LMFDB - Embedded newform 570.2.v.c.83.20

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			83.20
Character	$\chi$	$=$	570.83
Dual form			570.2.v.c.467.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.258819 - 0.965926i) q^{2} +(-1.66654 - 0.471844i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(1.46226 - 1.69168i) q^{5} +(-0.887099 + 1.48763i) q^{6} +(3.27081 - 3.27081i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(2.55473 + 1.57270i) q^{9} +O(q^{10})$	\(q+(0.258819 - 0.965926i) q^{2} +(-1.66654 - 0.471844i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(1.46226 - 1.69168i) q^{5} +(-0.887099 + 1.48763i) q^{6} +(3.27081 - 3.27081i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(2.55473 + 1.57270i) q^{9} +(-1.25558 - 1.85027i) q^{10} +1.50450i q^{11} +(1.20735 + 1.24190i) q^{12} +(5.77319 - 1.54692i) q^{13} +(-2.31281 - 4.00591i) q^{14} +(-3.23513 + 2.12931i) q^{15} +(0.500000 + 0.866025i) q^{16} +(-0.397886 + 1.48493i) q^{17} +(2.18032 - 2.06063i) q^{18} +(-2.87108 + 3.27977i) q^{19} +(-2.11220 + 0.733912i) q^{20} +(-6.99426 + 3.90763i) q^{21} +(1.45323 + 0.389392i) q^{22} +(-0.610391 - 2.27801i) q^{23} +(1.51207 - 0.844779i) q^{24} +(-0.723596 - 4.94736i) q^{25} -5.97685i q^{26} +(-3.51549 - 3.82640i) q^{27} +(-4.46802 + 1.19720i) q^{28} +(4.66388 - 8.07808i) q^{29} +(1.21944 + 3.67600i) q^{30} -2.56146 q^{31} +(0.965926 - 0.258819i) q^{32} +(0.709888 - 2.50731i) q^{33} +(1.33135 + 0.768656i) q^{34} +(-0.750409 - 10.3160i) q^{35} +(-1.42611 - 2.63936i) 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} +(1.96424 + 7.76731i) q^{42} +(-0.250824 + 0.936089i) q^{43} +(0.752248 - 1.30293i) q^{44} +(6.39618 - 2.02210i) q^{45} -2.35837 q^{46} +(-1.44523 + 0.387250i) q^{47} +(-0.424642 - 1.67919i) q^{48} -14.3964i q^{49} +(-4.96607 - 0.581532i) q^{50} +(1.36375 - 2.28696i) q^{51} +(-5.77319 - 1.54692i) q^{52} +(3.62088 + 13.5133i) q^{53} +(-4.60589 + 2.40536i) q^{54} +(2.54513 + 2.19996i) q^{55} +4.62563i q^{56} +(6.33232 - 4.11118i) q^{57} +(-6.59573 - 6.59573i) q^{58} +(0.204374 + 0.353985i) q^{59} +(3.86636 - 0.226468i) q^{60} +(3.40594 - 5.89926i) q^{61} +(-0.662955 + 2.47418i) q^{62} +(13.5000 - 3.21203i) q^{63} -1.00000i q^{64} +(5.82500 - 12.0284i) q^{65} +(-2.23814 - 1.33464i) 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} +(-2.91853 + 0.694400i) q^{72} +(0.323971 - 1.20908i) q^{73} +(4.35632 + 7.54537i) q^{74} +(-1.12848 + 8.58642i) q^{75} +(4.12631 - 1.40483i) q^{76} +(4.92093 + 4.92093i) q^{77} +(-2.82014 + 9.96067i) q^{78} +(-11.6452 + 6.72339i) q^{79} +(2.19617 + 0.420511i) q^{80} +(4.05325 + 8.03562i) 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} +(-11.5842 + 11.2618i) q^{87} +(-1.06384 - 1.06384i) q^{88} +(-4.16565 + 7.21512i) q^{89} +(-0.297747 - 6.70159i) q^{90} +(13.8233 - 23.9427i) q^{91} +(-0.610391 + 2.27801i) q^{92} +(4.26878 + 1.20861i) 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} +(-2.36612 + 3.84357i) 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
$3$	−1.66654	−	0.471844i	−0.962179	−	0.272419i
$3$	−1.66654	−	0.471844i	−0.962179	−	0.272419i
$4$	−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
$6$	−0.887099	+	1.48763i	−0.362157	+	0.607324i
$7$	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
$9$	2.55473	+	1.57270i	0.851575	+	0.524232i
$10$	−1.25558	−	1.85027i	−0.397050	−	0.585108i
$11$			1.50450i			0.453623i	0.973939	+	0.226811i	$0.0728301\pi$
$11$			1.50450i			0.453623i	−0.973939	+	0.226811i	$0.927170\pi$
$12$	1.20735	+	1.24190i	0.348531	+	0.358506i
$13$	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
$15$	−3.23513	+	2.12931i	−0.835307	+	0.549784i
$16$	0.500000	+	0.866025i	0.125000	+	0.216506i
$17$	−0.397886	+	1.48493i	−0.0965014	+	0.360148i	−0.997243	−	0.0742075i	$-0.976357\pi$
$17$	−0.397886	+	1.48493i	−0.0965014	+	0.360148i	0.900741	+	0.434356i	$0.143024\pi$
$18$	2.18032	−	2.06063i	0.513906	−	0.485696i
$19$	−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
$21$	−6.99426	+	3.90763i	−1.52627	+	0.852716i
$22$	1.45323	+	0.389392i	0.309830	+	0.0830187i
$23$	−0.610391	−	2.27801i	−0.127275	−	0.474998i	0.872635	−	0.488373i	$-0.162409\pi$
$23$	−0.610391	−	2.27801i	−0.127275	−	0.474998i	−0.999911	+	0.0133745i	$0.995743\pi$
$24$	1.51207	−	0.844779i	0.308650	−	0.172440i
$25$	−0.723596	−	4.94736i	−0.144719	−	0.989473i
$26$		−	5.97685i		−	1.17216i
$27$	−3.51549	−	3.82640i	−0.676557	−	0.736391i
$28$	−4.46802	+	1.19720i	−0.844375	+	0.226250i
$29$	4.66388	−	8.07808i	0.866062	−	1.50006i	7.24294e−5	−	1.00000i	$-0.499977\pi$
$29$	4.66388	−	8.07808i	0.866062	−	1.50006i	0.865989	−	0.500063i	$-0.166690\pi$
$30$	1.21944	+	3.67600i	0.222638	+	0.671143i
$31$	−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
$33$	0.709888	−	2.50731i	0.123576	−	0.436466i
$34$	1.33135	+	0.768656i	0.228325	+	0.131823i
$35$	−0.750409	−	10.3160i	−0.126842	−	1.74372i
$36$	−1.42611	−	2.63936i	−0.237685	−	0.439893i
$37$	−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	−0.879906	−	0.475147i	$-0.842395\pi$
$41$	−5.81640	+	3.35810i	−0.908370	+	0.524447i	−0.0284633	+	0.999595i	$0.509061\pi$
$42$	1.96424	+	7.76731i	0.303088	+	1.19852i
$43$	−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
$45$	6.39618	−	2.02210i	0.953486	−	0.301437i
$46$	−2.35837			−0.347723
$47$	−1.44523	+	0.387250i	−0.210809	+	0.0564861i	−0.362678	−	0.931915i	$-0.618138\pi$
$47$	−1.44523	+	0.387250i	−0.210809	+	0.0564861i	0.151869	+	0.988401i	$0.451471\pi$
$48$	−0.424642	−	1.67919i	−0.0612918	−	0.242370i
$49$		−	14.3964i		−	2.05664i
$50$	−4.96607	−	0.581532i	−0.702308	−	0.0822411i
$51$	1.36375	−	2.28696i	0.190963	−	0.320238i
$52$	−5.77319	−	1.54692i	−0.800598	−	0.214520i
$53$	3.62088	+	13.5133i	0.497366	+	1.85620i	0.516352	+	0.856376i	$0.327289\pi$
$53$	3.62088	+	13.5133i	0.497366	+	1.85620i	−0.0189862	+	0.999820i	$0.506044\pi$
$54$	−4.60589	+	2.40536i	−0.626783	+	0.327328i
$55$	2.54513	+	2.19996i	0.343186	+	0.296643i
$56$			4.62563i			0.618126i
$57$	6.33232	−	4.11118i	0.838736	−	0.544539i
$58$	−6.59573	−	6.59573i	−0.866062	−	0.866062i
$59$	0.204374	+	0.353985i	0.0266072	+	0.0460850i	0.879022	−	0.476781i	$-0.158196\pi$
$59$	0.204374	+	0.353985i	0.0266072	+	0.0460850i	−0.852415	+	0.522865i	$0.824863\pi$
$60$	3.86636	−	0.226468i	0.499144	−	0.0292370i
$61$	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
$63$	13.5000	−	3.21203i	1.70084	−	0.404678i
$64$		−	1.00000i		−	0.125000i
$65$	5.82500	−	12.0284i	0.722502	−	1.49194i
$66$	−2.23814	−	1.33464i	−0.275496	−	0.164282i
$67$	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	−0.821070	−	0.570828i	$-0.806622\pi$
$71$	−6.21221	+	3.58662i	−0.737254	+	0.425654i	0.0838162	+	0.996481i	$0.473289\pi$
$72$	−2.91853	+	0.694400i	−0.343952	+	0.0818358i
$73$	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
$75$	−1.12848	+	8.58642i	−0.130306	+	0.991474i
$76$	4.12631	−	1.40483i	0.473321	−	0.161145i
$77$	4.92093	+	4.92093i	0.560792	+	0.560792i
$78$	−2.82014	+	9.96067i	−0.319318	+	1.12782i
$79$	−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
$81$	4.05325	+	8.03562i	0.450361	+	0.892847i
$82$	1.73828	+	6.48735i	0.191961	+	0.716408i
$83$	9.42577	−	9.42577i	1.03461	−	1.03461i	0.0352334	−	0.999379i	$-0.488783\pi$
$83$	9.42577	−	9.42577i	1.03461	−	1.03461i	0.999379	−	0.0352334i	$-0.0112175\pi$
$84$	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
$87$	−11.5842	+	11.2618i	−1.24195	+	1.20740i
$88$	−1.06384	−	1.06384i	−0.113406	−	0.113406i
$89$	−4.16565	+	7.21512i	−0.441558	+	0.764801i	−0.997805	−	0.0662157i	$-0.978907\pi$
$89$	−4.16565	+	7.21512i	−0.441558	+	0.764801i	0.556247	+	0.831017i	$0.312241\pi$
$90$	−0.297747	−	6.70159i	−0.0313852	−	0.706410i
$91$	13.8233	−	23.9427i	1.44908	−	2.50988i
$92$	−0.610391	+	2.27801i	−0.0636377	+	0.237499i
$93$	4.26878	+	1.20861i	0.442652	+	0.125327i
$94$			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
$99$	−2.36612	+	3.84357i	−0.237804	+	0.386294i
$100$	−1.84703	+	4.64634i	−0.184703	+	0.464634i
$101$	7.67258	+	4.42977i	0.763450	+	0.440778i	0.830533	−	0.556969i	$-0.188036\pi$
$101$	7.67258	+	4.42977i	0.763450	+	0.440778i	−0.0670828	+	0.997747i	$0.521369\pi$
$102$	−1.85607	−	1.90919i	−0.183778	−	0.189038i
$103$	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
$105$	−3.61694	+	17.5461i	−0.352977	+	1.71232i
$106$	13.9900			1.35883
$107$	1.11305	+	1.11305i	0.107603	+	0.107603i	0.758858	−	0.651256i	$-0.225757\pi$
$107$	1.11305	+	1.11305i	0.107603	+	0.107603i	−0.651256	+	0.758858i	$0.725757\pi$
$108$	1.13131	+	5.07150i	0.108860	+	0.488006i
$109$	−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
$111$	13.1741	−	7.36026i	1.25043	−	0.698605i
$112$	4.46802	+	1.19720i	0.422188	+	0.113125i
$113$	9.39297	−	9.39297i	0.883617	−	0.883617i	−0.110284	−	0.993900i	$-0.535176\pi$
$113$	9.39297	−	9.39297i	0.883617	−	0.883617i	0.993900	+	0.110284i	$0.0351759\pi$
$114$	−2.33217	−	7.18060i	−0.218428	−	0.672525i
$115$	−4.74623	−	2.29845i	−0.442588	−	0.214332i
$116$	−8.07808	+	4.66388i	−0.750031	+	0.433031i
$117$	17.1818	+	5.12752i	1.58846	+	0.474039i
$118$	0.394819	−	0.105792i	0.0363461	−	0.00973890i
$119$	3.55552	+	6.15834i	0.325934	+	0.564534i
$120$	0.781935	−	3.79323i	0.0713806	−	0.346273i
$121$	8.73649			0.794227
$122$	−4.81673	−	4.81673i	−0.436086	−	0.436086i
$123$	11.2778	−	2.85198i	1.01688	−	0.257155i
$124$	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
$129$	0.859697	−	1.44168i	0.0756921	−	0.126933i
$130$	−10.1109	−	8.73971i	−0.886789	−	0.766523i
$131$	2.17528	−	1.25590i	0.190055	−	0.109729i	−0.401953	−	0.915660i	$-0.631668\pi$
$131$	2.17528	−	1.25590i	0.190055	−	0.109729i	0.592009	+	0.805932i	$0.298335\pi$
$132$	−1.86843	+	1.81645i	−0.162626	+	0.158101i
$133$	1.33676	+	20.1183i	0.115912	+	1.74448i
$134$	8.99713			0.777234
$135$	−11.6136	+	0.351916i	−0.999541	+	0.0302881i
$136$	−0.768656	−	1.33135i	−0.0659117	−	0.114162i
$137$	−3.65205	+	0.978564i	−0.312016	+	0.0836043i	−0.411429	−	0.911442i	$-0.634970\pi$
$137$	−3.65205	+	0.978564i	−0.312016	+	0.0836043i	0.0994132	+	0.995046i	$0.468303\pi$
$138$	3.93032	+	1.11278i	0.334571	+	0.0947264i
$139$	−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
$147$	−6.79288	+	23.9923i	−0.560267	+	1.97885i
$148$	8.41576	−	2.25500i	0.691772	−	0.185360i
$149$	3.50391	+	6.06896i	0.287052	+	0.497188i	0.973105	−	0.230363i	$-0.0739915\pi$
$149$	3.50391	+	6.06896i	0.287052	+	0.497188i	−0.686053	+	0.727552i	$0.740658\pi$
$150$	8.00177	+	3.31236i	0.653342	+	0.270453i
$151$	−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
$153$	−3.35183	+	3.16783i	−0.270980	+	0.256104i
$154$	6.02688	−	3.47962i	0.485660	−	0.280396i
$155$	−3.74552	+	4.33318i	−0.300847	+	0.348050i
$156$	8.89137	+	5.30206i	0.711879	+	0.424505i
$157$	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
$162$	8.81087	−	1.83537i	0.692247	−	0.144200i
$163$	−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
$165$	−3.20353	−	4.86724i	−0.249395	−	0.378914i
$166$	−6.66502	−	11.5442i	−0.517306	−	0.896001i
$167$	12.8441	−	3.44157i	0.993906	−	0.266316i	0.275016	−	0.961440i	$-0.411317\pi$
$167$	12.8441	−	3.44157i	0.993906	−	0.266316i	0.718890	+	0.695123i	$0.244650\pi$
$168$	2.18258	−	7.70881i	0.168389	−	0.594747i
$169$	19.6785	−	11.3614i	1.51373	−	0.873952i
$170$	3.24710	−	1.12825i	0.249042	−	0.0865330i
$171$	−12.4929	+	3.86358i	−0.955356	+	0.295456i
$172$	0.685264	−	0.685264i	0.0522509	−	0.0522509i
$173$	10.9463	+	2.93305i	0.832232	+	0.222996i	0.649687	−	0.760202i	$-0.274900\pi$
$173$	10.9463	+	2.93305i	0.832232	+	0.222996i	0.182545	+	0.983198i	$0.441567\pi$
$174$	7.87990	+	14.1042i	0.597374	+	1.06924i
$175$	−18.5487	−	13.8152i	−1.40215	−	1.04433i
$176$	−1.30293	+	0.752248i	−0.0982122	+	0.0567028i
$177$	−0.173571	−	0.686364i	−0.0130464	−	0.0515903i
$178$	5.89112	+	5.89112i	0.441558	+	0.441558i
$179$	3.81727			0.285316			0.142658	−	0.989772i	$-0.454435\pi$
$179$	3.81727			0.285316			0.142658	+	0.989772i	$0.454435\pi$
$180$	−6.55030	−	1.44690i	−0.488231	−	0.107845i
$181$	−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
$183$	−8.45968	+	8.22430i	−0.625358	+	0.607958i
$184$	2.04241	+	1.17919i	0.150568	+	0.0869307i
$185$	1.41344	+	19.4307i	0.103918	+	1.42857i
$186$	2.27227	−	3.81052i	0.166611	−	0.279401i
$187$	−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	$0.188944\pi$
$191$			15.4604i			1.11867i	−0.828940	+	0.559337i	$0.811056\pi$
$192$	−0.471844	+	1.66654i	−0.0340524	+	0.120272i
$193$	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
$195$	−15.3832	+	17.2974i	−1.10161	+	1.23869i
$196$	−7.19822	+	12.4677i	−0.514159	+	0.890549i
$197$	10.5903	+	10.5903i	0.754527	+	0.754527i	0.975321	−	0.220794i	$-0.0708648\pi$
$197$	10.5903	+	10.5903i	0.754527	+	0.754527i	−0.220794	+	0.975321i	$0.570865\pi$
$198$	3.10021	+	3.28028i	0.220322	+	0.233120i
$199$	−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
$204$	−2.32452	+	1.29869i	−0.162749	+	0.0909264i
$205$	−2.82424	+	14.7499i	−0.197253	+	1.03018i
$206$	2.04009	−	1.17784i	0.142140	−	0.0820643i
$207$	2.02324	−	6.77965i	0.140625	−	0.471218i
$208$	4.22627	+	4.22627i	0.293039	+	0.293039i
$209$	−4.93440	−	4.31953i	−0.341320	−	0.298788i
$210$	16.0121	+	8.03495i	1.10494	+	0.554464i
$211$	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
$213$	12.0452	−	3.04606i	0.825326	−	0.208713i
$214$	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
$219$	−1.11041	+	1.86212i	−0.0750344	+	0.125830i
$220$	−1.10417	−	3.17779i	−0.0744430	−	0.214247i
$221$			9.18828i			0.618071i
$222$	−3.69975	−	14.6302i	−0.248311	−	0.981913i
$223$	−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
$225$	5.93211	−	13.7772i	0.395474	−	0.918477i
$226$	−6.64184	−	11.5040i	−0.441808	−	0.765234i
$227$	−11.1096	−	11.1096i	−0.737368	−	0.737368i	0.234700	−	0.972068i	$-0.424589\pi$
$227$	−11.1096	−	11.1096i	−0.737368	−	0.737368i	−0.972068	+	0.234700i	$0.924589\pi$
$228$	−7.53953	+	0.394226i	−0.499318	+	0.0261083i
$229$		−	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
$231$	−5.87902	−	10.5228i	−0.386811	−	0.692352i
$232$	2.41420	+	9.00993i	0.158500	+	0.591531i
$233$	−14.4350	−	3.86784i	−0.945668	−	0.253391i	−0.247145	−	0.968979i	$-0.579492\pi$
$233$	−14.4350	−	3.86784i	−0.945668	−	0.253391i	−0.698523	+	0.715588i	$0.746159\pi$
$234$	9.39977	−	15.2692i	0.614482	−	0.998180i
$235$	−1.45820	+	3.01114i	−0.0951227	+	0.196425i
$236$		−	0.408747i		−	0.0266072i
$237$	22.5797	−	5.71006i	1.46671	−	0.370909i
$238$	6.86873	−	1.84047i	0.445234	−	0.119300i
$239$	−2.08267			−0.134717			−0.0673585	−	0.997729i	$-0.521457\pi$
$239$	−2.08267			−0.134717			−0.0673585	+	0.997729i	$0.521457\pi$
$240$	−3.46160	−	1.73705i	−0.223445	−	0.112126i
$241$	−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
$243$	−2.96335	−	15.3042i	−0.190099	−	0.981765i
$244$	−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
$249$	−20.1559	+	11.2609i	−1.27733	+	0.713633i
$250$	−8.24545	+	7.55067i	−0.521488	+	0.477546i
$251$	22.9496	+	13.2500i	1.44857	+	0.836331i	0.998396	−	0.0566115i	$-0.0180296\pi$
$251$	22.9496	+	13.2500i	1.44857	+	0.836331i	0.450171	+	0.892942i	$0.351363\pi$
$252$	−13.2974	−	3.96831i	−0.837657	−	0.249980i
$253$	3.42726	−	0.918331i	0.215470	−	0.0577350i
$254$	−12.1218			−0.760592
$255$	−1.87466	−	5.65116i	−0.117396	−	0.353889i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	0.927986	−	0.248653i	0.0578862	−	0.0155106i	−0.229760	−	0.973247i	$-0.573794\pi$
$257$	0.927986	−	0.248653i	0.0578862	−	0.0155106i	0.287646	+	0.957737i	$0.407127\pi$
$258$	−1.17005	−	1.20354i	−0.0728442	−	0.0749290i
$259$			40.3014i			2.50421i
$260$	−11.0588	+	7.50442i	−0.685838	+	0.465405i
$261$	24.6193	−	13.3024i	1.52390	−	0.823399i
$262$	−0.650102	−	2.42621i	−0.0401635	−	0.149892i
$263$	8.13123	+	2.17876i	0.501393	+	0.134348i	0.500647	−	0.865652i	$-0.333096\pi$
$263$	8.13123	+	2.17876i	0.501393	+	0.134348i	0.000746739		1.00000i	$0.499762\pi$
$264$	1.27097	+	2.27490i	0.0782226	+	0.140010i
$265$	28.1549	+	13.6346i	1.72954	+	0.837565i
$266$	19.7788	+	3.91578i	1.21271	+	0.240092i
$267$	10.3466	−	10.0588i	0.633205	−	0.615586i
$268$	2.32863	−	8.69056i	0.142244	−	0.530861i
$269$	−2.25938	−	3.91336i	−0.137757	−	0.238602i	0.788890	−	0.614534i	$-0.210656\pi$
$269$	−2.25938	−	3.91336i	−0.137757	−	0.238602i	−0.926647	+	0.375932i	$0.877323\pi$
$270$	−2.66590	+	11.3090i	−0.162242	+	0.688242i
$271$	−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
$273$	−34.3344	+	33.3791i	−2.07801	+	2.02020i
$274$			3.78088i			0.228411i
$275$	7.44329	−	1.08865i	0.448847	−	0.0656479i
$276$	2.09211	−	3.50839i	0.125930	−	0.211180i
$277$	−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
$279$	−6.54383	−	4.02840i	−0.391769	−	0.241174i
$280$	7.82511	+	6.76387i	0.467640	+	0.404219i
$281$	−21.7381	−	12.5505i	−1.29679	−	0.748700i	−0.316939	−	0.948446i	$-0.602655\pi$
$281$	−21.7381	−	12.5505i	−1.29679	−	0.748700i	−0.979848	+	0.199746i	$0.935988\pi$
$282$	0.705982	−	2.49351i	0.0420406	−	0.148486i
$283$	−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
$285$	2.30467	−	16.7239i	0.136517	−	0.990638i
$286$	8.99215			0.531717
$287$	−8.04065	+	30.0081i	−0.474624	+	1.77132i
$288$	2.87472	+	0.857897i	0.169394	+	0.0505520i
$289$	12.6757	+	7.31834i	0.745631	+	0.430490i
$290$	−20.8026	+	1.51323i	−1.22157	+	0.0888599i
$291$	−4.71560	−	2.81199i	−0.276433	−	0.164841i
$292$	−0.885106	+	0.885106i	−0.0517969	+	0.0517969i
$293$	6.80530	−	6.80530i	0.397570	−	0.397570i	−0.479805	−	0.877375i	$-0.659293\pi$
$293$	6.80530	−	6.80530i	0.397570	−	0.397570i	0.877375	+	0.479805i	$0.159293\pi$
$294$	21.4166	+	12.7711i	1.24904	+	0.744825i
$295$	0.897679	+	0.171883i	0.0522649	+	0.0100074i
$296$		−	8.71264i		−	0.506412i
$297$	5.75680	−	5.28904i	0.334043	−	0.306901i
$298$	6.76904	−	1.81376i	0.392120	−	0.105068i
$299$	−7.04781	−	12.2072i	−0.407586	−	0.705959i
$300$	5.27050	−	6.87181i	0.304293	−	0.396744i
$301$	2.24137	+	3.88217i	0.129191	+	0.223765i
$302$	−4.68018	+	17.4667i	−0.269314	+	1.00509i
$303$	−10.6965	−	11.0027i	−0.614499	−	0.632086i
$304$	−4.27591	−	0.846541i	−0.245240	−	0.0485524i
$305$	−4.99933	−	14.3880i	−0.286261	−	0.823856i
$306$	2.19237	+	4.05752i	0.125330	+	0.231953i
$307$	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
$309$	−1.99004	−	3.56196i	−0.113209	−	0.202633i
$310$	3.21612	+	4.73940i	0.182663	+	0.269180i
$311$			10.1728i			0.576844i	0.957503	+	0.288422i	$0.0931307\pi$
$311$			10.1728i			0.576844i	−0.957503	+	0.288422i	$0.906869\pi$
$312$	7.42265	−	7.21613i	0.420225	−	0.408533i
$313$	−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
$315$	14.3068	−	27.5346i	0.806097	−	1.55140i
$316$	13.4468			0.756440
$317$	−18.1359	+	4.85951i	−1.01861	+	0.272937i	−0.729225	−	0.684274i	$-0.760119\pi$
$317$	−18.1359	+	4.85951i	−1.01861	+	0.272937i	−0.289390	+	0.957211i	$0.593452\pi$
$318$	−23.3149	−	6.60111i	−1.30744	−	0.370172i
$319$	12.1534	+	7.01679i	0.680462	+	0.392865i
$320$	−1.69168	−	1.46226i	−0.0945681	−	0.0817428i
$321$	−1.32976	−	2.38014i	−0.0742200	−	0.132846i
$322$	−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
$327$	4.59998	−	1.16327i	0.254379	−	0.0643287i
$328$	1.73828	−	6.48735i	0.0959805	−	0.358204i
$329$	−3.46047	+	5.99372i	−0.190782	+	0.330444i
$330$	−5.53052	+	1.83464i	−0.304445	+	0.100994i
$331$	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
$333$	−25.4281	+	6.05005i	−1.39345	+	0.331541i
$334$		−	13.2972i		−	0.727590i
$335$	18.1068	+	8.76855i	0.989278	+	0.479077i
$336$	−6.88124	−	4.10339i	−0.375403	−	0.223858i
$337$	−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
$339$	−20.0858	+	11.2218i	−1.09091	+	0.609483i
$340$	−0.249396	−	3.42847i	−0.0135254	−	0.185935i
$341$		−	3.85371i		−	0.208690i
$342$	0.498533	+	13.0672i	0.0269576	+	0.706593i
$343$	−24.1924	−	24.1924i	−1.30627	−	1.30627i
$344$	−0.484555	−	0.839274i	−0.0261255	−	0.0452506i
$345$	6.82527	+	6.06995i	0.367460	+	0.326795i
$346$	5.66622	−	9.81418i	0.304618	−	0.527614i
$347$	3.30561	−	12.3367i	0.177454	−	0.662269i	−0.818666	−	0.574270i	$-0.805286\pi$
$347$	3.30561	−	12.3367i	0.177454	−	0.662269i	0.996121	−	0.0879993i	$-0.0280473\pi$
$348$	15.6631	−	3.96096i	0.839630	−	0.212330i
$349$		−	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
$351$	−26.2148	−	16.6523i	−1.39924	−	0.888837i
$352$	0.389392	+	1.45323i	0.0207547	+	0.0774575i
$353$	9.16982	−	9.16982i	0.488060	−	0.488060i	−0.419633	−	0.907694i	$-0.637841\pi$
$353$	9.16982	−	9.16982i	0.488060	−	0.488060i	0.907694	+	0.419633i	$0.137841\pi$
$354$	−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
$357$	−3.01964	−	11.9408i	−0.159817	−	0.631973i
$358$	0.987982	−	3.68720i	0.0522165	−	0.194875i
$359$	−2.39602	−	4.15003i	−0.126457	−	0.219030i	0.795844	−	0.605501i	$-0.207027\pi$
$359$	−2.39602	−	4.15003i	−0.126457	−	0.219030i	−0.922302	+	0.386471i	$0.873694\pi$
$360$	−3.09294	+	5.95262i	−0.163012	+	0.313731i
$361$	−2.51382	−	18.8330i	−0.132306	−	0.991209i
$362$	3.22962	+	3.22962i	0.169745	+	0.169745i
$363$	−14.5597	−	4.12226i	−0.764188	−	0.216363i
$364$	−23.9427	+	13.8233i	−1.25494	+	0.724540i
$365$	−1.57165	−	2.31604i	−0.0822638	−	0.121227i
$366$	5.75454	+	10.3000i	0.300794	+	0.538391i
$367$	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
$372$	−3.09257	−	3.18108i	−0.160342	−	0.164931i
$373$	−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
$375$	12.8754	+	14.4646i	0.664881	+	0.746949i
$376$	0.748109	−	1.29576i	0.0385808	−	0.0668238i
$377$	14.4293	−	53.8510i	0.743149	−	2.77347i
$378$	−7.19754	+	22.9325i	−0.370201	+	1.17952i
$379$		−	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	0.908255	−	0.418416i	$-0.137415\pi$
$383$	29.0741	+	7.79039i	1.48562	+	0.398071i	0.577364	+	0.816487i	$0.304081\pi$
$384$	1.48763	+	0.887099i	0.0759155	+	0.0452696i
$385$	15.5203	−	1.12899i	0.790989	−	0.0575385i
$386$	−9.95035	−	5.74484i	−0.506460	−	0.292405i
$387$	−2.11297	+	1.99698i	−0.107408	+	0.101512i
$388$	−2.24143	−	2.24143i	−0.113792	−	0.113792i
$389$	5.27510	−	9.13674i	0.267458	−	0.463251i	−0.700747	−	0.713410i	$-0.747150\pi$
$389$	5.27510	−	9.13674i	0.267458	−	0.463251i	0.968205	+	0.250159i	$0.0804829\pi$
$390$	12.7265	+	19.3359i	0.644433	+	0.979110i
$391$	3.62555			0.183352
$392$	10.1798	+	10.1798i	0.514159	+	0.514159i
$393$	−4.21779	+	1.06662i	−0.212760	+	0.0538037i
$394$	12.9704	−	7.48846i	0.653439	−	0.377263i
$395$	−5.65452	+	29.5314i	−0.284510	+	1.48589i
$396$	3.97090	−	2.14558i	0.199545	−	0.107819i
$397$	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
$399$	7.26493	−	34.1587i	0.363701	−	1.71008i
$400$	3.92274	−	3.10033i	0.196137	−	0.155017i
$401$	−21.9425	+	12.6685i	−1.09576	+	0.632636i	−0.935103	−	0.354375i	$-0.884694\pi$
$401$	−21.9425	+	12.6685i	−1.09576	+	0.632636i	−0.160654	+	0.987011i	$0.551360\pi$
$402$	−14.9941	−	4.24525i	−0.747838	−	0.211734i
$403$	−14.7878	+	3.96238i	−0.736633	+	0.197380i
$404$	−4.42977	−	7.67258i	−0.220389	−	0.381725i
$405$	19.5206	+	4.89334i	0.969988	+	0.243152i
$406$	−43.1468			−2.14134
$407$	−9.26885	−	9.26885i	−0.459440	−	0.459440i
$408$	0.652807	+	2.58144i	0.0323188	+	0.127800i
$409$	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
$414$	−6.02499	−	3.70900i	−0.296112	−	0.182287i
$415$	−2.16251	−	29.7283i	−0.106154	−	1.45931i
$416$	5.17610	−	2.98843i	0.253779	−	0.146520i
$417$	15.7514	+	16.2022i	0.771351	+	0.793427i
$418$	−5.44946	+	3.64829i	−0.266542	+	0.178444i
$419$	2.91774			0.142541			0.0712704	−	0.997457i	$-0.477295\pi$
$419$	2.91774			0.142541			0.0712704	+	0.997457i	$0.477295\pi$
$420$	11.9054	−	13.3869i	0.580924	−	0.653212i
$421$	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
$423$	−4.30121	−	1.28360i	−0.209132	−	0.0624108i
$424$	−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	0.276047	−	0.961144i	$-0.410976\pi$
$431$	−8.68424	−	5.01385i	−0.418305	−	0.241509i	−0.694352	+	0.719636i	$0.744309\pi$
$432$	1.55601	−	4.95770i	0.0748637	−	0.238528i
$433$	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
$435$	2.11245	+	36.0645i	0.101284	+	1.72916i
$436$	2.73940			0.131194
$437$	9.22384	+	4.53840i	0.441236	+	0.217101i
$438$	1.51127	+	1.55452i	0.0722113	+	0.0742780i
$439$	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
$441$	22.6412	−	36.7790i	1.07815	−	1.75138i
$442$	8.87520	+	2.37810i	0.422150	+	0.113115i
$443$	2.85504	+	10.6552i	0.135647	+	0.506242i	0.999994	+	0.00334646i	$0.00106521\pi$
$443$	2.85504	+	10.6552i	0.135647	+	0.506242i	−0.864347	+	0.502895i	$0.832268\pi$
$444$	−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
$447$	−2.97582	−	11.7675i	−0.140751	−	0.556582i
$448$	−3.27081	−	3.27081i	−0.154531	−	0.154531i
$449$	−19.4772			−0.919186			−0.459593	−	0.888130i	$-0.652005\pi$
$449$	−19.4772			−0.919186			−0.459593	+	0.888130i	$0.652005\pi$
$450$	−11.7724	−	9.29577i	−0.554955	−	0.438207i
$451$	−5.05225	−	8.75075i	−0.237901	−	0.412057i
$452$	−12.8310	+	3.43807i	−0.603521	+	0.161713i
$453$	30.1358	+	8.53227i	1.41590	+	0.400881i
$454$	−13.6064	+	7.85565i	−0.638579	+	0.368684i
$455$	−20.2903	−	58.3952i	−0.951222	−	2.73761i
$456$	−1.57058	+	7.38466i	−0.0735492	+	0.345819i
$457$	−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
$459$	7.08069	−	3.69779i	0.330498	−	0.172598i
$460$	2.96113	+	4.36363i	0.138063	+	0.203455i
$461$	−3.68820	+	2.12939i	−0.171777	+	0.0991754i	−0.583423	−	0.812168i	$-0.698287\pi$
$461$	−3.68820	+	2.12939i	−0.171777	+	0.0991754i	0.411647	+	0.911344i	$0.364954\pi$
$462$	−11.6859	+	2.95519i	−0.543677	+	0.137488i
$463$	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
$465$	8.28665	−	5.45413i	0.384284	−	0.252929i
$466$	−7.47210	+	12.9421i	−0.346138	+	0.599529i
$467$	−3.26000	−	3.26000i	−0.150855	−	0.150855i	0.627645	−	0.778500i	$-0.284019\pi$
$467$	−3.26000	−	3.26000i	−0.150855	−	0.150855i	−0.778500	+	0.627645i	$0.784019\pi$
$468$	−12.3161	−	13.0314i	−0.569311	−	0.602379i
$469$	36.0417	+	20.8087i	1.66425	+	0.960857i
$470$	2.53113	+	2.18786i	0.116752	+	0.100918i
$471$	−14.7020	−	8.76703i	−0.677432	−	0.403963i
$472$	−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
$477$	−12.0020	+	40.2174i	−0.549533	+	1.84143i
$478$	−0.539035	+	2.01171i	−0.0246549	+	0.0920134i
$479$	5.44532	−	9.43157i	0.248803	−	0.430939i	−0.714391	−	0.699747i	$-0.753296\pi$
$479$	5.44532	−	9.43157i	0.248803	−	0.430939i	0.963194	+	0.268807i	$0.0866295\pi$
$480$	−2.57379	+	2.89406i	−0.117477	+	0.132095i
$481$	−26.0371	+	45.0975i	−1.18719	+	2.05627i
$482$	15.3585	+	15.3585i	0.699560	+	0.699560i
$483$	13.1709	+	13.5478i	0.599295	+	0.616447i
$484$	−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
$489$	5.95483	+	10.6585i	0.269287	+	0.481996i
$490$	−26.6374	+	18.0759i	−1.20335	+	0.816587i
$491$	−14.7759	+	8.53085i	−0.666826	+	0.384992i	−0.794873	−	0.606776i	$-0.792462\pi$
$491$	−14.7759	+	8.53085i	−0.666826	+	0.384992i	0.128047	+	0.991768i	$0.459129\pi$
$492$	−11.1928	−	3.16900i	−0.504612	−	0.142870i
$493$	10.1397	+	10.1397i	0.456669	+	0.456669i
$494$	19.6027	+	17.1600i	0.881968	+	0.772065i
$495$	3.04224	+	9.62302i	0.136739	+	0.432523i
$496$	−1.28073	−	2.21829i	−0.0575065	−	0.0996041i
$497$	−8.58781	+	32.0502i	−0.385216	+	1.43765i
$498$	5.66050	+	22.3837i	0.253653	+	1.00304i
$499$	−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	0.985698	−	0.168520i	$-0.0538987\pi$
$503$	1.07201	+	4.00081i	0.0477987	+	0.178387i	−0.937900	+	0.346907i	$0.887232\pi$
$504$	−7.27471	+	11.8172i	−0.324041	+	0.526381i
$505$	18.7131	−	6.50212i	0.832721	−	0.289341i
$506$		−	3.54816i		−	0.157735i
$507$	−38.1558	+	9.64903i	−1.69456	+	0.428528i
$508$	−3.13737	+	11.7088i	−0.139198	+	0.519494i
$509$	−13.2715	+	22.9870i	−0.588250	+	1.01888i	0.406212	+	0.913779i	$0.366850\pi$
$509$	−13.2715	+	22.9870i	−0.588250	+	1.01888i	−0.994462	+	0.105100i	$0.966484\pi$
$510$	−5.94380	+	0.348153i	−0.263196	+	0.0154165i
$511$	−2.89502	−	5.01432i	−0.128068	−	0.221820i
$512$	0.707107	+	0.707107i	0.0312500	+	0.0312500i
$513$	22.6430	−	0.544120i	0.999711	−	0.0240235i
$514$		−	0.960722i		−	0.0423756i
$515$	5.25360	−	0.382160i	0.231501	−	0.0168400i
$516$	−1.46536	+	0.818684i	−0.0645089	+	0.0360405i
$517$	−0.582615	−	2.17435i	−0.0256234	−	0.0956278i
$518$	38.9282	+	10.4308i	1.71041	+	0.458302i
$519$	−16.8585	−	10.0530i	−0.740007	−	0.441278i
$520$	4.38649	+	12.6243i	0.192360	+	0.553611i
$521$		−	7.38031i		−	0.323337i	−0.986845	−	0.161669i	$-0.948312\pi$
$521$		−	7.38031i		−	0.323337i	0.986845	−	0.161669i	$-0.0516876\pi$
$522$	−6.47720	−	27.2234i	−0.283499	−	1.19153i
$523$	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
$525$	24.3935	+	31.7756i	1.06462	+	1.38680i
$526$	4.20904	−	7.29026i	0.183523	−	0.317871i
$527$	1.01917	−	3.80359i	0.0443957	−	0.165687i
$528$	2.52633	−	0.638872i	0.109945	−	0.0278033i
$529$	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
$534$	−7.03811	−	12.5975i	−0.304569	−	0.545147i
$535$	3.51050	−	0.255363i	0.151772	−	0.0110403i
$536$	−7.79175	−	4.49857i	−0.336552	−	0.194308i
$537$	−6.36164	−	1.80116i	−0.274525	−	0.0777256i
$538$	−4.36479	+	1.16954i	−0.188179	+	0.0504225i
$539$	21.6594			0.932936
$540$	10.2336	+	5.50204i	0.440386	+	0.236770i
$541$	−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
$543$	5.67222	−	5.51439i	0.243418	−	0.236645i
$544$			1.53731i			0.0659117i
$545$	−1.15195	+	6.01620i	−0.0493441	+	0.257706i
$546$	23.3553	+	41.8037i	0.999517	+	1.78903i
$547$	−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
$549$	17.9790	−	9.71449i	0.767325	−	0.414604i
$550$	0.874913	−	7.47143i	0.0373064	−	0.318583i
$551$	13.1039	+	38.4893i	0.558245	+	1.63970i
$552$	−2.84737	−	2.92886i	−0.121192	−	0.124661i
$553$	−16.0985	+	60.0804i	−0.684577	+	2.55488i
$554$	2.96610	+	5.13743i	0.126017	+	0.218268i
$555$	6.81272	−	33.0490i	0.289184	−	1.40285i
$556$	6.52316	+	11.2985i	0.276644	+	0.479161i
$557$	−12.6530	+	3.39037i	−0.536126	+	0.143655i	−0.516716	−	0.856157i	$-0.672846\pi$
$557$	−12.6530	+	3.39037i	−0.536126	+	0.143655i	−0.0194103	+	0.999812i	$0.506179\pi$
$558$	−5.58480	+	5.27823i	−0.236424	+	0.223445i
$559$			5.79223i			0.244985i
$560$	8.55868	−	5.80786i	0.361670	−	0.245427i
$561$	3.44072	+	2.05175i	0.145267	+	0.0866251i
$562$	−17.7491	+	17.7491i	−0.748700	+	0.748700i
$563$	3.51411	−	3.51411i	0.148102	−	0.148102i	−0.629168	−	0.777270i	$-0.716604\pi$
$563$	3.51411	−	3.51411i	0.148102	−	0.148102i	0.777270	+	0.629168i	$0.216604\pi$
$564$	−2.22582	−	1.32729i	−0.0937241	−	0.0558891i
$565$	−2.15499	−	29.6249i	−0.0906611	−	1.24633i
$566$	18.2607	+	10.5428i	0.767553	+	0.443147i
$567$	39.5404	+	13.0256i	1.66054	+	0.547023i
$568$	1.85657	−	6.92882i	0.0779000	−	0.290727i
$569$	22.6874			0.951107			0.475554	−	0.879687i	$-0.342248\pi$
$569$	22.6874			0.951107			0.475554	+	0.879687i	$0.342248\pi$
$570$	−15.5575	−	6.55460i	−0.651634	−	0.274542i
$571$	−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
$573$	7.29490	−	25.7654i	0.304749	−	1.07636i
$574$	26.9045	+	15.5333i	1.12297	+	0.648349i
$575$	−10.8285	+	4.66819i	−0.451578	+	0.194677i
$576$	1.57270	−	2.55473i	0.0655290	−	0.106447i
$577$	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
$579$	−10.1925	+	17.0924i	−0.423585	+	0.710337i
$580$	−3.92243	+	20.4854i	−0.162870	+	0.850609i
$581$		−	61.6599i		−	2.55808i
$582$	−3.93666	+	3.82712i	−0.163180	+	0.158639i
$583$	−20.3307	+	5.44760i	−0.842012	+	0.225617i
$584$	0.625865	+	1.08403i	0.0258985	+	0.0448575i
$585$	33.7984	−	21.5684i	1.39739	−	0.891743i
$586$	−4.81207	−	8.33476i	−0.198785	−	0.344306i
$587$	2.69293	−	10.0501i	0.111149	−	0.414814i	−0.887821	−	0.460189i	$-0.847782\pi$
$587$	2.69293	−	10.0501i	0.111149	−	0.414814i	0.998970	+	0.0453750i	$0.0144483\pi$
$588$	17.8790	−	17.3815i	0.737316	−	0.716801i
$589$	7.35415	−	8.40101i	0.303023	−	0.346157i
$590$	0.398362	−	0.822605i	0.0164003	−	0.0338661i
$591$	−12.6522	−	22.6461i	−0.520442	−	0.931537i
$592$	−8.41576	−	2.25500i	−0.345886	−	0.0926798i
$593$	−5.73743	−	21.4124i	−0.235608	−	0.879302i	−0.977874	−	0.209196i	$-0.932915\pi$
$593$	−5.73743	−	21.4124i	−0.235608	−	0.879302i	0.742266	−	0.670106i	$-0.233751\pi$
$594$	−3.61885	−	6.92955i	−0.148483	−	0.284323i
$595$	15.6171	+	2.99027i	0.640237	+	0.122589i
$596$		−	7.00783i		−	0.287052i
$597$	1.57902	+	1.62421i	0.0646250	+	0.0664746i
$598$	−13.6153	+	3.64822i	−0.556772	+	0.149187i
$599$	10.2909	−	17.8244i	0.420475	−	0.728284i	−0.575511	−	0.817794i	$-0.695197\pi$
$599$	10.2909	−	17.8244i	0.420475	−	0.728284i	0.995986	+	0.0895103i	$0.0285302\pi$
$600$	−5.27355	−	6.86947i	−0.215292	−	0.280445i
$601$	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
$603$	−7.71861	+	25.8642i	−0.314326	+	1.05327i
$604$	15.6602	+	9.04141i	0.637204	+	0.367890i
$605$	12.7750	−	14.7794i	0.519378	−	0.600868i
$606$	−13.3962	+	7.48435i	−0.544184	+	0.304031i
$607$	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
$612$	4.48669	−	1.06751i	0.181364	−	0.0431515i
$613$	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
$615$	11.6664	−	23.2488i	0.470434	−	0.937482i
$616$	−6.95924			−0.280396
$617$	−21.2202	+	5.68594i	−0.854294	+	0.228908i	−0.659284	−	0.751894i	$-0.729141\pi$
$617$	−21.2202	+	5.68594i	−0.854294	+	0.228908i	−0.195010	+	0.980801i	$0.562474\pi$
$618$	−3.95565	+	1.00032i	−0.159120	+	0.0402389i
$619$			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
$621$	−6.57075	+	10.3439i	−0.263675	+	0.415087i
$622$	9.82613	+	2.63290i	0.393992	+	0.105570i
$623$	9.97424	+	37.2244i	0.399610	+	1.49136i
$624$	−5.04912	−	9.03740i	−0.202126	−	0.361786i
$625$	−23.9528	+	7.15978i	−0.958113	+	0.286391i
$626$			20.8445i			0.833112i
$627$	6.18525	+	9.52694i	0.247015	+	0.380469i
$628$	−6.98820	−	6.98820i	−0.278859	−	0.278859i
$629$	−6.69702	−	11.5996i	−0.267028	−	0.462506i
$630$	−22.8935	−	20.9458i	−0.912100	−	0.834500i
$631$	−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
$633$	−7.16288	−	28.3247i	−0.284699	−	1.12580i
$634$			18.7757i			0.745678i
$635$	−24.3953	−	11.8139i	−0.968096	−	0.468819i
$636$	−12.4105	+	20.8120i	−0.492109	+	0.825250i
$637$	−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	−0.924070	−	0.382222i	$-0.875159\pi$
$641$	−26.7128	+	15.4226i	−1.05509	+	0.609157i	−0.131021	+	0.991380i	$0.541825\pi$
$642$	−2.64320	+	0.668426i	−0.104319	+	0.0263807i
$643$	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
$645$	−1.18177	−	3.56245i	−0.0465322	−	0.140271i
$646$	−6.34343	+	2.15966i	−0.249579	+	0.0849706i
$647$	33.1488	+	33.1488i	1.30322	+	1.30322i	0.926212	+	0.377004i	$0.123046\pi$
$647$	33.1488	+	33.1488i	1.30322	+	1.30322i	0.377004	+	0.926212i	$0.376954\pi$
$648$	−8.54812	−	2.81596i	−0.335802	−	0.110621i
$649$	−0.532569	+	0.307479i	−0.0209052	+	0.0120696i
$650$	−29.5697	+	4.32482i	−1.15982	+	0.169634i
$651$	17.9155	−	10.0093i	0.702165	−	0.392293i
$652$	1.82441	+	6.80879i	0.0714494	+	0.266653i
$653$	11.6345	−	11.6345i	0.455293	−	0.455293i	−0.441814	−	0.897107i	$-0.645665\pi$
$653$	11.6345	−	11.6345i	0.455293	−	0.455293i	0.897107	+	0.441814i	$0.145665\pi$
$654$	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
$657$	2.72917	−	2.57935i	0.106475	−	0.100630i
$658$	4.89385	+	4.89385i	0.190782	+	0.190782i
$659$	−7.58062	+	13.1300i	−0.295299	+	0.511473i	−0.975054	−	0.221966i	$-0.928753\pi$
$659$	−7.58062	+	13.1300i	−0.295299	+	0.511473i	0.679755	+	0.733439i	$0.262086\pi$
$660$	0.340721	+	5.81692i	0.0132625	+	0.226423i
$661$	−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
$663$	4.33544	−	15.3127i	0.168374	−	0.594695i
$664$			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
$669$	2.13701	−	3.58368i	0.0826215	−	0.138553i
$670$	13.1561	−	15.2203i	0.508266	−	0.588012i
$671$	8.87542	+	5.12422i	0.342632	+	0.197818i
$672$	−5.74457	+	5.58473i	−0.221602	+	0.215436i
$673$	−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
$675$	−16.3868	+	20.1612i	−0.630728	+	0.776004i
$676$	−22.7227			−0.873952
$677$	−11.9284	−	11.9284i	−0.458445	−	0.458445i	0.439700	−	0.898145i	$-0.355085\pi$
$677$	−11.9284	−	11.9284i	−0.458445	−	0.458445i	−0.898145	+	0.439700i	$0.855085\pi$
$678$	5.64080	+	22.3058i	0.216634	+	0.856649i
$679$	12.6982	−	7.33131i	0.487312	−	0.281350i
$680$	−3.37620	−	0.646457i	−0.129471	−	0.0247905i
$681$	13.2726	+	23.7565i	0.508606	+	0.910352i
$682$	−3.72239	−	0.997412i	−0.142538	−	0.0381929i
$683$	−12.7512	+	12.7512i	−0.487911	+	0.487911i	−0.907646	−	0.419736i	$-0.862123\pi$
$683$	−12.7512	+	12.7512i	−0.487911	+	0.487911i	0.419736	+	0.907646i	$0.362123\pi$
$684$	12.7510	+	2.90049i	0.487545	+	0.110903i
$685$	−3.68482	+	7.60903i	−0.140790	+	0.290726i
$686$	−29.6295	+	17.1066i	−1.13126	+	0.653134i
$687$	−0.218408	+	0.771411i	−0.00833278	+	0.0294312i
$688$	−0.936089	+	0.250824i	−0.0356880	+	0.00956258i
$689$	41.8081	+	72.4137i	1.59276	+	2.75874i
$690$	7.62963	−	5.02169i	0.290455	−	0.191172i
$691$	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
$693$	4.83249	+	20.3107i	0.183571	+	0.771541i
$694$	−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
$699$	22.2315	+	13.2570i	0.840872	+	0.501425i
$700$	9.15603	+	21.2386i	0.346065	+	0.802744i
$701$	−30.1018	+	17.3793i	−1.13693	+	0.656405i	−0.945668	−	0.325134i	$-0.894591\pi$
$701$	−30.1018	+	17.3793i	−1.13693	+	0.656405i	−0.191260	+	0.981539i	$0.561257\pi$
$702$	−22.8698	+	21.0116i	−0.863165	+	0.793030i
$703$	−2.51787	−	37.8940i	−0.0949632	−	1.42920i
$704$	1.50450			0.0567028
$705$	3.85095	−	4.33015i	0.145035	−	0.163083i
$706$	−6.48404	−	11.2307i	−0.244030	−	0.422673i
$707$	39.5845	−	10.6066i	1.48873	−	0.398904i
$708$	−0.192865	+	0.681194i	−0.00724831	+	0.0256008i
$709$	−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
$717$	3.47086	+	0.982697i	0.129622	+	0.0366995i
$718$	−4.62876	+	1.24027i	−0.172744	+	0.0462865i
$719$	9.45972	+	16.3847i	0.352788	+	0.611047i	0.986737	−	0.162328i	$-0.0519004\pi$
$719$	9.45972	+	16.3847i	0.352788	+	0.611047i	−0.633949	+	0.773375i	$0.718567\pi$
$720$	4.94928	+	4.52820i	0.184449	+	0.168756i
$721$	10.8965			0.405808
$722$	−18.8419	−	2.44617i	−0.701222	−	0.0910371i
$723$	26.9743	−	26.2238i	1.00319	−	0.975273i
$724$	3.95546	−	2.28368i	0.147003	−	0.0848724i
$725$	−43.3400	−	17.2287i	−1.60961	−	0.639857i
$726$	−7.75014	+	12.9967i	−0.287635	+	0.482353i
$727$	−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
$732$	11.4384	−	2.89261i	0.422777	−	0.106914i
$733$	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
$735$	30.6544	+	46.5744i	1.13071	+	1.71792i
$736$	−1.17919	−	2.04241i	−0.0434653	−	0.0752842i
$737$	−13.0749	+	3.50341i	−0.481621	+	0.129050i
$738$	−5.76181	+	19.3072i	−0.212095	+	0.710708i
$739$	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
$741$	30.1980	−	33.5302i	1.10935	−	1.23176i
$742$	45.7587	−	45.7587i	1.67986	−	1.67986i
$743$	−44.1174	−	11.8212i	−1.61851	−	0.433679i	−0.667947	−	0.744209i	$-0.732827\pi$
$743$	−44.1174	−	11.8212i	−1.61851	−	0.433679i	−0.950563	+	0.310530i	$0.899493\pi$
$744$	−3.87310	+	2.16387i	−0.141995	+	0.0793312i
$745$	15.3904	+	2.94687i	0.563860	+	0.107965i
$746$	−11.7571	+	6.78796i	−0.430457	+	0.248525i
$747$	38.9041	−	9.25638i	1.42343	−	0.338673i
$748$	1.63545	+	1.63545i	0.0597981	+	0.0597981i
$749$	7.28117			0.266048
$750$	17.3041	−	8.69294i	0.631857	−	0.317421i
$751$	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
$753$	−31.9946	−	32.9103i	−1.16595	−	1.19932i
$754$	−48.2815	−	27.8753i	−1.75831	−	1.01516i
$755$	−26.4418	+	30.5904i	−0.962314	+	1.11330i
$756$	20.2882	+	12.8877i	0.737876	+	0.468720i
$757$	−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	$0.0973219\pi$
$761$			16.6072i			0.602009i	−0.953623	+	0.301005i	$0.902678\pi$
$762$	20.2016	+	5.71962i	0.731826	+	0.207200i
$763$	−3.27962	+	12.2397i	−0.118730	+	0.443107i
$764$	7.73020	−	13.3891i	0.279669	−	0.484400i
$765$	0.457729	+	10.3024i	0.0165492	+	0.372485i
$766$	15.0499	−	26.0672i	0.543775	−	0.941845i
$767$	1.72748	+	1.72748i	0.0623755	+	0.0623755i
$768$	1.24190	−	1.20735i	0.0448132	−	0.0435663i
$769$	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	$-0.953043\pi$
$773$	−5.72773	−	21.3762i	−0.206012	−	0.768848i	0.783126	−	0.621863i	$-0.213624\pi$
$774$	1.38206	+	2.55783i	0.0496770	+	0.0919393i
$775$	1.85346	+	12.6725i	0.0665783	+	0.455209i
$776$	−2.74518	+	1.58493i	−0.0985463	+	0.0568958i
$777$	19.0160	−	67.1641i	0.682195	−	2.40950i
$778$	−7.46012	−	7.46012i	−0.267458	−	0.267458i
$779$	5.68554	−	28.7179i	0.203706	−	1.02892i
$780$	21.9709	−	7.28840i	0.786684	−	0.260967i
$781$	−5.39606	−	9.34624i	−0.193086	−	0.334435i
$782$	0.938361	−	3.50201i	0.0335557	−	0.125232i
$783$	−47.3058	+	10.5526i	−1.69057	+	0.377117i
$784$	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
$789$	−12.5230	−	7.46767i	−0.445831	−	0.265856i
$790$	27.0617	+	13.1051i	0.962811	+	0.466260i
$791$		−	61.4453i		−	2.18474i
$792$	−1.04472	−	4.39091i	−0.0371225	−	0.156024i
$793$	10.5375	−	39.3263i	0.374196	−	1.39652i
$794$	2.25091	−	3.89869i	0.0798818	−	0.138359i
$795$	−40.4880	−	36.0073i	−1.43596	−	1.27705i
$796$	0.653922	+	1.13263i	0.0231777	+	0.0401449i
$797$	−1.59055	−	1.59055i	−0.0563401	−	0.0563401i	0.678375	−	0.734715i	$-0.262684\pi$
$797$	−1.59055	−	1.59055i	−0.0563401	−	0.0563401i	−0.734715	+	0.678375i	$0.762684\pi$
$798$	−31.1145	−	15.8583i	−1.10144	−	0.561378i
$799$		−	2.30015i		−	0.0813735i
$800$	−1.97941	−	4.59151i	−0.0699828	−	0.162334i
$801$	−21.9893	+	11.8813i	−0.776953	+	0.419807i
$802$	6.55771	+	24.4737i	0.231561	+	0.864197i
$803$	1.81905	+	0.487414i	0.0641930	+	0.0172005i
$804$	−7.98135	+	13.3844i	−0.281481	+	0.472033i
$805$	−23.0418	+	8.00621i	−0.812118	+	0.282182i
$806$			15.3095i			0.539253i
$807$	1.91886	+	7.58786i	0.0675469	+	0.267105i
$808$	−8.55765	+	2.29302i	−0.301057	+	0.0806680i
$809$	−35.8571			−1.26067			−0.630334	−	0.776324i	$-0.717082\pi$
$809$	−35.8571			−1.26067			−0.630334	+	0.776324i	$0.717082\pi$
$810$	9.77891	−	17.5890i	0.343596	−	0.618014i
$811$	−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
$813$	5.93535	+	23.4705i	0.208162	+	0.823148i
$814$	−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
$819$	72.9695	−	39.4272i	2.54976	−	1.37770i
$820$	9.82083	−	11.3617i	0.342958	−	0.396768i
$821$	26.9842	+	15.5793i	0.941754	+	0.543722i	0.890510	−	0.454965i	$-0.150348\pi$
$821$	26.9842	+	15.5793i	0.941754	+	0.543722i	0.0512439	+	0.998686i	$0.483681\pi$
$822$	1.78399	−	6.30100i	0.0622237	−	0.219772i
$823$	−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
$825$	−12.9182	−	1.69780i	−0.449755	−	0.0591097i
$826$	0.945356	−	1.63741i	0.0328931	−	0.0569726i
$827$	−20.0906	+	5.38326i	−0.698618	+	0.187194i	−0.590611	−	0.806956i	$-0.701113\pi$
$827$	−20.0906	+	5.38326i	−0.698618	+	0.187194i	−0.108007	+	0.994150i	$0.534447\pi$
$828$	−5.14200	+	4.85973i	−0.178697	+	0.168887i
$829$		−	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
$831$	8.96987	−	5.01139i	0.311161	−	0.173843i
$832$	−1.54692	−	5.77319i	−0.0536299	−	0.200150i
$833$	21.3777	+	5.72814i	0.740694	+	0.198468i
$834$	19.7269	−	11.0213i	0.683088	−	0.381635i
$835$	12.9594	−	26.7606i	0.448477	−	0.926090i
$836$	2.11356	+	6.20802i	0.0730989	+	0.214709i
$837$	9.00479	+	9.80117i	0.311251	+	0.338778i
$838$	0.755166	−	2.81832i	0.0260868	−	0.0973571i
$839$	−27.8705	−	48.2731i	−0.962197	−	1.66657i	−0.716964	−	0.697110i	$-0.754469\pi$
$839$	−27.8705	−	48.2731i	−0.962197	−	1.66657i	−0.245233	−	0.969464i	$-0.578864\pi$
$840$	−9.84938	−	14.9645i	−0.339836	−	0.516325i
$841$	−29.0036	−	50.2358i	−1.00013	−	1.73227i
$842$	31.7911	−	8.51839i	1.09559	−	0.293563i
$843$	30.3056	+	31.1729i	1.04378	+	1.07365i
$844$		−	16.8680i		−	0.580622i
$845$	9.55517	−	49.9030i	0.328708	−	1.71672i
$846$	−2.35310	+	3.82243i	−0.0809011	+	0.131418i
$847$	28.5754	−	28.5754i	0.981864	−	0.981864i
$848$	−9.89243	+	9.89243i	−0.339707	+	0.339707i
$849$	18.7050	−	31.3676i	0.641954	−	1.07653i
$850$	2.83946	−	7.14287i	0.0973927	−	0.244999i
$851$	17.7948	+	10.2738i	0.609997	+	0.352182i
$852$	−11.9545	−	3.38465i	−0.409555	−	0.115956i
$853$	−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
$855$	−11.7319	+	26.7836i	−0.401223	+	0.915981i
$856$	−1.57409			−0.0538014
$857$	9.40068	−	35.0838i	0.321121	−	1.19844i	−0.597033	−	0.802216i	$-0.703654\pi$
$857$	9.40068	−	35.0838i	0.321121	−	1.19844i	0.918154	−	0.396223i	$-0.129679\pi$
$858$	−14.9858	−	4.24289i	−0.511606	−	0.144850i
$859$	−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
$861$	27.5592	−	46.2158i	0.939216	−	1.57503i
$862$	−7.09065	+	7.09065i	−0.241509	+	0.241509i
$863$	26.5413	−	26.5413i	0.903477	−	0.903477i	−0.0922582	−	0.995735i	$-0.529409\pi$
$863$	26.5413	−	26.5413i	0.903477	−	0.903477i	0.995735	+	0.0922582i	$0.0294085\pi$
$864$	−4.38605	−	2.78614i	−0.149216	−	0.0947864i
$865$	20.9681	−	14.2288i	0.712938	−	0.483794i
$866$		−	12.2500i		−	0.416271i
$867$	−17.6715	−	18.1773i	−0.600156	−	0.617333i
$868$	11.4446	−	3.06658i	0.388457	−	0.104087i
$869$	−10.1153	−	17.5202i	−0.343138	−	0.594333i
$870$	35.3824	+	7.29371i	1.19957	+	0.247280i
$871$	26.8873	+	46.5701i	0.911040	+	1.57797i
$872$	0.709010	−	2.64606i	0.0240101	−	0.0896069i
$873$	6.53192	+	6.91132i	0.221072	+	0.233913i
$874$	6.77107	−	7.73492i	0.229035	−	0.261637i
$875$	−50.4938	+	11.1771i	−1.70700	+	0.377856i
$876$	1.89270	−	1.05743i	0.0639484	−	0.0357274i
$877$	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
$879$	−14.5524	+	8.13028i	−0.490839	+	0.274228i
$880$	−0.632657	+	3.30413i	−0.0213269	+	0.111382i
$881$		−	35.6096i		−	1.19972i	−0.800106	−	0.599859i	$-0.795223\pi$
$881$		−	35.6096i		−	1.19972i	0.800106	−	0.599859i	$-0.204777\pi$
$882$	−29.6658	−	31.3889i	−0.998899	−	1.05692i
$883$	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
$885$	−1.41492	−	0.710014i	−0.0475619	−	0.0238669i
$886$	11.0310			0.370595
$887$	17.4913	−	4.68678i	0.587300	−	0.157367i	0.0470811	−	0.998891i	$-0.485008\pi$
$887$	17.4913	−	4.68678i	0.587300	−	0.157367i	0.540219	+	0.841524i	$0.318341\pi$
$888$	−4.11101	+	14.5200i	−0.137956	+	0.487259i
$889$	−48.5591	−	28.0356i	−1.62862	−	0.940283i
$890$	18.5803	−	1.35157i	0.622812	−	0.0453049i
$891$	−12.0896	+	6.09810i	−0.405015	+	0.204294i
$892$	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
$897$	5.98559	+	23.6692i	0.199853	+	0.790293i
$898$	−5.04107	+	18.8135i	−0.168223	+	0.627816i
$899$	−11.9464	+	20.6917i	−0.398433	+	0.690107i
$900$	−12.0259	+	8.96531i	−0.400865	+	0.298844i
$901$	−21.5070			−0.716502
$902$	−9.76020	+	2.61524i	−0.324979	+	0.0870779i
$903$	−1.90356	−	7.52738i	−0.0633466	−	0.250496i
$904$			13.2837i			0.441808i
$905$	3.35205	+	9.64718i	0.111426	+	0.320683i
$906$	16.0413	−	26.9006i	0.532935	−	0.893713i
$907$	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
$909$	12.6347	+	23.3835i	0.419065	+	0.775581i
$910$	−61.6570	+	4.48508i	−2.04391	+	0.148679i
$911$			39.6167i			1.31256i	0.754518	+	0.656280i	$0.227871\pi$
$911$			39.6167i			1.31256i	−0.754518	+	0.656280i	$0.772129\pi$
$912$	6.72654	+	3.42836i	0.222738	+	0.113524i
$913$	14.1810	+	14.1810i	0.469324	+	0.469324i
$914$	11.8484	+	20.5220i	0.391910	+	0.678808i
$915$	1.54268	+	26.3372i	0.0509993	+	0.870680i
$916$	−0.231441	+	0.400867i	−0.00764702	+	0.0132450i
$917$	3.00713	−	11.2228i	0.0993043	−	0.370609i
$918$	−1.73917	−	7.79648i	−0.0574011	−	0.257322i
$919$		−	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
$921$	−39.7440	−	23.7000i	−1.30961	−	0.780941i
$922$	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
$927$	1.63579	+	6.87514i	0.0537264	+	0.225809i
$928$	2.41420	−	9.00993i	0.0792501	−	0.295766i
$929$	8.94779	+	15.4980i	0.293567	+	0.508474i	0.974651	−	0.223732i	$-0.0718241\pi$
$929$	8.94779	+	15.4980i	0.293567	+	0.508474i	−0.681083	+	0.732206i	$0.738491\pi$
$930$	−3.12354	−	9.41593i	−0.102425	−	0.308760i
$931$	47.2171	+	41.3333i	1.54748	+	1.35465i
$932$	10.5671	+	10.5671i	0.346138	+	0.346138i
$933$	4.79996	−	16.9533i	0.157144	−	0.555027i
$934$	−3.99266	+	2.30517i	−0.130644	+	0.0754273i
$935$	−4.27946	+	2.90401i	−0.139953	+	0.0949712i
$936$	−15.7751	+	8.52364i	−0.515624	+	0.278604i
$937$	−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	−0.324111	−	0.946019i	$-0.605065\pi$
$941$	−40.0454	−	23.1202i	−1.30544	−	0.753698i	−0.981332	+	0.192321i	$0.938399\pi$
$942$	−12.2735	+	11.9320i	−0.399891	+	0.388764i
$943$	11.2001	+	11.2001i	0.364725	+	0.364725i
$944$	−0.204374	+	0.353985i	−0.00665179	+	0.0115212i
$945$	−36.8349	+	39.1370i	−1.19824	+	1.27313i
$946$	−0.729011	+	1.26268i	−0.0237022	+	0.0410534i
$947$	3.10306	−	11.5808i	0.100836	−	0.376325i	−0.897004	−	0.442023i	$-0.854261\pi$
$947$	3.10306	−	11.5808i	0.100836	−	0.376325i	0.997840	+	0.0656983i	$0.0209275\pi$
$948$	−22.4096	−	6.34478i	−0.727830	−	0.206069i
$949$		−	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	−0.283277	−	0.959038i	$-0.591422\pi$
$953$	−31.1214	−	8.33895i	−1.00812	−	0.270125i	−0.724844	+	0.688913i	$0.758088\pi$
$954$	35.7406	+	22.0020i	1.15715	+	0.712342i
$955$	26.1541	+	22.6071i	0.846327	+	0.731549i
$956$	1.80365	+	1.04134i	0.0583341	+	0.0336792i
$957$	−16.9434	−	17.4283i	−0.547702	−	0.563377i
$958$	−7.70084	−	7.70084i	−0.248803	−	0.248803i
$959$	−8.74447	+	15.1459i	−0.282374	+	0.489086i
$960$	2.12931	+	3.23513i	0.0687230	+	0.104413i
$961$	−24.4389			−0.788352
$962$	36.8220	+	36.8220i	1.18719	+	1.18719i
$963$	1.09305	+	4.59404i	0.0352230	+	0.148041i
$964$	18.8102	−	10.8601i	0.605837	−	0.349780i
$965$	−14.4262	−	21.2591i	−0.464397	−	0.684353i
$966$	16.4951	−	9.21565i	0.530720	−	0.296509i
$967$	−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
$969$	3.58527	+	11.0388i	0.115175	+	0.354618i
$970$	−2.32640	−	6.69538i	−0.0746963	−	0.214976i
$971$	−10.2078	+	5.89347i	−0.327584	+	0.189131i	−0.654768	−	0.755830i	$-0.727234\pi$
$971$	−10.2078	+	5.89347i	−0.327584	+	0.189131i	0.327184	+	0.944961i	$0.393900\pi$
$972$	−5.08576	+	14.7355i	−0.163126	+	0.472641i
$973$	−58.2912	+	15.6191i	−1.86873	+	0.500725i
$974$	8.85338	+	15.3345i	0.283681	+	0.491349i
$975$	6.76757	+	51.3167i	0.216736	+	1.64345i
$976$	6.81188			0.218043
$977$	−7.55488	−	7.55488i	−0.241702	−	0.241702i	0.575852	−	0.817554i	$-0.304670\pi$
$977$	−7.55488	−	7.55488i	−0.241702	−	0.241702i	−0.817554	+	0.575852i	$0.804670\pi$
$978$	11.8366	−	2.99329i	0.378492	−	0.0957150i
$979$	−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	−0.302177	−	0.953252i	$-0.597713\pi$
$983$	−32.6225	−	8.74117i	−1.04050	−	0.278800i	−0.738319	+	0.674452i	$0.764380\pi$
$984$	−5.95794	+	9.99125i	−0.189932	+	0.318509i
$985$	33.4012	−	2.42968i	1.06425	−	0.0774161i
$986$	12.4185	−	7.16985i	0.395487	−	0.228334i
$987$	8.59513	−	8.35598i	0.273586	−	0.265974i
$988$	21.6488	−	14.4934i	0.688742	−	0.461097i
$989$	2.28552			0.0726753
$990$	10.0825	−	0.447958i	0.320443	−	0.0142370i
$991$	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
$993$	−45.2562	−	12.8133i	−1.43616	−	0.406617i
$994$	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.83.20	yes	144
3.2	odd	2	inner	570.2.v.c.83.18	✓	144
5.2	odd	4	inner	570.2.v.c.197.27	yes	144
15.2	even	4	inner	570.2.v.c.197.12	yes	144
19.11	even	3	inner	570.2.v.c.353.12	yes	144
57.11	odd	6	inner	570.2.v.c.353.27	yes	144
95.87	odd	12	inner	570.2.v.c.467.18	yes	144
285.182	even	12	inner	570.2.v.c.467.20	yes	144

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

\(f(q)\)	\(=\)	\(q+(0.258819 - 0.965926i) q^{2} +(-1.66654 - 0.471844i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(1.46226 - 1.69168i) q^{5} +(-0.887099 + 1.48763i) q^{6} +(3.27081 - 3.27081i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(2.55473 + 1.57270i) q^{9} +O(q^{10})\)	\(q+(0.258819 - 0.965926i) q^{2} +(-1.66654 - 0.471844i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(1.46226 - 1.69168i) q^{5} +(-0.887099 + 1.48763i) q^{6} +(3.27081 - 3.27081i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(2.55473 + 1.57270i) q^{9} +(-1.25558 - 1.85027i) q^{10} +1.50450i q^{11} +(1.20735 + 1.24190i) q^{12} +(5.77319 - 1.54692i) q^{13} +(-2.31281 - 4.00591i) q^{14} +(-3.23513 + 2.12931i) q^{15} +(0.500000 + 0.866025i) q^{16} +(-0.397886 + 1.48493i) q^{17} +(2.18032 - 2.06063i) q^{18} +(-2.87108 + 3.27977i) q^{19} +(-2.11220 + 0.733912i) q^{20} +(-6.99426 + 3.90763i) q^{21} +(1.45323 + 0.389392i) q^{22} +(-0.610391 - 2.27801i) q^{23} +(1.51207 - 0.844779i) q^{24} +(-0.723596 - 4.94736i) q^{25} -5.97685i q^{26} +(-3.51549 - 3.82640i) q^{27} +(-4.46802 + 1.19720i) q^{28} +(4.66388 - 8.07808i) q^{29} +(1.21944 + 3.67600i) q^{30} -2.56146 q^{31} +(0.965926 - 0.258819i) q^{32} +(0.709888 - 2.50731i) q^{33} +(1.33135 + 0.768656i) q^{34} +(-0.750409 - 10.3160i) q^{35} +(-1.42611 - 2.63936i) 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} +(1.96424 + 7.76731i) q^{42} +(-0.250824 + 0.936089i) q^{43} +(0.752248 - 1.30293i) q^{44} +(6.39618 - 2.02210i) q^{45} -2.35837 q^{46} +(-1.44523 + 0.387250i) q^{47} +(-0.424642 - 1.67919i) q^{48} -14.3964i q^{49} +(-4.96607 - 0.581532i) q^{50} +(1.36375 - 2.28696i) q^{51} +(-5.77319 - 1.54692i) q^{52} +(3.62088 + 13.5133i) q^{53} +(-4.60589 + 2.40536i) q^{54} +(2.54513 + 2.19996i) q^{55} +4.62563i q^{56} +(6.33232 - 4.11118i) q^{57} +(-6.59573 - 6.59573i) q^{58} +(0.204374 + 0.353985i) q^{59} +(3.86636 - 0.226468i) q^{60} +(3.40594 - 5.89926i) q^{61} +(-0.662955 + 2.47418i) q^{62} +(13.5000 - 3.21203i) q^{63} -1.00000i q^{64} +(5.82500 - 12.0284i) q^{65} +(-2.23814 - 1.33464i) 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} +(-2.91853 + 0.694400i) q^{72} +(0.323971 - 1.20908i) q^{73} +(4.35632 + 7.54537i) q^{74} +(-1.12848 + 8.58642i) q^{75} +(4.12631 - 1.40483i) q^{76} +(4.92093 + 4.92093i) q^{77} +(-2.82014 + 9.96067i) q^{78} +(-11.6452 + 6.72339i) q^{79} +(2.19617 + 0.420511i) q^{80} +(4.05325 + 8.03562i) 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} +(-11.5842 + 11.2618i) q^{87} +(-1.06384 - 1.06384i) q^{88} +(-4.16565 + 7.21512i) q^{89} +(-0.297747 - 6.70159i) q^{90} +(13.8233 - 23.9427i) q^{91} +(-0.610391 + 2.27801i) q^{92} +(4.26878 + 1.20861i) 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} +(-2.36612 + 3.84357i) 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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