LMFDB - Embedded newform 572.2.j.a.463.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [572,2,Mod(463,572)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(572, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 0, 1]))

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

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

chi := DirichletCharacter("572.463");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 572 = 2^{2} \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	572.j (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:	$4.56744299562$
Analytic rank:	$0$
Dimension:	$140$
Relative dimension:	$70$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			463.14
Character	$\chi$	$=$	572.463
Dual form			572.2.j.a.551.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.11823 - 0.865774i) q^{2} -0.913063i q^{3} +(0.500870 + 1.93627i) q^{4} +(1.64493 + 1.64493i) q^{5} +(-0.790506 + 1.02101i) q^{6} +(-3.07399 - 3.07399i) q^{7} +(1.11628 - 2.59883i) q^{8} +2.16632 q^{9} +O(q^{10})$	\(q+(-1.11823 - 0.865774i) q^{2} -0.913063i q^{3} +(0.500870 + 1.93627i) q^{4} +(1.64493 + 1.64493i) q^{5} +(-0.790506 + 1.02101i) q^{6} +(-3.07399 - 3.07399i) q^{7} +(1.11628 - 2.59883i) q^{8} +2.16632 q^{9} +(-0.415270 - 3.26355i) q^{10} +(0.707107 + 0.707107i) q^{11} +(1.76793 - 0.457326i) q^{12} +(-2.81599 + 2.25171i) q^{13} +(0.776042 + 6.09881i) q^{14} +(1.50192 - 1.50192i) q^{15} +(-3.49826 + 1.93964i) q^{16} -3.95770i q^{17} +(-2.42244 - 1.87554i) q^{18} +(5.30162 - 5.30162i) q^{19} +(-2.36113 + 4.00892i) q^{20} +(-2.80675 + 2.80675i) q^{21} +(-0.178512 - 1.40290i) q^{22} +2.42028 q^{23} +(-2.37289 - 1.01924i) q^{24} +0.411591i q^{25} +(5.09839 - 0.0799068i) q^{26} -4.71717i q^{27} +(4.41240 - 7.49174i) q^{28} +6.63200 q^{29} +(-2.97982 + 0.379167i) q^{30} +(-4.00610 + 4.00610i) q^{31} +(5.59114 + 0.859747i) q^{32} +(0.645633 - 0.645633i) q^{33} +(-3.42647 + 4.42561i) q^{34} -10.1130i q^{35} +(1.08504 + 4.19457i) q^{36} +(6.40374 - 6.40374i) q^{37} +(-10.5184 + 1.33842i) q^{38} +(2.05595 + 2.57118i) q^{39} +(6.11110 - 2.43868i) q^{40} +(-6.99829 - 6.99829i) q^{41} +(5.56860 - 0.708575i) q^{42} +6.49245 q^{43} +(-1.01498 + 1.72332i) q^{44} +(3.56344 + 3.56344i) q^{45} +(-2.70643 - 2.09542i) q^{46} +(-1.10769 - 1.10769i) q^{47} +(1.77101 + 3.19413i) q^{48} +11.8989i q^{49} +(0.356345 - 0.460253i) q^{50} -3.61363 q^{51} +(-5.77035 - 4.32470i) q^{52} -2.83311 q^{53} +(-4.08401 + 5.27488i) q^{54} +2.32628i q^{55} +(-11.4202 + 4.55733i) q^{56} +(-4.84071 - 4.84071i) q^{57} +(-7.41609 - 5.74181i) q^{58} +(-8.97446 - 8.97446i) q^{59} +(3.66040 + 2.15586i) q^{60} -1.09975 q^{61} +(7.94811 - 1.01136i) q^{62} +(-6.65924 - 6.65924i) q^{63} +(-5.50782 - 5.80206i) q^{64} +(-8.33601 - 0.928214i) q^{65} +(-1.28094 + 0.162993i) q^{66} +(1.12474 - 1.12474i) q^{67} +(7.66316 - 1.98229i) q^{68} -2.20987i q^{69} +(-8.75558 + 11.3087i) q^{70} +(0.767629 - 0.767629i) q^{71} +(2.41822 - 5.62988i) q^{72} +(-3.00424 + 3.00424i) q^{73} +(-12.7050 + 1.61665i) q^{74} +0.375809 q^{75} +(12.9208 + 7.60992i) q^{76} -4.34728i q^{77} +(-0.0729599 - 4.65515i) q^{78} +5.41548i q^{79} +(-8.94496 - 2.56383i) q^{80} +2.19187 q^{81} +(1.76675 + 13.8846i) q^{82} +(-8.49263 + 8.49263i) q^{83} +(-6.84043 - 4.02880i) q^{84} +(6.51014 - 6.51014i) q^{85} +(-7.26004 - 5.62100i) q^{86} -6.05543i q^{87} +(2.62698 - 1.04832i) q^{88} +(5.20790 - 5.20790i) q^{89} +(-0.899605 - 7.06987i) q^{90} +(15.5781 + 1.73462i) q^{91} +(1.21225 + 4.68631i) q^{92} +(3.65782 + 3.65782i) q^{93} +(0.279642 + 2.19767i) q^{94} +17.4416 q^{95} +(0.785003 - 5.10506i) q^{96} +(6.70059 + 6.70059i) q^{97} +(10.3017 - 13.3056i) q^{98} +(1.53182 + 1.53182i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 140 q + 4 q^{5} - 12 q^{6} + 12 q^{8} - 140 q^{9}+O(q^{10}) $ 140 * q + 4 * q^5 - 12 * q^6 + 12 * q^8 - 140 * q^9	$ 140 q + 4 q^{5} - 12 q^{6} + 12 q^{8} - 140 q^{9} + 16 q^{14} - 12 q^{18} - 8 q^{20} - 16 q^{21} - 32 q^{26} - 20 q^{28} + 20 q^{32} - 8 q^{34} + 36 q^{37} - 80 q^{40} - 20 q^{41} - 20 q^{42} - 8 q^{44} - 20 q^{45} + 60 q^{46} + 20 q^{48} + 88 q^{50} - 8 q^{53} + 88 q^{54} - 80 q^{57} - 60 q^{58} + 12 q^{60} - 40 q^{61} - 20 q^{65} - 20 q^{66} - 80 q^{68} - 28 q^{70} + 20 q^{72} + 100 q^{73} - 136 q^{74} - 32 q^{76} - 88 q^{78} - 72 q^{80} + 140 q^{81} + 92 q^{84} + 24 q^{85} - 32 q^{86} - 60 q^{89} - 68 q^{92} - 80 q^{93} + 64 q^{94} + 100 q^{96} - 20 q^{97} + 92 q^{98}+O(q^{100}) $ 140 * q + 4 * q^5 - 12 * q^6 + 12 * q^8 - 140 * q^9 + 16 * q^14 - 12 * q^18 - 8 * q^20 - 16 * q^21 - 32 * q^26 - 20 * q^28 + 20 * q^32 - 8 * q^34 + 36 * q^37 - 80 * q^40 - 20 * q^41 - 20 * q^42 - 8 * q^44 - 20 * q^45 + 60 * q^46 + 20 * q^48 + 88 * q^50 - 8 * q^53 + 88 * q^54 - 80 * q^57 - 60 * q^58 + 12 * q^60 - 40 * q^61 - 20 * q^65 - 20 * q^66 - 80 * q^68 - 28 * q^70 + 20 * q^72 + 100 * q^73 - 136 * q^74 - 32 * q^76 - 88 * q^78 - 72 * q^80 + 140 * q^81 + 92 * q^84 + 24 * q^85 - 32 * q^86 - 60 * q^89 - 68 * q^92 - 80 * q^93 + 64 * q^94 + 100 * q^96 - 20 * q^97 + 92 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/572\mathbb{Z}\right)^\times$.

$n$	$287$	$353$	$365$
$\chi(n)$	$-1$	$e\left(\frac{1}{4}\right)$	$1$

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 $

$2$	−1.11823	−	0.865774i	−0.790707	−	0.612195i
$2$	−1.11823	−	0.865774i	−0.790707	−	0.612195i
$3$		−	0.913063i		−	0.527157i	−0.964638	−	0.263579i	$-0.915097\pi$
$3$		−	0.913063i		−	0.527157i	0.964638	−	0.263579i	$-0.0849028\pi$
$4$	0.500870	+	1.93627i	0.250435	+	0.968133i
$5$	1.64493	+	1.64493i	0.735635	+	0.735635i	0.971730	−	0.236095i	$-0.0758676\pi$
$5$	1.64493	+	1.64493i	0.735635	+	0.735635i	−0.236095	+	0.971730i	$0.575868\pi$
$6$	−0.790506	+	1.02101i	−0.322723	+	0.416827i
$7$	−3.07399	−	3.07399i	−1.16186	−	1.16186i	−0.984068	−	0.177792i	$-0.943105\pi$
$7$	−3.07399	−	3.07399i	−1.16186	−	1.16186i	−0.177792	−	0.984068i	$-0.556895\pi$
$8$	1.11628	−	2.59883i	0.394666	−	0.918825i
$9$	2.16632			0.722105
$10$	−0.415270	−	3.26355i	−0.131320	−	1.03202i
$11$	0.707107	+	0.707107i	0.213201	+	0.213201i
$11$	0.707107	+	0.707107i	0.213201	+	0.213201i
$12$	1.76793	−	0.457326i	0.510358	−	0.132019i
$13$	−2.81599	+	2.25171i	−0.781016	+	0.624511i
$13$	−2.81599	+	2.25171i	−0.781016	+	0.624511i
$14$	0.776042	+	6.09881i	0.207406	+	1.62998i
$15$	1.50192	−	1.50192i	0.387795	−	0.387795i
$16$	−3.49826	+	1.93964i	−0.874565	+	0.484909i
$17$		−	3.95770i		−	0.959883i	−0.877301	−	0.479941i	$-0.840658\pi$
$17$		−	3.95770i		−	0.959883i	0.877301	−	0.479941i	$-0.159342\pi$
$18$	−2.42244	−	1.87554i	−0.570974	−	0.442069i
$19$	5.30162	−	5.30162i	1.21627	−	1.21627i	0.247347	−	0.968927i	$-0.420441\pi$
$19$	5.30162	−	5.30162i	1.21627	−	1.21627i	0.968927	−	0.247347i	$-0.0795589\pi$
$20$	−2.36113	+	4.00892i	−0.527964	+	0.896422i
$21$	−2.80675	+	2.80675i	−0.612483	+	0.612483i
$22$	−0.178512	−	1.40290i	−0.0380589	−	0.299100i
$23$	2.42028			0.504663			0.252332	−	0.967641i	$-0.418803\pi$
$23$	2.42028			0.504663			0.252332	+	0.967641i	$0.418803\pi$
$24$	−2.37289	−	1.01924i	−0.484365	−	0.208051i
$25$			0.411591i			0.0823182i
$26$	5.09839	−	0.0799068i	0.999877	−	0.0156710i
$27$		−	4.71717i		−	0.907820i
$28$	4.41240	−	7.49174i	0.833865	−	1.41581i
$29$	6.63200			1.23153			0.615766	−	0.787929i	$-0.288847\pi$
$29$	6.63200			1.23153			0.615766	+	0.787929i	$0.288847\pi$
$30$	−2.97982	+	0.379167i	−0.544039	+	0.0692262i
$31$	−4.00610	+	4.00610i	−0.719517	+	0.719517i	−0.968506	−	0.248989i	$-0.919902\pi$
$31$	−4.00610	+	4.00610i	−0.719517	+	0.719517i	0.248989	+	0.968506i	$0.419902\pi$
$32$	5.59114	+	0.859747i	0.988383	+	0.151983i
$33$	0.645633	−	0.645633i	0.112390	−	0.112390i
$34$	−3.42647	+	4.42561i	−0.587635	+	0.758986i
$35$		−	10.1130i		−	1.70941i
$36$	1.08504	+	4.19457i	0.180840	+	0.699094i
$37$	6.40374	−	6.40374i	1.05277	−	1.05277i	0.0542409	−	0.998528i	$-0.482726\pi$
$37$	6.40374	−	6.40374i	1.05277	−	1.05277i	0.998528	−	0.0542409i	$-0.0172739\pi$
$38$	−10.5184	+	1.33842i	−1.70631	+	0.217120i
$39$	2.05595	+	2.57118i	0.329215	+	0.411718i
$40$	6.11110	−	2.43868i	0.966250	−	0.385590i
$41$	−6.99829	−	6.99829i	−1.09295	−	1.09295i	−0.995212	−	0.0977363i	$-0.968840\pi$
$41$	−6.99829	−	6.99829i	−1.09295	−	1.09295i	−0.0977363	−	0.995212i	$-0.531160\pi$
$42$	5.56860	−	0.708575i	0.859253	−	0.109336i
$43$	6.49245			0.990090			0.495045	−	0.868867i	$-0.335152\pi$
$43$	6.49245			0.990090			0.495045	+	0.868867i	$0.335152\pi$
$44$	−1.01498	+	1.72332i	−0.153014	+	0.259800i
$45$	3.56344	+	3.56344i	0.531206	+	0.531206i
$46$	−2.70643	−	2.09542i	−0.399041	−	0.308952i
$47$	−1.10769	−	1.10769i	−0.161574	−	0.161574i	0.621690	−	0.783264i	$-0.286446\pi$
$47$	−1.10769	−	1.10769i	−0.161574	−	0.161574i	−0.783264	+	0.621690i	$0.786446\pi$
$48$	1.77101	+	3.19413i	0.255623	+	0.461033i
$49$			11.8989i			1.69984i
$50$	0.356345	−	0.460253i	0.0503948	−	0.0650896i
$51$	−3.61363			−0.506009
$52$	−5.77035	−	4.32470i	−0.800204	−	0.599729i
$53$	−2.83311			−0.389157			−0.194579	−	0.980887i	$-0.562334\pi$
$53$	−2.83311			−0.389157			−0.194579	+	0.980887i	$0.562334\pi$
$54$	−4.08401	+	5.27488i	−0.555763	+	0.717820i
$55$			2.32628i			0.313676i
$56$	−11.4202	+	4.55733i	−1.52609	+	0.608999i
$57$	−4.84071	−	4.84071i	−0.641168	−	0.641168i
$58$	−7.41609	−	5.74181i	−0.973780	−	0.753937i
$59$	−8.97446	−	8.97446i	−1.16838	−	1.16838i	−0.982590	−	0.185785i	$-0.940517\pi$
$59$	−8.97446	−	8.97446i	−1.16838	−	1.16838i	−0.185785	−	0.982590i	$-0.559483\pi$
$60$	3.66040	+	2.15586i	0.472555	+	0.278320i
$61$	−1.09975			−0.140808			−0.0704040	−	0.997519i	$-0.522429\pi$
$61$	−1.09975			−0.140808			−0.0704040	+	0.997519i	$0.522429\pi$
$62$	7.94811	−	1.01136i	1.00941	−	0.128442i
$63$	−6.65924	−	6.65924i	−0.838985	−	0.838985i
$64$	−5.50782	−	5.80206i	−0.688478	−	0.725257i
$65$	−8.33601	−	0.928214i	−1.03396	−	0.115131i
$66$	−1.28094	+	0.162993i	−0.157673	+	0.0200630i
$67$	1.12474	−	1.12474i	0.137409	−	0.137409i	−0.635057	−	0.772466i	$-0.719023\pi$
$67$	1.12474	−	1.12474i	0.137409	−	0.137409i	0.772466	+	0.635057i	$0.219023\pi$
$68$	7.66316	−	1.98229i	0.929295	−	0.240388i
$69$		−	2.20987i		−	0.266037i
$70$	−8.75558	+	11.3087i	−1.04649	+	1.35164i
$71$	0.767629	−	0.767629i	0.0911008	−	0.0911008i	−0.660088	−	0.751189i	$-0.729481\pi$
$71$	0.767629	−	0.767629i	0.0911008	−	0.0911008i	0.751189	+	0.660088i	$0.229481\pi$
$72$	2.41822	−	5.62988i	0.284990	−	0.663488i
$73$	−3.00424	+	3.00424i	−0.351620	+	0.351620i	−0.860712	−	0.509092i	$-0.829981\pi$
$73$	−3.00424	+	3.00424i	−0.351620	+	0.351620i	0.509092	+	0.860712i	$0.329981\pi$
$74$	−12.7050	+	1.61665i	−1.47693	+	0.187932i
$75$	0.375809			0.0433946
$76$	12.9208	+	7.60992i	1.48211	+	0.872918i
$77$		−	4.34728i		−	0.495419i
$78$	−0.0729599	−	4.65515i	−0.00826108	−	0.527092i
$79$			5.41548i			0.609289i	0.952466	+	0.304645i	$0.0985377\pi$
$79$			5.41548i			0.609289i	−0.952466	+	0.304645i	$0.901462\pi$
$80$	−8.94496	−	2.56383i	−1.00008	−	0.286645i
$81$	2.19187			0.243541
$82$	1.76675	+	13.8846i	0.195105	+	1.53330i
$83$	−8.49263	+	8.49263i	−0.932187	+	0.932187i	−0.997842	−	0.0656556i	$-0.979086\pi$
$83$	−8.49263	+	8.49263i	−0.932187	+	0.932187i	0.0656556	+	0.997842i	$0.479086\pi$
$84$	−6.84043	−	4.02880i	−0.746352	−	0.439578i
$85$	6.51014	−	6.51014i	0.706124	−	0.706124i
$86$	−7.26004	−	5.62100i	−0.782871	−	0.606128i
$87$		−	6.05543i		−	0.649211i
$88$	2.62698	−	1.04832i	0.280037	−	0.111751i
$89$	5.20790	−	5.20790i	0.552037	−	0.552037i	−0.374992	−	0.927028i	$-0.622354\pi$
$89$	5.20790	−	5.20790i	0.552037	−	0.552037i	0.927028	+	0.374992i	$0.122354\pi$
$90$	−0.899605	−	7.06987i	−0.0948267	−	0.745230i
$91$	15.5781	+	1.73462i	1.63303	+	0.181837i
$92$	1.21225	+	4.68631i	0.126385	+	0.488582i
$93$	3.65782	+	3.65782i	0.379298	+	0.379298i
$94$	0.279642	+	2.19767i	0.0288429	+	0.226672i
$95$	17.4416			1.78947
$96$	0.785003	−	5.10506i	0.0801190	−	0.521033i
$97$	6.70059	+	6.70059i	0.680341	+	0.680341i	0.960077	−	0.279736i	$-0.0902468\pi$
$97$	6.70059	+	6.70059i	0.680341	+	0.680341i	−0.279736	+	0.960077i	$0.590247\pi$
$98$	10.3017	−	13.3056i	1.04063	−	1.34407i
$99$	1.53182	+	1.53182i	0.153953	+	0.153953i
$100$	−0.796950	+	0.206154i	−0.0796950	+	0.0206154i
$101$			14.2419i			1.41712i	0.705649	+	0.708561i	$0.250655\pi$
$101$			14.2419i			1.41712i	−0.705649	+	0.708561i	$0.749345\pi$
$102$	4.04086	+	3.12859i	0.400105	+	0.309776i
$103$	6.28623			0.619400			0.309700	−	0.950834i	$-0.399771\pi$
$103$	6.28623			0.619400			0.309700	+	0.950834i	$0.399771\pi$
$104$	2.70835	+	9.83183i	0.265576	+	0.964090i
$105$	−9.23381			−0.901128
$106$	3.16806	+	2.45283i	0.307710	+	0.238240i
$107$		−	12.6765i		−	1.22548i	−0.790284	−	0.612741i	$-0.790067\pi$
$107$		−	12.6765i		−	1.22548i	0.790284	−	0.612741i	$-0.209933\pi$
$108$	9.13370	−	2.36269i	0.878891	−	0.227350i
$109$	4.57155	+	4.57155i	0.437875	+	0.437875i	0.891296	−	0.453421i	$-0.149797\pi$
$109$	4.57155	+	4.57155i	0.437875	+	0.437875i	−0.453421	+	0.891296i	$0.649797\pi$
$110$	2.01404	−	2.60132i	0.192031	−	0.248026i
$111$	−5.84702	−	5.84702i	−0.554975	−	0.554975i
$112$	16.7160	+	4.79120i	1.57952	+	0.452725i
$113$	5.37310			0.505458			0.252729	−	0.967537i	$-0.418672\pi$
$113$	5.37310			0.505458			0.252729	+	0.967537i	$0.418672\pi$
$114$	1.22206	+	9.60398i	0.114456	+	0.899495i
$115$	3.98119	+	3.98119i	0.371248	+	0.371248i
$116$	3.32177	+	12.8413i	0.308418	+	1.19229i
$117$	−6.10033	+	4.87791i	−0.563976	+	0.450963i
$118$	2.26564	+	17.8054i	0.208569	+	1.63912i
$119$	−12.1659	+	12.1659i	−1.11525	+	1.11525i
$120$	−2.22667	−	5.57982i	−0.203266	−	0.509366i
$121$			1.00000i			0.0909091i
$122$	1.22977	+	0.952131i	0.111338	+	0.0862019i
$123$	−6.38988	+	6.38988i	−0.576156	+	0.576156i
$124$	−9.76341	−	5.75034i	−0.876781	−	0.516396i
$125$	7.54761	−	7.54761i	0.675079	−	0.675079i
$126$	1.68115	+	13.2119i	0.149769	+	1.17701i
$127$	0.909388			0.0806951			0.0403476	−	0.999186i	$-0.487153\pi$
$127$	0.909388			0.0806951			0.0403476	+	0.999186i	$0.487153\pi$
$128$	1.13573	+	11.2566i	0.100386	+	0.994949i
$129$		−	5.92802i		−	0.521933i
$130$	8.51794	+	8.25506i	0.747073	+	0.724017i
$131$			17.1589i			1.49918i	0.661904	+	0.749588i	$0.269748\pi$
$131$			17.1589i			1.49918i	−0.661904	+	0.749588i	$0.730252\pi$
$132$	1.57350	+	0.926740i	0.136955	+	0.0806623i
$133$	−32.5943			−2.82628
$134$	−2.23149	+	0.283946i	−0.192771	+	0.0245292i
$135$	7.75942	−	7.75942i	0.667824	−	0.667824i
$136$	−10.2854	−	4.41791i	−0.881964	−	0.378833i
$137$	4.25941	−	4.25941i	0.363906	−	0.363906i	−0.501343	−	0.865249i	$-0.667161\pi$
$137$	4.25941	−	4.25941i	0.363906	−	0.363906i	0.865249	+	0.501343i	$0.167161\pi$
$138$	−1.91325	+	2.47114i	−0.162866	+	0.210357i
$139$			11.7949i			1.00043i	0.865902	+	0.500214i	$0.166745\pi$
$139$			11.7949i			1.00043i	−0.865902	+	0.500214i	$0.833255\pi$
$140$	19.5815	−	5.06530i	1.65494	−	0.428096i
$141$	−1.01140	+	1.01140i	−0.0851748	+	0.0851748i
$142$	−1.52298	+	0.193791i	−0.127806	+	0.0162626i
$143$	−3.58340	−	0.399012i	−0.299659	−	0.0333670i
$144$	−7.57833	+	4.20186i	−0.631528	+	0.350155i
$145$	10.9092	+	10.9092i	0.905958	+	0.905958i
$146$	5.96043	−	0.758434i	0.493288	−	0.0627684i
$147$	10.8644			0.896081
$148$	15.6068	+	9.19191i	1.28287	+	0.755571i
$149$	−2.47156	−	2.47156i	−0.202478	−	0.202478i	0.598583	−	0.801061i	$-0.295731\pi$
$149$	−2.47156	−	2.47156i	−0.202478	−	0.202478i	−0.801061	+	0.598583i	$0.795731\pi$
$150$	−0.420240	−	0.325365i	−0.0343124	−	0.0265660i
$151$	13.4269	+	13.4269i	1.09266	+	1.09266i	0.995244	+	0.0974183i	$0.0310585\pi$
$151$	13.4269	+	13.4269i	1.09266	+	1.09266i	0.0974183	+	0.995244i	$0.468942\pi$
$152$	−7.85989	−	19.6961i	−0.637521	−	1.59756i
$153$		−	8.57363i		−	0.693137i
$154$	−3.76376	+	4.86125i	−0.303293	+	0.391731i
$155$	−13.1795			−1.05860
$156$	−3.94873	+	5.26869i	−0.316151	+	0.421833i
$157$	−3.92111			−0.312939			−0.156469	−	0.987683i	$-0.550011\pi$
$157$	−3.92111			−0.312939			−0.156469	+	0.987683i	$0.550011\pi$
$158$	4.68858	−	6.05575i	0.373004	−	0.481769i
$159$			2.58681i			0.205147i
$160$	7.78281	+	10.6113i	0.615285	+	0.838894i
$161$	−7.43992	−	7.43992i	−0.586348	−	0.586348i
$162$	−2.45101	−	1.89767i	−0.192570	−	0.149095i
$163$	5.41180	+	5.41180i	0.423885	+	0.423885i	0.886539	−	0.462654i	$-0.153103\pi$
$163$	5.41180	+	5.41180i	0.423885	+	0.423885i	−0.462654	+	0.886539i	$0.653103\pi$
$164$	10.0453	−	17.0558i	0.784408	−	1.33183i
$165$	2.12404			0.165356
$166$	16.8494	−	2.14400i	1.30777	−	0.166407i
$167$	−10.6658	−	10.6658i	−0.825343	−	0.825343i	0.161525	−	0.986869i	$-0.448359\pi$
$167$	−10.6658	−	10.6658i	−0.825343	−	0.825343i	−0.986869	+	0.161525i	$0.948359\pi$
$168$	4.16113	+	10.4274i	0.321038	+	0.804490i
$169$	2.85964	−	12.6816i	0.219972	−	0.975506i
$170$	−12.9161	+	1.64351i	−0.990622	+	0.126052i
$171$	11.4850	−	11.4850i	0.878278	−	0.878278i
$172$	3.25187	+	12.5711i	0.247953	+	0.958539i
$173$		−	11.8193i		−	0.898605i	−0.893380	−	0.449303i	$-0.851673\pi$
$173$		−	11.8193i		−	0.898605i	0.893380	−	0.449303i	$-0.148327\pi$
$174$	−5.24264	+	6.77136i	−0.397443	+	0.513335i
$175$	1.26523	−	1.26523i	0.0956422	−	0.0956422i
$176$	−3.84517	−	1.10211i	−0.289841	−	0.0830749i
$177$	−8.19425	+	8.19425i	−0.615917	+	0.615917i
$178$	−10.3325	+	1.31476i	−0.774453	+	0.0985452i
$179$	−10.3029			−0.770078			−0.385039	−	0.922900i	$-0.625812\pi$
$179$	−10.3029			−0.770078			−0.385039	+	0.922900i	$0.625812\pi$
$180$	−5.11495	+	8.68459i	−0.381246	+	0.647311i
$181$			15.4487i			1.14829i	0.818752	+	0.574147i	$0.194666\pi$
$181$			15.4487i			1.14829i	−0.818752	+	0.574147i	$0.805334\pi$
$182$	−15.9181	−	15.4268i	−1.17992	−	1.14351i
$183$			1.00414i			0.0742279i
$184$	2.70172	−	6.28990i	0.199173	−	0.463697i
$185$	21.0674			1.54891
$186$	−0.923433	−	7.25713i	−0.0677094	−	0.532119i
$187$	2.79852	−	2.79852i	0.204648	−	0.204648i
$188$	1.58998	−	2.69960i	0.115961	−	0.196889i
$189$	−14.5005	+	14.5005i	−1.05476	+	1.05476i
$190$	−19.5037	−	15.1005i	−1.41495	−	1.09550i
$191$			20.2823i			1.46758i	0.679377	+	0.733789i	$0.262250\pi$
$191$			20.2823i			1.46758i	−0.679377	+	0.733789i	$0.737750\pi$
$192$	−5.29764	+	5.02899i	−0.382325	+	0.362936i
$193$	−13.1892	+	13.1892i	−0.949377	+	0.949377i	−0.998779	−	0.0494022i	$-0.984268\pi$
$193$	−13.1892	+	13.1892i	−0.949377	+	0.949377i	0.0494022	+	0.998779i	$0.484268\pi$
$194$	−1.69159	−	13.2940i	−0.121449	−	0.954452i
$195$	−0.847518	+	7.61130i	−0.0606920	+	0.545057i
$196$	−23.0394	+	5.95978i	−1.64567	+	0.425698i
$197$	−5.70393	−	5.70393i	−0.406388	−	0.406388i	0.474089	−	0.880477i	$-0.342778\pi$
$197$	−5.70393	−	5.70393i	−0.406388	−	0.406388i	−0.880477	+	0.474089i	$0.842778\pi$
$198$	−0.386714	−	3.03913i	−0.0274825	−	0.215981i
$199$	10.7334			0.760867			0.380434	−	0.924808i	$-0.375775\pi$
$199$	10.7334			0.760867			0.380434	+	0.924808i	$0.375775\pi$
$200$	1.06965	+	0.459452i	0.0756360	+	0.0324882i
$201$	−1.02696	−	1.02696i	−0.0724361	−	0.0724361i
$202$	12.3303	−	15.9257i	0.867555	−	1.12053i
$203$	−20.3867	−	20.3867i	−1.43087	−	1.43087i
$204$	−1.80996	−	6.99695i	−0.126722	−	0.489884i
$205$		−	23.0234i		−	1.60802i
$206$	−7.02944	−	5.44245i	−0.489764	−	0.379194i
$207$	5.24309			0.364420
$208$	5.48359	−	13.3391i	0.380218	−	0.924897i
$209$	7.49762			0.518621
$210$	10.3255	+	7.99440i	0.712528	+	0.551666i
$211$			16.4418i			1.13190i	0.824440	+	0.565949i	$0.191490\pi$
$211$			16.4418i			1.13190i	−0.824440	+	0.565949i	$0.808510\pi$
$212$	−1.41902	−	5.48566i	−0.0974586	−	0.376756i
$213$	−0.700894	−	0.700894i	−0.0480245	−	0.0480245i
$214$	−10.9750	+	14.1752i	−0.750234	+	0.968997i
$215$	10.6796	+	10.6796i	0.728345	+	0.728345i
$216$	−12.2591	−	5.26570i	−0.834128	−	0.358285i
$217$	24.6294			1.67196
$218$	−1.15411	−	9.06997i	−0.0781660	−	0.614296i
$219$	2.74306	+	2.74306i	0.185359	+	0.185359i
$220$	−4.50430	+	1.16516i	−0.303680	+	0.0785554i
$221$	8.91157	+	11.1449i	0.599457	+	0.749684i
$222$	1.47610	+	11.6005i	0.0990697	+	0.778575i
$223$	−15.6039	+	15.6039i	−1.04492	+	1.04492i	−0.0459745	+	0.998943i	$0.514639\pi$
$223$	−15.6039	+	15.6039i	−1.04492	+	1.04492i	−0.998943	+	0.0459745i	$0.985361\pi$
$224$	−14.5443	−	19.8300i	−0.971779	−	1.32495i
$225$			0.891636i			0.0594424i
$226$	−6.00835	−	4.65189i	−0.399669	−	0.309439i
$227$	−4.95816	+	4.95816i	−0.329085	+	0.329085i	−0.852238	−	0.523154i	$-0.824755\pi$
$227$	−4.95816	+	4.95816i	−0.329085	+	0.329085i	0.523154	+	0.852238i	$0.324755\pi$
$228$	6.94834	−	11.7975i	0.460165	−	0.781307i
$229$	6.79089	−	6.79089i	0.448755	−	0.448755i	−0.446186	−	0.894940i	$-0.647218\pi$
$229$	6.79089	−	6.79089i	0.448755	−	0.448755i	0.894940	+	0.446186i	$0.147218\pi$
$230$	−1.00507	−	7.89870i	−0.0662723	−	0.520825i
$231$	−3.96934			−0.261164
$232$	7.40319	−	17.2354i	0.486043	−	1.13156i
$233$			3.20607i			0.210037i	0.994470	+	0.105018i	$0.0334901\pi$
$233$			3.20607i			0.210037i	−0.994470	+	0.105018i	$0.966510\pi$
$234$	11.0447	−	0.173103i	0.722017	−	0.0113161i
$235$		−	3.64416i		−	0.237719i
$236$	12.8819	−	21.8720i	0.838541	−	1.42375i
$237$	4.94468			0.321191
$238$	24.1372	−	3.07134i	1.56459	−	0.199085i
$239$	−11.5295	+	11.5295i	−0.745784	+	0.745784i	−0.973685	−	0.227900i	$-0.926814\pi$
$239$	−11.5295	+	11.5295i	−0.745784	+	0.745784i	0.227900	+	0.973685i	$0.426814\pi$
$240$	−2.34094	+	8.16731i	−0.151107	+	0.527198i
$241$	9.08751	−	9.08751i	0.585378	−	0.585378i	−0.350998	−	0.936376i	$-0.614158\pi$
$241$	9.08751	−	9.08751i	0.585378	−	0.585378i	0.936376	+	0.350998i	$0.114158\pi$
$242$	0.865774	−	1.11823i	0.0556541	−	0.0718824i
$243$		−	16.1528i		−	1.03620i
$244$	−0.550829	−	2.12940i	−0.0352632	−	0.136321i
$245$	−19.5728	+	19.5728i	−1.25046	+	1.25046i
$246$	12.6775	−	1.61315i	0.808290	−	0.102851i
$247$	−2.99164	+	26.8670i	−0.190353	+	1.70951i
$248$	5.93923	+	14.8831i	0.377141	+	0.945079i
$249$	7.75430	+	7.75430i	0.491409	+	0.491409i
$250$	−14.9745	+	1.90543i	−0.947070	+	0.120510i
$251$	15.9163			1.00463			0.502313	−	0.864686i	$-0.332483\pi$
$251$	15.9163			1.00463			0.502313	+	0.864686i	$0.332483\pi$
$252$	9.55865	−	16.2295i	0.602138	−	1.02236i
$253$	1.71140	+	1.71140i	0.107595	+	0.107595i
$254$	−1.01690	−	0.787325i	−0.0638062	−	0.0494011i
$255$	−5.94417	−	5.94417i	−0.372238	−	0.372238i
$256$	8.47563	−	13.5707i	0.529727	−	0.848168i
$257$			26.6809i			1.66431i	0.554542	+	0.832156i	$0.312893\pi$
$257$			26.6809i			1.66431i	−0.554542	+	0.832156i	$0.687107\pi$
$258$	−5.13233	+	6.62888i	−0.319525	+	0.412696i
$259$	−39.3701			−2.44634
$260$	−2.37799	−	16.6057i	−0.147476	−	1.02984i
$261$	14.3670			0.889295
$262$	14.8557	−	19.1875i	0.917788	−	1.18541i
$263$			0.297912i			0.0183701i	0.999958	+	0.00918503i	$0.00292373\pi$
$263$			0.297912i			0.0183701i	−0.999958	+	0.00918503i	$0.997076\pi$
$264$	−0.957181	−	2.39860i	−0.0589104	−	0.147624i
$265$	−4.66027	−	4.66027i	−0.286278	−	0.286278i
$266$	36.4478	+	28.2193i	2.23476	+	1.73023i
$267$	−4.75514	−	4.75514i	−0.291010	−	0.291010i
$268$	2.74115	+	1.61445i	0.167442	+	0.0986182i
$269$	−12.6355			−0.770399			−0.385200	−	0.922833i	$-0.625867\pi$
$269$	−12.6355			−0.770399			−0.385200	+	0.922833i	$0.625867\pi$
$270$	−15.3947	+	1.95890i	−0.936892	+	0.119215i
$271$	−15.7065	−	15.7065i	−0.954105	−	0.954105i	0.0448873	−	0.998992i	$-0.485707\pi$
$271$	−15.7065	−	15.7065i	−0.954105	−	0.954105i	−0.998992	+	0.0448873i	$0.985707\pi$
$272$	7.67649	+	13.8451i	0.465456	+	0.839480i
$273$	1.58381	−	14.2238i	0.0958568	−	0.860861i
$274$	−8.45067	+	1.07530i	−0.510524	+	0.0649615i
$275$	−0.291039	+	0.291039i	−0.0175503	+	0.0175503i
$276$	4.27890	−	1.10686i	0.257559	−	0.0666249i
$277$			2.54498i			0.152913i	0.997073	+	0.0764565i	$0.0243606\pi$
$277$			2.54498i			0.152913i	−0.997073	+	0.0764565i	$0.975639\pi$
$278$	10.2117	−	13.1894i	0.612457	−	0.791046i
$279$	−8.67848	+	8.67848i	−0.519567	+	0.519567i
$280$	−26.2820	−	11.2890i	−1.57065	−	0.674645i
$281$	1.67163	−	1.67163i	0.0997211	−	0.0997211i	−0.655486	−	0.755207i	$-0.727536\pi$
$281$	1.67163	−	1.67163i	0.0997211	−	0.0997211i	0.755207	+	0.655486i	$0.227536\pi$
$282$	2.00661	−	0.255331i	0.119492	−	0.0152047i
$283$	16.9054			1.00492			0.502460	−	0.864600i	$-0.332428\pi$
$283$	16.9054			1.00492			0.502460	+	0.864600i	$0.332428\pi$
$284$	1.87082	+	1.10185i	0.111013	+	0.0653829i
$285$		−	15.9253i		−	0.943331i
$286$	3.66161	+	3.54861i	0.216516	+	0.209833i
$287$			43.0254i			2.53971i
$288$	12.1122	+	1.86248i	0.713717	+	0.109748i
$289$	1.33662			0.0786250
$290$	−2.75407	−	21.6438i	−0.161724	−	1.27097i
$291$	6.11806	−	6.11806i	0.358647	−	0.358647i
$292$	−7.32175	−	4.31228i	−0.428473	−	0.252357i
$293$	2.37088	−	2.37088i	0.138508	−	0.138508i	−0.634453	−	0.772961i	$-0.718775\pi$
$293$	2.37088	−	2.37088i	0.138508	−	0.138508i	0.772961	+	0.634453i	$0.218775\pi$
$294$	−12.1489	−	9.40612i	−0.708537	−	0.548576i
$295$		−	29.5247i		−	1.71900i
$296$	−9.49384	−	23.7906i	−0.551818	−	1.38280i
$297$	3.33554	−	3.33554i	0.193548	−	0.193548i
$298$	0.623956	+	4.90358i	0.0361448	+	0.284057i
$299$	−6.81550	+	5.44976i	−0.394150	+	0.315168i
$300$	0.188231	+	0.727666i	0.0108675	+	0.0420118i
$301$	−19.9577	−	19.9577i	−1.15035	−	1.15035i
$302$	−3.38967	−	26.6389i	−0.195053	−	1.53290i
$303$	13.0038			0.747046
$304$	−8.26322	+	28.8296i	−0.473928	+	1.65349i
$305$	−1.80900	−	1.80900i	−0.103583	−	0.103583i
$306$	−7.42282	+	9.58727i	−0.424335	+	0.548068i
$307$	−20.1356	−	20.1356i	−1.14920	−	1.14920i	−0.986710	−	0.162491i	$-0.948047\pi$
$307$	−20.1356	−	20.1356i	−1.14920	−	1.14920i	−0.162491	−	0.986710i	$-0.551953\pi$
$308$	8.41750	−	2.17742i	0.479631	−	0.124070i
$309$		−	5.73972i		−	0.326521i
$310$	14.7377	+	11.4105i	0.837045	+	0.648072i
$311$	0.870576			0.0493658			0.0246829	−	0.999695i	$-0.492142\pi$
$311$	0.870576			0.0493658			0.0246829	+	0.999695i	$0.492142\pi$
$312$	8.97708	−	2.47290i	0.508227	−	0.140000i
$313$	−6.92987			−0.391699			−0.195850	−	0.980634i	$-0.562746\pi$
$313$	−6.92987			−0.391699			−0.195850	+	0.980634i	$0.562746\pi$
$314$	4.38470	+	3.39480i	0.247443	+	0.191579i
$315$		−	21.9080i		−	1.23437i
$316$	−10.4858	+	2.71245i	−0.589873	+	0.152587i
$317$	9.14907	+	9.14907i	0.513863	+	0.513863i	0.915708	−	0.401845i	$-0.131631\pi$
$317$	9.14907	+	9.14907i	0.513863	+	0.513863i	−0.401845	+	0.915708i	$0.631631\pi$
$318$	2.23959	−	2.89264i	0.125590	−	0.162211i
$319$	4.68953	+	4.68953i	0.262563	+	0.262563i
$320$	0.483994	−	18.6040i	0.0270561	−	1.03999i
$321$	−11.5744			−0.646022
$322$	1.87824	+	14.7608i	0.104670	+	0.822589i
$323$	−20.9822	−	20.9822i	−1.16748	−	1.16748i
$324$	1.09784	+	4.24405i	0.0609913	+	0.235781i
$325$	−0.926782	−	1.15904i	−0.0514086	−	0.0642919i
$326$	−1.36623	−	10.7370i	−0.0756686	−	0.594669i
$327$	4.17411	−	4.17411i	0.230829	−	0.230829i
$328$	−25.9994	+	10.3753i	−1.43558	+	0.572879i
$329$			6.81009i			0.375452i
$330$	−2.37516	−	1.83894i	−0.130749	−	0.101230i
$331$	−0.217296	+	0.217296i	−0.0119437	+	0.0119437i	−0.713053	−	0.701110i	$-0.752688\pi$
$331$	−0.217296	+	0.217296i	−0.0119437	+	0.0119437i	0.701110	+	0.713053i	$0.252688\pi$
$332$	−20.6977	−	12.1903i	−1.13593	−	0.669029i
$333$	13.8725	−	13.8725i	0.760210	−	0.760210i
$334$	2.69262	+	21.1609i	0.147334	+	1.15788i
$335$	3.70024			0.202166
$336$	4.37466	−	15.2628i	0.238657	−	0.832654i
$337$			20.1326i			1.09669i	0.836251	+	0.548346i	$0.184742\pi$
$337$			20.1326i			1.09669i	−0.836251	+	0.548346i	$0.815258\pi$
$338$	−14.1771	+	11.7051i	−0.771134	+	0.636673i
$339$		−	4.90598i		−	0.266456i
$340$	15.8661	+	9.34463i	0.860460	+	0.506784i
$341$	−5.66548			−0.306803
$342$	−22.7862	+	2.89943i	−1.23214	+	0.156783i
$343$	15.0590	−	15.0590i	0.813112	−	0.813112i
$344$	7.24741	−	16.8728i	0.390754	−	0.909719i
$345$	3.63508	−	3.63508i	0.195706	−	0.195706i
$346$	−10.2329	+	13.2167i	−0.550121	+	0.710533i
$347$		−	27.6979i		−	1.48690i	−0.668790	−	0.743452i	$-0.733187\pi$
$347$		−	27.6979i		−	1.48690i	0.668790	−	0.743452i	$-0.266813\pi$
$348$	11.7249	−	3.03298i	0.628523	−	0.162585i
$349$	15.2568	−	15.2568i	0.816676	−	0.816676i	−0.168949	−	0.985625i	$-0.554037\pi$
$349$	15.2568	−	15.2568i	0.816676	−	0.816676i	0.985625	+	0.168949i	$0.0540373\pi$
$350$	−2.51022	+	0.319412i	−0.134177	+	0.0170733i
$351$	10.6217	+	13.2835i	0.566944	+	0.709022i
$352$	3.34560	+	4.56147i	0.178321	+	0.243127i
$353$	1.08060	+	1.08060i	0.0575146	+	0.0575146i	0.735279	−	0.677764i	$-0.237051\pi$
$353$	1.08060	+	1.08060i	0.0575146	+	0.0575146i	−0.677764	+	0.735279i	$0.737051\pi$
$354$	16.2574	−	2.06867i	0.864072	−	0.109949i
$355$	2.52539			0.134034
$356$	12.6924	+	7.47541i	0.672694	+	0.396196i
$357$	11.1083	+	11.1083i	0.587912	+	0.587912i
$358$	11.5210	+	8.92002i	0.608906	+	0.471438i
$359$	6.67177	+	6.67177i	0.352123	+	0.352123i	0.860899	−	0.508776i	$-0.169902\pi$
$359$	6.67177	+	6.67177i	0.352123	+	0.352123i	−0.508776	+	0.860899i	$0.669902\pi$
$360$	13.2386	−	5.28296i	0.697734	−	0.278437i
$361$		−	37.2143i		−	1.95865i
$362$	13.3751	−	17.2752i	0.702980	−	0.907964i
$363$	0.913063			0.0479234
$364$	4.44390	+	31.0321i	0.232924	+	1.62652i
$365$	−9.88354			−0.517328
$366$	0.869356	−	1.12285i	0.0454419	−	0.0586925i
$367$		−	5.21010i		−	0.271965i	−0.990711	−	0.135982i	$-0.956581\pi$
$367$		−	5.21010i		−	0.271965i	0.990711	−	0.135982i	$-0.0434191\pi$
$368$	−8.46677	+	4.69446i	−0.441361	+	0.244716i
$369$	−15.1605	−	15.1605i	−0.789224	−	0.789224i
$370$	−23.5582	−	18.2396i	−1.22473	−	0.948233i
$371$	8.70896	+	8.70896i	0.452146	+	0.452146i
$372$	−5.25043	+	8.91461i	−0.272222	+	0.462201i
$373$	−32.9439			−1.70577			−0.852886	−	0.522098i	$-0.825150\pi$
$373$	−32.9439			−1.70577			−0.852886	+	0.522098i	$0.825150\pi$
$374$	−5.55226	+	0.706497i	−0.287101	+	0.0365321i
$375$	−6.89145	−	6.89145i	−0.355873	−	0.355873i
$376$	−4.11521	+	1.64221i	−0.212226	+	0.0846904i
$377$	−18.6757	+	14.9333i	−0.961846	+	0.769105i
$378$	28.7691	−	3.66072i	1.47972	−	0.188287i
$379$	−22.3547	+	22.3547i	−1.14828	+	1.14828i	−0.161393	+	0.986890i	$0.551599\pi$
$379$	−22.3547	+	22.3547i	−1.14828	+	1.14828i	−0.986890	+	0.161393i	$0.948401\pi$
$380$	8.73596	+	33.7716i	0.448145	+	1.73244i
$381$		−	0.830329i		−	0.0425390i
$382$	17.5599	−	22.6803i	0.898444	−	1.16042i
$383$	1.96868	−	1.96868i	0.100595	−	0.100595i	−0.655018	−	0.755613i	$-0.727339\pi$
$383$	1.96868	−	1.96868i	0.100595	−	0.100595i	0.755613	+	0.655018i	$0.227339\pi$
$384$	10.2779	−	1.03700i	0.524494	−	0.0529190i
$385$	7.15097	−	7.15097i	0.364447	−	0.364447i
$386$	26.1673	−	3.32966i	1.33188	−	0.169475i
$387$	14.0647			0.714949
$388$	−9.61800	+	16.3302i	−0.488280	+	0.829042i
$389$		−	36.8965i		−	1.87073i	−0.353690	−	0.935363i	$-0.615073\pi$
$389$		−	36.8965i		−	1.87073i	0.353690	−	0.935363i	$-0.384927\pi$
$390$	7.53739	−	7.77742i	0.381671	−	0.393825i
$391$		−	9.57874i		−	0.484418i
$392$	30.9231	+	13.2825i	1.56185	+	0.670867i
$393$	15.6671			0.790302
$394$	1.43998	+	11.3166i	0.0725452	+	0.570123i
$395$	−8.90809	+	8.90809i	−0.448215	+	0.448215i
$396$	−2.19877	+	3.73325i	−0.110492	+	0.187603i
$397$	−23.9650	+	23.9650i	−1.20277	+	1.20277i	−0.229449	+	0.973321i	$0.573692\pi$
$397$	−23.9650	+	23.9650i	−1.20277	+	1.20277i	−0.973321	+	0.229449i	$0.926308\pi$
$398$	−12.0023	−	9.29266i	−0.601623	−	0.465799i
$399$			29.7606i			1.48989i
$400$	−0.798337	−	1.43985i	−0.0399168	−	0.0719926i
$401$	3.74963	−	3.74963i	0.187248	−	0.187248i	−0.607257	−	0.794505i	$-0.707730\pi$
$401$	3.74963	−	3.74963i	0.187248	−	0.187248i	0.794505	+	0.607257i	$0.207730\pi$
$402$	0.259260	+	2.03749i	0.0129307	+	0.101621i
$403$	2.26059	−	20.3017i	0.112608	−	1.01130i
$404$	−27.5761	+	7.13334i	−1.37196	+	0.354897i
$405$	3.60548	+	3.60548i	0.179158	+	0.179158i
$406$	5.14671	+	40.4473i	0.255427	+	2.00737i
$407$	9.05626			0.448902
$408$	−4.03383	+	9.39120i	−0.199704	+	0.464934i
$409$	−5.58762	−	5.58762i	−0.276290	−	0.276290i	0.555336	−	0.831626i	$-0.312590\pi$
$409$	−5.58762	−	5.58762i	−0.276290	−	0.276290i	−0.831626	+	0.555336i	$0.812590\pi$
$410$	−19.9331	+	25.7454i	−0.984423	+	1.27147i
$411$	−3.88911	−	3.88911i	−0.191835	−	0.191835i
$412$	3.14858	+	12.1718i	0.155119	+	0.599662i
$413$			55.1749i			2.71498i
$414$	−5.86298	−	4.53934i	−0.288150	−	0.223096i
$415$	−27.9396			−1.37150
$416$	−17.6805	+	10.1686i	−0.866858	+	0.498555i
$417$	10.7695			0.527383
$418$	−8.38405	−	6.49125i	−0.410077	−	0.317497i
$419$		−	15.1662i		−	0.740918i	−0.928849	−	0.370459i	$-0.879200\pi$
$419$		−	15.1662i		−	0.740918i	0.928849	−	0.370459i	$-0.120800\pi$
$420$	−4.62494	−	17.8791i	−0.225674	−	0.872412i
$421$	1.71368	+	1.71368i	0.0835195	+	0.0835195i	0.747632	−	0.664113i	$-0.231191\pi$
$421$	1.71368	+	1.71368i	0.0835195	+	0.0835195i	−0.664113	+	0.747632i	$0.731191\pi$
$422$	14.2349	−	18.3857i	0.692942	−	0.895000i
$423$	−2.39962	−	2.39962i	−0.116673	−	0.116673i
$424$	−3.16255	+	7.36277i	−0.153587	+	0.357568i
$425$	1.62895			0.0790159
$426$	0.176944	+	1.39058i	0.00857295	+	0.0673736i
$427$	3.38061	+	3.38061i	0.163599	+	0.163599i
$428$	24.5451	−	6.34927i	1.18643	−	0.306904i
$429$	−0.364323	+	3.27187i	−0.0175897	+	0.157968i
$430$	−2.69612	−	21.1884i	−0.130018	−	1.02180i
$431$	2.74790	−	2.74790i	0.132362	−	0.132362i	−0.637822	−	0.770184i	$-0.720165\pi$
$431$	2.74790	−	2.74790i	0.132362	−	0.132362i	0.770184	+	0.637822i	$0.220165\pi$
$432$	9.14959	+	16.5019i	0.440210	+	0.793947i
$433$			18.6451i			0.896028i	0.894027	+	0.448014i	$0.147869\pi$
$433$			18.6451i			0.896028i	−0.894027	+	0.448014i	$0.852131\pi$
$434$	−27.5413	−	21.3235i	−1.32203	−	1.02356i
$435$	9.96077	−	9.96077i	0.477582	−	0.477582i
$436$	−6.56199	+	11.1415i	−0.314262	+	0.533581i
$437$	12.8314	−	12.8314i	0.613809	−	0.613809i
$438$	−0.692498	−	5.44224i	−0.0330888	−	0.260040i
$439$	30.7472			1.46748			0.733741	−	0.679429i	$-0.237772\pi$
$439$	30.7472			1.46748			0.733741	+	0.679429i	$0.237772\pi$
$440$	6.04561	+	2.59679i	0.288213	+	0.123797i
$441$			25.7767i			1.22746i
$442$	−0.316247	−	20.1779i	−0.0150423	−	0.959765i
$443$			36.7912i			1.74800i	0.485922	+	0.874002i	$0.338484\pi$
$443$			36.7912i			1.74800i	−0.485922	+	0.874002i	$0.661516\pi$
$444$	8.39280	−	14.2500i	0.398304	−	0.676275i
$445$	17.1333			0.812195
$446$	30.9583	−	3.93928i	1.46592	−	0.186530i
$447$	−2.25669	+	2.25669i	−0.106738	+	0.106738i
$448$	−0.904472	+	34.7665i	−0.0427323	+	1.64256i
$449$	5.45584	−	5.45584i	0.257477	−	0.257477i	−0.566550	−	0.824027i	$-0.691722\pi$
$449$	5.45584	−	5.45584i	0.257477	−	0.257477i	0.824027	+	0.566550i	$0.191722\pi$
$450$	0.771956	−	0.997053i	0.0363904	−	0.0470015i
$451$		−	9.89707i		−	0.466035i
$452$	2.69122	+	10.4037i	0.126584	+	0.489351i
$453$	12.2596	−	12.2596i	0.576004	−	0.576004i
$454$	9.83700	−	1.25171i	0.461673	−	0.0587456i
$455$	22.7715	+	28.4782i	1.06755	+	1.33508i
$456$	−17.9838	+	7.17657i	−0.842168	+	0.336074i
$457$	−2.81893	−	2.81893i	−0.131864	−	0.131864i	0.638094	−	0.769958i	$-0.279723\pi$
$457$	−2.81893	−	2.81893i	−0.131864	−	0.131864i	−0.769958	+	0.638094i	$0.779723\pi$
$458$	−13.4731	+	1.71439i	−0.629558	+	0.0801081i
$459$	−18.6691			−0.871401
$460$	−5.71459	+	9.70271i	−0.266444	+	0.452391i
$461$	−14.7532	−	14.7532i	−0.687127	−	0.687127i	0.274469	−	0.961596i	$-0.411498\pi$
$461$	−14.7532	−	14.7532i	−0.687127	−	0.687127i	−0.961596	+	0.274469i	$0.911498\pi$
$462$	4.43863	+	3.43655i	0.206504	+	0.159883i
$463$	18.7891	+	18.7891i	0.873202	+	0.873202i	0.992820	−	0.119618i	$-0.0381669\pi$
$463$	18.7891	+	18.7891i	0.873202	+	0.873202i	−0.119618	+	0.992820i	$0.538167\pi$
$464$	−23.2005	+	12.8637i	−1.07705	+	0.597180i
$465$			12.0337i			0.558051i
$466$	2.77573	−	3.58512i	0.128583	−	0.166077i
$467$	12.4762			0.577332			0.288666	−	0.957430i	$-0.406788\pi$
$467$	12.4762			0.577332			0.288666	+	0.957430i	$0.406788\pi$
$468$	−12.5004	−	9.36867i	−0.577831	−	0.433067i
$469$	−6.91489			−0.319300
$470$	−3.15502	+	4.07500i	−0.145530	+	0.187966i
$471$			3.58022i			0.164968i
$472$	−33.3411	+	13.3051i	−1.53465	+	0.612415i
$473$	4.59086	+	4.59086i	0.211088	+	0.211088i
$474$	−5.52928	−	4.28097i	−0.253968	−	0.196632i
$475$	2.18210	+	2.18210i	0.100122	+	0.100122i
$476$	−29.6500	−	17.4629i	−1.35901	−	0.800413i
$477$	−6.13741			−0.281013
$478$	22.8747	−	2.91068i	1.04626	−	0.133132i
$479$	14.9354	+	14.9354i	0.682418	+	0.682418i	0.960544	−	0.278126i	$-0.0897134\pi$
$479$	14.9354	+	14.9354i	0.682418	+	0.682418i	−0.278126	+	0.960544i	$0.589713\pi$
$480$	9.68875	−	7.10620i	0.442229	−	0.324352i
$481$	−3.61355	+	32.4522i	−0.164764	+	1.47969i
$482$	−18.0296	+	2.29418i	−0.821228	+	0.104497i
$483$	−6.79312	+	6.79312i	−0.309098	+	0.309098i
$484$	−1.93627	+	0.500870i	−0.0880121	+	0.0227668i
$485$			22.0440i			1.00097i
$486$	−13.9847	+	18.0626i	−0.634359	+	0.819334i
$487$	6.37880	−	6.37880i	0.289051	−	0.289051i	−0.547654	−	0.836705i	$-0.684479\pi$
$487$	6.37880	−	6.37880i	0.289051	−	0.289051i	0.836705	+	0.547654i	$0.184479\pi$
$488$	−1.22763	+	2.85805i	−0.0555721	+	0.129378i
$489$	4.94131	−	4.94131i	0.223454	−	0.223454i
$490$	38.8325	−	4.94123i	1.75427	−	0.223222i
$491$	−21.8577			−0.986425			−0.493213	−	0.869909i	$-0.664178\pi$
$491$	−21.8577			−0.986425			−0.493213	+	0.869909i	$0.664178\pi$
$492$	−15.5730	−	9.17201i	−0.702085	−	0.413506i
$493$		−	26.2475i		−	1.18213i
$494$	26.6061	−	27.4534i	1.19706	−	1.23519i
$495$			5.03946i			0.226507i
$496$	6.24400	−	21.7848i	0.280364	−	0.978164i
$497$	−4.71937			−0.211693
$498$	−1.95761	−	15.3846i	−0.0877224	−	0.689398i
$499$	17.2259	−	17.2259i	0.771137	−	0.771137i	−0.207169	−	0.978305i	$-0.566425\pi$
$499$	17.2259	−	17.2259i	0.771137	−	0.771137i	0.978305	+	0.207169i	$0.0664249\pi$
$500$	18.3946	+	10.8338i	0.822630	+	0.484503i
$501$	−9.73853	+	9.73853i	−0.435086	+	0.435086i
$502$	−17.7980	−	13.7799i	−0.794364	−	0.615027i
$503$			34.4119i			1.53435i	0.641437	+	0.767176i	$0.278339\pi$
$503$			34.4119i			1.53435i	−0.641437	+	0.767176i	$0.721661\pi$
$504$	−24.7398	+	9.87263i	−1.10200	+	0.439762i
$505$	−23.4269	+	23.4269i	−1.04249	+	1.04249i
$506$	−0.432049	−	3.39542i	−0.0192069	−	0.150945i
$507$	−11.5791	−	2.61103i	−0.514245	−	0.115960i
$508$	0.455485	+	1.76082i	0.0202089	+	0.0781237i
$509$	7.04387	+	7.04387i	0.312214	+	0.312214i	0.845767	−	0.533553i	$-0.179143\pi$
$509$	7.04387	+	7.04387i	0.312214	+	0.312214i	−0.533553	+	0.845767i	$0.679143\pi$
$510$	1.50063	+	11.7932i	0.0664490	+	0.522213i
$511$	18.4700			0.817066
$512$	−21.2268	+	7.83715i	−0.938103	+	0.346357i
$513$	−25.0086	−	25.0086i	−1.10416	−	1.10416i
$514$	23.0997	−	29.8354i	1.01888	−	1.31598i
$515$	10.3404	+	10.3404i	0.455653	+	0.455653i
$516$	11.4782	−	2.96917i	0.505301	−	0.130710i
$517$		−	1.56652i		−	0.0688953i
$518$	44.0248	+	34.0856i	1.93434	+	1.49764i
$519$	−10.7918			−0.473706
$520$	−11.7176	+	20.6277i	−0.513852	+	0.904585i
$521$	−2.29076			−0.100360			−0.0501800	−	0.998740i	$-0.515980\pi$
$521$	−2.29076			−0.100360			−0.0501800	+	0.998740i	$0.515980\pi$
$522$	−16.0656	−	12.4386i	−0.703172	−	0.544422i
$523$		−	37.0946i		−	1.62204i	−0.585022	−	0.811018i	$-0.698914\pi$
$523$		−	37.0946i		−	1.62204i	0.585022	−	0.811018i	$-0.301086\pi$
$524$	−33.2241	+	8.59435i	−1.45140	+	0.375446i
$525$	−1.15523	−	1.15523i	−0.0504185	−	0.0504185i
$526$	0.257925	−	0.333134i	0.0112461	−	0.0145253i
$527$	15.8549	+	15.8549i	0.690652	+	0.690652i
$528$	−1.00630	+	3.51088i	−0.0437935	+	0.152792i
$529$	−17.1422			−0.745315
$530$	1.17650	+	9.24598i	0.0511041	+	0.401620i
$531$	−19.4415	−	19.4415i	−0.843690	−	0.843690i
$532$	−16.3255	−	63.1112i	−0.707799	−	2.73622i
$533$	35.4652	+	3.94905i	1.53617	+	0.171052i
$534$	1.20046	+	9.43422i	0.0519488	+	0.408258i
$535$	20.8519	−	20.8519i	0.901508	−	0.901508i
$536$	−1.66748	−	4.17854i	−0.0720242	−	0.180485i
$537$			9.40724i			0.405952i
$538$	14.1294	+	10.9395i	0.609160	+	0.471634i
$539$	−8.41376	+	8.41376i	−0.362406	+	0.362406i
$540$	18.9108	+	11.1378i	0.813790	+	0.479297i
$541$	13.2271	−	13.2271i	0.568679	−	0.568679i	−0.363079	−	0.931758i	$-0.618275\pi$
$541$	13.2271	−	13.2271i	0.568679	−	0.568679i	0.931758	+	0.363079i	$0.118275\pi$
$542$	3.96518	+	31.1618i	0.170319	+	1.33852i
$543$	14.1057			0.605332
$544$	3.40262	−	22.1280i	0.145886	−	0.948732i
$545$			15.0398i			0.644233i
$546$	−14.0856	+	14.5342i	−0.602809	+	0.622006i
$547$		−	15.8172i		−	0.676295i	−0.941093	−	0.338147i	$-0.890200\pi$
$547$		−	15.8172i		−	0.676295i	0.941093	−	0.338147i	$-0.109800\pi$
$548$	10.3808	+	6.11394i	0.443444	+	0.261174i
$549$	−2.38240			−0.101678
$550$	0.577422	−	0.0734740i	0.0246214	−	0.00313294i
$551$	35.1603	−	35.1603i	1.49788	−	1.49788i
$552$	−5.74307	−	2.46684i	−0.244441	−	0.104996i
$553$	16.6471	−	16.6471i	0.707909	−	0.707909i
$554$	2.20338	−	2.84587i	0.0936126	−	0.120909i
$555$		−	19.2359i		−	0.816518i
$556$	−22.8380	+	5.90770i	−0.968548	+	0.250542i
$557$	7.18214	−	7.18214i	0.304317	−	0.304317i	−0.538383	−	0.842700i	$-0.680965\pi$
$557$	7.18214	−	7.18214i	0.304317	−	0.304317i	0.842700	+	0.538383i	$0.180965\pi$
$558$	17.2181	−	2.19092i	0.728901	−	0.0927490i
$559$	−18.2827	+	14.6191i	−0.773276	+	0.618322i
$560$	19.6155	+	35.3779i	0.828908	+	1.49499i
$561$	−2.55522	−	2.55522i	−0.107882	−	0.107882i
$562$	−3.31652	+	0.422010i	−0.139899	+	0.0178014i
$563$	21.8043			0.918941			0.459470	−	0.888193i	$-0.348039\pi$
$563$	21.8043			0.918941			0.459470	+	0.888193i	$0.348039\pi$
$564$	−2.46491	−	1.45175i	−0.103791	−	0.0611298i
$565$	8.83837	+	8.83837i	0.371833	+	0.371833i
$566$	−18.9041	−	14.6362i	−0.794597	−	0.615207i
$567$	−6.73780	−	6.73780i	−0.282961	−	0.282961i
$568$	−1.13805	−	2.85183i	−0.0477513	−	0.119660i
$569$		−	43.0719i		−	1.80567i	−0.429991	−	0.902833i	$-0.641483\pi$
$569$		−	43.0719i		−	1.80567i	0.429991	−	0.902833i	$-0.358517\pi$
$570$	−13.7877	+	17.8081i	−0.577502	+	0.745898i
$571$	9.53356			0.398967			0.199483	−	0.979901i	$-0.436074\pi$
$571$	9.53356			0.398967			0.199483	+	0.979901i	$0.436074\pi$
$572$	−1.02223	−	7.13828i	−0.0427414	−	0.298467i
$573$	18.5191			0.773645
$574$	37.2502	−	48.1122i	1.55480	−	2.00816i
$575$			0.996166i			0.0415430i
$576$	−11.9317	−	12.5691i	−0.497154	−	0.523712i
$577$	5.75389	+	5.75389i	0.239537	+	0.239537i	0.816659	−	0.577121i	$-0.195824\pi$
$577$	5.75389	+	5.75389i	0.239537	+	0.239537i	−0.577121	+	0.816659i	$0.695824\pi$
$578$	−1.49465	−	1.15721i	−0.0621693	−	0.0481338i
$579$	12.0425	+	12.0425i	0.500471	+	0.500471i
$580$	−15.6590	+	26.5872i	−0.650205	+	1.10397i
$581$	52.2125			2.16614
$582$	−12.1382	+	1.54453i	−0.503146	+	0.0640228i
$583$	−2.00331	−	2.00331i	−0.0829687	−	0.0829687i
$584$	4.45393	+	11.1611i	0.184305	+	0.461849i
$585$	−18.0584	−	2.01080i	−0.746624	−	0.0831366i
$586$	−4.70384	+	0.598539i	−0.194314	+	0.0247254i
$587$	−8.39717	+	8.39717i	−0.346588	+	0.346588i	−0.858837	−	0.512249i	$-0.828813\pi$
$587$	−8.39717	+	8.39717i	−0.346588	+	0.346588i	0.512249	+	0.858837i	$0.328813\pi$
$588$	5.44165	+	21.0364i	0.224410	+	0.867526i
$589$			42.4776i			1.75026i
$590$	−25.5617	+	33.0154i	−1.05236	+	1.35922i
$591$	−5.20805	+	5.20805i	−0.214231	+	0.214231i
$592$	−9.98102	+	34.8229i	−0.410218	+	1.43121i
$593$	−3.19550	+	3.19550i	−0.131224	+	0.131224i	−0.769668	−	0.638444i	$-0.779578\pi$
$593$	−3.19550	+	3.19550i	−0.131224	+	0.131224i	0.638444	+	0.769668i	$0.279578\pi$
$594$	−6.61773	+	0.842072i	−0.271529	+	0.0345506i
$595$	−40.0242			−1.64083
$596$	3.54767	−	6.02353i	0.145318	−	0.246734i
$597$		−	9.80023i		−	0.401097i
$598$	12.3395	−	0.193397i	0.504601	−	0.00790858i
$599$		−	11.0304i		−	0.450690i	−0.974279	−	0.225345i	$-0.927649\pi$
$599$		−	11.0304i		−	0.450690i	0.974279	−	0.225345i	$-0.0723509\pi$
$600$	0.419509	−	0.976662i	0.0171264	−	0.0398721i
$601$	35.4797			1.44725			0.723623	−	0.690195i	$-0.242475\pi$
$601$	35.4797			1.44725			0.723623	+	0.690195i	$0.242475\pi$
$602$	5.03842	+	39.5962i	0.205351	+	1.61382i
$603$	2.43654	−	2.43654i	0.0992237	−	0.0992237i
$604$	−19.2729	+	32.7231i	−0.784202	+	1.33148i
$605$	−1.64493	+	1.64493i	−0.0668759	+	0.0668759i
$606$	−14.5412	−	11.2583i	−0.590695	−	0.457338i
$607$		−	23.8892i		−	0.969631i	−0.874616	−	0.484815i	$-0.838887\pi$
$607$		−	23.8892i		−	0.969631i	0.874616	−	0.484815i	$-0.161113\pi$
$608$	34.2001	−	25.0840i	1.38700	−	1.01729i
$609$	−18.6144	+	18.6144i	−0.754292	+	0.754292i
$610$	0.456691	+	3.58907i	0.0184909	+	0.145317i
$611$	5.61346	+	0.625059i	0.227096	+	0.0252872i
$612$	16.6008	−	4.29427i	0.671049	−	0.173586i
$613$	32.0184	+	32.0184i	1.29321	+	1.29321i	0.932789	+	0.360423i	$0.117368\pi$
$613$	32.0184	+	32.0184i	1.29321	+	1.29321i	0.360423	+	0.932789i	$0.382632\pi$
$614$	5.08332	+	39.9491i	0.205146	+	1.61222i
$615$	−21.0218			−0.847681
$616$	−11.2978	−	4.85280i	−0.455203	−	0.195525i
$617$	−17.6482	−	17.6482i	−0.710488	−	0.710488i	0.256149	−	0.966637i	$-0.417546\pi$
$617$	−17.6482	−	17.6482i	−0.710488	−	0.710488i	−0.966637	+	0.256149i	$0.917546\pi$
$618$	−4.96930	+	6.41832i	−0.199895	+	0.258183i
$619$	−4.93452	−	4.93452i	−0.198335	−	0.198335i	0.600951	−	0.799286i	$-0.294789\pi$
$619$	−4.93452	−	4.93452i	−0.198335	−	0.198335i	−0.799286	+	0.600951i	$0.794789\pi$
$620$	−6.60122	−	25.5191i	−0.265111	−	1.02487i
$621$		−	11.4169i		−	0.458144i
$622$	−0.973502	−	0.753722i	−0.0390339	−	0.0302215i
$623$	−32.0181			−1.28278
$624$	−12.1794	−	5.00686i	−0.487566	−	0.200435i
$625$	26.8885			1.07554
$626$	7.74917	+	5.99970i	0.309719	+	0.239796i
$627$		−	6.84580i		−	0.273395i
$628$	−1.96397	−	7.59231i	−0.0783708	−	0.302966i
$629$	−25.3441	−	25.3441i	−1.01053	−	1.01053i
$630$	−18.9674	+	24.4981i	−0.755677	+	0.976028i
$631$	15.7289	+	15.7289i	0.626156	+	0.626156i	0.947099	−	0.320943i	$-0.104000\pi$
$631$	15.7289	+	15.7289i	0.626156	+	0.626156i	−0.320943	+	0.947099i	$0.604000\pi$
$632$	14.0739	+	6.04521i	0.559830	+	0.240466i
$633$	15.0124			0.596688
$634$	−2.30972	−	18.1518i	−0.0917307	−	0.720899i
$635$	1.49588	+	1.49588i	0.0593622	+	0.0593622i
$636$	−5.00875	+	1.29565i	−0.198610	+	0.0513760i
$637$	−26.7927	−	33.5071i	−1.06157	−	1.32760i
$638$	−1.18389	−	9.30404i	−0.0468707	−	0.368351i
$639$	1.66293	−	1.66293i	0.0657844	−	0.0657844i
$640$	−16.6481	+	20.3845i	−0.658072	+	0.805766i
$641$			10.3631i			0.409317i	0.978833	+	0.204659i	$0.0656084\pi$
$641$			10.3631i			0.409317i	−0.978833	+	0.204659i	$0.934392\pi$
$642$	12.9429	+	10.0208i	0.510814	+	0.395491i
$643$	−22.4337	+	22.4337i	−0.884699	+	0.884699i	−0.994008	−	0.109309i	$-0.965136\pi$
$643$	−22.4337	+	22.4337i	−0.884699	+	0.884699i	0.109309	+	0.994008i	$0.465136\pi$
$644$	10.6792	−	18.1321i	0.420821	−	0.714505i
$645$	9.75118	−	9.75118i	0.383952	−	0.383952i
$646$	5.29704	+	41.6287i	0.208409	+	1.63786i
$647$	31.3031			1.23065			0.615325	−	0.788273i	$-0.289025\pi$
$647$	31.3031			1.23065			0.615325	+	0.788273i	$0.289025\pi$
$648$	2.44675	−	5.69630i	0.0961174	−	0.223772i
$649$		−	12.6918i		−	0.498197i
$650$	0.0328889	+	2.09845i	0.00129001	+	0.0823081i
$651$		−	22.4882i		−	0.881383i
$652$	−7.76808	+	13.1893i	−0.304222	+	0.516533i
$653$	−18.5947			−0.727667			−0.363834	−	0.931464i	$-0.618532\pi$
$653$	−18.5947			−0.727667			−0.363834	+	0.931464i	$0.618532\pi$
$654$	−8.28145	+	1.05377i	−0.323830	+	0.0412058i
$655$	−28.2251	+	28.2251i	−1.10285	+	1.10285i
$656$	38.0559	+	10.9077i	1.48583	+	0.425874i
$657$	−6.50814	+	6.50814i	−0.253907	+	0.253907i
$658$	5.89600	−	7.61524i	0.229850	−	0.296873i
$659$		−	19.7433i		−	0.769089i	−0.923107	−	0.384544i	$-0.874359\pi$
$659$		−	19.7433i		−	0.769089i	0.923107	−	0.384544i	$-0.125641\pi$
$660$	1.06387	+	4.11271i	0.0414110	+	0.160087i
$661$	13.4724	−	13.4724i	0.524016	−	0.524016i	−0.394765	−	0.918782i	$-0.629174\pi$
$661$	13.4724	−	13.4724i	0.524016	−	0.524016i	0.918782	+	0.394765i	$0.129174\pi$
$662$	0.431117	−	0.0548574i	0.0167558	−	0.00213209i
$663$	10.1760	−	8.13683i	0.395201	−	0.316008i
$664$	12.5907	+	31.5511i	0.488614	+	1.22442i
$665$	−53.6153	−	53.6153i	−2.07911	−	2.07911i
$666$	−27.5231	+	3.50218i	−1.06650	+	0.135707i
$667$	16.0513			0.621509
$668$	15.3096	−	25.9940i	0.592348	−	1.00574i
$669$	14.2474	+	14.2474i	0.550836	+	0.550836i
$670$	−4.13771	−	3.20357i	−0.159854	−	0.123765i
$671$	−0.777637	−	0.777637i	−0.0300203	−	0.0300203i
$672$	−18.1060	+	13.2798i	−0.698455	+	0.512280i
$673$		−	29.3278i		−	1.13050i	−0.824919	−	0.565251i	$-0.808779\pi$
$673$		−	29.3278i		−	1.13050i	0.824919	−	0.565251i	$-0.191221\pi$
$674$	17.4303	−	22.5129i	0.671390	−	0.867163i
$675$	1.94155			0.0747301
$676$	25.9872	−	0.814792i	0.999509	−	0.0313382i
$677$	−15.6942			−0.603178			−0.301589	−	0.953438i	$-0.597517\pi$
$677$	−15.6942			−0.603178			−0.301589	+	0.953438i	$0.597517\pi$
$678$	−4.24747	+	5.48600i	−0.163123	+	0.210689i
$679$		−	41.1951i		−	1.58092i
$680$	−9.65158	−	24.1859i	−0.370121	−	0.927487i
$681$	4.52711	+	4.52711i	0.173479	+	0.173479i
$682$	6.33530	+	4.90503i	0.242591	+	0.187823i
$683$	−8.76602	−	8.76602i	−0.335422	−	0.335422i	0.519219	−	0.854641i	$-0.326223\pi$
$683$	−8.76602	−	8.76602i	−0.335422	−	0.335422i	−0.854641	+	0.519219i	$0.826223\pi$
$684$	27.9905	+	16.4855i	1.07024	+	0.630339i
$685$	14.0128			0.535403
$686$	−29.8772	+	3.80172i	−1.14072	+	0.145150i
$687$	−6.20051	−	6.20051i	−0.236564	−	0.236564i
$688$	−22.7123	+	12.5930i	−0.865897	+	0.480103i
$689$	7.97802	−	6.37933i	0.303938	−	0.243033i
$690$	−7.21201	+	0.917691i	−0.274557	+	0.0349359i
$691$	23.3516	−	23.3516i	0.888337	−	0.888337i	−0.106026	−	0.994363i	$-0.533813\pi$
$691$	23.3516	−	23.3516i	0.888337	−	0.888337i	0.994363	+	0.106026i	$0.0338128\pi$
$692$	22.8853	−	5.91993i	0.869970	−	0.225042i
$693$		−	9.41759i		−	0.357744i
$694$	−23.9802	+	30.9726i	−0.910275	+	1.17571i
$695$	−19.4018	+	19.4018i	−0.735950	+	0.735950i
$696$	−15.7370	−	6.75958i	−0.596511	−	0.256221i
$697$	−27.6971	+	27.6971i	−1.04910	+	1.04910i
$698$	−30.2695	+	3.85164i	−1.14572	+	0.145787i
$699$	2.92734			0.110722
$700$	3.08353	+	1.81610i	0.116547	+	0.0686423i
$701$			4.05559i			0.153178i	0.997063	+	0.0765888i	$0.0244029\pi$
$701$			4.05559i			0.153178i	−0.997063	+	0.0765888i	$0.975597\pi$
$702$	−0.376934	−	24.0500i	−0.0142265	−	0.907709i
$703$		−	67.9004i		−	2.56091i
$704$	0.208055	−	7.99729i	0.00784136	−	0.301409i
$705$	−3.32735			−0.125315
$706$	−0.272802	−	2.14391i	−0.0102670	−	0.0806873i
$707$	43.7795	−	43.7795i	1.64650	−	1.64650i
$708$	−19.9705	−	11.7620i	−0.750538	−	0.442043i
$709$	−25.3084	+	25.3084i	−0.950478	+	0.950478i	−0.998830	−	0.0483524i	$-0.984603\pi$
$709$	−25.3084	+	25.3084i	−0.950478	+	0.950478i	0.0483524	+	0.998830i	$0.484603\pi$
$710$	−2.82397	−	2.18642i	−0.105982	−	0.0820549i
$711$			11.7316i			0.439971i
$712$	−7.72095	−	19.3479i	−0.289355	−	0.725095i
$713$	−9.69589	+	9.69589i	−0.363114	+	0.363114i
$714$	−2.80433	−	22.0388i	−0.104949	−	0.824782i
$715$	−5.23810	−	6.55080i	−0.195894	−	0.244986i
$716$	−5.16043	−	19.9492i	−0.192854	−	0.745538i
$717$	10.5272	+	10.5272i	0.393146	+	0.393146i
$718$	−1.68432	−	13.2368i	−0.0628581	−	0.493993i
$719$	−26.9803			−1.00620			−0.503098	−	0.864229i	$-0.667807\pi$
$719$	−26.9803			−1.00620			−0.503098	+	0.864229i	$0.667807\pi$
$720$	−19.3776	−	5.55406i	−0.722161	−	0.206988i
$721$	−19.3238	−	19.3238i	−0.719656	−	0.719656i
$722$	−32.2192	+	41.6141i	−1.19907	+	1.54872i
$723$	−8.29747	−	8.29747i	−0.308586	−	0.308586i
$724$	−29.9128	+	7.73780i	−1.11170	+	0.287573i
$725$			2.72967i			0.101377i
$726$	−1.02101	−	0.790506i	−0.0378933	−	0.0293384i
$727$	−13.1675			−0.488354			−0.244177	−	0.969731i	$-0.578518\pi$
$727$	−13.1675			−0.488354			−0.244177	+	0.969731i	$0.578518\pi$
$728$	21.8975	−	38.5484i	0.811576	−	1.42870i
$729$	−8.17294			−0.302701
$730$	11.0521	+	8.55691i	0.409055	+	0.316706i
$731$		−	25.6952i		−	0.950370i
$732$	−1.94428	+	0.502942i	−0.0718625	+	0.0185893i
$733$	22.2907	+	22.2907i	0.823325	+	0.823325i	0.986583	−	0.163258i	$-0.0522003\pi$
$733$	22.2907	+	22.2907i	0.823325	+	0.823325i	−0.163258	+	0.986583i	$0.552200\pi$
$734$	−4.51077	+	5.82608i	−0.166496	+	0.215045i
$735$	17.8712	+	17.8712i	0.659189	+	0.659189i
$736$	13.5321	+	2.08083i	0.498801	+	0.0767004i
$737$	1.59062			0.0585914
$738$	3.82733	+	30.0785i	0.140886	+	1.10720i
$739$	25.2537	+	25.2537i	0.928974	+	0.928974i	0.997640	−	0.0686659i	$-0.0218743\pi$
$739$	25.2537	+	25.2537i	0.928974	+	0.928974i	−0.0686659	+	0.997640i	$0.521874\pi$
$740$	10.5520	+	40.7921i	0.387901	+	1.49955i
$741$	24.5313	+	2.73155i	0.901179	+	0.100346i
$742$	−2.19861	−	17.2786i	−0.0807136	−	0.634317i
$743$	−22.0188	+	22.0188i	−0.807792	+	0.807792i	−0.984299	−	0.176507i	$-0.943520\pi$
$743$	−22.0188	+	22.0188i	−0.807792	+	0.807792i	0.176507	+	0.984299i	$0.443520\pi$
$744$	13.5892	−	5.42289i	0.498205	−	0.198813i
$745$		−	8.13109i		−	0.297900i
$746$	36.8388	+	28.5220i	1.34877	+	1.04426i
$747$	−18.3977	+	18.3977i	−0.673137	+	0.673137i
$748$	6.82036	+	4.01698i	0.249377	+	0.146875i
$749$	−38.9674	+	38.9674i	−1.42384	+	1.42384i
$750$	1.73977	+	13.6726i	0.0635276	+	0.499254i
$751$	−20.2489			−0.738891			−0.369446	−	0.929252i	$-0.620452\pi$
$751$	−20.2489			−0.738891			−0.369446	+	0.929252i	$0.620452\pi$
$752$	6.02353	+	1.72648i	0.219655	+	0.0629582i
$753$		−	14.5326i		−	0.529596i
$754$	33.8125	−	0.529942i	1.23138	−	0.0192993i
$755$			44.1725i			1.60760i
$756$	−35.3398	−	20.8140i	−1.28530	−	0.757000i
$757$	−1.32154			−0.0480321			−0.0240161	−	0.999712i	$-0.507645\pi$
$757$	−1.32154			−0.0480321			−0.0240161	+	0.999712i	$0.507645\pi$
$758$	44.3518	−	5.64353i	1.61093	−	0.204982i
$759$	1.56261	−	1.56261i	0.0567193	−	0.0567193i
$760$	19.4697	−	45.3277i	0.706242	−	1.64421i
$761$	−31.2172	+	31.2172i	−1.13162	+	1.13162i	−0.141717	+	0.989907i	$0.545262\pi$
$761$	−31.2172	+	31.2172i	−1.13162	+	1.13162i	−0.989907	+	0.141717i	$0.954738\pi$
$762$	−0.718877	+	0.928497i	−0.0260422	+	0.0336359i
$763$		−	28.1058i		−	1.01750i
$764$	−39.2720	+	10.1588i	−1.42081	+	0.367533i
$765$	14.1030	−	14.1030i	0.509896	−	0.509896i
$766$	−3.90587	+	0.497003i	−0.141125	+	0.0179574i
$767$	45.4799	+	5.06418i	1.64218	+	0.182857i
$768$	−12.3909	−	7.73878i	−0.447118	−	0.279249i
$769$	31.4224	+	31.4224i	1.13312	+	1.13312i	0.989656	+	0.143464i	$0.0458242\pi$
$769$	31.4224	+	31.4224i	1.13312	+	1.13312i	0.143464	+	0.989656i	$0.454176\pi$
$770$	−14.1876	+	1.80529i	−0.511284	+	0.0650583i
$771$	24.3614			0.877354
$772$	−32.1438	−	18.9317i	−1.15688	−	0.681366i
$773$	−4.65084	−	4.65084i	−0.167279	−	0.167279i	0.618503	−	0.785782i	$-0.287739\pi$
$773$	−4.65084	−	4.65084i	−0.167279	−	0.167279i	−0.785782	+	0.618503i	$0.787739\pi$
$774$	−15.7276	−	12.1769i	−0.565315	−	0.437688i
$775$	−1.64888	−	1.64888i	−0.0592294	−	0.0592294i
$776$	24.8934	−	9.93392i	0.893622	−	0.356607i
$777$			35.9474i			1.28961i
$778$	−31.9440	+	41.2587i	−1.14525	+	1.47920i
$779$	−74.2045			−2.65865
$780$	−15.1620	+	2.17125i	−0.542887	+	0.0777433i
$781$	1.08559			0.0388455
$782$	−8.29303	+	10.7112i	−0.296558	+	0.383033i
$783$		−	31.2843i		−	1.11801i
$784$	−23.0794	−	41.6253i	−0.824266	−	1.48662i
$785$	−6.44995	−	6.44995i	−0.230209	−	0.230209i
$786$	−17.5194	−	13.5642i	−0.624897	−	0.483819i
$787$	34.4326	+	34.4326i	1.22739	+	1.22739i	0.964948	+	0.262441i	$0.0845275\pi$
$787$	34.4326	+	34.4326i	1.22739	+	1.22739i	0.262441	+	0.964948i	$0.415472\pi$
$788$	8.18741	−	13.9013i	0.291664	−	0.495212i
$789$	0.272013			0.00968391
$790$	17.6737	−	2.24888i	0.628801	−	0.0800117i
$791$	−16.5169	−	16.5169i	−0.587272	−	0.587272i
$792$	5.69087	−	2.27099i	0.202216	−	0.0806961i
$793$	3.09688	−	2.47630i	0.109973	−	0.0879361i
$794$	47.5466	−	6.05007i	1.68737	−	0.214709i
$795$	−4.25512	+	4.25512i	−0.150913	+	0.150913i
$796$	5.37601	+	20.7826i	0.190548	+	0.736621i
$797$		−	25.8903i		−	0.917080i	−0.888674	−	0.458540i	$-0.848373\pi$
$797$		−	25.8903i		−	0.917080i	0.888674	−	0.458540i	$-0.151627\pi$
$798$	25.7660	−	33.2792i	0.912105	−	1.17807i
$799$	−4.38392	+	4.38392i	−0.155092	+	0.155092i
$800$	−0.353864	+	2.30126i	−0.0125110	+	0.0813619i
$801$	11.2820	−	11.2820i	0.398629	−	0.398629i
$802$	−7.43928	+	0.946611i	−0.262690	+	0.0334260i
$803$	−4.24864			−0.149931
$804$	1.47409	−	2.50284i	0.0519873	−	0.0882684i
$805$		−	24.4763i		−	0.862677i
$806$	−20.1046	+	20.7448i	−0.708153	+	0.730704i
$807$			11.5370i			0.406121i
$808$	37.0123	+	15.8980i	1.30209	+	0.559290i
$809$	−24.5509			−0.863162			−0.431581	−	0.902074i	$-0.642044\pi$
$809$	−24.5509			−0.863162			−0.431581	+	0.902074i	$0.642044\pi$
$810$	−0.910218	−	7.15328i	−0.0319818	−	0.251341i
$811$	−7.72815	+	7.72815i	−0.271372	+	0.271372i	−0.829652	−	0.558280i	$-0.811461\pi$
$811$	−7.72815	+	7.72815i	−0.271372	+	0.271372i	0.558280	+	0.829652i	$0.311461\pi$
$812$	29.2630	−	49.6852i	1.02693	−	1.74361i
$813$	−14.3411	+	14.3411i	−0.502963	+	0.502963i
$814$	−10.1270	−	7.84068i	−0.354950	−	0.274816i
$815$			17.8041i			0.623649i
$816$	12.6414	−	7.00912i	0.442538	−	0.245368i
$817$	34.4205	−	34.4205i	1.20422	−	1.20422i
$818$	1.41062	+	11.0859i	0.0493211	+	0.387608i
$819$	33.7470	+	3.75773i	1.17922	+	0.131306i
$820$	44.5794	−	11.5317i	1.55678	−	0.402705i
$821$	−14.0543	−	14.0543i	−0.490499	−	0.490499i	0.417965	−	0.908463i	$-0.362744\pi$
$821$	−14.0543	−	14.0543i	−0.490499	−	0.490499i	−0.908463	+	0.417965i	$0.862744\pi$
$822$	0.981821	+	7.71600i	0.0342449	+	0.269126i
$823$	−2.65079			−0.0924008			−0.0462004	−	0.998932i	$-0.514711\pi$
$823$	−2.65079			−0.0924008			−0.0462004	+	0.998932i	$0.514711\pi$
$824$	7.01721	−	16.3368i	0.244456	−	0.569120i
$825$	0.265737	+	0.265737i	0.00925177	+	0.00925177i
$826$	47.7690	−	61.6981i	1.66209	−	2.14675i
$827$	33.7515	+	33.7515i	1.17365	+	1.17365i	0.981332	+	0.192323i	$0.0616020\pi$
$827$	33.7515	+	33.7515i	1.17365	+	1.17365i	0.192323	+	0.981332i	$0.438398\pi$
$828$	2.62611	+	10.1520i	0.0912635	+	0.352807i
$829$			25.8083i			0.896360i	0.893943	+	0.448180i	$0.147928\pi$
$829$			25.8083i			0.896360i	−0.893943	+	0.448180i	$0.852072\pi$
$830$	31.2428	+	24.1893i	1.08445	+	0.839624i
$831$	2.32373			0.0806092
$832$	28.5745	+	3.93656i	0.990643	+	0.136476i
$833$	47.0921			1.63164
$834$	−12.0427	−	9.32393i	−0.417005	−	0.322861i
$835$		−	35.0889i		−	1.21430i
$836$	3.75533	+	14.5174i	0.129881	+	0.502094i
$837$	18.8975	+	18.8975i	0.653192	+	0.653192i
$838$	−13.1305	+	16.9593i	−0.453586	+	0.585849i
$839$	−22.1346	−	22.1346i	−0.764171	−	0.764171i	0.212902	−	0.977074i	$-0.431708\pi$
$839$	−22.1346	−	22.1346i	−0.764171	−	0.764171i	−0.977074	+	0.212902i	$0.931708\pi$
$840$	−10.3075	+	23.9971i	−0.355644	+	0.827978i
$841$	14.9834			0.516670
$842$	−0.432625	−	3.39994i	−0.0149092	−	0.117170i
$843$	−1.52630	−	1.52630i	−0.0525687	−	0.0525687i
$844$	−31.8357	+	8.23519i	−1.09583	+	0.283467i
$845$	25.5642	−	16.1564i	0.879436	−	0.555797i
$846$	0.605793	+	4.76085i	0.0208276	+	0.163681i
$847$	3.07399	−	3.07399i	0.105624	−	0.105624i
$848$	9.91095	−	5.49520i	0.340343	−	0.188706i
$849$		−	15.4357i		−	0.529751i
$850$	−1.82154	−	1.41031i	−0.0624784	−	0.0483731i
$851$	15.4989	−	15.4989i	0.531294	−	0.531294i
$852$	1.00606	−	1.70817i	0.0344671	−	0.0585211i
$853$	−37.4684	+	37.4684i	−1.28289	+	1.28289i	−0.343879	+	0.939014i	$0.611741\pi$
$853$	−37.4684	+	37.4684i	−1.28289	+	1.28289i	−0.939014	+	0.343879i	$0.888259\pi$
$854$	−0.853449	−	6.70713i	−0.0292044	−	0.229513i
$855$	37.7840			1.29218
$856$	−32.9440	−	14.1505i	−1.12600	−	0.483656i
$857$			21.7166i			0.741827i	0.928667	+	0.370913i	$0.120955\pi$
$857$			21.7166i			0.741827i	−0.928667	+	0.370913i	$0.879045\pi$
$858$	3.24010	−	3.34328i	0.110615	−	0.114138i
$859$		−	23.4253i		−	0.799261i	−0.916676	−	0.399631i	$-0.869138\pi$
$859$		−	23.4253i		−	0.799261i	0.916676	−	0.399631i	$-0.130862\pi$
$860$	−15.3295	+	26.0277i	−0.522732	+	0.887538i
$861$	39.2849			1.33882
$862$	−5.45183	+	0.693718i	−0.185690	+	0.0236281i
$863$	6.61654	−	6.61654i	0.225230	−	0.225230i	−0.585467	−	0.810696i	$-0.699089\pi$
$863$	6.61654	−	6.61654i	0.225230	−	0.225230i	0.810696	+	0.585467i	$0.199089\pi$
$864$	4.05557	−	26.3744i	0.137973	−	0.897274i
$865$	19.4419	−	19.4419i	0.661046	−	0.661046i
$866$	16.1425	−	20.8495i	0.548544	−	0.708496i
$867$		−	1.22042i		−	0.0414477i
$868$	12.3361	+	47.6892i	0.418716	+	1.61868i
$869$	−3.82932	+	3.82932i	−0.129901	+	0.129901i
$870$	−19.7622	+	2.51464i	−0.670001	+	0.0852542i
$871$	−0.634678	+	5.69985i	−0.0215052	+	0.193132i
$872$	16.9838	−	6.77753i	0.575145	−	0.229516i
$873$	14.5156	+	14.5156i	0.491278	+	0.491278i
$874$	−25.4575	+	3.23934i	−0.861114	+	0.109572i
$875$	−46.4026			−1.56869
$876$	−3.93738	+	6.68522i	−0.133032	+	0.225873i
$877$	−8.50128	−	8.50128i	−0.287068	−	0.287068i	0.548852	−	0.835920i	$-0.315065\pi$
$877$	−8.50128	−	8.50128i	−0.287068	−	0.287068i	−0.835920	+	0.548852i	$0.815065\pi$
$878$	−34.3824	−	26.6201i	−1.16035	−	0.898386i
$879$	−2.16476	−	2.16476i	−0.0730157	−	0.0730157i
$880$	−4.51214	−	8.13794i	−0.152104	−	0.274330i
$881$		−	20.6755i		−	0.696575i	−0.937388	−	0.348287i	$-0.886763\pi$
$881$		−	20.6755i		−	0.696575i	0.937388	−	0.348287i	$-0.113237\pi$
$882$	22.3168	−	28.8242i	0.751445	−	0.970562i
$883$	−4.29902			−0.144674			−0.0723368	−	0.997380i	$-0.523046\pi$
$883$	−4.29902			−0.144674			−0.0723368	+	0.997380i	$0.523046\pi$
$884$	−17.1159	+	22.8373i	−0.575669	+	0.768102i
$885$	−26.9579			−0.906181
$886$	31.8529	−	41.1410i	1.07012	−	1.38216i
$887$			26.9120i			0.903615i	0.892115	+	0.451808i	$0.149221\pi$
$887$			26.9120i			0.903615i	−0.892115	+	0.451808i	$0.850779\pi$
$888$	−21.7223	+	8.66848i	−0.728954	+	0.290895i
$889$	−2.79545	−	2.79545i	−0.0937564	−	0.0937564i
$890$	−19.1589	−	14.8335i	−0.642208	−	0.497222i
$891$	1.54989	+	1.54989i	0.0519232	+	0.0519232i
$892$	−38.0289	−	22.3978i	−1.27330	−	0.749935i
$893$	−11.7451			−0.393036
$894$	4.47728	−	0.569711i	0.149743	−	0.0190540i
$895$	−16.9476	−	16.9476i	−0.566497	−	0.566497i
$896$	31.1113	−	38.0938i	1.03936	−	1.27262i
$897$	4.97597	+	6.22298i	0.166143	+	0.207779i
$898$	−10.8244	+	1.37735i	−0.361215	+	0.0459628i
$899$	−26.5685	+	26.5685i	−0.886108	+	0.886108i
$900$	−1.72645	+	0.446594i	−0.0575482	+	0.0148865i
$901$			11.2126i			0.373546i
$902$	−8.56863	+	11.0672i	−0.285304	+	0.368497i
$903$	−18.2227	+	18.2227i	−0.606413	+	0.606413i
$904$	5.99790	−	13.9638i	0.199487	−	0.464428i
$905$	−25.4121	+	25.4121i	−0.844726	+	0.844726i
$906$	−24.3230	+	3.09498i	−0.808078	+	0.102824i
$907$	21.9817			0.729890			0.364945	−	0.931029i	$-0.381088\pi$
$907$	21.9817			0.729890			0.364945	+	0.931029i	$0.381088\pi$
$908$	−12.0837	−	7.11693i	−0.401012	−	0.236184i
$909$			30.8525i			1.02331i
$910$	−0.808098	−	51.5601i	−0.0267882	−	1.70920i
$911$			6.77172i			0.224357i	0.993688	+	0.112179i	$0.0357829\pi$
$911$			6.77172i			0.224357i	−0.993688	+	0.112179i	$0.964217\pi$
$912$	26.3233	+	7.54484i	0.871651	+	0.249835i
$913$	−12.0104			−0.397486
$914$	0.711651	+	5.59277i	0.0235393	+	0.184992i
$915$	−1.65173	+	1.65173i	−0.0546047	+	0.0546047i
$916$	16.5503	+	9.74762i	0.546838	+	0.322070i
$917$	52.7462	−	52.7462i	1.74183	−	1.74183i
$918$	20.8764	+	16.1633i	0.689023	+	0.533467i
$919$		−	10.4170i		−	0.343624i	−0.985130	−	0.171812i	$-0.945038\pi$
$919$		−	10.4170i		−	0.343624i	0.985130	−	0.171812i	$-0.0549621\pi$
$920$	14.7906	−	5.90230i	0.487631	−	0.194593i
$921$	−18.3851	+	18.3851i	−0.605809	+	0.605809i
$922$	3.72452	+	29.2705i	0.122660	+	0.963972i
$923$	−0.433164	+	3.89011i	−0.0142578	+	0.128045i
$924$	−1.98812	−	7.68571i	−0.0654045	−	0.252841i
$925$	2.63572	+	2.63572i	0.0866621	+	0.0866621i
$926$	−4.74338	−	37.2776i	−0.155877	−	1.22502i
$927$	13.6180			0.447272
$928$	37.0804	+	5.70184i	1.21722	+	0.187172i
$929$	15.5512	+	15.5512i	0.510218	+	0.510218i	0.914593	−	0.404375i	$-0.132511\pi$
$929$	15.5512	+	15.5512i	0.510218	+	0.510218i	−0.404375	+	0.914593i	$0.632511\pi$
$930$	10.4185	−	13.4565i	0.341636	−	0.441255i
$931$	63.0832	+	63.0832i	2.06747	+	2.06747i
$932$	−6.20781	+	1.60582i	−0.203343	+	0.0526005i
$933$		−	0.794890i		−	0.0260235i
$934$	−13.9513	−	10.8016i	−0.456500	−	0.353440i
$935$	9.20673			0.301092
$936$	5.86715	+	21.2988i	0.191774	+	0.696175i
$937$	−35.6529			−1.16473			−0.582364	−	0.812928i	$-0.697872\pi$
$937$	−35.6529			−1.16473			−0.582364	+	0.812928i	$0.697872\pi$
$938$	7.73243	+	5.98673i	0.252473	+	0.195474i
$939$			6.32740i			0.206487i
$940$	7.05607	−	1.82525i	0.230144	−	0.0595331i
$941$	−24.0044	−	24.0044i	−0.782522	−	0.782522i	0.197734	−	0.980256i	$-0.436642\pi$
$941$	−24.0044	−	24.0044i	−0.782522	−	0.782522i	−0.980256	+	0.197734i	$0.936642\pi$
$942$	3.09966	−	4.00350i	0.100992	−	0.130441i
$943$	−16.9378	−	16.9378i	−0.551571	−	0.551571i
$944$	48.8022	+	13.9878i	1.58838	+	0.455264i
$945$	−47.7048			−1.55184
$946$	−1.15898	−	9.10827i	−0.0376817	−	0.296135i
$947$	−0.592048	−	0.592048i	−0.0192390	−	0.0192390i	0.697422	−	0.716661i	$-0.254330\pi$
$947$	−0.592048	−	0.592048i	−0.0192390	−	0.0192390i	−0.716661	+	0.697422i	$0.754330\pi$
$948$	2.47664	+	9.57421i	0.0804375	+	0.310956i
$949$	1.69526	−	15.2246i	0.0550304	−	0.494211i
$950$	−0.550880	−	4.32929i	−0.0178729	−	0.140461i
$951$	8.35368	−	8.35368i	0.270886	−	0.270886i
$952$	18.0366	+	45.1978i	0.584568	+	1.46487i
$953$		−	11.2346i		−	0.363924i	−0.983306	−	0.181962i	$-0.941755\pi$
$953$		−	11.2346i		−	0.363924i	0.983306	−	0.181962i	$-0.0582448\pi$
$954$	6.86303	+	5.31361i	0.222199	+	0.172035i
$955$	−33.3630	+	33.3630i	−1.07960	+	1.07960i
$956$	−28.0991	−	16.5495i	−0.908789	−	0.535248i
$957$	4.28184	−	4.28184i	0.138412	−	0.138412i
$958$	−3.77052	−	29.6320i	−0.121820	−	0.957366i
$959$	−26.1868			−0.845614
$960$	−16.9866	−	0.441917i	−0.548240	−	0.0142628i
$961$		−	1.09768i		−	0.0354092i
$962$	32.1371	−	33.1605i	1.03614	−	1.06914i
$963$		−	27.4613i		−	0.884927i
$964$	22.1475	+	13.0442i	0.713323	+	0.420125i
$965$	−43.3905			−1.39679
$966$	13.4776	−	1.71495i	0.433634	−	0.0551777i
$967$	−20.6703	+	20.6703i	−0.664712	+	0.664712i	−0.956487	−	0.291775i	$-0.905754\pi$
$967$	−20.6703	+	20.6703i	−0.664712	+	0.664712i	0.291775	+	0.956487i	$0.405754\pi$
$968$	2.59883	+	1.11628i	0.0835295	+	0.0358787i
$969$	−19.1581	+	19.1581i	−0.615446	+	0.615446i
$970$	19.0851	−	24.6502i	0.612786	−	0.791471i
$971$		−	23.3043i		−	0.747870i	−0.927455	−	0.373935i	$-0.878008\pi$
$971$		−	23.3043i		−	0.747870i	0.927455	−	0.373935i	$-0.121992\pi$
$972$	31.2762	−	8.09047i	1.00318	−	0.259502i
$973$	36.2574	−	36.2574i	1.16236	−	1.16236i
$974$	−12.6556	+	1.61036i	−0.405510	+	0.0515991i
$975$	−1.05827	+	0.846211i	−0.0338919	+	0.0271004i
$976$	3.84719	−	2.13310i	0.123146	−	0.0682790i
$977$	−11.5363	−	11.5363i	−0.369078	−	0.369078i	0.498063	−	0.867141i	$-0.334045\pi$
$977$	−11.5363	−	11.5363i	−0.369078	−	0.369078i	−0.867141	+	0.498063i	$0.834045\pi$
$978$	−9.80358	+	1.24746i	−0.313484	+	0.0398892i
$979$	7.36509			0.235389
$980$	−47.7016	−	28.0947i	−1.52377	−	0.897453i
$981$	9.90342	+	9.90342i	0.316192	+	0.316192i
$982$	24.4419	+	18.9239i	0.779973	+	0.603884i
$983$	27.0260	+	27.0260i	0.861996	+	0.861996i	0.991570	−	0.129573i	$-0.0413608\pi$
$983$	27.0260	+	27.0260i	0.861996	+	0.861996i	−0.129573	+	0.991570i	$0.541361\pi$
$984$	9.47328	+	23.7391i	0.301997	+	0.756775i
$985$		−	18.7651i		−	0.597907i
$986$	−22.7244	+	29.3507i	−0.723691	+	0.934715i
$987$	6.21804			0.197922
$988$	−53.5201	+	7.66426i	−1.70270	+	0.243833i
$989$	15.7136			0.499662
$990$	4.36304	−	5.63527i	0.138666	−	0.179101i
$991$			34.6700i			1.10133i	0.834726	+	0.550665i	$0.185626\pi$
$991$			34.6700i			1.10133i	−0.834726	+	0.550665i	$0.814374\pi$
$992$	−25.8429	+	18.9544i	−0.820513	+	0.601804i
$993$	0.198405	+	0.198405i	0.00629620	+	0.00629620i
$994$	5.27734	+	4.08591i	0.167387	+	0.129597i
$995$	17.6556	+	17.6556i	0.559721	+	0.559721i
$996$	−11.1305	+	18.8983i	−0.352683	+	0.598815i
$997$	−37.4186			−1.18506			−0.592529	−	0.805549i	$-0.701871\pi$
$997$	−37.4186			−1.18506			−0.592529	+	0.805549i	$0.701871\pi$
$998$	−34.1762	+	4.34875i	−1.08183	+	0.137657i
$999$	−30.2076	−	30.2076i	−0.955725	−	0.955725i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	572.2.j.a.463.14	✓	140
4.3	odd	2	inner	572.2.j.a.463.20	yes	140
13.5	odd	4	inner	572.2.j.a.551.20	yes	140
52.31	even	4	inner	572.2.j.a.551.14	yes	140

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
572.2.j.a.463.14	✓	140	1.1	even	1	trivial
572.2.j.a.463.20	yes	140	4.3	odd	2	inner
572.2.j.a.551.14	yes	140	52.31	even	4	inner
572.2.j.a.551.20	yes	140	13.5	odd	4	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:	\( N \)	\(=\)	\( 572 = 2^{2} \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	572.j (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.11823 - 0.865774i) q^{2} -0.913063i q^{3} +(0.500870 + 1.93627i) q^{4} +(1.64493 + 1.64493i) q^{5} +(-0.790506 + 1.02101i) q^{6} +(-3.07399 - 3.07399i) q^{7} +(1.11628 - 2.59883i) q^{8} +2.16632 q^{9} +O(q^{10})\)	\(q+(-1.11823 - 0.865774i) q^{2} -0.913063i q^{3} +(0.500870 + 1.93627i) q^{4} +(1.64493 + 1.64493i) q^{5} +(-0.790506 + 1.02101i) q^{6} +(-3.07399 - 3.07399i) q^{7} +(1.11628 - 2.59883i) q^{8} +2.16632 q^{9} +(-0.415270 - 3.26355i) q^{10} +(0.707107 + 0.707107i) q^{11} +(1.76793 - 0.457326i) q^{12} +(-2.81599 + 2.25171i) q^{13} +(0.776042 + 6.09881i) q^{14} +(1.50192 - 1.50192i) q^{15} +(-3.49826 + 1.93964i) q^{16} -3.95770i q^{17} +(-2.42244 - 1.87554i) q^{18} +(5.30162 - 5.30162i) q^{19} +(-2.36113 + 4.00892i) q^{20} +(-2.80675 + 2.80675i) q^{21} +(-0.178512 - 1.40290i) q^{22} +2.42028 q^{23} +(-2.37289 - 1.01924i) q^{24} +0.411591i q^{25} +(5.09839 - 0.0799068i) q^{26} -4.71717i q^{27} +(4.41240 - 7.49174i) q^{28} +6.63200 q^{29} +(-2.97982 + 0.379167i) q^{30} +(-4.00610 + 4.00610i) q^{31} +(5.59114 + 0.859747i) q^{32} +(0.645633 - 0.645633i) q^{33} +(-3.42647 + 4.42561i) q^{34} -10.1130i q^{35} +(1.08504 + 4.19457i) q^{36} +(6.40374 - 6.40374i) q^{37} +(-10.5184 + 1.33842i) q^{38} +(2.05595 + 2.57118i) q^{39} +(6.11110 - 2.43868i) q^{40} +(-6.99829 - 6.99829i) q^{41} +(5.56860 - 0.708575i) q^{42} +6.49245 q^{43} +(-1.01498 + 1.72332i) q^{44} +(3.56344 + 3.56344i) q^{45} +(-2.70643 - 2.09542i) q^{46} +(-1.10769 - 1.10769i) q^{47} +(1.77101 + 3.19413i) q^{48} +11.8989i q^{49} +(0.356345 - 0.460253i) q^{50} -3.61363 q^{51} +(-5.77035 - 4.32470i) q^{52} -2.83311 q^{53} +(-4.08401 + 5.27488i) q^{54} +2.32628i q^{55} +(-11.4202 + 4.55733i) q^{56} +(-4.84071 - 4.84071i) q^{57} +(-7.41609 - 5.74181i) q^{58} +(-8.97446 - 8.97446i) q^{59} +(3.66040 + 2.15586i) q^{60} -1.09975 q^{61} +(7.94811 - 1.01136i) q^{62} +(-6.65924 - 6.65924i) q^{63} +(-5.50782 - 5.80206i) q^{64} +(-8.33601 - 0.928214i) q^{65} +(-1.28094 + 0.162993i) q^{66} +(1.12474 - 1.12474i) q^{67} +(7.66316 - 1.98229i) q^{68} -2.20987i q^{69} +(-8.75558 + 11.3087i) q^{70} +(0.767629 - 0.767629i) q^{71} +(2.41822 - 5.62988i) q^{72} +(-3.00424 + 3.00424i) q^{73} +(-12.7050 + 1.61665i) q^{74} +0.375809 q^{75} +(12.9208 + 7.60992i) q^{76} -4.34728i q^{77} +(-0.0729599 - 4.65515i) q^{78} +5.41548i q^{79} +(-8.94496 - 2.56383i) q^{80} +2.19187 q^{81} +(1.76675 + 13.8846i) q^{82} +(-8.49263 + 8.49263i) q^{83} +(-6.84043 - 4.02880i) q^{84} +(6.51014 - 6.51014i) q^{85} +(-7.26004 - 5.62100i) q^{86} -6.05543i q^{87} +(2.62698 - 1.04832i) q^{88} +(5.20790 - 5.20790i) q^{89} +(-0.899605 - 7.06987i) q^{90} +(15.5781 + 1.73462i) q^{91} +(1.21225 + 4.68631i) q^{92} +(3.65782 + 3.65782i) q^{93} +(0.279642 + 2.19767i) q^{94} +17.4416 q^{95} +(0.785003 - 5.10506i) q^{96} +(6.70059 + 6.70059i) q^{97} +(10.3017 - 13.3056i) q^{98} +(1.53182 + 1.53182i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 140 q + 4 q^{5} - 12 q^{6} + 12 q^{8} - 140 q^{9}+O(q^{10}) \) 140 * q + 4 * q^5 - 12 * q^6 + 12 * q^8 - 140 * q^9	\( 140 q + 4 q^{5} - 12 q^{6} + 12 q^{8} - 140 q^{9} + 16 q^{14} - 12 q^{18} - 8 q^{20} - 16 q^{21} - 32 q^{26} - 20 q^{28} + 20 q^{32} - 8 q^{34} + 36 q^{37} - 80 q^{40} - 20 q^{41} - 20 q^{42} - 8 q^{44} - 20 q^{45} + 60 q^{46} + 20 q^{48} + 88 q^{50} - 8 q^{53} + 88 q^{54} - 80 q^{57} - 60 q^{58} + 12 q^{60} - 40 q^{61} - 20 q^{65} - 20 q^{66} - 80 q^{68} - 28 q^{70} + 20 q^{72} + 100 q^{73} - 136 q^{74} - 32 q^{76} - 88 q^{78} - 72 q^{80} + 140 q^{81} + 92 q^{84} + 24 q^{85} - 32 q^{86} - 60 q^{89} - 68 q^{92} - 80 q^{93} + 64 q^{94} + 100 q^{96} - 20 q^{97} + 92 q^{98}+O(q^{100}) \) 140 * q + 4 * q^5 - 12 * q^6 + 12 * q^8 - 140 * q^9 + 16 * q^14 - 12 * q^18 - 8 * q^20 - 16 * q^21 - 32 * q^26 - 20 * q^28 + 20 * q^32 - 8 * q^34 + 36 * q^37 - 80 * q^40 - 20 * q^41 - 20 * q^42 - 8 * q^44 - 20 * q^45 + 60 * q^46 + 20 * q^48 + 88 * q^50 - 8 * q^53 + 88 * q^54 - 80 * q^57 - 60 * q^58 + 12 * q^60 - 40 * q^61 - 20 * q^65 - 20 * q^66 - 80 * q^68 - 28 * q^70 + 20 * q^72 + 100 * q^73 - 136 * q^74 - 32 * q^76 - 88 * q^78 - 72 * q^80 + 140 * q^81 + 92 * q^84 + 24 * q^85 - 32 * q^86 - 60 * q^89 - 68 * q^92 - 80 * q^93 + 64 * q^94 + 100 * q^96 - 20 * q^97 + 92 * q^98

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