270	+	10.7969i	−0.261246	+	0.657077i
$271$		−	28.6391i		−	1.73970i	−0.493316	−	0.869850i	$-0.664215\pi$
$271$		−	28.6391i		−	1.73970i	0.493316	−	0.869850i	$-0.335785\pi$
$272$	0.446355	+	0.257703i	0.0270643	+	0.0156256i
$273$	1.37208	+	3.15859i	0.0830420	+	0.191167i
$274$	−9.34267	+	5.39400i	−0.564412	+	0.325863i
$275$	10.2984	+	12.9978i	0.621019	+	0.783796i
$276$	−10.2289	−	1.16907i	−0.615706	−	0.0703695i
$277$	−1.08182	+	1.87377i	−0.0650003	+	0.112584i	−0.896694	−	0.442651i	$-0.854038\pi$
$277$	−1.08182	+	1.87377i	−0.0650003	+	0.112584i	0.831694	+	0.555235i	$0.187371\pi$
$278$	−12.1714			−0.729993
$279$	−0.353366	−	0.0818420i	−0.0211555	−	0.00489975i
$280$	−0.165372	+	4.46341i	−0.00988289	+	0.266740i
$281$	−9.54055	+	16.5247i	−0.569141	+	0.985782i	0.427510	+	0.904011i	$0.359391\pi$
$281$	−9.54055	+	16.5247i	−0.569141	+	0.985782i	−0.996651	+	0.0817710i	$0.973942\pi$
$282$	−1.33090	−	0.985536i	−0.0792539	−	0.0586878i
$283$	0.195885	+	0.339283i	0.0116442	+	0.0201683i	0.871789	−	0.489882i	$-0.162960\pi$
$283$	0.195885	+	0.339283i	0.0116442	+	0.0201683i	−0.860145	+	0.510050i	$0.829627\pi$
$284$	0.851149	−	0.491411i	0.0505064	−	0.0291599i
$285$	10.3522	+	8.27645i	0.613210	+	0.490255i
$286$	3.15083	+	0.985338i	0.186312	+	0.0582642i
$287$	−8.34481			−0.492579
$288$	−0.676902	+	2.92264i	−0.0398869	+	0.172218i
$289$	16.7344			0.984374
$290$	8.32341	+	5.22569i	0.488767	+	0.306863i
$291$	−0.0521025	+	0.455877i	−0.00305430	+	0.0267240i
$292$	−5.44355	−	9.42850i	−0.318559	−	0.551761i
$293$	7.21267	−	4.16424i	0.421369	−	0.243277i	−0.274294	−	0.961646i	$-0.588444\pi$
$293$	7.21267	−	4.16424i	0.421369	−	0.243277i	0.695663	+	0.718368i	$0.255111\pi$
$294$	−4.78199	+	2.07727i	−0.278891	+	0.121149i
$295$	8.64208	+	5.42576i	0.503161	+	0.315900i
$296$	7.46673			0.433995
$297$	10.3537	−	13.7768i	0.600782	−	0.799413i
$298$		−	11.2903i		−	0.654030i
$299$	−2.95832	+	5.12396i	−0.171084	+	0.296326i
$300$	2.85323	+	8.17674i	0.164731	+	0.472084i
$301$	−0.163561	−	0.283296i	−0.00942751	−	0.0163289i
$302$	5.63493	+	9.75999i	0.324254	+	0.561624i
$303$	20.7852	+	2.37556i	1.19408	+	0.136472i
$304$	2.96367	+	1.71108i	0.169978	+	0.0981370i
$305$	0.488011	−	13.1714i	0.0279434	−	0.754195i
$306$	−0.451034	−	1.47897i	−0.0257839	−	0.0845474i
$307$	17.9818			1.02628			0.513139	−	0.858306i	$-0.328483\pi$
$307$	17.9818			1.02628			0.513139	+	0.858306i	$0.328483\pi$
$308$	1.97731	−	6.32289i	0.112668	−	0.360280i
$309$	26.1002	+	19.3273i	1.48479	+	1.09949i
$310$	−0.238979	+	0.126416i	−0.0135731	+	0.00717996i
$311$	16.9053	−	9.76030i	0.958614	−	0.553456i	0.0628677	−	0.998022i	$-0.479975\pi$
$311$	16.9053	−	9.76030i	0.958614	−	0.553456i	0.895746	+	0.444566i	$0.146642\pi$
$312$	1.38553	+	1.02599i	0.0784402	+	0.0580853i
$313$	7.50061	+	4.33048i	0.423959	+	0.244773i	0.696770	−	0.717295i	$-0.254620\pi$
$313$	7.50061	+	4.33048i	0.423959	+	0.244773i	−0.272811	+	0.962068i	$0.587953\pi$
$314$	6.31507			0.356380
$315$	9.50158	−	9.44799i	0.535354	−	0.532334i
$316$			7.98688i			0.449297i
$317$	8.19418	−	14.1927i	0.460231	−	0.797144i	−0.538741	−	0.842471i	$-0.681100\pi$
$317$	8.19418	−	14.1927i	0.460231	−	0.797144i	0.998972	+	0.0453278i	$0.0144332\pi$
$318$	0.305194	−	2.67033i	0.0171144	−	0.149745i
$319$	−9.87330	−	10.7242i	−0.552799	−	0.600442i
$320$	1.04557	+	1.97656i	0.0584490	+	0.110493i
$321$	0.837354	−	0.363743i	0.0467366	−	0.0203022i
$322$	10.2824	+	5.93657i	0.573018	+	0.330832i
$323$	−1.76380			−0.0981406
$324$	7.46839	−	5.02227i	0.414910	−	0.279015i
$325$	4.96326	+	0.368290i	0.275312	+	0.0204290i
$326$	2.89403	−	5.01260i	0.160285	−	0.277622i
$327$	−5.58837	+	2.42756i	−0.309037	+	0.134244i
$328$	−3.61799	+	2.08885i	−0.199770	+	0.115337i
$329$	0.954923	+	1.65398i	0.0526466	+	0.0911866i
$330$	−0.894331	−	12.8141i	−0.0492313	−	0.705391i
$331$	−6.38478	+	11.0588i	−0.350939	+	0.607844i	−0.986414	−	0.164277i	$-0.947471\pi$
$331$	−6.38478	+	11.0588i	−0.350939	+	0.607844i	0.635475	+	0.772121i	$0.280804\pi$
$332$			12.6904i			0.696475i
$333$	−16.3717	−	15.2884i	−0.897166	−	0.837797i
$334$	15.6860			0.858301
$335$	2.16576	+	1.35973i	0.118328	+	0.0742900i
$336$	2.05889	−	2.78040i	0.112322	−	0.151683i
$337$	−5.01115	−	8.67957i	−0.272975	−	0.472806i	0.696647	−	0.717414i	$-0.254674\pi$
$337$	−5.01115	−	8.67957i	−0.272975	−	0.472806i	−0.969622	+	0.244607i	$0.921341\pi$
$338$	−10.4003	+	6.00461i	−0.565701	+	0.326608i
$339$	−18.2655	+	24.6664i	−0.992048	+	1.33969i
$340$	−0.976061	−	0.612802i	−0.0529344	−	0.0332338i
$341$	0.391292	−	0.0877103i	0.0211897	−	0.00474978i
$342$	−2.99474	−	9.81997i	−0.161937	−	0.531003i
$343$	19.9949			1.07962
$344$	−0.141828	−	0.0818843i	−0.00764684	−	0.00441490i
$345$	22.7600	+	3.45918i	1.22536	+	0.186236i
$346$	5.34632	+	9.26010i	0.287420	+	0.497826i
$347$	−15.4613	+	8.92657i	−0.830005	+	0.479204i	−0.853854	−	0.520512i	$-0.825741\pi$
$347$	−15.4613	+	8.92657i	−0.830005	+	0.479204i	0.0238495	+	0.999716i	$0.492408\pi$
$348$	−3.03308	−	6.98231i	−0.162590	−	0.374291i
$349$	−22.1062	−	12.7630i	−1.18332	−	0.683188i	−0.226537	−	0.974003i	$-0.572740\pi$
$349$	−22.1062	−	12.7630i	−1.18332	−	0.683188i	−0.956779	+	0.290815i	$0.906074\pi$
$350$	0.739060	−	9.95996i	0.0395044	−	0.532382i
$351$	−0.937201	−	5.08653i	−0.0500241	−	0.271499i
$352$	−0.725438	−	3.23632i	−0.0386660	−	0.172496i
$353$	−13.1794	+	22.8274i	−0.701468	+	1.21498i	0.266483	+	0.963840i	$0.414138\pi$
$353$	−13.1794	+	22.8274i	−0.701468	+	1.21498i	−0.967951	+	0.251139i	$0.919195\pi$
$354$	−3.14921	−	7.24963i	−0.167378	−	0.385313i
$355$	−1.94261	+	1.02761i	−0.103103	+	0.0545398i
$356$	−8.46161	+	4.88531i	−0.448464	+	0.258921i
$357$	−0.202481	+	1.77163i	−0.0107164	+	0.0937645i
$358$	−7.40773	+	12.8306i	−0.391510	+	0.678116i
$359$	−26.1817			−1.38182			−0.690908	−	0.722943i	$-0.742789\pi$
$359$	−26.1817			−1.38182			−0.690908	+	0.722943i	$0.742789\pi$
$360$	1.75453	−	6.47469i	0.0924718	−	0.341246i
$361$	7.28886			0.383624
$362$	−6.67620	−	3.85450i	−0.350893	−	0.202588i
$363$	−3.71744	+	18.6864i	−0.195115	+	0.980780i
$364$	−0.994121	−	1.72187i	−0.0521061	−	0.0902504i
$365$	11.3832	+	21.5190i	0.595824	+	1.12636i
$366$	−6.07575	+	8.20489i	−0.317585	+	0.428877i
$367$	21.5842	+	12.4617i	1.12669	+	0.650493i	0.943100	−	0.332510i	$-0.107896\pi$
$367$	21.5842	+	12.4617i	1.12669	+	0.650493i	0.183588	+	0.983003i	$0.441229\pi$
$368$	5.94409			0.309857
$369$	12.2099	+	2.82789i	0.635621	+	0.147214i
$370$	−16.6847	−	0.618177i	−0.867394	−	0.0321375i
$371$	−1.54979	+	2.68431i	−0.0804609	+	0.139362i
$372$	0.208062	+	0.0237796i	0.0107875	+	0.00123291i
$373$	6.07758	+	10.5267i	0.314685	+	0.545051i	0.979371	−	0.202073i	$-0.0647677\pi$
$373$	6.07758	+	10.5267i	0.314685	+	0.545051i	−0.664685	+	0.747123i	$0.731434\pi$
$374$	1.15781	+	1.25760i	0.0598691	+	0.0650289i
$375$	−5.69868	−	18.5074i	−0.294279	−	0.955720i
$376$	0.828036	+	0.478067i	0.0427027	+	0.0246544i
$377$	−4.37486			−0.225317
$378$	−10.2073	+	1.88072i	−0.525009	+	0.0967336i
$379$	30.8256			1.58340			0.791701	−	0.610909i	$-0.209196\pi$
$379$	30.8256			1.58340			0.791701	+	0.610909i	$0.209196\pi$
$380$	−6.48077	−	4.06883i	−0.332456	−	0.208726i
$381$	−13.8528	−	31.8898i	−0.709699	−	1.63376i
$382$	−1.82651	−	3.16360i	−0.0934523	−	0.161864i
$383$	7.87038	+	13.6319i	0.402158	+	0.696558i	0.993986	−	0.109506i	$-0.0349270\pi$
$383$	7.87038	+	13.6319i	0.402158	+	0.696558i	−0.591828	+	0.806064i	$0.701594\pi$
$384$	0.196677	−	1.72085i	0.0100366	−	0.0878167i
$385$	−4.94185	+	13.9650i	−0.251860	+	0.711723i
$386$			18.5230i			0.942795i
$387$	0.143314	+	0.469938i	0.00728508	+	0.0238883i
$388$		−	0.264914i		−	0.0134490i
$389$	−18.9123	−	10.9190i	−0.958892	−	0.553617i	−0.0630604	−	0.998010i	$-0.520086\pi$
$389$	−18.9123	−	10.9190i	−0.958892	−	0.553617i	−0.895832	+	0.444393i	$0.853419\pi$
$390$	−3.01107	−	2.40732i	−0.152472	−	0.121899i
$391$	−2.65318	+	1.53181i	−0.134177	+	0.0774672i
$392$	2.60684	−	1.50506i	0.131665	−	0.0760170i
$393$	−9.86701	+	13.3247i	−0.497725	+	0.672144i
$394$	−4.31662	+	7.47661i	−0.217468	+	0.376666i
$395$	0.661242	−	17.8470i	0.0332707	−	0.897978i
$396$	−5.03585	+	8.58139i	−0.253061	+	0.431231i
$397$			19.6033i			0.983860i	0.870635	+	0.491930i	$0.163709\pi$
$397$			19.6033i			0.983860i	−0.870635	+	0.491930i	$0.836291\pi$
$398$	−20.3036	−	11.7223i	−1.01773	−	0.587586i
$399$	−1.34441	+	11.7631i	−0.0673049	+	0.588892i
$400$	−2.17272	−	4.50325i	−0.108636	−	0.225163i
$401$	−19.1726	+	11.0693i	−0.957436	+	0.552776i	−0.895383	−	0.445297i	$-0.853098\pi$
$401$	−19.1726	+	11.0693i	−0.957436	+	0.552776i	−0.0620529	+	0.998073i	$0.519765\pi$
$402$	−0.789212	−	1.81680i	−0.0393623	−	0.0906139i
$403$	0.0601741	−	0.104225i	0.00299749	−	0.00519180i
$404$	−12.0785			−0.600927
$405$	−17.1042	+	10.6041i	−0.849913	+	0.526923i
$406$			8.77918i			0.435704i
$407$	23.6356	+	7.39138i	1.17157	+	0.366377i
$408$	0.355681	+	0.818794i	0.0176088	+	0.0405364i
$409$	−1.35178	+	0.780450i	−0.0668412	+	0.0385908i	−0.533048	−	0.846085i	$-0.678954\pi$
$409$	−1.35178	+	0.780450i	−0.0668412	+	0.0385908i	0.466207	+	0.884676i	$0.345620\pi$
$410$	8.25746	−	4.36806i	0.407807	−	0.215723i
$411$	−18.5645	−	2.12175i	−0.915719	−	0.104658i
$412$	−16.2386	−	9.37534i	−0.800017	−	0.461890i
$413$			9.11530i			0.448535i
$414$	−13.0332	−	12.1707i	−0.640546	−	0.598159i
$415$	1.05065	−	28.3571i	0.0515743	−	1.39200i
$416$	−0.862025	−	0.497691i	−0.0422643	−	0.0244013i
$417$	−16.9421	−	12.5457i	−0.829660	−	0.614366i
$418$	7.68755	+	8.35010i	0.376010	+	0.408417i
$419$	−21.2005	+	12.2401i	−1.03571	+	0.597969i	−0.918616	−	0.395152i	$-0.870692\pi$
$419$	−21.2005	+	12.2401i	−1.03571	+	0.597969i	−0.117096	+	0.993121i	$0.537359\pi$
$420$	−4.83086	+	6.04243i	−0.235722	+	0.294840i
$421$	−9.90930	+	17.1634i	−0.482950	+	0.836493i	−0.999808	−	0.0195776i	$-0.993768\pi$
$421$	−9.90930	+	17.1634i	−0.482950	+	0.836493i	0.516859	+	0.856071i	$0.327101\pi$
$422$	−17.8801			−0.870389
$423$	−0.836716	−	2.74365i	−0.0406825	−	0.133401i
$424$			1.55175i			0.0753597i
$425$	2.13031	+	1.45014i	0.103335	+	0.0703419i
$426$	1.69129	+	0.193299i	0.0819432	+	0.00936535i
$427$	10.1966	−	5.88703i	0.493450	−	0.284893i
$428$	−0.456473	+	0.263545i	−0.0220645	+	0.0127389i
$429$	3.37019	+	4.61927i	0.162714	+	0.223021i
$430$	0.310140	+	0.194715i	0.0149563	+	0.00939000i
$431$	−23.0695			−1.11122			−0.555610	−	0.831443i	$-0.687515\pi$
$431$	−23.0695			−1.11122			−0.555610	+	0.831443i	$0.687515\pi$
$432$	−3.95473	+	3.37047i	−0.190272	+	0.162162i
$433$		−	26.8092i		−	1.28837i	−0.764870	−	0.644185i	$-0.777197\pi$
$433$		−	26.8092i		−	1.28837i	0.764870	−	0.644185i	$-0.222803\pi$
$434$	−0.209151	−	0.120754i	−0.0100396	−	0.00579636i
$435$	6.19946	+	15.8533i	0.297241	+	0.760108i
$436$	3.04643	−	1.75886i	0.145897	−	0.0842339i
$437$	−17.6164	+	10.1708i	−0.842705	+	0.486536i
$438$	2.14124	−	18.7350i	0.102312	−	0.895194i
$439$	6.59459	+	3.80739i	0.314742	+	0.181717i	0.649047	−	0.760749i	$-0.275168\pi$
$439$	6.59459	+	3.80739i	0.314742	+	0.181717i	−0.334304	+	0.942465i	$0.608501\pi$
$440$	1.35308	+	7.29172i	0.0645055	+	0.347619i
$441$	−8.79749	−	2.03756i	−0.418928	−	0.0970266i
$442$	0.513026			0.0244022
$443$	−5.24925	+	9.09197i	−0.249399	+	0.431973i	−0.963359	−	0.268214i	$-0.913567\pi$
$443$	−5.24925	+	9.09197i	−0.249399	+	0.431973i	0.713960	+	0.700187i	$0.246900\pi$
$444$	10.3934	+	7.69634i	0.493248	+	0.365252i
$445$	19.3122	−	10.2159i	0.915487	−	0.484278i
$446$	8.08949	+	14.0114i	0.383049	+	0.663460i
$447$	11.6375	−	15.7156i	0.550435	−	0.743324i
$448$	−0.998734	+	1.72986i	−0.0471857	+	0.0817281i
$449$			1.90268i			0.0897930i	0.998992	+	0.0448965i	$0.0142958\pi$
$449$			1.90268i			0.0897930i	−0.998992	+	0.0448965i	$0.985704\pi$
$450$	−4.45660	+	14.3227i	−0.210086	+	0.675177i
$451$	−13.5203	+	3.03066i	−0.636648	+	0.142708i
$452$	8.86031	−	15.3465i	0.416754	−	0.721839i
$453$	−2.21652	+	19.3937i	−0.104141	+	0.911196i
$454$	−11.6247	−	20.1345i	−0.545572	−	0.944958i
$455$	2.07884	+	3.92988i	0.0974577	+	0.184236i
$456$	2.36162	+	5.43656i	0.110593	+	0.254590i
$457$	−0.864576	+	1.49749i	−0.0404432	+	0.0700496i	−0.885538	−	0.464566i	$-0.846210\pi$
$457$	−0.864576	+	1.49749i	−0.0404432	+	0.0700496i	0.845095	+	0.534616i	$0.179544\pi$
$458$			21.9260i			1.02454i
$459$	0.896633	−	2.52358i	0.0418513	−	0.117791i
$460$	−13.2823	−	0.492117i	−0.619290	−	0.0229451i
$461$	8.06351	−	13.9664i	0.375555	−	0.650480i	−0.614855	−	0.788640i	$-0.710785\pi$
$461$	8.06351	−	13.9664i	0.375555	−	0.650480i	0.990410	+	0.138160i	$0.0441188\pi$
$462$	9.26966	−	6.76309i	0.431264	−	0.314647i
$463$	−3.94517	+	2.27775i	−0.183348	+	0.105856i	−0.588865	−	0.808232i	$-0.700425\pi$
$463$	−3.94517	+	2.27775i	−0.183348	+	0.105856i	0.405517	+	0.914088i	$0.367092\pi$
$464$	2.19758	+	3.80632i	0.102020	+	0.176704i
$465$	−0.462953	−	0.0703619i	−0.0214689	−	0.00326296i
$466$	−15.2104	+	26.3452i	−0.704610	+	1.22042i
$467$	−14.0697			−0.651067			−0.325533	−	0.945531i	$-0.605544\pi$
$467$	−14.0697			−0.651067			−0.325533	+	0.945531i	$0.605544\pi$
$468$	0.871062	+	2.85627i	0.0402648	+	0.132031i
$469$			2.28435i			0.105482i
$470$	−1.81070	−	1.13681i	−0.0835211	−	0.0524372i
$471$	8.79032	+	6.50926i	0.405036	+	0.299931i
$472$	2.28171	+	3.95204i	0.105024	+	0.181908i
$473$	−0.367891	−	0.399597i	−0.0169156	−	0.0183735i
$474$	−8.23249	+	11.1174i	−0.378131	+	0.510640i
$475$	14.1446	+	9.62849i	0.649001	+	0.441785i
$476$		−	1.02951i		−	0.0471875i
$477$	3.17726	−	3.40241i	0.145477	−	0.155786i
$478$			16.4168i			0.750887i
$479$	−11.5252	+	19.9622i	−0.526598	+	0.912095i	0.472922	+	0.881104i	$0.343199\pi$
$479$	−11.5252	+	19.9622i	−0.526598	+	0.912095i	−0.999520	+	0.0309901i	$0.990134\pi$
$480$	−0.581952	+	3.82901i	−0.0265624	+	0.174770i
$481$	6.43651	−	3.71612i	0.293479	−	0.169440i
$482$	14.3466	+	24.8491i	0.653471	+	1.13185i
$483$	8.19362	+	18.8621i	0.372822	+	0.858256i
$484$	0.907321	−	10.9625i	0.0412419	−	0.498296i
$485$	−0.0219325	+	0.591959i	−0.000995903	+	0.0268795i
$486$	15.5724	+	0.707254i	0.706379	+	0.0320817i
$487$		−	33.6486i		−	1.52476i	−0.647127	−	0.762382i	$-0.724030\pi$
$487$		−	33.6486i		−	1.52476i	0.647127	−	0.762382i	$-0.275970\pi$
$488$	2.94725	−	5.10478i	0.133416	−	0.231082i
$489$	9.19512	−	3.99432i	0.415818	−	0.180629i
$490$	−5.94968	+	3.14729i	−0.268779	+	0.142180i
$491$	−11.5903	−	20.0750i	−0.523063	−	0.905972i	−0.999640	−	0.0268390i	$-0.991456\pi$
$491$	−11.5903	−	20.0750i	−0.523063	−	0.905972i	0.476577	−	0.879133i	$-0.341877\pi$
$492$	−7.18918	−	0.821656i	−0.324113	−	0.0370431i
$493$	−1.96180	−	1.13265i	−0.0883551	−	0.0510118i
$494$	3.40635			0.153259
$495$	11.9632	−	18.7585i	0.537708	−	0.843131i
$496$	−0.120907			−0.00542887
$497$	−1.70014	−	0.981578i	−0.0762619	−	0.0440298i
$498$	−13.0806	+	17.6645i	−0.586157	+	0.791565i
$499$	−16.1278	−	27.9342i	−0.721980	−	1.25051i	−0.960205	−	0.279296i	$-0.909899\pi$
$499$	−16.1278	−	27.9342i	−0.721980	−	1.25051i	0.238225	−	0.971210i	$-0.423434\pi$
$500$	4.48218	+	10.2426i	0.200449	+	0.458061i
$501$	21.8343	+	16.1684i	0.975485	+	0.722350i
$502$	1.27257	−	2.20416i	0.0567978	−	0.0983766i
$503$		−	5.35769i		−	0.238887i	−0.992841	−	0.119444i	$-0.961889\pi$
$503$		−	5.35769i		−	0.238887i	0.992841	−	0.119444i	$-0.0381111\pi$
$504$	5.73179	−	1.74799i	0.255314	−	0.0778617i
$505$	26.9898	+	0.999989i	1.20103	+	0.0444989i
$506$	18.8157	+	5.88412i	0.836462	+	0.261581i
$507$	−20.6660	−	2.36194i	−0.917811	−	0.104897i
$508$	10.0368	+	17.3843i	0.445313	+	0.771304i
$509$	−20.0871	+	11.5973i	−0.890344	+	0.514041i	−0.874055	−	0.485827i	$-0.838519\pi$
$509$	−20.0871	+	11.5973i	−0.890344	+	0.514041i	−0.0162893	+	0.999867i	$0.505185\pi$
$510$	−0.726992	−	1.85907i	−0.0321917	−	0.0823211i
$511$	−10.8733	+	18.8331i	−0.481007	+	0.833128i
$512$			1.00000i			0.0441942i
$513$	5.95339	−	16.7558i	0.262849	−	0.739788i
$514$		−	14.0628i		−	0.620285i
$515$	35.5094	+	22.2939i	1.56473	+	0.982388i
$516$	−0.113016	−	0.260169i	−0.00497526	−	0.0114533i
$517$	2.14786	+	2.33298i	0.0944629	+	0.102604i
$518$	−7.45727	−	12.9164i	−0.327654	−	0.567513i
$519$	−2.10300	+	18.4004i	−0.0923113	+	0.807689i
$520$	1.88502	+	1.18347i	0.0826637	+	0.0518988i
$521$			23.2950i			1.02057i	0.860004	+	0.510287i	$0.170461\pi$
$521$			23.2950i			1.02057i	−0.860004	+	0.510287i	$0.829539\pi$
$522$	2.97509	−	12.8454i	0.130216	−	0.562230i
$523$	−17.1488			−0.749865			−0.374933	−	0.927052i	$-0.622334\pi$
$523$	−17.1488			−0.749865			−0.374933	+	0.927052i	$0.622334\pi$
$524$	4.78632	−	8.29015i	0.209091	−	0.362157i
$525$	11.2950	−	13.1021i	0.492953	−	0.571821i
$526$	−5.45111	−	9.44160i	−0.237680	−	0.411673i
$527$	0.0539674	−	0.0311581i	0.00235086	−	0.00135727i
$528$	2.32606	−	5.25257i	0.101229	−	0.228589i
$529$	−6.16613	+	10.6801i	−0.268093	+	0.464350i
$530$	0.128471	−	3.46744i	0.00558042	−	0.150616i
$531$	3.08900	−	13.3372i	0.134051	−	0.578787i
$532$		−	6.83565i		−	0.296363i
$533$	−2.07920	+	3.60128i	−0.0900601	+	0.155989i
$534$	−16.8138	−	1.92166i	−0.727603	−	0.0831582i
$535$	1.04182	−	0.551109i	0.0450420	−	0.0238265i
$536$	0.571812	+	0.990408i	0.0246985	+	0.0427791i
$537$	−23.5364	+	10.2241i	−1.01567	+	0.441202i
$538$	−7.59113	+	13.1482i	−0.327277	+	0.566860i
$539$	9.74170	−	2.18366i	0.419605	−	0.0940568i
$540$	9.11603	−	7.20403i	0.392292	−	0.310012i
$541$			12.2154i			0.525179i	0.964908	+	0.262590i	$0.0845766\pi$
$541$			12.2154i			0.525179i	−0.964908	+	0.262590i	$0.915423\pi$
$542$	−14.3195	+	24.8022i	−0.615077	+	1.06534i
$543$	−5.31996	−	12.2468i	−0.228301	−	0.525561i
$544$	−0.257703	−	0.446355i	−0.0110489	−	0.0191373i
$545$	−6.95297	+	3.67801i	−0.297832	+	0.157549i
$546$	0.391041	−	3.42146i	0.0167350	−	0.146425i
$547$	13.9579	−	24.1758i	0.596798	−	1.03368i	−0.396493	−	0.918038i	$-0.629773\pi$
$547$	13.9579	−	24.1758i	0.596798	−	1.03368i	0.993291	−	0.115646i	$-0.0368938\pi$
$548$	10.7880			0.460840
$549$	−16.9144	+	5.15829i	−0.721889	+	0.220150i
$550$	−2.41981	−	16.4056i	−0.103181	−	0.699538i
$551$	−13.0258	−	7.52045i	−0.554918	−	0.320382i
$552$	8.27394	+	6.12688i	0.352162	+	0.260777i
$553$	13.8162	−	7.97677i	0.587523	−	0.339207i
$554$	1.87377	−	1.08182i	0.0796088	−	0.0459621i
$555$	−22.5872	−	18.0582i	−0.958773	−	0.766528i
$556$	10.5408	+	6.08571i	0.447028	+	0.258092i
$557$			36.6139i			1.55138i	0.631114	+	0.775690i	$0.282598\pi$
$557$			36.6139i			1.55138i	−0.631114	+	0.775690i	$0.717402\pi$
$558$	0.265103	+	0.247560i	0.0112227	+	0.0104801i
$559$	−0.163012			−0.00689468
$560$	2.37492	−	3.78274i	0.100359	−	0.159850i
$561$	0.315357	+	2.94394i	0.0133144	+	0.124293i
$562$	16.5247	−	9.54055i	0.697053	−	0.402444i
$563$	33.3191	−	19.2368i	1.40423	−	0.810733i	0.409407	−	0.912352i	$-0.365735\pi$
$563$	33.3191	−	19.2368i	1.40423	−	0.810733i	0.994823	+	0.101619i	$0.0324021\pi$
$564$	0.659825	+	1.51895i	0.0277836	+	0.0639593i
$565$	−21.0692	+	33.5587i	−0.886389	+	1.41183i
$566$		−	0.391770i		−	0.0164673i
$567$	−16.1467	−	7.90334i	−0.678100	−	0.331909i
$568$	−0.982823			−0.0412383
$569$	9.59980	−	16.6273i	0.402445	−	0.697054i	−0.591576	−	0.806249i	$-0.701494\pi$
$569$	9.59980	−	16.6273i	0.402445	−	0.697054i	0.994020	+	0.109195i	$0.0348273\pi$
$570$	−4.82702	−	12.3437i	−0.202182	−	0.517021i
$571$	13.7386	−	7.93199i	0.574943	−	0.331944i	−0.184178	−	0.982893i	$-0.558962\pi$
$571$	13.7386	−	7.93199i	0.574943	−	0.331944i	0.759121	+	0.650949i	$0.225629\pi$
$572$	−2.23603	−	2.42874i	−0.0934931	−	0.101551i
$573$	0.718464	−	6.28628i	0.0300143	−	0.262613i
$574$	7.22682	+	4.17241i	0.301642	+	0.174153i
$575$	29.6390	+	2.19931i	1.23603	+	0.0917174i
$576$	2.04753	−	2.19263i	0.0853139	−	0.0913594i
$577$		−	20.2759i		−	0.844097i	−0.906573	−	0.422048i	$-0.861311\pi$
$577$		−	20.2759i		−	0.844097i	0.906573	−	0.422048i	$-0.138689\pi$
$578$	−14.4924	−	8.36718i	−0.602803	−	0.348029i
$579$	−19.0926	+	25.7833i	−0.793461	+	1.07152i
$580$	−4.59544	−	8.68729i	−0.190815	−	0.360720i
$581$	21.9526	−	12.6743i	0.910746	−	0.525819i
$582$	0.273060	−	0.368750i	0.0113187	−	0.0152852i
$583$	−1.53609	+	4.91199i	−0.0636185	+	0.203434i
$584$			10.8871i			0.450511i
$585$	−1.70994	−	6.45456i	−0.0706975	−	0.266863i
$586$	−8.32848			−0.344046
$587$	−8.05120	+	13.9451i	−0.332309	+	0.575575i	−0.982964	−	0.183798i	$-0.941161\pi$
$587$	−8.05120	+	13.9451i	−0.332309	+	0.575575i	0.650655	+	0.759373i	$0.274494\pi$
$588$	5.17996	+	0.592021i	0.213618	+	0.0244146i
$589$	0.358328	−	0.206881i	0.0147646	−	0.00852437i
$590$	−4.77138	−	9.01989i	−0.196434	−	0.371343i
$591$	−13.7151	+	5.95778i	−0.564164	+	0.245070i
$592$	−6.46637	−	3.73336i	−0.265766	−	0.153440i
$593$		−	18.6944i		−	0.767685i	−0.923399	−	0.383843i	$-0.874601\pi$
$593$		−	18.6944i		−	0.767685i	0.923399	−	0.383843i	$-0.125399\pi$
$594$	−15.8550	+	6.75424i	−0.650537	+	0.277130i
$595$	−0.0852340	+	2.30047i	−0.00349426	+	0.0943102i
$596$	−5.64515	+	9.77769i	−0.231234	+	0.400510i
$597$	−16.1791	−	37.2450i	−0.662165	−	1.52434i
$598$	5.12396	−	2.95832i	0.209534	−	0.120975i
$599$	−31.6112	+	18.2508i	−1.29160	+	0.745706i	−0.978938	−	0.204158i	$-0.934554\pi$
$599$	−31.6112	+	18.2508i	−1.29160	+	0.745706i	−0.312663	+	0.949864i	$0.601221\pi$
$600$	1.61740	−	8.50788i	0.0660301	−	0.347333i
$601$	−37.9146	−	21.8900i	−1.54657	−	0.892911i	−0.998400	−	0.0565419i	$-0.981993\pi$
$601$	−37.9146	−	21.8900i	−1.54657	−	0.892911i	−0.548167	−	0.836369i	$-0.684674\pi$
$602$			0.327122i			0.0133325i
$603$	0.774122	−	3.34240i	0.0315247	−	0.136113i
$604$		−	11.2699i		−	0.458564i
$605$	−2.93504	+	24.4210i	−0.119326	+	0.992855i
$606$	−16.8128	−	12.4499i	−0.682971	−	0.505743i
$607$	20.6217	+	35.7178i	0.837007	+	1.44974i	0.892385	+	0.451274i	$0.149030\pi$
$607$	20.6217	+	35.7178i	0.837007	+	1.44974i	−0.0553779	+	0.998465i	$0.517636\pi$
$608$	−1.71108	−	2.96367i	−0.0693934	−	0.120193i
$609$	−9.04916	+	12.2203i	−0.366690	+	0.495190i
$610$	−7.00835	+	11.1628i	−0.283760	+	0.451969i
$611$	0.951717			0.0385024
$612$	−0.348880	+	1.50635i	−0.0141026	+	0.0608905i
$613$	−12.8254			−0.518014			−0.259007	−	0.965875i	$-0.583395\pi$
$613$	−12.8254			−0.518014			−0.259007	+	0.965875i	$0.583395\pi$
$614$	−15.5727	−	8.99091i	−0.628464	−	0.362844i
$615$	15.9964	+	2.43122i	0.645039	+	0.0980362i
$616$	−4.87385	+	4.48712i	−0.196373	+	0.180791i
$617$	16.8244	+	29.1408i	0.677326	+	1.17316i	0.975783	+	0.218740i	$0.0701947\pi$
$617$	16.8244	+	29.1408i	0.677326	+	1.17316i	−0.298457	+	0.954423i	$0.596472\pi$
$618$	−12.9398	−	29.7880i	−0.520514	−	1.19825i
$619$	2.43442	−	4.21653i	0.0978475	−	0.169477i	−0.812946	−	0.582339i	$-0.802138\pi$
$619$	2.43442	−	4.21653i	0.0978475	−	0.169477i	0.910793	+	0.412862i	$0.135471\pi$
$620$	0.270170	+	0.0100100i	0.0108503	+	0.000402011i
$621$	−5.59666	−	30.3751i	−0.224586	−	1.21891i
$622$	−19.5206			−0.782705
$623$	16.9018	+	9.75826i	0.677156	+	0.390956i
$624$	−0.686909	−	1.58130i	−0.0274984	−	0.0633026i
$625$	−9.16760	−	23.2584i	−0.366704	−	0.930338i
$626$	−4.33048	−	7.50061i	−0.173081	−	0.299785i
$627$	2.09388	+	19.5470i	0.0836216	+	0.780630i
$628$	−5.46901	−	3.15753i	−0.218237	−	0.125999i
$629$	3.84840			0.153446
$630$	−12.9526	+	3.43141i	−0.516044	+	0.136711i
$631$	9.56679			0.380848			0.190424	−	0.981702i	$-0.439014\pi$
$631$	9.56679			0.380848			0.190424	+	0.981702i	$0.439014\pi$
$632$	3.99344	−	6.91684i	0.158851	−	0.275137i
$633$	−24.8884	−	18.4299i	−0.989224	−	0.732524i
$634$	−14.1927	+	8.19418i	−0.563666	+	0.325433i
$635$	−20.9884	−	39.6768i	−0.832899	−	1.57453i
$636$	−1.59947	+	2.15998i	−0.0634231	+	0.0856486i
$637$	1.49811	−	2.59480i	0.0593572	−	0.102810i
$638$	3.18841	+	14.2241i	0.126231	+	0.563138i
$639$	2.15496	+	2.01236i	0.0852490	+	0.0796078i
$640$	0.0827910	−	2.23453i	0.00327260	−	0.0883277i
$641$	24.2159	+	13.9810i	0.956469	+	0.552218i	0.895085	−	0.445896i	$-0.147115\pi$
$641$	24.2159	+	13.9810i	0.956469	+	0.552218i	0.0613847	+	0.998114i	$0.480448\pi$
$642$	−0.907042	−	0.103666i	−0.0357981	−	0.00409139i
$643$	29.4695	−	17.0142i	1.16216	−	0.670976i	0.210342	−	0.977628i	$-0.432542\pi$
$643$	29.4695	−	17.0142i	1.16216	−	0.670976i	0.951822	+	0.306652i	$0.0992088\pi$
$644$	−5.93657	−	10.2824i	−0.233934	−	0.405185i
$645$	0.230999	+	0.590713i	0.00909557	+	0.0232593i
$646$	1.52750	+	0.881901i	0.0600986	+	0.0346979i
$647$	−12.5526			−0.493492			−0.246746	−	0.969080i	$-0.579361\pi$
$647$	−12.5526			−0.493492			−0.246746	+	0.969080i	$0.579361\pi$
$648$	−8.97895	+	0.615219i	−0.352726	+	0.0241681i
$649$	3.31049	+	14.7687i	0.129948	+	0.579722i
$650$	−4.11416	−	2.80058i	−0.161371	−	0.109848i
$651$	−0.166663	−	0.383667i	−0.00653205	−	0.0150371i
$652$	−5.01260	+	2.89403i	−0.196309	+	0.113339i
$653$	13.5954	+	23.5479i	0.532028	+	0.921500i	0.999301	+	0.0373864i	$0.0119032\pi$
$653$	13.5954	+	23.5479i	0.532028	+	0.921500i	−0.467273	+	0.884113i	$0.654763\pi$
$654$	6.05345	+	0.691853i	0.236709	+	0.0270536i
$655$	−11.3815	+	18.1284i	−0.444714	+	0.708334i
$656$	4.17769			0.163112
$657$	22.2917	−	23.8713i	0.869681	−	0.931309i
$658$		−	1.90985i		−	0.0744535i
$659$	2.19251	−	3.79753i	0.0854079	−	0.147931i	−0.820157	−	0.572138i	$-0.806114\pi$
$659$	2.19251	−	3.79753i	0.0854079	−	0.147931i	0.905565	+	0.424208i	$0.139447\pi$
$660$	−5.63252	+	11.5445i	−0.219245	+	0.449368i
$661$	7.51802	+	13.0216i	0.292417	+	0.506481i	0.974381	−	0.224905i	$-0.0722072\pi$
$661$	7.51802	+	13.0216i	0.292417	+	0.506481i	−0.681964	+	0.731386i	$0.738874\pi$
$662$	11.0588	−	6.38478i	0.429811	−	0.248151i
$663$	0.714112	+	0.528803i	0.0277338	+	0.0205370i
$664$	6.34519	−	10.9902i	0.246241	−	0.426502i
$665$	−0.565930	+	15.2745i	−0.0219458	+	0.592319i
$666$	6.53416	+	21.4260i	0.253193	+	0.830240i
$667$	−26.1252			−1.01157
$668$	−13.5845	−	7.84301i	−0.525600	−	0.303455i
$669$	−3.18203	+	27.8416i	−0.123025	+	1.07642i
$670$	−1.19574	−	2.26044i	−0.0461954	−	0.0873285i
$671$	14.3826	−	13.2414i	0.555235	−	0.511179i
$672$	−3.17325	+	1.37845i	−0.122411	+	0.0531747i
$673$	20.5025	−	35.5113i	0.790312	−	1.36886i	−0.135462	−	0.990783i	$-0.543252\pi$
$673$	20.5025	−	35.5113i	0.790312	−	1.36886i	0.925774	−	0.378078i	$-0.123415\pi$
$674$			10.0223i			0.386045i
$675$	−20.9665	+	15.3429i	−0.807002	+	0.590549i
$676$	12.0092			0.461893
$677$	−7.56817	−	4.36948i	−0.290868	−	0.167933i	0.347465	−	0.937693i	$-0.387043\pi$
$677$	−7.56817	−	4.36948i	−0.290868	−	0.167933i	−0.638333	+	0.769760i	$0.720376\pi$
$678$	28.1516	−	12.2289i	1.08116	−	0.469650i
$679$	−0.458264	+	0.264579i	−0.0175865	+	0.0101536i
$680$	0.538893	+	1.01873i	0.0206656	+	0.0390666i
$681$	4.57260	−	40.0085i	0.175222	−	1.53313i
$682$	−0.382724	−	0.119687i	−0.0146553	−	0.00458304i
$683$	45.4630			1.73959			0.869797	−	0.493410i	$-0.164250\pi$
$683$	45.4630			1.73959			0.869797	+	0.493410i	$0.164250\pi$
$684$	−2.31646	+	10.0017i	−0.0885722	+	0.382425i
$685$	−24.1061	−	0.893148i	−0.921048	−	0.0341254i
$686$	−17.3161	−	9.99745i	−0.661131	−	0.381704i
$687$	−22.6003	+	30.5201i	−0.862254	+	1.16442i
$688$	0.0818843	+	0.141828i	0.00312181	+	0.00540713i
$689$	0.772292	+	1.33765i	0.0294220	+	0.0509604i
$690$	−17.9812	−	14.3757i	−0.684531	−	0.547275i
$691$	−3.21912	+	5.57568i	−0.122461	+	0.212109i	−0.920738	−	0.390182i	$-0.872412\pi$
$691$	−3.21912	+	5.57568i	−0.122461	+	0.212109i	0.798277	+	0.602291i	$0.205745\pi$
$692$		−	10.6926i		−	0.406473i
$693$	19.8741	+	0.140776i	0.754953	+	0.00534764i
$694$	17.8531			0.677696
$695$	−23.0499	−	14.4714i	−0.874331	−	0.548932i
$696$	−0.864426	+	7.56340i	−0.0327660	+	0.286690i
$697$	−1.86474	+	1.07661i	−0.0706319	+	0.0407794i
$698$	12.7630	+	22.1062i	0.483087	+	0.836731i
$699$	−48.3277	+	20.9933i	−1.82792	+	0.794041i
$700$	−5.62002	+	8.25605i	−0.212417	+	0.312049i
$701$	45.5913			1.72196			0.860979	−	0.508640i	$-0.169852\pi$
$701$	45.5913			1.72196			0.860979	+	0.508640i	$0.169852\pi$
$702$	−1.73163	+	4.87367i	−0.0653560	+	0.183945i
$703$	25.5523			0.963723
$704$	−0.989910	+	3.16545i	−0.0373086	+	0.119302i
$705$	−1.34865	−	3.44877i	−0.0507929	−	0.129888i
$706$	22.8274	−	13.1794i	0.859119	−	0.496013i
$707$	12.0632	+	20.8940i	0.453683	+	0.785802i
$708$	−0.897521	+	7.85297i	−0.0337309	+	0.295133i
$709$	17.7924	−	30.8173i	0.668207	−	1.15737i	−0.310198	−	0.950672i	$-0.600395\pi$
$709$	17.7924	−	30.8173i	0.668207	−	1.15737i	0.978405	−	0.206696i	$-0.0662712\pi$
$710$	2.19615	+	0.0813688i	0.0824201	+	0.00305372i
$711$	−22.9186	+	6.98935i	−0.859514	+	0.262121i
$712$	9.77063			0.366170
$713$	0.359340	−	0.622396i	0.0134574	−	0.0233089i
$714$	1.06117	−	1.43303i	0.0397132	−	0.0536300i
$715$	4.79541	+	5.61223i	0.179338	+	0.209886i
$716$	12.8306	−	7.40773i	0.479500	−	0.276840i
$717$	−16.9216	+	22.8515i	−0.631950	+	0.853406i
$718$	22.6740	+	13.0908i	0.846186	+	0.488546i
$719$		−	20.6731i		−	0.770977i	−0.922713	−	0.385489i	$-0.874033\pi$
$719$		−	20.6731i		−	0.770977i	0.922713	−	0.385489i	$-0.125967\pi$
$720$	−4.75681	+	4.72998i	−0.177276	+	0.176276i
$721$			37.4539i			1.39486i
$722$	−6.31233	−	3.64443i	−0.234921	−	0.135632i
$723$	−5.64331	+	49.3768i	−0.209877	+	1.83634i
$724$	3.85450	+	6.67620i	0.143252	+	0.248119i
$725$	9.54943	+	19.7925i	0.354657	+	0.735075i
$726$	12.5626	−	14.3242i	0.466241	−	0.531619i
$727$	28.1950	+	16.2784i	1.04569	+	0.603731i	0.921441	−	0.388519i	$-0.127013\pi$
$727$	28.1950	+	16.2784i	1.04569	+	0.603731i	0.124253	+	0.992251i	$0.460347\pi$
$728$			1.98824i			0.0736892i
$729$	20.9472	+	17.0357i	0.775821	+	0.630954i
$730$	0.901353	−	24.3276i	0.0333606	−	0.900404i
$731$	−0.0730990	−	0.0422037i	−0.00270366	−	0.00156096i
$732$	9.36420	−	4.06777i	0.346111	−	0.150349i
$733$	−24.9664	−	43.2432i	−0.922157	−	1.59722i	−0.796071	−	0.605203i	$-0.793092\pi$
$733$	−24.9664	−	43.2432i	−0.922157	−	1.59722i	−0.126086	−	0.992019i	$-0.540241\pi$
$734$	−12.4617	−	21.5842i	−0.459968	−	0.796688i
$735$	−11.5258	−	1.75175i	−0.425135	−	0.0646141i
$736$	−5.14774	−	2.97205i	−0.189748	−	0.109551i
$737$	0.829629	+	3.70113i	0.0305598	+	0.136333i
$738$	−9.16012	−	8.55397i	−0.337189	−	0.314876i
$739$			33.8069i			1.24361i	0.783174	+	0.621803i	$0.213599\pi$
$739$			33.8069i			1.24361i	−0.783174	+	0.621803i	$0.786401\pi$
$740$	14.1402	+	8.87769i	0.519806	+	0.326350i
$741$	4.74150	+	3.51110i	0.174183	+	0.128983i
$742$	2.68431	−	1.54979i	0.0985441	−	0.0568945i
$743$	−15.9525	+	9.21020i	−0.585242	+	0.337890i	−0.763214	−	0.646146i	$-0.776380\pi$
$743$	−15.9525	+	9.21020i	−0.585242	+	0.337890i	0.177972	+	0.984036i	$0.443046\pi$
$744$	−0.168297	−	0.124625i	−0.00617008	−	0.00456896i
$745$	13.4238	−	21.3812i	0.491810	−	0.783347i
$746$		−	12.1552i		−	0.445032i
$747$	−36.4154	+	11.1054i	−1.33237	+	0.406325i
$748$	−0.373896	−	1.66802i	−0.0136710	−	0.0609888i
$749$	0.911791	+	0.526423i	0.0333161	+	0.0192351i
$750$	−4.31851	+	18.8772i	−0.157690	+	0.689300i
$751$	−12.6964	−	21.9908i	−0.463298	−	0.802456i	0.535825	−	0.844329i	$-0.320001\pi$
$751$	−12.6964	−	21.9908i	−0.463298	−	0.802456i	−0.999123	+	0.0418731i	$0.986667\pi$
$752$	−0.478067	−	0.828036i	−0.0174333	−	0.0301954i
$753$	4.04332	−	1.75640i	0.147347	−	0.0640067i
$754$	3.78874	+	2.18743i	0.137978	+	0.0796614i
$755$	−0.933043	+	25.1829i	−0.0339569	+	0.916500i
$756$	9.78017	+	3.47492i	0.355701	+	0.126382i
$757$		−	10.7842i		−	0.391959i	−0.980608	−	0.195979i	$-0.937211\pi$
$757$		−	10.7842i		−	0.391959i	0.980608	−	0.195979i	$-0.0627886\pi$
$758$	−26.6957	−	15.4128i	−0.969632	−	0.559817i
$759$	20.1257	+	27.5848i	0.730516	+	1.00126i
$760$	3.57810	+	6.76409i	0.129791	+	0.245359i
$761$	9.92610	+	17.1925i	0.359821	+	0.623228i	0.987931	−	0.154897i	$-0.0495045\pi$
$761$	9.92610	+	17.1925i	0.359821	+	0.623228i	−0.628110	+	0.778125i	$0.716171\pi$
$762$	−3.94803	+	34.5437i	−0.143022	+	1.25139i
$763$	−6.08514	−	3.51326i	−0.220297	−	0.127189i
$764$			3.65302i			0.132161i
$765$	0.904297	−	3.33710i	0.0326949	−	0.120653i
$766$		−	15.7408i		−	0.568737i
$767$	3.93379	+	2.27118i	0.142041	+	0.0820074i
$768$	−1.03075	+	1.39196i	−0.0371940	+	0.0502280i
$769$	26.6153	−	15.3664i	0.959773	−	0.554125i	0.0636696	−	0.997971i	$-0.479720\pi$
$769$	26.6153	−	15.3664i	0.959773	−	0.554125i	0.896103	+	0.443846i	$0.146386\pi$
$770$	11.2623	−	9.62312i	0.405864	−	0.346793i
$771$	14.4953	−	19.5749i	0.522035	−	0.704973i
$772$	9.26150	−	16.0414i	0.333329	−	0.577342i
$773$	33.7838			1.21512			0.607560	−	0.794274i	$-0.292148\pi$
$773$	33.7838			1.21512			0.607560	+	0.794274i	$0.292148\pi$
$774$	0.110855	−	0.478636i	0.00398461	−	0.0172042i
$775$	−0.602876	−	0.0447353i	−0.0216559	−	0.00160694i
$776$	−0.132457	+	0.229422i	−0.00475493	+	0.00823578i
$777$	2.93335	−	25.6657i	0.105233	−	0.920751i
$778$	10.9190	+	18.9123i	0.391466	+	0.678039i
$779$	−12.3813	+	7.14836i	−0.443607	+	0.256117i
$780$	1.40401	+	3.59034i	0.0502715	+	0.128555i
$781$	−3.11108	−	0.972906i	−0.111323	−	0.0348133i
$782$	3.06363			0.109555
$783$	17.3817	−	14.8138i	0.621170	−	0.529401i
$784$	−3.01012			−0.107504
$785$	11.9593	+	7.50840i	0.426845	+	0.267986i
$786$	15.2074	−	6.60605i	0.542432	−	0.235630i
$787$	−14.1716	−	24.5459i	−0.505162	−	0.874966i	−0.999982	−	0.00597094i	$-0.998099\pi$
$787$	−14.1716	−	24.5459i	−0.505162	−	0.874966i	0.494820	−	0.868995i	$-0.335234\pi$
$788$	7.47661	−	4.31662i	0.266343	−	0.153773i
$789$	2.14422	−	18.7611i	0.0763361	−	0.667912i
$790$	−9.49613	+	15.1253i	−0.337857	+	0.538134i
$791$	−35.3964			−1.25855
$792$	8.65187	−	4.91378i	0.307431	−	0.174603i
$793$		−	5.86727i		−	0.208353i
$794$	9.80164	−	16.9769i	0.347847	−	0.602489i
$795$	3.75290	−	4.69412i	0.133102	−	0.166483i
$796$	11.7223	+	20.3036i	0.415486	+	0.719643i
$797$	9.37386	+	16.2360i	0.332039	+	0.575109i	0.982912	−	0.184078i	$-0.0589300\pi$
$797$	9.37386	+	16.2360i	0.332039	+	0.575109i	−0.650872	+	0.759187i	$0.725597\pi$
$798$	7.04585	−	9.51494i	0.249420	−	0.336825i
$799$	0.426775	+	0.246399i	0.0150982	+	0.00871697i
$800$	−0.369999	+	4.98629i	−0.0130814	+	0.176292i
$801$	−21.4233	−	20.0057i	−0.756956	−	0.706866i
$802$	22.1387			0.781743
$803$	−10.7772	+	34.4626i	−0.380321	+	1.21616i
$804$	−0.224925	+	1.96800i	−0.00793248	+	0.0694061i
$805$	12.4142	+	23.4680i	0.437542	+	0.827137i
$806$	−0.104225	+	0.0601741i	−0.00367116	+	0.00211954i
$807$	−24.1191	+	10.4772i	−0.849032	+	0.368816i
$808$	10.4603	+	6.03924i	0.367991	+	0.212460i
$809$	46.9291			1.64994			0.824970	−	0.565177i	$-0.191192\pi$
$809$	46.9291			1.64994			0.824970	+	0.565177i	$0.191192\pi$
$810$	20.1147	−	0.631352i	0.706759	−	0.0221834i
$811$			20.2237i			0.710151i	0.934838	+	0.355076i	$0.115545\pi$
$811$			20.2237i			0.710151i	−0.934838	+	0.355076i	$0.884455\pi$
$812$	4.38959	−	7.60300i	0.154044	−	0.266813i
$813$	−45.4971	+	19.7637i	−1.59565	+	0.693144i
$814$	−16.7733	−	18.2189i	−0.587904	−	0.638572i
$815$	11.4404	−	6.05181i	0.400741	−	0.211986i
$816$	0.101369	−	0.886937i	0.00354861	−	0.0310490i
$817$	−0.485356	−	0.280221i	−0.0169805	−	0.00980368i
$818$	1.56090			0.0545756
$819$	4.07099	−	4.35947i	0.142252	−	0.152332i
$820$	−9.33520	−	0.345875i	−0.325999	−	0.0120785i
$821$	10.2582	−	17.7678i	0.358014	−	0.620099i	−0.629615	−	0.776908i	$-0.716787\pi$
$821$	10.2582	−	17.7678i	0.358014	−	0.620099i	0.987629	+	0.156808i	$0.0501205\pi$
$822$	15.0164	+	11.1197i	0.523759	+	0.387845i
$823$	27.5503	−	15.9062i	0.960342	−	0.554454i	0.0640636	−	0.997946i	$-0.479594\pi$
$823$	27.5503	−	15.9062i	0.960342	−	0.554454i	0.896278	+	0.443492i	$0.146261\pi$
$824$	9.37534	+	16.2386i	0.326605	+	0.565697i
$825$	13.5418	−	25.3302i	0.471466	−	0.881884i
$826$	4.55765	−	7.89408i	0.158581	−	0.274670i
$827$		−	27.5608i		−	0.958383i	−0.877710	−	0.479191i	$-0.840930\pi$
$827$		−	27.5608i		−	0.958383i	0.877710	−	0.479191i	$-0.159070\pi$
$828$	5.20170	+	17.0568i	0.180772	+	0.592763i
$829$	19.3332			0.671471			0.335735	−	0.941956i	$-0.391015\pi$
$829$	19.3332			0.671471			0.335735	+	0.941956i	$0.391015\pi$
$830$	−15.0884	+	24.0326i	−0.523727	+	0.834185i
$831$	3.72330	+	0.425538i	0.129160	+	0.0147618i
$832$	0.497691	+	0.862025i	0.0172543	+	0.0298854i
$833$	1.34358	−	0.775719i	0.0465524	−	0.0268771i
$834$	8.39946	+	19.3360i	0.290849	+	0.669550i
$835$	29.7057	+	18.6502i	1.02801	+	0.645415i
$836$	−2.48256	−	11.0752i	−0.0858612	−	0.383043i
$837$	0.113840	+	0.617850i	0.00393488	+	0.0213560i
$838$	24.4802			0.845655
$839$	−34.5780	−	19.9636i	−1.19377	−	0.689221i	−0.234608	−	0.972090i	$-0.575381\pi$
$839$	−34.5780	−	19.9636i	−1.19377	−	0.689221i	−0.959159	+	0.282869i	$0.908714\pi$
$840$	7.20486	−	2.81747i	0.248591	−	0.0972119i
$841$	4.84130	+	8.38538i	0.166941	+	0.289151i
$842$	17.1634	−	9.90930i	0.591490	−	0.341497i
$843$	32.8357	+	3.75281i	1.13092	+	0.129254i
$844$	15.4846	+	8.94005i	0.533002	+	0.307729i
$845$	−26.8350	−	0.994255i	−0.923152	−	0.0342034i
$846$	−0.647209	+	2.79443i	−0.0222515	+	0.0960745i
$847$	−19.8698	+	9.37910i	−0.682733	+	0.322270i
$848$	0.775876	−	1.34386i	0.0266437	−	0.0461482i
$849$	0.403817	−	0.545328i	0.0138590	−	0.0187156i
$850$	−1.11983	−	2.32101i	−0.0384100	−	0.0796099i
$851$	38.4367	−	22.1915i	1.31759	−	0.760714i
$852$	−1.36805	−	1.01305i	−0.0468686	−	0.0347064i
$853$	−2.21498	+	3.83646i	−0.0758396	+	0.131358i	−0.901451	−	0.432881i	$-0.857497\pi$
$853$	−2.21498	+	3.83646i	−0.0758396	+	0.131358i	0.825611	+	0.564239i	$0.190830\pi$
$854$	−11.7741			−0.402900
$855$	6.00427	−	22.1574i	0.205342	−	0.757767i
$856$	0.527090			0.0180156
$857$	−41.6886	−	24.0690i	−1.42406	−	0.822180i	−0.427415	−	0.904056i	$-0.640576\pi$
$857$	−41.6886	−	24.0690i	−1.42406	−	0.822180i	−0.996643	+	0.0818759i	$0.973909\pi$
$858$	−0.609034	−	5.68550i	−0.0207921	−	0.194100i
$859$	13.5811	+	23.5231i	0.463380	+	0.802599i	0.999127	−	0.0417804i	$-0.0133030\pi$
$859$	13.5811	+	23.5231i	0.463380	+	0.802599i	−0.535746	+	0.844379i	$0.679970\pi$
$860$	−0.171231	−	0.323698i	−0.00583893	−	0.0110380i
$861$	5.75873	+	13.2569i	0.196257	+	0.451793i
$862$	19.9788	+	11.5348i	0.680480	+	0.392875i
$863$	−0.489737			−0.0166708			−0.00833542	−	0.999965i	$-0.502653\pi$
$863$	−0.489737			−0.0166708			−0.00833542	+	0.999965i	$0.502653\pi$
$864$	5.11014	−	0.941550i	0.173850	−	0.0320322i
$865$	−0.885255	+	23.8931i	−0.0300996	+	0.812389i
$866$	−13.4046	+	23.2175i	−0.455507	+	0.788962i
$867$	−11.5483	−	26.5848i	−0.392202	−	0.902868i
$868$	0.120754	+	0.209151i	0.00409865	+	0.00709906i
$869$	19.4881	−	17.9418i	0.661088	−	0.608633i
$870$	2.55777	−	16.8291i	0.0867165	−	0.570560i
$871$	0.985833	+	0.569171i	0.0334037	+	0.0192856i
$872$	−3.51771			−0.119125
$873$	0.760178	−	0.231827i	0.0257281	−	0.00784616i
$874$	20.3416			0.688065
$875$	13.2417	−	17.9831i	0.447650	−	0.607941i
$876$	−11.2219	+	15.1544i	−0.379152	+	0.512020i
$877$	25.1965	+	43.6416i	0.850825	+	1.47367i	0.880465	+	0.474111i	$0.157231\pi$
$877$	25.1965	+	43.6416i	0.850825	+	1.47367i	−0.0296401	+	0.999561i	$0.509436\pi$
$878$	−3.80739	−	6.59459i	−0.128493	−	0.222557i
$879$	−11.5929	−	8.58459i	−0.391019	−	0.289551i
$880$	2.47406	−	6.99135i	0.0834005	−	0.235679i
$881$		−	44.7551i		−	1.50784i	−0.656967	−	0.753919i	$-0.728161\pi$
$881$		−	44.7551i		−	1.50784i	0.656967	−	0.753919i	$-0.271839\pi$
$882$	6.60007	+	6.16332i	0.222236	+	0.207530i
$883$			9.73317i			0.327547i	0.986498	+	0.163774i	$0.0523667\pi$
$883$			9.73317i			0.327547i	−0.986498	+	0.163774i	$0.947633\pi$
$884$	−0.444294	−	0.256513i	−0.0149432	−	0.00862747i
$885$	2.65570	−	17.4734i	0.0892703	−	0.587363i
$886$	9.09197	−	5.24925i	0.305451	−	0.176352i
$887$	−42.4950	+	24.5345i	−1.42684	+	0.823788i	−0.996870	−	0.0790542i	$-0.974810\pi$
$887$	−42.4950	+	24.5345i	−1.42684	+	0.823788i	−0.429972	+	0.902842i	$0.641477\pi$
$888$	−5.15276	−	11.8619i	−0.172915	−	0.398060i
$889$	20.0483	−	34.7246i	0.672397	−	1.16463i
$890$	−21.8328	−	0.808920i	−0.731837	−	0.0271150i
$891$	−29.0314	−	6.94090i	−0.972589	−	0.232529i
$892$		−	16.1790i		−	0.541712i
$893$	2.83367	+	1.63602i	0.0948250	+	0.0547473i
$894$	−17.9362	+	7.79140i	−0.599876	+	0.260583i
$895$	−29.2836	+	15.4906i	−0.978843	+	0.517793i
$896$	1.72986	−	0.998734i	0.0577905	−	0.0333654i
$897$	10.1816	+	1.16367i	0.339955	+	0.0388537i
$898$	0.951340	−	1.64777i	0.0317466	−	0.0549868i
$899$	0.531404			0.0177233
$900$	11.0209	−	10.1755i	0.367362	−	0.339183i
$901$			0.799783i			0.0266446i
$902$	13.2243	+	4.13554i	0.440320	+	0.137698i
$903$	−0.337182	+	0.455341i	−0.0112207	+	0.0151528i
$904$	−15.3465	+	8.86031i	−0.510417	+	0.294689i
$905$	−8.06030	−	15.2373i	−0.267933	−	0.506505i
$906$	11.6164	−	15.6872i	0.385930	−	0.521172i
$907$	−25.5922	−	14.7757i	−0.849776	−	0.490618i	0.0107993	−	0.999942i	$-0.496562\pi$
$907$	−25.5922	−	14.7757i	−0.849776	−	0.490618i	−0.860575	+	0.509323i	$0.829896\pi$
$908$			23.2493i			0.771555i
$909$	−10.5699	−	34.6595i	−0.350582	−	1.14958i
$910$	0.164609	−	4.44280i	0.00545672	−	0.147277i
$911$	32.0646	+	18.5125i	1.06235	+	0.613346i	0.926081	−	0.377326i	$-0.123156\pi$
$911$	32.0646	+	18.5125i	1.06235	+	0.613346i	0.136267	+	0.990672i	$0.456490\pi$
$912$	0.673059	−	5.88901i	0.0222872	−	0.195005i
$913$	30.9647	−	28.5077i	1.02478	−	0.943469i
$914$	1.49749	−	0.864576i	0.0495325	−	0.0285976i
$915$	−21.2614	+	8.31430i	−0.702881	+	0.274862i
$916$	10.9630	−	18.9885i	0.362228	−	0.627398i
$917$	−19.1210			−0.631432
$918$	−2.03830	+	1.73717i	−0.0672738	+	0.0573350i
$919$		−	11.5747i		−	0.381814i	−0.981608	−	0.190907i	$-0.938857\pi$
$919$		−	11.5747i		−	0.381814i	0.981608	−	0.190907i	$-0.0611428\pi$
$920$	11.2567	+	7.06733i	0.371124	+	0.233003i
$921$	−12.4092	−	28.5666i	−0.408897	−	0.941301i
$922$	−13.9664	+	8.06351i	−0.459959	+	0.265557i
$923$	−0.847218	+	0.489142i	−0.0278865	+	0.0161003i
$924$	−11.4093	+	1.22217i	−0.375339	+	0.0402065i
$925$	−30.8619	−	21.0082i	−1.01473	−	0.690745i
$926$	4.55549			0.149703
$927$	12.6924	−	54.8014i	0.416872	−	1.79991i
$928$		−	4.39516i		−	0.144278i
$929$	−47.6610	−	27.5171i	−1.56371	−	0.902807i	−0.996877	−	0.0789722i	$-0.974836\pi$
$929$	−47.6610	−	27.5171i	−1.56371	−	0.902807i	−0.566830	−	0.823835i	$-0.691830\pi$
$930$	0.365748	+	0.292412i	0.0119934	+	0.00958856i
$931$	8.92102	−	5.15055i	0.292374	−	0.168802i
$932$	26.3452	−	15.2104i	0.862967	−	0.498234i
$933$	−27.1719	−	20.1209i	−0.889568	−	0.658728i
$934$	12.1847	+	7.03483i	0.398695	+	0.230187i
$935$	0.697386	+	3.75820i	0.0228070	+	0.122906i
$936$	0.673776	−	2.90914i	0.0220231	−	0.0950881i
$937$	24.6567			0.805500			0.402750	−	0.915310i	$-0.368054\pi$
$937$	24.6567			0.805500			0.402750	+	0.915310i	$0.368054\pi$
$938$	1.14218	−	1.97831i	0.0372934	−	0.0645940i
$939$	1.70341	−	14.9042i	0.0555887	−	0.486380i
$940$	0.999703	+	1.88985i	0.0326067	+	0.0616403i
$941$	3.71075	+	6.42721i	0.120967	+	0.209521i	0.920149	−	0.391568i	$-0.128067\pi$
$941$	3.71075	+	6.42721i	0.120967	+	0.209521i	−0.799182	+	0.601089i	$0.794734\pi$
$942$	−4.35801	−	10.0323i	−0.141992	−	0.326872i
$943$	−12.4163	+	21.5057i	−0.404331	+	0.700321i
$944$		−	4.56343i		−	0.148527i
$945$	−21.5664	−	8.57454i	−0.701556	−	0.278930i
$946$	0.118804	+	0.530007i	0.00386265	+	0.0172320i
$947$	9.01043	−	15.6065i	0.292800	−	0.507144i	−0.681671	−	0.731659i	$-0.738746\pi$
$947$	9.01043	−	15.6065i	0.292800	−	0.507144i	0.974471	+	0.224515i	$0.0720797\pi$
$948$	12.6883	−	5.51172i	0.412095	−	0.179012i
$949$	5.41840	+	9.38495i	0.175889	+	0.304648i
$950$	−7.43538	−	15.4108i	−0.241235	−	0.499993i
$951$	−28.2019	−	3.22321i	−0.914509	−	0.104520i
$952$	−0.514754	+	0.891581i	−0.0166833	+	0.0288963i
$953$		−	0.0792884i		−	0.00256840i	−0.999999	−	0.00128420i	$-0.999591\pi$
$953$		−	0.0792884i		−	0.00256840i	0.999999	−	0.00128420i	$-0.000408774\pi$
$954$	−4.45279	+	1.35794i	−0.144165	+	0.0439650i
$955$	0.302437	−	8.16279i	0.00978662	−	0.264142i
$956$	8.20840	−	14.2174i	0.265479	−	0.459822i
$957$	−10.2234	+	23.0859i	−0.330475	+	0.746260i
$958$	19.9622	−	11.5252i	0.644948	−	0.372361i
$959$	−10.7743	−	18.6617i	−0.347921	−	0.602618i
$960$	2.41849	−	3.02505i	0.0780565	−	0.0976329i
$961$	15.4927	−	26.8341i	0.499764	−	0.865617i
$962$	−7.43224			−0.239625
$963$	−1.15571	−	1.07923i	−0.0372423	−	0.0347778i
$964$		−	28.6933i		−	0.924148i
$965$	−22.0232	+	35.0783i	−0.708952	+	1.12921i
$966$	2.33517	−	20.4319i	0.0751330	−	0.657385i
$967$	0.339641	+	0.588275i	0.0109221	+	0.0189176i	0.871435	−	0.490511i	$-0.163190\pi$
$967$	0.339641	+	0.588275i	0.0109221	+	0.0189176i	−0.860513	+	0.509429i	$0.829857\pi$
$968$	−6.26702	+	9.04016i	−0.201430	+	0.290562i
$969$	1.21719	+	2.80204i	0.0391019	+	0.0900145i
$970$	0.314974	−	0.501686i	0.0101132	−	0.0161082i
$971$		−	49.2836i		−	1.58159i	−0.612083	−	0.790794i	$-0.709668\pi$
$971$		−	49.2836i		−	1.58159i	0.612083	−	0.790794i	$-0.290332\pi$
$972$	−13.1325	−	8.39870i	−0.421224	−	0.269389i
$973$		−	24.3120i		−	0.779408i
$974$	−16.8243	+	29.1406i	−0.539086	+	0.933724i
$975$	−2.84005	−	8.13897i	−0.0909545	−	0.260656i
$976$	−5.10478	+	2.94725i	−0.163400	+	0.0943390i
$977$	−12.3523	−	21.3947i	−0.395184	−	0.684479i	0.597941	−	0.801540i	$-0.295986\pi$
$977$	−12.3523	−	21.3947i	−0.395184	−	0.684479i	−0.993125	+	0.117062i	$0.962652\pi$
$978$	−9.96037	−	1.13838i	−0.318497	−	0.0364013i
$979$	30.9284	+	9.67204i	0.988477	+	0.309120i
$980$	6.72622	+	0.249211i	0.214861	+	0.00796075i
$981$	7.71303	+	7.20263i	0.246258	+	0.229962i
$982$			23.1806i			0.739723i
$983$	−2.55694	+	4.42875i	−0.0815537	+	0.141255i	−0.903917	−	0.427707i	$-0.859322\pi$
$983$	−2.55694	+	4.42875i	−0.0815537	+	0.141255i	0.822364	+	0.568962i	$0.192655\pi$
$984$	5.81518	+	4.30616i	0.185381	+	0.137275i
$985$	−17.0641	+	9.02665i	−0.543708	+	0.287613i
$986$	1.13265	+	1.96180i	0.0360708	+	0.0624765i
$987$	1.96858	−	2.65843i	0.0626605	−	0.0846187i
$988$	−2.94998	−	1.70317i	−0.0938515	−	0.0541852i
$989$	−0.973456			−0.0309541
$990$	−19.7397	+	10.2637i	−0.627369	+	0.326202i
$991$	19.0404			0.604837			0.302418	−	0.953175i	$-0.402206\pi$
$991$	19.0404			0.604837			0.302418	+	0.953175i	$0.402206\pi$
$992$	0.104708	+	0.0604533i	0.00332449	+	0.00191940i
$993$	21.9745	+	2.51148i	0.697339	+	0.0796993i
$994$	0.981578	+	1.70014i	0.0311338	+	0.0539253i
$995$	−24.5129	−	46.3397i	−0.777113	−	1.46907i
$996$	20.1604	−	8.75759i	0.638807	−	0.277495i
$997$	−26.6243	+	46.1147i	−0.843201	+	1.46047i	0.0439742	+	0.999033i	$0.485998\pi$
$997$	−26.6243	+	46.1147i	−0.843201	+	1.46047i	−0.887175	+	0.461434i	$0.847335\pi$
$998$			32.2556i			1.02103i
$999$	−12.9896	+	36.5592i	−0.410972	+	1.15668i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	990.2.o.a.659.14	yes	144
5.4	even	2	inner	990.2.o.a.659.59	yes	144
9.5	odd	6	inner	990.2.o.a.329.23	yes	144
11.10	odd	2	inner	990.2.o.a.659.50	yes	144
45.14	odd	6	inner	990.2.o.a.329.50	yes	144
55.54	odd	2	inner	990.2.o.a.659.23	yes	144
99.32	even	6	inner	990.2.o.a.329.59	yes	144
495.329	even	6	inner	990.2.o.a.329.14	✓	144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
990.2.o.a.329.14	✓	144	495.329	even	6	inner
990.2.o.a.329.23	yes	144	9.5	odd	6	inner
990.2.o.a.329.50	yes	144	45.14	odd	6	inner
990.2.o.a.329.59	yes	144	99.32	even	6	inner
990.2.o.a.659.14	yes	144	1.1	even	1	trivial
990.2.o.a.659.23	yes	144	55.54	odd	2	inner
990.2.o.a.659.50	yes	144	11.10	odd	2	inner
990.2.o.a.659.59	yes	144	5.4	even	2	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} +(-0.690097 - 1.58864i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-1.04557 - 1.97656i) q^{5} +(-0.196677 + 1.72085i) q^{6} +(0.998734 - 1.72986i) q^{7} -1.00000i q^{8} +(-2.04753 + 2.19263i) q^{9} +(-0.0827910 + 2.23453i) q^{10} +(0.989910 - 3.16545i) q^{11} +(1.03075 - 1.39196i) q^{12} +(-0.497691 - 0.862025i) q^{13} +(-1.72986 + 0.998734i) q^{14} +(-2.41849 + 3.02505i) q^{15} +(-0.500000 + 0.866025i) q^{16} -0.515407i q^{17} +(2.86953 - 0.875104i) q^{18} -3.42216i q^{19} +(1.18897 - 1.89377i) q^{20} +(-3.43734 - 0.392856i) q^{21} +(-2.44001 + 2.24641i) q^{22} +(-2.97205 - 5.14774i) q^{23} +(-1.58864 + 0.690097i) q^{24} +(-2.81357 + 4.13326i) q^{25} +0.995381i q^{26} +(4.89628 + 1.73966i) q^{27} +1.99747 q^{28} +(2.19758 - 3.80632i) q^{29} +(3.60700 - 1.41052i) q^{30} +(0.0604533 + 0.104708i) q^{31} +(0.866025 - 0.500000i) q^{32} +(-5.71188 + 0.611860i) q^{33} +(-0.257703 + 0.446355i) q^{34} +(-4.46341 - 0.165372i) q^{35} +(-2.92264 - 0.676902i) q^{36} +7.46673i q^{37} +(-1.71108 + 2.96367i) q^{38} +(-1.02599 + 1.38553i) q^{39} +(-1.97656 + 1.04557i) q^{40} +(-2.08885 - 3.61799i) q^{41} +(2.78040 + 2.05889i) q^{42} +(0.0818843 - 0.141828i) q^{43} +(3.23632 - 0.725438i) q^{44} +(6.47469 + 1.75453i) q^{45} +5.94409i q^{46} +(-0.478067 + 0.828036i) q^{47} +(1.72085 + 0.196677i) q^{48} +(1.50506 + 2.60684i) q^{49} +(4.50325 - 2.17272i) q^{50} +(-0.818794 + 0.355681i) q^{51} +(0.497691 - 0.862025i) q^{52} -1.55175 q^{53} +(-3.37047 - 3.95473i) q^{54} +(-7.29172 + 1.35308i) q^{55} +(-1.72986 - 0.998734i) q^{56} +(-5.43656 + 2.36162i) q^{57} +(-3.80632 + 2.19758i) q^{58} +(-3.95204 + 2.28171i) q^{59} +(-3.82901 - 0.581952i) q^{60} +(5.10478 + 2.94725i) q^{61} -0.120907i q^{62} +(1.74799 + 5.73179i) q^{63} -1.00000 q^{64} +(-1.18347 + 1.88502i) q^{65} +(5.25257 + 2.32606i) q^{66} +(-0.990408 + 0.571812i) q^{67} +(0.446355 - 0.257703i) q^{68} +(-6.12688 + 8.27394i) q^{69} +(3.78274 + 2.37492i) q^{70} -0.982823i q^{71} +(2.19263 + 2.04753i) q^{72} -10.8871 q^{73} +(3.73336 - 6.46637i) q^{74} +(8.50788 + 1.61740i) q^{75} +(2.96367 - 1.71108i) q^{76} +(-4.48712 - 4.87385i) q^{77} +(1.58130 - 0.686909i) q^{78} +(6.91684 + 3.99344i) q^{79} +(2.23453 + 0.0827910i) q^{80} +(-0.615219 - 8.97895i) q^{81} +4.17769i q^{82} +(10.9902 + 6.34519i) q^{83} +(-1.37845 - 3.17325i) q^{84} +(-1.01873 + 0.538893i) q^{85} +(-0.141828 + 0.0818843i) q^{86} +(-7.56340 - 0.864426i) q^{87} +(-3.16545 - 0.989910i) q^{88} +9.77063i q^{89} +(-4.72998 - 4.75681i) q^{90} -1.98824 q^{91} +(2.97205 - 5.14774i) q^{92} +(0.124625 - 0.168297i) q^{93} +(0.828036 - 0.478067i) q^{94} +(-6.76409 + 3.57810i) q^{95} +(-1.39196 - 1.03075i) q^{96} +(-0.229422 - 0.132457i) q^{97} -3.01012i q^{98} +(4.91378 + 8.65187i) 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

L-functions

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