LMFDB - Embedded newform 240.2.bl.a.109.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [240,2,Mod(109,240)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(240, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 3, 0, 2]))

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

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

chi := DirichletCharacter("240.109");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 240 = 2^{4} \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	240.bl (of order $4$, 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:	$1.91640964851$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			109.9
Character	$\chi$	$=$	240.109
Dual form			240.2.bl.a.229.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.550383 + 1.30272i) q^{2} +(0.707107 - 0.707107i) q^{3} +(-1.39416 - 1.43399i) q^{4} +(0.162008 + 2.23019i) q^{5} +(0.531983 + 1.31034i) q^{6} +2.93661 q^{7} +(2.63541 - 1.02695i) q^{8} -1.00000i q^{9} +O(q^{10})$	\(q+(-0.550383 + 1.30272i) q^{2} +(0.707107 - 0.707107i) q^{3} +(-1.39416 - 1.43399i) q^{4} +(0.162008 + 2.23019i) q^{5} +(0.531983 + 1.31034i) q^{6} +2.93661 q^{7} +(2.63541 - 1.02695i) q^{8} -1.00000i q^{9} +(-2.99448 - 1.01641i) q^{10} +(-0.663996 + 0.663996i) q^{11} +(-1.99980 - 0.0281646i) q^{12} +(1.12767 - 1.12767i) q^{13} +(-1.61626 + 3.82558i) q^{14} +(1.69154 + 1.46243i) q^{15} +(-0.112647 + 3.99841i) q^{16} +7.47528i q^{17} +(1.30272 + 0.550383i) q^{18} +(0.423555 + 0.423555i) q^{19} +(2.97220 - 3.34156i) q^{20} +(2.07650 - 2.07650i) q^{21} +(-0.499549 - 1.23045i) q^{22} +6.17642 q^{23} +(1.13735 - 2.58968i) q^{24} +(-4.94751 + 0.722620i) q^{25} +(0.848386 + 2.08968i) q^{26} +(-0.707107 - 0.707107i) q^{27} +(-4.09410 - 4.21107i) q^{28} +(-2.95128 - 2.95128i) q^{29} +(-2.83613 + 1.39871i) q^{30} +1.82581 q^{31} +(-5.14681 - 2.34740i) q^{32} +0.939032i q^{33} +(-9.73820 - 4.11426i) q^{34} +(0.475756 + 6.54921i) q^{35} +(-1.43399 + 1.39416i) q^{36} +(-5.53509 - 5.53509i) q^{37} +(-0.784891 + 0.318656i) q^{38} -1.59476i q^{39} +(2.71726 + 5.71108i) q^{40} -12.3694i q^{41} +(1.56223 + 3.84797i) q^{42} +(0.897614 + 0.897614i) q^{43} +(1.87788 + 0.0264474i) q^{44} +(2.23019 - 0.162008i) q^{45} +(-3.39939 + 8.04614i) q^{46} -4.12733i q^{47} +(2.74765 + 2.90696i) q^{48} +1.62370 q^{49} +(1.78165 - 6.84293i) q^{50} +(5.28582 + 5.28582i) q^{51} +(-3.18921 - 0.0449157i) q^{52} +(0.146479 + 0.146479i) q^{53} +(1.31034 - 0.531983i) q^{54} +(-1.58841 - 1.37327i) q^{55} +(7.73917 - 3.01577i) q^{56} +0.598997 q^{57} +(5.46902 - 2.22036i) q^{58} +(-7.72645 + 7.72645i) q^{59} +(-0.261172 - 4.46450i) q^{60} +(-7.37519 - 7.37519i) q^{61} +(-1.00489 + 2.37851i) q^{62} -2.93661i q^{63} +(5.89073 - 5.41289i) q^{64} +(2.69760 + 2.33222i) q^{65} +(-1.22330 - 0.516827i) q^{66} +(8.68265 - 8.68265i) q^{67} +(10.7195 - 10.4217i) q^{68} +(4.36739 - 4.36739i) q^{69} +(-8.79363 - 2.98479i) q^{70} -8.95735i q^{71} +(-1.02695 - 2.63541i) q^{72} +0.174246 q^{73} +(10.2571 - 4.16425i) q^{74} +(-2.98745 + 4.00938i) q^{75} +(0.0168705 - 1.19788i) q^{76} +(-1.94990 + 1.94990i) q^{77} +(2.07753 + 0.877729i) q^{78} +3.06488 q^{79} +(-8.93548 + 0.396552i) q^{80} -1.00000 q^{81} +(16.1139 + 6.80790i) q^{82} +(-9.18751 + 9.18751i) q^{83} +(-5.87264 - 0.0827084i) q^{84} +(-16.6713 + 1.21106i) q^{85} +(-1.66337 + 0.675308i) q^{86} -4.17374 q^{87} +(-1.06801 + 2.43179i) q^{88} +8.71473i q^{89} +(-1.01641 + 2.99448i) q^{90} +(3.31152 - 3.31152i) q^{91} +(-8.61090 - 8.85691i) q^{92} +(1.29104 - 1.29104i) q^{93} +(5.37676 + 2.27161i) q^{94} +(-0.875989 + 1.01323i) q^{95} +(-5.29921 + 1.97948i) q^{96} +10.5481i q^{97} +(-0.893654 + 2.11522i) q^{98} +(0.663996 + 0.663996i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q+O(q^{10}) $ 48 * q	$ 48 q + 12 q^{10} - 16 q^{14} - 4 q^{16} + 8 q^{19} - 4 q^{24} - 40 q^{26} - 8 q^{30} - 48 q^{31} - 28 q^{34} + 24 q^{35} - 4 q^{36} - 16 q^{40} - 40 q^{44} - 4 q^{46} + 48 q^{49} - 32 q^{50} + 8 q^{51} - 4 q^{54} + 48 q^{56} - 32 q^{59} - 24 q^{60} + 16 q^{61} + 48 q^{64} + 16 q^{65} + 24 q^{66} - 16 q^{69} + 40 q^{74} - 16 q^{75} + 60 q^{76} - 96 q^{79} + 72 q^{80} - 48 q^{81} + 16 q^{86} + 8 q^{90} - 32 q^{91} + 44 q^{94} - 48 q^{95} - 40 q^{96}+O(q^{100}) $ 48 * q + 12 * q^10 - 16 * q^14 - 4 * q^16 + 8 * q^19 - 4 * q^24 - 40 * q^26 - 8 * q^30 - 48 * q^31 - 28 * q^34 + 24 * q^35 - 4 * q^36 - 16 * q^40 - 40 * q^44 - 4 * q^46 + 48 * q^49 - 32 * q^50 + 8 * q^51 - 4 * q^54 + 48 * q^56 - 32 * q^59 - 24 * q^60 + 16 * q^61 + 48 * q^64 + 16 * q^65 + 24 * q^66 - 16 * q^69 + 40 * q^74 - 16 * q^75 + 60 * q^76 - 96 * q^79 + 72 * q^80 - 48 * q^81 + 16 * q^86 + 8 * q^90 - 32 * q^91 + 44 * q^94 - 48 * q^95 - 40 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/240\mathbb{Z}\right)^\times$.

$n$	$31$	$97$	$161$	$181$
$\chi(n)$	$1$	$-1$	$1$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−0.550383	+	1.30272i	−0.389179	+	0.921162i
$2$	−0.550383	+	1.30272i	−0.389179	+	0.921162i
$3$	0.707107	−	0.707107i	0.408248	−	0.408248i
$3$	0.707107	−	0.707107i	0.408248	−	0.408248i
$4$	−1.39416	−	1.43399i	−0.697079	−	0.716994i
$5$	0.162008	+	2.23019i	0.0724524	+	0.997372i
$5$	0.162008	+	2.23019i	0.0724524	+	0.997372i
$6$	0.531983	+	1.31034i	0.217181	+	0.534945i
$7$	2.93661			1.10994			0.554968	−	0.831872i	$-0.312731\pi$
$7$	2.93661			1.10994			0.554968	+	0.831872i	$0.312731\pi$
$8$	2.63541	−	1.02695i	0.931757	−	0.363083i
$9$		−	1.00000i		−	0.333333i
$10$	−2.99448	−	1.01641i	−0.946938	−	0.321416i
$11$	−0.663996	+	0.663996i	−0.200202	+	0.200202i	−0.800087	−	0.599884i	$-0.795213\pi$
$11$	−0.663996	+	0.663996i	−0.200202	+	0.200202i	0.599884	+	0.800087i	$0.295213\pi$
$12$	−1.99980	−	0.0281646i	−0.577293	−	0.00813041i
$13$	1.12767	−	1.12767i	0.312758	−	0.312758i	−0.533219	−	0.845977i	$-0.679018\pi$
$13$	1.12767	−	1.12767i	0.312758	−	0.312758i	0.845977	+	0.533219i	$0.179018\pi$
$14$	−1.61626	+	3.82558i	−0.431964	+	1.02243i
$15$	1.69154	+	1.46243i	0.436754	+	0.377597i
$16$	−0.112647	+	3.99841i	−0.0281618	+	0.999603i
$17$			7.47528i			1.81302i	0.422182	+	0.906511i	$0.361264\pi$
$17$			7.47528i			1.81302i	−0.422182	+	0.906511i	$0.638736\pi$
$18$	1.30272	+	0.550383i	0.307054	+	0.129726i
$19$	0.423555	+	0.423555i	0.0971702	+	0.0971702i	0.754021	−	0.656851i	$-0.228112\pi$
$19$	0.423555	+	0.423555i	0.0971702	+	0.0971702i	−0.656851	+	0.754021i	$0.728112\pi$
$20$	2.97220	−	3.34156i	0.664605	−	0.747195i
$21$	2.07650	−	2.07650i	0.453129	−	0.453129i
$22$	−0.499549	−	1.23045i	−0.106504	−	0.262333i
$23$	6.17642			1.28787			0.643936	−	0.765079i	$-0.277300\pi$
$23$	6.17642			1.28787			0.643936	+	0.765079i	$0.277300\pi$
$24$	1.13735	−	2.58968i	0.232160	−	0.528616i
$25$	−4.94751	+	0.722620i	−0.989501	+	0.144524i
$26$	0.848386	+	2.08968i	0.166382	+	0.409820i
$27$	−0.707107	−	0.707107i	−0.136083	−	0.136083i
$28$	−4.09410	−	4.21107i	−0.773713	−	0.795817i
$29$	−2.95128	−	2.95128i	−0.548038	−	0.548038i	0.377835	−	0.925873i	$-0.376669\pi$
$29$	−2.95128	−	2.95128i	−0.548038	−	0.548038i	−0.925873	+	0.377835i	$0.876669\pi$
$30$	−2.83613	+	1.39871i	−0.517803	+	0.255368i
$31$	1.82581			0.327924			0.163962	−	0.986467i	$-0.447572\pi$
$31$	1.82581			0.327924			0.163962	+	0.986467i	$0.447572\pi$
$32$	−5.14681	−	2.34740i	−0.909837	−	0.414966i
$33$			0.939032i			0.163465i
$34$	−9.73820	−	4.11426i	−1.67009	−	0.705591i
$35$	0.475756	+	6.54921i	0.0804175	+	1.10702i
$36$	−1.43399	+	1.39416i	−0.238998	+	0.232360i
$37$	−5.53509	−	5.53509i	−0.909963	−	0.909963i	0.0863055	−	0.996269i	$-0.472494\pi$
$37$	−5.53509	−	5.53509i	−0.909963	−	0.909963i	−0.996269	+	0.0863055i	$0.972494\pi$
$38$	−0.784891	+	0.318656i	−0.127326	+	0.0516929i
$39$		−	1.59476i		−	0.255366i
$40$	2.71726	+	5.71108i	0.429637	+	0.903002i
$41$		−	12.3694i		−	1.93178i	−0.258959	−	0.965888i	$-0.583380\pi$
$41$		−	12.3694i		−	1.93178i	0.258959	−	0.965888i	$-0.416620\pi$
$42$	1.56223	+	3.84797i	0.241057	+	0.593754i
$43$	0.897614	+	0.897614i	0.136885	+	0.136885i	0.772229	−	0.635344i	$-0.219142\pi$
$43$	0.897614	+	0.897614i	0.136885	+	0.136885i	−0.635344	+	0.772229i	$0.719142\pi$
$44$	1.87788	+	0.0264474i	0.283101	+	0.00398710i
$45$	2.23019	−	0.162008i	0.332457	−	0.0241508i
$46$	−3.39939	+	8.04614i	−0.501213	+	1.18634i
$47$		−	4.12733i		−	0.602033i	−0.953619	−	0.301017i	$-0.902674\pi$
$47$		−	4.12733i		−	0.602033i	0.953619	−	0.301017i	$-0.0973260\pi$
$48$	2.74765	+	2.90696i	0.396589	+	0.419583i
$49$	1.62370			0.231956
$50$	1.78165	−	6.84293i	0.251963	−	0.967737i
$51$	5.28582	+	5.28582i	0.740163	+	0.740163i
$52$	−3.18921	−	0.0449157i	−0.442263	−	0.00622869i
$53$	0.146479	+	0.146479i	0.0201204	+	0.0201204i	0.717095	−	0.696975i	$-0.245471\pi$
$53$	0.146479	+	0.146479i	0.0201204	+	0.0201204i	−0.696975	+	0.717095i	$0.745471\pi$
$54$	1.31034	−	0.531983i	0.178315	−	0.0723937i
$55$	−1.58841	−	1.37327i	−0.214181	−	0.185171i
$56$	7.73917	−	3.01577i	1.03419	−	0.402999i
$57$	0.598997			0.0793391
$58$	5.46902	−	2.22036i	0.718117	−	0.291547i
$59$	−7.72645	+	7.72645i	−1.00590	+	1.00590i	−0.00591515	+	0.999983i	$0.501883\pi$
$59$	−7.72645	+	7.72645i	−1.00590	+	1.00590i	−0.999983	+	0.00591515i	$0.998117\pi$
$60$	−0.261172	−	4.46450i	−0.0337172	−	0.576365i
$61$	−7.37519	−	7.37519i	−0.944297	−	0.944297i	0.0542318	−	0.998528i	$-0.482729\pi$
$61$	−7.37519	−	7.37519i	−0.944297	−	0.944297i	−0.998528	+	0.0542318i	$0.982729\pi$
$62$	−1.00489	+	2.37851i	−0.127621	+	0.302071i
$63$		−	2.93661i		−	0.369978i
$64$	5.89073	−	5.41289i	0.736341	−	0.676611i
$65$	2.69760	+	2.33222i	0.334597	+	0.289276i
$66$	−1.22330	−	0.516827i	−0.150577	−	0.0636170i
$67$	8.68265	−	8.68265i	1.06075	−	1.06075i	0.0627239	−	0.998031i	$-0.480021\pi$
$67$	8.68265	−	8.68265i	1.06075	−	1.06075i	0.998031	−	0.0627239i	$-0.0199787\pi$
$68$	10.7195	−	10.4217i	1.29993	−	1.26382i
$69$	4.36739	−	4.36739i	0.525772	−	0.525772i
$70$	−8.79363	−	2.98479i	−1.05104	−	0.356751i
$71$		−	8.95735i		−	1.06304i	−0.847045	−	0.531521i	$-0.821621\pi$
$71$		−	8.95735i		−	1.06304i	0.847045	−	0.531521i	$-0.178379\pi$
$72$	−1.02695	−	2.63541i	−0.121028	−	0.310586i
$73$	0.174246			0.0203940			0.0101970	−	0.999948i	$-0.496754\pi$
$73$	0.174246			0.0203940			0.0101970	+	0.999948i	$0.496754\pi$
$74$	10.2571	−	4.16425i	1.19236	−	0.484085i
$75$	−2.98745	+	4.00938i	−0.344961	+	0.462964i
$76$	0.0168705	−	1.19788i	0.00193518	−	0.137406i
$77$	−1.94990	+	1.94990i	−0.222212	+	0.222212i
$78$	2.07753	+	0.877729i	0.235234	+	0.0993832i
$79$	3.06488			0.344826			0.172413	−	0.985025i	$-0.444844\pi$
$79$	3.06488			0.344826			0.172413	+	0.985025i	$0.444844\pi$
$80$	−8.93548	+	0.396552i	−0.999017	+	0.0443359i
$81$	−1.00000			−0.111111
$82$	16.1139	+	6.80790i	1.77948	+	0.751807i
$83$	−9.18751	+	9.18751i	−1.00846	+	1.00846i	−0.00849620	+	0.999964i	$0.502704\pi$
$83$	−9.18751	+	9.18751i	−1.00846	+	1.00846i	−0.999964	+	0.00849620i	$0.997296\pi$
$84$	−5.87264	−	0.0827084i	−0.640758	−	0.00902423i
$85$	−16.6713	+	1.21106i	−1.80826	+	0.131358i
$86$	−1.66337	+	0.675308i	−0.179366	+	0.0728204i
$87$	−4.17374			−0.447471
$88$	−1.06801	+	2.43179i	−0.113850	+	0.259230i
$89$			8.71473i			0.923760i	0.886942	+	0.461880i	$0.152825\pi$
$89$			8.71473i			0.923760i	−0.886942	+	0.461880i	$0.847175\pi$
$90$	−1.01641	+	2.99448i	−0.107139	+	0.315646i
$91$	3.31152	−	3.31152i	0.347142	−	0.347142i
$92$	−8.61090	−	8.85691i	−0.897749	−	0.923397i
$93$	1.29104	−	1.29104i	0.133875	−	0.133875i
$94$	5.37676	+	2.27161i	0.554570	+	0.234299i
$95$	−0.875989	+	1.01323i	−0.0898746	+	0.103955i
$96$	−5.29921	+	1.97948i	−0.540849	+	0.202030i
$97$			10.5481i			1.07100i	0.844535	+	0.535500i	$0.179877\pi$
$97$			10.5481i			1.07100i	−0.844535	+	0.535500i	$0.820123\pi$
$98$	−0.893654	+	2.11522i	−0.0902727	+	0.213669i
$99$	0.663996	+	0.663996i	0.0667341	+	0.0667341i
$100$	7.93383	+	6.08722i	0.793383	+	0.608722i
$101$	−9.65550	+	9.65550i	−0.960758	+	0.960758i	−0.999259	−	0.0385005i	$-0.987742\pi$
$101$	−9.65550	+	9.65550i	−0.960758	+	0.960758i	0.0385005	+	0.999259i	$0.487742\pi$
$102$	−9.79517	+	3.97672i	−0.969866	+	0.393754i
$103$	14.5564			1.43428			0.717141	−	0.696928i	$-0.245450\pi$
$103$	14.5564			1.43428			0.717141	+	0.696928i	$0.245450\pi$
$104$	1.81380	−	4.12992i	0.177857	−	0.404972i
$105$	4.96740	+	4.29458i	0.484769	+	0.419108i
$106$	−0.271440	+	0.110201i	−0.0263646	+	0.0107037i
$107$	−5.86260	−	5.86260i	−0.566759	−	0.566759i	0.364460	−	0.931219i	$-0.381253\pi$
$107$	−5.86260	−	5.86260i	−0.566759	−	0.566759i	−0.931219	+	0.364460i	$0.881253\pi$
$108$	−0.0281646	+	1.99980i	−0.00271014	+	0.192431i
$109$	4.91625	+	4.91625i	0.470891	+	0.470891i	0.902203	−	0.431312i	$-0.141949\pi$
$109$	4.91625	+	4.91625i	0.470891	+	0.470891i	−0.431312	+	0.902203i	$0.641949\pi$
$110$	2.66321	−	1.31343i	0.253927	−	0.125231i
$111$	−7.82780			−0.742982
$112$	−0.330801	+	11.7418i	−0.0312577	+	1.10950i
$113$		−	12.8334i		−	1.20726i	−0.797263	−	0.603632i	$-0.793720\pi$
$113$		−	12.8334i		−	1.20726i	0.797263	−	0.603632i	$-0.206280\pi$
$114$	−0.329678	+	0.780326i	−0.0308771	+	0.0730842i
$115$	1.00063	+	13.7746i	0.0933094	+	1.28449i
$116$	−0.117551	+	8.34664i	−0.0109144	+	0.774966i
$117$	−1.12767	−	1.12767i	−0.104253	−	0.104253i
$118$	−5.81289	−	14.3179i	−0.535120	−	1.31807i
$119$			21.9520i			2.01234i
$120$	5.95974	+	2.11695i	0.544047	+	0.193250i
$121$			10.1182i			0.919838i
$122$	13.6670	−	5.54863i	1.23735	−	0.502349i
$123$	−8.74649	−	8.74649i	−0.788644	−	0.788644i
$124$	−2.54546	−	2.61818i	−0.228589	−	0.235120i
$125$	−2.41312	−	10.9168i	−0.215836	−	0.976430i
$126$	3.82558	+	1.61626i	0.340810	+	0.143988i
$127$			1.07042i			0.0949847i	0.998872	+	0.0474924i	$0.0151230\pi$
$127$			1.07042i			0.0949847i	−0.998872	+	0.0474924i	$0.984877\pi$
$128$	3.80932	+	10.6531i	0.336699	+	0.941612i
$129$	1.26942			0.111766
$130$	−4.52294	+	2.23061i	−0.396689	+	0.195637i
$131$	−10.9024	−	10.9024i	−0.952545	−	0.952545i	0.0463789	−	0.998924i	$-0.485232\pi$
$131$	−10.9024	−	10.9024i	−0.952545	−	0.952545i	−0.998924	+	0.0463789i	$0.985232\pi$
$132$	1.34656	−	1.30916i	0.117203	−	0.113948i
$133$	1.24382	+	1.24382i	0.107853	+	0.107853i
$134$	6.53228	+	16.0898i	0.564303	+	1.38995i
$135$	1.46243	−	1.69154i	0.125866	−	0.145585i
$136$	7.67678	+	19.7004i	0.658278	+	1.68930i
$137$	−10.0549			−0.859046			−0.429523	−	0.903056i	$-0.641318\pi$
$137$	−10.0549			−0.859046			−0.429523	+	0.903056i	$0.641318\pi$
$138$	3.28575	+	8.09322i	0.279701	+	0.688940i
$139$	2.90773	−	2.90773i	0.246630	−	0.246630i	−0.572956	−	0.819586i	$-0.694203\pi$
$139$	2.90773	−	2.90773i	0.246630	−	0.246630i	0.819586	+	0.572956i	$0.194203\pi$
$140$	8.72821	−	9.81286i	0.737669	−	0.829338i
$141$	−2.91847	−	2.91847i	−0.245779	−	0.245779i
$142$	11.6689	+	4.92997i	0.979234	+	0.413714i
$143$			1.49753i			0.125230i
$144$	3.99841	+	0.112647i	0.333201	+	0.00938725i
$145$	6.10378	−	7.06004i	0.506891	−	0.586305i
$146$	−0.0959021	+	0.226994i	−0.00793691	+	0.0187862i
$147$	1.14813	−	1.14813i	0.0946958	−	0.0946958i
$148$	−0.220467	+	15.6540i	−0.0181222	+	1.28675i
$149$	−1.26131	+	1.26131i	−0.103331	+	0.103331i	−0.756882	−	0.653551i	$-0.773278\pi$
$149$	−1.26131	+	1.26131i	−0.103331	+	0.103331i	0.653551	+	0.756882i	$0.273278\pi$
$150$	−3.57887	−	6.09850i	−0.292213	−	0.497941i
$151$		−	20.4739i		−	1.66614i	−0.553169	−	0.833069i	$-0.686582\pi$
$151$		−	20.4739i		−	1.66614i	0.553169	−	0.833069i	$-0.313418\pi$
$152$	1.55121	+	0.681268i	0.125820	+	0.0552581i
$153$	7.47528			0.604341
$154$	−1.46698	−	3.61336i	−0.118213	−	0.291173i
$155$	0.295796	+	4.07190i	0.0237589	+	0.327063i
$156$	−2.28687	+	2.22335i	−0.183096	+	0.178010i
$157$	−8.13344	+	8.13344i	−0.649119	+	0.649119i	−0.952780	−	0.303661i	$-0.901791\pi$
$157$	−8.13344	+	8.13344i	−0.649119	+	0.649119i	0.303661	+	0.952780i	$0.401791\pi$
$158$	−1.68686	+	3.99269i	−0.134199	+	0.317641i
$159$	0.207152			0.0164282
$160$	4.40133	−	11.8587i	0.347956	−	0.937511i
$161$	18.1377			1.42945
$162$	0.550383	−	1.30272i	0.0432421	−	0.102351i
$163$	−4.08947	+	4.08947i	−0.320312	+	0.320312i	−0.848887	−	0.528575i	$-0.822727\pi$
$163$	−4.08947	+	4.08947i	−0.320312	+	0.320312i	0.528575	+	0.848887i	$0.322727\pi$
$164$	−17.7376	+	17.2449i	−1.38507	+	1.34660i
$165$	−2.09422	+	0.152131i	−0.163035	+	0.0118434i
$166$	−6.91211	−	17.0254i	−0.536483	−	1.32143i
$167$	9.52867			0.737350			0.368675	−	0.929558i	$-0.379811\pi$
$167$	9.52867			0.737350			0.368675	+	0.929558i	$0.379811\pi$
$168$	3.33995	−	7.60489i	0.257682	−	0.586730i
$169$			10.4567i			0.804364i
$170$	7.59793	−	22.3846i	0.582734	−	1.71682i
$171$	0.423555	−	0.423555i	0.0323901	−	0.0323901i
$172$	0.0357526	−	2.53858i	0.00272611	−	0.193565i
$173$	6.18234	−	6.18234i	0.470035	−	0.470035i	−0.431891	−	0.901926i	$-0.642153\pi$
$173$	6.18234	−	6.18234i	0.470035	−	0.470035i	0.901926	+	0.431891i	$0.142153\pi$
$174$	2.29715	−	5.43721i	0.174147	−	0.412194i
$175$	−14.5289	+	2.12205i	−1.09828	+	0.160412i
$176$	−2.58013	−	2.72973i	−0.194485	−	0.205761i
$177$			10.9268i			0.821312i
$178$	−11.3529	−	4.79644i	−0.850933	−	0.359508i
$179$	−10.3548	−	10.3548i	−0.773954	−	0.773954i	0.204841	−	0.978795i	$-0.434332\pi$
$179$	−10.3548	−	10.3548i	−0.773954	−	0.773954i	−0.978795	+	0.204841i	$0.934332\pi$
$180$	−3.34156	−	2.97220i	−0.249065	−	0.221535i
$181$	5.98013	−	5.98013i	0.444500	−	0.444500i	−0.449021	−	0.893521i	$-0.648227\pi$
$181$	5.98013	−	5.98013i	0.444500	−	0.444500i	0.893521	+	0.449021i	$0.148227\pi$
$182$	2.49138	+	6.13659i	0.184673	+	0.454874i
$183$	−10.4301			−0.771015
$184$	16.2774	−	6.34290i	1.19998	−	0.467605i
$185$	11.4476	−	13.2410i	0.841643	−	0.973501i
$186$	0.971297	+	2.39243i	0.0712190	+	0.175421i
$187$	−4.96356	−	4.96356i	−0.362971	−	0.362971i
$188$	−5.91855	+	5.75415i	−0.431655	+	0.419665i
$189$	−2.07650	−	2.07650i	−0.151043	−	0.151043i
$190$	−0.837823	−	1.69883i	−0.0607821	−	0.123246i
$191$	−0.404932			−0.0292998			−0.0146499	−	0.999893i	$-0.504663\pi$
$191$	−0.404932			−0.0292998			−0.0146499	+	0.999893i	$0.504663\pi$
$192$	0.337885	−	7.99286i	0.0243848	−	0.576835i
$193$			6.48969i			0.467138i	0.972340	+	0.233569i	$0.0750405\pi$
$193$			6.48969i			0.467138i	−0.972340	+	0.233569i	$0.924959\pi$
$194$	−13.7412	−	5.80550i	−0.986564	−	0.416811i
$195$	3.55662	−	0.258365i	0.254695	−	0.0185019i
$196$	−2.26369	−	2.32836i	−0.161692	−	0.166311i
$197$	18.4425	+	18.4425i	1.31397	+	1.31397i	0.918460	+	0.395514i	$0.129434\pi$
$197$	18.4425	+	18.4425i	1.31397	+	1.31397i	0.395514	+	0.918460i	$0.370566\pi$
$198$	−1.23045	+	0.499549i	−0.0874445	+	0.0355014i
$199$		−	13.4696i		−	0.954833i	−0.878677	−	0.477417i	$-0.841573\pi$
$199$		−	13.4696i		−	0.954833i	0.878677	−	0.477417i	$-0.158427\pi$
$200$	−12.2966	+	6.98526i	−0.869500	+	0.493933i
$201$		−	12.2791i		−	0.866103i
$202$	−7.26419	−	17.8926i	−0.511107	−	1.25892i
$203$	−8.66676	−	8.66676i	−0.608287	−	0.608287i
$204$	0.210538	−	14.9491i	0.0147406	−	1.04664i
$205$	27.5861	−	2.00395i	1.92670	−	0.139962i
$206$	−8.01157	+	18.9629i	−0.558193	+	1.32121i
$207$		−	6.17642i		−	0.429291i
$208$	4.38185	+	4.63591i	0.303827	+	0.321442i
$209$	−0.562478			−0.0389074
$210$	−8.32860	+	4.10747i	−0.574728	+	0.283442i
$211$	6.07749	+	6.07749i	0.418392	+	0.418392i	0.884649	−	0.466257i	$-0.154398\pi$
$211$	6.07749	+	6.07749i	0.418392	+	0.418392i	−0.466257	+	0.884649i	$0.654398\pi$
$212$	0.00583434	−	0.414263i	0.000400704	−	0.0284517i
$213$	−6.33380	−	6.33380i	−0.433985	−	0.433985i
$214$	10.8640	−	4.41065i	0.742647	−	0.301506i
$215$	−1.85643	+	2.14727i	−0.126607	+	0.146443i
$216$	−2.58968	−	1.13735i	−0.176205	−	0.0773866i
$217$	5.36168			0.363975
$218$	−9.11032	+	3.69868i	−0.617028	+	0.250506i
$219$	0.123211	−	0.123211i	0.00832581	−	0.00832581i
$220$	0.245249	+	4.19231i	0.0165347	+	0.282646i
$221$	8.42963	+	8.42963i	0.567038	+	0.567038i
$222$	4.30828	−	10.1974i	0.289153	−	0.684407i
$223$			22.0794i			1.47855i	0.673405	+	0.739273i	$0.264831\pi$
$223$			22.0794i			1.47855i	−0.673405	+	0.739273i	$0.735169\pi$
$224$	−15.1142	−	6.89342i	−1.00986	−	0.460586i
$225$	0.722620	+	4.94751i	0.0481746	+	0.329834i
$226$	16.7183	+	7.06328i	1.11209	+	0.469842i
$227$	−5.55919	+	5.55919i	−0.368977	+	0.368977i	−0.867104	−	0.498127i	$-0.834021\pi$
$227$	−5.55919	+	5.55919i	−0.368977	+	0.368977i	0.498127	+	0.867104i	$0.334021\pi$
$228$	−0.835097	−	0.858955i	−0.0553056	−	0.0568857i
$229$	11.8223	−	11.8223i	0.781242	−	0.781242i	−0.198798	−	0.980040i	$-0.563704\pi$
$229$	11.8223	−	11.8223i	0.781242	−	0.781242i	0.980040	+	0.198798i	$0.0637038\pi$
$230$	−18.4952	−	6.27775i	−1.21954	−	0.413943i
$231$			2.75757i			0.181435i
$232$	−10.8086	−	4.74698i	−0.709622	−	0.311655i
$233$	−8.92024			−0.584385			−0.292192	−	0.956360i	$-0.594385\pi$
$233$	−8.92024			−0.584385			−0.292192	+	0.956360i	$0.594385\pi$
$234$	2.08968	−	0.848386i	0.136607	−	0.0554607i
$235$	9.20474	−	0.668663i	0.600451	−	0.0436188i
$236$	21.8515	+	0.307750i	1.42241	+	0.0200328i
$237$	2.16720	−	2.16720i	0.140775	−	0.140775i
$238$	−28.5973	−	12.0820i	−1.85369	−	0.783160i
$239$	22.9320			1.48335			0.741673	−	0.670762i	$-0.234033\pi$
$239$	22.9320			1.48335			0.741673	+	0.670762i	$0.234033\pi$
$240$	−6.03793	+	6.59874i	−0.389747	+	0.425947i
$241$	−6.48232			−0.417563			−0.208781	−	0.977962i	$-0.566950\pi$
$241$	−6.48232			−0.417563			−0.208781	+	0.977962i	$0.566950\pi$
$242$	−13.1812	−	5.56889i	−0.847320	−	0.357982i
$243$	−0.707107	+	0.707107i	−0.0453609	+	0.0453609i
$244$	−0.293759	+	20.8581i	−0.0188060	+	1.33530i
$245$	0.263052	+	3.62115i	0.0168058	+	0.231347i
$246$	16.2081	−	6.58031i	1.03339	−	0.419545i
$247$	0.955258			0.0607816
$248$	4.81174	−	1.87502i	0.305546	−	0.119064i
$249$			12.9931i			0.823404i
$250$	15.5497	+	2.86481i	0.983449	+	0.181186i
$251$	14.4218	−	14.4218i	0.910293	−	0.910293i	−0.0860018	−	0.996295i	$-0.527409\pi$
$251$	14.4218	−	14.4218i	0.910293	−	0.910293i	0.996295	+	0.0860018i	$0.0274091\pi$
$252$	−4.21107	+	4.09410i	−0.265272	+	0.257904i
$253$	−4.10112	+	4.10112i	−0.257835	+	0.257835i
$254$	−1.39446	−	0.589143i	−0.0874963	−	0.0369661i
$255$	−10.9320	+	12.6447i	−0.684591	+	0.791844i
$256$	−15.9746	−	0.900819i	−0.998414	−	0.0563012i
$257$		−	0.193739i		−	0.0120851i	−0.999982	−	0.00604256i	$-0.998077\pi$
$257$		−	0.193739i		−	0.0120851i	0.999982	−	0.00604256i	$-0.00192342\pi$
$258$	−0.698666	+	1.65370i	−0.0434970	+	0.102955i
$259$	−16.2544	−	16.2544i	−1.01000	−	1.01000i
$260$	−0.416508	−	7.11982i	−0.0258307	−	0.441552i
$261$	−2.95128	+	2.95128i	−0.182679	+	0.182679i
$262$	20.2032	−	8.20226i	1.24816	−	0.506738i
$263$	−16.5708			−1.02180			−0.510900	−	0.859640i	$-0.670688\pi$
$263$	−16.5708			−1.02180			−0.510900	+	0.859640i	$0.670688\pi$
$264$	0.964344	+	2.47473i	0.0593513	+	0.152309i
$265$	−0.302944	+	0.350406i	−0.0186097	+	0.0215253i
$266$	−2.30492	+	0.935770i	−0.141324	+	0.0573757i
$267$	6.16225	+	6.16225i	0.377123	+	0.377123i
$268$	−24.5558	−	0.345836i	−1.49999	−	0.0211253i
$269$	7.09381	+	7.09381i	0.432517	+	0.432517i	0.889484	−	0.456967i	$-0.151064\pi$
$269$	7.09381	+	7.09381i	0.432517	+	0.432517i	−0.456967	+	0.889484i	$0.651064\pi$
$270$	1.39871	+	2.83613i	0.0851228	+	0.172601i
$271$	2.62278			0.159323			0.0796613	−	0.996822i	$-0.474616\pi$
$271$	2.62278			0.159323			0.0796613	+	0.996822i	$0.474616\pi$
$272$	−29.8893	−	0.842068i	−1.81230	−	0.0510579i
$273$		−	4.68320i		−	0.283440i
$274$	5.53403	−	13.0987i	0.334323	−	0.791320i
$275$	2.80531	−	3.76494i	0.169166	−	0.227035i
$276$	−12.3516	−	0.173956i	−0.743480	−	0.0104709i
$277$	−7.97533	−	7.97533i	−0.479191	−	0.479191i	0.425682	−	0.904873i	$-0.360034\pi$
$277$	−7.97533	−	7.97533i	−0.479191	−	0.479191i	−0.904873	+	0.425682i	$0.860034\pi$
$278$	2.18759	+	5.38832i	0.131203	+	0.323170i
$279$		−	1.82581i		−	0.109308i
$280$	7.97955	+	16.7712i	0.476869	+	1.00227i
$281$			9.97850i			0.595267i	0.954680	+	0.297634i	$0.0961974\pi$
$281$			9.97850i			0.595267i	−0.954680	+	0.297634i	$0.903803\pi$
$282$	5.40822	−	2.19567i	0.322055	−	0.130750i
$283$	20.4056	+	20.4056i	1.21299	+	1.21299i	0.970040	+	0.242946i	$0.0781139\pi$
$283$	20.4056	+	20.4056i	1.21299	+	1.21299i	0.242946	+	0.970040i	$0.421886\pi$
$284$	−12.8447	+	12.4880i	−0.762195	+	0.741024i
$285$	0.0970426	+	1.33588i	0.00574831	+	0.0791306i
$286$	−1.95087	−	0.824216i	−0.115357	−	0.0487369i
$287$		−	36.3242i		−	2.14415i
$288$	−2.34740	+	5.14681i	−0.138322	+	0.303279i
$289$	−38.8798			−2.28705
$290$	5.83784	+	11.8372i	0.342810	+	0.695107i
$291$	7.45865	+	7.45865i	0.437234	+	0.437234i
$292$	−0.242927	−	0.249867i	−0.0142162	−	0.0146224i
$293$	4.65889	+	4.65889i	0.272175	+	0.272175i	0.829975	−	0.557800i	$-0.188354\pi$
$293$	4.65889	+	4.65889i	0.272175	+	0.272175i	−0.557800	+	0.829975i	$0.688354\pi$
$294$	0.863778	+	2.12760i	0.0503766	+	0.124084i
$295$	−18.4832	−	15.9797i	−1.07613	−	0.930374i
$296$	−20.2715	−	8.90292i	−1.17826	−	0.517472i
$297$	0.939032			0.0544882
$298$	−0.948931	−	2.33734i	−0.0549701	−	0.135398i
$299$	6.96494	−	6.96494i	0.402793	−	0.402793i
$300$	9.91438	−	1.30575i	0.572407	−	0.0753876i
$301$	2.63594	+	2.63594i	0.151933	+	0.151933i
$302$	26.6717	+	11.2685i	1.53478	+	0.648427i
$303$			13.6549i			0.784456i
$304$	−1.74126	+	1.64584i	−0.0998681	+	0.0943952i
$305$	15.2532	−	17.6429i	0.873398	−	1.01023i
$306$	−4.11426	+	9.73820i	−0.235197	+	0.556696i
$307$	9.05487	−	9.05487i	0.516789	−	0.516789i	−0.399810	−	0.916598i	$-0.630924\pi$
$307$	9.05487	−	9.05487i	0.516789	−	0.516789i	0.916598	+	0.399810i	$0.130924\pi$
$308$	5.51460	+	0.0776659i	0.314224	+	0.00442542i
$309$	10.2929	−	10.2929i	0.585543	−	0.585543i
$310$	−5.46734	−	1.85576i	−0.310524	−	0.105400i
$311$		−	3.39349i		−	0.192427i	−0.995361	−	0.0962137i	$-0.969327\pi$
$311$		−	3.39349i		−	0.192427i	0.995361	−	0.0962137i	$-0.0306732\pi$
$312$	−1.63775	−	4.20284i	−0.0927192	−	0.237939i
$313$	10.8943			0.615784			0.307892	−	0.951421i	$-0.400376\pi$
$313$	10.8943			0.615784			0.307892	+	0.951421i	$0.400376\pi$
$314$	−6.11909	−	15.0721i	−0.345320	−	0.850567i
$315$	6.54921	−	0.475756i	0.369006	−	0.0268058i
$316$	−4.27293	−	4.39501i	−0.240371	−	0.247239i
$317$	3.45776	−	3.45776i	0.194207	−	0.194207i	−0.603304	−	0.797511i	$-0.706149\pi$
$317$	3.45776	−	3.45776i	0.194207	−	0.194207i	0.797511	+	0.603304i	$0.206149\pi$
$318$	−0.114013	+	0.269861i	−0.00639352	+	0.0151331i
$319$	3.91927			0.219437
$320$	13.0261	+	12.2605i	0.728182	+	0.685384i
$321$	−8.29096			−0.462756
$322$	−9.98270	+	23.6284i	−0.556314	+	1.31676i
$323$	−3.16619	+	3.16619i	−0.176172	+	0.176172i
$324$	1.39416	+	1.43399i	0.0774532	+	0.0796660i
$325$	−4.76426	+	6.39401i	−0.264274	+	0.354676i
$326$	−3.07666	−	7.57820i	−0.170400	−	0.419718i
$327$	6.95263			0.384481
$328$	−12.7028	−	32.5984i	−0.701396	−	1.79995i
$329$		−	12.1204i		−	0.668218i
$330$	0.954439	−	2.81191i	0.0525401	−	0.154791i
$331$	−24.9246	+	24.9246i	−1.36998	+	1.36998i	−0.509526	+	0.860455i	$0.670179\pi$
$331$	−24.9246	+	24.9246i	−1.36998	+	1.36998i	−0.860455	+	0.509526i	$0.829821\pi$
$332$	25.9836	+	0.365945i	1.42604	+	0.0200838i
$333$	−5.53509	+	5.53509i	−0.303321	+	0.303321i
$334$	−5.24441	+	12.4132i	−0.286961	+	0.679219i
$335$	20.7706	+	17.9573i	1.13482	+	0.981113i
$336$	8.06879	+	8.53661i	0.440189	+	0.465710i
$337$		−	9.62502i		−	0.524308i	−0.965026	−	0.262154i	$-0.915567\pi$
$337$		−	9.62502i		−	0.524308i	0.965026	−	0.262154i	$-0.0844329\pi$
$338$	−13.6222	−	5.75521i	−0.740950	−	0.313042i
$339$	−9.07458	−	9.07458i	−0.492863	−	0.492863i
$340$	24.9791	+	22.2181i	1.35468	+	1.20494i
$341$	−1.21233	+	1.21233i	−0.0656512	+	0.0656512i
$342$	0.318656	+	0.784891i	0.0172310	+	0.0424420i
$343$	−15.7881			−0.852479
$344$	3.28739	+	1.44377i	0.177244	+	0.0778428i
$345$	10.4477	+	9.03256i	0.562483	+	0.486296i
$346$	4.65121	+	11.4565i	0.250050	+	0.615906i
$347$	15.9302	+	15.9302i	0.855178	+	0.855178i	0.990765	−	0.135588i	$-0.0432923\pi$
$347$	15.9302	+	15.9302i	0.855178	+	0.855178i	−0.135588	+	0.990765i	$0.543292\pi$
$348$	5.81885	+	5.98509i	0.311923	+	0.320834i
$349$	−4.56134	−	4.56134i	−0.244163	−	0.244163i	0.574407	−	0.818570i	$-0.305233\pi$
$349$	−4.56134	−	4.56134i	−0.244163	−	0.244163i	−0.818570	+	0.574407i	$0.805233\pi$
$350$	5.23202	−	20.0950i	0.279663	−	1.07413i
$351$	−1.59476			−0.0851221
$352$	4.97613	−	1.85880i	0.265229	−	0.0990742i
$353$		−	14.1314i		−	0.752141i	−0.926591	−	0.376070i	$-0.877275\pi$
$353$		−	14.1314i		−	0.752141i	0.926591	−	0.376070i	$-0.122725\pi$
$354$	−14.2346	−	6.01395i	−0.756561	−	0.319638i
$355$	19.9766	−	1.45117i	1.06025	−	0.0770199i
$356$	12.4968	−	12.1497i	0.662331	−	0.643934i
$357$	15.5224	+	15.5224i	0.821533	+	0.821533i
$358$	19.1885	−	7.79030i	1.01414	−	0.411730i
$359$			25.2588i			1.33311i	0.745456	+	0.666555i	$0.232232\pi$
$359$			25.2588i			1.33311i	−0.745456	+	0.666555i	$0.767768\pi$
$360$	5.71108	−	2.71726i	0.301001	−	0.143212i
$361$		−	18.6412i		−	0.981116i
$362$	4.49907	+	11.0818i	0.236466	+	0.582446i
$363$	7.15466	+	7.15466i	0.375522	+	0.375522i
$364$	−9.36547	−	0.131900i	−0.490884	−	0.00691345i
$365$	0.0282294	+	0.388602i	0.00147759	+	0.0203404i
$366$	5.74054	−	13.5875i	0.300063	−	0.710230i
$367$		−	3.01381i		−	0.157320i	−0.996902	−	0.0786598i	$-0.974936\pi$
$367$		−	3.01381i		−	0.157320i	0.996902	−	0.0786598i	$-0.0250641\pi$
$368$	−0.695755	+	24.6959i	−0.0362688	+	1.28736i
$369$	−12.3694			−0.643925
$370$	10.9488	+	22.2006i	0.569202	+	1.15416i
$371$	0.430151	+	0.430151i	0.0223323	+	0.0223323i
$372$	−3.65125	−	0.0514230i	−0.189308	−	0.00266616i
$373$	13.1060	+	13.1060i	0.678604	+	0.678604i	0.959684	−	0.281080i	$-0.0906927\pi$
$373$	13.1060	+	13.1060i	0.678604	+	0.678604i	−0.281080	+	0.959684i	$0.590693\pi$
$374$	9.19798	−	3.73427i	0.475616	−	0.193094i
$375$	−9.42569	−	6.01302i	−0.486740	−	0.310511i
$376$	−4.23858	−	10.8772i	−0.218588	−	0.560949i
$377$	−6.65611			−0.342807
$378$	3.84797	−	1.56223i	0.197918	−	0.0803523i
$379$	8.34584	−	8.34584i	0.428697	−	0.428697i	−0.459487	−	0.888184i	$-0.651967\pi$
$379$	8.34584	−	8.34584i	0.428697	−	0.428697i	0.888184	+	0.459487i	$0.151967\pi$
$380$	2.67423	−	0.156442i	0.137185	−	0.00802528i
$381$	0.756904	+	0.756904i	0.0387774	+	0.0387774i
$382$	0.222867	−	0.527513i	0.0114029	−	0.0269899i
$383$		−	25.5695i		−	1.30654i	−0.757124	−	0.653271i	$-0.773396\pi$
$383$		−	25.5695i		−	1.30654i	0.757124	−	0.653271i	$-0.226604\pi$
$384$	10.2265	+	4.83930i	0.521869	+	0.246955i
$385$	−4.66455	−	4.03275i	−0.237727	−	0.205528i
$386$	−8.45425	−	3.57181i	−0.430310	−	0.181801i
$387$	0.897614	−	0.897614i	0.0456283	−	0.0456283i
$388$	15.1259	−	14.7057i	0.767900	−	0.746571i
$389$	4.31954	−	4.31954i	0.219009	−	0.219009i	−0.589072	−	0.808081i	$-0.700506\pi$
$389$	4.31954	−	4.31954i	0.219009	−	0.219009i	0.808081	+	0.589072i	$0.200506\pi$
$390$	−1.62093	+	4.77548i	−0.0820788	+	0.241816i
$391$			46.1705i			2.33494i
$392$	4.27910	−	1.66746i	0.216127	−	0.0842195i
$393$	−15.4183			−0.777750
$394$	−34.1758	+	13.8750i	−1.72175	+	0.699011i
$395$	0.496537	+	6.83528i	0.0249835	+	0.343920i
$396$	0.0264474	−	1.87788i	0.00132903	−	0.0943669i
$397$	−23.5750	+	23.5750i	−1.18319	+	1.18319i	−0.204281	+	0.978912i	$0.565485\pi$
$397$	−23.5750	+	23.5750i	−1.18319	+	1.18319i	−0.978912	+	0.204281i	$0.934515\pi$
$398$	17.5471	+	7.41342i	0.879556	+	0.371601i
$399$	1.75902			0.0880613
$400$	−2.33201	−	19.8636i	−0.116601	−	0.993179i
$401$	17.1100			0.854430			0.427215	−	0.904150i	$-0.359495\pi$
$401$	17.1100			0.854430			0.427215	+	0.904150i	$0.359495\pi$
$402$	15.9963	+	6.75822i	0.797821	+	0.337069i
$403$	2.05890	−	2.05890i	0.102561	−	0.102561i
$404$	27.3072	+	0.384585i	1.35858	+	0.0191338i
$405$	−0.162008	−	2.23019i	−0.00805026	−	0.110819i
$406$	16.0604	−	6.52032i	0.797064	−	0.323598i
$407$	7.35056			0.364354
$408$	19.3586	+	8.50199i	0.958393	+	0.420911i
$409$			25.2659i			1.24932i	0.780897	+	0.624659i	$0.214762\pi$
$409$			25.2659i			1.24932i	−0.780897	+	0.624659i	$0.785238\pi$
$410$	−12.5723	+	37.0399i	−0.620904	+	1.82927i
$411$	−7.10987	+	7.10987i	−0.350704	+	0.350704i
$412$	−20.2939	−	20.8737i	−0.999807	−	1.02837i
$413$	−22.6896	+	22.6896i	−1.11648	+	1.11648i
$414$	8.04614	+	3.39939i	0.395446	+	0.167071i
$415$	−21.9784	−	19.0014i	−1.07888	−	0.932744i
$416$	−8.45098	+	3.15680i	−0.414343	+	0.154775i
$417$		−	4.11215i		−	0.201373i
$418$	0.309578	−	0.732751i	0.0151420	−	0.0358400i
$419$	−15.7885	−	15.7885i	−0.771317	−	0.771317i	0.207020	−	0.978337i	$-0.433624\pi$
$419$	−15.7885	−	15.7885i	−0.771317	−	0.771317i	−0.978337	+	0.207020i	$0.933624\pi$
$420$	−0.766962	−	13.1105i	−0.0374239	−	0.639728i
$421$	−4.64861	+	4.64861i	−0.226559	+	0.226559i	−0.811254	−	0.584694i	$-0.801214\pi$
$421$	−4.64861	+	4.64861i	−0.226559	+	0.226559i	0.584694	+	0.811254i	$0.301214\pi$
$422$	−11.2622	+	4.57232i	−0.548236	+	0.222577i
$423$	−4.12733			−0.200678
$424$	0.536457	+	0.235604i	0.0260527	+	0.0114419i
$425$	−5.40179	−	36.9840i	−0.262025	−	1.79399i
$426$	11.7372	−	4.76516i	0.568668	−	0.230873i
$427$	−21.6581	−	21.6581i	−1.04811	−	1.04811i
$428$	−0.233511	+	16.5803i	−0.0112872	+	0.801438i
$429$	1.05892	+	1.05892i	0.0511249	+	0.0511249i
$430$	−1.77555	−	3.60023i	−0.0856245	−	0.173618i
$431$	−28.6320			−1.37915			−0.689577	−	0.724213i	$-0.742203\pi$
$431$	−28.6320			−1.37915			−0.689577	+	0.724213i	$0.742203\pi$
$432$	2.90696	−	2.74765i	0.139861	−	0.132196i
$433$		−	6.14954i		−	0.295528i	−0.989023	−	0.147764i	$-0.952792\pi$
$433$		−	6.14954i		−	0.295528i	0.989023	−	0.147764i	$-0.0472076\pi$
$434$	−2.95098	+	6.98477i	−0.141651	+	0.335280i
$435$	−0.676180	−	9.30823i	−0.0324204	−	0.446295i
$436$	0.195818	−	13.9039i	0.00937797	−	0.665875i
$437$	2.61605	+	2.61605i	0.125143	+	0.125143i
$438$	0.0926960	+	0.228322i	0.00442919	+	0.0109097i
$439$			37.8541i			1.80668i	0.428926	+	0.903340i	$0.358892\pi$
$439$			37.8541i			1.80668i	−0.428926	+	0.903340i	$0.641108\pi$
$440$	−5.59639	−	1.98788i	−0.266797	−	0.0947687i
$441$		−	1.62370i		−	0.0773188i
$442$	−15.6210	+	6.34192i	−0.743013	+	0.301654i
$443$	−3.41746	−	3.41746i	−0.162368	−	0.162368i	0.621247	−	0.783615i	$-0.286627\pi$
$443$	−3.41746	−	3.41746i	−0.162368	−	0.162368i	−0.783615	+	0.621247i	$0.786627\pi$
$444$	10.9132	+	11.2250i	0.517917	+	0.532714i
$445$	−19.4355	+	1.41186i	−0.921332	+	0.0669286i
$446$	−28.7633	−	12.1521i	−1.36198	−	0.575420i
$447$			1.78376i			0.0843691i
$448$	17.2988	−	15.8955i	0.817291	−	0.750994i
$449$	−31.6935			−1.49571			−0.747855	−	0.663862i	$-0.768916\pi$
$449$	−31.6935			−1.49571			−0.747855	+	0.663862i	$0.768916\pi$
$450$	−6.84293	−	1.78165i	−0.322579	−	0.0839878i
$451$	8.21324	+	8.21324i	0.386746	+	0.386746i
$452$	−18.4029	+	17.8918i	−0.865601	+	0.841558i
$453$	−14.4772	−	14.4772i	−0.680198	−	0.680198i
$454$	−4.18239	−	10.3018i	−0.196289	−	0.483485i
$455$	7.92182	+	6.84883i	0.371381	+	0.321078i
$456$	1.57860	−	0.615143i	0.0739248	−	0.0288067i
$457$	−7.26208			−0.339706			−0.169853	−	0.985469i	$-0.554329\pi$
$457$	−7.26208			−0.339706			−0.169853	+	0.985469i	$0.554329\pi$
$458$	8.89439	+	21.9080i	0.415607	+	1.02369i
$459$	5.28582	−	5.28582i	0.246721	−	0.246721i
$460$	18.3576	−	20.6389i	0.855926	−	0.962292i
$461$	16.1568	+	16.1568i	0.752499	+	0.752499i	0.974945	−	0.222446i	$-0.0714041\pi$
$461$	16.1568	+	16.1568i	0.752499	+	0.752499i	−0.222446	+	0.974945i	$0.571404\pi$
$462$	−3.59235	−	1.51772i	−0.167131	−	0.0706108i
$463$		−	13.4637i		−	0.625710i	−0.949801	−	0.312855i	$-0.898715\pi$
$463$		−	13.4637i		−	0.625710i	0.949801	−	0.312855i	$-0.101285\pi$
$464$	12.1329	−	11.4680i	0.563255	−	0.532387i
$465$	3.08842	+	2.67011i	0.143222	+	0.123823i
$466$	4.90955	−	11.6206i	0.227430	−	0.538313i
$467$	10.5630	−	10.5630i	0.488795	−	0.488795i	−0.419131	−	0.907926i	$-0.637665\pi$
$467$	10.5630	−	10.5630i	0.488795	−	0.488795i	0.907926	+	0.419131i	$0.137665\pi$
$468$	−0.0449157	+	3.18921i	−0.00207623	+	0.147421i
$469$	25.4976	−	25.4976i	1.17737	−	1.17737i
$470$	−4.19505	+	12.3592i	−0.193503	+	0.570088i
$471$			11.5024i			0.530003i
$472$	−12.4276	+	28.2970i	−0.572027	+	1.30248i
$473$	−1.19202			−0.0548093
$474$	1.63047	+	4.01604i	0.0748898	+	0.184463i
$475$	−2.40161	−	1.78947i	−0.110193	−	0.0821066i
$476$	31.4789	−	30.6046i	1.44283	−	1.40276i
$477$	0.146479	−	0.146479i	0.00670679	−	0.00670679i
$478$	−12.6214	+	29.8739i	−0.577287	+	1.36640i
$479$	34.2747			1.56605			0.783026	−	0.621989i	$-0.213675\pi$
$479$	34.2747			1.56605			0.783026	+	0.621989i	$0.213675\pi$
$480$	−5.27314	−	11.4976i	−0.240685	−	0.524790i
$481$	−12.4835			−0.569197
$482$	3.56776	−	8.44465i	0.162507	−	0.384643i
$483$	12.8253	−	12.8253i	0.583573	−	0.583573i
$484$	14.5094	−	14.1064i	0.659519	−	0.641200i
$485$	−23.5243	+	1.70888i	−1.06818	+	0.0775964i
$486$	−0.531983	−	1.31034i	−0.0241312	−	0.0594383i
$487$	−33.4994			−1.51800			−0.759002	−	0.651088i	$-0.774313\pi$
$487$	−33.4994			−1.51800			−0.759002	+	0.651088i	$0.774313\pi$
$488$	−27.0106	−	11.8626i	−1.22271	−	0.536996i
$489$			5.78338i			0.261533i
$490$	−4.86212	−	1.65034i	−0.219648	−	0.0745545i
$491$	0.491541	−	0.491541i	0.0221829	−	0.0221829i	−0.695928	−	0.718111i	$-0.745007\pi$
$491$	0.491541	−	0.491541i	0.0221829	−	0.0221829i	0.718111	+	0.695928i	$0.245007\pi$
$492$	−0.348379	+	24.7364i	−0.0157061	+	1.11520i
$493$	22.0616	−	22.0616i	0.993606	−	0.993606i
$494$	−0.525757	+	1.24443i	−0.0236549	+	0.0559897i
$495$	−1.37327	+	1.58841i	−0.0617237	+	0.0713938i
$496$	−0.205672	+	7.30033i	−0.00923493	+	0.327794i
$497$		−	26.3043i		−	1.17991i
$498$	−16.9264	−	7.15118i	−0.758489	−	0.320452i
$499$	−0.863504	−	0.863504i	−0.0386557	−	0.0386557i	0.687515	−	0.726170i	$-0.258702\pi$
$499$	−0.863504	−	0.863504i	−0.0386557	−	0.0386557i	−0.726170	+	0.687515i	$0.758702\pi$
$500$	−12.2903	+	18.6801i	−0.549640	+	0.835402i
$501$	6.73779	−	6.73779i	0.301022	−	0.301022i
$502$	10.8500	+	26.7250i	0.484260	+	1.19279i
$503$	12.8335			0.572218			0.286109	−	0.958197i	$-0.407638\pi$
$503$	12.8335			0.572218			0.286109	+	0.958197i	$0.407638\pi$
$504$	−3.01577	−	7.73917i	−0.134333	−	0.344730i
$505$	−23.0979	−	19.9693i	−1.02784	−	0.888624i
$506$	−3.08542	−	7.59979i	−0.137164	−	0.337852i
$507$	7.39403	+	7.39403i	0.328380	+	0.328380i
$508$	1.53498	−	1.49234i	0.0681035	−	0.0662119i
$509$	−12.6692	−	12.6692i	−0.561554	−	0.561554i	0.368194	−	0.929749i	$-0.379976\pi$
$509$	−12.6692	−	12.6692i	−0.561554	−	0.561554i	−0.929749	+	0.368194i	$0.879976\pi$
$510$	−10.4557	−	21.2008i	−0.462988	−	0.938789i
$511$	0.511694			0.0226360
$512$	9.96567	−	20.3147i	0.440424	−	0.897790i
$513$		−	0.598997i		−	0.0264464i
$514$	0.252388	+	0.106631i	0.0111324	+	0.00470328i
$515$	2.35825	+	32.4635i	0.103917	+	1.43051i
$516$	−1.76977	−	1.82033i	−0.0779097	−	0.0801356i
$517$	2.74053	+	2.74053i	0.120529	+	0.120529i
$518$	30.1211	−	12.2288i	1.32345	−	0.537303i
$519$		−	8.74315i		−	0.383782i
$520$	9.50437	+	3.37603i	0.416794	+	0.148049i
$521$			30.2561i			1.32554i	0.748821	+	0.662772i	$0.230620\pi$
$521$			30.2561i			1.32554i	−0.748821	+	0.662772i	$0.769380\pi$
$522$	−2.22036	−	5.46902i	−0.0971823	−	0.239372i
$523$	4.01063	+	4.01063i	0.175373	+	0.175373i	0.789335	−	0.613962i	$-0.210425\pi$
$523$	4.01063	+	4.01063i	0.175373	+	0.175373i	−0.613962	+	0.789335i	$0.710425\pi$
$524$	−0.434249	+	30.8335i	−0.0189703	+	1.34697i
$525$	−8.77297	+	11.7740i	−0.382884	+	0.513860i
$526$	9.12029	−	21.5871i	0.397663	−	0.941243i
$527$			13.6484i			0.594534i
$528$	−3.75464	−	0.105779i	−0.163400	−	0.00460345i
$529$	15.1481			0.658615
$530$	−0.289745	−	0.587509i	−0.0125857	−	0.0255198i
$531$	7.72645	+	7.72645i	0.335299	+	0.335299i
$532$	0.0495421	−	3.51770i	0.00214792	−	0.152512i
$533$	−13.9486	−	13.9486i	−0.604179	−	0.604179i
$534$	−11.4193	+	4.63609i	−0.494160	+	0.200623i
$535$	12.1249	−	14.0245i	0.524206	−	0.606332i
$536$	13.9656	−	31.7990i	0.603223	−	1.37351i
$537$	−14.6439			−0.631931
$538$	−13.1456	+	5.33694i	−0.566745	+	0.230092i
$539$	−1.07813	+	1.07813i	−0.0464382	+	0.0464382i
$540$	−4.46450	+	0.261172i	−0.192122	+	0.0112391i
$541$	−5.53130	−	5.53130i	−0.237809	−	0.237809i	0.578133	−	0.815942i	$-0.303781\pi$
$541$	−5.53130	−	5.53130i	−0.237809	−	0.237809i	−0.815942	+	0.578133i	$0.803781\pi$
$542$	−1.44353	+	3.41675i	−0.0620051	+	0.146762i
$543$		−	8.45718i		−	0.362932i
$544$	17.5475	−	38.4739i	0.752343	−	1.64955i
$545$	−10.1677	+	11.7607i	−0.435537	+	0.503771i
$546$	6.10089	+	2.57755i	0.261094	+	0.110309i
$547$	22.6141	−	22.6141i	0.966908	−	0.966908i	−0.0325622	−	0.999470i	$-0.510367\pi$
$547$	22.6141	−	22.6141i	0.966908	−	0.966908i	0.999470	+	0.0325622i	$0.0103667\pi$
$548$	14.0181	+	14.4186i	0.598823	+	0.615931i
$549$	−7.37519	+	7.37519i	−0.314766	+	0.314766i
$550$	3.36067	+	5.72669i	0.143300	+	0.244187i
$551$		−	2.50006i		−	0.106506i
$552$	7.02473	−	15.9949i	0.298992	−	0.680790i
$553$	9.00038			0.382735
$554$	14.7791	−	6.00013i	0.627904	−	0.254921i
$555$	−1.26817	−	17.4575i	−0.0538308	−	0.741029i
$556$	−8.22349	−	0.115817i	−0.348753	−	0.00491173i
$557$	−6.08239	+	6.08239i	−0.257719	+	0.257719i	−0.824126	−	0.566407i	$-0.808333\pi$
$557$	−6.08239	+	6.08239i	−0.257719	+	0.257719i	0.566407	+	0.824126i	$0.308333\pi$
$558$	2.37851	+	1.00489i	0.100690	+	0.0425405i
$559$	2.02442			0.0856238
$560$	−26.2400	+	1.16452i	−1.10884	+	0.0492100i
$561$	−7.01953			−0.296365
$562$	−12.9992	−	5.49199i	−0.548338	−	0.231666i
$563$	23.1946	−	23.1946i	0.977536	−	0.977536i	−0.0222176	−	0.999753i	$-0.507073\pi$
$563$	23.1946	−	23.1946i	0.977536	−	0.977536i	0.999753	+	0.0222176i	$0.00707265\pi$
$564$	−0.116245	+	8.25385i	−0.00489478	+	0.347550i
$565$	28.6209	−	2.07912i	1.20409	−	0.0874692i
$566$	−37.8136	+	15.3519i	−1.58943	+	0.645288i
$567$	−2.93661			−0.123326
$568$	−9.19879	−	23.6062i	−0.385973	−	0.990496i
$569$			1.31584i			0.0551629i	0.999620	+	0.0275815i	$0.00878056\pi$
$569$			1.31584i			0.0551629i	−0.999620	+	0.0275815i	$0.991219\pi$
$570$	−1.79369	−	0.608825i	−0.0751292	−	0.0255009i
$571$	18.2083	−	18.2083i	0.761993	−	0.761993i	−0.214690	−	0.976682i	$-0.568874\pi$
$571$	18.2083	−	18.2083i	0.761993	−	0.761993i	0.976682	+	0.214690i	$0.0688740\pi$
$572$	2.14744	−	2.08780i	0.0897892	−	0.0872952i
$573$	−0.286330	+	0.286330i	−0.0119616	+	0.0119616i
$574$	47.3202	+	19.9922i	1.97511	+	0.834458i
$575$	−30.5579	+	4.46320i	−1.27435	+	0.186128i
$576$	−5.41289	−	5.89073i	−0.225537	−	0.245447i
$577$			8.13617i			0.338713i	0.985555	+	0.169357i	$0.0541689\pi$
$577$			8.13617i			0.338713i	−0.985555	+	0.169357i	$0.945831\pi$
$578$	21.3988	−	50.6495i	0.890072	−	2.10674i
$579$	4.58891	+	4.58891i	0.190708	+	0.190708i
$580$	−18.6337	+	1.09006i	−0.773721	+	0.0452625i
$581$	−26.9802	+	26.9802i	−1.11933	+	1.11933i
$582$	−13.8216	+	5.61142i	−0.572925	+	0.232601i
$583$	−0.194522			−0.00805629
$584$	0.459210	−	0.178943i	0.0190022	−	0.00740472i
$585$	2.33222	−	2.69760i	0.0964255	−	0.111532i
$586$	−8.63339	+	3.50505i	−0.356642	+	0.144792i
$587$	13.4231	+	13.4231i	0.554030	+	0.554030i	0.927601	−	0.373572i	$-0.121867\pi$
$587$	13.4231	+	13.4231i	0.554030	+	0.554030i	−0.373572	+	0.927601i	$0.621867\pi$
$588$	−3.24707	−	0.0457307i	−0.133907	−	0.00188590i
$589$	0.773329	+	0.773329i	0.0318645	+	0.0318645i
$590$	30.9899	−	15.2835i	1.27583	−	0.629211i
$591$	26.0816			1.07286
$592$	22.7551	−	21.5081i	0.935229	−	0.883976i
$593$			17.9386i			0.736649i	0.929697	+	0.368324i	$0.120068\pi$
$593$			17.9386i			0.736649i	−0.929697	+	0.368324i	$0.879932\pi$
$594$	−0.516827	+	1.22330i	−0.0212057	+	0.0501924i
$595$	−48.9572	+	3.55641i	−2.00705	+	0.145799i
$596$	3.56717	+	0.0502389i	0.146117	+	0.00205787i
$597$	−9.52443	−	9.52443i	−0.389809	−	0.389809i
$598$	5.23998	+	12.9067i	0.214279	+	0.527796i
$599$		−	3.98863i		−	0.162971i	−0.996675	−	0.0814855i	$-0.974034\pi$
$599$		−	3.98863i		−	0.162971i	0.996675	−	0.0814855i	$-0.0259664\pi$
$600$	−3.75568	+	13.6343i	−0.153325	+	0.556619i
$601$		−	20.7775i		−	0.847532i	−0.905772	−	0.423766i	$-0.860708\pi$
$601$		−	20.7775i		−	0.847532i	0.905772	−	0.423766i	$-0.139292\pi$
$602$	−4.88468	+	1.98312i	−0.199085	+	0.0808259i
$603$	−8.68265	−	8.68265i	−0.353585	−	0.353585i
$604$	−29.3593	+	28.5438i	−1.19461	+	1.16143i
$605$	−22.5656	+	1.63924i	−0.917421	+	0.0666445i
$606$	−17.7886	−	7.51544i	−0.722611	−	0.305294i
$607$			46.0393i			1.86868i	0.356384	+	0.934340i	$0.384010\pi$
$607$			46.0393i			1.86868i	−0.356384	+	0.934340i	$0.615990\pi$
$608$	−1.18570	−	3.17421i	−0.0480866	−	0.128731i
$609$	−12.2566			−0.496664
$610$	14.5887	+	29.5811i	0.590678	+	1.19770i
$611$	−4.65426	−	4.65426i	−0.188291	−	0.188291i
$612$	−10.4217	−	10.7195i	−0.421273	−	0.433309i
$613$	13.9783	+	13.9783i	0.564580	+	0.564580i	0.930605	−	0.366025i	$-0.119282\pi$
$613$	13.9783	+	13.9783i	0.564580	+	0.564580i	−0.366025	+	0.930605i	$0.619282\pi$
$614$	6.81231	+	16.7796i	0.274923	+	0.677169i
$615$	18.0893	−	20.9234i	0.729433	−	0.843711i
$616$	−3.13632	+	7.14124i	−0.126366	+	0.287729i
$617$	−33.5135			−1.34920			−0.674601	−	0.738182i	$-0.735684\pi$
$617$	−33.5135			−1.34920			−0.674601	+	0.738182i	$0.735684\pi$
$618$	7.74374	+	19.0738i	0.311499	+	0.767261i
$619$	−4.64277	+	4.64277i	−0.186609	+	0.186609i	−0.794228	−	0.607620i	$-0.792125\pi$
$619$	−4.64277	+	4.64277i	−0.186609	+	0.186609i	0.607620	+	0.794228i	$0.292125\pi$
$620$	5.42667	−	6.10103i	0.217940	−	0.245023i
$621$	−4.36739	−	4.36739i	−0.175257	−	0.175257i
$622$	4.42077	+	1.86772i	0.177257	+	0.0748887i
$623$			25.5918i			1.02531i
$624$	6.37652	+	0.179645i	0.255265	+	0.00719156i
$625$	23.9556	−	7.15033i	0.958226	−	0.286013i
$626$	−5.99605	+	14.1923i	−0.239650	+	0.567237i
$627$	−0.397732	+	0.397732i	−0.0158839	+	0.0158839i
$628$	23.0025	+	0.323960i	0.917902	+	0.0129274i
$629$	41.3764	−	41.3764i	1.64978	−	1.64978i
$630$	−2.98479	+	8.79363i	−0.118917	+	0.350347i
$631$			4.43412i			0.176519i	0.996097	+	0.0882597i	$0.0281305\pi$
$631$			4.43412i			0.176519i	−0.996097	+	0.0882597i	$0.971869\pi$
$632$	8.07721	−	3.14750i	0.321294	−	0.125201i
$633$	8.59487			0.341615
$634$	2.60140	+	6.40758i	0.103315	+	0.254478i
$635$	−2.38725	+	0.173418i	−0.0947351	+	0.00688187i
$636$	−0.288803	−	0.297054i	−0.0114518	−	0.0117789i
$637$	1.83099	−	1.83099i	0.0725464	−	0.0725464i
$638$	−2.15710	+	5.10571i	−0.0854004	+	0.202137i
$639$	−8.95735			−0.354347
$640$	−23.1414	+	10.2214i	−0.914743	+	0.404037i
$641$	−29.2735			−1.15623			−0.578116	−	0.815954i	$-0.696212\pi$
$641$	−29.2735			−1.15623			−0.578116	+	0.815954i	$0.696212\pi$
$642$	4.56320	−	10.8008i	0.180095	−	0.426274i
$643$	5.69367	−	5.69367i	0.224536	−	0.224536i	−0.585869	−	0.810406i	$-0.699247\pi$
$643$	5.69367	−	5.69367i	0.224536	−	0.224536i	0.810406	+	0.585869i	$0.199247\pi$
$644$	−25.2869	−	26.0093i	−0.996443	−	1.02491i
$645$	0.205656	+	2.83104i	0.00809771	+	0.111472i
$646$	−2.38205	−	5.86728i	−0.0937203	−	0.230845i
$647$	2.78788			0.109603			0.0548015	−	0.998497i	$-0.482547\pi$
$647$	2.78788			0.109603			0.0548015	+	0.998497i	$0.482547\pi$
$648$	−2.63541	+	1.02695i	−0.103529	+	0.0403426i
$649$		−	10.2607i		−	0.402766i
$650$	−5.70744	−	9.72565i	−0.223864	−	0.381472i
$651$	3.79128	−	3.79128i	0.148592	−	0.148592i
$652$	11.5656	+	0.162886i	0.452944	+	0.00637912i
$653$	19.9931	−	19.9931i	0.782389	−	0.782389i	−0.197844	−	0.980233i	$-0.563394\pi$
$653$	19.9931	−	19.9931i	0.782389	−	0.782389i	0.980233	+	0.197844i	$0.0633940\pi$
$654$	−3.82661	+	9.05733i	−0.149632	+	0.354170i
$655$	22.5481	−	26.0807i	0.881027	−	1.01906i
$656$	49.4580	+	1.39338i	1.93101	+	0.0544022i
$657$		−	0.174246i		−	0.00679799i
$658$	15.7895	+	6.67085i	0.615537	+	0.260057i
$659$	−6.26656	−	6.26656i	−0.244110	−	0.244110i	0.574438	−	0.818548i	$-0.305221\pi$
$659$	−6.26656	−	6.26656i	−0.244110	−	0.244110i	−0.818548	+	0.574438i	$0.805221\pi$
$660$	3.13783	+	2.79100i	0.122140	+	0.108639i
$661$	−2.89073	+	2.89073i	−0.112436	+	0.112436i	−0.761087	−	0.648650i	$-0.775334\pi$
$661$	−2.89073	+	2.89073i	−0.112436	+	0.112436i	0.648650	+	0.761087i	$0.275334\pi$
$662$	−18.7517	−	46.1879i	−0.728806	−	1.79514i
$663$	11.9213			0.462985
$664$	−14.7777	+	33.6480i	−0.573484	+	1.30579i
$665$	−2.57244	+	2.97546i	−0.0997550	+	0.115383i
$666$	−4.16425	−	10.2571i	−0.161362	−	0.397454i
$667$	−18.2283	−	18.2283i	−0.705803	−	0.705803i
$668$	−13.2845	−	13.6640i	−0.513991	−	0.528676i
$669$	15.6125	+	15.6125i	0.603614	+	0.603614i
$670$	−34.8251	+	17.1749i	−1.34541	+	0.663525i
$671$	9.79420			0.378101
$672$	−15.5617	+	5.81297i	−0.600307	+	0.224240i
$673$			30.9133i			1.19162i	0.803125	+	0.595810i	$0.203169\pi$
$673$			30.9133i			1.19162i	−0.803125	+	0.595810i	$0.796831\pi$
$674$	12.5387	+	5.29745i	0.482973	+	0.204050i
$675$	4.00938	+	2.98745i	0.154321	+	0.114987i
$676$	14.9948	−	14.5783i	0.576725	−	0.560705i
$677$	5.28850	+	5.28850i	0.203253	+	0.203253i	0.801392	−	0.598139i	$-0.204093\pi$
$677$	5.28850	+	5.28850i	0.203253	+	0.203253i	−0.598139	+	0.801392i	$0.704093\pi$
$678$	16.8161	−	6.82714i	0.645819	−	0.262195i
$679$			30.9757i			1.18874i
$680$	−42.6920	+	20.3123i	−1.63716	+	0.778942i
$681$			7.86189i			0.301268i
$682$	−0.912079	−	2.24657i	−0.0349253	−	0.0860255i
$683$	10.6055	+	10.6055i	0.405809	+	0.405809i	0.880274	−	0.474465i	$-0.157359\pi$
$683$	10.6055	+	10.6055i	0.405809	+	0.405809i	−0.474465	+	0.880274i	$0.657359\pi$
$684$	−1.19788	−	0.0168705i	−0.0458019	−	0.000645059i
$685$	−1.62897	−	22.4243i	−0.0622399	−	0.856788i
$686$	8.68951	−	20.5675i	0.331767	−	0.785271i
$687$		−	16.7193i		−	0.637882i
$688$	−3.69015	+	3.48792i	−0.140685	+	0.132976i
$689$	0.330358			0.0125856
$690$	−17.5171	+	8.63902i	−0.666865	+	0.328882i
$691$	32.1363	+	32.1363i	1.22252	+	1.22252i	0.966732	+	0.255790i	$0.0823357\pi$
$691$	32.1363	+	32.1363i	1.22252	+	1.22252i	0.255790	+	0.966732i	$0.417664\pi$
$692$	−17.4846	−	0.246247i	−0.664664	−	0.00936091i
$693$	1.94990	+	1.94990i	0.0740706	+	0.0740706i
$694$	−29.5203	+	11.9849i	−1.12057	+	0.454940i
$695$	6.95587	+	6.01372i	0.263851	+	0.228113i
$696$	−10.9995	+	4.28624i	−0.416935	+	0.162469i
$697$	92.4648			3.50235
$698$	8.45264	−	3.43167i	0.319937	−	0.129891i
$699$	−6.30756	+	6.30756i	−0.238574	+	0.238574i
$700$	23.2986	+	17.8758i	0.880604	+	0.675642i
$701$	13.0526	+	13.0526i	0.492989	+	0.492989i	0.909247	−	0.416258i	$-0.136659\pi$
$701$	13.0526	+	13.0526i	0.492989	+	0.492989i	−0.416258	+	0.909247i	$0.636659\pi$
$702$	0.877729	−	2.07753i	0.0331277	−	0.0784112i
$703$		−	4.68883i		−	0.176843i
$704$	−0.317285	+	7.50556i	−0.0119581	+	0.282876i
$705$	6.03592	−	6.98155i	0.227326	−	0.262940i
$706$	18.4093	+	7.77770i	0.692844	+	0.292718i
$707$	−28.3545	+	28.3545i	−1.06638	+	1.06638i
$708$	15.6690	−	15.2337i	0.588876	−	0.572519i
$709$	−7.03016	+	7.03016i	−0.264023	+	0.264023i	−0.826686	−	0.562663i	$-0.809777\pi$
$709$	−7.03016	+	7.03016i	−0.264023	+	0.264023i	0.562663	+	0.826686i	$0.309777\pi$
$710$	−9.10431	+	26.8226i	−0.341679	+	1.00663i
$711$		−	3.06488i		−	0.114942i
$712$	8.94964	+	22.9669i	0.335402	+	0.860720i
$713$	11.2769			0.422325
$714$	−28.7646	+	11.6781i	−1.07649	+	0.437042i
$715$	−3.33978	+	0.242613i	−0.124901	+	0.00907321i
$716$	−0.412439	+	29.2849i	−0.0154136	+	1.09443i
$717$	16.2153	−	16.2153i	0.605573	−	0.605573i
$718$	−32.9052	−	13.9020i	−1.22801	−	0.518819i
$719$	−15.9753			−0.595778			−0.297889	−	0.954601i	$-0.596282\pi$
$719$	−15.9753			−0.595778			−0.297889	+	0.954601i	$0.596282\pi$
$720$	0.396552	+	8.93548i	0.0147786	+	0.333006i
$721$	42.7464			1.59196
$722$	24.2843	+	10.2598i	0.903767	+	0.381830i
$723$	−4.58369	+	4.58369i	−0.170469	+	0.170469i
$724$	−16.9127	−	0.238193i	−0.628555	−	0.00885236i
$725$	16.7341	+	12.4688i	0.621489	+	0.463080i
$726$	−13.2583	+	5.38272i	−0.492062	+	0.199771i
$727$	9.60073			0.356071			0.178036	−	0.984024i	$-0.443026\pi$
$727$	9.60073			0.356071			0.178036	+	0.984024i	$0.443026\pi$
$728$	5.32642	−	12.1280i	0.197410	−	0.449493i
$729$			1.00000i			0.0370370i
$730$	−0.521777	−	0.177105i	−0.0193118	−	0.00655495i
$731$	−6.70992	+	6.70992i	−0.248175	+	0.248175i
$732$	14.5412	+	14.9566i	0.537458	+	0.552813i
$733$	−5.23740	+	5.23740i	−0.193448	+	0.193448i	−0.797184	−	0.603736i	$-0.793678\pi$
$733$	−5.23740	+	5.23740i	−0.193448	+	0.193448i	0.603736	+	0.797184i	$0.293678\pi$
$734$	3.92615	+	1.65875i	0.144917	+	0.0612255i
$735$	2.74655	+	2.37453i	0.101308	+	0.0875860i
$736$	−31.7889	−	14.4986i	−1.17175	−	0.534424i
$737$			11.5305i			0.424731i
$738$	6.80790	−	16.1139i	0.250602	−	0.593160i
$739$	−18.0809	−	18.0809i	−0.665118	−	0.665118i	0.291464	−	0.956582i	$-0.405858\pi$
$739$	−18.0809	−	18.0809i	−0.665118	−	0.665118i	−0.956582	+	0.291464i	$0.905858\pi$
$740$	−34.9472	+	2.04441i	−1.28469	+	0.0751538i
$741$	0.675469	−	0.675469i	0.0248140	−	0.0248140i
$742$	−0.797114	+	0.323619i	−0.0292630	+	0.0118804i
$743$	−5.96005			−0.218653			−0.109326	−	0.994006i	$-0.534869\pi$
$743$	−5.96005			−0.218653			−0.109326	+	0.994006i	$0.534869\pi$
$744$	2.07657	−	4.72825i	0.0761309	−	0.173346i
$745$	−3.01731	−	2.60862i	−0.110546	−	0.0955725i
$746$	−24.2868	+	9.86015i	−0.889203	+	0.361006i
$747$	9.18751	+	9.18751i	0.336153	+	0.336153i
$748$	−0.197702	+	14.0377i	−0.00722870	+	0.513268i
$749$	−17.2162	−	17.2162i	−0.629065	−	0.629065i
$750$	13.0210	−	8.96957i	0.475460	−	0.327522i
$751$	−32.6552			−1.19160			−0.595802	−	0.803131i	$-0.703166\pi$
$751$	−32.6552			−1.19160			−0.595802	+	0.803131i	$0.703166\pi$
$752$	16.5028	+	0.464932i	0.601795	+	0.0169543i
$753$		−	20.3954i		−	0.743251i
$754$	3.66341	−	8.67105i	0.133413	−	0.315781i
$755$	45.6606	−	3.31694i	1.66176	−	0.120716i
$756$	−0.0827084	+	5.87264i	−0.00300808	+	0.213586i
$757$	−34.0760	−	34.0760i	−1.23851	−	1.23851i	−0.960609	−	0.277903i	$-0.910361\pi$
$757$	−34.0760	−	34.0760i	−1.23851	−	1.23851i	−0.277903	−	0.960609i	$-0.589639\pi$
$758$	6.27889	+	15.4657i	0.228060	+	0.561740i
$759$			5.79986i			0.210521i
$760$	−1.26805	+	3.56987i	−0.0459969	+	0.129493i
$761$			29.5888i			1.07259i	0.844030	+	0.536296i	$0.180177\pi$
$761$			29.5888i			1.07259i	−0.844030	+	0.536296i	$0.819823\pi$
$762$	−1.40262	+	0.569447i	−0.0508116	+	0.0206289i
$763$	14.4371	+	14.4371i	0.522659	+	0.522659i
$764$	0.564539	+	0.580668i	0.0204243	+	0.0210078i
$765$	1.21106	+	16.6713i	0.0437859	+	0.602752i
$766$	33.3099	+	14.0730i	1.20354	+	0.508479i
$767$			17.4257i			0.629206i
$768$	−11.9327	+	10.6588i	−0.430586	+	0.384616i
$769$	29.1544			1.05133			0.525667	−	0.850690i	$-0.323816\pi$
$769$	29.1544			1.05133			0.525667	+	0.850690i	$0.323816\pi$
$770$	7.82083	−	3.85705i	0.281843	−	0.138998i
$771$	−0.136994	−	0.136994i	−0.00493373	−	0.00493373i
$772$	9.30615	−	9.04766i	0.334936	−	0.325632i
$773$	16.3728	+	16.3728i	0.588889	+	0.588889i	0.937331	−	0.348441i	$-0.113289\pi$
$773$	16.3728	+	16.3728i	0.588889	+	0.588889i	−0.348441	+	0.937331i	$0.613289\pi$
$774$	0.675308	+	1.66337i	0.0242735	+	0.0597886i
$775$	−9.03318	+	1.31936i	−0.324482	+	0.0473929i
$776$	10.8324	+	27.7986i	0.388862	+	0.997911i
$777$	−22.9872			−0.824662
$778$	3.24975	+	8.00455i	0.116509	+	0.286977i
$779$	5.23912	−	5.23912i	0.187711	−	0.187711i
$780$	−5.32899	−	4.73996i	−0.190808	−	0.169718i
$781$	5.94764	+	5.94764i	0.212823	+	0.212823i
$782$	−60.1472	−	25.4114i	−2.15086	−	0.908711i
$783$			4.17374i			0.149157i
$784$	−0.182904	+	6.49221i	−0.00653230	+	0.231864i
$785$	−19.4568	−	16.8214i	−0.694443	−	0.600383i
$786$	8.48596	−	20.0857i	0.302684	−	0.716434i
$787$	−27.4334	+	27.4334i	−0.977894	+	0.977894i	−0.999761	−	0.0218667i	$-0.993039\pi$
$787$	−27.4334	+	27.4334i	−0.977894	+	0.977894i	0.0218667	+	0.999761i	$0.493039\pi$
$788$	0.734578	−	52.1581i	0.0261682	−	1.85806i
$789$	−11.7173	+	11.7173i	−0.417148	+	0.417148i
$790$	−9.17774	−	3.11517i	−0.326529	−	0.110833i
$791$		−	37.6867i		−	1.33999i
$792$	2.43179	+	1.06801i	0.0864100	+	0.0379499i
$793$	−16.6335			−0.590673
$794$	−17.7363	−	43.6868i	−0.629438	−	1.55039i
$795$	0.0335604	+	0.461989i	0.00119026	+	0.0163850i
$796$	−19.3152	+	18.7787i	−0.684610	+	0.665594i
$797$	1.30833	−	1.30833i	0.0463434	−	0.0463434i	−0.683555	−	0.729899i	$-0.739567\pi$
$797$	1.30833	−	1.30833i	0.0463434	−	0.0463434i	0.729899	+	0.683555i	$0.239567\pi$
$798$	−0.968136	+	2.29151i	−0.0342716	+	0.0811187i
$799$	30.8530			1.09150
$800$	27.1602	+	7.89461i	0.960257	+	0.279117i
$801$	8.71473			0.307920
$802$	−9.41702	+	22.2895i	−0.332527	+	0.787069i
$803$	−0.115699	+	0.115699i	−0.00408292	+	0.00408292i
$804$	−17.6081	+	17.1190i	−0.620991	+	0.603742i
$805$	2.93847	+	40.4507i	0.103567	+	1.42570i
$806$	1.54899	+	3.81535i	0.0545607	+	0.134390i
$807$	10.0322			0.353149
$808$	−15.5304	+	35.3619i	−0.546357	+	1.24403i
$809$			5.40398i			0.189994i	0.995478	+	0.0949970i	$0.0302841\pi$
$809$			5.40398i			0.189994i	−0.995478	+	0.0949970i	$0.969716\pi$
$810$	2.99448	+	1.01641i	0.105215	+	0.0357129i
$811$	5.63507	−	5.63507i	0.197874	−	0.197874i	−0.601214	−	0.799088i	$-0.705316\pi$
$811$	5.63507	−	5.63507i	0.197874	−	0.197874i	0.799088	+	0.601214i	$0.205316\pi$
$812$	−0.345203	+	24.5109i	−0.0121143	+	0.860163i
$813$	1.85459	−	1.85459i	0.0650432	−	0.0650432i
$814$	−4.04562	+	9.57572i	−0.141799	+	0.335629i
$815$	−9.78282	−	8.45776i	−0.342677	−	0.296262i
$816$	−21.7303	+	20.5395i	−0.760714	+	0.719025i
$817$			0.760378i			0.0266023i
$818$	−32.9144	−	13.9059i	−1.15083	−	0.486209i
$819$	−3.31152	−	3.31152i	−0.115714	−	0.115714i
$820$	−41.3331	−	36.7644i	−1.44341	−	1.28387i
$821$	−11.6911	+	11.6911i	−0.408022	+	0.408022i	−0.881048	−	0.473027i	$-0.843161\pi$
$821$	−11.6911	+	11.6911i	−0.408022	+	0.408022i	0.473027	+	0.881048i	$0.343161\pi$
$822$	−5.34902	−	13.1753i	−0.186568	−	0.459542i
$823$	12.7721			0.445207			0.222604	−	0.974909i	$-0.428544\pi$
$823$	12.7721			0.445207			0.222604	+	0.974909i	$0.428544\pi$
$824$	38.3619	−	14.9487i	1.33640	−	0.520764i
$825$	−0.678563	−	4.64587i	−0.0236245	−	0.161748i
$826$	−17.0702	−	42.0461i	−0.593949	−	1.46297i
$827$	−0.00790410	−	0.00790410i	−0.000274852	−	0.000274852i	0.706969	−	0.707244i	$-0.250062\pi$
$827$	−0.00790410	−	0.00790410i	−0.000274852	−	0.000274852i	−0.707244	+	0.706969i	$0.750062\pi$
$828$	−8.85691	+	8.61090i	−0.307799	+	0.299250i
$829$	−2.93843	−	2.93843i	−0.102056	−	0.102056i	0.654235	−	0.756291i	$-0.272991\pi$
$829$	−2.93843	−	2.93843i	−0.102056	−	0.102056i	−0.756291	+	0.654235i	$0.772991\pi$
$830$	36.8501	−	18.1736i	1.27908	−	0.630814i
$831$	−11.2788			−0.391258
$832$	0.538846	−	12.7467i	0.0186811	−	0.441913i
$833$			12.1376i			0.420542i
$834$	5.35698	+	2.26326i	0.185497	+	0.0783701i
$835$	1.54372	+	21.2508i	0.0534228	+	0.735413i
$836$	0.784183	+	0.806587i	0.0271215	+	0.0278964i
$837$	−1.29104	−	1.29104i	−0.0446249	−	0.0446249i
$838$	29.2576	−	11.8782i	1.01069	−	0.410327i
$839$		−	39.0990i		−	1.34985i	−0.737888	−	0.674923i	$-0.764177\pi$
$839$		−	39.0990i		−	1.34985i	0.737888	−	0.674923i	$-0.235823\pi$
$840$	17.5015	+	6.21666i	0.603858	+	0.214495i
$841$		−	11.5799i		−	0.399308i
$842$	−3.49732	−	8.61435i	−0.120526	−	0.296870i
$843$	7.05586	+	7.05586i	0.243017	+	0.243017i
$844$	0.242071	−	17.1880i	0.00833241	−	0.591636i
$845$	−23.3205	+	1.69408i	−0.802250	+	0.0582781i
$846$	2.27161	−	5.37676i	0.0780996	−	0.184857i
$847$			29.7133i			1.02096i
$848$	−0.602182	+	0.569182i	−0.0206790	+	0.0195458i
$849$	28.8579			0.990399
$850$	51.1528	+	13.3183i	1.75453	+	0.456815i
$851$	−34.1870	−	34.1870i	−1.17192	−	1.17192i
$852$	−0.252280	+	17.9129i	−0.00864296	+	0.613687i
$853$	0.788780	+	0.788780i	0.0270073	+	0.0270073i	0.720481	−	0.693474i	$-0.243921\pi$
$853$	0.788780	+	0.788780i	0.0270073	+	0.0270073i	−0.693474	+	0.720481i	$0.743921\pi$
$854$	40.1346	−	16.2942i	1.37338	−	0.557575i
$855$	1.01323	+	0.875989i	0.0346517	+	0.0299582i
$856$	−21.4709	−	9.42970i	−0.733862	−	0.322300i
$857$	45.0264			1.53807			0.769036	−	0.639206i	$-0.220737\pi$
$857$	45.0264			1.53807			0.769036	+	0.639206i	$0.220737\pi$
$858$	−1.96228	+	0.796662i	−0.0669911	+	0.0271976i
$859$	−21.5188	+	21.5188i	−0.734212	+	0.734212i	−0.971451	−	0.237239i	$-0.923757\pi$
$859$	−21.5188	+	21.5188i	−0.734212	+	0.734212i	0.237239	+	0.971451i	$0.423757\pi$
$860$	5.66732	−	0.331537i	0.193254	−	0.0113053i
$861$	−25.6851	−	25.6851i	−0.875344	−	0.875344i
$862$	15.7585	−	37.2994i	0.536738	−	1.27042i
$863$			8.30436i			0.282684i	0.989961	+	0.141342i	$0.0451417\pi$
$863$			8.30436i			0.282684i	−0.989961	+	0.141342i	$0.954858\pi$
$864$	1.97948	+	5.29921i	0.0673433	+	0.180283i
$865$	14.7894	+	12.7862i	0.502855	+	0.434744i
$866$	8.01113	+	3.38460i	0.272229	+	0.115013i
$867$	−27.4922	+	27.4922i	−0.933684	+	0.933684i
$868$	−7.47503	−	7.68859i	−0.253719	−	0.260968i
$869$	−2.03507	+	2.03507i	−0.0690351	+	0.0690351i
$870$	12.4982	+	4.24221i	0.423728	+	0.143825i
$871$		−	19.5823i		−	0.663520i
$872$	18.0051	+	7.90755i	0.609729	+	0.267783i
$873$	10.5481			0.357000
$874$	−4.84781	+	1.96815i	−0.163980	+	0.0665738i
$875$	−7.08639	−	32.0585i	−0.239564	−	1.08377i
$876$	−0.348458	−	0.00490757i	−0.0117733	−	0.000165811i
$877$	17.6134	−	17.6134i	0.594764	−	0.594764i	−0.344151	−	0.938914i	$-0.611833\pi$
$877$	17.6134	−	17.6134i	0.594764	−	0.594764i	0.938914	+	0.344151i	$0.111833\pi$
$878$	−49.3133	−	20.8343i	−1.66424	−	0.703122i
$879$	6.58866			0.222230
$880$	5.66981	−	6.19643i	0.191129	−	0.208882i
$881$	32.5717			1.09737			0.548684	−	0.836030i	$-0.315129\pi$
$881$	32.5717			1.09737			0.548684	+	0.836030i	$0.315129\pi$
$882$	2.11522	+	0.893654i	0.0712232	+	0.0300909i
$883$	−11.6327	+	11.6327i	−0.391472	+	0.391472i	−0.875212	−	0.483740i	$-0.839278\pi$
$883$	−11.6327	+	11.6327i	−0.391472	+	0.391472i	0.483740	+	0.875212i	$0.339278\pi$
$884$	0.335758	−	23.8402i	0.0112928	−	0.801833i
$885$	−24.3690	+	1.77024i	−0.819153	+	0.0595060i
$886$	6.33290	−	2.57108i	0.212758	−	0.0863772i
$887$	−40.0203			−1.34375			−0.671875	−	0.740665i	$-0.734511\pi$
$887$	−40.0203			−1.34375			−0.671875	+	0.740665i	$0.734511\pi$
$888$	−20.6294	+	8.03880i	−0.692278	+	0.269764i
$889$			3.14342i			0.105427i
$890$	8.85772	−	26.0961i	0.296911	−	0.874744i
$891$	0.663996	−	0.663996i	0.0222447	−	0.0222447i
$892$	31.6616	−	30.7822i	1.06011	−	1.03066i
$893$	1.74815	−	1.74815i	0.0584997	−	0.0584997i
$894$	−2.32374	−	0.981752i	−0.0777176	−	0.0328347i
$895$	21.4156	−	24.7708i	0.715845	−	0.827995i
$896$	11.1865	+	31.2841i	0.373715	+	1.04513i
$897$		−	9.84991i		−	0.328879i
$898$	17.4436	−	41.2878i	0.582100	−	1.37779i
$899$	−5.38846	−	5.38846i	−0.179715	−	0.179715i
$900$	6.08722	−	7.93383i	0.202907	−	0.264461i
$901$	−1.09497	+	1.09497i	−0.0364787	+	0.0364787i
$902$	−15.2200	+	6.17912i	−0.506770	+	0.205742i
$903$	3.72779			0.124053
$904$	−13.1793	−	33.8212i	−0.438337	−	1.12488i
$905$	14.3057	+	12.3680i	0.475536	+	0.411126i
$906$	26.8277	−	10.8917i	0.891292	−	0.361854i
$907$	5.81050	+	5.81050i	0.192934	+	0.192934i	0.796963	−	0.604028i	$-0.206439\pi$
$907$	5.81050	+	5.81050i	0.192934	+	0.192934i	−0.604028	+	0.796963i	$0.706439\pi$
$908$	15.7222	+	0.221427i	0.521760	+	0.00734830i
$909$	9.65550	+	9.65550i	0.320253	+	0.320253i
$910$	−13.2821	+	6.55043i	−0.440299	+	0.217145i
$911$	10.4809			0.347248			0.173624	−	0.984812i	$-0.444452\pi$
$911$	10.4809			0.347248			0.173624	+	0.984812i	$0.444452\pi$
$912$	−0.0674753	+	2.39504i	−0.00223433	+	0.0793077i
$913$		−	12.2009i		−	0.403792i
$914$	3.99692	−	9.46045i	0.132206	−	0.312924i
$915$	−1.68976	−	23.2611i	−0.0558619	−	0.768989i
$916$	−33.4353	−	0.470892i	−1.10473	−	0.0155587i
$917$	−32.0161	−	32.0161i	−1.05726	−	1.05726i
$918$	3.97672	+	9.79517i	0.131251	+	0.323289i
$919$		−	51.8755i		−	1.71121i	−0.517626	−	0.855607i	$-0.673184\pi$
$919$		−	51.8755i		−	1.71121i	0.517626	−	0.855607i	$-0.326816\pi$
$920$	16.7830	+	35.2740i	0.553318	+	1.16295i
$921$		−	12.8055i		−	0.421956i
$922$	−29.9403	+	12.1554i	−0.986031	+	0.400317i
$923$	−10.1009	−	10.1009i	−0.332475	−	0.332475i
$924$	3.95433	−	3.84449i	0.130088	−	0.126475i
$925$	31.3847	+	23.3851i	1.03192	+	0.768898i
$926$	17.5394	+	7.41017i	0.576380	+	0.243513i
$927$		−	14.5564i		−	0.478094i
$928$	8.26183	+	22.1175i	0.271208	+	0.726043i
$929$	−5.54673			−0.181982			−0.0909912	−	0.995852i	$-0.529004\pi$
$929$	−5.54673			−0.181982			−0.0909912	+	0.995852i	$0.529004\pi$
$930$	−5.17821	+	2.55377i	−0.169800	+	0.0837415i
$931$	0.687724	+	0.687724i	0.0225393	+	0.0225393i
$932$	12.4362	+	12.7915i	0.407362	+	0.419000i
$933$	−2.39956	−	2.39956i	−0.0785581	−	0.0785581i
$934$	7.94691	+	19.5742i	0.260031	+	0.640489i
$935$	10.2655	−	11.8738i	0.335719	−	0.388315i
$936$	−4.12992	−	1.81380i	−0.134991	−	0.0592858i
$937$	9.31790			0.304402			0.152201	−	0.988350i	$-0.451364\pi$
$937$	9.31790			0.304402			0.152201	+	0.988350i	$0.451364\pi$
$938$	19.1828	+	47.2496i	0.626340	+	1.54276i
$939$	7.70346	−	7.70346i	0.251393	−	0.251393i
$940$	−13.7917	−	12.2673i	−0.449836	−	0.400114i
$941$	21.9832	+	21.9832i	0.716630	+	0.716630i	0.967914	−	0.251283i	$-0.0808526\pi$
$941$	21.9832	+	21.9832i	0.716630	+	0.716630i	−0.251283	+	0.967914i	$0.580853\pi$
$942$	−14.9844	−	6.33073i	−0.488219	−	0.206266i
$943$		−	76.3986i		−	2.48788i
$944$	−30.0232	−	31.7639i	−0.977171	−	1.03383i
$945$	4.29458	−	4.96740i	0.139703	−	0.161590i
$946$	0.656069	−	1.55287i	0.0213307	−	0.0504883i
$947$	−15.4966	+	15.4966i	−0.503572	+	0.503572i	−0.912546	−	0.408974i	$-0.865887\pi$
$947$	−15.4966	+	15.4966i	−0.503572	+	0.503572i	0.408974	+	0.912546i	$0.365887\pi$
$948$	−6.12916	−	0.0863211i	−0.199066	−	0.00280358i
$949$	0.196492	−	0.196492i	0.00637839	−	0.00637839i
$950$	3.65299	−	2.14373i	0.118519	−	0.0695518i
$951$		−	4.89001i		−	0.158569i
$952$	22.5437	+	57.8524i	0.730646	+	1.87501i
$953$	−5.72390			−0.185415			−0.0927076	−	0.995693i	$-0.529552\pi$
$953$	−5.72390			−0.185415			−0.0927076	+	0.995693i	$0.529552\pi$
$954$	0.110201	+	0.271440i	0.00356790	+	0.00878819i
$955$	−0.0656024	−	0.903075i	−0.00212284	−	0.0292228i
$956$	−31.9708	−	32.8842i	−1.03401	−	1.06355i
$957$	2.77134	−	2.77134i	0.0895848	−	0.0895848i
$958$	−18.8642	+	44.6504i	−0.609475	+	1.44259i
$959$	−29.5273			−0.953485
$960$	17.8804	−	0.541362i	0.577086	−	0.0174724i
$961$	−27.6664			−0.892466
$962$	6.87069	−	16.2625i	0.221520	−	0.524323i
$963$	−5.86260	+	5.86260i	−0.188920	+	0.188920i
$964$	9.03738	+	9.29557i	0.291074	+	0.299390i
$965$	−14.4733	+	1.05139i	−0.465911	+	0.0338453i
$966$	9.64897	+	23.7666i	0.310451	+	0.764679i
$967$	8.80514			0.283154			0.141577	−	0.989927i	$-0.454783\pi$
$967$	8.80514			0.283154			0.141577	+	0.989927i	$0.454783\pi$
$968$	10.3910	+	26.6656i	0.333978	+	0.857065i
$969$			4.47767i			0.143844i
$970$	10.7212	−	31.5861i	0.344236	−	1.01417i
$971$	−26.8032	+	26.8032i	−0.860157	+	0.860157i	−0.991356	−	0.131199i	$-0.958117\pi$
$971$	−26.8032	+	26.8032i	−0.860157	+	0.860157i	0.131199	+	0.991356i	$0.458117\pi$
$972$	1.99980	+	0.0281646i	0.0641437	+	0.000903379i
$973$	8.53888	−	8.53888i	0.273744	−	0.273744i
$974$	18.4375	−	43.6404i	0.590776	−	1.39833i
$975$	1.15241	+	7.89009i	0.0369065	+	0.252685i
$976$	30.3199	−	28.6583i	0.970515	−	0.917329i
$977$			36.2126i			1.15854i	0.815134	+	0.579272i	$0.196663\pi$
$977$			36.2126i			1.15854i	−0.815134	+	0.579272i	$0.803337\pi$
$978$	−7.53412	−	3.18307i	−0.240915	−	0.101783i
$979$	−5.78655	−	5.78655i	−0.184939	−	0.184939i
$980$	4.82595	−	5.42567i	0.154159	−	0.173317i
$981$	4.91625	−	4.91625i	0.156964	−	0.156964i
$982$	0.369804	+	0.910875i	0.0118009	+	0.0290672i
$983$	−15.7547			−0.502496			−0.251248	−	0.967923i	$-0.580841\pi$
$983$	−15.7547			−0.502496			−0.251248	+	0.967923i	$0.580841\pi$
$984$	−32.0328	−	14.0683i	−1.02117	−	0.448481i
$985$	−38.1425	+	44.1182i	−1.21532	+	1.40572i
$986$	16.5978	+	40.8825i	0.528581	+	1.30196i
$987$	−8.57040	−	8.57040i	−0.272799	−	0.272799i
$988$	−1.33178	−	1.36983i	−0.0423696	−	0.0435801i
$989$	5.54404	+	5.54404i	0.176290	+	0.176290i
$990$	−1.31343	−	2.66321i	−0.0417437	−	0.0846425i
$991$	12.5049			0.397230			0.198615	−	0.980078i	$-0.436356\pi$
$991$	12.5049			0.397230			0.198615	+	0.980078i	$0.436356\pi$
$992$	−9.39708	−	4.28590i	−0.298358	−	0.136078i
$993$			35.2487i			1.11859i
$994$	34.2671	+	14.4774i	1.08689	+	0.459196i
$995$	30.0397	−	2.18219i	0.952324	−	0.0691799i
$996$	18.6320	−	18.1144i	0.590376	−	0.573978i
$997$	4.59749	+	4.59749i	0.145604	+	0.145604i	0.776151	−	0.630547i	$-0.217169\pi$
$997$	4.59749	+	4.59749i	0.145604	+	0.145604i	−0.630547	+	0.776151i	$0.717169\pi$
$998$	1.60016	−	0.649646i	0.0506522	−	0.0205642i
$999$			7.82780i			0.247661i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	240.2.bl.a.109.9	✓	48
3.2	odd	2		720.2.bm.h.109.16		48
4.3	odd	2		960.2.bl.a.529.6		48
5.4	even	2	inner	240.2.bl.a.109.16	yes	48
8.3	odd	2		1920.2.bl.b.289.14		48
8.5	even	2		1920.2.bl.a.289.11		48
15.14	odd	2		720.2.bm.h.109.9		48
16.3	odd	4		1920.2.bl.b.1249.11		48
16.5	even	4	inner	240.2.bl.a.229.16	yes	48
16.11	odd	4		960.2.bl.a.49.13		48
16.13	even	4		1920.2.bl.a.1249.14		48
20.19	odd	2		960.2.bl.a.529.13		48
40.19	odd	2		1920.2.bl.b.289.11		48
40.29	even	2		1920.2.bl.a.289.14		48
48.5	odd	4		720.2.bm.h.469.9		48
80.19	odd	4		1920.2.bl.b.1249.14		48
80.29	even	4		1920.2.bl.a.1249.11		48
80.59	odd	4		960.2.bl.a.49.6		48
80.69	even	4	inner	240.2.bl.a.229.9	yes	48
240.149	odd	4		720.2.bm.h.469.16		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
240.2.bl.a.109.9	✓	48	1.1	even	1	trivial
240.2.bl.a.109.16	yes	48	5.4	even	2	inner
240.2.bl.a.229.9	yes	48	80.69	even	4	inner
240.2.bl.a.229.16	yes	48	16.5	even	4	inner
720.2.bm.h.109.9		48	15.14	odd	2
720.2.bm.h.109.16		48	3.2	odd	2
720.2.bm.h.469.9		48	48.5	odd	4
720.2.bm.h.469.16		48	240.149	odd	4
960.2.bl.a.49.6		48	80.59	odd	4
960.2.bl.a.49.13		48	16.11	odd	4
960.2.bl.a.529.6		48	4.3	odd	2
960.2.bl.a.529.13		48	20.19	odd	2
1920.2.bl.a.289.11		48	8.5	even	2
1920.2.bl.a.289.14		48	40.29	even	2
1920.2.bl.a.1249.11		48	80.29	even	4
1920.2.bl.a.1249.14		48	16.13	even	4
1920.2.bl.b.289.11		48	40.19	odd	2
1920.2.bl.b.289.14		48	8.3	odd	2
1920.2.bl.b.1249.11		48	16.3	odd	4
1920.2.bl.b.1249.14		48	80.19	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 240 = 2^{4} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	240.bl (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.550383 + 1.30272i) q^{2} +(0.707107 - 0.707107i) q^{3} +(-1.39416 - 1.43399i) q^{4} +(0.162008 + 2.23019i) q^{5} +(0.531983 + 1.31034i) q^{6} +2.93661 q^{7} +(2.63541 - 1.02695i) q^{8} -1.00000i q^{9} +O(q^{10})\)	\(q+(-0.550383 + 1.30272i) q^{2} +(0.707107 - 0.707107i) q^{3} +(-1.39416 - 1.43399i) q^{4} +(0.162008 + 2.23019i) q^{5} +(0.531983 + 1.31034i) q^{6} +2.93661 q^{7} +(2.63541 - 1.02695i) q^{8} -1.00000i q^{9} +(-2.99448 - 1.01641i) q^{10} +(-0.663996 + 0.663996i) q^{11} +(-1.99980 - 0.0281646i) q^{12} +(1.12767 - 1.12767i) q^{13} +(-1.61626 + 3.82558i) q^{14} +(1.69154 + 1.46243i) q^{15} +(-0.112647 + 3.99841i) q^{16} +7.47528i q^{17} +(1.30272 + 0.550383i) q^{18} +(0.423555 + 0.423555i) q^{19} +(2.97220 - 3.34156i) q^{20} +(2.07650 - 2.07650i) q^{21} +(-0.499549 - 1.23045i) q^{22} +6.17642 q^{23} +(1.13735 - 2.58968i) q^{24} +(-4.94751 + 0.722620i) q^{25} +(0.848386 + 2.08968i) q^{26} +(-0.707107 - 0.707107i) q^{27} +(-4.09410 - 4.21107i) q^{28} +(-2.95128 - 2.95128i) q^{29} +(-2.83613 + 1.39871i) q^{30} +1.82581 q^{31} +(-5.14681 - 2.34740i) q^{32} +0.939032i q^{33} +(-9.73820 - 4.11426i) q^{34} +(0.475756 + 6.54921i) q^{35} +(-1.43399 + 1.39416i) q^{36} +(-5.53509 - 5.53509i) q^{37} +(-0.784891 + 0.318656i) q^{38} -1.59476i q^{39} +(2.71726 + 5.71108i) q^{40} -12.3694i q^{41} +(1.56223 + 3.84797i) q^{42} +(0.897614 + 0.897614i) q^{43} +(1.87788 + 0.0264474i) q^{44} +(2.23019 - 0.162008i) q^{45} +(-3.39939 + 8.04614i) q^{46} -4.12733i q^{47} +(2.74765 + 2.90696i) q^{48} +1.62370 q^{49} +(1.78165 - 6.84293i) q^{50} +(5.28582 + 5.28582i) q^{51} +(-3.18921 - 0.0449157i) q^{52} +(0.146479 + 0.146479i) q^{53} +(1.31034 - 0.531983i) q^{54} +(-1.58841 - 1.37327i) q^{55} +(7.73917 - 3.01577i) q^{56} +0.598997 q^{57} +(5.46902 - 2.22036i) q^{58} +(-7.72645 + 7.72645i) q^{59} +(-0.261172 - 4.46450i) q^{60} +(-7.37519 - 7.37519i) q^{61} +(-1.00489 + 2.37851i) q^{62} -2.93661i q^{63} +(5.89073 - 5.41289i) q^{64} +(2.69760 + 2.33222i) q^{65} +(-1.22330 - 0.516827i) q^{66} +(8.68265 - 8.68265i) q^{67} +(10.7195 - 10.4217i) q^{68} +(4.36739 - 4.36739i) q^{69} +(-8.79363 - 2.98479i) q^{70} -8.95735i q^{71} +(-1.02695 - 2.63541i) q^{72} +0.174246 q^{73} +(10.2571 - 4.16425i) q^{74} +(-2.98745 + 4.00938i) q^{75} +(0.0168705 - 1.19788i) q^{76} +(-1.94990 + 1.94990i) q^{77} +(2.07753 + 0.877729i) q^{78} +3.06488 q^{79} +(-8.93548 + 0.396552i) q^{80} -1.00000 q^{81} +(16.1139 + 6.80790i) q^{82} +(-9.18751 + 9.18751i) q^{83} +(-5.87264 - 0.0827084i) q^{84} +(-16.6713 + 1.21106i) q^{85} +(-1.66337 + 0.675308i) q^{86} -4.17374 q^{87} +(-1.06801 + 2.43179i) q^{88} +8.71473i q^{89} +(-1.01641 + 2.99448i) q^{90} +(3.31152 - 3.31152i) q^{91} +(-8.61090 - 8.85691i) q^{92} +(1.29104 - 1.29104i) q^{93} +(5.37676 + 2.27161i) q^{94} +(-0.875989 + 1.01323i) q^{95} +(-5.29921 + 1.97948i) q^{96} +10.5481i q^{97} +(-0.893654 + 2.11522i) q^{98} +(0.663996 + 0.663996i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q+O(q^{10}) \) 48 * q	\( 48 q + 12 q^{10} - 16 q^{14} - 4 q^{16} + 8 q^{19} - 4 q^{24} - 40 q^{26} - 8 q^{30} - 48 q^{31} - 28 q^{34} + 24 q^{35} - 4 q^{36} - 16 q^{40} - 40 q^{44} - 4 q^{46} + 48 q^{49} - 32 q^{50} + 8 q^{51} - 4 q^{54} + 48 q^{56} - 32 q^{59} - 24 q^{60} + 16 q^{61} + 48 q^{64} + 16 q^{65} + 24 q^{66} - 16 q^{69} + 40 q^{74} - 16 q^{75} + 60 q^{76} - 96 q^{79} + 72 q^{80} - 48 q^{81} + 16 q^{86} + 8 q^{90} - 32 q^{91} + 44 q^{94} - 48 q^{95} - 40 q^{96}+O(q^{100}) \) 48 * q + 12 * q^10 - 16 * q^14 - 4 * q^16 + 8 * q^19 - 4 * q^24 - 40 * q^26 - 8 * q^30 - 48 * q^31 - 28 * q^34 + 24 * q^35 - 4 * q^36 - 16 * q^40 - 40 * q^44 - 4 * q^46 + 48 * q^49 - 32 * q^50 + 8 * q^51 - 4 * q^54 + 48 * q^56 - 32 * q^59 - 24 * q^60 + 16 * q^61 + 48 * q^64 + 16 * q^65 + 24 * q^66 - 16 * q^69 + 40 * q^74 - 16 * q^75 + 60 * q^76 - 96 * q^79 + 72 * q^80 - 48 * q^81 + 16 * q^86 + 8 * q^90 - 32 * q^91 + 44 * q^94 - 48 * q^95 - 40 * q^96

Introduction

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