LMFDB - Embedded newform 430.2.g.b.257.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [430,2,Mod(257,430)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(430, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("430.257");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 430 = 2 \cdot 5 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	430.g (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:	$3.43356728692$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$20$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			257.3
Character	$\chi$	$=$	430.257
Dual form			430.2.g.b.343.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 + 0.707107i) q^{2} +(-1.12833 - 1.12833i) q^{3} -1.00000i q^{4} +(-1.89019 - 1.19465i) q^{5} +1.59570 q^{6} +(0.600193 - 0.600193i) q^{7} +(0.707107 + 0.707107i) q^{8} -0.453751i q^{9} +O(q^{10})$	\(q+(-0.707107 + 0.707107i) q^{2} +(-1.12833 - 1.12833i) q^{3} -1.00000i q^{4} +(-1.89019 - 1.19465i) q^{5} +1.59570 q^{6} +(0.600193 - 0.600193i) q^{7} +(0.707107 + 0.707107i) q^{8} -0.453751i q^{9} +(2.18131 - 0.491820i) q^{10} +3.86104 q^{11} +(-1.12833 + 1.12833i) q^{12} +(-3.06758 + 3.06758i) q^{13} +0.848801i q^{14} +(0.784796 + 3.48071i) q^{15} -1.00000 q^{16} +(-3.44039 - 3.44039i) q^{17} +(0.320851 + 0.320851i) q^{18} -5.26434 q^{19} +(-1.19465 + 1.89019i) q^{20} -1.35443 q^{21} +(-2.73017 + 2.73017i) q^{22} +(-2.29351 + 2.29351i) q^{23} -1.59570i q^{24} +(2.14563 + 4.51623i) q^{25} -4.33821i q^{26} +(-3.89696 + 3.89696i) q^{27} +(-0.600193 - 0.600193i) q^{28} +1.15814 q^{29} +(-3.01617 - 1.90630i) q^{30} -8.29732 q^{31} +(0.707107 - 0.707107i) q^{32} +(-4.35652 - 4.35652i) q^{33} +4.86544 q^{34} +(-1.85150 + 0.417458i) q^{35} -0.453751 q^{36} +(-2.98811 + 2.98811i) q^{37} +(3.72245 - 3.72245i) q^{38} +6.92246 q^{39} +(-0.491820 - 2.18131i) q^{40} +6.25012 q^{41} +(0.957726 - 0.957726i) q^{42} +(4.40938 + 4.85359i) q^{43} -3.86104i q^{44} +(-0.542074 + 0.857675i) q^{45} -3.24351i q^{46} +(-8.96474 - 8.96474i) q^{47} +(1.12833 + 1.12833i) q^{48} +6.27954i q^{49} +(-4.71064 - 1.67627i) q^{50} +7.76378i q^{51} +(3.06758 + 3.06758i) q^{52} +(-0.712186 + 0.712186i) q^{53} -5.51114i q^{54} +(-7.29810 - 4.61259i) q^{55} +0.848801 q^{56} +(5.93991 + 5.93991i) q^{57} +(-0.818932 + 0.818932i) q^{58} -6.93170i q^{59} +(3.48071 - 0.784796i) q^{60} -0.0822438i q^{61} +(5.86709 - 5.86709i) q^{62} +(-0.272338 - 0.272338i) q^{63} +1.00000i q^{64} +(9.46297 - 2.13362i) q^{65} +6.16106 q^{66} +(-4.42045 - 4.42045i) q^{67} +(-3.44039 + 3.44039i) q^{68} +5.17566 q^{69} +(1.01402 - 1.60439i) q^{70} -6.42737i q^{71} +(0.320851 - 0.320851i) q^{72} +(0.675425 + 0.675425i) q^{73} -4.22582i q^{74} +(2.67481 - 7.51675i) q^{75} +5.26434i q^{76} +(2.31737 - 2.31737i) q^{77} +(-4.89492 + 4.89492i) q^{78} -8.61935i q^{79} +(1.89019 + 1.19465i) q^{80} +7.43286 q^{81} +(-4.41950 + 4.41950i) q^{82} +(-6.64942 + 6.64942i) q^{83} +1.35443i q^{84} +(2.39293 + 10.6130i) q^{85} +(-6.54991 - 0.314101i) q^{86} +(-1.30677 - 1.30677i) q^{87} +(2.73017 + 2.73017i) q^{88} +10.6483 q^{89} +(-0.223164 - 0.989772i) q^{90} +3.68228i q^{91} +(2.29351 + 2.29351i) q^{92} +(9.36210 + 9.36210i) q^{93} +12.6781 q^{94} +(9.95060 + 6.28905i) q^{95} -1.59570 q^{96} +(-0.895557 - 0.895557i) q^{97} +(-4.44030 - 4.44030i) q^{98} -1.75195i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q+O(q^{10}) $ 40 * q	$ 40 q - 8 q^{10} + 16 q^{11} - 24 q^{13} + 8 q^{15} - 40 q^{16} - 12 q^{17} - 16 q^{21} + 44 q^{23} + 24 q^{25} + 32 q^{31} - 64 q^{35} + 48 q^{36} - 28 q^{38} - 4 q^{40} + 8 q^{41} - 16 q^{43} - 28 q^{47} + 24 q^{52} - 80 q^{53} + 24 q^{56} + 64 q^{57} + 12 q^{58} + 24 q^{67} - 12 q^{68} + 40 q^{78} - 120 q^{81} + 48 q^{83} + 28 q^{87} - 44 q^{92} - 16 q^{95} - 60 q^{97}+O(q^{100}) $ 40 * q - 8 * q^10 + 16 * q^11 - 24 * q^13 + 8 * q^15 - 40 * q^16 - 12 * q^17 - 16 * q^21 + 44 * q^23 + 24 * q^25 + 32 * q^31 - 64 * q^35 + 48 * q^36 - 28 * q^38 - 4 * q^40 + 8 * q^41 - 16 * q^43 - 28 * q^47 + 24 * q^52 - 80 * q^53 + 24 * q^56 + 64 * q^57 + 12 * q^58 + 24 * q^67 - 12 * q^68 + 40 * q^78 - 120 * q^81 + 48 * q^83 + 28 * q^87 - 44 * q^92 - 16 * q^95 - 60 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/430\mathbb{Z}\right)^\times$.

$n$	$87$	$261$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$

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 $

$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$3$	−1.12833	−	1.12833i	−0.651441	−	0.651441i	0.301899	−	0.953340i	$-0.402379\pi$
$3$	−1.12833	−	1.12833i	−0.651441	−	0.651441i	−0.953340	+	0.301899i	$0.902379\pi$
$4$		−	1.00000i		−	0.500000i
$5$	−1.89019	−	1.19465i	−0.845318	−	0.534263i
$5$	−1.89019	−	1.19465i	−0.845318	−	0.534263i
$6$	1.59570			0.651441
$7$	0.600193	−	0.600193i	0.226852	−	0.226852i	−0.584524	−	0.811376i	$-0.698719\pi$
$7$	0.600193	−	0.600193i	0.226852	−	0.226852i	0.811376	+	0.584524i	$0.198719\pi$
$8$	0.707107	+	0.707107i	0.250000	+	0.250000i
$9$		−	0.453751i		−	0.151250i
$10$	2.18131	−	0.491820i	0.689791	−	0.155527i
$11$	3.86104			1.16415			0.582074	−	0.813136i	$-0.302241\pi$
$11$	3.86104			1.16415			0.582074	+	0.813136i	$0.302241\pi$
$12$	−1.12833	+	1.12833i	−0.325720	+	0.325720i
$13$	−3.06758	+	3.06758i	−0.850792	+	0.850792i	−0.990231	−	0.139438i	$-0.955470\pi$
$13$	−3.06758	+	3.06758i	−0.850792	+	0.850792i	0.139438	+	0.990231i	$0.455470\pi$
$14$			0.848801i			0.226852i
$15$	0.784796	+	3.48071i	0.202634	+	0.898715i
$16$	−1.00000			−0.250000
$17$	−3.44039	−	3.44039i	−0.834417	−	0.834417i	0.153701	−	0.988117i	$-0.450881\pi$
$17$	−3.44039	−	3.44039i	−0.834417	−	0.834417i	−0.988117	+	0.153701i	$0.950881\pi$
$18$	0.320851	+	0.320851i	0.0756252	+	0.0756252i
$19$	−5.26434			−1.20772			−0.603862	−	0.797089i	$-0.706372\pi$
$19$	−5.26434			−1.20772			−0.603862	+	0.797089i	$0.706372\pi$
$20$	−1.19465	+	1.89019i	−0.267132	+	0.422659i
$21$	−1.35443			−0.295561
$22$	−2.73017	+	2.73017i	−0.582074	+	0.582074i
$23$	−2.29351	+	2.29351i	−0.478230	+	0.478230i	−0.904565	−	0.426335i	$-0.859804\pi$
$23$	−2.29351	+	2.29351i	−0.478230	+	0.478230i	0.426335	+	0.904565i	$0.359804\pi$
$24$		−	1.59570i		−	0.325720i
$25$	2.14563	+	4.51623i	0.429125	+	0.903245i
$26$		−	4.33821i		−	0.850792i
$27$	−3.89696	+	3.89696i	−0.749971	+	0.749971i
$28$	−0.600193	−	0.600193i	−0.113426	−	0.113426i
$29$	1.15814			0.215062			0.107531	−	0.994202i	$-0.465706\pi$
$29$	1.15814			0.215062			0.107531	+	0.994202i	$0.465706\pi$
$30$	−3.01617	−	1.90630i	−0.550674	−	0.348041i
$31$	−8.29732			−1.49024			−0.745121	−	0.666929i	$-0.767608\pi$
$31$	−8.29732			−1.49024			−0.745121	+	0.666929i	$0.767608\pi$
$32$	0.707107	−	0.707107i	0.125000	−	0.125000i
$33$	−4.35652	−	4.35652i	−0.758374	−	0.758374i
$34$	4.86544			0.834417
$35$	−1.85150	+	0.417458i	−0.312960	+	0.0705633i
$36$	−0.453751			−0.0756252
$37$	−2.98811	+	2.98811i	−0.491242	+	0.491242i	−0.908697	−	0.417455i	$-0.862922\pi$
$37$	−2.98811	+	2.98811i	−0.491242	+	0.491242i	0.417455	+	0.908697i	$0.362922\pi$
$38$	3.72245	−	3.72245i	0.603862	−	0.603862i
$39$	6.92246			1.10848
$40$	−0.491820	−	2.18131i	−0.0777636	−	0.344895i
$41$	6.25012			0.976105			0.488052	−	0.872814i	$-0.337708\pi$
$41$	6.25012			0.976105			0.488052	+	0.872814i	$0.337708\pi$
$42$	0.957726	−	0.957726i	0.147780	−	0.147780i
$43$	4.40938	+	4.85359i	0.672425	+	0.740165i
$43$	4.40938	+	4.85359i	0.672425	+	0.740165i
$44$		−	3.86104i		−	0.582074i
$45$	−0.542074	+	0.857675i	−0.0808076	+	0.127855i
$46$		−	3.24351i		−	0.478230i
$47$	−8.96474	−	8.96474i	−1.30764	−	1.30764i	−0.923113	−	0.384529i	$-0.874364\pi$
$47$	−8.96474	−	8.96474i	−1.30764	−	1.30764i	−0.384529	−	0.923113i	$-0.625636\pi$
$48$	1.12833	+	1.12833i	0.162860	+	0.162860i
$49$			6.27954i			0.897077i
$50$	−4.71064	−	1.67627i	−0.666185	−	0.237060i
$51$			7.76378i			1.08715i
$52$	3.06758	+	3.06758i	0.425396	+	0.425396i
$53$	−0.712186	+	0.712186i	−0.0978263	+	0.0978263i	−0.754326	−	0.656500i	$-0.772036\pi$
$53$	−0.712186	+	0.712186i	−0.0978263	+	0.0978263i	0.656500	+	0.754326i	$0.272036\pi$
$54$		−	5.51114i		−	0.749971i
$55$	−7.29810	−	4.61259i	−0.984076	−	0.621962i
$56$	0.848801			0.113426
$57$	5.93991	+	5.93991i	0.786760	+	0.786760i
$58$	−0.818932	+	0.818932i	−0.107531	+	0.107531i
$59$		−	6.93170i		−	0.902431i	−0.892415	−	0.451216i	$-0.850991\pi$
$59$		−	6.93170i		−	0.902431i	0.892415	−	0.451216i	$-0.149009\pi$
$60$	3.48071	−	0.784796i	0.449358	−	0.101317i
$61$		−	0.0822438i		−	0.0105302i	−0.999986	−	0.00526512i	$-0.998324\pi$
$61$		−	0.0822438i		−	0.0105302i	0.999986	−	0.00526512i	$-0.00167595\pi$
$62$	5.86709	−	5.86709i	0.745121	−	0.745121i
$63$	−0.272338	−	0.272338i	−0.0343114	−	0.0343114i
$64$			1.00000i			0.125000i
$65$	9.46297	−	2.13362i	1.17374	−	0.264643i
$66$	6.16106			0.758374
$67$	−4.42045	−	4.42045i	−0.540044	−	0.540044i	0.383498	−	0.923542i	$-0.374719\pi$
$67$	−4.42045	−	4.42045i	−0.540044	−	0.540044i	−0.923542	+	0.383498i	$0.874719\pi$
$68$	−3.44039	+	3.44039i	−0.417208	+	0.417208i
$69$	5.17566			0.623077
$70$	1.01402	−	1.60439i	0.121199	−	0.191762i
$71$		−	6.42737i		−	0.762788i	−0.924412	−	0.381394i	$-0.875444\pi$
$71$		−	6.42737i		−	0.762788i	0.924412	−	0.381394i	$-0.124556\pi$
$72$	0.320851	−	0.320851i	0.0378126	−	0.0378126i
$73$	0.675425	+	0.675425i	0.0790526	+	0.0790526i	0.745527	−	0.666475i	$-0.232198\pi$
$73$	0.675425	+	0.675425i	0.0790526	+	0.0790526i	−0.666475	+	0.745527i	$0.732198\pi$
$74$		−	4.22582i		−	0.491242i
$75$	2.67481	−	7.51675i	0.308861	−	0.867960i
$76$			5.26434i			0.603862i
$77$	2.31737	−	2.31737i	0.264089	−	0.264089i
$78$	−4.89492	+	4.89492i	−0.554241	+	0.554241i
$79$		−	8.61935i		−	0.969753i	−0.874583	−	0.484876i	$-0.838865\pi$
$79$		−	8.61935i		−	0.969753i	0.874583	−	0.484876i	$-0.161135\pi$
$80$	1.89019	+	1.19465i	0.211330	+	0.133566i
$81$	7.43286			0.825873
$82$	−4.41950	+	4.41950i	−0.488052	+	0.488052i
$83$	−6.64942	+	6.64942i	−0.729868	+	0.729868i	−0.970593	−	0.240725i	$-0.922615\pi$
$83$	−6.64942	+	6.64942i	−0.729868	+	0.729868i	0.240725	+	0.970593i	$0.422615\pi$
$84$			1.35443i			0.147780i
$85$	2.39293	+	10.6130i	0.259549	+	1.15115i
$86$	−6.54991	−	0.314101i	−0.706295	−	0.0338704i
$87$	−1.30677	−	1.30677i	−0.140100	−	0.140100i
$88$	2.73017	+	2.73017i	0.291037	+	0.291037i
$89$	10.6483			1.12871			0.564357	−	0.825531i	$-0.309124\pi$
$89$	10.6483			1.12871			0.564357	+	0.825531i	$0.309124\pi$
$90$	−0.223164	−	0.989772i	−0.0235236	−	0.104331i
$91$			3.68228i			0.386007i
$92$	2.29351	+	2.29351i	0.239115	+	0.239115i
$93$	9.36210	+	9.36210i	0.970804	+	0.970804i
$94$	12.6781			1.30764
$95$	9.95060	+	6.28905i	1.02091	+	0.645243i
$96$	−1.59570			−0.162860
$97$	−0.895557	−	0.895557i	−0.0909300	−	0.0909300i	0.660179	−	0.751109i	$-0.270481\pi$
$97$	−0.895557	−	0.895557i	−0.0909300	−	0.0909300i	−0.751109	+	0.660179i	$0.770481\pi$
$98$	−4.44030	−	4.44030i	−0.448538	−	0.448538i
$99$		−	1.75195i		−	0.176078i
$100$	4.51623	−	2.14563i	0.451623	−	0.214563i
$101$	1.24688			0.124069			0.0620344	−	0.998074i	$-0.480241\pi$
$101$	1.24688			0.124069			0.0620344	+	0.998074i	$0.480241\pi$
$102$	−5.48982	−	5.48982i	−0.543573	−	0.543573i
$103$	−1.60123	+	1.60123i	−0.157773	+	0.157773i	−0.781579	−	0.623806i	$-0.785586\pi$
$103$	−1.60123	+	1.60123i	−0.157773	+	0.157773i	0.623806	+	0.781579i	$0.285586\pi$
$104$	−4.33821			−0.425396
$105$	2.56013	+	1.61807i	0.249843	+	0.157907i
$106$		−	1.00718i		−	0.0978263i
$107$	6.06708	+	6.06708i	0.586527	+	0.586527i	0.936689	−	0.350162i	$-0.113874\pi$
$107$	6.06708	+	6.06708i	0.586527	+	0.586527i	−0.350162	+	0.936689i	$0.613874\pi$
$108$	3.89696	+	3.89696i	0.374986	+	0.374986i
$109$			12.8239i			1.22831i	0.789187	+	0.614153i	$0.210502\pi$
$109$			12.8239i			1.22831i	−0.789187	+	0.614153i	$0.789498\pi$
$110$	8.42213	−	1.89894i	0.803019	−	0.181057i
$111$	6.74314			0.640030
$112$	−0.600193	+	0.600193i	−0.0567129	+	0.0567129i
$113$	−12.1461	−	12.1461i	−1.14261	−	1.14261i	−0.987971	−	0.154641i	$-0.950578\pi$
$113$	−12.1461	−	12.1461i	−1.14261	−	1.14261i	−0.154641	−	0.987971i	$-0.549422\pi$
$114$	−8.40030			−0.786760
$115$	7.07511	−	1.59523i	0.659757	−	0.148756i
$116$		−	1.15814i		−	0.107531i
$117$	1.39192	+	1.39192i	0.128683	+	0.128683i
$118$	4.90146	+	4.90146i	0.451216	+	0.451216i
$119$	−4.12980			−0.378578
$120$	−1.90630	+	3.01617i	−0.174020	+	0.275337i
$121$	3.90766			0.355242
$122$	0.0581551	+	0.0581551i	0.00526512	+	0.00526512i
$123$	−7.05218	−	7.05218i	−0.635874	−	0.635874i
$124$			8.29732i			0.745121i
$125$	1.33967	−	11.0998i	0.119824	−	0.992795i
$126$	0.385145			0.0343114
$127$	−8.86299	−	8.86299i	−0.786463	−	0.786463i	0.194449	−	0.980913i	$-0.437708\pi$
$127$	−8.86299	−	8.86299i	−0.786463	−	0.786463i	−0.980913	+	0.194449i	$0.937708\pi$
$128$	−0.707107	−	0.707107i	−0.0625000	−	0.0625000i
$129$	0.501210	−	10.4517i	0.0441291	−	0.920219i
$130$	−5.18264	+	8.20003i	−0.454547	+	0.719190i
$131$			8.38703i			0.732778i	0.930462	+	0.366389i	$0.119406\pi$
$131$			8.38703i			0.732778i	−0.930462	+	0.366389i	$0.880594\pi$
$132$	−4.35652	+	4.35652i	−0.379187	+	0.379187i
$133$	−3.15962	+	3.15962i	−0.273974	+	0.273974i
$134$	6.25146			0.540044
$135$	12.0215	−	2.71049i	1.03465	−	0.233282i
$136$		−	4.86544i		−	0.417208i
$137$	14.9722	−	14.9722i	1.27916	−	1.27916i	0.338027	−	0.941136i	$-0.390240\pi$
$137$	14.9722	−	14.9722i	1.27916	−	1.27916i	0.941136	−	0.338027i	$-0.109760\pi$
$138$	−3.65975	+	3.65975i	−0.311538	+	0.311538i
$139$		−	14.8010i		−	1.25540i	−0.778455	−	0.627700i	$-0.783996\pi$
$139$		−	14.8010i		−	1.25540i	0.778455	−	0.627700i	$-0.216004\pi$
$140$	0.417458	+	1.85150i	0.0352816	+	0.156480i
$141$			20.2303i			1.70370i
$142$	4.54484	+	4.54484i	0.381394	+	0.381394i
$143$	−11.8440	+	11.8440i	−0.990449	+	0.990449i
$144$			0.453751i			0.0378126i
$145$	−2.18911	−	1.38358i	−0.181796	−	0.114900i
$146$	−0.955196			−0.0790526
$147$	7.08538	−	7.08538i	0.584392	−	0.584392i
$148$	2.98811	+	2.98811i	0.245621	+	0.245621i
$149$	−21.3190			−1.74652			−0.873262	−	0.487251i	$-0.838000\pi$
$149$	−21.3190			−1.74652			−0.873262	+	0.487251i	$0.838000\pi$
$150$	3.42377	+	7.20653i	0.279550	+	0.588410i
$151$			4.59040i			0.373562i	0.982402	+	0.186781i	$0.0598054\pi$
$151$			4.59040i			0.373562i	−0.982402	+	0.186781i	$0.940195\pi$
$152$	−3.72245	−	3.72245i	−0.301931	−	0.301931i
$153$	−1.56108	+	1.56108i	−0.126206	+	0.126206i
$154$			3.27726i			0.264089i
$155$	15.6835	+	9.91239i	1.25973	+	0.796182i
$156$		−	6.92246i		−	0.554241i
$157$	8.33478	−	8.33478i	0.665188	−	0.665188i	−0.291410	−	0.956598i	$-0.594125\pi$
$157$	8.33478	−	8.33478i	0.665188	−	0.665188i	0.956598	+	0.291410i	$0.0941245\pi$
$158$	6.09480	+	6.09480i	0.484876	+	0.484876i
$159$	1.60716			0.127456
$160$	−2.18131	+	0.491820i	−0.172448	+	0.0388818i
$161$			2.75310i			0.216975i
$162$	−5.25582	+	5.25582i	−0.412936	+	0.412936i
$163$	−8.74375	−	8.74375i	−0.684863	−	0.684863i	0.276229	−	0.961092i	$-0.410915\pi$
$163$	−8.74375	−	8.74375i	−0.684863	−	0.684863i	−0.961092	+	0.276229i	$0.910915\pi$
$164$		−	6.25012i		−	0.488052i
$165$	3.03013	+	13.4392i	0.235896	+	1.04624i
$166$		−	9.40370i		−	0.729868i
$167$	4.14476	+	4.14476i	0.320731	+	0.320731i	0.849048	−	0.528317i	$-0.177177\pi$
$167$	4.14476	+	4.14476i	0.320731	+	0.320731i	−0.528317	+	0.849048i	$0.677177\pi$
$168$	−0.957726	−	0.957726i	−0.0738902	−	0.0738902i
$169$		−	5.82004i		−	0.447695i
$170$	−9.19661	−	5.81250i	−0.705348	−	0.445798i
$171$			2.38870i			0.182669i
$172$	4.85359	−	4.40938i	0.370083	−	0.336212i
$173$	14.3734	−	14.3734i	1.09279	−	1.09279i	0.0975573	−	0.995230i	$-0.468897\pi$
$173$	14.3734	−	14.3734i	1.09279	−	1.09279i	0.995230	−	0.0975573i	$-0.0311029\pi$
$174$	1.84805			0.140100
$175$	3.99840	+	1.42282i	0.302250	+	0.107555i
$176$	−3.86104			−0.291037
$177$	−7.82124	+	7.82124i	−0.587880	+	0.587880i
$178$	−7.52947	+	7.52947i	−0.564357	+	0.564357i
$179$	−25.0245			−1.87042			−0.935210	−	0.354094i	$-0.884789\pi$
$179$	−25.0245			−1.87042			−0.935210	+	0.354094i	$0.884789\pi$
$180$	0.857675	+	0.542074i	0.0639274	+	0.0404038i
$181$	−12.3805			−0.920235			−0.460118	−	0.887858i	$-0.652193\pi$
$181$	−12.3805			−0.920235			−0.460118	+	0.887858i	$0.652193\pi$
$182$	−2.60376	−	2.60376i	−0.193004	−	0.193004i
$183$	−0.0927979	+	0.0927979i	−0.00685982	+	0.00685982i
$184$	−3.24351			−0.239115
$185$	9.21783	−	2.07835i	0.677709	−	0.152803i
$186$	−13.2400			−0.970804
$187$	−13.2835	−	13.2835i	−0.971385	−	0.971385i
$188$	−8.96474	+	8.96474i	−0.653821	+	0.653821i
$189$			4.67786i			0.340265i
$190$	−11.4832	+	2.58911i	−0.833077	+	0.187834i
$191$		−	21.8481i		−	1.58087i	−0.612543	−	0.790437i	$-0.709853\pi$
$191$		−	21.8481i		−	1.58087i	0.612543	−	0.790437i	$-0.290147\pi$
$192$	1.12833	−	1.12833i	0.0814301	−	0.0814301i
$193$	16.3925	−	16.3925i	1.17996	−	1.17996i	0.200201	−	0.979755i	$-0.435840\pi$
$193$	16.3925	−	16.3925i	1.17996	−	1.17996i	0.979755	−	0.200201i	$-0.0641596\pi$
$194$	1.26651			0.0909300
$195$	−13.0848	−	8.26992i	−0.937019	−	0.592221i
$196$	6.27954			0.448538
$197$	8.22622	+	8.22622i	0.586094	+	0.586094i	0.936571	−	0.350477i	$-0.113981\pi$
$197$	8.22622	+	8.22622i	0.586094	+	0.586094i	−0.350477	+	0.936571i	$0.613981\pi$
$198$	1.23882	+	1.23882i	0.0880390	+	0.0880390i
$199$	−21.4309			−1.51919			−0.759597	−	0.650394i	$-0.774604\pi$
$199$	−21.4309			−1.51919			−0.759597	+	0.650394i	$0.774604\pi$
$200$	−1.67627	+	4.71064i	−0.118530	+	0.333093i
$201$			9.97543i			0.703613i
$202$	−0.881674	+	0.881674i	−0.0620344	+	0.0620344i
$203$	0.695110	−	0.695110i	0.0487872	−	0.0487872i
$204$	7.76378			0.543573
$205$	−11.8139	−	7.46670i	−0.825119	−	0.521497i
$206$		−	2.26448i		−	0.157773i
$207$	1.04068	+	1.04068i	0.0723325	+	0.0723325i
$208$	3.06758	−	3.06758i	0.212698	−	0.212698i
$209$	−20.3259			−1.40597
$210$	−2.95443	+	0.666136i	−0.203875	+	0.0459678i
$211$			1.82989i			0.125975i	0.998014	+	0.0629873i	$0.0200628\pi$
$211$			1.82989i			0.125975i	−0.998014	+	0.0629873i	$0.979937\pi$
$212$	0.712186	+	0.712186i	0.0489132	+	0.0489132i
$213$	−7.25218	+	7.25218i	−0.496911	+	0.496911i
$214$	−8.58015			−0.586527
$215$	−2.53623	−	14.4419i	−0.172969	−	0.984927i
$216$	−5.51114			−0.374986
$217$	−4.97999	+	4.97999i	−0.338064	+	0.338064i
$218$	−9.06786	−	9.06786i	−0.614153	−	0.614153i
$219$		−	1.52420i		−	0.102996i
$220$	−4.61259	+	7.29810i	−0.310981	+	0.492038i
$221$	21.1073			1.41983
$222$	−4.76812	+	4.76812i	−0.320015	+	0.320015i
$223$	7.67259	+	7.67259i	0.513794	+	0.513794i	0.915687	−	0.401893i	$-0.131647\pi$
$223$	7.67259	+	7.67259i	0.513794	+	0.513794i	−0.401893	+	0.915687i	$0.631647\pi$
$224$		−	0.848801i		−	0.0567129i
$225$	2.04924	−	0.973580i	0.136616	−	0.0649054i
$226$	17.1772			1.14261
$227$	−5.48731	+	5.48731i	−0.364205	+	0.364205i	−0.865359	−	0.501153i	$-0.832909\pi$
$227$	−5.48731	+	5.48731i	−0.364205	+	0.364205i	0.501153	+	0.865359i	$0.332909\pi$
$228$	5.93991	−	5.93991i	0.393380	−	0.393380i
$229$		−	12.1317i		−	0.801683i	−0.916147	−	0.400841i	$-0.868718\pi$
$229$		−	12.1317i		−	0.801683i	0.916147	−	0.400841i	$-0.131282\pi$
$230$	−3.87486	+	6.13085i	−0.255501	+	0.404256i
$231$	−5.22951			−0.344077
$232$	0.818932	+	0.818932i	0.0537655	+	0.0537655i
$233$	−14.1568	−	14.1568i	−0.927446	−	0.927446i	0.0700948	−	0.997540i	$-0.477670\pi$
$233$	−14.1568	−	14.1568i	−0.927446	−	0.927446i	−0.997540	+	0.0700948i	$0.977670\pi$
$234$	−1.96847			−0.128683
$235$	6.23533	+	27.6548i	0.406748	+	1.80400i
$236$	−6.93170			−0.451216
$237$	−9.72546	+	9.72546i	−0.631736	+	0.631736i
$238$	2.92021	−	2.92021i	0.189289	−	0.189289i
$239$		−	10.0050i		−	0.647173i	−0.946199	−	0.323586i	$-0.895111\pi$
$239$		−	10.0050i		−	0.647173i	0.946199	−	0.323586i	$-0.104889\pi$
$240$	−0.784796	−	3.48071i	−0.0506584	−	0.224679i
$241$			7.74645i			0.498993i	0.968376	+	0.249496i	$0.0802650\pi$
$241$			7.74645i			0.498993i	−0.968376	+	0.249496i	$0.919735\pi$
$242$	−2.76313	+	2.76313i	−0.177621	+	0.177621i
$243$	3.30419	+	3.30419i	0.211964	+	0.211964i
$244$	−0.0822438			−0.00526512
$245$	7.50184	−	11.8695i	0.479275	−	0.758315i
$246$	9.97330			0.635874
$247$	16.1488	−	16.1488i	1.02752	−	1.02752i
$248$	−5.86709	−	5.86709i	−0.372561	−	0.372561i
$249$	15.0055			0.950932
$250$	6.90145	+	8.79602i	0.436486	+	0.556309i
$251$	5.15375			0.325302			0.162651	−	0.986684i	$-0.447996\pi$
$251$	5.15375			0.325302			0.162651	+	0.986684i	$0.447996\pi$
$252$	−0.272338	+	0.272338i	−0.0171557	+	0.0171557i
$253$	−8.85534	+	8.85534i	−0.556731	+	0.556731i
$254$	12.5342			0.786463
$255$	9.27499	−	14.6750i	0.580822	−	0.918984i
$256$	1.00000			0.0625000
$257$	9.86993	−	9.86993i	0.615669	−	0.615669i	−0.328748	−	0.944418i	$-0.606627\pi$
$257$	9.86993	−	9.86993i	0.615669	−	0.615669i	0.944418	+	0.328748i	$0.106627\pi$
$258$	7.03604	+	7.74486i	0.438045	+	0.482174i
$259$			3.58689i			0.222878i
$260$	−2.13362	−	9.46297i	−0.132321	−	0.586869i
$261$		−	0.525509i		−	0.0325282i
$262$	−5.93052	−	5.93052i	−0.366389	−	0.366389i
$263$	−6.82082	−	6.82082i	−0.420590	−	0.420590i	0.464817	−	0.885407i	$-0.346120\pi$
$263$	−6.82082	−	6.82082i	−0.420590	−	0.420590i	−0.885407	+	0.464817i	$0.846120\pi$
$264$		−	6.16106i		−	0.379187i
$265$	2.19698	−	0.495354i	0.134959	−	0.0304293i
$266$		−	4.46838i		−	0.273974i
$267$	−12.0147	−	12.0147i	−0.735291	−	0.735291i
$268$	−4.42045	+	4.42045i	−0.270022	+	0.270022i
$269$			30.5711i			1.86395i	0.362520	+	0.931976i	$0.381916\pi$
$269$			30.5711i			1.86395i	−0.362520	+	0.931976i	$0.618084\pi$
$270$	−6.58388	+	10.4171i	−0.400682	+	0.633964i
$271$	12.7772			0.776159			0.388079	−	0.921626i	$-0.373139\pi$
$271$	12.7772			0.776159			0.388079	+	0.921626i	$0.373139\pi$
$272$	3.44039	+	3.44039i	0.208604	+	0.208604i
$273$	4.15482	−	4.15482i	0.251461	−	0.251461i
$274$			21.1739i			1.27916i
$275$	8.28435	+	17.4373i	0.499565	+	1.05151i
$276$		−	5.17566i		−	0.311538i
$277$	−19.0997	+	19.0997i	−1.14759	+	1.14759i	−0.160564	+	0.987025i	$0.551331\pi$
$277$	−19.0997	+	19.0997i	−1.14759	+	1.14759i	−0.987025	+	0.160564i	$0.948669\pi$
$278$	10.4659	+	10.4659i	0.627700	+	0.627700i
$279$			3.76492i			0.225400i
$280$	−1.60439	−	1.01402i	−0.0958809	−	0.0605993i
$281$	−11.8603			−0.707528			−0.353764	−	0.935335i	$-0.615098\pi$
$281$	−11.8603			−0.707528			−0.353764	+	0.935335i	$0.615098\pi$
$282$	−14.3050	−	14.3050i	−0.851851	−	0.851851i
$283$	2.97616	−	2.97616i	0.176914	−	0.176914i	−0.613095	−	0.790009i	$-0.710076\pi$
$283$	2.97616	−	2.97616i	0.176914	−	0.176914i	0.790009	+	0.613095i	$0.210076\pi$
$284$	−6.42737			−0.381394
$285$	−4.13144	−	18.3237i	−0.244725	−	1.08540i
$286$		−	16.7500i		−	0.990449i
$287$	3.75128	−	3.75128i	0.221431	−	0.221431i
$288$	−0.320851	−	0.320851i	−0.0189063	−	0.0189063i
$289$			6.67255i			0.392503i
$290$	2.52627	−	0.569599i	0.148348	−	0.0334480i
$291$			2.02096i			0.118471i
$292$	0.675425	−	0.675425i	0.0395263	−	0.0395263i
$293$	−3.57242	+	3.57242i	−0.208703	+	0.208703i	−0.803716	−	0.595013i	$-0.797147\pi$
$293$	−3.57242	+	3.57242i	−0.208703	+	0.208703i	0.595013	+	0.803716i	$0.297147\pi$
$294$			10.0202i			0.584392i
$295$	−8.28096	+	13.1022i	−0.482136	+	0.762841i
$296$	−4.22582			−0.245621
$297$	−15.0464	+	15.0464i	−0.873078	+	0.873078i
$298$	15.0748	−	15.0748i	0.873262	−	0.873262i
$299$		−	14.0710i		−	0.813749i
$300$	−7.51675	−	2.67481i	−0.433980	−	0.154430i
$301$	5.55957	+	0.266609i	0.320449	+	0.0153671i
$302$	−3.24591	−	3.24591i	−0.186781	−	0.186781i
$303$	−1.40689	−	1.40689i	−0.0808234	−	0.0808234i
$304$	5.26434			0.301931
$305$	−0.0982525	+	0.155456i	−0.00562592	+	0.00890140i
$306$		−	2.20770i		−	0.126206i
$307$	7.86832	+	7.86832i	0.449069	+	0.449069i	0.895045	−	0.445976i	$-0.147143\pi$
$307$	7.86832	+	7.86832i	0.449069	+	0.449069i	−0.445976	+	0.895045i	$0.647143\pi$
$308$	−2.31737	−	2.31737i	−0.132045	−	0.132045i
$309$	3.61342			0.205560
$310$	−18.0990	+	4.08079i	−1.02796	+	0.231773i
$311$	−22.6872			−1.28647			−0.643237	−	0.765667i	$-0.722409\pi$
$311$	−22.6872			−1.28647			−0.643237	+	0.765667i	$0.722409\pi$
$312$	4.89492	+	4.89492i	0.277120	+	0.277120i
$313$	−2.90495	−	2.90495i	−0.164197	−	0.164197i	0.620226	−	0.784423i	$-0.287041\pi$
$313$	−2.90495	−	2.90495i	−0.164197	−	0.164197i	−0.784423	+	0.620226i	$0.787041\pi$
$314$			11.7872i			0.665188i
$315$	0.189422	+	0.840120i	0.0106727	+	0.0473354i
$316$	−8.61935			−0.484876
$317$	22.1638	+	22.1638i	1.24485	+	1.24485i	0.957967	+	0.286879i	$0.0926176\pi$
$317$	22.1638	+	22.1638i	1.24485	+	1.24485i	0.286879	+	0.957967i	$0.407382\pi$
$318$	−1.13643	+	1.13643i	−0.0637280	+	0.0637280i
$319$	4.47165			0.250364
$320$	1.19465	−	1.89019i	0.0667829	−	0.105665i
$321$		−	13.6913i		−	0.764175i
$322$	−1.94673	−	1.94673i	−0.108487	−	0.108487i
$323$	18.1114	+	18.1114i	1.00774	+	1.00774i
$324$		−	7.43286i		−	0.412936i
$325$	−20.4357	−	7.27199i	−1.13357	−	0.403378i
$326$	12.3655			0.684863
$327$	14.4696	−	14.4696i	0.800168	−	0.800168i
$328$	4.41950	+	4.41950i	0.244026	+	0.244026i
$329$	−10.7612			−0.593282
$330$	−11.6456	−	7.36030i	−0.641067	−	0.405171i
$331$		−	2.27756i		−	0.125186i	−0.998039	−	0.0625929i	$-0.980063\pi$
$331$		−	2.27756i		−	0.125186i	0.998039	−	0.0625929i	$-0.0199370\pi$
$332$	6.64942	+	6.64942i	0.364934	+	0.364934i
$333$	1.35586	+	1.35586i	0.0743006	+	0.0743006i
$334$	−5.86157			−0.320731
$335$	3.07459	+	13.6364i	0.167983	+	0.745034i
$336$	1.35443			0.0738902
$337$	14.2943	+	14.2943i	0.778662	+	0.778662i	0.979603	−	0.200942i	$-0.0644001\pi$
$337$	14.2943	+	14.2943i	0.778662	+	0.778662i	−0.200942	+	0.979603i	$0.564400\pi$
$338$	4.11539	+	4.11539i	0.223848	+	0.223848i
$339$			27.4096i			1.48869i
$340$	10.6130	−	2.39293i	0.575573	−	0.129775i
$341$	−32.0363			−1.73486
$342$	−1.68907	−	1.68907i	−0.0913343	−	0.0913343i
$343$	7.97029	+	7.97029i	0.430355	+	0.430355i
$344$	−0.314101	+	6.54991i	−0.0169352	+	0.353148i
$345$	−9.78298	−	6.18310i	−0.526698	−	0.332887i
$346$			20.3270i			1.09279i
$347$	18.8781	−	18.8781i	1.01343	−	1.01343i	0.0135231	−	0.999909i	$-0.495695\pi$
$347$	18.8781	−	18.8781i	1.01343	−	1.01343i	0.999909	−	0.0135231i	$-0.00430466\pi$
$348$	−1.30677	+	1.30677i	−0.0700501	+	0.0700501i
$349$	28.2309			1.51117			0.755583	−	0.655053i	$-0.227354\pi$
$349$	28.2309			1.51117			0.755583	+	0.655053i	$0.227354\pi$
$350$	−3.83338	+	1.82121i	−0.204903	+	0.0973478i
$351$		−	23.9085i		−	1.27614i
$352$	2.73017	−	2.73017i	0.145519	−	0.145519i
$353$	6.31638	−	6.31638i	0.336187	−	0.336187i	−0.518743	−	0.854930i	$-0.673600\pi$
$353$	6.31638	−	6.31638i	0.336187	−	0.336187i	0.854930	+	0.518743i	$0.173600\pi$
$354$		−	11.0609i		−	0.587880i
$355$	−7.67845	+	12.1489i	−0.407530	+	0.644799i
$356$		−	10.6483i		−	0.564357i
$357$	4.65977	+	4.65977i	0.246621	+	0.246621i
$358$	17.6950	−	17.6950i	0.935210	−	0.935210i
$359$		−	15.6791i		−	0.827512i	−0.910388	−	0.413756i	$-0.864217\pi$
$359$		−	15.6791i		−	0.827512i	0.910388	−	0.413756i	$-0.135783\pi$
$360$	−0.989772	+	0.223164i	−0.0521656	+	0.0117618i
$361$	8.71333			0.458596
$362$	8.75433	−	8.75433i	0.460118	−	0.460118i
$363$	−4.40912	−	4.40912i	−0.231419	−	0.231419i
$364$	3.68228			0.193004
$365$	−0.469785	−	2.08358i	−0.0245897	−	0.109059i
$366$		−	0.131236i		−	0.00685982i
$367$	1.54680	+	1.54680i	0.0807425	+	0.0807425i	0.746325	−	0.665582i	$-0.231817\pi$
$367$	1.54680	+	1.54680i	0.0807425	+	0.0807425i	−0.665582	+	0.746325i	$0.731817\pi$
$368$	2.29351	−	2.29351i	0.119557	−	0.119557i
$369$		−	2.83600i		−	0.147636i
$370$	−5.04838	+	7.98761i	−0.262453	+	0.415256i
$371$			0.854899i			0.0443841i
$372$	9.36210	−	9.36210i	0.485402	−	0.485402i
$373$	7.99721	+	7.99721i	0.414080	+	0.414080i	0.883157	−	0.469077i	$-0.155413\pi$
$373$	7.99721	+	7.99721i	0.414080	+	0.414080i	−0.469077	+	0.883157i	$0.655413\pi$
$374$	18.7857			0.971385
$375$	−14.0358	+	11.0126i	−0.724805	+	0.568689i
$376$		−	12.6781i		−	0.653821i
$377$	−3.55270	+	3.55270i	−0.182973	+	0.182973i
$378$	−3.30775	−	3.30775i	−0.170132	−	0.170132i
$379$			22.6211i			1.16197i	0.813915	+	0.580984i	$0.197332\pi$
$379$			22.6211i			1.16197i	−0.813915	+	0.580984i	$0.802668\pi$
$380$	6.28905	−	9.95060i	0.322621	−	0.510455i
$381$			20.0007i			1.02467i
$382$	15.4490	+	15.4490i	0.790437	+	0.790437i
$383$	6.62759	+	6.62759i	0.338654	+	0.338654i	0.855861	−	0.517207i	$-0.173028\pi$
$383$	6.62759	+	6.62759i	0.338654	+	0.338654i	−0.517207	+	0.855861i	$0.673028\pi$
$384$			1.59570i			0.0814301i
$385$	−7.14872	+	1.61182i	−0.364332	+	0.0821461i
$386$			23.1825i			1.17996i
$387$	2.20232	−	2.00076i	0.111950	−	0.101705i
$388$	−0.895557	+	0.895557i	−0.0454650	+	0.0454650i
$389$	−16.4474			−0.833917			−0.416959	−	0.908925i	$-0.636904\pi$
$389$	−16.4474			−0.833917			−0.416959	+	0.908925i	$0.636904\pi$
$390$	15.1000	−	3.40461i	0.764620	−	0.172399i
$391$	15.7811			0.798086
$392$	−4.44030	+	4.44030i	−0.224269	+	0.224269i
$393$	9.46332	−	9.46332i	0.477361	−	0.477361i
$394$	−11.6336			−0.586094
$395$	−10.2971	+	16.2922i	−0.518104	+	0.819750i
$396$	−1.75195			−0.0880390
$397$	−6.44827	−	6.44827i	−0.323630	−	0.323630i	0.526528	−	0.850158i	$-0.323493\pi$
$397$	−6.44827	−	6.44827i	−0.323630	−	0.323630i	−0.850158	+	0.526528i	$0.823493\pi$
$398$	15.1539	−	15.1539i	0.759597	−	0.759597i
$399$	7.13019			0.356956
$400$	−2.14563	−	4.51623i	−0.107281	−	0.225811i
$401$	0.478182			0.0238793			0.0119396	−	0.999929i	$-0.496199\pi$
$401$	0.478182			0.0238793			0.0119396	+	0.999929i	$0.496199\pi$
$402$	−7.05369	−	7.05369i	−0.351806	−	0.351806i
$403$	25.4527	−	25.4527i	1.26789	−	1.26789i
$404$		−	1.24688i		−	0.0620344i
$405$	−14.0495	−	8.87966i	−0.698125	−	0.441234i
$406$			0.983035i			0.0487872i
$407$	−11.5372	+	11.5372i	−0.571879	+	0.571879i
$408$	−5.48982	+	5.48982i	−0.271786	+	0.271786i
$409$	16.3113			0.806542			0.403271	−	0.915081i	$-0.367873\pi$
$409$	16.3113			0.806542			0.403271	+	0.915081i	$0.367873\pi$
$410$	13.6334	−	3.07394i	0.673308	−	0.151811i
$411$	−33.7872			−1.66660
$412$	1.60123	+	1.60123i	0.0788867	+	0.0788867i
$413$	−4.16036	−	4.16036i	−0.204718	−	0.204718i
$414$	−1.47175			−0.0723325
$415$	20.5124	−	4.62493i	1.00691	−	0.227029i
$416$			4.33821i			0.212698i
$417$	−16.7003	+	16.7003i	−0.817819	+	0.817819i
$418$	14.3726	−	14.3726i	0.702985	−	0.702985i
$419$	11.8451			0.578672			0.289336	−	0.957228i	$-0.406565\pi$
$419$	11.8451			0.578672			0.289336	+	0.957228i	$0.406565\pi$
$420$	1.61807	−	2.56013i	0.0789537	−	0.124921i
$421$		−	20.6856i		−	1.00816i	−0.863658	−	0.504078i	$-0.831832\pi$
$421$		−	20.6856i		−	1.00816i	0.863658	−	0.504078i	$-0.168168\pi$
$422$	−1.29393	−	1.29393i	−0.0629873	−	0.0629873i
$423$	−4.06776	+	4.06776i	−0.197781	+	0.197781i
$424$	−1.00718			−0.0489132
$425$	8.15578	−	22.9194i	0.395614	−	1.11175i
$426$		−	10.2561i		−	0.496911i
$427$	−0.0493621	−	0.0493621i	−0.00238880	−	0.00238880i
$428$	6.06708	−	6.06708i	0.293263	−	0.293263i
$429$	26.7279			1.29044
$430$	12.0053	+	8.41856i	0.578948	+	0.405979i
$431$	−11.1801			−0.538526			−0.269263	−	0.963067i	$-0.586780\pi$
$431$	−11.1801			−0.538526			−0.269263	+	0.963067i	$0.586780\pi$
$432$	3.89696	−	3.89696i	0.187493	−	0.187493i
$433$	−7.04495	−	7.04495i	−0.338559	−	0.338559i	0.517266	−	0.855825i	$-0.326950\pi$
$433$	−7.04495	−	7.04495i	−0.338559	−	0.338559i	−0.855825	+	0.517266i	$0.826950\pi$
$434$		−	7.04278i		−	0.338064i
$435$	0.908908	+	4.03116i	0.0435788	+	0.193280i
$436$	12.8239			0.614153
$437$	12.0738	−	12.0738i	0.577570	−	0.577570i
$438$	1.07777	+	1.07777i	0.0514980	+	0.0514980i
$439$		−	0.523530i		−	0.0249867i	−0.999922	−	0.0124934i	$-0.996023\pi$
$439$		−	0.523530i		−	0.0249867i	0.999922	−	0.0124934i	$-0.00397686\pi$
$440$	−1.89894	−	8.42213i	−0.0905284	−	0.401509i
$441$	2.84935			0.135683
$442$	−14.9251	+	14.9251i	−0.709916	+	0.709916i
$443$	−13.1241	+	13.1241i	−0.623543	+	0.623543i	−0.946436	−	0.322892i	$-0.895345\pi$
$443$	−13.1241	+	13.1241i	−0.623543	+	0.623543i	0.322892	+	0.946436i	$0.395345\pi$
$444$		−	6.74314i		−	0.320015i
$445$	−20.1272	−	12.7210i	−0.954123	−	0.603031i
$446$	−10.8507			−0.513794
$447$	24.0549	+	24.0549i	1.13776	+	1.13776i
$448$	0.600193	+	0.600193i	0.0283565	+	0.0283565i
$449$	24.9867			1.17920			0.589599	−	0.807696i	$-0.299286\pi$
$449$	24.9867			1.17920			0.589599	+	0.807696i	$0.299286\pi$
$450$	−0.760608	+	2.13746i	−0.0358554	+	0.100761i
$451$	24.1320			1.13633
$452$	−12.1461	+	12.1461i	−0.571306	+	0.571306i
$453$	5.17948	−	5.17948i	0.243353	−	0.243353i
$454$		−	7.76022i		−	0.364205i
$455$	4.39903	−	6.96020i	0.206230	−	0.326299i
$456$			8.40030i			0.393380i
$457$	12.8655	−	12.8655i	0.601821	−	0.601821i	−0.338974	−	0.940796i	$-0.610080\pi$
$457$	12.8655	−	12.8655i	0.601821	−	0.601821i	0.940796	+	0.338974i	$0.110080\pi$
$458$	8.57838	+	8.57838i	0.400841	+	0.400841i
$459$	26.8141			1.25158
$460$	−1.59523	−	7.07511i	−0.0743778	−	0.329879i
$461$	−23.2926			−1.08484			−0.542422	−	0.840106i	$-0.682493\pi$
$461$	−23.2926			−1.08484			−0.542422	+	0.840106i	$0.682493\pi$
$462$	3.69782	−	3.69782i	0.172038	−	0.172038i
$463$	5.56236	+	5.56236i	0.258505	+	0.258505i	0.824446	−	0.565941i	$-0.191487\pi$
$463$	5.56236	+	5.56236i	0.258505	+	0.258505i	−0.565941	+	0.824446i	$0.691487\pi$
$464$	−1.15814			−0.0537655
$465$	−6.51171	−	28.8806i	−0.301973	−	1.33930i
$466$	20.0208			0.927446
$467$	11.3013	−	11.3013i	0.522962	−	0.522962i	−0.395502	−	0.918465i	$-0.629430\pi$
$467$	11.3013	−	11.3013i	0.522962	−	0.522962i	0.918465	+	0.395502i	$0.129430\pi$
$468$	1.39192	−	1.39192i	0.0643413	−	0.0643413i
$469$	−5.30624			−0.245020
$470$	−23.9639	−	15.1458i	−1.10537	−	0.698625i
$471$	−18.8087			−0.866660
$472$	4.90146	−	4.90146i	0.225608	−	0.225608i
$473$	17.0248	+	18.7399i	0.782802	+	0.861663i
$474$		−	13.7539i		−	0.631736i
$475$	−11.2953	−	23.7750i	−0.518265	−	1.09087i
$476$			4.12980i			0.189289i
$477$	0.323155	+	0.323155i	0.0147963	+	0.0147963i
$478$	7.07463	+	7.07463i	0.323586	+	0.323586i
$479$			3.82988i			0.174992i	0.996165	+	0.0874959i	$0.0278865\pi$
$479$			3.82988i			0.174992i	−0.996165	+	0.0874959i	$0.972114\pi$
$480$	3.01617	+	1.90630i	0.137669	+	0.0870102i
$481$		−	18.3325i		−	0.835890i
$482$	−5.47757	−	5.47757i	−0.249496	−	0.249496i
$483$	3.10640	−	3.10640i	0.141346	−	0.141346i
$484$		−	3.90766i		−	0.177621i
$485$	0.622895	+	2.76265i	0.0282842	+	0.125445i
$486$	−4.67284			−0.211964
$487$	−4.24902	−	4.24902i	−0.192541	−	0.192541i	0.604252	−	0.796793i	$-0.293472\pi$
$487$	−4.24902	−	4.24902i	−0.192541	−	0.192541i	−0.796793	+	0.604252i	$0.793472\pi$
$488$	0.0581551	−	0.0581551i	0.00263256	−	0.00263256i
$489$			19.7316i			0.892296i
$490$	3.08840	+	13.6976i	0.139520	+	0.618795i
$491$			13.8549i			0.625264i	0.949874	+	0.312632i	$0.101211\pi$
$491$			13.8549i			0.625264i	−0.949874	+	0.312632i	$0.898789\pi$
$492$	−7.05218	+	7.05218i	−0.317937	+	0.317937i
$493$	−3.98447	−	3.98447i	−0.179451	−	0.179451i
$494$			22.8378i			1.02752i
$495$	−2.09297	+	3.31152i	−0.0940720	+	0.148842i
$496$	8.29732			0.372561
$497$	−3.85766	−	3.85766i	−0.173040	−	0.173040i
$498$	−10.6105	+	10.6105i	−0.475466	+	0.475466i
$499$	−19.3183			−0.864805			−0.432402	−	0.901681i	$-0.642334\pi$
$499$	−19.3183			−0.864805			−0.432402	+	0.901681i	$0.642334\pi$
$500$	−11.0998	−	1.33967i	−0.496398	−	0.0599118i
$501$		−	9.35329i		−	0.417874i
$502$	−3.64425	+	3.64425i	−0.162651	+	0.162651i
$503$	−24.6429	−	24.6429i	−1.09877	−	1.09877i	−0.994555	−	0.104216i	$-0.966767\pi$
$503$	−24.6429	−	24.6429i	−1.09877	−	1.09877i	−0.104216	−	0.994555i	$-0.533233\pi$
$504$		−	0.385145i		−	0.0171557i
$505$	−2.35683	−	1.48958i	−0.104878	−	0.0662854i
$506$		−	12.5233i		−	0.556731i
$507$	−6.56691	+	6.56691i	−0.291647	+	0.291647i
$508$	−8.86299	+	8.86299i	−0.393232	+	0.393232i
$509$			21.2870i			0.943529i	0.881725	+	0.471765i	$0.156383\pi$
$509$			21.2870i			0.943529i	−0.881725	+	0.471765i	$0.843617\pi$
$510$	3.81838	+	16.9352i	0.169081	+	0.749903i
$511$	0.810771			0.0358664
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$	20.5150	−	20.5150i	0.905758	−	0.905758i
$514$			13.9582i			0.615669i
$515$	4.93952	−	1.11372i	0.217661	−	0.0490762i
$516$	−10.4517	−	0.501210i	−0.460109	−	0.0220645i
$517$	−34.6133	−	34.6133i	−1.52229	−	1.52229i
$518$	−2.53631	−	2.53631i	−0.111439	−	0.111439i
$519$	−32.4358			−1.42377
$520$	8.20003	+	5.18264i	0.359595	+	0.227274i
$521$			37.7486i			1.65380i	0.562351	+	0.826898i	$0.309897\pi$
$521$			37.7486i			1.65380i	−0.562351	+	0.826898i	$0.690103\pi$
$522$	0.371591	+	0.371591i	0.0162641	+	0.0162641i
$523$	−2.40075	−	2.40075i	−0.104978	−	0.104978i	0.652667	−	0.757645i	$-0.273650\pi$
$523$	−2.40075	−	2.40075i	−0.104978	−	0.104978i	−0.757645	+	0.652667i	$0.773650\pi$
$524$	8.38703			0.366389
$525$	−2.90610	−	6.11691i	−0.126833	−	0.266964i
$526$	9.64609			0.420590
$527$	28.5460	+	28.5460i	1.24348	+	1.24348i
$528$	4.35652	+	4.35652i	0.189593	+	0.189593i
$529$			12.4796i			0.542592i
$530$	−1.20323	+	1.90377i	−0.0522650	+	0.0826944i
$531$	−3.14527			−0.136493
$532$	3.15962	+	3.15962i	0.136987	+	0.136987i
$533$	−19.1727	+	19.1727i	−0.830462	+	0.830462i
$534$	16.9914			0.735291
$535$	−4.21989	−	18.7160i	−0.182442	−	0.809161i
$536$		−	6.25146i		−	0.270022i
$537$	28.2359	+	28.2359i	1.21847	+	1.21847i
$538$	−21.6170	−	21.6170i	−0.931976	−	0.931976i
$539$			24.2456i			1.04433i
$540$	−2.71049	−	12.0215i	−0.116641	−	0.517323i
$541$	−38.6118			−1.66005			−0.830026	−	0.557725i	$-0.811674\pi$
$541$	−38.6118			−1.66005			−0.830026	+	0.557725i	$0.811674\pi$
$542$	−9.03483	+	9.03483i	−0.388079	+	0.388079i
$543$	13.9693	+	13.9693i	0.599478	+	0.599478i
$544$	−4.86544			−0.208604
$545$	15.3200	−	24.2396i	0.656239	−	1.03831i
$546$			5.87580i			0.251461i
$547$	−21.0360	−	21.0360i	−0.899433	−	0.899433i	0.0959531	−	0.995386i	$-0.469410\pi$
$547$	−21.0360	−	21.0360i	−0.899433	−	0.899433i	−0.995386	+	0.0959531i	$0.969410\pi$
$548$	−14.9722	−	14.9722i	−0.639582	−	0.639582i
$549$	−0.0373182			−0.00159270
$550$	−18.1880	−	6.47214i	−0.775538	−	0.275973i
$551$	−6.09687			−0.259735
$552$	3.65975	+	3.65975i	0.155769	+	0.155769i
$553$	−5.17328	−	5.17328i	−0.219990	−	0.219990i
$554$		−	27.0111i		−	1.14759i
$555$	−12.7458	−	8.05568i	−0.541029	−	0.341945i
$556$	−14.8010			−0.627700
$557$	−22.2965	−	22.2965i	−0.944734	−	0.944734i	0.0538173	−	0.998551i	$-0.482861\pi$
$557$	−22.2965	−	22.2965i	−0.944734	−	0.944734i	−0.998551	+	0.0538173i	$0.982861\pi$
$558$	−2.66220	−	2.66220i	−0.112700	−	0.112700i
$559$	−28.4149	−	1.36263i	−1.20182	−	0.0576333i
$560$	1.85150	−	0.417458i	0.0782401	−	0.0176408i
$561$			29.9763i			1.26560i
$562$	8.38653	−	8.38653i	0.353764	−	0.353764i
$563$	−18.9159	+	18.9159i	−0.797209	+	0.797209i	−0.982654	−	0.185446i	$-0.940627\pi$
$563$	−18.9159	+	18.9159i	−0.797209	+	0.797209i	0.185446	+	0.982654i	$0.440627\pi$
$564$	20.2303			0.851851
$565$	8.44811	+	37.4688i	0.355415	+	1.57633i
$566$			4.20892i			0.176914i
$567$	4.46115	−	4.46115i	0.187351	−	0.187351i
$568$	4.54484	−	4.54484i	0.190697	−	0.190697i
$569$		−	23.5354i		−	0.986656i	−0.869843	−	0.493328i	$-0.835780\pi$
$569$		−	23.5354i		−	0.986656i	0.869843	−	0.493328i	$-0.164220\pi$
$570$	15.8781	+	10.0354i	0.665062	+	0.420337i
$571$		−	4.70919i		−	0.197074i	−0.995133	−	0.0985368i	$-0.968584\pi$
$571$		−	4.70919i		−	0.197074i	0.995133	−	0.0985368i	$-0.0314162\pi$
$572$	11.8440	+	11.8440i	0.495224	+	0.495224i
$573$	−24.6519	+	24.6519i	−1.02985	+	1.02985i
$574$			5.30511i			0.221431i
$575$	−15.2790	−	5.43699i	−0.637179	−	0.226738i
$576$	0.453751			0.0189063
$577$	−26.1487	+	26.1487i	−1.08859	+	1.08859i	−0.0929124	+	0.995674i	$0.529618\pi$
$577$	−26.1487	+	26.1487i	−1.08859	+	1.08859i	−0.995674	+	0.0929124i	$0.970382\pi$
$578$	−4.71821	−	4.71821i	−0.196252	−	0.196252i
$579$	−36.9922			−1.53734
$580$	−1.38358	+	2.18911i	−0.0574499	+	0.0908979i
$581$			7.98187i			0.331144i
$582$	−1.42904	−	1.42904i	−0.0592355	−	0.0592355i
$583$	−2.74978	+	2.74978i	−0.113884	+	0.113884i
$584$			0.955196i			0.0395263i
$585$	−0.968132	−	4.29384i	−0.0400273	−	0.177528i
$586$		−	5.05217i		−	0.208703i
$587$	−0.859208	+	0.859208i	−0.0354633	+	0.0354633i	−0.724616	−	0.689153i	$-0.757983\pi$
$587$	−0.859208	+	0.859208i	−0.0354633	+	0.0354633i	0.689153	+	0.724616i	$0.257983\pi$
$588$	−7.08538	−	7.08538i	−0.292196	−	0.292196i
$589$	43.6800			1.79980
$590$	−3.40915	−	15.1202i	−0.140353	−	0.622489i
$591$		−	18.5637i		−	0.763610i
$592$	2.98811	−	2.98811i	0.122811	−	0.122811i
$593$	−3.42036	−	3.42036i	−0.140457	−	0.140457i	0.633382	−	0.773839i	$-0.281666\pi$
$593$	−3.42036	−	3.42036i	−0.140457	−	0.140457i	−0.773839	+	0.633382i	$0.781666\pi$
$594$		−	21.2788i		−	0.873078i
$595$	7.80609	+	4.93366i	0.320019	+	0.202260i
$596$			21.3190i			0.873262i
$597$	24.1811	+	24.1811i	0.989665	+	0.989665i
$598$	9.94972	+	9.94972i	0.406874	+	0.406874i
$599$			8.86356i			0.362155i	0.983469	+	0.181078i	$0.0579586\pi$
$599$			8.86356i			0.362155i	−0.983469	+	0.181078i	$0.942041\pi$
$600$	7.20653	−	3.42377i	0.294205	−	0.139775i
$601$			7.79408i			0.317927i	0.987284	+	0.158963i	$0.0508152\pi$
$601$			7.79408i			0.317927i	−0.987284	+	0.158963i	$0.949185\pi$
$602$	−4.11973	+	3.74269i	−0.167908	+	0.152541i
$603$	−2.00578	+	2.00578i	−0.0816818	+	0.0816818i
$604$	4.59040			0.186781
$605$	−7.38621	−	4.66828i	−0.300292	−	0.189793i
$606$	1.98964			0.0808234
$607$	−8.20390	+	8.20390i	−0.332986	+	0.332986i	−0.853719	−	0.520733i	$-0.825659\pi$
$607$	−8.20390	+	8.20390i	−0.332986	+	0.332986i	0.520733	+	0.853719i	$0.325659\pi$
$608$	−3.72245	+	3.72245i	−0.150965	+	0.150965i
$609$	−1.56863			−0.0635639
$610$	−0.0404492	−	0.179399i	−0.00163774	−	0.00726366i
$611$	55.0001			2.22506
$612$	1.56108	+	1.56108i	0.0631029	+	0.0631029i
$613$	22.6331	−	22.6331i	0.914144	−	0.914144i	−0.0824513	−	0.996595i	$-0.526275\pi$
$613$	22.6331	−	22.6331i	0.914144	−	0.914144i	0.996595	+	0.0824513i	$0.0262749\pi$
$614$	−11.1275			−0.449069
$615$	4.90507	+	21.7548i	0.197792	+	0.877240i
$616$	3.27726			0.132045
$617$	13.3388	+	13.3388i	0.536999	+	0.536999i	0.922646	−	0.385647i	$-0.126022\pi$
$617$	13.3388	+	13.3388i	0.536999	+	0.536999i	−0.385647	+	0.922646i	$0.626022\pi$
$618$	−2.55507	+	2.55507i	−0.102780	+	0.102780i
$619$		−	30.7876i		−	1.23746i	−0.785605	−	0.618728i	$-0.787648\pi$
$619$		−	30.7876i		−	1.23746i	0.785605	−	0.618728i	$-0.212352\pi$
$620$	9.91239	−	15.6835i	0.398091	−	0.629864i
$621$		−	17.8755i		−	0.717317i
$622$	16.0423	−	16.0423i	0.643237	−	0.643237i
$623$	6.39102	−	6.39102i	0.256051	−	0.256051i
$624$	−6.92246			−0.277120
$625$	−15.7926	+	19.3803i	−0.631703	+	0.775210i
$626$	4.10821			0.164197
$627$	22.9342	+	22.9342i	0.915906	+	0.915906i
$628$	−8.33478	−	8.33478i	−0.332594	−	0.332594i
$629$	20.5605			0.819801
$630$	−0.727996	−	0.460113i	−0.0290041	−	0.0183313i
$631$			36.0519i			1.43520i	0.696454	+	0.717601i	$0.254760\pi$
$631$			36.0519i			1.43520i	−0.696454	+	0.717601i	$0.745240\pi$
$632$	6.09480	−	6.09480i	0.242438	−	0.242438i
$633$	2.06471	−	2.06471i	0.0820649	−	0.0820649i
$634$	−31.3444			−1.24485
$635$	6.16456	+	27.3409i	0.244633	+	1.08499i
$636$		−	1.60716i		−	0.0637280i
$637$	−19.2630	−	19.2630i	−0.763226	−	0.763226i
$638$	−3.16193	+	3.16193i	−0.125182	+	0.125182i
$639$	−2.91643			−0.115372
$640$	0.491820	+	2.18131i	0.0194409	+	0.0862238i
$641$			24.3449i			0.961566i	0.876840	+	0.480783i	$0.159647\pi$
$641$			24.3449i			0.961566i	−0.876840	+	0.480783i	$0.840353\pi$
$642$	9.68122	+	9.68122i	0.382087	+	0.382087i
$643$	27.6613	−	27.6613i	1.09085	−	1.09085i	0.0954162	−	0.995437i	$-0.469582\pi$
$643$	27.6613	−	27.6613i	1.09085	−	1.09085i	0.995437	−	0.0954162i	$-0.0304182\pi$
$644$	2.75310			0.108487
$645$	−13.4335	+	19.1569i	−0.528942	+	0.754301i
$646$	−25.6134			−1.00774
$647$	−29.5816	+	29.5816i	−1.16297	+	1.16297i	−0.179151	+	0.983822i	$0.557335\pi$
$647$	−29.5816	+	29.5816i	−1.16297	+	1.16297i	−0.983822	+	0.179151i	$0.942665\pi$
$648$	5.25582	+	5.25582i	0.206468	+	0.206468i
$649$		−	26.7636i		−	1.05056i
$650$	19.5923	−	9.30817i	0.768474	−	0.365096i
$651$	11.2381			0.440457
$652$	−8.74375	+	8.74375i	−0.342432	+	0.342432i
$653$	−17.5418	−	17.5418i	−0.686463	−	0.686463i	0.274985	−	0.961449i	$-0.411327\pi$
$653$	−17.5418	−	17.5418i	−0.686463	−	0.686463i	−0.961449	+	0.274985i	$0.911327\pi$
$654$			20.4630i			0.800168i
$655$	10.0196	−	15.8531i	0.391496	−	0.619430i
$656$	−6.25012			−0.244026
$657$	0.306475	−	0.306475i	0.0119567	−	0.0119567i
$658$	7.60929	−	7.60929i	0.296641	−	0.296641i
$659$			15.4145i			0.600464i	0.953866	+	0.300232i	$0.0970642\pi$
$659$			15.4145i			0.600464i	−0.953866	+	0.300232i	$0.902936\pi$
$660$	13.4392	−	3.03013i	0.523119	−	0.117948i
$661$	19.5394			0.759995			0.379997	−	0.924988i	$-0.375925\pi$
$661$	19.5394			0.759995			0.379997	+	0.924988i	$0.375925\pi$
$662$	1.61048	+	1.61048i	0.0625929	+	0.0625929i
$663$	−23.8160	−	23.8160i	−0.924936	−	0.924936i
$664$	−9.40370			−0.364934
$665$	9.74693	−	2.19764i	0.377970	−	0.0852209i
$666$	−1.91747			−0.0743006
$667$	−2.65622	+	2.65622i	−0.102849	+	0.102849i
$668$	4.14476	−	4.14476i	0.160366	−	0.160366i
$669$		−	17.3144i		−	0.669413i
$670$	−11.8164	−	7.46830i	−0.456509	−	0.288526i
$671$		−	0.317547i		−	0.0122588i
$672$	−0.957726	+	0.957726i	−0.0369451	+	0.0369451i
$673$	2.64638	+	2.64638i	0.102011	+	0.102011i	0.756270	−	0.654260i	$-0.227020\pi$
$673$	2.64638	+	2.64638i	0.102011	+	0.102011i	−0.654260	+	0.756270i	$0.727020\pi$
$674$	−20.2152			−0.778662
$675$	−25.9610	−	9.23814i	−0.999239	−	0.355576i
$676$	−5.82004			−0.223848
$677$	5.17419	−	5.17419i	0.198860	−	0.198860i	−0.600651	−	0.799511i	$-0.705092\pi$
$677$	5.17419	−	5.17419i	0.198860	−	0.198860i	0.799511	+	0.600651i	$0.205092\pi$
$678$	−19.3815	−	19.3815i	−0.744344	−	0.744344i
$679$	−1.07501			−0.0412553
$680$	−5.81250	+	9.19661i	−0.222899	+	0.352674i
$681$	12.3830			0.474516
$682$	22.6531	−	22.6531i	0.867432	−	0.867432i
$683$	18.1144	−	18.1144i	0.693128	−	0.693128i	−0.269791	−	0.962919i	$-0.586955\pi$
$683$	18.1144	−	18.1144i	0.693128	−	0.693128i	0.962919	+	0.269791i	$0.0869547\pi$
$684$	2.38870			0.0913343
$685$	−46.1869	+	10.4138i	−1.76471	+	0.397890i
$686$	−11.2717			−0.430355
$687$	−13.6885	+	13.6885i	−0.522249	+	0.522249i
$688$	−4.40938	−	4.85359i	−0.168106	−	0.185041i
$689$		−	4.36937i		−	0.166460i
$690$	11.2897	−	2.54550i	0.429793	−	0.0969054i
$691$		−	30.8756i		−	1.17456i	−0.809382	−	0.587282i	$-0.800198\pi$
$691$		−	30.8756i		−	1.17456i	0.809382	−	0.587282i	$-0.199802\pi$
$692$	−14.3734	−	14.3734i	−0.546394	−	0.546394i
$693$	−1.05151	−	1.05151i	−0.0399436	−	0.0399436i
$694$			26.6977i			1.01343i
$695$	−17.6819	+	27.9766i	−0.670715	+	1.06121i
$696$		−	1.84805i		−	0.0700501i
$697$	−21.5028	−	21.5028i	−0.814478	−	0.814478i
$698$	−19.9623	+	19.9623i	−0.755583	+	0.755583i
$699$			31.9471i			1.20835i
$700$	1.42282	−	3.99840i	0.0537775	−	0.151125i
$701$	43.8728			1.65705			0.828526	−	0.559951i	$-0.189180\pi$
$701$	43.8728			1.65705			0.828526	+	0.559951i	$0.189180\pi$
$702$	16.9058	+	16.9058i	0.638070	+	0.638070i
$703$	15.7304	−	15.7304i	0.593285	−	0.593285i
$704$			3.86104i			0.145519i
$705$	24.1682	−	38.2392i	0.910226	−	1.44017i
$706$			8.93272i			0.336187i
$707$	0.748366	−	0.748366i	0.0281452	−	0.0281452i
$708$	7.82124	+	7.82124i	0.293940	+	0.293940i
$709$			26.2366i			0.985337i	0.870217	+	0.492669i	$0.163978\pi$
$709$			26.2366i			0.985337i	−0.870217	+	0.492669i	$0.836022\pi$
$710$	−3.16111	−	14.0201i	−0.118634	−	0.526164i
$711$	−3.91104			−0.146676
$712$	7.52947	+	7.52947i	0.282179	+	0.282179i
$713$	19.0300	−	19.0300i	0.712679	−	0.712679i
$714$	−6.58990			−0.246621
$715$	36.5370	−	8.23800i	1.36640	−	0.308084i
$716$			25.0245i			0.935210i
$717$	−11.2890	+	11.2890i	−0.421594	+	0.421594i
$718$	11.0868	+	11.0868i	0.413756	+	0.413756i
$719$			2.78928i			0.104023i	0.998646	+	0.0520114i	$0.0165632\pi$
$719$			2.78928i			0.104023i	−0.998646	+	0.0520114i	$0.983437\pi$
$720$	0.542074	−	0.857675i	0.0202019	−	0.0319637i
$721$			1.92209i			0.0715824i
$722$	−6.16125	+	6.16125i	−0.229298	+	0.229298i
$723$	8.74054	−	8.74054i	0.325064	−	0.325064i
$724$			12.3805i			0.460118i
$725$	2.48494	+	5.23044i	0.0922885	+	0.194254i
$726$	6.23544			0.231419
$727$	3.70011	−	3.70011i	0.137229	−	0.137229i	−0.635155	−	0.772385i	$-0.719064\pi$
$727$	3.70011	−	3.70011i	0.137229	−	0.137229i	0.772385	+	0.635155i	$0.219064\pi$
$728$	−2.60376	+	2.60376i	−0.0965019	+	0.0965019i
$729$		−	29.7550i		−	1.10204i
$730$	1.80550	+	1.14112i	0.0668245	+	0.0422349i
$731$	1.52824	−	31.8682i	0.0565240	−	1.17869i
$732$	0.0927979	+	0.0927979i	0.00342991	+	0.00342991i
$733$	−24.1558	−	24.1558i	−0.892215	−	0.892215i	0.102516	−	0.994731i	$-0.467311\pi$
$733$	−24.1558	−	24.1558i	−0.892215	−	0.892215i	−0.994731	+	0.102516i	$0.967311\pi$
$734$	−2.18751			−0.0807425
$735$	−21.8572	+	4.92816i	−0.806216	+	0.181778i
$736$			3.24351i			0.119557i
$737$	−17.0675	−	17.0675i	−0.628691	−	0.628691i
$738$	2.00535	+	2.00535i	0.0738181	+	0.0738181i
$739$	−39.1365			−1.43966			−0.719829	−	0.694151i	$-0.755780\pi$
$739$	−39.1365			−1.43966			−0.719829	+	0.694151i	$0.755780\pi$
$740$	−2.07835	−	9.21783i	−0.0764016	−	0.338854i
$741$	−36.4422			−1.33874
$742$	−0.604505	−	0.604505i	−0.0221921	−	0.0221921i
$743$	34.0425	+	34.0425i	1.24890	+	1.24890i	0.956207	+	0.292693i	$0.0945513\pi$
$743$	34.0425	+	34.0425i	1.24890	+	1.24890i	0.292693	+	0.956207i	$0.405449\pi$
$744$			13.2400i			0.485402i
$745$	40.2970	+	25.4688i	1.47637	+	0.933104i
$746$	−11.3098			−0.414080
$747$	3.01718	+	3.01718i	0.110393	+	0.110393i
$748$	−13.2835	+	13.2835i	−0.485693	+	0.485693i
$749$	7.28284			0.266109
$750$	2.13770	−	17.7119i	0.0780579	−	0.646747i
$751$			29.1509i			1.06373i	0.846828	+	0.531866i	$0.178509\pi$
$751$			29.1509i			1.06373i	−0.846828	+	0.531866i	$0.821491\pi$
$752$	8.96474	+	8.96474i	0.326911	+	0.326911i
$753$	−5.81512	−	5.81512i	−0.211915	−	0.211915i
$754$		−	5.02427i		−	0.182973i
$755$	5.48392	−	8.67673i	0.199580	−	0.315778i
$756$	4.67786			0.170132
$757$	−10.7198	+	10.7198i	−0.389617	+	0.389617i	−0.874551	−	0.484934i	$-0.838844\pi$
$757$	−10.7198	+	10.7198i	−0.389617	+	0.389617i	0.484934	+	0.874551i	$0.338844\pi$
$758$	−15.9955	−	15.9955i	−0.580984	−	0.580984i
$759$	19.9835			0.725354
$760$	2.58911	+	11.4832i	0.0939170	+	0.416538i
$761$			3.34615i			0.121298i	0.998159	+	0.0606489i	$0.0193170\pi$
$761$			3.34615i			0.121298i	−0.998159	+	0.0606489i	$0.980683\pi$
$762$	−14.1426	−	14.1426i	−0.512334	−	0.512334i
$763$	7.69681	+	7.69681i	0.278643	+	0.278643i
$764$	−21.8481			−0.790437
$765$	4.81568	−	1.08579i	0.174111	−	0.0392569i
$766$	−9.37283			−0.338654
$767$	21.2635	+	21.2635i	0.767782	+	0.767782i
$768$	−1.12833	−	1.12833i	−0.0407150	−	0.0407150i
$769$			1.58365i			0.0571079i	0.999592	+	0.0285540i	$0.00909025\pi$
$769$			1.58365i			0.0571079i	−0.999592	+	0.0285540i	$0.990910\pi$
$770$	3.91518	−	6.19464i	0.141093	−	0.223239i
$771$	−22.2730			−0.802144
$772$	−16.3925	−	16.3925i	−0.589978	−	0.589978i
$773$	−2.70425	−	2.70425i	−0.0972650	−	0.0972650i	0.656800	−	0.754065i	$-0.271910\pi$
$773$	−2.70425	−	2.70425i	−0.0972650	−	0.0972650i	−0.754065	+	0.656800i	$0.771910\pi$
$774$	−0.142524	+	2.97203i	−0.00512291	+	0.106827i
$775$	−17.8029	−	37.4726i	−0.639501	−	1.34605i
$776$		−	1.26651i		−	0.0454650i
$777$	4.04718	−	4.04718i	0.145192	−	0.145192i
$778$	11.6301	−	11.6301i	0.416959	−	0.416959i
$779$	−32.9028			−1.17886
$780$	−8.26992	+	13.0848i	−0.296111	+	0.468510i
$781$		−	24.8164i		−	0.887999i
$782$	−11.1589	+	11.1589i	−0.399043	+	0.399043i
$783$	−4.51325	+	4.51325i	−0.161290	+	0.161290i
$784$		−	6.27954i		−	0.224269i
$785$	−25.7114	+	5.79716i	−0.917681	+	0.206910i
$786$			13.3832i			0.477361i
$787$	−3.12161	−	3.12161i	−0.111273	−	0.111273i	0.649278	−	0.760551i	$-0.275071\pi$
$787$	−3.12161	−	3.12161i	−0.111273	−	0.111273i	−0.760551	+	0.649278i	$0.775071\pi$
$788$	8.22622	−	8.22622i	0.293047	−	0.293047i
$789$			15.3922i			0.547978i
$790$	−4.23917	−	18.8015i	−0.150823	−	0.668927i
$791$	−14.5800			−0.518407
$792$	1.23882	−	1.23882i	0.0440195	−	0.0440195i
$793$	0.252289	+	0.252289i	0.00895904	+	0.00895904i
$794$	9.11924			0.323630
$795$	−3.03784	−	1.91999i	−0.107741	−	0.0680951i
$796$			21.4309i			0.759597i
$797$	25.9981	+	25.9981i	0.920900	+	0.920900i	0.997093	−	0.0761926i	$-0.0242764\pi$
$797$	25.9981	+	25.9981i	0.920900	+	0.920900i	−0.0761926	+	0.997093i	$0.524276\pi$
$798$	−5.04180	+	5.04180i	−0.178478	+	0.178478i
$799$			61.6844i			2.18224i
$800$	4.71064	+	1.67627i	0.166546	+	0.0592650i
$801$		−	4.83167i		−	0.170719i
$802$	−0.338126	+	0.338126i	−0.0119396	+	0.0119396i
$803$	2.60785	+	2.60785i	0.0920289	+	0.0920289i
$804$	9.97543			0.351806
$805$	3.28899	−	5.20388i	0.115922	−	0.183412i
$806$			35.9955i			1.26789i
$807$	34.4942	−	34.4942i	1.21425	−	1.21425i
$808$	0.881674	+	0.881674i	0.0310172	+	0.0310172i
$809$		−	46.2214i		−	1.62506i	−0.582920	−	0.812529i	$-0.698090\pi$
$809$		−	46.2214i		−	1.62506i	0.582920	−	0.812529i	$-0.301910\pi$
$810$	16.2134	−	3.65563i	0.569679	−	0.128446i
$811$		−	39.5860i		−	1.39005i	−0.718985	−	0.695025i	$-0.755393\pi$
$811$		−	39.5860i		−	1.39005i	0.718985	−	0.695025i	$-0.244607\pi$
$812$	−0.695110	−	0.695110i	−0.0243936	−	0.0243936i
$813$	−14.4169	−	14.4169i	−0.505621	−	0.505621i
$814$		−	16.3161i		−	0.571879i
$815$	6.08162	+	26.9731i	0.213030	+	0.944825i
$816$		−	7.76378i		−	0.271786i
$817$	−23.2125	−	25.5510i	−0.812103	−	0.893915i
$818$	−11.5338	+	11.5338i	−0.403271	+	0.403271i
$819$	1.67084			0.0583838
$820$	−7.46670	+	11.8139i	−0.260748	+	0.412559i
$821$	−12.8619			−0.448882			−0.224441	−	0.974488i	$-0.572056\pi$
$821$	−12.8619			−0.448882			−0.224441	+	0.974488i	$0.572056\pi$
$822$	23.8911	−	23.8911i	0.833299	−	0.833299i
$823$	−25.7628	+	25.7628i	−0.898035	+	0.898035i	−0.995262	−	0.0972270i	$-0.969003\pi$
$823$	−25.7628	+	25.7628i	−0.898035	+	0.898035i	0.0972270	+	0.995262i	$0.469003\pi$
$824$	−2.26448			−0.0788867
$825$	10.3276	−	29.0225i	0.359560	−	1.01043i
$826$	5.88364			0.204718
$827$	−29.5137	−	29.5137i	−1.02629	−	1.02629i	−0.999645	−	0.0266484i	$-0.991517\pi$
$827$	−29.5137	−	29.5137i	−1.02629	−	1.02629i	−0.0266484	−	0.999645i	$-0.508483\pi$
$828$	1.04068	−	1.04068i	0.0361662	−	0.0361662i
$829$	56.7451			1.97084			0.985419	−	0.170147i	$-0.0544243\pi$
$829$	56.7451			1.97084			0.985419	+	0.170147i	$0.0544243\pi$
$830$	−11.2341	+	17.7748i	−0.389942	+	0.616971i
$831$	43.1015			1.49517
$832$	−3.06758	−	3.06758i	−0.106349	−	0.106349i
$833$	21.6040	−	21.6040i	0.748536	−	0.748536i
$834$		−	23.6178i		−	0.817819i
$835$	−2.88284	−	12.7859i	−0.0997649	−	0.442475i
$836$			20.3259i			0.702985i
$837$	32.3344	−	32.3344i	1.11764	−	1.11764i
$838$	−8.37577	+	8.37577i	−0.289336	+	0.289336i
$839$	12.6979			0.438379			0.219190	−	0.975682i	$-0.429659\pi$
$839$	12.6979			0.438379			0.219190	+	0.975682i	$0.429659\pi$
$840$	0.666136	+	2.95443i	0.0229839	+	0.101938i
$841$	−27.6587			−0.953748
$842$	14.6269	+	14.6269i	0.504078	+	0.504078i
$843$	13.3824	+	13.3824i	0.460913	+	0.460913i
$844$	1.82989			0.0629873
$845$	−6.95291	+	11.0010i	−0.239187	+	0.378445i
$846$		−	5.75269i		−	0.197781i
$847$	2.34535	−	2.34535i	0.0805872	−	0.0805872i
$848$	0.712186	−	0.712186i	0.0244566	−	0.0244566i
$849$	−6.71616			−0.230498
$850$	10.4394	+	21.9734i	0.358069	+	0.753683i
$851$		−	13.7065i		−	0.469853i
$852$	7.25218	+	7.25218i	0.248456	+	0.248456i
$853$	−12.1701	+	12.1701i	−0.416695	+	0.416695i	−0.884063	−	0.467368i	$-0.845202\pi$
$853$	−12.1701	+	12.1701i	−0.416695	+	0.416695i	0.467368	+	0.884063i	$0.345202\pi$
$854$	0.0698086			0.00238880
$855$	2.85366	−	4.51510i	0.0975932	−	0.154413i
$856$			8.58015i			0.293263i
$857$	−39.3346	−	39.3346i	−1.34364	−	1.34364i	−0.892402	−	0.451241i	$-0.850981\pi$
$857$	−39.3346	−	39.3346i	−1.34364	−	1.34364i	−0.451241	−	0.892402i	$-0.649019\pi$
$858$	−18.8995	+	18.8995i	−0.645218	+	0.645218i
$859$	40.0488			1.36645			0.683223	−	0.730210i	$-0.260578\pi$
$859$	40.0488			1.36645			0.683223	+	0.730210i	$0.260578\pi$
$860$	−14.4419	+	2.53623i	−0.492464	+	0.0864847i
$861$	−8.46535			−0.288498
$862$	7.90552	−	7.90552i	0.269263	−	0.269263i
$863$	−6.12455	−	6.12455i	−0.208482	−	0.208482i	0.595140	−	0.803622i	$-0.297097\pi$
$863$	−6.12455	−	6.12455i	−0.208482	−	0.208482i	−0.803622	+	0.595140i	$0.797097\pi$
$864$			5.51114i			0.187493i
$865$	−44.3395	+	9.99724i	−1.50759	+	0.339916i
$866$	9.96306			0.338559
$867$	7.52883	−	7.52883i	0.255692	−	0.255692i
$868$	4.97999	+	4.97999i	0.169032	+	0.169032i
$869$		−	33.2797i		−	1.12894i
$870$	−3.49316	−	2.20777i	−0.118429	−	0.0748504i
$871$	27.1201			0.918930
$872$	−9.06786	+	9.06786i	−0.307076	+	0.307076i
$873$	−0.406360	+	0.406360i	−0.0137532	+	0.0137532i
$874$			17.0750i			0.577570i
$875$	−5.85796	−	7.46608i	−0.198035	−	0.252399i
$876$	−1.52420			−0.0514980
$877$	−14.6131	−	14.6131i	−0.493449	−	0.493449i	0.415942	−	0.909391i	$-0.363452\pi$
$877$	−14.6131	−	14.6131i	−0.493449	−	0.493449i	−0.909391	+	0.415942i	$0.863452\pi$
$878$	0.370192	+	0.370192i	0.0124934	+	0.0124934i
$879$	8.06173			0.271915
$880$	7.29810	+	4.61259i	0.246019	+	0.155490i
$881$	46.2924			1.55963			0.779816	−	0.626009i	$-0.215313\pi$
$881$	46.2924			1.55963			0.779816	+	0.626009i	$0.215313\pi$
$882$	−2.01479	+	2.01479i	−0.0678416	+	0.0678416i
$883$	17.8568	−	17.8568i	0.600929	−	0.600929i	−0.339630	−	0.940559i	$-0.610302\pi$
$883$	17.8568	−	17.8568i	0.600929	−	0.600929i	0.940559	+	0.339630i	$0.110302\pi$
$884$		−	21.1073i		−	0.709916i
$885$	24.1273	−	5.43998i	0.811029	−	0.182863i
$886$		−	18.5602i		−	0.623543i
$887$	4.75994	−	4.75994i	0.159823	−	0.159823i	−0.622665	−	0.782488i	$-0.713950\pi$
$887$	4.75994	−	4.75994i	0.159823	−	0.159823i	0.782488	+	0.622665i	$0.213950\pi$
$888$	4.76812	+	4.76812i	0.160008	+	0.160008i
$889$	−10.6390			−0.356821
$890$	23.2272	−	5.23704i	0.778577	−	0.175546i
$891$	28.6986			0.961439
$892$	7.67259	−	7.67259i	0.256897	−	0.256897i
$893$	47.1935	+	47.1935i	1.57927	+	1.57927i
$894$	−34.0187			−1.13776
$895$	47.3010	+	29.8955i	1.58110	+	0.999297i
$896$	−0.848801			−0.0283565
$897$	−15.8767	+	15.8767i	−0.530109	+	0.530109i
$898$	−17.6683	+	17.6683i	−0.589599	+	0.589599i
$899$	−9.60949			−0.320495
$900$	−0.973580	−	2.04924i	−0.0324527	−	0.0683081i
$901$	4.90040			0.163256
$902$	−17.0639	+	17.0639i	−0.568165	+	0.568165i
$903$	−5.97220	−	6.57385i	−0.198742	−	0.218764i
$904$		−	17.1772i		−	0.571306i
$905$	23.4015	+	14.7904i	0.777891	+	0.491648i
$906$			7.32489i			0.243353i
$907$	−37.8214	−	37.8214i	−1.25584	−	1.25584i	−0.953062	−	0.302776i	$-0.902087\pi$
$907$	−37.8214	−	37.8214i	−1.25584	−	1.25584i	−0.302776	−	0.953062i	$-0.597913\pi$
$908$	5.48731	+	5.48731i	0.182103	+	0.182103i
$909$		−	0.565771i		−	0.0187655i
$910$	1.81102	+	8.03218i	0.0600347	+	0.266264i
$911$			22.0824i			0.731623i	0.930689	+	0.365812i	$0.119209\pi$
$911$			22.0824i			0.731623i	−0.930689	+	0.365812i	$0.880791\pi$
$912$	−5.93991	−	5.93991i	−0.196690	−	0.196690i
$913$	−25.6737	+	25.6737i	−0.849675	+	0.849675i
$914$			18.1945i			0.601821i
$915$	0.286267	−	0.0645446i	0.00946368	−	0.00213378i
$916$	−12.1317			−0.400841
$917$	5.03384	+	5.03384i	0.166232	+	0.166232i
$918$	−18.9605	+	18.9605i	−0.625789	+	0.625789i
$919$		−	35.0510i		−	1.15623i	−0.815956	−	0.578114i	$-0.803789\pi$
$919$		−	35.0510i		−	1.15623i	0.815956	−	0.578114i	$-0.196211\pi$
$920$	6.13085	+	3.87486i	0.202128	+	0.127750i
$921$		−	17.7561i		−	0.585083i
$922$	16.4703	−	16.4703i	0.542422	−	0.542422i
$923$	19.7164	+	19.7164i	0.648975	+	0.648975i
$924$			5.22951i			0.172038i
$925$	−19.9063	−	7.08361i	−0.654516	−	0.232908i
$926$	−7.86636			−0.258505
$927$	0.726558	+	0.726558i	0.0238633	+	0.0238633i
$928$	0.818932	−	0.818932i	0.0268828	−	0.0268828i
$929$	−11.6744			−0.383025			−0.191513	−	0.981490i	$-0.561339\pi$
$929$	−11.6744			−0.383025			−0.191513	+	0.981490i	$0.561339\pi$
$930$	25.0261	+	15.8172i	0.820638	+	0.518665i
$931$		−	33.0576i		−	1.08342i
$932$	−14.1568	+	14.1568i	−0.463723	+	0.463723i
$933$	25.5986	+	25.5986i	0.838062	+	0.838062i
$934$			15.9825i			0.522962i
$935$	9.23919	+	40.9774i	0.302154	+	1.34010i
$936$			1.96847i			0.0643413i
$937$	31.0289	−	31.0289i	1.01367	−	1.01367i	0.0137650	−	0.999905i	$-0.495618\pi$
$937$	31.0289	−	31.0289i	1.01367	−	1.01367i	0.999905	−	0.0137650i	$-0.00438167\pi$
$938$	3.75208	−	3.75208i	0.122510	−	0.122510i
$939$			6.55546i			0.213929i
$940$	27.6548	−	6.23533i	0.901999	−	0.203374i
$941$	−38.5454			−1.25655			−0.628273	−	0.777993i	$-0.716238\pi$
$941$	−38.5454			−1.25655			−0.628273	+	0.777993i	$0.716238\pi$
$942$	13.2998	−	13.2998i	0.433330	−	0.433330i
$943$	−14.3347	+	14.3347i	−0.466802	+	0.466802i
$944$			6.93170i			0.225608i
$945$	5.58841	−	8.84204i	0.181791	−	0.287632i
$946$	−25.2895	−	1.21276i	−0.822232	−	0.0394301i
$947$	14.7145	+	14.7145i	0.478156	+	0.478156i	0.904541	−	0.426386i	$-0.140213\pi$
$947$	14.7145	+	14.7145i	0.478156	+	0.478156i	−0.426386	+	0.904541i	$0.640213\pi$
$948$	9.72546	+	9.72546i	0.315868	+	0.315868i
$949$	−4.14384			−0.134515
$950$	24.7984	+	8.82445i	0.804567	+	0.286303i
$951$		−	50.0162i		−	1.62189i
$952$	−2.92021	−	2.92021i	−0.0946444	−	0.0946444i
$953$	23.4050	+	23.4050i	0.758164	+	0.758164i	0.975988	−	0.217824i	$-0.0698959\pi$
$953$	23.4050	+	23.4050i	0.758164	+	0.758164i	−0.217824	+	0.975988i	$0.569896\pi$
$954$	−0.457011			−0.0147963
$955$	−26.1009	+	41.2971i	−0.844604	+	1.33634i
$956$	−10.0050			−0.323586
$957$	−5.04548	−	5.04548i	−0.163097	−	0.163097i
$958$	−2.70814	−	2.70814i	−0.0874959	−	0.0874959i
$959$		−	17.9725i		−	0.580361i
$960$	−3.48071	+	0.784796i	−0.112339	+	0.0253292i
$961$	37.8455			1.22082
$962$	12.9630	+	12.9630i	0.417945	+	0.417945i
$963$	2.75295	−	2.75295i	0.0887124	−	0.0887124i
$964$	7.74645			0.249496
$965$	−50.5681	+	11.4016i	−1.62785	+	0.367031i
$966$			4.39311i			0.141346i
$967$	28.1249	+	28.1249i	0.904436	+	0.904436i	0.995816	−	0.0913803i	$-0.0291279\pi$
$967$	28.1249	+	28.1249i	0.904436	+	0.904436i	−0.0913803	+	0.995816i	$0.529128\pi$
$968$	2.76313	+	2.76313i	0.0888104	+	0.0888104i
$969$		−	40.8712i		−	1.31297i
$970$	−2.39394	−	1.51303i	−0.0768648	−	0.0485806i
$971$	20.6482			0.662632			0.331316	−	0.943520i	$-0.392507\pi$
$971$	20.6482			0.662632			0.331316	+	0.943520i	$0.392507\pi$
$972$	3.30419	−	3.30419i	0.105982	−	0.105982i
$973$	−8.88343	−	8.88343i	−0.284790	−	0.284790i
$974$	6.00902			0.192541
$975$	14.8530	+	31.2634i	0.475677	+	1.00123i
$976$			0.0822438i			0.00263256i
$977$	−10.7498	−	10.7498i	−0.343918	−	0.343918i	0.513920	−	0.857838i	$-0.328193\pi$
$977$	−10.7498	−	10.7498i	−0.343918	−	0.343918i	−0.857838	+	0.513920i	$0.828193\pi$
$978$	−13.9524	−	13.9524i	−0.446148	−	0.446148i
$979$	41.1135			1.31399
$980$	−11.8695	−	7.50184i	−0.379158	−	0.239638i
$981$	5.81885			0.185782
$982$	−9.79691	−	9.79691i	−0.312632	−	0.312632i
$983$	18.3820	+	18.3820i	0.586293	+	0.586293i	0.936625	−	0.350332i	$-0.113931\pi$
$983$	18.3820	+	18.3820i	0.586293	+	0.586293i	−0.350332	+	0.936625i	$0.613931\pi$
$984$		−	9.97330i		−	0.317937i
$985$	−5.72166	−	25.3765i	−0.182307	−	0.808564i
$986$	5.63489			0.179451
$987$	12.1421	+	12.1421i	0.386488	+	0.386488i
$988$	−16.1488	−	16.1488i	−0.513761	−	0.513761i
$989$	−21.2447	−	1.01879i	−0.675543	−	0.0323956i
$990$	−0.861647	−	3.82155i	−0.0273849	−	0.121457i
$991$		−	38.1168i		−	1.21082i	−0.795914	−	0.605410i	$-0.793009\pi$
$991$		−	38.1168i		−	1.21082i	0.795914	−	0.605410i	$-0.206991\pi$
$992$	−5.86709	+	5.86709i	−0.186280	+	0.186280i
$993$	−2.56983	+	2.56983i	−0.0815512	+	0.0815512i
$994$	5.45556			0.173040
$995$	40.5084	+	25.6024i	1.28420	+	0.811650i
$996$		−	15.0055i		−	0.475466i
$997$	−40.5063	+	40.5063i	−1.28285	+	1.28285i	−0.343808	+	0.939040i	$0.611717\pi$
$997$	−40.5063	+	40.5063i	−1.28285	+	1.28285i	−0.939040	+	0.343808i	$0.888283\pi$
$998$	13.6601	−	13.6601i	0.432402	−	0.432402i
$999$		−	23.2891i		−	0.736835i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	430.2.g.b.257.3	✓	40
5.3	odd	4	inner	430.2.g.b.343.18	yes	40
43.42	odd	2	inner	430.2.g.b.257.18	yes	40
215.128	even	4	inner	430.2.g.b.343.3	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
430.2.g.b.257.3	✓	40	1.1	even	1	trivial
430.2.g.b.257.18	yes	40	43.42	odd	2	inner
430.2.g.b.343.3	yes	40	215.128	even	4	inner
430.2.g.b.343.18	yes	40	5.3	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:	\( N \)	\(=\)	\( 430 = 2 \cdot 5 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	430.g (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 + 0.707107i) q^{2} +(-1.12833 - 1.12833i) q^{3} -1.00000i q^{4} +(-1.89019 - 1.19465i) q^{5} +1.59570 q^{6} +(0.600193 - 0.600193i) q^{7} +(0.707107 + 0.707107i) q^{8} -0.453751i q^{9} +O(q^{10})\)	\(q+(-0.707107 + 0.707107i) q^{2} +(-1.12833 - 1.12833i) q^{3} -1.00000i q^{4} +(-1.89019 - 1.19465i) q^{5} +1.59570 q^{6} +(0.600193 - 0.600193i) q^{7} +(0.707107 + 0.707107i) q^{8} -0.453751i q^{9} +(2.18131 - 0.491820i) q^{10} +3.86104 q^{11} +(-1.12833 + 1.12833i) q^{12} +(-3.06758 + 3.06758i) q^{13} +0.848801i q^{14} +(0.784796 + 3.48071i) q^{15} -1.00000 q^{16} +(-3.44039 - 3.44039i) q^{17} +(0.320851 + 0.320851i) q^{18} -5.26434 q^{19} +(-1.19465 + 1.89019i) q^{20} -1.35443 q^{21} +(-2.73017 + 2.73017i) q^{22} +(-2.29351 + 2.29351i) q^{23} -1.59570i q^{24} +(2.14563 + 4.51623i) q^{25} -4.33821i q^{26} +(-3.89696 + 3.89696i) q^{27} +(-0.600193 - 0.600193i) q^{28} +1.15814 q^{29} +(-3.01617 - 1.90630i) q^{30} -8.29732 q^{31} +(0.707107 - 0.707107i) q^{32} +(-4.35652 - 4.35652i) q^{33} +4.86544 q^{34} +(-1.85150 + 0.417458i) q^{35} -0.453751 q^{36} +(-2.98811 + 2.98811i) q^{37} +(3.72245 - 3.72245i) q^{38} +6.92246 q^{39} +(-0.491820 - 2.18131i) q^{40} +6.25012 q^{41} +(0.957726 - 0.957726i) q^{42} +(4.40938 + 4.85359i) q^{43} -3.86104i q^{44} +(-0.542074 + 0.857675i) q^{45} -3.24351i q^{46} +(-8.96474 - 8.96474i) q^{47} +(1.12833 + 1.12833i) q^{48} +6.27954i q^{49} +(-4.71064 - 1.67627i) q^{50} +7.76378i q^{51} +(3.06758 + 3.06758i) q^{52} +(-0.712186 + 0.712186i) q^{53} -5.51114i q^{54} +(-7.29810 - 4.61259i) q^{55} +0.848801 q^{56} +(5.93991 + 5.93991i) q^{57} +(-0.818932 + 0.818932i) q^{58} -6.93170i q^{59} +(3.48071 - 0.784796i) q^{60} -0.0822438i q^{61} +(5.86709 - 5.86709i) q^{62} +(-0.272338 - 0.272338i) q^{63} +1.00000i q^{64} +(9.46297 - 2.13362i) q^{65} +6.16106 q^{66} +(-4.42045 - 4.42045i) q^{67} +(-3.44039 + 3.44039i) q^{68} +5.17566 q^{69} +(1.01402 - 1.60439i) q^{70} -6.42737i q^{71} +(0.320851 - 0.320851i) q^{72} +(0.675425 + 0.675425i) q^{73} -4.22582i q^{74} +(2.67481 - 7.51675i) q^{75} +5.26434i q^{76} +(2.31737 - 2.31737i) q^{77} +(-4.89492 + 4.89492i) q^{78} -8.61935i q^{79} +(1.89019 + 1.19465i) q^{80} +7.43286 q^{81} +(-4.41950 + 4.41950i) q^{82} +(-6.64942 + 6.64942i) q^{83} +1.35443i q^{84} +(2.39293 + 10.6130i) q^{85} +(-6.54991 - 0.314101i) q^{86} +(-1.30677 - 1.30677i) q^{87} +(2.73017 + 2.73017i) q^{88} +10.6483 q^{89} +(-0.223164 - 0.989772i) q^{90} +3.68228i q^{91} +(2.29351 + 2.29351i) q^{92} +(9.36210 + 9.36210i) q^{93} +12.6781 q^{94} +(9.95060 + 6.28905i) q^{95} -1.59570 q^{96} +(-0.895557 - 0.895557i) q^{97} +(-4.44030 - 4.44030i) q^{98} -1.75195i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q+O(q^{10}) \) 40 * q	\( 40 q - 8 q^{10} + 16 q^{11} - 24 q^{13} + 8 q^{15} - 40 q^{16} - 12 q^{17} - 16 q^{21} + 44 q^{23} + 24 q^{25} + 32 q^{31} - 64 q^{35} + 48 q^{36} - 28 q^{38} - 4 q^{40} + 8 q^{41} - 16 q^{43} - 28 q^{47} + 24 q^{52} - 80 q^{53} + 24 q^{56} + 64 q^{57} + 12 q^{58} + 24 q^{67} - 12 q^{68} + 40 q^{78} - 120 q^{81} + 48 q^{83} + 28 q^{87} - 44 q^{92} - 16 q^{95} - 60 q^{97}+O(q^{100}) \) 40 * q - 8 * q^10 + 16 * q^11 - 24 * q^13 + 8 * q^15 - 40 * q^16 - 12 * q^17 - 16 * q^21 + 44 * q^23 + 24 * q^25 + 32 * q^31 - 64 * q^35 + 48 * q^36 - 28 * q^38 - 4 * q^40 + 8 * q^41 - 16 * q^43 - 28 * q^47 + 24 * q^52 - 80 * q^53 + 24 * q^56 + 64 * q^57 + 12 * q^58 + 24 * q^67 - 12 * q^68 + 40 * q^78 - 120 * q^81 + 48 * q^83 + 28 * q^87 - 44 * q^92 - 16 * q^95 - 60 * q^97

Introduction

L-functions

Modular forms

Varieties

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Database

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