LMFDB - Embedded newform 936.2.db.a.61.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [936,2,Mod(61,936)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(936, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 3, 4, 4])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("936.61"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 936 = 2^{3} \cdot 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	936.db (of order $6$, degree $2$, 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:	$7.47399762919$
Analytic rank:	$0$
Dimension:	$328$
Relative dimension:	$164$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			61.4
Character	$\chi$	$=$	936.61
Dual form			936.2.db.a.445.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.40766 + 0.135961i) q^{2} +(-0.195465 + 1.72099i) q^{3} +(1.96303 - 0.382776i) q^{4} +(0.951819 - 0.549533i) q^{5} +(0.0411610 - 2.44914i) q^{6} -2.60565 q^{7} +(-2.71124 + 0.805715i) q^{8} +(-2.92359 - 0.672785i) q^{9} +(-1.26512 + 0.902967i) q^{10} +(0.683090 - 0.394382i) q^{11} +(0.275048 + 3.45316i) q^{12} +(-3.55254 + 0.616022i) q^{13} +(3.66788 - 0.354268i) q^{14} +(0.759691 + 1.74548i) q^{15} +(3.70697 - 1.50280i) q^{16} +(-2.29757 - 3.97951i) q^{17} +(4.20690 + 0.549559i) q^{18} +(2.63985 - 1.52412i) q^{19} +(1.65810 - 1.44308i) q^{20} +(0.509314 - 4.48429i) q^{21} +(-0.907939 + 0.648031i) q^{22} +8.58024 q^{23} +(-0.856672 - 4.82350i) q^{24} +(-1.89603 + 3.28402i) q^{25} +(4.91702 - 1.35016i) q^{26} +(1.72931 - 4.89995i) q^{27} +(-5.11497 + 0.997380i) q^{28} +(7.24161 - 4.18095i) q^{29} +(-1.30671 - 2.35376i) q^{30} +(-2.61428 - 4.52806i) q^{31} +(-5.01383 + 2.61944i) q^{32} +(0.545206 + 1.25268i) q^{33} +(3.77526 + 5.28943i) q^{34} +(-2.48011 + 1.43189i) q^{35} +(-5.99661 - 0.201618i) q^{36} +(-1.26850 - 0.732368i) q^{37} +(-3.50880 + 2.50436i) q^{38} +(-0.365768 - 6.23428i) q^{39} +(-2.13784 + 2.25681i) q^{40} -6.27993 q^{41} +(-0.107251 + 6.38162i) q^{42} -4.55721i q^{43} +(1.18996 - 1.03565i) q^{44} +(-3.15244 + 0.966238i) q^{45} +(-12.0781 + 1.16658i) q^{46} +(5.29828 - 9.17688i) q^{47} +(1.86172 + 6.67338i) q^{48} -0.210575 q^{49} +(2.22247 - 4.88057i) q^{50} +(7.29777 - 3.17623i) q^{51} +(-6.73793 + 2.56909i) q^{52} -0.616458i q^{53} +(-1.76808 + 7.13259i) q^{54} +(0.433452 - 0.750760i) q^{55} +(7.06455 - 2.09941i) q^{56} +(2.10699 + 4.84106i) q^{57} +(-9.62530 + 6.86994i) q^{58} +(8.58896 + 4.95884i) q^{59} +(2.15942 + 3.13564i) q^{60} -1.10166i q^{61} +(4.29566 + 6.01854i) q^{62} +(7.61785 + 1.75304i) q^{63} +(6.70165 - 4.36897i) q^{64} +(-3.04285 + 2.53858i) q^{65} +(-0.937782 - 1.68922i) q^{66} +13.1738i q^{67} +(-6.03346 - 6.93244i) q^{68} +(-1.67714 + 14.7665i) q^{69} +(3.29647 - 2.35282i) q^{70} +(-7.67022 - 13.2852i) q^{71} +(8.46862 - 0.531497i) q^{72} -3.19793 q^{73} +(1.88519 + 0.858461i) q^{74} +(-5.28114 - 3.90495i) q^{75} +(4.59871 - 4.00236i) q^{76} +(-1.77989 + 1.02762i) q^{77} +(1.36250 + 8.72603i) q^{78} +(7.48433 - 12.9632i) q^{79} +(2.70252 - 3.46749i) q^{80} +(8.09472 + 3.93389i) q^{81} +(8.84002 - 0.853828i) q^{82} +(1.72293 + 0.994734i) q^{83} +(-0.716680 - 8.99775i) q^{84} +(-4.37374 - 2.52518i) q^{85} +(0.619605 + 6.41502i) q^{86} +(5.77987 + 13.2799i) q^{87} +(-1.53426 + 1.61964i) q^{88} +(5.76546 - 9.98606i) q^{89} +(4.30620 - 1.78875i) q^{90} +(9.25668 - 1.60514i) q^{91} +(16.8433 - 3.28431i) q^{92} +(8.30372 - 3.61406i) q^{93} +(-6.21048 + 13.6383i) q^{94} +(1.67511 - 2.90137i) q^{95} +(-3.52799 - 9.14075i) q^{96} -11.3924 q^{97} +(0.296419 - 0.0286301i) q^{98} +(-2.26241 + 0.693438i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 328 q + q^{2} + q^{4} + q^{6} - 4 q^{7} - 2 q^{8} - 2 q^{9} - 4 q^{10} + 5 q^{12} - 6 q^{14} + 4 q^{15} + q^{16} - 4 q^{17} - 12 q^{18} - 18 q^{20} - 7 q^{22} + 44 q^{23} - 6 q^{24} + 144 q^{25} - 16 q^{26}+ \cdots + 39 q^{98}+O(q^{100}) $ 328 * q + q^2 + q^4 + q^6 - 4 * q^7 - 2 * q^8 - 2 * q^9 - 4 * q^10 + 5 * q^12 - 6 * q^14 + 4 * q^15 + q^16 - 4 * q^17 - 12 * q^18 - 18 * q^20 - 7 * q^22 + 44 * q^23 - 6 * q^24 + 144 * q^25 - 16 * q^26 - 10 * q^28 - 5 * q^30 - 4 * q^31 + q^32 - 14 * q^33 - 13 * q^36 + 6 * q^38 + 20 * q^39 + 8 * q^40 - 4 * q^41 - 46 * q^42 - 32 * q^44 - 6 * q^46 - 4 * q^47 - 46 * q^48 + 276 * q^49 + 68 * q^50 + 40 * q^54 - 14 * q^55 - 56 * q^56 - 20 * q^57 - 25 * q^58 - 41 * q^60 + 3 * q^62 - 58 * q^63 - 26 * q^64 - 22 * q^65 - 6 * q^66 - 64 * q^68 - 17 * q^70 - 4 * q^71 - 7 * q^72 - 16 * q^73 - 38 * q^74 - 18 * q^76 - q^78 - 4 * q^79 - 42 * q^80 - 2 * q^81 + 3 * q^82 + 6 * q^84 + 36 * q^86 - 2 * q^87 + 5 * q^88 - 4 * q^89 + 33 * q^90 + 28 * q^92 - 6 * q^94 + 56 * q^95 - 113 * q^96 - 4 * q^97 + 39 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/936\mathbb{Z}\right)^\times$.

$n$	$145$	$209$	$469$	$703$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$	$-1$	$1$

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 $

$2$	−1.40766	+	0.135961i	−0.995368	+	0.0961392i
$2$	−1.40766	+	0.135961i	−0.995368	+	0.0961392i
$3$	−0.195465	+	1.72099i	−0.112852	+	0.993612i
$3$	−0.195465	+	1.72099i	−0.112852	+	0.993612i
$4$	1.96303	−	0.382776i	0.981514	−	0.191388i
$5$	0.951819	−	0.549533i	0.425666	−	0.245759i	−0.271832	−	0.962345i	$-0.587630\pi$
$5$	0.951819	−	0.549533i	0.425666	−	0.245759i	0.697499	+	0.716586i	$0.254296\pi$
$6$	0.0411610	−	2.44914i	0.0168039	−	0.999859i
$7$	−2.60565			−0.984844			−0.492422	−	0.870357i	$-0.663888\pi$
$7$	−2.60565			−0.984844			−0.492422	+	0.870357i	$0.663888\pi$
$8$	−2.71124	+	0.805715i	−0.958568	+	0.284863i
$9$	−2.92359	−	0.672785i	−0.974529	−	0.224262i
$10$	−1.26512	+	0.902967i	−0.400067	+	0.285543i
$11$	0.683090	−	0.394382i	0.205959	−	0.118911i	−0.393473	−	0.919336i	$-0.628726\pi$
$11$	0.683090	−	0.394382i	0.205959	−	0.118911i	0.599432	+	0.800426i	$0.295393\pi$
$12$	0.275048	+	3.45316i	0.0793996	+	0.996843i
$13$	−3.55254	+	0.616022i	−0.985296	+	0.170854i
$13$	−3.55254	+	0.616022i	−0.985296	+	0.170854i
$14$	3.66788	−	0.354268i	0.980282	−	0.0946821i
$15$	0.759691	+	1.74548i	0.196151	+	0.450681i
$16$	3.70697	−	1.50280i	0.926741	−	0.375700i
$17$	−2.29757	−	3.97951i	−0.557243	−	0.965173i	−0.997725	−	0.0674115i	$-0.978526\pi$
$17$	−2.29757	−	3.97951i	−0.557243	−	0.965173i	0.440483	−	0.897761i	$-0.354807\pi$
$18$	4.20690	+	0.549559i	0.991575	+	0.129532i
$19$	2.63985	−	1.52412i	0.605624	−	0.349657i	−0.165627	−	0.986188i	$-0.552965\pi$
$19$	2.63985	−	1.52412i	0.605624	−	0.349657i	0.771251	+	0.636531i	$0.219631\pi$
$20$	1.65810	−	1.44308i	0.370762	−	0.322683i
$21$	0.509314	−	4.48429i	0.111141	−	0.978553i
$22$	−0.907939	+	0.648031i	−0.193573	+	0.138161i
$23$	8.58024			1.78910			0.894552	−	0.446964i	$-0.147495\pi$
$23$	8.58024			1.78910			0.894552	+	0.446964i	$0.147495\pi$
$24$	−0.856672	−	4.82350i	−0.174868	−	0.984592i
$25$	−1.89603	+	3.28402i	−0.379206	+	0.656803i
$26$	4.91702	−	1.35016i	0.964307	−	0.264788i
$27$	1.72931	−	4.89995i	0.332806	−	0.942995i
$28$	−5.11497	+	0.997380i	−0.966639	+	0.188487i
$29$	7.24161	−	4.18095i	1.34473	−	0.776383i	0.357236	−	0.934014i	$-0.383719\pi$
$29$	7.24161	−	4.18095i	1.34473	−	0.776383i	0.987498	+	0.157632i	$0.0503859\pi$
$30$	−1.30671	−	2.35376i	−0.238571	−	0.429736i
$31$	−2.61428	−	4.52806i	−0.469538	−	0.813263i	0.529856	−	0.848088i	$-0.322246\pi$
$31$	−2.61428	−	4.52806i	−0.469538	−	0.813263i	−0.999393	+	0.0348246i	$0.988913\pi$
$32$	−5.01383	+	2.61944i	−0.886329	+	0.463056i
$33$	0.545206	+	1.25268i	0.0949082	+	0.218063i
$34$	3.77526	+	5.28943i	0.647452	+	0.907129i
$35$	−2.48011	+	1.43189i	−0.419215	+	0.242034i
$36$	−5.99661	−	0.201618i	−0.999435	−	0.0336031i
$37$	−1.26850	−	0.732368i	−0.208540	−	0.120401i	0.392093	−	0.919926i	$-0.371751\pi$
$37$	−1.26850	−	0.732368i	−0.208540	−	0.120401i	−0.600633	+	0.799525i	$0.705085\pi$
$38$	−3.50880	+	2.50436i	−0.569203	+	0.406262i
$39$	−0.365768	−	6.23428i	−0.0585698	−	0.998283i
$40$	−2.13784	+	2.25681i	−0.338023	+	0.356833i
$41$	−6.27993			−0.980760			−0.490380	−	0.871509i	$-0.663142\pi$
$41$	−6.27993			−0.980760			−0.490380	+	0.871509i	$0.663142\pi$
$42$	−0.107251	+	6.38162i	−0.0165492	+	0.984705i
$43$		−	4.55721i		−	0.694968i	−0.937686	−	0.347484i	$-0.887036\pi$
$43$		−	4.55721i		−	0.694968i	0.937686	−	0.347484i	$-0.112964\pi$
$44$	1.18996	−	1.03565i	0.179394	−	0.156131i
$45$	−3.15244	+	0.966238i	−0.469938	+	0.144038i
$46$	−12.0781	+	1.16658i	−1.78082	+	0.172003i
$47$	5.29828	−	9.17688i	0.772833	−	1.33859i	−0.163171	−	0.986598i	$-0.552172\pi$
$47$	5.29828	−	9.17688i	0.772833	−	1.33859i	0.936004	−	0.351988i	$-0.114494\pi$
$48$	1.86172	+	6.67338i	0.268715	+	0.963220i
$49$	−0.210575			−0.0300822
$50$	2.22247	−	4.88057i	0.314304	−	0.690217i
$51$	7.29777	−	3.17623i	1.02189	−	0.444762i
$52$	−6.73793	+	2.56909i	−0.934383	+	0.356269i
$53$		−	0.616458i		−	0.0846770i	−0.999103	−	0.0423385i	$-0.986519\pi$
$53$		−	0.616458i		−	0.0846770i	0.999103	−	0.0423385i	$-0.0134808\pi$
$54$	−1.76808	+	7.13259i	−0.240606	+	0.970623i
$55$	0.433452	−	0.750760i	0.0584466	−	0.101232i
$56$	7.06455	−	2.09941i	0.944040	−	0.280546i
$57$	2.10699	+	4.84106i	0.279078	+	0.641214i
$58$	−9.62530	+	6.86994i	−1.26386	+	0.902068i
$59$	8.58896	+	4.95884i	1.11819	+	0.645586i	0.940938	−	0.338580i	$-0.109947\pi$
$59$	8.58896	+	4.95884i	1.11819	+	0.645586i	0.177250	+	0.984166i	$0.443280\pi$
$60$	2.15942	+	3.13564i	0.278780	+	0.404809i
$61$		−	1.10166i		−	0.141054i	−0.997510	−	0.0705268i	$-0.977532\pi$
$61$		−	1.10166i		−	0.141054i	0.997510	−	0.0705268i	$-0.0224680\pi$
$62$	4.29566	+	6.01854i	0.545549	+	0.764355i
$63$	7.61785	+	1.75304i	0.959759	+	0.220863i
$64$	6.70165	−	4.36897i	0.837706	−	0.546122i
$65$	−3.04285	+	2.53858i	−0.377419	+	0.314872i
$66$	−0.937782	−	1.68922i	−0.115433	−	0.207928i
$67$			13.1738i			1.60944i	0.593655	+	0.804720i	$0.297684\pi$
$67$			13.1738i			1.60944i	−0.593655	+	0.804720i	$0.702316\pi$
$68$	−6.03346	−	6.93244i	−0.731664	−	0.840682i
$69$	−1.67714	+	14.7665i	−0.201903	+	1.77767i
$70$	3.29647	−	2.35282i	0.394004	−	0.281216i
$71$	−7.67022	−	13.2852i	−0.910288	−	1.57666i	−0.813658	−	0.581344i	$-0.802527\pi$
$71$	−7.67022	−	13.2852i	−0.910288	−	1.57666i	−0.0966302	−	0.995320i	$-0.530806\pi$
$72$	8.46862	−	0.531497i	0.998036	−	0.0626375i
$73$	−3.19793			−0.374289			−0.187145	−	0.982332i	$-0.559923\pi$
$73$	−3.19793			−0.374289			−0.187145	+	0.982332i	$0.559923\pi$
$74$	1.88519	+	0.858461i	0.219149	+	0.0997940i
$75$	−5.28114	−	3.90495i	−0.609813	−	0.450904i
$76$	4.59871	−	4.00236i	0.527508	−	0.459102i
$77$	−1.77989	+	1.02762i	−0.202838	+	0.117108i
$78$	1.36250	+	8.72603i	0.154273	+	0.988028i
$79$	7.48433	−	12.9632i	0.842053	−	1.45848i	−0.0461034	−	0.998937i	$-0.514680\pi$
$79$	7.48433	−	12.9632i	0.842053	−	1.45848i	0.888156	−	0.459542i	$-0.151986\pi$
$80$	2.70252	−	3.46749i	0.302151	−	0.387677i
$81$	8.09472	+	3.93389i	0.899413	+	0.437099i
$82$	8.84002	−	0.853828i	0.976217	−	0.0942895i
$83$	1.72293	+	0.994734i	0.189116	+	0.109186i	0.591569	−	0.806255i	$-0.298509\pi$
$83$	1.72293	+	0.994734i	0.189116	+	0.109186i	−0.402453	+	0.915441i	$0.631842\pi$
$84$	−0.716680	−	8.99775i	−0.0781962	−	0.981735i
$85$	−4.37374	−	2.52518i	−0.474399	−	0.273894i
$86$	0.619605	+	6.41502i	0.0668137	+	0.691749i
$87$	5.77987	+	13.2799i	0.619667	+	1.42376i
$88$	−1.53426	+	1.61964i	−0.163553	+	0.172654i
$89$	5.76546	−	9.98606i	0.611137	−	1.05852i	−0.379912	−	0.925023i	$-0.624046\pi$
$89$	5.76546	−	9.98606i	0.611137	−	1.05852i	0.991049	−	0.133498i	$-0.0426210\pi$
$90$	4.30620	−	1.78875i	0.453914	−	0.188551i
$91$	9.25668	−	1.60514i	0.970363	−	0.168264i
$92$	16.8433	−	3.28431i	1.75603	−	0.342413i
$93$	8.30372	−	3.61406i	0.861056	−	0.374760i
$94$	−6.21048	+	13.6383i	−0.640563	+	1.40669i
$95$	1.67511	−	2.90137i	0.171862	−	0.297674i
$96$	−3.52799	−	9.14075i	−0.360074	−	0.932924i
$97$	−11.3924			−1.15673			−0.578363	−	0.815779i	$-0.696308\pi$
$97$	−11.3924			−1.15673			−0.578363	+	0.815779i	$0.696308\pi$
$98$	0.296419	−	0.0286301i	0.0299428	−	0.00289208i
$99$	−2.26241	+	0.693438i	−0.227380	+	0.0696931i
$100$	−2.46492	+	7.17237i	−0.246492	+	0.717237i
$101$	11.4610	−	6.61703i	1.14041	−	0.658419i	0.193881	−	0.981025i	$-0.437892\pi$
$101$	11.4610	−	6.61703i	1.14041	−	0.658419i	0.946533	+	0.322606i	$0.104559\pi$
$102$	−9.84096	+	5.46328i	−0.974400	+	0.540945i
$103$	5.32038	+	9.21518i	0.524233	+	0.907998i	0.999602	+	0.0282117i	$0.00898125\pi$
$103$	5.32038	+	9.21518i	0.524233	+	0.907998i	−0.475369	+	0.879787i	$0.657685\pi$
$104$	9.13544	−	4.53252i	0.895804	−	0.444450i
$105$	−1.97949	−	4.54812i	−0.193179	−	0.443851i
$106$	0.0838145	+	0.867765i	0.00814078	+	0.0842848i
$107$	2.41925	+	1.39675i	0.233877	+	0.135029i	0.612359	−	0.790579i	$-0.290221\pi$
$107$	2.41925	+	1.39675i	0.233877	+	0.135029i	−0.378482	+	0.925609i	$0.623554\pi$
$108$	1.51911	−	10.2807i	0.146176	−	0.989259i
$109$		−	16.2575i		−	1.55719i	−0.627529	−	0.778593i	$-0.715934\pi$
$109$		−	16.2575i		−	1.55719i	0.627529	−	0.778593i	$-0.284066\pi$
$110$	−0.508079	+	1.11575i	−0.0484435	+	0.106383i
$111$	1.50834	−	2.03992i	0.143166	−	0.193620i
$112$	−9.65906	+	3.91577i	−0.912696	+	0.370006i
$113$	7.62797	−	13.2120i	0.717579	−	1.24288i	−0.244377	−	0.969680i	$-0.578584\pi$
$113$	7.62797	−	13.2120i	0.717579	−	1.24288i	0.961956	−	0.273203i	$-0.0880831\pi$
$114$	−3.62413	−	6.52811i	−0.339431	−	0.611414i
$115$	8.16683	−	4.71512i	0.761561	−	0.439687i
$116$	12.6151	−	10.9792i	1.17129	−	1.01940i
$117$	10.8006	+	0.589100i	0.998516	+	0.0544623i
$118$	−12.7646	−	5.81261i	−1.17507	−	0.535094i
$119$	5.98667	+	10.3692i	0.548797	+	0.950545i
$120$	−3.46607	−	4.12032i	−0.316407	−	0.376132i
$121$	−5.18893	+	8.98748i	−0.471721	+	0.817044i
$122$	0.149784	+	1.55077i	0.0135608	+	0.140400i
$123$	1.22751	−	10.8077i	0.110680	−	0.974494i
$124$	−6.86513	−	7.88803i	−0.616507	−	0.708366i
$125$			9.66304i			0.864289i
$126$	−10.9617	−	1.43196i	−0.976547	−	0.127569i
$127$	−0.868706	+	1.50464i	−0.0770852	+	0.133516i	−0.901991	−	0.431755i	$-0.857895\pi$
$127$	−0.868706	+	1.50464i	−0.0770852	+	0.133516i	0.824906	+	0.565270i	$0.191228\pi$
$128$	−8.83965	+	7.06121i	−0.781322	+	0.624129i
$129$	7.84290	+	0.890775i	0.690529	+	0.0784284i
$130$	3.93815	−	3.98717i	0.345399	−	0.349698i
$131$	−13.7390	+	7.93221i	−1.20038	+	0.693041i	−0.960640	−	0.277796i	$-0.910396\pi$
$131$	−13.7390	+	7.93221i	−1.20038	+	0.693041i	−0.239742	+	0.970837i	$0.577063\pi$
$132$	1.54975	+	2.25035i	0.134888	+	0.195868i
$133$	−6.87854	+	3.97133i	−0.596445	+	0.344358i
$134$	−1.79113	−	18.5443i	−0.154730	−	1.60198i
$135$	−1.04669	−	5.61417i	−0.0900847	−	0.483191i
$136$	9.43562	+	8.93822i	0.809097	+	0.766446i
$137$	−19.1251			−1.63397			−0.816984	−	0.576661i	$-0.804355\pi$
$137$	−19.1251			−1.63397			−0.816984	+	0.576661i	$0.804355\pi$
$138$	0.353171	−	21.0142i	0.0300639	−	1.78885i
$139$	−8.44358	−	4.87490i	−0.716175	−	0.413484i	0.0971682	−	0.995268i	$-0.469022\pi$
$139$	−8.44358	−	4.87490i	−0.716175	−	0.413484i	−0.813343	+	0.581784i	$0.802355\pi$
$140$	−4.32043	+	3.76017i	−0.365143	+	0.317792i
$141$	14.7577	+	10.9120i	1.24282	+	0.918958i
$142$	12.6034	+	17.6582i	1.05765	+	1.48185i
$143$	−2.18375	+	1.82185i	−0.182615	+	0.152351i
$144$	−11.8487	+	1.89957i	−0.987391	+	0.158298i
$145$	4.59514	−	7.95901i	0.381605	−	0.660960i
$146$	4.50161	−	0.434795i	0.372556	−	0.0359839i
$147$	0.0411600	−	0.362397i	0.00339482	−	0.0298900i
$148$	−2.77043	−	0.952110i	−0.227728	−	0.0782629i
$149$	−0.291149	−	0.168095i	−0.0238519	−	0.0137709i	0.488027	−	0.872829i	$-0.337717\pi$
$149$	−0.291149	−	0.168095i	−0.0238519	−	0.0137709i	−0.511879	+	0.859058i	$0.671050\pi$
$150$	7.96499	+	4.77882i	0.650338	+	0.390189i
$151$	4.27767	−	7.40914i	0.348112	−	0.602947i	−0.637802	−	0.770200i	$-0.720156\pi$
$151$	4.27767	−	7.40914i	0.348112	−	0.602947i	0.985914	+	0.167253i	$0.0534897\pi$
$152$	−5.92927	+	6.25922i	−0.480927	+	0.507690i
$153$	4.03979	+	13.1802i	0.326598	+	1.06556i
$154$	2.36577	−	1.68854i	0.190639	−	0.136067i
$155$	−4.97663	−	2.87326i	−0.399733	−	0.230786i
$156$	−3.10434	−	12.0981i	−0.248546	−	0.968620i
$157$	0.808781	−	0.466950i	0.0645478	−	0.0372667i	−0.467379	−	0.884057i	$-0.654802\pi$
$157$	0.808781	−	0.466950i	0.0645478	−	0.0372667i	0.531927	+	0.846790i	$0.321468\pi$
$158$	−8.77291	+	19.2654i	−0.697935	+	1.53268i
$159$	1.06092	+	0.120496i	0.0841361	+	0.00955594i
$160$	−3.33279	+	5.24850i	−0.263481	+	0.414930i
$161$	−22.3571			−1.76199
$162$	−11.9295	−	4.43702i	−0.937270	−	0.348605i
$163$	2.43874	−	1.40800i	0.191017	−	0.110283i	−0.401442	−	0.915885i	$-0.631491\pi$
$163$	2.43874	−	1.40800i	0.191017	−	0.110283i	0.592458	+	0.805601i	$0.298157\pi$
$164$	−12.3277	+	2.40380i	−0.962630	+	0.187705i
$165$	1.20732	+	0.892712i	0.0939900	+	0.0694975i
$166$	−2.56055	−	1.16600i	−0.198737	−	0.0904990i
$167$	−4.39414			−0.340029			−0.170014	−	0.985442i	$-0.554381\pi$
$167$	−4.39414			−0.340029			−0.170014	+	0.985442i	$0.554381\pi$
$168$	2.23219	+	12.5684i	0.172217	+	0.969670i
$169$	12.2410	−	4.37688i	0.941618	−	0.336683i
$170$	6.50008	+	2.95994i	0.498533	+	0.227017i
$171$	−8.74324	+	2.67984i	−0.668612	+	0.204933i
$172$	−1.74439	−	8.94594i	−0.133008	−	0.682122i
$173$			16.5143i			1.25556i	0.778390	+	0.627781i	$0.216037\pi$
$173$			16.5143i			1.25556i	−0.778390	+	0.627781i	$0.783963\pi$
$174$	−9.94167	−	17.9078i	−0.753676	−	1.35759i
$175$	4.94039	−	8.55700i	0.373458	−	0.646849i
$176$	1.93951	−	2.48851i	0.146196	−	0.187578i
$177$	−10.2129	+	13.8122i	−0.767651	+	1.03819i
$178$	−6.75810	+	14.8409i	−0.506541	+	1.11237i
$179$	14.7604	+	8.52195i	1.10325	+	0.636960i	0.937072	−	0.349136i	$-0.113525\pi$
$179$	14.7604	+	8.52195i	1.10325	+	0.636960i	0.166175	+	0.986096i	$0.446858\pi$
$180$	−5.81848	+	3.10343i	−0.433684	+	0.231316i
$181$		−	3.54674i		−	0.263627i	−0.991275	−	0.131814i	$-0.957920\pi$
$181$		−	3.54674i		−	0.263627i	0.991275	−	0.131814i	$-0.0420800\pi$
$182$	−12.8120	+	3.51804i	−0.949692	+	0.260775i
$183$	1.89595	+	0.215337i	0.140153	+	0.0159181i
$184$	−23.2631	+	6.91323i	−1.71498	+	0.509650i
$185$	−1.60984			−0.118358
$186$	−11.1975	+	6.21636i	−0.821038	+	0.455805i
$187$	−3.13889	−	1.81224i	−0.229539	−	0.132524i
$188$	6.88798	−	20.0425i	0.502358	−	1.46175i
$189$	−4.50599	+	12.7676i	−0.327762	+	0.928703i
$190$	−1.96351	+	4.31190i	−0.142448	+	0.312818i
$191$	−2.44352			−0.176807			−0.0884035	−	0.996085i	$-0.528176\pi$
$191$	−2.44352			−0.176807			−0.0884035	+	0.996085i	$0.528176\pi$
$192$	6.20901	+	12.3874i	0.448097	+	0.893985i
$193$	0.542366			0.0390404			0.0195202	−	0.999809i	$-0.493786\pi$
$193$	0.542366			0.0390404			0.0195202	+	0.999809i	$0.493786\pi$
$194$	16.0367	−	1.54893i	1.15137	−	0.111207i
$195$	−3.77408	−	5.73290i	−0.270268	−	0.410541i
$196$	−0.413365	+	0.0806030i	−0.0295261	+	0.00575736i
$197$	−12.5387	−	7.23924i	−0.893348	−	0.515775i	−0.0183118	−	0.999832i	$-0.505829\pi$
$197$	−12.5387	−	7.23924i	−0.893348	−	0.515775i	−0.875036	+	0.484058i	$0.839162\pi$
$198$	3.09042	−	1.28373i	0.219627	−	0.0912305i
$199$	10.3208	+	17.8762i	0.731625	+	1.26721i	0.956189	+	0.292752i	$0.0945709\pi$
$199$	10.3208	+	17.8762i	0.731625	+	1.26721i	−0.224564	+	0.974459i	$0.572096\pi$
$200$	2.49460	−	10.4314i	0.176395	−	0.737612i
$201$	−22.6720	−	2.57502i	−1.59916	−	0.181628i
$202$	−15.2336	+	10.8728i	−1.07183	+	0.765007i
$203$	−18.8691	+	10.8941i	−1.32435	+	0.764616i
$204$	13.1100	−	9.02845i	0.917881	−	0.632118i
$205$	−5.97735	+	3.45103i	−0.417476	+	0.241030i
$206$	−8.74221	−	12.2485i	−0.609099	−	0.853393i
$207$	−25.0851	−	5.77265i	−1.74353	−	0.401227i
$208$	−12.2434	+	7.62232i	−0.848925	+	0.528513i
$209$	1.20217	−	2.08222i	0.0831559	−	0.144030i
$210$	3.40482	+	6.13308i	0.234955	+	0.423223i
$211$		−	13.3806i		−	0.921162i	−0.887618	−	0.460581i	$-0.847641\pi$
$211$		−	13.3806i		−	0.921162i	0.887618	−	0.460581i	$-0.152359\pi$
$212$	−0.235965	−	1.21012i	−0.0162061	−	0.0831117i
$213$	24.3629	−	10.6036i	1.66932	−	0.726543i
$214$	−3.59539	−	1.63723i	−0.245775	−	0.111919i
$215$	−2.50434	−	4.33764i	−0.170794	−	0.295825i
$216$	−0.740619	+	14.6783i	−0.0503927	+	0.998729i
$217$	6.81189	+	11.7985i	0.462421	+	0.800937i
$218$	2.21039	+	22.8851i	0.149707	+	1.54997i
$219$	0.625083	−	5.50359i	0.0422392	−	0.371898i
$220$	0.563505	−	1.63968i	0.0379915	−	0.110547i
$221$	10.6137	+	12.7220i	0.713953	+	0.855774i
$222$	−1.84589	+	3.07659i	−0.123888	+	0.206487i
$223$	−6.62393	−	11.4730i	−0.443571	−	0.768288i	0.554380	−	0.832263i	$-0.312955\pi$
$223$	−6.62393	−	11.4730i	−0.443571	−	0.768288i	−0.997951	+	0.0639756i	$0.979622\pi$
$224$	13.0643	−	6.82535i	0.872896	−	0.456038i
$225$	7.75264	−	8.32549i	0.516842	−	0.555033i
$226$	−8.94128	+	19.6352i	−0.594765	+	1.30611i
$227$		−	2.54766i		−	0.169094i	−0.996419	−	0.0845470i	$-0.973056\pi$
$227$		−	2.54766i		−	0.169094i	0.996419	−	0.0845470i	$-0.0269443\pi$
$228$	5.98912	+	8.69664i	0.396639	+	0.575949i
$229$	−13.7300	+	7.92704i	−0.907306	+	0.523834i	−0.879563	−	0.475782i	$-0.842165\pi$
$229$	−13.7300	+	7.92704i	−0.907306	+	0.523834i	−0.0277428	+	0.999615i	$0.508832\pi$
$230$	−10.8551	+	7.74768i	−0.715762	+	0.510867i
$231$	−1.42062	−	3.26404i	−0.0934697	−	0.214758i
$232$	−16.2651	+	17.1702i	−1.06786	+	1.12728i
$233$	−13.2878			−0.870510			−0.435255	−	0.900307i	$-0.643342\pi$
$233$	−13.2878			−0.870510			−0.435255	+	0.900307i	$0.643342\pi$
$234$	−15.2837	+	0.639211i	−0.999127	+	0.0417865i
$235$		−	11.6463i		−	0.759721i
$236$	18.7585	+	6.44670i	1.22107	+	0.419644i
$237$	20.8466	+	15.4143i	1.35413	+	1.00127i
$238$	−9.83703	−	13.7824i	−0.637640	−	0.893381i
$239$	2.19077	+	3.79453i	0.141709	+	0.245448i	0.928140	−	0.372230i	$-0.121407\pi$
$239$	2.19077	+	3.79453i	0.141709	+	0.245448i	−0.786431	+	0.617678i	$0.788073\pi$
$240$	5.43926	+	5.32878i	0.351102	+	0.343971i
$241$	1.26245			0.0813213			0.0406606	−	0.999173i	$-0.487054\pi$
$241$	1.26245			0.0813213			0.0406606	+	0.999173i	$0.487054\pi$
$242$	6.08231	−	13.3568i	0.390985	−	0.858610i
$243$	−8.35240	+	13.1620i	−0.535807	+	0.844341i
$244$	−0.421690	−	2.16260i	−0.0269959	−	0.138446i
$245$	−0.200429	+	0.115718i	−0.0128050	+	0.00739295i
$246$	−0.258488	+	15.3804i	−0.0164806	+	0.980621i
$247$	−8.43928	+	7.04070i	−0.536979	+	0.447989i
$248$	10.7363	+	10.1703i	0.681753	+	0.645814i
$249$	−2.04870	+	2.77070i	−0.129831	+	0.175586i
$250$	−1.31380	−	13.6023i	−0.0830921	−	0.860285i
$251$	−11.5952	+	6.69447i	−0.731880	+	0.422551i	−0.819110	−	0.573637i	$-0.805532\pi$
$251$	−11.5952	+	6.69447i	−0.731880	+	0.422551i	0.0872293	+	0.996188i	$0.472199\pi$
$252$	15.6251	+	0.525347i	0.984288	+	0.0330938i
$253$	5.86107	−	3.38389i	0.368482	−	0.212743i
$254$	1.01827	−	2.23614i	0.0638921	−	0.140308i
$255$	5.20071	−	7.03356i	0.325681	−	0.440459i
$256$	11.4832	−	11.1417i	0.717699	−	0.696353i
$257$	16.4295			1.02485			0.512424	−	0.858733i	$-0.328748\pi$
$257$	16.4295			1.02485			0.512424	+	0.858733i	$0.328748\pi$
$258$	−11.1613	−	0.187579i	−0.694870	−	0.0116782i
$259$	3.30527	+	1.90830i	0.205379	+	0.118576i
$260$	−5.00149	+	6.14803i	−0.310179	+	0.381284i
$261$	−23.9844	+	7.35132i	−1.48459	+	0.455035i
$262$	18.2614	−	13.0339i	1.12819	−	0.805234i
$263$	−5.61951	−	9.73328i	−0.346514	−	0.600180i	0.639114	−	0.769112i	$-0.279301\pi$
$263$	−5.61951	−	9.73328i	−0.346514	−	0.600180i	−0.985628	+	0.168932i	$0.945968\pi$
$264$	−2.48748	−	2.95702i	−0.153094	−	0.181992i
$265$	−0.338764	−	0.586756i	−0.0208101	−	0.0360441i
$266$	9.14272	−	6.52550i	0.560576	−	0.400104i
$267$	16.0589	+	11.8742i	0.982791	+	0.726689i
$268$	5.04262	+	25.8606i	0.308027	+	1.57969i
$269$	−6.99000	+	4.03568i	−0.426188	+	0.246060i	−0.697721	−	0.716369i	$-0.745803\pi$
$269$	−6.99000	+	4.03568i	−0.426188	+	0.246060i	0.271533	+	0.962429i	$0.412469\pi$
$270$	2.23670	+	7.76055i	0.136121	+	0.472292i
$271$	0.0161082	−	0.0279003i	0.000978506	−	0.00169482i	−0.865536	−	0.500847i	$-0.833022\pi$
$271$	0.0161082	−	0.0279003i	0.000978506	−	0.00169482i	0.866514	+	0.499152i	$0.166355\pi$
$272$	−14.4974	−	11.2991i	−0.879035	−	0.685110i
$273$	0.953065	+	16.2444i	0.0576821	+	0.983153i
$274$	26.9217	−	2.60028i	1.62640	−	0.157088i
$275$			2.99104i			0.180366i
$276$	2.35998	+	29.6290i	0.142054	+	1.78346i
$277$		−	5.71566i		−	0.343421i	−0.985147	−	0.171710i	$-0.945071\pi$
$277$		−	5.71566i		−	0.343421i	0.985147	−	0.171710i	$-0.0549293\pi$
$278$	12.5485	+	5.71422i	0.752610	+	0.342716i
$279$	4.59665	+	14.9970i	0.275194	+	0.897848i
$280$	5.57047	−	5.88046i	0.332899	−	0.351425i
$281$	10.6750	−	18.4896i	0.636814	−	1.10299i	−0.349313	−	0.937006i	$-0.613585\pi$
$281$	10.6750	−	18.4896i	0.636814	−	1.10299i	0.986128	−	0.165989i	$-0.0530816\pi$
$282$	−22.2574	−	13.3540i	−1.32541	−	0.795217i
$283$		−	21.1697i		−	1.25841i	−0.777241	−	0.629203i	$-0.783381\pi$
$283$		−	21.1697i		−	1.25841i	0.777241	−	0.629203i	$-0.216619\pi$
$284$	−20.1421	−	23.1433i	−1.19522	−	1.37330i
$285$	4.66579	+	3.44995i	0.276378	+	0.204358i
$286$	2.82629	−	2.86146i	0.167122	−	0.169202i
$287$	16.3633			0.965895
$288$	16.4207	−	4.28493i	0.967599	−	0.252492i
$289$	−2.05766	+	3.56398i	−0.121039	+	0.209646i
$290$	−5.38628	+	11.8284i	−0.316293	+	0.694585i
$291$	2.22682	−	19.6062i	0.130539	−	1.14934i
$292$	−6.27763	+	1.22409i	−0.367370	+	0.0716344i
$293$	−16.8083	−	9.70425i	−0.981949	−	0.566928i	−0.0790908	−	0.996867i	$-0.525202\pi$
$293$	−16.8083	−	9.70425i	−0.981949	−	0.566928i	−0.902858	+	0.429939i	$0.858535\pi$
$294$	−0.00866748	+	0.515729i	−0.000505498	+	0.0300779i
$295$	10.9002			0.634633
$296$	4.02929	+	0.963577i	0.234197	+	0.0560068i
$297$	−0.751176	−	4.02911i	−0.0435876	−	0.233793i
$298$	0.432694	+	0.197036i	0.0250653	+	0.0114140i
$299$	−30.4816	+	5.28561i	−1.76280	+	0.305675i
$300$	−11.8617	−	5.64403i	−0.684838	−	0.325858i
$301$			11.8745i			0.684436i
$302$	−5.01416	+	11.0112i	−0.288532	+	0.633621i
$303$	9.14758	+	21.0177i	0.525515	+	1.20743i
$304$	7.49540	−	9.61703i	0.429890	−	0.551574i
$305$	−0.605400	−	1.04858i	−0.0346651	−	0.0600418i
$306$	−7.47867	−	18.0040i	−0.427527	−	1.02922i
$307$			19.6660i			1.12240i	0.827682	+	0.561198i	$0.189659\pi$
$307$			19.6660i			1.12240i	−0.827682	+	0.561198i	$0.810341\pi$
$308$	−3.10064	+	2.69855i	−0.176675	+	0.153764i
$309$	−16.8991	+	7.35506i	−0.961358	+	0.418415i
$310$	7.39607	+	3.36795i	0.420069	+	0.191287i
$311$	−2.90685	−	5.03481i	−0.164832	−	0.285498i	0.771763	−	0.635910i	$-0.219375\pi$
$311$	−2.90685	−	5.03481i	−0.164832	−	0.285498i	−0.936596	+	0.350412i	$0.886042\pi$
$312$	6.01474	+	16.6079i	0.340517	+	0.940238i
$313$	−10.8847	+	18.8528i	−0.615237	+	1.06562i	0.375106	+	0.926982i	$0.377606\pi$
$313$	−10.8847	+	18.8528i	−0.615237	+	1.06562i	−0.990343	+	0.138640i	$0.955727\pi$
$314$	−1.07500	+	0.767271i	−0.0606660	+	0.0432996i
$315$	8.21417	−	2.51768i	0.462816	−	0.141855i
$316$	9.72994	−	28.3120i	0.547352	−	1.59268i
$317$	2.53961	+	1.46625i	0.142639	+	0.0823526i	0.569621	−	0.821907i	$-0.307090\pi$
$317$	2.53961	+	1.46625i	0.142639	+	0.0823526i	−0.426982	+	0.904260i	$0.640423\pi$
$318$	−1.50979	−	0.0253740i	−0.0846650	−	0.00142290i
$319$	3.29778	−	5.71192i	0.184640	−	0.319806i
$320$	3.97786	−	7.84125i	0.222369	−	0.438339i
$321$	−2.87667	+	3.89047i	−0.160560	+	0.217145i
$322$	31.4713	−	3.03971i	1.75383	−	0.169396i
$323$	−12.1305	−	7.00354i	−0.674959	−	0.389688i
$324$	17.3960	+	4.62388i	0.966443	+	0.256882i
$325$	4.71268	−	12.8346i	0.261413	−	0.711934i
$326$	−3.24148	+	2.31357i	−0.179529	+	0.128137i
$327$	27.9789	+	3.17777i	1.54724	+	0.175731i
$328$	17.0264	−	5.05983i	0.940125	−	0.279382i
$329$	−13.8055	+	23.9118i	−0.761120	+	1.31830i
$330$	−1.82088	−	1.09249i	−0.100236	−	0.0601395i
$331$		−	18.6157i		−	1.02321i	−0.859221	−	0.511604i	$-0.829051\pi$
$331$		−	18.6157i		−	1.02321i	0.859221	−	0.511604i	$-0.170949\pi$
$332$	3.76292	+	1.29320i	0.206517	+	0.0709734i
$333$	3.21584	+	2.99457i	0.176227	+	0.164101i
$334$	6.18546	−	0.597433i	0.338454	−	0.0326901i
$335$	7.23945	+	12.5391i	0.395533	+	0.685084i
$336$	−4.85098	−	17.3885i	−0.264643	−	0.948621i
$337$	−10.8924	−	18.8662i	−0.593346	−	1.02771i	−0.993778	−	0.111379i	$-0.964473\pi$
$337$	−10.8924	−	18.8662i	−0.593346	−	1.02771i	0.400432	−	0.916327i	$-0.368860\pi$
$338$	−16.6362	+	7.82548i	−0.904888	+	0.425650i
$339$	21.2467	+	15.7101i	1.15396	+	0.853257i
$340$	−9.55236	−	3.28284i	−0.518049	−	0.178037i
$341$	−3.57157	−	2.06205i	−0.193411	−	0.111666i
$342$	11.9432	−	4.96106i	0.645813	−	0.268263i
$343$	18.7883			1.01447
$344$	3.67182	+	12.3557i	0.197971	+	0.666175i
$345$	6.51833	+	14.9766i	0.350935	+	0.806315i
$346$	−2.24531	−	23.2466i	−0.120709	−	1.24975i
$347$	−28.5173	−	16.4645i	−1.53089	−	0.883860i	−0.999321	−	0.0368447i	$-0.988269\pi$
$347$	−28.5173	−	16.4645i	−1.53089	−	0.883860i	−0.531569	−	0.847015i	$-0.678397\pi$
$348$	16.4293	+	23.8565i	0.880703	+	1.27884i
$349$	−17.0399	+	9.83800i	−0.912126	+	0.526616i	−0.881115	−	0.472903i	$-0.843206\pi$
$349$	−17.0399	+	9.83800i	−0.912126	+	0.526616i	−0.0310116	+	0.999519i	$0.509873\pi$
$350$	−5.79098	+	12.7171i	−0.309541	+	0.679756i
$351$	−3.12497	+	18.4725i	−0.166799	+	0.985991i
$352$	−2.39184	+	3.76668i	−0.127485	+	0.200765i
$353$	−6.41454	−	11.1103i	−0.341412	−	0.591342i	0.643284	−	0.765628i	$-0.277572\pi$
$353$	−6.41454	−	11.1103i	−0.341412	−	0.591342i	−0.984695	+	0.174286i	$0.944238\pi$
$354$	12.4984	−	20.8315i	0.664285	−	1.10718i
$355$	−14.6013	−	8.43008i	−0.774958	−	0.447422i
$356$	7.49534	−	21.8098i	0.397252	−	1.15592i
$357$	−19.0155	+	8.27616i	−1.00641	+	0.438021i
$358$	−21.9364	−	9.98918i	−1.15937	−	0.527944i
$359$	−2.53795			−0.133948			−0.0669738	−	0.997755i	$-0.521334\pi$
$359$	−2.53795			−0.133948			−0.0669738	+	0.997755i	$0.521334\pi$
$360$	7.76851	−	5.15967i	0.409437	−	0.271939i
$361$	−4.85412	+	8.40758i	−0.255480	+	0.442504i
$362$	0.482220	+	4.99262i	0.0253449	+	0.262406i
$363$	−14.4531	−	10.6868i	−0.758590	−	0.560912i
$364$	17.5567	−	6.69416i	0.920222	−	0.350869i
$365$	−3.04385	+	1.75737i	−0.159322	+	0.0919848i
$366$	−2.69813	−	0.0453456i	−0.141034	−	0.00237025i
$367$	−16.0314	−	27.7672i	−0.836833	−	1.44944i	−0.892529	−	0.450989i	$-0.851071\pi$
$367$	−16.0314	−	27.7672i	−0.836833	−	1.44944i	0.0556967	−	0.998448i	$-0.482262\pi$
$368$	31.8067	−	12.8944i	1.65804	−	0.672166i
$369$	18.3599	+	4.22504i	0.955779	+	0.219947i
$370$	2.26611	−	0.218876i	0.117810	−	0.0113788i
$371$			1.60627i			0.0833936i
$372$	14.9171	−	10.2730i	0.773415	−	0.532628i
$373$	7.15520	+	4.13106i	0.370482	+	0.213898i	0.673669	−	0.739033i	$-0.264717\pi$
$373$	7.15520	+	4.13106i	0.370482	+	0.213898i	−0.303187	+	0.952931i	$0.598051\pi$
$374$	4.66490	+	2.12426i	0.241216	+	0.109843i
$375$	−16.6300	−	1.88879i	−0.858768	−	0.0975365i
$376$	−6.97095	+	29.1496i	−0.359499	+	1.50328i
$377$	−23.1505	+	19.3140i	−1.19231	+	0.994720i
$378$	4.60701	−	18.5851i	0.236959	−	0.955912i
$379$	2.16207	+	1.24827i	0.111058	+	0.0641193i	0.554500	−	0.832184i	$-0.312910\pi$
$379$	2.16207	+	1.24827i	0.111058	+	0.0641193i	−0.443442	+	0.896303i	$0.646243\pi$
$380$	2.17771	−	6.33667i	0.111714	−	0.325064i
$381$	−2.41967	−	1.78914i	−0.123963	−	0.0916602i
$382$	3.43965	−	0.332224i	0.175988	−	0.0169981i
$383$	3.99552	−	6.92044i	0.204161	−	0.353618i	−0.745704	−	0.666278i	$-0.767887\pi$
$383$	3.99552	−	6.92044i	0.204161	−	0.353618i	0.949865	+	0.312660i	$0.101220\pi$
$384$	−10.4244	−	16.5931i	−0.531968	−	0.846764i
$385$	−1.12942	+	1.95622i	−0.0575608	+	0.0996982i
$386$	−0.763468	+	0.0737408i	−0.0388595	+	0.00375331i
$387$	−3.06602	+	13.3234i	−0.155855	+	0.677267i
$388$	−22.3637	+	4.36075i	−1.13534	+	0.221383i
$389$	14.3211	+	8.26828i	0.726107	+	0.419218i	0.816996	−	0.576643i	$-0.195638\pi$
$389$	14.3211	+	8.26828i	0.726107	+	0.419218i	−0.0908891	+	0.995861i	$0.528971\pi$
$390$	6.09209	+	7.55686i	0.308485	+	0.382656i
$391$	−19.7137	−	34.1451i	−0.996965	−	1.72679i
$392$	0.570920	−	0.169664i	0.0288358	−	0.00856930i
$393$	−10.9657	−	25.1951i	−0.553148	−	1.27092i
$394$	18.6346	+	8.48563i	0.938796	+	0.427500i
$395$		−	16.4515i		−	0.827767i
$396$	−4.17574	+	2.22723i	−0.209839	+	0.111923i
$397$	−11.8706	+	6.85348i	−0.595767	+	0.343966i	−0.767375	−	0.641199i	$-0.778437\pi$
$397$	−11.8706	+	6.85348i	−0.595767	+	0.343966i	0.171608	+	0.985165i	$0.445104\pi$
$398$	−16.9587	−	23.7604i	−0.850064	−	1.19100i
$399$	−5.49008	−	12.6141i	−0.274848	−	0.631496i
$400$	−2.09329	+	15.0231i	−0.104665	+	0.751154i
$401$	−0.984984			−0.0491878			−0.0245939	−	0.999698i	$-0.507829\pi$
$401$	−0.984984			−0.0491878			−0.0245939	+	0.999698i	$0.507829\pi$
$402$	32.2646	+	0.542248i	1.60921	+	0.0270449i
$403$	12.0767	+	14.4756i	0.601583	+	0.721083i
$404$	19.9655	−	17.3764i	0.993320	−	0.864509i
$405$	9.86651	−	0.703965i	0.490271	−	0.0349803i
$406$	25.0802	−	17.9007i	1.24471	−	0.888396i
$407$	−1.15533			−0.0572677
$408$	−17.2269	+	14.4915i	−0.852858	+	0.717434i
$409$	9.69469	−	16.7917i	0.479371	−	0.830296i	−0.520349	−	0.853954i	$-0.674198\pi$
$409$	9.69469	−	16.7917i	0.479371	−	0.830296i	0.999720	+	0.0236582i	$0.00753135\pi$
$410$	7.94489	−	5.67057i	0.392370	−	0.280049i
$411$	3.73829	−	32.9140i	0.184396	−	1.62353i
$412$	13.9714	+	16.0531i	0.688322	+	0.790882i
$413$	−22.3799	−	12.9210i	−1.10124	−	0.635801i
$414$	36.0962	+	4.71535i	1.77403	+	0.231747i
$415$	2.18656			0.107334
$416$	16.1982	−	12.3943i	0.794182	−	0.607680i
$417$	10.0401	−	13.5784i	0.491664	−	0.664938i
$418$	−1.40915	+	3.09451i	−0.0689237	+	0.151358i
$419$			8.14810i			0.398061i	0.979993	+	0.199030i	$0.0637793\pi$
$419$			8.14810i			0.398061i	−0.979993	+	0.199030i	$0.936221\pi$
$420$	−5.62671	−	8.17038i	−0.274555	−	0.398674i
$421$	17.9654	+	10.3723i	0.875582	+	0.505517i	0.869199	−	0.494462i	$-0.164635\pi$
$421$	17.9654	+	10.3723i	0.875582	+	0.505517i	0.00638266	+	0.999980i	$0.497968\pi$
$422$	1.81925	+	18.8354i	0.0885598	+	0.916895i
$423$	−21.6640	+	23.2648i	−1.05334	+	1.13117i
$424$	0.496689	+	1.67137i	0.0241214	+	0.0811687i
$425$	17.4250			0.845238
$426$	−32.8531	+	18.2386i	−1.59174	+	0.883665i
$427$			2.87055i			0.138916i
$428$	5.28369	+	1.81584i	0.255397	+	0.0877718i
$429$	−2.70854	−	4.11432i	−0.130770	−	0.198641i
$430$	4.11501	+	5.76544i	0.198444	+	0.278034i
$431$	−11.6930	+	20.2528i	−0.563231	+	0.975545i	0.433981	+	0.900922i	$0.357109\pi$
$431$	−11.6930	+	20.2528i	−0.563231	+	0.975545i	−0.997212	+	0.0746227i	$0.976225\pi$
$432$	−0.953136	−	20.7627i	−0.0458578	−	0.998948i
$433$	−5.73141	−	9.92709i	−0.275434	−	0.477066i	0.694811	−	0.719193i	$-0.255488\pi$
$433$	−5.73141	−	9.92709i	−0.275434	−	0.477066i	−0.970245	+	0.242127i	$0.922155\pi$
$434$	−11.1930	−	15.6822i	−0.537281	−	0.752771i
$435$	12.7992	+	9.46387i	0.613673	+	0.453758i
$436$	−6.22297	−	31.9139i	−0.298026	−	1.52840i
$437$	22.6506	−	13.0773i	1.08352	−	0.625573i
$438$	−0.131630	+	7.83219i	−0.00628952	+	0.374236i
$439$	12.9756	+	22.4745i	0.619293	+	1.07265i	0.989615	+	0.143744i	$0.0459141\pi$
$439$	12.9756	+	22.4745i	0.619293	+	1.07265i	−0.370322	+	0.928904i	$0.620753\pi$
$440$	−0.570293	+	2.38473i	−0.0271876	+	0.113688i
$441$	0.615635	+	0.141672i	0.0293159	+	0.00674627i
$442$	−16.6702	−	16.4652i	−0.792919	−	0.783171i
$443$	11.8732	+	6.85501i	0.564114	+	0.325691i	0.754795	−	0.655961i	$-0.227736\pi$
$443$	11.8732	+	6.85501i	0.564114	+	0.325691i	−0.190681	+	0.981652i	$0.561070\pi$
$444$	2.18009	−	4.58177i	0.103462	−	0.217441i
$445$		−	12.6732i		−	0.600769i
$446$	10.8841	+	15.2495i	0.515379	+	0.722084i
$447$	0.346199	−	0.468207i	0.0163746	−	0.0221454i
$448$	−17.4622	+	11.3840i	−0.825010	+	0.537845i
$449$	9.12459	+	15.8042i	0.430616	+	0.745849i	0.996926	−	0.0783434i	$-0.0249631\pi$
$449$	9.12459	+	15.8042i	0.430616	+	0.745849i	−0.566311	+	0.824192i	$0.691630\pi$
$450$	−9.78115	+	12.7735i	−0.461088	+	0.602150i
$451$	−4.28975	+	2.47669i	−0.201997	+	0.116623i
$452$	9.91668	−	28.8554i	0.466442	−	1.35724i
$453$	11.9149	+	8.81003i	0.559810	+	0.413931i
$454$	0.346383	+	3.58624i	0.0162566	+	0.168311i
$455$	7.92860	−	6.61465i	0.371699	−	0.310099i
$456$	−9.61307	−	11.4276i	−0.450173	−	0.535149i
$457$	18.5796	+	32.1809i	0.869119	+	1.50536i	0.862898	+	0.505378i	$0.168647\pi$
$457$	18.5796	+	32.1809i	0.869119	+	1.50536i	0.00622085	+	0.999981i	$0.498020\pi$
$458$	18.2495	−	13.0254i	0.852743	−	0.608635i
$459$	−23.4726	+	4.37616i	−1.09561	+	0.204262i
$460$	14.2269	−	12.3820i	0.663332	−	0.577313i
$461$		−	26.6087i		−	1.23929i	−0.784882	−	0.619645i	$-0.787276\pi$
$461$		−	26.6087i		−	1.23929i	0.784882	−	0.619645i	$-0.212724\pi$
$462$	2.44353	+	4.40151i	0.113683	+	0.204777i
$463$	13.3735	+	23.1637i	0.621521	+	1.07651i	0.989203	+	0.146554i	$0.0468183\pi$
$463$	13.3735	+	23.1637i	0.621521	+	1.07651i	−0.367681	+	0.929952i	$0.619848\pi$
$464$	20.5613	−	26.3813i	0.954534	−	1.22472i
$465$	5.91760	−	8.00309i	0.274422	−	0.371135i
$466$	18.7047	−	1.80662i	0.866478	−	0.0836902i
$467$			0.685279i			0.0317109i	0.999874	+	0.0158555i	$0.00504716\pi$
$467$			0.685279i			0.0317109i	−0.999874	+	0.0158555i	$0.994953\pi$
$468$	21.4274	−	2.97779i	0.990481	−	0.137648i
$469$		−	34.3264i		−	1.58505i
$470$	1.58345	+	16.3941i	0.0730390	+	0.756202i
$471$	0.645526	+	1.48317i	0.0297443	+	0.0683410i
$472$	−27.2822	−	6.52435i	−1.25576	−	0.300307i
$473$	−1.79728	−	3.11298i	−0.0826391	−	0.143135i
$474$	−31.4408	−	18.8638i	−1.44412	−	0.866442i
$475$			11.5591i			0.530367i
$476$	15.7211	+	18.0635i	0.720575	+	0.827940i
$477$	−0.414743	+	1.80227i	−0.0189898	+	0.0825202i
$478$	−3.59978	−	5.04356i	−0.164650	−	0.230687i
$479$	2.94149	+	5.09481i	0.134400	+	0.232788i	0.925368	−	0.379070i	$-0.123756\pi$
$479$	2.94149	+	5.09481i	0.134400	+	0.232788i	−0.790968	+	0.611857i	$0.790423\pi$
$480$	−8.38115	−	6.76159i	−0.382545	−	0.308623i
$481$	4.95754	+	1.82034i	0.226045	+	0.0830005i
$482$	−1.77710	+	0.171644i	−0.0809446	+	0.00781816i
$483$	4.37003	−	38.4763i	0.198843	−	1.75073i
$484$	−6.74582	+	19.6289i	−0.306628	+	0.892222i
$485$	−10.8435	+	6.26052i	−0.492379	+	0.284275i
$486$	9.96785	−	19.6632i	0.452151	−	0.891942i
$487$	4.30239	+	7.45196i	0.194960	+	0.337681i	0.946887	−	0.321565i	$-0.104209\pi$
$487$	4.30239	+	7.45196i	0.194960	+	0.337681i	−0.751927	+	0.659246i	$0.770876\pi$
$488$	0.887627	+	2.98688i	0.0401810	+	0.135209i
$489$	1.94647	+	4.47225i	0.0880224	+	0.202242i
$490$	0.266404	−	0.190142i	0.0120349	−	0.00858976i
$491$			25.8347i			1.16591i	0.812506	+	0.582953i	$0.198103\pi$
$491$			25.8347i			1.16591i	−0.812506	+	0.582953i	$0.801897\pi$
$492$	−1.72728	−	21.6856i	−0.0778719	−	0.977663i
$493$	−33.2762	−	19.2120i	−1.49869	−	0.865267i
$494$	10.9224	−	11.0583i	0.491422	−	0.497538i
$495$	−1.77233	+	1.90329i	−0.0796605	+	0.0855467i
$496$	−16.4958	−	12.8566i	−0.740683	−	0.577279i
$497$	19.9859	+	34.6166i	0.896492	+	1.55277i
$498$	2.50716	−	4.17876i	0.112349	−	0.187255i
$499$	20.7450	−	11.9771i	0.928675	−	0.536171i	0.0422825	−	0.999106i	$-0.486537\pi$
$499$	20.7450	−	11.9771i	0.928675	−	0.536171i	0.886392	+	0.462935i	$0.153204\pi$
$500$	3.69878	+	18.9688i	0.165414	+	0.848312i
$501$	0.858900	−	7.56225i	0.0383728	−	0.337856i
$502$	15.4119	−	11.0001i	0.687866	−	0.490956i
$503$	−7.08931	−	12.2791i	−0.316097	−	0.547496i	0.663573	−	0.748111i	$-0.269039\pi$
$503$	−7.08931	−	12.2791i	−0.316097	−	0.547496i	−0.979670	+	0.200616i	$0.935706\pi$
$504$	−22.0663	+	1.38490i	−0.982910	+	0.0616882i
$505$	7.27254	−	12.5964i	0.323624	−	0.560533i
$506$	−7.79034	+	5.56026i	−0.346323	+	0.247184i
$507$	5.13986	+	21.9222i	0.228269	+	0.973598i
$508$	−1.12935	+	3.28618i	−0.0501070	+	0.145801i
$509$		−	32.2210i		−	1.42817i	−0.700058	−	0.714086i	$-0.746843\pi$
$509$		−	32.2210i		−	1.42817i	0.700058	−	0.714086i	$-0.253157\pi$
$510$	−6.36456	+	10.6080i	−0.281827	+	0.469729i
$511$	8.33269			0.368617
$512$	−14.6496	+	17.2450i	−0.647428	+	0.762127i
$513$	−2.90298	−	15.5708i	−0.128170	−	0.687468i
$514$	−23.1273	+	2.23378i	−1.02010	+	0.0985280i
$515$	10.1281	+	5.84745i	0.446297	+	0.257669i
$516$	15.7368	−	1.25345i	0.692774	−	0.0551802i
$517$		−	8.35818i		−	0.367592i
$518$	−4.91216	−	2.23685i	−0.215828	−	0.0982815i
$519$	−28.4210	−	3.22797i	−1.24754	−	0.141692i
$520$	6.20452	−	9.33436i	0.272086	−	0.409339i
$521$	5.44426			0.238517			0.119259	−	0.992863i	$-0.461948\pi$
$521$	5.44426			0.238517			0.119259	+	0.992863i	$0.461948\pi$
$522$	32.7624	−	13.6091i	1.43397	−	0.595655i
$523$	1.14504	+	0.661092i	0.0500693	+	0.0289075i	0.524826	−	0.851210i	$-0.324130\pi$
$523$	1.14504	+	0.661092i	0.0500693	+	0.0289075i	−0.474756	+	0.880117i	$0.657464\pi$
$524$	−23.9338	+	20.8301i	−1.04555	+	0.909968i
$525$	13.7608	+	10.1749i	0.600571	+	0.444071i
$526$	9.23373	+	12.9371i	0.402610	+	0.564086i
$527$	−12.0130	+	20.8071i	−0.523293	+	0.906370i
$528$	3.90358	+	3.82429i	0.169881	+	0.166431i
$529$	50.6205			2.20089
$530$	0.556641	+	0.779896i	0.0241790	+	0.0338765i
$531$	−21.7743	−	20.2761i	−0.944926	−	0.879909i
$532$	−11.9826	+	10.4288i	−0.519513	+	0.452144i
$533$	22.3097	−	3.86857i	0.966339	−	0.167566i
$534$	−24.2200	−	14.5315i	−1.04810	−	0.628838i
$535$	3.07024			0.132738
$536$	−10.6144	−	35.7174i	−0.458470	−	1.54276i
$537$	−17.5513	+	23.7368i	−0.757395	+	1.02432i
$538$	9.29087	−	6.63124i	0.400558	−	0.285893i
$539$	−0.143842	+	0.0830470i	−0.00619570	+	0.00357709i
$540$	−4.20365	−	10.6201i	−0.180896	−	0.457018i
$541$			8.27239i			0.355658i	0.984061	+	0.177829i	$0.0569073\pi$
$541$			8.27239i			0.355658i	−0.984061	+	0.177829i	$0.943093\pi$
$542$	−0.0188816	+	0.0414643i	−0.000811034	+	0.00178104i
$543$	6.10389	+	0.693263i	0.261943	+	0.0297508i
$544$	21.9437	+	13.9343i	0.940829	+	0.597426i
$545$	−8.93403	−	15.4742i	−0.382692	−	0.662842i
$546$	−3.55020	−	22.7370i	−0.151935	−	0.973054i
$547$	20.7704	+	11.9918i	0.888079	+	0.512733i	0.873314	−	0.487158i	$-0.161967\pi$
$547$	20.7704	+	11.9918i	0.888079	+	0.512733i	0.0147652	+	0.999891i	$0.495300\pi$
$548$	−37.5431	+	7.32062i	−1.60376	+	0.312721i
$549$	−0.741183	+	3.22081i	−0.0316329	+	0.137461i
$550$	−0.406666	−	4.21037i	−0.0173403	−	0.179531i
$551$	12.7445	−	22.0742i	0.542935	−	0.940391i
$552$	−7.35045	−	41.3867i	−0.312856	−	1.76154i
$553$	−19.5016	+	33.7777i	−0.829291	+	1.43637i
$554$	0.777109	+	8.04572i	0.0330162	+	0.341830i
$555$	0.314667	−	2.77051i	0.0133569	−	0.117602i
$556$	−18.4410	−	6.33758i	−0.782072	−	0.268773i
$557$	5.54287	+	3.20018i	0.234859	+	0.135596i	0.612812	−	0.790229i	$-0.290038\pi$
$557$	5.54287	+	3.20018i	0.234859	+	0.135596i	−0.377953	+	0.925825i	$0.623372\pi$
$558$	−8.50955	−	20.4858i	−0.360238	−	0.867232i
$559$	2.80734	+	16.1897i	0.118738	+	0.684750i
$560$	−7.04183	+	9.03508i	−0.297572	+	0.381802i
$561$	3.73239	−	5.04776i	0.157581	−	0.213117i
$562$	−12.5129	+	27.4785i	−0.527824	+	1.15911i
$563$	25.1750	+	14.5348i	1.06100	+	0.612568i	0.925708	−	0.378238i	$-0.123470\pi$
$563$	25.1750	+	14.5348i	1.06100	+	0.612568i	0.135291	+	0.990806i	$0.456803\pi$
$564$	33.1466	+	15.7717i	1.39572	+	0.664110i
$565$		−	16.7673i		−	0.705405i
$566$	2.87826	+	29.7998i	0.120982	+	1.25258i
$567$	−21.0920	−	10.2503i	−0.885782	−	0.430474i
$568$	31.4999	+	29.8394i	1.32171	+	1.25203i
$569$	−9.08529	−	15.7362i	−0.380875	−	0.659695i	0.610313	−	0.792161i	$-0.291044\pi$
$569$	−9.08529	−	15.7362i	−0.380875	−	0.659695i	−0.991188	+	0.132466i	$0.957711\pi$
$570$	−7.03693	−	4.22200i	−0.294744	−	0.176840i
$571$	−27.0813	+	15.6354i	−1.13332	+	0.654320i	−0.944767	−	0.327744i	$-0.893712\pi$
$571$	−27.0813	+	15.6354i	−1.13332	+	0.654320i	−0.188549	+	0.982064i	$0.560378\pi$
$572$	−3.58941	+	4.41224i	−0.150081	+	0.184485i
$573$	0.477623	−	4.20527i	0.0199530	−	0.175677i
$574$	−23.0340	+	2.22478i	−0.961421	+	0.0928604i
$575$	−16.2684	+	28.1776i	−0.678438	+	1.17509i
$576$	−22.5322	+	8.26431i	−0.938843	+	0.344346i
$577$	3.07397			0.127971			0.0639854	−	0.997951i	$-0.479619\pi$
$577$	3.07397			0.127971			0.0639854	+	0.997951i	$0.479619\pi$
$578$	2.41193	−	5.29664i	0.100323	−	0.220311i
$579$	−0.106014	+	0.933404i	−0.00440577	+	0.0387910i
$580$	5.97387	−	17.3827i	0.248051	−	0.721776i
$581$	−4.48936	−	2.59193i	−0.186250	−	0.107531i
$582$	−0.468924	+	27.9017i	−0.0194375	+	1.15656i
$583$	−0.243120	−	0.421096i	−0.0100690	−	0.0174400i
$584$	8.67035	−	2.57662i	0.358782	−	0.106621i
$585$	10.6039	−	5.37457i	0.438419	−	0.222211i
$586$	24.9798	+	11.3750i	1.03190	+	0.469898i
$587$	24.2313	−	13.9900i	1.00013	−	0.577428i	0.0918466	−	0.995773i	$-0.470723\pi$
$587$	24.2313	−	13.9900i	1.00013	−	0.577428i	0.908288	+	0.418345i	$0.137390\pi$
$588$	−0.0579183	−	0.727151i	−0.00238851	−	0.0299872i
$589$	−13.8026	−	7.96894i	−0.568726	−	0.328354i
$590$	−15.3438	+	1.48200i	−0.631693	+	0.0610131i
$591$	14.9095	−	20.1640i	0.613296	−	0.829435i
$592$	−5.80288	−	0.808565i	−0.238497	−	0.0332318i
$593$	15.1241			0.621070			0.310535	−	0.950562i	$-0.399492\pi$
$593$	15.1241			0.621070			0.310535	+	0.950562i	$0.399492\pi$
$594$	1.60521	+	5.56950i	0.0658624	+	0.228519i
$595$	11.3964	+	6.57974i	0.467209	+	0.269743i
$596$	−0.635877	−	0.218531i	−0.0260465	−	0.00895136i
$597$	−32.7821	+	14.2678i	−1.34168	+	0.583944i
$598$	42.1892	−	11.5847i	1.72524	−	0.473733i
$599$	18.8449	+	32.6403i	0.769982	+	1.33365i	0.937572	+	0.347791i	$0.113068\pi$
$599$	18.8449	+	32.6403i	0.769982	+	1.33365i	−0.167590	+	0.985857i	$0.553599\pi$
$600$	17.4647	+	6.33216i	0.712994	+	0.258509i
$601$	−14.3840	−	24.9138i	−0.586736	−	1.01626i	−0.994657	−	0.103239i	$-0.967079\pi$
$601$	−14.3840	−	24.9138i	−0.586736	−	1.01626i	0.407920	−	0.913018i	$-0.366254\pi$
$602$	−1.61448	−	16.7153i	−0.0658011	−	0.681265i
$603$	8.86315	−	38.5148i	0.360935	−	1.56845i
$604$	5.56115	−	16.1817i	0.226280	−	0.658426i
$605$			11.4059i			0.463717i
$606$	−15.7343	−	28.3421i	−0.639162	−	1.15132i
$607$	3.89315	−	6.74314i	0.158018	−	0.273696i	−0.776136	−	0.630566i	$-0.782823\pi$
$607$	3.89315	−	6.74314i	0.158018	−	0.273696i	0.934154	+	0.356870i	$0.116156\pi$
$608$	−9.24345	+	14.5566i	−0.374871	+	0.590349i
$609$	−15.0603	−	34.6029i	−0.610276	−	1.40218i
$610$	0.994767	+	1.39374i	0.0402769	+	0.0564310i
$611$	−13.1692	+	35.8651i	−0.532767	+	1.45095i
$612$	12.9753	+	24.3268i	0.524495	+	0.983353i
$613$	−21.5412	−	12.4368i	−0.870040	−	0.502318i	−0.00267850	−	0.999996i	$-0.500853\pi$
$613$	−21.5412	−	12.4368i	−0.870040	−	0.502318i	−0.867362	+	0.497679i	$0.834186\pi$
$614$	−2.67381	−	27.6831i	−0.107906	−	1.11720i
$615$	−4.77080	−	10.9615i	−0.192377	−	0.442010i
$616$	3.99775	−	4.22022i	0.161074	−	0.170037i
$617$	−11.2883	+	19.5520i	−0.454451	+	0.787132i	−0.998656	−	0.0518198i	$-0.983498\pi$
$617$	−11.2883	+	19.5520i	−0.454451	+	0.787132i	0.544205	+	0.838952i	$0.316831\pi$
$618$	22.7883	−	12.6511i	0.916679	−	0.508901i
$619$	21.7039	+	12.5308i	0.872355	+	0.503655i	0.868130	−	0.496337i	$-0.165322\pi$
$619$	21.7039	+	12.5308i	0.872355	+	0.503655i	0.00422503	+	0.999991i	$0.498655\pi$
$620$	−10.8691	−	3.73536i	−0.436513	−	0.150016i
$621$	14.8379	−	42.0427i	0.595425	−	1.68712i
$622$	4.77640	+	6.69209i	0.191516	+	0.268328i
$623$	−15.0228	+	26.0202i	−0.601875	+	1.04248i
$624$	−10.7248	−	22.5606i	−0.429334	−	0.903146i
$625$	−4.16998	−	7.22261i	−0.166799	−	0.288905i
$626$	12.7587	−	28.0182i	0.509939	−	1.11983i
$627$	3.34849	+	2.47592i	0.133726	+	0.0988787i
$628$	1.40892	−	1.22622i	0.0562222	−	0.0489314i
$629$			6.73067i			0.268369i
$630$	−11.2205	+	4.66085i	−0.447034	+	0.185693i
$631$	−20.2917	−	35.1462i	−0.807798	−	1.39915i	−0.914386	−	0.404844i	$-0.867326\pi$
$631$	−20.2917	−	35.1462i	−0.807798	−	1.39915i	0.106588	−	0.994303i	$-0.466008\pi$
$632$	−9.84714	+	41.1767i	−0.391698	+	1.63792i
$633$	23.0279	+	2.61545i	0.915277	+	0.103955i
$634$	−3.77427	−	1.71869i	−0.149895	−	0.0682579i
$635$			1.90953i			0.0757774i
$636$	2.12873	−	0.169556i	0.0844097	−	0.00672332i
$637$	0.748076	−	0.129719i	0.0296398	−	0.00513965i
$638$	−3.86556	+	8.48883i	−0.153039	+	0.336076i
$639$	13.4865	+	44.0009i	0.533516	+	1.74065i
$640$	−4.53337	+	11.5787i	−0.179197	+	0.457687i
$641$	13.0150			0.514062			0.257031	−	0.966403i	$-0.417256\pi$
$641$	13.0150			0.514062			0.257031	+	0.966403i	$0.417256\pi$
$642$	3.52042	−	5.86759i	0.138940	−	0.231575i
$643$	−6.21875	−	3.59040i	−0.245244	−	0.141592i	0.372341	−	0.928096i	$-0.378555\pi$
$643$	−6.21875	−	3.59040i	−0.245244	−	0.141592i	−0.617584	+	0.786505i	$0.711889\pi$
$644$	−43.8877	+	8.55776i	−1.72942	+	0.337223i
$645$	7.95453	−	3.46207i	0.313209	−	0.136319i
$646$	18.0279	+	8.20935i	0.709297	+	0.322993i
$647$	6.83502	−	11.8386i	0.268713	−	0.465424i	−0.699817	−	0.714322i	$-0.746735\pi$
$647$	6.83502	−	11.8386i	0.268713	−	0.465424i	0.968530	+	0.248898i	$0.0800685\pi$
$648$	−25.1163	−	4.14368i	−0.986663	−	0.162779i
$649$	7.82271			0.307068
$650$	−4.88886	+	18.7075i	−0.191757	+	0.733769i
$651$	−21.6366	+	9.41697i	−0.848006	+	0.369080i
$652$	4.24836	−	3.69744i	0.166379	−	0.144803i
$653$		−	34.4929i		−	1.34981i	−0.737903	−	0.674907i	$-0.764184\pi$
$653$		−	34.4929i		−	1.34981i	0.737903	−	0.674907i	$-0.235816\pi$
$654$	−39.8170	−	0.669175i	−1.55697	−	0.0261668i
$655$	−8.71802	+	15.1001i	−0.340641	+	0.590008i
$656$	−23.2795	+	9.43747i	−0.908911	+	0.368471i
$657$	9.34942	+	2.15152i	0.364756	+	0.0839387i
$658$	16.1824	−	35.5367i	0.630854	−	1.38537i
$659$			25.5180i			0.994042i	0.867739	+	0.497021i	$0.165573\pi$
$659$			25.5180i			0.994042i	−0.867739	+	0.497021i	$0.834427\pi$
$660$	2.71172	+	1.29028i	0.105554	+	0.0502243i
$661$			48.6855i			1.89365i	0.321753	+	0.946824i	$0.395728\pi$
$661$			48.6855i			1.89365i	−0.321753	+	0.946824i	$0.604272\pi$
$662$	2.53101	+	26.2046i	0.0983705	+	1.01847i
$663$	−23.9690	+	15.7793i	−0.930878	+	0.612816i
$664$	−5.47275	−	1.30877i	−0.212384	−	0.0507902i
$665$	−4.36475	+	7.55996i	−0.169258	+	0.293163i
$666$	−4.93397	−	3.77811i	−0.191187	−	0.146399i
$667$	62.1348	−	35.8735i	2.40587	−	1.38903i
$668$	−8.62582	+	1.68197i	−0.333743	+	0.0650773i
$669$	21.0396	−	9.15713i	0.813438	−	0.354035i
$670$	−11.8955	−	16.6665i	−0.459565	−	0.643884i
$671$	−0.434476	−	0.752535i	−0.0167728	−	0.0290513i
$672$	9.19271	+	23.8176i	0.354617	+	0.918784i
$673$	18.7563	+	32.4869i	0.723003	+	1.25228i	0.959791	+	0.280716i	$0.0905720\pi$
$673$	18.7563	+	32.4869i	0.723003	+	1.25228i	−0.236788	+	0.971561i	$0.576095\pi$
$674$	17.8979	+	25.0763i	0.689401	+	0.965901i
$675$	12.8127	+	14.9695i	0.493160	+	0.576177i
$676$	22.3541	−	13.2775i	0.859775	−	0.510673i
$677$	20.2093	+	11.6678i	0.776705	+	0.448431i	0.835261	−	0.549853i	$-0.185316\pi$
$677$	20.2093	+	11.6678i	0.776705	+	0.448431i	−0.0585564	+	0.998284i	$0.518650\pi$
$678$	−32.0442	−	19.2258i	−1.23065	−	0.738363i
$679$	29.6847			1.13920
$680$	13.8928	+	3.32238i	0.532766	+	0.127408i
$681$	4.38449	+	0.497978i	0.168014	+	0.0190826i
$682$	5.30792	+	2.41707i	0.203251	+	0.0925544i
$683$	31.0730	−	17.9400i	1.18897	−	0.686455i	0.230901	−	0.972977i	$-0.425833\pi$
$683$	31.0730	−	17.9400i	1.18897	−	0.686455i	0.958074	+	0.286522i	$0.0924993\pi$
$684$	−16.1375	+	8.60731i	−0.617031	+	0.329109i
$685$	−18.2036	+	10.5099i	−0.695525	+	0.401561i
$686$	−26.4475	+	2.55448i	−1.00977	+	0.0975304i
$687$	−10.9586	−	25.1787i	−0.418096	−	0.960626i
$688$	−6.84858	−	16.8934i	−0.261100	−	0.644056i
$689$	0.379751	+	2.18999i	0.0144674	+	0.0834319i
$690$	−11.2119	−	20.1958i	−0.426828	−	0.768842i
$691$	−15.3629	+	8.86976i	−0.584431	+	0.337421i	−0.762892	−	0.646525i	$-0.776221\pi$
$691$	−15.3629	+	8.86976i	−0.584431	+	0.337421i	0.178461	+	0.983947i	$0.442888\pi$
$692$	6.32129	+	32.4181i	0.240299	+	1.23235i
$693$	5.89504	−	1.80686i	0.223934	−	0.0686368i
$694$	42.3813	+	19.2992i	1.60877	+	0.732587i
$695$	−10.7157			−0.406469
$696$	−26.3705	−	31.3482i	−0.999570	−	1.18825i
$697$	14.4286	+	24.9910i	0.546521	+	0.946603i
$698$	22.6489	−	16.1654i	0.857273	−	0.611868i
$699$	2.59729	−	22.8681i	0.0982386	−	0.864949i
$700$	6.42271	−	18.6887i	0.242756	−	0.706367i
$701$		−	17.3881i		−	0.656739i	−0.944549	−	0.328370i	$-0.893501\pi$
$701$		−	17.3881i		−	0.656739i	0.944549	−	0.328370i	$-0.106499\pi$
$702$	1.88735	−	26.4280i	0.0712336	−	0.997460i
$703$	−4.46487			−0.168396
$704$	2.85478	−	5.62741i	0.107594	−	0.212091i
$705$	20.0431	+	2.27644i	0.754868	+	0.0857358i
$706$	10.5401	+	14.7674i	0.396681	+	0.555780i
$707$	−29.8634	+	17.2417i	−1.12313	+	0.648440i
$708$	−14.7613	+	31.0230i	−0.554764	+	1.16592i
$709$			12.1944i			0.457970i	0.973430	+	0.228985i	$0.0735406\pi$
$709$			12.1944i			0.457970i	−0.973430	+	0.228985i	$0.926459\pi$
$710$	21.6999	+	9.88149i	0.814383	+	0.370846i
$711$	−30.6026	+	32.8638i	−1.14769	+	1.23249i
$712$	−7.58562	+	31.7199i	−0.284283	+	1.18875i
$713$	−22.4311	−	38.8518i	−0.840052	−	1.45501i
$714$	25.6421	−	14.2354i	0.959632	−	0.532747i
$715$	−1.07737	+	2.93412i	−0.0402913	+	0.109730i
$716$	32.2372	+	11.0789i	1.20476	+	0.414038i
$717$	−6.95856	+	3.02859i	−0.259872	+	0.113105i
$718$	3.57257	−	0.345063i	0.133327	−	0.0128776i
$719$	−1.17357	−	2.03268i	−0.0437667	−	0.0758062i	0.843312	−	0.537424i	$-0.180602\pi$
$719$	−1.17357	−	2.03268i	−0.0437667	−	0.0758062i	−0.887079	+	0.461618i	$0.847269\pi$
$720$	−10.2339	+	8.31930i	−0.381396	+	0.310042i
$721$	−13.8631	−	24.0115i	−0.516288	−	0.894237i
$722$	5.68986	−	12.4950i	0.211755	−	0.465016i
$723$	−0.246764	+	2.17265i	−0.00917725	+	0.0808018i
$724$	−1.35761	−	6.96236i	−0.0504550	−	0.258754i
$725$			31.7088i			1.17763i
$726$	21.7981	+	13.0784i	0.809002	+	0.485383i
$727$	−12.2627	+	21.2395i	−0.454797	+	0.787731i	−0.998676	−	0.0514321i	$-0.983621\pi$
$727$	−12.2627	+	21.2395i	−0.454797	+	0.787731i	0.543880	+	0.839163i	$0.316955\pi$
$728$	−23.8038	+	11.8102i	−0.882227	+	0.437714i
$729$	−21.0190	−	16.9471i	−0.778480	−	0.627669i
$730$	4.04578	−	2.88763i	0.149741	−	0.106876i
$731$	−18.1355	+	10.4705i	−0.670765	+	0.387266i
$732$	3.80423	−	0.303011i	0.140608	−	0.0111996i
$733$	−10.9501	+	6.32202i	−0.404450	+	0.233509i	−0.688402	−	0.725329i	$-0.741688\pi$
$733$	−10.9501	+	6.32202i	−0.404450	+	0.233509i	0.283953	+	0.958838i	$0.408354\pi$
$734$	26.3421	+	36.9072i	0.972304	+	1.36227i
$735$	−0.159972	−	0.367555i	−0.00590066	−	0.0135575i
$736$	−43.0199	+	22.4754i	−1.58573	+	0.828455i
$737$	5.19552	+	8.99891i	0.191379	+	0.331479i
$738$	−26.4190	−	3.45119i	−0.972497	−	0.127040i
$739$	7.63333	+	4.40710i	0.280797	+	0.162118i	0.633784	−	0.773510i	$-0.281501\pi$
$739$	7.63333	+	4.40710i	0.280797	+	0.162118i	−0.352987	+	0.935628i	$0.614834\pi$
$740$	−3.16017	+	0.616208i	−0.116170	+	0.0226523i
$741$	−10.4674	−	15.9001i	−0.384528	−	0.584105i
$742$	−0.218391	−	2.26109i	−0.00801740	−	0.0830074i
$743$	2.15367			0.0790104			0.0395052	−	0.999219i	$-0.487422\pi$
$743$	2.15367			0.0790104			0.0395052	+	0.999219i	$0.487422\pi$
$744$	−19.6015	+	16.4890i	−0.718626	+	0.604516i
$745$	−0.369495			−0.0135372
$746$	−10.6338	−	4.84230i	−0.389330	−	0.177289i
$747$	−4.36789	−	4.06735i	−0.159813	−	0.148817i
$748$	−6.85542	−	2.35599i	−0.250659	−	0.0861435i
$749$	−6.30371	−	3.63945i	−0.230333	−	0.132983i
$750$	23.6662	+	0.397740i	0.864167	+	0.0145234i
$751$	22.5086			0.821351			0.410676	−	0.911782i	$-0.365293\pi$
$751$	22.5086			0.821351			0.410676	+	0.911782i	$0.365293\pi$
$752$	5.84951	−	41.9806i	0.213310	−	1.53088i
$753$	−9.25465	−	21.2637i	−0.337258	−	0.774891i
$754$	29.9622	−	30.3351i	1.09116	−	1.10474i
$755$		−	9.40287i		−	0.342206i
$756$	−3.95827	+	26.7879i	−0.143961	+	0.974265i
$757$	1.95836	+	1.13066i	0.0711777	+	0.0410945i	0.535166	−	0.844747i	$-0.320249\pi$
$757$	1.95836	+	1.13066i	0.0711777	+	0.0410945i	−0.463989	+	0.885841i	$0.653582\pi$
$758$	−3.21318	−	1.46319i	−0.116708	−	0.0531453i
$759$	4.67800	+	10.7483i	0.169801	+	0.390137i
$760$	−2.20394	+	9.21597i	−0.0799453	+	0.334298i
$761$	10.5918	−	18.3456i	0.383954	−	0.665028i	−0.607669	−	0.794190i	$-0.707895\pi$
$761$	10.5918	−	18.3456i	0.383954	−	0.665028i	0.991623	+	0.129162i	$0.0412288\pi$
$762$	3.64933	+	2.18952i	0.132201	+	0.0793179i
$763$			42.3614i			1.53359i
$764$	−4.79670	+	0.935320i	−0.173539	+	0.0338387i
$765$	11.0881	+	10.3252i	0.400891	+	0.373307i
$766$	−4.68343	+	10.2849i	−0.169219	+	0.371608i
$767$	−33.5674	−	12.3255i	−1.21205	−	0.445047i
$768$	16.9301	+	21.9402i	0.610911	+	0.791699i
$769$	−29.4608			−1.06238			−0.531191	−	0.847252i	$-0.678256\pi$
$769$	−29.4608			−1.06238			−0.531191	+	0.847252i	$0.678256\pi$
$770$	1.32388	−	2.90726i	0.0477093	−	0.104770i
$771$	−3.21140	+	28.2750i	−0.115656	+	1.01830i
$772$	1.06468	−	0.207604i	0.0383187	−	0.00747185i
$773$	9.18611	−	5.30360i	0.330401	−	0.190757i	−0.325618	−	0.945501i	$-0.605572\pi$
$773$	9.18611	−	5.30360i	0.330401	−	0.190757i	0.656019	+	0.754744i	$0.272239\pi$
$774$	2.50446	−	19.1717i	0.0900209	−	0.689113i
$775$	19.8270			0.712205
$776$	30.8876	−	9.17906i	1.10880	−	0.329509i
$777$	−3.93022	+	5.31531i	−0.140996	+	0.190686i
$778$	−21.2834	−	9.69183i	−0.763047	−	0.347469i
$779$	−16.5781	+	9.57136i	−0.593971	+	0.342929i
$780$	−9.60305	−	9.80922i	−0.343844	−	0.351226i
$781$	−10.4789	−	6.04999i	−0.374964	−	0.216486i
$782$	32.3927	+	45.3845i	1.15836	+	1.62295i
$783$	−7.96341	−	42.7137i	−0.284589	−	1.52646i
$784$	−0.780595	+	0.316452i	−0.0278784	+	0.0113019i
$785$	0.513209	−	0.888903i	0.0183172	−	0.0317263i
$786$	18.8616	+	33.9753i	0.672772	+	1.21186i
$787$	33.6703	+	19.4396i	1.20022	+	0.692946i	0.960604	−	0.277922i	$-0.0896458\pi$
$787$	33.6703	+	19.4396i	1.20022	+	0.692946i	0.239614	+	0.970868i	$0.422979\pi$
$788$	−27.3849	−	9.41132i	−0.975547	−	0.335264i
$789$	17.8493	−	7.76859i	0.635451	−	0.276569i
$790$	2.23677	+	23.1582i	0.0795808	+	0.823932i
$791$	−19.8758	+	34.4260i	−0.706703	+	1.22405i
$792$	5.57521	−	3.70293i	0.198107	−	0.131578i
$793$	0.678649	+	3.91370i	0.0240995	+	0.138980i
$794$	15.7780	−	11.2613i	0.559939	−	0.399650i
$795$	1.07602	−	0.468318i	0.0381623	−	0.0166095i
$796$	27.1027	+	31.1410i	0.960629	+	1.10376i
$797$	12.9218	+	7.46043i	0.457715	+	0.264262i	0.711083	−	0.703108i	$-0.248205\pi$
$797$	12.9218	+	7.46043i	0.457715	+	0.264262i	−0.253368	+	0.967370i	$0.581538\pi$
$798$	9.44322	+	17.0100i	0.334286	+	0.602147i
$799$	−48.6927			−1.72262
$800$	0.904090	−	21.4320i	0.0319644	−	0.757737i
$801$	−23.5743	+	25.3162i	−0.832956	+	0.894504i
$802$	1.38653	−	0.133920i	0.0489599	−	0.00472887i
$803$	−2.18447	+	1.26121i	−0.0770883	+	0.0445070i
$804$	−45.4914	+	3.62344i	−1.60436	+	0.127789i
$805$	−21.2799	+	12.2860i	−0.750019	+	0.433024i
$806$	−18.9680	−	18.7349i	−0.668121	−	0.659907i
$807$	−5.57905	−	12.8185i	−0.196392	−	0.451234i
$808$	−25.7422	+	27.1747i	−0.905606	+	0.956001i
$809$	2.40609	−	4.16747i	0.0845936	−	0.146520i	−0.820624	−	0.571468i	$-0.806374\pi$
$809$	2.40609	−	4.16747i	0.0845936	−	0.146520i	0.905218	+	0.424948i	$0.139707\pi$
$810$	−13.7930	+	2.33241i	−0.484637	+	0.0819525i
$811$			13.3466i			0.468663i	0.972157	+	0.234332i	$0.0752901\pi$
$811$			13.3466i			0.468663i	−0.972157	+	0.234332i	$0.924710\pi$
$812$	−32.8707	+	28.6081i	−1.15353	+	1.00395i
$813$	0.0448674	+	0.0331756i	0.00157357	+	0.00116352i
$814$	1.62632	−	0.157080i	0.0570024	−	0.00550567i
$815$	1.54749	−	2.68033i	0.0542062	−	0.0938879i
$816$	22.2794	−	22.7413i	0.779934	−	0.796104i
$817$	−6.94574	−	12.0304i	−0.243001	−	0.420889i
$818$	−11.3638	+	24.9551i	−0.397327	+	0.872536i
$819$	−28.1426	−	1.53499i	−0.983382	−	0.0536369i
$820$	−10.4127	+	9.06245i	−0.363629	+	0.316474i
$821$	22.8765	−	13.2078i	0.798396	−	0.460954i	−0.0445142	−	0.999009i	$-0.514174\pi$
$821$	22.8765	−	13.2078i	0.798396	−	0.460954i	0.842910	+	0.538055i	$0.180841\pi$
$822$	−0.787208	+	46.8401i	−0.0274570	+	1.63374i
$823$	15.9764	−	27.6720i	0.556904	−	0.964586i	−0.440849	−	0.897581i	$-0.645322\pi$
$823$	15.9764	−	27.6720i	0.556904	−	0.964586i	0.997753	−	0.0670045i	$-0.0213442\pi$
$824$	−21.8496	−	20.6978i	−0.761168	−	0.721043i
$825$	−5.14753	−	0.584643i	−0.179214	−	0.0203546i
$826$	33.2600	+	15.1456i	1.15726	+	0.526984i
$827$			15.6038i			0.542596i	0.962495	+	0.271298i	$0.0874529\pi$
$827$			15.6038i			0.542596i	−0.962495	+	0.271298i	$0.912547\pi$
$828$	−51.4524	−	1.72993i	−1.78809	−	0.0601193i
$829$	−32.0602	−	18.5100i	−1.11350	−	0.642878i	−0.173764	−	0.984787i	$-0.555593\pi$
$829$	−32.0602	−	18.5100i	−1.11350	−	0.642878i	−0.939733	+	0.341909i	$0.888926\pi$
$830$	−3.07793	+	0.297287i	−0.106837	+	0.0103190i
$831$	9.83657	+	1.11721i	0.341227	+	0.0387556i
$832$	−21.1165	+	19.6493i	−0.732082	+	0.681217i
$833$	0.483811	+	0.837986i	0.0167631	+	0.0290345i
$834$	−12.2869	+	20.4789i	−0.425460	+	0.709126i
$835$	−4.18242	+	2.41472i	−0.144739	+	0.0835649i
$836$	1.56287	−	4.54762i	0.0540531	−	0.157283i
$837$	−26.7081	+	4.97939i	−0.923168	+	0.172113i
$838$	−1.10783	−	11.4698i	−0.0382693	−	0.396217i
$839$	7.33950			0.253388			0.126694	−	0.991942i	$-0.459563\pi$
$839$	7.33950			0.253388			0.126694	+	0.991942i	$0.459563\pi$
$840$	9.03136	+	10.7361i	0.311612	+	0.370432i
$841$	20.4606	−	35.4389i	0.705540	−	1.22203i
$842$	−26.6995	−	12.1582i	−0.920126	−	0.418998i
$843$	29.7337	+	21.9855i	1.02408	+	0.757221i
$844$	−5.12179	−	26.2666i	−0.176299	−	0.904134i
$845$	9.24601	−	10.8928i	0.318072	−	0.374725i
$846$	27.3325	−	35.6945i	0.939712	−	1.22720i
$847$	13.5205	−	23.4183i	0.464571	−	0.804661i
$848$	−0.926412	−	2.28519i	−0.0318131	−	0.0784737i
$849$	36.4327	+	4.13793i	1.25037	+	0.142013i
$850$	−24.5286	+	2.36913i	−0.841323	+	0.0812605i
$851$	−10.8840	−	6.28389i	−0.373100	−	0.215409i
$852$	43.7664	−	30.1406i	1.49941	−	1.03260i
$853$	6.92791	+	3.99983i	0.237207	+	0.136952i	0.613892	−	0.789390i	$-0.289603\pi$
$853$	6.92791	+	3.99983i	0.237207	+	0.136952i	−0.376685	+	0.926341i	$0.622936\pi$
$854$	−0.390284	−	4.04077i	−0.0133553	−	0.138272i
$855$	−6.84932	+	7.35542i	−0.234242	+	0.251550i
$856$	−7.68454	−	1.83771i	−0.262652	−	0.0628115i
$857$	27.0704	−	46.8874i	0.924709	−	1.60164i	0.132680	−	0.991159i	$-0.457642\pi$
$857$	27.0704	−	46.8874i	0.924709	−	1.60164i	0.792029	−	0.610484i	$-0.209025\pi$
$858$	4.37210	+	5.42332i	0.149261	+	0.185149i
$859$	−45.2361	+	26.1171i	−1.54344	+	0.891103i	−0.544818	+	0.838554i	$0.683401\pi$
$859$	−45.2361	+	26.1171i	−1.54344	+	0.891103i	−0.998618	+	0.0525490i	$0.983265\pi$
$860$	−6.57643	−	7.55631i	−0.224254	−	0.257668i
$861$	−3.19845	+	28.1610i	−0.109003	+	0.959725i
$862$	13.7062	−	30.0990i	0.466834	−	1.02517i
$863$	−7.34392			−0.249990			−0.124995	−	0.992157i	$-0.539891\pi$
$863$	−7.34392			−0.249990			−0.124995	+	0.992157i	$0.539891\pi$
$864$	4.16463	+	29.0974i	0.141683	+	0.989912i
$865$	9.07517	+	15.7187i	0.308565	+	0.534450i
$866$	9.41759	+	13.1947i	0.320023	+	0.448376i
$867$	−5.73135	−	4.23784i	−0.194647	−	0.143925i
$868$	17.8881	+	20.5535i	0.607163	+	0.697630i
$869$		−	11.8067i		−	0.400516i
$870$	−19.3036	−	11.5817i	−0.654454	−	0.392658i
$871$	−8.11536	−	46.8005i	−0.274979	−	1.58577i
$872$	13.0989	+	44.0780i	0.443585	+	1.49267i
$873$	33.3068	+	7.66466i	1.12726	+	0.259409i
$874$	−30.1064	+	21.4880i	−1.01836	+	0.726844i
$875$		−	25.1785i		−	0.851190i
$876$	−0.879585	−	11.0430i	−0.0297184	−	0.373108i
$877$	17.9748	+	10.3778i	0.606966	+	0.350432i	0.771777	−	0.635893i	$-0.219368\pi$
$877$	17.9748	+	10.3778i	0.606966	+	0.350432i	−0.164811	+	0.986325i	$0.552701\pi$
$878$	−21.3210	−	29.8723i	−0.719548	−	1.00814i
$879$	19.9863	−	27.0299i	0.674121	−	0.911697i
$880$	0.478548	−	3.43443i	0.0161319	−	0.115775i
$881$	−15.6869	+	27.1706i	−0.528506	+	0.915400i	0.470941	+	0.882165i	$0.343914\pi$
$881$	−15.6869	+	27.1706i	−0.528506	+	0.915400i	−0.999448	+	0.0332353i	$0.989419\pi$
$882$	−0.885868	−	0.115723i	−0.0298287	−	0.00389661i
$883$		−	22.3215i		−	0.751180i	−0.926786	−	0.375590i	$-0.877440\pi$
$883$		−	22.3215i		−	0.751180i	0.926786	−	0.375590i	$-0.122560\pi$
$884$	25.7046	+	20.9110i	0.864540	+	0.703313i
$885$	−2.13060	+	18.7591i	−0.0716194	+	0.630579i
$886$	−17.6455	−	8.03524i	−0.592813	−	0.269949i
$887$	21.9309			0.736366			0.368183	−	0.929753i	$-0.379980\pi$
$887$	21.9309			0.736366			0.368183	+	0.929753i	$0.379980\pi$
$888$	−2.44589	+	6.74600i	−0.0820786	+	0.226381i
$889$	2.26355	−	3.92058i	0.0759169	−	0.131492i
$890$	1.72307	+	17.8396i	0.0577574	+	0.597986i
$891$	7.08088	−	0.505213i	0.237218	−	0.0169253i
$892$	−17.3945	−	19.9863i	−0.582412	−	0.669192i
$893$		−	32.3008i		−	1.08091i
$894$	−0.423673	+	0.706147i	−0.0141697	+	0.0236171i
$895$	18.7324			0.626154
$896$	23.0330	−	18.3991i	0.769480	−	0.614669i
$897$	−3.13838	−	53.4916i	−0.104787	−	1.78603i
$898$	−14.9931	−	21.0065i	−0.500326	−	0.700995i
$899$	−37.8631	−	21.8603i	−1.26281	−	0.729082i
$900$	12.0319	−	19.3107i	0.401062	−	0.643690i
$901$	−2.45320	+	1.41636i	−0.0817279	+	0.0471856i
$902$	5.70179	−	4.06958i	0.189849	−	0.135502i
$903$	−20.4359	−	2.32105i	−0.680063	−	0.0772397i
$904$	−10.0361	+	41.9670i	−0.333797	+	1.39580i
$905$	−1.94905	−	3.37585i	−0.0647886	−	0.112217i
$906$	−17.9700	−	10.7816i	−0.597012	−	0.358194i
$907$	42.7795	−	24.6988i	1.42047	−	0.820109i	0.424132	−	0.905601i	$-0.360579\pi$
$907$	42.7795	−	24.6988i	1.42047	−	0.820109i	0.996339	+	0.0854916i	$0.0272461\pi$
$908$	−0.975182	−	5.00113i	−0.0323625	−	0.165968i
$909$	−37.9591	+	11.6346i	−1.25902	+	0.385897i
$910$	−10.2615	+	10.3892i	−0.340164	+	0.344398i
$911$	20.4751	−	35.4639i	0.678370	−	1.17497i	−0.297101	−	0.954846i	$-0.596020\pi$
$911$	20.4751	−	35.4639i	0.678370	−	1.17497i	0.975472	−	0.220126i	$-0.0706467\pi$
$912$	15.0857	+	14.7793i	0.499537	+	0.489390i
$913$	1.56922			0.0519336
$914$	−30.5292	−	42.7737i	−1.00982	−	1.41483i
$915$	1.92293	−	0.836924i	0.0635702	−	0.0276679i
$916$	−23.9182	+	20.8165i	−0.790279	+	0.687798i
$917$	35.7991	−	20.6686i	1.18219	−	0.682537i
$918$	32.4465	−	9.35153i	1.07089	−	0.308646i
$919$	4.33945	+	7.51614i	0.143145	+	0.247935i	0.928679	−	0.370883i	$-0.120945\pi$
$919$	4.33945	+	7.51614i	0.143145	+	0.247935i	−0.785534	+	0.618818i	$0.787612\pi$
$920$	−18.3432	+	19.3640i	−0.604757	+	0.638411i
$921$	−33.8449	−	3.84401i	−1.11523	−	0.126664i
$922$	3.61776	+	37.4561i	0.119144	+	1.23355i
$923$	35.4327	+	42.4712i	1.16628	+	1.39796i
$924$	−4.03811	−	5.86362i	−0.132844	−	0.192899i
$925$	4.81022	−	2.77718i	0.158159	−	0.0913131i
$926$	−21.9748	−	30.7883i	−0.722137	−	1.01177i
$927$	−9.35478	−	30.5208i	−0.307251	−	1.00244i
$928$	−25.3565	+	39.9315i	−0.832369	+	1.31082i
$929$	−40.0287			−1.31330			−0.656650	−	0.754196i	$-0.728027\pi$
$929$	−40.0287			−1.31330			−0.656650	+	0.754196i	$0.728027\pi$
$930$	−7.24187	+	12.0702i	−0.237470	+	0.395798i
$931$	−0.555887	+	0.320942i	−0.0182185	+	0.0105184i
$932$	−26.0843	+	5.08623i	−0.854419	+	0.166605i
$933$	9.23302	−	4.01852i	0.302276	−	0.131560i
$934$	−0.0931715	−	0.964641i	−0.00304866	−	0.0315640i
$935$	−3.98354			−0.130276
$936$	−29.7577	+	7.10502i	−0.972660	+	0.232235i
$937$	−32.2151			−1.05242			−0.526211	−	0.850354i	$-0.676388\pi$
$937$	−32.2151			−1.05242			−0.526211	+	0.850354i	$0.676388\pi$
$938$	4.66707	+	48.3200i	0.152385	+	1.57770i
$939$	−30.3178	−	22.4174i	−0.989384	−	0.731564i
$940$	−4.45792	−	22.8620i	−0.145401	−	0.745677i
$941$	−6.40001	+	3.69505i	−0.208634	+	0.120455i	−0.600677	−	0.799492i	$-0.705102\pi$
$941$	−6.40001	+	3.69505i	−0.208634	+	0.120455i	0.392042	+	0.919947i	$0.371769\pi$
$942$	−1.11034	−	2.00004i	−0.0361767	−	0.0651649i
$943$	−53.8833			−1.75468
$944$	39.2911	+	5.47476i	1.27882	+	0.178188i
$945$	2.72731	+	14.6286i	0.0887194	+	0.475868i
$946$	2.95321	+	4.13767i	0.0960173	+	0.134527i
$947$	−33.6553	+	19.4309i	−1.09365	+	0.631420i	−0.934546	−	0.355842i	$-0.884194\pi$
$947$	−33.6553	+	19.4309i	−1.09365	+	0.631420i	−0.159105	+	0.987262i	$0.550861\pi$
$948$	46.8228	+	22.2791i	1.52073	+	0.723592i
$949$	11.3608	−	1.96999i	0.368786	−	0.0639487i
$950$	−1.57159	−	16.2713i	−0.0509891	−	0.527911i
$951$	−3.01979	+	4.08404i	−0.0979235	+	0.132434i
$952$	−24.5859	−	23.2899i	−0.796835	−	0.754830i
$953$	3.74946	+	6.49426i	0.121457	+	0.210370i	0.920342	−	0.391114i	$-0.127910\pi$
$953$	3.74946	+	6.49426i	0.121457	+	0.210370i	−0.798885	+	0.601483i	$0.794577\pi$
$954$	0.338780	−	2.59337i	0.0109684	−	0.0839636i
$955$	−2.32579	+	1.34279i	−0.0752607	+	0.0434518i
$956$	5.75301	+	6.61020i	0.186066	+	0.213789i
$957$	9.18554	+	6.79192i	0.296926	+	0.219551i
$958$	−4.83332	−	6.77184i	−0.156157	−	0.218788i
$959$	49.8334			1.60920
$960$	12.7171	+	8.37853i	0.410444	+	0.270416i
$961$	1.83113	−	3.17161i	0.0590687	−	0.102310i
$962$	−7.22605	−	1.88839i	−0.232977	−	0.0608842i
$963$	−6.13316	−	5.71116i	−0.197638	−	0.184039i
$964$	2.47822	−	0.483233i	0.0798180	−	0.0155639i
$965$	0.516234	−	0.298048i	0.0166182	−	0.00959450i
$966$	−0.920241	+	54.7558i	−0.0296083	+	1.76174i
$967$	−5.44937	−	9.43859i	−0.175240	−	0.303525i	0.765004	−	0.644025i	$-0.222737\pi$
$967$	−5.44937	−	9.43859i	−0.175240	−	0.303525i	−0.940244	+	0.340501i	$0.889403\pi$
$968$	6.82707	−	28.5480i	0.219430	−	0.917568i
$969$	14.4241	−	19.5075i	0.463369	−	0.626670i
$970$	14.4128	−	10.2870i	0.462769	−	0.330296i
$971$	16.5511	−	9.55578i	0.531150	−	0.306659i	−0.210335	−	0.977629i	$-0.567455\pi$
$971$	16.5511	−	9.55578i	0.531150	−	0.306659i	0.741485	+	0.670970i	$0.234122\pi$
$972$	−11.3579	+	29.0344i	−0.364306	+	0.931279i
$973$	22.0010	+	12.7023i	0.705321	+	0.407217i
$974$	−7.06950	−	9.90489i	−0.226521	−	0.317373i
$975$	21.1670	+	10.6192i	0.677886	+	0.340086i
$976$	−1.65558	−	4.08383i	−0.0529938	−	0.130720i
$977$	−9.42093			−0.301402			−0.150701	−	0.988579i	$-0.548153\pi$
$977$	−9.42093			−0.301402			−0.150701	+	0.988579i	$0.548153\pi$
$978$	−3.34803	−	6.03077i	−0.107058	−	0.192843i
$979$		−	9.09517i		−	0.290683i
$980$	−0.349155	+	0.303877i	−0.0111533	+	0.00970700i
$981$	−10.9378	+	47.5302i	−0.349217	+	1.51752i
$982$	−3.51253	−	36.3666i	−0.112089	−	1.16050i
$983$	−3.08894	+	5.35021i	−0.0985220	+	0.170645i	−0.911073	−	0.412245i	$-0.864745\pi$
$983$	−3.08894	+	5.35021i	−0.0985220	+	0.170645i	0.812551	+	0.582890i	$0.198078\pi$
$984$	5.37984	+	30.2912i	0.171503	+	0.965648i
$985$	−15.9128			−0.507024
$986$	49.4538	+	22.5198i	1.57493	+	0.717176i
$987$	−38.4533	−	28.4329i	−1.22398	−	0.905030i
$988$	−13.8715	+	17.0514i	−0.441313	+	0.542479i
$989$		−	39.1020i		−	1.24337i
$990$	2.23607	−	2.92016i	0.0710671	−	0.0928089i
$991$	−25.9079	+	44.8738i	−0.822992	+	1.42546i	0.0804529	+	0.996758i	$0.474363\pi$
$991$	−25.9079	+	44.8738i	−0.822992	+	1.42546i	−0.903445	+	0.428705i	$0.858970\pi$
$992$	24.9685	+	15.8550i	0.792751	+	0.503397i
$993$	32.0373	+	3.63871i	1.01667	+	0.115471i
$994$	−32.8400	−	46.0113i	−1.04162	−	1.45939i
$995$	19.6471	+	11.3433i	0.622856	+	0.359606i
$996$	−2.96109	+	6.22316i	−0.0938258	+	0.197188i
$997$		−	30.9424i		−	0.979956i	−0.871735	−	0.489978i	$-0.837005\pi$
$997$		−	30.9424i		−	0.979956i	0.871735	−	0.489978i	$-0.162995\pi$
$998$	−27.5736	+	19.6803i	−0.872826	+	0.622969i
$999$	−5.78220	+	4.94908i	−0.182941	+	0.156582i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	936.2.db.a.61.4	yes	328
8.5	even	2	inner	936.2.db.a.61.114	yes	328
9.4	even	3		936.2.cj.a.373.107	yes	328
13.3	even	3		936.2.cj.a.133.107	✓	328
72.13	even	6		936.2.cj.a.373.108	yes	328
104.29	even	6		936.2.cj.a.133.108	yes	328
117.94	even	3	inner	936.2.db.a.445.114	yes	328
936.445	even	6	inner	936.2.db.a.445.4	yes	328

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
936.2.cj.a.133.107	✓	328	13.3	even	3
936.2.cj.a.133.108	yes	328	104.29	even	6
936.2.cj.a.373.107	yes	328	9.4	even	3
936.2.cj.a.373.108	yes	328	72.13	even	6
936.2.db.a.61.4	yes	328	1.1	even	1	trivial
936.2.db.a.61.114	yes	328	8.5	even	2	inner
936.2.db.a.445.4	yes	328	936.445	even	6	inner
936.2.db.a.445.114	yes	328	117.94	even	3	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:	\( N \)	\(=\)	\( 936 = 2^{3} \cdot 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	936.db (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.40766 + 0.135961i) q^{2} +(-0.195465 + 1.72099i) q^{3} +(1.96303 - 0.382776i) q^{4} +(0.951819 - 0.549533i) q^{5} +(0.0411610 - 2.44914i) q^{6} -2.60565 q^{7} +(-2.71124 + 0.805715i) q^{8} +(-2.92359 - 0.672785i) q^{9} +(-1.26512 + 0.902967i) q^{10} +(0.683090 - 0.394382i) q^{11} +(0.275048 + 3.45316i) q^{12} +(-3.55254 + 0.616022i) q^{13} +(3.66788 - 0.354268i) q^{14} +(0.759691 + 1.74548i) q^{15} +(3.70697 - 1.50280i) q^{16} +(-2.29757 - 3.97951i) q^{17} +(4.20690 + 0.549559i) q^{18} +(2.63985 - 1.52412i) q^{19} +(1.65810 - 1.44308i) q^{20} +(0.509314 - 4.48429i) q^{21} +(-0.907939 + 0.648031i) q^{22} +8.58024 q^{23} +(-0.856672 - 4.82350i) q^{24} +(-1.89603 + 3.28402i) q^{25} +(4.91702 - 1.35016i) q^{26} +(1.72931 - 4.89995i) q^{27} +(-5.11497 + 0.997380i) q^{28} +(7.24161 - 4.18095i) q^{29} +(-1.30671 - 2.35376i) q^{30} +(-2.61428 - 4.52806i) q^{31} +(-5.01383 + 2.61944i) q^{32} +(0.545206 + 1.25268i) q^{33} +(3.77526 + 5.28943i) q^{34} +(-2.48011 + 1.43189i) q^{35} +(-5.99661 - 0.201618i) q^{36} +(-1.26850 - 0.732368i) q^{37} +(-3.50880 + 2.50436i) q^{38} +(-0.365768 - 6.23428i) q^{39} +(-2.13784 + 2.25681i) q^{40} -6.27993 q^{41} +(-0.107251 + 6.38162i) q^{42} -4.55721i q^{43} +(1.18996 - 1.03565i) q^{44} +(-3.15244 + 0.966238i) q^{45} +(-12.0781 + 1.16658i) q^{46} +(5.29828 - 9.17688i) q^{47} +(1.86172 + 6.67338i) q^{48} -0.210575 q^{49} +(2.22247 - 4.88057i) q^{50} +(7.29777 - 3.17623i) q^{51} +(-6.73793 + 2.56909i) q^{52} -0.616458i q^{53} +(-1.76808 + 7.13259i) q^{54} +(0.433452 - 0.750760i) q^{55} +(7.06455 - 2.09941i) q^{56} +(2.10699 + 4.84106i) q^{57} +(-9.62530 + 6.86994i) q^{58} +(8.58896 + 4.95884i) q^{59} +(2.15942 + 3.13564i) q^{60} -1.10166i q^{61} +(4.29566 + 6.01854i) q^{62} +(7.61785 + 1.75304i) q^{63} +(6.70165 - 4.36897i) q^{64} +(-3.04285 + 2.53858i) q^{65} +(-0.937782 - 1.68922i) q^{66} +13.1738i q^{67} +(-6.03346 - 6.93244i) q^{68} +(-1.67714 + 14.7665i) q^{69} +(3.29647 - 2.35282i) q^{70} +(-7.67022 - 13.2852i) q^{71} +(8.46862 - 0.531497i) q^{72} -3.19793 q^{73} +(1.88519 + 0.858461i) q^{74} +(-5.28114 - 3.90495i) q^{75} +(4.59871 - 4.00236i) q^{76} +(-1.77989 + 1.02762i) q^{77} +(1.36250 + 8.72603i) q^{78} +(7.48433 - 12.9632i) q^{79} +(2.70252 - 3.46749i) q^{80} +(8.09472 + 3.93389i) q^{81} +(8.84002 - 0.853828i) q^{82} +(1.72293 + 0.994734i) q^{83} +(-0.716680 - 8.99775i) q^{84} +(-4.37374 - 2.52518i) q^{85} +(0.619605 + 6.41502i) q^{86} +(5.77987 + 13.2799i) q^{87} +(-1.53426 + 1.61964i) q^{88} +(5.76546 - 9.98606i) q^{89} +(4.30620 - 1.78875i) q^{90} +(9.25668 - 1.60514i) q^{91} +(16.8433 - 3.28431i) q^{92} +(8.30372 - 3.61406i) q^{93} +(-6.21048 + 13.6383i) q^{94} +(1.67511 - 2.90137i) q^{95} +(-3.52799 - 9.14075i) q^{96} -11.3924 q^{97} +(0.296419 - 0.0286301i) q^{98} +(-2.26241 + 0.693438i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 328 q + q^{2} + q^{4} + q^{6} - 4 q^{7} - 2 q^{8} - 2 q^{9} - 4 q^{10} + 5 q^{12} - 6 q^{14} + 4 q^{15} + q^{16} - 4 q^{17} - 12 q^{18} - 18 q^{20} - 7 q^{22} + 44 q^{23} - 6 q^{24} + 144 q^{25} - 16 q^{26}+ \cdots + 39 q^{98}+O(q^{100}) \) 328 * q + q^2 + q^4 + q^6 - 4 * q^7 - 2 * q^8 - 2 * q^9 - 4 * q^10 + 5 * q^12 - 6 * q^14 + 4 * q^15 + q^16 - 4 * q^17 - 12 * q^18 - 18 * q^20 - 7 * q^22 + 44 * q^23 - 6 * q^24 + 144 * q^25 - 16 * q^26 - 10 * q^28 - 5 * q^30 - 4 * q^31 + q^32 - 14 * q^33 - 13 * q^36 + 6 * q^38 + 20 * q^39 + 8 * q^40 - 4 * q^41 - 46 * q^42 - 32 * q^44 - 6 * q^46 - 4 * q^47 - 46 * q^48 + 276 * q^49 + 68 * q^50 + 40 * q^54 - 14 * q^55 - 56 * q^56 - 20 * q^57 - 25 * q^58 - 41 * q^60 + 3 * q^62 - 58 * q^63 - 26 * q^64 - 22 * q^65 - 6 * q^66 - 64 * q^68 - 17 * q^70 - 4 * q^71 - 7 * q^72 - 16 * q^73 - 38 * q^74 - 18 * q^76 - q^78 - 4 * q^79 - 42 * q^80 - 2 * q^81 + 3 * q^82 + 6 * q^84 + 36 * q^86 - 2 * q^87 + 5 * q^88 - 4 * q^89 + 33 * q^90 + 28 * q^92 - 6 * q^94 + 56 * q^95 - 113 * q^96 - 4 * q^97 + 39 * q^98

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