LMFDB - Embedded newform 640.2.bm.a.341.59

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [640,2,Mod(21,640)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(640, base_ring=CyclotomicField(32))

chi = DirichletCharacter(H, H._module([0, 13, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("640.21");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

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

Embedding invariants

Embedding label			341.59
Character	$\chi$	$=$	640.341
Dual form			640.2.bm.a.381.59

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.34843 + 0.426318i) q^{2} +(1.96673 - 2.39647i) q^{3} +(1.63651 + 1.14972i) q^{4} +(-0.956940 + 0.290285i) q^{5} +(3.67365 - 2.39301i) q^{6} +(4.41320 + 0.877840i) q^{7} +(1.71656 + 2.24798i) q^{8} +(-1.28977 - 6.48409i) q^{9} +O(q^{10})$	\(q+(1.34843 + 0.426318i) q^{2} +(1.96673 - 2.39647i) q^{3} +(1.63651 + 1.14972i) q^{4} +(-0.956940 + 0.290285i) q^{5} +(3.67365 - 2.39301i) q^{6} +(4.41320 + 0.877840i) q^{7} +(1.71656 + 2.24798i) q^{8} +(-1.28977 - 6.48409i) q^{9} +(-1.41412 - 0.0165330i) q^{10} +(-3.98349 - 0.392339i) q^{11} +(5.97383 - 1.66066i) q^{12} +(-1.64713 + 5.42985i) q^{13} +(5.57663 + 3.06513i) q^{14} +(-1.18639 + 2.86419i) q^{15} +(1.35631 + 3.76303i) q^{16} +(-1.47073 - 3.55065i) q^{17} +(1.02513 - 9.29317i) q^{18} +(-2.49099 + 1.33146i) q^{19} +(-1.89978 - 0.625156i) q^{20} +(10.7833 - 8.84963i) q^{21} +(-5.20418 - 2.22727i) q^{22} +(-2.67686 + 4.00621i) q^{23} +(8.76324 + 0.307475i) q^{24} +(0.831470 - 0.555570i) q^{25} +(-4.53587 + 6.61955i) q^{26} +(-9.87322 - 5.27735i) q^{27} +(6.21296 + 6.51051i) q^{28} +(-0.771407 - 7.83223i) q^{29} +(-2.82081 + 3.35638i) q^{30} +(-5.27162 - 5.27162i) q^{31} +(0.224634 + 5.65239i) q^{32} +(-8.77469 + 8.77469i) q^{33} +(-0.469463 - 5.41479i) q^{34} +(-4.47799 + 0.441044i) q^{35} +(5.34415 - 12.0941i) q^{36} +(0.184376 - 0.344943i) q^{37} +(-3.92654 + 0.733424i) q^{38} +(9.77302 + 14.6264i) q^{39} +(-2.29520 - 1.65289i) q^{40} +(-1.69932 - 1.13545i) q^{41} +(18.3132 - 7.33596i) q^{42} +(2.05765 + 2.50725i) q^{43} +(-6.06793 - 5.22194i) q^{44} +(3.11646 + 5.83049i) q^{45} +(-5.31747 + 4.26088i) q^{46} +(2.54349 - 1.05355i) q^{47} +(11.6855 + 4.15053i) q^{48} +(12.2386 + 5.06937i) q^{49} +(1.35802 - 0.394675i) q^{50} +(-11.4016 - 3.45863i) q^{51} +(-8.93831 + 6.99225i) q^{52} +(-0.00307733 + 0.0312446i) q^{53} +(-11.0635 - 11.3252i) q^{54} +(3.92585 - 0.780900i) q^{55} +(5.60217 + 11.4276i) q^{56} +(-1.70830 + 8.58820i) q^{57} +(2.29883 - 10.8901i) q^{58} +(-0.326054 - 1.07486i) q^{59} +(-5.23454 + 3.32326i) q^{60} +(2.69514 + 2.21185i) q^{61} +(-4.86101 - 9.35578i) q^{62} -29.7478i q^{63} +(-2.10681 + 7.71760i) q^{64} -5.67417i q^{65} +(-15.5728 + 8.09122i) q^{66} +(-5.60405 - 4.59912i) q^{67} +(1.67538 - 7.50158i) q^{68} +(4.33609 + 14.2942i) q^{69} +(-6.22626 - 1.31433i) q^{70} +(1.81115 - 9.10528i) q^{71} +(12.3621 - 14.0297i) q^{72} +(4.08316 - 0.812192i) q^{73} +(0.395673 - 0.386528i) q^{74} +(0.303871 - 3.08525i) q^{75} +(-5.60731 - 0.684983i) q^{76} +(-17.2355 - 5.22833i) q^{77} +(6.94272 + 23.8890i) q^{78} +(8.94624 + 3.70565i) q^{79} +(-2.39026 - 3.20728i) q^{80} +(-13.7414 + 5.69186i) q^{81} +(-1.80735 - 2.25552i) q^{82} +(4.40291 + 8.23727i) q^{83} +(27.8215 - 2.08474i) q^{84} +(2.43810 + 2.97083i) q^{85} +(1.70570 + 4.25806i) q^{86} +(-20.2869 - 13.5553i) q^{87} +(-5.95594 - 9.62827i) q^{88} +(-3.03951 - 4.54894i) q^{89} +(1.71668 + 9.19058i) q^{90} +(-12.0356 + 22.5171i) q^{91} +(-8.98671 + 3.47856i) q^{92} +(-23.0012 + 2.26542i) q^{93} +(3.87885 - 0.336297i) q^{94} +(1.99722 - 1.99722i) q^{95} +(13.9876 + 10.5784i) q^{96} +(10.4315 + 10.4315i) q^{97} +(14.3416 + 12.0532i) q^{98} +(2.59380 + 26.3353i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 1024 q+O(q^{10}) $ 1024 * q	$ 1024 q - 192 q^{52} - 128 q^{54} - 32 q^{56} - 288 q^{58} - 192 q^{62} - 192 q^{64} - 192 q^{66} - 192 q^{68} - 288 q^{72} - 32 q^{74} - 128 q^{76} - 192 q^{78}+O(q^{100}) $ 1024 * q - 192 * q^52 - 128 * q^54 - 32 * q^56 - 288 * q^58 - 192 * q^62 - 192 * q^64 - 192 * q^66 - 192 * q^68 - 288 * q^72 - 32 * q^74 - 128 * q^76 - 192 * q^78

Display 100 coefficients 10 coefficients

Character values

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

$n$	$257$	$261$	$511$
$\chi(n)$	$1$	$e\left(\frac{29}{32}\right)$	$1$

Coefficient data

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

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

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

$2$	1.34843	+	0.426318i	0.953481	+	0.301452i
$2$	1.34843	+	0.426318i	0.953481	+	0.301452i
$3$	1.96673	−	2.39647i	1.13549	−	1.38360i	0.222848	−	0.974853i	$-0.428465\pi$
$3$	1.96673	−	2.39647i	1.13549	−	1.38360i	0.912646	−	0.408751i	$-0.134035\pi$
$4$	1.63651	+	1.14972i	0.818253	+	0.574858i
$5$	−0.956940	+	0.290285i	−0.427957	+	0.129819i
$5$	−0.956940	+	0.290285i	−0.427957	+	0.129819i
$6$	3.67365	−	2.39301i	1.49976	−	0.976943i
$7$	4.41320	+	0.877840i	1.66803	+	0.331792i	0.936674	−	0.350202i	$-0.113887\pi$
$7$	4.41320	+	0.877840i	1.66803	+	0.331792i	0.731358	+	0.681994i	$0.238887\pi$
$8$	1.71656	+	2.24798i	0.606897	+	0.794780i
$9$	−1.28977	−	6.48409i	−0.429922	−	2.16136i
$10$	−1.41412	−	0.0165330i	−0.447183	−	0.00522819i
$11$	−3.98349	−	0.392339i	−1.20107	−	0.118295i	−0.522374	−	0.852717i	$-0.674953\pi$
$11$	−3.98349	−	0.392339i	−1.20107	−	0.118295i	−0.678693	+	0.734422i	$0.737453\pi$
$12$	5.97383	−	1.66066i	1.72450	−	0.479391i
$13$	−1.64713	+	5.42985i	−0.456831	+	1.50597i	0.362135	+	0.932126i	$0.382048\pi$
$13$	−1.64713	+	5.42985i	−0.456831	+	1.50597i	−0.818966	+	0.573843i	$0.805452\pi$
$14$	5.57663	+	3.06513i	1.49042	+	0.819189i
$15$	−1.18639	+	2.86419i	−0.306324	+	0.739532i
$16$	1.35631	+	3.76303i	0.339077	+	0.940759i
$17$	−1.47073	−	3.55065i	−0.356704	−	0.861159i	−0.995759	−	0.0919983i	$-0.970675\pi$
$17$	−1.47073	−	3.55065i	−0.356704	−	0.861159i	0.639055	−	0.769161i	$-0.279325\pi$
$18$	1.02513	−	9.29317i	0.241625	−	2.19042i
$19$	−2.49099	+	1.33146i	−0.571471	+	0.305458i	−0.731705	−	0.681621i	$-0.761275\pi$
$19$	−2.49099	+	1.33146i	−0.571471	+	0.305458i	0.160234	+	0.987079i	$0.448775\pi$
$20$	−1.89978	−	0.625156i	−0.424805	−	0.139789i
$21$	10.7833	−	8.84963i	2.35311	−	1.93115i
$22$	−5.20418	−	2.22727i	−1.10953	−	0.474856i
$23$	−2.67686	+	4.00621i	−0.558165	+	0.835352i	−0.998032	−	0.0627105i	$-0.980026\pi$
$23$	−2.67686	+	4.00621i	−0.558165	+	0.835352i	0.439867	+	0.898063i	$0.355026\pi$
$24$	8.76324	+	0.307475i	1.78879	+	0.0627632i
$25$	0.831470	−	0.555570i	0.166294	−	0.111114i
$26$	−4.53587	+	6.61955i	−0.889557	+	1.29820i
$27$	−9.87322	−	5.27735i	−1.90010	−	1.01563i
$28$	6.21296	+	6.51051i	1.17414	+	1.23037i
$29$	−0.771407	−	7.83223i	−0.143247	−	1.45441i	−0.751010	−	0.660291i	$-0.770433\pi$
$29$	−0.771407	−	7.83223i	−0.143247	−	1.45441i	0.607763	−	0.794118i	$-0.292067\pi$
$30$	−2.82081	+	3.35638i	−0.515008	+	0.612788i
$31$	−5.27162	−	5.27162i	−0.946811	−	0.946811i	0.0518442	−	0.998655i	$-0.483490\pi$
$31$	−5.27162	−	5.27162i	−0.946811	−	0.946811i	−0.998655	+	0.0518442i	$0.983490\pi$
$32$	0.224634	+	5.65239i	0.0397101	+	0.999211i
$33$	−8.77469	+	8.77469i	−1.52748	+	1.52748i
$34$	−0.469463	−	5.41479i	−0.0805122	−	0.928628i
$35$	−4.47799	+	0.441044i	−0.756918	+	0.0745500i
$36$	5.34415	−	12.0941i	0.890691	−	2.01569i
$37$	0.184376	−	0.344943i	0.0303112	−	0.0567083i	−0.866310	−	0.499507i	$-0.833514\pi$
$37$	0.184376	−	0.344943i	0.0303112	−	0.0567083i	0.896621	+	0.442799i	$0.146014\pi$
$38$	−3.92654	+	0.733424i	−0.636968	+	0.118977i
$39$	9.77302	+	14.6264i	1.56494	+	2.34209i
$40$	−2.29520	−	1.65289i	−0.362904	−	0.261345i
$41$	−1.69932	−	1.13545i	−0.265390	−	0.177328i	0.415755	−	0.909477i	$-0.363517\pi$
$41$	−1.69932	−	1.13545i	−0.265390	−	0.177328i	−0.681144	+	0.732149i	$0.738517\pi$
$42$	18.3132	−	7.33596i	2.82579	−	1.13196i
$43$	2.05765	+	2.50725i	0.313788	+	0.382352i	0.905891	−	0.423510i	$-0.139202\pi$
$43$	2.05765	+	2.50725i	0.313788	+	0.382352i	−0.592103	+	0.805862i	$0.701702\pi$
$44$	−6.06793	−	5.22194i	−0.914774	−	0.787238i
$45$	3.11646	+	5.83049i	0.464574	+	0.869158i
$46$	−5.31747	+	4.26088i	−0.784018	+	0.628233i
$47$	2.54349	−	1.05355i	0.371006	−	0.153676i	−0.189387	−	0.981903i	$-0.560650\pi$
$47$	2.54349	−	1.05355i	0.371006	−	0.153676i	0.560393	+	0.828227i	$0.310650\pi$
$48$	11.6855	+	4.15053i	1.68666	+	0.599078i
$49$	12.2386	+	5.06937i	1.74836	+	0.724196i
$50$	1.35802	−	0.394675i	0.192054	−	0.0558155i
$51$	−11.4016	−	3.45863i	−1.59654	−	0.484304i
$52$	−8.93831	+	6.99225i	−1.23952	+	0.969651i
$53$	−0.00307733	+	0.0312446i	−0.000422704	+	0.00429178i	−0.995394	−	0.0958710i	$-0.969436\pi$
$53$	−0.00307733	+	0.0312446i	−0.000422704	+	0.00429178i	0.994971	+	0.100163i	$0.0319364\pi$
$54$	−11.0635	−	11.3252i	−1.50555	−	1.54117i
$55$	3.92585	−	0.780900i	0.529362	−	0.105297i
$56$	5.60217	+	11.4276i	0.748622	+	1.52708i
$57$	−1.70830	+	8.58820i	−0.226270	+	1.13754i
$58$	2.29883	−	10.8901i	0.301851	−	1.42993i
$59$	−0.326054	−	1.07486i	−0.0424486	−	0.139934i	0.933155	−	0.359475i	$-0.117044\pi$
$59$	−0.326054	−	1.07486i	−0.0424486	−	0.139934i	−0.975603	+	0.219541i	$0.929544\pi$
$60$	−5.23454	+	3.32326i	−0.675776	+	0.429031i
$61$	2.69514	+	2.21185i	0.345077	+	0.283198i	0.790927	−	0.611910i	$-0.209599\pi$
$61$	2.69514	+	2.21185i	0.345077	+	0.283198i	−0.445850	+	0.895108i	$0.647099\pi$
$62$	−4.86101	−	9.35578i	−0.617349	−	1.18818i
$63$		−	29.7478i		−	3.74787i
$64$	−2.10681	+	7.71760i	−0.263351	+	0.964700i
$65$		−	5.67417i		−	0.703795i
$66$	−15.5728	+	8.09122i	−1.91688	+	0.995960i
$67$	−5.60405	−	4.59912i	−0.684643	−	0.561872i	0.226475	−	0.974017i	$-0.427280\pi$
$67$	−5.60405	−	4.59912i	−0.684643	−	0.561872i	−0.911118	+	0.412145i	$0.864780\pi$
$68$	1.67538	−	7.50158i	0.203170	−	0.909700i
$69$	4.33609	+	14.2942i	0.522004	+	1.72082i
$70$	−6.22626	−	1.31433i	−0.744181	−	0.157093i
$71$	1.81115	−	9.10528i	0.214944	−	1.08060i	−0.711073	−	0.703118i	$-0.751791\pi$
$71$	1.81115	−	9.10528i	0.214944	−	1.08060i	0.926018	−	0.377480i	$-0.123209\pi$
$72$	12.3621	−	14.0297i	1.45689	−	1.65342i
$73$	4.08316	−	0.812192i	0.477898	−	0.0950599i	0.0497372	−	0.998762i	$-0.484162\pi$
$73$	4.08316	−	0.812192i	0.477898	−	0.0950599i	0.428161	+	0.903702i	$0.359162\pi$
$74$	0.395673	−	0.386528i	0.0459960	−	0.0449329i
$75$	0.303871	−	3.08525i	0.0350880	−	0.356254i
$76$	−5.60731	−	0.684983i	−0.643203	−	0.0785729i
$77$	−17.2355	−	5.22833i	−1.96417	−	0.595824i
$78$	6.94272	+	23.8890i	0.786108	+	2.70489i
$79$	8.94624	+	3.70565i	1.00653	+	0.416919i	0.824188	−	0.566316i	$-0.191632\pi$
$79$	8.94624	+	3.70565i	1.00653	+	0.416919i	0.182343	+	0.983235i	$0.441632\pi$
$80$	−2.39026	−	3.20728i	−0.267239	−	0.358585i
$81$	−13.7414	+	5.69186i	−1.52682	+	0.632429i
$82$	−1.80735	−	2.25552i	−0.199588	−	0.249081i
$83$	4.40291	+	8.23727i	0.483283	+	0.904158i	0.998879	+	0.0473269i	$0.0150702\pi$
$83$	4.40291	+	8.23727i	0.483283	+	0.904158i	−0.515597	+	0.856831i	$0.672430\pi$
$84$	27.8215	−	2.08474i	3.03557	−	0.227464i
$85$	2.43810	+	2.97083i	0.264449	+	0.322232i
$86$	1.70570	+	4.25806i	0.183931	+	0.459158i
$87$	−20.2869	−	13.5553i	−2.17498	−	1.45328i
$88$	−5.95594	−	9.62827i	−0.634906	−	1.02638i
$89$	−3.03951	−	4.54894i	−0.322187	−	0.482187i	0.634655	−	0.772796i	$-0.281142\pi$
$89$	−3.03951	−	4.54894i	−0.322187	−	0.482187i	−0.956842	+	0.290609i	$0.906142\pi$
$90$	1.71668	+	9.19058i	0.180954	+	0.968773i
$91$	−12.0356	+	22.5171i	−1.26168	+	2.36043i
$92$	−8.98671	+	3.47856i	−0.936929	+	0.362665i
$93$	−23.0012	+	2.26542i	−2.38511	+	0.234913i
$94$	3.87885	−	0.336297i	0.400073	−	0.0346864i
$95$	1.99722	−	1.99722i	0.204911	−	0.204911i
$96$	13.9876	+	10.5784i	1.42760	+	1.07966i
$97$	10.4315	+	10.4315i	1.05916	+	1.05916i	0.998136	+	0.0610232i	$0.0194363\pi$
$97$	10.4315	+	10.4315i	1.05916	+	1.05916i	0.0610232	+	0.998136i	$0.480564\pi$
$98$	14.3416	+	12.0532i	1.44872	+	1.21756i
$99$	2.59380	+	26.3353i	0.260687	+	2.64680i
$100$	1.99945	+	0.0467592i	0.199945	+	0.00467592i
$101$	12.5118	+	6.68771i	1.24497	+	0.665452i	0.956415	−	0.292011i	$-0.0943243\pi$
$101$	12.5118	+	6.68771i	1.24497	+	0.665452i	0.288558	+	0.957463i	$0.406824\pi$
$102$	−13.8997	−	9.52439i	−1.37627	−	0.943055i
$103$	−5.90393	+	3.94488i	−0.581731	+	0.388700i	−0.811333	−	0.584584i	$-0.801258\pi$
$103$	−5.90393	+	3.94488i	−0.581731	+	0.388700i	0.229602	+	0.973285i	$0.426258\pi$
$104$	−15.0336	+	5.61798i	−1.47416	+	0.550888i
$105$	−7.75007	+	11.5988i	−0.756329	+	1.13193i
$106$	−0.0174697	+	0.0408192i	−0.00169681	+	0.00396471i
$107$	9.99020	−	8.19874i	0.965789	−	0.792602i	−0.0124846	−	0.999922i	$-0.503974\pi$
$107$	9.99020	−	8.19874i	0.965789	−	0.792602i	0.978273	+	0.207320i	$0.0664741\pi$
$108$	−10.0901	−	19.9878i	−0.970924	−	1.92333i
$109$	−13.5897	+	7.26384i	−1.30166	+	0.695750i	−0.968944	−	0.247278i	$-0.920464\pi$
$109$	−13.5897	+	7.26384i	−1.30166	+	0.695750i	−0.332712	+	0.943028i	$0.607964\pi$
$110$	5.62663	+	0.620673i	0.536478	+	0.0591788i
$111$	−0.464028	−	1.12026i	−0.0440436	−	0.106331i
$112$	2.68232	+	17.7976i	0.253455	+	1.68172i
$113$	1.50810	−	3.64088i	0.141870	−	0.342505i	−0.836934	−	0.547304i	$-0.815654\pi$
$113$	1.50810	−	3.64088i	0.141870	−	0.342505i	0.978804	+	0.204799i	$0.0656541\pi$
$114$	−5.96482	+	10.8523i	−0.558656	+	1.01641i
$115$	1.39866	−	4.61076i	0.130425	−	0.429955i
$116$	7.74242	−	13.7044i	0.718866	−	1.27242i
$117$	37.3320	+	3.67688i	3.45135	+	0.339928i
$118$	0.0185702	−	1.58837i	0.00170953	−	0.146221i
$119$	−3.37371	−	16.9608i	−0.309267	−	1.55479i
$120$	−8.47516	+	2.24960i	−0.773672	+	0.205359i
$121$	4.92561	+	0.979765i	0.447783	+	0.0890696i
$122$	2.69125	+	4.13150i	0.243654	+	0.374048i
$123$	−6.06319	+	1.83925i	−0.546699	+	0.165839i
$124$	−2.56618	−	14.6879i	−0.230450	−	1.31901i
$125$	−0.634393	+	0.773010i	−0.0567419	+	0.0691402i
$126$	12.6820	−	40.1127i	1.12980	−	3.57352i
$127$	8.07978			0.716964			0.358482	−	0.933537i	$-0.383294\pi$
$127$	8.07978			0.716964			0.358482	+	0.933537i	$0.383294\pi$
$128$	−6.13103	+	9.50844i	−0.541911	+	0.840436i
$129$	10.0554			0.885329
$130$	2.41900	−	7.65121i	0.212160	−	0.671055i
$131$	−8.90430	+	10.8499i	−0.777972	+	0.947962i	−0.999631	−	0.0271626i	$-0.991353\pi$
$131$	−8.90430	+	10.8499i	−0.777972	+	0.947962i	0.221659	+	0.975124i	$0.428853\pi$
$132$	−24.4482	+	4.27144i	−2.12795	+	0.371781i
$133$	−12.1620	+	3.68931i	−1.05458	+	0.319904i
$134$	−5.59596	−	8.59068i	−0.483417	−	0.742122i
$135$	10.9800	+	2.18406i	0.945009	+	0.187974i
$136$	5.45718	−	9.40108i	0.467950	−	0.806136i
$137$	0.617539	+	3.10458i	0.0527599	+	0.265242i	0.998157	−	0.0606776i	$-0.0193261\pi$
$137$	0.617539	+	3.10458i	0.0527599	+	0.265242i	−0.945398	+	0.325920i	$0.894326\pi$
$138$	−0.246959	+	21.1232i	−0.0210226	+	1.79813i
$139$	7.24570	+	0.713639i	0.614572	+	0.0605301i	0.400514	−	0.916291i	$-0.368832\pi$
$139$	7.24570	+	0.713639i	0.614572	+	0.0605301i	0.214059	+	0.976821i	$0.431332\pi$
$140$	−7.83534	−	4.42664i	−0.662207	−	0.374120i
$141$	2.47757	−	8.16745i	0.208649	−	0.687823i
$142$	6.32395	−	11.5057i	0.530694	−	0.965534i
$143$	8.69165	−	20.9835i	0.726832	−	1.75473i
$144$	22.6505	−	13.6479i	1.88754	−	1.13732i
$145$	3.01177	+	7.27105i	0.250114	+	0.603828i
$146$	5.85210	+	0.645544i	0.484323	+	0.0534256i
$147$	36.2186	−	19.3592i	2.98726	−	1.59672i
$148$	0.698319	−	0.352522i	0.0574015	−	0.0289771i
$149$	−10.1935	+	8.36561i	−0.835086	+	0.685337i	−0.951428	−	0.307872i	$-0.900383\pi$
$149$	−10.1935	+	8.36561i	−0.835086	+	0.685337i	0.116342	+	0.993209i	$0.462883\pi$
$150$	1.72504	−	4.03069i	0.140849	−	0.329104i
$151$	9.39529	−	14.0610i	0.764578	−	1.14427i	−0.221037	−	0.975265i	$-0.570944\pi$
$151$	9.39529	−	14.0610i	0.764578	−	1.14427i	0.985615	−	0.169006i	$-0.0540558\pi$
$152$	−7.26903	−	3.31415i	−0.589596	−	0.268813i
$153$	−21.1258	+	14.1158i	−1.70792	+	1.14120i
$154$	−21.0119	−	14.3978i	−1.69319	−	1.16021i
$155$	6.57490	+	3.51436i	0.528108	+	0.282280i
$156$	−0.822539	+	35.1723i	−0.0658558	+	2.81604i
$157$	−0.0530309	−	0.538432i	−0.00423233	−	0.0429715i	0.992837	−	0.119480i	$-0.0381228\pi$
$157$	−0.0530309	−	0.538432i	−0.00423233	−	0.0429715i	−0.997069	+	0.0765085i	$0.975623\pi$
$158$	10.4836	+	8.81074i	0.834027	+	0.700945i
$159$	0.0688246	+	0.0688246i	0.00545815	+	0.00545815i
$160$	−1.85576	−	5.34379i	−0.146711	−	0.422464i
$161$	−15.3303	+	15.3303i	−1.20820	+	1.20820i
$162$	−20.9558	+	1.81687i	−1.64644	+	0.142747i
$163$	−18.7050	+	1.84228i	−1.46509	+	0.144299i	−0.798891	−	0.601476i	$-0.794579\pi$
$163$	−18.7050	+	1.84228i	−1.46509	+	0.144299i	−0.666198	+	0.745775i	$0.732079\pi$
$164$	−1.47551	−	3.81191i	−0.115218	−	0.297660i
$165$	5.84970	−	10.9440i	0.455398	−	0.851990i
$166$	2.42531	+	12.9844i	0.188241	+	1.00778i
$167$	14.2443	+	21.3181i	1.10226	+	1.64964i	0.656056	+	0.754712i	$0.272224\pi$
$167$	14.2443	+	21.3181i	1.10226	+	1.64964i	0.446201	+	0.894933i	$0.352776\pi$
$168$	38.4040	+	9.04967i	2.96293	+	0.698197i
$169$	−15.9611	−	10.6649i	−1.22778	−	0.820374i
$170$	2.02108	+	5.04535i	0.155010	+	0.386961i
$171$	11.8461	+	14.4345i	0.905893	+	1.10383i
$172$	0.484729	+	6.46884i	0.0369602	+	0.493245i
$173$	9.41235	+	17.6093i	0.715608	+	1.33881i	0.931984	+	0.362498i	$0.118076\pi$
$173$	9.41235	+	17.6093i	0.715608	+	1.33881i	−0.216376	+	0.976310i	$0.569424\pi$
$174$	−21.5765	−	26.9269i	−1.63571	−	2.04132i
$175$	4.15714	−	1.72194i	0.314250	−	0.130167i
$176$	−3.92645	−	15.5221i	−0.295967	−	1.17003i
$177$	−3.21712	−	1.33258i	−0.241814	−	0.100163i
$178$	−2.15926	−	7.42971i	−0.161843	−	0.556880i
$179$	−14.5118	−	4.40211i	−1.08466	−	0.329029i	−0.303167	−	0.952938i	$-0.598044\pi$
$179$	−14.5118	−	4.40211i	−1.08466	−	0.329029i	−0.781498	+	0.623908i	$0.785544\pi$
$180$	−1.60329	+	13.1247i	−0.119502	+	0.978255i
$181$	0.201257	−	2.04340i	0.0149593	−	0.151885i	−0.984803	−	0.173674i	$-0.944436\pi$
$181$	0.201257	−	2.04340i	0.0149593	−	0.151885i	0.999763	+	0.0217890i	$0.00693621\pi$
$182$	−25.8286	+	25.2316i	−1.91454	+	1.87029i
$183$	10.6013	−	2.10872i	0.783667	−	0.155881i
$184$	−13.6009	+	0.859387i	−1.00267	+	0.0633548i
$185$	−0.0763051	+	0.383611i	−0.00561006	+	0.0282037i
$186$	−31.9812	−	6.75105i	−2.34497	−	0.495011i
$187$	4.46557	+	14.7210i	0.326554	+	1.07651i
$188$	5.37372	+	1.20015i	0.391919	+	0.0875300i
$189$	−38.9398	−	31.9571i	−2.83245	−	2.32453i
$190$	3.54456	−	1.84166i	0.257149	−	0.133608i
$191$			3.36142i			0.243224i	0.992578	+	0.121612i	$0.0388063\pi$
$191$			3.36142i			0.243224i	−0.992578	+	0.121612i	$0.961194\pi$
$192$	14.3515	+	20.2274i	1.03573	+	1.45979i
$193$		−	1.80921i		−	0.130230i	−0.997878	−	0.0651149i	$-0.979259\pi$
$193$		−	1.80921i		−	0.130230i	0.997878	−	0.0651149i	$-0.0207414\pi$
$194$	9.61899	+	18.5133i	0.690603	+	1.32917i
$195$	−13.5980	−	11.1596i	−0.973773	−	0.799155i
$196$	14.2001	+	22.3669i	1.01430	+	1.59764i
$197$	−5.10013	−	16.8129i	−0.363369	−	1.19787i	−0.928017	−	0.372537i	$-0.878488\pi$
$197$	−5.10013	−	16.8129i	−0.363369	−	1.19787i	0.564648	−	0.825332i	$-0.309012\pi$
$198$	−7.72966	+	36.6170i	−0.549323	+	2.60226i
$199$	3.42516	−	17.2194i	0.242803	−	1.22065i	−0.646349	−	0.763042i	$-0.723705\pi$
$199$	3.42516	−	17.2194i	0.242803	−	1.22065i	0.889152	−	0.457611i	$-0.151295\pi$
$200$	2.67618	+	0.915453i	0.189235	+	0.0647323i
$201$	−22.0433	+	4.38469i	−1.55482	+	0.309272i
$202$	14.0202	+	14.3519i	0.986456	+	1.00980i
$203$	3.47107	−	35.2424i	0.243621	−	2.47353i
$204$	−14.6823	−	18.7686i	−1.02797	−	1.31407i
$205$	1.95575	+	0.593271i	0.136596	+	0.0414359i
$206$	−9.64278	+	2.80243i	−0.671844	+	0.195255i
$207$	29.4291	+	12.1900i	2.04547	+	0.847260i
$208$	−22.6667	+	1.16635i	−1.57165	+	0.0808721i
$209$	10.4452	−	4.32654i	0.722509	−	0.299273i
$210$	−15.3952	+	12.3361i	−1.06237	+	0.851274i
$211$	−5.63132	−	10.5355i	−0.387676	−	0.725291i	0.610073	−	0.792345i	$-0.291140\pi$
$211$	−5.63132	−	10.5355i	−0.387676	−	0.725291i	−0.997749	+	0.0670543i	$0.978640\pi$
$212$	−0.0409585	+	0.0475940i	−0.00281304	+	0.00326877i
$213$	−18.2585	−	22.2480i	−1.25105	−	1.52441i
$214$	16.9663	−	6.79640i	1.15979	−	0.464593i
$215$	−2.69686	−	1.80199i	−0.183925	−	0.122894i
$216$	−5.08466	−	31.2537i	−0.345967	−	2.12654i
$217$	−18.6371	−	27.8923i	−1.26517	−	1.89346i
$218$	−21.4214	+	4.00123i	−1.45084	+	0.270998i
$219$	6.08410	−	11.3826i	0.411125	−	0.769162i
$220$	7.32249	+	3.23566i	0.493682	+	0.218148i
$221$	21.7020	−	2.13746i	1.45983	−	0.143781i
$222$	−0.148120	−	1.70842i	−0.00994116	−	0.114661i
$223$	−3.89240	+	3.89240i	−0.260655	+	0.260655i	−0.825320	−	0.564665i	$-0.809005\pi$
$223$	−3.89240	+	3.89240i	−0.260655	+	0.260655i	0.564665	+	0.825320i	$0.309005\pi$
$224$	−3.97054	+	25.1423i	−0.265293	+	1.67989i
$225$	−4.67477	−	4.67477i	−0.311651	−	0.311651i
$226$	3.58573	−	4.26652i	0.238519	−	0.283805i
$227$	−1.15534	−	11.7303i	−0.0766823	−	0.778569i	−0.954229	−	0.299077i	$-0.903321\pi$
$227$	−1.15534	−	11.7303i	−0.0766823	−	0.778569i	0.877547	−	0.479491i	$-0.159179\pi$
$228$	−12.6696	+	12.0906i	−0.839067	+	0.800719i
$229$	17.7297	+	9.47670i	1.17161	+	0.626238i	0.938184	−	0.346136i	$-0.112507\pi$
$229$	17.7297	+	9.47670i	1.17161	+	0.626238i	0.233425	+	0.972375i	$0.425007\pi$
$230$	3.85163	−	5.62099i	0.253969	−	0.370637i
$231$	−46.4272	+	31.0217i	−3.05469	+	2.04108i
$232$	16.2825	−	15.1786i	1.06900	−	0.996526i
$233$	0.0246418	−	0.0368791i	0.00161434	−	0.00241603i	−0.830662	−	0.556778i	$-0.812038\pi$
$233$	0.0246418	−	0.0368791i	0.00161434	−	0.00241603i	0.832276	+	0.554362i	$0.187038\pi$
$234$	48.7719	+	20.8733i	3.18832	+	1.36453i
$235$	−2.12814	+	1.74652i	−0.138824	+	0.113930i
$236$	0.702189	−	2.13388i	0.0457086	−	0.138904i
$237$	26.4754	−	14.1514i	1.71976	−	0.919231i
$238$	2.68148	−	24.3086i	0.173815	−	1.57569i
$239$	−5.07104	−	12.2426i	−0.328018	−	0.791906i	−0.998739	−	0.0501965i	$-0.984015\pi$
$239$	−5.07104	−	12.2426i	−0.328018	−	0.791906i	0.670721	−	0.741710i	$-0.265985\pi$
$240$	−12.3872	−	0.579689i	−0.799588	−	0.0374188i
$241$	−0.0915683	+	0.221065i	−0.00589843	+	0.0142401i	−0.926801	−	0.375552i	$-0.877453\pi$
$241$	−0.0915683	+	0.221065i	−0.00589843	+	0.0142401i	0.920903	+	0.389792i	$0.127453\pi$
$242$	6.22413	+	3.42102i	0.400102	+	0.219911i
$243$	−3.63591	+	11.9860i	−0.233243	+	0.768901i
$244$	1.86762	+	6.71835i	0.119562	+	0.430098i
$245$	−13.1831	−	1.29842i	−0.842239	−	0.0829533i
$246$	−8.95987	−	0.104753i	−0.571260	−	0.00667883i
$247$	−3.12665	−	15.7188i	−0.198944	−	1.00016i
$248$	2.80141	−	20.8996i	0.177890	−	1.32712i
$249$	28.3998	+	5.64906i	1.79976	+	0.357995i
$250$	−1.18498	+	0.771895i	−0.0749447	+	0.0488189i
$251$	−1.50595	+	0.456825i	−0.0950548	+	0.0288346i	−0.337454	−	0.941342i	$-0.609566\pi$
$251$	−1.50595	+	0.456825i	−0.0950548	+	0.0288346i	0.242399	+	0.970177i	$0.422066\pi$
$252$	34.2015	−	48.6824i	2.15449	−	3.06670i
$253$	12.2350	−	14.9084i	0.769211	−	0.937286i
$254$	10.8950	+	3.44455i	0.683612	+	0.216130i
$255$	11.9146			0.746121
$256$	−12.3209	+	10.2077i	−0.770054	+	0.637979i
$257$	25.4362			1.58667			0.793334	−	0.608787i	$-0.208344\pi$
$257$	25.4362			1.58667			0.793334	+	0.608787i	$0.208344\pi$
$258$	13.5590	+	4.28680i	0.844145	+	0.266884i
$259$	1.11649	−	1.36045i	0.0693754	−	0.0845342i
$260$	6.52369	−	9.28582i	0.404582	−	0.575882i
$261$	−49.7900	+	15.1036i	−3.08192	+	0.934890i
$262$	−16.6323	+	10.8343i	−1.02755	+	0.669342i
$263$	13.9017	+	2.76522i	0.857215	+	0.170511i	0.604083	−	0.796921i	$-0.293539\pi$
$263$	13.9017	+	2.76522i	0.857215	+	0.170511i	0.253132	+	0.967432i	$0.418539\pi$
$264$	−34.7876	−	4.66299i	−2.14103	−	0.286987i
$265$	−0.00612502	−	0.0307926i	−0.000376257	−	0.00189157i
$266$	−17.9724	−	0.210122i	−1.10196	−	0.0128834i
$267$	−16.8793	−	1.66247i	−1.03300	−	0.101741i
$268$	−3.88338	−	13.9696i	−0.237215	−	0.853327i
$269$	4.54757	−	14.9913i	0.277270	−	0.914037i	−0.702120	−	0.712059i	$-0.747763\pi$
$269$	4.54757	−	14.9913i	0.277270	−	0.914037i	0.979390	−	0.201979i	$-0.0647371\pi$
$270$	13.8746	+	7.62602i	0.844383	+	0.464105i
$271$	3.29973	−	7.96626i	0.200444	−	0.483916i	−0.791411	−	0.611284i	$-0.790653\pi$
$271$	3.29973	−	7.96626i	0.200444	−	0.483916i	0.991855	+	0.127369i	$0.0406532\pi$
$272$	11.3665	−	10.3502i	0.689193	−	0.627571i
$273$	30.2907	+	73.1281i	1.83327	+	4.42592i
$274$	−0.490830	+	4.44956i	−0.0296521	+	0.268808i
$275$	−3.53012	+	1.88689i	−0.212874	+	0.113784i
$276$	−9.33820	+	28.3778i	−0.562093	+	1.70814i
$277$	3.69695	−	3.03401i	0.222128	−	0.182296i	−0.516747	−	0.856138i	$-0.672857\pi$
$277$	3.69695	−	3.03401i	0.222128	−	0.182296i	0.738875	+	0.673842i	$0.235357\pi$
$278$	9.46606	+	4.05126i	0.567736	+	0.242978i
$279$	−27.3825	+	40.9808i	−1.63935	+	2.45346i
$280$	−8.67822	−	9.30934i	−0.518623	−	0.556340i
$281$	−0.489549	+	0.327106i	−0.0292040	+	0.0195135i	−0.570087	−	0.821585i	$-0.693090\pi$
$281$	−0.489549	+	0.327106i	−0.0292040	+	0.0195135i	0.540883	+	0.841098i	$0.318090\pi$
$282$	6.82275	−	9.95697i	0.406289	−	0.592929i
$283$	−27.0399	−	14.4532i	−1.60736	−	0.859151i	−0.997792	−	0.0664151i	$-0.978844\pi$
$283$	−27.0399	−	14.4532i	−1.60736	−	0.859151i	−0.609566	−	0.792736i	$-0.708656\pi$
$284$	13.4324	−	12.8185i	0.797069	−	0.760640i
$285$	−0.858283	−	8.71429i	−0.0508403	−	0.516190i
$286$	20.6657	−	24.5893i	1.22199	−	1.45400i
$287$	−6.50270	−	6.50270i	−0.383842	−	0.383842i
$288$	36.3609	−	8.74681i	2.14259	−	0.515411i
$289$	1.57674	−	1.57674i	0.0927495	−	0.0927495i
$290$	0.961370	+	11.0884i	0.0564536	+	0.651136i
$291$	45.5148	−	4.48282i	2.66813	−	0.262788i
$292$	7.61591	+	3.36532i	0.445688	+	0.196940i
$293$	−0.293544	+	0.549182i	−0.0171490	+	0.0320836i	−0.890350	−	0.455277i	$-0.849540\pi$
$293$	−0.293544	+	0.549182i	−0.0171490	+	0.0320836i	0.873201	+	0.487361i	$0.162040\pi$
$294$	57.0913	−	10.6639i	3.32963	−	0.621930i
$295$	0.624029	+	0.933925i	0.0363323	+	0.0543752i
$296$	1.09192	−	0.177644i	0.0634664	−	0.0103254i
$297$	37.2593	+	24.8959i	2.16201	+	1.44461i
$298$	−17.3116	+	6.93473i	−1.00284	+	0.401718i
$299$	−17.3440	−	21.1337i	−1.00303	−	1.22219i
$300$	4.04445	−	4.69967i	0.233506	−	0.271336i
$301$	6.87984	+	12.8713i	0.396548	+	0.741888i
$302$	18.6633	−	14.9549i	1.07395	−	0.860558i
$303$	40.6343	−	16.8313i	2.33438	−	0.966932i
$304$	−8.38887	−	7.56780i	−0.481135	−	0.434043i
$305$	−3.22115	−	1.33425i	−0.184443	−	0.0763987i
$306$	−34.5045	+	10.0278i	−1.97249	+	0.573254i
$307$	−12.8228	−	3.88976i	−0.731837	−	0.222000i	−0.0976945	−	0.995216i	$-0.531147\pi$
$307$	−12.8228	−	3.88976i	−0.731837	−	0.222000i	−0.634143	+	0.773216i	$0.718647\pi$
$308$	−22.1949	−	28.3721i	−1.26467	−	1.61665i
$309$	−2.15766	+	21.9071i	−0.122745	+	1.24625i
$310$	7.36753	+	7.54184i	0.418448	+	0.428348i
$311$	−16.4253	+	3.26720i	−0.931394	+	0.185266i	−0.637392	−	0.770539i	$-0.719987\pi$
$311$	−16.4253	+	3.26720i	−0.931394	+	0.185266i	−0.294001	+	0.955805i	$0.594987\pi$
$312$	−16.1037	+	47.0766i	−0.911693	+	2.66519i
$313$	0.828187	−	4.16358i	0.0468119	−	0.235339i	−0.950295	−	0.311351i	$-0.899219\pi$
$313$	0.828187	−	4.16358i	0.0468119	−	0.235339i	0.997107	+	0.0760115i	$0.0242186\pi$
$314$	0.158035	−	0.748643i	0.00891841	−	0.0422484i
$315$	8.63532	+	28.4668i	0.486545	+	1.60392i
$316$	10.3801	+	16.3500i	0.583928	+	0.919757i
$317$	13.5154	+	11.0918i	0.759103	+	0.622979i	0.932208	−	0.361924i	$-0.117880\pi$
$317$	13.5154	+	11.0918i	0.759103	+	0.622979i	−0.173105	+	0.984903i	$0.555380\pi$
$318$	0.0634638	+	0.122146i	0.00355887	+	0.00684961i
$319$			31.5023i			1.76379i
$320$	−0.224208	−	7.99686i	−0.0125336	−	0.447038i
$321$		−	40.0660i		−	2.23626i
$322$	−27.2074	+	14.1362i	−1.51621	+	0.787782i
$323$	8.39111	+	6.88640i	0.466894	+	0.383170i
$324$	−29.0319	−	6.48390i	−1.61288	−	0.360216i
$325$	1.64713	+	5.42985i	0.0913661	+	0.301194i
$326$	−26.0077	−	5.49009i	−1.44043	−	0.304068i
$327$	−9.31972	+	46.8534i	−0.515381	+	2.59100i
$328$	−0.364528	−	5.76911i	−0.0201277	−	0.318546i
$329$	12.1498	−	2.41674i	0.669838	−	0.133239i
$330$	12.5535	−	12.2634i	0.691048	−	0.675076i
$331$	−0.743682	+	7.55073i	−0.0408764	+	0.415025i	0.952871	+	0.303375i	$0.0981136\pi$
$331$	−0.743682	+	7.55073i	−0.0408764	+	0.415025i	−0.993748	+	0.111650i	$0.964386\pi$
$332$	−2.26512	+	18.5425i	−0.124315	+	1.01765i
$333$	−2.47444	−	0.750614i	−0.135599	−	0.0411334i
$334$	10.1191	+	34.8185i	0.553693	+	1.90518i
$335$	6.69779	+	2.77432i	0.365940	+	0.151577i
$336$	47.9269	+	28.5751i	2.61463	+	1.55890i
$337$	8.27960	−	3.42952i	0.451018	−	0.186818i	−0.145599	−	0.989344i	$-0.546511\pi$
$337$	8.27960	−	3.42952i	0.451018	−	0.186818i	0.596618	+	0.802526i	$0.296511\pi$
$338$	−16.9757	−	21.1853i	−0.923359	−	1.15233i
$339$	−5.75923	−	10.7748i	−0.312798	−	0.585205i
$340$	0.574353	+	7.66490i	0.0311487	+	0.415688i
$341$	18.9312	+	23.0677i	1.02518	+	1.24919i
$342$	9.81990	+	24.5141i	0.530999	+	1.32557i
$343$	23.3718	+	15.6165i	1.26196	+	0.843212i
$344$	−2.10416	+	8.92941i	−0.113449	+	0.481441i
$345$	−8.29876	−	12.4200i	−0.446790	−	0.668669i
$346$	5.18472	+	27.7575i	0.278732	+	1.49225i
$347$	11.1778	−	20.9122i	0.600056	−	1.12263i	−0.380202	−	0.924904i	$-0.624145\pi$
$347$	11.1778	−	20.9122i	0.600056	−	1.12263i	0.980258	−	0.197723i	$-0.0633545\pi$
$348$	−17.6149	−	45.5074i	−0.944259	−	2.43945i
$349$	3.59510	−	0.354086i	0.192441	−	0.0189538i	−0.00133735	−	0.999999i	$-0.500426\pi$
$349$	3.59510	−	0.354086i	0.192441	−	0.0189538i	0.193778	+	0.981045i	$0.437926\pi$
$350$	6.33969	−	0.549653i	0.338871	−	0.0293802i
$351$	44.9176	−	44.9176i	2.39752	−	2.39752i
$352$	1.32283	−	22.6044i	0.0705070	−	1.20482i
$353$	5.23711	+	5.23711i	0.278743	+	0.278743i	0.832607	−	0.553864i	$-0.186847\pi$
$353$	5.23711	+	5.23711i	0.278743	+	0.278743i	−0.553864	+	0.832607i	$0.686847\pi$
$354$	−3.76995	−	3.16840i	−0.200371	−	0.168398i
$355$	0.909958	+	9.23896i	0.0482956	+	0.490353i
$356$	0.255818	−	10.9389i	0.0135583	−	0.579763i
$357$	−47.2812	−	25.2723i	−2.50239	−	1.33755i
$358$	−17.6914	−	12.1226i	−0.935021	−	0.640698i
$359$	−6.79741	+	4.54189i	−0.358754	+	0.239712i	−0.721865	−	0.692034i	$-0.756715\pi$
$359$	−6.79741	+	4.54189i	−0.358754	+	0.239712i	0.363111	+	0.931746i	$0.381715\pi$
$360$	−7.75720	+	17.0141i	−0.408840	+	0.896724i
$361$	−6.12361	+	9.16463i	−0.322295	+	0.482349i
$362$	1.14252	−	2.66957i	0.0600494	−	0.140310i
$363$	12.0353	−	9.87715i	0.631692	−	0.518416i
$364$	−45.5846	+	23.0118i	−2.38928	+	1.20615i
$365$	−3.67158	+	1.96250i	−0.192179	+	0.102722i
$366$	15.1940	+	1.67605i	0.794203	+	0.0876083i
$367$	−4.63586	−	11.1920i	−0.241990	−	0.584216i	0.755490	−	0.655160i	$-0.227399\pi$
$367$	−4.63586	−	11.1920i	−0.241990	−	0.584216i	−0.997480	+	0.0709442i	$0.977399\pi$
$368$	−18.7062	−	4.63947i	−0.975126	−	0.241849i
$369$	−5.17064	+	12.4830i	−0.269173	+	0.649840i
$370$	−0.266432	+	0.484742i	−0.0138511	+	0.0252005i
$371$	−0.0410086	+	0.135187i	−0.00212906	+	0.00701858i
$372$	−40.2461	−	22.7374i	−2.08667	−	1.17888i
$373$	35.4603	+	3.49254i	1.83607	+	0.180837i	0.955873	−	0.293779i	$-0.0949131\pi$
$373$	35.4603	+	3.49254i	1.83607	+	0.180837i	0.880193	+	0.474616i	$0.157413\pi$
$374$	−0.254334	+	21.7539i	−0.0131513	+	1.12487i
$375$	0.604815	+	3.04061i	0.0312325	+	0.157017i
$376$	6.73442	+	3.90923i	0.347301	+	0.201603i
$377$	43.7984	+	8.71205i	2.25573	+	0.448693i
$378$	−38.8836	−	59.6925i	−1.99996	−	3.07025i
$379$	18.3899	−	5.57851i	0.944625	−	0.286549i	0.219849	−	0.975534i	$-0.429443\pi$
$379$	18.3899	−	5.57851i	0.944625	−	0.286549i	0.724776	+	0.688985i	$0.241943\pi$
$380$	5.56471	−	0.972230i	0.285463	−	0.0498744i
$381$	15.8908	−	19.3630i	0.814109	−	0.991994i
$382$	−1.43303	+	4.53263i	−0.0733203	+	0.231909i
$383$	−30.3323			−1.54991			−0.774955	−	0.632017i	$-0.782227\pi$
$383$	−30.3323			−1.54991			−0.774955	+	0.632017i	$0.782227\pi$
$384$	10.7286	+	33.3934i	0.547492	+	1.70410i
$385$	18.0111			0.917929
$386$	0.771298	−	2.43959i	0.0392580	−	0.124172i
$387$	13.6034	−	16.5757i	0.691498	−	0.842592i
$388$	5.07797	+	29.0645i	0.257795	+	1.47553i
$389$	8.09641	−	2.45602i	0.410504	−	0.124525i	−0.0782767	−	0.996932i	$-0.524942\pi$
$389$	8.09641	−	2.45602i	0.410504	−	0.124525i	0.488781	+	0.872407i	$0.337442\pi$
$390$	−13.5784	−	20.8450i	−0.687568	−	1.05553i
$391$	18.1616	+	3.61256i	0.918471	+	0.182695i
$392$	9.61242	+	36.2139i	0.485501	+	1.82908i
$393$	8.48914	+	42.6778i	0.428221	+	2.15281i
$394$	0.290475	−	24.8452i	0.0146339	−	1.25168i
$395$	−9.63671	−	0.949134i	−0.484876	−	0.0477561i
$396$	−26.0334	+	46.0801i	−1.30823	+	2.31561i
$397$	−7.53049	+	24.8247i	−0.377944	+	1.24592i	0.537429	+	0.843309i	$0.319396\pi$
$397$	−7.53049	+	24.8247i	−0.377944	+	1.24592i	−0.915373	+	0.402606i	$0.868104\pi$
$398$	11.9595	−	21.7589i	0.599476	−	1.09068i
$399$	−15.0781	+	36.4018i	−0.754851	+	1.82237i
$400$	3.21836	+	2.37532i	0.160918	+	0.118766i
$401$	−4.50527	−	10.8767i	−0.224983	−	0.543156i	0.770571	−	0.637354i	$-0.219971\pi$
$401$	−4.50527	−	10.8767i	−0.224983	−	0.543156i	−0.995553	+	0.0941984i	$0.969971\pi$
$402$	−31.5931	−	3.48503i	−1.57572	−	0.173817i
$403$	37.3071	−	19.9411i	1.85840	−	0.993335i
$404$	12.7867	+	25.3295i	0.636163	+	1.26019i
$405$	11.4974	−	9.43568i	0.571311	−	0.468863i
$406$	19.7049	−	46.0419i	0.977939	−	2.28502i
$407$	−0.869794	+	1.30174i	−0.0431141	+	0.0645248i
$408$	−11.7966	−	31.5674i	−0.584019	−	1.56282i
$409$	0.413022	−	0.275973i	0.0204226	−	0.0136460i	−0.545317	−	0.838230i	$-0.683591\pi$
$409$	0.413022	−	0.275973i	0.0204226	−	0.0136460i	0.565740	+	0.824584i	$0.308591\pi$
$410$	2.38427	+	1.63376i	0.117751	+	0.0806854i
$411$	8.65457	+	4.62596i	0.426898	+	0.228182i
$412$	−14.1973	−	0.332018i	−0.699451	−	0.0163573i
$413$	−0.495390	−	5.02978i	−0.0243765	−	0.247499i
$414$	34.4862	+	28.9834i	1.69491	+	1.42446i
$415$	−6.60448	−	6.60448i	−0.324201	−	0.324201i
$416$	−31.0616	−	8.09047i	−1.52292	−	0.396668i
$417$	15.9606	−	15.9606i	0.781593	−	0.781593i
$418$	15.9291	−	1.38105i	0.779116	−	0.0675495i
$419$	−38.6970	+	3.81133i	−1.89047	+	0.186195i	−0.975899	−	0.218222i	$-0.929974\pi$
$419$	−38.6970	+	3.81133i	−1.89047	+	0.186195i	−0.914575	+	0.404417i	$0.867474\pi$
$420$	−26.0183	+	10.0711i	−1.26957	+	0.491421i
$421$	−17.5030	+	32.7457i	−0.853042	+	1.59593i	−0.0509724	+	0.998700i	$0.516232\pi$
$421$	−17.5030	+	32.7457i	−0.853042	+	1.59593i	−0.802070	+	0.597230i	$0.796268\pi$
$422$	−3.10197	−	16.6070i	−0.151001	−	0.808417i
$423$	−10.1118	−	15.1334i	−0.491653	−	0.735810i
$424$	−0.0755197	+	0.0467157i	−0.00366756	+	0.00226871i
$425$	−3.19550	−	2.13517i	−0.155005	−	0.103571i
$426$	−15.1355	−	37.7838i	−0.733317	−	1.83063i
$427$	9.95255	+	12.1272i	0.481637	+	0.586877i
$428$	25.7752	−	1.93141i	1.24589	−	0.0933583i
$429$	−33.1922	−	62.0982i	−1.60253	−	2.99813i
$430$	−2.86830	−	3.57957i	−0.138322	−	0.172622i
$431$	−21.2892	+	8.81826i	−1.02546	+	0.424761i	−0.831073	−	0.556163i	$-0.812273\pi$
$431$	−21.2892	+	8.81826i	−1.02546	+	0.424761i	−0.194390	+	0.980924i	$0.562273\pi$
$432$	6.46770	−	44.3110i	0.311178	−	2.13191i
$433$	−16.2221	−	6.71942i	−0.779585	−	0.322915i	−0.0428372	−	0.999082i	$-0.513640\pi$
$433$	−16.2221	−	6.71942i	−0.779585	−	0.322915i	−0.736748	+	0.676167i	$0.763640\pi$
$434$	−13.2397	−	45.5561i	−0.635527	−	2.18676i
$435$	23.3482	+	7.08260i	1.11946	+	0.339585i
$436$	−30.5910	−	3.73696i	−1.46504	−	0.178968i
$437$	1.33392	−	13.5435i	0.0638102	−	0.647876i
$438$	13.0565	−	12.7548i	0.623866	−	0.609447i
$439$	−3.92095	+	0.779925i	−0.187137	+	0.0372238i	−0.287769	−	0.957700i	$-0.592913\pi$
$439$	−3.92095	+	0.779925i	−0.187137	+	0.0372238i	0.100632	+	0.994924i	$0.467913\pi$
$440$	8.49442	+	7.48476i	0.404956	+	0.356822i
$441$	17.0854	−	85.8942i	0.813591	−	4.09020i
$442$	30.1747	+	6.36972i	1.43527	+	0.302977i
$443$	−9.06466	−	29.8822i	−0.430675	−	1.41974i	−0.857066	−	0.515206i	$-0.827715\pi$
$443$	−9.06466	−	29.8822i	−0.430675	−	1.41974i	0.426391	−	0.904539i	$-0.359785\pi$
$444$	0.528599	−	2.36682i	0.0250862	−	0.112324i
$445$	4.22911	+	3.47074i	0.200479	+	0.164529i
$446$	−6.90802	+	3.58922i	−0.327104	+	0.169954i
$447$			40.8814i			1.93362i
$448$	−16.0726	+	32.2098i	−0.759359	+	1.52177i
$449$		−	3.63995i		−	0.171780i	−0.996305	−	0.0858899i	$-0.972627\pi$
$449$		−	3.63995i		−	0.171780i	0.996305	−	0.0858899i	$-0.0273733\pi$
$450$	−4.31064	−	8.29652i	−0.203206	−	0.391101i
$451$	6.32375	+	5.18977i	0.297774	+	0.244377i
$452$	6.65399	−	4.22443i	0.312977	−	0.198701i
$453$	−15.2189	−	50.1699i	−0.715045	−	2.35719i
$454$	3.44296	−	16.3100i	0.161586	−	0.765467i
$455$	4.98101	−	25.0413i	0.233514	−	1.17395i
$456$	−22.2385	+	10.9020i	−1.04141	+	0.510532i
$457$	−13.1315	+	2.61201i	−0.614264	+	0.122185i	−0.492410	−	0.870363i	$-0.663884\pi$
$457$	−13.1315	+	2.61201i	−0.614264	+	0.122185i	−0.121854	+	0.992548i	$0.538884\pi$
$458$	19.8671	+	20.3371i	0.928327	+	0.950291i
$459$	−4.21719	+	42.8179i	−0.196842	+	1.99857i
$460$	7.58997	−	5.93747i	0.353884	−	0.276836i
$461$	−17.0696	−	5.17799i	−0.795008	−	0.241163i	−0.133449	−	0.991056i	$-0.542605\pi$
$461$	−17.0696	−	5.17799i	−0.795008	−	0.241163i	−0.661560	+	0.749893i	$0.730105\pi$
$462$	−75.8288	+	22.0377i	−3.52787	+	1.02529i
$463$	−18.0271	−	7.46709i	−0.837792	−	0.347025i	−0.0778096	−	0.996968i	$-0.524793\pi$
$463$	−18.0271	−	7.46709i	−0.837792	−	0.347025i	−0.759983	+	0.649943i	$0.774793\pi$
$464$	28.4267	−	13.5258i	1.31968	−	0.627917i
$465$	21.3531	−	8.84475i	0.990228	−	0.410166i
$466$	0.0489499	−	0.0392235i	0.00226756	−	0.00181699i
$467$	2.70705	+	5.06453i	0.125267	+	0.234359i	0.936736	−	0.350038i	$-0.113831\pi$
$467$	2.70705	+	5.06453i	0.125267	+	0.234359i	−0.811468	+	0.584397i	$0.801331\pi$
$468$	56.8667	+	48.9384i	2.62867	+	2.26218i
$469$	−20.6945	−	25.2163i	−0.955582	−	1.16438i
$470$	−3.61421	+	1.44779i	−0.166711	+	0.0667815i
$471$	−1.39463	−	0.931865i	−0.0642613	−	0.0429381i
$472$	1.85656	−	2.57802i	0.0854551	−	0.118663i
$473$	−7.21292	−	10.7949i	−0.331651	−	0.496350i
$474$	41.7331	−	7.79518i	1.91686	−	0.358044i
$475$	−1.33146	+	2.49099i	−0.0610916	+	0.114294i
$476$	13.9790	−	31.6352i	0.640725	−	1.45000i
$477$	0.206562	−	0.0203446i	0.00945783	−	0.000931515i
$478$	−1.61870	−	18.6701i	−0.0740376	−	0.853950i
$479$	4.41508	−	4.41508i	0.201730	−	0.201730i	−0.599011	−	0.800741i	$-0.704439\pi$
$479$	4.41508	−	4.41508i	0.201730	−	0.201730i	0.800741	+	0.599011i	$0.204439\pi$
$480$	−16.4560	−	6.06253i	−0.751112	−	0.276716i
$481$	1.56930	+	1.56930i	0.0715538	+	0.0715538i
$482$	−0.217717	+	0.259053i	−0.00991674	+	0.0117995i
$483$	6.58803	+	66.8894i	0.299766	+	3.04357i
$484$	6.93435	+	7.26644i	0.315198	+	0.330293i
$485$	−13.0104	−	6.95423i	−0.590774	−	0.315775i
$486$	−10.0126	+	14.6122i	−0.454180	+	0.662821i
$487$	4.95631	−	3.31170i	0.224592	−	0.150067i	−0.438184	−	0.898885i	$-0.644378\pi$
$487$	4.95631	−	3.31170i	0.224592	−	0.150067i	0.662776	+	0.748818i	$0.269378\pi$
$488$	−0.345796	+	9.85539i	−0.0156534	+	0.446133i
$489$	−32.3728	+	48.4493i	−1.46395	+	2.19095i
$490$	−17.2229	−	7.37103i	−0.778053	−	0.332989i
$491$	−12.8358	+	10.5341i	−0.579272	+	0.475396i	−0.877815	−	0.479000i	$-0.840999\pi$
$491$	−12.8358	+	10.5341i	−0.579272	+	0.475396i	0.298543	+	0.954396i	$0.403499\pi$
$492$	−12.0371	−	3.96100i	−0.542673	−	0.178576i
$493$	−26.6750	+	14.2581i	−1.20138	+	0.642151i
$494$	2.48512	−	22.5285i	0.111811	−	1.01361i
$495$	−10.1269	−	24.4484i	−0.455168	−	1.09887i
$496$	12.6873	−	26.9872i	0.569679	−	1.21176i
$497$	15.9859	−	38.5935i	0.717068	−	1.73115i
$498$	35.8867	+	19.7247i	1.60812	+	0.883883i
$499$	−4.30281	+	14.1844i	−0.192620	+	0.634983i	0.806427	+	0.591334i	$0.201398\pi$
$499$	−4.30281	+	14.1844i	−0.192620	+	0.634983i	−0.999047	+	0.0436493i	$0.986102\pi$
$500$	−1.92693	+	0.535665i	−0.0861750	+	0.0239557i
$501$	79.1030	+	7.79097i	3.53406	+	0.348075i
$502$	−2.22542	−	0.0260182i	−0.0993252	−	0.00116125i
$503$	5.50063	+	27.6535i	0.245261	+	1.23301i	0.885429	+	0.464775i	$0.153865\pi$
$503$	5.50063	+	27.6535i	0.245261	+	1.23301i	−0.640168	+	0.768235i	$0.721135\pi$
$504$	66.8723	−	51.0640i	2.97873	−	2.27457i
$505$	−13.9144	−	2.76775i	−0.619183	−	0.123163i
$506$	22.8538	−	14.8869i	1.01598	−	0.661805i
$507$	−56.9493	+	17.2754i	−2.52921	+	0.767226i
$508$	13.2226	+	9.28944i	0.586658	+	0.412152i
$509$	−17.0181	+	20.7367i	−0.754316	+	0.919136i	−0.998722	−	0.0505365i	$-0.983907\pi$
$509$	−17.0181	+	20.7367i	−0.754316	+	0.919136i	0.244406	+	0.969673i	$0.421407\pi$
$510$	16.0660	+	5.07940i	0.711413	+	0.224920i
$511$	18.7328			0.828689
$512$	−20.9655	+	8.51169i	−0.926552	+	0.376167i
$513$	31.6206			1.39608
$514$	34.2988	+	10.8439i	1.51286	+	0.478304i
$515$	4.50457	−	5.48883i	0.198495	−	0.241867i
$516$	16.4557	+	11.5609i	0.724423	+	0.508938i
$517$	−10.5453	+	3.19888i	−0.463782	+	0.140687i
$518$	2.08549	−	1.35849i	0.0916312	−	0.0596884i
$519$	60.7117	+	12.0763i	2.66495	+	0.530091i
$520$	12.7554	−	9.74009i	0.559362	−	0.427131i
$521$	8.64872	+	43.4801i	0.378907	+	1.90490i	0.423510	+	0.905891i	$0.360798\pi$
$521$	8.64872	+	43.4801i	0.378907	+	1.90490i	−0.0446025	+	0.999005i	$0.514202\pi$
$522$	−73.5770	−	0.860217i	−3.22038	−	0.0376507i
$523$	28.1021	+	2.76782i	1.22882	+	0.121028i	0.691517	−	0.722361i	$-0.256943\pi$
$523$	28.1021	+	2.76782i	1.22882	+	0.121028i	0.537304	+	0.843389i	$0.319443\pi$
$524$	−27.0463	+	7.51855i	−1.18152	+	0.328450i
$525$	4.04940	−	13.3491i	0.176730	−	0.582602i
$526$	17.5665	+	9.65523i	0.765938	+	0.420988i
$527$	−10.9646	+	26.4708i	−0.477624	+	1.15309i
$528$	−44.9207	−	21.1183i	−1.95492	−	0.919055i
$529$	−0.0823965	−	0.198923i	−0.00358246	−	0.00864882i
$530$	0.00486827	−	0.0441327i	0.000211464	−	0.00191700i
$531$	−6.54893	+	3.50048i	−0.284199	+	0.151908i
$532$	−24.1449	−	7.94529i	−1.04681	−	0.344472i
$533$	8.96432	−	7.35683i	0.388288	−	0.318660i
$534$	−22.0518	−	9.43766i	−0.954273	−	0.408407i
$535$	−7.18005	+	10.7457i	−0.310421	+	0.464577i
$536$	0.719018	−	20.4925i	0.0310569	−	0.885140i
$537$	−39.0904	+	26.1194i	−1.68688	+	1.12713i
$538$	12.5231	−	18.2760i	0.539910	−	0.787934i
$539$	−46.7632	−	24.9955i	−2.01423	−	1.07663i
$540$	15.4578	+	16.1981i	0.665199	+	0.697056i
$541$	−4.01209	−	40.7354i	−0.172493	−	1.75135i	−0.559094	−	0.829104i	$-0.688851\pi$
$541$	−4.01209	−	40.7354i	−0.172493	−	1.75135i	0.386601	−	0.922247i	$-0.373649\pi$
$542$	7.84560	−	9.33518i	0.336997	−	0.400980i
$543$	−4.50113	−	4.50113i	−0.193162	−	0.193162i
$544$	19.7393	−	9.11072i	0.846315	−	0.390619i
$545$	10.8959	−	10.8959i	0.466731	−	0.466731i
$546$	9.66892	+	111.521i	0.413792	+	4.77267i
$547$	−27.5564	+	2.71406i	−1.17823	+	0.116045i	−0.668111	−	0.744062i	$-0.732897\pi$
$547$	−27.5564	+	2.71406i	−1.17823	+	0.116045i	−0.510114	+	0.860107i	$0.670397\pi$
$548$	−2.55877	+	5.79066i	−0.109305	+	0.247365i
$549$	10.8657	−	20.3283i	0.463737	−	0.867591i
$550$	−5.56452	+	1.03938i	−0.237272	+	0.0443192i
$551$	12.3499	+	18.4829i	0.526122	+	0.787397i
$552$	−24.6898	+	34.2843i	−1.05087	+	1.45924i
$553$	36.2286	+	24.2072i	1.54060	+	1.02939i
$554$	6.27852	−	2.51507i	0.266749	−	0.106855i
$555$	0.769242	+	0.937325i	0.0326525	+	0.0397872i
$556$	11.0372	+	9.49837i	0.468080	+	0.402821i
$557$	−13.4489	−	25.1611i	−0.569847	−	1.06611i	−0.987517	−	0.157510i	$-0.949653\pi$
$557$	−13.4489	−	25.1611i	−0.569847	−	1.06611i	0.417670	−	0.908599i	$-0.362847\pi$
$558$	−54.3941	+	43.5860i	−2.30269	+	1.84514i
$559$	−17.0032	+	7.04295i	−0.719159	+	0.297885i
$560$	−7.73320	−	16.2526i	−0.326787	−	0.686799i
$561$	44.0610	+	18.2507i	1.86026	+	0.770544i
$562$	−0.799572	+	0.232375i	−0.0337279	+	0.00980215i
$563$	−41.3807	−	12.5527i	−1.74399	−	0.529033i	−0.752428	−	0.658674i	$-0.771118\pi$
$563$	−41.3807	−	12.5527i	−1.74399	−	0.529033i	−0.991561	+	0.129641i	$0.958618\pi$
$564$	13.4448	−	10.5176i	0.566128	−	0.442870i
$565$	−0.386272	+	3.92188i	−0.0162506	+	0.164995i
$566$	−30.2997	−	31.0166i	−1.27359	−	1.30373i
$567$	−65.6399	+	13.0566i	−2.75662	+	0.548325i
$568$	23.5774	−	11.5584i	0.989287	−	0.484978i
$569$	3.84119	−	19.3109i	0.161031	−	0.809557i	−0.812846	−	0.582479i	$-0.802083\pi$
$569$	3.84119	−	19.3109i	0.161031	−	0.809557i	0.973877	−	0.227078i	$-0.0729172\pi$
$570$	2.55772	−	12.1165i	0.107131	−	0.507504i
$571$	−7.20437	−	23.7496i	−0.301493	−	0.993891i	−0.968536	−	0.248872i	$-0.919940\pi$
$571$	−7.20437	−	23.7496i	−0.301493	−	0.993891i	0.667043	−	0.745019i	$-0.267560\pi$
$572$	38.3490	−	24.3467i	1.60345	−	1.01799i
$573$	8.05555	+	6.61102i	0.336526	+	0.276179i
$574$	−5.99620	−	11.5406i	−0.250276	−	0.481696i
$575$			4.81823i			0.200934i
$576$	52.7589	+	3.70686i	2.19829	+	0.154453i
$577$			3.94655i			0.164297i	0.996620	+	0.0821486i	$0.0261782\pi$
$577$			3.94655i			0.164297i	−0.996620	+	0.0821486i	$0.973822\pi$
$578$	2.79831	−	1.45393i	0.116394	−	0.0604754i
$579$	−4.33572	−	3.55823i	−0.180186	−	0.147875i
$580$	−3.43086	+	15.3618i	−0.142459	+	0.637864i
$581$	12.1999	+	40.2178i	0.506138	+	1.66851i
$582$	63.2845	+	13.3590i	2.62323	+	0.553749i
$583$	0.0245170	−	0.123255i	0.00101539	−	0.00510471i
$584$	8.83480	+	7.78468i	0.365587	+	0.322132i
$585$	−36.7919	+	7.31835i	−1.52116	+	0.302577i
$586$	−0.629948	+	0.615389i	−0.0260229	+	0.0254215i
$587$	−2.78384	+	28.2648i	−0.114902	+	1.16661i	0.748865	+	0.662723i	$0.230599\pi$
$587$	−2.78384	+	28.2648i	−0.114902	+	1.16661i	−0.863767	+	0.503892i	$0.831901\pi$
$588$	81.5296	+	9.95955i	3.36222	+	0.410725i
$589$	20.1505	+	6.11258i	0.830286	+	0.251865i
$590$	0.443308	+	1.52536i	0.0182507	+	0.0627982i
$591$	−50.3222	−	20.8441i	−2.06998	−	0.857414i
$592$	1.54810	+	0.225964i	0.0636267	+	0.00928705i
$593$	−42.8659	+	17.7556i	−1.76029	+	0.729136i	−0.763797	+	0.645457i	$0.776667\pi$
$593$	−42.8659	+	17.7556i	−1.76029	+	0.729136i	−0.996493	+	0.0836791i	$0.973333\pi$
$594$	39.6279	+	49.4546i	1.62595	+	2.02915i
$595$	8.15189	+	15.2511i	0.334195	+	0.625235i
$596$	−26.2998	+	1.97072i	−1.07728	+	0.0807239i
$597$	−34.5295	−	42.0743i	−1.41320	−	1.72199i
$598$	−14.3774	−	35.8913i	−0.587936	−	1.46770i
$599$	7.16841	+	4.78978i	0.292893	+	0.195705i	0.693332	−	0.720619i	$-0.256142\pi$
$599$	7.16841	+	4.78978i	0.292893	+	0.195705i	−0.400438	+	0.916324i	$0.631142\pi$
$600$	7.45719	−	4.61294i	0.304439	−	0.188322i
$601$	8.11616	+	12.1467i	0.331065	+	0.495474i	0.959238	−	0.282600i	$-0.0911969\pi$
$601$	8.11616	+	12.1467i	0.331065	+	0.495474i	−0.628173	+	0.778074i	$0.716197\pi$
$602$	3.78971	+	20.2890i	0.154457	+	0.826917i
$603$	−22.5932	+	42.2689i	−0.920067	+	1.72132i
$604$	31.5417	−	12.2091i	1.28341	−	0.496780i
$605$	−4.99793	+	0.492253i	−0.203195	+	0.0200129i
$606$	61.9679	−	5.37262i	2.51727	−	0.218248i
$607$	14.0514	−	14.0514i	0.570330	−	0.570330i	−0.361891	−	0.932221i	$-0.617869\pi$
$607$	14.0514	−	14.0514i	0.570330	−	0.570330i	0.932221	+	0.361891i	$0.117869\pi$
$608$	−8.08549	−	13.7809i	−0.327910	−	0.558891i
$609$	−77.6307	−	77.6307i	−3.14575	−	3.14575i
$610$	−3.77468	−	3.17237i	−0.152832	−	0.128445i
$611$	1.53116	+	15.5461i	0.0619439	+	0.628927i
$612$	−50.8018	−	1.18805i	−2.05354	−	0.0480240i
$613$	15.3908	+	8.22655i	0.621628	+	0.332267i	0.751965	−	0.659203i	$-0.229106\pi$
$613$	15.3908	+	8.22655i	0.621628	+	0.332267i	−0.130337	+	0.991470i	$0.541606\pi$
$614$	−15.6324	−	10.7117i	−0.630871	−	0.432287i
$615$	5.26821	−	3.52010i	0.212435	−	0.141944i
$616$	−17.8327	−	47.7198i	−0.718499	−	1.92269i
$617$	−4.66679	+	6.98434i	−0.187878	+	0.281179i	−0.913436	−	0.406981i	$-0.866581\pi$
$617$	−4.66679	+	6.98434i	−0.187878	+	0.281179i	0.725559	+	0.688160i	$0.241581\pi$
$618$	−12.2488	+	28.6203i	−0.492721	+	1.15128i
$619$	12.7412	−	10.4565i	0.512113	−	0.420280i	−0.342522	−	0.939510i	$-0.611281\pi$
$619$	12.7412	−	10.4565i	0.512113	−	0.420280i	0.854635	+	0.519230i	$0.173781\pi$
$620$	6.71935	+	13.3105i	0.269856	+	0.534564i
$621$	47.5714	−	25.4274i	1.90897	−	1.02037i
$622$	−23.5412	−	2.59682i	−0.943915	−	0.104123i
$623$	−9.42070	−	22.7436i	−0.377432	−	0.911202i
$624$	−41.7842	+	56.6140i	−1.67271	+	2.26638i
$625$	0.382683	−	0.923880i	0.0153073	−	0.0369552i
$626$	2.89176	−	5.26121i	0.115578	−	0.210280i
$627$	10.1745	−	33.5408i	0.406330	−	1.33949i
$628$	0.532258	−	0.942117i	0.0212394	−	0.0375946i
$629$	−1.49594	−	0.147337i	−0.0596470	−	0.00587472i
$630$	−0.491820	+	42.0668i	−0.0195946	+	1.67598i
$631$	4.23051	+	21.2682i	0.168414	+	0.846675i	0.968925	+	0.247356i	$0.0795618\pi$
$631$	4.23051	+	21.2682i	0.168414	+	0.846675i	−0.800510	+	0.599319i	$0.795438\pi$
$632$	7.02657	+	26.4720i	0.279502	+	1.05300i
$633$	−36.3232	−	7.22514i	−1.44372	−	0.287173i
$634$	13.4959	+	20.7184i	0.535992	+	0.822832i
$635$	−7.73186	+	2.34544i	−0.306830	+	0.0930758i
$636$	0.0335032	+	0.191761i	0.00132849	+	0.00760381i
$637$	−47.6844	+	58.1036i	−1.88932	+	2.30215i
$638$	−13.4300	+	42.4785i	−0.531697	+	1.68174i
$639$	−61.3754			−2.42797
$640$	3.10687	−	10.8788i	0.122810	−	0.430021i
$641$	−0.592703			−0.0234104			−0.0117052	−	0.999931i	$-0.503726\pi$
$641$	−0.592703			−0.0234104			−0.0117052	+	0.999931i	$0.503726\pi$
$642$	17.0808	−	54.0260i	0.674126	−	2.13224i
$643$	6.12492	−	7.46323i	0.241543	−	0.294321i	−0.638102	−	0.769952i	$-0.720280\pi$
$643$	6.12492	−	7.46323i	0.241543	−	0.294321i	0.879645	+	0.475631i	$0.157780\pi$
$644$	−42.7137	+	7.46267i	−1.68316	+	0.294070i
$645$	−9.62242	+	2.91893i	−0.378883	+	0.114933i
$646$	8.37899	+	12.8631i	0.329667	+	0.506091i
$647$	−32.1346	−	6.39198i	−1.26334	−	0.251295i	−0.482430	−	0.875935i	$-0.660246\pi$
$647$	−32.1346	−	6.39198i	−1.26334	−	0.251295i	−0.780913	+	0.624640i	$0.785246\pi$
$648$	−36.3831	−	21.1198i	−1.42926	−	0.829666i
$649$	0.877124	+	4.40960i	0.0344301	+	0.173092i
$650$	−0.0938111	+	8.02395i	−0.00367957	+	0.314725i
$651$	−103.497	−	10.1936i	−4.05638	−	0.399519i
$652$	−32.7290	−	18.4905i	−1.28177	−	0.724145i
$653$	11.8126	−	38.9410i	0.462263	−	1.52388i	−0.347819	−	0.937562i	$-0.613078\pi$
$653$	11.8126	−	38.9410i	0.462263	−	1.52388i	0.810082	−	0.586316i	$-0.199422\pi$
$654$	−32.5414	+	59.2052i	−1.27247	+	2.31510i
$655$	5.37132	−	12.9675i	0.209875	−	0.506682i
$656$	1.96794	−	7.93463i	0.0768350	−	0.309795i
$657$	−10.5326	−	25.4281i	−0.410918	−	0.992043i
$658$	17.4134	+	1.92087i	0.678844	+	0.0748831i
$659$	17.9267	−	9.58202i	0.698325	−	0.373263i	−0.0837156	−	0.996490i	$-0.526679\pi$
$659$	17.9267	−	9.58202i	0.698325	−	0.373263i	0.782041	+	0.623227i	$0.214179\pi$
$660$	22.1556	−	11.1845i	0.862405	−	0.435355i
$661$	−13.5154	+	11.0918i	−0.525689	+	0.431422i	−0.859438	−	0.511240i	$-0.829186\pi$
$661$	−13.5154	+	11.0918i	−0.525689	+	0.431422i	0.333749	+	0.942662i	$0.391686\pi$
$662$	−4.22181	+	9.86455i	−0.164085	+	0.383397i
$663$	37.5596	−	56.2119i	1.45869	−	2.18309i
$664$	−10.9593	+	24.0375i	−0.425304	+	0.932835i
$665$	10.5674	−	7.06090i	0.409785	−	0.273810i
$666$	−3.01660	−	2.06705i	−0.116891	−	0.0800964i
$667$	33.4425	+	17.8754i	1.29490	+	0.692138i
$668$	−1.19886	+	51.2641i	−0.0463853	+	1.98347i
$669$	1.67271	+	16.9834i	0.0646709	+	0.656614i
$670$	7.84874	+	6.59635i	0.303223	+	0.254839i
$671$	−9.86827	−	9.86827i	−0.380960	−	0.380960i
$672$	52.4439	+	58.9635i	2.02307	+	2.27457i
$673$	33.3855	−	33.3855i	1.28692	−	1.28692i	0.350264	−	0.936651i	$-0.386092\pi$
$673$	33.3855	−	33.3855i	1.28692	−	1.28692i	0.936651	−	0.350264i	$-0.113908\pi$
$674$	12.6265	−	1.09472i	0.486354	−	0.0421670i
$675$	−11.1412	+	1.09731i	−0.428826	+	0.0422356i
$676$	−13.8589	−	35.8039i	−0.533034	−	1.37707i
$677$	−0.0180389	+	0.0337483i	−0.000693290	+	0.00129705i	−0.882268	−	0.470748i	$-0.843984\pi$
$677$	−0.0180389	+	0.0337483i	−0.000693290	+	0.00129705i	0.881574	+	0.472045i	$0.156484\pi$
$678$	−3.17243	−	16.9842i	−0.121836	−	0.652275i
$679$	36.8791	+	55.1935i	1.41529	+	2.11813i
$680$	−2.49321	+	10.5804i	−0.0956102	+	0.405740i
$681$	−30.3836	−	20.3017i	−1.16430	−	0.777962i
$682$	15.6931	+	39.1758i	0.600921	+	1.50012i
$683$	−26.3736	−	32.1363i	−1.00916	−	1.22966i	−0.973117	−	0.230310i	$-0.926026\pi$
$683$	−26.3736	−	32.1363i	−1.00916	−	1.22966i	−0.0360392	−	0.999350i	$-0.511474\pi$
$684$	2.79063	+	37.2418i	0.106703	+	1.42398i
$685$	−1.49216	−	2.79163i	−0.0570125	−	0.106663i
$686$	24.8575	+	31.0215i	0.949064	+	1.18441i
$687$	57.5802	−	23.8505i	2.19682	−	0.909953i
$688$	−6.64407	+	11.1436i	−0.253303	+	0.424846i
$689$	−0.164585	−	0.0681733i	−0.00627018	−	0.00259719i
$690$	−5.89541	−	20.2853i	−0.224435	−	0.772249i
$691$	45.9481	+	13.9382i	1.74795	+	0.530235i	0.992203	−	0.124630i	$-0.0397745\pi$
$691$	45.9481	+	13.9382i	1.74795	+	0.530235i	0.755746	+	0.654865i	$0.227275\pi$
$692$	−4.84228	+	39.6392i	−0.184076	+	1.50686i
$693$	−11.6712	+	118.500i	−0.443353	+	4.50144i
$694$	23.9877	−	23.4333i	0.910560	−	0.889515i
$695$	−7.14086	+	1.42041i	−0.270868	+	0.0538791i
$696$	−4.35181	−	68.8729i	−0.164955	−	2.61062i
$697$	−1.53235	+	7.70364i	−0.0580418	+	0.291796i
$698$	4.99868	+	1.05519i	0.189203	+	0.0399397i
$699$	−0.0399158	−	0.131585i	−0.00150975	−	0.00497699i
$700$	8.78294	+	1.96156i	0.331964	+	0.0741399i
$701$	33.8198	+	27.7552i	1.27735	+	1.04830i	0.996060	+	0.0886764i	$0.0282637\pi$
$701$	33.8198	+	27.7552i	1.27735	+	1.04830i	0.281294	+	0.959622i	$0.409236\pi$
$702$	79.7172	−	41.4189i	3.00873	−	1.56326i
$703$			1.10474i			0.0416660i
$704$	11.4204	−	29.9164i	0.430422	−	1.12752i
$705$			8.53496i			0.321445i
$706$	4.82919	+	9.29454i	0.181749	+	0.349805i
$707$	49.3464	+	40.4975i	1.85586	+	1.52307i
$708$	−3.73276	−	5.87955i	−0.140286	−	0.220967i
$709$	6.24487	+	20.5866i	0.234531	+	0.773146i	0.992649	+	0.121028i	$0.0386191\pi$
$709$	6.24487	+	20.5866i	0.234531	+	0.773146i	−0.758118	+	0.652117i	$0.773881\pi$
$710$	−2.71172	+	12.8460i	−0.101769	+	0.482101i
$711$	12.4892	−	62.7877i	0.468383	−	2.35472i
$712$	5.00841	−	14.6413i	0.187698	−	0.548706i
$713$	35.2306	−	7.00781i	1.31940	−	0.262444i
$714$	−52.9812	−	54.2347i	−1.98277	−	2.02968i
$715$	−2.22620	+	22.6030i	−0.0832552	+	0.845305i
$716$	−18.6875	−	23.8886i	−0.698385	−	0.892757i
$717$	−39.3124	−	11.9253i	−1.46815	−	0.445358i
$718$	−11.1021	+	3.22654i	−0.414326	+	0.120413i
$719$	−15.0084	−	6.21667i	−0.559718	−	0.231843i	0.0848447	−	0.996394i	$-0.472961\pi$
$719$	−15.0084	−	6.21667i	−0.559718	−	0.231843i	−0.644563	+	0.764551i	$0.722961\pi$
$720$	−17.7134	+	19.6353i	−0.660141	+	0.731764i
$721$	−29.5182	+	12.2268i	−1.09931	+	0.455351i
$722$	−12.1643	+	9.74722i	−0.452708	+	0.362754i
$723$	0.349687	+	0.654218i	0.0130050	+	0.0243306i
$724$	2.67869	−	3.11265i	0.0995526	−	0.115681i
$725$	−4.99276	−	6.08369i	−0.185426	−	0.225943i
$726$	20.4396	−	8.18773i	0.758584	−	0.303875i
$727$	−13.6437	−	9.11645i	−0.506018	−	0.338111i	0.276215	−	0.961096i	$-0.410920\pi$
$727$	−13.6437	−	9.11645i	−0.506018	−	0.338111i	−0.782234	+	0.622985i	$0.785920\pi$
$728$	−71.2778	+	11.5962i	−2.64173	+	0.429783i
$729$	−3.21670	−	4.81414i	−0.119137	−	0.178301i
$730$	−5.78750	+	1.08103i	−0.214205	+	0.0400106i
$731$	5.87613	−	10.9935i	0.217337	−	0.406608i
$732$	19.7734	+	8.73749i	0.730848	+	0.322947i
$733$	−35.8059	+	3.52657i	−1.32252	+	0.130257i	−0.734510	−	0.678597i	$-0.762588\pi$
$733$	−35.8059	+	3.52657i	−1.32252	+	0.130257i	−0.588009	+	0.808854i	$0.700088\pi$
$734$	−1.47979	−	17.0679i	−0.0546200	−	0.629987i
$735$	−29.0393	+	29.0393i	−1.07113	+	1.07113i
$736$	−23.2460	−	14.2308i	−0.856858	−	0.524552i
$737$	20.5192	+	20.5192i	0.755836	+	0.755836i
$738$	−12.2940	+	14.6281i	−0.452547	+	0.538468i
$739$	3.35403	+	34.0540i	0.123380	+	1.25270i	0.835046	+	0.550180i	$0.185441\pi$
$739$	3.35403	+	34.0540i	0.123380	+	1.25270i	−0.711666	+	0.702518i	$0.752059\pi$
$740$	−0.565918	+	0.540054i	−0.0208036	+	0.0198528i
$741$	−43.8188	−	23.4217i	−1.60973	−	0.860416i
$742$	−0.112930	+	0.164807i	−0.00414579	+	0.00605027i
$743$	−12.6826	+	8.47422i	−0.465278	+	0.310889i	−0.766020	−	0.642817i	$-0.777766\pi$
$743$	−12.6826	+	8.47422i	−0.465278	+	0.310889i	0.300742	+	0.953706i	$0.402766\pi$
$744$	−44.5756	−	47.8174i	−1.63422	−	1.75307i
$745$	7.32619	−	10.9644i	0.268411	−	0.401705i
$746$	46.3267	+	19.8268i	1.69614	+	0.725910i
$747$	47.7325	−	39.1730i	1.74644	−	1.43327i
$748$	−9.61703	+	29.2251i	−0.351633	+	1.06858i
$749$	51.2859	−	27.4129i	1.87395	−	1.00164i
$750$	−0.480717	+	4.35788i	−0.0175533	+	0.159127i
$751$	16.6084	+	40.0962i	0.606048	+	1.46313i	0.867263	+	0.497849i	$0.165877\pi$
$751$	16.6084	+	40.0962i	0.606048	+	1.46313i	−0.261215	+	0.965281i	$0.584123\pi$
$752$	7.41429	+	8.14230i	0.270371	+	0.296919i
$753$	−1.86704	+	4.50742i	−0.0680386	+	0.164260i
$754$	55.3448	+	30.4196i	2.01554	+	1.10782i
$755$	−4.90903	+	16.1829i	−0.178658	+	0.588956i
$756$	−26.9837	−	97.0676i	−0.981388	−	3.53032i
$757$	9.12453	+	0.898688i	0.331637	+	0.0326634i	0.262465	−	0.964941i	$-0.415464\pi$
$757$	9.12453	+	0.898688i	0.331637	+	0.0326634i	0.0691714	+	0.997605i	$0.477964\pi$
$758$	27.1756	+	0.317721i	0.987063	+	0.0115401i
$759$	−11.6646	−	58.6419i	−0.423398	−	2.12857i
$760$	7.91807	+	1.06135i	0.287219	+	0.0384992i
$761$	−50.7840	−	10.1016i	−1.84092	−	0.366182i	−0.853095	−	0.521755i	$-0.825278\pi$
$761$	−50.7840	−	10.1016i	−1.84092	−	0.366182i	−0.987824	+	0.155573i	$0.950278\pi$
$762$	29.6823	−	19.3350i	1.07528	−	0.700433i
$763$	−66.3505	+	20.1272i	−2.40205	+	0.728654i
$764$	−3.86468	+	5.50099i	−0.139819	+	0.199019i
$765$	16.1186	−	19.6405i	0.582768	−	0.710104i
$766$	−40.9009	−	12.9312i	−1.47781	−	0.467223i
$767$	6.37336			0.230129
$768$	0.230550	+	49.6024i	0.00831925	+	1.78987i
$769$	−0.290658			−0.0104814			−0.00524070	−	0.999986i	$-0.501668\pi$
$769$	−0.290658			−0.0104814			−0.00524070	+	0.999986i	$0.501668\pi$
$770$	24.2866	+	7.67843i	0.875228	+	0.276711i
$771$	50.0262	−	60.9572i	1.80165	−	2.19532i
$772$	2.08008	−	2.96078i	0.0748636	−	0.106561i
$773$	20.8498	−	6.32471i	0.749914	−	0.227484i	0.107884	−	0.994163i	$-0.465593\pi$
$773$	20.8498	−	6.32471i	0.749914	−	0.227484i	0.642030	+	0.766680i	$0.278093\pi$
$774$	25.4097	−	16.5518i	0.913331	−	0.594943i
$775$	−7.31195	−	1.45444i	−0.262653	−	0.0522449i
$776$	−5.54345	+	41.3562i	−0.198998	+	1.48460i
$777$	−1.06444	−	5.35128i	−0.0381864	−	0.191976i
$778$	11.9644	+	0.139881i	0.428946	+	0.00501498i
$779$	5.74479	+	0.565813i	0.205829	+	0.0202723i
$780$	−9.42286	−	33.8966i	−0.337393	−	1.21369i
$781$	−10.7871	+	35.5602i	−0.385992	+	1.27244i
$782$	22.9495	+	12.6139i	0.820671	+	0.451071i
$783$	−33.7171	+	81.4003i	−1.20495	+	2.90901i
$784$	−2.47698	+	52.9297i	−0.0884636	+	1.89035i
$785$	0.207046	+	0.499853i	0.00738978	+	0.0178405i
$786$	−6.74731	+	61.1669i	−0.240669	+	2.18175i
$787$	38.2227	−	20.4305i	1.36249	−	0.728268i	0.381879	−	0.924212i	$-0.375277\pi$
$787$	38.2227	−	20.4305i	1.36249	−	0.728268i	0.980615	+	0.195944i	$0.0627772\pi$
$788$	10.9836	−	33.3781i	0.391276	−	1.18905i
$789$	33.9677	−	27.8766i	1.20928	−	0.992432i
$790$	−12.5898	−	5.38814i	−0.447924	−	0.191701i
$791$	9.85165	−	14.7440i	0.350284	−	0.524238i
$792$	−54.7488	+	51.0371i	−1.94541	+	1.81352i
$793$	−16.4492	+	10.9910i	−0.584129	+	0.390302i
$794$	−20.7375	+	30.2639i	−0.735946	+	1.07402i
$795$	−0.0858398	−	0.0458823i	−0.00304442	−	0.00162728i
$796$	25.4027	−	24.2418i	0.900376	−	0.859226i
$797$	1.74079	+	17.6746i	0.0616620	+	0.626065i	0.975502	+	0.219990i	$0.0706026\pi$
$797$	1.74079	+	17.6746i	0.0616620	+	0.626065i	−0.913840	+	0.406074i	$0.866897\pi$
$798$	−35.8505	+	42.6571i	−1.26909	+	1.51005i
$799$	−7.48156	−	7.48156i	−0.264679	−	0.264679i
$800$	3.32708	+	4.57499i	0.117630	+	0.161750i
$801$	−25.5755	+	25.5755i	−0.903666	+	0.903666i
$802$	−1.43810	−	16.5871i	−0.0507812	−	0.585710i
$803$	−16.5839	+	1.63337i	−0.585233	+	0.0576404i
$804$	−41.1152	−	18.1680i	−1.45002	−	0.640736i
$805$	10.2201	−	19.1204i	0.360210	−	0.673905i
$806$	58.8071	−	10.9844i	2.07139	−	0.386908i
$807$	−26.9824	−	40.3821i	−0.949827	−	1.42152i
$808$	6.44353	+	39.6062i	0.226683	+	1.39334i
$809$	−22.6200	−	15.1142i	−0.795276	−	0.531386i	0.0902818	−	0.995916i	$-0.471223\pi$
$809$	−22.6200	−	15.1142i	−0.795276	−	0.531386i	−0.885557	+	0.464530i	$0.846223\pi$
$810$	19.5260	−	7.82177i	0.686074	−	0.274829i
$811$	−0.572582	−	0.697694i	−0.0201061	−	0.0244993i	0.762860	−	0.646563i	$-0.223794\pi$
$811$	−0.572582	−	0.697694i	−0.0201061	−	0.0244993i	−0.782966	+	0.622064i	$0.786294\pi$
$812$	46.1991	−	53.6836i	1.62127	−	1.88393i
$813$	−12.6012	−	23.5752i	−0.441944	−	0.826819i
$814$	−1.72781	+	1.38449i	−0.0605596	+	0.0485264i
$815$	17.3648	−	7.19273i	0.608262	−	0.251950i
$816$	−2.44910	−	47.5954i	−0.0857358	−	1.66617i
$817$	−8.46388	−	3.50585i	−0.296114	−	0.122654i
$818$	0.674582	−	0.196050i	0.0235862	−	0.00685473i
$819$	161.526	+	48.9983i	5.64417	+	1.71214i
$820$	2.51851	+	3.21945i	0.0879502	+	0.112428i
$821$	−0.463439	+	4.70538i	−0.0161741	+	0.164219i	−0.999879	−	0.0155736i	$-0.995043\pi$
$821$	−0.463439	+	4.70538i	−0.0161741	+	0.164219i	0.983705	+	0.179792i	$0.0575426\pi$
$822$	9.69792	+	9.92736i	0.338254	+	0.346257i
$823$	−16.2224	+	3.22684i	−0.565478	+	0.112481i	−0.469547	−	0.882907i	$-0.655583\pi$
$823$	−16.2224	+	3.22684i	−0.565478	+	0.112481i	−0.0959308	+	0.995388i	$0.530583\pi$
$824$	−19.0025	−	6.50026i	−0.661983	−	0.226447i
$825$	−2.42093	+	12.1708i	−0.0842860	+	0.423734i
$826$	1.47629	−	6.99347i	0.0513665	−	0.243334i
$827$	−1.28742	−	4.24405i	−0.0447679	−	0.147580i	0.931707	−	0.363210i	$-0.118319\pi$
$827$	−1.28742	−	4.24405i	−0.0447679	−	0.147580i	−0.976475	+	0.215630i	$0.930819\pi$
$828$	34.1460	+	53.7841i	1.18666	+	1.86913i
$829$	17.1605	+	14.0833i	0.596009	+	0.489132i	0.883361	−	0.468693i	$-0.155275\pi$
$829$	17.1605	+	14.0833i	0.596009	+	0.489132i	−0.287352	+	0.957825i	$0.592775\pi$
$830$	−6.09005	−	11.7213i	−0.211389	−	0.406851i
$831$		−	14.8267i		−	0.514334i
$832$	−38.4352	−	24.1515i	−1.33250	−	0.837303i
$833$		−	50.9105i		−	1.76394i
$834$	28.3259	−	14.7174i	0.980847	−	0.509622i
$835$	−19.8193	−	16.2653i	−0.685874	−	0.562882i
$836$	22.0679	+	4.92859i	0.763235	+	0.170459i
$837$	24.2277	+	79.8680i	0.837432	+	2.76064i
$838$	−53.8049	−	11.3579i	−1.85866	−	0.392353i
$839$	−1.69075	+	8.49999i	−0.0583713	+	0.293452i	−0.998934	−	0.0461688i	$-0.985299\pi$
$839$	−1.69075	+	8.49999i	−0.0583713	+	0.293452i	0.940562	+	0.339621i	$0.110299\pi$
$840$	−39.3773	+	2.48810i	−1.35865	+	0.0858476i
$841$	−32.3060	+	6.42606i	−1.11400	+	0.221588i
$842$	−37.5615	+	36.6934i	−1.29446	+	1.26454i
$843$	−0.178912	+	1.81652i	−0.00616205	+	0.0625643i
$844$	2.89709	−	23.7158i	0.0997218	−	0.816330i
$845$	18.3697	+	5.57238i	0.631936	+	0.191696i
$846$	−7.18339	−	24.7171i	−0.246970	−	0.849791i
$847$	20.8776	+	8.64779i	0.717364	+	0.297142i
$848$	−0.121748	+	0.0307973i	−0.00418086	+	0.00105758i
$849$	−87.8169	+	36.3750i	−3.01387	+	1.24839i
$850$	−3.39864	−	4.24141i	−0.116572	−	0.145479i
$851$	0.888365	+	1.66201i	0.0304528	+	0.0569731i
$852$	−4.30123	−	57.4011i	−0.147358	−	1.96653i
$853$	−3.25287	−	3.96363i	−0.111376	−	0.135712i	0.714338	−	0.699800i	$-0.246728\pi$
$853$	−3.25287	−	3.96363i	−0.111376	−	0.135712i	−0.825714	+	0.564088i	$0.809228\pi$
$854$	8.25023	+	20.5956i	0.282317	+	0.704767i
$855$	−15.5261	−	10.3742i	−0.530982	−	0.354791i
$856$	35.5794	+	8.38407i	1.21608	+	0.286562i
$857$	10.3669	+	15.5151i	0.354125	+	0.529986i	0.965175	−	0.261607i	$-0.0842523\pi$
$857$	10.3669	+	15.5151i	0.354125	+	0.529986i	−0.611049	+	0.791593i	$0.709252\pi$
$858$	−18.2837	−	97.8853i	−0.624194	−	3.34175i
$859$	16.5949	−	31.0468i	0.566210	−	1.05930i	−0.422058	−	0.906569i	$-0.638692\pi$
$859$	16.5949	−	31.0468i	0.566210	−	1.05930i	0.988267	−	0.152735i	$-0.0488080\pi$
$860$	−2.34166	−	6.04959i	−0.0798500	−	0.206289i
$861$	−28.3726	+	2.79446i	−0.966936	+	0.0952349i
$862$	−32.4663	+	2.81483i	−1.10581	+	0.0958735i
$863$	−8.19853	+	8.19853i	−0.279081	+	0.279081i	−0.832742	−	0.553661i	$-0.813230\pi$
$863$	−8.19853	+	8.19853i	−0.279081	+	0.279081i	0.553661	+	0.832742i	$0.313230\pi$
$864$	27.6118	−	56.9928i	0.939371	−	1.93893i
$865$	−14.1188	−	14.1188i	−0.480052	−	0.480052i
$866$	−19.0097	−	15.9764i	−0.645977	−	0.542901i
$867$	−0.677586	−	6.87964i	−0.0230120	−	0.233645i
$868$	1.56857	−	67.0733i	0.0532409	−	2.27662i
$869$	−34.1834	−	18.2714i	−1.15959	−	0.619815i
$870$	28.4639	+	19.5041i	0.965017	+	0.661252i
$871$	34.2031	−	22.8538i	1.15893	−	0.774371i
$872$	−39.6566	−	18.0805i	−1.34294	−	0.612282i
$873$	54.1846	−	81.0931i	1.83387	−	2.74458i
$874$	7.57255	−	17.6938i	0.256145	−	0.598502i
$875$	−3.47828	+	2.85455i	−0.117587	+	0.0965015i
$876$	23.0434	−	11.6326i	0.778563	−	0.393030i
$877$	−6.22706	+	3.32843i	−0.210273	+	0.112393i	−0.573172	−	0.819435i	$-0.694287\pi$
$877$	−6.22706	+	3.32843i	−0.210273	+	0.112393i	0.362899	+	0.931829i	$0.381787\pi$
$878$	−5.61961	−	0.619898i	−0.189653	−	0.0209205i
$879$	0.738777	+	1.78357i	0.0249183	+	0.0601582i
$880$	8.26322	+	13.7140i	0.278553	+	0.462298i
$881$	6.78337	−	16.3765i	0.228538	−	0.551738i	−0.767462	−	0.641094i	$-0.778481\pi$
$881$	6.78337	−	16.3765i	0.228538	−	0.551738i	0.996000	+	0.0893557i	$0.0284808\pi$
$882$	59.6566	−	108.538i	2.00874	−	3.65467i
$883$	−3.26601	+	10.7666i	−0.109910	+	0.362324i	−0.994591	−	0.103873i	$-0.966876\pi$
$883$	−3.26601	+	10.7666i	−0.109910	+	0.362324i	0.884681	+	0.466197i	$0.154376\pi$
$884$	37.9729	+	21.4531i	1.27717	+	0.721546i
$885$	3.46542	+	0.341314i	0.116489	+	0.0114732i
$886$	0.516272	−	44.1583i	0.0173445	−	1.48353i
$887$	0.0191314	+	0.0961802i	0.000642371	+	0.00322942i	0.981105	−	0.193475i	$-0.0619760\pi$
$887$	0.0191314	+	0.0961802i	0.000642371	+	0.00322942i	−0.980463	+	0.196705i	$0.936976\pi$
$888$	1.72179	−	2.96613i	0.0577796	−	0.0995368i
$889$	35.6576	+	7.09275i	1.19592	+	0.237883i
$890$	4.22301	+	6.48299i	0.141556	+	0.217310i
$891$	56.9717	−	17.2822i	1.90862	−	0.578975i
$892$	−10.8451	+	1.89479i	−0.363121	+	0.0634422i
$893$	−4.93304	+	6.01093i	−0.165078	+	0.201148i
$894$	−17.4285	+	55.1256i	−0.582895	+	1.84368i
$895$	15.1648			0.506904
$896$	−35.4043	+	36.5806i	−1.18278	+	1.22207i
$897$	−84.7573			−2.82996
$898$	1.55177	−	4.90820i	0.0517834	−	0.163789i
$899$	−37.2220	+	45.3551i	−1.24142	+	1.51268i
$900$	−2.27564	−	13.0249i	−0.0758545	−	0.434165i
$901$	0.115465	−	0.0350258i	0.00384669	−	0.00116688i
$902$	6.31462	+	9.69394i	0.210254	+	0.322773i
$903$	44.3765	+	8.82703i	1.47676	+	0.293745i
$904$	10.7734	−	2.85962i	0.358317	−	0.0951097i
$905$	0.400576	+	2.01383i	0.0133156	+	0.0669421i
$906$	0.866781	−	74.1384i	0.0287969	−	2.46308i
$907$	−24.5657	−	2.41951i	−0.815692	−	0.0803387i	−0.318438	−	0.947944i	$-0.603158\pi$
$907$	−24.5657	−	2.41951i	−0.815692	−	0.0803387i	−0.497254	+	0.867605i	$0.665658\pi$
$908$	11.5958	−	20.5251i	0.384821	−	0.681148i
$909$	27.2264	−	89.7533i	0.903042	−	2.97693i
$910$	17.3921	−	31.6428i	0.576541	−	1.04895i
$911$	−1.89352	+	4.57136i	−0.0627351	+	0.151456i	−0.952138	−	0.305668i	$-0.901120\pi$
$911$	−1.89352	+	4.57136i	−0.0627351	+	0.151456i	0.889403	+	0.457124i	$0.151120\pi$
$912$	−34.6347	+	5.21986i	−1.14687	+	0.172847i
$913$	−14.3072	−	34.5405i	−0.473498	−	1.14312i
$914$	−18.8204	−	2.07607i	−0.622522	−	0.0686703i
$915$	−9.53264	+	5.09530i	−0.315139	+	0.168445i
$916$	18.1192	+	35.8928i	0.598675	+	1.18593i
$917$	−48.8209	+	40.0663i	−1.61221	+	1.32311i
$918$	−23.9406	+	55.9389i	−0.790157	+	1.84626i
$919$	−11.8762	+	17.7740i	−0.391760	+	0.586310i	−0.973956	−	0.226738i	$-0.927194\pi$
$919$	−11.8762	+	17.7740i	−0.391760	+	0.586310i	0.582196	+	0.813049i	$0.302194\pi$
$920$	12.7658	−	4.77051i	0.420875	−	0.157279i
$921$	−34.5408	+	23.0794i	−1.13816	+	0.760492i
$922$	−20.8096	−	14.2592i	−0.685327	−	0.469601i
$923$	46.4571	+	24.8318i	1.52915	+	0.817349i
$924$	−111.645	−	2.61092i	−3.67284	−	0.0858928i
$925$	−0.0383371	−	0.389243i	−0.00126052	−	0.0127982i
$926$	−21.1249	−	17.7541i	−0.694208	−	0.583436i
$927$	33.1936	+	33.1936i	1.09022	+	1.09022i
$928$	44.0976	−	6.11968i	1.44757	−	0.200888i
$929$	−16.1066	+	16.1066i	−0.528441	+	0.528441i	−0.920107	−	0.391667i	$-0.871899\pi$
$929$	−16.1066	+	16.1066i	−0.528441	+	0.528441i	0.391667	+	0.920107i	$0.371899\pi$
$930$	32.5638	−	2.82329i	1.06781	−	0.0925792i
$931$	−37.2357	+	3.66740i	−1.22035	+	0.120194i
$932$	0.0827270	−	0.0320218i	0.00270981	−	0.00104891i
$933$	−24.4745	+	45.7885i	−0.801258	+	1.49905i
$934$	1.49116	+	7.98321i	0.0487921	+	0.261219i
$935$	−8.54656	−	12.7908i	−0.279502	−	0.418305i
$936$	55.8173	+	90.2332i	1.82444	+	2.94936i
$937$	−25.0954	−	16.7682i	−0.819832	−	0.547794i	0.0734458	−	0.997299i	$-0.476600\pi$
$937$	−25.0954	−	16.7682i	−0.819832	−	0.547794i	−0.893278	+	0.449505i	$0.851600\pi$
$938$	−17.1548	−	42.8247i	−0.560125	−	1.39828i
$939$	−8.34908	−	10.1734i	−0.272462	−	0.331996i
$940$	−5.49071	+	0.411435i	−0.179087	+	0.0134195i
$941$	20.0304	+	37.4743i	0.652973	+	1.22163i	0.962641	+	0.270782i	$0.0872824\pi$
$941$	20.0304	+	37.4743i	0.652973	+	1.22163i	−0.309667	+	0.950845i	$0.600218\pi$
$942$	−1.48329	−	1.85111i	−0.0483282	−	0.0603123i
$943$	9.09771	−	3.76839i	0.296262	−	0.122716i
$944$	3.60249	−	2.68479i	0.117251	−	0.0873824i
$945$	46.5397	+	19.2774i	1.51394	+	0.627093i
$946$	−5.12404	−	17.6311i	−0.166597	−	0.573237i
$947$	−1.71117	−	0.519076i	−0.0556054	−	0.0168677i	0.262359	−	0.964970i	$-0.415499\pi$
$947$	−1.71117	−	0.519076i	−0.0556054	−	0.0168677i	−0.317965	+	0.948103i	$0.602999\pi$
$948$	59.5972	+	7.28032i	1.93563	+	0.236454i
$949$	−2.31541	+	23.5087i	−0.0751613	+	0.763126i
$950$	−2.85733	+	2.79129i	−0.0927039	+	0.0905613i
$951$	53.1625	−	10.5747i	1.72391	−	0.342908i
$952$	32.3363	−	36.6983i	1.04802	−	1.18940i
$953$	−10.0527	+	50.5381i	−0.325638	+	1.63709i	0.377480	+	0.926018i	$0.376791\pi$
$953$	−10.0527	+	50.5381i	−0.325638	+	1.63709i	−0.703118	+	0.711074i	$0.748209\pi$
$954$	0.287207	+	0.0606279i	0.00929867	+	0.00196290i
$955$	−0.975769	−	3.21668i	−0.0315751	−	0.104089i
$956$	5.77669	−	25.8653i	0.186831	−	0.836544i
$957$	75.4943	+	61.9566i	2.44038	+	2.00277i
$958$	7.83563	−	4.07118i	0.253158	−	0.131534i
$959$			14.2432i			0.459937i
$960$	−19.6052	−	15.1904i	−0.632755	−	0.490267i
$961$			24.5800i			0.792902i
$962$	1.44706	+	2.78510i	0.0466552	+	0.0897953i
$963$	−66.0464	−	54.2029i	−2.12831	−	1.74666i
$964$	−0.404014	+	0.256497i	−0.0130124	+	0.00826123i
$965$	0.525186	+	1.73131i	0.0169063	+	0.0557327i
$966$	−19.6327	+	93.0040i	−0.631670	+	2.99236i
$967$	11.6516	−	58.5765i	0.374690	−	1.88369i	−0.0862696	−	0.996272i	$-0.527495\pi$
$967$	11.6516	−	58.5765i	0.374690	−	1.88369i	0.460959	−	0.887421i	$-0.347505\pi$
$968$	6.25264	+	12.7545i	0.200967	+	0.409945i
$969$	33.0061	−	6.56533i	1.06031	−	0.210909i
$970$	−14.5789	−	14.9238i	−0.468101	−	0.479176i
$971$	3.41845	−	34.7081i	0.109703	−	1.11384i	−0.769912	−	0.638150i	$-0.779700\pi$
$971$	3.41845	−	34.7081i	0.109703	−	1.11384i	0.879615	−	0.475685i	$-0.157800\pi$
$972$	−19.7306	+	15.4349i	−0.632861	+	0.495074i
$973$	31.3502	+	9.50999i	1.00504	+	0.304876i
$974$	8.09505	−	2.35262i	0.259382	−	0.0753829i
$975$	16.2519	+	6.73177i	0.520478	+	0.215589i
$976$	−4.66781	+	13.1419i	−0.149413	+	0.420660i
$977$	40.3492	−	16.7132i	1.29089	−	0.534702i	0.371636	−	0.928378i	$-0.378797\pi$
$977$	40.3492	−	16.7132i	1.29089	−	0.534702i	0.919249	+	0.393676i	$0.128797\pi$
$978$	−64.3071	+	51.5292i	−2.05631	+	1.64772i
$979$	10.3231	+	19.3132i	0.329928	+	0.617252i
$980$	−20.0815	−	17.2817i	−0.641479	−	0.552045i
$981$	64.6269	+	78.7481i	2.06338	+	2.51423i
$982$	−21.7990	+	8.73229i	−0.695634	+	0.278659i
$983$	35.5812	+	23.7746i	1.13486	+	0.758292i	0.973519	−	0.228606i	$-0.0734167\pi$
$983$	35.5812	+	23.7746i	1.13486	+	0.758292i	0.161345	+	0.986898i	$0.448417\pi$
$984$	−14.5424	−	10.4727i	−0.463596	−	0.333858i
$985$	9.76105	+	14.6084i	0.311013	+	0.465464i
$986$	−42.0477	+	7.85395i	−1.33907	+	0.250121i
$987$	18.1037	−	33.8697i	0.576247	−	1.07808i
$988$	12.9553	−	29.3186i	0.412163	−	0.932749i
$989$	−15.5526	+	1.53180i	−0.494544	+	0.0487084i
$990$	−3.23254	−	37.2841i	−0.102737	−	1.18497i
$991$	−23.2451	+	23.2451i	−0.738404	+	0.738404i	−0.972269	−	0.233865i	$-0.924863\pi$
$991$	−23.2451	+	23.2451i	−0.738404	+	0.738404i	0.233865	+	0.972269i	$0.424863\pi$
$992$	28.6131	−	30.9815i	0.908466	−	0.983662i
$993$	16.6325	+	16.6325i	0.527816	+	0.527816i
$994$	38.0090	−	45.2254i	1.20557	−	1.43446i
$995$	1.72086	+	17.4722i	0.0545551	+	0.553907i
$996$	39.9816	+	41.8964i	1.26686	+	1.32754i
$997$	27.8603	+	14.8917i	0.882345	+	0.471623i	0.849349	−	0.527832i	$-0.176995\pi$
$997$	27.8603	+	14.8917i	0.882345	+	0.471623i	0.0329966	+	0.999455i	$0.489495\pi$
$998$	−11.8491	+	17.2923i	−0.375077	+	0.547379i
$999$	−3.64077	+	2.43268i	−0.115189	+	0.0769667i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	640.2.bm.a.341.59	✓	1024
128.125	even	32	inner	640.2.bm.a.381.59	yes	1024

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
640.2.bm.a.341.59	✓	1024	1.1	even	1	trivial
640.2.bm.a.381.59	yes	1024	128.125	even	32	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(1.34843 + 0.426318i) q^{2} +(1.96673 - 2.39647i) q^{3} +(1.63651 + 1.14972i) q^{4} +(-0.956940 + 0.290285i) q^{5} +(3.67365 - 2.39301i) q^{6} +(4.41320 + 0.877840i) q^{7} +(1.71656 + 2.24798i) q^{8} +(-1.28977 - 6.48409i) q^{9} +O(q^{10})\)	\(q+(1.34843 + 0.426318i) q^{2} +(1.96673 - 2.39647i) q^{3} +(1.63651 + 1.14972i) q^{4} +(-0.956940 + 0.290285i) q^{5} +(3.67365 - 2.39301i) q^{6} +(4.41320 + 0.877840i) q^{7} +(1.71656 + 2.24798i) q^{8} +(-1.28977 - 6.48409i) q^{9} +(-1.41412 - 0.0165330i) q^{10} +(-3.98349 - 0.392339i) q^{11} +(5.97383 - 1.66066i) q^{12} +(-1.64713 + 5.42985i) q^{13} +(5.57663 + 3.06513i) q^{14} +(-1.18639 + 2.86419i) q^{15} +(1.35631 + 3.76303i) q^{16} +(-1.47073 - 3.55065i) q^{17} +(1.02513 - 9.29317i) q^{18} +(-2.49099 + 1.33146i) q^{19} +(-1.89978 - 0.625156i) q^{20} +(10.7833 - 8.84963i) q^{21} +(-5.20418 - 2.22727i) q^{22} +(-2.67686 + 4.00621i) q^{23} +(8.76324 + 0.307475i) q^{24} +(0.831470 - 0.555570i) q^{25} +(-4.53587 + 6.61955i) q^{26} +(-9.87322 - 5.27735i) q^{27} +(6.21296 + 6.51051i) q^{28} +(-0.771407 - 7.83223i) q^{29} +(-2.82081 + 3.35638i) q^{30} +(-5.27162 - 5.27162i) q^{31} +(0.224634 + 5.65239i) q^{32} +(-8.77469 + 8.77469i) q^{33} +(-0.469463 - 5.41479i) q^{34} +(-4.47799 + 0.441044i) q^{35} +(5.34415 - 12.0941i) q^{36} +(0.184376 - 0.344943i) q^{37} +(-3.92654 + 0.733424i) q^{38} +(9.77302 + 14.6264i) q^{39} +(-2.29520 - 1.65289i) q^{40} +(-1.69932 - 1.13545i) q^{41} +(18.3132 - 7.33596i) q^{42} +(2.05765 + 2.50725i) q^{43} +(-6.06793 - 5.22194i) q^{44} +(3.11646 + 5.83049i) q^{45} +(-5.31747 + 4.26088i) q^{46} +(2.54349 - 1.05355i) q^{47} +(11.6855 + 4.15053i) q^{48} +(12.2386 + 5.06937i) q^{49} +(1.35802 - 0.394675i) q^{50} +(-11.4016 - 3.45863i) q^{51} +(-8.93831 + 6.99225i) q^{52} +(-0.00307733 + 0.0312446i) q^{53} +(-11.0635 - 11.3252i) q^{54} +(3.92585 - 0.780900i) q^{55} +(5.60217 + 11.4276i) q^{56} +(-1.70830 + 8.58820i) q^{57} +(2.29883 - 10.8901i) q^{58} +(-0.326054 - 1.07486i) q^{59} +(-5.23454 + 3.32326i) q^{60} +(2.69514 + 2.21185i) q^{61} +(-4.86101 - 9.35578i) q^{62} -29.7478i q^{63} +(-2.10681 + 7.71760i) q^{64} -5.67417i q^{65} +(-15.5728 + 8.09122i) q^{66} +(-5.60405 - 4.59912i) q^{67} +(1.67538 - 7.50158i) q^{68} +(4.33609 + 14.2942i) q^{69} +(-6.22626 - 1.31433i) q^{70} +(1.81115 - 9.10528i) q^{71} +(12.3621 - 14.0297i) q^{72} +(4.08316 - 0.812192i) q^{73} +(0.395673 - 0.386528i) q^{74} +(0.303871 - 3.08525i) q^{75} +(-5.60731 - 0.684983i) q^{76} +(-17.2355 - 5.22833i) q^{77} +(6.94272 + 23.8890i) q^{78} +(8.94624 + 3.70565i) q^{79} +(-2.39026 - 3.20728i) q^{80} +(-13.7414 + 5.69186i) q^{81} +(-1.80735 - 2.25552i) q^{82} +(4.40291 + 8.23727i) q^{83} +(27.8215 - 2.08474i) q^{84} +(2.43810 + 2.97083i) q^{85} +(1.70570 + 4.25806i) q^{86} +(-20.2869 - 13.5553i) q^{87} +(-5.95594 - 9.62827i) q^{88} +(-3.03951 - 4.54894i) q^{89} +(1.71668 + 9.19058i) q^{90} +(-12.0356 + 22.5171i) q^{91} +(-8.98671 + 3.47856i) q^{92} +(-23.0012 + 2.26542i) q^{93} +(3.87885 - 0.336297i) q^{94} +(1.99722 - 1.99722i) q^{95} +(13.9876 + 10.5784i) q^{96} +(10.4315 + 10.4315i) q^{97} +(14.3416 + 12.0532i) q^{98} +(2.59380 + 26.3353i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 1024 q+O(q^{10}) \) 1024 * q	\( 1024 q - 192 q^{52} - 128 q^{54} - 32 q^{56} - 288 q^{58} - 192 q^{62} - 192 q^{64} - 192 q^{66} - 192 q^{68} - 288 q^{72} - 32 q^{74} - 128 q^{76} - 192 q^{78}+O(q^{100}) \) 1024 * q - 192 * q^52 - 128 * q^54 - 32 * q^56 - 288 * q^58 - 192 * q^62 - 192 * q^64 - 192 * q^66 - 192 * q^68 - 288 * q^72 - 32 * q^74 - 128 * q^76 - 192 * q^78

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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