LMFDB - Embedded newform 384.2.v.a.373.17

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			373.17
Character	$\chi$	$=$	384.373
Dual form			384.2.v.a.349.17

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

$n$	$127$	$133$	$257$
$\chi(n)$	$1$	$e\left(\frac{21}{32}\right)$	$1$

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	−0.338541	−	0.940952i	$-0.609934\pi$
$5$	1.41300	−	2.64355i	0.631915	−	1.18223i	0.970456	−	0.241278i	$-0.0775665\pi$
$6$	−0.0625831	−	1.41283i	−0.0255495	−	0.576785i
$7$	−0.878507	+	4.41655i	−0.332044	+	1.66930i	0.349050	+	0.937104i	$0.386504\pi$
$7$	−0.878507	+	4.41655i	−0.332044	+	1.66930i	−0.681094	+	0.732196i	$0.738496\pi$
$8$	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	−0.975747	−	0.218902i	$-0.929753\pi$
$11$	−3.15547	+	2.58963i	−0.951410	+	0.780802i	0.0243368	+	0.999704i	$0.492253\pi$
$12$	1.99991	+	0.0192796i	0.577323	+	0.00556554i
$13$	−2.78393	+	1.48804i	−0.772124	+	0.412709i	−0.809893	−	0.586577i	$-0.800475\pi$
$13$	−2.78393	+	1.48804i	−0.772124	+	0.412709i	0.0377687	+	0.999287i	$0.487975\pi$
$14$	−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	0.945985	+	0.324209i	$0.105098\pi$
$17$	2.08762	+	5.03997i	0.506323	+	1.22237i	−0.439662	+	0.898163i	$0.644902\pi$
$18$	0.200763	+	1.39989i	0.0473203	+	0.329957i
$19$	−7.63218	−	2.31520i	−1.75094	−	0.531143i	−0.758266	−	0.651946i	$-0.773953\pi$
$19$	−7.63218	−	2.31520i	−1.75094	−	0.531143i	−0.992676	+	0.120803i	$0.961453\pi$
$20$	−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	0.710417	−	0.703781i	$-0.248506\pi$
$23$	1.59256	+	1.06412i	0.332072	+	0.221884i	−0.378344	+	0.925665i	$0.623506\pi$
$24$	−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	−0.997482	−	0.0709204i	$-0.977406\pi$
$29$	−3.94908	+	4.81196i	−0.733325	+	0.893559i	0.264157	+	0.964480i	$0.414906\pi$
$30$	−3.82331	−	1.83089i	−0.698037	−	0.334273i
$31$	−0.500935	−	0.500935i	−0.0899705	−	0.0899705i	0.660689	−	0.750660i	$-0.270264\pi$
$31$	−0.500935	−	0.500935i	−0.0899705	−	0.0899705i	−0.750660	+	0.660689i	$0.770264\pi$
$32$	−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	−0.997680	−	0.0680820i	$-0.978312\pi$
$37$	−1.25283	−	4.13002i	−0.205964	−	0.678971i	0.791716	−	0.610889i	$-0.209188\pi$
$38$	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	−0.706892	−	0.707322i	$-0.749903\pi$
$41$	1.39015	−	2.08050i	0.217104	−	0.324920i	0.923996	+	0.382402i	$0.124903\pi$
$42$	6.29481	+	0.964778i	0.971310	+	0.148868i
$43$	5.81683	+	0.572907i	0.887058	+	0.0873675i	0.531273	−	0.847201i	$-0.321714\pi$
$43$	5.81683	+	0.572907i	0.887058	+	0.0873675i	0.355784	+	0.934568i	$0.384214\pi$
$44$	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	−0.456750	−	0.889595i	$-0.650987\pi$
$47$	−1.03302	+	0.427893i	−0.150682	+	0.0624146i	0.306068	+	0.952010i	$0.400987\pi$
$48$	−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	0.762871	−	0.646551i	$-0.223789\pi$
$53$	−0.146227	−	0.178178i	−0.0200859	−	0.0244747i	−0.782957	+	0.622076i	$0.786289\pi$
$54$	−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	0.883766	−	0.467929i	$-0.155000\pi$
$59$	7.57124	+	4.04691i	0.985692	+	0.526863i	0.101926	+	0.994792i	$0.467500\pi$
$60$	2.87684	−	5.25960i	0.371399	−	0.679012i
$61$	0.985258	+	10.0035i	0.126149	+	1.28082i	0.824829	+	0.565382i	$0.191271\pi$
$61$	0.985258	+	10.0035i	0.126149	+	1.28082i	−0.698680	+	0.715434i	$0.746229\pi$
$62$	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	−0.883592	−	0.468258i	$-0.844882\pi$
$67$	−0.886724	−	9.00306i	−0.108331	−	1.09990i	0.775261	−	0.631641i	$-0.217618\pi$
$68$	−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	0.395452	−	0.918486i	$-0.370588\pi$
$71$	3.44894	+	0.686036i	0.409313	+	0.0814175i	0.0138609	+	0.999904i	$0.495588\pi$
$72$	−0.0979217	−	2.82673i	−0.0115402	−	0.333134i
$73$	1.10102	+	5.53521i	0.128865	+	0.647847i	0.990183	+	0.139781i	$0.0446397\pi$
$73$	1.10102	+	5.53521i	0.128865	+	0.647847i	−0.861318	+	0.508067i	$0.830360\pi$
$74$	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	0.629012	−	0.777396i	$-0.283460\pi$
$79$	4.65820	+	1.92949i	0.524089	+	0.217085i	−0.104923	+	0.994480i	$0.533460\pi$
$80$	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	0.622589	+	0.782549i	$0.286081\pi$
$83$	−3.00494	+	9.90597i	−0.329836	+	1.08732i	−0.952425	+	0.304773i	$0.901419\pi$
$84$	−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	−0.655747	−	0.754981i	$-0.727646\pi$
$89$	−1.97339	+	1.31858i	−0.209179	+	0.139769i	0.446568	+	0.894750i	$0.352646\pi$
$90$	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	0.999971	+	0.00759281i	$0.00241689\pi$
$97$	9.92335	+	9.92335i	1.00756	+	1.00756i	0.00759281	+	0.999971i	$0.497583\pi$
$98$	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	−0.151208	−	0.988502i	$-0.548316\pi$
$101$	2.73607	−	0.829978i	0.272249	−	0.0825859i	0.423457	+	0.905916i	$0.360816\pi$
$102$	6.98996	−	3.26487i	0.692109	−	0.323270i
$103$	−3.25873	−	4.87703i	−0.321092	−	0.480548i	0.635450	−	0.772142i	$-0.280815\pi$
$103$	−3.25873	−	4.87703i	−0.321092	−	0.480548i	−0.956542	+	0.291593i	$0.905815\pi$
$104$	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	−0.795657	−	0.605748i	$-0.792874\pi$
$107$	1.06427	−	10.8058i	0.102887	−	1.04463i	0.898544	−	0.438884i	$-0.144626\pi$
$108$	1.96524	−	0.371253i	0.189105	−	0.0357239i
$109$	−15.2326	−	4.62076i	−1.45902	−	0.442588i	−0.541642	−	0.840610i	$-0.682197\pi$
$109$	−15.2326	−	4.62076i	−1.45902	−	0.442588i	−0.917376	+	0.398021i	$0.869697\pi$
$110$	−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	−0.571851	−	0.820358i	$-0.693774\pi$
$113$	4.38588	−	10.5885i	0.412589	−	0.996078i	0.984440	−	0.175721i	$-0.0562256\pi$
$114$	−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	0.981800	−	0.189917i	$-0.0608220\pi$
$131$	22.6826	−	2.23404i	1.98179	−	0.195189i	0.999986	−	0.00527160i	$-0.00167801\pi$
$132$	−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	0.586188	−	0.810175i	$-0.300628\pi$
$137$	16.8290	−	3.34749i	1.43780	−	0.285995i	0.851607	+	0.524180i	$0.175628\pi$
$138$	1.40375	−	2.31661i	0.119495	−	0.197203i
$139$	14.2036	−	11.6566i	1.20474	−	0.988701i	0.204784	−	0.978807i	$-0.434351\pi$
$139$	14.2036	−	11.6566i	1.20474	−	0.988701i	0.999951	−	0.00989378i	$-0.00314934\pi$
$140$	−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	0.972715	+	0.232005i	$0.0745286\pi$
$149$	−0.324346	+	3.29314i	−0.0265715	+	0.269785i	−0.999286	+	0.0377798i	$0.987971\pi$
$150$	−4.54262	+	3.33522i	−0.370903	+	0.272319i
$151$	−17.4746	−	11.6762i	−1.42207	−	0.950194i	−0.999028	−	0.0440813i	$-0.985964\pi$
$151$	−17.4746	−	11.6762i	−1.42207	−	0.950194i	−0.423037	−	0.906112i	$-0.639036\pi$
$152$	−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	−0.856220	−	0.516612i	$-0.827193\pi$
$157$	−2.28664	+	2.78628i	−0.182494	+	0.222369i	0.673726	+	0.738982i	$0.264693\pi$
$158$	−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	0.931507	−	0.363723i	$-0.118495\pi$
$163$	9.65835	+	7.92640i	0.756500	+	0.620844i	−0.175007	+	0.984567i	$0.555995\pi$
$164$	−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	−0.483951	−	0.875095i	$-0.660799\pi$
$167$	1.80056	−	1.20309i	0.139331	−	0.0930982i	0.623282	+	0.781997i	$0.285799\pi$
$168$	−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	−0.898833	−	0.438291i	$-0.855584\pi$
$173$	1.21034	−	3.98997i	0.0920208	−	0.303352i	0.990854	+	0.134939i	$0.0430839\pi$
$174$	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	0.996252	+	0.0864980i	$0.0275676\pi$
$179$	6.88601	+	12.8828i	0.514684	+	0.962907i	−0.481568	+	0.876409i	$0.659932\pi$
$180$	−2.34746	+	5.51626i	−0.174969	+	0.411157i
$181$	6.28348	+	7.65644i	0.467047	+	0.569099i	0.952256	−	0.305299i	$-0.0987565\pi$
$181$	6.28348	+	7.65644i	0.467047	+	0.569099i	−0.485209	+	0.874398i	$0.661257\pi$
$182$	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	$-0.963611\pi$
$191$		−	3.15301i		−	0.228144i	0.993472	−	0.114072i	$-0.0363894\pi$
$192$	7.79787	+	1.78695i	0.562763	+	0.128962i
$193$			0.967727i			0.0696585i	0.999393	+	0.0348293i	$0.0110887\pi$
$193$			0.967727i			0.0696585i	−0.999393	+	0.0348293i	$0.988911\pi$
$194$	−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	0.391490	−	0.920182i	$-0.371960\pi$
$197$	−2.19116	−	1.17120i	−0.156114	−	0.0834446i	−0.547604	+	0.836738i	$0.684460\pi$
$198$	−4.25870	−	3.89741i	−0.302652	−	0.276977i
$199$	−20.0419	−	3.98659i	−1.42073	−	0.282602i	−0.575852	−	0.817554i	$-0.695330\pi$
$199$	−20.0419	−	3.98659i	−1.42073	−	0.282602i	−0.844882	+	0.534952i	$0.820330\pi$
$200$	−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	−0.980783	−	0.195103i	$-0.937496\pi$
$211$	−0.826492	+	2.72458i	−0.0568981	+	0.187568i	0.923885	+	0.382671i	$0.124996\pi$
$212$	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	−0.956110	−	0.293008i	$-0.905344\pi$
$223$	−9.90223	+	9.90223i	−0.663102	+	0.663102i	0.293008	+	0.956110i	$0.405344\pi$
$224$	−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	0.0575742	+	0.998341i	$0.481663\pi$
$227$	−14.0543	+	17.1252i	−0.932816	+	1.13664i	−0.990391	+	0.138299i	$0.955837\pi$
$228$	−15.2190	−	4.77732i	−1.00790	−	0.316386i
$229$	−24.9944	+	7.58196i	−1.65168	+	0.501030i	−0.972492	−	0.232938i	$-0.925166\pi$
$229$	−24.9944	+	7.58196i	−1.65168	+	0.501030i	−0.679184	+	0.733968i	$0.737666\pi$
$230$	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	0.00328136	−	0.999995i	$-0.498956\pi$
$233$	−14.0331	−	9.37660i	−0.919337	−	0.614282i	−0.922619	+	0.385713i	$0.873956\pi$
$234$	−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	0.983427	+	0.181305i	$0.0580320\pi$
$239$	6.43493	+	15.5353i	0.416241	+	1.00489i	−0.567186	+	0.823590i	$0.691968\pi$
$240$	−6.85221	+	9.83899i	−0.442308	+	0.635104i
$241$	−10.2936	+	24.8510i	−0.663071	+	1.60080i	0.129893	+	0.991528i	$0.458537\pi$
$241$	−10.2936	+	24.8510i	−0.663071	+	1.60080i	−0.792964	+	0.609268i	$0.791463\pi$
$242$	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	0.0375281	+	0.999296i	$0.488052\pi$
$251$	−12.8994	+	24.1332i	−0.814205	+	1.52327i	−0.851733	+	0.523975i	$0.824448\pi$
$252$	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	−0.886656	−	0.462429i	$-0.846978\pi$
$263$	1.77532	−	8.92515i	0.109471	−	0.550349i	0.996128	−	0.0879198i	$-0.0280219\pi$
$264$	−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	−0.742414	−	0.669941i	$-0.766319\pi$
$269$	−9.80533	+	5.24106i	−0.597842	+	0.319553i	0.144572	+	0.989494i	$0.453819\pi$
$270$	−4.10703	−	1.04982i	−0.249946	−	0.0638901i
$271$	−4.36059	+	10.5274i	−0.264887	+	0.639493i	−0.999228	−	0.0392873i	$-0.987491\pi$
$271$	−4.36059	+	10.5274i	−0.264887	+	0.639493i	0.734341	+	0.678781i	$0.237491\pi$
$272$	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	−0.882974	−	0.469422i	$-0.844462\pi$
$277$	1.24182	−	12.6084i	0.0746137	−	0.757565i	0.957587	−	0.288143i	$-0.0930378\pi$
$278$	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	0.828452	−	0.560061i	$-0.189222\pi$
$281$	−0.100773	−	0.150818i	−0.00601164	−	0.00899705i	−0.834463	+	0.551064i	$0.814222\pi$
$282$	0.669189	+	1.43271i	0.0398496	+	0.0853165i
$283$	5.32808	−	1.61625i	0.316721	−	0.0960763i	−0.127922	−	0.991784i	$-0.540831\pi$
$283$	5.32808	−	1.61625i	0.316721	−	0.0960763i	0.444643	+	0.895708i	$0.353331\pi$
$284$	−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	0.518449	+	0.855108i	$0.326510\pi$
$293$	9.62755	+	31.7378i	0.562447	+	1.85414i	0.0439982	+	0.999032i	$0.485990\pi$
$294$	−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	0.952629	−	0.304136i	$-0.0983678\pi$
$307$	2.98734	+	5.58892i	0.170496	+	0.318976i	−0.782132	+	0.623113i	$0.785868\pi$
$308$	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	0.937858	−	0.347018i	$-0.112806\pi$
$311$	−1.08294	−	5.44432i	−0.0614080	−	0.308719i	−0.999266	+	0.0382996i	$0.987806\pi$
$312$	−3.70028	−	8.12554i	−0.209487	−	0.460018i
$313$	9.70946	+	1.93133i	0.548811	+	0.109165i	0.461705	−	0.887034i	$-0.347238\pi$
$313$	9.70946	+	1.93133i	0.548811	+	0.109165i	0.0871063	+	0.996199i	$0.472238\pi$
$314$	−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	0.986797	−	0.161961i	$-0.0517820\pi$
$317$	−0.224979	−	2.28425i	−0.0126361	−	0.128296i	−0.999433	+	0.0336651i	$0.989282\pi$
$318$	−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	0.311840	−	0.950135i	$-0.399055\pi$
$331$	−12.3874	−	15.0941i	−0.680875	−	0.829649i	−0.992715	+	0.120486i	$0.961555\pi$
$332$	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	0.123219	−	0.992380i	$-0.460678\pi$
$337$	16.7433	−	6.93531i	0.912066	−	0.377790i	0.788847	+	0.614589i	$0.210678\pi$
$338$	−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	0.716704	+	0.697378i	$0.245650\pi$
$347$	9.46725	+	31.2094i	0.508229	+	1.67541i	−0.208475	+	0.978028i	$0.566850\pi$
$348$	−7.99056	+	9.54735i	−0.428339	+	0.511791i
$349$	26.9795	+	22.1415i	1.44418	+	1.18521i	0.948532	+	0.316680i	$0.102568\pi$
$349$	26.9795	+	22.1415i	1.44418	+	1.18521i	0.495645	+	0.868525i	$0.334932\pi$
$350$	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	−0.983599	−	0.180367i	$-0.942272\pi$
$353$	−21.8689	−	21.8689i	−1.16397	−	1.16397i	−0.180367	−	0.983599i	$-0.557728\pi$
$354$	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	0.918793	−	0.394740i	$-0.129165\pi$
$359$	3.83671	+	5.74205i	0.202494	+	0.303054i	−0.716299	+	0.697794i	$0.754165\pi$
$360$	−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	0.961939	−	0.273263i	$-0.0881028\pi$
$367$	1.69579	+	4.09401i	0.0885197	+	0.213706i	−0.873420	+	0.486968i	$0.838103\pi$
$368$	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	−0.854460	−	0.519518i	$-0.826112\pi$
$373$	−9.88104	+	8.10916i	−0.511621	+	0.419877i	0.342839	+	0.939394i	$0.388612\pi$
$374$	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	−0.217625	−	0.976033i	$-0.569831\pi$
$379$	13.9161	−	26.0352i	0.714823	−	1.33734i	0.932447	−	0.361306i	$-0.117669\pi$
$380$	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	−0.896163	−	0.443726i	$-0.853656\pi$
$389$	−0.578612	+	1.08251i	−0.0293368	+	0.0548853i	0.866826	+	0.498611i	$0.166156\pi$
$390$	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	−0.359425	−	0.933174i	$-0.617027\pi$
$397$	4.31961	−	2.30888i	0.216795	−	0.115879i	0.576220	+	0.817295i	$0.304527\pi$
$398$	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	0.750534	−	0.660832i	$-0.229796\pi$
$401$	−4.95524	−	11.9630i	−0.247453	−	0.597404i	−0.997986	+	0.0634286i	$0.979796\pi$
$402$	−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	0.737510	−	0.675336i	$-0.236001\pi$
$409$	−3.41077	−	5.10458i	−0.168652	−	0.252405i	−0.906162	+	0.422931i	$0.861001\pi$
$410$	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	0.714536	−	0.699599i	$-0.246638\pi$
$419$	3.43435	+	2.81849i	0.167779	+	0.137692i	−0.546757	+	0.837291i	$0.684138\pi$
$420$	20.7020	+	17.3263i	1.01015	+	0.845438i
$421$	−0.112416	−	0.370587i	−0.00547884	−	0.0180613i	0.954158	−	0.299302i	$-0.0967539\pi$
$421$	−0.112416	−	0.370587i	−0.00547884	−	0.0180613i	−0.959637	+	0.281241i	$0.909254\pi$
$422$	−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	−0.711375	−	0.702813i	$-0.751927\pi$
$431$	−14.8942	+	6.16938i	−0.717429	+	0.297169i	−0.00605420	+	0.999982i	$0.501927\pi$
$432$	−3.98756	+	0.315252i	−0.191851	+	0.0151676i
$433$	−8.77028	−	3.63277i	−0.421473	−	0.174580i	0.161859	−	0.986814i	$-0.448251\pi$
$433$	−8.77028	−	3.63277i	−0.421473	−	0.174580i	−0.583332	+	0.812234i	$0.698251\pi$
$434$	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	−0.999199	−	0.0400251i	$-0.987256\pi$
$439$	−1.91455	−	9.62509i	−0.0913764	−	0.459380i	0.907822	−	0.419355i	$-0.137744\pi$
$440$	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	0.565765	−	0.824567i	$-0.308581\pi$
$443$	4.09343	+	2.18799i	0.194485	+	0.103954i	−0.371280	+	0.928521i	$0.621081\pi$
$444$	−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	$0.0135672\pi$
$449$			1.80577i			0.0852195i	−0.999092	+	0.0426097i	$0.986433\pi$
$450$	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	0.995386	+	0.0959521i	$0.0305896\pi$
$457$	2.40473	+	12.0894i	0.112489	+	0.565518i	−0.882897	+	0.469566i	$0.844410\pi$
$458$	−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	0.972284	−	0.233801i	$-0.0751165\pi$
$461$	5.10393	+	9.54877i	0.237714	+	0.444731i	−0.734571	+	0.678532i	$0.762617\pi$
$462$	−22.3615	+	13.2569i	−1.04035	+	0.616766i
$463$	30.4630	+	12.6182i	1.41573	+	0.586416i	0.953785	−	0.300490i	$-0.0971501\pi$
$463$	30.4630	+	12.6182i	1.41573	+	0.586416i	0.461950	+	0.886906i	$0.347150\pi$
$464$	−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	−0.318853	−	0.947804i	$-0.603298\pi$
$467$	10.2181	−	33.6844i	0.472835	−	1.55873i	0.791688	−	0.610925i	$-0.209202\pi$
$468$	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	0.0748657	−	0.997194i	$-0.476147\pi$
$479$	23.4632	−	23.4632i	1.07206	−	1.07206i	0.997194	−	0.0748657i	$-0.0238528\pi$
$480$	−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	0.995483	+	0.0949374i	$0.0302651\pi$
$487$	15.4971	+	23.1930i	0.702239	+	1.05097i	−0.293244	+	0.956038i	$0.594735\pi$
$488$	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	−0.969577	−	0.244786i	$-0.921282\pi$
$491$	0.645371	−	6.55256i	0.0291252	−	0.295713i	0.998702	−	0.0509271i	$-0.0162176\pi$
$492$	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	−0.984319	−	0.176399i	$-0.943555\pi$
$499$	−30.9275	+	16.5311i	−1.38451	+	0.740034i	−0.400188	+	0.916433i	$0.631055\pi$
$500$	−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	0.0487638	−	0.998810i	$-0.484472\pi$
$503$	10.6765	−	2.12370i	0.476044	−	0.0946910i	0.427280	+	0.904119i	$0.359472\pi$
$504$	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	0.163463	−	0.986549i	$-0.447733\pi$
$509$	11.6472	−	1.14715i	0.516252	−	0.0508464i	0.352789	+	0.935703i	$0.385233\pi$
$510$	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	−0.306140	−	0.951986i	$-0.599038\pi$
$521$	−5.12812	+	1.02005i	−0.224667	+	0.0446891i	0.0814729	+	0.996676i	$0.474038\pi$
$522$	−7.52905	−	4.56221i	−0.329538	−	0.199683i
$523$	−21.8372	+	17.9213i	−0.954875	+	0.783646i	−0.976366	−	0.216123i	$-0.930659\pi$
$523$	−21.8372	+	17.9213i	−0.954875	+	0.783646i	0.0214912	+	0.999769i	$0.493159\pi$
$524$	−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	−0.915546	−	0.402214i	$-0.868241\pi$
$541$	−7.96509	+	9.70549i	−0.342446	+	0.417272i	0.573100	+	0.819486i	$0.305741\pi$
$542$	−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	0.405015	−	0.914310i	$-0.367266\pi$
$547$	−9.65254	−	7.92163i	−0.412713	−	0.338705i	−0.817727	+	0.575606i	$0.804766\pi$
$548$	−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	−0.842420	−	0.538821i	$-0.818870\pi$
$557$	3.71429	−	12.2444i	0.157380	−	0.518811i	0.999800	+	0.0200099i	$0.00636978\pi$
$558$	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	0.918192	−	0.396136i	$-0.129649\pi$
$563$	1.86729	+	3.49346i	0.0786971	+	0.147232i	−0.839495	+	0.543368i	$0.817149\pi$
$564$	−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	0.815406	−	0.578890i	$-0.196514\pi$
$569$	32.1360	+	6.39225i	1.34721	+	0.267977i	0.531805	+	0.846867i	$0.321514\pi$
$570$	24.9413	+	22.8254i	1.04468	+	0.956050i
$571$	−19.7859	−	10.5758i	−0.828015	−	0.442583i	0.00221956	−	0.999998i	$-0.499293\pi$
$571$	−19.7859	−	10.5758i	−0.828015	−	0.442583i	−0.830234	+	0.557414i	$0.811793\pi$
$572$	−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	$-0.920236\pi$
$577$		−	11.9129i		−	0.495941i	0.968768	−	0.247971i	$-0.0797636\pi$
$578$	−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	0.925434	−	0.378908i	$-0.123700\pi$
$587$	9.04347	+	11.0195i	0.373264	+	0.454824i	−0.552170	+	0.833731i	$0.686200\pi$
$588$	−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	−0.0461513	−	0.998934i	$-0.514696\pi$
$593$	15.2823	−	6.33013i	0.627568	−	0.259947i	0.673719	+	0.738987i	$0.264696\pi$
$594$	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	−0.503005	−	0.864283i	$-0.667772\pi$
$599$	11.9431	−	17.8741i	0.487980	−	0.730314i	0.990986	+	0.133969i	$0.0427723\pi$
$600$	9.75026	−	5.65408i	0.398053	−	0.230827i
$601$	−2.53430	+	1.69337i	−0.103376	+	0.0690739i	−0.606184	−	0.795325i	$-0.707300\pi$
$601$	−2.53430	+	1.69337i	−0.103376	+	0.0690739i	0.502808	+	0.864398i	$0.332300\pi$
$602$	−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	−0.458712	−	0.888585i	$-0.651689\pi$
$607$	10.5909	−	10.5909i	0.429873	−	0.429873i	0.888585	+	0.458712i	$0.151689\pi$
$608$	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	0.0584433	−	0.998291i	$-0.481386\pi$
$613$	16.3819	−	4.96939i	0.661658	−	0.200712i	0.603214	+	0.797579i	$0.293886\pi$
$614$	−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	0.582492	−	0.812836i	$-0.302078\pi$
$617$	1.35226	+	0.903548i	0.0544398	+	0.0363755i	−0.528053	+	0.849212i	$0.677078\pi$
$618$	−6.68647	+	4.90925i	−0.268969	+	0.197479i
$619$	−1.92749	+	19.5702i	−0.0774725	+	0.786591i	0.875436	+	0.483334i	$0.160574\pi$
$619$	−1.92749	+	19.5702i	−0.0774725	+	0.786591i	−0.952909	+	0.303257i	$0.901926\pi$
$620$	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	0.0586364	−	0.998279i	$-0.481325\pi$
$631$	12.4301	−	2.47250i	0.494834	−	0.0984287i	0.436198	+	0.899851i	$0.356325\pi$
$632$	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	0.0942873	−	0.995545i	$-0.469943\pi$
$643$	9.66078	−	0.951504i	0.380984	−	0.0375237i	0.286697	+	0.958021i	$0.407443\pi$
$644$	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	0.900259	+	0.435356i	$0.143377\pi$
$647$	−2.49466	+	12.5415i	−0.0980753	+	0.493058i	−0.998334	+	0.0577021i	$0.981623\pi$
$648$	−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	−0.581291	+	0.813696i	$0.697452\pi$
$653$	−40.3956	+	21.5919i	−1.58080	+	0.844957i	−0.999511	+	0.0312610i	$0.990048\pi$
$654$	−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	0.482373	−	0.875966i	$-0.339775\pi$
$659$	10.1860	+	3.08989i	0.396790	+	0.120365i	−0.0855823	+	0.996331i	$0.527275\pi$
$660$	4.54262	+	24.0465i	0.176821	+	0.936008i
$661$	−3.81075	+	38.6912i	−0.148221	+	1.50491i	0.577198	+	0.816604i	$0.304146\pi$
$661$	−3.81075	+	38.6912i	−0.148221	+	1.50491i	−0.725419	+	0.688308i	$0.758354\pi$
$662$	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	−0.448180	−	0.893943i	$-0.647928\pi$
$673$	11.5641	−	11.5641i	0.445764	−	0.445764i	0.893943	+	0.448180i	$0.147928\pi$
$674$	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	−0.988975	−	0.148083i	$-0.952690\pi$
$677$	−6.47730	−	21.3528i	−0.248943	−	0.820655i	0.740032	−	0.672572i	$-0.234810\pi$
$678$	−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	0.167226	−	0.985919i	$-0.446519\pi$
$683$	3.62992	+	0.357516i	0.138895	+	0.0136800i	−0.0283306	+	0.999599i	$0.509019\pi$
$684$	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	0.942406	−	0.334472i	$-0.108558\pi$
$691$	3.69934	+	6.92098i	0.140730	+	0.263286i	−0.801676	+	0.597759i	$0.796058\pi$
$692$	−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	0.982620	+	0.185626i	$0.0594312\pi$
$701$	1.45871	+	14.8105i	0.0550946	+	0.559385i	−0.927526	+	0.373759i	$0.878069\pi$
$702$	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	−0.0798618	−	0.996806i	$-0.525448\pi$
$709$	−25.3768	−	13.5642i	−0.953045	−	0.509413i	−0.873183	+	0.487393i	$0.837948\pi$
$710$	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	0.300325	−	0.953837i	$-0.402905\pi$
$719$	−4.33793	−	1.79683i	−0.161778	−	0.0670105i	−0.462103	+	0.886826i	$0.652905\pi$
$720$	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	−0.977322	−	0.211761i	$-0.932080\pi$
$727$	−10.9921	+	16.4509i	−0.407675	+	0.610129i	0.569646	+	0.821890i	$0.307080\pi$
$728$	−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	0.0154493	−	0.999881i	$-0.495082\pi$
$733$	−26.0507	−	21.3793i	−0.962205	−	0.789661i	−0.977654	+	0.210219i	$0.932582\pi$
$734$	−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	−0.602728	−	0.797947i	$-0.705920\pi$
$739$	8.08667	−	9.85364i	0.297473	−	0.362472i	0.900201	+	0.435475i	$0.143420\pi$
$740$	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	0.927053	−	0.374929i	$-0.122333\pi$
$743$	6.15748	+	9.21531i	0.225896	+	0.338077i	−0.701158	+	0.713006i	$0.747333\pi$
$744$	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	0.965782	+	0.259354i	$0.0835097\pi$
$751$	12.7776	+	30.8479i	0.466262	+	1.12566i	−0.499520	+	0.866302i	$0.666490\pi$
$752$	−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	−0.0462095	−	0.998932i	$-0.514714\pi$
$757$	25.4367	−	20.8754i	0.924513	−	0.758728i	0.970723	+	0.240203i	$0.0772142\pi$
$758$	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	−0.945614	−	0.325290i	$-0.894538\pi$
$761$	1.44835	−	7.28133i	0.0525025	−	0.263948i	0.998117	+	0.0613420i	$0.0195380\pi$
$762$	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	−0.0835357	−	0.996505i	$-0.526621\pi$
$773$	22.0042	−	41.1670i	0.791438	−	1.48068i	0.874973	−	0.484171i	$-0.160879\pi$
$774$	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	0.396412	−	0.918073i	$-0.370255\pi$
$787$	6.05853	+	1.83783i	0.215963	+	0.0655117i	−0.180449	+	0.983584i	$0.557755\pi$
$788$	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	−0.0489529	−	0.998801i	$-0.515588\pi$
$797$	26.5432	−	32.3429i	0.940207	−	1.14565i	0.989160	−	0.146844i	$-0.0469116\pi$
$798$	−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	−0.785732	−	0.618567i	$-0.787714\pi$
$809$	2.45848	−	3.67938i	0.0864356	−	0.129360i	0.872168	+	0.489207i	$0.162714\pi$
$810$	4.19015	+	0.642206i	0.147227	+	0.0225648i
$811$	−17.7169	−	1.74496i	−0.622123	−	0.0612738i	−0.217956	−	0.975959i	$-0.569939\pi$
$811$	−17.7169	−	1.74496i	−0.622123	−	0.0612738i	−0.404168	+	0.914685i	$0.632439\pi$
$812$	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	0.999993	−	0.00368821i	$-0.00117400\pi$
$821$	22.9594	+	27.9760i	0.801287	+	0.976371i	−0.198706	+	0.980059i	$0.563674\pi$
$822$	−5.78263	−	23.5669i	−0.201693	−	0.821991i
$823$	8.96315	+	45.0608i	0.312436	+	1.57072i	0.743712	+	0.668500i	$0.233063\pi$
$823$	8.96315	+	45.0608i	0.312436	+	1.57072i	−0.431276	+	0.902220i	$0.641937\pi$
$824$	−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	0.553612	−	0.832775i	$-0.313249\pi$
$827$	4.85298	+	2.59397i	0.168755	+	0.0902013i	−0.384857	+	0.922976i	$0.625749\pi$
$828$	−3.36083	−	1.83827i	−0.116797	−	0.0638844i
$829$	−0.132063	−	1.34085i	−0.00458672	−	0.0465698i	0.992619	−	0.121275i	$-0.0386984\pi$
$829$	−0.132063	−	1.34085i	−0.00458672	−	0.0465698i	−0.997206	+	0.0747054i	$0.976198\pi$
$830$	−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	−0.166442	−	0.986051i	$-0.553228\pi$
$839$	−20.2052	−	4.01906i	−0.697560	−	0.138753i	−0.531118	+	0.847298i	$0.678228\pi$
$840$	−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	−0.274531	−	0.961578i	$-0.588523\pi$
$853$	−21.3609	−	2.10386i	−0.731382	−	0.0720348i	−0.456851	+	0.889543i	$0.651023\pi$
$854$	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	−0.642263	−	0.766484i	$-0.722004\pi$
$857$	−5.26671	+	3.51910i	−0.179907	+	0.120210i	0.462356	+	0.886695i	$0.347004\pi$
$858$	−17.1281	−	6.22182i	−0.584743	−	0.212409i
$859$	7.17830	+	23.6637i	0.244920	+	0.807394i	0.990080	+	0.140508i	$0.0448735\pi$
$859$	7.17830	+	23.6637i	0.244920	+	0.807394i	−0.745159	+	0.666887i	$0.767627\pi$
$860$	−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	−0.948213	−	0.317634i	$-0.897112\pi$
$863$	−18.5244	+	18.5244i	−0.630579	+	0.630579i	0.317634	+	0.948213i	$0.397112\pi$
$864$	−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	0.565276	−	0.824902i	$-0.308770\pi$
$877$	17.0872	+	5.18335i	0.576994	+	0.175029i	0.0117185	+	0.999931i	$0.496270\pi$
$878$	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	−0.998094	−	0.0617176i	$-0.980342\pi$
$881$	−7.38164	+	17.8209i	−0.248694	+	0.600400i	0.749400	+	0.662118i	$0.230342\pi$
$882$	4.65031	−	18.1926i	0.156584	−	0.612576i
$883$	12.5319	−	6.69845i	0.421733	−	0.225421i	−0.246858	−	0.969052i	$-0.579398\pi$
$883$	12.5319	−	6.69845i	0.421733	−	0.225421i	0.668590	+	0.743631i	$0.266898\pi$
$884$	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	0.347879	−	0.937540i	$-0.386902\pi$
$887$	30.6182	−	6.09033i	1.02806	−	0.204493i	0.680179	+	0.733046i	$0.261902\pi$
$888$	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	0.304491	−	0.952515i	$-0.401514\pi$
$907$	39.0944	−	32.0839i	1.29811	−	1.06533i	0.993616	−	0.112814i	$-0.0359863\pi$
$908$	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	−0.807840	−	0.589402i	$-0.799363\pi$
$911$	5.43772	−	13.1278i	0.180160	−	0.434944i	0.987999	+	0.154458i	$0.0493632\pi$
$912$	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	0.452091	−	0.891972i	$-0.350678\pi$
$919$	−6.03195	−	4.03042i	−0.198976	−	0.132951i	−0.651067	+	0.759020i	$0.725678\pi$
$920$	−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	−0.453565	−	0.891223i	$-0.649848\pi$
$929$	13.3396	−	13.3396i	0.437658	−	0.437658i	0.891223	+	0.453565i	$0.149848\pi$
$930$	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	−0.814160	−	0.580641i	$-0.802802\pi$
$937$	1.03609	−	1.55062i	0.0338477	−	0.0506567i	0.848008	+	0.529984i	$0.177802\pi$
$938$	−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	−0.681239	−	0.732061i	$-0.738559\pi$
$941$	8.95429	−	29.5183i	0.291902	−	0.962270i	0.973141	−	0.230210i	$-0.0739412\pi$
$942$	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	0.862048	−	0.506827i	$-0.169182\pi$
$947$	−1.17836	−	2.20455i	−0.0382915	−	0.0716383i	−0.900339	+	0.435189i	$0.856682\pi$
$948$	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	0.637813	−	0.770191i	$-0.279839\pi$
$953$	28.7819	+	5.72508i	0.932337	+	0.185453i	0.294524	+	0.955644i	$0.404839\pi$
$954$	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	0.0128981	−	0.999917i	$-0.495894\pi$
$967$	−11.1275	−	2.21340i	−0.357837	−	0.0711782i	−0.370735	+	0.928739i	$0.620894\pi$
$968$	−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	0.963408	−	0.268039i	$-0.0863755\pi$
$971$	15.9721	+	19.4620i	0.512568	+	0.624566i	−0.450840	+	0.892605i	$0.648876\pi$
$972$	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	−0.125447	−	0.992100i	$-0.540036\pi$
$977$	15.2337	−	6.31001i	0.487370	−	0.201875i	0.612816	+	0.790225i	$0.290036\pi$
$978$	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	−0.560872	−	0.827903i	$-0.689534\pi$
$983$	13.1258	−	19.6441i	0.418647	−	0.626549i	0.979519	+	0.201353i	$0.0645340\pi$
$984$	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	0.235760	−	0.971811i	$-0.424242\pi$
$991$	38.0145	−	38.0145i	1.20757	−	1.20757i	0.971811	−	0.235760i	$-0.0757579\pi$
$992$	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	0.599907	−	0.800069i	$-0.295204\pi$
$997$	48.7272	−	14.7812i	1.54321	−	0.468127i	0.943300	+	0.331943i	$0.107704\pi$
$998$	−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.373.17	yes	512
128.93	even	32	inner	384.2.v.a.349.17	✓	512

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
384.2.v.a.349.17	✓	512	128.93	even	32	inner
384.2.v.a.373.17	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)

\(f(q)\)	\(=\)	\(q+(-0.0761996 + 1.41216i) q^{2} +(-0.995185 + 0.0980171i) q^{3} +(-1.98839 - 0.215212i) q^{4} +(1.41300 - 2.64355i) q^{5} +(-0.0625831 - 1.41283i) q^{6} +(-0.878507 + 4.41655i) q^{7} +(0.455428 - 2.79152i) q^{8} +(0.980785 - 0.195090i) q^{9} +O(q^{10})\)	\(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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