LMFDB - Embedded newform 680.2.ct.a.173.42

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [680,2,Mod(133,680)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(680, base_ring=CyclotomicField(16)) chi = DirichletCharacter(H, H._module([0, 8, 12, 9])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("680.133"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 680 = 2^{3} \cdot 5 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	680.ct (of order $16$, degree $8$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$5.42982733745$
Analytic rank:	$0$
Dimension:	$832$
Relative dimension:	$104$ over $\Q(\zeta_{16})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{16}]$

Embedding invariants

Embedding label			173.42
Character	$\chi$	$=$	680.173
Dual form			680.2.ct.a.397.42

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.422420 + 1.34965i) q^{2} +(0.863808 - 0.577178i) q^{3} +(-1.64312 - 1.14024i) q^{4} +(1.72803 - 1.41913i) q^{5} +(0.414100 + 1.40965i) q^{6} +(0.770271 + 3.87241i) q^{7} +(2.23302 - 1.73598i) q^{8} +(-0.735021 + 1.77450i) q^{9} +(1.18538 + 2.93170i) q^{10} +(-0.874343 + 0.173918i) q^{11} +(-2.07746 - 0.0365739i) q^{12} -2.28012 q^{13} +(-5.55179 - 0.596186i) q^{14} +(0.673594 - 2.22323i) q^{15} +(1.39971 + 3.74711i) q^{16} +(0.535855 + 4.08814i) q^{17} +(-2.08447 - 1.74161i) q^{18} +(5.94539 - 2.46266i) q^{19} +(-4.45751 + 0.361436i) q^{20} +(2.90044 + 2.90044i) q^{21} +(0.134611 - 1.25353i) q^{22} +(2.41192 + 1.61159i) q^{23} +(0.926924 - 2.78840i) q^{24} +(0.972154 - 4.90458i) q^{25} +(0.963168 - 3.07737i) q^{26} +(0.997318 + 5.01385i) q^{27} +(3.14983 - 7.24114i) q^{28} +(-1.30777 + 0.873827i) q^{29} +(2.71605 + 1.84826i) q^{30} +(0.405395 - 2.03806i) q^{31} +(-5.64856 + 0.306263i) q^{32} +(-0.654883 + 0.654883i) q^{33} +(-5.74392 - 1.00369i) q^{34} +(6.82649 + 5.59852i) q^{35} +(3.23108 - 2.07762i) q^{36} +(4.66437 + 6.98072i) q^{37} +(0.812285 + 9.06448i) q^{38} +(-1.96959 + 1.31603i) q^{39} +(1.39513 - 6.16876i) q^{40} +(-0.653766 + 0.978430i) q^{41} +(-5.13978 + 2.68938i) q^{42} +(5.12477 - 2.12275i) q^{43} +(1.63496 + 0.711193i) q^{44} +(1.24810 + 4.10947i) q^{45} +(-3.19393 + 2.57448i) q^{46} +2.65486 q^{47} +(3.37183 + 2.42890i) q^{48} +(-7.93510 + 3.28683i) q^{49} +(6.20882 + 3.38386i) q^{50} +(2.82246 + 3.22208i) q^{51} +(3.74652 + 2.59988i) q^{52} +(-1.01195 + 2.44306i) q^{53} +(-7.18825 - 0.771920i) q^{54} +(-1.26408 + 1.54134i) q^{55} +(8.44247 + 7.30998i) q^{56} +(3.71428 - 5.55881i) q^{57} +(-0.626933 - 2.13416i) q^{58} +(3.82876 - 9.24344i) q^{59} +(-3.64182 + 2.88499i) q^{60} +(-4.80516 + 7.19144i) q^{61} +(2.57942 + 1.40806i) q^{62} +(-7.43775 - 1.47946i) q^{63} +(1.97271 - 7.75296i) q^{64} +(-3.94011 + 3.23578i) q^{65} +(-0.607229 - 1.16050i) q^{66} +(0.596874 - 0.596874i) q^{67} +(3.78098 - 7.32831i) q^{68} +3.01361 q^{69} +(-10.4397 + 6.84847i) q^{70} +(-8.85604 - 1.76158i) q^{71} +(1.43919 + 5.23846i) q^{72} +(2.95504 - 14.8560i) q^{73} +(-11.3919 + 3.34648i) q^{74} +(-1.99106 - 4.79772i) q^{75} +(-12.5770 - 2.73271i) q^{76} +(-1.34696 - 3.25185i) q^{77} +(-0.944198 - 3.21417i) q^{78} +(-7.25794 + 1.44369i) q^{79} +(7.73635 + 4.48874i) q^{80} +(-0.319046 - 0.319046i) q^{81} +(-1.04438 - 1.29567i) q^{82} +(-16.6322 - 6.88930i) q^{83} +(-1.45858 - 8.07297i) q^{84} +(6.72756 + 6.30396i) q^{85} +(0.700169 + 7.81335i) q^{86} +(-0.625312 + 1.50964i) q^{87} +(-1.65050 + 1.90621i) q^{88} +(7.27719 + 7.27719i) q^{89} +(-6.07357 - 0.0514168i) q^{90} +(-1.75631 - 8.82956i) q^{91} +(-2.12547 - 5.39821i) q^{92} +(-0.826139 - 1.99447i) q^{93} +(-1.12146 + 3.58314i) q^{94} +(6.77896 - 12.6928i) q^{95} +(-4.70250 + 3.52478i) q^{96} +(-0.0315133 + 0.158428i) q^{97} +(-1.08413 - 12.0980i) q^{98} +(0.334044 - 1.67935i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 832 q - 8 q^{2} - 16 q^{6} - 16 q^{7} - 8 q^{8} - 8 q^{10} + 16 q^{12} + 32 q^{14} - 16 q^{15} - 16 q^{17} - 16 q^{18} - 8 q^{20} - 8 q^{22} - 16 q^{23} - 16 q^{25} - 48 q^{26} + 24 q^{28} + 56 q^{30} - 32 q^{31}+ \cdots - 16 q^{97}+O(q^{100}) $ 832 * q - 8 * q^2 - 16 * q^6 - 16 * q^7 - 8 * q^8 - 8 * q^10 + 16 * q^12 + 32 * q^14 - 16 * q^15 - 16 * q^17 - 16 * q^18 - 8 * q^20 - 8 * q^22 - 16 * q^23 - 16 * q^25 - 48 * q^26 + 24 * q^28 + 56 * q^30 - 32 * q^31 - 8 * q^32 + 48 * q^36 - 16 * q^38 - 96 * q^39 - 64 * q^40 - 32 * q^41 - 24 * q^42 - 32 * q^46 - 32 * q^47 - 136 * q^48 - 16 * q^52 + 64 * q^54 - 16 * q^55 - 16 * q^56 - 16 * q^57 - 64 * q^58 - 8 * q^60 - 8 * q^62 + 32 * q^63 - 96 * q^65 - 16 * q^66 - 64 * q^68 + 56 * q^70 - 32 * q^71 - 96 * q^73 - 16 * q^76 - 160 * q^78 + 40 * q^80 - 32 * q^81 - 8 * q^82 + 96 * q^84 - 32 * q^86 - 16 * q^87 - 96 * q^88 + 88 * q^90 - 120 * q^92 - 48 * q^94 - 16 * q^95 - 16 * q^96 - 16 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/680\mathbb{Z}\right)^\times$.

$n$	$137$	$241$	$341$	$511$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{1}{16}\right)$	$-1$	$1$

Coefficient data

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

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

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

$2$	−0.422420	+	1.34965i	−0.298696	+	0.954348i
$2$	−0.422420	+	1.34965i	−0.298696	+	0.954348i
$3$	0.863808	−	0.577178i	0.498720	−	0.333234i	−0.280637	−	0.959814i	$-0.590546\pi$
$3$	0.863808	−	0.577178i	0.498720	−	0.333234i	0.779357	+	0.626580i	$0.215546\pi$
$4$	−1.64312	−	1.14024i	−0.821561	−	0.570120i
$5$	1.72803	−	1.41913i	0.772797	−	0.634653i
$5$	1.72803	−	1.41913i	0.772797	−	0.634653i
$6$	0.414100	+	1.40965i	0.169056	+	0.575488i
$7$	0.770271	+	3.87241i	0.291135	+	1.46363i	0.798548	+	0.601931i	$0.205602\pi$
$7$	0.770271	+	3.87241i	0.291135	+	1.46363i	−0.507413	+	0.861703i	$0.669398\pi$
$8$	2.23302	−	1.73598i	0.789490	−	0.613763i
$9$	−0.735021	+	1.77450i	−0.245007	+	0.591499i
$10$	1.18538	+	2.93170i	0.374849	+	0.927086i
$11$	−0.874343	+	0.173918i	−0.263624	+	0.0524381i	−0.325133	−	0.945668i	$-0.605409\pi$
$11$	−0.874343	+	0.173918i	−0.263624	+	0.0524381i	0.0615083	+	0.998107i	$0.480409\pi$
$12$	−2.07746	−	0.0365739i	−0.599712	−	0.0105580i
$13$	−2.28012			−0.632391			−0.316196	−	0.948694i	$-0.602406\pi$
$13$	−2.28012			−0.632391			−0.316196	+	0.948694i	$0.602406\pi$
$14$	−5.55179	−	0.596186i	−1.48378	−	0.159337i
$15$	0.673594	−	2.22323i	0.173921	−	0.574036i
$16$	1.39971	+	3.74711i	0.349926	+	0.936777i
$17$	0.535855	+	4.08814i	0.129964	+	0.991519i
$17$	0.535855	+	4.08814i	0.129964	+	0.991519i
$18$	−2.08447	−	1.74161i	−0.491313	−	0.410500i
$19$	5.94539	−	2.46266i	1.36397	−	0.564973i	0.423820	−	0.905746i	$-0.360689\pi$
$19$	5.94539	−	2.46266i	1.36397	−	0.564973i	0.940145	+	0.340773i	$0.110689\pi$
$20$	−4.45751	+	0.361436i	−0.996729	+	0.0808194i
$21$	2.90044	+	2.90044i	0.632927	+	0.632927i
$22$	0.134611	−	1.25353i	0.0286993	−	0.267252i
$23$	2.41192	+	1.61159i	0.502919	+	0.336040i	0.781014	−	0.624514i	$-0.214703\pi$
$23$	2.41192	+	1.61159i	0.502919	+	0.336040i	−0.278094	+	0.960554i	$0.589703\pi$
$24$	0.926924	−	2.78840i	0.189208	−	0.569181i
$25$	0.972154	−	4.90458i	0.194431	−	0.980916i
$26$	0.963168	−	3.07737i	0.188893	−	0.603522i
$27$	0.997318	+	5.01385i	0.191934	+	0.964917i
$28$	3.14983	−	7.24114i	0.595262	−	1.36845i
$29$	−1.30777	+	0.873827i	−0.242848	+	0.162266i	−0.671038	−	0.741423i	$-0.734151\pi$
$29$	−1.30777	+	0.873827i	−0.242848	+	0.162266i	0.428190	+	0.903689i	$0.359151\pi$
$30$	2.71605	+	1.84826i	0.495881	+	0.337444i
$31$	0.405395	−	2.03806i	0.0728111	−	0.366046i	−0.927152	−	0.374686i	$-0.877750\pi$
$31$	0.405395	−	2.03806i	0.0728111	−	0.366046i	0.999963	+	0.00864049i	$0.00275039\pi$
$32$	−5.64856	+	0.306263i	−0.998533	+	0.0541402i
$33$	−0.654883	+	0.654883i	−0.114000	+	0.114000i
$34$	−5.74392	−	1.00369i	−0.985074	−	0.172132i
$35$	6.82649	+	5.59852i	1.15389	+	0.946323i
$36$	3.23108	−	2.07762i	0.538514	−	0.346269i
$37$	4.66437	+	6.98072i	0.766817	+	1.14762i	0.985141	+	0.171746i	$0.0549410\pi$
$37$	4.66437	+	6.98072i	0.766817	+	1.14762i	−0.218324	+	0.975876i	$0.570059\pi$
$38$	0.812285	+	9.06448i	0.131770	+	1.47045i
$39$	−1.96959	+	1.31603i	−0.315386	+	0.210734i
$40$	1.39513	−	6.16876i	0.220589	−	0.975367i
$41$	−0.653766	+	0.978430i	−0.102101	+	0.152805i	−0.879002	−	0.476817i	$-0.841790\pi$
$41$	−0.653766	+	0.978430i	−0.102101	+	0.152805i	0.776901	+	0.629622i	$0.216790\pi$
$42$	−5.13978	+	2.68938i	−0.793086	+	0.414980i
$43$	5.12477	−	2.12275i	0.781520	−	0.323716i	0.0439913	−	0.999032i	$-0.485993\pi$
$43$	5.12477	−	2.12275i	0.781520	−	0.323716i	0.737529	+	0.675316i	$0.235993\pi$
$44$	1.63496	+	0.711193i	0.246480	+	0.107216i
$45$	1.24810	+	4.10947i	0.186056	+	0.612603i
$46$	−3.19393	+	2.57448i	−0.470919	+	0.379586i
$47$	2.65486			0.387251			0.193625	−	0.981076i	$-0.437975\pi$
$47$	2.65486			0.387251			0.193625	+	0.981076i	$0.437975\pi$
$48$	3.37183	+	2.42890i	0.486681	+	0.350582i
$49$	−7.93510	+	3.28683i	−1.13359	+	0.469547i
$50$	6.20882	+	3.38386i	0.878060	+	0.478550i
$51$	2.82246	+	3.22208i	0.395223	+	0.451182i
$52$	3.74652	+	2.59988i	0.519548	+	0.360539i
$53$	−1.01195	+	2.44306i	−0.139002	+	0.335580i	−0.978016	−	0.208530i	$-0.933132\pi$
$53$	−1.01195	+	2.44306i	−0.139002	+	0.335580i	0.839014	+	0.544109i	$0.183132\pi$
$54$	−7.18825	−	0.771920i	−0.978197	−	0.105045i
$55$	−1.26408	+	1.54134i	−0.170448	+	0.207834i
$56$	8.44247	+	7.30998i	1.12817	+	0.976837i
$57$	3.71428	−	5.55881i	0.491968	−	0.736283i
$58$	−0.626933	−	2.13416i	−0.0823203	−	0.280229i
$59$	3.82876	−	9.24344i	0.498462	−	1.20339i	−0.451850	−	0.892094i	$-0.649236\pi$
$59$	3.82876	−	9.24344i	0.498462	−	1.20339i	0.950312	−	0.311300i	$-0.100764\pi$
$60$	−3.64182	+	2.88499i	−0.470157	+	0.372450i
$61$	−4.80516	+	7.19144i	−0.615238	+	0.920769i	−0.999997	−	0.00224780i	$-0.999285\pi$
$61$	−4.80516	+	7.19144i	−0.615238	+	0.920769i	0.384759	+	0.923017i	$0.374285\pi$
$62$	2.57942	+	1.40806i	0.327587	+	0.178824i
$63$	−7.43775	−	1.47946i	−0.937068	−	0.186394i
$64$	1.97271	−	7.75296i	0.246589	−	0.969120i
$65$	−3.94011	+	3.23578i	−0.488710	+	0.401349i
$66$	−0.607229	−	1.16050i	−0.0747447	−	0.142848i
$67$	0.596874	−	0.596874i	0.0729197	−	0.0729197i	−0.669706	−	0.742626i	$-0.733580\pi$
$67$	0.596874	−	0.596874i	0.0729197	−	0.0729197i	0.742626	+	0.669706i	$0.233580\pi$
$68$	3.78098	−	7.32831i	0.458511	−	0.888689i
$69$	3.01361			0.362796
$70$	−10.4397	+	6.84847i	−1.24778	+	0.818549i
$71$	−8.85604	−	1.76158i	−1.05102	−	0.209061i	−0.360786	−	0.932648i	$-0.617492\pi$
$71$	−8.85604	−	1.76158i	−1.05102	−	0.209061i	−0.690232	+	0.723588i	$0.742492\pi$
$72$	1.43919	+	5.23846i	0.169610	+	0.617359i
$73$	2.95504	−	14.8560i	0.345861	−	1.73876i	−0.281070	−	0.959687i	$-0.590689\pi$
$73$	2.95504	−	14.8560i	0.345861	−	1.73876i	0.626931	−	0.779075i	$-0.284311\pi$
$74$	−11.3919	+	3.34648i	−1.32428	+	0.389020i
$75$	−1.99106	−	4.79772i	−0.229908	−	0.553993i
$76$	−12.5770	−	2.73271i	−1.44268	−	0.313464i
$77$	−1.34696	−	3.25185i	−0.153500	−	0.370583i
$78$	−0.944198	−	3.21417i	−0.106909	−	0.363934i
$79$	−7.25794	+	1.44369i	−0.816582	+	0.162428i	−0.585673	−	0.810547i	$-0.699170\pi$
$79$	−7.25794	+	1.44369i	−0.816582	+	0.162428i	−0.230908	+	0.972975i	$0.574170\pi$
$80$	7.73635	+	4.48874i	0.864951	+	0.501857i
$81$	−0.319046	−	0.319046i	−0.0354495	−	0.0354495i
$82$	−1.04438	−	1.29567i	−0.115332	−	0.143082i
$83$	−16.6322	−	6.88930i	−1.82563	−	0.756199i	−0.971867	−	0.235531i	$-0.924317\pi$
$83$	−16.6322	−	6.88930i	−1.82563	−	0.756199i	−0.853759	−	0.520668i	$-0.825683\pi$
$84$	−1.45858	−	8.07297i	−0.159144	−	0.880833i
$85$	6.72756	+	6.30396i	0.729706	+	0.683761i
$86$	0.700169	+	7.81335i	0.0755012	+	0.842535i
$87$	−0.625312	+	1.50964i	−0.0670405	+	0.161850i
$88$	−1.65050	+	1.90621i	−0.175944	+	0.203202i
$89$	7.27719	+	7.27719i	0.771380	+	0.771380i	0.978348	−	0.206968i	$-0.0663595\pi$
$89$	7.27719	+	7.27719i	0.771380	+	0.771380i	−0.206968	+	0.978348i	$0.566359\pi$
$90$	−6.07357	−	0.0514168i	−0.640211	−	0.00541981i
$91$	−1.75631	−	8.82956i	−0.184111	−	0.925590i
$92$	−2.12547	−	5.39821i	−0.221596	−	0.562802i
$93$	−0.826139	−	1.99447i	−0.0856666	−	0.206817i
$94$	−1.12146	+	3.58314i	−0.115670	+	0.369572i
$95$	6.77896	−	12.6928i	0.695507	−	1.30225i
$96$	−4.70250	+	3.52478i	−0.479947	+	0.359746i
$97$	−0.0315133	+	0.158428i	−0.00319970	+	0.0160860i	−0.982352	−	0.187041i	$-0.940110\pi$
$97$	−0.0315133	+	0.158428i	−0.00319970	+	0.0160860i	0.979152	+	0.203127i	$0.0651103\pi$
$98$	−1.08413	−	12.0980i	−0.109514	−	1.22209i
$99$	0.334044	−	1.67935i	0.0335727	−	0.168781i
$100$	−7.18977	+	6.95034i	−0.718977	+	0.695034i
$101$	5.94421			0.591471			0.295736	−	0.955270i	$-0.404435\pi$
$101$	5.94421			0.591471			0.295736	+	0.955270i	$0.404435\pi$
$102$	−5.54095	+	2.44827i	−0.548636	+	0.242414i
$103$	9.94803	+	9.94803i	0.980209	+	0.980209i	0.999808	−	0.0195991i	$-0.00623897\pi$
$103$	9.94803	+	9.94803i	0.980209	+	0.980209i	−0.0195991	+	0.999808i	$0.506239\pi$
$104$	−5.09154	+	3.95825i	−0.499267	+	0.388139i
$105$	9.12812	+	0.895943i	0.890814	+	0.0874351i
$106$	−2.86981	−	2.39777i	−0.278741	−	0.232892i
$107$	3.93235	−	19.7693i	0.380155	−	1.91117i	−0.0308317	−	0.999525i	$-0.509816\pi$
$107$	3.93235	−	19.7693i	0.380155	−	1.91117i	0.410986	−	0.911642i	$-0.365184\pi$
$108$	4.07828	−	9.37556i	0.392433	−	0.902164i
$109$	−6.69807	+	10.0244i	−0.641559	+	0.960160i	0.358091	+	0.933687i	$0.383428\pi$
$109$	−6.69807	+	10.0244i	−0.641559	+	0.960160i	−0.999650	+	0.0264735i	$0.991572\pi$
$110$	−1.54630	−	2.35716i	−0.147434	−	0.224746i
$111$	8.05823	+	3.33783i	0.764853	+	0.316813i
$112$	−13.4322	+	8.30653i	−1.26922	+	0.784893i
$113$	3.00529	−	4.49773i	0.282714	−	0.423111i	−0.662749	−	0.748842i	$-0.730610\pi$
$113$	3.00529	−	4.49773i	0.282714	−	0.423111i	0.945463	+	0.325731i	$0.105610\pi$
$114$	5.93348	+	7.36114i	0.555721	+	0.689434i
$115$	6.45491	−	0.637944i	0.601923	−	0.0594886i
$116$	3.14521	+	0.0553715i	0.292025	+	0.00514112i
$117$	1.67593	−	4.04606i	0.154940	−	0.374059i
$118$	10.8581	+	9.07211i	0.999568	+	0.835155i
$119$	−15.4182	+	5.22402i	−1.41338	+	0.478885i
$120$	−2.35535	−	6.13386i	−0.215013	−	0.559942i
$121$	−9.42845	+	3.90539i	−0.857132	+	0.355035i
$122$	−7.67614	−	9.52311i	−0.694965	−	0.862182i
$123$			1.22252i			0.110230i
$124$	−2.98999	+	2.88653i	−0.268509	+	0.259218i
$125$	−5.28032	−	9.85486i	−0.472286	−	0.881445i
$126$	5.13861	−	9.41342i	0.457784	−	0.838614i
$127$	0.547142	+	1.32092i	0.0485510	+	0.117213i	0.946294	−	0.323306i	$-0.104794\pi$
$127$	0.547142	+	1.32092i	0.0485510	+	0.117213i	−0.897743	+	0.440519i	$0.854794\pi$
$128$	9.63049	+	5.93748i	0.851223	+	0.524804i
$129$	3.20161	−	4.79155i	0.281886	−	0.421873i
$130$	−2.70280	−	6.68463i	−0.237051	−	0.586281i
$131$	−6.01872	−	9.00765i	−0.525858	−	0.787002i	0.469532	−	0.882916i	$-0.344423\pi$
$131$	−6.01872	−	9.00765i	−0.525858	−	0.787002i	−0.995390	+	0.0959136i	$0.969423\pi$
$132$	1.82278	−	0.329329i	0.158652	−	0.0286645i
$133$	14.1160	+	21.1261i	1.22401	+	1.83186i
$134$	0.553441	+	1.05770i	0.0478100	+	0.0913717i
$135$	8.83869	+	7.24876i	0.760713	+	0.623874i
$136$	8.29351	+	8.19864i	0.711163	+	0.703027i
$137$	−2.31293	+	2.31293i	−0.197607	+	0.197607i	−0.798974	−	0.601366i	$-0.794623\pi$
$137$	−2.31293	+	2.31293i	−0.197607	+	0.197607i	0.601366	+	0.798974i	$0.294623\pi$
$138$	−1.27301	+	4.06732i	−0.108366	+	0.346233i
$139$	17.5793	+	3.49674i	1.49106	+	0.296590i	0.872292	−	0.488985i	$-0.162633\pi$
$139$	17.5793	+	3.49674i	1.49106	+	0.296590i	0.618766	+	0.785575i	$0.287633\pi$
$140$	−4.83311	−	16.9829i	−0.408473	−	1.43532i
$141$	2.29329	−	1.53233i	0.193130	−	0.129045i
$142$	6.11848	−	11.2085i	0.513452	−	0.940592i
$143$	1.99361	−	0.396553i	0.166714	−	0.0331614i
$144$	−7.67805	−	0.270429i	−0.639837	−	0.0225357i
$145$	−1.01980	+	3.36589i	−0.0846896	+	0.279522i
$146$	18.8022	+	10.2637i	1.55608	+	0.849433i
$147$	−4.95732	+	7.41915i	−0.408873	+	0.611921i
$148$	0.295566	−	16.7887i	0.0242953	−	1.38002i
$149$	−15.2950	−	15.2950i	−1.25301	−	1.25301i	−0.954362	−	0.298653i	$-0.903463\pi$
$149$	−15.2950	−	15.2950i	−1.25301	−	1.25301i	−0.298653	−	0.954362i	$-0.596537\pi$
$150$	7.31632	−	0.660588i	0.597375	−	0.0539368i
$151$	−3.68358	−	8.89295i	−0.299766	−	0.723698i	−0.999953	−	0.00973869i	$-0.996900\pi$
$151$	−3.68358	−	8.89295i	−0.299766	−	0.723698i	0.700187	−	0.713960i	$-0.253100\pi$
$152$	9.00100	−	15.8203i	0.730078	−	1.28319i
$153$	−7.64825	−	2.05399i	−0.618324	−	0.166055i
$154$	4.95785	−	0.444283i	0.399515	−	0.0358013i
$155$	−2.19173	−	4.09712i	−0.176044	−	0.329089i
$156$	4.73687	+	0.0833928i	0.379253	+	0.00667677i
$157$	−6.89136			−0.549990			−0.274995	−	0.961446i	$-0.588676\pi$
$157$	−6.89136			−0.549990			−0.274995	+	0.961446i	$0.588676\pi$
$158$	1.11741	−	10.4055i	0.0888965	−	0.827820i
$159$	0.535950	+	2.69440i	0.0425036	+	0.213680i
$160$	−9.32623	+	8.54525i	−0.737303	+	0.675562i
$161$	−4.38292	+	10.5813i	−0.345422	+	0.833923i
$162$	0.565372	−	0.295830i	0.0444198	−	0.0232426i
$163$	18.3387	−	3.64780i	1.43640	−	0.285718i	0.585341	−	0.810787i	$-0.300961\pi$
$163$	18.3387	−	3.64780i	1.43640	−	0.285718i	0.851059	+	0.525070i	$0.175961\pi$
$164$	2.18986	−	0.862231i	0.171000	−	0.0673289i
$165$	−0.202293	+	2.06102i	−0.0157485	+	0.160450i
$166$	16.3240	−	19.5376i	1.26698	−	1.51641i
$167$	−7.51585	−	11.2483i	−0.581594	−	0.870417i	0.417677	−	0.908596i	$-0.362844\pi$
$167$	−7.51585	−	11.2483i	−0.581594	−	0.870417i	−0.999271	+	0.0381784i	$0.987844\pi$
$168$	11.5118	+	1.44161i	0.888157	+	0.111222i
$169$	−7.80105			−0.600081
$170$	−11.3500	+	6.41694i	−0.870506	+	0.492157i
$171$			12.3602i			0.945206i
$172$	−10.8411	−	2.35553i	−0.826624	−	0.179607i
$173$	6.91780	−	4.62233i	0.525951	−	0.351429i	−0.264076	−	0.964502i	$-0.585067\pi$
$173$	6.91780	−	4.62233i	0.525951	−	0.351429i	0.790026	+	0.613073i	$0.210067\pi$
$174$	−1.77334	−	1.48165i	−0.134437	−	0.112324i
$175$	19.7414	−	0.0132726i	1.49231	−	0.00100331i
$176$	−1.87551	−	3.03282i	−0.141372	−	0.228608i
$177$	−2.02780	−	10.1944i	−0.152419	−	0.766261i
$178$	−12.8957	+	6.74764i	−0.966574	+	0.505757i
$179$	10.6251	+	4.40106i	0.794158	+	0.328951i	0.742614	−	0.669720i	$-0.233586\pi$
$179$	10.6251	+	4.40106i	0.794158	+	0.328951i	0.0515440	+	0.998671i	$0.483586\pi$
$180$	2.63499	−	8.17549i	0.196401	−	0.609365i
$181$	−11.2333	+	2.23443i	−0.834961	+	0.166084i	−0.594014	−	0.804454i	$-0.702458\pi$
$181$	−11.2333	+	2.23443i	−0.834961	+	0.166084i	−0.240946	+	0.970538i	$0.577458\pi$
$182$	12.6587	+	1.35938i	0.938328	+	0.100764i
$183$			8.98546i			0.664224i
$184$	8.18354	−	0.588343i	0.603299	−	0.0433732i
$185$	17.9667	+	5.44354i	1.32094	+	0.400217i
$186$	3.04083	−	0.272494i	0.222964	−	0.0199802i
$187$	−1.17952	−	3.48124i	−0.0862550	−	0.254573i
$188$	−4.36226	−	3.02718i	−0.318150	−	0.220779i
$189$	−18.6475	+	7.72405i	−1.35641	+	0.561842i
$190$	14.2673	+	14.5109i	1.03506	+	1.05273i
$191$	5.11132	−	5.11132i	0.369842	−	0.369842i	−0.497578	−	0.867419i	$-0.665777\pi$
$191$	5.11132	−	5.11132i	0.369842	−	0.369842i	0.867419	+	0.497578i	$0.165777\pi$
$192$	−2.77079	−	7.83568i	−0.199965	−	0.565491i
$193$	14.6808	+	9.80938i	1.05674	+	0.706094i	0.957343	−	0.288953i	$-0.0933072\pi$
$193$	14.6808	+	9.80938i	1.05674	+	0.706094i	0.0994016	+	0.995047i	$0.468307\pi$
$194$	−0.200511	−	0.109455i	−0.0143959	−	0.00785843i
$195$	−1.53588	+	5.06924i	−0.109986	+	0.363016i
$196$	16.7861	+	3.64726i	1.19901	+	0.260518i
$197$	−2.06555	−	10.3842i	−0.147164	−	0.739844i	−0.981931	−	0.189240i	$-0.939398\pi$
$197$	−2.06555	−	10.3842i	−0.147164	−	0.739844i	0.834767	−	0.550604i	$-0.185602\pi$
$198$	2.12543	+	1.16023i	0.151048	+	0.0824543i
$199$	0.727150	+	1.08826i	0.0515463	+	0.0771445i	0.856348	−	0.516400i	$-0.172728\pi$
$199$	0.727150	+	1.08826i	0.0515463	+	0.0771445i	−0.804801	+	0.593544i	$0.797728\pi$
$200$	−6.34344	−	12.6396i	−0.448549	−	0.893758i
$201$	0.171082	−	0.860087i	0.0120672	−	0.0606658i
$202$	−2.51095	+	8.02262i	−0.176670	+	0.564469i
$203$	−4.39116	−	4.39116i	−0.308199	−	0.308199i
$204$	−0.963700	−	8.51255i	−0.0674725	−	0.595998i
$205$	0.258792	+	2.61853i	0.0180748	+	0.182886i
$206$	−17.6286	+	9.22414i	−1.22825	+	0.642676i
$207$	−4.63257	+	3.09539i	−0.321986	+	0.215144i
$208$	−3.19150	−	8.54386i	−0.221290	−	0.592410i
$209$	−4.77001	+	3.18722i	−0.329948	+	0.220464i
$210$	−5.06511	+	11.9413i	−0.349526	+	0.824030i
$211$	−11.8854	−	7.94154i	−0.818222	−	0.546718i	0.0745553	−	0.997217i	$-0.476246\pi$
$211$	−11.8854	−	7.94154i	−0.818222	−	0.546718i	−0.892777	+	0.450498i	$0.851246\pi$
$212$	4.44842	−	2.86038i	0.305519	−	0.196452i
$213$	−8.66666	+	3.58985i	−0.593830	+	0.245972i
$214$	25.0205	+	13.6582i	1.71037	+	0.933657i
$215$	5.84329	−	10.9409i	0.398509	−	0.746161i
$216$	10.9310	+	9.46469i	0.743760	+	0.643990i
$217$	8.20446			0.556955
$218$	−10.7000	−	13.2746i	−0.724696	−	0.899066i
$219$	−6.02196	−	14.5383i	−0.406927	−	0.982408i
$220$	3.83453	−	1.09126i	0.258524	−	0.0735726i
$221$	−1.22181	−	9.32144i	−0.0821880	−	0.627028i
$222$	−7.90887	+	9.46585i	−0.530808	+	0.635306i
$223$	3.95573	+	1.63852i	0.264895	+	0.109723i	0.511178	−	0.859475i	$-0.329209\pi$
$223$	3.95573	+	1.63852i	0.264895	+	0.109723i	−0.246283	+	0.969198i	$0.579209\pi$
$224$	−5.53689	−	21.6376i	−0.369949	−	1.44573i
$225$	7.98861	+	5.33005i	0.532574	+	0.355337i
$226$	4.80088	+	5.95603i	0.319350	+	0.396189i
$227$	−3.16095	−	2.11208i	−0.209800	−	0.140184i	0.446231	−	0.894918i	$-0.352766\pi$
$227$	−3.16095	−	2.11208i	−0.209800	−	0.140184i	−0.656031	+	0.754734i	$0.727766\pi$
$228$	−12.4414	+	4.89864i	−0.823952	+	0.324420i
$229$	3.17302	−	7.66034i	0.209679	−	0.506210i	−0.783694	−	0.621147i	$-0.786667\pi$
$229$	3.17302	−	7.66034i	0.209679	−	0.506210i	0.993373	+	0.114938i	$0.0366668\pi$
$230$	−1.86568	+	8.98136i	−0.123019	+	0.592214i
$231$	−3.04041	−	2.03154i	−0.200045	−	0.133665i
$232$	−1.40333	+	4.22154i	−0.0921331	+	0.277158i
$233$	−12.8070	−	2.54747i	−0.839013	−	0.166890i	−0.243163	−	0.969985i	$-0.578185\pi$
$233$	−12.8070	−	2.54747i	−0.839013	−	0.166890i	−0.595851	+	0.803095i	$0.703185\pi$
$234$	4.75283	+	3.97107i	0.310702	+	0.259597i
$235$	4.58767	−	3.76758i	0.299266	−	0.245770i
$236$	−16.8309	+	10.8224i	−1.09560	+	0.704479i
$237$	−5.43619	+	5.43619i	−0.353119	+	0.353119i
$238$	−0.537661	−	23.0159i	−0.0348514	−	1.49190i
$239$		−	5.81216i		−	0.375957i	−0.982173	−	0.187979i	$-0.939806\pi$
$239$		−	5.81216i		−	0.375957i	0.982173	−	0.187979i	$-0.0601936\pi$
$240$	9.27353	−	0.587841i	0.598604	−	0.0379450i
$241$	−12.3194	−	2.45048i	−0.793561	−	0.157849i	−0.218368	−	0.975867i	$-0.570073\pi$
$241$	−12.3194	−	2.45048i	−0.793561	−	0.157849i	−0.575193	+	0.818018i	$0.695073\pi$
$242$	−1.28816	−	14.3748i	−0.0828058	−	0.924050i
$243$	−15.5013	−	3.08340i	−0.994409	−	0.197800i
$244$	16.0954	−	6.33737i	1.03040	−	0.405709i
$245$	−9.04764	+	16.9406i	−0.578033	+	1.08230i
$246$	−1.64997	−	0.516415i	−0.105198	−	0.0329254i
$247$	−13.5562	+	5.61516i	−0.862560	+	0.357284i
$248$	−2.63278	−	5.25477i	−0.167182	−	0.333678i
$249$	−18.3434	+	3.64873i	−1.16247	+	0.231229i
$250$	15.5311	−	2.96370i	0.982276	−	0.187441i
$251$	9.23711	−	9.23711i	0.583041	−	0.583041i	−0.352697	−	0.935738i	$-0.614735\pi$
$251$	9.23711	−	9.23711i	0.583041	−	0.583041i	0.935738	+	0.352697i	$0.114735\pi$
$252$	10.5342	+	10.9118i	0.663592	+	0.687376i
$253$	−2.38913	−	0.989609i	−0.150203	−	0.0622162i
$254$	−2.01390	+	0.180470i	−0.126364	+	0.0113237i
$255$	9.44983	+	1.56242i	0.591771	+	0.0978423i
$256$	−12.0816	+	10.4897i	−0.755103	+	0.655606i
$257$	11.5245	−	27.8225i	0.718877	−	1.73552i	0.0423523	−	0.999103i	$-0.486515\pi$
$257$	11.5245	−	27.8225i	0.718877	−	1.73552i	0.676525	−	0.736420i	$-0.263485\pi$
$258$	5.11450	+	6.34511i	0.318415	+	0.395029i
$259$	−23.4394	+	23.4394i	−1.45645	+	1.45645i
$260$	10.1636	−	0.824116i	0.630323	−	0.0511095i
$261$	−0.589362	−	2.96292i	−0.0364806	−	0.183400i
$262$	14.6996	−	4.31817i	0.908146	−	0.266777i
$263$	13.4304	−	5.56305i	0.828154	−	0.343032i	0.0719821	−	0.997406i	$-0.477068\pi$
$263$	13.4304	−	5.56305i	0.828154	−	0.343032i	0.756172	+	0.654373i	$0.227068\pi$
$264$	−0.325497	+	2.59923i	−0.0200329	+	0.159972i
$265$	1.71834	+	5.65775i	0.105557	+	0.347553i
$266$	−34.4757	+	10.1276i	−2.11384	+	0.620963i
$267$	10.4863	+	2.08586i	0.641753	+	0.127653i
$268$	−1.66132	+	0.300158i	−0.101481	+	0.0183350i
$269$	−1.19490	+	6.00716i	−0.0728542	+	0.366263i	−0.999964	−	0.00852785i	$-0.997285\pi$
$269$	−1.19490	+	6.00716i	−0.0728542	+	0.366263i	0.927109	+	0.374791i	$0.122285\pi$
$270$	−13.5169	+	8.86714i	−0.822615	+	0.539637i
$271$		−	5.05018i		−	0.306777i	−0.988166	−	0.153388i	$-0.950981\pi$
$271$		−	5.05018i		−	0.306777i	0.988166	−	0.153388i	$-0.0490185\pi$
$272$	−14.5687	+	7.73009i	−0.883354	+	0.468706i
$273$	−6.61334	−	6.61334i	−0.400258	−	0.400258i
$274$	−2.14463	−	4.09869i	−0.129562	−	0.247611i
$275$	0.00299678	+	4.45736i	0.000180713	+	0.268789i
$276$	−4.95173	−	3.43624i	−0.298059	−	0.206837i
$277$	2.71759	−	13.6623i	0.163284	−	0.820886i	−0.809131	−	0.587629i	$-0.800062\pi$
$277$	2.71759	−	13.6623i	0.163284	−	0.820886i	0.972415	−	0.233257i	$-0.0749385\pi$
$278$	−12.1452	+	22.2489i	−0.728423	+	1.33440i
$279$	3.31855	+	2.21739i	0.198677	+	0.132751i
$280$	24.9626	+	0.650890i	1.49180	+	0.0388981i
$281$	−23.3760	−	9.68267i	−1.39450	−	0.577619i	−0.446179	−	0.894944i	$-0.647216\pi$
$281$	−23.3760	−	9.68267i	−1.39450	−	0.577619i	−0.948317	+	0.317324i	$0.897216\pi$
$282$	1.09938	+	3.74243i	0.0654669	+	0.222858i
$283$	−1.29923	−	0.868117i	−0.0772311	−	0.0516042i	0.516355	−	0.856375i	$-0.327288\pi$
$283$	−1.29923	−	0.868117i	−0.0772311	−	0.0516042i	−0.593586	+	0.804770i	$0.702288\pi$
$284$	12.5429	+	12.9925i	0.744287	+	0.770963i
$285$	−1.47029	−	14.8768i	−0.0870923	−	0.881226i
$286$	−0.306930	+	2.85819i	−0.0181492	+	0.169008i
$287$	−4.29246	−	1.77800i	−0.253376	−	0.104952i
$288$	3.60834	−	10.2485i	0.212624	−	0.603896i
$289$	−16.4257	+	4.38129i	−0.966219	+	0.257723i
$290$	−4.11200	−	2.79819i	−0.241465	−	0.164316i
$291$	0.0642198	+	0.155040i	0.00376463	+	0.00908863i
$292$	−21.7949	+	21.0408i	−1.27545	+	1.23132i
$293$		−	2.86120i		−	0.167153i	−0.996501	−	0.0835765i	$-0.973366\pi$
$293$		−	2.86120i		−	0.167153i	0.996501	−	0.0835765i	$-0.0266343\pi$
$294$	−7.91921	−	9.82465i	−0.461857	−	0.572985i
$295$	−6.50142	−	21.4064i	−0.378528	−	1.24633i
$296$	22.5340	+	7.49078i	1.30976	+	0.435393i
$297$	−1.74400	−	4.21038i	−0.101197	−	0.244311i
$298$	27.1038	−	14.1820i	1.57008	−	0.821542i
$299$	−5.49946	−	3.67462i	−0.318042	−	0.212509i
$300$	−2.19900	+	10.1535i	−0.126959	+	0.586215i
$301$	12.1676	+	18.2101i	0.701330	+	1.04961i
$302$	13.5584	−	1.21499i	0.780199	−	0.0699151i
$303$	5.13466	−	3.43087i	0.294978	−	0.197098i
$304$	17.5496	+	18.8310i	1.00654	+	1.08003i
$305$	1.90211	+	19.2461i	0.108915	+	1.10203i
$306$	6.00295	−	9.45483i	0.343166	−	0.540497i
$307$	−5.63745	−	5.63745i	−0.321746	−	0.321746i	0.527690	−	0.849437i	$-0.323058\pi$
$307$	−5.63745	−	5.63745i	−0.321746	−	0.321746i	−0.849437	+	0.527690i	$0.823058\pi$
$308$	−1.49467	+	6.87905i	−0.0851667	+	0.391970i
$309$	14.3350	+	2.85140i	0.815488	+	0.162211i
$310$	6.45552	−	1.22737i	0.366649	−	0.0697097i
$311$	15.3185	+	22.9258i	0.868633	+	1.30000i	0.952815	+	0.303550i	$0.0981720\pi$
$311$	15.3185	+	22.9258i	0.868633	+	1.30000i	−0.0841828	+	0.996450i	$0.526828\pi$
$312$	−2.11350	+	6.35790i	−0.119653	+	0.359945i
$313$	10.2513	−	2.03911i	0.579438	−	0.115257i	0.103334	−	0.994647i	$-0.467049\pi$
$313$	10.2513	−	2.03911i	0.579438	−	0.115257i	0.476103	+	0.879389i	$0.342049\pi$
$314$	2.91105	−	9.30094i	0.164280	−	0.524882i
$315$	−14.9522	+	7.99856i	−0.842459	+	0.450668i
$316$	13.5718	+	5.90362i	0.763475	+	0.332105i
$317$	−9.84290	+	14.7309i	−0.552832	+	0.827372i	−0.997669	−	0.0682397i	$-0.978262\pi$
$317$	−9.84290	+	14.7309i	−0.552832	+	0.827372i	0.444837	+	0.895612i	$0.353262\pi$
$318$	−3.86291	−	0.414823i	−0.216621	−	0.0232621i
$319$	0.991469	−	0.991469i	0.0555116	−	0.0555116i
$320$	−7.59354	−	16.1969i	−0.424492	−	0.905432i
$321$	−8.01358	−	19.3465i	−0.447275	−	1.07982i
$322$	−12.4296	−	10.3852i	−0.692677	−	0.578742i
$323$	13.2536	+	22.9859i	0.737448	+	1.27897i
$324$	0.160443	+	0.888020i	0.00891348	+	0.0493345i
$325$	−2.21663	+	11.1830i	−0.122956	+	0.620323i
$326$	−2.82338	+	26.2918i	−0.156373	+	1.45617i
$327$			12.5251i			0.692640i
$328$	0.238670	+	3.31978i	0.0131784	+	0.183304i
$329$	2.04496	+	10.2807i	0.112742	+	0.566794i
$330$	−2.69620	−	1.14364i	−0.148421	−	0.0629553i
$331$	18.2151	+	7.54496i	1.00120	+	0.414709i	0.822235	−	0.569148i	$-0.192727\pi$
$331$	18.2151	+	7.54496i	1.00120	+	0.414709i	0.178960	+	0.983856i	$0.442727\pi$
$332$	19.4734	+	30.2847i	1.06874	+	1.66209i
$333$	−15.8157	+	3.14593i	−0.866693	+	0.172396i
$334$	18.3561	−	5.39230i	1.00440	−	0.295053i
$335$	0.184374	−	1.87845i	0.0100734	−	0.102631i
$336$	−6.80849	+	14.9280i	−0.371434	+	0.814390i
$337$	16.1850	+	24.2225i	0.881651	+	1.31948i	0.946871	+	0.321613i	$0.104225\pi$
$337$	16.1850	+	24.2225i	0.881651	+	1.31948i	−0.0652205	+	0.997871i	$0.520775\pi$
$338$	3.29532	−	10.5287i	0.179242	−	0.572686i
$339$		−	5.61977i		−	0.305224i
$340$	−3.86617	−	18.0292i	−0.209673	−	0.977772i
$341$			1.85247i			0.100317i
$342$	−16.6819	−	5.22118i	−0.902056	−	0.282329i
$343$	−3.48530	−	5.21612i	−0.188189	−	0.281644i
$344$	7.75863	−	13.6367i	0.418317	−	0.735239i
$345$	5.20759	−	4.27669i	0.280367	−	0.230249i
$346$	3.31632	+	11.2892i	0.178286	+	0.606911i
$347$	0.276973	−	0.0550933i	0.0148687	−	0.00295756i	−0.187650	−	0.982236i	$-0.560087\pi$
$347$	0.276973	−	0.0550933i	0.0148687	−	0.00295756i	0.202519	+	0.979278i	$0.435087\pi$
$348$	2.74881	−	1.76751i	0.147352	−	0.0947487i
$349$	−4.41812	−	1.83005i	−0.236497	−	0.0979602i	0.261288	−	0.965261i	$-0.415853\pi$
$349$	−4.41812	−	1.83005i	−0.236497	−	0.0979602i	−0.497784	+	0.867301i	$0.665853\pi$
$350$	−8.32124	+	26.6496i	−0.444789	+	1.42448i
$351$	−2.27400	−	11.4322i	−0.121377	−	0.610205i
$352$	4.88551	−	1.25016i	0.260399	−	0.0666339i
$353$			27.7209i			1.47543i	0.675110	+	0.737717i	$0.264096\pi$
$353$			27.7209i			1.47543i	−0.675110	+	0.737717i	$0.735904\pi$
$354$	14.6155	+	1.56951i	0.776806	+	0.0834184i
$355$	−17.8034	+	9.52380i	−0.944905	+	0.505471i
$356$	−3.65957	−	20.2550i	−0.193957	−	1.07352i
$357$	−10.3032	+	13.4116i	−0.545302	+	0.709817i
$358$	−10.4282	+	12.4811i	−0.551146	+	0.659647i
$359$	−3.49004	−	8.42569i	−0.184197	−	0.444691i	0.804627	−	0.593781i	$-0.202366\pi$
$359$	−3.49004	−	8.42569i	−0.184197	−	0.444691i	−0.988824	+	0.149090i	$0.952366\pi$
$360$	9.92100	+	7.00982i	0.522883	+	0.369450i
$361$	15.8479	−	15.8479i	0.834101	−	0.834101i
$362$	1.72944	−	16.1049i	0.0908974	−	0.846452i
$363$	−5.89026	+	8.81540i	−0.309159	+	0.462688i
$364$	−7.18199	+	16.5107i	−0.376438	+	0.865394i
$365$	−15.9762	−	29.8651i	−0.836230	−	1.56321i
$366$	−12.1272	−	3.79563i	−0.633901	−	0.198401i
$367$	−9.29863	+	1.84961i	−0.485384	+	0.0965489i	−0.431715	−	0.902010i	$-0.642092\pi$
$367$	−9.29863	+	1.84961i	−0.485384	+	0.0965489i	−0.0536689	+	0.998559i	$0.517092\pi$
$368$	−2.66283	+	11.2935i	−0.138810	+	0.588713i
$369$	−1.25569	−	1.87927i	−0.0653686	−	0.0978310i
$370$	−14.9364	+	21.9493i	−0.776505	+	1.14109i
$371$	−10.2400	−	2.03686i	−0.531634	−	0.105749i
$372$	−0.916733	+	4.21916i	−0.0475304	+	0.218753i
$373$	−21.2294	−	21.2294i	−1.09922	−	1.09922i	−0.994502	−	0.104714i	$-0.966607\pi$
$373$	−21.2294	−	21.2294i	−1.09922	−	1.09922i	−0.104714	−	0.994502i	$-0.533393\pi$
$374$	5.19671	−	0.121397i	0.268716	−	0.00627730i
$375$	−10.2492	−	5.46502i	−0.529266	−	0.282213i
$376$	5.92834	−	4.60879i	0.305731	−	0.237680i
$377$	2.98188	−	1.99243i	0.153575	−	0.102615i
$378$	−2.54771	−	28.4304i	−0.131040	−	1.46230i
$379$	−12.1218	−	18.1416i	−0.622656	−	0.931871i	−0.999983	−	0.00579091i	$-0.998157\pi$
$379$	−12.1218	−	18.1416i	−0.622656	−	0.931871i	0.377327	−	0.926080i	$-0.376843\pi$
$380$	−25.6115	+	13.1262i	−1.31384	+	0.673360i
$381$	1.23503	+	0.825221i	0.0632725	+	0.0422773i
$382$	4.73938	+	9.05762i	0.242488	+	0.463428i
$383$	4.04219	+	9.75871i	0.206546	+	0.498647i	0.992875	−	0.119162i	$-0.0380207\pi$
$383$	4.04219	+	9.75871i	0.206546	+	0.498647i	−0.786329	+	0.617809i	$0.788021\pi$
$384$	11.7459	−	0.429661i	0.599404	−	0.0219260i
$385$	−6.94238	−	3.70778i	−0.353816	−	0.188966i
$386$	−19.4407	+	15.6703i	−0.989505	+	0.797595i
$387$			10.6542i			0.541581i
$388$	0.232427	−	0.224384i	0.0117997	−	0.0113914i
$389$	8.99050	+	21.7050i	0.455837	+	1.10049i	0.970068	+	0.242835i	$0.0780774\pi$
$389$	8.99050	+	21.7050i	0.455837	+	1.10049i	−0.514231	+	0.857652i	$0.671923\pi$
$390$	−6.19292	−	4.21424i	−0.313591	−	0.213397i
$391$	−5.29597	+	10.7238i	−0.267829	+	0.542327i
$392$	−12.0133	+	21.1147i	−0.606764	+	1.06646i
$393$	−10.3980	−	4.30701i	−0.524511	−	0.217260i
$394$	14.8876	+	1.59872i	0.750026	+	0.0805425i
$395$	−10.4931	+	12.7947i	−0.527966	+	0.643770i
$396$	−2.46374	+	2.37849i	−0.123808	+	0.119524i
$397$	33.0727	+	22.0984i	1.65987	+	1.10909i	0.863678	+	0.504044i	$0.168155\pi$
$397$	33.0727	+	22.0984i	1.65987	+	1.10909i	0.796191	+	0.605045i	$0.206845\pi$
$398$	−1.77593	+	0.521699i	−0.0890194	+	0.0261504i
$399$	24.3870	+	10.1014i	1.22088	+	0.505704i
$400$	19.7387	−	3.22220i	0.986936	−	0.161110i
$401$	−28.1385	−	18.8015i	−1.40517	−	0.938903i	−0.999693	−	0.0247967i	$-0.992106\pi$
$401$	−28.1385	−	18.8015i	−1.40517	−	0.938903i	−0.405475	−	0.914106i	$-0.632894\pi$
$402$	1.08855	+	0.594219i	0.0542919	+	0.0296369i
$403$	−0.924349	+	4.64701i	−0.0460451	+	0.231484i
$404$	−9.76707	−	6.77783i	−0.485930	−	0.337209i
$405$	−1.00409	−	0.0985531i	−0.0498934	−	0.00489714i
$406$	7.78145	−	4.07162i	0.386187	−	0.202071i
$407$	−5.29232	−	5.29232i	−0.262331	−	0.262331i
$408$	11.8961	+	2.29521i	0.588943	+	0.113630i
$409$			27.5497i			1.36224i	0.732170	+	0.681122i	$0.238508\pi$
$409$			27.5497i			1.36224i	−0.732170	+	0.681122i	$0.761492\pi$
$410$	−3.64343	−	0.756841i	−0.179936	−	0.0373777i
$411$	−0.662956	+	3.33291i	−0.0327012	+	0.164400i
$412$	−5.00270	−	27.6890i	−0.246465	−	1.36414i
$413$	38.7436	+	7.70658i	1.90645	+	0.379216i
$414$	−2.22080	−	7.55991i	−0.109147	−	0.371549i
$415$	−38.5178	+	11.6984i	−1.89076	+	0.574251i
$416$	12.8794	−	0.698317i	0.631464	−	0.0342378i
$417$	17.2034	−	7.12588i	0.842454	−	0.348956i
$418$	−2.28669	−	7.78420i	−0.111846	−	0.380737i
$419$	7.40631	+	37.2340i	0.361822	+	1.81900i	0.547993	+	0.836483i	$0.315392\pi$
$419$	7.40631	+	37.2340i	0.361822	+	1.81900i	−0.186171	+	0.982517i	$0.559608\pi$
$420$	−13.9770	−	11.8804i	−0.682010	−	0.579704i
$421$	5.27775	−	5.27775i	0.257222	−	0.257222i	−0.566702	−	0.823923i	$-0.691781\pi$
$421$	5.27775	−	5.27775i	0.257222	−	0.257222i	0.823923	+	0.566702i	$0.191781\pi$
$422$	15.7389	−	12.6864i	0.766159	−	0.617566i
$423$	−1.95138	+	4.71104i	−0.0948791	+	0.229058i
$424$	1.98141	+	7.21211i	0.0962260	+	0.350251i
$425$	20.5715	+	1.34616i	0.997866	+	0.0652982i
$426$	−1.18408	−	13.2134i	−0.0573688	−	0.640191i
$427$	−31.5495	−	13.0682i	−1.52679	−	0.632416i
$428$	−29.0030	+	27.9995i	−1.40191	+	1.35341i
$429$	1.49321	−	1.49321i	0.0720929	−	0.0720929i
$430$	12.2980	+	12.5080i	0.593065	+	0.603192i
$431$	−11.9350	+	2.37401i	−0.574887	+	0.114352i	−0.473967	−	0.880543i	$-0.657178\pi$
$431$	−11.9350	+	2.37401i	−0.574887	+	0.114352i	−0.100919	+	0.994895i	$0.532178\pi$
$432$	−17.3915	+	10.7550i	−0.836749	+	0.517449i
$433$	−14.3702	+	5.95234i	−0.690588	+	0.286051i	−0.700245	−	0.713902i	$-0.746926\pi$
$433$	−14.3702	+	5.95234i	−0.690588	+	0.286051i	0.00965703	+	0.999953i	$0.496926\pi$
$434$	−3.46573	+	11.0732i	−0.166360	+	0.531529i
$435$	1.06181	+	3.49609i	0.0509099	+	0.167625i
$436$	22.4359	−	8.83386i	1.07449	−	0.423065i
$437$	18.3086	+	3.64180i	0.875818	+	0.174211i
$438$	22.1655	−	1.98629i	1.05911	−	0.0949085i
$439$	22.3059	+	4.43693i	1.06460	+	0.211763i	0.696160	−	0.717887i	$-0.254890\pi$
$439$	22.3059	+	4.43693i	1.06460	+	0.211763i	0.368445	+	0.929650i	$0.379890\pi$
$440$	−0.146963	+	5.63625i	−0.00700619	+	0.268698i
$441$		−	16.4967i		−	0.785557i
$442$	13.0968	+	2.28854i	0.622952	+	0.108855i
$443$	5.08940	−	5.08940i	0.241805	−	0.241805i	−0.575792	−	0.817596i	$-0.695306\pi$
$443$	5.08940	−	5.08940i	0.241805	−	0.241805i	0.817596	+	0.575792i	$0.195306\pi$
$444$	−9.43474	−	14.6728i	−0.447753	−	0.696339i
$445$	22.9024	+	2.24792i	1.08568	+	0.106562i
$446$	−3.88240	+	4.64671i	−0.183837	+	0.220028i
$447$	−22.0399	−	4.38400i	−1.04245	−	0.207356i
$448$	31.5422	+	1.66728i	1.49023	+	0.0787718i
$449$	15.3855	+	10.2803i	0.726087	+	0.485156i	0.862858	−	0.505447i	$-0.168672\pi$
$449$	15.3855	+	10.2803i	0.726087	+	0.485156i	−0.136770	+	0.990603i	$0.543672\pi$
$450$	−10.5683	+	8.53033i	−0.498193	+	0.402123i
$451$	0.401450	−	0.969185i	0.0189035	−	0.0456371i
$452$	−10.0666	+	3.96358i	−0.473491	+	0.186431i
$453$	−8.31472	−	5.55572i	−0.390660	−	0.261031i
$454$	4.18582	−	3.37400i	0.196450	−	0.158350i
$455$	−15.5652	−	12.7653i	−0.729709	−	0.598446i
$456$	−1.35597	−	18.8608i	−0.0634991	−	0.883240i
$457$	32.5865	+	13.4978i	1.52433	+	0.631399i	0.978454	−	0.206466i	$-0.0661962\pi$
$457$	32.5865	+	13.4978i	1.52433	+	0.631399i	0.545878	+	0.837865i	$0.316196\pi$
$458$	8.99845	+	7.51835i	0.420470	+	0.351310i
$459$	−19.9629	+	6.76387i	−0.931789	+	0.315710i
$460$	−11.3336	−	6.31193i	−0.528433	−	0.294295i
$461$	−6.13885	−	14.8205i	−0.285915	−	0.690260i	0.714037	−	0.700108i	$-0.246865\pi$
$461$	−6.13885	−	14.8205i	−0.285915	−	0.690260i	−0.999952	+	0.00984867i	$0.996865\pi$
$462$	4.02620	−	3.24534i	0.187316	−	0.150987i
$463$	−29.9900			−1.39376			−0.696878	−	0.717190i	$-0.745428\pi$
$463$	−29.9900			−1.39376			−0.696878	+	0.717190i	$0.745428\pi$
$464$	−5.10482	−	3.67727i	−0.236985	−	0.170713i
$465$	−4.25800	−	2.27411i	−0.197460	−	0.105459i
$466$	8.84812	−	16.2089i	0.409881	−	0.750862i
$467$	9.36967	−	3.88104i	0.433576	−	0.179593i	−0.155211	−	0.987881i	$-0.549606\pi$
$467$	9.36967	−	3.88104i	0.433576	−	0.179593i	0.588787	+	0.808288i	$0.299606\pi$
$468$	−7.36725	+	4.73721i	−0.340551	+	0.218978i
$469$	2.77110	+	1.85159i	0.127957	+	0.0854983i
$470$	3.14700	+	7.78326i	0.145161	+	0.359015i
$471$	−5.95281	+	3.97754i	−0.274291	+	0.183275i
$472$	−7.49680	−	27.2874i	−0.345068	−	1.25601i
$473$	−4.11162	+	2.74730i	−0.189053	+	0.126321i
$474$	−5.04062	−	9.63333i	−0.231523	−	0.442473i
$475$	−6.29848	−	31.5537i	−0.288994	−	1.44778i
$476$	31.2906	+	8.99673i	1.43420	+	0.412365i
$477$	−3.59139	−	3.59139i	−0.164439	−	0.164439i
$478$	7.84439	+	2.45517i	0.358794	+	0.112297i
$479$	3.28719	−	16.5258i	0.150195	−	0.755084i	−0.830111	−	0.557599i	$-0.811723\pi$
$479$	3.28719	−	16.5258i	0.150195	−	0.755084i	0.980306	−	0.197485i	$-0.0632773\pi$
$480$	−3.12394	+	12.7644i	−0.142588	+	0.582610i
$481$	−10.6353	−	15.9169i	−0.484928	−	0.725747i
$482$	8.51124	−	15.5917i	0.387676	−	0.710185i
$483$	2.32129	+	11.6699i	0.105622	+	0.531000i
$484$	19.9452	+	4.33365i	0.906599	+	0.196984i
$485$	0.170374	+	0.318490i	0.00773629	+	0.0144619i
$486$	10.7096	−	19.6189i	0.485796	−	0.889931i
$487$	7.27055	+	4.85803i	0.329460	+	0.220138i	0.709288	−	0.704919i	$-0.249017\pi$
$487$	7.27055	+	4.85803i	0.329460	+	0.220138i	−0.379828	+	0.925057i	$0.624017\pi$
$488$	1.75422	+	24.4003i	0.0794098	+	1.10455i
$489$	13.7357	−	13.7357i	0.621150	−	0.621150i
$490$	−19.0421	−	19.3672i	−0.860233	−	0.874922i
$491$	3.91165	−	1.62026i	0.176530	−	0.0731213i	−0.292668	−	0.956214i	$-0.594543\pi$
$491$	3.91165	−	1.62026i	0.176530	−	0.0731213i	0.469198	+	0.883093i	$0.344543\pi$
$492$	1.39396	−	2.00874i	0.0628446	−	0.0905611i
$493$	−4.27310	−	4.87812i	−0.192451	−	0.219699i
$494$	−1.85211	−	20.6681i	−0.0833303	−	0.929902i
$495$	−1.80598	−	3.37602i	−0.0811727	−	0.151741i
$496$	8.20426	−	1.33362i	0.368382	−	0.0598814i
$497$		−	35.6511i		−	1.59917i
$498$	2.82410	−	26.2985i	0.126551	−	1.17847i
$499$	7.61266	−	1.51425i	0.340789	−	0.0677872i	−0.0217289	−	0.999764i	$-0.506917\pi$
$499$	7.61266	−	1.51425i	0.340789	−	0.0677872i	0.362518	+	0.931977i	$0.381917\pi$
$500$	−2.56069	+	22.2136i	−0.114518	+	0.993421i
$501$	−12.9845	−	5.37836i	−0.580105	−	0.240287i
$502$	8.56495	+	16.3688i	0.382272	+	0.730576i
$503$	7.86838	+	39.5570i	0.350834	+	1.76376i	0.604633	+	0.796504i	$0.293320\pi$
$503$	7.86838	+	39.5570i	0.350834	+	1.76376i	−0.253800	+	0.967257i	$0.581680\pi$
$504$	−19.1769	+	9.60816i	−0.854208	+	0.427981i
$505$	10.2718	−	8.43559i	0.457087	−	0.375379i
$506$	2.34484	−	2.80646i	0.104241	−	0.124762i
$507$	−6.73861	+	4.50260i	−0.299272	+	0.199967i
$508$	0.607142	−	2.79430i	0.0269376	−	0.123977i
$509$		−	43.3283i		−	1.92049i	−0.279152	−	0.960247i	$-0.590053\pi$
$509$		−	43.3283i		−	1.92049i	0.279152	−	0.960247i	$-0.409947\pi$
$510$	−6.10051	+	12.0940i	−0.270135	+	0.535531i
$511$	59.8047			2.64560
$512$	−9.05392	−	20.7371i	−0.400131	−	0.916458i
$513$	18.2769	+	27.3533i	0.806943	+	1.20768i
$514$	32.6826	+	27.3068i	1.44157	+	1.20445i
$515$	31.3080	+	3.07294i	1.37960	+	0.135410i
$516$	−10.7242	+	4.22250i	−0.472105	+	0.185885i
$517$	−2.32126	+	0.461727i	−0.102089	+	0.0203067i
$518$	−21.7338	−	41.5363i	−0.954927	−	1.82500i
$519$	3.30775	−	7.98561i	0.145194	−	0.350529i
$520$	−3.18106	+	14.0655i	−0.139499	+	0.616814i
$521$	−4.28477	−	21.5410i	−0.187719	−	0.943729i	−0.953676	−	0.300836i	$-0.902734\pi$
$521$	−4.28477	−	21.5410i	−0.187719	−	0.943729i	0.765956	−	0.642892i	$-0.222266\pi$
$522$	4.24787	+	0.456164i	0.185924	+	0.0199657i
$523$	−16.7021			−0.730331			−0.365166	−	0.930943i	$-0.618988\pi$
$523$	−16.7021			−0.730331			−0.365166	+	0.930943i	$0.618988\pi$
$524$	−0.381387	+	21.6635i	−0.0166609	+	0.946373i
$525$	17.0451	−	11.4058i	0.743909	−	0.497788i
$526$	1.83492	+	20.4763i	0.0800063	+	0.892809i
$527$	8.54909	+	0.565207i	0.372404	+	0.0246208i
$528$	−3.37056	−	1.53727i	−0.146685	−	0.0669013i
$529$	−5.58160	−	13.4752i	−0.242678	−	0.585878i
$530$	−8.36185	−	0.0707886i	−0.363216	−	0.00307486i
$531$	13.5882	+	13.5882i	0.589680	+	0.589680i
$532$	0.894484	−	50.8084i	0.0387808	−	2.20282i
$533$	1.49067	−	2.23094i	0.0645679	−	0.0966327i
$534$	−7.24482	+	13.2718i	−0.313514	+	0.574326i
$535$	−21.2599	−	39.7423i	−0.919145	−	1.71821i
$536$	0.296665	−	2.36899i	0.0128140	−	0.102325i
$537$	11.7183	−	2.33091i	0.505680	−	0.100586i
$538$	−7.60283	−	4.15024i	−0.327781	−	0.178930i
$539$	6.36636	−	4.25387i	0.274219	−	0.183227i
$540$	−6.25774	−	21.9888i	−0.269290	−	0.946248i
$541$	23.3800	+	4.65057i	1.00518	+	0.199944i	0.670121	−	0.742252i	$-0.266242\pi$
$541$	23.3800	+	4.65057i	1.00518	+	0.199944i	0.335063	+	0.942196i	$0.391242\pi$
$542$	6.81599	+	2.13330i	0.292772	+	0.0916330i
$543$	−8.41370	+	8.41370i	−0.361067	+	0.361067i
$544$	−4.27885	−	22.9280i	−0.183454	−	0.983028i
$545$	2.65141	+	26.8278i	0.113574	+	1.14918i
$546$	11.7193	−	6.13211i	0.501541	−	0.262430i
$547$	1.17825	+	1.76337i	0.0503782	+	0.0753964i	0.855804	−	0.517301i	$-0.173063\pi$
$547$	1.17825	+	1.76337i	0.0503782	+	0.0753964i	−0.805425	+	0.592697i	$0.798063\pi$
$548$	6.43774	−	1.16314i	0.275006	−	0.0496867i
$549$	−9.22929	−	13.8126i	−0.393896	−	0.589508i
$550$	−6.01715	−	1.87883i	−0.256572	−	0.0801137i
$551$	−5.62329	+	8.41584i	−0.239560	+	0.358527i
$552$	6.72943	−	5.23158i	0.286424	−	0.222671i
$553$	−11.1811	−	26.9937i	−0.475471	−	1.14789i
$554$	17.2914	+	9.43902i	0.734639	+	0.401026i
$555$	18.6616	−	5.66780i	0.792143	−	0.240585i
$556$	−24.8979	−	25.7902i	−1.05590	−	1.09375i
$557$		−	15.7521i		−	0.667436i	−0.942673	−	0.333718i	$-0.891697\pi$
$557$		−	15.7521i		−	0.667436i	0.942673	−	0.333718i	$-0.108303\pi$
$558$	−4.39452	+	3.54222i	−0.186035	+	0.149954i
$559$	−11.6851	+	4.84012i	−0.494227	+	0.204715i
$560$	−11.4232	+	33.4159i	−0.482717	+	1.41208i
$561$	−3.02817	−	2.32633i	−0.127850	−	0.0982177i
$562$	22.9427	−	27.4594i	0.967781	−	1.15830i
$563$	5.13757	−	12.4032i	0.216523	−	0.522732i	−0.777877	−	0.628416i	$-0.783703\pi$
$563$	5.13757	−	12.4032i	0.216523	−	0.522732i	0.994400	+	0.105685i	$0.0337034\pi$
$564$	−5.51537	−	0.0970985i	−0.232239	−	0.00408858i
$565$	−1.18964	−	12.0371i	−0.0500484	−	0.506404i
$566$	1.72048	−	1.38680i	0.0723170	−	0.0582914i
$567$	0.989725	−	1.48123i	0.0415645	−	0.0622057i
$568$	−22.8337	+	11.4403i	−0.958083	+	0.480025i
$569$	26.3755	+	10.9251i	1.10572	+	0.458004i	0.859462	−	0.511200i	$-0.170799\pi$
$569$	26.3755	+	10.9251i	1.10572	+	0.458004i	0.246258	+	0.969204i	$0.420799\pi$
$570$	20.6996	+	4.29988i	0.867011	+	0.180102i
$571$	0.324508	−	0.485661i	0.0135802	−	0.0203243i	−0.824617	−	0.565691i	$-0.808610\pi$
$571$	0.324508	−	0.485661i	0.0135802	−	0.0203243i	0.838198	+	0.545367i	$0.183610\pi$
$572$	−3.72791	−	1.62160i	−0.155872	−	0.0678027i
$573$	1.46506	−	7.36534i	0.0612036	−	0.307691i
$574$	4.21290	−	5.04227i	0.175843	−	0.210460i
$575$	10.2489	−	10.2627i	0.427410	−	0.427985i
$576$	12.3076	+	9.19916i	0.512817	+	0.383298i
$577$	21.8681	+	21.8681i	0.910379	+	0.910379i	0.996302	−	0.0859228i	$-0.0273839\pi$
$577$	21.8681	+	21.8681i	0.910379	+	0.910379i	−0.0859228	+	0.996302i	$0.527384\pi$
$578$	1.02533	−	24.0198i	0.0426480	−	0.999090i
$579$	18.3431			0.762314
$580$	5.51358	−	4.36776i	0.228939	−	0.181362i
$581$	13.8669	−	69.7135i	0.575295	−	2.89220i
$582$	−0.236378	+	0.0211823i	−0.00979820	+	0.000878035i
$583$	0.459898	−	2.31206i	0.0190470	−	0.0957559i
$584$	−19.1911	−	38.3036i	−0.794134	−	1.58501i
$585$	−2.84582	−	9.37007i	−0.117660	−	0.387405i
$586$	3.86162	+	1.20863i	0.159522	+	0.0499279i
$587$	8.53473	+	20.6047i	0.352266	+	0.850445i	0.996340	+	0.0854819i	$0.0272430\pi$
$587$	8.53473	+	20.6047i	0.352266	+	0.850445i	−0.644074	+	0.764963i	$0.722757\pi$
$588$	16.6051	−	6.53805i	0.684783	−	0.269624i
$589$	−2.60881	−	13.1154i	−0.107494	−	0.540410i
$590$	31.6376	+	0.267833i	1.30250	+	0.0110265i
$591$	−7.77777	−	7.77777i	−0.319935	−	0.319935i
$592$	−19.6288	+	27.2488i	−0.806737	+	1.11992i
$593$	−8.80765	+	21.2635i	−0.361687	+	0.873189i	0.633367	+	0.773851i	$0.281672\pi$
$593$	−8.80765	+	21.2635i	−0.361687	+	0.873189i	−0.995054	+	0.0993374i	$0.968328\pi$
$594$	6.41924	−	0.575240i	0.263385	−	0.0236024i
$595$	−19.2295	+	30.9076i	−0.788333	+	1.26709i
$596$	7.69159	+	42.5715i	0.315060	+	1.74380i
$597$	1.25624	+	0.520350i	0.0514143	+	0.0212965i
$598$	7.28254	−	5.87012i	0.297805	−	0.240047i
$599$	−6.29900	−	6.29900i	−0.257370	−	0.257370i	0.566613	−	0.823984i	$-0.308253\pi$
$599$	−6.29900	−	6.29900i	−0.257370	−	0.257370i	−0.823984	+	0.566613i	$0.808253\pi$
$600$	−12.7748	−	7.25693i	−0.521531	−	0.296263i
$601$	−16.0052	+	3.18363i	−0.652866	+	0.129863i	−0.510401	−	0.859937i	$-0.670503\pi$
$601$	−16.0052	+	3.18363i	−0.652866	+	0.129863i	−0.142465	+	0.989800i	$0.545503\pi$
$602$	−29.7172	+	8.72974i	−1.21118	+	0.355797i
$603$	0.620436	+	1.49787i	0.0252661	+	0.0609978i
$604$	−4.08752	+	18.8124i	−0.166319	+	0.765465i
$605$	−10.7504	+	20.1288i	−0.437064	+	0.818352i
$606$	2.46150	+	8.37927i	0.0999915	+	0.340384i
$607$	−5.24399	+	26.3633i	−0.212847	+	1.07005i	0.715577	+	0.698533i	$0.246164\pi$
$607$	−5.24399	+	26.3633i	−0.212847	+	1.07005i	−0.928424	+	0.371521i	$0.878836\pi$
$608$	−32.8286	+	15.7313i	−1.33138	+	0.637990i
$609$	−6.32760	−	1.25864i	−0.256407	−	0.0510025i
$610$	−26.7791	−	5.56276i	−1.08425	−	0.225230i
$611$	−6.05339			−0.244894
$612$	10.2250	+	12.0958i	0.413320	+	0.488944i
$613$	27.1466	−	27.1466i	1.09644	−	1.09644i	0.101616	−	0.994824i	$-0.467599\pi$
$613$	27.1466	−	27.1466i	1.09644	−	1.09644i	0.994824	−	0.101616i	$-0.0324014\pi$
$614$	9.98997	−	5.22723i	0.403162	−	0.210954i
$615$	1.73491	+	2.11254i	0.0699581	+	0.0851858i
$616$	−8.65295	−	4.92313i	−0.348637	−	0.198359i
$617$	−27.0052	−	5.37167i	−1.08719	−	0.216255i	−0.381210	−	0.924488i	$-0.624493\pi$
$617$	−27.0052	−	5.37167i	−1.08719	−	0.216255i	−0.705979	+	0.708233i	$0.749493\pi$
$618$	−9.90378	+	18.1427i	−0.398389	+	0.729808i
$619$	7.12919	−	10.6696i	0.286546	−	0.428847i	−0.660073	−	0.751202i	$-0.729474\pi$
$619$	7.12919	−	10.6696i	0.286546	−	0.428847i	0.946619	+	0.322355i	$0.104474\pi$
$620$	−1.07042	+	9.23118i	−0.0429892	+	0.370733i
$621$	−5.67484	+	13.7003i	−0.227723	+	0.549773i
$622$	−37.4126	+	10.9904i	−1.50011	+	0.440673i
$623$	−22.5749	+	33.7857i	−0.904443	+	1.35359i
$624$	−7.68817	−	5.53819i	−0.307773	−	0.221705i
$625$	−23.1098	−	9.53602i	−0.924393	−	0.381441i
$626$	−1.57826	+	14.6970i	−0.0630801	+	0.587412i
$627$	−2.28078	+	5.50629i	−0.0910855	+	0.219900i
$628$	11.3234	+	7.85780i	0.451851	+	0.313561i
$629$	−26.0387	+	22.8092i	−1.03823	+	0.909463i
$630$	−4.47919	−	23.5590i	−0.178455	−	0.938612i
$631$	−2.80461	+	1.16171i	−0.111650	+	0.0462468i	−0.437809	−	0.899068i	$-0.644245\pi$
$631$	−2.80461	+	1.16171i	−0.111650	+	0.0462468i	0.326159	+	0.945315i	$0.394245\pi$
$632$	−13.7009	+	15.8235i	−0.544991	+	0.629423i
$633$	−14.8504			−0.590249
$634$	−15.7238	−	19.5071i	−0.624472	−	0.774727i
$635$	2.82003	+	1.50612i	0.111909	+	0.0597684i
$636$	2.19164	−	5.03835i	0.0869040	−	0.199784i
$637$	18.0930	−	7.49436i	0.716870	−	0.296937i
$638$	0.919323	+	1.75696i	0.0363963	+	0.0695585i
$639$	9.63528	−	14.4202i	0.381166	−	0.570455i
$640$	25.0678	−	3.40676i	0.990891	−	0.134664i
$641$	30.3051	−	20.2492i	1.19698	−	0.799796i	0.212822	−	0.977091i	$-0.431735\pi$
$641$	30.3051	−	20.2492i	1.19698	−	0.799796i	0.984158	+	0.177295i	$0.0567346\pi$
$642$	29.4962	−	2.64321i	1.16412	−	0.104319i
$643$	19.4002	+	29.0345i	0.765069	+	1.14501i	0.985512	+	0.169607i	$0.0542498\pi$
$643$	19.4002	+	29.0345i	0.765069	+	1.14501i	−0.220443	+	0.975400i	$0.570750\pi$
$644$	19.2669	−	12.3888i	0.759222	−	0.488187i
$645$	−1.26735	−	12.8234i	−0.0499019	−	0.504922i
$646$	−36.6216	+	8.17798i	−1.44086	+	0.321758i
$647$	−26.8220	+	26.8220i	−1.05448	+	1.05448i	−0.0560525	+	0.998428i	$0.517851\pi$
$647$	−26.8220	+	26.8220i	−1.05448	+	1.05448i	−0.998428	+	0.0560525i	$0.982149\pi$
$648$	−1.26629	−	0.158575i	−0.0497447	−	0.00622943i
$649$	−1.74005	+	8.74783i	−0.0683030	+	0.343382i
$650$	−14.1569	−	7.71561i	−0.555278	−	0.302631i
$651$	7.08708	−	4.73543i	0.277764	−	0.185596i
$652$	−34.2921	−	14.9168i	−1.34298	−	0.584186i
$653$	−4.75573	−	23.9087i	−0.186106	−	0.935618i	−0.955082	−	0.296341i	$-0.904234\pi$
$653$	−4.75573	−	23.9087i	−0.186106	−	0.935618i	0.768976	−	0.639277i	$-0.220766\pi$
$654$	−16.9045	−	5.29085i	−0.661020	−	0.206889i
$655$	−23.1835	−	7.02413i	−0.905855	−	0.274456i
$656$	−4.58137	−	1.08022i	−0.178872	−	0.0421754i
$657$	24.1899	+	16.1632i	0.943737	+	0.630585i
$658$	−14.7392	−	1.58279i	−0.574594	−	0.0617036i
$659$	−14.9828	−	14.9828i	−0.583648	−	0.583648i	0.352256	−	0.935904i	$-0.385415\pi$
$659$	−14.9828	−	14.9828i	−0.583648	−	0.583648i	−0.935904	+	0.352256i	$0.885415\pi$
$660$	2.68245	−	3.15584i	0.104414	−	0.122841i
$661$	−10.8667	+	4.50113i	−0.422665	+	0.175074i	−0.583870	−	0.811847i	$-0.698462\pi$
$661$	−10.8667	+	4.50113i	−0.422665	+	0.175074i	0.161204	+	0.986921i	$0.448462\pi$
$662$	−17.8775	+	21.3970i	−0.694829	+	0.831617i
$663$	−6.43554	−	7.34673i	−0.249936	−	0.285323i
$664$	−49.0998	+	13.4894i	−1.90544	+	0.523491i
$665$	54.3734	+	16.4740i	2.10851	+	0.638836i
$666$	2.43494	−	22.6746i	0.0943519	−	0.878621i
$667$	−4.56249			−0.176660
$668$	−0.476255	+	27.0522i	−0.0184269	+	1.04668i
$669$	4.36270	−	0.867796i	0.168672	−	0.0335509i
$670$	2.45738	+	1.04234i	0.0949367	+	0.0402690i
$671$	2.95064	−	7.12349i	0.113908	−	0.274999i
$672$	−17.2716	−	15.4950i	−0.666266	−	0.597732i
$673$	0.931095	+	4.68093i	0.0358911	+	0.180437i	0.994573	−	0.104045i	$-0.0331786\pi$
$673$	0.931095	+	4.68093i	0.0358911	+	0.180437i	−0.958682	+	0.284481i	$0.908179\pi$
$674$	−39.5288	+	11.6120i	−1.52259	+	0.447278i
$675$	25.5604	−	0.0171848i	0.983820	−	0.000661444i
$676$	12.8181	+	8.89507i	0.493004	+	0.342118i
$677$	−30.4945	+	20.3758i	−1.17200	+	0.783105i	−0.980138	−	0.198317i	$-0.936452\pi$
$677$	−30.4945	+	20.3758i	−1.17200	+	0.783105i	−0.191861	+	0.981422i	$0.561452\pi$
$678$	7.58473	+	2.37390i	0.291290	+	0.0911691i
$679$	−0.637773			−0.0244755
$680$	25.9663	+	2.39791i	0.995763	+	0.0919556i
$681$	−3.94950			−0.151345
$682$	−2.50019	−	0.782519i	−0.0957371	−	0.0299642i
$683$	2.20328	−	1.47218i	0.0843060	−	0.0563315i	−0.512703	−	0.858566i	$-0.671356\pi$
$683$	2.20328	−	1.47218i	0.0843060	−	0.0563315i	0.597009	+	0.802235i	$0.296356\pi$
$684$	14.0936	−	20.3093i	0.538881	−	0.776545i
$685$	−0.714464	+	7.27916i	−0.0272983	+	0.278122i
$686$	8.51222	−	2.50055i	0.324998	−	0.0954715i
$687$	−1.68050	−	8.44846i	−0.0641152	−	0.322329i
$688$	15.1273	+	16.2318i	0.576725	+	0.618833i
$689$	2.30736	−	5.57046i	0.0879034	−	0.212218i
$690$	3.57226	+	8.83500i	0.135994	+	0.336343i
$691$	16.6351	−	3.30892i	0.632828	−	0.125877i	0.131755	−	0.991282i	$-0.457939\pi$
$691$	16.6351	−	3.30892i	0.632828	−	0.125877i	0.501073	+	0.865405i	$0.332939\pi$
$692$	−16.6374	−	0.292902i	−0.632458	−	0.0111345i
$693$	6.76045			0.256808
$694$	−0.0426420	+	0.397089i	−0.00161867	+	0.0150733i
$695$	35.3399	−	18.9048i	1.34052	−	0.717101i
$696$	1.22438	+	4.45657i	0.0464098	+	0.168926i
$697$	−4.35028	−	2.14839i	−0.164779	−	0.0813760i
$698$	4.33623	−	5.18988i	0.164129	−	0.196440i
$699$	−12.5331	+	5.19139i	−0.474046	+	0.196356i
$700$	−32.4526	−	22.4881i	−1.22659	−	0.849970i
$701$	7.11271	+	7.11271i	0.268643	+	0.268643i	0.828553	−	0.559910i	$-0.189164\pi$
$701$	7.11271	+	7.11271i	0.268643	+	0.268643i	−0.559910	+	0.828553i	$0.689164\pi$
$702$	16.3901	+	1.76007i	0.618603	+	0.0664295i
$703$	44.9226	+	30.0163i	1.69429	+	1.13209i
$704$	−0.376452	+	7.12184i	−0.0141881	+	0.268414i
$705$	1.78830	−	5.90237i	0.0673512	−	0.222296i
$706$	−37.4136	−	11.7099i	−1.40808	−	0.440706i
$707$	4.57865	+	23.0184i	0.172198	+	0.865697i
$708$	−8.29218	+	19.0629i	−0.311639	+	0.716427i
$709$	29.4216	−	19.6589i	1.10495	−	0.738305i	0.137284	−	0.990532i	$-0.456163\pi$
$709$	29.4216	−	19.6589i	1.10495	−	0.738305i	0.967668	+	0.252226i	$0.0811628\pi$
$710$	−5.33332	−	28.0514i	−0.200156	−	1.05275i
$711$	2.77290	−	13.9403i	0.103992	−	0.522803i
$712$	28.8832	+	3.61698i	1.08244	+	0.135552i
$713$	4.26229	−	4.26229i	0.159624	−	0.159624i
$714$	−13.7487	−	19.5710i	−0.514533	−	0.732427i
$715$	2.88225	−	3.51444i	0.107790	−	0.131432i
$716$	−12.4401	−	19.3467i	−0.464908	−	0.723019i
$717$	−3.35465	−	5.02059i	−0.125282	−	0.187497i
$718$	12.8460	−	1.15116i	0.479409	−	0.0429608i
$719$	1.24932	−	0.834767i	0.0465916	−	0.0311315i	−0.532056	−	0.846709i	$-0.678581\pi$
$719$	1.24932	−	0.834767i	0.0465916	−	0.0311315i	0.578648	+	0.815577i	$0.303581\pi$
$720$	−13.6516	+	10.4288i	−0.508767	+	0.388659i
$721$	−30.8602	+	46.1856i	−1.14929	+	1.72004i
$722$	14.6947	+	28.0836i	0.546880	+	1.04516i
$723$	−12.0559	+	4.99373i	−0.448365	+	0.185719i
$724$	21.0054	+	9.13715i	0.780660	+	0.339580i
$725$	3.01440	+	7.26358i	0.111952	+	0.269763i
$726$	−9.40956	−	11.6736i	−0.349222	−	0.433248i
$727$	41.8750			1.55306			0.776528	−	0.630082i	$-0.216979\pi$
$727$	41.8750			1.55306			0.776528	+	0.630082i	$0.216979\pi$
$728$	−19.2498	−	16.6676i	−0.713447	−	0.617743i
$729$	−13.9193	+	5.76555i	−0.515528	+	0.213539i
$730$	47.0562	−	8.94663i	1.74163	−	0.331130i
$731$	11.4242	+	19.8133i	0.422540	+	0.732820i
$732$	10.2456	−	14.7642i	0.378687	−	0.545701i
$733$	−11.0820	+	26.7543i	−0.409323	+	0.988193i	0.575993	+	0.817454i	$0.304615\pi$
$733$	−11.0820	+	26.7543i	−0.409323	+	0.988193i	−0.985316	+	0.170739i	$0.945385\pi$
$734$	1.43159	−	13.3312i	0.0528410	−	0.492064i
$735$	1.96234	+	19.8556i	0.0723821	+	0.732383i
$736$	−14.1174	−	8.36448i	−0.520375	−	0.308319i
$737$	−0.418066	+	0.625679i	−0.0153996	+	0.0230472i
$738$	3.06679	−	0.900903i	0.112890	−	0.0331627i
$739$	−14.9807	+	36.1666i	−0.551074	+	1.33041i	0.365599	+	0.930772i	$0.380864\pi$
$739$	−14.9807	+	36.1666i	−0.551074	+	1.33041i	−0.916673	+	0.399638i	$0.869136\pi$
$740$	−23.3145	−	29.4307i	−0.857059	−	1.08189i
$741$	−8.46900	+	12.6748i	−0.311117	+	0.465619i
$742$	7.07463	−	12.9600i	0.259718	−	0.475777i
$743$	26.4800	+	5.26721i	0.971459	+	0.193235i	0.655215	−	0.755443i	$-0.272578\pi$
$743$	26.4800	+	5.26721i	0.971459	+	0.193235i	0.316244	+	0.948678i	$0.397578\pi$
$744$	−5.30716	−	3.01953i	−0.194570	−	0.110701i
$745$	−48.1357	−	4.72462i	−1.76356	−	0.173097i
$746$	37.6200	−	19.6846i	1.37737	−	0.720704i
$747$	24.4501	−	24.4501i	0.894582	−	0.894582i
$748$	−2.03135	+	7.06504i	−0.0742736	+	0.258323i
$749$	79.5837			2.90792
$750$	11.7053	−	11.5243i	0.427419	−	0.420808i
$751$	−25.9093	−	5.15368i	−0.945445	−	0.188061i	−0.301788	−	0.953375i	$-0.597583\pi$
$751$	−25.9093	−	5.15368i	−0.945445	−	0.188061i	−0.643657	+	0.765314i	$0.722583\pi$
$752$	3.71602	+	9.94804i	0.135509	+	0.362768i
$753$	2.64763	−	13.3105i	0.0964851	−	0.485063i
$754$	1.42948	+	4.86615i	0.0520586	+	0.177215i
$755$	−18.9856	−	10.1398i	−0.690955	−	0.369025i
$756$	39.4474	+	8.57107i	1.43469	+	0.311727i
$757$	10.7400	+	25.9287i	0.390353	+	0.942396i	0.989863	+	0.142028i	$0.0453623\pi$
$757$	10.7400	+	25.9287i	0.390353	+	0.942396i	−0.599510	+	0.800368i	$0.704638\pi$
$758$	29.6053	−	8.69688i	1.07531	−	0.315885i
$759$	−2.63493	+	0.524119i	−0.0956418	+	0.0190243i
$760$	−6.89699	−	40.1114i	−0.250180	−	1.45499i
$761$	22.5397	+	22.5397i	0.817062	+	0.817062i	0.985681	−	0.168619i	$-0.0539309\pi$
$761$	22.5397	+	22.5397i	0.817062	+	0.817062i	−0.168619	+	0.985681i	$0.553931\pi$
$762$	−1.63546	+	1.31827i	−0.0592466	+	0.0477560i
$763$	−43.9778	−	18.2162i	−1.59210	−	0.659471i
$764$	−14.2267	+	2.57039i	−0.514702	+	0.0929936i
$765$	−16.1313	+	7.30449i	−0.583227	+	0.264094i
$766$	−14.8784	+	1.33328i	−0.537577	+	0.0481733i
$767$	−8.73003	+	21.0762i	−0.315223	+	0.761016i
$768$	−4.38180	+	16.0343i	−0.158115	+	0.578590i
$769$	−6.93098	−	6.93098i	−0.249937	−	0.249937i	0.571007	−	0.820945i	$-0.306553\pi$
$769$	−6.93098	−	6.93098i	−0.249937	−	0.249937i	−0.820945	+	0.571007i	$0.806553\pi$
$770$	7.93681	−	7.80356i	0.286023	−	0.281221i
$771$	−6.10363	−	30.6850i	−0.219817	−	1.10509i
$772$	−12.9373	−	32.8576i	−0.465622	−	1.18257i
$773$	−19.1238	−	46.1690i	−0.687836	−	1.66058i	−0.749097	−	0.662460i	$-0.769512\pi$
$773$	−19.1238	−	46.1690i	−0.687836	−	1.66058i	0.0612613	−	0.998122i	$-0.480488\pi$
$774$	−14.3794	−	4.50053i	−0.516857	−	0.161768i
$775$	−9.60171	−	3.96960i	−0.344904	−	0.142592i
$776$	0.204659	+	0.408479i	0.00734684	+	0.0146636i
$777$	−6.71843	+	33.7758i	−0.241022	+	1.21170i
$778$	−33.0920	+	2.96543i	−1.18640	+	0.106316i
$779$	−1.47735	+	7.42715i	−0.0529316	+	0.266105i
$780$	8.30378	−	6.57811i	0.297323	−	0.235534i
$781$	8.04959			0.288037
$782$	−12.2363	−	11.6777i	−0.437570	−	0.417593i
$783$	−5.68551	−	5.68551i	−0.203183	−	0.203183i
$784$	−23.4229	−	25.1331i	−0.836532	−	0.897610i
$785$	−11.9085	+	9.77972i	−0.425031	+	0.349053i
$786$	10.2053	−	12.2144i	0.364011	−	0.435672i
$787$	−8.15868	+	41.0165i	−0.290826	+	1.46208i	0.508438	+	0.861098i	$0.330223\pi$
$787$	−8.15868	+	41.0165i	−0.290826	+	1.46208i	−0.799264	+	0.600980i	$0.794777\pi$
$788$	−8.44654	+	19.4177i	−0.300895	+	0.691728i
$789$	8.39041	−	12.5571i	0.298707	−	0.447046i
$790$	−12.8359	−	19.5668i	−0.456679	−	0.696155i
$791$	19.7320	+	8.17325i	0.701588	+	0.290607i
$792$	−2.16940	−	4.32991i	−0.0770864	−	0.153857i
$793$	10.9564	−	16.3973i	0.389071	−	0.582287i
$794$	−43.7958	+	35.3018i	−1.55425	+	1.25281i
$795$	4.74984	+	3.89542i	0.168459	+	0.138156i
$796$	0.0460771	−	2.61727i	0.00163316	−	0.0927665i
$797$	9.34070	−	22.5504i	0.330864	−	0.798777i	−0.667660	−	0.744467i	$-0.732704\pi$
$797$	9.34070	−	22.5504i	0.330864	−	0.798777i	0.998524	−	0.0543108i	$-0.0172962\pi$
$798$	−23.9350	+	28.6469i	−0.847289	+	1.01409i
$799$	1.42262	+	10.8534i	0.0503286	+	0.383967i
$800$	−3.98918	+	28.0015i	−0.141039	+	0.990004i
$801$	−18.2622	+	7.56446i	−0.645264	+	0.267277i
$802$	37.2618	−	30.0350i	1.31576	−	1.06057i
$803$			13.5032i			0.476516i
$804$	−1.26181	+	1.21815i	−0.0445007	+	0.0429610i
$805$	7.44241	+	24.5047i	0.262310	+	0.863677i
$806$	−5.88139	−	3.21054i	−0.207163	−	0.113086i
$807$	2.43504	+	5.87870i	0.0857174	+	0.206940i
$808$	13.2735	−	10.3191i	0.466961	−	0.363023i
$809$	−6.42823	+	9.62053i	−0.226005	+	0.338240i	−0.927091	−	0.374837i	$-0.877699\pi$
$809$	−6.42823	+	9.62053i	−0.226005	+	0.338240i	0.701086	+	0.713076i	$0.252699\pi$
$810$	0.557158	−	1.31354i	0.0195765	−	0.0461530i
$811$	−4.99087	−	7.46936i	−0.175253	−	0.262285i	0.733436	−	0.679759i	$-0.237915\pi$
$811$	−4.99087	−	7.46936i	−0.175253	−	0.262285i	−0.908689	+	0.417474i	$0.862915\pi$
$812$	2.20824	+	12.2222i	0.0774940	+	0.428915i
$813$	−2.91485	−	4.36239i	−0.102228	−	0.152996i
$814$	9.37838	−	4.90722i	0.328712	−	0.171998i
$815$	26.5131	−	32.3285i	0.928714	−	1.13242i
$816$	−8.12288	+	15.0860i	−0.284358	+	0.528116i
$817$	25.2411	−	25.2411i	0.883076	−	0.883076i
$818$	−37.1825	−	11.6375i	−1.30006	−	0.406897i
$819$	16.9590	+	3.37335i	0.592594	+	0.117874i
$820$	2.56053	−	4.59765i	0.0894175	−	0.160557i
$821$	−21.7785	+	14.5519i	−0.760075	+	0.507866i	−0.874180	−	0.485603i	$-0.838600\pi$
$821$	−21.7785	+	14.5519i	−0.760075	+	0.507866i	0.114104	+	0.993469i	$0.463600\pi$
$822$	−4.21822	−	2.30265i	−0.147127	−	0.0803140i
$823$	34.7808	−	6.91833i	1.21238	−	0.241158i	0.452825	−	0.891599i	$-0.350416\pi$
$823$	34.7808	−	6.91833i	1.21238	−	0.241158i	0.759556	+	0.650441i	$0.225416\pi$
$824$	39.4837	+	4.94448i	1.37548	+	0.172249i
$825$	2.57528	+	3.84857i	0.0896597	+	0.133990i
$826$	−26.7673	+	49.0350i	−0.931352	+	1.70615i
$827$	26.2452	−	39.2787i	0.912635	−	1.36585i	−0.0179735	−	0.999838i	$-0.505721\pi$
$827$	26.2452	−	39.2787i	0.912635	−	1.36585i	0.930608	−	0.366016i	$-0.119279\pi$
$828$	11.1414	+	0.196144i	0.387189	+	0.00681649i
$829$	11.5594	+	11.5594i	0.401476	+	0.401476i	0.878753	−	0.477277i	$-0.158376\pi$
$829$	11.5594	+	11.5594i	0.401476	+	0.401476i	−0.477277	+	0.878753i	$0.658376\pi$
$830$	0.481927	−	56.9272i	0.0167279	−	1.97597i
$831$	−5.53808	−	13.3701i	−0.192114	−	0.463804i
$832$	−4.49802	+	17.6777i	−0.155941	+	0.612863i
$833$	−17.6891	−	30.6785i	−0.612889	−	1.06295i
$834$	2.35040	+	26.2287i	0.0813879	+	0.908226i
$835$	−28.9503	−	8.77136i	−1.00187	−	0.303545i
$836$	11.4719	+	0.201964i	0.396764	+	0.00698505i
$837$	10.6228			0.367179
$838$	−53.3815	−	5.73245i	−1.84403	−	0.198024i
$839$	−7.31573	−	36.7787i	−0.252567	−	1.26974i	−0.873866	−	0.486167i	$-0.838395\pi$
$839$	−7.31573	−	36.7787i	−0.252567	−	1.26974i	0.621299	−	0.783574i	$-0.286605\pi$
$840$	21.9386	−	13.8456i	0.756953	−	0.477719i
$841$	−10.1511	+	24.5070i	−0.350039	+	0.845068i
$842$	4.89370	+	9.35255i	0.168648	+	0.322310i
$843$	−25.7810	+	5.12816i	−0.887945	+	0.176623i
$844$	10.4738	+	26.6011i	0.360525	+	0.915647i
$845$	−13.4804	+	11.0707i	−0.463741	+	0.380843i
$846$	−5.53396	−	4.62371i	−0.190262	−	0.158967i
$847$	−22.3857	−	33.5026i	−0.769183	−	1.15116i
$848$	−10.5708	−	0.372315i	−0.363004	−	0.0127854i
$849$	−1.62334			−0.0557129
$850$	−10.5067	+	27.1958i	−0.360376	+	0.932807i
$851$			24.3540i			0.834843i
$852$	18.3337	+	3.98351i	0.628101	+	0.136473i
$853$	9.69693	−	6.47928i	0.332017	−	0.221846i	−0.378376	−	0.925652i	$-0.623517\pi$
$853$	9.69693	−	6.47928i	0.332017	−	0.221846i	0.710393	+	0.703806i	$0.248517\pi$
$854$	30.9647	−	37.0606i	1.05959	−	1.26819i
$855$	17.5407	+	21.3587i	0.599878	+	0.730453i
$856$	−25.5381	−	50.9715i	−0.872875	−	1.74217i
$857$	−6.89226	−	34.6497i	−0.235435	−	1.18361i	−0.899833	−	0.436234i	$-0.856312\pi$
$857$	−6.89226	−	34.6497i	−0.235435	−	1.18361i	0.664398	−	0.747379i	$-0.268688\pi$
$858$	1.38455	+	2.64608i	0.0472679	+	0.0903356i
$859$	−30.0127	−	12.4317i	−1.02402	−	0.424163i	−0.193470	−	0.981106i	$-0.561974\pi$
$859$	−30.0127	−	12.4317i	−1.02402	−	0.424163i	−0.830551	+	0.556943i	$0.811974\pi$
$860$	−22.0765	+	11.3144i	−0.752801	+	0.385819i
$861$	−4.73408	+	0.941668i	−0.161337	+	0.0320919i
$862$	1.83747	−	17.1109i	0.0625846	−	0.582798i
$863$		−	19.9564i		−	0.679325i	−0.940547	−	0.339663i	$-0.889687\pi$
$863$		−	19.9564i		−	0.679325i	0.940547	−	0.339663i	$-0.110313\pi$
$864$	−7.16897	−	28.0156i	−0.243893	−	0.953110i
$865$	5.39448	−	17.8048i	0.183418	−	0.605380i
$866$	−1.96332	−	21.9092i	−0.0667164	−	0.744504i
$867$	−11.6599	+	13.2652i	−0.395990	+	0.450508i
$868$	−13.4809	−	9.35505i	−0.457573	−	0.317531i
$869$	6.09484	−	2.52457i	0.206753	−	0.0856400i
$870$	−5.16704	−	0.0437424i	−0.175179	−	0.00148301i
$871$	−1.36094	+	1.36094i	−0.0461138	+	0.0461138i
$872$	2.44526	+	34.0123i	0.0828070	+	1.15180i
$873$	−0.257968	−	0.172368i	−0.00873088	−	0.00583379i
$874$	−12.6491	+	23.1718i	−0.427861	+	0.783799i
$875$	34.0948	−	28.0385i	1.15261	−	0.947873i
$876$	−6.68233	+	30.7547i	−0.225775	+	1.03911i
$877$	6.64180	+	33.3906i	0.224277	+	1.12752i	0.914706	+	0.404119i	$0.132422\pi$
$877$	6.64180	+	33.3906i	0.224277	+	1.12752i	−0.690429	+	0.723400i	$0.742578\pi$
$878$	−15.4108	+	28.2310i	−0.520089	+	0.952751i
$879$	−1.65142	−	2.47153i	−0.0557011	−	0.0833625i
$880$	−7.54490	−	2.57921i	−0.254338	−	0.0869453i
$881$	−8.88494	+	44.6676i	−0.299341	+	1.50489i	0.479430	+	0.877580i	$0.340844\pi$
$881$	−8.88494	+	44.6676i	−0.299341	+	1.50489i	−0.778771	+	0.627309i	$0.784156\pi$
$882$	22.2648	+	6.96853i	0.749695	+	0.234643i
$883$	−13.6254	−	13.6254i	−0.458530	−	0.458530i	0.439642	−	0.898173i	$-0.355105\pi$
$883$	−13.6254	−	13.6254i	−0.458530	−	0.458530i	−0.898173	+	0.439642i	$0.855105\pi$
$884$	−8.62109	+	16.7094i	−0.289959	+	0.561999i
$885$	−17.9713	−	14.7386i	−0.604098	−	0.495431i
$886$	4.71906	+	9.01878i	0.158540	+	0.302992i
$887$	28.3870	−	18.9676i	0.953141	−	0.636869i	0.0213148	−	0.999773i	$-0.493215\pi$
$887$	28.3870	−	18.9676i	0.953141	−	0.636869i	0.931826	+	0.362904i	$0.118215\pi$
$888$	23.7886	−	6.53554i	0.798292	−	0.219318i
$889$	−4.69369	+	3.13622i	−0.157421	+	0.105186i
$890$	−12.7083	+	29.9608i	−0.425985	+	1.00429i
$891$	0.334443	+	0.223468i	0.0112043	+	0.00748645i
$892$	−4.63144	−	7.20276i	−0.155072	−	0.241166i
$893$	15.7842	−	6.53801i	0.528197	−	0.218786i
$894$	15.2270	−	27.8943i	0.509266	−	0.932924i
$895$	24.6061	−	7.47323i	0.822493	−	0.249802i
$896$	−15.5743	+	41.8667i	−0.520301	+	1.39867i
$897$	−6.87139			−0.229429
$898$	−20.3739	+	16.4225i	−0.679887	+	0.548026i
$899$	1.25074	+	3.01956i	0.0417147	+	0.100708i
$900$	−7.04873	−	17.8669i	−0.234958	−	0.595562i
$901$	−10.5298	−	2.82785i	−0.350799	−	0.0942095i
$902$	1.13848	+	0.951220i	0.0379073	+	0.0316722i
$903$	21.0210	+	8.70717i	0.699534	+	0.289757i
$904$	−1.09714	−	15.2606i	−0.0364903	−	0.507562i
$905$	−16.2404	+	19.8026i	−0.539850	+	0.658260i
$906$	11.0106	−	8.87514i	0.365803	−	0.294857i
$907$	0.716904	+	0.479020i	0.0238044	+	0.0159056i	0.567416	−	0.823432i	$-0.307943\pi$
$907$	0.716904	+	0.479020i	0.0238044	+	0.0159056i	−0.543611	+	0.839337i	$0.682943\pi$
$908$	2.78555	+	7.07464i	0.0924418	+	0.234780i
$909$	−4.36912	+	10.5480i	−0.144914	+	0.349855i
$910$	23.8038	−	15.6153i	0.789087	−	0.517643i
$911$	11.7222	+	7.83250i	0.388373	+	0.259502i	0.734393	−	0.678725i	$-0.237467\pi$
$911$	11.7222	+	7.83250i	0.388373	+	0.259502i	−0.346020	+	0.938227i	$0.612467\pi$
$912$	26.0284	+	6.13711i	0.861886	+	0.203220i
$913$	15.7405	+	3.13097i	0.520933	+	0.103620i
$914$	−31.9825	+	38.2787i	−1.05789	+	1.26615i
$915$	12.7515	+	15.5271i	0.421552	+	0.513310i
$916$	−13.9483	+	8.96888i	−0.460864	+	0.296340i
$917$	30.2453	−	30.2453i	0.998787	−	0.998787i
$918$	−0.696143	−	29.8002i	−0.0229761	−	0.983552i
$919$		−	47.4915i		−	1.56660i	−0.621644	−	0.783300i	$-0.713535\pi$
$919$		−	47.4915i		−	1.56660i	0.621644	−	0.783300i	$-0.286465\pi$
$920$	13.3065	−	12.6302i	0.438701	−	0.416404i
$921$	−8.12349	−	1.61586i	−0.267678	−	0.0532445i
$922$	22.5957	−	2.02484i	0.744150	−	0.0666847i
$923$	20.1928	+	4.01660i	0.664655	+	0.132208i
$924$	2.67933	+	6.80487i	0.0881435	+	0.223864i
$925$	38.7720	−	16.0904i	1.27481	−	0.529050i
$926$	12.6684	−	40.4761i	0.416309	−	1.33013i
$927$	−24.9648	+	10.3407i	−0.819950	+	0.339635i
$928$	7.11942	−	5.33638i	0.233706	−	0.175175i
$929$	−0.833125	+	0.165719i	−0.0273339	+	0.00543706i	−0.208738	−	0.977972i	$-0.566936\pi$
$929$	−0.833125	+	0.165719i	−0.0273339	+	0.00543706i	0.181404	+	0.983409i	$0.441936\pi$
$930$	4.86792	−	4.78620i	0.159626	−	0.156946i
$931$	−39.0829	+	39.0829i	−1.28089	+	1.28089i
$932$	18.1387	+	18.7888i	0.594154	+	0.615449i
$933$	26.4645	+	10.9619i	0.866408	+	0.358878i
$934$	1.28013	+	14.2852i	0.0418870	+	0.467427i
$935$	−6.97856	−	4.34179i	−0.228223	−	0.141992i
$936$	−3.28152	−	11.9443i	−0.107260	−	0.390412i
$937$	3.76373	−	9.08644i	0.122956	−	0.296841i	−0.850402	−	0.526134i	$-0.823641\pi$
$937$	3.76373	−	9.08644i	0.122956	−	0.296841i	0.973358	+	0.229292i	$0.0736412\pi$
$938$	−3.66956	+	2.95787i	−0.119816	+	0.0965778i
$939$	7.67822	−	7.67822i	0.250569	−	0.250569i
$940$	−11.8340	+	0.959560i	−0.385984	+	0.0312974i
$941$	4.61268	+	23.1895i	0.150369	+	0.755956i	0.980211	+	0.197957i	$0.0634306\pi$
$941$	4.61268	+	23.1895i	0.150369	+	0.755956i	−0.829842	+	0.557999i	$0.811569\pi$
$942$	−2.85371	−	9.71442i	−0.0929790	−	0.316513i
$943$	−3.15366	+	1.30629i	−0.102697	+	0.0425386i
$944$	39.9953	+	1.40868i	1.30174	+	0.0458485i
$945$	−21.2620	+	39.8106i	−0.691652	+	1.29504i
$946$	−1.97107	−	6.70978i	−0.0640849	−	0.218154i
$947$	−19.6819	−	3.91498i	−0.639576	−	0.127220i	−0.135359	−	0.990797i	$-0.543219\pi$
$947$	−19.6819	−	3.91498i	−0.639576	−	0.127220i	−0.504217	+	0.863577i	$0.668219\pi$
$948$	15.1309	−	2.73377i	0.491429	−	0.0887887i
$949$	−6.73784	+	33.8734i	−0.218720	+	1.09958i
$950$	45.2472	+	4.82816i	1.46801	+	0.156646i
$951$			18.4058i			0.596849i
$952$	−25.3602	+	38.4311i	−0.821930	+	1.24556i
$953$	−37.0796	−	37.0796i	−1.20112	−	1.20112i	−0.973825	−	0.227300i	$-0.927010\pi$
$953$	−37.0796	−	37.0796i	−1.20112	−	1.20112i	−0.227300	−	0.973825i	$-0.572990\pi$
$954$	6.36421	−	3.33006i	0.206049	−	0.107815i
$955$	1.57888	−	16.0861i	0.0510915	−	0.520534i
$956$	−6.62725	+	9.55009i	−0.214341	+	0.308872i
$957$	0.284185	−	1.42869i	0.00918639	−	0.0461831i
$958$	20.9155	+	11.4174i	0.675750	+	0.368879i
$959$	−10.7382	−	7.17505i	−0.346755	−	0.231694i
$960$	−15.9078	−	9.60815i	−0.513423	−	0.310102i
$961$	24.6509	+	10.2108i	0.795191	+	0.329379i
$962$	25.9748	−	7.63037i	0.837461	−	0.246013i
$963$	32.1901	+	21.5088i	1.03731	+	0.693110i
$964$	17.4481	+	18.0735i	0.561966	+	0.582108i
$965$	39.2895	−	3.88302i	1.26477	−	0.124999i
$966$	−16.7309	−	1.79667i	−0.538308	−	0.0578069i
$967$	−30.7352	−	12.7309i	−0.988377	−	0.409399i	−0.170855	−	0.985296i	$-0.554653\pi$
$967$	−30.7352	−	12.7309i	−0.988377	−	0.409399i	−0.817522	+	0.575897i	$0.804653\pi$
$968$	−14.2742	+	25.0884i	−0.458789	+	0.806373i
$969$	24.7155	+	12.2058i	0.793976	+	0.392106i
$970$	−0.501820	+	0.0954093i	−0.0161125	+	0.00306341i
$971$	−8.86801	−	21.4093i	−0.284588	−	0.687056i	0.715343	−	0.698773i	$-0.246270\pi$
$971$	−8.86801	−	21.4093i	−0.284588	−	0.687056i	−0.999931	+	0.0117170i	$0.996270\pi$
$972$	21.9547	+	22.7416i	0.704198	+	0.729438i
$973$			70.7678i			2.26871i
$974$	−9.62788	+	7.76059i	−0.308497	+	0.248665i
$975$	4.53986	+	10.9394i	0.145392	+	0.350341i
$976$	−33.6729	−	7.93958i	−1.07784	−	0.254140i
$977$	−6.30843	−	15.2299i	−0.201824	−	0.487247i	0.790267	−	0.612762i	$-0.209942\pi$
$977$	−6.30843	−	15.2299i	−0.201824	−	0.487247i	−0.992092	+	0.125515i	$0.959942\pi$
$978$	12.7362	+	24.3407i	0.407259	+	0.778329i
$979$	−7.62839	−	5.09713i	−0.243804	−	0.162905i
$980$	34.1828	−	17.5191i	1.09193	−	0.559626i
$981$	−12.8650	−	19.2538i	−0.410747	−	0.614727i
$982$	0.534428	+	5.96380i	0.0170543	+	0.190313i
$983$	−35.6767	+	23.8384i	−1.13791	+	0.760326i	−0.974089	−	0.226164i	$-0.927382\pi$
$983$	−35.6767	+	23.8384i	−1.13791	+	0.760326i	−0.163820	+	0.986490i	$0.552382\pi$
$984$	2.12227	+	2.72990i	0.0676554	+	0.0870259i
$985$	−18.3058	−	15.0129i	−0.583272	−	0.478351i
$986$	8.38880	−	3.70659i	0.267154	−	0.118042i
$987$	7.70025	+	7.70025i	0.245102	+	0.245102i
$988$	28.6771	+	6.23092i	0.912341	+	0.198232i
$989$	15.7815	+	3.13914i	0.501823	+	0.0998188i
$990$	5.31933	−	1.01135i	0.169059	−	0.0321427i
$991$	13.7159	+	20.5273i	0.435700	+	0.652071i	0.982731	−	0.185041i	$-0.0592419\pi$
$991$	13.7159	+	20.5273i	0.435700	+	0.652071i	−0.547031	+	0.837113i	$0.684242\pi$
$992$	−1.66571	+	11.6362i	−0.0528865	+	0.369451i
$993$	20.0892	−	3.99599i	0.637511	−	0.126809i
$994$	48.1166	+	15.0597i	1.52617	+	0.477666i
$995$	2.80091	+	0.848619i	0.0887949	+	0.0269030i
$996$	34.3009	+	14.9206i	1.08687	+	0.472777i
$997$	7.40967	−	11.0894i	0.234667	−	0.351203i	−0.695382	−	0.718640i	$-0.744765\pi$
$997$	7.40967	−	11.0894i	0.234667	−	0.351203i	0.930048	+	0.367437i	$0.119765\pi$
$998$	−1.17202	+	10.9141i	−0.0370998	+	0.345479i
$999$	−30.3484	+	30.3484i	−0.960182	+	0.960182i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	680.2.ct.a.173.42	yes	832
5.2	odd	4		680.2.cf.a.37.11	✓	832
8.5	even	2	inner	680.2.ct.a.173.38	yes	832
17.6	odd	16		680.2.cf.a.533.17	yes	832
40.37	odd	4		680.2.cf.a.37.17	yes	832
85.57	even	16	inner	680.2.ct.a.397.38	yes	832
136.125	odd	16		680.2.cf.a.533.11	yes	832
680.397	even	16	inner	680.2.ct.a.397.42	yes	832

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
680.2.cf.a.37.11	✓	832	5.2	odd	4
680.2.cf.a.37.17	yes	832	40.37	odd	4
680.2.cf.a.533.11	yes	832	136.125	odd	16
680.2.cf.a.533.17	yes	832	17.6	odd	16
680.2.ct.a.173.38	yes	832	8.5	even	2	inner
680.2.ct.a.173.42	yes	832	1.1	even	1	trivial
680.2.ct.a.397.38	yes	832	85.57	even	16	inner
680.2.ct.a.397.42	yes	832	680.397	even	16	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:	\( N \)	\(=\)	\( 680 = 2^{3} \cdot 5 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	680.ct (of order \(16\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.422420 + 1.34965i) q^{2} +(0.863808 - 0.577178i) q^{3} +(-1.64312 - 1.14024i) q^{4} +(1.72803 - 1.41913i) q^{5} +(0.414100 + 1.40965i) q^{6} +(0.770271 + 3.87241i) q^{7} +(2.23302 - 1.73598i) q^{8} +(-0.735021 + 1.77450i) q^{9} +(1.18538 + 2.93170i) q^{10} +(-0.874343 + 0.173918i) q^{11} +(-2.07746 - 0.0365739i) q^{12} -2.28012 q^{13} +(-5.55179 - 0.596186i) q^{14} +(0.673594 - 2.22323i) q^{15} +(1.39971 + 3.74711i) q^{16} +(0.535855 + 4.08814i) q^{17} +(-2.08447 - 1.74161i) q^{18} +(5.94539 - 2.46266i) q^{19} +(-4.45751 + 0.361436i) q^{20} +(2.90044 + 2.90044i) q^{21} +(0.134611 - 1.25353i) q^{22} +(2.41192 + 1.61159i) q^{23} +(0.926924 - 2.78840i) q^{24} +(0.972154 - 4.90458i) q^{25} +(0.963168 - 3.07737i) q^{26} +(0.997318 + 5.01385i) q^{27} +(3.14983 - 7.24114i) q^{28} +(-1.30777 + 0.873827i) q^{29} +(2.71605 + 1.84826i) q^{30} +(0.405395 - 2.03806i) q^{31} +(-5.64856 + 0.306263i) q^{32} +(-0.654883 + 0.654883i) q^{33} +(-5.74392 - 1.00369i) q^{34} +(6.82649 + 5.59852i) q^{35} +(3.23108 - 2.07762i) q^{36} +(4.66437 + 6.98072i) q^{37} +(0.812285 + 9.06448i) q^{38} +(-1.96959 + 1.31603i) q^{39} +(1.39513 - 6.16876i) q^{40} +(-0.653766 + 0.978430i) q^{41} +(-5.13978 + 2.68938i) q^{42} +(5.12477 - 2.12275i) q^{43} +(1.63496 + 0.711193i) q^{44} +(1.24810 + 4.10947i) q^{45} +(-3.19393 + 2.57448i) q^{46} +2.65486 q^{47} +(3.37183 + 2.42890i) q^{48} +(-7.93510 + 3.28683i) q^{49} +(6.20882 + 3.38386i) q^{50} +(2.82246 + 3.22208i) q^{51} +(3.74652 + 2.59988i) q^{52} +(-1.01195 + 2.44306i) q^{53} +(-7.18825 - 0.771920i) q^{54} +(-1.26408 + 1.54134i) q^{55} +(8.44247 + 7.30998i) q^{56} +(3.71428 - 5.55881i) q^{57} +(-0.626933 - 2.13416i) q^{58} +(3.82876 - 9.24344i) q^{59} +(-3.64182 + 2.88499i) q^{60} +(-4.80516 + 7.19144i) q^{61} +(2.57942 + 1.40806i) q^{62} +(-7.43775 - 1.47946i) q^{63} +(1.97271 - 7.75296i) q^{64} +(-3.94011 + 3.23578i) q^{65} +(-0.607229 - 1.16050i) q^{66} +(0.596874 - 0.596874i) q^{67} +(3.78098 - 7.32831i) q^{68} +3.01361 q^{69} +(-10.4397 + 6.84847i) q^{70} +(-8.85604 - 1.76158i) q^{71} +(1.43919 + 5.23846i) q^{72} +(2.95504 - 14.8560i) q^{73} +(-11.3919 + 3.34648i) q^{74} +(-1.99106 - 4.79772i) q^{75} +(-12.5770 - 2.73271i) q^{76} +(-1.34696 - 3.25185i) q^{77} +(-0.944198 - 3.21417i) q^{78} +(-7.25794 + 1.44369i) q^{79} +(7.73635 + 4.48874i) q^{80} +(-0.319046 - 0.319046i) q^{81} +(-1.04438 - 1.29567i) q^{82} +(-16.6322 - 6.88930i) q^{83} +(-1.45858 - 8.07297i) q^{84} +(6.72756 + 6.30396i) q^{85} +(0.700169 + 7.81335i) q^{86} +(-0.625312 + 1.50964i) q^{87} +(-1.65050 + 1.90621i) q^{88} +(7.27719 + 7.27719i) q^{89} +(-6.07357 - 0.0514168i) q^{90} +(-1.75631 - 8.82956i) q^{91} +(-2.12547 - 5.39821i) q^{92} +(-0.826139 - 1.99447i) q^{93} +(-1.12146 + 3.58314i) q^{94} +(6.77896 - 12.6928i) q^{95} +(-4.70250 + 3.52478i) q^{96} +(-0.0315133 + 0.158428i) q^{97} +(-1.08413 - 12.0980i) q^{98} +(0.334044 - 1.67935i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 832 q - 8 q^{2} - 16 q^{6} - 16 q^{7} - 8 q^{8} - 8 q^{10} + 16 q^{12} + 32 q^{14} - 16 q^{15} - 16 q^{17} - 16 q^{18} - 8 q^{20} - 8 q^{22} - 16 q^{23} - 16 q^{25} - 48 q^{26} + 24 q^{28} + 56 q^{30} - 32 q^{31}+ \cdots - 16 q^{97}+O(q^{100}) \) 832 * q - 8 * q^2 - 16 * q^6 - 16 * q^7 - 8 * q^8 - 8 * q^10 + 16 * q^12 + 32 * q^14 - 16 * q^15 - 16 * q^17 - 16 * q^18 - 8 * q^20 - 8 * q^22 - 16 * q^23 - 16 * q^25 - 48 * q^26 + 24 * q^28 + 56 * q^30 - 32 * q^31 - 8 * q^32 + 48 * q^36 - 16 * q^38 - 96 * q^39 - 64 * q^40 - 32 * q^41 - 24 * q^42 - 32 * q^46 - 32 * q^47 - 136 * q^48 - 16 * q^52 + 64 * q^54 - 16 * q^55 - 16 * q^56 - 16 * q^57 - 64 * q^58 - 8 * q^60 - 8 * q^62 + 32 * q^63 - 96 * q^65 - 16 * q^66 - 64 * q^68 + 56 * q^70 - 32 * q^71 - 96 * q^73 - 16 * q^76 - 160 * q^78 + 40 * q^80 - 32 * q^81 - 8 * q^82 + 96 * q^84 - 32 * q^86 - 16 * q^87 - 96 * q^88 + 88 * q^90 - 120 * q^92 - 48 * q^94 - 16 * q^95 - 16 * q^96 - 16 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more