LMFDB - Embedded newform 384.2.v.a.229.20

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			229.20
Character	$\chi$	$=$	384.229
Dual form			384.2.v.a.109.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.526803 + 1.31243i) q^{2} +(-0.881921 + 0.471397i) q^{3} +(-1.44496 + 1.38279i) q^{4} +(-2.24332 - 2.73349i) q^{5} +(-1.08328 - 0.909129i) q^{6} +(3.89436 - 2.60213i) q^{7} +(-2.57602 - 1.16795i) q^{8} +(0.555570 - 0.831470i) q^{9} +O(q^{10})$	\(q+(0.526803 + 1.31243i) q^{2} +(-0.881921 + 0.471397i) q^{3} +(-1.44496 + 1.38279i) q^{4} +(-2.24332 - 2.73349i) q^{5} +(-1.08328 - 0.909129i) q^{6} +(3.89436 - 2.60213i) q^{7} +(-2.57602 - 1.16795i) q^{8} +(0.555570 - 0.831470i) q^{9} +(2.40573 - 4.38421i) q^{10} +(-0.156087 + 0.0473485i) q^{11} +(0.622497 - 1.90066i) q^{12} +(2.21559 + 1.81829i) q^{13} +(5.46668 + 3.74027i) q^{14} +(3.26699 + 1.35323i) q^{15} +(0.175800 - 3.99613i) q^{16} +(1.46421 - 0.606495i) q^{17} +(1.38392 + 0.291127i) q^{18} +(-0.843043 - 8.55956i) q^{19} +(7.02133 + 0.847744i) q^{20} +(-2.20788 + 4.13066i) q^{21} +(-0.144369 - 0.179910i) q^{22} +(-1.83632 + 0.365267i) q^{23} +(2.82242 - 0.184288i) q^{24} +(-1.46404 + 7.36023i) q^{25} +(-1.21920 + 3.86569i) q^{26} +(-0.0980171 + 0.995185i) q^{27} +(-2.02899 + 9.14503i) q^{28} +(1.58392 - 5.22147i) q^{29} +(-0.0549638 + 5.00058i) q^{30} +(5.96896 + 5.96896i) q^{31} +(5.33727 - 1.87445i) q^{32} +(0.115337 - 0.115337i) q^{33} +(1.56733 + 1.60217i) q^{34} +(-15.8492 - 4.80779i) q^{35} +(0.346971 + 1.96967i) q^{36} +(0.516036 + 0.0508251i) q^{37} +(10.7897 - 5.61564i) q^{38} +(-2.81111 - 0.559165i) q^{39} +(2.58625 + 9.66161i) q^{40} +(0.115849 + 0.582411i) q^{41} +(-6.58433 - 0.721653i) q^{42} +(-8.00926 - 4.28104i) q^{43} +(0.160066 - 0.284252i) q^{44} +(-3.51913 + 0.346604i) q^{45} +(-1.44677 - 2.21762i) q^{46} +(-3.84272 - 9.27715i) q^{47} +(1.72872 + 3.60715i) q^{48} +(5.71619 - 13.8001i) q^{49} +(-10.4311 + 1.95594i) q^{50} +(-1.00542 + 1.22510i) q^{51} +(-5.71574 + 0.436342i) q^{52} +(3.13382 + 10.3308i) q^{53} +(-1.35775 + 0.395626i) q^{54} +(0.479579 + 0.320445i) q^{55} +(-13.0711 + 2.15472i) q^{56} +(4.77844 + 7.15145i) q^{57} +(7.68724 - 0.671905i) q^{58} +(-2.05845 + 1.68932i) q^{59} +(-6.59188 + 2.56219i) q^{60} +(2.62372 + 4.90863i) q^{61} +(-4.68939 + 10.9783i) q^{62} -4.68371i q^{63} +(5.27178 + 6.01734i) q^{64} -10.1353i q^{65} +(0.212131 + 0.0906118i) q^{66} +(-4.68583 - 8.76657i) q^{67} +(-1.27706 + 2.90105i) q^{68} +(1.44730 - 1.18777i) q^{69} +(-2.03949 - 23.3337i) q^{70} +(-4.85535 - 7.26655i) q^{71} +(-2.40228 + 1.49301i) q^{72} +(4.96699 + 3.31883i) q^{73} +(0.205145 + 0.704037i) q^{74} +(-2.17842 - 7.18129i) q^{75} +(13.0542 + 11.2024i) q^{76} +(-0.484653 + 0.590551i) q^{77} +(-0.747037 - 3.98396i) q^{78} +(-0.986760 + 2.38225i) q^{79} +(-11.3178 + 8.48405i) q^{80} +(-0.382683 - 0.923880i) q^{81} +(-0.703345 + 0.458860i) q^{82} +(13.1741 - 1.29754i) q^{83} +(-2.52153 - 9.02166i) q^{84} +(-4.94253 - 2.64183i) q^{85} +(1.39927 - 12.7669i) q^{86} +(1.06449 + 5.35158i) q^{87} +(0.457385 + 0.0603313i) q^{88} +(2.92443 + 0.581706i) q^{89} +(-2.30878 - 4.43603i) q^{90} +(13.3597 + 1.31582i) q^{91} +(2.14832 - 3.06703i) q^{92} +(-8.07790 - 2.45040i) q^{93} +(10.1513 - 9.93054i) q^{94} +(-21.5062 + 21.5062i) q^{95} +(-3.82344 + 4.16909i) q^{96} +(2.72128 + 2.72128i) q^{97} +(21.1230 + 0.232173i) q^{98} +(-0.0473485 + 0.156087i) 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 $\left(\mathbb{Z}/384\mathbb{Z}\right)^\times$.

$n$	$127$	$133$	$257$
$\chi(n)$	$1$	$e\left(\frac{9}{32}\right)$	$1$

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 $

$2$	0.526803	+	1.31243i	0.372506	+	0.928030i
$2$	0.526803	+	1.31243i	0.372506	+	0.928030i
$3$	−0.881921	+	0.471397i	−0.509177	+	0.272161i
$3$	−0.881921	+	0.471397i	−0.509177	+	0.272161i
$4$	−1.44496	+	1.38279i	−0.722478	+	0.691394i
$5$	−2.24332	−	2.73349i	−1.00324	−	1.22245i	−0.974851	−	0.222856i	$-0.928462\pi$
$5$	−2.24332	−	2.73349i	−1.00324	−	1.22245i	−0.0283901	−	0.999597i	$-0.509038\pi$
$6$	−1.08328	−	0.909129i	−0.442245	−	0.371150i
$7$	3.89436	−	2.60213i	1.47193	−	0.983512i	0.477442	−	0.878663i	$-0.341564\pi$
$7$	3.89436	−	2.60213i	1.47193	−	0.983512i	0.994488	−	0.104849i	$-0.0334358\pi$
$8$	−2.57602	−	1.16795i	−0.910761	−	0.412933i
$9$	0.555570	−	0.831470i	0.185190	−	0.277157i
$10$	2.40573	−	4.38421i	0.760759	−	1.38641i
$11$	−0.156087	+	0.0473485i	−0.0470620	+	0.0142761i	−0.313728	−	0.949513i	$-0.601578\pi$
$11$	−0.156087	+	0.0473485i	−0.0470620	+	0.0142761i	0.266666	+	0.963789i	$0.414078\pi$
$12$	0.622497	−	1.90066i	0.179699	−	0.548672i
$13$	2.21559	+	1.81829i	0.614494	+	0.504302i	0.889377	−	0.457175i	$-0.151139\pi$
$13$	2.21559	+	1.81829i	0.614494	+	0.504302i	−0.274882	+	0.961478i	$0.588639\pi$
$14$	5.46668	+	3.74027i	1.46103	+	0.999630i
$15$	3.26699	+	1.35323i	0.843532	+	0.349402i
$16$	0.175800	−	3.99613i	0.0439499	−	0.999034i
$17$	1.46421	−	0.606495i	0.355122	−	0.147097i	−0.197988	−	0.980204i	$-0.563441\pi$
$17$	1.46421	−	0.606495i	0.355122	−	0.147097i	0.553110	+	0.833108i	$0.313441\pi$
$18$	1.38392	+	0.291127i	0.326194	+	0.0686194i
$19$	−0.843043	−	8.55956i	−0.193407	−	1.96370i	−0.259081	−	0.965856i	$-0.583420\pi$
$19$	−0.843043	−	8.55956i	−0.193407	−	1.96370i	0.0656733	−	0.997841i	$-0.479080\pi$
$20$	7.02133	+	0.847744i	1.57002	+	0.189561i
$21$	−2.20788	+	4.13066i	−0.481800	+	0.901384i
$22$	−0.144369	−	0.179910i	−0.0307796	−	0.0383570i
$23$	−1.83632	+	0.365267i	−0.382899	+	0.0761634i	−0.382787	−	0.923837i	$-0.625036\pi$
$23$	−1.83632	+	0.365267i	−0.382899	+	0.0761634i	−0.000112122		1.00000i	$0.500036\pi$
$24$	2.82242	−	0.184288i	0.576123	−	0.0376175i
$25$	−1.46404	+	7.36023i	−0.292808	+	1.47205i
$26$	−1.21920	+	3.86569i	−0.239105	+	0.758125i
$27$	−0.0980171	+	0.995185i	−0.0188634	+	0.191523i
$28$	−2.02899	+	9.14503i	−0.383444	+	1.72825i
$29$	1.58392	−	5.22147i	0.294126	−	0.969602i	−0.677984	−	0.735076i	$-0.737146\pi$
$29$	1.58392	−	5.22147i	0.294126	−	0.969602i	0.972110	−	0.234526i	$-0.0753538\pi$
$30$	−0.0549638	+	5.00058i	−0.0100350	+	0.912977i
$31$	5.96896	+	5.96896i	1.07206	+	1.07206i	0.997194	+	0.0748628i	$0.0238519\pi$
$31$	5.96896	+	5.96896i	1.07206	+	1.07206i	0.0748628	+	0.997194i	$0.476148\pi$
$32$	5.33727	−	1.87445i	0.943505	−	0.331359i
$33$	0.115337	−	0.115337i	0.0200775	−	0.0200775i
$34$	1.56733	+	1.60217i	0.268795	+	0.274770i
$35$	−15.8492	−	4.80779i	−2.67900	−	0.812665i
$36$	0.346971	+	1.96967i	0.0578284	+	0.328279i
$37$	0.516036	+	0.0508251i	0.0848358	+	0.00835560i	0.140346	−	0.990103i	$-0.455179\pi$
$37$	0.516036	+	0.0508251i	0.0848358	+	0.00835560i	−0.0555102	+	0.998458i	$0.517679\pi$
$38$	10.7897	−	5.61564i	1.75032	−	0.910977i
$39$	−2.81111	−	0.559165i	−0.450138	−	0.0895380i
$40$	2.58625	+	9.66161i	0.408922	+	1.52763i
$41$	0.115849	+	0.582411i	0.0180925	+	0.0909573i	0.988777	−	0.149402i	$-0.0477348\pi$
$41$	0.115849	+	0.582411i	0.0180925	+	0.0909573i	−0.970684	+	0.240359i	$0.922735\pi$
$42$	−6.58433	−	0.721653i	−1.01598	−	0.111353i
$43$	−8.00926	−	4.28104i	−1.22140	−	0.652852i	−0.270610	−	0.962689i	$-0.587225\pi$
$43$	−8.00926	−	4.28104i	−1.22140	−	0.652852i	−0.950790	+	0.309837i	$0.899725\pi$
$44$	0.160066	−	0.284252i	0.0241309	−	0.0428526i
$45$	−3.51913	+	0.346604i	−0.524601	+	0.0516687i
$46$	−1.44677	−	2.21762i	−0.213314	−	0.326970i
$47$	−3.84272	−	9.27715i	−0.560519	−	1.35321i	−0.909352	−	0.416027i	$-0.863422\pi$
$47$	−3.84272	−	9.27715i	−0.560519	−	1.35321i	0.348834	−	0.937185i	$-0.386578\pi$
$48$	1.72872	+	3.60715i	0.249520	+	0.520647i
$49$	5.71619	−	13.8001i	0.816598	−	1.97144i
$50$	−10.4311	+	1.95594i	−1.47518	+	0.276612i
$51$	−1.00542	+	1.22510i	−0.140786	+	0.171549i
$52$	−5.71574	+	0.436342i	−0.792630	+	0.0605098i
$53$	3.13382	+	10.3308i	0.430463	+	1.41905i	0.857347	+	0.514740i	$0.172111\pi$
$53$	3.13382	+	10.3308i	0.430463	+	1.41905i	−0.426884	+	0.904307i	$0.640389\pi$
$54$	−1.35775	+	0.395626i	−0.184766	+	0.0538378i
$55$	0.479579	+	0.320445i	0.0646665	+	0.0432087i
$56$	−13.0711	+	2.15472i	−1.74670	+	0.287936i
$57$	4.77844	+	7.15145i	0.632920	+	0.947232i
$58$	7.68724	−	0.671905i	1.00938	−	0.0882255i
$59$	−2.05845	+	1.68932i	−0.267987	+	0.219931i	−0.758783	−	0.651343i	$-0.774206\pi$
$59$	−2.05845	+	1.68932i	−0.267987	+	0.219931i	0.490796	+	0.871274i	$0.336706\pi$
$60$	−6.59188	+	2.56219i	−0.851008	+	0.330777i
$61$	2.62372	+	4.90863i	0.335933	+	0.628486i	0.992003	−	0.126214i	$-0.0402826\pi$
$61$	2.62372	+	4.90863i	0.335933	+	0.628486i	−0.656070	+	0.754700i	$0.727783\pi$
$62$	−4.68939	+	10.9783i	−0.595553	+	1.39425i
$63$		−	4.68371i		−	0.590092i
$64$	5.27178	+	6.01734i	0.658973	+	0.752167i
$65$		−	10.1353i		−	1.25713i
$66$	0.212131	+	0.0906118i	0.0261115	+	0.0111535i
$67$	−4.68583	−	8.76657i	−0.572465	−	1.07101i	−0.986962	−	0.160956i	$-0.948542\pi$
$67$	−4.68583	−	8.76657i	−0.572465	−	1.07101i	0.414496	−	0.910051i	$-0.363958\pi$
$68$	−1.27706	+	2.90105i	−0.154867	+	0.351803i
$69$	1.44730	−	1.18777i	0.174235	−	0.142991i
$70$	−2.03949	−	23.3337i	−0.243766	−	2.78891i
$71$	−4.85535	−	7.26655i	−0.576224	−	0.862380i	0.422815	−	0.906216i	$-0.361042\pi$
$71$	−4.85535	−	7.26655i	−0.576224	−	0.862380i	−0.999039	+	0.0438358i	$0.986042\pi$
$72$	−2.40228	+	1.49301i	−0.283111	+	0.175952i
$73$	4.96699	+	3.31883i	0.581342	+	0.388440i	0.811187	−	0.584787i	$-0.198822\pi$
$73$	4.96699	+	3.31883i	0.581342	+	0.388440i	−0.229845	+	0.973227i	$0.573822\pi$
$74$	0.205145	+	0.704037i	0.0238476	+	0.0818427i
$75$	−2.17842	−	7.18129i	−0.251542	−	0.829224i
$76$	13.0542	+	11.2024i	1.49742	+	1.28501i
$77$	−0.484653	+	0.590551i	−0.0552313	+	0.0672995i
$78$	−0.747037	−	3.98396i	−0.0845852	−	0.451095i
$79$	−0.986760	+	2.38225i	−0.111019	+	0.268024i	−0.969618	−	0.244624i	$-0.921335\pi$
$79$	−0.986760	+	2.38225i	−0.111019	+	0.268024i	0.858599	+	0.512648i	$0.171335\pi$
$80$	−11.3178	+	8.48405i	−1.26536	+	0.948545i
$81$	−0.382683	−	0.923880i	−0.0425204	−	0.102653i
$82$	−0.703345	+	0.458860i	−0.0776715	+	0.0506726i
$83$	13.1741	−	1.29754i	1.44605	−	0.142423i	0.655673	−	0.755045i	$-0.272385\pi$
$83$	13.1741	−	1.29754i	1.44605	−	0.142423i	0.790376	+	0.612622i	$0.209885\pi$
$84$	−2.52153	−	9.02166i	−0.275121	−	0.984344i
$85$	−4.94253	−	2.64183i	−0.536092	−	0.286547i
$86$	1.39927	−	12.7669i	0.150887	−	1.37669i
$87$	1.06449	+	5.35158i	0.114126	+	0.573749i
$88$	0.457385	+	0.0603313i	0.0487574	+	0.00643134i
$89$	2.92443	+	0.581706i	0.309989	+	0.0616607i	0.347633	−	0.937631i	$-0.386985\pi$
$89$	2.92443	+	0.581706i	0.309989	+	0.0616607i	−0.0376442	+	0.999291i	$0.511985\pi$
$90$	−2.30878	−	4.43603i	−0.243367	−	0.467599i
$91$	13.3597	+	1.31582i	1.40048	+	0.137935i
$92$	2.14832	−	3.06703i	0.223977	−	0.319760i
$93$	−8.07790	−	2.45040i	−0.837639	−	0.254095i
$94$	10.1513	−	9.93054i	1.04702	−	1.02426i
$95$	−21.5062	+	21.5062i	−2.20649	+	2.20649i
$96$	−3.82344	+	4.16909i	−0.390228	+	0.425506i
$97$	2.72128	+	2.72128i	0.276304	+	0.276304i	0.831632	−	0.555328i	$-0.187407\pi$
$97$	2.72128	+	2.72128i	0.276304	+	0.276304i	−0.555328	+	0.831632i	$0.687407\pi$
$98$	21.1230	+	0.232173i	2.13374	+	0.0234530i
$99$	−0.0473485	+	0.156087i	−0.00475870	+	0.0156873i
$100$	−8.06216	−	12.6597i	−0.806216	−	1.26597i
$101$	−0.858422	+	8.71571i	−0.0854162	+	0.867245i	0.853040	+	0.521846i	$0.174756\pi$
$101$	−0.858422	+	8.71571i	−0.0854162	+	0.867245i	−0.938456	+	0.345399i	$0.887744\pi$
$102$	−2.13752	−	0.674152i	−0.211646	−	0.0667510i
$103$	−1.61226	+	8.10536i	−0.158860	+	0.798645i	0.816383	+	0.577511i	$0.195976\pi$
$103$	−1.61226	+	8.10536i	−0.158860	+	0.798645i	−0.975243	+	0.221134i	$0.929024\pi$
$104$	−3.58374	−	7.27165i	−0.351415	−	0.713044i
$105$	16.2441	−	3.23115i	1.58526	−	0.315328i
$106$	−11.9076	+	9.55523i	−1.15657	+	0.928086i
$107$	−9.62251	+	18.0025i	−0.930243	+	1.74036i	−0.321701	+	0.946841i	$0.604255\pi$
$107$	−9.62251	+	18.0025i	−0.930243	+	1.74036i	−0.608542	+	0.793521i	$0.708245\pi$
$108$	−1.23450	−	1.57354i	−0.118790	−	0.151414i
$109$	0.357472	+	3.62947i	0.0342396	+	0.347640i	0.997007	+	0.0773096i	$0.0246330\pi$
$109$	0.357472	+	3.62947i	0.0342396	+	0.347640i	−0.962768	+	0.270331i	$0.912867\pi$
$110$	−0.167918	+	0.798227i	−0.0160103	+	0.0761079i
$111$	−0.479062	+	0.198434i	−0.0454706	+	0.0188345i
$112$	−9.71383	−	16.0198i	−0.917871	−	1.51373i
$113$	−0.767769	−	0.318020i	−0.0722256	−	0.0299168i	0.346278	−	0.938132i	$-0.387445\pi$
$113$	−0.767769	−	0.318020i	−0.0722256	−	0.0299168i	−0.418504	+	0.908215i	$0.637445\pi$
$114$	−6.86849	+	10.0388i	−0.643293	+	0.940219i
$115$	5.11790	+	4.20015i	0.477246	+	0.391666i
$116$	4.93149	+	9.73501i	0.457877	+	0.903873i
$117$	2.74277	−	0.832009i	0.253569	−	0.0769193i
$118$	−3.30152	−	1.81163i	−0.303930	−	0.166774i
$119$	4.12397	−	6.17196i	0.378044	−	0.565783i
$120$	−6.83532	−	7.30163i	−0.623977	−	0.666545i
$121$	−9.12404	+	6.09649i	−0.829459	+	0.554227i
$122$	−5.06006	+	6.02933i	−0.458116	+	0.545870i
$123$	−0.376716	−	0.459030i	−0.0339673	−	0.0413893i
$124$	−16.8787	−	0.371088i	−1.51575	−	0.0333247i
$125$	7.81034	−	4.17471i	0.698578	−	0.373398i
$126$	6.14705	−	2.46739i	0.547623	−	0.219813i
$127$	6.86017			0.608741			0.304371	−	0.952554i	$-0.401554\pi$
$127$	6.86017			0.608741			0.304371	+	0.952554i	$0.401554\pi$
$128$	−5.12015	+	10.0888i	−0.452562	+	0.891733i
$129$	9.08160			0.799590
$130$	13.3019	−	5.33930i	1.16665	−	0.468288i
$131$	6.96093	−	3.72070i	0.608179	−	0.325079i	−0.138399	−	0.990377i	$-0.544195\pi$
$131$	6.96093	−	3.72070i	0.608179	−	0.325079i	0.746578	+	0.665298i	$0.231695\pi$
$132$	−0.00717043	+	0.326142i	−0.000624106	+	0.0283871i
$133$	−25.5562	−	31.1403i	−2.21600	−	2.70021i
$134$	9.03702	−	10.7681i	0.780680	−	0.930222i
$135$	2.94021	−	1.96459i	0.253053	−	0.169085i
$136$	−4.48019	−	0.147779i	−0.384173	−	0.0126720i
$137$	−1.26519	+	1.89349i	−0.108093	+	0.161772i	−0.881572	−	0.472049i	$-0.843514\pi$
$137$	−1.26519	+	1.89349i	−0.108093	+	0.161772i	0.773480	+	0.633821i	$0.218514\pi$
$138$	2.32131	+	1.27377i	0.197603	+	0.108430i
$139$	−5.96677	+	1.81000i	−0.506095	+	0.153522i	−0.532999	−	0.846116i	$-0.678935\pi$
$139$	−5.96677	+	1.81000i	−0.506095	+	0.153522i	0.0269044	+	0.999638i	$0.491435\pi$
$140$	29.5495	−	14.9690i	2.49739	−	1.26511i
$141$	7.76220	+	6.37027i	0.653695	+	0.536473i
$142$	6.97904	−	10.2004i	0.585668	−	0.855995i
$143$	−0.431918	−	0.178906i	−0.0361188	−	0.0149609i
$144$	−3.22500	−	2.36631i	−0.268750	−	0.197192i
$145$	−17.8260	+	7.38379i	−1.48037	+	0.613190i
$146$	−1.73912	+	8.26721i	−0.143931	+	0.684199i
$147$	1.46409	+	14.8652i	0.120756	+	1.22606i
$148$	−0.815930	+	0.640128i	−0.0670691	+	0.0526182i
$149$	−6.64868	+	12.4388i	−0.544681	+	1.01903i	0.447508	+	0.894280i	$0.352312\pi$
$149$	−6.64868	+	12.4388i	−0.544681	+	1.01903i	−0.992189	+	0.124746i	$0.960188\pi$
$150$	8.27736	−	6.64215i	0.675843	−	0.542330i
$151$	2.92600	−	0.582018i	0.238115	−	0.0473640i	−0.0745902	−	0.997214i	$-0.523765\pi$
$151$	2.92600	−	0.582018i	0.238115	−	0.0473640i	0.312705	+	0.949850i	$0.398765\pi$
$152$	−7.82545	+	23.0342i	−0.634727	+	1.86832i
$153$	0.309188	−	1.55439i	0.0249964	−	0.125665i
$154$	−1.03037	−	0.324970i	−0.0830299	−	0.0261868i
$155$	2.92582	−	29.7063i	0.235007	−	2.38607i
$156$	4.83514	−	3.07920i	0.387121	−	0.246533i
$157$	−2.91501	+	9.60951i	−0.232643	+	0.766922i	0.760429	+	0.649421i	$0.224988\pi$
$157$	−2.91501	+	9.60951i	−0.232643	+	0.766922i	−0.993073	+	0.117501i	$0.962512\pi$
$158$	−3.64637	−	0.0400789i	−0.290089	−	0.00318851i
$159$	−7.63369	−	7.63369i	−0.605391	−	0.605391i
$160$	−17.0970	−	10.3844i	−1.35163	−	0.820957i
$161$	−6.20082	+	6.20082i	−0.488693	+	0.488693i
$162$	1.01093	−	0.988949i	0.0794262	−	0.0776992i
$163$	18.6252	+	5.64988i	1.45884	+	0.442533i	0.917318	−	0.398156i	$-0.130350\pi$
$163$	18.6252	+	5.64988i	1.45884	+	0.442533i	0.541518	+	0.840689i	$0.317850\pi$
$164$	−0.972747	−	0.681365i	−0.0759588	−	0.0532056i
$165$	−0.574008	−	0.0565348i	−0.0446864	−	0.00440123i
$166$	8.64311	+	16.6066i	0.670835	+	1.28892i
$167$	12.3918	+	2.46488i	0.958907	+	0.190738i	0.649644	−	0.760238i	$-0.274918\pi$
$167$	12.3918	+	2.46488i	0.958907	+	0.190738i	0.309262	+	0.950977i	$0.399918\pi$
$168$	10.5120	−	8.06197i	0.811016	−	0.621995i
$169$	−0.933505	−	4.69304i	−0.0718080	−	0.361003i
$170$	0.863491	−	7.87846i	0.0662267	−	0.604250i
$171$	−7.58538	−	4.05447i	−0.580069	−	0.310053i
$172$	17.4928	−	4.88918i	1.33381	−	0.372797i
$173$	6.29511	−	0.620014i	0.478608	−	0.0471388i	0.144163	−	0.989554i	$-0.453951\pi$
$173$	6.29511	−	0.620014i	0.478608	−	0.0471388i	0.334445	+	0.942415i	$0.391451\pi$
$174$	−6.46280	+	4.21631i	−0.489944	+	0.319637i
$175$	13.4508	+	32.4730i	1.01678	+	2.45473i
$176$	0.161771	+	0.632069i	0.0121939	+	0.0476440i
$177$	1.01905	−	2.46020i	0.0765962	−	0.184920i
$178$	0.777151	+	4.14456i	0.0582499	+	0.310648i
$179$	5.52542	−	6.73274i	0.412989	−	0.503229i	−0.524419	−	0.851460i	$-0.675718\pi$
$179$	5.52542	−	6.73274i	0.412989	−	0.503229i	0.937409	+	0.348231i	$0.113218\pi$
$180$	4.60571	−	5.36704i	0.343290	−	0.400035i
$181$	4.33564	+	14.2927i	0.322265	+	1.06237i	0.957110	+	0.289726i	$0.0935643\pi$
$181$	4.33564	+	14.2927i	0.322265	+	1.06237i	−0.634844	+	0.772640i	$0.718936\pi$
$182$	5.31103	+	18.2269i	0.393679	+	1.35107i
$183$	−4.62782	−	3.09221i	−0.342099	−	0.228583i
$184$	5.15701	+	1.20380i	0.380180	+	0.0887451i
$185$	−1.01870	−	1.52460i	−0.0748965	−	0.112091i
$186$	−1.03947	−	11.8926i	−0.0762180	−	0.872006i
$187$	−0.199827	+	0.163994i	−0.0146128	+	0.0119924i
$188$	18.3809	+	8.09141i	1.34056	+	0.590127i
$189$	2.20788	+	4.13066i	0.160600	+	0.300461i
$190$	−39.5550	−	16.8959i	−2.86962	−	1.22576i
$191$		−	2.05819i		−	0.148926i	−0.997224	−	0.0744628i	$-0.976276\pi$
$191$		−	2.05819i		−	0.148926i	0.997224	−	0.0744628i	$-0.0237242\pi$
$192$	−7.48585	−	2.82172i	−0.540245	−	0.203640i
$193$		−	2.04091i		−	0.146908i	−0.997299	−	0.0734539i	$-0.976598\pi$
$193$		−	2.04091i		−	0.146908i	0.997299	−	0.0734539i	$-0.0234022\pi$
$194$	−2.13792	+	5.00507i	−0.153493	+	0.359343i
$195$	4.77774	+	8.93852i	0.342141	+	0.640101i
$196$	10.8230	+	27.8448i	0.773068	+	1.98891i
$197$	8.65441	−	7.10249i	0.616601	−	0.506032i	−0.273453	−	0.961885i	$-0.588166\pi$
$197$	8.65441	−	7.10249i	0.616601	−	0.506032i	0.890055	+	0.455854i	$0.150666\pi$
$198$	−0.229797	+	0.0200855i	−0.0163310	+	0.00142741i
$199$	−2.82804	−	4.23247i	−0.200475	−	0.300032i	0.717587	−	0.696469i	$-0.245247\pi$
$199$	−2.82804	−	4.23247i	−0.200475	−	0.300032i	−0.918062	+	0.396437i	$0.870247\pi$
$200$	12.3678	−	17.2502i	0.874535	−	1.21977i
$201$	8.26507	+	5.52254i	0.582973	+	0.389530i
$202$	−11.8910	+	3.46484i	−0.836647	+	0.243785i
$203$	−7.41860	−	24.4558i	−0.520683	−	1.71646i
$204$	−0.241274	−	3.16050i	−0.0168926	−	0.221279i
$205$	1.33213	−	1.62320i	0.0930399	−	0.113369i
$206$	−11.4871	+	2.15395i	−0.800342	+	0.150073i
$207$	−0.716496	+	1.72978i	−0.0497999	+	0.120228i
$208$	7.65563	−	8.53414i	0.530822	−	0.591736i
$209$	0.536870	+	1.29612i	0.0371361	+	0.0896545i
$210$	12.7981	+	19.6171i	0.883154	+	1.35371i
$211$	7.05541	−	0.694897i	0.485715	−	0.0478387i	0.147803	−	0.989017i	$-0.452780\pi$
$211$	7.05541	−	0.694897i	0.485715	−	0.0478387i	0.337911	+	0.941178i	$0.390280\pi$
$212$	−18.8135	−	10.5942i	−1.29212	−	0.727611i
$213$	7.70746	+	4.11973i	0.528107	+	0.282279i
$214$	−28.6962	−	3.14514i	−1.96163	−	0.214998i
$215$	6.26513	+	31.4969i	0.427278	+	2.14807i
$216$	1.41482	−	2.44914i	0.0962664	−	0.166643i
$217$	38.7773	+	7.71328i	2.63237	+	0.523612i
$218$	−4.57512	+	2.38117i	−0.309866	+	0.161273i
$219$	−5.94498	−	0.585529i	−0.401724	−	0.0395664i
$220$	−1.13608	+	0.200127i	−0.0765944	+	0.0134926i
$221$	4.34687	+	1.31861i	0.292402	+	0.0886991i
$222$	−0.512803	−	0.524201i	−0.0344171	−	0.0351821i
$223$	8.15183	−	8.15183i	0.545887	−	0.545887i	−0.379362	−	0.925248i	$-0.623856\pi$
$223$	8.15183	−	8.15183i	0.545887	−	0.545887i	0.925248	+	0.379362i	$0.123856\pi$
$224$	15.9077	−	21.1880i	1.06288	−	1.41569i
$225$	5.30643	+	5.30643i	0.353762	+	0.353762i
$226$	0.0129169	−	1.17518i	0.000859222	−	0.0781717i
$227$	3.86049	−	12.7263i	0.256230	−	0.844677i	−0.730585	−	0.682822i	$-0.760752\pi$
$227$	3.86049	−	12.7263i	0.256230	−	0.844677i	0.986815	−	0.161855i	$-0.0517477\pi$
$228$	−16.7936	−	3.72596i	−1.11218	−	0.246758i
$229$	−1.40999	+	14.3159i	−0.0931748	+	0.946020i	0.829001	+	0.559248i	$0.188910\pi$
$229$	−1.40999	+	14.3159i	−0.0931748	+	0.946020i	−0.922175	+	0.386772i	$0.873590\pi$
$230$	−2.81629	+	8.92955i	−0.185700	+	0.588797i
$231$	0.149042	−	0.749283i	0.00980622	−	0.0492992i
$232$	−10.1786	+	11.6007i	−0.668259	+	0.761622i
$233$	0.0419802	−	0.00835038i	0.00275021	−	0.000547052i	−0.193715	−	0.981058i	$-0.562054\pi$
$233$	0.0419802	−	0.00835038i	0.00275021	−	0.000547052i	0.196465	+	0.980511i	$0.437054\pi$
$234$	2.53685	+	3.16139i	0.165839	+	0.206667i
$235$	−16.7385	+	31.3156i	−1.09190	+	2.04281i
$236$	0.638392	−	5.28740i	0.0415558	−	0.344180i
$237$	−0.252740	−	2.56611i	−0.0164172	−	0.166687i
$238$	10.2728	+	2.16103i	0.665887	+	0.140079i
$239$	−10.0495	+	4.16264i	−0.650048	+	0.269259i	−0.683244	−	0.730190i	$-0.739431\pi$
$239$	−10.0495	+	4.16264i	−0.650048	+	0.269259i	0.0331960	+	0.999449i	$0.489431\pi$
$240$	5.98202	−	12.8174i	0.386138	−	0.827361i
$241$	−17.4007	−	7.20761i	−1.12088	−	0.464283i	−0.256208	−	0.966622i	$-0.582473\pi$
$241$	−17.4007	−	7.20761i	−1.12088	−	0.464283i	−0.864671	+	0.502339i	$0.832473\pi$
$242$	−12.8078	−	8.76304i	−0.823317	−	0.563309i
$243$	0.773010	+	0.634393i	0.0495886	+	0.0406963i
$244$	−10.5787	−	3.46472i	−0.677235	−	0.221806i
$245$	−50.5456	+	15.3328i	−3.22924	+	0.979579i
$246$	0.403990	−	0.736233i	0.0257575	−	0.0469405i
$247$	13.6959	−	20.4974i	0.871449	−	1.30422i
$248$	−8.40472	−	22.3476i	−0.533700	−	1.41908i
$249$	−11.0069	+	7.35457i	−0.697533	+	0.466077i
$250$	9.59354	+	8.05129i	0.606749	+	0.509208i
$251$	1.70567	+	2.07836i	0.107661	+	0.131185i	0.824053	−	0.566513i	$-0.191708\pi$
$251$	1.70567	+	2.07836i	0.107661	+	0.131185i	−0.716392	+	0.697698i	$0.754208\pi$
$252$	6.47657	+	6.76775i	0.407986	+	0.426328i
$253$	0.269331	−	0.143960i	0.0169327	−	0.00905071i
$254$	3.61396	+	9.00351i	0.226760	+	0.564930i
$255$	5.60427			0.350953
$256$	−15.9382	−	1.40504i	−0.996137	−	0.0878150i
$257$	24.9721			1.55772			0.778858	−	0.627200i	$-0.215799\pi$
$257$	24.9721			1.55772			0.778858	+	0.627200i	$0.215799\pi$
$258$	4.78422	+	11.9190i	0.297852	+	0.742043i
$259$	2.14188	−	1.14486i	0.133090	−	0.0711382i
$260$	14.0149	+	14.6450i	0.869170	+	0.908247i
$261$	−3.46152	−	4.21787i	−0.214262	−	0.261080i
$262$	8.55020	+	7.17568i	0.528233	+	0.443315i
$263$	9.62918	−	6.43401i	0.593761	−	0.396738i	−0.222069	−	0.975031i	$-0.571281\pi$
$263$	9.62918	−	6.43401i	0.593761	−	0.396738i	0.815829	+	0.578293i	$0.196281\pi$
$264$	−0.431817	+	0.162402i	−0.0265765	+	0.00999516i
$265$	21.2090	−	31.7415i	1.30286	−	1.94987i
$266$	27.4064	−	49.9456i	1.68040	−	3.06236i
$267$	−2.85333	+	0.865549i	−0.174621	+	0.0529708i
$268$	18.8931	+	6.18781i	1.15408	+	0.377981i
$269$	1.58850	+	1.30365i	0.0968527	+	0.0794849i	0.681574	−	0.731750i	$-0.261296\pi$
$269$	1.58850	+	1.30365i	0.0968527	+	0.0794849i	−0.584721	+	0.811235i	$0.698796\pi$
$270$	4.12730	+	2.82388i	0.251179	+	0.171856i
$271$	0.522407	+	0.216388i	0.0317340	+	0.0131446i	0.398494	−	0.917171i	$-0.369533\pi$
$271$	0.522407	+	0.216388i	0.0317340	+	0.0131446i	−0.366760	+	0.930316i	$0.619533\pi$
$272$	−2.16623	−	5.95779i	−0.131347	−	0.361244i
$273$	−12.4025	+	5.13728i	−0.750633	+	0.310923i
$274$	−3.15159	−	0.662980i	−0.190394	−	0.0400521i
$275$	−0.119978	−	1.21816i	−0.00723495	−	0.0734576i
$276$	−0.448856	+	3.71759i	−0.0270180	+	0.223773i
$277$	12.0704	−	22.5821i	0.725238	−	1.35682i	−0.200889	−	0.979614i	$-0.564383\pi$
$277$	12.0704	−	22.5821i	0.725238	−	1.35682i	0.926127	−	0.377211i	$-0.123117\pi$
$278$	−5.51881	−	6.87746i	−0.330996	−	0.412483i
$279$	8.27918	−	1.64683i	0.495662	−	0.0985933i
$280$	35.2125	+	30.8960i	2.10435	+	1.84639i
$281$	1.49650	−	7.52343i	0.0892739	−	0.448810i	−0.910131	−	0.414320i	$-0.864019\pi$
$281$	1.49650	−	7.52343i	0.0892739	−	0.448810i	0.999405	−	0.0344898i	$-0.0109806\pi$
$282$	−4.27140	+	13.5432i	−0.254358	+	0.806488i
$283$	0.954034	−	9.68647i	0.0567114	−	0.575801i	−0.924275	−	0.381726i	$-0.875330\pi$
$283$	0.954034	−	9.68647i	0.0567114	−	0.575801i	0.980987	−	0.194074i	$-0.0621703\pi$
$284$	17.0639	+	3.78593i	1.01255	+	0.224654i
$285$	8.82884	−	29.1048i	0.522975	−	1.72402i
$286$	0.00726659	−	0.661112i	0.000429683	−	0.0390924i
$287$	1.96666	+	1.96666i	0.116089	+	0.116089i
$288$	1.40668	−	5.47917i	0.0828893	−	0.322863i
$289$	−10.2447	+	10.2447i	−0.602632	+	0.602632i
$290$	−19.0815	−	19.5057i	−1.12051	−	1.14541i
$291$	−3.68276	−	1.11715i	−0.215887	−	0.0654886i
$292$	−11.7663	+	2.07271i	−0.688572	+	0.121296i
$293$	29.1423	+	2.87027i	1.70251	+	0.167683i	0.902030	−	0.431674i	$-0.142077\pi$
$293$	29.1423	+	2.87027i	1.70251	+	0.167683i	0.800482	+	0.599357i	$0.204577\pi$
$294$	−18.7383	+	9.75255i	−1.09284	+	0.568780i
$295$	9.23550	+	1.83705i	0.537711	+	0.106957i
$296$	−1.26996	−	0.733632i	−0.0738149	−	0.0426415i
$297$	−0.0318213	−	0.159976i	−0.00184646	−	0.00928278i
$298$	−19.8276	−	2.17314i	−1.14858	−	0.125887i
$299$	−4.73269	−	2.52968i	−0.273699	−	0.146295i
$300$	13.0779	+	7.36436i	0.755054	+	0.425181i
$301$	−42.3307	+	4.16921i	−2.43990	+	0.240309i
$302$	2.30529	+	3.53357i	0.132654	+	0.203334i
$303$	−3.35149	−	8.09122i	−0.192538	−	0.464829i
$304$	−34.3533	+	1.86414i	−1.97030	+	0.106916i
$305$	7.53186	−	18.1835i	0.431273	−	1.04118i
$306$	2.20292	−	0.413071i	0.125932	−	0.0236137i
$307$	−6.31619	+	7.69630i	−0.360484	+	0.439251i	−0.921396	−	0.388624i	$-0.872951\pi$
$307$	−6.31619	+	7.69630i	−0.360484	+	0.439251i	0.560912	+	0.827875i	$0.310451\pi$
$308$	−0.116304	−	1.52349i	−0.00662704	−	0.0868090i
$309$	−2.39896	−	7.90830i	−0.136472	−	0.449887i
$310$	40.5289	−	11.8095i	2.30189	−	0.670732i
$311$	0.578935	+	0.386832i	0.0328284	+	0.0219352i	0.571876	−	0.820340i	$-0.306216\pi$
$311$	0.578935	+	0.386832i	0.0328284	+	0.0219352i	−0.539048	+	0.842275i	$0.681216\pi$
$312$	6.58841	+	4.72366i	0.372995	+	0.267425i
$313$	6.24834	+	9.35130i	0.353177	+	0.528567i	0.964939	−	0.262475i	$-0.0845389\pi$
$313$	6.24834	+	9.35130i	0.353177	+	0.528567i	−0.611762	+	0.791042i	$0.709539\pi$
$314$	−14.1475	+	1.23656i	−0.798387	+	0.0697833i
$315$	−12.8029	+	10.5070i	−0.721359	+	0.592004i
$316$	−1.86832	−	4.80673i	−0.105101	−	0.270399i
$317$	−0.464040	−	0.868158i	−0.0260631	−	0.0487606i	0.868553	−	0.495597i	$-0.165051\pi$
$317$	−0.464040	−	0.868158i	−0.0260631	−	0.0487606i	−0.894616	+	0.446836i	$0.852551\pi$
$318$	5.99725	−	14.0402i	0.336309	−	0.787333i
$319$			0.890000i			0.0498304i
$320$	4.62205	−	27.9091i	0.258380	−	1.56017i
$321$		−	20.4128i		−	1.13933i
$322$	−11.4048	−	4.87154i	−0.635563	−	0.271481i
$323$	−6.42571	−	12.0217i	−0.357536	−	0.668903i
$324$	1.83049	+	0.805796i	0.101694	+	0.0447665i
$325$	−16.6267	+	13.6452i	−0.922285	+	0.756900i
$326$	2.39671	+	27.4207i	0.132742	+	1.51869i
$327$	−2.02618	−	3.03240i	−0.112048	−	0.167692i
$328$	0.381799	−	1.63561i	0.0210813	−	0.0903114i
$329$	−39.1053	−	26.1293i	−2.15594	−	1.44056i
$330$	−0.228191	−	0.783129i	−0.0125615	−	0.0431098i
$331$	−3.49767	−	11.5303i	−0.192249	−	0.633761i	−0.999076	−	0.0429733i	$-0.986317\pi$
$331$	−3.49767	−	11.5303i	−0.192249	−	0.633761i	0.806827	−	0.590788i	$-0.201183\pi$
$332$	−17.2418	+	20.0919i	−0.946268	+	1.10269i
$333$	0.328954	−	0.400831i	0.0180266	−	0.0219654i
$334$	3.29305	+	17.5619i	0.180188	+	0.960945i
$335$	−13.4515	+	32.4749i	−0.734936	+	1.77429i
$336$	16.1185	+	9.54917i	0.879338	+	0.520950i
$337$	−8.15665	−	19.6919i	−0.444321	−	1.07269i	−0.974417	−	0.224748i	$-0.927844\pi$
$337$	−8.15665	−	19.6919i	−0.444321	−	1.07269i	0.530096	−	0.847938i	$-0.322156\pi$
$338$	5.66753	−	3.69747i	0.308273	−	0.201116i
$339$	0.827025	−	0.0814549i	0.0449178	−	0.00442402i
$340$	10.7948	−	3.01712i	0.585432	−	0.163626i
$341$	−1.21430	−	0.649056i	−0.0657580	−	0.0351484i
$342$	1.32521	−	12.0912i	0.0716594	−	0.653818i
$343$	−7.25251	−	36.4608i	−0.391599	−	1.96870i
$344$	15.6320	+	20.3825i	0.842820	+	1.09895i
$345$	−6.49352	−	1.29164i	−0.349599	−	0.0695396i
$346$	4.13001	+	7.93528i	0.222031	+	0.426603i
$347$	−16.1401	−	1.58967i	−0.866449	−	0.0853377i	−0.344982	−	0.938609i	$-0.612115\pi$
$347$	−16.1401	−	1.58967i	−0.866449	−	0.0853377i	−0.521467	+	0.853272i	$0.674615\pi$
$348$	−8.93824	−	6.26083i	−0.479140	−	0.335616i
$349$	21.0288	+	6.37903i	1.12565	+	0.341462i	0.797592	−	0.603197i	$-0.206107\pi$
$349$	21.0288	+	6.37903i	1.12565	+	0.341462i	0.328056	+	0.944658i	$0.393607\pi$
$350$	−35.5327	+	34.7601i	−1.89930	+	1.85801i
$351$	−2.02670	+	2.02670i	−0.108177	+	0.108177i
$352$	−0.744326	+	0.545289i	−0.0396727	+	0.0290640i
$353$	−14.6790	−	14.6790i	−0.781283	−	0.781283i	0.198765	−	0.980047i	$-0.436307\pi$
$353$	−14.6790	−	14.6790i	−0.781283	−	0.781283i	−0.980047	+	0.198765i	$0.936307\pi$
$354$	3.76568	+	0.0413903i	0.200144	+	0.00219987i
$355$	−8.97093	+	29.5732i	−0.476128	+	1.56958i
$356$	−5.03005	+	3.20333i	−0.266592	+	0.169776i
$357$	−0.727577	+	7.38721i	−0.0385075	+	0.390973i
$358$	11.7471	+	3.70491i	0.620852	+	0.195810i
$359$	−3.71872	+	18.6952i	−0.196266	+	0.986697i	0.749538	+	0.661961i	$0.230276\pi$
$359$	−3.71872	+	18.6952i	−0.196266	+	0.986697i	−0.945805	+	0.324736i	$0.894724\pi$
$360$	9.47018	+	3.21731i	0.499122	+	0.169567i
$361$	−53.9204	+	10.7254i	−2.83791	+	0.564496i
$362$	−16.4741	+	13.2197i	−0.865862	+	0.694810i
$363$	5.17282	−	9.67767i	0.271503	−	0.507946i
$364$	−21.1237	+	16.5724i	−1.10718	+	0.868628i
$365$	−2.07052	−	21.0224i	−0.108376	−	1.10036i
$366$	1.62037	−	7.70269i	0.0846980	−	0.402626i
$367$	−24.0500	+	9.96183i	−1.25540	+	0.520003i	−0.908494	−	0.417897i	$-0.862767\pi$
$367$	−24.0500	+	9.96183i	−1.25540	+	0.520003i	−0.346905	+	0.937900i	$0.612767\pi$
$368$	1.13683	+	7.40240i	0.0592614	+	0.385877i
$369$	0.548619	+	0.227245i	0.0285600	+	0.0118299i
$370$	1.46427	−	2.14014i	0.0761239	−	0.111261i
$371$	39.0863	+	32.0773i	2.02926	+	1.66537i
$372$	15.0606	−	7.62929i	0.780856	−	0.395560i
$373$	3.74325	−	1.13550i	0.193818	−	0.0587941i	−0.191883	−	0.981418i	$-0.561459\pi$
$373$	3.74325	−	1.13550i	0.193818	−	0.0587941i	0.385701	+	0.922624i	$0.373959\pi$
$374$	−0.320501	−	0.175867i	−0.0165727	−	0.00909388i
$375$	−4.92016	+	7.36354i	−0.254076	+	0.380251i
$376$	−0.936322	+	28.3863i	−0.0482871	+	1.46391i
$377$	13.0034	−	8.68862i	0.669711	−	0.447487i
$378$	−4.25809	+	5.07374i	−0.219013	+	0.260965i
$379$	−14.1885	−	17.2887i	−0.728813	−	0.888062i	0.268351	−	0.963321i	$-0.413521\pi$
$379$	−14.1885	−	17.2887i	−0.728813	−	0.888062i	−0.997164	+	0.0752597i	$0.976021\pi$
$380$	1.33703	−	60.8141i	0.0685884	−	3.11970i
$381$	−6.05013	+	3.23386i	−0.309957	+	0.165676i
$382$	2.70124	−	1.08426i	0.138207	−	0.0554757i
$383$	24.6264			1.25835			0.629174	−	0.777265i	$-0.283393\pi$
$383$	24.6264			1.25835			0.629174	+	0.777265i	$0.283393\pi$
$384$	−0.240258	−	11.3112i	−0.0122606	−	0.577220i
$385$	2.70149			0.137681
$386$	2.67856	−	1.07516i	0.136335	−	0.0547241i
$387$	−8.00926	+	4.28104i	−0.407133	+	0.217617i
$388$	−7.69508	−	0.169181i	−0.390659	−	0.00858886i
$389$	20.7210	+	25.2486i	1.05060	+	1.28015i	0.958710	+	0.284384i	$0.0917891\pi$
$389$	20.7210	+	25.2486i	1.05060	+	1.28015i	0.0918847	+	0.995770i	$0.470711\pi$
$390$	−9.21428	+	10.9793i	−0.466583	+	0.555959i
$391$	−2.46722	+	1.64854i	−0.124773	+	0.0833705i
$392$	−30.8429	+	28.8731i	−1.55780	+	1.45831i
$393$	−4.38507	+	6.56272i	−0.221198	+	0.331045i
$394$	13.8807	+	7.61671i	0.699300	+	0.383724i
$395$	8.72546	−	2.64684i	0.439026	−	0.133177i
$396$	−0.147419	−	0.291012i	−0.00740807	−	0.0146239i
$397$	−17.9576	−	14.7374i	−0.901265	−	0.739649i	0.0648136	−	0.997897i	$-0.479355\pi$
$397$	−17.9576	−	14.7374i	−0.901265	−	0.739649i	−0.966079	+	0.258248i	$0.916855\pi$
$398$	4.06500	−	5.94129i	0.203760	−	0.297810i
$399$	37.2180	+	15.4162i	1.86323	+	0.771775i
$400$	29.1551	+	7.14443i	1.45775	+	0.357222i
$401$	0.761948	−	0.315609i	0.0380499	−	0.0157608i	−0.363577	−	0.931564i	$-0.618445\pi$
$401$	0.761948	−	0.315609i	0.0380499	−	0.0157608i	0.401627	+	0.915803i	$0.368445\pi$
$402$	−2.89390	+	13.7566i	−0.144335	+	0.686119i
$403$	2.37148	+	24.0781i	0.118132	+	1.19941i
$404$	−10.8116	−	13.7808i	−0.537896	−	0.685622i
$405$	−1.66693	+	3.11861i	−0.0828306	+	0.154965i
$406$	28.1885	−	22.6198i	1.39897	−	1.12260i
$407$	−0.0829531	+	0.0165004i	−0.00411183	+	0.000817894i
$408$	4.02083	−	1.98162i	0.199061	−	0.0981046i
$409$	−1.37208	+	6.89791i	−0.0678450	+	0.341080i	−0.999767	−	0.0215785i	$-0.993131\pi$
$409$	−1.37208	+	6.89791i	−0.0678450	+	0.341080i	0.931922	+	0.362658i	$0.118131\pi$
$410$	2.83211	+	0.893220i	0.139868	+	0.0441130i
$411$	0.223213	−	2.26632i	0.0110103	−	0.111789i
$412$	−8.87834	−	13.9413i	−0.437405	−	0.686838i
$413$	−3.62050	+	11.9352i	−0.178153	+	0.587292i
$414$	−2.64767	−	0.0291017i	−0.130126	−	0.00143027i
$415$	−33.1005	−	33.1005i	−1.62484	−	1.62484i
$416$	15.2335	+	5.55167i	0.746883	+	0.272193i
$417$	4.40899	−	4.40899i	0.215909	−	0.215909i
$418$	−1.41824	+	1.38741i	−0.0693686	+	0.0678602i
$419$	2.32583	+	0.705532i	0.113624	+	0.0344675i	0.346585	−	0.938019i	$-0.387341\pi$
$419$	2.32583	+	0.705532i	0.113624	+	0.0344675i	−0.232961	+	0.972486i	$0.574841\pi$
$420$	−19.0040	+	27.1310i	−0.927301	+	1.32386i
$421$	−13.0474	−	1.28506i	−0.635893	−	0.0626300i	−0.225066	−	0.974343i	$-0.572260\pi$
$421$	−13.0474	−	1.28506i	−0.635893	−	0.0626300i	−0.410827	+	0.911714i	$0.634760\pi$
$422$	4.62882	+	8.89368i	0.225327	+	0.432937i
$423$	−9.84857	−	1.95900i	−0.478854	−	0.0952500i
$424$	3.99310	−	30.2725i	0.193922	−	1.47016i
$425$	2.32028	+	11.6648i	0.112550	+	0.565828i
$426$	−1.34654	+	12.2858i	−0.0652402	+	0.595249i
$427$	22.9906	+	12.2887i	1.11259	+	0.594693i
$428$	−10.9894	−	39.3186i	−0.531195	−	1.90054i
$429$	0.465254	−	0.0458235i	0.0224627	−	0.00221238i
$430$	−38.0371	+	24.8152i	−1.83431	+	1.19670i
$431$	10.0187	+	24.1873i	0.482585	+	1.16506i	0.958377	+	0.285505i	$0.0921612\pi$
$431$	10.0187	+	24.1873i	0.482585	+	1.16506i	−0.475793	+	0.879557i	$0.657839\pi$
$432$	3.95966	+	0.566643i	0.190509	+	0.0272626i
$433$	0.203324	−	0.490867i	0.00977111	−	0.0235895i	−0.918919	−	0.394447i	$-0.870936\pi$
$433$	0.203324	−	0.490867i	0.00977111	−	0.0235895i	0.928690	+	0.370857i	$0.120936\pi$
$434$	10.3048	+	54.9559i	0.494648	+	2.63797i
$435$	12.2405	−	14.9151i	0.586886	−	0.715123i
$436$	−5.53531	−	4.75012i	−0.265093	−	0.227489i
$437$	4.67462	+	15.4101i	0.223617	+	0.737167i
$438$	−2.36337	−	8.11084i	−0.112926	−	0.387551i
$439$	0.108801	+	0.0726984i	0.00519278	+	0.00346971i	0.558164	−	0.829731i	$-0.311506\pi$
$439$	0.108801	+	0.0726984i	0.00519278	+	0.00346971i	−0.552971	+	0.833200i	$0.686506\pi$
$440$	−0.861143	−	1.38560i	−0.0410534	−	0.0660558i
$441$	−8.29862	−	12.4198i	−0.395172	−	0.591417i
$442$	0.559360	+	6.39961i	0.0266061	+	0.304399i
$443$	18.7595	−	15.3955i	0.891292	−	0.731464i	−0.0727119	−	0.997353i	$-0.523165\pi$
$443$	18.7595	−	15.3955i	0.891292	−	0.731464i	0.964004	+	0.265889i	$0.0856654\pi$
$444$	0.417832	−	0.949169i	0.0198294	−	0.0450456i
$445$	−4.97034	−	9.29885i	−0.235617	−	0.440808i
$446$	14.9931	+	6.40431i	0.709945	+	0.303253i
$447$		−	14.1042i		−	0.667106i
$448$	36.1881	+	9.71582i	1.70973	+	0.459030i
$449$			4.56687i			0.215524i	0.994177	+	0.107762i	$0.0343684\pi$
$449$			4.56687i			0.215524i	−0.994177	+	0.107762i	$0.965632\pi$
$450$	−4.16889	+	9.75978i	−0.196523	+	0.460080i
$451$	−0.0456588	−	0.0854216i	−0.00214999	−	0.00402235i
$452$	1.54915	−	0.602135i	0.0728657	−	0.0283221i
$453$	−2.30614	+	1.89260i	−0.108352	+	0.0889223i
$454$	18.7362	−	1.63764i	0.879333	−	0.0768584i
$455$	−26.3733	−	39.4705i	−1.23640	−	1.85040i
$456$	−3.95684	−	24.0033i	−0.185296	−	1.12406i
$457$	24.8964	+	16.6353i	1.16461	+	0.778165i	0.978880	−	0.204437i	$-0.0655362\pi$
$457$	24.8964	+	16.6353i	1.16461	+	0.778165i	0.185726	+	0.982602i	$0.440536\pi$
$458$	−19.5314	+	5.69113i	−0.912643	+	0.265929i
$459$	0.460057	+	1.51660i	0.0214736	+	0.0707890i
$460$	−13.2031	+	1.00793i	−0.615596	+	0.0469949i
$461$	6.55117	−	7.98263i	0.305119	−	0.371788i	−0.597766	−	0.801670i	$-0.703945\pi$
$461$	6.55117	−	7.98263i	0.305119	−	0.371788i	0.902885	+	0.429882i	$0.141445\pi$
$462$	1.06190	−	0.199118i	0.0494040	−	0.00926379i
$463$	−12.8769	+	31.0876i	−0.598441	+	1.44476i	0.276729	+	0.960948i	$0.410750\pi$
$463$	−12.8769	+	31.0876i	−0.598441	+	1.44476i	−0.875170	+	0.483816i	$0.839250\pi$
$464$	−20.5872	−	7.24747i	−0.955739	−	0.336455i
$465$	11.4231	+	27.5779i	0.529735	+	1.27889i
$466$	0.0330746	+	0.0506972i	0.00153215	+	0.00234850i
$467$	−14.8904	+	1.46657i	−0.689045	+	0.0678650i	−0.436479	−	0.899715i	$-0.643775\pi$
$467$	−14.8904	+	1.46657i	−0.689045	+	0.0678650i	−0.252566	+	0.967580i	$0.581275\pi$
$468$	−2.81269	+	4.99488i	−0.130017	+	0.230888i
$469$	−41.0601	−	21.9471i	−1.89598	−	1.01342i
$470$	−49.9175	−	5.47104i	−2.30252	−	0.252360i
$471$	−1.95908	−	9.84895i	−0.0902696	−	0.453816i
$472$	7.27565	−	1.94757i	0.334889	−	0.0896442i
$473$	1.45284	+	0.288988i	0.0668018	+	0.0132877i
$474$	3.23470	−	1.68354i	0.148575	−	0.0773275i
$475$	64.2346	+	6.32655i	2.94728	+	0.290282i
$476$	2.57555	+	14.6208i	0.118050	+	0.670143i
$477$	10.3308	+	3.13382i	0.473015	+	0.143488i
$478$	−10.7573	−	10.9964i	−0.492027	−	0.502963i
$479$	3.06998	−	3.06998i	0.140271	−	0.140271i	−0.633484	−	0.773755i	$-0.718376\pi$
$479$	3.06998	−	3.06998i	0.140271	−	0.140271i	0.773755	+	0.633484i	$0.218376\pi$
$480$	19.9733	+	1.09874i	0.911654	+	0.0501506i
$481$	1.05091	+	1.05091i	0.0479174	+	0.0479174i
$482$	0.292750	−	26.6343i	0.0133344	−	1.21316i
$483$	2.54559	−	8.39168i	0.115828	−	0.381835i
$484$	4.75370	−	21.4258i	0.216077	−	0.973899i
$485$	1.33390	−	13.5433i	0.0605691	−	0.614969i
$486$	−0.425374	+	1.34872i	−0.0192953	+	0.0611794i
$487$	7.16380	−	36.0149i	0.324623	−	1.63199i	−0.381832	−	0.924232i	$-0.624707\pi$
$487$	7.16380	−	36.0149i	0.324623	−	1.63199i	0.706455	−	0.707758i	$-0.250293\pi$
$488$	−1.02571	−	15.7091i	−0.0464319	−	0.711118i
$489$	−19.0893	+	3.79709i	−0.863247	+	0.171710i
$490$	−46.7509	−	58.2603i	−2.11199	−	2.63193i
$491$	−11.1731	+	20.9034i	−0.504236	+	0.943359i	0.493069	+	0.869990i	$0.335875\pi$
$491$	−11.1731	+	20.9034i	−0.504236	+	0.943359i	−0.997305	+	0.0733685i	$0.976625\pi$
$492$	1.17908	+	0.142360i	0.0531570	+	0.00641809i
$493$	−0.847612	−	8.60595i	−0.0381745	−	0.387592i
$494$	34.1165	+	7.17686i	1.53497	+	0.322902i
$495$	0.532880	−	0.220726i	0.0239512	−	0.00992090i
$496$	24.9021	−	22.8034i	1.11814	−	1.02390i
$497$	−37.8170	−	15.6643i	−1.69632	−	0.702640i
$498$	−15.4508	−	10.5714i	−0.692369	−	0.473715i
$499$	−32.3065	−	26.5132i	−1.44624	−	1.18690i	−0.947338	−	0.320236i	$-0.896238\pi$
$499$	−32.3065	−	26.5132i	−1.44624	−	1.18690i	−0.498899	−	0.866660i	$-0.666262\pi$
$500$	−5.51286	+	16.8323i	−0.246543	+	0.752764i
$501$	−12.0905	+	3.66762i	−0.540165	+	0.163857i
$502$	−1.82916	+	3.33346i	−0.0816392	+	0.148779i
$503$	−2.28891	+	3.42559i	−0.102057	+	0.152740i	−0.878984	−	0.476852i	$-0.841778\pi$
$503$	−2.28891	+	3.42559i	−0.102057	+	0.152740i	0.776926	+	0.629592i	$0.216778\pi$
$504$	−5.47034	+	12.0653i	−0.243668	+	0.537433i
$505$	25.7500	−	17.2056i	1.14586	−	0.765639i
$506$	0.330823	+	0.277640i	0.0147069	+	0.0123426i
$507$	3.03556	+	3.69884i	0.134814	+	0.164271i
$508$	−9.91265	+	9.48615i	−0.439803	+	0.420880i
$509$	31.2540	−	16.7056i	1.38531	−	0.740464i	0.400863	−	0.916138i	$-0.368710\pi$
$509$	31.2540	−	16.7056i	1.38531	−	0.740464i	0.984448	+	0.175674i	$0.0562105\pi$
$510$	2.95235	+	7.35523i	0.130732	+	0.325695i
$511$	27.9793			1.23773
$512$	−6.55227	−	21.6580i	−0.289572	−	0.957156i
$513$	8.60097			0.379742
$514$	13.1554	+	32.7742i	0.580259	+	1.44561i
$515$	25.7727	−	13.7758i	1.13568	−	0.607034i
$516$	−13.1225	+	12.5579i	−0.577687	+	0.552831i
$517$	1.03906	+	1.26610i	0.0456977	+	0.0556829i
$518$	2.63090	+	2.20796i	0.115595	+	0.0970123i
$519$	−5.25952	+	3.51430i	−0.230867	+	0.154261i
$520$	−11.8375	+	26.1087i	−0.519110	+	1.14494i
$521$	−18.7765	+	28.1010i	−0.822613	+	1.23113i	0.147642	+	0.989041i	$0.452832\pi$
$521$	−18.7765	+	28.1010i	−0.822613	+	1.23113i	−0.970255	+	0.242086i	$0.922168\pi$
$522$	3.71213	−	6.76499i	0.162476	−	0.296096i
$523$	12.5893	−	3.81894i	0.550494	−	0.166990i	−0.00277076	−	0.999996i	$-0.500882\pi$
$523$	12.5893	−	3.81894i	0.550494	−	0.166990i	0.553264	+	0.833006i	$0.313382\pi$
$524$	−4.91332	+	15.0017i	−0.214639	+	0.655354i
$525$	−27.1702	−	22.2980i	−1.18580	−	0.973164i
$526$	13.5169	+	9.24819i	0.589364	+	0.403240i
$527$	12.3599	+	5.11965i	0.538407	+	0.223016i
$528$	−0.440625	−	0.481177i	−0.0191757	−	0.0209405i
$529$	−18.0106	+	7.46023i	−0.783069	+	0.324358i
$530$	52.8316	+	11.1139i	2.29486	+	0.482755i
$531$	0.261010	+	2.65007i	0.0113269	+	0.115003i
$532$	79.9880	+	9.65762i	3.46792	+	0.418711i
$533$	−0.802318	+	1.50103i	−0.0347522	+	0.0650169i
$534$	−2.63912	−	3.28883i	−0.114206	−	0.142322i
$535$	70.7958	−	14.0822i	3.06077	−	0.608825i
$536$	1.83188	+	28.0557i	0.0791250	+	1.21182i
$537$	−1.69919	+	8.54241i	−0.0733255	+	0.368632i
$538$	−0.874124	+	2.77157i	−0.0376862	+	0.119491i
$539$	−0.238809	+	2.42467i	−0.0102862	+	0.104438i
$540$	−1.53187	+	6.90442i	−0.0659213	+	0.297119i
$541$	−11.8498	+	39.0635i	−0.509462	+	1.67947i	0.204156	+	0.978938i	$0.434555\pi$
$541$	−11.8498	+	39.0635i	−0.509462	+	1.67947i	−0.713619	+	0.700534i	$0.752945\pi$
$542$	−0.00878897	+	0.799617i	−0.000377519	+	0.0343465i
$543$	−10.5612	−	10.5612i	−0.453225	−	0.453225i
$544$	6.67802	−	5.98161i	0.286318	−	0.256459i
$545$	9.11919	−	9.11919i	0.390623	−	0.390623i
$546$	−13.2760	−	13.5711i	−0.568161	−	0.580790i
$547$	16.7651	+	5.08565i	0.716825	+	0.217447i	0.627568	−	0.778562i	$-0.284051\pi$
$547$	16.7651	+	5.08565i	0.716825	+	0.217447i	0.0892576	+	0.996009i	$0.471551\pi$
$548$	−0.790150	−	4.48550i	−0.0337535	−	0.191611i
$549$	5.53904	+	0.545547i	0.236400	+	0.0232834i
$550$	1.53554	−	0.799192i	0.0654758	−	0.0340777i
$551$	−46.0288	−	9.15569i	−1.96089	−	0.390046i
$552$	−5.11555	+	1.36935i	−0.217732	+	0.0582832i
$553$	2.35612	+	11.8450i	0.100192	+	0.503701i
$554$	35.9961	+	3.94523i	1.52933	+	0.167617i
$555$	1.61710	+	0.864360i	0.0686423	+	0.0366901i
$556$	6.11888	−	10.8661i	0.259498	−	0.460827i
$557$	40.8034	−	4.01878i	1.72889	−	0.170281i	0.815884	−	0.578216i	$-0.196251\pi$
$557$	40.8034	−	4.01878i	1.72889	−	0.170281i	0.913011	+	0.407935i	$0.133751\pi$
$558$	6.52286	+	9.99831i	0.276135	+	0.423262i
$559$	−9.96107	−	24.0482i	−0.421308	−	1.01713i
$560$	−21.9989	+	62.4902i	−0.929622	+	2.64069i
$561$	0.0989257	−	0.238828i	0.00417665	−	0.0100833i
$562$	10.6624	−	1.99931i	0.449764	−	0.0843357i
$563$	−11.8655	+	14.4582i	−0.500072	+	0.609340i	−0.960474	−	0.278371i	$-0.910205\pi$
$563$	−11.8655	+	14.4582i	−0.500072	+	0.609340i	0.460401	+	0.887711i	$0.347705\pi$
$564$	−20.0248	+	1.52870i	−0.843195	+	0.0643699i
$565$	0.853043	+	2.81211i	0.0358878	+	0.118306i
$566$	13.2154	−	3.85076i	0.555486	−	0.161859i
$567$	−3.89436	−	2.60213i	−0.163548	−	0.109279i
$568$	4.02052	+	24.3896i	0.168697	+	1.02336i
$569$	−8.98366	−	13.4450i	−0.376614	−	0.563643i	0.593945	−	0.804506i	$-0.297570\pi$
$569$	−8.98366	−	13.4450i	−0.376614	−	0.563643i	−0.970559	+	0.240862i	$0.922570\pi$
$570$	42.8491	−	3.74524i	1.79475	−	0.156871i
$571$	−27.0640	+	22.2109i	−1.13259	+	0.929496i	−0.998112	−	0.0614199i	$-0.980437\pi$
$571$	−27.0640	+	22.2109i	−1.13259	+	0.929496i	−0.134482	+	0.990916i	$0.542937\pi$
$572$	0.871493	−	0.338739i	0.0364389	−	0.0141634i
$573$	0.970225	+	1.81516i	0.0405317	+	0.0758296i
$574$	−1.54507	+	3.61716i	−0.0644899	+	0.150977i
$575$		−	14.0505i		−	0.585946i
$576$	7.93208	−	1.04027i	0.330503	−	0.0433447i
$577$		−	9.26843i		−	0.385850i	−0.981214	−	0.192925i	$-0.938203\pi$
$577$		−	9.26843i		−	0.385850i	0.981214	−	0.192925i	$-0.0617974\pi$
$578$	−18.8425	−	8.04857i	−0.783745	−	0.334776i
$579$	0.962078	+	1.79992i	0.0399826	+	0.0748022i
$580$	15.5477	−	35.3189i	0.645581	−	1.46654i
$581$	47.9284	−	39.3339i	1.98841	−	1.63184i
$582$	−0.473902	−	5.42189i	−0.0196439	−	0.224745i
$583$	−0.978297	−	1.46412i	−0.0405169	−	0.0606379i
$584$	−8.91883	−	14.3506i	−0.369064	−	0.593831i
$585$	−8.42718	−	5.63086i	−0.348421	−	0.232808i
$586$	11.5852	+	39.7594i	0.478581	+	1.64244i
$587$	7.74380	+	25.5279i	0.319621	+	1.05365i	0.958679	+	0.284490i	$0.0918243\pi$
$587$	7.74380	+	25.5279i	0.319621	+	1.05365i	−0.639058	+	0.769158i	$0.720676\pi$
$588$	−22.6709	−	19.4550i	−0.934934	−	0.802312i
$589$	46.0596	−	56.1237i	1.89785	−	2.31254i
$590$	2.45428	+	13.0887i	0.101041	+	0.538855i
$591$	−4.28442	+	10.3435i	−0.176237	+	0.425475i
$592$	0.293823	−	2.05322i	0.0120761	−	0.0843866i
$593$	9.60061	+	23.1779i	0.394250	+	0.951803i	0.989003	+	0.147895i	$0.0472497\pi$
$593$	9.60061	+	23.1779i	0.394250	+	0.951803i	−0.594753	+	0.803908i	$0.702750\pi$
$594$	0.193195	−	0.126039i	0.00792688	−	0.00517146i
$595$	−26.1224	+	2.57283i	−1.07091	+	0.105476i
$596$	−7.59316	−	27.1672i	−0.311028	−	1.11281i
$597$	4.48928	+	2.39957i	0.183734	+	0.0982080i
$598$	0.826832	−	7.54398i	0.0338117	−	0.308496i
$599$	2.49321	+	12.5342i	0.101870	+	0.512135i	0.997703	+	0.0677436i	$0.0215800\pi$
$599$	2.49321	+	12.5342i	0.101870	+	0.512135i	−0.895833	+	0.444391i	$0.853420\pi$
$600$	−2.77573	+	21.0434i	−0.113319	+	0.859095i
$601$	0.939398	+	0.186858i	0.0383189	+	0.00762210i	0.214213	−	0.976787i	$-0.431281\pi$
$601$	0.939398	+	0.186858i	0.0383189	+	0.00762210i	−0.175894	+	0.984409i	$0.556281\pi$
$602$	−27.7718	−	53.3599i	−1.13189	−	2.17479i
$603$	−9.89245	−	0.974321i	−0.402852	−	0.0396774i
$604$	−3.42314	+	4.88703i	−0.139286	+	0.198851i
$605$	37.1328	+	11.2641i	1.50966	+	0.457951i
$606$	8.85360	−	8.66109i	0.359653	−	0.351833i
$607$	−1.48671	+	1.48671i	−0.0603438	+	0.0603438i	−0.736635	−	0.676291i	$-0.763586\pi$
$607$	−1.48671	+	1.48671i	−0.0603438	+	0.0603438i	0.676291	+	0.736635i	$0.263586\pi$
$608$	−20.5440	−	44.1044i	−0.833170	−	1.78867i
$609$	18.0710	+	18.0710i	0.732275	+	0.732275i
$610$	27.8324	+	0.305919i	1.12690	+	0.0123863i
$611$	8.35464	−	27.5415i	0.337992	−	1.11421i
$612$	1.70263	+	2.67357i	0.0688248	+	0.108073i
$613$	1.67694	−	17.0263i	0.0677311	−	0.687685i	−0.900032	−	0.435824i	$-0.856457\pi$
$613$	1.67694	−	17.0263i	0.0677311	−	0.687685i	0.967763	−	0.251862i	$-0.0810428\pi$
$614$	−13.4283	−	4.23514i	−0.541921	−	0.170916i
$615$	−0.409660	+	2.05950i	−0.0165191	+	0.0830470i
$616$	1.93821	−	0.955222i	0.0780927	−	0.0384870i
$617$	6.31861	−	1.25685i	0.254377	−	0.0505988i	−0.0662542	−	0.997803i	$-0.521105\pi$
$617$	6.31861	−	1.25685i	0.254377	−	0.0505988i	0.320632	+	0.947204i	$0.396105\pi$
$618$	9.11533	−	7.31458i	0.366672	−	0.294236i
$619$	0.116722	−	0.218372i	0.00469146	−	0.00877710i	−0.879565	−	0.475779i	$-0.842166\pi$
$619$	0.116722	−	0.218372i	0.00469146	−	0.00877710i	0.884256	+	0.467002i	$0.154666\pi$
$620$	36.8499	+	46.9702i	1.47993	+	1.88637i
$621$	−0.183517	−	1.86328i	−0.00736429	−	0.0747708i
$622$	−0.202706	+	0.963598i	−0.00812777	+	0.0386368i
$623$	12.9025	−	5.34438i	0.516926	−	0.214118i
$624$	−2.72869	+	11.1353i	−0.109235	+	0.445768i
$625$	5.73334	+	2.37483i	0.229334	+	0.0949931i
$626$	−8.98130	+	13.1268i	−0.358965	+	0.524653i
$627$	−1.08446	−	0.889997i	−0.0433093	−	0.0355430i
$628$	−9.07583	−	17.9162i	−0.362165	−	0.714933i
$629$	0.786409	−	0.238555i	0.0313562	−	0.00951179i
$630$	−20.5344	−	11.2677i	−0.818109	−	0.448918i
$631$	−18.9657	+	28.3842i	−0.755012	+	1.12996i	0.232528	+	0.972590i	$0.425300\pi$
$631$	−18.9657	+	28.3842i	−0.755012	+	1.12996i	−0.987540	+	0.157366i	$0.949700\pi$
$632$	5.32427	−	4.98424i	0.211788	−	0.198262i
$633$	−5.89475	+	3.93874i	−0.234295	+	0.156551i
$634$	0.894940	−	1.06637i	0.0355426	−	0.0423509i
$635$	−15.3895	−	18.7522i	−0.610715	−	0.744158i
$636$	21.5861	+	0.474584i	0.855945	+	0.0188185i
$637$	37.7573	−	20.1817i	1.49600	−	0.799628i
$638$	−1.16806	+	0.468855i	−0.0462441	+	0.0185621i
$639$	−8.73940			−0.345725
$640$	39.0638	−	8.63650i	1.54413	−	0.341388i
$641$	−9.84987			−0.389047			−0.194523	−	0.980898i	$-0.562316\pi$
$641$	−9.84987			−0.389047			−0.194523	+	0.980898i	$0.562316\pi$
$642$	26.7904	−	10.7535i	1.05733	−	0.424407i
$643$	−23.5008	+	12.5614i	−0.926779	+	0.495374i	−0.864471	−	0.502683i	$-0.832346\pi$
$643$	−23.5008	+	12.5614i	−0.926779	+	0.495374i	−0.0623085	+	0.998057i	$0.519846\pi$
$644$	0.385503	−	17.5343i	0.0151909	−	0.690949i
$645$	−20.3729	−	24.8244i	−0.802182	−	0.977462i
$646$	12.3925	−	14.7664i	0.487578	−	0.580975i
$647$	−37.3004	+	24.9234i	−1.46643	+	0.979838i	−0.471228	+	0.882011i	$0.656189\pi$
$647$	−37.3004	+	24.9234i	−1.46643	+	0.979838i	−0.995203	+	0.0978267i	$0.968811\pi$
$648$	−0.0932451	+	2.82689i	−0.00366301	+	0.111051i
$649$	0.241310	−	0.361146i	0.00947225	−	0.0141762i
$650$	−26.6674	−	14.6331i	−1.04598	−	0.573958i
$651$	−37.8345	+	11.4770i	−1.48285	+	0.449818i
$652$	−34.7252	+	17.5908i	−1.35994	+	0.688909i
$653$	−27.7205	−	22.7496i	−1.08479	−	0.890262i	−0.0903835	−	0.995907i	$-0.528809\pi$
$653$	−27.7205	−	22.7496i	−1.08479	−	0.890262i	−0.994404	+	0.105645i	$0.966309\pi$
$654$	2.91241	−	4.25670i	0.113884	−	0.166450i
$655$	−25.7860	−	10.6809i	−1.00754	−	0.417339i
$656$	2.34776	−	0.360560i	0.0916646	−	0.0140775i
$657$	5.51902	−	2.28605i	0.215317	−	0.0891874i
$658$	13.6922	−	65.0880i	0.533776	−	2.53740i
$659$	3.58725	+	36.4220i	0.139739	+	1.41880i	0.767828	+	0.640657i	$0.221338\pi$
$659$	3.58725	+	36.4220i	0.139739	+	1.41880i	−0.628088	+	0.778142i	$0.716162\pi$
$660$	0.907592	−	0.712040i	0.0353280	−	0.0277161i
$661$	−3.83288	+	7.17082i	−0.149082	+	0.278913i	−0.945366	−	0.326010i	$-0.894296\pi$
$661$	−3.83288	+	7.17082i	−0.149082	+	0.278913i	0.796285	+	0.604922i	$0.206796\pi$
$662$	13.2901	−	10.6646i	0.516535	−	0.414493i
$663$	−4.45518	+	0.886190i	−0.173025	+	0.0344168i
$664$	−35.4523	−	12.0443i	−1.37582	−	0.467408i
$665$	−27.7910	+	139.715i	−1.07769	+	5.41792i
$666$	0.699358	+	0.220570i	0.0270996	+	0.00854693i
$667$	−1.00135	+	10.1668i	−0.0387723	+	0.393662i
$668$	−21.3140	+	13.5736i	−0.824665	+	0.525177i
$669$	−3.34652	+	11.0320i	−0.129384	+	0.426522i
$670$	−49.7074	−	0.546357i	−1.92036	−	0.0211076i
$671$	−0.641945	−	0.641945i	−0.0247820	−	0.0247820i
$672$	−4.04135	+	26.1850i	−0.155898	+	1.01011i
$673$	10.3991	−	10.3991i	0.400855	−	0.400855i	−0.477680	−	0.878534i	$-0.658522\pi$
$673$	10.3991	−	10.3991i	0.400855	−	0.400855i	0.878534	+	0.477680i	$0.158522\pi$
$674$	21.5473	−	21.0788i	0.829972	−	0.811925i
$675$	−7.18129	−	2.17842i	−0.276408	−	0.0838474i
$676$	7.83835	+	5.49041i	0.301475	+	0.211170i
$677$	−14.3492	−	1.41327i	−0.551485	−	0.0543165i	−0.181563	−	0.983379i	$-0.558116\pi$
$677$	−14.3492	−	1.41327i	−0.551485	−	0.0543165i	−0.369922	+	0.929063i	$0.620616\pi$
$678$	0.542584	+	1.04250i	0.0208378	+	0.0400371i
$679$	17.6788	+	3.51653i	0.678449	+	0.134952i
$680$	9.64652	+	12.5781i	0.369927	+	0.482346i
$681$	2.59451	+	13.0435i	0.0994217	+	0.499826i
$682$	0.212146	−	1.93561i	0.00812348	−	0.0741183i
$683$	30.7325	+	16.4269i	1.17595	+	0.628557i	0.939319	−	0.343044i	$-0.111458\pi$
$683$	30.7325	+	16.4269i	1.17595	+	0.628557i	0.236627	+	0.971600i	$0.423958\pi$
$684$	16.5670	−	4.63043i	0.633456	−	0.177049i
$685$	8.01406	−	0.789316i	0.306202	−	0.0301582i
$686$	44.0317	−	28.7261i	1.68114	−	1.09677i
$687$	−5.50496	−	13.2901i	−0.210027	−	0.507051i
$688$	−18.5156	+	31.2535i	−0.705902	+	1.19153i
$689$	−11.8411	+	28.5870i	−0.451111	+	1.08908i
$690$	−1.72562	−	9.20275i	−0.0656931	−	0.350343i
$691$	23.4293	−	28.5487i	0.891292	−	1.08604i	−0.104511	−	0.994524i	$-0.533328\pi$
$691$	23.4293	−	28.5487i	0.891292	−	1.08604i	0.995803	−	0.0915190i	$-0.0291722\pi$
$692$	−8.23882	+	9.60069i	−0.313193	+	0.364964i
$693$	0.221767	+	0.731066i	0.00842422	+	0.0277709i
$694$	−6.41635	−	22.0203i	−0.243561	−	0.835879i
$695$	18.3330	+	12.2497i	0.695409	+	0.464657i
$696$	3.50822	−	15.0291i	0.132979	−	0.569675i
$697$	0.522856	+	0.782509i	0.0198046	+	0.0296396i
$698$	2.70602	+	30.9594i	0.102424	+	1.17183i
$699$	−0.0330869	+	0.0271537i	−0.00125146	+	0.00102705i
$700$	−64.3390	−	28.3226i	−2.43179	−	1.07049i
$701$	−1.16621	−	2.18183i	−0.0440471	−	0.0824064i	0.858935	−	0.512085i	$-0.171127\pi$
$701$	−1.16621	−	2.18183i	−0.0440471	−	0.0824064i	−0.902982	+	0.429679i	$0.858627\pi$
$702$	−3.72758	−	1.59223i	−0.140688	−	0.0600950i
$703$		−	4.45989i		−	0.168208i
$704$	−1.10777	−	0.689618i	−0.0417506	−	0.0259909i
$705$		−	35.5084i		−	1.33732i
$706$	11.5322	−	26.9981i	0.434021	−	1.01609i
$707$	19.3364	+	36.1758i	0.727219	+	1.36053i
$708$	1.92945	+	4.96400i	0.0725132	+	0.186559i
$709$	15.2059	−	12.4792i	0.571069	−	0.468664i	−0.303993	−	0.952674i	$-0.598320\pi$
$709$	15.2059	−	12.4792i	0.571069	−	0.468664i	0.875063	+	0.484010i	$0.160820\pi$
$710$	−43.5387	+	3.80552i	−1.63398	+	0.142819i
$711$	1.43255	+	2.14397i	0.0537249	+	0.0804051i
$712$	−6.85400	−	4.91408i	−0.256864	−	0.184163i
$713$	−13.1412	−	8.78065i	−0.492141	−	0.328838i
$714$	−10.0785	+	2.93671i	−0.377179	+	0.109904i
$715$	0.479891	+	1.58199i	0.0179469	+	0.0591630i
$716$	1.32596	+	17.3690i	0.0495534	+	0.649110i
$717$	6.90061	−	8.40842i	0.257708	−	0.314018i
$718$	−26.4953	+	4.96815i	−0.988795	+	0.185410i
$719$	15.2589	−	36.8383i	0.569062	−	1.37384i	−0.333284	−	0.942827i	$-0.608157\pi$
$719$	15.2589	−	36.8383i	0.569062	−	1.37384i	0.902346	−	0.431012i	$-0.141843\pi$
$720$	0.766415	+	14.1239i	0.0285626	+	0.526365i
$721$	14.8125	+	35.7605i	0.551645	+	1.33179i
$722$	−42.4818	−	65.1166i	−1.58101	−	2.42339i
$723$	18.7437	−	1.84609i	0.697086	−	0.0686570i
$724$	−26.0285	−	14.6570i	−0.967343	−	0.544725i
$725$	36.1123	+	19.3024i	1.34118	+	0.716874i
$726$	15.4263	+	1.69075i	0.572525	+	0.0627497i
$727$	−4.64827	−	23.3684i	−0.172395	−	0.866686i	−0.966057	−	0.258328i	$-0.916828\pi$
$727$	−4.64827	−	23.3684i	−0.172395	−	0.866686i	0.793663	−	0.608358i	$-0.208172\pi$
$728$	−32.8781	−	18.9931i	−1.21855	−	0.703931i
$729$	−0.980785	−	0.195090i	−0.0363254	−	0.00722557i
$730$	26.4997	−	13.7921i	0.980798	−	0.510468i
$731$	−14.3236	−	1.41075i	−0.529779	−	0.0521787i
$732$	10.9629	−	1.93118i	0.405200	−	0.0713785i
$733$	25.1630	+	7.63312i	0.929418	+	0.281936i	0.718467	−	0.695561i	$-0.244844\pi$
$733$	25.1630	+	7.63312i	0.929418	+	0.281936i	0.210951	+	0.977497i	$0.432344\pi$
$734$	−25.7438	−	26.3161i	−0.950222	−	0.971343i
$735$	37.3494	−	37.3494i	1.37765	−	1.37765i
$736$	−9.11626	+	5.39162i	−0.336030	+	0.198738i
$737$	1.14648	+	1.14648i	0.0422312	+	0.0422312i
$738$	−0.00922997	+	0.839739i	−0.000339760	+	0.0309112i
$739$	2.11838	−	6.98338i	0.0779260	−	0.256888i	−0.909318	−	0.416102i	$-0.863396\pi$
$739$	2.11838	−	6.98338i	0.0779260	−	0.256888i	0.987244	+	0.159214i	$0.0508960\pi$
$740$	3.58017	+	0.794326i	0.131610	+	0.0292000i
$741$	−2.41632	+	24.5333i	−0.0887656	+	0.901252i
$742$	−21.5085	+	68.1966i	−0.789602	+	2.50357i
$743$	−8.38174	+	42.1378i	−0.307496	+	1.54589i	0.449989	+	0.893034i	$0.351428\pi$
$743$	−8.38174	+	42.1378i	−0.307496	+	1.54589i	−0.757485	+	0.652853i	$0.773572\pi$
$744$	17.9469	+	15.7469i	0.657965	+	0.577309i
$745$	48.9164	−	9.73008i	1.79216	−	0.356483i
$746$	3.46223	+	4.31458i	0.126761	+	0.157968i
$747$	6.24029	−	11.6748i	0.228320	−	0.427157i
$748$	0.0619730	−	0.513283i	0.00226596	−	0.0187675i
$749$	9.37117	+	95.1470i	0.342415	+	3.47660i
$750$	−12.2561	−	2.57824i	−0.447529	−	0.0941440i
$751$	17.3924	−	7.20415i	0.634656	−	0.262883i	−0.0420738	−	0.999115i	$-0.513396\pi$
$751$	17.3924	−	7.20415i	0.634656	−	0.262883i	0.676730	+	0.736231i	$0.263396\pi$
$752$	−37.7483	+	13.7251i	−1.37654	+	0.500503i
$753$	−2.48400	−	1.02890i	−0.0905218	−	0.0374954i
$754$	18.2535	+	12.4889i	0.664753	+	0.454820i
$755$	−8.15489	−	6.69255i	−0.296787	−	0.243567i
$756$	−8.90212	−	2.91559i	−0.323767	−	0.106039i
$757$	−11.5427	+	3.50143i	−0.419525	+	0.127262i	−0.492988	−	0.870036i	$-0.664095\pi$
$757$	−11.5427	+	3.50143i	−0.419525	+	0.127262i	0.0734621	+	0.997298i	$0.476595\pi$
$758$	15.2157	−	27.7292i	0.552660	−	1.00717i
$759$	−0.169666	+	0.253924i	−0.00615850	+	0.00921684i
$760$	80.5188	−	30.2823i	2.92072	−	1.09845i
$761$	3.17567	−	2.12192i	0.115118	−	0.0769194i	−0.496678	−	0.867935i	$-0.665447\pi$
$761$	3.17567	−	2.12192i	0.115118	−	0.0769194i	0.611796	+	0.791015i	$0.290447\pi$
$762$	−7.43145	−	6.23677i	−0.269213	−	0.225935i
$763$	10.8365	+	13.2043i	0.392306	+	0.478027i
$764$	2.84604	+	2.97400i	0.102966	+	0.107596i
$765$	−4.94253	+	2.64183i	−0.178697	+	0.0955157i
$766$	12.9732	+	32.3204i	0.468742	+	1.16778i
$767$	−7.63236			−0.275588
$768$	14.7186	−	6.27408i	0.531110	−	0.226396i

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)

\(f(q)\)	\(=\)	\(q+(0.526803 + 1.31243i) q^{2} +(-0.881921 + 0.471397i) q^{3} +(-1.44496 + 1.38279i) q^{4} +(-2.24332 - 2.73349i) q^{5} +(-1.08328 - 0.909129i) q^{6} +(3.89436 - 2.60213i) q^{7} +(-2.57602 - 1.16795i) q^{8} +(0.555570 - 0.831470i) q^{9} +O(q^{10})\)	\(q+(0.526803 + 1.31243i) q^{2} +(-0.881921 + 0.471397i) q^{3} +(-1.44496 + 1.38279i) q^{4} +(-2.24332 - 2.73349i) q^{5} +(-1.08328 - 0.909129i) q^{6} +(3.89436 - 2.60213i) q^{7} +(-2.57602 - 1.16795i) q^{8} +(0.555570 - 0.831470i) q^{9} +(2.40573 - 4.38421i) q^{10} +(-0.156087 + 0.0473485i) q^{11} +(0.622497 - 1.90066i) q^{12} +(2.21559 + 1.81829i) q^{13} +(5.46668 + 3.74027i) q^{14} +(3.26699 + 1.35323i) q^{15} +(0.175800 - 3.99613i) q^{16} +(1.46421 - 0.606495i) q^{17} +(1.38392 + 0.291127i) q^{18} +(-0.843043 - 8.55956i) q^{19} +(7.02133 + 0.847744i) q^{20} +(-2.20788 + 4.13066i) q^{21} +(-0.144369 - 0.179910i) q^{22} +(-1.83632 + 0.365267i) q^{23} +(2.82242 - 0.184288i) q^{24} +(-1.46404 + 7.36023i) q^{25} +(-1.21920 + 3.86569i) q^{26} +(-0.0980171 + 0.995185i) q^{27} +(-2.02899 + 9.14503i) q^{28} +(1.58392 - 5.22147i) q^{29} +(-0.0549638 + 5.00058i) q^{30} +(5.96896 + 5.96896i) q^{31} +(5.33727 - 1.87445i) q^{32} +(0.115337 - 0.115337i) q^{33} +(1.56733 + 1.60217i) q^{34} +(-15.8492 - 4.80779i) q^{35} +(0.346971 + 1.96967i) q^{36} +(0.516036 + 0.0508251i) q^{37} +(10.7897 - 5.61564i) q^{38} +(-2.81111 - 0.559165i) q^{39} +(2.58625 + 9.66161i) q^{40} +(0.115849 + 0.582411i) q^{41} +(-6.58433 - 0.721653i) q^{42} +(-8.00926 - 4.28104i) q^{43} +(0.160066 - 0.284252i) q^{44} +(-3.51913 + 0.346604i) q^{45} +(-1.44677 - 2.21762i) q^{46} +(-3.84272 - 9.27715i) q^{47} +(1.72872 + 3.60715i) q^{48} +(5.71619 - 13.8001i) q^{49} +(-10.4311 + 1.95594i) q^{50} +(-1.00542 + 1.22510i) q^{51} +(-5.71574 + 0.436342i) q^{52} +(3.13382 + 10.3308i) q^{53} +(-1.35775 + 0.395626i) q^{54} +(0.479579 + 0.320445i) q^{55} +(-13.0711 + 2.15472i) q^{56} +(4.77844 + 7.15145i) q^{57} +(7.68724 - 0.671905i) q^{58} +(-2.05845 + 1.68932i) q^{59} +(-6.59188 + 2.56219i) q^{60} +(2.62372 + 4.90863i) q^{61} +(-4.68939 + 10.9783i) q^{62} -4.68371i q^{63} +(5.27178 + 6.01734i) q^{64} -10.1353i q^{65} +(0.212131 + 0.0906118i) q^{66} +(-4.68583 - 8.76657i) q^{67} +(-1.27706 + 2.90105i) q^{68} +(1.44730 - 1.18777i) q^{69} +(-2.03949 - 23.3337i) q^{70} +(-4.85535 - 7.26655i) q^{71} +(-2.40228 + 1.49301i) q^{72} +(4.96699 + 3.31883i) q^{73} +(0.205145 + 0.704037i) q^{74} +(-2.17842 - 7.18129i) q^{75} +(13.0542 + 11.2024i) q^{76} +(-0.484653 + 0.590551i) q^{77} +(-0.747037 - 3.98396i) q^{78} +(-0.986760 + 2.38225i) q^{79} +(-11.3178 + 8.48405i) q^{80} +(-0.382683 - 0.923880i) q^{81} +(-0.703345 + 0.458860i) q^{82} +(13.1741 - 1.29754i) q^{83} +(-2.52153 - 9.02166i) q^{84} +(-4.94253 - 2.64183i) q^{85} +(1.39927 - 12.7669i) q^{86} +(1.06449 + 5.35158i) q^{87} +(0.457385 + 0.0603313i) q^{88} +(2.92443 + 0.581706i) q^{89} +(-2.30878 - 4.43603i) q^{90} +(13.3597 + 1.31582i) q^{91} +(2.14832 - 3.06703i) q^{92} +(-8.07790 - 2.45040i) q^{93} +(10.1513 - 9.93054i) q^{94} +(-21.5062 + 21.5062i) q^{95} +(-3.82344 + 4.16909i) q^{96} +(2.72128 + 2.72128i) q^{97} +(21.1230 + 0.232173i) q^{98} +(-0.0473485 + 0.156087i) 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

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Database

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