LMFDB - Embedded newform 558.2.g.a.439.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [558,2,Mod(211,558)] 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("558.211"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(558, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([2, 2])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 558 = 2 \cdot 3^{2} \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	558.g (of order $3$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [32,-16] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$4.45565243279$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			439.6
Character	$\chi$	$=$	558.439
Dual form			558.2.g.a.211.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.735824 - 1.56798i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.112175 - 0.194293i) q^{5} +(1.72582 + 0.146748i) q^{6} +(1.36938 + 2.37184i) q^{7} +1.00000 q^{8} +(-1.91712 + 2.30752i) q^{9} +(0.112175 + 0.194293i) q^{10} -1.78900 q^{11} +(-0.989999 + 1.42123i) q^{12} +(-2.36086 + 4.08914i) q^{13} -2.73877 q^{14} +(-0.387188 - 0.0329228i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(1.76904 - 3.06407i) q^{17} +(-1.03981 - 2.81404i) q^{18} +(1.48549 - 2.57295i) q^{19} -0.224350 q^{20} +(2.71138 - 3.89243i) q^{21} +(0.894500 - 1.54932i) q^{22} +(4.28596 + 7.42350i) q^{23} +(-0.735824 - 1.56798i) q^{24} +(2.47483 + 4.28654i) q^{25} +(-2.36086 - 4.08914i) q^{26} +(5.02881 + 1.30809i) q^{27} +(1.36938 - 2.37184i) q^{28} +(2.91652 - 5.05156i) q^{29} +(0.222106 - 0.318853i) q^{30} +(-0.472281 + 5.54770i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(1.31639 + 2.80512i) q^{33} +(1.76904 + 3.06407i) q^{34} +0.614442 q^{35} +(2.95693 + 0.506521i) q^{36} +(-5.39234 + 9.33981i) q^{37} +(1.48549 + 2.57295i) q^{38} +(8.14887 + 0.692902i) q^{39} +(0.112175 - 0.194293i) q^{40} +(-1.86216 + 3.22535i) q^{41} +(2.01525 + 4.29434i) q^{42} +(4.34890 + 7.53252i) q^{43} +(0.894500 + 1.54932i) q^{44} +(0.233280 + 0.631329i) q^{45} -8.57192 q^{46} +(3.95276 - 6.84638i) q^{47} +(1.72582 + 0.146748i) q^{48} +(-0.250427 + 0.433752i) q^{49} -4.94967 q^{50} +(-6.10611 - 0.519205i) q^{51} +4.72173 q^{52} +(-1.39044 - 2.40831i) q^{53} +(-3.64724 + 3.70103i) q^{54} +(-0.200681 + 0.347589i) q^{55} +(1.36938 + 2.37184i) q^{56} +(-5.12740 - 0.435985i) q^{57} +(2.91652 + 5.05156i) q^{58} -0.735683 q^{59} +(0.165082 + 0.351776i) q^{60} +(0.690085 - 1.19526i) q^{61} +(-4.56831 - 3.18286i) q^{62} +(-8.09835 - 1.38724i) q^{63} +1.00000 q^{64} +(0.529660 + 0.917397i) q^{65} +(-3.08750 - 0.262531i) q^{66} +(5.77895 - 10.0094i) q^{67} -3.53808 q^{68} +(8.48619 - 12.1827i) q^{69} +(-0.307221 + 0.532123i) q^{70} +(5.76848 + 9.99131i) q^{71} +(-1.91712 + 2.30752i) q^{72} +(-1.13722 - 1.96972i) q^{73} +(-5.39234 - 9.33981i) q^{74} +(4.90016 - 7.03463i) q^{75} -2.97099 q^{76} +(-2.44983 - 4.24323i) q^{77} +(-4.67450 + 6.71067i) q^{78} +(7.08665 + 12.2744i) q^{79} +(0.112175 + 0.194293i) q^{80} +(-1.64926 - 8.84759i) q^{81} +(-1.86216 - 3.22535i) q^{82} -10.9608 q^{83} +(-4.72663 - 0.401908i) q^{84} +(-0.396884 - 0.687424i) q^{85} -8.69780 q^{86} +(-10.0668 - 0.855985i) q^{87} -1.78900 q^{88} -13.3870 q^{89} +(-0.663387 - 0.113638i) q^{90} -12.9317 q^{91} +(4.28596 - 7.42350i) q^{92} +(9.04620 - 3.34160i) q^{93} +(3.95276 + 6.84638i) q^{94} +(-0.333271 - 0.577242i) q^{95} +(-0.989999 + 1.42123i) q^{96} +(6.40336 - 11.0909i) q^{97} +(-0.250427 - 0.433752i) q^{98} +(3.42973 - 4.12814i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 16 q^{2} + 4 q^{3} - 16 q^{4} - q^{5} - 2 q^{6} + q^{7} + 32 q^{8} + 12 q^{9} - q^{10} + 4 q^{11} - 2 q^{12} - 10 q^{13} - 2 q^{14} - 13 q^{15} - 16 q^{16} - 4 q^{17} - 6 q^{18} + 4 q^{19} + 2 q^{20}+ \cdots + 19 q^{99}+O(q^{100}) $ 32 * q - 16 * q^2 + 4 * q^3 - 16 * q^4 - q^5 - 2 * q^6 + q^7 + 32 * q^8 + 12 * q^9 - q^10 + 4 * q^11 - 2 * q^12 - 10 * q^13 - 2 * q^14 - 13 * q^15 - 16 * q^16 - 4 * q^17 - 6 * q^18 + 4 * q^19 + 2 * q^20 + 10 * q^21 - 2 * q^22 - q^23 + 4 * q^24 - 19 * q^25 - 10 * q^26 + 7 * q^27 + q^28 - 3 * q^29 + 14 * q^30 - q^31 - 16 * q^32 - 7 * q^33 - 4 * q^34 - 6 * q^36 - 19 * q^37 + 4 * q^38 + 19 * q^39 - q^40 + 10 * q^41 - 11 * q^42 - 13 * q^43 - 2 * q^44 + 14 * q^45 + 2 * q^46 - 6 * q^47 - 2 * q^48 - 13 * q^49 + 38 * q^50 + 20 * q^51 + 20 * q^52 - 7 * q^53 - 17 * q^54 - 11 * q^55 + q^56 - 5 * q^57 - 3 * q^58 + 12 * q^59 - q^60 + 7 * q^61 + 11 * q^62 - 42 * q^63 + 32 * q^64 - 8 * q^65 + 5 * q^66 - 8 * q^67 + 8 * q^68 + 43 * q^69 + 7 * q^71 + 12 * q^72 + 7 * q^73 - 19 * q^74 - 41 * q^75 - 8 * q^76 - q^77 - 11 * q^78 - 34 * q^79 - q^80 + 10 * q^82 - 28 * q^83 + q^84 + 13 * q^85 + 26 * q^86 - 54 * q^87 + 4 * q^88 + 2 * q^89 - 19 * q^90 + 24 * q^91 - q^92 - 15 * q^93 - 6 * q^94 + 21 * q^95 - 2 * q^96 + 10 * q^97 - 13 * q^98 + 19 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/558\mathbb{Z}\right)^\times$.

$n$	$127$	$497$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$3$	−0.735824	−	1.56798i	−0.424828	−	0.905274i
$3$	−0.735824	−	1.56798i	−0.424828	−	0.905274i
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	0.112175	−	0.194293i	0.0501662	−	0.0868903i	−0.839852	−	0.542816i	$-0.817358\pi$
$5$	0.112175	−	0.194293i	0.0501662	−	0.0868903i	0.890018	+	0.455925i	$0.150692\pi$
$6$	1.72582	+	0.146748i	0.704564	+	0.0599094i
$7$	1.36938	+	2.37184i	0.517579	+	0.896472i	0.999792	+	0.0204184i	$0.00649983\pi$
$7$	1.36938	+	2.37184i	0.517579	+	0.896472i	−0.482213	+	0.876054i	$0.660167\pi$
$8$	1.00000			0.353553
$9$	−1.91712	+	2.30752i	−0.639042	+	0.769172i
$10$	0.112175	+	0.194293i	0.0354728	+	0.0614407i
$11$	−1.78900			−0.539404			−0.269702	−	0.962944i	$-0.586925\pi$
$11$	−1.78900			−0.539404			−0.269702	+	0.962944i	$0.586925\pi$
$12$	−0.989999	+	1.42123i	−0.285788	+	0.410275i
$13$	−2.36086	+	4.08914i	−0.654786	+	1.13412i	0.327162	+	0.944968i	$0.393908\pi$
$13$	−2.36086	+	4.08914i	−0.654786	+	1.13412i	−0.981947	+	0.189154i	$0.939425\pi$
$14$	−2.73877			−0.731967
$15$	−0.387188	−	0.0329228i	−0.0999716	−	0.00850063i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	1.76904	−	3.06407i	0.429056	−	0.743146i	−0.567734	−	0.823212i	$-0.692180\pi$
$17$	1.76904	−	3.06407i	0.429056	−	0.743146i	0.996790	+	0.0800659i	$0.0255131\pi$
$18$	−1.03981	−	2.81404i	−0.245084	−	0.663275i
$19$	1.48549	−	2.57295i	0.340796	−	0.590276i	−0.643785	−	0.765207i	$-0.722637\pi$
$19$	1.48549	−	2.57295i	0.340796	−	0.590276i	0.984581	+	0.174931i	$0.0559702\pi$
$20$	−0.224350			−0.0501662
$21$	2.71138	−	3.89243i	0.591671	−	0.849397i
$22$	0.894500	−	1.54932i	0.190708	−	0.330316i
$23$	4.28596	+	7.42350i	0.893684	+	1.54791i	0.835425	+	0.549605i	$0.185222\pi$
$23$	4.28596	+	7.42350i	0.893684	+	1.54791i	0.0582596	+	0.998301i	$0.481445\pi$
$24$	−0.735824	−	1.56798i	−0.150200	−	0.320063i
$25$	2.47483	+	4.28654i	0.494967	+	0.857307i
$26$	−2.36086	−	4.08914i	−0.463003	−	0.801946i
$27$	5.02881	+	1.30809i	0.967795	+	0.251742i
$28$	1.36938	−	2.37184i	0.258789	−	0.448236i
$29$	2.91652	−	5.05156i	0.541585	−	0.938052i	−0.457229	−	0.889349i	$-0.651158\pi$
$29$	2.91652	−	5.05156i	0.541585	−	0.938052i	0.998813	−	0.0487028i	$-0.0155087\pi$
$30$	0.222106	−	0.318853i	0.0405508	−	0.0582144i
$31$	−0.472281	+	5.54770i	−0.0848241	+	0.996396i
$31$	−0.472281	+	5.54770i	−0.0848241	+	0.996396i
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$	1.31639	+	2.80512i	0.229154	+	0.488308i
$34$	1.76904	+	3.06407i	0.303388	+	0.525484i
$35$	0.614442			0.103860
$36$	2.95693	+	0.506521i	0.492822	+	0.0844201i
$37$	−5.39234	+	9.33981i	−0.886496	+	1.53546i	−0.0425065	+	0.999096i	$0.513534\pi$
$37$	−5.39234	+	9.33981i	−0.886496	+	1.53546i	−0.843989	+	0.536360i	$0.819799\pi$
$38$	1.48549	+	2.57295i	0.240979	+	0.417388i
$39$	8.14887	+	0.692902i	1.30486	+	0.110953i
$40$	0.112175	−	0.194293i	0.0177364	−	0.0307204i
$41$	−1.86216	+	3.22535i	−0.290820	+	0.503716i	−0.974004	−	0.226531i	$-0.927262\pi$
$41$	−1.86216	+	3.22535i	−0.290820	+	0.503716i	0.683184	+	0.730247i	$0.260595\pi$
$42$	2.01525	+	4.29434i	0.310960	+	0.662630i
$43$	4.34890	+	7.53252i	0.663201	+	1.14870i	0.979770	+	0.200129i	$0.0641360\pi$
$43$	4.34890	+	7.53252i	0.663201	+	1.14870i	−0.316568	+	0.948570i	$0.602531\pi$
$44$	0.894500	+	1.54932i	0.134851	+	0.233569i
$45$	0.233280	+	0.631329i	0.0347754	+	0.0941130i
$46$	−8.57192			−1.26386
$47$	3.95276	−	6.84638i	0.576570	−	0.998648i	−0.419300	−	0.907848i	$-0.637724\pi$
$47$	3.95276	−	6.84638i	0.576570	−	0.998648i	0.995869	−	0.0907998i	$-0.0289423\pi$
$48$	1.72582	+	0.146748i	0.249101	+	0.0211812i
$49$	−0.250427	+	0.433752i	−0.0357753	+	0.0619646i
$50$	−4.94967			−0.699989
$51$	−6.10611	−	0.519205i	−0.855026	−	0.0727033i
$52$	4.72173			0.654786
$53$	−1.39044	−	2.40831i	−0.190992	−	0.330807i	0.754587	−	0.656199i	$-0.227837\pi$
$53$	−1.39044	−	2.40831i	−0.190992	−	0.330807i	−0.945579	+	0.325392i	$0.894504\pi$
$54$	−3.64724	+	3.70103i	−0.496327	+	0.503647i
$55$	−0.200681	+	0.347589i	−0.0270598	+	0.0468690i
$56$	1.36938	+	2.37184i	0.182992	+	0.316951i
$57$	−5.12740	−	0.435985i	−0.679141	−	0.0577477i
$58$	2.91652	+	5.05156i	0.382958	+	0.663303i
$59$	−0.735683			−0.0957777			−0.0478889	−	0.998853i	$-0.515249\pi$
$59$	−0.735683			−0.0957777			−0.0478889	+	0.998853i	$0.515249\pi$
$60$	0.165082	+	0.351776i	0.0213120	+	0.0454141i
$61$	0.690085	−	1.19526i	0.0883564	−	0.153038i	−0.818460	−	0.574563i	$-0.805172\pi$
$61$	0.690085	−	1.19526i	0.0883564	−	0.153038i	0.906816	+	0.421526i	$0.138505\pi$
$62$	−4.56831	−	3.18286i	−0.580176	−	0.404223i
$63$	−8.09835	−	1.38724i	−1.02030	−	0.174776i
$64$	1.00000			0.125000
$65$	0.529660	+	0.917397i	0.0656962	+	0.113789i
$66$	−3.08750	−	0.262531i	−0.380044	−	0.0323154i
$67$	5.77895	−	10.0094i	0.706012	−	1.22285i	−0.260314	−	0.965524i	$-0.583826\pi$
$67$	5.77895	−	10.0094i	0.706012	−	1.22285i	0.966325	−	0.257324i	$-0.0828407\pi$
$68$	−3.53808			−0.429056
$69$	8.48619	−	12.1827i	1.02162	−	1.46662i
$70$	−0.307221	+	0.532123i	−0.0367200	+	0.0636008i
$71$	5.76848	+	9.99131i	0.684593	+	1.18575i	0.973565	+	0.228412i	$0.0733534\pi$
$71$	5.76848	+	9.99131i	0.684593	+	1.18575i	−0.288972	+	0.957338i	$0.593313\pi$
$72$	−1.91712	+	2.30752i	−0.225935	+	0.271943i
$73$	−1.13722	−	1.96972i	−0.133101	−	0.230538i	0.791769	−	0.610820i	$-0.209160\pi$
$73$	−1.13722	−	1.96972i	−0.133101	−	0.230538i	−0.924870	+	0.380282i	$0.875827\pi$
$74$	−5.39234	−	9.33981i	−0.626847	−	1.08573i
$75$	4.90016	−	7.03463i	0.565822	−	0.812289i
$76$	−2.97099			−0.340796
$77$	−2.44983	−	4.24323i	−0.279184	−	0.483560i
$78$	−4.67450	+	6.71067i	−0.529283	+	0.759834i
$79$	7.08665	+	12.2744i	0.797310	+	1.38098i	0.921362	+	0.388706i	$0.127078\pi$
$79$	7.08665	+	12.2744i	0.797310	+	1.38098i	−0.124051	+	0.992276i	$0.539589\pi$
$80$	0.112175	+	0.194293i	0.0125415	+	0.0217226i
$81$	−1.64926	−	8.84759i	−0.183252	−	0.983066i
$82$	−1.86216	−	3.22535i	−0.205641	−	0.356181i
$83$	−10.9608			−1.20310			−0.601551	−	0.798834i	$-0.705450\pi$
$83$	−10.9608			−1.20310			−0.601551	+	0.798834i	$0.705450\pi$
$84$	−4.72663	−	0.401908i	−0.515718	−	0.0438517i
$85$	−0.396884	−	0.687424i	−0.0430482	−	0.0745616i
$86$	−8.69780			−0.937908
$87$	−10.0668	−	0.855985i	−1.07927	−	0.0917712i
$88$	−1.78900			−0.190708
$89$	−13.3870			−1.41902			−0.709509	−	0.704697i	$-0.751083\pi$
$89$	−13.3870			−1.41902			−0.709509	+	0.704697i	$0.751083\pi$
$90$	−0.663387	−	0.113638i	−0.0699271	−	0.0119785i
$91$	−12.9317			−1.35561
$92$	4.28596	−	7.42350i	0.446842	−	0.773953i
$93$	9.04620	−	3.34160i	0.938047	−	0.346508i
$94$	3.95276	+	6.84638i	0.407696	+	0.706151i
$95$	−0.333271	−	0.577242i	−0.0341928	−	0.0592237i
$96$	−0.989999	+	1.42123i	−0.101041	+	0.145054i
$97$	6.40336	−	11.0909i	0.650162	−	1.12611i	−0.332921	−	0.942955i	$-0.608034\pi$
$97$	6.40336	−	11.0909i	0.650162	−	1.12611i	0.983083	−	0.183160i	$-0.0586325\pi$
$98$	−0.250427	−	0.433752i	−0.0252969	−	0.0438156i
$99$	3.42973	−	4.12814i	0.344701	−	0.414894i
$100$	2.47483	−	4.28654i	0.247483	−	0.428654i
$101$	−5.60050	+	9.70035i	−0.557270	+	0.965221i	0.440453	+	0.897776i	$0.354818\pi$
$101$	−5.60050	+	9.70035i	−0.557270	+	0.965221i	−0.997723	+	0.0674448i	$0.978515\pi$
$102$	3.50270	−	5.02844i	0.346819	−	0.497890i
$103$	−8.34800	+	14.4592i	−0.822553	+	1.42470i	0.0812228	+	0.996696i	$0.474117\pi$
$103$	−8.34800	+	14.4592i	−0.822553	+	1.42470i	−0.903775	+	0.428007i	$0.859216\pi$
$104$	−2.36086	+	4.08914i	−0.231502	+	0.400973i
$105$	−0.452122	−	0.963434i	−0.0441226	−	0.0940215i
$106$	2.78088			0.270103
$107$	1.71895	−	2.97731i	0.166177	−	0.287827i	−0.770896	−	0.636961i	$-0.780191\pi$
$107$	1.71895	−	2.97731i	0.166177	−	0.287827i	0.937073	+	0.349134i	$0.113524\pi$
$108$	−1.38157	−	5.00912i	−0.132941	−	0.482003i
$109$	1.05340			0.100897			0.0504486	−	0.998727i	$-0.483935\pi$
$109$	1.05340			0.100897			0.0504486	+	0.998727i	$0.483935\pi$
$110$	−0.200681	−	0.347589i	−0.0191342	−	0.0331414i
$111$	18.6125	+	1.58263i	1.76662	+	0.150216i
$112$	−2.73877			−0.258789
$113$	8.77559	−	15.1998i	0.825539	−	1.42987i	−0.0759685	−	0.997110i	$-0.524205\pi$
$113$	8.77559	−	15.1998i	0.825539	−	1.42987i	0.901507	−	0.432764i	$-0.142462\pi$
$114$	2.94128	−	4.22247i	0.275476	−	0.395470i
$115$	1.92311			0.179331
$116$	−5.83304			−0.541585
$117$	−4.90968	−	13.2871i	−0.453900	−	1.22839i
$118$	0.367841	−	0.637120i	0.0338625	−	0.0586516i
$119$	9.68999			0.888280
$120$	−0.387188	−	0.0329228i	−0.0353453	−	0.00300543i
$121$	−7.79948			−0.709044
$122$	0.690085	+	1.19526i	0.0624774	+	0.108214i
$123$	6.42751	+	0.546534i	0.579549	+	0.0492794i
$124$	5.04059	−	2.36484i	0.452658	−	0.212369i
$125$	2.23221			0.199655
$126$	5.25056	−	6.31975i	0.467757	−	0.563008i
$127$	−2.79724	+	4.84496i	−0.248215	+	0.429921i	−0.963031	−	0.269392i	$-0.913177\pi$
$127$	−2.79724	+	4.84496i	−0.248215	+	0.429921i	0.714816	+	0.699313i	$0.246511\pi$
$128$	−0.500000	+	0.866025i	−0.0441942	+	0.0765466i
$129$	8.61081	−	12.3616i	0.758140	−	1.08838i
$130$	−1.05932			−0.0929084
$131$	−4.10066			−0.358276			−0.179138	−	0.983824i	$-0.557331\pi$
$131$	−4.10066			−0.358276			−0.179138	+	0.983824i	$0.557331\pi$
$132$	1.77111	−	2.54258i	0.154155	−	0.221304i
$133$	8.13685			0.705555
$134$	5.77895	+	10.0094i	0.499226	+	0.864684i
$135$	0.818258	−	0.830326i	0.0704244	−	0.0714631i
$136$	1.76904	−	3.06407i	0.151694	−	0.262742i
$137$	−3.70226			−0.316305			−0.158153	−	0.987415i	$-0.550554\pi$
$137$	−3.70226			−0.316305			−0.158153	+	0.987415i	$0.550554\pi$
$138$	6.30743	+	13.4406i	0.536924	+	1.14414i
$139$	0.308876	+	0.534988i	0.0261985	+	0.0453771i	0.878827	−	0.477140i	$-0.158326\pi$
$139$	0.308876	+	0.534988i	0.0261985	+	0.0453771i	−0.852629	+	0.522517i	$0.824993\pi$
$140$	−0.307221	−	0.532123i	−0.0259649	−	0.0449726i
$141$	−13.6435	−	1.16012i	−1.14899	−	0.0976994i
$142$	−11.5370			−0.968161
$143$	4.22358	−	7.31546i	0.353194	−	0.611750i
$144$	−1.03981	−	2.81404i	−0.0866505	−	0.234503i
$145$	−0.654321	−	1.13332i	−0.0543384	−	0.0941169i
$146$	2.27443			0.188233
$147$	0.864385	+	0.0734991i	0.0712933	+	0.00606210i
$148$	10.7847			0.886496
$149$	−22.8854			−1.87485			−0.937423	−	0.348192i	$-0.886796\pi$
$149$	−22.8854			−1.87485			−0.937423	+	0.348192i	$0.886796\pi$
$150$	3.64209	+	7.76098i	0.297375	+	0.633681i
$151$	5.86565	−	10.1596i	0.477340	−	0.826777i	−0.522323	−	0.852748i	$-0.674934\pi$
$151$	5.86565	−	10.1596i	0.477340	−	0.826777i	0.999663	+	0.0259706i	$0.00826763\pi$
$152$	1.48549	−	2.57295i	0.120490	−	0.208694i
$153$	3.67892	+	9.95630i	0.297423	+	0.804919i
$154$	4.89965			0.394825
$155$	1.02490	+	0.714073i	0.0823219	+	0.0573557i
$156$	−3.47436	−	7.40358i	−0.278172	−	0.592761i
$157$	−8.39260	−	14.5364i	−0.669802	−	1.16013i	−0.977959	−	0.208796i	$-0.933045\pi$
$157$	−8.39260	−	14.5364i	−0.669802	−	1.16013i	0.308157	−	0.951336i	$-0.400288\pi$
$158$	−14.1733			−1.12757
$159$	−2.75307	+	3.95228i	−0.218332	+	0.313436i
$160$	−0.224350			−0.0177364
$161$	−11.7383	+	20.3312i	−0.925104	+	1.60233i
$162$	8.48687	+	2.99549i	0.666792	+	0.235348i
$163$	4.45804			0.349181			0.174591	−	0.984641i	$-0.444140\pi$
$163$	4.45804			0.349181			0.174591	+	0.984641i	$0.444140\pi$
$164$	3.72432			0.290820
$165$	0.692679	+	0.0588988i	0.0539250	+	0.00458527i
$166$	5.48039	−	9.49232i	0.425361	−	0.736747i
$167$	−2.98695			−0.231138			−0.115569	−	0.993299i	$-0.536869\pi$
$167$	−2.98695			−0.231138			−0.115569	+	0.993299i	$0.536869\pi$
$168$	2.71138	−	3.89243i	0.209187	−	0.300307i
$169$	−4.64736	−	8.04946i	−0.357489	−	0.619189i
$170$	0.793769			0.0608793
$171$	3.08925	+	8.36047i	0.236241	+	0.639341i
$172$	4.34890	−	7.53252i	0.331601	−	0.574349i
$173$	15.7592			1.19815			0.599077	−	0.800692i	$-0.295534\pi$
$173$	15.7592			1.19815			0.599077	+	0.800692i	$0.295534\pi$
$174$	5.77471	−	8.29011i	0.437779	−	0.628472i
$175$	−6.77800	+	11.7398i	−0.512368	+	0.887448i
$176$	0.894500	−	1.54932i	0.0674254	−	0.116784i
$177$	0.541333	+	1.15354i	0.0406891	+	0.0867051i
$178$	6.69349	−	11.5935i	0.501698	−	0.868967i
$179$	7.69486	−	13.3279i	0.575141	−	0.996173i	−0.420885	−	0.907114i	$-0.638281\pi$
$179$	7.69486	−	13.3279i	0.575141	−	0.996173i	0.996026	−	0.0890594i	$-0.0283861\pi$
$180$	0.430107	−	0.517691i	0.0320583	−	0.0385864i
$181$	−4.56933	−	7.91432i	−0.339636	−	0.588267i	0.644728	−	0.764412i	$-0.276971\pi$
$181$	−4.56933	−	7.91432i	−0.339636	−	0.588267i	−0.984364	+	0.176145i	$0.943637\pi$
$182$	6.46586	−	11.1992i	0.479281	−	0.830140i
$183$	−2.38193	−	0.202537i	−0.176077	−	0.0149719i
$184$	4.28596	+	7.42350i	0.315965	+	0.547268i
$185$	1.20977	+	2.09539i	0.0889442	+	0.154056i
$186$	−1.62918	+	9.50504i	−0.119458	+	0.696943i
$187$	−3.16481	+	5.48162i	−0.231434	+	0.400856i
$188$	−7.90552			−0.576570
$189$	3.78379	+	13.7188i	0.275230	+	0.997897i
$190$	0.666541			0.0483560
$191$	−3.16267			−0.228843			−0.114421	−	0.993432i	$-0.536501\pi$
$191$	−3.16267			−0.228843			−0.114421	+	0.993432i	$0.536501\pi$
$192$	−0.735824	−	1.56798i	−0.0531036	−	0.113159i
$193$	4.12497			0.296922			0.148461	−	0.988918i	$-0.452568\pi$
$193$	4.12497			0.296922			0.148461	+	0.988918i	$0.452568\pi$
$194$	6.40336	+	11.0909i	0.459734	+	0.796283i
$195$	1.04872	−	1.50554i	0.0751007	−	0.107814i
$196$	0.500854			0.0357753
$197$	−2.14925	−	3.72261i	−0.153128	−	0.265225i	0.779248	−	0.626716i	$-0.215601\pi$
$197$	−2.14925	−	3.72261i	−0.153128	−	0.265225i	−0.932376	+	0.361491i	$0.882268\pi$
$198$	1.86021	+	5.03431i	0.132199	+	0.357773i
$199$	−2.73087	−	4.73000i	−0.193586	−	0.335301i	0.752850	−	0.658192i	$-0.228678\pi$
$199$	−2.73087	−	4.73000i	−0.193586	−	0.335301i	−0.946436	+	0.322891i	$0.895345\pi$
$200$	2.47483	+	4.28654i	0.174997	+	0.303104i
$201$	−19.9469	−	1.69609i	−1.40695	−	0.119633i
$202$	−5.60050	−	9.70035i	−0.394050	−	0.682514i
$203$	15.9754			1.12125
$204$	2.60341	+	5.54765i	0.182275	+	0.388413i
$205$	0.417775	+	0.723608i	0.0291787	+	0.0505390i
$206$	−8.34800	−	14.4592i	−0.581633	−	1.00742i
$207$	−25.3466	−	4.34185i	−1.76171	−	0.301780i
$208$	−2.36086	−	4.08914i	−0.163696	−	0.283531i
$209$	−2.65755	+	4.60301i	−0.183826	+	0.318397i
$210$	1.06042	+	0.0901679i	0.0731759	+	0.00622218i
$211$	10.7402			0.739384			0.369692	−	0.929154i	$-0.379463\pi$
$211$	10.7402			0.739384			0.369692	+	0.929154i	$0.379463\pi$
$212$	−1.39044	+	2.40831i	−0.0954958	+	0.165404i
$213$	11.4216	−	16.3967i	0.782594	−	1.12348i
$214$	1.71895	+	2.97731i	0.117505	+	0.203524i
$215$	1.95135			0.133081
$216$	5.02881	+	1.30809i	0.342167	+	0.0890041i
$217$	−13.8050	+	6.47676i	−0.937145	+	0.439671i
$218$	−0.526699	+	0.912269i	−0.0356725	+	0.0617866i
$219$	−2.25169	+	3.23250i	−0.152155	+	0.218432i
$220$	0.401362			0.0270598
$221$	8.35293	+	14.4677i	0.561879	+	0.973203i
$222$	−10.6768	+	15.3276i	−0.716582	+	1.02872i
$223$	6.87299	+	11.9044i	0.460249	+	0.797175i	0.998973	−	0.0453075i	$-0.0144268\pi$
$223$	6.87299	+	11.9044i	0.460249	+	0.797175i	−0.538724	+	0.842482i	$0.681093\pi$
$224$	1.36938	−	2.37184i	0.0914958	−	0.158475i
$225$	−14.6358	−	2.50711i	−0.975721	−	0.167141i
$226$	8.77559	+	15.1998i	0.583744	+	1.01107i
$227$	12.9311			0.858267			0.429133	−	0.903241i	$-0.358819\pi$
$227$	12.9311			0.858267			0.429133	+	0.903241i	$0.358819\pi$
$228$	2.18613	+	4.65845i	0.144780	+	0.308514i
$229$	−24.6591			−1.62952			−0.814758	−	0.579801i	$-0.803130\pi$
$229$	−24.6591			−1.62952			−0.814758	+	0.579801i	$0.803130\pi$
$230$	−0.961554	+	1.66546i	−0.0634030	+	0.109817i
$231$	−4.85065	+	6.96355i	−0.319149	+	0.458168i
$232$	2.91652	−	5.05156i	0.191479	−	0.331651i
$233$	16.0453			1.05116			0.525581	−	0.850744i	$-0.323848\pi$
$233$	16.0453			1.05116			0.525581	+	0.850744i	$0.323848\pi$
$234$	13.9618	+	2.39165i	0.912713	+	0.156347i
$235$	−0.886802	−	1.53599i	−0.0578486	−	0.100197i
$236$	0.367841	+	0.637120i	0.0239444	+	0.0414730i
$237$	14.0315	−	20.1436i	0.911447	−	1.30846i
$238$	−4.84500	+	8.39178i	−0.314054	+	0.543958i
$239$	3.31957	−	5.74966i	0.214725	−	0.371915i	−0.738462	−	0.674295i	$-0.764448\pi$
$239$	3.31957	−	5.74966i	0.214725	−	0.371915i	0.953188	+	0.302380i	$0.0977811\pi$
$240$	0.222106	−	0.318853i	0.0143369	−	0.0205819i
$241$	−9.00343	−	15.5944i	−0.579962	−	1.00452i	−0.995483	−	0.0949403i	$-0.969734\pi$
$241$	−9.00343	−	15.5944i	−0.579962	−	1.00452i	0.415521	−	0.909584i	$-0.363599\pi$
$242$	3.89974	−	6.75455i	0.250685	−	0.434199i
$243$	−12.6593	+	9.09629i	−0.812094	+	0.583527i
$244$	−1.38017			−0.0883564
$245$	0.0561832	+	0.0973122i	0.00358942	+	0.00621705i
$246$	−3.68707	+	5.29312i	−0.235079	+	0.337477i
$247$	7.01410	+	12.1488i	0.446297	+	0.773008i
$248$	−0.472281	+	5.54770i	−0.0299898	+	0.352279i
$249$	8.06522	+	17.1863i	0.511112	+	1.08914i
$250$	−1.11610	+	1.93315i	−0.0705886	+	0.122263i
$251$	−6.79471	+	11.7688i	−0.428878	+	0.742839i	−0.996774	−	0.0802615i	$-0.974424\pi$
$251$	−6.79471	+	11.7688i	−0.428878	+	0.742839i	0.567895	+	0.823101i	$0.307758\pi$
$252$	2.84779	+	7.70700i	0.179394	+	0.485495i
$253$	−7.66758	−	13.2806i	−0.482056	−	0.834946i
$254$	−2.79724	−	4.84496i	−0.175514	−	0.304000i
$255$	−0.785830	+	1.12813i	−0.0492106	+	0.0706462i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	5.42227	−	9.39164i	0.338232	−	0.585835i	−0.645868	−	0.763449i	$-0.723505\pi$
$257$	5.42227	−	9.39164i	0.338232	−	0.585835i	0.984100	+	0.177614i	$0.0568379\pi$
$258$	6.40006	+	13.6380i	0.398450	+	0.849064i
$259$	−29.5368			−1.83533
$260$	0.529660	−	0.917397i	0.0328481	−	0.0568946i
$261$	6.06523	+	16.4144i	0.375428	+	1.01603i
$262$	2.05033	−	3.55128i	0.126670	−	0.219399i
$263$	−13.3671	+	23.1525i	−0.824252	+	1.42765i	0.0782384	+	0.996935i	$0.475070\pi$
$263$	−13.3671	+	23.1525i	−0.824252	+	1.42765i	−0.902490	+	0.430711i	$0.858263\pi$
$264$	1.31639	+	2.80512i	0.0810182	+	0.172643i
$265$	−0.623890			−0.0383253
$266$	−4.06843	+	7.04672i	−0.249451	+	0.432062i
$267$	9.85047	+	20.9905i	0.602839	+	1.28460i
$268$	−11.5579			−0.706012
$269$	3.70614	+	6.41922i	0.225967	+	0.391387i	0.956609	−	0.291374i	$-0.0941124\pi$
$269$	3.70614	+	6.41922i	0.225967	+	0.391387i	−0.730642	+	0.682761i	$0.760779\pi$
$270$	0.309954	+	1.12380i	0.0188632	+	0.0683920i
$271$	6.12866			0.372290			0.186145	−	0.982522i	$-0.440401\pi$
$271$	6.12866			0.372290			0.186145	+	0.982522i	$0.440401\pi$
$272$	1.76904	+	3.06407i	0.107264	+	0.185787i
$273$	9.51548	+	20.2767i	0.575903	+	1.22720i
$274$	1.85113	−	3.20625i	0.111831	−	0.193697i
$275$	−4.42747	−	7.66861i	−0.266987	−	0.462435i
$276$	−14.7936	−	1.25791i	−0.890471	−	0.0757172i
$277$	−2.79415	+	4.83961i	−0.167884	+	0.290784i	−0.937676	−	0.347511i	$-0.887027\pi$
$277$	−2.79415	+	4.83961i	−0.167884	+	0.290784i	0.769792	+	0.638295i	$0.220360\pi$
$278$	−0.617751			−0.0370503
$279$	−11.8960	−	11.7254i	−0.712194	−	0.701983i
$280$	0.614442			0.0367200
$281$	−0.195272	+	0.338221i	−0.0116489	+	0.0201766i	−0.871791	−	0.489878i	$-0.837041\pi$
$281$	−0.195272	+	0.338221i	−0.0116489	+	0.0201766i	0.860142	+	0.510054i	$0.170375\pi$
$282$	7.82646	−	11.2356i	0.466059	−	0.669070i
$283$	−3.41935	−	5.92249i	−0.203259	−	0.352056i	0.746317	−	0.665590i	$-0.231820\pi$
$283$	−3.41935	−	5.92249i	−0.203259	−	0.352056i	−0.949577	+	0.313535i	$0.898487\pi$
$284$	5.76848	−	9.99131i	0.342296	−	0.592875i
$285$	−0.659875	+	0.947310i	−0.0390876	+	0.0561138i
$286$	4.22358	+	7.31546i	0.249746	+	0.432572i
$287$	−10.2000			−0.602090
$288$	2.95693	+	0.506521i	0.174239	+	0.0298470i
$289$	2.24098	+	3.88149i	0.131822	+	0.228323i
$290$	1.30864			0.0768461
$291$	−22.1021	−	1.87935i	−1.29565	−	0.110170i
$292$	−1.13722	+	1.96972i	−0.0665506	+	0.115269i
$293$	22.4628			1.31229			0.656144	−	0.754635i	$-0.272186\pi$
$293$	22.4628			1.31229			0.656144	+	0.754635i	$0.272186\pi$
$294$	−0.495845	+	0.711830i	−0.0289182	+	0.0415148i
$295$	−0.0825252	+	0.142938i	−0.00480480	+	0.00832216i
$296$	−5.39234	+	9.33981i	−0.313424	+	0.542866i
$297$	−8.99653	−	2.34017i	−0.522032	−	0.135790i
$298$	11.4427	−	19.8194i	0.662858	−	1.14810i
$299$	−40.4743			−2.34069
$300$	−8.54225	−	0.726352i	−0.493187	−	0.0419359i
$301$	−11.9106	+	20.6298i	−0.686518	+	1.18908i
$302$	5.86565	+	10.1596i	0.337530	+	0.584620i
$303$	19.3309	+	1.64372i	1.11053	+	0.0944292i
$304$	1.48549	+	2.57295i	0.0851990	+	0.147569i
$305$	−0.154821	−	0.268157i	−0.00886500	−	0.0153546i
$306$	−10.4619	−	1.79211i	−0.598065	−	0.102448i
$307$	15.2405	−	26.3973i	0.869819	−	1.50657i	0.00763772	−	0.999971i	$-0.497569\pi$
$307$	15.2405	−	26.3973i	0.869819	−	1.50657i	0.862181	−	0.506600i	$-0.169098\pi$
$308$	−2.44983	+	4.24323i	−0.139592	+	0.241780i
$309$	28.8143	+	2.45010i	1.63919	+	0.139381i
$310$	−1.13086	+	0.530552i	−0.0642283	+	0.0301333i
$311$	8.10219	+	14.0334i	0.459433	+	0.795761i	0.998931	−	0.0462258i	$-0.0147194\pi$
$311$	8.10219	+	14.0334i	0.459433	+	0.795761i	−0.539498	+	0.841987i	$0.681386\pi$
$312$	8.14887	+	0.692902i	0.461339	+	0.0392279i
$313$	5.78194	+	10.0146i	0.326815	+	0.566059i	0.981878	−	0.189515i	$-0.0606914\pi$
$313$	5.78194	+	10.0146i	0.326815	+	0.566059i	−0.655063	+	0.755574i	$0.727358\pi$
$314$	16.7852			0.947244
$315$	−1.17796	+	1.41784i	−0.0663707	+	0.0798860i
$316$	7.08665	−	12.2744i	0.398655	−	0.690491i
$317$	2.97721	+	5.15668i	0.167217	+	0.289628i	0.937440	−	0.348146i	$-0.113189\pi$
$317$	2.97721	+	5.15668i	0.167217	+	0.289628i	−0.770223	+	0.637774i	$0.779855\pi$
$318$	−2.04624	−	4.36037i	−0.114747	−	0.244517i
$319$	−5.21765	+	9.03724i	−0.292133	+	0.505988i
$320$	0.112175	−	0.194293i	0.00627077	−	0.0108613i
$321$	−5.93320	−	0.504503i	−0.331159	−	0.0281586i
$322$	−11.7383	−	20.3312i	−0.654147	−	1.13302i
$323$	−5.25581	−	9.10332i	−0.292441	−	0.506522i
$324$	−6.83761	+	5.85210i	−0.379867	+	0.325117i
$325$	−23.3710			−1.29639
$326$	−2.22902	+	3.86078i	−0.123454	+	0.213829i
$327$	−0.775115	−	1.65171i	−0.0428640	−	0.0913396i
$328$	−1.86216	+	3.22535i	−0.102821	+	0.178090i
$329$	21.6514			1.19368
$330$	−0.397348	+	0.570428i	−0.0218733	+	0.0314011i
$331$	23.3496			1.28341			0.641705	−	0.766952i	$-0.278227\pi$
$331$	23.3496			1.28341			0.641705	+	0.766952i	$0.278227\pi$
$332$	5.48039	+	9.49232i	0.300776	+	0.520959i
$333$	−11.2140	−	30.3485i	−0.614522	−	1.66309i
$334$	1.49348	−	2.58678i	0.0817194	−	0.141542i
$335$	−1.29651	−	2.24562i	−0.0708358	−	0.122691i
$336$	2.01525	+	4.29434i	0.109941	+	0.234275i
$337$	10.6393	+	18.4279i	0.579561	+	1.00383i	0.995530	+	0.0944506i	$0.0301094\pi$
$337$	10.6393	+	18.4279i	0.579561	+	1.00383i	−0.415968	+	0.909379i	$0.636557\pi$
$338$	9.29471			0.505566
$339$	−30.2902	−	2.57559i	−1.64514	−	0.139887i
$340$	−0.396884	+	0.687424i	−0.0215241	+	0.0372808i
$341$	0.844909	−	9.92483i	0.0457544	−	0.537459i
$342$	−8.78501	−	1.50487i	−0.475039	−	0.0813739i
$343$	17.7997			0.961091
$344$	4.34890	+	7.53252i	0.234477	+	0.406126i
$345$	−1.41507	−	3.01540i	−0.0761848	−	0.162344i
$346$	−7.87962	+	13.6479i	−0.423611	+	0.733716i
$347$	11.0811			0.594863			0.297431	−	0.954743i	$-0.403870\pi$
$347$	11.0811			0.594863			0.297431	+	0.954743i	$0.403870\pi$
$348$	4.29210	+	9.14610i	0.230080	+	0.490282i
$349$	10.6149	−	18.3855i	0.568201	−	0.984154i	−0.428543	−	0.903522i	$-0.640973\pi$
$349$	10.6149	−	18.3855i	0.568201	−	0.984154i	0.996744	−	0.0806321i	$-0.0256939\pi$
$350$	−6.77800	−	11.7398i	−0.362299	−	0.627521i
$351$	−17.2213	+	17.4753i	−0.919204	+	0.932761i
$352$	0.894500	+	1.54932i	0.0476770	+	0.0825790i
$353$	6.68694	+	11.5821i	0.355910	+	0.616454i	0.987273	−	0.159033i	$-0.0508377\pi$
$353$	6.68694	+	11.5821i	0.355910	+	0.616454i	−0.631364	+	0.775487i	$0.717504\pi$
$354$	−1.26966	−	0.107960i	−0.0674816	−	0.00573799i
$355$	2.58832			0.137374
$356$	6.69349	+	11.5935i	0.354754	+	0.614453i
$357$	−7.13013	−	15.1937i	−0.377367	−	0.804137i
$358$	7.69486	+	13.3279i	0.406686	+	0.704401i
$359$	3.50147	+	6.06472i	0.184800	+	0.320084i	0.943509	−	0.331346i	$-0.107503\pi$
$359$	3.50147	+	6.06472i	0.184800	+	0.320084i	−0.758709	+	0.651430i	$0.774169\pi$
$360$	0.233280	+	0.631329i	0.0122949	+	0.0332740i
$361$	5.08661	+	8.81027i	0.267716	+	0.463698i
$362$	9.13867			0.480318
$363$	5.73905	+	12.2294i	0.301222	+	0.641879i
$364$	6.46586	+	11.1992i	0.338903	+	0.586997i
$365$	−0.510269			−0.0267087
$366$	1.36637	−	1.96154i	0.0714211	−	0.102532i
$367$	11.4584			0.598122			0.299061	−	0.954234i	$-0.403327\pi$
$367$	11.4584			0.598122			0.299061	+	0.954234i	$0.403327\pi$
$368$	−8.57192			−0.446842
$369$	−3.87257	−	10.4804i	−0.201598	−	0.545586i
$370$	−2.41954			−0.125786
$371$	3.80809	−	6.59581i	0.197706	−	0.342437i
$372$	−7.41701	−	6.16343i	−0.384554	−	0.319559i
$373$	−14.8554	−	25.7303i	−0.769183	−	1.33226i	−0.938006	−	0.346618i	$-0.887330\pi$
$373$	−14.8554	−	25.7303i	−0.769183	−	1.33226i	0.168823	−	0.985646i	$-0.446003\pi$
$374$	−3.16481	−	5.48162i	−0.163649	−	0.283448i
$375$	−1.64251	−	3.50006i	−0.0848190	−	0.180742i
$376$	3.95276	−	6.84638i	0.203848	−	0.353075i
$377$	13.7710	+	23.8521i	0.709244	+	1.22845i
$378$	−13.7727	−	3.58255i	−0.708393	−	0.184266i
$379$	−9.90644	+	17.1585i	−0.508860	+	0.881371i	0.491088	+	0.871110i	$0.336599\pi$
$379$	−9.90644	+	17.1585i	−0.508860	+	0.881371i	−0.999947	+	0.0102606i	$0.996734\pi$
$380$	−0.333271	+	0.577242i	−0.0170964	+	0.0296119i
$381$	9.65508	+	0.820976i	0.494645	+	0.0420599i
$382$	1.58133	−	2.73895i	0.0809081	−	0.140137i
$383$	2.14961	−	3.72324i	0.109840	−	0.190249i	−0.805865	−	0.592099i	$-0.798299\pi$
$383$	2.14961	−	3.72324i	0.109840	−	0.190249i	0.915705	+	0.401850i	$0.131633\pi$
$384$	1.72582	+	0.146748i	0.0880705	+	0.00748868i
$385$	−1.09924			−0.0560223
$386$	−2.06248	+	3.57233i	−0.104978	+	0.181827i
$387$	−25.7188	−	4.40562i	−1.30736	−	0.223950i
$388$	−12.8067			−0.650162
$389$	12.9883	+	22.4965i	0.658535	+	1.14062i	0.980995	+	0.194034i	$0.0621571\pi$
$389$	12.9883	+	22.4965i	0.658535	+	1.14062i	−0.322459	+	0.946583i	$0.604510\pi$
$390$	0.779473	+	1.66099i	0.0394701	+	0.0841076i
$391$	30.3282			1.53376
$392$	−0.250427	+	0.433752i	−0.0126485	+	0.0219078i
$393$	3.01737	+	6.42976i	0.152206	+	0.324338i
$394$	4.29850			0.216555
$395$	3.17978			0.159992
$396$	−5.28995	−	0.906165i	−0.265830	−	0.0455365i
$397$	16.3125	−	28.2541i	0.818703	−	1.41803i	−0.0879354	−	0.996126i	$-0.528027\pi$
$397$	16.3125	−	28.2541i	0.818703	−	1.41803i	0.906638	−	0.421909i	$-0.138640\pi$
$398$	5.46173			0.273772
$399$	−5.98730	−	12.7584i	−0.299740	−	0.638720i
$400$	−4.94967			−0.247483
$401$	−16.1852	−	28.0336i	−0.808249	−	1.39993i	−0.914075	−	0.405544i	$-0.867082\pi$
$401$	−16.1852	−	28.0336i	−0.808249	−	1.39993i	0.105826	−	0.994385i	$-0.466251\pi$
$402$	11.4423	−	16.4265i	0.570691	−	0.819278i
$403$	−21.5703	−	15.0286i	−1.07449	−	0.748627i
$404$	11.2010			0.557270
$405$	−1.90403	−	0.672038i	−0.0946120	−	0.0333939i
$406$	−7.98768	+	13.8351i	−0.396422	+	0.686623i
$407$	9.64690	−	16.7089i	0.478179	−	0.828230i
$408$	−6.10611	−	0.519205i	−0.302297	−	0.0257045i
$409$	14.0840			0.696408			0.348204	−	0.937419i	$-0.386792\pi$
$409$	14.0840			0.696408			0.348204	+	0.937419i	$0.386792\pi$
$410$	−0.835550			−0.0412649
$411$	2.72421	+	5.80507i	0.134376	+	0.286343i
$412$	16.6960			0.822553
$413$	−1.00743	−	1.74492i	−0.0495725	−	0.0858621i
$414$	16.4334	−	19.7798i	0.807659	−	0.972126i
$415$	−1.22953	+	2.12960i	−0.0603550	+	0.104538i
$416$	4.72173			0.231502
$417$	0.611573	−	0.877968i	0.0299489	−	0.0429943i
$418$	−2.65755	−	4.60301i	−0.129985	−	0.225141i
$419$	−4.78040	−	8.27989i	−0.233538	−	0.404499i	0.725309	−	0.688423i	$-0.241697\pi$
$419$	−4.78040	−	8.27989i	−0.233538	−	0.404499i	−0.958847	+	0.283924i	$0.908364\pi$
$420$	−0.608297	+	0.873266i	−0.0296819	+	0.0426110i
$421$	19.4558			0.948217			0.474108	−	0.880467i	$-0.342770\pi$
$421$	19.4558			0.948217			0.474108	+	0.880467i	$0.342770\pi$
$422$	−5.37008	+	9.30126i	−0.261412	+	0.452778i
$423$	8.22021	+	22.2464i	0.399680	+	1.08166i
$424$	−1.39044	−	2.40831i	−0.0675257	−	0.116958i
$425$	17.5123			0.849473
$426$	8.48918	+	18.0897i	0.411302	+	0.876451i
$427$	3.77997			0.182925
$428$	−3.43790			−0.166177
$429$	−14.5783	−	1.23960i	−0.703848	−	0.0598485i
$430$	−0.975675	+	1.68992i	−0.0470513	+	0.0814952i
$431$	17.2586	−	29.8928i	0.831318	−	1.43989i	−0.0656750	−	0.997841i	$-0.520920\pi$
$431$	17.2586	−	29.8928i	0.831318	−	1.43989i	0.896993	−	0.442044i	$-0.145747\pi$
$432$	−3.64724	+	3.70103i	−0.175478	+	0.178066i
$433$	−2.01297			−0.0967373			−0.0483687	−	0.998830i	$-0.515402\pi$
$433$	−2.01297			−0.0967373			−0.0483687	+	0.998830i	$0.515402\pi$
$434$	1.29347	−	15.1939i	0.0620884	−	0.729329i
$435$	−1.29555	+	1.85989i	−0.0621171	+	0.0891747i
$436$	−0.526699	−	0.912269i	−0.0252243	−	0.0436898i
$437$	25.4671			1.21826
$438$	−1.67358	−	3.56627i	−0.0799669	−	0.170403i
$439$	0.356224			0.0170017			0.00850083	−	0.999964i	$-0.497294\pi$
$439$	0.356224			0.0170017			0.00850083	+	0.999964i	$0.497294\pi$
$440$	−0.200681	+	0.347589i	−0.00956708	+	0.0165707i
$441$	−0.520790	−	1.40942i	−0.0247995	−	0.0671153i
$442$	−16.7059			−0.794617
$443$	−16.0429			−0.762223			−0.381112	−	0.924529i	$-0.624459\pi$
$443$	−16.0429			−0.762223			−0.381112	+	0.924529i	$0.624459\pi$
$444$	−7.93564	−	16.9102i	−0.376609	−	0.802522i
$445$	−1.50168	+	2.60099i	−0.0711866	+	0.123299i
$446$	−13.7460			−0.650891
$447$	16.8396	+	35.8839i	0.796488	+	1.69725i
$448$	1.36938	+	2.37184i	0.0646973	+	0.112059i
$449$	2.96595			0.139972			0.0699859	−	0.997548i	$-0.477705\pi$
$449$	2.96595			0.139972			0.0699859	+	0.997548i	$0.477705\pi$
$450$	9.48913	−	11.4214i	0.447322	−	0.538412i
$451$	3.33140	−	5.77015i	0.156870	−	0.271706i
$452$	−17.5512			−0.825539
$453$	−20.2462	−	1.72154i	−0.951248	−	0.0808850i
$454$	−6.46555	+	11.1987i	−0.303443	+	0.525579i
$455$	−1.45061	+	2.51254i	−0.0680059	+	0.117790i
$456$	−5.12740	−	0.435985i	−0.240113	−	0.0204169i
$457$	0.0613990	−	0.106346i	0.00287213	−	0.00497467i	−0.864586	−	0.502485i	$-0.832419\pi$
$457$	0.0613990	−	0.106346i	0.00287213	−	0.00497467i	0.867458	+	0.497511i	$0.165752\pi$
$458$	12.3295	−	21.3554i	0.576121	−	0.997871i
$459$	12.9042	−	13.0946i	0.602319	−	0.611202i
$460$	−0.961554	−	1.66546i	−0.0448327	−	0.0776525i
$461$	4.52857	−	7.84371i	0.210916	−	0.365318i	−0.741085	−	0.671411i	$-0.765689\pi$
$461$	4.52857	−	7.84371i	0.210916	−	0.365318i	0.952002	+	0.306093i	$0.0990219\pi$
$462$	−3.60529	−	7.68256i	−0.167733	−	0.357425i
$463$	−10.3734	−	17.9672i	−0.482091	−	0.835005i	0.517698	−	0.855563i	$-0.326789\pi$
$463$	−10.3734	−	17.9672i	−0.482091	−	0.835005i	−0.999789	+	0.0205579i	$0.993456\pi$
$464$	2.91652	+	5.05156i	0.135396	+	0.234513i
$465$	0.365507	−	2.13245i	0.0169500	−	0.0988902i
$466$	−8.02264	+	13.8956i	−0.371642	+	0.643702i
$467$	−9.66564			−0.447273			−0.223636	−	0.974673i	$-0.571793\pi$
$467$	−9.66564			−0.447273			−0.223636	+	0.974673i	$0.571793\pi$
$468$	−9.05214	+	10.8955i	−0.418435	+	0.503643i
$469$	31.6544			1.46167
$470$	1.77360			0.0818102
$471$	−16.6173	+	23.8557i	−0.765686	+	1.09921i
$472$	−0.735683			−0.0338625
$473$	−7.78018	−	13.4757i	−0.357733	−	0.619612i
$474$	10.4291	+	22.2235i	0.479023	+	1.02076i
$475$	14.7054			0.674730
$476$	−4.84500	−	8.39178i	−0.222070	−	0.384637i
$477$	8.22287	+	1.40857i	0.376499	+	0.0644941i
$478$	3.31957	+	5.74966i	0.151834	+	0.262983i
$479$	−3.35560	−	5.81208i	−0.153321	−	0.265561i	0.779125	−	0.626868i	$-0.215664\pi$
$479$	−3.35560	−	5.81208i	−0.153321	−	0.265561i	−0.932447	+	0.361308i	$0.882330\pi$
$480$	0.165082	+	0.351776i	0.00753493	+	0.0160563i
$481$	−25.4612	−	44.1001i	−1.16093	−	2.01079i
$482$	18.0069			0.820190
$483$	40.5163	+	3.44512i	1.84355	+	0.156758i
$484$	3.89974	+	6.75455i	0.177261	+	0.307025i
$485$	−1.43659	−	2.48825i	−0.0652323	−	0.112986i
$486$	−1.54798	−	15.5114i	−0.0702176	−	0.703612i
$487$	−16.6092	−	28.7680i	−0.752635	−	1.30360i	−0.946541	−	0.322582i	$-0.895449\pi$
$487$	−16.6092	−	28.7680i	−0.752635	−	1.30360i	0.193906	−	0.981020i	$-0.437884\pi$
$488$	0.690085	−	1.19526i	0.0312387	−	0.0541070i
$489$	−3.28034	−	6.99013i	−0.148342	−	0.316104i
$490$	−0.112366			−0.00507620
$491$	−15.1123	+	26.1753i	−0.682008	+	1.18127i	0.292359	+	0.956309i	$0.405560\pi$
$491$	−15.1123	+	26.1753i	−0.682008	+	1.18127i	−0.974367	+	0.224964i	$0.927774\pi$
$492$	−2.74044	−	5.83966i	−0.123549	−	0.263272i
$493$	−10.3189	−	17.8729i	−0.464740	−	0.804953i
$494$	−14.0282			−0.631159
$495$	−0.417338	−	1.12945i	−0.0187580	−	0.0507649i
$496$	−4.56831	−	3.18286i	−0.205123	−	0.142914i
$497$	−15.7985	+	27.3639i	−0.708661	+	1.22744i
$498$	−18.9164	−	1.60847i	−0.847663	−	0.0720772i
$499$	−4.78644			−0.214270			−0.107135	−	0.994244i	$-0.534168\pi$
$499$	−4.78644			−0.214270			−0.107135	+	0.994244i	$0.534168\pi$
$500$	−1.11610	−	1.93315i	−0.0499137	−	0.0864530i
$501$	2.19787	+	4.68349i	0.0981938	+	0.209243i
$502$	−6.79471	−	11.7688i	−0.303263	−	0.525267i
$503$	12.9266	−	22.3896i	0.576370	−	0.998302i	−0.419521	−	0.907745i	$-0.637802\pi$
$503$	12.9266	−	22.3896i	0.576370	−	0.998302i	0.995891	−	0.0905566i	$-0.0288646\pi$
$504$	−8.09835	−	1.38724i	−0.360729	−	0.0617927i
$505$	1.25647	+	2.17627i	0.0559122	+	0.0968428i
$506$	15.3352			0.681731
$507$	−9.20175	+	13.2100i	−0.408664	+	0.586675i
$508$	5.59448			0.248215
$509$	4.29896	−	7.44601i	0.190548	−	0.330039i	−0.754884	−	0.655858i	$-0.772307\pi$
$509$	4.29896	−	7.44601i	0.190548	−	0.330039i	0.945432	+	0.325820i	$0.105640\pi$
$510$	−0.584074	−	1.24461i	−0.0258632	−	0.0551124i
$511$	3.11457	−	5.39460i	0.137781	−	0.238643i
$512$	1.00000			0.0441942
$513$	10.8359	−	10.9957i	0.478417	−	0.485473i
$514$	5.42227	+	9.39164i	0.239166	+	0.414248i
$515$	1.87287	+	3.24391i	0.0825286	+	0.142944i
$516$	−15.0109	−	1.27638i	−0.660817	−	0.0561896i
$517$	−7.07149	+	12.2482i	−0.311004	+	0.538674i
$518$	14.7684	−	25.5796i	0.648886	−	1.12390i
$519$	−11.5960	−	24.7102i	−0.509010	−	1.08466i
$520$	0.529660	+	0.917397i	0.0232271	+	0.0402305i
$521$	−12.5385	+	21.7173i	−0.549321	+	0.951453i	0.449000	+	0.893532i	$0.351780\pi$
$521$	−12.5385	+	21.7173i	−0.549321	+	0.951453i	−0.998321	+	0.0579208i	$0.981553\pi$
$522$	−17.2479	−	2.95456i	−0.754920	−	0.129317i
$523$	18.6718			0.816460			0.408230	−	0.912879i	$-0.366146\pi$
$523$	18.6718			0.816460			0.408230	+	0.912879i	$0.366146\pi$
$524$	2.05033	+	3.55128i	0.0895691	+	0.155138i
$525$	23.3952	+	1.98931i	1.02105	+	0.0868206i
$526$	−13.3671	−	23.1525i	−0.582834	−	1.00950i
$527$	16.1631	+	11.2612i	0.704074	+	0.490546i
$528$	−3.08750	−	0.262531i	−0.134366	−	0.0114252i
$529$	−25.2389	+	43.7150i	−1.09734	+	1.90065i
$530$	0.311945	−	0.540305i	0.0135500	−	0.0234693i
$531$	1.41040	−	1.69760i	0.0612060	−	0.0736696i
$532$	−4.06843	−	7.04672i	−0.176389	−	0.305514i
$533$	−8.79261	−	15.2292i	−0.380850	−	0.659652i
$534$	−23.1036	−	1.96451i	−0.999789	−	0.0850125i
$535$	−0.385646	−	0.667958i	−0.0166729	−	0.0288784i
$536$	5.77895	−	10.0094i	0.249613	−	0.432342i
$537$	−26.5599	−	2.25840i	−1.14615	−	0.0974573i
$538$	−7.41228			−0.319566
$539$	0.448013	−	0.775982i	0.0192973	−	0.0334239i
$540$	−1.12821	−	0.293469i	−0.0485505	−	0.0126289i
$541$	−16.3304	+	28.2850i	−0.702097	+	1.21607i	0.265632	+	0.964075i	$0.414419\pi$
$541$	−16.3304	+	28.2850i	−0.702097	+	1.21607i	−0.967729	+	0.251993i	$0.918914\pi$
$542$	−3.06433	+	5.30758i	−0.131624	+	0.227980i
$543$	−9.04727	+	12.9882i	−0.388255	+	0.557376i
$544$	−3.53808			−0.151694
$545$	0.118165	−	0.204667i	0.00506162	−	0.00876699i
$546$	−22.3179	−	1.89770i	−0.955116	−	0.0812140i
$547$	−6.43449			−0.275119			−0.137559	−	0.990494i	$-0.543926\pi$
$547$	−6.43449			−0.275119			−0.137559	+	0.990494i	$0.543926\pi$
$548$	1.85113	+	3.20625i	0.0790763	+	0.136964i
$549$	1.43511	+	3.88385i	0.0612489	+	0.165759i
$550$	8.85495			0.377576
$551$	−8.66496	−	15.0081i	−0.369140	−	0.639368i
$552$	8.48619	−	12.1827i	0.361196	−	0.518530i
$553$	−19.4087	+	33.6168i	−0.825342	+	1.42953i
$554$	−2.79415	−	4.83961i	−0.118712	−	0.205615i
$555$	2.39534	−	3.43873i	0.101677	−	0.145966i
$556$	0.308876	−	0.534988i	0.0130992	−	0.0226886i
$557$	33.7425			1.42972			0.714858	−	0.699269i	$-0.246491\pi$
$557$	33.7425			1.42972			0.714858	+	0.699269i	$0.246491\pi$
$558$	16.1025	−	4.43951i	0.681673	−	0.187940i
$559$	−41.0687			−1.73702
$560$	−0.307221	+	0.532123i	−0.0129825	+	0.0224863i
$561$	10.9238	+	0.928858i	0.461204	+	0.0392164i
$562$	−0.195272	−	0.338221i	−0.00823705	−	0.0142670i
$563$	8.89487	−	15.4064i	0.374874	−	0.649301i	−0.615434	−	0.788188i	$-0.711019\pi$
$563$	8.89487	−	15.4064i	0.374874	−	0.649301i	0.990308	+	0.138888i	$0.0443527\pi$
$564$	5.81708	+	12.3957i	0.244943	+	0.521953i
$565$	−1.96880	−	3.41007i	−0.0828282	−	0.143463i
$566$	6.83871			0.287452
$567$	18.7266	−	16.0276i	0.786445	−	0.673094i
$568$	5.76848	+	9.99131i	0.242040	+	0.419226i
$569$	−45.2192			−1.89569			−0.947843	−	0.318737i	$-0.896741\pi$
$569$	−45.2192			−1.89569			−0.947843	+	0.318737i	$0.896741\pi$
$570$	−0.490457	−	1.04512i	−0.0205430	−	0.0437754i
$571$	1.55123	−	2.68681i	0.0649170	−	0.112439i	−0.831740	−	0.555165i	$-0.812655\pi$
$571$	1.55123	−	2.68681i	0.0649170	−	0.112439i	0.896657	+	0.442726i	$0.145988\pi$
$572$	−8.44717			−0.353194
$573$	2.32717	+	4.95900i	0.0972189	+	0.207165i
$574$	5.10002	−	8.83350i	0.212871	−	0.368703i
$575$	−21.2141	+	36.7438i	−0.884688	+	1.53232i
$576$	−1.91712	+	2.30752i	−0.0798802	+	0.0961465i
$577$	7.64425	−	13.2402i	0.318234	−	0.551198i	−0.661885	−	0.749605i	$-0.730243\pi$
$577$	7.64425	−	13.2402i	0.318234	−	0.551198i	0.980120	+	0.198407i	$0.0635768\pi$
$578$	−4.48196			−0.186425
$579$	−3.03525	−	6.46787i	−0.126141	−	0.268796i
$580$	−0.654321	+	1.13332i	−0.0271692	+	0.0470585i
$581$	−15.0095	−	25.9973i	−0.622700	−	1.07855i
$582$	12.6786	−	18.2013i	0.525546	−	0.754469i
$583$	2.48750	+	4.30847i	0.103022	+	0.178439i
$584$	−1.13722	−	1.96972i	−0.0470584	−	0.0815075i
$585$	−3.13233	−	0.536567i	−0.129506	−	0.0221843i
$586$	−11.2314	+	19.4533i	−0.463964	+	0.803609i
$587$	19.8677	−	34.4118i	0.820027	−	1.42033i	−0.0856346	−	0.996327i	$-0.527292\pi$
$587$	19.8677	−	34.4118i	0.820027	−	1.42033i	0.905661	−	0.424002i	$-0.139375\pi$
$588$	−0.368540	−	0.785329i	−0.0151984	−	0.0323864i
$589$	13.5724	+	9.45623i	0.559241	+	0.389637i
$590$	−0.0825252	−	0.142938i	−0.00339751	−	0.00588466i
$591$	−4.25551	+	6.10917i	−0.175048	+	0.251298i
$592$	−5.39234	−	9.33981i	−0.221624	−	0.383864i
$593$	19.0789			0.783475			0.391738	−	0.920077i	$-0.371874\pi$
$593$	19.0789			0.783475			0.391738	+	0.920077i	$0.371874\pi$
$594$	6.52491	−	6.62114i	0.267720	−	0.271669i
$595$	1.08697	−	1.88269i	0.0445616	−	0.0771830i
$596$	11.4427	+	19.8194i	0.468712	+	0.811832i
$597$	−5.40711	+	7.76239i	−0.221298	+	0.317694i
$598$	20.2371	−	35.0517i	0.827558	−	1.43337i
$599$	7.11725	−	12.3274i	0.290803	−	0.503685i	−0.683197	−	0.730234i	$-0.739411\pi$
$599$	7.11725	−	12.3274i	0.290803	−	0.503685i	0.974000	+	0.226549i	$0.0727443\pi$
$600$	4.90016	−	7.03463i	0.200048	−	0.287188i
$601$	−3.91930	−	6.78843i	−0.159872	−	0.276906i	0.774951	−	0.632022i	$-0.217775\pi$
$601$	−3.91930	−	6.78843i	−0.159872	−	0.276906i	−0.934822	+	0.355116i	$0.884441\pi$
$602$	−11.9106	−	20.6298i	−0.485441	−	0.840809i
$603$	12.0180	+	32.5244i	0.489410	+	1.32450i
$604$	−11.7313			−0.477340
$605$	−0.874906	+	1.51538i	−0.0355700	+	0.0616091i
$606$	−11.0890	+	15.9192i	−0.450459	+	0.646674i
$607$	11.9645	−	20.7231i	0.485623	−	0.841123i	−0.514241	−	0.857646i	$-0.671926\pi$
$607$	11.9645	−	20.7231i	0.485623	−	0.841123i	0.999863	+	0.0165227i	$0.00525959\pi$
$608$	−2.97099			−0.120490
$609$	−11.7551	−	25.0490i	−0.476339	−	1.01504i
$610$	0.309641			0.0125370
$611$	18.6639	+	32.3268i	0.755059	+	1.30780i
$612$	6.78295	−	8.16419i	0.274184	−	0.330018i
$613$	18.3904	−	31.8532i	0.742783	−	1.28654i	−0.208441	−	0.978035i	$-0.566839\pi$
$613$	18.3904	−	31.8532i	0.742783	−	1.28654i	0.951224	−	0.308502i	$-0.0998277\pi$
$614$	15.2405	+	26.3973i	0.615055	+	1.06531i
$615$	0.827194	−	1.18751i	0.0333557	−	0.0478851i
$616$	−2.44983	−	4.24323i	−0.0987064	−	0.170964i
$617$	−33.1858			−1.33601			−0.668005	−	0.744157i	$-0.732851\pi$
$617$	−33.1858			−1.33601			−0.668005	+	0.744157i	$0.732851\pi$
$618$	−16.5290	+	23.7289i	−0.664894	+	0.954516i
$619$	11.7191	−	20.2981i	0.471032	−	0.815851i	−0.528419	−	0.848983i	$-0.677215\pi$
$619$	11.7191	−	20.2981i	0.471032	−	0.815851i	0.999451	+	0.0331329i	$0.0105485\pi$
$620$	0.105956	−	1.24463i	0.00425530	−	0.0499854i
$621$	11.8427	+	42.9378i	0.475230	+	1.72303i
$622$	−16.2044			−0.649736
$623$	−18.3319	−	31.7518i	−0.734453	−	1.27211i
$624$	−4.67450	+	6.71067i	−0.187130	+	0.268642i
$625$	−12.1238	+	20.9990i	−0.484951	+	0.839959i
$626$	−11.5639			−0.462186
$627$	9.17292	+	0.779978i	0.366331	+	0.0311493i
$628$	−8.39260	+	14.5364i	−0.334901	+	0.580066i
$629$	19.0786	+	33.0450i	0.760712	+	1.31759i
$630$	−0.638901	−	1.72906i	−0.0254544	−	0.0688875i
$631$	−2.50285	−	4.33506i	−0.0996367	−	0.172576i	0.811898	−	0.583800i	$-0.198435\pi$
$631$	−2.50285	−	4.33506i	−0.0996367	−	0.172576i	−0.911534	+	0.411224i	$0.865101\pi$
$632$	7.08665	+	12.2744i	0.281892	+	0.488251i
$633$	−7.90288	−	16.8404i	−0.314111	−	0.669345i
$634$	−5.95443			−0.236480
$635$	0.627560	+	1.08697i	0.0249040	+	0.0431349i
$636$	4.79931	+	0.408087i	0.190305	+	0.0161817i
$637$	−1.18245	−	2.04806i	−0.0468503	−	0.0811471i
$638$	−5.21765	−	9.03724i	−0.206569	−	0.357788i
$639$	−34.1140	−	5.84371i	−1.34953	−	0.231174i
$640$	0.112175	+	0.194293i	0.00443410	+	0.00768009i
$641$	−18.8549			−0.744726			−0.372363	−	0.928087i	$-0.621452\pi$
$641$	−18.8549			−0.744726			−0.372363	+	0.928087i	$0.621452\pi$
$642$	3.40351	−	4.88605i	0.134326	−	0.192837i
$643$	9.95142	+	17.2364i	0.392446	+	0.679736i	0.992772	−	0.120020i	$-0.0382958\pi$
$643$	9.95142	+	17.2364i	0.392446	+	0.679736i	−0.600326	+	0.799755i	$0.704962\pi$
$644$	23.4765			0.925104
$645$	−1.43585	−	3.05968i	−0.0565366	−	0.120475i
$646$	10.5116			0.413574
$647$	−13.7789			−0.541705			−0.270852	−	0.962621i	$-0.587306\pi$
$647$	−13.7789			−0.541705			−0.270852	+	0.962621i	$0.587306\pi$
$648$	−1.64926	−	8.84759i	−0.0647892	−	0.347566i
$649$	1.31614			0.0516628
$650$	11.6855	−	20.2399i	0.458343	−	0.793873i
$651$	20.3135	+	16.8802i	0.796148	+	0.661588i
$652$	−2.22902	−	3.86078i	−0.0872953	−	0.151200i
$653$	6.86535	+	11.8911i	0.268662	+	0.465336i	0.968517	−	0.248949i	$-0.0800852\pi$
$653$	6.86535	+	11.8911i	0.268662	+	0.465336i	−0.699855	+	0.714285i	$0.746752\pi$
$654$	1.81798	+	0.154583i	0.0710885	+	0.00604469i
$655$	−0.459991	+	0.796728i	−0.0179733	+	0.0311308i
$656$	−1.86216	−	3.22535i	−0.0727051	−	0.125929i
$657$	6.72534	+	1.15205i	0.262381	+	0.0449457i
$658$	−10.8257	+	18.7507i	−0.422030	+	0.730977i
$659$	7.21984	−	12.5051i	0.281245	−	0.487131i	−0.690447	−	0.723383i	$-0.742586\pi$
$659$	7.21984	−	12.5051i	0.281245	−	0.487131i	0.971692	+	0.236253i	$0.0759193\pi$
$660$	−0.295332	−	0.629327i	−0.0114958	−	0.0244965i
$661$	4.97137	−	8.61066i	0.193364	−	0.334916i	−0.752999	−	0.658022i	$-0.771394\pi$
$661$	4.97137	−	8.61066i	0.193364	−	0.334916i	0.946363	+	0.323106i	$0.104727\pi$
$662$	−11.6748	+	20.2213i	−0.453754	+	0.785925i
$663$	16.5388	−	23.7429i	0.642313	−	0.922099i
$664$	−10.9608			−0.425361
$665$	0.912751	−	1.58093i	0.0353950	−	0.0613059i
$666$	31.8896	+	5.46267i	1.23570	+	0.211674i
$667$	50.0004			1.93602
$668$	1.49348	+	2.58678i	0.0577844	+	0.100085i
$669$	13.6085	−	19.5362i	0.526135	−	0.755314i
$670$	2.59301			0.100177
$671$	−1.23456	+	2.13832i	−0.0476597	+	0.0825491i
$672$	−4.72663	−	0.401908i	−0.182334	−	0.0155039i
$673$	−11.7409			−0.452580			−0.226290	−	0.974060i	$-0.572660\pi$
$673$	−11.7409			−0.452580			−0.226290	+	0.974060i	$0.572660\pi$
$674$	−21.2787			−0.819624
$675$	6.83830	+	24.7935i	0.263206	+	0.954301i
$676$	−4.64736	+	8.04946i	−0.178744	+	0.309595i
$677$	−15.5831			−0.598908			−0.299454	−	0.954111i	$-0.596804\pi$
$677$	−15.5831			−0.598908			−0.299454	+	0.954111i	$0.596804\pi$
$678$	17.3757	−	24.9443i	0.667308	−	0.957981i
$679$	35.0746			1.34604
$680$	−0.396884	−	0.687424i	−0.0152198	−	0.0263615i
$681$	−9.51502	−	20.2757i	−0.364616	−	0.776967i
$682$	8.17270	+	5.69413i	0.312949	+	0.218039i
$683$	−38.0819			−1.45717			−0.728583	−	0.684958i	$-0.759821\pi$
$683$	−38.0819			−1.45717			−0.728583	+	0.684958i	$0.759821\pi$
$684$	5.69576	−	6.85561i	0.217783	−	0.262131i
$685$	−0.415301	+	0.719322i	−0.0158678	+	0.0274839i
$686$	−8.89983	+	15.4150i	−0.339797	+	0.588546i
$687$	18.1447	+	38.6649i	0.692265	+	1.47516i
$688$	−8.69780			−0.331601
$689$	13.1306			0.500234
$690$	3.31895	+	0.282212i	0.126350	+	0.0107436i
$691$	−17.5904			−0.669170			−0.334585	−	0.942366i	$-0.608596\pi$
$691$	−17.5904			−0.669170			−0.334585	+	0.942366i	$0.608596\pi$
$692$	−7.87962	−	13.6479i	−0.299538	−	0.518816i
$693$	14.4879	+	2.48178i	0.550351	+	0.0942749i
$694$	−5.54053	+	9.59648i	−0.210316	+	0.364278i
$695$	0.138592			0.00525711
$696$	−10.0668	−	0.855985i	−0.381581	−	0.0324460i
$697$	6.58847	+	11.4116i	0.249556	+	0.432244i
$698$	10.6149	+	18.3855i	0.401779	+	0.695902i
$699$	−11.8065	−	25.1587i	−0.446563	−	0.951589i
$700$	13.5560			0.512368
$701$	−16.3743	+	28.3611i	−0.618448	+	1.07118i	0.371321	+	0.928505i	$0.378905\pi$
$701$	−16.3743	+	28.3611i	−0.618448	+	1.07118i	−0.989769	+	0.142679i	$0.954428\pi$
$702$	−6.52338	−	23.6517i	−0.246209	−	0.892676i
$703$	16.0206	+	27.7485i	0.604228	+	1.04655i
$704$	−1.78900			−0.0674254
$705$	−1.75586	+	2.52070i	−0.0661297	+	0.0949352i
$706$	−13.3739			−0.503332
$707$	−30.6769			−1.15373
$708$	0.728325	−	1.04558i	0.0273721	−	0.0392952i
$709$	18.2831	−	31.6673i	0.686637	−	1.18929i	−0.286283	−	0.958145i	$-0.592420\pi$
$709$	18.2831	−	31.6673i	0.686637	−	1.18929i	0.972919	−	0.231145i	$-0.0742470\pi$
$710$	−1.29416	+	2.24155i	−0.0485689	+	0.0841238i
$711$	−41.9095	−	7.17907i	−1.57173	−	0.269236i
$712$	−13.3870			−0.501698
$713$	−43.2075	+	20.2712i	−1.61813	+	0.759164i
$714$	16.7232	+	1.42198i	0.625851	+	0.0532164i
$715$	−0.947560	−	1.64122i	−0.0354367	−	0.0613782i
$716$	−15.3897			−0.575141
$717$	−11.4580	−	0.974278i	−0.427906	−	0.0363851i
$718$	−7.00294			−0.261347
$719$	6.97255	−	12.0768i	0.260032	−	0.450389i	−0.706218	−	0.707995i	$-0.749600\pi$
$719$	6.97255	−	12.0768i	0.260032	−	0.450389i	0.966250	+	0.257605i	$0.0829334\pi$
$720$	−0.663387	−	0.113638i	−0.0247230	−	0.00423503i
$721$	−45.7265			−1.70294
$722$	−10.1732			−0.378608
$723$	−17.8268	+	25.5920i	−0.662985	+	0.951775i
$724$	−4.56933	+	7.91432i	−0.169818	+	0.294133i
$725$	28.8716			1.07227
$726$	−13.4605	−	1.14455i	−0.499567	−	0.0424784i
$727$	21.7643	+	37.6968i	0.807191	+	1.39810i	0.914802	+	0.403903i	$0.132347\pi$
$727$	21.7643	+	37.6968i	0.807191	+	1.39810i	−0.107610	+	0.994193i	$0.534320\pi$
$728$	−12.9317			−0.479281
$729$	23.5778	+	13.1562i	0.873252	+	0.487268i
$730$	0.255134	−	0.441906i	0.00944295	−	0.0163557i
$731$	30.7736			1.13820
$732$	1.01556	+	2.16408i	0.0375363	+	0.0799867i
$733$	6.33597	−	10.9742i	0.234024	−	0.405342i	−0.724964	−	0.688786i	$-0.758144\pi$
$733$	6.33597	−	10.9742i	0.234024	−	0.405342i	0.958989	+	0.283444i	$0.0914771\pi$
$734$	−5.72919	+	9.92324i	−0.211468	+	0.366274i
$735$	0.111243	−	0.159699i	0.00410325	−	0.00589058i
$736$	4.28596	−	7.42350i	0.157983	−	0.273634i
$737$	−10.3385	+	17.9069i	−0.380825	+	0.659608i
$738$	11.0125	+	1.88644i	0.405377	+	0.0694409i
$739$	16.2768	+	28.1922i	0.598751	+	1.03707i	0.993006	+	0.118066i	$0.0376695\pi$
$739$	16.2768	+	28.1922i	0.598751	+	1.03707i	−0.394254	+	0.919001i	$0.628997\pi$
$740$	1.20977	−	2.09539i	0.0444721	−	0.0770279i
$741$	13.8879	−	19.9373i	0.510185	−	0.732417i
$742$	3.80809	+	6.59581i	0.139800	+	0.242140i
$743$	−13.2807	−	23.0029i	−0.487222	−	0.843894i	0.512670	−	0.858586i	$-0.328657\pi$
$743$	−13.2807	−	23.0029i	−0.487222	−	0.843894i	−0.999892	+	0.0146920i	$0.995323\pi$
$744$	9.04620	−	3.34160i	0.331650	−	0.122509i
$745$	−2.56717	+	4.44647i	−0.0940538	+	0.162906i
$746$	29.7108			1.08779
$747$	21.0132	−	25.2922i	0.768833	−	0.925393i
$748$	6.32963			0.231434
$749$	9.41561			0.344039
$750$	3.85239	+	0.327571i	0.140670	+	0.0119612i
$751$	45.9117			1.67534			0.837671	−	0.546175i	$-0.183917\pi$
$751$	45.9117			1.67534			0.837671	+	0.546175i	$0.183917\pi$
$752$	3.95276	+	6.84638i	0.144142	+	0.249662i
$753$	23.4529	+	1.99421i	0.854673	+	0.0726732i
$754$	−27.5420			−1.00302
$755$	−1.31596	−	2.27931i	−0.0478926	−	0.0829525i
$756$	9.98895	−	10.1363i	0.363295	−	0.368653i
$757$	22.5384	+	39.0376i	0.819171	+	1.41885i	0.906294	+	0.422648i	$0.138899\pi$
$757$	22.5384	+	39.0376i	0.819171	+	1.41885i	−0.0871233	+	0.996198i	$0.527767\pi$
$758$	−9.90644	−	17.1585i	−0.359818	−	0.623223i
$759$	−15.1818	+	21.7948i	−0.551064	+	0.791102i
$760$	−0.333271	−	0.577242i	−0.0120890	−	0.0209388i
$761$	2.74399			0.0994695			0.0497348	−	0.998762i	$-0.484162\pi$
$761$	2.74399			0.0994695			0.0497348	+	0.998762i	$0.484162\pi$
$762$	−5.53853	+	7.95106i	−0.200640	+	0.288036i
$763$	1.44251	+	2.49849i	0.0522222	+	0.0904515i
$764$	1.58133	+	2.73895i	0.0572107	+	0.0990918i
$765$	2.34712	+	0.402060i	0.0848603	+	0.0145365i
$766$	2.14961	+	3.72324i	0.0776687	+	0.134526i
$767$	1.73685	−	3.00831i	0.0627139	−	0.108624i
$768$	−0.989999	+	1.42123i	−0.0357235	+	0.0512843i
$769$	7.88382			0.284298			0.142149	−	0.989845i	$-0.454599\pi$
$769$	7.88382			0.284298			0.142149	+	0.989845i	$0.454599\pi$
$770$	0.549618	−	0.951967i	0.0198069	−	0.0343065i
$771$	−18.7157	−	1.59141i	−0.674031	−	0.0573132i
$772$	−2.06248	−	3.57233i	−0.0742304	−	0.128571i
$773$	−16.8186			−0.604922			−0.302461	−	0.953162i	$-0.597808\pi$
$773$	−16.8186			−0.604922			−0.302461	+	0.953162i	$0.597808\pi$
$774$	16.6748	−	20.0703i	0.599362	−	0.721413i
$775$	−24.9492	+	11.7052i	−0.896203	+	0.420462i
$776$	6.40336	−	11.0909i	0.229867	−	0.398142i
$777$	21.7339	+	46.3131i	0.779698	+	1.66147i
$778$	−25.9767			−0.931310
$779$	5.53245	+	9.58249i	0.198221	+	0.343328i
$780$	−1.82820	−	0.155452i	−0.0654600	−	0.00556609i
$781$	−10.3198	−	17.8744i	−0.369272	−	0.639598i
$782$	−15.1641	+	26.2650i	−0.542267	+	0.939233i
$783$	21.2745	−	21.5883i	0.760289	−	0.771502i
$784$	−0.250427	−	0.433752i	−0.00894382	−	0.0154911i
$785$	−3.76576			−0.134406
$786$	−7.07701	−	0.601762i	−0.252429	−	0.0214641i
$787$	29.7799			1.06154			0.530769	−	0.847517i	$-0.321903\pi$
$787$	29.7799			1.06154			0.530769	+	0.847517i	$0.321903\pi$
$788$	−2.14925	+	3.72261i	−0.0765639	+	0.132613i
$789$	46.1385	+	3.92318i	1.64258	+	0.139669i
$790$	−1.58989	+	2.75377i	−0.0565657	+	0.0979747i
$791$	48.0686			1.70912
$792$	3.42973	−	4.12814i	0.121870	−	0.146687i
$793$	3.25839	+	5.64370i	0.115709	+	0.200414i
$794$	16.3125	+	28.2541i	0.578910	+	1.00270i
$795$	0.459074	+	0.978247i	0.0162817	+	0.0346949i
$796$	−2.73087	+	4.73000i	−0.0967930	+	0.167650i
$797$	−0.963067	+	1.66808i	−0.0341136	+	0.0590865i	−0.882578	−	0.470166i	$-0.844194\pi$
$797$	−0.963067	+	1.66808i	−0.0341136	+	0.0590865i	0.848465	+	0.529252i	$0.177527\pi$
$798$	14.0428	+	1.19406i	0.497109	+	0.0422694i
$799$	−13.9852	−	24.2231i	−0.494761	−	0.856951i
$800$	2.47483	−	4.28654i	0.0874986	−	0.151552i
$801$	25.6645	−	30.8907i	0.906811	−	1.09147i
$802$	32.3704			1.14304
$803$	2.03448	+	3.52382i	0.0717952	+	0.124353i
$804$	8.50459	+	18.1226i	0.299934	+	0.639134i
$805$	2.63348	+	4.56131i	0.0928178	+	0.160765i
$806$	23.8003	−	11.1661i	0.838329	−	0.393311i
$807$	7.33815	−	10.5346i	0.258315	−	0.370835i
$808$	−5.60050	+	9.70035i	−0.197025	+	0.341257i
$809$	−1.87914	+	3.25477i	−0.0660672	+	0.114432i	−0.897167	−	0.441692i	$-0.854379\pi$
$809$	−1.87914	+	3.25477i	−0.0660672	+	0.114432i	0.831100	+	0.556123i	$0.187712\pi$
$810$	1.53402	−	1.31292i	0.0538999	−	0.0461312i
$811$	−23.2559	−	40.2804i	−0.816626	−	1.41444i	−0.908155	−	0.418635i	$-0.862509\pi$
$811$	−23.2559	−	40.2804i	−0.816626	−	1.41444i	0.0915291	−	0.995802i	$-0.470825\pi$
$812$	−7.98768	−	13.8351i	−0.280313	−	0.485516i
$813$	−4.50962	−	9.60962i	−0.158159	−	0.337024i
$814$	9.64690	+	16.7089i	0.338124	+	0.585647i
$815$	0.500081	−	0.866165i	0.0175171	−	0.0303405i
$816$	3.50270	−	5.02844i	0.122619	−	0.176031i
$817$	25.8411			0.904065
$818$	−7.04199	+	12.1971i	−0.246218	+	0.426461i
$819$	24.7917	−	29.8402i	0.866293	−	1.04270i
$820$	0.417775	−	0.723608i	0.0145893	−	0.0252695i
$821$	−0.281005	+	0.486714i	−0.00980713	+	0.0169864i	−0.870887	−	0.491483i	$-0.836455\pi$
$821$	−0.281005	+	0.486714i	−0.00980713	+	0.0169864i	0.861080	+	0.508469i	$0.169788\pi$
$822$	−6.38944	−	0.543297i	−0.222857	−	0.0189497i
$823$	−21.0731			−0.734561			−0.367280	−	0.930110i	$-0.619711\pi$
$823$	−21.0731			−0.734561			−0.367280	+	0.930110i	$0.619711\pi$
$824$	−8.34800	+	14.4592i	−0.290816	+	0.503709i
$825$	−8.76639	+	12.5849i	−0.305206	+	0.438152i
$826$	2.01486			0.0701061
$827$	−6.53573	−	11.3202i	−0.227270	−	0.393643i	0.729728	−	0.683737i	$-0.239647\pi$
$827$	−6.53573	−	11.3202i	−0.227270	−	0.393643i	−0.956998	+	0.290095i	$0.906313\pi$
$828$	8.91313	+	24.1217i	0.309753	+	0.838287i
$829$	28.2189			0.980085			0.490042	−	0.871699i	$-0.336981\pi$
$829$	28.2189			0.980085			0.490042	+	0.871699i	$0.336981\pi$
$830$	−1.22953	−	2.12960i	−0.0426775	−	0.0739195i
$831$	9.64442	+	0.820070i	0.334561	+	0.0284479i
$832$	−2.36086	+	4.08914i	−0.0818482	+	0.141765i
$833$	0.886031	+	1.53465i	0.0306992	+	0.0531725i
$834$	0.454557	+	0.968622i	0.0157400	+	0.0335406i
$835$	−0.335061	+	0.580344i	−0.0115953	+	0.0200836i
$836$	5.31510			0.183826
$837$	−9.63188	+	27.2805i	−0.332927	+	0.942953i
$838$	9.56079			0.330272
$839$	23.1977	−	40.1796i	0.800874	−	1.38715i	−0.118168	−	0.992994i	$-0.537702\pi$
$839$	23.1977	−	40.1796i	0.800874	−	1.38715i	0.919042	−	0.394161i	$-0.128965\pi$
$840$	−0.452122	−	0.963434i	−0.0155997	−	0.0332416i
$841$	−2.51220	−	4.35126i	−0.0866276	−	0.150043i
$842$	−9.72789	+	16.8492i	−0.335245	+	0.580662i
$843$	0.674010	+	0.0573114i	0.0232141	+	0.00197391i
$844$	−5.37008	−	9.30126i	−0.184846	−	0.320162i
$845$	−2.08527			−0.0717354
$846$	−23.3761	−	4.00431i	−0.803686	−	0.137671i
$847$	−10.6805	−	18.4991i	−0.366986	−	0.635638i
$848$	2.78088			0.0954958
$849$	−6.77031	+	9.71939i	−0.232356	+	0.333569i
$850$	−8.75617	+	15.1661i	−0.300334	+	0.520194i
$851$	−92.4455			−3.16899
$852$	−19.9108	−	1.69302i	−0.682131	−	0.0580020i
$853$	−14.3991	+	24.9400i	−0.493017	+	0.853930i	−0.999968	−	0.00804459i	$-0.997439\pi$
$853$	−14.3991	+	24.9400i	−0.493017	+	0.853930i	0.506951	+	0.861975i	$0.330773\pi$
$854$	−1.88998	+	3.27355i	−0.0646739	+	0.112019i
$855$	1.97092	+	0.337617i	0.0674039	+	0.0115463i
$856$	1.71895	−	2.97731i	0.0587525	−	0.101762i
$857$	−32.6456			−1.11515			−0.557576	−	0.830126i	$-0.688269\pi$
$857$	−32.6456			−1.11515			−0.557576	+	0.830126i	$0.688269\pi$
$858$	8.36268	−	12.0054i	0.285497	−	0.409857i
$859$	3.39601	−	5.88206i	0.115870	−	0.200693i	−0.802257	−	0.596979i	$-0.796368\pi$
$859$	3.39601	−	5.88206i	0.115870	−	0.200693i	0.918127	+	0.396286i	$0.129701\pi$
$860$	−0.975675	−	1.68992i	−0.0332703	−	0.0576258i
$861$	7.50544	+	15.9935i	0.255785	+	0.545056i
$862$	17.2586	+	29.8928i	0.587831	+	1.01815i
$863$	−24.2090	−	41.9311i	−0.824083	−	1.42735i	−0.902618	−	0.430442i	$-0.858358\pi$
$863$	−24.2090	−	41.9311i	−0.824083	−	1.42735i	0.0785358	−	0.996911i	$-0.474976\pi$
$864$	−1.38157	−	5.00912i	−0.0470019	−	0.170414i
$865$	1.76779	−	3.06191i	0.0601067	−	0.104108i
$866$	1.00649	−	1.74329i	0.0342018	−	0.0592393i
$867$	4.43714	−	6.36991i	0.150693	−	0.216334i
$868$	12.5115	+	8.71711i	0.424669	+	0.295878i
$869$	−12.6780	−	21.9590i	−0.430072	−	0.744906i
$870$	−0.962931	−	2.05193i	−0.0326464	−	0.0695668i
$871$	27.2866	+	47.2619i	0.924573	+	1.60141i
$872$	1.05340			0.0356725
$873$	13.3165	+	36.0386i	0.450695	+	1.21972i
$874$	−12.7335	+	22.0551i	−0.430718	+	0.746026i
$875$	3.05675	+	5.29444i	0.103337	+	0.178985i
$876$	3.92527	+	0.333768i	0.132623	+	0.0112770i
$877$	8.41916	−	14.5824i	0.284295	−	0.492413i	−0.688143	−	0.725575i	$-0.741574\pi$
$877$	8.41916	−	14.5824i	0.284295	−	0.492413i	0.972438	+	0.233162i	$0.0749073\pi$
$878$	−0.178112	+	0.308499i	−0.00601099	+	0.0104113i
$879$	−16.5286	−	35.2212i	−0.557498	−	1.18798i
$880$	−0.200681	−	0.347589i	−0.00676495	−	0.0117172i
$881$	9.10158	+	15.7644i	0.306640	+	0.531116i	0.977625	−	0.210355i	$-0.0674619\pi$
$881$	9.10158	+	15.7644i	0.306640	+	0.531116i	−0.670985	+	0.741471i	$0.734129\pi$
$882$	1.48099	+	0.253693i	0.0498675	+	0.00854228i
$883$	27.0039			0.908752			0.454376	−	0.890810i	$-0.349862\pi$
$883$	27.0039			0.908752			0.454376	+	0.890810i	$0.349862\pi$
$884$	8.35293	−	14.4677i	0.280940	−	0.486602i
$885$	0.284848	+	0.0242207i	0.00957505	+	0.000814171i
$886$	8.02147	−	13.8936i	0.269487	−	0.466765i
$887$	0.627232			0.0210604			0.0105302	−	0.999945i	$-0.496648\pi$
$887$	0.627232			0.0210604			0.0105302	+	0.999945i	$0.496648\pi$
$888$	18.6125	+	1.58263i	0.624593	+	0.0531095i
$889$	−15.3220			−0.513883
$890$	−1.50168	−	2.60099i	−0.0503366	−	0.0871855i
$891$	2.95053	+	15.8283i	0.0988466	+	0.530269i
$892$	6.87299	−	11.9044i	0.230125	−	0.398587i
$893$	−11.7436	−	20.3405i	−0.392985	−	0.680670i
$894$	−39.4962	−	3.35838i	−1.32095	−	0.112321i
$895$	−1.72634	−	2.99011i	−0.0577052	−	0.0999484i
$896$	−2.73877			−0.0914958
$897$	29.7820	+	63.4629i	0.994390	+	2.11896i
$898$	−1.48298	+	2.56859i	−0.0494875	+	0.0857149i
$899$	26.6471	+	18.5657i	0.888732	+	0.619202i
$900$	5.14669	+	13.9285i	0.171556	+	0.464285i
$901$	−9.83899			−0.327784
$902$	3.33140	+	5.77015i	0.110923	+	0.192125i
$903$	41.1113	+	3.49571i	1.36810	+	0.116330i
$904$	8.77559	−	15.1998i	0.291872	−	0.505537i
$905$	−2.05026			−0.0681529
$906$	11.6140	−	16.6729i	0.385849	−	0.553921i
$907$	−8.22342	+	14.2434i	−0.273054	+	0.472944i	−0.969642	−	0.244527i	$-0.921367\pi$
$907$	−8.22342	+	14.2434i	−0.273054	+	0.472944i	0.696588	+	0.717471i	$0.254701\pi$
$908$	−6.46555	−	11.1987i	−0.214567	−	0.371640i
$909$	−11.6469	−	31.5200i	−0.386302	−	1.04545i
$910$	−1.45061	−	2.51254i	−0.0480874	−	0.0832898i
$911$	−20.4664	−	35.4488i	−0.678082	−	1.17447i	−0.975558	−	0.219742i	$-0.929478\pi$
$911$	−20.4664	−	35.4488i	−0.678082	−	1.17447i	0.297476	−	0.954729i	$-0.403855\pi$
$912$	2.94128	−	4.22247i	0.0973954	−	0.139820i
$913$	19.6088			0.648958
$914$	0.0613990	+	0.106346i	0.00203090	+	0.00351762i
$915$	−0.306544	+	0.440072i	−0.0101340	+	0.0145483i
$916$	12.3295	+	21.3554i	0.407379	+	0.705601i
$917$	−5.61538	−	9.72612i	−0.185436	−	0.321185i
$918$	4.88810	+	17.7227i	0.161331	+	0.584936i
$919$	13.1639	+	22.8005i	0.434237	+	0.752120i	0.997233	−	0.0743394i	$-0.0236848\pi$
$919$	13.1639	+	22.8005i	0.434237	+	0.752120i	−0.562996	+	0.826459i	$0.690351\pi$
$920$	1.92311			0.0634030
$921$	−52.6047	−	4.47300i	−1.73338	−	0.147390i
$922$	4.52857	+	7.84371i	0.149140	+	0.258319i
$923$	−54.4744			−1.79305
$924$	8.45594	+	0.719012i	0.278180	+	0.0236538i
$925$	−53.3806			−1.75514
$926$	20.7467			0.681779
$927$	−17.3606	−	46.9831i	−0.570196	−	1.54313i
$928$	−5.83304			−0.191479
$929$	4.85121	−	8.40254i	0.159163	−	0.275678i	−0.775404	−	0.631465i	$-0.782454\pi$
$929$	4.85121	−	8.40254i	0.159163	−	0.275678i	0.934567	+	0.355787i	$0.115787\pi$
$930$	1.66401	+	1.38277i	0.0545649	+	0.0453427i
$931$	0.744016	+	1.28867i	0.0243841	+	0.0422346i
$932$	−8.02264	−	13.8956i	−0.262790	−	0.455166i
$933$	16.0423	−	23.0302i	0.525202	−	0.753974i
$934$	4.83282	−	8.37069i	0.158135	−	0.273897i
$935$	0.710026	+	1.22980i	0.0232203	+	0.0402188i
$936$	−4.90968	−	13.2871i	−0.160478	−	0.434303i
$937$	−0.255570	+	0.442660i	−0.00834911	+	0.0144611i	−0.870170	−	0.492752i	$-0.835991\pi$
$937$	−0.255570	+	0.442660i	−0.00834911	+	0.0144611i	0.861821	+	0.507213i	$0.169324\pi$
$938$	−15.8272	+	27.4135i	−0.516777	+	0.895084i
$939$	11.4482	−	16.4350i	0.373599	−	0.536335i
$940$	−0.886802	+	1.53599i	−0.0289243	+	0.0500983i
$941$	−25.6020	+	44.3440i	−0.834603	+	1.44557i	0.0597504	+	0.998213i	$0.480970\pi$
$941$	−25.6020	+	44.3440i	−0.834603	+	1.44557i	−0.894353	+	0.447361i	$0.852364\pi$
$942$	−12.3510	−	26.3189i	−0.402416	−	0.857515i
$943$	−31.9245			−1.03961
$944$	0.367841	−	0.637120i	0.0119722	−	0.0207365i
$945$	3.08991	+	0.803744i	0.100515	+	0.0261458i
$946$	15.5604			0.505911
$947$	28.5943	+	49.5268i	0.929189	+	1.60940i	0.784681	+	0.619900i	$0.212827\pi$
$947$	28.5943	+	49.5268i	0.929189	+	1.60940i	0.144508	+	0.989504i	$0.453840\pi$
$948$	−24.4606	−	2.07990i	−0.794443	−	0.0675519i
$949$	10.7393			0.348611
$950$	−7.35270	+	12.7353i	−0.238553	+	0.413186i
$951$	5.89487	−	8.46262i	0.191154	−	0.274419i
$952$	9.68999			0.314054
$953$	9.12093			0.295456			0.147728	−	0.989028i	$-0.452804\pi$
$953$	9.12093			0.295456			0.147728	+	0.989028i	$0.452804\pi$
$954$	−5.33129	+	6.41693i	−0.172607	+	0.207756i
$955$	−0.354772	+	0.614484i	−0.0114802	+	0.0198842i
$956$	−6.63914			−0.214725
$957$	18.0095	+	1.53136i	0.582164	+	0.0495017i
$958$	6.71121			0.216829
$959$	−5.06982	−	8.78118i	−0.163713	−	0.283559i
$960$	−0.387188	−	0.0329228i	−0.0124964	−	0.00106258i
$961$	−30.5539	−	5.24014i	−0.985610	−	0.169037i
$962$	50.9224			1.64180
$963$	3.57474	+	9.67437i	0.115195	+	0.311752i
$964$	−9.00343	+	15.5944i	−0.289981	+	0.502262i
$965$	0.462718	−	0.801451i	0.0148954	−	0.0257996i
$966$	−23.2417	+	33.3656i	−0.747790	+	1.07352i
$967$	13.7545			0.442314			0.221157	−	0.975238i	$-0.429017\pi$
$967$	13.7545			0.442314			0.221157	+	0.975238i	$0.429017\pi$
$968$	−7.79948			−0.250685
$969$	−10.4065	+	14.9394i	−0.334304	+	0.479924i
$970$	2.87318			0.0922524
$971$	5.73336	+	9.93048i	0.183992	+	0.318684i	0.943237	−	0.332122i	$-0.107764\pi$
$971$	5.73336	+	9.93048i	0.183992	+	0.318684i	−0.759244	+	0.650806i	$0.774431\pi$
$972$	14.2073	+	6.41512i	0.455698	+	0.205765i
$973$	−0.845939	+	1.46521i	−0.0271196	+	0.0469725i
$974$	33.2184			1.06439
$975$	17.1969	+	36.6452i	0.550743	+	1.17359i
$976$	0.690085	+	1.19526i	0.0220891	+	0.0382594i
$977$	11.2070	+	19.4111i	0.358544	+	0.621016i	0.987718	−	0.156248i	$-0.0499400\pi$
$977$	11.2070	+	19.4111i	0.358544	+	0.621016i	−0.629174	+	0.777265i	$0.716607\pi$
$978$	7.69380	+	0.654207i	0.246020	+	0.0209192i
$979$	23.9493			0.765423
$980$	0.0561832	−	0.0973122i	0.00179471	−	0.00310853i
$981$	−2.01949	+	2.43073i	−0.0644775	+	0.0776073i
$982$	−15.1123	−	26.1753i	−0.482253	−	0.835286i
$983$	−38.9311			−1.24171			−0.620855	−	0.783925i	$-0.713214\pi$
$983$	−38.9311			−1.24171			−0.620855	+	0.783925i	$0.713214\pi$
$984$	6.42751	+	0.546534i	0.204902	+	0.0174229i
$985$	−0.964368			−0.0307273
$986$	20.6378			0.657241
$987$	−15.9316	−	33.9490i	−0.507109	−	1.08061i
$988$	7.01410	−	12.1488i	0.223148	−	0.386504i
$989$	−37.2784	+	64.5681i	−1.18539	+	2.05315i
$990$	1.18680	+	0.203298i	0.0377189	+	0.00646123i
$991$	−56.3923			−1.79136			−0.895679	−	0.444700i	$-0.853310\pi$
$991$	−56.3923			−1.79136			−0.895679	+	0.444700i	$0.853310\pi$
$992$	5.04059	−	2.36484i	0.160039	−	0.0750838i
$993$	−17.1812	−	36.6117i	−0.545229	−	1.16184i
$994$	−15.7985	−	27.3639i	−0.501099	−	0.867929i
$995$	−1.22534			−0.0388458
$996$	10.8512	−	15.5778i	0.343832	−	0.493602i
$997$	27.8110			0.880782			0.440391	−	0.897806i	$-0.354840\pi$
$997$	27.8110			0.880782			0.440391	+	0.897806i	$0.354840\pi$
$998$	2.39322	−	4.14518i	0.0757560	−	0.131213i
$999$	−39.3344	+	39.9145i	−1.24448	+	1.26284i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	558.2.g.a.439.6	yes	32
3.2	odd	2		1674.2.g.b.1369.9		32
9.4	even	3		558.2.h.a.67.16	yes	32
9.5	odd	6		1674.2.h.b.253.8		32
31.25	even	3		558.2.h.a.25.16	yes	32
93.56	odd	6		1674.2.h.b.397.8		32
279.149	odd	6		1674.2.g.b.955.9		32
279.211	even	3	inner	558.2.g.a.211.6	✓	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
558.2.g.a.211.6	✓	32	279.211	even	3	inner
558.2.g.a.439.6	yes	32	1.1	even	1	trivial
558.2.h.a.25.16	yes	32	31.25	even	3
558.2.h.a.67.16	yes	32	9.4	even	3
1674.2.g.b.955.9		32	279.149	odd	6
1674.2.g.b.1369.9		32	3.2	odd	2
1674.2.h.b.253.8		32	9.5	odd	6
1674.2.h.b.397.8		32	93.56	odd	6

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:	\( N \)	\(=\)	\( 558 = 2 \cdot 3^{2} \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	558.g (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.735824 - 1.56798i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.112175 - 0.194293i) q^{5} +(1.72582 + 0.146748i) q^{6} +(1.36938 + 2.37184i) q^{7} +1.00000 q^{8} +(-1.91712 + 2.30752i) q^{9} +(0.112175 + 0.194293i) q^{10} -1.78900 q^{11} +(-0.989999 + 1.42123i) q^{12} +(-2.36086 + 4.08914i) q^{13} -2.73877 q^{14} +(-0.387188 - 0.0329228i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(1.76904 - 3.06407i) q^{17} +(-1.03981 - 2.81404i) q^{18} +(1.48549 - 2.57295i) q^{19} -0.224350 q^{20} +(2.71138 - 3.89243i) q^{21} +(0.894500 - 1.54932i) q^{22} +(4.28596 + 7.42350i) q^{23} +(-0.735824 - 1.56798i) q^{24} +(2.47483 + 4.28654i) q^{25} +(-2.36086 - 4.08914i) q^{26} +(5.02881 + 1.30809i) q^{27} +(1.36938 - 2.37184i) q^{28} +(2.91652 - 5.05156i) q^{29} +(0.222106 - 0.318853i) q^{30} +(-0.472281 + 5.54770i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(1.31639 + 2.80512i) q^{33} +(1.76904 + 3.06407i) q^{34} +0.614442 q^{35} +(2.95693 + 0.506521i) q^{36} +(-5.39234 + 9.33981i) q^{37} +(1.48549 + 2.57295i) q^{38} +(8.14887 + 0.692902i) q^{39} +(0.112175 - 0.194293i) q^{40} +(-1.86216 + 3.22535i) q^{41} +(2.01525 + 4.29434i) q^{42} +(4.34890 + 7.53252i) q^{43} +(0.894500 + 1.54932i) q^{44} +(0.233280 + 0.631329i) q^{45} -8.57192 q^{46} +(3.95276 - 6.84638i) q^{47} +(1.72582 + 0.146748i) q^{48} +(-0.250427 + 0.433752i) q^{49} -4.94967 q^{50} +(-6.10611 - 0.519205i) q^{51} +4.72173 q^{52} +(-1.39044 - 2.40831i) q^{53} +(-3.64724 + 3.70103i) q^{54} +(-0.200681 + 0.347589i) q^{55} +(1.36938 + 2.37184i) q^{56} +(-5.12740 - 0.435985i) q^{57} +(2.91652 + 5.05156i) q^{58} -0.735683 q^{59} +(0.165082 + 0.351776i) q^{60} +(0.690085 - 1.19526i) q^{61} +(-4.56831 - 3.18286i) q^{62} +(-8.09835 - 1.38724i) q^{63} +1.00000 q^{64} +(0.529660 + 0.917397i) q^{65} +(-3.08750 - 0.262531i) q^{66} +(5.77895 - 10.0094i) q^{67} -3.53808 q^{68} +(8.48619 - 12.1827i) q^{69} +(-0.307221 + 0.532123i) q^{70} +(5.76848 + 9.99131i) q^{71} +(-1.91712 + 2.30752i) q^{72} +(-1.13722 - 1.96972i) q^{73} +(-5.39234 - 9.33981i) q^{74} +(4.90016 - 7.03463i) q^{75} -2.97099 q^{76} +(-2.44983 - 4.24323i) q^{77} +(-4.67450 + 6.71067i) q^{78} +(7.08665 + 12.2744i) q^{79} +(0.112175 + 0.194293i) q^{80} +(-1.64926 - 8.84759i) q^{81} +(-1.86216 - 3.22535i) q^{82} -10.9608 q^{83} +(-4.72663 - 0.401908i) q^{84} +(-0.396884 - 0.687424i) q^{85} -8.69780 q^{86} +(-10.0668 - 0.855985i) q^{87} -1.78900 q^{88} -13.3870 q^{89} +(-0.663387 - 0.113638i) q^{90} -12.9317 q^{91} +(4.28596 - 7.42350i) q^{92} +(9.04620 - 3.34160i) q^{93} +(3.95276 + 6.84638i) q^{94} +(-0.333271 - 0.577242i) q^{95} +(-0.989999 + 1.42123i) q^{96} +(6.40336 - 11.0909i) q^{97} +(-0.250427 - 0.433752i) q^{98} +(3.42973 - 4.12814i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 16 q^{2} + 4 q^{3} - 16 q^{4} - q^{5} - 2 q^{6} + q^{7} + 32 q^{8} + 12 q^{9} - q^{10} + 4 q^{11} - 2 q^{12} - 10 q^{13} - 2 q^{14} - 13 q^{15} - 16 q^{16} - 4 q^{17} - 6 q^{18} + 4 q^{19} + 2 q^{20}+ \cdots + 19 q^{99}+O(q^{100}) \) 32 * q - 16 * q^2 + 4 * q^3 - 16 * q^4 - q^5 - 2 * q^6 + q^7 + 32 * q^8 + 12 * q^9 - q^10 + 4 * q^11 - 2 * q^12 - 10 * q^13 - 2 * q^14 - 13 * q^15 - 16 * q^16 - 4 * q^17 - 6 * q^18 + 4 * q^19 + 2 * q^20 + 10 * q^21 - 2 * q^22 - q^23 + 4 * q^24 - 19 * q^25 - 10 * q^26 + 7 * q^27 + q^28 - 3 * q^29 + 14 * q^30 - q^31 - 16 * q^32 - 7 * q^33 - 4 * q^34 - 6 * q^36 - 19 * q^37 + 4 * q^38 + 19 * q^39 - q^40 + 10 * q^41 - 11 * q^42 - 13 * q^43 - 2 * q^44 + 14 * q^45 + 2 * q^46 - 6 * q^47 - 2 * q^48 - 13 * q^49 + 38 * q^50 + 20 * q^51 + 20 * q^52 - 7 * q^53 - 17 * q^54 - 11 * q^55 + q^56 - 5 * q^57 - 3 * q^58 + 12 * q^59 - q^60 + 7 * q^61 + 11 * q^62 - 42 * q^63 + 32 * q^64 - 8 * q^65 + 5 * q^66 - 8 * q^67 + 8 * q^68 + 43 * q^69 + 7 * q^71 + 12 * q^72 + 7 * q^73 - 19 * q^74 - 41 * q^75 - 8 * q^76 - q^77 - 11 * q^78 - 34 * q^79 - q^80 + 10 * q^82 - 28 * q^83 + q^84 + 13 * q^85 + 26 * q^86 - 54 * q^87 + 4 * q^88 + 2 * q^89 - 19 * q^90 + 24 * q^91 - q^92 - 15 * q^93 - 6 * q^94 + 21 * q^95 - 2 * q^96 + 10 * q^97 - 13 * q^98 + 19 * q^99

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