LMFDB - Embedded newform 384.2.v.a.349.17

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			349.17
Character	$\chi$	$=$	384.349
Dual form			384.2.v.a.373.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.0761996 - 1.41216i) q^{2} +(-0.995185 - 0.0980171i) q^{3} +(-1.98839 + 0.215212i) q^{4} +(1.41300 + 2.64355i) q^{5} +(-0.0625831 + 1.41283i) q^{6} +(-0.878507 - 4.41655i) q^{7} +(0.455428 + 2.79152i) q^{8} +(0.980785 + 0.195090i) q^{9} +O(q^{10})$	\(q+(-0.0761996 - 1.41216i) q^{2} +(-0.995185 - 0.0980171i) q^{3} +(-1.98839 + 0.215212i) q^{4} +(1.41300 + 2.64355i) q^{5} +(-0.0625831 + 1.41283i) q^{6} +(-0.878507 - 4.41655i) q^{7} +(0.455428 + 2.79152i) q^{8} +(0.980785 + 0.195090i) q^{9} +(3.62544 - 2.19682i) q^{10} +(-3.15547 - 2.58963i) q^{11} +(1.99991 - 0.0192796i) q^{12} +(-2.78393 - 1.48804i) q^{13} +(-6.16993 + 1.57713i) q^{14} +(-1.14709 - 2.76931i) q^{15} +(3.90737 - 0.855849i) q^{16} +(2.08762 - 5.03997i) q^{17} +(0.200763 - 1.39989i) q^{18} +(-7.63218 + 2.31520i) q^{19} +(-3.37852 - 4.95230i) q^{20} +(0.441379 + 4.48139i) q^{21} +(-3.41652 + 4.65336i) q^{22} +(1.59256 - 1.06412i) q^{23} +(-0.179618 - 2.82272i) q^{24} +(-2.21390 + 3.31333i) q^{25} +(-1.88922 + 4.04475i) q^{26} +(-0.956940 - 0.290285i) q^{27} +(2.69731 + 8.59275i) q^{28} +(-3.94908 - 4.81196i) q^{29} +(-3.82331 + 1.83089i) q^{30} +(-0.500935 + 0.500935i) q^{31} +(-1.50634 - 5.45261i) q^{32} +(2.88645 + 2.88645i) q^{33} +(-7.27631 - 2.56401i) q^{34} +(10.4340 - 8.56298i) q^{35} +(-1.99217 - 0.176838i) q^{36} +(-1.25283 + 4.13002i) q^{37} +(3.85100 + 10.6014i) q^{38} +(2.62468 + 1.75375i) q^{39} +(-6.73599 + 5.14837i) q^{40} +(1.39015 + 2.08050i) q^{41} +(6.29481 - 0.964778i) q^{42} +(5.81683 - 0.572907i) q^{43} +(6.83162 + 4.47009i) q^{44} +(0.870124 + 2.86841i) q^{45} +(-1.62406 - 2.16787i) q^{46} +(-1.03302 - 0.427893i) q^{47} +(-3.97244 + 0.468739i) q^{48} +(-12.2670 + 5.08116i) q^{49} +(4.84765 + 2.87390i) q^{50} +(-2.57157 + 4.81108i) q^{51} +(5.85578 + 2.35967i) q^{52} +(-0.146227 + 0.178178i) q^{53} +(-0.337010 + 1.37347i) q^{54} +(2.38710 - 12.0008i) q^{55} +(11.9288 - 4.46379i) q^{56} +(7.82236 - 1.55596i) q^{57} +(-6.49434 + 5.94340i) q^{58} +(7.57124 - 4.04691i) q^{59} +(2.87684 + 5.25960i) q^{60} +(0.985258 - 10.0035i) q^{61} +(0.745571 + 0.669229i) q^{62} -4.50308i q^{63} +(-7.58517 + 2.54267i) q^{64} -9.46207i q^{65} +(3.85618 - 4.29607i) q^{66} +(-0.886724 + 9.00306i) q^{67} +(-3.06634 + 10.4707i) q^{68} +(-1.68920 + 0.902894i) q^{69} +(-12.8874 - 14.0820i) q^{70} +(3.44894 - 0.686036i) q^{71} +(-0.0979217 + 2.82673i) q^{72} +(1.10102 - 5.53521i) q^{73} +(5.92771 + 1.45449i) q^{74} +(2.52800 - 3.08038i) q^{75} +(14.6775 - 6.24604i) q^{76} +(-8.66512 + 16.2113i) q^{77} +(2.27658 - 3.84009i) q^{78} +(4.65820 - 1.92949i) q^{79} +(7.78360 + 9.11998i) q^{80} +(0.923880 + 0.382683i) q^{81} +(2.83207 - 2.12164i) q^{82} +(-3.00494 - 9.90597i) q^{83} +(-1.84208 - 8.81576i) q^{84} +(16.2732 - 1.60277i) q^{85} +(-1.25228 - 8.17063i) q^{86} +(3.45841 + 5.17587i) q^{87} +(5.79191 - 9.98795i) q^{88} +(-1.97339 - 1.31858i) q^{89} +(3.98435 - 1.44733i) q^{90} +(-4.12632 + 13.6026i) q^{91} +(-2.93762 + 2.45862i) q^{92} +(0.547623 - 0.449422i) q^{93} +(-0.525537 + 1.49140i) q^{94} +(-16.9046 - 16.9046i) q^{95} +(0.964633 + 5.57400i) q^{96} +(9.92335 - 9.92335i) q^{97} +(8.11015 + 16.9358i) q^{98} +(-2.58963 - 3.15547i) 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 $\left(\mathbb{Z}/384\mathbb{Z}\right)^\times$.

$n$	$127$	$133$	$257$
$\chi(n)$	$1$	$e\left(\frac{11}{32}\right)$	$1$

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 $

$2$	−0.0761996	−	1.41216i	−0.0538813	−	0.998547i
$2$	−0.0761996	−	1.41216i	−0.0538813	−	0.998547i
$3$	−0.995185	−	0.0980171i	−0.574570	−	0.0565902i
$3$	−0.995185	−	0.0980171i	−0.574570	−	0.0565902i
$4$	−1.98839	+	0.215212i	−0.994194	+	0.107606i
$5$	1.41300	+	2.64355i	0.631915	+	1.18223i	0.970456	+	0.241278i	$0.0775665\pi$
$5$	1.41300	+	2.64355i	0.631915	+	1.18223i	−0.338541	+	0.940952i	$0.609934\pi$
$6$	−0.0625831	+	1.41283i	−0.0255495	+	0.576785i
$7$	−0.878507	−	4.41655i	−0.332044	−	1.66930i	−0.681094	−	0.732196i	$-0.738496\pi$
$7$	−0.878507	−	4.41655i	−0.332044	−	1.66930i	0.349050	−	0.937104i	$-0.386504\pi$
$8$	0.455428	+	2.79152i	0.161018	+	0.986951i
$9$	0.980785	+	0.195090i	0.326928	+	0.0650301i
$10$	3.62544	−	2.19682i	1.14646	−	0.694697i
$11$	−3.15547	−	2.58963i	−0.951410	−	0.780802i	0.0243368	−	0.999704i	$-0.492253\pi$
$11$	−3.15547	−	2.58963i	−0.951410	−	0.780802i	−0.975747	+	0.218902i	$0.929753\pi$
$12$	1.99991	−	0.0192796i	0.577323	−	0.00556554i
$13$	−2.78393	−	1.48804i	−0.772124	−	0.412709i	0.0377687	−	0.999287i	$-0.487975\pi$
$13$	−2.78393	−	1.48804i	−0.772124	−	0.412709i	−0.809893	+	0.586577i	$0.800475\pi$
$14$	−6.16993	+	1.57713i	−1.64898	+	0.421506i
$15$	−1.14709	−	2.76931i	−0.296177	−	0.715034i
$16$	3.90737	−	0.855849i	0.976842	−	0.213962i
$17$	2.08762	−	5.03997i	0.506323	−	1.22237i	−0.439662	−	0.898163i	$-0.644902\pi$
$17$	2.08762	−	5.03997i	0.506323	−	1.22237i	0.945985	−	0.324209i	$-0.105098\pi$
$18$	0.200763	−	1.39989i	0.0473203	−	0.329957i
$19$	−7.63218	+	2.31520i	−1.75094	+	0.531143i	−0.992676	−	0.120803i	$-0.961453\pi$
$19$	−7.63218	+	2.31520i	−1.75094	+	0.531143i	−0.758266	+	0.651946i	$0.773953\pi$
$20$	−3.37852	−	4.95230i	−0.755461	−	1.10737i
$21$	0.441379	+	4.48139i	0.0963168	+	0.977920i
$22$	−3.41652	+	4.65336i	−0.728405	+	0.992099i
$23$	1.59256	−	1.06412i	0.332072	−	0.221884i	−0.378344	−	0.925665i	$-0.623506\pi$
$23$	1.59256	−	1.06412i	0.332072	−	0.221884i	0.710417	+	0.703781i	$0.248506\pi$
$24$	−0.179618	−	2.82272i	−0.0366644	−	0.576185i
$25$	−2.21390	+	3.31333i	−0.442780	+	0.662667i
$26$	−1.88922	+	4.04475i	−0.370507	+	0.793240i
$27$	−0.956940	−	0.290285i	−0.184163	−	0.0558653i
$28$	2.69731	+	8.59275i	0.509743	+	1.62388i
$29$	−3.94908	−	4.81196i	−0.733325	−	0.893559i	0.264157	−	0.964480i	$-0.414906\pi$
$29$	−3.94908	−	4.81196i	−0.733325	−	0.893559i	−0.997482	+	0.0709204i	$0.977406\pi$
$30$	−3.82331	+	1.83089i	−0.698037	+	0.334273i
$31$	−0.500935	+	0.500935i	−0.0899705	+	0.0899705i	−0.750660	−	0.660689i	$-0.770264\pi$
$31$	−0.500935	+	0.500935i	−0.0899705	+	0.0899705i	0.660689	+	0.750660i	$0.270264\pi$
$32$	−1.50634	−	5.45261i	−0.266285	−	0.963894i
$33$	2.88645	+	2.88645i	0.502466	+	0.502466i
$34$	−7.27631	−	2.56401i	−1.24788	−	0.439725i
$35$	10.4340	−	8.56298i	1.76367	−	1.44741i
$36$	−1.99217	−	0.176838i	−0.332028	−	0.0294731i
$37$	−1.25283	+	4.13002i	−0.205964	+	0.678971i	0.791716	+	0.610889i	$0.209188\pi$
$37$	−1.25283	+	4.13002i	−0.205964	+	0.678971i	−0.997680	+	0.0680820i	$0.978312\pi$
$38$	3.85100	+	10.6014i	0.624714	+	1.71978i
$39$	2.62468	+	1.75375i	0.420284	+	0.280825i
$40$	−6.73599	+	5.14837i	−1.06505	+	0.814029i
$41$	1.39015	+	2.08050i	0.217104	+	0.324920i	0.923996	−	0.382402i	$-0.124903\pi$
$41$	1.39015	+	2.08050i	0.217104	+	0.324920i	−0.706892	+	0.707322i	$0.749903\pi$
$42$	6.29481	−	0.964778i	0.971310	−	0.148868i
$43$	5.81683	−	0.572907i	0.887058	−	0.0873675i	0.355784	−	0.934568i	$-0.384214\pi$
$43$	5.81683	−	0.572907i	0.887058	−	0.0873675i	0.531273	+	0.847201i	$0.321714\pi$
$44$	6.83162	+	4.47009i	1.02990	+	0.673891i
$45$	0.870124	+	2.86841i	0.129710	+	0.427598i
$46$	−1.62406	−	2.16787i	−0.239454	−	0.319635i
$47$	−1.03302	−	0.427893i	−0.150682	−	0.0624146i	0.306068	−	0.952010i	$-0.400987\pi$
$47$	−1.03302	−	0.427893i	−0.150682	−	0.0624146i	−0.456750	+	0.889595i	$0.650987\pi$
$48$	−3.97244	+	0.468739i	−0.573372	+	0.0676567i
$49$	−12.2670	+	5.08116i	−1.75243	+	0.725880i
$50$	4.84765	+	2.87390i	0.685561	+	0.406431i
$51$	−2.57157	+	4.81108i	−0.360092	+	0.673686i
$52$	5.85578	+	2.35967i	0.812051	+	0.327228i
$53$	−0.146227	+	0.178178i	−0.0200859	+	0.0244747i	−0.782957	−	0.622076i	$-0.786289\pi$
$53$	−0.146227	+	0.178178i	−0.0200859	+	0.0244747i	0.762871	+	0.646551i	$0.223789\pi$
$54$	−0.337010	+	1.37347i	−0.0458612	+	0.186906i
$55$	2.38710	−	12.0008i	0.321877	−	1.61819i
$56$	11.9288	−	4.46379i	1.59405	−	0.596499i
$57$	7.82236	−	1.55596i	1.03610	−	0.206092i
$58$	−6.49434	+	5.94340i	−0.852749	+	0.780406i
$59$	7.57124	−	4.04691i	0.985692	−	0.526863i	0.101926	−	0.994792i	$-0.467500\pi$
$59$	7.57124	−	4.04691i	0.985692	−	0.526863i	0.883766	+	0.467929i	$0.155000\pi$
$60$	2.87684	+	5.25960i	0.371399	+	0.679012i
$61$	0.985258	−	10.0035i	0.126149	−	1.28082i	−0.698680	−	0.715434i	$-0.746229\pi$
$61$	0.985258	−	10.0035i	0.126149	−	1.28082i	0.824829	−	0.565382i	$-0.191271\pi$
$62$	0.745571	+	0.669229i	0.0946876	+	0.0849921i
$63$		−	4.50308i		−	0.567334i
$64$	−7.58517	+	2.54267i	−0.948146	+	0.317834i
$65$		−	9.46207i		−	1.17363i
$66$	3.85618	−	4.29607i	0.474663	−	0.528810i
$67$	−0.886724	+	9.00306i	−0.108331	+	1.09990i	0.775261	+	0.631641i	$0.217618\pi$
$67$	−0.886724	+	9.00306i	−0.108331	+	1.09990i	−0.883592	+	0.468258i	$0.844882\pi$
$68$	−3.06634	+	10.4707i	−0.371849	+	1.26976i
$69$	−1.68920	+	0.902894i	−0.203355	+	0.108696i
$70$	−12.8874	−	14.0820i	−1.54033	−	1.68312i
$71$	3.44894	−	0.686036i	0.409313	−	0.0814175i	0.0138609	−	0.999904i	$-0.495588\pi$
$71$	3.44894	−	0.686036i	0.409313	−	0.0814175i	0.395452	+	0.918486i	$0.370588\pi$
$72$	−0.0979217	+	2.82673i	−0.0115402	+	0.333134i
$73$	1.10102	−	5.53521i	0.128865	−	0.647847i	−0.861318	−	0.508067i	$-0.830360\pi$
$73$	1.10102	−	5.53521i	0.128865	−	0.647847i	0.990183	−	0.139781i	$-0.0446397\pi$
$74$	5.92771	+	1.45449i	0.689083	+	0.169081i
$75$	2.52800	−	3.08038i	0.291908	−	0.355691i
$76$	14.6775	−	6.24604i	1.68362	−	0.716470i
$77$	−8.66512	+	16.2113i	−0.987482	+	1.84745i
$78$	2.27658	−	3.84009i	0.257772	−	0.434805i
$79$	4.65820	−	1.92949i	0.524089	−	0.217085i	−0.104923	−	0.994480i	$-0.533460\pi$
$79$	4.65820	−	1.92949i	0.524089	−	0.217085i	0.629012	+	0.777396i	$0.283460\pi$
$80$	7.78360	+	9.11998i	0.870233	+	1.01965i
$81$	0.923880	+	0.382683i	0.102653	+	0.0425204i
$82$	2.83207	−	2.12164i	0.312750	−	0.234296i
$83$	−3.00494	−	9.90597i	−0.329836	−	1.08732i	−0.952425	−	0.304773i	$-0.901419\pi$
$83$	−3.00494	−	9.90597i	−0.329836	−	1.08732i	0.622589	−	0.782549i	$-0.286081\pi$
$84$	−1.84208	−	8.81576i	−0.200988	−	0.961878i
$85$	16.2732	−	1.60277i	1.76508	−	0.173845i
$86$	−1.25228	−	8.17063i	−0.135036	−	0.881061i
$87$	3.45841	+	5.17587i	0.370780	+	0.554912i
$88$	5.79191	−	9.98795i	0.617420	−	1.06472i
$89$	−1.97339	−	1.31858i	−0.209179	−	0.139769i	0.446568	−	0.894750i	$-0.352646\pi$
$89$	−1.97339	−	1.31858i	−0.209179	−	0.139769i	−0.655747	+	0.754981i	$0.727646\pi$
$90$	3.98435	−	1.44733i	0.419988	−	0.152561i
$91$	−4.12632	+	13.6026i	−0.432556	+	1.42594i
$92$	−2.93762	+	2.45862i	−0.306268	+	0.256328i
$93$	0.547623	−	0.449422i	0.0567858	−	0.0466029i
$94$	−0.525537	+	1.49140i	−0.0542050	+	0.153826i
$95$	−16.9046	−	16.9046i	−1.73438	−	1.73438i
$96$	0.964633	+	5.57400i	0.0984524	+	0.568894i
$97$	9.92335	−	9.92335i	1.00756	−	1.00756i	0.00759281	−	0.999971i	$-0.497583\pi$
$97$	9.92335	−	9.92335i	1.00756	−	1.00756i	0.999971	−	0.00759281i	$-0.00241689\pi$
$98$	8.11015	+	16.9358i	0.819249	+	1.71077i
$99$	−2.58963	−	3.15547i	−0.260267	−	0.317137i
$100$	3.68902	−	7.06465i	0.368902	−	0.706465i
$101$	2.73607	+	0.829978i	0.272249	+	0.0825859i	0.423457	−	0.905916i	$-0.360816\pi$
$101$	2.73607	+	0.829978i	0.272249	+	0.0825859i	−0.151208	+	0.988502i	$0.548316\pi$
$102$	6.98996	+	3.26487i	0.692109	+	0.323270i
$103$	−3.25873	+	4.87703i	−0.321092	+	0.480548i	−0.956542	−	0.291593i	$-0.905815\pi$
$103$	−3.25873	+	4.87703i	−0.321092	+	0.480548i	0.635450	+	0.772142i	$0.280815\pi$
$104$	2.88602	−	8.44911i	0.282998	−	0.828503i
$105$	−11.2231	+	7.49903i	−1.09526	+	0.731831i
$106$	0.262759	+	0.192919i	0.0255214	+	0.0187380i
$107$	1.06427	+	10.8058i	0.102887	+	1.04463i	0.898544	+	0.438884i	$0.144626\pi$
$107$	1.06427	+	10.8058i	0.102887	+	1.04463i	−0.795657	+	0.605748i	$0.792874\pi$
$108$	1.96524	+	0.371253i	0.189105	+	0.0357239i
$109$	−15.2326	+	4.62076i	−1.45902	+	0.442588i	−0.917376	−	0.398021i	$-0.869697\pi$
$109$	−15.2326	+	4.62076i	−1.45902	+	0.442588i	−0.541642	+	0.840610i	$0.682197\pi$
$110$	−17.1289	−	2.45652i	−1.63318	−	0.234220i
$111$	1.65161	−	3.98734i	0.156764	−	0.378461i
$112$	−7.21255	−	16.5052i	−0.681522	−	1.55960i
$113$	4.38588	+	10.5885i	0.412589	+	0.996078i	0.984440	+	0.175721i	$0.0562256\pi$
$113$	4.38588	+	10.5885i	0.412589	+	0.996078i	−0.571851	+	0.820358i	$0.693774\pi$
$114$	−2.79333	−	10.9279i	−0.261619	−	1.02349i
$115$	5.06334	+	2.70641i	0.472159	+	0.252374i
$116$	8.88789	+	8.71816i	0.825220	+	0.809461i
$117$	−2.44014	−	2.00257i	−0.225591	−	0.185138i
$118$	−6.29181	−	10.3834i	−0.579208	−	0.955872i
$119$	−24.0933	−	4.79245i	−2.20863	−	0.439323i
$120$	7.20818	−	4.46334i	0.658014	−	0.407445i
$121$	1.10483	+	5.55435i	0.100439	+	0.504941i
$122$	−14.2016	−	0.629079i	−1.28575	−	0.0569541i
$123$	−1.17953	−	2.20674i	−0.106354	−	0.198975i
$124$	0.888245	−	1.10386i	0.0797668	−	0.0991295i
$125$	3.02806	+	0.298238i	0.270838	+	0.0266752i
$126$	−6.35906	+	0.343133i	−0.566510	+	0.0305687i
$127$	−12.1852			−1.08126			−0.540631	−	0.841260i	$-0.681815\pi$
$127$	−12.1852			−1.08126			−0.540631	+	0.841260i	$0.681815\pi$
$128$	4.16864	+	10.5177i	0.368460	+	0.929644i
$129$	−5.84497			−0.514621
$130$	−13.3619	+	0.721006i	−1.17192	+	0.0632364i
$131$	22.6826	+	2.23404i	1.98179	+	0.195189i	0.999986	+	0.00527160i	$0.00167801\pi$
$131$	22.6826	+	2.23404i	1.98179	+	0.195189i	0.981800	+	0.189917i	$0.0608220\pi$
$132$	−6.36057	−	5.11818i	−0.553617	−	0.445480i
$133$	16.9301	+	31.6740i	1.46803	+	2.74648i
$134$	12.7813	+	0.566166i	1.10414	+	0.0489093i
$135$	−0.584780	−	2.93989i	−0.0503299	−	0.253025i
$136$	15.0199	+	3.53230i	1.28795	+	0.302892i
$137$	16.8290	+	3.34749i	1.43780	+	0.285995i	0.851607	−	0.524180i	$-0.175628\pi$
$137$	16.8290	+	3.34749i	1.43780	+	0.285995i	0.586188	+	0.810175i	$0.300628\pi$
$138$	1.40375	+	2.31661i	0.119495	+	0.197203i
$139$	14.2036	+	11.6566i	1.20474	+	0.988701i	0.999951	+	0.00989378i	$0.00314934\pi$
$139$	14.2036	+	11.6566i	1.20474	+	0.988701i	0.204784	+	0.978807i	$0.434351\pi$
$140$	−18.9040	+	19.2720i	−1.59768	+	1.62879i
$141$	0.986110	+	0.527087i	0.0830454	+	0.0443887i
$142$	−1.23160	−	4.81817i	−0.103354	−	0.404332i
$143$	4.93114	+	11.9048i	0.412363	+	0.995532i
$144$	3.99926	−	0.0771149i	0.333271	−	0.00642624i
$145$	7.14058	−	17.2389i	0.592993	−	1.43161i
$146$	−7.90050	−	1.13304i	−0.653850	−	0.0937708i
$147$	12.7060	−	3.85432i	1.04797	−	0.317899i
$148$	1.60228	−	8.48170i	0.131706	−	0.697192i
$149$	−0.324346	−	3.29314i	−0.0265715	−	0.269785i	−0.999286	−	0.0377798i	$-0.987971\pi$
$149$	−0.324346	−	3.29314i	−0.0265715	−	0.269785i	0.972715	−	0.232005i	$-0.0745286\pi$
$150$	−4.54262	−	3.33522i	−0.370903	−	0.272319i
$151$	−17.4746	+	11.6762i	−1.42207	+	0.950194i	−0.423037	+	0.906112i	$0.639036\pi$
$151$	−17.4746	+	11.6762i	−1.42207	+	0.950194i	−0.999028	+	0.0440813i	$0.985964\pi$
$152$	−9.93883	−	20.2510i	−0.806145	−	1.64257i
$153$	3.03076	−	4.53585i	0.245022	−	0.366702i
$154$	23.5532	+	11.0012i	1.89797	+	0.886505i
$155$	−2.03207	−	0.616421i	−0.163220	−	0.0495121i
$156$	−5.59630	−	2.92228i	−0.448062	−	0.233969i
$157$	−2.28664	−	2.78628i	−0.182494	−	0.222369i	0.673726	−	0.738982i	$-0.264693\pi$
$157$	−2.28664	−	2.78628i	−0.182494	−	0.222369i	−0.856220	+	0.516612i	$0.827193\pi$
$158$	−3.07970	−	6.43110i	−0.245008	−	0.511631i
$159$	0.162988	−	0.162988i	0.0129258	−	0.0129258i
$160$	12.2858	−	11.6866i	0.971275	−	0.923909i
$161$	−6.09881	−	6.09881i	−0.480653	−	0.480653i
$162$	0.470011	−	1.33383i	0.0369275	−	0.104795i
$163$	9.65835	−	7.92640i	0.756500	−	0.620844i	−0.175007	−	0.984567i	$-0.555995\pi$
$163$	9.65835	−	7.92640i	0.756500	−	0.620844i	0.931507	+	0.363723i	$0.118495\pi$
$164$	−3.21190	−	3.83767i	−0.250807	−	0.299671i
$165$	−3.55189	+	11.7090i	−0.276514	+	0.911546i
$166$	−13.7598	+	4.99829i	−1.06797	+	0.387943i
$167$	1.80056	+	1.20309i	0.139331	+	0.0930982i	0.623282	−	0.781997i	$-0.285799\pi$
$167$	1.80056	+	1.20309i	0.139331	+	0.0930982i	−0.483951	+	0.875095i	$0.660799\pi$
$168$	−12.3089	+	3.27307i	−0.949651	+	0.252523i
$169$	−1.68640	−	2.52387i	−0.129723	−	0.194144i
$170$	−3.50338	−	22.8582i	−0.268697	−	1.75315i
$171$	−7.93720	+	0.781746i	−0.606973	+	0.0597816i
$172$	−11.4428	+	2.39101i	−0.872506	+	0.182313i
$173$	1.21034	+	3.98997i	0.0920208	+	0.303352i	0.990854	−	0.134939i	$-0.0430839\pi$
$173$	1.21034	+	3.98997i	0.0920208	+	0.303352i	−0.898833	+	0.438291i	$0.855584\pi$
$174$	7.04562	−	5.27822i	0.534127	−	0.400141i
$175$	16.5784	+	6.86701i	1.25321	+	0.519097i
$176$	−14.5459	−	7.41802i	−1.09644	−	0.559154i
$177$	−7.93145	+	3.28531i	−0.596164	+	0.246939i
$178$	−1.71167	+	2.88721i	−0.128295	+	0.216406i
$179$	6.88601	−	12.8828i	0.514684	−	0.962907i	−0.481568	−	0.876409i	$-0.659932\pi$
$179$	6.88601	−	12.8828i	0.514684	−	0.962907i	0.996252	−	0.0864980i	$-0.0275676\pi$
$180$	−2.34746	−	5.51626i	−0.174969	−	0.411157i
$181$	6.28348	−	7.65644i	0.467047	−	0.569099i	−0.485209	−	0.874398i	$-0.661257\pi$
$181$	6.28348	−	7.65644i	0.467047	−	0.569099i	0.952256	+	0.305299i	$0.0987565\pi$
$182$	19.5235	+	4.79050i	1.44718	+	0.355096i
$183$	−1.96103	+	9.85875i	−0.144963	+	0.728780i
$184$	3.69580	+	3.96105i	0.272458	+	0.292012i
$185$	−12.6881	+	2.52383i	−0.932851	+	0.185556i
$186$	−0.676385	−	0.739085i	−0.0495949	−	0.0541923i
$187$	−19.6391	+	10.4973i	−1.43615	+	0.767639i
$188$	2.14614	+	0.628498i	0.156523	+	0.0458379i
$189$	−0.441379	+	4.48139i	−0.0321056	+	0.325973i
$190$	−22.5839	+	25.1602i	−1.63841	+	1.82531i
$191$			3.15301i			0.228144i	0.993472	+	0.114072i	$0.0363894\pi$
$191$			3.15301i			0.228144i	−0.993472	+	0.114072i	$0.963611\pi$
$192$	7.79787	−	1.78695i	0.562763	−	0.128962i
$193$		−	0.967727i		−	0.0696585i	−0.999393	−	0.0348293i	$-0.988911\pi$
$193$		−	0.967727i		−	0.0696585i	0.999393	−	0.0348293i	$-0.0110887\pi$
$194$	−14.7695	−	13.2572i	−1.06039	−	0.951812i
$195$	−0.927445	+	9.41651i	−0.0664157	+	0.674330i
$196$	23.2980	−	12.7433i	1.66414	−	0.910237i
$197$	−2.19116	+	1.17120i	−0.156114	+	0.0834446i	−0.547604	−	0.836738i	$-0.684460\pi$
$197$	−2.19116	+	1.17120i	−0.156114	+	0.0834446i	0.391490	+	0.920182i	$0.371960\pi$
$198$	−4.25870	+	3.89741i	−0.302652	+	0.276977i
$199$	−20.0419	+	3.98659i	−1.42073	+	0.282602i	−0.844882	−	0.534952i	$-0.820330\pi$
$199$	−20.0419	+	3.98659i	−1.42073	+	0.282602i	−0.575852	+	0.817554i	$0.695330\pi$
$200$	−10.2575	−	4.67116i	−0.725315	−	0.330301i
$201$	1.76491	−	8.87280i	0.124487	−	0.625839i
$202$	0.963574	−	3.92701i	0.0677968	−	0.276304i
$203$	−17.7830	+	21.6687i	−1.24812	+	1.52084i
$204$	4.07788	−	10.1197i	0.285509	−	0.708522i
$205$	−3.53562	+	6.61467i	−0.246938	+	0.461989i
$206$	7.13546	+	4.23022i	0.497151	+	0.294733i
$207$	1.76956	−	0.732977i	0.122993	−	0.0509454i
$208$	−12.1514	−	3.43171i	−0.842548	−	0.237946i
$209$	30.0786	+	12.4590i	2.08058	+	0.861805i
$210$	11.4450	+	15.2774i	0.789782	+	1.05424i
$211$	−0.826492	−	2.72458i	−0.0568981	−	0.187568i	0.923885	−	0.382671i	$-0.124996\pi$
$211$	−0.826492	−	2.72458i	−0.0568981	−	0.187568i	−0.980783	+	0.195103i	$0.937496\pi$
$212$	0.252410	−	0.385757i	0.0173356	−	0.0264939i
$213$	−3.49957	+	0.344678i	−0.239787	+	0.0236169i
$214$	15.1783	−	2.32632i	1.03757	−	0.159024i
$215$	9.73370	+	14.5675i	0.663833	+	0.993497i
$216$	0.374518	−	2.80352i	0.0254827	−	0.190756i
$217$	2.65248	+	1.77233i	0.180062	+	0.120314i
$218$	7.68596	+	21.1587i	0.520559	+	1.43305i
$219$	−1.63827	+	5.40064i	−0.110704	+	0.364941i
$220$	−2.16378	+	24.3759i	−0.145882	+	1.64343i
$221$	−13.3115	+	10.9245i	−0.895428	+	0.734859i
$222$	−5.75660	−	2.02850i	−0.386358	−	0.136144i
$223$	−9.90223	−	9.90223i	−0.663102	−	0.663102i	0.293008	−	0.956110i	$-0.405344\pi$
$223$	−9.90223	−	9.90223i	−0.663102	−	0.663102i	−0.956110	+	0.293008i	$0.905344\pi$
$224$	−22.7584	+	11.4430i	−1.52061	+	0.764565i
$225$	−2.81776	+	2.81776i	−0.187851	+	0.187851i
$226$	14.6184	−	7.00040i	0.972400	−	0.465660i
$227$	−14.0543	−	17.1252i	−0.932816	−	1.13664i	−0.990391	−	0.138299i	$-0.955837\pi$
$227$	−14.0543	−	17.1252i	−0.932816	−	1.13664i	0.0575742	−	0.998341i	$-0.481663\pi$
$228$	−15.2190	+	4.77732i	−1.00790	+	0.316386i
$229$	−24.9944	−	7.58196i	−1.65168	−	0.501030i	−0.679184	−	0.733968i	$-0.737666\pi$
$229$	−24.9944	−	7.58196i	−1.65168	−	0.501030i	−0.972492	+	0.232938i	$0.925166\pi$
$230$	3.43606	−	7.35647i	0.226567	−	0.485071i
$231$	10.2124	−	15.2839i	0.671926	−	1.00561i
$232$	11.6342	−	13.2154i	0.763821	−	0.867636i
$233$	−14.0331	+	9.37660i	−0.919337	+	0.614282i	−0.922619	−	0.385713i	$-0.873956\pi$
$233$	−14.0331	+	9.37660i	−0.919337	+	0.614282i	0.00328136	+	0.999995i	$0.498956\pi$
$234$	−2.64201	+	3.59846i	−0.172714	+	0.235239i
$235$	−0.328514	−	3.33546i	−0.0214299	−	0.217582i
$236$	−14.1836	+	9.67625i	−0.923275	+	0.629870i
$237$	−4.82490	+	1.46362i	−0.313411	+	0.0950721i
$238$	−4.93181	+	34.3887i	−0.319681	+	2.22909i
$239$	6.43493	−	15.5353i	0.416241	−	1.00489i	−0.567186	−	0.823590i	$-0.691968\pi$
$239$	6.43493	−	15.5353i	0.416241	−	1.00489i	0.983427	−	0.181305i	$-0.0580320\pi$
$240$	−6.85221	−	9.83899i	−0.442308	−	0.635104i
$241$	−10.2936	−	24.8510i	−0.663071	−	1.60080i	−0.792964	−	0.609268i	$-0.791463\pi$
$241$	−10.2936	−	24.8510i	−0.663071	−	1.60080i	0.129893	−	0.991528i	$-0.458537\pi$
$242$	7.75944	−	1.98343i	0.498796	−	0.127500i
$243$	−0.881921	−	0.471397i	−0.0565753	−	0.0302401i
$244$	0.193797	+	20.1029i	0.0124066	+	1.28695i
$245$	−30.7656	−	25.2487i	−1.96554	−	1.61308i
$246$	−3.02639	+	1.83383i	−0.192956	+	0.116921i
$247$	24.6926	+	4.91166i	1.57115	+	0.312522i
$248$	−1.62651	−	1.17023i	−0.103283	−	0.0743097i
$249$	2.01952	+	10.1528i	0.127982	+	0.643408i
$250$	0.190422	−	4.29883i	0.0120434	−	0.271882i
$251$	−12.8994	−	24.1332i	−0.814205	−	1.52327i	−0.851733	−	0.523975i	$-0.824448\pi$
$251$	−12.8994	−	24.1332i	−0.814205	−	1.52327i	0.0375281	−	0.999296i	$-0.488052\pi$
$252$	0.969116	+	8.95386i	0.0610486	+	0.564040i
$253$	−7.78095	−	0.766357i	−0.489184	−	0.0481805i
$254$	0.928508	+	17.2075i	0.0582598	+	1.07969i
$255$	−16.3519			−1.02400
$256$	14.5350	−	6.68824i	0.908440	−	0.418015i
$257$	20.6047			1.28528			0.642642	−	0.766166i	$-0.277838\pi$
$257$	20.6047			1.28528			0.642642	+	0.766166i	$0.277838\pi$
$258$	0.445384	+	8.25403i	0.0277284	+	0.513873i
$259$	19.3411	+	1.90493i	1.20180	+	0.118367i
$260$	2.03635	+	18.8143i	0.126289	+	1.16681i
$261$	−2.93443	−	5.48993i	−0.181637	−	0.339818i
$262$	1.42642	−	32.2016i	0.0881242	−	1.98942i
$263$	1.77532	+	8.92515i	0.109471	+	0.550349i	0.996128	+	0.0879198i	$0.0280219\pi$
$263$	1.77532	+	8.92515i	0.109471	+	0.550349i	−0.886656	+	0.462429i	$0.846978\pi$
$264$	−6.74301	+	9.37215i	−0.415004	+	0.576816i
$265$	−0.677642	−	0.134791i	−0.0416272	−	0.00828017i
$266$	43.4387	−	26.3216i	2.66340	−	1.61388i
$267$	1.83464	+	1.50565i	0.112278	+	0.0921445i
$268$	−0.174415	−	18.0924i	−0.0106541	−	1.10517i
$269$	−9.80533	−	5.24106i	−0.597842	−	0.319553i	0.144572	−	0.989494i	$-0.453819\pi$
$269$	−9.80533	−	5.24106i	−0.597842	−	0.319553i	−0.742414	+	0.669941i	$0.766319\pi$
$270$	−4.10703	+	1.04982i	−0.249946	+	0.0638901i
$271$	−4.36059	−	10.5274i	−0.264887	−	0.639493i	0.734341	−	0.678781i	$-0.237491\pi$
$271$	−4.36059	−	10.5274i	−0.264887	−	0.639493i	−0.999228	+	0.0392873i	$0.987491\pi$
$272$	3.84366	−	21.4797i	0.233056	−	1.30240i
$273$	5.43974	−	13.1327i	0.329228	−	0.794827i
$274$	3.44483	−	24.0202i	0.208110	−	1.45112i
$275$	15.5662	−	4.72195i	0.938676	−	0.284744i
$276$	3.16446	−	2.15884i	0.190478	−	0.129947i
$277$	1.24182	+	12.6084i	0.0746137	+	0.757565i	0.957587	+	0.288143i	$0.0930378\pi$
$277$	1.24182	+	12.6084i	0.0746137	+	0.757565i	−0.882974	+	0.469422i	$0.844462\pi$
$278$	15.3787	−	20.9460i	0.922352	−	1.25626i
$279$	−0.589037	+	0.393582i	−0.0352647	+	0.0235631i
$280$	28.6557	+	25.2270i	1.71250	+	1.50760i
$281$	−0.100773	+	0.150818i	−0.00601164	+	0.00899705i	−0.834463	−	0.551064i	$-0.814222\pi$
$281$	−0.100773	+	0.150818i	−0.00601164	+	0.00899705i	0.828452	+	0.560061i	$0.189222\pi$
$282$	0.669189	−	1.43271i	0.0398496	−	0.0853165i
$283$	5.32808	+	1.61625i	0.316721	+	0.0960763i	0.444643	−	0.895708i	$-0.353331\pi$
$283$	5.32808	+	1.61625i	0.316721	+	0.0960763i	−0.127922	+	0.991784i	$0.540831\pi$
$284$	−6.71018	+	2.10636i	−0.398176	+	0.124989i
$285$	15.1663	+	18.4802i	0.898373	+	1.09467i
$286$	16.4358	−	7.87070i	0.971867	−	0.465404i
$287$	7.96739	−	7.96739i	0.470300	−	0.470300i
$288$	−0.413640	−	5.64171i	−0.0243740	−	0.332441i
$289$	−9.02230	−	9.02230i	−0.530724	−	0.530724i
$290$	−24.8882	−	8.77004i	−1.46148	−	0.514995i
$291$	−10.8482	+	8.90291i	−0.635934	+	0.521898i
$292$	−0.998014	+	11.2431i	−0.0584044	+	0.657952i
$293$	9.62755	−	31.7378i	0.562447	−	1.85414i	0.0439982	−	0.999032i	$-0.485990\pi$
$293$	9.62755	−	31.7378i	0.562447	−	1.85414i	0.518449	−	0.855108i	$-0.326510\pi$
$294$	−6.41110	−	17.6492i	−0.373903	−	1.02932i
$295$	21.3964	+	14.2966i	1.24575	+	0.832381i
$296$	−12.0996	−	1.61637i	−0.703276	−	0.0939495i
$297$	2.26787	+	3.39410i	0.131595	+	0.196946i
$298$	−4.62573	+	0.708965i	−0.267961	+	0.0410692i
$299$	−6.01705	+	0.592627i	−0.347975	+	0.0342725i
$300$	−4.36371	+	6.66904i	−0.251939	+	0.385037i
$301$	−7.64040	−	25.1870i	−0.440385	−	1.45176i
$302$	17.8202	+	23.7872i	1.02544	+	1.36880i
$303$	−2.64154	−	1.09416i	−0.151753	−	0.0628581i
$304$	−27.8403	+	15.5783i	−1.59675	+	0.893478i
$305$	27.8369	−	11.5304i	1.59393	−	0.660229i
$306$	−6.63629	−	3.93428i	−0.379371	−	0.224908i
$307$	2.98734	−	5.58892i	0.170496	−	0.318976i	−0.782132	−	0.623113i	$-0.785868\pi$
$307$	2.98734	−	5.58892i	0.170496	−	0.318976i	0.952629	+	0.304136i	$0.0983678\pi$
$308$	13.7408	−	34.0992i	0.782952	−	1.94298i
$309$	3.72107	−	4.53414i	0.211684	−	0.257938i
$310$	−0.715641	+	2.91657i	−0.0406457	+	0.165650i
$311$	−1.08294	+	5.44432i	−0.0614080	+	0.308719i	−0.999266	−	0.0382996i	$-0.987806\pi$
$311$	−1.08294	+	5.44432i	−0.0614080	+	0.308719i	0.937858	+	0.347018i	$0.112806\pi$
$312$	−3.70028	+	8.12554i	−0.209487	+	0.460018i
$313$	9.70946	−	1.93133i	0.548811	−	0.109165i	0.0871063	−	0.996199i	$-0.472238\pi$
$313$	9.70946	−	1.93133i	0.548811	−	0.109165i	0.461705	+	0.887034i	$0.347238\pi$
$314$	−3.76043	+	3.44142i	−0.212213	+	0.194210i
$315$	11.9041	−	6.36287i	0.670719	−	0.358507i
$316$	−8.84706	+	4.83908i	−0.497686	+	0.272219i
$317$	−0.224979	+	2.28425i	−0.0126361	+	0.128296i	−0.999433	−	0.0336651i	$-0.989282\pi$
$317$	−0.224979	+	2.28425i	−0.0126361	+	0.128296i	0.986797	+	0.161961i	$0.0517820\pi$
$318$	−0.242584	−	0.217745i	−0.0136034	−	0.0122105i
$319$			25.4107i			1.42272i
$320$	−17.4395	−	16.4589i	−0.974900	−	0.920082i
$321$		−	10.8580i		−	0.606036i
$322$	−8.14776	+	9.07721i	−0.454057	+	0.505853i
$323$	−4.26460	+	43.2992i	−0.237289	+	2.40923i
$324$	−1.91939	−	0.562093i	−0.106633	−	0.0312274i
$325$	11.0937	−	5.92972i	0.615369	−	0.328922i
$326$	−11.9293	−	13.0351i	−0.660703	−	0.721950i
$327$	15.6122	−	3.10545i	0.863354	−	0.171732i
$328$	−5.17465	+	4.82814i	−0.285722	+	0.266589i
$329$	−0.982292	+	4.93832i	−0.0541555	+	0.272258i
$330$	16.8057	+	4.12361i	0.925121	+	0.226998i
$331$	−12.3874	+	15.0941i	−0.680875	+	0.829649i	−0.992715	−	0.120486i	$-0.961555\pi$
$331$	−12.3874	+	15.0941i	−0.680875	+	0.829649i	0.311840	+	0.950135i	$0.399055\pi$
$332$	8.10688	+	19.0502i	0.444923	+	1.04552i
$333$	−2.03448	+	3.80625i	−0.111489	+	0.208581i
$334$	1.56176	−	2.63435i	0.0854556	−	0.144145i
$335$	−25.0529	+	10.3773i	−1.36879	+	0.566971i
$336$	5.56003	+	17.1327i	0.303324	+	0.934665i
$337$	16.7433	+	6.93531i	0.912066	+	0.377790i	0.788847	−	0.614589i	$-0.210678\pi$
$337$	16.7433	+	6.93531i	0.912066	+	0.377790i	0.123219	+	0.992380i	$0.460678\pi$
$338$	−3.43561	+	2.57378i	−0.186872	+	0.139995i
$339$	−3.32691	−	10.9674i	−0.180693	−	0.595665i
$340$	−32.0125	+	6.68912i	−1.73612	+	0.362768i
$341$	2.87792	−	0.283450i	0.155848	−	0.0153497i
$342$	1.70876	+	11.1490i	0.0923993	+	0.602870i
$343$	15.7054	+	23.5048i	0.848013	+	1.26914i
$344$	4.24843	+	15.9769i	0.229060	+	0.861415i
$345$	−4.77368	−	3.18967i	−0.257007	−	0.171726i
$346$	5.54224	−	2.01323i	0.297953	−	0.108232i
$347$	9.46725	−	31.2094i	0.508229	−	1.67541i	−0.208475	−	0.978028i	$-0.566850\pi$
$347$	9.46725	−	31.2094i	0.508229	−	1.67541i	0.716704	−	0.697378i	$-0.245650\pi$
$348$	−7.99056	−	9.54735i	−0.428339	−	0.511791i
$349$	26.9795	−	22.1415i	1.44418	−	1.18521i	0.495645	−	0.868525i	$-0.334932\pi$
$349$	26.9795	−	22.1415i	1.44418	−	1.18521i	0.948532	−	0.316680i	$-0.102568\pi$
$350$	8.43404	−	23.9346i	0.450819	−	1.27936i
$351$	2.23210	+	2.23210i	0.119141	+	0.119141i
$352$	−9.36703	+	21.1064i	−0.499264	+	1.12497i
$353$	−21.8689	+	21.8689i	−1.16397	+	1.16397i	−0.180367	+	0.983599i	$0.557728\pi$
$353$	−21.8689	+	21.8689i	−1.16397	+	1.16397i	−0.983599	+	0.180367i	$0.942272\pi$
$354$	5.24376	+	10.9501i	0.278703	+	0.581993i
$355$	6.68693	+	8.14805i	0.354905	+	0.432453i
$356$	4.20764	+	2.19714i	0.223004	+	0.116448i
$357$	23.5075	+	7.13093i	1.24415	+	0.377409i
$358$	−18.7173	−	8.74248i	−0.989240	−	0.462054i
$359$	3.83671	−	5.74205i	0.202494	−	0.303054i	−0.716299	−	0.697794i	$-0.754165\pi$
$359$	3.83671	−	5.74205i	0.202494	−	0.303054i	0.918793	+	0.394740i	$0.129165\pi$
$360$	−7.61096	+	3.73532i	−0.401133	+	0.196869i
$361$	37.0921	−	24.7842i	1.95222	−	1.30443i
$362$	−11.2909	−	8.28985i	−0.593437	−	0.435705i
$363$	−0.555087	−	5.63590i	−0.0291345	−	0.295808i
$364$	5.27727	−	27.9354i	0.276604	−	1.46421i
$365$	16.1883	−	4.91068i	0.847336	−	0.257036i
$366$	14.0716	+	2.01805i	0.735532	+	0.105485i
$367$	1.69579	−	4.09401i	0.0885197	−	0.213706i	−0.873420	−	0.486968i	$-0.838103\pi$
$367$	1.69579	−	4.09401i	0.0885197	−	0.213706i	0.961939	+	0.273263i	$0.0881028\pi$
$368$	5.31201	−	5.52089i	0.276908	−	0.287796i
$369$	0.957550	+	2.31173i	0.0498480	+	0.120344i
$370$	4.53088	+	17.7254i	0.235549	+	0.921498i
$371$	0.915396	+	0.489289i	0.0475250	+	0.0254026i
$372$	−0.992165	+	1.01148i	−0.0514414	+	0.0524428i
$373$	−9.88104	−	8.10916i	−0.511621	−	0.419877i	0.342839	−	0.939394i	$-0.388612\pi$
$373$	−9.88104	−	8.10916i	−0.511621	−	0.419877i	−0.854460	+	0.519518i	$0.826112\pi$
$374$	16.3204	+	26.9336i	0.843906	+	1.39270i
$375$	−2.98425	−	0.593604i	−0.154106	−	0.0306536i
$376$	0.724003	−	3.07858i	0.0373376	−	0.158766i
$377$	3.83356	+	19.2726i	0.197438	+	0.992589i
$378$	6.36208	+	0.281817i	0.327230	+	0.0144951i
$379$	13.9161	+	26.0352i	0.714823	+	1.33734i	0.932447	+	0.361306i	$0.117669\pi$
$379$	13.9161	+	26.0352i	0.714823	+	1.33734i	−0.217625	+	0.976033i	$0.569831\pi$
$380$	37.2510	+	29.9749i	1.91094	+	1.53768i
$381$	12.1265	+	1.19436i	0.621261	+	0.0611889i
$382$	4.45255	−	0.240258i	0.227812	−	0.0122927i
$383$	−20.8865			−1.06725			−0.533626	−	0.845720i	$-0.679171\pi$
$383$	−20.8865			−1.06725			−0.533626	+	0.845720i	$0.679171\pi$
$384$	−3.11766	−	10.8757i	−0.159097	−	0.554997i
$385$	−55.0992			−2.80811
$386$	−1.36659	+	0.0737404i	−0.0695574	+	0.00375329i
$387$	5.81683	+	0.572907i	0.295686	+	0.0291225i
$388$	−17.5958	+	21.8671i	−0.893294	+	1.11013i
$389$	−0.578612	−	1.08251i	−0.0293368	−	0.0548853i	0.866826	−	0.498611i	$-0.166156\pi$
$389$	−0.578612	−	1.08251i	−0.0293368	−	0.0548853i	−0.896163	+	0.443726i	$0.853656\pi$
$390$	13.3683	+	0.592166i	0.676929	+	0.0299855i
$391$	−2.03844	−	10.2479i	−0.103089	−	0.518261i
$392$	−19.7709	−	31.9295i	−0.998581	−	1.61268i
$393$	−22.3544	−	4.44656i	−1.12763	−	0.224299i
$394$	1.82089	+	3.00503i	0.0917350	+	0.151391i
$395$	11.6828	+	9.58779i	0.587823	+	0.482414i
$396$	5.82828	+	5.71698i	0.292882	+	0.287289i
$397$	4.31961	+	2.30888i	0.216795	+	0.115879i	0.576220	−	0.817295i	$-0.304527\pi$
$397$	4.31961	+	2.30888i	0.216795	+	0.115879i	−0.359425	+	0.933174i	$0.617027\pi$
$398$	7.15688	+	27.9986i	0.358742	+	1.40344i
$399$	−13.7440	−	33.1809i	−0.688060	−	1.66112i
$400$	−5.81480	+	14.8412i	−0.290740	+	0.742059i
$401$	−4.95524	+	11.9630i	−0.247453	+	0.597404i	−0.997986	−	0.0634286i	$-0.979796\pi$
$401$	−4.95524	+	11.9630i	−0.247453	+	0.597404i	0.750534	+	0.660832i	$0.229796\pi$
$402$	−12.6643	−	1.81623i	−0.631637	−	0.0905853i
$403$	2.13998	−	0.649157i	0.106600	−	0.0323368i
$404$	−5.61899	−	1.06148i	−0.279555	−	0.0528107i
$405$	0.293805	+	2.98305i	0.0145993	+	0.148229i
$406$	31.9546	+	23.4613i	1.58588	+	1.16436i
$407$	14.6485	−	9.78780i	0.726098	−	0.485163i
$408$	−14.6014	−	4.98750i	−0.722876	−	0.246918i
$409$	−3.41077	+	5.10458i	−0.168652	+	0.252405i	−0.906162	−	0.422931i	$-0.861001\pi$
$409$	−3.41077	+	5.10458i	−0.168652	+	0.252405i	0.737510	+	0.675336i	$0.236001\pi$
$410$	9.61038	+	4.48882i	0.474623	+	0.221687i
$411$	−16.4198	−	4.98090i	−0.809930	−	0.245689i
$412$	5.43002	−	10.3987i	0.267518	−	0.512310i
$413$	−24.5248	−	29.8835i	−1.20679	−	1.47047i
$414$	−1.16992	−	2.44305i	−0.0574984	−	0.120069i
$415$	21.9409	−	21.9409i	1.07704	−	1.07704i
$416$	−3.92018	+	17.4212i	−0.192203	+	0.854145i
$417$	−12.9927	−	12.9927i	−0.636254	−	0.636254i
$418$	15.3021	−	43.4252i	0.748449	−	2.12399i
$419$	3.43435	−	2.81849i	0.167779	−	0.137692i	−0.546757	−	0.837291i	$-0.684138\pi$
$419$	3.43435	−	2.81849i	0.167779	−	0.137692i	0.714536	+	0.699599i	$0.246638\pi$
$420$	20.7020	−	17.3263i	1.01015	−	0.845438i
$421$	−0.112416	+	0.370587i	−0.00547884	+	0.0180613i	−0.959637	−	0.281241i	$-0.909254\pi$
$421$	−0.112416	+	0.370587i	−0.00547884	+	0.0180613i	0.954158	+	0.299302i	$0.0967539\pi$
$422$	−3.78456	+	1.37475i	−0.184230	+	0.0669218i
$423$	−0.929698	−	0.621204i	−0.0452035	−	0.0302040i
$424$	−0.563985	−	0.327049i	−0.0273895	−	0.0158829i
$425$	12.0773	+	18.0750i	0.585836	+	0.876765i
$426$	0.753406	+	4.91569i	0.0365026	+	0.238166i
$427$	−45.0465	+	4.43669i	−2.17995	+	0.214707i
$428$	−4.44171	−	21.2570i	−0.214698	−	1.02749i
$429$	−3.74052	−	12.3308i	−0.180594	−	0.595339i
$430$	19.8300	−	14.8556i	0.956285	−	0.716400i
$431$	−14.8942	−	6.16938i	−0.717429	−	0.297169i	−0.00605420	−	0.999982i	$-0.501927\pi$
$431$	−14.8942	−	6.16938i	−0.717429	−	0.297169i	−0.711375	+	0.702813i	$0.751927\pi$
$432$	−3.98756	−	0.315252i	−0.191851	−	0.0151676i
$433$	−8.77028	+	3.63277i	−0.421473	+	0.174580i	−0.583332	−	0.812234i	$-0.698251\pi$
$433$	−8.77028	+	3.63277i	−0.421473	+	0.174580i	0.161859	+	0.986814i	$0.448251\pi$
$434$	2.30069	−	3.88077i	0.110437	−	0.186283i
$435$	−8.79590	+	16.4560i	−0.421731	+	0.789004i
$436$	29.2939	−	12.4661i	1.40292	−	0.597017i
$437$	−9.69109	+	11.8086i	−0.463588	+	0.564883i
$438$	7.75140	+	1.90197i	0.370376	+	0.0908794i
$439$	−1.91455	+	9.62509i	−0.0913764	+	0.459380i	0.907822	+	0.419355i	$0.137744\pi$
$439$	−1.91455	+	9.62509i	−0.0913764	+	0.459380i	−0.999199	+	0.0400251i	$0.987256\pi$
$440$	34.5876	+	1.19816i	1.64890	+	0.0571200i
$441$	−13.0226	+	2.59035i	−0.620123	+	0.123350i
$442$	16.4414	+	17.9655i	0.782038	+	0.854533i
$443$	4.09343	−	2.18799i	0.194485	−	0.103954i	−0.371280	−	0.928521i	$-0.621081\pi$
$443$	4.09343	−	2.18799i	0.194485	−	0.103954i	0.565765	+	0.824567i	$0.308581\pi$
$444$	−2.42591	+	8.28381i	−0.115129	+	0.393132i
$445$	0.697309	−	7.07990i	0.0330556	−	0.335619i
$446$	−13.2290	+	14.7381i	−0.626410	+	0.697868i
$447$			3.30908i			0.156514i
$448$	17.8935	+	31.2666i	0.845387	+	1.47721i
$449$		−	1.80577i		−	0.0852195i	−0.999092	−	0.0426097i	$-0.986433\pi$
$449$		−	1.80577i		−	0.0852195i	0.999092	−	0.0426097i	$-0.0135672\pi$
$450$	4.19383	+	3.76441i	0.197699	+	0.177456i
$451$	1.00116	−	10.1649i	0.0471427	−	0.478647i
$452$	−10.9996	−	20.1101i	−0.517377	−	0.945898i
$453$	18.5349	−	9.90714i	0.870848	−	0.465478i
$454$	−23.1126	+	21.1518i	−1.08473	+	0.992705i
$455$	−41.7897	+	8.31249i	−1.95913	+	0.389696i
$456$	7.90602	+	21.1276i	0.370234	+	0.989392i
$457$	2.40473	−	12.0894i	0.112489	−	0.565518i	−0.882897	−	0.469566i	$-0.844410\pi$
$457$	2.40473	−	12.0894i	0.112489	−	0.565518i	0.995386	−	0.0959521i	$-0.0305896\pi$
$458$	−8.80238	+	35.8738i	−0.411308	+	1.67627i
$459$	−3.46076	+	4.21694i	−0.161534	+	0.196830i
$460$	−10.6503	−	4.29170i	−0.496574	−	0.200102i
$461$	5.10393	−	9.54877i	0.237714	−	0.444731i	−0.734571	−	0.678532i	$-0.762617\pi$
$461$	5.10393	−	9.54877i	0.237714	−	0.444731i	0.972284	+	0.233801i	$0.0751165\pi$
$462$	−22.3615	−	13.2569i	−1.04035	−	0.616766i
$463$	30.4630	−	12.6182i	1.41573	−	0.586416i	0.461950	−	0.886906i	$-0.347150\pi$
$463$	30.4630	−	12.6182i	1.41573	−	0.586416i	0.953785	+	0.300490i	$0.0971501\pi$
$464$	−19.5488	−	15.4223i	−0.907531	−	0.715962i
$465$	1.96186	+	0.812630i	0.0909792	+	0.0376848i
$466$	14.3106	+	19.1024i	0.662924	+	0.884904i
$467$	10.2181	+	33.6844i	0.472835	+	1.55873i	0.791688	+	0.610925i	$0.209202\pi$
$467$	10.2181	+	33.6844i	0.472835	+	1.55873i	−0.318853	+	0.947804i	$0.603298\pi$
$468$	5.28292	+	3.45674i	0.244203	+	0.159788i
$469$	40.5415	−	3.99299i	1.87203	−	0.184379i
$470$	−4.68517	+	0.718076i	−0.216111	+	0.0331224i
$471$	2.00253	+	2.99699i	0.0922716	+	0.138094i
$472$	14.7452	+	19.2922i	0.678703	+	0.887995i
$473$	−19.8384	−	13.2556i	−0.912172	−	0.609494i
$474$	2.43451	+	6.70200i	0.111821	+	0.307833i
$475$	9.22585	−	30.4136i	0.423311	−	1.39547i
$476$	48.9382	+	4.34409i	2.24308	+	0.199111i
$477$	−0.178178	+	0.146227i	−0.00815823	+	0.00669528i
$478$	−22.4286	−	7.90336i	−1.02586	−	0.361491i
$479$	23.4632	+	23.4632i	1.07206	+	1.07206i	0.997194	+	0.0748657i	$0.0238528\pi$
$479$	23.4632	+	23.4632i	1.07206	+	1.07206i	0.0748657	+	0.997194i	$0.476147\pi$
$480$	−13.3721	+	10.4261i	−0.610350	+	0.475886i
$481$	9.63344	−	9.63344i	0.439247	−	0.439247i
$482$	−34.3092	+	16.4299i	−1.56274	+	0.748361i
$483$	5.47165	+	6.66723i	0.248969	+	0.303369i
$484$	−3.39219	−	10.8064i	−0.154190	−	0.491201i
$485$	40.2546	+	12.2111i	1.82787	+	0.554477i
$486$	−0.598485	+	1.28133i	−0.0271478	+	0.0581225i
$487$	15.4971	−	23.1930i	0.702239	−	1.05097i	−0.293244	−	0.956038i	$-0.594735\pi$
$487$	15.4971	−	23.1930i	0.702239	−	1.05097i	0.995483	−	0.0949374i	$-0.0302651\pi$
$488$	28.3737	−	1.80550i	1.28442	−	0.0817312i
$489$	−10.3888	+	6.94155i	−0.469796	+	0.313908i
$490$	−33.3108	+	45.3699i	−1.50483	+	2.04960i
$491$	0.645371	+	6.55256i	0.0291252	+	0.295713i	0.998702	+	0.0509271i	$0.0162176\pi$
$491$	0.645371	+	6.55256i	0.0291252	+	0.295713i	−0.969577	+	0.244786i	$0.921282\pi$
$492$	2.82028	+	4.13401i	0.127148	+	0.186375i
$493$	−32.4963	+	9.85766i	−1.46356	+	0.443967i
$494$	5.05448	−	35.2442i	0.227412	−	1.58571i
$495$	4.68247	−	11.3045i	0.210462	−	0.508099i
$496$	−1.52861	+	2.38606i	−0.0686367	+	0.107137i
$497$	−6.05983	−	14.6297i	−0.271820	−	0.656233i
$498$	14.1835	−	3.62552i	0.635578	−	0.162464i
$499$	−30.9275	−	16.5311i	−1.38451	−	0.740034i	−0.400188	−	0.916433i	$-0.631055\pi$
$499$	−30.9275	−	16.5311i	−1.38451	−	0.740034i	−0.984319	+	0.176399i	$0.943555\pi$
$500$	−6.08514	+	0.0586623i	−0.272136	+	0.00262346i
$501$	−1.67396	−	1.37379i	−0.0747872	−	0.0613762i
$502$	−33.0969	+	20.0550i	−1.47719	+	0.895098i
$503$	10.6765	+	2.12370i	0.476044	+	0.0946910i	0.427280	−	0.904119i	$-0.359472\pi$
$503$	10.6765	+	2.12370i	0.476044	+	0.0946910i	0.0487638	+	0.998810i	$0.484472\pi$
$504$	12.5704	−	2.05083i	0.559932	−	0.0913511i
$505$	1.67200	+	8.40569i	0.0744028	+	0.374048i
$506$	−0.489313	+	11.0463i	−0.0217526	+	0.491070i
$507$	1.43089	+	2.67702i	0.0635483	+	0.118890i
$508$	24.2289	−	2.62240i	1.07498	−	0.116350i
$509$	11.6472	+	1.14715i	0.516252	+	0.0508464i	0.352789	−	0.935703i	$-0.385233\pi$
$509$	11.6472	+	1.14715i	0.516252	+	0.0508464i	0.163463	+	0.986549i	$0.447733\pi$
$510$	1.24601	+	23.0915i	0.0551743	+	1.02251i
$511$	−25.4138			−1.12424
$512$	−10.5524	−	20.0162i	−0.466355	−	0.884597i
$513$	7.97561			0.352132
$514$	−1.57007	−	29.0971i	−0.0692528	−	1.28342i
$515$	−17.4973	−	1.72333i	−0.771021	−	0.0759390i
$516$	11.6221	−	1.25791i	0.511633	−	0.0553763i
$517$	2.15160	+	4.02535i	0.0946271	+	0.177035i
$518$	1.21628	−	27.4578i	0.0534403	−	1.20643i
$519$	−0.813430	−	4.08939i	−0.0357056	−	0.179504i
$520$	26.4136	−	4.30929i	1.15831	−	0.188975i
$521$	−5.12812	−	1.02005i	−0.224667	−	0.0446891i	0.0814729	−	0.996676i	$-0.474038\pi$
$521$	−5.12812	−	1.02005i	−0.224667	−	0.0446891i	−0.306140	+	0.951986i	$0.599038\pi$
$522$	−7.52905	+	4.56221i	−0.329538	+	0.199683i
$523$	−21.8372	−	17.9213i	−0.954875	−	0.783646i	0.0214912	−	0.999769i	$-0.493159\pi$
$523$	−21.8372	−	17.9213i	−0.954875	−	0.783646i	−0.976366	+	0.216123i	$0.930659\pi$
$524$	−45.5825	+	0.439427i	−1.99128	+	0.0191965i
$525$	−15.8255	−	8.45892i	−0.690682	−	0.369177i
$526$	12.4685	−	3.18713i	0.543651	−	0.138966i
$527$	1.47893	+	3.57046i	0.0644233	+	0.155532i
$528$	13.7488	+	8.80805i	0.598339	+	0.383321i
$529$	−7.39780	+	17.8599i	−0.321644	+	0.776517i
$530$	−0.138711	+	0.967210i	−0.00602522	+	0.0420129i
$531$	8.21528	−	2.49208i	0.356513	−	0.108147i
$532$	−40.4802	−	59.3366i	−1.75504	−	2.57257i
$533$	−0.774199	−	7.86058i	−0.0335343	−	0.340479i
$534$	1.98642	−	2.70554i	0.0859609	−	0.117080i
$535$	−27.0617	+	18.0820i	−1.16998	+	0.781754i
$536$	−25.5361	+	1.62494i	−1.10299	+	0.0701866i
$537$	−8.11559	+	12.1458i	−0.350213	+	0.524131i
$538$	−6.65405	+	14.2461i	−0.286876	+	0.614191i
$539$	51.8665	+	15.7335i	2.23405	+	0.677691i
$540$	1.79547	+	5.71978i	0.0772647	+	0.246140i
$541$	−7.96509	−	9.70549i	−0.342446	−	0.417272i	0.573100	−	0.819486i	$-0.305741\pi$
$541$	−7.96509	−	9.70549i	−0.342446	−	0.417272i	−0.915546	+	0.402214i	$0.868241\pi$
$542$	−14.5341	+	6.96003i	−0.624292	+	0.298959i
$543$	−7.00368	+	7.00368i	−0.300557	+	0.300557i
$544$	−30.6256	−	3.79111i	−1.31306	−	0.162543i
$545$	−33.7389	−	33.7389i	−1.44522	−	1.44522i
$546$	−18.9600	−	6.68107i	−0.811412	−	0.285924i
$547$	−9.65254	+	7.92163i	−0.412713	+	0.338705i	−0.817727	−	0.575606i	$-0.804766\pi$
$547$	−9.65254	+	7.92163i	−0.412713	+	0.338705i	0.405015	+	0.914310i	$0.367266\pi$
$548$	−34.1829	−	3.03431i	−1.46022	−	0.129619i
$549$	2.91791	−	9.61906i	0.124533	−	0.410532i
$550$	−7.85428	−	21.6221i	−0.334908	−	0.921970i
$551$	41.2807	+	27.5829i	1.75862	+	1.17507i
$552$	−3.28976	−	4.30422i	−0.140021	−	0.183200i
$553$	−12.6140	−	18.8781i	−0.536400	−	0.802780i
$554$	17.7104	−	2.71440i	0.752444	−	0.115324i
$555$	12.8744	−	1.26802i	0.546489	−	0.0538245i
$556$	−30.7509	−	20.1211i	−1.30413	−	0.853323i
$557$	3.71429	+	12.2444i	0.157380	+	0.518811i	0.999800	−	0.0200099i	$-0.00636978\pi$
$557$	3.71429	+	12.2444i	0.157380	+	0.518811i	−0.842420	+	0.538821i	$0.818870\pi$
$558$	0.600685	+	0.801823i	0.0254290	+	0.0339439i
$559$	−17.0462	−	7.06075i	−0.720976	−	0.298638i
$560$	33.4409	−	42.3887i	1.41314	−	1.79125i
$561$	20.5734	−	8.52179i	0.868611	−	0.359790i
$562$	0.220658	+	0.130816i	0.00930790	+	0.00551813i
$563$	1.86729	−	3.49346i	0.0786971	−	0.147232i	−0.839495	−	0.543368i	$-0.817149\pi$
$563$	1.86729	−	3.49346i	0.0786971	−	0.147232i	0.918192	+	0.396136i	$0.129649\pi$
$564$	−2.07420	−	0.835830i	−0.0873397	−	0.0351948i
$565$	−21.7938	+	26.5558i	−0.916872	+	1.11721i
$566$	1.87641	−	7.64725i	0.0788714	−	0.321438i
$567$	0.878507	−	4.41655i	0.0368938	−	0.185478i
$568$	3.48583	+	9.31534i	0.146262	+	0.390863i
$569$	32.1360	−	6.39225i	1.34721	−	0.267977i	0.531805	−	0.846867i	$-0.321514\pi$
$569$	32.1360	−	6.39225i	1.34721	−	0.267977i	0.815406	+	0.578890i	$0.196514\pi$
$570$	24.9413	−	22.8254i	1.04468	−	0.956050i
$571$	−19.7859	+	10.5758i	−0.828015	+	0.442583i	−0.830234	−	0.557414i	$-0.811793\pi$
$571$	−19.7859	+	10.5758i	−0.828015	+	0.442583i	0.00221956	+	0.999998i	$0.499293\pi$
$572$	−12.3671	−	22.6102i	−0.517094	−	0.945379i
$573$	0.309049	−	3.13783i	0.0129107	−	0.131085i
$574$	−11.8583	−	10.6441i	−0.494957	−	0.444277i
$575$			7.63254i			0.318299i
$576$	−7.93547	+	1.01402i	−0.330645	+	0.0422509i
$577$			11.9129i			0.495941i	0.968768	+	0.247971i	$0.0797636\pi$
$577$			11.9129i			0.495941i	−0.968768	+	0.247971i	$0.920236\pi$
$578$	−12.0534	+	13.4284i	−0.501357	+	0.558549i
$579$	−0.0948539	+	0.963068i	−0.00394199	+	0.0400237i
$580$	−10.4882	+	35.8143i	−0.435500	+	1.48711i
$581$	−41.1104	+	21.9740i	−1.70555	+	0.911634i
$582$	13.3990	+	14.6410i	0.555405	+	0.606890i
$583$	0.922831	−	0.183563i	0.0382198	−	0.00760239i
$584$	15.9531	+	0.552636i	0.660143	+	0.0228682i
$585$	1.84596	−	9.28026i	0.0763210	−	0.383691i
$586$	−45.5524	−	11.1772i	−1.88175	−	0.461727i
$587$	9.04347	−	11.0195i	0.373264	−	0.454824i	−0.552170	−	0.833731i	$-0.686200\pi$
$587$	9.04347	−	11.0195i	0.373264	−	0.454824i	0.925434	+	0.378908i	$0.123700\pi$
$588$	−24.4349	+	10.3983i	−1.00768	+	0.428821i
$589$	2.66346	−	4.98299i	0.109746	−	0.205320i
$590$	18.5587	−	31.3045i	0.764049	−	1.28879i
$591$	2.29541	−	0.950790i	0.0944205	−	0.0391103i
$592$	−1.36058	+	17.2097i	−0.0559197	+	0.707316i
$593$	15.2823	+	6.33013i	0.627568	+	0.259947i	0.673719	−	0.738987i	$-0.264696\pi$
$593$	15.2823	+	6.33013i	0.627568	+	0.259947i	−0.0461513	+	0.998934i	$0.514696\pi$
$594$	4.62020	−	3.46122i	0.189569	−	0.142016i
$595$	−21.3748	−	70.4634i	−0.876283	−	2.88872i
$596$	1.35365	+	6.47824i	0.0554476	+	0.265359i
$597$	20.3362	−	2.00294i	0.832304	−	0.0819748i
$598$	1.29538	+	8.45187i	0.0529720	+	0.345623i
$599$	11.9431	+	17.8741i	0.487980	+	0.730314i	0.990986	−	0.133969i	$-0.0427723\pi$
$599$	11.9431	+	17.8741i	0.487980	+	0.730314i	−0.503005	+	0.864283i	$0.667772\pi$
$600$	9.75026	+	5.65408i	0.398053	+	0.230827i
$601$	−2.53430	−	1.69337i	−0.103376	−	0.0690739i	0.502808	−	0.864398i	$-0.332300\pi$
$601$	−2.53430	−	1.69337i	−0.103376	−	0.0690739i	−0.606184	+	0.795325i	$0.707300\pi$
$602$	−34.9859	+	12.7087i	−1.42592	+	0.517968i
$603$	−2.62610	+	8.65708i	−0.106943	+	0.352544i
$604$	32.2335	−	26.9775i	1.31156	−	1.09770i
$605$	−13.1220	+	10.7690i	−0.533487	+	0.437821i
$606$	−1.34385	+	3.81366i	−0.0545901	+	0.154919i
$607$	10.5909	+	10.5909i	0.429873	+	0.429873i	0.888585	−	0.458712i	$-0.151689\pi$
$607$	10.5909	+	10.5909i	0.429873	+	0.429873i	−0.458712	+	0.888585i	$0.651689\pi$
$608$	24.1205	+	38.1278i	0.978215	+	1.54629i
$609$	19.8213	−	19.8213i	0.803198	−	0.803198i
$610$	−18.4039	−	38.4315i	−0.745153	−	1.55604i
$611$	2.23915	+	2.72841i	0.0905863	+	0.110380i
$612$	−5.05015	+	9.67129i	−0.204140	+	0.390939i
$613$	16.3819	+	4.96939i	0.661658	+	0.200712i	0.603214	−	0.797579i	$-0.293886\pi$
$613$	16.3819	+	4.96939i	0.661658	+	0.200712i	0.0584433	+	0.998291i	$0.481386\pi$
$614$	−8.12007	−	3.79272i	−0.327699	−	0.153062i
$615$	4.16694	−	6.23627i	0.168027	−	0.251471i
$616$	−49.2005	−	16.8058i	−1.98235	−	0.677125i
$617$	1.35226	−	0.903548i	0.0544398	−	0.0363755i	−0.528053	−	0.849212i	$-0.677078\pi$
$617$	1.35226	−	0.903548i	0.0544398	−	0.0363755i	0.582492	+	0.812836i	$0.302078\pi$
$618$	−6.68647	−	4.90925i	−0.268969	−	0.197479i
$619$	−1.92749	−	19.5702i	−0.0774725	−	0.786591i	−0.952909	−	0.303257i	$-0.901926\pi$
$619$	−1.92749	−	19.5702i	−0.0774725	−	0.786591i	0.875436	−	0.483334i	$-0.160574\pi$
$620$	4.17320	+	0.788358i	0.167600	+	0.0316612i
$621$	−1.83289	+	0.556000i	−0.0735512	+	0.0223115i
$622$	7.77076	+	1.11443i	0.311579	+	0.0446846i
$623$	−4.08993	+	9.87396i	−0.163859	+	0.395592i
$624$	11.7565	+	4.60623i	0.470637	+	0.184397i
$625$	11.1151	+	26.8341i	0.444602	+	1.07336i
$626$	−3.46720	−	13.5641i	−0.138577	−	0.542132i
$627$	−28.7126	−	15.3472i	−1.14667	−	0.612908i
$628$	5.14637	+	5.04809i	0.205363	+	0.201441i
$629$	18.1997	+	14.9361i	0.725671	+	0.595543i
$630$	−9.89247	−	16.3256i	−0.394125	−	0.650428i
$631$	12.4301	+	2.47250i	0.494834	+	0.0984287i	0.436198	−	0.899851i	$-0.356325\pi$
$631$	12.4301	+	2.47250i	0.494834	+	0.0984287i	0.0586364	+	0.998279i	$0.481325\pi$
$632$	7.50769	+	12.1247i	0.298640	+	0.482296i
$633$	0.555457	+	2.79247i	0.0220774	+	0.110991i
$634$	3.24287	+	0.143647i	0.128791	+	0.00570496i
$635$	−17.2178	−	32.2121i	−0.683266	−	1.27830i
$636$	−0.289006	+	0.359159i	−0.0114598	+	0.0142416i
$637$	41.7115	+	4.10823i	1.65267	+	0.162774i
$638$	35.8839	−	1.93628i	1.42066	−	0.0766581i
$639$	3.51650			0.139111
$640$	−21.9137	+	25.8816i	−0.866217	+	1.02306i
$641$	−15.2506			−0.602363			−0.301181	−	0.953567i	$-0.597381\pi$
$641$	−15.2506			−0.602363			−0.301181	+	0.953567i	$0.597381\pi$
$642$	−15.3333	+	0.827378i	−0.605156	+	0.0326540i
$643$	9.66078	+	0.951504i	0.380984	+	0.0375237i	0.286697	−	0.958021i	$-0.407443\pi$
$643$	9.66078	+	0.951504i	0.380984	+	0.0375237i	0.0942873	+	0.995545i	$0.469943\pi$
$644$	13.4393	+	10.8143i	0.529584	+	0.426141i
$645$	−8.25897	−	15.4514i	−0.325197	−	0.608400i
$646$	61.4703	+	2.72291i	2.41852	+	0.107132i
$647$	−2.49466	−	12.5415i	−0.0980753	−	0.493058i	−0.998334	−	0.0577021i	$-0.981623\pi$
$647$	−2.49466	−	12.5415i	−0.0980753	−	0.493058i	0.900259	−	0.435356i	$-0.143377\pi$
$648$	−0.647508	+	2.75331i	−0.0254365	+	0.108160i
$649$	−34.3708	−	6.83678i	−1.34917	−	0.268367i
$650$	−9.21905	−	15.2143i	−0.361601	−	0.596753i
$651$	−2.46599	−	2.02378i	−0.0966497	−	0.0793184i
$652$	−17.4987	+	17.8394i	−0.685301	+	0.698643i
$653$	−40.3956	−	21.5919i	−1.58080	−	0.844957i	−0.999511	−	0.0312610i	$-0.990048\pi$
$653$	−40.3956	−	21.5919i	−1.58080	−	0.844957i	−0.581291	−	0.813696i	$-0.697452\pi$
$654$	−5.57503	−	21.8102i	−0.218001	−	0.852847i
$655$	26.1448	+	63.1191i	1.02156	+	2.46627i
$656$	7.21241	+	6.93953i	0.281597	+	0.270943i
$657$	2.15973	−	5.21405i	0.0842592	−	0.203420i
$658$	7.04854	+	1.01086i	0.274781	+	0.0394072i
$659$	10.1860	−	3.08989i	0.396790	−	0.120365i	−0.0855823	−	0.996331i	$-0.527275\pi$
$659$	10.1860	−	3.08989i	0.396790	−	0.120365i	0.482373	+	0.875966i	$0.339775\pi$
$660$	4.54262	−	24.0465i	0.176821	−	0.936008i
$661$	−3.81075	−	38.6912i	−0.148221	−	1.50491i	−0.725419	−	0.688308i	$-0.758354\pi$
$661$	−3.81075	−	38.6912i	−0.148221	−	1.50491i	0.577198	−	0.816604i	$-0.304146\pi$
$662$	22.2592	+	16.3429i	0.865130	+	0.635184i
$663$	14.3182	−	9.56711i	0.556072	−	0.371556i
$664$	26.2842	−	12.8998i	1.02002	−	0.500610i
$665$	−59.8093	+	89.5110i	−2.31931	+	3.47109i
$666$	5.53006	+	2.58298i	0.214285	+	0.100088i
$667$	−11.4097	−	3.46108i	−0.441783	−	0.134014i
$668$	−3.83913	−	2.00472i	−0.148540	−	0.0775648i
$669$	8.88396	+	10.8251i	0.343474	+	0.418524i
$670$	16.5634	+	34.5880i	0.639899	+	1.33625i
$671$	−29.0143	+	29.0143i	−1.12008	+	1.12008i
$672$	23.7704	−	9.15715i	0.916964	−	0.353245i
$673$	11.5641	+	11.5641i	0.445764	+	0.445764i	0.893943	−	0.448180i	$-0.147928\pi$
$673$	11.5641	+	11.5641i	0.445764	+	0.445764i	−0.448180	+	0.893943i	$0.647928\pi$
$674$	8.51792	−	24.1727i	0.328098	−	0.931097i
$675$	3.08038	−	2.52800i	0.118564	−	0.0973028i
$676$	3.89638	+	4.65550i	0.149861	+	0.179058i
$677$	−6.47730	+	21.3528i	−0.248943	+	0.820655i	0.740032	+	0.672572i	$0.234810\pi$
$677$	−6.47730	+	21.3528i	−0.248943	+	0.820655i	−0.988975	+	0.148083i	$0.952690\pi$
$678$	−15.2342	+	5.53384i	−0.585064	+	0.212526i
$679$	−52.5448	−	35.1093i	−2.01648	−	1.34737i
$680$	11.8854	+	44.6970i	0.455786	+	1.71405i
$681$	12.3081	+	18.4203i	0.471646	+	0.705868i
$682$	−0.619573	−	4.04248i	−0.0237247	−	0.154795i
$683$	3.62992	−	0.357516i	0.138895	−	0.0136800i	−0.0283306	−	0.999599i	$-0.509019\pi$
$683$	3.62992	−	0.357516i	0.138895	−	0.0136800i	0.167226	+	0.985919i	$0.446519\pi$
$684$	15.6140	−	3.26259i	0.597016	−	0.124748i
$685$	14.9302	+	49.2181i	0.570452	+	1.88053i
$686$	31.9958	−	23.9696i	1.22161	−	0.915164i
$687$	24.1309	+	9.99533i	0.920650	+	0.381346i
$688$	22.2382	−	7.21689i	0.847822	−	0.275141i
$689$	0.672224	−	0.278444i	0.0256097	−	0.0106079i
$690$	−4.14057	+	6.98425i	−0.157629	+	0.265886i
$691$	3.69934	−	6.92098i	0.140730	−	0.263286i	−0.801676	−	0.597759i	$-0.796058\pi$
$691$	3.69934	−	6.92098i	0.140730	−	0.263286i	0.942406	+	0.334472i	$0.108558\pi$
$692$	−3.26532	−	7.67312i	−0.124129	−	0.291688i
$693$	−11.6613	+	14.2093i	−0.442976	+	0.539768i
$694$	−44.7940	−	10.9911i	−1.70036	−	0.417218i
$695$	−10.7450	+	54.0188i	−0.407581	+	2.04905i
$696$	−12.8735	+	12.0114i	−0.487969	+	0.455293i
$697$	13.3878	−	2.66299i	0.507098	−	0.100868i
$698$	−33.3231	−	36.4121i	−1.26130	−	1.37822i
$699$	14.8846	−	7.95597i	0.562986	−	0.300922i
$700$	−34.4422	−	10.0864i	−1.30179	−	0.381230i
$701$	1.45871	−	14.8105i	0.0550946	−	0.559385i	−0.927526	−	0.373759i	$-0.878069\pi$
$701$	1.45871	−	14.8105i	0.0550946	−	0.559385i	0.982620	−	0.185626i	$-0.0594312\pi$
$702$	2.98200	−	3.32217i	0.112548	−	0.125387i
$703$		−	34.4216i		−	1.29824i
$704$	30.5194	+	11.6194i	1.15024	+	0.437924i
$705$			3.35160i			0.126229i
$706$	32.5488	+	29.2160i	1.22499	+	1.09956i
$707$	1.26198	−	12.8131i	0.0474618	−	0.481888i
$708$	15.0638	−	8.23942i	0.566131	−	0.309656i
$709$	−25.3768	+	13.5642i	−0.953045	+	0.509413i	−0.873183	−	0.487393i	$-0.837948\pi$
$709$	−25.3768	+	13.5642i	−0.953045	+	0.509413i	−0.0798618	+	0.996806i	$0.525448\pi$
$710$	10.9968	−	10.0639i	0.412702	−	0.377691i
$711$	4.94512	−	0.983646i	0.185457	−	0.0368896i
$712$	2.78210	−	6.10927i	0.104263	−	0.228955i
$713$	−0.264717	+	1.33082i	−0.00991374	+	0.0498397i
$714$	8.27874	−	33.7397i	0.309824	−	1.26268i
$715$	−24.5032	+	29.8573i	−0.916369	+	1.11660i
$716$	−10.9195	+	27.0980i	−0.408081	+	1.01270i
$717$	−7.92667	+	14.8298i	−0.296027	+	0.553827i
$718$	−8.40104	−	4.98051i	−0.313524	−	0.185871i
$719$	−4.33793	+	1.79683i	−0.161778	+	0.0670105i	−0.462103	−	0.886826i	$-0.652905\pi$
$719$	−4.33793	+	1.79683i	−0.161778	+	0.0670105i	0.300325	+	0.953837i	$0.402905\pi$
$720$	5.85482	+	10.4633i	0.218196	+	0.389942i
$721$	24.4025	+	10.1078i	0.908796	+	0.376436i
$722$	−37.8256	−	50.4914i	−1.40772	−	1.87910i
$723$	7.80824	+	25.7403i	0.290392	+	0.957293i
$724$	−10.8462	+	16.5762i	−0.403097	+	0.616051i
$725$	24.6865	−	2.43141i	0.916833	−	0.0903002i
$726$	−7.91648	+	1.21332i	−0.293808	+	0.0450307i
$727$	−10.9921	−	16.4509i	−0.407675	−	0.610129i	0.569646	−	0.821890i	$-0.307080\pi$
$727$	−10.9921	−	16.4509i	−0.407675	−	0.610129i	−0.977322	+	0.211761i	$0.932080\pi$
$728$	−39.8513	−	5.32368i	−1.47699	−	0.197309i
$729$	0.831470	+	0.555570i	0.0307952	+	0.0205767i
$730$	−8.16820	−	22.4863i	−0.302319	−	0.832255i
$731$	9.25591	−	30.5126i	0.342342	−	1.12855i
$732$	1.77756	−	20.0250i	0.0657005	−	0.740147i
$733$	−26.0507	+	21.3793i	−0.962205	+	0.789661i	−0.977654	−	0.210219i	$-0.932582\pi$
$733$	−26.0507	+	21.3793i	−0.962205	+	0.789661i	0.0154493	+	0.999881i	$0.495082\pi$
$734$	−5.91061	−	2.08277i	−0.218165	−	0.0768764i
$735$	28.1427	+	28.1427i	1.03806	+	1.03806i
$736$	−8.20115	−	7.08071i	−0.302298	−	0.260998i
$737$	26.1126	−	26.1126i	0.961870	−	0.961870i
$738$	3.19156	−	1.52837i	0.117483	−	0.0562599i
$739$	8.08667	+	9.85364i	0.297473	+	0.362472i	0.900201	−	0.435475i	$-0.143420\pi$
$739$	8.08667	+	9.85364i	0.297473	+	0.362472i	−0.602728	+	0.797947i	$0.705920\pi$
$740$	24.6858	−	7.74899i	0.907468	−	0.284859i
$741$	−24.0923	−	7.30831i	−0.885052	−	0.268478i
$742$	0.621202	−	1.32997i	0.0228050	−	0.0488247i
$743$	6.15748	−	9.21531i	0.225896	−	0.338077i	−0.701158	−	0.713006i	$-0.747333\pi$
$743$	6.15748	−	9.21531i	0.225896	−	0.338077i	0.927053	+	0.374929i	$0.122333\pi$
$744$	1.50397	+	1.32402i	0.0551384	+	0.0485410i
$745$	8.24727	−	5.51065i	0.302157	−	0.201895i
$746$	−10.6985	+	14.5715i	−0.391700	+	0.533501i
$747$	−1.01465	−	10.3019i	−0.0371239	−	0.376926i
$748$	36.7909	−	25.0993i	1.34521	−	0.917720i
$749$	46.7892	−	14.1933i	1.70964	−	0.518614i
$750$	−0.610864	+	4.25946i	−0.0223056	+	0.155534i
$751$	12.7776	−	30.8479i	0.466262	−	1.12566i	−0.499520	−	0.866302i	$-0.666490\pi$
$751$	12.7776	−	30.8479i	0.466262	−	1.12566i	0.965782	−	0.259354i	$-0.0835097\pi$
$752$	−4.40262	−	0.787821i	−0.160547	−	0.0287289i
$753$	10.4719	+	25.2813i	0.381616	+	0.921302i
$754$	26.9239	−	6.88216i	0.980509	−	0.250633i
$755$	−55.5582	−	29.6965i	−2.02197	−	1.08077i
$756$	−0.0868176	−	9.00574i	−0.00315753	−	0.327535i
$757$	25.4367	+	20.8754i	0.924513	+	0.758728i	0.970723	−	0.240203i	$-0.0772142\pi$
$757$	25.4367	+	20.8754i	0.924513	+	0.758728i	−0.0462095	+	0.998932i	$0.514714\pi$
$758$	35.7055	−	21.6356i	1.29688	−	0.785842i
$759$	7.66837	+	1.52533i	0.278344	+	0.0553661i
$760$	39.4908	−	54.8885i	1.43248	−	1.99101i
$761$	1.44835	+	7.28133i	0.0525025	+	0.263948i	0.998117	−	0.0613420i	$-0.0195380\pi$
$761$	1.44835	+	7.28133i	0.0525025	+	0.263948i	−0.945614	+	0.325290i	$0.894538\pi$
$762$	0.762588	−	17.2156i	0.0276257	−	0.623656i
$763$	33.7898	+	63.2162i	1.22327	+	2.28858i
$764$	−0.678565	−	6.26941i	−0.0245496	−	0.226819i
$765$	16.2732	+	1.60277i	0.588359	+	0.0579483i
$766$	1.59155	+	29.4951i	0.0575049	+	1.06570i
$767$	−27.0998			−0.978518
$768$	−15.1206	+	5.23135i	−0.545618	+	0.188770i
$769$	−11.8285			−0.426548			−0.213274	−	0.976992i	$-0.568413\pi$
$769$	−11.8285			−0.426548			−0.213274	+	0.976992i	$0.568413\pi$
$770$	4.19854	+	77.8088i	0.151305	+	2.80403i
$771$	−20.5055	−	2.01961i	−0.738486	−	0.0727346i
$772$	0.208266	+	1.92422i	0.00749568	+	0.0692541i
$773$	22.0042	+	41.1670i	0.791438	+	1.48068i	0.874973	+	0.484171i	$0.160879\pi$
$773$	22.0042	+	41.1670i	0.791438	+	1.48068i	−0.0835357	+	0.996505i	$0.526621\pi$
$774$	0.365796	−	8.25794i	0.0131483	−	0.296825i
$775$	−0.550745	−	2.76878i	−0.0197833	−	0.0994576i
$776$	32.2206	+	23.1819i	1.15665	+	0.832181i
$777$	−19.0612	−	3.79151i	−0.683818	−	0.136020i
$778$	−1.48458	+	0.899579i	−0.0532249	+	0.0322515i
$779$	−15.4266	−	12.6603i	−0.552716	−	0.453602i
$780$	−0.182425	−	18.9233i	−0.00653186	−	0.677561i
$781$	−12.6596	−	6.76669i	−0.452996	−	0.242131i
$782$	−14.3164	+	3.65950i	−0.511954	+	0.130863i
$783$	2.38219	+	5.75112i	0.0851326	+	0.205528i
$784$	−43.5830	+	30.3527i	−1.55654	+	1.08402i
$785$	4.13462	−	9.98187i	0.147571	−	0.356268i
$786$	−4.57586	+	31.9068i	−0.163216	+	1.13808i
$787$	6.05853	−	1.83783i	0.215963	−	0.0655117i	−0.180449	−	0.983584i	$-0.557755\pi$
$787$	6.05853	−	1.83783i	0.215963	−	0.0655117i	0.396412	+	0.918073i	$0.370255\pi$
$788$	4.10482	−	2.80037i	0.146228	−	0.0997589i
$789$	−0.891957	−	9.05619i	−0.0317545	−	0.322409i
$790$	12.6493	−	17.2285i	0.450041	−	0.612963i
$791$	42.9114	−	28.6725i	1.52576	−	1.01948i
$792$	7.62917	−	8.66609i	0.271091	−	0.307936i
$793$	−17.6285	+	26.3830i	−0.626007	+	0.936886i
$794$	2.93136	−	6.27592i	0.104030	−	0.222724i
$795$	0.661167	+	0.200563i	0.0234492	+	0.00711323i
$796$	38.9932	−	12.2401i	1.38208	−	0.433840i
$797$	26.5432	+	32.3429i	0.940207	+	1.14565i	0.989160	+	0.146844i	$0.0469116\pi$
$797$	26.5432	+	32.3429i	0.940207	+	1.14565i	−0.0489529	+	0.998801i	$0.515588\pi$
$798$	−45.8095	+	21.9371i	−1.62164	+	0.776564i
$799$	−4.31313	+	4.31313i	−0.152588	+	0.152588i
$800$	21.4012	+	7.08053i	0.756646	+	0.250335i
$801$	−1.67823	−	1.67823i	−0.0592973	−	0.0592973i
$802$	17.2712	+	6.08601i	0.609869	+	0.214904i
$803$	−17.8084	+	14.6150i	−0.628444	+	0.515751i
$804$	−1.59979	+	18.0224i	−0.0564203	+	0.635600i
$805$	7.50483	−	24.7401i	0.264511	−	0.871974i
$806$	−1.07978	−	2.97253i	−0.0380336	−	0.104703i
$807$	9.24441	+	6.17691i	0.325418	+	0.217438i
$808$	−1.07082	+	8.01579i	−0.0376712	+	0.281995i
$809$	2.45848	+	3.67938i	0.0864356	+	0.129360i	0.872168	−	0.489207i	$-0.162714\pi$
$809$	2.45848	+	3.67938i	0.0864356	+	0.129360i	−0.785732	+	0.618567i	$0.787714\pi$
$810$	4.19015	−	0.642206i	0.147227	−	0.0225648i
$811$	−17.7169	+	1.74496i	−0.622123	+	0.0612738i	−0.404168	−	0.914685i	$-0.632439\pi$
$811$	−17.7169	+	1.74496i	−0.622123	+	0.0612738i	−0.217956	+	0.975959i	$0.569939\pi$
$812$	30.6961	−	46.9128i	1.07722	−	1.64632i
$813$	3.30772	+	10.9041i	0.116007	+	0.382424i
$814$	−14.9381	−	19.9402i	−0.523582	−	0.698902i
$815$	34.6011	+	14.3322i	1.21202	+	0.502037i
$816$	−5.93053	+	20.9995i	−0.207610	+	0.735131i
$817$	−43.0687	+	17.8396i	−1.50678	+	0.624129i
$818$	7.46838	+	4.42758i	0.261126	+	0.154807i
$819$	−6.70078	+	12.5363i	−0.234144	+	0.438053i
$820$	5.60662	−	13.9134i	0.195792	−	0.485878i
$821$	22.9594	−	27.9760i	0.801287	−	0.976371i	−0.198706	−	0.980059i	$-0.563674\pi$
$821$	22.9594	−	27.9760i	0.801287	−	0.976371i	0.999993	+	0.00368821i	$0.00117400\pi$
$822$	−5.78263	+	23.5669i	−0.201693	+	0.821991i
$823$	8.96315	−	45.0608i	0.312436	−	1.57072i	−0.431276	−	0.902220i	$-0.641937\pi$
$823$	8.96315	−	45.0608i	0.312436	−	1.57072i	0.743712	−	0.668500i	$-0.233063\pi$
$824$	−15.0985	−	6.87567i	−0.525980	−	0.239525i
$825$	−15.9541	+	3.17346i	−0.555449	+	0.110486i
$826$	−40.3315	+	36.9100i	−1.40331	+	1.28426i
$827$	4.85298	−	2.59397i	0.168755	−	0.0902013i	−0.384857	−	0.922976i	$-0.625749\pi$
$827$	4.85298	−	2.59397i	0.168755	−	0.0902013i	0.553612	+	0.832775i	$0.313249\pi$
$828$	−3.36083	+	1.83827i	−0.116797	+	0.0638844i
$829$	−0.132063	+	1.34085i	−0.00458672	+	0.0465698i	−0.997206	−	0.0747054i	$-0.976198\pi$
$829$	−0.132063	+	1.34085i	−0.00458672	+	0.0465698i	0.992619	+	0.121275i	$0.0386984\pi$
$830$	−32.6559	−	29.3121i	−1.13350	−	1.01744i
$831$		−	12.6694i		−	0.439497i
$832$	24.9002	+	4.20843i	0.863260	+	0.145901i
$833$			72.4329i			2.50965i
$834$	−17.3577	+	19.3378i	−0.601048	+	0.669612i
$835$	−0.636238	+	6.45983i	−0.0220179	+	0.223552i
$836$	−62.4893	−	18.3000i	−2.16124	−	0.632918i
$837$	0.624778	−	0.333951i	0.0215955	−	0.0115430i
$838$	−4.24186	−	4.63507i	−0.146533	−	0.160116i
$839$	−20.2052	+	4.01906i	−0.697560	+	0.138753i	−0.531118	−	0.847298i	$-0.678228\pi$
$839$	−20.2052	+	4.01906i	−0.697560	+	0.138753i	−0.166442	+	0.986051i	$0.553228\pi$
$840$	−26.0450	−	27.9142i	−0.898638	−	0.963133i
$841$	−1.90217	+	9.56287i	−0.0655922	+	0.329754i
$842$	0.531894	+	0.130511i	0.0183303	+	0.00449772i
$843$	0.115071	−	0.140214i	0.00396325	−	0.00482924i
$844$	2.22975	+	5.23965i	0.0767511	+	0.180356i
$845$	4.28908	−	8.02431i	0.147549	−	0.276045i
$846$	−0.806397	+	1.36022i	−0.0277245	+	0.0467652i
$847$	23.5605	−	9.75907i	0.809547	−	0.335326i
$848$	−0.418870	+	0.821357i	−0.0143840	+	0.0282055i
$849$	−5.14400	−	2.13071i	−0.176542	−	0.0731259i
$850$	24.6044	−	18.4324i	0.843926	−	0.632226i
$851$	2.39962	+	7.91048i	0.0822578	+	0.271168i
$852$	6.88433	−	1.43850i	0.235853	−	0.0492823i
$853$	−21.3609	+	2.10386i	−0.731382	+	0.0720348i	−0.456851	−	0.889543i	$-0.651023\pi$
$853$	−21.3609	+	2.10386i	−0.731382	+	0.0720348i	−0.274531	+	0.961578i	$0.588523\pi$
$854$	9.69784	+	63.2748i	0.331853	+	2.16522i
$855$	−13.2819	−	19.8777i	−0.454231	−	0.679804i
$856$	−29.6798	+	7.89218i	−1.01443	+	0.269749i
$857$	−5.26671	−	3.51910i	−0.179907	−	0.120210i	0.462356	−	0.886695i	$-0.347004\pi$
$857$	−5.26671	−	3.51910i	−0.179907	−	0.120210i	−0.642263	+	0.766484i	$0.722004\pi$
$858$	−17.1281	+	6.22182i	−0.584743	+	0.212409i
$859$	7.17830	−	23.6637i	0.244920	−	0.807394i	−0.745159	−	0.666887i	$-0.767627\pi$
$859$	7.17830	−	23.6637i	0.244920	−	0.807394i	0.990080	−	0.140508i	$-0.0448735\pi$
$860$	−22.4895	−	26.8711i	−0.766885	−	0.916295i
$861$	−8.70997	+	7.14808i	−0.296835	+	0.243606i
$862$	−7.57722	+	21.5031i	−0.258081	+	0.732399i
$863$	−18.5244	−	18.5244i	−0.630579	−	0.630579i	0.317634	−	0.948213i	$-0.397112\pi$
$863$	−18.5244	−	18.5244i	−0.630579	−	0.630579i	−0.948213	+	0.317634i	$0.897112\pi$
$864$	−0.141336	+	5.65509i	−0.00480835	+	0.192390i
$865$	−8.83744	+	8.83744i	−0.300482	+	0.300482i
$866$	5.79834	+	12.1082i	0.197036	+	0.411454i
$867$	8.09452	+	9.86320i	0.274904	+	0.334972i
$868$	−5.65558	−	2.95323i	−0.191963	−	0.100239i
$869$	−19.6955	−	5.97456i	−0.668124	−	0.202673i
$870$	23.9087	+	11.1673i	0.810581	+	0.378606i
$871$	15.8655	−	23.7444i	0.537583	−	0.804550i
$872$	−19.8363	−	40.4177i	−0.671741	−	1.36872i
$873$	11.6686	−	7.79673i	0.394923	−	0.263879i
$874$	17.4141	+	12.7856i	0.589042	+	0.432478i
$875$	−1.34299	−	13.6356i	−0.0454013	−	0.460967i
$876$	2.09522	−	11.0911i	0.0707911	−	0.374735i
$877$	17.0872	−	5.18335i	0.576994	−	0.175029i	0.0117185	−	0.999931i	$-0.496270\pi$
$877$	17.0872	−	5.18335i	0.576994	−	0.175029i	0.565276	+	0.824902i	$0.308770\pi$
$878$	13.7380	+	1.97022i	0.463636	+	0.0664917i
$879$	−12.6920	+	30.6413i	−0.428092	+	1.03350i
$880$	−0.943569	−	48.9345i	−0.0318077	−	1.64958i
$881$	−7.38164	−	17.8209i	−0.248694	−	0.600400i	0.749400	−	0.662118i	$-0.230342\pi$
$881$	−7.38164	−	17.8209i	−0.248694	−	0.600400i	−0.998094	+	0.0617176i	$0.980342\pi$
$882$	4.65031	+	18.1926i	0.156584	+	0.612576i
$883$	12.5319	+	6.69845i	0.421733	+	0.225421i	0.668590	−	0.743631i	$-0.266898\pi$
$883$	12.5319	+	6.69845i	0.421733	+	0.225421i	−0.246858	+	0.969052i	$0.579398\pi$
$884$	24.1173	−	24.5869i	0.811154	−	0.826946i
$885$	−19.8921	−	16.3250i	−0.668664	−	0.548758i
$886$	−3.40170	−	5.61386i	−0.114282	−	0.188601i
$887$	30.6182	+	6.09033i	1.02806	+	0.204493i	0.680179	−	0.733046i	$-0.261902\pi$
$887$	30.6182	+	6.09033i	1.02806	+	0.204493i	0.347879	+	0.937540i	$0.386902\pi$
$888$	11.8829	+	2.79455i	0.398765	+	0.0937791i
$889$	10.7048	+	53.8166i	0.359027	+	1.80495i
$890$	−10.0511	−	0.445226i	−0.336913	−	0.0149240i
$891$	−1.92427	−	3.60005i	−0.0644654	−	0.120606i
$892$	21.8205	+	17.5584i	0.730606	+	0.587898i
$893$	8.87489	+	0.874100i	0.296987	+	0.0292506i
$894$	4.67294	−	0.252150i	0.156287	−	0.00843317i
$895$	43.7863			1.46361
$896$	42.7899	−	27.6509i	1.42951	−	0.923753i
$897$	6.04616			0.201875
$898$	−2.55003	+	0.137599i	−0.0850957	+	0.00459173i
$899$	4.38871	+	0.432250i	0.146372	+	0.0144164i
$900$	4.99638	−	6.20921i	0.166546	−	0.206974i
$901$	0.592746	+	1.10895i	0.0197472	+	0.0369445i
$902$	−14.4308	−	0.639231i	−0.480492	−	0.0212841i
$903$	5.13485	+	25.8146i	0.170877	+	0.859057i
$904$	−27.5604	+	17.0656i	−0.916647	+	0.567592i
$905$	29.1187	+	5.79208i	0.967939	+	0.192535i
$906$	−15.4028	−	25.4194i	−0.511724	−	0.844502i
$907$	39.0944	+	32.0839i	1.29811	+	1.06533i	0.993616	+	0.112814i	$0.0359863\pi$
$907$	39.0944	+	32.0839i	1.29811	+	1.06533i	0.304491	+	0.952515i	$0.401514\pi$
$908$	31.6309	+	31.0269i	1.04971	+	1.02966i
$909$	2.52158	+	1.34781i	0.0836355	+	0.0447041i
$910$	14.9229	+	58.3803i	0.494690	+	1.93529i
$911$	5.43772	+	13.1278i	0.180160	+	0.434944i	0.987999	−	0.154458i	$-0.0493632\pi$
$911$	5.43772	+	13.1278i	0.180160	+	0.434944i	−0.807840	+	0.589402i	$0.799363\pi$
$912$	29.2332	−	12.7745i	0.968007	−	0.423005i
$913$	−16.1708	+	39.0397i	−0.535174	+	1.29203i
$914$	−17.2554	−	2.47465i	−0.570758	−	0.0818543i
$915$	−28.8330	+	8.74639i	−0.953189	+	0.289147i
$916$	51.3302	+	9.69679i	1.69600	+	0.320391i
$917$	−10.0601	−	102.141i	−0.332212	−	3.37301i
$918$	6.21871	+	4.56581i	0.205248	+	0.150694i
$919$	−6.03195	+	4.03042i	−0.198976	+	0.132951i	−0.651067	−	0.759020i	$-0.725678\pi$
$919$	−6.03195	+	4.03042i	−0.198976	+	0.132951i	0.452091	+	0.891972i	$0.350678\pi$
$920$	−5.24902	+	15.3670i	−0.173055	+	0.506635i
$921$	−3.52076	+	5.26919i	−0.116013	+	0.173626i
$922$	−13.8733	−	6.47994i	−0.456893	−	0.213406i
$923$	−10.6225	−	3.22229i	−0.349643	−	0.106063i
$924$	−17.0169	+	32.5882i	−0.559815	+	1.07207i
$925$	−10.9105	−	13.2945i	−0.358735	−	0.437120i
$926$	−20.1401	−	42.0571i	−0.661846	−	1.38208i
$927$	−4.14758	+	4.14758i	−0.136224	+	0.136224i
$928$	−20.2891	+	28.7812i	−0.666023	+	0.944790i
$929$	13.3396	+	13.3396i	0.437658	+	0.437658i	0.891223	−	0.453565i	$-0.149848\pi$
$929$	13.3396	+	13.3396i	0.437658	+	0.437658i	−0.453565	+	0.891223i	$0.649848\pi$
$930$	0.998070	−	2.83238i	0.0327280	−	0.0928775i
$931$	81.8601	−	67.1809i	2.68286	−	2.20176i
$932$	25.8852	−	21.6644i	0.847899	−	0.709641i
$933$	1.61136	−	5.31195i	0.0527537	−	0.173906i
$934$	46.7892	−	16.9963i	1.53099	−	0.556135i
$935$	−55.5002	−	37.0840i	−1.81505	−	1.21278i
$936$	4.47891	−	7.72372i	0.146398	−	0.252458i
$937$	1.03609	+	1.55062i	0.0338477	+	0.0506567i	0.848008	−	0.529984i	$-0.177802\pi$
$937$	1.03609	+	1.55062i	0.0338477	+	0.0506567i	−0.814160	+	0.580641i	$0.802802\pi$
$938$	−8.72798	−	56.9468i	−0.284979	−	1.85938i
$939$	−9.85201	+	0.970338i	−0.321508	+	0.0316658i
$940$	1.37105	+	6.56149i	0.0447186	+	0.214012i
$941$	8.95429	+	29.5183i	0.291902	+	0.962270i	0.973141	+	0.230210i	$0.0739412\pi$
$941$	8.95429	+	29.5183i	0.291902	+	0.962270i	−0.681239	+	0.732061i	$0.738559\pi$
$942$	4.07964	−	3.05626i	0.132922	−	0.0995783i
$943$	4.42779	+	1.83405i	0.144189	+	0.0597250i
$944$	26.1201	−	22.2926i	0.850136	−	0.725563i
$945$	−12.4704	+	5.16542i	−0.405663	+	0.168031i
$946$	−17.2074	+	29.0251i	−0.559460	+	0.943687i
$947$	−1.17836	+	2.20455i	−0.0382915	+	0.0716383i	−0.900339	−	0.435189i	$-0.856682\pi$
$947$	−1.17836	+	2.20455i	−0.0382915	+	0.0716383i	0.862048	+	0.506827i	$0.169182\pi$
$948$	9.27878	−	3.94861i	0.301361	−	0.128245i
$949$	−11.3018	+	13.7713i	−0.366872	+	0.447035i
$950$	−43.6518	−	10.7109i	−1.41625	−	0.347507i
$951$	0.447792	−	2.25120i	0.0145206	−	0.0730002i
$952$	2.40547	−	69.4395i	0.0779619	−	2.25055i
$953$	28.7819	−	5.72508i	0.932337	−	0.185453i	0.294524	−	0.955644i	$-0.404839\pi$
$953$	28.7819	−	5.72508i	0.932337	−	0.185453i	0.637813	+	0.770191i	$0.279839\pi$
$954$	0.220073	+	0.240474i	0.00712513	+	0.00778563i
$955$	−8.33512	+	4.45522i	−0.269718	+	0.144167i
$956$	−9.45175	+	32.2750i	−0.305691	+	1.04385i
$957$	2.49068	−	25.2883i	0.0805122	−	0.817454i
$958$	31.3458	−	34.9216i	1.01274	−	1.12827i
$959$		−	77.2668i		−	2.49507i
$960$	15.7423	+	18.0891i	0.508081	+	0.583822i
$961$			30.4981i			0.983811i
$962$	−14.3380	−	12.8699i	−0.462276	−	0.414942i
$963$	−1.06427	+	10.8058i	−0.0342957	+	0.348210i
$964$	25.8160	+	47.1982i	0.831477	+	1.52015i
$965$	2.55823	−	1.36740i	0.0823524	−	0.0440183i
$966$	8.99825	−	8.23488i	0.289514	−	0.264953i
$967$	−11.1275	+	2.21340i	−0.357837	+	0.0711782i	−0.370735	−	0.928739i	$-0.620894\pi$
$967$	−11.1275	+	2.21340i	−0.357837	+	0.0711782i	0.0128981	+	0.999917i	$0.495894\pi$
$968$	−15.0019	+	5.61376i	−0.482180	+	0.180433i
$969$	8.48813	−	42.6727i	0.272678	−	1.37084i
$970$	14.1766	−	57.7764i	0.455184	−	1.85509i
$971$	15.9721	−	19.4620i	0.512568	−	0.624566i	−0.450840	−	0.892605i	$-0.648876\pi$
$971$	15.9721	−	19.4620i	0.512568	−	0.624566i	0.963408	+	0.268039i	$0.0863755\pi$
$972$	1.85505	+	0.747519i	0.0595008	+	0.0239767i
$973$	39.0041	−	72.9715i	1.25041	−	2.33936i
$974$	−33.9331	−	20.1170i	−1.08729	−	0.644591i
$975$	−11.6215	+	4.81379i	−0.372187	+	0.154165i
$976$	−4.71172	−	39.9305i	−0.150818	−	1.27815i
$977$	15.2337	+	6.31001i	0.487370	+	0.201875i	0.612816	−	0.790225i	$-0.290036\pi$
$977$	15.2337	+	6.31001i	0.487370	+	0.201875i	−0.125447	+	0.992100i	$0.540036\pi$
$978$	10.5942	+	14.1416i	0.338765	+	0.452200i
$979$	2.81235	+	9.27107i	0.0898831	+	0.296305i
$980$	66.6077	+	43.5830i	2.12771	+	1.39221i
$981$	−15.8414	+	1.56024i	−0.505776	+	0.0498146i
$982$	9.20408	−	1.41067i	0.293714	−	0.0450162i
$983$	13.1258	+	19.6441i	0.418647	+	0.626549i	0.979519	−	0.201353i	$-0.0645340\pi$
$983$	13.1258	+	19.6441i	0.418647	+	0.626549i	−0.560872	+	0.827903i	$0.689534\pi$
$984$	5.62297	−	4.29769i	0.179254	−	0.137005i
$985$	−6.19224	−	4.13753i	−0.197301	−	0.131833i
$986$	16.3968	+	45.1389i	0.522180	+	1.43751i
$987$	1.46160	−	4.81825i	0.0465233	−	0.153367i
$988$	−50.1555	−	4.45215i	−1.59566	−	0.141642i
$989$	8.65402	−	7.10217i	0.275182	−	0.225836i
$990$	−16.3205	−	5.75100i	−0.518701	−	0.182779i
$991$	38.0145	+	38.0145i	1.20757	+	1.20757i	0.971811	+	0.235760i	$0.0757579\pi$
$991$	38.0145	+	38.0145i	1.20757	+	1.20757i	0.235760	+	0.971811i	$0.424242\pi$
$992$	3.48598	+	1.97683i	0.110680	+	0.0627643i
$993$	13.8073	−	13.8073i	0.438161	−	0.438161i
$994$	−20.1977	+	9.67222i	−0.640633	+	0.306784i
$995$	−38.8581	−	47.3487i	−1.23188	−	1.50105i
$996$	−6.20059	−	19.7531i	−0.196473	−	0.625901i
$997$	48.7272	+	14.7812i	1.54321	+	0.468127i	0.943300	−	0.331943i	$-0.107704\pi$
$997$	48.7272	+	14.7812i	1.54321	+	0.468127i	0.599907	+	0.800069i	$0.295204\pi$
$998$	−20.9879	+	44.9343i	−0.664360	+	1.42237i
$999$	2.39776	−	3.58851i	0.0758619	−	0.113535i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	384.2.v.a.349.17	✓	512
128.117	even	32	inner	384.2.v.a.373.17	yes	512

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
384.2.v.a.349.17	✓	512	1.1	even	1	trivial
384.2.v.a.373.17	yes	512	128.117	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)

\(f(q)\)	\(=\)	\(q+(-0.0761996 - 1.41216i) q^{2} +(-0.995185 - 0.0980171i) q^{3} +(-1.98839 + 0.215212i) q^{4} +(1.41300 + 2.64355i) q^{5} +(-0.0625831 + 1.41283i) q^{6} +(-0.878507 - 4.41655i) q^{7} +(0.455428 + 2.79152i) q^{8} +(0.980785 + 0.195090i) q^{9} +O(q^{10})\)	\(q+(-0.0761996 - 1.41216i) q^{2} +(-0.995185 - 0.0980171i) q^{3} +(-1.98839 + 0.215212i) q^{4} +(1.41300 + 2.64355i) q^{5} +(-0.0625831 + 1.41283i) q^{6} +(-0.878507 - 4.41655i) q^{7} +(0.455428 + 2.79152i) q^{8} +(0.980785 + 0.195090i) q^{9} +(3.62544 - 2.19682i) q^{10} +(-3.15547 - 2.58963i) q^{11} +(1.99991 - 0.0192796i) q^{12} +(-2.78393 - 1.48804i) q^{13} +(-6.16993 + 1.57713i) q^{14} +(-1.14709 - 2.76931i) q^{15} +(3.90737 - 0.855849i) q^{16} +(2.08762 - 5.03997i) q^{17} +(0.200763 - 1.39989i) q^{18} +(-7.63218 + 2.31520i) q^{19} +(-3.37852 - 4.95230i) q^{20} +(0.441379 + 4.48139i) q^{21} +(-3.41652 + 4.65336i) q^{22} +(1.59256 - 1.06412i) q^{23} +(-0.179618 - 2.82272i) q^{24} +(-2.21390 + 3.31333i) q^{25} +(-1.88922 + 4.04475i) q^{26} +(-0.956940 - 0.290285i) q^{27} +(2.69731 + 8.59275i) q^{28} +(-3.94908 - 4.81196i) q^{29} +(-3.82331 + 1.83089i) q^{30} +(-0.500935 + 0.500935i) q^{31} +(-1.50634 - 5.45261i) q^{32} +(2.88645 + 2.88645i) q^{33} +(-7.27631 - 2.56401i) q^{34} +(10.4340 - 8.56298i) q^{35} +(-1.99217 - 0.176838i) q^{36} +(-1.25283 + 4.13002i) q^{37} +(3.85100 + 10.6014i) q^{38} +(2.62468 + 1.75375i) q^{39} +(-6.73599 + 5.14837i) q^{40} +(1.39015 + 2.08050i) q^{41} +(6.29481 - 0.964778i) q^{42} +(5.81683 - 0.572907i) q^{43} +(6.83162 + 4.47009i) q^{44} +(0.870124 + 2.86841i) q^{45} +(-1.62406 - 2.16787i) q^{46} +(-1.03302 - 0.427893i) q^{47} +(-3.97244 + 0.468739i) q^{48} +(-12.2670 + 5.08116i) q^{49} +(4.84765 + 2.87390i) q^{50} +(-2.57157 + 4.81108i) q^{51} +(5.85578 + 2.35967i) q^{52} +(-0.146227 + 0.178178i) q^{53} +(-0.337010 + 1.37347i) q^{54} +(2.38710 - 12.0008i) q^{55} +(11.9288 - 4.46379i) q^{56} +(7.82236 - 1.55596i) q^{57} +(-6.49434 + 5.94340i) q^{58} +(7.57124 - 4.04691i) q^{59} +(2.87684 + 5.25960i) q^{60} +(0.985258 - 10.0035i) q^{61} +(0.745571 + 0.669229i) q^{62} -4.50308i q^{63} +(-7.58517 + 2.54267i) q^{64} -9.46207i q^{65} +(3.85618 - 4.29607i) q^{66} +(-0.886724 + 9.00306i) q^{67} +(-3.06634 + 10.4707i) q^{68} +(-1.68920 + 0.902894i) q^{69} +(-12.8874 - 14.0820i) q^{70} +(3.44894 - 0.686036i) q^{71} +(-0.0979217 + 2.82673i) q^{72} +(1.10102 - 5.53521i) q^{73} +(5.92771 + 1.45449i) q^{74} +(2.52800 - 3.08038i) q^{75} +(14.6775 - 6.24604i) q^{76} +(-8.66512 + 16.2113i) q^{77} +(2.27658 - 3.84009i) q^{78} +(4.65820 - 1.92949i) q^{79} +(7.78360 + 9.11998i) q^{80} +(0.923880 + 0.382683i) q^{81} +(2.83207 - 2.12164i) q^{82} +(-3.00494 - 9.90597i) q^{83} +(-1.84208 - 8.81576i) q^{84} +(16.2732 - 1.60277i) q^{85} +(-1.25228 - 8.17063i) q^{86} +(3.45841 + 5.17587i) q^{87} +(5.79191 - 9.98795i) q^{88} +(-1.97339 - 1.31858i) q^{89} +(3.98435 - 1.44733i) q^{90} +(-4.12632 + 13.6026i) q^{91} +(-2.93762 + 2.45862i) q^{92} +(0.547623 - 0.449422i) q^{93} +(-0.525537 + 1.49140i) q^{94} +(-16.9046 - 16.9046i) q^{95} +(0.964633 + 5.57400i) q^{96} +(9.92335 - 9.92335i) q^{97} +(8.11015 + 16.9358i) q^{98} +(-2.58963 - 3.15547i) 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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