LMFDB - Embedded newform 540.2.be.a.491.60

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [540,2,Mod(11,540)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(540, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([9, 13, 0])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("540.11"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 540 = 2^{2} \cdot 3^{3} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	540.be (of order $18$, degree $6$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$4.31192170915$
Analytic rank:	$0$
Dimension:	$432$
Relative dimension:	$72$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			491.60
Character	$\chi$	$=$	540.491
Dual form			540.2.be.a.11.60

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.17623 - 0.785164i) q^{2} +(1.42519 - 0.984291i) q^{3} +(0.767034 - 1.84707i) q^{4} +(0.342020 + 0.939693i) q^{5} +(0.903523 - 2.27676i) q^{6} +(-0.242074 + 0.0426842i) q^{7} +(-0.548043 - 2.77482i) q^{8} +(1.06234 - 2.80561i) q^{9} +(1.14011 + 0.836753i) q^{10} +(-1.13736 - 0.413964i) q^{11} +(-0.724881 - 3.38741i) q^{12} +(0.576076 + 0.483385i) q^{13} +(-0.251221 + 0.240275i) q^{14} +(1.41238 + 1.00259i) q^{15} +(-2.82332 - 2.83353i) q^{16} +(3.50104 + 2.02132i) q^{17} +(-0.953302 - 4.13415i) q^{18} +(-4.99450 + 2.88358i) q^{19} +(1.99802 + 0.0890420i) q^{20} +(-0.302989 + 0.299105i) q^{21} +(-1.66282 + 0.406095i) q^{22} +(0.615990 - 3.49345i) q^{23} +(-3.51230 - 3.41522i) q^{24} +(-0.766044 + 0.642788i) q^{25} +(1.05713 + 0.116258i) q^{26} +(-1.24749 - 5.04418i) q^{27} +(-0.106839 + 0.479868i) q^{28} +(4.09856 + 4.88448i) q^{29} +(2.44848 + 0.0703356i) q^{30} +(7.42673 + 1.30953i) q^{31} +(-5.54566 - 1.11611i) q^{32} +(-2.02841 + 0.529512i) q^{33} +(5.70510 - 0.371347i) q^{34} +(-0.122904 - 0.212877i) q^{35} +(-4.36729 - 4.11422i) q^{36} +(-3.85088 + 6.66992i) q^{37} +(-3.61060 + 7.31326i) q^{38} +(1.29681 + 0.121890i) q^{39} +(2.42004 - 1.46404i) q^{40} +(-2.19561 + 2.61663i) q^{41} +(-0.121538 + 0.589712i) q^{42} +(-0.00223415 + 0.00613829i) q^{43} +(-1.63701 + 1.78325i) q^{44} +(2.99975 + 0.0387019i) q^{45} +(-2.01839 - 4.59276i) q^{46} +(-0.367791 - 2.08585i) q^{47} +(-6.81278 - 1.25935i) q^{48} +(-6.52107 + 2.37348i) q^{49} +(-0.396351 + 1.35754i) q^{50} +(6.97922 - 0.565264i) q^{51} +(1.33471 - 0.693278i) q^{52} -0.559092i q^{53} +(-5.42785 - 4.95363i) q^{54} -1.21035i q^{55} +(0.251108 + 0.648321i) q^{56} +(-4.27984 + 9.02569i) q^{57} +(8.65597 + 2.52722i) q^{58} +(-5.91537 + 2.15302i) q^{59} +(2.93520 - 1.83973i) q^{60} +(-0.311420 - 1.76615i) q^{61} +(9.76375 - 4.29089i) q^{62} +(-0.137411 + 0.724510i) q^{63} +(-7.39930 + 3.04145i) q^{64} +(-0.257204 + 0.706662i) q^{65} +(-1.97013 + 2.21547i) q^{66} +(-6.42340 + 7.65512i) q^{67} +(6.41894 - 4.91623i) q^{68} +(-2.56067 - 5.58515i) q^{69} +(-0.311707 - 0.153892i) q^{70} +(4.04403 - 7.00447i) q^{71} +(-8.36727 - 1.41022i) q^{72} +(7.23690 + 12.5347i) q^{73} +(0.707463 + 10.8689i) q^{74} +(-0.459070 + 1.67011i) q^{75} +(1.49521 + 11.4370i) q^{76} +(0.292995 + 0.0516629i) q^{77} +(1.62105 - 0.874838i) q^{78} +(-5.69121 - 6.78252i) q^{79} +(1.69701 - 3.62217i) q^{80} +(-6.74285 - 5.96103i) q^{81} +(-0.528061 + 4.80167i) q^{82} +(10.6221 - 8.91300i) q^{83} +(0.320064 + 0.789064i) q^{84} +(-0.701999 + 3.98123i) q^{85} +(0.00219169 + 0.00897422i) q^{86} +(10.6490 + 2.92714i) q^{87} +(-0.525357 + 3.38284i) q^{88} +(2.75507 - 1.59064i) q^{89} +(3.55878 - 2.30977i) q^{90} +(-0.160086 - 0.0924257i) q^{91} +(-5.98016 - 3.81737i) q^{92} +(11.8735 - 5.44373i) q^{93} +(-2.07034 - 2.16466i) q^{94} +(-4.41790 - 3.70706i) q^{95} +(-9.00220 + 3.86786i) q^{96} +(-1.59179 - 0.579364i) q^{97} +(-5.80671 + 7.91186i) q^{98} +(-2.36968 + 2.75121i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 432 q + 18 q^{12} + 30 q^{14} + 30 q^{24} + 12 q^{29} - 24 q^{30} + 60 q^{33} - 60 q^{36} - 60 q^{38} + 60 q^{41} - 60 q^{42} - 72 q^{44} + 12 q^{45} - 150 q^{48} + 54 q^{52} - 84 q^{54} - 84 q^{56} - 12 q^{57}+ \cdots + 36 q^{97}+O(q^{100}) $ 432 * q + 18 * q^12 + 30 * q^14 + 30 * q^24 + 12 * q^29 - 24 * q^30 + 60 * q^33 - 60 * q^36 - 60 * q^38 + 60 * q^41 - 60 * q^42 - 72 * q^44 + 12 * q^45 - 150 * q^48 + 54 * q^52 - 84 * q^54 - 84 * q^56 - 12 * q^57 + 54 * q^58 - 198 * q^62 - 48 * q^66 - 138 * q^68 - 48 * q^69 - 84 * q^72 - 84 * q^74 - 48 * q^77 - 78 * q^78 - 66 * q^84 + 54 * q^86 - 36 * q^89 + 120 * q^92 - 54 * q^94 + 210 * q^96 + 36 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/540\mathbb{Z}\right)^\times$.

$n$	$217$	$271$	$461$
$\chi(n)$	$1$	$-1$	$e\left(\frac{5}{18}\right)$

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 $

$2$	1.17623	−	0.785164i	0.831720	−	0.555195i
$2$	1.17623	−	0.785164i	0.831720	−	0.555195i
$3$	1.42519	−	0.984291i	0.822835	−	0.568281i
$3$	1.42519	−	0.984291i	0.822835	−	0.568281i
$4$	0.767034	−	1.84707i	0.383517	−	0.923534i
$5$	0.342020	+	0.939693i	0.152956	+	0.420243i
$5$	0.342020	+	0.939693i	0.152956	+	0.420243i
$6$	0.903523	−	2.27676i	0.368862	−	0.929484i
$7$	−0.242074	+	0.0426842i	−0.0914955	+	0.0161331i	−0.219208	−	0.975678i	$-0.570347\pi$
$7$	−0.242074	+	0.0426842i	−0.0914955	+	0.0161331i	0.127713	+	0.991811i	$0.459236\pi$
$8$	−0.548043	−	2.77482i	−0.193762	−	0.981048i
$9$	1.06234	−	2.80561i	0.354114	−	0.935202i
$10$	1.14011	+	0.836753i	0.360534	+	0.264604i
$11$	−1.13736	−	0.413964i	−0.342926	−	0.124815i	0.164815	−	0.986324i	$-0.447297\pi$
$11$	−1.13736	−	0.413964i	−0.342926	−	0.124815i	−0.507741	+	0.861510i	$0.669519\pi$
$12$	−0.724881	−	3.38741i	−0.209255	−	0.977861i
$13$	0.576076	+	0.483385i	0.159775	+	0.134067i	0.719170	−	0.694834i	$-0.244522\pi$
$13$	0.576076	+	0.483385i	0.159775	+	0.134067i	−0.559395	+	0.828901i	$0.688967\pi$
$14$	−0.251221	+	0.240275i	−0.0671416	+	0.0642161i
$15$	1.41238	+	1.00259i	0.364674	+	0.258869i
$16$	−2.82332	−	2.83353i	−0.705829	−	0.708382i
$17$	3.50104	+	2.02132i	0.849126	+	0.490243i	0.860356	−	0.509694i	$-0.170241\pi$
$17$	3.50104	+	2.02132i	0.849126	+	0.490243i	−0.0112297	+	0.999937i	$0.503575\pi$
$18$	−0.953302	−	4.13415i	−0.224696	−	0.974429i
$19$	−4.99450	+	2.88358i	−1.14582	+	0.661538i	−0.947865	−	0.318674i	$-0.896763\pi$
$19$	−4.99450	+	2.88358i	−1.14582	+	0.661538i	−0.197953	+	0.980212i	$0.563429\pi$
$20$	1.99802	+	0.0890420i	0.446770	+	0.0199104i
$21$	−0.302989	+	0.299105i	−0.0661175	+	0.0652700i
$22$	−1.66282	+	0.406095i	−0.354515	+	0.0865798i
$23$	0.615990	−	3.49345i	0.128443	−	0.728435i	−0.850761	−	0.525554i	$-0.823858\pi$
$23$	0.615990	−	3.49345i	0.128443	−	0.728435i	0.979203	−	0.202882i	$-0.0650306\pi$
$24$	−3.51230	−	3.41522i	−0.716945	−	0.697129i
$25$	−0.766044	+	0.642788i	−0.153209	+	0.128558i
$26$	1.05713	+	0.116258i	0.207321	+	0.0228000i
$27$	−1.24749	−	5.04418i	−0.240080	−	0.970753i
$28$	−0.106839	+	0.479868i	−0.0201906	+	0.0906865i
$29$	4.09856	+	4.88448i	0.761084	+	0.907025i	0.997916	−	0.0645258i	$-0.0205535\pi$
$29$	4.09856	+	4.88448i	0.761084	+	0.907025i	−0.236832	+	0.971551i	$0.576109\pi$
$30$	2.44848	+	0.0703356i	0.447029	+	0.0128415i
$31$	7.42673	+	1.30953i	1.33388	+	0.235199i	0.794706	−	0.606995i	$-0.207625\pi$
$31$	7.42673	+	1.30953i	1.33388	+	0.235199i	0.539175	+	0.842194i	$0.318736\pi$
$32$	−5.54566	−	1.11611i	−0.980343	−	0.197303i
$33$	−2.02841	+	0.529512i	−0.353102	+	0.0921762i
$34$	5.70510	−	0.371347i	0.978416	−	0.0636854i
$35$	−0.122904	−	0.212877i	−0.0207746	−	0.0359827i
$36$	−4.36729	−	4.11422i	−0.727882	−	0.685703i
$37$	−3.85088	+	6.66992i	−0.633081	+	1.09653i	0.353837	+	0.935307i	$0.384877\pi$
$37$	−3.85088	+	6.66992i	−0.633081	+	1.09653i	−0.986918	+	0.161222i	$0.948457\pi$
$38$	−3.61060	+	7.31326i	−0.585717	+	1.18637i
$39$	1.29681	+	0.121890i	0.207656	+	0.0195180i
$40$	2.42004	−	1.46404i	0.382642	−	0.231485i
$41$	−2.19561	+	2.61663i	−0.342897	+	0.408648i	−0.909741	−	0.415177i	$-0.863720\pi$
$41$	−2.19561	+	2.61663i	−0.342897	+	0.408648i	0.566844	+	0.823825i	$0.308164\pi$
$42$	−0.121538	+	0.589712i	−0.0187537	+	0.0909945i
$43$	−0.00223415	+	0.00613829i	−0.000340705	+	0.000936080i	−0.939863	−	0.341552i	$-0.889047\pi$
$43$	−0.00223415	+	0.00613829i	−0.000340705	+	0.000936080i	0.939522	+	0.342488i	$0.111270\pi$
$44$	−1.63701	+	1.78325i	−0.246789	+	0.268835i
$45$	2.99975	+	0.0387019i	0.447176	+	0.00576934i
$46$	−2.01839	−	4.59276i	−0.297595	−	0.677165i
$47$	−0.367791	−	2.08585i	−0.0536478	−	0.304252i	0.946163	−	0.323690i	$-0.104923\pi$
$47$	−0.367791	−	2.08585i	−0.0536478	−	0.304252i	−0.999811	+	0.0194379i	$0.993812\pi$
$48$	−6.81278	−	1.25935i	−0.983341	−	0.181772i
$49$	−6.52107	+	2.37348i	−0.931581	+	0.339068i
$50$	−0.396351	+	1.35754i	−0.0560524	+	0.191985i
$51$	6.97922	−	0.565264i	0.977286	−	0.0791527i
$52$	1.33471	−	0.693278i	0.185092	−	0.0961404i
$53$		−	0.559092i		−	0.0767971i	−0.999263	−	0.0383986i	$-0.987774\pi$
$53$		−	0.559092i		−	0.0767971i	0.999263	−	0.0383986i	$-0.0122257\pi$
$54$	−5.42785	−	4.95363i	−0.738636	−	0.674104i
$55$		−	1.21035i		−	0.163204i
$56$	0.251108	+	0.648321i	0.0335558	+	0.0866355i
$57$	−4.27984	+	9.02569i	−0.566879	+	1.19548i
$58$	8.65597	+	2.52722i	1.13658	+	0.331841i
$59$	−5.91537	+	2.15302i	−0.770115	+	0.280299i	−0.697045	−	0.717028i	$-0.745502\pi$
$59$	−5.91537	+	2.15302i	−0.770115	+	0.280299i	−0.0730705	+	0.997327i	$0.523280\pi$
$60$	2.93520	−	1.83973i	0.378933	−	0.237508i
$61$	−0.311420	−	1.76615i	−0.0398733	−	0.226132i	0.958359	−	0.285566i	$-0.0921816\pi$
$61$	−0.311420	−	1.76615i	−0.0398733	−	0.226132i	−0.998232	+	0.0594337i	$0.981071\pi$
$62$	9.76375	−	4.29089i	1.24000	−	0.544944i
$63$	−0.137411	+	0.724510i	−0.0173121	+	0.0912797i
$64$	−7.39930	+	3.04145i	−0.924912	+	0.380181i
$65$	−0.257204	+	0.706662i	−0.0319022	+	0.0876506i
$66$	−1.97013	+	2.21547i	−0.242506	+	0.272705i
$67$	−6.42340	+	7.65512i	−0.784744	+	0.935221i	−0.999137	−	0.0415261i	$-0.986778\pi$
$67$	−6.42340	+	7.65512i	−0.784744	+	0.935221i	0.214394	+	0.976747i	$0.431222\pi$
$68$	6.41894	−	4.91623i	0.778411	−	0.596180i
$69$	−2.56067	−	5.58515i	−0.308268	−	0.672373i
$70$	−0.311707	−	0.153892i	−0.0372561	−	0.0183936i
$71$	4.04403	−	7.00447i	0.479939	−	0.831278i	−0.519797	−	0.854290i	$-0.673992\pi$
$71$	4.04403	−	7.00447i	0.479939	−	0.831278i	0.999735	+	0.0230121i	$0.00732561\pi$
$72$	−8.36727	−	1.41022i	−0.986093	−	0.166196i
$73$	7.23690	+	12.5347i	0.847015	+	1.46707i	0.883860	+	0.467752i	$0.154936\pi$
$73$	7.23690	+	12.5347i	0.847015	+	1.46707i	−0.0368445	+	0.999321i	$0.511731\pi$
$74$	0.707463	+	10.8689i	0.0822409	+	1.26349i
$75$	−0.459070	+	1.67011i	−0.0530089	+	0.192847i
$76$	1.49521	+	11.4370i	0.171512	+	1.31191i
$77$	0.292995	+	0.0516629i	0.0333898	+	0.00588753i
$78$	1.62105	−	0.874838i	0.183548	−	0.0990559i
$79$	−5.69121	−	6.78252i	−0.640312	−	0.763094i	0.344108	−	0.938930i	$-0.388181\pi$
$79$	−5.69121	−	6.78252i	−0.640312	−	0.763094i	−0.984419	+	0.175837i	$0.943737\pi$
$80$	1.69701	−	3.62217i	0.189732	−	0.404971i
$81$	−6.74285	−	5.96103i	−0.749206	−	0.662337i
$82$	−0.528061	+	4.80167i	−0.0583146	+	0.530255i
$83$	10.6221	−	8.91300i	1.16593	−	0.978329i	0.165958	−	0.986133i	$-0.446929\pi$
$83$	10.6221	−	8.91300i	1.16593	−	0.978329i	0.999970	+	0.00780394i	$0.00248410\pi$
$84$	0.320064	+	0.789064i	0.0349218	+	0.0860939i
$85$	−0.701999	+	3.98123i	−0.0761425	+	0.431825i
$86$	0.00219169	+	0.00897422i	0.000236336	+	0.000967715i
$87$	10.6490	+	2.92714i	1.14169	+	0.313822i
$88$	−0.525357	+	3.38284i	−0.0560033	+	0.360612i
$89$	2.75507	−	1.59064i	0.292037	−	0.168608i	−0.346823	−	0.937931i	$-0.612740\pi$
$89$	2.75507	−	1.59064i	0.292037	−	0.168608i	0.638860	+	0.769323i	$0.279406\pi$
$90$	3.55878	−	2.30977i	0.375129	−	0.243472i
$91$	−0.160086	−	0.0924257i	−0.0167816	−	0.00968885i
$92$	−5.98016	−	3.81737i	−0.623474	−	0.397988i
$93$	11.8735	−	5.44373i	1.23122	−	0.564489i
$94$	−2.07034	−	2.16466i	−0.213539	−	0.223268i
$95$	−4.41790	−	3.70706i	−0.453267	−	0.380336i
$96$	−9.00220	+	3.86786i	−0.918783	+	0.394762i
$97$	−1.59179	−	0.579364i	−0.161622	−	0.0588255i	0.259942	−	0.965624i	$-0.416296\pi$
$97$	−1.59179	−	0.579364i	−0.161622	−	0.0588255i	−0.421564	+	0.906799i	$0.638519\pi$
$98$	−5.80671	+	7.91186i	−0.586566	+	0.799219i
$99$	−2.36968	+	2.75121i	−0.238162	+	0.276507i
$100$	0.599690	+	1.90798i	0.0599690	+	0.190798i
$101$	11.5220	−	2.03164i	1.14648	−	0.202156i	0.432044	−	0.901853i	$-0.357793\pi$
$101$	11.5220	−	2.03164i	1.14648	−	0.202156i	0.714440	+	0.699696i	$0.246681\pi$
$102$	7.76534	−	6.14472i	0.768884	−	0.608417i
$103$	3.48523	+	9.57560i	0.343410	+	0.943512i	0.984397	+	0.175960i	$0.0563030\pi$
$103$	3.48523	+	9.57560i	0.343410	+	0.943512i	−0.640987	+	0.767552i	$0.721475\pi$
$104$	1.02559	−	1.86343i	0.100568	−	0.182724i
$105$	−0.384695	−	0.182416i	−0.0375424	−	0.0178020i
$106$	−0.438979	−	0.657620i	−0.0426374	−	0.0638737i
$107$	−11.4554			−1.10744			−0.553719	−	0.832704i	$-0.686792\pi$
$107$	−11.4554			−1.10744			−0.553719	+	0.832704i	$0.686792\pi$
$108$	−10.2738	−	1.56486i	−0.988598	−	0.150579i
$109$	19.9338			1.90932			0.954658	−	0.297706i	$-0.0962216\pi$
$109$	19.9338			1.90932			0.954658	+	0.297706i	$0.0962216\pi$
$110$	−0.950324	−	1.42365i	−0.0906098	−	0.135740i
$111$	1.07690	+	13.2963i	0.102215	+	1.26203i
$112$	0.804399	+	0.565413i	0.0760086	+	0.0534265i
$113$	1.34706	+	3.70102i	0.126721	+	0.348162i	0.986788	−	0.162019i	$-0.0518006\pi$
$113$	1.34706	+	3.70102i	0.126721	+	0.348162i	−0.860067	+	0.510181i	$0.829578\pi$
$114$	2.05257	+	13.9767i	0.192241	+	1.30904i
$115$	3.49345	−	0.615990i	0.325766	−	0.0574413i
$116$	12.1657	−	3.82376i	1.12956	−	0.355028i
$117$	1.96818	−	1.10272i	0.181958	−	0.101947i
$118$	−5.26736	+	7.17698i	−0.484900	+	0.660694i
$119$	−0.933790	−	0.339872i	−0.0856004	−	0.0311560i
$120$	2.00798	−	4.46856i	0.183303	−	0.407922i
$121$	−7.30427	−	6.12901i	−0.664025	−	0.557183i
$122$	−1.75302	−	1.83288i	−0.158711	−	0.165942i
$123$	−0.553644	+	5.89031i	−0.0499204	+	0.531112i
$124$	8.11536	−	12.7132i	0.728780	−	1.14168i
$125$	−0.866025	−	0.500000i	−0.0774597	−	0.0447214i
$126$	0.407233	+	0.960081i	0.0362792	+	0.0855308i
$127$	−13.5059	+	7.79761i	−1.19845	+	0.691926i	−0.960210	−	0.279280i	$-0.909904\pi$
$127$	−13.5059	+	7.79761i	−1.19845	+	0.691926i	−0.238241	+	0.971206i	$0.576571\pi$
$128$	−6.31524	+	9.38710i	−0.558194	+	0.829711i
$129$	0.00285776	+	0.0109473i	0.000251612	+	0.000963856i
$130$	0.252315	+	1.03314i	0.0221295	+	0.0906127i
$131$	2.27248	−	12.8879i	0.198547	−	1.12602i	−0.708729	−	0.705481i	$-0.750731\pi$
$131$	2.27248	−	12.8879i	0.198547	−	1.12602i	0.907276	−	0.420536i	$-0.138158\pi$
$132$	−0.577818	+	4.15277i	−0.0502926	+	0.361452i
$133$	1.08596	−	0.911226i	0.0941644	−	0.0790133i
$134$	−1.54488	+	14.0476i	−0.133457	+	1.21353i
$135$	4.31331	−	2.89747i	0.371231	−	0.249374i
$136$	3.69010	−	10.8225i	0.316424	−	0.928025i
$137$	−4.66524	−	5.55981i	−0.398578	−	0.475007i	0.529008	−	0.848617i	$-0.322564\pi$
$137$	−4.66524	−	5.55981i	−0.398578	−	0.475007i	−0.927586	+	0.373610i	$0.878120\pi$
$138$	−7.39720	−	4.55888i	−0.629691	−	0.388077i
$139$	−14.8508	−	2.61860i	−1.25963	−	0.222107i	−0.496321	−	0.868139i	$-0.665316\pi$
$139$	−14.8508	−	2.61860i	−1.25963	−	0.222107i	−0.763311	+	0.646032i	$0.776427\pi$
$140$	−0.487469	+	0.0637290i	−0.0411987	+	0.00538609i
$141$	−2.57725	−	2.61072i	−0.217044	−	0.219862i
$142$	−0.742947	−	11.4141i	−0.0623468	−	0.957850i
$143$	−0.455100	−	0.788257i	−0.0380574	−	0.0659173i
$144$	−10.9491	+	4.91094i	−0.912425	+	0.409245i
$145$	−3.18812	+	5.52198i	−0.264759	+	0.458576i
$146$	18.3540	+	9.06151i	1.51899	+	0.749936i
$147$	−6.95759	+	9.80129i	−0.573852	+	0.808397i
$148$	9.36604	+	12.2289i	0.769884	+	1.00521i
$149$	4.51542	−	5.38127i	0.369918	−	0.440851i	−0.548687	−	0.836028i	$-0.684872\pi$
$149$	4.51542	−	5.38127i	0.369918	−	0.440851i	0.918605	+	0.395177i	$0.129317\pi$
$150$	0.771336	+	2.32487i	0.0629793	+	0.189825i
$151$	−0.161803	+	0.444550i	−0.0131673	+	0.0361770i	−0.946102	−	0.323868i	$-0.895017\pi$
$151$	−0.161803	+	0.444550i	−0.0131673	+	0.0361770i	0.932935	+	0.360045i	$0.117239\pi$
$152$	10.7386	+	12.2785i	0.871017	+	0.995921i
$153$	9.39034	−	7.67519i	0.759164	−	0.620503i
$154$	0.385193	−	0.169282i	0.0310397	−	0.0136411i
$155$	1.30953	+	7.42673i	0.105184	+	0.596530i
$156$	1.21984	−	2.30180i	0.0976651	−	0.184292i
$157$	−20.0093	+	7.28278i	−1.59691	+	0.581229i	−0.978793	−	0.204853i	$-0.934328\pi$
$157$	−20.0093	+	7.28278i	−1.59691	+	0.581229i	−0.618122	+	0.786082i	$0.712106\pi$
$158$	−12.0196	−	3.50927i	−0.956226	−	0.279183i
$159$	−0.550309	−	0.796813i	−0.0436423	−	0.0631914i
$160$	−0.847923	−	5.59294i	−0.0670342	−	0.442161i
$161$			0.871968i			0.0687207i
$162$	−12.6115	−	1.71730i	−0.990856	−	0.134924i
$163$			2.97419i			0.232957i	0.993193	+	0.116478i	$0.0371606\pi$
$163$			2.97419i			0.232957i	−0.993193	+	0.116478i	$0.962839\pi$
$164$	3.14898	+	6.06248i	0.245894	+	0.473400i
$165$	−1.19134	−	1.72498i	−0.0927455	−	0.134290i
$166$	5.49586	−	18.8238i	0.426562	−	1.46101i
$167$	15.7978	−	5.74993i	1.22247	−	0.444943i	0.351458	−	0.936204i	$-0.385686\pi$
$167$	15.7978	−	5.74993i	1.22247	−	0.444943i	0.871013	+	0.491261i	$0.163464\pi$
$168$	0.996014	+	0.676818i	0.0768441	+	0.0522176i
$169$	−2.15922	−	12.2456i	−0.166094	−	0.941967i
$170$	2.30021	+	5.23403i	0.176418	+	0.401432i
$171$	2.78431	+	17.0760i	0.212921	+	1.30583i
$172$	0.00962416	+	0.00883491i	0.000733835	+	0.000673656i
$173$	1.77604	−	4.87963i	0.135030	−	0.370991i	−0.853687	−	0.520786i	$-0.825639\pi$
$173$	1.77604	−	4.87963i	0.135030	−	0.370991i	0.988717	+	0.149795i	$0.0478612\pi$
$174$	14.8239	−	4.91822i	1.12380	−	0.372849i
$175$	0.158003	−	0.188300i	0.0119439	−	0.0142342i
$176$	2.03814	+	4.39149i	0.153631	+	0.331021i
$177$	−6.31134	+	8.89090i	−0.474389	+	0.668281i
$178$	1.99168	−	4.03414i	0.149283	−	0.302372i
$179$	−4.51117	+	7.81358i	−0.337181	+	0.584014i	−0.983901	−	0.178713i	$-0.942807\pi$
$179$	−4.51117	+	7.81358i	−0.337181	+	0.584014i	0.646720	+	0.762727i	$0.276140\pi$
$180$	2.37240	−	5.51106i	0.176828	−	0.410770i
$181$	−2.39263	−	4.14416i	−0.177843	−	0.308033i	0.763298	−	0.646046i	$-0.223579\pi$
$181$	−2.39263	−	4.14416i	−0.177843	−	0.308033i	−0.941141	+	0.338013i	$0.890245\pi$
$182$	−0.260867	+	0.0169799i	−0.0193368	+	0.00125864i
$183$	−2.18224	−	2.21058i	−0.161316	−	0.163410i
$184$	−10.0313	+	0.205298i	−0.739517	+	0.0151348i
$185$	−7.58476	−	1.33740i	−0.557642	−	0.0983274i
$186$	9.69172	−	15.7257i	0.710632	−	1.15307i
$187$	−3.14517	−	3.74827i	−0.229998	−	0.274101i
$188$	−4.13481	−	0.920581i	−0.301562	−	0.0671402i
$189$	0.517292	+	1.16782i	0.0376275	+	0.0849463i
$190$	−8.10711	−	0.891575i	−0.588152	−	0.0646817i
$191$	10.2501	−	8.60085i	0.741671	−	0.622336i	−0.191615	−	0.981470i	$-0.561373\pi$
$191$	10.2501	−	8.60085i	0.741671	−	0.622336i	0.933286	+	0.359135i	$0.116928\pi$
$192$	−7.55175	+	11.6177i	−0.545001	+	0.838436i
$193$	1.34642	−	7.63593i	0.0969175	−	0.549646i	−0.897225	−	0.441573i	$-0.854421\pi$
$193$	1.34642	−	7.63593i	0.0969175	−	0.549646i	0.994143	−	0.108074i	$-0.0344682\pi$
$194$	−2.32721	+	0.568351i	−0.167084	+	0.0408052i
$195$	0.328996	+	1.26029i	0.0235599	+	0.0902514i
$196$	−0.617914	+	13.8654i	−0.0441367	+	0.990385i
$197$	−6.93764	+	4.00545i	−0.494286	+	0.285376i	−0.726351	−	0.687324i	$-0.758785\pi$
$197$	−6.93764	+	4.00545i	−0.494286	+	0.285376i	0.232065	+	0.972700i	$0.425452\pi$
$198$	−0.627146	+	5.09664i	−0.0445693	+	0.362203i
$199$	−8.00596	−	4.62224i	−0.567528	−	0.327662i	0.188634	−	0.982048i	$-0.439594\pi$
$199$	−8.00596	−	4.62224i	−0.567528	−	0.327662i	−0.756161	+	0.654385i	$0.772927\pi$
$200$	2.20345	+	1.77336i	0.155807	+	0.125396i
$201$	−1.61972	+	17.2325i	−0.114246	+	1.21549i
$202$	11.9574	−	11.4364i	0.841318	−	0.804660i
$203$	−1.20065	−	1.00746i	−0.0842689	−	0.0707100i
$204$	4.30922	−	13.3247i	0.301706	−	0.932913i
$205$	−3.20977	−	1.16826i	−0.224180	−	0.0815948i
$206$	11.6179	+	8.52663i	0.809454	+	0.594078i
$207$	−9.14686	−	5.43947i	−0.635751	−	0.378069i
$208$	−0.256760	−	2.99708i	−0.0178031	−	0.207810i
$209$	6.87423	−	1.21211i	0.475501	−	0.0838436i
$210$	−0.595716	+	0.0874850i	−0.0411083	+	0.00603704i
$211$	7.08402	+	19.4632i	0.487684	+	1.33990i	0.902772	+	0.430119i	$0.141528\pi$
$211$	7.08402	+	19.4632i	0.487684	+	1.33990i	−0.415088	+	0.909781i	$0.636249\pi$
$212$	−1.03268	−	0.428842i	−0.0709248	−	0.0294530i
$213$	−1.13091	−	13.9632i	−0.0774890	−	0.956744i
$214$	−13.4742	+	8.99439i	−0.921078	+	0.614844i
$215$	−0.00653223			−0.000445494
$216$	−13.3130	+	6.22599i	−0.905838	+	0.423625i
$217$	−1.85372			−0.125839
$218$	23.4468	−	15.6513i	1.58802	−	1.06004i
$219$	22.6517	+	10.7411i	1.53066	+	0.725817i
$220$	−2.23560	−	0.928380i	−0.150724	−	0.0625914i
$221$	1.03979	+	2.85679i	0.0699435	+	0.192168i
$222$	11.7065	+	14.7940i	0.785687	+	0.992906i
$223$	−8.66402	+	1.52770i	−0.580185	+	0.102302i	−0.456036	−	0.889961i	$-0.650731\pi$
$223$	−8.66402	+	1.52770i	−0.580185	+	0.102302i	−0.124149	+	0.992264i	$0.539620\pi$
$224$	1.39010	+	0.0334701i	0.0928800	+	0.00223631i
$225$	0.989607	+	2.83208i	0.0659738	+	0.188805i
$226$	4.49036	+	3.29558i	0.298694	+	0.219219i
$227$	9.34078	+	3.39976i	0.619969	+	0.225650i	0.632860	−	0.774267i	$-0.281881\pi$
$227$	9.34078	+	3.39976i	0.619969	+	0.225650i	−0.0128905	+	0.999917i	$0.504103\pi$
$228$	13.3883	+	14.8282i	0.886660	+	0.982020i
$229$	0.471602	+	0.395721i	0.0311643	+	0.0261500i	0.658237	−	0.752811i	$-0.271303\pi$
$229$	0.471602	+	0.395721i	0.0311643	+	0.0261500i	−0.627072	+	0.778961i	$0.715747\pi$
$230$	3.62545	−	3.46748i	0.239055	−	0.228639i
$231$	0.468425	−	0.214763i	0.0308201	−	0.0141303i
$232$	11.3074	−	14.0497i	0.742366	−	0.922408i
$233$	−24.0677	−	13.8955i	−1.57673	−	0.910324i	−0.995312	−	0.0967173i	$-0.969166\pi$
$233$	−24.0677	−	13.8955i	−1.57673	−	0.910324i	−0.581416	−	0.813607i	$-0.697501\pi$
$234$	1.44921	−	2.84240i	0.0947380	−	0.185813i
$235$	1.83426	−	1.05901i	0.119654	−	0.0690823i
$236$	−0.560519	+	12.5775i	−0.0364867	+	0.818727i
$237$	−14.7870	−	4.06459i	−0.960522	−	0.264023i
$238$	−1.36521	+	0.333411i	−0.0884932	+	0.0216118i
$239$	2.81587	−	15.9696i	0.182143	−	1.03299i	−0.747428	−	0.664343i	$-0.768711\pi$
$239$	2.81587	−	15.9696i	0.182143	−	1.03299i	0.929571	−	0.368643i	$-0.120178\pi$
$240$	−1.14670	−	6.83265i	−0.0740194	−	0.441045i
$241$	19.0856	−	16.0147i	1.22941	−	1.03160i	0.231135	−	0.972922i	$-0.425756\pi$
$241$	19.0856	−	16.0147i	1.22941	−	1.03160i	0.998277	−	0.0586770i	$-0.0186882\pi$
$242$	−13.4038	−	1.47407i	−0.861628	−	0.0947571i
$243$	−15.4773	−	1.85868i	−0.992866	−	0.119235i
$244$	−3.50107	−	0.779484i	−0.224133	−	0.0499014i
$245$	−4.46067	−	5.31603i	−0.284982	−	0.339628i
$246$	3.97365	+	7.36306i	0.253351	+	0.469452i
$247$	−4.27109	−	0.753109i	−0.271763	−	0.0479192i
$248$	−0.436444	−	21.3256i	−0.0277142	−	1.35417i
$249$	6.36554	−	23.1580i	0.403400	−	1.46758i
$250$	−1.41123	+	0.0918572i	−0.0892538	+	0.00580956i
$251$	−2.54978	−	4.41635i	−0.160941	−	0.278757i	0.774266	−	0.632861i	$-0.218119\pi$
$251$	−2.54978	−	4.41635i	−0.160941	−	0.278757i	−0.935206	+	0.354103i	$0.884786\pi$
$252$	1.23282	+	0.809531i	0.0776604	+	0.0509957i
$253$	−2.14676	+	3.71831i	−0.134966	+	0.233768i
$254$	−9.76359	+	19.7761i	−0.612622	+	1.24086i
$255$	2.91821	+	6.36499i	0.182745	+	0.398591i
$256$	−0.0577577	+	15.9999i	−0.00360986	+	0.999993i
$257$	−16.3635	+	19.5013i	−1.02073	+	1.21646i	−0.0446563	+	0.999002i	$0.514219\pi$
$257$	−16.3635	+	19.5013i	−1.02073	+	1.21646i	−0.976071	+	0.217453i	$0.930225\pi$
$258$	0.0119568	+	0.0106327i	0.000744399	+	0.000661965i
$259$	0.647499	−	1.77899i	0.0402336	−	0.110541i
$260$	1.10797	+	1.01711i	0.0687133	+	0.0630783i
$261$	18.0580	−	6.30997i	1.11776	−	0.390577i
$262$	−7.44613	−	16.9434i	−0.460023	−	1.04676i
$263$	1.20783	+	6.84992i	0.0744778	+	0.422384i	0.999135	+	0.0415839i	$0.0132404\pi$
$263$	1.20783	+	6.84992i	0.0744778	+	0.422384i	−0.924657	+	0.380800i	$0.875649\pi$
$264$	2.58096	+	5.33830i	0.158847	+	0.328549i
$265$	0.525374	−	0.191221i	0.0322735	−	0.0117466i
$266$	0.561873	−	1.92447i	0.0344507	−	0.117997i
$267$	2.36085	−	4.97876i	0.144482	−	0.304695i
$268$	9.21255	+	17.7362i	0.562746	+	1.08341i
$269$		−	2.27064i		−	0.138443i	−0.997601	−	0.0692215i	$-0.977948\pi$
$269$		−	2.27064i		−	0.138443i	0.997601	−	0.0692215i	$-0.0220515\pi$
$270$	2.79846	−	6.79475i	0.170309	−	0.413515i
$271$		−	22.6376i		−	1.37513i	−0.726121	−	0.687567i	$-0.758679\pi$
$271$		−	22.6376i		−	1.37513i	0.726121	−	0.687567i	$-0.241321\pi$
$272$	−4.15706	−	15.6271i	−0.252059	−	0.947534i
$273$	−0.319127	+	0.0258469i	−0.0193145	+	0.00156432i
$274$	−9.85276	−	2.87664i	−0.595227	−	0.173784i
$275$	1.13736	−	0.413964i	0.0685852	−	0.0249630i
$276$	−12.2803	+	0.445727i	−0.739186	+	0.0268296i
$277$	−4.60351	−	26.1078i	−0.276598	−	1.56867i	−0.733839	−	0.679323i	$-0.762273\pi$
$277$	−4.60351	−	26.1078i	−0.276598	−	1.56867i	0.457241	−	0.889343i	$-0.348838\pi$
$278$	−19.5240	+	8.58027i	−1.17097	+	0.514610i
$279$	11.5638	−	19.4453i	0.692305	−	1.16416i
$280$	−0.523338	+	0.457703i	−0.0312754	+	0.0273530i
$281$	2.73352	−	7.51029i	0.163068	−	0.448026i	−0.831067	−	0.556173i	$-0.812269\pi$
$281$	2.73352	−	7.51029i	0.163068	−	0.448026i	0.994135	+	0.108146i	$0.0344915\pi$
$282$	−5.08129	−	1.04724i	−0.302586	−	0.0623621i
$283$	−0.717765	+	0.855400i	−0.0426667	+	0.0508482i	−0.786956	−	0.617009i	$-0.788344\pi$
$283$	−0.717765	+	0.855400i	−0.0426667	+	0.0508482i	0.744289	+	0.667858i	$0.232788\pi$
$284$	−9.83582	−	12.8423i	−0.583649	−	0.762049i
$285$	−9.94517	−	0.934769i	−0.589101	−	0.0553710i
$286$	−1.15421	−	0.569843i	−0.0682501	−	0.0336955i
$287$	0.419812	−	0.727136i	0.0247807	−	0.0429215i
$288$	−9.02276	+	14.3732i	−0.531671	+	0.846951i
$289$	−0.328491	−	0.568964i	−0.0193230	−	0.0334684i
$290$	0.585703	+	8.99831i	0.0343937	+	0.528399i
$291$	−2.83887	+	0.741079i	−0.166417	+	0.0434428i
$292$	28.7033	−	3.75252i	1.67974	−	0.219600i
$293$	−10.6830	−	1.88371i	−0.624110	−	0.110047i	−0.147355	−	0.989084i	$-0.547076\pi$
$293$	−10.6830	−	1.88371i	−0.624110	−	0.110047i	−0.476755	+	0.879036i	$0.658187\pi$
$294$	−0.488100	+	16.9914i	−0.0284665	+	0.990960i
$295$	−4.04635	−	4.82225i	−0.235588	−	0.280762i
$296$	20.6183	+	7.03012i	1.19842	+	0.408617i
$297$	−0.669268	+	6.25345i	−0.0388349	+	0.362862i
$298$	1.08599	−	9.87496i	0.0629099	−	0.572041i
$299$	2.04354	−	1.71473i	0.118181	−	0.0991656i
$300$	2.73268	+	2.12896i	0.157771	+	0.122916i
$301$	0.000278823	−	0.00158128i	1.60711e−5	−	9.11437e-5i
$302$	0.158727	+	0.649935i	0.00913373	+	0.0373996i
$303$	14.4214	−	14.2365i	0.828486	−	0.817866i
$304$	22.2718	+	6.01081i	1.27737	+	0.344743i
$305$	1.55313	−	0.896698i	0.0889318	−	0.0513448i
$306$	5.01892	−	16.4008i	0.286912	−	0.937569i
$307$	−13.8771	−	8.01193i	−0.792006	−	0.457265i	0.0486623	−	0.998815i	$-0.484504\pi$
$307$	−13.8771	−	8.01193i	−0.792006	−	0.457265i	−0.840668	+	0.541550i	$0.817838\pi$
$308$	0.320162	−	0.501554i	0.0182429	−	0.0285787i
$309$	14.3923	+	10.2166i	0.818749	+	0.581201i
$310$	7.37152	+	7.70735i	0.418674	+	0.437748i
$311$	−15.6782	−	13.1556i	−0.889032	−	0.745986i	0.0789841	−	0.996876i	$-0.474832\pi$
$311$	−15.6782	−	13.1556i	−0.889032	−	0.745986i	−0.968016	+	0.250890i	$0.919277\pi$
$312$	−0.372484	−	3.66522i	−0.0210878	−	0.207502i
$313$	−2.95000	−	1.07371i	−0.166744	−	0.0606898i	0.257299	−	0.966332i	$-0.417167\pi$
$313$	−2.95000	−	1.07371i	−0.166744	−	0.0606898i	−0.424043	+	0.905642i	$0.639390\pi$
$314$	−17.8173	+	24.2768i	−1.00549	+	1.37002i
$315$	−0.727814	+	0.118673i	−0.0410077	+	0.00668648i
$316$	−16.8931	+	5.30963i	−0.950313	+	0.298690i
$317$	11.9008	−	2.09843i	0.668415	−	0.117860i	0.170865	−	0.985295i	$-0.445344\pi$
$317$	11.9008	−	2.09843i	0.668415	−	0.117860i	0.497551	+	0.867435i	$0.334233\pi$
$318$	−1.27292	−	0.505152i	−0.0713817	−	0.0283275i
$319$	−2.63953	−	7.25206i	−0.147785	−	0.406037i
$320$	−5.38873	−	5.91283i	−0.301239	−	0.330537i
$321$	−16.3262	+	11.2755i	−0.911238	+	0.629335i
$322$	0.684638	+	1.02563i	0.0381534	+	0.0571564i
$323$	−23.3146			−1.29726
$324$	−16.1824	+	7.88219i	−0.899024	+	0.437900i
$325$	−0.752014			−0.0417142
$326$	2.33523	+	3.49834i	0.129336	+	0.193755i
$327$	28.4095	−	19.6207i	1.57105	−	1.08503i
$328$	8.46396	+	4.65841i	0.467344	+	0.257217i
$329$	0.178066	+	0.489231i	0.00981707	+	0.0269722i
$330$	−2.75568	−	1.09358i	−0.151695	−	0.0601996i
$331$	2.67053	−	0.470887i	0.146786	−	0.0258823i	−0.0997724	−	0.995010i	$-0.531811\pi$
$331$	2.67053	−	0.470887i	0.146786	−	0.0258823i	0.246558	+	0.969128i	$0.420700\pi$
$332$	−8.31540	−	26.4563i	−0.456367	−	1.45198i
$333$	14.6222	+	17.8898i	0.801293	+	0.980355i
$334$	14.0672	−	19.1671i	0.769723	−	1.04878i
$335$	−9.39039	−	3.41782i	−0.513052	−	0.186736i
$336$	1.70295	+	0.0140589i	0.0929038	+	0.000766978i
$337$	25.5023	+	21.3989i	1.38920	+	1.16567i	0.965664	+	0.259793i	$0.0836545\pi$
$337$	25.5023	+	21.3989i	1.38920	+	1.16567i	0.423532	+	0.905881i	$0.360790\pi$
$338$	−12.1545	−	12.7083i	−0.661119	−	0.691238i
$339$	5.56269	+	3.94876i	0.302124	+	0.214467i
$340$	6.81515	+	4.35038i	0.369603	+	0.235933i
$341$	−7.90475	−	4.56381i	−0.428066	−	0.247144i
$342$	16.6824	+	17.8991i	0.902082	+	0.967873i
$343$	2.96741	−	1.71323i	0.160225	−	0.0925060i
$344$	0.0182571	+	0.00283534i	0.000984356	+	0.000152871i
$345$	4.37253	−	4.31648i	0.235409	−	0.232391i
$346$	−1.74228	−	7.13405i	−0.0936655	−	0.383529i
$347$	−1.99901	+	11.3370i	−0.107313	+	0.608600i	0.882959	+	0.469451i	$0.155548\pi$
$347$	−1.99901	+	11.3370i	−0.107313	+	0.608600i	−0.990271	+	0.139150i	$0.955563\pi$
$348$	13.5748	−	17.4242i	0.727684	−	0.934034i
$349$	−3.19522	+	2.68111i	−0.171036	+	0.143516i	−0.724288	−	0.689498i	$-0.757831\pi$
$349$	−3.19522	+	2.68111i	−0.171036	+	0.143516i	0.553252	+	0.833014i	$0.313387\pi$
$350$	0.0380009	−	0.345543i	0.00203123	−	0.0184700i
$351$	1.71963	−	3.50885i	0.0917872	−	0.187289i
$352$	5.84536	+	3.56512i	0.311559	+	0.190022i
$353$	−21.3342	−	25.4251i	−1.13551	−	1.35324i	−0.926929	−	0.375236i	$-0.877562\pi$
$353$	−21.3342	−	25.4251i	−1.13551	−	1.35324i	−0.208576	−	0.978006i	$-0.566883\pi$
$354$	−0.442763	+	15.4132i	−0.0235326	+	0.819201i
$355$	7.96519	+	1.40448i	0.422749	+	0.0745420i
$356$	−0.824788	−	6.30888i	−0.0437137	−	0.334370i
$357$	−1.66536	+	0.434738i	−0.0881403	+	0.0230088i
$358$	0.828767	+	12.7326i	0.0438017	+	0.672938i
$359$	14.6260	+	25.3330i	0.771931	+	1.33702i	0.936503	+	0.350659i	$0.114042\pi$
$359$	14.6260	+	25.3330i	0.771931	+	1.33702i	−0.164572	+	0.986365i	$0.552624\pi$
$360$	−1.53660	−	8.34499i	−0.0809860	−	0.439820i
$361$	7.13004	−	12.3496i	0.375265	−	0.649978i
$362$	−6.06813	−	2.99588i	−0.318934	−	0.157460i
$363$	−16.4427	−	1.54549i	−0.863019	−	0.0811171i
$364$	−0.293508	+	0.224796i	−0.0153840	+	0.0117825i
$365$	−9.30358	+	11.0876i	−0.486972	+	0.580350i
$366$	−4.30248	−	0.886729i	−0.224894	−	0.0463501i
$367$	−1.18410	+	3.25328i	−0.0618093	+	0.169820i	−0.966753	−	0.255711i	$-0.917690\pi$
$367$	−1.18410	+	3.25328i	−0.0618093	+	0.169820i	0.904944	+	0.425531i	$0.139913\pi$
$368$	−11.6379	+	8.11770i	−0.606669	+	0.423164i
$369$	5.00873	+	8.93977i	0.260744	+	0.465386i
$370$	−9.97150	+	4.38219i	−0.518393	+	0.227819i
$371$	0.0238644	+	0.135342i	0.00123898	+	0.00702659i
$372$	−0.947572	−	26.1067i	−0.0491293	−	1.35357i
$373$	−16.7643	+	6.10171i	−0.868024	+	0.315935i	−0.737367	−	0.675493i	$-0.763931\pi$
$373$	−16.7643	+	6.10171i	−0.868024	+	0.315935i	−0.130657	+	0.991428i	$0.541709\pi$
$374$	−6.64246	−	1.93935i	−0.343473	−	0.100282i
$375$	−1.72640	+	0.139825i	−0.0891508	+	0.00722053i
$376$	−5.58629	+	2.16369i	−0.288091	+	0.111584i
$377$			4.79502i			0.246956i
$378$	1.52538	+	0.967464i	0.0784573	+	0.0497610i
$379$			16.9816i			0.872288i	0.899877	+	0.436144i	$0.143656\pi$
$379$			16.9816i			0.872288i	−0.899877	+	0.436144i	$0.856344\pi$
$380$	−10.2359	+	5.31672i	−0.525089	+	0.272742i
$381$	−11.5733	+	24.4068i	−0.592919	+	1.25040i
$382$	5.30339	−	18.1646i	0.271345	−	0.929381i
$383$	6.14396	−	2.23622i	0.313942	−	0.114265i	−0.180244	−	0.983622i	$-0.557689\pi$
$383$	6.14396	−	2.23622i	0.313942	−	0.114265i	0.494185	+	0.869357i	$0.335466\pi$
$384$	0.239211	+	19.5945i	0.0122072	+	0.999925i
$385$	0.0516629	+	0.292995i	0.00263298	+	0.0149324i
$386$	−4.41176	−	10.0388i	−0.224553	−	0.510960i
$387$	0.0148482	+	0.0127891i	0.000754776	+	0.000650108i
$388$	−2.29108	+	2.49575i	−0.116312	+	0.126703i
$389$	7.21948	−	19.8353i	0.366042	−	1.00569i	−0.610810	−	0.791777i	$-0.709156\pi$
$389$	7.21948	−	19.8353i	0.366042	−	1.00569i	0.976852	−	0.213915i	$-0.0686216\pi$
$390$	1.37651	+	1.22408i	0.0697023	+	0.0619836i
$391$	9.21800	−	10.9856i	0.466174	−	0.555565i
$392$	10.1598	+	16.7941i	0.513148	+	0.848228i
$393$	−9.44669	−	20.6044i	−0.476522	−	1.03936i
$394$	−5.01532	+	10.1585i	−0.252668	+	0.511778i
$395$	4.42698	−	7.66775i	0.222745	−	0.385806i
$396$	3.26403	+	6.48724i	0.164024	+	0.325996i
$397$	2.58386	+	4.47538i	0.129680	+	0.224613i	0.923553	−	0.383471i	$-0.125272\pi$
$397$	2.58386	+	4.47538i	0.129680	+	0.224613i	−0.793872	+	0.608084i	$0.791938\pi$
$398$	−13.0461	+	0.849173i	−0.653941	+	0.0425652i
$399$	0.650786	−	2.36757i	0.0325800	−	0.118527i
$400$	3.98414	+	0.355815i	0.199207	+	0.0177907i
$401$	28.9861	+	5.11104i	1.44750	+	0.255233i	0.841511	−	0.540241i	$-0.181667\pi$
$401$	28.9861	+	5.11104i	1.44750	+	0.255233i	0.605988	+	0.795474i	$0.292778\pi$
$402$	11.6252	+	21.5411i	0.579811	+	1.07437i
$403$	3.64535	+	4.34436i	0.181588	+	0.216408i
$404$	5.08520	−	22.8403i	0.252998	−	1.13635i
$405$	3.29535	−	8.37500i	0.163747	−	0.416157i
$406$	−2.20326	−	0.242302i	−0.109346	−	0.0120253i
$407$	7.14094	−	5.99196i	0.353963	−	0.297010i
$408$	−5.39342	−	19.0563i	−0.267014	−	0.943429i
$409$	4.15265	−	23.5508i	0.205335	−	1.16451i	−0.691576	−	0.722303i	$-0.743083\pi$
$409$	4.15265	−	23.5508i	0.205335	−	1.16451i	0.896911	−	0.442210i	$-0.145805\pi$
$410$	−4.69270	+	1.14605i	−0.231756	+	0.0565995i
$411$	−12.1213	−	3.33185i	−0.597901	−	0.164348i
$412$	20.3601	+	0.907350i	1.00307	+	0.0447019i
$413$	1.34006	−	0.773683i	0.0659399	−	0.0380704i
$414$	−15.0297	+	0.783720i	−0.738669	+	0.0385177i
$415$	12.0085	+	6.93308i	0.589472	+	0.340332i
$416$	−2.65521	−	3.32365i	−0.130182	−	0.162955i
$417$	−23.7428	+	10.8855i	−1.16269	+	0.533067i
$418$	7.13397	−	6.82313i	0.348934	−	0.333730i
$419$	−5.42215	−	4.54972i	−0.264889	−	0.222268i	0.500663	−	0.865642i	$-0.333090\pi$
$419$	−5.42215	−	4.54972i	−0.264889	−	0.222268i	−0.765552	+	0.643374i	$0.777534\pi$
$420$	−0.632009	+	0.570638i	−0.0308389	+	0.0278443i
$421$	−5.67293	−	2.06478i	−0.276482	−	0.100631i	0.200058	−	0.979784i	$-0.435887\pi$
$421$	−5.67293	−	2.06478i	−0.276482	−	0.100631i	−0.476540	+	0.879153i	$0.658109\pi$
$422$	23.6142	+	17.3311i	1.14952	+	0.843663i
$423$	−6.24279	−	1.18401i	−0.303535	−	0.0575684i
$424$	−1.55138	+	0.306406i	−0.0753417	+	0.0148804i
$425$	−3.98123	+	0.701999i	−0.193118	+	0.0340519i
$426$	−12.2936	−	15.5360i	−0.595629	−	0.752722i
$427$	0.150774	+	0.414247i	0.00729644	+	0.0200468i
$428$	−8.78670	+	21.1589i	−0.424721	+	1.02276i
$429$	−1.42448	−	0.675466i	−0.0687745	−	0.0326118i
$430$	−0.00768341	+	0.00512887i	−0.000370527	+	0.000247336i
$431$	−37.4475			−1.80378			−0.901892	−	0.431961i	$-0.857822\pi$
$431$	−37.4475			−1.80378			−0.901892	+	0.431961i	$0.857822\pi$
$432$	−10.7708	+	17.7761i	−0.518209	+	0.855254i
$433$	38.6912			1.85938			0.929691	−	0.368339i	$-0.120074\pi$
$433$	38.6912			1.85938			0.929691	+	0.368339i	$0.120074\pi$
$434$	−2.18040	+	1.45547i	−0.104662	+	0.0698649i
$435$	0.891557	+	11.0079i	0.0427469	+	0.527789i
$436$	15.2899	−	36.8191i	0.732255	−	1.76332i
$437$	6.99708	+	19.2243i	0.334716	+	0.919623i
$438$	35.0772	−	5.15133i	1.67605	−	0.246140i
$439$	38.8989	−	6.85893i	1.85654	−	0.327359i	0.870283	−	0.492553i	$-0.163936\pi$
$439$	38.8989	−	6.85893i	1.85654	−	0.327359i	0.986261	+	0.165194i	$0.0528251\pi$
$440$	−3.35851	+	0.663324i	−0.160111	+	0.0316227i
$441$	−0.268575	+	20.8170i	−0.0127893	+	0.991286i
$442$	3.46607	+	2.54384i	0.164864	+	0.120998i
$443$	−1.16058	−	0.422415i	−0.0551406	−	0.0200696i	0.314303	−	0.949323i	$-0.398229\pi$
$443$	−1.16058	−	0.422415i	−0.0551406	−	0.0200696i	−0.369443	+	0.929253i	$0.620452\pi$
$444$	25.3852	+	8.20962i	1.20473	+	0.389611i
$445$	2.43700	+	2.04489i	0.115525	+	0.0969370i
$446$	−8.99138	+	8.59960i	−0.425754	+	0.407203i
$447$	1.13861	−	12.1138i	0.0538543	−	0.572965i
$448$	1.66136	−	1.05209i	0.0784918	−	0.0497065i
$449$	−29.0321	−	16.7617i	−1.37011	−	0.791032i	−0.379166	−	0.925328i	$-0.623789\pi$
$449$	−29.0321	−	16.7617i	−1.37011	−	0.791032i	−0.990941	+	0.134296i	$0.957123\pi$
$450$	3.38765	+	2.55417i	0.159696	+	0.120405i
$451$	3.58038	−	2.06713i	0.168594	−	0.0973376i
$452$	7.86927	+	0.350695i	0.370139	+	0.0164953i
$453$	0.206966	+	0.792830i	0.00972412	+	0.0372504i
$454$	13.6563	−	3.33514i	0.640921	−	0.156526i
$455$	0.0320991	−	0.182043i	0.00150483	−	0.00853432i
$456$	27.3903	+	6.92935i	1.28267	+	0.324496i
$457$	23.3125	−	19.5615i	1.09051	−	0.915047i	0.0937598	−	0.995595i	$-0.470111\pi$
$457$	23.3125	−	19.5615i	1.09051	−	0.915047i	0.996751	+	0.0805478i	$0.0256670\pi$
$458$	0.865418	+	0.0951739i	0.0404383	+	0.00444718i
$459$	5.82842	−	20.1815i	0.272047	−	0.941990i
$460$	1.54182	−	6.92513i	0.0718878	−	0.322886i
$461$	18.5602	+	22.1191i	0.864432	+	1.03019i	0.999227	+	0.0393169i	$0.0125182\pi$
$461$	18.5602	+	22.1191i	0.864432	+	1.03019i	−0.134794	+	0.990874i	$0.543037\pi$
$462$	0.382352	−	0.620401i	0.0177886	−	0.0288637i
$463$	8.89287	+	1.56805i	0.413287	+	0.0728736i	0.376426	−	0.926447i	$-0.377153\pi$
$463$	8.89287	+	1.56805i	0.413287	+	0.0728736i	0.0368609	+	0.999320i	$0.488264\pi$
$464$	2.26876	−	25.4038i	0.105324	−	1.17934i
$465$	9.17640	+	9.29556i	0.425546	+	0.431071i
$466$	−39.2194	+	2.55280i	−1.81680	+	0.118256i
$467$	18.7300	+	32.4413i	0.866721	+	1.50120i	0.865328	+	0.501205i	$0.167110\pi$
$467$	18.7300	+	32.4413i	0.866721	+	1.50120i	0.00139232	+	0.999999i	$0.499557\pi$
$468$	−0.527141	−	4.48118i	−0.0243671	−	0.207143i
$469$	1.22819	−	2.12728i	0.0567125	−	0.0982289i
$470$	1.32602	−	2.68584i	0.0611646	−	0.123889i
$471$	−21.3487	+	30.0743i	−0.983696	+	1.38575i
$472$	9.21612	+	15.2342i	0.424206	+	0.701209i
$473$	0.00508206	−	0.00605657i	0.000233674	−	0.000278481i
$474$	−20.5843	+	6.82937i	−0.945470	+	0.313683i
$475$	1.97248	−	5.41935i	0.0905037	−	0.248657i
$476$	−1.34401	+	1.46408i	−0.0616028	+	0.0671060i
$477$	−1.56859	−	0.593947i	−0.0718209	−	0.0271950i
$478$	−9.22664	−	20.9948i	−0.422017	−	0.960281i
$479$	5.83268	+	33.0788i	0.266502	+	1.51141i	0.764724	+	0.644358i	$0.222875\pi$
$479$	5.83268	+	33.0788i	0.266502	+	1.51141i	−0.498222	+	0.867049i	$0.666014\pi$
$480$	−6.71354	−	7.13641i	−0.306430	−	0.325731i
$481$	−5.44254	+	1.98092i	−0.248159	+	0.0903223i
$482$	9.87487	−	33.8223i	0.449788	−	1.54056i
$483$	0.858270	+	1.24272i	0.0390526	+	0.0565458i
$484$	−16.9233	+	8.79032i	−0.769242	+	0.399560i
$485$		−	1.69395i		−	0.0769182i
$486$	−19.6642	+	9.96595i	−0.891985	+	0.452064i
$487$			34.4221i			1.55981i	0.625896	+	0.779906i	$0.284733\pi$
$487$			34.4221i			1.55981i	−0.625896	+	0.779906i	$0.715267\pi$
$488$	−4.73009	+	1.83206i	−0.214121	+	0.0829336i
$489$	2.92747	+	4.23880i	0.132385	+	0.191685i
$490$	−9.42073	−	2.75051i	−0.425585	−	0.124255i
$491$	−21.2867	+	7.74773i	−0.960656	+	0.349650i	−0.774291	−	0.632830i	$-0.781893\pi$
$491$	−21.2867	+	7.74773i	−0.960656	+	0.349650i	−0.186366	+	0.982480i	$0.559671\pi$
$492$	10.4551	+	5.54069i	0.471354	+	0.249793i
$493$	4.47611	+	25.3853i	0.201594	+	1.14330i
$494$	−5.61510	+	2.46768i	−0.252635	+	0.111026i
$495$	−3.39577	−	1.28581i	−0.152628	−	0.0577927i
$496$	−17.2574	−	24.7411i	−0.774881	−	1.11091i
$497$	−0.679976	+	1.86822i	−0.0305011	+	0.0838011i
$498$	−10.6955	−	32.2371i	−0.479275	−	1.44458i
$499$	−14.8999	+	17.7570i	−0.667012	+	0.794914i	−0.988374	−	0.152042i	$-0.951415\pi$
$499$	−14.8999	+	17.7570i	−0.667012	+	0.794914i	0.321362	+	0.946956i	$0.395859\pi$
$500$	−1.58780	+	1.21609i	−0.0710088	+	0.0543852i
$501$	16.8553	−	23.7444i	0.753039	−	1.06082i
$502$	−6.46668	−	3.19264i	−0.288622	−	0.142495i
$503$	1.13319	−	1.96274i	0.0505265	−	0.0875144i	−0.839656	−	0.543119i	$-0.817243\pi$
$503$	1.13319	−	1.96274i	0.0505265	−	0.0875144i	0.890182	+	0.455604i	$0.150577\pi$
$504$	2.08570	−	0.0157722i	0.0929043	−	0.000702548i
$505$	5.84988	+	10.1323i	0.260316	+	0.450881i
$506$	0.394392	+	6.05915i	0.0175328	+	0.269362i
$507$	−15.1305	−	15.3270i	−0.671969	−	0.680695i
$508$	4.04326	+	30.9273i	0.179391	+	1.37218i
$509$	29.1173	+	5.13417i	1.29060	+	0.227568i	0.776477	−	0.630146i	$-0.217005\pi$
$509$	29.1173	+	5.13417i	1.29060	+	0.227568i	0.514127	+	0.857714i	$0.328116\pi$
$510$	8.43005	+	5.19542i	0.373289	+	0.230057i
$511$	−2.28690	−	2.72542i	−0.101167	−	0.120566i
$512$	12.4946	+	18.8649i	0.552189	+	0.833719i
$513$	20.7759	+	21.5959i	0.917278	+	0.953484i
$514$	−3.93555	+	35.7860i	−0.173590	+	1.57845i
$515$	−7.80610	+	6.55010i	−0.343978	+	0.288632i
$516$	0.0224124	+	0.00311847i	0.000986651	+	0.000137283i
$517$	−0.445156	+	2.52461i	−0.0195779	+	0.111032i
$518$	−0.635191	−	2.60089i	−0.0279087	−	0.114277i
$519$	−2.27178	−	8.70255i	−0.0997200	−	0.381999i
$520$	2.10182	+	0.326414i	0.0921709	+	0.0143142i
$521$	−33.1255	+	19.1250i	−1.45125	+	0.837882i	−0.998553	−	0.0537801i	$-0.982873\pi$
$521$	−33.1255	+	19.1250i	−1.45125	+	0.837882i	−0.452701	+	0.891662i	$0.649540\pi$
$522$	16.2860	−	21.6005i	0.712819	−	0.945427i
$523$	−23.0691	−	13.3189i	−1.00874	−	0.582397i	−0.0979179	−	0.995194i	$-0.531218\pi$
$523$	−23.0691	−	13.3189i	−1.00874	−	0.582397i	−0.910823	+	0.412798i	$0.864552\pi$
$524$	−22.0617	−	14.0828i	−0.963769	−	0.615212i
$525$	0.0398419	−	0.423885i	0.00173884	−	0.0184998i
$526$	6.79900	+	7.10874i	0.296450	+	0.309956i
$527$	23.3543	+	19.5966i	1.01733	+	0.853640i
$528$	7.22724	+	4.25259i	0.314525	+	0.185070i
$529$	9.78817	+	3.56260i	0.425573	+	0.154896i
$530$	0.467821	−	0.637425i	0.0203209	−	0.0276880i
$531$	−0.243629	+	18.8834i	−0.0105726	+	0.819471i
$532$	−0.850130	−	2.70478i	−0.0368578	−	0.117267i
$533$	−2.52968	+	0.446050i	−0.109572	+	0.0193206i
$534$	−1.13224	−	7.70982i	−0.0489968	−	0.333637i
$535$	−3.91799	−	10.7646i	−0.169389	−	0.465393i
$536$	24.7619	+	13.6285i	1.06955	+	0.588661i
$537$	1.26155	+	15.5762i	0.0544399	+	0.672161i
$538$	−1.78282	−	2.67079i	−0.0768629	−	0.115146i
$539$	8.39932			0.361784
$540$	−2.04336	−	10.1894i	−0.0879324	−	0.438484i
$541$	−27.1433			−1.16698			−0.583491	−	0.812120i	$-0.698314\pi$
$541$	−27.1433			−1.16698			−0.583491	+	0.812120i	$0.698314\pi$
$542$	−17.7742	−	26.6270i	−0.763467	−	1.14373i
$543$	−7.48902	−	3.55118i	−0.321385	−	0.152396i
$544$	−17.1595	−	15.1171i	−0.735708	−	0.648141i
$545$	6.81777	+	18.7317i	0.292041	+	0.802377i
$546$	−0.355073	+	0.280969i	−0.0151957	+	0.0120244i
$547$	−21.9345	+	3.86764i	−0.937850	+	0.165368i	−0.621624	−	0.783316i	$-0.713527\pi$
$547$	−21.9345	+	3.86764i	−0.937850	+	0.165368i	−0.316226	+	0.948684i	$0.602416\pi$
$548$	−13.8478	+	4.35244i	−0.591547	+	0.185927i
$549$	−5.28596	−	1.00254i	−0.225599	−	0.0427872i
$550$	1.01276	−	1.37993i	0.0431844	−	0.0588404i
$551$	−34.5551	−	12.5770i	−1.47210	−	0.535799i
$552$	−14.0945	+	10.1663i	−0.599900	+	0.432707i
$553$	1.66720	+	1.39895i	0.0708967	+	0.0594894i
$554$	−25.9137	−	27.0943i	−1.10097	−	1.15113i
$555$	−12.1261	+	5.55956i	−0.514725	+	0.235990i
$556$	−16.2278	+	25.4220i	−0.688214	+	1.07813i
$557$	0.0559126	+	0.0322812i	0.00236909	+	0.00136780i	0.501184	−	0.865341i	$-0.332898\pi$
$557$	0.0559126	+	0.0322812i	0.00236909	+	0.00136780i	−0.498815	+	0.866708i	$0.666231\pi$
$558$	−1.66611	−	31.9516i	−0.0705321	−	1.35262i
$559$	−0.00425420	+	0.00245616i	−0.000179933	+	0.000103885i
$560$	−0.256194	+	0.949271i	−0.0108262	+	0.0401140i
$561$	−8.17187	−	2.24624i	−0.345017	−	0.0948364i
$562$	−2.68156	−	10.9801i	−0.113115	−	0.463167i
$563$	−5.59927	+	31.7550i	−0.235981	+	1.33831i	0.604557	+	0.796562i	$0.293350\pi$
$563$	−5.59927	+	31.7550i	−0.235981	+	1.33831i	−0.840538	+	0.541753i	$0.817761\pi$
$564$	−6.79901	+	2.75785i	−0.286290	+	0.116126i
$565$	−3.01710	+	2.53164i	−0.126930	+	0.106507i
$566$	−0.172628	+	1.56971i	−0.00725610	+	0.0659798i
$567$	1.88671	+	1.15520i	0.0792345	+	0.0485138i
$568$	−21.6525	−	7.38273i	−0.908518	−	0.309773i
$569$	17.6067	+	20.9828i	0.738111	+	0.879646i	0.996255	−	0.0864600i	$-0.0275555\pi$
$569$	17.6067	+	20.9828i	0.738111	+	0.879646i	−0.258144	+	0.966106i	$0.583111\pi$
$570$	−12.4318	+	6.70909i	−0.520709	+	0.281013i
$571$	23.2461	+	4.09892i	0.972820	+	0.171534i	0.637399	−	0.770534i	$-0.280010\pi$
$571$	23.2461	+	4.09892i	0.972820	+	0.171534i	0.335421	+	0.942068i	$0.391121\pi$
$572$	−1.80504	+	0.235981i	−0.0754725	+	0.00986686i
$573$	6.14261	−	22.3469i	0.256611	−	0.933556i
$574$	−0.0771255	−	1.18490i	−0.00321916	−	0.0494568i
$575$	1.77367	+	3.07209i	0.0739672	+	0.128115i
$576$	0.672508	+	23.9906i	0.0280212	+	0.999607i
$577$	−2.98212	+	5.16519i	−0.124147	+	0.215030i	−0.921399	−	0.388617i	$-0.872953\pi$
$577$	−2.98212	+	5.16519i	−0.124147	+	0.215030i	0.797252	+	0.603647i	$0.206286\pi$
$578$	−0.833111	−	0.411312i	−0.0346529	−	0.0171083i
$579$	−5.59707	−	12.2079i	−0.232606	−	0.507344i
$580$	7.75408	+	10.1242i	0.321971	+	0.420385i
$581$	−2.19089	+	2.61100i	−0.0908935	+	0.108323i
$582$	−2.75729	+	3.10066i	−0.114293	+	0.128526i
$583$	−0.231444	+	0.635887i	−0.00958543	+	0.0263358i
$584$	30.8154	−	26.9507i	1.27515	−	1.11523i
$585$	1.70938	+	1.47233i	0.0706740	+	0.0608733i
$586$	−14.0447	+	6.17227i	−0.580183	+	0.254974i
$587$	2.33966	+	13.2689i	0.0965681	+	0.547665i	0.994256	+	0.107032i	$0.0341348\pi$
$587$	2.33966	+	13.2689i	0.0965681	+	0.547665i	−0.897687	+	0.440633i	$0.854754\pi$
$588$	12.7669	+	20.3691i	0.526500	+	0.840006i
$589$	−40.8690	+	14.8751i	−1.68398	+	0.612918i
$590$	−8.54570	−	2.49503i	−0.351821	−	0.102719i
$591$	−5.94494	+	12.5372i	−0.244542	+	0.515711i
$592$	29.7717	−	7.91973i	1.22361	−	0.325499i
$593$		−	1.15177i		−	0.0472976i	−0.999720	−	0.0236488i	$-0.992472\pi$
$593$		−	1.15177i		−	0.0472976i	0.999720	−	0.0236488i	$-0.00752835\pi$
$594$	4.12278	+	7.88099i	0.169160	+	0.323361i
$595$		−	0.993718i		−	0.0407385i
$596$	−6.47609	−	12.4679i	−0.265271	−	0.510706i
$597$	−15.9597	+	1.29261i	−0.653185	+	0.0529030i
$598$	1.05733	−	3.62143i	0.0432372	−	0.148091i
$599$	15.0200	−	5.46685i	0.613702	−	0.223369i	−0.0164201	−	0.999865i	$-0.505227\pi$
$599$	15.0200	−	5.46685i	0.613702	−	0.223369i	0.630122	+	0.776496i	$0.283005\pi$
$600$	4.88584	+	0.358549i	0.199464	+	0.0146377i
$601$	−5.34867	−	30.3338i	−0.218177	−	1.23734i	−0.875308	−	0.483566i	$-0.839341\pi$
$601$	−5.34867	−	30.3338i	−0.218177	−	1.23734i	0.657131	−	0.753776i	$-0.271770\pi$
$602$	−0.000913608	−	0.00207888i	−3.72359e−5	−	8.47287e-5i
$603$	14.6534	+	26.1539i	0.596732	+	1.06507i
$604$	0.697006	+	0.639846i	0.0283608	+	0.0260350i
$605$	3.26118	−	8.96002i	0.132586	−	0.364277i
$606$	5.78485	−	28.0685i	0.234993	−	1.14021i
$607$	25.8106	−	30.7598i	1.04762	−	1.24850i	0.0798109	−	0.996810i	$-0.474568\pi$
$607$	25.8106	−	30.7598i	1.04762	−	1.24850i	0.967807	−	0.251693i	$-0.0809872\pi$
$608$	30.9162	−	10.4169i	1.25382	−	0.422461i
$609$	−2.70279	−	0.254041i	−0.109523	−	0.0102943i
$610$	1.12278	−	2.27418i	0.0454600	−	0.0920790i
$611$	0.796392	−	1.37939i	0.0322186	−	0.0558042i
$612$	−6.97389	−	23.2317i	−0.281903	−	0.939087i
$613$	11.8991	+	20.6099i	0.480601	+	0.832426i	0.999752	−	0.0222566i	$-0.00708508\pi$
$613$	11.8991	+	20.6099i	0.480601	+	0.832426i	−0.519151	+	0.854683i	$0.673752\pi$
$614$	−22.6133	+	1.47191i	−0.912599	+	0.0594013i
$615$	−5.72444	+	1.49435i	−0.230832	+	0.0602580i
$616$	−0.0172183	−	0.841322i	−0.000693746	−	0.0338978i
$617$	15.3067	+	2.69898i	0.616224	+	0.108657i	0.473043	−	0.881039i	$-0.343156\pi$
$617$	15.3067	+	2.69898i	0.616224	+	0.108657i	0.143181	+	0.989696i	$0.454267\pi$
$618$	24.9504	+	0.716730i	1.00365	+	0.0288311i
$619$	6.32644	+	7.53956i	0.254281	+	0.303040i	0.878050	−	0.478568i	$-0.158844\pi$
$619$	6.32644	+	7.53956i	0.254281	+	0.303040i	−0.623769	+	0.781608i	$0.714400\pi$
$620$	14.7221	+	3.27776i	0.591255	+	0.131638i
$621$	−18.3900	+	1.25088i	−0.737967	+	0.0501962i
$622$	−28.7705	−	3.16402i	−1.15359	−	0.126866i
$623$	−0.599036	+	0.502651i	−0.0239999	+	0.0201383i
$624$	−3.31593	−	4.01868i	−0.132743	−	0.160876i
$625$	0.173648	−	0.984808i	0.00694593	−	0.0393923i
$626$	−4.31292	+	1.05330i	−0.172379	+	0.0420984i
$627$	8.60403	−	8.49374i	0.343612	−	0.339207i
$628$	−1.89601	+	42.5446i	−0.0756590	+	1.69772i
$629$	−26.9642	+	15.5678i	−1.07513	+	0.620728i
$630$	−0.762899	+	0.711041i	−0.0303946	+	0.0283285i
$631$	32.2698	+	18.6310i	1.28464	+	0.741687i	0.977693	−	0.210039i	$-0.0673591\pi$
$631$	32.2698	+	18.6310i	1.28464	+	0.741687i	0.306947	+	0.951726i	$0.400692\pi$
$632$	−15.7013	+	19.5092i	−0.624564	+	0.776036i
$633$	29.2535	+	20.7660i	1.16272	+	0.825375i
$634$	12.3505	−	11.8123i	0.490499	−	0.469127i
$635$	−11.9466	−	10.0244i	−0.474088	−	0.397807i
$636$	−1.89387	+	0.405275i	−0.0750969	+	0.0160702i
$637$	−4.90393	−	1.78489i	−0.194301	−	0.0707198i
$638$	−8.79875	−	6.45762i	−0.348346	−	0.255660i
$639$	−15.3556	−	18.7871i	−0.607460	−	0.743207i
$640$	−10.9809	−	2.72381i	−0.434059	−	0.107668i
$641$	26.3552	−	4.64713i	1.04097	−	0.183551i	0.373069	−	0.927804i	$-0.378305\pi$
$641$	26.3552	−	4.64713i	1.04097	−	0.183551i	0.667898	+	0.744253i	$0.267194\pi$
$642$	−10.3502	+	26.0813i	−0.408492	+	1.02935i
$643$	10.1102	+	27.7775i	0.398707	+	1.09544i	0.962915	+	0.269806i	$0.0869595\pi$
$643$	10.1102	+	27.7775i	0.398707	+	1.09544i	−0.564208	+	0.825633i	$0.690818\pi$
$644$	1.61058	+	0.668829i	0.0634659	+	0.0263556i
$645$	−0.00930968	+	0.00642961i	−0.000366568	+	0.000253166i
$646$	−27.4233	+	18.3058i	−1.07896	+	0.720231i
$647$	26.4918			1.04150			0.520749	−	0.853710i	$-0.325653\pi$
$647$	26.4918			1.04150			0.520749	+	0.853710i	$0.325653\pi$
$648$	−12.8454	+	21.9771i	−0.504617	+	0.863344i
$649$	7.61916			0.299078
$650$	−0.884541	+	0.590454i	−0.0346946	+	0.0231595i
$651$	−2.64190	+	1.82460i	−0.103544	+	0.0715116i
$652$	5.49354	+	2.28131i	0.215143	+	0.0893429i
$653$	16.2621	+	44.6796i	0.636383	+	1.74845i	0.662798	+	0.748798i	$0.269369\pi$
$653$	16.2621	+	44.6796i	0.636383	+	1.74845i	−0.0264146	+	0.999651i	$0.508409\pi$
$654$	18.0107	−	45.3846i	0.704273	−	1.77468i
$655$	12.8879	−	2.27248i	0.503570	−	0.0887930i
$656$	13.6132	−	1.16624i	0.531506	−	0.0455342i
$657$	42.8554	−	6.98777i	1.67195	−	0.272619i
$658$	0.593573	+	0.435637i	0.0231399	+	0.0169829i
$659$	−1.02802	−	0.374169i	−0.0400460	−	0.0145756i	0.321919	−	0.946767i	$-0.395672\pi$
$659$	−1.02802	−	0.374169i	−0.0400460	−	0.0145756i	−0.361966	+	0.932191i	$0.617894\pi$
$660$	−4.09995	+	0.877360i	−0.159590	+	0.0341512i
$661$	18.9495	+	15.9005i	0.737051	+	0.618459i	0.932044	−	0.362346i	$-0.118024\pi$
$661$	18.9495	+	15.9005i	0.737051	+	0.618459i	−0.194993	+	0.980805i	$0.562468\pi$
$662$	2.77144	−	2.65068i	0.107715	−	0.103022i
$663$	4.29380	+	3.04802i	0.166757	+	0.118375i
$664$	−30.5534	−	24.5898i	−1.18570	−	0.954268i
$665$	1.22769	+	0.708808i	0.0476078	+	0.0274864i
$666$	31.2455	+	9.56168i	1.21074	+	0.370508i
$667$	19.5884	−	11.3093i	0.758464	−	0.437900i
$668$	1.49694	−	33.5900i	0.0579185	−	1.29964i
$669$	−10.8442	+	10.7052i	−0.419260	+	0.413886i
$670$	−13.7288	+	3.35285i	−0.530390	+	0.129532i
$671$	−0.376927	+	2.13766i	−0.0145511	+	0.0825235i
$672$	2.01410	−	1.32056i	0.0776958	−	0.0509418i
$673$	−33.8620	+	28.4136i	−1.30528	+	1.09526i	−0.316079	+	0.948733i	$0.602366\pi$
$673$	−33.8620	+	28.4136i	−1.30528	+	1.09526i	−0.989206	+	0.146531i	$0.953189\pi$
$674$	46.7982	+	5.14661i	1.80260	+	0.198240i
$675$	4.19797	+	3.06220i	0.161580	+	0.117864i
$676$	−24.2746	−	5.40454i	−0.933638	−	0.207867i
$677$	−20.2474	−	24.1299i	−0.778170	−	0.927387i	0.220679	−	0.975346i	$-0.429173\pi$
$677$	−20.2474	−	24.1299i	−0.778170	−	0.927387i	−0.998849	+	0.0479594i	$0.984728\pi$
$678$	9.64343	+	0.277020i	0.370354	+	0.0106389i
$679$	0.410061	+	0.0723048i	0.0157367	+	0.00277480i
$680$	11.4319	−	0.233964i	0.438395	−	0.00897210i
$681$	16.6588	−	4.34872i	0.638365	−	0.166643i
$682$	−12.8811	+	0.838438i	−0.493245	+	0.0321054i
$683$	11.0324	+	19.1086i	0.422141	+	0.731170i	0.996149	−	0.0876798i	$-0.0279452\pi$
$683$	11.0324	+	19.1086i	0.422141	+	0.731170i	−0.574007	+	0.818850i	$0.694612\pi$
$684$	33.6761	+	7.95503i	1.28764	+	0.304168i
$685$	3.62891	−	6.28546i	0.138654	−	0.240155i
$686$	2.14519	−	4.34506i	0.0819035	−	0.165895i
$687$	1.06163	+	0.0997848i	0.0405036	+	0.00380703i
$688$	0.0237007	−	0.0109998i	0.000903582	−	0.000419363i
$689$	0.270257	−	0.322079i	0.0102960	−	0.0122702i
$690$	1.75395	−	8.51032i	0.0667718	−	0.323982i
$691$	5.57347	−	15.3130i	0.212025	−	0.582533i	−0.787400	−	0.616442i	$-0.788573\pi$
$691$	5.57347	−	15.3130i	0.212025	−	0.582533i	0.999425	+	0.0339088i	$0.0107956\pi$
$692$	−7.65072	−	7.02331i	−0.290837	−	0.266986i
$693$	0.456207	−	0.767144i	0.0173299	−	0.0291414i
$694$	6.55008	+	14.9044i	0.248638	+	0.565764i
$695$	−2.61860	−	14.8508i	−0.0993293	−	0.563325i
$696$	2.28619	−	31.1533i	0.0866579	−	1.18086i
$697$	−12.9760	+	4.72286i	−0.491500	+	0.178891i
$698$	−1.65320	+	5.66237i	−0.0625747	+	0.214324i
$699$	−47.9783	+	3.88588i	−1.81471	+	0.146977i
$700$	−0.226610	−	0.436275i	−0.00856505	−	0.0164896i
$701$		−	8.06276i		−	0.304526i	−0.988340	−	0.152263i	$-0.951344\pi$
$701$		−	8.06276i		−	0.304526i	0.988340	−	0.152263i	$-0.0486561\pi$
$702$	−0.732340	−	5.47741i	−0.0276404	−	0.206731i
$703$		−	44.4173i		−	1.67523i
$704$	9.67470	−	0.396166i	0.364629	−	0.0149311i
$705$	1.57180	−	3.31474i	0.0591974	−	0.124840i
$706$	−45.0568	−	13.1549i	−1.69574	−	0.495092i
$707$	−2.70247	+	0.983617i	−0.101637	+	0.0369927i
$708$	11.5811	+	18.4771i	0.435244	+	0.694412i
$709$	−0.0913452	−	0.518044i	−0.00343054	−	0.0194556i	0.983044	−	0.183367i	$-0.0586998\pi$
$709$	−0.0913452	−	0.518044i	−0.00343054	−	0.0194556i	−0.986475	+	0.163912i	$0.947589\pi$
$710$	10.4716	−	4.60200i	0.392994	−	0.172710i
$711$	−25.0751	+	8.76194i	−0.940390	+	0.328598i
$712$	−5.92364	−	6.77310i	−0.221998	−	0.253832i
$713$	9.14958	−	25.1383i	0.342655	−	0.941436i
$714$	−1.61751	+	1.81894i	−0.0605337	+	0.0680719i
$715$	0.585065	−	0.697254i	0.0218802	−	0.0260758i
$716$	10.9720	+	14.3257i	0.410042	+	0.535377i
$717$	−11.7056	−	25.5314i	−0.437152	−	0.953486i
$718$	37.0941	+	18.3136i	1.38434	+	0.683457i
$719$	23.3686	−	40.4756i	0.871503	−	1.50949i	0.0110603	−	0.999939i	$-0.496479\pi$
$719$	23.3686	−	40.4756i	0.871503	−	1.50949i	0.860442	−	0.509548i	$-0.170187\pi$
$720$	−8.35958	−	8.60914i	−0.311543	−	0.320844i
$721$	−1.25241	−	2.16924i	−0.0466423	−	0.0807868i
$722$	−1.30989	−	20.1242i	−0.0487491	−	0.748945i
$723$	11.4375	−	41.6098i	0.425365	−	1.54749i
$724$	−9.48978	+	1.24064i	−0.352685	+	0.0461081i
$725$	−6.27936	−	1.10722i	−0.233210	−	0.0411212i
$726$	−20.5539	+	11.0924i	−0.762826	+	0.411677i
$727$	−8.80102	−	10.4886i	−0.326412	−	0.389002i	0.577735	−	0.816224i	$-0.303937\pi$
$727$	−8.80102	−	10.4886i	−0.326412	−	0.389002i	−0.904147	+	0.427222i	$0.859492\pi$
$728$	−0.168731	+	0.494864i	−0.00625359	+	0.0183409i
$729$	−23.8875	+	12.5851i	−0.884724	+	0.466116i
$730$	−2.23758	+	20.3464i	−0.0828166	+	0.753053i
$731$	−0.0202293	+	0.0169744i	−0.000748209	+	0.000627822i
$732$	−5.75694	+	2.33516i	−0.212782	+	0.0863099i
$733$	4.79457	−	27.1913i	0.177091	−	1.00434i	−0.758611	−	0.651544i	$-0.774122\pi$
$733$	4.79457	−	27.1913i	0.177091	−	1.00434i	0.935702	−	0.352791i	$-0.114767\pi$
$734$	1.16159	+	4.75631i	0.0428750	+	0.175559i
$735$	−11.5898	−	3.18575i	−0.427497	−	0.117508i
$736$	−7.31515	+	18.6860i	−0.269640	+	0.688774i
$737$	10.4747	−	6.04754i	0.385839	−	0.222764i
$738$	12.9106	+	6.58255i	0.475246	+	0.242307i
$739$	6.47095	+	3.73600i	0.238038	+	0.137431i	0.614275	−	0.789092i	$-0.289449\pi$
$739$	6.47095	+	3.73600i	0.238038	+	0.137431i	−0.376237	+	0.926524i	$0.622782\pi$
$740$	−8.28803	+	12.9837i	−0.304674	+	0.477291i
$741$	−6.82840	+	3.13067i	−0.250848	+	0.115008i
$742$	0.134335	+	0.140455i	0.00493161	+	0.00515628i
$743$	34.1696	+	28.6717i	1.25356	+	1.05186i	0.996337	+	0.0855095i	$0.0272518\pi$
$743$	34.1696	+	28.6717i	1.25356	+	1.05186i	0.257223	+	0.966352i	$0.417193\pi$
$744$	−21.6126	−	29.9634i	−0.792355	−	1.09851i
$745$	6.60111	+	2.40261i	0.241846	+	0.0880247i
$746$	−14.9279	+	20.3398i	−0.546547	+	0.744692i
$747$	−13.7221	−	39.2701i	−0.502064	−	1.43682i
$748$	−9.33577	+	2.93430i	−0.341350	+	0.107289i
$749$	2.77306	−	0.488966i	0.101326	−	0.0178664i
$750$	−1.92086	+	1.51997i	−0.0701397	+	0.0555015i
$751$	−4.73072	−	12.9976i	−0.172627	−	0.474288i	0.822964	−	0.568094i	$-0.192319\pi$
$751$	−4.73072	−	12.9976i	−0.172627	−	0.474288i	−0.995590	+	0.0938060i	$0.970097\pi$
$752$	−4.87191	+	6.93115i	−0.177660	+	0.252753i
$753$	−7.98089	−	3.78442i	−0.290840	−	0.137912i
$754$	3.76487	+	5.64004i	0.137109	+	0.205398i
$755$	−0.473080			−0.0172172
$756$	2.55382	−	0.0597173i	0.0928815	−	0.00217190i
$757$	−34.6538			−1.25951			−0.629756	−	0.776793i	$-0.716845\pi$
$757$	−34.6538			−1.25951			−0.629756	+	0.776793i	$0.716845\pi$
$758$	13.3334	+	19.9743i	0.484290	+	0.725500i
$759$	0.600343	+	7.41234i	0.0217911	+	0.269051i
$760$	−7.86523	+	14.2905i	−0.285302	+	0.518371i
$761$	−7.04978	−	19.3691i	−0.255554	−	0.702130i	−0.999428	−	0.0338099i	$-0.989236\pi$
$761$	−7.04978	−	19.3691i	−0.255554	−	0.702130i	0.743874	−	0.668320i	$-0.232986\pi$
$762$	5.55045	+	37.7949i	0.201071	+	1.36917i
$763$	−4.82547	+	0.850860i	−0.174694	+	0.0308032i
$764$	−8.02418	−	25.5298i	−0.290305	−	0.923634i
$765$	10.4240	+	6.19897i	0.376881	+	0.224124i
$766$	5.47091	−	7.45433i	0.197672	−	0.269336i
$767$	−4.44844	−	1.61910i	−0.160624	−	0.0584623i
$768$	15.6662	+	22.8598i	0.565307	+	0.824881i
$769$	5.07800	+	4.26095i	0.183117	+	0.153654i	0.729739	−	0.683726i	$-0.239642\pi$
$769$	5.07800	+	4.26095i	0.183117	+	0.153654i	−0.546621	+	0.837380i	$0.684086\pi$
$770$	0.290816	+	0.304065i	0.0104803	+	0.0109578i
$771$	−4.12621	+	43.8995i	−0.148602	+	1.58100i
$772$	−13.0713	−	8.34395i	−0.470447	−	0.300305i
$773$	43.1871	+	24.9341i	1.55333	+	0.896817i	0.997867	+	0.0652773i	$0.0207932\pi$
$773$	43.1871	+	24.9341i	1.55333	+	0.896817i	0.555465	+	0.831540i	$0.312540\pi$
$774$	0.0275064	+	0.00338469i	0.000988699	+	0.000121660i
$775$	−6.53096	+	3.77065i	−0.234599	+	0.135446i
$776$	−0.735264	+	4.73445i	−0.0263944	+	0.169957i
$777$	−0.828232	−	3.17273i	−0.0297127	−	0.113821i
$778$	−7.08224	−	28.9994i	−0.253911	−	1.03968i
$779$	3.42074	−	19.4000i	0.122561	−	0.695075i
$780$	2.58020	+	0.359009i	0.0923858	+	0.0128546i
$781$	−7.49911	+	6.29250i	−0.268339	+	0.225164i
$782$	2.21700	−	20.1592i	0.0792798	−	0.720893i
$783$	19.5253	−	26.7672i	0.697776	−	0.956583i
$784$	25.1364	+	11.7766i	0.897727	+	0.420591i
$785$	−13.6872	−	16.3117i	−0.488516	−	0.582190i
$786$	−27.2894	−	16.8184i	−0.973379	−	0.599891i
$787$	−25.5084	−	4.49783i	−0.909278	−	0.160330i	−0.300602	−	0.953750i	$-0.597188\pi$
$787$	−25.5084	−	4.49783i	−0.909278	−	0.160330i	−0.608675	+	0.793419i	$0.708299\pi$
$788$	2.07693	+	15.8866i	0.0739875	+	0.565937i
$789$	8.46370	+	8.57360i	0.301316	+	0.305228i
$790$	−0.813300	−	12.4949i	−0.0289359	−	0.444550i
$791$	−0.484063	−	0.838423i	−0.0172113	−	0.0298109i
$792$	8.93280	+	5.06768i	0.317413	+	0.180072i
$793$	0.674329	−	1.16797i	0.0239461	−	0.0414759i
$794$	6.55313	+	3.23532i	0.232562	+	0.114817i
$795$	0.560542	−	0.789647i	0.0198804	−	0.0280059i
$796$	−14.6784	+	11.2421i	−0.520264	+	0.398467i
$797$	15.1867	−	18.0989i	0.537942	−	0.641094i	−0.426783	−	0.904354i	$-0.640353\pi$
$797$	15.1867	−	18.0989i	0.537942	−	0.641094i	0.964725	+	0.263260i	$0.0847976\pi$
$798$	−1.09346	−	3.29578i	−0.0387080	−	0.116669i
$799$	2.92852	−	8.04605i	0.103604	−	0.284649i
$800$	4.96564	−	2.70969i	0.175562	−	0.0958019i
$801$	−1.53588	−	9.41945i	−0.0542677	−	0.332820i
$802$	38.1074	−	16.7471i	1.34562	−	0.591362i
$803$	−3.04203	−	17.2522i	−0.107351	−	0.608818i
$804$	30.5872	+	16.2097i	1.07873	+	0.571671i
$805$	−0.819382	+	0.298231i	−0.0288794	+	0.0105112i
$806$	7.69881	+	2.24777i	0.271179	+	0.0791743i
$807$	−2.23497	−	3.23609i	−0.0786745	−	0.113916i
$808$	−11.9520	−	30.8582i	−0.420471	−	1.08559i
$809$		−	26.8566i		−	0.944229i	−0.881537	−	0.472115i	$-0.843491\pi$
$809$		−	26.8566i		−	0.944229i	0.881537	−	0.472115i	$-0.156509\pi$
$810$	−2.69967	−	12.4383i	−0.0948567	−	0.437038i
$811$		−	41.4068i		−	1.45399i	−0.686644	−	0.726994i	$-0.740917\pi$
$811$		−	41.4068i		−	1.45399i	0.686644	−	0.726994i	$-0.259083\pi$
$812$	−2.78179	+	1.44492i	−0.0976216	+	0.0507067i
$813$	−22.2819	−	32.2629i	−0.781462	−	1.13151i
$814$	3.69471	−	12.6547i	0.129500	−	0.443548i
$815$	−2.79483	+	1.01723i	−0.0978985	+	0.0356321i
$816$	−21.3062	−	18.1799i	−0.745868	−	0.636424i
$817$	−0.00654174	−	0.0371001i	−0.000228867	−	0.00129797i
$818$	−13.6068	−	30.9617i	−0.475751	−	1.08255i
$819$	−0.429377	+	0.350951i	−0.0150036	+	0.0122632i
$820$	−4.61985	+	5.03256i	−0.161332	+	0.175745i
$821$	−11.7386	+	32.2516i	−0.409681	+	1.12559i	0.547679	+	0.836689i	$0.315512\pi$
$821$	−11.7386	+	32.2516i	−0.409681	+	1.12559i	−0.957359	+	0.288900i	$0.906711\pi$
$822$	−16.8735	+	5.59822i	−0.588532	+	0.195260i
$823$	24.1949	−	28.8343i	0.843380	−	1.00510i	−0.156468	−	0.987683i	$-0.550011\pi$
$823$	24.1949	−	28.8343i	0.843380	−	1.00510i	0.999848	−	0.0174181i	$-0.00554464\pi$
$824$	24.6605	−	14.9187i	0.859091	−	0.519719i
$825$	1.21349	−	1.70947i	0.0422483	−	0.0595161i
$826$	0.968748	−	1.96219i	0.0337071	−	0.0682735i
$827$	11.8331	−	20.4955i	0.411476	−	0.712697i	−0.583576	−	0.812059i	$-0.698347\pi$
$827$	11.8331	−	20.4955i	0.411476	−	0.712697i	0.995051	+	0.0993619i	$0.0316801\pi$
$828$	−17.0630	+	12.7226i	−0.592981	+	0.442141i
$829$	18.2491	+	31.6084i	0.633818	+	1.09780i	0.986764	+	0.162161i	$0.0518464\pi$
$829$	18.2491	+	31.6084i	0.633818	+	1.09780i	−0.352947	+	0.935643i	$0.614820\pi$
$830$	19.5683	−	1.27371i	0.679226	−	0.0442110i
$831$	−32.2586	−	32.6774i	−1.11904	−	1.13357i
$832$	−5.73275	−	1.82461i	−0.198747	−	0.0632569i
$833$	−27.6281	−	4.87158i	−0.957256	−	0.168790i
$834$	−19.3800	+	31.4459i	−0.671075	+	1.08888i
$835$	10.8063	+	12.8785i	0.373969	+	0.445678i
$836$	3.03392	−	13.6269i	0.104930	−	0.471296i
$837$	−2.65925	−	39.0954i	−0.0919173	−	1.35134i
$838$	−9.94997	−	1.09424i	−0.343716	−	0.0378000i
$839$	−20.2912	+	17.0264i	−0.700531	+	0.587816i	−0.921925	−	0.387369i	$-0.873384\pi$
$839$	−20.2912	+	17.0264i	−0.700531	+	0.587816i	0.221393	+	0.975185i	$0.428940\pi$
$840$	−0.295344	+	1.16743i	−0.0101903	+	0.0402802i
$841$	−2.02411	+	11.4793i	−0.0697967	+	0.395837i
$842$	−8.29386	+	2.02553i	−0.285825	+	0.0698043i
$843$	−3.49652	−	13.3942i	−0.120426	−	0.461320i
$844$	41.3835	+	1.84426i	1.42448	+	0.0634821i
$845$	10.7686	−	6.21724i	0.370450	−	0.213879i
$846$	−8.27259	+	3.50895i	−0.284418	+	0.120640i
$847$	2.02979	+	1.17190i	0.0697444	+	0.0402669i
$848$	−1.58420	+	1.57849i	−0.0544017	+	0.0542057i
$849$	−0.180991	+	1.92560i	−0.00621161	+	0.0660864i
$850$	−4.13166	+	3.95163i	−0.141715	+	0.135540i
$851$	20.9290	+	17.5615i	0.717435	+	0.602000i
$852$	−26.6585	−	8.62139i	−0.913304	−	0.295364i
$853$	−23.8105	−	8.66631i	−0.815256	−	0.296729i	−0.0994627	−	0.995041i	$-0.531712\pi$
$853$	−23.8105	−	8.66631i	−0.815256	−	0.296729i	−0.715793	+	0.698312i	$0.753935\pi$
$854$	0.502596	+	0.368868i	0.0171985	+	0.0126224i
$855$	−15.0939	+	8.45672i	−0.516199	+	0.289214i
$856$	6.27807	+	31.7868i	0.214580	+	1.08645i
$857$	49.8823	−	8.79559i	1.70395	−	0.300452i	0.764876	−	0.644178i	$-0.222800\pi$
$857$	49.8823	−	8.79559i	1.70395	−	0.300452i	0.939070	+	0.343726i	$0.111689\pi$
$858$	−2.20587	+	0.323947i	−0.0753070	+	0.0110594i
$859$	−16.3264	−	44.8564i	−0.557049	−	1.53048i	−0.823896	−	0.566740i	$-0.808204\pi$
$859$	−16.3264	−	44.8564i	−0.557049	−	1.53048i	0.266848	−	0.963739i	$-0.414018\pi$
$860$	−0.00501044	+	0.0120655i	−0.000170855	+	0.000411429i
$861$	−0.117400	−	1.44952i	−0.00400100	−	0.0493997i
$862$	−44.0469	+	29.4025i	−1.50024	+	1.00145i
$863$	−36.7547			−1.25114			−0.625572	−	0.780166i	$-0.715134\pi$
$863$	−36.7547			−1.25114			−0.625572	+	0.780166i	$0.715134\pi$
$864$	1.28828	+	29.3656i	0.0438281	+	0.999039i
$865$	5.19279			0.176560
$866$	45.5098	−	30.3790i	1.54649	−	1.03232i
$867$	−1.02819	−	0.487551i	−0.0349191	−	0.0165581i
$868$	−1.42186	+	3.42394i	−0.0482612	+	0.116216i
$869$	3.66522	+	10.0701i	0.124334	+	0.341605i
$870$	9.69170	+	12.2478i	0.328579	+	0.415240i
$871$	−7.40074	+	1.30495i	−0.250764	+	0.0442165i
$872$	−10.9246	−	55.3129i	−0.369954	−	1.87313i
$873$	−3.31649	+	3.85045i	−0.112246	+	0.130318i
$874$	23.3244	+	17.1184i	0.788960	+	0.579037i
$875$	0.230985	+	0.0840715i	0.00780870	+	0.00284214i
$876$	37.2142	−	33.6005i	1.25735	−	1.13526i
$877$	8.14964	+	6.83836i	0.275194	+	0.230915i	0.769930	−	0.638128i	$-0.220291\pi$
$877$	8.14964	+	6.83836i	0.275194	+	0.230915i	−0.494736	+	0.869043i	$0.664735\pi$
$878$	40.3687	−	38.6097i	1.36238	−	1.30301i
$879$	−17.0795	+	7.83058i	−0.576078	+	0.264119i
$880$	−3.42956	+	3.41720i	−0.115611	+	0.115194i
$881$	−19.2671	−	11.1239i	−0.649125	−	0.374772i	0.138996	−	0.990293i	$-0.455612\pi$
$881$	−19.2671	−	11.1239i	−0.649125	−	0.374772i	−0.788121	+	0.615521i	$0.788946\pi$
$882$	16.0289	+	24.6965i	0.539720	+	0.831573i
$883$	43.7766	−	25.2744i	1.47320	−	0.850552i	0.473654	−	0.880711i	$-0.342935\pi$
$883$	43.7766	−	25.2744i	1.47320	−	0.850552i	0.999545	+	0.0301587i	$0.00960127\pi$
$884$	6.07423	+	0.270699i	0.204298	+	0.00910459i
$885$	−10.5133	−	2.88985i	−0.353401	−	0.0971412i
$886$	−1.69677	+	0.414386i	−0.0570041	+	0.0139216i
$887$	−6.48419	+	36.7737i	−0.217718	+	1.23474i	0.658410	+	0.752659i	$0.271229\pi$
$887$	−6.48419	+	36.7737i	−0.217718	+	1.23474i	−0.876128	+	0.482079i	$0.839882\pi$
$888$	36.3047	−	10.2752i	1.21831	−	0.344812i
$889$	2.93658	−	2.46409i	0.0984899	−	0.0826428i
$890$	4.47205	+	0.491811i	0.149903	+	0.0164855i
$891$	5.20138	+	9.57113i	0.174253	+	0.320645i
$892$	−3.82383	+	17.1748i	−0.128031	+	0.575056i
$893$	7.85163	+	9.35721i	0.262745	+	0.313127i
$894$	−8.17209	−	15.1427i	−0.273315	−	0.506446i
$895$	−8.88527	−	1.56671i	−0.297002	−	0.0523695i
$896$	1.12808	−	2.54194i	0.0376864	−	0.0849202i
$897$	1.22464	−	4.45526i	0.0408895	−	0.148757i
$898$	−47.3090	+	3.07936i	−1.57872	+	0.102760i
$899$	24.0426	+	41.6429i	0.801864	+	1.38887i
$900$	5.99011	+	0.344431i	0.199670	+	0.0114810i
$901$	1.13011	−	1.95740i	0.0376493	−	0.0652105i
$902$	2.58831	−	5.24261i	0.0861814	−	0.174560i
$903$	−0.00115907	−	0.00252808i	−3.85714e−5	−	8.41291e-5i
$904$	9.53142	−	5.76617i	0.317010	−	0.191780i
$905$	3.07591	−	3.66573i	0.102247	−	0.121853i
$906$	0.865942	+	0.770048i	0.0287690	+	0.0255831i
$907$	−7.11240	+	19.5412i	−0.236163	+	0.648854i	0.763831	+	0.645417i	$0.223316\pi$
$907$	−7.11240	+	19.5412i	−0.236163	+	0.648854i	−0.999994	+	0.00343704i	$0.998906\pi$
$908$	13.4443	−	14.6453i	0.446164	−	0.486022i
$909$	6.54035	−	34.4846i	0.216930	−	1.14378i
$910$	−0.105178	−	0.239328i	−0.00348661	−	0.00793364i
$911$	−5.45823	−	30.9552i	−0.180839	−	1.02559i	−0.931186	−	0.364546i	$-0.881224\pi$
$911$	−5.45823	−	30.9552i	−0.180839	−	1.02559i	0.750346	−	0.661045i	$-0.229887\pi$
$912$	37.6579	−	13.3553i	1.24698	−	0.442240i
$913$	−15.7708	+	5.74010i	−0.521937	+	0.189970i
$914$	12.0618	−	41.3129i	0.398970	−	1.36651i
$915$	1.33089	−	2.80670i	0.0439979	−	0.0927865i
$916$	1.09266	−	0.567549i	0.0361024	−	0.0187523i
$917$			3.21682i			0.106229i
$918$	−8.99019	−	28.3143i	−0.296721	−	0.934511i
$919$			50.8721i			1.67812i	0.544042	+	0.839058i	$0.316893\pi$
$919$			50.8721i			1.67812i	−0.544042	+	0.839058i	$0.683107\pi$
$920$	−3.62382	−	9.35612i	−0.119474	−	0.308462i
$921$	−27.6635	+	2.24054i	−0.911545	+	0.0738282i
$922$	39.1982	+	11.4444i	1.29092	+	0.376902i
$923$	5.71553	−	2.08028i	0.188129	−	0.0684733i
$924$	−0.0373830	−	1.02994i	−0.00122981	−	0.0338826i
$925$	−1.33740	−	7.58476i	−0.0439734	−	0.249385i
$926$	11.6912	−	5.13797i	0.384198	−	0.168844i
$927$	30.5679	+	0.394378i	1.00398	+	0.0129531i
$928$	−17.2776	−	31.6621i	−0.567165	−	1.03936i
$929$	−0.188361	+	0.517518i	−0.00617993	+	0.0169792i	−0.942744	−	0.333517i	$-0.891765\pi$
$929$	−0.188361	+	0.517518i	−0.00617993	+	0.0169792i	0.936564	+	0.350496i	$0.113987\pi$
$930$	18.0921	+	3.72873i	0.593263	+	0.122270i
$931$	25.7254	−	30.6583i	0.843116	−	1.00479i
$932$	−44.1267	+	33.7964i	−1.44542	+	1.10704i
$933$	−35.2934	−	3.31731i	−1.15546	−	0.108604i
$934$	47.5025	+	23.4523i	1.55433	+	0.767383i
$935$	2.44651	−	4.23748i	0.0800095	−	0.138581i
$936$	−4.13851	−	4.85701i	−0.135271	−	0.158756i
$937$	−19.6313	−	34.0025i	−0.641328	−	1.11081i	−0.985137	−	0.171773i	$-0.945051\pi$
$937$	−19.6313	−	34.0025i	−0.641328	−	1.11081i	0.343809	−	0.939040i	$-0.388283\pi$
$938$	−0.225636	−	3.46651i	−0.00736727	−	0.113185i
$939$	−5.26116	+	1.37341i	−0.171691	+	0.0448196i
$940$	−0.549125	−	4.20031i	−0.0179105	−	0.136999i
$941$	23.3759	+	4.12180i	0.762032	+	0.134367i	0.541141	−	0.840932i	$-0.317992\pi$
$941$	23.3759	+	4.12180i	0.762032	+	0.134367i	0.220891	+	0.975299i	$0.429104\pi$
$942$	−1.49769	+	52.1365i	−0.0487973	+	1.69870i
$943$	7.78858	+	9.28207i	0.253631	+	0.302266i
$944$	22.8016	+	10.6827i	0.742128	+	0.347692i
$945$	−0.920466	+	0.885513i	−0.0299428	+	0.0288057i
$946$	0.00122228	−	0.0111142i	3.97396e−5	−	0.000361353i
$947$	−5.89399	+	4.94565i	−0.191529	+	0.160712i	−0.733510	−	0.679679i	$-0.762119\pi$
$947$	−5.89399	+	4.94565i	−0.191529	+	0.160712i	0.541981	+	0.840391i	$0.317675\pi$
$948$	−18.8497	+	24.1950i	−0.612211	+	0.785817i
$949$	−1.89007	+	10.7191i	−0.0613544	+	0.347958i
$950$	−1.93499	−	7.92313i	−0.0627793	−	0.257060i
$951$	14.8954	−	14.7045i	0.483018	−	0.476826i
$952$	−0.431327	+	2.77737i	−0.0139794	+	0.0900150i
$953$	17.5585	−	10.1374i	0.568777	−	0.328383i	−0.187884	−	0.982191i	$-0.560163\pi$
$953$	17.5585	−	10.1374i	0.568777	−	0.328383i	0.756661	+	0.653808i	$0.226830\pi$
$954$	−2.31137	+	0.532983i	−0.0748334	+	0.0172560i
$955$	11.5879	+	6.69027i	0.374975	+	0.216492i
$956$	−27.3370	−	17.4503i	−0.884143	−	0.564384i
$957$	−10.9000	−	7.73750i	−0.352346	−	0.250118i
$958$	32.8328	+	34.3286i	1.06078	+	1.10911i
$959$	1.36665	+	1.14676i	0.0441314	+	0.0370307i
$960$	−13.4999	−	3.12284i	−0.435708	−	0.100789i
$961$	24.3110	+	8.84849i	0.784227	+	0.285435i
$962$	−4.84633	+	6.60331i	−0.156252	+	0.212899i
$963$	−12.1696	+	32.1394i	−0.392160	+	1.03568i
$964$	−14.9410	−	47.5362i	−0.481216	−	1.53104i
$965$	7.63593	−	1.34642i	0.245809	−	0.0433428i
$966$	1.98526	+	0.787843i	0.0638748	+	0.0253484i
$967$	4.84704	+	13.3171i	0.155870	+	0.428250i	0.992907	−	0.118897i	$-0.0379360\pi$
$967$	4.84704	+	13.3171i	0.155870	+	0.428250i	−0.837036	+	0.547147i	$0.815714\pi$
$968$	−13.0039	+	23.6270i	−0.417960	+	0.759402i
$969$	−33.2278	+	22.9483i	−1.06743	+	0.737207i
$970$	−1.33003	−	1.99247i	−0.0427046	−	0.0639744i
$971$	−31.0109			−0.995187			−0.497593	−	0.867410i	$-0.665783\pi$
$971$	−31.0109			−0.995187			−0.497593	+	0.867410i	$0.665783\pi$
$972$	−15.3047	+	27.1619i	−0.490898	+	0.871217i
$973$	3.70678			0.118834
$974$	27.0270	+	40.4883i	0.866000	+	1.29733i
$975$	−1.07176	+	0.740200i	−0.0343239	+	0.0237054i
$976$	−4.12520	+	5.86882i	−0.132044	+	0.187856i
$977$	−12.0775	−	33.1827i	−0.386393	−	1.06161i	−0.968613	−	0.248575i	$-0.920038\pi$
$977$	−12.0775	−	33.1827i	−0.386393	−	1.06161i	0.582219	−	0.813032i	$-0.302185\pi$
$978$	6.77153	+	2.68725i	0.216530	+	0.0859289i
$979$	−3.79197	+	0.668626i	−0.121192	+	0.0213694i
$980$	−13.2405	+	4.16160i	−0.422954	+	0.132937i
$981$	21.1766	−	55.9265i	0.676116	−	1.78560i
$982$	−18.9548	+	25.8267i	−0.604873	+	0.824163i
$983$	13.8628	+	5.04565i	0.442155	+	0.160931i	0.553498	−	0.832851i	$-0.313293\pi$
$983$	13.8628	+	5.04565i	0.442155	+	0.160931i	−0.111343	+	0.993782i	$0.535515\pi$
$984$	16.6480	−	1.69188i	0.530719	−	0.0539351i
$985$	−6.13670	−	5.14930i	−0.195532	−	0.164070i
$986$	25.1965	+	26.3444i	0.802421	+	0.838978i
$987$	0.735323	+	0.521980i	0.0234056	+	0.0166148i
$988$	−4.66712	+	7.31133i	−0.148481	+	0.232605i
$989$	0.0200676	+	0.0115860i	0.000638112	+	0.000368414i
$990$	−5.00377	+	1.15383i	−0.159030	+	0.0366711i
$991$	−2.11784	+	1.22274i	−0.0672754	+	0.0388415i	−0.533260	−	0.845951i	$-0.679033\pi$
$991$	−2.11784	+	1.22274i	−0.0672754	+	0.0388415i	0.465985	+	0.884793i	$0.345700\pi$
$992$	−39.7245	−	15.5513i	−1.26125	−	0.493754i
$993$	3.34253	−	3.29969i	0.106072	−	0.104712i
$994$	0.667051	+	2.73135i	0.0211576	+	0.0866331i
$995$	1.60529	−	9.10404i	0.0508911	−	0.288618i
$996$	−37.8918	−	29.5205i	−1.20065	−	0.935394i
$997$	24.0778	−	20.2037i	0.762551	−	0.639856i	−0.176239	−	0.984347i	$-0.556393\pi$
$997$	24.0778	−	20.2037i	0.762551	−	0.639856i	0.938789	+	0.344491i	$0.111949\pi$
$998$	−3.58354	+	32.5852i	−0.113435	+	1.03147i
$999$	38.4482	+	11.1039i	1.21645	+	0.351311i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	540.2.be.a.491.60	yes	432
4.3	odd	2	inner	540.2.be.a.491.20	yes	432
27.11	odd	18	inner	540.2.be.a.11.20	✓	432
108.11	even	18	inner	540.2.be.a.11.60	yes	432

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
540.2.be.a.11.20	✓	432	27.11	odd	18	inner
540.2.be.a.11.60	yes	432	108.11	even	18	inner
540.2.be.a.491.20	yes	432	4.3	odd	2	inner
540.2.be.a.491.60	yes	432	1.1	even	1	trivial

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 540 = 2^{2} \cdot 3^{3} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	540.be (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(1.17623 - 0.785164i) q^{2} +(1.42519 - 0.984291i) q^{3} +(0.767034 - 1.84707i) q^{4} +(0.342020 + 0.939693i) q^{5} +(0.903523 - 2.27676i) q^{6} +(-0.242074 + 0.0426842i) q^{7} +(-0.548043 - 2.77482i) q^{8} +(1.06234 - 2.80561i) q^{9} +(1.14011 + 0.836753i) q^{10} +(-1.13736 - 0.413964i) q^{11} +(-0.724881 - 3.38741i) q^{12} +(0.576076 + 0.483385i) q^{13} +(-0.251221 + 0.240275i) q^{14} +(1.41238 + 1.00259i) q^{15} +(-2.82332 - 2.83353i) q^{16} +(3.50104 + 2.02132i) q^{17} +(-0.953302 - 4.13415i) q^{18} +(-4.99450 + 2.88358i) q^{19} +(1.99802 + 0.0890420i) q^{20} +(-0.302989 + 0.299105i) q^{21} +(-1.66282 + 0.406095i) q^{22} +(0.615990 - 3.49345i) q^{23} +(-3.51230 - 3.41522i) q^{24} +(-0.766044 + 0.642788i) q^{25} +(1.05713 + 0.116258i) q^{26} +(-1.24749 - 5.04418i) q^{27} +(-0.106839 + 0.479868i) q^{28} +(4.09856 + 4.88448i) q^{29} +(2.44848 + 0.0703356i) q^{30} +(7.42673 + 1.30953i) q^{31} +(-5.54566 - 1.11611i) q^{32} +(-2.02841 + 0.529512i) q^{33} +(5.70510 - 0.371347i) q^{34} +(-0.122904 - 0.212877i) q^{35} +(-4.36729 - 4.11422i) q^{36} +(-3.85088 + 6.66992i) q^{37} +(-3.61060 + 7.31326i) q^{38} +(1.29681 + 0.121890i) q^{39} +(2.42004 - 1.46404i) q^{40} +(-2.19561 + 2.61663i) q^{41} +(-0.121538 + 0.589712i) q^{42} +(-0.00223415 + 0.00613829i) q^{43} +(-1.63701 + 1.78325i) q^{44} +(2.99975 + 0.0387019i) q^{45} +(-2.01839 - 4.59276i) q^{46} +(-0.367791 - 2.08585i) q^{47} +(-6.81278 - 1.25935i) q^{48} +(-6.52107 + 2.37348i) q^{49} +(-0.396351 + 1.35754i) q^{50} +(6.97922 - 0.565264i) q^{51} +(1.33471 - 0.693278i) q^{52} -0.559092i q^{53} +(-5.42785 - 4.95363i) q^{54} -1.21035i q^{55} +(0.251108 + 0.648321i) q^{56} +(-4.27984 + 9.02569i) q^{57} +(8.65597 + 2.52722i) q^{58} +(-5.91537 + 2.15302i) q^{59} +(2.93520 - 1.83973i) q^{60} +(-0.311420 - 1.76615i) q^{61} +(9.76375 - 4.29089i) q^{62} +(-0.137411 + 0.724510i) q^{63} +(-7.39930 + 3.04145i) q^{64} +(-0.257204 + 0.706662i) q^{65} +(-1.97013 + 2.21547i) q^{66} +(-6.42340 + 7.65512i) q^{67} +(6.41894 - 4.91623i) q^{68} +(-2.56067 - 5.58515i) q^{69} +(-0.311707 - 0.153892i) q^{70} +(4.04403 - 7.00447i) q^{71} +(-8.36727 - 1.41022i) q^{72} +(7.23690 + 12.5347i) q^{73} +(0.707463 + 10.8689i) q^{74} +(-0.459070 + 1.67011i) q^{75} +(1.49521 + 11.4370i) q^{76} +(0.292995 + 0.0516629i) q^{77} +(1.62105 - 0.874838i) q^{78} +(-5.69121 - 6.78252i) q^{79} +(1.69701 - 3.62217i) q^{80} +(-6.74285 - 5.96103i) q^{81} +(-0.528061 + 4.80167i) q^{82} +(10.6221 - 8.91300i) q^{83} +(0.320064 + 0.789064i) q^{84} +(-0.701999 + 3.98123i) q^{85} +(0.00219169 + 0.00897422i) q^{86} +(10.6490 + 2.92714i) q^{87} +(-0.525357 + 3.38284i) q^{88} +(2.75507 - 1.59064i) q^{89} +(3.55878 - 2.30977i) q^{90} +(-0.160086 - 0.0924257i) q^{91} +(-5.98016 - 3.81737i) q^{92} +(11.8735 - 5.44373i) q^{93} +(-2.07034 - 2.16466i) q^{94} +(-4.41790 - 3.70706i) q^{95} +(-9.00220 + 3.86786i) q^{96} +(-1.59179 - 0.579364i) q^{97} +(-5.80671 + 7.91186i) q^{98} +(-2.36968 + 2.75121i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 432 q + 18 q^{12} + 30 q^{14} + 30 q^{24} + 12 q^{29} - 24 q^{30} + 60 q^{33} - 60 q^{36} - 60 q^{38} + 60 q^{41} - 60 q^{42} - 72 q^{44} + 12 q^{45} - 150 q^{48} + 54 q^{52} - 84 q^{54} - 84 q^{56} - 12 q^{57}+ \cdots + 36 q^{97}+O(q^{100}) \) 432 * q + 18 * q^12 + 30 * q^14 + 30 * q^24 + 12 * q^29 - 24 * q^30 + 60 * q^33 - 60 * q^36 - 60 * q^38 + 60 * q^41 - 60 * q^42 - 72 * q^44 + 12 * q^45 - 150 * q^48 + 54 * q^52 - 84 * q^54 - 84 * q^56 - 12 * q^57 + 54 * q^58 - 198 * q^62 - 48 * q^66 - 138 * q^68 - 48 * q^69 - 84 * q^72 - 84 * q^74 - 48 * q^77 - 78 * q^78 - 66 * q^84 + 54 * q^86 - 36 * q^89 + 120 * q^92 - 54 * q^94 + 210 * q^96 + 36 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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