LMFDB - Embedded newform 357.2.bj.a.26.10

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [357,2,Mod(26,357)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(357, base_ring=CyclotomicField(24)) chi = DirichletCharacter(H, H._module([12, 20, 3])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("357.26"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 357 = 3 \cdot 7 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	357.bj (of order $24$, degree $8$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$2.85065935216$
Analytic rank:	$0$
Dimension:	$352$
Relative dimension:	$44$ over $\Q(\zeta_{24})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{24}]$

Embedding invariants

Embedding label			26.10
Character	$\chi$	$=$	357.26
Dual form			357.2.bj.a.206.10

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.61484 + 0.432695i) q^{2} +(1.70456 - 0.307393i) q^{3} +(0.688428 - 0.397464i) q^{4} +(-1.64076 - 2.13829i) q^{5} +(-2.61957 + 1.23394i) q^{6} +(-2.63988 - 0.176109i) q^{7} +(1.42457 - 1.42457i) q^{8} +(2.81102 - 1.04794i) q^{9} +(3.57479 + 2.74304i) q^{10} +(-3.01128 + 3.92438i) q^{11} +(1.05129 - 0.889118i) q^{12} -4.15052 q^{13} +(4.33919 - 0.857876i) q^{14} +(-3.45407 - 3.14047i) q^{15} +(-2.47897 + 4.29371i) q^{16} +(-2.79152 + 3.03437i) q^{17} +(-4.08591 + 2.90856i) q^{18} +(-2.13274 + 0.571466i) q^{19} +(-1.97944 - 0.819911i) q^{20} +(-4.55396 + 0.511294i) q^{21} +(3.16468 - 7.64020i) q^{22} +(-0.0442863 - 0.00583040i) q^{23} +(1.99035 - 2.86616i) q^{24} +(-0.586062 + 2.18721i) q^{25} +(6.70242 - 1.79591i) q^{26} +(4.46941 - 2.65035i) q^{27} +(-1.88737 + 0.928021i) q^{28} +(4.59170 + 1.90195i) q^{29} +(6.93662 + 3.57679i) q^{30} +(-7.96718 + 1.04890i) q^{31} +(1.10242 - 4.11429i) q^{32} +(-3.92657 + 7.61497i) q^{33} +(3.19490 - 6.10790i) q^{34} +(3.95485 + 5.93378i) q^{35} +(1.51867 - 1.83871i) q^{36} +(3.74525 - 2.87383i) q^{37} +(3.19676 - 1.84565i) q^{38} +(-7.07479 + 1.27584i) q^{39} +(-5.38351 - 0.708753i) q^{40} +(-1.92244 - 4.64118i) q^{41} +(7.13268 - 2.79613i) q^{42} +(-7.46037 - 7.46037i) q^{43} +(-0.513251 + 3.89853i) q^{44} +(-6.85301 - 4.29135i) q^{45} +(0.0740379 - 0.00974728i) q^{46} +(-7.89894 - 4.56046i) q^{47} +(-2.90569 + 8.08088i) q^{48} +(6.93797 + 0.929815i) q^{49} -3.78558i q^{50} +(-3.82556 + 6.03035i) q^{51} +(-2.85733 + 1.64968i) q^{52} +(2.12102 - 7.91574i) q^{53} +(-6.07058 + 6.21378i) q^{54} +13.3322 q^{55} +(-4.01157 + 3.50981i) q^{56} +(-3.45971 + 1.62968i) q^{57} +(-8.23782 - 1.08453i) q^{58} +(-1.66054 + 6.19722i) q^{59} +(-3.62610 - 0.789118i) q^{60} +(-0.922226 + 7.00500i) q^{61} +(12.4119 - 5.14116i) q^{62} +(-7.60531 + 2.27138i) q^{63} -2.79497i q^{64} +(6.81002 + 8.87499i) q^{65} +(3.04582 - 13.9959i) q^{66} +(-0.363981 - 0.630434i) q^{67} +(-0.715708 + 3.19848i) q^{68} +(-0.0772806 + 0.00367504i) q^{69} +(-8.95397 - 7.87085i) q^{70} +(2.68599 - 6.48456i) q^{71} +(2.51163 - 5.49735i) q^{72} +(2.06170 + 15.6602i) q^{73} +(-4.80448 + 6.26133i) q^{74} +(-0.326642 + 3.90838i) q^{75} +(-1.24110 + 1.24110i) q^{76} +(8.64055 - 9.82959i) q^{77} +(10.8726 - 5.12150i) q^{78} +(1.37950 - 10.4784i) q^{79} +(13.2486 - 1.74421i) q^{80} +(6.80366 - 5.89154i) q^{81} +(5.11264 + 6.66293i) q^{82} +(-1.30506 + 1.30506i) q^{83} +(-2.93186 + 2.16203i) q^{84} +(11.0686 + 0.990381i) q^{85} +(15.2754 + 8.81923i) q^{86} +(8.41146 + 1.83052i) q^{87} +(1.30077 + 9.88032i) q^{88} +(-2.24326 - 1.29515i) q^{89} +(12.9233 + 3.96457i) q^{90} +(10.9569 + 0.730944i) q^{91} +(-0.0328053 + 0.0135884i) q^{92} +(-13.2581 + 4.23696i) q^{93} +(14.7288 + 3.94657i) q^{94} +(4.72128 + 3.62277i) q^{95} +(0.614434 - 7.35191i) q^{96} +(1.65844 + 0.686947i) q^{97} +(-11.6060 + 1.50052i) q^{98} +(-4.35227 + 14.1871i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 352 q - 12 q^{3} - 16 q^{7} - 4 q^{9} - 24 q^{10} - 12 q^{12} - 24 q^{15} + 112 q^{16} - 24 q^{18} - 24 q^{19} - 80 q^{22} - 60 q^{24} - 8 q^{25} - 72 q^{28} - 24 q^{31} + 24 q^{33} - 64 q^{36} - 40 q^{37}+ \cdots + 256 q^{99}+O(q^{100}) $ 352 * q - 12 * q^3 - 16 * q^7 - 4 * q^9 - 24 * q^10 - 12 * q^12 - 24 * q^15 + 112 * q^16 - 24 * q^18 - 24 * q^19 - 80 * q^22 - 60 * q^24 - 8 * q^25 - 72 * q^28 - 24 * q^31 + 24 * q^33 - 64 * q^36 - 40 * q^37 - 24 * q^39 - 24 * q^40 + 68 * q^42 - 48 * q^45 - 40 * q^46 + 48 * q^49 - 20 * q^51 - 240 * q^52 - 16 * q^57 - 8 * q^58 + 44 * q^60 - 24 * q^61 + 88 * q^63 - 12 * q^66 - 16 * q^67 + 64 * q^70 - 120 * q^73 - 156 * q^75 - 176 * q^78 - 24 * q^79 + 120 * q^82 - 104 * q^84 + 112 * q^85 + 132 * q^87 - 24 * q^88 - 96 * q^91 - 8 * q^93 - 120 * q^94 + 60 * q^96 + 256 * q^99

Character values

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

$n$	$52$	$190$	$239$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{8}\right)$	$-1$

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 $

$2$	−1.61484	+	0.432695i	−1.14186	+	0.305961i	−0.779700	−	0.626153i	$-0.784628\pi$
$2$	−1.61484	+	0.432695i	−1.14186	+	0.305961i	−0.362163	+	0.932115i	$0.617962\pi$
$3$	1.70456	−	0.307393i	0.984126	−	0.177473i
$3$	1.70456	−	0.307393i	0.984126	−	0.177473i
$4$	0.688428	−	0.397464i	0.344214	−	0.198732i
$5$	−1.64076	−	2.13829i	−0.733772	−	0.956270i	0.266199	−	0.963918i	$-0.414232\pi$
$5$	−1.64076	−	2.13829i	−0.733772	−	0.956270i	−0.999971	+	0.00764793i	$0.997566\pi$
$6$	−2.61957	+	1.23394i	−1.06944	+	0.503755i
$7$	−2.63988	−	0.176109i	−0.997782	−	0.0665630i
$7$	−2.63988	−	0.176109i	−0.997782	−	0.0665630i
$8$	1.42457	−	1.42457i	0.503661	−	0.503661i
$9$	2.81102	−	1.04794i	0.937006	−	0.349312i
$10$	3.57479	+	2.74304i	1.13045	+	0.867424i
$11$	−3.01128	+	3.92438i	−0.907936	+	1.18324i	0.0746082	+	0.997213i	$0.476229\pi$
$11$	−3.01128	+	3.92438i	−0.907936	+	1.18324i	−0.982544	+	0.186032i	$0.940437\pi$
$12$	1.05129	−	0.889118i	0.303480	−	0.256666i
$13$	−4.15052			−1.15115			−0.575573	−	0.817750i	$-0.695221\pi$
$13$	−4.15052			−1.15115			−0.575573	+	0.817750i	$0.695221\pi$
$14$	4.33919	−	0.857876i	1.15970	−	0.229277i
$15$	−3.45407	−	3.14047i	−0.891836	−	0.810865i
$16$	−2.47897	+	4.29371i	−0.619743	+	1.07343i
$17$	−2.79152	+	3.03437i	−0.677043	+	0.735943i
$17$	−2.79152	+	3.03437i	−0.677043	+	0.735943i
$18$	−4.08591	+	2.90856i	−0.963057	+	0.685554i
$19$	−2.13274	+	0.571466i	−0.489284	+	0.131103i	−0.495022	−	0.868880i	$-0.664840\pi$
$19$	−2.13274	+	0.571466i	−0.489284	+	0.131103i	0.00573824	+	0.999984i	$0.498173\pi$
$20$	−1.97944	−	0.819911i	−0.442616	−	0.183338i
$21$	−4.55396	+	0.511294i	−0.993756	+	0.111573i
$22$	3.16468	−	7.64020i	0.674711	−	1.62890i
$23$	−0.0442863	−	0.00583040i	−0.00923432	−	0.00121572i	0.125908	−	0.992042i	$-0.459816\pi$
$23$	−0.0442863	−	0.00583040i	−0.00923432	−	0.00121572i	−0.135142	+	0.990826i	$0.543149\pi$
$24$	1.99035	−	2.86616i	0.406279	−	0.585052i
$25$	−0.586062	+	2.18721i	−0.117212	+	0.437443i
$26$	6.70242	−	1.79591i	1.31445	−	0.352206i
$27$	4.46941	−	2.65035i	0.860138	−	0.510061i
$28$	−1.88737	+	0.928021i	−0.356679	+	0.175379i
$29$	4.59170	+	1.90195i	0.852658	+	0.353182i	0.765832	−	0.643041i	$-0.222328\pi$
$29$	4.59170	+	1.90195i	0.852658	+	0.353182i	0.0868261	+	0.996223i	$0.472328\pi$
$30$	6.93662	+	3.57679i	1.26645	+	0.653030i
$31$	−7.96718	+	1.04890i	−1.43095	+	0.188388i	−0.805832	−	0.592145i	$-0.798281\pi$
$31$	−7.96718	+	1.04890i	−1.43095	+	0.188388i	−0.625115	+	0.780532i	$0.714948\pi$
$32$	1.10242	−	4.11429i	0.194882	−	0.727310i
$33$	−3.92657	+	7.61497i	−0.683528	+	1.32560i
$34$	3.19490	−	6.10790i	0.547921	−	1.04750i
$35$	3.95485	+	5.93378i	0.668492	+	1.00299i
$36$	1.51867	−	1.83871i	0.253111	−	0.306451i
$37$	3.74525	−	2.87383i	0.615716	−	0.472455i	−0.253201	−	0.967414i	$-0.581483\pi$
$37$	3.74525	−	2.87383i	0.615716	−	0.472455i	0.868917	+	0.494958i	$0.164817\pi$
$38$	3.19676	−	1.84565i	0.518583	−	0.299404i
$39$	−7.07479	+	1.27584i	−1.13287	+	0.204298i
$40$	−5.38351	−	0.708753i	−0.851208	−	0.112064i
$41$	−1.92244	−	4.64118i	−0.300235	−	0.724830i	−0.999946	−	0.0104047i	$-0.996688\pi$
$41$	−1.92244	−	4.64118i	−0.300235	−	0.724830i	0.699711	−	0.714426i	$-0.253312\pi$
$42$	7.13268	−	2.79613i	1.10060	−	0.431453i
$43$	−7.46037	−	7.46037i	−1.13770	−	1.13770i	−0.988862	−	0.148834i	$-0.952448\pi$
$43$	−7.46037	−	7.46037i	−1.13770	−	1.13770i	−0.148834	−	0.988862i	$-0.547552\pi$
$44$	−0.513251	+	3.89853i	−0.0773755	+	0.587725i
$45$	−6.85301	−	4.29135i	−1.02159	−	0.639716i
$46$	0.0740379	−	0.00974728i	0.0109163	−	0.00143716i
$47$	−7.89894	−	4.56046i	−1.15218	−	0.665211i	−0.202762	−	0.979228i	$-0.564992\pi$
$47$	−7.89894	−	4.56046i	−1.15218	−	0.665211i	−0.949417	+	0.314017i	$0.898325\pi$
$48$	−2.90569	+	8.08088i	−0.419401	+	1.16637i
$49$	6.93797	+	0.929815i	0.991139	+	0.132831i
$50$		−	3.78558i		−	0.535362i
$51$	−3.82556	+	6.03035i	−0.535685	+	0.844418i
$52$	−2.85733	+	1.64968i	−0.396241	+	0.228770i
$53$	2.12102	−	7.91574i	0.291344	−	1.08731i	−0.652733	−	0.757588i	$-0.726378\pi$
$53$	2.12102	−	7.91574i	0.291344	−	1.08731i	0.944078	−	0.329723i	$-0.106956\pi$
$54$	−6.07058	+	6.21378i	−0.826102	+	0.845589i
$55$	13.3322			1.79772
$56$	−4.01157	+	3.50981i	−0.536069	+	0.469019i
$57$	−3.45971	+	1.62968i	−0.458250	+	0.215857i
$58$	−8.23782	−	1.08453i	−1.08168	−	0.142406i
$59$	−1.66054	+	6.19722i	−0.216184	+	0.806810i	0.769562	+	0.638572i	$0.220474\pi$
$59$	−1.66054	+	6.19722i	−0.216184	+	0.806810i	−0.985746	+	0.168238i	$0.946192\pi$
$60$	−3.62610	−	0.789118i	−0.468127	−	0.101875i
$61$	−0.922226	+	7.00500i	−0.118079	+	0.896898i	0.825187	+	0.564860i	$0.191070\pi$
$61$	−0.922226	+	7.00500i	−0.118079	+	0.896898i	−0.943266	+	0.332039i	$0.892264\pi$
$62$	12.4119	−	5.14116i	1.57631	−	0.652928i
$63$	−7.60531	+	2.27138i	−0.958180	+	0.286167i
$64$		−	2.79497i		−	0.349371i
$65$	6.81002	+	8.87499i	0.844679	+	1.10081i
$66$	3.04582	−	13.9959i	0.374915	−	1.72278i
$67$	−0.363981	−	0.630434i	−0.0444674	−	0.0770197i	0.842935	−	0.538015i	$-0.180826\pi$
$67$	−0.363981	−	0.630434i	−0.0444674	−	0.0770197i	−0.887402	+	0.460996i	$0.847492\pi$
$68$	−0.715708	+	3.19848i	−0.0867923	+	0.387872i
$69$	−0.0772806	+	0.00367504i	−0.00930349	+	0.000442423i
$70$	−8.95397	−	7.87085i	−1.07020	−	0.940746i
$71$	2.68599	−	6.48456i	0.318769	−	0.769575i	−0.680551	−	0.732700i	$-0.738260\pi$
$71$	2.68599	−	6.48456i	0.318769	−	0.769575i	0.999320	−	0.0368749i	$-0.0117403\pi$
$72$	2.51163	−	5.49735i	0.295999	−	0.647868i
$73$	2.06170	+	15.6602i	0.241304	+	1.83288i	0.498933	+	0.866641i	$0.333725\pi$
$73$	2.06170	+	15.6602i	0.241304	+	1.83288i	−0.257629	+	0.966244i	$0.582941\pi$
$74$	−4.80448	+	6.26133i	−0.558510	+	0.727864i
$75$	−0.326642	+	3.90838i	−0.0377173	+	0.451301i
$76$	−1.24110	+	1.24110i	−0.142364	+	0.142364i
$77$	8.64055	−	9.82959i	0.984682	−	1.12019i
$78$	10.8726	−	5.12150i	1.23108	−	0.579896i
$79$	1.37950	−	10.4784i	0.155206	−	1.17891i	−0.719584	−	0.694405i	$-0.755668\pi$
$79$	1.37950	−	10.4784i	0.155206	−	1.17891i	0.874790	−	0.484502i	$-0.160999\pi$
$80$	13.2486	−	1.74421i	1.48124	−	0.195008i
$81$	6.80366	−	5.89154i	0.755962	−	0.654615i
$82$	5.11264	+	6.66293i	0.564597	+	0.735797i
$83$	−1.30506	+	1.30506i	−0.143249	+	0.143249i	−0.775095	−	0.631845i	$-0.782298\pi$
$83$	−1.30506	+	1.30506i	−0.143249	+	0.143249i	0.631845	+	0.775095i	$0.282298\pi$
$84$	−2.93186	+	2.16203i	−0.319892	+	0.235896i
$85$	11.0686	+	0.990381i	1.20056	+	0.107422i
$86$	15.2754	+	8.81923i	1.64718	+	0.951002i
$87$	8.41146	+	1.83052i	0.901803	+	0.196252i
$88$	1.30077	+	9.88032i	0.138662	+	1.05325i
$89$	−2.24326	−	1.29515i	−0.237785	−	0.137285i	0.376373	−	0.926468i	$-0.377171\pi$
$89$	−2.24326	−	1.29515i	−0.237785	−	0.137285i	−0.614158	+	0.789183i	$0.710504\pi$
$90$	12.9233	+	3.96457i	1.36224	+	0.417902i
$91$	10.9569	+	0.730944i	1.14859	+	0.0766238i
$92$	−0.0328053	+	0.0135884i	−0.00342019	+	0.00141669i
$93$	−13.2581	+	4.23696i	−1.37480	+	0.439352i
$94$	14.7288	+	3.94657i	1.51916	+	0.407058i
$95$	4.72128	+	3.62277i	0.484393	+	0.371688i
$96$	0.614434	−	7.35191i	0.0627104	−	0.750351i
$97$	1.65844	+	0.686947i	0.168389	+	0.0697489i	0.465285	−	0.885161i	$-0.345952\pi$
$97$	1.65844	+	0.686947i	0.168389	+	0.0697489i	−0.296897	+	0.954910i	$0.595952\pi$
$98$	−11.6060	+	1.50052i	−1.17239	+	0.151576i
$99$	−4.35227	+	14.1871i	−0.437420	+	1.42586i
$100$	0.465877	+	1.73868i	0.0465877	+	0.173868i
$101$	−2.51385	−	4.35411i	−0.250137	−	0.433250i	0.713426	−	0.700730i	$-0.247142\pi$
$101$	−2.51385	−	4.35411i	−0.250137	−	0.433250i	−0.963563	+	0.267480i	$0.913809\pi$
$102$	3.56836	−	11.3933i	0.353320	−	1.12811i
$103$	9.21963	+	5.32296i	0.908437	+	0.524487i	0.879928	−	0.475107i	$-0.157591\pi$
$103$	9.21963	+	5.32296i	0.908437	+	0.524487i	0.0285093	+	0.999594i	$0.490924\pi$
$104$	−5.91270	+	5.91270i	−0.579788	+	0.579788i
$105$	8.56527	+	8.89876i	0.835885	+	0.868430i
$106$			13.7004i			1.33070i
$107$	3.53019	−	2.70881i	0.341276	−	0.261870i	−0.423876	−	0.905720i	$-0.639331\pi$
$107$	3.53019	−	2.70881i	0.341276	−	0.261870i	0.765152	+	0.643850i	$0.222664\pi$
$108$	2.02345	−	3.60101i	0.194706	−	0.346507i
$109$	−0.483403	+	0.629983i	−0.0463016	+	0.0603414i	−0.815930	−	0.578150i	$-0.803775\pi$
$109$	−0.483403	+	0.629983i	−0.0463016	+	0.0603414i	0.769629	+	0.638492i	$0.220441\pi$
$110$	−21.5294	+	5.76879i	−2.05275	+	0.550033i
$111$	5.50059	−	6.04987i	0.522093	−	0.574228i
$112$	7.30036	−	10.8983i	0.689819	−	1.02979i
$113$	−0.543834	−	1.31293i	−0.0511596	−	0.123510i	0.896233	−	0.443583i	$-0.146293\pi$
$113$	−0.543834	−	1.31293i	−0.0511596	−	0.123510i	−0.947393	+	0.320072i	$0.896293\pi$
$114$	4.88172	−	4.12867i	0.457215	−	0.386686i
$115$	0.0601962	+	0.104263i	0.00561333	+	0.00972257i
$116$	3.91701	−	0.515684i	0.363685	−	0.0478801i
$117$	−11.6672	+	4.34948i	−1.07863	+	0.402109i
$118$		−	10.7260i		−	0.987411i
$119$	7.90367	−	7.51878i	0.724528	−	0.689245i
$120$	−9.39436	+	0.446744i	−0.857584	+	0.0407820i
$121$	−3.48592	−	13.0096i	−0.316902	−	1.18269i
$122$	−1.54178	−	11.7110i	−0.139586	−	1.06026i
$123$	−4.70357	−	7.32020i	−0.424107	−	0.660041i
$124$	−5.06793	+	3.88876i	−0.455113	+	0.349221i
$125$	−6.81195	+	2.82160i	−0.609280	+	0.252372i
$126$	11.2985	−	6.95870i	1.00655	−	0.619930i
$127$	−6.97574	−	6.97574i	−0.618996	−	0.618996i	0.326278	−	0.945274i	$-0.394206\pi$
$127$	−6.97574	−	6.97574i	−0.618996	−	0.618996i	−0.945274	+	0.326278i	$0.894206\pi$
$128$	3.41421	+	12.7420i	0.301776	+	1.12624i
$129$	−15.0099	−	10.4234i	−1.32155	−	0.917725i
$130$	−14.8372	−	11.3850i	−1.30131	−	0.998532i
$131$	5.84019	+	7.61109i	0.510260	+	0.664984i	0.975448	−	0.220228i	$-0.0706801\pi$
$131$	5.84019	+	7.61109i	0.510260	+	0.664984i	−0.465189	+	0.885212i	$0.654013\pi$
$132$	0.323515	+	6.80303i	0.0281583	+	0.592128i
$133$	5.73083	−	1.13301i	0.496926	−	0.0982443i
$134$	0.860556	+	0.860556i	0.0743407	+	0.0743407i
$135$	−13.0005	−	5.20827i	−1.11890	−	0.448257i
$136$	0.345957	+	8.29938i	0.0296656	+	0.711666i
$137$	7.31429	−	4.22291i	0.624902	−	0.360788i	−0.153873	−	0.988091i	$-0.549175\pi$
$137$	7.31429	−	4.22291i	0.624902	−	0.360788i	0.778775	+	0.627303i	$0.215841\pi$
$138$	0.123206	−	0.0393735i	0.0104880	−	0.00335170i
$139$	−5.24896	+	12.6721i	−0.445211	+	1.07483i	0.528884	+	0.848694i	$0.322611\pi$
$139$	−5.24896	+	12.6721i	−0.445211	+	1.07483i	−0.974095	+	0.226140i	$0.927389\pi$
$140$	5.08110	+	2.51307i	0.429431	+	0.212393i
$141$	−14.8660	−	5.34547i	−1.25195	−	0.450170i
$142$	−1.53161	+	11.6337i	−0.128530	+	0.976281i
$143$	12.4984	−	16.2882i	1.04517	−	1.36209i
$144$	−2.46891	+	14.6675i	−0.205742	+	1.22229i
$145$	−3.46700	−	12.9390i	−0.287919	−	1.07453i
$146$	−10.1054	−	24.3966i	−0.836328	−	2.01907i
$147$	12.1120	−	0.547761i	0.998979	−	0.0451786i
$148$	1.43609	−	3.46703i	0.118046	−	0.284988i
$149$	−7.18152	+	12.4388i	−0.588333	+	1.01902i	0.406117	+	0.913821i	$0.366882\pi$
$149$	−7.18152	+	12.4388i	−0.588333	+	1.01902i	−0.994451	+	0.105202i	$0.966451\pi$
$150$	−1.16366	−	6.45274i	−0.0950125	−	0.526864i
$151$	−6.10583	−	1.63605i	−0.496885	−	0.133140i	0.00166892	−	0.999999i	$-0.499469\pi$
$151$	−6.10583	−	1.63605i	−0.496885	−	0.133140i	−0.498554	+	0.866859i	$0.666135\pi$
$152$	−2.22414	+	3.85233i	−0.180402	+	0.312465i
$153$	−4.66719	+	11.4550i	−0.377320	+	0.926083i
$154$	−9.69989	+	19.6119i	−0.781639	+	1.58037i
$155$	15.3151	+	15.3151i	1.23014	+	1.23014i
$156$	−4.36338	+	3.69030i	−0.349350	+	0.295460i
$157$	−1.79372	−	3.10681i	−0.143154	−	0.247950i	0.785529	−	0.618825i	$-0.212391\pi$
$157$	−1.79372	−	3.10681i	−0.143154	−	0.247950i	−0.928683	+	0.370875i	$0.879058\pi$
$158$	2.30626	+	17.5178i	0.183476	+	1.39364i
$159$	1.18215	−	14.1448i	0.0937505	−	1.12176i
$160$	−10.6063	+	4.39329i	−0.838504	+	0.347320i
$161$	0.115884	+	0.0231908i	0.00913292	+	0.00182769i
$162$	−8.43757	+	12.4578i	−0.662918	+	0.978776i
$163$	16.3905	+	2.15785i	1.28380	+	0.169016i	0.741377	−	0.671088i	$-0.234173\pi$
$163$	16.3905	+	2.15785i	1.28380	+	0.169016i	0.542425	+	0.840104i	$0.317506\pi$
$164$	−3.16816	−	2.43102i	−0.247392	−	0.189831i
$165$	22.7255	−	4.09824i	1.76918	−	0.319047i
$166$	1.54277	−	2.67216i	0.119742	−	0.207400i
$167$	−12.2178	−	5.06080i	−0.945445	−	0.391616i	−0.143928	−	0.989588i	$-0.545973\pi$
$167$	−12.2178	−	5.06080i	−0.945445	−	0.391616i	−0.801517	+	0.597972i	$0.795973\pi$
$168$	−5.75906	+	7.21580i	−0.444321	+	0.556711i
$169$	4.22681			0.325139
$170$	−18.3025	+	3.19001i	−1.40374	+	0.244663i
$171$	−5.39631	+	3.84138i	−0.412666	+	0.293757i
$172$	−8.10116	−	2.17070i	−0.617708	−	0.165514i
$173$	2.02775	−	1.55595i	0.154167	−	0.118297i	−0.528798	−	0.848748i	$-0.677357\pi$
$173$	2.02775	−	1.55595i	0.154167	−	0.118297i	0.682965	+	0.730451i	$0.260690\pi$
$174$	−14.3752	+	0.683606i	−1.08978	+	0.0518240i
$175$	1.93232	−	5.67078i	0.146070	−	0.428671i
$176$	−9.38525	−	22.6580i	−0.707440	−	1.70791i
$177$	−0.925503	+	11.0740i	−0.0695650	+	0.832369i
$178$	4.18291	+	1.12081i	0.313522	+	0.0840081i
$179$	−21.1442	−	5.66558i	−1.58040	−	0.423466i	−0.641347	−	0.767251i	$-0.721624\pi$
$179$	−21.1442	−	5.66558i	−1.58040	−	0.423466i	−0.939048	+	0.343785i	$0.888291\pi$
$180$	−6.42346	−	0.230458i	−0.478776	−	0.0171774i
$181$	−2.84943	−	6.87914i	−0.211797	−	0.511322i	0.781903	−	0.623400i	$-0.214249\pi$
$181$	−2.84943	−	6.87914i	−0.211797	−	0.511322i	−0.993699	+	0.112078i	$0.964249\pi$
$182$	−18.0099	+	3.56063i	−1.33498	+	0.263931i
$183$	0.581302	+	12.2239i	0.0429710	+	0.903616i
$184$	−0.0713946	+	0.0547830i	−0.00526328	+	0.00403866i
$185$	−12.2901	−	3.29314i	−0.903590	−	0.242116i
$186$	19.5763	−	12.5787i	1.43541	−	0.922315i
$187$	−3.50197	−	20.0923i	−0.256089	−	1.46930i
$188$	−7.25047			−0.528795
$189$	−12.2655	+	6.20952i	−0.892182	+	0.451676i
$190$	−9.19166	−	3.80731i	−0.666833	−	0.276211i
$191$	−9.24341	+	16.0100i	−0.668829	+	1.15845i	0.309402	+	0.950931i	$0.399871\pi$
$191$	−9.24341	+	16.0100i	−0.668829	+	1.15845i	−0.978232	+	0.207515i	$0.933462\pi$
$192$	−0.859153	−	4.76418i	−0.0620040	−	0.343825i
$193$	4.59625	+	3.52682i	0.330845	+	0.253866i	0.760803	−	0.648982i	$-0.224805\pi$
$193$	4.59625	+	3.52682i	0.330845	+	0.253866i	−0.429958	+	0.902849i	$0.641472\pi$
$194$	−2.97534	−	0.391712i	−0.213617	−	0.0281233i
$195$	14.3362	+	13.0346i	1.02663	+	0.933425i
$196$	5.14586	−	2.11748i	0.367562	−	0.151249i
$197$	13.2100	−	5.47178i	0.941176	−	0.389848i	0.141269	−	0.989971i	$-0.454882\pi$
$197$	13.2100	−	5.47178i	0.941176	−	0.389848i	0.799908	+	0.600123i	$0.204882\pi$
$198$	0.889519	−	24.7931i	0.0632154	−	1.76197i
$199$	−0.981578	−	7.45582i	−0.0695822	−	0.528529i	−0.990368	−	0.138461i	$-0.955785\pi$
$199$	−0.981578	−	7.45582i	−0.0695822	−	0.528529i	0.920786	−	0.390069i	$-0.127549\pi$
$200$	2.28095	+	3.95072i	0.161287	+	0.279358i
$201$	−0.814217	−	0.962724i	−0.0574304	−	0.0679053i
$202$	5.94345	+	5.94345i	0.418180	+	0.418180i
$203$	−11.7866	−	5.82956i	−0.827258	−	0.409155i
$204$	−0.236775	+	5.67198i	−0.0165776	+	0.397118i
$205$	−6.76990	+	11.7258i	−0.472830	+	0.818966i
$206$	−17.1914	−	4.60643i	−1.19778	−	0.320945i
$207$	−0.130599	+	0.0300198i	−0.00907729	+	0.00208652i
$208$	10.2890	−	17.8211i	0.713415	−	1.23567i
$209$	4.17963	−	10.0905i	0.289111	−	0.697976i
$210$	−17.6820	−	10.6639i	−1.22017	−	0.735880i
$211$	4.35571	+	10.5156i	0.299860	+	0.723925i	0.999951	+	0.00987235i	$0.00314252\pi$
$211$	4.35571	+	10.5156i	0.299860	+	0.723925i	−0.700092	+	0.714053i	$0.746857\pi$
$212$	−1.68606	−	6.29245i	−0.115799	−	0.432167i
$213$	2.58512	−	11.8789i	0.177129	−	0.813932i
$214$	−4.52860	+	5.90178i	−0.309569	+	0.403438i
$215$	−3.71169	+	28.1931i	−0.253135	+	1.92275i
$216$	2.59137	−	10.1426i	0.176321	−	0.690116i
$217$	21.2171	−	1.36588i	1.44031	−	0.0927219i
$218$	0.508027	−	1.22649i	0.0344080	−	0.0830682i
$219$	8.32811	+	26.0599i	0.562761	+	1.76096i
$220$	9.17829	−	5.29909i	0.618800	−	0.357264i
$221$	11.5863	−	12.5942i	0.779376	−	0.847179i
$222$	−6.26482	+	12.1496i	−0.420467	+	0.815431i
$223$	−14.3858	−	14.3858i	−0.963343	−	0.963343i	0.0360089	−	0.999351i	$-0.488536\pi$
$223$	−14.3858	−	14.3858i	−0.963343	−	0.963343i	−0.999351	+	0.0360089i	$0.988536\pi$
$224$	−3.63483	+	10.6671i	−0.242862	+	0.712725i
$225$	0.644628	+	6.76245i	0.0429752	+	0.450830i
$226$	1.44630	+	1.88486i	0.0962066	+	0.125379i
$227$	−18.6137	−	14.2828i	−1.23544	−	0.947984i	−0.235721	−	0.971821i	$-0.575745\pi$
$227$	−18.6137	−	14.2828i	−1.23544	−	0.947984i	−0.999716	+	0.0238367i	$0.992412\pi$
$228$	−1.73402	+	2.49703i	−0.114838	+	0.165370i
$229$	−3.13941	−	11.7165i	−0.207458	−	0.774245i	−0.988686	−	0.149999i	$-0.952073\pi$
$229$	−3.13941	−	11.7165i	−0.207458	−	0.774245i	0.781228	−	0.624246i	$-0.214594\pi$
$230$	−0.142321	−	0.142321i	−0.00938439	−	0.00938439i
$231$	11.7068	−	19.4111i	0.770248	−	1.27716i
$232$	9.25065	−	3.83174i	0.607335	−	0.251566i
$233$	9.55488	−	7.33172i	0.625961	−	0.480317i	−0.246407	−	0.969166i	$-0.579250\pi$
$233$	9.55488	−	7.33172i	0.625961	−	0.480317i	0.872368	+	0.488850i	$0.162583\pi$
$234$	16.9586	−	12.0720i	1.10862	−	0.789174i
$235$	3.20874	+	24.3728i	0.209315	+	1.58991i
$236$	1.32001	+	4.92635i	0.0859254	+	0.320678i
$237$	−0.869534	−	18.2850i	−0.0564823	−	1.18774i
$238$	−9.50982	+	15.5615i	−0.616430	+	1.00870i
$239$			17.8282i			1.15321i	0.817023	+	0.576605i	$0.195623\pi$
$239$			17.8282i			1.15321i	−0.817023	+	0.576605i	$0.804377\pi$
$240$	22.0468	−	7.04562i	1.42311	−	0.454793i
$241$	−2.96671	+	0.390575i	−0.191103	+	0.0251591i	−0.225470	−	0.974250i	$-0.572392\pi$
$241$	−2.96671	+	0.390575i	−0.191103	+	0.0251591i	0.0343672	+	0.999409i	$0.489058\pi$
$242$	11.2584	+	19.5001i	0.723717	+	1.25352i
$243$	9.78620	−	12.1338i	0.627785	−	0.778387i
$244$	2.14935	+	5.18899i	0.137598	+	0.332191i
$245$	−9.39536	−	16.3610i	−0.600248	−	1.04526i
$246$	10.7629	+	9.78574i	0.686219	+	0.623916i
$247$	8.85198	−	2.37188i	0.563238	−	0.150919i
$248$	−9.85556	+	12.8440i	−0.625829	+	0.815596i
$249$	−1.82339	+	2.62572i	−0.115552	+	0.166398i
$250$	9.77931	−	7.50393i	0.618498	−	0.474590i
$251$			27.6331i			1.74419i	0.489339	+	0.872094i	$0.337238\pi$
$251$			27.6331i			1.74419i	−0.489339	+	0.872094i	$0.662762\pi$
$252$	−4.33292	+	4.58652i	−0.272948	+	0.288924i
$253$	0.156239	−	0.156239i	0.00982267	−	0.00982267i
$254$	14.2831	+	8.24632i	0.896198	+	0.517420i
$255$	19.1714	−	1.71424i	1.20056	−	0.107350i
$256$	−8.23182	−	14.2579i	−0.514489	−	0.891121i
$257$	−1.28477	−	4.79482i	−0.0801416	−	0.299092i	0.914208	−	0.405245i	$-0.132814\pi$
$257$	−1.28477	−	4.79482i	−0.0801416	−	0.299092i	−0.994350	+	0.106152i	$0.966147\pi$
$258$	28.7487	+	10.3373i	1.78981	+	0.643575i
$259$	−10.3931	+	6.92701i	−0.645798	+	0.430424i
$260$	8.21570	+	3.40306i	0.509516	+	0.211049i
$261$	14.9005	+	0.534594i	0.922317	+	0.0330905i
$262$	−12.7242	−	9.76366i	−0.786106	−	0.603201i
$263$	−18.4746	−	4.95026i	−1.13919	−	0.305246i	−0.360567	−	0.932733i	$-0.617417\pi$
$263$	−18.4746	−	4.95026i	−1.13919	−	0.305246i	−0.778627	+	0.627488i	$0.784083\pi$
$264$	5.25437	+	16.4417i	0.323384	+	1.01192i
$265$	−20.4062	+	8.45253i	−1.25354	+	0.519235i
$266$	−8.76411	+	4.30932i	−0.537362	+	0.264222i
$267$	−4.22189	−	1.51809i	−0.258375	−	0.0929056i
$268$	−0.501150	−	0.289339i	−0.0306126	−	0.0176742i
$269$	0.955601	+	7.25851i	0.0582640	+	0.442559i	0.995568	+	0.0940458i	$0.0299800\pi$
$269$	0.955601	+	7.25851i	0.0582640	+	0.442559i	−0.937304	+	0.348513i	$0.886687\pi$
$270$	23.2472	+	2.78529i	1.41478	+	0.169507i
$271$	0.996751	+	0.575475i	0.0605483	+	0.0349576i	0.529969	−	0.848017i	$-0.322204\pi$
$271$	0.996751	+	0.575475i	0.0605483	+	0.0349576i	−0.469420	+	0.882975i	$0.655537\pi$
$272$	−6.10860	−	19.5081i	−0.370388	−	1.18285i
$273$	18.9013	−	2.12213i	1.14396	−	0.128437i
$274$	−9.98417	+	9.98417i	−0.603166	+	0.603166i
$275$	−6.81866	−	8.88624i	−0.411180	−	0.535861i
$276$	−0.0517414	+	0.0332463i	−0.00311447	+	0.00200119i
$277$	5.85255	−	0.770503i	0.351646	−	0.0462951i	0.0473657	−	0.998878i	$-0.484917\pi$
$277$	5.85255	−	0.770503i	0.351646	−	0.0462951i	0.304280	+	0.952583i	$0.401584\pi$
$278$	2.99307	−	22.7346i	0.179512	−	1.36353i
$279$	−21.2967	+	11.2976i	−1.27500	+	0.676368i
$280$	14.0870	+	2.81911i	0.841861	+	0.168474i
$281$	−1.82394	+	1.82394i	−0.108807	+	0.108807i	−0.759414	−	0.650607i	$-0.774514\pi$
$281$	−1.82394	+	1.82394i	−0.108807	+	0.108807i	0.650607	+	0.759414i	$0.274514\pi$
$282$	26.3192	+	2.19962i	1.56729	+	0.130986i
$283$	−18.4199	+	24.0053i	−1.09495	+	1.42696i	−0.200555	+	0.979682i	$0.564275\pi$
$283$	−18.4199	+	24.0053i	−1.09495	+	1.42696i	−0.894393	+	0.447282i	$0.852392\pi$
$284$	−0.728267	−	5.53174i	−0.0432147	−	0.328248i
$285$	9.16130	+	4.72392i	0.542668	+	0.279821i
$286$	−13.1350	+	31.7108i	−0.776692	+	1.87510i
$287$	4.25766	+	12.5907i	0.251322	+	0.743207i
$288$	−1.21259	−	12.7206i	−0.0714524	−	0.749569i
$289$	−1.41482	−	16.9410i	−0.0832247	−	0.996531i
$290$	11.1973	+	19.3943i	0.657527	+	1.13887i
$291$	3.03806	+	0.661148i	0.178094	+	0.0387572i
$292$	7.64369	+	9.96145i	0.447313	+	0.582950i
$293$		−	22.7145i		−	1.32699i	−0.748179	−	0.663497i	$-0.769072\pi$
$293$		−	22.7145i		−	1.32699i	0.748179	−	0.663497i	$-0.230928\pi$
$294$	−19.3219	+	6.12533i	−1.12687	+	0.357237i
$295$	15.9760	−	6.61747i	0.930158	−	0.385284i
$296$	1.24140	−	9.42934i	0.0721547	−	0.548069i
$297$	−3.05767	+	25.5206i	−0.177424	+	1.48086i
$298$	6.21481	−	23.1940i	0.360015	−	1.34359i
$299$	0.183811	+	0.0241992i	0.0106301	+	0.00139947i
$300$	1.32857	+	2.82047i	0.0767051	+	0.162840i
$301$	18.3807	+	21.0084i	1.05944	+	1.21090i
$302$	10.5678			0.608111
$303$	−5.62341	−	6.64908i	−0.323056	−	0.381980i
$304$	2.83330	−	10.5740i	0.162501	−	0.606461i
$305$	16.4918	−	9.52157i	0.944320	−	0.545203i
$306$	2.58024	−	20.5175i	0.147502	−	1.17291i
$307$		−	19.5978i		−	1.11851i	−0.828996	−	0.559254i	$-0.811088\pi$
$307$		−	19.5978i		−	1.11851i	0.828996	−	0.559254i	$-0.188912\pi$
$308$	2.04149	−	10.2013i	0.116325	−	0.581272i
$309$	17.3516	+	6.23923i	0.987099	+	0.354937i
$310$	−31.3582	−	18.1047i	−1.78102	−	1.02828i
$311$	28.2820	−	3.72339i	1.60372	−	0.211134i	0.725097	−	0.688646i	$-0.241795\pi$
$311$	28.2820	−	3.72339i	1.60372	−	0.211134i	0.878625	+	0.477512i	$0.158461\pi$
$312$	−8.26100	+	11.8960i	−0.467687	+	0.673481i
$313$	−1.76349	+	13.3951i	−0.0996785	+	0.757133i	0.866485	+	0.499203i	$0.166374\pi$
$313$	−1.76349	+	13.3951i	−0.0996785	+	0.757133i	−0.966164	+	0.257930i	$0.916959\pi$
$314$	4.24087	+	4.24087i	0.239326	+	0.239326i
$315$	17.3354	+	12.5355i	0.976739	+	0.706297i
$316$	−3.21508	−	7.76189i	−0.180863	−	0.436641i
$317$	10.7371	+	1.41356i	0.603055	+	0.0793937i	0.425871	−	0.904784i	$-0.359968\pi$
$317$	10.7371	+	1.41356i	0.603055	+	0.0793937i	0.177184	+	0.984178i	$0.443301\pi$
$318$	4.21141	+	23.3531i	0.236164	+	1.30958i
$319$	−21.2909	+	12.2923i	−1.19206	+	0.688236i
$320$	−5.97644	+	4.58588i	−0.334093	+	0.256359i
$321$	5.18473	−	5.70247i	0.289384	−	0.318281i
$322$	−0.197168	+	0.0126929i	−0.0109878	+	0.000707349i
$323$	4.21955	−	8.06678i	0.234782	−	0.448848i
$324$	2.34215	−	6.76011i	0.130120	−	0.375562i
$325$	2.43246	−	9.07807i	0.134929	−	0.503561i
$326$	−27.4017	+	3.60750i	−1.51764	+	0.199801i
$327$	−0.630335	+	1.22244i	−0.0348576	+	0.0676008i
$328$	−9.35032	−	3.87303i	−0.516285	−	0.213852i
$329$	20.0492	+	13.4302i	1.10535	+	0.740428i
$330$	−34.9248	+	16.4512i	−1.92255	+	0.905609i
$331$	−1.77586	+	0.475840i	−0.0976100	+	0.0261545i	−0.307293	−	0.951615i	$-0.599423\pi$
$331$	−1.77586	+	0.475840i	−0.0976100	+	0.0261545i	0.209683	+	0.977769i	$0.432757\pi$
$332$	−0.379727	+	1.41716i	−0.0208402	+	0.0777767i
$333$	7.51638	−	12.0032i	0.411895	−	0.657770i
$334$	21.9196	+	2.88577i	1.19939	+	0.157903i
$335$	−0.750840	+	1.81269i	−0.0410228	+	0.0990378i
$336$	9.09381	−	20.8209i	0.496108	−	1.13587i
$337$	−30.7955	−	12.7559i	−1.67754	−	0.694860i	−0.678335	−	0.734752i	$-0.737298\pi$
$337$	−30.7955	−	12.7559i	−1.67754	−	0.694860i	−0.999204	+	0.0398930i	$0.987298\pi$
$338$	−6.82561	+	1.82892i	−0.371264	+	0.0994800i
$339$	−1.33058	−	2.07079i	−0.0722672	−	0.112470i
$340$	8.01356	−	3.71756i	0.434596	−	0.201613i
$341$	19.8751	−	34.4247i	1.07630	−	1.86420i
$342$	7.05203	−	8.53816i	0.381330	−	0.461691i
$343$	−18.1517	−	3.67644i	−0.980099	−	0.198509i
$344$	−21.2556			−1.14603
$345$	0.134658	+	0.159218i	0.00724972	+	0.00857201i
$346$	−2.60124	+	3.39000i	−0.139844	+	0.182248i
$347$	24.3072	+	18.6516i	1.30488	+	1.00127i	0.998786	+	0.0492690i	$0.0156891\pi$
$347$	24.3072	+	18.6516i	1.30488	+	1.00127i	0.306095	+	0.952001i	$0.400978\pi$
$348$	6.51825	−	2.08307i	0.349415	−	0.111665i
$349$	2.00398	−	2.00398i	0.107271	−	0.107271i	−0.651434	−	0.758705i	$-0.725832\pi$
$349$	2.00398	−	2.00398i	0.107271	−	0.107271i	0.758705	+	0.651434i	$0.225832\pi$
$350$	−0.666676	+	9.99350i	−0.0356353	+	0.534175i
$351$	−18.5504	+	11.0003i	−0.990146	+	0.587155i
$352$	12.8263	+	16.7156i	0.683646	+	0.890944i
$353$	8.95054	−	5.16759i	0.476389	−	0.275043i	−0.242521	−	0.970146i	$-0.577974\pi$
$353$	8.95054	−	5.16759i	0.476389	−	0.275043i	0.718910	+	0.695103i	$0.244641\pi$
$354$	−3.29710	−	18.2831i	−0.175239	−	0.971736i
$355$	−18.2729	+	4.89621i	−0.969825	+	0.259864i
$356$	−2.05910			−0.109132
$357$	11.1610	−	15.2457i	0.590704	−	0.806888i
$358$	36.5960			1.93416
$359$	−19.0599	+	5.10709i	−1.00594	+	0.269542i	−0.723934	−	0.689869i	$-0.757668\pi$
$359$	−19.0599	+	5.10709i	−1.00594	+	0.269542i	−0.282010	+	0.959411i	$0.591001\pi$
$360$	−15.8759	+	3.64926i	−0.836733	+	0.192333i
$361$	−12.2325	+	7.06242i	−0.643815	+	0.371707i
$362$	7.57794	+	9.87576i	0.398288	+	0.519059i
$363$	−9.94101	−	21.1041i	−0.521768	−	1.10768i
$364$	7.83355	−	3.85177i	0.410590	−	0.201887i
$365$	30.1032	−	30.1032i	1.57567	−	1.57567i
$366$	−6.22792	−	19.4881i	−0.325539	−	1.01866i
$367$	−0.344918	−	0.264665i	−0.0180046	−	0.0138154i	0.599720	−	0.800210i	$-0.295279\pi$
$367$	−0.344918	−	0.264665i	−0.0180046	−	0.0138154i	−0.617725	+	0.786395i	$0.711945\pi$
$368$	0.134818	−	0.175699i	0.00702790	−	0.00915893i
$369$	−10.2677	−	11.0318i	−0.534514	−	0.574295i
$370$	21.2715			1.10585
$371$	−6.99327	+	20.5231i	−0.363073	+	1.06551i
$372$	−7.44319	+	8.18645i	−0.385911	+	0.424448i
$373$	−8.04028	+	13.9262i	−0.416310	+	0.721070i	−0.995565	−	0.0940767i	$-0.970010\pi$
$373$	−8.04028	+	13.9262i	−0.416310	+	0.721070i	0.579255	+	0.815146i	$0.303343\pi$
$374$	14.3490	+	30.9306i	0.741967	+	1.59938i
$375$	−10.7440	+	6.90353i	−0.554818	+	0.356497i
$376$	−17.7493	+	4.75590i	−0.915349	+	0.245267i
$377$	−19.0579	−	7.89406i	−0.981534	−	0.406565i
$378$	17.1199	−	15.3346i	0.880554	−	0.788726i
$379$	−5.61581	+	13.5578i	−0.288465	+	0.696416i	−0.999980	−	0.00625443i	$-0.998009\pi$
$379$	−5.61581	+	13.5578i	−0.288465	+	0.696416i	0.711516	+	0.702670i	$0.248009\pi$
$380$	4.69018	+	0.617474i	0.240601	+	0.0316757i
$381$	−14.0348	−	9.74624i	−0.719026	−	0.499315i
$382$	7.99915	−	29.8532i	0.409272	−	1.52742i
$383$	21.2600	−	5.69659i	1.08633	−	0.291082i	0.329145	−	0.944279i	$-0.393239\pi$
$383$	21.2600	−	5.69659i	1.08633	−	0.291082i	0.757188	+	0.653197i	$0.226573\pi$
$384$	9.73651	+	20.6699i	0.496864	+	1.05481i
$385$	−35.1956	−	2.34793i	−1.79373	−	0.119662i
$386$	−8.94823	−	3.70648i	−0.455453	−	0.188655i
$387$	−28.7892	−	13.1533i	−1.46344	−	0.668618i
$388$	1.41475	−	0.186255i	0.0718231	−	0.00945569i
$389$	0.214891	−	0.801985i	0.0108954	−	0.0406623i	−0.960264	−	0.279093i	$-0.909966\pi$
$389$	0.214891	−	0.801985i	0.0108954	−	0.0406623i	0.971160	+	0.238431i	$0.0766329\pi$
$390$	−28.7906	−	14.8455i	−1.45787	−	0.751733i
$391$	0.141318	−	0.118105i	0.00714674	−	0.00597284i
$392$	11.2082	−	8.55903i	0.566099	−	0.432296i
$393$	12.2945	+	11.1783i	0.620177	+	0.563870i
$394$	−18.9645	+	14.5520i	−0.955416	+	0.733117i
$395$	−24.6691	+	14.2427i	−1.24124	+	0.716630i
$396$	2.64265	+	11.4967i	0.132798	+	0.577731i
$397$	21.7599	+	2.86475i	1.09210	+	0.143778i	0.654995	−	0.755633i	$-0.272671\pi$
$397$	21.7599	+	2.86475i	1.09210	+	0.143778i	0.437104	+	0.899411i	$0.356004\pi$
$398$	4.81118	+	11.6152i	0.241163	+	0.582219i
$399$	9.42023	−	3.69289i	0.471601	−	0.184876i
$400$	−7.93842	−	7.93842i	−0.396921	−	0.396921i
$401$	0.142312	−	1.08096i	0.00710670	−	0.0539807i	−0.987524	−	0.157468i	$-0.949667\pi$
$401$	0.142312	−	1.08096i	0.00710670	−	0.0539807i	0.994631	+	0.103487i	$0.0330002\pi$
$402$	1.73139	+	1.20234i	0.0863541	+	0.0599671i
$403$	33.0679	−	4.35347i	1.64723	−	0.216862i
$404$	−3.46120	−	1.99833i	−0.172201	−	0.0994205i
$405$	−23.7610	−	4.88154i	−1.18069	−	0.242566i
$406$	21.5559	+	4.31379i	1.06980	+	0.214090i
$407$			23.3517i			1.15750i
$408$	3.14087	+	14.0404i	0.155496	+	0.695104i
$409$	6.31767	−	3.64751i	0.312389	−	0.180358i	−0.335606	−	0.942002i	$-0.608941\pi$
$409$	6.31767	−	3.64751i	0.312389	−	0.180358i	0.647995	+	0.761645i	$0.275608\pi$
$410$	5.85860	−	21.8646i	0.289335	−	1.07981i
$411$	11.1695	−	9.44655i	0.550952	−	0.465964i
$412$	8.46274			0.416929
$413$	5.47502	−	16.0675i	0.269408	−	0.790631i
$414$	0.197908	−	0.104987i	0.00972663	−	0.00515982i
$415$	4.93190	+	0.649297i	0.242097	+	0.0318727i
$416$	−4.57562	+	17.0764i	−0.224338	+	0.837241i
$417$	−5.05182	+	23.2138i	−0.247389	+	1.13678i
$418$	−2.38331	+	18.1031i	−0.116572	+	0.885450i
$419$	21.6688	−	8.97553i	1.05859	−	0.438483i	0.215641	−	0.976473i	$-0.430816\pi$
$419$	21.6688	−	8.97553i	1.05859	−	0.438483i	0.842952	+	0.537989i	$0.180816\pi$
$420$	9.43351	+	2.72177i	0.460308	+	0.132809i
$421$			6.06915i			0.295792i	0.989003	+	0.147896i	$0.0472501\pi$
$421$			6.06915i			0.295792i	−0.989003	+	0.147896i	$0.952750\pi$
$422$	−11.5838	−	15.0963i	−0.563892	−	0.734878i
$423$	−26.9832	−	4.54194i	−1.31197	−	0.220837i
$424$	−8.25498	−	14.2981i	−0.400897	−	0.694375i
$425$	−5.00081	−	7.88398i	−0.242575	−	0.382429i
$426$	0.965411	+	20.3011i	0.0467743	+	0.983593i
$427$	3.66821	−	18.3300i	0.177517	−	0.887049i
$428$	1.35363	−	3.26794i	0.0654300	−	0.157962i
$429$	16.2973	−	31.6061i	0.786841	−	1.52596i
$430$	−6.20522	−	47.1334i	−0.299242	−	2.27297i
$431$	−22.1427	+	28.8569i	−1.06658	+	1.38999i	−0.150675	+	0.988583i	$0.548145\pi$
$431$	−22.1427	+	28.8569i	−1.06658	+	1.38999i	−0.915901	+	0.401405i	$0.868522\pi$
$432$	0.300290	+	25.7605i	0.0144477	+	1.23940i
$433$	−13.2743	+	13.2743i	−0.637924	+	0.637924i	−0.950043	−	0.312119i	$-0.898961\pi$
$433$	−13.2743	+	13.2743i	−0.637924	+	0.637924i	0.312119	+	0.950043i	$0.398961\pi$
$434$	−33.6712	+	11.3862i	−1.61627	+	0.546556i
$435$	−9.88705	−	20.9895i	−0.474048	−	1.00637i
$436$	−0.0823925	+	0.625833i	−0.00394589	+	0.0299720i
$437$	0.0977829	−	0.0128734i	0.00467759	−	0.000615817i
$438$	−24.7245	−	38.4790i	−1.18138	−	1.83860i
$439$	4.09611	+	5.33815i	0.195496	+	0.254776i	0.880807	−	0.473475i	$-0.157000\pi$
$439$	4.09611	+	5.33815i	0.195496	+	0.254776i	−0.685311	+	0.728250i	$0.740334\pi$
$440$	18.9927	−	18.9927i	0.905441	−	0.905441i
$441$	20.4772	−	4.65682i	0.975103	−	0.221753i
$442$	−13.2605	+	25.3509i	−0.630737	+	1.20582i
$443$	−27.3063	−	15.7653i	−1.29736	−	0.749032i	−0.317414	−	0.948287i	$-0.602815\pi$
$443$	−27.3063	−	15.7653i	−1.29736	−	0.749032i	−0.979948	+	0.199255i	$0.936148\pi$
$444$	1.38216	−	6.35119i	0.0655943	−	0.301414i
$445$	0.911268	+	6.92177i	0.0431982	+	0.328123i
$446$	29.4553	+	17.0061i	1.39475	+	0.805260i
$447$	−8.41772	+	23.4101i	−0.398145	+	1.10726i
$448$	−0.492219	+	7.37839i	−0.0232552	+	0.348596i
$449$	4.17166	−	1.72796i	0.196873	−	0.0815474i	−0.282069	−	0.959394i	$-0.591021\pi$
$449$	4.17166	−	1.72796i	0.196873	−	0.0815474i	0.478942	+	0.877847i	$0.341021\pi$
$450$	−3.96705	−	10.6413i	−0.187008	−	0.501638i
$451$	24.0027	+	6.43152i	1.13025	+	0.302848i
$452$	−0.896234	−	0.687704i	−0.0421553	−	0.0323469i
$453$	−10.9106	−	0.911853i	−0.512626	−	0.0428426i
$454$	36.2383	+	15.0104i	1.70075	+	0.704472i
$455$	−16.4147	−	24.6283i	−0.769533	−	1.15459i
$456$	−2.60699	+	7.25019i	−0.122084	+	0.339521i
$457$	−5.27741	−	19.6956i	−0.246867	−	0.921320i	−0.972436	−	0.233171i	$-0.925090\pi$
$457$	−5.27741	−	19.6956i	−0.246867	−	0.921320i	0.725569	−	0.688150i	$-0.241577\pi$
$458$	10.1393	+	17.5618i	0.473778	+	0.820608i
$459$	−4.43430	+	20.9604i	−0.206975	+	0.978346i
$460$	0.0828816	+	0.0478517i	0.00386437	+	0.00223110i
$461$	−15.1771	+	15.1771i	−0.706868	+	0.706868i	−0.965875	−	0.259007i	$-0.916605\pi$
$461$	−15.1771	+	15.1771i	−0.706868	+	0.706868i	0.259007	+	0.965875i	$0.416605\pi$
$462$	−10.5054	+	36.4113i	−0.488757	+	1.69401i
$463$		−	3.10812i		−	0.144447i	−0.997388	−	0.0722234i	$-0.976991\pi$
$463$		−	3.10812i		−	0.144447i	0.997388	−	0.0722234i	$-0.0230094\pi$
$464$	−19.5491	+	15.0006i	−0.907544	+	0.696383i
$465$	30.8132	+	21.3977i	1.42893	+	0.992294i
$466$	−12.2572	+	15.9739i	−0.567804	+	0.739976i
$467$	6.63090	−	1.77674i	0.306841	−	0.0822179i	−0.102113	−	0.994773i	$-0.532560\pi$
$467$	6.63090	−	1.77674i	0.306841	−	0.0822179i	0.408954	+	0.912555i	$0.365894\pi$
$468$	−6.30326	+	7.63159i	−0.291368	+	0.352771i
$469$	0.849843	+	1.72837i	0.0392421	+	0.0798088i
$470$	−15.7276	−	37.9698i	−0.725460	−	1.75142i
$471$	−4.01250	−	4.74436i	−0.184886	−	0.218608i
$472$	6.46281	+	11.1939i	0.297475	+	0.515242i
$473$	51.7426	−	6.81204i	2.37913	−	0.313218i
$474$	9.31597	+	29.1511i	0.427897	+	1.33895i
$475$		−	4.99967i		−	0.229401i
$476$	2.45267	−	8.31756i	0.112418	−	0.381235i
$477$	−2.33297	−	24.4740i	−0.106820	−	1.12059i
$478$	−7.71417	−	28.7897i	−0.352838	−	1.31681i
$479$	0.677515	+	5.14624i	0.0309565	+	0.235138i	0.999928	−	0.0120364i	$-0.00383139\pi$
$479$	0.677515	+	5.14624i	0.0309565	+	0.235138i	−0.968971	+	0.247174i	$0.920498\pi$
$480$	−16.7286	+	10.7489i	−0.763554	+	0.490619i
$481$	−15.5447	+	11.9279i	−0.708779	+	0.543865i
$482$	4.62176	−	1.91440i	0.210515	−	0.0871983i
$483$	0.204659	+	0.00390813i	0.00931231	+	0.000177826i
$484$	−7.57067	−	7.57067i	−0.344121	−	0.344121i
$485$	−1.25221	−	4.67333i	−0.0568601	−	0.212205i
$486$	−10.5529	+	23.8286i	−0.478688	+	1.08089i
$487$	4.99470	+	3.83257i	0.226331	+	0.173670i	0.715702	−	0.698406i	$-0.246107\pi$
$487$	4.99470	+	3.83257i	0.226331	+	0.173670i	−0.489371	+	0.872076i	$0.662773\pi$
$488$	8.66533	+	11.2929i	0.392261	+	0.511204i
$489$	28.6018	−	1.36015i	1.29342	−	0.0615079i
$490$	22.2513	+	22.3550i	1.00521	+	1.00990i
$491$	23.5027	+	23.5027i	1.06066	+	1.06066i	0.998037	+	0.0626233i	$0.0199467\pi$
$491$	23.5027	+	23.5027i	1.06066	+	1.06066i	0.0626233	+	0.998037i	$0.480053\pi$
$492$	−6.14759	−	3.16993i	−0.277155	−	0.142912i
$493$	−18.5890	+	8.62361i	−0.837209	+	0.388388i
$494$	−13.2682	+	7.66041i	−0.596965	+	0.344658i
$495$	37.4772	−	13.9713i	1.68447	−	0.627965i
$496$	15.2468	−	36.8089i	0.684599	−	1.65277i
$497$	−8.23269	+	16.6454i	−0.369287	+	0.746650i
$498$	1.80834	−	5.02909i	0.0810336	−	0.225359i
$499$	−0.267951	+	2.03529i	−0.0119951	+	0.0911120i	−0.996395	−	0.0848323i	$-0.972965\pi$
$499$	−0.267951	+	2.03529i	−0.0119951	+	0.0911120i	0.984400	+	0.175944i	$0.0562979\pi$
$500$	−3.56805	+	4.64998i	−0.159568	+	0.207953i
$501$	−22.3817	−	4.87073i	−0.999939	−	0.217608i
$502$	−11.9567	−	44.6230i	−0.533654	−	1.99162i
$503$	4.69022	+	11.3232i	0.209127	+	0.504877i	0.993286	−	0.115683i	$-0.0369056\pi$
$503$	4.69022	+	11.3232i	0.209127	+	0.504877i	−0.784159	+	0.620559i	$0.786906\pi$
$504$	−7.59855	+	14.0700i	−0.338466	+	0.626729i
$505$	−5.18570	+	12.5194i	−0.230761	+	0.557105i
$506$	−0.184697	+	0.319905i	−0.00821079	+	0.0142215i
$507$	7.20483	−	1.29929i	0.319978	−	0.0577035i
$508$	−7.57490	−	2.02969i	−0.336082	−	0.0900528i
$509$	−1.21403	+	2.10276i	−0.0538109	+	0.0932033i	−0.891676	−	0.452674i	$-0.850470\pi$
$509$	−1.21403	+	2.10276i	−0.0538109	+	0.0932033i	0.837865	+	0.545877i	$0.183803\pi$
$510$	−30.2170	+	11.0636i	−1.33803	+	0.489905i
$511$	−2.68475	−	41.7041i	−0.118766	−	1.84488i
$512$	0.806819	+	0.806819i	0.0356567	+	0.0356567i
$513$	−8.01750	+	8.20663i	−0.353981	+	0.362332i
$514$	4.14938	+	7.18694i	0.183021	+	0.317002i
$515$	−3.74524	−	28.4479i	−0.165035	−	1.25357i
$516$	−14.4761	−	1.20984i	−0.637276	−	0.0532602i
$517$	41.6829	−	17.2656i	1.83321	−	0.759341i
$518$	13.7860	−	15.6831i	0.605720	−	0.689074i
$519$	2.97813	−	3.27552i	0.130725	−	0.143779i
$520$	22.3444	+	2.94169i	0.979866	+	0.129002i
$521$	−7.82380	−	6.00341i	−0.342767	−	0.263014i	0.423004	−	0.906128i	$-0.360976\pi$
$521$	−7.82380	−	6.00341i	−0.342767	−	0.263014i	−0.765771	+	0.643114i	$0.777642\pi$
$522$	−24.2932	+	5.58408i	−1.06328	+	0.244408i
$523$	1.95491	−	3.38600i	0.0854821	−	0.148059i	−0.820114	−	0.572200i	$-0.806090\pi$
$523$	1.95491	−	3.38600i	0.0854821	−	0.148059i	0.905597	+	0.424140i	$0.139424\pi$
$524$	7.04569	+	2.91842i	0.307792	+	0.127492i
$525$	1.55060	−	10.2601i	0.0676736	−	0.447789i
$526$	31.9755			1.39420
$527$	19.0578	−	27.1034i	0.830171	−	1.18064i
$528$	−22.9626	−	35.7368i	−0.999318	−	1.55525i
$529$	−22.2144	−	5.95232i	−0.965842	−	0.258797i
$530$	29.2954	−	22.4791i	1.27251	−	0.976431i
$531$	1.82648	+	19.1607i	0.0792626	+	0.831502i
$532$	3.49493	−	3.05779i	0.151524	−	0.132572i
$533$	7.97912	+	19.2633i	0.345614	+	0.834386i
$534$	7.47453	+	0.624682i	0.323455	+	0.0270326i
$535$	−11.5844	−	3.10403i	−0.500838	−	0.134199i
$536$	−1.41661	−	0.379580i	−0.0611883	−	0.0163954i
$537$	−37.7831	−	3.15771i	−1.63046	−	0.136265i
$538$	−4.68386	−	11.3078i	−0.201935	−	0.487515i
$539$	−24.5411	+	24.4273i	−1.05706	+	1.05216i
$540$	−11.0200	+	1.58170i	−0.474224	+	0.0680653i
$541$	16.0520	−	12.3171i	0.690128	−	0.529554i	−0.203100	−	0.979158i	$-0.565102\pi$
$541$	16.0520	−	12.3171i	0.690128	−	0.529554i	0.893228	+	0.449604i	$0.148435\pi$
$542$	−1.85860	−	0.498010i	−0.0798336	−	0.0213913i
$543$	−6.97161	−	10.8500i	−0.299181	−	0.465617i
$544$	9.40685	+	14.8303i	0.403315	+	0.635843i
$545$	2.14023			0.0916775
$546$	−29.6043	+	11.6054i	−1.26695	+	0.496665i
$547$	38.3493	+	15.8848i	1.63970	+	0.679184i	0.996267	−	0.0863218i	$-0.0275113\pi$
$547$	38.3493	+	15.8848i	1.63970	+	0.679184i	0.643429	+	0.765506i	$0.277511\pi$
$548$	3.35691	−	5.81434i	0.143400	−	0.248376i
$549$	4.74840	+	20.6576i	0.202657	+	0.881646i
$550$	14.8561	+	11.3995i	0.633464	+	0.486074i
$551$	−10.8798	−	1.43235i	−0.463495	−	0.0610203i
$552$	−0.104856	+	0.115327i	−0.00446297	+	0.00490864i
$553$	−5.48706	+	27.4187i	−0.233333	+	1.16596i
$554$	−9.11754	+	3.77661i	−0.387367	+	0.160453i
$555$	−21.9615	−	1.83543i	−0.932215	−	0.0779096i
$556$	1.42318	+	10.8101i	0.0603561	+	0.458450i
$557$	8.35192	+	14.4660i	0.353882	+	0.612942i	0.986926	−	0.161174i	$-0.0515280\pi$
$557$	8.35192	+	14.4660i	0.353882	+	0.612942i	−0.633044	+	0.774116i	$0.718195\pi$
$558$	29.5024	−	27.4587i	1.24893	−	1.16242i
$559$	30.9644	+	30.9644i	1.30966	+	1.30966i
$560$	−35.2819	+	2.27131i	−1.49093	+	0.0959805i
$561$	−12.1455	−	33.1720i	−0.512785	−	1.40052i
$562$	2.15616	−	3.73458i	0.0909522	−	0.157534i
$563$	−30.5750	−	8.19254i	−1.28858	−	0.345274i	−0.451460	−	0.892292i	$-0.649097\pi$
$563$	−30.5750	−	8.19254i	−1.28858	−	0.345274i	−0.837121	+	0.547017i	$0.815763\pi$
$564$	−12.3588	+	2.22874i	−0.520401	+	0.0938470i
$565$	−1.91512	+	3.31708i	−0.0805696	+	0.139551i
$566$	19.3582	−	46.7348i	0.813685	−	1.96441i
$567$	−18.9984	+	14.3548i	−0.797859	+	0.602844i
$568$	−5.41132	−	13.0641i	−0.227054	−	0.548156i
$569$	−6.65239	−	24.8270i	−0.278883	−	1.04080i	−0.953195	−	0.302357i	$-0.902226\pi$
$569$	−6.65239	−	24.8270i	−0.278883	−	1.04080i	0.674312	−	0.738446i	$-0.264440\pi$
$570$	−16.8380	−	3.66432i	−0.705267	−	0.153481i
$571$	−8.73388	+	11.3822i	−0.365502	+	0.476331i	−0.939511	−	0.342517i	$-0.888720\pi$
$571$	−8.73388	+	11.3822i	−0.365502	+	0.476331i	0.574010	+	0.818848i	$0.305387\pi$
$572$	2.13026	−	16.1809i	0.0890706	−	0.676558i
$573$	−10.8345	+	30.1314i	−0.452619	+	1.25876i
$574$	−12.3234	−	18.4897i	−0.514368	−	0.771746i
$575$	0.0387068	−	0.0934465i	0.00161419	−	0.00389699i
$576$	−2.92895	−	7.85671i	−0.122039	−	0.327363i
$577$	18.7725	−	10.8383i	0.781511	−	0.451205i	−0.0554546	−	0.998461i	$-0.517661\pi$
$577$	18.7725	−	10.8383i	0.781511	−	0.451205i	0.836965	+	0.547256i	$0.184327\pi$
$578$	9.61500	+	26.7448i	0.399931	+	1.11244i
$579$	8.91868	+	4.59881i	0.370648	+	0.191120i
$580$	−7.52957	−	7.52957i	−0.312649	−	0.312649i
$581$	3.67505	−	3.21538i	0.152467	−	0.133397i
$582$	−5.19205	+	0.246905i	−0.215217	+	0.0102346i
$583$	24.6774	+	32.1602i	1.02203	+	1.33194i
$584$	25.2460	+	19.3720i	1.04469	+	0.801617i
$585$	28.4435	+	17.8113i	1.17600	+	0.736407i
$586$	9.82843	+	36.6802i	0.406009	+	1.51524i
$587$	15.2485	+	15.2485i	0.629373	+	0.629373i	0.947910	−	0.318537i	$-0.103192\pi$
$587$	15.2485	+	15.2485i	0.629373	+	0.629373i	−0.318537	+	0.947910i	$0.603192\pi$
$588$	8.12051	−	5.19117i	0.334884	−	0.214080i
$589$	16.3925	−	6.79000i	0.675441	−	0.279777i
$590$	−22.9353	+	17.5989i	−0.944231	+	0.724534i
$591$	20.8353	−	13.3876i	0.857048	−	0.550693i
$592$	3.05502	+	23.2052i	0.125560	+	0.953726i
$593$	−8.60095	−	32.0992i	−0.353199	−	1.31815i	−0.882736	−	0.469869i	$-0.844301\pi$
$593$	−8.60095	−	32.0992i	−0.353199	−	1.31815i	0.529538	−	0.848286i	$-0.322365\pi$
$594$	−6.10500	−	42.5347i	−0.250491	−	1.74522i
$595$	−29.0453	−	4.56377i	−1.19074	−	0.187096i
$596$			11.4176i			0.467683i
$597$	−3.96502	−	12.4071i	−0.162277	−	0.507790i
$598$	−0.307296	+	0.0404563i	−0.0125663	+	0.00165438i
$599$	−11.9623	−	20.7193i	−0.488765	−	0.846566i	0.511151	−	0.859491i	$-0.329219\pi$
$599$	−11.9623	−	20.7193i	−0.488765	−	0.846566i	−0.999916	+	0.0129246i	$0.995886\pi$
$600$	5.10243	+	6.03307i	0.208306	+	0.246299i
$601$	−1.42133	−	3.43140i	−0.0579774	−	0.139970i	0.892236	−	0.451569i	$-0.149135\pi$
$601$	−1.42133	−	3.43140i	−0.0579774	−	0.139970i	−0.950214	+	0.311599i	$0.899135\pi$
$602$	−38.7720	−	25.9719i	−1.58023	−	1.05853i
$603$	−1.68381	−	1.39073i	−0.0685701	−	0.0566350i
$604$	−4.85369	+	1.30054i	−0.197494	+	0.0529184i
$605$	−22.0987	+	28.7996i	−0.898441	+	1.17087i
$606$	11.9579	+	8.30397i	0.485757	+	0.337326i
$607$	−8.64514	+	6.63365i	−0.350895	+	0.269251i	−0.769136	−	0.639085i	$-0.779313\pi$
$607$	−8.64514	+	6.63365i	−0.350895	+	0.269251i	0.418241	+	0.908336i	$0.362647\pi$
$608$			9.40470i			0.381411i
$609$	−21.8829	−	6.31368i	−0.886740	−	0.255843i
$610$	−22.5117	+	22.5117i	−0.911473	+	0.911473i
$611$	32.7847	+	18.9283i	1.32633	+	0.765756i
$612$	1.33993	+	9.74099i	0.0541635	+	0.393756i
$613$	18.0881	+	31.3295i	0.730571	+	1.26539i	0.956640	+	0.291274i	$0.0940792\pi$
$613$	18.0881	+	31.3295i	0.730571	+	1.26539i	−0.226069	+	0.974111i	$0.572588\pi$
$614$	8.47988	+	31.6473i	0.342220	+	1.27718i
$615$	−7.93524	+	22.0683i	−0.319980	+	0.889880i
$616$	−1.69386	−	26.3120i	−0.0682477	−	1.06014i
$617$	−41.2427	−	17.0833i	−1.66037	−	0.687747i	−0.662264	−	0.749271i	$-0.730404\pi$
$617$	−41.2427	−	17.0833i	−1.66037	−	0.687747i	−0.998106	+	0.0615236i	$0.980404\pi$
$618$	−30.7197	−	2.56739i	−1.23573	−	0.103276i
$619$	−8.45417	−	6.48711i	−0.339802	−	0.260739i	0.424737	−	0.905317i	$-0.360367\pi$
$619$	−8.45417	−	6.48711i	−0.339802	−	0.260739i	−0.764539	+	0.644578i	$0.777033\pi$
$620$	16.6306	+	4.45614i	0.667899	+	0.178963i
$621$	−0.213386	+	0.0913158i	−0.00856289	+	0.00366438i
$622$	−44.0597	+	18.2501i	−1.76663	+	0.731763i
$623$	5.69386	+	3.81410i	0.228120	+	0.152809i
$624$	12.0601	−	33.5398i	0.482792	−	1.34267i
$625$	27.0152	+	15.5972i	1.08061	+	0.623890i
$626$	−2.94821	−	22.3939i	−0.117834	−	0.895041i
$627$	4.02266	−	18.4846i	0.160650	−	0.738206i
$628$	−2.46969	−	1.42588i	−0.0985514	−	0.0568987i
$629$	−1.73467	+	19.3868i	−0.0691660	+	0.773004i
$630$	−33.4179	−	12.7419i	−1.33140	−	0.507650i
$631$	3.19507	−	3.19507i	0.127194	−	0.127194i	−0.640644	−	0.767838i	$-0.721333\pi$
$631$	3.19507	−	3.19507i	0.127194	−	0.127194i	0.767838	+	0.640644i	$0.221333\pi$
$632$	−12.9619	−	16.8923i	−0.515598	−	0.671940i
$633$	10.6570	+	16.5856i	0.423577	+	0.659216i
$634$	−17.9503	+	2.36320i	−0.712897	+	0.0938547i
$635$	−3.47058	+	26.3616i	−0.137726	+	1.04613i
$636$	−4.80823	−	10.2075i	−0.190659	−	0.404756i
$637$	−28.7962	−	3.85921i	−1.14095	−	0.152908i
$638$	29.0625	−	29.0625i	1.15060	−	1.15060i
$639$	0.754971	−	21.0430i	0.0298662	−	0.832447i
$640$	21.6441	−	28.2072i	0.855559	−	1.11499i
$641$	−2.13616	−	16.2257i	−0.0843732	−	0.640878i	−0.980420	−	0.196918i	$-0.936907\pi$
$641$	−2.13616	−	16.2257i	−0.0843732	−	0.640878i	0.896047	−	0.443960i	$-0.146427\pi$
$642$	−5.90508	+	11.4520i	−0.233055	+	0.451973i
$643$	−1.18266	+	2.85519i	−0.0466395	+	0.112598i	−0.945482	−	0.325673i	$-0.894409\pi$
$643$	−1.18266	+	2.85519i	−0.0466395	+	0.112598i	0.898843	+	0.438271i	$0.144409\pi$
$644$	0.0889952	−	0.0300945i	0.00350690	−	0.00118589i
$645$	2.33957	+	49.1977i	0.0921206	+	1.93716i
$646$	−3.32343	+	14.8523i	−0.130759	+	0.584357i
$647$	−3.93865	−	6.82194i	−0.154844	−	0.268198i	0.778158	−	0.628069i	$-0.216154\pi$
$647$	−3.93865	−	6.82194i	−0.154844	−	0.268198i	−0.933002	+	0.359870i	$0.882821\pi$
$648$	1.29938	−	18.0852i	0.0510444	−	0.710453i
$649$	−19.3199	−	25.1782i	−0.758372	−	0.988330i
$650$			15.7121i			0.616281i
$651$	35.7459	−	8.85021i	1.40099	−	0.346867i
$652$	12.1413	−	5.02911i	0.475492	−	0.196955i
$653$	−4.21222	+	31.9950i	−0.164837	+	1.25206i	0.686378	+	0.727245i	$0.259200\pi$
$653$	−4.21222	+	31.9950i	−0.164837	+	1.25206i	−0.851215	+	0.524817i	$0.824134\pi$
$654$	0.488948	−	2.24678i	0.0191194	−	0.0878560i
$655$	6.69230	−	24.9760i	0.261490	−	0.975893i
$656$	24.6935	+	3.25097i	0.964121	+	0.126929i
$657$	22.2063	+	41.8605i	0.866352	+	1.63313i
$658$	−38.1873	−	13.0124i	−1.48870	−	0.507275i
$659$	−10.0346			−0.390893			−0.195447	−	0.980714i	$-0.562616\pi$
$659$	−10.0346			−0.390893			−0.195447	+	0.980714i	$0.562616\pi$
$660$	14.0160	−	11.8539i	0.545572	−	0.461414i
$661$	−1.80346	+	6.73059i	−0.0701463	+	0.261790i	−0.992089	−	0.125537i	$-0.959935\pi$
$661$	−1.80346	+	6.73059i	−0.0701463	+	0.261790i	0.921943	+	0.387326i	$0.126601\pi$
$662$	2.66183	−	1.53681i	0.103455	−	0.0597298i
$663$	15.8781	−	25.0291i	0.616653	−	0.972049i
$664$			3.71830i			0.144298i
$665$	−11.8256	−	10.3951i	−0.458578	−	0.403106i
$666$	−6.94403	+	22.6355i	−0.269076	+	0.877108i
$667$	−0.192260	−	0.111002i	−0.00744435	−	0.00429800i
$668$	−10.4226	+	1.37216i	−0.403262	+	0.0530905i
$669$	−28.9434	−	20.0993i	−1.11902	−	0.777082i
$670$	0.428145	−	3.25208i	0.0165407	−	0.125639i
$671$	−24.7132	−	24.7132i	−0.954042	−	0.954042i
$672$	−2.91677	+	19.3000i	−0.112517	+	0.744513i
$673$	−11.6614	−	28.1532i	−0.449515	−	1.08522i	−0.972504	−	0.232885i	$-0.925183\pi$
$673$	−11.6614	−	28.1532i	−0.449515	−	1.08522i	0.522989	−	0.852339i	$-0.324817\pi$
$674$	55.2492	+	7.27370i	2.12812	+	0.280172i
$675$	3.17754	+	11.3288i	0.122303	+	0.436047i
$676$	2.90985	−	1.68000i	0.111917	−	0.0646155i
$677$	−11.9850	+	9.19638i	−0.460619	+	0.353445i	−0.812855	−	0.582466i	$-0.802088\pi$
$677$	−11.9850	+	9.19638i	−0.460619	+	0.353445i	0.352236	+	0.935911i	$0.385421\pi$
$678$	3.04469	+	2.76826i	0.116931	+	0.106314i
$679$	−4.25710	−	2.10553i	−0.163373	−	0.0808026i
$680$	17.1788	−	14.3571i	0.658777	−	0.550569i
$681$	−36.1186	−	18.6241i	−1.38407	−	0.713678i
$682$	−17.1997	+	64.1903i	−0.658612	+	2.45797i
$683$	−9.25698	+	1.21871i	−0.354209	+	0.0466325i	−0.305531	−	0.952182i	$-0.598834\pi$
$683$	−9.25698	+	1.21871i	−0.354209	+	0.0466325i	−0.0486775	+	0.998815i	$0.515501\pi$
$684$	−2.18816	+	4.78935i	−0.0836665	+	0.183125i
$685$	−21.0308	−	8.71125i	−0.803546	−	0.332840i
$686$	30.9028	−	1.91728i	1.17988	−	0.0732020i
$687$	−8.95286	−	19.0063i	−0.341573	−	0.725136i
$688$	50.5267	−	13.5386i	1.92631	−	0.516154i
$689$	−8.80332	+	32.8544i	−0.335380	+	1.25165i
$690$	−0.286343	−	0.198846i	−0.0109009	−	0.00756994i
$691$	−30.1850	−	3.97393i	−1.14829	−	0.151176i	−0.467734	−	0.883869i	$-0.654929\pi$
$691$	−30.1850	−	3.97393i	−1.14829	−	0.151176i	−0.680558	+	0.732694i	$0.738263\pi$
$692$	0.777528	−	1.87712i	0.0295572	−	0.0713573i
$693$	13.9880	−	36.6859i	0.531359	−	1.39358i
$694$	−47.3227	−	19.6017i	−1.79634	−	0.744070i
$695$	35.7089	−	9.56816i	1.35451	−	0.362941i
$696$	14.5904	−	9.37500i	0.553047	−	0.355358i
$697$	19.4496	+	7.12255i	0.736706	+	0.269786i
$698$	−2.36900	+	4.10322i	−0.0896679	+	0.155309i
$699$	14.0331	−	15.4344i	0.530781	−	0.583784i
$700$	−0.923665	−	4.67195i	−0.0349113	−	0.176583i
$701$	−7.62405			−0.287957			−0.143978	−	0.989581i	$-0.545990\pi$
$701$	−7.62405			−0.287957			−0.143978	+	0.989581i	$0.545990\pi$
$702$	25.1961	−	25.7904i	0.950964	−	0.973397i
$703$	−6.34535	+	8.26942i	−0.239319	+	0.311887i
$704$	10.9685	+	8.41643i	0.413391	+	0.317206i
$705$	12.9615	+	40.5585i	0.488159	+	1.52752i
$706$	−12.2177	+	12.2177i	−0.459818	+	0.459818i
$707$	5.86946	+	11.9370i	0.220744	+	0.448939i
$708$	3.76436	+	7.99147i	0.141473	+	0.300338i
$709$	−1.21985	−	1.58974i	−0.0458124	−	0.0597038i	0.769885	−	0.638182i	$-0.220313\pi$
$709$	−1.21985	−	1.58974i	−0.0458124	−	0.0597038i	−0.815698	+	0.578478i	$0.803647\pi$
$710$	27.3892	−	15.8132i	1.02790	−	0.593458i
$711$	−7.10284	−	30.9005i	−0.266377	−	1.15886i
$712$	−5.04071	+	1.35065i	−0.188908	+	0.0506179i
$713$	0.358952			0.0134429
$714$	−11.4265	+	29.4487i	−0.427627	+	1.10209i
$715$	−55.3357			−2.06944
$716$	−16.8082	+	4.50373i	−0.628150	+	0.168312i
$717$	5.48026	+	30.3892i	0.204664	+	1.13490i
$718$	28.5689	−	16.4943i	1.06618	−	0.615560i
$719$	0.195753	+	0.255110i	0.00730035	+	0.00951400i	0.796989	−	0.603993i	$-0.206425\pi$
$719$	0.195753	+	0.255110i	0.00730035	+	0.00951400i	−0.789689	+	0.613507i	$0.789758\pi$
$720$	35.4142	−	18.7867i	1.31981	−	0.700138i
$721$	−23.4013	−	15.6756i	−0.871511	−	0.583792i
$722$	16.6976	−	16.6976i	0.621420	−	0.621420i
$723$	−4.93686	+	1.57770i	−0.183604	+	0.0586754i
$724$	−4.69584	−	3.60325i	−0.174520	−	0.133914i
$725$	−6.85098	+	8.92838i	−0.254439	+	0.331592i
$726$	25.1848	+	29.7783i	0.934694	+	1.10518i
$727$	−19.3681			−0.718322			−0.359161	−	0.933276i	$-0.616937\pi$
$727$	−19.3681			−0.718322			−0.359161	+	0.933276i	$0.616937\pi$
$728$	16.6501	−	14.5676i	0.617094	−	0.539909i
$729$	12.9513	−	23.6910i	0.479676	−	0.877446i
$730$	−35.5863	+	61.6372i	−1.31711	+	2.28130i
$731$	43.4633	−	1.81175i	1.60755	−	0.0670101i
$732$	5.25874	+	8.18423i	0.194369	+	0.302498i
$733$	−2.91598	+	0.781333i	−0.107704	+	0.0288592i	−0.312269	−	0.949994i	$-0.601089\pi$
$733$	−2.91598	+	0.781333i	−0.107704	+	0.0288592i	0.204564	+	0.978853i	$0.434422\pi$
$734$	0.671507	+	0.278147i	0.0247858	+	0.0102666i
$735$	−21.0442	−	25.0001i	−0.776226	−	0.922143i
$736$	−0.0728100	+	0.175779i	−0.00268381	+	0.00647930i
$737$	3.57011	+	0.470014i	0.131507	+	0.0173132i
$738$	21.3541	+	13.3719i	0.786054	+	0.492226i
$739$	9.76907	−	36.4587i	0.359361	−	1.34115i	−0.515546	−	0.856862i	$-0.672411\pi$
$739$	9.76907	−	36.4587i	0.359361	−	1.34115i	0.874907	−	0.484292i	$-0.160923\pi$
$740$	−9.76979	+	2.61781i	−0.359144	+	0.0962325i
$741$	14.3596	−	6.76404i	0.527513	−	0.248483i
$742$	2.41277	−	36.1675i	0.0885754	−	1.32775i
$743$	−3.09070	−	1.28021i	−0.113387	−	0.0469663i	0.325269	−	0.945622i	$-0.394545\pi$
$743$	−3.09070	−	1.28021i	−0.113387	−	0.0469663i	−0.438656	+	0.898655i	$0.644545\pi$
$744$	−12.8512	+	24.9229i	−0.471147	+	0.913717i
$745$	38.3808	−	5.05293i	1.40616	−	0.185125i
$746$	6.95797	−	25.9675i	0.254749	−	0.950738i
$747$	−2.30094	+	5.03618i	−0.0841868	+	0.184264i
$748$	−10.3968	−	12.4402i	−0.380146	−	0.454859i
$749$	−9.79633	+	6.52924i	−0.357950	+	0.238573i
$750$	14.3627	−	15.7970i	0.524453	−	0.576823i
$751$	−15.0059	+	11.5144i	−0.547574	+	0.420168i	−0.845149	−	0.534530i	$-0.820489\pi$
$751$	−15.0059	+	11.5144i	−0.547574	+	0.420168i	0.297576	+	0.954698i	$0.403822\pi$
$752$	39.1625	−	22.6105i	1.42811	−	0.824520i
$753$	8.49422	+	47.1022i	0.309547	+	1.71650i
$754$	34.1912	+	4.50136i	1.24517	+	0.163930i
$755$	6.51988	+	15.7404i	0.237283	+	0.572851i
$756$	−5.97584	+	9.14989i	−0.217339	+	0.332778i
$757$	2.27639	+	2.27639i	0.0827369	+	0.0827369i	0.747264	−	0.664527i	$-0.231367\pi$
$757$	2.27639	+	2.27639i	0.0827369	+	0.0827369i	−0.664527	+	0.747264i	$0.731367\pi$
$758$	3.20226	−	24.3235i	0.116311	−	0.883471i
$759$	0.218291	−	0.314345i	0.00792348	−	0.0114100i
$760$	11.8867	−	1.56491i	0.431175	−	0.0567652i
$761$	37.7218	+	21.7787i	1.36741	+	0.789477i	0.990597	−	0.136810i	$-0.0436851\pi$
$761$	37.7218	+	21.7787i	1.36741	+	0.789477i	0.376817	+	0.926288i	$0.377018\pi$
$762$	26.8811	+	9.66581i	0.973800	+	0.350155i
$763$	1.38707	−	1.57795i	0.0502154	−	0.0571256i
$764$			14.6957i			0.531671i
$765$	32.1518	−	8.81518i	1.16245	−	0.318714i
$766$	−31.8665	+	18.3981i	−1.15138	+	0.664752i
$767$	6.89211	−	25.7217i	0.248860	−	0.928757i
$768$	−18.4144	−	21.7730i	−0.664472	−	0.785667i
$769$	40.1172			1.44666			0.723331	−	0.690502i	$-0.242610\pi$
$769$	40.1172			1.44666			0.723331	+	0.690502i	$0.242610\pi$
$770$	57.8511	−	11.4374i	2.08481	−	0.412176i
$771$	−3.66385	−	7.77810i	−0.131950	−	0.280122i
$772$	4.56597	+	0.601122i	0.164333	+	0.0216348i
$773$	−11.0166	+	41.1146i	−0.396241	+	1.47879i	0.423416	+	0.905936i	$0.360831\pi$
$773$	−11.0166	+	41.1146i	−0.396241	+	1.47879i	−0.819657	+	0.572855i	$0.805836\pi$
$774$	52.1813	+	8.78343i	1.87562	+	0.315714i
$775$	2.37509	−	18.0406i	0.0853159	−	0.648039i
$776$	3.34116	−	1.38395i	0.119941	−	0.0496810i
$777$	−15.5864	+	15.0023i	−0.559158	+	0.538203i
$778$			1.38806i			0.0497643i
$779$	6.75234	+	8.79982i	0.241928	+	0.315286i
$780$	15.0502	+	3.27525i	0.538883	+	0.117273i
$781$	17.3596	+	30.0677i	0.621175	+	1.07591i
$782$	−0.177102	+	0.251868i	−0.00633314	+	0.00900679i
$783$	25.5630	−	3.66906i	0.913548	−	0.131121i
$784$	−21.1914	+	27.4846i	−0.756836	+	0.981594i
$785$	−3.70018	+	8.93302i	−0.132065	+	0.318833i
$786$	−24.6905	−	12.7314i	−0.880679	−	0.454112i
$787$	−3.94708	−	29.9811i	−0.140698	−	1.06871i	−0.905471	−	0.424409i	$-0.860482\pi$
$787$	−3.94708	−	29.9811i	−0.140698	−	1.06871i	0.764772	−	0.644301i	$-0.222851\pi$
$788$	6.91933	−	9.01744i	0.246491	−	0.321233i
$789$	−33.0127	−	2.75903i	−1.17528	−	0.0982239i
$790$	33.6739	−	33.6739i	1.19806	−	1.19806i
$791$	1.20444	+	3.56176i	0.0428249	+	0.126642i
$792$	14.0104	+	26.4106i	0.497839	+	0.938462i
$793$	3.82772	−	29.0744i	0.135926	−	1.03246i
$794$	−36.3783	+	4.78930i	−1.29102	+	0.169966i
$795$	−32.1853	+	20.6805i	−1.14149	+	0.733463i
$796$	−3.63917	−	4.74266i	−0.128987	−	0.168099i
$797$	0.623342	−	0.623342i	0.0220799	−	0.0220799i	−0.695981	−	0.718061i	$-0.745030\pi$
$797$	0.623342	−	0.623342i	0.0220799	−	0.0220799i	0.718061	+	0.695981i	$0.245030\pi$
$798$	−13.6143	+	10.0395i	−0.481940	+	0.355395i
$799$	35.8882	−	11.2377i	1.26963	−	0.397562i
$800$	8.35274	+	4.82246i	0.295314	+	0.170500i
$801$	−7.66309	−	1.28989i	−0.270762	−	0.0455760i
$802$	0.237917	+	1.80716i	0.00840114	+	0.0638130i
$803$	−67.6648	−	39.0663i	−2.38784	−	1.37862i
$804$	−0.943178	−	0.339144i	−0.0332633	−	0.0119607i
$805$	−0.140549	−	0.285843i	−0.00495372	−	0.0100746i
$806$	−51.5156	+	21.3385i	−1.81456	+	0.751616i
$807$	3.86009	+	12.0788i	0.135882	+	0.425193i
$808$	−9.78387	−	2.62158i	−0.344195	−	0.0922268i
$809$	6.66155	+	5.11159i	0.234208	+	0.179714i	0.719197	−	0.694806i	$-0.244510\pi$
$809$	6.66155	+	5.11159i	0.234208	+	0.179714i	−0.484989	+	0.874520i	$0.661177\pi$
$810$	40.4824	−	2.39835i	1.42241	−	0.0842695i
$811$	−34.6783	−	14.3642i	−1.21772	−	0.504396i	−0.321036	−	0.947067i	$-0.604031\pi$
$811$	−34.6783	−	14.3642i	−1.21772	−	0.504396i	−0.896684	+	0.442671i	$0.854031\pi$
$812$	−10.4313	+	0.671526i	−0.366066	+	0.0235659i
$813$	1.87591	+	0.674534i	0.0657912	+	0.0236570i
$814$	−10.1042	−	37.7092i	−0.354151	−	1.32171i
$815$	−22.2788	−	38.5881i	−0.780394	−	1.35168i
$816$	−16.4091	−	31.3749i	−0.574433	−	1.09834i
$817$	20.1744	+	11.6477i	0.705812	+	0.407501i
$818$	−8.62376	+	8.62376i	−0.301523	+	0.301523i
$819$	31.5660	−	9.42742i	1.10301	−	0.329421i
$820$			10.7632i			0.375866i
$821$	−33.6696	+	25.8356i	−1.17508	+	0.901667i	−0.996609	−	0.0822787i	$-0.973780\pi$
$821$	−33.6696	+	25.8356i	−1.17508	+	0.901667i	−0.178466	+	0.983946i	$0.557114\pi$
$822$	−13.9495	+	20.0876i	−0.486545	+	0.700637i
$823$	−3.13800	+	4.08952i	−0.109384	+	0.142552i	−0.844837	−	0.535024i	$-0.820303\pi$
$823$	−3.13800	+	4.08952i	−0.109384	+	0.142552i	0.735453	+	0.677575i	$0.236969\pi$
$824$	20.7169	−	5.55108i	0.721708	−	0.193381i
$825$	−14.3543	−	13.0511i	−0.499754	−	0.454381i
$826$	−1.88895	+	28.3155i	−0.0657250	+	0.985221i
$827$	18.6904	+	45.1227i	0.649931	+	1.56907i	0.812876	+	0.582436i	$0.197900\pi$
$827$	18.6904	+	45.1227i	0.649931	+	1.56907i	−0.162946	+	0.986635i	$0.552100\pi$
$828$	−0.0779765	+	0.0725751i	−0.00270987	+	0.00252216i
$829$	−21.4309	−	37.1194i	−0.744326	−	1.28921i	−0.950509	−	0.310697i	$-0.899438\pi$
$829$	−21.4309	−	37.1194i	−0.744326	−	1.28921i	0.206183	−	0.978513i	$-0.433896\pi$
$830$	−8.24517	+	1.08550i	−0.286194	+	0.0376782i
$831$	9.73916	−	3.11240i	0.337848	−	0.107968i
$832$			11.6006i			0.402177i
$833$	−22.1889	+	18.4568i	−0.768800	+	0.639490i
$834$	−1.88660	−	39.6724i	−0.0653277	−	1.37374i
$835$	9.22517	+	34.4288i	0.319250	+	1.19146i
$836$	−1.13325	−	8.60785i	−0.0391941	−	0.297709i
$837$	−32.8286	+	25.8038i	−1.13472	+	0.891909i
$838$	−31.1080	+	23.8700i	−1.07461	+	0.824577i
$839$	12.1669	−	5.03969i	0.420047	−	0.173989i	−0.162640	−	0.986685i	$-0.552001\pi$
$839$	12.1669	−	5.03969i	0.420047	−	0.173989i	0.582688	+	0.812696i	$0.302001\pi$
$840$	24.8787	+	0.475079i	0.858397	+	0.0163918i
$841$	−3.03976	−	3.03976i	−0.104819	−	0.104819i
$842$	−2.62609	−	9.80069i	−0.0905010	−	0.337754i
$843$	−2.54834	+	3.66968i	−0.0877696	+	0.126390i
$844$	7.17818	+	5.50801i	0.247083	+	0.189594i
$845$	−6.93519	−	9.03812i	−0.238578	−	0.310921i
$846$	45.5387	−	4.34096i	1.56565	−	0.149245i
$847$	6.91131	+	34.9578i	0.237475	+	1.20116i
$848$	28.7299	+	28.7299i	0.986590	+	0.986590i
$849$	−24.0187	+	46.5804i	−0.824318	+	1.59864i
$850$	11.4869	+	10.5675i	0.393996	+	0.362463i
$851$	−0.182619	+	0.105435i	−0.00626009	+	0.00361427i
$852$	−2.94179	−	9.20529i	−0.100784	−	0.315368i
$853$	5.38162	−	12.9924i	0.184263	−	0.444851i	−0.804574	−	0.593853i	$-0.797606\pi$
$853$	5.38162	−	12.9924i	0.184263	−	0.444851i	0.988837	+	0.149002i	$0.0476061\pi$
$854$	2.00771	+	31.1872i	0.0687024	+	1.06720i
$855$	17.0680	+	5.23606i	0.583715	+	0.179070i
$856$	1.17011	−	8.88788i	0.0399936	−	0.303781i
$857$	24.3725	−	31.7628i	0.832547	−	1.08500i	−0.162609	−	0.986691i	$-0.551991\pi$
$857$	24.3725	−	31.7628i	0.832547	−	1.08500i	0.995156	−	0.0983059i	$-0.0313424\pi$
$858$	−12.6417	+	58.0905i	−0.431582	+	1.98318i
$859$	−5.03477	−	18.7900i	−0.171784	−	0.641107i	−0.997077	−	0.0764024i	$-0.975657\pi$
$859$	−5.03477	−	18.7900i	−0.171784	−	0.641107i	0.825293	−	0.564705i	$-0.191010\pi$
$860$	8.65052	+	20.8842i	0.294980	+	0.712145i
$861$	11.1277	+	20.1528i	0.379232	+	0.686806i
$862$	23.2706	−	56.1803i	0.792601	−	1.91351i
$863$	14.7307	−	25.5144i	0.501440	−	0.868520i	−0.498559	−	0.866856i	$-0.666137\pi$
$863$	14.7307	−	25.5144i	0.501440	−	0.868520i	0.999999	−	0.00166365i	$-0.000529557\pi$
$864$	−5.97715	−	21.3103i	−0.203347	−	0.724989i
$865$	−6.65412	−	1.78297i	−0.226247	−	0.0606227i
$866$	15.6922	−	27.1797i	0.533242	−	0.923602i
$867$	−7.61919	−	28.4420i	−0.258761	−	0.965941i
$868$	14.0636	−	9.37336i	0.477349	−	0.318153i
$869$	36.9670	+	36.9670i	1.25402	+	1.25402i
$870$	25.0481	+	29.6166i	0.849209	+	1.00410i
$871$	1.51071	+	2.61663i	0.0511885	+	0.0886610i
$872$	0.208813	+	1.58609i	0.00707131	+	0.0537119i
$873$	5.38177	+	0.193085i	0.182145	+	0.00653494i
$874$	−0.152333	+	0.0630986i	−0.00515275	+	0.00213434i
$875$	18.4797	−	6.24906i	0.624727	−	0.211257i
$876$	16.0912	+	14.6302i	0.543670	+	0.494310i
$877$	−44.4109	−	5.84681i	−1.49965	−	0.197433i	−0.664431	−	0.747349i	$-0.731326\pi$
$877$	−44.4109	−	5.84681i	−1.49965	−	0.197433i	−0.835220	+	0.549917i	$0.814660\pi$
$878$	−8.92434	−	6.84788i	−0.301182	−	0.231105i
$879$	−6.98226	−	38.7181i	−0.235506	−	1.30593i
$880$	−33.0503	+	57.2447i	−1.11412	+	1.92972i
$881$	−19.4721	−	8.06562i	−0.656033	−	0.271738i	0.0297354	−	0.999558i	$-0.490534\pi$
$881$	−19.4721	−	8.06562i	−0.656033	−	0.271738i	−0.685768	+	0.727820i	$0.740534\pi$
$882$	−31.0523	+	16.3804i	−1.04559	+	0.551556i
$883$	25.6678			0.863790			0.431895	−	0.901924i	$-0.357845\pi$
$883$	25.6678			0.863790			0.431895	+	0.901924i	$0.357845\pi$
$884$	2.97056	−	13.2753i	0.0999107	−	0.446498i
$885$	25.1978	−	16.1908i	0.847015	−	0.544246i
$886$	50.9169	+	13.6431i	1.71059	+	0.458350i
$887$	2.16678	−	1.66263i	0.0727534	−	0.0558256i	−0.571744	−	0.820432i	$-0.693733\pi$
$887$	2.16678	−	1.66263i	0.0727534	−	0.0558256i	0.644498	+	0.764606i	$0.277066\pi$
$888$	−0.782482	−	16.4544i	−0.0262584	−	0.552174i
$889$	17.1866	+	19.6436i	0.576421	+	0.658826i
$890$	−4.46656	−	10.7832i	−0.149720	−	0.361455i
$891$	2.63289	+	44.4412i	0.0882052	+	1.48884i
$892$	−15.6214	−	4.18574i	−0.523043	−	0.140149i
$893$	19.4525	+	5.21229i	0.650954	+	0.174423i
$894$	3.46383	−	41.4459i	0.115848	−	1.38616i
$895$	22.5781	+	54.5083i	0.754702	+	1.82201i
$896$	−6.76913	−	34.2387i	−0.226141	−	1.14383i
$897$	0.320755	−	0.0152533i	0.0107097	−	0.000509294i
$898$	−5.98888	+	4.59543i	−0.199852	+	0.153351i
$899$	−38.5779	−	10.3369i	−1.28664	−	0.344755i
$900$	3.13161	+	4.39925i	0.104387	+	0.146642i
$901$	18.0984	+	28.5329i	0.602947	+	0.950569i
$902$	−41.5434			−1.38325
$903$	37.7887	+	30.1598i	1.25753	+	1.00366i
$904$	−2.64509	−	1.09563i	−0.0879743	−	0.0364402i
$905$	−10.0343	+	17.3799i	−0.333552	+	0.577729i
$906$	18.0135	−	3.24848i	0.598457	−	0.107923i
$907$	−4.99215	−	3.83061i	−0.165762	−	0.127193i	0.522550	−	0.852609i	$-0.324981\pi$
$907$	−4.99215	−	3.83061i	−0.165762	−	0.127193i	−0.688311	+	0.725416i	$0.741648\pi$
$908$	−18.4911	−	2.43440i	−0.613650	−	0.0807885i
$909$	−11.6293	−	9.60513i	−0.385719	−	0.318582i
$910$	37.1636	+	32.6681i	1.23196	+	1.08294i
$911$	−40.3095	+	16.6967i	−1.33551	+	0.553187i	−0.932223	−	0.361886i	$-0.882133\pi$
$911$	−40.3095	+	16.6967i	−1.33551	+	0.553187i	−0.403289	+	0.915073i	$0.632133\pi$
$912$	1.57914	−	18.8949i	0.0522905	−	0.625673i
$913$	−1.19165	−	9.05148i	−0.0394379	−	0.299560i
$914$	17.0443	+	29.5217i	0.563777	+	0.976490i
$915$	25.1844	−	21.2995i	0.832571	−	0.704140i
$916$	−6.81813	−	6.81813i	−0.225277	−	0.225277i
$917$	−14.0770	−	21.1209i	−0.464865	−	0.697473i
$918$	−1.90876	−	35.7663i	−0.0629985	−	1.18046i
$919$	12.2089	−	21.1465i	0.402736	−	0.697559i	−0.591319	−	0.806438i	$-0.701393\pi$
$919$	12.2089	−	21.1465i	0.402736	−	0.697559i	0.994055	+	0.108879i	$0.0347260\pi$
$920$	0.234283	+	0.0627760i	0.00772409	+	0.00206966i
$921$	−6.02423	−	33.4056i	−0.198505	−	1.10075i
$922$	17.9415	−	31.0756i	0.590873	−	1.02342i
$923$	−11.1483	+	26.9143i	−0.366949	+	0.885894i
$924$	0.344034	−	18.0162i	0.0113179	−	0.592689i
$925$	4.09074	+	9.87591i	0.134503	+	0.324718i
$926$	1.34487	+	5.01912i	0.0441951	+	0.164938i
$927$	31.4947	+	5.30135i	1.03442	+	0.174119i
$928$	12.8871	−	16.7949i	0.423041	−	0.551318i
$929$	1.19093	−	9.04598i	0.0390730	−	0.296789i	−0.960740	−	0.277450i	$-0.910511\pi$
$929$	1.19093	−	9.04598i	0.0390730	−	0.296789i	0.999813	−	0.0193386i	$-0.00615607\pi$
$930$	−59.0170	−	21.2211i	−1.93524	−	0.695868i
$931$	−15.3282	+	1.98176i	−0.502363	+	0.0649496i
$932$	3.66375	−	8.84508i	0.120010	−	0.289730i
$933$	47.0636	−	15.0404i	1.54079	−	0.492400i
$934$	−9.93905	+	5.73831i	−0.325216	+	0.187763i
$935$	−37.2172	+	40.4550i	−1.21713	+	1.32302i
$936$	−10.4246	+	22.8168i	−0.340738	+	0.745792i
$937$	−3.38191	−	3.38191i	−0.110482	−	0.110482i	0.649705	−	0.760187i	$-0.274893\pi$
$937$	−3.38191	−	3.38191i	−0.110482	−	0.110482i	−0.760187	+	0.649705i	$0.774893\pi$
$938$	−2.12022	−	2.42332i	−0.0692275	−	0.0791242i
$939$	1.11157	+	23.3747i	0.0362748	+	0.762805i
$940$	11.8963	+	15.5036i	0.388015	+	0.505671i
$941$	−37.2285	−	28.5664i	−1.21361	−	0.931239i	−0.214648	−	0.976692i	$-0.568860\pi$
$941$	−37.2285	−	28.5664i	−1.21361	−	0.931239i	−0.998966	+	0.0454528i	$0.985527\pi$
$942$	8.53240	+	5.92518i	0.278001	+	0.193053i
$943$	0.0580777	+	0.216749i	0.00189127	+	0.00705832i
$944$	−22.4926	−	22.4926i	−0.732073	−	0.732073i
$945$	33.4025	+	16.0387i	1.08658	+	0.521740i
$946$	−80.6084	+	33.3891i	−2.62081	+	1.08557i
$947$	3.47064	−	2.66312i	0.112781	−	0.0865397i	−0.550831	−	0.834617i	$-0.685689\pi$
$947$	3.47064	−	2.66312i	0.112781	−	0.0865397i	0.663612	+	0.748077i	$0.269023\pi$
$948$	−7.86624	−	12.2423i	−0.255483	−	0.397611i
$949$	−8.55713	−	64.9978i	−0.277776	−	2.10992i
$950$	2.16333	+	8.07366i	0.0701877	+	0.261944i
$951$	18.7365	−	0.891004i	0.607572	−	0.0288928i
$952$	0.548311	−	21.9703i	0.0177708	−	0.712062i
$953$		−	21.4025i		−	0.693295i	−0.937996	−	0.346647i	$-0.887320\pi$
$953$		−	21.4025i		−	0.693295i	0.937996	−	0.346647i	$-0.112680\pi$
$954$	14.3571	+	38.5121i	0.464830	+	1.24688i
$955$	49.4003	−	6.50367i	1.59856	−	0.210454i
$956$	7.08607	+	12.2734i	0.229180	+	0.396951i
$957$	−32.5129	+	27.4975i	−1.05099	+	0.888869i
$958$	−3.32083	−	8.01719i	−0.107291	−	0.259024i
$959$	−20.0526	+	9.85988i	−0.647532	+	0.318392i
$960$	−8.77750	+	9.65400i	−0.283293	+	0.311582i
$961$	32.4320	−	8.69013i	1.04619	−	0.280327i
$962$	19.9411	−	25.9878i	0.642927	−	0.837879i
$963$	7.08477	−	11.3139i	0.228304	−	0.364586i
$964$	−1.88713	+	1.44804i	−0.0607803	+	0.0466384i
$965$		−	15.6148i		−	0.502657i
$966$	−0.332182	+	0.0822439i	−0.0106878	+	0.00264615i
$967$	−37.0583	+	37.0583i	−1.19172	+	1.19172i	−0.215131	+	0.976585i	$0.569018\pi$
$967$	−37.0583	+	37.0583i	−1.19172	+	1.19172i	−0.976585	+	0.215131i	$0.930982\pi$
$968$	−23.4990	−	13.5672i	−0.755288	−	0.436066i
$969$	4.71278	−	15.0473i	0.151396	−	0.483390i
$970$	4.04425	+	7.00484i	0.129853	+	0.224912i
$971$	2.47002	+	9.21823i	0.0792666	+	0.295827i	0.994167	−	0.107853i	$-0.0343976\pi$
$971$	2.47002	+	9.21823i	0.0792666	+	0.295827i	−0.914900	+	0.403680i	$0.867731\pi$
$972$	1.91432	−	12.2429i	0.0614020	−	0.392693i
$973$	16.0883	−	32.5285i	0.515767	−	1.04282i
$974$	−9.72396	−	4.02780i	−0.311576	−	0.129059i
$975$	1.35573	−	16.2218i	0.0434182	−	0.519513i
$976$	−27.7912	−	21.3250i	−0.889576	−	0.682596i
$977$	−39.0718	−	10.4693i	−1.25002	−	0.334941i	−0.427674	−	0.903933i	$-0.640667\pi$
$977$	−39.0718	−	10.4693i	−1.25002	−	0.334941i	−0.822343	+	0.568992i	$0.807334\pi$
$978$	−45.5988	+	14.5723i	−1.45809	+	0.465970i
$979$	11.8377	−	4.90336i	0.378336	−	0.156712i
$980$	−12.9709	−	7.52903i	−0.414341	−	0.240506i
$981$	−0.698673	+	2.27747i	−0.0223069	+	0.0727140i
$982$	−48.1225	−	27.7835i	−1.53565	−	0.886608i
$983$	−1.62386	−	12.3345i	−0.0517932	−	0.393408i	−0.997632	−	0.0687726i	$-0.978092\pi$
$983$	−1.62386	−	12.3345i	−0.0517932	−	0.393408i	0.945839	−	0.324636i	$-0.105242\pi$
$984$	−17.1287	−	3.72757i	−0.546042	−	0.118831i
$985$	−33.3748	−	19.2689i	−1.06341	−	0.613959i
$986$	26.2869	−	21.9691i	0.837146	−	0.699639i
$987$	38.3032	+	16.7295i	1.21921	+	0.532505i
$988$	5.15121	−	5.15121i	0.163882	−	0.163882i
$989$	0.286895	+	0.373889i	0.00912273	+	0.0118890i
$990$	−54.4743	+	38.7776i	−1.73131	+	1.23243i
$991$	−18.0609	+	2.37776i	−0.573722	+	0.0755319i	−0.411804	−	0.911272i	$-0.635101\pi$
$991$	−18.0609	+	2.37776i	−0.573722	+	0.0755319i	−0.161918	+	0.986804i	$0.551768\pi$
$992$	−4.46771	+	33.9356i	−0.141850	+	1.07746i
$993$	−2.88078	+	1.35698i	−0.0914188	+	0.0430625i
$994$	6.09208	−	30.4420i	0.193229	−	0.965560i
$995$	−14.3321	+	14.3321i	−0.454359	+	0.454359i
$996$	−0.211641	+	2.53235i	−0.00670609	+	0.0802406i
$997$	1.94471	−	2.53439i	0.0615895	−	0.0802650i	−0.761543	−	0.648115i	$-0.775558\pi$
$997$	1.94471	−	2.53439i	0.0615895	−	0.0802650i	0.823132	+	0.567850i	$0.192224\pi$
$998$	−0.447961	−	3.40260i	−0.0141800	−	0.107708i
$999$	9.12240	−	22.7706i	0.288620	−	0.720429i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	357.2.bj.a.26.10	✓	352
3.2	odd	2	inner	357.2.bj.a.26.35	yes	352
7.3	odd	6	inner	357.2.bj.a.332.35	yes	352
17.2	even	8	inner	357.2.bj.a.257.10	yes	352
21.17	even	6	inner	357.2.bj.a.332.10	yes	352
51.2	odd	8	inner	357.2.bj.a.257.35	yes	352
119.87	odd	24	inner	357.2.bj.a.206.35	yes	352
357.206	even	24	inner	357.2.bj.a.206.10	yes	352

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
357.2.bj.a.26.10	✓	352	1.1	even	1	trivial
357.2.bj.a.26.35	yes	352	3.2	odd	2	inner
357.2.bj.a.206.10	yes	352	357.206	even	24	inner
357.2.bj.a.206.35	yes	352	119.87	odd	24	inner
357.2.bj.a.257.10	yes	352	17.2	even	8	inner
357.2.bj.a.257.35	yes	352	51.2	odd	8	inner
357.2.bj.a.332.10	yes	352	21.17	even	6	inner
357.2.bj.a.332.35	yes	352	7.3	odd	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 357 = 3 \cdot 7 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	357.bj (of order \(24\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.61484 + 0.432695i) q^{2} +(1.70456 - 0.307393i) q^{3} +(0.688428 - 0.397464i) q^{4} +(-1.64076 - 2.13829i) q^{5} +(-2.61957 + 1.23394i) q^{6} +(-2.63988 - 0.176109i) q^{7} +(1.42457 - 1.42457i) q^{8} +(2.81102 - 1.04794i) q^{9} +(3.57479 + 2.74304i) q^{10} +(-3.01128 + 3.92438i) q^{11} +(1.05129 - 0.889118i) q^{12} -4.15052 q^{13} +(4.33919 - 0.857876i) q^{14} +(-3.45407 - 3.14047i) q^{15} +(-2.47897 + 4.29371i) q^{16} +(-2.79152 + 3.03437i) q^{17} +(-4.08591 + 2.90856i) q^{18} +(-2.13274 + 0.571466i) q^{19} +(-1.97944 - 0.819911i) q^{20} +(-4.55396 + 0.511294i) q^{21} +(3.16468 - 7.64020i) q^{22} +(-0.0442863 - 0.00583040i) q^{23} +(1.99035 - 2.86616i) q^{24} +(-0.586062 + 2.18721i) q^{25} +(6.70242 - 1.79591i) q^{26} +(4.46941 - 2.65035i) q^{27} +(-1.88737 + 0.928021i) q^{28} +(4.59170 + 1.90195i) q^{29} +(6.93662 + 3.57679i) q^{30} +(-7.96718 + 1.04890i) q^{31} +(1.10242 - 4.11429i) q^{32} +(-3.92657 + 7.61497i) q^{33} +(3.19490 - 6.10790i) q^{34} +(3.95485 + 5.93378i) q^{35} +(1.51867 - 1.83871i) q^{36} +(3.74525 - 2.87383i) q^{37} +(3.19676 - 1.84565i) q^{38} +(-7.07479 + 1.27584i) q^{39} +(-5.38351 - 0.708753i) q^{40} +(-1.92244 - 4.64118i) q^{41} +(7.13268 - 2.79613i) q^{42} +(-7.46037 - 7.46037i) q^{43} +(-0.513251 + 3.89853i) q^{44} +(-6.85301 - 4.29135i) q^{45} +(0.0740379 - 0.00974728i) q^{46} +(-7.89894 - 4.56046i) q^{47} +(-2.90569 + 8.08088i) q^{48} +(6.93797 + 0.929815i) q^{49} -3.78558i q^{50} +(-3.82556 + 6.03035i) q^{51} +(-2.85733 + 1.64968i) q^{52} +(2.12102 - 7.91574i) q^{53} +(-6.07058 + 6.21378i) q^{54} +13.3322 q^{55} +(-4.01157 + 3.50981i) q^{56} +(-3.45971 + 1.62968i) q^{57} +(-8.23782 - 1.08453i) q^{58} +(-1.66054 + 6.19722i) q^{59} +(-3.62610 - 0.789118i) q^{60} +(-0.922226 + 7.00500i) q^{61} +(12.4119 - 5.14116i) q^{62} +(-7.60531 + 2.27138i) q^{63} -2.79497i q^{64} +(6.81002 + 8.87499i) q^{65} +(3.04582 - 13.9959i) q^{66} +(-0.363981 - 0.630434i) q^{67} +(-0.715708 + 3.19848i) q^{68} +(-0.0772806 + 0.00367504i) q^{69} +(-8.95397 - 7.87085i) q^{70} +(2.68599 - 6.48456i) q^{71} +(2.51163 - 5.49735i) q^{72} +(2.06170 + 15.6602i) q^{73} +(-4.80448 + 6.26133i) q^{74} +(-0.326642 + 3.90838i) q^{75} +(-1.24110 + 1.24110i) q^{76} +(8.64055 - 9.82959i) q^{77} +(10.8726 - 5.12150i) q^{78} +(1.37950 - 10.4784i) q^{79} +(13.2486 - 1.74421i) q^{80} +(6.80366 - 5.89154i) q^{81} +(5.11264 + 6.66293i) q^{82} +(-1.30506 + 1.30506i) q^{83} +(-2.93186 + 2.16203i) q^{84} +(11.0686 + 0.990381i) q^{85} +(15.2754 + 8.81923i) q^{86} +(8.41146 + 1.83052i) q^{87} +(1.30077 + 9.88032i) q^{88} +(-2.24326 - 1.29515i) q^{89} +(12.9233 + 3.96457i) q^{90} +(10.9569 + 0.730944i) q^{91} +(-0.0328053 + 0.0135884i) q^{92} +(-13.2581 + 4.23696i) q^{93} +(14.7288 + 3.94657i) q^{94} +(4.72128 + 3.62277i) q^{95} +(0.614434 - 7.35191i) q^{96} +(1.65844 + 0.686947i) q^{97} +(-11.6060 + 1.50052i) q^{98} +(-4.35227 + 14.1871i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 352 q - 12 q^{3} - 16 q^{7} - 4 q^{9} - 24 q^{10} - 12 q^{12} - 24 q^{15} + 112 q^{16} - 24 q^{18} - 24 q^{19} - 80 q^{22} - 60 q^{24} - 8 q^{25} - 72 q^{28} - 24 q^{31} + 24 q^{33} - 64 q^{36} - 40 q^{37}+ \cdots + 256 q^{99}+O(q^{100}) \) 352 * q - 12 * q^3 - 16 * q^7 - 4 * q^9 - 24 * q^10 - 12 * q^12 - 24 * q^15 + 112 * q^16 - 24 * q^18 - 24 * q^19 - 80 * q^22 - 60 * q^24 - 8 * q^25 - 72 * q^28 - 24 * q^31 + 24 * q^33 - 64 * q^36 - 40 * q^37 - 24 * q^39 - 24 * q^40 + 68 * q^42 - 48 * q^45 - 40 * q^46 + 48 * q^49 - 20 * q^51 - 240 * q^52 - 16 * q^57 - 8 * q^58 + 44 * q^60 - 24 * q^61 + 88 * q^63 - 12 * q^66 - 16 * q^67 + 64 * q^70 - 120 * q^73 - 156 * q^75 - 176 * q^78 - 24 * q^79 + 120 * q^82 - 104 * q^84 + 112 * q^85 + 132 * q^87 - 24 * q^88 - 96 * q^91 - 8 * q^93 - 120 * q^94 + 60 * q^96 + 256 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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