LMFDB - Embedded newform 570.2.v.c.83.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [570,2,Mod(83,570)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(570, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 9, 4]))

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

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

chi := DirichletCharacter("570.83");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 570 = 2 \cdot 3 \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	570.v (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$4.55147291521$
Analytic rank:	$0$
Dimension:	$144$
Relative dimension:	$36$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			83.18
Character	$\chi$	$=$	570.83
Dual form			570.2.v.c.467.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.258819 + 0.965926i) q^{2} +(1.67919 + 0.424642i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(-1.46226 + 1.69168i) q^{5} +(-0.844779 + 1.51207i) q^{6} +(3.27081 - 3.27081i) q^{7} +(0.707107 - 0.707107i) q^{8} +(2.63936 + 1.42611i) q^{9} +O(q^{10})$	\(q+(-0.258819 + 0.965926i) q^{2} +(1.67919 + 0.424642i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(-1.46226 + 1.69168i) q^{5} +(-0.844779 + 1.51207i) q^{6} +(3.27081 - 3.27081i) q^{7} +(0.707107 - 0.707107i) q^{8} +(2.63936 + 1.42611i) q^{9} +(-1.25558 - 1.85027i) q^{10} -1.50450i q^{11} +(-1.24190 - 1.20735i) q^{12} +(5.77319 - 1.54692i) q^{13} +(2.31281 + 4.00591i) q^{14} +(-3.17377 + 2.21972i) q^{15} +(0.500000 + 0.866025i) q^{16} +(0.397886 - 1.48493i) q^{17} +(-2.06063 + 2.18032i) q^{18} +(-2.87108 + 3.27977i) q^{19} +(2.11220 - 0.733912i) q^{20} +(6.88124 - 4.10339i) q^{21} +(1.45323 + 0.389392i) q^{22} +(0.610391 + 2.27801i) q^{23} +(1.48763 - 0.887099i) q^{24} +(-0.723596 - 4.94736i) q^{25} +5.97685i q^{26} +(3.82640 + 3.51549i) q^{27} +(-4.46802 + 1.19720i) q^{28} +(-4.66388 + 8.07808i) q^{29} +(-1.32266 - 3.64013i) q^{30} -2.56146 q^{31} +(-0.965926 + 0.258819i) q^{32} +(0.638872 - 2.52633i) q^{33} +(1.33135 + 0.768656i) q^{34} +(0.750409 + 10.3160i) q^{35} +(-1.57270 - 2.55473i) q^{36} +(-6.16077 + 6.16077i) q^{37} +(-2.42493 - 3.62212i) q^{38} +(10.3512 - 0.146037i) q^{39} +(0.162228 + 2.23018i) q^{40} +(5.81640 - 3.35810i) q^{41} +(2.18258 + 7.70881i) q^{42} +(-0.250824 + 0.936089i) q^{43} +(-0.752248 + 1.30293i) q^{44} +(-6.27195 + 2.37962i) q^{45} -2.35837 q^{46} +(1.44523 - 0.387250i) q^{47} +(0.471844 + 1.66654i) q^{48} -14.3964i q^{49} +(4.96607 + 0.581532i) q^{50} +(1.29869 - 2.32452i) q^{51} +(-5.77319 - 1.54692i) q^{52} +(-3.62088 - 13.5133i) q^{53} +(-4.38605 + 2.78614i) q^{54} +(2.54513 + 2.19996i) q^{55} -4.62563i q^{56} +(-6.21382 + 4.28818i) q^{57} +(-6.59573 - 6.59573i) q^{58} +(-0.204374 - 0.353985i) q^{59} +(3.85843 - 0.335451i) q^{60} +(3.40594 - 5.89926i) q^{61} +(0.662955 - 2.47418i) q^{62} +(13.2974 - 3.96831i) q^{63} -1.00000i q^{64} +(-5.82500 + 12.0284i) q^{65} +(2.27490 + 1.27097i) q^{66} +(2.32863 + 8.69056i) q^{67} +(-1.08704 + 1.08704i) q^{68} +(0.0576237 + 4.08441i) q^{69} +(-10.1587 - 1.94513i) q^{70} +(6.21221 - 3.58662i) q^{71} +(2.87472 - 0.857897i) q^{72} +(0.323971 - 1.20908i) q^{73} +(-4.35632 - 7.54537i) q^{74} +(0.885804 - 8.61483i) q^{75} +(4.12631 - 1.40483i) q^{76} +(-4.92093 - 4.92093i) q^{77} +(-2.53802 + 10.0363i) q^{78} +(-11.6452 + 6.72339i) q^{79} +(-2.19617 - 0.420511i) q^{80} +(4.93243 + 7.52803i) q^{81} +(1.73828 + 6.48735i) q^{82} +(-9.42577 + 9.42577i) q^{83} +(-8.01103 + 0.113021i) q^{84} +(1.93022 + 2.84445i) q^{85} +(-0.839274 - 0.484555i) q^{86} +(-11.2618 + 11.5842i) q^{87} +(-1.06384 - 1.06384i) q^{88} +(4.16565 - 7.21512i) q^{89} +(-0.675237 - 6.67413i) q^{90} +(13.8233 - 23.9427i) q^{91} +(0.610391 - 2.27801i) q^{92} +(-4.30118 - 1.08770i) q^{93} +1.49622i q^{94} +(-1.35008 - 9.65284i) q^{95} +(-1.73188 + 0.0244337i) q^{96} +(3.06185 + 0.820421i) q^{97} +(13.9059 + 3.72608i) q^{98} +(2.14558 - 3.97090i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q - 4 q^{3} + 8 q^{6}+O(q^{10}) $ 144 * q - 4 * q^3 + 8 * q^6	$ 144 q - 4 q^{3} + 8 q^{6} - 16 q^{10} - 8 q^{12} - 32 q^{13} + 4 q^{15} + 72 q^{16} + 32 q^{18} - 24 q^{21} + 8 q^{22} + 40 q^{25} - 16 q^{27} - 8 q^{30} - 16 q^{33} - 16 q^{37} + 8 q^{40} - 44 q^{42} - 16 q^{43} - 56 q^{45} - 48 q^{46} + 4 q^{48} + 32 q^{51} + 32 q^{52} + 8 q^{55} - 64 q^{57} + 32 q^{58} - 24 q^{60} + 76 q^{63} + 16 q^{66} - 56 q^{67} - 8 q^{70} + 16 q^{72} + 88 q^{73} + 32 q^{75} + 48 q^{76} - 56 q^{81} - 152 q^{87} - 16 q^{88} - 4 q^{90} + 80 q^{91} - 52 q^{93} + 16 q^{96} + 32 q^{97}+O(q^{100}) $ 144 * q - 4 * q^3 + 8 * q^6 - 16 * q^10 - 8 * q^12 - 32 * q^13 + 4 * q^15 + 72 * q^16 + 32 * q^18 - 24 * q^21 + 8 * q^22 + 40 * q^25 - 16 * q^27 - 8 * q^30 - 16 * q^33 - 16 * q^37 + 8 * q^40 - 44 * q^42 - 16 * q^43 - 56 * q^45 - 48 * q^46 + 4 * q^48 + 32 * q^51 + 32 * q^52 + 8 * q^55 - 64 * q^57 + 32 * q^58 - 24 * q^60 + 76 * q^63 + 16 * q^66 - 56 * q^67 - 8 * q^70 + 16 * q^72 + 88 * q^73 + 32 * q^75 + 48 * q^76 - 56 * q^81 - 152 * q^87 - 16 * q^88 - 4 * q^90 + 80 * q^91 - 52 * q^93 + 16 * q^96 + 32 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/570\mathbb{Z}\right)^\times$.

$n$	$191$	$211$	$457$
$\chi(n)$	$-1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$	−0.258819	+	0.965926i	−0.183013	+	0.683013i
$2$	−0.258819	+	0.965926i	−0.183013	+	0.683013i
$3$	1.67919	+	0.424642i	0.969481	+	0.245167i
$3$	1.67919	+	0.424642i	0.969481	+	0.245167i
$4$	−0.866025	−	0.500000i	−0.433013	−	0.250000i
$5$	−1.46226	+	1.69168i	−0.653942	+	0.756544i
$5$	−1.46226	+	1.69168i	−0.653942	+	0.756544i
$6$	−0.844779	+	1.51207i	−0.344880	+	0.617299i
$7$	3.27081	−	3.27081i	1.23625	−	1.23625i	0.274730	−	0.961521i	$-0.411411\pi$
$7$	3.27081	−	3.27081i	1.23625	−	1.23625i	0.961521	−	0.274730i	$-0.0885885\pi$
$8$	0.707107	−	0.707107i	0.250000	−	0.250000i
$9$	2.63936	+	1.42611i	0.879786	+	0.475370i
$10$	−1.25558	−	1.85027i	−0.397050	−	0.585108i
$11$		−	1.50450i		−	0.453623i	−0.973939	−	0.226811i	$-0.927170\pi$
$11$		−	1.50450i		−	0.453623i	0.973939	−	0.226811i	$-0.0728301\pi$
$12$	−1.24190	−	1.20735i	−0.358506	−	0.348531i
$13$	5.77319	−	1.54692i	1.60120	−	0.429039i	0.655792	−	0.754941i	$-0.272335\pi$
$13$	5.77319	−	1.54692i	1.60120	−	0.429039i	0.945404	+	0.325902i	$0.105668\pi$
$14$	2.31281	+	4.00591i	0.618126	+	1.07063i
$15$	−3.17377	+	2.21972i	−0.819464	+	0.573130i
$16$	0.500000	+	0.866025i	0.125000	+	0.216506i
$17$	0.397886	−	1.48493i	0.0965014	−	0.360148i	−0.900741	−	0.434356i	$-0.856976\pi$
$17$	0.397886	−	1.48493i	0.0965014	−	0.360148i	0.997243	+	0.0742075i	$0.0236427\pi$
$18$	−2.06063	+	2.18032i	−0.485696	+	0.513906i
$19$	−2.87108	+	3.27977i	−0.658671	+	0.752431i
$19$	−2.87108	+	3.27977i	−0.658671	+	0.752431i
$20$	2.11220	−	0.733912i	0.472301	−	0.164108i
$21$	6.88124	−	4.10339i	1.50161	−	0.895434i
$22$	1.45323	+	0.389392i	0.309830	+	0.0830187i
$23$	0.610391	+	2.27801i	0.127275	+	0.474998i	0.999911	−	0.0133745i	$-0.00425738\pi$
$23$	0.610391	+	2.27801i	0.127275	+	0.474998i	−0.872635	+	0.488373i	$0.837591\pi$
$24$	1.48763	−	0.887099i	0.303662	−	0.181078i
$25$	−0.723596	−	4.94736i	−0.144719	−	0.989473i
$26$			5.97685i			1.17216i
$27$	3.82640	+	3.51549i	0.736391	+	0.676557i
$28$	−4.46802	+	1.19720i	−0.844375	+	0.226250i
$29$	−4.66388	+	8.07808i	−0.866062	+	1.50006i	−7.24294e−5		1.00000i	$0.500023\pi$
$29$	−4.66388	+	8.07808i	−0.866062	+	1.50006i	−0.865989	+	0.500063i	$0.833310\pi$
$30$	−1.32266	−	3.64013i	−0.241483	−	0.664595i
$31$	−2.56146			−0.460052			−0.230026	−	0.973185i	$-0.573881\pi$
$31$	−2.56146			−0.460052			−0.230026	+	0.973185i	$0.573881\pi$
$32$	−0.965926	+	0.258819i	−0.170753	+	0.0457532i
$33$	0.638872	−	2.52633i	0.111213	−	0.439778i
$34$	1.33135	+	0.768656i	0.228325	+	0.131823i
$35$	0.750409	+	10.3160i	0.126842	+	1.74372i
$36$	−1.57270	−	2.55473i	−0.262116	−	0.425788i
$37$	−6.16077	+	6.16077i	−1.01282	+	1.01282i	−0.0129072	+	0.999917i	$0.504109\pi$
$37$	−6.16077	+	6.16077i	−1.01282	+	1.01282i	−0.999917	+	0.0129072i	$0.995891\pi$
$38$	−2.42493	−	3.62212i	−0.393375	−	0.587585i
$39$	10.3512	−	0.146037i	1.65752	−	0.0233846i
$40$	0.162228	+	2.23018i	0.0256506	+	0.352622i
$41$	5.81640	−	3.35810i	0.908370	−	0.524447i	0.0284633	−	0.999595i	$-0.490939\pi$
$41$	5.81640	−	3.35810i	0.908370	−	0.524447i	0.879906	+	0.475147i	$0.157605\pi$
$42$	2.18258	+	7.70881i	0.336779	+	1.18949i
$43$	−0.250824	+	0.936089i	−0.0382503	+	0.142752i	−0.982410	−	0.186735i	$-0.940209\pi$
$43$	−0.250824	+	0.936089i	−0.0382503	+	0.142752i	0.944160	+	0.329488i	$0.106876\pi$
$44$	−0.752248	+	1.30293i	−0.113406	+	0.196424i
$45$	−6.27195	+	2.37962i	−0.934968	+	0.354733i
$46$	−2.35837			−0.347723
$47$	1.44523	−	0.387250i	0.210809	−	0.0564861i	−0.151869	−	0.988401i	$-0.548529\pi$
$47$	1.44523	−	0.387250i	0.210809	−	0.0564861i	0.362678	+	0.931915i	$0.381862\pi$
$48$	0.471844	+	1.66654i	0.0681049	+	0.240545i
$49$		−	14.3964i		−	2.05664i
$50$	4.96607	+	0.581532i	0.702308	+	0.0822411i
$51$	1.29869	−	2.32452i	0.181853	−	0.325498i
$52$	−5.77319	−	1.54692i	−0.800598	−	0.214520i
$53$	−3.62088	−	13.5133i	−0.497366	−	1.85620i	−0.516352	−	0.856376i	$-0.672711\pi$
$53$	−3.62088	−	13.5133i	−0.497366	−	1.85620i	0.0189862	−	0.999820i	$-0.493956\pi$
$54$	−4.38605	+	2.78614i	−0.596866	+	0.379146i
$55$	2.54513	+	2.19996i	0.343186	+	0.296643i
$56$		−	4.62563i		−	0.618126i
$57$	−6.21382	+	4.28818i	−0.823040	+	0.567983i
$58$	−6.59573	−	6.59573i	−0.866062	−	0.866062i
$59$	−0.204374	−	0.353985i	−0.0266072	−	0.0460850i	0.852415	−	0.522865i	$-0.175137\pi$
$59$	−0.204374	−	0.353985i	−0.0266072	−	0.0460850i	−0.879022	+	0.476781i	$0.841804\pi$
$60$	3.85843	−	0.335451i	0.498121	−	0.0433066i
$61$	3.40594	−	5.89926i	0.436086	−	0.755323i	−0.561297	−	0.827614i	$-0.689698\pi$
$61$	3.40594	−	5.89926i	0.436086	−	0.755323i	0.997384	+	0.0722908i	$0.0230310\pi$
$62$	0.662955	−	2.47418i	0.0841953	−	0.314221i
$63$	13.2974	−	3.96831i	1.67531	−	0.499960i
$64$		−	1.00000i		−	0.125000i
$65$	−5.82500	+	12.0284i	−0.722502	+	1.49194i
$66$	2.27490	+	1.27097i	0.280021	+	0.156445i
$67$	2.32863	+	8.69056i	0.284487	+	1.06172i	0.949213	+	0.314634i	$0.101882\pi$
$67$	2.32863	+	8.69056i	0.284487	+	1.06172i	−0.664726	+	0.747087i	$0.731452\pi$
$68$	−1.08704	+	1.08704i	−0.131823	+	0.131823i
$69$	0.0576237	+	4.08441i	0.00693708	+	0.491705i
$70$	−10.1587	−	1.94513i	−1.21419	−	0.232487i
$71$	6.21221	−	3.58662i	0.737254	−	0.425654i	−0.0838162	−	0.996481i	$-0.526711\pi$
$71$	6.21221	−	3.58662i	0.737254	−	0.425654i	0.821070	+	0.570828i	$0.193378\pi$
$72$	2.87472	−	0.857897i	0.338789	−	0.101104i
$73$	0.323971	−	1.20908i	0.0379180	−	0.141512i	−0.944372	−	0.328880i	$-0.893329\pi$
$73$	0.323971	−	1.20908i	0.0379180	−	0.141512i	0.982290	+	0.187368i	$0.0599956\pi$
$74$	−4.35632	−	7.54537i	−0.506412	−	0.877131i
$75$	0.885804	−	8.61483i	0.102284	−	0.994755i
$76$	4.12631	−	1.40483i	0.473321	−	0.161145i
$77$	−4.92093	−	4.92093i	−0.560792	−	0.560792i
$78$	−2.53802	+	10.0363i	−0.287374	+	1.13638i
$79$	−11.6452	+	6.72339i	−1.31019	+	0.756440i	−0.982128	−	0.188215i	$-0.939730\pi$
$79$	−11.6452	+	6.72339i	−1.31019	+	0.756440i	−0.328065	+	0.944655i	$0.606396\pi$
$80$	−2.19617	−	0.420511i	−0.245539	−	0.0470146i
$81$	4.93243	+	7.52803i	0.548047	+	0.836447i
$82$	1.73828	+	6.48735i	0.191961	+	0.716408i
$83$	−9.42577	+	9.42577i	−1.03461	+	1.03461i	−0.0352334	+	0.999379i	$0.511217\pi$
$83$	−9.42577	+	9.42577i	−1.03461	+	1.03461i	−0.999379	+	0.0352334i	$0.988783\pi$
$84$	−8.01103	+	0.113021i	−0.874075	+	0.0123316i
$85$	1.93022	+	2.84445i	0.209362	+	0.308524i
$86$	−0.839274	−	0.484555i	−0.0905012	−	0.0522509i
$87$	−11.2618	+	11.5842i	−1.20740	+	1.24195i
$88$	−1.06384	−	1.06384i	−0.113406	−	0.113406i
$89$	4.16565	−	7.21512i	0.441558	−	0.764801i	−0.556247	−	0.831017i	$-0.687759\pi$
$89$	4.16565	−	7.21512i	0.441558	−	0.764801i	0.997805	+	0.0662157i	$0.0210926\pi$
$90$	−0.675237	−	6.67413i	−0.0711762	−	0.703515i
$91$	13.8233	−	23.9427i	1.44908	−	2.50988i
$92$	0.610391	−	2.27801i	0.0636377	−	0.237499i
$93$	−4.30118	−	1.08770i	−0.446011	−	0.112790i
$94$			1.49622i			0.154323i
$95$	−1.35008	−	9.65284i	−0.138515	−	0.990360i
$96$	−1.73188	+	0.0244337i	−0.176759	+	0.00249375i
$97$	3.06185	+	0.820421i	0.310884	+	0.0833012i	0.410888	−	0.911686i	$-0.365219\pi$
$97$	3.06185	+	0.820421i	0.310884	+	0.0833012i	−0.100004	+	0.994987i	$0.531885\pi$
$98$	13.9059	+	3.72608i	1.40471	+	0.376390i
$99$	2.14558	−	3.97090i	0.215638	−	0.399091i
$100$	−1.84703	+	4.64634i	−0.184703	+	0.464634i
$101$	−7.67258	−	4.42977i	−0.763450	−	0.440778i	0.0670828	−	0.997747i	$-0.478631\pi$
$101$	−7.67258	−	4.42977i	−0.763450	−	0.440778i	−0.830533	+	0.556969i	$0.811964\pi$
$102$	1.90919	+	1.85607i	0.189038	+	0.183778i
$103$	1.66572	+	1.66572i	0.164129	+	0.164129i	0.784393	−	0.620264i	$-0.212975\pi$
$103$	1.66572	+	1.66572i	0.164129	+	0.164129i	−0.620264	+	0.784393i	$0.712975\pi$
$104$	2.98843	−	5.17610i	0.293039	−	0.507559i
$105$	−3.12051	+	17.6411i	−0.304531	+	1.72160i
$106$	13.9900			1.35883
$107$	−1.11305	−	1.11305i	−0.107603	−	0.107603i	0.651256	−	0.758858i	$-0.274243\pi$
$107$	−1.11305	−	1.11305i	−0.107603	−	0.107603i	−0.758858	+	0.651256i	$0.774243\pi$
$108$	−1.55601	−	4.95770i	−0.149727	−	0.477055i
$109$	−2.37239	+	1.36970i	−0.227234	+	0.131194i	−0.609295	−	0.792943i	$-0.708548\pi$
$109$	−2.37239	+	1.36970i	−0.227234	+	0.131194i	0.382061	+	0.924137i	$0.375214\pi$
$110$	−2.78373	+	1.88902i	−0.265418	+	0.180111i
$111$	−12.9612	+	7.72898i	−1.23022	+	0.733602i
$112$	4.46802	+	1.19720i	0.422188	+	0.113125i
$113$	−9.39297	+	9.39297i	−0.883617	+	0.883617i	−0.993900	−	0.110284i	$-0.964824\pi$
$113$	−9.39297	+	9.39297i	−0.883617	+	0.883617i	0.110284	+	0.993900i	$0.464824\pi$
$114$	−2.53381	−	7.11195i	−0.237313	−	0.666095i
$115$	−4.74623	−	2.29845i	−0.442588	−	0.214332i
$116$	8.07808	−	4.66388i	0.750031	−	0.433031i
$117$	17.4436	+	4.15032i	1.61266	+	0.383697i
$118$	0.394819	−	0.105792i	0.0363461	−	0.00973890i
$119$	−3.55552	−	6.15834i	−0.325934	−	0.564534i
$120$	−0.674614	+	3.81378i	−0.0615835	+	0.348149i
$121$	8.73649			0.794227
$122$	4.81673	+	4.81673i	0.436086	+	0.436086i
$123$	11.1928	−	3.16900i	1.00922	−	0.285739i
$124$	2.21829	+	1.28073i	0.199208	+	0.115013i
$125$	9.42747	+	6.01023i	0.843218	+	0.537572i
$126$	0.391478	+	13.8714i	0.0348756	+	1.23576i
$127$	−3.13737	−	11.7088i	−0.278396	−	1.03899i	−0.953531	−	0.301294i	$-0.902581\pi$
$127$	−3.13737	−	11.7088i	−0.278396	−	1.03899i	0.675135	−	0.737694i	$-0.264085\pi$
$128$	0.965926	+	0.258819i	0.0853766	+	0.0228766i
$129$	−0.818684	+	1.46536i	−0.0720811	+	0.129018i
$130$	−10.1109	−	8.73971i	−0.886789	−	0.766523i
$131$	−2.17528	+	1.25590i	−0.190055	+	0.109729i	−0.592009	−	0.805932i	$-0.701665\pi$
$131$	−2.17528	+	1.25590i	−0.190055	+	0.109729i	0.401953	+	0.915660i	$0.368332\pi$
$132$	−1.81645	+	1.86843i	−0.158101	+	0.162626i
$133$	1.33676	+	20.1183i	0.115912	+	1.74448i
$134$	−8.99713			−0.777234
$135$	−11.5423	+	1.33250i	−0.993402	+	0.114683i
$136$	−0.768656	−	1.33135i	−0.0659117	−	0.114162i
$137$	3.65205	−	0.978564i	0.312016	−	0.0836043i	−0.0994132	−	0.995046i	$-0.531697\pi$
$137$	3.65205	−	0.978564i	0.312016	−	0.0836043i	0.411429	+	0.911442i	$0.365030\pi$
$138$	−3.96015	−	1.00146i	−0.337110	−	0.0852502i
$139$	−11.2985	−	6.52316i	−0.958322	−	0.553288i	−0.0626660	−	0.998035i	$-0.519960\pi$
$139$	−11.2985	−	6.52316i	−0.958322	−	0.553288i	−0.895656	+	0.444747i	$0.853294\pi$
$140$	4.50811	−	9.30909i	0.381005	−	0.786762i
$141$	2.59127	−	0.0365581i	0.218224	−	0.00307875i
$142$	1.85657	+	6.92882i	0.155800	+	0.581454i
$143$	−2.32734	−	8.68575i	−0.194622	−	0.726339i
$144$	0.0846324	+	2.99881i	0.00705270	+	0.249900i
$145$	−6.84577	−	19.7021i	−0.568510	−	1.63617i
$146$	1.08403	+	0.625865i	0.0897149	+	0.0517969i
$147$	6.11334	−	24.1744i	0.504220	−	1.99387i
$148$	8.41576	−	2.25500i	0.691772	−	0.185360i
$149$	−3.50391	−	6.06896i	−0.287052	−	0.497188i	0.686053	−	0.727552i	$-0.259342\pi$
$149$	−3.50391	−	6.06896i	−0.287052	−	0.497188i	−0.973105	+	0.230363i	$0.926008\pi$
$150$	8.09203	+	3.08530i	0.660711	+	0.251914i
$151$	−18.0828			−1.47156			−0.735779	−	0.677221i	$-0.763184\pi$
$151$	−18.0828			−1.47156			−0.735779	+	0.677221i	$0.763184\pi$
$152$	0.288990	+	4.34931i	0.0234402	+	0.352776i
$153$	3.16783	−	3.35183i	0.256104	−	0.270980i
$154$	6.02688	−	3.47962i	0.485660	−	0.280396i
$155$	3.74552	−	4.33318i	0.300847	−	0.348050i
$156$	−9.03740	−	5.04912i	−0.723571	−	0.404253i
$157$	9.54605	+	2.55786i	0.761858	+	0.204139i	0.618772	−	0.785571i	$-0.287631\pi$
$157$	9.54605	+	2.55786i	0.761858	+	0.204139i	0.143086	+	0.989710i	$0.454297\pi$
$158$	−3.48028	−	12.9886i	−0.276876	−	1.03332i
$159$	−0.341828	−	24.2290i	−0.0271087	−	1.92148i
$160$	0.974594	−	2.01250i	0.0770484	−	0.159102i
$161$	9.44742	+	5.45447i	0.744561	+	0.429873i
$162$	−8.54812	+	2.81596i	−0.671604	+	0.221243i
$163$	−4.98438	−	4.98438i	−0.390407	−	0.390407i	0.484426	−	0.874832i	$-0.339029\pi$
$163$	−4.98438	−	4.98438i	−0.390407	−	0.390407i	−0.874832	+	0.484426i	$0.839029\pi$
$164$	−6.71620			−0.524447
$165$	3.33956	+	4.77493i	0.259985	+	0.371727i
$166$	−6.66502	−	11.5442i	−0.517306	−	0.896001i
$167$	−12.8441	+	3.44157i	−0.993906	+	0.266316i	−0.718890	−	0.695123i	$-0.755350\pi$
$167$	−12.8441	+	3.44157i	−0.993906	+	0.266316i	−0.275016	+	0.961440i	$0.588683\pi$
$168$	1.96424	−	7.76731i	0.151544	−	0.599261i
$169$	19.6785	−	11.3614i	1.51373	−	0.873952i
$170$	−3.24710	+	1.12825i	−0.249042	+	0.0865330i
$171$	−12.2551	+	4.56202i	−0.937172	+	0.348867i
$172$	0.685264	−	0.685264i	0.0522509	−	0.0522509i
$173$	−10.9463	−	2.93305i	−0.832232	−	0.222996i	−0.182545	−	0.983198i	$-0.558433\pi$
$173$	−10.9463	−	2.93305i	−0.832232	−	0.222996i	−0.649687	+	0.760202i	$0.725100\pi$
$174$	−8.27466	−	13.8763i	−0.627300	−	1.05196i
$175$	−18.5487	−	13.8152i	−1.40215	−	1.04433i
$176$	1.30293	−	0.752248i	0.0982122	−	0.0567028i
$177$	−0.192865	−	0.681194i	−0.0144966	−	0.0512017i
$178$	5.89112	+	5.89112i	0.441558	+	0.441558i
$179$	−3.81727			−0.285316			−0.142658	−	0.989772i	$-0.545565\pi$
$179$	−3.81727			−0.285316			−0.142658	+	0.989772i	$0.545565\pi$
$180$	6.62148	+	1.07516i	0.493536	+	0.0801380i
$181$	−2.28368	+	3.95546i	−0.169745	+	0.294007i	−0.938330	−	0.345741i	$-0.887628\pi$
$181$	−2.28368	+	3.95546i	−0.169745	+	0.294007i	0.768585	+	0.639747i	$0.220961\pi$
$182$	19.5492	+	19.5492i	1.44908	+	1.44908i
$183$	8.22430	−	8.45968i	0.607958	−	0.625358i
$184$	2.04241	+	1.17919i	0.150568	+	0.0869307i
$185$	−1.41344	−	19.4307i	−0.103918	−	1.42857i
$186$	2.16387	−	3.87310i	0.158662	−	0.283990i
$187$	−2.23407	−	0.598617i	−0.163371	−	0.0437752i
$188$	−1.44523	−	0.387250i	−0.105405	−	0.0282431i
$189$	24.0140	−	1.01692i	1.74676	−	0.0739701i
$190$	9.67335	+	1.19426i	0.701779	+	0.0866408i
$191$		−	15.4604i		−	1.11867i	−0.828940	−	0.559337i	$-0.811056\pi$
$191$		−	15.4604i		−	1.11867i	0.828940	−	0.559337i	$-0.188944\pi$
$192$	0.424642	−	1.67919i	0.0306459	−	0.121185i
$193$	2.97375	−	11.0982i	0.214055	−	0.798864i	−0.772442	−	0.635085i	$-0.780965\pi$
$193$	2.97375	−	11.0982i	0.214055	−	0.798864i	0.986497	−	0.163779i	$-0.0523684\pi$
$194$	−1.58493	+	2.74518i	−0.113792	+	0.197093i
$195$	−14.8891	+	17.7245i	−1.06623	+	1.26928i
$196$	−7.19822	+	12.4677i	−0.514159	+	0.890549i
$197$	−10.5903	−	10.5903i	−0.754527	−	0.754527i	0.220794	−	0.975321i	$-0.429135\pi$
$197$	−10.5903	−	10.5903i	−0.754527	−	0.754527i	−0.975321	+	0.220794i	$0.929135\pi$
$198$	3.28028	+	3.10021i	0.233120	+	0.220322i
$199$	−1.13263	−	0.653922i	−0.0802898	−	0.0463553i	0.459318	−	0.888272i	$-0.348094\pi$
$199$	−1.13263	−	0.653922i	−0.0802898	−	0.0463553i	−0.539607	+	0.841917i	$0.681427\pi$
$200$	−4.00997	−	2.98666i	−0.283548	−	0.211188i
$201$	0.219833	+	15.5819i	0.0155058	+	1.09907i
$202$	6.26464	−	6.26464i	0.440778	−	0.440778i
$203$	11.1672	+	41.6766i	0.783785	+	2.92512i
$204$	−2.28696	+	1.36375i	−0.160119	+	0.0954815i
$205$	−2.82424	+	14.7499i	−0.197253	+	1.03018i
$206$	−2.04009	+	1.17784i	−0.142140	+	0.0820643i
$207$	−1.63765	+	6.88297i	−0.113825	+	0.478400i
$208$	4.22627	+	4.22627i	0.293039	+	0.293039i
$209$	4.93440	+	4.31953i	0.341320	+	0.298788i
$210$	−16.2324	−	7.58004i	−1.12014	−	0.523073i
$211$	8.43402	+	14.6082i	0.580622	+	1.00567i	0.995406	+	0.0957468i	$0.0305239\pi$
$211$	8.43402	+	14.6082i	0.580622	+	1.00567i	−0.414784	+	0.909920i	$0.636143\pi$
$212$	−3.62088	+	13.5133i	−0.248683	+	0.928098i
$213$	11.9545	−	3.38465i	0.819110	−	0.231913i
$214$	1.36320	−	0.787047i	0.0931868	−	0.0538014i
$215$	−1.21680	−	1.79312i	−0.0829849	−	0.122290i
$216$	5.19150	−	0.219845i	0.353237	−	0.0149586i
$217$	−8.37806	+	8.37806i	−0.568740	+	0.568740i
$218$	−0.709010	−	2.64606i	−0.0480202	−	0.179214i
$219$	1.05743	−	1.89270i	0.0714548	−	0.127897i
$220$	−1.10417	−	3.17779i	−0.0744430	−	0.214247i
$221$		−	9.18828i		−	0.618071i
$222$	−4.11101	−	14.5200i	−0.275913	−	0.974517i
$223$	−0.623490	+	2.32690i	−0.0417520	+	0.155821i	−0.983655	−	0.180065i	$-0.942369\pi$
$223$	−0.623490	+	2.32690i	−0.0417520	+	0.155821i	0.941903	+	0.335886i	$0.109036\pi$
$224$	−2.31281	+	4.00591i	−0.154531	+	0.267656i
$225$	5.14565	−	14.0898i	0.343044	−	0.939320i
$226$	−6.64184	−	11.5040i	−0.441808	−	0.765234i
$227$	11.1096	+	11.1096i	0.737368	+	0.737368i	0.972068	−	0.234700i	$-0.0754109\pi$
$227$	11.1096	+	11.1096i	0.737368	+	0.737368i	−0.234700	+	0.972068i	$0.575411\pi$
$228$	7.52541	−	0.606766i	0.498383	−	0.0401840i
$229$		−	0.462881i		−	0.0305881i	−0.999883	−	0.0152940i	$-0.995132\pi$
$229$		−	0.462881i		−	0.0305881i	0.999883	−	0.0152940i	$-0.00486843\pi$
$230$	3.44855	−	3.98962i	0.227391	−	0.263068i
$231$	−6.17354	−	10.3528i	−0.406189	−	0.681164i
$232$	2.41420	+	9.00993i	0.158500	+	0.591531i
$233$	14.4350	+	3.86784i	0.945668	+	0.253391i	0.698523	−	0.715588i	$-0.253841\pi$
$233$	14.4350	+	3.86784i	0.945668	+	0.253391i	0.247145	+	0.968979i	$0.420508\pi$
$234$	−8.52364	+	15.7751i	−0.557208	+	1.03125i
$235$	−1.45820	+	3.01114i	−0.0951227	+	0.196425i
$236$			0.408747i			0.0266072i
$237$	−22.4096	+	6.34478i	−1.45566	+	0.412138i
$238$	6.86873	−	1.84047i	0.445234	−	0.119300i
$239$	2.08267			0.134717			0.0673585	−	0.997729i	$-0.478543\pi$
$239$	2.08267			0.134717			0.0673585	+	0.997729i	$0.478543\pi$
$240$	−3.50922	−	1.63871i	−0.226519	−	0.105778i
$241$	−10.8601	+	18.8102i	−0.699560	+	1.21167i	0.269059	+	0.963124i	$0.413287\pi$
$241$	−10.8601	+	18.8102i	−0.699560	+	1.21167i	−0.968619	+	0.248550i	$0.920046\pi$
$242$	−2.26117	+	8.43880i	−0.145354	+	0.542467i
$243$	5.08576	+	14.7355i	0.326252	+	0.945283i
$244$	−5.89926	+	3.40594i	−0.377662	+	0.218043i
$245$	24.3543	+	21.0513i	1.55594	+	1.34492i
$246$	0.164102	+	11.6316i	0.0104627	+	0.741607i
$247$	−11.5017	+	23.3761i	−0.731838	+	1.48739i
$248$	−1.81123	+	1.81123i	−0.115013	+	0.115013i
$249$	−19.8302	+	11.8251i	−1.25669	+	0.749384i
$250$	−8.24545	+	7.55067i	−0.521488	+	0.477546i
$251$	−22.9496	−	13.2500i	−1.44857	−	0.836331i	−0.450171	−	0.892942i	$-0.648637\pi$
$251$	−22.9496	−	13.2500i	−1.44857	−	0.836331i	−0.998396	+	0.0566115i	$0.981970\pi$
$252$	−13.5000	−	3.21203i	−0.850422	−	0.202339i
$253$	3.42726	−	0.918331i	0.215470	−	0.0577350i
$254$	12.1218			0.760592
$255$	2.03333	+	5.59602i	0.127332	+	0.350437i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−0.927986	+	0.248653i	−0.0578862	+	0.0155106i	−0.287646	−	0.957737i	$-0.592873\pi$
$257$	−0.927986	+	0.248653i	−0.0578862	+	0.0155106i	0.229760	+	0.973247i	$0.426206\pi$
$258$	−1.20354	−	1.17005i	−0.0749290	−	0.0728442i
$259$			40.3014i			2.50421i
$260$	11.0588	−	7.50442i	0.685838	−	0.465405i
$261$	−23.8299	+	14.6698i	−1.47503	+	0.908035i
$262$	−0.650102	−	2.42621i	−0.0401635	−	0.149892i
$263$	−8.13123	−	2.17876i	−0.501393	−	0.134348i	−0.000746739	−	1.00000i	$-0.500238\pi$
$263$	−8.13123	−	2.17876i	−0.501393	−	0.134348i	−0.500647	+	0.865652i	$0.666904\pi$
$264$	−1.33464	−	2.23814i	−0.0821412	−	0.137748i
$265$	28.1549	+	13.6346i	1.72954	+	0.837565i
$266$	−19.7788	−	3.91578i	−1.21271	−	0.240092i
$267$	10.0588	−	10.3466i	0.615586	−	0.633205i
$268$	2.32863	−	8.69056i	0.142244	−	0.530861i
$269$	2.25938	+	3.91336i	0.137757	+	0.238602i	0.926647	−	0.375932i	$-0.122677\pi$
$269$	2.25938	+	3.91336i	0.137757	+	0.238602i	−0.788890	+	0.614534i	$0.789344\pi$
$270$	1.70027	−	11.4939i	0.103475	−	0.699495i
$271$	−6.98865	−	12.1047i	−0.424530	−	0.735308i	0.571846	−	0.820361i	$-0.306227\pi$
$271$	−6.98865	−	12.1047i	−0.424530	−	0.735308i	−0.996376	+	0.0850530i	$0.972894\pi$
$272$	1.48493	−	0.397886i	0.0900371	−	0.0241254i
$273$	33.3791	−	34.3344i	2.02020	−	2.07801i
$274$			3.78088i			0.228411i
$275$	−7.44329	+	1.08865i	−0.448847	+	0.0656479i
$276$	1.99230	−	3.56601i	0.119922	−	0.214649i
$277$	−4.19469	+	4.19469i	−0.252035	+	0.252035i	−0.821804	−	0.569770i	$-0.807032\pi$
$277$	−4.19469	+	4.19469i	−0.252035	+	0.252035i	0.569770	+	0.821804i	$0.307032\pi$
$278$	9.22515	−	9.22515i	0.553288	−	0.553288i
$279$	−6.76061	−	3.65292i	−0.404747	−	0.218695i
$280$	7.82511	+	6.76387i	0.467640	+	0.404219i
$281$	21.7381	+	12.5505i	1.29679	+	0.748700i	0.979848	−	0.199746i	$-0.0640117\pi$
$281$	21.7381	+	12.5505i	1.29679	+	0.748700i	0.316939	+	0.948446i	$0.397345\pi$
$282$	−0.635357	+	2.51243i	−0.0378349	+	0.149613i
$283$	−5.45735	+	20.3671i	−0.324406	+	1.21070i	0.590502	+	0.807036i	$0.298930\pi$
$283$	−5.45735	+	20.3671i	−0.324406	+	1.21070i	−0.914908	+	0.403663i	$0.867737\pi$
$284$	−7.17324			−0.425654
$285$	1.83196	−	16.7823i	0.108516	−	0.994095i
$286$	8.99215			0.531717
$287$	8.04065	−	30.0081i	0.474624	−	1.77132i
$288$	−2.91853	−	0.694400i	−0.171976	−	0.0409179i
$289$	12.6757	+	7.31834i	0.745631	+	0.430490i
$290$	20.8026	−	1.51323i	1.22157	−	0.0888599i
$291$	4.79305	+	2.67784i	0.280974	+	0.156977i
$292$	−0.885106	+	0.885106i	−0.0517969	+	0.0517969i
$293$	−6.80530	+	6.80530i	−0.397570	+	0.397570i	−0.877375	−	0.479805i	$-0.840707\pi$
$293$	−6.80530	+	6.80530i	−0.397570	+	0.397570i	0.479805	+	0.877375i	$0.340707\pi$
$294$	21.7684	+	12.1618i	1.26956	+	0.709292i
$295$	0.897679	+	0.171883i	0.0522649	+	0.0100074i
$296$			8.71264i			0.506412i
$297$	5.28904	−	5.75680i	0.306901	−	0.334043i
$298$	6.76904	−	1.81376i	0.392120	−	0.105068i
$299$	7.04781	+	12.2072i	0.407586	+	0.705959i
$300$	−5.07455	+	7.01776i	−0.292979	+	0.405171i
$301$	2.24137	+	3.88217i	0.129191	+	0.223765i
$302$	4.68018	−	17.4667i	0.269314	−	1.00509i
$303$	−11.0027	−	10.6965i	−0.632086	−	0.614499i
$304$	−4.27591	−	0.846541i	−0.245240	−	0.0485524i
$305$	4.99933	+	14.3880i	0.286261	+	0.823856i
$306$	2.41773	+	3.92741i	0.138212	+	0.224515i
$307$	25.8059	+	6.91468i	1.47282	+	0.394642i	0.903898	−	0.427748i	$-0.140693\pi$
$307$	25.8059	+	6.91468i	1.47282	+	0.394642i	0.568925	+	0.822390i	$0.307360\pi$
$308$	1.80118	+	6.72211i	0.102632	+	0.383028i
$309$	2.08973	+	3.50440i	0.118881	+	0.199358i
$310$	3.21612	+	4.73940i	0.182663	+	0.269180i
$311$		−	10.1728i		−	0.576844i	−0.957503	−	0.288422i	$-0.906869\pi$
$311$		−	10.1728i		−	0.576844i	0.957503	−	0.288422i	$-0.0931307\pi$
$312$	7.21613	−	7.42265i	0.408533	−	0.420225i
$313$	−20.1342	+	5.39494i	−1.13805	+	0.304940i	−0.778168	−	0.628057i	$-0.783851\pi$
$313$	−20.1342	+	5.39494i	−1.13805	+	0.304940i	−0.359885	+	0.932997i	$0.617184\pi$
$314$	−4.94140	+	8.55876i	−0.278859	+	0.482999i
$315$	−12.7311	+	28.2977i	−0.717316	+	1.59439i
$316$	13.4468			0.756440
$317$	18.1359	−	4.85951i	1.01861	−	0.272937i	0.289390	−	0.957211i	$-0.406548\pi$
$317$	18.1359	−	4.85951i	1.01861	−	0.272937i	0.729225	+	0.684274i	$0.239881\pi$
$318$	23.4919	+	5.94075i	1.31736	+	0.333140i
$319$	12.1534	+	7.01679i	0.680462	+	0.392865i
$320$	1.69168	+	1.46226i	0.0945681	+	0.0817428i
$321$	−1.39638	−	2.34167i	−0.0779382	−	0.130700i
$322$	−7.71379	+	7.71379i	−0.429873	+	0.429873i
$323$	3.72787	+	5.56832i	0.207424	+	0.309830i
$324$	−0.507592	−	8.98567i	−0.0281996	−	0.499204i
$325$	−11.8306	−	27.4427i	−0.656246	−	1.52225i
$326$	6.10460	−	3.52449i	0.338102	−	0.195203i
$327$	−4.56533	+	1.29257i	−0.252463	+	0.0714794i
$328$	1.73828	−	6.48735i	0.0959805	−	0.358204i
$329$	3.46047	−	5.99372i	0.190782	−	0.330444i
$330$	−5.47657	+	1.98993i	−0.301475	+	0.109542i
$331$	27.1558			1.49262			0.746308	−	0.665601i	$-0.231825\pi$
$331$	27.1558			1.49262			0.746308	+	0.665601i	$0.231825\pi$
$332$	12.8758	−	3.45007i	0.706653	−	0.189347i
$333$	−25.0464	+	7.47455i	−1.37253	+	0.409603i
$334$		−	13.2972i		−	0.727590i
$335$	−18.1068	−	8.76855i	−0.989278	−	0.479077i
$336$	6.99426	+	3.90763i	0.381568	+	0.213179i
$337$	−19.1199	−	5.12316i	−1.04153	−	0.279076i	−0.302781	−	0.953060i	$-0.597915\pi$
$337$	−19.1199	−	5.12316i	−1.04153	−	0.279076i	−0.738746	+	0.673984i	$0.764582\pi$
$338$	5.88108	+	21.9485i	0.319889	+	1.19384i
$339$	−19.7612	+	11.7839i	−1.07328	+	0.640016i
$340$	−0.249396	−	3.42847i	−0.0135254	−	0.185935i
$341$			3.85371i			0.208690i
$342$	−1.23472	−	13.0183i	−0.0667659	−	0.703948i
$343$	−24.1924	−	24.1924i	−1.30627	−	1.30627i
$344$	0.484555	+	0.839274i	0.0261255	+	0.0452506i
$345$	−6.99380	−	5.87499i	−0.376533	−	0.316299i
$346$	5.66622	−	9.81418i	0.304618	−	0.527614i
$347$	−3.30561	+	12.3367i	−0.177454	+	0.662269i	0.818666	+	0.574270i	$0.194714\pi$
$347$	−3.30561	+	12.3367i	−0.177454	+	0.662269i	−0.996121	+	0.0879993i	$0.971953\pi$
$348$	15.5451	−	4.40125i	0.833306	−	0.235932i
$349$		−	20.4630i		−	1.09536i	−0.836689	−	0.547679i	$-0.815512\pi$
$349$		−	20.4630i		−	1.09536i	0.836689	−	0.547679i	$-0.184488\pi$
$350$	18.1452	−	14.3410i	0.969900	−	0.766559i
$351$	27.5287	+	14.3765i	1.46938	+	0.767359i
$352$	0.389392	+	1.45323i	0.0207547	+	0.0774575i
$353$	−9.16982	+	9.16982i	−0.488060	+	0.488060i	−0.907694	−	0.419633i	$-0.862159\pi$
$353$	−9.16982	+	9.16982i	−0.488060	+	0.488060i	0.419633	+	0.907694i	$0.362159\pi$
$354$	0.707900	−	0.00998720i	0.0376245	−	0.000530814i
$355$	−3.01643	+	15.7537i	−0.160095	+	0.836118i
$356$	−7.21512	+	4.16565i	−0.382401	+	0.220779i
$357$	−3.35530	−	11.8508i	−0.177581	−	0.627213i
$358$	0.987982	−	3.68720i	0.0522165	−	0.194875i
$359$	2.39602	+	4.15003i	0.126457	+	0.219030i	0.922302	−	0.386471i	$-0.126306\pi$
$359$	2.39602	+	4.15003i	0.126457	+	0.219030i	−0.795844	+	0.605501i	$0.792973\pi$
$360$	−2.75229	+	6.11759i	−0.145059	+	0.322425i
$361$	−2.51382	−	18.8330i	−0.132306	−	0.991209i
$362$	−3.22962	−	3.22962i	−0.169745	−	0.169745i
$363$	14.6702	+	3.70988i	0.769987	+	0.194718i
$364$	−23.9427	+	13.8233i	−1.25494	+	0.724540i
$365$	1.57165	+	2.31604i	0.0822638	+	0.121227i
$366$	6.04282	+	10.1336i	0.315863	+	0.529691i
$367$	2.54101	+	9.48318i	0.132640	+	0.495018i	0.999996	−	0.00266881i	$-0.000849511\pi$
$367$	2.54101	+	9.48318i	0.132640	+	0.495018i	−0.867357	+	0.497687i	$0.834183\pi$
$368$	−1.66762	+	1.66762i	−0.0869307	+	0.0869307i
$369$	20.1406	−	0.568408i	1.04848	−	0.0295902i
$370$	19.1345	+	3.66376i	0.994753	+	0.190470i
$371$	−56.0428	−	32.3563i	−2.90959	−	1.67986i
$372$	3.18108	+	3.09257i	0.164931	+	0.160342i
$373$	−9.59962	−	9.59962i	−0.497049	−	0.497049i	0.413469	−	0.910518i	$-0.364317\pi$
$373$	−9.59962	−	9.59962i	−0.497049	−	0.497049i	−0.910518	+	0.413469i	$0.864317\pi$
$374$	1.15644	−	2.00301i	0.0597981	−	0.103573i
$375$	13.2783	+	14.0956i	0.685689	+	0.727895i
$376$	0.748109	−	1.29576i	0.0385808	−	0.0668238i
$377$	−14.4293	+	53.8510i	−0.743149	+	2.77347i
$378$	−5.23300	+	23.4589i	−0.269156	+	1.20660i
$379$		−	11.3908i		−	0.585104i	−0.956250	−	0.292552i	$-0.905495\pi$
$379$		−	11.3908i		−	0.585104i	0.956250	−	0.292552i	$-0.0945045\pi$
$380$	−3.65722	+	9.03464i	−0.187611	+	0.463467i
$381$	−0.296182	−	20.9936i	−0.0151738	−	1.07553i
$382$	14.9336	+	4.00144i	0.764069	+	0.204732i
$383$	−29.0741	−	7.79039i	−1.48562	−	0.398071i	−0.577364	−	0.816487i	$-0.695919\pi$
$383$	−29.0741	−	7.79039i	−1.48562	−	0.398071i	−0.908255	+	0.418416i	$0.862585\pi$
$384$	1.51207	+	0.844779i	0.0771624	+	0.0431099i
$385$	15.5203	−	1.12899i	0.790989	−	0.0575385i
$386$	9.95035	+	5.74484i	0.506460	+	0.292405i
$387$	−1.99698	+	2.11297i	−0.101512	+	0.107408i
$388$	−2.24143	−	2.24143i	−0.113792	−	0.113792i
$389$	−5.27510	+	9.13674i	−0.267458	+	0.463251i	−0.968205	−	0.250159i	$-0.919517\pi$
$389$	−5.27510	+	9.13674i	−0.267458	+	0.463251i	0.700747	+	0.713410i	$0.252850\pi$
$390$	−13.2670	−	18.9692i	−0.671798	−	0.960541i
$391$	3.62555			0.183352
$392$	−10.1798	−	10.1798i	−0.514159	−	0.514159i
$393$	−4.18602	+	1.18518i	−0.211157	+	0.0597844i
$394$	12.9704	−	7.48846i	0.653439	−	0.377263i
$395$	5.65452	−	29.5314i	0.284510	−	1.48589i
$396$	−3.84357	+	2.36612i	−0.193147	+	0.118902i
$397$	4.34842	+	1.16516i	0.218241	+	0.0584775i	0.366283	−	0.930504i	$-0.380630\pi$
$397$	4.34842	+	1.16516i	0.218241	+	0.0584775i	−0.148042	+	0.988981i	$0.547297\pi$
$398$	0.924786	−	0.924786i	0.0463553	−	0.0463553i
$399$	−6.29839	+	34.3501i	−0.315314	+	1.71965i
$400$	3.92274	−	3.10033i	0.196137	−	0.155017i
$401$	21.9425	−	12.6685i	1.09576	−	0.632636i	0.160654	−	0.987011i	$-0.448640\pi$
$401$	21.9425	−	12.6685i	1.09576	−	0.632636i	0.935103	+	0.354375i	$0.115306\pi$
$402$	−15.1079	−	3.82056i	−0.753513	−	0.190552i
$403$	−14.7878	+	3.96238i	−0.736633	+	0.197380i
$404$	4.42977	+	7.67258i	0.220389	+	0.381725i
$405$	−19.9475	−	2.66382i	−0.991201	−	0.132366i
$406$	−43.1468			−2.14134
$407$	9.26885	+	9.26885i	0.459440	+	0.459440i
$408$	−0.725372	−	2.56200i	−0.0359113	−	0.126838i
$409$	3.52423	+	2.03471i	0.174262	+	0.100610i	0.584594	−	0.811326i	$-0.301254\pi$
$409$	3.52423	+	2.03471i	0.174262	+	0.100610i	−0.410332	+	0.911936i	$0.634587\pi$
$410$	−13.5164	−	6.54557i	−0.667526	−	0.323263i
$411$	6.54802	−	0.0923809i	0.322990	−	0.00455681i
$412$	−0.609697	−	2.27542i	−0.0300376	−	0.112102i
$413$	−1.82629	−	0.489352i	−0.0898658	−	0.0240795i
$414$	−6.22458	−	3.36329i	−0.305922	−	0.165297i
$415$	−2.16251	−	29.7283i	−0.106154	−	1.45931i
$416$	−5.17610	+	2.98843i	−0.253779	+	0.146520i
$417$	−16.2022	−	15.7514i	−0.793427	−	0.771351i
$418$	−5.44946	+	3.64829i	−0.266542	+	0.178444i
$419$	−2.91774			−0.142541			−0.0712704	−	0.997457i	$-0.522705\pi$
$419$	−2.91774			−0.142541			−0.0712704	+	0.997457i	$0.522705\pi$
$420$	11.5230	−	13.7174i	0.562265	−	0.669341i
$421$	16.4563	+	28.5031i	0.802029	+	1.38916i	0.918278	+	0.395936i	$0.129580\pi$
$421$	16.4563	+	28.5031i	0.802029	+	1.38916i	−0.116249	+	0.993220i	$0.537087\pi$
$422$	−16.2933	+	4.36577i	−0.793144	+	0.212522i
$423$	4.36675	+	1.03897i	0.212319	+	0.0505166i
$424$	−12.1157	−	6.99500i	−0.588391	−	0.339707i
$425$	−7.63439	−	0.893997i	−0.370322	−	0.0433652i
$426$	0.175269	+	12.4232i	0.00849180	+	0.601905i
$427$	−8.15519	−	30.4356i	−0.394657	−	1.47288i
$428$	0.407405	+	1.52046i	0.0196927	+	0.0734941i
$429$	−0.219711	−	15.5733i	−0.0106078	−	0.751886i
$430$	2.04695	−	0.711242i	0.0987127	−	0.0342991i
$431$	8.68424	+	5.01385i	0.418305	+	0.241509i	0.694352	−	0.719636i	$-0.255691\pi$
$431$	8.68424	+	5.01385i	0.418305	+	0.241509i	−0.276047	+	0.961144i	$0.589024\pi$
$432$	−1.13131	+	5.07150i	−0.0544299	+	0.244003i
$433$	11.8326	−	3.17053i	0.568637	−	0.152366i	0.0369655	−	0.999317i	$-0.488231\pi$
$433$	11.8326	−	3.17053i	0.568637	−	0.152366i	0.531671	+	0.846951i	$0.321564\pi$
$434$	−5.92418	−	10.2610i	−0.284370	−	0.492543i
$435$	−3.12901	−	35.9905i	−0.150025	−	1.72561i
$436$	2.73940			0.131194
$437$	−9.22384	−	4.53840i	−0.441236	−	0.217101i
$438$	1.55452	+	1.51127i	0.0742780	+	0.0722113i
$439$	17.9077	−	10.3390i	0.854690	−	0.493456i	−0.00754041	−	0.999972i	$-0.502400\pi$
$439$	17.9077	−	10.3390i	0.854690	−	0.493456i	0.862231	+	0.506516i	$0.169067\pi$
$440$	3.35529	−	0.244072i	0.159957	−	0.0116357i
$441$	20.5309	−	37.9974i	0.977662	−	1.80940i
$442$	8.87520	+	2.37810i	0.422150	+	0.113115i
$443$	−2.85504	−	10.6552i	−0.135647	−	0.506242i	−0.999994	−	0.00334646i	$-0.998935\pi$
$443$	−2.85504	−	10.6552i	−0.135647	−	0.506242i	0.864347	−	0.502895i	$-0.167732\pi$
$444$	15.0892	−	0.212882i	0.716103	−	0.0101029i
$445$	6.11445	+	17.5973i	0.289853	+	0.834194i
$446$	−2.08624	−	1.20449i	−0.0987863	−	0.0570343i
$447$	−3.30660	−	11.6788i	−0.156397	−	0.552390i
$448$	−3.27081	−	3.27081i	−0.154531	−	0.154531i
$449$	19.4772			0.919186			0.459593	−	0.888130i	$-0.347995\pi$
$449$	19.4772			0.919186			0.459593	+	0.888130i	$0.347995\pi$
$450$	12.2779	+	8.61703i	0.578786	+	0.406210i
$451$	−5.05225	−	8.75075i	−0.237901	−	0.412057i
$452$	12.8310	−	3.43807i	0.603521	−	0.161713i
$453$	−30.3645	−	7.67872i	−1.42665	−	0.360778i
$454$	−13.6064	+	7.85565i	−0.638579	+	0.368684i
$455$	20.2903	+	58.3952i	0.951222	+	2.73761i
$456$	−1.36163	+	7.42603i	−0.0637641	+	0.347756i
$457$	−16.7562	+	16.7562i	−0.783821	+	0.783821i	−0.980473	−	0.196653i	$-0.936993\pi$
$457$	−16.7562	+	16.7562i	−0.783821	+	0.783821i	0.196653	+	0.980473i	$0.436993\pi$
$458$	0.447109	+	0.119803i	0.0208920	+	0.00559800i
$459$	6.74272	−	4.28317i	0.314723	−	0.199921i
$460$	2.96113	+	4.36363i	0.138063	+	0.203455i
$461$	3.68820	−	2.12939i	0.171777	−	0.0991754i	−0.411647	−	0.911344i	$-0.635046\pi$
$461$	3.68820	−	2.12939i	0.171777	−	0.0991754i	0.583423	+	0.812168i	$0.301713\pi$
$462$	11.5979	−	3.28368i	0.539582	−	0.152770i
$463$	3.05272	+	3.05272i	0.141872	+	0.141872i	0.774476	−	0.632604i	$-0.218014\pi$
$463$	3.05272	+	3.05272i	0.141872	+	0.141872i	−0.632604	+	0.774476i	$0.718014\pi$
$464$	−9.32777			−0.433031
$465$	8.12949	−	5.68573i	0.376996	−	0.263670i
$466$	−7.47210	+	12.9421i	−0.346138	+	0.599529i
$467$	3.26000	+	3.26000i	0.150855	+	0.150855i	0.778500	−	0.627645i	$-0.215981\pi$
$467$	3.26000	+	3.26000i	0.150855	+	0.150855i	−0.627645	+	0.778500i	$0.715981\pi$
$468$	−13.0314	−	12.3161i	−0.602379	−	0.569311i
$469$	36.0417	+	20.8087i	1.66425	+	0.960857i
$470$	−2.53113	−	2.18786i	−0.116752	−	0.100918i
$471$	14.9435	+	8.34878i	0.688558	+	0.384692i
$472$	−0.394819	−	0.105792i	−0.0181730	−	0.00486945i
$473$	1.40834	+	0.377364i	0.0647556	+	0.0173512i
$474$	−0.328554	−	23.2882i	−0.0150910	−	1.06966i
$475$	18.3037	+	11.8310i	0.839833	+	0.542845i
$476$			7.11104i			0.325934i
$477$	9.71465	−	40.8302i	0.444803	−	1.86949i
$478$	−0.539035	+	2.01171i	−0.0246549	+	0.0920134i
$479$	−5.44532	+	9.43157i	−0.248803	+	0.430939i	−0.963194	−	0.268807i	$-0.913370\pi$
$479$	−5.44532	+	9.43157i	−0.248803	+	0.430939i	0.714391	+	0.699747i	$0.246704\pi$
$480$	2.49112	−	2.96552i	0.113704	−	0.135357i
$481$	−26.0371	+	45.0975i	−1.18719	+	2.05627i
$482$	−15.3585	−	15.3585i	−0.699560	−	0.699560i
$483$	13.5478	+	13.1709i	0.616447	+	0.599295i
$484$	−7.56602	−	4.36825i	−0.343910	−	0.198557i
$485$	−5.86512	+	3.98002i	−0.266321	+	0.180724i
$486$	−15.5497	+	1.09864i	−0.705348	+	0.0498354i
$487$	−12.5206	+	12.5206i	−0.567361	+	0.567361i	−0.931388	−	0.364027i	$-0.881402\pi$
$487$	−12.5206	+	12.5206i	−0.567361	+	0.567361i	0.364027	+	0.931388i	$0.381402\pi$
$488$	−1.76305	−	6.57977i	−0.0798093	−	0.297852i
$489$	−6.25315	−	10.4863i	−0.282777	−	0.474207i
$490$	−26.6374	+	18.0759i	−1.20335	+	0.816587i
$491$	14.7759	−	8.53085i	0.666826	−	0.384992i	−0.128047	−	0.991768i	$-0.540871\pi$
$491$	14.7759	−	8.53085i	0.666826	−	0.384992i	0.794873	+	0.606776i	$0.207538\pi$
$492$	−11.2778	−	2.85198i	−0.508442	−	0.128577i
$493$	10.1397	+	10.1397i	0.456669	+	0.456669i
$494$	−19.6027	−	17.1600i	−0.881968	−	0.772065i
$495$	3.58013	+	9.43613i	0.160915	+	0.424122i
$496$	−1.28073	−	2.21829i	−0.0575065	−	0.0996041i
$497$	8.58781	−	32.0502i	0.385216	−	1.43765i
$498$	−6.28971	−	22.2151i	−0.281849	−	0.995482i
$499$	−12.5840	+	7.26540i	−0.563339	+	0.325244i	−0.754485	−	0.656318i	$-0.772113\pi$
$499$	−12.5840	+	7.26540i	−0.563339	+	0.325244i	0.191145	+	0.981562i	$0.438780\pi$
$500$	−5.15931	−	9.91875i	−0.230731	−	0.443580i
$501$	−23.0291	+	0.324899i	−1.02886	+	0.0145154i
$502$	18.7383	−	18.7383i	0.836331	−	0.836331i
$503$	−1.07201	−	4.00081i	−0.0477987	−	0.178387i	0.937900	−	0.346907i	$-0.112768\pi$
$503$	−1.07201	−	4.00081i	−0.0477987	−	0.178387i	−0.985698	+	0.168520i	$0.946101\pi$
$504$	6.59665	−	12.2087i	0.293838	−	0.543818i
$505$	18.7131	−	6.50212i	0.832721	−	0.289341i
$506$			3.54816i			0.157735i
$507$	37.8684	−	10.7216i	1.68180	−	0.476163i
$508$	−3.13737	+	11.7088i	−0.139198	+	0.519494i
$509$	13.2715	−	22.9870i	0.588250	−	1.01888i	−0.406212	−	0.913779i	$-0.633150\pi$
$509$	13.2715	−	22.9870i	0.588250	−	1.01888i	0.994462	−	0.105100i	$-0.0335163\pi$
$510$	−5.93161	+	0.515693i	−0.262656	+	0.0228353i
$511$	−2.89502	−	5.01432i	−0.128068	−	0.221820i
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$	−22.5159	+	2.45647i	−0.994101	+	0.108456i
$514$		−	0.960722i		−	0.0423756i
$515$	−5.25360	+	0.382160i	−0.231501	+	0.0168400i
$516$	1.44168	−	0.859697i	0.0634665	−	0.0378461i
$517$	−0.582615	−	2.17435i	−0.0256234	−	0.0956278i
$518$	−38.9282	−	10.4308i	−1.71041	−	0.458302i
$519$	−17.1354	−	9.57341i	−0.752161	−	0.420226i
$520$	4.38649	+	12.6243i	0.192360	+	0.553611i
$521$			7.38031i			0.323337i	0.986845	+	0.161669i	$0.0516876\pi$
$521$			7.38031i			0.323337i	−0.986845	+	0.161669i	$0.948312\pi$
$522$	−8.00226	−	26.8147i	−0.350250	−	1.17365i
$523$	37.8870	−	10.1518i	1.65668	−	0.443906i	0.695208	−	0.718808i	$-0.255312\pi$
$523$	37.8870	−	10.1518i	1.65668	−	0.443906i	0.961472	+	0.274902i	$0.0886454\pi$
$524$	2.51180			0.109729
$525$	−25.2802	−	31.0748i	−1.10332	−	1.35622i
$526$	4.20904	−	7.29026i	0.183523	−	0.317871i
$527$	−1.01917	+	3.80359i	−0.0443957	+	0.165687i
$528$	2.50731	−	0.709888i	0.109116	−	0.0308939i
$529$	15.1018	−	8.71905i	0.656601	−	0.379089i
$530$	−20.4570	+	23.6667i	−0.888596	+	1.02802i
$531$	−0.0345932	−	1.22575i	−0.00150122	−	0.0531932i
$532$	8.90148	−	18.0913i	0.385928	−	0.784359i
$533$	28.3845	−	28.3845i	1.22947	−	1.22947i
$534$	7.39069	+	12.3939i	0.319827	+	0.536338i
$535$	3.51050	−	0.255363i	0.151772	−	0.0110403i
$536$	7.79175	+	4.49857i	0.336552	+	0.194308i
$537$	−6.40992	−	1.62097i	−0.276608	−	0.0699501i
$538$	−4.36479	+	1.16954i	−0.188179	+	0.0504225i
$539$	−21.6594			−0.932936
$540$	10.6622	+	4.61716i	0.458827	+	0.198691i
$541$	−0.475900	+	0.824283i	−0.0204605	+	0.0354387i	−0.876074	−	0.482176i	$-0.839847\pi$
$541$	−0.475900	+	0.824283i	−0.0204605	+	0.0354387i	0.855614	+	0.517615i	$0.173180\pi$
$542$	13.5010	−	3.61759i	0.579919	−	0.155389i
$543$	−5.51439	+	5.67222i	−0.236645	+	0.243418i
$544$			1.53731i			0.0659117i
$545$	1.15195	−	6.01620i	0.0493441	−	0.257706i
$546$	24.5254	+	41.1282i	1.04959	+	1.76012i
$547$	−5.08007	−	18.9591i	−0.217208	−	0.810631i	−0.985378	−	0.170385i	$-0.945499\pi$
$547$	−5.08007	−	18.9591i	−0.217208	−	0.810631i	0.768170	−	0.640246i	$-0.221168\pi$
$548$	−3.65205	−	0.978564i	−0.156008	−	0.0418022i
$549$	17.4025	−	10.7130i	0.742720	−	0.457221i
$550$	0.874913	−	7.47143i	0.0373064	−	0.318583i
$551$	−13.1039	−	38.4893i	−0.558245	−	1.63970i
$552$	2.92886	+	2.84737i	0.124661	+	0.121192i
$553$	−16.0985	+	60.0804i	−0.684577	+	2.55488i
$554$	−2.96610	−	5.13743i	−0.126017	−	0.218268i
$555$	5.87767	−	33.2281i	0.249493	−	1.41045i
$556$	6.52316	+	11.2985i	0.276644	+	0.479161i
$557$	12.6530	−	3.39037i	0.536126	−	0.143655i	0.0194103	−	0.999812i	$-0.493821\pi$
$557$	12.6530	−	3.39037i	0.536126	−	0.143655i	0.516716	+	0.856157i	$0.327154\pi$
$558$	5.27823	−	5.58480i	0.223445	−	0.236424i
$559$			5.79223i			0.244985i
$560$	−8.55868	+	5.80786i	−0.361670	+	0.245427i
$561$	−3.49723	−	1.95387i	−0.147653	−	0.0824925i
$562$	−17.7491	+	17.7491i	−0.748700	+	0.748700i
$563$	−3.51411	+	3.51411i	−0.148102	+	0.148102i	−0.777270	−	0.629168i	$-0.783396\pi$
$563$	−3.51411	+	3.51411i	−0.148102	+	0.148102i	0.629168	+	0.777270i	$0.283396\pi$
$564$	−2.26238	−	1.26397i	−0.0952634	−	0.0532229i
$565$	−2.15499	−	29.6249i	−0.0906611	−	1.24633i
$566$	−18.2607	−	10.5428i	−0.767553	−	0.443147i
$567$	40.7558	+	8.48973i	1.71158	+	0.356535i
$568$	1.85657	−	6.92882i	0.0779000	−	0.290727i
$569$	−22.6874			−0.951107			−0.475554	−	0.879687i	$-0.657752\pi$
$569$	−22.6874			−0.951107			−0.475554	+	0.879687i	$0.657752\pi$
$570$	15.7363	+	6.11310i	0.659120	+	0.256050i
$571$	−23.6711			−0.990604			−0.495302	−	0.868721i	$-0.664943\pi$
$571$	−23.6711			−0.990604			−0.495302	+	0.868721i	$0.664943\pi$
$572$	−2.32734	+	8.68575i	−0.0973109	+	0.363169i
$573$	6.56513	−	25.9609i	0.274262	−	1.08453i
$574$	26.9045	+	15.5333i	1.12297	+	0.648349i
$575$	10.8285	−	4.66819i	0.451578	−	0.194677i
$576$	1.42611	−	2.63936i	0.0594212	−	0.109973i
$577$	7.59331	−	7.59331i	0.316113	−	0.316113i	−0.531159	−	0.847272i	$-0.678243\pi$
$577$	7.59331	−	7.59331i	0.316113	−	0.316113i	0.847272	+	0.531159i	$0.178243\pi$
$578$	−10.3497	+	10.3497i	−0.430490	+	0.430490i
$579$	9.70624	−	17.3732i	0.403378	−	0.722004i
$580$	−3.92243	+	20.4854i	−0.162870	+	0.850609i
$581$			61.6599i			2.55808i
$582$	−3.82712	+	3.93666i	−0.158639	+	0.163180i
$583$	−20.3307	+	5.44760i	−0.842012	+	0.225617i
$584$	−0.625865	−	1.08403i	−0.0258985	−	0.0448575i
$585$	−32.5281	+	23.4402i	−1.34487	+	0.969135i
$586$	−4.81207	−	8.33476i	−0.198785	−	0.344306i
$587$	−2.69293	+	10.0501i	−0.111149	+	0.414814i	−0.998970	−	0.0453750i	$-0.985552\pi$
$587$	−2.69293	+	10.0501i	−0.111149	+	0.414814i	0.887821	+	0.460189i	$0.152218\pi$
$588$	−17.3815	+	17.8790i	−0.716801	+	0.737316i
$589$	7.35415	−	8.40101i	0.303023	−	0.346157i
$590$	−0.398362	+	0.822605i	−0.0164003	+	0.0338661i
$591$	−13.2860	−	22.2802i	−0.546514	−	0.916484i
$592$	−8.41576	−	2.25500i	−0.345886	−	0.0926798i
$593$	5.73743	+	21.4124i	0.235608	+	0.879302i	0.977874	+	0.209196i	$0.0670846\pi$
$593$	5.73743	+	21.4124i	0.235608	+	0.879302i	−0.742266	+	0.670106i	$0.766249\pi$
$594$	4.19174	+	6.59879i	0.171989	+	0.270752i
$595$	15.6171	+	2.99027i	0.640237	+	0.122589i
$596$			7.00783i			0.287052i
$597$	−1.62421	−	1.57902i	−0.0664746	−	0.0646250i
$598$	−13.6153	+	3.64822i	−0.556772	+	0.149187i
$599$	−10.2909	+	17.8244i	−0.420475	+	0.728284i	−0.995986	−	0.0895103i	$-0.971470\pi$
$599$	−10.2909	+	17.8244i	−0.420475	+	0.728284i	0.575511	+	0.817794i	$0.304803\pi$
$600$	−5.46525	−	6.71796i	−0.223118	−	0.274260i
$601$	30.8635			1.25895			0.629474	−	0.777021i	$-0.283270\pi$
$601$	30.8635			1.25895			0.629474	+	0.777021i	$0.283270\pi$
$602$	−4.33000	+	1.16022i	−0.176478	+	0.0472870i
$603$	−6.24761	+	26.2584i	−0.254422	+	1.06932i
$604$	15.6602	+	9.04141i	0.637204	+	0.367890i
$605$	−12.7750	+	14.7794i	−0.519378	+	0.600868i
$606$	13.1797	−	7.85929i	0.535390	−	0.319262i
$607$	27.4679	−	27.4679i	1.11489	−	1.11489i	0.122407	−	0.992480i	$-0.460939\pi$
$607$	27.4679	−	27.4679i	1.11489	−	1.11489i	0.992480	−	0.122407i	$-0.0390614\pi$
$608$	1.92438	−	3.91111i	0.0780440	−	0.158616i
$609$	1.05424	+	74.7250i	0.0427198	+	3.02801i
$610$	−15.1917	+	1.10508i	−0.615094	+	0.0447434i
$611$	7.74458	−	4.47133i	0.313312	−	0.180891i
$612$	−4.41934	+	1.31885i	−0.178641	+	0.0533115i
$613$	3.55128	−	13.2536i	0.143435	−	0.535306i	−0.856385	−	0.516337i	$-0.827295\pi$
$613$	3.55128	−	13.2536i	0.143435	−	0.535306i	0.999820	−	0.0189686i	$-0.00603825\pi$
$614$	−13.3581	+	23.1370i	−0.539091	+	0.933732i
$615$	−11.0059	+	23.5687i	−0.443800	+	0.950380i
$616$	−6.95924			−0.280396
$617$	21.2202	−	5.68594i	0.854294	−	0.228908i	0.195010	−	0.980801i	$-0.437526\pi$
$617$	21.2202	−	5.68594i	0.854294	−	0.228908i	0.659284	+	0.751894i	$0.270859\pi$
$618$	−3.92585	+	1.11152i	−0.157921	+	0.0447118i
$619$			41.9681i			1.68684i	0.537254	+	0.843420i	$0.319462\pi$
$619$			41.9681i			1.68684i	−0.537254	+	0.843420i	$0.680538\pi$
$620$	−5.41031	+	1.87989i	−0.217283	+	0.0754981i
$621$	−5.67273	+	10.8624i	−0.227639	+	0.435893i
$622$	9.82613	+	2.63290i	0.393992	+	0.105570i
$623$	−9.97424	−	37.2244i	−0.399610	−	1.49136i
$624$	5.30206	+	8.89137i	0.212252	+	0.355939i
$625$	−23.9528	+	7.15978i	−0.958113	+	0.286391i
$626$		−	20.8445i		−	0.833112i
$627$	6.45155	+	9.34866i	0.257650	+	0.373349i
$628$	−6.98820	−	6.98820i	−0.278859	−	0.278859i
$629$	6.69702	+	11.5996i	0.267028	+	0.462506i
$630$	−24.0384	−	19.6213i	−0.957714	−	0.781730i
$631$	−15.3909	+	26.6578i	−0.612703	+	1.06123i	0.378080	+	0.925773i	$0.376584\pi$
$631$	−15.3909	+	26.6578i	−0.612703	+	1.06123i	−0.990783	+	0.135459i	$0.956749\pi$
$632$	−3.48028	+	12.9886i	−0.138438	+	0.516658i
$633$	7.95909	+	28.1113i	0.316345	+	1.11732i
$634$			18.7757i			0.745678i
$635$	24.3953	+	11.8139i	0.968096	+	0.468819i
$636$	−11.8185	+	21.1538i	−0.468633	+	0.838804i
$637$	−22.2702	−	83.1135i	−0.882377	−	3.29308i
$638$	−9.92325	+	9.92325i	−0.392865	+	0.392865i
$639$	21.5112	−	0.607089i	0.850969	−	0.0240161i
$640$	−1.85027	+	1.25558i	−0.0731385	+	0.0496312i
$641$	26.7128	−	15.4226i	1.05509	−	0.609157i	0.131021	−	0.991380i	$-0.458175\pi$
$641$	26.7128	−	15.4226i	1.05509	−	0.609157i	0.924070	+	0.382222i	$0.124841\pi$
$642$	2.62329	−	0.742727i	0.103533	−	0.0293131i
$643$	7.65231	−	28.5588i	0.301777	−	1.12625i	−0.633906	−	0.773410i	$-0.718550\pi$
$643$	7.65231	−	28.5588i	0.301777	−	1.12625i	0.935684	−	0.352839i	$-0.114784\pi$
$644$	−5.45447	−	9.44742i	−0.214936	−	0.372281i
$645$	−1.28180	−	3.52769i	−0.0504708	−	0.138903i
$646$	−6.34343	+	2.15966i	−0.249579	+	0.0849706i
$647$	−33.1488	−	33.1488i	−1.30322	−	1.30322i	−0.926212	−	0.377004i	$-0.876954\pi$
$647$	−33.1488	−	33.1488i	−1.30322	−	1.30322i	−0.377004	−	0.926212i	$-0.623046\pi$
$648$	8.81087	+	1.83537i	0.346124	+	0.0721000i
$649$	−0.532569	+	0.307479i	−0.0209052	+	0.0120696i
$650$	29.5697	−	4.32482i	1.15982	−	0.169634i
$651$	−17.6260	+	10.5107i	−0.690819	+	0.411946i
$652$	1.82441	+	6.80879i	0.0714494	+	0.266653i
$653$	−11.6345	+	11.6345i	−0.455293	+	0.455293i	−0.897107	−	0.441814i	$-0.854335\pi$
$653$	−11.6345	+	11.6345i	−0.455293	+	0.455293i	0.441814	+	0.897107i	$0.354335\pi$
$654$	−0.0669337	−	4.74431i	−0.00261732	−	0.185517i
$655$	1.05624	−	5.51635i	0.0412708	−	0.215542i
$656$	5.81640	+	3.35810i	0.227092	+	0.131112i
$657$	2.57935	−	2.72917i	0.100630	−	0.106475i
$658$	4.89385	+	4.89385i	0.190782	+	0.190782i
$659$	7.58062	−	13.1300i	0.295299	−	0.511473i	−0.679755	−	0.733439i	$-0.737914\pi$
$659$	7.58062	−	13.1300i	0.295299	−	0.511473i	0.975054	+	0.221966i	$0.0712474\pi$
$660$	−0.504685	−	5.80499i	−0.0196448	−	0.225959i
$661$	−17.1392	+	29.6860i	−0.666639	+	1.15465i	0.312200	+	0.950017i	$0.398934\pi$
$661$	−17.1392	+	29.6860i	−0.666639	+	1.15465i	−0.978838	+	0.204636i	$0.934399\pi$
$662$	−7.02843	+	26.2304i	−0.273168	+	1.01948i
$663$	3.90173	−	15.4289i	0.151531	−	0.599208i
$664$			13.3300i			0.517306i
$665$	−35.9885	−	27.1568i	−1.39557	−	1.05309i
$666$	−0.737371	−	26.1275i	−0.0285726	−	1.01242i
$667$	−21.2488	−	5.69359i	−0.822755	−	0.220457i
$668$	12.8441	+	3.44157i	0.496953	+	0.133158i
$669$	−2.03506	+	3.64254i	−0.0786799	+	0.140829i
$670$	13.1561	−	15.2203i	0.508266	−	0.588012i
$671$	−8.87542	−	5.12422i	−0.342632	−	0.197818i
$672$	−5.58473	+	5.74457i	−0.215436	+	0.221602i
$673$	−5.55175	−	5.55175i	−0.214004	−	0.214004i	0.591962	−	0.805966i	$-0.298354\pi$
$673$	−5.55175	−	5.55175i	−0.214004	−	0.214004i	−0.805966	+	0.591962i	$0.798354\pi$
$674$	9.89719	−	17.1424i	0.381225	−	0.660302i
$675$	14.6236	−	21.4744i	0.562864	−	0.826549i
$676$	−22.7227			−0.873952
$677$	11.9284	+	11.9284i	0.458445	+	0.458445i	0.898145	−	0.439700i	$-0.144915\pi$
$677$	11.9284	+	11.9284i	0.458445	+	0.458445i	−0.439700	+	0.898145i	$0.644915\pi$
$678$	−6.26782	−	22.1378i	−0.240714	−	0.850197i
$679$	12.6982	−	7.33131i	0.487312	−	0.281350i
$680$	3.37620	+	0.646457i	0.129471	+	0.0247905i
$681$	13.9375	+	23.3727i	0.534085	+	0.895642i
$682$	−3.72239	−	0.997412i	−0.142538	−	0.0381929i
$683$	12.7512	−	12.7512i	0.487911	−	0.487911i	−0.419736	−	0.907646i	$-0.637877\pi$
$683$	12.7512	−	12.7512i	0.487911	−	0.487911i	0.907646	+	0.419736i	$0.137877\pi$
$684$	12.8943	+	2.17673i	0.493024	+	0.0832294i
$685$	−3.68482	+	7.60903i	−0.140790	+	0.290726i
$686$	29.6295	−	17.1066i	1.13126	−	0.653134i
$687$	0.196559	−	0.777266i	0.00749919	−	0.0296545i
$688$	−0.936089	+	0.250824i	−0.0356880	+	0.00956258i
$689$	−41.8081	−	72.4137i	−1.59276	−	2.75874i
$690$	7.48493	−	5.23493i	0.284946	−	0.199290i
$691$	14.0219			0.533418			0.266709	−	0.963777i	$-0.414064\pi$
$691$	14.0219			0.533418			0.266709	+	0.963777i	$0.414064\pi$
$692$	8.01325	+	8.01325i	0.304618	+	0.304618i
$693$	−5.97031	−	20.0059i	−0.226793	−	0.759960i
$694$	−11.0608	−	6.38595i	−0.419862	−	0.242407i
$695$	27.5564	−	9.57486i	1.04527	−	0.363195i
$696$	0.227912	+	16.1546i	0.00863898	+	0.612337i
$697$	−2.67228	−	9.97309i	−0.101220	−	0.377758i
$698$	19.7657	+	5.29620i	0.748143	+	0.200464i
$699$	22.5966	+	12.6245i	0.854683	+	0.477504i
$700$	9.15603	+	21.2386i	0.346065	+	0.802744i
$701$	30.1018	−	17.3793i	1.13693	−	0.656405i	0.191260	−	0.981539i	$-0.438743\pi$
$701$	30.1018	−	17.3793i	1.13693	−	0.656405i	0.945668	+	0.325134i	$0.105409\pi$
$702$	−21.0116	+	22.8698i	−0.793030	+	0.863165i
$703$	−2.51787	−	37.8940i	−0.0949632	−	1.42920i
$704$	−1.50450			−0.0567028
$705$	−3.72726	+	4.43706i	−0.140377	+	0.167109i
$706$	−6.48404	−	11.2307i	−0.244030	−	0.422673i
$707$	−39.5845	+	10.6066i	−1.48873	+	0.398904i
$708$	−0.173571	+	0.686364i	−0.00652320	+	0.0257951i
$709$	−39.2828	−	22.6799i	−1.47530	−	0.851762i	−0.475683	−	0.879617i	$-0.657799\pi$
$709$	−39.2828	−	22.6799i	−1.47530	−	0.851762i	−0.999612	+	0.0278548i	$0.991132\pi$
$710$	−14.4362	−	6.99100i	−0.541780	−	0.262367i
$711$	−40.3243	+	1.13803i	−1.51228	+	0.0426795i
$712$	−2.15630	−	8.04742i	−0.0808108	−	0.301590i
$713$	−1.56349	−	5.83503i	−0.0585533	−	0.218524i
$714$	12.3154	−	0.173749i	0.460894	−	0.00650239i
$715$	18.0967	+	8.76369i	0.676779	+	0.327743i
$716$	3.30585	+	1.90863i	0.123545	+	0.0713290i
$717$	3.49720	+	0.884390i	0.130605	+	0.0330282i
$718$	−4.62876	+	1.24027i	−0.172744	+	0.0462865i
$719$	−9.45972	−	16.3847i	−0.352788	−	0.611047i	0.633949	−	0.773375i	$-0.281433\pi$
$719$	−9.45972	−	16.3847i	−0.352788	−	0.611047i	−0.986737	+	0.162328i	$0.948100\pi$
$720$	−5.19679	−	4.24186i	−0.193673	−	0.158085i
$721$	10.8965			0.405808
$722$	18.8419	+	2.44617i	0.701222	+	0.0910371i
$723$	−26.2238	+	26.9743i	−0.975273	+	1.00319i
$724$	3.95546	−	2.28368i	0.147003	−	0.0848724i
$725$	43.3400	+	17.2287i	1.60961	+	0.639857i
$726$	−7.38041	+	13.2102i	−0.273913	+	0.490275i
$727$	−20.3872	−	5.46273i	−0.756119	−	0.202602i	−0.139889	−	0.990167i	$-0.544674\pi$
$727$	−20.3872	−	5.46273i	−0.756119	−	0.202602i	−0.616231	+	0.787566i	$0.711341\pi$
$728$	−7.15549	−	26.7047i	−0.265200	−	0.989740i
$729$	2.28265	+	26.9033i	0.0845426	+	0.996420i
$730$	−2.64390	+	0.918660i	−0.0978551	+	0.0340011i
$731$	1.29023	+	0.744912i	0.0477207	+	0.0275516i
$732$	−11.3523	+	3.21415i	−0.419593	+	0.118798i
$733$	27.0660	+	27.0660i	0.999706	+	0.999706i	1.00000		0.000293575i	$-9.34479e-5\pi$
$733$	27.0660	+	27.0660i	0.999706	+	0.999706i	−0.000293575		1.00000i	$0.500093\pi$
$734$	−9.81771			−0.362378
$735$	31.9561	+	45.6910i	1.17872	+	1.68534i
$736$	−1.17919	−	2.04241i	−0.0434653	−	0.0752842i
$737$	13.0749	−	3.50341i	0.481621	−	0.129050i
$738$	−4.66373	+	19.6014i	−0.171674	+	0.721539i
$739$	13.3663	−	7.71701i	0.491686	−	0.283875i	−0.233588	−	0.972336i	$-0.575047\pi$
$739$	13.3663	−	7.71701i	0.491686	−	0.283875i	0.725274	+	0.688461i	$0.241713\pi$
$740$	−8.49128	+	17.5342i	−0.312146	+	0.644570i
$741$	−29.2401	+	34.3688i	−1.07416	+	1.26257i
$742$	45.7587	−	45.7587i	1.67986	−	1.67986i
$743$	44.1174	+	11.8212i	1.61851	+	0.433679i	0.950563	−	0.310530i	$-0.100507\pi$
$743$	44.1174	+	11.8212i	1.61851	+	0.433679i	0.667947	+	0.744209i	$0.267173\pi$
$744$	−3.81052	+	2.27227i	−0.139700	+	0.0833055i
$745$	15.3904	+	2.94687i	0.563860	+	0.107965i
$746$	11.7571	−	6.78796i	0.430457	−	0.248525i
$747$	−38.3202	+	11.4358i	−1.40206	+	0.418414i
$748$	1.63545	+	1.63545i	0.0597981	+	0.0597981i
$749$	−7.28117			−0.266048
$750$	−17.0520	+	9.17765i	−0.622651	+	0.335120i
$751$	6.38204	−	11.0540i	0.232884	−	0.403367i	−0.725772	−	0.687936i	$-0.758517\pi$
$751$	6.38204	−	11.0540i	0.232884	−	0.403367i	0.958656	+	0.284569i	$0.0918504\pi$
$752$	1.05799	+	1.05799i	0.0385808	+	0.0385808i
$753$	−32.9103	−	31.9946i	−1.19932	−	1.16595i
$754$	−48.2815	−	27.8753i	−1.75831	−	1.01516i
$755$	26.4418	−	30.5904i	0.962314	−	1.11330i
$756$	−21.3052	−	11.1263i	−0.774861	−	0.404660i
$757$	−11.6311	−	3.11655i	−0.422740	−	0.113273i	0.0411761	−	0.999152i	$-0.486890\pi$
$757$	−11.6311	−	3.11655i	−0.422740	−	0.113273i	−0.463916	+	0.885879i	$0.653556\pi$
$758$	11.0026	+	2.94815i	0.399634	+	0.107082i
$759$	6.14498	−	0.0866946i	0.223049	−	0.00314681i
$760$	−7.78024	−	5.87094i	−0.282219	−	0.212961i
$761$		−	16.6072i		−	0.602009i	−0.953623	−	0.301005i	$-0.902678\pi$
$761$		−	16.6072i		−	0.602009i	0.953623	−	0.301005i	$-0.0973219\pi$
$762$	20.3549	+	5.14745i	0.737380	+	0.186472i
$763$	−3.27962	+	12.2397i	−0.118730	+	0.443107i
$764$	−7.73020	+	13.3891i	−0.279669	+	0.484400i
$765$	1.03805	+	10.2602i	0.0375307	+	0.370959i
$766$	15.0499	−	26.0672i	0.543775	−	0.941845i
$767$	−1.72748	−	1.72748i	−0.0623755	−	0.0623755i
$768$	−1.20735	+	1.24190i	−0.0435663	+	0.0448132i
$769$	2.08571	+	1.20418i	0.0752125	+	0.0434240i	0.537135	−	0.843497i	$-0.319507\pi$
$769$	2.08571	+	1.20418i	0.0752125	+	0.0434240i	−0.461922	+	0.886920i	$0.652840\pi$
$770$	−2.92644	+	15.2837i	−0.105462	+	0.550786i
$771$	−1.66385	+	0.0234740i	−0.0599222	+	0.000845395i
$772$	−8.12443	+	8.12443i	−0.292405	+	0.292405i
$773$	5.72773	+	21.3762i	0.206012	+	0.768848i	0.989139	+	0.146986i	$0.0469571\pi$
$773$	5.72773	+	21.3762i	0.206012	+	0.768848i	−0.783126	+	0.621863i	$0.786376\pi$
$774$	−1.52412	−	2.47581i	−0.0547832	−	0.0889912i
$775$	1.85346	+	12.6725i	0.0665783	+	0.455209i
$776$	2.74518	−	1.58493i	0.0985463	−	0.0568958i
$777$	−17.1137	+	67.6738i	−0.613950	+	2.42778i
$778$	−7.46012	−	7.46012i	−0.267458	−	0.267458i
$779$	−5.68554	+	28.7179i	−0.203706	+	1.02892i
$780$	21.7565	−	7.90532i	0.779009	−	0.283056i
$781$	−5.39606	−	9.34624i	−0.193086	−	0.334435i
$782$	−0.938361	+	3.50201i	−0.0335557	+	0.125232i
$783$	−46.2443	+	14.5141i	−1.65264	+	0.518693i
$784$	12.4677	−	7.19822i	0.445275	−	0.257079i
$785$	−18.2859	+	12.4087i	−0.652651	+	0.442884i
$786$	−0.0613726	−	4.35014i	−0.00218909	−	0.155164i
$787$	−5.47888	+	5.47888i	−0.195301	+	0.195301i	−0.797982	−	0.602681i	$-0.794099\pi$
$787$	−5.47888	+	5.47888i	−0.195301	+	0.195301i	0.602681	+	0.797982i	$0.294099\pi$
$788$	3.87631	+	14.4666i	0.138088	+	0.515351i
$789$	−12.7287	−	7.11141i	−0.453153	−	0.253173i
$790$	27.0617	+	13.1051i	0.962811	+	0.466260i
$791$			61.4453i			2.18474i
$792$	−1.29070	−	4.32500i	−0.0458631	−	0.153682i
$793$	10.5375	−	39.3263i	0.374196	−	1.39652i
$794$	−2.25091	+	3.89869i	−0.0798818	+	0.138359i
$795$	41.4877	+	34.8508i	1.47142	+	1.23603i
$796$	0.653922	+	1.13263i	0.0231777	+	0.0401449i
$797$	1.59055	+	1.59055i	0.0563401	+	0.0563401i	0.734715	−	0.678375i	$-0.237316\pi$
$797$	1.59055	+	1.59055i	0.0563401	+	0.0563401i	−0.678375	+	0.734715i	$0.737316\pi$
$798$	−31.5495	−	14.9742i	−1.11684	−	0.530082i
$799$		−	2.30015i		−	0.0813735i
$800$	1.97941	+	4.59151i	0.0699828	+	0.162334i
$801$	21.2842	−	13.1026i	0.752040	−	0.462958i
$802$	6.55771	+	24.4737i	0.231561	+	0.864197i
$803$	−1.81905	−	0.487414i	−0.0641930	−	0.0172005i
$804$	7.60059	−	13.6043i	0.268052	−	0.479786i
$805$	−23.0418	+	8.00621i	−0.812118	+	0.282182i
$806$		−	15.3095i		−	0.539253i
$807$	2.13215	+	7.53071i	0.0750553	+	0.265093i
$808$	−8.55765	+	2.29302i	−0.301057	+	0.0806680i
$809$	35.8571			1.26067			0.630334	−	0.776324i	$-0.282918\pi$
$809$	35.8571			1.26067			0.630334	+	0.776324i	$0.282918\pi$
$810$	7.73585	−	18.5784i	0.271810	−	0.652778i
$811$	−4.50197	+	7.79765i	−0.158086	+	0.273812i	−0.934178	−	0.356806i	$-0.883866\pi$
$811$	−4.50197	+	7.79765i	−0.158086	+	0.273812i	0.776093	+	0.630619i	$0.217199\pi$
$812$	11.1672	−	41.6766i	0.391892	−	1.46256i
$813$	−6.59511	−	23.2938i	−0.231300	−	0.816948i
$814$	−11.3520	+	6.55406i	−0.397886	+	0.229720i
$815$	15.7205	−	1.14355i	0.550664	−	0.0400566i
$816$	2.66244	−	0.0375622i	0.0932039	−	0.00131494i
$817$	−2.35002	−	3.51023i	−0.0822168	−	0.122807i
$818$	−2.87752	+	2.87752i	−0.100610	+	0.100610i
$819$	70.6297	−	43.4799i	2.46800	−	1.51931i
$820$	9.82083	−	11.3617i	0.342958	−	0.396768i
$821$	−26.9842	−	15.5793i	−0.941754	−	0.543722i	−0.0512439	−	0.998686i	$-0.516319\pi$
$821$	−26.9842	−	15.5793i	−0.941754	−	0.543722i	−0.890510	+	0.454965i	$0.849652\pi$
$822$	−1.60552	+	6.34882i	−0.0559989	+	0.221440i
$823$	−13.9193	+	3.72966i	−0.485196	+	0.130008i	−0.493121	−	0.869961i	$-0.664144\pi$
$823$	−13.9193	+	3.72966i	−0.485196	+	0.130008i	0.00792527	+	0.999969i	$0.497477\pi$
$824$	2.35569			0.0820643
$825$	−12.9610	−	1.33269i	−0.451243	−	0.0463982i
$826$	0.945356	−	1.63741i	0.0328931	−	0.0569726i
$827$	20.0906	−	5.38326i	0.698618	−	0.187194i	0.108007	−	0.994150i	$-0.465553\pi$
$827$	20.0906	−	5.38326i	0.698618	−	0.187194i	0.590611	+	0.806956i	$0.298887\pi$
$828$	4.85973	−	5.14200i	0.168887	−	0.178697i
$829$		−	18.5190i		−	0.643190i	−0.946877	−	0.321595i	$-0.895781\pi$
$829$		−	18.5190i		−	0.643190i	0.946877	−	0.321595i	$-0.104219\pi$
$830$	29.2751	+	5.60544i	1.01615	+	0.194568i
$831$	−8.82493	+	5.26244i	−0.306133	+	0.182552i
$832$	−1.54692	−	5.77319i	−0.0536299	−	0.200150i
$833$	−21.3777	−	5.72814i	−0.740694	−	0.198468i
$834$	19.4082	−	11.5734i	0.672050	−	0.400754i
$835$	12.9594	−	26.7606i	0.448477	−	0.926090i
$836$	−2.11356	−	6.20802i	−0.0730989	−	0.214709i
$837$	−9.80117	−	9.00479i	−0.338778	−	0.311251i
$838$	0.755166	−	2.81832i	0.0260868	−	0.0973571i
$839$	27.8705	+	48.2731i	0.962197	+	1.66657i	0.716964	+	0.697110i	$0.245531\pi$
$839$	27.8705	+	48.2731i	0.962197	+	1.66657i	0.245233	+	0.969464i	$0.421136\pi$
$840$	10.2676	+	14.6807i	0.354267	+	0.506532i
$841$	−29.0036	−	50.2358i	−1.00013	−	1.73227i
$842$	−31.7911	+	8.51839i	−1.09559	+	0.293563i
$843$	31.1729	+	30.3056i	1.07365	+	1.04378i
$844$		−	16.8680i		−	0.580622i
$845$	−9.55517	+	49.9030i	−0.328708	+	1.71672i
$846$	−2.13377	+	3.94905i	−0.0733605	+	0.135771i
$847$	28.5754	−	28.5754i	0.981864	−	0.981864i
$848$	9.89243	−	9.89243i	0.339707	−	0.339707i
$849$	−17.8127	+	31.8828i	−0.611329	+	1.09422i
$850$	2.83946	−	7.14287i	0.0973927	−	0.244999i
$851$	−17.7948	−	10.2738i	−0.609997	−	0.352182i
$852$	−12.0452	−	3.04606i	−0.412663	−	0.104356i
$853$	−10.7222	+	40.0158i	−0.367121	+	1.37011i	0.497402	+	0.867520i	$0.334287\pi$
$853$	−10.7222	+	40.0158i	−0.367121	+	1.37011i	−0.864523	+	0.502594i	$0.832379\pi$
$854$	31.5092			1.07822
$855$	10.2027	−	27.4027i	0.348923	−	0.937151i
$856$	−1.57409			−0.0538014
$857$	−9.40068	+	35.0838i	−0.321121	+	1.19844i	0.597033	+	0.802216i	$0.296346\pi$
$857$	−9.40068	+	35.0838i	−0.321121	+	1.19844i	−0.918154	+	0.396223i	$0.870321\pi$
$858$	15.0995	+	3.81844i	0.515489	+	0.130359i
$859$	−30.9724	−	17.8819i	−1.05677	−	0.610124i	−0.132230	−	0.991219i	$-0.542214\pi$
$859$	−30.9724	−	17.8819i	−1.05677	−	0.610124i	−0.924536	+	0.381095i	$0.875547\pi$
$860$	0.157217	+	2.16129i	0.00536106	+	0.0736992i
$861$	26.2445	−	46.9749i	0.894409	−	1.60090i
$862$	−7.09065	+	7.09065i	−0.241509	+	0.241509i
$863$	−26.5413	+	26.5413i	−0.903477	+	0.903477i	−0.995735	−	0.0922582i	$-0.970591\pi$
$863$	−26.5413	+	26.5413i	−0.903477	+	0.903477i	0.0922582	+	0.995735i	$0.470591\pi$
$864$	−4.60589	−	2.40536i	−0.156696	−	0.0818320i
$865$	20.9681	−	14.2288i	0.712938	−	0.483794i
$866$			12.2500i			0.416271i
$867$	18.1773	+	17.6715i	0.617333	+	0.600156i
$868$	11.4446	−	3.06658i	0.388457	−	0.104087i
$869$	10.1153	+	17.5202i	0.343138	+	0.594333i
$870$	35.5740	+	6.29264i	1.20607	+	0.213341i
$871$	26.8873	+	46.5701i	0.911040	+	1.57797i
$872$	−0.709010	+	2.64606i	−0.0240101	+	0.0896069i
$873$	6.91132	+	6.53192i	0.233913	+	0.221072i
$874$	6.77107	−	7.73492i	0.229035	−	0.261637i
$875$	50.4938	−	11.1771i	1.70700	−	0.377856i
$876$	−1.86212	+	1.11041i	−0.0629150	+	0.0375172i
$877$	12.9458	+	3.46882i	0.437150	+	0.117134i	0.470680	−	0.882304i	$-0.344009\pi$
$877$	12.9458	+	3.46882i	0.437150	+	0.117134i	−0.0335308	+	0.999438i	$0.510675\pi$
$878$	5.35188	+	19.9735i	0.180617	+	0.674073i
$879$	−14.3172	+	8.53758i	−0.482908	+	0.287965i
$880$	−0.632657	+	3.30413i	−0.0213269	+	0.111382i
$881$			35.6096i			1.19972i	0.800106	+	0.599859i	$0.204777\pi$
$881$			35.6096i			1.19972i	−0.800106	+	0.599859i	$0.795223\pi$
$882$	31.3889	+	29.6658i	1.05692	+	0.998899i
$883$	8.94681	−	2.39729i	0.301084	−	0.0806753i	−0.105114	−	0.994460i	$-0.533521\pi$
$883$	8.94681	−	2.39729i	0.301084	−	0.0806753i	0.406198	+	0.913785i	$0.366854\pi$
$884$	−4.59414	+	7.95729i	−0.154518	+	0.267633i
$885$	1.43438	+	0.669816i	0.0482163	+	0.0225156i
$886$	11.0310			0.370595
$887$	−17.4913	+	4.68678i	−0.587300	+	0.157367i	−0.540219	−	0.841524i	$-0.681659\pi$
$887$	−17.4913	+	4.68678i	−0.587300	+	0.157367i	−0.0470811	+	0.998891i	$0.514992\pi$
$888$	−3.69975	+	14.6302i	−0.124156	+	0.490957i
$889$	−48.5591	−	28.0356i	−1.62862	−	0.940283i
$890$	−18.5803	+	1.35157i	−0.622812	+	0.0453049i
$891$	11.3259	−	7.42081i	0.379431	−	0.248607i
$892$	1.70341	−	1.70341i	0.0570343	−	0.0570343i
$893$	−2.87929	+	5.85187i	−0.0963518	+	0.195825i
$894$	12.1367	−	0.171227i	0.405912	−	0.00572669i
$895$	5.58184	−	6.45762i	0.186580	−	0.215854i
$896$	4.00591	−	2.31281i	0.133828	−	0.0772657i
$897$	6.65094	+	23.4910i	0.222068	+	0.784340i
$898$	−5.04107	+	18.8135i	−0.168223	+	0.627816i
$899$	11.9464	−	20.6917i	0.398433	−	0.690107i
$900$	−11.5012	+	9.62929i	−0.383372	+	0.320976i
$901$	−21.5070			−0.716502
$902$	9.76020	−	2.61524i	0.324979	−	0.0870779i
$903$	2.11516	+	7.47068i	0.0703880	+	0.248609i
$904$			13.2837i			0.441808i
$905$	−3.35205	−	9.64718i	−0.111426	−	0.320683i
$906$	15.2760	−	27.3424i	0.507511	−	0.908392i
$907$	36.4411	+	9.76435i	1.21001	+	0.324220i	0.806764	−	0.590874i	$-0.201217\pi$
$907$	36.4411	+	9.76435i	1.21001	+	0.324220i	0.403241	+	0.915094i	$0.367884\pi$
$908$	−4.06638	−	15.1759i	−0.134948	−	0.503631i
$909$	−13.9334	−	22.6337i	−0.462140	−	0.750712i
$910$	−61.6570	+	4.48508i	−2.04391	+	0.148679i
$911$		−	39.6167i		−	1.31256i	−0.754518	−	0.656280i	$-0.772129\pi$
$911$		−	39.6167i		−	1.31256i	0.754518	−	0.656280i	$-0.227871\pi$
$912$	−6.82058	−	3.23723i	−0.225852	−	0.107195i
$913$	14.1810	+	14.1810i	0.469324	+	0.469324i
$914$	−11.8484	−	20.5220i	−0.391910	−	0.678808i
$915$	2.28506	+	26.2832i	0.0755416	+	0.868895i
$916$	−0.231441	+	0.400867i	−0.00764702	+	0.0132450i
$917$	−3.00713	+	11.2228i	−0.0993043	+	0.370609i
$918$	2.39208	+	7.62154i	0.0789503	+	0.251548i
$919$		−	23.1523i		−	0.763725i	−0.924219	−	0.381862i	$-0.875283\pi$
$919$		−	23.1523i		−	0.763725i	0.924219	−	0.381862i	$-0.124717\pi$
$920$	−4.98134	+	1.73084i	−0.164230	+	0.0570640i
$921$	40.3968	+	22.5693i	1.33112	+	0.743685i
$922$	1.10225	+	4.11366i	0.0363007	+	0.135476i
$923$	30.3161	−	30.3161i	0.997866	−	0.997866i
$924$	0.170040	+	12.0526i	0.00559390	+	0.396500i
$925$	34.9375	+	26.0217i	1.14874	+	0.855587i
$926$	−3.73881	+	2.15860i	−0.122865	+	0.0709361i
$927$	2.02094	+	6.77194i	0.0663763	+	0.222420i
$928$	2.41420	−	9.00993i	0.0792501	−	0.295766i
$929$	−8.94779	−	15.4980i	−0.293567	−	0.508474i	0.681083	−	0.732206i	$-0.261509\pi$
$929$	−8.94779	−	15.4980i	−0.293567	−	0.508474i	−0.974651	+	0.223732i	$0.928176\pi$
$930$	3.38793	+	9.32406i	0.111095	+	0.305748i
$931$	47.2171	+	41.3333i	1.54748	+	1.35465i
$932$	−10.5671	−	10.5671i	−0.346138	−	0.346138i
$933$	4.31978	−	17.0820i	0.141423	−	0.559240i
$934$	−3.99266	+	2.30517i	−0.130644	+	0.0754273i
$935$	4.27946	−	2.90401i	0.139953	−	0.0949712i
$936$	15.2692	−	9.39977i	0.499090	−	0.307241i
$937$	−11.7003	−	43.6662i	−0.382233	−	1.42651i	−0.842483	−	0.538724i	$-0.818907\pi$
$937$	−11.7003	−	43.6662i	−0.382233	−	1.42651i	0.460249	−	0.887790i	$-0.347760\pi$
$938$	−29.4280	+	29.4280i	−0.960857	+	0.960857i
$939$	−36.1001	+	0.509307i	−1.17808	+	0.0166206i
$940$	2.76841	−	1.87862i	0.0902957	−	0.0612739i
$941$	40.0454	+	23.1202i	1.30544	+	0.753698i	0.981332	−	0.192321i	$-0.0616015\pi$
$941$	40.0454	+	23.1202i	1.30544	+	0.753698i	0.324111	+	0.946019i	$0.394935\pi$
$942$	−11.9320	+	12.2735i	−0.388764	+	0.399891i
$943$	11.2001	+	11.2001i	0.364725	+	0.364725i
$944$	0.204374	−	0.353985i	0.00665179	−	0.0115212i
$945$	−33.3943	+	42.1110i	−1.08632	+	1.36987i
$946$	−0.729011	+	1.26268i	−0.0237022	+	0.0410534i
$947$	−3.10306	+	11.5808i	−0.100836	+	0.376325i	−0.997840	−	0.0656983i	$-0.979072\pi$
$947$	−3.10306	+	11.5808i	−0.100836	+	0.376325i	0.897004	+	0.442023i	$0.145739\pi$
$948$	22.5797	+	5.71006i	0.733354	+	0.185454i
$949$		−	7.48140i		−	0.242857i
$950$	−16.1653	+	14.6179i	−0.524470	+	0.474269i
$951$	32.5172	−	0.458759i	1.05444	−	0.0148763i
$952$	−6.86873	−	1.84047i	−0.222617	−	0.0596500i
$953$	31.1214	+	8.33895i	1.00812	+	0.270125i	0.724844	−	0.688913i	$-0.241912\pi$
$953$	31.1214	+	8.33895i	1.00812	+	0.270125i	0.283277	+	0.959038i	$0.408578\pi$
$954$	36.9246	+	19.9513i	1.19548	+	0.645947i
$955$	26.1541	+	22.6071i	0.846327	+	0.731549i
$956$	−1.80365	−	1.04134i	−0.0583341	−	0.0336792i
$957$	17.4283	+	16.9434i	0.563377	+	0.547702i
$958$	−7.70084	−	7.70084i	−0.248803	−	0.248803i
$959$	8.74447	−	15.1459i	0.282374	−	0.489086i
$960$	2.21972	+	3.17377i	0.0716413	+	0.102433i
$961$	−24.4389			−0.788352
$962$	−36.8220	−	36.8220i	−1.18719	−	1.18719i
$963$	−1.35041	−	4.52508i	−0.0435163	−	0.145819i
$964$	18.8102	−	10.8601i	0.605837	−	0.349780i
$965$	14.4262	+	21.2591i	0.464397	+	0.684353i
$966$	−16.2285	+	9.67732i	−0.522144	+	0.311363i
$967$	−4.92486	−	1.31961i	−0.158373	−	0.0424359i	0.178761	−	0.983892i	$-0.442791\pi$
$967$	−4.92486	−	1.31961i	−0.158373	−	0.0424359i	−0.337134	+	0.941457i	$0.609458\pi$
$968$	6.17763	−	6.17763i	0.198557	−	0.198557i
$969$	3.89526	+	10.9333i	0.125134	+	0.351228i
$970$	−2.32640	−	6.69538i	−0.0746963	−	0.214976i
$971$	10.2078	−	5.89347i	0.327584	−	0.189131i	−0.327184	−	0.944961i	$-0.606100\pi$
$971$	10.2078	−	5.89347i	0.327584	−	0.189131i	0.654768	+	0.755830i	$0.272766\pi$
$972$	2.96335	−	15.3042i	0.0950495	−	0.490882i
$973$	−58.2912	+	15.6191i	−1.86873	+	0.500725i
$974$	−8.85338	−	15.3345i	−0.283681	−	0.491349i
$975$	−8.21256	−	51.1054i	−0.263013	−	1.63668i
$976$	6.81188			0.218043
$977$	7.55488	+	7.55488i	0.241702	+	0.241702i	0.817554	−	0.575852i	$-0.195330\pi$
$977$	7.55488	+	7.55488i	0.241702	+	0.241702i	−0.575852	+	0.817554i	$0.695330\pi$
$978$	11.7474	−	3.32602i	0.375641	−	0.106354i
$979$	−10.8551	−	6.26720i	−0.346931	−	0.200301i
$980$	−10.5657	−	30.4081i	−0.337510	−	0.971352i
$981$	−8.21494	+	0.231842i	−0.262283	+	0.00740215i
$982$	4.41589	+	16.4803i	0.140917	+	0.525909i
$983$	32.6225	+	8.74117i	1.04050	+	0.278800i	0.738319	−	0.674452i	$-0.235620\pi$
$983$	32.6225	+	8.74117i	1.04050	+	0.278800i	0.302177	+	0.953252i	$0.402287\pi$
$984$	5.67371	−	10.1554i	0.180871	−	0.323741i
$985$	33.4012	−	2.42968i	1.06425	−	0.0774161i
$986$	−12.4185	+	7.16985i	−0.395487	+	0.228334i
$987$	8.35598	−	8.59513i	0.265974	−	0.273586i
$988$	21.6488	−	14.4934i	0.688742	−	0.461097i
$989$	−2.28552			−0.0726753
$990$	−10.0412	+	1.01589i	−0.319130	+	0.0322871i
$991$	1.71559	+	2.97149i	0.0544975	+	0.0943924i	0.891987	−	0.452061i	$-0.149311\pi$
$991$	1.71559	+	2.97149i	0.0544975	+	0.0943924i	−0.837490	+	0.546453i	$0.815978\pi$
$992$	2.47418	−	0.662955i	0.0785553	−	0.0210488i
$993$	45.5997	+	11.5315i	1.44706	+	0.365940i
$994$	28.7354	+	16.5904i	0.911431	+	0.526215i
$995$	2.76242	−	0.959843i	0.0875747	−	0.0304291i
$996$	23.0860	−	0.325702i	0.731509	−	0.0103203i
$997$	2.01789	+	7.53085i	0.0639071	+	0.238504i	0.990490	−	0.137587i	$-0.0439346\pi$
$997$	2.01789	+	7.53085i	0.0639071	+	0.238504i	−0.926583	+	0.376091i	$0.877268\pi$
$998$	−3.76085	−	14.0357i	−0.119048	−	0.444292i
$999$	−45.2317	+	1.91543i	−1.43107	+	0.0606015i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	570.2.v.c.83.18	✓	144
3.2	odd	2	inner	570.2.v.c.83.20	yes	144
5.2	odd	4	inner	570.2.v.c.197.12	yes	144
15.2	even	4	inner	570.2.v.c.197.27	yes	144
19.11	even	3	inner	570.2.v.c.353.27	yes	144
57.11	odd	6	inner	570.2.v.c.353.12	yes	144
95.87	odd	12	inner	570.2.v.c.467.20	yes	144
285.182	even	12	inner	570.2.v.c.467.18	yes	144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.2.v.c.83.18	✓	144	1.1	even	1	trivial
570.2.v.c.83.20	yes	144	3.2	odd	2	inner
570.2.v.c.197.12	yes	144	5.2	odd	4	inner
570.2.v.c.197.27	yes	144	15.2	even	4	inner
570.2.v.c.353.12	yes	144	57.11	odd	6	inner
570.2.v.c.353.27	yes	144	19.11	even	3	inner
570.2.v.c.467.18	yes	144	285.182	even	12	inner
570.2.v.c.467.20	yes	144	95.87	odd	12	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:	\( N \)	\(=\)	\( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	570.v (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.258819 + 0.965926i) q^{2} +(1.67919 + 0.424642i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(-1.46226 + 1.69168i) q^{5} +(-0.844779 + 1.51207i) q^{6} +(3.27081 - 3.27081i) q^{7} +(0.707107 - 0.707107i) q^{8} +(2.63936 + 1.42611i) q^{9} +O(q^{10})\)	\(q+(-0.258819 + 0.965926i) q^{2} +(1.67919 + 0.424642i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(-1.46226 + 1.69168i) q^{5} +(-0.844779 + 1.51207i) q^{6} +(3.27081 - 3.27081i) q^{7} +(0.707107 - 0.707107i) q^{8} +(2.63936 + 1.42611i) q^{9} +(-1.25558 - 1.85027i) q^{10} -1.50450i q^{11} +(-1.24190 - 1.20735i) q^{12} +(5.77319 - 1.54692i) q^{13} +(2.31281 + 4.00591i) q^{14} +(-3.17377 + 2.21972i) q^{15} +(0.500000 + 0.866025i) q^{16} +(0.397886 - 1.48493i) q^{17} +(-2.06063 + 2.18032i) q^{18} +(-2.87108 + 3.27977i) q^{19} +(2.11220 - 0.733912i) q^{20} +(6.88124 - 4.10339i) q^{21} +(1.45323 + 0.389392i) q^{22} +(0.610391 + 2.27801i) q^{23} +(1.48763 - 0.887099i) q^{24} +(-0.723596 - 4.94736i) q^{25} +5.97685i q^{26} +(3.82640 + 3.51549i) q^{27} +(-4.46802 + 1.19720i) q^{28} +(-4.66388 + 8.07808i) q^{29} +(-1.32266 - 3.64013i) q^{30} -2.56146 q^{31} +(-0.965926 + 0.258819i) q^{32} +(0.638872 - 2.52633i) q^{33} +(1.33135 + 0.768656i) q^{34} +(0.750409 + 10.3160i) q^{35} +(-1.57270 - 2.55473i) q^{36} +(-6.16077 + 6.16077i) q^{37} +(-2.42493 - 3.62212i) q^{38} +(10.3512 - 0.146037i) q^{39} +(0.162228 + 2.23018i) q^{40} +(5.81640 - 3.35810i) q^{41} +(2.18258 + 7.70881i) q^{42} +(-0.250824 + 0.936089i) q^{43} +(-0.752248 + 1.30293i) q^{44} +(-6.27195 + 2.37962i) q^{45} -2.35837 q^{46} +(1.44523 - 0.387250i) q^{47} +(0.471844 + 1.66654i) q^{48} -14.3964i q^{49} +(4.96607 + 0.581532i) q^{50} +(1.29869 - 2.32452i) q^{51} +(-5.77319 - 1.54692i) q^{52} +(-3.62088 - 13.5133i) q^{53} +(-4.38605 + 2.78614i) q^{54} +(2.54513 + 2.19996i) q^{55} -4.62563i q^{56} +(-6.21382 + 4.28818i) q^{57} +(-6.59573 - 6.59573i) q^{58} +(-0.204374 - 0.353985i) q^{59} +(3.85843 - 0.335451i) q^{60} +(3.40594 - 5.89926i) q^{61} +(0.662955 - 2.47418i) q^{62} +(13.2974 - 3.96831i) q^{63} -1.00000i q^{64} +(-5.82500 + 12.0284i) q^{65} +(2.27490 + 1.27097i) q^{66} +(2.32863 + 8.69056i) q^{67} +(-1.08704 + 1.08704i) q^{68} +(0.0576237 + 4.08441i) q^{69} +(-10.1587 - 1.94513i) q^{70} +(6.21221 - 3.58662i) q^{71} +(2.87472 - 0.857897i) q^{72} +(0.323971 - 1.20908i) q^{73} +(-4.35632 - 7.54537i) q^{74} +(0.885804 - 8.61483i) q^{75} +(4.12631 - 1.40483i) q^{76} +(-4.92093 - 4.92093i) q^{77} +(-2.53802 + 10.0363i) q^{78} +(-11.6452 + 6.72339i) q^{79} +(-2.19617 - 0.420511i) q^{80} +(4.93243 + 7.52803i) q^{81} +(1.73828 + 6.48735i) q^{82} +(-9.42577 + 9.42577i) q^{83} +(-8.01103 + 0.113021i) q^{84} +(1.93022 + 2.84445i) q^{85} +(-0.839274 - 0.484555i) q^{86} +(-11.2618 + 11.5842i) q^{87} +(-1.06384 - 1.06384i) q^{88} +(4.16565 - 7.21512i) q^{89} +(-0.675237 - 6.67413i) q^{90} +(13.8233 - 23.9427i) q^{91} +(0.610391 - 2.27801i) q^{92} +(-4.30118 - 1.08770i) q^{93} +1.49622i q^{94} +(-1.35008 - 9.65284i) q^{95} +(-1.73188 + 0.0244337i) q^{96} +(3.06185 + 0.820421i) q^{97} +(13.9059 + 3.72608i) q^{98} +(2.14558 - 3.97090i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q - 4 q^{3} + 8 q^{6}+O(q^{10}) \) 144 * q - 4 * q^3 + 8 * q^6	\( 144 q - 4 q^{3} + 8 q^{6} - 16 q^{10} - 8 q^{12} - 32 q^{13} + 4 q^{15} + 72 q^{16} + 32 q^{18} - 24 q^{21} + 8 q^{22} + 40 q^{25} - 16 q^{27} - 8 q^{30} - 16 q^{33} - 16 q^{37} + 8 q^{40} - 44 q^{42} - 16 q^{43} - 56 q^{45} - 48 q^{46} + 4 q^{48} + 32 q^{51} + 32 q^{52} + 8 q^{55} - 64 q^{57} + 32 q^{58} - 24 q^{60} + 76 q^{63} + 16 q^{66} - 56 q^{67} - 8 q^{70} + 16 q^{72} + 88 q^{73} + 32 q^{75} + 48 q^{76} - 56 q^{81} - 152 q^{87} - 16 q^{88} - 4 q^{90} + 80 q^{91} - 52 q^{93} + 16 q^{96} + 32 q^{97}+O(q^{100}) \) 144 * q - 4 * q^3 + 8 * q^6 - 16 * q^10 - 8 * q^12 - 32 * q^13 + 4 * q^15 + 72 * q^16 + 32 * q^18 - 24 * q^21 + 8 * q^22 + 40 * q^25 - 16 * q^27 - 8 * q^30 - 16 * q^33 - 16 * q^37 + 8 * q^40 - 44 * q^42 - 16 * q^43 - 56 * q^45 - 48 * q^46 + 4 * q^48 + 32 * q^51 + 32 * q^52 + 8 * q^55 - 64 * q^57 + 32 * q^58 - 24 * q^60 + 76 * q^63 + 16 * q^66 - 56 * q^67 - 8 * q^70 + 16 * q^72 + 88 * q^73 + 32 * q^75 + 48 * q^76 - 56 * q^81 - 152 * q^87 - 16 * q^88 - 4 * q^90 + 80 * q^91 - 52 * q^93 + 16 * q^96 + 32 * q^97

Introduction

L-functions

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