LMFDB - Embedded newform 357.2.bl.a.10.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [357,2,Mod(10,357)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("357.10"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(357, base_ring=CyclotomicField(48)) chi = DirichletCharacter(H, H._module([0, 8, 9])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 357 = 3 \cdot 7 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	357.bl (of order $48$, degree $16$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$2.85065935216$
Analytic rank:	$0$
Dimension:	$384$
Relative dimension:	$24$ over $\Q(\zeta_{48})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{48}]$

Embedding invariants

Embedding label			10.6
Character	$\chi$	$=$	357.10
Dual form			357.2.bl.a.250.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.52158 + 0.200320i) q^{2} +(-0.442289 - 0.896873i) q^{3} +(0.343232 - 0.0919687i) q^{4} +(0.535735 - 0.469827i) q^{5} +(0.852640 + 1.27607i) q^{6} +(-0.930484 + 2.47673i) q^{7} +(2.33194 - 0.965923i) q^{8} +(-0.608761 + 0.793353i) q^{9} +(-0.721050 + 0.822199i) q^{10} +(-1.33819 + 0.0877095i) q^{11} +(-0.234292 - 0.267159i) q^{12} +(-4.27660 - 4.27660i) q^{13} +(0.919668 - 3.95495i) q^{14} +(-0.658325 - 0.272687i) q^{15} +(-3.97022 + 2.29221i) q^{16} +(3.64894 + 1.91970i) q^{17} +(0.767356 - 1.32910i) q^{18} +(1.01085 + 7.67818i) q^{19} +(0.140672 - 0.210531i) q^{20} +(2.63286 - 0.260905i) q^{21} +(2.01859 - 0.401523i) q^{22} +(4.34502 + 2.14272i) q^{23} +(-1.89770 - 1.66424i) q^{24} +(-0.586356 + 4.45382i) q^{25} +(7.36389 + 5.65051i) q^{26} +(0.980785 + 0.195090i) q^{27} +(-0.0915898 + 0.935669i) q^{28} +(0.642640 + 3.23077i) q^{29} +(1.05632 + 0.283040i) q^{30} +(-1.55853 + 0.768583i) q^{31} +(1.57686 - 1.20997i) q^{32} +(0.670530 + 1.16139i) q^{33} +(-5.93671 - 2.19003i) q^{34} +(0.665143 + 1.76404i) q^{35} +(-0.135983 + 0.328291i) q^{36} +(-0.378313 + 5.77194i) q^{37} +(-3.07619 - 11.4805i) q^{38} +(-1.94408 + 5.72706i) q^{39} +(0.795488 - 1.61309i) q^{40} +(0.182285 - 0.916407i) q^{41} +(-3.95384 + 0.924402i) q^{42} +(1.49978 + 3.62079i) q^{43} +(-0.451243 + 0.153176i) q^{44} +(0.0466040 + 0.711040i) q^{45} +(-7.04053 - 2.38994i) q^{46} +(-1.50648 + 5.62228i) q^{47} +(3.81180 + 2.54696i) q^{48} +(-5.26840 - 4.60912i) q^{49} -6.89431i q^{50} +(0.107843 - 4.12170i) q^{51} +(-1.86118 - 1.07455i) q^{52} +(0.460735 + 0.600442i) q^{53} +(-1.53143 - 0.100375i) q^{54} +(-0.675707 + 0.675707i) q^{55} +(0.222496 + 6.67438i) q^{56} +(6.43926 - 4.30258i) q^{57} +(-1.62502 - 4.78715i) q^{58} +(7.03394 + 0.926036i) q^{59} +(-0.251037 - 0.0330496i) q^{60} +(0.387921 + 1.14278i) q^{61} +(2.21747 - 1.48167i) q^{62} +(-1.39848 - 2.24594i) q^{63} +(4.32639 - 4.32639i) q^{64} +(-4.30039 - 0.281863i) q^{65} +(-1.25292 - 1.63283i) q^{66} +(11.1135 + 6.41639i) q^{67} +(1.42898 + 0.323314i) q^{68} -4.84463i q^{69} +(-1.36544 - 2.55089i) q^{70} +(-13.0855 - 8.74348i) q^{71} +(-0.653280 + 2.43807i) q^{72} +(-14.2830 - 4.84844i) q^{73} +(-0.580601 - 8.85826i) q^{74} +(4.25385 - 1.44399i) q^{75} +(1.05311 + 2.54243i) q^{76} +(1.02793 - 3.39595i) q^{77} +(1.81082 - 9.10363i) q^{78} +(-4.02463 + 8.16115i) q^{79} +(-1.05005 + 3.09333i) q^{80} +(-0.258819 - 0.965926i) q^{81} +(-0.0937864 + 1.43090i) q^{82} +(4.50672 - 10.8802i) q^{83} +(0.879685 - 0.331691i) q^{84} +(2.85679 - 0.685920i) q^{85} +(-3.00736 - 5.20890i) q^{86} +(2.61336 - 2.00530i) q^{87} +(-3.03586 + 1.49712i) q^{88} +(-16.3601 - 4.38367i) q^{89} +(-0.213348 - 1.07257i) q^{90} +(14.5713 - 6.61269i) q^{91} +(1.68841 + 0.335846i) q^{92} +(1.37864 + 1.05787i) q^{93} +(1.16598 - 8.85653i) q^{94} +(4.14897 + 3.63855i) q^{95} +(-1.78262 - 0.879091i) q^{96} +(8.94789 - 1.77985i) q^{97} +(8.93960 + 5.95778i) q^{98} +(0.745053 - 1.11505i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 384 q - 16 q^{11} + 32 q^{14} - 64 q^{22} - 16 q^{25} - 48 q^{28} - 64 q^{30} - 64 q^{35} - 32 q^{37} - 48 q^{42} - 64 q^{44} + 32 q^{46} - 64 q^{49} + 80 q^{56} - 32 q^{58} - 288 q^{61} - 528 q^{68} + 176 q^{70}+ \cdots + 32 q^{99}+O(q^{100}) $ 384 * q - 16 * q^11 + 32 * q^14 - 64 * q^22 - 16 * q^25 - 48 * q^28 - 64 * q^30 - 64 * q^35 - 32 * q^37 - 48 * q^42 - 64 * q^44 + 32 * q^46 - 64 * q^49 + 80 * q^56 - 32 * q^58 - 288 * q^61 - 528 * q^68 + 176 * q^70 + 64 * q^71 - 48 * q^73 - 128 * q^74 + 96 * q^77 + 128 * q^78 - 480 * q^80 - 240 * q^82 + 32 * q^85 - 144 * q^87 - 96 * q^88 - 64 * q^91 + 320 * q^92 - 192 * q^94 - 64 * q^95 + 32 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/357\mathbb{Z}\right)^\times$.

$n$	$52$	$190$	$239$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{3}{16}\right)$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−1.52158	+	0.200320i	−1.07592	+	0.141648i	−0.647601	−	0.761980i	$-0.724228\pi$
$2$	−1.52158	+	0.200320i	−1.07592	+	0.141648i	−0.428320	+	0.903627i	$0.640894\pi$
$3$	−0.442289	−	0.896873i	−0.255355	−	0.517810i
$3$	−0.442289	−	0.896873i	−0.255355	−	0.517810i
$4$	0.343232	−	0.0919687i	0.171616	−	0.0459844i
$5$	0.535735	−	0.469827i	0.239588	−	0.210113i	−0.531128	−	0.847291i	$-0.678232\pi$
$5$	0.535735	−	0.469827i	0.239588	−	0.210113i	0.770717	+	0.637178i	$0.219898\pi$
$6$	0.852640	+	1.27607i	0.348089	+	0.520952i
$7$	−0.930484	+	2.47673i	−0.351690	+	0.936117i
$7$	−0.930484	+	2.47673i	−0.351690	+	0.936117i
$8$	2.33194	−	0.965923i	0.824467	−	0.341505i
$9$	−0.608761	+	0.793353i	−0.202920	+	0.264451i
$10$	−0.721050	+	0.822199i	−0.228016	+	0.260002i
$11$	−1.33819	+	0.0877095i	−0.403479	+	0.0264454i	−0.265792	−	0.964030i	$-0.585633\pi$
$11$	−1.33819	+	0.0877095i	−0.403479	+	0.0264454i	−0.137687	+	0.990476i	$0.543967\pi$
$12$	−0.234292	−	0.267159i	−0.0676342	−	0.0771221i
$13$	−4.27660	−	4.27660i	−1.18612	−	1.18612i	−0.978132	−	0.207984i	$-0.933310\pi$
$13$	−4.27660	−	4.27660i	−1.18612	−	1.18612i	−0.207984	−	0.978132i	$-0.566690\pi$
$14$	0.919668	−	3.95495i	0.245792	−	1.05700i
$15$	−0.658325	−	0.272687i	−0.169979	−	0.0704075i
$16$	−3.97022	+	2.29221i	−0.992555	+	0.573052i
$17$	3.64894	+	1.91970i	0.884998	+	0.465596i
$17$	3.64894	+	1.91970i	0.884998	+	0.465596i
$18$	0.767356	−	1.32910i	0.180868	−	0.313272i
$19$	1.01085	+	7.67818i	0.231905	+	1.76150i	0.571196	+	0.820814i	$0.306480\pi$
$19$	1.01085	+	7.67818i	0.231905	+	1.76150i	−0.339291	+	0.940682i	$0.610187\pi$
$20$	0.140672	−	0.210531i	0.0314552	−	0.0470761i
$21$	2.63286	−	0.260905i	0.574536	−	0.0569342i
$22$	2.01859	−	0.401523i	0.430366	−	0.0856050i
$23$	4.34502	+	2.14272i	0.905998	+	0.446789i	0.834724	−	0.550668i	$-0.185627\pi$
$23$	4.34502	+	2.14272i	0.905998	+	0.446789i	0.0712739	+	0.997457i	$0.477294\pi$
$24$	−1.89770	−	1.66424i	−0.387367	−	0.339712i
$25$	−0.586356	+	4.45382i	−0.117271	+	0.890764i
$26$	7.36389	+	5.65051i	1.44418	+	1.10816i
$27$	0.980785	+	0.195090i	0.188752	+	0.0375451i
$28$	−0.0915898	+	0.935669i	−0.0173088	+	0.176825i
$29$	0.642640	+	3.23077i	0.119335	+	0.599939i	0.993455	+	0.114228i	$0.0364393\pi$
$29$	0.642640	+	3.23077i	0.119335	+	0.599939i	−0.874119	+	0.485711i	$0.838561\pi$
$30$	1.05632	+	0.283040i	0.192857	+	0.0516758i
$31$	−1.55853	+	0.768583i	−0.279921	+	0.138042i	−0.576830	−	0.816864i	$-0.695711\pi$
$31$	−1.55853	+	0.768583i	−0.279921	+	0.138042i	0.296910	+	0.954906i	$0.404044\pi$
$32$	1.57686	−	1.20997i	0.278753	−	0.213895i
$33$	0.670530	+	1.16139i	0.116724	+	0.202172i
$34$	−5.93671	−	2.19003i	−1.01814	−	0.375586i
$35$	0.665143	+	1.76404i	0.112430	+	0.298177i
$36$	−0.135983	+	0.328291i	−0.0226638	+	0.0547152i
$37$	−0.378313	+	5.77194i	−0.0621942	+	0.948900i	0.846752	+	0.531987i	$0.178555\pi$
$37$	−0.378313	+	5.77194i	−0.0621942	+	0.948900i	−0.908946	+	0.416913i	$0.863112\pi$
$38$	−3.07619	−	11.4805i	−0.499023	−	1.86238i
$39$	−1.94408	+	5.72706i	−0.311301	+	0.917064i
$40$	0.795488	−	1.61309i	0.125778	−	0.255052i
$41$	0.182285	−	0.916407i	0.0284681	−	0.143119i	−0.963937	−	0.266130i	$-0.914255\pi$
$41$	0.182285	−	0.916407i	0.0284681	−	0.143119i	0.992405	+	0.123011i	$0.0392551\pi$
$42$	−3.95384	+	0.924402i	−0.610091	+	0.142638i
$43$	1.49978	+	3.62079i	0.228714	+	0.552166i	0.996021	−	0.0891145i	$-0.0284037\pi$
$43$	1.49978	+	3.62079i	0.228714	+	0.552166i	−0.767307	+	0.641280i	$0.778404\pi$
$44$	−0.451243	+	0.153176i	−0.0680274	+	0.0230922i
$45$	0.0466040	+	0.711040i	0.00694732	+	0.105996i
$46$	−7.04053	−	2.38994i	−1.03807	−	0.352377i
$47$	−1.50648	+	5.62228i	−0.219743	+	0.820093i	0.764699	+	0.644387i	$0.222887\pi$
$47$	−1.50648	+	5.62228i	−0.219743	+	0.820093i	−0.984443	+	0.175706i	$0.943779\pi$
$48$	3.81180	+	2.54696i	0.550186	+	0.367623i
$49$	−5.26840	−	4.60912i	−0.752629	−	0.658445i
$50$		−	6.89431i		−	0.975002i
$51$	0.107843	−	4.12170i	0.0151010	−	0.577153i
$52$	−1.86118	−	1.07455i	−0.258099	−	0.149014i
$53$	0.460735	+	0.600442i	0.0632868	+	0.0824770i	0.823924	−	0.566700i	$-0.191780\pi$
$53$	0.460735	+	0.600442i	0.0632868	+	0.0824770i	−0.760637	+	0.649177i	$0.775113\pi$
$54$	−1.53143	−	0.100375i	−0.208401	−	0.0136593i
$55$	−0.675707	+	0.675707i	−0.0911123	+	0.0911123i
$56$	0.222496	+	6.67438i	0.0297323	+	0.891901i
$57$	6.43926	−	4.30258i	0.852901	−	0.569890i
$58$	−1.62502	−	4.78715i	−0.213375	−	0.628583i
$59$	7.03394	+	0.926036i	0.915741	+	0.120560i	0.573644	−	0.819105i	$-0.305529\pi$
$59$	7.03394	+	0.926036i	0.915741	+	0.120560i	0.342097	+	0.939664i	$0.388863\pi$
$60$	−0.251037	−	0.0330496i	−0.0324087	−	0.00426669i
$61$	0.387921	+	1.14278i	0.0496682	+	0.146318i	0.968934	−	0.247320i	$-0.0795498\pi$
$61$	0.387921	+	1.14278i	0.0496682	+	0.146318i	−0.919266	+	0.393638i	$0.871217\pi$
$62$	2.21747	−	1.48167i	0.281619	−	0.188172i
$63$	−1.39848	−	2.24594i	−0.176192	−	0.282962i
$64$	4.32639	−	4.32639i	0.540799	−	0.540799i
$65$	−4.30039	−	0.281863i	−0.533398	−	0.0349607i
$66$	−1.25292	−	1.63283i	−0.154223	−	0.200988i
$67$	11.1135	+	6.41639i	1.35773	+	0.783886i	0.989318	−	0.145776i	$-0.0465678\pi$
$67$	11.1135	+	6.41639i	1.35773	+	0.783886i	0.368413	+	0.929662i	$0.379901\pi$
$68$	1.42898	+	0.323314i	0.173290	+	0.0392076i
$69$		−	4.84463i		−	0.583225i
$70$	−1.36544	−	2.55089i	−0.163202	−	0.304890i
$71$	−13.0855	−	8.74348i	−1.55297	−	1.03766i	−0.975164	−	0.221484i	$-0.928910\pi$
$71$	−13.0855	−	8.74348i	−1.55297	−	1.03766i	−0.577803	−	0.816176i	$-0.696090\pi$
$72$	−0.653280	+	2.43807i	−0.0769898	+	0.287330i
$73$	−14.2830	−	4.84844i	−1.67170	−	0.567467i	−0.684794	−	0.728737i	$-0.740108\pi$
$73$	−14.2830	−	4.84844i	−1.67170	−	0.567467i	−0.986910	+	0.161270i	$0.948441\pi$
$74$	−0.580601	−	8.85826i	−0.0674935	−	1.02975i
$75$	4.25385	−	1.44399i	0.491192	−	0.166737i
$76$	1.05311	+	2.54243i	0.120800	+	0.291637i
$77$	1.02793	−	3.39595i	0.117143	−	0.387004i
$78$	1.81082	−	9.10363i	0.205035	−	1.03078i
$79$	−4.02463	+	8.16115i	−0.452807	+	0.918201i	0.544056	+	0.839049i	$0.316888\pi$
$79$	−4.02463	+	8.16115i	−0.452807	+	0.918201i	−0.996863	+	0.0791522i	$0.974779\pi$
$80$	−1.05005	+	3.09333i	−0.117399	+	0.345845i
$81$	−0.258819	−	0.965926i	−0.0287577	−	0.107325i
$82$	−0.0937864	+	1.43090i	−0.0103570	+	0.158017i
$83$	4.50672	−	10.8802i	0.494676	−	1.19425i	−0.457639	−	0.889138i	$-0.651305\pi$
$83$	4.50672	−	10.8802i	0.494676	−	1.19425i	0.952315	−	0.305116i	$-0.0986954\pi$
$84$	0.879685	−	0.331691i	0.0959815	−	0.0361905i
$85$	2.85679	−	0.685920i	0.309863	−	0.0743984i
$86$	−3.00736	−	5.20890i	−0.324292	−	0.561690i
$87$	2.61336	−	2.00530i	0.280181	−	0.214991i
$88$	−3.03586	+	1.49712i	−0.323624	+	0.159594i
$89$	−16.3601	−	4.38367i	−1.73416	−	0.464668i	−0.753028	−	0.657989i	$-0.771407\pi$
$89$	−16.3601	−	4.38367i	−1.73416	−	0.464668i	−0.981136	+	0.193321i	$0.938074\pi$
$90$	−0.213348	−	1.07257i	−0.0224888	−	0.113059i
$91$	14.5713	−	6.61269i	1.52749	−	0.693198i
$92$	1.68841	+	0.335846i	0.176029	+	0.0350144i
$93$	1.37864	+	1.05787i	0.142959	+	0.109696i
$94$	1.16598	−	8.85653i	0.120262	−	0.913481i
$95$	4.14897	+	3.63855i	0.425675	+	0.373307i
$96$	−1.78262	−	0.879091i	−0.181938	−	0.0897218i
$97$	8.94789	−	1.77985i	0.908521	−	0.180716i	0.281357	−	0.959603i	$-0.409216\pi$
$97$	8.94789	−	1.77985i	0.908521	−	0.180716i	0.627164	+	0.778887i	$0.284216\pi$
$98$	8.93960	+	5.95778i	0.903036	+	0.601827i
$99$	0.745053	−	1.11505i	0.0748806	−	0.112067i
$100$	0.208356	+	1.58262i	0.0208356	+	0.158262i
$101$	−0.473922	+	0.820857i	−0.0471570	+	0.0816783i	−0.888640	−	0.458605i	$-0.848349\pi$
$101$	−0.473922	+	0.820857i	−0.0471570	+	0.0816783i	0.841483	+	0.540283i	$0.181683\pi$
$102$	0.661567	+	6.29310i	0.0655049	+	0.623110i
$103$	11.7818	−	6.80223i	1.16090	−	0.670244i	0.209377	−	0.977835i	$-0.432856\pi$
$103$	11.7818	−	6.80223i	1.16090	−	0.670244i	0.951519	+	0.307591i	$0.0995230\pi$
$104$	−14.1037	−	5.84193i	−1.38298	−	0.572848i
$105$	1.28793	−	1.37676i	0.125689	−	0.134358i
$106$	−0.821327	−	0.821327i	−0.0797743	−	0.0797743i
$107$	−0.295865	−	0.337370i	−0.0286024	−	0.0326148i	0.737362	−	0.675498i	$-0.236071\pi$
$107$	−0.295865	−	0.337370i	−0.0286024	−	0.0326148i	−0.765964	+	0.642883i	$0.777738\pi$
$108$	0.354579	−	0.0232403i	0.0341194	−	0.00223630i
$109$	0.951971	−	1.08552i	0.0911823	−	0.103974i	−0.704449	−	0.709754i	$-0.748806\pi$
$109$	0.951971	−	1.08552i	0.0911823	−	0.103974i	0.795631	+	0.605781i	$0.207139\pi$
$110$	0.892785	−	1.16350i	0.0851237	−	0.110935i
$111$	5.34401	−	2.21356i	0.507231	−	0.210102i
$112$	−1.98296	−	11.9660i	−0.187372	−	1.13068i
$113$	6.27093	+	9.38510i	0.589919	+	0.882876i	0.999569	−	0.0293667i	$-0.00934906\pi$
$113$	6.27093	+	9.38510i	0.589919	+	0.882876i	−0.409650	+	0.912243i	$0.634349\pi$
$114$	−8.93597	+	7.83664i	−0.836930	+	0.733968i
$115$	3.33449	−	0.893474i	0.310943	−	0.0833169i
$116$	0.517704	+	1.04980i	0.0480676	+	0.0974715i
$117$	5.99629	−	0.789426i	0.554357	−	0.0729825i
$118$	−10.8882			−1.00234
$119$	−8.14986	+	7.25119i	−0.747096	+	0.664716i
$120$	−1.79857			−0.164186
$121$	−9.12284	+	1.20104i	−0.829349	+	0.109186i
$122$	−0.819174	−	1.66112i	−0.0741646	−	0.150391i
$123$	−0.902523	+	0.241830i	−0.0813777	+	0.0218051i
$124$	−0.464253	+	0.407139i	−0.0416911	+	0.0365621i
$125$	3.75780	+	5.62394i	0.336107	+	0.503020i
$126$	2.57781	+	3.13724i	0.229650	+	0.279488i
$127$	−8.42470	+	3.48963i	−0.747571	+	0.309654i	−0.723750	−	0.690062i	$-0.757583\pi$
$127$	−8.42470	+	3.48963i	−0.747571	+	0.309654i	−0.0238211	+	0.999716i	$0.507583\pi$
$128$	−8.13624	+	10.6034i	−0.719149	+	0.937213i
$129$	2.58405	−	2.94655i	0.227513	−	0.259429i
$130$	6.59986	−	0.432578i	0.578846	−	0.0379396i
$131$	4.03941	+	4.60606i	0.352925	+	0.402433i	0.900876	−	0.434077i	$-0.142925\pi$
$131$	4.03941	+	4.60606i	0.352925	+	0.402433i	−0.547951	+	0.836510i	$0.684592\pi$
$132$	0.336959	+	0.336959i	0.0293285	+	0.0293285i
$133$	−19.9574	−	4.64081i	−1.73052	−	0.402409i
$134$	−18.1954	−	7.53680i	−1.57185	−	0.651080i
$135$	0.617100	−	0.356283i	0.0531115	−	0.0306640i
$136$	10.3634	+	0.952041i	0.888655	+	0.0816368i
$137$	3.44501	−	5.96693i	0.294327	−	0.509789i	−0.680501	−	0.732747i	$-0.738238\pi$
$137$	3.44501	−	5.96693i	0.294327	−	0.509789i	0.974828	+	0.222958i	$0.0715712\pi$
$138$	0.970476	+	7.37150i	0.0826124	+	0.627504i
$139$	−4.48641	+	6.71439i	−0.380533	+	0.569507i	−0.971456	−	0.237220i	$-0.923764\pi$
$139$	−4.48641	+	6.71439i	−0.380533	+	0.569507i	0.590923	+	0.806728i	$0.298764\pi$
$140$	0.390535	+	0.544302i	0.0330062	+	0.0460020i
$141$	5.70877	−	1.13554i	0.480765	−	0.0956301i
$142$	21.6622	+	10.6826i	1.81785	+	0.896465i
$143$	6.09800	+	5.34780i	0.509940	+	0.447206i
$144$	0.598386	−	4.54519i	0.0498655	−	0.378766i
$145$	1.86219	+	1.42891i	0.154646	+	0.118664i
$146$	22.7041	+	4.51612i	1.87900	+	0.373757i
$147$	−1.80364	+	6.76365i	−0.148761	+	0.557856i
$148$	0.400989	+	2.01591i	0.0329611	+	0.165706i
$149$	−18.7478	−	5.02345i	−1.53588	−	0.411537i	−0.610946	−	0.791672i	$-0.709211\pi$
$149$	−18.7478	−	5.02345i	−1.53588	−	0.411537i	−0.924931	+	0.380135i	$0.875877\pi$
$150$	−6.18332	+	3.04927i	−0.504866	+	0.248972i
$151$	1.84384	−	1.41483i	0.150049	−	0.115137i	−0.531009	−	0.847366i	$-0.678187\pi$
$151$	1.84384	−	1.41483i	0.150049	−	0.115137i	0.681058	+	0.732229i	$0.261520\pi$
$152$	9.77378	+	16.9287i	0.792758	+	1.37310i
$153$	−3.74433	+	1.72626i	−0.302711	+	0.139560i
$154$	−0.883803	+	5.37313i	−0.0712188	+	0.432979i
$155$	−0.473860	+	1.14400i	−0.0380613	+	0.0918882i
$156$	−0.140558	+	2.14450i	−0.0112537	+	0.171698i
$157$	−5.73411	−	21.4000i	−0.457632	−	1.70790i	−0.680233	−	0.732996i	$-0.738122\pi$
$157$	−5.73411	−	21.4000i	−0.457632	−	1.70790i	0.222602	−	0.974909i	$-0.428545\pi$
$158$	4.48897	−	13.2241i	0.357123	−	1.05205i
$159$	0.334742	−	0.678789i	0.0265468	−	0.0538315i
$160$	0.276305	−	1.38908i	0.0218438	−	0.109816i
$161$	−9.34992	+	8.76767i	−0.736877	+	0.690989i
$162$	0.587309	+	1.41789i	0.0461433	+	0.111400i
$163$	6.25531	−	2.12339i	0.489953	−	0.166317i	−0.0655197	−	0.997851i	$-0.520871\pi$
$163$	6.25531	−	2.12339i	0.489953	−	0.166317i	0.555473	+	0.831535i	$0.312537\pi$
$164$	−0.0217148	−	0.331305i	−0.00169564	−	0.0258705i
$165$	0.904880	+	0.307165i	0.0704448	+	0.0239128i
$166$	−4.67782	+	17.4579i	−0.363069	+	1.35499i
$167$	11.1291	+	7.43622i	0.861195	+	0.575432i	0.905863	−	0.423570i	$-0.139223\pi$
$167$	11.1291	+	7.43622i	0.861195	+	0.575432i	−0.0446687	+	0.999002i	$0.514223\pi$
$168$	5.88766	−	3.15155i	0.454243	−	0.243148i
$169$			23.5786i			1.81374i
$170$	−4.20944	+	1.61596i	−0.322849	+	0.123938i
$171$	−6.70688	−	3.87222i	−0.512888	−	0.296116i
$172$	0.847772	+	1.10484i	0.0646420	+	0.0842431i
$173$	14.3899	+	0.943164i	1.09404	+	0.0717074i	0.601722	−	0.798706i	$-0.294482\pi$
$173$	14.3899	+	0.943164i	1.09404	+	0.0717074i	0.492322	+	0.870413i	$0.336148\pi$
$174$	−3.57473	+	3.57473i	−0.271000	+	0.271000i
$175$	−10.4853	−	5.59645i	−0.792616	−	0.423052i
$176$	5.11185	−	3.41563i	0.385320	−	0.257463i
$177$	−2.28050	−	6.71813i	−0.171413	−	0.504965i
$178$	25.7713	+	3.39286i	1.93164	+	0.254305i
$179$	−8.11550	−	1.06843i	−0.606581	−	0.0798579i	−0.179022	−	0.983845i	$-0.557293\pi$
$179$	−8.11550	−	1.06843i	−0.606581	−	0.0798579i	−0.427559	+	0.903987i	$0.640627\pi$
$180$	0.0813895	+	0.239766i	0.00606641	+	0.0178711i
$181$	4.06061	−	2.71322i	0.301823	−	0.201672i	−0.395431	−	0.918496i	$-0.629405\pi$
$181$	4.06061	−	2.71322i	0.301823	−	0.201672i	0.697254	+	0.716824i	$0.254405\pi$
$182$	−20.8468	+	12.9807i	−1.54527	+	0.962191i
$183$	0.853353	−	0.853353i	0.0630817	−	0.0630817i
$184$	12.2020	+	0.799764i	0.899547	+	0.0589594i
$185$	2.50914	+	3.26997i	0.184475	+	0.240413i
$186$	−2.30963	−	1.33347i	−0.169350	−	0.0977744i
$187$	−5.05134	−	2.24887i	−0.369391	−	0.164454i
$188$			2.06829i			0.150846i
$189$	−1.39579	+	2.24761i	−0.101529	+	0.163490i
$190$	−7.04187	−	4.70523i	−0.510871	−	0.341353i
$191$	−4.14822	+	15.4814i	−0.300155	+	1.12019i	0.636882	+	0.770961i	$0.280224\pi$
$191$	−4.14822	+	15.4814i	−0.300155	+	1.12019i	−0.937037	+	0.349231i	$0.886443\pi$
$192$	−5.79374	−	1.96671i	−0.418127	−	0.141935i
$193$	0.959851	+	14.6445i	0.0690916	+	1.05413i	0.881849	+	0.471532i	$0.156299\pi$
$193$	0.959851	+	14.6445i	0.0690916	+	1.05413i	−0.812758	+	0.582602i	$0.802035\pi$
$194$	−13.2584	+	4.50062i	−0.951898	+	0.323126i
$195$	1.64922	+	3.98157i	0.118103	+	0.285126i
$196$	−2.23218	−	1.09747i	−0.159441	−	0.0783906i
$197$	2.06578	−	10.3854i	0.147181	−	0.739928i	−0.834741	−	0.550642i	$-0.814383\pi$
$197$	2.06578	−	10.3854i	0.147181	−	0.739928i	0.981922	−	0.189285i	$-0.0606171\pi$
$198$	−0.910292	+	1.84589i	−0.0646916	+	0.131182i
$199$	−1.64109	+	4.83450i	−0.116334	+	0.342708i	−0.989464	−	0.144779i	$-0.953753\pi$
$199$	−1.64109	+	4.83450i	−0.116334	+	0.342708i	0.873130	+	0.487487i	$0.162086\pi$
$200$	2.93470	+	10.9524i	0.207514	+	0.774454i
$201$	0.839304	−	12.8053i	0.0591999	−	0.903216i
$202$	0.556677	−	1.34394i	0.0391676	−	0.0945590i
$203$	−8.59971	−	1.41453i	−0.603582	−	0.0992806i
$204$	−0.342052	−	1.42462i	−0.0239484	−	0.0997430i
$205$	−0.332897	−	0.576594i	−0.0232505	−	0.0402711i
$206$	−16.5644	+	12.7103i	−1.15409	+	0.885567i
$207$	−4.34502	+	2.14272i	−0.301999	+	0.148930i
$208$	26.7819	+	7.17619i	1.85699	+	0.497579i
$209$	−2.02616	−	10.1862i	−0.140152	−	0.704593i
$210$	−1.68390	+	2.35286i	−0.116200	+	0.162363i
$211$	−1.93403	−	0.384703i	−0.133144	−	0.0264840i	0.128068	−	0.991765i	$-0.459122\pi$
$211$	−1.93403	−	0.384703i	−0.133144	−	0.0264840i	−0.261212	+	0.965281i	$0.584122\pi$
$212$	0.213361	+	0.163718i	0.0146537	+	0.0112442i
$213$	−2.05420	+	15.6032i	−0.140751	+	1.06911i
$214$	0.517765	+	0.454068i	0.0353937	+	0.0310394i
$215$	2.50463	+	1.23515i	0.170815	+	0.0842364i
$216$	2.47558	−	0.492423i	0.168442	−	0.0335052i
$217$	−0.453386	−	4.57522i	−0.0307778	−	0.310586i
$218$	−1.23105	+	1.84240i	−0.0833774	+	0.124783i
$219$	1.96879	+	14.9545i	0.133039	+	1.01053i
$220$	−0.169780	+	0.294068i	−0.0114466	+	0.0198261i
$221$	−7.39526	−	23.8149i	−0.497459	−	1.60196i
$222$	−7.68794	+	4.43863i	−0.515980	+	0.297901i
$223$	−6.41443	−	2.65694i	−0.429542	−	0.177922i	0.157429	−	0.987530i	$-0.449680\pi$
$223$	−6.41443	−	2.65694i	−0.429542	−	0.177922i	−0.586970	+	0.809608i	$0.699680\pi$
$224$	1.52953	+	5.03133i	0.102196	+	0.336170i
$225$	−3.17650	−	3.17650i	−0.211767	−	0.211767i
$226$	−11.4218	−	13.0240i	−0.759764	−	0.866344i
$227$	25.6616	−	1.68195i	1.70322	−	0.111635i	0.817523	−	0.575896i	$-0.195347\pi$
$227$	25.6616	−	1.68195i	1.70322	−	0.111635i	0.885698	+	0.464261i	$0.153680\pi$
$228$	1.81446	−	2.06899i	0.120165	−	0.137022i
$229$	5.28975	−	6.89373i	0.349556	−	0.455551i	−0.585174	−	0.810907i	$-0.698974\pi$
$229$	5.28975	−	6.89373i	0.349556	−	0.455551i	0.934731	+	0.355357i	$0.115641\pi$
$230$	−4.89472	+	2.02746i	−0.322748	+	0.133687i
$231$	−3.50037	+	0.580067i	−0.230308	+	0.0381656i
$232$	4.61928	+	6.91323i	0.303270	+	0.453876i
$233$	−11.4564	+	10.0470i	−0.750534	+	0.658201i	−0.946607	−	0.322389i	$-0.895514\pi$
$233$	−11.4564	+	10.0470i	−0.750534	+	0.658201i	0.196073	+	0.980589i	$0.437181\pi$
$234$	−8.96570	+	2.40235i	−0.586106	+	0.157047i
$235$	1.83442	+	3.71984i	0.119664	+	0.242656i
$236$	2.49944	−	0.329058i	0.162700	−	0.0214198i
$237$	9.09956			0.591080
$238$	10.9481	−	12.6659i	0.709661	−	0.821006i
$239$	−2.29895			−0.148707			−0.0743534	−	0.997232i	$-0.523689\pi$
$239$	−2.29895			−0.148707			−0.0743534	+	0.997232i	$0.523689\pi$
$240$	3.23875	−	0.426389i	0.209060	−	0.0275233i
$241$	9.90660	+	20.0886i	0.638140	+	1.29402i	0.940165	+	0.340720i	$0.110671\pi$
$241$	9.90660	+	20.0886i	0.638140	+	1.29402i	−0.302025	+	0.953300i	$0.597663\pi$
$242$	13.6406	−	3.65498i	0.876848	−	0.234951i
$243$	−0.751840	+	0.659346i	−0.0482305	+	0.0422971i
$244$	0.238247	+	0.356561i	0.0152522	+	0.0228265i
$245$	−4.98796	+	0.00597205i	−0.318669	+	0.000381540i
$246$	1.32482	−	0.548758i	0.0844674	−	0.0349875i
$247$	28.5135	−	37.1595i	1.81427	−	2.36440i
$248$	−2.89202	+	3.29772i	−0.183643	+	0.209405i
$249$	−11.7514	+	0.770228i	−0.744715	+	0.0488112i
$250$	−6.84438	−	7.80452i	−0.432877	−	0.493601i
$251$	12.4496	+	12.4496i	0.785809	+	0.785809i	0.980804	−	0.194995i	$-0.0624690\pi$
$251$	12.4496	+	12.4496i	0.785809	+	0.785809i	−0.194995	+	0.980804i	$0.562469\pi$
$252$	−0.686560	−	0.642262i	−0.0432492	−	0.0404587i
$253$	−6.00239	−	2.48627i	−0.377367	−	0.156310i
$254$	12.1198	−	6.99739i	0.760466	−	0.439055i
$255$	−1.87871	−	2.25881i	−0.117649	−	0.141452i
$256$	4.13745	−	7.16627i	0.258590	−	0.447892i
$257$	−3.11232	−	23.6404i	−0.194141	−	1.47465i	−0.759880	−	0.650063i	$-0.774742\pi$
$257$	−3.11232	−	23.6404i	−0.194141	−	1.47465i	0.565739	−	0.824584i	$-0.308591\pi$
$258$	−3.34160	+	5.00105i	−0.208039	+	0.311352i
$259$	−13.9435	−	6.30767i	−0.866408	−	0.391939i
$260$	−1.50195	+	0.298757i	−0.0931473	+	0.0185281i
$261$	−2.95436	−	1.45693i	−0.182870	−	0.0901815i
$262$	−7.06897	−	6.19932i	−0.436723	−	0.382996i
$263$	2.37646	−	18.0510i	0.146539	−	1.11307i	−0.747237	−	0.664558i	$-0.768620\pi$
$263$	2.37646	−	18.0510i	0.146539	−	1.11307i	0.893776	−	0.448514i	$-0.148047\pi$
$264$	2.68545	+	2.06062i	0.165278	+	0.126822i
$265$	0.528936	+	0.105212i	0.0324923	+	0.00646312i
$266$	31.2964	+	3.06351i	1.91891	+	0.187836i
$267$	3.30428	+	16.6117i	0.202219	+	1.01662i
$268$	4.40462	+	1.18021i	0.269055	+	0.0720930i
$269$	27.5869	−	13.6044i	1.68200	−	0.829472i	0.687336	−	0.726340i	$-0.258780\pi$
$269$	27.5869	−	13.6044i	1.68200	−	0.829472i	0.994668	−	0.103133i	$-0.0328866\pi$
$270$	−0.867598	+	0.665731i	−0.0528003	+	0.0405151i
$271$	−5.54904	−	9.61122i	−0.337080	−	0.583840i	0.646802	−	0.762658i	$-0.276106\pi$
$271$	−5.54904	−	9.61122i	−0.337080	−	0.583840i	−0.983882	+	0.178818i	$0.942773\pi$
$272$	−18.8874	+	0.742492i	−1.14522	+	0.0450202i
$273$	−12.3755	−	10.1439i	−0.748997	−	0.613936i
$274$	−4.04657	+	9.76928i	−0.244462	+	0.590184i
$275$	0.394013	−	6.01148i	0.0237599	−	0.362506i
$276$	−0.445554	−	1.66283i	−0.0268192	−	0.100091i
$277$	−6.00100	+	17.6784i	−0.360565	+	1.06219i	0.603690	+	0.797219i	$0.293696\pi$
$277$	−6.00100	+	17.6784i	−0.360565	+	1.06219i	−0.964256	+	0.264973i	$0.914637\pi$
$278$	5.48142	−	11.1152i	0.328754	−	0.666647i
$279$	0.339016	−	1.70435i	0.0202964	−	0.102037i
$280$	3.25500	+	3.47117i	0.194524	+	0.207442i
$281$	−4.11051	−	9.92364i	−0.245212	−	0.591995i	0.752573	−	0.658508i	$-0.228812\pi$
$281$	−4.11051	−	9.92364i	−0.245212	−	0.591995i	−0.997786	+	0.0665139i	$0.978812\pi$
$282$	−8.45888	+	2.87140i	−0.503719	+	0.170990i
$283$	0.0544598	+	0.830897i	0.00323730	+	0.0493917i	0.999172	−	0.0406873i	$-0.0129547\pi$
$283$	0.0544598	+	0.830897i	0.00323730	+	0.0493917i	−0.995935	+	0.0900789i	$0.971288\pi$
$284$	−5.29550	−	1.79758i	−0.314230	−	0.106667i
$285$	1.42827	−	5.33038i	0.0846035	−	0.315745i
$286$	−10.3499	−	6.91557i	−0.612001	−	0.408926i
$287$	2.10008	+	1.30417i	0.123964	+	0.0769828i
$288$			1.98759i			0.117120i
$289$	9.62950	+	14.0097i	0.566441	+	0.824102i
$290$	−3.11971	−	1.80117i	−0.183196	−	0.105768i
$291$	−5.55385	−	7.23791i	−0.325572	−	0.424294i
$292$	−5.34830	−	0.350546i	−0.312986	−	0.0205142i
$293$	2.71671	−	2.71671i	0.158712	−	0.158712i	−0.623284	−	0.781996i	$-0.714202\pi$
$293$	2.71671	−	2.71671i	0.158712	−	0.158712i	0.781996	+	0.623284i	$0.214202\pi$
$294$	1.38949	−	10.6527i	0.0810365	−	0.621281i
$295$	4.20341	−	2.80863i	0.244732	−	0.163525i
$296$	4.69304	+	13.8253i	0.272778	+	0.803577i
$297$	−1.32959	−	0.175043i	−0.0771504	−	0.0101570i
$298$	29.5326	+	3.88804i	1.71078	+	0.225228i
$299$	−9.41832	−	27.7455i	−0.544676	−	1.60456i
$300$	1.32725	−	0.886843i	0.0766291	−	0.0512019i
$301$	−10.3633	+	0.345468i	−0.597328	+	0.0199125i
$302$	−2.52213	+	2.52213i	−0.145132	+	0.145132i
$303$	0.945814	+	0.0619919i	0.0543356	+	0.00356134i
$304$	−21.6133	−	28.1670i	−1.23961	−	1.61549i
$305$	0.744731	+	0.429971i	0.0426432	+	0.0246200i
$306$	5.35151	−	3.37671i	0.305925	−	0.193034i
$307$			0.155536i			0.00887691i	0.999990	+	0.00443845i	$0.00141281\pi$
$307$			0.155536i			0.00887691i	−0.999990	+	0.00443845i	$0.998587\pi$
$308$	0.0404974	−	1.26013i	0.00230755	−	0.0718028i
$309$	−11.3117	−	7.55823i	−0.643500	−	0.429973i
$310$	0.491850	−	1.83561i	0.0279352	−	0.104256i
$311$	4.30158	+	1.46019i	0.243920	+	0.0827997i	0.440722	−	0.897643i	$-0.354722\pi$
$311$	4.30158	+	1.46019i	0.243920	+	0.0827997i	−0.196802	+	0.980443i	$0.563056\pi$
$312$	0.998425	+	15.2330i	0.0565247	+	0.862400i
$313$	−1.24849	+	0.423807i	−0.0705691	+	0.0239550i	−0.356501	−	0.934295i	$-0.616030\pi$
$313$	−1.24849	+	0.423807i	−0.0705691	+	0.0239550i	0.285932	+	0.958250i	$0.407697\pi$
$314$	13.0118	+	31.4132i	0.734296	+	1.77275i
$315$	−1.80442	−	0.546186i	−0.101668	−	0.0307741i
$316$	−0.630812	+	3.17131i	−0.0354860	+	0.178400i
$317$	3.87359	−	7.85487i	0.217563	−	0.441173i	−0.760542	−	0.649289i	$-0.775066\pi$
$317$	3.87359	−	7.85487i	0.217563	−	0.441173i	0.978104	+	0.208116i	$0.0667331\pi$
$318$	−0.373362	+	1.09989i	−0.0209371	+	0.0616787i
$319$	−1.14334	−	4.26701i	−0.0640149	−	0.238907i
$320$	0.285144	−	4.35046i	0.0159400	−	0.243198i
$321$	−0.171720	+	0.414568i	−0.00958447	+	0.0231390i
$322$	12.4703	−	15.2137i	0.694944	−	0.847826i
$323$	−11.0513	+	29.9577i	−0.614909	+	1.66689i
$324$	−0.177670	−	0.307733i	−0.00987055	−	0.0170963i
$325$	21.5548	−	16.5396i	1.19565	−	0.917452i
$326$	−9.09260	+	4.48398i	−0.503593	+	0.248344i
$327$	−1.39462	−	0.373686i	−0.0771224	−	0.0206649i
$328$	−0.460101	−	2.31308i	−0.0254048	−	0.127719i
$329$	−12.5231	−	8.96259i	−0.690421	−	0.494124i
$330$	−1.43838	−	0.286112i	−0.0791803	−	0.0157499i
$331$	3.33514	+	2.55914i	0.183316	+	0.140663i	0.696343	−	0.717709i	$-0.254809\pi$
$331$	3.33514	+	2.55914i	0.183316	+	0.140663i	−0.513027	+	0.858372i	$0.671476\pi$
$332$	0.546213	−	4.14890i	0.0299774	−	0.227701i
$333$	−4.34888	−	3.81387i	−0.238317	−	0.208999i
$334$	−18.4234	−	9.08544i	−1.00809	−	0.497133i
$335$	8.96849	−	1.78394i	0.490001	−	0.0974673i
$336$	−9.85496	+	7.07090i	−0.537632	+	0.385749i
$337$	−14.5634	+	21.7956i	−0.793316	+	1.18728i	0.185520	+	0.982640i	$0.440603\pi$
$337$	−14.5634	+	21.7956i	−0.793316	+	1.18728i	−0.978837	+	0.204642i	$0.934397\pi$
$338$	−4.72328	−	35.8768i	−0.256912	−	1.95144i
$339$	5.64368	−	9.77515i	0.306523	−	0.530913i
$340$	0.917460	−	0.498165i	0.0497562	−	0.0270168i
$341$	2.01820	−	1.16521i	0.109292	−	0.0630995i
$342$	10.9807	+	4.54837i	0.593771	+	0.245948i
$343$	16.3177	−	8.75971i	0.881073	−	0.472980i
$344$	6.99481	+	6.99481i	0.377135	+	0.377135i
$345$	−2.27614	−	2.59544i	−0.122543	−	0.139734i
$346$	−22.0843	+	1.44748i	−1.18726	+	0.0778172i
$347$	−5.76809	+	6.57725i	−0.309647	+	0.353085i	−0.885642	−	0.464368i	$-0.846281\pi$
$347$	−5.76809	+	6.57725i	−0.309647	+	0.353085i	0.575995	+	0.817453i	$0.304615\pi$
$348$	0.712563	−	0.928630i	0.0381974	−	0.0497798i
$349$	−5.12270	+	2.12189i	−0.274212	+	0.113582i	−0.515552	−	0.856858i	$-0.672413\pi$
$349$	−5.12270	+	2.12189i	−0.274212	+	0.113582i	0.241340	+	0.970441i	$0.422413\pi$
$350$	17.0754	+	6.41504i	0.912716	+	0.342898i
$351$	−3.36010	−	5.02875i	−0.179349	−	0.268415i
$352$	−2.00402	+	1.75747i	−0.106814	+	0.0936737i
$353$	−2.27925	+	0.610723i	−0.121312	+	0.0325055i	−0.318964	−	0.947767i	$-0.603335\pi$
$353$	−2.27925	+	0.610723i	−0.121312	+	0.0325055i	0.197652	+	0.980272i	$0.436668\pi$
$354$	4.81574	+	9.76535i	0.255954	+	0.519023i
$355$	−11.1183	+	1.46375i	−0.590099	+	0.0776880i
$356$	−6.01846			−0.318978
$357$	10.1080	+	4.10227i	0.534971	+	0.217115i
$358$	12.5624			0.663945
$359$	−21.3176	+	2.80652i	−1.12510	+	0.148122i	−0.670031	−	0.742334i	$-0.733719\pi$
$359$	−21.3176	+	2.80652i	−1.12510	+	0.148122i	−0.455070	+	0.890456i	$0.650386\pi$
$360$	0.795488	+	1.61309i	0.0419259	+	0.0850174i
$361$	−39.5800	+	10.6054i	−2.08316	+	0.558181i
$362$	−5.63505	+	4.94180i	−0.296171	+	0.259735i
$363$	5.11211	+	7.65082i	0.268316	+	0.401564i
$364$	4.39318	−	3.60979i	0.230265	−	0.189204i
$365$	−9.92986	+	4.11308i	−0.519753	+	0.215289i
$366$	−1.12750	+	1.46939i	−0.0589355	+	0.0768063i
$367$	−13.0845	+	14.9200i	−0.683006	+	0.778819i	−0.984638	−	0.174605i	$-0.944135\pi$
$367$	−13.0845	+	14.9200i	−0.683006	+	0.778819i	0.301633	+	0.953424i	$0.402468\pi$
$368$	−22.1622	+	1.45259i	−1.15529	+	0.0757214i
$369$	0.616066	+	0.702489i	0.0320711	+	0.0365701i
$370$	−4.47290	−	4.47290i	−0.232535	−	0.232535i
$371$	−1.91584	+	0.582416i	−0.0994654	+	0.0302375i
$372$	0.570485	+	0.236303i	0.0295783	+	0.0122517i
$373$	20.8074	−	12.0132i	1.07737	−	0.622018i	0.147181	−	0.989110i	$-0.452980\pi$
$373$	20.8074	−	12.0132i	1.07737	−	0.622018i	0.930185	+	0.367092i	$0.119647\pi$
$374$	8.13653	+	2.40996i	0.420730	+	0.124616i
$375$	3.38193	−	5.85767i	0.174642	−	0.302489i
$376$	1.91765	+	14.5660i	0.0988952	+	0.751183i
$377$	11.0684	−	16.5650i	0.570051	−	0.853142i
$378$	1.67357	−	3.69953i	0.0860791	−	0.190283i
$379$	−11.3559	+	2.25884i	−0.583315	+	0.116029i	−0.477922	−	0.878402i	$-0.658610\pi$
$379$	−11.3559	+	2.25884i	−0.583315	+	0.116029i	−0.105393	+	0.994431i	$0.533610\pi$
$380$	1.75869	+	0.867290i	0.0902189	+	0.0444911i
$381$	6.85590	+	6.01246i	0.351238	+	0.308028i
$382$	3.21063	−	24.3871i	0.164270	−	1.24775i
$383$	−2.57132	−	1.97304i	−0.131388	−	0.100818i	0.540977	−	0.841038i	$-0.318055\pi$
$383$	−2.57132	−	1.97304i	−0.131388	−	0.100818i	−0.672365	+	0.740220i	$0.734721\pi$
$384$	13.1084	+	2.60743i	0.668936	+	0.133060i
$385$	−1.04481	−	2.30228i	−0.0532485	−	0.117335i
$386$	−4.39408	−	22.0905i	−0.223653	−	1.12438i
$387$	−3.78558	−	1.01434i	−0.192432	−	0.0515619i
$388$	2.90751	−	1.43383i	0.147607	−	0.0727915i
$389$	20.9633	−	16.0857i	1.06288	−	0.815578i	0.0794473	−	0.996839i	$-0.474684\pi$
$389$	20.9633	−	16.0857i	1.06288	−	0.815578i	0.983435	+	0.181261i	$0.0580178\pi$
$390$	−3.30701	−	5.72791i	−0.167457	−	0.290044i
$391$	11.7413	+	16.1598i	0.593783	+	0.817236i
$392$	−16.7377	−	5.65933i	−0.845380	−	0.285840i
$393$	2.34447	−	5.66004i	0.118263	−	0.285511i
$394$	−1.06285	+	16.2160i	−0.0535458	+	0.816951i
$395$	1.67819	+	6.26310i	0.0844390	+	0.315131i
$396$	0.153176	−	0.451243i	0.00769739	−	0.0226758i
$397$	6.16056	−	12.4924i	0.309190	−	0.626974i	−0.685707	−	0.727878i	$-0.740507\pi$
$397$	6.16056	−	12.4924i	0.309190	−	0.626974i	0.994896	+	0.100904i	$0.0321734\pi$
$398$	1.52861	−	7.68483i	0.0766222	−	0.385206i
$399$	4.66470	+	19.9518i	0.233527	+	0.998839i
$400$	−7.88111	−	19.0267i	−0.394055	−	0.951334i
$401$	24.4098	−	8.28602i	1.21897	−	0.413784i	0.363478	−	0.931603i	$-0.381589\pi$
$401$	24.4098	−	8.28602i	1.21897	−	0.413784i	0.855490	+	0.517819i	$0.173256\pi$
$402$	1.28809	+	19.6524i	0.0642440	+	0.980175i
$403$	9.95215	+	3.37830i	0.495752	+	0.168285i
$404$	−0.0871720	+	0.325330i	−0.00433697	+	0.0161858i
$405$	−0.592477	−	0.395880i	−0.0294404	−	0.0196715i
$406$	13.3685	+	0.429629i	0.663469	+	0.0213221i
$407$		−	7.75712i		−	0.384506i
$408$	−3.72976	−	9.71573i	−0.184651	−	0.481000i
$409$	−4.33940	−	2.50536i	−0.214570	−	0.123882i	0.388864	−	0.921295i	$-0.372868\pi$
$409$	−4.33940	−	2.50536i	−0.214570	−	0.123882i	−0.603433	+	0.797413i	$0.706201\pi$
$410$	0.622033	+	0.810649i	0.0307200	+	0.0400351i
$411$	−6.87527	−	0.450629i	−0.339132	−	0.0222279i
$412$	3.41830	−	3.41830i	0.168408	−	0.168408i
$413$	−8.83851	+	16.5595i	−0.434915	+	0.814841i
$414$	6.18207	−	4.13072i	0.303832	−	0.203014i
$415$	−2.69740	−	7.94628i	−0.132410	−	0.390067i
$416$	−11.9182	−	1.56906i	−0.584337	−	0.0769294i
$417$	8.00625	+	1.05404i	0.392068	+	0.0516167i
$418$	5.12347	+	15.0932i	0.250597	+	0.738235i
$419$	−1.47653	+	0.986586i	−0.0721332	+	0.0481979i	−0.591114	−	0.806588i	$-0.701312\pi$
$419$	−1.47653	+	0.986586i	−0.0721332	+	0.0481979i	0.518981	+	0.854786i	$0.326312\pi$
$420$	0.315441	−	0.590999i	0.0153919	−	0.0288378i
$421$	9.81186	−	9.81186i	0.478201	−	0.478201i	−0.426355	−	0.904556i	$-0.640203\pi$
$421$	9.81186	−	9.81186i	0.478201	−	0.478201i	0.904556	+	0.426355i	$0.140203\pi$
$422$	3.01985	+	0.197931i	0.147004	+	0.00963515i
$423$	−3.54336	−	4.61780i	−0.172284	−	0.224525i
$424$	1.65439	+	0.955162i	0.0803443	+	0.0463868i
$425$	−10.6896	+	15.1261i	−0.518520	+	0.733723i
$426$		−	24.1530i		−	1.17022i
$427$	−3.19131	−	0.102560i	−0.154438	−	0.00496323i
$428$	−0.132578	−	0.0885857i	−0.00640840	−	0.00428195i
$429$	2.09922	−	7.83440i	0.101351	−	0.378248i
$430$	−4.05843	−	1.37765i	−0.195715	−	0.0664362i
$431$	2.29846	+	35.0677i	0.110713	+	1.68915i	0.586784	+	0.809743i	$0.300394\pi$
$431$	2.29846	+	35.0677i	0.110713	+	1.68915i	−0.476072	+	0.879406i	$0.657940\pi$
$432$	−4.34112	+	1.47361i	−0.208862	+	0.0708992i
$433$	4.98035	+	12.0236i	0.239340	+	0.577819i	0.997215	−	0.0745817i	$-0.0237621\pi$
$433$	4.98035	+	12.0236i	0.239340	+	0.577819i	−0.757875	+	0.652400i	$0.773762\pi$
$434$	1.60637	+	6.87075i	0.0771083	+	0.329807i
$435$	0.457923	−	2.30214i	0.0219557	−	0.110379i
$436$	0.226914	−	0.460135i	0.0108672	−	0.0220365i
$437$	−12.0601	+	35.5278i	−0.576911	+	1.69952i
$438$	−5.99137	−	22.3601i	−0.286279	−	1.06841i
$439$	−1.53837	+	23.4710i	−0.0734224	+	1.12021i	0.789125	+	0.614233i	$0.210534\pi$
$439$	−1.53837	+	23.4710i	−0.0734224	+	1.12021i	−0.862547	+	0.505976i	$0.831132\pi$
$440$	−0.923030	+	2.22839i	−0.0440037	+	0.106234i
$441$	6.86386	−	1.37385i	0.326850	−	0.0654215i
$442$	16.0231	+	34.7548i	0.762141	+	1.65312i
$443$	12.5544	+	21.7449i	0.596477	+	1.03313i	0.993337	+	0.115250i	$0.0367668\pi$
$443$	12.5544	+	21.7449i	0.596477	+	1.03313i	−0.396859	+	0.917880i	$0.629900\pi$
$444$	1.63066	−	1.25125i	0.0773876	−	0.0593816i
$445$	−10.8242	+	5.33792i	−0.513118	+	0.253042i
$446$	10.2923	+	2.75782i	0.487355	+	0.130586i
$447$	3.78653	+	19.0362i	0.179097	+	0.900380i
$448$	6.68968	+	14.7409i	0.316057	+	0.696444i
$449$	17.9276	+	3.56603i	0.846057	+	0.168291i	0.599039	−	0.800720i	$-0.295549\pi$
$449$	17.9276	+	3.56603i	0.846057	+	0.168291i	0.247018	+	0.969011i	$0.420549\pi$
$450$	5.46962	+	4.19699i	0.257840	+	0.197848i
$451$	−0.163554	+	1.24231i	−0.00770144	+	0.0584982i
$452$	3.01552	+	2.64454i	0.141838	+	0.124389i
$453$	−2.08443	−	1.02793i	−0.0979350	−	0.0482962i
$454$	−38.7093	+	7.69976i	−1.81672	+	0.361368i
$455$	4.69954	−	10.3886i	0.220318	−	0.487027i
$456$	10.8600	−	16.2532i	0.508568	−	0.761126i
$457$	−1.07930	−	8.19811i	−0.0504876	−	0.383492i	−0.997970	−	0.0636839i	$-0.979715\pi$
$457$	−1.07930	−	8.19811i	−0.0504876	−	0.383492i	0.947482	−	0.319808i	$-0.103618\pi$
$458$	−6.66783	+	11.5490i	−0.311567	+	0.539650i
$459$	3.20431	+	2.59469i	0.149564	+	0.121110i
$460$	1.06233	−	0.613338i	0.0495315	−	0.0285970i
$461$	−10.5964	−	4.38917i	−0.493523	−	0.204424i	0.122019	−	0.992528i	$-0.461063\pi$
$461$	−10.5964	−	4.38917i	−0.493523	−	0.204424i	−0.615543	+	0.788104i	$0.711063\pi$
$462$	5.20991	−	1.58381i	0.242387	−	0.0736857i
$463$	19.0806	+	19.0806i	0.886749	+	0.886749i	0.994209	−	0.107460i	$-0.0342718\pi$
$463$	19.0806	+	19.0806i	0.886749	+	0.886749i	−0.107460	+	0.994209i	$0.534272\pi$
$464$	−9.95701	−	11.3538i	−0.462243	−	0.527087i
$465$	1.23560	−	0.0809857i	0.0572997	−	0.00375562i
$466$	15.4192	−	17.5823i	0.714283	−	0.814483i
$467$	−6.54707	+	8.53230i	−0.302962	+	0.394828i	−0.919880	−	0.392199i	$-0.871714\pi$
$467$	−6.54707	+	8.53230i	−0.302962	+	0.394828i	0.616918	+	0.787027i	$0.288381\pi$
$468$	1.98551	−	0.822427i	0.0917805	−	0.0380167i
$469$	−26.2326	+	21.5548i	−1.21131	+	0.995310i
$470$	−3.53638	−	5.29257i	−0.163121	−	0.244128i
$471$	−16.6569	+	14.6077i	−0.767511	+	0.673089i
$472$	17.2972	−	4.63478i	0.796170	−	0.213333i
$473$	−2.32457	−	4.71376i	−0.106884	−	0.216739i
$474$	−13.8457	+	1.82283i	−0.635956	+	0.0837251i
$475$	−34.7899			−1.59627
$476$	−2.13041	+	3.23837i	−0.0976472	+	0.148431i
$477$	−0.756840			−0.0346533
$478$	3.49804	−	0.460526i	0.159997	−	0.0210640i
$479$	−13.8321	−	28.0487i	−0.632004	−	1.28158i	−0.943513	−	0.331335i	$-0.892501\pi$
$479$	−13.8321	−	28.0487i	−0.632004	−	1.28158i	0.311509	−	0.950243i	$-0.399166\pi$
$480$	−1.36803	+	0.366563i	−0.0624419	+	0.0167313i
$481$	26.3022	−	23.0664i	1.19928	−	1.05174i
$482$	−19.0978	−	28.5820i	−0.869883	−	1.30187i
$483$	11.9988	+	4.50785i	0.545966	+	0.205114i
$484$	−3.02079	+	1.25125i	−0.137309	+	0.0568751i
$485$	3.95748	−	5.15749i	0.179700	−	0.234190i
$486$	1.01191	−	1.15386i	0.0459010	−	0.0523400i
$487$	−22.7356	+	1.49017i	−1.03025	+	0.0675260i	−0.571138	−	0.820854i	$-0.693498\pi$
$487$	−22.7356	+	1.49017i	−1.03025	+	0.0675260i	−0.459109	+	0.888380i	$0.651831\pi$
$488$	2.00845	+	2.29019i	0.0909180	+	0.103672i
$489$	−4.67106	−	4.67106i	−0.211233	−	0.211233i
$490$	7.58839	−	1.00828i	0.342809	−	0.0455492i
$491$	33.9555	+	14.0648i	1.53239	+	0.634737i	0.980026	−	0.198867i	$-0.0637262\pi$
$491$	33.9555	+	14.0648i	1.53239	+	0.634737i	0.552363	+	0.833604i	$0.313726\pi$
$492$	−0.287534	+	0.166008i	−0.0129630	+	0.00748421i
$493$	−3.85715	+	13.0226i	−0.173717	+	0.586506i
$494$	−35.9418	+	62.2531i	−1.61710	+	2.80090i
$495$	−0.124730	−	0.947418i	−0.00560620	−	0.0425833i
$496$	4.42596	−	6.62392i	0.198732	−	0.297423i
$497$	33.8311	−	24.2737i	1.51753	−	1.08882i
$498$	17.7264	−	3.52601i	0.794341	−	0.158004i
$499$	4.39160	+	2.16570i	0.196595	+	0.0969499i	0.537922	−	0.842995i	$-0.319210\pi$
$499$	4.39160	+	2.16570i	0.196595	+	0.0969499i	−0.341327	+	0.939945i	$0.610876\pi$
$500$	1.80702	+	1.58472i	0.0808125	+	0.0708707i
$501$	1.74707	−	13.2703i	0.0780534	−	0.592875i
$502$	−21.4369	−	16.4491i	−0.956777	−	0.734161i
$503$	11.4269	+	2.27295i	0.509499	+	0.101346i	0.443144	−	0.896450i	$-0.353863\pi$
$503$	11.4269	+	2.27295i	0.509499	+	0.101346i	0.0663551	+	0.997796i	$0.478863\pi$
$504$	−5.43059	−	3.88659i	−0.241898	−	0.173122i
$505$	0.131764	+	0.662423i	0.00586343	+	0.0294775i
$506$	9.63117	+	2.58066i	0.428158	+	0.114725i
$507$	21.1470	−	10.4286i	0.939173	−	0.463149i
$508$	−2.57069	+	1.97256i	−0.114056	+	0.0875182i
$509$	−14.7366	−	25.5245i	−0.653187	−	1.13135i	−0.982345	−	0.187078i	$-0.940098\pi$
$509$	−14.7366	−	25.5245i	−0.653187	−	1.13135i	0.329159	−	0.944275i	$-0.393235\pi$
$510$	3.31110	+	3.06061i	0.146618	+	0.135526i
$511$	25.2984	−	30.8639i	1.11914	−	1.36534i
$512$	5.36939	−	12.9629i	0.237296	−	0.572882i
$513$	−0.506510	+	7.72785i	−0.0223630	+	0.341193i
$514$	9.47129	+	35.3474i	0.417761	+	1.55910i
$515$	3.11606	−	9.17961i	0.137310	−	0.404502i
$516$	0.615939	−	1.24900i	0.0271152	−	0.0549842i
$517$	1.52283	−	7.65580i	0.0669741	−	0.336702i
$518$	22.4798	+	6.80447i	0.987704	+	0.298971i
$519$	−5.51859	−	13.3231i	−0.242239	−	0.584817i
$520$	−10.3005	+	3.49656i	−0.451708	+	0.153334i
$521$	−1.18918	−	18.1434i	−0.0520989	−	0.794876i	−0.941345	−	0.337446i	$-0.890437\pi$
$521$	−1.18918	−	18.1434i	−0.0520989	−	0.794876i	0.889246	−	0.457429i	$-0.151230\pi$
$522$	4.78715	+	1.62502i	0.209528	+	0.0711251i
$523$	2.76761	−	10.3289i	0.121019	−	0.451649i	−0.878648	−	0.477471i	$-0.841554\pi$
$523$	2.76761	−	10.3289i	0.121019	−	0.451649i	0.999667	+	0.0258217i	$0.00822023\pi$
$524$	1.81007	+	1.20945i	0.0790731	+	0.0528350i
$525$	−0.381767	+	11.8792i	−0.0166617	+	0.518453i
$526$			27.9421i			1.21833i
$527$	−7.16244	−	0.187402i	−0.312001	−	0.00816338i
$528$	−5.32430	−	3.07399i	−0.231710	−	0.133778i
$529$	0.286378	+	0.373216i	0.0124512	+	0.0162268i
$530$	−0.825896	−	0.0541321i	−0.0358746	−	0.00235135i
$531$	−5.01667	+	5.01667i	−0.217705	+	0.217705i
$532$	−7.27682	+	0.242579i	−0.315490	+	0.0105171i
$533$	−4.69867	+	3.13955i	−0.203522	+	0.135989i
$534$	−8.35540	−	24.6142i	−0.361573	−	1.06516i
$535$	−0.317011	−	0.0417353i	−0.0137056	−	0.00180437i
$536$	32.1138	+	4.22787i	1.38711	+	0.182616i
$537$	2.63115	+	7.75112i	0.113543	+	0.334486i
$538$	−39.2505	+	26.2264i	−1.69221	+	1.13070i
$539$	7.45438	+	5.70578i	0.321083	+	0.245765i
$540$	0.179042	−	0.179042i	0.00770473	−	0.00770473i
$541$	−14.3462	−	0.940297i	−0.616789	−	0.0404265i	−0.246193	−	0.969221i	$-0.579180\pi$
$541$	−14.3462	−	0.940297i	−0.616789	−	0.0404265i	−0.370596	+	0.928794i	$0.620847\pi$
$542$	10.3686	+	13.5127i	0.445371	+	0.580419i
$543$	−4.22937	−	2.44183i	−0.181500	−	0.104789i
$544$	8.07666	−	1.38800i	0.346284	−	0.0595101i
$545$		−	1.02881i		−	0.0440694i
$546$	20.8623	+	12.9557i	0.892824	+	0.554453i
$547$	22.9790	+	15.3541i	0.982512	+	0.656493i	0.939488	−	0.342581i	$-0.111301\pi$
$547$	22.9790	+	15.3541i	0.982512	+	0.656493i	0.0430232	+	0.999074i	$0.486301\pi$
$548$	0.633666	−	2.36488i	0.0270689	−	0.101022i
$549$	−1.14278	−	0.387921i	−0.0487726	−	0.0165561i
$550$	0.604696	+	9.22588i	0.0257843	+	0.393393i
$551$	−24.1568	+	8.20013i	−1.02911	+	0.349337i
$552$	−4.67954	−	11.2974i	−0.199174	−	0.480850i
$553$	−16.4681	−	17.5618i	−0.700296	−	0.746802i
$554$	5.58968	−	28.1012i	0.237483	−	1.19391i
$555$	1.82299	−	3.69665i	0.0773814	−	0.156914i
$556$	−0.922367	+	2.71720i	−0.0391171	+	0.115235i
$557$	−3.53451	−	13.1910i	−0.149762	−	0.558920i	−0.999497	−	0.0317100i	$-0.989905\pi$
$557$	−3.53451	−	13.1910i	−0.149762	−	0.558920i	0.849735	−	0.527210i	$-0.176762\pi$
$558$	−0.174426	+	2.66122i	−0.00738403	+	0.112658i
$559$	9.07072	−	21.8987i	0.383650	−	0.926214i
$560$	−6.68431	−	5.47898i	−0.282464	−	0.231529i
$561$	0.217198	+	5.52506i	0.00917011	+	0.233268i
$562$	8.24237	+	14.2762i	0.347684	+	0.602206i
$563$	−18.2257	+	13.9851i	−0.768124	+	0.589402i	−0.916736	−	0.399494i	$-0.869186\pi$
$563$	−18.2257	+	13.9851i	−0.768124	+	0.589402i	0.148612	+	0.988896i	$0.452519\pi$
$564$	1.85500	−	0.914783i	0.0781094	−	0.0385193i
$565$	7.76893	+	2.08168i	0.326842	+	0.0875769i
$566$	−0.249310	−	1.25337i	−0.0104793	−	0.0526830i
$567$	2.63317	+	0.257753i	0.110583	+	0.0108246i
$568$	−38.9603	−	7.74968i	−1.63474	−	0.325169i
$569$	−6.41622	−	4.92334i	−0.268982	−	0.206397i	0.465459	−	0.885069i	$-0.345889\pi$
$569$	−6.41622	−	4.92334i	−0.268982	−	0.206397i	−0.734441	+	0.678672i	$0.762556\pi$
$570$	−1.10545	+	8.39673i	−0.0463022	+	0.351700i
$571$	4.92401	+	4.31824i	0.206063	+	0.180713i	0.756157	−	0.654390i	$-0.227075\pi$
$571$	4.92401	+	4.31824i	0.206063	+	0.180713i	−0.550094	+	0.835103i	$0.685408\pi$
$572$	2.58486	+	1.27471i	0.108078	+	0.0532983i
$573$	15.7195	−	3.12681i	0.656693	−	0.130624i
$574$	−3.45670	−	1.56372i	−0.144280	−	0.0652682i
$575$	−12.0910	+	18.0955i	−0.504231	+	0.754635i
$576$	0.798617	+	6.06610i	0.0332757	+	0.252754i
$577$	5.87474	−	10.1754i	0.244569	−	0.423605i	−0.717442	−	0.696619i	$-0.754687\pi$
$577$	5.87474	−	10.1754i	0.244569	−	0.423605i	0.962010	+	0.273013i	$0.0880203\pi$
$578$	−17.4585	−	19.3880i	−0.726178	−	0.806434i
$579$	12.7097	−	7.33796i	0.528198	−	0.304955i
$580$	0.770577	+	0.319184i	0.0319965	+	0.0132534i
$581$	22.7539	+	21.2858i	0.943989	+	0.883082i
$582$	9.90053	+	9.90053i	0.410390	+	0.410390i
$583$	−0.669215	−	0.763093i	−0.0277160	−	0.0316041i
$584$	−37.9905	+	2.49003i	−1.57206	+	0.103038i
$585$	2.84153	−	3.24014i	0.117483	−	0.133963i
$586$	−3.58948	+	4.67791i	−0.148280	+	0.193243i
$587$	−11.4819	+	4.75595i	−0.473908	+	0.196299i	−0.606837	−	0.794827i	$-0.707562\pi$
$587$	−11.4819	+	4.75595i	−0.473908	+	0.196299i	0.132929	+	0.991126i	$0.457562\pi$
$588$	0.00297812	+	2.48738i	0.000122816	+	0.102578i
$589$	−7.47676	−	11.1898i	−0.308075	−	0.461066i
$590$	−5.83321	+	5.11559i	−0.240149	+	0.210605i
$591$	−10.2280	+	2.74059i	−0.420725	+	0.112733i
$592$	−11.7285	−	23.7830i	−0.482038	−	0.977476i
$593$	−12.8289	+	1.68896i	−0.526821	+	0.0693573i	−0.389246	−	0.921134i	$-0.627264\pi$
$593$	−12.8289	+	1.68896i	−0.526821	+	0.0693573i	−0.137576	+	0.990491i	$0.543931\pi$
$594$	2.05814			0.0844465
$595$	−0.959360	+	7.71375i	−0.0393299	+	0.316233i
$596$	−6.89683			−0.282505
$597$	5.06177	−	0.666394i	0.207164	−	0.0272737i
$598$	19.8887	+	40.3303i	0.813310	+	1.64923i
$599$	−10.9476	+	2.93341i	−0.447308	+	0.119856i	−0.475440	−	0.879748i	$-0.657711\pi$
$599$	−10.9476	+	2.93341i	−0.447308	+	0.119856i	0.0281313	+	0.999604i	$0.491044\pi$
$600$	8.52496	−	7.47619i	0.348030	−	0.305214i
$601$	3.86067	+	5.77790i	0.157480	+	0.235685i	0.901816	−	0.432119i	$-0.142234\pi$
$601$	3.86067	+	5.77790i	0.157480	+	0.235685i	−0.744336	+	0.667805i	$0.767234\pi$
$602$	15.6993	−	2.60163i	0.639857	−	0.106034i
$603$	−11.8559	+	4.91089i	−0.482811	+	0.199987i
$604$	0.502744	−	0.655189i	0.0204564	−	0.0266593i
$605$	−4.32314	+	4.92960i	−0.175761	+	0.200417i
$606$	−1.45155	+	0.0951397i	−0.0589653	+	0.00386479i
$607$	−14.2082	−	16.2013i	−0.576692	−	0.657591i	0.387788	−	0.921749i	$-0.373239\pi$
$607$	−14.2082	−	16.2013i	−0.576692	−	0.657591i	−0.964479	+	0.264158i	$0.914906\pi$
$608$	10.8843	+	10.8843i	0.441419	+	0.441419i
$609$	2.53490	+	8.33848i	0.102719	+	0.337892i
$610$	−1.21930	−	0.505051i	−0.0493681	−	0.0204489i
$611$	30.4869	−	17.6016i	1.23337	−	0.712085i
$612$	−1.12641	+	0.936869i	−0.0455326	+	0.0378707i
$613$	−3.64545	+	6.31411i	−0.147239	+	0.255025i	−0.930206	−	0.367038i	$-0.880372\pi$
$613$	−3.64545	+	6.31411i	−0.147239	+	0.255025i	0.782967	+	0.622063i	$0.213705\pi$
$614$	−0.0311570	−	0.236661i	−0.00125739	−	0.00955085i
$615$	−0.369895	+	0.553587i	−0.0149156	+	0.0223228i
$616$	−0.883149	−	8.91206i	−0.0355831	−	0.359077i
$617$	8.35603	−	1.66212i	0.336401	−	0.0669143i	−0.0239995	−	0.999712i	$-0.507640\pi$
$617$	8.35603	−	1.66212i	0.336401	−	0.0669143i	0.360401	+	0.932798i	$0.382640\pi$
$618$	18.7257	+	9.23451i	0.753260	+	0.371466i
$619$	12.6595	+	11.1021i	0.508830	+	0.446232i	0.874863	−	0.484370i	$-0.160951\pi$
$619$	12.6595	+	11.1021i	0.508830	+	0.446232i	−0.366033	+	0.930602i	$0.619284\pi$
$620$	−0.0574317	+	0.436237i	−0.00230651	+	0.0175197i
$621$	3.84350	+	2.94922i	0.154234	+	0.118348i
$622$	−6.83771	−	1.36011i	−0.274167	−	0.0545353i
$623$	26.0799	−	36.4406i	1.04487	−	1.45996i
$624$	−5.40920	−	27.1939i	−0.216541	−	1.08863i
$625$	−17.0404	−	4.56597i	−0.681617	−	0.182639i
$626$	1.81479	−	0.894955i	0.0725336	−	0.0357696i
$627$	−8.23957	+	6.32244i	−0.329057	+	0.252494i
$628$	−3.93626	−	6.81780i	−0.157074	−	0.272060i
$629$	−12.4608	+	20.3352i	−0.496846	+	0.810817i
$630$	2.85499	+	0.469604i	0.113745	+	0.0187095i
$631$	−0.0197611	+	0.0477075i	−0.000786677	+	0.00189921i	−0.924272	−	0.381734i	$-0.875327\pi$
$631$	−0.0197611	+	0.0477075i	−0.000786677	+	0.00189921i	0.923486	+	0.383633i	$0.125327\pi$
$632$	−1.50218	+	22.9188i	−0.0597535	+	0.911663i
$633$	0.510371	+	1.90473i	0.0202854	+	0.0757062i
$634$	−4.32050	+	12.7278i	−0.171589	+	0.505485i
$635$	−2.87389	+	5.82767i	−0.114047	+	0.231264i
$636$	0.0524667	−	0.263768i	0.00208044	−	0.0104591i
$637$	2.81950	+	42.2422i	0.111713	+	1.67370i
$638$	2.59446	+	6.26357i	0.102716	+	0.247977i
$639$	14.9026	−	5.05876i	0.589539	−	0.200122i
$640$	0.622874	+	9.50322i	0.0246213	+	0.375648i
$641$	34.1866	+	11.6048i	1.35029	+	0.458361i	0.900532	−	0.434791i	$-0.143178\pi$
$641$	34.1866	+	11.6048i	1.35029	+	0.458361i	0.449756	+	0.893151i	$0.351511\pi$
$642$	0.178239	−	0.665199i	0.00703455	−	0.0262533i
$643$	−29.3910	−	19.6384i	−1.15907	−	0.774464i	−0.181149	−	0.983456i	$-0.557982\pi$
$643$	−29.3910	−	19.6384i	−1.15907	−	0.774464i	−0.977917	+	0.208992i	$0.932982\pi$
$644$	−2.40284	+	3.86924i	−0.0946852	+	0.152470i
$645$		−	2.79263i		−	0.109960i
$646$	10.8143	−	47.7969i	0.425482	−	1.88055i
$647$	−38.6095	−	22.2912i	−1.51789	−	0.876357i	−0.999778	−	0.0210468i	$-0.993300\pi$
$647$	−38.6095	−	22.2912i	−1.51789	−	0.876357i	−0.518116	−	0.855310i	$-0.673367\pi$
$648$	−1.53656	−	2.00249i	−0.0603619	−	0.0786651i
$649$	−9.49396	−	0.622267i	−0.372671	−	0.0244261i
$650$	−29.4842	+	29.4842i	−1.15647	+	1.15647i
$651$	−3.90286	+	2.43020i	−0.152965	+	0.0952469i
$652$	1.95174	−	1.30411i	0.0764359	−	0.0510728i
$653$	6.99576	+	20.6088i	0.273765	+	0.806486i	0.993662	+	0.112405i	$0.0358555\pi$
$653$	6.99576	+	20.6088i	0.273765	+	0.806486i	−0.719897	+	0.694081i	$0.755811\pi$
$654$	2.19688	+	0.289225i	0.0859047	+	0.0113096i
$655$	4.32811	+	0.569806i	0.169113	+	0.0222642i
$656$	1.37688	+	4.05617i	0.0537583	+	0.158367i
$657$	12.5415	−	8.37996i	0.489290	−	0.326933i
$658$	20.8503	+	11.1287i	0.812830	+	0.433841i
$659$	8.51953	−	8.51953i	0.331874	−	0.331874i	−0.521424	−	0.853298i	$-0.674599\pi$
$659$	8.51953	−	8.51953i	0.331874	−	0.331874i	0.853298	+	0.521424i	$0.174599\pi$
$660$	0.338833	+	0.0222083i	0.0131891	+	0.000864458i
$661$	9.32649	+	12.1545i	0.362759	+	0.472756i	0.938700	−	0.344735i	$-0.112031\pi$
$661$	9.32649	+	12.1545i	0.362759	+	0.472756i	−0.575942	+	0.817491i	$0.695364\pi$
$662$	−5.58734	−	3.22585i	−0.217158	−	0.125376i
$663$	−18.0880	+	17.1656i	−0.702482	+	0.666659i
$664$		−	29.7251i		−	1.15356i
$665$	−12.8723	+	6.89027i	−0.499165	+	0.267193i
$666$	7.38117	+	4.93194i	0.286015	+	0.191109i
$667$	−4.13037	+	15.4147i	−0.159928	+	0.596861i
$668$	4.50376	+	1.52882i	0.174256	+	0.0591518i
$669$	0.454089	+	6.92806i	0.0175561	+	0.267854i
$670$	−13.2889	+	4.51099i	−0.513397	+	0.174275i
$671$	−0.619343	−	1.49523i	−0.0239095	−	0.0577226i
$672$	3.83597	−	3.59709i	0.147976	−	0.138761i
$673$	0.603108	−	3.03203i	0.0232481	−	0.116876i	−0.967419	−	0.253182i	$-0.918523\pi$
$673$	0.603108	−	3.03203i	0.0232481	−	0.116876i	0.990667	+	0.136306i	$0.0435229\pi$
$674$	17.7932	−	36.0811i	0.685370	−	1.38979i
$675$	−1.44399	+	4.25385i	−0.0555791	+	0.163731i
$676$	2.16850	+	8.09295i	0.0834038	+	0.311267i
$677$	−2.26063	+	34.4906i	−0.0868832	+	1.32558i	0.702502	+	0.711682i	$0.252066\pi$
$677$	−2.26063	+	34.4906i	−0.0868832	+	1.32558i	−0.789385	+	0.613899i	$0.789600\pi$
$678$	−6.62917	+	16.0042i	−0.254592	+	0.614639i
$679$	−3.91766	+	23.8176i	−0.150346	+	0.914037i
$680$	5.99934	−	4.35897i	0.230064	−	0.167159i
$681$	−12.8583	−	22.2713i	−0.492733	−	0.853438i
$682$	−2.83744	+	2.17724i	−0.108651	+	0.0833710i
$683$	31.4346	−	15.5018i	1.20281	−	0.593160i	0.273290	−	0.961932i	$-0.411888\pi$
$683$	31.4346	−	15.5018i	1.20281	−	0.593160i	0.929520	+	0.368771i	$0.120221\pi$
$684$	−2.65814	−	0.712246i	−0.101636	−	0.0272334i
$685$	−0.957814	−	4.81526i	−0.0365962	−	0.183982i
$686$	−23.0740	+	16.5974i	−0.880969	+	0.633691i
$687$	−8.52239	−	1.69521i	−0.325150	−	0.0646763i
$688$	−14.2541	−	10.9375i	−0.543431	−	0.416989i
$689$	0.597469	−	4.53823i	0.0227618	−	0.172893i
$690$	3.98325	+	3.49322i	0.151640	+	0.132985i
$691$	17.8753	+	8.81512i	0.680008	+	0.335343i	0.749279	−	0.662255i	$-0.230400\pi$
$691$	17.8753	+	8.81512i	0.680008	+	0.335343i	−0.0692704	+	0.997598i	$0.522067\pi$
$692$	5.02581	−	0.999696i	0.191053	−	0.0380028i
$693$	2.06842	+	2.88283i	0.0785728	+	0.109510i
$694$	7.45907	−	11.1633i	0.283142	−	0.423752i
$695$	0.751075	+	5.70498i	0.0284899	+	0.216402i
$696$	4.15724	−	7.20055i	0.157580	−	0.272936i
$697$	2.42437	−	2.99398i	0.0918296	−	0.113405i
$698$	7.36955	−	4.25481i	0.278942	−	0.161047i
$699$	14.0779	+	5.83126i	0.532476	+	0.220559i
$700$	−4.11359	−	0.956560i	−0.155479	−	0.0361546i
$701$	17.2730	+	17.2730i	0.652392	+	0.652392i	0.953568	−	0.301176i	$-0.0973792\pi$
$701$	17.2730	+	17.2730i	0.652392	+	0.652392i	−0.301176	+	0.953568i	$0.597379\pi$
$702$	6.12003	+	6.97856i	0.230986	+	0.263389i
$703$	−44.7004	+	2.92982i	−1.68591	+	0.110500i
$704$	−5.41006	+	6.16899i	−0.203899	+	0.232503i
$705$	2.52488	−	3.29049i	0.0950924	−	0.123927i
$706$	3.34572	−	1.38584i	0.125918	−	0.0521569i
$707$	−1.59207	−	1.93757i	−0.0598758	−	0.0728698i
$708$	−1.40060	−	2.09614i	−0.0526377	−	0.0787778i
$709$	34.2354	−	30.0236i	1.28574	−	1.12756i	0.300978	−	0.953631i	$-0.402687\pi$
$709$	34.2354	−	30.0236i	1.28574	−	1.12756i	0.984758	−	0.173929i	$-0.0556464\pi$
$710$	16.6242	−	4.45444i	0.623895	−	0.167172i
$711$	−4.02463	−	8.16115i	−0.150936	−	0.306067i
$712$	−42.3850	+	5.58010i	−1.58845	+	0.209123i
$713$	−8.41871			−0.315283
$714$	−16.2019	−	4.21710i	−0.606341	−	0.157821i
$715$	5.77946			0.216139
$716$	−2.88376	+	0.379654i	−0.107771	+	0.0141884i
$717$	1.01680	+	2.06187i	0.0379731	+	0.0770018i
$718$	31.8743	−	8.54069i	1.18954	−	0.318736i
$719$	0.00837645	−	0.00734595i	0.000312389	−	0.000273958i	−0.659190	−	0.751977i	$-0.729101\pi$
$719$	0.00837645	−	0.00734595i	0.000312389	−	0.000273958i	0.659502	+	0.751703i	$0.270767\pi$
$720$	−1.81488	−	2.71616i	−0.0676366	−	0.101225i
$721$	5.88452	+	35.5097i	0.219151	+	1.32245i
$722$	58.0998	−	24.0657i	2.16225	−	0.895633i
$723$	13.6353	−	17.7699i	0.507104	−	0.660870i
$724$	1.14420	−	1.30471i	0.0425239	−	0.0484892i
$725$	−14.7661	+	0.967819i	−0.548398	+	0.0359439i
$726$	−9.31111	−	10.6173i	−0.345568	−	0.394044i
$727$	12.6217	+	12.6217i	0.468111	+	0.468111i	0.901302	−	0.433191i	$-0.142612\pi$
$727$	12.6217	+	12.6217i	0.468111	+	0.468111i	−0.433191	+	0.901302i	$0.642612\pi$
$728$	27.5921	−	29.4952i	1.02263	−	1.09316i
$729$	0.923880	+	0.382683i	0.0342178	+	0.0141735i
$730$	14.2852	−	8.24754i	0.528718	−	0.305255i
$731$	−1.47823	+	16.0912i	−0.0546742	+	0.595154i
$732$	0.214416	−	0.371380i	0.00792505	−	0.0137266i
$733$	3.56928	+	27.1113i	0.131834	+	1.00138i	0.921646	+	0.388031i	$0.126845\pi$
$733$	3.56928	+	27.1113i	0.131834	+	1.00138i	−0.789812	+	0.613349i	$0.789822\pi$
$734$	16.9204	−	25.3231i	0.624542	−	0.934693i
$735$	2.21147	+	4.47092i	0.0815714	+	0.164912i
$736$	9.44414	−	1.87856i	0.348115	−	0.0692445i
$737$	−15.4347	−	7.61157i	−0.568546	−	0.280376i
$738$	−1.07812	−	0.945484i	−0.0396861	−	0.0348038i
$739$	3.63786	−	27.6323i	0.133821	−	1.01647i	−0.784360	−	0.620306i	$-0.787008\pi$
$739$	3.63786	−	27.6323i	0.133821	−	1.01647i	0.918180	−	0.396163i	$-0.129658\pi$
$740$	1.16195	+	0.891597i	0.0427142	+	0.0327757i
$741$	−45.9386	−	9.13775i	−1.68760	−	0.335684i
$742$	2.79844	−	1.26998i	0.102734	−	0.0466223i
$743$	−9.81499	−	49.3433i	−0.360077	−	1.81023i	−0.557805	−	0.829972i	$-0.688356\pi$
$743$	−9.81499	−	49.3433i	−0.360077	−	1.81023i	0.197728	−	0.980257i	$-0.436644\pi$
$744$	4.23674	+	1.13523i	0.155326	+	0.0416196i
$745$	−12.4040	+	6.11697i	−0.454447	+	0.224109i
$746$	−29.2537	+	22.4471i	−1.07105	+	0.821848i
$747$	5.88831	+	10.1989i	0.215442	+	0.373156i
$748$	−1.94061	−	0.307320i	−0.0709557	−	0.0112367i
$749$	1.11087	−	0.418862i	0.0405904	−	0.0153049i
$750$	−3.97247	+	9.59039i	−0.145054	+	0.350192i
$751$	1.42326	−	21.7147i	0.0519353	−	0.792380i	−0.889869	−	0.456217i	$-0.849204\pi$
$751$	1.42326	−	21.7147i	0.0519353	−	0.792380i	0.941804	−	0.336163i	$-0.109129\pi$
$752$	−6.90635	−	25.7748i	−0.251849	−	0.939911i
$753$	5.65937	−	16.6720i	0.206239	−	0.607561i
$754$	−13.5232	+	27.4223i	−0.492485	+	0.998660i
$755$	0.323085	−	1.62426i	0.0117583	−	0.0591128i
$756$	−0.272370	+	0.899822i	−0.00990600	+	0.0327262i
$757$	−13.5386	−	32.6851i	−0.492069	−	1.18796i	−0.953665	−	0.300870i	$-0.902723\pi$
$757$	−13.5386	−	32.6851i	−0.492069	−	1.18796i	0.461596	−	0.887090i	$-0.347277\pi$
$758$	16.8265	−	5.71183i	0.611166	−	0.207463i
$759$	0.424920	+	6.48303i	0.0154236	+	0.235319i
$760$	13.1897	+	4.47731i	0.478441	+	0.162409i
$761$	5.75320	−	21.4712i	0.208553	−	0.778331i	−0.779784	−	0.626049i	$-0.784671\pi$
$761$	5.75320	−	21.4712i	0.208553	−	0.778331i	0.988337	−	0.152282i	$-0.0486623\pi$
$762$	−11.6362	−	7.77508i	−0.421536	−	0.281661i
$763$	1.80274	+	3.36783i	0.0652635	+	0.121924i
$764$			5.69521i			0.206045i
$765$	−1.19493	+	2.68401i	−0.0432027	+	0.0970405i
$766$	4.30771	+	2.48706i	0.155644	+	0.0898611i
$767$	−26.1211	−	34.0417i	−0.943178	−	1.22917i
$768$	−8.25718	−	0.541204i	−0.297955	−	0.0195290i
$769$	−26.4704	+	26.4704i	−0.954547	+	0.954547i	−0.999011	−	0.0444643i	$-0.985842\pi$
$769$	−26.4704	+	26.4704i	−0.954547	+	0.954547i	0.0444643	+	0.999011i	$0.485842\pi$
$770$	2.05096	+	3.29381i	0.0739114	+	0.118701i
$771$	−19.8259	+	13.2472i	−0.714012	+	0.477088i
$772$	1.67629	+	4.93818i	0.0603309	+	0.177729i
$773$	8.08420	+	1.06431i	0.290768	+	0.0382804i	0.274499	−	0.961587i	$-0.411488\pi$
$773$	8.08420	+	1.06431i	0.290768	+	0.0382804i	0.0162690	+	0.999868i	$0.494821\pi$
$774$	5.96326	+	0.785078i	0.214345	+	0.0282190i
$775$	−2.50927	−	7.39208i	−0.0901358	−	0.265531i
$776$	19.1468	−	12.7935i	0.687330	−	0.459259i
$777$	0.509885	+	15.2954i	0.0182920	+	0.548719i
$778$	−28.6751	+	28.6751i	−1.02805	+	1.02805i
$779$	7.22060	+	0.473263i	0.258705	+	0.0169564i
$780$	0.932245	+	1.21493i	0.0333797	+	0.0435013i
$781$	18.2778	+	10.5527i	0.654031	+	0.377605i
$782$	−21.1025	−	22.2364i	−0.754624	−	0.795173i
$783$			3.29406i			0.117720i
$784$	31.4817	+	6.22293i	1.12435	+	0.222248i
$785$	−13.1263	−	8.77069i	−0.468497	−	0.313039i
$786$	−2.43348	+	9.08186i	−0.0867993	+	0.323939i
$787$	8.89082	+	3.01803i	0.316923	+	0.107581i	0.475368	−	0.879787i	$-0.342315\pi$
$787$	8.89082	+	3.01803i	0.316923	+	0.107581i	−0.158445	+	0.987368i	$0.550648\pi$
$788$	−0.246088	−	3.75458i	−0.00876653	−	0.133751i
$789$	−17.2405	+	5.85237i	−0.613779	+	0.208350i
$790$	−3.80813	−	9.19365i	−0.135487	−	0.327095i
$791$	−29.0794	+	6.79872i	−1.03394	+	0.241735i
$792$	0.660369	−	3.31990i	0.0234652	−	0.117968i
$793$	3.22822	−	6.54619i	0.114638	−	0.232462i
$794$	−6.87132	+	20.2423i	−0.243854	+	0.718371i
$795$	−0.139581	−	0.520922i	−0.00495042	−	0.0184752i
$796$	−0.118652	+	1.81028i	−0.00420552	+	0.0641638i
$797$	17.5076	−	42.2672i	0.620152	−	1.49718i	−0.231372	−	0.972865i	$-0.574322\pi$
$797$	17.5076	−	42.2672i	0.620152	−	1.49718i	0.851524	−	0.524315i	$-0.175678\pi$
$798$	−11.0945	−	29.4239i	−0.392740	−	1.04159i
$799$	−16.2902	+	17.6233i	−0.576304	+	0.623469i
$800$	4.46439	+	7.73254i	0.157840	+	0.273387i
$801$	13.4372	−	10.3107i	0.474779	−	0.364311i
$802$	−35.4817	+	17.4976i	−1.25290	+	0.617863i
$803$	19.5387	+	5.23537i	0.689504	+	0.184752i
$804$	−0.889611	−	4.47238i	−0.0313742	−	0.157729i
$805$	−0.889793	+	9.09000i	−0.0313611	+	0.320380i
$806$	−15.8197	−	3.14674i	−0.557227	−	0.110839i
$807$	−24.4028	−	18.7249i	−0.859018	−	0.659147i
$808$	−0.312275	+	2.37196i	−0.0109858	+	0.0834454i
$809$	36.9865	+	32.4363i	1.30037	+	1.14040i	0.981261	+	0.192681i	$0.0617184\pi$
$809$	36.9865	+	32.4363i	1.30037	+	1.14040i	0.319113	+	0.947717i	$0.396615\pi$
$810$	0.980805	+	0.483680i	0.0344620	+	0.0169948i
$811$	16.5157	−	3.28518i	0.579945	−	0.115358i	0.103604	−	0.994619i	$-0.466963\pi$
$811$	16.5157	−	3.28518i	0.579945	−	0.115358i	0.476341	+	0.879260i	$0.341963\pi$
$812$	−3.08179	+	0.305393i	−0.108150	+	0.0107172i
$813$	−6.16576	+	9.22771i	−0.216243	+	0.323630i
$814$	1.55391	+	11.8031i	0.0544644	+	0.413698i
$815$	2.35356	−	4.07649i	0.0824417	−	0.142793i
$816$	9.01962	+	16.6112i	0.315750	+	0.581509i
$817$	−26.2850	+	15.1757i	−0.919597	+	0.530929i
$818$	7.10463	+	2.94284i	0.248408	+	0.102894i
$819$	−3.62425	+	15.5857i	−0.126642	+	0.544610i
$820$	−0.167289	−	0.167289i	−0.00584200	−	0.00584200i
$821$	−7.67625	−	8.75309i	−0.267903	−	0.305485i	0.602209	−	0.798338i	$-0.294287\pi$
$821$	−7.67625	−	8.75309i	−0.267903	−	0.305485i	−0.870112	+	0.492853i	$0.835954\pi$
$822$	10.5516	−	0.691585i	0.368028	−	0.0241218i
$823$	20.1981	−	23.0316i	0.704063	−	0.802829i	−0.283680	−	0.958919i	$-0.591555\pi$
$823$	20.1981	−	23.0316i	0.704063	−	0.802829i	0.987743	+	0.156089i	$0.0498888\pi$
$824$	20.9041	−	27.2427i	0.728229	−	0.949046i
$825$	−5.56580	+	2.30543i	−0.193776	+	0.0802647i
$826$	10.1313	−	26.9672i	0.352513	−	0.938309i
$827$	22.0148	+	32.9474i	0.765528	+	1.14569i	0.985415	+	0.170168i	$0.0544312\pi$
$827$	22.0148	+	32.9474i	0.765528	+	1.14569i	−0.219887	+	0.975525i	$0.570569\pi$
$828$	−1.29428	+	1.13506i	−0.0449795	+	0.0394460i
$829$	26.8747	−	7.20105i	0.933397	−	0.250103i	0.240094	−	0.970750i	$-0.422822\pi$
$829$	26.8747	−	7.20105i	0.933397	−	0.250103i	0.693303	+	0.720647i	$0.256155\pi$
$830$	5.69611	+	11.5506i	0.197715	+	0.400926i
$831$	18.5094	−	2.43681i	0.642085	−	0.0845322i
$832$	−37.0045			−1.28290
$833$	−10.3759	−	26.9321i	−0.359505	−	0.933143i
$834$	−12.3933			−0.429145
$835$	9.45599	−	1.24490i	0.327238	−	0.0430817i
$836$	−1.63225	−	3.30988i	−0.0564527	−	0.114475i
$837$	−1.67853	+	0.449760i	−0.0580184	+	0.0155460i
$838$	2.04903	−	1.79695i	0.0707825	−	0.0620746i
$839$	−5.39489	−	8.07402i	−0.186252	−	0.278746i	0.726579	−	0.687083i	$-0.241109\pi$
$839$	−5.39489	−	8.07402i	−0.186252	−	0.278746i	−0.912831	+	0.408337i	$0.866109\pi$
$840$	1.67354	−	4.45458i	0.0577427	−	0.153698i
$841$	16.7676	−	6.94538i	0.578194	−	0.239496i
$842$	−12.9640	+	16.8951i	−0.446770	+	0.582243i
$843$	−7.08221	+	8.07571i	−0.243924	+	0.278142i
$844$	−0.699202	+	0.0458281i	−0.0240675	+	0.00157747i
$845$	11.0779	+	12.6319i	0.381091	+	0.434551i
$846$	6.31655	+	6.31655i	0.217168	+	0.217168i
$847$	5.51399	−	23.7124i	0.189463	−	0.814767i
$848$	−3.20556	−	1.32778i	−0.110079	−	0.0455963i
$849$	0.721122	−	0.416340i	0.0247488	−	0.0142887i
$850$	13.2350	−	25.1569i	0.453957	−	0.862875i
$851$	−14.0114	+	24.2685i	−0.480306	+	0.831914i
$852$	0.729939	+	5.54444i	0.0250073	+	0.189949i
$853$	11.3080	−	16.9237i	0.387179	−	0.579455i	−0.585769	−	0.810478i	$-0.699207\pi$
$853$	11.3080	−	16.9237i	0.387179	−	0.579455i	0.972948	+	0.231023i	$0.0742074\pi$
$854$	4.87638	−	0.483229i	0.166866	−	0.0165358i
$855$	−5.41239	+	1.07659i	−0.185100	+	0.0368186i
$856$	−1.01581	−	0.500944i	−0.0347198	−	0.0171219i
$857$	42.2714	+	37.0710i	1.44396	+	1.26632i	0.905949	+	0.423386i	$0.139159\pi$
$857$	42.2714	+	37.0710i	1.44396	+	1.26632i	0.538014	+	0.842936i	$0.319175\pi$
$858$	−1.62475	+	12.3412i	−0.0554680	+	0.421322i
$859$	−13.0750	−	10.0328i	−0.446114	−	0.342315i	0.361148	−	0.932509i	$-0.382385\pi$
$859$	−13.0750	−	10.0328i	−0.446114	−	0.342315i	−0.807262	+	0.590193i	$0.799052\pi$
$860$	0.973265	+	0.193594i	0.0331881	+	0.00660152i
$861$	0.240834	−	2.46033i	0.00820760	−	0.0838477i
$862$	−10.5220	−	52.8979i	−0.358382	−	1.80171i
$863$	37.0180	+	9.91895i	1.26011	+	0.337645i	0.826233	−	0.563328i	$-0.190479\pi$
$863$	37.0180	+	9.91895i	1.26011	+	0.337645i	0.433875	+	0.900973i	$0.357146\pi$
$864$	1.78262	−	0.879091i	0.0606459	−	0.0299073i
$865$	8.15230	−	6.25548i	0.277187	−	0.212693i
$866$	−9.98658	−	17.2973i	−0.339358	−	0.587785i
$867$	8.30593	−	14.8328i	0.282084	−	0.503748i
$868$	−0.576394	−	1.52866i	−0.0195641	−	0.0518863i
$869$	4.66991	−	11.2742i	0.158416	−	0.382450i
$870$	−0.235604	+	3.59462i	−0.00798772	+	0.121869i
$871$	−20.0877	−	74.9684i	−0.680646	−	2.54021i
$872$	1.17142	−	3.45089i	0.0396693	−	0.116862i
$873$	−4.03508	+	8.18234i	−0.136567	+	0.276930i
$874$	11.2334	−	56.4743i	0.379977	−	1.91027i
$875$	−17.4256	+	4.07407i	−0.589091	+	0.137729i
$876$	2.05110	+	4.95179i	0.0693002	+	0.167305i
$877$	−26.2761	+	8.91953i	−0.887280	+	0.301191i	−0.727620	−	0.685981i	$-0.759373\pi$
$877$	−26.2761	+	8.91953i	−0.887280	+	0.301191i	−0.159661	+	0.987172i	$0.551040\pi$
$878$	−2.36095	−	36.0212i	−0.0796784	−	1.21566i
$879$	−3.63811	−	1.23497i	−0.122710	−	0.0416546i
$880$	1.13384	−	4.23156i	0.0382219	−	0.142646i
$881$	−2.52607	−	1.68786i	−0.0851054	−	0.0568656i	0.512290	−	0.858813i	$-0.328797\pi$
$881$	−2.52607	−	1.68786i	−0.0851054	−	0.0568656i	−0.597395	+	0.801947i	$0.703797\pi$
$882$	−10.1687	+	3.46540i	−0.342398	+	0.116686i
$883$		−	20.3369i		−	0.684390i	−0.939629	−	0.342195i	$-0.888830\pi$
$883$		−	20.3369i		−	0.684390i	0.939629	−	0.342195i	$-0.111170\pi$
$884$	−4.72851	−	7.49389i	−0.159037	−	0.252047i
$885$	−4.37810	−	2.52770i	−0.147168	−	0.0849677i
$886$	−23.4585	−	30.5717i	−0.788103	−	1.02708i
$887$	7.45825	+	0.488839i	0.250424	+	0.0164136i	0.190098	−	0.981765i	$-0.439119\pi$
$887$	7.45825	+	0.488839i	0.250424	+	0.0164136i	0.0603256	+	0.998179i	$0.480786\pi$
$888$	10.3238	−	10.3238i	0.346445	−	0.346445i
$889$	−0.803821	−	24.1128i	−0.0269593	−	0.808716i
$890$	15.4007	−	10.2904i	0.516231	−	0.344935i
$891$	0.431070	+	1.26989i	0.0144414	+	0.0425429i
$892$	−2.44599	−	0.322021i	−0.0818979	−	0.0107821i
$893$	−44.6917	−	5.88377i	−1.49555	−	0.196893i
$894$	−9.57485	−	28.2066i	−0.320231	−	0.943369i
$895$	−4.84974	+	3.24049i	−0.162109	+	0.108318i
$896$	−18.6910	−	30.0175i	−0.624423	−	1.00282i
$897$	−20.7185	+	20.7185i	−0.691772	+	0.691772i
$898$	−27.9927	−	1.83474i	−0.934128	−	0.0612260i
$899$	−3.48469	−	4.54134i	−0.116221	−	0.151462i
$900$	−1.38242	−	0.798138i	−0.0460805	−	0.0266046i
$901$	0.528526	+	3.07545i	0.0176078	+	0.102458i
$902$		−	1.92304i		−	0.0640304i
$903$	4.89339	+	9.14172i	0.162842	+	0.304217i
$904$	23.6887	+	15.8283i	0.787876	+	0.526442i
$905$	0.900672	−	3.36135i	0.0299393	−	0.111735i
$906$	3.37754	+	1.14652i	0.112211	+	0.0380906i
$907$	−2.83913	−	43.3168i	−0.0942719	−	1.43831i	−0.738900	−	0.673815i	$-0.764654\pi$
$907$	−2.83913	−	43.3168i	−0.0942719	−	1.43831i	0.644628	−	0.764496i	$-0.277012\pi$
$908$	8.65320	−	2.93737i	0.287166	−	0.0974799i
$909$	−0.362724	−	0.875693i	−0.0120308	−	0.0290449i
$910$	−5.06968	+	16.7486i	−0.168058	+	0.555210i
$911$	−2.53022	+	12.7203i	−0.0838299	+	0.421442i	0.915966	+	0.401255i	$0.131426\pi$
$911$	−2.53022	+	12.7203i	−0.0838299	+	0.421442i	−0.999796	+	0.0201864i	$0.993574\pi$
$912$	−15.7029	+	31.8423i	−0.519974	+	1.05440i
$913$	−5.07654	+	14.9550i	−0.168009	+	0.494939i
$914$	3.28449	+	12.2579i	0.108641	+	0.405455i
$915$	0.0562429	−	0.858100i	0.00185933	−	0.0283679i
$916$	1.18160	−	2.85264i	0.0390412	−	0.0942539i
$917$	−15.1666	+	5.71866i	−0.500845	+	0.188847i
$918$	−5.39539	−	3.30614i	−0.178074	−	0.109119i
$919$	17.2896	+	29.9465i	0.570331	+	0.987843i	0.996532	+	0.0832138i	$0.0265184\pi$
$919$	17.2896	+	29.9465i	0.570331	+	0.987843i	−0.426201	+	0.904629i	$0.640148\pi$
$920$	6.91282	−	5.30439i	0.227909	−	0.174881i
$921$	0.139496	−	0.0687918i	0.00459655	−	0.00226677i
$922$	17.0025	+	4.55581i	0.559948	+	0.150038i
$923$	18.5693	+	93.3540i	0.611215	+	3.07278i
$924$	−1.14809	+	0.521022i	−0.0377695	+	0.0171404i
$925$	−25.4853	−	5.06935i	−0.837952	−	0.166679i
$926$	−32.8549	−	25.2104i	−1.07968	−	0.828466i
$927$	−1.77574	+	13.4881i	−0.0583229	+	0.443006i
$928$	4.92249	+	4.31691i	0.161589	+	0.141710i
$929$	−15.1708	−	7.48143i	−0.497739	−	0.245458i	0.176050	−	0.984381i	$-0.443668\pi$
$929$	−15.1708	−	7.48143i	−0.497739	−	0.245458i	−0.673789	+	0.738923i	$0.735335\pi$
$930$	−1.86385	+	0.370743i	−0.0611180	+	0.0121571i
$931$	30.0641	−	45.1109i	0.985309	−	1.47845i
$932$	−3.00819	+	4.50208i	−0.0985367	+	0.147471i
$933$	−0.592936	−	4.50379i	−0.0194118	−	0.147448i
$934$	8.25271	−	14.2941i	0.270037	−	0.467718i
$935$	−3.76277	+	1.16846i	−0.123056	+	0.0382127i
$936$	13.2205	−	7.63285i	0.432125	−	0.249488i
$937$	52.9585	+	21.9361i	1.73008	+	0.716621i	0.999426	+	0.0338705i	$0.0107834\pi$
$937$	52.9585	+	21.9361i	1.73008	+	0.716621i	0.730651	+	0.682751i	$0.239217\pi$
$938$	35.5972	−	38.0524i	1.16229	−	1.24245i
$939$	0.932295	+	0.932295i	0.0304243	+	0.0304243i
$940$	0.971741	+	1.10806i	0.0316947	+	0.0361409i
$941$	−19.0768	+	1.25036i	−0.621887	+	0.0407606i	−0.373090	−	0.927795i	$-0.621702\pi$
$941$	−19.0768	+	1.25036i	−0.621887	+	0.0407606i	−0.248797	+	0.968556i	$0.580035\pi$
$942$	22.4187	−	25.5636i	0.730440	−	0.832907i
$943$	2.75564	−	3.59122i	0.0897359	−	0.116946i
$944$	−30.0490	+	12.4467i	−0.978010	+	0.405105i
$945$	0.308216	+	1.85991i	0.0100263	+	0.0605028i
$946$	4.48128	+	6.70671i	0.145699	+	0.218054i
$947$	−8.04793	+	7.05784i	−0.261522	+	0.229349i	−0.780058	−	0.625707i	$-0.784811\pi$
$947$	−8.04793	+	7.05784i	−0.261522	+	0.229349i	0.518536	+	0.855056i	$0.326477\pi$
$948$	3.12326	−	0.836875i	0.101439	−	0.0271804i
$949$	40.3480	+	81.8177i	1.30975	+	2.65592i
$950$	52.9357	−	6.96912i	1.71746	−	0.226108i
$951$	−8.75806			−0.284000
$952$	−12.0009	+	24.7815i	−0.388952	+	0.803174i
$953$	6.01930			0.194984			0.0974921	−	0.995236i	$-0.468918\pi$
$953$	6.01930			0.194984			0.0974921	+	0.995236i	$0.468918\pi$
$954$	1.15159	−	0.151610i	0.0372843	−	0.00490856i
$955$	5.05122	+	10.2429i	0.163454	+	0.331451i
$956$	−0.789073	+	0.211432i	−0.0255204	+	0.00683818i
$957$	−3.32128	+	2.91268i	−0.107362	+	0.0941537i
$958$	26.6654	+	39.9076i	0.861519	+	1.28935i
$959$	11.5730	+	14.0845i	0.373711	+	0.454812i
$960$	−4.02792	+	1.66842i	−0.130001	+	0.0538480i
$961$	−17.0333	+	22.1982i	−0.549461	+	0.716072i
$962$	−35.4002	+	40.3662i	−1.14135	+	1.30146i
$963$	0.447765	−	0.0293481i	0.0144290	−	0.000945728i
$964$	5.24778	+	5.98395i	0.169020	+	0.192730i
$965$	7.39461	+	7.39461i	0.238041	+	0.238041i
$966$	−19.1602	−	4.45545i	−0.616471	−	0.143352i
$967$	5.97556	+	2.47516i	0.192161	+	0.0795957i	0.476689	−	0.879072i	$-0.341837\pi$
$967$	5.97556	+	2.47516i	0.192161	+	0.0795957i	−0.284528	+	0.958668i	$0.591837\pi$
$968$	−20.1138	+	11.6127i	−0.646483	+	0.373247i
$969$	31.7561	−	3.33839i	1.02015	−	0.107244i
$970$	−4.98848	+	8.64031i	−0.160171	+	0.277424i
$971$	−6.24138	−	47.4080i	−0.200296	−	1.52140i	−0.735995	−	0.676987i	$-0.763285\pi$
$971$	−6.24138	−	47.4080i	−0.200296	−	1.52140i	0.535700	−	0.844409i	$-0.320048\pi$
$972$	−0.197416	+	0.295454i	−0.00633213	+	0.00947670i
$973$	−12.4552	−	17.3593i	−0.399296	−	0.556513i
$974$	34.2956	−	6.82181i	1.09890	−	0.218585i
$975$	−24.3674	−	12.0167i	−0.780380	−	0.384841i
$976$	−4.15961	−	3.64788i	−0.133146	−	0.116766i
$977$	2.50742	−	19.0457i	0.0802194	−	0.609327i	−0.903364	−	0.428874i	$-0.858910\pi$
$977$	2.50742	−	19.0457i	0.0802194	−	0.609327i	0.983584	−	0.180453i	$-0.0577563\pi$
$978$	8.04311	+	6.17170i	0.257190	+	0.197349i
$979$	22.2773	+	4.43124i	0.711987	+	0.141623i
$980$	−1.71148	+	0.460786i	−0.0546711	+	0.0147193i
$981$	0.281674	+	1.41607i	0.00899315	+	0.0452116i
$982$	−54.4835	−	14.5988i	−1.73864	−	0.465867i
$983$	−50.4259	+	24.8673i	−1.60834	+	0.793143i	−1.00000		0.000536365i	$-0.999829\pi$
$983$	−50.4259	+	24.8673i	−1.60834	+	0.793143i	−0.608336	+	0.793680i	$0.708163\pi$
$984$	−1.87104	+	1.43570i	−0.0596467	+	0.0457685i
$985$	−3.77262	−	6.53438i	−0.120206	−	0.208203i
$986$	3.26030	−	20.5875i	0.103829	−	0.655641i
$987$	−2.49947	+	15.1957i	−0.0795591	+	0.483684i
$988$	6.36923	−	15.3767i	0.202632	−	0.489198i
$989$	−1.24179	+	18.9460i	−0.0394865	+	0.602448i
$990$	0.379574	+	1.41659i	0.0120636	+	0.0450221i
$991$	8.19409	−	24.1390i	0.260294	−	0.766801i	−0.735694	−	0.677314i	$-0.763144\pi$
$991$	8.19409	−	24.1390i	0.260294	−	0.766801i	0.995988	−	0.0894873i	$-0.0285228\pi$
$992$	−1.52763	+	3.09773i	−0.0485024	+	0.0983530i
$993$	0.820131	−	4.12308i	0.0260261	−	0.130842i
$994$	−46.6143	+	43.7115i	−1.47852	+	1.38644i
$995$	1.39219	+	3.36104i	0.0441354	+	0.106552i
$996$	−3.96262	+	1.34513i	−0.125560	+	0.0426220i
$997$	−1.13634	−	17.3372i	−0.0359883	−	0.549076i	−0.977344	−	0.211659i	$-0.932113\pi$
$997$	−1.13634	−	17.3372i	−0.0359883	−	0.549076i	0.941355	−	0.337417i	$-0.109553\pi$
$998$	−7.11601	−	2.41556i	−0.225253	−	0.0764632i
$999$	−1.49709	+	5.58722i	−0.0473659	+	0.176772i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	357.2.bl.a.10.6	✓	384
7.5	odd	6	inner	357.2.bl.a.61.19	yes	384
17.12	odd	16	inner	357.2.bl.a.199.19	yes	384
119.12	even	48	inner	357.2.bl.a.250.6	yes	384

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
357.2.bl.a.10.6	✓	384	1.1	even	1	trivial
357.2.bl.a.61.19	yes	384	7.5	odd	6	inner
357.2.bl.a.199.19	yes	384	17.12	odd	16	inner
357.2.bl.a.250.6	yes	384	119.12	even	48	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 357 = 3 \cdot 7 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	357.bl (of order \(48\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.52158 + 0.200320i) q^{2} +(-0.442289 - 0.896873i) q^{3} +(0.343232 - 0.0919687i) q^{4} +(0.535735 - 0.469827i) q^{5} +(0.852640 + 1.27607i) q^{6} +(-0.930484 + 2.47673i) q^{7} +(2.33194 - 0.965923i) q^{8} +(-0.608761 + 0.793353i) q^{9} +(-0.721050 + 0.822199i) q^{10} +(-1.33819 + 0.0877095i) q^{11} +(-0.234292 - 0.267159i) q^{12} +(-4.27660 - 4.27660i) q^{13} +(0.919668 - 3.95495i) q^{14} +(-0.658325 - 0.272687i) q^{15} +(-3.97022 + 2.29221i) q^{16} +(3.64894 + 1.91970i) q^{17} +(0.767356 - 1.32910i) q^{18} +(1.01085 + 7.67818i) q^{19} +(0.140672 - 0.210531i) q^{20} +(2.63286 - 0.260905i) q^{21} +(2.01859 - 0.401523i) q^{22} +(4.34502 + 2.14272i) q^{23} +(-1.89770 - 1.66424i) q^{24} +(-0.586356 + 4.45382i) q^{25} +(7.36389 + 5.65051i) q^{26} +(0.980785 + 0.195090i) q^{27} +(-0.0915898 + 0.935669i) q^{28} +(0.642640 + 3.23077i) q^{29} +(1.05632 + 0.283040i) q^{30} +(-1.55853 + 0.768583i) q^{31} +(1.57686 - 1.20997i) q^{32} +(0.670530 + 1.16139i) q^{33} +(-5.93671 - 2.19003i) q^{34} +(0.665143 + 1.76404i) q^{35} +(-0.135983 + 0.328291i) q^{36} +(-0.378313 + 5.77194i) q^{37} +(-3.07619 - 11.4805i) q^{38} +(-1.94408 + 5.72706i) q^{39} +(0.795488 - 1.61309i) q^{40} +(0.182285 - 0.916407i) q^{41} +(-3.95384 + 0.924402i) q^{42} +(1.49978 + 3.62079i) q^{43} +(-0.451243 + 0.153176i) q^{44} +(0.0466040 + 0.711040i) q^{45} +(-7.04053 - 2.38994i) q^{46} +(-1.50648 + 5.62228i) q^{47} +(3.81180 + 2.54696i) q^{48} +(-5.26840 - 4.60912i) q^{49} -6.89431i q^{50} +(0.107843 - 4.12170i) q^{51} +(-1.86118 - 1.07455i) q^{52} +(0.460735 + 0.600442i) q^{53} +(-1.53143 - 0.100375i) q^{54} +(-0.675707 + 0.675707i) q^{55} +(0.222496 + 6.67438i) q^{56} +(6.43926 - 4.30258i) q^{57} +(-1.62502 - 4.78715i) q^{58} +(7.03394 + 0.926036i) q^{59} +(-0.251037 - 0.0330496i) q^{60} +(0.387921 + 1.14278i) q^{61} +(2.21747 - 1.48167i) q^{62} +(-1.39848 - 2.24594i) q^{63} +(4.32639 - 4.32639i) q^{64} +(-4.30039 - 0.281863i) q^{65} +(-1.25292 - 1.63283i) q^{66} +(11.1135 + 6.41639i) q^{67} +(1.42898 + 0.323314i) q^{68} -4.84463i q^{69} +(-1.36544 - 2.55089i) q^{70} +(-13.0855 - 8.74348i) q^{71} +(-0.653280 + 2.43807i) q^{72} +(-14.2830 - 4.84844i) q^{73} +(-0.580601 - 8.85826i) q^{74} +(4.25385 - 1.44399i) q^{75} +(1.05311 + 2.54243i) q^{76} +(1.02793 - 3.39595i) q^{77} +(1.81082 - 9.10363i) q^{78} +(-4.02463 + 8.16115i) q^{79} +(-1.05005 + 3.09333i) q^{80} +(-0.258819 - 0.965926i) q^{81} +(-0.0937864 + 1.43090i) q^{82} +(4.50672 - 10.8802i) q^{83} +(0.879685 - 0.331691i) q^{84} +(2.85679 - 0.685920i) q^{85} +(-3.00736 - 5.20890i) q^{86} +(2.61336 - 2.00530i) q^{87} +(-3.03586 + 1.49712i) q^{88} +(-16.3601 - 4.38367i) q^{89} +(-0.213348 - 1.07257i) q^{90} +(14.5713 - 6.61269i) q^{91} +(1.68841 + 0.335846i) q^{92} +(1.37864 + 1.05787i) q^{93} +(1.16598 - 8.85653i) q^{94} +(4.14897 + 3.63855i) q^{95} +(-1.78262 - 0.879091i) q^{96} +(8.94789 - 1.77985i) q^{97} +(8.93960 + 5.95778i) q^{98} +(0.745053 - 1.11505i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 384 q - 16 q^{11} + 32 q^{14} - 64 q^{22} - 16 q^{25} - 48 q^{28} - 64 q^{30} - 64 q^{35} - 32 q^{37} - 48 q^{42} - 64 q^{44} + 32 q^{46} - 64 q^{49} + 80 q^{56} - 32 q^{58} - 288 q^{61} - 528 q^{68} + 176 q^{70}+ \cdots + 32 q^{99}+O(q^{100}) \) 384 * q - 16 * q^11 + 32 * q^14 - 64 * q^22 - 16 * q^25 - 48 * q^28 - 64 * q^30 - 64 * q^35 - 32 * q^37 - 48 * q^42 - 64 * q^44 + 32 * q^46 - 64 * q^49 + 80 * q^56 - 32 * q^58 - 288 * q^61 - 528 * q^68 + 176 * q^70 + 64 * q^71 - 48 * q^73 - 128 * q^74 + 96 * q^77 + 128 * q^78 - 480 * q^80 - 240 * q^82 + 32 * q^85 - 144 * q^87 - 96 * q^88 - 64 * q^91 + 320 * q^92 - 192 * q^94 - 64 * q^95 + 32 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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