LMFDB - Embedded newform 208.2.n.a.157.11

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [208,2,Mod(53,208)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(208, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([0, 1, 0])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("208.53"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 208 = 2^{4} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	208.n (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$1.66088836204$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			157.11
Character	$\chi$	$=$	208.157
Dual form			208.2.n.a.53.11

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.0872990 - 1.41152i) q^{2} +(-0.316792 - 0.316792i) q^{3} +(-1.98476 + 0.246448i) q^{4} +(-2.69572 + 2.69572i) q^{5} +(-0.419501 + 0.474812i) q^{6} +1.94658i q^{7} +(0.521133 + 2.78000i) q^{8} -2.79929i q^{9} +(4.04038 + 3.56972i) q^{10} +(-3.78495 + 3.78495i) q^{11} +(0.706828 + 0.550682i) q^{12} +(0.707107 + 0.707107i) q^{13} +(2.74763 - 0.169934i) q^{14} +1.70796 q^{15} +(3.87853 - 0.978279i) q^{16} -1.40999 q^{17} +(-3.95124 + 0.244375i) q^{18} +(-2.81181 - 2.81181i) q^{19} +(4.68599 - 6.01470i) q^{20} +(0.616660 - 0.616660i) q^{21} +(5.67295 + 5.01210i) q^{22} +1.87751i q^{23} +(0.715592 - 1.04577i) q^{24} -9.53379i q^{25} +(0.936363 - 1.05982i) q^{26} +(-1.83717 + 1.83717i) q^{27} +(-0.479730 - 3.86349i) q^{28} +(4.67785 + 4.67785i) q^{29} +(-0.149103 - 2.41082i) q^{30} -5.23075 q^{31} +(-1.71945 - 5.38920i) q^{32} +2.39808 q^{33} +(0.123090 + 1.99022i) q^{34} +(-5.24743 - 5.24743i) q^{35} +(0.689878 + 5.55590i) q^{36} +(0.980035 - 0.980035i) q^{37} +(-3.72344 + 4.21438i) q^{38} -0.448011i q^{39} +(-8.89893 - 6.08928i) q^{40} +6.55469i q^{41} +(-0.924260 - 0.816592i) q^{42} +(-5.25230 + 5.25230i) q^{43} +(6.57942 - 8.44501i) q^{44} +(7.54609 + 7.54609i) q^{45} +(2.65014 - 0.163905i) q^{46} -3.38423 q^{47} +(-1.53860 - 0.918775i) q^{48} +3.21083 q^{49} +(-13.4571 + 0.832291i) q^{50} +(0.446672 + 0.446672i) q^{51} +(-1.57770 - 1.22917i) q^{52} +(4.86540 - 4.86540i) q^{53} +(2.75357 + 2.43281i) q^{54} -20.4063i q^{55} +(-5.41150 + 1.01443i) q^{56} +1.78151i q^{57} +(6.19448 - 7.01123i) q^{58} +(1.57147 - 1.57147i) q^{59} +(-3.38989 + 0.420924i) q^{60} +(-4.55651 - 4.55651i) q^{61} +(0.456640 + 7.38330i) q^{62} +5.44903 q^{63} +(-7.45684 + 2.89750i) q^{64} -3.81232 q^{65} +(-0.209350 - 3.38494i) q^{66} +(8.66069 + 8.66069i) q^{67} +(2.79848 - 0.347488i) q^{68} +(0.594781 - 0.594781i) q^{69} +(-6.94874 + 7.86493i) q^{70} +7.61497i q^{71} +(7.78203 - 1.45880i) q^{72} -13.6310i q^{73} +(-1.46889 - 1.29778i) q^{74} +(-3.02023 + 3.02023i) q^{75} +(6.27372 + 4.88779i) q^{76} +(-7.36771 - 7.36771i) q^{77} +(-0.632375 + 0.0391109i) q^{78} +9.62325 q^{79} +(-7.81825 + 13.0926i) q^{80} -7.23386 q^{81} +(9.25205 - 0.572218i) q^{82} +(-6.65402 - 6.65402i) q^{83} +(-1.07195 + 1.37590i) q^{84} +(3.80093 - 3.80093i) q^{85} +(7.87223 + 6.95519i) q^{86} -2.96381i q^{87} +(-12.4946 - 8.54972i) q^{88} +9.24830i q^{89} +(9.99266 - 11.3102i) q^{90} +(-1.37644 + 1.37644i) q^{91} +(-0.462709 - 3.72641i) q^{92} +(1.65706 + 1.65706i) q^{93} +(0.295440 + 4.77690i) q^{94} +15.1597 q^{95} +(-1.16255 + 2.25196i) q^{96} +13.9970 q^{97} +(-0.280302 - 4.53214i) q^{98} +(10.5952 + 10.5952i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 4 q^{4} - 12 q^{8} - 4 q^{10} - 8 q^{11} + 8 q^{12} - 4 q^{14} - 16 q^{15} + 12 q^{16} - 16 q^{19} - 28 q^{20} + 12 q^{22} + 28 q^{24} - 16 q^{29} + 4 q^{30} + 24 q^{31} - 20 q^{32} - 40 q^{34} + 24 q^{35}+ \cdots - 40 q^{99}+O(q^{100}) $ 48 * q - 4 * q^4 - 12 * q^8 - 4 * q^10 - 8 * q^11 + 8 * q^12 - 4 * q^14 - 16 * q^15 + 12 * q^16 - 16 * q^19 - 28 * q^20 + 12 * q^22 + 28 * q^24 - 16 * q^29 + 4 * q^30 + 24 * q^31 - 20 * q^32 - 40 * q^34 + 24 * q^35 + 8 * q^36 - 16 * q^37 + 32 * q^40 + 40 * q^42 - 8 * q^43 + 20 * q^44 - 32 * q^46 - 40 * q^47 - 52 * q^48 - 48 * q^49 - 16 * q^50 - 24 * q^51 - 8 * q^52 + 16 * q^53 + 20 * q^54 + 20 * q^56 - 16 * q^58 - 68 * q^60 + 32 * q^61 - 32 * q^62 + 40 * q^63 + 32 * q^64 - 32 * q^66 + 16 * q^67 + 40 * q^68 + 32 * q^69 - 60 * q^70 + 40 * q^72 + 72 * q^74 - 40 * q^75 - 28 * q^76 + 16 * q^77 + 32 * q^79 - 52 * q^80 - 48 * q^81 + 40 * q^82 + 40 * q^83 - 36 * q^84 - 32 * q^85 - 72 * q^86 - 8 * q^88 + 28 * q^90 + 36 * q^92 + 28 * q^94 - 48 * q^95 + 68 * q^96 + 64 * q^98 - 40 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/208\mathbb{Z}\right)^\times$.

$n$	$53$	$79$	$145$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$	−0.0872990	−	1.41152i	−0.0617297	−	0.998093i
$2$	−0.0872990	−	1.41152i	−0.0617297	−	0.998093i
$3$	−0.316792	−	0.316792i	−0.182900	−	0.182900i	0.609718	−	0.792618i	$-0.291283\pi$
$3$	−0.316792	−	0.316792i	−0.182900	−	0.182900i	−0.792618	+	0.609718i	$0.791283\pi$
$4$	−1.98476	+	0.246448i	−0.992379	+	0.123224i
$5$	−2.69572	+	2.69572i	−1.20556	+	1.20556i	−0.233112	+	0.972450i	$0.574891\pi$
$5$	−2.69572	+	2.69572i	−1.20556	+	1.20556i	−0.972450	+	0.233112i	$0.925109\pi$
$6$	−0.419501	+	0.474812i	−0.171261	+	0.193841i
$7$			1.94658i			0.735738i	0.929878	+	0.367869i	$0.119912\pi$
$7$			1.94658i			0.735738i	−0.929878	+	0.367869i	$0.880088\pi$
$8$	0.521133	+	2.78000i	0.184248	+	0.982880i
$9$		−	2.79929i		−	0.933095i
$10$	4.04038	+	3.56972i	1.27768	+	1.12884i
$11$	−3.78495	+	3.78495i	−1.14121	+	1.14121i	−0.152977	+	0.988230i	$0.548886\pi$
$11$	−3.78495	+	3.78495i	−1.14121	+	1.14121i	−0.988230	+	0.152977i	$0.951114\pi$
$12$	0.706828	+	0.550682i	0.204044	+	0.158968i
$13$	0.707107	+	0.707107i	0.196116	+	0.196116i
$13$	0.707107	+	0.707107i	0.196116	+	0.196116i
$14$	2.74763	−	0.169934i	0.734334	−	0.0454169i
$15$	1.70796			0.440994
$16$	3.87853	−	0.978279i	0.969632	−	0.244570i
$17$	−1.40999			−0.341972			−0.170986	−	0.985273i	$-0.554695\pi$
$17$	−1.40999			−0.341972			−0.170986	+	0.985273i	$0.554695\pi$
$18$	−3.95124	+	0.244375i	−0.931316	+	0.0575997i
$19$	−2.81181	−	2.81181i	−0.645073	−	0.645073i	0.306725	−	0.951798i	$-0.400767\pi$
$19$	−2.81181	−	2.81181i	−0.645073	−	0.645073i	−0.951798	+	0.306725i	$0.900767\pi$
$20$	4.68599	−	6.01470i	1.04782	−	1.34493i
$21$	0.616660	−	0.616660i	0.134566	−	0.134566i
$22$	5.67295	+	5.01210i	1.20948	+	1.06858i
$23$			1.87751i			0.391488i	0.980655	+	0.195744i	$0.0627122\pi$
$23$			1.87751i			0.391488i	−0.980655	+	0.195744i	$0.937288\pi$
$24$	0.715592	−	1.04577i	0.146070	−	0.213467i
$25$		−	9.53379i		−	1.90676i
$26$	0.936363	−	1.05982i	0.183636	−	0.207848i
$27$	−1.83717	+	1.83717i	−0.353563	+	0.353563i
$28$	−0.479730	−	3.86349i	−0.0906605	−	0.730130i
$29$	4.67785	+	4.67785i	0.868654	+	0.868654i	0.992323	−	0.123669i	$-0.0394662\pi$
$29$	4.67785	+	4.67785i	0.868654	+	0.868654i	−0.123669	+	0.992323i	$0.539466\pi$
$30$	−0.149103	−	2.41082i	−0.0272224	−	0.440153i
$31$	−5.23075			−0.939471			−0.469736	−	0.882807i	$-0.655651\pi$
$31$	−5.23075			−0.939471			−0.469736	+	0.882807i	$0.655651\pi$
$32$	−1.71945	−	5.38920i	−0.303958	−	0.952685i
$33$	2.39808			0.417453
$34$	0.123090	+	1.99022i	0.0211098	+	0.341320i
$35$	−5.24743	−	5.24743i	−0.886977	−	0.886977i
$36$	0.689878	+	5.55590i	0.114980	+	0.925984i
$37$	0.980035	−	0.980035i	0.161117	−	0.161117i	−0.621945	−	0.783061i	$-0.713657\pi$
$37$	0.980035	−	0.980035i	0.161117	−	0.161117i	0.783061	+	0.621945i	$0.213657\pi$
$38$	−3.72344	+	4.21438i	−0.604022	+	0.683663i
$39$		−	0.448011i		−	0.0717392i
$40$	−8.89893	−	6.08928i	−1.40704	−	0.962800i
$41$			6.55469i			1.02367i	0.859084	+	0.511835i	$0.171034\pi$
$41$			6.55469i			1.02367i	−0.859084	+	0.511835i	$0.828966\pi$
$42$	−0.924260	−	0.816592i	−0.142616	−	0.126003i
$43$	−5.25230	+	5.25230i	−0.800968	+	0.800968i	−0.983247	−	0.182279i	$-0.941653\pi$
$43$	−5.25230	+	5.25230i	−0.800968	+	0.800968i	0.182279	+	0.983247i	$0.441653\pi$
$44$	6.57942	−	8.44501i	0.991885	−	1.27313i
$45$	7.54609	+	7.54609i	1.12490	+	1.12490i
$46$	2.65014	−	0.163905i	0.390742	−	0.0241665i
$47$	−3.38423			−0.493641			−0.246820	−	0.969061i	$-0.579386\pi$
$47$	−3.38423			−0.493641			−0.246820	+	0.969061i	$0.579386\pi$
$48$	−1.53860	−	0.918775i	−0.222077	−	0.132614i
$49$	3.21083			0.458690
$50$	−13.4571	+	0.832291i	−1.90312	+	0.117704i
$51$	0.446672	+	0.446672i	0.0625467	+	0.0625467i
$52$	−1.57770	−	1.22917i	−0.218788	−	0.170455i
$53$	4.86540	−	4.86540i	0.668314	−	0.668314i	−0.289012	−	0.957326i	$-0.593327\pi$
$53$	4.86540	−	4.86540i	0.668314	−	0.668314i	0.957326	+	0.289012i	$0.0933267\pi$
$54$	2.75357	+	2.43281i	0.374714	+	0.331063i
$55$		−	20.4063i		−	2.75159i
$56$	−5.41150	+	1.01443i	−0.723142	+	0.135558i
$57$			1.78151i			0.235967i
$58$	6.19448	−	7.01123i	0.813376	−	0.920619i
$59$	1.57147	−	1.57147i	0.204588	−	0.204588i	−0.597374	−	0.801963i	$-0.703789\pi$
$59$	1.57147	−	1.57147i	0.204588	−	0.204588i	0.801963	+	0.597374i	$0.203789\pi$
$60$	−3.38989	+	0.420924i	−0.437633	+	0.0543410i
$61$	−4.55651	−	4.55651i	−0.583401	−	0.583401i	0.352435	−	0.935836i	$-0.385354\pi$
$61$	−4.55651	−	4.55651i	−0.583401	−	0.583401i	−0.935836	+	0.352435i	$0.885354\pi$
$62$	0.456640	+	7.38330i	0.0579933	+	0.937680i
$63$	5.44903			0.686513
$64$	−7.45684	+	2.89750i	−0.932105	+	0.362188i
$65$	−3.81232			−0.472860
$66$	−0.209350	−	3.38494i	−0.0257692	−	0.416657i
$67$	8.66069	+	8.66069i	1.05807	+	1.05807i	0.998206	+	0.0598658i	$0.0190673\pi$
$67$	8.66069	+	8.66069i	1.05807	+	1.05807i	0.0598658	+	0.998206i	$0.480933\pi$
$68$	2.79848	−	0.347488i	0.339366	−	0.0421392i
$69$	0.594781	−	0.594781i	0.0716032	−	0.0716032i
$70$	−6.94874	+	7.86493i	−0.830533	+	0.940039i
$71$			7.61497i			0.903731i	0.892086	+	0.451865i	$0.149241\pi$
$71$			7.61497i			0.903731i	−0.892086	+	0.451865i	$0.850759\pi$
$72$	7.78203	−	1.45880i	0.917120	−	0.171921i
$73$		−	13.6310i		−	1.59539i	−0.603062	−	0.797695i	$-0.706053\pi$
$73$		−	13.6310i		−	1.59539i	0.603062	−	0.797695i	$-0.293947\pi$
$74$	−1.46889	−	1.29778i	−0.170755	−	0.150864i
$75$	−3.02023	+	3.02023i	−0.348746	+	0.348746i
$76$	6.27372	+	4.88779i	0.719645	+	0.560668i
$77$	−7.36771	−	7.36771i	−0.839629	−	0.839629i
$78$	−0.632375	+	0.0391109i	−0.0716024	+	0.00442844i
$79$	9.62325			1.08270			0.541350	−	0.840797i	$-0.317913\pi$
$79$	9.62325			1.08270			0.541350	+	0.840797i	$0.317913\pi$
$80$	−7.81825	+	13.0926i	−0.874107	+	1.46379i
$81$	−7.23386			−0.803762
$82$	9.25205	−	0.572218i	1.02172	−	0.0631909i
$83$	−6.65402	−	6.65402i	−0.730374	−	0.730374i	0.240320	−	0.970694i	$-0.422748\pi$
$83$	−6.65402	−	6.65402i	−0.730374	−	0.730374i	−0.970694	+	0.240320i	$0.922748\pi$
$84$	−1.07195	+	1.37590i	−0.116959	+	0.150123i
$85$	3.80093	−	3.80093i	0.412269	−	0.412269i
$86$	7.87223	+	6.95519i	0.848884	+	0.749997i
$87$		−	2.96381i		−	0.317753i
$88$	−12.4946	−	8.54972i	−1.33193	−	0.911404i
$89$			9.24830i			0.980318i	0.871633	+	0.490159i	$0.163061\pi$
$89$			9.24830i			0.980318i	−0.871633	+	0.490159i	$0.836939\pi$
$90$	9.99266	−	11.3102i	1.05332	−	1.19220i
$91$	−1.37644	+	1.37644i	−0.144290	+	0.144290i
$92$	−0.462709	−	3.72641i	−0.0482408	−	0.388505i
$93$	1.65706	+	1.65706i	0.171829	+	0.171829i
$94$	0.295440	+	4.77690i	0.0304723	+	0.492699i
$95$	15.1597			1.55535
$96$	−1.16255	+	2.25196i	−0.118652	+	0.229840i
$97$	13.9970			1.42118			0.710588	−	0.703609i	$-0.248429\pi$
$97$	13.9970			1.42118			0.710588	+	0.703609i	$0.248429\pi$
$98$	−0.280302	−	4.53214i	−0.0283148	−	0.457815i
$99$	10.5952	+	10.5952i	1.06485	+	1.06485i
$100$	2.34958	+	18.9223i	0.234958	+	1.89223i
$101$	−10.1513	+	10.1513i	−1.01009	+	1.01009i	−0.0101401	+	0.999949i	$0.503228\pi$
$101$	−10.1513	+	10.1513i	−1.01009	+	1.01009i	−0.999949	+	0.0101401i	$0.996772\pi$
$102$	0.591491	−	0.669480i	0.0585664	−	0.0662884i
$103$			19.3196i			1.90361i	0.306697	+	0.951807i	$0.400776\pi$
$103$			19.3196i			1.90361i	−0.306697	+	0.951807i	$0.599224\pi$
$104$	−1.59726	+	2.33426i	−0.156625	+	0.228893i
$105$			3.32468i			0.324456i
$106$	−7.29233	−	6.44284i	−0.708294	−	0.625784i
$107$	5.65743	−	5.65743i	0.546924	−	0.546924i	−0.378626	−	0.925550i	$-0.623603\pi$
$107$	5.65743	−	5.65743i	0.546924	−	0.546924i	0.925550	+	0.378626i	$0.123603\pi$
$108$	3.19356	−	4.09910i	0.307301	−	0.394436i
$109$	10.0292	+	10.0292i	0.960626	+	0.960626i	0.999254	−	0.0386278i	$-0.0122987\pi$
$109$	10.0292	+	10.0292i	0.960626	+	0.960626i	−0.0386278	+	0.999254i	$0.512299\pi$
$110$	−28.8039	+	1.78145i	−2.74634	+	0.169855i
$111$	−0.620934			−0.0589365
$112$	1.90430	+	7.54986i	0.179939	+	0.713395i
$113$	−3.03193			−0.285220			−0.142610	−	0.989779i	$-0.545549\pi$
$113$	−3.03193			−0.285220			−0.142610	+	0.989779i	$0.545549\pi$
$114$	2.51464	−	0.155524i	0.235517	−	0.0145662i
$115$	−5.06124	−	5.06124i	−0.471964	−	0.471964i
$116$	−10.4372	−	8.13154i	−0.969073	−	0.754995i
$117$	1.97939	−	1.97939i	0.182995	−	0.182995i
$118$	−2.35535	−	2.08097i	−0.216827	−	0.191569i
$119$		−	2.74465i		−	0.251602i
$120$	0.890075	+	4.74814i	0.0812524	+	0.433444i
$121$		−	17.6518i		−	1.60470i
$122$	−6.03381	+	6.82937i	−0.546276	+	0.618302i
$123$	2.07647	−	2.07647i	0.187229	−	0.187229i
$124$	10.3818	−	1.28911i	0.932311	−	0.115765i
$125$	12.2218	+	12.2218i	1.09315	+	1.09315i
$126$	−0.475695	−	7.69140i	−0.0423783	−	0.685204i
$127$	2.52036			0.223646			0.111823	−	0.993728i	$-0.464331\pi$
$127$	2.52036			0.223646			0.111823	+	0.993728i	$0.464331\pi$
$128$	4.74085	+	10.2725i	0.419036	+	0.907970i
$129$	3.32777			0.292994
$130$	0.332812	+	5.38115i	0.0291895	+	0.471958i
$131$	4.32480	+	4.32480i	0.377859	+	0.377859i	0.870329	−	0.492470i	$-0.163906\pi$
$131$	4.32480	+	4.32480i	0.377859	+	0.377859i	−0.492470	+	0.870329i	$0.663906\pi$
$132$	−4.75962	+	0.591003i	−0.414271	+	0.0514402i
$133$	5.47340	−	5.47340i	0.474604	−	0.474604i
$134$	11.4686	−	12.9808i	0.990740	−	1.12137i
$135$		−	9.90496i		−	0.852484i
$136$	−0.734790	−	3.91977i	−0.0630078	−	0.336118i
$137$		−	2.82814i		−	0.241625i	−0.992675	−	0.120812i	$-0.961450\pi$
$137$		−	2.82814i		−	0.241625i	0.992675	−	0.120812i	$-0.0385499\pi$
$138$	−0.891466	−	0.787619i	−0.0758866	−	0.0670466i
$139$	−9.25198	+	9.25198i	−0.784743	+	0.784743i	−0.980627	−	0.195884i	$-0.937242\pi$
$139$	−9.25198	+	9.25198i	−0.784743	+	0.784743i	0.195884	+	0.980627i	$0.437242\pi$
$140$	11.7081	+	9.12166i	0.989514	+	0.770921i
$141$	1.07210	+	1.07210i	0.0902868	+	0.0902868i
$142$	10.7487	−	0.664779i	0.902007	−	0.0557870i
$143$	−5.35273			−0.447618
$144$	−2.73848	−	10.8571i	−0.228207	−	0.904759i
$145$	−25.2203			−2.09443
$146$	−19.2404	+	1.18997i	−1.59235	+	0.0984829i
$147$	−1.01716	−	1.01716i	−0.0838944	−	0.0838944i
$148$	−1.70361	+	2.18666i	−0.140035	+	0.179742i
$149$	−11.8722	+	11.8722i	−0.972605	+	0.972605i	−0.999635	−	0.0270299i	$-0.991395\pi$
$149$	−11.8722	+	11.8722i	−0.972605	+	0.972605i	0.0270299	+	0.999635i	$0.491395\pi$
$150$	4.52676	+	3.99944i	0.369609	+	0.326553i
$151$		−	0.659670i		−	0.0536832i	−0.999640	−	0.0268416i	$-0.991455\pi$
$151$		−	0.659670i		−	0.0536832i	0.999640	−	0.0268416i	$-0.00854497\pi$
$152$	6.35151	−	9.28216i	0.515176	−	0.752883i
$153$			3.94696i			0.319093i
$154$	−9.75645	+	11.0428i	−0.786197	+	0.889857i
$155$	14.1006	−	14.1006i	1.13259	−	1.13259i
$156$	0.110411	+	0.889194i	0.00883999	+	0.0711925i
$157$	1.01263	+	1.01263i	0.0808166	+	0.0808166i	0.746360	−	0.665543i	$-0.231800\pi$
$157$	1.01263	+	1.01263i	0.0808166	+	0.0808166i	−0.665543	+	0.746360i	$0.731800\pi$
$158$	−0.840100	−	13.5834i	−0.0668347	−	1.08064i
$159$	−3.08264			−0.244469
$160$	19.1629	+	9.89262i	1.51496	+	0.782080i
$161$	−3.65473			−0.288033
$162$	0.631509	+	10.2107i	0.0496160	+	0.802229i
$163$	−18.0271	−	18.0271i	−1.41199	−	1.41199i	−0.745649	−	0.666339i	$-0.767861\pi$
$163$	−18.0271	−	18.0271i	−1.41199	−	1.41199i	−0.666339	−	0.745649i	$-0.732139\pi$
$164$	−1.61539	−	13.0095i	−0.126141	−	1.01587i
$165$	−6.46456	+	6.46456i	−0.503265	+	0.503265i
$166$	−8.81137	+	9.97315i	−0.683895	+	0.774067i
$167$			1.01314i			0.0783990i	0.999231	+	0.0391995i	$0.0124808\pi$
$167$			1.01314i			0.0783990i	−0.999231	+	0.0391995i	$0.987519\pi$
$168$	2.03568	+	1.39296i	0.157056	+	0.107469i
$169$			1.00000i			0.0769231i
$170$	−5.69689	−	5.03326i	−0.436932	−	0.386033i
$171$	−7.87105	+	7.87105i	−0.601914	+	0.601914i
$172$	9.13013	−	11.7190i	0.696166	−	0.893563i
$173$	−10.5855	−	10.5855i	−0.804803	−	0.804803i	0.179039	−	0.983842i	$-0.442701\pi$
$173$	−10.5855	−	10.5855i	−0.804803	−	0.804803i	−0.983842	+	0.179039i	$0.942701\pi$
$174$	−4.18346	+	0.258737i	−0.317147	+	0.0196148i
$175$	18.5583			1.40287
$176$	−10.9773	+	18.3828i	−0.827446	+	1.38565i
$177$	−0.995659			−0.0748383
$178$	13.0541	−	0.807367i	0.978448	−	0.0605147i
$179$	−9.79314	−	9.79314i	−0.731973	−	0.731973i	0.239037	−	0.971010i	$-0.423168\pi$
$179$	−9.79314	−	9.79314i	−0.731973	−	0.731973i	−0.971010	+	0.239037i	$0.923168\pi$
$180$	−16.8369	−	13.1174i	−1.25495	−	0.977716i
$181$	−15.7866	+	15.7866i	−1.17341	+	1.17341i	−0.192015	+	0.981392i	$0.561502\pi$
$181$	−15.7866	+	15.7866i	−1.17341	+	1.17341i	−0.981392	+	0.192015i	$0.938498\pi$
$182$	2.06303	+	1.82270i	0.152922	+	0.135108i
$183$			2.88693i			0.213408i
$184$	−5.21949	+	0.978433i	−0.384786	+	0.0721310i
$185$			5.28380i			0.388473i
$186$	2.19431	−	2.48363i	0.160894	−	0.182108i
$187$	5.33674	−	5.33674i	0.390261	−	0.390261i
$188$	6.71688	−	0.834036i	0.489878	−	0.0608283i
$189$	−3.57619	−	3.57619i	−0.260129	−	0.260129i
$190$	−1.32342	−	21.3981i	−0.0960113	−	1.55238i
$191$	−6.85385			−0.495928			−0.247964	−	0.968769i	$-0.579761\pi$
$191$	−6.85385			−0.495928			−0.247964	+	0.968769i	$0.579761\pi$
$192$	3.28017	+	1.44436i	0.236726	+	0.104238i
$193$	1.74605			0.125683			0.0628417	−	0.998024i	$-0.479984\pi$
$193$	1.74605			0.125683			0.0628417	+	0.998024i	$0.479984\pi$
$194$	−1.22192	−	19.7569i	−0.0877287	−	1.41847i
$195$	1.20771	+	1.20771i	0.0864861	+	0.0864861i
$196$	−6.37272	+	0.791303i	−0.455194	+	0.0565216i
$197$	13.3926	−	13.3926i	0.954181	−	0.954181i	−0.0448147	−	0.998995i	$-0.514270\pi$
$197$	13.3926	−	13.3926i	0.954181	−	0.954181i	0.998995	+	0.0448147i	$0.0142698\pi$
$198$	14.0303	−	15.8802i	0.997091	−	1.12856i
$199$			6.60203i			0.468005i	0.972236	+	0.234003i	$0.0751825\pi$
$199$			6.60203i			0.468005i	−0.972236	+	0.234003i	$0.924818\pi$
$200$	26.5040	−	4.96837i	1.87411	−	0.351317i
$201$		−	5.48727i		−	0.387042i
$202$	15.2149	+	13.4425i	1.07051	+	0.945810i
$203$	−9.10579	+	9.10579i	−0.639101	+	0.639101i
$204$	−0.996618	−	0.776455i	−0.0697772	−	0.0543627i
$205$	−17.6696	−	17.6696i	−1.23410	−	1.23410i
$206$	27.2699	−	1.68658i	1.89998	−	0.117510i
$207$	5.25569			0.365296
$208$	3.43428	+	2.05079i	0.238124	+	0.142196i
$209$	21.2851			1.47232
$210$	4.69285	−	0.290242i	0.323837	−	0.0200286i
$211$	18.8246	+	18.8246i	1.29594	+	1.29594i	0.931051	+	0.364889i	$0.118893\pi$
$211$	18.8246	+	18.8246i	1.29594	+	1.29594i	0.364889	+	0.931051i	$0.381107\pi$
$212$	−8.45757	+	10.8557i	−0.580868	+	0.745573i
$213$	2.41236	−	2.41236i	0.165292	−	0.165292i
$214$	−8.47944	−	7.49166i	−0.579642	−	0.512120i
$215$		−	28.3174i		−	1.93123i
$216$	−6.06474	−	4.14992i	−0.412653	−	0.282366i
$217$		−	10.1821i		−	0.691204i
$218$	13.2809	−	15.0320i	0.899495	−	1.01809i
$219$	−4.31819	+	4.31819i	−0.291796	+	0.291796i
$220$	5.02910	+	40.5016i	0.339062	+	2.73062i
$221$	−0.997012	−	0.997012i	−0.0670663	−	0.0670663i
$222$	0.0542069	+	0.876459i	0.00363813	+	0.0588241i
$223$	9.28188			0.621561			0.310780	−	0.950482i	$-0.399410\pi$
$223$	9.28188			0.621561			0.310780	+	0.950482i	$0.399410\pi$
$224$	10.4905	−	3.34704i	0.700926	−	0.223634i
$225$	−26.6878			−1.77919
$226$	0.264684	+	4.27962i	0.0176065	+	0.284676i
$227$	−12.1525	−	12.1525i	−0.806590	−	0.806590i	0.177526	−	0.984116i	$-0.443191\pi$
$227$	−12.1525	−	12.1525i	−0.806590	−	0.806590i	−0.984116	+	0.177526i	$0.943191\pi$
$228$	−0.439051	−	3.53588i	−0.0290768	−	0.234169i
$229$	−8.18281	+	8.18281i	−0.540735	+	0.540735i	−0.923744	−	0.383009i	$-0.874888\pi$
$229$	−8.18281	+	8.18281i	−0.540735	+	0.540735i	0.383009	+	0.923744i	$0.374888\pi$
$230$	−6.70219	+	7.58587i	−0.441929	+	0.500198i
$231$			4.66806i			0.307136i
$232$	−10.5666	+	15.4422i	−0.693735	+	1.01383i
$233$			10.2927i			0.674296i	0.941452	+	0.337148i	$0.109462\pi$
$233$			10.2927i			0.674296i	−0.941452	+	0.337148i	$0.890538\pi$
$234$	−2.96675	−	2.62115i	−0.193942	−	0.171350i
$235$	9.12293	−	9.12293i	0.595114	−	0.595114i
$236$	−2.73170	+	3.50628i	−0.177819	+	0.228239i
$237$	−3.04857	−	3.04857i	−0.198026	−	0.198026i
$238$	−3.87412	+	0.239605i	−0.251122	+	0.0155313i
$239$	−4.98041			−0.322156			−0.161078	−	0.986942i	$-0.551497\pi$
$239$	−4.98041			−0.322156			−0.161078	+	0.986942i	$0.551497\pi$
$240$	6.62438	−	1.67086i	0.427602	−	0.107854i
$241$	0.737586			0.0475121			0.0237560	−	0.999718i	$-0.492438\pi$
$241$	0.737586			0.0475121			0.0237560	+	0.999718i	$0.492438\pi$
$242$	−24.9157	+	1.54098i	−1.60164	+	0.0990580i
$243$	7.80313	+	7.80313i	0.500571	+	0.500571i
$244$	10.1665	+	7.92063i	0.650844	+	0.507066i
$245$	−8.65550	+	8.65550i	−0.552979	+	0.552979i
$246$	−3.11225	−	2.74970i	−0.198430	−	0.175315i
$247$		−	3.97650i		−	0.253018i
$248$	−2.72592	−	14.5415i	−0.173096	−	0.923387i
$249$			4.21588i			0.267171i
$250$	16.1844	−	18.3183i	1.02359	−	1.15855i
$251$	8.12530	−	8.12530i	0.512864	−	0.512864i	−0.402539	−	0.915403i	$-0.631872\pi$
$251$	8.12530	−	8.12530i	0.512864	−	0.512864i	0.915403	+	0.402539i	$0.131872\pi$
$252$	−10.8150	+	1.34290i	−0.681281	+	0.0845949i
$253$	−7.10630	−	7.10630i	−0.446769	−	0.446769i
$254$	−0.220025	−	3.55753i	−0.0138056	−	0.223219i
$255$	−2.40821			−0.150808
$256$	14.0859	−	7.58856i	0.880371	−	0.474285i
$257$	−0.345258			−0.0215366			−0.0107683	−	0.999942i	$-0.503428\pi$
$257$	−0.345258			−0.0215366			−0.0107683	+	0.999942i	$0.503428\pi$
$258$	−0.290511	−	4.69720i	−0.0180864	−	0.292435i
$259$	1.90772	+	1.90772i	0.118540	+	0.118540i
$260$	7.56653	−	0.939539i	0.469257	−	0.0582677i
$261$	13.0946	−	13.0946i	0.810537	−	0.810537i
$262$	5.72697	−	6.48207i	0.353813	−	0.400464i
$263$			14.8561i			0.916067i	0.888935	+	0.458033i	$0.151446\pi$
$263$			14.8561i			0.916067i	−0.888935	+	0.458033i	$0.848554\pi$
$264$	1.24972	+	6.66668i	0.0769150	+	0.410306i
$265$			26.2315i			1.61139i
$266$	−8.20362	−	7.24798i	−0.502996	−	0.444402i
$267$	2.92978	−	2.92978i	0.179300	−	0.179300i
$268$	−19.3238	−	15.0550i	−1.18039	−	0.919629i
$269$	1.65331	+	1.65331i	0.100804	+	0.100804i	0.755710	−	0.654906i	$-0.227292\pi$
$269$	1.65331	+	1.65331i	0.100804	+	0.100804i	−0.654906	+	0.755710i	$0.727292\pi$
$270$	−13.9810	+	0.864693i	−0.850858	+	0.0526236i
$271$	−10.4677			−0.635867			−0.317933	−	0.948113i	$-0.602989\pi$
$271$	−10.4677			−0.635867			−0.317933	+	0.948113i	$0.602989\pi$
$272$	−5.46867	+	1.37936i	−0.331587	+	0.0836360i
$273$	0.872089			0.0527812
$274$	−3.99197	+	0.246894i	−0.241164	+	0.0149154i
$275$	36.0850	+	36.0850i	2.17601	+	2.17601i
$276$	−1.03391	+	1.32708i	−0.0622342	+	0.0798807i
$277$	−6.67776	+	6.67776i	−0.401228	+	0.401228i	−0.878665	−	0.477438i	$-0.841566\pi$
$277$	−6.67776	+	6.67776i	−0.401228	+	0.401228i	0.477438	+	0.878665i	$0.341566\pi$
$278$	13.8670	+	12.2516i	0.831688	+	0.734804i
$279$			14.6424i			0.876616i
$280$	11.8533	−	17.3225i	0.708368	−	1.03522i
$281$			18.8671i			1.12552i	0.826621	+	0.562760i	$0.190260\pi$
$281$			18.8671i			1.12552i	−0.826621	+	0.562760i	$0.809740\pi$
$282$	1.41969	−	1.60687i	0.0845412	−	0.0956880i
$283$	15.8367	−	15.8367i	0.941395	−	0.941395i	−0.0569799	−	0.998375i	$-0.518147\pi$
$283$	15.8367	−	15.8367i	0.941395	−	0.941395i	0.998375	+	0.0569799i	$0.0181471\pi$
$284$	−1.87669	−	15.1139i	−0.111361	−	0.896843i
$285$	−4.80246	−	4.80246i	−0.284473	−	0.284473i
$286$	0.467288	+	7.55547i	0.0276313	+	0.446764i
$287$	−12.7592			−0.753153
$288$	−15.0859	+	4.81323i	−0.888946	+	0.283622i
$289$	−15.0119			−0.883055
$290$	2.20171	+	35.5989i	0.129289	+	2.09044i
$291$	−4.43412	−	4.43412i	−0.259933	−	0.259933i
$292$	3.35933	+	27.0543i	0.196590	+	1.58323i
$293$	0.726156	−	0.726156i	0.0424225	−	0.0424225i	−0.685577	−	0.728000i	$-0.740450\pi$
$293$	0.726156	−	0.726156i	0.0424225	−	0.0424225i	0.728000	+	0.685577i	$0.240450\pi$
$294$	−1.34695	+	1.52454i	−0.0785556	+	0.0889131i
$295$			8.47249i			0.493287i
$296$	3.23523	+	2.21377i	0.188044	+	0.128673i
$297$		−	13.9072i		−	0.806976i
$298$	17.7942	+	15.7213i	1.03079	+	0.910711i
$299$	−1.32760	+	1.32760i	−0.0767772	+	0.0767772i
$300$	5.25009	−	6.73875i	0.303114	−	0.389062i
$301$	−10.2240	−	10.2240i	−0.589303	−	0.589303i
$302$	−0.931136	+	0.0575885i	−0.0535808	+	0.00331385i
$303$	6.43167			0.369490
$304$	−13.6564	−	8.15494i	−0.783248	−	0.467718i
$305$	24.5661			1.40665
$306$	5.57120	−	0.344565i	0.318484	−	0.0196975i
$307$	−7.41062	−	7.41062i	−0.422946	−	0.422946i	0.463270	−	0.886217i	$-0.346676\pi$
$307$	−7.41062	−	7.41062i	−0.422946	−	0.422946i	−0.886217	+	0.463270i	$0.846676\pi$
$308$	16.4389	+	12.8074i	0.936692	+	0.729767i
$309$	6.12028	−	6.12028i	0.348171	−	0.348171i
$310$	−21.1343	−	18.6723i	−1.20035	−	1.06052i
$311$		−	1.96144i		−	0.111223i	−0.998452	−	0.0556115i	$-0.982289\pi$
$311$		−	1.96144i		−	0.111223i	0.998452	−	0.0556115i	$-0.0177108\pi$
$312$	1.24547	−	0.233473i	0.0705110	−	0.0132178i
$313$			25.8880i			1.46328i	0.681692	+	0.731639i	$0.261244\pi$
$313$			25.8880i			1.46328i	−0.681692	+	0.731639i	$0.738756\pi$
$314$	1.34094	−	1.51774i	0.0756737	−	0.0856512i
$315$	−14.6891	+	14.6891i	−0.827634	+	0.827634i
$316$	−19.0998	+	2.37163i	−1.07445	+	0.133415i
$317$	−0.109471	−	0.109471i	−0.00614851	−	0.00614851i	0.704026	−	0.710174i	$-0.251384\pi$
$317$	−0.109471	−	0.109471i	−0.00614851	−	0.00614851i	−0.710174	+	0.704026i	$0.751384\pi$
$318$	0.269111	+	4.35119i	0.0150910	+	0.244003i
$319$	−35.4109			−1.98263
$320$	12.2907	−	27.9124i	0.687071	−	1.56035i
$321$	−3.58445			−0.200065
$322$	0.319054	+	5.15871i	0.0177802	+	0.287483i
$323$	3.96461	+	3.96461i	0.220597	+	0.220597i
$324$	14.3575	−	1.78277i	0.797637	−	0.0990428i
$325$	6.74141	−	6.74141i	0.373946	−	0.373946i
$326$	−23.8717	+	27.0192i	−1.32213	+	1.49646i
$327$		−	6.35435i		−	0.351397i
$328$	−18.2221	+	3.41586i	−1.00615	+	0.188609i
$329$		−	6.58767i		−	0.363190i
$330$	9.68918	+	8.56048i	0.533372	+	0.471239i
$331$	7.47754	−	7.47754i	0.411003	−	0.411003i	−0.471085	−	0.882088i	$-0.656138\pi$
$331$	7.47754	−	7.47754i	0.411003	−	0.411003i	0.882088	+	0.471085i	$0.156138\pi$
$332$	14.8465	+	11.5668i	0.814807	+	0.634808i
$333$	−2.74340	−	2.74340i	−0.150337	−	0.150337i
$334$	1.43006	−	0.0884459i	0.0782495	−	0.00483955i
$335$	−46.6936			−2.55114
$336$	1.78847	−	2.99500i	0.0975689	−	0.163391i
$337$	−2.94962			−0.160676			−0.0803380	−	0.996768i	$-0.525600\pi$
$337$	−2.94962			−0.160676			−0.0803380	+	0.996768i	$0.525600\pi$
$338$	1.41152	−	0.0872990i	0.0767764	−	0.00474844i
$339$	0.960490	+	0.960490i	0.0521666	+	0.0521666i
$340$	−6.60719	+	8.48065i	−0.358325	+	0.459928i
$341$	19.7982	−	19.7982i	1.07213	−	1.07213i
$342$	11.7973	+	10.4230i	0.637923	+	0.563611i
$343$			19.8762i			1.07321i
$344$	−17.3386	−	11.8643i	−0.934833	−	0.639679i
$345$			3.20672i			0.172644i
$346$	−14.0175	+	15.8658i	−0.753588	+	0.852948i
$347$	25.0508	−	25.0508i	1.34480	−	1.34480i	0.453581	−	0.891215i	$-0.350146\pi$
$347$	25.0508	−	25.0508i	1.34480	−	1.34480i	0.891215	−	0.453581i	$-0.149854\pi$
$348$	0.730424	+	5.88244i	0.0391548	+	0.315332i
$349$	11.2227	+	11.2227i	0.600735	+	0.600735i	0.940508	−	0.339773i	$-0.110350\pi$
$349$	11.2227	+	11.2227i	0.600735	+	0.600735i	−0.339773	+	0.940508i	$0.610350\pi$
$350$	−1.62012	−	26.1953i	−0.0865990	−	1.40020i
$351$	−2.59815			−0.138679
$352$	26.9059	+	13.8898i	1.43409	+	0.740331i
$353$	0.552517			0.0294075			0.0147038	−	0.999892i	$-0.495319\pi$
$353$	0.552517			0.0294075			0.0147038	+	0.999892i	$0.495319\pi$
$354$	0.0869200	+	1.40539i	0.00461975	+	0.0746956i
$355$	−20.5278	−	20.5278i	−1.08950	−	1.08950i
$356$	−2.27922	−	18.3556i	−0.120799	−	0.972847i
$357$	−0.869483	+	0.869483i	−0.0460179	+	0.0460179i
$358$	−12.9682	+	14.6781i	−0.685393	+	0.775762i
$359$		−	19.1512i		−	1.01076i	−0.862896	−	0.505382i	$-0.831352\pi$
$359$		−	19.1512i		−	1.01076i	0.862896	−	0.505382i	$-0.168648\pi$
$360$	−17.0456	+	24.9107i	−0.898384	+	1.31291i
$361$		−	3.18748i		−	0.167762i
$362$	23.6612	+	20.9049i	1.24360	+	1.09874i
$363$	−5.59193	+	5.59193i	−0.293500	+	0.293500i
$364$	2.39268	−	3.07112i	0.125410	−	0.160970i
$365$	36.7454	+	36.7454i	1.92334	+	1.92334i
$366$	4.07495	−	0.252026i	0.213001	−	0.0131736i
$367$	−19.3629			−1.01073			−0.505367	−	0.862905i	$-0.668643\pi$
$367$	−19.3629			−1.01073			−0.505367	+	0.862905i	$0.668643\pi$
$368$	1.83673	+	7.28198i	0.0957462	+	0.379600i
$369$	18.3485			0.955182
$370$	7.45817	−	0.461270i	0.387732	−	0.0239803i
$371$	9.47088	+	9.47088i	0.491703	+	0.491703i
$372$	−3.69724	−	2.88048i	−0.191693	−	0.149346i
$373$	−0.0772409	+	0.0772409i	−0.00399938	+	0.00399938i	−0.709104	−	0.705104i	$-0.750900\pi$
$373$	−0.0772409	+	0.0772409i	−0.00399938	+	0.00399938i	0.705104	+	0.709104i	$0.250900\pi$
$374$	−7.99879	−	7.06700i	−0.413607	−	0.365426i
$375$		−	7.74355i		−	0.399875i
$376$	−1.76363	−	9.40817i	−0.0909524	−	0.485189i
$377$			6.61547i			0.340714i
$378$	−4.73565	+	5.36005i	−0.243576	+	0.275691i
$379$	23.6224	−	23.6224i	1.21340	−	1.21340i	0.243501	−	0.969901i	$-0.421704\pi$
$379$	23.6224	−	23.6224i	1.21340	−	1.21340i	0.969901	−	0.243501i	$-0.0782958\pi$
$380$	−30.0883	+	3.73607i	−1.54350	+	0.191656i
$381$	−0.798430	−	0.798430i	−0.0409048	−	0.0409048i
$382$	0.598335	+	9.67433i	0.0306135	+	0.494982i
$383$	5.27887			0.269738			0.134869	−	0.990863i	$-0.456939\pi$
$383$	5.27887			0.269738			0.134869	+	0.990863i	$0.456939\pi$
$384$	1.75238	−	4.75611i	0.0894260	−	0.242709i
$385$	39.7225			2.02445
$386$	−0.152428	−	2.46458i	−0.00775840	−	0.125444i
$387$	14.7027	+	14.7027i	0.747380	+	0.747380i
$388$	−27.7806	+	3.44952i	−1.41034	+	0.175123i
$389$	19.3372	−	19.3372i	0.980437	−	0.980437i	−0.0193749	−	0.999812i	$-0.506168\pi$
$389$	19.3372	−	19.3372i	0.980437	−	0.980437i	0.999812	+	0.0193749i	$0.00616761\pi$
$390$	1.59927	−	1.81014i	0.0809824	−	0.0916599i
$391$		−	2.64727i		−	0.133878i
$392$	1.67327	+	8.92612i	0.0845128	+	0.450837i
$393$		−	2.74012i		−	0.138221i
$394$	−20.0730	−	17.7347i	−1.01126	−	0.893460i
$395$	−25.9416	+	25.9416i	−1.30526	+	1.30526i
$396$	−23.6400	−	18.4177i	−1.18795	−	0.925524i
$397$	−13.5510	−	13.5510i	−0.680107	−	0.680107i	0.279917	−	0.960024i	$-0.409693\pi$
$397$	−13.5510	−	13.5510i	−0.680107	−	0.680107i	−0.960024	+	0.279917i	$0.909693\pi$
$398$	9.31887	−	0.576350i	0.467113	−	0.0288898i
$399$	−3.46786			−0.173610
$400$	−9.32671	−	36.9771i	−0.466335	−	1.84885i
$401$	−4.77141			−0.238273			−0.119136	−	0.992878i	$-0.538013\pi$
$401$	−4.77141			−0.238273			−0.119136	+	0.992878i	$0.538013\pi$
$402$	−7.74538	+	0.479033i	−0.386304	+	0.0238920i
$403$	−3.69870	−	3.69870i	−0.184245	−	0.184245i
$404$	17.6460	−	22.6496i	0.877924	−	1.12686i
$405$	19.5004	−	19.5004i	0.968985	−	0.968985i
$406$	13.6479	+	12.0581i	0.677334	+	0.598431i
$407$			7.41878i			0.367735i
$408$	−1.00898	+	1.47453i	−0.0499517	+	0.0729999i
$409$			12.2843i			0.607421i	0.952764	+	0.303711i	$0.0982256\pi$
$409$			12.2843i			0.607421i	−0.952764	+	0.303711i	$0.901774\pi$
$410$	−23.3984	+	26.4835i	−1.15556	+	1.30793i
$411$	−0.895932	+	0.895932i	−0.0441931	+	0.0441931i
$412$	−4.76127	−	38.3447i	−0.234571	−	1.88911i
$413$	3.05899	+	3.05899i	0.150523	+	0.150523i
$414$	−0.458817	−	7.41850i	−0.0225496	−	0.364599i
$415$	35.8747			1.76102
$416$	2.59491	−	5.02657i	0.127226	−	0.246448i
$417$	5.86190			0.287059
$418$	−1.85817	−	30.0443i	−0.0908860	−	1.46951i
$419$	13.4383	+	13.4383i	0.656502	+	0.656502i	0.954551	−	0.298049i	$-0.0963358\pi$
$419$	13.4383	+	13.4383i	0.656502	+	0.656502i	−0.298049	+	0.954551i	$0.596336\pi$
$420$	−0.819361	−	6.59869i	−0.0399807	−	0.321983i
$421$	16.6784	−	16.6784i	0.812856	−	0.812856i	−0.172205	−	0.985061i	$-0.555089\pi$
$421$	16.6784	−	16.6784i	0.812856	−	0.812856i	0.985061	+	0.172205i	$0.0550892\pi$
$422$	24.9279	−	28.2146i	1.21347	−	1.37347i
$423$			9.47343i			0.460614i
$424$	16.0613	+	10.9903i	0.780008	+	0.533736i
$425$			13.4425i			0.652059i
$426$	−3.61568	−	3.19449i	−0.175180	−	0.154774i
$427$	8.86961	−	8.86961i	0.429230	−	0.429230i
$428$	−9.83436	+	12.6229i	−0.475362	+	0.610150i
$429$	1.69570	+	1.69570i	0.0818693	+	0.0818693i
$430$	−39.9705	+	2.47208i	−1.92755	+	0.119214i
$431$	−19.7507			−0.951360			−0.475680	−	0.879618i	$-0.657798\pi$
$431$	−19.7507			−0.951360			−0.475680	+	0.879618i	$0.657798\pi$
$432$	−5.32824	+	8.92276i	−0.256355	+	0.429296i
$433$	27.7090			1.33161			0.665804	−	0.746126i	$-0.268088\pi$
$433$	27.7090			1.33161			0.665804	+	0.746126i	$0.268088\pi$
$434$	−14.3722	+	0.888885i	−0.689886	+	0.0426678i
$435$	7.98959	+	7.98959i	0.383071	+	0.383071i
$436$	−22.3773	−	17.4339i	−1.07168	−	0.834933i
$437$	5.27920	−	5.27920i	0.252539	−	0.252539i
$438$	6.47217	+	5.71823i	0.309252	+	0.273227i
$439$		−	15.4354i		−	0.736693i	−0.929689	−	0.368347i	$-0.879924\pi$
$439$		−	15.4354i		−	0.736693i	0.929689	−	0.368347i	$-0.120076\pi$
$440$	56.7297	−	10.6344i	2.70448	−	0.506976i
$441$		−	8.98803i		−	0.428002i
$442$	−1.32026	+	1.49434i	−0.0627984	+	0.0710783i
$443$	0.277623	−	0.277623i	0.0131903	−	0.0131903i	−0.700481	−	0.713671i	$-0.747031\pi$
$443$	0.277623	−	0.277623i	0.0131903	−	0.0131903i	0.713671	+	0.700481i	$0.247031\pi$
$444$	1.23240	−	0.153028i	0.0584873	−	0.00726239i
$445$	−24.9308	−	24.9308i	−1.18183	−	1.18183i
$446$	−0.810298	−	13.1015i	−0.0383687	−	0.620375i
$447$	7.52200			0.355778
$448$	−5.64021	−	14.5153i	−0.266475	−	0.685785i
$449$	10.4762			0.494401			0.247200	−	0.968964i	$-0.420489\pi$
$449$	10.4762			0.494401			0.247200	+	0.968964i	$0.420489\pi$
$450$	2.32982	+	37.6703i	0.109829	+	1.77579i
$451$	−24.8092	−	24.8092i	−1.16822	−	1.16822i
$452$	6.01764	−	0.747212i	0.283046	−	0.0351459i
$453$	−0.208978	+	0.208978i	−0.00981865	+	0.00981865i
$454$	−16.0926	+	18.2144i	−0.755261	+	0.854842i
$455$		−	7.42098i		−	0.347901i
$456$	−4.95262	+	0.928406i	−0.231928	+	0.0434766i
$457$		−	2.75908i		−	0.129064i	−0.997916	−	0.0645321i	$-0.979445\pi$
$457$		−	2.75908i		−	0.129064i	0.997916	−	0.0645321i	$-0.0205555\pi$
$458$	12.2645	+	10.8358i	0.573083	+	0.506325i
$459$	2.59038	−	2.59038i	0.120909	−	0.120909i
$460$	11.2927	+	8.79801i	0.526524	+	0.410209i
$461$	2.08207	+	2.08207i	0.0969718	+	0.0969718i	0.753928	−	0.656957i	$-0.228157\pi$
$461$	2.08207	+	2.08207i	0.0969718	+	0.0969718i	−0.656957	+	0.753928i	$0.728157\pi$
$462$	6.58904	−	0.407517i	0.306550	−	0.0189594i
$463$	13.4010			0.622798			0.311399	−	0.950279i	$-0.399202\pi$
$463$	13.4010			0.622798			0.311399	+	0.950279i	$0.399202\pi$
$464$	22.7194	+	13.5669i	1.05472	+	0.629828i
$465$	−8.93393			−0.414301
$466$	14.5283	−	0.898541i	0.673010	−	0.0416241i
$467$	5.25333	+	5.25333i	0.243095	+	0.243095i	0.818129	−	0.575034i	$-0.195011\pi$
$467$	5.25333	+	5.25333i	0.243095	+	0.243095i	−0.575034	+	0.818129i	$0.695011\pi$
$468$	−3.44080	+	4.41644i	−0.159051	+	0.204150i
$469$	−16.8587	+	16.8587i	−0.778464	+	0.778464i
$470$	−13.6736	−	12.0807i	−0.630716	−	0.557243i
$471$		−	0.641585i		−	0.0295627i
$472$	5.18764	+	3.54975i	0.238781	+	0.163391i
$473$		−	39.7594i		−	1.82814i
$474$	−4.03696	+	4.56924i	−0.185424	+	0.209872i
$475$	−26.8072	+	26.8072i	−1.23000	+	1.23000i
$476$	0.676414	+	5.44747i	0.0310034	+	0.249684i
$477$	−13.6196	−	13.6196i	−0.623600	−	0.623600i
$478$	0.434785	+	7.02993i	0.0198866	+	0.321542i
$479$	34.9353			1.59623			0.798116	−	0.602504i	$-0.205830\pi$
$479$	34.9353			1.59623			0.798116	+	0.602504i	$0.205830\pi$
$480$	−2.93675	−	9.20456i	−0.134044	−	0.420129i
$481$	1.38598			0.0631952
$482$	−0.0643905	−	1.04111i	−0.00293291	−	0.0474215i
$483$	1.15779	+	1.15779i	0.0526811	+	0.0526811i
$484$	4.35024	+	35.0345i	0.197738	+	1.59248i
$485$	−37.7318	+	37.7318i	−1.71331	+	1.71331i
$486$	10.3330	−	11.6954i	0.468716	−	0.530516i
$487$			26.1284i			1.18399i	0.805942	+	0.591995i	$0.201660\pi$
$487$			26.1284i			1.18399i	−0.805942	+	0.591995i	$0.798340\pi$
$488$	10.2926	−	15.0417i	0.465923	−	0.680904i
$489$			11.4216i			0.516505i
$490$	12.9730	+	11.4618i	0.586060	+	0.517790i
$491$	−6.40729	+	6.40729i	−0.289157	+	0.289157i	−0.836747	−	0.547590i	$-0.815545\pi$
$491$	−6.40729	+	6.40729i	−0.289157	+	0.289157i	0.547590	+	0.836747i	$0.315545\pi$
$492$	−3.60955	+	4.63304i	−0.162731	+	0.208873i
$493$	−6.59570	−	6.59570i	−0.297056	−	0.297056i
$494$	−5.61289	+	0.347144i	−0.252536	+	0.0156187i
$495$	−57.1232			−2.56750
$496$	−20.2876	+	5.11714i	−0.910941	+	0.229766i
$497$	−14.8231			−0.664909
$498$	5.95078	−	0.368042i	0.266661	−	0.0164924i
$499$	0.662277	+	0.662277i	0.0296476	+	0.0296476i	0.721775	−	0.692128i	$-0.243326\pi$
$499$	0.662277	+	0.662277i	0.0296476	+	0.0296476i	−0.692128	+	0.721775i	$0.743326\pi$
$500$	−27.2694	−	21.2453i	−1.21953	−	0.950120i
$501$	0.320954	−	0.320954i	0.0143392	−	0.0143392i
$502$	−12.1783	−	10.7597i	−0.543545	−	0.480227i
$503$			10.2028i			0.454920i	0.973787	+	0.227460i	$0.0730422\pi$
$503$			10.2028i			0.454920i	−0.973787	+	0.227460i	$0.926958\pi$
$504$	2.83967	+	15.1483i	0.126489	+	0.674760i
$505$		−	54.7299i		−	2.43545i
$506$	−9.41029	+	10.6510i	−0.418338	+	0.473496i
$507$	0.316792	−	0.316792i	0.0140692	−	0.0140692i
$508$	−5.00231	+	0.621138i	−0.221941	+	0.0275585i
$509$	−21.1446	−	21.1446i	−0.937219	−	0.937219i	0.0609233	−	0.998142i	$-0.480596\pi$
$509$	−21.1446	−	21.1446i	−0.937219	−	0.937219i	−0.998142	+	0.0609233i	$0.980596\pi$
$510$	0.210234	+	3.39922i	0.00930932	+	0.150520i
$511$	26.5338			1.17379
$512$	−11.9411	−	19.2201i	−0.527726	−	0.849415i
$513$	10.3315			0.456147
$514$	0.0301407	+	0.487338i	0.00132945	+	0.0214955i
$515$	−52.0801	−	52.0801i	−2.29492	−	2.29492i
$516$	−6.60482	+	0.820122i	−0.290761	+	0.0361039i
$517$	12.8092	−	12.8092i	0.563346	−	0.563346i
$518$	2.52623	−	2.85931i	0.110996	−	0.125631i
$519$			6.70682i			0.294397i
$520$	−1.98673	−	10.5983i	−0.0871237	−	0.464765i
$521$			19.3973i			0.849810i	0.905238	+	0.424905i	$0.139693\pi$
$521$			19.3973i			0.849810i	−0.905238	+	0.424905i	$0.860307\pi$
$522$	−19.6264	−	17.3401i	−0.859025	−	0.758957i
$523$	10.2516	−	10.2516i	0.448271	−	0.448271i	−0.446508	−	0.894780i	$-0.647333\pi$
$523$	10.2516	−	10.2516i	0.448271	−	0.448271i	0.894780	+	0.446508i	$0.147333\pi$
$524$	−9.64951	−	7.51783i	−0.421541	−	0.328418i
$525$	−5.87911	−	5.87911i	−0.256585	−	0.256585i
$526$	20.9696	−	1.29692i	0.914320	−	0.0565485i
$527$	7.37530			0.321273
$528$	9.30104	−	2.34600i	0.404776	−	0.102096i
$529$	19.4749			0.846737
$530$	37.0262	−	2.28998i	1.60831	−	0.0994704i
$531$	−4.39900	−	4.39900i	−0.190900	−	0.190900i
$532$	−9.51447	+	12.2123i	−0.412505	+	0.529470i
$533$	−4.63487	+	4.63487i	−0.200758	+	0.200758i
$534$	−4.39121	−	3.87967i	−0.190026	−	0.167890i
$535$			30.5017i			1.31870i
$536$	−19.5634	+	28.5901i	−0.845010	+	1.23491i
$537$			6.20477i			0.267756i
$538$	2.18935	−	2.47801i	0.0943895	−	0.106835i
$539$	−12.1528	+	12.1528i	−0.523460	+	0.523460i
$540$	2.44106	+	19.6590i	0.105046	+	0.845987i
$541$	7.32414	+	7.32414i	0.314889	+	0.314889i	0.846800	−	0.531911i	$-0.178526\pi$
$541$	7.32414	+	7.32414i	0.314889	+	0.314889i	−0.531911	+	0.846800i	$0.678526\pi$
$542$	0.913819	+	14.7753i	0.0392519	+	0.634654i
$543$	10.0021			0.429232
$544$	2.42440	+	7.59871i	0.103945	+	0.325792i
$545$	−54.0719			−2.31619
$546$	−0.0761325	−	1.23097i	−0.00325817	−	0.0526806i
$547$	−4.57498	−	4.57498i	−0.195612	−	0.195612i	0.602504	−	0.798116i	$-0.294170\pi$
$547$	−4.57498	−	4.57498i	−0.195612	−	0.195612i	−0.798116	+	0.602504i	$0.794170\pi$
$548$	0.696990	+	5.61318i	0.0297739	+	0.239783i
$549$	−12.7550	+	12.7550i	−0.544369	+	0.544369i
$550$	47.7844	−	54.0847i	2.03753	−	2.30618i
$551$		−	26.3064i		−	1.12069i
$552$	1.96345	+	1.34353i	0.0835701	+	0.0571845i
$553$			18.7324i			0.796583i
$554$	10.0087	+	8.84280i	0.425230	+	0.375695i
$555$	1.67386	−	1.67386i	0.0710516	−	0.0710516i
$556$	16.0828	−	20.6431i	0.682063	−	0.875461i
$557$	12.0550	+	12.0550i	0.510787	+	0.510787i	0.914768	−	0.403980i	$-0.132374\pi$
$557$	12.0550	+	12.0550i	0.510787	+	0.510787i	−0.403980	+	0.914768i	$0.632374\pi$
$558$	20.6680	−	1.27826i	0.874944	−	0.0541133i
$559$	−7.42787			−0.314166
$560$	−25.4857	−	15.2188i	−1.07697	−	0.643113i
$561$	−3.38127			−0.142757
$562$	26.6313	−	1.64708i	1.12337	−	0.0694780i
$563$	6.86170	+	6.86170i	0.289186	+	0.289186i	0.836758	−	0.547572i	$-0.184448\pi$
$563$	6.86170	+	6.86170i	0.289186	+	0.289186i	−0.547572	+	0.836758i	$0.684448\pi$
$564$	−2.39207	−	1.86364i	−0.100724	−	0.0784732i
$565$	8.17322	−	8.17322i	0.343850	−	0.343850i
$566$	−23.7363	−	20.9713i	−0.997712	−	0.881488i
$567$		−	14.0813i		−	0.591358i
$568$	−21.1696	+	3.96841i	−0.888259	+	0.166511i
$569$			21.9148i			0.918718i	0.888251	+	0.459359i	$0.151921\pi$
$569$			21.9148i			0.918718i	−0.888251	+	0.459359i	$0.848079\pi$
$570$	−6.35950	+	7.19801i	−0.266370	+	0.301491i
$571$	−21.0410	+	21.0410i	−0.880539	+	0.880539i	−0.993589	−	0.113050i	$-0.963938\pi$
$571$	−21.0410	+	21.0410i	−0.880539	+	0.880539i	0.113050	+	0.993589i	$0.463938\pi$
$572$	10.6239	−	1.31917i	0.444207	−	0.0551573i
$573$	2.17124	+	2.17124i	0.0907051	+	0.0907051i
$574$	1.11387	+	18.0098i	0.0464919	+	0.751717i
$575$	17.8998			0.746474
$576$	8.11093	+	20.8738i	0.337956	+	0.869743i
$577$	19.0020			0.791063			0.395531	−	0.918452i	$-0.370560\pi$
$577$	19.0020			0.791063			0.395531	+	0.918452i	$0.370560\pi$
$578$	1.31053	+	21.1896i	0.0545107	+	0.881371i
$579$	−0.553135	−	0.553135i	−0.0229875	−	0.0229875i
$580$	50.0562	−	6.21549i	2.07847	−	0.258084i
$581$	12.9526	−	12.9526i	0.537364	−	0.537364i
$582$	−5.87174	+	6.64593i	−0.243391	+	0.275483i
$583$			36.8306i			1.52537i
$584$	37.8943	−	7.10357i	1.56808	−	0.293948i
$585$			10.6718i			0.441224i
$586$	−1.08837	−	0.961589i	−0.0449603	−	0.0397229i
$587$	3.76524	−	3.76524i	0.155408	−	0.155408i	−0.625120	−	0.780528i	$-0.714950\pi$
$587$	3.76524	−	3.76524i	0.155408	−	0.155408i	0.780528	+	0.625120i	$0.214950\pi$
$588$	2.26950	+	1.76815i	0.0935928	+	0.0729172i
$589$	14.7079	+	14.7079i	0.606027	+	0.606027i
$590$	11.9591	−	0.739640i	0.492347	−	0.0304505i
$591$	−8.48531			−0.349039
$592$	2.84235	−	4.75984i	0.116820	−	0.195628i
$593$	−11.4157			−0.468788			−0.234394	−	0.972142i	$-0.575311\pi$
$593$	−11.4157			−0.468788			−0.234394	+	0.972142i	$0.575311\pi$
$594$	−19.6302	+	1.21408i	−0.805437	+	0.0498144i
$595$	7.39881	+	7.39881i	0.303322	+	0.303322i
$596$	20.6375	−	26.4892i	0.845344	−	1.08504i
$597$	2.09147	−	2.09147i	0.0855981	−	0.0855981i
$598$	1.98983	+	1.75803i	0.0813702	+	0.0718913i
$599$		−	25.1267i		−	1.02665i	−0.858194	−	0.513326i	$-0.828413\pi$
$599$		−	25.1267i		−	1.02665i	0.858194	−	0.513326i	$-0.171587\pi$
$600$	−9.97018	−	6.82231i	−0.407031	−	0.278519i
$601$			2.10270i			0.0857708i	0.999080	+	0.0428854i	$0.0136550\pi$
$601$			2.10270i			0.0857708i	−0.999080	+	0.0428854i	$0.986345\pi$
$602$	−13.5388	+	15.3239i	−0.551801	+	0.624556i
$603$	24.2438	−	24.2438i	0.987282	−	0.987282i
$604$	0.162574	+	1.30929i	0.00661506	+	0.0532741i
$605$	47.5842	+	47.5842i	1.93457	+	1.93457i
$606$	−0.561479	−	9.07842i	−0.0228085	−	0.368785i
$607$	−33.2148			−1.34815			−0.674073	−	0.738665i	$-0.735457\pi$
$607$	−33.2148			−1.34815			−0.674073	+	0.738665i	$0.735457\pi$
$608$	−10.3186	+	19.9882i	−0.418476	+	0.810627i
$609$	5.76928			0.233783
$610$	−2.14460	−	34.6755i	−0.0868323	−	1.40397i
$611$	−2.39301	−	2.39301i	−0.0968109	−	0.0968109i
$612$	−0.972720	−	7.83376i	−0.0393199	−	0.316661i
$613$	−28.1428	+	28.1428i	−1.13668	+	1.13668i	−0.147637	+	0.989042i	$0.547167\pi$
$613$	−28.1428	+	28.1428i	−1.13668	+	1.13668i	−0.989042	+	0.147637i	$0.952833\pi$
$614$	−9.81327	+	11.1072i	−0.396032	+	0.448248i
$615$			11.1952i			0.451433i
$616$	16.6427	−	24.3218i	0.670554	−	0.979954i
$617$		−	14.1655i		−	0.570281i	−0.958486	−	0.285141i	$-0.907960\pi$
$617$		−	14.1655i		−	0.570281i	0.958486	−	0.285141i	$-0.0920403\pi$
$618$	−9.17317	−	8.10458i	−0.368999	−	0.326014i
$619$	4.36024	−	4.36024i	0.175253	−	0.175253i	−0.614030	−	0.789283i	$-0.710453\pi$
$619$	4.36024	−	4.36024i	0.175253	−	0.175253i	0.789283	+	0.614030i	$0.210453\pi$
$620$	−24.5113	+	31.4614i	−0.984397	+	1.26352i
$621$	−3.44930	−	3.44930i	−0.138416	−	0.138416i
$622$	−2.76860	+	0.171232i	−0.111011	+	0.00686576i
$623$	−18.0025			−0.721257
$624$	−0.438280	−	1.73762i	−0.0175452	−	0.0695606i
$625$	−18.2243			−0.728971
$626$	36.5414	−	2.26000i	1.46049	−	0.0903277i
$627$	−6.74295	−	6.74295i	−0.269288	−	0.269288i
$628$	−2.25938	−	1.76026i	−0.0901592	−	0.0702421i
$629$	−1.38184	+	1.38184i	−0.0550975	+	0.0550975i
$630$	22.0162	+	19.4515i	0.877146	+	0.774966i
$631$			29.6217i			1.17922i	0.807688	+	0.589610i	$0.200719\pi$
$631$			29.6217i			1.17922i	−0.807688	+	0.589610i	$0.799281\pi$
$632$	5.01499	+	26.7527i	0.199486	+	1.06416i
$633$		−	11.9270i		−	0.474054i
$634$	−0.144964	+	0.164077i	−0.00575724	+	0.00651633i
$635$	−6.79418	+	6.79418i	−0.269619	+	0.269619i
$636$	6.11828	−	0.759709i	0.242606	−	0.0301244i
$637$	2.27040	+	2.27040i	0.0899565	+	0.0899565i
$638$	3.09133	+	49.9830i	0.122387	+	1.97885i
$639$	21.3165			0.843267
$640$	−40.4718	−	14.9118i	−1.59979	−	0.589441i
$641$	20.7799			0.820757			0.410379	−	0.911915i	$-0.365397\pi$
$641$	20.7799			0.820757			0.410379	+	0.911915i	$0.365397\pi$
$642$	0.312919	+	5.05951i	0.0123499	+	0.199683i
$643$	5.76964	+	5.76964i	0.227532	+	0.227532i	0.811661	−	0.584129i	$-0.198564\pi$
$643$	5.76964	+	5.76964i	0.227532	+	0.227532i	−0.584129	+	0.811661i	$0.698564\pi$
$644$	7.25375	−	0.900700i	0.285838	−	0.0354925i
$645$	−8.97073	+	8.97073i	−0.353222	+	0.353222i
$646$	5.25001	−	5.94222i	0.206559	−	0.233794i
$647$		−	25.4317i		−	0.999821i	−0.866077	−	0.499911i	$-0.833366\pi$
$647$		−	25.4317i		−	0.999821i	0.866077	−	0.499911i	$-0.166634\pi$
$648$	−3.76980	−	20.1102i	−0.148092	−	0.790002i
$649$			11.8959i			0.466955i
$650$	−10.1041	−	8.92709i	−0.396317	−	0.350149i
$651$	−3.22560	+	3.22560i	−0.126421	+	0.126421i
$652$	40.2221	+	31.3366i	1.57522	+	1.22724i
$653$	−11.4792	−	11.4792i	−0.449215	−	0.449215i	0.445878	−	0.895094i	$-0.352891\pi$
$653$	−11.4792	−	11.4792i	−0.449215	−	0.449215i	−0.895094	+	0.445878i	$0.852891\pi$
$654$	−8.96928	+	0.554729i	−0.350726	+	0.0216916i
$655$	−23.3169			−0.911065
$656$	6.41231	+	25.4225i	0.250359	+	0.992583i
$657$	−38.1571			−1.48865
$658$	−9.29860	+	0.575097i	−0.362497	+	0.0224196i
$659$	10.5724	+	10.5724i	0.411842	+	0.411842i	0.882380	−	0.470538i	$-0.155940\pi$
$659$	10.5724	+	10.5724i	0.411842	+	0.411842i	−0.470538	+	0.882380i	$0.655940\pi$
$660$	11.2374	−	14.4238i	0.437416	−	0.561444i
$661$	−13.3203	+	13.3203i	−0.518099	+	0.518099i	−0.916996	−	0.398897i	$-0.869393\pi$
$661$	−13.3203	+	13.3203i	−0.518099	+	0.518099i	0.398897	+	0.916996i	$0.369393\pi$
$662$	−11.2075	−	9.90189i	−0.435590	−	0.384848i
$663$			0.631690i			0.0245328i
$664$	15.0306	−	21.9658i	0.583300	−	0.852440i
$665$			29.5095i			1.14433i
$666$	−3.63286	+	4.11185i	−0.140770	+	0.159331i
$667$	−8.78271	+	8.78271i	−0.340068	+	0.340068i
$668$	−0.249686	−	2.01083i	−0.00966063	−	0.0778015i
$669$	−2.94042	−	2.94042i	−0.113683	−	0.113683i
$670$	4.07630	+	65.9088i	0.157481	+	2.54628i
$671$	34.4924			1.33156
$672$	−4.38362	−	2.26299i	−0.169102	−	0.0872968i
$673$	23.4159			0.902616			0.451308	−	0.892368i	$-0.350958\pi$
$673$	23.4159			0.902616			0.451308	+	0.892368i	$0.350958\pi$
$674$	0.257499	+	4.16344i	0.00991849	+	0.160370i
$675$	17.5152	+	17.5152i	0.674159	+	0.674159i
$676$	−0.246448	−	1.98476i	−0.00947877	−	0.0763368i
$677$	26.7272	−	26.7272i	1.02721	−	1.02721i	0.0275903	−	0.999619i	$-0.491217\pi$
$677$	26.7272	−	26.7272i	1.02721	−	1.02721i	0.999619	−	0.0275903i	$-0.00878337\pi$
$678$	1.27190	−	1.43960i	0.0488469	−	0.0552874i
$679$			27.2462i			1.04561i
$680$	12.5474	+	8.58581i	0.481170	+	0.329251i
$681$			7.69963i			0.295050i
$682$	−29.6738	−	26.2171i	−1.13627	−	1.00390i
$683$	−4.14571	+	4.14571i	−0.158631	+	0.158631i	−0.781960	−	0.623329i	$-0.785780\pi$
$683$	−4.14571	+	4.14571i	−0.158631	+	0.158631i	0.623329	+	0.781960i	$0.285780\pi$
$684$	13.6823	−	17.5619i	0.523157	−	0.671497i
$685$	7.62388	+	7.62388i	0.291293	+	0.291293i
$686$	28.0556	−	1.73517i	1.07117	−	0.0662491i
$687$	5.18449			0.197801
$688$	−15.2330	+	25.5094i	−0.580752	+	0.972537i
$689$	6.88071			0.262134
$690$	4.52634	−	0.279944i	0.172315	−	0.0106573i
$691$	35.7485	+	35.7485i	1.35994	+	1.35994i	0.873985	+	0.485954i	$0.161528\pi$
$691$	35.7485	+	35.7485i	1.35994	+	1.35994i	0.485954	+	0.873985i	$0.338472\pi$
$692$	23.6185	+	18.4009i	0.897840	+	0.699498i
$693$	−20.6243	+	20.6243i	−0.783453	+	0.783453i
$694$	−37.5465	−	33.1727i	−1.42525	−	1.25922i
$695$		−	49.8815i		−	1.89211i
$696$	8.23939	−	1.54454i	0.312313	−	0.0585455i
$697$		−	9.24203i		−	0.350067i
$698$	14.8612	−	16.8207i	0.562506	−	0.636673i
$699$	3.26064	−	3.26064i	0.123329	−	0.123329i
$700$	−36.8337	+	4.57365i	−1.39218	+	0.172868i
$701$	−22.1069	−	22.1069i	−0.834965	−	0.834965i	0.153226	−	0.988191i	$-0.451034\pi$
$701$	−22.1069	−	22.1069i	−0.834965	−	0.834965i	−0.988191	+	0.153226i	$0.951034\pi$
$702$	0.226815	+	3.66732i	0.00856060	+	0.138414i
$703$	−5.51134			−0.207864
$704$	17.2569	−	39.1907i	0.650394	−	1.47706i
$705$	−5.78014			−0.217693
$706$	−0.0482342	−	0.779887i	−0.00181532	−	0.0293514i
$707$	−19.7602	−	19.7602i	−0.743160	−	0.743160i
$708$	1.97614	−	0.245378i	0.0742679	−	0.00922187i
$709$	−21.1243	+	21.1243i	−0.793338	+	0.793338i	−0.982035	−	0.188697i	$-0.939574\pi$
$709$	−21.1243	+	21.1243i	−0.793338	+	0.793338i	0.188697	+	0.982035i	$0.439574\pi$
$710$	−27.1833	+	30.7674i	−1.02017	+	1.15468i
$711$		−	26.9382i		−	1.01026i
$712$	−25.7103	+	4.81959i	−0.963534	+	0.180622i
$713$		−	9.82081i		−	0.367792i
$714$	1.30319	+	1.15138i	0.0487708	+	0.0430895i
$715$	14.4295	−	14.4295i	0.539631	−	0.539631i
$716$	21.8505	+	17.0235i	0.816591	+	0.636198i
$717$	1.57775	+	1.57775i	0.0589223	+	0.0589223i
$718$	−27.0323	+	1.67188i	−1.00884	+	0.0623941i
$719$	−6.02460			−0.224680			−0.112340	−	0.993670i	$-0.535835\pi$
$719$	−6.02460			−0.224680			−0.112340	+	0.993670i	$0.535835\pi$
$720$	36.6499	+	21.8855i	1.36586	+	0.815625i
$721$	−37.6071			−1.40056
$722$	−4.49918	+	0.278264i	−0.167442	+	0.0103559i
$723$	−0.233661	−	0.233661i	−0.00868995	−	0.00868995i
$724$	27.4420	−	35.2231i	1.01987	−	1.30906i
$725$	44.5976	−	44.5976i	1.65631	−	1.65631i
$726$	8.38127	+	7.40493i	0.311058	+	0.274823i
$727$		−	49.0509i		−	1.81920i	−0.415487	−	0.909599i	$-0.636389\pi$
$727$		−	49.0509i		−	1.81920i	0.415487	−	0.909599i	$-0.363611\pi$
$728$	−4.54381	−	3.10920i	−0.168405	−	0.115235i
$729$			16.7576i			0.620654i
$730$	48.6589	−	55.0745i	1.80095	−	2.03840i
$731$	7.40568	−	7.40568i	0.273909	−	0.273909i
$732$	−0.711478	−	5.72986i	−0.0262970	−	0.211782i
$733$	7.75465	+	7.75465i	0.286424	+	0.286424i	0.835665	−	0.549240i	$-0.185083\pi$
$733$	7.75465	+	7.75465i	0.286424	+	0.286424i	−0.549240	+	0.835665i	$0.685083\pi$
$734$	1.69036	+	27.3310i	0.0623923	+	1.00881i
$735$	5.48398			0.202280
$736$	10.1183	−	3.22829i	0.372965	−	0.118996i
$737$	−65.5607			−2.41496
$738$	−1.60180	−	25.8991i	−0.0589631	−	0.953361i
$739$	−35.6106	−	35.6106i	−1.30996	−	1.30996i	−0.921442	−	0.388517i	$-0.872988\pi$
$739$	−35.6106	−	35.6106i	−1.30996	−	1.30996i	−0.388517	−	0.921442i	$-0.627012\pi$
$740$	−1.30218	−	10.4871i	−0.0478691	−	0.385512i
$741$	−1.25972	+	1.25972i	−0.0462770	+	0.0462770i
$742$	12.5415	−	14.1951i	0.460413	−	0.521118i
$743$		−	39.6393i		−	1.45422i	−0.686519	−	0.727112i	$-0.740862\pi$
$743$		−	39.6393i		−	1.45422i	0.686519	−	0.727112i	$-0.259138\pi$
$744$	−3.74309	+	5.47018i	−0.137228	+	0.200547i
$745$		−	64.0080i		−	2.34507i
$746$	0.115770	+	0.102284i	0.00423863	+	0.00374487i
$747$	−18.6265	+	18.6265i	−0.681508	+	0.681508i
$748$	−9.27690	+	11.9074i	−0.339197	+	0.435376i
$749$	11.0126	+	11.0126i	0.402393	+	0.402393i
$750$	−10.9302	+	0.676004i	−0.399113	+	0.0246842i
$751$	−11.1125			−0.405500			−0.202750	−	0.979230i	$-0.564988\pi$
$751$	−11.1125			−0.405500			−0.202750	+	0.979230i	$0.564988\pi$
$752$	−13.1258	+	3.31072i	−0.478650	+	0.120730i
$753$	−5.14805			−0.187606
$754$	9.33785	−	0.577524i	0.340064	−	0.0210322i
$755$	1.77829	+	1.77829i	0.0647184	+	0.0647184i
$756$	7.97921	+	6.21652i	0.290201	+	0.226093i
$757$	−7.47336	+	7.47336i	−0.271624	+	0.271624i	−0.829754	−	0.558130i	$-0.811519\pi$
$757$	−7.47336	+	7.47336i	−0.271624	+	0.271624i	0.558130	+	0.829754i	$0.311519\pi$
$758$	−35.4056	−	31.2812i	−1.28599	−	1.13618i
$759$			4.50243i			0.163428i
$760$	7.90020	+	42.1440i	0.286571	+	1.52872i
$761$		−	12.8301i		−	0.465090i	−0.972586	−	0.232545i	$-0.925295\pi$
$761$		−	12.8301i		−	0.465090i	0.972586	−	0.232545i	$-0.0747053\pi$
$762$	−1.05729	+	1.19670i	−0.0383017	+	0.0433518i
$763$	−19.5227	+	19.5227i	−0.706769	+	0.706769i
$764$	13.6032	−	1.68912i	0.492148	−	0.0611101i
$765$	−10.6399	−	10.6399i	−0.384686	−	0.384686i
$766$	−0.460840	−	7.45121i	−0.0166508	−	0.269223i
$767$	2.22240			0.0802461
$768$	−6.86630	−	2.05832i	−0.247766	−	0.0742731i
$769$	−37.6661			−1.35827			−0.679137	−	0.734012i	$-0.737646\pi$
$769$	−37.6661			−1.35827			−0.679137	+	0.734012i	$0.737646\pi$
$770$	−3.46774	−	56.0690i	−0.124969	−	2.02059i
$771$	0.109375	+	0.109375i	0.00393904	+	0.00393904i
$772$	−3.46549	+	0.430311i	−0.124726	+	0.0154872i
$773$	−10.5123	+	10.5123i	−0.378103	+	0.378103i	−0.870417	−	0.492315i	$-0.836151\pi$
$773$	−10.5123	+	10.5123i	−0.378103	+	0.378103i	0.492315	+	0.870417i	$0.336151\pi$
$774$	19.4696	−	22.0366i	0.699819	−	0.792090i
$775$			49.8689i			1.79135i
$776$	7.29427	+	38.9116i	0.261849	+	1.39684i
$777$		−	1.20870i		−	0.0433618i
$778$	−28.9830	−	25.6067i	−1.03909	−	0.918045i
$779$	18.4305	−	18.4305i	0.660342	−	0.660342i
$780$	−2.69465	−	2.09938i	−0.0964841	−	0.0751698i
$781$	−28.8223	−	28.8223i	−1.03134	−	1.03134i
$782$	−3.73666	+	0.231104i	−0.133623	+	0.00826426i
$783$	−17.1880			−0.614248
$784$	12.4533	−	3.14109i	0.444761	−	0.112182i
$785$	−5.45952			−0.194859
$786$	−3.86772	+	0.239210i	−0.137957	+	0.00853232i
$787$	16.3508	+	16.3508i	0.582841	+	0.582841i	0.935683	−	0.352842i	$-0.114785\pi$
$787$	16.3508	+	16.3508i	0.582841	+	0.582841i	−0.352842	+	0.935683i	$0.614785\pi$
$788$	−23.2804	+	29.8816i	−0.829331	+	1.06449i
$789$	4.70629	−	4.70629i	0.167548	−	0.167548i
$790$	38.8816	+	34.3523i	1.38335	+	1.22220i
$791$		−	5.90189i		−	0.209847i
$792$	−23.9331	+	34.9761i	−0.850426	+	1.24282i
$793$		−	6.44388i		−	0.228829i
$794$	−17.9445	+	20.3105i	−0.636827	+	0.720793i
$795$	8.30992	−	8.30992i	0.294722	−	0.294722i
$796$	−1.62706	−	13.1034i	−0.0576695	−	0.464439i
$797$	−17.0148	−	17.0148i	−0.602696	−	0.602696i	0.338331	−	0.941027i	$-0.390138\pi$
$797$	−17.0148	−	17.0148i	−0.602696	−	0.602696i	−0.941027	+	0.338331i	$0.890138\pi$
$798$	0.302741	+	4.89494i	0.0107169	+	0.173279i
$799$	4.77172			0.168811
$800$	−51.3795	+	16.3929i	−1.81654	+	0.579575i
$801$	25.8886			0.914730
$802$	0.416539	+	6.73493i	0.0147085	+	0.237819i
$803$	51.5928	+	51.5928i	1.82067	+	1.82067i
$804$	1.35233	+	10.8909i	0.0476929	+	0.384093i
$805$	9.85211	−	9.85211i	0.347241	−	0.347241i
$806$	−4.89789	+	5.54367i	−0.172521	+	0.195268i
$807$		−	1.04751i		−	0.0368742i
$808$	−33.5107	−	22.9304i	−1.17890	−	0.806689i
$809$			40.9024i			1.43805i	0.694984	+	0.719025i	$0.255412\pi$
$809$			40.9024i			1.43805i	−0.694984	+	0.719025i	$0.744588\pi$
$810$	−29.2276	−	25.8228i	−1.02695	−	0.907322i
$811$	−16.1269	+	16.1269i	−0.566291	+	0.566291i	−0.931087	−	0.364796i	$-0.881139\pi$
$811$	−16.1269	+	16.1269i	−0.566291	+	0.566291i	0.364796	+	0.931087i	$0.381139\pi$
$812$	15.8287	−	20.3169i	0.555478	−	0.712983i
$813$	3.31608	+	3.31608i	0.116300	+	0.116300i
$814$	10.4717	−	0.647652i	0.367034	−	0.0227002i
$815$	97.1917			3.40448
$816$	2.16940	+	1.29546i	0.0759442	+	0.0453502i
$817$	29.5369			1.03337
$818$	17.3395	−	1.07241i	0.606263	−	0.0374959i
$819$	3.85305	+	3.85305i	0.134636	+	0.134636i
$820$	39.4245	+	30.7152i	1.37676	+	1.07262i
$821$	1.81720	−	1.81720i	0.0634209	−	0.0634209i	−0.674685	−	0.738106i	$-0.735721\pi$
$821$	1.81720	−	1.81720i	0.0634209	−	0.0634209i	0.738106	+	0.674685i	$0.235721\pi$
$822$	1.34284	+	1.18641i	0.0468368	+	0.0413808i
$823$			38.3121i			1.33547i	0.744397	+	0.667737i	$0.232737\pi$
$823$			38.3121i			1.33547i	−0.744397	+	0.667737i	$0.767263\pi$
$824$	−53.7085	+	10.0681i	−1.87102	+	0.350737i
$825$		−	22.8628i		−	0.795982i
$826$	4.05077	−	4.58487i	0.140944	−	0.159528i
$827$	−6.65111	+	6.65111i	−0.231282	+	0.231282i	−0.813228	−	0.581946i	$-0.802292\pi$
$827$	−6.65111	+	6.65111i	−0.231282	+	0.231282i	0.581946	+	0.813228i	$0.302292\pi$
$828$	−10.4313	+	1.29525i	−0.362512	+	0.0450132i
$829$	23.3602	+	23.3602i	0.811332	+	0.811332i	0.984834	−	0.173502i	$-0.0555083\pi$
$829$	23.3602	+	23.3602i	0.811332	+	0.811332i	−0.173502	+	0.984834i	$0.555508\pi$
$830$	−3.13183	−	50.6378i	−0.108707	−	1.75766i
$831$	4.23092			0.146769
$832$	−7.32163	−	3.22394i	−0.253832	−	0.111770i
$833$	−4.52723			−0.156859
$834$	−0.511738	−	8.27417i	−0.0177200	−	0.286511i
$835$	−2.73113	−	2.73113i	−0.0945148	−	0.0945148i
$836$	−42.2458	+	5.24567i	−1.46110	+	0.181425i
$837$	9.60976	−	9.60976i	0.332162	−	0.332162i
$838$	17.7952	−	20.1415i	0.614724	−	0.695776i
$839$		−	47.1496i		−	1.62778i	−0.581016	−	0.813892i	$-0.697345\pi$
$839$		−	47.1496i		−	1.62778i	0.581016	−	0.813892i	$-0.302655\pi$
$840$	−9.24263	+	1.73260i	−0.318901	+	0.0597804i
$841$			14.7645i			0.509120i
$842$	−24.9979	−	22.0858i	−0.861483	−	0.761129i
$843$	5.97696	−	5.97696i	0.205857	−	0.205857i
$844$	−42.0016	−	32.7230i	−1.44575	−	1.12637i
$845$	−2.69572	−	2.69572i	−0.0927355	−	0.0927355i
$846$	13.3719	−	0.827020i	0.459735	−	0.0284335i
$847$	34.3605			1.18064
$848$	14.1109	−	23.6303i	0.484569	−	0.811467i
$849$	−10.0339			−0.344362
$850$	18.9744	−	1.17352i	0.650815	−	0.0402514i
$851$	1.84003	+	1.84003i	0.0630754	+	0.0630754i
$852$	−4.19343	+	5.38247i	−0.143665	+	0.184400i
$853$	−32.0963	+	32.0963i	−1.09896	+	1.09896i	−0.104423	+	0.994533i	$0.533300\pi$
$853$	−32.0963	+	32.0963i	−1.09896	+	1.09896i	−0.994533	+	0.104423i	$0.966700\pi$
$854$	−13.2939	−	11.7453i	−0.454908	−	0.401915i
$855$		−	42.4363i		−	1.45129i
$856$	18.6759	+	12.7794i	0.638330	+	0.436791i
$857$		−	12.2891i		−	0.419789i	−0.977724	−	0.209894i	$-0.932688\pi$
$857$		−	12.2891i		−	0.419789i	0.977724	−	0.209894i	$-0.0673120\pi$
$858$	2.24548	−	2.54154i	0.0766594	−	0.0867669i
$859$	11.9167	−	11.9167i	0.406592	−	0.406592i	−0.473957	−	0.880548i	$-0.657175\pi$
$859$	11.9167	−	11.9167i	0.406592	−	0.406592i	0.880548	+	0.473957i	$0.157175\pi$
$860$	6.97878	+	56.2033i	0.237974	+	1.91652i
$861$	4.04202	+	4.04202i	0.137752	+	0.137752i
$862$	1.72422	+	27.8785i	0.0587272	+	0.949546i
$863$	7.67225			0.261166			0.130583	−	0.991437i	$-0.458315\pi$
$863$	7.67225			0.261166			0.130583	+	0.991437i	$0.458315\pi$
$864$	13.0598	+	6.74195i	0.444302	+	0.229366i
$865$	57.0712			1.94048
$866$	−2.41897	−	39.1117i	−0.0821998	−	1.32907i
$867$	4.75566	+	4.75566i	0.161511	+	0.161511i
$868$	2.50935	+	20.2090i	0.0851729	+	0.685937i
$869$	−36.4235	+	36.4235i	−1.23558	+	1.23558i
$870$	10.5800	−	11.9749i	0.358694	−	0.405988i
$871$			12.2481i			0.415010i
$872$	−22.6547	+	33.1079i	−0.767186	+	1.12117i
$873$		−	39.1815i		−	1.32609i
$874$	−7.91255	−	6.99081i	−0.267646	−	0.236468i
$875$	−23.7908	+	23.7908i	−0.804275	+	0.804275i
$876$	7.50636	−	9.63478i	0.253616	−	0.325529i
$877$	11.6940	+	11.6940i	0.394877	+	0.394877i	0.876421	−	0.481545i	$-0.159924\pi$
$877$	11.6940	+	11.6940i	0.394877	+	0.394877i	−0.481545	+	0.876421i	$0.659924\pi$
$878$	−21.7874	+	1.34750i	−0.735288	+	0.0454759i
$879$	−0.460081			−0.0155181
$880$	−19.9631	−	79.1465i	−0.672956	−	2.66803i
$881$	−44.8587			−1.51133			−0.755664	−	0.654959i	$-0.772686\pi$
$881$	−44.8587			−1.51133			−0.755664	+	0.654959i	$0.772686\pi$
$882$	−12.6868	+	0.784646i	−0.427185	+	0.0264204i
$883$	6.56651	+	6.56651i	0.220981	+	0.220981i	0.808911	−	0.587931i	$-0.200057\pi$
$883$	6.56651	+	6.56651i	0.220981	+	0.220981i	−0.587931	+	0.808911i	$0.700057\pi$
$884$	2.22454	+	1.73312i	0.0748193	+	0.0582910i
$885$	2.68402	−	2.68402i	0.0902222	−	0.0902222i
$886$	−0.416106	−	0.367633i	−0.0139794	−	0.0123509i
$887$			24.2248i			0.813390i	0.913564	+	0.406695i	$0.133319\pi$
$887$			24.2248i			0.813390i	−0.913564	+	0.406695i	$0.866681\pi$
$888$	−0.323589	−	1.72620i	−0.0108589	−	0.0579275i
$889$			4.90608i			0.164545i
$890$	−33.0138	+	37.3667i	−1.10663	+	1.25253i
$891$	27.3798	−	27.3798i	0.917259	−	0.917259i
$892$	−18.4223	+	2.28750i	−0.616824	+	0.0765911i
$893$	9.51580	+	9.51580i	0.318434	+	0.318434i
$894$	−0.656663	−	10.6174i	−0.0219621	−	0.355100i
$895$	52.7991			1.76488
$896$	−19.9962	+	9.22843i	−0.668028	+	0.308300i
$897$	0.841147			0.0280851
$898$	−0.914559	−	14.7873i	−0.0305192	−	0.493458i
$899$	−24.4687	−	24.4687i	−0.816076	−	0.816076i
$900$	52.9689	−	6.57716i	1.76563	−	0.219239i
$901$	−6.86015	+	6.86015i	−0.228545	+	0.228545i
$902$	−32.8528	+	37.1844i	−1.09388	+	1.23811i
$903$			6.47777i			0.215567i
$904$	−1.58004	−	8.42877i	−0.0525512	−	0.280337i
$905$		−	85.1123i		−	2.82923i
$906$	0.313220	+	0.276733i	0.0104060	+	0.00919382i
$907$	9.86594	−	9.86594i	0.327593	−	0.327593i	−0.524077	−	0.851671i	$-0.675590\pi$
$907$	9.86594	−	9.86594i	0.327593	−	0.327593i	0.851671	+	0.524077i	$0.175590\pi$
$908$	27.1147	+	21.1248i	0.899834	+	0.701052i
$909$	28.4163	+	28.4163i	0.942509	+	0.942509i
$910$	−10.4748	+	0.647844i	−0.347238	+	0.0214758i
$911$	2.49568			0.0826856			0.0413428	−	0.999145i	$-0.486836\pi$
$911$	2.49568			0.0826856			0.0413428	+	0.999145i	$0.486836\pi$
$912$	1.74282	+	6.90965i	0.0577105	+	0.228801i
$913$	50.3703			1.66701
$914$	−3.89448	+	0.240865i	−0.128818	+	0.00796710i
$915$	−7.78235	−	7.78235i	−0.257277	−	0.257277i
$916$	14.2243	−	18.2575i	0.469983	−	0.603246i
$917$	−8.41855	+	8.41855i	−0.278005	+	0.278005i
$918$	−3.88250	−	3.43023i	−0.128142	−	0.113214i
$919$			3.25239i			0.107286i	0.998560	+	0.0536432i	$0.0170834\pi$
$919$			3.25239i			0.107286i	−0.998560	+	0.0536432i	$0.982917\pi$
$920$	11.4327	−	16.7079i	0.376925	−	0.550842i
$921$			4.69525i			0.154714i
$922$	2.75712	−	3.12064i	0.0908008	−	0.102773i
$923$	−5.38460	+	5.38460i	−0.177236	+	0.177236i
$924$	−1.15043	−	9.26497i	−0.0378465	−	0.304795i
$925$	−9.34346	−	9.34346i	−0.307211	−	0.307211i
$926$	−1.16989	−	18.9158i	−0.0384451	−	0.621610i
$927$	54.0810			1.77625
$928$	17.1665	−	33.2532i	0.563519	−	1.09159i
$929$	−48.0050			−1.57499			−0.787497	−	0.616318i	$-0.788624\pi$
$929$	−48.0050			−1.57499			−0.787497	+	0.616318i	$0.788624\pi$
$930$	0.779923	+	12.6104i	0.0255747	+	0.413511i
$931$	−9.02824	−	9.02824i	−0.295889	−	0.295889i
$932$	−2.53661	−	20.4285i	−0.0830894	−	0.669157i
$933$	−0.621368	+	0.621368i	−0.0203427	+	0.0203427i
$934$	6.95655	−	7.87377i	0.227625	−	0.257638i
$935$			28.7727i			0.940967i
$936$	6.53425	+	4.47120i	0.213579	+	0.146146i
$937$			0.692149i			0.0226115i	0.999936	+	0.0113058i	$0.00359881\pi$
$937$			0.692149i			0.0226115i	−0.999936	+	0.0113058i	$0.996401\pi$
$938$	25.2681	+	22.3246i	0.825033	+	0.728925i
$939$	8.20111	−	8.20111i	0.267633	−	0.267633i
$940$	−15.8585	+	20.3551i	−0.517247	+	0.663911i
$941$	42.5844	+	42.5844i	1.38821	+	1.38821i	0.829076	+	0.559135i	$0.188867\pi$
$941$	42.5844	+	42.5844i	1.38821	+	1.38821i	0.559135	+	0.829076i	$0.311133\pi$
$942$	−0.905608	+	0.0560097i	−0.0295063	+	0.00182489i
$943$	−12.3065			−0.400755
$944$	4.55766	−	7.63233i	0.148339	−	0.248411i
$945$	19.2808			0.627204
$946$	−56.1211	+	3.47096i	−1.82465	+	0.112851i
$947$	−31.6502	−	31.6502i	−1.02849	−	1.02849i	−0.999582	−	0.0289124i	$-0.990796\pi$
$947$	−31.6502	−	31.6502i	−1.02849	−	1.02849i	−0.0289124	−	0.999582i	$-0.509204\pi$
$948$	6.80198	+	5.29935i	0.220918	+	0.172115i
$949$	9.63858	−	9.63858i	0.312882	−	0.312882i
$950$	40.1790	+	35.4986i	1.30358	+	1.15173i
$951$			0.0693591i			0.00224912i
$952$	7.63014	−	1.43033i	0.247294	−	0.0463572i
$953$		−	48.6867i		−	1.57712i	−0.614959	−	0.788559i	$-0.710828\pi$
$953$		−	48.6867i		−	1.57712i	0.614959	−	0.788559i	$-0.289172\pi$
$954$	−18.0354	+	20.4133i	−0.583916	+	0.660906i
$955$	18.4761	−	18.4761i	0.597871	−	0.597871i
$956$	9.88491	−	1.22741i	0.319701	−	0.0396973i
$957$	11.2179	+	11.2179i	0.362622	+	0.362622i
$958$	−3.04981	−	49.3117i	−0.0985350	−	1.59319i
$959$	5.50520			0.177772
$960$	−12.7360	+	4.94882i	−0.411053	+	0.159723i
$961$	−3.63921			−0.117394
$962$	−0.120995	−	1.95633i	−0.00390102	−	0.0630747i
$963$	−15.8368	−	15.8368i	−0.510332	−	0.510332i
$964$	−1.46393	+	0.181776i	−0.0471500	+	0.00585463i
$965$	−4.70686	+	4.70686i	−0.151519	+	0.151519i
$966$	1.53316	−	1.73531i	0.0493287	−	0.0558327i
$967$		−	17.7914i		−	0.572133i	−0.958210	−	0.286066i	$-0.907652\pi$
$967$		−	17.7914i		−	0.572133i	0.958210	−	0.286066i	$-0.0923478\pi$
$968$	49.0719	−	9.19890i	1.57723	−	0.295664i
$969$		−	2.51191i		−	0.0806943i
$970$	56.5531	+	49.9652i	1.81581	+	1.60429i
$971$	−20.2005	+	20.2005i	−0.648265	+	0.648265i	−0.952574	−	0.304308i	$-0.901575\pi$
$971$	−20.2005	+	20.2005i	−0.648265	+	0.648265i	0.304308	+	0.952574i	$0.401575\pi$
$972$	−17.4104	−	13.5643i	−0.558438	−	0.435074i
$973$	−18.0097	−	18.0097i	−0.577365	−	0.577365i
$974$	36.8806	−	2.28098i	1.18173	−	0.0730874i
$975$	−4.27125			−0.136789
$976$	−22.1301	−	13.2150i	−0.708367	−	0.423002i
$977$	14.2989			0.457463			0.228731	−	0.973490i	$-0.426542\pi$
$977$	14.2989			0.457463			0.228731	+	0.973490i	$0.426542\pi$
$978$	16.1218	−	0.997098i	0.515520	−	0.0318837i
$979$	−35.0044	−	35.0044i	−1.11874	−	1.11874i
$980$	15.0459	−	19.3122i	0.480625	−	0.616905i
$981$	28.0747	−	28.0747i	0.896355	−	0.896355i
$982$	9.60334	+	8.48464i	0.306455	+	0.270756i
$983$			54.7212i			1.74533i	0.488316	+	0.872667i	$0.337612\pi$
$983$			54.7212i			1.74533i	−0.488316	+	0.872667i	$0.662388\pi$
$984$	6.85472	+	4.69048i	0.218520	+	0.149527i
$985$			72.2052i			2.30065i
$986$	−8.73415	+	9.88574i	−0.278152	+	0.314826i
$987$	−2.08692	+	2.08692i	−0.0664274	+	0.0664274i
$988$	0.979999	+	7.89238i	0.0311779	+	0.251090i
$989$	−9.86126	−	9.86126i	−0.313570	−	0.313570i
$990$	4.98680	+	80.6303i	0.158491	+	2.56260i
$991$	56.2551			1.78700			0.893500	−	0.449062i	$-0.148242\pi$
$991$	56.2551			1.78700			0.893500	+	0.449062i	$0.148242\pi$
$992$	8.99401	+	28.1896i	0.285560	+	0.895020i
$993$	−4.73765			−0.150345
$994$	1.29404	+	20.9231i	0.0410446	+	0.663641i
$995$	−17.7972	−	17.7972i	−0.564210	−	0.564210i
$996$	−1.03899	−	8.36750i	−0.0329218	−	0.265134i
$997$	3.94123	−	3.94123i	0.124820	−	0.124820i	−0.641937	−	0.766757i	$-0.721869\pi$
$997$	3.94123	−	3.94123i	0.124820	−	0.124820i	0.766757	+	0.641937i	$0.221869\pi$
$998$	0.876998	−	0.992631i	0.0277609	−	0.0314212i
$999$			3.60098i			0.113930i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	208.2.n.a.157.11	yes	48
4.3	odd	2		832.2.n.a.209.14		48
8.3	odd	2		1664.2.n.a.417.11		48
8.5	even	2		1664.2.n.b.417.14		48
16.3	odd	4		1664.2.n.a.1249.11		48
16.5	even	4	inner	208.2.n.a.53.11	✓	48
16.11	odd	4		832.2.n.a.625.14		48
16.13	even	4		1664.2.n.b.1249.14		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
208.2.n.a.53.11	✓	48	16.5	even	4	inner
208.2.n.a.157.11	yes	48	1.1	even	1	trivial
832.2.n.a.209.14		48	4.3	odd	2
832.2.n.a.625.14		48	16.11	odd	4
1664.2.n.a.417.11		48	8.3	odd	2
1664.2.n.a.1249.11		48	16.3	odd	4
1664.2.n.b.417.14		48	8.5	even	2
1664.2.n.b.1249.14		48	16.13	even	4

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:	\( N \)	\(=\)	\( 208 = 2^{4} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	208.n (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.0872990 - 1.41152i) q^{2} +(-0.316792 - 0.316792i) q^{3} +(-1.98476 + 0.246448i) q^{4} +(-2.69572 + 2.69572i) q^{5} +(-0.419501 + 0.474812i) q^{6} +1.94658i q^{7} +(0.521133 + 2.78000i) q^{8} -2.79929i q^{9} +(4.04038 + 3.56972i) q^{10} +(-3.78495 + 3.78495i) q^{11} +(0.706828 + 0.550682i) q^{12} +(0.707107 + 0.707107i) q^{13} +(2.74763 - 0.169934i) q^{14} +1.70796 q^{15} +(3.87853 - 0.978279i) q^{16} -1.40999 q^{17} +(-3.95124 + 0.244375i) q^{18} +(-2.81181 - 2.81181i) q^{19} +(4.68599 - 6.01470i) q^{20} +(0.616660 - 0.616660i) q^{21} +(5.67295 + 5.01210i) q^{22} +1.87751i q^{23} +(0.715592 - 1.04577i) q^{24} -9.53379i q^{25} +(0.936363 - 1.05982i) q^{26} +(-1.83717 + 1.83717i) q^{27} +(-0.479730 - 3.86349i) q^{28} +(4.67785 + 4.67785i) q^{29} +(-0.149103 - 2.41082i) q^{30} -5.23075 q^{31} +(-1.71945 - 5.38920i) q^{32} +2.39808 q^{33} +(0.123090 + 1.99022i) q^{34} +(-5.24743 - 5.24743i) q^{35} +(0.689878 + 5.55590i) q^{36} +(0.980035 - 0.980035i) q^{37} +(-3.72344 + 4.21438i) q^{38} -0.448011i q^{39} +(-8.89893 - 6.08928i) q^{40} +6.55469i q^{41} +(-0.924260 - 0.816592i) q^{42} +(-5.25230 + 5.25230i) q^{43} +(6.57942 - 8.44501i) q^{44} +(7.54609 + 7.54609i) q^{45} +(2.65014 - 0.163905i) q^{46} -3.38423 q^{47} +(-1.53860 - 0.918775i) q^{48} +3.21083 q^{49} +(-13.4571 + 0.832291i) q^{50} +(0.446672 + 0.446672i) q^{51} +(-1.57770 - 1.22917i) q^{52} +(4.86540 - 4.86540i) q^{53} +(2.75357 + 2.43281i) q^{54} -20.4063i q^{55} +(-5.41150 + 1.01443i) q^{56} +1.78151i q^{57} +(6.19448 - 7.01123i) q^{58} +(1.57147 - 1.57147i) q^{59} +(-3.38989 + 0.420924i) q^{60} +(-4.55651 - 4.55651i) q^{61} +(0.456640 + 7.38330i) q^{62} +5.44903 q^{63} +(-7.45684 + 2.89750i) q^{64} -3.81232 q^{65} +(-0.209350 - 3.38494i) q^{66} +(8.66069 + 8.66069i) q^{67} +(2.79848 - 0.347488i) q^{68} +(0.594781 - 0.594781i) q^{69} +(-6.94874 + 7.86493i) q^{70} +7.61497i q^{71} +(7.78203 - 1.45880i) q^{72} -13.6310i q^{73} +(-1.46889 - 1.29778i) q^{74} +(-3.02023 + 3.02023i) q^{75} +(6.27372 + 4.88779i) q^{76} +(-7.36771 - 7.36771i) q^{77} +(-0.632375 + 0.0391109i) q^{78} +9.62325 q^{79} +(-7.81825 + 13.0926i) q^{80} -7.23386 q^{81} +(9.25205 - 0.572218i) q^{82} +(-6.65402 - 6.65402i) q^{83} +(-1.07195 + 1.37590i) q^{84} +(3.80093 - 3.80093i) q^{85} +(7.87223 + 6.95519i) q^{86} -2.96381i q^{87} +(-12.4946 - 8.54972i) q^{88} +9.24830i q^{89} +(9.99266 - 11.3102i) q^{90} +(-1.37644 + 1.37644i) q^{91} +(-0.462709 - 3.72641i) q^{92} +(1.65706 + 1.65706i) q^{93} +(0.295440 + 4.77690i) q^{94} +15.1597 q^{95} +(-1.16255 + 2.25196i) q^{96} +13.9970 q^{97} +(-0.280302 - 4.53214i) q^{98} +(10.5952 + 10.5952i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 4 q^{4} - 12 q^{8} - 4 q^{10} - 8 q^{11} + 8 q^{12} - 4 q^{14} - 16 q^{15} + 12 q^{16} - 16 q^{19} - 28 q^{20} + 12 q^{22} + 28 q^{24} - 16 q^{29} + 4 q^{30} + 24 q^{31} - 20 q^{32} - 40 q^{34} + 24 q^{35}+ \cdots - 40 q^{99}+O(q^{100}) \) 48 * q - 4 * q^4 - 12 * q^8 - 4 * q^10 - 8 * q^11 + 8 * q^12 - 4 * q^14 - 16 * q^15 + 12 * q^16 - 16 * q^19 - 28 * q^20 + 12 * q^22 + 28 * q^24 - 16 * q^29 + 4 * q^30 + 24 * q^31 - 20 * q^32 - 40 * q^34 + 24 * q^35 + 8 * q^36 - 16 * q^37 + 32 * q^40 + 40 * q^42 - 8 * q^43 + 20 * q^44 - 32 * q^46 - 40 * q^47 - 52 * q^48 - 48 * q^49 - 16 * q^50 - 24 * q^51 - 8 * q^52 + 16 * q^53 + 20 * q^54 + 20 * q^56 - 16 * q^58 - 68 * q^60 + 32 * q^61 - 32 * q^62 + 40 * q^63 + 32 * q^64 - 32 * q^66 + 16 * q^67 + 40 * q^68 + 32 * q^69 - 60 * q^70 + 40 * q^72 + 72 * q^74 - 40 * q^75 - 28 * q^76 + 16 * q^77 + 32 * q^79 - 52 * q^80 - 48 * q^81 + 40 * q^82 + 40 * q^83 - 36 * q^84 - 32 * q^85 - 72 * q^86 - 8 * q^88 + 28 * q^90 + 36 * q^92 + 28 * q^94 - 48 * q^95 + 68 * q^96 + 64 * q^98 - 40 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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