LMFDB - Embedded newform 342.3.l.a.151.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [342,3,Mod(151,342)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(342, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 3]))

N = Newforms(chi, 3, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("342.151");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 342 = 2 \cdot 3^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	342.l (of order $6$, degree $2$, 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:	$9.31882504112$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$40$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			151.14
Character	$\chi$	$=$	342.151
Dual form			342.3.l.a.265.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.22474 - 0.707107i) q^{2} +(1.11114 + 2.78664i) q^{3} +(1.00000 + 1.73205i) q^{4} +(1.92987 + 3.34264i) q^{5} +(0.609589 - 4.19862i) q^{6} +(-2.60142 + 4.50580i) q^{7} -2.82843i q^{8} +(-6.53073 + 6.19270i) q^{9} +O(q^{10})$	\(q+(-1.22474 - 0.707107i) q^{2} +(1.11114 + 2.78664i) q^{3} +(1.00000 + 1.73205i) q^{4} +(1.92987 + 3.34264i) q^{5} +(0.609589 - 4.19862i) q^{6} +(-2.60142 + 4.50580i) q^{7} -2.82843i q^{8} +(-6.53073 + 6.19270i) q^{9} -5.45850i q^{10} +(-4.45159 + 7.71037i) q^{11} +(-3.71546 + 4.71119i) q^{12} +(1.57311 - 0.908234i) q^{13} +(6.37216 - 3.67897i) q^{14} +(-7.17036 + 9.09200i) q^{15} +(-2.00000 + 3.46410i) q^{16} -1.92601 q^{17} +(12.3774 - 2.96655i) q^{18} +(-8.21402 - 17.1327i) q^{19} +(-3.85974 + 6.68527i) q^{20} +(-15.4466 - 2.24266i) q^{21} +(10.9041 - 6.29549i) q^{22} +(8.65856 + 14.9971i) q^{23} +(7.88181 - 3.14278i) q^{24} +(5.05119 - 8.74892i) q^{25} -2.56887 q^{26} +(-24.5134 - 11.3178i) q^{27} -10.4057 q^{28} +(-12.8972 - 7.44619i) q^{29} +(15.2109 - 6.06516i) q^{30} +(-0.120044 + 0.0693073i) q^{31} +(4.89898 - 2.82843i) q^{32} +(-26.4324 - 3.83766i) q^{33} +(2.35887 + 1.36189i) q^{34} -20.0816 q^{35} +(-17.2568 - 5.11886i) q^{36} -24.7669i q^{37} +(-2.05458 + 26.7914i) q^{38} +(4.27886 + 3.37451i) q^{39} +(9.45440 - 5.45850i) q^{40} +(-22.0925 + 12.7551i) q^{41} +(17.3323 + 13.6691i) q^{42} +(-12.4303 + 21.5299i) q^{43} -17.8063 q^{44} +(-33.3034 - 9.87874i) q^{45} -24.4901i q^{46} +(-24.5533 + 42.5276i) q^{47} +(-11.8755 - 1.72418i) q^{48} +(10.9652 + 18.9923i) q^{49} +(-12.3728 + 7.14347i) q^{50} +(-2.14006 - 5.36709i) q^{51} +(3.14621 + 1.81647i) q^{52} +88.1629i q^{53} +(22.0197 + 31.1951i) q^{54} -34.3640 q^{55} +(12.7443 + 7.35793i) q^{56} +(38.6158 - 41.9264i) q^{57} +(10.5305 + 18.2394i) q^{58} +(-20.8669 + 12.0475i) q^{59} +(-22.9182 - 3.32744i) q^{60} +(16.2635 - 28.1692i) q^{61} +0.196031 q^{62} +(-10.9138 - 45.5360i) q^{63} -8.00000 q^{64} +(6.07179 + 3.50555i) q^{65} +(29.6593 + 23.3907i) q^{66} +(37.3293 - 21.5521i) q^{67} +(-1.92601 - 3.33594i) q^{68} +(-32.1705 + 40.7921i) q^{69} +(24.5949 + 14.1999i) q^{70} +95.9893i q^{71} +(17.5156 + 18.4717i) q^{72} +15.1298 q^{73} +(-17.5129 + 30.3332i) q^{74} +(29.9927 + 4.35458i) q^{75} +(21.4607 - 31.3598i) q^{76} +(-23.1609 - 40.1159i) q^{77} +(-2.85438 - 7.15853i) q^{78} +(26.9445 + 15.5564i) q^{79} -15.4390 q^{80} +(4.30094 - 80.8857i) q^{81} +36.0769 q^{82} +(-14.8960 + 25.8007i) q^{83} +(-11.5622 - 28.9969i) q^{84} +(-3.71694 - 6.43793i) q^{85} +(30.4479 - 17.5791i) q^{86} +(6.41928 - 44.2136i) q^{87} +(21.8082 + 12.5910i) q^{88} +63.5313i q^{89} +(33.8029 + 35.6480i) q^{90} +9.45080i q^{91} +(-17.3171 + 29.9941i) q^{92} +(-0.326520 - 0.257509i) q^{93} +(60.1431 - 34.7237i) q^{94} +(41.4164 - 60.5204i) q^{95} +(13.3253 + 10.5089i) q^{96} +(-65.5439 - 37.8418i) q^{97} -31.0143i q^{98} +(-18.6759 - 77.9217i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q + 80 q^{4} + 8 q^{6} - 4 q^{7} + 4 q^{9}+O(q^{10}) $ 80 * q + 80 * q^4 + 8 * q^6 - 4 * q^7 + 4 * q^9	$ 80 q + 80 q^{4} + 8 q^{6} - 4 q^{7} + 4 q^{9} + 12 q^{11} - 160 q^{16} + 96 q^{17} + 40 q^{19} - 48 q^{23} - 16 q^{24} - 200 q^{25} - 16 q^{28} + 40 q^{30} + 432 q^{35} - 8 q^{36} + 24 q^{38} + 88 q^{42} + 28 q^{43} + 48 q^{44} + 380 q^{45} + 240 q^{47} - 228 q^{49} - 64 q^{54} - 120 q^{57} - 28 q^{61} - 144 q^{62} + 44 q^{63} - 640 q^{64} + 16 q^{66} + 96 q^{68} - 368 q^{73} - 24 q^{74} + 40 q^{76} - 456 q^{77} + 652 q^{81} - 192 q^{82} - 84 q^{83} + 492 q^{87} + 96 q^{92} + 504 q^{93} - 324 q^{95} - 64 q^{96} - 604 q^{99}+O(q^{100}) $ 80 * q + 80 * q^4 + 8 * q^6 - 4 * q^7 + 4 * q^9 + 12 * q^11 - 160 * q^16 + 96 * q^17 + 40 * q^19 - 48 * q^23 - 16 * q^24 - 200 * q^25 - 16 * q^28 + 40 * q^30 + 432 * q^35 - 8 * q^36 + 24 * q^38 + 88 * q^42 + 28 * q^43 + 48 * q^44 + 380 * q^45 + 240 * q^47 - 228 * q^49 - 64 * q^54 - 120 * q^57 - 28 * q^61 - 144 * q^62 + 44 * q^63 - 640 * q^64 + 16 * q^66 + 96 * q^68 - 368 * q^73 - 24 * q^74 + 40 * q^76 - 456 * q^77 + 652 * q^81 - 192 * q^82 - 84 * q^83 + 492 * q^87 + 96 * q^92 + 504 * q^93 - 324 * q^95 - 64 * q^96 - 604 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/342\mathbb{Z}\right)^\times$.

$n$	$191$	$325$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$-1$

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 $

$2$	−1.22474	−	0.707107i	−0.612372	−	0.353553i
$2$	−1.22474	−	0.707107i	−0.612372	−	0.353553i
$3$	1.11114	+	2.78664i	0.370380	+	0.928880i
$3$	1.11114	+	2.78664i	0.370380	+	0.928880i
$4$	1.00000	+	1.73205i	0.250000	+	0.433013i
$5$	1.92987	+	3.34264i	0.385974	+	0.668527i	0.991904	−	0.126991i	$-0.0405320\pi$
$5$	1.92987	+	3.34264i	0.385974	+	0.668527i	−0.605930	+	0.795518i	$0.707199\pi$
$6$	0.609589	−	4.19862i	0.101598	−	0.699770i
$7$	−2.60142	+	4.50580i	−0.371632	+	0.643685i	−0.989817	−	0.142348i	$-0.954535\pi$
$7$	−2.60142	+	4.50580i	−0.371632	+	0.643685i	0.618185	+	0.786033i	$0.287868\pi$
$8$		−	2.82843i		−	0.353553i
$9$	−6.53073	+	6.19270i	−0.725637	+	0.688078i
$10$		−	5.45850i		−	0.545850i
$11$	−4.45159	+	7.71037i	−0.404690	+	0.700943i	−0.994285	−	0.106755i	$-0.965954\pi$
$11$	−4.45159	+	7.71037i	−0.404690	+	0.700943i	0.589596	+	0.807699i	$0.299287\pi$
$12$	−3.71546	+	4.71119i	−0.309622	+	0.392599i
$13$	1.57311	−	0.908234i	0.121008	−	0.0698641i	−0.438274	−	0.898841i	$-0.644410\pi$
$13$	1.57311	−	0.908234i	0.121008	−	0.0698641i	0.559282	+	0.828977i	$0.311077\pi$
$14$	6.37216	−	3.67897i	0.455154	−	0.262783i
$15$	−7.17036	+	9.09200i	−0.478024	+	0.606133i
$16$	−2.00000	+	3.46410i	−0.125000	+	0.216506i
$17$	−1.92601			−0.113294			−0.0566472	−	0.998394i	$-0.518041\pi$
$17$	−1.92601			−0.113294			−0.0566472	+	0.998394i	$0.518041\pi$
$18$	12.3774	−	2.96655i	0.687632	−	0.164808i
$19$	−8.21402	−	17.1327i	−0.432317	−	0.901722i
$19$	−8.21402	−	17.1327i	−0.432317	−	0.901722i
$20$	−3.85974	+	6.68527i	−0.192987	+	0.334264i
$21$	−15.4466	−	2.24266i	−0.735551	−	0.106793i
$22$	10.9041	−	6.29549i	0.495642	−	0.286159i
$23$	8.65856	+	14.9971i	0.376459	+	0.652046i	0.990544	−	0.137194i	$-0.0438082\pi$
$23$	8.65856	+	14.9971i	0.376459	+	0.652046i	−0.614085	+	0.789240i	$0.710475\pi$
$24$	7.88181	−	3.14278i	0.328409	−	0.130949i
$25$	5.05119	−	8.74892i	0.202048	−	0.349957i
$26$	−2.56887			−0.0988028
$27$	−24.5134	−	11.3178i	−0.907903	−	0.419179i
$28$	−10.4057			−0.371632
$29$	−12.8972	−	7.44619i	−0.444730	−	0.256765i	0.260872	−	0.965373i	$-0.415990\pi$
$29$	−12.8972	−	7.44619i	−0.444730	−	0.256765i	−0.705602	+	0.708608i	$0.749323\pi$
$30$	15.2109	−	6.06516i	0.507029	−	0.202172i
$31$	−0.120044	+	0.0693073i	−0.00387238	+	0.00223572i	−0.501935	−	0.864905i	$-0.667378\pi$
$31$	−0.120044	+	0.0693073i	−0.00387238	+	0.00223572i	0.498063	+	0.867141i	$0.334045\pi$
$32$	4.89898	−	2.82843i	0.153093	−	0.0883883i
$33$	−26.4324	−	3.83766i	−0.800981	−	0.116293i
$34$	2.35887	+	1.36189i	0.0693784	+	0.0400556i
$35$	−20.0816			−0.573761
$36$	−17.2568	−	5.11886i	−0.479356	−	0.142191i
$37$		−	24.7669i		−	0.669376i	−0.942329	−	0.334688i	$-0.891369\pi$
$37$		−	24.7669i		−	0.669376i	0.942329	−	0.334688i	$-0.108631\pi$
$38$	−2.05458	+	26.7914i	−0.0540678	+	0.705037i
$39$	4.27886	+	3.37451i	0.109714	+	0.0865259i
$40$	9.45440	−	5.45850i	0.236360	−	0.136463i
$41$	−22.0925	+	12.7551i	−0.538841	+	0.311100i	−0.744609	−	0.667501i	$-0.767364\pi$
$41$	−22.0925	+	12.7551i	−0.538841	+	0.311100i	0.205768	+	0.978601i	$0.434031\pi$
$42$	17.3323	+	13.6691i	0.412674	+	0.325454i
$43$	−12.4303	+	21.5299i	−0.289077	+	0.500696i	−0.973590	−	0.228305i	$-0.926682\pi$
$43$	−12.4303	+	21.5299i	−0.289077	+	0.500696i	0.684513	+	0.729001i	$0.260015\pi$
$44$	−17.8063			−0.404690
$45$	−33.3034	−	9.87874i	−0.740076	−	0.219528i
$46$		−	24.4901i		−	0.532393i
$47$	−24.5533	+	42.5276i	−0.522411	+	0.904843i	0.477249	+	0.878768i	$0.341634\pi$
$47$	−24.5533	+	42.5276i	−0.522411	+	0.904843i	−0.999660	+	0.0260747i	$0.991699\pi$
$48$	−11.8755	−	1.72418i	−0.247406	−	0.0359204i
$49$	10.9652	+	18.9923i	0.223780	+	0.387598i
$50$	−12.3728	+	7.14347i	−0.247457	+	0.142869i
$51$	−2.14006	−	5.36709i	−0.0419620	−	0.105237i
$52$	3.14621	+	1.81647i	0.0605041	+	0.0349321i
$53$			88.1629i			1.66345i	0.555187	+	0.831725i	$0.312647\pi$
$53$			88.1629i			1.66345i	−0.555187	+	0.831725i	$0.687353\pi$
$54$	22.0197	+	31.1951i	0.407773	+	0.577686i
$55$	−34.3640			−0.624799
$56$	12.7443	+	7.35793i	0.227577	+	0.131392i
$57$	38.6158	−	41.9264i	0.677470	−	0.735551i
$58$	10.5305	+	18.2394i	0.181560	+	0.314472i
$59$	−20.8669	+	12.0475i	−0.353676	+	0.204195i	−0.666303	−	0.745681i	$-0.732124\pi$
$59$	−20.8669	+	12.0475i	−0.353676	+	0.204195i	0.312627	+	0.949876i	$0.398791\pi$
$60$	−22.9182	−	3.32744i	−0.381969	−	0.0554573i
$61$	16.2635	−	28.1692i	0.266615	−	0.461791i	−0.701370	−	0.712797i	$-0.747428\pi$
$61$	16.2635	−	28.1692i	0.266615	−	0.461791i	0.967985	+	0.251006i	$0.0807615\pi$
$62$	0.196031			0.00316178
$63$	−10.9138	−	45.5360i	−0.173236	−	0.722793i
$64$	−8.00000			−0.125000
$65$	6.07179	+	3.50555i	0.0934121	+	0.0539315i
$66$	29.6593	+	23.3907i	0.449383	+	0.354404i
$67$	37.3293	−	21.5521i	0.557154	−	0.321673i	−0.194848	−	0.980833i	$-0.562421\pi$
$67$	37.3293	−	21.5521i	0.557154	−	0.321673i	0.752003	+	0.659160i	$0.229088\pi$
$68$	−1.92601	−	3.33594i	−0.0283236	−	0.0490579i
$69$	−32.1705	+	40.7921i	−0.466240	+	0.591190i
$70$	24.5949	+	14.1999i	0.351356	+	0.202855i
$71$			95.9893i			1.35196i	0.736919	+	0.675981i	$0.236280\pi$
$71$			95.9893i			1.35196i	−0.736919	+	0.675981i	$0.763720\pi$
$72$	17.5156	+	18.4717i	0.243272	+	0.256551i
$73$	15.1298			0.207257			0.103629	−	0.994616i	$-0.466955\pi$
$73$	15.1298			0.207257			0.103629	+	0.994616i	$0.466955\pi$
$74$	−17.5129	+	30.3332i	−0.236660	+	0.409907i
$75$	29.9927	+	4.35458i	0.399903	+	0.0580610i
$76$	21.4607	−	31.3598i	0.282378	−	0.412629i
$77$	−23.1609	−	40.1159i	−0.300791	−	0.520986i
$78$	−2.85438	−	7.15853i	−0.0365946	−	0.0917760i
$79$	26.9445	+	15.5564i	0.341069	+	0.196916i	0.660745	−	0.750611i	$-0.270241\pi$
$79$	26.9445	+	15.5564i	0.341069	+	0.196916i	−0.319676	+	0.947527i	$0.603574\pi$
$80$	−15.4390			−0.192987
$81$	4.30094	−	80.8857i	0.0530980	−	0.998589i
$82$	36.0769			0.439962
$83$	−14.8960	+	25.8007i	−0.179470	+	0.310851i	−0.941699	−	0.336456i	$-0.890772\pi$
$83$	−14.8960	+	25.8007i	−0.179470	+	0.310851i	0.762229	+	0.647307i	$0.224105\pi$
$84$	−11.5622	−	28.9969i	−0.137645	−	0.345201i
$85$	−3.71694	−	6.43793i	−0.0437287	−	0.0757404i
$86$	30.4479	−	17.5791i	0.354045	−	0.204408i
$87$	6.41928	−	44.2136i	0.0737848	−	0.508202i
$88$	21.8082	+	12.5910i	0.247821	+	0.143079i
$89$			63.5313i			0.713835i	0.934136	+	0.356917i	$0.116172\pi$
$89$			63.5313i			0.713835i	−0.934136	+	0.356917i	$0.883828\pi$
$90$	33.8029	+	35.6480i	0.375587	+	0.396089i
$91$			9.45080i			0.103855i
$92$	−17.3171	+	29.9941i	−0.188230	+	0.326023i
$93$	−0.326520	−	0.257509i	−0.00351097	−	0.00276891i
$94$	60.1431	−	34.7237i	0.639821	−	0.369401i
$95$	41.4164	−	60.5204i	0.435962	−	0.637057i
$96$	13.3253	+	10.5089i	0.138805	+	0.109468i
$97$	−65.5439	−	37.8418i	−0.675710	−	0.390122i	0.122526	−	0.992465i	$-0.460900\pi$
$97$	−65.5439	−	37.8418i	−0.675710	−	0.390122i	−0.798237	+	0.602344i	$0.794234\pi$
$98$		−	31.0143i		−	0.316472i
$99$	−18.6759	−	77.9217i	−0.188646	−	0.787088i
$100$	20.2048			0.202048
$101$	64.7217	−	112.101i	0.640809	−	1.10991i	−0.344444	−	0.938807i	$-0.611932\pi$
$101$	64.7217	−	112.101i	0.640809	−	1.10991i	0.985253	−	0.171107i	$-0.0547343\pi$
$102$	−1.17407	+	8.08656i	−0.0115105	+	0.0792800i
$103$	2.92871	−	1.69089i	0.0284341	−	0.0164164i	−0.485716	−	0.874117i	$-0.661441\pi$
$103$	2.92871	−	1.69089i	0.0284341	−	0.0164164i	0.514150	+	0.857700i	$0.328108\pi$
$104$	−2.56887	−	4.44942i	−0.0247007	−	0.0427829i
$105$	−22.3135	−	55.9603i	−0.212510	−	0.532955i
$106$	62.3406	−	107.977i	0.588119	−	1.01865i
$107$			95.0206i			0.888043i	0.896016	+	0.444022i	$0.146449\pi$
$107$			95.0206i			0.888043i	−0.896016	+	0.444022i	$0.853551\pi$
$108$	−4.91031	−	53.7763i	−0.0454659	−	0.497929i
$109$		−	28.0002i		−	0.256883i	−0.991717	−	0.128441i	$-0.959003\pi$
$109$		−	28.0002i		−	0.256883i	0.991717	−	0.128441i	$-0.0409974\pi$
$110$	42.0871	+	24.2990i	0.382610	+	0.220900i
$111$	69.0165	−	27.5195i	0.621770	−	0.247924i
$112$	−10.4057	−	18.0232i	−0.0929079	−	0.160921i
$113$	108.618	−	62.7106i	0.961221	−	0.554961i	0.0646727	−	0.997907i	$-0.479400\pi$
$113$	108.618	−	62.7106i	0.961221	−	0.554961i	0.896549	+	0.442945i	$0.146066\pi$
$114$	−76.9409	+	24.0436i	−0.674920	+	0.210909i
$115$	−33.4198	+	57.8848i	−0.290607	+	0.503346i
$116$		−	29.7848i		−	0.256765i
$117$	−4.64912	+	15.6732i	−0.0397361	+	0.133959i
$118$	34.0755			0.288776
$119$	5.01035	−	8.67819i	0.0421038	−	0.0729259i
$120$	25.7160	+	20.2809i	0.214300	+	0.169007i
$121$	20.8667	+	36.1423i	0.172452	+	0.298696i
$122$	−39.8373	+	23.0001i	−0.326535	+	0.188525i
$123$	−60.0917	−	47.3911i	−0.488551	−	0.385293i
$124$	−0.240088	−	0.138615i	−0.00193619	−	0.00111786i
$125$	135.486			1.08389
$126$	−18.8321	+	63.4872i	−0.149461	+	0.503867i
$127$		−	166.123i		−	1.30806i	−0.756469	−	0.654029i	$-0.773077\pi$
$127$		−	166.123i		−	1.30806i	0.756469	−	0.654029i	$-0.226923\pi$
$128$	9.79796	+	5.65685i	0.0765466	+	0.0441942i
$129$	−73.8079	−	10.7160i	−0.572155	−	0.0830699i
$130$	−4.95759	−	8.58680i	−0.0381353	−	0.0660523i
$131$	58.0701	+	100.580i	0.443283	+	0.767789i	0.997931	−	0.0642960i	$-0.0204802\pi$
$131$	58.0701	+	100.580i	0.443283	+	0.767789i	−0.554647	+	0.832085i	$0.687147\pi$
$132$	−19.7854	−	49.6199i	−0.149889	−	0.375908i
$133$	98.5646	+	7.55871i	0.741088	+	0.0568324i
$134$	−60.9586			−0.454915
$135$	−9.47627	−	103.781i	−0.0701946	−	0.768750i
$136$			5.44757i			0.0400556i
$137$	129.268	−	223.899i	0.943564	−	1.63430i	0.184963	−	0.982745i	$-0.440783\pi$
$137$	129.268	−	223.899i	0.943564	−	1.63430i	0.758601	−	0.651556i	$-0.225883\pi$
$138$	68.2451	−	27.2119i	0.494530	−	0.197188i
$139$	99.6419	+	172.585i	0.716848	+	1.24162i	0.962242	+	0.272194i	$0.0877494\pi$
$139$	99.6419	+	172.585i	0.716848	+	1.24162i	−0.245394	+	0.969423i	$0.578917\pi$
$140$	−20.0816	−	34.7824i	−0.143440	−	0.248446i
$141$	−145.791	−	21.1671i	−1.03398	−	0.150122i
$142$	67.8747	−	117.562i	0.477991	−	0.827904i
$143$			16.1723i			0.113093i
$144$	−8.39068	−	35.0085i	−0.0582686	−	0.243115i
$145$		−	57.4808i		−	0.396419i
$146$	−18.5301	−	10.6984i	−0.126919	−	0.0732765i
$147$	−40.7408	+	51.6592i	−0.277148	+	0.351423i
$148$	42.8976	−	24.7669i	0.289848	−	0.167344i
$149$	4.52486	+	7.83729i	0.0303682	+	0.0525993i	0.880810	−	0.473470i	$-0.156999\pi$
$149$	4.52486	+	7.83729i	0.0303682	+	0.0525993i	−0.850442	+	0.526069i	$0.823665\pi$
$150$	−33.6542	−	26.5413i	−0.224362	−	0.176942i
$151$	86.8534	+	50.1448i	0.575188	+	0.332085i	0.759219	−	0.650835i	$-0.225581\pi$
$151$	86.8534	+	50.1448i	0.575188	+	0.332085i	−0.184031	+	0.982921i	$0.558915\pi$
$152$	−48.4586	+	23.2328i	−0.318807	+	0.152847i
$153$	12.5782	−	11.9272i	0.0822106	−	0.0779554i
$154$			65.5090i			0.425383i
$155$	−0.463338	−	0.267508i	−0.00298928	−	0.00172586i
$156$	−1.56596	+	10.7857i	−0.0100382	+	0.0691392i
$157$	93.1462	+	161.334i	0.593288	+	1.02760i	0.993786	+	0.111307i	$0.0355037\pi$
$157$	93.1462	+	161.334i	0.593288	+	1.02760i	−0.400498	+	0.916298i	$0.631163\pi$
$158$	−22.0001	−	38.1052i	−0.139241	−	0.241172i
$159$	−245.678	+	97.9614i	−1.54515	+	0.616109i
$160$	18.9088	+	10.9170i	0.118180	+	0.0682313i
$161$	−90.0983			−0.559617
$162$	−62.4624	+	96.0232i	−0.385570	+	0.592736i
$163$	188.909			1.15895			0.579475	−	0.814990i	$-0.303258\pi$
$163$	188.909			1.15895			0.579475	+	0.814990i	$0.303258\pi$
$164$	−44.1850	−	25.5102i	−0.269420	−	0.155550i
$165$	−38.1832	−	95.7600i	−0.231413	−	0.580364i
$166$	36.4876	−	21.0661i	0.219805	−	0.126904i
$167$	−3.82026	+	2.20563i	−0.0228758	+	0.0132074i	−0.511394	−	0.859346i	$-0.670871\pi$
$167$	−3.82026	+	2.20563i	−0.0228758	+	0.0132074i	0.488518	+	0.872554i	$0.337537\pi$
$168$	−6.34319	+	43.6895i	−0.0377571	+	0.260057i
$169$	−82.8502	+	143.501i	−0.490238	+	0.849117i
$170$			10.5131i			0.0618418i
$171$	159.741	+	61.0222i	0.934160	+	0.356855i
$172$	−49.7212			−0.289077
$173$	1.24351	+	0.717940i	0.00718791	+	0.00414994i	0.503590	−	0.863943i	$-0.332012\pi$
$173$	1.24351	+	0.717940i	0.00718791	+	0.00414994i	−0.496402	+	0.868093i	$0.665346\pi$
$174$	−39.1257	+	49.6112i	−0.224860	+	0.285122i
$175$	26.2806	+	45.5193i	0.150175	+	0.260110i
$176$	−17.8063	−	30.8415i	−0.101172	−	0.175236i
$177$	−56.7582	−	44.7621i	−0.320668	−	0.252893i
$178$	44.9234	−	77.8096i	0.252379	−	0.437133i
$179$			133.988i			0.748538i	0.927320	+	0.374269i	$0.122106\pi$
$179$			133.988i			0.748538i	−0.927320	+	0.374269i	$0.877894\pi$
$180$	−16.1929	−	67.5619i	−0.0899607	−	0.375344i
$181$		−	8.14248i		−	0.0449861i	−0.999747	−	0.0224930i	$-0.992840\pi$
$181$		−	8.14248i		−	0.0449861i	0.999747	−	0.0224930i	$-0.00716036\pi$
$182$	6.68272	−	11.5748i	0.0367183	−	0.0635979i
$183$	96.5686	+	14.0206i	0.527697	+	0.0766152i
$184$	42.4181	−	24.4901i	0.230533	−	0.133098i
$185$	82.7868	−	47.7970i	0.447496	−	0.258362i
$186$	0.217818	+	0.546267i	0.00117106	+	0.00293692i
$187$	8.57378	−	14.8502i	0.0458491	−	0.0794130i
$188$	−98.2133			−0.522411
$189$	114.766	−	81.0099i	0.607225	−	0.428624i
$190$	−93.5189	+	44.8362i	−0.492205	+	0.235980i
$191$	−9.07869	+	15.7248i	−0.0475324	+	0.0823286i	−0.888813	−	0.458271i	$-0.848469\pi$
$191$	−9.07869	+	15.7248i	−0.0475324	+	0.0823286i	0.841280	+	0.540599i	$0.181802\pi$
$192$	−8.88913	−	22.2931i	−0.0462975	−	0.116110i
$193$	−8.07058	+	4.65955i	−0.0418165	+	0.0241428i	−0.520763	−	0.853702i	$-0.674352\pi$
$193$	−8.07058	+	4.65955i	−0.0418165	+	0.0241428i	0.478946	+	0.877844i	$0.341019\pi$
$194$	53.5164	+	92.6931i	0.275858	+	0.477799i
$195$	−3.02209	+	20.8150i	−0.0154979	+	0.106744i
$196$	−21.9304	+	37.9846i	−0.111890	+	0.193799i
$197$	−272.525			−1.38338			−0.691688	−	0.722196i	$-0.743133\pi$
$197$	−272.525			−1.38338			−0.691688	+	0.722196i	$0.743133\pi$
$198$	−32.2258	+	108.640i	−0.162756	+	0.548687i
$199$	−253.479			−1.27376			−0.636882	−	0.770961i	$-0.719776\pi$
$199$	−253.479			−1.27376			−0.636882	+	0.770961i	$0.719776\pi$
$200$	−24.7457	−	14.2869i	−0.123728	−	0.0714347i
$201$	101.536	+	80.0760i	0.505155	+	0.398388i
$202$	−158.535	+	91.5303i	−0.784828	+	0.453120i
$203$	67.1020	−	38.7414i	0.330552	−	0.190844i
$204$	7.15600	−	9.07378i	0.0350784	−	0.0444793i
$205$	−85.2713	−	49.2314i	−0.415957	−	0.240153i
$206$	−4.78257			−0.0232164
$207$	−149.419	−	44.3220i	−0.721831	−	0.214116i
$208$			7.26587i			0.0349321i
$209$	168.665	+	12.9346i	0.807010	+	0.0618879i
$210$	−12.2415	+	84.3152i	−0.0582931	+	0.401501i
$211$	−299.964	+	173.184i	−1.42163	+	0.820777i	−0.996438	−	0.0843267i	$-0.973126\pi$
$211$	−299.964	+	173.184i	−1.42163	+	0.820777i	−0.425190	+	0.905104i	$0.639793\pi$
$212$	−152.703	+	88.1629i	−0.720295	+	0.415863i
$213$	−267.488	+	106.658i	−1.25581	+	0.500740i
$214$	67.1897	−	116.376i	0.313971	−	0.543813i
$215$	−95.9555			−0.446305
$216$	−32.0117	+	69.3343i	−0.148202	+	0.320992i
$217$		−	0.721190i		−	0.00332346i
$218$	−19.7992	+	34.2932i	−0.0908218	+	0.157308i
$219$	16.8113	+	42.1612i	0.0767640	+	0.192517i
$220$	−34.3640	−	59.5201i	−0.156200	−	0.270546i
$221$	−3.02981	+	1.74926i	−0.0137096	+	0.00791522i
$222$	−103.987	−	15.0976i	−0.468409	−	0.0680073i
$223$	218.516	+	126.160i	0.979893	+	0.565741i	0.902238	−	0.431239i	$-0.141923\pi$
$223$	218.516	+	126.160i	0.979893	+	0.565741i	0.0776552	+	0.996980i	$0.475257\pi$
$224$			29.4317i			0.131392i
$225$	21.1915	+	88.4174i	0.0941843	+	0.392966i
$226$	−177.372			−0.784834
$227$	86.5843	+	49.9895i	0.381429	+	0.220218i	0.678440	−	0.734656i	$-0.262656\pi$
$227$	86.5843	+	49.9895i	0.381429	+	0.220218i	−0.297011	+	0.954874i	$0.595990\pi$
$228$	111.234	+	24.9581i	0.487870	+	0.109465i
$229$	183.038	+	317.030i	0.799290	+	1.38441i	0.920079	+	0.391733i	$0.128124\pi$
$229$	183.038	+	317.030i	0.799290	+	1.38441i	−0.120788	+	0.992678i	$0.538542\pi$
$230$	81.8615	−	47.2627i	0.355919	−	0.205490i
$231$	86.0535	−	109.116i	0.372526	−	0.472362i
$232$	−21.0610	+	36.4787i	−0.0907802	+	0.157236i
$233$	72.9160			0.312944			0.156472	−	0.987682i	$-0.449988\pi$
$233$	72.9160			0.312944			0.156472	+	0.987682i	$0.449988\pi$
$234$	16.7766	−	15.9083i	0.0716950	−	0.0679840i
$235$	−189.539			−0.806549
$236$	−41.7338	−	24.0950i	−0.176838	−	0.102098i
$237$	−13.4110	+	92.3698i	−0.0565864	+	0.389746i
$238$	−12.2728	+	7.08571i	−0.0515664	+	0.0297719i
$239$	169.400	+	293.409i	0.708787	+	1.22765i	0.965307	+	0.261116i	$0.0840905\pi$
$239$	169.400	+	293.409i	0.708787	+	1.22765i	−0.256521	+	0.966539i	$0.582576\pi$
$240$	−17.1549	−	43.0229i	−0.0714786	−	0.179262i
$241$	−271.037	−	156.483i	−1.12463	−	0.649307i	−0.182054	−	0.983289i	$-0.558274\pi$
$241$	−271.037	−	156.483i	−1.12463	−	0.649307i	−0.942580	+	0.333981i	$0.891608\pi$
$242$		−	59.0201i		−	0.243885i
$243$	230.178	−	77.8903i	0.947236	−	0.320536i
$244$	65.0541			0.266615
$245$	−42.3229	+	73.3053i	−0.172746	+	0.299205i
$246$	40.0865	+	100.533i	0.162953	+	0.408672i
$247$	−28.4820	−	19.4913i	−0.115312	−	0.0789123i
$248$	0.196031	+	0.339535i	0.000790446	+	0.00136909i
$249$	−88.4487	−	12.8417i	−0.355216	−	0.0515730i
$250$	−165.936	−	95.8032i	−0.663744	−	0.383213i
$251$	431.498			1.71912			0.859558	−	0.511038i	$-0.170739\pi$
$251$	431.498			1.71912			0.859558	+	0.511038i	$0.170739\pi$
$252$	67.9568	−	64.4393i	0.269670	−	0.255712i
$253$	−154.177			−0.609396
$254$	−117.467	+	203.459i	−0.462468	+	0.801019i
$255$	13.8102	−	17.5112i	0.0541575	−	0.0686715i
$256$	−8.00000	−	13.8564i	−0.0312500	−	0.0541266i
$257$	−130.545	+	75.3699i	−0.507955	+	0.293268i	−0.731993	−	0.681312i	$-0.761410\pi$
$257$	−130.545	+	75.3699i	−0.507955	+	0.293268i	0.224037	+	0.974581i	$0.428076\pi$
$258$	82.8185	+	65.3145i	0.321002	+	0.253157i
$259$	111.595	+	64.4292i	0.430867	+	0.248761i
$260$			14.0222i			0.0539315i
$261$	130.340	−	31.2393i	0.499387	−	0.119691i
$262$		−	164.247i		−	0.626897i
$263$	78.8276	−	136.533i	0.299725	−	0.519139i	−0.676348	−	0.736582i	$-0.736438\pi$
$263$	78.8276	−	136.533i	0.299725	−	0.519139i	0.976073	+	0.217443i	$0.0697718\pi$
$264$	−10.8545	+	74.7621i	−0.0411157	+	0.283190i
$265$	−294.696	+	170.143i	−1.11206	+	0.642049i
$266$	−115.372	−	78.9532i	−0.433728	−	0.296817i
$267$	−177.039	+	70.5922i	−0.663067	+	0.264390i
$268$	74.6587	+	43.1042i	0.278577	+	0.160837i
$269$		−	427.232i		−	1.58822i	−0.607773	−	0.794111i	$-0.707937\pi$
$269$		−	427.232i		−	1.58822i	0.607773	−	0.794111i	$-0.292063\pi$
$270$	−61.7785	+	133.806i	−0.228809	+	0.495579i
$271$	−126.115			−0.465370			−0.232685	−	0.972552i	$-0.574751\pi$
$271$	−126.115			−0.465370			−0.232685	+	0.972552i	$0.574751\pi$
$272$	3.85201	−	6.67188i	0.0141618	−	0.0245290i
$273$	−26.3360	+	10.5012i	−0.0964688	+	0.0384658i
$274$	−316.641	+	182.813i	−1.15563	+	0.667201i
$275$	44.9717	+	77.8932i	0.163533	+	0.283248i
$276$	−102.825	−	14.9289i	−0.372553	−	0.0540902i
$277$	274.455	−	475.370i	0.990811	−	1.71614i	0.378274	−	0.925694i	$-0.376518\pi$
$277$	274.455	−	475.370i	0.990811	−	1.71614i	0.612537	−	0.790442i	$-0.290149\pi$
$278$		−	281.830i		−	1.01378i
$279$	0.354774	−	1.19602i	0.00127159	−	0.00428682i
$280$			56.7995i			0.202855i
$281$	−372.487	−	215.056i	−1.32558	−	0.765322i	−0.340965	−	0.940076i	$-0.610754\pi$
$281$	−372.487	−	215.056i	−1.32558	−	0.765322i	−0.984612	+	0.174754i	$0.944087\pi$
$282$	163.590	+	129.014i	0.580106	+	0.457498i
$283$	35.7112	+	61.8537i	0.126188	+	0.218564i	0.922197	−	0.386721i	$-0.126392\pi$
$283$	35.7112	+	61.8537i	0.126188	+	0.218564i	−0.796009	+	0.605285i	$0.793059\pi$
$284$	−166.258	+	95.9893i	−0.585416	+	0.337990i
$285$	214.668	+	48.1659i	0.753221	+	0.169003i
$286$	11.4356	−	19.8070i	0.0399845	−	0.0692551i
$287$		−	132.726i		−	0.462459i
$288$	−14.4783	+	48.8096i	−0.0502720	+	0.169478i
$289$	−285.291			−0.987164
$290$	−40.6450	+	70.3993i	−0.140155	+	0.242756i
$291$	32.6230	−	224.695i	0.112106	−	0.772147i
$292$	15.1298	+	26.2055i	0.0518143	+	0.0897450i
$293$	190.841	−	110.182i	0.651335	−	0.376049i	−0.137632	−	0.990483i	$-0.543949\pi$
$293$	190.841	−	110.182i	0.651335	−	0.376049i	0.788968	+	0.614435i	$0.210616\pi$
$294$	86.4256	−	34.4612i	0.293965	−	0.117215i
$295$	−80.5409	−	46.5003i	−0.273020	−	0.157628i
$296$	−70.0514			−0.236660
$297$	196.388	−	138.625i	0.661240	−	0.466751i
$298$		−	12.7982i		−	0.0429471i
$299$	27.2417	+	15.7280i	0.0911093	+	0.0526020i
$300$	22.4503	+	56.3034i	0.0748345	+	0.187678i
$301$	−64.6729	−	112.017i	−0.214860	−	0.372149i
$302$	−70.9155	−	122.829i	−0.234820	−	0.406720i
$303$	384.301	+	55.7958i	1.26832	+	0.184145i
$304$	75.7775	+	5.81122i	0.249268	+	0.0191158i
$305$	125.546			0.411626
$306$	−23.8389	+	5.71360i	−0.0779049	+	0.0186719i
$307$		−	264.466i		−	0.861453i	−0.902482	−	0.430727i	$-0.858257\pi$
$307$		−	264.466i		−	0.861453i	0.902482	−	0.430727i	$-0.141743\pi$
$308$	46.3218	−	80.2318i	0.150396	−	0.260493i
$309$	7.96613	+	6.28245i	0.0257804	+	0.0203316i
$310$	0.378314	+	0.655259i	0.00122037	+	0.00211374i
$311$	24.1544	+	41.8366i	0.0776667	+	0.134523i	0.902243	−	0.431228i	$-0.141920\pi$
$311$	24.1544	+	41.8366i	0.0776667	+	0.134523i	−0.824576	+	0.565751i	$0.808586\pi$
$312$	9.54455	−	12.1025i	0.0305915	−	0.0387899i
$313$	−21.5582	+	37.3398i	−0.0688759	+	0.119297i	−0.898407	−	0.439164i	$-0.855275\pi$
$313$	−21.5582	+	37.3398i	−0.0688759	+	0.119297i	0.829531	+	0.558461i	$0.188608\pi$
$314$		−	263.457i		−	0.839036i
$315$	131.148	−	124.360i	0.416342	−	0.394792i
$316$			62.2255i			0.196916i
$317$	−506.486	−	292.420i	−1.59775	−	0.922460i	−0.991920	−	0.126864i	$-0.959509\pi$
$317$	−506.486	−	292.420i	−1.59775	−	0.922460i	−0.605827	−	0.795596i	$-0.707158\pi$
$318$	370.162	+	53.7431i	1.16403	+	0.169003i
$319$	114.826	−	66.2947i	0.359956	−	0.207820i
$320$	−15.4390	−	26.7411i	−0.0482468	−	0.0835659i
$321$	−264.788	+	105.581i	−0.824886	+	0.328914i
$322$	110.347	+	63.7091i	0.342694	+	0.197854i
$323$	15.8203	+	32.9977i	0.0489791	+	0.102160i
$324$	144.399	−	73.4363i	0.445676	−	0.226655i
$325$		−	18.3507i		−	0.0564636i
$326$	−231.365	−	133.579i	−0.709709	−	0.409751i
$327$	78.0266	−	31.1122i	0.238613	−	0.0951444i
$328$	36.0769	+	62.4870i	0.109990	+	0.190509i
$329$	−127.747	−	221.265i	−0.388289	−	0.672537i
$330$	−20.9479	+	144.281i	−0.0634784	+	0.437216i
$331$	332.551	+	191.998i	1.00468	+	0.580055i	0.909631	−	0.415417i	$-0.136364\pi$
$331$	332.551	+	191.998i	1.00468	+	0.580055i	0.0950534	+	0.995472i	$0.469698\pi$
$332$	−59.5841			−0.179470
$333$	153.374	+	161.746i	0.460583	+	0.485724i
$334$	6.23846			0.0186780
$335$	144.082	+	83.1856i	0.430094	+	0.248315i
$336$	38.6620	−	49.0232i	0.115065	−	0.145902i
$337$	57.2392	−	33.0471i	0.169849	−	0.0980625i	−0.412666	−	0.910883i	$-0.635402\pi$
$337$	57.2392	−	33.0471i	0.169849	−	0.0980625i	0.582515	+	0.812820i	$0.302069\pi$
$338$	202.941	−	117.168i	0.600416	−	0.346651i
$339$	295.442	+	232.999i	0.871510	+	0.687313i
$340$	7.43389	−	12.8759i	0.0218644	−	0.0378702i
$341$		−	1.23411i		−	0.00361909i
$342$	−152.493	−	187.691i	−0.445886	−	0.548803i
$343$	−369.040			−1.07592
$344$	60.8958	+	35.1582i	0.177023	+	0.102204i
$345$	−198.438	−	28.8108i	−0.575183	−	0.0835096i
$346$	−1.01532	−	1.75859i	−0.00293445	−	0.00508262i
$347$	61.5728	+	106.647i	0.177443	+	0.307340i	0.941004	−	0.338395i	$-0.109884\pi$
$347$	61.5728	+	106.647i	0.177443	+	0.307340i	−0.763561	+	0.645736i	$0.776551\pi$
$348$	82.9994	−	33.0951i	0.238504	−	0.0951008i
$349$	207.769	−	359.866i	0.595327	−	1.03114i	−0.398174	−	0.917310i	$-0.630356\pi$
$349$	207.769	−	359.866i	0.595327	−	1.03114i	0.993501	−	0.113826i	$-0.0363107\pi$
$350$		−	74.3327i		−	0.212379i
$351$	−48.8414	+	4.45971i	−0.139149	+	0.0127057i
$352$			50.3640i			0.143079i
$353$	45.4106	−	78.6535i	0.128642	−	0.222815i	−0.794509	−	0.607253i	$-0.792272\pi$
$353$	45.4106	−	78.6535i	0.128642	−	0.222815i	0.923151	+	0.384438i	$0.125605\pi$
$354$	37.8627	+	94.9562i	0.106957	+	0.268238i
$355$	−320.857	+	185.247i	−0.903823	+	0.521822i
$356$	−110.039	+	63.5313i	−0.309099	+	0.178459i
$357$	29.7502	+	4.31937i	0.0833339	+	0.0120991i
$358$	94.7440	−	164.101i	0.264648	−	0.458384i
$359$	519.637			1.44746			0.723729	−	0.690085i	$-0.242427\pi$
$359$	519.637			1.44746			0.723729	+	0.690085i	$0.242427\pi$
$360$	−27.9413	+	94.1963i	−0.0776147	+	0.261656i
$361$	−226.060	+	281.457i	−0.626204	+	0.779659i
$362$	−5.75760	+	9.97246i	−0.0159050	+	0.0275482i
$363$	−77.5296	+	98.3073i	−0.213580	+	0.270819i
$364$	−16.3693	+	9.45080i	−0.0449705	+	0.0259637i
$365$	29.1985	+	50.5733i	0.0799959	+	0.138557i
$366$	−108.358	−	85.4560i	−0.296060	−	0.233486i
$367$	−40.5303	+	70.2006i	−0.110437	+	0.191282i	−0.915946	−	0.401300i	$-0.868558\pi$
$367$	−40.5303	+	70.2006i	−0.110437	+	0.191282i	0.805510	+	0.592583i	$0.201892\pi$
$368$	−69.2685			−0.188230
$369$	65.2916	−	220.112i	0.176942	−	0.596510i
$370$	−135.190			−0.365379
$371$	−397.244	−	229.349i	−1.07074	−	0.618191i
$372$	0.119498	−	0.823058i	0.000321231	−	0.00221252i
$373$	228.571	−	131.966i	0.612792	−	0.353796i	−0.161265	−	0.986911i	$-0.551558\pi$
$373$	228.571	−	131.966i	0.612792	−	0.353796i	0.774057	+	0.633115i	$0.218224\pi$
$374$	−21.0014	+	12.1252i	−0.0561534	+	0.0324202i
$375$	150.544	+	377.551i	0.401451	+	1.00680i
$376$	120.286	+	69.4473i	0.319910	+	0.184700i
$377$	−27.0515			−0.0717547
$378$	−197.841	+	18.0649i	−0.523389	+	0.0477907i
$379$			632.212i			1.66811i	0.551684	+	0.834053i	$0.313985\pi$
$379$			632.212i			1.66811i	−0.551684	+	0.834053i	$0.686015\pi$
$380$	146.241	+	11.2149i	0.384844	+	0.0295129i
$381$	462.926	−	184.586i	1.21503	−	0.484479i
$382$	22.2382	−	12.8392i	0.0582151	−	0.0336105i
$383$	18.5524	−	10.7112i	0.0484396	−	0.0279666i	−0.475585	−	0.879670i	$-0.657763\pi$
$383$	18.5524	−	10.7112i	0.0484396	−	0.0279666i	0.524024	+	0.851703i	$0.324430\pi$
$384$	−4.87671	+	33.5890i	−0.0126998	+	0.0874712i
$385$	89.3952	−	154.837i	0.232195	−	0.402174i
$386$	13.1792			0.0341430
$387$	−52.1493	−	217.583i	−0.134753	−	0.562231i
$388$		−	151.367i		−	0.390122i
$389$	−111.164	+	192.541i	−0.285768	+	0.494964i	−0.972795	−	0.231667i	$-0.925582\pi$
$389$	−111.164	+	192.541i	−0.285768	+	0.494964i	0.687027	+	0.726632i	$0.258915\pi$
$390$	18.4198	−	23.3562i	0.0472301	−	0.0598876i
$391$	−16.6764	−	28.8844i	−0.0426507	−	0.0738732i
$392$	53.7183	−	31.0143i	0.137036	−	0.0791180i
$393$	−215.757	+	273.580i	−0.549001	+	0.696131i
$394$	333.774	+	192.704i	0.847141	+	0.489097i
$395$			120.087i			0.304018i
$396$	116.288	−	110.269i	0.293658	−	0.278458i
$397$	−1.43653			−0.00361846			−0.00180923	−	0.999998i	$-0.500576\pi$
$397$	−1.43653			−0.00361846			−0.00180923	+	0.999998i	$0.500576\pi$
$398$	310.447	+	179.237i	0.780018	+	0.450344i
$399$	88.4558	+	283.063i	0.221694	+	0.709431i
$400$	20.2048	+	34.9957i	0.0505119	+	0.0874892i
$401$	−123.964	+	71.5706i	−0.309137	+	0.178480i	−0.646540	−	0.762880i	$-0.723785\pi$
$401$	−123.964	+	71.5706i	−0.309137	+	0.178480i	0.337403	+	0.941360i	$0.390451\pi$
$402$	−67.7335	−	169.870i	−0.168491	−	0.422561i
$403$	−0.125894	+	0.218056i	−0.000312393	+	0.000541081i
$404$	258.887			0.640809
$405$	278.672	−	141.723i	0.688078	−	0.349932i
$406$	−109.577			−0.269894
$407$	190.962	+	110.252i	0.469195	+	0.270890i
$408$	−15.1804	+	6.05301i	−0.0372069	+	0.0148358i
$409$	9.82032	−	5.66976i	0.0240106	−	0.0138625i	−0.487947	−	0.872873i	$-0.662254\pi$
$409$	9.82032	−	5.66976i	0.0240106	−	0.0138625i	0.511957	+	0.859011i	$0.328921\pi$
$410$	69.6237	+	120.592i	0.169814	+	0.294126i
$411$	767.562	+	111.441i	1.86755	+	0.271145i
$412$	5.85743	+	3.38179i	0.0142171	+	0.00820822i
$413$		−	125.363i		−	0.303542i
$414$	151.660	+	159.938i	0.366328	+	0.386324i
$415$	−114.990			−0.277083
$416$	5.13775	−	8.89884i	0.0123503	−	0.0213914i
$417$	−370.216	+	469.432i	−0.887808	+	1.12574i
$418$	−197.426	−	135.106i	−0.472310	−	0.323220i
$419$	−108.022	−	187.100i	−0.257809	−	0.446538i	0.707846	−	0.706367i	$-0.249667\pi$
$419$	−108.022	−	187.100i	−0.257809	−	0.446538i	−0.965655	+	0.259829i	$0.916334\pi$
$420$	74.6126	−	94.6085i	0.177649	−	0.225258i
$421$	−265.389	−	153.222i	−0.630377	−	0.363948i	0.150521	−	0.988607i	$-0.451905\pi$
$421$	−265.389	−	153.222i	−0.630377	−	0.363948i	−0.780898	+	0.624659i	$0.785238\pi$
$422$	489.838			1.16075
$423$	−103.010	−	429.788i	−0.243521	−	1.01605i
$424$	249.362			0.588119
$425$	−9.72863	+	16.8505i	−0.0228909	+	0.0396482i
$426$	403.022	+	58.5140i	0.946062	+	0.137357i
$427$	84.6166	+	146.560i	0.198165	+	0.343232i
$428$	−164.581	+	95.0206i	−0.384534	+	0.222011i
$429$	−45.0665	+	17.9697i	−0.105050	+	0.0418875i
$430$	117.521	+	67.8508i	0.273305	+	0.157793i
$431$			22.7370i			0.0527540i	0.999652	+	0.0263770i	$0.00839704\pi$
$431$			22.7370i			0.0527540i	−0.999652	+	0.0263770i	$0.991603\pi$
$432$	88.2329	−	62.2812i	0.204243	−	0.144169i
$433$			508.681i			1.17478i	0.809303	+	0.587392i	$0.199845\pi$
$433$			508.681i			1.17478i	−0.809303	+	0.587392i	$0.800155\pi$
$434$	−0.509959	+	0.883274i	−0.00117502	+	0.00203519i
$435$	160.178	−	63.8692i	0.368226	−	0.146826i
$436$	48.4978	−	28.0002i	0.111234	−	0.0642207i
$437$	185.819	−	271.531i	0.425215	−	0.621352i
$438$	9.22294	−	63.5242i	0.0210569	−	0.145032i
$439$	−287.494	−	165.985i	−0.654883	−	0.378097i	0.135441	−	0.990785i	$-0.456755\pi$
$439$	−287.494	−	165.985i	−0.654883	−	0.378097i	−0.790325	+	0.612688i	$0.790088\pi$
$440$			97.1960i			0.220900i
$441$	−189.224	−	56.1293i	−0.429080	−	0.127277i
$442$	4.94766			0.0111938
$443$	−82.4575	+	142.821i	−0.186134	+	0.322394i	−0.943958	−	0.330065i	$-0.892929\pi$
$443$	−82.4575	+	142.821i	−0.186134	+	0.322394i	0.757824	+	0.652459i	$0.226263\pi$
$444$	116.682	+	92.0205i	0.262797	+	0.207253i
$445$	−212.362	+	122.607i	−0.477218	+	0.275522i
$446$	−178.418	−	309.028i	−0.400040	−	0.692889i
$447$	−16.8120	+	21.3175i	−0.0376106	+	0.0476901i
$448$	20.8114	−	36.0464i	0.0464540	−	0.0804606i
$449$			521.089i			1.16055i	0.814419	+	0.580277i	$0.197056\pi$
$449$			521.089i			1.16055i	−0.814419	+	0.580277i	$0.802944\pi$
$450$	36.5664	−	123.273i	0.0812587	−	0.273941i
$451$		−	227.122i		−	0.503596i
$452$	217.236	+	125.421i	0.480611	+	0.277481i
$453$	−43.2293	+	297.747i	−0.0954289	+	0.657279i
$454$	−70.6958	−	122.449i	−0.155718	−	0.269711i
$455$	−31.5906	+	18.2388i	−0.0694298	+	0.0400853i
$456$	−118.586	−	109.222i	−0.260056	−	0.239522i
$457$	159.906	−	276.965i	0.349903	−	0.606050i	−0.636329	−	0.771418i	$-0.719548\pi$
$457$	159.906	−	276.965i	0.349903	−	0.606050i	0.986232	+	0.165368i	$0.0528812\pi$
$458$		−	517.708i		−	1.13037i
$459$	47.2129	+	21.7982i	0.102860	+	0.0474907i
$460$	−133.679			−0.290607
$461$	−74.5442	+	129.114i	−0.161701	+	0.280074i	−0.935479	−	0.353383i	$-0.885031\pi$
$461$	−74.5442	+	129.114i	−0.161701	+	0.280074i	0.773778	+	0.633457i	$0.218365\pi$
$462$	−182.550	+	72.7897i	−0.395130	+	0.157553i
$463$	−436.324	−	755.735i	−0.942384	−	1.63226i	−0.760905	−	0.648863i	$-0.775245\pi$
$463$	−436.324	−	755.735i	−0.942384	−	1.63226i	−0.181479	−	0.983395i	$-0.558088\pi$
$464$	51.5887	−	29.7848i	0.111183	−	0.0641913i
$465$	0.230616	−	1.58840i	0.000495948	−	0.00341591i
$466$	−89.3035	−	51.5594i	−0.191638	−	0.110642i
$467$	−333.138			−0.713357			−0.356678	−	0.934227i	$-0.616091\pi$
$467$	−333.138			−0.713357			−0.356678	+	0.934227i	$0.616091\pi$
$468$	−31.7959	+	7.62070i	−0.0679400	+	0.0162835i
$469$			224.265i			0.478176i
$470$	232.137	+	134.024i	0.493909	+	0.285158i
$471$	−346.081	+	438.830i	−0.734780	+	0.931698i
$472$	34.0755	+	59.0205i	0.0721939	+	0.125043i
$473$	−110.669	−	191.685i	−0.233973	−	0.405253i
$474$	81.7404	−	103.646i	0.172448	−	0.218663i
$475$	−191.383	−	14.6768i	−0.402912	−	0.0308985i
$476$	20.0414			0.0421038
$477$	−545.966	−	575.768i	−1.14458	−	1.20706i
$478$		−	479.136i		−	1.00238i
$479$	275.991	−	478.030i	0.576181	−	0.997975i	−0.419731	−	0.907648i	$-0.637876\pi$
$479$	275.991	−	478.030i	0.576181	−	0.997975i	0.995912	−	0.0903262i	$-0.0287910\pi$
$480$	−9.41142	+	64.8224i	−0.0196071	+	0.135047i
$481$	−22.4941	−	38.9610i	−0.0467654	−	0.0810000i
$482$	221.300	+	383.304i	0.459130	+	0.795236i
$483$	−100.112	−	251.072i	−0.207271	−	0.519817i
$484$	−41.7335	+	72.2845i	−0.0862262	+	0.149348i
$485$		−	292.119i		−	0.602308i
$486$	−336.987	−	67.3650i	−0.693388	−	0.138611i
$487$		−	302.930i		−	0.622032i	−0.950405	−	0.311016i	$-0.899331\pi$
$487$		−	302.930i		−	0.622032i	0.950405	−	0.311016i	$-0.100669\pi$
$488$	−79.6746	−	46.0002i	−0.163268	−	0.0942626i
$489$	209.904	+	526.421i	0.429252	+	1.07653i
$490$	103.669	−	59.8536i	0.211570	−	0.122150i
$491$	26.1582	+	45.3073i	0.0532753	+	0.0922755i	0.891433	−	0.453152i	$-0.149701\pi$
$491$	26.1582	+	45.3073i	0.0532753	+	0.0922755i	−0.838158	+	0.545428i	$0.816367\pi$
$492$	21.9920	−	151.473i	0.0446993	−	0.307872i
$493$	24.8400	+	14.3414i	0.0503855	+	0.0290901i
$494$	21.1008	+	44.0118i	0.0427141	+	0.0890926i
$495$	224.422	−	212.806i	0.453377	−	0.429910i
$496$		−	0.554458i		−	0.00111786i
$497$	−432.508	−	249.709i	−0.870237	−	0.502432i
$498$	99.2467	+	78.2705i	0.199291	+	0.157170i
$499$	379.181	+	656.760i	0.759881	+	1.31615i	0.942911	+	0.333045i	$0.108076\pi$
$499$	379.181	+	656.760i	0.759881	+	1.31615i	−0.183030	+	0.983107i	$0.558590\pi$
$500$	135.486	+	234.669i	0.270972	+	0.469338i
$501$	−10.3911	−	8.19493i	−0.0207408	−	0.0163571i
$502$	−528.475	−	305.115i	−1.05274	−	0.607800i
$503$	−335.670			−0.667337			−0.333668	−	0.942691i	$-0.608287\pi$
$503$	−335.670			−0.667337			−0.333668	+	0.942691i	$0.608287\pi$
$504$	−128.795	+	30.8690i	−0.255546	+	0.0612481i
$505$	499.618			0.989343
$506$	188.828	+	109.020i	0.373178	+	0.215454i
$507$	−491.943	−	71.4242i	−0.970303	−	0.140876i
$508$	287.734	−	166.123i	0.566406	−	0.327014i
$509$	−16.2090	+	9.35825i	−0.0318447	+	0.0183856i	−0.515838	−	0.856686i	$-0.672519\pi$
$509$	−16.2090	+	9.35825i	−0.0318447	+	0.0183856i	0.483993	+	0.875072i	$0.339186\pi$
$510$	−29.2962	+	11.6815i	−0.0574436	+	0.0229050i
$511$	−39.3589	+	68.1717i	−0.0770234	+	0.133408i
$512$			22.6274i			0.0441942i
$513$	7.44819	+	512.946i	0.0145189	+	0.999895i
$514$	213.178			0.414744
$515$	11.3041	+	6.52642i	0.0219497	+	0.0126727i
$516$	−55.2473	−	138.555i	−0.107068	−	0.268518i
$517$	−218.603	−	378.631i	−0.422829	−	0.732361i
$518$	−91.1167	−	157.819i	−0.175901	−	0.304669i
$519$	−0.618928	+	4.26294i	−0.00119254	+	0.00821376i
$520$	9.91519	−	17.1736i	0.0190677	−	0.0330262i
$521$		−	117.234i		−	0.225018i	−0.993651	−	0.112509i	$-0.964111\pi$
$521$		−	117.234i		−	0.225018i	0.993651	−	0.112509i	$-0.0358887\pi$
$522$	−181.723	−	53.9042i	−0.348128	−	0.103265i
$523$		−	656.669i		−	1.25558i	−0.778382	−	0.627790i	$-0.783959\pi$
$523$		−	656.669i		−	1.25558i	0.778382	−	0.627790i	$-0.216041\pi$
$524$	−116.140	+	201.161i	−0.221642	+	0.383895i
$525$	−97.6445	+	123.813i	−0.185990	+	0.235834i
$526$	−193.087	+	111.479i	−0.367086	+	0.211937i
$527$	0.231205	−	0.133486i	0.000438719	−	0.000253295i
$528$	66.1588	−	83.8891i	0.125301	−	0.158881i
$529$	114.559	−	198.422i	0.216557	−	0.375088i
$530$	481.237			0.907995
$531$	61.6695	−	207.902i	0.116139	−	0.391528i
$532$	85.4726	+	178.278i	0.160663	+	0.335108i
$533$	−23.1692	+	40.1303i	−0.0434695	+	0.0752913i
$534$	266.744	+	38.7279i	0.499520	+	0.0725242i
$535$	−317.619	+	183.378i	−0.593681	+	0.342762i
$536$	−60.9586	−	105.583i	−0.113729	−	0.196984i
$537$	−373.377	+	148.880i	−0.695302	+	0.277244i
$538$	−302.098	+	523.250i	−0.561521	+	0.972583i
$539$	−195.250			−0.362245
$540$	170.278	−	120.195i	0.315330	−	0.222583i
$541$	795.600			1.47061			0.735305	−	0.677737i	$-0.237039\pi$
$541$	795.600			1.47061			0.735305	+	0.677737i	$0.237039\pi$
$542$	154.459	+	89.1769i	0.284980	+	0.164533i
$543$	22.6902	−	9.04744i	0.0417867	−	0.0166620i
$544$	−9.43546	+	5.44757i	−0.0173446	+	0.0100139i
$545$	93.5946	−	54.0369i	0.171733	−	0.0991502i
$546$	39.6803	+	5.76110i	0.0726745	+	0.0105515i
$547$	−30.3322	−	17.5123i	−0.0554520	−	0.0320152i	0.472018	−	0.881589i	$-0.343526\pi$
$547$	−30.3322	−	17.5123i	−0.0554520	−	0.0320152i	−0.527470	+	0.849574i	$0.676859\pi$
$548$	517.073			0.943564
$549$	68.2310	+	284.681i	0.124282	+	0.518544i
$550$		−	127.199i		−	0.231271i
$551$	−21.6357	+	282.127i	−0.0392663	+	0.512027i
$552$	115.378	+	90.9920i	0.209017	+	0.164841i
$553$	−140.188	+	80.9375i	−0.253504	+	0.146361i
$554$	−672.274	+	388.138i	−1.21349	+	0.700609i
$555$	225.181	+	177.588i	0.405731	+	0.319978i
$556$	−199.284	+	345.170i	−0.358424	+	0.620809i
$557$	−688.716			−1.23647			−0.618237	−	0.785992i	$-0.712153\pi$
$557$	−688.716			−1.23647			−0.618237	+	0.785992i	$0.712153\pi$
$558$	−1.28022	+	1.21396i	−0.00229431	+	0.00217555i
$559$			45.1585i			0.0807844i
$560$	40.1633	−	69.5649i	0.0717202	−	0.124223i
$561$	50.9089	+	7.39136i	0.0907467	+	0.0131753i
$562$	304.134	+	526.776i	0.541165	+	0.937324i
$563$	274.981	−	158.760i	0.488421	−	0.281990i	−0.235498	−	0.971875i	$-0.575672\pi$
$563$	274.981	−	158.760i	0.488421	−	0.281990i	0.723919	+	0.689885i	$0.242339\pi$
$564$	−109.129	−	273.685i	−0.193491	−	0.485258i
$565$	419.238	+	242.047i	0.742013	+	0.428402i
$566$		−	101.007i		−	0.178457i
$567$	353.266	+	229.797i	0.623044	+	0.405286i
$568$	271.499			0.477991
$569$	782.086	+	451.537i	1.37449	+	0.793563i	0.991490	−	0.130184i	$-0.0415569\pi$
$569$	782.086	+	451.537i	1.37449	+	0.793563i	0.383002	+	0.923748i	$0.374890\pi$
$570$	−228.855	−	210.784i	−0.401500	−	0.369797i
$571$	110.083	+	190.670i	0.192790	+	0.333923i	0.946174	−	0.323659i	$-0.104913\pi$
$571$	110.083	+	190.670i	0.192790	+	0.333923i	−0.753384	+	0.657581i	$0.771580\pi$
$572$	−28.0113	+	16.1723i	−0.0489708	+	0.0282733i
$573$	−53.9070	−	7.82664i	−0.0940785	−	0.0136591i
$574$	−93.8512	+	162.555i	−0.163504	+	0.283197i
$575$	174.944			0.304251
$576$	52.2459	−	49.5416i	0.0907046	−	0.0860097i
$577$	334.209			0.579219			0.289609	−	0.957145i	$-0.406475\pi$
$577$	334.209			0.579219			0.289609	+	0.957145i	$0.406475\pi$
$578$	349.408	+	201.731i	0.604512	+	0.349015i
$579$	−21.9521	−	17.3124i	−0.0379137	−	0.0299005i
$580$	99.5596	−	57.4808i	0.171654	−	0.0991048i
$581$	−77.5017	−	134.237i	−0.133394	−	0.231044i
$582$	−198.838	+	252.126i	−0.341646	+	0.433206i
$583$	−679.769	−	392.465i	−1.16598	−	0.673181i
$584$		−	42.7935i		−	0.0732765i
$585$	−61.3620	+	14.7070i	−0.104892	+	0.0251401i
$586$	−311.642			−0.531813
$587$	142.064	−	246.063i	0.242018	−	0.419187i	−0.719271	−	0.694729i	$-0.755524\pi$
$587$	142.064	−	246.063i	0.242018	−	0.419187i	0.961289	+	0.275542i	$0.0888574\pi$
$588$	−130.217	−	18.9059i	−0.221458	−	0.0321530i
$589$	2.17346	+	1.48738i	0.00369009	+	0.00252527i
$590$	65.7614	+	113.902i	0.111460	+	0.193054i
$591$	−302.814	−	759.429i	−0.512375	−	1.28499i
$592$	85.7951	+	49.5338i	0.144924	+	0.0836720i
$593$	−703.480			−1.18631			−0.593153	−	0.805089i	$-0.702117\pi$
$593$	−703.480			−1.18631			−0.593153	+	0.805089i	$0.702117\pi$
$594$	−338.548	+	30.9128i	−0.569947	+	0.0520418i
$595$	38.6774			0.0650040
$596$	−9.04972	+	15.6746i	−0.0151841	+	0.0262996i
$597$	−281.651	−	706.355i	−0.471777	−	1.18317i
$598$	−22.2427	−	38.5255i	−0.0371952	−	0.0644240i
$599$	−814.261	+	470.114i	−1.35937	+	0.784831i	−0.989538	−	0.144269i	$-0.953917\pi$
$599$	−814.261	+	470.114i	−1.35937	+	0.784831i	−0.369828	+	0.929100i	$0.620583\pi$
$600$	12.3166	−	84.8321i	0.0205277	−	0.141387i
$601$	705.469	+	407.303i	1.17383	+	0.677709i	0.954578	−	0.297961i	$-0.0963064\pi$
$601$	705.469	+	407.303i	1.17383	+	0.677709i	0.219248	+	0.975669i	$0.429640\pi$
$602$			182.923i			0.303858i
$603$	−110.322	+	371.920i	−0.182956	+	0.616784i
$604$			200.579i			0.332085i
$605$	−80.5403	+	139.500i	−0.133124	+	0.230578i
$606$	−431.217	−	340.077i	−0.711579	−	0.561184i
$607$	589.399	−	340.290i	0.971004	−	0.560609i	0.0714615	−	0.997443i	$-0.477234\pi$
$607$	589.399	−	340.290i	0.971004	−	0.560609i	0.899542	+	0.436834i	$0.143900\pi$
$608$	−88.6990	−	60.7000i	−0.145886	−	0.0998356i
$609$	182.518	+	143.942i	0.299701	+	0.236358i
$610$	−153.762	−	88.7744i	−0.252068	−	0.145532i
$611$			89.2007i			0.145991i
$612$	33.2367	+	9.85895i	0.0543083	+	0.0161094i
$613$	410.858			0.670242			0.335121	−	0.942175i	$-0.391223\pi$
$613$	410.858			0.670242			0.335121	+	0.942175i	$0.391223\pi$
$614$	−187.006	+	323.904i	−0.304570	+	0.527530i
$615$	42.4418	−	292.323i	0.0690111	−	0.475323i
$616$	−113.465	+	65.5090i	−0.184196	+	0.106346i
$617$	−146.972	−	254.563i	−0.238204	−	0.412582i	0.721995	−	0.691898i	$-0.243225\pi$
$617$	−146.972	−	254.563i	−0.238204	−	0.412582i	−0.960199	+	0.279317i	$0.909892\pi$
$618$	−5.31411	−	13.3273i	−0.00859888	−	0.0215652i
$619$	−543.317	+	941.053i	−0.877734	+	1.52028i	−0.0239118	+	0.999714i	$0.507612\pi$
$619$	−543.317	+	941.053i	−0.877734	+	1.52028i	−0.853822	+	0.520565i	$0.825721\pi$
$620$		−	1.07003i		−	0.00172586i
$621$	−42.5162	−	465.625i	−0.0684641	−	0.749799i
$622$		−	68.3188i		−	0.109837i
$623$	−286.259	−	165.272i	−0.459485	−	0.265284i
$624$	−20.2474	+	8.07340i	−0.0324477	+	0.0129381i
$625$	135.191	+	234.158i	0.216306	+	0.374652i
$626$	52.8065	−	30.4878i	0.0843554	−	0.0487026i
$627$	151.367	+	484.381i	0.241414	+	0.772538i
$628$	−186.292	+	322.668i	−0.296644	+	0.513802i
$629$			47.7012i			0.0758366i
$630$	−248.558	+	59.5732i	−0.394537	+	0.0945607i
$631$	−966.349			−1.53146			−0.765728	−	0.643164i	$-0.777621\pi$
$631$	−966.349			−1.53146			−0.765728	+	0.643164i	$0.777621\pi$
$632$	44.0001	−	76.2104i	0.0696204	−	0.120586i
$633$	−815.903	−	643.459i	−1.28895	−	1.01652i
$634$	413.544	+	716.279i	0.652278	+	1.12978i
$635$	555.290	−	320.597i	0.874472	−	0.504877i
$636$	−415.352	−	327.566i	−0.653070	−	0.515041i
$637$	34.4989	+	19.9179i	0.0541583	+	0.0312683i
$638$	−187.510			−0.293903
$639$	−594.433	−	626.880i	−0.930255	−	0.981033i
$640$			43.6680i			0.0682313i
$641$	351.472	+	202.922i	0.548318	+	0.316571i	0.748443	−	0.663199i	$-0.230802\pi$
$641$	351.472	+	202.922i	0.548318	+	0.316571i	−0.200125	+	0.979770i	$0.564135\pi$
$642$	398.955	+	57.9235i	0.621426	+	0.0902235i
$643$	−437.226	−	757.298i	−0.679979	−	1.17776i	−0.974987	−	0.222263i	$-0.928656\pi$
$643$	−437.226	−	757.298i	−0.679979	−	1.17776i	0.295008	−	0.955495i	$-0.404678\pi$
$644$	−90.0983	−	156.055i	−0.139904	−	0.242321i
$645$	−106.620	−	267.394i	−0.165302	−	0.414564i
$646$	3.95712	−	51.6004i	0.00612558	−	0.0798767i
$647$	−818.931			−1.26573			−0.632867	−	0.774260i	$-0.718122\pi$
$647$	−818.931			−1.26573			−0.632867	+	0.774260i	$0.718122\pi$
$648$	−228.779	−	12.1649i	−0.353055	−	0.0187730i
$649$		−	214.522i		−	0.330543i
$650$	−12.9759	+	22.4749i	−0.0199629	+	0.0345767i
$651$	2.00970	−	0.801344i	0.00308709	−	0.00123094i
$652$	188.909	+	327.200i	0.289738	+	0.501840i
$653$	−18.0356	−	31.2385i	−0.0276195	−	0.0478384i	0.851885	−	0.523728i	$-0.175459\pi$
$653$	−18.0356	−	31.2385i	−0.0276195	−	0.0478384i	−0.879505	+	0.475890i	$0.842126\pi$
$654$	−117.562	−	17.0686i	−0.179759	−	0.0260988i
$655$	−224.136	+	388.215i	−0.342192	+	0.592694i
$656$		−	102.041i		−	0.155550i
$657$	−98.8085	+	93.6942i	−0.150393	+	0.142609i
$658$			361.324i			0.549124i
$659$	−776.872	−	448.527i	−1.17887	−	0.680618i	−0.223114	−	0.974792i	$-0.571622\pi$
$659$	−776.872	−	448.527i	−1.17887	−	0.680618i	−0.955752	+	0.294174i	$0.904955\pi$
$660$	127.678	−	161.895i	0.193452	−	0.245296i
$661$	929.059	−	536.393i	1.40554	−	0.811486i	0.410582	−	0.911824i	$-0.365325\pi$
$661$	929.059	−	536.393i	1.40554	−	0.811486i	0.994954	+	0.100337i	$0.0319921\pi$
$662$	−271.526	−	470.297i	−0.410161	−	0.710419i
$663$	−8.24112	−	6.49932i	−0.0124300	−	0.00980290i
$664$	72.9753	+	42.1323i	0.109903	+	0.0634522i
$665$	164.951	+	344.053i	0.248047	+	0.517373i
$666$	−73.4723	−	306.550i	−0.110319	−	0.460285i
$667$		−	257.893i		−	0.386646i
$668$	−7.64052	−	4.41126i	−0.0114379	−	0.00660368i
$669$	−108.761	+	749.108i	−0.162573	+	1.11974i
$670$	−117.642	−	203.762i	−0.175585	−	0.304123i
$671$	144.797	+	250.796i	0.215793	+	0.373764i
$672$	−82.0157	+	32.7028i	−0.122047	+	0.0486649i
$673$	869.027	+	501.733i	1.29127	+	0.745517i	0.978880	−	0.204436i	$-0.0655361\pi$
$673$	869.027	+	501.733i	1.29127	+	0.745517i	0.312393	+	0.949953i	$0.398869\pi$
$674$	−93.4712			−0.138681
$675$	−222.841	+	157.297i	−0.330135	+	0.233033i
$676$	−331.401			−0.490238
$677$	463.414	+	267.552i	0.684512	+	0.395203i	0.801553	−	0.597924i	$-0.204008\pi$
$677$	463.414	+	267.552i	0.684512	+	0.395203i	−0.117041	+	0.993127i	$0.537341\pi$
$678$	−197.086	−	494.273i	−0.290687	−	0.729017i
$679$	341.015	−	196.885i	0.502231	−	0.289963i
$680$	−18.2092	+	10.5131i	−0.0267783	+	0.0154604i
$681$	−43.0954	+	296.825i	−0.0632825	+	0.435866i
$682$	−0.872648	+	1.51147i	−0.00127954	+	0.00221623i
$683$			707.067i			1.03524i	0.855611	+	0.517619i	$0.173181\pi$
$683$			707.067i			1.03524i	−0.855611	+	0.517619i	$0.826819\pi$
$684$	54.0478	+	337.702i	0.0790173	+	0.493717i
$685$	997.885			1.45677
$686$	451.980	+	260.951i	0.658863	+	0.380394i
$687$	−680.069	+	862.325i	−0.989911	+	1.25520i
$688$	−49.7212	−	86.1196i	−0.0722692	−	0.125174i
$689$	80.0725	+	138.690i	0.116216	+	0.201291i
$690$	222.664	+	175.603i	0.322701	+	0.254497i
$691$	59.6066	−	103.242i	0.0862614	−	0.149409i	−0.819667	−	0.572841i	$-0.805841\pi$
$691$	59.6066	−	103.242i	0.0862614	−	0.149409i	0.905928	+	0.423432i	$0.139175\pi$
$692$			2.87176i			0.00414994i
$693$	399.683	+	118.558i	0.576744	+	0.171079i
$694$		−	174.154i		−	0.250942i
$695$	−384.592	+	666.133i	−0.553370	+	0.958465i
$696$	−125.055	−	18.1565i	−0.179677	−	0.0260869i
$697$	42.5502	−	24.5664i	0.0610477	−	0.0352459i
$698$	−508.928	+	293.830i	−0.729123	+	0.420959i
$699$	81.0199	+	203.191i	0.115908	+	0.290688i
$700$	−52.5612	+	91.0386i	−0.0750874	+	0.130055i
$701$	392.596			0.560051			0.280025	−	0.959993i	$-0.409657\pi$
$701$	392.596			0.560051			0.280025	+	0.959993i	$0.409657\pi$
$702$	62.9718	+	29.0741i	0.0897034	+	0.0414161i
$703$	−424.324	+	203.436i	−0.603591	+	0.289383i
$704$	35.6127	−	61.6830i	0.0505862	−	0.0876179i
$705$	−210.605	−	528.177i	−0.298730	−	0.749188i
$706$	−111.233	+	64.2203i	−0.157554	+	0.0909637i
$707$	336.737	+	583.246i	0.476290	+	0.824958i
$708$	20.7720	−	143.070i	0.0293390	−	0.202076i
$709$	132.035	−	228.692i	0.186228	−	0.322555i	−0.757762	−	0.652531i	$-0.773707\pi$
$709$	132.035	−	228.692i	0.186228	−	0.322555i	0.943989	+	0.329976i	$0.107041\pi$
$710$	523.957			0.737968
$711$	−272.303	+	65.2643i	−0.382986	+	0.0917923i
$712$	179.694			0.252379
$713$	−2.07881	−	1.20020i	−0.00291558	−	0.00168331i
$714$	−33.3821	−	26.3267i	−0.0467537	−	0.0368721i
$715$	−54.0582	+	31.2105i	−0.0756058	+	0.0436511i
$716$	−232.075	+	133.988i	−0.324126	+	0.187134i
$717$	−629.400	+	798.076i	−0.877824	+	1.11308i
$718$	−636.423	−	367.439i	−0.886383	−	0.511753i
$719$	659.840			0.917719			0.458860	−	0.888509i	$-0.348258\pi$
$719$	659.840			0.917719			0.458860	+	0.888509i	$0.348258\pi$
$720$	100.828	−	95.6089i	0.140039	−	0.132790i
$721$			17.5949i			0.0244035i
$722$	475.886	−	184.865i	0.659121	−	0.256045i
$723$	134.902	−	929.156i	0.186587	−	1.28514i
$724$	14.1032	−	8.14248i	0.0194795	−	0.0112465i
$725$	−130.292	+	75.2243i	−0.179714	+	0.103758i
$726$	164.468	−	65.5796i	0.226540	−	0.0903300i
$727$	217.618	−	376.926i	0.299337	−	0.518468i	−0.676647	−	0.736307i	$-0.736568\pi$
$727$	217.618	−	376.926i	0.299337	−	0.518468i	0.975985	+	0.217840i	$0.0699011\pi$
$728$	26.7309			0.0367183
$729$	472.813	+	554.877i	0.648577	+	0.761149i
$730$		−	82.5859i		−	0.113131i
$731$	23.9408	−	41.4667i	0.0327508	−	0.0567260i
$732$	72.2842	+	181.282i	0.0987489	+	0.247653i
$733$	59.6987	+	103.401i	0.0814444	+	0.141066i	0.903871	−	0.427806i	$-0.140713\pi$
$733$	59.6987	+	103.401i	0.0814444	+	0.141066i	−0.822426	+	0.568872i	$0.807380\pi$
$734$	99.2786	−	57.3185i	0.135257	−	0.0780906i
$735$	−251.302	−	36.4860i	−0.341908	−	0.0496409i
$736$	84.8362	+	48.9802i	0.115267	+	0.0665492i
$737$			383.764i			0.520711i
$738$	−235.608	+	223.413i	−0.319253	+	0.302728i
$739$	364.707			0.493514			0.246757	−	0.969077i	$-0.420635\pi$
$739$	364.707			0.493514			0.246757	+	0.969077i	$0.420635\pi$
$740$	165.574	+	95.5939i	0.223748	+	0.129181i
$741$	22.6678	−	101.027i	0.0305908	−	0.136339i
$742$	324.348	+	561.788i	0.437127	+	0.757126i
$743$	−542.318	+	313.108i	−0.729903	+	0.421410i	−0.818387	−	0.574668i	$-0.805131\pi$
$743$	−542.318	+	313.108i	−0.729903	+	0.421410i	0.0884834	+	0.996078i	$0.471798\pi$
$744$	−0.728345	+	0.923538i	−0.000978958	+	0.00124131i
$745$	−17.4648	+	30.2499i	−0.0234427	+	0.0406039i
$746$	−373.256			−0.500343
$747$	−62.4938	−	260.744i	−0.0836597	−	0.349054i
$748$	34.2951			0.0458491
$749$	−428.144	−	247.189i	−0.571620	−	0.330025i
$750$	82.5908	−	568.855i	0.110121	−	0.758473i
$751$	1271.04	−	733.837i	1.69247	−	0.977146i	0.739949	−	0.672663i	$-0.234850\pi$
$751$	1271.04	−	733.837i	1.69247	−	0.977146i	0.952518	−	0.304483i	$-0.0984837\pi$
$752$	−98.2133	−	170.110i	−0.130603	−	0.226211i
$753$	479.455	+	1202.43i	0.636727	+	1.59685i
$754$	33.1312	+	19.1283i	0.0439406	+	0.0253691i
$755$			387.092i			0.512705i
$756$	255.079	+	117.770i	0.337406	+	0.155780i
$757$	84.5134			0.111643			0.0558213	−	0.998441i	$-0.482222\pi$
$757$	84.5134			0.111643			0.0558213	+	0.998441i	$0.482222\pi$
$758$	447.041	−	774.299i	0.589764	−	1.02150i
$759$	−171.313	−	429.637i	−0.225708	−	0.566056i
$760$	−171.178	−	117.143i	−0.225234	−	0.154136i
$761$	−303.316	−	525.360i	−0.398576	−	0.690354i	0.594974	−	0.803745i	$-0.297162\pi$
$761$	−303.316	−	525.360i	−0.398576	−	0.690354i	−0.993550	+	0.113391i	$0.963829\pi$
$762$	−697.489	−	101.267i	−0.915340	−	0.132896i
$763$	126.163	+	72.8405i	0.165352	+	0.0954659i
$764$	−36.3148			−0.0475324
$765$	64.1425	+	19.0265i	0.0838465	+	0.0248713i
$766$	−30.2959			−0.0395507
$767$	−21.8839	+	37.9041i	−0.0285318	+	0.0494186i
$768$	29.7237	−	37.6895i	0.0387027	−	0.0490749i
$769$	708.547	+	1227.24i	0.921387	+	1.59589i	0.797271	+	0.603622i	$0.206276\pi$
$769$	708.547	+	1227.24i	0.921387	+	1.59589i	0.124117	+	0.992268i	$0.460390\pi$
$770$	−218.973	+	126.424i	−0.284380	+	0.164187i
$771$	−355.082	−	280.034i	−0.460548	−	0.363209i
$772$	−16.1412	−	9.31911i	−0.0209083	−	0.0120714i
$773$		−	851.164i		−	1.10112i	−0.834796	−	0.550559i	$-0.814415\pi$
$773$		−	851.164i		−	1.10112i	0.834796	−	0.550559i	$-0.185585\pi$
$774$	−89.9850	+	303.359i	−0.116260	+	0.391937i
$775$			1.40034i			0.00180689i
$776$	−107.033	+	185.386i	−0.137929	+	0.238900i
$777$	−55.5437	+	382.564i	−0.0714848	+	0.492361i
$778$	272.294	−	157.209i	0.349993	−	0.202068i
$779$	399.998	+	273.733i	0.513476	+	0.351391i
$780$	−39.0748	+	15.5806i	−0.0500959	+	0.0199752i
$781$	−740.113	−	427.305i	−0.947648	−	0.547125i
$782$			47.1681i			0.0603172i
$783$	231.879	+	328.500i	0.296142	+	0.419540i
$784$	−87.7216			−0.111890
$785$	−359.520	+	622.707i	−0.457988	+	0.793258i
$786$	457.698	−	182.502i	0.582313	−	0.232190i
$787$	−301.758	+	174.220i	−0.383429	+	0.221373i	−0.679309	−	0.733852i	$-0.737720\pi$
$787$	−301.758	+	174.220i	−0.383429	+	0.221373i	0.295880	+	0.955225i	$0.404387\pi$
$788$	−272.525	−	472.027i	−0.345844	−	0.599019i
$789$	468.058	+	67.9564i	0.593230	+	0.0861298i
$790$	84.9145	−	147.076i	0.107487	−	0.186173i
$791$			652.548i			0.824965i
$792$	−220.396	+	52.8235i	−0.278278	+	0.0666963i
$793$		−	59.0843i		−	0.0745073i
$794$	1.75938	+	1.01578i	0.00221584	+	0.00127932i
$795$	−801.577	−	632.160i	−1.00827	−	0.795170i
$796$	−253.479	−	439.039i	−0.318441	−	0.551556i
$797$	1316.86	−	760.289i	1.65227	−	0.953939i	0.676134	−	0.736779i	$-0.263654\pi$
$797$	1316.86	−	760.289i	1.65227	−	0.953939i	0.976136	−	0.217160i	$-0.0696793\pi$
$798$	91.8200	−	409.228i	0.115063	−	0.512817i
$799$	47.2899	−	81.9084i	0.0591863	−	0.102514i
$800$		−	57.1477i		−	0.0714347i
$801$	−393.430	−	414.906i	−0.491174	−	0.517985i
$802$	202.432			0.252409
$803$	−67.3515	+	116.656i	−0.0838749	+	0.145276i
$804$	−37.1596	+	255.942i	−0.0462185	+	0.318336i
$805$	−173.878	−	301.166i	−0.215998	−	0.374119i
$806$	0.308377	−	0.178042i	0.000382602	−	0.000220895i
$807$	1190.54	−	474.714i	1.47527	−	0.588246i
$808$	−317.070	−	183.061i	−0.392414	−	0.226560i
$809$	−1595.60			−1.97231			−0.986156	−	0.165818i	$-0.946974\pi$
$809$	−1595.60			−1.97231			−0.986156	+	0.165818i	$0.946974\pi$
$810$	−441.515	−	23.4767i	−0.545080	−	0.0289835i
$811$		−	722.550i		−	0.890937i	−0.895298	−	0.445469i	$-0.853037\pi$
$811$		−	722.550i		−	0.890937i	0.895298	−	0.445469i	$-0.146963\pi$
$812$	134.204	+	77.4828i	0.165276	+	0.0954221i
$813$	−140.132	−	351.438i	−0.172364	−	0.432273i
$814$	−155.920	−	270.061i	−0.191548	−	0.331771i
$815$	364.570	+	631.454i	0.447325	+	0.774790i
$816$	22.8723	+	3.32077i	0.0280297	+	0.00406958i
$817$	470.969	+	36.1176i	0.576461	+	0.0442076i
$818$	−16.0365			−0.0196045
$819$	−58.5260	−	61.7206i	−0.0714603	−	0.0753610i
$820$		−	196.926i		−	0.240153i
$821$	353.569	−	612.399i	0.430656	−	0.745918i	−0.566274	−	0.824217i	$-0.691616\pi$
$821$	353.569	−	612.399i	0.430656	−	0.745918i	0.996930	+	0.0782990i	$0.0249489\pi$
$822$	−861.267	−	679.235i	−1.04777	−	0.826320i
$823$	−357.430	−	619.087i	−0.434302	−	0.752233i	0.562937	−	0.826500i	$-0.309671\pi$
$823$	−357.430	−	619.087i	−0.434302	−	0.752233i	−0.997238	+	0.0742674i	$0.976338\pi$
$824$	−4.78257	−	8.28366i	−0.00580409	−	0.0100530i
$825$	−167.090	+	211.870i	−0.202534	+	0.256812i
$826$	−88.6448	+	153.537i	−0.107318	+	0.185881i
$827$			114.879i			0.138910i	0.997585	+	0.0694552i	$0.0221261\pi$
$827$			114.879i			0.138910i	−0.997585	+	0.0694552i	$0.977874\pi$
$828$	−72.6512	−	303.123i	−0.0877429	−	0.366091i
$829$		−	229.259i		−	0.276548i	−0.990394	−	0.138274i	$-0.955844\pi$
$829$		−	229.259i		−	0.276548i	0.990394	−	0.138274i	$-0.0441555\pi$
$830$	140.833	+	81.3099i	0.169678	+	0.0979637i
$831$	1629.64	+	236.604i	1.96106	+	0.284722i
$832$	−12.5849	+	7.26587i	−0.0151260	+	0.00873302i
$833$	−21.1190	−	36.5792i	−0.0253530	−	0.0439127i
$834$	785.359	−	313.153i	0.941677	−	0.375483i
$835$	−14.7452	−	8.51316i	−0.0176589	−	0.0101954i
$836$	146.262	+	305.071i	0.174954	+	0.364918i
$837$	3.72709	−	0.340320i	0.00445291	−	0.000406596i
$838$			305.532i			0.364597i
$839$	−709.831	−	409.821i	−0.846044	−	0.488464i	0.0132703	−	0.999912i	$-0.495776\pi$
$839$	−709.831	−	409.821i	−0.846044	−	0.488464i	−0.859314	+	0.511448i	$0.829109\pi$
$840$	−158.280	+	63.1122i	−0.188428	+	0.0751336i
$841$	−309.608	−	536.258i	−0.368143	−	0.637643i
$842$	216.689	+	375.316i	0.257350	+	0.445744i
$843$	185.397	−	1276.94i	0.219925	−	1.51476i
$844$	−599.927	−	346.368i	−0.710814	−	0.410389i
$845$	−639.561			−0.756877
$846$	−177.746	+	599.219i	−0.210101	+	0.708297i
$847$	−217.133			−0.256355
$848$	−305.405	−	176.326i	−0.360148	−	0.207931i
$849$	−132.684	+	168.243i	−0.156282	+	0.198165i
$850$	23.8302	−	13.7584i	0.0280355	−	0.0161863i
$851$	371.431	−	214.446i	0.436464	−	0.251993i
$852$	−452.224	−	356.644i	−0.530779	−	0.418597i
$853$	454.140	−	786.594i	0.532403	−	0.922150i	−0.466881	−	0.884320i	$-0.654622\pi$
$853$	454.140	−	786.594i	0.532403	−	0.922150i	0.999284	−	0.0378295i	$-0.0120444\pi$
$854$		−	239.332i		−	0.280248i
$855$	104.305	+	651.722i	0.121995	+	0.762248i
$856$	268.759			0.313971
$857$	1364.14	+	787.588i	1.59177	+	0.919006i	0.993004	+	0.118078i	$0.0376734\pi$
$857$	1364.14	+	787.588i	1.59177	+	0.919006i	0.598761	+	0.800928i	$0.295660\pi$
$858$	67.9014	+	9.85846i	0.0791392	+	0.0114901i
$859$	−331.866	−	574.809i	−0.386340	−	0.669161i	0.605614	−	0.795759i	$-0.292928\pi$
$859$	−331.866	−	574.809i	−0.386340	−	0.669161i	−0.991954	+	0.126598i	$0.959594\pi$
$860$	−95.9555	−	166.200i	−0.111576	−	0.193256i
$861$	369.859	−	147.477i	0.429569	−	0.171286i
$862$	16.0775	−	27.8470i	0.0186514	−	0.0323051i
$863$			557.342i			0.645820i	0.946430	+	0.322910i	$0.104661\pi$
$863$			557.342i			0.645820i	−0.946430	+	0.322910i	$0.895339\pi$
$864$	−152.102	+	13.8885i	−0.176044	+	0.0160746i
$865$			5.54213i			0.00640708i
$866$	359.692	−	623.005i	0.415349	−	0.719405i
$867$	−316.998	−	795.002i	−0.365626	−	0.916957i
$868$	1.24914	−	0.721190i	0.00143910	−	0.000830864i
$869$	−239.891	+	138.501i	−0.276054	+	0.159380i
$870$	−241.340	−	35.0396i	−0.277402	−	0.0402754i
$871$	39.1487	−	67.8075i	0.0449468	−	0.0778502i
$872$	−79.1966			−0.0908218
$873$	662.393	−	158.759i	0.758754	−	0.181855i
$874$	−419.582	+	201.162i	−0.480071	+	0.230163i
$875$	−352.457	+	610.473i	−0.402808	+	0.697684i
$876$	−56.2141	+	71.2793i	−0.0641714	+	0.0813690i
$877$	472.398	−	272.739i	0.538652	−	0.310991i	−0.205881	−	0.978577i	$-0.566006\pi$
$877$	472.398	−	272.739i	0.538652	−	0.310991i	0.744532	+	0.667586i	$0.232673\pi$
$878$	234.738	+	406.578i	0.267355	+	0.463073i
$879$	519.090	+	409.378i	0.590546	+	0.465731i
$880$	68.7279	−	119.040i	0.0780999	−	0.135273i
$881$	461.377			0.523697			0.261848	−	0.965109i	$-0.415668\pi$
$881$	461.377			0.523697			0.261848	+	0.965109i	$0.415668\pi$
$882$	192.062	+	202.546i	0.217757	+	0.229644i
$883$	1266.08			1.43384			0.716921	−	0.697154i	$-0.245551\pi$
$883$	1266.08			1.43384			0.716921	+	0.697154i	$0.245551\pi$
$884$	−6.05962	−	3.49853i	−0.00685478	−	0.00395761i
$885$	40.0874	−	276.107i	0.0452965	−	0.311985i
$886$	201.979	−	116.613i	0.227967	−	0.131617i
$887$	796.362	−	459.780i	0.897815	−	0.518354i	0.0213246	−	0.999773i	$-0.493212\pi$
$887$	796.362	−	459.780i	0.897815	−	0.518354i	0.876491	+	0.481419i	$0.159878\pi$
$888$	−77.8370	−	195.208i	−0.0876543	−	0.219829i
$889$	748.518	+	432.157i	0.841977	+	0.486116i
$890$	346.785			0.389647
$891$	604.513	+	393.232i	0.678466	+	0.441337i
$892$			504.641i			0.565741i
$893$	930.295	+	71.3424i	1.04176	+	0.0798907i
$894$	35.6641	−	14.2206i	0.0398927	−	0.0159068i
$895$	−447.874	+	258.580i	−0.500418	+	0.288916i
$896$	−50.9773	+	29.4317i	−0.0568943	+	0.0328479i
$897$	−13.5589	+	93.3888i	−0.0151158	+	0.104112i
$898$	368.465	−	638.201i	0.410318	−	0.710691i
$899$	2.06430			0.00229622
$900$	−131.952	+	125.122i	−0.146613	+	0.139025i
$901$		−	169.802i		−	0.188460i
$902$	−160.599	+	278.166i	−0.178048	+	0.308388i
$903$	240.290	−	304.687i	0.266102	−	0.337416i
$904$	−177.372	−	307.218i	−0.196209	−	0.339843i
$905$	27.2173	−	15.7139i	0.0300744	−	0.0173635i
$906$	263.484	−	334.097i	0.290821	−	0.368760i
$907$	244.376	+	141.091i	0.269433	+	0.155557i	0.628630	−	0.777704i	$-0.283616\pi$
$907$	244.376	+	141.091i	0.269433	+	0.155557i	−0.359197	+	0.933262i	$0.616949\pi$
$908$			199.958i			0.220218i
$909$	271.529	+	1132.91i	0.298712	+	1.24632i
$910$	51.5872			0.0566892
$911$	428.423	+	247.350i	0.470278	+	0.271515i	0.716356	−	0.697735i	$-0.245809\pi$
$911$	428.423	+	247.350i	0.470278	+	0.271515i	−0.246078	+	0.969250i	$0.579142\pi$
$912$	68.0057	+	217.622i	0.0745677	+	0.238620i
$913$	−132.622	−	229.708i	−0.145259	−	0.251597i
$914$	−391.687	+	226.141i	−0.428542	+	0.247419i
$915$	139.499	+	349.851i	0.152458	+	0.382351i
$916$	−366.075	+	634.061i	−0.399645	+	0.692206i
$917$	−604.260			−0.658953
$918$	−42.4101	−	60.0818i	−0.0461984	−	0.0654486i
$919$	358.442			0.390035			0.195017	−	0.980800i	$-0.437524\pi$
$919$	358.442			0.390035			0.195017	+	0.980800i	$0.437524\pi$
$920$	163.723	+	94.5255i	0.177960	+	0.102745i
$921$	736.972	−	293.859i	0.800187	−	0.319065i
$922$	182.595	−	105.421i	0.198043	−	0.114340i
$923$	87.1807	+	151.001i	0.0944536	+	0.163598i
$924$	275.047	+	39.9335i	0.297670	+	0.0432181i
$925$	−216.684	−	125.102i	−0.234253	−	0.135246i
$926$			1234.11i			1.33273i
$927$	−8.65545	+	29.1794i	−0.00933706	+	0.0314773i
$928$	−84.2440			−0.0907802
$929$	−137.255	+	237.732i	−0.147745	+	0.255901i	−0.930394	−	0.366562i	$-0.880535\pi$
$929$	−137.255	+	237.732i	−0.147745	+	0.255901i	0.782649	+	0.622463i	$0.213868\pi$
$930$	−1.40561	+	1.78231i	−0.00151141	+	0.00191646i
$931$	235.321	−	343.867i	0.252762	−	0.369352i
$932$	72.9160	+	126.294i	0.0782360	+	0.135509i
$933$	−89.7446	+	113.796i	−0.0961893	+	0.121968i
$934$	408.009	+	235.564i	0.436840	+	0.252210i
$935$	66.1852			0.0707863
$936$	44.3305	+	13.1497i	0.0473617	+	0.0140488i
$937$	1314.34			1.40271			0.701354	−	0.712813i	$-0.252579\pi$
$937$	1314.34			1.40271			0.701354	+	0.712813i	$0.252579\pi$
$938$	158.579	−	274.667i	0.169061	−	0.292822i
$939$	−128.007	−	18.5850i	−0.136322	−	0.0197924i
$940$	−189.539	−	328.291i	−0.201637	−	0.349246i
$941$	−425.930	+	245.911i	−0.452636	+	0.261329i	−0.708943	−	0.705266i	$-0.750828\pi$
$941$	−425.930	+	245.911i	−0.452636	+	0.261329i	0.256307	+	0.966595i	$0.417494\pi$
$942$	734.161	−	292.738i	0.779364	−	0.310762i
$943$	−382.578	−	220.882i	−0.405703	−	0.234233i
$944$		−	96.3801i		−	0.102098i
$945$	492.269	+	227.281i	0.520920	+	0.240509i
$946$			313.020i			0.330887i
$947$	537.752	−	931.414i	0.567848	−	0.983542i	−0.428930	−	0.903338i	$-0.641109\pi$
$947$	537.752	−	931.414i	0.567848	−	0.983542i	0.996778	−	0.0802043i	$-0.0255573\pi$
$948$	−173.400	+	69.1413i	−0.182912	+	0.0729339i
$949$	23.8008	−	13.7414i	0.0250798	−	0.0144798i
$950$	224.018	+	153.304i	0.235808	+	0.161372i
$951$	252.092	−	1736.31i	0.265081	−	1.82578i
$952$	−24.5456	−	14.1714i	−0.0257832	−	0.0148859i
$953$		−	156.471i		−	0.164188i	−0.996625	−	0.0820938i	$-0.973839\pi$
$953$		−	156.471i		−	0.164188i	0.996625	−	0.0820938i	$-0.0261607\pi$
$954$	261.540	+	1091.23i	0.274151	+	1.14384i
$955$	−70.0828			−0.0733852
$956$	−338.800	+	586.819i	−0.354393	+	0.613827i
$957$	312.327	+	246.316i	0.326361	+	0.257383i
$958$	−676.036	+	390.310i	−0.705675	+	0.407421i
$959$	672.563	+	1164.91i	0.701317	+	1.21472i
$960$	57.3629	−	72.7360i	0.0597530	−	0.0757666i
$961$	−480.490	+	832.234i	−0.499990	+	0.866008i
$962$			63.6231i			0.0661362i
$963$	−588.434	−	620.554i	−0.611043	−	0.644397i
$964$		−	625.932i		−	0.649307i
$965$	−31.1504	−	17.9847i	−0.0322802	−	0.0186370i
$966$	−54.9229	+	378.288i	−0.0568560	+	0.391603i
$967$	−594.394	−	1029.52i	−0.614678	−	1.06465i	−0.990441	−	0.137938i	$-0.955953\pi$
$967$	−594.394	−	1029.52i	−0.614678	−	1.06465i	0.375763	−	0.926716i	$-0.377381\pi$
$968$	102.226	−	59.0201i	0.105605	−	0.0609712i
$969$	−74.3742	+	80.7504i	−0.0767536	+	0.0833338i
$970$	−206.559	+	357.771i	−0.212948	+	0.368837i
$971$		−	17.7822i		−	0.0183133i	−0.999958	−	0.00915666i	$-0.997085\pi$
$971$		−	17.7822i		−	0.0183133i	0.999958	−	0.00915666i	$-0.00291470\pi$
$972$	365.088	+	320.790i	0.375605	+	0.330031i
$973$	−1036.84			−1.06561
$974$	−214.204	+	371.012i	−0.219922	+	0.380915i
$975$	51.1367	−	20.3902i	0.0524479	−	0.0209130i
$976$	65.0541	+	112.677i	0.0666538	+	0.115448i
$977$	−272.656	+	157.418i	−0.279075	+	0.161124i	−0.633005	−	0.774148i	$-0.718179\pi$
$977$	−272.656	+	157.418i	−0.279075	+	0.161124i	0.353929	+	0.935272i	$0.384845\pi$
$978$	115.157	−	793.157i	0.117747	−	0.810999i
$979$	−489.850	−	282.815i	−0.500357	−	0.288881i
$980$	−169.291			−0.172746
$981$	173.397	+	182.862i	0.176755	+	0.186404i
$982$		−	73.9865i		−	0.0753427i
$983$	−1010.72	−	583.541i	−1.02820	−	0.593633i	−0.111733	−	0.993738i	$-0.535640\pi$
$983$	−1010.72	−	583.541i	−1.02820	−	0.593633i	−0.916469	+	0.400105i	$0.868974\pi$
$984$	−134.042	+	169.965i	−0.136222	+	0.172729i
$985$	−525.938	−	910.952i	−0.533948	−	0.924824i
$986$	−20.2818	−	35.1291i	−0.0205698	−	0.0356279i
$987$	474.640	−	601.842i	0.480891	−	0.609769i
$988$	5.27794	−	68.8237i	0.00534205	−	0.0696596i
$989$	−430.514			−0.435302
$990$	−425.336	+	101.942i	−0.429632	+	0.102972i
$991$		−	1737.30i		−	1.75308i	−0.481329	−	0.876540i	$-0.659846\pi$
$991$		−	1737.30i		−	1.75308i	0.481329	−	0.876540i	$-0.340154\pi$
$992$	−0.392061	+	0.679070i	−0.000395223	+	0.000684547i
$993$	−165.519	+	1140.04i	−0.166686	+	1.14807i
$994$	353.141	+	611.659i	0.355273	+	0.615351i
$995$	−489.182	−	847.288i	−0.491640	−	0.851546i
$996$	−66.2063	−	166.039i	−0.0664722	−	0.166706i
$997$	−275.492	+	477.167i	−0.276321	+	0.478603i	−0.970468	−	0.241231i	$-0.922449\pi$
$997$	−275.492	+	477.167i	−0.276321	+	0.478603i	0.694146	+	0.719834i	$0.255782\pi$
$998$		−	1072.48i		−	1.07463i
$999$	−280.308	+	607.121i	−0.280589	+	0.607729i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	342.3.l.a.151.14	✓	80
3.2	odd	2		1026.3.l.a.721.33		80
9.4	even	3	inner	342.3.l.a.265.27	yes	80
9.5	odd	6		1026.3.l.a.37.11		80
19.18	odd	2	inner	342.3.l.a.151.27	yes	80
57.56	even	2		1026.3.l.a.721.11		80
171.94	odd	6	inner	342.3.l.a.265.14	yes	80
171.113	even	6		1026.3.l.a.37.33		80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
342.3.l.a.151.14	✓	80	1.1	even	1	trivial
342.3.l.a.151.27	yes	80	19.18	odd	2	inner
342.3.l.a.265.14	yes	80	171.94	odd	6	inner
342.3.l.a.265.27	yes	80	9.4	even	3	inner
1026.3.l.a.37.11		80	9.5	odd	6
1026.3.l.a.37.33		80	171.113	even	6
1026.3.l.a.721.11		80	57.56	even	2
1026.3.l.a.721.33		80	3.2	odd	2

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:	\( N \)	\(=\)	\( 342 = 2 \cdot 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	342.l (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.22474 - 0.707107i) q^{2} +(1.11114 + 2.78664i) q^{3} +(1.00000 + 1.73205i) q^{4} +(1.92987 + 3.34264i) q^{5} +(0.609589 - 4.19862i) q^{6} +(-2.60142 + 4.50580i) q^{7} -2.82843i q^{8} +(-6.53073 + 6.19270i) q^{9} +O(q^{10})\)	\(q+(-1.22474 - 0.707107i) q^{2} +(1.11114 + 2.78664i) q^{3} +(1.00000 + 1.73205i) q^{4} +(1.92987 + 3.34264i) q^{5} +(0.609589 - 4.19862i) q^{6} +(-2.60142 + 4.50580i) q^{7} -2.82843i q^{8} +(-6.53073 + 6.19270i) q^{9} -5.45850i q^{10} +(-4.45159 + 7.71037i) q^{11} +(-3.71546 + 4.71119i) q^{12} +(1.57311 - 0.908234i) q^{13} +(6.37216 - 3.67897i) q^{14} +(-7.17036 + 9.09200i) q^{15} +(-2.00000 + 3.46410i) q^{16} -1.92601 q^{17} +(12.3774 - 2.96655i) q^{18} +(-8.21402 - 17.1327i) q^{19} +(-3.85974 + 6.68527i) q^{20} +(-15.4466 - 2.24266i) q^{21} +(10.9041 - 6.29549i) q^{22} +(8.65856 + 14.9971i) q^{23} +(7.88181 - 3.14278i) q^{24} +(5.05119 - 8.74892i) q^{25} -2.56887 q^{26} +(-24.5134 - 11.3178i) q^{27} -10.4057 q^{28} +(-12.8972 - 7.44619i) q^{29} +(15.2109 - 6.06516i) q^{30} +(-0.120044 + 0.0693073i) q^{31} +(4.89898 - 2.82843i) q^{32} +(-26.4324 - 3.83766i) q^{33} +(2.35887 + 1.36189i) q^{34} -20.0816 q^{35} +(-17.2568 - 5.11886i) q^{36} -24.7669i q^{37} +(-2.05458 + 26.7914i) q^{38} +(4.27886 + 3.37451i) q^{39} +(9.45440 - 5.45850i) q^{40} +(-22.0925 + 12.7551i) q^{41} +(17.3323 + 13.6691i) q^{42} +(-12.4303 + 21.5299i) q^{43} -17.8063 q^{44} +(-33.3034 - 9.87874i) q^{45} -24.4901i q^{46} +(-24.5533 + 42.5276i) q^{47} +(-11.8755 - 1.72418i) q^{48} +(10.9652 + 18.9923i) q^{49} +(-12.3728 + 7.14347i) q^{50} +(-2.14006 - 5.36709i) q^{51} +(3.14621 + 1.81647i) q^{52} +88.1629i q^{53} +(22.0197 + 31.1951i) q^{54} -34.3640 q^{55} +(12.7443 + 7.35793i) q^{56} +(38.6158 - 41.9264i) q^{57} +(10.5305 + 18.2394i) q^{58} +(-20.8669 + 12.0475i) q^{59} +(-22.9182 - 3.32744i) q^{60} +(16.2635 - 28.1692i) q^{61} +0.196031 q^{62} +(-10.9138 - 45.5360i) q^{63} -8.00000 q^{64} +(6.07179 + 3.50555i) q^{65} +(29.6593 + 23.3907i) q^{66} +(37.3293 - 21.5521i) q^{67} +(-1.92601 - 3.33594i) q^{68} +(-32.1705 + 40.7921i) q^{69} +(24.5949 + 14.1999i) q^{70} +95.9893i q^{71} +(17.5156 + 18.4717i) q^{72} +15.1298 q^{73} +(-17.5129 + 30.3332i) q^{74} +(29.9927 + 4.35458i) q^{75} +(21.4607 - 31.3598i) q^{76} +(-23.1609 - 40.1159i) q^{77} +(-2.85438 - 7.15853i) q^{78} +(26.9445 + 15.5564i) q^{79} -15.4390 q^{80} +(4.30094 - 80.8857i) q^{81} +36.0769 q^{82} +(-14.8960 + 25.8007i) q^{83} +(-11.5622 - 28.9969i) q^{84} +(-3.71694 - 6.43793i) q^{85} +(30.4479 - 17.5791i) q^{86} +(6.41928 - 44.2136i) q^{87} +(21.8082 + 12.5910i) q^{88} +63.5313i q^{89} +(33.8029 + 35.6480i) q^{90} +9.45080i q^{91} +(-17.3171 + 29.9941i) q^{92} +(-0.326520 - 0.257509i) q^{93} +(60.1431 - 34.7237i) q^{94} +(41.4164 - 60.5204i) q^{95} +(13.3253 + 10.5089i) q^{96} +(-65.5439 - 37.8418i) q^{97} -31.0143i q^{98} +(-18.6759 - 77.9217i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q + 80 q^{4} + 8 q^{6} - 4 q^{7} + 4 q^{9}+O(q^{10}) \) 80 * q + 80 * q^4 + 8 * q^6 - 4 * q^7 + 4 * q^9	\( 80 q + 80 q^{4} + 8 q^{6} - 4 q^{7} + 4 q^{9} + 12 q^{11} - 160 q^{16} + 96 q^{17} + 40 q^{19} - 48 q^{23} - 16 q^{24} - 200 q^{25} - 16 q^{28} + 40 q^{30} + 432 q^{35} - 8 q^{36} + 24 q^{38} + 88 q^{42} + 28 q^{43} + 48 q^{44} + 380 q^{45} + 240 q^{47} - 228 q^{49} - 64 q^{54} - 120 q^{57} - 28 q^{61} - 144 q^{62} + 44 q^{63} - 640 q^{64} + 16 q^{66} + 96 q^{68} - 368 q^{73} - 24 q^{74} + 40 q^{76} - 456 q^{77} + 652 q^{81} - 192 q^{82} - 84 q^{83} + 492 q^{87} + 96 q^{92} + 504 q^{93} - 324 q^{95} - 64 q^{96} - 604 q^{99}+O(q^{100}) \) 80 * q + 80 * q^4 + 8 * q^6 - 4 * q^7 + 4 * q^9 + 12 * q^11 - 160 * q^16 + 96 * q^17 + 40 * q^19 - 48 * q^23 - 16 * q^24 - 200 * q^25 - 16 * q^28 + 40 * q^30 + 432 * q^35 - 8 * q^36 + 24 * q^38 + 88 * q^42 + 28 * q^43 + 48 * q^44 + 380 * q^45 + 240 * q^47 - 228 * q^49 - 64 * q^54 - 120 * q^57 - 28 * q^61 - 144 * q^62 + 44 * q^63 - 640 * q^64 + 16 * q^66 + 96 * q^68 - 368 * q^73 - 24 * q^74 + 40 * q^76 - 456 * q^77 + 652 * q^81 - 192 * q^82 - 84 * q^83 + 492 * q^87 + 96 * q^92 + 504 * q^93 - 324 * q^95 - 64 * q^96 - 604 * q^99

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