LMFDB - Embedded newform 585.2.bt.b.376.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [585,2,Mod(376,585)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(585, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 0, 3]))

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

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

chi := DirichletCharacter("585.376");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 585 = 3^{2} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	585.bt (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:	$4.67124851824$
Analytic rank:	$0$
Dimension:	$108$
Relative dimension:	$54$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			376.19
Character	$\chi$	$=$	585.376
Dual form			585.2.bt.b.571.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.883008 - 0.509805i) q^{2} +(-0.597446 + 1.62575i) q^{3} +(-0.480198 - 0.831727i) q^{4} +(-0.866025 + 0.500000i) q^{5} +(1.35636 - 1.13097i) q^{6} +(-3.32453 - 1.91942i) q^{7} +3.01845i q^{8} +(-2.28612 - 1.94260i) q^{9} +O(q^{10})$	\(q+(-0.883008 - 0.509805i) q^{2} +(-0.597446 + 1.62575i) q^{3} +(-0.480198 - 0.831727i) q^{4} +(-0.866025 + 0.500000i) q^{5} +(1.35636 - 1.13097i) q^{6} +(-3.32453 - 1.91942i) q^{7} +3.01845i q^{8} +(-2.28612 - 1.94260i) q^{9} +1.01961 q^{10} +(-1.97745 - 1.14168i) q^{11} +(1.63907 - 0.283769i) q^{12} +(3.56410 - 0.545131i) q^{13} +(1.95706 + 3.38972i) q^{14} +(-0.295470 - 1.70666i) q^{15} +(0.578424 - 1.00186i) q^{16} +7.50452 q^{17} +(1.02831 + 2.88080i) q^{18} +2.31692i q^{19} +(0.831727 + 0.480198i) q^{20} +(5.10672 - 4.25810i) q^{21} +(1.16407 + 2.01622i) q^{22} +(1.68012 + 2.91006i) q^{23} +(-4.90724 - 1.80336i) q^{24} +(0.500000 - 0.866025i) q^{25} +(-3.42504 - 1.33564i) q^{26} +(4.52400 - 2.55605i) q^{27} +3.68680i q^{28} +(-4.07714 + 7.06182i) q^{29} +(-0.609162 + 1.65763i) q^{30} +(-3.49528 + 2.01800i) q^{31} +(4.20660 - 2.42868i) q^{32} +(3.03750 - 2.53274i) q^{33} +(-6.62655 - 3.82584i) q^{34} +3.83884 q^{35} +(-0.517922 + 2.83426i) q^{36} -0.546920i q^{37} +(1.18118 - 2.04586i) q^{38} +(-1.24312 + 6.12002i) q^{39} +(-1.50922 - 2.61405i) q^{40} +(6.35971 - 3.67178i) q^{41} +(-6.68007 + 1.15651i) q^{42} +(-0.826744 + 1.43196i) q^{43} +2.19293i q^{44} +(2.95113 + 0.539279i) q^{45} -3.42614i q^{46} +(7.13335 + 4.11844i) q^{47} +(1.28319 + 1.53893i) q^{48} +(3.86833 + 6.70015i) q^{49} +(-0.883008 + 0.509805i) q^{50} +(-4.48355 + 12.2005i) q^{51} +(-2.16488 - 2.70259i) q^{52} +7.10215 q^{53} +(-5.29782 - 0.0493446i) q^{54} +2.28336 q^{55} +(5.79367 - 10.0349i) q^{56} +(-3.76673 - 1.38424i) q^{57} +(7.20030 - 4.15710i) q^{58} +(6.45792 - 3.72848i) q^{59} +(-1.27759 + 1.06529i) q^{60} +(5.77492 - 10.0025i) q^{61} +4.11515 q^{62} +(3.87161 + 10.8462i) q^{63} -7.26631 q^{64} +(-2.81404 + 2.25415i) q^{65} +(-3.97334 + 0.687894i) q^{66} +(-6.43546 + 3.71551i) q^{67} +(-3.60366 - 6.24172i) q^{68} +(-5.73480 + 0.992853i) q^{69} +(-3.38972 - 1.95706i) q^{70} +7.19213i q^{71} +(5.86362 - 6.90052i) q^{72} +7.74780i q^{73} +(-0.278822 + 0.482935i) q^{74} +(1.10922 + 1.33028i) q^{75} +(1.92705 - 1.11258i) q^{76} +(4.38272 + 7.59109i) q^{77} +(4.21770 - 4.77028i) q^{78} +(6.19823 - 10.7357i) q^{79} +1.15685i q^{80} +(1.45265 + 8.88199i) q^{81} -7.48756 q^{82} +(5.81320 + 3.35625i) q^{83} +(-5.99382 - 2.20267i) q^{84} +(-6.49911 + 3.75226i) q^{85} +(1.46004 - 0.842957i) q^{86} +(-9.04487 - 10.8475i) q^{87} +(3.44610 - 5.96882i) q^{88} -6.46613i q^{89} +(-2.33095 - 1.98069i) q^{90} +(-12.8953 - 5.02870i) q^{91} +(1.61358 - 2.79481i) q^{92} +(-1.19252 - 6.88809i) q^{93} +(-4.19920 - 7.27323i) q^{94} +(-1.15846 - 2.00651i) q^{95} +(1.43521 + 8.28988i) q^{96} +(10.1032 + 5.83306i) q^{97} -7.88838i q^{98} +(2.30285 + 6.45139i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 108 q - 6 q^{3} + 52 q^{4} - 14 q^{9}+O(q^{10}) $ 108 * q - 6 * q^3 + 52 * q^4 - 14 * q^9	$ 108 q - 6 q^{3} + 52 q^{4} - 14 q^{9} - 8 q^{10} - 36 q^{12} - 4 q^{13} - 8 q^{14} - 64 q^{16} + 36 q^{17} + 24 q^{22} - 22 q^{23} + 54 q^{25} + 40 q^{26} + 48 q^{27} - 16 q^{29} + 20 q^{30} - 40 q^{35} - 76 q^{36} - 12 q^{38} + 26 q^{39} - 52 q^{42} - 6 q^{43} - 68 q^{48} + 58 q^{49} + 34 q^{51} + 22 q^{52} - 116 q^{53} + 24 q^{55} + 40 q^{56} + 18 q^{61} + 152 q^{62} - 216 q^{64} + 2 q^{65} - 72 q^{66} - 134 q^{69} + 32 q^{74} + 40 q^{77} - 34 q^{78} + 18 q^{79} + 34 q^{81} + 88 q^{82} + 60 q^{87} + 8 q^{90} + 16 q^{91} + 176 q^{92} - 76 q^{94} - 56 q^{95}+O(q^{100}) $ 108 * q - 6 * q^3 + 52 * q^4 - 14 * q^9 - 8 * q^10 - 36 * q^12 - 4 * q^13 - 8 * q^14 - 64 * q^16 + 36 * q^17 + 24 * q^22 - 22 * q^23 + 54 * q^25 + 40 * q^26 + 48 * q^27 - 16 * q^29 + 20 * q^30 - 40 * q^35 - 76 * q^36 - 12 * q^38 + 26 * q^39 - 52 * q^42 - 6 * q^43 - 68 * q^48 + 58 * q^49 + 34 * q^51 + 22 * q^52 - 116 * q^53 + 24 * q^55 + 40 * q^56 + 18 * q^61 + 152 * q^62 - 216 * q^64 + 2 * q^65 - 72 * q^66 - 134 * q^69 + 32 * q^74 + 40 * q^77 - 34 * q^78 + 18 * q^79 + 34 * q^81 + 88 * q^82 + 60 * q^87 + 8 * q^90 + 16 * q^91 + 176 * q^92 - 76 * q^94 - 56 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/585\mathbb{Z}\right)^\times$.

$n$	$326$	$352$	$496$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$-1$

Coefficient data

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

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

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

$2$	−0.883008	−	0.509805i	−0.624381	−	0.360486i	0.154192	−	0.988041i	$-0.450723\pi$
$2$	−0.883008	−	0.509805i	−0.624381	−	0.360486i	−0.778573	+	0.627554i	$0.784056\pi$
$3$	−0.597446	+	1.62575i	−0.344936	+	0.938626i
$3$	−0.597446	+	1.62575i	−0.344936	+	0.938626i
$4$	−0.480198	−	0.831727i	−0.240099	−	0.415864i
$5$	−0.866025	+	0.500000i	−0.387298	+	0.223607i
$5$	−0.866025	+	0.500000i	−0.387298	+	0.223607i
$6$	1.35636	−	1.13097i	0.553733	−	0.461716i
$7$	−3.32453	−	1.91942i	−1.25655	−	0.725472i	−0.284151	−	0.958779i	$-0.591712\pi$
$7$	−3.32453	−	1.91942i	−1.25655	−	0.725472i	−0.972403	+	0.233307i	$0.925045\pi$
$8$			3.01845i			1.06718i
$9$	−2.28612	−	1.94260i	−0.762038	−	0.647532i
$10$	1.01961			0.322429
$11$	−1.97745	−	1.14168i	−0.596222	−	0.344229i	0.171332	−	0.985213i	$-0.445193\pi$
$11$	−1.97745	−	1.14168i	−0.596222	−	0.344229i	−0.767554	+	0.640984i	$0.778526\pi$
$12$	1.63907	−	0.283769i	0.473159	−	0.0819169i
$13$	3.56410	−	0.545131i	0.988504	−	0.151192i
$13$	3.56410	−	0.545131i	0.988504	−	0.151192i
$14$	1.95706	+	3.38972i	0.523046	+	0.905942i
$15$	−0.295470	−	1.70666i	−0.0762901	−	0.440658i
$16$	0.578424	−	1.00186i	0.144606	−	0.250465i
$17$	7.50452			1.82011			0.910057	−	0.414483i	$-0.136037\pi$
$17$	7.50452			1.82011			0.910057	+	0.414483i	$0.136037\pi$
$18$	1.02831	+	2.88080i	0.242376	+	0.679011i
$19$			2.31692i			0.531539i	0.964037	+	0.265769i	$0.0856260\pi$
$19$			2.31692i			0.531539i	−0.964037	+	0.265769i	$0.914374\pi$
$20$	0.831727	+	0.480198i	0.185980	+	0.107376i
$21$	5.10672	−	4.25810i	1.11438	−	0.929194i
$22$	1.16407	+	2.01622i	0.248180	+	0.429860i
$23$	1.68012	+	2.91006i	0.350330	+	0.606789i	0.986307	−	0.164919i	$-0.0527362\pi$
$23$	1.68012	+	2.91006i	0.350330	+	0.606789i	−0.635977	+	0.771708i	$0.719403\pi$
$24$	−4.90724	−	1.80336i	−1.00169	−	0.368110i
$25$	0.500000	−	0.866025i	0.100000	−	0.173205i
$26$	−3.42504	−	1.33564i	−0.671706	−	0.261941i
$27$	4.52400	−	2.55605i	0.870645	−	0.491912i
$28$			3.68680i			0.696740i
$29$	−4.07714	+	7.06182i	−0.757107	+	1.31135i	0.187213	+	0.982319i	$0.440054\pi$
$29$	−4.07714	+	7.06182i	−0.757107	+	1.31135i	−0.944320	+	0.329028i	$0.893279\pi$
$30$	−0.609162	+	1.65763i	−0.111217	+	0.302640i
$31$	−3.49528	+	2.01800i	−0.627771	+	0.362444i	−0.779888	−	0.625919i	$-0.784724\pi$
$31$	−3.49528	+	2.01800i	−0.627771	+	0.362444i	0.152117	+	0.988362i	$0.451391\pi$
$32$	4.20660	−	2.42868i	0.743629	−	0.429334i
$33$	3.03750	−	2.53274i	0.528761	−	0.440893i
$34$	−6.62655	−	3.82584i	−1.13644	−	0.656127i
$35$	3.83884			0.648882
$36$	−0.517922	+	2.83426i	−0.0863203	+	0.472376i
$37$		−	0.546920i		−	0.0899131i	−0.998989	−	0.0449565i	$-0.985685\pi$
$37$		−	0.546920i		−	0.0899131i	0.998989	−	0.0449565i	$-0.0143149\pi$
$38$	1.18118	−	2.04586i	0.191613	−	0.331883i
$39$	−1.24312	+	6.12002i	−0.199058	+	0.979988i
$40$	−1.50922	−	2.61405i	−0.238629	−	0.413318i
$41$	6.35971	−	3.67178i	0.993219	−	0.573436i	0.0869844	−	0.996210i	$-0.472277\pi$
$41$	6.35971	−	3.67178i	0.993219	−	0.573436i	0.906235	+	0.422774i	$0.138944\pi$
$42$	−6.68007	+	1.15651i	−1.03076	+	0.178453i
$43$	−0.826744	+	1.43196i	−0.126077	+	0.218372i	−0.922154	−	0.386824i	$-0.873572\pi$
$43$	−0.826744	+	1.43196i	−0.126077	+	0.218372i	0.796076	+	0.605196i	$0.206905\pi$
$44$			2.19293i			0.330596i
$45$	2.95113	+	0.539279i	0.439929	+	0.0803910i
$46$		−	3.42614i		−	0.505157i
$47$	7.13335	+	4.11844i	1.04051	+	0.600737i	0.919977	−	0.391973i	$-0.128207\pi$
$47$	7.13335	+	4.11844i	1.04051	+	0.600737i	0.120530	+	0.992710i	$0.461541\pi$
$48$	1.28319	+	1.53893i	0.185213	+	0.222125i
$49$	3.86833	+	6.70015i	0.552619	+	0.957164i
$50$	−0.883008	+	0.509805i	−0.124876	+	0.0720973i
$51$	−4.48355	+	12.2005i	−0.627823	+	1.70841i
$52$	−2.16488	−	2.70259i	−0.300214	−	0.374782i
$53$	7.10215			0.975555			0.487778	−	0.872968i	$-0.337808\pi$
$53$	7.10215			0.975555			0.487778	+	0.872968i	$0.337808\pi$
$54$	−5.29782	−	0.0493446i	−0.720942	−	0.00671495i
$55$	2.28336			0.307888
$56$	5.79367	−	10.0349i	0.774211	−	1.34097i
$57$	−3.76673	−	1.38424i	−0.498916	−	0.183347i
$58$	7.20030	−	4.15710i	0.945446	−	0.545853i
$59$	6.45792	−	3.72848i	0.840750	−	0.485407i	−0.0167693	−	0.999859i	$-0.505338\pi$
$59$	6.45792	−	3.72848i	0.840750	−	0.485407i	0.857519	+	0.514452i	$0.172005\pi$
$60$	−1.27759	+	1.06529i	−0.164937	+	0.137528i
$61$	5.77492	−	10.0025i	0.739403	−	1.28068i	−0.213362	−	0.976973i	$-0.568441\pi$
$61$	5.77492	−	10.0025i	0.739403	−	1.28068i	0.952765	−	0.303710i	$-0.0982254\pi$
$62$	4.11515			0.522624
$63$	3.87161	+	10.8462i	0.487777	+	1.36650i
$64$	−7.26631			−0.908289
$65$	−2.81404	+	2.25415i	−0.349039	+	0.279593i
$66$	−3.97334	+	0.687894i	−0.489084	+	0.0846739i
$67$	−6.43546	+	3.71551i	−0.786217	+	0.453922i	−0.838629	−	0.544703i	$-0.816642\pi$
$67$	−6.43546	+	3.71551i	−0.786217	+	0.453922i	0.0524124	+	0.998626i	$0.483309\pi$
$68$	−3.60366	−	6.24172i	−0.437008	−	0.756919i
$69$	−5.73480	+	0.992853i	−0.690389	+	0.119525i
$70$	−3.38972	−	1.95706i	−0.405149	−	0.233913i
$71$			7.19213i			0.853549i	0.904358	+	0.426774i	$0.140350\pi$
$71$			7.19213i			0.853549i	−0.904358	+	0.426774i	$0.859650\pi$
$72$	5.86362	−	6.90052i	0.691035	−	0.813234i
$73$			7.74780i			0.906811i	0.891304	+	0.453406i	$0.149791\pi$
$73$			7.74780i			0.906811i	−0.891304	+	0.453406i	$0.850209\pi$
$74$	−0.278822	+	0.482935i	−0.0324125	+	0.0561400i
$75$	1.10922	+	1.33028i	0.128081	+	0.153607i
$76$	1.92705	−	1.11258i	0.221048	−	0.127622i
$77$	4.38272	+	7.59109i	0.499457	+	0.865085i
$78$	4.21770	−	4.77028i	0.477560	−	0.540128i
$79$	6.19823	−	10.7357i	0.697356	−	1.20786i	−0.272025	−	0.962290i	$-0.587693\pi$
$79$	6.19823	−	10.7357i	0.697356	−	1.20786i	0.969380	−	0.245565i	$-0.0789735\pi$
$80$			1.15685i			0.129339i
$81$	1.45265	+	8.88199i	0.161405	+	0.986888i
$82$	−7.48756			−0.826863
$83$	5.81320	+	3.35625i	0.638082	+	0.368397i	0.783875	−	0.620918i	$-0.213240\pi$
$83$	5.81320	+	3.35625i	0.638082	+	0.368397i	−0.145793	+	0.989315i	$0.546573\pi$
$84$	−5.99382	−	2.20267i	−0.653979	−	0.240331i
$85$	−6.49911	+	3.75226i	−0.704927	+	0.406990i
$86$	1.46004	−	0.842957i	0.157441	−	0.0908984i
$87$	−9.04487	−	10.8475i	−0.969712	−	1.16297i
$88$	3.44610	−	5.96882i	0.367355	−	0.636278i
$89$		−	6.46613i		−	0.685408i	−0.939443	−	0.342704i	$-0.888657\pi$
$89$		−	6.46613i		−	0.685408i	0.939443	−	0.342704i	$-0.111343\pi$
$90$	−2.33095	−	1.98069i	−0.245703	−	0.208783i
$91$	−12.8953	−	5.02870i	−1.35180	−	0.527151i
$92$	1.61358	−	2.79481i	0.168228	−	0.291379i
$93$	−1.19252	−	6.88809i	−0.123658	−	0.714262i
$94$	−4.19920	−	7.27323i	−0.433115	−	0.750177i
$95$	−1.15846	−	2.00651i	−0.118856	−	0.205864i
$96$	1.43521	+	8.28988i	0.146480	+	0.846083i
$97$	10.1032	+	5.83306i	1.02582	+	0.592257i	0.915784	−	0.401670i	$-0.131570\pi$
$97$	10.1032	+	5.83306i	1.02582	+	0.592257i	0.110035	+	0.993928i	$0.464904\pi$
$98$		−	7.88838i		−	0.796847i
$99$	2.30285	+	6.45139i	0.231445	+	0.648389i
$100$	−0.960396			−0.0960396
$101$	−1.51884	+	2.63071i	−0.151130	+	0.261765i	−0.931643	−	0.363374i	$-0.881625\pi$
$101$	−1.51884	+	2.63071i	−0.151130	+	0.261765i	0.780513	+	0.625140i	$0.214958\pi$
$102$	10.1789	−	8.48737i	1.00786	−	0.840375i
$103$	−9.34492	−	16.1859i	−0.920783	−	1.59484i	−0.798207	−	0.602383i	$-0.794218\pi$
$103$	−9.34492	−	16.1859i	−0.920783	−	1.59484i	−0.122575	−	0.992459i	$-0.539115\pi$
$104$	1.64545	+	10.7581i	0.161350	+	1.05491i
$105$	−2.29350	+	6.24098i	−0.223823	+	0.609058i
$106$	−6.27125	−	3.62071i	−0.609118	−	0.351674i
$107$	−6.42736			−0.621357			−0.310678	−	0.950515i	$-0.600556\pi$
$107$	−6.42736			−0.621357			−0.310678	+	0.950515i	$0.600556\pi$
$108$	−4.29836	−	2.53533i	−0.413609	−	0.243962i
$109$		−	0.188689i		−	0.0180731i	−0.999959	−	0.00903656i	$-0.997124\pi$
$109$		−	0.188689i		−	0.0180731i	0.999959	−	0.00903656i	$-0.00287646\pi$
$110$	−2.01622	−	1.16407i	−0.192239	−	0.110989i
$111$	0.889154	+	0.326755i	0.0843948	+	0.0310143i
$112$	−3.84597	+	2.22047i	−0.363410	+	0.209815i
$113$	0.0907879	+	0.157249i	0.00854061	+	0.0147928i	0.870264	−	0.492585i	$-0.163948\pi$
$113$	0.0907879	+	0.157249i	0.00854061	+	0.0147928i	−0.861724	+	0.507378i	$0.830615\pi$
$114$	2.62037	+	3.14259i	0.245420	+	0.294331i
$115$	−2.91006	−	1.68012i	−0.271364	−	0.156672i
$116$	7.83135			0.727122
$117$	−9.20692	−	5.67738i	−0.851180	−	0.524874i
$118$	−7.60319			−0.699931
$119$	−24.9490	−	14.4043i	−2.28707	−	1.32044i
$120$	5.15147	−	0.891862i	0.470263	−	0.0814155i
$121$	−2.89314	−	5.01106i	−0.263013	−	0.455551i
$122$	−10.1986	+	5.88817i	−0.923338	+	0.533089i
$123$	2.16980	+	12.5330i	0.195645	+	1.13006i
$124$	3.35685	+	1.93808i	0.301454	+	0.174045i
$125$			1.00000i			0.0894427i
$126$	2.11080	−	11.5511i	0.188045	−	1.02905i
$127$	9.18483			0.815022			0.407511	−	0.913200i	$-0.366397\pi$
$127$	9.18483			0.815022			0.407511	+	0.913200i	$0.366397\pi$
$128$	−1.99699	−	1.15296i	−0.176511	−	0.101909i
$129$	−1.83408	−	2.19960i	−0.161481	−	0.193664i
$130$	3.63399	−	0.555821i	0.318722	−	0.0487487i
$131$	0.668898	+	1.15857i	0.0584419	+	0.101224i	0.893766	−	0.448533i	$-0.148053\pi$
$131$	0.668898	+	1.15857i	0.0584419	+	0.101224i	−0.835324	+	0.549758i	$0.814720\pi$
$132$	−3.56515	−	1.31016i	−0.310306	−	0.114035i
$133$	4.44715	−	7.70268i	0.385616	−	0.667907i
$134$	7.57675			0.654531
$135$	−2.63988	+	4.47561i	−0.227204	+	0.385199i
$136$			22.6520i			1.94239i
$137$	0.388221	+	0.224140i	0.0331680	+	0.0191495i	0.516492	−	0.856292i	$-0.327237\pi$
$137$	0.388221	+	0.224140i	0.0331680	+	0.0191495i	−0.483324	+	0.875441i	$0.660571\pi$
$138$	5.57004	+	2.04693i	0.474153	+	0.174247i
$139$	9.89704	+	17.1422i	0.839456	+	1.45398i	0.890350	+	0.455276i	$0.150459\pi$
$139$	9.89704	+	17.1422i	0.839456	+	1.45398i	−0.0508945	+	0.998704i	$0.516207\pi$
$140$	−1.84340	−	3.19287i	−0.155796	−	0.269846i
$141$	−10.9573	+	9.13649i	−0.922775	+	0.769431i
$142$	3.66658	−	6.35071i	0.307693	−	0.532939i
$143$	−7.67018	−	2.99109i	−0.641413	−	0.250128i
$144$	−3.26855	+	1.16672i	−0.272379	+	0.0972269i
$145$		−	8.15429i		−	0.677177i
$146$	3.94986	−	6.84137i	0.326893	−	0.566196i
$147$	−13.2039	+	2.28596i	−1.08904	+	0.188542i
$148$	−0.454888	+	0.262630i	−0.0373916	+	0.0215880i
$149$	−9.24192	+	5.33582i	−0.757127	+	0.437128i	−0.828263	−	0.560339i	$-0.810671\pi$
$149$	−9.24192	+	5.33582i	−0.757127	+	0.437128i	0.0711360	+	0.997467i	$0.477338\pi$
$150$	−0.301264	−	1.74013i	−0.0245981	−	0.142081i
$151$	12.1571	+	7.01893i	0.989334	+	0.571192i	0.905075	−	0.425251i	$-0.139814\pi$
$151$	12.1571	+	7.01893i	0.989334	+	0.571192i	0.0842590	+	0.996444i	$0.473148\pi$
$152$	−6.99351			−0.567249
$153$	−17.1562	−	14.5783i	−1.38700	−	1.17858i
$154$		−	8.93732i		−	0.720190i
$155$	2.01800	−	3.49528i	0.162090	−	0.280748i
$156$	5.68713	−	1.90489i	0.455335	−	0.152513i
$157$	6.23726	+	10.8032i	0.497787	+	0.862193i	0.999997	−	0.00255322i	$-0.000812715\pi$
$157$	6.23726	+	10.8032i	0.497787	+	0.862193i	−0.502210	+	0.864746i	$0.667479\pi$
$158$	−10.9462	+	6.31978i	−0.870831	+	0.502775i
$159$	−4.24315	+	11.5463i	−0.336504	+	0.915682i
$160$	−2.42868	+	4.20660i	−0.192004	+	0.332561i
$161$		−	12.8994i		−	1.01662i
$162$	3.24538	−	8.58344i	0.254981	−	0.674379i
$163$		−	8.11257i		−	0.635425i	−0.948187	−	0.317713i	$-0.897085\pi$
$163$		−	8.11257i		−	0.635425i	0.948187	−	0.317713i	$-0.102915\pi$
$164$	−6.10784	−	3.52636i	−0.476942	−	0.275363i
$165$	−1.36418	+	3.71216i	−0.106202	+	0.288992i
$166$	−3.42207	−	5.92720i	−0.265604	−	0.460040i
$167$	7.32936	−	4.23161i	0.567163	−	0.327452i	−0.188852	−	0.982005i	$-0.560477\pi$
$167$	7.32936	−	4.23161i	0.567163	−	0.327452i	0.756015	+	0.654554i	$0.227143\pi$
$168$	12.8529	+	15.4144i	0.991619	+	1.18924i
$169$	12.4057	−	3.88581i	0.954282	−	0.298908i
$170$	7.65169			0.586857
$171$	4.50084	−	5.29675i	0.344188	−	0.405053i
$172$	1.58800			0.121084
$173$	−13.0267	+	22.5630i	−0.990404	+	1.71543i	−0.375514	+	0.926817i	$0.622534\pi$
$173$	−13.0267	+	22.5630i	−0.990404	+	1.71543i	−0.614890	+	0.788613i	$0.710800\pi$
$174$	2.45660	+	14.1895i	0.186234	+	1.07570i
$175$	−3.32453	+	1.91942i	−0.251311	+	0.145094i
$176$	−2.28760	+	1.32075i	−0.172435	+	0.0995551i
$177$	2.20331	+	12.7265i	0.165611	+	0.956584i
$178$	−3.29646	+	5.70964i	−0.247080	+	0.427956i
$179$	−19.3448			−1.44590			−0.722948	−	0.690902i	$-0.757213\pi$
$179$	−19.3448			−1.44590			−0.722948	+	0.690902i	$0.757213\pi$
$180$	−0.968594	−	2.71350i	−0.0721948	−	0.202252i
$181$	−9.00966			−0.669683			−0.334841	−	0.942274i	$-0.608683\pi$
$181$	−9.00966			−0.669683			−0.334841	+	0.942274i	$0.608683\pi$
$182$	8.82300	+	11.0145i	0.654004	+	0.816447i
$183$	12.8113	+	15.3645i	0.947036	+	1.13578i
$184$	−8.78386	+	5.07136i	−0.647555	+	0.373866i
$185$	0.273460	+	0.473647i	0.0201052	+	0.0348232i
$186$	−2.45858	+	6.69019i	−0.180272	+	0.490549i
$187$	−14.8398	−	8.56776i	−1.08519	−	0.626536i
$188$		−	7.91067i		−	0.576945i
$189$	−19.9463	−	0.185783i	−1.45088	−	0.0135137i
$190$			2.36236i			0.171383i
$191$	0.575599	−	0.996967i	0.0416489	−	0.0721380i	−0.844450	−	0.535635i	$-0.820072\pi$
$191$	0.575599	−	0.996967i	0.0416489	−	0.0721380i	0.886098	+	0.463497i	$0.153406\pi$
$192$	4.34123	−	11.8132i	0.313301	−	0.852544i
$193$	14.7966	−	8.54284i	1.06509	−	0.614927i	0.138251	−	0.990397i	$-0.455852\pi$
$193$	14.7966	−	8.54284i	1.06509	−	0.614927i	0.926835	+	0.375470i	$0.122519\pi$
$194$	−5.94744	−	10.3013i	−0.427002	−	0.739588i
$195$	−1.98344	−	5.92165i	−0.142037	−	0.424058i
$196$	3.71513	−	6.43480i	0.265367	−	0.459628i
$197$			23.3323i			1.66236i	0.556006	+	0.831178i	$0.312333\pi$
$197$			23.3323i			1.66236i	−0.556006	+	0.831178i	$0.687667\pi$
$198$	1.25551	−	6.87063i	0.0892255	−	0.488274i
$199$	−22.4339			−1.59030			−0.795148	−	0.606415i	$-0.792607\pi$
$199$	−22.4339			−1.59030			−0.795148	+	0.606415i	$0.792607\pi$
$200$	2.61405	+	1.50922i	0.184841	+	0.106718i
$201$	−2.19565	−	12.6823i	−0.154869	−	0.894538i
$202$	2.68230	−	1.54862i	0.188726	−	0.108961i
$203$	27.1092	−	15.6515i	1.90269	−	1.09852i
$204$	12.3005	−	2.12955i	0.861204	−	0.149098i
$205$	−3.67178	+	6.35971i	−0.256448	+	0.444181i
$206$			19.0563i			1.32772i
$207$	1.81211	−	9.91653i	0.125950	−	0.689246i
$208$	1.51542	−	3.88605i	0.105075	−	0.269449i
$209$	2.64518	−	4.58159i	0.182971	−	0.316915i
$210$	5.20686	−	4.34160i	0.359308	−	0.299599i
$211$	−1.42676	−	2.47121i	−0.0982219	−	0.170125i	0.812727	−	0.582645i	$-0.197982\pi$
$211$	−1.42676	−	2.47121i	−0.0982219	−	0.170125i	−0.910949	+	0.412520i	$0.864649\pi$
$212$	−3.41044	−	5.90705i	−0.234230	−	0.405698i
$213$	−11.6926	−	4.29691i	−0.801163	−	0.294420i
$214$	5.67541	+	3.27670i	0.387963	+	0.223991i
$215$		−	1.65349i		−	0.112767i
$216$	7.71531	+	13.6555i	0.524960	+	0.929137i
$217$	15.4936			1.05177
$218$	−0.0961945	+	0.166614i	−0.00651511	+	0.0112845i
$219$	−12.5960	−	4.62889i	−0.851157	−	0.312792i
$220$	−1.09646	−	1.89913i	−0.0739236	−	0.128039i
$221$	26.7469	−	4.09095i	1.79919	−	0.275187i
$222$	−0.618549	−	0.741823i	−0.0415143	−	0.0497879i
$223$	7.75167	+	4.47543i	0.519090	+	0.299697i	0.736562	−	0.676370i	$-0.236448\pi$
$223$	7.75167	+	4.47543i	0.519090	+	0.299697i	−0.217472	+	0.976067i	$0.569781\pi$
$224$	−18.6466			−1.24588
$225$	−2.82539	+	1.00854i	−0.188360	+	0.0672358i
$226$		−	0.185137i		−	0.0123151i
$227$	10.4464	+	6.03126i	0.693355	+	0.400309i	0.804868	−	0.593454i	$-0.202236\pi$
$227$	10.4464	+	6.03126i	0.693355	+	0.400309i	−0.111513	+	0.993763i	$0.535570\pi$
$228$	0.657470	+	3.79760i	0.0435420	+	0.251503i
$229$	19.0488	−	10.9978i	1.25878	−	0.726755i	0.285940	−	0.958247i	$-0.407694\pi$
$229$	19.0488	−	10.9978i	1.25878	−	0.726755i	0.972837	+	0.231492i	$0.0743608\pi$
$230$	1.71307	+	2.96712i	0.112956	+	0.195646i
$231$	−14.9596	+	2.58993i	−0.984272	+	0.170405i
$232$	−21.3157	−	12.3067i	−1.39945	−	0.807971i
$233$	18.6627			1.22263			0.611316	−	0.791387i	$-0.290641\pi$
$233$	18.6627			1.22263			0.611316	+	0.791387i	$0.290641\pi$
$234$	5.23543	+	9.70690i	0.342251	+	0.634560i
$235$	−8.23689			−0.537315
$236$	−6.20216	−	3.58082i	−0.403726	−	0.233091i
$237$	13.7504	+	16.4907i	0.893182	+	1.07119i
$238$	14.6868	+	25.4383i	0.952003	+	1.64892i
$239$	−0.139921	+	0.0807834i	−0.00905073	+	0.00522544i	−0.504519	−	0.863401i	$-0.668330\pi$
$239$	−0.139921	+	0.0807834i	−0.00905073	+	0.00522544i	0.495468	+	0.868626i	$0.334997\pi$
$240$	−1.88074	−	0.691154i	−0.121401	−	0.0446138i
$241$	−1.45945	−	0.842613i	−0.0940114	−	0.0542775i	0.452257	−	0.891888i	$-0.350619\pi$
$241$	−1.45945	−	0.842613i	−0.0940114	−	0.0542775i	−0.546269	+	0.837610i	$0.683952\pi$
$242$			5.89975i			0.379250i
$243$	−15.3078	−	2.94488i	−0.981994	−	0.188914i
$244$	−11.0924			−0.710120
$245$	−6.70015	−	3.86833i	−0.428057	−	0.247139i
$246$	4.47342	−	12.1729i	0.285215	−	0.776115i
$247$	1.26303	+	8.25775i	0.0803645	+	0.525428i
$248$	−6.09123	−	10.5503i	−0.386794	−	0.669946i
$249$	−8.92950	+	7.44562i	−0.565884	+	0.471847i
$250$	0.509805	−	0.883008i	0.0322429	−	0.0558463i
$251$	16.3409			1.03143			0.515714	−	0.856761i	$-0.327527\pi$
$251$	16.3409			1.03143			0.515714	+	0.856761i	$0.327527\pi$
$252$	7.16197	−	8.42846i	0.451162	−	0.530943i
$253$		−	7.67264i		−	0.482375i
$254$	−8.11028	−	4.68247i	−0.508884	−	0.293804i
$255$	−2.21736	−	12.8077i	−0.138857	−	0.802049i
$256$	8.44188	+	14.6218i	0.527618	+	0.913861i
$257$	0.0607070	+	0.105148i	0.00378680	+	0.00655893i	0.867913	−	0.496717i	$-0.165461\pi$
$257$	0.0607070	+	0.105148i	0.00378680	+	0.00655893i	−0.864126	+	0.503276i	$0.832128\pi$
$258$	0.498137	+	2.87729i	0.0310127	+	0.179132i
$259$	−1.04977	+	1.81825i	−0.0652294	+	0.112981i
$260$	3.22613	+	1.25807i	0.200076	+	0.0780225i
$261$	23.0391	−	8.22390i	1.42608	−	0.509046i
$262$		−	1.36403i		−	0.0842700i
$263$	−3.71682	+	6.43773i	−0.229189	+	0.396967i	−0.957568	−	0.288207i	$-0.906941\pi$
$263$	−3.71682	+	6.43773i	−0.229189	+	0.396967i	0.728379	+	0.685175i	$0.240274\pi$
$264$	7.64494	+	9.16854i	0.470513	+	0.564284i
$265$	−6.15064	+	3.55107i	−0.377831	+	0.218141i
$266$	−7.85373	+	4.53435i	−0.481543	+	0.278019i
$267$	10.5123	+	3.86316i	0.643342	+	0.236422i
$268$	6.18059	+	3.56837i	0.377540	+	0.217973i
$269$	11.1991			0.682823			0.341412	−	0.939914i	$-0.389095\pi$
$269$	11.1991			0.682823			0.341412	+	0.939914i	$0.389095\pi$
$270$	4.61272	−	2.60618i	0.280721	−	0.158607i
$271$			15.2574i			0.926821i	0.886144	+	0.463410i	$0.153374\pi$
$271$			15.2574i			0.926821i	−0.886144	+	0.463410i	$0.846626\pi$
$272$	4.34079	−	7.51848i	0.263199	−	0.455875i
$273$	15.8797	−	17.9601i	0.961080	−	1.08700i
$274$	−0.228535	−	0.395834i	−0.0138063	−	0.0239132i
$275$	−1.97745	+	1.14168i	−0.119244	+	0.0688458i
$276$	3.57962	+	4.29303i	0.215468	+	0.258410i
$277$	−2.37420	+	4.11224i	−0.142652	+	0.247080i	−0.928494	−	0.371346i	$-0.878896\pi$
$277$	−2.37420	+	4.11224i	−0.142652	+	0.247080i	0.785843	+	0.618427i	$0.212230\pi$
$278$		−	20.1822i		−	1.21045i
$279$	11.9108	+	2.17653i	0.713079	+	0.130306i
$280$			11.5873i			0.692476i
$281$	−11.8137	−	6.82064i	−0.704746	−	0.406885i	0.104367	−	0.994539i	$-0.466718\pi$
$281$	−11.8137	−	6.82064i	−0.704746	−	0.406885i	−0.809113	+	0.587654i	$0.800052\pi$
$282$	14.3332	−	2.48148i	0.853533	−	0.147770i
$283$	−3.90498	−	6.76362i	−0.232127	−	0.402056i	0.726307	−	0.687371i	$-0.241235\pi$
$283$	−3.90498	−	6.76362i	−0.232127	−	0.402056i	−0.958434	+	0.285315i	$0.907902\pi$
$284$	5.98189	−	3.45365i	0.354960	−	0.204936i
$285$	3.95421	−	0.684582i	0.234227	−	0.0405512i
$286$	5.24796	+	6.55146i	0.310318	+	0.387396i
$287$	−28.1907			−1.66405
$288$	−14.3347	−	2.61948i	−0.844682	−	0.154354i
$289$	39.3179			2.31282
$290$	−4.15710	+	7.20030i	−0.244113	+	0.422816i
$291$	−15.5192	+	12.9402i	−0.909750	+	0.758571i
$292$	6.44405	−	3.72048i	0.377110	−	0.217724i
$293$	−5.15813	+	2.97805i	−0.301341	+	0.173979i	−0.643045	−	0.765828i	$-0.722329\pi$
$293$	−5.15813	+	2.97805i	−0.301341	+	0.173979i	0.341704	+	0.939808i	$0.388996\pi$
$294$	12.8245	+	4.71289i	0.747941	+	0.274861i
$295$	−3.72848	+	6.45792i	−0.217081	+	0.375995i
$296$	1.65085			0.0959537
$297$	−11.8642	−	0.110504i	−0.688428	−	0.00641212i
$298$	10.8809			0.630315
$299$	7.57449	+	9.45586i	0.438044	+	0.546846i
$300$	0.573785	−	1.56136i	0.0331275	−	0.0901453i
$301$	5.49707	−	3.17374i	0.316846	−	0.182931i
$302$	−7.15657	−	12.3955i	−0.411814	−	0.713283i
$303$	−3.36944	−	4.04096i	−0.193569	−	0.232147i
$304$	2.32123	+	1.34016i	0.133132	+	0.0768636i
$305$			11.5498i			0.661342i
$306$	7.71700	+	21.6190i	0.441152	+	1.23588i
$307$		−	7.80536i		−	0.445475i	−0.974878	−	0.222738i	$-0.928501\pi$
$307$		−	7.80536i		−	0.445475i	0.974878	−	0.222738i	$-0.0714993\pi$
$308$	4.20915	−	7.29045i	0.239838	−	0.415412i
$309$	31.8973	−	5.52230i	1.81457	−	0.314152i
$310$	−3.56382	+	2.05757i	−0.202411	+	0.116862i
$311$	4.84636	+	8.39414i	0.274812	+	0.475988i	0.970088	−	0.242755i	$-0.0780511\pi$
$311$	4.84636	+	8.39414i	0.274812	+	0.475988i	−0.695276	+	0.718743i	$0.744718\pi$
$312$	−18.4730	−	3.75228i	−1.04583	−	0.212431i
$313$	13.6176	−	23.5864i	0.769714	−	1.33318i	−0.168004	−	0.985786i	$-0.553732\pi$
$313$	13.6176	−	23.5864i	0.769714	−	1.33318i	0.937718	−	0.347397i	$-0.112934\pi$
$314$		−	12.7191i		−	0.717782i
$315$	−8.77602	−	7.45731i	−0.494473	−	0.420172i
$316$	−11.9055			−0.669738
$317$	19.4508	+	11.2299i	1.09246	+	0.630734i	0.934231	−	0.356668i	$-0.116087\pi$
$317$	19.4508	+	11.2299i	1.09246	+	0.630734i	0.158232	+	0.987402i	$0.449420\pi$
$318$	9.63310	−	8.03230i	0.540198	−	0.450429i
$319$	16.1247	−	9.30958i	0.902808	−	0.521236i
$320$	6.29281	−	3.63316i	0.351779	−	0.203100i
$321$	3.84001	−	10.4493i	0.214328	−	0.583222i
$322$	−6.57619	+	11.3903i	−0.366477	+	0.634757i
$323$			17.3874i			0.967461i
$324$	6.68984	−	5.47332i	0.371658	−	0.304073i
$325$	1.30995	−	3.35917i	0.0726632	−	0.186333i
$326$	−4.13583	+	7.16346i	−0.229062	+	0.396748i
$327$	0.306761	+	0.112731i	0.0169639	+	0.00623407i
$328$	11.0831	+	19.1964i	0.611960	+	1.05995i
$329$	−15.8100	−	27.3838i	−0.871635	−	1.50972i
$330$	3.09706	−	2.58240i	0.170488	−	0.142157i
$331$	1.13312	+	0.654208i	0.0622820	+	0.0359585i	0.530818	−	0.847486i	$-0.321885\pi$
$331$	1.13312	+	0.654208i	0.0622820	+	0.0359585i	−0.468536	+	0.883445i	$0.655218\pi$
$332$		−	6.44667i		−	0.353807i
$333$	−1.06244	+	1.25032i	−0.0582216	+	0.0685172i
$334$	−8.62918			−0.472168
$335$	3.71551	−	6.43546i	0.203000	−	0.351607i
$336$	−1.31217	−	7.57920i	−0.0715847	−	0.413479i
$337$	12.9160	+	22.3712i	0.703580	+	1.21864i	0.967201	+	0.254011i	$0.0817499\pi$
$337$	12.9160	+	22.3712i	0.703580	+	1.21864i	−0.263621	+	0.964626i	$0.584917\pi$
$338$	−12.9353	−	2.89327i	−0.703588	−	0.157373i
$339$	−0.309889	+	0.0536503i	−0.0168308	+	0.00291388i
$340$	6.24172	+	3.60366i	0.338505	+	0.195436i
$341$	9.21564			0.499055
$342$	−6.67459	+	2.38252i	−0.360921	+	0.128832i
$343$		−	2.82795i		−	0.152695i
$344$	−4.32231	−	2.49549i	−0.233043	−	0.134548i
$345$	4.47006	−	3.72724i	0.240660	−	0.200668i
$346$	23.0054	−	13.2822i	1.23678	−	0.714054i
$347$	8.22130	+	14.2397i	0.441342	+	0.764428i	0.997789	−	0.0664556i	$-0.0211691\pi$
$347$	8.22130	+	14.2397i	0.441342	+	0.764428i	−0.556447	+	0.830883i	$0.687836\pi$
$348$	−4.67881	+	12.7318i	−0.250811	+	0.682496i
$349$	−6.19279	−	3.57541i	−0.331492	−	0.191387i	0.325011	−	0.945710i	$-0.394632\pi$
$349$	−6.19279	−	3.57541i	−0.331492	−	0.191387i	−0.656504	+	0.754323i	$0.727965\pi$
$350$	3.91412			0.209218
$351$	14.7306	−	11.5762i	0.786263	−	0.617892i
$352$	−11.0911			−0.591158
$353$	−23.2529	−	13.4251i	−1.23763	−	0.714544i	−0.269018	−	0.963135i	$-0.586699\pi$
$353$	−23.2529	−	13.4251i	−1.23763	−	0.714544i	−0.968608	+	0.248591i	$0.920032\pi$
$354$	4.54250	−	12.3609i	0.241431	−	0.656973i
$355$	−3.59606	−	6.22857i	−0.190859	−	0.330578i
$356$	−5.37806	+	3.10502i	−0.285036	+	0.164566i
$357$	38.3235	−	31.9550i	2.02829	−	1.69124i
$358$	17.0816	+	9.86206i	0.902790	+	0.521226i
$359$		−	25.3831i		−	1.33967i	−0.742512	−	0.669833i	$-0.766366\pi$
$359$		−	25.3831i		−	1.33967i	0.742512	−	0.669833i	$-0.233634\pi$
$360$	−1.62779	+	8.90784i	−0.0857919	+	0.469484i
$361$	13.6319			0.717467
$362$	7.95560	+	4.59317i	0.418137	+	0.241412i
$363$	9.87523	−	1.70967i	0.518315	−	0.0897346i
$364$	2.00979	+	13.1401i	0.105342	+	0.688731i
$365$	−3.87390	−	6.70979i	−0.202769	−	0.351206i
$366$	−3.47956	−	20.0982i	−0.181879	−	1.05055i
$367$	2.75102	−	4.76491i	0.143602	−	0.248726i	−0.785248	−	0.619181i	$-0.787465\pi$
$367$	2.75102	−	4.76491i	0.143602	−	0.248726i	0.928851	+	0.370455i	$0.120798\pi$
$368$	3.88729			0.202639
$369$	−21.6718	−	3.96023i	−1.12819	−	0.206161i
$370$		−	0.557645i		−	0.0289906i
$371$	−23.6113	−	13.6320i	−1.22584	−	0.707738i
$372$	−5.15637	+	4.29950i	−0.267345	+	0.222919i
$373$	−11.5270	−	19.9654i	−0.596847	−	1.03377i	−0.993283	−	0.115708i	$-0.963086\pi$
$373$	−11.5270	−	19.9654i	−0.596847	−	1.03377i	0.396436	−	0.918062i	$-0.370247\pi$
$374$	8.73577	+	15.1308i	0.451716	+	0.782395i
$375$	−1.62575	−	0.597446i	−0.0839533	−	0.0308520i
$376$	−12.4313	+	21.5317i	−0.641096	+	1.11041i
$377$	−10.6817	+	27.3916i	−0.550138	+	1.41074i
$378$	17.5180	+	10.3328i	0.901031	+	0.531461i
$379$			13.1674i			0.676363i	0.941081	+	0.338181i	$0.109812\pi$
$379$			13.1674i			0.676363i	−0.941081	+	0.338181i	$0.890188\pi$
$380$	−1.11258	+	1.92705i	−0.0570743	+	0.0988555i
$381$	−5.48744	+	14.9322i	−0.281130	+	0.765001i
$382$	−1.01652	+	0.586886i	−0.0520095	+	0.0300277i
$383$	−31.5880	+	18.2373i	−1.61407	+	0.931884i	−0.625656	+	0.780099i	$0.715169\pi$
$383$	−31.5880	+	18.2373i	−1.61407	+	0.931884i	−0.988414	+	0.151785i	$0.951498\pi$
$384$	3.06752	−	2.55777i	0.156539	−	0.130526i
$385$	−7.59109	−	4.38272i	−0.386878	−	0.223364i
$386$	−17.4207			−0.886692
$387$	4.67176	−	1.66760i	0.237479	−	0.0847691i
$388$		−	11.2041i		−	0.568802i
$389$	−9.44003	+	16.3506i	−0.478629	+	0.829009i	−0.999700	−	0.0245043i	$-0.992199\pi$
$389$	−9.44003	+	16.3506i	−0.478629	+	0.829009i	0.521071	+	0.853513i	$0.325533\pi$
$390$	−1.26749	+	6.24003i	−0.0641820	+	0.315976i
$391$	12.6085	+	21.8386i	0.637640	+	1.10443i
$392$	−20.2241	+	11.6764i	−1.02147	+	0.589746i
$393$	−2.28317	+	0.395279i	−0.115170	+	0.0199392i
$394$	11.8949	−	20.6026i	0.599257	−	1.03794i
$395$			12.3965i			0.623734i
$396$	4.25997	−	5.01329i	0.214072	−	0.251927i
$397$			24.1425i			1.21168i	0.795587	+	0.605840i	$0.207163\pi$
$397$			24.1425i			1.21168i	−0.795587	+	0.605840i	$0.792837\pi$
$398$	19.8093	+	11.4369i	0.992951	+	0.573280i
$399$	9.86569	+	11.8319i	0.493902	+	0.592335i
$400$	−0.578424	−	1.00186i	−0.0289212	−	0.0500930i
$401$	16.9146	−	9.76567i	0.844676	−	0.487674i	−0.0141747	−	0.999900i	$-0.504512\pi$
$401$	16.9146	−	9.76567i	0.844676	−	0.487674i	0.858851	+	0.512225i	$0.171179\pi$
$402$	−4.52670	+	12.3179i	−0.225771	+	0.614360i
$403$	−11.3575	+	9.09775i	−0.565756	+	0.453191i
$404$	2.91738			0.145145
$405$	−5.69903	−	6.96571i	−0.283187	−	0.346129i
$406$	−31.9168			−1.58401
$407$	−0.624407	+	1.08150i	−0.0309507	+	0.0536082i
$408$	−36.8265	−	13.5334i	−1.82318	−	0.670002i
$409$	20.9244	−	12.0807i	1.03465	−	0.597354i	0.116335	−	0.993210i	$-0.462885\pi$
$409$	20.9244	−	12.0807i	1.03465	−	0.597354i	0.918313	+	0.395856i	$0.129552\pi$
$410$	6.48442	−	3.74378i	0.320243	−	0.184892i
$411$	−0.596336	+	0.497239i	−0.0294151	+	0.0245270i
$412$	−8.97483	+	15.5449i	−0.442158	+	0.765840i
$413$	−28.6261			−1.40860
$414$	−6.65560	+	7.83255i	−0.327105	+	0.384949i
$415$	−6.71251			−0.329504
$416$	13.6688	−	10.9492i	0.670169	−	0.536830i
$417$	−33.7818	+	5.84856i	−1.65430	+	0.286405i
$418$	−4.67143	+	2.69705i	−0.228487	+	0.131917i
$419$	1.42009	+	2.45966i	0.0693758	+	0.120162i	0.898627	−	0.438714i	$-0.144566\pi$
$419$	1.42009	+	2.45966i	0.0693758	+	0.120162i	−0.829251	+	0.558876i	$0.811233\pi$
$420$	6.29213	−	1.08934i	0.307025	−	0.0531544i
$421$	−27.4313	−	15.8375i	−1.33692	−	0.771872i	−0.350571	−	0.936536i	$-0.614013\pi$
$421$	−27.4313	−	15.8375i	−1.33692	−	0.771872i	−0.986350	+	0.164664i	$0.947346\pi$
$422$			2.90947i			0.141631i
$423$	−8.30720	−	23.2725i	−0.403910	−	1.13155i
$424$			21.4375i			1.04110i
$425$	3.75226	−	6.49911i	0.182011	−	0.315253i
$426$	8.13406	+	9.75515i	0.394097	+	0.472638i
$427$	−38.3978	+	22.1690i	−1.85820	+	1.07283i
$428$	3.08641	+	5.34581i	0.149187	+	0.258400i
$429$	9.44529	−	10.6828i	0.456023	−	0.515769i
$430$	−0.842957	+	1.46004i	−0.0406510	+	0.0704096i
$431$		−	21.7562i		−	1.04796i	−0.851731	−	0.523979i	$-0.824447\pi$
$431$		−	21.7562i		−	1.04796i	0.851731	−	0.523979i	$-0.175553\pi$
$432$	0.0559863	−	6.01089i	0.00269364	−	0.289199i
$433$	25.9173			1.24551			0.622753	−	0.782419i	$-0.286014\pi$
$433$	25.9173			1.24551			0.622753	+	0.782419i	$0.286014\pi$
$434$	−13.6809	−	7.89869i	−0.656706	−	0.379149i
$435$	13.2568	+	4.87175i	0.635616	+	0.233583i
$436$	−0.156938	+	0.0906080i	−0.00751595	+	0.00433934i
$437$	−6.74238	+	3.89272i	−0.322532	+	0.186214i
$438$	8.76251	+	10.5088i	0.418689	+	0.502132i
$439$	−12.0337	+	20.8429i	−0.574336	+	0.994778i	0.421778	+	0.906699i	$0.361406\pi$
$439$	−12.0337	+	20.8429i	−0.574336	+	0.994778i	−0.996113	+	0.0880792i	$0.971927\pi$
$440$			6.89220i			0.328573i
$441$	4.17222	−	22.8319i	0.198677	−	1.08723i
$442$	−25.7033	−	10.0234i	−1.22258	−	0.476763i
$443$	9.26668	−	16.0504i	0.440273	−	0.762575i	−0.557436	−	0.830220i	$-0.688215\pi$
$443$	9.26668	−	16.0504i	0.440273	−	0.762575i	0.997710	+	0.0676443i	$0.0215483\pi$
$444$	−0.155199	−	0.896441i	−0.00736540	−	0.0425432i
$445$	3.23306	+	5.59983i	0.153262	+	0.265457i
$446$	−4.56319	−	7.90368i	−0.216073	−	0.374250i
$447$	−3.15316	−	18.2129i	−0.149139	−	0.861441i
$448$	24.1571	+	13.9471i	1.14131	+	0.658938i
$449$			22.1356i			1.04465i	0.852748	+	0.522323i	$0.174934\pi$
$449$			22.1356i			1.04465i	−0.852748	+	0.522323i	$0.825066\pi$
$450$	3.00900	+	0.549854i	0.141846	+	0.0259204i
$451$	−16.7680			−0.789573
$452$	0.0871924	−	0.151022i	0.00410118	−	0.00710346i
$453$	−18.6743	+	15.5710i	−0.877393	+	0.731590i
$454$	−6.14953	−	10.6513i	−0.288612	−	0.499890i
$455$	13.6820	−	2.09267i	0.641423	−	0.0981058i
$456$	4.17825	−	11.3697i	0.195665	−	0.532435i
$457$	−17.3428	−	10.0128i	−0.811260	−	0.468381i	0.0361334	−	0.999347i	$-0.488496\pi$
$457$	−17.3428	−	10.0128i	−0.811260	−	0.468381i	−0.847393	+	0.530966i	$0.821829\pi$
$458$	−22.4269			−1.04794
$459$	33.9505	−	19.1820i	1.58467	−	0.895337i
$460$			3.22717i			0.150467i
$461$	4.75751	+	2.74675i	0.221580	+	0.127929i	0.606681	−	0.794945i	$-0.292500\pi$
$461$	4.75751	+	2.74675i	0.221580	+	0.127929i	−0.385102	+	0.922874i	$0.625834\pi$
$462$	14.5298	+	5.33957i	0.675989	+	0.248419i
$463$	−29.8153	+	17.2139i	−1.38563	+	0.799996i	−0.992820	−	0.119622i	$-0.961832\pi$
$463$	−29.8153	+	17.2139i	−1.38563	+	0.799996i	−0.392814	+	0.919618i	$0.628498\pi$
$464$	4.71663	+	8.16945i	0.218964	+	0.379257i
$465$	4.47680	+	5.36901i	0.207607	+	0.248982i
$466$	−16.4793	−	9.51431i	−0.763388	−	0.440742i
$467$	15.2175			0.704182			0.352091	−	0.935966i	$-0.385471\pi$
$467$	15.2175			0.704182			0.352091	+	0.935966i	$0.385471\pi$
$468$	−0.300885	+	10.3839i	−0.0139084	+	0.479997i
$469$	28.5265			1.31723
$470$	7.27323	+	4.19920i	0.335489	+	0.193695i
$471$	−21.2898	+	3.68585i	−0.980981	+	0.169835i
$472$	11.2542	+	19.4929i	0.518018	+	0.897233i
$473$	3.26968	−	1.88775i	0.150340	−	0.0867990i
$474$	−3.73461	−	21.5715i	−0.171536	−	0.990810i
$475$	2.00651	+	1.15846i	0.0920652	+	0.0531539i
$476$			27.6677i			1.26815i
$477$	−16.2363	−	13.7966i	−0.743411	−	0.631703i
$478$	0.164735			0.00753480
$479$	34.7928	+	20.0877i	1.58973	+	0.917828i	0.993351	+	0.115122i	$0.0367258\pi$
$479$	34.7928	+	20.0877i	1.58973	+	0.917828i	0.596374	+	0.802707i	$0.296608\pi$
$480$	−5.38787	−	6.46164i	−0.245921	−	0.294932i
$481$	−0.298143	−	1.94928i	−0.0135942	−	0.0888795i
$482$	0.859137	+	1.48807i	0.0391326	+	0.0677797i
$483$	20.9712	+	7.70672i	0.954224	+	0.350668i
$484$	−2.77856	+	4.81261i	−0.126298	+	0.218755i
$485$	−11.6661			−0.529731
$486$	12.0156	+	10.4043i	0.545037	+	0.471950i
$487$			31.1250i			1.41041i	0.709005	+	0.705203i	$0.249144\pi$
$487$			31.1250i			1.41041i	−0.709005	+	0.705203i	$0.750856\pi$
$488$	30.1919	+	17.4313i	1.36672	+	0.789078i
$489$	13.1890	+	4.84683i	0.596427	+	0.219181i
$490$	3.94419	+	6.83154i	0.178180	+	0.308617i
$491$	−9.68601	−	16.7767i	−0.437124	−	0.757120i	0.560343	−	0.828261i	$-0.310669\pi$
$491$	−9.68601	−	16.7767i	−0.437124	−	0.757120i	−0.997466	+	0.0711405i	$0.977336\pi$
$492$	9.38208	−	7.82299i	0.422977	−	0.352688i
$493$	−30.5970	+	52.9956i	−1.37802	+	2.38680i
$494$	3.09458	−	7.93556i	0.139232	−	0.357038i
$495$	−5.22002	−	4.43564i	−0.234622	−	0.199367i
$496$			4.66904i			0.209646i
$497$	13.8047	−	23.9105i	0.619226	−	1.07253i
$498$	11.6806	−	2.02224i	0.523422	−	0.0906187i
$499$	14.5593	−	8.40584i	0.651766	−	0.376297i	−0.137367	−	0.990520i	$-0.543864\pi$
$499$	14.5593	−	8.40584i	0.651766	−	0.376297i	0.789132	+	0.614223i	$0.210531\pi$
$500$	0.831727	−	0.480198i	0.0371960	−	0.0214751i
$501$	2.50063	+	14.4439i	0.111720	+	0.645304i
$502$	−14.4291	−	8.33066i	−0.644004	−	0.371816i
$503$	7.16252			0.319361			0.159681	−	0.987169i	$-0.448954\pi$
$503$	7.16252			0.319361			0.159681	+	0.987169i	$0.448954\pi$
$504$	−32.7388	+	11.6862i	−1.45830	+	0.520547i
$505$		−	3.03768i		−	0.135175i
$506$	−3.91155	+	6.77500i	−0.173890	+	0.301186i
$507$	−1.09438	+	22.4900i	−0.0486030	+	0.998818i
$508$	−4.41054	−	7.63927i	−0.195686	−	0.338938i
$509$	−19.7416	+	11.3978i	−0.875033	+	0.505201i	−0.869018	−	0.494781i	$-0.835248\pi$
$509$	−19.7416	+	11.3978i	−0.875033	+	0.505201i	−0.00601565	+	0.999982i	$0.501915\pi$
$510$	−4.57147	+	12.4397i	−0.202428	+	0.550840i
$511$	14.8713	−	25.7578i	0.657866	−	1.13946i
$512$		−	12.6030i		−	0.556979i
$513$	5.92218	+	10.4818i	0.261470	+	0.462781i
$514$		−	0.123795i		−	0.00546036i
$515$	16.1859	+	9.34492i	0.713235	+	0.411786i
$516$	−0.948747	+	2.58170i	−0.0417663	+	0.113653i
$517$	−9.40388	−	16.2880i	−0.413582	−	0.716345i
$518$	1.85391	−	1.07035i	0.0814560	−	0.0470287i
$519$	−28.8989	−	34.6583i	−1.26852	−	1.52133i
$520$	−6.80403	−	8.49403i	−0.298377	−	0.372488i
$521$	−38.1592			−1.67179			−0.835893	−	0.548892i	$-0.815050\pi$
$521$	−38.1592			−1.67179			−0.835893	+	0.548892i	$0.815050\pi$
$522$	−24.5363	−	4.48367i	−1.07392	−	0.196245i
$523$	−3.45918			−0.151259			−0.0756297	−	0.997136i	$-0.524097\pi$
$523$	−3.45918			−0.151259			−0.0756297	+	0.997136i	$0.524097\pi$
$524$	0.642407	−	1.11268i	0.0280637	−	0.0486077i
$525$	−1.13426	−	6.55160i	−0.0495033	−	0.285935i
$526$	6.56397	−	3.78971i	0.286203	−	0.165239i
$527$	−26.2304	+	15.1441i	−1.14261	+	0.659689i
$528$	−0.780484	−	4.50814i	−0.0339662	−	0.196192i
$529$	5.85438	−	10.1401i	0.254538	−	0.440873i
$530$	7.24142			0.314547
$531$	−22.0065	−	4.02139i	−0.955000	−	0.174513i
$532$	−8.54204			−0.370345
$533$	20.6651	−	16.5535i	0.895103	−	0.717010i
$534$	−7.31298	−	8.77042i	−0.316464	−	0.379533i
$535$	5.56626	−	3.21368i	0.240650	−	0.138940i
$536$	−11.2151	−	19.4251i	−0.484418	−	0.839037i
$537$	11.5575	−	31.4497i	0.498742	−	1.35716i
$538$	−9.88893	−	5.70937i	−0.426342	−	0.246149i
$539$		−	17.6656i		−	0.760910i
$540$	4.99015	+	0.0464789i	0.214742	+	0.00200014i
$541$		−	39.9806i		−	1.71890i	−0.511218	−	0.859451i	$-0.670806\pi$
$541$		−	39.9806i		−	1.71890i	0.511218	−	0.859451i	$-0.329194\pi$
$542$	7.77829	−	13.4724i	0.334106	−	0.578689i
$543$	5.38279	−	14.6474i	0.230998	−	0.628582i
$544$	31.5685	−	18.2261i	1.35349	−	0.781438i
$545$	0.0943444	+	0.163409i	0.00404127	+	0.00699969i
$546$	−23.1780	+	7.76342i	−0.991928	+	0.332244i
$547$	5.20013	−	9.00689i	0.222341	−	0.385107i	−0.733177	−	0.680038i	$-0.761963\pi$
$547$	5.20013	−	9.00689i	0.222341	−	0.385107i	0.955519	+	0.294931i	$0.0952967\pi$
$548$		−	0.430526i		−	0.0183911i
$549$	−32.6329	+	11.6484i	−1.39274	+	0.497143i
$550$	2.32813			0.0992719
$551$	−16.3617	−	9.44643i	−0.697032	−	0.402432i
$552$	−2.99688	−	17.3102i	−0.127555	−	0.736772i
$553$	−41.2124	+	23.7940i	−1.75253	+	1.01182i
$554$	4.19288	−	2.42076i	0.178138	−	0.102848i
$555$	−0.933408	+	0.161599i	−0.0396210	+	0.00685948i
$556$	9.50508	−	16.4633i	0.403105	−	0.698198i
$557$		−	27.0548i		−	1.14635i	−0.819433	−	0.573175i	$-0.805712\pi$
$557$		−	27.0548i		−	1.14635i	0.819433	−	0.573175i	$-0.194288\pi$
$558$	−9.40770	−	7.99407i	−0.398260	−	0.338416i
$559$	−2.16599	+	5.55435i	−0.0916118	+	0.234924i
$560$	2.22047	−	3.84597i	0.0938322	−	0.162522i
$561$	22.7950	−	19.0070i	0.962405	−	0.802476i
$562$	6.95439	+	12.0454i	0.293353	+	0.508103i
$563$	6.78259	+	11.7478i	0.285852	+	0.495110i	0.972815	−	0.231582i	$-0.0743901\pi$
$563$	6.78259	+	11.7478i	0.285852	+	0.495110i	−0.686963	+	0.726692i	$0.741057\pi$
$564$	12.8608	+	4.72620i	0.541536	+	0.199009i
$565$	−0.157249	−	0.0907879i	−0.00661553	−	0.00381948i
$566$			7.96311i			0.334714i
$567$	12.2189	−	32.3167i	0.513145	−	1.35717i
$568$	−21.7091			−0.910892
$569$	4.61124	−	7.98690i	0.193313	−	0.334828i	−0.753033	−	0.657983i	$-0.771410\pi$
$569$	4.61124	−	7.98690i	0.193313	−	0.334828i	0.946346	+	0.323154i	$0.104743\pi$
$570$	−3.84060	−	1.41138i	−0.160865	−	0.0591163i
$571$	5.96082	+	10.3244i	0.249453	+	0.432064i	0.963374	−	0.268161i	$-0.0864160\pi$
$571$	5.96082	+	10.3244i	0.249453	+	0.432064i	−0.713922	+	0.700226i	$0.753083\pi$
$572$	1.19543	+	7.81582i	0.0499836	+	0.326796i
$573$	1.27693	+	1.53141i	0.0533444	+	0.0639757i
$574$	24.8926	+	14.3718i	1.03900	+	0.599866i
$575$	3.36025			0.140132
$576$	16.6116	+	14.1155i	0.692151	+	0.588146i
$577$		−	34.5550i		−	1.43854i	−0.694730	−	0.719271i	$-0.744476\pi$
$577$		−	34.5550i		−	1.43854i	0.694730	−	0.719271i	$-0.255524\pi$
$578$	−34.7180	−	20.0444i	−1.44408	−	0.833739i
$579$	5.04831	+	29.1595i	0.209801	+	1.21183i
$580$	−6.78215	+	3.91567i	−0.281613	+	0.162589i
$581$	−12.8841	−	22.3159i	−0.534523	−	0.925821i
$582$	20.3006	−	3.51459i	0.841485	−	0.145684i
$583$	−14.0441	−	8.10837i	−0.581648	−	0.335815i
$584$	−23.3863			−0.967733
$585$	10.8121	+	0.313293i	0.447026	+	0.0129531i
$586$	6.07289			0.250869
$587$	22.8226	+	13.1766i	0.941990	+	0.543858i	0.890584	−	0.454820i	$-0.150296\pi$
$587$	22.8226	+	13.1766i	0.941990	+	0.543858i	0.0514064	+	0.998678i	$0.483630\pi$
$588$	8.24177	+	9.88432i	0.339885	+	0.407622i
$589$	−4.67555	−	8.09830i	−0.192653	−	0.333685i
$590$	6.58456	−	3.80160i	0.271082	−	0.156509i
$591$	−37.9324	−	13.9398i	−1.56033	−	0.573406i
$592$	−0.547937	−	0.316351i	−0.0225201	−	0.0130020i
$593$		−	24.2830i		−	0.997183i	−0.866837	−	0.498592i	$-0.833851\pi$
$593$		−	24.2830i		−	0.997183i	0.866837	−	0.498592i	$-0.166149\pi$
$594$	10.4198	+	6.14598i	0.427530	+	0.252173i
$595$	28.8086			1.18104
$596$	8.87590	+	5.12450i	0.363571	+	0.209908i
$597$	13.4031	−	36.4719i	0.548550	−	1.49269i
$598$	−1.86769	−	12.2111i	−0.0763757	−	0.499350i
$599$	−8.31375	−	14.3998i	−0.339691	−	0.588362i	0.644684	−	0.764449i	$-0.276989\pi$
$599$	−8.31375	−	14.3998i	−0.339691	−	0.588362i	−0.984374	+	0.176088i	$0.943656\pi$
$600$	−4.01538	+	3.34811i	−0.163927	+	0.136686i
$601$	4.96659	−	8.60238i	0.202591	−	0.350898i	−0.746771	−	0.665081i	$-0.768397\pi$
$601$	4.96659	−	8.60238i	0.202591	−	0.350898i	0.949363	+	0.314182i	$0.101730\pi$
$602$	−6.47195			−0.263777
$603$	21.9299	+	4.00740i	0.893056	+	0.163194i
$604$		−	13.4819i		−	0.548571i
$605$	5.01106	+	2.89314i	0.203729	+	0.117623i
$606$	0.915145	+	5.28596i	0.0371752	+	0.214727i
$607$	−14.1047	−	24.4300i	−0.572492	−	0.991585i	−0.996309	−	0.0858373i	$-0.972643\pi$
$607$	−14.1047	−	24.4300i	−0.572492	−	0.991585i	0.423817	−	0.905748i	$-0.360690\pi$
$608$	5.62707	+	9.74637i	0.228208	+	0.395268i
$609$	9.24910	+	53.4236i	0.374793	+	2.16483i
$610$	5.88817	−	10.1986i	0.238405	−	0.412929i
$611$	27.6691	+	10.7899i	1.11937	+	0.436514i
$612$	−3.88675	+	21.2697i	−0.157113	+	0.859778i
$613$			12.3008i			0.496826i	0.968654	+	0.248413i	$0.0799090\pi$
$613$			12.3008i			0.496826i	−0.968654	+	0.248413i	$0.920091\pi$
$614$	−3.97921	+	6.89219i	−0.160588	+	0.278146i
$615$	−8.14559	−	9.76897i	−0.328462	−	0.393923i
$616$	−22.9133	+	13.2290i	−0.923204	+	0.533012i
$617$	−0.597139	+	0.344759i	−0.0240399	+	0.0138795i	−0.511972	−	0.859002i	$-0.671085\pi$
$617$	−0.597139	+	0.344759i	−0.0240399	+	0.0138795i	0.487932	+	0.872882i	$0.337751\pi$
$618$	−30.9808	−	11.3851i	−1.24623	−	0.457978i
$619$	1.92390	+	1.11076i	0.0773280	+	0.0446454i	0.538165	−	0.842839i	$-0.319118\pi$
$619$	1.92390	+	1.11076i	0.0773280	+	0.0446454i	−0.460837	+	0.887485i	$0.652451\pi$
$620$	−3.87616			−0.155670
$621$	15.0391	+	8.87063i	0.603500	+	0.355966i
$622$		−	9.88279i		−	0.396264i
$623$	−12.4112	+	21.4968i	−0.497244	+	0.861253i
$624$	5.41235	+	4.78539i	0.216668	+	0.191569i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	−24.0489	+	13.8847i	−0.961189	+	0.554943i
$627$	5.86816	+	7.03766i	0.234352	+	0.281057i
$628$	5.99024	−	10.3754i	0.239036	−	0.414023i
$629$		−	4.10437i		−	0.163652i
$630$	3.94753	+	11.0589i	0.157273	+	0.440598i
$631$		−	31.5030i		−	1.25412i	−0.778973	−	0.627058i	$-0.784259\pi$
$631$		−	31.5030i		−	1.25412i	0.778973	−	0.627058i	$-0.215741\pi$
$632$	32.4050	+	18.7090i	1.28900	+	0.744206i
$633$	4.86998	−	0.843128i	0.193564	−	0.0335113i
$634$	−11.4501	−	19.8322i	−0.454742	−	0.787637i
$635$	−7.95429	+	4.59241i	−0.315657	+	0.182244i
$636$	11.6409	−	2.01537i	0.461593	−	0.0799145i
$637$	17.4396	+	21.7713i	0.690982	+	0.862610i
$638$	−18.9843			−0.751595
$639$	13.9714	−	16.4420i	0.552700	−	0.650437i
$640$	2.30593			0.0911498
$641$	−23.6797	+	41.0145i	−0.935294	+	1.61998i	−0.161184	+	0.986924i	$0.551531\pi$
$641$	−23.6797	+	41.0145i	−0.935294	+	1.61998i	−0.774109	+	0.633052i	$0.781802\pi$
$642$	−8.71785	+	7.26914i	−0.344066	+	0.286890i
$643$	16.4867	−	9.51859i	0.650171	−	0.375377i	−0.138350	−	0.990383i	$-0.544180\pi$
$643$	16.4867	−	9.51859i	0.650171	−	0.375377i	0.788522	+	0.615007i	$0.210847\pi$
$644$	−10.7288	+	6.19428i	−0.422774	+	0.244089i
$645$	2.68816	+	0.987871i	0.105846	+	0.0388974i
$646$	8.86419	−	15.3532i	0.348757	−	0.604064i
$647$	31.9873			1.25755			0.628774	−	0.777588i	$-0.283557\pi$
$647$	31.9873			1.25755			0.628774	+	0.777588i	$0.283557\pi$
$648$	−26.8098	+	4.38474i	−1.05319	+	0.172249i
$649$	−17.0269			−0.668365
$650$	−2.86922	+	2.29835i	−0.112540	+	0.0901488i
$651$	−9.25657	+	25.1886i	−0.362794	+	0.987220i
$652$	−6.74745	+	3.89564i	−0.264250	+	0.152565i
$653$	−6.18188	−	10.7073i	−0.241916	−	0.419010i	0.719344	−	0.694654i	$-0.244442\pi$
$653$	−6.18188	−	10.7073i	−0.241916	−	0.419010i	−0.961260	+	0.275644i	$0.911109\pi$
$654$	−0.213401	−	0.255931i	−0.00834464	−	0.0100077i
$655$	−1.15857	−	0.668898i	−0.0452689	−	0.0261360i
$656$		−	8.49538i		−	0.331689i
$657$	15.0508	−	17.7124i	0.587189	−	0.691025i
$658$			32.2401i			1.25685i
$659$	−1.24479	+	2.15604i	−0.0484901	+	0.0839874i	−0.889252	−	0.457418i	$-0.848774\pi$
$659$	−1.24479	+	2.15604i	−0.0484901	+	0.0839874i	0.840762	+	0.541406i	$0.182108\pi$
$660$	3.74259	−	0.647945i	0.145680	−	0.0252212i
$661$	−0.890000	+	0.513842i	−0.0346170	+	0.0199861i	−0.517209	−	0.855859i	$-0.673029\pi$
$661$	−0.890000	+	0.513842i	−0.0346170	+	0.0199861i	0.482592	+	0.875845i	$0.339696\pi$
$662$	−0.667037	−	1.15534i	−0.0259251	−	0.0449036i
$663$	−9.32899	+	45.9278i	−0.362308	+	1.78369i
$664$	−10.1307	+	17.5469i	−0.393147	+	0.680950i
$665$			8.89429i			0.344906i
$666$	1.57557	−	0.562405i	0.0610520	−	0.0217928i
$667$	−27.4004			−1.06095
$668$	−7.03909	−	4.06402i	−0.272351	−	0.157242i
$669$	−11.9071	+	9.92844i	−0.460356	+	0.383856i
$670$	−6.56166	+	3.78837i	−0.253499	+	0.146358i
$671$	−22.8392	+	13.1862i	−0.881697	+	0.509048i
$672$	11.1404	−	30.3147i	0.429749	−	1.16942i
$673$	−2.59568	+	4.49585i	−0.100056	+	0.173302i	−0.911708	−	0.410840i	$-0.865236\pi$
$673$	−2.59568	+	4.49585i	−0.100056	+	0.173302i	0.811651	+	0.584142i	$0.198569\pi$
$674$		−	26.3386i		−	1.01452i
$675$	0.0483956	−	5.19593i	0.00186275	−	0.199991i
$676$	−9.18911	−	8.45217i	−0.353427	−	0.325084i
$677$	−9.95304	+	17.2392i	−0.382526	+	0.662555i	−0.991423	−	0.130695i	$-0.958279\pi$
$677$	−9.95304	+	17.2392i	−0.382526	+	0.662555i	0.608896	+	0.793250i	$0.291613\pi$
$678$	0.300985	+	0.110609i	0.0115593	+	0.00424792i
$679$	−22.3922	−	38.7844i	−0.859332	−	1.48841i
$680$	−11.3260	−	19.6172i	−0.434333	−	0.752286i
$681$	−16.0465	+	13.3799i	−0.614903	+	0.512720i
$682$	−8.13748	−	4.69818i	−0.311600	−	0.179902i
$683$			9.73809i			0.372618i	0.982491	+	0.186309i	$0.0596525\pi$
$683$			9.73809i			0.372618i	−0.982491	+	0.186309i	$0.940348\pi$
$684$	−6.56675	−	1.19998i	−0.251086	−	0.0458826i
$685$	−0.448279			−0.0171279
$686$	−1.44170	+	2.49710i	−0.0550445	+	0.0953398i
$687$	6.49905	+	37.5391i	0.247954	+	1.43221i
$688$	0.956417	+	1.65656i	0.0364631	+	0.0631559i
$689$	25.3128	−	3.87160i	0.964341	−	0.147496i
$690$	−5.84726	+	1.01232i	−0.222601	+	0.0385385i
$691$	22.4051	+	12.9356i	0.852331	+	0.492093i	0.861437	−	0.507865i	$-0.169565\pi$
$691$	22.4051	+	12.9356i	0.852331	+	0.492093i	−0.00910599	+	0.999959i	$0.502899\pi$
$692$	25.0216			0.951180
$693$	4.72702	−	25.8680i	0.179565	−	0.982642i
$694$		−	16.7650i		−	0.636392i
$695$	−17.1422	−	9.89704i	−0.650240	−	0.375416i
$696$	32.7425	−	27.3015i	1.24110	−	1.03486i
$697$	47.7266	−	27.5550i	1.80777	−	1.04372i
$698$	3.64552	+	6.31423i	0.137985	+	0.238997i
$699$	−11.1499	+	30.3408i	−0.421729	+	1.14759i
$700$	3.19287	+	1.84340i	0.120679	+	0.0696740i
$701$	11.8618			0.448016			0.224008	−	0.974587i	$-0.428086\pi$
$701$	11.8618			0.448016			0.224008	+	0.974587i	$0.428086\pi$
$702$	−18.9089	+	2.71214i	−0.713669	+	0.102363i
$703$	1.26717			0.0477923
$704$	14.3687	+	8.29579i	0.541542	+	0.312659i
$705$	4.92110	−	13.3911i	0.185339	−	0.504338i
$706$	13.6883	+	23.7089i	0.515167	+	0.892295i
$707$	10.0989	−	5.83058i	0.379807	−	0.219281i
$708$	9.52697	−	7.94381i	0.358045	−	0.298546i
$709$	28.7325	+	16.5887i	1.07907	+	0.623001i	0.930645	−	0.365922i	$-0.119246\pi$
$709$	28.7325	+	16.5887i	1.07907	+	0.623001i	0.148425	+	0.988924i	$0.452580\pi$
$710$			7.33316i			0.275209i
$711$	−35.0249	+	12.5023i	−1.31354	+	0.468872i
$712$	19.5177			0.731456
$713$	−11.7450	−	6.78098i	−0.439854	−	0.253950i
$714$	−50.1308	+	8.67902i	−1.87610	+	0.324804i
$715$	8.13812	−	1.24473i	0.304348	−	0.0465502i
$716$	9.28932	+	16.0896i	0.347158	+	0.601296i
$717$	−0.0477382	−	0.275740i	−0.00178281	−	0.0102977i
$718$	−12.9404	+	22.4134i	−0.482932	+	0.836462i
$719$	−9.95480			−0.371251			−0.185626	−	0.982621i	$-0.559431\pi$
$719$	−9.95480			−0.371251			−0.185626	+	0.982621i	$0.559431\pi$
$720$	2.24729	−	2.64469i	0.0837514	−	0.0985617i
$721$			71.7473i			2.67201i
$722$	−12.0370	−	6.94959i	−0.447972	−	0.258637i
$723$	2.24182	−	1.86928i	0.0833742	−	0.0695193i
$724$	4.32642	+	7.49358i	0.160790	+	0.278497i
$725$	4.07714	+	7.06182i	0.151421	+	0.262269i
$726$	−9.59150	−	3.52478i	−0.355974	−	0.130817i
$727$	10.3803	−	17.9792i	0.384983	−	0.666811i	−0.606784	−	0.794867i	$-0.707541\pi$
$727$	10.3803	−	17.9792i	0.384983	−	0.666811i	0.991767	+	0.128056i	$0.0408738\pi$
$728$	15.1789	−	38.9238i	0.562567	−	1.44261i
$729$	13.9332	−	23.1272i	0.516044	−	0.856562i
$730$			7.89973i			0.292382i
$731$	−6.20432	+	10.7462i	−0.229475	+	0.397463i
$732$	6.62713	−	18.0335i	0.244946	−	0.666537i
$733$	16.4787	−	9.51396i	0.608653	−	0.351406i	−0.163785	−	0.986496i	$-0.552370\pi$
$733$	16.4787	−	9.51396i	0.608653	−	0.351406i	0.772438	+	0.635090i	$0.219037\pi$
$734$	−4.85834	+	2.80497i	−0.179325	+	0.103533i
$735$	10.2919	−	8.58164i	0.379623	−	0.316538i
$736$	14.1352	+	8.16097i	0.521031	+	0.300817i
$737$	16.9677			0.625013
$738$	17.1174	+	14.5453i	0.630101	+	0.535420i
$739$		−	16.5319i		−	0.608136i	−0.952650	−	0.304068i	$-0.901655\pi$
$739$		−	16.5319i		−	0.608136i	0.952650	−	0.304068i	$-0.0983450\pi$
$740$	0.262630	−	0.454888i	0.00965447	−	0.0167220i
$741$	−14.1796	−	2.88020i	−0.520901	−	0.105807i
$742$	13.8993	+	24.0743i	0.510260	+	0.883796i
$743$	−28.4897	+	16.4486i	−1.04519	+	0.603439i	−0.921298	−	0.388857i	$-0.872870\pi$
$743$	−28.4897	+	16.4486i	−1.04519	+	0.603439i	−0.123889	+	0.992296i	$0.539537\pi$
$744$	20.7914	−	3.59956i	0.762248	−	0.131966i
$745$	5.33582	−	9.24192i	0.195489	−	0.338598i
$746$			23.5062i			0.860622i
$747$	−6.76981	−	18.9655i	−0.247694	−	0.693911i
$748$			16.4569i			0.601723i
$749$	21.3680	+	12.3368i	0.780768	+	0.450777i
$750$	1.13097	+	1.35636i	0.0412971	+	0.0495274i
$751$	1.83181	+	3.17279i	0.0668437	+	0.115777i	0.897510	−	0.440993i	$-0.145374\pi$
$751$	1.83181	+	3.17279i	0.0668437	+	0.115777i	−0.830667	+	0.556770i	$0.812040\pi$
$752$	8.25220	−	4.76441i	0.300927	−	0.173740i
$753$	−9.76280	+	26.5662i	−0.355776	+	0.968125i
$754$	23.3965	−	18.7414i	0.852049	−	0.682523i
$755$	−14.0379			−0.510890
$756$	9.42366	+	16.6791i	0.342735	+	0.606613i
$757$	21.2758			0.773284			0.386642	−	0.922230i	$-0.373635\pi$
$757$	21.2758			0.773284			0.386642	+	0.922230i	$0.373635\pi$
$758$	6.71279	−	11.6269i	0.243820	−	0.422308i
$759$	12.4738	+	4.58399i	0.452770	+	0.166388i
$760$	6.05656	−	3.49676i	0.219695	−	0.126841i
$761$	11.3826	−	6.57174i	0.412619	−	0.238226i	−0.279296	−	0.960205i	$-0.590101\pi$
$761$	11.3826	−	6.57174i	0.412619	−	0.238226i	0.691914	+	0.721980i	$0.256768\pi$
$762$	12.4580	−	10.3877i	0.451305	−	0.376308i
$763$	−0.362173	+	0.627302i	−0.0131115	+	0.0227098i
$764$	−1.10561			−0.0399994
$765$	22.1468	+	4.04703i	0.800721	+	0.146321i
$766$	37.1899			1.34373
$767$	20.9842	−	16.8091i	0.757695	−	0.606942i
$768$	−28.8149	+	4.98865i	−1.03977	+	0.180012i
$769$	−43.1583	+	24.9175i	−1.55633	+	0.898547i	−0.558726	+	0.829353i	$0.688709\pi$
$769$	−43.1583	+	24.9175i	−1.55633	+	0.898547i	−0.997603	+	0.0691942i	$0.977957\pi$
$770$	4.46866	+	7.73995i	0.161039	+	0.278928i
$771$	−0.207213	+	0.0358742i	−0.00746258	+	0.00129198i
$772$	−14.2106	−	8.20451i	−0.511452	−	0.295287i
$773$		−	18.0797i		−	0.650281i	−0.945666	−	0.325141i	$-0.894588\pi$
$773$		−	18.0797i		−	0.650281i	0.945666	−	0.325141i	$-0.105412\pi$
$774$	−4.97535	−	0.909178i	−0.178835	−	0.0326797i
$775$			4.03600i			0.144977i
$776$	−17.6068	+	30.4958i	−0.632047	+	1.09474i
$777$	−2.32884	−	2.79297i	−0.0835467	−	0.100197i
$778$	16.6712	−	9.62515i	0.597693	−	0.345078i
$779$	8.50723	+	14.7350i	0.304803	+	0.527935i
$780$	−3.97276	+	4.49325i	−0.142247	+	0.160884i
$781$	8.21110	−	14.2220i	0.293816	−	0.508905i
$782$		−	25.7115i		−	0.919443i
$783$	−0.394632	+	42.3691i	−0.0141030	+	1.51415i
$784$	8.95014			0.319648
$785$	−10.8032	−	6.23726i	−0.385584	−	0.222617i
$786$	2.21757	+	0.814935i	0.0790981	+	0.0290678i
$787$	−39.6275	+	22.8790i	−1.41257	+	0.815547i	−0.995630	−	0.0933874i	$-0.970230\pi$
$787$	−39.6275	+	22.8790i	−1.41257	+	0.815547i	−0.416939	+	0.908934i	$0.636897\pi$
$788$	19.4061	−	11.2041i	0.691314	−	0.399130i
$789$	−8.24552	−	9.88882i	−0.293548	−	0.352051i
$790$	6.31978	−	10.9462i	0.224848	−	0.389447i
$791$		−	0.697040i		−	0.0247839i
$792$	−19.4732	+	6.95103i	−0.691949	+	0.246994i
$793$	15.1298	−	38.7979i	0.537274	−	1.37775i
$794$	12.3080	−	21.3181i	0.436794	−	0.756550i
$795$	−2.09847	−	12.1210i	−0.0744252	−	0.429887i
$796$	10.7727	+	18.6589i	0.381829	+	0.661347i
$797$	22.6184	+	39.1762i	0.801185	+	1.38769i	0.918837	+	0.394638i	$0.129130\pi$
$797$	22.6184	+	39.1762i	0.801185	+	1.38769i	−0.117651	+	0.993055i	$0.537537\pi$
$798$	−2.67953	−	15.4772i	−0.0948545	−	0.547888i
$799$	53.5324	+	30.9070i	1.89384	+	1.09341i
$800$		−	4.85736i		−	0.171734i
$801$	−12.5611	+	14.7823i	−0.443824	+	0.522307i
$802$	−19.9143			−0.703200
$803$	8.84550	−	15.3208i	0.312151	−	0.540661i
$804$	−9.49384	+	7.91618i	−0.334822	+	0.279182i
$805$	6.44972	+	11.1712i	0.227323	+	0.393734i
$806$	14.6668	−	2.24329i	0.516616	−	0.0790167i
$807$	−6.69088	+	18.2070i	−0.235530	+	0.640916i
$808$	−7.94066	−	4.58454i	−0.279351	−	0.161284i
$809$	10.8941			0.383016			0.191508	−	0.981491i	$-0.438662\pi$
$809$	10.8941			0.383016			0.191508	+	0.981491i	$0.438662\pi$
$810$	1.48113	+	9.05617i	0.0520417	+	0.318201i
$811$		−	15.5249i		−	0.545155i	−0.962134	−	0.272577i	$-0.912124\pi$
$811$		−	15.5249i		−	0.545155i	0.962134	−	0.272577i	$-0.0878760\pi$
$812$	−26.0355	−	15.0316i	−0.913669	−	0.527507i
$813$	−24.8047	−	9.11548i	−0.869938	−	0.319694i
$814$	1.10271	−	0.636651i	0.0386501	−	0.0223146i
$815$	4.05628	+	7.02569i	0.142085	+	0.246099i
$816$	9.62976	+	11.5489i	0.337109	+	0.404293i
$817$	−3.31775	−	1.91550i	−0.116073	−	0.0670150i
$818$	−24.6353			−0.861352
$819$	19.7114	+	36.5465i	0.688773	+	1.27704i
$820$	7.05272			0.246292
$821$	−37.4158	−	21.6020i	−1.30582	−	0.753916i	−0.324425	−	0.945911i	$-0.605171\pi$
$821$	−37.4158	−	21.6020i	−1.30582	−	0.753916i	−0.981396	+	0.191996i	$0.938504\pi$
$822$	0.780064	−	0.135051i	0.0272079	−	0.00471043i
$823$	−16.4269	−	28.4523i	−0.572607	−	0.991784i	−0.996297	−	0.0859771i	$-0.972599\pi$
$823$	−16.4269	−	28.4523i	−0.572607	−	0.991784i	0.423690	−	0.905807i	$-0.360735\pi$
$824$	48.8562	−	28.2072i	1.70199	−	0.982643i
$825$	−0.674664	−	3.89692i	−0.0234888	−	0.135673i
$826$	25.2770	+	14.5937i	0.879501	+	0.507780i
$827$		−	22.0099i		−	0.765359i	−0.923881	−	0.382680i	$-0.875001\pi$
$827$		−	22.0099i		−	0.765359i	0.923881	−	0.382680i	$-0.124999\pi$
$828$	−9.11802	+	3.25471i	−0.316873	+	0.113109i
$829$	−16.6541			−0.578419			−0.289210	−	0.957266i	$-0.593392\pi$
$829$	−16.6541			−0.578419			−0.289210	+	0.957266i	$0.593392\pi$
$830$	5.92720	+	3.42207i	0.205736	+	0.118782i
$831$	−5.26700	−	6.31669i	−0.182710	−	0.219124i
$832$	−25.8979	+	3.96109i	−0.897847	+	0.137326i
$833$	29.0300	+	50.2814i	1.00583	+	1.74215i
$834$	32.8112	+	12.0578i	1.13616	+	0.417528i
$835$	−4.23161	+	7.32936i	−0.146441	+	0.253643i
$836$	−5.08085			−0.175725
$837$	−10.6545	+	18.0636i	−0.368275	+	0.624368i
$838$		−	2.89587i		−	0.100036i
$839$	−8.84015	−	5.10386i	−0.305196	−	0.176205i	0.339579	−	0.940578i	$-0.389715\pi$
$839$	−8.84015	−	5.10386i	−0.305196	−	0.176205i	−0.644775	+	0.764373i	$0.723049\pi$
$840$	−18.8381	−	6.92281i	−0.649976	−	0.238860i
$841$	−18.7462	−	32.4694i	−0.646421	−	1.11963i
$842$	16.1481	+	27.9692i	0.556499	+	0.963884i
$843$	18.1467	−	15.1311i	0.625005	−	0.521144i
$844$	−1.37025	+	2.37334i	−0.0471660	+	0.0816939i
$845$	−8.80072	+	9.56804i	−0.302754	+	0.329151i
$846$	−4.52909	+	24.7848i	−0.155713	+	0.852119i
$847$			22.2126i			0.763233i
$848$	4.10805	−	7.11535i	0.141071	−	0.244342i
$849$	13.3290	−	2.30761i	0.457449	−	0.0791970i
$850$	−6.62655	+	3.82584i	−0.227289	+	0.131225i
$851$	1.59157	−	0.918893i	0.0545583	−	0.0314992i
$852$	2.04090	+	11.7884i	0.0699201	+	0.403865i
$853$	−41.0378	−	23.6932i	−1.40511	−	0.811240i	−0.410198	−	0.911997i	$-0.634540\pi$
$853$	−41.0378	−	23.6932i	−1.40511	−	0.811240i	−0.994911	+	0.100757i	$0.967874\pi$
$854$	45.2074			1.54697
$855$	−1.24947	+	6.83755i	−0.0427309	+	0.233839i
$856$		−	19.4007i		−	0.663101i
$857$	4.16755	−	7.21840i	0.142361	−	0.246576i	−0.786024	−	0.618195i	$-0.787864\pi$
$857$	4.16755	−	7.21840i	0.142361	−	0.246576i	0.928385	+	0.371619i	$0.121197\pi$
$858$	−13.7864	+	4.61772i	−0.470660	+	0.157646i
$859$	−3.88143	−	6.72284i	−0.132433	−	0.229380i	0.792181	−	0.610286i	$-0.208946\pi$
$859$	−3.88143	−	6.72284i	−0.132433	−	0.229380i	−0.924614	+	0.380906i	$0.875612\pi$
$860$	−1.37525	+	0.794002i	−0.0468957	+	0.0270752i
$861$	16.8424	−	45.8310i	0.573989	−	1.56192i
$862$	−11.0914	+	19.2109i	−0.377775	+	0.654325i
$863$			55.9535i			1.90468i	0.305038	+	0.952340i	$0.401331\pi$
$863$			55.9535i			1.90468i	−0.305038	+	0.952340i	$0.598669\pi$
$864$	12.8228	−	21.7397i	0.436242	−	0.739598i
$865$		−	26.0535i		−	0.885844i
$866$	−22.8852	−	13.2128i	−0.777670	−	0.448988i
$867$	−23.4903	+	63.9210i	−0.797773	+	2.17087i
$868$	−7.43997	−	12.8864i	−0.252529	−	0.437393i
$869$	−24.5133	+	14.1528i	−0.831558	+	0.480100i
$870$	−9.22224	−	11.0602i	−0.312663	−	0.374975i
$871$	−20.9112	+	16.7506i	−0.708549	+	0.567574i
$872$	0.569548			0.0192873
$873$	−11.7657	−	32.9614i	−0.398209	−	1.11557i
$874$	7.93810			0.268510
$875$	1.91942	−	3.32453i	0.0648882	−	0.112390i
$876$	2.19858	+	12.6992i	0.0742832	+	0.429066i
$877$	−27.9976	+	16.1644i	−0.945413	+	0.545835i	−0.891653	−	0.452719i	$-0.850454\pi$
$877$	−27.9976	+	16.1644i	−0.945413	+	0.545835i	−0.0537601	+	0.998554i	$0.517121\pi$
$878$	21.2516	−	12.2696i	0.717208	−	0.414080i
$879$	−1.75985	−	10.1650i	−0.0593583	−	0.342859i
$880$	1.32075	−	2.28760i	0.0445224	−	0.0771151i
$881$	−42.5371			−1.43311			−0.716555	−	0.697530i	$-0.754282\pi$
$881$	−42.5371			−1.43311			−0.716555	+	0.697530i	$0.754282\pi$
$882$	−15.3239	+	18.0338i	−0.515984	+	0.607228i
$883$	36.8578			1.24036			0.620182	−	0.784458i	$-0.287059\pi$
$883$	36.8578			1.24036			0.620182	+	0.784458i	$0.287059\pi$
$884$	−16.2464	−	20.2817i	−0.546424	−	0.682146i
$885$	−8.27139	−	9.91984i	−0.278040	−	0.333452i
$886$	−16.3651	+	9.44839i	−0.549796	+	0.317425i
$887$	−7.88144	−	13.6511i	−0.264633	−	0.458358i	0.702834	−	0.711353i	$-0.251917\pi$
$887$	−7.88144	−	13.6511i	−0.264633	−	0.458358i	−0.967467	+	0.252996i	$0.918584\pi$
$888$	−0.986294	+	2.68387i	−0.0330979	+	0.0900647i
$889$	−30.5352	−	17.6295i	−1.02412	−	0.591275i
$890$		−	6.59293i		−	0.220995i
$891$	7.26785	−	19.2221i	0.243482	−	0.643965i
$892$		−	8.59637i		−	0.287828i
$893$	−9.54212	+	16.5274i	−0.319315	+	0.553069i
$894$	−6.50076	+	17.6896i	−0.217418	+	0.591630i
$895$	16.7531	−	9.67239i	0.559993	−	0.323312i
$896$	4.42604	+	7.66613i	0.147864	+	0.256107i
$897$	−19.8982	+	6.66485i	−0.664382	+	0.222533i
$898$	11.2849	−	19.5459i	0.376581	−	0.652257i
$899$		−	32.9107i		−	1.09763i
$900$	2.19558	+	1.86566i	0.0731859	+	0.0621887i
$901$	53.2983			1.77562
$902$	14.8062	+	8.54839i	0.492994	+	0.284630i
$903$	1.87549	+	10.8330i	0.0624124	+	0.360500i
$904$	−0.474649	+	0.274039i	−0.0157866	+	0.00911439i
$905$	7.80260	−	4.50483i	0.259367	−	0.149746i
$906$	24.4277	−	4.22911i	0.811556	−	0.140503i
$907$	11.7945	−	20.4286i	0.391629	−	0.678321i	−0.601036	−	0.799222i	$-0.705245\pi$
$907$	11.7945	−	20.4286i	0.391629	−	0.678321i	0.992665	+	0.120901i	$0.0385784\pi$
$908$		−	11.5848i		−	0.384455i
$909$	8.58264	−	3.06361i	0.284668	−	0.101614i
$910$	−13.1482	−	5.12731i	−0.435858	−	0.169969i
$911$	−2.45500	+	4.25219i	−0.0813379	+	0.140881i	−0.903825	−	0.427903i	$-0.859253\pi$
$911$	−2.45500	+	4.25219i	−0.0813379	+	0.140881i	0.822487	+	0.568784i	$0.192586\pi$
$912$	−3.56558	+	2.97306i	−0.118068	+	0.0984479i
$913$	−7.66353	−	13.2736i	−0.253626	−	0.439293i
$914$	10.2092	+	17.6828i	0.337690	+	0.584896i
$915$	−18.7771	−	6.90041i	−0.620753	−	0.228121i
$916$	−18.2943	−	10.5622i	−0.604462	−	0.348986i
$917$		−	5.13558i		−	0.169592i
$918$	−39.7576	−	0.370308i	−1.31220	−	0.0122220i
$919$	−37.6341			−1.24143			−0.620717	−	0.784035i	$-0.713158\pi$
$919$	−37.6341			−1.24143			−0.620717	+	0.784035i	$0.713158\pi$
$920$	5.07136	−	8.78386i	0.167198	−	0.289595i
$921$	12.6895	+	4.66328i	0.418135	+	0.153660i
$922$	−2.80062	−	4.85081i	−0.0922334	−	0.159753i
$923$	3.92065	+	25.6335i	0.129050	+	0.843737i
$924$	9.33770	+	11.1987i	0.307188	+	0.368409i
$925$	−0.473647	−	0.273460i	−0.0155734	−	0.00899131i
$926$	35.1028			1.15355
$927$	−10.0790	+	55.1562i	−0.331039	+	1.81157i
$928$			39.6084i			1.30021i
$929$	4.04204	+	2.33367i	0.132615	+	0.0765654i	0.564840	−	0.825201i	$-0.308938\pi$
$929$	4.04204	+	2.33367i	0.132615	+	0.0765654i	−0.432225	+	0.901766i	$0.642271\pi$
$930$	−1.21590	−	7.02317i	−0.0398711	−	0.230299i
$931$	−15.5237	+	8.96263i	−0.508770	+	0.293738i
$932$	−8.96177	−	15.5222i	−0.293553	−	0.508448i
$933$	−16.5422	+	2.86391i	−0.541568	+	0.0937603i
$934$	−13.4372	−	7.75796i	−0.439678	−	0.253848i
$935$	17.1355			0.560391
$936$	17.1369	−	27.7906i	0.560136	−	0.908365i
$937$	−45.6433			−1.49110			−0.745550	−	0.666450i	$-0.767813\pi$
$937$	−45.6433			−1.49110			−0.745550	+	0.666450i	$0.767813\pi$
$938$	−25.1891	−	14.5430i	−0.822454	−	0.474844i
$939$	30.2098	+	36.2305i	0.985859	+	1.18234i
$940$	3.95534	+	6.85084i	0.129009	+	0.223450i
$941$	31.9448	−	18.4433i	1.04137	−	0.601236i	0.121150	−	0.992634i	$-0.461342\pi$
$941$	31.9448	−	18.4433i	1.04137	−	0.601236i	0.920221	+	0.391398i	$0.128009\pi$
$942$	20.6781	+	7.59900i	0.673729	+	0.247589i
$943$	21.3702	+	12.3381i	0.695909	+	0.401783i
$944$		−	8.62657i		−	0.280771i
$945$	17.3669	−	9.81227i	0.564946	−	0.319193i
$946$	−3.84954			−0.125159
$947$	22.7786	+	13.1512i	0.740205	+	0.427358i	0.822144	−	0.569280i	$-0.192778\pi$
$947$	22.7786	+	13.1512i	0.740205	+	0.427358i	−0.0819386	+	0.996637i	$0.526111\pi$
$948$	7.11291	−	19.3554i	0.231017	−	0.628633i
$949$	4.22356	+	27.6139i	0.137103	+	0.896387i
$950$	−1.18118	−	2.04586i	−0.0383225	−	0.0663765i
$951$	−29.8778	+	24.9128i	−0.968854	+	0.807852i
$952$	43.4787	−	75.3073i	1.40915	−	2.44072i
$953$	44.7832			1.45067			0.725335	−	0.688396i	$-0.241685\pi$
$953$	44.7832			1.45067			0.725335	+	0.688396i	$0.241685\pi$
$954$	7.30324	+	20.4599i	0.236451	+	0.662413i
$955$			1.15120i			0.0372519i
$956$	0.134379	+	0.0775840i	0.00434614	+	0.00250925i
$957$	5.50141	+	31.7766i	0.177835	+	1.02719i
$958$	−20.4816	−	35.4751i	−0.661729	−	1.14615i
$959$	−0.860436	−	1.49032i	−0.0277849	−	0.0481249i
$960$	2.14698	+	12.4011i	0.0692935	+	0.400245i
$961$	−7.35534	+	12.7398i	−0.237269	+	0.410962i
$962$	−0.730489	+	1.87322i	−0.0235519	+	0.0603952i
$963$	14.6937	+	12.4858i	0.473498	+	0.402348i
$964$			1.61849i			0.0521279i
$965$	−8.54284	+	14.7966i	−0.275004	+	0.476321i
$966$	−14.5888	−	17.4963i	−0.469388	−	0.562935i
$967$	39.6702	−	22.9036i	1.27571	−	0.736531i	0.299652	−	0.954048i	$-0.403129\pi$
$967$	39.6702	−	22.9036i	1.27571	−	0.736531i	0.976056	+	0.217518i	$0.0697960\pi$
$968$	15.1256	−	8.73279i	0.486157	−	0.280683i
$969$	−28.2676	−	10.3880i	−0.908085	−	0.333712i
$970$	10.3013	+	5.94744i	0.330754	+	0.190961i
$971$	47.1484			1.51306			0.756532	−	0.653957i	$-0.226892\pi$
$971$	47.1484			1.51306			0.756532	+	0.653957i	$0.226892\pi$
$972$	4.90142	+	14.1460i	0.157213	+	0.453734i
$973$		−	75.9862i		−	2.43601i
$974$	15.8677	−	27.4836i	0.508432	−	0.880631i
$975$	4.67854	+	4.13658i	0.149833	+	0.132477i
$976$	−6.68070	−	11.5713i	−0.213844	−	0.370389i
$977$	0.391867	−	0.226244i	0.0125369	−	0.00723820i	−0.493718	−	0.869622i	$-0.664363\pi$
$977$	0.391867	−	0.226244i	0.0125369	−	0.00723820i	0.506255	+	0.862384i	$0.331029\pi$
$978$	−9.17505	−	11.0036i	−0.293386	−	0.351856i
$979$	−7.38224	+	12.7864i	−0.235937	+	0.408656i
$980$			7.43027i			0.237351i
$981$	−0.366546	+	0.431364i	−0.0117029	+	0.0137724i
$982$			19.7519i			0.630309i
$983$	−32.8628	−	18.9733i	−1.04816	−	0.605155i	−0.126026	−	0.992027i	$-0.540222\pi$
$983$	−32.8628	−	18.9733i	−1.04816	−	0.605155i	−0.922134	+	0.386872i	$0.873556\pi$
$984$	−37.8301	+	6.54944i	−1.20598	+	0.208789i
$985$	−11.6661	−	20.2063i	−0.371714	−	0.643828i
$986$	54.0348	−	31.1970i	1.72082	−	0.993516i
$987$	53.9648	−	9.34279i	1.71772	−	0.297384i
$988$	6.26170	−	5.01585i	0.199211	−	0.159575i
$989$	−5.55613			−0.176675
$990$	2.34801	+	6.57790i	0.0746246	+	0.209059i
$991$	31.1373			0.989109			0.494555	−	0.869147i	$-0.335331\pi$
$991$	31.1373			0.989109			0.494555	+	0.869147i	$0.335331\pi$
$992$	−9.80217	+	16.9779i	−0.311219	+	0.539047i
$993$	−1.74056	+	1.45132i	−0.0552349	+	0.0460561i
$994$	−24.3793	+	14.0754i	−0.773265	+	0.446445i
$995$	19.4283	−	11.2169i	0.615919	−	0.355601i
$996$	10.4807	+	3.85154i	0.332092	+	0.122041i
$997$	−24.1727	+	41.8684i	−0.765557	+	1.32598i	0.174394	+	0.984676i	$0.444203\pi$
$997$	−24.1727	+	41.8684i	−0.765557	+	1.32598i	−0.939951	+	0.341308i	$0.889130\pi$
$998$	−17.1414			−0.542600
$999$	−1.39796	−	2.47427i	−0.0442294	−	0.0782824i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	585.2.bt.b.376.19	✓	108
9.4	even	3	inner	585.2.bt.b.571.36	yes	108
13.12	even	2	inner	585.2.bt.b.376.36	yes	108
117.103	even	6	inner	585.2.bt.b.571.19	yes	108

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
585.2.bt.b.376.19	✓	108	1.1	even	1	trivial
585.2.bt.b.376.36	yes	108	13.12	even	2	inner
585.2.bt.b.571.19	yes	108	117.103	even	6	inner
585.2.bt.b.571.36	yes	108	9.4	even	3	inner

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:	\( N \)	\(=\)	\( 585 = 3^{2} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	585.bt (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.883008 - 0.509805i) q^{2} +(-0.597446 + 1.62575i) q^{3} +(-0.480198 - 0.831727i) q^{4} +(-0.866025 + 0.500000i) q^{5} +(1.35636 - 1.13097i) q^{6} +(-3.32453 - 1.91942i) q^{7} +3.01845i q^{8} +(-2.28612 - 1.94260i) q^{9} +O(q^{10})\)	\(q+(-0.883008 - 0.509805i) q^{2} +(-0.597446 + 1.62575i) q^{3} +(-0.480198 - 0.831727i) q^{4} +(-0.866025 + 0.500000i) q^{5} +(1.35636 - 1.13097i) q^{6} +(-3.32453 - 1.91942i) q^{7} +3.01845i q^{8} +(-2.28612 - 1.94260i) q^{9} +1.01961 q^{10} +(-1.97745 - 1.14168i) q^{11} +(1.63907 - 0.283769i) q^{12} +(3.56410 - 0.545131i) q^{13} +(1.95706 + 3.38972i) q^{14} +(-0.295470 - 1.70666i) q^{15} +(0.578424 - 1.00186i) q^{16} +7.50452 q^{17} +(1.02831 + 2.88080i) q^{18} +2.31692i q^{19} +(0.831727 + 0.480198i) q^{20} +(5.10672 - 4.25810i) q^{21} +(1.16407 + 2.01622i) q^{22} +(1.68012 + 2.91006i) q^{23} +(-4.90724 - 1.80336i) q^{24} +(0.500000 - 0.866025i) q^{25} +(-3.42504 - 1.33564i) q^{26} +(4.52400 - 2.55605i) q^{27} +3.68680i q^{28} +(-4.07714 + 7.06182i) q^{29} +(-0.609162 + 1.65763i) q^{30} +(-3.49528 + 2.01800i) q^{31} +(4.20660 - 2.42868i) q^{32} +(3.03750 - 2.53274i) q^{33} +(-6.62655 - 3.82584i) q^{34} +3.83884 q^{35} +(-0.517922 + 2.83426i) q^{36} -0.546920i q^{37} +(1.18118 - 2.04586i) q^{38} +(-1.24312 + 6.12002i) q^{39} +(-1.50922 - 2.61405i) q^{40} +(6.35971 - 3.67178i) q^{41} +(-6.68007 + 1.15651i) q^{42} +(-0.826744 + 1.43196i) q^{43} +2.19293i q^{44} +(2.95113 + 0.539279i) q^{45} -3.42614i q^{46} +(7.13335 + 4.11844i) q^{47} +(1.28319 + 1.53893i) q^{48} +(3.86833 + 6.70015i) q^{49} +(-0.883008 + 0.509805i) q^{50} +(-4.48355 + 12.2005i) q^{51} +(-2.16488 - 2.70259i) q^{52} +7.10215 q^{53} +(-5.29782 - 0.0493446i) q^{54} +2.28336 q^{55} +(5.79367 - 10.0349i) q^{56} +(-3.76673 - 1.38424i) q^{57} +(7.20030 - 4.15710i) q^{58} +(6.45792 - 3.72848i) q^{59} +(-1.27759 + 1.06529i) q^{60} +(5.77492 - 10.0025i) q^{61} +4.11515 q^{62} +(3.87161 + 10.8462i) q^{63} -7.26631 q^{64} +(-2.81404 + 2.25415i) q^{65} +(-3.97334 + 0.687894i) q^{66} +(-6.43546 + 3.71551i) q^{67} +(-3.60366 - 6.24172i) q^{68} +(-5.73480 + 0.992853i) q^{69} +(-3.38972 - 1.95706i) q^{70} +7.19213i q^{71} +(5.86362 - 6.90052i) q^{72} +7.74780i q^{73} +(-0.278822 + 0.482935i) q^{74} +(1.10922 + 1.33028i) q^{75} +(1.92705 - 1.11258i) q^{76} +(4.38272 + 7.59109i) q^{77} +(4.21770 - 4.77028i) q^{78} +(6.19823 - 10.7357i) q^{79} +1.15685i q^{80} +(1.45265 + 8.88199i) q^{81} -7.48756 q^{82} +(5.81320 + 3.35625i) q^{83} +(-5.99382 - 2.20267i) q^{84} +(-6.49911 + 3.75226i) q^{85} +(1.46004 - 0.842957i) q^{86} +(-9.04487 - 10.8475i) q^{87} +(3.44610 - 5.96882i) q^{88} -6.46613i q^{89} +(-2.33095 - 1.98069i) q^{90} +(-12.8953 - 5.02870i) q^{91} +(1.61358 - 2.79481i) q^{92} +(-1.19252 - 6.88809i) q^{93} +(-4.19920 - 7.27323i) q^{94} +(-1.15846 - 2.00651i) q^{95} +(1.43521 + 8.28988i) q^{96} +(10.1032 + 5.83306i) q^{97} -7.88838i q^{98} +(2.30285 + 6.45139i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 108 q - 6 q^{3} + 52 q^{4} - 14 q^{9}+O(q^{10}) \) 108 * q - 6 * q^3 + 52 * q^4 - 14 * q^9	\( 108 q - 6 q^{3} + 52 q^{4} - 14 q^{9} - 8 q^{10} - 36 q^{12} - 4 q^{13} - 8 q^{14} - 64 q^{16} + 36 q^{17} + 24 q^{22} - 22 q^{23} + 54 q^{25} + 40 q^{26} + 48 q^{27} - 16 q^{29} + 20 q^{30} - 40 q^{35} - 76 q^{36} - 12 q^{38} + 26 q^{39} - 52 q^{42} - 6 q^{43} - 68 q^{48} + 58 q^{49} + 34 q^{51} + 22 q^{52} - 116 q^{53} + 24 q^{55} + 40 q^{56} + 18 q^{61} + 152 q^{62} - 216 q^{64} + 2 q^{65} - 72 q^{66} - 134 q^{69} + 32 q^{74} + 40 q^{77} - 34 q^{78} + 18 q^{79} + 34 q^{81} + 88 q^{82} + 60 q^{87} + 8 q^{90} + 16 q^{91} + 176 q^{92} - 76 q^{94} - 56 q^{95}+O(q^{100}) \) 108 * q - 6 * q^3 + 52 * q^4 - 14 * q^9 - 8 * q^10 - 36 * q^12 - 4 * q^13 - 8 * q^14 - 64 * q^16 + 36 * q^17 + 24 * q^22 - 22 * q^23 + 54 * q^25 + 40 * q^26 + 48 * q^27 - 16 * q^29 + 20 * q^30 - 40 * q^35 - 76 * q^36 - 12 * q^38 + 26 * q^39 - 52 * q^42 - 6 * q^43 - 68 * q^48 + 58 * q^49 + 34 * q^51 + 22 * q^52 - 116 * q^53 + 24 * q^55 + 40 * q^56 + 18 * q^61 + 152 * q^62 - 216 * q^64 + 2 * q^65 - 72 * q^66 - 134 * q^69 + 32 * q^74 + 40 * q^77 - 34 * q^78 + 18 * q^79 + 34 * q^81 + 88 * q^82 + 60 * q^87 + 8 * q^90 + 16 * q^91 + 176 * q^92 - 76 * q^94 - 56 * q^95

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