LMFDB - Embedded newform 384.2.v.a.13.12

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			13.12
Character	$\chi$	$=$	384.13
Dual form			384.2.v.a.325.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.607361 + 1.27715i) q^{2} +(-0.290285 - 0.956940i) q^{3} +(-1.26223 - 1.55138i) q^{4} +(0.269039 + 2.73160i) q^{5} +(1.39846 + 0.210471i) q^{6} +(0.857384 - 1.28317i) q^{7} +(2.74797 - 0.669804i) q^{8} +(-0.831470 + 0.555570i) q^{9} +O(q^{10})$	\(q+(-0.607361 + 1.27715i) q^{2} +(-0.290285 - 0.956940i) q^{3} +(-1.26223 - 1.55138i) q^{4} +(0.269039 + 2.73160i) q^{5} +(1.39846 + 0.210471i) q^{6} +(0.857384 - 1.28317i) q^{7} +(2.74797 - 0.669804i) q^{8} +(-0.831470 + 0.555570i) q^{9} +(-3.65206 - 1.31546i) q^{10} +(-5.50570 + 2.94286i) q^{11} +(-1.11818 + 1.65822i) q^{12} +(5.53992 + 0.545635i) q^{13} +(1.11805 + 1.87435i) q^{14} +(2.53588 - 1.05039i) q^{15} +(-0.813572 + 3.91639i) q^{16} +(3.96432 + 1.64207i) q^{17} +(-0.204545 - 1.39934i) q^{18} +(-2.47517 + 2.03132i) q^{19} +(3.89816 - 3.86527i) q^{20} +(-1.47680 - 0.447982i) q^{21} +(-0.414526 - 8.81898i) q^{22} +(-1.24331 + 6.25056i) q^{23} +(-1.43866 - 2.43521i) q^{24} +(-2.48531 + 0.494359i) q^{25} +(-4.06159 + 6.74392i) q^{26} +(0.773010 + 0.634393i) q^{27} +(-3.07289 + 0.289515i) q^{28} +(-1.87108 + 3.50055i) q^{29} +(-0.198680 + 3.87666i) q^{30} +(-1.60293 + 1.60293i) q^{31} +(-4.50769 - 3.41771i) q^{32} +(4.41436 + 4.41436i) q^{33} +(-4.50495 + 4.06570i) q^{34} +(3.73576 + 1.99680i) q^{35} +(1.91140 + 0.588672i) q^{36} +(-3.90148 + 4.75396i) q^{37} +(-1.09098 - 4.39491i) q^{38} +(-1.08601 - 5.45977i) q^{39} +(2.56894 + 7.32615i) q^{40} +(1.19260 + 0.237222i) q^{41} +(1.46909 - 1.61401i) q^{42} +(-1.18922 + 3.92032i) q^{43} +(11.5149 + 4.82689i) q^{44} +(-1.74129 - 2.12177i) q^{45} +(-7.22776 - 5.38424i) q^{46} +(4.43305 - 10.7023i) q^{47} +(3.98392 - 0.358328i) q^{48} +(1.76738 + 4.26683i) q^{49} +(0.878109 - 3.47437i) q^{50} +(0.420586 - 4.27029i) q^{51} +(-6.14615 - 9.28325i) q^{52} +(-3.21836 - 6.02112i) q^{53} +(-1.27971 + 0.601945i) q^{54} +(-9.51994 - 14.2476i) q^{55} +(1.49660 - 4.10038i) q^{56} +(2.66236 + 1.77893i) q^{57} +(-3.33430 - 4.51575i) q^{58} +(12.4050 - 1.22179i) q^{59} +(-4.83041 - 2.60828i) q^{60} +(0.672244 - 0.203923i) q^{61} +(-1.07363 - 3.02074i) q^{62} +1.54325i q^{63} +(7.10273 - 3.68121i) q^{64} +15.2796i q^{65} +(-8.31891 + 2.95669i) q^{66} +(5.38202 - 1.63262i) q^{67} +(-2.45638 - 8.22284i) q^{68} +(6.34233 - 0.624665i) q^{69} +(-4.81917 + 3.55834i) q^{70} +(-4.06093 - 2.71343i) q^{71} +(-1.91273 + 2.08361i) q^{72} +(-3.68754 - 5.51879i) q^{73} +(-3.70192 - 7.87014i) q^{74} +(1.19452 + 2.23479i) q^{75} +(6.27559 + 1.27595i) q^{76} +(-0.944324 + 9.58788i) q^{77} +(7.63254 + 1.92904i) q^{78} +(-1.22482 - 2.95698i) q^{79} +(-10.9169 - 1.16869i) q^{80} +(0.382683 - 0.923880i) q^{81} +(-1.02731 + 1.37905i) q^{82} +(7.62729 + 9.29388i) q^{83} +(1.16906 + 2.85653i) q^{84} +(-3.41893 + 11.2707i) q^{85} +(-4.28456 - 3.89986i) q^{86} +(3.89296 + 0.774358i) q^{87} +(-13.1584 + 11.7746i) q^{88} +(-1.91480 - 9.62637i) q^{89} +(3.76741 - 0.935211i) q^{90} +(5.44998 - 6.64082i) q^{91} +(11.2663 - 5.96076i) q^{92} +(1.99921 + 1.06860i) q^{93} +(10.9760 + 12.1619i) q^{94} +(-6.21467 - 6.21467i) q^{95} +(-1.96204 + 5.30570i) q^{96} +(9.90497 - 9.90497i) q^{97} +(-6.52282 - 0.334296i) q^{98} +(2.94286 - 5.50570i) 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 $\left(\mathbb{Z}/384\mathbb{Z}\right)^\times$.

$n$	$127$	$133$	$257$
$\chi(n)$	$1$	$e\left(\frac{15}{32}\right)$	$1$

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 $

$2$	−0.607361	+	1.27715i	−0.429469	+	0.903082i
$2$	−0.607361	+	1.27715i	−0.429469	+	0.903082i
$3$	−0.290285	−	0.956940i	−0.167596	−	0.552490i
$3$	−0.290285	−	0.956940i	−0.167596	−	0.552490i
$4$	−1.26223	−	1.55138i	−0.631113	−	0.775691i
$5$	0.269039	+	2.73160i	0.120318	+	1.22161i	0.845851	+	0.533420i	$0.179093\pi$
$5$	0.269039	+	2.73160i	0.120318	+	1.22161i	−0.725533	+	0.688187i	$0.758407\pi$
$6$	1.39846	+	0.210471i	0.570921	+	0.0859244i
$7$	0.857384	−	1.28317i	0.324061	−	0.484991i	−0.633292	−	0.773913i	$-0.718297\pi$
$7$	0.857384	−	1.28317i	0.324061	−	0.484991i	0.957353	+	0.288922i	$0.0932968\pi$
$8$	2.74797	−	0.669804i	0.971556	−	0.236811i
$9$	−0.831470	+	0.555570i	−0.277157	+	0.185190i
$10$	−3.65206	−	1.31546i	−1.15488	−	0.415985i
$11$	−5.50570	+	2.94286i	−1.66003	+	0.887305i	−0.670681	+	0.741746i	$0.733998\pi$
$11$	−5.50570	+	2.94286i	−1.66003	+	0.887305i	−0.989350	+	0.145559i	$0.953502\pi$
$12$	−1.11818	+	1.65822i	−0.322789	+	0.478686i
$13$	5.53992	+	0.545635i	1.53650	+	0.151332i	0.830555	−	0.556937i	$-0.188023\pi$
$13$	5.53992	+	0.545635i	1.53650	+	0.151332i	0.705943	+	0.708268i	$0.250523\pi$
$14$	1.11805	+	1.87435i	0.298812	+	0.500942i
$15$	2.53588	−	1.05039i	0.654761	−	0.271211i
$16$	−0.813572	+	3.91639i	−0.203393	+	0.979097i
$17$	3.96432	+	1.64207i	0.961489	+	0.398262i	0.807537	−	0.589817i	$-0.200800\pi$
$17$	3.96432	+	1.64207i	0.961489	+	0.398262i	0.153952	+	0.988078i	$0.450800\pi$
$18$	−0.204545	−	1.39934i	−0.0482116	−	0.329828i
$19$	−2.47517	+	2.03132i	−0.567844	+	0.466017i	−0.873974	−	0.485972i	$-0.838466\pi$
$19$	−2.47517	+	2.03132i	−0.567844	+	0.466017i	0.306130	+	0.951990i	$0.400966\pi$
$20$	3.89816	−	3.86527i	0.871655	−	0.864301i
$21$	−1.47680	−	0.447982i	−0.322264	−	0.0977576i
$22$	−0.414526	−	8.81898i	−0.0883772	−	1.88021i
$23$	−1.24331	+	6.25056i	−0.259249	+	1.30333i	0.603364	+	0.797466i	$0.293827\pi$
$23$	−1.24331	+	6.25056i	−0.259249	+	1.30333i	−0.862612	+	0.505865i	$0.831173\pi$
$24$	−1.43866	−	2.43521i	−0.293665	−	0.497086i
$25$	−2.48531	+	0.494359i	−0.497062	+	0.0988718i
$26$	−4.06159	+	6.74392i	−0.796543	+	1.32259i
$27$	0.773010	+	0.634393i	0.148766	+	0.122089i
$28$	−3.07289	+	0.289515i	−0.580722	+	0.0547132i
$29$	−1.87108	+	3.50055i	−0.347451	+	0.650035i	−0.993572	−	0.113200i	$-0.963890\pi$
$29$	−1.87108	+	3.50055i	−0.347451	+	0.650035i	0.646121	+	0.763235i	$0.276390\pi$
$30$	−0.198680	+	3.87666i	−0.0362739	+	0.707779i
$31$	−1.60293	+	1.60293i	−0.287895	+	0.287895i	−0.836247	−	0.548353i	$-0.815255\pi$
$31$	−1.60293	+	1.60293i	−0.287895	+	0.287895i	0.548353	+	0.836247i	$0.315255\pi$
$32$	−4.50769	−	3.41771i	−0.796854	−	0.604172i
$33$	4.41436	+	4.41436i	0.768441	+	0.768441i
$34$	−4.50495	+	4.06570i	−0.772592	+	0.697262i
$35$	3.73576	+	1.99680i	0.631458	+	0.337522i
$36$	1.91140	+	0.588672i	0.318567	+	0.0981120i
$37$	−3.90148	+	4.75396i	−0.641399	+	0.781547i	−0.987664	−	0.156590i	$-0.949950\pi$
$37$	−3.90148	+	4.75396i	−0.641399	+	0.781547i	0.346265	+	0.938137i	$0.387450\pi$
$38$	−1.09098	−	4.39491i	−0.176980	−	0.712949i
$39$	−1.08601	−	5.45977i	−0.173902	−	0.874262i
$40$	2.56894	+	7.32615i	0.406186	+	1.15837i
$41$	1.19260	+	0.237222i	0.186252	+	0.0370479i	0.287335	−	0.957830i	$-0.407231\pi$
$41$	1.19260	+	0.237222i	0.186252	+	0.0370479i	−0.101083	+	0.994878i	$0.532231\pi$
$42$	1.46909	−	1.61401i	0.226685	−	0.249047i
$43$	−1.18922	+	3.92032i	−0.181354	+	0.597844i	0.818378	+	0.574681i	$0.194874\pi$
$43$	−1.18922	+	3.92032i	−0.181354	+	0.597844i	−0.999732	+	0.0231631i	$0.992626\pi$
$44$	11.5149	+	4.82689i	1.73594	+	0.727681i
$45$	−1.74129	−	2.12177i	−0.259576	−	0.316295i
$46$	−7.22776	−	5.38424i	−1.06568	−	0.793863i
$47$	4.43305	−	10.7023i	0.646627	−	1.56110i	−0.170951	−	0.985279i	$-0.554684\pi$
$47$	4.43305	−	10.7023i	0.646627	−	1.56110i	0.817579	−	0.575817i	$-0.195316\pi$
$48$	3.98392	−	0.358328i	0.575029	−	0.0517202i
$49$	1.76738	+	4.26683i	0.252483	+	0.609547i
$50$	0.878109	−	3.47437i	0.124183	−	0.491350i
$51$	0.420586	−	4.27029i	0.0588939	−	0.597960i
$52$	−6.14615	−	9.28325i	−0.852317	−	1.28736i
$53$	−3.21836	−	6.02112i	−0.442075	−	0.827065i	0.557921	−	0.829894i	$-0.311599\pi$
$53$	−3.21836	−	6.02112i	−0.442075	−	0.827065i	−0.999996	+	0.00282966i	$0.999099\pi$
$54$	−1.27971	+	0.601945i	−0.174147	+	0.0819143i
$55$	−9.51994	−	14.2476i	−1.28367	−	1.92115i
$56$	1.49660	−	4.10038i	0.199992	−	0.547937i
$57$	2.66236	+	1.77893i	0.352638	+	0.235625i
$58$	−3.33430	−	4.51575i	−0.437816	−	0.592947i
$59$	12.4050	−	1.22179i	1.61500	−	0.159063i	0.750209	−	0.661201i	$-0.229953\pi$
$59$	12.4050	−	1.22179i	1.61500	−	0.159063i	0.864788	+	0.502137i	$0.167453\pi$
$60$	−4.83041	−	2.60828i	−0.623604	−	0.336727i
$61$	0.672244	−	0.203923i	0.0860720	−	0.0261097i	−0.246955	−	0.969027i	$-0.579430\pi$
$61$	0.672244	−	0.203923i	0.0860720	−	0.0261097i	0.333027	+	0.942917i	$0.391930\pi$
$62$	−1.07363	−	3.02074i	−0.136351	−	0.383634i
$63$			1.54325i			0.194431i
$64$	7.10273	−	3.68121i	0.887841	−	0.460151i
$65$			15.2796i			1.89520i
$66$	−8.31891	+	2.95669i	−1.02399	+	0.363944i
$67$	5.38202	−	1.63262i	0.657519	−	0.199456i	0.0561434	−	0.998423i	$-0.482120\pi$
$67$	5.38202	−	1.63262i	0.657519	−	0.199456i	0.601375	+	0.798967i	$0.294620\pi$
$68$	−2.45638	−	8.22284i	−0.297880	−	0.997166i
$69$	6.34233	−	0.624665i	0.763526	−	0.0752008i
$70$	−4.81917	+	3.55834i	−0.576001	+	0.425304i
$71$	−4.06093	−	2.71343i	−0.481944	−	0.322025i	0.290755	−	0.956798i	$-0.406094\pi$
$71$	−4.06093	−	2.71343i	−0.481944	−	0.322025i	−0.772699	+	0.634773i	$0.781094\pi$
$72$	−1.91273	+	2.08361i	−0.225418	+	0.245556i
$73$	−3.68754	−	5.51879i	−0.431593	−	0.645925i	0.550387	−	0.834910i	$-0.314480\pi$
$73$	−3.68754	−	5.51879i	−0.431593	−	0.645925i	−0.981980	+	0.188985i	$0.939480\pi$
$74$	−3.70192	−	7.87014i	−0.430340	−	0.914885i
$75$	1.19452	+	2.23479i	0.137931	+	0.258051i
$76$	6.27559	+	1.27595i	0.719859	+	0.146362i
$77$	−0.944324	+	9.58788i	−0.107616	+	1.09264i
$78$	7.63254	+	1.92904i	0.864215	+	0.218421i
$79$	−1.22482	−	2.95698i	−0.137803	−	0.332687i	0.839880	−	0.542773i	$-0.182626\pi$
$79$	−1.22482	−	2.95698i	−0.137803	−	0.332687i	−0.977683	+	0.210086i	$0.932626\pi$
$80$	−10.9169	−	1.16869i	−1.22054	−	0.130663i
$81$	0.382683	−	0.923880i	0.0425204	−	0.102653i
$82$	−1.02731	+	1.37905i	−0.113447	+	0.152290i
$83$	7.62729	+	9.29388i	0.837204	+	1.02014i	0.999443	+	0.0333841i	$0.0106285\pi$
$83$	7.62729	+	9.29388i	0.837204	+	1.02014i	−0.162239	+	0.986751i	$0.551872\pi$
$84$	1.16906	+	2.85653i	0.127555	+	0.311673i
$85$	−3.41893	+	11.2707i	−0.370835	+	1.22248i
$86$	−4.28456	−	3.89986i	−0.462016	−	0.420533i
$87$	3.89296	+	0.774358i	0.417369	+	0.0830199i
$88$	−13.1584	+	11.7746i	−1.40269	+	1.25518i
$89$	−1.91480	−	9.62637i	−0.202969	−	1.02039i	−0.939123	−	0.343580i	$-0.888360\pi$
$89$	−1.91480	−	9.62637i	−0.202969	−	1.02039i	0.736154	−	0.676814i	$-0.236640\pi$
$90$	3.76741	−	0.935211i	0.397120	−	0.0985799i
$91$	5.44998	−	6.64082i	0.571313	−	0.696147i
$92$	11.2663	−	5.96076i	1.17460	−	0.621452i
$93$	1.99921	+	1.06860i	0.207309	+	0.110809i
$94$	10.9760	+	12.1619i	1.13209	+	1.25440i
$95$	−6.21467	−	6.21467i	−0.637612	−	0.637612i
$96$	−1.96204	+	5.30570i	−0.200250	+	0.541510i
$97$	9.90497	−	9.90497i	1.00570	−	1.00570i	0.00571375	−	0.999984i	$-0.498181\pi$
$97$	9.90497	−	9.90497i	1.00570	−	1.00570i	0.999984	−	0.00571375i	$-0.00181875\pi$
$98$	−6.52282	−	0.334296i	−0.658904	−	0.0337690i
$99$	2.94286	−	5.50570i	0.295768	−	0.553343i
$100$	3.90396	+	3.23167i	0.390396	+	0.323167i
$101$	−9.24655	−	7.58845i	−0.920066	−	0.755079i	0.0497894	−	0.998760i	$-0.484145\pi$
$101$	−9.24655	−	7.58845i	−0.920066	−	0.755079i	−0.969855	+	0.243681i	$0.921645\pi$
$102$	5.19835	+	3.13076i	0.514713	+	0.309991i
$103$	13.4671	−	2.67878i	1.32696	−	0.263948i	0.519801	−	0.854287i	$-0.326006\pi$
$103$	13.4671	−	2.67878i	1.32696	−	0.263948i	0.807155	+	0.590339i	$0.201006\pi$
$104$	15.5890	−	2.21127i	1.52863	−	0.216833i
$105$	0.826389	−	4.15454i	0.0806473	−	0.405442i
$106$	9.64458	−	0.453332i	0.936764	−	0.0440315i
$107$	4.55882	+	1.38290i	0.440718	+	0.133690i	0.502842	−	0.864378i	$-0.332288\pi$
$107$	4.55882	+	1.38290i	0.440718	+	0.133690i	−0.0621245	+	0.998068i	$0.519788\pi$
$108$	0.00847249	−	1.99998i	0.000815266	−	0.192448i
$109$	6.05675	−	4.97065i	0.580132	−	0.476102i	−0.297970	−	0.954575i	$-0.596310\pi$
$109$	6.05675	−	4.97065i	0.580132	−	0.476102i	0.878102	+	0.478473i	$0.158810\pi$
$110$	23.9784	−	3.50496i	2.28625	−	0.334185i
$111$	5.68180	+	2.35348i	0.539292	+	0.223382i
$112$	4.32783	+	4.40179i	0.408942	+	0.415931i
$113$	−8.46081	+	3.50458i	−0.795926	+	0.329683i	−0.743323	−	0.668932i	$-0.766752\pi$
$113$	−8.46081	+	3.50458i	−0.795926	+	0.329683i	−0.0526024	+	0.998616i	$0.516752\pi$
$114$	−3.88898	+	2.31978i	−0.364236	+	0.217267i
$115$	−17.4085	−	1.71459i	−1.62335	−	0.159886i
$116$	7.79241	−	1.51572i	0.723507	−	0.140731i
$117$	−4.90942	+	2.62414i	−0.453876	+	0.242602i
$118$	−5.97392	+	16.5851i	−0.549944	+	1.52679i
$119$	5.50600	−	3.67899i	0.504734	−	0.337252i
$120$	6.26497	−	4.58500i	0.571911	−	0.418551i
$121$	15.5410	−	23.2588i	1.41282	−	2.11444i
$122$	−0.147854	+	0.982412i	−0.0133861	+	0.0889434i
$123$	−0.119185	−	1.21011i	−0.0107466	−	0.109112i
$124$	4.51001	+	0.463497i	0.405011	+	0.0416232i
$125$	1.96485	+	6.47725i	0.175742	+	0.579343i
$126$	−1.97096	−	0.937309i	−0.175587	−	0.0835022i
$127$	−11.9689			−1.06207			−0.531033	−	0.847351i	$-0.678196\pi$
$127$	−11.9689			−1.06207			−0.531033	+	0.847351i	$0.678196\pi$
$128$	0.387537	+	11.3071i	0.0342538	+	0.999413i
$129$	4.09673			0.360697
$130$	−19.5144	−	9.28025i	−1.71152	−	0.813932i
$131$	0.236543	+	0.779777i	0.0206668	+	0.0681294i	0.966667	−	0.256036i	$-0.0824166\pi$
$131$	0.236543	+	0.779777i	0.0206668	+	0.0681294i	−0.946000	+	0.324165i	$0.894917\pi$
$132$	1.27644	−	12.4203i	0.111100	−	1.08105i
$133$	0.484349	+	4.91768i	0.0419984	+	0.426417i
$134$	−1.18373	+	7.86524i	−0.102259	+	0.679453i
$135$	−1.52494	+	2.28223i	−0.131246	+	0.196423i
$136$	11.9937	+	1.85706i	1.02845	+	0.159242i
$137$	−12.7032	+	8.48804i	−1.08531	+	0.725182i	−0.963591	−	0.267382i	$-0.913841\pi$
$137$	−12.7032	+	8.48804i	−1.08531	+	0.725182i	−0.121721	+	0.992564i	$0.538841\pi$
$138$	−3.05429	+	8.47950i	−0.259998	+	0.721823i
$139$	−16.8642	+	9.01408i	−1.43040	+	0.764565i	−0.991017	−	0.133735i	$-0.957303\pi$
$139$	−16.8642	+	9.01408i	−1.43040	+	0.764565i	−0.439383	+	0.898300i	$0.644803\pi$
$140$	−1.61756	−	8.31601i	−0.136709	−	0.702831i
$141$	−11.5283	−	1.13544i	−0.970862	−	0.0956216i
$142$	5.93191	−	3.53839i	0.497795	−	0.296935i
$143$	−32.1069	+	13.2991i	−2.68491	+	1.11213i
$144$	−1.49937	−	3.70835i	−0.124947	−	0.309030i
$145$	−10.0655	−	4.16926i	−0.835892	−	0.346238i
$146$	9.28799	−	1.35764i	0.768679	−	0.112359i
$147$	3.57006	−	2.92987i	0.294453	−	0.241652i
$148$	12.2998	+	0.0521052i	1.01103	+	0.00428302i
$149$	13.2330	+	4.01419i	1.08409	+	0.328855i	0.781271	−	0.624192i	$-0.214572\pi$
$149$	13.2330	+	4.01419i	1.08409	+	0.328855i	0.302820	+	0.953048i	$0.402072\pi$
$150$	−3.57966	+	0.168258i	−0.292278	+	0.0137382i
$151$	0.115979	−	0.583066i	0.00943823	−	0.0474492i	−0.975779	−	0.218758i	$-0.929800\pi$
$151$	0.115979	−	0.583066i	0.00943823	−	0.0474492i	0.985217	+	0.171309i	$0.0547995\pi$
$152$	−5.44113	+	7.23990i	−0.441334	+	0.587234i
$153$	−4.20850	+	0.837123i	−0.340237	+	0.0676773i
$154$	−11.6716	−	7.02934i	−0.940526	−	0.566441i
$155$	−4.80981	−	3.94731i	−0.386333	−	0.317055i
$156$	−7.09939	+	8.57628i	−0.568406	+	0.686652i
$157$	0.447846	−	0.837861i	0.0357420	−	0.0668686i	−0.863416	−	0.504492i	$-0.831680\pi$
$157$	0.447846	−	0.837861i	0.0357420	−	0.0668686i	0.899158	+	0.437624i	$0.144180\pi$
$158$	4.52042	+	0.231673i	0.359626	+	0.0184309i
$159$	−4.82761	+	4.82761i	−0.382855	+	0.382855i
$160$	8.12307	−	13.2327i	0.642185	−	1.04613i
$161$	6.95450	+	6.95450i	0.548092	+	0.548092i
$162$	0.947506	+	1.04987i	0.0744431	+	0.0824858i
$163$	7.25991	+	3.88051i	0.568640	+	0.303945i	0.730548	−	0.682861i	$-0.239265\pi$
$163$	7.25991	+	3.88051i	0.568640	+	0.303945i	−0.161908	+	0.986806i	$0.551765\pi$
$164$	−1.13731	−	2.14960i	−0.0888086	−	0.167856i
$165$	−10.8706	+	13.2459i	−0.846276	+	1.03119i
$166$	−16.5022	+	4.09646i	−1.28082	+	0.317947i
$167$	−1.72564	−	8.67536i	−0.133534	−	0.671319i	−0.988327	−	0.152350i	$-0.951316\pi$
$167$	−1.72564	−	8.67536i	−0.133534	−	0.671319i	0.854793	−	0.518969i	$-0.173684\pi$
$168$	−4.35826	−	0.241878i	−0.336247	−	0.0186613i
$169$	17.6428	+	3.50938i	1.35714	+	0.269952i
$170$	−12.3179	−	11.2119i	−0.944736	−	0.859911i
$171$	0.929489	−	3.06412i	0.0710798	−	0.234319i
$172$	7.58298	−	3.10340i	0.578197	−	0.236632i
$173$	−8.65546	−	10.5467i	−0.658063	−	0.801852i	0.331880	−	0.943322i	$-0.392317\pi$
$173$	−8.65546	−	10.5467i	−0.658063	−	0.801852i	−0.989943	+	0.141470i	$0.954817\pi$
$174$	−3.35340	+	4.50158i	−0.254221	+	0.341264i
$175$	−1.49652	+	3.61292i	−0.113126	+	0.273111i
$176$	−7.04609	−	23.9567i	−0.531119	−	1.80580i
$177$	−4.77017	−	11.5162i	−0.358548	−	0.865611i
$178$	13.4573	+	3.40119i	1.00867	+	0.254930i
$179$	0.332475	−	3.37568i	0.0248504	−	0.252310i	−0.974731	−	0.223381i	$-0.928290\pi$
$179$	0.332475	−	3.37568i	0.0248504	−	0.252310i	0.999581	−	0.0289286i	$-0.00920955\pi$
$180$	−1.09377	+	5.37956i	−0.0815249	+	0.400969i
$181$	−0.00348186	−	0.00651409i	−0.000258804	−	0.000484189i	0.881792	−	0.471639i	$-0.156337\pi$
$181$	−0.00348186	−	0.00651409i	−0.000258804	−	0.000484189i	−0.882051	+	0.471155i	$0.843837\pi$
$182$	5.17122	+	10.9938i	0.383316	+	0.814916i
$183$	−0.390284	−	0.584102i	−0.0288506	−	0.0431780i
$184$	0.770054	+	18.0092i	0.0567691	+	1.32765i
$185$	−14.0356	−	9.37826i	−1.03191	−	0.689503i
$186$	−2.57901	+	1.90427i	−0.189102	+	0.139628i
$187$	−26.6587	+	2.62566i	−1.94948	+	0.192007i
$188$	−22.1989	+	6.63141i	−1.61902	+	0.483645i
$189$	1.47680	−	0.447982i	0.107421	−	0.0325859i
$190$	11.7116	−	4.16252i	0.849650	−	0.301981i
$191$		−	21.9685i		−	1.58959i	−0.606880	−	0.794794i	$-0.707579\pi$
$191$		−	21.9685i		−	1.58959i	0.606880	−	0.794794i	$-0.292421\pi$
$192$	−5.58451	−	5.72829i	−0.403027	−	0.413404i
$193$			13.9813i			1.00640i	0.864170	+	0.503199i	$0.167844\pi$
$193$			13.9813i			1.00640i	−0.864170	+	0.503199i	$0.832156\pi$
$194$	6.63425	+	18.6660i	0.476311	+	1.34014i
$195$	14.6217	−	4.43544i	1.04708	−	0.317629i
$196$	4.38865	−	8.12758i	0.313475	−	0.580541i
$197$	−21.2024	+	2.08825i	−1.51061	+	0.148782i	−0.819126	−	0.573614i	$-0.805541\pi$
$197$	−21.2024	+	2.08825i	−1.51061	+	0.148782i	−0.691480	+	0.722396i	$0.743041\pi$
$198$	5.24423	+	7.10242i	0.372691	+	0.504747i
$199$	18.1744	+	12.1437i	1.28835	+	0.860846i	0.995449	−	0.0952974i	$-0.0303802\pi$
$199$	18.1744	+	12.1437i	1.28835	+	0.860846i	0.292899	+	0.956144i	$0.405380\pi$
$200$	−6.49844	+	3.02315i	−0.459509	+	0.213769i
$201$	−3.12464	−	4.67635i	−0.220395	−	0.329844i
$202$	15.3076	−	7.20031i	1.07704	−	0.506612i
$203$	2.88755	+	5.40222i	0.202666	+	0.379161i
$204$	−7.15572	+	4.73758i	−0.501001	+	0.331697i
$205$	−0.327141	+	3.32152i	−0.0228485	+	0.231985i
$206$	−4.75820	+	18.8265i	−0.331520	+	1.31171i
$207$	−2.43885	−	5.88790i	−0.169512	−	0.409237i
$208$	−6.64404	+	21.2526i	−0.460682	+	1.47360i
$209$	7.64967	−	18.4679i	0.529139	−	1.27745i
$210$	4.80406	+	3.57873i	0.331511	+	0.246956i
$211$	−3.34818	−	4.07977i	−0.230499	−	0.280863i	0.644898	−	0.764269i	$-0.276900\pi$
$211$	−3.34818	−	4.07977i	−0.230499	−	0.280863i	−0.875397	+	0.483405i	$0.839400\pi$
$212$	−5.27877	+	12.5929i	−0.362547	+	0.864885i
$213$	−1.41776	+	4.67374i	−0.0971435	+	0.320239i
$214$	−4.53503	+	4.98238i	−0.310008	+	0.340589i
$215$	−11.0287	−	2.19374i	−0.752150	−	0.149612i
$216$	2.54913	+	1.22553i	0.173446	+	0.0833868i
$217$	0.682498	+	3.43115i	0.0463310	+	0.232922i
$218$	2.66963	+	10.7544i	0.180810	+	0.728377i
$219$	−4.21072	+	5.13077i	−0.284534	+	0.346705i
$220$	−10.0872	+	32.7528i	−0.680076	+	2.20819i
$221$	21.0661	+	11.2600i	1.41706	+	0.757432i
$222$	−6.45664	+	5.82710i	−0.433342	+	0.391089i
$223$	0.728363	+	0.728363i	0.0487748	+	0.0487748i	0.731074	−	0.682299i	$-0.239020\pi$
$223$	0.728363	+	0.728363i	0.0487748	+	0.0487748i	−0.682299	+	0.731074i	$0.739020\pi$
$224$	−8.25031	+	2.85381i	−0.551247	+	0.190678i
$225$	1.79181	−	1.79181i	0.119454	−	0.119454i
$226$	0.662885	−	12.9343i	0.0440945	−	0.860375i
$227$	9.58574	−	17.9337i	0.636228	−	1.19030i	−0.332718	−	0.943026i	$-0.607966\pi$
$227$	9.58574	−	17.9337i	0.636228	−	1.19030i	0.968946	−	0.247272i	$-0.0795343\pi$
$228$	−0.600697	−	6.37575i	−0.0397821	−	0.422244i
$229$	−5.74268	−	4.71289i	−0.379487	−	0.311437i	0.425242	−	0.905080i	$-0.360189\pi$
$229$	−5.74268	−	4.71289i	−0.379487	−	0.311437i	−0.804728	+	0.593643i	$0.797689\pi$
$230$	12.7630	−	21.1919i	0.841569	−	1.39735i
$231$	9.44915	−	1.87955i	0.621708	−	0.123665i
$232$	−2.79700	+	10.8727i	−0.183632	+	0.713826i
$233$	−4.70844	+	23.6709i	−0.308460	+	1.55073i	0.446392	+	0.894837i	$0.352709\pi$
$233$	−4.70844	+	23.6709i	−0.308460	+	1.55073i	−0.754852	+	0.655895i	$0.772291\pi$
$234$	−0.369632	−	7.86386i	−0.0241636	−	0.514077i
$235$	30.4271	+	9.22997i	1.98485	+	0.602097i
$236$	−17.5534	−	17.7028i	−1.14263	−	1.15235i
$237$	−2.47411	+	2.03045i	−0.160711	+	0.131892i
$238$	1.35450	+	9.26646i	0.0877989	+	0.600655i
$239$	−5.62642	−	2.33054i	−0.363943	−	0.150750i	0.193216	−	0.981156i	$-0.438108\pi$
$239$	−5.62642	−	2.33054i	−0.363943	−	0.150750i	−0.557158	+	0.830406i	$0.688108\pi$
$240$	2.05064	+	10.7861i	0.132368	+	0.696237i
$241$	18.6884	−	7.74098i	1.20382	−	0.498640i	0.311592	−	0.950216i	$-0.399138\pi$
$241$	18.6884	−	7.74098i	1.20382	−	0.498640i	0.892233	+	0.451576i	$0.149138\pi$
$242$	20.2660	+	33.9747i	1.30275	+	2.18398i
$243$	−0.995185	−	0.0980171i	−0.0638411	−	0.00628780i
$244$	−1.16489	−	0.785510i	−0.0745742	−	0.0502871i
$245$	−11.1798	+	5.97570i	−0.714248	+	0.381774i
$246$	1.61788	+	0.582754i	0.103152	+	0.0371550i
$247$	−14.8206	+	9.90283i	−0.943014	+	0.630102i
$248$	−3.33116	+	5.47846i	−0.211529	+	0.347882i
$249$	6.67960	−	9.99673i	0.423303	−	0.633517i
$250$	−9.46580	−	1.42462i	−0.598670	−	0.0901006i
$251$	2.34554	+	23.8146i	0.148049	+	1.50317i	0.726340	+	0.687336i	$0.241220\pi$
$251$	2.34554	+	23.8146i	0.148049	+	1.50317i	−0.578291	+	0.815831i	$0.696280\pi$
$252$	2.39417	−	1.94793i	0.150819	−	0.122708i
$253$	−11.5492	−	38.0726i	−0.726091	−	2.39360i
$254$	7.26942	−	15.2860i	0.456124	−	0.959132i
$255$	11.7779			0.737558
$256$	−14.6762	−	6.37253i	−0.917263	−	0.398283i
$257$	27.0192			1.68541			0.842707	−	0.538373i	$-0.180961\pi$
$257$	27.0192			1.68541			0.842707	+	0.538373i	$0.180961\pi$
$258$	−2.48819	+	5.23214i	−0.154908	+	0.325739i
$259$	2.75506	+	9.08221i	0.171191	+	0.564341i
$260$	23.7045	−	19.2863i	1.47009	−	1.19609i
$261$	−0.389052	−	3.95012i	−0.0240817	−	0.244506i
$262$	−1.13956	−	0.171505i	−0.0704022	−	0.0105956i
$263$	3.53885	−	5.29626i	0.218215	−	0.326581i	−0.706170	−	0.708042i	$-0.749579\pi$
$263$	3.53885	−	5.29626i	0.218215	−	0.326581i	0.924385	+	0.381461i	$0.124579\pi$
$264$	15.0873	+	9.17379i	0.928559	+	0.564608i
$265$	15.5814	−	10.4112i	0.957158	−	0.639553i
$266$	−6.57479	−	2.36822i	−0.403126	−	0.145205i
$267$	−8.65603	+	4.62674i	−0.529740	+	0.283152i
$268$	−9.32615	−	6.28884i	−0.569685	−	0.384152i
$269$	−18.2010	−	1.79264i	−1.10973	−	0.109299i	−0.473499	−	0.880795i	$-0.657009\pi$
$269$	−18.2010	−	1.79264i	−1.10973	−	0.109299i	−0.636235	+	0.771495i	$0.719509\pi$
$270$	−1.98856	−	3.33371i	−0.121020	−	0.202883i
$271$	1.89028	−	0.782978i	0.114826	−	0.0475625i	−0.324531	−	0.945875i	$-0.605206\pi$
$271$	1.89028	−	0.782978i	0.114826	−	0.0475625i	0.439357	+	0.898313i	$0.355206\pi$
$272$	−9.65626	+	14.1899i	−0.585497	+	0.860387i
$273$	−7.93691	−	3.28758i	−0.480364	−	0.198973i
$274$	−3.12505	−	21.3793i	−0.188791	−	1.29157i
$275$	12.2285	−	10.0357i	0.737408	−	0.605175i
$276$	−8.97454	−	9.05090i	−0.540204	−	0.544800i
$277$	4.36127	+	1.32298i	0.262043	+	0.0794900i	0.418573	−	0.908183i	$-0.362531\pi$
$277$	4.36127	+	1.32298i	0.262043	+	0.0794900i	−0.156529	+	0.987673i	$0.550031\pi$
$278$	−1.26971	−	27.0129i	−0.0761521	−	1.62012i
$279$	0.442247	−	2.22333i	0.0264767	−	0.133107i
$280$	11.6032	+	2.98494i	0.693426	+	0.178384i
$281$	−2.07315	+	0.412374i	−0.123674	+	0.0246002i	−0.256539	−	0.966534i	$-0.582582\pi$
$281$	−2.07315	+	0.412374i	−0.123674	+	0.0246002i	0.132865	+	0.991134i	$0.457582\pi$
$282$	8.45200	−	14.0338i	0.503309	−	0.835701i
$283$	3.98537	+	3.27071i	0.236906	+	0.194424i	0.745354	−	0.666669i	$-0.232281\pi$
$283$	3.98537	+	3.27071i	0.236906	+	0.194424i	−0.508448	+	0.861093i	$0.669781\pi$
$284$	0.916250	+	9.72502i	0.0543695	+	0.577074i
$285$	−4.14305	+	7.75109i	−0.245413	+	0.459135i
$286$	2.51550	−	49.0827i	0.148745	−	2.90232i
$287$	1.32691	−	1.32691i	0.0783250	−	0.0783250i
$288$	5.64678	+	0.337390i	0.332740	+	0.0198809i
$289$	0.998603	+	0.998603i	0.0587414	+	0.0587414i
$290$	11.4381	−	10.3229i	0.671671	−	0.606180i
$291$	−12.3537	−	6.60320i	−0.724188	−	0.387087i
$292$	−3.90724	+	12.6867i	−0.228654	+	0.742435i
$293$	14.1595	−	17.2534i	0.827207	−	1.00795i	−0.172530	−	0.985004i	$-0.555194\pi$
$293$	14.1595	−	17.2534i	0.827207	−	1.00795i	0.999737	−	0.0229501i	$-0.00730588\pi$
$294$	1.57357	+	6.33899i	0.0917726	+	0.369697i
$295$	6.67487	+	33.5568i	0.388626	+	1.95375i
$296$	−7.53693	+	15.6770i	−0.438075	+	0.911206i
$297$	−6.12289	−	1.21792i	−0.355286	−	0.0706708i
$298$	−13.1639	+	14.4625i	−0.762567	+	0.837790i
$299$	−10.2984	+	33.9492i	−0.595571	+	1.96333i
$300$	1.95926	−	4.67396i	0.113118	−	0.269851i
$301$	4.01081	+	4.88718i	0.231179	+	0.281693i
$302$	0.674221	+	0.502254i	0.0387971	+	0.0289015i
$303$	−4.57756	+	11.0512i	−0.262974	+	0.634875i
$304$	−5.94172	−	11.3464i	−0.340781	−	0.650759i
$305$	0.737895	+	1.78144i	0.0422517	+	0.102005i
$306$	1.48695	−	5.88332i	0.0850030	−	0.336327i
$307$	0.961956	−	9.76690i	0.0549017	−	0.557426i	−0.927909	−	0.372808i	$-0.878395\pi$
$307$	0.961956	−	9.76690i	0.0549017	−	0.557426i	0.982810	−	0.184618i	$-0.0591049\pi$
$308$	16.0664	−	10.6371i	0.915469	−	0.606103i
$309$	−6.47274	−	12.1096i	−0.368221	−	0.688893i
$310$	7.96259	−	3.74541i	0.452245	−	0.212725i
$311$	13.5695	+	20.3082i	0.769456	+	1.15157i	0.984571	+	0.174983i	$0.0559871\pi$
$311$	13.5695	+	20.3082i	0.769456	+	1.15157i	−0.215116	+	0.976589i	$0.569013\pi$
$312$	−6.64131	−	14.2759i	−0.375990	−	0.808213i
$313$	0.400851	+	0.267840i	0.0226574	+	0.0151392i	0.566847	−	0.823823i	$-0.308163\pi$
$313$	0.400851	+	0.267840i	0.0226574	+	0.0151392i	−0.544190	+	0.838962i	$0.683163\pi$
$314$	0.798071	+	1.08085i	0.0450377	+	0.0609959i
$315$	−4.21554	+	0.415194i	−0.237518	+	0.0233935i
$316$	−3.04141	+	5.63255i	−0.171093	+	0.316856i
$317$	16.2606	−	4.93259i	0.913285	−	0.277042i	0.201541	−	0.979480i	$-0.435405\pi$
$317$	16.2606	−	4.93259i	0.913285	−	0.277042i	0.711745	+	0.702438i	$0.247905\pi$
$318$	−3.23349	−	9.09769i	−0.181325	−	0.510173i
$319$		−	24.7793i		−	1.38737i
$320$	11.9665	+	18.4114i	0.668946	+	1.02923i
$321$		−	4.76396i		−	0.265898i
$322$	−13.1058	+	4.65805i	−0.730360	+	0.259583i
$323$	−13.1480	+	3.98839i	−0.731572	+	0.221920i
$324$	−1.91632	+	0.572456i	−0.106462	+	0.0318031i
$325$	−14.0382	+	1.38264i	−0.778697	+	0.0766950i
$326$	−9.36538	+	6.91514i	−0.518700	+	0.382994i
$327$	−6.51480	−	4.35305i	−0.360269	−	0.240724i
$328$	3.43612	−	0.146925i	0.189728	−	0.00811259i
$329$	−9.93204	−	14.8644i	−0.547571	−	0.819498i
$330$	−10.3146	−	21.9284i	−0.567800	−	1.20712i
$331$	8.43007	+	15.7716i	0.463359	+	0.866883i	0.999738	+	0.0229057i	$0.00729174\pi$
$331$	8.43007	+	15.7716i	0.463359	+	0.866883i	−0.536379	+	0.843977i	$0.680208\pi$
$332$	4.79099	−	23.5638i	0.262940	−	1.29323i
$333$	0.602799	−	6.12032i	0.0330332	−	0.335391i
$334$	12.1278	+	3.06517i	0.663605	+	0.167719i
$335$	5.90763	+	14.2623i	0.322768	+	0.779231i
$336$	2.95595	−	5.41925i	0.161260	−	0.295644i
$337$	2.80491	−	6.77166i	0.152793	−	0.368876i	−0.828886	−	0.559418i	$-0.811025\pi$
$337$	2.80491	−	6.77166i	0.152793	−	0.368876i	0.981679	+	0.190542i	$0.0610247\pi$
$338$	−15.1976	+	20.4011i	−0.826638	+	1.10967i
$339$	5.80972	+	7.07916i	0.315541	+	0.384487i
$340$	21.8006	−	8.92210i	1.18230	−	0.483869i
$341$	4.10805	−	13.5424i	0.222464	−	0.733364i
$342$	3.34880	+	3.04812i	0.181082	+	0.164824i
$343$	17.5855	+	3.49798i	0.949530	+	0.188873i
$344$	−0.642091	+	11.5695i	−0.0346192	+	0.623785i
$345$	3.41266	+	17.1566i	0.183732	+	0.923681i
$346$	18.7267	−	4.64867i	1.00675	−	0.249914i
$347$	0.345923	−	0.421509i	0.0185701	−	0.0226278i	−0.763643	−	0.645639i	$-0.776591\pi$
$347$	0.345923	−	0.421509i	0.0185701	−	0.0226278i	0.782213	+	0.623011i	$0.214091\pi$
$348$	−3.71247	−	7.01688i	−0.199009	−	0.376144i
$349$	11.1529	+	5.96135i	0.597001	+	0.319104i	0.742075	−	0.670317i	$-0.233842\pi$
$349$	11.1529	+	5.96135i	0.597001	+	0.319104i	−0.145074	+	0.989421i	$0.546342\pi$
$350$	−3.70531	−	4.10562i	−0.198057	−	0.219455i
$351$	3.93627	+	3.93627i	0.210103	+	0.210103i
$352$	34.8758	+	5.55143i	1.85889	+	0.295892i
$353$	−22.1452	+	22.1452i	−1.17867	+	1.17867i	−0.198585	+	0.980084i	$0.563635\pi$
$353$	−22.1452	+	22.1452i	−1.17867	+	1.17867i	−0.980084	+	0.198585i	$0.936365\pi$
$354$	17.6051	+	0.902269i	0.935702	+	0.0479550i
$355$	6.31944	−	11.8228i	0.335401	−	0.627492i
$356$	−12.5173	+	15.1213i	−0.663414	+	0.801425i
$357$	−5.11888	−	4.20096i	−0.270920	−	0.222338i
$358$	4.10932	+	2.47488i	0.217184	+	0.130801i
$359$	25.8235	−	5.13661i	1.36291	−	0.271100i	0.541147	−	0.840928i	$-0.317990\pi$
$359$	25.8235	−	5.13661i	1.36291	−	0.271100i	0.821764	+	0.569828i	$0.192990\pi$
$360$	−6.20619	−	4.66424i	−0.327095	−	0.245827i
$361$	−1.70650	+	8.57917i	−0.0898159	+	0.451535i
$362$	0.0104342		0.000490448i	0.000548410		2.57774e-5i
$363$	−26.7686	−	8.12017i	−1.40499	−	0.426198i
$364$	−17.1816	−	0.0727859i	−0.900558	−	0.00381502i
$365$	14.0830	−	11.5576i	0.737138	−	0.604954i
$366$	0.983029	−	0.143691i	0.0513838	−	0.00751086i
$367$	−15.0989	−	6.25415i	−0.788154	−	0.326464i	−0.0479527	−	0.998850i	$-0.515270\pi$
$367$	−15.0989	−	6.25415i	−0.788154	−	0.326464i	−0.740201	+	0.672386i	$0.765270\pi$
$368$	−23.4681	−	9.95458i	−1.22336	−	0.518918i
$369$	−1.12340	+	0.465329i	−0.0584820	+	0.0242240i
$370$	20.5021	−	12.2295i	1.06585	−	0.635783i
$371$	−10.4855	−	1.03273i	−0.544378	−	0.0536165i
$372$	−0.865649	−	4.45036i	−0.0448818	−	0.230740i
$373$	11.6937	−	6.25039i	0.605475	−	0.323633i	−0.140016	−	0.990149i	$-0.544715\pi$
$373$	11.6937	−	6.25039i	0.605475	−	0.323633i	0.745490	+	0.666516i	$0.232215\pi$
$374$	12.8381	−	35.6419i	0.663843	−	1.84300i
$375$	5.62798	−	3.76049i	0.290628	−	0.194191i
$376$	5.01345	−	32.3790i	0.258549	−	1.66982i
$377$	−12.2757	+	18.3718i	−0.632229	+	0.946198i
$378$	−0.324809	+	2.15818i	−0.0167064	+	0.111005i
$379$	−1.78473	−	18.1206i	−0.0916752	−	0.930794i	−0.925496	−	0.378758i	$-0.876351\pi$
$379$	−1.78473	−	18.1206i	−0.0916752	−	0.930794i	0.833821	−	0.552036i	$-0.186149\pi$
$380$	−1.79701	+	17.4856i	−0.0921847	+	0.896995i
$381$	3.47438	+	11.4535i	0.177998	+	0.586780i
$382$	28.0571	+	13.3428i	1.43553	+	0.682678i
$383$	17.1598			0.876824			0.438412	−	0.898774i	$-0.355541\pi$
$383$	17.1598			0.876824			0.438412	+	0.898774i	$0.355541\pi$
$384$	10.7077	−	3.65312i	0.546425	−	0.186422i
$385$	−26.4443			−1.34772
$386$	−17.8563	−	8.49172i	−0.908860	−	0.432217i
$387$	−1.18922	−	3.92032i	−0.0604513	−	0.199281i
$388$	−27.8687	−	2.86408i	−1.41482	−	0.145402i
$389$	0.287229	+	2.91628i	0.0145631	+	0.147861i	0.999716	−	0.0238156i	$-0.00758145\pi$
$389$	0.287229	+	2.91628i	0.0145631	+	0.147861i	−0.985153	+	0.171677i	$0.945081\pi$
$390$	−3.21592	+	21.3680i	−0.162844	+	1.08201i
$391$	−15.1928	+	22.7376i	−0.768332	+	1.14989i
$392$	7.71464	+	10.5413i	0.389648	+	0.532418i
$393$	0.677535	−	0.452715i	0.0341771	−	0.0228364i
$394$	10.2105	−	28.3469i	0.514396	−	1.42810i
$395$	7.74776	−	4.14127i	0.389832	−	0.208370i
$396$	−12.2560	+	2.38394i	−0.615887	+	0.119797i
$397$	−18.9112	−	1.86259i	−0.949125	−	0.0934806i	−0.388407	−	0.921488i	$-0.626975\pi$
$397$	−18.9112	−	1.86259i	−0.949125	−	0.0934806i	−0.560717	+	0.828007i	$0.689475\pi$
$398$	−26.5478	+	15.8358i	−1.33072	+	0.793776i
$399$	4.56533	−	1.89102i	0.228552	−	0.0946694i
$400$	0.0858763	−	10.1356i	0.00429382	−	0.506782i
$401$	3.08275	+	1.27692i	0.153945	+	0.0637661i	0.458326	−	0.888784i	$-0.348449\pi$
$401$	3.08275	+	1.27692i	0.153945	+	0.0637661i	−0.304380	+	0.952551i	$0.598449\pi$
$402$	7.87019	−	1.15040i	0.392529	−	0.0573768i
$403$	−9.75472	+	8.00549i	−0.485917	+	0.398782i
$404$	−0.101346	+	23.9233i	−0.00504214	+	1.19023i
$405$	2.62662	+	0.796777i	0.130518	+	0.0395922i
$406$	−8.65323	+	0.406735i	−0.429452	+	0.0201859i
$407$	7.49012	−	37.6554i	0.371271	−	1.86651i
$408$	−1.70449	−	12.0163i	−0.0843850	−	0.594898i
$409$	28.1776	−	5.60487i	1.39329	−	0.277143i	0.559322	−	0.828951i	$-0.311062\pi$
$409$	28.1776	−	5.60487i	1.39329	−	0.277143i	0.833972	+	0.551808i	$0.186062\pi$
$410$	−4.04338	−	2.43517i	−0.199689	−	0.120264i
$411$	11.8101	+	9.69230i	0.582550	+	0.478086i
$412$	−21.1544	−	17.5114i	−1.04220	−	0.862727i
$413$	9.06811	−	16.9652i	0.446213	−	0.834805i
$414$	9.00099	+	0.461304i	0.442375	+	0.0226718i
$415$	−23.3351	+	23.3351i	−1.14547	+	1.14547i
$416$	−23.1074	−	21.3934i	−1.13293	−	1.04890i
$417$	13.5213	+	13.5213i	0.662143	+	0.662143i
$418$	18.9402	+	20.9865i	0.926396	+	1.02648i
$419$	1.88980	+	1.01012i	0.0923228	+	0.0493476i	0.516912	−	0.856039i	$-0.327081\pi$
$419$	1.88980	+	1.01012i	0.0923228	+	0.0493476i	−0.424589	+	0.905386i	$0.639581\pi$
$420$	−7.48837	+	3.96192i	−0.365395	+	0.193322i
$421$	−11.8024	+	14.3812i	−0.575212	+	0.700898i	−0.976613	−	0.215004i	$-0.931023\pi$
$421$	−11.8024	+	14.3812i	−0.575212	+	0.700898i	0.401401	+	0.915902i	$0.368523\pi$
$422$	7.24404	−	1.79824i	0.352634	−	0.0875369i
$423$	2.25995	+	11.3615i	0.109883	+	0.552417i
$424$	−12.8769	−	14.3902i	−0.625359	−	0.698851i
$425$	−10.6643	−	2.12127i	−0.517296	−	0.102897i
$426$	−5.10797	−	4.64934i	−0.247482	−	0.225261i
$427$	0.314704	−	1.03744i	0.0152296	−	0.0502053i
$428$	−3.60885	−	8.81801i	−0.174440	−	0.426235i
$429$	22.0466	+	26.8638i	1.06442	+	1.29700i
$430$	9.50013	−	12.7529i	0.458137	−	0.614999i
$431$	−2.38748	+	5.76389i	−0.115001	+	0.277637i	−0.970891	−	0.239521i	$-0.923010\pi$
$431$	−2.38748	+	5.76389i	−0.115001	+	0.277637i	0.855890	+	0.517157i	$0.173010\pi$
$432$	−3.11343	+	2.51129i	−0.149795	+	0.120824i
$433$	7.60286	+	18.3549i	0.365370	+	0.882082i	0.994496	+	0.104778i	$0.0334131\pi$
$433$	7.60286	+	18.3549i	0.365370	+	0.882082i	−0.629126	+	0.777304i	$0.716587\pi$
$434$	−4.79662	−	1.21229i	−0.230245	−	0.0581919i
$435$	−1.06788	+	10.8423i	−0.0512007	+	0.519850i
$436$	−15.3564	−	3.12226i	−0.735437	−	0.149529i
$437$	−9.61949	−	17.9968i	−0.460162	−	0.860903i
$438$	−3.99534	−	8.49395i	−0.190905	−	0.405856i
$439$	1.78528	+	2.67186i	0.0852067	+	0.127521i	0.871625	−	0.490174i	$-0.163067\pi$
$439$	1.78528	+	2.67186i	0.0852067	+	0.127521i	−0.786418	+	0.617695i	$0.788067\pi$
$440$	−35.7037	−	32.7756i	−1.70210	−	1.56251i
$441$	−3.84004	−	2.56583i	−0.182859	−	0.122183i
$442$	−27.1755	+	20.0656i	−1.29260	+	0.954424i
$443$	6.48538	−	0.638754i	0.308129	−	0.0303481i	0.0572293	−	0.998361i	$-0.481773\pi$
$443$	6.48538	−	0.638754i	0.308129	−	0.0303481i	0.250900	+	0.968013i	$0.419273\pi$
$444$	−3.52057	−	11.7853i	−0.167079	−	0.559304i
$445$	25.7802	−	7.82034i	1.22210	−	0.370720i
$446$	−1.37261	+	0.487850i	−0.0649949	+	0.0231004i
$447$		−	13.8285i		−	0.654064i
$448$	1.36616	−	12.2702i	0.0645452	−	0.579711i
$449$		−	27.9353i		−	1.31835i	−0.751990	−	0.659175i	$-0.770906\pi$
$449$		−	27.9353i		−	1.31835i	0.751990	−	0.659175i	$-0.229094\pi$
$450$	1.20013	+	3.37668i	0.0565749	+	0.159178i
$451$	−7.26419	+	2.20357i	−0.342058	+	0.103762i
$452$	16.1164	+	8.70237i	0.758051	+	0.409325i
$453$	−0.591626	+	0.0582701i	−0.0277970	+	0.00273777i
$454$	17.0820	+	23.1346i	0.801697	+	1.08576i
$455$	19.6063	+	13.1005i	0.919157	+	0.614161i
$456$	8.50763	+	3.10520i	0.398406	+	0.145414i
$457$	−15.8823	−	23.7696i	−0.742944	−	1.11189i	−0.989747	−	0.142829i	$-0.954380\pi$
$457$	−15.8823	−	23.7696i	−0.742944	−	1.11189i	0.246803	−	0.969066i	$-0.420620\pi$
$458$	9.50695	−	4.47184i	0.444231	−	0.208955i
$459$	2.02274	+	3.78428i	0.0944134	+	0.176635i
$460$	19.3135	+	29.1714i	0.900496	+	1.36013i
$461$	0.982621	−	9.97672i	0.0457652	−	0.464662i	−0.944803	−	0.327640i	$-0.893747\pi$
$461$	0.982621	−	9.97672i	0.0457652	−	0.464662i	0.990568	−	0.137022i	$-0.0437532\pi$
$462$	−3.33857	+	13.2096i	−0.155324	+	0.614564i
$463$	−6.75440	−	16.3066i	−0.313904	−	0.757831i	−0.999553	−	0.0298986i	$-0.990482\pi$
$463$	−6.75440	−	16.3066i	−0.313904	−	0.757831i	0.685649	−	0.727932i	$-0.259518\pi$
$464$	−12.1872	−	10.1758i	−0.565779	−	0.472401i
$465$	−2.38112	+	5.74854i	−0.110422	+	0.266582i
$466$	−27.3716	−	20.3902i	−1.26796	−	0.944556i
$467$	4.09031	+	4.98405i	0.189277	+	0.230635i	0.858999	−	0.511977i	$-0.171087\pi$
$467$	4.09031	+	4.98405i	0.189277	+	0.230635i	−0.669722	+	0.742612i	$0.733587\pi$
$468$	10.2678	+	4.30413i	0.474631	+	0.198958i
$469$	2.51954	−	8.30581i	0.116341	−	0.383527i
$470$	−30.2683	+	33.2541i	−1.39617	+	1.53390i
$471$	−0.931786	−	0.185344i	−0.0429344	−	0.00854019i
$472$	33.2703	−	11.6664i	1.53139	−	0.536988i
$473$	−4.98948	−	25.0838i	−0.229417	−	1.15335i
$474$	−1.09051	−	4.39303i	−0.0500889	−	0.201778i
$475$	5.14737	−	6.27209i	0.236178	−	0.287783i
$476$	−12.6573	−	3.89819i	−0.580148	−	0.178673i
$477$	6.02112	+	3.21836i	0.275688	+	0.147358i
$478$	6.39371	−	5.77030i	0.292442	−	0.263927i
$479$	1.53866	+	1.53866i	0.0703031	+	0.0703031i	0.741384	−	0.671081i	$-0.234170\pi$
$479$	1.53866	+	1.53866i	0.0703031	+	0.0703031i	−0.671081	+	0.741384i	$0.734170\pi$
$480$	−15.0209	−	3.93205i	−0.685606	−	0.179473i
$481$	−24.2078	+	24.2078i	−1.10378	+	1.10378i
$482$	−1.46419	+	28.5694i	−0.0666922	+	1.30130i
$483$	4.63626	−	8.67383i	0.210957	−	0.394673i
$484$	−55.6996	+	5.24778i	−2.53180	+	0.238535i
$485$	29.7212	+	24.3916i	1.34957	+	1.10756i
$486$	0.729619	−	1.21147i	0.0330962	−	0.0549533i
$487$	2.20948	−	0.439493i	0.100121	−	0.0199153i	−0.144775	−	0.989465i	$-0.546246\pi$
$487$	2.20948	−	0.439493i	0.100121	−	0.0199153i	0.244897	+	0.969549i	$0.421246\pi$
$488$	1.71072	−	1.01065i	0.0774407	−	0.0457498i
$489$	1.60597	−	8.07376i	0.0726245	−	0.365108i
$490$	−0.841727	−	17.9076i	−0.0380254	−	0.808984i
$491$	38.1824	+	11.5825i	1.72315	+	0.522711i	0.987901	−	0.155087i	$-0.0495659\pi$
$491$	38.1824	+	11.5825i	1.72315	+	0.522711i	0.735248	+	0.677799i	$0.237066\pi$
$492$	−1.72690	+	1.71233i	−0.0778546	+	0.0771978i
$493$	−13.1657	+	10.8048i	−0.592954	+	0.486625i
$494$	−3.64593	−	24.9428i	−0.164038	−	1.12223i
$495$	15.8311	+	6.55745i	0.711554	+	0.294735i
$496$	−4.97360	−	7.58179i	−0.223321	−	0.340433i
$497$	−6.96355	+	2.88440i	−0.312358	+	0.129383i
$498$	8.71040	+	14.6025i	0.390322	+	0.654353i
$499$	−19.8978	−	1.95976i	−0.890749	−	0.0877311i	−0.357721	−	0.933829i	$-0.616446\pi$
$499$	−19.8978	−	1.95976i	−0.890749	−	0.0877311i	−0.533028	+	0.846097i	$0.678946\pi$
$500$	7.56860	−	11.2240i	0.338478	−	0.501952i
$501$	−7.80087	+	4.16965i	−0.348517	+	0.186286i
$502$	−31.8395	−	11.4685i	−1.42106	−	0.511863i
$503$	−13.9350	+	9.31104i	−0.621329	+	0.415159i	−0.825998	−	0.563672i	$-0.809388\pi$
$503$	−13.9350	+	9.31104i	−0.621329	+	0.415159i	0.204669	+	0.978831i	$0.434388\pi$
$504$	1.03367	+	4.24081i	0.0460435	+	0.188901i
$505$	18.2409	−	27.2994i	0.811709	−	1.21481i
$506$	55.6389	+	8.37374i	2.47345	+	0.372258i
$507$	−1.76318	−	17.9019i	−0.0783055	−	0.795049i
$508$	15.1074	+	18.5683i	0.670283	+	0.823835i
$509$	−10.7456	−	35.4235i	−0.476291	−	1.57012i	−0.785333	−	0.619073i	$-0.787509\pi$
$509$	−10.7456	−	35.4235i	−0.476291	−	1.57012i	0.309042	−	0.951048i	$-0.399991\pi$
$510$	−7.15340	+	15.0421i	−0.316758	+	0.666075i
$511$	−10.2432			−0.453130
$512$	17.0524	−	14.8733i	0.753618	−	0.657313i
$513$	−3.20199			−0.141371
$514$	−16.4104	+	34.5076i	−0.723833	+	1.52207i
$515$	10.9405	+	36.0661i	0.482097	+	1.58926i
$516$	−5.17099	−	6.35559i	−0.227640	−	0.279789i
$517$	7.08840	+	71.9697i	0.311747	+	3.16522i
$518$	−13.2727	−	1.99755i	−0.583167	−	0.0877675i
$519$	−7.58003	+	11.3443i	−0.332726	+	0.497960i
$520$	10.2344	+	41.9880i	0.448806	+	1.84130i
$521$	2.85015	−	1.90441i	0.124867	−	0.0834337i	−0.491568	−	0.870839i	$-0.663576\pi$
$521$	2.85015	−	1.90441i	0.124867	−	0.0834337i	0.616435	+	0.787405i	$0.288576\pi$
$522$	5.28119	+	1.90227i	0.231151	+	0.0832600i
$523$	15.2013	−	8.12528i	0.664708	−	0.355294i	−0.104288	−	0.994547i	$-0.533256\pi$
$523$	15.2013	−	8.12528i	0.664708	−	0.355294i	0.768996	+	0.639253i	$0.220756\pi$
$524$	0.911161	−	1.35122i	0.0398043	−	0.0590284i
$525$	3.89176	+	0.383305i	0.169850	+	0.0167288i
$526$	4.61476	+	7.73638i	0.201213	+	0.337322i
$527$	−8.98665	+	3.72239i	−0.391465	+	0.162150i
$528$	−20.8797	+	13.6969i	−0.908674	+	0.596083i
$529$	−16.2744	−	6.74109i	−0.707584	−	0.293091i
$530$	3.83309	+	26.2231i	0.166499	+	1.13906i
$531$	−9.63561	+	7.90774i	−0.418150	+	0.343167i
$532$	7.01784	−	6.95863i	0.304262	−	0.301695i
$533$	6.47746	+	1.96492i	0.280570	+	0.0851100i
$534$	−0.651715	−	13.8652i	−0.0282025	−	0.600004i
$535$	−2.55103	+	12.8249i	−0.110291	+	0.554470i
$536$	13.6961	−	8.09129i	0.591583	−	0.349491i
$537$	−3.32684	+	0.661749i	−0.143564	+	0.0285566i
$538$	13.3440	−	22.1566i	0.575302	−	0.955239i
$539$	−22.2873	−	18.2907i	−0.959982	−	0.787837i
$540$	5.46542	−	0.514929i	0.235194	−	0.0221590i
$541$	12.4800	−	23.3484i	0.536556	−	1.00383i	−0.456890	−	0.889523i	$-0.651037\pi$
$541$	12.4800	−	23.3484i	0.536556	−	1.00383i	0.993446	−	0.114303i	$-0.0364634\pi$
$542$	−0.148099	+	2.88972i	−0.00636139	+	0.124124i
$543$	−0.00522287	+	0.00522287i	−0.000224135	+	0.000224135i
$544$	−12.2578	−	20.9509i	−0.525547	−	0.898261i
$545$	15.2073	+	15.2073i	0.651409	+	0.651409i
$546$	9.01930	−	8.13989i	0.385990	−	0.348355i
$547$	−24.9645	−	13.3438i	−1.06740	−	0.570539i	−0.158421	−	0.987372i	$-0.550640\pi$
$547$	−24.9645	−	13.3438i	−1.06740	−	0.570539i	−0.908983	+	0.416832i	$0.863140\pi$
$548$	29.2026	+	8.99377i	1.24747	+	0.384195i
$549$	−0.445657	+	0.543035i	−0.0190202	+	0.0231762i
$550$	5.38996	+	21.7130i	0.229829	+	0.925844i
$551$	−2.47949	−	12.4652i	−0.105630	−	0.531037i
$552$	17.0101	−	5.96468i	0.724000	−	0.253873i
$553$	−4.84444	−	0.963620i	−0.206007	−	0.0409773i
$554$	−4.33851	+	4.76647i	−0.184325	+	0.202508i
$555$	−4.90013	+	16.1536i	−0.207999	+	0.685680i
$556$	35.2707	+	14.7850i	1.49581	+	0.627022i
$557$	−22.7487	−	27.7194i	−0.963893	−	1.17451i	−0.984618	−	0.174721i	$-0.944098\pi$
$557$	−22.7487	−	27.7194i	−0.963893	−	1.17451i	0.0207252	−	0.999785i	$-0.493402\pi$
$558$	2.57092	+	1.91518i	0.108836	+	0.0810759i
$559$	−8.72724	+	21.0694i	−0.369123	+	0.891141i
$560$	−10.8596	+	13.0061i	−0.458901	+	0.549610i
$561$	10.2512	+	24.7486i	0.432807	+	1.04489i
$562$	0.732483	−	2.89818i	0.0308980	−	0.122252i
$563$	−0.260558	+	2.64549i	−0.0109812	+	0.111494i	−0.999113	−	0.0421163i	$-0.986590\pi$
$563$	−0.260558	+	2.64549i	−0.0109812	+	0.111494i	0.988132	+	0.153610i	$0.0490900\pi$
$564$	12.7899	+	19.3181i	0.538551	+	0.813437i
$565$	−11.8494	−	22.1686i	−0.498507	−	0.932642i
$566$	−6.59775	+	3.10342i	−0.277324	+	0.130446i
$567$	−0.857384	−	1.28317i	−0.0360067	−	0.0538879i
$568$	−12.9768	−	4.73640i	−0.544495	−	0.198735i
$569$	9.57546	+	6.39812i	0.401424	+	0.268223i	0.739852	−	0.672769i	$-0.234895\pi$
$569$	9.57546	+	6.39812i	0.401424	+	0.268223i	−0.338428	+	0.940992i	$0.609895\pi$
$570$	−7.38299	−	9.99900i	−0.309239	−	0.418812i
$571$	26.4717	−	2.60724i	1.10781	−	0.109110i	0.472472	−	0.881346i	$-0.343362\pi$
$571$	26.4717	−	2.60724i	1.10781	−	0.109110i	0.635336	+	0.772236i	$0.280862\pi$
$572$	61.1581	+	33.0236i	2.55715	+	1.38078i
$573$	−21.0226	+	6.37713i	−0.878231	+	0.266408i
$574$	0.888750	+	2.50058i	0.0370957	+	0.104372i
$575$		−	16.1492i		−	0.673469i
$576$	−3.86053	+	7.00687i	−0.160856	+	0.291953i
$577$		−	24.4488i		−	1.01782i	−0.860821	−	0.508908i	$-0.830049\pi$
$577$		−	24.4488i		−	1.01782i	0.860821	−	0.508908i	$-0.169951\pi$
$578$	−1.88188	+	0.668854i	−0.0782758	+	0.0278207i
$579$	13.3793	−	4.05857i	0.556025	−	0.168668i
$580$	6.23679	+	20.8779i	0.258969	+	0.866909i
$581$	18.4651	−	1.81865i	0.766061	−	0.0754504i
$582$	15.9365	−	11.7670i	0.660587	−	0.487759i
$583$	35.4386	+	23.6793i	1.46772	+	0.980697i
$584$	−13.8298	−	12.6956i	−0.572280	−	0.525346i
$585$	−8.48891	−	12.7045i	−0.350973	−	0.525268i
$586$	13.4353	+	28.5628i	0.555006	+	1.17992i
$587$	5.98065	+	11.1890i	0.246848	+	0.461820i	0.974579	−	0.224042i	$-0.0719253\pi$
$587$	5.98065	+	11.1890i	0.246848	+	0.461820i	−0.727732	+	0.685862i	$0.759425\pi$
$588$	−9.05156	−	1.84036i	−0.373280	−	0.0758953i
$589$	0.711462	−	7.22360i	0.0293153	−	0.297643i
$590$	−46.9111	−	11.8563i	−1.93130	−	0.488116i
$591$	8.15305	+	19.6832i	0.335372	+	0.809659i
$592$	−15.4442	−	19.1474i	−0.634754	−	0.786953i
$593$	−15.5260	+	37.4831i	−0.637577	+	1.53925i	0.192321	+	0.981332i	$0.438399\pi$
$593$	−15.5260	+	37.4831i	−0.637577	+	1.53925i	−0.829898	+	0.557915i	$0.811601\pi$
$594$	5.27427	−	7.08014i	0.216406	−	0.290501i
$595$	11.5308	+	14.0504i	0.472718	+	0.576009i
$596$	−10.4755	−	25.5963i	−0.429094	−	1.04846i
$597$	6.34508	−	20.9169i	0.259687	−	0.856073i
$598$	−37.1034	−	33.7720i	−1.51727	−	1.38104i
$599$	−38.5645	−	7.67096i	−1.57570	−	0.313427i	−0.671658	−	0.740861i	$-0.734418\pi$
$599$	−38.5645	−	7.67096i	−1.57570	−	0.313427i	−0.904046	+	0.427434i	$0.859418\pi$
$600$	4.77938	+	5.34105i	0.195117	+	0.218047i
$601$	6.37976	+	32.0732i	0.260236	+	1.30829i	0.860893	+	0.508786i	$0.169906\pi$
$601$	6.37976	+	32.0732i	0.260236	+	1.30829i	−0.600657	+	0.799507i	$0.705094\pi$
$602$	−8.67767	+	2.15412i	−0.353676	+	0.0877954i
$603$	−3.56795	+	4.34757i	−0.145298	+	0.177047i
$604$	−1.05095	+	0.556033i	−0.0427625	+	0.0226247i
$605$	67.7148	+	36.1943i	2.75300	+	1.47151i
$606$	−11.3338	−	12.5583i	−0.460405	−	0.510146i
$607$	4.83355	+	4.83355i	0.196188	+	0.196188i	0.798363	−	0.602176i	$-0.205699\pi$
$607$	4.83355	+	4.83355i	0.196188	+	0.196188i	−0.602176	+	0.798363i	$0.705699\pi$
$608$	18.0998	−	0.697127i	0.734043	−	0.0282722i
$609$	4.33139	−	4.33139i	0.175517	−	0.175517i
$610$	−2.72333	−	0.139572i	−0.110264	−	0.00565109i
$611$	30.3983	−	56.8713i	1.22979	−	2.30077i
$612$	6.61077	+	5.47235i	0.267225	+	0.221207i
$613$	22.7852	+	18.6993i	0.920284	+	0.755257i	0.969898	−	0.243511i	$-0.0782992\pi$
$613$	22.7852	+	18.6993i	0.920284	+	0.755257i	−0.0496143	+	0.998768i	$0.515799\pi$
$614$	11.8895	+	7.16059i	0.479823	+	0.288978i
$615$	3.27346	−	0.651131i	0.131999	−	0.0262561i
$616$	3.82702	+	26.9798i	0.154195	+	1.08705i
$617$	−0.220821	+	1.11014i	−0.00888991	+	0.0446926i	−0.984976	−	0.172693i	$-0.944753\pi$
$617$	−0.220821	+	1.11014i	−0.00888991	+	0.0446926i	0.976086	+	0.217386i	$0.0697530\pi$
$618$	19.3971	−	0.911738i	0.780266	−	0.0366755i
$619$	−18.9964	−	5.76250i	−0.763530	−	0.231614i	−0.115581	−	0.993298i	$-0.536873\pi$
$619$	−18.9964	−	5.76250i	−0.763530	−	0.231614i	−0.647949	+	0.761684i	$0.724373\pi$
$620$	−0.0527173	+	12.4442i	−0.00211718	+	0.499773i
$621$	−4.92641	+	4.04300i	−0.197690	+	0.162240i
$622$	−34.1782	+	4.99589i	−1.37042	+	0.200317i
$623$	−13.9940	−	5.79648i	−0.560656	−	0.232231i
$624$	22.2661	+	0.188654i	0.891358	+	0.00755222i
$625$	−28.8702	+	11.9584i	−1.15481	+	0.478337i
$626$	−0.585533	+	0.349271i	−0.0234026	+	0.0139597i
$627$	−19.8933	−	1.95932i	−0.794462	−	0.0782476i
$628$	−1.86513	+	0.362790i	−0.0744266	+	0.0144769i
$629$	−23.2731	+	12.4397i	−0.927958	+	0.496004i
$630$	2.03009	−	5.63604i	0.0808805	−	0.224545i
$631$	6.04512	−	4.03922i	0.240652	−	0.160799i	−0.429396	−	0.903116i	$-0.641273\pi$
$631$	6.04512	−	4.03922i	0.240652	−	0.160799i	0.670048	+	0.742318i	$0.266273\pi$
$632$	−5.34638	−	7.30533i	−0.212668	−	0.290590i
$633$	−2.93217	+	4.38831i	−0.116543	+	0.174420i
$634$	−3.57638	+	23.7631i	−0.142036	+	0.943752i
$635$	−3.22009	−	32.6941i	−0.127785	−	1.29743i
$636$	13.5830	+	1.39593i	0.538601	+	0.0553524i
$637$	7.46301	+	24.6022i	0.295695	+	0.974776i
$638$	31.6469	+	15.0500i	1.25291	+	0.595834i
$639$	4.88404			0.193210
$640$	−30.7821	+	4.10064i	−1.21677	+	0.162092i
$641$	−22.8564			−0.902774			−0.451387	−	0.892328i	$-0.649071\pi$
$641$	−22.8564			−0.902774			−0.451387	+	0.892328i	$0.649071\pi$
$642$	6.08429	+	2.89344i	0.240128	+	0.114195i
$643$	−1.04656	−	3.45006i	−0.0412725	−	0.136057i	0.933883	−	0.357579i	$-0.116398\pi$
$643$	−1.04656	−	3.45006i	−0.0412725	−	0.136057i	−0.975155	+	0.221522i	$0.928898\pi$
$644$	2.01094	−	19.5672i	0.0792420	−	0.771057i
$645$	1.10218	+	11.1906i	0.0433982	+	0.440630i
$646$	2.89178	−	19.2143i	0.113776	−	0.755977i
$647$	−9.72627	+	14.5564i	−0.382379	+	0.572271i	−0.971874	−	0.235501i	$-0.924327\pi$
$647$	−9.72627	+	14.5564i	−0.382379	+	0.572271i	0.589495	+	0.807772i	$0.299327\pi$
$648$	0.432786	−	2.79512i	0.0170015	−	0.109803i
$649$	−64.7028	+	43.2330i	−2.53981	+	1.69704i
$650$	6.76039	−	18.7686i	0.265164	−	0.736165i
$651$	3.08529	−	1.64912i	0.120922	−	0.0646341i
$652$	−3.14351	−	16.1610i	−0.123109	−	0.632913i
$653$	15.1683	+	1.49395i	0.593582	+	0.0584627i	0.390348	−	0.920667i	$-0.372355\pi$
$653$	15.1683	+	1.49395i	0.593582	+	0.0584627i	0.203234	+	0.979130i	$0.434855\pi$
$654$	9.51633	−	5.67650i	0.372118	−	0.221969i
$655$	−2.06640	+	0.855929i	−0.0807408	+	0.0334439i
$656$	−1.89932	+	4.47768i	−0.0741559	+	0.174824i
$657$	6.13215	+	2.54002i	0.239238	+	0.0990956i
$658$	25.0163	−	3.65669i	0.975239	−	0.142553i
$659$	8.45255	−	6.93683i	0.329264	−	0.270220i	−0.455207	−	0.890386i	$-0.650435\pi$
$659$	8.45255	−	6.93683i	0.329264	−	0.270220i	0.784471	+	0.620166i	$0.212935\pi$
$660$	34.2706	+	0.145180i	1.33398	+	0.00565112i
$661$	−21.4005	−	6.49177i	−0.832383	−	0.252501i	−0.154799	−	0.987946i	$-0.549473\pi$
$661$	−21.4005	−	6.49177i	−0.832383	−	0.252501i	−0.677584	+	0.735445i	$0.736973\pi$
$662$	−25.2627	+	1.18745i	−0.981864	+	0.0461514i
$663$	4.66003	−	23.4276i	0.180981	−	0.909852i
$664$	27.1847	+	20.4306i	1.05497	+	0.792859i
$665$	−13.3028	+	2.64609i	−0.515861	+	0.102611i
$666$	7.45045	+	4.48711i	0.288699	+	0.173872i
$667$	−19.5540	−	16.0476i	−0.757135	−	0.621365i
$668$	−11.2807	+	13.6274i	−0.436461	+	0.527259i
$669$	0.485567	−	0.908432i	0.0187731	−	0.0351220i
$670$	−21.8031	−	1.11742i	−0.842329	−	0.0431696i
$671$	−3.10106	+	3.10106i	−0.119715	+	0.119715i
$672$	5.12587	+	7.06663i	0.197735	+	0.272601i
$673$	20.9988	+	20.9988i	0.809442	+	0.809442i	0.984549	−	0.175107i	$-0.0560271\pi$
$673$	20.9988	+	20.9988i	0.809442	+	0.809442i	−0.175107	+	0.984549i	$0.556027\pi$
$674$	6.94483	+	7.69513i	0.267505	+	0.296405i
$675$	−2.23479	−	1.19452i	−0.0860170	−	0.0459771i
$676$	−16.8248	−	31.8004i	−0.647110	−	1.22309i
$677$	15.6424	−	19.0604i	0.601188	−	0.732550i	−0.380132	−	0.924932i	$-0.624121\pi$
$677$	15.6424	−	19.0604i	0.601188	−	0.732550i	0.981320	+	0.192382i	$0.0616214\pi$
$678$	−12.5697	+	3.12028i	−0.482738	+	0.119834i
$679$	−4.21735	−	21.2021i	−0.161847	−	0.813661i
$680$	−1.84597	+	33.2616i	−0.0707899	+	1.27552i
$681$	−19.9440	−	3.96712i	−0.764257	−	0.152020i
$682$	14.8007	+	13.4717i	0.566747	+	0.515860i
$683$	3.05021	−	10.0552i	0.116713	−	0.384752i	−0.879047	−	0.476734i	$-0.841820\pi$
$683$	3.05021	−	10.0552i	0.116713	−	0.384752i	0.995761	+	0.0919825i	$0.0293204\pi$
$684$	−5.92684	+	2.42561i	−0.226618	+	0.0927457i
$685$	−26.6036	−	32.4165i	−1.01647	−	1.23857i
$686$	−15.1482	+	20.3348i	−0.578362	+	0.776388i
$687$	−2.84295	+	6.86348i	−0.108465	+	0.261858i
$688$	−14.3860	−	7.84690i	−0.548461	−	0.299160i
$689$	−14.5441	−	35.1126i	−0.554087	−	1.33768i
$690$	−23.9843	−	6.06177i	−0.913067	−	0.230768i
$691$	0.208606	−	2.11801i	0.00793574	−	0.0805729i	−0.990401	−	0.138223i	$-0.955861\pi$
$691$	0.208606	−	2.11801i	0.00793574	−	0.0805729i	0.998337	+	0.0576503i	$0.0183609\pi$
$692$	−5.43683	+	26.7403i	−0.206677	+	1.01651i
$693$	−4.54156	−	8.49667i	−0.172520	−	0.322762i
$694$	0.328230	+	0.697804i	0.0124594	+	0.0264883i
$695$	−29.1600	−	43.6410i	−1.10610	−	1.65540i
$696$	11.2164	−	0.479603i	0.425158	−	0.0181793i
$697$	4.33830	+	2.89876i	0.164325	+	0.109798i
$698$	−14.3874	+	10.6232i	−0.544570	+	0.402096i
$699$	24.0184	−	2.36561i	0.908461	−	0.0894756i
$700$	7.49396	−	2.23864i	0.283245	−	0.0846128i
$701$	20.9613	−	6.35855i	0.791699	−	0.240159i	0.131565	−	0.991307i	$-0.458000\pi$
$701$	20.9613	−	6.35855i	0.791699	−	0.240159i	0.660134	+	0.751148i	$0.270500\pi$
$702$	−7.41795	+	2.63647i	−0.279972	+	0.0995073i
$703$		−	19.6920i		−	0.742699i
$704$	−28.2722	+	41.1699i	−1.06555	+	1.55165i
$705$		−	31.7963i		−	1.19752i
$706$	−14.8326	−	41.7328i	−0.558233	−	1.57064i
$707$	−17.6651	+	5.35864i	−0.664363	+	0.201532i
$708$	−11.8450	+	21.9364i	−0.445162	+	0.824420i
$709$	−34.9015	+	3.43750i	−1.31075	+	0.129098i	−0.729139	−	0.684366i	$-0.760079\pi$
$709$	−34.9015	+	3.43750i	−1.31075	+	0.129098i	−0.581616	+	0.813464i	$0.697579\pi$
$710$	11.2614	+	15.2516i	0.422632	+	0.572383i
$711$	2.66122	+	1.77817i	0.0998034	+	0.0666865i
$712$	−11.7096	−	25.1705i	−0.438836	−	0.943304i
$713$	−8.02626	−	12.0121i	−0.300586	−	0.449858i
$714$	8.47426	−	3.98608i	0.317141	−	0.149175i
$715$	−44.9658	−	84.1250i	−1.68162	−	3.14610i
$716$	−5.65663	+	3.74507i	−0.211398	+	0.139960i
$717$	−0.596923	+	6.06066i	−0.0222925	+	0.226340i
$718$	−9.12394	+	36.1002i	−0.340502	+	1.34725i
$719$	−2.11444	−	5.10471i	−0.0788553	−	0.190373i	0.879535	−	0.475834i	$-0.157854\pi$
$719$	−2.11444	−	5.10471i	−0.0788553	−	0.190373i	−0.958391	+	0.285460i	$0.907854\pi$
$720$	9.72634	−	5.09336i	0.362479	−	0.189818i
$721$	8.10918	−	19.5773i	0.302002	−	0.729097i
$722$	−9.92042	−	7.39011i	−0.369200	−	0.275031i
$723$	−12.8326	−	15.6366i	−0.477250	−	0.581531i
$724$	−0.00571096	+	0.0136239i	−0.000212246	+	0.000506330i
$725$	2.91969	−	9.62493i	0.108435	−	0.357461i
$726$	26.6289	−	29.2557i	0.988290	−	1.08578i
$727$	24.8817	+	4.94928i	0.922812	+	0.183559i	0.633559	−	0.773694i	$-0.281593\pi$
$727$	24.8817	+	4.94928i	0.922812	+	0.183559i	0.289253	+	0.957253i	$0.406593\pi$
$728$	10.5284	−	21.8992i	0.390207	−	0.811639i
$729$	0.195090	+	0.980785i	0.00722557	+	0.0363254i
$730$	6.20736	+	25.0058i	0.229745	+	0.925505i
$731$	−11.1519	+	13.5886i	−0.412468	+	0.502594i
$732$	−0.413538	+	1.34275i	−0.0152848	+	0.0496294i
$733$	−14.2090	−	7.59488i	−0.524822	−	0.280523i	0.187635	−	0.982239i	$-0.439918\pi$
$733$	−14.2090	−	7.59488i	−0.524822	−	0.280523i	−0.712457	+	0.701716i	$0.752418\pi$
$734$	17.1579	−	15.4850i	0.633311	−	0.571561i
$735$	8.96370	+	8.96370i	0.330631	+	0.330631i
$736$	26.9671	−	23.9263i	0.994020	−	0.881934i
$737$	−24.8272	+	24.8272i	−0.914523	+	0.914523i
$738$	0.0880161	−	1.71738i	0.00323992	−	0.0632175i
$739$	−12.5039	+	23.3931i	−0.459963	+	0.860531i	0.539860	+	0.841755i	$0.318477\pi$
$739$	−12.5039	+	23.3931i	−0.459963	+	0.860531i	−0.999824	+	0.0187762i	$0.994023\pi$
$740$	3.16678	+	33.6120i	0.116413	+	1.23560i
$741$	13.7786	+	11.3078i	0.506170	+	0.415403i
$742$	7.68740	−	12.7643i	0.282214	−	0.468591i
$743$	−26.2011	+	5.21173i	−0.961226	+	0.191200i	−0.650675	−	0.759357i	$-0.725514\pi$
$743$	−26.2011	+	5.21173i	−0.961226	+	0.191200i	−0.310552	+	0.950557i	$0.600514\pi$
$744$	6.20954	+	1.59741i	0.227653	+	0.0585639i
$745$	−7.40496	+	37.2272i	−0.271297	+	1.36390i
$746$	0.880419	+	18.7308i	0.0322344	+	0.685783i
$747$	−11.5053	−	3.49008i	−0.420955	−	0.127695i
$748$	37.7227	+	38.0437i	1.37928	+	1.39102i
$749$	5.68315	−	4.66404i	0.207658	−	0.170420i
$750$	1.38450	+	9.47175i	0.0505549	+	0.345859i
$751$	40.2506	+	16.6723i	1.46876	+	0.608382i	0.966577	−	0.256377i	$-0.0825288\pi$
$751$	40.2506	+	16.6723i	1.46876	+	0.608382i	0.502187	+	0.864759i	$0.332529\pi$
$752$	38.3079	+	26.0687i	1.39695	+	0.950627i
$753$	22.1083	−	9.15756i	0.805672	−	0.333720i
$754$	−16.0078	−	26.8362i	−0.582971	−	0.977317i
$755$	1.62390	+	0.159940i	0.0590999	+	0.00582083i
$756$	−2.55904	−	1.72562i	−0.0930715	−	0.0627603i
$757$	40.0262	−	21.3944i	1.45478	−	0.777594i	0.460833	−	0.887487i	$-0.347551\pi$
$757$	40.0262	−	21.3944i	1.45478	−	0.777594i	0.993943	+	0.109893i	$0.0350507\pi$
$758$	24.2267	+	8.72639i	0.879954	+	0.316957i
$759$	−33.0806	+	22.1038i	−1.20075	+	0.802316i
$760$	−21.2404	−	12.9151i	−0.770469	−	0.468482i
$761$	14.1463	−	21.1714i	0.512801	−	0.767461i	−0.481226	−	0.876597i	$-0.659808\pi$
$761$	14.1463	−	21.1714i	0.512801	−	0.767461i	0.994027	+	0.109136i	$0.0348082\pi$
$762$	−16.7380	−	2.51910i	−0.606355	−	0.0912573i
$763$	−1.18520	−	12.0336i	−0.0429072	−	0.435644i
$764$	−34.0816	+	27.7293i	−1.23303	+	1.00321i
$765$	−3.41893	−	11.2707i	−0.123612	−	0.407493i
$766$	−10.4222	+	21.9156i	−0.376569	+	0.791844i
$767$	69.3895			2.50551
$768$	−1.83785	+	15.8941i	−0.0663177	+	0.573529i
$769$	8.22516			0.296607			0.148304	−	0.988942i	$-0.452619\pi$
$769$	8.22516			0.296607			0.148304	+	0.988942i	$0.452619\pi$
$770$	16.0612	−	33.7733i	0.578806	−	1.21711i
$771$	−7.84327	−	25.8558i	−0.282468	−	0.931174i
$772$	21.6904	−	17.6476i	0.780654	−	0.635151i
$773$	−3.09827	−	31.4573i	−0.111437	−	1.13144i	−0.874470	−	0.485079i	$-0.838791\pi$
$773$	−3.09827	−	31.4573i	−0.111437	−	1.13144i	0.763033	−	0.646359i	$-0.223709\pi$
$774$	5.72913	+	0.862241i	0.205929	+	0.0309926i
$775$	3.19135	−	4.77620i	0.114637	−	0.171566i
$776$	20.5842	−	33.8530i	0.738930	−	1.21525i
$777$	7.89138	−	5.27285i	0.283102	−	0.189162i
$778$	−3.89898	−	1.40440i	−0.139785	−	0.0503502i
$779$	−3.43376	+	1.83538i	−0.123027	+	0.0657595i
$780$	−25.3369	−	17.0853i	−0.907208	−	0.611752i
$781$	30.3435	+	2.98857i	1.08578	+	0.106940i
$782$	−19.8118	−	33.2134i	−0.708470	−	1.18771i
$783$	−3.66709	+	1.51896i	−0.131051	+	0.0542831i
$784$	−18.1484	+	3.45037i	−0.648159	+	0.123227i
$785$	2.40919	+	0.997918i	0.0859876	+	0.0356172i
$786$	0.166676	+	1.14028i	0.00594515	+	0.0406723i
$787$	−7.82740	+	6.42378i	−0.279017	+	0.228983i	−0.763485	−	0.645826i	$-0.776513\pi$
$787$	−7.82740	+	6.42378i	−0.279017	+	0.228983i	0.484468	+	0.874809i	$0.339013\pi$
$788$	30.0018	+	30.2571i	1.06877	+	1.07786i
$789$	−6.09548	−	1.84904i	−0.217005	−	0.0658277i
$790$	0.583332	+	12.4103i	0.0207540	+	0.441539i
$791$	−2.75720	+	13.8614i	−0.0980348	+	0.492854i
$792$	4.39916	−	17.1007i	0.156317	−	0.607645i
$793$	3.83545	−	0.762918i	0.136201	−	0.0270920i
$794$	13.8647	−	23.0212i	0.492040	−	0.816990i
$795$	−14.4859	−	11.8883i	−0.513762	−	0.421634i
$796$	−4.10060	−	43.5235i	−0.145342	−	1.54265i
$797$	−10.8678	+	20.3323i	−0.384959	+	0.720207i	−0.997532	−	0.0702065i	$-0.977634\pi$
$797$	−10.8678	+	20.3323i	−0.384959	+	0.720207i	0.612574	+	0.790413i	$0.290134\pi$
$798$	−0.357683	+	6.97914i	−0.0126618	+	0.247059i
$799$	35.1481	−	35.1481i	1.24345	−	1.24345i
$800$	12.8926	+	6.26566i	0.455821	+	0.221525i
$801$	6.94023	+	6.94023i	0.245221	+	0.245221i
$802$	−3.50315	+	3.16158i	−0.123701	+	0.111639i
$803$	36.5435	+	19.5329i	1.28959	+	0.689301i
$804$	−3.31081	+	10.7501i	−0.116763	+	0.379127i
$805$	−17.1259	+	20.8679i	−0.603607	+	0.735498i
$806$	−4.29958	−	17.3205i	−0.151446	−	0.610087i
$807$	3.56802	+	17.9376i	0.125600	+	0.631435i
$808$	−30.4921	−	14.6595i	−1.07271	−	0.515719i
$809$	31.9442	+	6.35409i	1.12310	+	0.223398i	0.721498	−	0.692417i	$-0.243454\pi$
$809$	31.9442	+	6.35409i	1.12310	+	0.223398i	0.401600	+	0.915815i	$0.368454\pi$
$810$	−2.61291	+	2.87066i	−0.0918084	+	0.100865i
$811$	1.35326	−	4.46110i	0.0475193	−	0.156650i	−0.929970	−	0.367636i	$-0.880167\pi$
$811$	1.35326	−	4.46110i	0.0475193	−	0.156650i	0.977489	+	0.210986i	$0.0676673\pi$
$812$	4.73617	−	11.2985i	0.166207	−	0.396500i
$813$	−1.29798	−	1.58159i	−0.0455222	−	0.0554689i
$814$	43.5424	+	32.4364i	1.52616	+	1.13690i
$815$	−8.64677	+	20.8752i	−0.302883	+	0.731225i
$816$	16.3819	+	5.12136i	0.573482	+	0.179284i
$817$	−5.01992	−	12.1192i	−0.175625	−	0.423996i
$818$	−9.95571	+	39.3912i	−0.348093	+	1.37728i
$819$	−0.842051	+	8.54949i	−0.0294236	+	0.298743i
$820$	5.56587	−	3.68498i	0.194369	−	0.128685i
$821$	−0.526701	−	0.985388i	−0.0183820	−	0.0343903i	0.872563	−	0.488502i	$-0.162457\pi$
$821$	−0.526701	−	0.985388i	−0.0183820	−	0.0343903i	−0.890945	+	0.454112i	$0.849957\pi$
$822$	−19.5515	+	9.19655i	−0.681938	+	0.320767i
$823$	−3.68451	−	5.51426i	−0.128434	−	0.192215i	0.761680	−	0.647954i	$-0.224375\pi$
$823$	−3.68451	−	5.51426i	−0.128434	−	0.192215i	−0.890113	+	0.455739i	$0.849375\pi$
$824$	35.2131	−	16.3816i	1.22671	−	0.570679i
$825$	−13.1533	−	8.78877i	−0.457940	−	0.305986i
$826$	16.1595	+	21.8854i	0.562263	+	0.761489i
$827$	−46.7203	+	4.60155i	−1.62462	+	0.160011i	−0.868937	−	0.494922i	$-0.835197\pi$
$827$	−46.7203	+	4.60155i	−1.62462	+	0.160011i	−0.755686	+	0.654934i	$0.772697\pi$
$828$	−6.05600	+	11.2154i	−0.210461	+	0.389763i
$829$	−27.8939	+	8.46151i	−0.968794	+	0.293880i	−0.734744	−	0.678344i	$-0.762698\pi$
$829$	−27.8939	+	8.46151i	−0.968794	+	0.293880i	−0.234050	+	0.972225i	$0.575198\pi$
$830$	−15.6296	−	43.9752i	−0.542511	−	1.52640i
$831$		−	4.55752i		−	0.158098i
$832$	41.3572	−	16.5181i	1.43380	−	0.572662i
$833$			19.8172i			0.686626i
$834$	−25.4811	+	9.05646i	−0.882339	+	0.313600i
$835$	23.2333	−	7.04775i	0.804022	−	0.243897i
$836$	−38.3064	+	11.4431i	−1.32486	+	0.395769i
$837$	−2.25597	+	0.222194i	−0.0779777	+	0.00768013i
$838$	−2.43786	+	1.80005i	−0.0842146	+	0.0621818i
$839$	−15.2137	−	10.1655i	−0.525235	−	0.350951i	0.264513	−	0.964382i	$-0.414789\pi$
$839$	−15.2137	−	10.1655i	−0.525235	−	0.350951i	−0.789748	+	0.613431i	$0.789789\pi$
$840$	−0.511829	−	11.9701i	−0.0176598	−	0.413007i
$841$	7.35865	+	11.0130i	0.253747	+	0.379759i
$842$	−11.1987	−	23.8080i	−0.385932	−	0.820477i
$843$	0.996420	+	1.86417i	0.0343185	+	0.0642055i
$844$	−2.10312	+	10.3439i	−0.0723925	+	0.356052i
$845$	−4.83960	+	49.1372i	−0.166487	+	1.69037i
$846$	−15.8830	−	4.01426i	−0.546069	−	0.138013i
$847$	−16.5203	−	39.8834i	−0.567643	−	1.37041i
$848$	26.1994	−	7.70572i	0.899692	−	0.264616i
$849$	1.97298	−	4.76320i	0.0677126	−	0.163473i
$850$	9.18628	−	12.3316i	0.315087	−	0.422970i
$851$	−24.8642	−	30.2971i	−0.852332	−	1.03857i
$852$	9.04029	−	3.69982i	0.309715	−	0.126754i
$853$	−10.4215	+	34.3550i	−0.356825	+	1.17629i	0.576450	+	0.817132i	$0.304437\pi$
$853$	−10.4215	+	34.3550i	−0.356825	+	1.17629i	−0.933275	+	0.359162i	$0.883063\pi$
$854$	1.13383	+	1.03203i	0.0387988	+	0.0353152i
$855$	8.62000	+	1.71462i	0.294798	+	0.0586389i
$856$	13.4538	+	0.746668i	0.459841	+	0.0255206i
$857$	6.50216	+	32.6886i	0.222110	+	1.11662i	0.917423	+	0.397914i	$0.130266\pi$
$857$	6.50216	+	32.6886i	0.222110	+	1.11662i	−0.695313	+	0.718707i	$0.744734\pi$
$858$	−47.6994	+	11.8408i	−1.62843	+	0.404237i
$859$	−34.9519	+	42.5890i	−1.19254	+	1.45312i	−0.332345	+	0.943158i	$0.607840\pi$
$859$	−34.9519	+	42.5890i	−1.19254	+	1.45312i	−0.860198	+	0.509960i	$0.829660\pi$
$860$	10.5174	+	19.8787i	0.358639	+	0.677858i
$861$	−1.65495	−	0.884592i	−0.0564007	−	0.0301468i
$862$	−5.91129	−	6.54993i	−0.201339	−	0.223091i
$863$	16.3525	+	16.3525i	0.556645	+	0.556645i	0.928351	−	0.371706i	$-0.121227\pi$
$863$	16.3525	+	16.3525i	0.556645	+	0.556645i	−0.371706	+	0.928351i	$0.621227\pi$
$864$	−1.31631	−	5.50157i	−0.0447819	−	0.187167i
$865$	26.4807	−	26.4807i	0.900371	−	0.900371i
$866$	−28.0597	−	1.43807i	−0.953507	−	0.0488675i
$867$	0.665725	−	1.24548i	0.0226092	−	0.0422988i
$868$	4.46156	−	5.38970i	0.151435	−	0.182938i
$869$	15.4455	+	12.6758i	0.523952	+	0.429997i
$870$	−13.1987	−	7.94904i	−0.447478	−	0.269498i
$871$	30.7068	−	6.10796i	1.04046	−	0.206960i
$872$	13.3144	−	17.7161i	0.450884	−	0.599941i
$873$	−2.73278	+	13.7386i	−0.0924904	+	0.464981i
$874$	28.8271	−	1.35498i	0.975091	−	0.0458330i
$875$	9.99602	+	3.03226i	0.337927	+	0.102509i
$876$	13.2747	+	0.0562352i	0.448509	+	0.00190001i
$877$	23.5981	−	19.3664i	0.796850	−	0.653958i	−0.145210	−	0.989401i	$-0.546386\pi$
$877$	23.5981	−	19.3664i	0.796850	−	0.653958i	0.942061	+	0.335443i	$0.108886\pi$
$878$	−4.49667	+	0.657287i	−0.151755	+	0.0221824i
$879$	−20.6208	−	8.54140i	−0.695521	−	0.288094i
$880$	63.5443	−	25.6924i	2.14208	−	0.866089i
$881$	42.7470	−	17.7064i	1.44018	−	0.596543i	0.480340	−	0.877082i	$-0.340513\pi$
$881$	42.7470	−	17.7064i	1.44018	−	0.596543i	0.959843	+	0.280539i	$0.0905133\pi$
$882$	5.60925	−	3.34592i	0.188873	−	0.112663i
$883$	−51.7505	−	5.09698i	−1.74154	−	0.171527i	−0.823317	−	0.567581i	$-0.807879\pi$
$883$	−51.7505	−	5.09698i	−1.74154	−	0.171527i	−0.918227	+	0.396054i	$0.870379\pi$
$884$	−9.12149	−	46.8942i	−0.306789	−	1.57722i
$885$	30.1743	−	16.1285i	1.01430	−	0.542153i
$886$	−3.12318	+	8.67075i	−0.104925	+	0.291300i
$887$	−34.3520	+	22.9533i	−1.15343	+	0.770696i	−0.976921	−	0.213603i	$-0.931480\pi$
$887$	−34.3520	+	22.9533i	−1.15343	+	0.770696i	−0.176508	+	0.984299i	$0.556480\pi$
$888$	17.1898	+	2.66161i	0.576852	+	0.0893177i
$889$	−10.2619	+	15.3580i	−0.344174	+	0.515092i
$890$	−5.67014	+	37.6750i	−0.190063	+	1.26287i
$891$	0.611906	+	6.21278i	0.0204996	+	0.208136i
$892$	0.210611	−	2.04933i	0.00705176	−	0.0686166i
$893$	10.7673	+	35.4951i	0.360315	+	1.18780i
$894$	17.6610	+	8.39887i	0.590673	+	0.280900i
$895$	9.31044			0.311214
$896$	14.8411	+	9.19722i	0.495807	+	0.307258i
$897$	35.4768			1.18454
$898$	35.6776	+	16.9668i	1.19058	+	0.566190i
$899$	−2.61192	−	8.61034i	−0.0871124	−	0.287171i
$900$	−5.04145	−	0.518112i	−0.168048	−	0.0172704i
$901$	−2.87146	−	29.1544i	−0.0956622	−	0.971275i
$902$	1.59770	−	10.6158i	0.0531975	−	0.353468i
$903$	3.51247	−	5.25678i	0.116888	−	0.174935i
$904$	−20.9027	+	15.2976i	−0.695213	+	0.508790i
$905$	0.0168571	−	0.0112636i	0.000560350	−	0.000374414i
$906$	0.284911	−	0.790986i	0.00946552	−	0.0262788i
$907$	37.5926	−	20.0937i	1.24824	−	0.667199i	0.291065	−	0.956703i	$-0.405991\pi$
$907$	37.5926	−	20.0937i	1.24824	−	0.667199i	0.957177	+	0.289504i	$0.0934905\pi$
$908$	−39.9213	+	7.76518i	−1.32484	+	0.257697i
$909$	11.9041	+	1.17246i	0.394835	+	0.0388879i
$910$	−28.6394	+	17.0834i	−0.949387	+	0.566311i
$911$	−9.26150	+	3.83624i	−0.306847	+	0.127100i	−0.530793	−	0.847501i	$-0.678106\pi$
$911$	−9.26150	+	3.83624i	−0.306847	+	0.127100i	0.223946	+	0.974601i	$0.428106\pi$
$912$	−9.13301	+	8.97955i	−0.302424	+	0.297343i
$913$	−69.3441	−	28.7233i	−2.29495	−	0.950601i
$914$	40.0036	−	5.84741i	1.32320	−	0.193415i
$915$	1.49053	−	1.22325i	0.0492753	−	0.0404392i
$916$	−0.0629419	+	14.8578i	−0.00207966	+	0.490916i
$917$	1.20339	+	0.365045i	0.0397395	+	0.0120548i
$918$	−6.06162	+	0.284920i	−0.200063	+	0.00940375i
$919$	8.04777	−	40.4589i	0.265472	−	1.33462i	−0.586041	−	0.810281i	$-0.699314\pi$
$919$	8.04777	−	40.4589i	0.265472	−	1.33462i	0.851513	−	0.524334i	$-0.175686\pi$
$920$	−48.9866	+	6.94864i	−1.61504	+	0.229090i
$921$	−9.62558	+	1.91465i	−0.317174	+	0.0630898i
$922$	12.1450	+	7.31442i	0.399973	+	0.240888i
$923$	−21.0167	−	17.2480i	−0.691774	−	0.567724i
$924$	−14.8429	−	12.2868i	−0.488294	−	0.404207i
$925$	7.34621	−	13.7438i	0.241542	−	0.451893i
$926$	24.9283	+	1.27758i	0.819195	+	0.0419840i
$927$	−9.70926	+	9.70926i	−0.318894	+	0.318894i
$928$	20.3981	−	9.38454i	0.669601	−	0.308063i
$929$	15.4667	+	15.4667i	0.507446	+	0.507446i	0.913742	−	0.406296i	$-0.133180\pi$
$929$	15.4667	+	15.4667i	0.507446	+	0.507446i	−0.406296	+	0.913742i	$0.633180\pi$
$930$	−5.89555	−	6.53249i	−0.193323	−	0.214209i
$931$	−13.0419	−	6.97102i	−0.427430	−	0.228466i
$932$	42.6657	−	22.5734i	1.39756	−	0.739418i
$933$	15.4947	−	18.8804i	0.507274	−	0.618115i
$934$	−8.84968	+	2.19682i	−0.289570	+	0.0718821i
$935$	−14.3445	−	72.1145i	−0.469114	−	2.35840i
$936$	−11.7333	+	10.4994i	−0.383515	+	0.343184i
$937$	26.5653	+	5.28416i	0.867850	+	0.172626i	0.608883	−	0.793260i	$-0.291618\pi$
$937$	26.5653	+	5.28416i	0.867850	+	0.172626i	0.258967	+	0.965886i	$0.416618\pi$
$938$	9.07749	+	8.26245i	0.296391	+	0.269779i
$939$	0.139946	−	0.461340i	0.00456697	−	0.0150553i
$940$	−24.0867	−	58.8544i	−0.785622	−	1.91962i
$941$	−24.5643	−	29.9317i	−0.800772	−	0.975744i	0.199219	−	0.979955i	$-0.436160\pi$
$941$	−24.5643	−	29.9317i	−0.800772	−	0.975744i	−0.999991	+	0.00421106i	$0.998660\pi$
$942$	0.802642	−	1.07746i	0.0261515	−	0.0351056i
$943$	−2.96555	+	7.15946i	−0.0965714	+	0.233144i
$944$	−5.30738	+	49.5769i	−0.172741	+	1.61359i
$945$	1.62102	+	3.91349i	0.0527318	+	0.127306i
$946$	35.0662	+	8.86261i	1.14010	+	0.288148i
$947$	5.01047	−	50.8722i	0.162819	−	1.65312i	−0.472836	−	0.881151i	$-0.656770\pi$
$947$	5.01047	−	50.8722i	0.162819	−	1.65312i	0.635654	−	0.771974i	$-0.280730\pi$
$948$	6.27289	+	1.27540i	0.203734	+	0.0414232i
$949$	−17.4174	−	32.5857i	−0.565394	−	1.05778i
$950$	4.88409	+	10.3834i	0.158461	+	0.336882i
$951$	−9.44040	−	14.1286i	−0.306126	−	0.458150i
$952$	12.6661	−	13.7977i	0.410512	−	0.447186i
$953$	13.2818	+	8.87461i	0.430239	+	0.287477i	0.751774	−	0.659421i	$-0.229199\pi$
$953$	13.2818	+	8.87461i	0.430239	+	0.287477i	−0.321534	+	0.946898i	$0.604199\pi$
$954$	−7.76732	+	5.73517i	−0.251476	+	0.185683i
$955$	60.0092	−	5.91039i	1.94185	−	0.191256i
$956$	3.48625	+	11.6704i	0.112753	+	0.377447i
$957$	−23.7123	+	7.19305i	−0.766510	+	0.232518i
$958$	−2.89962	+	1.03058i	−0.0936825	+	0.0332965i
$959$			23.5779i			0.761369i
$960$	14.1449	−	16.7958i	0.456525	−	0.542081i
$961$			25.8612i			0.834233i
$962$	−16.2141	−	45.6199i	−0.522765	−	1.47084i
$963$	−4.55882	+	1.38290i	−0.146906	+	0.0445635i
$964$	−35.5982	−	19.2220i	−1.14654	−	0.619097i
$965$	−38.1914	+	3.76152i	−1.22942	+	0.121088i
$966$	8.26190	+	11.1893i	0.265822	+	0.360011i
$967$	19.9115	+	13.3044i	0.640309	+	0.427841i	0.832889	−	0.553440i	$-0.186685\pi$
$967$	19.9115	+	13.3044i	0.640309	+	0.427841i	−0.192580	+	0.981281i	$0.561685\pi$
$968$	27.1275	−	74.3240i	0.871912	−	2.38886i
$969$	7.63331	+	11.4240i	0.245217	+	0.366993i
$970$	−49.2032	+	23.1440i	−1.57982	+	0.743108i
$971$	−12.0623	−	22.5669i	−0.387096	−	0.724206i	0.610608	−	0.791933i	$-0.290925\pi$
$971$	−12.0623	−	22.5669i	−0.387096	−	0.724206i	−0.997704	+	0.0677274i	$0.978425\pi$
$972$	1.10409	+	1.66763i	0.0354136	+	0.0534893i
$973$	−2.89250	+	29.3680i	−0.0927293	+	0.941496i
$974$	−0.780653	+	3.08877i	−0.0250137	+	0.0989706i
$975$	5.39817	+	13.0323i	0.172880	+	0.417368i
$976$	0.251723	+	2.79868i	0.00805746	+	0.0895834i
$977$	−6.95069	+	16.7804i	−0.222372	+	0.536854i	−0.995211	−	0.0977483i	$-0.968836\pi$
$977$	−6.95069	+	16.7804i	−0.222372	+	0.536854i	0.772839	+	0.634602i	$0.218836\pi$
$978$	9.33600	+	6.95475i	0.298532	+	0.222388i
$979$	38.8714	+	47.3649i	1.24233	+	1.51379i
$980$	23.3820	+	9.80138i	0.746910	+	0.313094i
$981$	−2.27446	+	7.49790i	−0.0726180	+	0.239389i
$982$	−37.9831	+	41.7299i	−1.21209	+	1.33166i
$983$	25.9639	+	5.16453i	0.828118	+	0.164723i	0.590912	−	0.806736i	$-0.298768\pi$
$983$	25.9639	+	5.16453i	0.828118	+	0.164723i	0.237207	+	0.971459i	$0.423768\pi$
$984$	−1.13805	−	3.24551i	−0.0362798	−	0.103463i
$985$	−11.4085	−	57.3544i	−0.363505	−	1.82746i
$986$	−5.80305	−	23.3770i	−0.184807	−	0.744477i
$987$	−11.3412	+	13.8193i	−0.360994	+	0.439872i
$988$	34.0701	+	10.4929i	1.08391	+	0.333822i
$989$	−23.0256	−	12.3075i	−0.732173	−	0.391354i
$990$	−17.9900	+	16.2359i	−0.571761	+	0.516012i
$991$	−20.6360	−	20.6360i	−0.655523	−	0.655523i	0.298794	−	0.954318i	$-0.403416\pi$
$991$	−20.6360	−	20.6360i	−0.655523	−	0.655523i	−0.954318	+	0.298794i	$0.903416\pi$
$992$	12.7039	−	1.74715i	0.403348	−	0.0554720i
$993$	12.6453	−	12.6453i	0.401287	−	0.401287i
$994$	0.545579	−	10.6454i	0.0173047	−	0.337651i
$995$	−28.2822	+	52.9122i	−0.896605	+	1.67743i
$996$	−23.9399	+	2.25552i	−0.758565	+	0.0714688i
$997$	6.72010	+	5.51504i	0.212828	+	0.174663i	0.734767	−	0.678319i	$-0.237291\pi$
$997$	6.72010	+	5.51504i	0.212828	+	0.174663i	−0.521940	+	0.852982i	$0.674791\pi$
$998$	14.5881	−	24.2222i	0.461777	−	0.766741i
$999$	−6.03176	+	1.19979i	−0.190837	+	0.0379597i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	384.2.v.a.13.12	✓	512
128.69	even	32	inner	384.2.v.a.325.12	yes	512

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
384.2.v.a.13.12	✓	512	1.1	even	1	trivial
384.2.v.a.325.12	yes	512	128.69	even	32	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 384 = 2^{7} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	384.v (of order \(32\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.607361 + 1.27715i) q^{2} +(-0.290285 - 0.956940i) q^{3} +(-1.26223 - 1.55138i) q^{4} +(0.269039 + 2.73160i) q^{5} +(1.39846 + 0.210471i) q^{6} +(0.857384 - 1.28317i) q^{7} +(2.74797 - 0.669804i) q^{8} +(-0.831470 + 0.555570i) q^{9} +O(q^{10})\)	\(q+(-0.607361 + 1.27715i) q^{2} +(-0.290285 - 0.956940i) q^{3} +(-1.26223 - 1.55138i) q^{4} +(0.269039 + 2.73160i) q^{5} +(1.39846 + 0.210471i) q^{6} +(0.857384 - 1.28317i) q^{7} +(2.74797 - 0.669804i) q^{8} +(-0.831470 + 0.555570i) q^{9} +(-3.65206 - 1.31546i) q^{10} +(-5.50570 + 2.94286i) q^{11} +(-1.11818 + 1.65822i) q^{12} +(5.53992 + 0.545635i) q^{13} +(1.11805 + 1.87435i) q^{14} +(2.53588 - 1.05039i) q^{15} +(-0.813572 + 3.91639i) q^{16} +(3.96432 + 1.64207i) q^{17} +(-0.204545 - 1.39934i) q^{18} +(-2.47517 + 2.03132i) q^{19} +(3.89816 - 3.86527i) q^{20} +(-1.47680 - 0.447982i) q^{21} +(-0.414526 - 8.81898i) q^{22} +(-1.24331 + 6.25056i) q^{23} +(-1.43866 - 2.43521i) q^{24} +(-2.48531 + 0.494359i) q^{25} +(-4.06159 + 6.74392i) q^{26} +(0.773010 + 0.634393i) q^{27} +(-3.07289 + 0.289515i) q^{28} +(-1.87108 + 3.50055i) q^{29} +(-0.198680 + 3.87666i) q^{30} +(-1.60293 + 1.60293i) q^{31} +(-4.50769 - 3.41771i) q^{32} +(4.41436 + 4.41436i) q^{33} +(-4.50495 + 4.06570i) q^{34} +(3.73576 + 1.99680i) q^{35} +(1.91140 + 0.588672i) q^{36} +(-3.90148 + 4.75396i) q^{37} +(-1.09098 - 4.39491i) q^{38} +(-1.08601 - 5.45977i) q^{39} +(2.56894 + 7.32615i) q^{40} +(1.19260 + 0.237222i) q^{41} +(1.46909 - 1.61401i) q^{42} +(-1.18922 + 3.92032i) q^{43} +(11.5149 + 4.82689i) q^{44} +(-1.74129 - 2.12177i) q^{45} +(-7.22776 - 5.38424i) q^{46} +(4.43305 - 10.7023i) q^{47} +(3.98392 - 0.358328i) q^{48} +(1.76738 + 4.26683i) q^{49} +(0.878109 - 3.47437i) q^{50} +(0.420586 - 4.27029i) q^{51} +(-6.14615 - 9.28325i) q^{52} +(-3.21836 - 6.02112i) q^{53} +(-1.27971 + 0.601945i) q^{54} +(-9.51994 - 14.2476i) q^{55} +(1.49660 - 4.10038i) q^{56} +(2.66236 + 1.77893i) q^{57} +(-3.33430 - 4.51575i) q^{58} +(12.4050 - 1.22179i) q^{59} +(-4.83041 - 2.60828i) q^{60} +(0.672244 - 0.203923i) q^{61} +(-1.07363 - 3.02074i) q^{62} +1.54325i q^{63} +(7.10273 - 3.68121i) q^{64} +15.2796i q^{65} +(-8.31891 + 2.95669i) q^{66} +(5.38202 - 1.63262i) q^{67} +(-2.45638 - 8.22284i) q^{68} +(6.34233 - 0.624665i) q^{69} +(-4.81917 + 3.55834i) q^{70} +(-4.06093 - 2.71343i) q^{71} +(-1.91273 + 2.08361i) q^{72} +(-3.68754 - 5.51879i) q^{73} +(-3.70192 - 7.87014i) q^{74} +(1.19452 + 2.23479i) q^{75} +(6.27559 + 1.27595i) q^{76} +(-0.944324 + 9.58788i) q^{77} +(7.63254 + 1.92904i) q^{78} +(-1.22482 - 2.95698i) q^{79} +(-10.9169 - 1.16869i) q^{80} +(0.382683 - 0.923880i) q^{81} +(-1.02731 + 1.37905i) q^{82} +(7.62729 + 9.29388i) q^{83} +(1.16906 + 2.85653i) q^{84} +(-3.41893 + 11.2707i) q^{85} +(-4.28456 - 3.89986i) q^{86} +(3.89296 + 0.774358i) q^{87} +(-13.1584 + 11.7746i) q^{88} +(-1.91480 - 9.62637i) q^{89} +(3.76741 - 0.935211i) q^{90} +(5.44998 - 6.64082i) q^{91} +(11.2663 - 5.96076i) q^{92} +(1.99921 + 1.06860i) q^{93} +(10.9760 + 12.1619i) q^{94} +(-6.21467 - 6.21467i) q^{95} +(-1.96204 + 5.30570i) q^{96} +(9.90497 - 9.90497i) q^{97} +(-6.52282 - 0.334296i) q^{98} +(2.94286 - 5.50570i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 512 q+O(q^{10}) \) 512 * q	\( 512 q - 96 q^{50} - 96 q^{52} - 32 q^{54} - 224 q^{56} - 192 q^{60} - 192 q^{62} - 192 q^{64} - 192 q^{66} - 192 q^{68} - 192 q^{70} - 224 q^{74} - 32 q^{76} - 96 q^{78} - 96 q^{80}+O(q^{100}) \) 512 * q - 96 * q^50 - 96 * q^52 - 32 * q^54 - 224 * q^56 - 192 * q^60 - 192 * q^62 - 192 * q^64 - 192 * q^66 - 192 * q^68 - 192 * q^70 - 224 * q^74 - 32 * q^76 - 96 * q^78 - 96 * q^80

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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