LMFDB - Embedded newform 990.2.o.a.659.59

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			659.59
Character	$\chi$	$=$	990.659
Dual form			990.2.o.a.329.59

$q$-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} +(1.18897 + 1.89377i) 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} +(-2.18801 + 3.19572i) q^{15} +(-0.500000 + 0.866025i) q^{16} +0.515407i q^{17} +(-2.86953 + 0.875104i) q^{18} -3.42216i q^{19} +(-1.04557 + 1.97656i) 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} +(-2.17272 + 4.50325i) q^{25} +0.995381i q^{26} +(-4.89628 - 1.73966i) q^{27} -1.99747 q^{28} +(2.19758 - 3.80632i) q^{29} +(-3.49273 + 1.67357i) 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} +(-1.89377 + 1.18897i) 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} +(-6.58677 - 1.27059i) q^{45} +5.94409i q^{46} +(0.478067 - 0.828036i) q^{47} +(-1.72085 - 0.196677i) q^{48} +(1.50506 + 2.60684i) q^{49} +(-4.13326 + 2.81357i) q^{50} +(-0.818794 + 0.355681i) q^{51} +(-0.497691 + 0.862025i) q^{52} +1.55175 q^{53} +(-3.37047 - 3.95473i) q^{54} +(7.17160 - 1.88895i) 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} +(-3.86158 - 0.297011i) q^{60} +(5.10478 + 2.94725i) q^{61} +0.120907i q^{62} +(-1.74799 - 5.73179i) q^{63} -1.00000 q^{64} +(-1.04074 + 1.96743i) 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} +(-3.94811 - 2.08849i) q^{70} -0.982823i q^{71} +(-2.19263 - 2.04753i) q^{72} +10.8871 q^{73} +(3.73336 - 6.46637i) q^{74} +(-8.65342 - 0.343977i) 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} +(-0.976061 + 0.612802i) q^{85} +(-0.141828 + 0.0818843i) q^{86} +(7.56340 + 0.864426i) q^{87} +(3.16545 + 0.989910i) q^{88} +9.77063i q^{89} +(-5.06902 - 4.39375i) q^{90} -1.98824 q^{91} +(-2.97205 + 5.14774i) q^{92} +(-0.124625 + 0.168297i) q^{93} +(0.828036 - 0.478067i) q^{94} +(6.48077 - 4.06883i) 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
$5$	1.18897	+	1.89377i	0.531722	+	0.846919i
$5$	1.18897	+	1.89377i	0.531722	+	0.846919i
$6$	−0.196677	+	1.72085i	−0.0802930	+	0.702533i
$7$	−0.998734	+	1.72986i	−0.377486	+	0.653825i	−0.990696	−	0.136095i	$-0.956545\pi$
$7$	−0.998734	+	1.72986i	−0.377486	+	0.653825i	0.613210	+	0.789920i	$0.289878\pi$
$8$			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	0.926753	−	0.375672i	$-0.122588\pi$
$13$	0.497691	+	0.862025i	0.138035	+	0.239083i	−0.788718	+	0.614755i	$0.789255\pi$
$14$	−1.72986	+	0.998734i	−0.462324	+	0.266923i
$15$	−2.18801	+	3.19572i	−0.564941	+	0.825131i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$			0.515407i			0.125005i	0.998045	+	0.0625023i	$0.0199081\pi$
$17$			0.515407i			0.125005i	−0.998045	+	0.0625023i	$0.980092\pi$
$18$	−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	$-0.128406\pi$
$20$	−1.04557	+	1.97656i	−0.233796	+	0.441972i
$21$	−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	$0.0460850\pi$
$23$	2.97205	+	5.14774i	0.619715	+	1.07338i	−0.369823	+	0.929102i	$0.620582\pi$
$24$	−1.58864	+	0.690097i	−0.324279	+	0.140865i
$25$	−2.17272	+	4.50325i	−0.434543	+	0.900651i
$26$			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	$0.0328651\pi$
$30$	−3.49273	+	1.67357i	−0.637682	+	0.305551i
$31$	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	$-0.789656\pi$
$37$		−	7.46673i		−	1.22752i	0.789492	−	0.613761i	$-0.210344\pi$
$38$	1.71108	−	2.96367i	0.277573	−	0.480771i
$39$	−1.02599	+	1.38553i	−0.164290	+	0.221862i
$40$	−1.89377	+	1.18897i	−0.299431	+	0.187992i
$41$	−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	−0.872201	−	0.489147i	$-0.837308\pi$
$43$	−0.0818843	+	0.141828i	−0.0124872	+	0.0216285i	0.859714	+	0.510775i	$0.170642\pi$
$44$	3.23632	−	0.725438i	0.487893	−	0.109364i
$45$	−6.58677	−	1.27059i	−0.981898	−	0.189409i
$46$			5.94409i			0.876409i
$47$	0.478067	−	0.828036i	0.0697332	−	0.120781i	−0.829051	−	0.559174i	$-0.811119\pi$
$47$	0.478067	−	0.828036i	0.0697332	−	0.120781i	0.898784	+	0.438392i	$0.144452\pi$
$48$	−1.72085	−	0.196677i	−0.248383	−	0.0283879i
$49$	1.50506	+	2.60684i	0.215009	+	0.372406i
$50$	−4.13326	+	2.81357i	−0.584531	+	0.397899i
$51$	−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	$-0.466012\pi$
$53$	1.55175			0.213149			0.106575	+	0.994305i	$0.466012\pi$
$54$	−3.37047	−	3.95473i	−0.458663	−	0.538171i
$55$	7.17160	−	1.88895i	0.967018	−	0.254707i
$56$	−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	$0.429337\pi$
$60$	−3.86158	−	0.297011i	−0.498528	−	0.0383439i
$61$	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
$65$	−1.04074	+	1.96743i	−0.129088	+	0.244030i
$66$	5.25257	+	2.32606i	0.646546	+	0.286318i
$67$	0.990408	−	0.571812i	0.120998	−	0.0698580i	−0.438280	−	0.898839i	$-0.644412\pi$
$67$	0.990408	−	0.571812i	0.120998	−	0.0698580i	0.559277	+	0.828981i	$0.311079\pi$
$68$	−0.446355	+	0.257703i	−0.0541286	+	0.0312511i
$69$	−6.12688	+	8.27394i	−0.737590	+	0.996065i
$70$	−3.94811	−	2.08849i	−0.471890	−	0.249622i
$71$		−	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	$-0.280126\pi$
$73$	10.8871			1.27424			0.637119	+	0.770766i	$0.280126\pi$
$74$	3.73336	−	6.46637i	0.433995	−	0.751701i
$75$	−8.65342	−	0.343977i	−0.999211	−	0.0397191i
$76$	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	−0.244375	−	0.969681i	$-0.578583\pi$
$83$	−10.9902	−	6.34519i	−1.20633	−	0.696475i	−0.961956	+	0.273206i	$0.911916\pi$
$84$	−1.37845	−	3.17325i	−0.150401	−	0.346230i
$85$	−0.976061	+	0.612802i	−0.105869	+	0.0664677i
$86$	−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	$0.826735\pi$
$90$	−5.06902	−	4.39375i	−0.534321	−	0.463142i
$91$	−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
$95$	6.48077	−	4.06883i	0.664913	−	0.417453i
$96$	−1.39196	−	1.03075i	−0.142066	−	0.105201i
$97$	0.229422	+	0.132457i	0.0232943	+	0.0134490i	0.511602	−	0.859223i	$-0.329052\pi$
$97$	0.229422	+	0.132457i	0.0232943	+	0.0134490i	−0.488308	+	0.872672i	$0.662386\pi$
$98$			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	$-0.291750\pi$
$103$	16.2386	−	9.37534i	1.60003	−	0.923780i	0.991479	−	0.130268i	$-0.0415837\pi$
$104$	−0.862025	+	0.497691i	−0.0845285	+	0.0488026i
$105$	−3.34290	−	6.97662i	−0.326234	−	0.680848i
$106$	1.34386	+	0.775876i	0.130527	+	0.0753597i
$107$		−	0.527090i		−	0.0509557i	−0.999675	−	0.0254779i	$-0.991889\pi$
$107$		−	0.527090i		−	0.0509557i	0.999675	−	0.0254779i	$-0.00811073\pi$
$108$	−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	$-0.0538819\pi$
$110$	7.15527	+	1.94992i	0.682228	+	0.185917i
$111$	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	$0.147004\pi$
$113$	8.86031	+	15.3465i	0.833508	+	1.44368i	−0.0617322	+	0.998093i	$0.519662\pi$
$114$	5.88901	+	0.673059i	0.551556	+	0.0630378i
$115$	−6.21496	+	11.7489i	−0.579548	+	1.09559i
$116$	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
$120$	−3.19572	−	2.18801i	−0.291728	−	0.199737i
$121$	−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	$-0.849733\pi$
$127$	−20.0737			−1.78125			−0.890625	+	0.454738i	$0.849733\pi$
$128$	−0.866025	−	0.500000i	−0.0765466	−	0.0441942i
$129$	−0.281821	−	0.0322095i	−0.0248129	−	0.00283589i
$130$	−1.88502	+	1.18347i	−0.165327	+	0.103798i
$131$	−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
$135$	−2.52700	−	11.3408i	−0.217489	−	0.976063i
$136$	−0.515407			−0.0441958
$137$	−5.39400	+	9.34267i	−0.460840	+	0.798199i	−0.999003	−	0.0446423i	$-0.985785\pi$
$137$	−5.39400	+	9.34267i	−0.460840	+	0.798199i	0.538163	+	0.842841i	$0.319119\pi$
$138$	−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	$0.160686\pi$
$140$	−2.37492	−	3.78274i	−0.200718	−	0.319700i
$141$	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	$0.680297\pi$
$150$	−7.32209	−	4.62460i	−0.597846	−	0.377597i
$151$	−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
$155$	−0.126416	+	0.238979i	−0.0101540	+	0.0191953i
$156$	−1.71290	−	0.195769i	−0.137142	−	0.0156740i
$157$	5.46901	−	3.15753i	0.436474	−	0.251999i	−0.265627	−	0.964076i	$-0.585579\pi$
$157$	5.46901	−	3.15753i	0.436474	−	0.251999i	0.702101	+	0.712077i	$0.252245\pi$
$158$	3.99344	+	6.91684i	0.317701	+	0.550274i
$159$	1.07086	+	2.46517i	0.0849246	+	0.195501i
$160$	−1.97656	−	1.04557i	−0.156261	−	0.0826594i
$161$	−11.8731			−0.935735
$162$	3.95668	−	8.08361i	0.310866	−	0.635108i
$163$		−	5.78806i		−	0.453356i	−0.973970	−	0.226678i	$-0.927214\pi$
$163$		−	5.78806i		−	0.453356i	0.973970	−	0.226678i	$-0.0727864\pi$
$164$	2.08885	−	3.61799i	0.163112	−	0.282517i
$165$	7.94996	+	10.0895i	0.618904	+	0.785467i
$166$	−6.34519	−	10.9902i	−0.492482	−	0.853004i
$167$	13.5845	−	7.84301i	1.05120	−	0.606910i	0.128215	−	0.991746i	$-0.459075\pi$
$167$	13.5845	−	7.84301i	1.05120	−	0.606910i	0.922985	+	0.384836i	$0.125742\pi$
$168$	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	0.808848	−	0.588018i	$-0.200092\pi$
$173$	9.26010	+	5.34632i	0.704033	+	0.406473i	−0.104815	+	0.994492i	$0.533425\pi$
$174$	6.11788	+	4.53031i	0.463795	+	0.343442i
$175$	−5.62002	−	8.25605i	−0.424834	−	0.624098i
$176$	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	$-0.186777\pi$
$180$	−2.19302	−	6.33961i	−0.163458	−	0.472527i
$181$	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
$185$	14.1402	−	8.87769i	1.03961	−	0.652700i
$186$	−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	$0.0656088\pi$
$193$	9.26150	+	16.0414i	0.666657	+	1.15468i	−0.312176	+	0.950024i	$0.601058\pi$
$194$	0.132457	+	0.229422i	0.00950986	+	0.0164716i
$195$	−3.84374	−	0.295639i	−0.275256	−	0.0211711i
$196$	−1.50506	+	2.60684i	−0.107504	+	0.186203i
$197$			8.63325i			0.615094i	0.951533	+	0.307547i	$0.0995081\pi$
$197$			8.63325i			0.615094i	−0.951533	+	0.307547i	$0.900492\pi$
$198$	−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	$0.187785\pi$
$200$	−4.50325	−	2.17272i	−0.318428	−	0.153634i
$201$	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
$205$	4.36806	−	8.25746i	0.305079	−	0.576726i
$206$	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
$210$	0.593270	−	7.71338i	0.0409395	−	0.532274i
$211$	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
$220$	5.22168	+	5.26631i	0.352046	+	0.355055i
$221$	−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	0.889419	−	0.457093i	$-0.151110\pi$
$223$	14.0114	+	8.08949i	0.938273	+	0.541712i	0.0488548	+	0.998806i	$0.484443\pi$
$224$		−	1.99747i		−	0.133461i
$225$	−5.42524	−	13.9845i	−0.361683	−	0.932301i
$226$			17.7206i			1.17876i
$227$	−20.1345	−	11.6247i	−1.33637	−	0.771555i	−0.350105	−	0.936710i	$-0.613854\pi$
$227$	−20.1345	−	11.6247i	−1.33637	−	0.771555i	−0.986268	+	0.165155i	$0.947187\pi$
$228$	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	$-0.424576\pi$
$230$	−11.2567	+	7.06733i	−0.742247	+	0.466006i
$231$	−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	$0.473242\pi$
$233$			30.4209i			1.99294i	−0.0839648	+	0.996469i	$0.526758\pi$
$234$	−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	$-0.344834\pi$
$240$	−1.67357	−	3.49273i	−0.108028	−	0.225455i
$241$	−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
$245$	−3.14729	+	5.94968i	−0.201073	+	0.380111i
$246$	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
$250$	−10.2426	−	4.48218i	−0.647796	−	0.283478i
$251$			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
$255$	−1.64710	−	1.12771i	−0.103145	−	0.0706202i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−7.03142	−	12.1788i	−0.438608	−	0.759691i	0.558975	−	0.829185i	$-0.311195\pi$
$257$	−7.03142	−	12.1788i	−0.438608	−	0.759691i	−0.997582	+	0.0694939i	$0.977862\pi$
$258$	−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	0.179811	−	0.983701i	$-0.442451\pi$
$263$	−9.44160	−	5.45111i	−0.582194	−	0.336130i	−0.762005	+	0.647571i	$0.775785\pi$
$264$	0.611860	+	5.71188i	0.0376574	+	0.351542i
$265$	1.84498	+	2.93866i	0.113336	+	0.180520i
$266$	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	$-0.153169\pi$
$270$	3.48197	−	11.0849i	0.211906	−	0.674608i
$271$		−	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
$275$	12.1040	+	11.3354i	0.729901	+	0.683553i
$276$	−10.2289	−	1.16907i	−0.615706	−	0.0703695i
$277$	1.08182	−	1.87377i	0.0650003	−	0.112584i	−0.831694	−	0.555235i	$-0.812629\pi$
$277$	1.08182	−	1.87377i	0.0650003	−	0.112584i	0.896694	+	0.442651i	$0.145962\pi$
$278$	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	0.860145	−	0.510050i	$-0.170373\pi$
$283$	−0.195885	−	0.339283i	−0.0116442	−	0.0201683i	−0.871789	+	0.489882i	$0.837040\pi$
$284$	0.851149	−	0.491411i	0.0505064	−	0.0291599i
$285$	10.9362	+	7.48770i	0.647807	+	0.443533i
$286$	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
$290$	8.68729	+	4.59544i	0.510135	+	0.269853i
$291$	−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	−0.695663	−	0.718368i	$-0.744889\pi$
$293$	−7.21267	+	4.16424i	−0.421369	+	0.243277i	0.274294	+	0.961646i	$0.411556\pi$
$294$	−4.78199	+	2.07727i	−0.278891	+	0.121149i
$295$	−9.01989	−	4.77138i	−0.525158	−	0.277800i
$296$	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
$300$	−4.02882	−	7.66607i	−0.232604	−	0.442601i
$301$	−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	$-0.671517\pi$
$307$	−17.9818			−1.02628			−0.513139	+	0.858306i	$0.671517\pi$
$308$	−1.97731	+	6.32289i	−0.112668	+	0.360280i
$309$	26.1002	+	19.3273i	1.48479	+	1.09949i
$310$	−0.228969	+	0.143754i	−0.0130046	+	0.00816468i
$311$	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	0.272811	−	0.962068i	$-0.412047\pi$
$313$	−7.50061	−	4.33048i	−0.423959	−	0.244773i	−0.696770	+	0.717295i	$0.745380\pi$
$314$	6.31507			0.356380
$315$	8.77638	−	10.1252i	0.494493	−	0.570490i
$316$			7.98688i			0.449297i
$317$	−8.19418	+	14.1927i	−0.460231	+	0.797144i	−0.998972	−	0.0453278i	$-0.985567\pi$
$317$	−8.19418	+	14.1927i	−0.460231	+	0.797144i	0.538741	+	0.842471i	$0.318900\pi$
$318$	−0.305194	+	2.67033i	−0.0171144	+	0.149745i
$319$	−9.87330	−	10.7242i	−0.552799	−	0.600442i
$320$	−1.18897	−	1.89377i	−0.0664652	−	0.105865i
$321$	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
$330$	1.84012	+	12.7127i	0.101295	+	0.699814i
$331$	−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
$335$	2.26044	+	1.19574i	0.123501	+	0.0653301i
$336$	2.05889	−	2.78040i	0.112322	−	0.151683i
$337$	5.01115	+	8.67957i	0.272975	+	0.472806i	0.969622	−	0.244607i	$-0.0786591\pi$
$337$	5.01115	+	8.67957i	0.272975	+	0.472806i	−0.696647	+	0.717414i	$0.745326\pi$
$338$	10.4003	−	6.00461i	0.565701	−	0.326608i
$339$	−18.2655	+	24.6664i	−0.992048	+	1.33969i
$340$	−1.01873	−	0.538893i	−0.0552485	−	0.0292256i
$341$	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
$345$	−22.9536	−	1.76546i	−1.23578	−	0.0950492i
$346$	5.34632	+	9.26010i	0.287420	+	0.497826i
$347$	15.4613	−	8.92657i	0.830005	−	0.479204i	−0.0238495	−	0.999716i	$-0.507592\pi$
$347$	15.4613	−	8.92657i	0.830005	−	0.479204i	0.853854	+	0.520512i	$0.174259\pi$
$348$	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	$-0.585862\pi$
$353$	13.1794	−	22.8274i	0.701468	−	1.21498i	0.967951	−	0.251139i	$-0.0808050\pi$
$354$	−3.14921	−	7.24963i	−0.167378	−	0.385313i
$355$	1.86124	−	1.16854i	0.0987843	−	0.0620198i
$356$	−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	$0.742789\pi$
$360$	1.27059	−	6.58677i	0.0669662	−	0.347153i
$361$	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
$365$	12.9444	+	20.6176i	0.677540	+	1.07918i
$366$	−6.07575	+	8.20489i	−0.317585	+	0.428877i
$367$	−21.5842	−	12.4617i	−1.12669	−	0.650493i	−0.183588	−	0.983003i	$-0.558771\pi$
$367$	−21.5842	−	12.4617i	−1.12669	−	0.650493i	−0.943100	+	0.332510i	$0.892104\pi$
$368$	−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	0.664685	−	0.747123i	$-0.268566\pi$
$373$	−6.07758	−	10.5267i	−0.314685	−	0.545051i	−0.979371	+	0.202073i	$0.935232\pi$
$374$	1.15781	+	1.25760i	0.0598691	+	0.0650289i
$375$	−9.63721	−	16.7966i	−0.497664	−	0.867370i
$376$	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	$0.209196\pi$
$380$	6.76409	+	3.57810i	0.346991	+	0.183552i
$381$	−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	0.591828	−	0.806064i	$-0.298406\pi$
$383$	−7.87038	−	13.6319i	−0.402158	−	0.696558i	−0.993986	+	0.109506i	$0.965073\pi$
$384$	0.196677	−	1.72085i	0.0100366	−	0.0878167i
$385$	−3.89490	+	14.2924i	−0.198502	+	0.728409i
$386$			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	$0.853419\pi$
$390$	−3.18096	−	2.17790i	−0.161074	−	0.110282i
$391$	−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	$-0.836291\pi$
$397$		−	19.6033i		−	0.983860i	0.870635	−	0.491930i	$-0.163709\pi$
$398$	20.3036	+	11.7223i	1.01773	+	0.587586i
$399$	−1.34441	+	11.7631i	−0.0673049	+	0.588892i
$400$	−2.81357	−	4.13326i	−0.140679	−	0.206663i
$401$	−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
$405$	16.2726	−	11.8407i	0.808591	−	0.588372i
$406$			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	$0.345620\pi$
$410$	7.91158	−	4.96714i	0.390725	−	0.245309i
$411$	−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	$0.537359\pi$
$420$	4.37048	−	6.38335i	0.213257	−	0.311475i
$421$	−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
$425$	−2.32101	−	1.11983i	−0.112585	−	0.0543199i
$426$	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
$430$	−0.323698	−	0.171231i	−0.0156101	−	0.00825750i
$431$	−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	$0.222803\pi$
$433$			26.8092i			1.28837i	−0.764870	+	0.644185i	$0.777197\pi$
$434$	−0.209151	−	0.120754i	−0.0100396	−	0.00579636i
$435$	7.35560	+	15.3511i	0.352674	+	0.736029i
$436$	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	$0.608501\pi$
$440$	1.88895	+	7.17160i	0.0900524	+	0.341893i
$441$	−8.79749	−	2.03756i	−0.418928	−	0.0970266i
$442$	−0.513026			−0.0244022
$443$	5.24925	−	9.09197i	0.249399	−	0.431973i	−0.713960	−	0.700187i	$-0.753100\pi$
$443$	5.24925	−	9.09197i	0.249399	−	0.431973i	0.963359	+	0.268214i	$0.0864335\pi$
$444$	10.3934	+	7.69634i	0.493248	+	0.365252i
$445$	−18.5033	+	11.6169i	−0.877141	+	0.550696i
$446$	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	$0.985704\pi$
$450$	2.29386	−	14.8236i	0.108134	−	0.698790i
$451$	−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
$455$	−2.36395	−	3.76527i	−0.110824	−	0.176519i
$456$	2.36162	+	5.43656i	0.110593	+	0.254590i
$457$	0.864576	−	1.49749i	0.0404432	−	0.0700496i	−0.845095	−	0.534616i	$-0.820456\pi$
$457$	0.864576	−	1.49749i	0.0404432	−	0.0700496i	0.885538	+	0.464566i	$0.153790\pi$
$458$		−	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	−0.405517	−	0.914088i	$-0.632908\pi$
$463$	3.94517	−	2.27775i	0.183348	−	0.105856i	0.588865	+	0.808232i	$0.299575\pi$
$464$	2.19758	+	3.80632i	0.102020	+	0.176704i
$465$	−0.466891	−	0.0359106i	−0.0216515	−	0.00166531i
$466$	−15.2104	+	26.3452i	−0.704610	+	1.22042i
$467$	14.0697			0.651067			0.325533	−	0.945531i	$-0.394456\pi$
$467$	14.0697			0.651067			0.325533	+	0.945531i	$0.394456\pi$
$468$	−0.871062	−	2.85627i	−0.0402648	−	0.132031i
$469$			2.28435i			0.105482i
$470$	1.88985	+	0.999703i	0.0871725	+	0.0461129i
$471$	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
$475$	15.4108	+	7.43538i	0.707098	+	0.341158i
$476$		−	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	$0.990134\pi$
$480$	0.297011	−	3.86158i	0.0135566	−	0.176256i
$481$	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	$0.275970\pi$
$487$			33.6486i			1.52476i	−0.647127	+	0.762382i	$0.724030\pi$
$488$	−2.94725	+	5.10478i	−0.133416	+	0.231082i
$489$	9.19512	−	3.99432i	0.415818	−	0.180629i
$490$	−5.70047	+	3.57893i	−0.257521	+	0.161680i
$491$	−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
$495$	−10.5423	+	19.5923i	−0.473842	+	0.880610i
$496$	−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	$-0.423434\pi$
$500$	−6.62922	−	9.00296i	−0.296468	−	0.402625i
$501$	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	$0.0381111\pi$
$503$			5.35769i			0.238887i	−0.992841	+	0.119444i	$0.961889\pi$
$504$	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	$0.505185\pi$
$510$	−0.862570	−	1.80018i	−0.0381952	−	0.0797132i
$511$	−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
$515$	37.0618	+	19.6051i	1.63314	+	0.863905i
$516$	−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
$520$	−1.96743	−	1.04074i	−0.0862775	−	0.0456394i
$521$			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	$-0.377666\pi$
$523$	17.1488			0.749865			0.374933	+	0.927052i	$0.377666\pi$
$524$	4.78632	−	8.29015i	0.209091	−	0.362157i
$525$	9.23750	−	14.6256i	0.403157	−	0.638316i
$526$	−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
$535$	0.998186	−	0.626692i	0.0431554	−	0.0270943i
$536$	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
$540$	8.55794	−	7.85886i	0.368275	−	0.338191i
$541$			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
$545$	6.66173	−	4.18244i	0.285357	−	0.179156i
$546$	0.391041	−	3.42146i	0.0167350	−	0.146425i
$547$	−13.9579	+	24.1758i	−0.596798	+	1.03368i	0.396493	+	0.918038i	$0.370227\pi$
$547$	−13.9579	+	24.1758i	−0.596798	+	1.03368i	−0.993291	+	0.115646i	$0.963106\pi$
$548$	−10.7880			−0.460840
$549$	−16.9144	+	5.15829i	−0.721889	+	0.220150i
$550$	4.81468	+	15.8688i	0.205299	+	0.676648i
$551$	−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
$555$	23.8616	+	16.3373i	1.01287	+	0.693478i
$556$	10.5408	+	6.08571i	0.447028	+	0.258092i
$557$		−	36.6139i		−	1.55138i	−0.631114	−	0.775690i	$-0.717402\pi$
$557$		−	36.6139i		−	1.55138i	0.631114	−	0.775690i	$-0.282598\pi$
$558$	−0.265103	−	0.247560i	−0.0112227	−	0.0104801i
$559$	−0.163012			−0.00689468
$560$	2.08849	−	3.94811i	0.0882548	−	0.166838i
$561$	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	−0.994823	−	0.101619i	$-0.967598\pi$
$563$	−33.3191	+	19.2368i	−1.40423	+	0.810733i	−0.409407	+	0.912352i	$0.634265\pi$
$564$	0.659825	+	1.51895i	0.0277836	+	0.0639593i
$565$	−18.5281	+	35.0258i	−0.779484	+	1.47355i
$566$		−	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	$0.0348273\pi$
$570$	5.72722	+	11.9527i	0.239887	+	0.500642i
$571$	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	$0.138689\pi$
$577$			20.2759i			0.844097i	−0.906573	+	0.422048i	$0.861311\pi$
$578$	14.4924	+	8.36718i	0.602803	+	0.348029i
$579$	−19.0926	+	25.7833i	−0.793461	+	1.07152i
$580$	5.22569	+	8.32341i	0.216985	+	0.345611i
$581$	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
$585$	−2.18289	−	6.31033i	−0.0902514	−	0.260900i
$586$	−8.32848			−0.344046
$587$	8.05120	−	13.9451i	0.332309	−	0.575575i	−0.650655	−	0.759373i	$-0.725506\pi$
$587$	8.05120	−	13.9451i	0.332309	−	0.575575i	0.982964	+	0.183798i	$0.0588391\pi$
$588$	−5.17996	−	0.592021i	−0.213618	−	0.0244146i
$589$	0.358328	−	0.206881i	0.0147646	−	0.00852437i
$590$	−5.42576	−	8.64208i	−0.223375	−	0.355789i
$591$	−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	$0.125399\pi$
$593$			18.6944i			0.767685i	−0.923399	+	0.383843i	$0.874601\pi$
$594$	−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	$0.601221\pi$
$600$	0.343977	−	8.65342i	0.0140428	−	0.353274i
$601$	−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
$605$	1.11984	−	24.5712i	0.0455281	−	0.998963i
$606$	−16.8128	−	12.4499i	−0.682971	−	0.505743i
$607$	−20.6217	−	35.7178i	−0.837007	−	1.44974i	−0.892385	−	0.451274i	$-0.850970\pi$
$607$	−20.6217	−	35.7178i	−0.837007	−	1.44974i	0.0553779	−	0.998465i	$-0.482364\pi$
$608$	1.71108	+	2.96367i	0.0693934	+	0.120193i
$609$	−9.04916	+	12.2203i	−0.366690	+	0.495190i
$610$	−6.16309	+	11.6508i	−0.249536	+	0.471728i
$611$	0.951717			0.0385024
$612$	0.348880	−	1.50635i	0.0141026	−	0.0608905i
$613$	12.8254			0.518014			0.259007	−	0.965875i	$-0.416605\pi$
$613$	12.8254			0.518014			0.259007	+	0.965875i	$0.416605\pi$
$614$	−15.5727	−	8.99091i	−0.628464	−	0.362844i
$615$	16.1325	+	1.24082i	0.650525	+	0.0500347i
$616$	−4.87385	+	4.48712i	−0.196373	+	0.180791i
$617$	−16.8244	−	29.1408i	−0.677326	−	1.17316i	−0.975783	−	0.218740i	$-0.929805\pi$
$617$	−16.8244	−	29.1408i	−0.677326	−	1.17316i	0.298457	−	0.954423i	$-0.403528\pi$
$618$	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
$625$	−15.5586	−	19.5686i	−0.622344	−	0.782744i
$626$	−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
$630$	12.6632	−	4.38049i	0.504513	−	0.174523i
$631$	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
$635$	−23.8669	−	38.0149i	−0.947130	−	1.50857i
$636$	−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	−0.951822	−	0.306652i	$-0.900791\pi$
$643$	−29.4695	+	17.0142i	−1.16216	+	0.670976i	−0.210342	+	0.977628i	$0.567458\pi$
$644$	−5.93657	−	10.2824i	−0.233934	−	0.405185i
$645$	−0.274078	−	0.571999i	−0.0107918	−	0.0225224i
$646$	1.52750	+	0.881901i	0.0600986	+	0.0346979i
$647$	12.5526			0.493492			0.246746	−	0.969080i	$-0.420639\pi$
$647$	12.5526			0.493492			0.246746	+	0.969080i	$0.420639\pi$
$648$	8.97895	−	0.615219i	0.352726	−	0.0241681i
$649$	3.31049	+	14.7687i	0.129948	+	0.579722i
$650$	−4.48245	−	2.16268i	−0.175816	−	0.0848274i
$651$	−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	$-0.988097\pi$
$653$	−13.5954	−	23.5479i	−0.532028	−	0.921500i	0.467273	−	0.884113i	$-0.345237\pi$
$654$	6.05345	+	0.691853i	0.236709	+	0.0270536i
$655$	10.0088	−	18.9209i	0.391078	−	0.739300i
$656$	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	$0.139447\pi$
$660$	−4.76279	+	11.9296i	−0.185391	+	0.464360i
$661$	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
$670$	1.35973	+	2.16576i	0.0525310	+	0.0836706i
$671$	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	$0.456748\pi$
$673$	−20.5025	+	35.5113i	−0.790312	+	1.36886i	−0.925774	+	0.378078i	$0.876585\pi$
$674$			10.0223i			0.386045i
$675$	18.4724	−	18.2694i	0.711002	−	0.703190i
$676$	12.0092			0.461893
$677$	7.56817	+	4.36948i	0.290868	+	0.167933i	0.638333	−	0.769760i	$-0.279624\pi$
$677$	7.56817	+	4.36948i	0.290868	+	0.167933i	−0.347465	+	0.937693i	$0.612957\pi$
$678$	−28.1516	+	12.2289i	−1.08116	+	0.469650i
$679$	−0.458264	+	0.264579i	−0.0175865	+	0.0101536i
$680$	−0.612802	−	0.976061i	−0.0234999	−	0.0374302i
$681$	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	$-0.835750\pi$
$683$	−45.4630			−1.73959			−0.869797	+	0.493410i	$0.835750\pi$
$684$	−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
$690$	−18.9957	−	13.0057i	−0.723152	−	0.495120i
$691$	−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
$695$	24.0575	+	12.7261i	0.912554	+	0.482727i
$696$	−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
$700$	4.33993	−	8.99511i	0.164034	−	0.339983i
$701$	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
$705$	1.60016	+	3.33952i	0.0602654	+	0.125773i
$706$	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
$715$	5.19757	+	5.24199i	0.194378	+	0.196039i
$716$	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	$-0.125967\pi$
$720$	4.39375	−	5.06902i	0.163746	−	0.188911i
$721$			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
$725$	12.3661	+	18.1663i	0.459265	+	0.674680i
$726$	12.5626	−	14.3242i	0.466241	−	0.531619i
$727$	−28.1950	−	16.2784i	−1.04569	−	0.603731i	−0.124253	−	0.992251i	$-0.539653\pi$
$727$	−28.1950	−	16.2784i	−1.04569	−	0.603731i	−0.921441	+	0.388519i	$0.872987\pi$
$728$		−	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	$0.206908\pi$
$733$	24.9664	+	43.2432i	0.922157	+	1.59722i	0.126086	+	0.992019i	$0.459759\pi$
$734$	−12.4617	−	21.5842i	−0.459968	−	0.796688i
$735$	−11.6238	−	0.894039i	−0.428751	−	0.0329771i
$736$	−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	$0.786401\pi$
$740$	14.7584	+	7.80697i	0.542531	+	0.286990i
$741$	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	−0.177972	−	0.984036i	$-0.556954\pi$
$743$	15.9525	−	9.21020i	0.585242	−	0.337890i	0.763214	+	0.646146i	$0.223620\pi$
$744$	−0.168297	−	0.124625i	−0.00617008	−	0.00456896i
$745$	−11.8048	+	22.3160i	−0.432494	+	0.817593i
$746$		−	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
$750$	0.0522039	−	19.3648i	0.00190622	−	0.707104i
$751$	−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	$0.0627886\pi$
$757$			10.7842i			0.391959i	−0.980608	+	0.195979i	$0.937211\pi$
$758$	26.6957	+	15.4128i	0.969632	+	0.559817i
$759$	20.1257	+	27.5848i	0.730516	+	1.00126i
$760$	4.06883	+	6.48077i	0.147592	+	0.235082i
$761$	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
$765$	0.654873	−	3.39487i	0.0236770	−	0.122742i
$766$		−	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	$0.146386\pi$
$770$	−10.5193	+	10.4301i	−0.379089	+	0.375876i
$771$	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	$-0.707852\pi$
$773$	−33.7838			−1.21512			−0.607560	+	0.794274i	$0.707852\pi$
$774$	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
$780$	−1.66584	−	3.47660i	−0.0596466	−	0.124482i
$781$	−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
$785$	12.4821	+	6.60283i	0.445505	+	0.235665i
$786$	15.2074	−	6.60605i	0.542432	−	0.235630i
$787$	14.1716	+	24.5459i	0.505162	+	0.874966i	0.999982	+	0.00597094i	$0.00190062\pi$
$787$	14.1716	+	24.5459i	0.505162	+	0.874966i	−0.494820	+	0.868995i	$0.664766\pi$
$788$	−7.47661	+	4.31662i	−0.266343	+	0.153773i
$789$	2.14422	−	18.7611i	0.0763361	−	0.667912i
$790$	−8.35083	+	15.7865i	−0.297109	+	0.561660i
$791$	−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
$795$	−3.39524	+	4.95896i	−0.120417	+	0.175876i
$796$	11.7223	+	20.3036i	0.415486	+	0.719643i
$797$	−9.37386	−	16.2360i	−0.332039	−	0.575109i	0.650872	−	0.759187i	$-0.274403\pi$
$797$	−9.37386	−	16.2360i	−0.332039	−	0.575109i	−0.982912	+	0.184078i	$0.941070\pi$
$798$	−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
$805$	−14.1168	−	22.4850i	−0.497551	−	0.792491i
$806$	−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	$0.191192\pi$
$810$	20.0128	−	2.11810i	0.703179	−	0.0744226i
$811$			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
$815$	10.9612	−	6.88180i	0.383955	−	0.241059i
$816$	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	−0.896278	−	0.443492i	$-0.853739\pi$
$823$	−27.5503	+	15.9062i	−0.960342	+	0.554454i	−0.0640636	+	0.997946i	$0.520406\pi$
$824$	9.37534	+	16.2386i	0.326605	+	0.565697i
$825$	−9.65495	+	27.0515i	−0.336142	+	0.941811i
$826$	4.55765	−	7.89408i	0.158581	−	0.274670i
$827$			27.5608i			0.958383i	0.877710	+	0.479191i	$0.159070\pi$
$827$			27.5608i			0.958383i	−0.877710	+	0.479191i	$0.840930\pi$
$828$	−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	$0.391015\pi$
$830$	13.2687	−	25.0833i	0.460562	−	0.870654i
$831$	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
$835$	31.0044	+	16.4008i	1.07295	+	0.567573i
$836$	−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	$0.908714\pi$
$840$	6.97662	−	3.34290i	0.240716	−	0.115341i
$841$	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
$850$	−1.45014	−	2.13031i	−0.0497392	−	0.0730690i
$851$	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	−0.825611	−	0.564239i	$-0.809170\pi$
$853$	2.21498	−	3.83646i	0.0758396	−	0.131358i	0.901451	+	0.432881i	$0.142503\pi$
$854$	−11.7741			−0.402900
$855$	−4.34817	+	22.5410i	−0.148704	+	0.770885i
$856$	0.527090			0.0180156
$857$	41.6886	+	24.0690i	1.42406	+	0.822180i	0.996643	−	0.0818759i	$-0.0260911\pi$
$857$	41.6886	+	24.0690i	1.42406	+	0.822180i	0.427415	+	0.904056i	$0.359424\pi$
$858$	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	$0.679970\pi$
$860$	−0.194715	−	0.310140i	−0.00663974	−	0.0105757i
$861$	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	$-0.497347\pi$
$863$	0.489737			0.0166708			0.00833542	+	0.999965i	$0.497347\pi$
$864$	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
$870$	−1.30541	+	16.9722i	−0.0442575	+	0.575413i
$871$	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
$875$	8.95302	−	20.4592i	0.302667	−	0.691647i
$876$	−11.2219	+	15.1544i	−0.379152	+	0.512020i
$877$	−25.1965	−	43.6416i	−0.850825	−	1.47367i	−0.880465	−	0.474111i	$-0.842769\pi$
$877$	−25.1965	−	43.6416i	−0.850825	−	1.47367i	0.0296401	−	0.999561i	$-0.490564\pi$
$878$	3.80739	+	6.59459i	0.128493	+	0.222557i
$879$	−11.5929	−	8.58459i	−0.391019	−	0.289551i
$880$	−1.94992	+	7.15527i	−0.0657317	+	0.241204i
$881$		−	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	$-0.947633\pi$
$883$		−	9.73317i		−	0.327547i	0.986498	−	0.163774i	$-0.0523667\pi$
$884$	−0.444294	−	0.256513i	−0.0149432	−	0.00862747i
$885$	1.35539	−	17.6220i	0.0455609	−	0.592358i
$886$	9.09197	−	5.24925i	0.305451	−	0.176352i
$887$	42.4950	−	24.5345i	1.42684	−	0.823788i	0.429972	−	0.902842i	$-0.358523\pi$
$887$	42.4950	−	24.5345i	1.42684	−	0.823788i	0.996870	+	0.0790542i	$0.0251900\pi$
$888$	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
$895$	28.0570	−	17.6151i	0.937843	−	0.588807i
$896$	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
$900$	9.39833	−	11.6907i	0.313278	−	0.389689i
$901$			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
$905$	9.16575	+	14.5991i	0.304680	+	0.485290i
$906$	11.6164	−	15.6872i	0.385930	−	0.521172i
$907$	25.5922	+	14.7757i	0.849776	+	0.490618i	0.860575	−	0.509323i	$-0.170104\pi$
$907$	25.5922	+	14.7757i	0.849776	+	0.490618i	−0.0107993	+	0.999942i	$0.503438\pi$
$908$		−	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
$915$	−20.5879	+	9.86484i	−0.680614	+	0.326122i
$916$	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	$-0.0611428\pi$
$920$	−11.7489	−	6.21496i	−0.387348	−	0.204901i
$921$	−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
$925$	33.6246	+	16.2231i	1.10557	+	0.533412i
$926$	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	$-0.691830\pi$
$930$	−0.386384	−	0.264545i	−0.0126700	−	0.00867477i
$931$	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
$935$	0.973580	+	3.69629i	0.0318395	+	0.120882i
$936$	0.673776	−	2.90914i	0.0220231	−	0.0950881i
$937$	−24.6567			−0.805500			−0.402750	−	0.915310i	$-0.631946\pi$
$937$	−24.6567			−0.805500			−0.402750	+	0.915310i	$0.631946\pi$
$938$	−1.14218	+	1.97831i	−0.0372934	+	0.0645940i
$939$	1.70341	−	14.9042i	0.0555887	−	0.486380i
$940$	1.13681	+	1.81070i	0.0370787	+	0.0590584i
$941$	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
$945$	22.1418	+	6.95512i	0.720273	+	0.226250i
$946$	0.118804	+	0.530007i	0.00386265	+	0.0172320i
$947$	−9.01043	+	15.6065i	−0.292800	+	0.507144i	−0.974471	−	0.224515i	$-0.927920\pi$
$947$	−9.01043	+	15.6065i	−0.292800	+	0.507144i	0.681671	+	0.731659i	$0.261254\pi$
$948$	−12.6883	+	5.51172i	−0.412095	+	0.179012i
$949$	5.41840	+	9.38495i	0.175889	+	0.304648i
$950$	9.62849	+	14.1446i	0.312389	+	0.458913i
$951$	−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	$0.000408774\pi$
$953$			0.0792884i			0.00256840i	−0.999999	+	0.00128420i	$0.999591\pi$
$954$	−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
$960$	2.18801	−	3.19572i	0.0706177	−	0.103141i
$961$	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
$965$	−19.3671	+	36.6118i	−0.623448	+	1.17858i
$966$	2.33517	−	20.4319i	0.0751330	−	0.657385i
$967$	−0.339641	−	0.588275i	−0.0109221	−	0.0189176i	0.860513	−	0.509429i	$-0.170143\pi$
$967$	−0.339641	−	0.588275i	−0.0109221	−	0.0189176i	−0.871435	+	0.490511i	$0.836810\pi$
$968$	6.26702	−	9.04016i	0.201430	−	0.290562i
$969$	1.21719	+	2.80204i	0.0391019	+	0.0900145i
$970$	−0.276986	+	0.523618i	−0.00889347	+	0.0168124i
$971$		−	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
$975$	−4.01021	−	7.63066i	−0.128429	−	0.244377i
$976$	−5.10478	+	2.94725i	−0.163400	+	0.0943390i
$977$	12.3523	+	21.3947i	0.395184	+	0.684479i	0.993125	−	0.117062i	$-0.0373475\pi$
$977$	12.3523	+	21.3947i	0.395184	+	0.684479i	−0.597941	+	0.801540i	$0.704014\pi$
$978$	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	−0.822364	−	0.568962i	$-0.807345\pi$
$983$	2.55694	−	4.42875i	0.0815537	−	0.141255i	0.903917	+	0.427707i	$0.140678\pi$
$984$	5.81518	+	4.30616i	0.185381	+	0.137275i
$985$	−16.3494	+	10.2646i	−0.520934	+	0.327059i
$986$	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
$990$	−18.9261	+	11.6963i	−0.601510	+	0.371733i
$991$	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
$995$	27.8749	+	44.3987i	0.883693	+	1.40753i
$996$	20.1604	−	8.75759i	0.638807	−	0.277495i
$997$	26.6243	−	46.1147i	0.843201	−	1.46047i	−0.0439742	−	0.999033i	$-0.514002\pi$
$997$	26.6243	−	46.1147i	0.843201	−	1.46047i	0.887175	−	0.461434i	$-0.152665\pi$
$998$		−	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.659.59	yes	144
5.4	even	2	inner	990.2.o.a.659.14	yes	144
9.5	odd	6	inner	990.2.o.a.329.50	yes	144
11.10	odd	2	inner	990.2.o.a.659.23	yes	144
45.14	odd	6	inner	990.2.o.a.329.23	yes	144
55.54	odd	2	inner	990.2.o.a.659.50	yes	144
99.32	even	6	inner	990.2.o.a.329.14	✓	144
495.329	even	6	inner	990.2.o.a.329.59	yes	144

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

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} +(1.18897 + 1.89377i) 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} +(-2.18801 + 3.19572i) q^{15} +(-0.500000 + 0.866025i) q^{16} +0.515407i q^{17} +(-2.86953 + 0.875104i) q^{18} -3.42216i q^{19} +(-1.04557 + 1.97656i) 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} +(-2.17272 + 4.50325i) q^{25} +0.995381i q^{26} +(-4.89628 - 1.73966i) q^{27} -1.99747 q^{28} +(2.19758 - 3.80632i) q^{29} +(-3.49273 + 1.67357i) 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} +(-1.89377 + 1.18897i) 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} +(-6.58677 - 1.27059i) q^{45} +5.94409i q^{46} +(0.478067 - 0.828036i) q^{47} +(-1.72085 - 0.196677i) q^{48} +(1.50506 + 2.60684i) q^{49} +(-4.13326 + 2.81357i) q^{50} +(-0.818794 + 0.355681i) q^{51} +(-0.497691 + 0.862025i) q^{52} +1.55175 q^{53} +(-3.37047 - 3.95473i) q^{54} +(7.17160 - 1.88895i) 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} +(-3.86158 - 0.297011i) q^{60} +(5.10478 + 2.94725i) q^{61} +0.120907i q^{62} +(-1.74799 - 5.73179i) q^{63} -1.00000 q^{64} +(-1.04074 + 1.96743i) 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} +(-3.94811 - 2.08849i) q^{70} -0.982823i q^{71} +(-2.19263 - 2.04753i) q^{72} +10.8871 q^{73} +(3.73336 - 6.46637i) q^{74} +(-8.65342 - 0.343977i) 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} +(-0.976061 + 0.612802i) q^{85} +(-0.141828 + 0.0818843i) q^{86} +(7.56340 + 0.864426i) q^{87} +(3.16545 + 0.989910i) q^{88} +9.77063i q^{89} +(-5.06902 - 4.39375i) q^{90} -1.98824 q^{91} +(-2.97205 + 5.14774i) q^{92} +(-0.124625 + 0.168297i) q^{93} +(0.828036 - 0.478067i) q^{94} +(6.48077 - 4.06883i) 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

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more