LMFDB - Embedded newform 384.2.v.a.325.12

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			325.12
Character	$\chi$	$=$	384.325
Dual form			384.2.v.a.13.12

$q$-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 $\left(\mathbb{Z}/384\mathbb{Z}\right)^\times$.

$n$	$127$	$133$	$257$
$\chi(n)$	$1$	$e\left(\frac{17}{32}\right)$	$1$

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	−0.725533	−	0.688187i	$-0.758407\pi$
$5$	0.269039	−	2.73160i	0.120318	−	1.22161i	0.845851	−	0.533420i	$-0.179093\pi$
$6$	1.39846	−	0.210471i	0.570921	−	0.0859244i
$7$	0.857384	+	1.28317i	0.324061	+	0.484991i	0.957353	−	0.288922i	$-0.0932968\pi$
$7$	0.857384	+	1.28317i	0.324061	+	0.484991i	−0.633292	+	0.773913i	$0.718297\pi$
$8$	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	−0.989350	−	0.145559i	$-0.953502\pi$
$11$	−5.50570	−	2.94286i	−1.66003	−	0.887305i	−0.670681	−	0.741746i	$-0.733998\pi$
$12$	−1.11818	−	1.65822i	−0.322789	−	0.478686i
$13$	5.53992	−	0.545635i	1.53650	−	0.151332i	0.705943	−	0.708268i	$-0.250523\pi$
$13$	5.53992	−	0.545635i	1.53650	−	0.151332i	0.830555	+	0.556937i	$0.188023\pi$
$14$	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	0.153952	−	0.988078i	$-0.450800\pi$
$17$	3.96432	−	1.64207i	0.961489	−	0.398262i	0.807537	+	0.589817i	$0.200800\pi$
$18$	−0.204545	+	1.39934i	−0.0482116	+	0.329828i
$19$	−2.47517	−	2.03132i	−0.567844	−	0.466017i	0.306130	−	0.951990i	$-0.400966\pi$
$19$	−2.47517	−	2.03132i	−0.567844	−	0.466017i	−0.873974	+	0.485972i	$0.838466\pi$
$20$	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	−0.862612	−	0.505865i	$-0.831173\pi$
$23$	−1.24331	−	6.25056i	−0.259249	−	1.30333i	0.603364	−	0.797466i	$-0.293827\pi$
$24$	−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	0.646121	−	0.763235i	$-0.276390\pi$
$29$	−1.87108	−	3.50055i	−0.347451	−	0.650035i	−0.993572	+	0.113200i	$0.963890\pi$
$30$	−0.198680	−	3.87666i	−0.0362739	−	0.707779i
$31$	−1.60293	−	1.60293i	−0.287895	−	0.287895i	0.548353	−	0.836247i	$-0.315255\pi$
$31$	−1.60293	−	1.60293i	−0.287895	−	0.287895i	−0.836247	+	0.548353i	$0.815255\pi$
$32$	−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	0.346265	−	0.938137i	$-0.387450\pi$
$37$	−3.90148	−	4.75396i	−0.641399	−	0.781547i	−0.987664	+	0.156590i	$0.949950\pi$
$38$	−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	−0.101083	−	0.994878i	$-0.532231\pi$
$41$	1.19260	−	0.237222i	0.186252	−	0.0370479i	0.287335	+	0.957830i	$0.407231\pi$
$42$	1.46909	+	1.61401i	0.226685	+	0.249047i
$43$	−1.18922	−	3.92032i	−0.181354	−	0.597844i	−0.999732	−	0.0231631i	$-0.992626\pi$
$43$	−1.18922	−	3.92032i	−0.181354	−	0.597844i	0.818378	−	0.574681i	$-0.194874\pi$
$44$	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	0.817579	+	0.575817i	$0.195316\pi$
$47$	4.43305	+	10.7023i	0.646627	+	1.56110i	−0.170951	+	0.985279i	$0.554684\pi$
$48$	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	−0.999996	−	0.00282966i	$-0.999099\pi$
$53$	−3.21836	+	6.02112i	−0.442075	+	0.827065i	0.557921	+	0.829894i	$0.311599\pi$
$54$	−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	0.864788	−	0.502137i	$-0.167453\pi$
$59$	12.4050	+	1.22179i	1.61500	+	0.159063i	0.750209	+	0.661201i	$0.229953\pi$
$60$	−4.83041	+	2.60828i	−0.623604	+	0.336727i
$61$	0.672244	+	0.203923i	0.0860720	+	0.0261097i	0.333027	−	0.942917i	$-0.391930\pi$
$61$	0.672244	+	0.203923i	0.0860720	+	0.0261097i	−0.246955	+	0.969027i	$0.579430\pi$
$62$	−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	0.601375	−	0.798967i	$-0.294620\pi$
$67$	5.38202	+	1.63262i	0.657519	+	0.199456i	0.0561434	+	0.998423i	$0.482120\pi$
$68$	−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	−0.772699	−	0.634773i	$-0.781094\pi$
$71$	−4.06093	+	2.71343i	−0.481944	+	0.322025i	0.290755	+	0.956798i	$0.406094\pi$
$72$	−1.91273	−	2.08361i	−0.225418	−	0.245556i
$73$	−3.68754	+	5.51879i	−0.431593	+	0.645925i	−0.981980	−	0.188985i	$-0.939480\pi$
$73$	−3.68754	+	5.51879i	−0.431593	+	0.645925i	0.550387	+	0.834910i	$0.314480\pi$
$74$	−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	−0.977683	−	0.210086i	$-0.932626\pi$
$79$	−1.22482	+	2.95698i	−0.137803	+	0.332687i	0.839880	+	0.542773i	$0.182626\pi$
$80$	−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	−0.162239	−	0.986751i	$-0.551872\pi$
$83$	7.62729	−	9.29388i	0.837204	−	1.02014i	0.999443	−	0.0333841i	$-0.0106285\pi$
$84$	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	0.736154	+	0.676814i	$0.236640\pi$
$89$	−1.91480	+	9.62637i	−0.202969	+	1.02039i	−0.939123	+	0.343580i	$0.888360\pi$
$90$	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	0.999984	+	0.00571375i	$0.00181875\pi$
$97$	9.90497	+	9.90497i	1.00570	+	1.00570i	0.00571375	+	0.999984i	$0.498181\pi$
$98$	−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	−0.969855	−	0.243681i	$-0.921645\pi$
$101$	−9.24655	+	7.58845i	−0.920066	+	0.755079i	0.0497894	+	0.998760i	$0.484145\pi$
$102$	5.19835	−	3.13076i	0.514713	−	0.309991i
$103$	13.4671	+	2.67878i	1.32696	+	0.263948i	0.807155	−	0.590339i	$-0.201006\pi$
$103$	13.4671	+	2.67878i	1.32696	+	0.263948i	0.519801	+	0.854287i	$0.326006\pi$
$104$	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	−0.0621245	−	0.998068i	$-0.519788\pi$
$107$	4.55882	−	1.38290i	0.440718	−	0.133690i	0.502842	+	0.864378i	$0.332288\pi$
$108$	0.00847249	+	1.99998i	0.000815266	+	0.192448i
$109$	6.05675	+	4.97065i	0.580132	+	0.476102i	0.878102	−	0.478473i	$-0.158810\pi$
$109$	6.05675	+	4.97065i	0.580132	+	0.476102i	−0.297970	+	0.954575i	$0.596310\pi$
$110$	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	−0.0526024	−	0.998616i	$-0.516752\pi$
$113$	−8.46081	−	3.50458i	−0.795926	−	0.329683i	−0.743323	+	0.668932i	$0.766752\pi$
$114$	−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	−0.946000	−	0.324165i	$-0.894917\pi$
$131$	0.236543	−	0.779777i	0.0206668	−	0.0681294i	0.966667	+	0.256036i	$0.0824166\pi$
$132$	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	−0.121721	−	0.992564i	$-0.538841\pi$
$137$	−12.7032	−	8.48804i	−1.08531	−	0.725182i	−0.963591	+	0.267382i	$0.913841\pi$
$138$	−3.05429	−	8.47950i	−0.259998	−	0.721823i
$139$	−16.8642	−	9.01408i	−1.43040	−	0.764565i	−0.439383	−	0.898300i	$-0.644803\pi$
$139$	−16.8642	−	9.01408i	−1.43040	−	0.764565i	−0.991017	+	0.133735i	$0.957303\pi$
$140$	−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	0.302820	−	0.953048i	$-0.402072\pi$
$149$	13.2330	−	4.01419i	1.08409	−	0.328855i	0.781271	+	0.624192i	$0.214572\pi$
$150$	−3.57966	−	0.168258i	−0.292278	−	0.0137382i
$151$	0.115979	+	0.583066i	0.00943823	+	0.0474492i	0.985217	−	0.171309i	$-0.0547995\pi$
$151$	0.115979	+	0.583066i	0.00943823	+	0.0474492i	−0.975779	+	0.218758i	$0.929800\pi$
$152$	−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	0.899158	−	0.437624i	$-0.144180\pi$
$157$	0.447846	+	0.837861i	0.0357420	+	0.0668686i	−0.863416	+	0.504492i	$0.831680\pi$
$158$	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	−0.161908	−	0.986806i	$-0.551765\pi$
$163$	7.25991	−	3.88051i	0.568640	−	0.303945i	0.730548	+	0.682861i	$0.239265\pi$
$164$	−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	0.854793	+	0.518969i	$0.173684\pi$
$167$	−1.72564	+	8.67536i	−0.133534	+	0.671319i	−0.988327	+	0.152350i	$0.951316\pi$
$168$	−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	−0.989943	−	0.141470i	$-0.954817\pi$
$173$	−8.65546	+	10.5467i	−0.658063	+	0.801852i	0.331880	+	0.943322i	$0.392317\pi$
$174$	−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	0.999581	+	0.0289286i	$0.00920955\pi$
$179$	0.332475	+	3.37568i	0.0248504	+	0.252310i	−0.974731	+	0.223381i	$0.928290\pi$
$180$	−1.09377	−	5.37956i	−0.0815249	−	0.400969i
$181$	−0.00348186	+	0.00651409i	−0.000258804	+	0.000484189i	−0.882051	−	0.471155i	$-0.843837\pi$
$181$	−0.00348186	+	0.00651409i	−0.000258804	+	0.000484189i	0.881792	+	0.471639i	$0.156337\pi$
$182$	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	$0.292421\pi$
$191$			21.9685i			1.58959i	−0.606880	+	0.794794i	$0.707579\pi$
$192$	−5.58451	+	5.72829i	−0.403027	+	0.413404i
$193$		−	13.9813i		−	1.00640i	−0.864170	−	0.503199i	$-0.832156\pi$
$193$		−	13.9813i		−	1.00640i	0.864170	−	0.503199i	$-0.167844\pi$
$194$	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	−0.691480	−	0.722396i	$-0.743041\pi$
$197$	−21.2024	−	2.08825i	−1.51061	−	0.148782i	−0.819126	+	0.573614i	$0.805541\pi$
$198$	5.24423	−	7.10242i	0.372691	−	0.504747i
$199$	18.1744	−	12.1437i	1.28835	−	0.860846i	0.292899	−	0.956144i	$-0.405380\pi$
$199$	18.1744	−	12.1437i	1.28835	−	0.860846i	0.995449	+	0.0952974i	$0.0303802\pi$
$200$	−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	−0.875397	−	0.483405i	$-0.839400\pi$
$211$	−3.34818	+	4.07977i	−0.230499	+	0.280863i	0.644898	+	0.764269i	$0.276900\pi$
$212$	−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	−0.682299	−	0.731074i	$-0.739020\pi$
$223$	0.728363	−	0.728363i	0.0487748	−	0.0487748i	0.731074	+	0.682299i	$0.239020\pi$
$224$	−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	0.968946	+	0.247272i	$0.0795343\pi$
$227$	9.58574	+	17.9337i	0.636228	+	1.19030i	−0.332718	+	0.943026i	$0.607966\pi$
$228$	−0.600697	+	6.37575i	−0.0397821	+	0.422244i
$229$	−5.74268	+	4.71289i	−0.379487	+	0.311437i	−0.804728	−	0.593643i	$-0.797689\pi$
$229$	−5.74268	+	4.71289i	−0.379487	+	0.311437i	0.425242	+	0.905080i	$0.360189\pi$
$230$	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	−0.754852	−	0.655895i	$-0.772291\pi$
$233$	−4.70844	−	23.6709i	−0.308460	−	1.55073i	0.446392	−	0.894837i	$-0.352709\pi$
$234$	−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	−0.557158	−	0.830406i	$-0.688108\pi$
$239$	−5.62642	+	2.33054i	−0.363943	+	0.150750i	0.193216	+	0.981156i	$0.438108\pi$
$240$	2.05064	−	10.7861i	0.132368	−	0.696237i
$241$	18.6884	+	7.74098i	1.20382	+	0.498640i	0.892233	−	0.451576i	$-0.149138\pi$
$241$	18.6884	+	7.74098i	1.20382	+	0.498640i	0.311592	+	0.950216i	$0.399138\pi$
$242$	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	−0.578291	−	0.815831i	$-0.696280\pi$
$251$	2.34554	−	23.8146i	0.148049	−	1.50317i	0.726340	−	0.687336i	$-0.241220\pi$
$252$	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	0.924385	−	0.381461i	$-0.124579\pi$
$263$	3.53885	+	5.29626i	0.218215	+	0.326581i	−0.706170	+	0.708042i	$0.749579\pi$
$264$	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	−0.636235	−	0.771495i	$-0.719509\pi$
$269$	−18.2010	+	1.79264i	−1.10973	+	0.109299i	−0.473499	+	0.880795i	$0.657009\pi$
$270$	−1.98856	+	3.33371i	−0.121020	+	0.202883i
$271$	1.89028	+	0.782978i	0.114826	+	0.0475625i	0.439357	−	0.898313i	$-0.355206\pi$
$271$	1.89028	+	0.782978i	0.114826	+	0.0475625i	−0.324531	+	0.945875i	$0.605206\pi$
$272$	−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	−0.156529	−	0.987673i	$-0.550031\pi$
$277$	4.36127	−	1.32298i	0.262043	−	0.0794900i	0.418573	+	0.908183i	$0.362531\pi$
$278$	−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	0.132865	−	0.991134i	$-0.457582\pi$
$281$	−2.07315	−	0.412374i	−0.123674	−	0.0246002i	−0.256539	+	0.966534i	$0.582582\pi$
$282$	8.45200	+	14.0338i	0.503309	+	0.835701i
$283$	3.98537	−	3.27071i	0.236906	−	0.194424i	−0.508448	−	0.861093i	$-0.669781\pi$
$283$	3.98537	−	3.27071i	0.236906	−	0.194424i	0.745354	+	0.666669i	$0.232281\pi$
$284$	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	0.999737	+	0.0229501i	$0.00730588\pi$
$293$	14.1595	+	17.2534i	0.827207	+	1.00795i	−0.172530	+	0.985004i	$0.555194\pi$
$294$	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	0.982810	+	0.184618i	$0.0591049\pi$
$307$	0.961956	+	9.76690i	0.0549017	+	0.557426i	−0.927909	+	0.372808i	$0.878395\pi$
$308$	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	−0.215116	−	0.976589i	$-0.569013\pi$
$311$	13.5695	−	20.3082i	0.769456	−	1.15157i	0.984571	−	0.174983i	$-0.0559871\pi$
$312$	−6.64131	+	14.2759i	−0.375990	+	0.808213i
$313$	0.400851	−	0.267840i	0.0226574	−	0.0151392i	−0.544190	−	0.838962i	$-0.683163\pi$
$313$	0.400851	−	0.267840i	0.0226574	−	0.0151392i	0.566847	+	0.823823i	$0.308163\pi$
$314$	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	0.711745	−	0.702438i	$-0.247905\pi$
$317$	16.2606	+	4.93259i	0.913285	+	0.277042i	0.201541	+	0.979480i	$0.435405\pi$
$318$	−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	−0.536379	−	0.843977i	$-0.680208\pi$
$331$	8.43007	−	15.7716i	0.463359	−	0.866883i	0.999738	−	0.0229057i	$-0.00729174\pi$
$332$	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	0.981679	−	0.190542i	$-0.0610247\pi$
$337$	2.80491	+	6.77166i	0.152793	+	0.368876i	−0.828886	+	0.559418i	$0.811025\pi$
$338$	−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	0.782213	−	0.623011i	$-0.214091\pi$
$347$	0.345923	+	0.421509i	0.0185701	+	0.0226278i	−0.763643	+	0.645639i	$0.776591\pi$
$348$	−3.71247	+	7.01688i	−0.199009	+	0.376144i
$349$	11.1529	−	5.96135i	0.597001	−	0.319104i	−0.145074	−	0.989421i	$-0.546342\pi$
$349$	11.1529	−	5.96135i	0.597001	−	0.319104i	0.742075	+	0.670317i	$0.233842\pi$
$350$	−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	−0.980084	−	0.198585i	$-0.936365\pi$
$353$	−22.1452	−	22.1452i	−1.17867	−	1.17867i	−0.198585	−	0.980084i	$-0.563635\pi$
$354$	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	0.821764	−	0.569828i	$-0.192990\pi$
$359$	25.8235	+	5.13661i	1.36291	+	0.271100i	0.541147	+	0.840928i	$0.317990\pi$
$360$	−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	−0.740201	−	0.672386i	$-0.765270\pi$
$367$	−15.0989	+	6.25415i	−0.788154	+	0.326464i	−0.0479527	+	0.998850i	$0.515270\pi$
$368$	−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	0.745490	−	0.666516i	$-0.232215\pi$
$373$	11.6937	+	6.25039i	0.605475	+	0.323633i	−0.140016	+	0.990149i	$0.544715\pi$
$374$	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	0.833821	+	0.552036i	$0.186149\pi$
$379$	−1.78473	+	18.1206i	−0.0916752	+	0.930794i	−0.925496	+	0.378758i	$0.876351\pi$
$380$	−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	−0.985153	−	0.171677i	$-0.945081\pi$
$389$	0.287229	−	2.91628i	0.0145631	−	0.147861i	0.999716	+	0.0238156i	$0.00758145\pi$
$390$	−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	−0.560717	−	0.828007i	$-0.689475\pi$
$397$	−18.9112	+	1.86259i	−0.949125	+	0.0934806i	−0.388407	+	0.921488i	$0.626975\pi$
$398$	−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	−0.304380	−	0.952551i	$-0.598449\pi$
$401$	3.08275	−	1.27692i	0.153945	−	0.0637661i	0.458326	+	0.888784i	$0.348449\pi$
$402$	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	0.833972	−	0.551808i	$-0.186062\pi$
$409$	28.1776	+	5.60487i	1.39329	+	0.277143i	0.559322	+	0.828951i	$0.311062\pi$
$410$	−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	−0.424589	−	0.905386i	$-0.639581\pi$
$419$	1.88980	−	1.01012i	0.0923228	−	0.0493476i	0.516912	+	0.856039i	$0.327081\pi$
$420$	−7.48837	−	3.96192i	−0.365395	−	0.193322i
$421$	−11.8024	−	14.3812i	−0.575212	−	0.700898i	0.401401	−	0.915902i	$-0.368523\pi$
$421$	−11.8024	−	14.3812i	−0.575212	−	0.700898i	−0.976613	+	0.215004i	$0.931023\pi$
$422$	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	0.855890	−	0.517157i	$-0.173010\pi$
$431$	−2.38748	−	5.76389i	−0.115001	−	0.277637i	−0.970891	+	0.239521i	$0.923010\pi$
$432$	−3.11343	−	2.51129i	−0.149795	−	0.120824i
$433$	7.60286	−	18.3549i	0.365370	−	0.882082i	−0.629126	−	0.777304i	$-0.716587\pi$
$433$	7.60286	−	18.3549i	0.365370	−	0.882082i	0.994496	−	0.104778i	$-0.0334131\pi$
$434$	−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	−0.786418	−	0.617695i	$-0.788067\pi$
$439$	1.78528	−	2.67186i	0.0852067	−	0.127521i	0.871625	+	0.490174i	$0.163067\pi$
$440$	−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	0.250900	−	0.968013i	$-0.419273\pi$
$443$	6.48538	+	0.638754i	0.308129	+	0.0303481i	0.0572293	+	0.998361i	$0.481773\pi$
$444$	−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	$0.229094\pi$
$449$			27.9353i			1.31835i	−0.751990	+	0.659175i	$0.770906\pi$
$450$	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	0.246803	+	0.969066i	$0.420620\pi$
$457$	−15.8823	+	23.7696i	−0.742944	+	1.11189i	−0.989747	+	0.142829i	$0.954380\pi$
$458$	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	0.990568	+	0.137022i	$0.0437532\pi$
$461$	0.982621	+	9.97672i	0.0457652	+	0.464662i	−0.944803	+	0.327640i	$0.893747\pi$
$462$	−3.33857	−	13.2096i	−0.155324	−	0.614564i
$463$	−6.75440	+	16.3066i	−0.313904	+	0.757831i	0.685649	+	0.727932i	$0.259518\pi$
$463$	−6.75440	+	16.3066i	−0.313904	+	0.757831i	−0.999553	+	0.0298986i	$0.990482\pi$
$464$	−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	−0.669722	−	0.742612i	$-0.733587\pi$
$467$	4.09031	−	4.98405i	0.189277	−	0.230635i	0.858999	+	0.511977i	$0.171087\pi$
$468$	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	−0.671081	−	0.741384i	$-0.734170\pi$
$479$	1.53866	−	1.53866i	0.0703031	−	0.0703031i	0.741384	+	0.671081i	$0.234170\pi$
$480$	−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	0.244897	−	0.969549i	$-0.421246\pi$
$487$	2.20948	+	0.439493i	0.100121	+	0.0199153i	−0.144775	+	0.989465i	$0.546246\pi$
$488$	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	0.735248	−	0.677799i	$-0.237066\pi$
$491$	38.1824	−	11.5825i	1.72315	−	0.522711i	0.987901	+	0.155087i	$0.0495659\pi$
$492$	−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	−0.533028	−	0.846097i	$-0.678946\pi$
$499$	−19.8978	+	1.95976i	−0.890749	+	0.0877311i	−0.357721	+	0.933829i	$0.616446\pi$
$500$	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	0.204669	−	0.978831i	$-0.434388\pi$
$503$	−13.9350	−	9.31104i	−0.621329	−	0.415159i	−0.825998	+	0.563672i	$0.809388\pi$
$504$	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	0.309042	+	0.951048i	$0.399991\pi$
$509$	−10.7456	+	35.4235i	−0.476291	+	1.57012i	−0.785333	+	0.619073i	$0.787509\pi$
$510$	−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	0.616435	−	0.787405i	$-0.288576\pi$
$521$	2.85015	+	1.90441i	0.124867	+	0.0834337i	−0.491568	+	0.870839i	$0.663576\pi$
$522$	5.28119	−	1.90227i	0.231151	−	0.0832600i
$523$	15.2013	+	8.12528i	0.664708	+	0.355294i	0.768996	−	0.639253i	$-0.220756\pi$
$523$	15.2013	+	8.12528i	0.664708	+	0.355294i	−0.104288	+	0.994547i	$0.533256\pi$
$524$	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	0.993446	+	0.114303i	$0.0364634\pi$
$541$	12.4800	+	23.3484i	0.536556	+	1.00383i	−0.456890	+	0.889523i	$0.651037\pi$
$542$	−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	−0.908983	−	0.416832i	$-0.863140\pi$
$547$	−24.9645	+	13.3438i	−1.06740	+	0.570539i	−0.158421	+	0.987372i	$0.550640\pi$
$548$	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	0.0207252	+	0.999785i	$0.493402\pi$
$557$	−22.7487	+	27.7194i	−0.963893	+	1.17451i	−0.984618	+	0.174721i	$0.944098\pi$
$558$	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	0.988132	−	0.153610i	$-0.0490900\pi$
$563$	−0.260558	−	2.64549i	−0.0109812	−	0.111494i	−0.999113	+	0.0421163i	$0.986590\pi$
$564$	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	−0.338428	−	0.940992i	$-0.609895\pi$
$569$	9.57546	−	6.39812i	0.401424	−	0.268223i	0.739852	+	0.672769i	$0.234895\pi$
$570$	−7.38299	+	9.99900i	−0.309239	+	0.418812i
$571$	26.4717	+	2.60724i	1.10781	+	0.109110i	0.635336	−	0.772236i	$-0.280862\pi$
$571$	26.4717	+	2.60724i	1.10781	+	0.109110i	0.472472	+	0.881346i	$0.343362\pi$
$572$	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	$0.169951\pi$
$577$			24.4488i			1.01782i	−0.860821	+	0.508908i	$0.830049\pi$
$578$	−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	−0.727732	−	0.685862i	$-0.759425\pi$
$587$	5.98065	−	11.1890i	0.246848	−	0.461820i	0.974579	+	0.224042i	$0.0719253\pi$
$588$	−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	−0.829898	−	0.557915i	$-0.811601\pi$
$593$	−15.5260	−	37.4831i	−0.637577	−	1.53925i	0.192321	−	0.981332i	$-0.438399\pi$
$594$	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	−0.904046	−	0.427434i	$-0.859418\pi$
$599$	−38.5645	+	7.67096i	−1.57570	+	0.313427i	−0.671658	+	0.740861i	$0.734418\pi$
$600$	4.77938	−	5.34105i	0.195117	−	0.218047i
$601$	6.37976	−	32.0732i	0.260236	−	1.30829i	−0.600657	−	0.799507i	$-0.705094\pi$
$601$	6.37976	−	32.0732i	0.260236	−	1.30829i	0.860893	−	0.508786i	$-0.169906\pi$
$602$	−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	−0.602176	−	0.798363i	$-0.705699\pi$
$607$	4.83355	−	4.83355i	0.196188	−	0.196188i	0.798363	+	0.602176i	$0.205699\pi$
$608$	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	−0.0496143	−	0.998768i	$-0.515799\pi$
$613$	22.7852	−	18.6993i	0.920284	−	0.755257i	0.969898	+	0.243511i	$0.0782992\pi$
$614$	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	0.976086	−	0.217386i	$-0.0697530\pi$
$617$	−0.220821	−	1.11014i	−0.00888991	−	0.0446926i	−0.984976	+	0.172693i	$0.944753\pi$
$618$	19.3971	+	0.911738i	0.780266	+	0.0366755i
$619$	−18.9964	+	5.76250i	−0.763530	+	0.231614i	−0.647949	−	0.761684i	$-0.724373\pi$
$619$	−18.9964	+	5.76250i	−0.763530	+	0.231614i	−0.115581	+	0.993298i	$0.536873\pi$
$620$	−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	0.670048	−	0.742318i	$-0.266273\pi$
$631$	6.04512	+	4.03922i	0.240652	+	0.160799i	−0.429396	+	0.903116i	$0.641273\pi$
$632$	−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	−0.975155	−	0.221522i	$-0.928898\pi$
$643$	−1.04656	+	3.45006i	−0.0412725	+	0.136057i	0.933883	+	0.357579i	$0.116398\pi$
$644$	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	0.589495	−	0.807772i	$-0.299327\pi$
$647$	−9.72627	−	14.5564i	−0.382379	−	0.572271i	−0.971874	+	0.235501i	$0.924327\pi$
$648$	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	0.203234	−	0.979130i	$-0.434855\pi$
$653$	15.1683	−	1.49395i	0.593582	−	0.0584627i	0.390348	+	0.920667i	$0.372355\pi$
$654$	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	0.784471	−	0.620166i	$-0.212935\pi$
$659$	8.45255	+	6.93683i	0.329264	+	0.270220i	−0.455207	+	0.890386i	$0.650435\pi$
$660$	34.2706	−	0.145180i	1.33398	−	0.00565112i
$661$	−21.4005	+	6.49177i	−0.832383	+	0.252501i	−0.677584	−	0.735445i	$-0.736973\pi$
$661$	−21.4005	+	6.49177i	−0.832383	+	0.252501i	−0.154799	+	0.987946i	$0.549473\pi$
$662$	−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	−0.175107	−	0.984549i	$-0.556027\pi$
$673$	20.9988	−	20.9988i	0.809442	−	0.809442i	0.984549	+	0.175107i	$0.0560271\pi$
$674$	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	0.981320	−	0.192382i	$-0.0616214\pi$
$677$	15.6424	+	19.0604i	0.601188	+	0.732550i	−0.380132	+	0.924932i	$0.624121\pi$
$678$	−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	0.995761	−	0.0919825i	$-0.0293204\pi$
$683$	3.05021	+	10.0552i	0.116713	+	0.384752i	−0.879047	+	0.476734i	$0.841820\pi$
$684$	−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	0.998337	−	0.0576503i	$-0.0183609\pi$
$691$	0.208606	+	2.11801i	0.00793574	+	0.0805729i	−0.990401	+	0.138223i	$0.955861\pi$
$692$	−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	0.660134	−	0.751148i	$-0.270500\pi$
$701$	20.9613	+	6.35855i	0.791699	+	0.240159i	0.131565	+	0.991307i	$0.458000\pi$
$702$	−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	−0.581616	−	0.813464i	$-0.697579\pi$
$709$	−34.9015	−	3.43750i	−1.31075	−	0.129098i	−0.729139	+	0.684366i	$0.760079\pi$
$710$	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	−0.958391	−	0.285460i	$-0.907854\pi$
$719$	−2.11444	+	5.10471i	−0.0788553	+	0.190373i	0.879535	+	0.475834i	$0.157854\pi$
$720$	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	0.289253	−	0.957253i	$-0.406593\pi$
$727$	24.8817	−	4.94928i	0.922812	−	0.183559i	0.633559	+	0.773694i	$0.281593\pi$
$728$	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	−0.712457	−	0.701716i	$-0.752418\pi$
$733$	−14.2090	+	7.59488i	−0.524822	+	0.280523i	0.187635	+	0.982239i	$0.439918\pi$
$734$	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	−0.999824	−	0.0187762i	$-0.994023\pi$
$739$	−12.5039	−	23.3931i	−0.459963	−	0.860531i	0.539860	−	0.841755i	$-0.318477\pi$
$740$	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	−0.310552	−	0.950557i	$-0.600514\pi$
$743$	−26.2011	−	5.21173i	−0.961226	−	0.191200i	−0.650675	+	0.759357i	$0.725514\pi$
$744$	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	0.502187	−	0.864759i	$-0.332529\pi$
$751$	40.2506	−	16.6723i	1.46876	−	0.608382i	0.966577	+	0.256377i	$0.0825288\pi$
$752$	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	0.993943	−	0.109893i	$-0.0350507\pi$
$757$	40.0262	+	21.3944i	1.45478	+	0.777594i	0.460833	+	0.887487i	$0.347551\pi$
$758$	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	0.994027	−	0.109136i	$-0.0348082\pi$
$761$	14.1463	+	21.1714i	0.512801	+	0.767461i	−0.481226	+	0.876597i	$0.659808\pi$
$762$	−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	0.763033	+	0.646359i	$0.223709\pi$
$773$	−3.09827	+	31.4573i	−0.111437	+	1.13144i	−0.874470	+	0.485079i	$0.838791\pi$
$774$	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	0.484468	−	0.874809i	$-0.339013\pi$
$787$	−7.82740	−	6.42378i	−0.279017	−	0.228983i	−0.763485	+	0.645826i	$0.776513\pi$
$788$	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	0.612574	−	0.790413i	$-0.290134\pi$
$797$	−10.8678	−	20.3323i	−0.384959	−	0.720207i	−0.997532	+	0.0702065i	$0.977634\pi$
$798$	−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	0.401600	−	0.915815i	$-0.368454\pi$
$809$	31.9442	−	6.35409i	1.12310	−	0.223398i	0.721498	+	0.692417i	$0.243454\pi$
$810$	−2.61291	−	2.87066i	−0.0918084	−	0.100865i
$811$	1.35326	+	4.46110i	0.0475193	+	0.156650i	0.977489	−	0.210986i	$-0.0676673\pi$
$811$	1.35326	+	4.46110i	0.0475193	+	0.156650i	−0.929970	+	0.367636i	$0.880167\pi$
$812$	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	−0.890945	−	0.454112i	$-0.849957\pi$
$821$	−0.526701	+	0.985388i	−0.0183820	+	0.0343903i	0.872563	+	0.488502i	$0.162457\pi$
$822$	−19.5515	−	9.19655i	−0.681938	−	0.320767i
$823$	−3.68451	+	5.51426i	−0.128434	+	0.192215i	−0.890113	−	0.455739i	$-0.849375\pi$
$823$	−3.68451	+	5.51426i	−0.128434	+	0.192215i	0.761680	+	0.647954i	$0.224375\pi$
$824$	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	−0.755686	−	0.654934i	$-0.772697\pi$
$827$	−46.7203	−	4.60155i	−1.62462	−	0.160011i	−0.868937	+	0.494922i	$0.835197\pi$
$828$	−6.05600	−	11.2154i	−0.210461	−	0.389763i
$829$	−27.8939	−	8.46151i	−0.968794	−	0.293880i	−0.234050	−	0.972225i	$-0.575198\pi$
$829$	−27.8939	−	8.46151i	−0.968794	−	0.293880i	−0.734744	+	0.678344i	$0.762698\pi$
$830$	−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	−0.789748	−	0.613431i	$-0.789789\pi$
$839$	−15.2137	+	10.1655i	−0.525235	+	0.350951i	0.264513	+	0.964382i	$0.414789\pi$
$840$	−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	−0.933275	−	0.359162i	$-0.883063\pi$
$853$	−10.4215	−	34.3550i	−0.356825	−	1.17629i	0.576450	−	0.817132i	$-0.304437\pi$
$854$	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	−0.695313	−	0.718707i	$-0.744734\pi$
$857$	6.50216	−	32.6886i	0.222110	−	1.11662i	0.917423	−	0.397914i	$-0.130266\pi$
$858$	−47.6994	−	11.8408i	−1.62843	−	0.404237i
$859$	−34.9519	−	42.5890i	−1.19254	−	1.45312i	−0.860198	−	0.509960i	$-0.829660\pi$
$859$	−34.9519	−	42.5890i	−1.19254	−	1.45312i	−0.332345	−	0.943158i	$-0.607840\pi$
$860$	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	−0.371706	−	0.928351i	$-0.621227\pi$
$863$	16.3525	−	16.3525i	0.556645	−	0.556645i	0.928351	+	0.371706i	$0.121227\pi$
$864$	−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	0.942061	−	0.335443i	$-0.108886\pi$
$877$	23.5981	+	19.3664i	0.796850	+	0.653958i	−0.145210	+	0.989401i	$0.546386\pi$
$878$	−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	0.959843	−	0.280539i	$-0.0905133\pi$
$881$	42.7470	+	17.7064i	1.44018	+	0.596543i	0.480340	+	0.877082i	$0.340513\pi$
$882$	5.60925	+	3.34592i	0.188873	+	0.112663i
$883$	−51.7505	+	5.09698i	−1.74154	+	0.171527i	−0.918227	−	0.396054i	$-0.870379\pi$
$883$	−51.7505	+	5.09698i	−1.74154	+	0.171527i	−0.823317	+	0.567581i	$0.807879\pi$
$884$	−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	−0.176508	−	0.984299i	$-0.556480\pi$
$887$	−34.3520	−	22.9533i	−1.15343	−	0.770696i	−0.976921	+	0.213603i	$0.931480\pi$
$888$	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	0.957177	−	0.289504i	$-0.0934905\pi$
$907$	37.5926	+	20.0937i	1.24824	+	0.667199i	0.291065	+	0.956703i	$0.405991\pi$
$908$	−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	0.223946	−	0.974601i	$-0.428106\pi$
$911$	−9.26150	−	3.83624i	−0.306847	−	0.127100i	−0.530793	+	0.847501i	$0.678106\pi$
$912$	−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	0.851513	+	0.524334i	$0.175686\pi$
$919$	8.04777	+	40.4589i	0.265472	+	1.33462i	−0.586041	+	0.810281i	$0.699314\pi$
$920$	−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	−0.406296	−	0.913742i	$-0.633180\pi$
$929$	15.4667	−	15.4667i	0.507446	−	0.507446i	0.913742	+	0.406296i	$0.133180\pi$
$930$	−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	0.258967	−	0.965886i	$-0.416618\pi$
$937$	26.5653	−	5.28416i	0.867850	−	0.172626i	0.608883	+	0.793260i	$0.291618\pi$
$938$	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	−0.999991	−	0.00421106i	$-0.998660\pi$
$941$	−24.5643	+	29.9317i	−0.800772	+	0.975744i	0.199219	+	0.979955i	$0.436160\pi$
$942$	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	0.635654	+	0.771974i	$0.280730\pi$
$947$	5.01047	+	50.8722i	0.162819	+	1.65312i	−0.472836	+	0.881151i	$0.656770\pi$
$948$	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	−0.321534	−	0.946898i	$-0.604199\pi$
$953$	13.2818	−	8.87461i	0.430239	−	0.287477i	0.751774	+	0.659421i	$0.229199\pi$
$954$	−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	−0.192580	−	0.981281i	$-0.561685\pi$
$967$	19.9115	−	13.3044i	0.640309	−	0.427841i	0.832889	+	0.553440i	$0.186685\pi$
$968$	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	−0.997704	−	0.0677274i	$-0.978425\pi$
$971$	−12.0623	+	22.5669i	−0.387096	+	0.724206i	0.610608	+	0.791933i	$0.290925\pi$
$972$	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	0.772839	−	0.634602i	$-0.218836\pi$
$977$	−6.95069	−	16.7804i	−0.222372	−	0.536854i	−0.995211	+	0.0977483i	$0.968836\pi$
$978$	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	0.237207	−	0.971459i	$-0.423768\pi$
$983$	25.9639	−	5.16453i	0.828118	−	0.164723i	0.590912	+	0.806736i	$0.298768\pi$
$984$	−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	−0.954318	−	0.298794i	$-0.903416\pi$
$991$	−20.6360	+	20.6360i	−0.655523	+	0.655523i	0.298794	+	0.954318i	$0.403416\pi$
$992$	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	−0.521940	−	0.852982i	$-0.674791\pi$
$997$	6.72010	−	5.51504i	0.212828	−	0.174663i	0.734767	+	0.678319i	$0.237291\pi$
$998$	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.325.12	yes	512
128.13	even	32	inner	384.2.v.a.13.12	✓	512

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
384.2.v.a.13.12	✓	512	128.13	even	32	inner
384.2.v.a.325.12	yes	512	1.1	even	1	trivial

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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