LMFDB - Embedded newform 384.2.v.a.229.8

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			229.8
Character	$\chi$	$=$	384.229
Dual form			384.2.v.a.109.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.08380 + 0.908505i) q^{2} +(0.881921 - 0.471397i) q^{3} +(0.349236 - 1.96927i) q^{4} +(1.51317 + 1.84381i) q^{5} +(-0.527558 + 1.31213i) q^{6} +(1.69750 - 1.13424i) q^{7} +(1.41059 + 2.45158i) q^{8} +(0.555570 - 0.831470i) q^{9} +O(q^{10})$	\(q+(-1.08380 + 0.908505i) q^{2} +(0.881921 - 0.471397i) q^{3} +(0.349236 - 1.96927i) q^{4} +(1.51317 + 1.84381i) q^{5} +(-0.527558 + 1.31213i) q^{6} +(1.69750 - 1.13424i) q^{7} +(1.41059 + 2.45158i) q^{8} +(0.555570 - 0.831470i) q^{9} +(-3.31508 - 0.623587i) q^{10} +(1.92877 - 0.585085i) q^{11} +(-0.620310 - 1.90137i) q^{12} +(-1.76228 - 1.44627i) q^{13} +(-0.809292 + 2.77147i) q^{14} +(2.20366 + 0.912787i) q^{15} +(-3.75607 - 1.37548i) q^{16} +(-1.20049 + 0.497260i) q^{17} +(0.153269 + 1.40588i) q^{18} +(0.0663842 + 0.674010i) q^{19} +(4.15941 - 2.33592i) q^{20} +(0.962390 - 1.80051i) q^{21} +(-1.55884 + 2.38641i) q^{22} +(4.83916 - 0.962569i) q^{23} +(2.39970 + 1.49715i) q^{24} +(-0.134477 + 0.676061i) q^{25} +(3.22390 - 0.0335811i) q^{26} +(0.0980171 - 0.995185i) q^{27} +(-1.64079 - 3.73897i) q^{28} +(-1.28397 + 4.23268i) q^{29} +(-3.21760 + 1.01276i) q^{30} +(3.94232 + 3.94232i) q^{31} +(5.32045 - 1.92167i) q^{32} +(1.42521 - 1.42521i) q^{33} +(0.849328 - 1.62958i) q^{34} +(4.65993 + 1.41357i) q^{35} +(-1.44337 - 1.38445i) q^{36} +(1.45144 + 0.142954i) q^{37} +(-0.684289 - 0.670180i) q^{38} +(-2.23596 - 0.444760i) q^{39} +(-2.38576 + 6.31052i) q^{40} +(-1.24514 - 6.25974i) q^{41} +(0.592732 + 2.82572i) q^{42} +(-3.63120 - 1.94092i) q^{43} +(-0.478597 - 4.00260i) q^{44} +(2.37374 - 0.233793i) q^{45} +(-4.37017 + 5.43963i) q^{46} +(3.99335 + 9.64079i) q^{47} +(-3.96095 + 0.557532i) q^{48} +(-1.08375 + 2.61641i) q^{49} +(-0.468460 - 0.854887i) q^{50} +(-0.824333 + 1.00445i) q^{51} +(-3.46355 + 2.96533i) q^{52} +(1.42674 + 4.70334i) q^{53} +(0.797900 + 1.16763i) q^{54} +(3.99734 + 2.67094i) q^{55} +(5.17516 + 2.56162i) q^{56} +(0.376272 + 0.563131i) q^{57} +(-2.45385 - 5.75386i) q^{58} +(-6.73143 + 5.52434i) q^{59} +(2.56712 - 4.02083i) q^{60} +(-3.92102 - 7.33571i) q^{61} +(-7.85429 - 0.691058i) q^{62} -2.04157i q^{63} +(-4.02045 + 6.91636i) q^{64} -5.43776i q^{65} +(-0.249829 + 2.83946i) q^{66} +(2.13980 + 4.00329i) q^{67} +(0.559986 + 2.53776i) q^{68} +(3.81401 - 3.13007i) q^{69} +(-6.33466 + 2.70154i) q^{70} +(-8.27472 - 12.3840i) q^{71} +(2.82209 + 0.189157i) q^{72} +(-6.01751 - 4.02077i) q^{73} +(-1.70294 + 1.16371i) q^{74} +(0.200095 + 0.659625i) q^{75} +(1.35049 + 0.104660i) q^{76} +(2.61047 - 3.18086i) q^{77} +(2.82740 - 1.54935i) q^{78} +(2.42450 - 5.85326i) q^{79} +(-3.14746 - 9.00680i) q^{80} +(-0.382683 - 0.923880i) q^{81} +(7.03649 + 5.65308i) q^{82} +(4.16177 - 0.409899i) q^{83} +(-3.20958 - 2.52401i) q^{84} +(-2.73340 - 1.46103i) q^{85} +(5.69882 - 1.19540i) q^{86} +(0.862911 + 4.33815i) q^{87} +(4.15509 + 3.90320i) q^{88} +(-10.0964 - 2.00831i) q^{89} +(-2.36025 + 2.40994i) q^{90} +(-4.63189 - 0.456202i) q^{91} +(-0.205552 - 9.86579i) q^{92} +(5.33521 + 1.61842i) q^{93} +(-13.0867 - 6.82069i) q^{94} +(-1.14229 + 1.14229i) q^{95} +(3.78635 - 4.20280i) q^{96} +(-9.11913 - 9.11913i) q^{97} +(-1.20246 - 3.82026i) q^{98} +(0.585085 - 1.92877i) 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 $

$2$	−1.08380	+	0.908505i	−0.766361	+	0.642410i
$2$	−1.08380	+	0.908505i	−0.766361	+	0.642410i
$3$	0.881921	−	0.471397i	0.509177	−	0.272161i
$3$	0.881921	−	0.471397i	0.509177	−	0.272161i
$4$	0.349236	−	1.96927i	0.174618	−	0.984636i
$5$	1.51317	+	1.84381i	0.676711	+	0.824575i	0.992239	−	0.124341i	$-0.0396818\pi$
$5$	1.51317	+	1.84381i	0.676711	+	0.824575i	−0.315529	+	0.948916i	$0.602182\pi$
$6$	−0.527558	+	1.31213i	−0.215375	+	0.535674i
$7$	1.69750	−	1.13424i	0.641596	−	0.428701i	−0.191756	−	0.981443i	$-0.561418\pi$
$7$	1.69750	−	1.13424i	0.641596	−	0.428701i	0.833353	+	0.552742i	$0.186418\pi$
$8$	1.41059	+	2.45158i	0.498720	+	0.866763i
$9$	0.555570	−	0.831470i	0.185190	−	0.277157i
$10$	−3.31508	−	0.623587i	−1.04832	−	0.197196i
$11$	1.92877	−	0.585085i	0.581545	−	0.176410i	0.0142132	−	0.999899i	$-0.495476\pi$
$11$	1.92877	−	0.585085i	0.581545	−	0.176410i	0.567332	+	0.823489i	$0.307976\pi$
$12$	−0.620310	−	1.90137i	−0.179068	−	0.548879i
$13$	−1.76228	−	1.44627i	−0.488769	−	0.401123i	0.357471	−	0.933924i	$-0.383639\pi$
$13$	−1.76228	−	1.44627i	−0.488769	−	0.401123i	−0.846240	+	0.532802i	$0.821139\pi$
$14$	−0.809292	+	2.77147i	−0.216292	+	0.740708i
$15$	2.20366	+	0.912787i	0.568983	+	0.235681i
$16$	−3.75607	−	1.37548i	−0.939017	−	0.343870i
$17$	−1.20049	+	0.497260i	−0.291162	+	0.120603i	−0.523484	−	0.852036i	$-0.675368\pi$
$17$	−1.20049	+	0.497260i	−0.291162	+	0.120603i	0.232321	+	0.972639i	$0.425368\pi$
$18$	0.153269	+	1.40588i	0.0361258	+	0.331370i
$19$	0.0663842	+	0.674010i	0.0152296	+	0.154629i	0.999792	−	0.0204066i	$-0.00649608\pi$
$19$	0.0663842	+	0.674010i	0.0152296	+	0.154629i	−0.984562	+	0.175035i	$0.943996\pi$
$20$	4.15941	−	2.33592i	0.930072	−	0.522329i
$21$	0.962390	−	1.80051i	0.210011	−	0.392902i
$22$	−1.55884	+	2.38641i	−0.332346	+	0.508784i
$23$	4.83916	−	0.962569i	1.00903	−	0.200709i	0.337218	−	0.941427i	$-0.390514\pi$
$23$	4.83916	−	0.962569i	1.00903	−	0.200709i	0.671817	+	0.740717i	$0.265514\pi$
$24$	2.39970	+	1.49715i	0.489836	+	0.305604i
$25$	−0.134477	+	0.676061i	−0.0268954	+	0.135212i
$26$	3.22390	−	0.0335811i	0.632259	−	0.00658579i
$27$	0.0980171	−	0.995185i	0.0188634	−	0.191523i
$28$	−1.64079	−	3.73897i	−0.310080	−	0.706598i
$29$	−1.28397	+	4.23268i	−0.238427	+	0.785989i	0.753306	+	0.657670i	$0.228458\pi$
$29$	−1.28397	+	4.23268i	−0.238427	+	0.785989i	−0.991733	+	0.128318i	$0.959042\pi$
$30$	−3.21760	+	1.01276i	−0.587450	+	0.184904i
$31$	3.94232	+	3.94232i	0.708061	+	0.708061i	0.966127	−	0.258066i	$-0.0830853\pi$
$31$	3.94232	+	3.94232i	0.708061	+	0.708061i	−0.258066	+	0.966127i	$0.583085\pi$
$32$	5.32045	−	1.92167i	0.940532	−	0.339706i
$33$	1.42521	−	1.42521i	0.248098	−	0.248098i
$34$	0.849328	−	1.62958i	0.145658	−	0.279471i
$35$	4.65993	+	1.41357i	0.787671	+	0.238937i
$36$	−1.44337	−	1.38445i	−0.240561	−	0.230741i
$37$	1.45144	+	0.142954i	0.238615	+	0.0235015i	0.216618	−	0.976257i	$-0.430498\pi$
$37$	1.45144	+	0.142954i	0.238615	+	0.0235015i	0.0219972	+	0.999758i	$0.492998\pi$
$38$	−0.684289	−	0.670180i	−0.111006	−	0.108718i
$39$	−2.23596	−	0.444760i	−0.358040	−	0.0712187i
$40$	−2.38576	+	6.31052i	−0.377221	+	0.997780i
$41$	−1.24514	−	6.25974i	−0.194458	−	0.977607i	−0.947530	−	0.319668i	$-0.896429\pi$
$41$	−1.24514	−	6.25974i	−0.194458	−	0.977607i	0.753071	−	0.657939i	$-0.228571\pi$
$42$	0.592732	+	2.82572i	0.0914606	+	0.436018i
$43$	−3.63120	−	1.94092i	−0.553752	−	0.295987i	0.170687	−	0.985325i	$-0.445401\pi$
$43$	−3.63120	−	1.94092i	−0.553752	−	0.295987i	−0.724439	+	0.689339i	$0.757901\pi$
$44$	−0.478597	−	4.00260i	−0.0721513	−	0.603415i
$45$	2.37374	−	0.233793i	0.353856	−	0.0348518i
$46$	−4.37017	+	5.43963i	−0.644347	+	0.802030i
$47$	3.99335	+	9.64079i	0.582489	+	1.40625i	0.890549	+	0.454887i	$0.150320\pi$
$47$	3.99335	+	9.64079i	0.582489	+	1.40625i	−0.308060	+	0.951367i	$0.599680\pi$
$48$	−3.96095	+	0.557532i	−0.571714	+	0.0804729i
$49$	−1.08375	+	2.61641i	−0.154822	+	0.373773i
$50$	−0.468460	−	0.854887i	−0.0662502	−	0.120899i
$51$	−0.824333	+	1.00445i	−0.115430	+	0.140651i
$52$	−3.46355	+	2.96533i	−0.480308	+	0.411217i
$53$	1.42674	+	4.70334i	0.195978	+	0.646053i	0.998760	+	0.0497806i	$0.0158522\pi$
$53$	1.42674	+	4.70334i	0.195978	+	0.646053i	−0.802782	+	0.596272i	$0.796648\pi$
$54$	0.797900	+	1.16763i	0.108580	+	0.158894i
$55$	3.99734	+	2.67094i	0.539001	+	0.360149i
$56$	5.17516	+	2.56162i	0.691559	+	0.342310i
$57$	0.376272	+	0.563131i	0.0498384	+	0.0745885i
$58$	−2.45385	−	5.75386i	−0.322206	−	0.755519i
$59$	−6.73143	+	5.52434i	−0.876358	+	0.719208i	−0.960807	−	0.277219i	$-0.910587\pi$
$59$	−6.73143	+	5.52434i	−0.876358	+	0.719208i	0.0844487	+	0.996428i	$0.473087\pi$
$60$	2.56712	−	4.02083i	0.331414	−	0.519087i
$61$	−3.92102	−	7.33571i	−0.502035	−	0.939242i	−0.997504	−	0.0706158i	$-0.977504\pi$
$61$	−3.92102	−	7.33571i	−0.502035	−	0.939242i	0.495468	−	0.868626i	$-0.334996\pi$
$62$	−7.85429	−	0.691058i	−0.997496	−	0.0877645i
$63$		−	2.04157i		−	0.257214i
$64$	−4.02045	+	6.91636i	−0.502556	+	0.864544i
$65$		−	5.43776i		−	0.674471i
$66$	−0.249829	+	2.83946i	−0.0307519	+	0.349513i
$67$	2.13980	+	4.00329i	0.261418	+	0.489079i	0.978049	−	0.208373i	$-0.0668168\pi$
$67$	2.13980	+	4.00329i	0.261418	+	0.489079i	−0.716631	+	0.697452i	$0.754317\pi$
$68$	0.559986	+	2.53776i	0.0679083	+	0.307748i
$69$	3.81401	−	3.13007i	0.459152	−	0.376817i
$70$	−6.33466	+	2.70154i	−0.757136	+	0.322896i
$71$	−8.27472	−	12.3840i	−0.982028	−	1.46971i	−0.880026	−	0.474925i	$-0.842475\pi$
$71$	−8.27472	−	12.3840i	−0.982028	−	1.46971i	−0.102002	−	0.994784i	$-0.532525\pi$
$72$	2.82209	+	0.189157i	0.332587	+	0.0222924i
$73$	−6.01751	−	4.02077i	−0.704297	−	0.470596i	0.151134	−	0.988513i	$-0.451708\pi$
$73$	−6.01751	−	4.02077i	−0.704297	−	0.470596i	−0.855431	+	0.517917i	$0.826708\pi$
$74$	−1.70294	+	1.16371i	−0.197963	+	0.135278i
$75$	0.200095	+	0.659625i	0.0231050	+	0.0761669i
$76$	1.35049	+	0.104660i	0.154912	+	0.0120053i
$77$	2.61047	−	3.18086i	0.297490	−	0.362493i
$78$	2.82740	−	1.54935i	0.320140	−	0.175430i
$79$	2.42450	−	5.85326i	0.272778	−	0.658543i	−0.726822	−	0.686826i	$-0.759004\pi$
$79$	2.42450	−	5.85326i	0.272778	−	0.658543i	0.999600	+	0.0282820i	$0.00900365\pi$
$80$	−3.14746	−	9.00680i	−0.351896	−	1.00699i
$81$	−0.382683	−	0.923880i	−0.0425204	−	0.102653i
$82$	7.03649	+	5.65308i	0.777050	+	0.624278i
$83$	4.16177	−	0.409899i	0.456814	−	0.0449922i	0.133006	−	0.991115i	$-0.457537\pi$
$83$	4.16177	−	0.409899i	0.456814	−	0.0449922i	0.323807	+	0.946123i	$0.395037\pi$
$84$	−3.20958	−	2.52401i	−0.350194	−	0.275392i
$85$	−2.73340	−	1.46103i	−0.296479	−	0.158471i
$86$	5.69882	−	1.19540i	0.614519	−	0.128904i
$87$	0.862911	+	4.33815i	0.0925138	+	0.465098i
$88$	4.15509	+	3.90320i	0.442934	+	0.416083i
$89$	−10.0964	−	2.00831i	−1.07022	−	0.212880i	−0.371615	−	0.928387i	$-0.621196\pi$
$89$	−10.0964	−	2.00831i	−1.07022	−	0.212880i	−0.698606	+	0.715507i	$0.746196\pi$
$90$	−2.36025	+	2.40994i	−0.248793	+	0.254030i
$91$	−4.63189	−	0.456202i	−0.485554	−	0.0478229i
$92$	−0.205552	−	9.86579i	−0.0214303	−	1.02858i
$93$	5.33521	+	1.61842i	0.553235	+	0.167822i
$94$	−13.0867	−	6.82069i	−1.34979	−	0.703501i
$95$	−1.14229	+	1.14229i	−0.117197	+	0.117197i
$96$	3.78635	−	4.20280i	0.386443	−	0.428947i
$97$	−9.11913	−	9.11913i	−0.925907	−	0.925907i	0.0715310	−	0.997438i	$-0.477212\pi$
$97$	−9.11913	−	9.11913i	−0.925907	−	0.925907i	−0.997438	+	0.0715310i	$0.977212\pi$
$98$	−1.20246	−	3.82026i	−0.121466	−	0.385905i
$99$	0.585085	−	1.92877i	0.0588033	−	0.193848i
$100$	1.28439	+	0.500927i	0.128439	+	0.0500927i
$101$	−1.15741	+	11.7513i	−0.115166	+	1.16930i	0.747759	+	0.663970i	$0.231130\pi$
$101$	−1.15741	+	11.7513i	−0.115166	+	1.16930i	−0.862925	+	0.505332i	$0.831370\pi$
$102$	−0.0191403	−	1.83753i	−0.00189517	−	0.181943i
$103$	1.07543	−	5.40655i	0.105965	−	0.532723i	−0.890941	−	0.454120i	$-0.849954\pi$
$103$	1.07543	−	5.40655i	0.105965	−	0.532723i	0.996906	−	0.0786035i	$-0.0250461\pi$
$104$	1.05977	−	6.36047i	0.103919	−	0.623695i
$105$	4.77604	−	0.950014i	0.466094	−	0.0927119i
$106$	−5.81931	−	3.80126i	−0.565221	−	0.369211i
$107$	−1.12667	+	2.10785i	−0.108919	+	0.203773i	−0.930476	−	0.366354i	$-0.880606\pi$
$107$	−1.12667	+	2.10785i	−0.108919	+	0.203773i	0.821557	+	0.570127i	$0.193106\pi$
$108$	−1.92556	−	0.540577i	−0.185287	−	0.0520170i
$109$	−1.65828	−	16.8367i	−0.158834	−	1.61267i	−0.662699	−	0.748886i	$-0.730589\pi$
$109$	−1.65828	−	16.8367i	−0.158834	−	1.61267i	0.503865	−	0.863782i	$-0.331911\pi$
$110$	−6.75887	+	0.736849i	−0.644433	+	0.0702558i
$111$	1.34744	−	0.558129i	0.127894	−	0.0529752i
$112$	−7.93606	+	1.92538i	−0.749888	+	0.181932i
$113$	−15.6486	−	6.48185i	−1.47209	−	0.609761i	−0.504758	−	0.863261i	$-0.668418\pi$
$113$	−15.6486	−	6.48185i	−1.47209	−	0.609761i	−0.967335	+	0.253500i	$0.918418\pi$
$114$	−0.919410	−	0.268475i	−0.0861106	−	0.0251450i
$115$	9.09727	+	7.46594i	0.848325	+	0.696202i
$116$	7.88689	+	4.00669i	0.732279	+	0.372012i
$117$	−2.18160	+	0.661781i	−0.201689	+	0.0611817i
$118$	2.27662	−	12.1028i	0.209580	−	1.11415i
$119$	−1.47383	+	2.20574i	−0.135106	+	0.202200i
$120$	0.870706	+	6.69002i	0.0794842	+	0.610712i
$121$	−5.76835	+	3.85429i	−0.524395	+	0.350390i
$122$	10.9141	+	4.38816i	0.988119	+	0.397286i
$123$	−4.04894	−	4.93364i	−0.365080	−	0.444852i
$124$	9.14029	−	6.38670i	0.820822	−	0.573542i
$125$	9.06790	−	4.84689i	0.811057	−	0.433519i
$126$	1.85478	+	2.21265i	0.165237	+	0.197119i
$127$	13.4180			1.19066			0.595328	−	0.803483i	$-0.297022\pi$
$127$	13.4180			1.19066			0.595328	+	0.803483i	$0.297022\pi$
$128$	−1.92619	−	11.1485i	−0.170253	−	0.985400i
$129$	−4.11737			−0.362514
$130$	4.94023	+	5.89343i	0.433287	+	0.516888i
$131$	−15.5513	+	8.31234i	−1.35872	+	0.726253i	−0.979951	−	0.199237i	$-0.936154\pi$
$131$	−15.5513	+	8.31234i	−1.35872	+	0.726253i	−0.378772	+	0.925490i	$0.623654\pi$
$132$	−2.30890	−	3.30437i	−0.200964	−	0.287608i
$133$	0.877174	+	1.06884i	0.0760607	+	0.0926802i
$134$	−5.95612	−	2.39473i	−0.514530	−	0.206873i
$135$	1.98324	−	1.32516i	0.170690	−	0.114052i
$136$	−2.91248	−	2.24167i	−0.249743	−	0.192221i
$137$	−3.67875	+	5.50564i	−0.314297	+	0.470378i	−0.954662	−	0.297692i	$-0.903783\pi$
$137$	−3.67875	+	5.50564i	−0.314297	+	0.470378i	0.640365	+	0.768071i	$0.278783\pi$
$138$	−1.28992	+	6.85741i	−0.109806	+	0.583742i
$139$	−11.8681	+	3.60016i	−1.00664	+	0.305361i	−0.750209	−	0.661201i	$-0.770047\pi$
$139$	−11.8681	+	3.60016i	−1.00664	+	0.305361i	−0.256433	+	0.966562i	$0.582547\pi$
$140$	4.41112	−	8.68300i	0.372808	−	0.733847i
$141$	8.06645	+	6.61997i	0.679318	+	0.557502i
$142$	20.2190	+	5.90412i	1.69674	+	0.495463i
$143$	−4.24522	−	1.75843i	−0.355003	−	0.147047i
$144$	−3.23043	+	2.35888i	−0.269203	+	0.196573i
$145$	−9.74710	+	4.03738i	−0.809452	+	0.335286i
$146$	10.1747	−	1.10924i	0.842061	−	0.0918011i
$147$	0.277583	+	2.81835i	0.0228947	+	0.232454i
$148$	0.788410	−	2.80835i	0.0648069	−	0.230845i
$149$	−6.57456	+	12.3001i	−0.538609	+	1.00767i	0.454531	+	0.890731i	$0.349807\pi$
$149$	−6.57456	+	12.3001i	−0.538609	+	1.00767i	−0.993140	+	0.116935i	$0.962693\pi$
$150$	−0.816135	−	0.533113i	−0.0666372	−	0.0435285i
$151$	19.7401	−	3.92656i	1.60643	−	0.319539i	0.691259	−	0.722607i	$-0.257056\pi$
$151$	19.7401	−	3.92656i	1.60643	−	0.319539i	0.915170	+	0.403068i	$0.132056\pi$
$152$	−1.55875	+	1.11350i	−0.126431	+	0.0903168i
$153$	−0.253501	+	1.27444i	−0.0204943	+	0.103032i
$154$	0.0606128	+	5.81903i	0.00488431	+	0.468911i
$155$	−1.30346	+	13.2343i	−0.104697	+	1.06300i
$156$	−1.65673	+	4.24789i	−0.132645	+	0.340103i
$157$	−6.23968	+	20.5695i	−0.497981	+	1.64162i	0.242948	+	0.970039i	$0.421885\pi$
$157$	−6.23968	+	20.5695i	−0.497981	+	1.64162i	−0.740929	+	0.671583i	$0.765615\pi$
$158$	2.69005	+	8.54643i	0.214009	+	0.679917i
$159$	3.47541	+	3.47541i	0.275618	+	0.275618i
$160$	11.5939	+	6.90207i	0.916581	+	0.545656i
$161$	7.12272	−	7.12272i	0.561349	−	0.561349i
$162$	1.25410	+	0.653629i	0.0985315	+	0.0513539i
$163$	18.9985	+	5.76313i	1.48808	+	0.451403i	0.926587	−	0.376080i	$-0.122728\pi$
$163$	18.9985	+	5.76313i	1.48808	+	0.451403i	0.561490	+	0.827483i	$0.310228\pi$
$164$	−12.7620	+	0.265894i	−0.996543	+	0.0207628i
$165$	4.78441	+	0.471223i	0.372466	+	0.0366847i
$166$	−4.13812	+	4.22524i	−0.321181	+	0.327942i
$167$	−17.0695	−	3.39533i	−1.32087	−	0.262738i	−0.516207	−	0.856464i	$-0.672656\pi$
$167$	−17.0695	−	3.39533i	−1.32087	−	0.262738i	−0.804667	+	0.593726i	$0.797656\pi$
$168$	5.77162	−	0.180409i	0.445290	−	0.0139188i
$169$	−1.52222	−	7.65274i	−0.117094	−	0.588672i
$170$	4.28981	−	0.899845i	0.329014	−	0.0690150i
$171$	0.597300	+	0.319264i	0.0456767	+	0.0244147i
$172$	−5.09033	+	6.47298i	−0.388134	+	0.493560i
$173$	2.13477	−	0.210257i	0.162304	−	0.0159855i	−0.0165389	−	0.999863i	$-0.505265\pi$
$173$	2.13477	−	0.210257i	0.162304	−	0.0159855i	0.178843	+	0.983878i	$0.442765\pi$
$174$	−4.87645	−	3.91772i	−0.369683	−	0.297001i
$175$	0.538538	+	1.30015i	0.0407097	+	0.0982818i
$176$	−8.04936	−	0.455363i	−0.606743	−	0.0343243i
$177$	−3.33244	+	8.04521i	−0.250481	+	0.604715i
$178$	12.7671	−	6.99607i	0.956932	−	0.524378i
$179$	−5.32959	+	6.49412i	−0.398352	+	0.485393i	−0.933099	−	0.359619i	$-0.882907\pi$
$179$	−5.32959	+	6.49412i	−0.398352	+	0.485393i	0.534747	+	0.845012i	$0.320407\pi$
$180$	0.368593	−	4.75619i	0.0274733	−	0.354506i
$181$	2.84738	+	9.38655i	0.211644	+	0.697697i	0.996911	+	0.0785395i	$0.0250257\pi$
$181$	2.84738	+	9.38655i	0.211644	+	0.697697i	−0.785267	+	0.619157i	$0.787474\pi$
$182$	5.43450	−	3.71367i	0.402832	−	0.275276i
$183$	−6.91606	−	4.62117i	−0.511250	−	0.341606i
$184$	9.18590	+	10.5058i	0.677193	+	0.774496i
$185$	1.93269	+	2.89248i	0.142095	+	0.212660i
$186$	−7.25263	+	3.09303i	−0.531788	+	0.226792i
$187$	−2.02453	+	1.66149i	−0.148048	+	0.121500i
$188$	20.3800	−	4.49708i	1.48636	−	0.327983i
$189$	−0.962390	−	1.80051i	−0.0700036	−	0.130967i
$190$	0.200235	−	2.27579i	0.0145266	−	0.165103i
$191$		−	2.66457i		−	0.192801i	−0.995343	−	0.0964006i	$-0.969267\pi$
$191$		−	2.66457i		−	0.192801i	0.995343	−	0.0964006i	$-0.0307330\pi$
$192$	−0.285374	+	7.99491i	−0.0205951	+	0.576983i
$193$		−	5.89897i		−	0.424617i	−0.977203	−	0.212309i	$-0.931902\pi$
$193$		−	5.89897i		−	0.424617i	0.977203	−	0.212309i	$-0.0680982\pi$
$194$	18.1681	+	1.59852i	1.30439	+	0.114767i
$195$	−2.56334	−	4.79568i	−0.183565	−	0.343425i
$196$	4.77395	+	3.04795i	0.340996	+	0.217711i
$197$	−9.21547	+	7.56294i	−0.656575	+	0.538837i	−0.902629	−	0.430419i	$-0.858366\pi$
$197$	−9.21547	+	7.56294i	−0.656575	+	0.538837i	0.246054	+	0.969256i	$0.420866\pi$
$198$	1.11818	+	2.62195i	0.0794657	+	0.186334i
$199$	3.34864	+	5.01159i	0.237379	+	0.355262i	0.930963	−	0.365113i	$-0.118970\pi$
$199$	3.34864	+	5.01159i	0.237379	+	0.355262i	−0.693585	+	0.720375i	$0.743970\pi$
$200$	−1.84711	+	0.623967i	−0.130610	+	0.0441212i
$201$	3.77427	+	2.52189i	0.266217	+	0.177880i
$202$	−9.42176	−	13.7876i	−0.662913	−	0.970091i
$203$	2.62131	+	8.64131i	0.183980	+	0.606501i
$204$	1.69015	+	1.97413i	0.118334	+	0.138217i
$205$	9.65763	−	11.7679i	0.674518	−	0.821903i
$206$	3.74633	+	6.83664i	0.261019	+	0.476331i
$207$	1.88815	−	4.55839i	0.131235	−	0.316830i
$208$	4.62994	+	7.85627i	0.321029	+	0.544734i
$209$	0.522393	+	1.26117i	0.0361347	+	0.0872368i
$210$	−4.31317	+	5.36868i	−0.297637	+	0.370474i
$211$	−3.89162	+	0.383291i	−0.267910	+	0.0263869i	−0.231080	−	0.972935i	$-0.574226\pi$
$211$	−3.89162	+	0.383291i	−0.267910	+	0.0263869i	−0.0368301	+	0.999322i	$0.511726\pi$
$212$	9.76042	−	1.16707i	0.670349	−	0.0801547i
$213$	−13.1354	−	7.02103i	−0.900024	−	0.481073i
$214$	−0.693910	−	3.30806i	−0.0474347	−	0.226134i
$215$	−1.91596	−	9.63216i	−0.130667	−	0.656908i
$216$	2.57803	−	1.16350i	0.175413	−	0.0791665i
$217$	11.1636	+	2.22058i	0.757836	+	0.150743i
$218$	17.0935	+	16.7411i	1.15772	+	1.13385i
$219$	−7.20235	−	0.709370i	−0.486690	−	0.0479348i
$220$	6.65582	−	6.93906i	0.448735	−	0.467832i
$221$	2.83478	+	0.859921i	0.190688	+	0.0578445i
$222$	−0.953292	+	1.82906i	−0.0639807	+	0.122758i
$223$	16.6668	−	16.6668i	1.11609	−	1.11609i	0.123780	−	0.992310i	$-0.460498\pi$
$223$	16.6668	−	16.6668i	1.11609	−	1.11609i	0.992310	−	0.123780i	$-0.0395018\pi$
$224$	6.85187	−	9.29668i	0.457810	−	0.621161i
$225$	0.487413	+	0.487413i	0.0324942	+	0.0324942i
$226$	22.8487	−	7.19179i	1.51987	−	0.478391i
$227$	8.67960	−	28.6128i	0.576085	−	1.89910i	0.169339	−	0.985558i	$-0.445837\pi$
$227$	8.67960	−	28.6128i	0.576085	−	1.89910i	0.406747	−	0.913541i	$-0.366663\pi$
$228$	1.24037	−	0.544316i	0.0821452	−	0.0360482i
$229$	−0.468204	+	4.75376i	−0.0309398	+	0.314137i	0.967242	+	0.253857i	$0.0816993\pi$
$229$	−0.468204	+	4.75376i	−0.0309398	+	0.314137i	−0.998182	+	0.0602800i	$0.980801\pi$
$230$	−16.6424	+	0.173353i	−1.09737	+	0.0114305i
$231$	0.802778	−	4.03584i	0.0528189	−	0.265538i
$232$	−12.1879	+	2.82284i	−0.800174	+	0.185329i
$233$	27.0721	−	5.38498i	1.77355	−	0.352782i	0.803432	−	0.595397i	$-0.203005\pi$
$233$	27.0721	−	5.38498i	1.77355	−	0.352782i	0.970123	+	0.242615i	$0.0780052\pi$
$234$	1.76318	−	2.69923i	0.115263	−	0.176454i
$235$	−11.7331	+	21.9511i	−0.765384	+	1.43193i
$236$	8.52808	+	15.1853i	0.555131	+	0.988481i
$237$	−0.620990	−	6.30502i	−0.0403376	−	0.409555i
$238$	−0.406595	−	3.72956i	−0.0263557	−	0.241752i
$239$	−25.2426	+	10.4558i	−1.63281	+	0.676331i	−0.995542	−	0.0943146i	$-0.969934\pi$
$239$	−25.2426	+	10.4558i	−1.63281	+	0.676331i	−0.637264	+	0.770645i	$0.719934\pi$
$240$	−7.02159	−	6.45959i	−0.453241	−	0.416964i
$241$	−5.67671	−	2.35137i	−0.365669	−	0.151465i	0.192280	−	0.981340i	$-0.438412\pi$
$241$	−5.67671	−	2.35137i	−0.365669	−	0.151465i	−0.557949	+	0.829875i	$0.688412\pi$
$242$	2.75008	−	9.41784i	0.176782	−	0.605402i
$243$	−0.773010	−	0.634393i	−0.0495886	−	0.0406963i
$244$	−15.8154	+	5.15966i	−1.01248	+	0.330314i
$245$	−6.46406	+	1.96085i	−0.412974	+	0.125274i
$246$	8.87047	+	1.66859i	0.565560	+	0.106386i
$247$	0.857812	−	1.28381i	0.0545813	−	0.0816866i
$248$	−4.10388	+	15.2259i	−0.260597	+	0.966845i
$249$	3.47713	−	2.32334i	0.220354	−	0.147236i
$250$	−5.42434	+	13.4913i	−0.343065	+	0.853264i
$251$	0.538913	+	0.656667i	0.0340159	+	0.0414484i	0.789741	−	0.613441i	$-0.210215\pi$
$251$	0.538913	+	0.656667i	0.0340159	+	0.0414484i	−0.755725	+	0.654889i	$0.772715\pi$
$252$	−4.02041	−	0.712990i	−0.253262	−	0.0449141i
$253$	8.77043	−	4.68789i	0.551392	−	0.294725i
$254$	−14.5424	+	12.1903i	−0.912472	+	0.764889i
$255$	−3.09937			−0.194090
$256$	12.2161	+	10.3328i	0.763506	+	0.645800i
$257$	17.0076			1.06090			0.530451	−	0.847716i	$-0.322023\pi$
$257$	17.0076			1.06090			0.530451	+	0.847716i	$0.322023\pi$
$258$	4.46240	−	3.74065i	0.277817	−	0.232883i
$259$	2.62597	−	1.40361i	0.163170	−	0.0872159i
$260$	−10.7084	−	1.89906i	−0.664109	−	0.117775i
$261$	2.80601	+	3.41913i	0.173688	+	0.211639i
$262$	9.30266	−	23.1373i	0.574720	−	1.42943i
$263$	7.66863	−	5.12402i	0.472868	−	0.315960i	−0.296201	−	0.955126i	$-0.595720\pi$
$263$	7.66863	−	5.12402i	0.472868	−	0.315960i	0.769070	+	0.639165i	$0.220720\pi$
$264$	5.50442	+	1.48362i	0.338773	+	0.0913106i
$265$	−6.51313	+	9.74759i	−0.400099	+	0.598790i
$266$	−1.92173	−	0.361489i	−0.117829	−	0.0221643i
$267$	−9.85098	+	2.98826i	−0.602870	+	0.182879i
$268$	8.63086	−	2.81576i	0.527214	−	0.172000i
$269$	0.629886	+	0.516934i	0.0384048	+	0.0315180i	0.653400	−	0.757013i	$-0.273342\pi$
$269$	0.629886	+	0.516934i	0.0384048	+	0.0315180i	−0.614995	+	0.788531i	$0.710842\pi$
$270$	−0.945519	+	3.23799i	−0.0575425	+	0.197058i
$271$	−9.81622	−	4.06601i	−0.596293	−	0.246993i	0.0640624	−	0.997946i	$-0.479594\pi$
$271$	−9.81622	−	4.06601i	−0.596293	−	0.246993i	−0.660355	+	0.750953i	$0.729594\pi$
$272$	5.19310	−	0.216489i	0.314878	−	0.0131266i
$273$	−4.30002	+	1.78113i	−0.260249	+	0.107799i
$274$	−1.01488	−	9.30916i	−0.0613112	−	0.562387i
$275$	0.136179	+	1.38265i	0.00821189	+	0.0833767i
$276$	−4.83198	−	8.60395i	−0.290851	−	0.517897i
$277$	−9.52208	+	17.8146i	−0.572126	+	1.07037i	0.414908	+	0.909863i	$0.363814\pi$
$277$	−9.52208	+	17.8146i	−0.572126	+	1.07037i	−0.987034	+	0.160510i	$0.948686\pi$
$278$	9.59189	−	14.6841i	0.575284	−	0.880694i
$279$	5.46815	−	1.08768i	0.327370	−	0.0651178i
$280$	3.10778	+	13.4181i	0.185725	+	0.801887i
$281$	2.32655	−	11.6964i	0.138790	−	0.697747i	−0.847244	−	0.531204i	$-0.821740\pi$
$281$	2.32655	−	11.6964i	0.138790	−	0.697747i	0.986034	−	0.166542i	$-0.0532603\pi$
$282$	−14.7567	+	0.153710i	−0.878747	+	0.00915329i
$283$	1.71295	−	17.3918i	0.101824	−	1.03384i	−0.799493	−	0.600676i	$-0.794898\pi$
$283$	1.71295	−	17.3918i	0.101824	−	1.03384i	0.901317	−	0.433161i	$-0.142602\pi$
$284$	−27.2773	+	11.9702i	−1.61861	+	0.710303i
$285$	−0.468939	+	1.54589i	−0.0277776	+	0.0915703i
$286$	6.19851	−	1.95103i	0.366525	−	0.115367i
$287$	−9.21365	−	9.21365i	−0.543865	−	0.543865i
$288$	1.35808	−	5.49141i	0.0800255	−	0.323585i
$289$	−10.8269	+	10.8269i	−0.636877	+	0.636877i
$290$	6.89590	−	13.2310i	0.404941	−	0.776951i
$291$	−12.3411	−	3.74363i	−0.723447	−	0.219455i
$292$	−10.0195	+	10.4459i	−0.586349	+	0.611302i
$293$	−1.00922	−	0.0993990i	−0.0589590	−	0.00580695i	0.0684946	−	0.997651i	$-0.478180\pi$
$293$	−1.00922	−	0.0993990i	−0.0589590	−	0.00580695i	−0.127454	+	0.991845i	$0.540680\pi$
$294$	−2.86133	−	2.80234i	−0.166876	−	0.163436i
$295$	−20.3716	−	4.05217i	−1.18608	−	0.235926i
$296$	1.69693	+	3.75996i	0.0986318	+	0.218543i
$297$	−0.393216	−	1.97683i	−0.0228167	−	0.114707i
$298$	−4.04925	−	19.3039i	−0.234567	−	1.11824i
$299$	−9.92010	−	5.30241i	−0.573694	−	0.306646i
$300$	1.36886	−	0.163677i	0.0790313	−	0.00944990i
$301$	−8.36543	+	0.823923i	−0.482175	+	0.0474901i
$302$	−17.8270	+	22.1896i	−1.02583	+	1.27687i
$303$	4.51880	+	10.9094i	0.259598	+	0.626726i
$304$	0.677745	−	2.62294i	0.0388713	−	0.150436i
$305$	7.59245	−	18.3298i	0.434742	−	1.04956i
$306$	−0.883088	−	1.61154i	−0.0504828	−	0.0921255i
$307$	0.0565020	−	0.0688478i	0.00322474	−	0.00392935i	−0.771396	−	0.636356i	$-0.780441\pi$
$307$	0.0565020	−	0.0688478i	0.00322474	−	0.00392935i	0.774620	+	0.632427i	$0.217941\pi$
$308$	−5.35232	−	6.25159i	−0.304977	−	0.356217i
$309$	−1.60019	−	5.27510i	−0.0910314	−	0.300090i
$310$	−10.6107	−	15.5275i	−0.602648	−	0.881901i
$311$	−12.9406	−	8.64666i	−0.733796	−	0.490307i	0.131658	−	0.991295i	$-0.457970\pi$
$311$	−12.9406	−	8.64666i	−0.733796	−	0.490307i	−0.865454	+	0.500988i	$0.832970\pi$
$312$	−2.06367	−	6.10901i	−0.116832	−	0.345854i
$313$	15.0027	+	22.4532i	0.848005	+	1.26913i	0.961282	+	0.275566i	$0.0888651\pi$
$313$	15.0027	+	22.4532i	0.848005	+	1.26913i	−0.113277	+	0.993563i	$0.536135\pi$
$314$	−11.9249	−	27.9619i	−0.672962	−	1.57798i
$315$	3.76426	−	3.08925i	0.212092	−	0.174059i
$316$	−10.6799	−	6.81867i	−0.600794	−	0.383580i
$317$	11.8589	+	22.1864i	0.666062	+	1.24611i	0.957198	+	0.289432i	$0.0934665\pi$
$317$	11.8589	+	22.1864i	0.666062	+	1.24611i	−0.291137	+	0.956681i	$0.594033\pi$
$318$	−6.92407	−	0.609214i	−0.388283	−	0.0341630i
$319$			8.91508i			0.499149i
$320$	−18.8360	+	3.05271i	−1.05297	+	0.170651i
$321$			2.39006i			0.133400i
$322$	−1.24856	+	14.1906i	−0.0695795	+	0.790812i
$323$	−0.414852	−	0.776134i	−0.0230830	−	0.0431852i
$324$	−1.95302	+	0.430956i	−0.108501	+	0.0239420i
$325$	1.21475	−	0.996922i	0.0673824	−	0.0552993i
$326$	−25.8264	+	11.0142i	−1.43039	+	0.610019i
$327$	−9.39926	−	14.0670i	−0.519780	−	0.777906i
$328$	13.5898	−	11.8825i	0.750373	−	0.656102i
$329$	17.7137	+	11.8359i	0.976585	+	0.652533i
$330$	−5.61344	+	3.83595i	−0.309010	+	0.211162i
$331$	−5.16241	−	17.0182i	−0.283751	−	0.935403i	−0.976735	−	0.214450i	$-0.931204\pi$
$331$	−5.16241	−	17.0182i	−0.283751	−	0.935403i	0.692984	−	0.720953i	$-0.256296\pi$
$332$	0.646237	−	8.33881i	0.0354669	−	0.457652i
$333$	0.925237	−	1.12741i	0.0507027	−	0.0617814i
$334$	21.5845	−	11.8278i	1.18105	−	0.647191i
$335$	−4.14339	+	10.0030i	−0.226378	+	0.546524i
$336$	−6.09136	+	5.43907i	−0.332311	+	0.296726i
$337$	−8.27412	−	19.9755i	−0.450720	−	1.08813i	−0.972049	−	0.234779i	$-0.924563\pi$
$337$	−8.27412	−	19.9755i	−0.450720	−	1.08813i	0.521329	−	0.853356i	$-0.325437\pi$
$338$	8.60234	+	6.91107i	0.467906	+	0.375913i
$339$	−16.8563	+	1.66020i	−0.915510	+	0.0901699i
$340$	−3.83178	+	4.87257i	−0.207807	+	0.264252i
$341$	9.91040	+	5.29722i	0.536678	+	0.286861i
$342$	−0.937405	+	0.196633i	−0.0506891	+	0.0106327i
$343$	3.91599	+	19.6870i	0.211444	+	1.06300i
$344$	−0.363842	−	11.6400i	−0.0196170	−	0.627587i
$345$	11.5425	+	2.29594i	0.621427	+	0.123609i
$346$	−2.12264	+	2.16733i	−0.114114	+	0.116516i
$347$	17.7051	+	1.74380i	0.950461	+	0.0936122i	0.561350	−	0.827579i	$-0.310282\pi$
$347$	17.7051	+	1.74380i	0.950461	+	0.0936122i	0.389111	+	0.921191i	$0.372782\pi$
$348$	8.84435	−	0.184271i	0.474107	−	0.00987795i
$349$	19.1039	+	5.79511i	1.02261	+	0.310205i	0.756679	−	0.653787i	$-0.226821\pi$
$349$	19.1039	+	5.79511i	1.02261	+	0.310205i	0.265931	+	0.963992i	$0.414321\pi$
$350$	−1.76486	−	0.919831i	−0.0943355	−	0.0491670i
$351$	−1.61204	+	1.61204i	−0.0860442	+	0.0860442i
$352$	9.13757	−	6.81936i	0.487034	−	0.363473i
$353$	5.11721	+	5.11721i	0.272361	+	0.272361i	0.830050	−	0.557689i	$-0.188312\pi$
$353$	5.11721	+	5.11721i	0.272361	+	0.272361i	−0.557689	+	0.830050i	$0.688312\pi$
$354$	−3.69743	−	11.7469i	−0.196516	−	0.624342i
$355$	10.3126	−	33.9961i	0.547336	−	1.80432i
$356$	−7.48094	+	19.1813i	−0.396489	+	1.01661i
$357$	−0.260022	+	2.64005i	−0.0137618	+	0.139726i
$358$	−0.123748	−	11.8803i	−0.00654030	−	0.627892i
$359$	1.84862	−	9.29362i	0.0975662	−	0.490498i	−0.900845	−	0.434142i	$-0.857052\pi$
$359$	1.84862	−	9.29362i	0.0975662	−	0.490498i	0.998411	−	0.0563565i	$-0.0179483\pi$
$360$	3.92155	+	5.48962i	0.206684	+	0.289328i
$361$	18.1850	−	3.61723i	0.957107	−	0.190380i
$362$	−11.6137	−	7.58626i	−0.610403	−	0.398725i
$363$	−3.27033	+	6.11836i	−0.171648	+	0.321130i
$364$	−2.51601	+	8.96214i	−0.131875	+	0.469744i
$365$	−1.69201	−	17.1792i	−0.0885637	−	0.899203i
$366$	11.6940	−	1.27487i	0.611253	−	0.0666386i
$367$	12.8204	−	5.31038i	0.669219	−	0.277200i	−0.0220929	−	0.999756i	$-0.507033\pi$
$367$	12.8204	−	5.31038i	0.669219	−	0.277200i	0.691312	+	0.722556i	$0.257033\pi$
$368$	−19.5002	−	3.04070i	−1.01652	−	0.158507i
$369$	−5.89655	−	2.44243i	−0.306962	−	0.127148i
$370$	−4.72249	−	1.37900i	−0.245510	−	0.0716909i
$371$	7.75660	+	6.36567i	0.402702	+	0.330489i
$372$	5.05035	−	9.94127i	0.261848	−	0.515431i
$373$	17.6137	−	5.34306i	0.912003	−	0.276653i	0.200794	−	0.979634i	$-0.435648\pi$
$373$	17.6137	−	5.34306i	0.912003	−	0.276653i	0.711209	+	0.702981i	$0.248148\pi$
$374$	0.684710	−	3.64002i	0.0354055	−	0.188221i
$375$	5.71236	−	8.54916i	0.294985	−	0.441476i
$376$	−18.0021	+	23.3892i	−0.928389	+	1.20621i
$377$	8.38430	−	5.60221i	0.431814	−	0.288529i
$378$	2.67881	+	1.07705i	0.137783	+	0.0553973i
$379$	7.58167	+	9.23829i	0.389444	+	0.474539i	0.930418	−	0.366501i	$-0.119444\pi$
$379$	7.58167	+	9.23829i	0.389444	+	0.474539i	−0.540974	+	0.841039i	$0.681944\pi$
$380$	1.85056	+	2.64842i	0.0949315	+	0.135861i
$381$	11.8336	−	6.32520i	0.606255	−	0.324050i
$382$	2.42077	+	2.88785i	0.123858	+	0.147755i
$383$	8.84381			0.451898			0.225949	−	0.974139i	$-0.427452\pi$
$383$	8.84381			0.451898			0.225949	+	0.974139i	$0.427452\pi$
$384$	−6.95413	−	8.92413i	−0.354876	−	0.455408i
$385$	9.81497			0.500217
$386$	5.35925	+	6.39330i	0.272779	+	0.325410i
$387$	−3.63120	+	1.94092i	−0.184584	+	0.0986623i
$388$	−21.1428	+	14.7733i	−1.07336	+	0.750002i
$389$	2.11087	+	2.57211i	0.107026	+	0.130411i	0.823768	−	0.566927i	$-0.191868\pi$
$389$	2.11087	+	2.57211i	0.107026	+	0.130411i	−0.716743	+	0.697338i	$0.754368\pi$
$390$	7.13504	+	2.86873i	0.361297	+	0.145264i
$391$	−5.33073	+	3.56188i	−0.269586	+	0.180132i
$392$	−7.94308	+	1.03379i	−0.401186	+	0.0522143i
$393$	−9.79661	+	14.6617i	−0.494174	+	0.739583i
$394$	3.11674	−	16.5690i	0.157019	−	0.834735i
$395$	14.4610	−	4.38668i	0.727610	−	0.220718i
$396$	−3.59394	−	1.82579i	−0.180602	−	0.0917492i
$397$	−16.2736	−	13.3554i	−0.816747	−	0.670287i	0.130267	−	0.991479i	$-0.458417\pi$
$397$	−16.2736	−	13.3554i	−0.816747	−	0.670287i	−0.947014	+	0.321192i	$0.895917\pi$
$398$	−8.18231	−	2.38930i	−0.410142	−	0.119765i
$399$	1.27745	+	0.529136i	0.0639523	+	0.0264899i
$400$	1.43501	−	2.35436i	0.0717507	−	0.117718i
$401$	−25.1296	+	10.4090i	−1.25491	+	0.519801i	−0.908344	−	0.418224i	$-0.862653\pi$
$401$	−25.1296	+	10.4090i	−1.25491	+	0.519801i	−0.346567	+	0.938025i	$0.612653\pi$
$402$	−6.38170	+	0.695730i	−0.318290	+	0.0346998i
$403$	−1.24583	−	12.6491i	−0.0620592	−	0.630098i
$404$	22.7374	+	6.38324i	1.13123	+	0.317578i
$405$	1.12439	−	2.10358i	0.0558713	−	0.104528i
$406$	−10.6917	−	6.98396i	−0.530618	−	0.346608i
$407$	2.88313	−	0.573489i	0.142911	−	0.0284268i
$408$	−3.62529	−	0.604040i	−0.179479	−	0.0299045i
$409$	−6.84766	+	34.4255i	−0.338595	+	1.70223i	0.318085	+	0.948062i	$0.396960\pi$
$409$	−6.84766	+	34.4255i	−0.338595	+	1.70223i	−0.656680	+	0.754170i	$0.728040\pi$
$410$	0.224242	+	21.5280i	0.0110745	+	1.06319i
$411$	−0.649027	+	6.58969i	−0.0320142	+	0.325045i
$412$	−10.2714	−	4.00597i	−0.506035	−	0.197360i
$413$	−5.16073	+	17.0126i	−0.253943	+	0.837137i
$414$	2.09495	+	6.65576i	0.102961	+	0.327113i
$415$	7.05325	+	7.05325i	0.346230	+	0.346230i
$416$	−12.1554	−	4.30828i	−0.595967	−	0.211231i
$417$	−8.76965	+	8.76965i	−0.429452	+	0.429452i
$418$	−1.71195	−	0.892255i	−0.0837340	−	0.0436416i
$419$	−6.49854	−	1.97131i	−0.317475	−	0.0963049i	0.127526	−	0.991835i	$-0.459296\pi$
$419$	−6.49854	−	1.97131i	−0.317475	−	0.0963049i	−0.445000	+	0.895530i	$0.646796\pi$
$420$	−0.202871	−	9.73711i	−0.00989910	−	0.475122i
$421$	−4.89233	−	0.481853i	−0.238438	−	0.0234841i	−0.0219076	−	0.999760i	$-0.506974\pi$
$421$	−4.89233	−	0.481853i	−0.238438	−	0.0234841i	−0.216530	+	0.976276i	$0.569474\pi$
$422$	3.86951	−	3.95097i	0.188365	−	0.192330i
$423$	10.2346	+	2.03579i	0.497624	+	0.0989835i
$424$	−9.51804	+	10.1323i	−0.462237	+	0.492066i
$425$	−0.174740	−	0.878477i	−0.00847613	−	0.0426124i
$426$	20.6148	−	4.32423i	0.998790	−	0.209509i
$427$	−14.9764	−	8.00504i	−0.724758	−	0.387391i
$428$	3.75745	+	2.95485i	0.181623	+	0.142828i
$429$	−4.57287	+	0.450389i	−0.220780	+	0.0217450i
$430$	10.8274	+	8.69866i	0.522142	+	0.419486i
$431$	8.48833	+	20.4926i	0.408868	+	0.987095i	0.985436	+	0.170046i	$0.0543916\pi$
$431$	8.48833	+	20.4926i	0.408868	+	0.987095i	−0.576568	+	0.817049i	$0.695608\pi$
$432$	−1.73702	+	3.60316i	−0.0835723	+	0.173357i
$433$	14.2471	−	34.3955i	0.684672	−	1.65294i	−0.0705781	−	0.997506i	$-0.522484\pi$
$433$	14.2471	−	34.3955i	0.684672	−	1.65294i	0.755250	−	0.655437i	$-0.227516\pi$
$434$	−14.1165	+	7.73554i	−0.677614	+	0.371318i
$435$	−6.69297	+	8.15540i	−0.320903	+	0.391022i
$436$	−33.7353	−	2.61440i	−1.61563	−	0.125207i
$437$	0.970025	+	3.19774i	0.0464026	+	0.152969i
$438$	8.45036	−	5.77456i	0.403774	−	0.275919i
$439$	−6.83927	−	4.56985i	−0.326421	−	0.218107i	0.381552	−	0.924348i	$-0.375390\pi$
$439$	−6.83927	−	4.56985i	−0.326421	−	0.218107i	−0.707972	+	0.706240i	$0.750390\pi$
$440$	−0.909383	+	13.5674i	−0.0433531	+	0.646800i
$441$	1.57337	+	2.35471i	0.0749223	+	0.112129i
$442$	−3.85357	+	1.64343i	−0.183296	+	0.0781701i
$443$	21.0794	−	17.2994i	1.00151	−	0.821920i	0.0174687	−	0.999847i	$-0.494439\pi$
$443$	21.0794	−	17.2994i	1.00151	−	0.821920i	0.984044	+	0.177928i	$0.0569393\pi$
$444$	−0.628532	−	2.84840i	−0.0298288	−	0.135179i
$445$	−11.5747	−	21.6548i	−0.548695	−	1.02654i
$446$	−2.92156	+	33.2053i	−0.138340	+	1.57232i
$447$			13.9470i			0.659669i
$448$	1.02005	+	16.3007i	0.0481927	+	0.770135i
$449$			20.3796i			0.961773i	0.876783	+	0.480887i	$0.159685\pi$
$449$			20.3796i			0.961773i	−0.876783	+	0.480887i	$0.840315\pi$
$450$	−0.971075	−	0.0854399i	−0.0457769	−	0.00402767i
$451$	−6.06407	−	11.3451i	−0.285546	−	0.534218i
$452$	−18.2296	+	28.5526i	−0.857447	+	1.34300i
$453$	15.5583	−	12.7683i	0.730992	−	0.599909i
$454$	16.5880	+	38.8960i	0.778511	+	1.82548i
$455$	−6.16770	−	9.23062i	−0.289146	−	0.432738i
$456$	−0.849791	+	1.71681i	−0.0397951	+	0.0803969i
$457$	−7.29165	−	4.87212i	−0.341089	−	0.227908i	0.373214	−	0.927745i	$-0.378256\pi$
$457$	−7.29165	−	4.87212i	−0.341089	−	0.227908i	−0.714302	+	0.699837i	$0.753256\pi$
$458$	−3.81138	−	5.57748i	−0.178094	−	0.260619i
$459$	0.377197	+	1.24345i	0.0176060	+	0.0580394i
$460$	17.8796	−	15.3076i	0.833639	−	0.713722i
$461$	2.03479	−	2.47940i	0.0947697	−	0.115477i	−0.723466	−	0.690360i	$-0.757452\pi$
$461$	2.03479	−	2.47940i	0.0947697	−	0.115477i	0.818236	+	0.574883i	$0.194952\pi$
$462$	2.79653	+	5.10336i	0.130106	+	0.237430i
$463$	−6.41839	+	15.4954i	−0.298288	+	0.720130i	0.701683	+	0.712489i	$0.252432\pi$
$463$	−6.41839	+	15.4954i	−0.298288	+	0.720130i	−0.999971	+	0.00764102i	$0.997568\pi$
$464$	10.6446	−	14.1322i	0.494165	−	0.656069i
$465$	5.08904	+	12.2860i	0.235999	+	0.569751i
$466$	−24.4484	+	30.4314i	−1.13255	+	1.40971i
$467$	25.8069	−	2.54176i	1.19420	−	0.117618i	0.518686	−	0.854965i	$-0.326421\pi$
$467$	25.8069	−	2.54176i	1.19420	−	0.117618i	0.675515	+	0.737346i	$0.263921\pi$
$468$	0.541335	+	4.52728i	0.0250232	+	0.209274i
$469$	8.17300	+	4.36856i	0.377394	+	0.201721i
$470$	−7.22638	−	34.4502i	−0.333328	−	1.58907i
$471$	4.19347	+	21.0820i	0.193225	+	0.971408i
$472$	−23.0387	−	8.71002i	−1.06044	−	0.400911i
$473$	−8.13933	−	1.61901i	−0.374247	−	0.0744424i
$474$	6.40117	+	6.26919i	0.294016	+	0.287954i
$475$	−0.464599	−	0.0457591i	−0.0213173	−	0.00209957i
$476$	3.82900	+	3.67270i	0.175502	+	0.168338i
$477$	4.70334	+	1.42674i	0.215351	+	0.0653260i
$478$	17.8587	−	34.2650i	0.816837	−	1.56725i
$479$	9.47205	−	9.47205i	0.432789	−	0.432789i	−0.456787	−	0.889576i	$-0.651000\pi$
$479$	9.47205	−	9.47205i	0.432789	−	0.432789i	0.889576	+	0.456787i	$0.151000\pi$
$480$	13.4785	+	0.621737i	0.615209	+	0.0283783i
$481$	−2.35109	−	2.35109i	−0.107201	−	0.107201i
$482$	8.28864	−	2.60891i	0.377537	−	0.118833i
$483$	2.92405	−	9.63930i	0.133049	−	0.438603i
$484$	5.57563	+	12.7055i	0.253438	+	0.577523i
$485$	3.01509	−	30.6127i	0.136908	−	1.39005i
$486$	1.41414	−	0.0147301i	0.0641466	−	0.000668169i
$487$	−3.13023	+	15.7367i	−0.141844	+	0.713099i	0.842758	+	0.538292i	$0.180930\pi$
$487$	−3.13023	+	15.7367i	−0.141844	+	0.713099i	−0.984603	+	0.174807i	$0.944070\pi$
$488$	12.4531	−	19.9604i	0.563725	−	0.903564i
$489$	19.4719	−	3.87320i	0.880550	−	0.175152i
$490$	5.22429	−	7.99781i	0.236010	−	0.361304i
$491$	5.49651	−	10.2833i	0.248054	−	0.464077i	−0.726822	−	0.686826i	$-0.759003\pi$
$491$	5.49651	−	10.2833i	0.248054	−	0.464077i	0.974876	+	0.222750i	$0.0715033\pi$
$492$	−11.1297	+	6.25045i	−0.501767	+	0.281792i
$493$	−0.563348	−	5.71976i	−0.0253719	−	0.257605i
$494$	0.236650	+	2.17071i	0.0106474	+	0.0976650i
$495$	4.44161	−	1.83977i	0.199635	−	0.0826917i
$496$	−9.38503	−	20.2302i	−0.421400	−	0.908362i
$497$	−28.0927	−	11.6364i	−1.26013	−	0.521964i
$498$	−1.65774	+	5.67702i	−0.0742849	+	0.254394i
$499$	15.7143	+	12.8964i	0.703469	+	0.577322i	0.916650	−	0.399691i	$-0.130882\pi$
$499$	15.7143	+	12.8964i	0.703469	+	0.577322i	−0.213181	+	0.977013i	$0.568382\pi$
$500$	−6.37802	−	19.5499i	−0.285234	−	0.874297i
$501$	−16.6545	+	5.05208i	−0.744066	+	0.225710i
$502$	−1.18066	−	0.222089i	−0.0526953	−	0.00991233i
$503$	7.61772	−	11.4007i	0.339657	−	0.508333i	−0.621841	−	0.783143i	$-0.713615\pi$
$503$	7.61772	−	11.4007i	0.339657	−	0.508333i	0.961498	+	0.274810i	$0.0886151\pi$
$504$	5.00507	−	2.87983i	0.222943	−	0.128278i
$505$	−23.4185	+	15.6478i	−1.04211	+	0.696316i
$506$	−5.24640	+	13.0487i	−0.233231	+	0.580086i
$507$	−4.94996	−	6.03154i	−0.219835	−	0.267870i
$508$	4.68605	−	26.4237i	0.207910	−	1.17236i
$509$	13.2481	−	7.08127i	0.587213	−	0.313872i	−0.150900	−	0.988549i	$-0.548217\pi$
$509$	13.2481	−	7.08127i	0.587213	−	0.313872i	0.738113	+	0.674677i	$0.235717\pi$
$510$	3.35909	−	2.81580i	0.148743	−	0.124686i
$511$	−14.7753			−0.653619
$512$	−22.6272	−	0.100274i	−0.999990	−	0.00443154i
$513$	0.677271			0.0299023
$514$	−18.4327	+	15.4515i	−0.813034	+	0.681534i
$515$	11.5959	−	6.19815i	0.510978	−	0.273123i
$516$	−1.43793	+	8.10823i	−0.0633015	+	0.356945i
$517$	13.3429	+	16.2584i	0.586821	+	0.715043i
$518$	−1.57083	+	3.90693i	−0.0690183	+	0.171661i
$519$	1.78359	−	1.19175i	0.0782908	−	0.0523122i
$520$	13.3311	−	7.67047i	0.584607	−	0.336372i
$521$	20.9054	−	31.2872i	0.915884	−	1.37072i	−0.0128285	−	0.999918i	$-0.504084\pi$
$521$	20.9054	−	31.2872i	0.915884	−	1.37072i	0.928713	−	0.370800i	$-0.120916\pi$
$522$	−6.14744	−	1.15637i	−0.269066	−	0.0506131i
$523$	−28.9348	+	8.77727i	−1.26523	+	0.383803i	−0.850420	−	0.526105i	$-0.823652\pi$
$523$	−28.9348	+	8.77727i	−1.26523	+	0.383803i	−0.414810	+	0.909908i	$0.636152\pi$
$524$	10.9382	+	33.5277i	0.477837	+	1.46467i
$525$	1.08783	+	0.892761i	0.0474769	+	0.0389633i
$526$	−3.65605	+	12.5204i	−0.159411	+	0.545915i
$527$	−6.69308	−	2.77236i	−0.291555	−	0.120766i
$528$	−7.31355	+	3.39285i	−0.318282	+	0.147655i
$529$	1.24170	−	0.514328i	0.0539869	−	0.0223621i
$530$	−1.79682	−	16.4816i	−0.0780489	−	0.715916i
$531$	0.853541	+	8.66614i	0.0370405	+	0.376079i
$532$	2.41118	−	1.35412i	0.104538	−	0.0587085i
$533$	−6.85898	+	12.8322i	−0.297095	+	0.555826i
$534$	7.96162	−	12.1883i	0.344533	−	0.527441i
$535$	−5.59130	+	1.11218i	−0.241733	+	0.0480837i
$536$	−6.79597	+	10.8929i	−0.293541	+	0.470501i
$537$	−1.63897	+	8.23965i	−0.0707267	+	0.355567i
$538$	−1.15231	+	0.0120028i	−0.0496795	+	0.000517476i
$539$	−0.559485	+	5.68054i	−0.0240987	+	0.244678i
$540$	−1.91698	−	4.36834i	−0.0824938	−	0.187983i
$541$	−0.412556	+	1.36002i	−0.0177372	+	0.0584716i	−0.965362	−	0.260913i	$-0.915976\pi$
$541$	−0.412556	+	1.36002i	−0.0177372	+	0.0584716i	0.947625	+	0.319385i	$0.103476\pi$
$542$	14.3328	−	4.51135i	0.615646	−	0.193779i
$543$	6.93595	+	6.93595i	0.297650	+	0.297650i
$544$	−5.43159	+	4.95259i	−0.232878	+	0.212341i
$545$	28.5344	−	28.5344i	1.22228	−	1.22228i
$546$	3.04219	−	5.83697i	0.130194	−	0.249799i
$547$	30.1818	+	9.15554i	1.29048	+	0.391462i	0.859609	−	0.510952i	$-0.170707\pi$
$547$	30.1818	+	9.15554i	1.29048	+	0.391462i	0.430869	+	0.902414i	$0.358207\pi$
$548$	9.55735	+	9.16722i	0.408270	+	0.391604i
$549$	−8.27782	−	0.815295i	−0.353289	−	0.0347959i
$550$	−1.40373	−	1.37479i	−0.0598553	−	0.0586212i
$551$	−2.93810	−	0.584425i	−0.125167	−	0.0248973i
$552$	13.0536	+	4.93506i	0.555599	+	0.210050i
$553$	−2.52338	−	12.6859i	−0.107305	−	0.539459i
$554$	−5.86461	−	27.9582i	−0.249164	−	1.18783i
$555$	3.06799	+	1.63988i	0.130229	+	0.0696088i
$556$	2.94492	+	24.6289i	0.124892	+	1.04450i
$557$	−21.2870	+	2.09659i	−0.901960	+	0.0888353i	−0.538355	−	0.842718i	$-0.680954\pi$
$557$	−21.2870	+	2.09659i	−0.901960	+	0.0888353i	−0.363605	+	0.931553i	$0.618454\pi$
$558$	−4.93820	+	6.14667i	−0.209051	+	0.260209i
$559$	3.59211	+	8.67213i	0.151930	+	0.366792i
$560$	−15.5587	−	11.7191i	−0.657473	−	0.495223i
$561$	−1.00226	+	2.41966i	−0.0423153	+	0.102158i
$562$	8.10470	+	14.7902i	0.341876	+	0.623886i
$563$	−10.6132	+	12.9322i	−0.447292	+	0.545027i	−0.947028	−	0.321151i	$-0.895930\pi$
$563$	−10.6132	+	12.9322i	−0.447292	+	0.545027i	0.499736	+	0.866178i	$0.333430\pi$
$564$	15.8536	−	13.5731i	0.667558	−	0.571531i
$565$	−11.7277	−	38.6611i	−0.493388	−	1.62648i
$566$	13.9441	+	20.4054i	0.586113	+	0.857705i
$567$	−1.69750	−	1.13424i	−0.0712885	−	0.0476334i
$568$	18.6880	−	37.7549i	0.784132	−	1.58416i
$569$	4.05247	+	6.06495i	0.169888	+	0.254256i	0.906638	−	0.421910i	$-0.138640\pi$
$569$	4.05247	+	6.06495i	0.169888	+	0.254256i	−0.736749	+	0.676166i	$0.763640\pi$
$570$	−0.896210	−	2.10146i	−0.0375381	−	0.0880205i
$571$	19.2534	−	15.8008i	0.805729	−	0.661245i	−0.138563	−	0.990354i	$-0.544248\pi$
$571$	19.2534	−	15.8008i	0.805729	−	0.661245i	0.944292	+	0.329109i	$0.106748\pi$
$572$	−4.94541	+	7.74590i	−0.206778	+	0.323872i
$573$	−1.25607	−	2.34994i	−0.0524730	−	0.0981700i
$574$	18.3564	+	1.61508i	0.766181	+	0.0674123i
$575$			3.40101i			0.141832i
$576$	3.51710	+	7.18540i	0.146546	+	0.299392i
$577$			37.5944i			1.56507i	0.622604	+	0.782537i	$0.286075\pi$
$577$			37.5944i			1.56507i	−0.622604	+	0.782537i	$0.713925\pi$
$578$	1.89787	−	21.5705i	0.0789412	−	0.897213i
$579$	−2.78076	−	5.20243i	−0.115564	−	0.216206i
$580$	4.54667	+	20.6047i	0.188790	+	0.855563i
$581$	6.59970	−	5.41624i	0.273802	−	0.224703i
$582$	16.7763	−	7.15461i	0.695402	−	0.296568i
$583$	5.50371	+	8.23688i	0.227940	+	0.341137i
$584$	1.36897	−	20.4241i	0.0566483	−	0.845154i
$585$	−4.52133	−	3.02106i	−0.186934	−	0.124905i
$586$	1.18409	−	0.809149i	0.0489143	−	0.0334256i
$587$	−3.43548	−	11.3253i	−0.141797	−	0.467443i	0.857061	−	0.515215i	$-0.172288\pi$
$587$	−3.43548	−	11.3253i	−0.141797	−	0.467443i	−0.998858	+	0.0477719i	$0.984788\pi$
$588$	5.64704	+	0.437632i	0.232880	+	0.0180476i
$589$	−2.39545	+	2.91887i	−0.0987029	+	0.120270i
$590$	25.7601	−	14.1160i	1.06053	−	0.581147i
$591$	−4.56217	+	11.0141i	−0.187663	+	0.453058i
$592$	−5.25507	−	2.53337i	−0.215982	−	0.104121i
$593$	9.66916	+	23.3434i	0.397065	+	0.958599i	0.988359	+	0.152143i	$0.0486173\pi$
$593$	9.66916	+	23.3434i	0.397065	+	0.958599i	−0.591294	+	0.806456i	$0.701383\pi$
$594$	2.22213	+	1.78524i	0.0911749	+	0.0732494i
$595$	−6.29712	+	0.620212i	−0.258157	+	0.0254262i
$596$	21.9263	+	17.2428i	0.898134	+	0.706291i
$597$	5.31568	+	2.84129i	0.217556	+	0.116286i
$598$	15.5686	−	3.26573i	0.636649	−	0.133546i
$599$	0.831567	+	4.18057i	0.0339769	+	0.170813i	0.994048	−	0.108943i	$-0.0347465\pi$
$599$	0.831567	+	4.18057i	0.0339769	+	0.170813i	−0.960071	+	0.279756i	$0.909746\pi$
$600$	−1.33487	+	1.42101i	−0.0544958	+	0.0580125i
$601$	−22.9442	−	4.56389i	−0.935914	−	0.186165i	−0.296505	−	0.955031i	$-0.595821\pi$
$601$	−22.9442	−	4.56389i	−0.935914	−	0.186165i	−0.639410	+	0.768866i	$0.720821\pi$
$602$	8.31790	−	8.49300i	0.339012	−	0.346149i
$603$	4.51742	+	0.444927i	0.183964	+	0.0181188i
$604$	−0.838498	−	40.2450i	−0.0341180	−	1.63755i
$605$	−15.8351	−	4.80351i	−0.643786	−	0.195290i
$606$	−14.8087	−	7.71818i	−0.601561	−	0.313530i
$607$	−13.0111	+	13.0111i	−0.528104	+	0.528104i	−0.920007	−	0.391902i	$-0.871817\pi$
$607$	−13.0111	+	13.0111i	−0.528104	+	0.528104i	0.391902	+	0.920007i	$0.371817\pi$
$608$	1.64842	+	3.45847i	0.0668521	+	0.140259i
$609$	6.38528	+	6.38528i	0.258745	+	0.258745i
$610$	8.42404	+	26.7636i	0.341079	+	1.08363i
$611$	6.90576	−	22.7652i	0.279377	−	0.920983i
$612$	2.42118	+	0.944291i	0.0978704	+	0.0381707i
$613$	0.0488905	−	0.496393i	0.00197467	−	0.0200491i	−0.994147	−	0.108037i	$-0.965544\pi$
$613$	0.0488905	−	0.496393i	0.00197467	−	0.0200491i	0.996122	+	0.0879876i	$0.0280436\pi$
$614$	0.00131193	+	0.125949i	5.29450e−5	+	0.00508291i
$615$	2.96994	−	14.9309i	0.119760	−	0.602072i
$616$	11.4804	+	1.91285i	0.462560	+	0.0770710i
$617$	8.14754	−	1.62065i	0.328008	−	0.0652448i	−0.0283396	−	0.999598i	$-0.509022\pi$
$617$	8.14754	−	1.62065i	0.328008	−	0.0652448i	0.356347	+	0.934354i	$0.384022\pi$
$618$	6.52674	+	4.26337i	0.262544	+	0.171498i
$619$	−22.3380	+	41.7914i	−0.897840	+	1.67974i	−0.179841	+	0.983696i	$0.557558\pi$
$619$	−22.3380	+	41.7914i	−0.897840	+	1.67974i	−0.717999	+	0.696044i	$0.754942\pi$
$620$	25.6067	+	7.18875i	1.02839	+	0.288707i
$621$	−0.483613	−	4.91021i	−0.0194067	−	0.197040i
$622$	21.8806	−	2.38541i	0.877331	−	0.0956462i
$623$	−19.4167	+	8.04264i	−0.777912	+	0.322222i
$624$	7.78666	+	4.74607i	0.311716	+	0.189995i
$625$	25.8422	+	10.7042i	1.03369	+	0.428167i
$626$	−36.6588	−	10.7046i	−1.46518	−	0.427844i
$627$	1.05522	+	0.865997i	0.0421414	+	0.0345846i
$628$	38.3278	+	19.4712i	1.52944	+	0.776987i
$629$	−1.81353	+	0.550127i	−0.0723100	+	0.0219350i
$630$	−1.27310	+	6.76797i	−0.0507214	+	0.269642i
$631$	4.23687	−	6.34093i	0.168667	−	0.252428i	−0.737501	−	0.675346i	$-0.763994\pi$
$631$	4.23687	−	6.34093i	0.168667	−	0.252428i	0.906168	+	0.422918i	$0.138994\pi$
$632$	17.7697	−	2.31273i	0.706841	−	0.0919953i
$633$	−3.25142	+	2.17253i	−0.129232	+	0.0863504i
$634$	−33.0091	−	13.2717i	−1.31096	−	0.527088i
$635$	20.3037	+	24.7402i	0.805730	+	0.981784i
$636$	8.05777	−	5.63029i	0.319511	−	0.223256i
$637$	5.69392	−	3.04346i	0.225601	−	0.120586i
$638$	−8.09940	−	9.66215i	−0.320658	−	0.382528i
$639$	−14.8941			−0.589201
$640$	17.6411	−	20.4212i	0.697324	−	0.807217i
$641$	−29.3557			−1.15948			−0.579740	−	0.814801i	$-0.696846\pi$
$641$	−29.3557			−1.15948			−0.579740	+	0.814801i	$0.696846\pi$
$642$	−2.17138	−	2.59034i	−0.0856977	−	0.102233i
$643$	−8.03090	+	4.29260i	−0.316708	+	0.169284i	−0.622089	−	0.782946i	$-0.713716\pi$
$643$	−8.03090	+	4.29260i	−0.316708	+	0.169284i	0.305382	+	0.952230i	$0.401216\pi$
$644$	−11.5391	−	16.5141i	−0.454703	−	0.650746i
$645$	−6.23029	−	7.59163i	−0.245317	−	0.298920i
$646$	1.15474	+	0.464277i	0.0454325	+	0.0182667i
$647$	25.8065	−	17.2434i	1.01456	−	0.677907i	0.0670877	−	0.997747i	$-0.478629\pi$
$647$	25.8065	−	17.2434i	1.01456	−	0.677907i	0.947471	+	0.319840i	$0.103629\pi$
$648$	1.72515	−	2.24140i	0.0677703	−	0.0880504i
$649$	−9.75116	+	14.5936i	−0.382766	+	0.572850i
$650$	−0.410838	+	2.18407i	−0.0161144	+	0.0856663i
$651$	10.8922	−	3.30411i	0.426899	−	0.129498i
$652$	17.9841	−	35.4005i	0.704313	−	1.38639i
$653$	8.72044	+	7.15668i	0.341257	+	0.280062i	0.789374	−	0.613912i	$-0.210405\pi$
$653$	8.72044	+	7.15668i	0.341257	+	0.280062i	−0.448117	+	0.893975i	$0.647905\pi$
$654$	22.9668	+	6.70649i	0.898074	+	0.262245i
$655$	−38.8581	−	16.0956i	−1.51831	−	0.628906i
$656$	−3.93332	+	25.2247i	−0.153570	+	0.984858i
$657$	−6.68630	+	2.76956i	−0.260858	+	0.108051i
$658$	−29.9510	+	3.26524i	−1.16761	+	0.127292i
$659$	0.0329596	+	0.334644i	0.00128392	+	0.0130359i	0.995805	−	0.0914971i	$-0.0291652\pi$
$659$	0.0329596	+	0.334644i	0.00128392	+	0.0130359i	−0.994521	+	0.104533i	$0.966665\pi$
$660$	2.59885	−	9.25724i	0.101160	−	0.360337i
$661$	−22.4908	+	42.0774i	−0.874793	+	1.63662i	−0.108531	+	0.994093i	$0.534615\pi$
$661$	−22.4908	+	42.0774i	−0.874793	+	1.63662i	−0.766262	+	0.642529i	$0.777885\pi$
$662$	21.0561	+	13.7542i	0.818369	+	0.534572i
$663$	2.90542	−	0.577923i	0.112837	−	0.0224447i
$664$	6.87546	+	9.62470i	0.266820	+	0.373511i
$665$	−0.643417	+	3.23468i	−0.0249507	+	0.125435i
$666$	0.0214832	+	2.06246i	0.000832457	+	0.0799188i
$667$	−2.13909	+	21.7185i	−0.0828258	+	0.840944i
$668$	−12.6476	+	32.4286i	−0.489350	+	1.25470i
$669$	6.84212	−	22.5554i	0.264532	−	0.872044i
$670$	−4.59721	−	14.6056i	−0.177606	−	0.564262i
$671$	−11.8548	−	11.8548i	−0.457648	−	0.457648i
$672$	1.66038	−	11.4289i	0.0640506	−	0.440879i
$673$	−0.279123	+	0.279123i	−0.0107594	+	0.0107594i	−0.712466	−	0.701707i	$-0.752422\pi$
$673$	−0.279123	+	0.279123i	−0.0107594	+	0.0107594i	0.701707	+	0.712466i	$0.252422\pi$
$674$	27.1153	+	14.1323i	1.04444	+	0.544357i
$675$	0.659625	+	0.200095i	0.0253890	+	0.00770166i
$676$	−15.6019	+	0.325064i	−0.600075	+	0.0125025i
$677$	−7.67266	−	0.755691i	−0.294884	−	0.0290436i	−0.0505067	−	0.998724i	$-0.516084\pi$
$677$	−7.67266	−	0.755691i	−0.294884	−	0.0290436i	−0.244378	+	0.969680i	$0.578584\pi$
$678$	16.7605	−	17.1134i	0.643685	−	0.657236i
$679$	−25.8230	−	5.13652i	−0.990996	−	0.197121i
$680$	−0.273884	−	8.76207i	−0.0105030	−	0.336010i
$681$	−5.83326	−	29.3258i	−0.223531	−	1.12377i
$682$	−15.5534	+	3.26254i	−0.595571	+	0.124929i
$683$	−29.0987	−	15.5536i	−1.11343	−	0.595142i	−0.191112	−	0.981568i	$-0.561209\pi$
$683$	−29.0987	−	15.5536i	−1.11343	−	0.595142i	−0.922320	+	0.386426i	$0.873709\pi$
$684$	0.837315	−	1.06475i	0.0320156	−	0.0407117i
$685$	−15.7179	+	1.54808i	−0.600550	+	0.0591490i
$686$	−22.1299	−	17.7790i	−0.844923	−	0.678807i
$687$	1.82799	+	4.41315i	0.0697421	+	0.168372i
$688$	10.9693	+	12.2849i	0.418202	+	0.468356i
$689$	4.28797	−	10.3521i	0.163358	−	0.394382i
$690$	−14.5956	+	7.99808i	−0.555645	+	0.304482i
$691$	11.7794	−	14.3532i	0.448108	−	0.546022i	−0.499140	−	0.866521i	$-0.666351\pi$
$691$	11.7794	−	14.3532i	0.448108	−	0.546022i	0.947249	+	0.320499i	$0.103851\pi$
$692$	0.331486	−	4.27738i	0.0126012	−	0.162601i
$693$	−1.19449	−	3.93772i	−0.0453750	−	0.149581i
$694$	−20.7730	+	14.1953i	−0.788533	+	0.538845i
$695$	−24.5965	−	16.4349i	−0.932999	−	0.623410i
$696$	−9.41808	+	8.23486i	−0.356991	+	0.312141i
$697$	4.60750	+	6.89561i	0.174522	+	0.261190i
$698$	−25.9697	+	11.0753i	−0.982967	+	0.419206i
$699$	21.3370	−	17.5108i	0.807040	−	0.662321i
$700$	2.74842	−	0.606471i	0.103880	−	0.0229224i
$701$	7.43403	+	13.9081i	0.280780	+	0.525302i	0.982292	−	0.187355i	$-0.0599916\pi$
$701$	7.43403	+	13.9081i	0.280780	+	0.525302i	−0.701513	+	0.712657i	$0.747492\pi$
$702$	0.282578	−	3.21167i	0.0106652	−	0.121217i
$703$			0.987774i			0.0372546i
$704$	−3.70786	+	15.6923i	−0.139745	+	0.591428i
$705$			24.8901i			0.937416i
$706$	−10.1950	−	0.897008i	−0.383695	−	0.0337593i
$707$	11.3641	+	21.2607i	0.427391	+	0.799592i
$708$	14.6794	+	9.37215i	0.551686	+	0.352227i
$709$	33.3091	−	27.3361i	1.25095	−	1.02663i	0.252697	−	0.967545i	$-0.418682\pi$
$709$	33.3091	−	27.3361i	1.25095	−	1.02663i	0.998253	−	0.0590830i	$-0.0188177\pi$
$710$	19.7088	+	46.2139i	0.739660	+	1.73438i
$711$	−3.51983	−	5.26780i	−0.132004	−	0.197558i
$712$	−9.31846	−	27.5851i	−0.349224	−	1.03380i
$713$	22.8722	+	15.2827i	0.856572	+	0.572343i
$714$	−2.11669	−	3.09751i	−0.0792151	−	0.115922i
$715$	−3.18155	−	10.4882i	−0.118983	−	0.392235i
$716$	10.9274	+	12.7634i	0.408377	+	0.476990i
$717$	−17.3331	+	21.1205i	−0.647318	+	0.788759i
$718$	6.43978	+	11.7519i	0.240330	+	0.438576i
$719$	−2.98195	+	7.19908i	−0.111208	+	0.268480i	−0.969679	−	0.244382i	$-0.921415\pi$
$719$	−2.98195	+	7.19908i	−0.111208	+	0.268480i	0.858471	+	0.512862i	$0.171415\pi$
$720$	−9.23751	−	2.38689i	−0.344262	−	0.0889543i
$721$	−4.30676	−	10.3974i	−0.160392	−	0.387221i
$722$	−16.4226	+	20.4416i	−0.611187	+	0.760756i
$723$	−6.11484	+	0.602259i	−0.227413	+	0.0223983i
$724$	19.4791	−	2.32915i	0.723934	−	0.0865620i
$725$	−2.68889	−	1.43724i	−0.0998627	−	0.0533777i
$726$	−2.01418	−	9.60218i	−0.0747534	−	0.356370i
$727$	6.69139	+	33.6399i	0.248170	+	1.24763i	0.880915	+	0.473274i	$0.156928\pi$
$727$	6.69139	+	33.6399i	0.248170	+	1.24763i	−0.632745	+	0.774360i	$0.718072\pi$
$728$	−5.41531	−	11.9990i	−0.200705	−	0.444711i
$729$	−0.980785	−	0.195090i	−0.0363254	−	0.00722557i
$730$	17.4412	+	17.0816i	0.645529	+	0.632220i
$731$	5.32436	+	0.524404i	0.196929	+	0.0193958i
$732$	−11.5157	+	12.0057i	−0.425631	+	0.443745i
$733$	−22.6194	−	6.86151i	−0.835466	−	0.253436i	−0.156567	−	0.987667i	$-0.550043\pi$
$733$	−22.6194	−	6.86151i	−0.835466	−	0.253436i	−0.678899	+	0.734232i	$0.737543\pi$
$734$	−9.07021	+	17.4028i	−0.334788	+	0.642348i
$735$	−4.77646	+	4.77646i	−0.176182	+	0.176182i
$736$	23.8968	−	14.4205i	0.880847	−	0.531548i
$737$	6.46944	+	6.46944i	0.238305	+	0.238305i
$738$	8.60962	−	2.70994i	0.316925	−	0.0997544i
$739$	−2.93218	+	9.66611i	−0.107862	+	0.355574i	−0.994211	−	0.107444i	$-0.965733\pi$
$739$	−2.93218	+	9.66611i	−0.107862	+	0.355574i	0.886349	+	0.463018i	$0.153233\pi$
$740$	6.37105	−	2.79584i	0.234205	−	0.102777i
$741$	0.151340	−	1.53659i	0.00555963	−	0.0564479i
$742$	−14.1898	+	0.147805i	−0.520925	+	0.00542611i
$743$	−4.87900	+	24.5284i	−0.178993	+	0.899860i	0.781998	+	0.623281i	$0.214201\pi$
$743$	−4.87900	+	24.5284i	−0.178993	+	0.899860i	−0.960991	+	0.276579i	$0.910799\pi$
$744$	3.55814	+	15.3626i	0.130448	+	0.563220i
$745$	−32.6275	+	6.49001i	−1.19538	+	0.237776i
$746$	−14.2355	+	21.7929i	−0.521198	+	0.797896i
$747$	1.97134	−	3.68811i	0.0721275	−	0.134941i
$748$	2.56489	+	4.56710i	0.0937816	+	0.166990i
$749$	0.478273	+	4.85598i	0.0174757	+	0.177434i
$750$	1.57591	+	14.4553i	0.0575440	+	0.527832i
$751$	28.4472	−	11.7832i	1.03805	−	0.429976i	0.202441	−	0.979295i	$-0.435113\pi$
$751$	28.4472	−	11.7832i	1.03805	−	0.429976i	0.835613	+	0.549319i	$0.185113\pi$
$752$	−1.73856	−	41.7042i	−0.0633986	−	1.52080i
$753$	0.784829	+	0.325087i	0.0286008	+	0.0118468i
$754$	−3.99725	+	13.6889i	−0.145571	+	0.498519i
$755$	37.1100	+	30.4554i	1.35057	+	1.10839i
$756$	−3.88179	+	1.26641i	−0.141179	+	0.0460588i
$757$	−15.5544	+	4.71838i	−0.565335	+	0.171493i	−0.559999	−	0.828493i	$-0.689199\pi$
$757$	−15.5544	+	4.71838i	−0.565335	+	0.171493i	−0.00533603	+	0.999986i	$0.501699\pi$
$758$	−16.6100	−	3.12445i	−0.603303	−	0.113485i
$759$	5.52497	−	8.26870i	0.200544	−	0.300135i
$760$	−4.41173	−	1.18911i	−0.160030	−	0.0431334i
$761$	29.5964	−	19.7757i	1.07287	−	0.716867i	0.111953	−	0.993713i	$-0.464289\pi$
$761$	29.5964	−	19.7757i	1.07287	−	0.716867i	0.960914	+	0.276846i	$0.0892892\pi$
$762$	−7.07878	+	17.6062i	−0.256437	+	0.637804i
$763$	−21.9118	−	26.6996i	−0.793260	−	0.966590i
$764$	−5.24726	−	0.930562i	−0.189839	−	0.0336666i
$765$	−2.73340	+	1.46103i	−0.0988264	+	0.0528238i
$766$	−9.58490	+	8.03465i	−0.346317	+	0.290304i
$767$	19.8524			0.716828
$768$	15.6445	+	3.35409i	0.564522	+	0.121030i

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)

\(f(q)\)	\(=\)	\(q+(-1.08380 + 0.908505i) q^{2} +(0.881921 - 0.471397i) q^{3} +(0.349236 - 1.96927i) q^{4} +(1.51317 + 1.84381i) q^{5} +(-0.527558 + 1.31213i) q^{6} +(1.69750 - 1.13424i) q^{7} +(1.41059 + 2.45158i) q^{8} +(0.555570 - 0.831470i) q^{9} +O(q^{10})\)	\(q+(-1.08380 + 0.908505i) q^{2} +(0.881921 - 0.471397i) q^{3} +(0.349236 - 1.96927i) q^{4} +(1.51317 + 1.84381i) q^{5} +(-0.527558 + 1.31213i) q^{6} +(1.69750 - 1.13424i) q^{7} +(1.41059 + 2.45158i) q^{8} +(0.555570 - 0.831470i) q^{9} +(-3.31508 - 0.623587i) q^{10} +(1.92877 - 0.585085i) q^{11} +(-0.620310 - 1.90137i) q^{12} +(-1.76228 - 1.44627i) q^{13} +(-0.809292 + 2.77147i) q^{14} +(2.20366 + 0.912787i) q^{15} +(-3.75607 - 1.37548i) q^{16} +(-1.20049 + 0.497260i) q^{17} +(0.153269 + 1.40588i) q^{18} +(0.0663842 + 0.674010i) q^{19} +(4.15941 - 2.33592i) q^{20} +(0.962390 - 1.80051i) q^{21} +(-1.55884 + 2.38641i) q^{22} +(4.83916 - 0.962569i) q^{23} +(2.39970 + 1.49715i) q^{24} +(-0.134477 + 0.676061i) q^{25} +(3.22390 - 0.0335811i) q^{26} +(0.0980171 - 0.995185i) q^{27} +(-1.64079 - 3.73897i) q^{28} +(-1.28397 + 4.23268i) q^{29} +(-3.21760 + 1.01276i) q^{30} +(3.94232 + 3.94232i) q^{31} +(5.32045 - 1.92167i) q^{32} +(1.42521 - 1.42521i) q^{33} +(0.849328 - 1.62958i) q^{34} +(4.65993 + 1.41357i) q^{35} +(-1.44337 - 1.38445i) q^{36} +(1.45144 + 0.142954i) q^{37} +(-0.684289 - 0.670180i) q^{38} +(-2.23596 - 0.444760i) q^{39} +(-2.38576 + 6.31052i) q^{40} +(-1.24514 - 6.25974i) q^{41} +(0.592732 + 2.82572i) q^{42} +(-3.63120 - 1.94092i) q^{43} +(-0.478597 - 4.00260i) q^{44} +(2.37374 - 0.233793i) q^{45} +(-4.37017 + 5.43963i) q^{46} +(3.99335 + 9.64079i) q^{47} +(-3.96095 + 0.557532i) q^{48} +(-1.08375 + 2.61641i) q^{49} +(-0.468460 - 0.854887i) q^{50} +(-0.824333 + 1.00445i) q^{51} +(-3.46355 + 2.96533i) q^{52} +(1.42674 + 4.70334i) q^{53} +(0.797900 + 1.16763i) q^{54} +(3.99734 + 2.67094i) q^{55} +(5.17516 + 2.56162i) q^{56} +(0.376272 + 0.563131i) q^{57} +(-2.45385 - 5.75386i) q^{58} +(-6.73143 + 5.52434i) q^{59} +(2.56712 - 4.02083i) q^{60} +(-3.92102 - 7.33571i) q^{61} +(-7.85429 - 0.691058i) q^{62} -2.04157i q^{63} +(-4.02045 + 6.91636i) q^{64} -5.43776i q^{65} +(-0.249829 + 2.83946i) q^{66} +(2.13980 + 4.00329i) q^{67} +(0.559986 + 2.53776i) q^{68} +(3.81401 - 3.13007i) q^{69} +(-6.33466 + 2.70154i) q^{70} +(-8.27472 - 12.3840i) q^{71} +(2.82209 + 0.189157i) q^{72} +(-6.01751 - 4.02077i) q^{73} +(-1.70294 + 1.16371i) q^{74} +(0.200095 + 0.659625i) q^{75} +(1.35049 + 0.104660i) q^{76} +(2.61047 - 3.18086i) q^{77} +(2.82740 - 1.54935i) q^{78} +(2.42450 - 5.85326i) q^{79} +(-3.14746 - 9.00680i) q^{80} +(-0.382683 - 0.923880i) q^{81} +(7.03649 + 5.65308i) q^{82} +(4.16177 - 0.409899i) q^{83} +(-3.20958 - 2.52401i) q^{84} +(-2.73340 - 1.46103i) q^{85} +(5.69882 - 1.19540i) q^{86} +(0.862911 + 4.33815i) q^{87} +(4.15509 + 3.90320i) q^{88} +(-10.0964 - 2.00831i) q^{89} +(-2.36025 + 2.40994i) q^{90} +(-4.63189 - 0.456202i) q^{91} +(-0.205552 - 9.86579i) q^{92} +(5.33521 + 1.61842i) q^{93} +(-13.0867 - 6.82069i) q^{94} +(-1.14229 + 1.14229i) q^{95} +(3.78635 - 4.20280i) q^{96} +(-9.11913 - 9.11913i) q^{97} +(-1.20246 - 3.82026i) q^{98} +(0.585085 - 1.92877i) 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

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