LMFDB - Embedded newform 336.2.bs.a.187.32

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [336,2,Mod(19,336)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("336.19"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(336, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([6, 9, 0, 10])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 336 = 2^{4} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	336.bs (of order $12$, degree $4$, 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:	$2.68297350792$
Analytic rank:	$0$
Dimension:	$128$
Relative dimension:	$32$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			187.32
Character	$\chi$	$=$	336.187
Dual form			336.2.bs.a.115.32

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.41354 - 0.0438036i) q^{2} +(0.965926 + 0.258819i) q^{3} +(1.99616 - 0.123836i) q^{4} +(0.137704 + 0.513920i) q^{5} +(1.37671 + 0.323539i) q^{6} +(1.08086 + 2.41490i) q^{7} +(2.81622 - 0.262485i) q^{8} +(0.866025 + 0.500000i) q^{9} +(0.217161 + 0.720412i) q^{10} +(-6.25340 - 1.67559i) q^{11} +(1.96020 + 0.397029i) q^{12} +(-3.08799 - 3.08799i) q^{13} +(1.63361 + 3.36620i) q^{14} +0.532049i q^{15} +(3.96933 - 0.494393i) q^{16} +(-1.95705 + 1.12990i) q^{17} +(1.24606 + 0.668833i) q^{18} +(0.0316062 + 0.117956i) q^{19} +(0.338522 + 1.00881i) q^{20} +(0.419005 + 2.61236i) q^{21} +(-8.91279 - 2.09459i) q^{22} +(2.16025 - 3.74167i) q^{23} +(2.78820 + 0.475350i) q^{24} +(4.08498 - 2.35846i) q^{25} +(-4.50025 - 4.22972i) q^{26} +(0.707107 + 0.707107i) q^{27} +(2.45662 + 4.68669i) q^{28} +(4.37123 - 4.37123i) q^{29} +(0.0233056 + 0.752070i) q^{30} +(1.25747 + 2.17799i) q^{31} +(5.58913 - 0.872712i) q^{32} +(-5.60664 - 3.23700i) q^{33} +(-2.71686 + 1.68288i) q^{34} +(-1.09223 + 0.888016i) q^{35} +(1.79065 + 0.890836i) q^{36} +(-2.07025 + 0.554721i) q^{37} +(0.0498434 + 0.165351i) q^{38} +(-2.18354 - 3.78200i) q^{39} +(0.522702 + 1.41117i) q^{40} -8.63061 q^{41} +(0.706709 + 3.67431i) q^{42} +(-2.21407 + 2.21407i) q^{43} +(-12.6903 - 2.57036i) q^{44} +(-0.137704 + 0.513920i) q^{45} +(2.88969 - 5.38361i) q^{46} +(-4.58222 + 7.93663i) q^{47} +(3.96204 + 0.549791i) q^{48} +(-4.66350 + 5.22033i) q^{49} +(5.67095 - 3.51271i) q^{50} +(-2.18280 + 0.584880i) q^{51} +(-6.54654 - 5.78173i) q^{52} +(2.23326 - 8.33463i) q^{53} +(1.03049 + 0.968546i) q^{54} -3.44448i q^{55} +(3.67781 + 6.51719i) q^{56} +0.122117i q^{57} +(5.98741 - 6.37036i) q^{58} +(-1.49402 + 5.57577i) q^{59} +(0.0658867 + 1.06206i) q^{60} +(9.61887 - 2.57737i) q^{61} +(1.87288 + 3.02359i) q^{62} +(-0.271401 + 2.63179i) q^{63} +(7.86220 - 1.47843i) q^{64} +(1.16175 - 2.01221i) q^{65} +(-8.06697 - 4.33002i) q^{66} +(-1.99445 + 7.44337i) q^{67} +(-3.76666 + 2.49782i) q^{68} +(3.05506 - 3.05506i) q^{69} +(-1.50500 + 1.30309i) q^{70} -3.75185 q^{71} +(2.57016 + 1.18079i) q^{72} +(-0.753853 - 1.30571i) q^{73} +(-2.90207 + 0.874802i) q^{74} +(4.55620 - 1.22083i) q^{75} +(0.0776984 + 0.231546i) q^{76} +(-2.71264 - 16.9124i) q^{77} +(-3.25218 - 5.25035i) q^{78} +(4.23158 + 2.44310i) q^{79} +(0.800672 + 1.97184i) q^{80} +(0.500000 + 0.866025i) q^{81} +(-12.1997 + 0.378051i) q^{82} +(-10.6169 + 10.6169i) q^{83} +(1.15991 + 5.16281i) q^{84} +(-0.850172 - 0.850172i) q^{85} +(-3.03269 + 3.22666i) q^{86} +(5.35364 - 3.09093i) q^{87} +(-18.0508 - 3.07741i) q^{88} +(5.81809 - 10.0772i) q^{89} +(-0.172138 + 0.732475i) q^{90} +(4.11952 - 10.7949i) q^{91} +(3.84886 - 7.73649i) q^{92} +(0.650912 + 2.42924i) q^{93} +(-6.12947 + 11.4194i) q^{94} +(-0.0562677 + 0.0324861i) q^{95} +(5.62456 + 0.603598i) q^{96} +15.5828i q^{97} +(-6.36335 + 7.58339i) q^{98} +(-4.57780 - 4.57780i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 128 q + 4 q^{4} - 24 q^{8} + 36 q^{10} - 8 q^{11} - 32 q^{14} - 4 q^{16} + 4 q^{18} + 16 q^{22} + 16 q^{23} - 32 q^{28} + 32 q^{29} - 24 q^{35} - 16 q^{37} + 60 q^{40} - 20 q^{42} - 16 q^{43} - 12 q^{44}+ \cdots - 16 q^{99}+O(q^{100}) $ 128 * q + 4 * q^4 - 24 * q^8 + 36 * q^10 - 8 * q^11 - 32 * q^14 - 4 * q^16 + 4 * q^18 + 16 * q^22 + 16 * q^23 - 32 * q^28 + 32 * q^29 - 24 * q^35 - 16 * q^37 + 60 * q^40 - 20 * q^42 - 16 * q^43 - 12 * q^44 - 20 * q^46 - 32 * q^50 - 144 * q^52 - 16 * q^53 - 56 * q^56 - 40 * q^58 - 96 * q^59 - 24 * q^60 - 32 * q^64 - 72 * q^66 + 16 * q^67 - 60 * q^68 + 28 * q^70 + 128 * q^71 - 4 * q^72 - 72 * q^74 + 72 * q^78 - 36 * q^80 + 64 * q^81 - 60 * q^82 + 24 * q^84 - 44 * q^86 - 48 * q^88 - 8 * q^91 + 56 * q^92 + 36 * q^94 + 60 * q^96 + 148 * q^98 - 16 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/336\mathbb{Z}\right)^\times$.

$n$	$85$	$113$	$127$	$241$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$	$-1$	$e\left(\frac{5}{6}\right)$

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 $

$2$	1.41354	−	0.0438036i	0.999520	−	0.0309738i
$2$	1.41354	−	0.0438036i	0.999520	−	0.0309738i
$3$	0.965926	+	0.258819i	0.557678	+	0.149429i
$3$	0.965926	+	0.258819i	0.557678	+	0.149429i
$4$	1.99616	−	0.123836i	0.998081	−	0.0619179i
$5$	0.137704	+	0.513920i	0.0615833	+	0.229832i	0.989857	−	0.142065i	$-0.0453742\pi$
$5$	0.137704	+	0.513920i	0.0615833	+	0.229832i	−0.928274	+	0.371897i	$0.878708\pi$
$6$	1.37671	+	0.323539i	0.562038	+	0.132084i
$7$	1.08086	+	2.41490i	0.408525	+	0.912747i
$7$	1.08086	+	2.41490i	0.408525	+	0.912747i
$8$	2.81622	−	0.262485i	0.995685	−	0.0928025i
$9$	0.866025	+	0.500000i	0.288675	+	0.166667i
$10$	0.217161	+	0.720412i	0.0686725	+	0.227814i
$11$	−6.25340	−	1.67559i	−1.88547	−	0.505210i	−0.999109	−	0.0422154i	$-0.986558\pi$
$11$	−6.25340	−	1.67559i	−1.88547	−	0.505210i	−0.886361	−	0.462995i	$-0.846775\pi$
$12$	1.96020	+	0.397029i	0.565860	+	0.114612i
$13$	−3.08799	−	3.08799i	−0.856455	−	0.856455i	0.134463	−	0.990919i	$-0.457069\pi$
$13$	−3.08799	−	3.08799i	−0.856455	−	0.856455i	−0.990919	+	0.134463i	$0.957069\pi$
$14$	1.63361	+	3.36620i	0.436601	+	0.899655i
$15$			0.532049i			0.137374i
$16$	3.96933	−	0.494393i	0.992332	−	0.123598i
$17$	−1.95705	+	1.12990i	−0.474653	+	0.274041i	−0.718186	−	0.695852i	$-0.755027\pi$
$17$	−1.95705	+	1.12990i	−0.474653	+	0.274041i	0.243532	+	0.969893i	$0.421694\pi$
$18$	1.24606	+	0.668833i	0.293699	+	0.157645i
$19$	0.0316062	+	0.117956i	0.00725097	+	0.0270610i	0.969457	−	0.245263i	$-0.0788744\pi$
$19$	0.0316062	+	0.117956i	0.00725097	+	0.0270610i	−0.962206	+	0.272324i	$0.912208\pi$
$20$	0.338522	+	1.00881i	0.0756958	+	0.225578i
$21$	0.419005	+	2.61236i	0.0914344	+	0.570064i
$22$	−8.91279	−	2.09459i	−1.90021	−	0.446567i
$23$	2.16025	−	3.74167i	0.450444	−	0.780192i	−0.547970	−	0.836498i	$-0.684599\pi$
$23$	2.16025	−	3.74167i	0.450444	−	0.780192i	0.998414	+	0.0563065i	$0.0179324\pi$
$24$	2.78820	+	0.475350i	0.569138	+	0.0970305i
$25$	4.08498	−	2.35846i	0.816995	−	0.471692i
$26$	−4.50025	−	4.22972i	−0.882572	−	0.829517i
$27$	0.707107	+	0.707107i	0.136083	+	0.136083i
$28$	2.45662	+	4.68669i	0.464257	+	0.885701i
$29$	4.37123	−	4.37123i	0.811717	−	0.811717i	−0.173174	−	0.984891i	$-0.555402\pi$
$29$	4.37123	−	4.37123i	0.811717	−	0.811717i	0.984891	+	0.173174i	$0.0554023\pi$
$30$	0.0233056	+	0.752070i	0.00425501	+	0.137309i
$31$	1.25747	+	2.17799i	0.225848	+	0.391179i	0.956573	−	0.291492i	$-0.0941516\pi$
$31$	1.25747	+	2.17799i	0.225848	+	0.391179i	−0.730726	+	0.682671i	$0.760818\pi$
$32$	5.58913	−	0.872712i	0.988028	−	0.154275i
$33$	−5.60664	−	3.23700i	−0.975991	−	0.563489i
$34$	−2.71686	+	1.68288i	−0.465937	+	0.288612i
$35$	−1.09223	+	0.888016i	−0.184620	+	0.150102i
$36$	1.79065	+	0.890836i	0.298441	+	0.148473i
$37$	−2.07025	+	0.554721i	−0.340346	+	0.0911956i	−0.424944	−	0.905220i	$-0.639706\pi$
$37$	−2.07025	+	0.554721i	−0.340346	+	0.0911956i	0.0845975	+	0.996415i	$0.473040\pi$
$38$	0.0498434	+	0.165351i	0.00808567	+	0.0268234i
$39$	−2.18354	−	3.78200i	−0.349646	−	0.605605i
$40$	0.522702	+	1.41117i	0.0826465	+	0.223125i
$41$	−8.63061			−1.34787			−0.673937	−	0.738789i	$-0.735398\pi$
$41$	−8.63061			−1.34787			−0.673937	+	0.738789i	$0.735398\pi$
$42$	0.706709	+	3.67431i	0.109048	+	0.566959i
$43$	−2.21407	+	2.21407i	−0.337643	+	0.337643i	−0.855480	−	0.517836i	$-0.826738\pi$
$43$	−2.21407	+	2.21407i	−0.337643	+	0.337643i	0.517836	+	0.855480i	$0.326738\pi$
$44$	−12.6903	−	2.57036i	−1.91313	−	0.387496i
$45$	−0.137704	+	0.513920i	−0.0205278	+	0.0766106i
$46$	2.88969	−	5.38361i	0.426062	−	0.793769i
$47$	−4.58222	+	7.93663i	−0.668385	+	1.15768i	0.309970	+	0.950746i	$0.399681\pi$
$47$	−4.58222	+	7.93663i	−0.668385	+	1.15768i	−0.978356	+	0.206931i	$0.933652\pi$
$48$	3.96204	+	0.549791i	0.571871	+	0.0793556i
$49$	−4.66350	+	5.22033i	−0.666214	+	0.745761i
$50$	5.67095	−	3.51271i	0.801993	−	0.496772i
$51$	−2.18280	+	0.584880i	−0.305653	+	0.0818995i
$52$	−6.54654	−	5.78173i	−0.907842	−	0.801782i
$53$	2.23326	−	8.33463i	0.306761	−	1.14485i	−0.624657	−	0.780899i	$-0.714761\pi$
$53$	2.23326	−	8.33463i	0.306761	−	1.14485i	0.931418	−	0.363950i	$-0.118572\pi$
$54$	1.03049	+	0.968546i	0.140232	+	0.131802i
$55$		−	3.44448i		−	0.464454i
$56$	3.67781	+	6.51719i	0.491468	+	0.870896i
$57$			0.122117i			0.0161748i
$58$	5.98741	−	6.37036i	0.786186	−	0.836470i
$59$	−1.49402	+	5.57577i	−0.194505	+	0.725904i	0.797889	+	0.602804i	$0.205950\pi$
$59$	−1.49402	+	5.57577i	−0.194505	+	0.725904i	−0.992394	+	0.123099i	$0.960717\pi$
$60$	0.0658867	+	1.06206i	0.00850593	+	0.137111i
$61$	9.61887	−	2.57737i	1.23157	−	0.329998i	0.416380	−	0.909191i	$-0.363299\pi$
$61$	9.61887	−	2.57737i	1.23157	−	0.329998i	0.815191	+	0.579192i	$0.196632\pi$
$62$	1.87288	+	3.02359i	0.237855	+	0.383996i
$63$	−0.271401	+	2.63179i	−0.0341933	+	0.331575i
$64$	7.86220	−	1.47843i	0.982775	−	0.184804i
$65$	1.16175	−	2.01221i	0.144097	−	0.249584i
$66$	−8.06697	−	4.33002i	−0.992976	−	0.532988i
$67$	−1.99445	+	7.44337i	−0.243660	+	0.909352i	0.730392	+	0.683028i	$0.239337\pi$
$67$	−1.99445	+	7.44337i	−0.243660	+	0.909352i	−0.974052	+	0.226324i	$0.927329\pi$
$68$	−3.76666	+	2.49782i	−0.456775	+	0.302905i
$69$	3.05506	−	3.05506i	0.367786	−	0.367786i
$70$	−1.50500	+	1.30309i	−0.179882	+	0.155748i
$71$	−3.75185			−0.445262			−0.222631	−	0.974903i	$-0.571465\pi$
$71$	−3.75185			−0.445262			−0.222631	+	0.974903i	$0.571465\pi$
$72$	2.57016	+	1.18079i	0.302896	+	0.139158i
$73$	−0.753853	−	1.30571i	−0.0882318	−	0.152822i	0.818532	−	0.574461i	$-0.194788\pi$
$73$	−0.753853	−	1.30571i	−0.0882318	−	0.152822i	−0.906764	+	0.421639i	$0.861455\pi$
$74$	−2.90207	+	0.874802i	−0.337359	+	0.101694i
$75$	4.55620	−	1.22083i	0.526105	−	0.140969i
$76$	0.0776984	+	0.231546i	0.00891262	+	0.0265601i
$77$	−2.71264	−	16.9124i	−0.309133	−	1.92735i
$78$	−3.25218	−	5.25035i	−0.368237	−	0.594485i
$79$	4.23158	+	2.44310i	0.476090	+	0.274871i	0.718786	−	0.695232i	$-0.244698\pi$
$79$	4.23158	+	2.44310i	0.476090	+	0.274871i	−0.242696	+	0.970102i	$0.578032\pi$
$80$	0.800672	+	1.97184i	0.0895179	+	0.220458i
$81$	0.500000	+	0.866025i	0.0555556	+	0.0962250i
$82$	−12.1997	+	0.378051i	−1.34723	+	0.0417488i
$83$	−10.6169	+	10.6169i	−1.16536	+	1.16536i	−0.182076	+	0.983284i	$0.558282\pi$
$83$	−10.6169	+	10.6169i	−1.16536	+	1.16536i	−0.983284	+	0.182076i	$0.941718\pi$
$84$	1.15991	+	5.16281i	0.126556	+	0.563309i
$85$	−0.850172	−	0.850172i	−0.0922141	−	0.0922141i
$86$	−3.03269	+	3.22666i	−0.327023	+	0.347939i
$87$	5.35364	−	3.09093i	0.573971	−	0.331382i
$88$	−18.0508	−	3.07741i	−1.92422	−	0.328053i
$89$	5.81809	−	10.0772i	0.616717	−	1.06818i	−0.373364	−	0.927685i	$-0.621796\pi$
$89$	5.81809	−	10.0772i	0.616717	−	1.06818i	0.990081	−	0.140500i	$-0.0448709\pi$
$90$	−0.172138	+	0.732475i	−0.0181450	+	0.0772097i
$91$	4.11952	−	10.7949i	0.431843	−	1.13161i
$92$	3.84886	−	7.73649i	0.401272	−	0.806585i
$93$	0.650912	+	2.42924i	0.0674964	+	0.251900i
$94$	−6.12947	+	11.4194i	−0.632207	+	1.17782i
$95$	−0.0562677	+	0.0324861i	−0.00577294	+	0.00333301i
$96$	5.62456	+	0.603598i	0.574054	+	0.0616045i
$97$			15.5828i			1.58219i	0.611694	+	0.791095i	$0.290489\pi$
$97$			15.5828i			1.58219i	−0.611694	+	0.791095i	$0.709511\pi$
$98$	−6.36335	+	7.58339i	−0.642795	+	0.766038i
$99$	−4.57780	−	4.57780i	−0.460087	−	0.460087i
$100$	7.86221	−	5.21374i	0.786221	−	0.521374i
$101$	−2.94694	−	0.789630i	−0.293231	−	0.0785711i	0.109205	−	0.994019i	$-0.465170\pi$
$101$	−2.94694	−	0.789630i	−0.293231	−	0.0785711i	−0.402436	+	0.915448i	$0.631836\pi$
$102$	−3.05985	+	0.922362i	−0.302970	+	0.0913275i
$103$	14.8691	+	8.58468i	1.46510	+	0.845873i	0.999240	−	0.0389870i	$-0.0124131\pi$
$103$	14.8691	+	8.58468i	1.46510	+	0.845873i	0.465856	+	0.884860i	$0.345746\pi$
$104$	−9.50702	−	7.88592i	−0.932240	−	0.773278i
$105$	−1.28485	+	0.575069i	−0.125388	+	0.0561210i
$106$	2.79170	−	11.8791i	0.271154	−	1.15380i
$107$	2.87018	+	10.7117i	0.277471	+	1.03554i	0.954167	+	0.299274i	$0.0967444\pi$
$107$	2.87018	+	10.7117i	0.277471	+	1.03554i	−0.676696	+	0.736262i	$0.736589\pi$
$108$	1.49907	+	1.32393i	0.144248	+	0.127396i
$109$	−4.68125	−	1.25434i	−0.448382	−	0.120144i	0.0275600	−	0.999620i	$-0.491226\pi$
$109$	−4.68125	−	1.25434i	−0.448382	−	0.120144i	−0.475942	+	0.879476i	$0.657893\pi$
$110$	−0.150880	−	4.86889i	−0.0143859	−	0.464231i
$111$	−2.14328			−0.203431
$112$	5.48419	+	9.05117i	0.518207	+	0.855255i
$113$	−9.24690			−0.869875			−0.434938	−	0.900461i	$-0.643230\pi$
$113$	−9.24690			−0.869875			−0.434938	+	0.900461i	$0.643230\pi$
$114$	0.00534917	+	0.172617i	0.000500995	+	0.0161671i
$115$	2.22039	+	0.594953i	0.207053	+	0.0554796i
$116$	8.18437	−	9.26700i	0.759900	−	0.860420i
$117$	−1.13028	−	4.21828i	−0.104495	−	0.389980i
$118$	−1.86762	+	7.94699i	−0.171928	+	0.731580i
$119$	−4.84389	−	3.50481i	−0.444038	−	0.321286i
$120$	0.139655	+	1.49837i	0.0127487	+	0.136782i
$121$	26.7711	+	15.4563i	2.43373	+	1.40512i
$122$	13.4837	−	4.06454i	1.22076	−	0.367986i
$123$	−8.33653	−	2.23377i	−0.751679	−	0.201412i
$124$	2.77982	+	4.19191i	0.249635	+	0.376445i
$125$	3.65566	+	3.65566i	0.326972	+	0.326972i
$126$	−0.268353	+	3.73202i	−0.0239068	+	0.332475i
$127$		−	7.84213i		−	0.695876i	−0.937518	−	0.347938i	$-0.886882\pi$
$127$		−	7.84213i		−	0.695876i	0.937518	−	0.347938i	$-0.113118\pi$
$128$	11.0487	−	2.43421i	0.976580	−	0.215156i
$129$	−2.71168	+	1.56559i	−0.238750	+	0.137842i
$130$	1.55403	−	2.89522i	0.136298	−	0.253928i
$131$	−4.29440	−	16.0269i	−0.375204	−	1.40028i	−0.853047	−	0.521834i	$-0.825248\pi$
$131$	−4.29440	−	16.0269i	−0.375204	−	1.40028i	0.477844	−	0.878445i	$-0.341419\pi$
$132$	−11.5926	−	5.76727i	−1.00901	−	0.501976i
$133$	−0.250691	+	0.203820i	−0.0217376	+	0.0176734i
$134$	−2.49317	+	10.6088i	−0.215377	+	0.916463i
$135$	−0.266024	+	0.460768i	−0.0228957	+	0.0396566i
$136$	−5.21489	+	3.69575i	−0.447173	+	0.316908i
$137$	5.50614	−	3.17897i	0.470421	−	0.271598i	−0.245995	−	0.969271i	$-0.579115\pi$
$137$	5.50614	−	3.17897i	0.470421	−	0.271598i	0.716416	+	0.697673i	$0.245781\pi$
$138$	4.18461	−	4.45226i	0.356218	−	0.379001i
$139$	−3.90174	−	3.90174i	−0.330941	−	0.330941i	0.522003	−	0.852944i	$-0.325185\pi$
$139$	−3.90174	−	3.90174i	−0.330941	−	0.330941i	−0.852944	+	0.522003i	$0.825185\pi$
$140$	−2.07029	+	1.90788i	−0.174972	+	0.161245i
$141$	−6.48024	+	6.48024i	−0.545734	+	0.545734i
$142$	−5.30337	+	0.164344i	−0.445049	+	0.0137915i
$143$	14.1362	+	24.4847i	1.18213	+	2.04751i
$144$	3.68474	+	1.55651i	0.307061	+	0.129709i
$145$	2.84840	+	1.64452i	0.236547	+	0.136570i
$146$	−1.12279	−	1.81265i	−0.0929230	−	0.150016i
$147$	−5.85571	+	3.83545i	−0.482971	+	0.316342i
$148$	−4.06385	+	1.36368i	−0.334047	+	0.112094i
$149$	−3.55507	+	0.952578i	−0.291243	+	0.0780382i	−0.401482	−	0.915867i	$-0.631505\pi$
$149$	−3.55507	+	0.952578i	−0.291243	+	0.0780382i	0.110240	+	0.993905i	$0.464838\pi$
$150$	6.38687	−	1.92526i	0.521486	−	0.157197i
$151$	5.20716	+	9.01907i	0.423753	+	0.733962i	0.996303	−	0.0859081i	$-0.0273792\pi$
$151$	5.20716	+	9.01907i	0.423753	+	0.733962i	−0.572550	+	0.819870i	$0.694046\pi$
$152$	0.119972	+	0.323894i	0.00973101	+	0.0262713i
$153$	−2.25980			−0.182694
$154$	−4.57523	−	23.7875i	−0.368682	−	1.91685i
$155$	−0.946156	+	0.946156i	−0.0759971	+	0.0759971i
$156$	−4.82705	−	7.27909i	−0.386473	−	0.582794i
$157$	4.99405	−	18.6380i	0.398568	−	1.48748i	−0.417048	−	0.908884i	$-0.636935\pi$
$157$	4.99405	−	18.6380i	0.398568	−	1.48748i	0.815617	−	0.578593i	$-0.196398\pi$
$158$	6.08850	+	3.26806i	0.484375	+	0.259992i
$159$	4.31432	−	7.47262i	0.342148	−	0.592618i
$160$	1.21815	+	2.75219i	0.0963033	+	0.217580i
$161$	11.3707	+	1.17259i	0.896135	+	0.0924131i
$162$	0.744703	+	1.20226i	0.0585094	+	0.0944581i
$163$	8.76426	−	2.34838i	0.686470	−	0.183939i	0.101307	−	0.994855i	$-0.467697\pi$
$163$	8.76426	−	2.34838i	0.686470	−	0.183939i	0.585162	+	0.810916i	$0.301031\pi$
$164$	−17.2281	+	1.06878i	−1.34529	+	0.0834575i
$165$	0.891497	−	3.32711i	0.0694029	−	0.259015i
$166$	−14.5424	+	15.4725i	−1.12871	+	1.20090i
$167$		−	12.5652i		−	0.972326i	−0.873868	−	0.486163i	$-0.838396\pi$
$167$		−	12.5652i		−	0.972326i	0.873868	−	0.486163i	$-0.161604\pi$
$168$	1.86572	+	7.24701i	0.143943	+	0.559119i
$169$			6.07140i			0.467031i
$170$	−1.23899	−	1.16451i	−0.0950261	−	0.0893136i
$171$	−0.0316062	+	0.117956i	−0.00241699	+	0.00902033i
$172$	−4.14547	+	4.69383i	−0.316089	+	0.357901i
$173$	3.74006	−	1.00215i	0.284352	−	0.0761918i	−0.113824	−	0.993501i	$-0.536310\pi$
$173$	3.74006	−	1.00215i	0.284352	−	0.0761918i	0.398176	+	0.917309i	$0.369643\pi$
$174$	7.43217	−	4.60364i	0.563431	−	0.349001i
$175$	10.1107	+	7.31565i	0.764299	+	0.553011i
$176$	−25.6502	−	3.55935i	−1.93346	−	0.268296i
$177$	−2.88623	+	4.99910i	−0.216943	+	0.375756i
$178$	7.78266	−	14.4994i	0.583335	−	1.08677i
$179$	−0.184288	+	0.687772i	−0.0137743	+	0.0514065i	−0.972471	−	0.233024i	$-0.925138\pi$
$179$	−0.184288	+	0.687772i	−0.0137743	+	0.0514065i	0.958697	+	0.284431i	$0.0918045\pi$
$180$	−0.211239	+	1.04292i	−0.0157448	+	0.0777347i
$181$	−2.77496	+	2.77496i	−0.206261	+	0.206261i	−0.802676	−	0.596415i	$-0.796591\pi$
$181$	−2.77496	+	2.77496i	−0.206261	+	0.206261i	0.596415	+	0.802676i	$0.296591\pi$
$182$	5.35023	−	15.4394i	0.396586	−	1.14444i
$183$	9.95819			0.736131
$184$	5.10162	−	11.1044i	0.376096	−	0.818627i
$185$	−0.570164	−	0.987553i	−0.0419193	−	0.0726064i
$186$	1.02650	+	3.40530i	0.0752664	+	0.249689i
$187$	14.1314	−	3.78651i	1.03339	−	0.276897i
$188$	−8.16401	+	16.4103i	−0.595422	+	1.19684i
$189$	−0.943312	+	2.47187i	−0.0686158	+	0.179802i
$190$	−0.0781133	+	0.0483850i	−0.00566693	+	0.00351022i
$191$	18.2274	+	10.5236i	1.31889	+	0.761460i	0.983550	−	0.180638i	$-0.0578163\pi$
$191$	18.2274	+	10.5236i	1.31889	+	0.761460i	0.335337	+	0.942098i	$0.391150\pi$
$192$	7.97695	+	0.606831i	0.575687	+	0.0437943i
$193$	−9.22014	−	15.9697i	−0.663680	−	1.14953i	−0.979641	−	0.200756i	$-0.935660\pi$
$193$	−9.22014	−	15.9697i	−0.663680	−	1.14953i	0.315961	−	0.948772i	$-0.397673\pi$
$194$	0.682581	+	22.0268i	0.0490064	+	1.58143i
$195$	1.64296	−	1.64296i	0.117655	−	0.117655i
$196$	−8.66263	+	10.9981i	−0.618760	+	0.785580i
$197$	16.7792	+	16.7792i	1.19547	+	1.19547i	0.975510	+	0.219955i	$0.0705911\pi$
$197$	16.7792	+	16.7792i	1.19547	+	1.19547i	0.219955	+	0.975510i	$0.429409\pi$
$198$	−6.67141	−	6.27036i	−0.474116	−	0.445615i
$199$	−15.5584	+	8.98263i	−1.10290	+	0.636762i	−0.936982	−	0.349377i	$-0.886393\pi$
$199$	−15.5584	+	8.98263i	−1.10290	+	0.636762i	−0.165922	+	0.986139i	$0.553060\pi$
$200$	10.8851	−	7.71420i	0.769695	−	0.545476i
$201$	−3.85297	+	6.67354i	−0.271768	+	0.470715i
$202$	−4.20019	−	0.987083i	−0.295524	−	0.0694509i
$203$	15.2808	+	5.83142i	1.07250	+	0.409285i
$204$	−4.28480	+	1.43782i	−0.299996	+	0.100668i
$205$	−1.18847	−	4.43544i	−0.0830065	−	0.309784i
$206$	21.3940	+	11.4834i	1.49059	+	0.800088i
$207$	3.74167	−	2.16025i	0.260064	−	0.150148i
$208$	−13.7839	−	10.7306i	−0.955745	−	0.744032i
$209$		−	0.790585i		−	0.0546859i
$210$	−1.79098	+	0.869161i	−0.123590	+	0.0599778i
$211$	−18.3628	−	18.3628i	−1.26415	−	1.26415i	−0.949063	−	0.315086i	$-0.897967\pi$
$211$	−18.3628	−	18.3628i	−1.26415	−	1.26415i	−0.315086	−	0.949063i	$-0.602033\pi$
$212$	3.42582	−	16.9138i	0.235286	−	1.16165i
$213$	−3.62400	−	0.971049i	−0.248313	−	0.0665352i
$214$	4.52631	+	15.0156i	0.309412	+	1.02644i
$215$	−1.44274	−	0.832969i	−0.0983943	−	0.0568080i
$216$	2.17697	+	1.80576i	0.148124	+	0.122867i
$217$	−3.90050	+	5.39076i	−0.264783	+	0.365948i
$218$	−6.67205	−	1.56799i	−0.451889	−	0.106198i
$219$	−0.390223	−	1.45633i	−0.0263688	−	0.0984098i
$220$	−0.426550	−	6.87574i	−0.0287580	−	0.463562i
$221$	9.53247	+	2.55422i	0.641223	+	0.171815i
$222$	−3.02960	+	0.0938832i	−0.203333	+	0.00630103i
$223$	−14.4404			−0.967003			−0.483501	−	0.875344i	$-0.660635\pi$
$223$	−14.4404			−0.967003			−0.483501	+	0.875344i	$0.660635\pi$
$224$	8.14856	+	12.5539i	0.544449	+	0.838794i
$225$	4.71692			0.314462
$226$	−13.0708	+	0.405047i	−0.869458	+	0.0269433i
$227$	8.35405	+	2.23846i	0.554478	+	0.148572i	0.525168	−	0.850999i	$-0.324002\pi$
$227$	8.35405	+	2.23846i	0.554478	+	0.148572i	0.0293095	+	0.999570i	$0.490669\pi$
$228$	0.0151225	+	0.243766i	0.00100151	+	0.0161438i
$229$	1.03487	+	3.86219i	0.0683861	+	0.255220i	0.991652	−	0.128940i	$-0.0411575\pi$
$229$	1.03487	+	3.86219i	0.0683861	+	0.255220i	−0.923266	+	0.384161i	$0.874491\pi$
$230$	3.16466	+	0.743725i	0.208672	+	0.0490398i
$231$	1.75705	−	17.0382i	0.115605	−	1.12103i
$232$	11.1630	−	13.4577i	0.732885	−	0.883544i
$233$	1.28842	+	0.743869i	0.0844071	+	0.0487325i	0.541609	−	0.840630i	$-0.317815\pi$
$233$	1.28842	+	0.743869i	0.0844071	+	0.0487325i	−0.457202	+	0.889363i	$0.651148\pi$
$234$	−1.78247	−	5.91317i	−0.116524	−	0.386556i
$235$	−4.70978	−	1.26198i	−0.307232	−	0.0823227i
$236$	−2.29183	+	11.3152i	−0.149186	+	0.736554i
$237$	3.45507	+	3.45507i	0.224431	+	0.224431i
$238$	−7.00052	−	4.74199i	−0.453777	−	0.307378i
$239$		−	14.3545i		−	0.928518i	−0.885699	−	0.464259i	$-0.846321\pi$
$239$		−	14.3545i		−	0.928518i	0.885699	−	0.464259i	$-0.153679\pi$
$240$	0.263041	+	2.11188i	0.0169792	+	0.136321i
$241$	1.73344	−	1.00080i	0.111661	−	0.0644673i	−0.443130	−	0.896458i	$-0.646132\pi$
$241$	1.73344	−	1.00080i	0.111661	−	0.0644673i	0.554790	+	0.831990i	$0.312799\pi$
$242$	38.5189	+	20.6753i	2.47609	+	1.32906i
$243$	0.258819	+	0.965926i	0.0166032	+	0.0619642i
$244$	18.8817	−	6.33601i	1.20877	−	0.405621i
$245$	−3.32501	−	1.67780i	−0.212427	−	0.107191i
$246$	−11.8818	−	2.79234i	−0.757557	−	0.178033i
$247$	0.266648	−	0.461848i	0.0169664	−	0.0293867i
$248$	4.11299	+	5.80365i	0.261175	+	0.368532i
$249$	−13.0030	+	7.50731i	−0.824034	+	0.475757i
$250$	5.32753	+	5.00727i	0.336942	+	0.316687i
$251$	0.867999	+	0.867999i	0.0547876	+	0.0547876i	0.733970	−	0.679182i	$-0.237665\pi$
$251$	0.867999	+	0.867999i	0.0547876	+	0.0547876i	−0.679182	+	0.733970i	$0.737665\pi$
$252$	−0.215851	+	5.28710i	−0.0135973	+	0.333056i
$253$	−19.7784	+	19.7784i	−1.24346	+	1.24346i
$254$	−0.343513	−	11.0851i	−0.0215539	−	0.695542i
$255$	−0.601162	−	1.04124i	−0.0376463	−	0.0652052i
$256$	15.5112	−	3.92481i	0.969447	−	0.245301i
$257$	9.37793	+	5.41435i	0.584979	+	0.337738i	0.763110	−	0.646269i	$-0.223672\pi$
$257$	9.37793	+	5.41435i	0.584979	+	0.337738i	−0.178131	+	0.984007i	$0.557005\pi$
$258$	−3.76447	+	2.33179i	−0.234366	+	0.145171i
$259$	−3.57724	−	4.39987i	−0.222279	−	0.273394i
$260$	2.06986	−	4.16057i	0.128367	−	0.258027i
$261$	5.97121	−	1.59998i	0.369609	−	0.0990364i
$262$	−6.77232	−	22.4665i	−0.418395	−	1.38799i
$263$	0.00452051	+	0.00782974i	0.000278746	+	0.000482803i	0.866165	−	0.499759i	$-0.166578\pi$
$263$	0.00452051	+	0.00782974i	0.000278746	+	0.000482803i	−0.865886	+	0.500241i	$0.833245\pi$
$264$	−16.6392	−	7.64443i	−1.02407	−	0.470482i
$265$	4.59086			0.282014
$266$	−0.345432	+	0.299087i	−0.0211798	+	0.0183382i
$267$	8.22803	−	8.22803i	0.503547	−	0.503547i
$268$	−3.05948	+	15.1052i	−0.186888	+	0.922695i
$269$	−3.27363	+	12.2174i	−0.199597	+	0.744905i	0.791432	+	0.611257i	$0.209336\pi$
$269$	−3.27363	+	12.2174i	−0.199597	+	0.744905i	−0.991029	+	0.133648i	$0.957331\pi$
$270$	−0.355852	+	0.662964i	−0.0216564	+	0.0403467i
$271$	13.3599	−	23.1400i	0.811555	−	1.40565i	−0.100220	−	0.994965i	$-0.531955\pi$
$271$	13.3599	−	23.1400i	0.811555	−	1.40565i	0.911775	−	0.410690i	$-0.134712\pi$
$272$	−7.20954	+	5.45250i	−0.437143	+	0.330606i
$273$	6.77307	−	9.36084i	0.409925	−	0.566544i
$274$	7.64387	−	4.73477i	0.461783	−	0.286038i
$275$	−29.4968	+	7.90364i	−1.77872	+	0.476607i
$276$	5.72007	−	6.47672i	0.344308	−	0.389853i
$277$	−6.08279	+	22.7013i	−0.365480	+	1.36399i	0.501290	+	0.865279i	$0.332859\pi$
$277$	−6.08279	+	22.7013i	−0.365480	+	1.36399i	−0.866770	+	0.498709i	$0.833808\pi$
$278$	−5.68616	−	5.34434i	−0.341033	−	0.320532i
$279$			2.51493i			0.150565i
$280$	−2.84286	+	2.78754i	−0.169893	+	0.166588i
$281$			12.2705i			0.732000i	0.930615	+	0.366000i	$0.119273\pi$
$281$			12.2705i			0.732000i	−0.930615	+	0.366000i	$0.880727\pi$
$282$	−8.87618	+	9.44390i	−0.528569	+	0.562376i
$283$	5.48764	−	20.4802i	0.326207	−	1.21742i	−0.586887	−	0.809669i	$-0.699647\pi$
$283$	5.48764	−	20.4802i	0.326207	−	1.21742i	0.913093	−	0.407750i	$-0.133687\pi$
$284$	−7.48929	+	0.464613i	−0.444408	+	0.0275697i
$285$	−0.0627584	+	0.0168161i	−0.00371749	+	0.000996098i
$286$	21.0546	+	33.9907i	1.24498	+	2.00991i
$287$	−9.32845	−	20.8421i	−0.550641	−	1.23027i
$288$	5.27668	+	2.03877i	0.310932	+	0.120136i
$289$	−5.94665	+	10.2999i	−0.349803	+	0.605876i
$290$	4.09835	+	2.19982i	0.240663	+	0.129178i
$291$	−4.03312	+	15.0518i	−0.236425	+	0.882352i
$292$	−1.66651	−	2.51306i	−0.0975249	−	0.147066i
$293$	9.97513	−	9.97513i	0.582753	−	0.582753i	−0.352906	−	0.935659i	$-0.614806\pi$
$293$	9.97513	−	9.97513i	0.582753	−	0.582753i	0.935659	+	0.352906i	$0.114806\pi$
$294$	−8.10925	+	5.67804i	−0.472941	+	0.331150i
$295$	−3.07123			−0.178814
$296$	−5.68467	+	2.10563i	−0.330415	+	0.122387i
$297$	−3.23700	−	5.60664i	−0.187830	−	0.325330i
$298$	−4.98349	+	1.50223i	−0.288686	+	0.0870217i
$299$	−18.2251	+	4.88340i	−1.05398	+	0.282414i
$300$	8.94373	−	3.00119i	0.516367	−	0.173274i
$301$	−7.73987	−	2.95367i	−0.446119	−	0.170247i
$302$	7.75557	+	12.5207i	0.446283	+	0.720484i
$303$	−2.64215	−	1.52545i	−0.151788	−	0.0876346i
$304$	0.183772	+	0.452581i	0.0105401	+	0.0259573i
$305$	2.64912	+	4.58841i	0.151688	+	0.262732i
$306$	−3.19431	+	0.0989874i	−0.182606	+	0.00565873i
$307$	19.3504	−	19.3504i	1.10438	−	1.10438i	0.110510	−	0.993875i	$-0.464752\pi$
$307$	19.3504	−	19.3504i	1.10438	−	1.10438i	0.993875	−	0.110510i	$-0.0352484\pi$
$308$	−7.50922	−	33.4240i	−0.427878	−	1.90451i
$309$	12.1406	+	12.1406i	0.690653	+	0.690653i
$310$	−1.29598	+	1.37887i	−0.0736067	+	0.0783145i
$311$	7.44749	−	4.29981i	0.422309	−	0.243820i	−0.273756	−	0.961799i	$-0.588266\pi$
$311$	7.44749	−	4.29981i	0.422309	−	0.243820i	0.696065	+	0.717979i	$0.254933\pi$
$312$	−7.14205	−	10.0778i	−0.404339	−	0.570544i
$313$	−8.82075	+	15.2780i	−0.498578	+	0.863563i	−0.999999	−	0.00164098i	$-0.999478\pi$
$313$	−8.82075	+	15.2780i	−0.498578	+	0.863563i	0.501420	+	0.865204i	$0.332811\pi$
$314$	6.24285	−	26.5643i	0.352304	−	1.49911i
$315$	−1.38990	+	0.222931i	−0.0783122	+	0.0125607i
$316$	8.74947	+	4.35281i	0.492196	+	0.244865i
$317$	−2.11388	−	7.88911i	−0.118727	−	0.443097i	0.880811	−	0.473468i	$-0.156998\pi$
$317$	−2.11388	−	7.88911i	−0.118727	−	0.443097i	−0.999539	+	0.0303708i	$0.990331\pi$
$318$	5.77112	−	10.7518i	0.323628	−	0.602931i
$319$	−34.6594	+	20.0106i	−1.94056	+	1.12038i
$320$	1.84246	+	3.83695i	0.102996	+	0.214492i
$321$			11.0895i			0.618957i
$322$	16.1242	+	1.15942i	0.898568	+	0.0646120i
$323$	−0.195134	−	0.195134i	−0.0108575	−	0.0108575i
$324$	1.10533	+	1.66681i	0.0614070	+	0.0926005i
$325$	−19.8973	−	5.33146i	−1.10370	−	0.295736i
$326$	12.2857	−	3.70342i	0.680443	−	0.205113i
$327$	−4.19709	−	2.42319i	−0.232100	−	0.134003i
$328$	−24.3057	+	2.26541i	−1.34206	+	0.125086i
$329$	−24.1189	−	2.48724i	−1.32972	−	0.137126i
$330$	1.11442	−	4.74204i	0.0613470	−	0.261041i
$331$	−7.62628	−	28.4617i	−0.419178	−	1.56439i	−0.776317	−	0.630343i	$-0.782914\pi$
$331$	−7.62628	−	28.4617i	−0.419178	−	1.56439i	0.357139	−	0.934051i	$-0.383752\pi$
$332$	−19.8784	+	22.5079i	−1.09097	+	1.23528i
$333$	−2.07025	−	0.554721i	−0.113449	−	0.0303985i
$334$	−0.550401	−	17.7614i	−0.0301166	−	0.971859i
$335$	−4.09994			−0.224004
$336$	2.95470	+	10.1622i	0.161192	+	0.554392i
$337$	−18.9391			−1.03168			−0.515839	−	0.856686i	$-0.672520\pi$
$337$	−18.9391			−1.03168			−0.515839	+	0.856686i	$0.672520\pi$
$338$	0.265949	+	8.58214i	0.0144657	+	0.466807i
$339$	−8.93182	−	2.39327i	−0.485110	−	0.129985i
$340$	−1.80236	−	1.59180i	−0.0977469	−	0.0863275i
$341$	−4.21400	−	15.7269i	−0.228201	−	0.851657i
$342$	−0.0395096	+	0.168120i	−0.00213644	+	0.00909086i
$343$	−17.6471	−	5.61946i	−0.952856	−	0.303422i
$344$	−5.65416	+	6.81648i	−0.304852	+	0.367520i
$345$	1.99075	+	1.14936i	0.107178	+	0.0618795i
$346$	5.24281	−	1.58040i	0.281855	−	0.0849627i
$347$	−10.2122	−	2.73635i	−0.548219	−	0.146895i	−0.0259306	−	0.999664i	$-0.508255\pi$
$347$	−10.2122	−	2.73635i	−0.548219	−	0.146895i	−0.522288	+	0.852769i	$0.674922\pi$
$348$	10.3040	−	6.83296i	0.552351	−	0.366285i
$349$	−23.1048	−	23.1048i	−1.23677	−	1.23677i	−0.961312	−	0.275461i	$-0.911170\pi$
$349$	−23.1048	−	23.1048i	−1.23677	−	1.23677i	−0.275461	−	0.961312i	$-0.588830\pi$
$350$	14.6123	+	9.89805i	0.781061	+	0.529073i
$351$		−	4.36708i		−	0.233098i
$352$	−36.4133	−	3.90769i	−1.94084	−	0.208281i
$353$	9.52429	−	5.49885i	0.506927	−	0.292674i	−0.224643	−	0.974441i	$-0.572122\pi$
$353$	9.52429	−	5.49885i	0.506927	−	0.292674i	0.731569	+	0.681767i	$0.238788\pi$
$354$	−3.86081	+	7.19283i	−0.205200	+	0.382295i
$355$	−0.516646	−	1.92815i	−0.0274207	−	0.102335i
$356$	10.3659	−	20.8363i	0.549394	−	1.10432i
$357$	−3.77172	−	4.63908i	−0.199621	−	0.245526i
$358$	−0.230371	+	0.980263i	−0.0121755	+	0.0518085i
$359$	−13.0644	+	22.6283i	−0.689515	+	1.19427i	0.282480	+	0.959273i	$0.408843\pi$
$359$	−13.0644	+	22.6283i	−0.689515	+	1.19427i	−0.971995	+	0.235001i	$0.924491\pi$
$360$	−0.252910	+	1.48346i	−0.0133295	+	0.0781850i
$361$	16.4416	−	9.49254i	0.865346	−	0.499608i
$362$	−3.80095	+	4.04405i	−0.199773	+	0.212551i
$363$	21.8585	+	21.8585i	1.14727	+	1.14727i
$364$	6.88644	−	22.0585i	0.360948	−	1.15618i
$365$	0.567222	−	0.567222i	0.0296898	−	0.0296898i
$366$	14.0763	−	0.436204i	0.735777	−	0.0228008i
$367$	−2.41396	−	4.18109i	−0.126007	−	0.218251i	0.796119	−	0.605140i	$-0.206883\pi$
$367$	−2.41396	−	4.18109i	−0.126007	−	0.218251i	−0.922126	+	0.386889i	$0.873550\pi$
$368$	6.72490	−	15.9199i	0.350560	−	0.829884i
$369$	−7.47432	−	4.31530i	−0.389098	−	0.224646i
$370$	−0.849205	−	1.37097i	−0.0441481	−	0.0712731i
$371$	22.5411	−	3.61545i	1.17028	−	0.187705i
$372$	1.60015	+	4.76855i	0.0829641	+	0.247238i
$373$	−0.596413	+	0.159809i	−0.0308811	+	0.00827457i	−0.274227	−	0.961665i	$-0.588422\pi$
$373$	−0.596413	+	0.159809i	−0.0308811	+	0.00827457i	0.243345	+	0.969940i	$0.421755\pi$
$374$	19.8094	−	5.97137i	1.02432	−	0.308772i
$375$	2.58494	+	4.47725i	0.133486	+	0.231204i
$376$	−10.8213	+	23.5541i	−0.558065	+	1.21471i
$377$	−26.9967			−1.39040
$378$	−1.22513	+	3.53540i	−0.0630138	+	0.181841i
$379$	−16.6366	+	16.6366i	−0.854562	+	0.854562i	−0.990691	−	0.136129i	$-0.956534\pi$
$379$	−16.6366	+	16.6366i	−0.854562	+	0.854562i	0.136129	+	0.990691i	$0.456534\pi$
$380$	−0.108296	+	0.0718156i	−0.00555549	+	0.00368406i
$381$	2.02969	−	7.57491i	0.103984	−	0.388075i
$382$	26.2260	+	14.0770i	1.34184	+	0.720243i
$383$	7.35153	−	12.7332i	0.375646	−	0.650637i	−0.614778	−	0.788700i	$-0.710754\pi$
$383$	7.35153	−	12.7332i	0.375646	−	0.650637i	0.990423	+	0.138063i	$0.0440877\pi$
$384$	11.3023	+	0.508358i	0.576767	+	0.0259421i
$385$	8.31808	−	3.72299i	0.423929	−	0.189741i
$386$	−13.7325	−	22.1699i	−0.698967	−	1.12842i
$387$	−3.02448	+	0.810407i	−0.153743	+	0.0411953i
$388$	1.92970	+	31.1057i	0.0979658	+	1.57915i
$389$	−1.22720	+	4.57999i	−0.0622217	+	0.232215i	−0.990033	−	0.140835i	$-0.955021\pi$
$389$	−1.22720	+	4.57999i	−0.0622217	+	0.232215i	0.927811	+	0.373050i	$0.121688\pi$
$390$	2.25042	−	2.39435i	0.113954	−	0.121243i
$391$			9.76349i			0.493761i
$392$	−11.7632	+	15.9257i	−0.594130	+	0.804369i
$393$		−	16.5923i		−	0.836970i
$394$	24.4529	+	22.9829i	1.23192	+	1.15786i
$395$	−0.672852	+	2.51112i	−0.0338549	+	0.126348i
$396$	−9.70493	−	8.57114i	−0.487691	−	0.430716i
$397$	−7.86954	+	2.10864i	−0.394961	+	0.105830i	−0.450833	−	0.892608i	$-0.648873\pi$
$397$	−7.86954	+	2.10864i	−0.394961	+	0.105830i	0.0558716	+	0.998438i	$0.482206\pi$
$398$	−21.5988	+	13.3788i	−1.08265	+	0.670617i
$399$	−0.294901	+	0.131991i	−0.0147635	+	0.00660782i
$400$	15.0486	−	11.3811i	0.752430	−	0.569055i
$401$	3.76720	−	6.52497i	0.188125	−	0.325842i	−0.756500	−	0.653993i	$-0.773092\pi$
$401$	3.76720	−	6.52497i	0.188125	−	0.325842i	0.944625	+	0.328152i	$0.106426\pi$
$402$	−5.15399	+	9.60206i	−0.257057	+	0.478907i
$403$	2.84259	−	10.6087i	0.141599	−	0.528456i
$404$	−5.98035	−	1.21129i	−0.297534	−	0.0602641i
$405$	−0.376215	+	0.376215i	−0.0186943	+	0.0186943i
$406$	21.8553	+	7.57356i	1.08466	+	0.375869i
$407$	13.8756			0.687786
$408$	−5.99373	+	2.22010i	−0.296734	+	0.109912i
$409$	−8.32166	−	14.4135i	−0.411480	−	0.712704i	0.583572	−	0.812061i	$-0.301655\pi$
$409$	−8.32166	−	14.4135i	−0.411480	−	0.712704i	−0.995052	+	0.0993575i	$0.968321\pi$
$410$	−1.87424	−	6.21759i	−0.0925619	−	0.307065i
$411$	6.14130	−	1.64556i	0.302928	−	0.0811693i
$412$	30.7442	+	15.2951i	1.51466	+	0.753535i
$413$	−15.0798	+	2.41869i	−0.742027	+	0.119016i
$414$	5.19435	−	3.21749i	0.255288	−	0.158131i
$415$	−6.91826	−	3.99426i	−0.339604	−	0.196070i
$416$	−19.9541	−	14.5643i	−0.978331	−	0.714072i
$417$	−2.75895	−	4.77864i	−0.135106	−	0.234011i
$418$	−0.0346305	−	1.11752i	−0.00169383	−	0.0546597i
$419$	0.524487	−	0.524487i	0.0256229	−	0.0256229i	−0.694179	−	0.719802i	$-0.744233\pi$
$419$	0.524487	−	0.524487i	0.0256229	−	0.0256229i	0.719802	+	0.694179i	$0.244233\pi$
$420$	−2.49355	+	1.30704i	−0.121673	+	0.0637770i
$421$	12.7438	+	12.7438i	0.621094	+	0.621094i	0.945811	−	0.324717i	$-0.105269\pi$
$421$	12.7438	+	12.7438i	0.621094	+	0.621094i	−0.324717	+	0.945811i	$0.605269\pi$
$422$	−26.7608	−	25.1521i	−1.30270	−	1.22439i
$423$	−7.93663	+	4.58222i	−0.385892	+	0.222795i
$424$	4.10163	−	24.0584i	0.199193	−	1.16838i
$425$	−5.32966	+	9.23124i	−0.258526	+	0.447781i
$426$	−5.16519	−	1.21387i	−0.250254	−	0.0588121i
$427$	16.6207	+	20.4429i	0.804333	+	0.989299i
$428$	7.05584	+	21.0268i	0.341057	+	1.01637i
$429$	7.31745	+	27.3091i	0.353290	+	1.31850i
$430$	−2.07586	−	1.11423i	−0.100107	−	0.0537331i
$431$	−14.3339	+	8.27570i	−0.690441	+	0.398626i	−0.803777	−	0.594930i	$-0.797180\pi$
$431$	−14.3339	+	8.27570i	−0.690441	+	0.398626i	0.113336	+	0.993557i	$0.463846\pi$
$432$	3.15633	+	2.45715i	0.151859	+	0.118220i
$433$		−	27.6006i		−	1.32640i	−0.748441	−	0.663201i	$-0.769198\pi$
$433$		−	27.6006i		−	1.32640i	0.748441	−	0.663201i	$-0.230802\pi$
$434$	−5.27736	+	7.79088i	−0.253321	+	0.373974i
$435$	2.32571	+	2.32571i	0.111509	+	0.111509i
$436$	−9.49987	−	1.92415i	−0.454961	−	0.0921503i
$437$	0.509630	+	0.136555i	0.0243789	+	0.00653231i
$438$	−0.615386	−	2.04148i	−0.0294043	−	0.0975458i
$439$	6.31007	+	3.64312i	0.301163	+	0.173877i	0.642965	−	0.765895i	$-0.277704\pi$
$439$	6.31007	+	3.64312i	0.301163	+	0.173877i	−0.341802	+	0.939772i	$0.611037\pi$
$440$	−0.904125	−	9.70042i	−0.0431025	−	0.462449i
$441$	−6.64887	+	2.18919i	−0.316613	+	0.104247i
$442$	13.5864	+	3.19292i	0.646237	+	0.151872i
$443$	−1.66883	−	6.22816i	−0.0792885	−	0.295909i	0.914883	−	0.403719i	$-0.132283\pi$
$443$	−1.66883	−	6.22816i	−0.0792885	−	0.295909i	−0.994171	+	0.107810i	$0.965616\pi$
$444$	−4.27833	+	0.265414i	−0.203041	+	0.0125960i
$445$	5.98007	+	1.60235i	0.283482	+	0.0759589i
$446$	−20.4121	+	0.632542i	−0.966539	+	0.0299517i
$447$	−3.68048			−0.174081
$448$	12.0682	+	17.3885i	0.570168	+	0.821528i
$449$	−6.83595			−0.322609			−0.161304	−	0.986905i	$-0.551570\pi$
$449$	−6.83595			−0.322609			−0.161304	+	0.986905i	$0.551570\pi$
$450$	6.66754	−	0.206618i	0.314311	−	0.00974007i
$451$	53.9706	+	14.4614i	2.54138	+	0.680960i
$452$	−18.4583	+	1.14510i	−0.868206	+	0.0538608i
$453$	2.69543	+	10.0595i	0.126642	+	0.472635i
$454$	11.9068	+	2.79820i	0.558813	+	0.131326i
$455$	6.11498	+	0.630601i	0.286675	+	0.0295630i
$456$	0.0320539	+	0.343909i	0.00150106	+	0.0161050i
$457$	24.7993	+	14.3179i	1.16006	+	0.669764i	0.951320	−	0.308206i	$-0.0997288\pi$
$457$	24.7993	+	14.3179i	1.16006	+	0.669764i	0.208745	+	0.977970i	$0.433062\pi$
$458$	1.63200	+	5.41400i	0.0762584	+	0.252980i
$459$	−2.18280	−	0.584880i	−0.101884	−	0.0272998i
$460$	4.50594	+	0.912658i	0.210091	+	0.0425529i
$461$	25.0731	+	25.0731i	1.16777	+	1.16777i	0.982731	+	0.185040i	$0.0592415\pi$
$461$	25.0731	+	25.0731i	1.16777	+	1.16777i	0.185040	+	0.982731i	$0.440759\pi$
$462$	1.73732	−	24.1611i	0.0808272	−	1.12407i
$463$		−	3.36642i		−	0.156451i	−0.996936	−	0.0782254i	$-0.975075\pi$
$463$		−	3.36642i		−	0.156451i	0.996936	−	0.0782254i	$-0.0249254\pi$
$464$	15.1898	−	19.5120i	0.705166	−	0.905820i
$465$	−1.15880	+	0.669033i	−0.0537380	+	0.0310257i
$466$	1.85381	+	0.995047i	0.0858760	+	0.0460947i
$467$	3.90263	+	14.5648i	0.180592	+	0.673979i	0.995531	+	0.0944323i	$0.0301036\pi$
$467$	3.90263	+	14.5648i	0.180592	+	0.673979i	−0.814939	+	0.579546i	$0.803230\pi$
$468$	−2.77860	−	8.28040i	−0.128441	−	0.382761i
$469$	−20.1307	+	3.22883i	−0.929550	+	0.149094i
$470$	−6.71272	−	1.57755i	−0.309635	−	0.0727670i
$471$	9.64776	−	16.7104i	0.444545	−	0.769975i
$472$	−2.74394	+	16.0948i	−0.126300	+	0.740822i
$473$	17.5554	−	10.1356i	0.807197	−	0.466035i
$474$	5.03521	+	4.73252i	0.231275	+	0.217372i
$475$	0.407306	+	0.407306i	0.0186885	+	0.0186885i
$476$	−10.1032	−	6.39633i	−0.463080	−	0.293175i
$477$	6.10137	−	6.10137i	0.279363	−	0.279363i
$478$	−0.628780	−	20.2907i	−0.0287597	−	0.928073i
$479$	−4.63917	−	8.03529i	−0.211969	−	0.367142i	0.740361	−	0.672209i	$-0.234654\pi$
$479$	−4.63917	−	8.03529i	−0.211969	−	0.367142i	−0.952331	+	0.305067i	$0.901321\pi$
$480$	0.464325	+	2.97369i	0.0211935	+	0.135730i
$481$	8.10588	+	4.67993i	0.369596	+	0.213387i
$482$	2.40644	−	1.49060i	0.109610	−	0.0678949i
$483$	10.6797	+	4.07558i	0.485945	+	0.185446i
$484$	55.3534	+	27.5380i	2.51607	+	1.25173i
$485$	−8.00829	+	2.14581i	−0.363638	+	0.0974364i
$486$	0.408161	+	1.35403i	0.0185145	+	0.0614202i
$487$	−5.16994	−	8.95459i	−0.234272	−	0.405771i	0.724789	−	0.688971i	$-0.241937\pi$
$487$	−5.16994	−	8.95459i	−0.234272	−	0.405771i	−0.959061	+	0.283200i	$0.908604\pi$
$488$	26.4124	−	9.78325i	1.19563	−	0.442867i
$489$	9.07343			0.410315
$490$	−4.77351	−	2.22598i	−0.215645	−	0.100560i
$491$	−12.8416	+	12.8416i	−0.579534	+	0.579534i	−0.934775	−	0.355241i	$-0.884399\pi$
$491$	−12.8416	+	12.8416i	−0.579534	+	0.579534i	0.355241	+	0.934775i	$0.384399\pi$
$492$	−16.9177	−	3.42660i	−0.762708	−	0.154483i
$493$	−3.61564	+	13.4938i	−0.162840	+	0.607728i
$494$	0.356685	−	0.664518i	0.0160480	−	0.0298981i
$495$	1.72224	−	2.98301i	0.0774089	−	0.134076i
$496$	6.06808	+	8.02350i	0.272465	+	0.360266i
$497$	−4.05521	−	9.06034i	−0.181901	−	0.406412i
$498$	−18.0514	+	11.1814i	−0.808903	+	0.501052i
$499$	−5.62933	+	1.50838i	−0.252004	+	0.0675241i	−0.382609	−	0.923910i	$-0.624974\pi$
$499$	−5.62933	+	1.50838i	−0.252004	+	0.0675241i	0.130606	+	0.991434i	$0.458308\pi$
$500$	7.74998	+	6.84458i	0.346590	+	0.306099i
$501$	3.25212	−	12.1371i	0.145294	−	0.542244i
$502$	1.26497	+	1.18893i	0.0564583	+	0.0530643i
$503$		−	22.7236i		−	1.01319i	−0.862183	−	0.506597i	$-0.830903\pi$
$503$		−	22.7236i		−	1.01319i	0.862183	−	0.506597i	$-0.169097\pi$
$504$	−0.0735185	+	7.48295i	−0.00327478	+	0.333317i
$505$		−	1.62322i		−	0.0722326i
$506$	−27.0911	+	28.8239i	−1.20435	+	1.28138i
$507$	−1.57140	+	5.86453i	−0.0697881	+	0.260453i
$508$	−0.971136	−	15.6542i	−0.0430872	−	0.694541i
$509$	2.62635	−	0.703729i	0.116411	−	0.0311922i	−0.200143	−	0.979767i	$-0.564141\pi$
$509$	2.62635	−	0.703729i	0.116411	−	0.0311922i	0.316554	+	0.948574i	$0.397474\pi$
$510$	−0.895374	−	1.44550i	−0.0396478	−	0.0640079i
$511$	2.33836	−	3.23177i	0.103443	−	0.142965i
$512$	21.7536	−	6.22731i	0.961384	−	0.275211i
$513$	−0.0610586	+	0.105757i	−0.00269580	+	0.00466927i
$514$	13.4932	+	7.24258i	0.595159	+	0.319457i
$515$	−2.36430	+	8.82367i	−0.104183	+	0.388817i
$516$	−5.21907	+	3.46097i	−0.229757	+	0.152361i
$517$	41.9530	−	41.9530i	1.84509	−	1.84509i
$518$	−5.24928	−	6.06267i	−0.230640	−	0.266379i
$519$	3.87200			0.169962
$520$	2.74357	−	5.97177i	0.120314	−	0.261880i
$521$	−8.61770	−	14.9263i	−0.377548	−	0.653932i	0.613157	−	0.789961i	$-0.289899\pi$
$521$	−8.61770	−	14.9263i	−0.377548	−	0.653932i	−0.990705	+	0.136029i	$0.956566\pi$
$522$	8.37043	−	2.52319i	0.366364	−	0.110437i
$523$	−18.6595	+	4.99979i	−0.815921	+	0.218625i	−0.642563	−	0.766233i	$-0.722129\pi$
$523$	−18.6595	+	4.99979i	−0.815921	+	0.218625i	−0.173359	+	0.984859i	$0.555462\pi$
$524$	−10.5570	−	31.4605i	−0.461186	−	1.37436i
$525$	7.87278	+	9.68323i	0.343596	+	0.422611i
$526$	0.00673286	+	0.0108696i	0.000293567	+	0.000473937i
$527$	−4.92184	−	2.84162i	−0.214399	−	0.123783i
$528$	−23.8550	−	10.0768i	−1.03815	−	0.438537i
$529$	2.16661	+	3.75269i	0.0942006	+	0.163160i
$530$	6.48934	−	0.201096i	0.281879	−	0.00873505i
$531$	−4.08175	+	4.08175i	−0.177133	+	0.177133i
$532$	−0.475179	+	0.437902i	−0.0206016	+	0.0189854i
$533$	26.6513	+	26.6513i	1.15439	+	1.15439i
$534$	11.2702	−	11.9910i	0.487709	−	0.518902i
$535$	−5.10970	+	2.95009i	−0.220912	+	0.127543i
$536$	−3.66302	+	21.4857i	−0.158219	+	0.928040i
$537$	−0.356017	+	0.616640i	−0.0153633	+	0.0266100i
$538$	−4.09223	+	17.4131i	−0.176428	+	0.750730i
$539$	37.9098	−	24.8306i	1.63289	−	1.06953i
$540$	−0.473968	+	0.952711i	−0.0203964	+	0.0409981i
$541$	−0.457338	−	1.70681i	−0.0196625	−	0.0733814i	0.955397	−	0.295323i	$-0.0954272\pi$
$541$	−0.457338	−	1.70681i	−0.0196625	−	0.0733814i	−0.975060	+	0.221942i	$0.928761\pi$
$542$	17.8711	−	33.2944i	0.767627	−	1.43012i
$543$	−3.39862	+	1.96219i	−0.145849	+	0.0842057i
$544$	−9.95210	+	8.02310i	−0.426693	+	0.343988i
$545$		−	2.57851i		−	0.110451i
$546$	9.16393	−	13.5286i	0.392180	−	0.578969i
$547$	26.0358	+	26.0358i	1.11321	+	1.11321i	0.992714	+	0.120496i	$0.0384484\pi$
$547$	26.0358	+	26.0358i	1.11321	+	1.11321i	0.120496	+	0.992714i	$0.461552\pi$
$548$	10.5975	−	7.02760i	0.452702	−	0.300204i
$549$	9.61887	+	2.57737i	0.410524	+	0.109999i
$550$	−41.3485	+	12.4641i	−1.76311	+	0.531473i
$551$	0.653772	+	0.377455i	0.0278516	+	0.0160801i
$552$	7.80181	−	9.40563i	0.332067	−	0.400330i
$553$	−1.32612	+	12.8595i	−0.0563925	+	0.546841i
$554$	−7.60384	+	32.3555i	−0.323056	+	1.37465i
$555$	−0.295139	−	1.10147i	−0.0125279	−	0.0467549i
$556$	−8.27168	−	7.30533i	−0.350798	−	0.309815i
$557$	15.4511	+	4.14011i	0.654685	+	0.175422i	0.570846	−	0.821057i	$-0.306615\pi$
$557$	15.4511	+	4.14011i	0.654685	+	0.175422i	0.0838386	+	0.996479i	$0.473282\pi$
$558$	0.110163	+	3.55494i	0.00466357	+	0.150493i
$559$	13.6741			0.578352
$560$	−3.89638	+	4.06482i	−0.164652	+	0.171770i
$561$	14.6299			0.617676
$562$	0.537494	+	17.3448i	0.0226728	+	0.731648i
$563$	−17.5348	−	4.69845i	−0.739006	−	0.198016i	−0.130369	−	0.991465i	$-0.541616\pi$
$563$	−17.5348	−	4.69845i	−0.739006	−	0.198016i	−0.608636	+	0.793450i	$0.708283\pi$
$564$	−12.1331	+	13.7381i	−0.510896	+	0.578478i
$565$	−1.27334	−	4.75216i	−0.0535698	−	0.199925i
$566$	6.85987	−	29.1898i	0.288342	−	1.22694i
$567$	−1.55094	+	2.14350i	−0.0651333	+	0.0900185i
$568$	−10.5660	+	0.984804i	−0.443341	+	0.0413215i
$569$	1.31806	+	0.760981i	0.0552558	+	0.0319020i	0.527373	−	0.849634i	$-0.323177\pi$
$569$	1.31806	+	0.760981i	0.0552558	+	0.0319020i	−0.472118	+	0.881536i	$0.656510\pi$
$570$	−0.0879746	+	0.0265191i	−0.00368485	+	0.00111076i
$571$	−33.4722	−	8.96886i	−1.40077	−	0.375335i	−0.522148	−	0.852855i	$-0.674869\pi$
$571$	−33.4722	−	8.96886i	−1.40077	−	0.375335i	−0.878621	+	0.477519i	$0.841536\pi$
$572$	31.2503	+	47.1248i	1.30664	+	1.97039i
$573$	14.8826	+	14.8826i	0.621729	+	0.621729i
$574$	−14.0990	−	29.0524i	−0.588483	−	1.21262i
$575$		−	20.3795i		−	0.849884i
$576$	7.54808	+	2.65074i	0.314503	+	0.110448i
$577$	15.2440	−	8.80112i	0.634615	−	0.366395i	−0.147922	−	0.988999i	$-0.547258\pi$
$577$	15.2440	−	8.80112i	0.634615	−	0.366395i	0.782537	+	0.622604i	$0.213925\pi$
$578$	−7.95462	+	14.8197i	−0.330869	+	0.616420i
$579$	−4.77270	−	17.8119i	−0.198346	−	0.740239i
$580$	5.88952	+	2.93000i	0.244549	+	0.121662i
$581$	−37.1143	−	14.1635i	−1.53976	−	0.587600i
$582$	−5.04163	+	21.4529i	−0.208982	+	0.889251i
$583$	−27.9309	+	48.3777i	−1.15678	+	2.00360i
$584$	−2.46575	−	3.47930i	−0.102033	−	0.143974i
$585$	2.01221	−	1.16175i	0.0831947	−	0.0480325i
$586$	13.6632	−	14.5371i	0.564424	−	0.600524i
$587$	20.4769	+	20.4769i	0.845173	+	0.845173i	0.989526	−	0.144353i	$-0.0461101\pi$
$587$	20.4769	+	20.4769i	0.845173	+	0.845173i	−0.144353	+	0.989526i	$0.546110\pi$
$588$	−11.2140	+	8.38132i	−0.462457	+	0.345640i
$589$	−0.217164	+	0.217164i	−0.00894809	+	0.00894809i
$590$	−4.34130	+	0.134531i	−0.178728	+	0.00553855i
$591$	11.8647	+	20.5502i	0.488047	+	0.845321i
$592$	−7.94324	+	3.22539i	−0.326465	+	0.132563i
$593$	14.0356	+	8.10348i	0.576375	+	0.332770i	0.759691	−	0.650284i	$-0.225350\pi$
$593$	14.0356	+	8.10348i	0.576375	+	0.332770i	−0.183316	+	0.983054i	$0.558683\pi$
$594$	−4.82120	−	7.78339i	−0.197816	−	0.319356i
$595$	1.13417	−	2.97200i	0.0464963	−	0.121840i
$596$	−6.97853	+	2.34174i	−0.285852	+	0.0959216i
$597$	−17.3531	+	4.64975i	−0.710215	+	0.190302i
$598$	−25.5479	+	7.70118i	−1.04473	+	0.314925i
$599$	5.90260	+	10.2236i	0.241174	+	0.417725i	0.961049	−	0.276378i	$-0.0891343\pi$
$599$	5.90260	+	10.2236i	0.241174	+	0.417725i	−0.719875	+	0.694104i	$0.755801\pi$
$600$	12.5108	−	4.63406i	0.510752	−	0.189185i
$601$	−8.58028			−0.349997			−0.174999	−	0.984569i	$-0.555992\pi$
$601$	−8.58028			−0.349997			−0.174999	+	0.984569i	$0.555992\pi$
$602$	−11.0700	−	3.83609i	−0.451178	−	0.156347i
$603$	−5.44893	+	5.44893i	−0.221897	+	0.221897i
$604$	11.5112	+	17.3587i	0.468385	+	0.706315i
$605$	−4.25679	+	15.8866i	−0.173063	+	0.645881i
$606$	−3.80159	−	2.04054i	−0.154429	−	0.0828912i
$607$	8.54772	−	14.8051i	0.346941	−	0.600920i	−0.638763	−	0.769403i	$-0.720554\pi$
$607$	8.54772	−	14.8051i	0.346941	−	0.600920i	0.985704	+	0.168484i	$0.0538870\pi$
$608$	0.279593	+	0.631689i	0.0113390	+	0.0256184i
$609$	13.2508	+	9.58767i	0.536950	+	0.388512i
$610$	3.94562	+	6.36984i	0.159753	+	0.257907i
$611$	38.6581	−	10.3584i	1.56394	−	0.419057i
$612$	−4.51093	+	0.279844i	−0.182344	+	0.0113120i
$613$	−1.04144	+	3.88672i	−0.0420635	+	0.156983i	−0.983763	−	0.179472i	$-0.942561\pi$
$613$	−1.04144	+	3.88672i	−0.0420635	+	0.156983i	0.941700	+	0.336455i	$0.109228\pi$
$614$	26.5048	−	28.2001i	1.06965	−	1.13806i
$615$		−	4.59190i		−	0.185163i
$616$	−12.0786	−	46.9171i	−0.486662	−	1.89034i
$617$		−	37.6707i		−	1.51657i	−0.651925	−	0.758283i	$-0.726038\pi$
$617$		−	37.6707i		−	1.51657i	0.651925	−	0.758283i	$-0.273962\pi$
$618$	17.6929	+	16.6293i	0.711714	+	0.668929i
$619$	−10.5851	+	39.5040i	−0.425450	+	1.58780i	0.337489	+	0.941330i	$0.390422\pi$
$619$	−10.5851	+	39.5040i	−0.425450	+	1.58780i	−0.762939	+	0.646471i	$0.776244\pi$
$620$	−1.77151	+	2.00585i	−0.0711457	+	0.0805568i
$621$	4.17329	−	1.11823i	0.167468	−	0.0448730i
$622$	10.3389	−	6.40416i	0.414554	−	0.256783i
$623$	30.6240	+	3.15807i	1.22693	+	0.126526i
$624$	−10.5370	−	13.9325i	−0.421817	−	0.557746i
$625$	10.4170	−	18.0428i	0.416680	−	0.721711i
$626$	−11.7992	+	21.9823i	−0.471591	+	0.878591i
$627$	0.204619	−	0.763647i	0.00817168	−	0.0304971i
$628$	7.66087	−	37.8230i	0.305702	−	1.50930i
$629$	3.42479	−	3.42479i	0.136555	−	0.136555i
$630$	−1.95491	+	0.376004i	−0.0778856	+	0.0149804i
$631$	10.0961			0.401919			0.200960	−	0.979600i	$-0.435594\pi$
$631$	10.0961			0.401919			0.200960	+	0.979600i	$0.435594\pi$
$632$	12.5583	+	5.76959i	0.499544	+	0.229502i
$633$	−12.9845	−	22.4898i	−0.516087	−	0.893888i
$634$	−3.33362	−	11.0589i	−0.132395	−	0.439207i
$635$	4.03022	−	1.07990i	0.159935	−	0.0428543i
$636$	7.68671	−	15.4508i	0.304798	−	0.612666i
$637$	30.5212	−	1.71948i	1.20929	−	0.0681284i
$638$	−48.1158	+	29.8039i	−1.90492	+	1.17995i
$639$	−3.24919	−	1.87592i	−0.128536	−	0.0742104i
$640$	2.77245	+	5.34296i	0.109591	+	0.211199i
$641$	−8.60375	−	14.9021i	−0.339828	−	0.588599i	0.644572	−	0.764543i	$-0.277035\pi$
$641$	−8.60375	−	14.9021i	−0.339828	−	0.588599i	−0.984400	+	0.175945i	$0.943702\pi$
$642$	0.485761	+	15.6754i	0.0191715	+	0.618660i
$643$	0.510936	−	0.510936i	0.0201493	−	0.0201493i	−0.696960	−	0.717110i	$-0.745465\pi$
$643$	0.510936	−	0.510936i	0.0201493	−	0.0201493i	0.717110	+	0.696960i	$0.245465\pi$
$644$	22.8429	+	0.932584i	0.900138	+	0.0367489i
$645$	−1.17800	−	1.17800i	−0.0463835	−	0.0463835i
$646$	−0.284376	−	0.267281i	−0.0111886	−	0.0105160i
$647$	−22.6226	+	13.0612i	−0.889386	+	0.513487i	−0.873742	−	0.486391i	$-0.838313\pi$
$647$	−22.6226	+	13.0612i	−0.889386	+	0.513487i	−0.0156442	+	0.999878i	$0.504980\pi$
$648$	1.63543	+	2.30768i	0.0642457	+	0.0906541i
$649$	18.6854	−	32.3641i	0.733468	−	1.27040i
$650$	−28.3591	−	6.66464i	−1.11233	−	0.261409i
$651$	−5.16283	+	4.19755i	−0.202347	+	0.164515i
$652$	17.2041	−	5.77307i	0.673763	−	0.226091i
$653$	−4.95648	−	18.4979i	−0.193962	−	0.723877i	−0.992533	−	0.121976i	$-0.961077\pi$
$653$	−4.95648	−	18.4979i	−0.193962	−	0.723877i	0.798571	−	0.601901i	$-0.205590\pi$
$654$	−6.03888	−	3.24142i	−0.236139	−	0.126750i
$655$	7.64519	−	4.41395i	0.298722	−	0.172467i
$656$	−34.2577	+	4.26691i	−1.33754	+	0.166595i
$657$		−	1.50771i		−	0.0588212i
$658$	−34.2019	−	2.45930i	−1.33333	−	0.0958737i
$659$	7.67275	+	7.67275i	0.298888	+	0.298888i	0.840578	−	0.541690i	$-0.182215\pi$
$659$	7.67275	+	7.67275i	0.298888	+	0.298888i	−0.541690	+	0.840578i	$0.682215\pi$
$660$	1.36756	−	6.75185i	0.0532321	−	0.262816i
$661$	−38.9014	−	10.4236i	−1.51309	−	0.405431i	−0.595629	−	0.803259i	$-0.703097\pi$
$661$	−38.9014	−	10.4236i	−1.51309	−	0.405431i	−0.917460	+	0.397828i	$0.869764\pi$
$662$	−12.0267	−	39.8975i	−0.467432	−	1.55066i
$663$	8.54658	+	4.93437i	0.331922	+	0.191635i
$664$	−27.1129	+	32.6864i	−1.05218	+	1.26848i
$665$	−0.139268	−	0.100768i	−0.00540059	−	0.00390761i
$666$	−2.95067	−	0.693433i	−0.114336	−	0.0268700i
$667$	−6.91273	−	25.7987i	−0.267662	−	0.998928i
$668$	−1.55602	−	25.0822i	−0.0602043	−	0.970460i
$669$	−13.9484	−	3.73746i	−0.539276	−	0.144498i
$670$	−5.79541	+	0.179592i	−0.223896	+	0.00693824i
$671$	−64.4692			−2.48881
$672$	4.62171	+	14.2352i	0.178286	+	0.549133i
$673$	−0.953677			−0.0367616			−0.0183808	−	0.999831i	$-0.505851\pi$
$673$	−0.953677			−0.0367616			−0.0183808	+	0.999831i	$0.505851\pi$
$674$	−26.7711	+	0.829600i	−1.03118	+	0.0319550i
$675$	4.55620	+	1.22083i	0.175368	+	0.0469898i
$676$	0.751857	+	12.1195i	0.0289176	+	0.466135i
$677$	10.5233	+	39.2733i	0.404441	+	1.50940i	0.805084	+	0.593161i	$0.202120\pi$
$677$	10.5233	+	39.2733i	0.404441	+	1.50940i	−0.400642	+	0.916235i	$0.631213\pi$
$678$	−12.7303	−	2.99173i	−0.488903	−	0.114897i
$679$	−37.6308	+	16.8427i	−1.44414	+	0.646365i
$680$	−2.61743	−	2.17112i	−0.100374	−	0.0832585i
$681$	7.49003	+	4.32437i	0.287019	+	0.165710i
$682$	−6.64553	−	22.0459i	−0.254470	−	0.844180i
$683$	4.50593	+	1.20736i	0.172415	+	0.0461983i	0.343993	−	0.938972i	$-0.388220\pi$
$683$	4.50593	+	1.20736i	0.172415	+	0.0461983i	−0.171579	+	0.985170i	$0.554887\pi$
$684$	−0.0484840	+	0.239374i	−0.00185383	+	0.00915268i
$685$	2.39195	+	2.39195i	0.0913919	+	0.0913919i
$686$	−25.1910	−	7.17030i	−0.961797	−	0.273763i
$687$			3.99843i			0.152550i
$688$	−7.69377	+	9.88301i	−0.293322	+	0.376786i
$689$	−32.6336	+	18.8410i	−1.24324	+	0.717785i
$690$	2.86434	+	1.53746i	0.109044	+	0.0585301i
$691$	0.900846	+	3.36200i	0.0342698	+	0.127897i	0.980942	−	0.194303i	$-0.0622445\pi$
$691$	0.900846	+	3.36200i	0.0342698	+	0.127897i	−0.946672	+	0.322200i	$0.895578\pi$
$692$	7.34167	−	2.46360i	0.279088	−	0.0936520i
$693$	6.10699	−	16.0029i	0.231985	−	0.607900i
$694$	−14.5551	−	3.42059i	−0.552506	−	0.129844i
$695$	1.46789	−	2.54247i	0.0556804	−	0.0964413i
$696$	14.2657	−	10.1100i	0.540741	−	0.383218i
$697$	16.8905	−	9.75173i	0.639773	−	0.369373i
$698$	−33.6716	−	31.6474i	−1.27449	−	1.19787i
$699$	1.05199	+	1.05199i	0.0397899	+	0.0397899i
$700$	21.0886	+	13.3512i	0.797074	+	0.504627i
$701$	−27.1670	+	27.1670i	−1.02608	+	1.02608i	−0.0264314	+	0.999651i	$0.508414\pi$
$701$	−27.1670	+	27.1670i	−1.02608	+	1.02608i	−0.999651	+	0.0264314i	$0.991586\pi$
$702$	−0.191294	−	6.17302i	−0.00721992	−	0.232986i
$703$	−0.130865	−	0.226666i	−0.00493568	−	0.00854886i
$704$	−51.6427	−	3.92862i	−1.94636	−	0.148065i
$705$	−4.22268	−	2.43796i	−0.159035	−	0.0918190i
$706$	13.2220	−	8.19001i	0.497618	−	0.308235i
$707$	−1.27834	−	7.97004i	−0.0480769	−	0.299744i
$708$	−5.14232	+	10.3364i	−0.193260	+	0.388467i
$709$	−40.1041	+	10.7459i	−1.50614	+	0.403569i	−0.915152	−	0.403110i	$-0.867929\pi$
$709$	−40.1041	+	10.7459i	−1.50614	+	0.403569i	−0.590990	+	0.806679i	$0.701263\pi$
$710$	−0.814756	−	2.70287i	−0.0305773	−	0.101437i
$711$	2.44310	+	4.23158i	0.0916236	+	0.158697i
$712$	13.7399	−	29.9069i	0.514925	−	1.12081i
$713$	10.8658			0.406927
$714$	−5.53467	−	6.39228i	−0.207130	−	0.239225i
$715$	−10.6365	+	10.6365i	−0.397784	+	0.397784i
$716$	−0.282698	+	1.39573i	−0.0105649	+	0.0521607i
$717$	3.71523	−	13.8654i	0.138748	−	0.517814i
$718$	−17.4758	+	32.5581i	−0.652193	+	1.21506i
$719$	−24.4734	+	42.3891i	−0.912703	+	1.58085i	−0.102474	+	0.994736i	$0.532676\pi$
$719$	−24.4734	+	42.3891i	−0.912703	+	1.58085i	−0.810230	+	0.586113i	$0.800658\pi$
$720$	−0.292516	+	2.10800i	−0.0109014	+	0.0785604i
$721$	−4.65978	+	45.1862i	−0.173539	+	1.68282i
$722$	22.8249	−	14.1382i	0.849456	−	0.526171i
$723$	1.93340	−	0.518053i	0.0719039	−	0.0192666i
$724$	−5.19563	+	5.88291i	−0.193094	+	0.218636i
$725$	7.54699	−	28.1658i	0.280288	−	1.04605i
$726$	31.8552	+	29.9402i	1.18226	+	1.11119i
$727$		−	21.3746i		−	0.792739i	−0.918091	−	0.396369i	$-0.870270\pi$
$727$		−	21.3746i		−	0.792739i	0.918091	−	0.396369i	$-0.129730\pi$
$728$	8.76798	−	31.4821i	0.324963	−	1.16680i
$729$			1.00000i			0.0370370i
$730$	0.776942	−	0.826635i	0.0287559	−	0.0305951i
$731$	1.83136	−	6.83473i	0.0677353	−	0.252792i
$732$	19.8782	−	1.23318i	0.734718	−	0.0455796i
$733$	−14.0396	+	3.76190i	−0.518565	+	0.138949i	−0.508603	−	0.861001i	$-0.669838\pi$
$733$	−14.0396	+	3.76190i	−0.518565	+	0.138949i	−0.00996222	+	0.999950i	$0.503171\pi$
$734$	−3.59536	−	5.80438i	−0.132707	−	0.214244i
$735$	−2.77747	−	2.48121i	−0.102448	−	0.0915207i
$736$	8.80854	−	22.7979i	0.324687	−	0.840343i
$737$	24.9441	−	43.2045i	0.918828	−	1.59146i
$738$	−10.7542	−	5.77243i	−0.395869	−	0.212486i
$739$	5.50536	−	20.5463i	0.202518	−	0.755807i	−0.787674	−	0.616092i	$-0.788715\pi$
$739$	5.50536	−	20.5463i	0.202518	−	0.755807i	0.990192	−	0.139715i	$-0.0446185\pi$
$740$	−1.26043	−	1.90071i	−0.0463345	−	0.0698715i
$741$	0.377097	−	0.377097i	0.0138530	−	0.0138530i
$742$	31.7043	−	6.09794i	1.16390	−	0.223862i
$743$	35.9378			1.31843			0.659214	−	0.751955i	$-0.270889\pi$
$743$	35.9378			1.31843			0.659214	+	0.751955i	$0.270889\pi$
$744$	2.47075	+	6.67041i	0.0905821	+	0.244549i
$745$	−0.979097	−	1.69585i	−0.0358713	−	0.0621310i
$746$	−0.836051	+	0.252020i	−0.0306100	+	0.00922711i
$747$	−14.5030	+	3.88607i	−0.530637	+	0.142184i
$748$	27.7397	−	9.30846i	1.01427	−	0.340351i
$749$	−22.7654	+	18.5090i	−0.831828	+	0.676304i
$750$	3.85002	+	6.21551i	0.140583	+	0.226958i
$751$	−21.0586	−	12.1582i	−0.768438	−	0.443658i	0.0638792	−	0.997958i	$-0.479653\pi$
$751$	−21.0586	−	12.1582i	−0.768438	−	0.443658i	−0.832317	+	0.554300i	$0.812986\pi$
$752$	−14.2645	+	33.7685i	−0.520174	+	1.23141i
$753$	0.613768	+	1.06308i	0.0223669	+	0.0387407i
$754$	−38.1607	+	1.18255i	−1.38973	+	0.0430659i
$755$	−3.91803	+	3.91803i	−0.142592	+	0.142592i
$756$	−1.57690	+	5.05108i	−0.0573512	+	0.183706i
$757$	−7.63746	−	7.63746i	−0.277588	−	0.277588i	0.554557	−	0.832146i	$-0.312888\pi$
$757$	−7.63746	−	7.63746i	−0.277588	−	0.277588i	−0.832146	+	0.554557i	$0.812888\pi$
$758$	−22.7876	+	24.2451i	−0.827683	+	0.880621i
$759$	−24.2235	+	13.9855i	−0.879258	+	0.507640i
$760$	−0.149935	+	0.106258i	−0.00543871	+	0.00385437i
$761$	1.18820	−	2.05803i	0.0430723	−	0.0746035i	−0.843686	−	0.536838i	$-0.819619\pi$
$761$	1.18820	−	2.05803i	0.0430723	−	0.0746035i	0.886758	+	0.462234i	$0.152952\pi$
$762$	2.53723	−	10.7963i	0.0919142	−	0.391109i
$763$	−2.03066	−	12.6605i	−0.0735148	−	0.458341i
$764$	37.6880	+	18.7496i	1.36350	+	0.678336i
$765$	−0.311185	−	1.16136i	−0.0112509	−	0.0419889i
$766$	9.83388	−	18.3209i	0.355313	−	0.661960i
$767$	21.8315	−	12.6044i	0.788289	−	0.455119i
$768$	15.9984	+	0.223502i	0.577294	+	0.00806494i
$769$			20.1727i			0.727447i	0.931507	+	0.363724i	$0.118495\pi$
$769$			20.1727i			0.727447i	−0.931507	+	0.363724i	$0.881505\pi$
$770$	11.5948	−	5.62694i	0.417848	−	0.202781i
$771$	7.65705	+	7.65705i	0.275762	+	0.275762i
$772$	−20.3825	−	30.7364i	−0.733583	−	1.10623i
$773$	−10.3499	−	2.77324i	−0.372260	−	0.0997467i	0.0678386	−	0.997696i	$-0.478390\pi$
$773$	−10.3499	−	2.77324i	−0.372260	−	0.0997467i	−0.440098	+	0.897950i	$0.645056\pi$
$774$	−4.23971	+	1.27802i	−0.152393	+	0.0459376i
$775$	10.2734	+	5.93137i	0.369033	+	0.213061i
$776$	4.09024	+	43.8845i	0.146831	+	1.57536i
$777$	−2.31658	−	5.17580i	−0.0831067	−	0.185681i
$778$	−1.53408	+	6.52773i	−0.0549993	+	0.234031i
$779$	−0.272781	−	1.01803i	−0.00977339	−	0.0364748i
$780$	3.07616	−	3.48308i	0.110144	−	0.124714i
$781$	23.4618	+	6.28656i	0.839528	+	0.224951i
$782$	0.427676	+	13.8010i	0.0152936	+	0.493524i
$783$	6.18185			0.220921
$784$	−15.9301	+	23.0268i	−0.568931	+	0.822385i
$785$	10.2662			0.366415
$786$	−0.726801	−	23.4538i	−0.0259242	−	0.836569i
$787$	7.37662	+	1.97656i	0.262948	+	0.0704568i	0.387884	−	0.921708i	$-0.373206\pi$
$787$	7.37662	+	1.97656i	0.262948	+	0.0704568i	−0.124936	+	0.992165i	$0.539873\pi$
$788$	35.5718	+	31.4161i	1.26719	+	1.11915i
$789$	0.00233999	+	0.00873295i	8.33057e−5	+	0.000310901i
$790$	−0.841104	+	3.57903i	−0.0299251	+	0.127336i
$791$	−9.99458	−	22.3304i	−0.355366	−	0.793976i
$792$	−14.0937	−	11.6905i	−0.500798	−	0.415404i
$793$	−37.6619	−	21.7441i	−1.33741	−	0.772156i
$794$	−11.0315	+	3.32535i	−0.391494	+	0.118012i
$795$	4.43443	+	1.18820i	0.157273	+	0.0421412i
$796$	−29.9447	+	19.8575i	−1.06136	+	0.703829i
$797$	38.9100	+	38.9100i	1.37826	+	1.37826i	0.847553	+	0.530711i	$0.178075\pi$
$797$	38.9100	+	38.9100i	1.37826	+	1.37826i	0.530711	+	0.847553i	$0.321925\pi$
$798$	−0.411071	+	0.199492i	−0.0145518	+	0.00706193i
$799$		−	20.7098i		−	0.732660i
$800$	20.7732	−	16.7468i	0.734444	−	0.592087i
$801$	10.0772	−	5.81809i	0.356062	−	0.205572i
$802$	5.03925	−	9.38830i	0.177942	−	0.331512i
$803$	2.52630	+	9.42828i	0.0891512	+	0.332717i
$804$	−6.86474	+	13.7986i	−0.242101	+	0.486640i
$805$	0.963176	+	6.00509i	0.0339475	+	0.211652i
$806$	3.55340	−	15.1203i	0.125163	−	0.532588i
$807$	−6.32417	+	10.9538i	−0.222621	+	0.385591i
$808$	−8.50649	−	1.45024i	−0.299257	−	0.0510194i
$809$	2.52237	−	1.45629i	0.0886819	−	0.0512005i	−0.455003	−	0.890490i	$-0.650362\pi$
$809$	2.52237	−	1.45629i	0.0886819	−	0.0512005i	0.543685	+	0.839289i	$0.317029\pi$
$810$	−0.515314	+	0.548273i	−0.0181063	+	0.0192644i
$811$	−2.45352	−	2.45352i	−0.0861548	−	0.0861548i	0.662716	−	0.748871i	$-0.269404\pi$
$811$	−2.45352	−	2.45352i	−0.0861548	−	0.0861548i	−0.748871	+	0.662716i	$0.769404\pi$
$812$	31.2250	+	9.74815i	1.09578	+	0.342093i
$813$	18.8937	−	18.8937i	0.662632	−	0.662632i
$814$	19.6136	−	0.607799i	0.687456	−	0.0213033i
$815$	2.41375	+	4.18074i	0.0845501	+	0.146445i
$816$	−8.37510	+	3.40074i	−0.293187	+	0.119050i
$817$	−0.331142	−	0.191185i	−0.0115852	−	0.00668872i
$818$	−12.3943	−	20.0095i	−0.433357	−	0.699617i
$819$	8.96505	−	7.28888i	0.313264	−	0.254694i
$820$	−2.92165	−	8.70668i	−0.102028	−	0.304050i
$821$	−7.23667	+	1.93906i	−0.252561	+	0.0676736i	−0.382878	−	0.923799i	$-0.625067\pi$
$821$	−7.23667	+	1.93906i	−0.252561	+	0.0676736i	0.130317	+	0.991472i	$0.458401\pi$
$822$	8.60886	−	2.59506i	0.300268	−	0.0905132i
$823$	22.3471	+	38.7063i	0.778971	+	1.34922i	0.932535	+	0.361079i	$0.117591\pi$
$823$	22.3471	+	38.7063i	0.778971	+	1.34922i	−0.153564	+	0.988139i	$0.549075\pi$
$824$	44.1280	+	20.2734i	1.53727	+	0.706259i
$825$	−30.5373			−1.06317
$826$	−21.2098	+	4.07945i	−0.737985	+	0.141942i
$827$	32.9750	−	32.9750i	1.14665	−	1.14665i	0.159447	−	0.987207i	$-0.449029\pi$
$827$	32.9750	−	32.9750i	1.14665	−	1.14665i	0.987207	−	0.159447i	$-0.0509710\pi$
$828$	7.20146	−	4.77557i	0.250268	−	0.165962i
$829$	7.56065	−	28.2167i	0.262592	−	0.980008i	−0.701115	−	0.713048i	$-0.747314\pi$
$829$	7.56065	−	28.2167i	0.262592	−	0.980008i	0.963708	−	0.266960i	$-0.0860192\pi$
$830$	−9.95416	−	5.34298i	−0.345514	−	0.185457i
$831$	−11.7511	+	20.3534i	−0.407639	+	0.706052i
$832$	−28.8438	−	19.7130i	−0.999980	−	0.683427i
$833$	3.22823	−	15.4857i	0.111851	−	0.536548i
$834$	−4.10919	−	6.63392i	−0.142290	−	0.229714i
$835$	6.45751	−	1.73029i	0.223471	−	0.0598790i
$836$	−0.0979027	−	1.57814i	−0.00338604	−	0.0545810i
$837$	−0.650912	+	2.42924i	−0.0224988	+	0.0839667i
$838$	0.718407	−	0.764356i	0.0248170	−	0.0264042i
$839$		−	5.52046i		−	0.190588i	−0.995449	−	0.0952938i	$-0.969621\pi$
$839$		−	5.52046i		−	0.190588i	0.995449	−	0.0952938i	$-0.0303790\pi$
$840$	−3.46746	+	1.95677i	−0.119639	+	0.0675151i
$841$		−	9.21532i		−	0.317770i
$842$	18.5720	+	17.4556i	0.640033	+	0.601558i
$843$	−3.17585	+	11.8524i	−0.109382	+	0.408220i
$844$	−38.9292	−	34.3812i	−1.34000	−	1.18345i
$845$	−3.12021	+	0.836059i	−0.107339	+	0.0287613i
$846$	−11.0180	+	6.82478i	−0.378806	+	0.234641i
$847$	−8.38970	+	81.3555i	−0.288274	+	2.79541i
$848$	4.74395	−	34.1870i	0.162908	−	1.17399i
$849$	10.6013	−	18.3620i	0.363836	−	0.630183i
$850$	−7.12930	+	13.2821i	−0.244533	+	0.455573i
$851$	−2.39668	+	8.94451i	−0.0821570	+	0.306614i
$852$	−7.35435	−	1.48959i	−0.251956	−	0.0510325i
$853$	34.1830	−	34.1830i	1.17040	−	1.17040i	0.188292	−	0.982113i	$-0.439705\pi$
$853$	34.1830	−	34.1830i	1.17040	−	1.17040i	0.982113	−	0.188292i	$-0.0602950\pi$
$854$	24.3894	+	28.1687i	0.834589	+	0.963912i
$855$	−0.0649723			−0.00222201
$856$	10.8947	+	29.4130i	0.372374	+	1.00532i
$857$	14.2392	+	24.6629i	0.486400	+	0.842470i	0.999878	−	0.0156331i	$-0.00497638\pi$
$857$	14.2392	+	24.6629i	0.486400	+	0.842470i	−0.513478	+	0.858103i	$0.671643\pi$
$858$	11.5397	+	38.2818i	0.393959	+	1.30692i
$859$	30.2932	−	8.11704i	1.03359	−	0.276950i	0.298136	−	0.954523i	$-0.403635\pi$
$859$	30.2932	−	8.11704i	1.03359	−	0.276950i	0.735455	+	0.677574i	$0.236968\pi$
$860$	−2.98310	−	1.48408i	−0.101723	−	0.0506066i
$861$	−3.61627	−	22.5463i	−0.123242	−	0.768375i
$862$	−19.8990	+	12.3259i	−0.677763	+	0.419821i
$863$	−3.70091	−	2.13672i	−0.125980	−	0.0727348i	0.435685	−	0.900099i	$-0.356506\pi$
$863$	−3.70091	−	2.13672i	−0.125980	−	0.0727348i	−0.561666	+	0.827364i	$0.689839\pi$
$864$	4.56921	+	3.33501i	0.155448	+	0.113459i
$865$	1.03005	+	1.78409i	0.0350226	+	0.0606609i
$866$	−1.20901	−	39.0145i	−0.0410837	−	1.32577i
$867$	−8.40983	+	8.40983i	−0.285613	+	0.285613i
$868$	−7.11847	+	11.2438i	−0.241616	+	0.381641i
$869$	−22.3681	−	22.3681i	−0.758786	−	0.758786i
$870$	3.38934	+	3.18560i	0.114910	+	0.108002i
$871$	29.1439	−	16.8262i	0.987504	−	0.570136i
$872$	−13.5127	−	2.30373i	−0.457597	−	0.0780142i
$873$	−7.79138	+	13.4951i	−0.263698	+	0.456739i
$874$	0.726362	+	0.170702i	0.0245695	+	0.00577407i
$875$	−4.87681	+	12.7793i	−0.164866	+	0.432019i
$876$	−0.959295	−	2.85875i	−0.0324116	−	0.0965883i
$877$	3.16718	+	11.8201i	0.106948	+	0.399135i	0.998559	−	0.0536671i	$-0.0170910\pi$
$877$	3.16718	+	11.8201i	0.106948	+	0.399135i	−0.891611	+	0.452802i	$0.850424\pi$
$878$	9.07909	+	4.87328i	0.306404	+	0.164465i
$879$	12.2170	−	7.05348i	0.412069	−	0.237908i
$880$	−1.70293	−	13.6723i	−0.0574056	−	0.460892i
$881$			55.3474i			1.86470i	0.361557	+	0.932350i	$0.382245\pi$
$881$			55.3474i			1.86470i	−0.361557	+	0.932350i	$0.617755\pi$
$882$	−9.30252	+	3.38574i	−0.313232	+	0.114004i
$883$	−7.09926	−	7.09926i	−0.238909	−	0.238909i	0.577489	−	0.816398i	$-0.304033\pi$
$883$	−7.09926	−	7.09926i	−0.238909	−	0.238909i	−0.816398	+	0.577489i	$0.804033\pi$
$884$	19.3447	+	3.91817i	0.650631	+	0.131782i
$885$	−2.96658	−	0.794894i	−0.0997206	−	0.0267201i
$886$	−2.63177	−	8.73062i	−0.0884159	−	0.293311i
$887$	−46.0761	−	26.6021i	−1.54708	−	0.893210i	−0.998362	−	0.0572050i	$-0.981781\pi$
$887$	−46.0761	−	26.6021i	−1.54708	−	0.893210i	−0.548722	−	0.836005i	$-0.684886\pi$
$888$	−6.03594	+	0.562579i	−0.202553	+	0.0188789i
$889$	18.9380	−	8.47622i	0.635159	−	0.284283i
$890$	8.52322	+	2.00303i	0.285699	+	0.0671419i
$891$	−1.67559	−	6.25340i	−0.0561345	−	0.209497i
$892$	−28.8254	+	1.78824i	−0.965147	+	0.0598747i
$893$	−1.08100	−	0.289653i	−0.0361743	−	0.00969288i
$894$	−5.20248	+	0.161218i	−0.173997	+	0.00539194i
$895$	−0.378837			−0.0126631
$896$	17.8205	+	24.0506i	0.595340	+	0.803474i
$897$	−18.8680			−0.629984
$898$	−9.66286	+	0.299439i	−0.322454	+	0.00999242i
$899$	15.0172	+	4.02384i	0.500851	+	0.134203i
$900$	9.41575	−	0.584124i	0.313858	−	0.0194708i
$901$	5.04672	+	18.8346i	0.168131	+	0.627472i
$902$	76.9228	+	18.0776i	2.56125	+	0.601917i
$903$	−6.71167	−	4.85625i	−0.223350	−	0.161606i
$904$	−26.0413	+	2.42717i	−0.866121	+	0.0807266i
$905$	−1.80823	−	1.04398i	−0.0601076	−	0.0347031i
$906$	4.25072	+	14.1013i	0.141221	+	0.468486i
$907$	43.1506	+	11.5622i	1.43279	+	0.383915i	0.890003	−	0.455955i	$-0.150702\pi$
$907$	43.1506	+	11.5622i	1.43279	+	0.383915i	0.542788	+	0.839870i	$0.317369\pi$
$908$	16.9532	+	3.43380i	0.562613	+	0.113955i
$909$	−2.15731	−	2.15731i	−0.0715534	−	0.0715534i
$910$	8.67136	+	0.623519i	0.287453	+	0.0206694i
$911$		−	33.2113i		−	1.10034i	−0.835053	−	0.550169i	$-0.814563\pi$
$911$		−	33.2113i		−	1.10034i	0.835053	−	0.550169i	$-0.185437\pi$
$912$	0.0603738	+	0.484723i	0.00199918	+	0.0160508i
$913$	84.1816	−	48.6023i	2.78600	−	1.60850i
$914$	35.6819	+	19.1526i	1.18025	+	0.633511i
$915$	1.37129	+	5.11771i	0.0453333	+	0.169186i
$916$	2.54404	+	7.58140i	0.0840576	+	0.250496i
$917$	34.0618	−	27.6934i	1.12482	−	0.914515i
$918$	−3.11109	−	0.731134i	−0.102681	−	0.0241310i
$919$	20.2101	−	35.0049i	0.666669	−	1.15471i	−0.312161	−	0.950029i	$-0.601053\pi$
$919$	20.2101	−	35.0049i	0.666669	−	1.15471i	0.978830	−	0.204676i	$-0.0656140\pi$
$920$	6.40928	+	1.09270i	0.211308	+	0.0360252i
$921$	23.6993	−	13.6828i	0.780918	−	0.450863i
$922$	36.5400	+	34.3434i	1.20338	+	1.13104i
$923$	11.5857	+	11.5857i	0.381347	+	0.381347i
$924$	1.39741	−	34.2286i	0.0459716	−	1.12604i
$925$	−7.14862	+	7.14862i	−0.235045	+	0.235045i
$926$	−0.147461	−	4.75855i	−0.00484588	−	0.156376i
$927$	8.58468	+	14.8691i	0.281958	+	0.488365i
$928$	20.6166	−	28.2462i	0.676771	−	0.927227i
$929$	−51.0649	−	29.4823i	−1.67538	−	0.967284i	−0.964541	−	0.263934i	$-0.914980\pi$
$929$	−51.0649	−	29.4823i	−1.67538	−	0.967284i	−0.710844	−	0.703350i	$-0.751687\pi$
$930$	−1.60870	+	0.996461i	−0.0527513	+	0.0326753i
$931$	−0.763165	−	0.385093i	−0.0250117	−	0.0126209i
$932$	2.66401	+	1.32533i	0.0872626	+	0.0434127i
$933$	8.30660	−	2.22575i	0.271946	−	0.0728677i
$934$	6.15449	+	20.4169i	0.201381	+	0.668062i
$935$	3.89192	+	6.74100i	0.127279	+	0.220454i
$936$	−4.29037	−	11.5829i	−0.140235	−	0.378600i
$937$	−51.0514			−1.66778			−0.833888	−	0.551934i	$-0.813890\pi$
$937$	−51.0514			−1.66778			−0.833888	+	0.551934i	$0.813890\pi$
$938$	−28.3140	+	5.44586i	−0.924486	+	0.177814i
$939$	−12.4744	+	12.4744i	−0.407087	+	0.407087i
$940$	−9.55777	−	1.93588i	−0.311740	−	0.0631416i
$941$	0.108289	−	0.404141i	0.00353013	−	0.0131746i	−0.964138	−	0.265400i	$-0.914496\pi$
$941$	0.108289	−	0.404141i	0.00353013	−	0.0131746i	0.967668	+	0.252226i	$0.0811625\pi$
$942$	12.9055	−	24.0433i	0.420483	−	0.783375i
$943$	−18.6443	+	32.2929i	−0.607142	+	1.05160i
$944$	−3.17365	+	22.8707i	−0.103294	+	0.744378i
$945$	−1.40024	−	0.144399i	−0.0455499	−	0.00469729i
$946$	24.3712	−	15.0960i	0.792374	−	0.490814i
$947$	−11.8005	+	3.16192i	−0.383463	+	0.102749i	−0.445401	−	0.895331i	$-0.646939\pi$
$947$	−11.8005	+	3.16192i	−0.383463	+	0.102749i	0.0619374	+	0.998080i	$0.480272\pi$
$948$	7.32474	+	6.46902i	0.237897	+	0.210104i
$949$	−1.70414	+	6.35992i	−0.0553186	+	0.206452i
$950$	0.593582	+	0.557899i	0.0192584	+	0.0181006i
$951$		−	8.16741i		−	0.264846i
$952$	−14.5614	−	8.59888i	−0.471938	−	0.278691i
$953$			35.0073i			1.13400i	0.823719	+	0.566998i	$0.191895\pi$
$953$			35.0073i			1.13400i	−0.823719	+	0.566998i	$0.808105\pi$
$954$	8.35724	−	8.89177i	0.270576	−	0.287882i
$955$	−2.89829	+	10.8166i	−0.0937864	+	0.350015i
$956$	−1.77761	−	28.6540i	−0.0574919	−	0.926737i
$957$	−38.6576	+	10.3583i	−1.24962	+	0.334835i
$958$	−6.90961	−	11.1549i	−0.223239	−	0.360400i
$959$	13.6282	+	9.86077i	0.440079	+	0.318421i
$960$	0.786599	+	4.18308i	0.0253874	+	0.135008i
$961$	12.3376	−	21.3693i	0.397986	−	0.689332i
$962$	11.6629	+	6.26018i	0.376029	+	0.201836i
$963$	−2.87018	+	10.7117i	−0.0924903	+	0.345179i
$964$	3.33629	−	2.21242i	0.107455	−	0.0712574i
$965$	6.93752	−	6.93752i	0.223327	−	0.223327i
$966$	15.2747	+	5.29317i	0.491456	+	0.170305i
$967$	−43.4971			−1.39877			−0.699387	−	0.714743i	$-0.746543\pi$
$967$	−43.4971			−1.39877			−0.699387	+	0.714743i	$0.746543\pi$
$968$	79.4503	+	36.5013i	2.55363	+	1.17320i
$969$	−0.137980	−	0.238989i	−0.00443256	−	0.00767743i
$970$	−11.2260	+	3.38398i	−0.360445	+	0.108653i
$971$	−55.3893	+	14.8415i	−1.77753	+	0.476287i	−0.990129	−	0.140158i	$-0.955239\pi$
$971$	−55.3893	+	14.8415i	−1.77753	+	0.476287i	−0.787398	+	0.616445i	$0.788572\pi$
$972$	0.636261	+	1.89609i	0.0204081	+	0.0608172i
$973$	5.20510	−	13.6395i	0.166868	−	0.437264i
$974$	−7.70013	−	12.4312i	−0.246728	−	0.398320i
$975$	−17.8394	−	10.2996i	−0.571319	−	0.329851i
$976$	36.9062	−	14.9859i	1.18134	−	0.479688i
$977$	14.5405	+	25.1848i	0.465191	+	0.805734i	0.999210	−	0.0397379i	$-0.0126523\pi$
$977$	14.5405	+	25.1848i	0.465191	+	0.805734i	−0.534019	+	0.845472i	$0.679319\pi$
$978$	12.8256	−	0.397449i	0.410118	−	0.0127090i
$979$	−53.2682	+	53.2682i	−1.70246	+	1.70246i
$980$	−6.84504	−	2.93741i	−0.218657	−	0.0938321i
$981$	−3.42691	−	3.42691i	−0.109413	−	0.109413i
$982$	−17.5896	+	18.7146i	−0.561305	+	0.597206i
$983$	33.9117	−	19.5789i	1.08161	−	0.624470i	0.150283	−	0.988643i	$-0.451982\pi$
$983$	33.9117	−	19.5789i	1.08161	−	0.624470i	0.931331	+	0.364173i	$0.118648\pi$
$984$	−24.0638	−	4.10256i	−0.767127	−	0.130785i
$985$	−6.31257	+	10.9337i	−0.201135	+	0.348377i
$986$	−4.51976	+	19.2323i	−0.143939	+	0.612480i
$987$	−22.6533	−	8.64492i	−0.721064	−	0.275171i
$988$	0.475079	−	0.954943i	0.0151143	−	0.0303808i
$989$	3.50137	+	13.0673i	0.111337	+	0.415516i
$990$	2.30378	−	4.29202i	0.0732189	−	0.136410i
$991$	4.95458	−	2.86053i	0.157387	−	0.0908676i	−0.419238	−	0.907876i	$-0.637703\pi$
$991$	4.95458	−	2.86053i	0.157387	−	0.0908676i	0.576625	+	0.817009i	$0.304369\pi$
$992$	8.92890	+	11.0757i	0.283493	+	0.351653i
$993$		−	29.4657i		−	0.935065i
$994$	−6.12905	−	12.6295i	−0.194402	−	0.400582i
$995$	−6.75881	−	6.75881i	−0.214269	−	0.214269i
$996$	−25.0265	+	16.5961i	−0.792996	+	0.525866i
$997$	4.51940	+	1.21097i	0.143131	+	0.0383518i	0.329673	−	0.944095i	$-0.393061\pi$
$997$	4.51940	+	1.21097i	0.143131	+	0.0383518i	−0.186542	+	0.982447i	$0.559728\pi$
$998$	−7.89119	+	2.37873i	−0.249791	+	0.0752973i
$999$	−1.85613	−	1.07164i	−0.0587254	−	0.0339051i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	336.2.bs.a.187.32	yes	128
7.3	odd	6	inner	336.2.bs.a.283.13	yes	128
16.3	odd	4	inner	336.2.bs.a.19.13	✓	128
112.3	even	12	inner	336.2.bs.a.115.32	yes	128

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
336.2.bs.a.19.13	✓	128	16.3	odd	4	inner
336.2.bs.a.115.32	yes	128	112.3	even	12	inner
336.2.bs.a.187.32	yes	128	1.1	even	1	trivial
336.2.bs.a.283.13	yes	128	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:	\( N \)	\(=\)	\( 336 = 2^{4} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	336.bs (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.41354 - 0.0438036i) q^{2} +(0.965926 + 0.258819i) q^{3} +(1.99616 - 0.123836i) q^{4} +(0.137704 + 0.513920i) q^{5} +(1.37671 + 0.323539i) q^{6} +(1.08086 + 2.41490i) q^{7} +(2.81622 - 0.262485i) q^{8} +(0.866025 + 0.500000i) q^{9} +(0.217161 + 0.720412i) q^{10} +(-6.25340 - 1.67559i) q^{11} +(1.96020 + 0.397029i) q^{12} +(-3.08799 - 3.08799i) q^{13} +(1.63361 + 3.36620i) q^{14} +0.532049i q^{15} +(3.96933 - 0.494393i) q^{16} +(-1.95705 + 1.12990i) q^{17} +(1.24606 + 0.668833i) q^{18} +(0.0316062 + 0.117956i) q^{19} +(0.338522 + 1.00881i) q^{20} +(0.419005 + 2.61236i) q^{21} +(-8.91279 - 2.09459i) q^{22} +(2.16025 - 3.74167i) q^{23} +(2.78820 + 0.475350i) q^{24} +(4.08498 - 2.35846i) q^{25} +(-4.50025 - 4.22972i) q^{26} +(0.707107 + 0.707107i) q^{27} +(2.45662 + 4.68669i) q^{28} +(4.37123 - 4.37123i) q^{29} +(0.0233056 + 0.752070i) q^{30} +(1.25747 + 2.17799i) q^{31} +(5.58913 - 0.872712i) q^{32} +(-5.60664 - 3.23700i) q^{33} +(-2.71686 + 1.68288i) q^{34} +(-1.09223 + 0.888016i) q^{35} +(1.79065 + 0.890836i) q^{36} +(-2.07025 + 0.554721i) q^{37} +(0.0498434 + 0.165351i) q^{38} +(-2.18354 - 3.78200i) q^{39} +(0.522702 + 1.41117i) q^{40} -8.63061 q^{41} +(0.706709 + 3.67431i) q^{42} +(-2.21407 + 2.21407i) q^{43} +(-12.6903 - 2.57036i) q^{44} +(-0.137704 + 0.513920i) q^{45} +(2.88969 - 5.38361i) q^{46} +(-4.58222 + 7.93663i) q^{47} +(3.96204 + 0.549791i) q^{48} +(-4.66350 + 5.22033i) q^{49} +(5.67095 - 3.51271i) q^{50} +(-2.18280 + 0.584880i) q^{51} +(-6.54654 - 5.78173i) q^{52} +(2.23326 - 8.33463i) q^{53} +(1.03049 + 0.968546i) q^{54} -3.44448i q^{55} +(3.67781 + 6.51719i) q^{56} +0.122117i q^{57} +(5.98741 - 6.37036i) q^{58} +(-1.49402 + 5.57577i) q^{59} +(0.0658867 + 1.06206i) q^{60} +(9.61887 - 2.57737i) q^{61} +(1.87288 + 3.02359i) q^{62} +(-0.271401 + 2.63179i) q^{63} +(7.86220 - 1.47843i) q^{64} +(1.16175 - 2.01221i) q^{65} +(-8.06697 - 4.33002i) q^{66} +(-1.99445 + 7.44337i) q^{67} +(-3.76666 + 2.49782i) q^{68} +(3.05506 - 3.05506i) q^{69} +(-1.50500 + 1.30309i) q^{70} -3.75185 q^{71} +(2.57016 + 1.18079i) q^{72} +(-0.753853 - 1.30571i) q^{73} +(-2.90207 + 0.874802i) q^{74} +(4.55620 - 1.22083i) q^{75} +(0.0776984 + 0.231546i) q^{76} +(-2.71264 - 16.9124i) q^{77} +(-3.25218 - 5.25035i) q^{78} +(4.23158 + 2.44310i) q^{79} +(0.800672 + 1.97184i) q^{80} +(0.500000 + 0.866025i) q^{81} +(-12.1997 + 0.378051i) q^{82} +(-10.6169 + 10.6169i) q^{83} +(1.15991 + 5.16281i) q^{84} +(-0.850172 - 0.850172i) q^{85} +(-3.03269 + 3.22666i) q^{86} +(5.35364 - 3.09093i) q^{87} +(-18.0508 - 3.07741i) q^{88} +(5.81809 - 10.0772i) q^{89} +(-0.172138 + 0.732475i) q^{90} +(4.11952 - 10.7949i) q^{91} +(3.84886 - 7.73649i) q^{92} +(0.650912 + 2.42924i) q^{93} +(-6.12947 + 11.4194i) q^{94} +(-0.0562677 + 0.0324861i) q^{95} +(5.62456 + 0.603598i) q^{96} +15.5828i q^{97} +(-6.36335 + 7.58339i) q^{98} +(-4.57780 - 4.57780i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 128 q + 4 q^{4} - 24 q^{8} + 36 q^{10} - 8 q^{11} - 32 q^{14} - 4 q^{16} + 4 q^{18} + 16 q^{22} + 16 q^{23} - 32 q^{28} + 32 q^{29} - 24 q^{35} - 16 q^{37} + 60 q^{40} - 20 q^{42} - 16 q^{43} - 12 q^{44}+ \cdots - 16 q^{99}+O(q^{100}) \) 128 * q + 4 * q^4 - 24 * q^8 + 36 * q^10 - 8 * q^11 - 32 * q^14 - 4 * q^16 + 4 * q^18 + 16 * q^22 + 16 * q^23 - 32 * q^28 + 32 * q^29 - 24 * q^35 - 16 * q^37 + 60 * q^40 - 20 * q^42 - 16 * q^43 - 12 * q^44 - 20 * q^46 - 32 * q^50 - 144 * q^52 - 16 * q^53 - 56 * q^56 - 40 * q^58 - 96 * q^59 - 24 * q^60 - 32 * q^64 - 72 * q^66 + 16 * q^67 - 60 * q^68 + 28 * q^70 + 128 * q^71 - 4 * q^72 - 72 * q^74 + 72 * q^78 - 36 * q^80 + 64 * q^81 - 60 * q^82 + 24 * q^84 - 44 * q^86 - 48 * q^88 - 8 * q^91 + 56 * q^92 + 36 * q^94 + 60 * q^96 + 148 * q^98 - 16 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

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Database

Properties

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