LMFDB - Embedded newform 430.2.g.b.257.18

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			257.18
Character	$\chi$	$=$	430.257
Dual form			430.2.g.b.343.18

$q$-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} +(-4.85359 - 4.40938i) 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	0.953340	−	0.301899i	$-0.0976206\pi$
$3$	1.12833	+	1.12833i	0.651441	+	0.651441i	−0.301899	+	0.953340i	$0.597621\pi$
$4$		−	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	−0.811376	−	0.584524i	$-0.801281\pi$
$7$	−0.600193	+	0.600193i	−0.226852	+	0.226852i	0.584524	+	0.811376i	$0.301281\pi$
$8$	−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	$-0.293628\pi$
$19$	5.26434			1.20772			0.603862	+	0.797089i	$0.293628\pi$
$20$	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	$-0.534294\pi$
$29$	−1.15814			−0.215062			−0.107531	+	0.994202i	$0.534294\pi$
$30$	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	−0.417455	−	0.908697i	$-0.637078\pi$
$37$	2.98811	−	2.98811i	0.491242	−	0.491242i	0.908697	+	0.417455i	$0.137078\pi$
$38$	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
$43$	−4.85359	−	4.40938i	−0.740165	−	0.672425i
$43$	−4.85359	−	4.40938i	−0.740165	−	0.672425i
$44$		−	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	$0.00167595\pi$
$61$			0.0822438i			0.0105302i	−0.999986	+	0.00526512i	$0.998324\pi$
$62$	−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	$0.124556\pi$
$71$			6.42737i			0.762788i	−0.924412	+	0.381394i	$0.875444\pi$
$72$	−0.320851	+	0.320851i	−0.0378126	+	0.0378126i
$73$	−0.675425	−	0.675425i	−0.0790526	−	0.0790526i	0.666475	−	0.745527i	$-0.267802\pi$
$73$	−0.675425	−	0.675425i	−0.0790526	−	0.0790526i	−0.745527	+	0.666475i	$0.767802\pi$
$74$		−	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	$-0.690876\pi$
$89$	−10.6483			−1.12871			−0.564357	+	0.825531i	$0.690876\pi$
$90$	−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	$0.0494221\pi$
$113$	12.1461	+	12.1461i	1.14261	+	1.14261i	0.154641	+	0.987971i	$0.450578\pi$
$114$	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	$-0.880594\pi$
$131$		−	8.38703i		−	0.732778i	0.930462	−	0.366389i	$-0.119406\pi$
$132$	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	$0.609760\pi$
$137$	−14.9722	+	14.9722i	−1.27916	+	1.27916i	−0.941136	+	0.338027i	$0.890240\pi$
$138$	−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	$-0.162000\pi$
$149$	21.3190			1.74652			0.873262	+	0.487251i	$0.162000\pi$
$150$	3.42377	+	7.20653i	0.279550	+	0.588410i
$151$		−	4.59040i		−	0.373562i	−0.982402	−	0.186781i	$-0.940195\pi$
$151$		−	4.59040i		−	0.373562i	0.982402	−	0.186781i	$-0.0598054\pi$
$152$	−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	−0.956598	−	0.291410i	$-0.905875\pi$
$157$	−8.33478	+	8.33478i	−0.665188	+	0.665188i	0.291410	+	0.956598i	$0.405875\pi$
$158$	−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	0.961092	−	0.276229i	$-0.0890847\pi$
$163$	8.74375	+	8.74375i	0.684863	+	0.684863i	−0.276229	+	0.961092i	$0.589085\pi$
$164$		−	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
$172$	−4.40938	+	4.85359i	−0.336212	+	0.370083i
$173$	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	$-0.115211\pi$
$179$	25.0245			1.87042			0.935210	+	0.354094i	$0.115211\pi$
$180$	−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	$0.290147\pi$
$191$			21.8481i			1.58087i	−0.612543	+	0.790437i	$0.709853\pi$
$192$	−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	$-0.225396\pi$
$199$	21.4309			1.51919			0.759597	+	0.650394i	$0.225396\pi$
$200$	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	$-0.979937\pi$
$211$		−	1.82989i		−	0.125975i	0.998014	−	0.0629873i	$-0.0200628\pi$
$212$	0.712186	+	0.712186i	0.0489132	+	0.0489132i
$213$	−7.25218	+	7.25218i	−0.496911	+	0.496911i
$214$	8.58015			0.586527
$215$	−3.90653	−	14.1329i	−0.266423	−	0.963856i
$216$	−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	0.401893	−	0.915687i	$-0.368353\pi$
$223$	−7.67259	−	7.67259i	−0.513794	−	0.513794i	−0.915687	+	0.401893i	$0.868353\pi$
$224$		−	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	−0.501153	−	0.865359i	$-0.667091\pi$
$227$	5.48731	−	5.48731i	0.364205	−	0.364205i	0.865359	+	0.501153i	$0.167091\pi$
$228$	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	0.997540	−	0.0700948i	$-0.0223302\pi$
$233$	14.1568	+	14.1568i	0.927446	+	0.927446i	−0.0700948	+	0.997540i	$0.522330\pi$
$234$	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	$-0.919735\pi$
$241$		−	7.74645i		−	0.498993i	0.968376	−	0.249496i	$-0.0802650\pi$
$242$	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	−0.944418	−	0.328748i	$-0.893373\pi$
$257$	−9.86993	+	9.86993i	−0.615669	+	0.615669i	0.328748	+	0.944418i	$0.393373\pi$
$258$	−7.74486	−	7.03604i	−0.482174	−	0.438045i
$259$			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	0.885407	−	0.464817i	$-0.153880\pi$
$263$	6.82082	+	6.82082i	0.420590	+	0.420590i	−0.464817	+	0.885407i	$0.653880\pi$
$264$		−	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	$-0.448669\pi$
$277$	19.0997	−	19.0997i	1.14759	−	1.14759i	0.987025	−	0.160564i	$-0.0513314\pi$
$278$	−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	0.784423	−	0.620226i	$-0.212959\pi$
$313$	2.90495	+	2.90495i	0.164197	+	0.164197i	−0.620226	+	0.784423i	$0.712959\pi$
$314$			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	$0.0199370\pi$
$331$			2.27756i			0.125186i	−0.998039	+	0.0625929i	$0.980063\pi$
$332$	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	$0.504305\pi$
$347$	−18.8781	+	18.8781i	−1.01343	+	1.01343i	−0.999909	+	0.0135231i	$0.995695\pi$
$348$	−1.30677	+	1.30677i	−0.0700501	+	0.0700501i
$349$	−28.2309			−1.51117			−0.755583	−	0.655053i	$-0.772646\pi$
$349$	−28.2309			−1.51117			−0.755583	+	0.655053i	$0.772646\pi$
$350$	−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	0.469077	−	0.883157i	$-0.344587\pi$
$373$	−7.99721	−	7.99721i	−0.414080	−	0.414080i	−0.883157	+	0.469077i	$0.844587\pi$
$374$	−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	0.517207	−	0.855861i	$-0.326972\pi$
$383$	−6.62759	−	6.62759i	−0.338654	−	0.338654i	−0.855861	+	0.517207i	$0.826972\pi$
$384$			1.59570i			0.0814301i
$385$	−7.14872	+	1.61182i	−0.364332	+	0.0821461i
$386$		−	23.1825i		−	1.17996i
$387$	−2.00076	+	2.20232i	−0.101705	+	0.111950i
$388$	−0.895557	+	0.895557i	−0.0454650	+	0.0454650i
$389$	16.4474			0.833917			0.416959	−	0.908925i	$-0.363096\pi$
$389$	16.4474			0.833917			0.416959	+	0.908925i	$0.363096\pi$
$390$	−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	$-0.632127\pi$
$409$	−16.3113			−0.806542			−0.403271	+	0.915081i	$0.632127\pi$
$410$	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	$-0.593435\pi$
$419$	−11.8451			−0.578672			−0.289336	+	0.957228i	$0.593435\pi$
$420$	−1.61807	+	2.56013i	−0.0789537	+	0.124921i
$421$			20.6856i			1.00816i	0.863658	+	0.504078i	$0.168168\pi$
$421$			20.6856i			1.00816i	−0.863658	+	0.504078i	$0.831832\pi$
$422$	−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
$430$	−12.7558	−	7.23114i	−0.615140	−	0.348716i
$431$	−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	0.855825	−	0.517266i	$-0.173050\pi$
$433$	7.04495	+	7.04495i	0.338559	+	0.338559i	−0.517266	+	0.855825i	$0.673050\pi$
$434$		−	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	$-0.700714\pi$
$449$	−24.9867			−1.17920			−0.589599	+	0.807696i	$0.700714\pi$
$450$	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	−0.940796	−	0.338974i	$-0.889920\pi$
$457$	−12.8655	+	12.8655i	−0.601821	+	0.601821i	0.338974	+	0.940796i	$0.389920\pi$
$458$	−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	0.565941	−	0.824446i	$-0.308513\pi$
$463$	−5.56236	−	5.56236i	−0.258505	−	0.258505i	−0.824446	+	0.565941i	$0.808513\pi$
$464$	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	−0.918465	−	0.395502i	$-0.870570\pi$
$467$	−11.3013	+	11.3013i	−0.522962	+	0.522962i	0.395502	+	0.918465i	$0.370570\pi$
$468$	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
$473$	−18.7399	−	17.0248i	−0.861663	−	0.782802i
$474$		−	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	$-0.898789\pi$
$491$		−	13.8549i		−	0.625264i	0.949874	−	0.312632i	$-0.101211\pi$
$492$	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	$-0.357666\pi$
$499$	19.3183			0.864805			0.432402	+	0.901681i	$0.357666\pi$
$500$	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	$0.0332335\pi$
$503$	24.6429	+	24.6429i	1.09877	+	1.09877i	0.104216	+	0.994555i	$0.466767\pi$
$504$		−	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	$-0.690103\pi$
$521$		−	37.7486i		−	1.65380i	0.562351	−	0.826898i	$-0.309897\pi$
$522$	0.371591	+	0.371591i	0.0162641	+	0.0162641i
$523$	2.40075	+	2.40075i	0.104978	+	0.104978i	0.757645	−	0.652667i	$-0.226350\pi$
$523$	2.40075	+	2.40075i	0.104978	+	0.104978i	−0.652667	+	0.757645i	$0.726350\pi$
$524$	−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	$0.0314162\pi$
$571$			4.70919i			0.197074i	−0.995133	+	0.0985368i	$0.968584\pi$
$572$	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	$-0.470382\pi$
$577$	26.1487	−	26.1487i	1.08859	−	1.08859i	0.995674	−	0.0929124i	$-0.0296176\pi$
$578$	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	−0.689153	−	0.724616i	$-0.742017\pi$
$587$	0.859208	−	0.859208i	0.0354633	−	0.0354633i	0.724616	+	0.689153i	$0.242017\pi$
$588$	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	0.773839	−	0.633382i	$-0.218334\pi$
$593$	3.42036	+	3.42036i	0.140457	+	0.140457i	−0.633382	+	0.773839i	$0.718334\pi$
$594$		−	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	$-0.949185\pi$
$601$		−	7.79408i		−	0.317927i	0.987284	−	0.158963i	$-0.0508152\pi$
$602$	3.74269	−	4.11973i	0.152541	−	0.167908i
$603$	−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	−0.520733	−	0.853719i	$-0.674341\pi$
$607$	8.20390	−	8.20390i	0.332986	−	0.332986i	0.853719	+	0.520733i	$0.174341\pi$
$608$	−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	$-0.745240\pi$
$631$		−	36.0519i		−	1.43520i	0.696454	−	0.717601i	$-0.254760\pi$
$632$	−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	$-0.840353\pi$
$641$		−	24.3449i		−	0.961566i	0.876840	−	0.480783i	$-0.159647\pi$
$642$	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
$645$	11.5387	−	20.3544i	0.454336	−	0.801454i
$646$	−25.6134			−1.00774
$647$	29.5816	−	29.5816i	1.16297	−	1.16297i	0.179151	−	0.983822i	$-0.442665\pi$
$647$	29.5816	−	29.5816i	1.16297	−	1.16297i	0.983822	−	0.179151i	$-0.0573351\pi$
$648$	−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	0.961449	−	0.274985i	$-0.0886729\pi$
$653$	17.5418	+	17.5418i	0.686463	+	0.686463i	−0.274985	+	0.961449i	$0.588673\pi$
$654$			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	0.654260	−	0.756270i	$-0.272980\pi$
$673$	−2.64638	−	2.64638i	−0.102011	−	0.102011i	−0.756270	+	0.654260i	$0.772980\pi$
$674$	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	−0.799511	−	0.600651i	$-0.794908\pi$
$677$	−5.17419	+	5.17419i	−0.198860	+	0.198860i	0.600651	+	0.799511i	$0.294908\pi$
$678$	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
$688$	4.85359	+	4.40938i	0.185041	+	0.168106i
$689$		−	4.36937i		−	0.166460i
$690$	−11.2897	+	2.54550i	−0.429793	+	0.0969054i
$691$			30.8756i			1.17456i	0.809382	+	0.587282i	$0.199802\pi$
$691$			30.8756i			1.17456i	−0.809382	+	0.587282i	$0.800198\pi$
$692$	−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	−0.772385	−	0.635155i	$-0.780936\pi$
$727$	−3.70011	+	3.70011i	−0.137229	+	0.137229i	0.635155	+	0.772385i	$0.280936\pi$
$728$	−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	0.994731	−	0.102516i	$-0.0326894\pi$
$733$	24.1558	+	24.1558i	0.892215	+	0.892215i	−0.102516	+	0.994731i	$0.532689\pi$
$734$	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	$-0.244220\pi$
$739$	39.1365			1.43966			0.719829	+	0.694151i	$0.244220\pi$
$740$	−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	$-0.905449\pi$
$743$	−34.0425	−	34.0425i	−1.24890	−	1.24890i	−0.292693	−	0.956207i	$-0.594551\pi$
$744$			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	$-0.821491\pi$
$751$		−	29.1509i		−	1.06373i	0.846828	−	0.531866i	$-0.178509\pi$
$752$	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	−0.484934	−	0.874551i	$-0.661156\pi$
$757$	10.7198	−	10.7198i	0.389617	−	0.389617i	0.874551	+	0.484934i	$0.161156\pi$
$758$	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	$-0.980683\pi$
$761$		−	3.34615i		−	0.121298i	0.998159	−	0.0606489i	$-0.0193170\pi$
$762$	−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	0.754065	−	0.656800i	$-0.228090\pi$
$773$	2.70425	+	2.70425i	0.0972650	+	0.0972650i	−0.656800	+	0.754065i	$0.728090\pi$
$774$	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	$0.244607\pi$
$811$			39.5860i			1.39005i	−0.718985	+	0.695025i	$0.755393\pi$
$812$	−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
$817$	−25.5510	−	23.2125i	−0.893915	−	0.812103i
$818$	−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	$-0.945576\pi$
$829$	−56.7451			−1.97084			−0.985419	+	0.170147i	$0.945576\pi$
$830$	−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	$-0.570341\pi$
$839$	−12.6979			−0.438379			−0.219190	+	0.975682i	$0.570341\pi$
$840$	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	$-0.739422\pi$
$859$	−40.0488			−1.36645			−0.683223	+	0.730210i	$0.739422\pi$
$860$	−14.1329	+	3.90653i	−0.481928	+	0.133212i
$861$	−8.46535			−0.288498
$862$	−7.90552	+	7.90552i	−0.269263	+	0.269263i
$863$	6.12455	+	6.12455i	0.208482	+	0.208482i	0.803622	−	0.595140i	$-0.202903\pi$
$863$	6.12455	+	6.12455i	0.208482	+	0.208482i	−0.595140	+	0.803622i	$0.702903\pi$
$864$			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	−0.782488	−	0.622665i	$-0.786050\pi$
$887$	−4.75994	+	4.75994i	−0.159823	+	0.159823i	0.622665	+	0.782488i	$0.286050\pi$
$888$	−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
$903$	6.57385	+	5.97220i	0.218764	+	0.198742i
$904$		−	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	$-0.880791\pi$
$911$		−	22.0824i		−	0.731623i	0.930689	−	0.365812i	$-0.119209\pi$
$912$	−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	$-0.438661\pi$
$929$	11.6744			0.383025			0.191513	+	0.981490i	$0.438661\pi$
$930$	−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	$0.504382\pi$
$937$	−31.0289	+	31.0289i	−1.01367	+	1.01367i	−0.999905	+	0.0137650i	$0.995618\pi$
$938$	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	0.217824	−	0.975988i	$-0.430104\pi$
$953$	−23.4050	−	23.4050i	−0.758164	−	0.758164i	−0.975988	+	0.217824i	$0.930104\pi$
$954$	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	0.350332	−	0.936625i	$-0.386069\pi$
$983$	−18.3820	−	18.3820i	−0.586293	−	0.586293i	−0.936625	+	0.350332i	$0.886069\pi$
$984$		−	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	$0.206991\pi$
$991$			38.1168i			1.21082i	−0.795914	+	0.605410i	$0.793009\pi$
$992$	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	$-0.388283\pi$
$997$	40.5063	−	40.5063i	1.28285	−	1.28285i	0.939040	−	0.343808i	$-0.111717\pi$
$998$	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.257.18	yes	40
5.3	odd	4	inner	430.2.g.b.343.3	yes	40
43.42	odd	2	inner	430.2.g.b.257.3	✓	40
215.128	even	4	inner	430.2.g.b.343.18	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
430.2.g.b.257.3	✓	40	43.42	odd	2	inner
430.2.g.b.257.18	yes	40	1.1	even	1	trivial
430.2.g.b.343.3	yes	40	5.3	odd	4	inner
430.2.g.b.343.18	yes	40	215.128	even	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} +(-4.85359 - 4.40938i) 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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