LMFDB - Embedded newform 240.2.t.b.59.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [240,2,Mod(59,240)]

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([2, 1, 2, 2]))

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

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

chi := DirichletCharacter("240.59");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 240 = 2^{4} \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	240.t (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:	$80$
Relative dimension:	$40$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			59.8
Character	$\chi$	$=$	240.59
Dual form			240.2.t.b.179.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.22048 - 0.714442i) q^{2} +(1.62793 + 0.591463i) q^{3} +(0.979146 + 1.74392i) q^{4} +(-0.258204 + 2.22111i) q^{5} +(-1.56430 - 1.88493i) q^{6} -4.18600i q^{7} +(0.0509042 - 2.82797i) q^{8} +(2.30034 + 1.92573i) q^{9} +O(q^{10})$	\(q+(-1.22048 - 0.714442i) q^{2} +(1.62793 + 0.591463i) q^{3} +(0.979146 + 1.74392i) q^{4} +(-0.258204 + 2.22111i) q^{5} +(-1.56430 - 1.88493i) q^{6} -4.18600i q^{7} +(0.0509042 - 2.82797i) q^{8} +(2.30034 + 1.92573i) q^{9} +(1.90199 - 2.52635i) q^{10} +(0.975442 + 0.975442i) q^{11} +(0.562519 + 3.41812i) q^{12} +(2.97668 + 2.97668i) q^{13} +(-2.99066 + 5.10893i) q^{14} +(-1.73404 + 3.46311i) q^{15} +(-2.08255 + 3.41511i) q^{16} -0.313777 q^{17} +(-1.43171 - 3.99377i) q^{18} +(4.54172 + 4.54172i) q^{19} +(-4.12627 + 1.72450i) q^{20} +(2.47586 - 6.81454i) q^{21} +(-0.493612 - 1.88740i) q^{22} -0.374730 q^{23} +(1.75551 - 4.57364i) q^{24} +(-4.86666 - 1.14700i) q^{25} +(-1.50631 - 5.75964i) q^{26} +(2.60582 + 4.49552i) q^{27} +(7.30007 - 4.09871i) q^{28} +(-4.71030 - 4.71030i) q^{29} +(4.59055 - 2.98778i) q^{30} -5.53854i q^{31} +(4.98161 - 2.68022i) q^{32} +(1.01102 + 2.16489i) q^{33} +(0.382959 + 0.224175i) q^{34} +(9.29757 + 1.08084i) q^{35} +(-1.10595 + 5.89719i) q^{36} +(-4.61988 + 4.61988i) q^{37} +(-2.29829 - 8.78787i) q^{38} +(3.08524 + 6.60643i) q^{39} +(6.26809 + 0.843256i) q^{40} +3.91134 q^{41} +(-7.89034 + 6.54815i) q^{42} +(-6.73708 - 6.73708i) q^{43} +(-0.745998 + 2.65620i) q^{44} +(-4.87121 + 4.61209i) q^{45} +(0.457351 + 0.267723i) q^{46} -6.23699i q^{47} +(-5.41016 + 4.32783i) q^{48} -10.5226 q^{49} +(5.12020 + 4.87684i) q^{50} +(-0.510808 - 0.185587i) q^{51} +(-2.27650 + 8.10570i) q^{52} +(-7.81306 - 7.81306i) q^{53} +(0.0314419 - 7.34840i) q^{54} +(-2.41843 + 1.91470i) q^{55} +(-11.8379 - 0.213085i) q^{56} +(4.70737 + 10.0799i) q^{57} +(2.38360 + 9.11407i) q^{58} +(-0.720910 - 0.720910i) q^{59} +(-7.73728 + 0.366845i) q^{60} +(3.20512 - 3.20512i) q^{61} +(-3.95696 + 6.75968i) q^{62} +(8.06109 - 9.62925i) q^{63} +(-7.99482 - 0.287911i) q^{64} +(-7.38012 + 5.84294i) q^{65} +(0.312762 - 3.36453i) q^{66} +(1.59395 - 1.59395i) q^{67} +(-0.307233 - 0.547203i) q^{68} +(-0.610036 - 0.221639i) q^{69} +(-10.5753 - 7.96172i) q^{70} +3.80582i q^{71} +(5.56299 - 6.40727i) q^{72} -6.36328 q^{73} +(8.93910 - 2.33784i) q^{74} +(-7.24420 - 4.74569i) q^{75} +(-3.47341 + 12.3674i) q^{76} +(4.08320 - 4.08320i) q^{77} +(0.954430 - 10.2672i) q^{78} -2.22600i q^{79} +(-7.04762 - 5.50736i) q^{80} +(1.58316 + 8.85966i) q^{81} +(-4.77371 - 2.79442i) q^{82} +(3.88632 + 3.88632i) q^{83} +(14.3083 - 2.35471i) q^{84} +(0.0810184 - 0.696933i) q^{85} +(3.40922 + 13.0357i) q^{86} +(-4.88210 - 10.4540i) q^{87} +(2.80817 - 2.70887i) q^{88} +0.399515 q^{89} +(9.24028 - 2.14877i) q^{90} +(12.4604 - 12.4604i) q^{91} +(-0.366915 - 0.653501i) q^{92} +(3.27584 - 9.01638i) q^{93} +(-4.45597 + 7.61213i) q^{94} +(-11.2603 + 8.91497i) q^{95} +(9.69498 - 1.41679i) q^{96} +0.0633091i q^{97} +(12.8426 + 7.51780i) q^{98} +(0.365419 + 4.12229i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q - 8 q^{4} - 4 q^{6}+O(q^{10}) $ 80 * q - 8 * q^4 - 4 * q^6	$ 80 q - 8 q^{4} - 4 q^{6} + 16 q^{10} - 32 q^{16} + 16 q^{19} + 8 q^{21} - 56 q^{24} + 8 q^{30} - 16 q^{34} - 40 q^{36} - 8 q^{39} - 8 q^{40} - 12 q^{45} - 24 q^{46} - 112 q^{49} + 32 q^{51} + 60 q^{54} - 40 q^{55} + 40 q^{60} + 16 q^{61} - 32 q^{64} - 56 q^{66} - 40 q^{69} + 48 q^{70} - 36 q^{75} - 128 q^{76} + 64 q^{81} + 128 q^{84} - 64 q^{85} + 72 q^{90} + 48 q^{91} + 56 q^{94} - 24 q^{96} - 8 q^{99}+O(q^{100}) $ 80 * q - 8 * q^4 - 4 * q^6 + 16 * q^10 - 32 * q^16 + 16 * q^19 + 8 * q^21 - 56 * q^24 + 8 * q^30 - 16 * q^34 - 40 * q^36 - 8 * q^39 - 8 * q^40 - 12 * q^45 - 24 * q^46 - 112 * q^49 + 32 * q^51 + 60 * q^54 - 40 * q^55 + 40 * q^60 + 16 * q^61 - 32 * q^64 - 56 * q^66 - 40 * q^69 + 48 * q^70 - 36 * q^75 - 128 * q^76 + 64 * q^81 + 128 * q^84 - 64 * q^85 + 72 * q^90 + 48 * q^91 + 56 * q^94 - 24 * q^96 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	−1.22048	−	0.714442i	−0.863010	−	0.505187i
$2$	−1.22048	−	0.714442i	−0.863010	−	0.505187i
$3$	1.62793	+	0.591463i	0.939889	+	0.341481i
$3$	1.62793	+	0.591463i	0.939889	+	0.341481i
$4$	0.979146	+	1.74392i	0.489573	+	0.871962i
$5$	−0.258204	+	2.22111i	−0.115472	+	0.993311i
$5$	−0.258204	+	2.22111i	−0.115472	+	0.993311i
$6$	−1.56430	−	1.88493i	−0.638622	−	0.769521i
$7$		−	4.18600i		−	1.58216i	−0.611713	−	0.791080i	$-0.709519\pi$
$7$		−	4.18600i		−	1.58216i	0.611713	−	0.791080i	$-0.290481\pi$
$8$	0.0509042	−	2.82797i	0.0179973	−	0.999838i
$9$	2.30034	+	1.92573i	0.766781	+	0.641908i
$10$	1.90199	−	2.52635i	0.601461	−	0.798902i
$11$	0.975442	+	0.975442i	0.294107	+	0.294107i	0.838700	−	0.544593i	$-0.183316\pi$
$11$	0.975442	+	0.975442i	0.294107	+	0.294107i	−0.544593	+	0.838700i	$0.683316\pi$
$12$	0.562519	+	3.41812i	0.162385	+	0.986727i
$13$	2.97668	+	2.97668i	0.825582	+	0.825582i	0.986902	−	0.161320i	$-0.0515752\pi$
$13$	2.97668	+	2.97668i	0.825582	+	0.825582i	−0.161320	+	0.986902i	$0.551575\pi$
$14$	−2.99066	+	5.10893i	−0.799286	+	1.36542i
$15$	−1.73404	+	3.46311i	−0.447728	+	0.894170i
$16$	−2.08255	+	3.41511i	−0.520637	+	0.853778i
$17$	−0.313777			−0.0761021			−0.0380510	−	0.999276i	$-0.512115\pi$
$17$	−0.313777			−0.0761021			−0.0380510	+	0.999276i	$0.512115\pi$
$18$	−1.43171	−	3.99377i	−0.337456	−	0.941341i
$19$	4.54172	+	4.54172i	1.04194	+	1.04194i	0.999081	+	0.0428606i	$0.0136471\pi$
$19$	4.54172	+	4.54172i	1.04194	+	1.04194i	0.0428606	+	0.999081i	$0.486353\pi$
$20$	−4.12627	+	1.72450i	−0.922662	+	0.385611i
$21$	2.47586	−	6.81454i	0.540278	−	1.48705i
$22$	−0.493612	−	1.88740i	−0.105238	−	0.402396i
$23$	−0.374730			−0.0781366			−0.0390683	−	0.999237i	$-0.512439\pi$
$23$	−0.374730			−0.0781366			−0.0390683	+	0.999237i	$0.512439\pi$
$24$	1.75551	−	4.57364i	0.358341	−	0.933591i
$25$	−4.86666	−	1.14700i	−0.973332	−	0.229400i
$26$	−1.50631	−	5.75964i	−0.295413	−	1.12956i
$27$	2.60582	+	4.49552i	0.501489	+	0.865164i
$28$	7.30007	−	4.09871i	1.37958	−	0.774583i
$29$	−4.71030	−	4.71030i	−0.874681	−	0.874681i	0.118297	−	0.992978i	$-0.462257\pi$
$29$	−4.71030	−	4.71030i	−0.874681	−	0.874681i	−0.992978	+	0.118297i	$0.962257\pi$
$30$	4.59055	−	2.98778i	0.838116	−	0.545492i
$31$		−	5.53854i		−	0.994751i	−0.867535	−	0.497375i	$-0.834297\pi$
$31$		−	5.53854i		−	0.994751i	0.867535	−	0.497375i	$-0.165703\pi$
$32$	4.98161	−	2.68022i	0.880632	−	0.473801i
$33$	1.01102	+	2.16489i	0.175996	+	0.376860i
$34$	0.382959	+	0.224175i	0.0656768	+	0.0384457i
$35$	9.29757	+	1.08084i	1.57158	+	0.182696i
$36$	−1.10595	+	5.89719i	−0.184325	+	0.982865i
$37$	−4.61988	+	4.61988i	−0.759503	+	0.759503i	−0.976232	−	0.216729i	$-0.930461\pi$
$37$	−4.61988	+	4.61988i	−0.759503	+	0.759503i	0.216729	+	0.976232i	$0.430461\pi$
$38$	−2.29829	−	8.78787i	−0.372831	−	1.42558i
$39$	3.08524	+	6.60643i	0.494034	+	1.05788i
$40$	6.26809	+	0.843256i	0.991072	+	0.133330i
$41$	3.91134			0.610848			0.305424	−	0.952216i	$-0.401202\pi$
$41$	3.91134			0.610848			0.305424	+	0.952216i	$0.401202\pi$
$42$	−7.89034	+	6.54815i	−1.21751	+	1.01040i
$43$	−6.73708	−	6.73708i	−1.02740	−	1.02740i	−0.999614	−	0.0277811i	$-0.991156\pi$
$43$	−6.73708	−	6.73708i	−1.02740	−	1.02740i	−0.0277811	−	0.999614i	$-0.508844\pi$
$44$	−0.745998	+	2.65620i	−0.112463	+	0.400437i
$45$	−4.87121	+	4.61209i	−0.726156	+	0.687529i
$46$	0.457351	+	0.267723i	0.0674327	+	0.0394736i
$47$		−	6.23699i		−	0.909759i	−0.890553	−	0.454880i	$-0.849682\pi$
$47$		−	6.23699i		−	0.909759i	0.890553	−	0.454880i	$-0.150318\pi$
$48$	−5.41016	+	4.32783i	−0.780890	+	0.624669i
$49$	−10.5226			−1.50323
$50$	5.12020	+	4.87684i	0.724106	+	0.689689i
$51$	−0.510808	−	0.185587i	−0.0715275	−	0.0259874i
$52$	−2.27650	+	8.10570i	−0.315694	+	1.12406i
$53$	−7.81306	−	7.81306i	−1.07321	−	1.07321i	−0.997100	−	0.0761074i	$-0.975751\pi$
$53$	−7.81306	−	7.81306i	−1.07321	−	1.07321i	−0.0761074	−	0.997100i	$-0.524249\pi$
$54$	0.0314419	−	7.34840i	0.00427870	−	0.999991i
$55$	−2.41843	+	1.91470i	−0.326101	+	0.258178i
$56$	−11.8379	−	0.213085i	−1.58190	−	0.0284747i
$57$	4.70737	+	10.0799i	0.623506	+	1.33511i
$58$	2.38360	+	9.11407i	0.312982	+	1.19674i
$59$	−0.720910	−	0.720910i	−0.0938545	−	0.0938545i	0.658621	−	0.752475i	$-0.271140\pi$
$59$	−0.720910	−	0.720910i	−0.0938545	−	0.0938545i	−0.752475	+	0.658621i	$0.771140\pi$
$60$	−7.73728	+	0.366845i	−0.998878	+	0.0473595i
$61$	3.20512	−	3.20512i	0.410373	−	0.410373i	−0.471495	−	0.881869i	$-0.656286\pi$
$61$	3.20512	−	3.20512i	0.410373	−	0.410373i	0.881869	+	0.471495i	$0.156286\pi$
$62$	−3.95696	+	6.75968i	−0.502535	+	0.858480i
$63$	8.06109	−	9.62925i	1.01560	−	1.21317i
$64$	−7.99482	−	0.287911i	−0.999352	−	0.0359889i
$65$	−7.38012	+	5.84294i	−0.915391	+	0.724727i
$66$	0.312762	−	3.36453i	0.0384983	−	0.414144i
$67$	1.59395	−	1.59395i	0.194732	−	0.194732i	−0.603005	−	0.797737i	$-0.706030\pi$
$67$	1.59395	−	1.59395i	0.194732	−	0.194732i	0.797737	+	0.603005i	$0.206030\pi$
$68$	−0.307233	−	0.547203i	−0.0372575	−	0.0663581i
$69$	−0.610036	−	0.221639i	−0.0734397	−	0.0266822i
$70$	−10.5753	−	7.96172i	−1.26399	−	0.951608i
$71$			3.80582i			0.451667i	0.974166	+	0.225834i	$0.0725106\pi$
$71$			3.80582i			0.451667i	−0.974166	+	0.225834i	$0.927489\pi$
$72$	5.56299	−	6.40727i	0.655604	−	0.755104i
$73$	−6.36328			−0.744765			−0.372383	−	0.928079i	$-0.621459\pi$
$73$	−6.36328			−0.744765			−0.372383	+	0.928079i	$0.621459\pi$
$74$	8.93910	−	2.33784i	1.03915	−	0.271768i
$75$	−7.24420	−	4.74569i	−0.836488	−	0.547985i
$76$	−3.47341	+	12.3674i	−0.398427	+	1.41864i
$77$	4.08320	−	4.08320i	0.465324	−	0.465324i
$78$	0.954430	−	10.2672i	0.108068	−	1.16254i
$79$		−	2.22600i		−	0.250444i	−0.992129	−	0.125222i	$-0.960036\pi$
$79$		−	2.22600i		−	0.250444i	0.992129	−	0.125222i	$-0.0399644\pi$
$80$	−7.04762	−	5.50736i	−0.787948	−	0.615742i
$81$	1.58316	+	8.85966i	0.175907	+	0.984407i
$82$	−4.77371	−	2.79442i	−0.527168	−	0.308592i
$83$	3.88632	+	3.88632i	0.426579	+	0.426579i	0.887461	−	0.460882i	$-0.152467\pi$
$83$	3.88632	+	3.88632i	0.426579	+	0.426579i	−0.460882	+	0.887461i	$0.652467\pi$
$84$	14.3083	−	2.35471i	1.56116	−	0.256920i
$85$	0.0810184	−	0.696933i	0.00878767	−	0.0755930i
$86$	3.40922	+	13.0357i	0.367626	+	1.40568i
$87$	−4.88210	−	10.4540i	−0.523416	−	1.12079i
$88$	2.80817	−	2.70887i	0.299352	−	0.288766i
$89$	0.399515			0.0423485			0.0211743	−	0.999776i	$-0.493260\pi$
$89$	0.399515			0.0423485			0.0211743	+	0.999776i	$0.493260\pi$
$90$	9.24028	−	2.14877i	0.974011	−	0.226500i
$91$	12.4604	−	12.4604i	1.30620	−	1.30620i
$92$	−0.366915	−	0.653501i	−0.0382536	−	0.0681322i
$93$	3.27584	−	9.01638i	0.339689	−	0.934955i
$94$	−4.45597	+	7.61213i	−0.459598	+	0.785131i
$95$	−11.2603	+	8.91497i	−1.15529	+	0.914656i
$96$	9.69498	−	1.41679i	0.989490	−	0.144601i
$97$			0.0633091i			0.00642807i	0.999995	+	0.00321403i	$0.00102306\pi$
$97$			0.0633091i			0.00642807i	−0.999995	+	0.00321403i	$0.998977\pi$
$98$	12.8426	+	7.51780i	1.29730	+	0.759412i
$99$	0.365419	+	4.12229i	0.0367260	+	0.414305i
$100$	−2.76489	−	9.61017i	−0.276489	−	0.961017i
$101$	−9.71331	+	9.71331i	−0.966511	+	0.966511i	−0.999457	−	0.0329465i	$-0.989511\pi$
$101$	−9.71331	+	9.71331i	−0.966511	+	0.966511i	0.0329465	+	0.999457i	$0.489511\pi$
$102$	0.490840	+	0.591448i	0.0486004	+	0.0585621i
$103$			8.62944i			0.850284i	0.905127	+	0.425142i	$0.139776\pi$
$103$			8.62944i			0.850284i	−0.905127	+	0.425142i	$0.860224\pi$
$104$	8.56948	−	8.26643i	0.840306	−	0.810590i
$105$	14.4966	+	7.25871i	1.41472	+	0.708377i
$106$	3.95371	+	15.1177i	0.384019	+	1.46836i
$107$	4.34517	−	4.34517i	0.420063	−	0.420063i	−0.465162	−	0.885225i	$-0.654004\pi$
$107$	4.34517	−	4.34517i	0.420063	−	0.420063i	0.885225	+	0.465162i	$0.154004\pi$
$108$	−5.28838	+	8.94612i	−0.508875	+	0.860841i
$109$	0.147011	−	0.147011i	0.0140811	−	0.0140811i	−0.700031	−	0.714112i	$-0.746831\pi$
$109$	0.147011	−	0.147011i	0.0140811	−	0.0140811i	0.714112	+	0.700031i	$0.246831\pi$
$110$	4.31959	−	0.609031i	0.411856	−	0.0580688i
$111$	−10.2533	+	4.78837i	−0.973204	+	0.454492i
$112$	14.2957	+	8.71755i	1.35081	+	0.823731i
$113$	−6.83896			−0.643355			−0.321678	−	0.946849i	$-0.604247\pi$
$113$	−6.83896			−0.643355			−0.321678	+	0.946849i	$0.604247\pi$
$114$	1.45624	−	15.6654i	0.136389	−	1.46720i
$115$	0.0967567	−	0.832317i	0.00902261	−	0.0776139i
$116$	3.60234	−	12.8265i	0.334469	−	1.19091i
$117$	1.11512	+	12.5796i	0.103093	+	1.16299i
$118$	0.364808	+	1.39490i	0.0335833	+	0.128411i
$119$			1.31347i			0.120406i
$120$	9.70528	+	5.08011i	0.885967	+	0.463748i
$121$		−	9.09703i		−	0.827002i
$122$	−6.20166	+	1.62191i	−0.561472	+	0.146841i
$123$	6.36740	+	2.31341i	0.574130	+	0.208593i
$124$	9.65879	−	5.42304i	0.867385	−	0.487003i
$125$	3.80420	−	10.5132i	0.340258	−	0.940332i
$126$	−16.7179	+	5.99313i	−1.48935	+	0.533910i
$127$	3.91564			0.347457			0.173729	−	0.984794i	$-0.444418\pi$
$127$	3.91564			0.347457			0.173729	+	0.984794i	$0.444418\pi$
$128$	9.55182	+	6.06322i	0.844270	+	0.535918i
$129$	−6.98280	−	14.9523i	−0.614801	−	1.31647i
$130$	13.1817	−	1.85853i	1.15611	−	0.163004i
$131$	13.5343	−	13.5343i	1.18249	−	1.18249i	0.203397	−	0.979096i	$-0.434802\pi$
$131$	13.5343	−	13.5343i	1.18249	−	1.18249i	0.979096	−	0.203397i	$-0.0651982\pi$
$132$	−2.78548	+	3.88289i	−0.242445	+	0.337962i
$133$	19.0116	−	19.0116i	1.64852	−	1.64852i
$134$	−3.08417	+	0.806601i	−0.266432	+	0.0696797i
$135$	−10.6579	+	4.62704i	−0.917285	+	0.398232i
$136$	−0.0159726	+	0.887351i	−0.00136963	+	0.0760897i
$137$			5.07778i			0.433824i	0.976191	+	0.216912i	$0.0695985\pi$
$137$			5.07778i			0.433824i	−0.976191	+	0.216912i	$0.930401\pi$
$138$	0.586189	+	0.706341i	0.0498997	+	0.0601277i
$139$	−7.98030	+	7.98030i	−0.676880	+	0.676880i	−0.959293	−	0.282413i	$-0.908865\pi$
$139$	−7.98030	+	7.98030i	−0.676880	+	0.676880i	0.282413	+	0.959293i	$0.408865\pi$
$140$	7.21877	+	17.2726i	0.610098	+	1.45980i
$141$	3.68895	−	10.1534i	0.310666	−	0.855072i
$142$	2.71903	−	4.64493i	0.228176	−	0.389794i
$143$			5.80715i			0.485619i
$144$	−11.3671	+	3.84552i	−0.947262	+	0.320460i
$145$	11.6783	−	9.24588i	0.969832	−	0.767829i
$146$	7.76626	+	4.54619i	0.642740	+	0.376245i
$147$	−17.1301	−	6.22373i	−1.41287	−	0.513325i
$148$	−12.5803	−	3.53318i	−1.03409	−	0.290426i
$149$	−0.910619	+	0.910619i	−0.0746008	+	0.0746008i	−0.743423	−	0.668822i	$-0.766799\pi$
$149$	−0.910619	+	0.910619i	−0.0746008	+	0.0746008i	0.668822	+	0.743423i	$0.266799\pi$
$150$	5.45089	+	10.9676i	0.445063	+	0.895499i
$151$	−2.80934			−0.228621			−0.114310	−	0.993445i	$-0.536466\pi$
$151$	−2.80934			−0.228621			−0.114310	+	0.993445i	$0.536466\pi$
$152$	13.0750	−	12.6126i	1.06053	−	1.02302i
$153$	−0.721795	−	0.604248i	−0.0583536	−	0.0488506i
$154$	−7.90068	+	2.06626i	−0.636655	+	0.166504i
$155$	12.3017	+	1.43007i	0.988097	+	0.114866i
$156$	−8.50021	+	11.8491i	−0.680562	+	0.948686i
$157$	−1.51250	−	1.51250i	−0.120710	−	0.120710i	0.644171	−	0.764881i	$-0.277202\pi$
$157$	−1.51250	−	1.51250i	−0.120710	−	0.120710i	−0.764881	+	0.644171i	$0.777202\pi$
$158$	−1.59035	+	2.71679i	−0.126521	+	0.216136i
$159$	−8.09802	−	17.3403i	−0.642215	−	1.37517i
$160$	4.66680	+	11.7567i	0.368943	+	0.929452i
$161$			1.56862i			0.123625i
$162$	4.39749	−	11.9441i	0.345499	−	0.938419i
$163$	−4.92406	+	4.92406i	−0.385682	+	0.385682i	−0.873144	−	0.487462i	$-0.837923\pi$
$163$	−4.92406	+	4.92406i	−0.385682	+	0.385682i	0.487462	+	0.873144i	$0.337923\pi$
$164$	3.82977	+	6.82108i	0.299055	+	0.532637i
$165$	−5.06952	+	1.68660i	−0.394661	+	0.131302i
$166$	−1.96663	−	7.51973i	−0.152640	−	0.583644i
$167$	−14.9625			−1.15783			−0.578917	−	0.815387i	$-0.696524\pi$
$167$	−14.9625			−1.15783			−0.578917	+	0.815387i	$0.696524\pi$
$168$	−19.1453	−	7.34856i	−1.47709	−	0.566953i
$169$			4.72121i			0.363170i
$170$	−0.596799	+	0.792710i	−0.0457724	+	0.0607981i
$171$	1.70141	+	19.1936i	0.130110	+	1.46777i
$172$	5.15238	−	18.3455i	0.392865	−	1.39883i
$173$	−3.43166	+	3.43166i	−0.260904	+	0.260904i	−0.825421	−	0.564517i	$-0.809062\pi$
$173$	−3.43166	+	3.43166i	−0.260904	+	0.260904i	0.564517	+	0.825421i	$0.309062\pi$
$174$	−1.51029	+	16.2469i	−0.114495	+	1.23168i
$175$	−4.80134	+	20.3719i	−0.362947	+	1.53997i
$176$	−5.36265	+	1.29984i	−0.404225	+	0.0979792i
$177$	−0.747203	−	1.59999i	−0.0561632	−	0.120262i
$178$	−0.487600	−	0.285430i	−0.0365472	−	0.0213939i
$179$	0.917781	−	0.917781i	0.0685982	−	0.0685982i	−0.671975	−	0.740574i	$-0.734554\pi$
$179$	0.917781	−	0.917781i	0.0685982	−	0.0685982i	0.740574	+	0.671975i	$0.234554\pi$
$180$	−12.8128	−	3.97911i	−0.955006	−	0.296585i
$181$	1.12485	+	1.12485i	0.0836095	+	0.0836095i	0.747675	−	0.664065i	$-0.231170\pi$
$181$	1.12485	+	1.12485i	0.0836095	+	0.0836095i	−0.664065	+	0.747675i	$0.731170\pi$
$182$	−24.1099	+	6.30543i	−1.78714	+	0.467390i
$183$	7.11343	−	3.32202i	0.525840	−	0.245571i
$184$	−0.0190753	+	1.05972i	−0.00140625	+	0.0781239i
$185$	−9.06839	−	11.4541i	−0.666721	−	0.842124i
$186$	−10.4398	+	8.66392i	−0.765481	+	0.635269i
$187$	−0.306071	−	0.306071i	−0.0223821	−	0.0223821i
$188$	10.8768	−	6.10693i	0.793276	−	0.445393i
$189$	18.8183	−	10.9080i	1.36883	−	0.793437i
$190$	20.1123	−	2.83568i	1.45910	−	0.205722i
$191$	17.7963			1.28769			0.643847	−	0.765154i	$-0.277337\pi$
$191$	17.7963			1.28769			0.643847	+	0.765154i	$0.277337\pi$
$192$	−12.8448	−	5.19734i	−0.926990	−	0.375085i
$193$			12.0738i			0.869092i	0.900650	+	0.434546i	$0.143091\pi$
$193$			12.0738i			0.869092i	−0.900650	+	0.434546i	$0.856909\pi$
$194$	0.0452307	−	0.0772675i	0.00324737	−	0.00554749i
$195$	−15.4702	+	5.14686i	−1.10785	+	0.368574i
$196$	−10.3032	−	18.3507i	−0.735941	−	1.31076i
$197$	15.7762	+	15.7762i	1.12401	+	1.12401i	0.991133	+	0.132874i	$0.0424206\pi$
$197$	15.7762	+	15.7762i	1.12401	+	1.12401i	0.132874	+	0.991133i	$0.457579\pi$
$198$	2.49915	−	5.29224i	0.177607	−	0.376103i
$199$	−24.3324			−1.72488			−0.862440	−	0.506159i	$-0.831065\pi$
$199$	−24.3324			−1.72488			−0.862440	+	0.506159i	$0.831065\pi$
$200$	−3.49141	+	13.7044i	−0.246880	+	0.969046i
$201$	3.53761	−	1.65209i	0.249524	−	0.116529i
$202$	18.7945	−	4.91531i	1.32238	−	0.345840i
$203$	−19.7173	+	19.7173i	−1.38389	+	1.38389i
$204$	−0.176506	−	1.07253i	−0.0123579	−	0.0750920i
$205$	−1.00992	+	8.68751i	−0.0705360	+	0.606762i
$206$	6.16523	−	10.5321i	0.429552	−	0.733804i
$207$	−0.862008	−	0.721627i	−0.0599137	−	0.0501565i
$208$	−16.3648	+	3.96662i	−1.13469	+	0.275036i
$209$			8.86037i			0.612884i
$210$	−12.5069	−	19.2161i	−0.863055	−	1.32603i
$211$	−11.4688	−	11.4688i	−0.789548	−	0.789548i	0.191872	−	0.981420i	$-0.438544\pi$
$211$	−11.4688	−	11.4688i	−0.789548	−	0.789548i	−0.981420	+	0.191872i	$0.938544\pi$
$212$	5.97527	−	21.2755i	0.410383	−	1.46121i
$213$	−2.25100	+	6.19562i	−0.154236	+	0.424517i
$214$	−8.40756	+	2.19882i	−0.574729	+	0.150309i
$215$	16.7033	−	13.2243i	1.13916	−	0.901887i
$216$	12.8458	−	7.14032i	0.874049	−	0.485838i
$217$	−23.1843			−1.57386
$218$	−0.284454	+	0.0743932i	−0.0192657	+	0.00503854i
$219$	−10.3590	−	3.76364i	−0.699996	−	0.254323i
$220$	−5.70709	−	2.34278i	−0.384772	−	0.157950i
$221$	−0.934012	−	0.934012i	−0.0628285	−	0.0628285i
$222$	15.9350	+	1.48130i	1.06949	+	0.0994183i
$223$	2.46705			0.165206			0.0826031	−	0.996583i	$-0.473677\pi$
$223$	2.46705			0.165206			0.0826031	+	0.996583i	$0.473677\pi$
$224$	−11.2194	−	20.8530i	−0.749628	−	1.39330i
$225$	−8.98619	−	12.0103i	−0.599080	−	0.800690i
$226$	8.34682	+	4.88604i	0.555222	+	0.325014i
$227$	0.313124	+	0.313124i	0.0207828	+	0.0207828i	0.717422	−	0.696639i	$-0.245322\pi$
$227$	0.313124	+	0.313124i	0.0207828	+	0.0207828i	−0.696639	+	0.717422i	$0.745322\pi$
$228$	−12.9694	+	18.0790i	−0.858916	+	1.19731i
$229$	20.3545	+	20.3545i	1.34506	+	1.34506i	0.890937	+	0.454128i	$0.150049\pi$
$229$	20.3545	+	20.3545i	1.34506	+	1.34506i	0.454128	+	0.890937i	$0.349951\pi$
$230$	−0.712731	+	0.946699i	−0.0469961	+	0.0624235i
$231$	9.06225	−	4.23213i	0.596252	−	0.278454i
$232$	−13.5604	+	13.0808i	−0.890282	+	0.858798i
$233$			12.3539i			0.809332i	0.914465	+	0.404666i	$0.132612\pi$
$233$			12.3539i			0.809332i	−0.914465	+	0.404666i	$0.867388\pi$
$234$	7.62644	−	16.1499i	0.498556	−	1.05575i
$235$	13.8531	+	1.61042i	0.903673	+	0.105052i
$236$	0.551337	−	1.96309i	0.0358890	−	0.127786i
$237$	1.31660	−	3.62378i	0.0855221	−	0.235390i
$238$	0.938398	−	1.60307i	0.0608273	−	0.103911i
$239$	18.0079			1.16483			0.582416	−	0.812891i	$-0.302108\pi$
$239$	18.0079			1.16483			0.582416	+	0.812891i	$0.302108\pi$
$240$	−8.21567	−	13.1340i	−0.530319	−	0.847798i
$241$	15.6851			1.01037			0.505184	−	0.863011i	$-0.331424\pi$
$241$	15.6851			1.01037			0.505184	+	0.863011i	$0.331424\pi$
$242$	−6.49929	+	11.1027i	−0.417791	+	0.713711i
$243$	−2.66287	+	15.3593i	−0.170823	+	0.985302i
$244$	8.72777	+	2.45121i	0.558738	+	0.156922i
$245$	2.71698	−	23.3719i	0.173581	−	1.49318i
$246$	−6.11850	−	7.37261i	−0.390101	−	0.470061i
$247$			27.0385i			1.72042i
$248$	−15.6628	−	0.281935i	−0.994590	−	0.0179029i
$249$	4.02806	+	8.62529i	0.255268	+	0.546605i
$250$	−12.1540	+	10.1133i	−0.768689	+	0.639622i
$251$	−17.8578	−	17.8578i	−1.12717	−	1.12717i	−0.990635	−	0.136539i	$-0.956402\pi$
$251$	−17.8578	−	17.8578i	−1.12717	−	1.12717i	−0.136539	−	0.990635i	$-0.543598\pi$
$252$	24.6857	+	4.62950i	1.55505	+	0.291631i
$253$	−0.365527	−	0.365527i	−0.0229805	−	0.0229805i
$254$	−4.77897	−	2.79750i	−0.299859	−	0.175531i
$255$	0.544102	−	1.08664i	0.0340730	−	0.0680482i
$256$	−7.32600	−	14.2243i	−0.457875	−	0.889017i
$257$	24.6791			1.53944			0.769721	−	0.638380i	$-0.220395\pi$
$257$	24.6791			1.53944			0.769721	+	0.638380i	$0.220395\pi$
$258$	−2.16015	+	23.2377i	−0.134485	+	1.44672i
$259$	19.3388	+	19.3388i	1.20166	+	1.20166i
$260$	−17.4159	−	7.14928i	−1.08009	−	0.443380i
$261$	−1.76457	−	19.9061i	−0.109224	−	1.23215i
$262$	−26.1877	+	6.84886i	−1.61788	+	0.423124i
$263$	6.88949			0.424824			0.212412	−	0.977180i	$-0.431868\pi$
$263$	6.88949			0.424824			0.212412	+	0.977180i	$0.431868\pi$
$264$	6.17372	−	2.74893i	0.379966	−	0.169185i
$265$	19.3710	−	15.3363i	1.18995	−	0.942102i
$266$	−36.7861	+	9.62063i	−2.25550	+	0.589879i
$267$	0.650384	+	0.236298i	0.0398029	+	0.0144612i
$268$	4.34044	+	1.21902i	0.265135	+	0.0744635i
$269$	16.2552	+	16.2552i	0.991098	+	0.991098i	0.999961	−	0.00886261i	$-0.00282109\pi$
$269$	16.2552	+	16.2552i	0.991098	+	0.991098i	−0.00886261	+	0.999961i	$0.502821\pi$
$270$	16.3135	+	1.96722i	0.992808	+	0.119721i
$271$		−	4.62155i		−	0.280739i	−0.990099	−	0.140370i	$-0.955171\pi$
$271$		−	4.62155i		−	0.280739i	0.990099	−	0.140370i	$-0.0448291\pi$
$272$	0.653455	−	1.07158i	0.0396215	−	0.0649743i
$273$	27.6545	−	12.9148i	1.67373	−	0.781641i
$274$	3.62778	−	6.19734i	0.219162	−	0.374395i
$275$	−3.62832	−	5.86598i	−0.218796	−	0.353732i
$276$	−0.210793	−	1.28087i	−0.0126882	−	0.0770995i
$277$	9.65538	−	9.65538i	0.580136	−	0.580136i	−0.354805	−	0.934940i	$-0.615453\pi$
$277$	9.65538	−	9.65538i	0.580136	−	0.580136i	0.934940	+	0.354805i	$0.115453\pi$
$278$	15.4413	−	4.03834i	0.926105	−	0.242203i
$279$	10.6657	−	12.7405i	0.638539	−	0.762756i
$280$	3.52987	−	26.2382i	0.210950	−	1.56803i
$281$	9.30710			0.555215			0.277607	−	0.960695i	$-0.410459\pi$
$281$	9.30710			0.555215			0.277607	+	0.960695i	$0.410459\pi$
$282$	−11.7563	+	9.75651i	−0.700079	+	0.580992i
$283$	−6.44536	−	6.44536i	−0.383137	−	0.383137i	0.489094	−	0.872231i	$-0.337327\pi$
$283$	−6.44536	−	6.44536i	−0.383137	−	0.383137i	−0.872231	+	0.489094i	$0.837327\pi$
$284$	−6.63706	+	3.72645i	−0.393837	+	0.221124i
$285$	−23.6040	+	7.85291i	−1.39818	+	0.465167i
$286$	4.14887	−	7.08752i	0.245328	−	0.419094i
$287$		−	16.3729i		−	0.966460i
$288$	16.6208	+	3.42778i	0.979389	+	0.201984i
$289$	−16.9015			−0.994208
$290$	−20.8588	+	2.94094i	−1.22487	+	0.172698i
$291$	−0.0374450	+	0.103063i	−0.00219506	+	0.00604167i
$292$	−6.23058	−	11.0971i	−0.364617	−	0.649407i
$293$	−6.80859	−	6.80859i	−0.397762	−	0.397762i	0.479681	−	0.877443i	$-0.340752\pi$
$293$	−6.80859	−	6.80859i	−0.397762	−	0.397762i	−0.877443	+	0.479681i	$0.840752\pi$
$294$	16.4605	+	19.8344i	0.959996	+	1.15677i
$295$	1.78736	−	1.41508i	0.104064	−	0.0823891i
$296$	12.8297	+	13.3000i	0.745711	+	0.773049i
$297$	−1.84330	+	6.92695i	−0.106959	+	0.401942i
$298$	1.76198	−	0.460809i	0.102069	−	0.0266939i
$299$	−1.11545	−	1.11545i	−0.0645081	−	0.0645081i
$300$	1.18299	−	17.2801i	0.0683000	−	0.997665i
$301$	−28.2014	+	28.2014i	−1.62550	+	1.62550i
$302$	3.42874	+	2.00711i	0.197302	+	0.115496i
$303$	−21.5577	+	10.0676i	−1.23846	+	0.578367i
$304$	−24.9688	+	6.05214i	−1.43206	+	0.347114i
$305$	6.29135	+	7.94650i	0.360242	+	0.455015i
$306$	0.449236	+	1.25315i	0.0256811	+	0.0716380i
$307$	22.8375	−	22.8375i	1.30340	−	1.30340i	0.377319	−	0.926083i	$-0.376846\pi$
$307$	22.8375	−	22.8375i	1.30340	−	1.30340i	0.926083	−	0.377319i	$-0.123154\pi$
$308$	11.1189	+	3.12275i	0.633555	+	0.177935i
$309$	−5.10399	+	14.0482i	−0.290356	+	0.799172i
$310$	−13.9923	−	10.5342i	−0.794709	−	0.598304i
$311$			12.6770i			0.718847i	0.933175	+	0.359424i	$0.117027\pi$
$311$			12.6770i			0.718847i	−0.933175	+	0.359424i	$0.882973\pi$
$312$	18.8398	−	8.38868i	1.06660	−	0.474915i
$313$	−2.60725			−0.147370			−0.0736852	−	0.997282i	$-0.523476\pi$
$313$	−2.60725			−0.147370			−0.0736852	+	0.997282i	$0.523476\pi$
$314$	0.765383	+	2.92657i	0.0431930	+	0.165156i
$315$	19.3062	+	20.3909i	1.08778	+	1.14890i
$316$	3.88197	−	2.17958i	0.218378	−	0.122611i
$317$	−21.7776	+	21.7776i	−1.22315	+	1.22315i	−0.256644	+	0.966506i	$0.582617\pi$
$317$	−21.7776	+	21.7776i	−1.22315	+	1.22315i	−0.966506	+	0.256644i	$0.917383\pi$
$318$	−2.50515	+	26.9491i	−0.140482	+	1.51123i
$319$		−	9.18926i		−	0.514500i
$320$	2.70377	−	17.6830i	0.151146	−	0.988512i
$321$	9.64366	−	4.50365i	0.538256	−	0.251369i
$322$	1.12069	−	1.91447i	0.0624535	−	0.106689i
$323$	−1.42509	−	1.42509i	−0.0792939	−	0.0792939i
$324$	−13.9004	+	11.4358i	−0.772246	+	0.635323i
$325$	−11.0722	−	17.9007i	−0.614177	−	0.992953i
$326$	9.52768	−	2.49177i	0.527689	−	0.138006i
$327$	0.326275	−	0.152373i	0.0180431	−	0.00842622i
$328$	0.199103	−	11.0611i	0.0109937	−	0.610750i
$329$	−26.1081			−1.43938
$330$	7.39223	+	1.56341i	0.406929	+	0.0860630i
$331$	5.38860	−	5.38860i	0.296184	−	0.296184i	−0.543333	−	0.839517i	$-0.682838\pi$
$331$	5.38860	−	5.38860i	0.296184	−	0.296184i	0.839517	+	0.543333i	$0.182838\pi$
$332$	−2.97218	+	10.5827i	−0.163119	+	0.580802i
$333$	−19.5239	+	1.73069i	−1.06990	+	0.0948413i
$334$	18.2614	+	10.6898i	0.999222	+	0.584922i
$335$	3.12878	+	3.95190i	0.170943	+	0.215916i
$336$	18.1163	+	22.6470i	0.988326	+	1.23549i
$337$			1.17400i			0.0639519i	0.999489	+	0.0319759i	$0.0101800\pi$
$337$			1.17400i			0.0639519i	−0.999489	+	0.0319759i	$0.989820\pi$
$338$	3.37303	−	5.76215i	0.183469	−	0.313420i
$339$	−11.1334	−	4.04499i	−0.604682	−	0.219694i
$340$	1.29473	−	0.541109i	0.0702164	−	0.0293458i
$341$	5.40252	−	5.40252i	0.292563	−	0.292563i
$342$	11.6362	−	24.6410i	0.629213	−	1.33243i
$343$			14.7457i			0.796192i
$344$	−19.3952	+	18.7093i	−1.04572	+	1.00874i
$345$	0.649798	−	1.29773i	0.0349839	−	0.0698674i
$346$	6.63999	−	1.73655i	0.356968	−	0.0933576i
$347$	7.64341	−	7.64341i	0.410320	−	0.410320i	−0.471530	−	0.881850i	$-0.656298\pi$
$347$	7.64341	−	7.64341i	0.410320	−	0.410320i	0.881850	+	0.471530i	$0.156298\pi$
$348$	13.4508	−	18.7500i	0.721037	−	1.00511i
$349$	14.8727	−	14.8727i	0.796117	−	0.796117i	−0.186364	−	0.982481i	$-0.559670\pi$
$349$	14.8727	−	14.8727i	0.796117	−	0.796117i	0.982481	+	0.186364i	$0.0596704\pi$
$350$	20.4144	−	21.4332i	1.09120	−	1.14565i
$351$	−5.62505	+	21.1384i	−0.300243	+	1.12828i
$352$	7.47367	+	2.24487i	0.398348	+	0.119652i
$353$	−15.0672			−0.801944			−0.400972	−	0.916090i	$-0.631328\pi$
$353$	−15.0672			−0.801944			−0.400972	+	0.916090i	$0.631328\pi$
$354$	−0.231150	+	2.48658i	−0.0122855	+	0.132160i
$355$	−8.45314	−	0.982676i	−0.448646	−	0.0521550i
$356$	0.391183	+	0.696724i	0.0207327	+	0.0369263i
$357$	−0.776869	+	2.13824i	−0.0411163	+	0.113168i
$358$	−1.77584	+	0.464433i	−0.0938558	+	0.0245460i
$359$		−	26.7692i		−	1.41282i	−0.707801	−	0.706412i	$-0.750312\pi$
$359$		−	26.7692i		−	1.41282i	0.707801	−	0.706412i	$-0.249688\pi$
$360$	12.7949	+	14.0104i	0.674349	+	0.738413i
$361$			22.2544i			1.17128i
$362$	−0.569218	−	2.17650i	−0.0299174	−	0.114394i
$363$	5.38055	−	14.8094i	0.282406	−	0.777290i
$364$	33.9305	+	9.52943i	1.77844	+	0.499478i
$365$	1.64302	−	14.1335i	0.0859997	−	0.739783i
$366$	−11.0552	−	1.02768i	−0.577864	−	0.0537175i
$367$	8.45642			0.441421			0.220711	−	0.975339i	$-0.429162\pi$
$367$	8.45642			0.441421			0.220711	+	0.975339i	$0.429162\pi$
$368$	0.780393	−	1.27975i	0.0406808	−	0.0667113i
$369$	8.99742	+	7.53216i	0.468387	+	0.392109i
$370$	2.88448	+	20.4584i	0.149957	+	1.06358i
$371$	−32.7055	+	32.7055i	−1.69799	+	1.69799i
$372$	18.9314	−	3.11554i	0.981548	−	0.161533i
$373$	−23.9476	+	23.9476i	−1.23996	+	1.23996i	−0.279944	+	0.960016i	$0.590316\pi$
$373$	−23.9476	+	23.9476i	−1.23996	+	1.23996i	−0.960016	+	0.279944i	$0.909684\pi$
$374$	0.154884	+	0.592224i	0.00800885	+	0.0306232i
$375$	12.4112	−	14.8648i	0.640910	−	0.767616i
$376$	−17.6380	−	0.317489i	−0.909612	−	0.0163732i
$377$		−	28.0421i		−	1.44424i
$378$	−30.7604	−	0.131616i	−1.58215	−	0.00676959i
$379$	−20.3433	+	20.3433i	−1.04497	+	1.04497i	−0.0460265	+	0.998940i	$0.514656\pi$
$379$	−20.3433	+	20.3433i	−1.04497	+	1.04497i	−0.998940	+	0.0460265i	$0.985344\pi$
$380$	−26.5726	−	10.9081i	−1.36314	−	0.559576i
$381$	6.37441	+	2.31596i	0.326571	+	0.118650i
$382$	−21.7200	−	12.7144i	−1.11129	−	0.650526i
$383$			10.1582i			0.519062i	0.965735	+	0.259531i	$0.0835680\pi$
$383$			10.1582i			0.519062i	−0.965735	+	0.259531i	$0.916432\pi$
$384$	11.9636	+	15.5201i	0.610514	+	0.792006i
$385$	8.01495	+	10.1235i	0.408479	+	0.515944i
$386$	8.62603	−	14.7358i	0.439053	−	0.750035i
$387$	−2.52384	−	28.4714i	−0.128294	−	1.44728i
$388$	−0.110406	+	0.0619889i	−0.00560503	+	0.00314701i
$389$	−8.96467	+	8.96467i	−0.454527	+	0.454527i	−0.896854	−	0.442327i	$-0.854153\pi$
$389$	−8.96467	+	8.96467i	−0.454527	+	0.454527i	0.442327	+	0.896854i	$0.354153\pi$
$390$	22.5582	+	4.77094i	1.14228	+	0.241586i
$391$	0.117582			0.00594636
$392$	−0.535645	+	29.7576i	−0.0270542	+	1.50299i
$393$	30.0379	−	14.0279i	1.51521	−	0.707613i
$394$	−7.98337	−	30.5257i	−0.402196	−	1.53786i
$395$	4.94419	+	0.574761i	0.248769	+	0.0289194i
$396$	−6.83116	+	4.67358i	−0.343279	+	0.234856i
$397$	24.2782	+	24.2782i	1.21849	+	1.21849i	0.968162	+	0.250326i	$0.0805379\pi$
$397$	24.2782	+	24.2782i	1.21849	+	1.21849i	0.250326	+	0.968162i	$0.419462\pi$
$398$	29.6973	+	17.3841i	1.48859	+	0.871386i
$399$	42.1944	−	19.7050i	2.11236	−	0.986486i
$400$	14.0522	−	14.2315i	0.702609	−	0.711576i
$401$		−	16.0990i		−	0.803945i	−0.915652	−	0.401972i	$-0.868325\pi$
$401$		−	16.0990i		−	0.803945i	0.915652	−	0.401972i	$-0.131675\pi$
$402$	−5.49790	−	0.511078i	−0.274211	−	0.0254903i
$403$	16.4864	−	16.4864i	0.821248	−	0.821248i
$404$	−26.4500	−	7.42854i	−1.31594	−	0.369583i
$405$	−20.0871	+	1.22879i	−0.998134	+	0.0610588i
$406$	38.1515	−	9.97774i	1.89343	−	0.495187i
$407$	−9.01285			−0.446750
$408$	−0.550837	+	1.43510i	−0.0272705	+	0.0710482i
$409$		−	27.3395i		−	1.35185i	−0.736970	−	0.675925i	$-0.763744\pi$
$409$		−	27.3395i		−	1.35185i	0.736970	−	0.675925i	$-0.236256\pi$
$410$	7.43931	−	9.88141i	0.367402	−	0.488008i
$411$	−3.00332	+	8.26630i	−0.148143	+	0.407747i
$412$	−15.0491	+	8.44948i	−0.741416	+	0.416276i
$413$	−3.01773	+	3.01773i	−0.148493	+	0.148493i
$414$	0.536503	+	1.49659i	0.0263677	+	0.0735532i
$415$	−9.63541	+	7.62848i	−0.472984	+	0.374468i
$416$	22.8068	+	6.85048i	1.11819	+	0.335873i
$417$	−17.7114	+	8.27135i	−0.867333	+	0.405050i
$418$	6.33022	−	10.8139i	0.309621	−	0.528925i
$419$	−20.3104	+	20.3104i	−0.992226	+	0.992226i	−0.999970	−	0.00774352i	$-0.997535\pi$
$419$	−20.3104	+	20.3104i	−0.992226	+	0.992226i	0.00774352	+	0.999970i	$0.497535\pi$
$420$	1.53561	+	32.3883i	0.0749303	+	1.58038i
$421$	19.5824	+	19.5824i	0.954387	+	0.954387i	0.999004	−	0.0446175i	$-0.0142069\pi$
$421$	19.5824	+	19.5824i	0.954387	+	0.954387i	−0.0446175	+	0.999004i	$0.514207\pi$
$422$	5.80368	+	22.1913i	0.282519	+	1.08026i
$423$	12.0107	−	14.3472i	0.583982	−	0.697586i
$424$	−22.4928	+	21.6974i	−1.09235	+	1.05372i
$425$	1.52705	+	0.359901i	0.0740726	+	0.0174578i
$426$	7.17371	−	5.95343i	0.347567	−	0.288445i
$427$	−13.4166	−	13.4166i	−0.649277	−	0.649277i
$428$	11.8322	+	3.32309i	0.571931	+	0.160628i
$429$	−3.43471	+	9.45367i	−0.165830	+	0.456427i
$430$	−29.8341	+	4.20639i	−1.43873	+	0.202850i
$431$	−29.2879			−1.41075			−0.705375	−	0.708834i	$-0.749222\pi$
$431$	−29.2879			−1.41075			−0.705375	+	0.708834i	$0.749222\pi$
$432$	−20.7795	−	0.462981i	−0.999752	−	0.0222752i
$433$		−	20.5034i		−	0.985332i	−0.870218	−	0.492666i	$-0.836022\pi$
$433$		−	20.5034i		−	0.985332i	0.870218	−	0.492666i	$-0.163978\pi$
$434$	28.2960	+	16.5639i	1.35825	+	0.795091i
$435$	24.4801	−	8.14441i	1.17373	−	0.390494i
$436$	0.400321	+	0.112431i	0.0191719	+	0.00538446i
$437$	−1.70192	−	1.70192i	−0.0814138	−	0.0814138i
$438$	9.95406	+	11.9944i	0.475623	+	0.573112i
$439$	15.9350			0.760534			0.380267	−	0.924877i	$-0.375832\pi$
$439$	15.9350			0.760534			0.380267	+	0.924877i	$0.375832\pi$
$440$	5.29161	+	6.93670i	0.252268	+	0.330694i
$441$	−24.2056	−	20.2637i	−1.15265	−	0.964937i
$442$	0.472646	+	1.80724i	0.0224815	+	0.0859617i
$443$	6.17870	−	6.17870i	0.293559	−	0.293559i	−0.544926	−	0.838484i	$-0.683442\pi$
$443$	6.17870	−	6.17870i	0.293559	−	0.293559i	0.838484	+	0.544926i	$0.183442\pi$
$444$	−18.3901	−	13.1925i	−0.872755	−	0.626090i
$445$	−0.103156	+	0.887367i	−0.00489008	+	0.0420652i
$446$	−3.01099	−	1.76257i	−0.142575	−	0.0834600i
$447$	−2.02103	+	0.943832i	−0.0955912	+	0.0446417i
$448$	−1.20520	+	33.4663i	−0.0569401	+	1.58114i
$449$		−	37.7180i		−	1.78002i	−0.455937	−	0.890012i	$-0.650696\pi$
$449$		−	37.7180i		−	1.78002i	0.455937	−	0.890012i	$-0.349304\pi$
$450$	2.38678	+	21.0785i	0.112514	+	0.993650i
$451$	3.81528	+	3.81528i	0.179655	+	0.179655i
$452$	−6.69634	−	11.9266i	−0.314969	−	0.560982i
$453$	−4.57342	−	1.66162i	−0.214878	−	0.0780697i
$454$	−0.158453	−	0.605871i	−0.00743657	−	0.0284349i
$455$	24.4586	+	30.8932i	1.14663	+	1.44830i
$456$	28.7452	−	12.7992i	1.34612	−	0.599376i
$457$	15.0222			0.702711			0.351356	−	0.936242i	$-0.385721\pi$
$457$	15.0222			0.702711			0.351356	+	0.936242i	$0.385721\pi$
$458$	−10.3002	−	39.3844i	−0.481296	−	1.84031i
$459$	−0.817645	−	1.41059i	−0.0381644	−	0.0658407i
$460$	1.54624	−	0.646223i	0.0720936	−	0.0301303i
$461$	−2.57111	−	2.57111i	−0.119749	−	0.119749i	0.644693	−	0.764442i	$-0.276985\pi$
$461$	−2.57111	−	2.57111i	−0.119749	−	0.119749i	−0.764442	+	0.644693i	$0.776985\pi$
$462$	−14.0839	−	1.30922i	−0.655243	−	0.0609105i
$463$	16.4245			0.763312			0.381656	−	0.924304i	$-0.375354\pi$
$463$	16.4245			0.763312			0.381656	+	0.924304i	$0.375354\pi$
$464$	25.8956	−	6.27679i	1.20218	−	0.291393i
$465$	19.1805	+	9.60406i	0.889476	+	0.445378i
$466$	8.82615	−	15.0777i	0.408864	−	0.698462i
$467$	−6.12767	−	6.12767i	−0.283555	−	0.283555i	0.550970	−	0.834525i	$-0.314258\pi$
$467$	−6.12767	−	6.12767i	−0.283555	−	0.283555i	−0.834525	+	0.550970i	$0.814258\pi$
$468$	−20.8461	+	14.2620i	−0.963611	+	0.659261i
$469$	−6.67228	−	6.67228i	−0.308097	−	0.308097i
$470$	−15.7568	−	11.8627i	−0.726808	−	0.547185i
$471$	−1.56766	−	3.35683i	−0.0722340	−	0.154675i
$472$	−2.07541	+	2.00201i	−0.0955284	+	0.0921502i
$473$		−	13.1433i		−	0.604328i
$474$	−4.19586	+	3.48212i	−0.192722	+	0.159939i
$475$	−16.8937	−	27.3123i	−0.775134	−	1.25318i
$476$	−2.29059	+	1.28608i	−0.104989	+	0.0589473i
$477$	−2.92692	−	33.0186i	−0.134014	−	1.51182i
$478$	−21.9782	−	12.8656i	−1.00526	−	0.588457i
$479$	−7.10184			−0.324491			−0.162246	−	0.986750i	$-0.551874\pi$
$479$	−7.10184			−0.324491			−0.162246	+	0.986750i	$0.551874\pi$
$480$	0.643567	+	21.8994i	0.0293747	+	0.999568i
$481$	−27.5038			−1.25406
$482$	−19.1434	−	11.2061i	−0.871958	−	0.510425i
$483$	−0.927780	+	2.55361i	−0.0422155	+	0.116193i
$484$	15.8645	−	8.90731i	0.721115	−	0.404878i
$485$	−0.140617	−	0.0163466i	−0.00638507	−	0.000742263i
$486$	14.2233	−	16.8433i	0.645183	−	0.764028i
$487$		−	24.6603i		−	1.11746i	−0.829348	−	0.558732i	$-0.811288\pi$
$487$		−	24.6603i		−	1.11746i	0.829348	−	0.558732i	$-0.188712\pi$
$488$	−8.90082	−	9.22713i	−0.402921	−	0.417693i
$489$	−10.9285	+	5.10365i	−0.494202	+	0.230795i
$490$	−20.0139	+	26.5838i	−0.904135	+	1.20093i
$491$	27.0103	+	27.0103i	1.21896	+	1.21896i	0.967997	+	0.250960i	$0.0807463\pi$
$491$	27.0103	+	27.0103i	1.21896	+	1.21896i	0.250960	+	0.967997i	$0.419254\pi$
$492$	2.20020	+	13.3694i	0.0991928	+	0.602741i
$493$	1.47798	+	1.47798i	0.0665650	+	0.0665650i
$494$	19.3174	−	32.9999i	0.869131	−	1.48474i
$495$	−9.25040	−	0.252754i	−0.415775	−	0.0113605i
$496$	18.9147	+	11.5343i	0.849297	+	0.517904i
$497$	15.9312			0.714610
$498$	1.24609	−	13.4048i	0.0558388	−	0.600684i
$499$	1.14980	+	1.14980i	0.0514722	+	0.0514722i	0.732374	−	0.680902i	$-0.238412\pi$
$499$	1.14980	+	1.14980i	0.0514722	+	0.0514722i	−0.680902	+	0.732374i	$0.738412\pi$
$500$	22.0592	−	3.65975i	0.986515	−	0.163669i
$501$	−24.3580	−	8.84976i	−1.08823	−	0.395378i
$502$	9.03673	+	34.5534i	0.403329	+	1.54219i
$503$	−11.6414			−0.519064			−0.259532	−	0.965735i	$-0.583568\pi$
$503$	−11.6414			−0.519064			−0.259532	+	0.965735i	$0.583568\pi$
$504$	−26.8209	−	23.2867i	−1.19470	−	1.03727i
$505$	−19.0663	−	24.0823i	−0.848440	−	1.07165i
$506$	0.184971	+	0.707267i	0.00822297	+	0.0314419i
$507$	−2.79242	+	7.68583i	−0.124016	+	0.341340i
$508$	3.83399	+	6.82859i	0.170106	+	0.302970i
$509$	17.3227	+	17.3227i	0.767814	+	0.767814i	0.977721	−	0.209907i	$-0.0673162\pi$
$509$	17.3227	+	17.3227i	0.767814	+	0.767814i	−0.209907	+	0.977721i	$0.567316\pi$
$510$	−1.44041	+	0.937496i	−0.0637824	+	0.0415130i
$511$			26.6367i			1.17834i
$512$	−1.22117	+	22.5944i	−0.0539687	+	0.998543i
$513$	−8.58252	+	32.2523i	−0.378927	+	1.42397i
$514$	−30.1204	−	17.6318i	−1.32855	−	0.777706i
$515$	−19.1669	−	2.22815i	−0.844596	−	0.0981842i
$516$	19.2384	−	26.8179i	0.846925	−	1.18059i
$517$	6.08383	−	6.08383i	0.267566	−	0.267566i
$518$	−9.78619	−	37.4191i	−0.429981	−	1.64410i
$519$	−7.61621	+	3.55682i	−0.334315	+	0.156127i
$520$	16.1480	+	21.1682i	0.708135	+	0.928286i
$521$	−32.6757			−1.43155			−0.715775	−	0.698331i	$-0.753927\pi$
$521$	−32.6757			−1.43155			−0.715775	+	0.698331i	$0.753927\pi$
$522$	−12.0681	+	25.5556i	−0.528207	+	1.11854i
$523$	22.2033	+	22.2033i	0.970882	+	0.970882i	0.999588	−	0.0287060i	$-0.00913867\pi$
$523$	22.2033	+	22.2033i	0.970882	+	0.970882i	−0.0287060	+	0.999588i	$0.509139\pi$
$524$	36.8547	+	10.3507i	1.61001	+	0.452173i
$525$	−19.8655	+	30.3242i	−0.867000	+	1.32346i
$526$	−8.40849	−	4.92214i	−0.366627	−	0.214615i
$527$			1.73786i			0.0757026i
$528$	−9.49885	−	1.05575i	−0.413384	−	0.0459456i
$529$	−22.8596			−0.993895
$530$	−34.5989	+	4.87819i	−1.50288	+	0.211895i
$531$	−0.270066	−	3.04662i	−0.0117199	−	0.132212i
$532$	51.7700	+	14.5397i	2.24452	+	0.630376i
$533$	11.6428	+	11.6428i	0.504305	+	0.504305i
$534$	−0.624960	−	0.753059i	−0.0270447	−	0.0325881i
$535$	8.52916	+	10.7730i	0.368748	+	0.465759i
$536$	−4.42650	−	4.58878i	−0.191196	−	0.198205i
$537$	2.03692	−	0.951255i	0.0878997	−	0.0410497i
$538$	−8.22577	−	31.4526i	−0.354638	−	1.35602i
$539$	−10.2642	−	10.2642i	−0.442111	−	0.442111i
$540$	−18.5048	−	14.0560i	−0.796321	−	0.604874i
$541$	−22.0381	+	22.0381i	−0.947491	+	0.947491i	−0.998689	−	0.0511971i	$-0.983696\pi$
$541$	−22.0381	+	22.0381i	−0.947491	+	0.947491i	0.0511971	+	0.998689i	$0.483696\pi$
$542$	−3.30183	+	5.64051i	−0.141826	+	0.242281i
$543$	1.16588	+	2.49649i	0.0500326	+	0.107135i
$544$	−1.56311	+	0.840991i	−0.0670179	+	0.0360572i
$545$	0.288568	+	0.364486i	0.0123609	+	0.0156129i
$546$	−42.9787	−	3.99525i	−1.83932	−	0.170981i
$547$	−19.7700	+	19.7700i	−0.845304	+	0.845304i	−0.989543	−	0.144239i	$-0.953927\pi$
$547$	−19.7700	+	19.7700i	−0.845304	+	0.845304i	0.144239	+	0.989543i	$0.453927\pi$
$548$	−8.85527	+	4.97189i	−0.378279	+	0.212389i
$549$	13.5451	−	1.20070i	0.578089	−	0.0512445i
$550$	0.237391	+	9.75153i	0.0101224	+	0.415807i
$551$		−	42.7857i		−	1.82273i
$552$	−0.657841	+	1.71388i	−0.0279996	+	0.0729476i
$553$	−9.31804			−0.396243
$554$	−18.6824	+	4.88600i	−0.793740	+	0.207586i
$555$	−7.98806	−	24.0102i	−0.339074	−	1.01918i
$556$	−21.7309	−	6.10316i	−0.921596	−	0.258832i
$557$	−14.5534	+	14.5534i	−0.616649	+	0.616649i	−0.944670	−	0.328021i	$-0.893618\pi$
$557$	−14.5534	+	14.5534i	−0.616649	+	0.616649i	0.328021	+	0.944670i	$0.393618\pi$
$558$	−22.1197	+	7.92956i	−0.936400	+	0.335685i
$559$		−	40.1082i		−	1.69640i
$560$	−23.0538	+	29.5014i	−0.974202	+	1.24666i
$561$	−0.317234	−	0.679294i	−0.0133936	−	0.0286798i
$562$	−11.3591	−	6.64938i	−0.479156	−	0.280487i
$563$	−31.4961	−	31.4961i	−1.32740	−	1.32740i	−0.907629	−	0.419774i	$-0.862109\pi$
$563$	−31.4961	−	31.4961i	−1.32740	−	1.32740i	−0.419774	−	0.907629i	$-0.637891\pi$
$564$	21.3188	−	3.50843i	0.897684	−	0.147732i
$565$	1.76585	−	15.1901i	0.0742897	−	0.639052i
$566$	3.26160	+	12.4713i	0.137095	+	0.524207i
$567$	37.0866	−	6.62713i	1.55749	−	0.278313i
$568$	10.7627	+	0.193732i	0.451594	+	0.00812881i
$569$	36.6819			1.53778			0.768892	−	0.639379i	$-0.220808\pi$
$569$	36.6819			1.53778			0.768892	+	0.639379i	$0.220808\pi$
$570$	34.4187	+	7.27934i	1.44164	+	0.304898i
$571$	11.2374	−	11.2374i	0.470269	−	0.470269i	−0.431732	−	0.902002i	$-0.642098\pi$
$571$	11.2374	−	11.2374i	0.470269	−	0.470269i	0.902002	+	0.431732i	$0.142098\pi$
$572$	−10.1272	+	5.68605i	−0.423441	+	0.237746i
$573$	28.9712	+	10.5258i	1.21029	+	0.439723i
$574$	−11.6975	+	19.9828i	−0.488243	+	0.834065i
$575$	1.82368	+	0.429814i	0.0760529	+	0.0179245i
$576$	−17.8364	−	16.0581i	−0.743183	−	0.669088i
$577$			36.2264i			1.50813i	0.656802	+	0.754063i	$0.271909\pi$
$577$			36.2264i			1.50813i	−0.656802	+	0.754063i	$0.728091\pi$
$578$	20.6280	+	12.0752i	0.858012	+	0.502261i
$579$	−7.14120	+	19.6554i	−0.296778	+	0.816849i
$580$	27.5589	+	11.3130i	1.14432	+	0.469748i
$581$	16.2681	−	16.2681i	0.674916	−	0.674916i
$582$	0.119333	−	0.0990343i	0.00494653	−	0.00410510i
$583$		−	15.2424i		−	0.631275i
$584$	−0.323917	+	17.9952i	−0.0134038	+	0.744645i
$585$	−28.2287	−	0.771309i	−1.16711	−	0.0318897i
$586$	3.44541	+	13.1741i	0.142329	+	0.544217i
$587$	−12.0457	+	12.0457i	−0.497178	+	0.497178i	−0.910558	−	0.413381i	$-0.864348\pi$
$587$	−12.0457	+	12.0457i	−0.497178	+	0.497178i	0.413381	+	0.910558i	$0.364348\pi$
$588$	−5.91918	−	35.9676i	−0.244103	−	1.48328i
$589$	25.1545	−	25.1545i	1.03647	−	1.03647i
$590$	−3.19243	+	0.450110i	−0.131430	+	0.0185307i
$591$	16.3516	+	35.0136i	0.672614	+	1.44027i
$592$	−6.15629	−	25.3985i	−0.253022	−	1.04387i
$593$	−12.2879			−0.504605			−0.252303	−	0.967648i	$-0.581188\pi$
$593$	−12.2879			−0.504605			−0.252303	+	0.967648i	$0.581188\pi$
$594$	7.19861	−	7.13727i	0.295363	−	0.292846i
$595$	−2.91736	−	0.339143i	−0.119600	−	0.0139035i
$596$	−2.47968	−	0.696422i	−0.101572	−	0.0285266i
$597$	−39.6116	−	14.3917i	−1.62120	−	0.589014i
$598$	0.564461	+	2.15831i	0.0230825	+	0.0882598i
$599$			26.2095i			1.07089i	0.844569	+	0.535447i	$0.179857\pi$
$599$			26.2095i			1.07089i	−0.844569	+	0.535447i	$0.820143\pi$
$600$	−13.7894	+	20.2448i	−0.562950	+	0.826491i
$601$			25.6918i			1.04799i	0.851721	+	0.523996i	$0.175559\pi$
$601$			25.6918i			1.04799i	−0.851721	+	0.523996i	$0.824441\pi$
$602$	54.5676	−	14.2710i	2.22401	−	0.581643i
$603$	6.73615	−	0.597124i	0.274317	−	0.0243168i
$604$	−2.75075	−	4.89928i	−0.111927	−	0.199349i
$605$	20.2055	+	2.34889i	0.821470	+	0.0954958i
$606$	33.5035	+	3.11444i	1.36098	+	0.126515i
$607$	−8.85963			−0.359601			−0.179801	−	0.983703i	$-0.557545\pi$
$607$	−8.85963			−0.359601			−0.179801	+	0.983703i	$0.557545\pi$
$608$	34.7979	+	10.4522i	1.41124	+	0.423895i
$609$	−43.7606	+	20.4365i	−1.77327	+	0.828128i
$610$	−2.00116	−	14.1933i	−0.0810246	−	0.574672i
$611$	18.5655	−	18.5655i	0.751080	−	0.751080i
$612$	0.347021	−	1.85040i	0.0140275	−	0.0747981i
$613$	9.70021	−	9.70021i	0.391788	−	0.391788i	−0.483536	−	0.875324i	$-0.660648\pi$
$613$	9.70021	−	9.70021i	0.391788	−	0.391788i	0.875324	+	0.483536i	$0.160648\pi$
$614$	−44.1887	+	11.5566i	−1.78331	+	0.466388i
$615$	−6.78243	+	13.5454i	−0.273494	+	0.546202i
$616$	−11.3393	−	11.7550i	−0.456874	−	0.473623i
$617$			22.4614i			0.904261i	0.891952	+	0.452130i	$0.149336\pi$
$617$			22.4614i			0.904261i	−0.891952	+	0.452130i	$0.850664\pi$
$618$	16.2659	−	13.4990i	0.654311	−	0.543010i
$619$	24.1499	−	24.1499i	0.970665	−	0.970665i	−0.0289171	−	0.999582i	$-0.509206\pi$
$619$	24.1499	−	24.1499i	0.970665	−	0.970665i	0.999582	+	0.0289171i	$0.00920588\pi$
$620$	9.55123	+	22.8535i	0.383586	+	0.917818i
$621$	−0.976477	−	1.68461i	−0.0391847	−	0.0676010i
$622$	9.05699	−	15.4720i	0.363152	−	0.620372i
$623$		−	1.67237i		−	0.0670021i
$624$	−28.9869	−	3.22174i	−1.16040	−	0.128973i
$625$	22.3688	+	11.1641i	0.894752	+	0.446564i
$626$	3.18210	+	1.86273i	0.127182	+	0.0744495i
$627$	−5.24058	+	14.4241i	−0.209288	+	0.576043i
$628$	1.15673	−	4.11864i	0.0461584	−	0.164352i
$629$	1.44961	−	1.44961i	0.0577997	−	0.0577997i
$630$	−8.99476	−	38.6798i	−0.358360	−	1.54104i
$631$	−1.52136			−0.0605645			−0.0302823	−	0.999541i	$-0.509641\pi$
$631$	−1.52136			−0.0605645			−0.0302823	+	0.999541i	$0.509641\pi$
$632$	−6.29506	−	0.113313i	−0.250404	−	0.00450734i
$633$	−11.8871	−	25.4539i	−0.472471	−	1.01170i
$634$	42.1379	−	11.0203i	1.67351	−	0.437672i
$635$	−1.01103	+	8.69708i	−0.0401217	+	0.345133i
$636$	22.3110	−	31.1010i	0.884690	−	1.23324i
$637$	−31.3224	−	31.3224i	−1.24104	−	1.24104i
$638$	−6.56519	+	11.2153i	−0.259918	+	0.444018i
$639$	−7.32896	+	8.75469i	−0.289929	+	0.346330i
$640$	−15.9334	+	19.6501i	−0.629823	+	0.776739i
$641$			12.8149i			0.506157i	0.967446	+	0.253078i	$0.0814431\pi$
$641$			12.8149i			0.506157i	−0.967446	+	0.253078i	$0.918557\pi$
$642$	−14.9875	−	1.39322i	−0.591509	−	0.0549859i
$643$	7.79142	−	7.79142i	0.307264	−	0.307264i	−0.536584	−	0.843847i	$-0.680285\pi$
$643$	7.79142	−	7.79142i	0.307264	−	0.307264i	0.843847	+	0.536584i	$0.180285\pi$
$644$	−2.73556	+	1.53591i	−0.107796	+	0.0605233i
$645$	35.0136	−	11.6488i	1.37866	−	0.458672i
$646$	0.721149	+	2.75743i	0.0283732	+	0.108490i
$647$	20.4705			0.804777			0.402389	−	0.915469i	$-0.368180\pi$
$647$	20.4705			0.804777			0.402389	+	0.915469i	$0.368180\pi$
$648$	25.1354	−	4.02615i	0.987413	−	0.158162i
$649$		−	1.40641i		−	0.0552065i
$650$	0.724427	+	29.7580i	0.0284144	+	1.16720i
$651$	−37.7426	−	13.7127i	−1.47925	−	0.537442i
$652$	−13.4086	−	3.76582i	−0.525120	−	0.147481i
$653$	−2.36644	+	2.36644i	−0.0926061	+	0.0926061i	−0.751892	−	0.659286i	$-0.770859\pi$
$653$	−2.36644	+	2.36644i	−0.0926061	+	0.0926061i	0.659286	+	0.751892i	$0.270859\pi$
$654$	−0.507074	−	0.0471370i	−0.0198282	−	0.00184320i
$655$	26.5665	+	33.5557i	1.03804	+	1.31113i
$656$	−8.14555	+	13.3577i	−0.318030	+	0.521529i
$657$	−14.6377	−	12.2539i	−0.571072	−	0.478071i
$658$	31.8644	+	18.6527i	1.24220	+	0.727158i
$659$	14.0445	−	14.0445i	0.547094	−	0.547094i	−0.378505	−	0.925599i	$-0.623562\pi$
$659$	14.0445	−	14.0445i	0.547094	−	0.547094i	0.925599	+	0.378505i	$0.123562\pi$
$660$	−7.90510	−	7.18943i	−0.307706	−	0.279848i
$661$	−13.5921	−	13.5921i	−0.528672	−	0.528672i	0.391504	−	0.920176i	$-0.371955\pi$
$661$	−13.5921	−	13.5921i	−0.528672	−	0.528672i	−0.920176	+	0.391504i	$0.871955\pi$
$662$	−10.4265	+	2.72684i	−0.405238	+	0.105982i
$663$	−0.968078	−	2.07294i	−0.0375970	−	0.0805065i
$664$	11.1882	−	10.7926i	0.434187	−	0.418833i
$665$	37.3181	+	47.1358i	1.44713	+	1.82785i
$666$	25.0650	+	11.8364i	0.971251	+	0.458652i
$667$	1.76509	+	1.76509i	0.0683446	+	0.0683446i
$668$	−14.6505	−	26.0935i	−0.566844	−	1.00959i
$669$	4.01620	+	1.45917i	0.155275	+	0.0564148i
$670$	−0.995205	−	7.05855i	−0.0384481	−	0.272696i
$671$	6.25282			0.241387
$672$	−5.93069	−	40.5832i	−0.228781	−	1.56553i
$673$			0.604185i			0.0232896i	0.999932	+	0.0116448i	$0.00370674\pi$
$673$			0.604185i			0.0232896i	−0.999932	+	0.0116448i	$0.996293\pi$
$674$	0.838755	−	1.43284i	0.0323076	−	0.0551911i
$675$	−7.52527	−	24.8671i	−0.289648	−	0.957133i
$676$	−8.23344	+	4.62276i	−0.316671	+	0.177798i
$677$	12.3653	+	12.3653i	0.475238	+	0.475238i	0.903605	−	0.428367i	$-0.140911\pi$
$677$	12.3653	+	12.3653i	0.475238	+	0.475238i	−0.428367	+	0.903605i	$0.640911\pi$
$678$	10.6982	+	12.8910i	0.410861	+	0.495075i
$679$	0.265012			0.0101702
$680$	−1.96678	−	0.264594i	−0.0754226	−	0.0101467i
$681$	0.324545	+	0.694947i	0.0124366	+	0.0266304i
$682$	−10.4535	+	2.73389i	−0.400284	+	0.104686i
$683$	23.9254	−	23.9254i	0.915480	−	0.915480i	−0.0812166	−	0.996696i	$-0.525881\pi$
$683$	23.9254	−	23.9254i	0.915480	−	0.915480i	0.996696	+	0.0812166i	$0.0258806\pi$
$684$	−31.8063	+	21.7605i	−1.21614	+	0.832033i
$685$	−11.2783	−	1.31110i	−0.430922	−	0.0500947i
$686$	10.5349	−	17.9968i	0.402226	−	0.687122i
$687$	21.0969	+	45.1748i	0.804897	+	1.72352i
$688$	37.0382	−	8.97761i	1.41207	−	0.342268i
$689$		−	46.5139i		−	1.77204i
$690$	−1.72022	+	1.11961i	−0.0654876	+	0.0426228i
$691$	−9.58653	−	9.58653i	−0.364689	−	0.364689i	0.500847	−	0.865536i	$-0.333022\pi$
$691$	−9.58653	−	9.58653i	−0.364689	−	0.364689i	−0.865536	+	0.500847i	$0.833022\pi$
$692$	−9.34464	−	2.62446i	−0.355230	−	0.0997669i
$693$	17.2559	−	1.52964i	0.655497	−	0.0581064i
$694$	−14.7894	+	3.86786i	−0.561398	+	0.146822i
$695$	−15.6646	−	19.7857i	−0.594191	−	0.750513i
$696$	−29.8122	+	13.2743i	−1.13003	+	0.503160i
$697$	−1.22729			−0.0464868
$698$	−28.7775	+	7.52616i	−1.08924	+	0.284869i
$699$	−7.30688	+	20.1114i	−0.276372	+	0.760682i
$700$	−40.2282	+	11.5739i	−1.52048	+	0.437450i
$701$	10.0636	+	10.0636i	0.380097	+	0.380097i	0.871137	−	0.491040i	$-0.163383\pi$
$701$	10.0636	+	10.0636i	0.380097	+	0.380097i	−0.491040	+	0.871137i	$0.663383\pi$
$702$	21.9674	−	21.7802i	0.829107	−	0.822042i
$703$	−41.9644			−1.58272
$704$	−7.51764	−	8.07932i	−0.283332	−	0.304501i
$705$	21.5994	+	10.8152i	0.813479	+	0.407324i
$706$	18.3892	+	10.7646i	0.692086	+	0.405131i
$707$	40.6599	+	40.6599i	1.52917	+	1.52917i
$708$	2.05863	−	2.86969i	0.0773682	−	0.107849i
$709$	8.71875	+	8.71875i	0.327440	+	0.327440i	0.851612	−	0.524173i	$-0.175625\pi$
$709$	8.71875	+	8.71875i	0.327440	+	0.327440i	−0.524173	+	0.851612i	$0.675625\pi$
$710$	9.61483	+	7.23861i	0.360838	+	0.271660i
$711$	4.28666	−	5.12056i	0.160762	−	0.192036i
$712$	0.0203370	−	1.12982i	0.000762161	−	0.0423417i
$713$			2.07546i			0.0777264i
$714$	2.47580	−	2.05466i	0.0926547	−	0.0768937i
$715$	−12.8983	−	1.49943i	−0.482370	−	0.0560755i
$716$	2.49918	+	0.701900i	0.0933989	+	0.0262312i
$717$	29.3156	+	10.6510i	1.09481	+	0.397768i
$718$	−19.1250	+	32.6713i	−0.713740	+	1.21928i
$719$	−2.54190			−0.0947970			−0.0473985	−	0.998876i	$-0.515093\pi$
$719$	−2.54190			−0.0947970			−0.0473985	+	0.998876i	$0.515093\pi$
$720$	−5.60629	−	26.2406i	−0.208934	−	0.977930i
$721$	36.1229			1.34529
$722$	15.8995	−	27.1611i	0.591717	−	1.01083i
$723$	25.5344	+	9.27718i	0.949634	+	0.345022i
$724$	−0.860262	+	3.06305i	−0.0319714	+	0.113837i
$725$	17.5207	+	28.3262i	0.650704	+	1.05201i
$726$	−17.1473	+	14.2305i	−0.636395	+	0.528142i
$727$		−	7.05180i		−	0.261537i	−0.991413	−	0.130768i	$-0.958256\pi$
$727$		−	7.05180i		−	0.261537i	0.991413	−	0.130768i	$-0.0417444\pi$
$728$	−34.6033	−	35.8718i	−1.28248	−	1.32950i
$729$	−13.4194	+	23.4290i	−0.497017	+	0.867741i
$730$	−12.1029	+	16.0759i	−0.447947	+	0.594995i
$731$	2.11394	+	2.11394i	0.0781869	+	0.0781869i
$732$	12.7584	+	9.15255i	0.471565	+	0.338288i
$733$	−15.7665	−	15.7665i	−0.582348	−	0.582348i	0.353200	−	0.935548i	$-0.385094\pi$
$733$	−15.7665	−	15.7665i	−0.582348	−	0.582348i	−0.935548	+	0.353200i	$0.885094\pi$
$734$	−10.3209	−	6.04162i	−0.380951	−	0.223000i
$735$	18.2467	−	36.4409i	0.673038	−	1.34414i
$736$	−1.86676	+	1.00436i	−0.0688096	+	0.0370212i
$737$	3.10961			0.114544
$738$	−5.59989	−	15.6210i	−0.206135	−	0.575017i
$739$	14.0549	+	14.0549i	0.517018	+	0.517018i	0.916668	−	0.399650i	$-0.130868\pi$
$739$	14.0549	+	14.0549i	0.517018	+	0.517018i	−0.399650	+	0.916668i	$0.630868\pi$
$740$	11.0959	−	27.0298i	0.407892	−	0.993637i
$741$	−15.9922	+	44.0168i	−0.587490	+	1.61700i
$742$	63.2826	−	16.5503i	2.32318	−	0.607579i
$743$	−16.0741			−0.589703			−0.294852	−	0.955543i	$-0.595270\pi$
$743$	−16.0741			−0.589703			−0.294852	+	0.955543i	$0.595270\pi$
$744$	−25.3313	−	9.72294i	−0.928690	−	0.356460i
$745$	−1.78746	−	2.25771i	−0.0654875	−	0.0827161i
$746$	46.3368	−	12.1184i	1.69651	−	0.443687i
$747$	1.45589	+	16.4239i	0.0532682	+	0.600918i
$748$	0.234077	−	0.833453i	0.00855869	−	0.0304741i
$749$	−18.1889	−	18.1889i	−0.664607	−	0.664607i
$750$	−25.7676	+	9.27516i	−0.940901	+	0.338681i
$751$		−	24.8503i		−	0.906802i	−0.891307	−	0.453401i	$-0.850211\pi$
$751$		−	24.8503i		−	0.906802i	0.891307	−	0.453401i	$-0.149789\pi$
$752$	21.3000	+	12.9888i	0.776733	+	0.473654i
$753$	−18.5091	−	39.6335i	−0.674509	−	1.44433i
$754$	−20.0344	+	34.2248i	−0.729612	+	1.24640i
$755$	0.725382	−	6.23985i	0.0263993	−	0.227091i
$756$	37.4485	+	22.1372i	1.36199	+	0.805121i
$757$	−22.7349	+	22.7349i	−0.826314	+	0.826314i	−0.987005	−	0.160691i	$-0.948628\pi$
$757$	−22.7349	+	22.7349i	−0.826314	+	0.826314i	0.160691	+	0.987005i	$0.448628\pi$
$758$	39.3628	−	10.2945i	1.42972	−	0.373914i
$759$	−0.378859	−	0.811251i	−0.0137517	−	0.0294465i
$760$	24.6381	+	32.2977i	0.893716	+	1.17156i
$761$	11.9396			0.432809			0.216404	−	0.976304i	$-0.430567\pi$
$761$	11.9396			0.432809			0.216404	+	0.976304i	$0.430567\pi$
$762$	−6.12523	−	7.38073i	−0.221894	−	0.267376i
$763$	−0.615387	−	0.615387i	−0.0222785	−	0.0222785i
$764$	17.4252	+	31.0354i	0.630421	+	1.12282i
$765$	1.52847	−	1.44717i	0.0552620	−	0.0523224i
$766$	7.25748	−	12.3979i	0.262223	−	0.447956i
$767$		−	4.29183i		−	0.154969i
$768$	−3.51312	−	27.4892i	−0.126769	−	0.991932i
$769$	7.36786			0.265692			0.132846	−	0.991137i	$-0.457588\pi$
$769$	7.36786			0.265692			0.132846	+	0.991137i	$0.457588\pi$
$770$	−2.54940	−	18.0818i	−0.0918742	−	0.651623i
$771$	40.1760	+	14.5968i	1.44690	+	0.525690i
$772$	−21.0558	+	11.8220i	−0.757815	+	0.425484i
$773$	18.7360	+	18.7360i	0.673886	+	0.673886i	0.958610	−	0.284723i	$-0.0919017\pi$
$773$	18.7360	+	18.7360i	0.673886	+	0.673886i	−0.284723	+	0.958610i	$0.591902\pi$
$774$	−17.2608	+	36.5519i	−0.620428	+	1.31383i
$775$	−6.35269	+	26.9542i	−0.228195	+	0.968223i
$776$	0.179036	+	0.00322270i	0.00642703	+	0.000115688i
$777$	20.0441	+	42.9205i	0.719080	+	1.53977i
$778$	17.3459	−	4.53647i	0.621882	−	0.162640i
$779$	17.7642	+	17.7642i	0.636468	+	0.636468i
$780$	−24.1233	−	21.9394i	−0.863754	−	0.785556i
$781$	−3.71235	+	3.71235i	−0.132838	+	0.132838i
$782$	−0.143506	−	0.0840052i	−0.00513176	−	0.00300402i
$783$	8.90109	−	33.4495i	0.318099	−	1.19539i
$784$	21.9138	−	35.9359i	0.782637	−	1.28343i
$785$	3.74996	−	2.96889i	0.133842	−	0.105964i
$786$	−46.6828	−	4.33957i	−1.66512	−	0.154787i
$787$	−27.6338	+	27.6338i	−0.985038	+	0.985038i	−0.999890	−	0.0148519i	$-0.995272\pi$
$787$	−27.6338	+	27.6338i	−0.985038	+	0.985038i	0.0148519	+	0.999890i	$0.495272\pi$
$788$	−12.0653	+	42.9597i	−0.429808	+	1.53038i
$789$	11.2156	+	4.07487i	0.399287	+	0.145069i
$790$	−5.62365	−	4.23382i	−0.200081	−	0.150633i
$791$			28.6279i			1.01789i
$792$	11.6763	−	0.823552i	0.414899	−	0.0292636i
$793$	19.0812			0.677594
$794$	−12.2857	−	46.9764i	−0.436004	−	1.66713i
$795$	40.6057	−	13.5093i	1.44013	−	0.479125i
$796$	−23.8250	−	42.4339i	−0.844455	−	1.50403i
$797$	9.09598	−	9.09598i	0.322196	−	0.322196i	−0.527413	−	0.849609i	$-0.676838\pi$
$797$	9.09598	−	9.09598i	0.322196	−	0.322196i	0.849609	+	0.527413i	$0.176838\pi$
$798$	−65.5755	−	6.09582i	−2.32135	−	0.215790i
$799$			1.95702i			0.0692345i
$800$	−27.3180	+	7.32984i	−0.965837	+	0.259149i
$801$	0.919022	+	0.769356i	0.0324720	+	0.0271839i
$802$	−11.5018	+	19.6485i	−0.406142	+	0.693812i
$803$	−6.20701	−	6.20701i	−0.219041	−	0.219041i
$804$	6.34495	+	4.55169i	0.223769	+	0.160526i
$805$	−3.48408	−	0.405024i	−0.122798	−	0.0142752i
$806$	−31.9000	+	8.34278i	−1.12363	+	0.293862i
$807$	16.8481	+	36.0768i	0.593081	+	1.26996i
$808$	26.9745	+	27.9634i	0.948959	+	0.983749i
$809$	21.9660			0.772285			0.386142	−	0.922439i	$-0.373807\pi$
$809$	21.9660			0.772285			0.386142	+	0.922439i	$0.373807\pi$
$810$	25.3938	+	12.8513i	0.892246	+	0.451550i
$811$	−12.7359	+	12.7359i	−0.447217	+	0.447217i	−0.894428	−	0.447211i	$-0.852417\pi$
$811$	−12.7359	+	12.7359i	−0.447217	+	0.447217i	0.447211	+	0.894428i	$0.352417\pi$
$812$	−53.6917	−	15.0794i	−1.88421	−	0.529183i
$813$	2.73347	−	7.52358i	0.0958671	−	0.263864i
$814$	11.0000	+	6.43915i	0.385550	+	0.225692i
$815$	−9.66548	−	12.2083i	−0.338567	−	0.427638i
$816$	1.69758	−	1.35797i	0.0594273	−	0.0475386i
$817$		−	61.1958i		−	2.14097i
$818$	−19.5325	+	33.3673i	−0.682937	+	1.16666i
$819$	52.6584	−	4.66789i	1.84003	−	0.163109i
$820$	−16.1392	+	6.74511i	−0.563606	+	0.235550i
$821$	8.04026	−	8.04026i	0.280607	−	0.280607i	−0.552744	−	0.833351i	$-0.686419\pi$
$821$	8.04026	−	8.04026i	0.280607	−	0.280607i	0.833351	+	0.552744i	$0.186419\pi$
$822$	9.57128	−	7.94316i	0.333837	−	0.277050i
$823$		−	23.5015i		−	0.819210i	−0.912263	−	0.409605i	$-0.865667\pi$
$823$		−	23.5015i		−	0.819210i	0.912263	−	0.409605i	$-0.134333\pi$
$824$	24.4038	+	0.439275i	0.850147	+	0.0153029i
$825$	−2.43716	−	11.6954i	−0.0848509	−	0.407183i
$826$	5.83908	−	1.52709i	0.203167	−	0.0531342i
$827$	0.624561	−	0.624561i	0.0217181	−	0.0217181i	−0.696164	−	0.717882i	$-0.745112\pi$
$827$	0.624561	−	0.624561i	0.0217181	−	0.0217181i	0.717882	+	0.696164i	$0.245112\pi$
$828$	0.414432	−	2.20985i	0.0144025	−	0.0767978i
$829$	10.0700	−	10.0700i	0.349744	−	0.349744i	−0.510270	−	0.860014i	$-0.670455\pi$
$829$	10.0700	−	10.0700i	0.349744	−	0.349744i	0.860014	+	0.510270i	$0.170455\pi$
$830$	17.2099	−	2.42648i	0.597366	−	0.0842243i
$831$	21.4291	−	10.0075i	0.743368	−	0.347158i
$832$	−22.9410	−	24.6550i	−0.795335	−	0.854759i
$833$	3.30175			0.114399
$834$	27.5259	+	2.55877i	0.953143	+	0.0886030i
$835$	3.86338	−	33.2334i	0.133698	−	1.15009i
$836$	−15.4518	+	8.67559i	−0.534412	+	0.300052i
$837$	24.8986	−	14.4324i	0.860622	−	0.498857i
$838$	39.2990	−	10.2778i	1.35756	−	0.355042i
$839$			21.9404i			0.757466i	0.925506	+	0.378733i	$0.123640\pi$
$839$			21.9404i			0.757466i	−0.925506	+	0.378733i	$0.876360\pi$
$840$	21.2653	−	40.6263i	0.733724	−	1.40174i
$841$			15.3739i			0.530135i
$842$	−9.90944	−	37.8904i	−0.341502	−	1.30579i
$843$	15.1513	+	5.50480i	0.521840	+	0.189595i
$844$	8.77113	−	31.2305i	0.301915	−	1.07500i
$845$	−10.4863	−	1.21904i	−0.360741	−	0.0419361i
$846$	−24.9091	+	8.92954i	−0.856394	+	0.307004i
$847$	−38.0802			−1.30845
$848$	42.9536	−	10.4114i	1.47503	−	0.357530i
$849$	−6.68044	−	14.3048i	−0.229272	−	0.490940i
$850$	−1.60660	−	1.53024i	−0.0551060	−	0.0524867i
$851$	1.73121	−	1.73121i	0.0593450	−	0.0593450i
$852$	−13.0088	+	2.14085i	−0.445673	+	0.0733442i
$853$	−21.9267	+	21.9267i	−0.750756	+	0.750756i	−0.974620	−	0.223864i	$-0.928133\pi$
$853$	−21.9267	+	21.9267i	−0.750756	+	0.750756i	0.223864	+	0.974620i	$0.428133\pi$
$854$	6.78934	+	25.9602i	0.232326	+	0.888338i
$855$	−43.0704	−	1.17684i	−1.47298	−	0.0402470i
$856$	−12.0668	−	12.5092i	−0.412435	−	0.427555i
$857$		−	42.1646i		−	1.44031i	−0.693811	−	0.720157i	$-0.744070\pi$
$857$		−	42.1646i		−	1.44031i	0.693811	−	0.720157i	$-0.255930\pi$
$858$	10.9461	−	9.08411i	0.373694	−	0.310127i
$859$	−13.5837	+	13.5837i	−0.463471	+	0.463471i	−0.899791	−	0.436320i	$-0.856282\pi$
$859$	−13.5837	+	13.5837i	−0.463471	+	0.463471i	0.436320	+	0.899791i	$0.356282\pi$
$860$	39.4171	+	16.1809i	1.34411	+	0.551764i
$861$	9.68394	−	26.6540i	0.330028	−	0.908365i
$862$	35.7454	+	20.9245i	1.21749	+	0.712692i
$863$			25.6050i			0.871605i	0.900042	+	0.435802i	$0.143535\pi$
$863$			25.6050i			0.871605i	−0.900042	+	0.435802i	$0.856465\pi$
$864$	25.0301	+	15.4108i	0.851543	+	0.524285i
$865$	−6.73602	−	8.50815i	−0.229032	−	0.289286i
$866$	−14.6485	+	25.0240i	−0.497777	+	0.850352i
$867$	−27.5146	−	9.99663i	−0.934445	−	0.339503i
$868$	−22.7008	−	40.4317i	−0.770517	−	1.37234i
$869$	2.17133	−	2.17133i	0.0736574	−	0.0736574i
$870$	−35.6962	−	7.54954i	−1.21022	−	0.255953i
$871$	9.48935			0.321534
$872$	−0.408258	−	0.423225i	−0.0138254	−	0.0143322i
$873$	−0.121916	+	0.145633i	−0.00412623	+	0.00492892i
$874$	0.861237	+	3.29308i	0.0291318	+	0.111390i
$875$	−44.0084	−	15.9244i	−1.48776	−	0.538343i
$876$	−3.57947	−	21.7505i	−0.120939	−	0.734880i
$877$	−8.86408	−	8.86408i	−0.299319	−	0.299319i	0.541428	−	0.840747i	$-0.317884\pi$
$877$	−8.86408	−	8.86408i	−0.299319	−	0.299319i	−0.840747	+	0.541428i	$0.817884\pi$
$878$	−19.4483	−	11.3846i	−0.656349	−	0.384212i
$879$	−7.05691	−	15.1110i	−0.238024	−	0.509680i
$880$	−1.50244	−	12.2467i	−0.0506471	−	0.412835i
$881$			46.3504i			1.56158i	0.624791	+	0.780792i	$0.285184\pi$
$881$			46.3504i			1.56158i	−0.624791	+	0.780792i	$0.714816\pi$
$882$	15.0653	+	42.0249i	0.507275	+	1.41505i
$883$	−18.1184	+	18.1184i	−0.609732	+	0.609732i	−0.942876	−	0.333144i	$-0.891891\pi$
$883$	−18.1184	+	18.1184i	−0.609732	+	0.609732i	0.333144	+	0.942876i	$0.391891\pi$
$884$	0.714313	−	2.54338i	0.0240249	−	0.0855432i
$885$	3.74668	−	1.24650i	0.125943	−	0.0419006i
$886$	−11.9553	+	3.12666i	−0.401646	+	0.105042i
$887$	−52.9154			−1.77673			−0.888363	−	0.459141i	$-0.848157\pi$
$887$	−52.9154			−1.77673			−0.888363	+	0.459141i	$0.848157\pi$
$888$	13.0194	+	29.2399i	0.436904	+	0.981226i
$889$		−	16.3909i		−	0.549733i
$890$	0.759872	−	1.00932i	0.0254710	−	0.0338323i
$891$	−7.09780	+	10.1864i	−0.237785	+	0.341256i
$892$	2.41561	+	4.30236i	0.0808805	+	0.144054i
$893$	28.3267	−	28.3267i	0.947916	−	0.947916i
$894$	3.14094	+	0.291977i	0.105049	+	0.00976518i
$895$	1.80152	+	2.27547i	0.0602181	+	0.0760605i
$896$	25.3807	−	39.9840i	0.847908	−	1.33577i
$897$	−1.15613	−	2.47563i	−0.0386022	−	0.0826588i
$898$	−26.9473	+	46.0341i	−0.899244	+	1.53618i
$899$	−26.0882	+	26.0882i	−0.870090	+	0.870090i
$900$	12.1463	−	27.4311i	0.404878	−	0.914371i
$901$	2.45156	+	2.45156i	0.0816733	+	0.0816733i
$902$	−1.93068	−	7.38228i	−0.0642847	−	0.245803i
$903$	−62.5902	+	29.2300i	−2.08287	+	0.972714i
$904$	−0.348132	+	19.3404i	−0.0115787	+	0.643251i
$905$	−2.78886	+	2.20798i	−0.0927048	+	0.0733956i
$906$	4.39464	+	5.29542i	0.146002	+	0.175928i
$907$	17.7862	+	17.7862i	0.590581	+	0.590581i	0.937788	−	0.347207i	$-0.112870\pi$
$907$	17.7862	+	17.7862i	0.590581	+	0.590581i	−0.347207	+	0.937788i	$0.612870\pi$
$908$	−0.239471	+	0.852659i	−0.00794712	+	0.0282965i
$909$	−41.0491	+	3.63879i	−1.36151	+	0.120691i
$910$	−7.77981	−	55.1788i	−0.257898	−	1.82916i
$911$	−60.0703			−1.99022			−0.995108	−	0.0987897i	$-0.968503\pi$
$911$	−60.0703			−1.99022			−0.995108	+	0.0987897i	$0.968503\pi$
$912$	−44.2272	−	4.91563i	−1.46451	−	0.162773i
$913$			7.58176i			0.250920i
$914$	−18.3344	−	10.7325i	−0.606447	−	0.355000i
$915$	5.54185	+	16.6575i	0.183208	+	0.550679i
$916$	−15.5667	+	55.4268i	−0.514338	+	1.83135i
$917$	−56.6544	−	56.6544i	−1.87089	−	1.87089i
$918$	−0.00986574	+	2.30576i	−0.000325618	+	0.0761014i
$919$	9.57060			0.315705			0.157853	−	0.987463i	$-0.449543\pi$
$919$	9.57060			0.315705			0.157853	+	0.987463i	$0.449543\pi$
$920$	−2.34884	−	0.315993i	−0.0774390	−	0.0104180i
$921$	50.6854	−	23.6704i	1.67014	−	0.779966i
$922$	1.30108	+	4.97490i	0.0428489	+	0.163840i
$923$	−11.3287	+	11.3287i	−0.372888	+	0.372888i
$924$	16.2538	+	11.6600i	0.534710	+	0.383586i
$925$	27.7824	−	17.1844i	0.913479	−	0.565019i
$926$	−20.0458	−	11.7344i	−0.658746	−	0.385615i
$927$	−16.6179	+	19.8507i	−0.545805	+	0.651982i
$928$	−36.0895	−	10.8402i	−1.18470	−	0.355848i
$929$			50.9760i			1.67247i	0.548373	+	0.836234i	$0.315247\pi$
$929$			50.9760i			1.67247i	−0.548373	+	0.836234i	$0.684753\pi$
$930$	−16.5479	−	25.4249i	−0.542628	−	0.833717i
$931$	−47.7908	−	47.7908i	−1.56628	−	1.56628i
$932$	−21.5443	+	12.0963i	−0.705707	+	0.396227i
$933$	−7.49798	+	20.6373i	−0.245473	+	0.675636i
$934$	3.10084	+	11.8566i	0.101463	+	0.387959i
$935$	0.758846	−	0.600789i	0.0248169	−	0.0196479i
$936$	35.6316	−	2.51317i	1.16466	−	0.0821454i
$937$	17.6069			0.575193			0.287597	−	0.957752i	$-0.407144\pi$
$937$	17.6069			0.575193			0.287597	+	0.957752i	$0.407144\pi$
$938$	3.37643	+	12.9103i	0.110244	+	0.421538i
$939$	−4.24443	−	1.54209i	−0.138512	−	0.0503242i
$940$	10.7557	+	25.7355i	0.350813	+	0.839400i
$941$	−39.2607	−	39.2607i	−1.27986	−	1.27986i	−0.940744	−	0.339118i	$-0.889872\pi$
$941$	−39.2607	−	39.2607i	−1.27986	−	1.27986i	−0.339118	−	0.940744i	$-0.610128\pi$
$942$	−0.484961	+	5.21695i	−0.0158009	+	0.169978i
$943$	−1.46570			−0.0477296
$944$	3.96332	−	0.960661i	0.128995	−	0.0312668i
$945$	19.3688	+	44.6139i	0.630068	+	1.45129i
$946$	−9.39010	+	16.0411i	−0.305298	+	0.521541i
$947$	39.2434	+	39.2434i	1.27524	+	1.27524i	0.943302	+	0.331937i	$0.107702\pi$
$947$	39.2434	+	39.2434i	1.27524	+	1.27524i	0.331937	+	0.943302i	$0.392298\pi$
$948$	7.60874	−	1.25217i	0.247120	−	0.0406685i
$949$	−18.9414	−	18.9414i	−0.614865	−	0.614865i
$950$	1.10531	+	45.4037i	0.0358609	+	1.47309i
$951$	−48.3331	+	22.5718i	−1.56731	+	0.731942i
$952$	3.71445	+	0.0668611i	0.120386	+	0.00216698i
$953$			41.3618i			1.33984i	0.742433	+	0.669921i	$0.233672\pi$
$953$			41.3618i			1.33984i	−0.742433	+	0.669921i	$0.766328\pi$
$954$	−20.0176	+	42.3896i	−0.648093	+	1.37241i
$955$	−4.59507	+	39.5275i	−0.148693	+	1.27908i
$956$	17.6323	+	31.4044i	0.570270	+	1.01569i
$957$	5.43510	−	14.9595i	0.175692	−	0.483572i
$958$	8.66766	+	5.07385i	0.280039	+	0.163929i
$959$	21.2556			0.686380
$960$	14.8604	−	27.1876i	0.479618	−	0.877477i
$961$	0.324597			0.0104709
$962$	33.5678	+	19.6498i	1.08227	+	0.633536i
$963$	18.3630	−	1.62778i	0.591739	−	0.0524545i
$964$	15.3580	+	27.3537i	0.494649	+	0.881004i
$965$	−26.8173	−	3.11750i	−0.863278	−	0.100356i
$966$	2.95675	−	2.45379i	0.0951317	−	0.0789494i
$967$			10.8477i			0.348838i	0.984672	+	0.174419i	$0.0558048\pi$
$967$			10.8477i			0.348838i	−0.984672	+	0.174419i	$0.944195\pi$
$968$	−25.7261	−	0.463077i	−0.826868	−	0.0148838i
$969$	−1.47706	−	3.16283i	−0.0474501	−	0.101605i
$970$	0.159941	+	0.120413i	0.00513540	+	0.00386623i
$971$	−8.94529	−	8.94529i	−0.287068	−	0.287068i	0.548852	−	0.835920i	$-0.315065\pi$
$971$	−8.94529	−	8.94529i	−0.287068	−	0.287068i	−0.835920	+	0.548852i	$0.815065\pi$
$972$	−29.3929	+	10.3952i	−0.942776	+	0.333426i
$973$	33.4055	+	33.4055i	1.07093	+	1.07093i
$974$	−17.6183	+	30.0974i	−0.564528	+	0.964383i
$975$	−7.43727	−	35.6900i	−0.238183	−	1.14300i
$976$	4.27103	+	17.6207i	0.136712	+	0.564023i
$977$	−11.4126			−0.365122			−0.182561	−	0.983194i	$-0.558439\pi$
$977$	−11.4126			−0.365122			−0.182561	+	0.983194i	$0.558439\pi$
$978$	16.9842	+	1.57883i	0.543096	+	0.0504855i
$979$	0.389704	+	0.389704i	0.0124550	+	0.0124550i
$980$	43.4191	−	18.1463i	1.38697	−	0.579662i
$981$	0.621278	−	0.0550730i	0.0198359	−	0.00175835i
$982$	−13.6683	−	52.2628i	−0.436172	−	1.66777i
$983$	1.96842			0.0627828			0.0313914	−	0.999507i	$-0.490006\pi$
$983$	1.96842			0.0627828			0.0313914	+	0.999507i	$0.490006\pi$
$984$	6.86638	−	17.8891i	0.218892	−	0.570282i
$985$	−39.1141	+	30.9672i	−1.24628	+	0.986697i
$986$	−0.747917	−	2.85978i	−0.0238185	−	0.0910741i
$987$	−42.5022	−	15.4419i	−1.35286	−	0.491523i
$988$	−47.1530	+	26.4746i	−1.50014	+	0.842269i
$989$	2.52459	+	2.52459i	0.0802772	+	0.0802772i
$990$	11.1094	+	6.91736i	0.353079	+	0.219848i
$991$		−	38.9711i		−	1.23796i	−0.785408	−	0.618979i	$-0.787547\pi$
$991$		−	38.9711i		−	1.23796i	0.785408	−	0.618979i	$-0.212453\pi$
$992$	−14.8445	−	27.5908i	−0.471314	−	0.876010i
$993$	11.9594	−	5.58513i	0.379521	−	0.177239i
$994$	−19.4437	−	11.3819i	−0.616716	−	0.361011i
$995$	6.28272	−	54.0450i	0.199176	−	1.71334i
$996$	−11.0978	+	15.4701i	−0.351647	+	0.490187i
$997$	23.0890	−	23.0890i	0.731236	−	0.731236i	−0.239628	−	0.970865i	$-0.577026\pi$
$997$	23.0890	−	23.0890i	0.731236	−	0.731236i	0.970865	+	0.239628i	$0.0770256\pi$
$998$	−0.581844	−	2.22478i	−0.0184180	−	0.0704241i
$999$	−32.8073	−	8.73021i	−1.03798	−	0.276212i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	240.2.t.b.59.8	yes	80
3.2	odd	2	inner	240.2.t.b.59.34	yes	80
4.3	odd	2		960.2.t.b.719.6		80
5.4	even	2	inner	240.2.t.b.59.33	yes	80
12.11	even	2		960.2.t.b.719.26		80
15.14	odd	2	inner	240.2.t.b.59.7	✓	80
16.3	odd	4	inner	240.2.t.b.179.7	yes	80
16.13	even	4		960.2.t.b.239.15		80
20.19	odd	2		960.2.t.b.719.35		80
48.29	odd	4		960.2.t.b.239.35		80
48.35	even	4	inner	240.2.t.b.179.33	yes	80
60.59	even	2		960.2.t.b.719.15		80
80.19	odd	4	inner	240.2.t.b.179.34	yes	80
80.29	even	4		960.2.t.b.239.26		80
240.29	odd	4		960.2.t.b.239.6		80
240.179	even	4	inner	240.2.t.b.179.8	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
240.2.t.b.59.7	✓	80	15.14	odd	2	inner
240.2.t.b.59.8	yes	80	1.1	even	1	trivial
240.2.t.b.59.33	yes	80	5.4	even	2	inner
240.2.t.b.59.34	yes	80	3.2	odd	2	inner
240.2.t.b.179.7	yes	80	16.3	odd	4	inner
240.2.t.b.179.8	yes	80	240.179	even	4	inner
240.2.t.b.179.33	yes	80	48.35	even	4	inner
240.2.t.b.179.34	yes	80	80.19	odd	4	inner
960.2.t.b.239.6		80	240.29	odd	4
960.2.t.b.239.15		80	16.13	even	4
960.2.t.b.239.26		80	80.29	even	4
960.2.t.b.239.35		80	48.29	odd	4
960.2.t.b.719.6		80	4.3	odd	2
960.2.t.b.719.15		80	60.59	even	2
960.2.t.b.719.26		80	12.11	even	2
960.2.t.b.719.35		80	20.19	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-1.22048 - 0.714442i) q^{2} +(1.62793 + 0.591463i) q^{3} +(0.979146 + 1.74392i) q^{4} +(-0.258204 + 2.22111i) q^{5} +(-1.56430 - 1.88493i) q^{6} -4.18600i q^{7} +(0.0509042 - 2.82797i) q^{8} +(2.30034 + 1.92573i) q^{9} +O(q^{10})\)	\(q+(-1.22048 - 0.714442i) q^{2} +(1.62793 + 0.591463i) q^{3} +(0.979146 + 1.74392i) q^{4} +(-0.258204 + 2.22111i) q^{5} +(-1.56430 - 1.88493i) q^{6} -4.18600i q^{7} +(0.0509042 - 2.82797i) q^{8} +(2.30034 + 1.92573i) q^{9} +(1.90199 - 2.52635i) q^{10} +(0.975442 + 0.975442i) q^{11} +(0.562519 + 3.41812i) q^{12} +(2.97668 + 2.97668i) q^{13} +(-2.99066 + 5.10893i) q^{14} +(-1.73404 + 3.46311i) q^{15} +(-2.08255 + 3.41511i) q^{16} -0.313777 q^{17} +(-1.43171 - 3.99377i) q^{18} +(4.54172 + 4.54172i) q^{19} +(-4.12627 + 1.72450i) q^{20} +(2.47586 - 6.81454i) q^{21} +(-0.493612 - 1.88740i) q^{22} -0.374730 q^{23} +(1.75551 - 4.57364i) q^{24} +(-4.86666 - 1.14700i) q^{25} +(-1.50631 - 5.75964i) q^{26} +(2.60582 + 4.49552i) q^{27} +(7.30007 - 4.09871i) q^{28} +(-4.71030 - 4.71030i) q^{29} +(4.59055 - 2.98778i) q^{30} -5.53854i q^{31} +(4.98161 - 2.68022i) q^{32} +(1.01102 + 2.16489i) q^{33} +(0.382959 + 0.224175i) q^{34} +(9.29757 + 1.08084i) q^{35} +(-1.10595 + 5.89719i) q^{36} +(-4.61988 + 4.61988i) q^{37} +(-2.29829 - 8.78787i) q^{38} +(3.08524 + 6.60643i) q^{39} +(6.26809 + 0.843256i) q^{40} +3.91134 q^{41} +(-7.89034 + 6.54815i) q^{42} +(-6.73708 - 6.73708i) q^{43} +(-0.745998 + 2.65620i) q^{44} +(-4.87121 + 4.61209i) q^{45} +(0.457351 + 0.267723i) q^{46} -6.23699i q^{47} +(-5.41016 + 4.32783i) q^{48} -10.5226 q^{49} +(5.12020 + 4.87684i) q^{50} +(-0.510808 - 0.185587i) q^{51} +(-2.27650 + 8.10570i) q^{52} +(-7.81306 - 7.81306i) q^{53} +(0.0314419 - 7.34840i) q^{54} +(-2.41843 + 1.91470i) q^{55} +(-11.8379 - 0.213085i) q^{56} +(4.70737 + 10.0799i) q^{57} +(2.38360 + 9.11407i) q^{58} +(-0.720910 - 0.720910i) q^{59} +(-7.73728 + 0.366845i) q^{60} +(3.20512 - 3.20512i) q^{61} +(-3.95696 + 6.75968i) q^{62} +(8.06109 - 9.62925i) q^{63} +(-7.99482 - 0.287911i) q^{64} +(-7.38012 + 5.84294i) q^{65} +(0.312762 - 3.36453i) q^{66} +(1.59395 - 1.59395i) q^{67} +(-0.307233 - 0.547203i) q^{68} +(-0.610036 - 0.221639i) q^{69} +(-10.5753 - 7.96172i) q^{70} +3.80582i q^{71} +(5.56299 - 6.40727i) q^{72} -6.36328 q^{73} +(8.93910 - 2.33784i) q^{74} +(-7.24420 - 4.74569i) q^{75} +(-3.47341 + 12.3674i) q^{76} +(4.08320 - 4.08320i) q^{77} +(0.954430 - 10.2672i) q^{78} -2.22600i q^{79} +(-7.04762 - 5.50736i) q^{80} +(1.58316 + 8.85966i) q^{81} +(-4.77371 - 2.79442i) q^{82} +(3.88632 + 3.88632i) q^{83} +(14.3083 - 2.35471i) q^{84} +(0.0810184 - 0.696933i) q^{85} +(3.40922 + 13.0357i) q^{86} +(-4.88210 - 10.4540i) q^{87} +(2.80817 - 2.70887i) q^{88} +0.399515 q^{89} +(9.24028 - 2.14877i) q^{90} +(12.4604 - 12.4604i) q^{91} +(-0.366915 - 0.653501i) q^{92} +(3.27584 - 9.01638i) q^{93} +(-4.45597 + 7.61213i) q^{94} +(-11.2603 + 8.91497i) q^{95} +(9.69498 - 1.41679i) q^{96} +0.0633091i q^{97} +(12.8426 + 7.51780i) q^{98} +(0.365419 + 4.12229i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q - 8 q^{4} - 4 q^{6}+O(q^{10}) \) 80 * q - 8 * q^4 - 4 * q^6	\( 80 q - 8 q^{4} - 4 q^{6} + 16 q^{10} - 32 q^{16} + 16 q^{19} + 8 q^{21} - 56 q^{24} + 8 q^{30} - 16 q^{34} - 40 q^{36} - 8 q^{39} - 8 q^{40} - 12 q^{45} - 24 q^{46} - 112 q^{49} + 32 q^{51} + 60 q^{54} - 40 q^{55} + 40 q^{60} + 16 q^{61} - 32 q^{64} - 56 q^{66} - 40 q^{69} + 48 q^{70} - 36 q^{75} - 128 q^{76} + 64 q^{81} + 128 q^{84} - 64 q^{85} + 72 q^{90} + 48 q^{91} + 56 q^{94} - 24 q^{96} - 8 q^{99}+O(q^{100}) \) 80 * q - 8 * q^4 - 4 * q^6 + 16 * q^10 - 32 * q^16 + 16 * q^19 + 8 * q^21 - 56 * q^24 + 8 * q^30 - 16 * q^34 - 40 * q^36 - 8 * q^39 - 8 * q^40 - 12 * q^45 - 24 * q^46 - 112 * q^49 + 32 * q^51 + 60 * q^54 - 40 * q^55 + 40 * q^60 + 16 * q^61 - 32 * q^64 - 56 * q^66 - 40 * q^69 + 48 * q^70 - 36 * q^75 - 128 * q^76 + 64 * q^81 + 128 * q^84 - 64 * q^85 + 72 * q^90 + 48 * q^91 + 56 * q^94 - 24 * q^96 - 8 * q^99

Introduction

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