LMFDB - Embedded newform 384.2.v.a.37.32

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [384,2,Mod(13,384)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(384, base_ring=CyclotomicField(32))

chi = DirichletCharacter(H, H._module([0, 15, 0]))

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

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

chi := DirichletCharacter("384.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 384 = 2^{7} \cdot 3 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	384.v (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:	$3.06625543762$
Analytic rank:	$0$
Dimension:	$512$
Relative dimension:	$32$ over $\Q(\zeta_{32})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{32}]$

Embedding invariants

Embedding label			37.32
Character	$\chi$	$=$	384.37
Dual form			384.2.v.a.301.32

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.41418 + 0.00986600i) q^{2} +(0.471397 + 0.881921i) q^{3} +(1.99981 + 0.0279046i) q^{4} +(1.72253 - 1.41364i) q^{5} +(0.657938 + 1.25185i) q^{6} +(-2.19144 + 1.46427i) q^{7} +(2.82781 + 0.0591922i) q^{8} +(-0.555570 + 0.831470i) q^{9} +O(q^{10})$	\(q+(1.41418 + 0.00986600i) q^{2} +(0.471397 + 0.881921i) q^{3} +(1.99981 + 0.0279046i) q^{4} +(1.72253 - 1.41364i) q^{5} +(0.657938 + 1.25185i) q^{6} +(-2.19144 + 1.46427i) q^{7} +(2.82781 + 0.0591922i) q^{8} +(-0.555570 + 0.831470i) q^{9} +(2.44991 - 1.98215i) q^{10} +(-0.262068 - 0.863924i) q^{11} +(0.918092 + 1.77682i) q^{12} +(0.448755 - 0.546809i) q^{13} +(-3.11353 + 2.04912i) q^{14} +(2.05871 + 0.852747i) q^{15} +(3.99844 + 0.111607i) q^{16} +(2.25114 - 0.932454i) q^{17} +(-0.793879 + 1.17037i) q^{18} +(-5.01848 + 0.494277i) q^{19} +(3.48416 - 2.77894i) q^{20} +(-2.32441 - 1.24242i) q^{21} +(-0.362088 - 1.22433i) q^{22} +(-3.32646 + 0.661674i) q^{23} +(1.28082 + 2.52181i) q^{24} +(-0.00673583 + 0.0338633i) q^{25} +(0.640015 - 0.768859i) q^{26} +(-0.995185 - 0.0980171i) q^{27} +(-4.42331 + 2.86711i) q^{28} +(-2.81116 - 0.852757i) q^{29} +(2.90297 + 1.22625i) q^{30} +(-2.02144 - 2.02144i) q^{31} +(5.65341 + 0.197282i) q^{32} +(0.638375 - 0.638375i) q^{33} +(3.19272 - 1.29645i) q^{34} +(-1.70486 + 5.62016i) q^{35} +(-1.13423 + 1.64727i) q^{36} +(0.822345 - 8.34941i) q^{37} +(-7.10190 + 0.649484i) q^{38} +(0.693785 + 0.138002i) q^{39} +(4.95465 - 3.89554i) q^{40} +(1.16181 + 5.84083i) q^{41} +(-3.27488 - 1.77994i) q^{42} +(1.19961 - 2.24431i) q^{43} +(-0.499978 - 1.73499i) q^{44} +(0.218415 + 2.21760i) q^{45} +(-4.71074 + 0.902907i) q^{46} +(0.201268 + 0.485904i) q^{47} +(1.78642 + 3.57892i) q^{48} +(-0.0204723 + 0.0494245i) q^{49} +(-0.00985977 + 0.0478223i) q^{50} +(1.88353 + 1.54577i) q^{51} +(0.912681 - 1.08099i) q^{52} +(-5.66382 + 1.71810i) q^{53} +(-1.40640 - 0.148432i) q^{54} +(-1.67270 - 1.11766i) q^{55} +(-6.28364 + 4.01097i) q^{56} +(-2.80161 - 4.19290i) q^{57} +(-3.96708 - 1.23369i) q^{58} +(6.94644 + 8.46427i) q^{59} +(4.09323 + 1.76277i) q^{60} +(4.29691 - 2.29675i) q^{61} +(-2.83874 - 2.87863i) q^{62} -2.63562i q^{63} +(7.99299 + 0.334768i) q^{64} -1.57627i q^{65} +(0.909074 - 0.896478i) q^{66} +(-4.28589 + 2.29085i) q^{67} +(4.52787 - 1.80191i) q^{68} +(-2.15163 - 2.62177i) q^{69} +(-2.46642 + 7.93109i) q^{70} +(-6.69894 - 10.0257i) q^{71} +(-1.62026 + 2.31835i) q^{72} +(-9.11407 - 6.08983i) q^{73} +(1.24532 - 11.7995i) q^{74} +(-0.0330400 + 0.0100226i) q^{75} +(-10.0498 + 0.848419i) q^{76} +(1.83933 + 1.50950i) q^{77} +(0.979774 + 0.202005i) q^{78} +(3.21767 - 7.76815i) q^{79} +(7.04519 - 5.46011i) q^{80} +(-0.382683 - 0.923880i) q^{81} +(1.58539 + 8.27145i) q^{82} +(0.213301 + 2.16568i) q^{83} +(-4.61370 - 2.54947i) q^{84} +(2.55950 - 4.78848i) q^{85} +(1.71860 - 3.16202i) q^{86} +(-0.573109 - 2.88121i) q^{87} +(-0.689942 - 2.45852i) q^{88} +(-11.8485 - 2.35682i) q^{89} +(0.286999 + 3.13824i) q^{90} +(-0.182741 + 1.85540i) q^{91} +(-6.67074 + 1.23040i) q^{92} +(0.829852 - 2.73566i) q^{93} +(0.279835 + 0.689141i) q^{94} +(-7.94572 + 7.94572i) q^{95} +(2.49101 + 5.07886i) q^{96} +(-10.0739 - 10.0739i) q^{97} +(-0.0294391 + 0.0696932i) q^{98} +(0.863924 + 0.262068i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 512 q+O(q^{10}) $ 512 * q	$ 512 q - 96 q^{50} - 96 q^{52} - 32 q^{54} - 224 q^{56} - 192 q^{60} - 192 q^{62} - 192 q^{64} - 192 q^{66} - 192 q^{68} - 192 q^{70} - 224 q^{74} - 32 q^{76} - 96 q^{78} - 96 q^{80}+O(q^{100}) $ 512 * q - 96 * q^50 - 96 * q^52 - 32 * q^54 - 224 * q^56 - 192 * q^60 - 192 * q^62 - 192 * q^64 - 192 * q^66 - 192 * q^68 - 192 * q^70 - 224 * q^74 - 32 * q^76 - 96 * q^78 - 96 * q^80

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/384\mathbb{Z}\right)^\times$.

$n$	$127$	$133$	$257$
$\chi(n)$	$1$	$e\left(\frac{25}{32}\right)$	$1$

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 $

$2$	1.41418	+	0.00986600i	0.999976	+	0.00697632i
$2$	1.41418	+	0.00986600i	0.999976	+	0.00697632i
$3$	0.471397	+	0.881921i	0.272161	+	0.509177i
$3$	0.471397	+	0.881921i	0.272161	+	0.509177i
$4$	1.99981	+	0.0279046i	0.999903	+	0.0139523i
$5$	1.72253	−	1.41364i	0.770337	−	0.632199i	−0.164864	−	0.986316i	$-0.552719\pi$
$5$	1.72253	−	1.41364i	0.770337	−	0.632199i	0.935201	+	0.354117i	$0.115219\pi$
$6$	0.657938	+	1.25185i	0.268602	+	0.511064i
$7$	−2.19144	+	1.46427i	−0.828286	+	0.553443i	−0.895894	−	0.444269i	$-0.853464\pi$
$7$	−2.19144	+	1.46427i	−0.828286	+	0.553443i	0.0676072	+	0.997712i	$0.478464\pi$
$8$	2.82781	+	0.0591922i	0.999781	+	0.0209276i
$9$	−0.555570	+	0.831470i	−0.185190	+	0.277157i
$10$	2.44991	−	1.98215i	0.774729	−	0.626810i
$11$	−0.262068	−	0.863924i	−0.0790166	−	0.260483i	0.908528	−	0.417825i	$-0.137207\pi$
$11$	−0.262068	−	0.863924i	−0.0790166	−	0.260483i	−0.987544	+	0.157342i	$0.949707\pi$
$12$	0.918092	+	1.77682i	0.265030	+	0.512925i
$13$	0.448755	−	0.546809i	0.124462	−	0.151658i	−0.707051	−	0.707162i	$-0.749975\pi$
$13$	0.448755	−	0.546809i	0.124462	−	0.151658i	0.831513	+	0.555505i	$0.187475\pi$
$14$	−3.11353	+	2.04912i	−0.832127	+	0.547651i
$15$	2.05871	+	0.852747i	0.531557	+	0.220178i
$16$	3.99844	+	0.111607i	0.999611	+	0.0279019i
$17$	2.25114	−	0.932454i	0.545982	−	0.226153i	−0.0926046	−	0.995703i	$-0.529519\pi$
$17$	2.25114	−	0.932454i	0.545982	−	0.226153i	0.638587	+	0.769550i	$0.279519\pi$
$18$	−0.793879	+	1.17037i	−0.187119	+	0.275858i
$19$	−5.01848	+	0.494277i	−1.15132	+	0.113395i	−0.655613	−	0.755097i	$-0.727590\pi$
$19$	−5.01848	+	0.494277i	−1.15132	+	0.113395i	−0.495704	+	0.868492i	$0.665090\pi$
$20$	3.48416	−	2.77894i	0.779083	−	0.621390i
$21$	−2.32441	−	1.24242i	−0.507228	−	0.271119i
$22$	−0.362088	−	1.22433i	−0.0771975	−	0.261028i
$23$	−3.32646	+	0.661674i	−0.693615	+	0.137969i	−0.529294	−	0.848438i	$-0.677543\pi$
$23$	−3.32646	+	0.661674i	−0.693615	+	0.137969i	−0.164321	+	0.986407i	$0.552543\pi$
$24$	1.28082	+	2.52181i	0.261446	+	0.514762i
$25$	−0.00673583	+	0.0338633i	−0.00134717	+	0.00677266i
$26$	0.640015	−	0.768859i	0.125517	−	0.150786i
$27$	−0.995185	−	0.0980171i	−0.191523	−	0.0188634i
$28$	−4.42331	+	2.86711i	−0.835927	+	0.541833i
$29$	−2.81116	−	0.852757i	−0.522020	−	0.158353i	0.0182681	−	0.999833i	$-0.494185\pi$
$29$	−2.81116	−	0.852757i	−0.522020	−	0.158353i	−0.540288	+	0.841480i	$0.681685\pi$
$30$	2.90297	+	1.22625i	0.530008	+	0.223881i
$31$	−2.02144	−	2.02144i	−0.363062	−	0.363062i	0.501877	−	0.864939i	$-0.332643\pi$
$31$	−2.02144	−	2.02144i	−0.363062	−	0.363062i	−0.864939	+	0.501877i	$0.832643\pi$
$32$	5.65341	+	0.197282i	0.999392	+	0.0348748i
$33$	0.638375	−	0.638375i	0.111127	−	0.111127i
$34$	3.19272	−	1.29645i	0.547547	−	0.222339i
$35$	−1.70486	+	5.62016i	−0.288173	+	0.949980i
$36$	−1.13423	+	1.64727i	−0.189039	+	0.274546i
$37$	0.822345	−	8.34941i	0.135193	−	1.37263i	−0.653071	−	0.757297i	$-0.726520\pi$
$37$	0.822345	−	8.34941i	0.135193	−	1.37263i	0.788263	−	0.615338i	$-0.210980\pi$
$38$	−7.10190	+	0.649484i	−1.15208	+	0.105360i
$39$	0.693785	+	0.138002i	0.111094	+	0.0220981i
$40$	4.95465	−	3.89554i	0.783399	−	0.615939i
$41$	1.16181	+	5.84083i	0.181445	+	0.912185i	0.959008	+	0.283380i	$0.0914557\pi$
$41$	1.16181	+	5.84083i	0.181445	+	0.912185i	−0.777563	+	0.628805i	$0.783544\pi$
$42$	−3.27488	−	1.77994i	−0.505324	−	0.274651i
$43$	1.19961	−	2.24431i	0.182938	−	0.342254i	−0.773690	−	0.633564i	$-0.781591\pi$
$43$	1.19961	−	2.24431i	0.182938	−	0.342254i	0.956629	+	0.291310i	$0.0940913\pi$
$44$	−0.499978	−	1.73499i	−0.0753746	−	0.261560i
$45$	0.218415	+	2.21760i	0.0325594	+	0.330581i
$46$	−4.71074	+	0.902907i	−0.694561	+	0.133126i
$47$	0.201268	+	0.485904i	0.0293579	+	0.0708764i	0.937879	−	0.346964i	$-0.112787\pi$
$47$	0.201268	+	0.485904i	0.0293579	+	0.0708764i	−0.908521	+	0.417840i	$0.862787\pi$
$48$	1.78642	+	3.57892i	0.257848	+	0.516573i
$49$	−0.0204723	+	0.0494245i	−0.00292462	+	0.00706065i
$50$	−0.00985977	+	0.0478223i	−0.00139438	+	0.00676310i
$51$	1.88353	+	1.54577i	0.263747	+	0.216452i
$52$	0.912681	−	1.08099i	0.126566	−	0.149906i
$53$	−5.66382	+	1.71810i	−0.777985	+	0.235999i	−0.654212	−	0.756311i	$-0.727000\pi$
$53$	−5.66382	+	1.71810i	−0.777985	+	0.235999i	−0.123773	+	0.992311i	$0.539500\pi$
$54$	−1.40640	−	0.148432i	−0.191387	−	0.0201991i
$55$	−1.67270	−	1.11766i	−0.225546	−	0.150705i
$56$	−6.28364	+	4.01097i	−0.839687	+	0.535988i
$57$	−2.80161	−	4.19290i	−0.371082	−	0.555363i
$58$	−3.96708	−	1.23369i	−0.520903	−	0.161991i
$59$	6.94644	+	8.46427i	0.904350	+	1.10195i	0.994365	+	0.106013i	$0.0338086\pi$
$59$	6.94644	+	8.46427i	0.904350	+	1.10195i	−0.0900148	+	0.995940i	$0.528691\pi$
$60$	4.09323	+	1.76277i	0.528434	+	0.227573i
$61$	4.29691	−	2.29675i	0.550163	−	0.294068i	−0.172798	−	0.984957i	$-0.555281\pi$
$61$	4.29691	−	2.29675i	0.550163	−	0.294068i	0.722961	+	0.690889i	$0.242781\pi$
$62$	−2.83874	−	2.87863i	−0.360520	−	0.365586i
$63$		−	2.63562i		−	0.332057i
$64$	7.99299	+	0.334768i	0.999124	+	0.0418460i
$65$		−	1.57627i		−	0.195512i
$66$	0.909074	−	0.896478i	0.111899	−	0.110349i
$67$	−4.28589	+	2.29085i	−0.523604	+	0.279872i	−0.711950	−	0.702230i	$-0.752188\pi$
$67$	−4.28589	+	2.29085i	−0.523604	+	0.279872i	0.188345	+	0.982103i	$0.439688\pi$
$68$	4.52787	−	1.80191i	0.549085	−	0.218514i
$69$	−2.15163	−	2.62177i	−0.259026	−	0.315623i
$70$	−2.46642	+	7.93109i	−0.294794	+	0.947946i
$71$	−6.69894	−	10.0257i	−0.795018	−	1.18983i	−0.978386	−	0.206785i	$-0.933700\pi$
$71$	−6.69894	−	10.0257i	−0.795018	−	1.18983i	0.183368	−	0.983044i	$-0.441300\pi$
$72$	−1.62026	+	2.31835i	−0.190950	+	0.273220i
$73$	−9.11407	−	6.08983i	−1.06672	−	0.712760i	−0.107155	−	0.994242i	$-0.534174\pi$
$73$	−9.11407	−	6.08983i	−1.06672	−	0.712760i	−0.959567	+	0.281482i	$0.909174\pi$
$74$	1.24532	−	11.7995i	0.144765	−	1.37166i
$75$	−0.0330400	+	0.0100226i	−0.00381513	+	0.00115731i
$76$	−10.0498	+	0.848419i	−1.15279	+	0.0973203i
$77$	1.83933	+	1.50950i	0.209611	+	0.172023i
$78$	0.979774	+	0.202005i	0.110938	+	0.0228725i
$79$	3.21767	−	7.76815i	0.362017	−	0.873985i	−0.632989	−	0.774161i	$-0.718172\pi$
$79$	3.21767	−	7.76815i	0.362017	−	0.873985i	0.995005	−	0.0998240i	$-0.0318280\pi$
$80$	7.04519	−	5.46011i	0.787676	−	0.610459i
$81$	−0.382683	−	0.923880i	−0.0425204	−	0.102653i
$82$	1.58539	+	8.27145i	0.175077	+	0.913428i
$83$	0.213301	+	2.16568i	0.0234128	+	0.237714i	0.999768	+	0.0215415i	$0.00685742\pi$
$83$	0.213301	+	2.16568i	0.0234128	+	0.237714i	−0.976355	+	0.216173i	$0.930643\pi$
$84$	−4.61370	−	2.54947i	−0.503396	−	0.278170i
$85$	2.55950	−	4.78848i	0.277616	−	0.519384i
$86$	1.71860	−	3.16202i	0.185322	−	0.340969i
$87$	−0.573109	−	2.88121i	−0.0614437	−	0.308898i
$88$	−0.689942	−	2.45852i	−0.0735480	−	0.262079i
$89$	−11.8485	−	2.35682i	−1.25594	−	0.249822i	−0.478113	−	0.878299i	$-0.658679\pi$
$89$	−11.8485	−	2.35682i	−1.25594	−	0.249822i	−0.777829	+	0.628476i	$0.783679\pi$
$90$	0.286999	+	3.13824i	0.0302523	+	0.330800i
$91$	−0.182741	+	1.85540i	−0.0191565	+	0.194499i
$92$	−6.67074	+	1.23040i	−0.695473	+	0.128278i
$93$	0.829852	−	2.73566i	0.0860517	−	0.283674i
$94$	0.279835	+	0.689141i	0.0288628	+	0.0710794i
$95$	−7.94572	+	7.94572i	−0.815214	+	0.815214i
$96$	2.49101	+	5.07886i	0.254238	+	0.518359i
$97$	−10.0739	−	10.0739i	−1.02285	−	1.02285i	−0.999733	−	0.0231153i	$-0.992642\pi$
$97$	−10.0739	−	10.0739i	−1.02285	−	1.02285i	−0.0231153	−	0.999733i	$-0.507358\pi$
$98$	−0.0294391	+	0.0696932i	−0.00297380	+	0.00704007i
$99$	0.863924	+	0.262068i	0.0868276	+	0.0263389i
$100$	−0.0144153	+	0.0675321i	−0.00144153	+	0.00675321i
$101$	−1.18015	−	0.116234i	−0.117429	−	0.0115657i	0.0391319	−	0.999234i	$-0.487541\pi$
$101$	−1.18015	−	0.116234i	−0.117429	−	0.0115657i	−0.156561	+	0.987668i	$0.550041\pi$
$102$	2.64840	+	2.20459i	0.262231	+	0.218287i
$103$	−1.68588	+	8.47549i	−0.166115	+	0.835115i	0.804403	+	0.594084i	$0.202485\pi$
$103$	−1.68588	+	8.47549i	−0.166115	+	0.835115i	−0.970518	+	0.241031i	$0.922515\pi$
$104$	1.30136	−	1.51971i	0.127609	−	0.149020i
$105$	−5.76020	+	1.14577i	−0.562138	+	0.111816i
$106$	−8.02660	+	2.37382i	−0.779613	+	0.230566i
$107$	16.7192	+	8.93661i	1.61631	+	0.863935i	0.996884	+	0.0788778i	$0.0251337\pi$
$107$	16.7192	+	8.93661i	1.61631	+	0.863935i	0.619424	+	0.785057i	$0.287366\pi$
$108$	−1.98744	−	0.223785i	−0.191242	−	0.0215338i
$109$	18.1302	−	1.78567i	1.73656	−	0.171036i	0.820382	−	0.571816i	$-0.193761\pi$
$109$	18.1302	−	1.78567i	1.73656	−	0.171036i	0.916174	+	0.400780i	$0.131261\pi$
$110$	−2.35447	−	1.59707i	−0.224490	−	0.152275i
$111$	7.75117	−	3.21064i	0.735709	−	0.304741i
$112$	−8.92577	+	5.61023i	−0.843406	+	0.530117i
$113$	15.3352	+	6.35205i	1.44261	+	0.597550i	0.960430	−	0.278520i	$-0.0898439\pi$
$113$	15.3352	+	6.35205i	1.44261	+	0.597550i	0.482183	+	0.876070i	$0.339844\pi$
$114$	−3.92061	−	5.95715i	−0.367198	−	0.557939i
$115$	−4.79454	+	5.84217i	−0.447094	+	0.544785i
$116$	−5.59798	−	1.78379i	−0.519760	−	0.165621i
$117$	0.205341	+	0.676917i	0.0189837	+	0.0625810i
$118$	9.74001	+	12.0385i	0.896640	+	1.10824i
$119$	−3.56788	+	5.33970i	−0.327067	+	0.489490i
$120$	5.77117	+	2.53326i	0.526833	+	0.231254i
$121$	8.46848	−	5.65846i	0.769862	−	0.514405i
$122$	6.09926	−	3.20562i	0.552201	−	0.290223i
$123$	−4.60348	+	3.77798i	−0.415082	+	0.340649i
$124$	−3.98609	−	4.09890i	−0.357961	−	0.368092i
$125$	5.28842	+	9.89393i	0.473010	+	0.884940i
$126$	0.0260030	−	3.72724i	0.00231654	−	0.332049i
$127$	−16.2087			−1.43829			−0.719147	−	0.694858i	$-0.755467\pi$
$127$	−16.2087			−1.43829			−0.719147	+	0.694858i	$0.755467\pi$
$128$	11.3002	+	0.552281i	0.998808	+	0.0488152i
$129$	2.54479			0.224057
$130$	0.0155515	−	2.22913i	0.00136396	−	0.195508i
$131$	10.0970	+	18.8902i	0.882180	+	1.65044i	0.752209	+	0.658925i	$0.228988\pi$
$131$	10.0970	+	18.8902i	0.882180	+	1.65044i	0.129971	+	0.991518i	$0.458512\pi$
$132$	1.29444	−	1.25881i	0.112666	−	0.109565i
$133$	10.2739	−	8.43160i	0.890863	−	0.731112i
$134$	−6.08361	+	3.19739i	−0.525544	+	0.276213i
$135$	−1.85279	+	1.23800i	−0.159463	+	0.106550i
$136$	6.42099	−	2.50355i	0.550596	−	0.214678i
$137$	−5.21938	+	7.81135i	−0.445921	+	0.667369i	−0.984536	−	0.175184i	$-0.943948\pi$
$137$	−5.21938	+	7.81135i	−0.445921	+	0.667369i	0.538614	+	0.842552i	$0.318948\pi$
$138$	−3.01692	−	3.72887i	−0.256817	−	0.317423i
$139$	−1.46426	−	4.82702i	−0.124197	−	0.409423i	0.872689	−	0.488276i	$-0.162374\pi$
$139$	−1.46426	−	4.82702i	−0.124197	−	0.409423i	−0.996886	+	0.0788535i	$0.974874\pi$
$140$	−3.56621	+	11.1916i	−0.301400	+	0.945866i
$141$	−0.333652	+	0.406556i	−0.0280986	+	0.0342382i
$142$	−9.37459	−	14.2442i	−0.786698	−	1.19535i
$143$	−0.590006	−	0.244389i	−0.0493388	−	0.0204368i
$144$	−2.31421	+	3.26258i	−0.192851	+	0.271881i
$145$	−6.04779	+	2.50508i	−0.502242	+	0.208035i
$146$	−12.8288	−	8.70203i	−1.06172	−	0.720185i
$147$	−0.0532391	+	0.00524360i	−0.00439109	+	0.000432485i
$148$	1.87752	−	16.6742i	0.154331	−	1.37061i
$149$	4.80943	+	2.57069i	0.394004	+	0.210599i	0.656487	−	0.754337i	$-0.272042\pi$
$149$	4.80943	+	2.57069i	0.394004	+	0.210599i	−0.262484	+	0.964936i	$0.584542\pi$
$150$	−0.0468234	+	0.0138478i	−0.00382312	+	0.00113066i
$151$	17.8099	−	3.54262i	1.44935	−	0.288294i	0.593216	−	0.805043i	$-0.297858\pi$
$151$	17.8099	−	3.54262i	1.44935	−	0.288294i	0.856137	+	0.516749i	$0.172858\pi$
$152$	−14.2205	+	1.10067i	−1.15344	+	0.0892757i
$153$	−0.475361	+	2.38980i	−0.0384306	+	0.193204i
$154$	2.58625	+	2.15285i	0.208406	+	0.173481i
$155$	−6.33958	−	0.624394i	−0.509208	−	0.0501526i
$156$	1.38358	+	0.295338i	0.110775	+	0.0236459i
$157$	−1.12611	−	0.341601i	−0.0898731	−	0.0272627i	0.245028	−	0.969516i	$-0.421203\pi$
$157$	−1.12611	−	0.341601i	−0.0898731	−	0.0272627i	−0.334901	+	0.942253i	$0.608703\pi$
$158$	4.62701	−	10.9538i	0.368105	−	0.871438i
$159$	−4.18513	−	4.18513i	−0.331903	−	0.331903i
$160$	10.0170	−	7.65207i	0.791916	−	0.604949i
$161$	6.32087	−	6.32087i	0.498154	−	0.498154i
$162$	−0.532068	−	1.31031i	−0.0418032	−	0.102947i
$163$	−2.43154	+	8.01570i	−0.190453	+	0.627838i	0.808759	+	0.588140i	$0.200140\pi$
$163$	−2.43154	+	8.01570i	−0.190453	+	0.627838i	−0.999212	+	0.0396981i	$0.987360\pi$
$164$	2.16042	+	11.7129i	0.168700	+	0.914628i
$165$	0.197185	−	2.00205i	0.0153508	−	0.155859i
$166$	0.280279	+	3.06476i	0.0217539	+	0.237872i
$167$	16.7466	+	3.33111i	1.29589	+	0.257769i	0.794401	−	0.607394i	$-0.207785\pi$
$167$	16.7466	+	3.33111i	1.29589	+	0.257769i	0.501491	+	0.865163i	$0.332785\pi$
$168$	−6.49945	−	3.65092i	−0.501443	−	0.281675i
$169$	2.43855	+	12.2594i	0.187581	+	0.943034i
$170$	3.66683	−	6.74652i	0.281233	−	0.517434i
$171$	2.37714	−	4.44732i	0.181784	−	0.340095i
$172$	2.46161	−	4.45470i	0.187696	−	0.339668i
$173$	−0.359346	−	3.64851i	−0.0273206	−	0.277391i	−0.999133	−	0.0416348i	$-0.986743\pi$
$173$	−0.359346	−	3.64851i	−0.0273206	−	0.277391i	0.971812	−	0.235756i	$-0.0757566\pi$
$174$	−0.782052	−	4.08020i	−0.0592872	−	0.309320i
$175$	−0.0348240	−	0.0840725i	−0.00263245	−	0.00635529i
$176$	−0.951445	−	3.48360i	−0.0717179	−	0.262586i
$177$	−4.19029	+	10.1162i	−0.314961	+	0.760383i
$178$	−16.7327	−	3.44986i	−1.25417	−	0.258578i
$179$	4.49968	+	3.69279i	0.336322	+	0.276012i	0.787361	−	0.616492i	$-0.211447\pi$
$179$	4.49968	+	3.69279i	0.336322	+	0.276012i	−0.451040	+	0.892504i	$0.648947\pi$
$180$	0.374906	+	4.44087i	0.0279438	+	0.331003i
$181$	17.4333	−	5.28834i	1.29581	−	0.393079i	0.434276	−	0.900780i	$-0.357004\pi$
$181$	17.4333	−	5.28834i	1.29581	−	0.393079i	0.861534	+	0.507701i	$0.169504\pi$
$182$	−0.276734	+	2.62206i	−0.0205129	+	0.194360i
$183$	4.05110	+	2.70686i	0.299466	+	0.200097i
$184$	−9.44576	+	1.67419i	−0.696351	+	0.123423i
$185$	−10.3866	−	15.5446i	−0.763635	−	1.14286i
$186$	1.20055	−	3.86052i	0.0880286	−	0.283067i
$187$	−1.39552	−	1.70045i	−0.102051	−	0.124349i
$188$	0.388938	+	0.977329i	0.0283662	+	0.0712791i
$189$	2.32441	−	1.24242i	0.169076	−	0.0903730i
$190$	−11.3151	+	11.1583i	−0.820881	+	0.809507i
$191$		−	22.2962i		−	1.61330i	−0.591030	−	0.806650i	$-0.701278\pi$
$191$		−	22.2962i		−	1.61330i	0.591030	−	0.806650i	$-0.298722\pi$
$192$	3.47263	+	7.20700i	0.250616	+	0.520120i
$193$			19.5429i			1.40673i	0.710831	+	0.703363i	$0.248319\pi$
$193$			19.5429i			1.40673i	−0.710831	+	0.703363i	$0.751681\pi$
$194$	−14.1469	−	14.3457i	−1.01569	−	1.02996i
$195$	1.39015	−	0.743049i	0.0995505	−	0.0532109i
$196$	−0.0423198	+	0.0982682i	−0.00302284	+	0.00701916i
$197$	2.16014	+	2.63214i	0.153904	+	0.187532i	0.844254	−	0.535943i	$-0.180044\pi$
$197$	2.16014	+	2.63214i	0.153904	+	0.187532i	−0.690351	+	0.723475i	$0.742544\pi$
$198$	1.21916	+	0.379135i	0.0866417	+	0.0269440i
$199$	3.35800	+	5.02560i	0.238042	+	0.356256i	0.931186	−	0.364544i	$-0.118775\pi$
$199$	3.35800	+	5.02560i	0.238042	+	0.356256i	−0.693144	+	0.720799i	$0.743775\pi$
$200$	−0.0210521	+	0.0953603i	−0.00148861	+	0.00674299i
$201$	−4.04071	−	2.69991i	−0.285009	−	0.190437i
$202$	−1.66779	−	0.176019i	−0.117345	−	0.0123847i
$203$	7.40917	−	2.24755i	0.520021	−	0.157747i
$204$	3.72356	+	3.14381i	0.260702	+	0.220111i
$205$	10.2581	+	8.41860i	0.716456	+	0.587980i
$206$	−2.46775	+	11.9692i	−0.171937	+	0.833935i
$207$	1.29792	−	3.13346i	0.0902117	−	0.217790i
$208$	1.85535	−	2.13630i	0.128645	−	0.148126i
$209$	1.74220	+	4.20605i	0.120511	+	0.290938i
$210$	−8.15726	+	1.56350i	−0.562904	+	0.107892i
$211$	−1.38711	−	14.0836i	−0.0954926	−	0.969552i	−0.916875	−	0.399174i	$-0.869297\pi$
$211$	−1.38711	−	14.0836i	−0.0954926	−	0.969552i	0.821382	−	0.570378i	$-0.193203\pi$
$212$	−11.3745	+	3.27782i	−0.781202	+	0.225122i
$213$	5.68400	−	10.6340i	0.389461	−	0.728631i
$214$	23.5558	+	12.8029i	1.61024	+	0.875189i
$215$	−1.10629	−	5.56169i	−0.0754483	−	0.379304i
$216$	−2.80839	−	0.336081i	−0.191087	−	0.0228674i
$217$	7.38982	+	1.46993i	0.501654	+	0.0997851i
$218$	25.6569	−	2.34638i	1.73771	−	0.158917i
$219$	1.07441	−	10.9086i	0.0726016	−	0.737136i
$220$	−3.31388	−	2.28178i	−0.223422	−	0.153838i
$221$	0.500337	−	1.64939i	0.0336563	−	0.110950i
$222$	10.9932	−	4.46395i	0.737817	−	0.299601i
$223$	−11.0520	+	11.0520i	−0.740094	+	0.740094i	−0.972596	−	0.232502i	$-0.925309\pi$
$223$	−11.0520	+	11.0520i	−0.740094	+	0.740094i	0.232502	+	0.972596i	$0.425309\pi$
$224$	−12.6780	+	7.84581i	−0.847084	+	0.524220i
$225$	−0.0244141	−	0.0244141i	−0.00162761	−	0.00162761i
$226$	21.6240	+	9.13423i	1.43841	+	0.607600i
$227$	−3.23076	−	0.980041i	−0.214433	−	0.0650476i	0.181240	−	0.983439i	$-0.441989\pi$
$227$	−3.23076	−	0.980041i	−0.214433	−	0.0650476i	−0.395673	+	0.918391i	$0.629489\pi$
$228$	−5.48567	−	8.46316i	−0.363297	−	0.560487i
$229$	−24.6922	−	2.43197i	−1.63171	−	0.160709i	−0.759724	−	0.650245i	$-0.774666\pi$
$229$	−24.6922	−	2.43197i	−1.63171	−	0.160709i	−0.871983	+	0.489536i	$0.837166\pi$
$230$	−6.83798	+	8.21457i	−0.450883	+	0.541653i
$231$	−0.464205	+	2.33371i	−0.0305424	+	0.153547i
$232$	−7.89895	−	2.57783i	−0.518592	−	0.169243i
$233$	−19.3112	+	3.84123i	−1.26512	+	0.251647i	−0.781651	−	0.623716i	$-0.785622\pi$
$233$	−19.3112	+	3.84123i	−1.26512	+	0.251647i	−0.483465	+	0.875364i	$0.660622\pi$
$234$	0.283710	+	0.959308i	0.0185467	+	0.0627119i
$235$	1.03358	+	0.552461i	0.0674235	+	0.0360386i
$236$	13.6553	+	17.1207i	0.888887	+	1.11446i
$237$	8.36770	−	0.824146i	0.543540	−	0.0535341i
$238$	−5.09830	+	7.51610i	−0.330474	+	0.487196i
$239$	15.4958	−	6.41858i	1.00234	−	0.415183i	0.179686	−	0.983724i	$-0.442492\pi$
$239$	15.4958	−	6.41858i	1.00234	−	0.415183i	0.822655	+	0.568541i	$0.192492\pi$
$240$	8.13647	+	3.63943i	0.525207	+	0.234924i
$241$	19.1279	+	7.92303i	1.23213	+	0.510367i	0.901248	−	0.433304i	$-0.142652\pi$
$241$	19.1279	+	7.92303i	1.23213	+	0.510367i	0.330887	+	0.943670i	$0.392652\pi$
$242$	12.0318	−	7.91852i	0.773432	−	0.509022i
$243$	0.634393	−	0.773010i	0.0406963	−	0.0495886i
$244$	8.65707	−	4.47314i	0.554212	−	0.286363i
$245$	0.0346044	+	0.114076i	0.00221080	+	0.00728802i
$246$	−6.54742	+	5.29732i	−0.417448	+	0.337745i
$247$	−1.98179	+	2.96596i	−0.126098	+	0.188719i
$248$	−5.59660	−	5.83591i	−0.355384	−	0.370581i
$249$	−1.80941	+	1.20901i	−0.114667	+	0.0766178i
$250$	7.38115	+	14.0440i	0.466825	+	0.888218i
$251$	15.1774	−	12.4557i	0.957986	−	0.786199i	−0.0189301	−	0.999821i	$-0.506026\pi$
$251$	15.1774	−	12.4557i	0.957986	−	0.786199i	0.976916	+	0.213622i	$0.0685260\pi$
$252$	0.0735459	−	5.27073i	0.00463296	−	0.332025i
$253$	1.44340	+	2.70040i	0.0907456	+	0.169773i
$254$	−22.9221	−	0.159915i	−1.43826	−	0.0100340i
$255$	5.42960			0.340015
$256$	15.9751	+	0.892512i	0.998443	+	0.0557820i
$257$	−6.14199			−0.383127			−0.191563	−	0.981480i	$-0.561356\pi$
$257$	−6.14199			−0.383127			−0.191563	+	0.981480i	$0.561356\pi$
$258$	3.59879	+	0.0251069i	0.224051	+	0.00156309i
$259$	10.4237	+	19.5014i	0.647697	+	1.21176i
$260$	0.0439852	−	3.15224i	0.00272785	−	0.195493i
$261$	2.27084	−	1.86363i	0.140562	−	0.115356i
$262$	14.0926	+	26.8137i	0.870644	+	1.65656i
$263$	9.09126	−	6.07458i	0.560591	−	0.374575i	−0.242755	−	0.970088i	$-0.578051\pi$
$263$	9.09126	−	6.07458i	0.560591	−	0.374575i	0.803346	+	0.595513i	$0.203051\pi$
$264$	1.84299	−	1.76741i	0.113428	−	0.108777i
$265$	−7.32729	+	10.9661i	−0.450112	+	0.673640i
$266$	14.6124	−	11.8224i	0.895942	−	0.724880i
$267$	−3.50683	−	11.5605i	−0.214614	−	0.707489i
$268$	−8.63487	+	4.46167i	−0.527458	+	0.272540i
$269$	−15.0945	+	18.3927i	−0.920327	+	1.12142i	0.0719533	+	0.997408i	$0.477077\pi$
$269$	−15.0945	+	18.3927i	−0.920327	+	1.12142i	−0.992280	+	0.124014i	$0.960423\pi$
$270$	−2.63239	+	1.73247i	−0.160202	+	0.105435i
$271$	−26.1214	−	10.8198i	−1.58676	−	0.657259i	−0.597296	−	0.802021i	$-0.703758\pi$
$271$	−26.1214	−	10.8198i	−1.58676	−	0.657259i	−0.989466	+	0.144762i	$0.953758\pi$
$272$	9.10513	−	3.47712i	0.552080	−	0.210831i
$273$	−1.72246	+	0.713466i	−0.104248	+	0.0431809i
$274$	−7.45820	+	10.9952i	−0.450566	+	0.664241i
$275$	0.0310206	−	0.00305526i	0.00187061	−	0.000184239i
$276$	−4.22968	−	5.30306i	−0.254597	−	0.319207i
$277$	17.5389	+	9.37475i	1.05381	+	0.563274i	0.904921	−	0.425580i	$-0.139930\pi$
$277$	17.5389	+	9.37475i	1.05381	+	0.563274i	0.148891	+	0.988854i	$0.452430\pi$
$278$	−2.02310	−	6.84072i	−0.121338	−	0.410279i
$279$	2.80382	−	0.557715i	0.167860	−	0.0333895i
$280$	−5.15367	+	15.7918i	−0.307991	+	0.943741i
$281$	3.32162	−	16.6989i	0.198151	−	0.996172i	−0.745821	−	0.666146i	$-0.767943\pi$
$281$	3.32162	−	16.6989i	0.198151	−	0.996172i	0.943972	−	0.330026i	$-0.107057\pi$
$282$	−0.475855	+	0.571651i	−0.0283367	+	0.0340413i
$283$	7.56743	+	0.745327i	0.449837	+	0.0443051i	0.320400	−	0.947282i	$-0.396183\pi$
$283$	7.56743	+	0.745327i	0.449837	+	0.0443051i	0.129438	+	0.991588i	$0.458683\pi$
$284$	−13.1168	−	20.2363i	−0.778340	−	1.20081i
$285$	−10.7531	−	3.26191i	−0.636958	−	0.193219i
$286$	−0.831963	−	0.351430i	−0.0491950	−	0.0207805i
$287$	−11.0986	−	11.0986i	−0.655131	−	0.655131i
$288$	−3.30490	+	4.59104i	−0.194743	+	0.270529i
$289$	−7.82264	+	7.82264i	−0.460155	+	0.460155i
$290$	−8.57738	+	3.48296i	−0.503681	+	0.204527i
$291$	4.13558	−	13.6332i	0.242432	−	0.799191i
$292$	−18.0564	−	12.4328i	−1.05667	−	0.727574i
$293$	−0.892833	+	9.06509i	−0.0521599	+	0.529588i	0.933231	+	0.359278i	$0.116977\pi$
$293$	−0.892833	+	9.06509i	−0.0521599	+	0.529588i	−0.985390	+	0.170310i	$0.945523\pi$
$294$	−0.0753414	+	0.00689013i	−0.00439400	+	0.000401840i
$295$	23.9309	+	4.76014i	1.39331	+	0.277146i
$296$	2.81965	−	23.5619i	0.163889	−	1.36950i
$297$	0.176127	+	0.885451i	0.0102199	+	0.0513791i
$298$	6.77603	+	3.68287i	0.392525	+	0.213343i
$299$	−1.13096	+	2.11587i	−0.0654049	+	0.122364i
$300$	−0.0663533	+	0.0191212i	−0.00383091	+	0.00110397i
$301$	0.657412	+	6.67482i	0.0378926	+	0.384730i
$302$	25.2214	−	4.83418i	1.45133	−	0.278176i
$303$	−0.453808	−	1.09559i	−0.0260706	−	0.0629399i
$304$	−20.1213	+	1.41624i	−1.15403	+	0.0812268i
$305$	4.15476	−	10.0305i	0.237901	−	0.574344i
$306$	−0.695823	+	3.37492i	−0.0397776	+	0.192931i
$307$	−21.3157	−	17.4934i	−1.21655	−	0.998400i	−0.999754	−	0.0221834i	$-0.992938\pi$
$307$	−21.3157	−	17.4934i	−1.21655	−	0.998400i	−0.216799	−	0.976216i	$-0.569562\pi$
$308$	3.63618	+	3.07003i	0.207190	+	0.174931i
$309$	−8.26943	+	2.50850i	−0.470432	+	0.142704i
$310$	−8.95915	−	0.945552i	−0.508845	−	0.0537037i
$311$	−9.41458	−	6.29062i	−0.533852	−	0.356709i	0.259237	−	0.965814i	$-0.416529\pi$
$311$	−9.41458	−	6.29062i	−0.533852	−	0.356709i	−0.793090	+	0.609105i	$0.791529\pi$
$312$	1.95372	+	0.431311i	0.110608	+	0.0244182i
$313$	12.4469	+	18.6282i	0.703543	+	1.05293i	0.995338	+	0.0964451i	$0.0307472\pi$
$313$	12.4469	+	18.6282i	0.703543	+	1.05293i	−0.291796	+	0.956481i	$0.594253\pi$
$314$	−1.58915	−	0.494195i	−0.0896807	−	0.0278890i
$315$	−3.72582	−	4.53993i	−0.209926	−	0.255796i
$316$	6.65149	−	15.4450i	0.374175	−	0.868849i
$317$	9.14592	−	4.88860i	0.513686	−	0.274571i	−0.194120	−	0.980978i	$-0.562185\pi$
$317$	9.14592	−	4.88860i	0.513686	−	0.274571i	0.707806	+	0.706407i	$0.249685\pi$
$318$	−5.87724	−	5.95982i	−0.329579	−	0.334210i
$319$			2.65211i			0.148490i
$320$	14.2414	−	10.7226i	0.796117	−	0.599410i
$321$			18.9577i			1.05812i
$322$	9.00120	−	8.87648i	0.501617	−	0.494667i
$323$	−10.8364	+	5.79219i	−0.602954	+	0.322286i
$324$	−0.739512	−	1.85826i	−0.0410840	−	0.103237i
$325$	0.0154940	+	0.0188796i	0.000859455	+	0.00104725i
$326$	−3.51771	+	11.3116i	−0.194828	+	0.626494i
$327$	10.1213	+	15.1476i	0.559711	+	0.837666i
$328$	2.93965	+	16.5855i	0.162315	+	0.915782i
$329$	−1.15256	−	0.770118i	−0.0635428	−	0.0424580i
$330$	0.298607	−	2.82931i	0.0164377	−	0.155748i
$331$	2.41546	−	0.732723i	0.132766	−	0.0402741i	−0.223202	−	0.974772i	$-0.571651\pi$
$331$	2.41546	−	0.732723i	0.132766	−	0.0402741i	0.355968	+	0.934498i	$0.384151\pi$
$332$	0.366128	+	4.33689i	0.0200939	+	0.238018i
$333$	6.48541	+	5.32244i	0.355398	+	0.291668i
$334$	23.6499	+	4.87601i	1.29406	+	0.266803i
$335$	−4.14411	+	10.0048i	−0.226417	+	0.546618i
$336$	−9.15536	−	5.22718i	−0.499466	−	0.285166i
$337$	−3.21050	−	7.75082i	−0.174887	−	0.422214i	0.811994	−	0.583666i	$-0.198382\pi$
$337$	−3.21050	−	7.75082i	−0.174887	−	0.422214i	−0.986881	+	0.161452i	$0.948382\pi$
$338$	3.32760	+	17.3611i	0.180998	+	0.944320i
$339$	1.62696	+	16.5188i	0.0883642	+	0.897176i
$340$	5.25212	−	9.50461i	0.284836	−	0.515460i
$341$	−1.21662	+	2.27613i	−0.0658835	+	0.123259i
$342$	3.40558	−	6.26585i	0.184153	−	0.338818i
$343$	−3.62680	−	18.2331i	−0.195829	−	0.984497i
$344$	3.52510	−	6.27546i	0.190061	−	0.338350i
$345$	−7.41247	−	1.47443i	−0.399074	−	0.0793807i
$346$	−0.472184	−	5.16319i	−0.0253848	−	0.277575i
$347$	2.87953	−	29.2363i	0.154581	−	1.56949i	−0.534730	−	0.845023i	$-0.679587\pi$
$347$	2.87953	−	29.2363i	0.154581	−	1.56949i	0.689312	−	0.724465i	$-0.257913\pi$
$348$	−1.06571	−	5.77786i	−0.0571279	−	0.309726i
$349$	−4.26957	+	14.0749i	−0.228545	+	0.753412i	0.765402	+	0.643552i	$0.222540\pi$
$349$	−4.26957	+	14.0749i	−0.228545	+	0.753412i	−0.993947	+	0.109860i	$0.964960\pi$
$350$	−0.0484179	−	0.119237i	−0.00258804	−	0.00637350i
$351$	−0.500191	+	0.500191i	−0.0266982	+	0.0266982i
$352$	−1.31114	−	4.93582i	−0.0698843	−	0.263080i
$353$	−4.58788	−	4.58788i	−0.244188	−	0.244188i	0.574392	−	0.818580i	$-0.305239\pi$
$353$	−4.58788	−	4.58788i	−0.244188	−	0.244188i	−0.818580	+	0.574392i	$0.805239\pi$
$354$	−6.02562	+	14.2648i	−0.320258	+	0.758168i
$355$	−25.7118	−	7.79959i	−1.36464	−	0.413959i
$356$	−23.6290	−	5.04381i	−1.25233	−	0.267321i
$357$	−6.39108	−	0.629467i	−0.338252	−	0.0333149i
$358$	6.32692	+	5.26666i	0.334388	+	0.278352i
$359$	0.123415	−	0.620451i	0.00651361	−	0.0327462i	−0.977392	−	0.211436i	$-0.932186\pi$
$359$	0.123415	−	0.620451i	0.00651361	−	0.0327462i	0.983905	+	0.178690i	$0.0571859\pi$
$360$	0.486371	+	6.28389i	0.0256340	+	0.331190i
$361$	6.30588	−	1.25432i	0.331888	−	0.0660167i
$362$	24.7060	−	7.30667i	1.29852	−	0.384030i
$363$	8.98233	+	4.80115i	0.471450	+	0.251995i
$364$	−0.417220	+	3.70534i	−0.0218683	+	0.194213i
$365$	−24.3080	+	2.39413i	−1.27234	+	0.125315i
$366$	5.70227	+	3.86795i	0.298062	+	0.202181i
$367$	−12.9690	+	5.37194i	−0.676976	+	0.280413i	−0.694562	−	0.719433i	$-0.744402\pi$
$367$	−12.9690	+	5.37194i	−0.676976	+	0.280413i	0.0175859	+	0.999845i	$0.494402\pi$
$368$	−13.3745	+	2.27441i	−0.697195	+	0.118562i
$369$	−5.50194	−	2.27898i	−0.286420	−	0.118639i
$370$	−14.5351	−	22.0853i	−0.755643	−	1.14816i
$371$	9.89615	−	12.0585i	0.513782	−	0.626046i
$372$	1.73588	−	5.44762i	0.0900012	−	0.282446i
$373$	−8.09392	−	26.6821i	−0.419087	−	1.38155i	−0.871788	−	0.489883i	$-0.837039\pi$
$373$	−8.09392	−	26.6821i	−0.419087	−	1.38155i	0.452700	−	0.891663i	$-0.350461\pi$
$374$	−1.95674	−	2.41851i	−0.101181	−	0.125058i
$375$	−6.23272	+	9.32793i	−0.321857	+	0.481692i
$376$	0.540385	+	1.38596i	0.0278682	+	0.0714752i
$377$	−1.72782	+	1.15449i	−0.0889872	+	0.0594594i
$378$	3.29939	−	1.73408i	0.169702	−	0.0891913i
$379$	−3.31635	+	2.72166i	−0.170350	+	0.139802i	−0.715705	−	0.698402i	$-0.753895\pi$
$379$	−3.31635	+	2.72166i	−0.170350	+	0.139802i	0.545356	+	0.838205i	$0.316395\pi$
$380$	−16.1116	+	15.6682i	−0.826509	+	0.803761i
$381$	−7.64075	−	14.2948i	−0.391447	−	0.732346i
$382$	0.219975	−	31.5309i	0.0112549	−	1.61326i
$383$	−20.3571			−1.04020			−0.520099	−	0.854106i	$-0.674105\pi$
$383$	−20.3571			−1.04020			−0.520099	+	0.854106i	$0.674105\pi$
$384$	4.83982	+	10.2262i	0.246981	+	0.521856i
$385$	5.30217			0.270224
$386$	−0.192810	+	27.6371i	−0.00981376	+	1.40669i
$387$	1.19961	+	2.24431i	0.0609795	+	0.114085i
$388$	−19.8647	−	20.4269i	−1.00848	−	1.03702i
$389$	−15.8857	+	13.0371i	−0.805439	+	0.661007i	−0.944220	−	0.329316i	$-0.893182\pi$
$389$	−15.8857	+	13.0371i	−0.805439	+	0.661007i	0.138780	+	0.990323i	$0.455682\pi$
$390$	1.97325	−	1.03709i	0.0999193	−	0.0525151i
$391$	−6.87136	+	4.59129i	−0.347499	+	0.232192i
$392$	−0.0608173	+	0.138551i	−0.00307174	+	0.00699790i
$393$	−11.9000	+	17.8095i	−0.600273	+	0.898372i
$394$	3.02886	+	3.74363i	0.152592	+	0.188601i
$395$	−5.43885	−	17.9295i	−0.273658	−	0.902130i
$396$	1.72037	+	0.548193i	0.0864517	+	0.0275477i
$397$	−19.2215	+	23.4215i	−0.964701	+	1.17549i	0.0197448	+	0.999805i	$0.493715\pi$
$397$	−19.2215	+	23.4215i	−0.964701	+	1.17549i	−0.984446	+	0.175687i	$0.943785\pi$
$398$	4.69923	+	7.14023i	0.235551	+	0.357908i
$399$	12.2791	+	5.08617i	0.614724	+	0.254627i
$400$	−0.0307122	+	0.134649i	−0.00153561	+	0.00673244i
$401$	3.24389	−	1.34366i	0.161992	−	0.0670994i	−0.300214	−	0.953872i	$-0.597058\pi$
$401$	3.24389	−	1.34366i	0.161992	−	0.0670994i	0.462206	+	0.886773i	$0.347058\pi$
$402$	−5.68765	−	3.85803i	−0.283674	−	0.192421i
$403$	−2.01248	+	0.198212i	−0.100249	+	0.00987363i
$404$	−2.35682	−	0.265377i	−0.117256	−	0.0132030i
$405$	−1.96522	−	1.05043i	−0.0976523	−	0.0521963i
$406$	10.5001	−	3.10533i	0.521109	−	0.154115i
$407$	−7.42877	+	1.47767i	−0.368230	+	0.0732456i
$408$	5.23477	+	4.48264i	0.259160	+	0.221924i
$409$	2.06812	−	10.3971i	0.102262	−	0.514104i	−0.895370	−	0.445323i	$-0.853089\pi$
$409$	2.06812	−	10.3971i	0.102262	−	0.514104i	0.997632	−	0.0687815i	$-0.0219111\pi$
$410$	14.4237	+	12.0066i	0.712337	+	0.592964i
$411$	−9.34939	−	0.920835i	−0.461171	−	0.0454214i
$412$	−3.60794	+	16.9023i	−0.177750	+	0.832716i
$413$	−27.6167	−	8.37744i	−1.35893	−	0.412227i
$414$	1.86641	−	4.41847i	0.0917289	−	0.217156i
$415$	3.42891	+	3.42891i	0.168318	+	0.168318i
$416$	2.64487	−	3.00281i	0.129676	−	0.147225i
$417$	3.56680	−	3.56680i	0.174667	−	0.174667i
$418$	2.42229	+	5.96529i	0.118478	+	0.291772i
$419$	−6.09950	+	20.1074i	−0.297980	+	0.982308i	0.672291	+	0.740287i	$0.265310\pi$
$419$	−6.09950	+	20.1074i	−0.297980	+	0.982308i	−0.970271	+	0.242021i	$0.922190\pi$
$420$	−11.5512	+	2.13059i	−0.563643	+	0.103962i
$421$	1.85898	−	18.8745i	0.0906011	−	0.919889i	−0.837221	−	0.546865i	$-0.815821\pi$
$421$	1.85898	−	18.8745i	0.0906011	−	0.919889i	0.927822	−	0.373024i	$-0.121679\pi$
$422$	−1.82267	−	19.9304i	−0.0887263	−	0.970195i
$423$	−0.515833	−	0.102606i	−0.0250806	−	0.00498885i
$424$	−16.1179	+	4.52320i	−0.782754	+	0.219666i
$425$	0.0164127	+	0.0825120i	0.000796131	+	0.00400242i
$426$	8.14311	−	14.9823i	0.394535	−	0.725896i
$427$	−6.05335	+	11.3250i	−0.292942	+	0.548056i
$428$	33.1858	+	18.3380i	1.60410	+	0.886402i
$429$	−0.0625955	−	0.635543i	−0.00302214	−	0.0306843i
$430$	−1.50962	−	7.87614i	−0.0728003	−	0.379821i
$431$	−12.4388	−	30.0299i	−0.599156	−	1.44649i	−0.874442	−	0.485129i	$-0.838773\pi$
$431$	−12.4388	−	30.0299i	−0.599156	−	1.44649i	0.275286	−	0.961362i	$-0.411227\pi$
$432$	−3.96825	−	0.502986i	−0.190922	−	0.0241999i
$433$	7.76244	−	18.7402i	0.373039	−	0.900596i	−0.620193	−	0.784449i	$-0.712946\pi$
$433$	7.76244	−	18.7402i	0.373039	−	0.900596i	0.993232	−	0.116147i	$-0.0370543\pi$
$434$	10.4360	+	2.15165i	0.500945	+	0.103282i
$435$	−5.06019	−	4.15279i	−0.242618	−	0.199111i
$436$	36.3067	−	3.06507i	1.73877	−	0.146790i
$437$	16.3667	−	4.96479i	0.782926	−	0.237498i
$438$	1.62703	−	15.4161i	0.0777423	−	0.736612i
$439$	−11.8419	−	7.91251i	−0.565183	−	0.377643i	0.239907	−	0.970796i	$-0.422883\pi$
$439$	−11.8419	−	7.91251i	−0.565183	−	0.377643i	−0.805090	+	0.593153i	$0.797883\pi$
$440$	−4.66391	−	3.25954i	−0.222343	−	0.155392i
$441$	−0.0297212	−	0.0444809i	−0.00141530	−	0.00211814i
$442$	0.723839	−	2.32760i	0.0344295	−	0.110712i
$443$	−8.19855	−	9.98997i	−0.389525	−	0.474638i	0.540917	−	0.841076i	$-0.318077\pi$
$443$	−8.19855	−	9.98997i	−0.389525	−	0.474638i	−0.930442	+	0.366438i	$0.880577\pi$
$444$	15.5904	−	6.20436i	0.739889	−	0.294446i
$445$	−23.7411	+	12.6899i	−1.12544	+	0.601558i
$446$	−15.7385	+	15.5204i	−0.745239	+	0.734913i
$447$			5.45335i			0.257935i
$448$	−18.0064	+	10.9703i	−0.850720	+	0.518298i
$449$		−	22.5429i		−	1.06387i	−0.846786	−	0.531934i	$-0.821466\pi$
$449$		−	22.5429i		−	1.06387i	0.846786	−	0.531934i	$-0.178534\pi$
$450$	−0.0342850	−	0.0347668i	−0.00161621	−	0.00163892i
$451$	4.74156	−	2.53442i	0.223271	−	0.119341i
$452$	30.4902	+	13.1308i	1.43414	+	0.617620i
$453$	11.5199	+	14.0370i	0.541250	+	0.659515i
$454$	−4.55921	−	1.41783i	−0.213974	−	0.0665419i
$455$	2.30809	+	3.45430i	0.108205	+	0.161940i
$456$	−7.67422	−	12.0225i	−0.359378	−	0.563007i
$457$	−11.8613	−	7.92550i	−0.554850	−	0.370739i	0.246308	−	0.969192i	$-0.420782\pi$
$457$	−11.8613	−	7.92550i	−0.554850	−	0.370739i	−0.801158	+	0.598453i	$0.795782\pi$
$458$	−34.8952	−	3.68286i	−1.63055	−	0.172089i
$459$	−2.33170	+	0.707313i	−0.108834	+	0.0330146i
$460$	−9.75118	+	11.5494i	−0.454651	+	0.538494i
$461$	10.4337	+	8.56271i	0.485945	+	0.398805i	0.845213	−	0.534429i	$-0.179473\pi$
$461$	10.4337	+	8.56271i	0.485945	+	0.398805i	−0.359268	+	0.933235i	$0.616973\pi$
$462$	−0.679493	+	3.29571i	−0.0316129	+	0.153330i
$463$	6.78388	−	16.3777i	0.315274	−	0.761138i	−0.684219	−	0.729277i	$-0.739857\pi$
$463$	6.78388	−	16.3777i	0.315274	−	0.761138i	0.999492	−	0.0318609i	$-0.0101433\pi$
$464$	−11.1451	−	3.72345i	−0.517398	−	0.172857i
$465$	−2.43779	−	5.88535i	−0.113050	−	0.272927i
$466$	−27.3473	+	5.24166i	−1.26684	+	0.242815i
$467$	−1.97234	−	20.0255i	−0.0912691	−	0.926671i	−0.926380	−	0.376589i	$-0.877097\pi$
$467$	−1.97234	−	20.0255i	−0.0912691	−	0.926671i	0.835111	−	0.550081i	$-0.185403\pi$
$468$	0.391752	+	1.35943i	0.0181087	+	0.0628398i
$469$	6.03783	−	11.2960i	0.278801	−	0.521600i
$470$	1.45622	+	0.791477i	0.0671704	+	0.0365081i
$471$	−0.229578	−	1.15417i	−0.0105784	−	0.0531812i
$472$	19.1422	+	24.3465i	0.881091	+	1.12064i
$473$	−2.25329	−	0.448207i	−0.103606	−	0.0206086i
$474$	11.8416	−	1.08293i	0.543901	−	0.0497408i
$475$	0.0170658	−	0.173272i	0.000783031	−	0.00795025i
$476$	−7.28406	+	10.5788i	−0.333864	+	0.484879i
$477$	1.71810	−	5.66382i	0.0786664	−	0.259328i
$478$	21.9772	−	8.92414i	1.00521	−	0.408181i
$479$	−1.40366	+	1.40366i	−0.0641350	+	0.0641350i	−0.738447	−	0.674312i	$-0.764440\pi$
$479$	−1.40366	+	1.40366i	−0.0641350	+	0.0641350i	0.674312	+	0.738447i	$0.264440\pi$
$480$	11.4705	+	5.22707i	0.523555	+	0.238582i
$481$	−4.19651	−	4.19651i	−0.191344	−	0.191344i
$482$	26.9721	+	11.3933i	1.22854	+	0.518950i
$483$	8.55414	+	2.59487i	0.389227	+	0.118071i
$484$	17.0932	−	11.0795i	0.776964	−	0.503614i
$485$	−31.5934	−	3.11168i	−1.43458	−	0.141294i
$486$	0.904772	−	1.08692i	0.0410413	−	0.0493035i
$487$	−0.844540	+	4.24579i	−0.0382697	+	0.192395i	−0.995191	−	0.0979522i	$-0.968771\pi$
$487$	−0.844540	+	4.24579i	−0.0382697	+	0.192395i	0.956921	+	0.290347i	$0.0937708\pi$
$488$	12.2868	−	6.24041i	0.556196	−	0.282490i
$489$	−8.21544	+	1.63415i	−0.371515	+	0.0738989i
$490$	0.0478114	+	0.161665i	0.00215990	+	0.00730326i
$491$	24.3924	+	13.0380i	1.10081	+	0.588396i	0.918730	−	0.394887i	$-0.129216\pi$
$491$	24.3924	+	13.0380i	1.10081	+	0.588396i	0.182082	+	0.983283i	$0.441716\pi$
$492$	−9.31149	+	7.42676i	−0.419794	+	0.334824i
$493$	−7.12349	+	0.701602i	−0.320826	+	0.0315986i
$494$	−2.83187	+	4.17485i	−0.127412	+	0.187835i
$495$	1.85860	−	0.769858i	0.0835379	−	0.0346025i
$496$	−7.85702	−	8.30824i	−0.352791	−	0.373051i
$497$	29.3607	+	12.1616i	1.31701	+	0.545522i
$498$	−2.57076	+	1.69190i	−0.115198	+	0.0758160i
$499$	17.1960	−	20.9534i	0.769798	−	0.938001i	−0.229580	−	0.973290i	$-0.573735\pi$
$499$	17.1960	−	20.9534i	0.769798	−	0.938001i	0.999377	+	0.0352889i	$0.0112351\pi$
$500$	10.2997	+	19.9335i	0.460617	+	0.891453i
$501$	4.95653	+	16.3395i	0.221441	+	0.729994i
$502$	21.5864	−	17.4649i	0.963448	−	0.779497i
$503$	−11.3610	+	17.0029i	−0.506562	+	0.758124i	−0.993317	−	0.115415i	$-0.963180\pi$
$503$	−11.3610	+	17.0029i	−0.506562	+	0.758124i	0.486755	+	0.873538i	$0.338180\pi$
$504$	0.156008	−	7.45303i	0.00694916	−	0.331984i
$505$	−2.19715	+	1.46809i	−0.0977717	+	0.0653290i
$506$	2.01458	+	3.83310i	0.0895590	+	0.170402i
$507$	−9.66234	+	7.92967i	−0.429119	+	0.352169i
$508$	−32.4143	−	0.452298i	−1.43815	−	0.0200675i
$509$	10.1610	+	19.0099i	0.450380	+	0.842601i	0.999974	+	0.00716942i	$0.00228212\pi$
$509$	10.1610	+	19.0099i	0.450380	+	0.842601i	−0.549595	+	0.835431i	$0.685218\pi$
$510$	7.67843	+	0.0535685i	0.340007	+	0.00237205i
$511$	28.8901			1.27802
$512$	22.5828	+	1.41978i	0.998030	+	0.0627461i
$513$	5.04276			0.222643
$514$	−8.68588	−	0.0605969i	−0.383118	−	0.00267281i
$515$	9.07732	+	16.9825i	0.399995	+	0.748337i
$516$	5.08909	+	0.0710114i	0.224035	+	0.00312610i
$517$	0.367038	−	0.301220i	0.0161423	−	0.0132477i
$518$	14.5486	+	27.6813i	0.639228	+	1.21625i
$519$	3.04830	−	2.03681i	0.133806	−	0.0894060i
$520$	0.0933029	−	4.45739i	0.00409160	−	0.195470i
$521$	1.65462	−	2.47631i	0.0724902	−	0.108489i	−0.793453	−	0.608631i	$-0.791719\pi$
$521$	1.65462	−	2.47631i	0.0724902	−	0.108489i	0.865943	+	0.500142i	$0.166719\pi$
$522$	3.22976	−	2.61310i	0.141363	−	0.114372i
$523$	6.31700	+	20.8244i	0.276223	+	0.910586i	0.979802	+	0.199969i	$0.0640842\pi$
$523$	6.31700	+	20.8244i	0.276223	+	0.910586i	−0.703579	+	0.710617i	$0.748416\pi$
$524$	19.6649	+	38.0584i	0.859067	+	1.66259i
$525$	0.0577294	−	0.0703435i	0.00251952	−	0.00307004i
$526$	12.9166	−	8.50086i	0.563190	−	0.370655i
$527$	−6.43546	−	2.66566i	−0.280333	−	0.116118i
$528$	2.62375	−	2.48126i	0.114184	−	0.107983i
$529$	−10.6217	+	4.39965i	−0.461813	+	0.191289i
$530$	−10.4703	+	15.4357i	−0.454801	+	0.670484i
$531$	−10.8970	+	1.07326i	−0.472890	+	0.0465756i
$532$	20.7811	−	16.5749i	0.900977	−	0.718612i
$533$	3.71519	+	1.98581i	0.160923	+	0.0860151i
$534$	−4.84523	−	16.3832i	−0.209674	−	0.708969i
$535$	41.4324	−	8.24142i	1.79128	−	0.356308i
$536$	−12.2553	+	6.22441i	−0.529347	+	0.268853i
$537$	−1.13562	+	5.70913i	−0.0490055	+	0.246367i
$538$	−21.5278	+	25.8616i	−0.928128	+	1.11497i
$539$	0.0480642	+	0.00473391i	0.00207027	+	0.000203904i
$540$	−3.73977	+	2.42405i	−0.160934	+	0.104314i
$541$	−11.8171	−	3.58468i	−0.508057	−	0.154117i	0.0258412	−	0.999666i	$-0.491774\pi$
$541$	−11.8171	−	3.58468i	−0.508057	−	0.154117i	−0.533899	+	0.845549i	$0.679274\pi$
$542$	−36.8336	−	15.5589i	−1.58214	−	0.668312i
$543$	12.8819	+	12.8819i	0.552816	+	0.552816i
$544$	12.9106	−	4.82744i	0.553537	−	0.206975i
$545$	28.7054	−	28.7054i	1.22960	−	1.22960i
$546$	−2.44291	+	0.991975i	−0.104547	+	0.0424526i
$547$	−0.264155	+	0.870804i	−0.0112945	+	0.0372329i	−0.962406	−	0.271613i	$-0.912443\pi$
$547$	−0.264155	+	0.870804i	−0.0112945	+	0.0372329i	0.951112	+	0.308846i	$0.0999428\pi$
$548$	−10.6557	+	15.4755i	−0.455189	+	0.661082i
$549$	−0.477560	+	4.84875i	−0.0203818	+	0.206940i
$550$	0.0438988	−	0.00401464i	0.00187185	−	0.000171185i
$551$	14.5293	+	2.89005i	0.618967	+	0.123120i
$552$	−5.92920	−	7.54121i	−0.252364	−	0.320975i
$553$	4.32336	+	21.7350i	0.183848	+	0.924266i
$554$	24.7107	+	13.4306i	1.04986	+	0.570612i
$555$	8.81290	−	16.4878i	0.374087	−	0.699867i
$556$	−2.79354	−	9.69396i	−0.118472	−	0.411115i
$557$	2.68026	+	27.2131i	0.113566	+	1.15306i	0.867960	+	0.496634i	$0.165431\pi$
$557$	2.68026	+	27.2131i	0.113566	+	1.15306i	−0.754394	+	0.656422i	$0.772069\pi$
$558$	3.97061	−	0.761047i	0.168089	−	0.0322177i
$559$	−0.688879	−	1.66310i	−0.0291365	−	0.0703417i
$560$	−7.44402	+	22.2816i	−0.314567	+	0.941569i
$561$	0.841817	−	2.03233i	0.0355416	−	0.0858049i
$562$	4.86211	−	23.5824i	0.205096	−	0.994766i
$563$	3.04192	+	2.49644i	0.128202	+	0.105212i	0.696309	−	0.717742i	$-0.254824\pi$
$563$	3.04192	+	2.49644i	0.128202	+	0.105212i	−0.568107	+	0.822954i	$0.692324\pi$
$564$	−0.678584	+	0.803722i	−0.0285735	+	0.0338428i
$565$	35.3948	−	10.7369i	1.48907	−	0.451704i
$566$	10.6944	+	1.12869i	0.449517	+	0.0474422i
$567$	2.19144	+	1.46427i	0.0920318	+	0.0614937i
$568$	−18.3499	−	28.7472i	−0.769944	−	1.20621i
$569$	16.1102	+	24.1106i	0.675374	+	1.01077i	0.997936	+	0.0642199i	$0.0204559\pi$
$569$	16.1102	+	24.1106i	0.675374	+	1.01077i	−0.322562	+	0.946548i	$0.604544\pi$
$570$	−15.1746	−	4.71902i	−0.635595	−	0.197658i
$571$	−14.0031	−	17.0628i	−0.586012	−	0.714057i	0.392615	−	0.919703i	$-0.371571\pi$
$571$	−14.0031	−	17.0628i	−0.586012	−	0.714057i	−0.978627	+	0.205646i	$0.934071\pi$
$572$	−1.17308	−	0.505193i	−0.0490489	−	0.0211232i
$573$	19.6635	−	10.5104i	0.821456	−	0.439077i
$574$	−15.5859	−	15.8049i	−0.650544	−	0.659685i
$575$		−	0.117102i		−	0.00488349i
$576$	−4.71902	+	6.45994i	−0.196626	+	0.269164i
$577$		−	22.0932i		−	0.919751i	−0.887983	−	0.459876i	$-0.847894\pi$
$577$		−	22.0932i		−	0.919751i	0.887983	−	0.459876i	$-0.152106\pi$
$578$	−11.1398	+	10.9854i	−0.463354	+	0.456934i
$579$	−17.2353	+	9.21244i	−0.716273	+	0.382856i
$580$	−12.1643	+	4.84091i	−0.505096	+	0.201008i
$581$	−3.63858	−	4.43363i	−0.150954	−	0.183938i
$582$	5.98295	−	19.2389i	0.248001	−	0.797480i
$583$	2.96862	+	4.44285i	0.122947	+	0.184004i
$584$	−25.4124	−	17.7603i	−1.05157	−	0.734928i
$585$	1.31062	+	0.875729i	0.0541875	+	0.0362070i
$586$	−1.35206	+	12.8109i	−0.0558532	+	0.529211i
$587$	−6.32961	+	1.92007i	−0.261251	+	0.0792497i	−0.418193	−	0.908358i	$-0.637336\pi$
$587$	−6.32961	+	1.92007i	−0.261251	+	0.0792497i	0.156942	+	0.987608i	$0.449836\pi$
$588$	−0.106614	+	0.00900056i	−0.00439670	+	0.000371177i
$589$	11.1437	+	9.14541i	0.459169	+	0.376830i
$590$	33.7956	+	6.96780i	1.39134	+	0.286860i
$591$	−1.30306	+	3.14585i	−0.0536005	+	0.129403i
$592$	4.21996	−	33.2929i	0.173439	−	1.36833i
$593$	0.493025	+	1.19027i	0.0202461	+	0.0488784i	0.933679	−	0.358110i	$-0.116579\pi$
$593$	0.493025	+	1.19027i	0.0202461	+	0.0488784i	−0.913433	+	0.406989i	$0.866579\pi$
$594$	0.240339	+	1.25392i	0.00986125	+	0.0514491i
$595$	1.40266	+	14.2415i	0.0575036	+	0.583843i
$596$	9.54618	+	5.27509i	0.391027	+	0.216076i
$597$	−2.84924	+	5.33055i	−0.116611	+	0.218165i
$598$	−1.62025	+	2.98106i	−0.0662569	+	0.121905i
$599$	0.578558	+	2.90861i	0.0236392	+	0.118842i	0.990803	−	0.135311i	$-0.0432033\pi$
$599$	0.578558	+	2.90861i	0.0236392	+	0.118842i	−0.967164	+	0.254153i	$0.918203\pi$
$600$	−0.0940241	+	0.0263862i	−0.00383852	+	0.00107721i
$601$	−5.78714	−	1.15113i	−0.236062	−	0.0469557i	0.0756412	−	0.997135i	$-0.475900\pi$
$601$	−5.78714	−	1.15113i	−0.236062	−	0.0469557i	−0.311704	+	0.950179i	$0.600900\pi$
$602$	0.863845	+	9.44587i	0.0352077	+	0.384985i
$603$	0.476336	−	4.83632i	0.0193979	−	0.196950i
$604$	35.7153	−	6.58757i	1.45323	−	0.268044i
$605$	6.58815	−	21.7182i	0.267846	−	0.882971i
$606$	−0.630956	−	1.55384i	−0.0256309	−	0.0631203i
$607$	−20.9435	+	20.9435i	−0.850070	+	0.850070i	−0.990141	−	0.140072i	$-0.955267\pi$
$607$	−20.9435	+	20.9435i	−0.850070	+	0.850070i	0.140072	+	0.990141i	$0.455267\pi$
$608$	−28.4690	+	1.80430i	−1.15457	+	0.0731739i
$609$	5.47481	+	5.47481i	0.221851	+	0.221851i
$610$	5.97454	−	14.1439i	0.241902	−	0.572670i
$611$	0.356017	+	0.107997i	0.0144029	+	0.00436907i
$612$	−1.01732	+	4.76587i	−0.0411225	+	0.192649i
$613$	−31.1548	−	3.06848i	−1.25833	−	0.123935i	−0.553221	−	0.833035i	$-0.686601\pi$
$613$	−31.1548	−	3.06848i	−1.25833	−	0.123935i	−0.705108	+	0.709100i	$0.749101\pi$
$614$	−29.9717	−	24.9491i	−1.20956	−	1.00686i
$615$	−2.58891	+	13.0153i	−0.104395	+	0.524829i
$616$	5.11191	+	4.37744i	0.205965	+	0.176372i
$617$	39.6631	−	7.88947i	1.59677	−	0.317618i	0.685074	−	0.728474i	$-0.259770\pi$
$617$	39.6631	−	7.88947i	1.59677	−	0.317618i	0.911701	+	0.410855i	$0.134770\pi$
$618$	−11.7192	+	3.46589i	−0.471416	+	0.139418i
$619$	39.1015	+	20.9002i	1.57162	+	0.840049i	0.999807	+	0.0196655i	$0.00626014\pi$
$619$	39.1015	+	20.9002i	1.57162	+	0.840049i	0.571814	+	0.820383i	$0.306240\pi$
$620$	−12.6605	−	1.42557i	−0.508458	−	0.0572523i
$621$	3.37530	−	0.332438i	0.135446	−	0.0133403i
$622$	−13.2518	−	8.98895i	−0.531351	−	0.360424i
$623$	29.4164	−	12.1847i	1.17854	−	0.488168i
$624$	2.75866	+	0.629226i	0.110435	+	0.0251892i
$625$	22.9364	+	9.50057i	0.917456	+	0.380023i
$626$	17.4184	+	26.4664i	0.696180	+	1.05781i
$627$	−2.88813	+	3.51920i	−0.115341	+	0.140543i
$628$	−2.24246	−	0.714558i	−0.0894839	−	0.0285140i
$629$	−5.93422	−	19.5625i	−0.236613	−	0.780009i
$630$	−5.22419	−	6.45703i	−0.208137	−	0.257254i
$631$	−4.99796	+	7.47998i	−0.198966	+	0.297773i	−0.917514	−	0.397704i	$-0.869807\pi$
$631$	−4.99796	+	7.47998i	−0.198966	+	0.297773i	0.718548	+	0.695477i	$0.244807\pi$
$632$	9.55877	−	21.7764i	0.380228	−	0.866218i
$633$	11.7667	−	7.86227i	0.467685	−	0.312497i
$634$	12.9822	−	6.82312i	0.515589	−	0.270981i
$635$	−27.9200	+	22.9133i	−1.10797	+	0.909288i
$636$	−8.25267	−	8.48624i	−0.327240	−	0.336501i
$637$	0.0178388	+	0.0333740i	0.000706797	+	0.00132232i
$638$	−0.0261657	+	3.75056i	−0.00103591	+	0.148486i
$639$	12.0578			0.476998
$640$	20.2456	−	15.0231i	0.800279	−	0.593841i
$641$	−20.5968			−0.813525			−0.406762	−	0.913534i	$-0.633342\pi$
$641$	−20.5968			−0.813525			−0.406762	+	0.913534i	$0.633342\pi$
$642$	−0.187037	+	26.8096i	−0.00738176	+	1.05809i
$643$	−13.7497	−	25.7238i	−0.542234	−	1.01445i	−0.992580	−	0.121594i	$-0.961199\pi$
$643$	−13.7497	−	25.7238i	−0.542234	−	1.01445i	0.450346	−	0.892854i	$-0.351301\pi$
$644$	12.8169	−	12.4641i	0.505056	−	0.491155i
$645$	4.38347	−	3.59742i	0.172599	−	0.141648i
$646$	−15.3818	+	8.08428i	−0.605188	+	0.318072i
$647$	−13.1490	+	8.78590i	−0.516941	+	0.345409i	−0.786516	−	0.617570i	$-0.788117\pi$
$647$	−13.1490	+	8.78590i	−0.516941	+	0.345409i	0.269574	+	0.962980i	$0.413117\pi$
$648$	−1.02747	−	2.63521i	−0.0403628	−	0.103521i
$649$	5.49204	−	8.21942i	0.215581	−	0.322640i
$650$	0.0217251	+	0.0268519i	0.000852128	+	0.00105322i
$651$	2.18718	+	7.21016i	0.0857222	+	0.282588i
$652$	−5.08627	+	15.9620i	−0.199194	+	0.625120i
$653$	13.6473	−	16.6293i	0.534059	−	0.650753i	−0.434166	−	0.900833i	$-0.642957\pi$
$653$	13.6473	−	16.6293i	0.534059	−	0.650753i	0.968225	+	0.250080i	$0.0804568\pi$
$654$	14.1639	+	21.5213i	0.553853	+	0.841551i
$655$	44.0963	+	18.2653i	1.72298	+	0.713683i
$656$	3.99357	+	23.4839i	0.155923	+	0.916892i
$657$	10.1270	−	4.19475i	0.395092	−	0.163653i
$658$	−1.62233	−	1.10046i	−0.0632451	−	0.0429002i
$659$	16.1287	−	1.58854i	0.628285	−	0.0618807i	0.221137	−	0.975243i	$-0.429023\pi$
$659$	16.1287	−	1.58854i	0.628285	−	0.0618807i	0.407148	+	0.913362i	$0.366523\pi$
$660$	0.450197	−	3.99821i	0.0175239	−	0.155630i
$661$	−19.9081	−	10.6411i	−0.774334	−	0.413890i	0.0363761	−	0.999338i	$-0.488419\pi$
$661$	−19.9081	−	10.6411i	−0.774334	−	0.413890i	−0.810710	+	0.585448i	$0.800919\pi$
$662$	3.42313	−	1.01237i	0.133044	−	0.0393469i
$663$	1.69049	−	0.336259i	0.0656531	−	0.0130592i
$664$	0.474982	+	6.13675i	0.0184329	+	0.238152i
$665$	5.77786	−	29.0473i	0.224056	−	1.12641i
$666$	9.11902	+	7.59087i	0.353355	+	0.294140i
$667$	9.91547	+	0.976589i	0.383929	+	0.0378137i
$668$	33.3970	+	7.12888i	1.29217	+	0.275825i
$669$	−14.9568	−	4.53710i	−0.578264	−	0.175414i
$670$	−5.95922	+	14.1076i	−0.230225	+	0.545025i
$671$	−3.11030	−	3.11030i	−0.120072	−	0.120072i
$672$	−12.8957	−	7.48250i	−0.497464	−	0.288644i
$673$	−7.33024	+	7.33024i	−0.282560	+	0.282560i	−0.834129	−	0.551569i	$-0.814029\pi$
$673$	−7.33024	+	7.33024i	−0.282560	+	0.282560i	0.551569	+	0.834129i	$0.314029\pi$
$674$	−4.46375	−	10.9927i	−0.171937	−	0.423424i
$675$	0.0100226	−	0.0330400i	0.000385769	−	0.00127171i
$676$	4.53454	+	24.5845i	0.174405	+	0.945559i
$677$	−2.07111	+	21.0283i	−0.0795993	+	0.808185i	0.869652	+	0.493666i	$0.164343\pi$
$677$	−2.07111	+	21.0283i	−0.0795993	+	0.808185i	−0.949251	+	0.314519i	$0.898157\pi$
$678$	2.13783	+	23.3766i	0.0821030	+	0.897771i
$679$	36.8272	+	7.32539i	1.41330	+	0.281123i
$680$	7.52121	−	13.3894i	0.288425	−	0.513460i
$681$	−0.658651	−	3.31126i	−0.0252396	−	0.126888i
$682$	−1.74297	+	3.20685i	−0.0667418	+	0.122797i
$683$	−9.16569	+	17.1478i	−0.350715	+	0.656142i	−0.993987	−	0.109496i	$-0.965076\pi$
$683$	−9.16569	+	17.1478i	−0.350715	+	0.656142i	0.643272	+	0.765638i	$0.277576\pi$
$684$	4.87792	−	8.82743i	0.186512	−	0.337525i
$685$	2.05193	+	20.8336i	0.0784001	+	0.796010i
$686$	−4.94905	−	25.8207i	−0.188956	−	0.985839i
$687$	−9.49502	−	22.9230i	−0.362258	−	0.874567i
$688$	5.04704	−	8.83985i	0.192417	−	0.337016i
$689$	−1.60219	+	3.86804i	−0.0610387	+	0.147360i
$690$	−10.4680	−	2.15824i	−0.398510	−	0.0821628i
$691$	−28.4980	−	23.3877i	−1.08412	−	0.889711i	−0.0897763	−	0.995962i	$-0.528615\pi$
$691$	−28.4980	−	23.3877i	−1.08412	−	0.889711i	−0.994339	+	0.106251i	$0.966115\pi$
$692$	−0.616813	−	7.30633i	−0.0234477	−	0.277745i
$693$	−2.27698	+	0.690713i	−0.0864952	+	0.0262380i
$694$	4.36061	−	41.3170i	0.165527	−	1.56837i
$695$	−9.34590	−	6.24473i	−0.354510	−	0.236876i
$696$	−1.45010	−	8.18144i	−0.0549658	−	0.310117i
$697$	8.06172	+	12.0652i	0.305359	+	0.457002i
$698$	−6.17681	+	19.8623i	−0.233796	+	0.751800i
$699$	−12.4909	−	15.2202i	−0.472448	−	0.575680i
$700$	−0.0672952	−	0.169100i	−0.00254352	−	0.00639140i
$701$	36.0366	−	19.2620i	1.36108	−	0.727514i	0.380716	−	0.924692i	$-0.375678\pi$
$701$	36.0366	−	19.2620i	1.36108	−	0.727514i	0.980368	+	0.197178i	$0.0631777\pi$
$702$	−0.712294	+	0.702424i	−0.0268838	+	0.0265113i
$703$			42.3078i			1.59567i
$704$	−1.80550	−	6.99307i	−0.0680472	−	0.263561i
$705$			1.17197i			0.0441388i
$706$	−6.44283	−	6.53335i	−0.242479	−	0.245886i
$707$	2.75642	−	1.47334i	0.103666	−	0.0554105i
$708$	−8.66204	+	20.1136i	−0.325540	+	0.755915i
$709$	−4.02812	−	4.90828i	−0.151279	−	0.184334i	0.691856	−	0.722035i	$-0.256793\pi$
$709$	−4.02812	−	4.90828i	−0.151279	−	0.184334i	−0.843136	+	0.537701i	$0.819293\pi$
$710$	−36.2842	−	11.2837i	−1.36172	−	0.423469i
$711$	4.67134	+	6.99115i	0.175189	+	0.262189i
$712$	−33.3659	−	7.36597i	−1.25044	−	0.276051i
$713$	8.06179	+	5.38672i	0.301916	+	0.201734i
$714$	−9.03193	−	0.953233i	−0.338011	−	0.0356739i
$715$	−1.36178	+	0.413091i	−0.0509276	+	0.0154487i
$716$	8.89544	+	7.51043i	0.332438	+	0.280678i
$717$	12.9654	+	10.6404i	0.484200	+	0.397373i
$718$	0.180653	−	0.876211i	0.00674190	−	0.0326999i
$719$	1.66867	−	4.02853i	0.0622310	−	0.150239i	−0.889705	−	0.456536i	$-0.849090\pi$
$719$	1.66867	−	4.02853i	0.0622310	−	0.150239i	0.951936	+	0.306297i	$0.0990900\pi$
$720$	0.625818	+	8.89134i	0.0233229	+	0.331361i
$721$	−8.71593	−	21.0421i	−0.324598	−	0.783649i
$722$	8.93001	−	1.71161i	0.332341	−	0.0636997i
$723$	2.02933	+	20.6042i	0.0754717	+	0.766277i
$724$	35.0108	−	10.0892i	1.30117	−	0.374962i
$725$	0.0478127	−	0.0894513i	0.00177572	−	0.00332214i
$726$	12.6553	+	6.87831i	0.469681	+	0.255278i
$727$	−5.28446	−	26.5668i	−0.195990	−	0.985307i	−0.946071	−	0.323961i	$-0.894985\pi$
$727$	−5.28446	−	26.5668i	−0.195990	−	0.985307i	0.750081	−	0.661346i	$-0.230015\pi$
$728$	−0.626581	+	5.23590i	−0.0232226	+	0.194055i
$729$	0.980785	+	0.195090i	0.0363254	+	0.00722557i
$730$	−34.3996	+	3.14591i	−1.27318	+	0.116435i
$731$	0.607774	−	6.17084i	0.0224793	−	0.228237i
$732$	8.02587	+	5.52623i	0.296645	+	0.204255i
$733$	3.22315	−	10.6253i	0.119050	−	0.392454i	−0.877081	−	0.480343i	$-0.840512\pi$
$733$	3.22315	−	10.6253i	0.119050	−	0.392454i	0.996130	+	0.0878890i	$0.0280121\pi$
$734$	−18.3935	+	7.46893i	−0.678916	+	0.275683i
$735$	−0.0842932	+	0.0842932i	−0.00310920	+	0.00310920i
$736$	−18.9364	+	3.08447i	−0.698005	+	0.113695i
$737$	3.10232	+	3.10232i	0.114275	+	0.114275i
$738$	−7.75825	−	3.27717i	−0.285585	−	0.120634i
$739$	−36.8355	−	11.1739i	−1.35502	−	0.411039i	−0.472503	−	0.881329i	$-0.656650\pi$
$739$	−36.8355	−	11.1739i	−1.35502	−	0.411039i	−0.882512	+	0.470289i	$0.844150\pi$
$740$	−20.3373	−	31.3760i	−0.747615	−	1.15340i
$741$	−3.54995	−	0.349640i	−0.130411	−	0.0128443i
$742$	14.1139	−	16.9552i	0.518137	−	0.622446i
$743$	−1.99408	+	10.0249i	−0.0731558	+	0.367779i	−0.999970	−	0.00774113i	$-0.997536\pi$
$743$	−1.99408	+	10.0249i	−0.0731558	+	0.367779i	0.926814	+	0.375520i	$0.122536\pi$
$744$	2.50859	−	7.68679i	0.0919694	−	0.281811i
$745$	11.9184	−	2.37072i	0.436656	−	0.0868563i
$746$	−11.1830	−	37.8131i	−0.409439	−	1.38444i
$747$	−1.91920	−	1.02583i	−0.0702199	−	0.0375333i
$748$	−2.74332	−	3.43951i	−0.100306	−	0.125761i
$749$	−49.7248	+	4.89747i	−1.81690	+	0.178949i
$750$	−8.90622	+	13.1299i	−0.325209	+	0.479435i
$751$	−17.5930	+	7.28725i	−0.641977	+	0.265916i	−0.679832	−	0.733368i	$-0.737947\pi$
$751$	−17.5930	+	7.28725i	−0.641977	+	0.265916i	0.0378551	+	0.999283i	$0.487947\pi$
$752$	0.750528	+	1.96532i	0.0273689	+	0.0716679i
$753$	18.1395	+	7.51364i	0.661041	+	0.273812i
$754$	−2.45484	+	1.61561i	−0.0893999	+	0.0588371i
$755$	25.6701	−	31.2791i	0.934231	−	1.13836i
$756$	4.68304	−	2.41974i	0.170320	−	0.0880052i
$757$	−0.629191	−	2.07416i	−0.0228683	−	0.0753868i	0.944764	−	0.327753i	$-0.106291\pi$
$757$	−0.629191	−	2.07416i	−0.0228683	−	0.0753868i	−0.967632	+	0.252366i	$0.918791\pi$
$758$	−4.71677	+	3.81620i	−0.171321	+	0.138610i
$759$	−1.70113	+	2.54592i	−0.0617472	+	0.0924112i
$760$	−22.9393	+	21.9987i	−0.832096	+	0.797975i
$761$	−0.0960806	+	0.0641990i	−0.00348292	+	0.00232721i	−0.557310	−	0.830304i	$-0.688167\pi$
$761$	−0.0960806	+	0.0641990i	−0.00348292	+	0.00232721i	0.553828	+	0.832631i	$0.313167\pi$
$762$	−10.6644	−	20.2908i	−0.386329	−	0.735060i
$763$	−37.1165	+	30.4607i	−1.34371	+	1.10275i
$764$	0.622167	−	44.5881i	0.0225092	−	1.61314i
$765$	2.55950	+	4.78848i	0.0925388	+	0.173128i
$766$	−28.7886	−	0.200843i	−1.04017	−	0.00725675i
$767$	7.74559			0.279677
$768$	6.74348	+	14.5095i	0.243334	+	0.523566i
$769$	−18.6668			−0.673143			−0.336572	−	0.941658i	$-0.609267\pi$
$769$	−18.6668			−0.673143			−0.336572	+	0.941658i	$0.609267\pi$
$770$	7.49822	+	0.0523113i	0.270217	+	0.00188517i
$771$	−2.89532	−	5.41675i	−0.104272	−	0.195080i
$772$	−0.545335	+	39.0819i	−0.0196270	+	1.40659i
$773$	−33.2421	+	27.2811i	−1.19564	+	0.981233i	−0.195636	+	0.980677i	$0.562677\pi$
$773$	−33.2421	+	27.2811i	−1.19564	+	0.981233i	−1.00000		0.000556602i	$0.999823\pi$
$774$	1.67432	+	3.18569i	0.0601821	+	0.114507i
$775$	0.0820689	−	0.0548367i	0.00294800	−	0.00196979i
$776$	−27.8907	−	29.0833i	−1.00122	−	1.04403i
$777$	−12.2850	+	18.3858i	−0.440721	+	0.659586i
$778$	−22.5939	+	18.2801i	−0.810031	+	0.655372i
$779$	−8.71752	−	28.7378i	−0.312338	−	1.02964i
$780$	2.80076	−	1.44716i	0.100283	−	0.0518167i
$781$	−6.90584	+	8.41479i	−0.247110	+	0.301105i
$782$	−9.76263	+	6.42512i	−0.349111	+	0.229762i
$783$	2.71404	+	1.12419i	0.0969920	+	0.0401754i
$784$	−0.0873735	+	0.195336i	−0.00312048	+	0.00697630i
$785$	−2.42265	+	1.00349i	−0.0864680	+	0.0358162i
$786$	−17.0044	+	25.0685i	−0.606526	+	0.894163i
$787$	15.4295	−	1.51967i	0.550003	−	0.0541705i	0.180801	−	0.983520i	$-0.442131\pi$
$787$	15.4295	−	1.51967i	0.550003	−	0.0541705i	0.369202	+	0.929349i	$0.379631\pi$
$788$	4.24641	+	5.32404i	0.151272	+	0.189661i
$789$	9.64289	+	5.15423i	0.343296	+	0.183496i
$790$	−7.51461	−	25.4091i	−0.267358	−	0.904017i
$791$	−42.9073	+	8.53479i	−1.52561	+	0.303462i
$792$	2.42750	+	0.792217i	0.0862574	+	0.0281502i
$793$	0.672377	−	3.38027i	0.0238768	−	0.120037i
$794$	−27.4138	+	32.9326i	−0.972878	+	1.16873i
$795$	−13.1253	−	1.29273i	−0.465506	−	0.0458483i
$796$	6.57511	+	10.1439i	0.233049	+	0.359542i
$797$	−8.64933	−	2.62375i	−0.306375	−	0.0929378i	0.133354	−	0.991069i	$-0.457425\pi$
$797$	−8.64933	−	2.62375i	−0.306375	−	0.0929378i	−0.439729	+	0.898131i	$0.644925\pi$
$798$	17.3147	+	7.31390i	0.612933	+	0.258909i
$799$	0.906166	+	0.906166i	0.0320578	+	0.0320578i
$800$	−0.0447611	+	0.190114i	−0.00158254	+	0.00672156i
$801$	8.54231	−	8.54231i	0.301828	−	0.301828i
$802$	4.60070	−	1.86818i	0.162456	−	0.0659676i
$803$	−2.87264	+	9.46981i	−0.101373	+	0.334183i
$804$	−8.00529	−	5.51206i	−0.282325	−	0.194395i
$805$	1.95242	−	19.8233i	0.0688139	−	0.698679i
$806$	−2.84796	+	0.260452i	−0.100315	+	0.00917402i
$807$	−23.3364	−	4.64190i	−0.821480	−	0.163403i
$808$	−3.33035	−	0.398544i	−0.117161	−	0.0140207i
$809$	−6.61060	−	33.2337i	−0.232416	−	1.16843i	−0.904009	−	0.427514i	$-0.859389\pi$
$809$	−6.61060	−	33.2337i	−0.232416	−	1.16843i	0.671592	−	0.740921i	$-0.265611\pi$
$810$	−2.76880	−	1.50488i	−0.0972858	−	0.0528762i
$811$	13.2159	−	24.7252i	0.464073	−	0.868220i	−0.535644	−	0.844444i	$-0.679931\pi$
$811$	13.2159	−	24.7252i	0.464073	−	0.868220i	0.999717	−	0.0237762i	$-0.00756891\pi$
$812$	14.8796	−	4.28790i	0.522172	−	0.150476i
$813$	−2.77130	−	28.1375i	−0.0971937	−	0.986824i
$814$	−10.5202	+	2.01640i	−0.368732	+	0.0706749i
$815$	7.14293	+	17.2446i	0.250206	+	0.604051i
$816$	7.35868	+	6.39091i	0.257605	+	0.223727i
$817$	−4.91089	+	11.8559i	−0.171810	+	0.414787i
$818$	3.02726	−	14.6830i	0.105846	−	0.513378i
$819$	−1.44118	−	1.18275i	−0.0503590	−	0.0413286i
$820$	20.2793	+	17.1218i	0.708183	+	0.597919i
$821$	37.5172	−	11.3807i	1.30936	−	0.397189i	0.442959	−	0.896542i	$-0.353929\pi$
$821$	37.5172	−	11.3807i	1.30936	−	0.397189i	0.866399	+	0.499353i	$0.166429\pi$
$822$	−13.2126	−	1.39447i	−0.460843	−	0.0486376i
$823$	9.87852	+	6.60062i	0.344344	+	0.230083i	0.715701	−	0.698407i	$-0.246107\pi$
$823$	9.87852	+	6.60062i	0.344344	+	0.230083i	−0.371357	+	0.928490i	$0.621107\pi$
$824$	−5.26903	+	23.8673i	−0.183555	+	0.831455i
$825$	0.0173175	+	0.0259175i	0.000602918	+	0.000902330i
$826$	−38.9723	−	12.1197i	−1.35602	−	0.421697i
$827$	16.3291	+	19.8971i	0.567820	+	0.691891i	0.975189	−	0.221373i	$-0.0710538\pi$
$827$	16.3291	+	19.8971i	0.567820	+	0.691891i	−0.407369	+	0.913264i	$0.633554\pi$
$828$	2.68303	−	6.23009i	0.0932416	−	0.216511i
$829$	1.67104	−	0.893192i	0.0580378	−	0.0310218i	−0.442123	−	0.896955i	$-0.645774\pi$
$829$	1.67104	−	0.893192i	0.0580378	−	0.0310218i	0.500160	+	0.865933i	$0.333274\pi$
$830$	4.81526	+	4.88292i	0.167140	+	0.169489i
$831$			19.8872i			0.689878i
$832$	3.76995	−	4.22042i	0.130699	−	0.146317i
$833$			0.130351i			0.00451640i
$834$	5.07929	−	5.00891i	0.175881	−	0.173444i
$835$	33.5555	−	17.9358i	1.16124	−	0.620693i
$836$	3.36670	+	8.45989i	0.116440	+	0.292591i
$837$	1.81357	+	2.20985i	0.0626863	+	0.0763835i
$838$	−8.82416	+	28.3752i	−0.304826	+	0.980206i
$839$	8.47159	+	12.6786i	0.292472	+	0.437715i	0.948385	−	0.317121i	$-0.102716\pi$
$839$	8.47159	+	12.6786i	0.292472	+	0.437715i	−0.655913	+	0.754836i	$0.727716\pi$
$840$	−16.3566	+	2.89907i	−0.564355	+	0.100027i
$841$	−16.9372	−	11.3171i	−0.584040	−	0.390243i
$842$	2.81515	−	26.6736i	0.0970164	−	0.919234i
$843$	16.2929	−	4.94240i	0.561157	−	0.170225i
$844$	−2.38095	−	28.2031i	−0.0819558	−	0.970790i
$845$	21.5309	+	17.6700i	0.740686	+	0.607865i
$846$	−0.728468	−	0.150192i	−0.0250452	−	0.00516370i
$847$	−10.2726	+	24.8003i	−0.352972	+	0.852150i
$848$	−22.8382	+	6.23760i	−0.784267	+	0.214200i
$849$	2.90994	+	7.02522i	0.0998690	+	0.241105i
$850$	0.0223964	+	0.116849i	0.000768190	+	0.00400788i
$851$	2.78909	+	28.3181i	0.0956088	+	0.970732i
$852$	11.6636	−	21.1073i	0.399589	−	0.723126i
$853$	−22.1816	+	41.4988i	−0.759483	+	1.42089i	0.142801	+	0.989751i	$0.454389\pi$
$853$	−22.1816	+	41.4988i	−0.759483	+	1.42089i	−0.902284	+	0.431142i	$0.858111\pi$
$854$	−8.67226	+	15.9559i	−0.296759	+	0.545999i
$855$	−2.19222	−	11.0210i	−0.0749724	−	0.376912i
$856$	46.7498	+	26.2607i	1.59787	+	0.897571i
$857$	−24.2774	−	4.82907i	−0.829300	−	0.164958i	−0.237852	−	0.971301i	$-0.576443\pi$
$857$	−24.2774	−	4.82907i	−0.829300	−	0.164958i	−0.591448	+	0.806343i	$0.701443\pi$
$858$	−0.0822510	−	0.899389i	−0.00280800	−	0.0307046i
$859$	−3.16310	+	32.1155i	−0.107923	+	1.09577i	0.776831	+	0.629709i	$0.216826\pi$
$859$	−3.16310	+	32.1155i	−0.107923	+	1.09577i	−0.884755	+	0.466057i	$0.845674\pi$
$860$	−2.05717	−	11.1532i	−0.0701488	−	0.380320i
$861$	4.55626	−	15.0200i	0.155277	−	0.511879i
$862$	−17.2944	−	42.5904i	−0.589051	−	1.45064i
$863$	−28.1946	+	28.1946i	−0.959754	+	0.959754i	−0.999221	−	0.0394671i	$-0.987434\pi$
$863$	−28.1946	+	28.1946i	−0.959754	+	0.959754i	0.0394671	+	0.999221i	$0.487434\pi$
$864$	−5.60685	−	0.750463i	−0.190749	−	0.0255313i
$865$	−5.77666	−	5.77666i	−0.196412	−	0.196412i
$866$	11.1624	−	26.4254i	0.379313	−	0.897972i
$867$	−10.5865	−	3.21139i	−0.359537	−	0.109064i
$868$	14.7372	+	3.14578i	0.500212	+	0.106775i
$869$	−7.55434	−	0.744038i	−0.256263	−	0.0252397i
$870$	−7.11505	−	5.92272i	−0.241223	−	0.200799i
$871$	−0.670652	+	3.37160i	−0.0227242	+	0.114242i
$872$	51.3744	−	3.97636i	1.73976	−	0.134656i
$873$	13.9729	−	2.77938i	0.472910	−	0.0940677i
$874$	23.1945	−	6.85963i	0.784564	−	0.232030i
$875$	−26.0767	−	13.9383i	−0.881552	−	0.471199i
$876$	2.45300	−	21.7851i	0.0828792	−	0.736051i
$877$	24.5815	−	2.42106i	0.830057	−	0.0817535i	0.325942	−	0.945390i	$-0.394319\pi$
$877$	24.5815	−	2.42106i	0.830057	−	0.0817535i	0.504115	+	0.863636i	$0.331819\pi$
$878$	−16.6685	−	11.3065i	−0.562535	−	0.381577i
$879$	−8.41557	+	3.48585i	−0.283850	+	0.117575i
$880$	−6.56344	−	4.65559i	−0.221254	−	0.156940i
$881$	33.8440	+	14.0186i	1.14023	+	0.472300i	0.871247	−	0.490844i	$-0.163312\pi$
$881$	33.8440	+	14.0186i	1.14023	+	0.472300i	0.268985	+	0.963144i	$0.413312\pi$
$882$	−0.0415922	−	0.0631972i	−0.00140048	−	0.00212796i
$883$	23.4895	−	28.6220i	0.790484	−	0.963207i	−0.209409	−	0.977828i	$-0.567154\pi$
$883$	23.4895	−	28.6220i	0.790484	−	0.963207i	0.999893	+	0.0146207i	$0.00465409\pi$
$884$	1.04660	−	3.28450i	0.0352010	−	0.110470i
$885$	7.08286	+	23.3490i	0.238088	+	0.784870i
$886$	−11.4957	−	14.2085i	−0.386204	−	0.477343i
$887$	−18.1709	+	27.1947i	−0.610119	+	0.913108i	−0.999970	−	0.00777050i	$-0.997527\pi$
$887$	−18.1709	+	27.1947i	−0.610119	+	0.913108i	0.389851	+	0.920878i	$0.372527\pi$
$888$	22.1089	−	8.62027i	0.741925	−	0.289277i
$889$	35.5205	−	23.7340i	1.19132	−	0.796014i
$890$	−33.6993	+	17.7115i	−1.12960	+	0.593692i
$891$	−0.697872	+	0.572729i	−0.0233796	+	0.0191871i
$892$	−22.4102	+	21.7934i	−0.750348	+	0.729696i
$893$	−1.25023	−	2.33901i	−0.0418373	−	0.0782722i
$894$	−0.0538028	+	7.71202i	−0.00179943	+	0.257928i
$895$	12.9711			0.433576
$896$	−25.5724	+	15.3363i	−0.854315	+	0.512350i
$897$	−2.39916			−0.0801056
$898$	0.222409	−	31.8798i	0.00742187	−	1.06384i
$899$	3.95881	+	7.40641i	0.132034	+	0.247018i
$900$	−0.0481422	−	0.0495047i	−0.00160474	−	0.00165016i
$901$	−11.1480	+	9.14894i	−0.371394	+	0.304795i
$902$	6.73042	−	3.53734i	0.224098	−	0.117780i
$903$	−5.57676	+	3.72627i	−0.185583	+	0.124003i
$904$	42.9890	+	18.8701i	1.42979	+	0.627610i
$905$	22.5535	−	33.7538i	0.749705	−	1.12201i
$906$	16.1527	+	19.9645i	0.536636	+	0.663275i
$907$	−3.75776	−	12.3877i	−0.124774	−	0.411326i	0.872192	−	0.489164i	$-0.162698\pi$
$907$	−3.75776	−	12.3877i	−0.124774	−	0.411326i	−0.996966	+	0.0778386i	$0.975198\pi$
$908$	−6.43354	−	2.05004i	−0.213505	−	0.0680331i
$909$	0.752300	−	0.916680i	0.0249522	−	0.0304044i
$910$	3.22998	+	4.90778i	0.107073	+	0.162691i
$911$	38.9358	+	16.1277i	1.29000	+	0.534336i	0.918986	−	0.394291i	$-0.129010\pi$
$911$	38.9358	+	16.1277i	1.29000	+	0.534336i	0.371015	+	0.928627i	$0.379010\pi$
$912$	−10.7341	−	17.0778i	−0.355442	−	0.565501i
$913$	1.81508	−	0.751832i	0.0600705	−	0.0248820i
$914$	−16.6959	−	11.3251i	−0.552250	−	0.374601i
$915$	10.8046	−	1.06416i	0.357190	−	0.0351802i
$916$	−49.3118	−	5.55249i	−1.62931	−	0.183460i
$917$	−49.7874	−	26.6119i	−1.64412	−	0.878802i
$918$	−3.30442	+	0.977263i	−0.109062	+	0.0322545i
$919$	11.3366	−	2.25498i	0.373959	−	0.0743851i	−0.00453281	−	0.999990i	$-0.501443\pi$
$919$	11.3366	−	2.25498i	0.373959	−	0.0743851i	0.378492	+	0.925605i	$0.376443\pi$
$920$	−13.9039	+	16.2367i	−0.458397	+	0.535309i
$921$	5.37961	−	27.0451i	0.177264	−	0.891167i
$922$	14.6706	+	12.2121i	0.483151	+	0.402185i
$923$	−8.48832	−	0.836027i	−0.279396	−	0.0275182i
$924$	−0.993440	+	4.65402i	−0.0326818	+	0.153106i
$925$	0.277200	+	0.0840876i	0.00911427	+	0.00276478i
$926$	9.75520	−	23.0941i	0.320576	−	0.758920i
$927$	−6.11049	−	6.11049i	−0.200695	−	0.200695i
$928$	−15.7244	−	5.37558i	−0.516180	−	0.176462i
$929$	6.70873	−	6.70873i	0.220106	−	0.220106i	−0.588437	−	0.808543i	$-0.700256\pi$
$929$	6.70873	−	6.70873i	0.220106	−	0.220106i	0.808543	+	0.588437i	$0.200256\pi$
$930$	−3.38941	−	8.34699i	−0.111143	−	0.273709i
$931$	0.0783104	−	0.258155i	0.00256652	−	0.00846068i
$932$	−38.7257	+	7.14284i	−1.26850	+	0.233971i
$933$	1.10983	−	11.2683i	0.0363342	−	0.368908i
$934$	−2.59167	−	28.3391i	−0.0848021	−	0.927285i
$935$	−4.80765	−	0.956300i	−0.157227	−	0.0312744i
$936$	0.540595	+	1.92635i	0.0176699	+	0.0629646i
$937$	0.946104	+	4.75639i	0.0309079	+	0.155384i	0.993157	−	0.116785i	$-0.0372589\pi$
$937$	0.946104	+	4.75639i	0.0309079	+	0.155384i	−0.962249	+	0.272169i	$0.912259\pi$
$938$	8.65001	−	15.9150i	0.282433	−	0.519642i
$939$	−10.5611	+	19.7585i	−0.344649	+	0.644793i
$940$	2.05155	+	1.13366i	0.0669141	+	0.0369758i
$941$	−5.60426	−	56.9010i	−0.182694	−	1.85492i	−0.452193	−	0.891920i	$-0.649358\pi$
$941$	−5.60426	−	56.9010i	−0.182694	−	1.85492i	0.269499	−	0.963001i	$-0.413142\pi$
$942$	−0.313277	−	1.63446i	−0.0102071	−	0.0532537i
$943$	−7.72946	−	18.6606i	−0.251706	−	0.607671i
$944$	26.8303	+	34.6192i	0.873251	+	1.12676i
$945$	2.24752	−	5.42599i	0.0731118	−	0.176507i
$946$	−3.18213	−	0.656076i	−0.103460	−	0.0213309i
$947$	−18.2359	−	14.9658i	−0.592588	−	0.486325i	0.289647	−	0.957134i	$-0.406462\pi$
$947$	−18.2359	−	14.9658i	−0.592588	−	0.486325i	−0.882235	+	0.470809i	$0.843962\pi$
$948$	16.7568	−	1.41463i	0.544234	−	0.0459452i
$949$	−7.41996	+	2.25082i	−0.240862	+	0.0730647i
$950$	0.0258436	−	0.244869i	0.000838476	−	0.00794459i
$951$	8.62272	+	5.76151i	0.279611	+	0.186830i
$952$	−10.4053	+	14.8885i	−0.337239	+	0.482538i
$953$	6.86159	+	10.2691i	0.222269	+	0.332648i	0.925799	−	0.378017i	$-0.123394\pi$
$953$	6.86159	+	10.2691i	0.222269	+	0.332648i	−0.703530	+	0.710666i	$0.748394\pi$
$954$	2.48558	−	7.99270i	0.0804736	−	0.258773i
$955$	−31.5189	−	38.4058i	−1.01993	−	1.24278i
$956$	31.1677	−	12.4035i	1.00804	−	0.401158i
$957$	−2.33895	+	1.25020i	−0.0756076	+	0.0404131i
$958$	−1.99888	+	1.97118i	−0.0645809	+	0.0636861i
$959$		−	24.7607i		−	0.799564i
$960$	16.1698	+	7.50519i	0.521878	+	0.242229i
$961$		−	22.8275i		−	0.736372i
$962$	−5.89321	−	5.97601i	−0.190005	−	0.192674i
$963$	−16.7192	+	8.93661i	−0.538769	+	0.287978i
$964$	38.0309	+	16.3783i	1.22489	+	0.527508i
$965$	27.6266	+	33.6631i	0.889331	+	1.08365i
$966$	12.0715	+	3.75401i	0.388394	+	0.120783i
$967$	5.65662	+	8.46573i	0.181905	+	0.272240i	0.911204	−	0.411955i	$-0.135154\pi$
$967$	5.65662	+	8.46573i	0.181905	+	0.272240i	−0.729300	+	0.684195i	$0.760154\pi$
$968$	24.2822	−	15.4998i	0.780459	−	0.498181i
$969$	−10.2165	−	6.82645i	−0.328201	−	0.219297i
$970$	−44.6480	−	4.71217i	−1.43356	−	0.151299i
$971$	6.91348	−	2.09718i	0.221864	−	0.0673017i	−0.177396	−	0.984140i	$-0.556767\pi$
$971$	6.91348	−	2.09718i	0.221864	−	0.0673017i	0.399260	+	0.916838i	$0.369267\pi$
$972$	1.29023	−	1.52817i	0.0413843	−	0.0490160i
$973$	10.2769	+	8.43405i	0.329463	+	0.270383i
$974$	−1.23622	+	5.99597i	−0.0396110	+	0.192123i
$975$	−0.00934643	+	0.0225643i	−0.000299325	+	0.000722636i
$976$	17.4373	−	8.70384i	0.558154	−	0.278603i
$977$	10.9657	+	26.4735i	0.350823	+	0.846963i	0.996519	+	0.0833675i	$0.0265675\pi$
$977$	10.9657	+	26.4735i	0.350823	+	0.846963i	−0.645696	+	0.763595i	$0.723432\pi$
$978$	−11.6342	+	2.22993i	−0.372021	+	0.0713053i
$979$	1.06901	+	10.8539i	0.0341658	+	0.346891i
$980$	0.0660189	+	0.229094i	0.00210890	+	0.00731815i
$981$	−8.58786	+	16.0668i	−0.274189	+	0.512972i
$982$	34.3665	+	18.6787i	1.09668	+	0.596061i
$983$	−0.151243	−	0.760349i	−0.00482390	−	0.0242514i	0.978298	−	0.207201i	$-0.0664354\pi$
$983$	−0.151243	−	0.760349i	−0.00482390	−	0.0242514i	−0.983122	+	0.182950i	$0.941435\pi$
$984$	−13.2414	+	10.4109i	−0.422120	+	0.331888i
$985$	7.44179	+	1.48026i	0.237115	+	0.0471652i
$986$	−10.0808	+	0.921911i	−0.321038	+	0.0293596i
$987$	0.135869	−	1.37950i	0.00432476	−	0.0439100i
$988$	−4.04596	+	5.87604i	−0.128719	+	0.186942i
$989$	−2.50545	+	8.25935i	−0.0796686	+	0.262632i
$990$	2.63599	−	1.07038i	0.0837773	−	0.0340189i
$991$	−30.0306	+	30.0306i	−0.953954	+	0.953954i	−0.998986	−	0.0450319i	$-0.985661\pi$
$991$	−30.0306	+	30.0306i	−0.953954	+	0.953954i	0.0450319	+	0.998986i	$0.485661\pi$
$992$	−11.0293	−	11.8269i	−0.350179	−	0.375503i
$993$	1.78485	+	1.78485i	0.0566404	+	0.0566404i
$994$	41.4013	+	17.4883i	1.31317	+	0.554696i
$995$	12.8886	+	3.90973i	0.408597	+	0.123947i
$996$	−3.65220	+	2.36729i	−0.115725	+	0.0750105i
$997$	53.2855	+	5.24817i	1.68757	+	0.166211i	0.895755	−	0.444549i	$-0.146636\pi$
$997$	53.2855	+	5.24817i	1.68757	+	0.166211i	0.791816	+	0.610760i	$0.209136\pi$
$998$	24.5249	−	29.4621i	0.776323	−	0.932608i
$999$	−1.63677	+	8.22860i	−0.0517851	+	0.260341i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	384.2.v.a.37.32	✓	512
128.45	even	32	inner	384.2.v.a.301.32	yes	512

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
384.2.v.a.37.32	✓	512	1.1	even	1	trivial
384.2.v.a.301.32	yes	512	128.45	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:	\( N \)	\(=\)	\( 384 = 2^{7} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	384.v (of order \(32\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(1.41418 + 0.00986600i) q^{2} +(0.471397 + 0.881921i) q^{3} +(1.99981 + 0.0279046i) q^{4} +(1.72253 - 1.41364i) q^{5} +(0.657938 + 1.25185i) q^{6} +(-2.19144 + 1.46427i) q^{7} +(2.82781 + 0.0591922i) q^{8} +(-0.555570 + 0.831470i) q^{9} +O(q^{10})\)	\(q+(1.41418 + 0.00986600i) q^{2} +(0.471397 + 0.881921i) q^{3} +(1.99981 + 0.0279046i) q^{4} +(1.72253 - 1.41364i) q^{5} +(0.657938 + 1.25185i) q^{6} +(-2.19144 + 1.46427i) q^{7} +(2.82781 + 0.0591922i) q^{8} +(-0.555570 + 0.831470i) q^{9} +(2.44991 - 1.98215i) q^{10} +(-0.262068 - 0.863924i) q^{11} +(0.918092 + 1.77682i) q^{12} +(0.448755 - 0.546809i) q^{13} +(-3.11353 + 2.04912i) q^{14} +(2.05871 + 0.852747i) q^{15} +(3.99844 + 0.111607i) q^{16} +(2.25114 - 0.932454i) q^{17} +(-0.793879 + 1.17037i) q^{18} +(-5.01848 + 0.494277i) q^{19} +(3.48416 - 2.77894i) q^{20} +(-2.32441 - 1.24242i) q^{21} +(-0.362088 - 1.22433i) q^{22} +(-3.32646 + 0.661674i) q^{23} +(1.28082 + 2.52181i) q^{24} +(-0.00673583 + 0.0338633i) q^{25} +(0.640015 - 0.768859i) q^{26} +(-0.995185 - 0.0980171i) q^{27} +(-4.42331 + 2.86711i) q^{28} +(-2.81116 - 0.852757i) q^{29} +(2.90297 + 1.22625i) q^{30} +(-2.02144 - 2.02144i) q^{31} +(5.65341 + 0.197282i) q^{32} +(0.638375 - 0.638375i) q^{33} +(3.19272 - 1.29645i) q^{34} +(-1.70486 + 5.62016i) q^{35} +(-1.13423 + 1.64727i) q^{36} +(0.822345 - 8.34941i) q^{37} +(-7.10190 + 0.649484i) q^{38} +(0.693785 + 0.138002i) q^{39} +(4.95465 - 3.89554i) q^{40} +(1.16181 + 5.84083i) q^{41} +(-3.27488 - 1.77994i) q^{42} +(1.19961 - 2.24431i) q^{43} +(-0.499978 - 1.73499i) q^{44} +(0.218415 + 2.21760i) q^{45} +(-4.71074 + 0.902907i) q^{46} +(0.201268 + 0.485904i) q^{47} +(1.78642 + 3.57892i) q^{48} +(-0.0204723 + 0.0494245i) q^{49} +(-0.00985977 + 0.0478223i) q^{50} +(1.88353 + 1.54577i) q^{51} +(0.912681 - 1.08099i) q^{52} +(-5.66382 + 1.71810i) q^{53} +(-1.40640 - 0.148432i) q^{54} +(-1.67270 - 1.11766i) q^{55} +(-6.28364 + 4.01097i) q^{56} +(-2.80161 - 4.19290i) q^{57} +(-3.96708 - 1.23369i) q^{58} +(6.94644 + 8.46427i) q^{59} +(4.09323 + 1.76277i) q^{60} +(4.29691 - 2.29675i) q^{61} +(-2.83874 - 2.87863i) q^{62} -2.63562i q^{63} +(7.99299 + 0.334768i) q^{64} -1.57627i q^{65} +(0.909074 - 0.896478i) q^{66} +(-4.28589 + 2.29085i) q^{67} +(4.52787 - 1.80191i) q^{68} +(-2.15163 - 2.62177i) q^{69} +(-2.46642 + 7.93109i) q^{70} +(-6.69894 - 10.0257i) q^{71} +(-1.62026 + 2.31835i) q^{72} +(-9.11407 - 6.08983i) q^{73} +(1.24532 - 11.7995i) q^{74} +(-0.0330400 + 0.0100226i) q^{75} +(-10.0498 + 0.848419i) q^{76} +(1.83933 + 1.50950i) q^{77} +(0.979774 + 0.202005i) q^{78} +(3.21767 - 7.76815i) q^{79} +(7.04519 - 5.46011i) q^{80} +(-0.382683 - 0.923880i) q^{81} +(1.58539 + 8.27145i) q^{82} +(0.213301 + 2.16568i) q^{83} +(-4.61370 - 2.54947i) q^{84} +(2.55950 - 4.78848i) q^{85} +(1.71860 - 3.16202i) q^{86} +(-0.573109 - 2.88121i) q^{87} +(-0.689942 - 2.45852i) q^{88} +(-11.8485 - 2.35682i) q^{89} +(0.286999 + 3.13824i) q^{90} +(-0.182741 + 1.85540i) q^{91} +(-6.67074 + 1.23040i) q^{92} +(0.829852 - 2.73566i) q^{93} +(0.279835 + 0.689141i) q^{94} +(-7.94572 + 7.94572i) q^{95} +(2.49101 + 5.07886i) q^{96} +(-10.0739 - 10.0739i) q^{97} +(-0.0294391 + 0.0696932i) q^{98} +(0.863924 + 0.262068i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 512 q+O(q^{10}) \) 512 * q	\( 512 q - 96 q^{50} - 96 q^{52} - 32 q^{54} - 224 q^{56} - 192 q^{60} - 192 q^{62} - 192 q^{64} - 192 q^{66} - 192 q^{68} - 192 q^{70} - 224 q^{74} - 32 q^{76} - 96 q^{78} - 96 q^{80}+O(q^{100}) \) 512 * q - 96 * q^50 - 96 * q^52 - 32 * q^54 - 224 * q^56 - 192 * q^60 - 192 * q^62 - 192 * q^64 - 192 * q^66 - 192 * q^68 - 192 * q^70 - 224 * q^74 - 32 * q^76 - 96 * q^78 - 96 * q^80

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more