LMFDB - Embedded newform 1338.2.e.i.1075.7

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1338,2,Mod(931,1338)] 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("1338.931"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1338, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 4])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 1338 = 2 \cdot 3 \cdot 223 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1338.e (of order $3$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [14,14,7] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$10.6839837904$
Analytic rank:	$0$
Dimension:	$14$
Relative dimension:	$7$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} + \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} + 25 x^{12} - 30 x^{11} + 502 x^{10} - 434 x^{9} + 3060 x^{8} - 1136 x^{7} + 13014 x^{6} + \cdots + 961 $ x^14 + 25x^12 - 30x^11 + 502x^10 - 434x^9 + 3060x^8 - 1136x^7 + 13014x^6 - 2882x^5 + 18706x^4 + 14706x^3 + 12571x^2 + 3720x + 961
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			1075.7
Root			$0.820326 + 1.42085i$ of defining polynomial
Character	$\chi$	$=$	1338.1075
Dual form			1338.2.e.i.931.7

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.00000 q^{2} +(0.500000 + 0.866025i) q^{3} +1.00000 q^{4} +(1.68125 - 2.91200i) q^{5} +(0.500000 + 0.866025i) q^{6} +3.43032 q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(1.68125 - 2.91200i) q^{10} +(1.32033 - 2.28687i) q^{11} +(0.500000 + 0.866025i) q^{12} -5.85224 q^{13} +3.43032 q^{14} +3.36249 q^{15} +1.00000 q^{16} +1.53062 q^{17} +(-0.500000 + 0.866025i) q^{18} +(3.92799 + 6.80347i) q^{19} +(1.68125 - 2.91200i) q^{20} +(1.71516 + 2.97075i) q^{21} +(1.32033 - 2.28687i) q^{22} +(-0.904391 - 1.56645i) q^{23} +(0.500000 + 0.866025i) q^{24} +(-3.15318 - 5.46146i) q^{25} -5.85224 q^{26} -1.00000 q^{27} +3.43032 q^{28} +(0.320326 - 0.554821i) q^{29} +3.36249 q^{30} +(-3.52202 - 6.10032i) q^{31} +1.00000 q^{32} +2.64065 q^{33} +1.53062 q^{34} +(5.76722 - 9.98912i) q^{35} +(-0.500000 + 0.866025i) q^{36} +(-3.18680 + 5.51970i) q^{37} +(3.92799 + 6.80347i) q^{38} +(-2.92612 - 5.06819i) q^{39} +(1.68125 - 2.91200i) q^{40} -5.60351 q^{41} +(1.71516 + 2.97075i) q^{42} +(-3.02359 - 5.23702i) q^{43} +(1.32033 - 2.28687i) q^{44} +(1.68125 + 2.91200i) q^{45} +(-0.904391 - 1.56645i) q^{46} +(-0.895792 + 1.55156i) q^{47} +(0.500000 + 0.866025i) q^{48} +4.76712 q^{49} +(-3.15318 - 5.46146i) q^{50} +(0.765311 + 1.32556i) q^{51} -5.85224 q^{52} +(1.90926 - 3.30693i) q^{53} -1.00000 q^{54} +(-4.43958 - 7.68959i) q^{55} +3.43032 q^{56} +(-3.92799 + 6.80347i) q^{57} +(0.320326 - 0.554821i) q^{58} +12.0662 q^{59} +3.36249 q^{60} +(6.69855 + 11.6022i) q^{61} +(-3.52202 - 6.10032i) q^{62} +(-1.71516 + 2.97075i) q^{63} +1.00000 q^{64} +(-9.83905 + 17.0417i) q^{65} +2.64065 q^{66} +(-4.73320 - 8.19815i) q^{67} +1.53062 q^{68} +(0.904391 - 1.56645i) q^{69} +(5.76722 - 9.98912i) q^{70} +(3.29893 + 5.71392i) q^{71} +(-0.500000 + 0.866025i) q^{72} +(-4.03786 + 6.99379i) q^{73} +(-3.18680 + 5.51970i) q^{74} +(3.15318 - 5.46146i) q^{75} +(3.92799 + 6.80347i) q^{76} +(4.52915 - 7.84471i) q^{77} +(-2.92612 - 5.06819i) q^{78} +(-5.82315 + 10.0860i) q^{79} +(1.68125 - 2.91200i) q^{80} +(-0.500000 - 0.866025i) q^{81} -5.60351 q^{82} +(-7.21722 + 12.5006i) q^{83} +(1.71516 + 2.97075i) q^{84} +(2.57335 - 4.45718i) q^{85} +(-3.02359 - 5.23702i) q^{86} +0.640652 q^{87} +(1.32033 - 2.28687i) q^{88} +(4.41021 + 7.63871i) q^{89} +(1.68125 + 2.91200i) q^{90} -20.0751 q^{91} +(-0.904391 - 1.56645i) q^{92} +(3.52202 - 6.10032i) q^{93} +(-0.895792 + 1.55156i) q^{94} +26.4156 q^{95} +(0.500000 + 0.866025i) q^{96} +(4.27730 - 7.40850i) q^{97} +4.76712 q^{98} +(1.32033 + 2.28687i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q + 14 q^{2} + 7 q^{3} + 14 q^{4} + 3 q^{5} + 7 q^{6} + 4 q^{7} + 14 q^{8} - 7 q^{9} + 3 q^{10} + 7 q^{11} + 7 q^{12} - 12 q^{13} + 4 q^{14} + 6 q^{15} + 14 q^{16} + 6 q^{17} - 7 q^{18} - 6 q^{19} + 3 q^{20}+ \cdots + 7 q^{99}+O(q^{100}) $ 14 * q + 14 * q^2 + 7 * q^3 + 14 * q^4 + 3 * q^5 + 7 * q^6 + 4 * q^7 + 14 * q^8 - 7 * q^9 + 3 * q^10 + 7 * q^11 + 7 * q^12 - 12 * q^13 + 4 * q^14 + 6 * q^15 + 14 * q^16 + 6 * q^17 - 7 * q^18 - 6 * q^19 + 3 * q^20 + 2 * q^21 + 7 * q^22 - 14 * q^23 + 7 * q^24 - 16 * q^25 - 12 * q^26 - 14 * q^27 + 4 * q^28 - 7 * q^29 + 6 * q^30 - 19 * q^31 + 14 * q^32 + 14 * q^33 + 6 * q^34 + q^35 - 7 * q^36 - 9 * q^37 - 6 * q^38 - 6 * q^39 + 3 * q^40 + 10 * q^41 + 2 * q^42 + 20 * q^43 + 7 * q^44 + 3 * q^45 - 14 * q^46 + q^47 + 7 * q^48 + 62 * q^49 - 16 * q^50 + 3 * q^51 - 12 * q^52 + 10 * q^53 - 14 * q^54 - 24 * q^55 + 4 * q^56 + 6 * q^57 - 7 * q^58 - 6 * q^59 + 6 * q^60 + 4 * q^61 - 19 * q^62 - 2 * q^63 + 14 * q^64 + 3 * q^65 + 14 * q^66 + 3 * q^67 + 6 * q^68 + 14 * q^69 + q^70 + 31 * q^71 - 7 * q^72 - 45 * q^73 - 9 * q^74 + 16 * q^75 - 6 * q^76 - 14 * q^77 - 6 * q^78 - 41 * q^79 + 3 * q^80 - 7 * q^81 + 10 * q^82 - q^83 + 2 * q^84 - 9 * q^85 + 20 * q^86 - 14 * q^87 + 7 * q^88 - 24 * q^89 + 3 * q^90 + 74 * q^91 - 14 * q^92 + 19 * q^93 + q^94 - 8 * q^95 + 7 * q^96 - 13 * q^97 + 62 * q^98 + 7 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1338\mathbb{Z}\right)^\times$.

$n$	$893$	$895$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$

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 $

$2$	1.00000			0.707107
$2$	1.00000			0.707107
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$4$	1.00000			0.500000
$5$	1.68125	−	2.91200i	0.751876	−	1.30229i	−0.195036	−	0.980796i	$-0.562483\pi$
$5$	1.68125	−	2.91200i	0.751876	−	1.30229i	0.946912	−	0.321491i	$-0.104184\pi$
$6$	0.500000	+	0.866025i	0.204124	+	0.353553i
$7$	3.43032			1.29654			0.648270	−	0.761410i	$-0.275493\pi$
$7$	3.43032			1.29654			0.648270	+	0.761410i	$0.275493\pi$
$8$	1.00000			0.353553
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	1.68125	−	2.91200i	0.531657	−	0.920856i
$11$	1.32033	−	2.28687i	0.398093	−	0.689518i	−0.595397	−	0.803431i	$-0.703005\pi$
$11$	1.32033	−	2.28687i	0.398093	−	0.689518i	0.993491	+	0.113914i	$0.0363387\pi$
$12$	0.500000	+	0.866025i	0.144338	+	0.250000i
$13$	−5.85224			−1.62312			−0.811560	−	0.584270i	$-0.801381\pi$
$13$	−5.85224			−1.62312			−0.811560	+	0.584270i	$0.801381\pi$
$14$	3.43032			0.916793
$15$	3.36249			0.868192
$16$	1.00000			0.250000
$17$	1.53062			0.371230			0.185615	−	0.982623i	$-0.440572\pi$
$17$	1.53062			0.371230			0.185615	+	0.982623i	$0.440572\pi$
$18$	−0.500000	+	0.866025i	−0.117851	+	0.204124i
$19$	3.92799	+	6.80347i	0.901142	+	1.56082i	0.826014	+	0.563649i	$0.190603\pi$
$19$	3.92799	+	6.80347i	0.901142	+	1.56082i	0.0751274	+	0.997174i	$0.476064\pi$
$20$	1.68125	−	2.91200i	0.375938	−	0.651144i
$21$	1.71516	+	2.97075i	0.374279	+	0.648270i
$22$	1.32033	−	2.28687i	0.281494	−	0.487563i
$23$	−0.904391	−	1.56645i	−0.188579	−	0.326628i	0.756198	−	0.654343i	$-0.227055\pi$
$23$	−0.904391	−	1.56645i	−0.188579	−	0.326628i	−0.944777	+	0.327715i	$0.893721\pi$
$24$	0.500000	+	0.866025i	0.102062	+	0.176777i
$25$	−3.15318	−	5.46146i	−0.630635	−	1.09229i
$26$	−5.85224			−1.14772
$27$	−1.00000			−0.192450
$28$	3.43032			0.648270
$29$	0.320326	−	0.554821i	0.0594830	−	0.103028i	−0.834750	−	0.550628i	$-0.814388\pi$
$29$	0.320326	−	0.554821i	0.0594830	−	0.103028i	0.894233	+	0.447601i	$0.147721\pi$
$30$	3.36249			0.613904
$31$	−3.52202	−	6.10032i	−0.632574	−	1.09565i	−0.987024	−	0.160575i	$-0.948665\pi$
$31$	−3.52202	−	6.10032i	−0.632574	−	1.09565i	0.354450	−	0.935075i	$-0.384668\pi$
$32$	1.00000			0.176777
$33$	2.64065			0.459678
$34$	1.53062			0.262500
$35$	5.76722	−	9.98912i	0.974838	−	1.68847i
$36$	−0.500000	+	0.866025i	−0.0833333	+	0.144338i
$37$	−3.18680	+	5.51970i	−0.523906	+	0.907432i	0.475706	+	0.879604i	$0.342192\pi$
$37$	−3.18680	+	5.51970i	−0.523906	+	0.907432i	−0.999613	+	0.0278282i	$0.991141\pi$
$38$	3.92799	+	6.80347i	0.637203	+	1.10367i
$39$	−2.92612	−	5.06819i	−0.468554	−	0.811560i
$40$	1.68125	−	2.91200i	0.265828	−	0.460428i
$41$	−5.60351			−0.875121			−0.437561	−	0.899189i	$-0.644157\pi$
$41$	−5.60351			−0.875121			−0.437561	+	0.899189i	$0.644157\pi$
$42$	1.71516	+	2.97075i	0.264655	+	0.458396i
$43$	−3.02359	−	5.23702i	−0.461094	−	0.798638i	0.537922	−	0.842995i	$-0.319210\pi$
$43$	−3.02359	−	5.23702i	−0.461094	−	0.798638i	−0.999016	+	0.0443567i	$0.985876\pi$
$44$	1.32033	−	2.28687i	0.199047	−	0.344759i
$45$	1.68125	+	2.91200i	0.250625	+	0.434096i
$46$	−0.904391	−	1.56645i	−0.133345	−	0.230961i
$47$	−0.895792	+	1.55156i	−0.130665	+	0.226318i	−0.923933	−	0.382554i	$-0.875044\pi$
$47$	−0.895792	+	1.55156i	−0.130665	+	0.226318i	0.793268	+	0.608872i	$0.208378\pi$
$48$	0.500000	+	0.866025i	0.0721688	+	0.125000i
$49$	4.76712			0.681018
$50$	−3.15318	−	5.46146i	−0.445926	−	0.772367i
$51$	0.765311	+	1.32556i	0.107165	+	0.185615i
$52$	−5.85224			−0.811560
$53$	1.90926	−	3.30693i	0.262257	−	0.454242i	−0.704585	−	0.709620i	$-0.748867\pi$
$53$	1.90926	−	3.30693i	0.262257	−	0.454242i	0.966841	+	0.255378i	$0.0822000\pi$
$54$	−1.00000			−0.136083
$55$	−4.43958	−	7.68959i	−0.598634	−	1.03686i
$56$	3.43032			0.458396
$57$	−3.92799	+	6.80347i	−0.520274	+	0.901142i
$58$	0.320326	−	0.554821i	0.0420609	−	0.0728515i
$59$	12.0662			1.57088			0.785442	−	0.618935i	$-0.212436\pi$
$59$	12.0662			1.57088			0.785442	+	0.618935i	$0.212436\pi$
$60$	3.36249			0.434096
$61$	6.69855	+	11.6022i	0.857662	+	1.48551i	0.874153	+	0.485650i	$0.161417\pi$
$61$	6.69855	+	11.6022i	0.857662	+	1.48551i	−0.0164914	+	0.999864i	$0.505250\pi$
$62$	−3.52202	−	6.10032i	−0.447297	−	0.774742i
$63$	−1.71516	+	2.97075i	−0.216090	+	0.374279i
$64$	1.00000			0.125000
$65$	−9.83905	+	17.0417i	−1.22038	+	2.11377i
$66$	2.64065			0.325042
$67$	−4.73320	−	8.19815i	−0.578253	−	1.00156i	−0.995680	−	0.0928531i	$-0.970401\pi$
$67$	−4.73320	−	8.19815i	−0.578253	−	1.00156i	0.417427	−	0.908711i	$-0.362932\pi$
$68$	1.53062			0.185615
$69$	0.904391	−	1.56645i	0.108876	−	0.188579i
$70$	5.76722	−	9.98912i	0.689314	−	1.19393i
$71$	3.29893	+	5.71392i	0.391511	+	0.678118i	0.992649	−	0.121028i	$-0.0386190\pi$
$71$	3.29893	+	5.71392i	0.391511	+	0.678118i	−0.601138	+	0.799145i	$0.705286\pi$
$72$	−0.500000	+	0.866025i	−0.0589256	+	0.102062i
$73$	−4.03786	+	6.99379i	−0.472596	+	0.818561i	−0.999508	−	0.0313592i	$-0.990016\pi$
$73$	−4.03786	+	6.99379i	−0.472596	+	0.818561i	0.526912	+	0.849920i	$0.323350\pi$
$74$	−3.18680	+	5.51970i	−0.370458	+	0.641652i
$75$	3.15318	−	5.46146i	0.364097	−	0.630635i
$76$	3.92799	+	6.80347i	0.450571	+	0.780412i
$77$	4.52915	−	7.84471i	0.516144	−	0.893988i
$78$	−2.92612	−	5.06819i	−0.331318	−	0.573859i
$79$	−5.82315	+	10.0860i	−0.655155	+	1.13476i	0.326700	+	0.945128i	$0.394063\pi$
$79$	−5.82315	+	10.0860i	−0.655155	+	1.13476i	−0.981855	+	0.189634i	$0.939270\pi$
$80$	1.68125	−	2.91200i	0.187969	−	0.325572i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	−5.60351			−0.618804
$83$	−7.21722	+	12.5006i	−0.792192	+	1.37212i	0.132414	+	0.991194i	$0.457727\pi$
$83$	−7.21722	+	12.5006i	−0.792192	+	1.37212i	−0.924607	+	0.380923i	$0.875606\pi$
$84$	1.71516	+	2.97075i	0.187140	+	0.324135i
$85$	2.57335	−	4.45718i	0.279119	−	0.483449i
$86$	−3.02359	−	5.23702i	−0.326043	−	0.564722i
$87$	0.640652			0.0686851
$88$	1.32033	−	2.28687i	0.140747	−	0.243781i
$89$	4.41021	+	7.63871i	0.467481	+	0.809701i	0.999310	−	0.0371509i	$-0.0118282\pi$
$89$	4.41021	+	7.63871i	0.467481	+	0.809701i	−0.531828	+	0.846852i	$0.678495\pi$
$90$	1.68125	+	2.91200i	0.177219	+	0.306952i
$91$	−20.0751			−2.10444
$92$	−0.904391	−	1.56645i	−0.0942893	−	0.163314i
$93$	3.52202	−	6.10032i	0.365217	−	0.632574i
$94$	−0.895792	+	1.55156i	−0.0923939	+	0.160031i
$95$	26.4156			2.71019
$96$	0.500000	+	0.866025i	0.0510310	+	0.0883883i
$97$	4.27730	−	7.40850i	0.434294	−	0.752219i	−0.562944	−	0.826495i	$-0.690331\pi$
$97$	4.27730	−	7.40850i	0.434294	−	0.752219i	0.997238	+	0.0742759i	$0.0236645\pi$
$98$	4.76712			0.481552
$99$	1.32033	+	2.28687i	0.132698	+	0.229839i
$100$	−3.15318	−	5.46146i	−0.315318	−	0.546146i
$101$	−7.97016	−	13.8047i	−0.793061	−	1.37362i	−0.924063	−	0.382240i	$-0.875153\pi$
$101$	−7.97016	−	13.8047i	−0.793061	−	1.37362i	0.131002	−	0.991382i	$-0.458181\pi$
$102$	0.765311	+	1.32556i	0.0757771	+	0.131250i
$103$	13.5572			1.33583			0.667914	−	0.744239i	$-0.267188\pi$
$103$	13.5572			1.33583			0.667914	+	0.744239i	$0.267188\pi$
$104$	−5.85224			−0.573859
$105$	11.5344			1.12565
$106$	1.90926	−	3.30693i	0.185443	−	0.321197i
$107$	0.876590	−	1.51830i	0.0847432	−	0.146780i	−0.820539	−	0.571591i	$-0.806326\pi$
$107$	0.876590	−	1.51830i	0.0847432	−	0.146780i	0.905282	+	0.424812i	$0.139660\pi$
$108$	−1.00000			−0.0962250
$109$	4.27095	−	7.39751i	0.409083	−	0.708553i	−0.585704	−	0.810525i	$-0.699182\pi$
$109$	4.27095	−	7.39751i	0.409083	−	0.708553i	0.994787	+	0.101972i	$0.0325153\pi$
$110$	−4.43958	−	7.68959i	−0.423298	−	0.733173i
$111$	−6.37359			−0.604955
$112$	3.43032			0.324135
$113$	1.57848	+	2.73400i	0.148491	+	0.257193i	0.930670	−	0.365860i	$-0.119225\pi$
$113$	1.57848	+	2.73400i	0.148491	+	0.257193i	−0.782179	+	0.623054i	$0.785892\pi$
$114$	−3.92799	+	6.80347i	−0.367890	+	0.637203i
$115$	−6.08201			−0.567151
$116$	0.320326	−	0.554821i	0.0297415	−	0.0515138i
$117$	2.92612	−	5.06819i	0.270520	−	0.468554i
$118$	12.0662			1.11078
$119$	5.25053			0.481315
$120$	3.36249			0.306952
$121$	2.01348	+	3.48745i	0.183044	+	0.317041i
$122$	6.69855	+	11.6022i	0.606459	+	1.05042i
$123$	−2.80175	−	4.85278i	−0.252626	−	0.437561i
$124$	−3.52202	−	6.10032i	−0.316287	−	0.547825i
$125$	−4.39259			−0.392885
$126$	−1.71516	+	2.97075i	−0.152799	+	0.264655i
$127$	−4.64156	−	8.03942i	−0.411872	−	0.713383i	0.583222	−	0.812313i	$-0.301792\pi$
$127$	−4.64156	−	8.03942i	−0.411872	−	0.713383i	−0.995094	+	0.0989292i	$0.968458\pi$
$128$	1.00000			0.0883883
$129$	3.02359	−	5.23702i	0.266213	−	0.461094i
$130$	−9.83905	+	17.0417i	−0.862942	+	1.49466i
$131$	−0.217929	−	0.377465i	−0.0190406	−	0.0329792i	0.856348	−	0.516399i	$-0.172728\pi$
$131$	−0.217929	−	0.377465i	−0.0190406	−	0.0329792i	−0.875389	+	0.483420i	$0.839395\pi$
$132$	2.64065			0.229839
$133$	13.4743	+	23.3381i	1.16837	+	2.02367i
$134$	−4.73320	−	8.19815i	−0.408887	−	0.708212i
$135$	−1.68125	+	2.91200i	−0.144699	+	0.250625i
$136$	1.53062			0.131250
$137$	−4.70021	−	8.14100i	−0.401566	−	0.695532i	0.592349	−	0.805681i	$-0.298201\pi$
$137$	−4.70021	−	8.14100i	−0.401566	−	0.695532i	−0.993915	+	0.110149i	$0.964867\pi$
$138$	0.904391	−	1.56645i	0.0769869	−	0.133345i
$139$	4.15049	+	7.18885i	0.352040	+	0.609751i	0.986607	−	0.163117i	$-0.0521549\pi$
$139$	4.15049	+	7.18885i	0.352040	+	0.609751i	−0.634567	+	0.772868i	$0.718822\pi$
$140$	5.76722	−	9.98912i	0.487419	−	0.844234i
$141$	−1.79158			−0.150879
$142$	3.29893	+	5.71392i	0.276840	+	0.479501i
$143$	−7.72686	+	13.3833i	−0.646153	+	1.11917i
$144$	−0.500000	+	0.866025i	−0.0416667	+	0.0721688i
$145$	−1.07709	−	1.86558i	−0.0894477	−	0.154928i
$146$	−4.03786	+	6.99379i	−0.334176	+	0.578810i
$147$	2.38356	+	4.12845i	0.196593	+	0.340509i
$148$	−3.18680	+	5.51970i	−0.261953	+	0.453716i
$149$	−4.47847	+	7.75694i	−0.366891	+	0.635473i	−0.989078	−	0.147396i	$-0.952911\pi$
$149$	−4.47847	+	7.75694i	−0.366891	+	0.635473i	0.622187	+	0.782869i	$0.286244\pi$
$150$	3.15318	−	5.46146i	0.257456	−	0.445926i
$151$	−3.52522	+	6.10586i	−0.286878	+	0.496888i	−0.973063	−	0.230539i	$-0.925951\pi$
$151$	−3.52522	+	6.10586i	−0.286878	+	0.496888i	0.686184	+	0.727428i	$0.259284\pi$
$152$	3.92799	+	6.80347i	0.318602	+	0.551834i
$153$	−0.765311	+	1.32556i	−0.0618717	+	0.107165i
$154$	4.52915	−	7.84471i	0.364969	−	0.632145i
$155$	−23.6855			−1.90247
$156$	−2.92612	−	5.06819i	−0.234277	−	0.405780i
$157$	−19.4984			−1.55614			−0.778072	−	0.628175i	$-0.783802\pi$
$157$	−19.4984			−1.55614			−0.778072	+	0.628175i	$0.783802\pi$
$158$	−5.82315	+	10.0860i	−0.463265	+	0.802398i
$159$	3.81851			0.302828
$160$	1.68125	−	2.91200i	0.132914	−	0.230214i
$161$	−3.10235	−	5.37344i	−0.244500	−	0.423486i
$162$	−0.500000	−	0.866025i	−0.0392837	−	0.0680414i
$163$	−17.1562			−1.34378			−0.671889	−	0.740652i	$-0.734517\pi$
$163$	−17.1562			−1.34378			−0.671889	+	0.740652i	$0.734517\pi$
$164$	−5.60351			−0.437561
$165$	4.43958	−	7.68959i	0.345621	−	0.598634i
$166$	−7.21722	+	12.5006i	−0.560165	+	0.970234i
$167$	0.0473273			0.00366230			0.00183115	−	0.999998i	$-0.499417\pi$
$167$	0.0473273			0.00366230			0.00183115	+	0.999998i	$0.499417\pi$
$168$	1.71516	+	2.97075i	0.132328	+	0.229198i
$169$	21.2487			1.63452
$170$	2.57335	−	4.45718i	0.197367	−	0.341850i
$171$	−7.85597			−0.600761
$172$	−3.02359	−	5.23702i	−0.230547	−	0.399319i
$173$	6.60870	+	11.4466i	0.502450	+	0.870269i	0.999996	+	0.00283140i	$0.000901264\pi$
$173$	6.60870	+	11.4466i	0.502450	+	0.870269i	−0.497546	+	0.867438i	$0.665765\pi$
$174$	0.640652			0.0485677
$175$	−10.8164	−	18.7346i	−0.817644	−	1.41620i
$176$	1.32033	−	2.28687i	0.0995233	−	0.172379i
$177$	6.03309	+	10.4496i	0.453475	+	0.785442i
$178$	4.41021	+	7.63871i	0.330559	+	0.572545i
$179$	−7.64767	+	13.2461i	−0.571613	+	0.990063i	0.424787	+	0.905293i	$0.360349\pi$
$179$	−7.64767	+	13.2461i	−0.571613	+	0.990063i	−0.996401	+	0.0847701i	$0.972984\pi$
$180$	1.68125	+	2.91200i	0.125313	+	0.217048i
$181$	0.550259	+	0.953076i	0.0409004	+	0.0708416i	0.885751	−	0.464161i	$-0.153644\pi$
$181$	0.550259	+	0.953076i	0.0409004	+	0.0708416i	−0.844851	+	0.535002i	$0.820311\pi$
$182$	−20.0751			−1.48806
$183$	−6.69855	+	11.6022i	−0.495171	+	0.857662i
$184$	−0.904391	−	1.56645i	−0.0666726	−	0.115480i
$185$	10.7156	+	18.5599i	0.787825	+	1.36455i
$186$	3.52202	−	6.10032i	0.258247	−	0.447297i
$187$	2.02092	−	3.50034i	0.147784	−	0.255970i
$188$	−0.895792	+	1.55156i	−0.0653323	+	0.113159i
$189$	−3.43032			−0.249519
$190$	26.4156			1.91639
$191$	−2.68742			−0.194455			−0.0972274	−	0.995262i	$-0.530997\pi$
$191$	−2.68742			−0.194455			−0.0972274	+	0.995262i	$0.530997\pi$
$192$	0.500000	+	0.866025i	0.0360844	+	0.0625000i
$193$	15.2039			1.09440			0.547199	−	0.837002i	$-0.315694\pi$
$193$	15.2039			1.09440			0.547199	+	0.837002i	$0.315694\pi$
$194$	4.27730	−	7.40850i	0.307092	−	0.531899i
$195$	−19.6781			−1.40918
$196$	4.76712			0.340509
$197$	−13.0540			−0.930058			−0.465029	−	0.885296i	$-0.653956\pi$
$197$	−13.0540			−0.930058			−0.465029	+	0.885296i	$0.653956\pi$
$198$	1.32033	+	2.28687i	0.0938315	+	0.162521i
$199$	−9.36374	−	16.2185i	−0.663778	−	1.14970i	−0.979615	−	0.200883i	$-0.935619\pi$
$199$	−9.36374	−	16.2185i	−0.663778	−	1.14970i	0.315837	−	0.948813i	$-0.397715\pi$
$200$	−3.15318	−	5.46146i	−0.222963	−	0.386184i
$201$	4.73320	−	8.19815i	0.333855	−	0.578253i
$202$	−7.97016	−	13.8047i	−0.560779	−	0.971297i
$203$	1.09882	−	1.90322i	0.0771222	−	0.133580i
$204$	0.765311	+	1.32556i	0.0535825	+	0.0928076i
$205$	−9.42088	+	16.3174i	−0.657983	+	1.13966i
$206$	13.5572			0.944573
$207$	1.80878			0.125719
$208$	−5.85224			−0.405780
$209$	20.7449			1.43495
$210$	11.5344			0.795952
$211$	6.98152	+	12.0923i	0.480627	+	0.832471i	0.999753	−	0.0222269i	$-0.00707563\pi$
$211$	6.98152	+	12.0923i	0.480627	+	0.832471i	−0.519126	+	0.854698i	$0.673742\pi$
$212$	1.90926	−	3.30693i	0.131128	−	0.227121i
$213$	−3.29893	+	5.71392i	−0.226039	+	0.391511i
$214$	0.876590	−	1.51830i	0.0599225	−	0.103789i
$215$	−20.3336			−1.38674
$216$	−1.00000			−0.0680414
$217$	−12.0817	−	20.9261i	−0.820158	−	1.42056i
$218$	4.27095	−	7.39751i	0.289265	−	0.501023i
$219$	−8.07573			−0.545707
$220$	−4.43958	−	7.68959i	−0.299317	−	0.518432i
$221$	−8.95757			−0.602551
$222$	−6.37359			−0.427768
$223$	−1.06649	−	14.8951i	−0.0714172	−	0.997447i
$223$	−1.06649	−	14.8951i	−0.0714172	−	0.997447i
$224$	3.43032			0.229198
$225$	6.30635			0.420423
$226$	1.57848	+	2.73400i	0.104999	+	0.181863i
$227$	9.82781			0.652294			0.326147	−	0.945319i	$-0.394249\pi$
$227$	9.82781			0.652294			0.326147	+	0.945319i	$0.394249\pi$
$228$	−3.92799	+	6.80347i	−0.260137	+	0.450571i
$229$	−8.75138	−	15.1578i	−0.578307	−	1.00166i	−0.995674	−	0.0929193i	$-0.970380\pi$
$229$	−8.75138	−	15.1578i	−0.578307	−	1.00166i	0.417366	−	0.908738i	$-0.362953\pi$
$230$	−6.08201			−0.401036
$231$	9.05829			0.595992
$232$	0.320326	−	0.554821i	0.0210304	−	0.0364258i
$233$	−9.67829	+	16.7633i	−0.634046	+	1.09820i	0.352671	+	0.935747i	$0.385274\pi$
$233$	−9.67829	+	16.7633i	−0.634046	+	1.09820i	−0.986716	+	0.162452i	$0.948060\pi$
$234$	2.92612	−	5.06819i	0.191286	−	0.331318i
$235$	3.01209	+	5.21710i	0.196487	+	0.340326i
$236$	12.0662			0.785442
$237$	−11.6463			−0.756508
$238$	5.25053			0.340341
$239$	−24.8377			−1.60662			−0.803308	−	0.595563i	$-0.796929\pi$
$239$	−24.8377			−1.60662			−0.803308	+	0.595563i	$0.796929\pi$
$240$	3.36249			0.217048
$241$	1.92602	−	3.33597i	0.124066	−	0.214889i	−0.797301	−	0.603581i	$-0.793740\pi$
$241$	1.92602	−	3.33597i	0.124066	−	0.214889i	0.921367	+	0.388693i	$0.127073\pi$
$242$	2.01348	+	3.48745i	0.129431	+	0.224182i
$243$	0.500000	−	0.866025i	0.0320750	−	0.0555556i
$244$	6.69855	+	11.6022i	0.428831	+	0.742757i
$245$	8.01471	−	13.8819i	0.512041	−	0.886881i
$246$	−2.80175	−	4.85278i	−0.178633	−	0.309402i
$247$	−22.9875	−	39.8155i	−1.46266	−	2.53340i
$248$	−3.52202	−	6.10032i	−0.223649	−	0.387371i
$249$	−14.4344			−0.914745
$250$	−4.39259			−0.277812
$251$	23.8654			1.50637			0.753184	−	0.657810i	$-0.228517\pi$
$251$	23.8654			1.50637			0.753184	+	0.657810i	$0.228517\pi$
$252$	−1.71516	+	2.97075i	−0.108045	+	0.187140i
$253$	−4.77636			−0.300287
$254$	−4.64156	−	8.03942i	−0.291238	−	0.504438i
$255$	5.14670			0.322299
$256$	1.00000			0.0625000
$257$	21.5636			1.34510			0.672549	−	0.740053i	$-0.265199\pi$
$257$	21.5636			1.34510			0.672549	+	0.740053i	$0.265199\pi$
$258$	3.02359	−	5.23702i	0.188241	−	0.326043i
$259$	−10.9317	+	18.9343i	−0.679266	+	1.17652i
$260$	−9.83905	+	17.0417i	−0.610192	+	1.05688i
$261$	0.320326	+	0.554821i	0.0198277	+	0.0343425i
$262$	−0.217929	−	0.377465i	−0.0134637	−	0.0233198i
$263$	−11.4232	+	19.7855i	−0.704383	+	1.22003i	0.262531	+	0.964924i	$0.415443\pi$
$263$	−11.4232	+	19.7855i	−0.704383	+	1.22003i	−0.966914	+	0.255104i	$0.917890\pi$
$264$	2.64065			0.162521
$265$	−6.41986	−	11.1195i	−0.394369	−	0.683067i
$266$	13.4743	+	23.3381i	0.826160	+	1.43095i
$267$	−4.41021	+	7.63871i	−0.269900	+	0.467481i
$268$	−4.73320	−	8.19815i	−0.289127	−	0.500782i
$269$	3.04919	+	5.28136i	0.185913	+	0.322010i	0.943884	−	0.330278i	$-0.107143\pi$
$269$	3.04919	+	5.28136i	0.185913	+	0.322010i	−0.757971	+	0.652288i	$0.773809\pi$
$270$	−1.68125	+	2.91200i	−0.102317	+	0.177219i
$271$	−10.6875	−	18.5113i	−0.649218	−	1.12448i	−0.983310	−	0.181938i	$-0.941763\pi$
$271$	−10.6875	−	18.5113i	−0.649218	−	1.12448i	0.334092	−	0.942541i	$-0.391570\pi$
$272$	1.53062			0.0928076
$273$	−10.0375	−	17.3855i	−0.607499	−	1.05222i
$274$	−4.70021	−	8.14100i	−0.283950	−	0.491816i
$275$	−16.6529			−1.00421
$276$	0.904391	−	1.56645i	0.0544379	−	0.0942893i
$277$	−13.3182			−0.800211			−0.400106	−	0.916469i	$-0.631027\pi$
$277$	−13.3182			−0.800211			−0.400106	+	0.916469i	$0.631027\pi$
$278$	4.15049	+	7.18885i	0.248930	+	0.431159i
$279$	7.04405			0.421716
$280$	5.76722	−	9.98912i	0.344657	−	0.596964i
$281$	3.84808	−	6.66507i	0.229557	−	0.397605i	−0.728120	−	0.685450i	$-0.759606\pi$
$281$	3.84808	−	6.66507i	0.229557	−	0.397605i	0.957677	+	0.287845i	$0.0929389\pi$
$282$	−1.79158			−0.106687
$283$	−26.0594			−1.54907			−0.774536	−	0.632530i	$-0.782016\pi$
$283$	−26.0594			−1.54907			−0.774536	+	0.632530i	$0.782016\pi$
$284$	3.29893	+	5.71392i	0.195756	+	0.339059i
$285$	13.2078	+	22.8766i	0.782364	+	1.35509i
$286$	−7.72686	+	13.3833i	−0.456899	+	0.791372i
$287$	−19.2219			−1.13463
$288$	−0.500000	+	0.866025i	−0.0294628	+	0.0510310i
$289$	−14.6572			−0.862188
$290$	−1.07709	−	1.86558i	−0.0632491	−	0.109551i
$291$	8.55460			0.501480
$292$	−4.03786	+	6.99379i	−0.236298	+	0.409280i
$293$	13.8929	−	24.0632i	0.811631	−	1.40579i	−0.100090	−	0.994978i	$-0.531913\pi$
$293$	13.8929	−	24.0632i	0.811631	−	1.40579i	0.911722	−	0.410808i	$-0.134753\pi$
$294$	2.38356	+	4.12845i	0.139012	+	0.240776i
$295$	20.2862	−	35.1368i	1.18111	−	2.04574i
$296$	−3.18680	+	5.51970i	−0.185229	+	0.320826i
$297$	−1.32033	+	2.28687i	−0.0766131	+	0.132698i
$298$	−4.47847	+	7.75694i	−0.259431	+	0.449347i
$299$	5.29271	+	9.16725i	0.306085	+	0.530156i
$300$	3.15318	−	5.46146i	0.182049	−	0.315318i
$301$	−10.3719	−	17.9647i	−0.597827	−	1.03547i
$302$	−3.52522	+	6.10586i	−0.202854	+	0.351353i
$303$	7.97016	−	13.8047i	0.457874	−	0.793061i
$304$	3.92799	+	6.80347i	0.225285	+	0.390206i
$305$	45.0477			2.57942
$306$	−0.765311	+	1.32556i	−0.0437499	+	0.0757771i
$307$	4.98307	+	8.63093i	0.284399	+	0.492593i	0.972463	−	0.233056i	$-0.0748727\pi$
$307$	4.98307	+	8.63093i	0.284399	+	0.492593i	−0.688064	+	0.725650i	$0.741539\pi$
$308$	4.52915	−	7.84471i	0.258072	−	0.446994i
$309$	6.77858	+	11.7409i	0.385620	+	0.667914i
$310$	−23.6855			−1.34525
$311$	12.9852	−	22.4910i	0.736321	−	1.27535i	−0.217820	−	0.975989i	$-0.569894\pi$
$311$	12.9852	−	22.4910i	0.736321	−	1.27535i	0.954141	−	0.299357i	$-0.0967722\pi$
$312$	−2.92612	−	5.06819i	−0.165659	−	0.286930i
$313$	−2.12041	−	3.67266i	−0.119853	−	0.207591i	0.799856	−	0.600191i	$-0.204909\pi$
$313$	−2.12041	−	3.67266i	−0.119853	−	0.207591i	−0.919709	+	0.392600i	$0.871576\pi$
$314$	−19.4984			−1.10036
$315$	5.76722	+	9.98912i	0.324946	+	0.562823i
$316$	−5.82315	+	10.0860i	−0.327578	+	0.567381i
$317$	8.43404	−	14.6082i	0.473703	−	0.820478i	−0.525844	−	0.850581i	$-0.676250\pi$
$317$	8.43404	−	14.6082i	0.473703	−	0.820478i	0.999547	+	0.0301034i	$0.00958366\pi$
$318$	3.81851			0.214132
$319$	−0.845869	−	1.46509i	−0.0473596	−	0.0820292i
$320$	1.68125	−	2.91200i	0.0939845	−	0.162786i
$321$	1.75318			0.0978530
$322$	−3.10235	−	5.37344i	−0.172887	−	0.299450i
$323$	6.01226	+	10.4135i	0.334531	+	0.579425i
$324$	−0.500000	−	0.866025i	−0.0277778	−	0.0481125i
$325$	18.4531	+	31.9618i	1.02360	+	1.77292i
$326$	−17.1562			−0.950194
$327$	8.54191			0.472369
$328$	−5.60351			−0.309402
$329$	−3.07286	+	5.32234i	−0.169412	+	0.293430i
$330$	4.43958	−	7.68959i	0.244391	−	0.423298i
$331$	4.13258			0.227147			0.113574	−	0.993530i	$-0.463770\pi$
$331$	4.13258			0.227147			0.113574	+	0.993530i	$0.463770\pi$
$332$	−7.21722	+	12.5006i	−0.396096	+	0.686059i
$333$	−3.18680	−	5.51970i	−0.174635	−	0.302477i
$334$	0.0473273			0.00258963
$335$	−31.8307			−1.73910
$336$	1.71516	+	2.97075i	0.0935698	+	0.162068i
$337$	−1.03630	+	1.79492i	−0.0564507	+	0.0977755i	−0.892870	−	0.450315i	$-0.851312\pi$
$337$	−1.03630	+	1.79492i	−0.0564507	+	0.0977755i	0.836419	+	0.548090i	$0.184645\pi$
$338$	21.2487			1.15578
$339$	−1.57848	+	2.73400i	−0.0857311	+	0.148491i
$340$	2.57335	−	4.45718i	0.139560	−	0.241724i
$341$	−18.6009			−1.00729
$342$	−7.85597			−0.424802
$343$	−7.65949			−0.413573
$344$	−3.02359	−	5.23702i	−0.163021	−	0.282361i
$345$	−3.04101	−	5.26718i	−0.163722	−	0.283575i
$346$	6.60870	+	11.4466i	0.355286	+	0.615373i
$347$	−10.6601	−	18.4638i	−0.572262	−	0.991187i	−0.996333	−	0.0855583i	$-0.972733\pi$
$347$	−10.6601	−	18.4638i	−0.572262	−	0.991187i	0.424071	−	0.905629i	$-0.360601\pi$
$348$	0.640652			0.0343425
$349$	−12.9119	+	22.3641i	−0.691160	+	1.19712i	0.280298	+	0.959913i	$0.409567\pi$
$349$	−12.9119	+	22.3641i	−0.691160	+	1.19712i	−0.971458	+	0.237211i	$0.923767\pi$
$350$	−10.8164	−	18.7346i	−0.578162	−	1.00141i
$351$	5.85224			0.312369
$352$	1.32033	−	2.28687i	0.0703736	−	0.121891i
$353$	15.1245	−	26.1964i	0.804997	−	1.39429i	−0.111297	−	0.993787i	$-0.535500\pi$
$353$	15.1245	−	26.1964i	0.804997	−	1.39429i	0.916293	−	0.400508i	$-0.131166\pi$
$354$	6.03309	+	10.4496i	0.320655	+	0.555391i
$355$	22.1853			1.17747
$356$	4.41021	+	7.63871i	0.233741	+	0.404851i
$357$	2.62526	+	4.54709i	0.138944	+	0.240658i
$358$	−7.64767	+	13.2461i	−0.404192	+	0.700081i
$359$	−5.74869			−0.303404			−0.151702	−	0.988426i	$-0.548475\pi$
$359$	−5.74869			−0.303404			−0.151702	+	0.988426i	$0.548475\pi$
$360$	1.68125	+	2.91200i	0.0886094	+	0.153476i
$361$	−21.3581	+	36.9934i	−1.12411	+	1.94702i
$362$	0.550259	+	0.953076i	0.0289210	+	0.0500926i
$363$	−2.01348	+	3.48745i	−0.105680	+	0.183044i
$364$	−20.0751			−1.05222
$365$	13.5773	+	23.5165i	0.710668	+	1.23091i
$366$	−6.69855	+	11.6022i	−0.350139	+	0.606459i
$367$	−5.93840	+	10.2856i	−0.309982	+	0.536905i	−0.978358	−	0.206919i	$-0.933656\pi$
$367$	−5.93840	+	10.2856i	−0.309982	+	0.536905i	0.668376	+	0.743824i	$0.266990\pi$
$368$	−0.904391	−	1.56645i	−0.0471446	−	0.0816569i
$369$	2.80175	−	4.85278i	0.145854	−	0.252626i
$370$	10.7156	+	18.5599i	0.557076	+	0.964885i
$371$	6.54937	−	11.3438i	0.340026	−	0.588943i
$372$	3.52202	−	6.10032i	0.182608	−	0.316287i
$373$	9.56648	−	16.5696i	0.495333	−	0.857943i	−0.504652	−	0.863323i	$-0.668379\pi$
$373$	9.56648	−	16.5696i	0.495333	−	0.857943i	0.999986	+	0.00538012i	$0.00171255\pi$
$374$	2.02092	−	3.50034i	0.104499	−	0.180998i
$375$	−2.19630	−	3.80410i	−0.113416	−	0.196443i
$376$	−0.895792	+	1.55156i	−0.0461969	+	0.0800154i
$377$	−1.87462	+	3.24694i	−0.0965480	+	0.167226i
$378$	−3.43032			−0.176437
$379$	−12.8802	−	22.3092i	−0.661611	−	1.14594i	−0.980192	−	0.198049i	$-0.936540\pi$
$379$	−12.8802	−	22.3092i	−0.661611	−	1.14594i	0.318581	−	0.947896i	$-0.396794\pi$
$380$	26.4156			1.35509
$381$	4.64156	−	8.03942i	0.237794	−	0.411872i
$382$	−2.68742			−0.137500
$383$	0.801373	−	1.38802i	0.0409482	−	0.0709244i	−0.844825	−	0.535043i	$-0.820295\pi$
$383$	0.801373	−	1.38802i	0.0409482	−	0.0709244i	0.885773	+	0.464118i	$0.153629\pi$
$384$	0.500000	+	0.866025i	0.0255155	+	0.0441942i
$385$	−15.2292	−	26.3778i	−0.776153	−	1.34434i
$386$	15.2039			0.773856
$387$	6.04719			0.307396
$388$	4.27730	−	7.40850i	0.217147	−	0.376110i
$389$	−7.72986	+	13.3885i	−0.391920	+	0.678825i	−0.992703	−	0.120587i	$-0.961522\pi$
$389$	−7.72986	+	13.3885i	−0.391920	+	0.678825i	0.600783	+	0.799412i	$0.294856\pi$
$390$	−19.6781			−0.996440
$391$	−1.38428	−	2.39764i	−0.0700061	−	0.121254i
$392$	4.76712			0.240776
$393$	0.217929	−	0.377465i	0.0109931	−	0.0190406i
$394$	−13.0540			−0.657650
$395$	19.5803	+	33.9140i	0.985191	+	1.70640i
$396$	1.32033	+	2.28687i	0.0663489	+	0.114920i
$397$	9.92942			0.498343			0.249172	−	0.968459i	$-0.419842\pi$
$397$	9.92942			0.498343			0.249172	+	0.968459i	$0.419842\pi$
$398$	−9.36374	−	16.2185i	−0.469362	−	0.812958i
$399$	−13.4743	+	23.3381i	−0.674557	+	1.16837i
$400$	−3.15318	−	5.46146i	−0.157659	−	0.273073i
$401$	2.85507	+	4.94513i	0.142576	+	0.246948i	0.928466	−	0.371418i	$-0.121128\pi$
$401$	2.85507	+	4.94513i	0.142576	+	0.246948i	−0.785890	+	0.618366i	$0.787795\pi$
$402$	4.73320	−	8.19815i	0.236071	−	0.408887i
$403$	20.6117	+	35.7005i	1.02674	+	1.77837i
$404$	−7.97016	−	13.8047i	−0.396531	−	0.686811i
$405$	−3.36249			−0.167084
$406$	1.09882	−	1.90322i	0.0545336	−	0.0944550i
$407$	8.41522	+	14.5756i	0.417127	+	0.722485i
$408$	0.765311	+	1.32556i	0.0378885	+	0.0656249i
$409$	−0.228104	+	0.395087i	−0.0112790	+	0.0195358i	−0.871610	−	0.490200i	$-0.836924\pi$
$409$	−0.228104	+	0.395087i	−0.0112790	+	0.0195358i	0.860331	+	0.509736i	$0.170257\pi$
$410$	−9.42088	+	16.3174i	−0.465264	+	0.805861i
$411$	4.70021	−	8.14100i	0.231844	−	0.401566i
$412$	13.5572			0.667914
$413$	41.3909			2.03671
$414$	1.80878			0.0888968
$415$	24.2678	+	42.0331i	1.19126	+	2.06332i
$416$	−5.85224			−0.286930
$417$	−4.15049	+	7.18885i	−0.203250	+	0.352040i
$418$	20.7449			1.01467
$419$	−32.0750			−1.56697			−0.783484	−	0.621412i	$-0.786559\pi$
$419$	−32.0750			−1.56697			−0.783484	+	0.621412i	$0.786559\pi$
$420$	11.5344			0.562823
$421$	−2.43218	−	4.21267i	−0.118537	−	0.205313i	0.800651	−	0.599131i	$-0.204487\pi$
$421$	−2.43218	−	4.21267i	−0.118537	−	0.205313i	−0.919188	+	0.393818i	$0.871154\pi$
$422$	6.98152	+	12.0923i	0.339855	+	0.588646i
$423$	−0.895792	−	1.55156i	−0.0435549	−	0.0754393i
$424$	1.90926	−	3.30693i	0.0927217	−	0.160599i
$425$	−4.82632	−	8.35943i	−0.234111	−	0.405492i
$426$	−3.29893	+	5.71392i	−0.159834	+	0.276840i
$427$	22.9782	+	39.7994i	1.11199	+	1.92603i
$428$	0.876590	−	1.51830i	0.0423716	−	0.0733898i
$429$	−15.4537			−0.746113
$430$	−20.3336			−0.980574
$431$	14.1890			0.683459			0.341730	−	0.939798i	$-0.388987\pi$
$431$	14.1890			0.683459			0.341730	+	0.939798i	$0.388987\pi$
$432$	−1.00000			−0.0481125
$433$	2.03787			0.0979336			0.0489668	−	0.998800i	$-0.484407\pi$
$433$	2.03787			0.0979336			0.0489668	+	0.998800i	$0.484407\pi$
$434$	−12.0817	−	20.9261i	−0.579939	−	1.00448i
$435$	1.07709	−	1.86558i	0.0516427	−	0.0894477i
$436$	4.27095	−	7.39751i	0.204542	−	0.354276i
$437$	7.10487	−	12.3060i	0.339872	−	0.588676i
$438$	−8.07573			−0.385873
$439$	1.35115			0.0644869			0.0322434	−	0.999480i	$-0.489735\pi$
$439$	1.35115			0.0644869			0.0322434	+	0.999480i	$0.489735\pi$
$440$	−4.43958	−	7.68959i	−0.211649	−	0.366587i
$441$	−2.38356	+	4.12845i	−0.113503	+	0.196593i
$442$	−8.95757			−0.426068
$443$	14.0780	+	24.3839i	0.668868	+	1.15851i	0.978221	+	0.207566i	$0.0665542\pi$
$443$	14.0780	+	24.3839i	0.668868	+	1.15851i	−0.309353	+	0.950947i	$0.600113\pi$
$444$	−6.37359			−0.302477
$445$	29.6586			1.40595
$446$	−1.06649	−	14.8951i	−0.0504996	−	0.705301i
$447$	−8.95694			−0.423649
$448$	3.43032			0.162068
$449$	20.8849	+	36.1738i	0.985622	+	1.70715i	0.639141	+	0.769089i	$0.279290\pi$
$449$	20.8849	+	36.1738i	0.985622	+	1.70715i	0.346480	+	0.938057i	$0.387377\pi$
$450$	6.30635			0.297284
$451$	−7.39846	+	12.8145i	−0.348380	+	0.603411i
$452$	1.57848	+	2.73400i	0.0742453	+	0.128597i
$453$	−7.05044			−0.331259
$454$	9.82781			0.461242
$455$	−33.7511	+	58.4587i	−1.58228	+	2.74059i
$456$	−3.92799	+	6.80347i	−0.183945	+	0.318602i
$457$	5.50347	−	9.53228i	0.257441	−	0.445901i	−0.708114	−	0.706098i	$-0.750454\pi$
$457$	5.50347	−	9.53228i	0.257441	−	0.445901i	0.965556	+	0.260196i	$0.0837873\pi$
$458$	−8.75138	−	15.1578i	−0.408925	−	0.708279i
$459$	−1.53062			−0.0714433
$460$	−6.08201			−0.283575
$461$	−34.8496			−1.62311			−0.811554	−	0.584278i	$-0.801378\pi$
$461$	−34.8496			−1.62311			−0.811554	+	0.584278i	$0.801378\pi$
$462$	9.05829			0.421430
$463$	28.7050			1.33403			0.667017	−	0.745042i	$-0.267571\pi$
$463$	28.7050			1.33403			0.667017	+	0.745042i	$0.267571\pi$
$464$	0.320326	−	0.554821i	0.0148708	−	0.0257569i
$465$	−11.8428	−	20.5123i	−0.549195	−	0.951234i
$466$	−9.67829	+	16.7633i	−0.448338	+	0.776544i
$467$	10.2597	+	17.7704i	0.474764	+	0.822315i	0.999582	−	0.0288991i	$-0.00920016\pi$
$467$	10.2597	+	17.7704i	0.474764	+	0.822315i	−0.524819	+	0.851214i	$0.675867\pi$
$468$	2.92612	−	5.06819i	0.135260	−	0.234277i
$469$	−16.2364	−	28.1223i	−0.749729	−	1.29857i
$470$	3.01209	+	5.21710i	0.138937	+	0.240647i
$471$	−9.74921	−	16.8861i	−0.449220	−	0.778072i
$472$	12.0662			0.555391
$473$	−15.9685			−0.734233
$474$	−11.6463			−0.534932
$475$	24.7713	−	42.9051i	1.13658	−	1.96862i
$476$	5.25053			0.240658
$477$	1.90926	+	3.30693i	0.0874189	+	0.151414i
$478$	−24.8377			−1.13605
$479$	21.0954			0.963875			0.481938	−	0.876206i	$-0.339933\pi$
$479$	21.0954			0.963875			0.481938	+	0.876206i	$0.339933\pi$
$480$	3.36249			0.153476
$481$	18.6499	−	32.3026i	0.850362	−	1.47287i
$482$	1.92602	−	3.33597i	0.0877279	−	0.151949i
$483$	3.10235	−	5.37344i	0.141162	−	0.244500i
$484$	2.01348	+	3.48745i	0.0915218	+	0.158520i
$485$	−14.3824	−	24.9110i	−0.653071	−	1.13115i
$486$	0.500000	−	0.866025i	0.0226805	−	0.0392837i
$487$	20.6286			0.934770			0.467385	−	0.884054i	$-0.345196\pi$
$487$	20.6286			0.934770			0.467385	+	0.884054i	$0.345196\pi$
$488$	6.69855	+	11.6022i	0.303229	+	0.525209i
$489$	−8.57810	−	14.8577i	−0.387915	−	0.671889i
$490$	8.01471	−	13.8819i	0.362068	−	0.627120i
$491$	−0.701973	−	1.21585i	−0.0316796	−	0.0548707i	0.849751	−	0.527184i	$-0.176752\pi$
$491$	−0.701973	−	1.21585i	−0.0316796	−	0.0548707i	−0.881431	+	0.472314i	$0.843419\pi$
$492$	−2.80175	−	4.85278i	−0.126313	−	0.218780i
$493$	0.490298	−	0.849221i	0.0220819	−	0.0382470i
$494$	−22.9875	−	39.8155i	−1.03426	−	1.79139i
$495$	8.87917			0.399089
$496$	−3.52202	−	6.10032i	−0.158143	−	0.273913i
$497$	11.3164	+	19.6006i	0.507610	+	0.879207i
$498$	−14.4344			−0.646822
$499$	−9.59184	+	16.6136i	−0.429390	+	0.743725i	−0.996819	−	0.0796971i	$-0.974605\pi$
$499$	−9.59184	+	16.6136i	−0.429390	+	0.743725i	0.567429	+	0.823422i	$0.307938\pi$
$500$	−4.39259			−0.196443
$501$	0.0236637	+	0.0409866i	0.00105721	+	0.00183115i
$502$	23.8654			1.06516
$503$	17.5554	−	30.4069i	0.782758	−	1.35578i	−0.147571	−	0.989052i	$-0.547145\pi$
$503$	17.5554	−	30.4069i	0.782758	−	1.35578i	0.930329	−	0.366726i	$-0.119521\pi$
$504$	−1.71516	+	2.97075i	−0.0763994	+	0.132328i
$505$	−53.5992			−2.38513
$506$	−4.77636			−0.212335
$507$	10.6244	+	18.4019i	0.471844	+	0.817258i
$508$	−4.64156	−	8.03942i	−0.205936	−	0.356692i
$509$	8.13621	−	14.0923i	0.360631	−	0.624631i	−0.627434	−	0.778670i	$-0.715895\pi$
$509$	8.13621	−	14.0923i	0.360631	−	0.624631i	0.988065	+	0.154039i	$0.0492280\pi$
$510$	5.14670			0.227900
$511$	−13.8512	+	23.9910i	−0.612740	+	1.06130i
$512$	1.00000			0.0441942
$513$	−3.92799	−	6.80347i	−0.173425	−	0.300381i
$514$	21.5636			0.951128
$515$	22.7929	−	39.4785i	1.00438	−	1.73963i
$516$	3.02359	−	5.23702i	0.133106	−	0.230547i
$517$	2.36547	+	4.09712i	0.104033	+	0.180191i
$518$	−10.9317	+	18.9343i	−0.480313	+	0.831927i
$519$	−6.60870	+	11.4466i	−0.290090	+	0.502450i
$520$	−9.83905	+	17.0417i	−0.431471	+	0.747330i
$521$	5.39513	−	9.34464i	0.236365	−	0.409396i	−0.723304	−	0.690530i	$-0.757377\pi$
$521$	5.39513	−	9.34464i	0.236365	−	0.409396i	0.959668	+	0.281134i	$0.0907106\pi$
$522$	0.320326	+	0.554821i	0.0140203	+	0.0242838i
$523$	3.72399	−	6.45013i	0.162839	−	0.282045i	−0.773047	−	0.634349i	$-0.781268\pi$
$523$	3.72399	−	6.45013i	0.162839	−	0.282045i	0.935886	+	0.352304i	$0.114602\pi$
$524$	−0.217929	−	0.377465i	−0.00952029	−	0.0164896i
$525$	10.8164	−	18.7346i	0.472067	−	0.817644i
$526$	−11.4232	+	19.7855i	−0.498074	+	0.862690i
$527$	−5.39089	−	9.33729i	−0.234831	−	0.406739i
$528$	2.64065			0.114920
$529$	9.86415	−	17.0852i	0.428876	−	0.742835i
$530$	−6.41986	−	11.1195i	−0.278861	−	0.483001i
$531$	−6.03309	+	10.4496i	−0.261814	+	0.453475i
$532$	13.4743	+	23.3381i	0.584183	+	1.01184i
$533$	32.7931			1.42043
$534$	−4.41021	+	7.63871i	−0.190848	+	0.330559i
$535$	−2.94753	−	5.10527i	−0.127433	−	0.220720i
$536$	−4.73320	−	8.19815i	−0.204443	−	0.354106i
$537$	−15.2953			−0.660042
$538$	3.04919	+	5.28136i	0.131460	+	0.227695i
$539$	6.29416	−	10.9018i	0.271109	−	0.469574i
$540$	−1.68125	+	2.91200i	−0.0723493	+	0.125313i
$541$	−19.0345			−0.818357			−0.409178	−	0.912454i	$-0.634185\pi$
$541$	−19.0345			−0.818357			−0.409178	+	0.912454i	$0.634185\pi$
$542$	−10.6875	−	18.5113i	−0.459067	−	0.795127i
$543$	−0.550259	+	0.953076i	−0.0236139	+	0.0409004i
$544$	1.53062			0.0656249
$545$	−14.3610	−	24.8741i	−0.615160	−	1.06549i
$546$	−10.0375	−	17.3855i	−0.429567	−	0.744032i
$547$	−13.1057	−	22.6998i	−0.560360	−	0.970572i	−0.997465	−	0.0711616i	$-0.977329\pi$
$547$	−13.1057	−	22.6998i	−0.560360	−	0.970572i	0.437105	−	0.899411i	$-0.356004\pi$
$548$	−4.70021	−	8.14100i	−0.200783	−	0.347766i
$549$	−13.3971			−0.571775
$550$	−16.6529			−0.710081
$551$	5.03294			0.214411
$552$	0.904391	−	1.56645i	0.0384934	−	0.0666726i
$553$	−19.9753	+	34.5982i	−0.849435	+	1.47127i
$554$	−13.3182			−0.565835
$555$	−10.7156	+	18.5599i	−0.454851	+	0.787825i
$556$	4.15049	+	7.18885i	0.176020	+	0.304875i
$557$	43.9128			1.86065			0.930323	−	0.366741i	$-0.119527\pi$
$557$	43.9128			1.86065			0.930323	+	0.366741i	$0.119527\pi$
$558$	7.04405			0.298198
$559$	17.6948	+	30.6483i	0.748410	+	1.29628i
$560$	5.76722	−	9.98912i	0.243709	−	0.422117i
$561$	4.04184			0.170647
$562$	3.84808	−	6.66507i	0.162321	−	0.281149i
$563$	−8.06897	+	13.9759i	−0.340067	+	0.589013i	−0.984445	−	0.175694i	$-0.943783\pi$
$563$	−8.06897	+	13.9759i	−0.340067	+	0.589013i	0.644378	+	0.764707i	$0.277116\pi$
$564$	−1.79158			−0.0754393
$565$	10.6152			0.446586
$566$	−26.0594			−1.09536
$567$	−1.71516	−	2.97075i	−0.0720300	−	0.124760i
$568$	3.29893	+	5.71392i	0.138420	+	0.239751i
$569$	4.06657	+	7.04350i	0.170479	+	0.295279i	0.938588	−	0.345041i	$-0.112135\pi$
$569$	4.06657	+	7.04350i	0.170479	+	0.295279i	−0.768108	+	0.640320i	$0.778802\pi$
$570$	13.2078	+	22.8766i	0.553215	+	0.958196i
$571$	−23.1445			−0.968566			−0.484283	−	0.874911i	$-0.660920\pi$
$571$	−23.1445			−0.968566			−0.484283	+	0.874911i	$0.660920\pi$
$572$	−7.72686	+	13.3833i	−0.323076	+	0.559585i
$573$	−1.34371	−	2.32737i	−0.0561343	−	0.0972274i
$574$	−19.2219			−0.802305
$575$	−5.70341	+	9.87859i	−0.237849	+	0.411966i
$576$	−0.500000	+	0.866025i	−0.0208333	+	0.0360844i
$577$	17.6409	+	30.5549i	0.734400	+	1.27202i	0.954986	+	0.296650i	$0.0958696\pi$
$577$	17.6409	+	30.5549i	0.734400	+	1.27202i	−0.220586	+	0.975367i	$0.570797\pi$
$578$	−14.6572			−0.609659
$579$	7.60193	+	13.1669i	0.315926	+	0.547199i
$580$	−1.07709	−	1.86558i	−0.0447239	−	0.0774640i
$581$	−24.7574	+	42.8811i	−1.02711	+	1.77901i
$582$	8.55460			0.354600
$583$	−5.04168	−	8.73245i	−0.208805	−	0.361661i
$584$	−4.03786	+	6.99379i	−0.167088	+	0.289405i
$585$	−9.83905	−	17.0417i	−0.406795	−	0.704589i
$586$	13.8929	−	24.0632i	0.573910	−	0.994041i
$587$	−2.47082			−0.101982			−0.0509909	−	0.998699i	$-0.516238\pi$
$587$	−2.47082			−0.101982			−0.0509909	+	0.998699i	$0.516238\pi$
$588$	2.38356	+	4.12845i	0.0982965	+	0.170254i
$589$	27.6689	−	47.9240i	1.14008	−	1.97467i
$590$	20.2862	−	35.1368i	0.835171	−	1.44656i
$591$	−6.52699	−	11.3051i	−0.268485	−	0.465029i
$592$	−3.18680	+	5.51970i	−0.130977	+	0.226858i
$593$	−7.92679	−	13.7296i	−0.325514	−	0.563807i	0.656102	−	0.754672i	$-0.272204\pi$
$593$	−7.92679	−	13.7296i	−0.325514	−	0.563807i	−0.981616	+	0.190865i	$0.938871\pi$
$594$	−1.32033	+	2.28687i	−0.0541736	+	0.0938315i
$595$	8.82743	−	15.2896i	0.361889	−	0.626811i
$596$	−4.47847	+	7.75694i	−0.183445	+	0.317737i
$597$	9.36374	−	16.2185i	0.383232	−	0.663778i
$598$	5.29271	+	9.16725i	0.216435	+	0.374877i
$599$	14.5732	−	25.2415i	0.595444	−	1.03134i	−0.398040	−	0.917368i	$-0.630310\pi$
$599$	14.5732	−	25.2415i	0.595444	−	1.03134i	0.993484	−	0.113971i	$-0.0363571\pi$
$600$	3.15318	−	5.46146i	0.128728	−	0.222963i
$601$	16.5336			0.674419			0.337209	−	0.941430i	$-0.390517\pi$
$601$	16.5336			0.674419			0.337209	+	0.941430i	$0.390517\pi$
$602$	−10.3719	−	17.9647i	−0.422727	−	0.732185i
$603$	9.46641			0.385502
$604$	−3.52522	+	6.10586i	−0.143439	+	0.248444i
$605$	13.5406			0.550504
$606$	7.97016	−	13.8047i	0.323766	−	0.560779i
$607$	−6.61248	−	11.4531i	−0.268392	−	0.464869i	0.700055	−	0.714089i	$-0.253159\pi$
$607$	−6.61248	−	11.4531i	−0.268392	−	0.464869i	−0.968447	+	0.249220i	$0.919826\pi$
$608$	3.92799	+	6.80347i	0.159301	+	0.275917i
$609$	2.19764			0.0890530
$610$	45.0477			1.82393
$611$	5.24239	−	9.08008i	0.212084	−	0.367341i
$612$	−0.765311	+	1.32556i	−0.0309359	+	0.0535825i
$613$	15.2525			0.616043			0.308021	−	0.951379i	$-0.400333\pi$
$613$	15.2525			0.616043			0.308021	+	0.951379i	$0.400333\pi$
$614$	4.98307	+	8.63093i	0.201100	+	0.348316i
$615$	−18.8418			−0.759773
$616$	4.52915	−	7.84471i	0.182484	−	0.316072i
$617$	31.0947			1.25182			0.625912	−	0.779894i	$-0.284727\pi$
$617$	31.0947			1.25182			0.625912	+	0.779894i	$0.284727\pi$
$618$	6.77858	+	11.7409i	0.272675	+	0.472286i
$619$	2.00126	+	3.46629i	0.0804376	+	0.139322i	0.903438	−	0.428719i	$-0.141035\pi$
$619$	2.00126	+	3.46629i	0.0804376	+	0.139322i	−0.823000	+	0.568041i	$0.807702\pi$
$620$	−23.6855			−0.951234
$621$	0.904391	+	1.56645i	0.0362920	+	0.0628595i
$622$	12.9852	−	22.4910i	0.520658	−	0.901806i
$623$	15.1284	+	26.2032i	0.606108	+	1.04981i
$624$	−2.92612	−	5.06819i	−0.117139	−	0.202890i
$625$	8.38085	−	14.5161i	0.335234	−	0.580642i
$626$	−2.12041	−	3.67266i	−0.0847488	−	0.146789i
$627$	10.3724	+	17.9656i	0.414235	+	0.717477i
$628$	−19.4984			−0.778072
$629$	−4.87778	+	8.44857i	−0.194490	+	0.336866i
$630$	5.76722	+	9.98912i	0.229771	+	0.397976i
$631$	7.27173	+	12.5950i	0.289483	+	0.501399i	0.973686	−	0.227892i	$-0.0731833\pi$
$631$	7.27173	+	12.5950i	0.289483	+	0.501399i	−0.684203	+	0.729291i	$0.739850\pi$
$632$	−5.82315	+	10.0860i	−0.231632	+	0.401199i
$633$	−6.98152	+	12.0923i	−0.277490	+	0.480627i
$634$	8.43404	−	14.6082i	0.334959	−	0.580165i
$635$	−31.2144			−1.23871
$636$	3.81851			0.151414
$637$	−27.8984			−1.10537
$638$	−0.845869	−	1.46509i	−0.0334883	−	0.0580034i
$639$	−6.59787			−0.261008
$640$	1.68125	−	2.91200i	0.0664571	−	0.115107i
$641$	32.6511			1.28964			0.644821	−	0.764334i	$-0.276932\pi$
$641$	32.6511			1.28964			0.644821	+	0.764334i	$0.276932\pi$
$642$	1.75318			0.0691925
$643$	−41.1687			−1.62353			−0.811767	−	0.583982i	$-0.801494\pi$
$643$	−41.1687			−1.62353			−0.811767	+	0.583982i	$0.801494\pi$
$644$	−3.10235	−	5.37344i	−0.122250	−	0.211743i
$645$	−10.1668	−	17.6094i	−0.400318	−	0.693371i
$646$	6.01226	+	10.4135i	0.236549	+	0.409715i
$647$	20.8314	−	36.0811i	0.818969	−	1.41850i	−0.0874741	−	0.996167i	$-0.527880\pi$
$647$	20.8314	−	36.0811i	0.818969	−	1.41850i	0.906443	−	0.422329i	$-0.138787\pi$
$648$	−0.500000	−	0.866025i	−0.0196419	−	0.0340207i
$649$	15.9313	−	27.5938i	0.625358	−	1.08315i
$650$	18.4531	+	31.9618i	0.723792	+	1.25364i
$651$	12.0817	−	20.9261i	0.473518	−	0.820158i
$652$	−17.1562			−0.671889
$653$	39.9335			1.56272			0.781359	−	0.624082i	$-0.214527\pi$
$653$	39.9335			1.56272			0.781359	+	0.624082i	$0.214527\pi$
$654$	8.54191			0.334015
$655$	−1.46557			−0.0572646
$656$	−5.60351			−0.218780
$657$	−4.03786	−	6.99379i	−0.157532	−	0.272854i
$658$	−3.07286	+	5.32234i	−0.119792	+	0.207487i
$659$	−17.7208	+	30.6934i	−0.690306	+	1.19564i	0.281432	+	0.959581i	$0.409191\pi$
$659$	−17.7208	+	30.6934i	−0.690306	+	1.19564i	−0.971738	+	0.236063i	$0.924143\pi$
$660$	4.43958	−	7.68959i	0.172811	−	0.299317i
$661$	19.8097			0.770509			0.385255	−	0.922810i	$-0.374114\pi$
$661$	19.8097			0.770509			0.385255	+	0.922810i	$0.374114\pi$
$662$	4.13258			0.160617
$663$	−4.47878	−	7.75748i	−0.173942	−	0.301276i
$664$	−7.21722	+	12.5006i	−0.280082	+	0.485117i
$665$	90.6142			3.51387
$666$	−3.18680	−	5.51970i	−0.123486	−	0.213884i
$667$	−1.15880			−0.0448689
$668$	0.0473273			0.00183115
$669$	12.3663	−	8.37113i	0.478107	−	0.323647i
$670$	−31.8307			−1.22973
$671$	35.3771			1.36572
$672$	1.71516	+	2.97075i	0.0661638	+	0.114599i
$673$	32.8376			1.26580			0.632899	−	0.774235i	$-0.281865\pi$
$673$	32.8376			1.26580			0.632899	+	0.774235i	$0.281865\pi$
$674$	−1.03630	+	1.79492i	−0.0399167	+	0.0691377i
$675$	3.15318	+	5.46146i	0.121366	+	0.210212i
$676$	21.2487			0.817258
$677$	−42.6068			−1.63751			−0.818755	−	0.574143i	$-0.805335\pi$
$677$	−42.6068			−1.63751			−0.818755	+	0.574143i	$0.805335\pi$
$678$	−1.57848	+	2.73400i	−0.0606210	+	0.104999i
$679$	14.6725	−	25.4136i	0.563080	−	0.975283i
$680$	2.57335	−	4.45718i	0.0986835	−	0.170925i
$681$	4.91390	+	8.51113i	0.188301	+	0.326147i
$682$	−18.6009			−0.712264
$683$	−44.9142			−1.71859			−0.859297	−	0.511478i	$-0.829098\pi$
$683$	−44.9142			−1.71859			−0.859297	+	0.511478i	$0.829098\pi$
$684$	−7.85597			−0.300381
$685$	−31.6088			−1.20771
$686$	−7.65949			−0.292441
$687$	8.75138	−	15.1578i	0.333886	−	0.578307i
$688$	−3.02359	−	5.23702i	−0.115273	−	0.199659i
$689$	−11.1734	+	19.3529i	−0.425674	+	0.737289i
$690$	−3.04101	−	5.26718i	−0.115769	−	0.200518i
$691$	3.37232	−	5.84103i	0.128289	−	0.222203i	−0.794725	−	0.606970i	$-0.792385\pi$
$691$	3.37232	−	5.84103i	0.128289	−	0.222203i	0.923014	+	0.384767i	$0.125718\pi$
$692$	6.60870	+	11.4466i	0.251225	+	0.435135i
$693$	4.52915	+	7.84471i	0.172048	+	0.297996i
$694$	−10.6601	−	18.4638i	−0.404651	−	0.700875i
$695$	27.9120			1.05876
$696$	0.640652			0.0242838
$697$	−8.57685			−0.324872
$698$	−12.9119	+	22.3641i	−0.488724	+	0.846495i
$699$	−19.3566			−0.732133
$700$	−10.8164	−	18.7346i	−0.408822	−	0.708101i
$701$	−4.52008			−0.170721			−0.0853605	−	0.996350i	$-0.527204\pi$
$701$	−4.52008			−0.170721			−0.0853605	+	0.996350i	$0.527204\pi$
$702$	5.85224			0.220879
$703$	−50.0708			−1.88846
$704$	1.32033	−	2.28687i	0.0497617	−	0.0861897i
$705$	−3.01209	+	5.21710i	−0.113442	+	0.196487i
$706$	15.1245	−	26.1964i	0.569219	−	0.985915i
$707$	−27.3402	−	47.3547i	−1.02824	−	1.78096i
$708$	6.03309	+	10.4496i	0.226738	+	0.392721i
$709$	−13.8752	+	24.0326i	−0.521096	+	0.902564i	0.478603	+	0.878031i	$0.341143\pi$
$709$	−13.8752	+	24.0326i	−0.521096	+	0.902564i	−0.999699	+	0.0245331i	$0.992190\pi$
$710$	22.1853			0.832598
$711$	−5.82315	−	10.0860i	−0.218385	−	0.378254i
$712$	4.41021	+	7.63871i	0.165280	+	0.286273i
$713$	−6.37057	+	11.0342i	−0.238580	+	0.413232i
$714$	2.62526	+	4.54709i	0.0982481	+	0.170171i
$715$	25.9815	+	45.0013i	0.971653	+	1.68295i
$716$	−7.64767	+	13.2461i	−0.285807	+	0.495032i
$717$	−12.4188	−	21.5101i	−0.463790	−	0.803308i
$718$	−5.74869			−0.214539
$719$	4.74456	+	8.21783i	0.176942	+	0.306473i	0.940832	−	0.338874i	$-0.110046\pi$
$719$	4.74456	+	8.21783i	0.176942	+	0.306473i	−0.763889	+	0.645347i	$0.776713\pi$
$720$	1.68125	+	2.91200i	0.0626563	+	0.108524i
$721$	46.5055			1.73195
$722$	−21.3581	+	36.9934i	−0.794868	+	1.37675i
$723$	3.85204			0.143259
$724$	0.550259	+	0.953076i	0.0204502	+	0.0354208i
$725$	−4.04018			−0.150048
$726$	−2.01348	+	3.48745i	−0.0747272	+	0.129431i
$727$	26.1186	−	45.2388i	0.968687	−	1.67781i	0.269321	−	0.963050i	$-0.413201\pi$
$727$	26.1186	−	45.2388i	0.968687	−	1.67781i	0.699365	−	0.714764i	$-0.253466\pi$
$728$	−20.0751			−0.744032
$729$	1.00000			0.0370370
$730$	13.5773	+	23.5165i	0.502518	+	0.870386i
$731$	−4.62798	−	8.01590i	−0.171172	−	0.296479i
$732$	−6.69855	+	11.6022i	−0.247586	+	0.428831i
$733$	3.43847			0.127003			0.0635013	−	0.997982i	$-0.479773\pi$
$733$	3.43847			0.127003			0.0635013	+	0.997982i	$0.479773\pi$
$734$	−5.93840	+	10.2856i	−0.219190	+	0.379649i
$735$	16.0294			0.591254
$736$	−0.904391	−	1.56645i	−0.0333363	−	0.0577402i
$737$	−24.9975			−0.920794
$738$	2.80175	−	4.85278i	0.103134	−	0.178633i
$739$	−4.44567	+	7.70013i	−0.163537	+	0.283254i	−0.936135	−	0.351642i	$-0.885624\pi$
$739$	−4.44567	+	7.70013i	−0.163537	+	0.283254i	0.772598	+	0.634895i	$0.218957\pi$
$740$	10.7156	+	18.5599i	0.393913	+	0.682277i
$741$	22.9875	−	39.8155i	0.844467	−	1.46266i
$742$	6.54937	−	11.3438i	0.240435	−	0.416446i
$743$	−1.67093	+	2.89413i	−0.0613004	+	0.106175i	−0.895047	−	0.445972i	$-0.852858\pi$
$743$	−1.67093	+	2.89413i	−0.0613004	+	0.106175i	0.833747	+	0.552147i	$0.186191\pi$
$744$	3.52202	−	6.10032i	0.129124	−	0.223649i
$745$	15.0588	+	26.0826i	0.551712	+	0.955594i
$746$	9.56648	−	16.5696i	0.350254	−	0.606657i
$747$	−7.21722	−	12.5006i	−0.264064	−	0.457373i
$748$	2.02092	−	3.50034i	0.0738921	−	0.127985i
$749$	3.00699	−	5.20826i	0.109873	−	0.190306i
$750$	−2.19630	−	3.80410i	−0.0801974	−	0.138906i
$751$	−18.5868			−0.678243			−0.339121	−	0.940743i	$-0.610130\pi$
$751$	−18.5868			−0.678243			−0.339121	+	0.940743i	$0.610130\pi$
$752$	−0.895792	+	1.55156i	−0.0326662	+	0.0565795i
$753$	11.9327	+	20.6680i	0.434851	+	0.753184i
$754$	−1.87462	+	3.24694i	−0.0682698	+	0.118247i
$755$	11.8535	+	20.5309i	0.431394	+	0.747197i
$756$	−3.43032			−0.124760
$757$	−23.2265	+	40.2294i	−0.844180	+	1.46216i	0.0421508	+	0.999111i	$0.486579\pi$
$757$	−23.2265	+	40.2294i	−0.844180	+	1.46216i	−0.886331	+	0.463052i	$0.846754\pi$
$758$	−12.8802	−	22.3092i	−0.467830	−	0.810305i
$759$	−2.38818	−	4.13645i	−0.0866855	−	0.150144i
$760$	26.4156			0.958196
$761$	−11.4447	−	19.8228i	−0.414870	−	0.718575i	0.580545	−	0.814228i	$-0.302839\pi$
$761$	−11.4447	−	19.8228i	−0.414870	−	0.718575i	−0.995415	+	0.0956529i	$0.969506\pi$
$762$	4.64156	−	8.03942i	0.168146	−	0.291238i
$763$	14.6508	−	25.3759i	0.530393	−	0.918668i
$764$	−2.68742			−0.0972274
$765$	2.57335	+	4.45718i	0.0930397	+	0.161150i
$766$	0.801373	−	1.38802i	0.0289548	−	0.0501511i
$767$	−70.6142			−2.54973
$768$	0.500000	+	0.866025i	0.0180422	+	0.0312500i
$769$	−10.3408	−	17.9108i	−0.372898	−	0.645879i	0.617112	−	0.786876i	$-0.288303\pi$
$769$	−10.3408	−	17.9108i	−0.372898	−	0.645879i	−0.990010	+	0.140997i	$0.954969\pi$
$770$	−15.2292	−	26.3778i	−0.548823	−	0.950589i
$771$	10.7818	+	18.6746i	0.388296	+	0.672549i
$772$	15.2039			0.547199
$773$	−20.5992			−0.740903			−0.370452	−	0.928852i	$-0.620797\pi$
$773$	−20.5992			−0.740903			−0.370452	+	0.928852i	$0.620797\pi$
$774$	6.04719			0.217362
$775$	−22.2111	+	38.4708i	−0.797847	+	1.38191i
$776$	4.27730	−	7.40850i	0.153546	−	0.265950i
$777$	−21.8635			−0.784349
$778$	−7.72986	+	13.3885i	−0.277129	+	0.480002i
$779$	−22.0105	−	38.1233i	−0.788608	−	1.36591i
$780$	−19.6781			−0.704589
$781$	17.4227			0.623432
$782$	−1.38428	−	2.39764i	−0.0495018	−	0.0857396i
$783$	−0.320326	+	0.554821i	−0.0114475	+	0.0198277i
$784$	4.76712			0.170254
$785$	−32.7816	+	56.7795i	−1.17003	+	2.02655i
$786$	0.217929	−	0.377465i	0.00777328	−	0.0134637i
$787$	48.3319			1.72285			0.861423	−	0.507888i	$-0.169574\pi$
$787$	48.3319			1.72285			0.861423	+	0.507888i	$0.169574\pi$
$788$	−13.0540			−0.465029
$789$	−22.8463			−0.813351
$790$	19.5803	+	33.9140i	0.696635	+	1.20661i
$791$	5.41469	+	9.37851i	0.192524	+	0.333462i
$792$	1.32033	+	2.28687i	0.0469157	+	0.0812604i
$793$	−39.2015	−	67.8991i	−1.39209	−	2.41117i
$794$	9.92942			0.352382
$795$	6.41986	−	11.1195i	0.227689	−	0.394369i
$796$	−9.36374	−	16.2185i	−0.331889	−	0.574848i
$797$	2.45990			0.0871342			0.0435671	−	0.999051i	$-0.486128\pi$
$797$	2.45990			0.0871342			0.0435671	+	0.999051i	$0.486128\pi$
$798$	−13.4743	+	23.3381i	−0.476984	+	0.826160i
$799$	−1.37112	+	2.37485i	−0.0485067	+	0.0840160i
$800$	−3.15318	−	5.46146i	−0.111482	−	0.193092i
$801$	−8.82042			−0.311654
$802$	2.85507	+	4.94513i	0.100816	+	0.174619i
$803$	10.6626	+	18.4682i	0.376275	+	0.651727i
$804$	4.73320	−	8.19815i	0.166927	−	0.289127i
$805$	−20.8633			−0.735334
$806$	20.6117	+	35.7005i	0.726017	+	1.25750i
$807$	−3.04919	+	5.28136i	−0.107337	+	0.185913i
$808$	−7.97016	−	13.8047i	−0.280389	−	0.485649i
$809$	−3.99653	+	6.92220i	−0.140511	+	0.243371i	−0.927689	−	0.373354i	$-0.878208\pi$
$809$	−3.99653	+	6.92220i	−0.140511	+	0.243371i	0.787178	+	0.616725i	$0.211541\pi$
$810$	−3.36249			−0.118146
$811$	22.1783	+	38.4140i	0.778786	+	1.34890i	0.932642	+	0.360804i	$0.117498\pi$
$811$	22.1783	+	38.4140i	0.778786	+	1.34890i	−0.153855	+	0.988093i	$0.549169\pi$
$812$	1.09882	−	1.90322i	0.0385611	−	0.0667898i
$813$	10.6875	−	18.5113i	0.374826	−	0.649218i
$814$	8.41522	+	14.5756i	0.294953	+	0.510874i
$815$	−28.8438	+	49.9589i	−1.01035	+	1.74998i
$816$	0.765311	+	1.32556i	0.0267912	+	0.0464038i
$817$	23.7533	−	41.1419i	0.831022	−	1.43937i
$818$	−0.228104	+	0.395087i	−0.00797546	+	0.0138139i
$819$	10.0375	−	17.3855i	0.350740	−	0.607499i
$820$	−9.42088	+	16.3174i	−0.328991	+	0.569830i
$821$	−15.7628	−	27.3020i	−0.550127	−	0.952847i	−0.998265	−	0.0588829i	$-0.981246\pi$
$821$	−15.7628	−	27.3020i	−0.550127	−	0.952847i	0.448138	−	0.893964i	$-0.352087\pi$
$822$	4.70021	−	8.14100i	0.163939	−	0.283950i
$823$	7.67960	−	13.3015i	0.267694	−	0.463659i	−0.700572	−	0.713582i	$-0.747072\pi$
$823$	7.67960	−	13.3015i	0.267694	−	0.463659i	0.968266	+	0.249922i	$0.0804051\pi$
$824$	13.5572			0.472286
$825$	−8.32644	−	14.4218i	−0.289889	−	0.502103i
$826$	41.3909			1.44017
$827$	11.9359	−	20.6737i	0.415053	−	0.718893i	−0.580381	−	0.814345i	$-0.697096\pi$
$827$	11.9359	−	20.6737i	0.415053	−	0.718893i	0.995434	+	0.0954519i	$0.0304296\pi$
$828$	1.80878			0.0628595
$829$	−0.539039	+	0.933643i	−0.0187216	+	0.0324268i	−0.875234	−	0.483699i	$-0.839293\pi$
$829$	−0.539039	+	0.933643i	−0.0187216	+	0.0324268i	0.856513	+	0.516126i	$0.172626\pi$
$830$	24.2678	+	42.0331i	0.842349	+	1.45899i
$831$	−6.65909	−	11.5339i	−0.231001	−	0.400106i
$832$	−5.85224			−0.202890
$833$	7.29667			0.252814
$834$	−4.15049	+	7.18885i	−0.143720	+	0.248930i
$835$	0.0795688	−	0.137817i	0.00275359	−	0.00476936i
$836$	20.7449			0.717477
$837$	3.52202	+	6.10032i	0.121739	+	0.210858i
$838$	−32.0750			−1.10801
$839$	18.9686	−	32.8545i	0.654867	−	1.13426i	−0.327060	−	0.945004i	$-0.606058\pi$
$839$	18.9686	−	32.8545i	0.654867	−	1.13426i	0.981927	−	0.189260i	$-0.0606088\pi$
$840$	11.5344			0.397976
$841$	14.2948	+	24.7593i	0.492924	+	0.853769i
$842$	−2.43218	−	4.21267i	−0.0838186	−	0.145178i
$843$	7.69616			0.265070
$844$	6.98152	+	12.0923i	0.240314	+	0.416236i
$845$	35.7243	−	61.8763i	1.22895	−	2.12861i
$846$	−0.895792	−	1.55156i	−0.0307980	−	0.0533436i
$847$	6.90689	+	11.9631i	0.237323	+	0.411056i
$848$	1.90926	−	3.30693i	0.0655642	−	0.113560i
$849$	−13.0297	−	22.5681i	−0.447178	−	0.774536i
$850$	−4.82632	−	8.35943i	−0.165541	−	0.286726i
$851$	11.5284			0.395190
$852$	−3.29893	+	5.71392i	−0.113020	+	0.195756i
$853$	17.4900	+	30.2937i	0.598848	+	1.03723i	0.992991	+	0.118186i	$0.0377079\pi$
$853$	17.4900	+	30.2937i	0.598848	+	1.03723i	−0.394144	+	0.919049i	$0.628959\pi$
$854$	22.9782	+	39.7994i	0.786298	+	1.36191i
$855$	−13.2078	+	22.8766i	−0.451698	+	0.782364i
$856$	0.876590	−	1.51830i	0.0299612	−	0.0518944i
$857$	−17.4502	+	30.2247i	−0.596088	+	1.03245i	0.397305	+	0.917687i	$0.369946\pi$
$857$	−17.4502	+	30.2247i	−0.596088	+	1.03245i	−0.993392	+	0.114768i	$0.963388\pi$
$858$	−15.4537			−0.527582
$859$	13.5060			0.460817			0.230409	−	0.973094i	$-0.425994\pi$
$859$	13.5060			0.460817			0.230409	+	0.973094i	$0.425994\pi$
$860$	−20.3336			−0.693371
$861$	−9.61093	−	16.6466i	−0.327540	−	0.567315i
$862$	14.1890			0.483279
$863$	15.0514	−	26.0698i	0.512356	−	0.887426i	−0.487542	−	0.873100i	$-0.662106\pi$
$863$	15.0514	−	26.0698i	0.512356	−	0.887426i	0.999897	−	0.0143262i	$-0.00456034\pi$
$864$	−1.00000			−0.0340207
$865$	44.4434			1.51112
$866$	2.03787			0.0692495
$867$	−7.32860	−	12.6935i	−0.248892	−	0.431094i
$868$	−12.0817	−	20.9261i	−0.410079	−	0.710278i
$869$	15.3769	+	26.6336i	0.521626	+	0.903482i
$870$	1.07709	−	1.86558i	0.0365169	−	0.0632491i
$871$	27.6998	+	47.9775i	0.938574	+	1.62566i
$872$	4.27095	−	7.39751i	0.144633	−	0.250511i
$873$	4.27730	+	7.40850i	0.144765	+	0.250740i
$874$	7.10487	−	12.3060i	0.240326	−	0.416256i
$875$	−15.0680			−0.509392
$876$	−8.07573			−0.272854
$877$	37.8631			1.27855			0.639273	−	0.768980i	$-0.279235\pi$
$877$	37.8631			1.27855			0.639273	+	0.768980i	$0.279235\pi$
$878$	1.35115			0.0455991
$879$	27.7858			0.937191
$880$	−4.43958	−	7.68959i	−0.149658	−	0.259216i
$881$	9.01079	−	15.6071i	0.303581	−	0.525818i	−0.673363	−	0.739312i	$-0.735151\pi$
$881$	9.01079	−	15.6071i	0.303581	−	0.525818i	0.976944	+	0.213494i	$0.0684843\pi$
$882$	−2.38356	+	4.12845i	−0.0802587	+	0.139012i
$883$	20.5397	−	35.5757i	0.691215	−	1.19722i	−0.280225	−	0.959934i	$-0.590409\pi$
$883$	20.5397	−	35.5757i	0.691215	−	1.19722i	0.971440	−	0.237285i	$-0.0762575\pi$
$884$	−8.95757			−0.301276
$885$	40.5725			1.36383
$886$	14.0780	+	24.3839i	0.472961	+	0.819193i
$887$	−5.29745	+	9.17545i	−0.177871	+	0.308082i	−0.941151	−	0.337986i	$-0.890254\pi$
$887$	−5.29745	+	9.17545i	−0.177871	+	0.308082i	0.763280	+	0.646068i	$0.223588\pi$
$888$	−6.37359			−0.213884
$889$	−15.9221	−	27.5778i	−0.534009	−	0.924931i
$890$	29.6586			0.994158
$891$	−2.64065			−0.0884652
$892$	−1.06649	−	14.8951i	−0.0357086	−	0.498723i
$893$	−14.0746			−0.470989
$894$	−8.95694			−0.299565
$895$	25.7152	+	44.5401i	0.859565	+	1.48881i
$896$	3.43032			0.114599
$897$	−5.29271	+	9.16725i	−0.176719	+	0.306085i
$898$	20.8849	+	36.1738i	0.696940	+	1.20713i
$899$	−4.51278			−0.150510
$900$	6.30635			0.210212
$901$	2.92235	−	5.06166i	0.0973576	−	0.168628i
$902$	−7.39846	+	12.8145i	−0.246342	+	0.426676i
$903$	10.3719	−	17.9647i	0.345156	−	0.597827i
$904$	1.57848	+	2.73400i	0.0524993	+	0.0909315i
$905$	3.70048			0.123008
$906$	−7.05044			−0.234235
$907$	−32.2076			−1.06944			−0.534718	−	0.845030i	$-0.679582\pi$
$907$	−32.2076			−1.06944			−0.534718	+	0.845030i	$0.679582\pi$
$908$	9.82781			0.326147
$909$	15.9403			0.528707
$910$	−33.7511	+	58.4587i	−1.11884	+	1.93789i
$911$	−15.0932	−	26.1422i	−0.500060	−	0.866129i	−1.00000		6.88529e-5i	$-0.999978\pi$
$911$	−15.0932	−	26.1422i	−0.500060	−	0.866129i	0.499940	−	0.866060i	$-0.333355\pi$
$912$	−3.92799	+	6.80347i	−0.130069	+	0.225285i
$913$	19.0582	+	33.0097i	0.630733	+	1.09246i
$914$	5.50347	−	9.53228i	0.182038	−	0.315300i
$915$	22.5238	+	39.0124i	0.744615	+	1.28971i
$916$	−8.75138	−	15.1578i	−0.289154	−	0.500829i
$917$	−0.747568	−	1.29483i	−0.0246869	−	0.0427589i
$918$	−1.53062			−0.0505181
$919$	18.6651			0.615703			0.307852	−	0.951434i	$-0.400390\pi$
$919$	18.6651			0.615703			0.307852	+	0.951434i	$0.400390\pi$
$920$	−6.08201			−0.200518
$921$	−4.98307	+	8.63093i	−0.164198	+	0.284399i
$922$	−34.8496			−1.14771
$923$	−19.3061	−	33.4392i	−0.635470	−	1.10067i
$924$	9.05829			0.297996
$925$	40.1941			1.32157
$926$	28.7050			0.943305
$927$	−6.77858	+	11.7409i	−0.222638	+	0.385620i
$928$	0.320326	−	0.554821i	0.0105152	−	0.0182129i
$929$	−8.39620	+	14.5427i	−0.275470	+	0.477129i	−0.970254	−	0.242090i	$-0.922167\pi$
$929$	−8.39620	+	14.5427i	−0.275470	+	0.477129i	0.694783	+	0.719219i	$0.255500\pi$
$930$	−11.8428	−	20.5123i	−0.388340	−	0.672624i
$931$	18.7252	+	32.4330i	0.613694	+	1.06295i
$932$	−9.67829	+	16.7633i	−0.317023	+	0.549100i
$933$	25.9703			0.850231
$934$	10.2597	+	17.7704i	0.335709	+	0.581465i
$935$	−6.79533	−	11.7699i	−0.222231	−	0.384915i
$936$	2.92612	−	5.06819i	0.0956432	−	0.165659i
$937$	−13.8837	−	24.0473i	−0.453562	−	0.785592i	0.545042	−	0.838408i	$-0.316514\pi$
$937$	−13.8837	−	24.0473i	−0.453562	−	0.785592i	−0.998604	+	0.0528164i	$0.983180\pi$
$938$	−16.2364	−	28.1223i	−0.530138	−	0.918226i
$939$	2.12041	−	3.67266i	0.0691971	−	0.119853i
$940$	3.01209	+	5.21710i	0.0982436	+	0.170163i
$941$	32.5006			1.05949			0.529745	−	0.848157i	$-0.322287\pi$
$941$	32.5006			1.05949			0.529745	+	0.848157i	$0.322287\pi$
$942$	−9.74921	−	16.8861i	−0.317646	−	0.550180i
$943$	5.06776	+	8.77762i	0.165029	+	0.285839i
$944$	12.0662			0.392721
$945$	−5.76722	+	9.98912i	−0.187608	+	0.324946i
$946$	−15.9685			−0.519181
$947$	−19.9617	−	34.5747i	−0.648668	−	1.12353i	−0.983441	−	0.181228i	$-0.941993\pi$
$947$	−19.9617	−	34.5747i	−0.648668	−	1.12353i	0.334773	−	0.942299i	$-0.391340\pi$
$948$	−11.6463			−0.378254
$949$	23.6305	−	40.9293i	0.767080	−	1.32862i
$950$	24.7713	−	42.9051i	0.803686	−	1.39202i
$951$	16.8681			0.546985
$952$	5.25053			0.170171
$953$	−8.12502	−	14.0729i	−0.263195	−	0.455867i	0.703894	−	0.710305i	$-0.251443\pi$
$953$	−8.12502	−	14.0729i	−0.263195	−	0.455867i	−0.967089	+	0.254438i	$0.918110\pi$
$954$	1.90926	+	3.30693i	0.0618145	+	0.107066i
$955$	−4.51821	+	7.82577i	−0.146206	+	0.253236i
$956$	−24.8377			−0.803308
$957$	0.845869	−	1.46509i	0.0273431	−	0.0473596i
$958$	21.0954			0.681563
$959$	−16.1232	−	27.9263i	−0.520646	−	0.901786i
$960$	3.36249			0.108524
$961$	−9.30929	+	16.1242i	−0.300300	+	0.520134i
$962$	18.6499	−	32.3026i	0.601297	−	1.04148i
$963$	0.876590	+	1.51830i	0.0282477	+	0.0489265i
$964$	1.92602	−	3.33597i	0.0620330	−	0.107444i
$965$	25.5614	−	44.2737i	0.822852	−	1.42522i
$966$	3.10235	−	5.37344i	0.0998166	−	0.172887i
$967$	−16.6011	+	28.7540i	−0.533856	+	0.924666i	0.465362	+	0.885121i	$0.345924\pi$
$967$	−16.6011	+	28.7540i	−0.533856	+	0.924666i	−0.999218	+	0.0395454i	$0.987409\pi$
$968$	2.01348	+	3.48745i	0.0647157	+	0.112091i
$969$	−6.01226	+	10.4135i	−0.193142	+	0.334531i
$970$	−14.3824	−	24.9110i	−0.461791	−	0.799845i
$971$	15.8313	−	27.4207i	0.508052	−	0.879972i	−0.491905	−	0.870649i	$-0.663699\pi$
$971$	15.8313	−	27.4207i	0.508052	−	0.879972i	0.999957	−	0.00932250i	$-0.00296749\pi$
$972$	0.500000	−	0.866025i	0.0160375	−	0.0277778i
$973$	14.2375	+	24.6601i	0.456434	+	0.790567i
$974$	20.6286			0.660982
$975$	−18.4531	+	31.9618i	−0.590973	+	1.02360i
$976$	6.69855	+	11.6022i	0.214415	+	0.371379i
$977$	−1.79436	+	3.10793i	−0.0574067	+	0.0994313i	−0.893301	−	0.449460i	$-0.851617\pi$
$977$	−1.79436	+	3.10793i	−0.0574067	+	0.0994313i	0.835894	+	0.548891i	$0.184950\pi$
$978$	−8.57810	−	14.8577i	−0.274297	−	0.475097i
$979$	23.2917			0.744404
$980$	8.01471	−	13.8819i	0.256020	−	0.443440i
$981$	4.27095	+	7.39751i	0.136361	+	0.236184i
$982$	−0.701973	−	1.21585i	−0.0224009	−	0.0387994i
$983$	−26.2023			−0.835725			−0.417862	−	0.908510i	$-0.637221\pi$
$983$	−26.2023			−0.835725			−0.417862	+	0.908510i	$0.637221\pi$
$984$	−2.80175	−	4.85278i	−0.0893167	−	0.154701i
$985$	−21.9470	+	38.0132i	−0.699288	+	1.21120i
$986$	0.490298	−	0.849221i	0.0156143	−	0.0270447i
$987$	−6.14571			−0.195620
$988$	−22.9875	−	39.8155i	−0.731330	−	1.26670i
$989$	−5.46902	+	9.47263i	−0.173905	+	0.301212i
$990$	8.87917			0.282199
$991$	15.3451	+	26.5785i	0.487452	+	0.844292i	0.999896	−	0.0144285i	$-0.00459290\pi$
$991$	15.3451	+	26.5785i	0.487452	+	0.844292i	−0.512443	+	0.858721i	$0.671260\pi$
$992$	−3.52202	−	6.10032i	−0.111824	−	0.193685i
$993$	2.06629	+	3.57892i	0.0655718	+	0.113574i
$994$	11.3164	+	19.6006i	0.358935	+	0.621693i
$995$	−62.9710			−1.99631
$996$	−14.4344			−0.457373
$997$	39.2107			1.24182			0.620908	−	0.783883i	$-0.286764\pi$
$997$	39.2107			1.24182			0.620908	+	0.783883i	$0.286764\pi$
$998$	−9.59184	+	16.6136i	−0.303624	+	0.525893i
$999$	3.18680	−	5.51970i	0.100826	−	0.174635i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1338.2.e.i.1075.7	yes	14
223.39	even	3	inner	1338.2.e.i.931.7	✓	14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1338.2.e.i.931.7	✓	14	223.39	even	3	inner
1338.2.e.i.1075.7	yes	14	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 1338 = 2 \cdot 3 \cdot 223 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1338.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +(0.500000 + 0.866025i) q^{3} +1.00000 q^{4} +(1.68125 - 2.91200i) q^{5} +(0.500000 + 0.866025i) q^{6} +3.43032 q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(1.68125 - 2.91200i) q^{10} +(1.32033 - 2.28687i) q^{11} +(0.500000 + 0.866025i) q^{12} -5.85224 q^{13} +3.43032 q^{14} +3.36249 q^{15} +1.00000 q^{16} +1.53062 q^{17} +(-0.500000 + 0.866025i) q^{18} +(3.92799 + 6.80347i) q^{19} +(1.68125 - 2.91200i) q^{20} +(1.71516 + 2.97075i) q^{21} +(1.32033 - 2.28687i) q^{22} +(-0.904391 - 1.56645i) q^{23} +(0.500000 + 0.866025i) q^{24} +(-3.15318 - 5.46146i) q^{25} -5.85224 q^{26} -1.00000 q^{27} +3.43032 q^{28} +(0.320326 - 0.554821i) q^{29} +3.36249 q^{30} +(-3.52202 - 6.10032i) q^{31} +1.00000 q^{32} +2.64065 q^{33} +1.53062 q^{34} +(5.76722 - 9.98912i) q^{35} +(-0.500000 + 0.866025i) q^{36} +(-3.18680 + 5.51970i) q^{37} +(3.92799 + 6.80347i) q^{38} +(-2.92612 - 5.06819i) q^{39} +(1.68125 - 2.91200i) q^{40} -5.60351 q^{41} +(1.71516 + 2.97075i) q^{42} +(-3.02359 - 5.23702i) q^{43} +(1.32033 - 2.28687i) q^{44} +(1.68125 + 2.91200i) q^{45} +(-0.904391 - 1.56645i) q^{46} +(-0.895792 + 1.55156i) q^{47} +(0.500000 + 0.866025i) q^{48} +4.76712 q^{49} +(-3.15318 - 5.46146i) q^{50} +(0.765311 + 1.32556i) q^{51} -5.85224 q^{52} +(1.90926 - 3.30693i) q^{53} -1.00000 q^{54} +(-4.43958 - 7.68959i) q^{55} +3.43032 q^{56} +(-3.92799 + 6.80347i) q^{57} +(0.320326 - 0.554821i) q^{58} +12.0662 q^{59} +3.36249 q^{60} +(6.69855 + 11.6022i) q^{61} +(-3.52202 - 6.10032i) q^{62} +(-1.71516 + 2.97075i) q^{63} +1.00000 q^{64} +(-9.83905 + 17.0417i) q^{65} +2.64065 q^{66} +(-4.73320 - 8.19815i) q^{67} +1.53062 q^{68} +(0.904391 - 1.56645i) q^{69} +(5.76722 - 9.98912i) q^{70} +(3.29893 + 5.71392i) q^{71} +(-0.500000 + 0.866025i) q^{72} +(-4.03786 + 6.99379i) q^{73} +(-3.18680 + 5.51970i) q^{74} +(3.15318 - 5.46146i) q^{75} +(3.92799 + 6.80347i) q^{76} +(4.52915 - 7.84471i) q^{77} +(-2.92612 - 5.06819i) q^{78} +(-5.82315 + 10.0860i) q^{79} +(1.68125 - 2.91200i) q^{80} +(-0.500000 - 0.866025i) q^{81} -5.60351 q^{82} +(-7.21722 + 12.5006i) q^{83} +(1.71516 + 2.97075i) q^{84} +(2.57335 - 4.45718i) q^{85} +(-3.02359 - 5.23702i) q^{86} +0.640652 q^{87} +(1.32033 - 2.28687i) q^{88} +(4.41021 + 7.63871i) q^{89} +(1.68125 + 2.91200i) q^{90} -20.0751 q^{91} +(-0.904391 - 1.56645i) q^{92} +(3.52202 - 6.10032i) q^{93} +(-0.895792 + 1.55156i) q^{94} +26.4156 q^{95} +(0.500000 + 0.866025i) q^{96} +(4.27730 - 7.40850i) q^{97} +4.76712 q^{98} +(1.32033 + 2.28687i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q + 14 q^{2} + 7 q^{3} + 14 q^{4} + 3 q^{5} + 7 q^{6} + 4 q^{7} + 14 q^{8} - 7 q^{9} + 3 q^{10} + 7 q^{11} + 7 q^{12} - 12 q^{13} + 4 q^{14} + 6 q^{15} + 14 q^{16} + 6 q^{17} - 7 q^{18} - 6 q^{19} + 3 q^{20}+ \cdots + 7 q^{99}+O(q^{100}) \) 14 * q + 14 * q^2 + 7 * q^3 + 14 * q^4 + 3 * q^5 + 7 * q^6 + 4 * q^7 + 14 * q^8 - 7 * q^9 + 3 * q^10 + 7 * q^11 + 7 * q^12 - 12 * q^13 + 4 * q^14 + 6 * q^15 + 14 * q^16 + 6 * q^17 - 7 * q^18 - 6 * q^19 + 3 * q^20 + 2 * q^21 + 7 * q^22 - 14 * q^23 + 7 * q^24 - 16 * q^25 - 12 * q^26 - 14 * q^27 + 4 * q^28 - 7 * q^29 + 6 * q^30 - 19 * q^31 + 14 * q^32 + 14 * q^33 + 6 * q^34 + q^35 - 7 * q^36 - 9 * q^37 - 6 * q^38 - 6 * q^39 + 3 * q^40 + 10 * q^41 + 2 * q^42 + 20 * q^43 + 7 * q^44 + 3 * q^45 - 14 * q^46 + q^47 + 7 * q^48 + 62 * q^49 - 16 * q^50 + 3 * q^51 - 12 * q^52 + 10 * q^53 - 14 * q^54 - 24 * q^55 + 4 * q^56 + 6 * q^57 - 7 * q^58 - 6 * q^59 + 6 * q^60 + 4 * q^61 - 19 * q^62 - 2 * q^63 + 14 * q^64 + 3 * q^65 + 14 * q^66 + 3 * q^67 + 6 * q^68 + 14 * q^69 + q^70 + 31 * q^71 - 7 * q^72 - 45 * q^73 - 9 * q^74 + 16 * q^75 - 6 * q^76 - 14 * q^77 - 6 * q^78 - 41 * q^79 + 3 * q^80 - 7 * q^81 + 10 * q^82 - q^83 + 2 * q^84 - 9 * q^85 + 20 * q^86 - 14 * q^87 + 7 * q^88 - 24 * q^89 + 3 * q^90 + 74 * q^91 - 14 * q^92 + 19 * q^93 + q^94 - 8 * q^95 + 7 * q^96 - 13 * q^97 + 62 * q^98 + 7 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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