LMFDB - Embedded newform 140.2.o.a.131.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [140,2,Mod(31,140)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(140, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 0, 1]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("140.31");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 140 = 2^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	140.o (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$1.11790562830$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			131.4
Character	$\chi$	$=$	140.131
Dual form			140.2.o.a.31.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.950668 - 1.04701i) q^{2} +(1.36859 + 2.37047i) q^{3} +(-0.192463 + 1.99072i) q^{4} +(-0.866025 - 0.500000i) q^{5} +(1.18083 - 3.68646i) q^{6} +(-1.02440 + 2.43939i) q^{7} +(2.26727 - 1.69100i) q^{8} +(-2.24609 + 3.89033i) q^{9} +O(q^{10})$	\(q+(-0.950668 - 1.04701i) q^{2} +(1.36859 + 2.37047i) q^{3} +(-0.192463 + 1.99072i) q^{4} +(-0.866025 - 0.500000i) q^{5} +(1.18083 - 3.68646i) q^{6} +(-1.02440 + 2.43939i) q^{7} +(2.26727 - 1.69100i) q^{8} +(-2.24609 + 3.89033i) q^{9} +(0.299797 + 1.38207i) q^{10} +(0.0868131 - 0.0501216i) q^{11} +(-4.98234 + 2.26825i) q^{12} +4.11735i q^{13} +(3.52793 - 1.24649i) q^{14} -2.73718i q^{15} +(-3.92592 - 0.766277i) q^{16} +(4.67424 - 2.69867i) q^{17} +(6.20850 - 1.34674i) q^{18} +(3.72967 - 6.45997i) q^{19} +(1.16204 - 1.62778i) q^{20} +(-7.18448 + 0.910218i) q^{21} +(-0.135008 - 0.0432453i) q^{22} +(1.30623 + 0.754151i) q^{23} +(7.11143 + 3.06021i) q^{24} +(0.500000 + 0.866025i) q^{25} +(4.31091 - 3.91424i) q^{26} -4.08434 q^{27} +(-4.65897 - 2.50878i) q^{28} -2.37688 q^{29} +(-2.86586 + 2.60215i) q^{30} +(-2.72129 - 4.71341i) q^{31} +(2.92994 + 4.83895i) q^{32} +(0.237623 + 0.137192i) q^{33} +(-7.26919 - 2.32844i) q^{34} +(2.10685 - 1.60037i) q^{35} +(-7.31227 - 5.22007i) q^{36} +(-0.519260 + 0.899386i) q^{37} +(-10.3093 + 2.23629i) q^{38} +(-9.76007 + 5.63498i) q^{39} +(-2.80901 + 0.330814i) q^{40} -7.99125i q^{41} +(7.78306 + 6.65691i) q^{42} +7.04778i q^{43} +(0.0830696 + 0.182467i) q^{44} +(3.89033 - 2.24609i) q^{45} +(-0.452184 - 2.08458i) q^{46} +(2.22188 - 3.84841i) q^{47} +(-3.55654 - 10.3550i) q^{48} +(-4.90122 - 4.99781i) q^{49} +(0.431404 - 1.34681i) q^{50} +(12.7943 + 7.38677i) q^{51} +(-8.19649 - 0.792437i) q^{52} +(-3.07131 - 5.31966i) q^{53} +(3.88285 + 4.27635i) q^{54} -0.100243 q^{55} +(1.80242 + 7.26301i) q^{56} +20.4176 q^{57} +(2.25962 + 2.48862i) q^{58} +(4.26148 + 7.38111i) q^{59} +(5.44896 + 0.526805i) q^{60} +(6.84408 + 3.95143i) q^{61} +(-2.34795 + 7.33010i) q^{62} +(-7.18914 - 9.46432i) q^{63} +(2.28103 - 7.66791i) q^{64} +(2.05868 - 3.56573i) q^{65} +(-0.0822594 - 0.379218i) q^{66} +(-0.0950895 + 0.0549000i) q^{67} +(4.47268 + 9.82449i) q^{68} +4.12850i q^{69} +(-3.67852 - 0.684471i) q^{70} -6.73221i q^{71} +(1.48607 + 12.6186i) q^{72} +(-5.32344 + 3.07349i) q^{73} +(1.43531 - 0.311345i) q^{74} +(-1.36859 + 2.37047i) q^{75} +(12.1422 + 8.66802i) q^{76} +(0.0333347 + 0.263115i) q^{77} +(15.1785 + 4.86190i) q^{78} +(3.70178 + 2.13723i) q^{79} +(3.01680 + 2.62657i) q^{80} +(1.14846 + 1.98919i) q^{81} +(-8.36692 + 7.59702i) q^{82} -6.50159 q^{83} +(-0.429245 - 14.4774i) q^{84} -5.39735 q^{85} +(7.37910 - 6.70009i) q^{86} +(-3.25298 - 5.63433i) q^{87} +(0.112073 - 0.260440i) q^{88} +(-2.76417 - 1.59589i) q^{89} +(-6.05009 - 1.93794i) q^{90} +(-10.0438 - 4.21781i) q^{91} +(-1.75270 + 2.45519i) q^{92} +(7.44866 - 12.9015i) q^{93} +(-6.14160 + 1.33223i) q^{94} +(-6.45997 + 3.72967i) q^{95} +(-7.46070 + 13.5679i) q^{96} -11.0691i q^{97} +(-0.573332 + 9.88288i) q^{98} +0.450309i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 2 q^{2} - 2 q^{4} - 4 q^{8} - 16 q^{9}+O(q^{10}) $ 32 * q + 2 * q^2 - 2 * q^4 - 4 * q^8 - 16 * q^9	$ 32 q + 2 q^{2} - 2 q^{4} - 4 q^{8} - 16 q^{9} - 30 q^{12} + 2 q^{14} - 14 q^{16} - 12 q^{21} - 8 q^{22} + 36 q^{24} + 16 q^{25} + 30 q^{26} + 2 q^{28} - 40 q^{29} + 2 q^{32} + 60 q^{36} + 8 q^{37} - 60 q^{38} - 62 q^{42} - 18 q^{44} + 12 q^{45} + 2 q^{46} - 16 q^{49} + 4 q^{50} - 36 q^{52} - 8 q^{53} + 12 q^{54} - 4 q^{56} + 48 q^{57} + 2 q^{58} + 14 q^{60} + 24 q^{61} + 4 q^{64} + 4 q^{65} + 24 q^{66} + 60 q^{68} - 4 q^{70} + 4 q^{72} - 72 q^{73} + 38 q^{74} - 40 q^{77} + 120 q^{78} - 36 q^{81} + 42 q^{82} - 20 q^{84} + 28 q^{86} + 4 q^{88} - 60 q^{89} - 4 q^{92} - 8 q^{93} + 18 q^{94} - 60 q^{96} + 78 q^{98}+O(q^{100}) $ 32 * q + 2 * q^2 - 2 * q^4 - 4 * q^8 - 16 * q^9 - 30 * q^12 + 2 * q^14 - 14 * q^16 - 12 * q^21 - 8 * q^22 + 36 * q^24 + 16 * q^25 + 30 * q^26 + 2 * q^28 - 40 * q^29 + 2 * q^32 + 60 * q^36 + 8 * q^37 - 60 * q^38 - 62 * q^42 - 18 * q^44 + 12 * q^45 + 2 * q^46 - 16 * q^49 + 4 * q^50 - 36 * q^52 - 8 * q^53 + 12 * q^54 - 4 * q^56 + 48 * q^57 + 2 * q^58 + 14 * q^60 + 24 * q^61 + 4 * q^64 + 4 * q^65 + 24 * q^66 + 60 * q^68 - 4 * q^70 + 4 * q^72 - 72 * q^73 + 38 * q^74 - 40 * q^77 + 120 * q^78 - 36 * q^81 + 42 * q^82 - 20 * q^84 + 28 * q^86 + 4 * q^88 - 60 * q^89 - 4 * q^92 - 8 * q^93 + 18 * q^94 - 60 * q^96 + 78 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/140\mathbb{Z}\right)^\times$.

$n$	$57$	$71$	$101$
$\chi(n)$	$1$	$-1$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$	−0.950668	−	1.04701i	−0.672223	−	0.740348i
$2$	−0.950668	−	1.04701i	−0.672223	−	0.740348i
$3$	1.36859	+	2.37047i	0.790157	+	1.36859i	0.925870	+	0.377843i	$0.123334\pi$
$3$	1.36859	+	2.37047i	0.790157	+	1.36859i	−0.135713	+	0.990748i	$0.543332\pi$
$4$	−0.192463	+	1.99072i	−0.0962313	+	0.995359i
$5$	−0.866025	−	0.500000i	−0.387298	−	0.223607i
$5$	−0.866025	−	0.500000i	−0.387298	−	0.223607i
$6$	1.18083	−	3.68646i	0.482073	−	1.50499i
$7$	−1.02440	+	2.43939i	−0.387186	+	0.922002i
$7$	−1.02440	+	2.43939i	−0.387186	+	0.922002i
$8$	2.26727	−	1.69100i	0.801601	−	0.597859i
$9$	−2.24609	+	3.89033i	−0.748695	+	1.29678i
$10$	0.299797	+	1.38207i	0.0948041	+	0.437049i
$11$	0.0868131	−	0.0501216i	0.0261751	−	0.0151122i	−0.486855	−	0.873483i	$-0.661856\pi$
$11$	0.0868131	−	0.0501216i	0.0261751	−	0.0151122i	0.513030	+	0.858370i	$0.328523\pi$
$12$	−4.98234	+	2.26825i	−1.43828	+	0.654788i
$13$			4.11735i			1.14195i	0.820968	+	0.570974i	$0.193434\pi$
$13$			4.11735i			1.14195i	−0.820968	+	0.570974i	$0.806566\pi$
$14$	3.52793	−	1.24649i	0.942878	−	0.333138i
$15$		−	2.73718i		−	0.706738i
$16$	−3.92592	−	0.766277i	−0.981479	−	0.191569i
$17$	4.67424	−	2.69867i	1.13367	−	0.654525i	0.188815	−	0.982013i	$-0.439535\pi$
$17$	4.67424	−	2.69867i	1.13367	−	0.654525i	0.944855	+	0.327488i	$0.106202\pi$
$18$	6.20850	−	1.34674i	1.46336	−	0.317429i
$19$	3.72967	−	6.45997i	0.855645	−	1.48202i	−0.0204012	−	0.999792i	$-0.506494\pi$
$19$	3.72967	−	6.45997i	0.855645	−	1.48202i	0.876046	−	0.482228i	$-0.160172\pi$
$20$	1.16204	−	1.62778i	0.259839	−	0.363983i
$21$	−7.18448	+	0.910218i	−1.56778	+	0.198626i
$22$	−0.135008	−	0.0432453i	−0.0287838	−	0.00921993i
$23$	1.30623	+	0.754151i	0.272367	+	0.157251i	0.629963	−	0.776625i	$-0.283070\pi$
$23$	1.30623	+	0.754151i	0.272367	+	0.157251i	−0.357596	+	0.933877i	$0.616403\pi$
$24$	7.11143	+	3.06021i	1.45162	+	0.624662i
$25$	0.500000	+	0.866025i	0.100000	+	0.173205i
$26$	4.31091	−	3.91424i	0.845440	−	0.767645i
$27$	−4.08434			−0.786032
$28$	−4.65897	−	2.50878i	−0.880463	−	0.474115i
$29$	−2.37688			−0.441376			−0.220688	−	0.975344i	$-0.570830\pi$
$29$	−2.37688			−0.441376			−0.220688	+	0.975344i	$0.570830\pi$
$30$	−2.86586	+	2.60215i	−0.523232	+	0.475086i
$31$	−2.72129	−	4.71341i	−0.488758	−	0.846553i	0.511159	−	0.859486i	$-0.329217\pi$
$31$	−2.72129	−	4.71341i	−0.488758	−	0.846553i	−0.999916	+	0.0129330i	$0.995883\pi$
$32$	2.92994	+	4.83895i	0.517945	+	0.855414i
$33$	0.237623	+	0.137192i	0.0413649	+	0.0238820i
$34$	−7.26919	−	2.32844i	−1.24666	−	0.399324i
$35$	2.10685	−	1.60037i	0.356122	−	0.270512i
$36$	−7.31227	−	5.22007i	−1.21871	−	0.870011i
$37$	−0.519260	+	0.899386i	−0.0853659	+	0.147858i	−0.905547	−	0.424246i	$-0.860539\pi$
$37$	−0.519260	+	0.899386i	−0.0853659	+	0.147858i	0.820181	+	0.572104i	$0.193873\pi$
$38$	−10.3093	+	2.23629i	−1.67240	+	0.362773i
$39$	−9.76007	+	5.63498i	−1.56286	+	0.902318i
$40$	−2.80901	+	0.330814i	−0.444144	+	0.0523063i
$41$		−	7.99125i		−	1.24802i	−0.781415	−	0.624012i	$-0.785502\pi$
$41$		−	7.99125i		−	1.24802i	0.781415	−	0.624012i	$-0.214498\pi$
$42$	7.78306	+	6.65691i	1.20095	+	1.02718i
$43$			7.04778i			1.07478i	0.843335	+	0.537388i	$0.180589\pi$
$43$			7.04778i			1.07478i	−0.843335	+	0.537388i	$0.819411\pi$
$44$	0.0830696	+	0.182467i	0.0125232	+	0.0275079i
$45$	3.89033	−	2.24609i	0.579937	−	0.334827i
$46$	−0.452184	−	2.08458i	−0.0666710	−	0.307355i
$47$	2.22188	−	3.84841i	0.324095	−	0.561348i	−0.657234	−	0.753686i	$-0.728274\pi$
$47$	2.22188	−	3.84841i	0.324095	−	0.561348i	0.981329	+	0.192338i	$0.0616071\pi$
$48$	−3.55654	−	10.3550i	−0.513342	−	1.49461i
$49$	−4.90122	−	4.99781i	−0.700174	−	0.713973i
$50$	0.431404	−	1.34681i	0.0610097	−	0.190467i
$51$	12.7943	+	7.38677i	1.79155	+	1.03435i
$52$	−8.19649	−	0.792437i	−1.13665	−	0.109891i
$53$	−3.07131	−	5.31966i	−0.421876	−	0.730711i	0.574247	−	0.818682i	$-0.305295\pi$
$53$	−3.07131	−	5.31966i	−0.421876	−	0.730711i	−0.996123	+	0.0879710i	$0.971962\pi$
$54$	3.88285	+	4.27635i	0.528389	+	0.581938i
$55$	−0.100243			−0.0135168
$56$	1.80242	+	7.26301i	0.240858	+	0.970560i
$57$	20.4176			2.70437
$58$	2.25962	+	2.48862i	0.296703	+	0.326772i
$59$	4.26148	+	7.38111i	0.554798	+	0.960938i	0.997919	+	0.0644767i	$0.0205378\pi$
$59$	4.26148	+	7.38111i	0.554798	+	0.960938i	−0.443121	+	0.896462i	$0.646129\pi$
$60$	5.44896	+	0.526805i	0.703458	+	0.0680103i
$61$	6.84408	+	3.95143i	0.876295	+	0.505929i	0.869435	−	0.494048i	$-0.164483\pi$
$61$	6.84408	+	3.95143i	0.876295	+	0.505929i	0.00685975	+	0.999976i	$0.497816\pi$
$62$	−2.34795	+	7.33010i	−0.298190	+	0.930924i
$63$	−7.18914	−	9.46432i	−0.905747	−	1.19239i
$64$	2.28103	−	7.66791i	0.285129	−	0.958489i
$65$	2.05868	−	3.56573i	0.255348	−	0.442275i
$66$	−0.0822594	−	0.379218i	−0.0101254	−	0.0466785i
$67$	−0.0950895	+	0.0549000i	−0.0116170	+	0.00670710i	−0.505797	−	0.862652i	$-0.668802\pi$
$67$	−0.0950895	+	0.0549000i	−0.0116170	+	0.00670710i	0.494180	+	0.869359i	$0.335468\pi$
$68$	4.47268	+	9.82449i	0.542393	+	1.19139i
$69$			4.12850i			0.497013i
$70$	−3.67852	−	0.684471i	−0.439667	−	0.0818100i
$71$		−	6.73221i		−	0.798967i	−0.916740	−	0.399483i	$-0.869190\pi$
$71$		−	6.73221i		−	0.798967i	0.916740	−	0.399483i	$-0.130810\pi$
$72$	1.48607	+	12.6186i	0.175135	+	1.48711i
$73$	−5.32344	+	3.07349i	−0.623062	+	0.359725i	−0.778060	−	0.628190i	$-0.783796\pi$
$73$	−5.32344	+	3.07349i	−0.623062	+	0.359725i	0.154998	+	0.987915i	$0.450463\pi$
$74$	1.43531	−	0.311345i	0.166851	−	0.0361932i
$75$	−1.36859	+	2.37047i	−0.158031	+	0.273718i
$76$	12.1422	+	8.66802i	1.39280	+	0.994290i
$77$	0.0333347	+	0.263115i	0.00379884	+	0.0299848i
$78$	15.1785	+	4.86190i	1.71862	+	0.550502i
$79$	3.70178	+	2.13723i	0.416483	+	0.240457i	0.693572	−	0.720388i	$-0.256036\pi$
$79$	3.70178	+	2.13723i	0.416483	+	0.240457i	−0.277088	+	0.960844i	$0.589369\pi$
$80$	3.01680	+	2.62657i	0.337289	+	0.293660i
$81$	1.14846	+	1.98919i	0.127607	+	0.221021i
$82$	−8.36692	+	7.59702i	−0.923972	+	0.838951i
$83$	−6.50159			−0.713642			−0.356821	−	0.934173i	$-0.616139\pi$
$83$	−6.50159			−0.713642			−0.356821	+	0.934173i	$0.616139\pi$
$84$	−0.429245	−	14.4774i	−0.0468345	−	1.57962i
$85$	−5.39735			−0.585425
$86$	7.37910	−	6.70009i	0.795709	−	0.722490i
$87$	−3.25298	−	5.63433i	−0.348756	−	0.604063i
$88$	0.112073	−	0.260440i	0.0119470	−	0.0277630i
$89$	−2.76417	−	1.59589i	−0.293001	−	0.169164i	0.346293	−	0.938126i	$-0.387440\pi$
$89$	−2.76417	−	1.59589i	−0.293001	−	0.169164i	−0.639294	+	0.768962i	$0.720774\pi$
$90$	−6.05009	−	1.93794i	−0.637735	−	0.204277i
$91$	−10.0438	−	4.21781i	−1.05288	−	0.442147i
$92$	−1.75270	+	2.45519i	−0.182732	+	0.255971i
$93$	7.44866	−	12.9015i	0.772391	−	1.33782i
$94$	−6.14160	+	1.33223i	−0.633457	+	0.137409i
$95$	−6.45997	+	3.72967i	−0.662779	+	0.382656i
$96$	−7.46070	+	13.5679i	−0.761454	+	1.38477i
$97$		−	11.0691i		−	1.12390i	−0.827173	−	0.561948i	$-0.810052\pi$
$97$		−	11.0691i		−	1.12390i	0.827173	−	0.561948i	$-0.189948\pi$
$98$	−0.573332	+	9.88288i	−0.0579152	+	0.998322i
$99$			0.450309i			0.0452578i
$100$	−1.82024	+	0.828682i	−0.182024	+	0.0828682i
$101$	−6.20412	+	3.58195i	−0.617333	+	0.356418i	−0.775830	−	0.630942i	$-0.782669\pi$
$101$	−6.20412	+	3.58195i	−0.617333	+	0.356418i	0.158497	+	0.987359i	$0.449335\pi$
$102$	−4.42906	−	20.4181i	−0.438542	−	2.02169i
$103$	2.44304	−	4.23147i	0.240720	−	0.416939i	−0.720200	−	0.693767i	$-0.755950\pi$
$103$	2.44304	−	4.23147i	0.240720	−	0.416939i	0.960920	+	0.276828i	$0.0892832\pi$
$104$	6.96245	+	9.33516i	0.682724	+	0.915388i
$105$	6.67705	+	2.80397i	0.651613	+	0.273639i
$106$	−2.64995	+	8.27292i	−0.257386	+	0.803537i
$107$	6.55470	+	3.78436i	0.633667	+	0.365848i	0.782171	−	0.623064i	$-0.214112\pi$
$107$	6.55470	+	3.78436i	0.633667	+	0.365848i	−0.148504	+	0.988912i	$0.547446\pi$
$108$	0.786083	−	8.13077i	0.0756409	−	0.782384i
$109$	9.02662	+	15.6346i	0.864593	+	1.49752i	0.867451	+	0.497523i	$0.165757\pi$
$109$	9.02662	+	15.6346i	0.864593	+	1.49752i	−0.00285729	+	0.999996i	$0.500910\pi$
$110$	0.0952979	+	0.104956i	0.00908630	+	0.0100071i
$111$	−2.84262			−0.269810
$112$	5.89095	−	8.79185i	0.556642	−	0.830752i
$113$	−18.1432			−1.70677			−0.853384	−	0.521283i	$-0.825453\pi$
$113$	−18.1432			−1.70677			−0.853384	+	0.521283i	$0.825453\pi$
$114$	−19.4103	−	21.3774i	−1.81794	−	2.00218i
$115$	−0.754151	−	1.30623i	−0.0703250	−	0.121806i
$116$	0.457461	−	4.73170i	0.0424742	−	0.439328i
$117$	−16.0179	−	9.24793i	−1.48085	−	0.854971i
$118$	3.67684	−	11.4788i	0.338481	−	1.05671i
$119$	1.79483	+	14.1668i	0.164531	+	1.29867i
$120$	−4.62858	−	6.20593i	−0.422529	−	0.566522i
$121$	−5.49498	+	9.51758i	−0.499543	+	0.865234i
$122$	−2.36925	−	10.9223i	−0.214502	−	0.988861i
$123$	18.9430	−	10.9368i	1.70803	−	0.986134i
$124$	9.90682	−	4.51016i	0.889658	−	0.405025i
$125$		−	1.00000i		−	0.0894427i
$126$	−3.07476	+	16.5245i	−0.273922	+	1.47212i
$127$			4.37573i			0.388283i	0.980974	+	0.194141i	$0.0621921\pi$
$127$			4.37573i			0.388283i	−0.980974	+	0.194141i	$0.937808\pi$
$128$	−10.1969	+	4.90137i	−0.901286	+	0.433224i
$129$	−16.7065	+	9.64553i	−1.47093	+	0.849241i
$130$	−5.69048	+	1.23437i	−0.499088	+	0.108261i
$131$	−1.49073	+	2.58201i	−0.130245	+	0.225592i	−0.923771	−	0.382945i	$-0.874910\pi$
$131$	−1.49073	+	2.58201i	−0.130245	+	0.225592i	0.793526	+	0.608537i	$0.208243\pi$
$132$	−0.318844	+	0.446637i	−0.0277518	+	0.0388747i
$133$	11.9377	+	15.7157i	1.03513	+	1.36272i
$134$	0.147879	+	0.0473681i	0.0127748	+	0.00409198i
$135$	3.53714	+	2.04217i	0.304429	+	0.175762i
$136$	6.03431	−	14.0228i	0.517438	−	1.20244i
$137$	0.762377	+	1.32048i	0.0651342	+	0.112816i	0.896754	−	0.442530i	$-0.145919\pi$
$137$	0.762377	+	1.32048i	0.0651342	+	0.112816i	−0.831619	+	0.555346i	$0.812586\pi$
$138$	4.32258	−	3.92483i	0.367963	−	0.334104i
$139$	7.16082			0.607373			0.303686	−	0.952772i	$-0.401783\pi$
$139$	7.16082			0.607373			0.303686	+	0.952772i	$0.401783\pi$
$140$	2.78040	+	4.50215i	0.234987	+	0.380501i
$141$	12.1634			1.02434
$142$	−7.04870	+	6.40010i	−0.591514	+	0.537084i
$143$	0.206368	+	0.357440i	0.0172574	+	0.0298907i
$144$	11.7990	−	13.5520i	0.983251	−	1.12933i
$145$	2.05844	+	1.18844i	0.170944	+	0.0986947i
$146$	8.27880	+	2.65183i	0.685158	+	0.219467i
$147$	5.13939	−	18.4581i	0.423890	−	1.52240i
$148$	−1.69048	−	1.20680i	−0.138957	−	0.0991983i
$149$	10.5236	−	18.2275i	0.862129	−	1.49325i	−0.00774027	−	0.999970i	$-0.502464\pi$
$149$	10.5236	−	18.2275i	0.862129	−	1.49325i	0.869870	−	0.493282i	$-0.164203\pi$
$150$	3.78298	−	0.820599i	0.308879	−	0.0670016i
$151$	−3.31081	+	1.91150i	−0.269430	+	0.155555i	−0.628628	−	0.777706i	$-0.716383\pi$
$151$	−3.31081	+	1.91150i	−0.269430	+	0.155555i	0.359199	+	0.933261i	$0.383050\pi$
$152$	−2.46765	−	20.9534i	−0.200153	−	1.69954i
$153$			24.2458i			1.96016i
$154$	0.243794	−	0.285037i	0.0196455	−	0.0229689i
$155$			5.44258i			0.437158i
$156$	−9.33920	−	20.5141i	−0.747735	−	1.64244i
$157$	−1.11209	+	0.642065i	−0.0887543	+	0.0512423i	−0.543720	−	0.839266i	$-0.682985\pi$
$157$	−1.11209	+	0.642065i	−0.0887543	+	0.0512423i	0.454966	+	0.890509i	$0.349651\pi$
$158$	−1.28147	−	5.90760i	−0.101948	−	0.469983i
$159$	8.40673	−	14.5609i	0.666697	−	1.15475i
$160$	−0.117927	−	5.65562i	−0.00932296	−	0.447116i
$161$	−3.17776	+	2.41384i	−0.250443	+	0.190238i
$162$	0.990900	−	3.09351i	0.0778525	−	0.243049i
$163$	−7.44875	−	4.30054i	−0.583431	−	0.336844i	0.179064	−	0.983837i	$-0.442693\pi$
$163$	−7.44875	−	4.30054i	−0.583431	−	0.336844i	−0.762496	+	0.646993i	$0.776026\pi$
$164$	15.9083	+	1.53802i	1.24223	+	0.120099i
$165$	−0.137192	−	0.237623i	−0.0106804	−	0.0184989i
$166$	6.18085	+	6.80723i	0.479727	+	0.528343i
$167$	−8.10448			−0.627144			−0.313572	−	0.949565i	$-0.601526\pi$
$167$	−8.10448			−0.627144			−0.313572	+	0.949565i	$0.601526\pi$
$168$	−14.7500	+	14.2127i	−1.13799	+	1.09653i
$169$	−3.95261			−0.304047
$170$	5.13109	+	5.65108i	0.393536	+	0.433418i
$171$	16.7543	+	29.0193i	1.28123	+	2.21916i
$172$	−14.0301	−	1.35643i	−1.06979	−	0.103427i
$173$	−6.95744	−	4.01688i	−0.528964	−	0.305398i	0.211630	−	0.977350i	$-0.432123\pi$
$173$	−6.95744	−	4.01688i	−0.528964	−	0.305398i	−0.740595	+	0.671952i	$0.765456\pi$
$174$	−2.80670	+	8.76228i	−0.212775	+	0.664267i
$175$	−2.62477	+	0.332538i	−0.198414	+	0.0251375i
$176$	−0.379228	+	0.130250i	−0.0285854	+	0.00981797i
$177$	−11.6645	+	20.2034i	−0.876755	+	1.51858i
$178$	0.956887	+	4.41128i	0.0717217	+	0.330639i
$179$	−7.66309	+	4.42429i	−0.572766	+	0.330687i	−0.758253	−	0.651960i	$-0.773947\pi$
$179$	−7.66309	+	4.42429i	−0.572766	+	0.330687i	0.185487	+	0.982647i	$0.440614\pi$
$180$	3.72258	+	8.17684i	0.277465	+	0.609466i
$181$		−	21.3610i		−	1.58775i	−0.608082	−	0.793874i	$-0.708061\pi$
$181$		−	21.3610i		−	1.58775i	0.608082	−	0.793874i	$-0.291939\pi$
$182$	5.13224	+	14.5257i	0.380427	+	1.07672i
$183$			21.6316i			1.59905i
$184$	4.23684	−	0.498968i	0.312344	−	0.0367844i
$185$	0.899386	−	0.519260i	0.0661241	−	0.0381768i
$186$	−20.5892	+	4.46617i	−1.50967	+	0.327476i
$187$	0.270524	−	0.468561i	0.0197826	−	0.0342645i
$188$	7.23347	+	5.16381i	0.527555	+	0.376610i
$189$	4.18399	−	9.96329i	0.304341	−	0.724723i
$190$	10.0463	+	3.21799i	0.728835	+	0.233457i
$191$	−21.6710	−	12.5117i	−1.56806	−	0.905317i	−0.996396	−	0.0848269i	$-0.972966\pi$
$191$	−21.6710	−	12.5117i	−1.56806	−	0.905317i	−0.571660	−	0.820491i	$-0.693700\pi$
$192$	21.2984	−	5.08712i	1.53708	−	0.367131i
$193$	−4.08078	−	7.06813i	−0.293741	−	0.508775i	0.680950	−	0.732330i	$-0.261567\pi$
$193$	−4.08078	−	7.06813i	−0.293741	−	0.508775i	−0.974691	+	0.223555i	$0.928234\pi$
$194$	−11.5894	+	10.5230i	−0.832074	+	0.755509i
$195$	11.2700			0.807058
$196$	10.8925	−	8.79505i	0.778038	−	0.628218i
$197$	−12.4517			−0.887149			−0.443574	−	0.896238i	$-0.646290\pi$
$197$	−12.4517			−0.887149			−0.443574	+	0.896238i	$0.646290\pi$
$198$	0.471478	−	0.428094i	0.0335065	−	0.0304233i
$199$	−11.5867	−	20.0687i	−0.821358	−	1.42263i	−0.904671	−	0.426110i	$-0.859884\pi$
$199$	−11.5867	−	20.0687i	−0.821358	−	1.42263i	0.0833132	−	0.996523i	$-0.473450\pi$
$200$	2.59808	+	1.11801i	0.183712	+	0.0790555i
$201$	−0.260277	−	0.150271i	−0.0183586	−	0.0105993i
$202$	9.64840	+	3.09054i	0.678859	+	0.217449i
$203$	2.43487	−	5.79814i	0.170895	−	0.406949i
$204$	−17.1674	+	24.0481i	−1.20196	+	1.68370i
$205$	−3.99562	+	6.92062i	−0.279067	+	0.483357i
$206$	−6.75291	+	1.46483i	−0.470498	+	0.102060i
$207$	−5.86780	+	3.38778i	−0.407840	+	0.235467i
$208$	3.15504	−	16.1644i	0.218762	−	1.12080i
$209$		−	0.747747i		−	0.0517228i
$210$	−3.41187	−	9.65658i	−0.235441	−	0.666367i
$211$			10.9759i			0.755613i	0.925885	+	0.377807i	$0.123322\pi$
$211$			10.9759i			0.755613i	−0.925885	+	0.377807i	$0.876678\pi$
$212$	11.1811	−	5.09027i	0.767918	−	0.349601i
$213$	15.9585	−	9.21365i	1.09346	−	0.631309i
$214$	−2.26908	−	10.4605i	−0.155111	−	0.715066i
$215$	3.52389	−	6.10355i	0.240327	−	0.416259i
$216$	−9.26031	+	6.90663i	−0.630084	+	0.469936i
$217$	14.2855	−	1.80987i	0.969764	−	0.122862i
$218$	7.78824	−	24.3142i	0.527486	−	1.64677i
$219$	−14.5712	−	8.41270i	−0.984633	−	0.568478i
$220$	0.0192930	−	0.199556i	0.00130074	−	0.0134540i
$221$	11.1114	+	19.2455i	0.747434	+	1.29459i
$222$	2.70239	+	2.97626i	0.181372	+	0.199753i
$223$	14.9798			1.00312			0.501559	−	0.865123i	$-0.332760\pi$
$223$	14.9798			1.00312			0.501559	+	0.865123i	$0.332760\pi$
$224$	−14.8055	+	2.19024i	−0.989234	+	0.146342i
$225$	−4.49217			−0.299478
$226$	17.2481	+	18.9961i	1.14733	+	1.26360i
$227$	−0.753708	−	1.30546i	−0.0500254	−	0.0866465i	0.839928	−	0.542697i	$-0.182597\pi$
$227$	−0.753708	−	1.30546i	−0.0500254	−	0.0866465i	−0.889954	+	0.456051i	$0.849264\pi$
$228$	−3.92962	+	40.6456i	−0.260245	+	2.69182i
$229$	7.38329	+	4.26274i	0.487901	+	0.281690i	0.723703	−	0.690111i	$-0.242438\pi$
$229$	7.38329	+	4.26274i	0.487901	+	0.281690i	−0.235802	+	0.971801i	$0.575772\pi$
$230$	−0.650688	+	2.03139i	−0.0429051	+	0.133946i
$231$	−0.578085	+	0.439116i	−0.0380352	+	0.0288917i
$232$	−5.38904	+	4.01931i	−0.353808	+	0.263881i
$233$	10.6117	−	18.3799i	0.695193	−	1.20411i	−0.274922	−	0.961467i	$-0.588652\pi$
$233$	10.6117	−	18.3799i	0.695193	−	1.20411i	0.970115	−	0.242644i	$-0.0780146\pi$
$234$	5.54500	+	25.5626i	0.362488	+	1.67108i
$235$	−3.84841	+	2.22188i	−0.251043	+	0.144940i
$236$	−15.5139	+	7.06283i	−1.00987	+	0.459751i
$237$			11.7000i			0.759994i
$238$	13.1265	−	15.3471i	0.850865	−	0.994806i
$239$		−	10.1532i		−	0.656754i	−0.944547	−	0.328377i	$-0.893498\pi$
$239$		−	10.1532i		−	0.656754i	0.944547	−	0.328377i	$-0.106502\pi$
$240$	−2.09744	+	10.7460i	−0.135389	+	0.693648i
$241$	16.4985	−	9.52539i	1.06276	−	0.613584i	0.136565	−	0.990631i	$-0.456394\pi$
$241$	16.4985	−	9.52539i	1.06276	−	0.613584i	0.926194	+	0.377047i	$0.123060\pi$
$242$	15.1889	−	3.29475i	0.976379	−	0.211795i
$243$	−9.27006	+	16.0562i	−0.594674	+	1.03001i
$244$	−9.18342	+	12.8641i	−0.587908	+	0.823542i
$245$	1.74567	+	6.77884i	0.111527	+	0.433084i
$246$	−29.4594	−	9.43632i	−1.87826	−	0.601638i
$247$	26.5980	+	15.3564i	1.69239	+	0.977102i
$248$	−14.1403	−	6.08488i	−0.897909	−	0.386390i
$249$	−8.89801	−	15.4118i	−0.563889	−	0.976684i
$250$	−1.04701	+	0.950668i	−0.0662188	+	0.0601255i
$251$	−9.46184			−0.597226			−0.298613	−	0.954374i	$-0.596524\pi$
$251$	−9.46184			−0.597226			−0.298613	+	0.954374i	$0.596524\pi$
$252$	20.2244	−	12.4900i	1.27402	−	0.786798i
$253$	0.151197			0.00950567
$254$	4.58143	−	4.15986i	0.287465	−	0.261013i
$255$	−7.38677	−	12.7943i	−0.462577	−	0.801207i
$256$	14.8256	+	6.01668i	0.926602	+	0.376043i
$257$	2.37760	+	1.37271i	0.148310	+	0.0856270i	0.572319	−	0.820031i	$-0.306044\pi$
$257$	2.37760	+	1.37271i	0.148310	+	0.0856270i	−0.424008	+	0.905658i	$0.639377\pi$
$258$	25.9813	+	8.32224i	1.61753	+	0.518120i
$259$	−1.66202	−	2.18801i	−0.103273	−	0.135956i
$260$	6.70215	+	4.78452i	0.415650	+	0.296723i
$261$	5.33868	−	9.24686i	0.330456	−	0.572367i
$262$	4.12058	−	0.893830i	0.254570	−	0.0552210i
$263$	−22.2367	+	12.8384i	−1.37117	+	0.791648i	−0.991076	−	0.133298i	$-0.957443\pi$
$263$	−22.2367	+	12.8384i	−1.37117	+	0.791648i	−0.380098	+	0.924946i	$0.624110\pi$
$264$	0.770748	−	0.0907700i	0.0474363	−	0.00558651i
$265$			6.14261i			0.377338i
$266$	5.10570	−	27.4393i	0.313051	−	1.68241i
$267$		−	8.73650i		−	0.534665i
$268$	−0.0909892	−	0.199863i	−0.00555805	−	0.0122086i
$269$	7.10140	−	4.10000i	0.432980	−	0.249981i	−0.267635	−	0.963520i	$-0.586242\pi$
$269$	7.10140	−	4.10000i	0.432980	−	0.249981i	0.700615	+	0.713539i	$0.252909\pi$
$270$	−1.22447	−	5.64485i	−0.0745191	−	0.343535i
$271$	3.20364	−	5.54886i	0.194607	−	0.337069i	−0.752165	−	0.658975i	$-0.770990\pi$
$271$	3.20364	−	5.54886i	0.194607	−	0.337069i	0.946772	+	0.321906i	$0.104324\pi$
$272$	−20.4186	+	7.01301i	−1.23806	+	0.425226i
$273$	−3.74769	−	29.5810i	−0.226821	−	1.79033i
$274$	0.657785	−	2.05355i	0.0397382	−	0.124059i
$275$	0.0868131	+	0.0501216i	0.00523503	+	0.00302244i
$276$	−8.21868	−	0.794582i	−0.494706	−	0.0478282i
$277$	−7.98456	−	13.8297i	−0.479746	−	0.830944i	0.519984	−	0.854176i	$-0.325938\pi$
$277$	−7.98456	−	13.8297i	−0.479746	−	0.830944i	−0.999730	+	0.0232316i	$0.992604\pi$
$278$	−6.80756	−	7.49745i	−0.408290	−	0.449667i
$279$	24.4490			1.46372
$280$	2.07057	−	7.19116i	0.123740	−	0.429754i
$281$	−9.68409			−0.577704			−0.288852	−	0.957374i	$-0.593274\pi$
$281$	−9.68409			−0.577704			−0.288852	+	0.957374i	$0.593274\pi$
$282$	−11.5633	−	12.7352i	−0.688587	−	0.758370i
$283$	13.0633	+	22.6264i	0.776535	+	1.34500i	0.933928	+	0.357462i	$0.116358\pi$
$283$	13.0633	+	22.6264i	0.776535	+	1.34500i	−0.157393	+	0.987536i	$0.550309\pi$
$284$	13.4019	+	1.29570i	0.795259	+	0.0768856i
$285$	−17.6821	−	10.2088i	−1.04740	−	0.604716i
$286$	0.178056	−	0.555877i	0.0105287	−	0.0328697i
$287$	19.4937	+	8.18622i	1.15068	+	0.483217i
$288$	−25.4060	+	0.529749i	−1.49706	+	0.0312158i
$289$	6.06569	−	10.5061i	0.356805	−	0.618005i
$290$	−0.712582	−	3.28502i	−0.0418443	−	0.192903i
$291$	26.2389	−	15.1491i	1.53815	−	0.888053i
$292$	−5.09389	−	11.1890i	−0.298097	−	0.654787i
$293$			16.2389i			0.948684i	0.880341	+	0.474342i	$0.157314\pi$
$293$			16.2389i			0.948684i	−0.880341	+	0.474342i	$0.842686\pi$
$294$	−24.2117	+	12.1666i	−1.41206	+	0.709568i
$295$		−	8.52297i		−	0.496226i
$296$	0.343557	+	2.91722i	0.0199689	+	0.169560i
$297$	−0.354574	+	0.204714i	−0.0205745	+	0.0118787i
$298$	−29.0888	+	6.30990i	−1.68507	+	0.365523i
$299$	−3.10511	+	5.37821i	−0.179573	+	0.311030i
$300$	−4.45553	−	3.18071i	−0.257240	−	0.183638i
$301$	−17.1923	−	7.21973i	−0.990945	−	0.416138i
$302$	5.14883	+	1.64925i	0.296282	+	0.0949039i
$303$	−16.9818	−	9.80446i	−0.975580	−	0.563251i
$304$	−19.5925	+	22.5034i	−1.12371	+	1.29066i
$305$	−3.95143	−	6.84408i	−0.226258	−	0.391891i
$306$	25.3856	−	23.0497i	1.45120	−	1.31766i
$307$	−23.5437			−1.34371			−0.671854	−	0.740684i	$-0.734502\pi$
$307$	−23.5437			−1.34371			−0.671854	+	0.740684i	$0.734502\pi$
$308$	−0.530204	+	0.0157201i	−0.0302112	+	0.000895737i
$309$	13.3741			0.760825
$310$	5.69844	−	5.17408i	0.323649	−	0.293868i
$311$	−2.69773	−	4.67261i	−0.152974	−	0.264959i	0.779345	−	0.626595i	$-0.215552\pi$
$311$	−2.69773	−	4.67261i	−0.152974	−	0.264959i	−0.932320	+	0.361635i	$0.882219\pi$
$312$	−12.6000	+	29.2803i	−0.713333	+	1.65767i
$313$	28.1990	+	16.2807i	1.59390	+	0.920240i	0.992629	+	0.121197i	$0.0386732\pi$
$313$	28.1990	+	16.2807i	1.59390	+	0.920240i	0.601274	+	0.799043i	$0.294660\pi$
$314$	1.72948	+	0.553979i	0.0975999	+	0.0312628i
$315$	1.49382	+	11.7909i	0.0841672	+	0.664343i
$316$	−4.96707	+	6.95787i	−0.279420	+	0.391411i
$317$	−6.85587	+	11.8747i	−0.385064	+	0.666951i	−0.991778	−	0.127970i	$-0.959154\pi$
$317$	−6.85587	+	11.8747i	−0.385064	+	0.666951i	0.606714	+	0.794920i	$0.292487\pi$
$318$	−23.2374	+	5.04062i	−1.30309	+	0.282664i
$319$	−0.206344	+	0.119133i	−0.0115531	+	0.00667017i
$320$	−5.80939	+	5.50009i	−0.324755	+	0.307464i
$321$			20.7170i			1.15631i
$322$	5.54832	+	1.03239i	0.309196	+	0.0575328i
$323$		−	40.2606i		−	2.24016i
$324$	−4.18095	+	1.90341i	−0.232275	+	0.105745i
$325$	−3.56573	+	2.05868i	−0.197791	+	0.114195i
$326$	2.57858	+	11.8873i	0.142814	+	0.658377i
$327$	−24.7075	+	42.7947i	−1.36633	+	2.36655i
$328$	−13.5132	−	18.1183i	−0.746142	−	1.00042i
$329$	7.11167	+	9.36233i	0.392079	+	0.516162i
$330$	−0.118370	+	0.369542i	−0.00651607	+	0.0203426i
$331$	−4.92495	−	2.84342i	−0.270700	−	0.156289i	0.358506	−	0.933527i	$-0.383286\pi$
$331$	−4.92495	−	2.84342i	−0.270700	−	0.156289i	−0.629206	+	0.777239i	$0.716620\pi$
$332$	1.25131	−	12.9428i	0.0686747	−	0.710330i
$333$	−2.33261	−	4.04019i	−0.127826	−	0.221401i
$334$	7.70467	+	8.48548i	0.421581	+	0.464305i
$335$	0.109800			0.00599901
$336$	28.9031	+	1.93186i	1.57680	+	0.105392i
$337$	−14.7219			−0.801955			−0.400978	−	0.916088i	$-0.631330\pi$
$337$	−14.7219			−0.801955			−0.400978	+	0.916088i	$0.631330\pi$
$338$	3.75762	+	4.13843i	0.204388	+	0.225101i
$339$	−24.8306	−	43.0079i	−1.34861	−	2.33587i
$340$	1.03879	−	10.7446i	0.0563362	−	0.582708i
$341$	−0.472487	−	0.272790i	−0.0255866	−	0.0147724i
$342$	14.4557	−	45.1296i	0.781677	−	2.44033i
$343$	17.2124	−	6.83621i	0.929381	−	0.369121i
$344$	11.9178	+	15.9792i	0.642564	+	0.861542i
$345$	2.06425	−	3.57539i	0.111135	−	0.192492i
$346$	2.40850	+	11.1032i	0.129482	+	0.596913i
$347$	13.3966	−	7.73454i	0.719168	−	0.415212i	−0.0952784	−	0.995451i	$-0.530374\pi$
$347$	13.3966	−	7.73454i	0.719168	−	0.415212i	0.814446	+	0.580239i	$0.197041\pi$
$348$	11.8424	−	5.39137i	0.634821	−	0.289008i
$349$		−	11.5290i		−	0.617132i	−0.951203	−	0.308566i	$-0.900151\pi$
$349$		−	11.5290i		−	0.617132i	0.951203	−	0.308566i	$-0.0998491\pi$
$350$	2.84345	+	2.43203i	0.151989	+	0.129997i
$351$		−	16.8167i		−	0.897608i
$352$	0.496893	+	0.273231i	0.0264845	+	0.0145633i
$353$	17.6983	−	10.2181i	0.941985	−	0.543855i	0.0514030	−	0.998678i	$-0.483631\pi$
$353$	17.6983	−	10.2181i	0.941985	−	0.543855i	0.890582	+	0.454823i	$0.150297\pi$
$354$	32.2422	−	6.99394i	1.71366	−	0.371724i
$355$	−3.36611	+	5.83027i	−0.178654	+	0.309438i
$356$	3.70897	−	5.19553i	0.196575	−	0.275362i
$357$	−31.1256	+	23.6431i	−1.64734	+	1.25133i
$358$	11.9173	+	3.81731i	0.629850	+	0.201751i
$359$	18.3761	+	10.6095i	0.969856	+	0.559946i	0.899192	−	0.437554i	$-0.144155\pi$
$359$	18.3761	+	10.6095i	0.969856	+	0.559946i	0.0706634	+	0.997500i	$0.477488\pi$
$360$	5.02231	−	11.6710i	0.264699	−	0.615118i
$361$	−18.3208	−	31.7326i	−0.964255	−	1.67014i
$362$	−22.3652	+	20.3072i	−1.17549	+	1.06732i
$363$	−30.0815			−1.57887
$364$	10.3295	−	19.1826i	0.541415	−	1.00544i
$365$	6.14698			0.321748
$366$	22.6485	−	20.5644i	1.18386	−	1.07492i
$367$	3.82574	+	6.62637i	0.199702	+	0.345894i	0.948432	−	0.316982i	$-0.102669\pi$
$367$	3.82574	+	6.62637i	0.199702	+	0.345894i	−0.748730	+	0.662875i	$0.769336\pi$
$368$	−4.55025	−	3.96167i	−0.237198	−	0.206516i
$369$	31.0886	+	17.9490i	1.61841	+	0.934389i
$370$	−1.39869	−	0.448022i	−0.0727143	−	0.0232916i
$371$	16.1229	−	2.04265i	0.837062	−	0.106049i
$372$	24.2496	+	17.3112i	1.25728	+	0.897546i
$373$	−12.8172	+	22.2000i	−0.663647	+	1.14947i	0.316003	+	0.948758i	$0.397659\pi$
$373$	−12.8172	+	22.2000i	−0.663647	+	1.14947i	−0.979650	+	0.200713i	$0.935674\pi$
$374$	−0.747766	+	0.162204i	−0.0386661	+	0.00838738i
$375$	2.37047	−	1.36859i	0.122411	−	0.0706738i
$376$	−1.47006	−	12.4826i	−0.0758125	−	0.643740i
$377$		−	9.78647i		−	0.504029i
$378$	−14.4093	+	5.09109i	−0.741132	+	0.261857i
$379$			29.1039i			1.49497i	0.664279	+	0.747485i	$0.268739\pi$
$379$			29.1039i			1.49497i	−0.664279	+	0.747485i	$0.731261\pi$
$380$	−6.18141	−	13.5778i	−0.317100	−	0.696527i
$381$	−10.3725	+	5.98858i	−0.531401	+	0.306804i
$382$	7.50196	+	34.5842i	0.383834	+	1.76948i
$383$	4.32161	−	7.48525i	0.220824	−	0.382478i	−0.734234	−	0.678896i	$-0.762459\pi$
$383$	4.32161	−	7.48525i	0.220824	−	0.382478i	0.955058	+	0.296418i	$0.0957920\pi$
$384$	−25.5739	−	17.4635i	−1.30506	−	0.891178i
$385$	0.102689	−	0.244532i	0.00523351	−	0.0124625i
$386$	−3.52093	+	10.9921i	−0.179211	+	0.559481i
$387$	−27.4182	−	15.8299i	−1.39375	−	0.804679i
$388$	22.0354	+	2.13038i	1.11868	+	0.108154i
$389$	7.08846	+	12.2776i	0.359399	+	0.622498i	0.987861	−	0.155343i	$-0.0496483\pi$
$389$	7.08846	+	12.2776i	0.359399	+	0.622498i	−0.628461	+	0.777841i	$0.716315\pi$
$390$	−10.7140	−	11.7998i	−0.542523	−	0.597504i
$391$	8.14084			0.411700
$392$	−19.5637	−	3.04343i	−0.988115	−	0.153716i
$393$	−8.16078			−0.411657
$394$	11.8375	+	13.0371i	0.596362	+	0.656799i
$395$	−2.13723	−	3.70178i	−0.107536	−	0.186257i
$396$	−0.896438	−	0.0866677i	−0.0450477	−	0.00435521i
$397$	0.151559	+	0.0875029i	0.00760655	+	0.00439164i	0.503798	−	0.863821i	$-0.331935\pi$
$397$	0.151559	+	0.0875029i	0.00760655	+	0.00439164i	−0.496192	+	0.868213i	$0.665269\pi$
$398$	−9.99708	+	31.2101i	−0.501108	+	1.56442i
$399$	−20.9157	+	49.8063i	−1.04710	+	2.49344i
$400$	−1.29934	−	3.78308i	−0.0649671	−	0.189154i
$401$	−12.0285	+	20.8339i	−0.600674	+	1.04040i	0.392046	+	0.919946i	$0.371768\pi$
$401$	−12.0285	+	20.8339i	−0.600674	+	1.04040i	−0.992719	+	0.120452i	$0.961566\pi$
$402$	0.0901017	+	0.415371i	0.00449386	+	0.0207168i
$403$	19.4068	−	11.2045i	0.966721	−	0.558136i
$404$	−5.93659	−	13.0401i	−0.295357	−	0.648767i
$405$		−	2.29692i		−	0.114135i
$406$	−8.38547	+	2.96276i	−0.416164	+	0.147039i
$407$			0.104105i			0.00516027i
$408$	41.4991	−	4.88729i	2.05451	−	0.241957i
$409$	−10.3372	+	5.96818i	−0.511141	+	0.295108i	−0.733303	−	0.679902i	$-0.762022\pi$
$409$	−10.3372	+	5.96818i	−0.511141	+	0.295108i	0.222161	+	0.975010i	$0.428689\pi$
$410$	11.0445	−	2.39575i	0.545448	−	0.118318i
$411$	−2.08676	+	3.61438i	−0.102932	+	0.178284i
$412$	7.95347	+	5.67780i	0.391839	+	0.279725i
$413$	−22.3708	+	2.83421i	−1.10080	+	0.139463i
$414$	9.12536	+	2.92300i	0.448487	+	0.143658i
$415$	5.63054	+	3.25079i	0.276392	+	0.159575i
$416$	−19.9237	+	12.0636i	−0.976839	+	0.591467i
$417$	9.80023	+	16.9745i	0.479919	+	0.831245i
$418$	−0.782899	+	0.710859i	−0.0382929	+	0.0347692i
$419$	30.1003			1.47050			0.735249	−	0.677798i	$-0.237065\pi$
$419$	30.1003			1.47050			0.735249	+	0.677798i	$0.237065\pi$
$420$	−6.86699	+	12.7525i	−0.335075	+	0.622256i
$421$	6.78256			0.330562			0.165281	−	0.986247i	$-0.447147\pi$
$421$	6.78256			0.330562			0.165281	+	0.986247i	$0.447147\pi$
$422$	11.4919	−	10.4344i	0.559417	−	0.507941i
$423$	9.98107	+	17.2877i	0.485296	+	0.840557i
$424$	−15.9590	−	6.86753i	−0.775039	−	0.333517i
$425$	4.67424	+	2.69867i	0.226734	+	0.130905i
$426$	−24.8180	−	7.94961i	−1.20244	−	0.385160i
$427$	−16.6501	+	12.6475i	−0.805756	+	0.612056i
$428$	−8.79513	+	12.3202i	−0.425128	+	0.595520i
$429$	−0.564868	+	0.978379i	−0.0272721	+	0.0472366i
$430$	−9.74053	+	2.11290i	−0.469730	+	0.101893i
$431$	13.8010	−	7.96802i	0.664772	−	0.383806i	−0.129321	−	0.991603i	$-0.541280\pi$
$431$	13.8010	−	7.96802i	0.664772	−	0.383806i	0.794093	+	0.607797i	$0.207946\pi$
$432$	16.0348	+	3.12974i	0.771474	+	0.150580i
$433$		−	15.1291i		−	0.727057i	−0.931583	−	0.363529i	$-0.881572\pi$
$433$		−	15.1291i		−	0.727057i	0.931583	−	0.363529i	$-0.118428\pi$
$434$	−15.4757	−	13.2365i	−0.742858	−	0.635373i
$435$			6.50596i			0.311937i
$436$	−32.8613	+	14.9604i	−1.57377	+	0.716472i
$437$	9.74360	−	5.62547i	0.466099	−	0.269103i
$438$	5.04421	+	23.2539i	0.241021	+	1.11112i
$439$	−2.18337	+	3.78171i	−0.104207	+	0.180491i	−0.913414	−	0.407032i	$-0.866564\pi$
$439$	−2.18337	+	3.78171i	−0.104207	+	0.180491i	0.809207	+	0.587523i	$0.199897\pi$
$440$	−0.227278	+	0.169511i	−0.0108351	+	0.00808113i
$441$	30.4517	−	7.84186i	1.45008	−	0.373422i
$442$	9.58701	−	29.9298i	0.456007	−	1.42362i
$443$	−12.2094	−	7.04909i	−0.580086	−	0.334913i	0.181082	−	0.983468i	$-0.442040\pi$
$443$	−12.2094	−	7.04909i	−0.580086	−	0.334913i	−0.761167	+	0.648555i	$0.775373\pi$
$444$	0.547098	−	5.65886i	0.0259641	−	0.268558i
$445$	1.59589	+	2.76417i	0.0756526	+	0.131034i
$446$	−14.2408	−	15.6840i	−0.674320	−	0.742657i
$447$	57.6102			2.72487
$448$	16.3683	+	13.4193i	0.773330	+	0.634003i
$449$	17.0120			0.802848			0.401424	−	0.915892i	$-0.368515\pi$
$449$	17.0120			0.802848			0.401424	+	0.915892i	$0.368515\pi$
$450$	4.27056	+	4.70335i	0.201316	+	0.221718i
$451$	−0.400534	−	0.693745i	−0.0188604	−	0.0326672i
$452$	3.49188	−	36.1180i	0.164244	−	1.69885i
$453$	−9.06228	−	5.23211i	−0.425783	−	0.245826i
$454$	−0.650306	+	2.03020i	−0.0305204	+	0.0952820i
$455$	6.58930	+	8.67464i	0.308911	+	0.406674i
$456$	46.2922	−	34.5261i	2.16783	−	1.61683i
$457$	−5.83234	+	10.1019i	−0.272825	+	0.472548i	−0.969584	−	0.244758i	$-0.921291\pi$
$457$	−5.83234	+	10.1019i	−0.272825	+	0.472548i	0.696759	+	0.717306i	$0.254625\pi$
$458$	−2.55591	−	11.7828i	−0.119430	−	0.550575i
$459$	−19.0912	+	11.0223i	−0.891101	+	0.514477i
$460$	2.74548	−	1.24990i	0.128009	−	0.0582770i
$461$			26.4488i			1.23184i	0.787808	+	0.615921i	$0.211216\pi$
$461$			26.4488i			1.23184i	−0.787808	+	0.615921i	$0.788784\pi$
$462$	1.00933	+	0.187808i	0.0469581	+	0.00873761i
$463$			3.13685i			0.145782i	0.997340	+	0.0728909i	$0.0232225\pi$
$463$			3.13685i			0.145782i	−0.997340	+	0.0728909i	$0.976778\pi$
$464$	9.33144	+	1.82135i	0.433201	+	0.0845541i
$465$	−12.9015	+	7.44866i	−0.598291	+	0.345424i
$466$	−29.3322	+	6.36269i	−1.35879	+	0.294746i
$467$	−4.07057	+	7.05043i	−0.188363	+	0.326255i	−0.944705	−	0.327922i	$-0.893652\pi$
$467$	−4.07057	+	7.05043i	−0.188363	+	0.326255i	0.756341	+	0.654177i	$0.226985\pi$
$468$	21.4929	−	30.1072i	0.993508	−	1.39171i
$469$	−0.0365127	−	0.288200i	−0.00168600	−	0.0133078i
$470$	5.98489	+	1.91706i	0.276062	+	0.0884272i
$471$	−3.04399	−	1.75745i	−0.140260	−	0.0809789i
$472$	22.1434	+	9.52880i	1.01923	+	0.438599i
$473$	0.353246	+	0.611839i	0.0162422	+	0.0281324i
$474$	12.2500	−	11.1228i	0.562660	−	0.510886i
$475$	7.45934			0.342258
$476$	−28.5475	+	0.846412i	−1.30847	+	0.0387952i
$477$	27.5937			1.26343
$478$	−10.6305	+	9.65229i	−0.486227	+	0.441485i
$479$	12.3904	+	21.4608i	0.566131	+	0.980567i	0.996944	+	0.0781258i	$0.0248936\pi$
$479$	12.3904	+	21.4608i	0.566131	+	0.980567i	−0.430813	+	0.902441i	$0.641773\pi$
$480$	13.2451	−	8.01978i	0.604553	−	0.366051i
$481$	−3.70309	−	2.13798i	−0.168846	−	0.0974835i
$482$	−25.6577	−	8.21858i	−1.16868	−	0.374346i
$483$	−10.0710	−	4.22923i	−0.458247	−	0.192437i
$484$	−17.8892	−	12.7707i	−0.813147	−	0.580487i
$485$	−5.53454	+	9.58611i	−0.251311	+	0.435283i
$486$	25.6238	−	5.55827i	1.16232	−	0.252128i
$487$	10.9938	−	6.34726i	0.498175	−	0.287622i	−0.229784	−	0.973242i	$-0.573802\pi$
$487$	10.9938	−	6.34726i	0.498175	−	0.287622i	0.727960	+	0.685620i	$0.240469\pi$
$488$	22.1993	−	2.61438i	1.00491	−	0.118347i
$489$		−	23.5427i		−	1.06464i
$490$	5.43796	−	8.27216i	0.245662	−	0.373698i
$491$			9.51192i			0.429267i	0.976695	+	0.214633i	$0.0688557\pi$
$491$			9.51192i			0.429267i	−0.976695	+	0.214633i	$0.931144\pi$
$492$	18.1262	+	39.8151i	0.817191	+	1.79500i
$493$	−11.1101	+	6.41443i	−0.500375	+	0.288892i
$494$	−9.20758	−	42.4472i	−0.414269	−	1.90979i
$495$	0.225155	−	0.389979i	0.0101199	−	0.0175283i
$496$	7.07177	+	20.5897i	0.317532	+	0.924506i
$497$	16.4225	+	6.89647i	0.736649	+	0.309349i
$498$	−7.67728	+	23.9678i	−0.344027	+	1.07402i
$499$	−7.35497	−	4.24639i	−0.329254	−	0.190095i	0.326256	−	0.945281i	$-0.394213\pi$
$499$	−7.35497	−	4.24639i	−0.329254	−	0.190095i	−0.655510	+	0.755187i	$0.727546\pi$
$500$	1.99072	+	0.192463i	0.0890276	+	0.00860719i
$501$	−11.0917	−	19.2114i	−0.495542	−	0.858303i
$502$	8.99507	+	9.90665i	0.401469	+	0.442155i
$503$	−10.4796			−0.467261			−0.233630	−	0.972325i	$-0.575061\pi$
$503$	−10.4796			−0.467261			−0.233630	+	0.972325i	$0.575061\pi$
$504$	−32.3039	−	9.30134i	−1.43893	−	0.414315i
$505$	7.16390			0.318790
$506$	−0.143738	−	0.158305i	−0.00638993	−	0.00703751i
$507$	−5.40951	−	9.36955i	−0.240245	−	0.416116i
$508$	−8.71084	−	0.842164i	−0.386481	−	0.0373650i
$509$	−19.7483	−	11.4017i	−0.875329	−	0.505371i	−0.00621337	−	0.999981i	$-0.501978\pi$
$509$	−19.7483	−	11.4017i	−0.875329	−	0.505371i	−0.869115	+	0.494609i	$0.835311\pi$
$510$	−6.37336	+	19.8971i	−0.282217	+	0.881059i
$511$	−2.04411	−	16.1344i	−0.0904259	−	0.713744i
$512$	−7.79472	−	21.2425i	−0.344481	−	0.938793i
$513$	−15.2332	+	26.3847i	−0.672564	+	1.16492i
$514$	−0.823066	−	3.79435i	−0.0363039	−	0.167362i
$515$	−4.23147	+	2.44304i	−0.186461	+	0.107653i
$516$	−15.9861	−	35.1144i	−0.703751	−	1.54583i
$517$		−	0.445456i		−	0.0195912i
$518$	−0.710838	+	3.82022i	−0.0312324	+	0.167851i
$519$		−	21.9899i		−	0.965248i
$520$	−1.36208	−	11.5657i	−0.0597311	−	0.507190i
$521$	−7.88048	+	4.54980i	−0.345250	+	0.199330i	−0.662591	−	0.748981i	$-0.730543\pi$
$521$	−7.88048	+	4.54980i	−0.345250	+	0.199330i	0.317341	+	0.948311i	$0.397210\pi$
$522$	−14.7569	+	3.20104i	−0.645891	+	0.140106i
$523$	2.38048	−	4.12311i	0.104091	−	0.180291i	−0.809275	−	0.587429i	$-0.800140\pi$
$523$	2.38048	−	4.12311i	0.104091	−	0.180291i	0.913366	+	0.407138i	$0.133473\pi$
$524$	−4.85315	−	3.46456i	−0.212011	−	0.151350i
$525$	−4.38051	−	5.76683i	−0.191181	−	0.251685i
$526$	34.5816	+	11.0771i	1.50783	+	0.482982i
$527$	−25.4399	−	14.6877i	−1.10818	−	0.639808i
$528$	−0.827762	−	0.720689i	−0.0360237	−	0.0313640i
$529$	−10.3625	−	17.9484i	−0.450544	−	0.780365i
$530$	6.43138	−	5.83958i	0.279361	−	0.253655i
$531$	−38.2866			−1.66150
$532$	−33.5831	+	20.7399i	−1.45601	+	0.899190i
$533$	32.9028			1.42518
$534$	−9.14721	+	8.30551i	−0.395838	+	0.359414i
$535$	−3.78436	−	6.55470i	−0.163612	−	0.283384i
$536$	−0.122758	+	0.285270i	−0.00530233	+	0.0123218i
$537$	−20.9753	−	12.1101i	−0.905150	−	0.522588i
$538$	−11.0438	−	3.53751i	−0.476133	−	0.152513i
$539$	−0.675988	−	0.188219i	−0.0291168	−	0.00810715i
$540$	−4.74615	+	6.64842i	−0.204242	+	0.286102i
$541$	11.2312	−	19.4530i	0.482867	−	0.836350i	−0.516939	−	0.856022i	$-0.672929\pi$
$541$	11.2312	−	19.4530i	0.482867	−	0.836350i	0.999806	+	0.0196717i	$0.00626211\pi$
$542$	−8.85531	+	1.92088i	−0.380368	+	0.0825089i
$543$	50.6355	−	29.2344i	2.17298	−	1.25457i
$544$	26.7540	+	14.7115i	1.14707	+	0.630749i
$545$		−	18.0532i		−	0.773316i
$546$	−27.4089	+	32.0456i	−1.17299	+	1.37143i
$547$		−	24.4644i		−	1.04602i	−0.852326	−	0.523012i	$-0.824808\pi$
$547$		−	24.4644i		−	1.04602i	0.852326	−	0.523012i	$-0.175192\pi$
$548$	−2.77542	+	1.26353i	−0.118560	+	0.0539755i
$549$	−30.7448	+	17.7505i	−1.31215	+	0.757573i
$550$	−0.0300526	−	0.138543i	−0.00128145	−	0.00590750i
$551$	−8.86498	+	15.3546i	−0.377661	+	0.654128i
$552$	6.98130	+	9.36043i	0.297144	+	0.398406i
$553$	−9.00562	+	6.84071i	−0.382958	+	0.290897i
$554$	−6.88915	+	21.5073i	−0.292692	+	0.913759i
$555$	2.46178	+	1.42131i	0.104497	+	0.0603313i
$556$	−1.37819	+	14.2552i	−0.0584483	+	0.604554i
$557$	4.21627	+	7.30280i	0.178649	+	0.309430i	0.941418	−	0.337242i	$-0.109494\pi$
$557$	4.21627	+	7.30280i	0.178649	+	0.309430i	−0.762769	+	0.646671i	$0.776161\pi$
$558$	−23.2429	−	25.5983i	−0.983948	−	1.08366i
$559$	−29.0182			−1.22734
$560$	−9.49764	+	4.66849i	−0.401349	+	0.197280i
$561$	1.48095			0.0625255
$562$	9.20635	+	10.1393i	0.388346	+	0.427702i
$563$	13.5833	+	23.5269i	0.572467	+	0.991541i	0.996312	+	0.0858067i	$0.0273467\pi$
$563$	13.5833	+	23.5269i	0.572467	+	0.991541i	−0.423845	+	0.905735i	$0.639320\pi$
$564$	−2.34100	+	24.2139i	−0.0985738	+	1.01959i
$565$	15.7125	+	9.07159i	0.661028	+	0.381645i
$566$	11.2712	−	35.1876i	0.473762	−	1.47905i
$567$	−6.02888	+	0.763813i	−0.253189	+	0.0320771i
$568$	−11.3842	−	15.2638i	−0.477669	−	0.640453i
$569$	−7.11643	+	12.3260i	−0.298336	+	0.516733i	−0.975755	−	0.218864i	$-0.929765\pi$
$569$	−7.11643	+	12.3260i	−0.298336	+	0.516733i	0.677419	+	0.735597i	$0.263098\pi$
$570$	6.12112	+	28.2185i	0.256386	+	1.18194i
$571$	−14.5870	+	8.42181i	−0.610447	+	0.352442i	−0.773140	−	0.634235i	$-0.781315\pi$
$571$	−14.5870	+	8.42181i	−0.610447	+	0.352442i	0.162693	+	0.986677i	$0.447982\pi$
$572$	−0.751281	+	0.342027i	−0.0314126	+	0.0143009i
$573$		−	68.4938i		−	2.86137i
$574$	−9.96101	−	28.1925i	−0.415764	−	1.17673i
$575$			1.50830i			0.0629006i
$576$	24.7073	+	26.0968i	1.02947	+	1.08737i
$577$	1.86487	−	1.07668i	0.0776356	−	0.0448230i	−0.460680	−	0.887566i	$-0.652394\pi$
$577$	1.86487	−	1.07668i	0.0776356	−	0.0448230i	0.538315	+	0.842744i	$0.319061\pi$
$578$	−16.7664	+	3.63695i	−0.697392	+	0.151277i
$579$	11.1699	−	19.3468i	0.464203	−	0.804024i
$580$	−2.76202	+	3.86904i	−0.114687	+	0.160653i
$581$	6.66021	−	15.8599i	0.276312	−	0.657979i
$582$	−40.8057	−	13.0707i	−1.69145	−	0.541799i
$583$	−0.533259	−	0.307877i	−0.0220853	−	0.0127510i
$584$	−6.87241	+	15.9704i	−0.284382	+	0.660859i
$585$	9.24793	+	16.0179i	0.382355	+	0.662258i
$586$	17.0023	−	15.4378i	0.702357	−	0.637728i
$587$	−11.3061			−0.466652			−0.233326	−	0.972399i	$-0.574961\pi$
$587$	−11.3061			−0.466652			−0.233326	+	0.972399i	$0.574961\pi$
$588$	35.7558	+	13.7836i	1.47454	+	0.568425i
$589$	−40.5980			−1.67281
$590$	−8.92364	+	8.10251i	−0.367380	+	0.333575i
$591$	−17.0413	−	29.5164i	−0.700986	−	1.21414i
$592$	2.72775	−	3.13301i	0.112110	−	0.128766i
$593$	14.7570	+	8.51993i	0.605996	+	0.349872i	0.771397	−	0.636355i	$-0.219558\pi$
$593$	14.7570	+	8.51993i	0.605996	+	0.349872i	−0.165401	+	0.986226i	$0.552892\pi$
$594$	0.551420	+	0.176629i	0.0226250	+	0.00724716i
$595$	5.52904	−	13.1662i	0.226668	−	0.539763i
$596$	34.2603	+	24.4577i	1.40336	+	1.00183i
$597$	31.7149	−	54.9318i	1.29800	−	2.24821i
$598$	8.58296	−	1.86180i	0.350984	−	0.0761348i
$599$	3.39864	−	1.96221i	0.138865	−	0.0801736i	−0.428958	−	0.903324i	$-0.641119\pi$
$599$	3.39864	−	1.96221i	0.138865	−	0.0801736i	0.567823	+	0.823151i	$0.307786\pi$
$600$	0.905498	+	7.68879i	0.0369668	+	0.313893i
$601$		−	8.98026i		−	0.366312i	−0.983084	−	0.183156i	$-0.941369\pi$
$601$		−	8.98026i		−	0.366312i	0.983084	−	0.183156i	$-0.0586314\pi$
$602$	8.78498	+	24.8640i	0.358049	+	1.01338i
$603$		−	0.493240i		−	0.0200863i
$604$	−3.16804	−	6.95877i	−0.128906	−	0.283149i
$605$	9.51758	−	5.49498i	0.386945	−	0.223403i
$606$	5.87869	+	27.1009i	0.238806	+	1.10090i
$607$	18.7895	−	32.5444i	0.762644	−	1.32094i	−0.178840	−	0.983878i	$-0.557234\pi$
$607$	18.7895	−	32.5444i	0.762644	−	1.32094i	0.941483	−	0.337059i	$-0.109432\pi$
$608$	42.1872	−	0.879659i	1.71092	−	0.0356749i
$609$	17.0767	−	2.16348i	0.691981	−	0.0876687i
$610$	−3.40933	+	10.6436i	−0.138040	+	0.430948i
$611$	15.8453	+	9.14827i	0.641031	+	0.370099i
$612$	−48.2666	−	4.66641i	−1.95106	−	0.188629i
$613$	23.1299	+	40.0621i	0.934207	+	1.61809i	0.776042	+	0.630681i	$0.217224\pi$
$613$	23.1299	+	40.0621i	0.934207	+	1.61809i	0.158165	+	0.987413i	$0.449442\pi$
$614$	22.3822	+	24.6505i	0.903272	+	0.994812i
$615$	−21.8735			−0.882025
$616$	0.520507	+	0.540184i	0.0209718	+	0.0217646i
$617$	−42.8844			−1.72646			−0.863231	−	0.504809i	$-0.831563\pi$
$617$	−42.8844			−1.72646			−0.863231	+	0.504809i	$0.831563\pi$
$618$	−12.7143	−	14.0028i	−0.511445	−	0.563276i
$619$	−14.7503	−	25.5483i	−0.592865	−	1.02687i	−0.993844	−	0.110785i	$-0.964664\pi$
$619$	−14.7503	−	25.5483i	−0.592865	−	1.02687i	0.400980	−	0.916087i	$-0.368670\pi$
$620$	−10.8346	−	1.04749i	−0.435129	−	0.0420683i
$621$	−5.33508	−	3.08021i	−0.214090	−	0.123605i
$622$	−2.32762	+	7.26665i	−0.0933293	+	0.291366i
$623$	6.72461	−	5.10804i	0.269416	−	0.204649i
$624$	42.6352	−	14.6435i	1.70677	−	0.586210i
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	−9.76181	−	45.0022i	−0.390160	−	1.79865i
$627$	1.77251	−	1.02336i	0.0707873	−	0.0408691i
$628$	−1.06413	−	2.33743i	−0.0424636	−	0.0932735i
$629$			5.60526i			0.223496i
$630$	10.9251	−	12.7733i	0.435266	−	0.508900i
$631$			20.5872i			0.819563i	0.912184	+	0.409781i	$0.134395\pi$
$631$			20.5872i			0.819563i	−0.912184	+	0.409781i	$0.865605\pi$
$632$	12.0070	−	1.41405i	0.477613	−	0.0562478i
$633$	−26.0181	+	15.0215i	−1.03413	+	0.597053i
$634$	18.9506	−	4.11074i	0.752625	−	0.163258i
$635$	2.18786	−	3.78949i	0.0868227	−	0.150381i
$636$	27.3686	+	19.5378i	1.08524	+	0.774726i
$637$	20.5777	−	20.1800i	0.815320	−	0.799562i
$638$	0.320899	+	0.102789i	0.0127045	+	0.00406945i
$639$	26.1906	+	15.1211i	1.03608	+	0.598182i
$640$	11.2815	+	0.853736i	0.445939	+	0.0337469i
$641$	18.4263	+	31.9153i	0.727795	+	1.26058i	0.957813	+	0.287392i	$0.0927883\pi$
$641$	18.4263	+	31.9153i	0.727795	+	1.26058i	−0.230018	+	0.973186i	$0.573878\pi$
$642$	21.6909	−	19.6949i	0.856071	−	0.777297i
$643$	−48.4719			−1.91154			−0.955772	−	0.294108i	$-0.904977\pi$
$643$	−48.4719			−1.91154			−0.955772	+	0.294108i	$0.904977\pi$
$644$	−4.19368	−	6.79061i	−0.165254	−	0.267587i
$645$	19.2911			0.759585
$646$	−42.1533	+	38.2745i	−1.65850	+	1.50589i
$647$	19.5933	+	33.9366i	0.770292	+	1.33418i	0.937403	+	0.348247i	$0.113223\pi$
$647$	19.5933	+	33.9366i	0.770292	+	1.33418i	−0.167111	+	0.985938i	$0.553444\pi$
$648$	5.96759	+	2.56799i	0.234429	+	0.100880i
$649$	0.739905	+	0.427185i	0.0290438	+	0.0167685i
$650$	5.54528	+	1.77624i	0.217504	+	0.0696700i
$651$	23.8413	+	31.3864i	0.934413	+	1.23013i
$652$	9.99477	−	14.0007i	0.391425	−	0.548309i
$653$	−3.44161	+	5.96105i	−0.134681	+	0.233274i	−0.925475	−	0.378808i	$-0.876334\pi$
$653$	−3.44161	+	5.96105i	−0.134681	+	0.233274i	0.790795	+	0.612082i	$0.209668\pi$
$654$	68.2951	−	14.8145i	2.67055	−	0.579291i
$655$	2.58201	−	1.49073i	0.100888	−	0.0582475i
$656$	−6.12351	+	31.3730i	−0.239083	+	1.22491i
$657$		−	27.6133i		−	1.07730i
$658$	3.04163	−	16.3465i	0.118575	−	0.637251i
$659$		−	40.9792i		−	1.59632i	−0.602444	−	0.798161i	$-0.705806\pi$
$659$		−	40.9792i		−	1.59632i	0.602444	−	0.798161i	$-0.294194\pi$
$660$	0.499445	−	0.227377i	0.0194409	−	0.00885063i
$661$	10.4696	−	6.04460i	0.407219	−	0.235108i	−0.282375	−	0.959304i	$-0.591122\pi$
$661$	10.4696	−	6.04460i	0.407219	−	0.235108i	0.689594	+	0.724196i	$0.257789\pi$
$662$	1.70490	+	7.85962i	0.0662627	+	0.305473i
$663$	−30.4139	+	52.6785i	−1.18118	+	2.04586i
$664$	−14.7409	+	10.9942i	−0.572056	+	0.426657i
$665$	−2.48052	−	19.5790i	−0.0961903	−	0.759243i
$666$	−2.01259	+	6.28314i	−0.0779863	+	0.243467i
$667$	−3.10475	−	1.79253i	−0.120216	−	0.0694070i
$668$	1.55981	−	16.1337i	0.0603508	−	0.624233i
$669$	20.5012	+	35.5091i	0.792621	+	1.37286i
$670$	−0.104383	−	0.114962i	−0.00403268	−	0.00444136i
$671$	0.792208			0.0305828
$672$	−25.4546	−	32.0984i	−0.981932	−	1.23822i
$673$	29.0006			1.11789			0.558945	−	0.829205i	$-0.311206\pi$
$673$	29.0006			1.11789			0.558945	+	0.829205i	$0.311206\pi$
$674$	13.9957	+	15.4140i	0.539093	+	0.593726i
$675$	−2.04217	−	3.53714i	−0.0786032	−	0.136145i
$676$	0.760730	−	7.86853i	0.0292588	−	0.302636i
$677$	41.8361	+	24.1541i	1.60789	+	0.928317i	0.989841	+	0.142178i	$0.0454106\pi$
$677$	41.8361	+	24.1541i	1.60789	+	0.928317i	0.618051	+	0.786138i	$0.287923\pi$
$678$	−21.4240	+	66.8841i	−0.822786	+	2.56867i
$679$	27.0018	+	11.3392i	1.03623	+	0.435157i
$680$	−12.2373	+	9.12692i	−0.469277	+	0.350001i
$681$	2.06304	−	3.57329i	0.0790558	−	0.136929i
$682$	0.163563	+	0.754032i	0.00626317	+	0.0288734i
$683$	11.4528	−	6.61231i	0.438231	−	0.253013i	−0.264616	−	0.964354i	$-0.585245\pi$
$683$	11.4528	−	6.61231i	0.438231	−	0.253013i	0.702847	+	0.711341i	$0.251912\pi$
$684$	−60.9938	+	27.7680i	−2.33216	+	1.06173i
$685$		−	1.52475i		−	0.0582578i
$686$	−23.5208	−	11.5226i	−0.898030	−	0.439934i
$687$			23.3358i			0.890317i
$688$	5.40055	−	27.6690i	0.205894	−	1.05487i
$689$	21.9029	−	12.6457i	0.834435	−	0.481761i
$690$	−5.70588	+	1.23771i	−0.217219	+	0.0471189i
$691$	−19.9447	+	34.5453i	−0.758733	+	1.31416i	0.184763	+	0.982783i	$0.440848\pi$
$691$	−19.9447	+	34.5453i	−0.758733	+	1.31416i	−0.943497	+	0.331382i	$0.892485\pi$
$692$	9.33552	−	13.0772i	0.354883	−	0.497121i
$693$	−1.09848	−	0.461296i	−0.0417277	−	0.0175232i
$694$	−20.8339	−	6.67342i	−0.790843	−	0.253320i
$695$	−6.20145	−	3.58041i	−0.235234	−	0.135813i
$696$	−16.9030	−	7.27376i	−0.640708	−	0.275711i
$697$	−21.5658	−	37.3530i	−0.816862	−	1.41485i
$698$	−12.0710	+	10.9602i	−0.456893	+	0.414851i
$699$	58.0921			2.19725
$700$	−0.156820	−	5.28918i	−0.00592724	−	0.199912i
$701$	−5.82647			−0.220063			−0.110031	−	0.993928i	$-0.535095\pi$
$701$	−5.82647			−0.220063			−0.110031	+	0.993928i	$0.535095\pi$
$702$	−17.6072	+	15.9871i	−0.664543	+	0.603393i
$703$	3.87334	+	6.70882i	0.146086	+	0.253028i
$704$	−0.186304	−	0.780004i	−0.00702160	−	0.0293975i
$705$	−10.5338	−	6.08169i	−0.396726	−	0.229050i
$706$	−27.5237	−	8.81627i	−1.03587	−	0.331805i
$707$	−2.38227	−	18.8036i	−0.0895946	−	0.707182i
$708$	−37.9744	−	27.1091i	−1.42716	−	1.01882i
$709$	8.29615	−	14.3694i	0.311569	−	0.539653i	−0.667134	−	0.744938i	$-0.732479\pi$
$709$	8.29615	−	14.3694i	0.311569	−	0.539653i	0.978702	+	0.205286i	$0.0658123\pi$
$710$	9.30440	−	2.01830i	0.349188	−	0.0757453i
$711$	−16.6290	+	9.60078i	−0.623638	+	0.360058i
$712$	−8.96577	+	1.05589i	−0.336006	+	0.0395710i
$713$		−	8.20905i		−	0.307431i
$714$	54.3447	+	10.1121i	2.03380	+	0.378434i
$715$		−	0.412736i		−	0.0154355i
$716$	−7.33265	−	16.1066i	−0.274034	−	0.601930i
$717$	24.0678	−	13.8955i	0.898828	−	0.518938i
$718$	−6.36137	−	29.3261i	−0.237404	−	1.09444i
$719$	1.69923	−	2.94314i	0.0633704	−	0.109761i	−0.832600	−	0.553875i	$-0.813148\pi$
$719$	1.69923	−	2.94314i	0.0633704	−	0.109761i	0.895970	+	0.444115i	$0.146482\pi$
$720$	−16.9942	+	5.83687i	−0.633338	+	0.217527i
$721$	7.81954	+	10.2942i	0.291215	+	0.383377i
$722$	−15.8074	+	49.3493i	−0.588290	+	1.83659i
$723$	45.1593	+	26.0727i	1.67949	+	0.969655i
$724$	42.5237	+	4.11119i	1.58038	+	0.152791i
$725$	−1.18844	−	2.05844i	−0.0441376	−	0.0764486i
$726$	28.5975	+	31.4957i	1.06135	+	1.16891i
$727$	−14.3045			−0.530526			−0.265263	−	0.964176i	$-0.585459\pi$
$727$	−14.3045			−0.530526			−0.265263	+	0.964176i	$0.585459\pi$
$728$	−29.9044	+	7.42118i	−1.10833	+	0.275047i
$729$	−43.8569			−1.62433
$730$	−5.84373	−	6.43595i	−0.216286	−	0.238205i
$731$	19.0197	+	32.9430i	0.703468	+	1.21844i
$732$	−43.0624	−	4.16327i	−1.59163	−	0.153879i
$733$	−42.8607	−	24.7457i	−1.58310	−	0.914001i	−0.994404	−	0.105645i	$-0.966309\pi$
$733$	−42.8607	−	24.7457i	−1.58310	−	0.914001i	−0.588693	−	0.808357i	$-0.700357\pi$
$734$	3.30088	−	10.3051i	0.121838	−	0.380367i
$735$	−13.6799	+	13.4155i	−0.504591	+	0.494839i
$736$	0.177870	+	8.53039i	0.00655637	+	0.314434i
$737$	−0.00550334	+	0.00953207i	−0.000202718	+	0.000351118i
$738$	−10.7621	−	49.6137i	−0.396159	−	1.82630i
$739$	−23.2184	+	13.4052i	−0.854104	+	0.493117i	−0.862033	−	0.506852i	$-0.830809\pi$
$739$	−23.2184	+	13.4052i	−0.854104	+	0.493117i	0.00792968	+	0.999969i	$0.497476\pi$
$740$	0.860603	+	1.89036i	0.0316364	+	0.0694911i
$741$			84.0664i			3.08826i
$742$	−17.4662	−	14.9390i	−0.641206	−	0.548428i
$743$			22.2896i			0.817727i	0.912596	+	0.408863i	$0.134075\pi$
$743$			22.2896i			0.817727i	−0.912596	+	0.408863i	$0.865925\pi$
$744$	−4.92824	−	41.8468i	−0.180678	−	1.53418i
$745$	−18.2275	+	10.5236i	−0.667803	+	0.385556i
$746$	35.4285	−	7.68509i	1.29713	−	0.281371i
$747$	14.6031	−	25.2933i	0.534300	−	0.925435i
$748$	0.880706	+	0.628717i	0.0322018	+	0.0229882i
$749$	−15.9461	+	12.1128i	−0.582659	+	0.442591i
$750$	−3.68646	−	1.18083i	−0.134610	−	0.0431179i
$751$	−11.1427	−	6.43324i	−0.406603	−	0.234752i	0.282726	−	0.959201i	$-0.408761\pi$
$751$	−11.1427	−	6.43324i	−0.406603	−	0.234752i	−0.689329	+	0.724448i	$0.742095\pi$
$752$	−11.6719	+	13.4060i	−0.425629	+	0.488865i
$753$	−12.9494	−	22.4290i	−0.471902	−	0.817359i
$754$	−10.2465	+	9.30368i	−0.373157	+	0.338820i
$755$	3.82299			0.139133
$756$	19.0288	+	10.2467i	0.692072	+	0.372669i
$757$	−3.66830			−0.133327			−0.0666633	−	0.997776i	$-0.521235\pi$
$757$	−3.66830			−0.133327			−0.0666633	+	0.997776i	$0.521235\pi$
$758$	30.4721	−	27.6682i	1.10680	−	1.00495i
$759$	0.206927	+	0.358408i	0.00751097	+	0.0130094i
$760$	−8.33964	+	19.3800i	−0.302511	+	0.702986i
$761$	−2.56137	−	1.47880i	−0.0928494	−	0.0536066i	0.452856	−	0.891583i	$-0.350405\pi$
$761$	−2.56137	−	1.47880i	−0.0928494	−	0.0536066i	−0.545706	+	0.837977i	$0.683738\pi$
$762$	16.1309	+	5.16700i	0.584362	+	0.187181i
$763$	−47.3856	+	6.00339i	−1.71547	+	0.217337i
$764$	29.0782	−	40.7327i	1.05201	−	1.47366i
$765$	12.1229	−	20.9975i	0.438305	−	0.759166i
$766$	−11.9456	+	2.59121i	−0.431610	+	0.0936243i
$767$	−30.3906	+	17.5460i	−1.09734	+	0.633551i
$768$	6.02788	+	43.3781i	0.217512	+	1.56527i
$769$			32.6324i			1.17676i	0.808586	+	0.588378i	$0.200233\pi$
$769$			32.6324i			1.17676i	−0.808586	+	0.588378i	$0.799767\pi$
$770$	−0.353650	+	0.124952i	−0.0127447	+	0.00450296i
$771$			7.51469i			0.270635i
$772$	14.8560	−	6.76334i	0.534681	−	0.243418i
$773$	−4.76043	+	2.74844i	−0.171221	+	0.0988544i	−0.583161	−	0.812356i	$-0.698184\pi$
$773$	−4.76043	+	2.74844i	−0.171221	+	0.0988544i	0.411941	+	0.911211i	$0.364851\pi$
$774$	9.49151	+	43.7561i	0.341165	+	1.57278i
$775$	2.72129	−	4.71341i	0.0977516	−	0.169311i
$776$	−18.7178	−	25.0966i	−0.671931	−	0.900916i
$777$	2.91198	−	6.93425i	0.104467	−	0.248765i
$778$	6.11598	−	19.0936i	0.219269	−	0.684538i
$779$	−51.6233	−	29.8047i	−1.84960	−	1.06786i
$780$	−2.16904	+	22.4353i	−0.0776642	+	0.803313i
$781$	−0.337429	−	0.584444i	−0.0120742	−	0.0209131i
$782$	−7.73923	−	8.52354i	−0.276754	−	0.304801i
$783$	9.70800			0.346936
$784$	15.4121	+	23.3767i	0.550431	+	0.834881i
$785$	1.28413			0.0458325
$786$	7.75819	+	8.54443i	0.276725	+	0.304770i
$787$	−15.7430	−	27.2677i	−0.561177	−	0.971987i	−0.997394	−	0.0721455i	$-0.977015\pi$
$787$	−15.7430	−	27.2677i	−0.561177	−	0.971987i	0.436217	−	0.899841i	$-0.356318\pi$
$788$	2.39649	−	24.7879i	0.0853715	−	0.883031i
$789$	−60.8659	−	35.1410i	−2.16689	−	1.25105i
$790$	−1.84402	+	5.75687i	−0.0656072	+	0.204820i
$791$	18.5858	−	44.2582i	0.660837	−	1.57364i
$792$	0.761473	+	1.02097i	0.0270578	+	0.0362787i
$793$	−16.2694	+	28.1795i	−0.577745	+	1.00068i
$794$	−0.0524662	−	0.241870i	−0.00186195	−	0.00858366i
$795$	−14.5609	+	8.40673i	−0.516421	+	0.298156i
$796$	42.1812	−	19.2033i	1.49507	−	0.680644i
$797$			20.2691i			0.717968i	0.933344	+	0.358984i	$0.116877\pi$
$797$			20.2691i			0.717968i	−0.933344	+	0.358984i	$0.883123\pi$
$798$	72.0317	−	25.4503i	2.54989	−	0.900930i
$799$		−	23.9845i		−	0.848512i
$800$	−2.72568	+	4.95688i	−0.0963675	+	0.175252i
$801$	12.4171	−	7.16902i	0.438737	−	0.253305i
$802$	33.2484	−	7.21220i	1.17404	−	0.254672i
$803$	−0.308096	+	0.533638i	−0.0108725	+	0.0188317i
$804$	0.349241	−	0.489217i	0.0123168	−	0.0172534i
$805$	3.95895	−	0.501568i	0.139535	−	0.0176780i
$806$	−30.1806	−	9.66734i	−1.06307	−	0.340518i
$807$	19.4378	+	11.2224i	0.684244	+	0.395049i
$808$	−8.00934	+	18.6124i	−0.281768	+	0.654783i
$809$	15.6376	+	27.0851i	0.549789	+	0.952262i	0.998289	+	0.0584790i	$0.0186251\pi$
$809$	15.6376	+	27.0851i	0.549789	+	0.952262i	−0.448500	+	0.893783i	$0.648042\pi$
$810$	−2.40490	+	2.18361i	−0.0844995	+	0.0767241i
$811$	51.4855			1.80790			0.903950	−	0.427638i	$-0.140654\pi$
$811$	51.4855			1.80790			0.903950	+	0.427638i	$0.140654\pi$
$812$	11.0738	+	5.96307i	0.388615	+	0.209263i
$813$	17.5379			0.615080
$814$	0.108999	−	0.0989688i	0.00382040	−	0.00346886i
$815$	4.30054	+	7.44875i	0.150641	+	0.260918i
$816$	−44.5689	−	38.8038i	−1.56022	−	1.35840i
$817$	45.5285	+	26.2859i	1.59284	+	0.919626i
$818$	16.0760	+	5.14940i	0.562084	+	0.180044i
$819$	38.9680	−	29.6002i	1.36165	−	1.03432i
$820$	−13.0080	−	9.28612i	−0.454259	−	0.324285i
$821$	24.0601	−	41.6733i	0.839702	−	1.45441i	−0.0504413	−	0.998727i	$-0.516063\pi$
$821$	24.0601	−	41.6733i	0.839702	−	1.45441i	0.890144	−	0.455680i	$-0.150604\pi$
$822$	5.76812	−	1.25121i	0.201186	−	0.0436410i
$823$	21.3892	−	12.3490i	0.745580	−	0.430461i	−0.0785148	−	0.996913i	$-0.525018\pi$
$823$	21.3892	−	12.3490i	0.745580	−	0.430461i	0.824095	+	0.566452i	$0.191684\pi$
$824$	−1.61638	−	13.7251i	−0.0563094	−	0.478135i
$825$			0.274384i			0.00955282i
$826$	24.2347	+	20.7281i	0.843232	+	0.721223i
$827$		−	19.9120i		−	0.692408i	−0.938159	−	0.346204i	$-0.887470\pi$
$827$		−	19.9120i		−	0.692408i	0.938159	−	0.346204i	$-0.112530\pi$
$828$	−5.61477	−	12.3332i	−0.195127	−	0.428607i
$829$	−13.8257	+	7.98225i	−0.480185	+	0.277235i	−0.720494	−	0.693461i	$-0.756085\pi$
$829$	−13.8257	+	7.98225i	−0.480185	+	0.277235i	0.240308	+	0.970697i	$0.422751\pi$
$830$	−1.94916	−	8.98566i	−0.0676562	−	0.311897i
$831$	21.8552	−	37.8543i	0.758149	−	1.31315i
$832$	31.5715	+	9.39183i	1.09455	+	0.325603i
$833$	−36.3969	−	10.1342i	−1.26108	−	0.351128i
$834$	8.45572	−	26.3981i	0.292798	−	0.914090i
$835$	7.01869	+	4.05224i	0.242892	+	0.140234i
$836$	1.48855	+	0.143913i	0.0514827	+	0.00497735i
$837$	11.1147	+	19.2512i	0.384179	+	0.665418i
$838$	−28.6154	−	31.5154i	−0.988503	−	1.08868i
$839$	−14.5375			−0.501889			−0.250944	−	0.968002i	$-0.580741\pi$
$839$	−14.5375			−0.501889			−0.250944	+	0.968002i	$0.580741\pi$
$840$	19.8802	−	4.93354i	0.685931	−	0.170223i
$841$	−23.3504			−0.805187
$842$	−6.44796	−	7.10141i	−0.222211	−	0.244731i
$843$	−13.2536	−	22.9558i	−0.456477	−	0.790641i
$844$	−21.8500	−	2.11245i	−0.752106	−	0.0727136i
$845$	3.42306	+	1.97631i	0.117757	+	0.0679870i
$846$	8.61174	−	26.8851i	0.296078	−	0.924330i
$847$	−17.5880	−	23.1542i	−0.604331	−	0.795586i
$848$	7.98136	+	23.2380i	0.274081	+	0.797996i
$849$	−35.7568	+	61.9325i	−1.22717	+	2.12552i
$850$	−1.61811	−	7.45952i	−0.0555007	−	0.255860i
$851$	−1.35655	+	0.783202i	−0.0465018	+	0.0268478i
$852$	15.2704	+	33.5422i	0.523154	+	1.14914i
$853$			36.2299i			1.24049i	0.784408	+	0.620245i	$0.212967\pi$
$853$			36.2299i			1.24049i	−0.784408	+	0.620245i	$0.787033\pi$
$854$	29.0708	+	5.40928i	0.994783	+	0.185102i
$855$		−	33.5086i		−	1.14597i
$856$	21.2606	−	2.50384i	0.726674	−	0.0855794i
$857$	−32.9576	+	19.0281i	−1.12581	+	0.649986i	−0.942878	−	0.333139i	$-0.891892\pi$
$857$	−32.9576	+	19.0281i	−1.12581	+	0.649986i	−0.182932	+	0.983126i	$0.558559\pi$
$858$	1.56137	−	0.338691i	0.0533045	−	0.0115627i
$859$	−13.3104	+	23.0543i	−0.454145	+	0.786602i	−0.998639	−	0.0521630i	$-0.983388\pi$
$859$	−13.3104	+	23.0543i	−0.454145	+	0.786602i	0.544494	+	0.838765i	$0.316722\pi$
$860$	11.4722	+	8.18977i	0.391200	+	0.279269i
$861$	7.27378	+	57.4129i	0.247890	+	1.95663i
$862$	−21.4628	−	6.87487i	−0.731025	−	0.234159i
$863$	−20.1195	−	11.6160i	−0.684876	−	0.395413i	0.116814	−	0.993154i	$-0.462732\pi$
$863$	−20.1195	−	11.6160i	−0.684876	−	0.395413i	−0.801690	+	0.597741i	$0.796065\pi$
$864$	−11.9669	−	19.7639i	−0.407122	−	0.672383i
$865$	4.01688	+	6.95744i	0.136578	+	0.236560i
$866$	−15.8403	+	14.3827i	−0.538276	+	0.488745i
$867$	33.2058			1.12773
$868$	0.853505	+	28.7868i	0.0289698	+	0.977086i
$869$	0.428484			0.0145353
$870$	6.81181	−	6.18501i	0.230942	−	0.209691i
$871$	−0.226043	−	0.391517i	−0.00765916	−	0.0132661i
$872$	46.9038	+	20.1838i	1.58836	+	0.683509i
$873$	43.0624	+	24.8621i	1.45744	+	0.841455i
$874$	−15.1528	−	4.85370i	−0.512553	−	0.164179i
$875$	2.43939	+	1.02440i	0.0824663	+	0.0346310i
$876$	19.5517	−	27.3881i	0.660592	−	0.925358i
$877$	1.28202	−	2.22052i	0.0432907	−	0.0749817i	−0.843568	−	0.537022i	$-0.819549\pi$
$877$	1.28202	−	2.22052i	0.0432907	−	0.0749817i	0.886859	+	0.462040i	$0.152882\pi$
$878$	6.03515	−	1.30914i	0.203676	−	0.0441812i
$879$	−38.4937	+	22.2244i	−1.29836	+	0.749609i
$880$	0.393546	+	0.0768140i	0.0132664	+	0.00258940i
$881$		−	11.4074i		−	0.384324i	−0.981363	−	0.192162i	$-0.938450\pi$
$881$		−	11.4074i		−	0.384324i	0.981363	−	0.192162i	$-0.0615498\pi$
$882$	−37.1599	−	24.4282i	−1.25124	−	0.822542i
$883$			15.8634i			0.533845i	0.963718	+	0.266922i	$0.0860068\pi$
$883$			15.8634i			0.533845i	−0.963718	+	0.266922i	$0.913993\pi$
$884$	−40.4509	+	18.4156i	−1.36051	+	0.619385i
$885$	20.2034	−	11.6645i	0.679131	−	0.392097i
$886$	4.22659	+	19.4847i	0.141995	+	0.654601i
$887$	13.5260	−	23.4277i	0.454159	−	0.786626i	−0.544480	−	0.838774i	$-0.683273\pi$
$887$	13.5260	−	23.4277i	0.454159	−	0.786626i	0.998639	+	0.0521471i	$0.0166065\pi$
$888$	−6.44499	+	4.80687i	−0.216280	+	0.161308i
$889$	−10.6741	−	4.48249i	−0.357997	−	0.150338i
$890$	1.37695	−	4.29872i	0.0461554	−	0.144093i
$891$	0.199403	+	0.115125i	0.00668024	+	0.00385684i
$892$	−2.88304	+	29.8205i	−0.0965314	+	0.998463i
$893$	−16.5738	−	28.7066i	−0.554620	−	0.960629i
$894$	−54.7681	−	60.3185i	−1.83172	−	2.01735i
$895$	8.84857			0.295775
$896$	−1.51065	−	29.8951i	−0.0504674	−	0.998726i
$897$	−16.9985			−0.567563
$898$	−16.1728	−	17.8118i	−0.539693	−	0.594387i
$899$	6.46818	+	11.2032i	0.215726	+	0.373648i
$900$	0.864575	−	8.94264i	0.0288192	−	0.298088i
$901$	−28.7121	−	16.5769i	−0.956537	−	0.552257i
$902$	−0.345584	+	1.07888i	−0.0115067	+	0.0359229i
$903$	−6.41502	−	50.6346i	−0.213478	−	1.68501i
$904$	−41.1355	+	30.6801i	−1.36815	+	1.02041i
$905$	−10.6805	+	18.4991i	−0.355031	+	0.614932i
$906$	3.13714	+	14.4623i	0.104225	+	0.480478i
$907$	−9.02842	+	5.21256i	−0.299784	+	0.173080i	−0.642346	−	0.766415i	$-0.722039\pi$
$907$	−9.02842	+	5.21256i	−0.299784	+	0.173080i	0.342562	+	0.939495i	$0.388705\pi$
$908$	2.74387	−	1.24917i	0.0910584	−	0.0414551i
$909$		−	32.1815i		−	1.06739i
$910$	2.81821	−	15.1458i	0.0934228	−	0.502077i
$911$			43.7727i			1.45026i	0.688614	+	0.725128i	$0.258219\pi$
$911$			43.7727i			1.45026i	−0.688614	+	0.725128i	$0.741781\pi$
$912$	−80.1577	−	15.6455i	−2.65429	−	0.518075i
$913$	−0.564423	+	0.325870i	−0.0186797	+	0.0107847i
$914$	16.1214	−	3.49704i	0.533250	−	0.115672i
$915$	10.8158	−	18.7335i	0.357559	−	0.619310i
$916$	−9.90692	+	13.8776i	−0.327334	+	0.458529i
$917$	−4.77143	−	6.28147i	−0.157567	−	0.207432i
$918$	29.6899	+	9.51014i	0.979912	+	0.313881i
$919$	43.5772	+	25.1593i	1.43748	+	0.829929i	0.997674	−	0.0681637i	$-0.0217140\pi$
$919$	43.5772	+	25.1593i	1.43748	+	0.829929i	0.439806	+	0.898093i	$0.355047\pi$
$920$	−3.91870	−	1.68630i	−0.129196	−	0.0555958i
$921$	−32.2216	−	55.8095i	−1.06174	−	1.83899i
$922$	27.6922	−	25.1440i	0.911993	−	0.828073i
$923$	27.7189			0.912379
$924$	−0.762896	−	1.23532i	−0.0250974	−	0.0406390i
$925$	−1.03852			−0.0341464
$926$	3.28432	−	2.98210i	0.107929	−	0.0979980i
$927$	10.9745	+	19.0085i	0.360451	+	0.624320i
$928$	−6.96412	−	11.5016i	−0.228609	−	0.377559i
$929$	−16.4494	−	9.49704i	−0.539686	−	0.311588i	0.205266	−	0.978706i	$-0.434194\pi$
$929$	−16.4494	−	9.49704i	−0.539686	−	0.311588i	−0.744952	+	0.667118i	$0.767527\pi$
$930$	20.0638	+	6.42677i	0.657919	+	0.210742i
$931$	−50.5656	+	13.0216i	−1.65722	+	0.426765i
$932$	34.5469	+	24.6623i	1.13162	+	0.807840i
$933$	7.38419	−	12.7898i	0.241747	−	0.418719i
$934$	11.2516	−	2.44069i	0.368164	−	0.0798617i
$935$	−0.468561	+	0.270524i	−0.0153236	+	0.00884707i
$936$	−51.9551	+	6.11869i	−1.69821	+	0.199996i
$937$			44.7192i			1.46091i	0.682959	+	0.730457i	$0.260693\pi$
$937$			44.7192i			1.46091i	−0.682959	+	0.730457i	$0.739307\pi$
$938$	−0.267037	+	0.312211i	−0.00871905	+	0.0101941i
$939$			89.1265i			2.90853i
$940$	−3.68246	−	8.08873i	−0.120109	−	0.263825i
$941$	8.88040	−	5.12710i	0.289493	−	0.167139i	−0.348220	−	0.937413i	$-0.613214\pi$
$941$	8.88040	−	5.12710i	0.289493	−	0.167139i	0.637713	+	0.770274i	$0.279881\pi$
$942$	1.05376	+	4.85784i	0.0343332	+	0.158277i
$943$	6.02661	−	10.4384i	0.196253	−	0.339921i
$944$	−11.0743	−	32.2431i	−0.360436	−	1.04942i
$945$	−8.60509	+	6.53647i	−0.279924	+	0.212631i
$946$	0.304783	−	0.951508i	0.00990936	−	0.0309362i
$947$	21.6242	+	12.4847i	0.702691	+	0.405699i	0.808349	−	0.588704i	$-0.200362\pi$
$947$	21.6242	+	12.4847i	0.702691	+	0.405699i	−0.105658	+	0.994403i	$0.533695\pi$
$948$	−23.2913	−	2.25180i	−0.756467	−	0.0731352i
$949$	−12.6546	−	21.9185i	−0.410787	−	0.711504i
$950$	−7.09135	−	7.81000i	−0.230074	−	0.253390i
$951$	−37.5316			−1.21704
$952$	28.0254	+	29.0849i	0.908309	+	0.942648i
$953$	26.3831			0.854633			0.427317	−	0.904102i	$-0.359459\pi$
$953$	26.3831			0.854633			0.427317	+	0.904102i	$0.359459\pi$
$954$	−26.2324	−	28.8909i	−0.849305	−	0.935376i
$955$	12.5117	+	21.6710i	0.404870	+	0.701256i
$956$	20.2121	+	1.95410i	0.653706	+	0.0632003i
$957$	−0.564803	−	0.326089i	−0.0182575	−	0.0105410i
$958$	10.6905	−	33.3749i	0.345395	−	1.07829i
$959$	−4.00213	+	0.507039i	−0.129235	+	0.0163731i
$960$	−20.9885	−	6.24361i	−0.677400	−	0.201512i
$961$	0.689177	−	1.19369i	0.0222315	−	0.0385061i
$962$	1.28192	+	5.90968i	0.0413307	+	0.190536i
$963$	−29.4448	+	17.0000i	−0.948846	+	0.547817i
$964$	15.7870	+	34.6771i	0.508466	+	1.11687i
$965$			8.16157i			0.262730i
$966$	5.14613	+	14.5650i	0.165574	+	0.468623i
$967$			47.1287i			1.51556i	0.652512	+	0.757778i	$0.273715\pi$
$967$			47.1287i			1.51556i	−0.652512	+	0.757778i	$0.726285\pi$
$968$	3.63563	+	30.8709i	0.116854	+	0.992229i
$969$	95.4367	−	55.1004i	3.06587	−	1.77008i
$970$	15.2983	−	3.31848i	0.491198	−	0.106550i
$971$	27.6416	−	47.8767i	0.887062	−	1.53644i	0.0437306	−	0.999043i	$-0.486076\pi$
$971$	27.6416	−	47.8767i	0.887062	−	1.53644i	0.843332	−	0.537394i	$-0.180591\pi$
$972$	−30.1792	−	21.5443i	−0.968000	−	0.691033i
$973$	−7.33553	+	17.4680i	−0.235166	+	0.559998i
$974$	−17.0971	−	5.47647i	−0.547826	−	0.175477i
$975$	−9.76007	−	5.63498i	−0.312572	−	0.180464i
$976$	−23.8414	−	20.7575i	−0.763144	−	0.664430i
$977$	−4.22669	−	7.32085i	−0.135224	−	0.234215i	0.790459	−	0.612515i	$-0.209842\pi$
$977$	−4.22669	−	7.32085i	−0.135224	−	0.234215i	−0.925683	+	0.378300i	$0.876509\pi$
$978$	−24.6495	+	22.3813i	−0.788204	+	0.715675i
$979$	−0.319954			−0.0102258
$980$	−13.8307	+	2.17047i	−0.441806	+	0.0693332i
$981$	−81.0982			−2.58927
$982$	9.95908	−	9.04267i	0.317807	−	0.288563i
$983$	−16.4461	−	28.4854i	−0.524548	−	0.908543i	−0.999591	−	0.0285811i	$-0.990901\pi$
$983$	−16.4461	−	28.4854i	−0.524548	−	0.908543i	0.475044	−	0.879962i	$-0.342432\pi$
$984$	24.4549	−	56.8292i	0.779593	−	1.81165i
$985$	10.7835	+	6.22586i	0.343591	+	0.198372i
$986$	17.2780	+	5.53442i	0.550244	+	0.176252i
$987$	−12.4602	+	29.6712i	−0.396611	+	0.944445i
$988$	−35.6893	+	49.9936i	−1.13543	+	1.59051i
$989$	−5.31509	+	9.20601i	−0.169010	+	0.292734i
$990$	−0.622359	+	0.135001i	−0.0197799	+	0.00429062i
$991$	26.5344	−	15.3196i	0.842893	−	0.486645i	−0.0153535	−	0.999882i	$-0.504887\pi$
$991$	26.5344	−	15.3196i	0.842893	−	0.486645i	0.858247	+	0.513238i	$0.171554\pi$
$992$	14.8347	−	26.9782i	0.471004	−	0.856559i
$993$		−	15.5659i		−	0.493970i
$994$	−8.39163	−	23.7508i	−0.266166	−	0.753328i
$995$			23.1734i			0.734645i
$996$	32.3931	−	14.7472i	1.02641	−	0.467284i
$997$	36.7799	−	21.2349i	1.16483	−	0.672516i	0.212374	−	0.977188i	$-0.431880\pi$
$997$	36.7799	−	21.2349i	1.16483	−	0.672516i	0.952457	+	0.304673i	$0.0985471\pi$
$998$	2.54611	+	11.7376i	0.0805957	+	0.371548i
$999$	2.12084	−	3.67340i	0.0671003	−	0.116221i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	140.2.o.a.131.4	yes	32
4.3	odd	2	inner	140.2.o.a.131.16	yes	32
5.2	odd	4		700.2.t.d.299.12		32
5.3	odd	4		700.2.t.c.299.5		32
5.4	even	2		700.2.p.c.551.13		32
7.2	even	3		980.2.g.a.391.15		32
7.3	odd	6	inner	140.2.o.a.31.16	yes	32
7.4	even	3		980.2.o.f.31.16		32
7.5	odd	6		980.2.g.a.391.16		32
7.6	odd	2		980.2.o.f.411.4		32
20.3	even	4		700.2.t.c.299.9		32
20.7	even	4		700.2.t.d.299.8		32
20.19	odd	2		700.2.p.c.551.1		32
28.3	even	6	inner	140.2.o.a.31.4	✓	32
28.11	odd	6		980.2.o.f.31.4		32
28.19	even	6		980.2.g.a.391.13		32
28.23	odd	6		980.2.g.a.391.14		32
28.27	even	2		980.2.o.f.411.16		32
35.3	even	12		700.2.t.d.199.8		32
35.17	even	12		700.2.t.c.199.9		32
35.24	odd	6		700.2.p.c.451.1		32
140.3	odd	12		700.2.t.d.199.12		32
140.59	even	6		700.2.p.c.451.13		32
140.87	odd	12		700.2.t.c.199.5		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
140.2.o.a.31.4	✓	32	28.3	even	6	inner
140.2.o.a.31.16	yes	32	7.3	odd	6	inner
140.2.o.a.131.4	yes	32	1.1	even	1	trivial
140.2.o.a.131.16	yes	32	4.3	odd	2	inner
700.2.p.c.451.1		32	35.24	odd	6
700.2.p.c.451.13		32	140.59	even	6
700.2.p.c.551.1		32	20.19	odd	2
700.2.p.c.551.13		32	5.4	even	2
700.2.t.c.199.5		32	140.87	odd	12
700.2.t.c.199.9		32	35.17	even	12
700.2.t.c.299.5		32	5.3	odd	4
700.2.t.c.299.9		32	20.3	even	4
700.2.t.d.199.8		32	35.3	even	12
700.2.t.d.199.12		32	140.3	odd	12
700.2.t.d.299.8		32	20.7	even	4
700.2.t.d.299.12		32	5.2	odd	4
980.2.g.a.391.13		32	28.19	even	6
980.2.g.a.391.14		32	28.23	odd	6
980.2.g.a.391.15		32	7.2	even	3
980.2.g.a.391.16		32	7.5	odd	6
980.2.o.f.31.4		32	28.11	odd	6
980.2.o.f.31.16		32	7.4	even	3
980.2.o.f.411.4		32	7.6	odd	2
980.2.o.f.411.16		32	28.27	even	2

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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 140 = 2^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	140.o (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.950668 - 1.04701i) q^{2} +(1.36859 + 2.37047i) q^{3} +(-0.192463 + 1.99072i) q^{4} +(-0.866025 - 0.500000i) q^{5} +(1.18083 - 3.68646i) q^{6} +(-1.02440 + 2.43939i) q^{7} +(2.26727 - 1.69100i) q^{8} +(-2.24609 + 3.89033i) q^{9} +O(q^{10})\)	\(q+(-0.950668 - 1.04701i) q^{2} +(1.36859 + 2.37047i) q^{3} +(-0.192463 + 1.99072i) q^{4} +(-0.866025 - 0.500000i) q^{5} +(1.18083 - 3.68646i) q^{6} +(-1.02440 + 2.43939i) q^{7} +(2.26727 - 1.69100i) q^{8} +(-2.24609 + 3.89033i) q^{9} +(0.299797 + 1.38207i) q^{10} +(0.0868131 - 0.0501216i) q^{11} +(-4.98234 + 2.26825i) q^{12} +4.11735i q^{13} +(3.52793 - 1.24649i) q^{14} -2.73718i q^{15} +(-3.92592 - 0.766277i) q^{16} +(4.67424 - 2.69867i) q^{17} +(6.20850 - 1.34674i) q^{18} +(3.72967 - 6.45997i) q^{19} +(1.16204 - 1.62778i) q^{20} +(-7.18448 + 0.910218i) q^{21} +(-0.135008 - 0.0432453i) q^{22} +(1.30623 + 0.754151i) q^{23} +(7.11143 + 3.06021i) q^{24} +(0.500000 + 0.866025i) q^{25} +(4.31091 - 3.91424i) q^{26} -4.08434 q^{27} +(-4.65897 - 2.50878i) q^{28} -2.37688 q^{29} +(-2.86586 + 2.60215i) q^{30} +(-2.72129 - 4.71341i) q^{31} +(2.92994 + 4.83895i) q^{32} +(0.237623 + 0.137192i) q^{33} +(-7.26919 - 2.32844i) q^{34} +(2.10685 - 1.60037i) q^{35} +(-7.31227 - 5.22007i) q^{36} +(-0.519260 + 0.899386i) q^{37} +(-10.3093 + 2.23629i) q^{38} +(-9.76007 + 5.63498i) q^{39} +(-2.80901 + 0.330814i) q^{40} -7.99125i q^{41} +(7.78306 + 6.65691i) q^{42} +7.04778i q^{43} +(0.0830696 + 0.182467i) q^{44} +(3.89033 - 2.24609i) q^{45} +(-0.452184 - 2.08458i) q^{46} +(2.22188 - 3.84841i) q^{47} +(-3.55654 - 10.3550i) q^{48} +(-4.90122 - 4.99781i) q^{49} +(0.431404 - 1.34681i) q^{50} +(12.7943 + 7.38677i) q^{51} +(-8.19649 - 0.792437i) q^{52} +(-3.07131 - 5.31966i) q^{53} +(3.88285 + 4.27635i) q^{54} -0.100243 q^{55} +(1.80242 + 7.26301i) q^{56} +20.4176 q^{57} +(2.25962 + 2.48862i) q^{58} +(4.26148 + 7.38111i) q^{59} +(5.44896 + 0.526805i) q^{60} +(6.84408 + 3.95143i) q^{61} +(-2.34795 + 7.33010i) q^{62} +(-7.18914 - 9.46432i) q^{63} +(2.28103 - 7.66791i) q^{64} +(2.05868 - 3.56573i) q^{65} +(-0.0822594 - 0.379218i) q^{66} +(-0.0950895 + 0.0549000i) q^{67} +(4.47268 + 9.82449i) q^{68} +4.12850i q^{69} +(-3.67852 - 0.684471i) q^{70} -6.73221i q^{71} +(1.48607 + 12.6186i) q^{72} +(-5.32344 + 3.07349i) q^{73} +(1.43531 - 0.311345i) q^{74} +(-1.36859 + 2.37047i) q^{75} +(12.1422 + 8.66802i) q^{76} +(0.0333347 + 0.263115i) q^{77} +(15.1785 + 4.86190i) q^{78} +(3.70178 + 2.13723i) q^{79} +(3.01680 + 2.62657i) q^{80} +(1.14846 + 1.98919i) q^{81} +(-8.36692 + 7.59702i) q^{82} -6.50159 q^{83} +(-0.429245 - 14.4774i) q^{84} -5.39735 q^{85} +(7.37910 - 6.70009i) q^{86} +(-3.25298 - 5.63433i) q^{87} +(0.112073 - 0.260440i) q^{88} +(-2.76417 - 1.59589i) q^{89} +(-6.05009 - 1.93794i) q^{90} +(-10.0438 - 4.21781i) q^{91} +(-1.75270 + 2.45519i) q^{92} +(7.44866 - 12.9015i) q^{93} +(-6.14160 + 1.33223i) q^{94} +(-6.45997 + 3.72967i) q^{95} +(-7.46070 + 13.5679i) q^{96} -11.0691i q^{97} +(-0.573332 + 9.88288i) q^{98} +0.450309i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 2 q^{2} - 2 q^{4} - 4 q^{8} - 16 q^{9}+O(q^{10}) \) 32 * q + 2 * q^2 - 2 * q^4 - 4 * q^8 - 16 * q^9	\( 32 q + 2 q^{2} - 2 q^{4} - 4 q^{8} - 16 q^{9} - 30 q^{12} + 2 q^{14} - 14 q^{16} - 12 q^{21} - 8 q^{22} + 36 q^{24} + 16 q^{25} + 30 q^{26} + 2 q^{28} - 40 q^{29} + 2 q^{32} + 60 q^{36} + 8 q^{37} - 60 q^{38} - 62 q^{42} - 18 q^{44} + 12 q^{45} + 2 q^{46} - 16 q^{49} + 4 q^{50} - 36 q^{52} - 8 q^{53} + 12 q^{54} - 4 q^{56} + 48 q^{57} + 2 q^{58} + 14 q^{60} + 24 q^{61} + 4 q^{64} + 4 q^{65} + 24 q^{66} + 60 q^{68} - 4 q^{70} + 4 q^{72} - 72 q^{73} + 38 q^{74} - 40 q^{77} + 120 q^{78} - 36 q^{81} + 42 q^{82} - 20 q^{84} + 28 q^{86} + 4 q^{88} - 60 q^{89} - 4 q^{92} - 8 q^{93} + 18 q^{94} - 60 q^{96} + 78 q^{98}+O(q^{100}) \) 32 * q + 2 * q^2 - 2 * q^4 - 4 * q^8 - 16 * q^9 - 30 * q^12 + 2 * q^14 - 14 * q^16 - 12 * q^21 - 8 * q^22 + 36 * q^24 + 16 * q^25 + 30 * q^26 + 2 * q^28 - 40 * q^29 + 2 * q^32 + 60 * q^36 + 8 * q^37 - 60 * q^38 - 62 * q^42 - 18 * q^44 + 12 * q^45 + 2 * q^46 - 16 * q^49 + 4 * q^50 - 36 * q^52 - 8 * q^53 + 12 * q^54 - 4 * q^56 + 48 * q^57 + 2 * q^58 + 14 * q^60 + 24 * q^61 + 4 * q^64 + 4 * q^65 + 24 * q^66 + 60 * q^68 - 4 * q^70 + 4 * q^72 - 72 * q^73 + 38 * q^74 - 40 * q^77 + 120 * q^78 - 36 * q^81 + 42 * q^82 - 20 * q^84 + 28 * q^86 + 4 * q^88 - 60 * q^89 - 4 * q^92 - 8 * q^93 + 18 * q^94 - 60 * q^96 + 78 * q^98

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