LMFDB - Embedded newform 540.2.be.a.491.20

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			491.20
Character	$\chi$	$=$	540.491
Dual form			540.2.be.a.11.20

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.977486 + 1.02202i) q^{2} +(-1.42519 + 0.984291i) q^{3} +(-0.0890420 - 1.99802i) q^{4} +(0.342020 + 0.939693i) q^{5} +(0.387142 - 2.41870i) q^{6} +(0.242074 - 0.0426842i) q^{7} +(2.12905 + 1.86203i) q^{8} +(1.06234 - 2.80561i) q^{9} +(-1.29470 - 0.568986i) q^{10} +(1.13736 + 0.413964i) q^{11} +(2.09353 + 2.75991i) q^{12} +(0.576076 + 0.483385i) q^{13} +(-0.193000 + 0.289128i) q^{14} +(-1.41238 - 1.00259i) q^{15} +(-3.98414 + 0.355815i) q^{16} +(3.50104 + 2.02132i) q^{17} +(1.82896 + 3.82817i) q^{18} +(4.99450 - 2.88358i) q^{19} +(1.84707 - 0.767034i) q^{20} +(-0.302989 + 0.299105i) q^{21} +(-1.53483 + 0.757756i) q^{22} +(-0.615990 + 3.49345i) q^{23} +(-4.86708 - 0.558150i) 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} +(2.40525 - 0.463450i) q^{30} +(-7.42673 - 1.30953i) q^{31} +(3.53080 - 4.41967i) q^{32} +(-2.02841 + 0.529512i) q^{33} +(-5.48805 + 1.60231i) q^{34} +(0.122904 + 0.212877i) q^{35} +(-5.70024 - 1.87276i) q^{36} +(-3.85088 + 6.66992i) q^{37} +(-1.93499 + 7.92313i) q^{38} +(-1.29681 - 0.121890i) q^{39} +(-1.02156 + 2.63750i) q^{40} +(-2.19561 + 2.61663i) q^{41} +(-0.00952332 - 0.602030i) q^{42} +(0.00223415 - 0.00613829i) q^{43} +(0.725835 - 2.30932i) q^{44} +(2.99975 + 0.0387019i) q^{45} +(-2.96825 - 4.04435i) q^{46} +(0.367791 + 2.08585i) q^{47} +(5.32794 - 4.42866i) q^{48} +(-6.52107 + 2.37348i) q^{49} +(0.0918572 - 1.41123i) q^{50} +(-6.97922 + 0.565264i) q^{51} +(0.914517 - 1.19405i) q^{52} -0.559092i q^{53} +(-6.37465 - 3.65566i) q^{54} +1.21035i q^{55} +(0.594867 + 0.359873i) q^{56} +(-4.27984 + 9.02569i) q^{57} +(-8.99831 - 0.585703i) q^{58} +(5.91537 - 2.15302i) q^{59} +(-1.87744 + 2.91122i) q^{60} +(-0.311420 - 1.76615i) q^{61} +(8.59790 - 6.31021i) q^{62} +(0.137411 - 0.724510i) q^{63} +(1.06568 + 7.92870i) q^{64} +(-0.257204 + 0.706662i) q^{65} +(1.44158 - 2.59067i) q^{66} +(6.42340 - 7.65512i) q^{67} +(3.72690 - 7.17511i) q^{68} +(-2.56067 - 5.58515i) q^{69} +(-0.337701 - 0.0824734i) q^{70} +(-4.04403 + 7.00447i) q^{71} +(7.48590 - 3.99515i) q^{72} +(7.23690 + 12.5347i) q^{73} +(-3.05260 - 10.4554i) q^{74} +(0.459070 - 1.67011i) q^{75} +(-6.20616 - 9.72234i) q^{76} +(0.292995 + 0.0516629i) q^{77} +(1.39219 - 1.20622i) 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} +(0.624595 + 0.578743i) q^{84} +(-0.701999 + 3.98123i) q^{85} +(0.00408959 + 0.00828344i) q^{86} +(-10.6490 - 2.92714i) q^{87} +(1.65067 + 2.99914i) q^{88} +(2.75507 - 1.59064i) q^{89} +(-2.97177 + 3.02797i) q^{90} +(0.160086 + 0.0924257i) q^{91} +(7.03482 + 0.919694i) q^{92} +(11.8735 - 5.44373i) q^{93} +(-2.49128 - 1.66300i) q^{94} +(4.41790 + 3.70706i) q^{95} +(-0.681819 + 9.77421i) q^{96} +(-1.59179 - 0.579364i) q^{97} +(3.94852 - 8.98469i) 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 $

$2$	−0.977486	+	1.02202i	−0.691187	+	0.722676i
$2$	−0.977486	+	1.02202i	−0.691187	+	0.722676i
$3$	−1.42519	+	0.984291i	−0.822835	+	0.568281i
$3$	−1.42519	+	0.984291i	−0.822835	+	0.568281i
$4$	−0.0890420	−	1.99802i	−0.0445210	−	0.999008i
$5$	0.342020	+	0.939693i	0.152956	+	0.420243i
$5$	0.342020	+	0.939693i	0.152956	+	0.420243i
$6$	0.387142	−	2.41870i	0.158050	−	0.987431i
$7$	0.242074	−	0.0426842i	0.0914955	−	0.0161331i	−0.127713	−	0.991811i	$-0.540764\pi$
$7$	0.242074	−	0.0426842i	0.0914955	−	0.0161331i	0.219208	+	0.975678i	$0.429653\pi$
$8$	2.12905	+	1.86203i	0.752732	+	0.658327i
$9$	1.06234	−	2.80561i	0.354114	−	0.935202i
$10$	−1.29470	−	0.568986i	−0.409421	−	0.179929i
$11$	1.13736	+	0.413964i	0.342926	+	0.124815i	0.507741	−	0.861510i	$-0.330481\pi$
$11$	1.13736	+	0.413964i	0.342926	+	0.124815i	−0.164815	+	0.986324i	$0.552703\pi$
$12$	2.09353	+	2.75991i	0.604351	+	0.796719i
$13$	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	$0.688967\pi$
$14$	−0.193000	+	0.289128i	−0.0515815	+	0.0772726i
$15$	−1.41238	−	1.00259i	−0.364674	−	0.258869i
$16$	−3.98414	+	0.355815i	−0.996036	+	0.0889537i
$17$	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	$0.503575\pi$
$18$	1.82896	+	3.82817i	0.431089	+	0.902309i
$19$	4.99450	−	2.88358i	1.14582	−	0.661538i	0.197953	−	0.980212i	$-0.436571\pi$
$19$	4.99450	−	2.88358i	1.14582	−	0.661538i	0.947865	+	0.318674i	$0.103237\pi$
$20$	1.84707	−	0.767034i	0.413017	−	0.171514i
$21$	−0.302989	+	0.299105i	−0.0661175	+	0.0652700i
$22$	−1.53483	+	0.757756i	−0.327227	+	0.161554i
$23$	−0.615990	+	3.49345i	−0.128443	+	0.728435i	0.850761	+	0.525554i	$0.176142\pi$
$23$	−0.615990	+	3.49345i	−0.128443	+	0.728435i	−0.979203	+	0.202882i	$0.934969\pi$
$24$	−4.86708	−	0.558150i	−0.993489	−	0.113932i
$25$	−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	$0.576109\pi$
$30$	2.40525	−	0.463450i	0.439136	−	0.0846141i
$31$	−7.42673	−	1.30953i	−1.33388	−	0.235199i	−0.539175	−	0.842194i	$-0.681264\pi$
$31$	−7.42673	−	1.30953i	−1.33388	−	0.235199i	−0.794706	+	0.606995i	$0.792375\pi$
$32$	3.53080	−	4.41967i	0.624162	−	0.781295i
$33$	−2.02841	+	0.529512i	−0.353102	+	0.0921762i
$34$	−5.48805	+	1.60231i	−0.941192	+	0.274793i
$35$	0.122904	+	0.212877i	0.0207746	+	0.0359827i
$36$	−5.70024	−	1.87276i	−0.950040	−	0.312127i
$37$	−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	$0.948457\pi$
$38$	−1.93499	+	7.92313i	−0.313897	+	1.28530i
$39$	−1.29681	−	0.121890i	−0.207656	−	0.0195180i
$40$	−1.02156	+	2.63750i	−0.161523	+	0.417026i
$41$	−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	$0.308164\pi$
$42$	−0.00952332	−	0.602030i	−0.00146948	−	0.0928953i
$43$	0.00223415	−	0.00613829i	0.000340705	−	0.000936080i	−0.939522	−	0.342488i	$-0.888730\pi$
$43$	0.00223415	−	0.00613829i	0.000340705	−	0.000936080i	0.939863	+	0.341552i	$0.110953\pi$
$44$	0.725835	−	2.30932i	0.109424	−	0.348143i
$45$	2.99975	+	0.0387019i	0.447176	+	0.00576934i
$46$	−2.96825	−	4.04435i	−0.437644	−	0.596307i
$47$	0.367791	+	2.08585i	0.0536478	+	0.304252i	0.999811	−	0.0194379i	$-0.00618765\pi$
$47$	0.367791	+	2.08585i	0.0536478	+	0.304252i	−0.946163	+	0.323690i	$0.895077\pi$
$48$	5.32794	−	4.42866i	0.769022	−	0.639222i
$49$	−6.52107	+	2.37348i	−0.931581	+	0.339068i
$50$	0.0918572	−	1.41123i	0.0129906	−	0.199578i
$51$	−6.97922	+	0.565264i	−0.977286	+	0.0791527i
$52$	0.914517	−	1.19405i	0.126821	−	0.165585i
$53$		−	0.559092i		−	0.0767971i	−0.999263	−	0.0383986i	$-0.987774\pi$
$53$		−	0.559092i		−	0.0767971i	0.999263	−	0.0383986i	$-0.0122257\pi$
$54$	−6.37465	−	3.65566i	−0.867480	−	0.497472i
$55$			1.21035i			0.163204i
$56$	0.594867	+	0.359873i	0.0794924	+	0.0480901i
$57$	−4.27984	+	9.02569i	−0.566879	+	1.19548i
$58$	−8.99831	−	0.585703i	−1.18154	−	0.0769066i
$59$	5.91537	−	2.15302i	0.770115	−	0.280299i	0.0730705	−	0.997327i	$-0.476720\pi$
$59$	5.91537	−	2.15302i	0.770115	−	0.280299i	0.697045	+	0.717028i	$0.254498\pi$
$60$	−1.87744	+	2.91122i	−0.242377	+	0.375837i
$61$	−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	$0.981071\pi$
$62$	8.59790	−	6.31021i	1.09193	−	0.801397i
$63$	0.137411	−	0.724510i	0.0173121	−	0.0912797i
$64$	1.06568	+	7.92870i	0.133210	+	0.991088i
$65$	−0.257204	+	0.706662i	−0.0319022	+	0.0876506i
$66$	1.44158	−	2.59067i	0.177446	−	0.318889i
$67$	6.42340	−	7.65512i	0.784744	−	0.935221i	−0.214394	−	0.976747i	$-0.568778\pi$
$67$	6.42340	−	7.65512i	0.784744	−	0.935221i	0.999137	+	0.0415261i	$0.0132220\pi$
$68$	3.72690	−	7.17511i	0.451953	−	0.870110i
$69$	−2.56067	−	5.58515i	−0.308268	−	0.672373i
$70$	−0.337701	−	0.0824734i	−0.0403630	−	0.00985746i
$71$	−4.04403	+	7.00447i	−0.479939	+	0.831278i	−0.999735	−	0.0230121i	$-0.992674\pi$
$71$	−4.04403	+	7.00447i	−0.479939	+	0.831278i	0.519797	+	0.854290i	$0.326008\pi$
$72$	7.48590	−	3.99515i	0.882222	−	0.470833i
$73$	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	$0.511731\pi$
$74$	−3.05260	−	10.4554i	−0.354857	−	1.21542i
$75$	0.459070	−	1.67011i	0.0530089	−	0.192847i
$76$	−6.20616	−	9.72234i	−0.711895	−	1.11523i
$77$	0.292995	+	0.0516629i	0.0333898	+	0.00588753i
$78$	1.39219	−	1.20622i	0.157634	−	0.136577i
$79$	5.69121	+	6.78252i	0.640312	+	0.763094i	0.984419	−	0.175837i	$-0.0562630\pi$
$79$	5.69121	+	6.78252i	0.640312	+	0.763094i	−0.344108	+	0.938930i	$0.611819\pi$
$80$	−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	−0.999970	−	0.00780394i	$-0.997516\pi$
$83$	−10.6221	+	8.91300i	−1.16593	+	0.978329i	−0.165958	+	0.986133i	$0.553071\pi$
$84$	0.624595	+	0.578743i	0.0681489	+	0.0631461i
$85$	−0.701999	+	3.98123i	−0.0761425	+	0.431825i
$86$	0.00408959	+	0.00828344i	0.000440992	+	0.000893226i
$87$	−10.6490	−	2.92714i	−1.14169	−	0.313822i
$88$	1.65067	+	2.99914i	0.175962	+	0.319710i
$89$	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	$0.279406\pi$
$90$	−2.97177	+	3.02797i	−0.313252	+	0.319176i
$91$	0.160086	+	0.0924257i	0.0167816	+	0.00968885i
$92$	7.03482	+	0.919694i	0.733431	+	0.0958848i
$93$	11.8735	−	5.44373i	1.23122	−	0.564489i
$94$	−2.49128	−	1.66300i	−0.256956	−	0.171525i
$95$	4.41790	+	3.70706i	0.453267	+	0.380336i
$96$	−0.681819	+	9.77421i	−0.0695879	+	0.997576i
$97$	−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	$0.638519\pi$
$98$	3.94852	−	8.98469i	0.398861	−	0.907591i
$99$	2.36968	−	2.75121i	0.238162	−	0.276507i
$100$	1.35251	+	1.47333i	0.135251	+	0.147333i
$101$	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	$0.246681\pi$
$102$	6.24438	−	7.68543i	0.618286	−	0.760971i
$103$	−3.48523	−	9.57560i	−0.343410	−	0.943512i	−0.984397	−	0.175960i	$-0.943697\pi$
$103$	−3.48523	−	9.57560i	−0.343410	−	0.943512i	0.640987	−	0.767552i	$-0.278525\pi$
$104$	0.326414	+	2.10182i	0.0320076	+	0.206100i
$105$	−0.384695	−	0.182416i	−0.0375424	−	0.0178020i
$106$	0.571402	+	0.546504i	0.0554994	+	0.0530812i
$107$	11.4554			1.10744			0.553719	−	0.832704i	$-0.313208\pi$
$107$	11.4554			1.10744			0.553719	+	0.832704i	$0.313208\pi$
$108$	9.96728	−	2.94165i	0.959102	−	0.283060i
$109$	19.9338			1.90932			0.954658	−	0.297706i	$-0.0962216\pi$
$109$	19.9338			1.90932			0.954658	+	0.297706i	$0.0962216\pi$
$110$	−1.23700	−	1.18310i	−0.117943	−	0.112804i
$111$	−1.07690	−	13.2963i	−0.102215	−	1.26203i
$112$	−0.949271	+	0.256194i	−0.0896977	+	0.0242080i
$113$	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	$0.829578\pi$
$114$	−5.04093	−	13.1966i	−0.472127	−	1.23597i
$115$	−3.49345	+	0.615990i	−0.325766	+	0.0574413i
$116$	9.39433	−	8.62392i	0.872241	−	0.800711i
$117$	1.96818	−	1.10272i	0.181958	−	0.101947i
$118$	−3.58177	+	8.15015i	−0.329728	+	0.750283i
$119$	0.933790	+	0.339872i	0.0856004	+	0.0311560i
$120$	−1.14015	−	4.76446i	−0.104081	−	0.434934i
$121$	−7.30427	−	6.12901i	−0.664025	−	0.557183i
$122$	2.10945	+	1.40811i	0.190980	+	0.127484i
$123$	0.553644	−	5.89031i	0.0499204	−	0.531112i
$124$	−1.95518	+	14.9553i	−0.175580	+	1.34303i
$125$	−0.866025	−	0.500000i	−0.0774597	−	0.0447214i
$126$	0.606146	+	0.848635i	0.0539997	+	0.0756024i
$127$	13.5059	−	7.79761i	1.19845	−	0.691926i	0.238241	−	0.971206i	$-0.423429\pi$
$127$	13.5059	−	7.79761i	1.19845	−	0.691926i	0.960210	+	0.279280i	$0.0900958\pi$
$128$	−9.14496	−	6.66105i	−0.808308	−	0.588759i
$129$	0.00285776	+	0.0109473i	0.000251612	+	0.000963856i
$130$	−0.470808	−	0.953619i	−0.0412926	−	0.0836379i
$131$	−2.27248	+	12.8879i	−0.198547	+	1.12602i	0.708729	+	0.705481i	$0.249269\pi$
$131$	−2.27248	+	12.8879i	−0.198547	+	1.12602i	−0.907276	+	0.420536i	$0.861842\pi$
$132$	1.23859	+	4.00566i	0.107805	+	0.348648i
$133$	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	$0.878120\pi$
$138$	8.21114	+	2.84236i	0.698979	+	0.241958i
$139$	14.8508	+	2.61860i	1.25963	+	0.222107i	0.763311	−	0.646032i	$-0.223573\pi$
$139$	14.8508	+	2.61860i	1.25963	+	0.222107i	0.496321	+	0.868139i	$0.334684\pi$
$140$	0.414387	−	0.264520i	0.0350221	−	0.0223560i
$141$	−2.57725	−	2.61072i	−0.217044	−	0.219862i
$142$	−3.20571	−	10.9799i	−0.269017	−	0.921409i
$143$	0.455100	+	0.788257i	0.0380574	+	0.0659173i
$144$	−3.23425	+	11.5559i	−0.269521	+	0.962995i
$145$	−3.18812	+	5.52198i	−0.264759	+	0.458576i
$146$	−19.8846	−	4.85623i	−1.64566	−	0.401905i
$147$	6.95759	−	9.80129i	0.573852	−	0.808397i
$148$	13.6695	+	7.10022i	1.12363	+	0.583635i
$149$	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	$0.129317\pi$
$150$	1.25814	+	2.10168i	0.102727	+	0.171602i
$151$	0.161803	−	0.444550i	0.0131673	−	0.0361770i	−0.932935	−	0.360045i	$-0.882761\pi$
$151$	0.161803	−	0.444550i	0.0131673	−	0.0361770i	0.946102	+	0.323868i	$0.104983\pi$
$152$	16.0028	+	3.16065i	1.29800	+	0.256362i
$153$	9.39034	−	7.67519i	0.759164	−	0.620503i
$154$	−0.339199	+	0.248946i	−0.0273334	+	0.0200607i
$155$	−1.30953	−	7.42673i	−0.105184	−	0.596530i
$156$	−0.128068	+	2.60190i	−0.0102537	+	0.208319i
$157$	−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	$0.712106\pi$
$158$	−12.4949	−	0.813300i	−0.994044	−	0.0647027i
$159$	0.550309	+	0.796813i	0.0436423	+	0.0631914i
$160$	5.36073	+	1.80625i	0.423803	+	0.142796i
$161$			0.871968i			0.0687207i
$162$	12.6833	−	1.06449i	0.996496	−	0.0836345i
$163$		−	2.97419i		−	0.232957i	−0.993193	−	0.116478i	$-0.962839\pi$
$163$		−	2.97419i		−	0.232957i	0.993193	−	0.116478i	$-0.0371606\pi$
$164$	5.42356	+	4.15388i	0.423509	+	0.324363i
$165$	−1.19134	−	1.72498i	−0.0927455	−	0.134290i
$166$	1.27371	−	19.5683i	0.0988589	−	1.51880i
$167$	−15.7978	+	5.74993i	−1.22247	+	0.444943i	−0.871013	−	0.491261i	$-0.836536\pi$
$167$	−15.7978	+	5.74993i	−1.22247	+	0.444943i	−0.351458	+	0.936204i	$0.614314\pi$
$168$	−1.20202	+	0.0726337i	−0.0927378	+	0.00560381i
$169$	−2.15922	−	12.2456i	−0.166094	−	0.941967i
$170$	−3.38270	−	4.60906i	−0.259441	−	0.353498i
$171$	−2.78431	−	17.0760i	−0.212921	−	1.30583i
$172$	−0.0124633	−	0.00391731i	−0.000950321	−	0.000298692i
$173$	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	$0.0478612\pi$
$174$	13.4008	−	8.02222i	1.01591	−	0.608163i
$175$	−0.158003	+	0.188300i	−0.0119439	+	0.0142342i
$176$	−4.67869	−	1.24460i	−0.352670	−	0.0938156i
$177$	−6.31134	+	8.89090i	−0.474389	+	0.668281i
$178$	−1.06738	+	4.37056i	−0.0800035	+	0.327587i
$179$	4.51117	−	7.81358i	0.337181	−	0.584014i	−0.646720	−	0.762727i	$-0.723860\pi$
$179$	4.51117	−	7.81358i	0.337181	−	0.584014i	0.983901	+	0.178713i	$0.0571933\pi$
$180$	−0.189777	−	5.99700i	−0.0141451	−	0.446990i
$181$	−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	$0.890245\pi$
$182$	−0.250943	+	0.0732660i	−0.0186011	+	0.00543084i
$183$	2.18224	+	2.21058i	0.161316	+	0.163410i
$184$	−7.81639	+	6.29073i	−0.576232	+	0.463759i
$185$	−7.58476	−	1.33740i	−0.557642	−	0.0983274i
$186$	−6.04257	+	17.4561i	−0.443063	+	1.27994i
$187$	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	−0.933286	−	0.359135i	$-0.883072\pi$
$191$	−10.2501	+	8.60085i	−0.741671	+	0.622336i	0.191615	+	0.981470i	$0.438627\pi$
$192$	−9.32295	−	10.2510i	−0.672826	−	0.739801i
$193$	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	$-0.0344682\pi$
$194$	2.14807	−	1.06052i	0.154223	−	0.0761407i
$195$	−0.328996	−	1.26029i	−0.0235599	−	0.0902514i
$196$	5.32289	+	12.8179i	0.380207	+	0.915562i
$197$	−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	$0.425452\pi$
$198$	0.495448	+	5.11113i	0.0352100	+	0.363232i
$199$	8.00596	+	4.62224i	0.567528	+	0.327662i	0.756161	−	0.654385i	$-0.227073\pi$
$199$	8.00596	+	4.62224i	0.567528	+	0.327662i	−0.188634	+	0.982048i	$0.560406\pi$
$200$	−2.82783	−	0.0578738i	−0.199958	−	0.00409230i
$201$	−1.61972	+	17.2325i	−0.114246	+	1.21549i
$202$	−9.18624	+	13.7616i	−0.646342	+	0.968264i
$203$	1.20065	+	1.00746i	0.0842689	+	0.0707100i
$204$	1.75085	+	13.8943i	0.122584	+	0.972793i
$205$	−3.20977	−	1.16826i	−0.224180	−	0.0815948i
$206$	13.1932	+	5.79804i	0.919214	+	0.403969i
$207$	9.14686	+	5.43947i	0.635751	+	0.378069i
$208$	−2.46716	−	1.72090i	−0.171067	−	0.119323i
$209$	6.87423	−	1.21211i	0.475501	−	0.0838436i
$210$	0.562466	−	0.214856i	0.0388139	−	0.0148264i
$211$	−7.08402	−	19.4632i	−0.487684	−	1.33990i	−0.902772	−	0.430119i	$-0.858472\pi$
$211$	−7.08402	−	19.4632i	−0.487684	−	1.33990i	0.415088	−	0.909781i	$-0.363751\pi$
$212$	−1.11707	+	0.0497826i	−0.0767210	+	0.00341908i
$213$	−1.13091	−	13.9632i	−0.0774890	−	0.956744i
$214$	−11.1975	+	11.7077i	−0.765447	+	0.800319i
$215$	0.00653223			0.000445494
$216$	−6.73646	+	13.0622i	−0.458358	+	0.888768i
$217$	−1.85372			−0.125839
$218$	−19.4850	+	20.3727i	−1.31969	+	1.37982i
$219$	−22.6517	−	10.7411i	−1.53066	−	0.725817i
$220$	2.41830	−	0.107772i	0.163042	−	0.00726599i
$221$	1.03979	+	2.85679i	0.0699435	+	0.192168i
$222$	14.6417	+	11.8963i	0.982688	+	0.798430i
$223$	8.66402	−	1.52770i	0.580185	−	0.102302i	0.124149	−	0.992264i	$-0.460380\pi$
$223$	8.66402	−	1.52770i	0.580185	−	0.102302i	0.456036	+	0.889961i	$0.349269\pi$
$224$	0.666064	−	1.22060i	0.0445033	−	0.0815546i
$225$	0.989607	+	2.83208i	0.0659738	+	0.188805i
$226$	−5.09924	−	2.24097i	−0.339196	−	0.149067i
$227$	−9.34078	−	3.39976i	−0.619969	−	0.225650i	0.0128905	−	0.999917i	$-0.495897\pi$
$227$	−9.34078	−	3.39976i	−0.619969	−	0.225650i	−0.632860	+	0.774267i	$0.718119\pi$
$228$	18.4146	+	7.74754i	1.21954	+	0.513093i
$229$	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	$0.715747\pi$
$230$	2.78525	−	4.17249i	0.183654	−	0.275126i
$231$	−0.468425	+	0.214763i	−0.0308201	+	0.0141303i
$232$	−0.369017	+	18.0309i	−0.0242272	+	1.18379i
$233$	−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	$-0.697501\pi$
$234$	−0.796866	+	3.08941i	−0.0520927	+	0.201961i
$235$	−1.83426	+	1.05901i	−0.119654	+	0.0690823i
$236$	−4.82848	−	11.6273i	−0.314307	−	0.756872i
$237$	−14.7870	−	4.06459i	−0.960522	−	0.264023i
$238$	−1.26012	+	0.622130i	−0.0816815	+	0.0403267i
$239$	−2.81587	+	15.9696i	−0.182143	+	1.03299i	0.747428	+	0.664343i	$0.231289\pi$
$239$	−2.81587	+	15.9696i	−0.182143	+	1.03299i	−0.929571	+	0.368643i	$0.879822\pi$
$240$	5.98384	+	3.49194i	0.386255	+	0.225404i
$241$	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
$246$	5.47883	+	6.32353i	0.349317	+	0.403174i
$247$	4.27109	+	0.753109i	0.271763	+	0.0479192i
$248$	−13.3735	−	16.6169i	−0.849216	−	1.05517i
$249$	6.36554	−	23.1580i	0.403400	−	1.46758i
$250$	1.35754	−	0.396351i	0.0858582	−	0.0250674i
$251$	2.54978	+	4.41635i	0.160941	+	0.278757i	0.935206	−	0.354103i	$-0.115214\pi$
$251$	2.54978	+	4.41635i	0.160941	+	0.278757i	−0.774266	+	0.632861i	$0.781881\pi$
$252$	−1.45982	−	0.210037i	−0.0919600	−	0.0132311i
$253$	−2.14676	+	3.71831i	−0.134966	+	0.233768i
$254$	−5.23249	+	21.4253i	−0.328315	+	1.34434i
$255$	−2.91821	−	6.36499i	−0.182745	−	0.398591i
$256$	15.7468	−	2.83523i	0.984174	−	0.177202i
$257$	−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	$0.930225\pi$
$258$	−0.0139818	−	0.00778014i	−0.000870466	−	0.000484371i
$259$	−0.647499	+	1.77899i	−0.0402336	+	0.110541i
$260$	1.43482	+	0.450975i	0.0889840	+	0.0279683i
$261$	18.0580	−	6.30997i	1.11776	−	0.390577i
$262$	−10.9503	−	14.9202i	−0.676512	−	0.921774i
$263$	−1.20783	−	6.84992i	−0.0744778	−	0.422384i	−0.999135	−	0.0415839i	$-0.986760\pi$
$263$	−1.20783	−	6.84992i	−0.0744778	−	0.422384i	0.924657	−	0.380800i	$-0.124351\pi$
$264$	−5.30456	−	2.64961i	−0.326473	−	0.163072i
$265$	0.525374	−	0.191221i	0.0322735	−	0.0117466i
$266$	−0.130218	+	2.00058i	−0.00798420	+	0.122663i
$267$	−2.36085	+	4.97876i	−0.144482	+	0.304695i
$268$	−15.8670	−	12.1524i	−0.969231	−	0.742329i
$269$		−	2.27064i		−	0.138443i	−0.997601	−	0.0692215i	$-0.977948\pi$
$269$		−	2.27064i		−	0.138443i	0.997601	−	0.0692215i	$-0.0220515\pi$
$270$	1.25494	−	7.24052i	0.0763731	−	0.440644i
$271$			22.6376i			1.37513i	0.726121	+	0.687567i	$0.241321\pi$
$271$			22.6376i			1.37513i	−0.726121	+	0.687567i	$0.758679\pi$
$272$	−14.6679	−	6.80753i	−0.889369	−	0.412767i
$273$	−0.319127	+	0.0258469i	−0.0193145	+	0.00156432i
$274$	10.2424	+	0.666683i	0.618768	+	0.0402758i
$275$	−1.13736	+	0.413964i	−0.0685852	+	0.0249630i
$276$	−10.9312	+	5.61357i	−0.657982	+	0.337897i
$277$	−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	$-0.348838\pi$
$278$	−17.1928	+	12.6182i	−1.03115	+	0.756788i
$279$	−11.5638	+	19.4453i	−0.692305	+	1.16416i
$280$	−0.134714	+	0.682076i	−0.00805068	+	0.0407618i
$281$	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	$0.0344915\pi$
$282$	5.18743	−	0.0820583i	0.308907	−	0.00488650i
$283$	0.717765	−	0.855400i	0.0426667	−	0.0508482i	−0.744289	−	0.667858i	$-0.767212\pi$
$283$	0.717765	−	0.855400i	0.0426667	−	0.0508482i	0.786956	+	0.617009i	$0.211656\pi$
$284$	14.3551	+	7.45636i	0.851821	+	0.442453i
$285$	−9.94517	−	0.934769i	−0.589101	−	0.0553710i
$286$	−1.25047	−	0.305389i	−0.0739416	−	0.0180580i
$287$	−0.419812	+	0.727136i	−0.0247807	+	0.0429215i
$288$	−8.64894	−	14.6012i	−0.509644	−	0.860386i
$289$	−0.328491	−	0.568964i	−0.0193230	−	0.0334684i
$290$	−2.52722	−	8.65597i	−0.148404	−	0.508296i
$291$	2.83887	−	0.741079i	0.166417	−	0.0434428i
$292$	24.4001	−	15.5756i	1.42791	−	0.911491i
$293$	−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	$0.658187\pi$
$294$	3.21615	+	16.6914i	0.187570	+	0.973462i
$295$	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
$300$	−3.37778	−	0.768521i	−0.195016	−	0.0443706i
$301$	0.000278823	−	0.00158128i	1.60711e−5	−	9.11437e-5i
$302$	0.296178	+	0.599907i	0.0170431	+	0.0345208i
$303$	−14.4214	+	14.2365i	−0.828486	+	0.817866i
$304$	−18.8728	+	13.2657i	−1.08243	+	0.760840i
$305$	1.55313	−	0.896698i	0.0889318	−	0.0513448i
$306$	−1.33475	+	17.0995i	−0.0763023	+	0.977513i
$307$	13.8771	+	8.01193i	0.792006	+	0.457265i	0.840668	−	0.541550i	$-0.182162\pi$
$307$	13.8771	+	8.01193i	0.792006	+	0.457265i	−0.0486623	+	0.998815i	$0.515496\pi$
$308$	0.0771345	−	0.590009i	0.00439514	−	0.0336189i
$309$	14.3923	+	10.2166i	0.818749	+	0.581201i
$310$	8.87031	+	5.92116i	0.503800	+	0.336299i
$311$	15.6782	+	13.1556i	0.889032	+	0.745986i	0.968016	−	0.250890i	$-0.0807232\pi$
$311$	15.6782	+	13.1556i	0.889032	+	0.745986i	−0.0789841	+	0.996876i	$0.525168\pi$
$312$	−2.53401	−	2.67421i	−0.143460	−	0.151397i
$313$	−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	$0.639390\pi$
$314$	12.1157	−	27.5687i	0.683726	−	1.55579i
$315$	0.727814	−	0.118673i	0.0410077	−	0.00668648i
$316$	13.0448	−	11.9751i	0.733830	−	0.673650i
$317$	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	$0.334233\pi$
$318$	−1.35228	−	0.216448i	−0.0758319	−	0.0121378i
$319$	2.63953	+	7.25206i	0.147785	+	0.406037i
$320$	−7.08606	+	3.71319i	−0.396123	+	0.207573i
$321$	−16.3262	+	11.2755i	−0.911238	+	0.629335i
$322$	−0.891167	−	0.852336i	−0.0496628	−	0.0474988i
$323$	23.3146			1.29726
$324$	−11.3098	+	14.0031i	−0.628325	+	0.777951i
$325$	−0.752014			−0.0417142
$326$	3.03968	+	2.90723i	0.168352	+	0.161017i
$327$	−28.4095	+	19.6207i	−1.57105	+	1.08503i
$328$	−9.54679	+	1.48262i	−0.527133	+	0.0818642i
$329$	0.178066	+	0.489231i	0.00981707	+	0.0269722i
$330$	2.92748	+	0.468578i	0.161152	+	0.0257943i
$331$	−2.67053	+	0.470887i	−0.146786	+	0.0258823i	−0.246558	−	0.969128i	$-0.579300\pi$
$331$	−2.67053	+	0.470887i	−0.146786	+	0.0258823i	0.0997724	+	0.995010i	$0.468189\pi$
$332$	18.7541	+	20.4295i	1.02927	+	1.12121i
$333$	14.6222	+	17.8898i	0.801293	+	0.980355i
$334$	9.56560	−	21.7661i	0.523406	−	1.19099i
$335$	9.39039	+	3.41782i	0.513052	+	0.186736i
$336$	1.10072	−	1.29948i	0.0600494	−	0.0708926i
$337$	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	$0.360790\pi$
$338$	14.6258	+	9.76311i	0.795539	+	0.531043i
$339$	−5.56269	−	3.94876i	−0.302124	−	0.214467i
$340$	8.01708	+	1.04811i	0.434787	+	0.0568417i
$341$	−7.90475	−	4.56381i	−0.428066	−	0.247144i
$342$	20.1736	+	13.8459i	1.09086	+	0.748700i
$343$	−2.96741	+	1.71323i	−0.160225	+	0.0925060i
$344$	0.0161863	−	0.00890864i	0.000872707	−	0.000480322i
$345$	4.37253	−	4.31648i	0.235409	−	0.232391i
$346$	3.25102	+	6.58492i	0.174776	+	0.354007i
$347$	1.99901	−	11.3370i	0.107313	−	0.608600i	−0.882959	−	0.469451i	$-0.844452\pi$
$347$	1.99901	−	11.3370i	0.107313	−	0.608600i	0.990271	−	0.139150i	$-0.0444369\pi$
$348$	−4.90027	+	21.5375i	−0.262682	+	1.15453i
$349$	−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	$-0.566883\pi$
$354$	−2.91742	−	15.1410i	−0.155059	−	0.804737i
$355$	−7.96519	−	1.40448i	−0.422749	−	0.0745420i
$356$	−3.42344	−	5.36304i	−0.181442	−	0.284241i
$357$	−1.66536	+	0.434738i	−0.0881403	+	0.0230088i
$358$	3.57601	+	12.2482i	0.188998	+	0.647336i
$359$	−14.6260	−	25.3330i	−0.771931	−	1.33702i	−0.936503	−	0.350659i	$-0.885958\pi$
$359$	−14.6260	−	25.3330i	−0.771931	−	1.33702i	0.164572	−	0.986365i	$-0.447376\pi$
$360$	6.31454	+	5.66803i	0.332806	+	0.298731i
$361$	7.13004	−	12.3496i	0.375265	−	0.649978i
$362$	6.57417	+	1.60555i	0.345531	+	0.0843856i
$363$	16.4427	+	1.54549i	0.863019	+	0.0811171i
$364$	0.170414	−	0.328084i	0.00893211	−	0.0171963i
$365$	−9.30358	+	11.0876i	−0.486972	+	0.580350i
$366$	−4.39236	+	0.0694813i	−0.229592	+	0.00363184i
$367$	1.18410	−	3.25328i	0.0618093	−	0.169820i	−0.904944	−	0.425531i	$-0.860087\pi$
$367$	1.18410	−	3.25328i	0.0618093	−	0.169820i	0.966753	+	0.255711i	$0.0823096\pi$
$368$	1.21117	−	14.1376i	0.0631366	−	0.736973i
$369$	5.00873	+	8.93977i	0.260744	+	0.465386i
$370$	8.78084	−	6.44447i	0.456494	−	0.335032i
$371$	−0.0238644	−	0.135342i	−0.00123898	−	0.00702659i
$372$	−11.9339	−	23.2387i	−0.618744	−	1.20487i
$373$	−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	$0.541709\pi$
$374$	−6.90517	−	0.449459i	−0.357058	−	0.0232410i
$375$	1.72640	−	0.139825i	0.0891508	−	0.00722053i
$376$	−3.10087	+	5.12570i	−0.159915	+	0.264338i
$377$			4.79502i			0.246956i
$378$	−1.69918	−	0.612844i	−0.0873963	−	0.0315213i
$379$		−	16.9816i		−	0.872288i	−0.899877	−	0.436144i	$-0.856344\pi$
$379$		−	16.9816i		−	0.872288i	0.899877	−	0.436144i	$-0.143656\pi$
$380$	7.01338	−	9.15712i	0.359779	−	0.469750i
$381$	−11.5733	+	24.4068i	−0.592919	+	1.25040i
$382$	1.22910	−	18.8830i	0.0628862	−	0.966138i
$383$	−6.14396	+	2.23622i	−0.313942	+	0.114265i	−0.494185	−	0.869357i	$-0.664534\pi$
$383$	−6.14396	+	2.23622i	−0.313942	+	0.114265i	0.180244	+	0.983622i	$0.442311\pi$
$384$	19.5897	+	0.491972i	0.999685	+	0.0251058i
$385$	0.0516629	+	0.292995i	0.00263298	+	0.0149324i
$386$	6.48795	+	8.84008i	0.330228	+	0.449948i
$387$	−0.0148482	−	0.0127891i	−0.000754776	−	0.000650108i
$388$	−1.01584	+	3.23201i	−0.0515716	+	0.164080i
$389$	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	$-0.0686216\pi$
$390$	1.60963	+	0.895678i	0.0815068	+	0.0453544i
$391$	−9.21800	+	10.9856i	−0.466174	+	0.555565i
$392$	−18.3031	−	7.08920i	−0.924449	−	0.358058i
$393$	−9.44669	−	20.6044i	−0.476522	−	1.03936i
$394$	2.68781	−	11.0057i	0.135410	−	0.554457i
$395$	−4.42698	+	7.66775i	−0.222745	+	0.385806i
$396$	−5.70796	−	4.48970i	−0.286836	−	0.225616i
$397$	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	$0.791938\pi$
$398$	−12.5497	+	3.66406i	−0.629061	+	0.183663i
$399$	−0.650786	+	2.36757i	−0.0325800	+	0.118527i
$400$	2.82332	−	2.83353i	0.141166	−	0.141676i
$401$	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	$0.292778\pi$
$402$	−16.0287	−	18.4999i	−0.799438	−	0.922692i
$403$	−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
$408$	−15.9116	−	11.7921i	−0.787743	−	0.583794i
$409$	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	$-0.145805\pi$
$410$	4.33148	−	2.13848i	0.213917	−	0.105612i
$411$	12.1213	+	3.33185i	0.597901	+	0.164348i
$412$	−18.8219	+	7.81618i	−0.927287	+	0.385076i
$413$	1.34006	−	0.773683i	0.0659399	−	0.0380704i
$414$	−14.5002	+	4.03125i	−0.712644	+	0.198125i
$415$	−12.0085	−	6.93308i	−0.589472	−	0.340332i
$416$	4.17041	−	0.839332i	0.204471	−	0.0411516i
$417$	−23.7428	+	10.8855i	−1.16269	+	0.533067i
$418$	−5.48067	+	8.21041i	−0.268068	+	0.401584i
$419$	5.42215	+	4.54972i	0.264889	+	0.222268i	0.765552	−	0.643374i	$-0.222466\pi$
$419$	5.42215	+	4.54972i	0.264889	+	0.222268i	−0.500663	+	0.865642i	$0.666910\pi$
$420$	−0.330217	+	0.784869i	−0.0161129	+	0.0382977i
$421$	−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	$0.658109\pi$
$422$	26.8162	+	11.7850i	1.30539	+	0.573684i
$423$	6.24279	+	1.18401i	0.303535	+	0.0575684i
$424$	1.04105	−	1.19033i	0.0505577	−	0.0578076i
$425$	−3.98123	+	0.701999i	−0.193118	+	0.0340519i
$426$	15.3761	+	12.4930i	0.744975	+	0.605290i
$427$	−0.150774	−	0.414247i	−0.00729644	−	0.0200468i
$428$	−1.02001	−	22.8881i	−0.0493042	−	1.10634i
$429$	−1.42448	−	0.675466i	−0.0687745	−	0.0326118i
$430$	−0.00638516	+	0.00667606i	−0.000307920	+	0.000321948i
$431$	37.4475			1.80378			0.901892	−	0.431961i	$-0.142178\pi$
$431$	37.4475			1.80378			0.901892	+	0.431961i	$0.142178\pi$
$432$	−6.76497	−	19.6529i	−0.325480	−	0.945549i
$433$	38.6912			1.85938			0.929691	−	0.368339i	$-0.120074\pi$
$433$	38.6912			1.85938			0.929691	+	0.368339i	$0.120074\pi$
$434$	1.81198	−	1.89453i	0.0869780	−	0.0909405i
$435$	−0.891557	−	11.0079i	−0.0427469	−	0.527789i
$436$	−1.77495	−	39.8281i	−0.0850046	−	1.90742i
$437$	6.99708	+	19.2243i	0.334716	+	0.919623i
$438$	33.1194	−	12.6512i	1.58250	−	0.604498i
$439$	−38.8989	+	6.85893i	−1.85654	+	0.327359i	−0.986261	−	0.165194i	$-0.947175\pi$
$439$	−38.8989	+	6.85893i	−1.85654	+	0.327359i	−0.870283	+	0.492553i	$0.836064\pi$
$440$	−2.25371	+	2.57689i	−0.107441	+	0.122849i
$441$	−0.268575	+	20.8170i	−0.0127893	+	0.991286i
$442$	−3.93606	−	1.72979i	−0.187219	−	0.0822777i
$443$	1.16058	+	0.422415i	0.0551406	+	0.0200696i	0.369443	−	0.929253i	$-0.379548\pi$
$443$	1.16058	+	0.422415i	0.0551406	+	0.0200696i	−0.314303	+	0.949323i	$0.601771\pi$
$444$	−26.4704	+	3.33559i	−1.25623	+	0.158300i
$445$	2.43700	+	2.04489i	0.115525	+	0.0969370i
$446$	−6.90762	+	10.3481i	−0.327085	+	0.489996i
$447$	−1.13861	+	12.1138i	−0.0538543	+	0.572965i
$448$	0.596404	+	1.87385i	0.0281774	+	0.0885310i
$449$	−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	$0.957123\pi$
$450$	−3.86176	−	1.75692i	−0.182045	−	0.0828221i
$451$	−3.58038	+	2.06713i	−0.168594	+	0.0973376i
$452$	7.27475	−	3.02099i	0.342175	−	0.142096i
$453$	0.206966	+	0.792830i	0.00972412	+	0.0372504i
$454$	12.6051	−	6.22322i	0.591587	−	0.292070i
$455$	−0.0320991	+	0.182043i	−0.00150483	+	0.00853432i
$456$	−25.9181	+	11.2469i	−1.21373	+	0.526685i
$457$	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	$0.543037\pi$
$462$	0.238388	−	0.688666i	0.0110908	−	0.0320396i
$463$	−8.89287	−	1.56805i	−0.413287	−	0.0728736i	−0.0368609	−	0.999320i	$-0.511736\pi$
$463$	−8.89287	−	1.56805i	−0.413287	−	0.0728736i	−0.376426	+	0.926447i	$0.622847\pi$
$464$	−18.0672	−	18.0021i	−0.838750	−	0.835728i
$465$	9.17640	+	9.29556i	0.425546	+	0.431071i
$466$	37.7273	−	11.0150i	1.74768	−	0.510259i
$467$	−18.7300	−	32.4413i	−0.866721	−	1.50120i	−0.865328	−	0.501205i	$-0.832890\pi$
$467$	−18.7300	−	32.4413i	−0.866721	−	1.50120i	−0.00139232	−	0.999999i	$-0.500443\pi$
$468$	−2.37851	−	3.83427i	−0.109947	−	0.177239i
$469$	1.22819	−	2.12728i	0.0567125	−	0.0982289i
$470$	0.710637	−	2.90982i	0.0327792	−	0.134220i
$471$	21.3487	−	30.0743i	0.983696	−	1.38575i
$472$	16.6031	+	6.43072i	0.764218	+	0.295998i
$473$	0.00508206	−	0.00605657i	0.000233674	−	0.000278481i
$474$	18.6082	−	11.1396i	0.854704	−	0.511657i
$475$	−1.97248	+	5.41935i	−0.0905037	+	0.248657i
$476$	0.595923	−	1.89599i	0.0273141	−	0.0869026i
$477$	−1.56859	−	0.593947i	−0.0718209	−	0.0271950i
$478$	−13.5687	−	18.4879i	−0.620619	−	0.845618i
$479$	−5.83268	−	33.0788i	−0.266502	−	1.51141i	−0.764724	−	0.644358i	$-0.777125\pi$
$479$	−5.83268	−	33.0788i	−0.266502	−	1.51141i	0.498222	−	0.867049i	$-0.333986\pi$
$480$	−9.41795	+	2.70228i	−0.429868	+	0.123341i
$481$	−5.44254	+	1.98092i	−0.248159	+	0.0903223i
$482$	−2.28857	+	35.1600i	−0.104242	+	1.60149i
$483$	−0.858270	−	1.24272i	−0.0390526	−	0.0565458i
$484$	−11.5955	+	15.1398i	−0.527067	+	0.688173i
$485$		−	1.69395i		−	0.0769182i
$486$	−17.0284	+	14.0012i	−0.772424	+	0.635107i
$487$		−	34.4221i		−	1.55981i	−0.625896	−	0.779906i	$-0.715267\pi$
$487$		−	34.4221i		−	1.55981i	0.625896	−	0.779906i	$-0.284733\pi$
$488$	2.62560	−	4.34009i	0.118855	−	0.196467i
$489$	2.92747	+	4.23880i	0.132385	+	0.191685i
$490$	9.79332	+	0.637450i	0.442417	+	0.0287971i
$491$	21.2867	−	7.74773i	0.960656	−	0.349650i	0.186366	−	0.982480i	$-0.440329\pi$
$491$	21.2867	−	7.74773i	0.960656	−	0.349650i	0.774291	+	0.632830i	$0.218107\pi$
$492$	−11.8182	−	0.581705i	−0.532807	−	0.0262253i
$493$	4.47611	+	25.3853i	0.201594	+	1.14330i
$494$	−4.94462	+	3.62898i	−0.222469	+	0.163275i
$495$	3.39577	+	1.28581i	0.152628	+	0.0577927i
$496$	30.0551	+	2.57483i	1.34951	+	0.115613i
$497$	−0.679976	+	1.86822i	−0.0305011	+	0.0838011i
$498$	17.4456	+	29.1423i	0.781758	+	1.30590i
$499$	14.8999	−	17.7570i	0.667012	−	0.794914i	−0.321362	−	0.946956i	$-0.604141\pi$
$499$	14.8999	−	17.7570i	0.667012	−	0.794914i	0.988374	+	0.152042i	$0.0485851\pi$
$500$	−0.921896	+	1.77485i	−0.0412284	+	0.0793739i
$501$	16.8553	−	23.7444i	0.753039	−	1.06082i
$502$	−7.00596	−	1.71100i	−0.312691	−	0.0763655i
$503$	−1.13319	+	1.96274i	−0.0505265	+	0.0875144i	−0.890182	−	0.455604i	$-0.849423\pi$
$503$	−1.13319	+	1.96274i	−0.0505265	+	0.0875144i	0.839656	+	0.543119i	$0.182757\pi$
$504$	1.64161	−	1.28665i	0.0731233	−	0.0573121i
$505$	5.84988	+	10.1323i	0.260316	+	0.450881i
$506$	−1.70174	−	5.82862i	−0.0756517	−	0.259114i
$507$	15.1305	+	15.3270i	0.671969	+	0.680695i
$508$	−16.7823	−	26.2906i	−0.744596	−	1.16646i
$509$	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	$0.328116\pi$
$510$	9.35764	+	3.23923i	0.414363	+	0.143435i
$511$	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
$516$	0.0216184	−	0.00668463i	0.000951698	−	0.000294274i
$517$	−0.445156	+	2.52461i	−0.0195779	+	0.111032i
$518$	−1.18524	−	2.40069i	−0.0520763	−	0.105480i
$519$	2.27178	+	8.70255i	0.0997200	+	0.381999i
$520$	−1.86343	+	1.02559i	−0.0817166	+	0.0449753i
$521$	−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	$0.649540\pi$
$522$	−11.2025	+	24.6235i	−0.490322	+	1.07774i
$523$	23.0691	+	13.3189i	1.00874	+	0.582397i	0.910823	−	0.412798i	$-0.135448\pi$
$523$	23.0691	+	13.3189i	1.00874	+	0.582397i	0.0979179	+	0.995194i	$0.468782\pi$
$524$	25.9525	+	3.39289i	1.13374	+	0.148219i
$525$	0.0398419	−	0.423885i	0.00173884	−	0.0184998i
$526$	8.18138	+	5.46128i	0.356725	+	0.238123i
$527$	−23.3543	−	19.5966i	−1.01733	−	0.853640i
$528$	7.89308	−	2.83139i	0.343502	−	0.123221i
$529$	9.78817	+	3.56260i	0.425573	+	0.154896i
$530$	−0.318115	+	0.723857i	−0.0138180	+	0.0314424i
$531$	0.243629	−	18.8834i	0.0105726	−	0.819471i
$532$	−1.91734	−	2.08862i	−0.0831273	−	0.0905533i
$533$	−2.52968	+	0.446050i	−0.109572	+	0.0193206i
$534$	−2.78068	−	7.27950i	−0.120332	−	0.315015i
$535$	3.91799	+	10.7646i	0.169389	+	0.465393i
$536$	27.9298	−	4.33752i	1.20638	−	0.187352i
$537$	1.26155	+	15.5762i	0.0544399	+	0.672161i
$538$	2.32063	+	2.21951i	0.100049	+	0.0956901i
$539$	−8.39932			−0.361784
$540$	6.17326	+	8.36008i	0.265655	+	0.359760i
$541$	−27.1433			−1.16698			−0.583491	−	0.812120i	$-0.698314\pi$
$541$	−27.1433			−1.16698			−0.583491	+	0.812120i	$0.698314\pi$
$542$	−23.1360	−	22.1279i	−0.993776	−	0.950475i
$543$	7.48902	+	3.55118i	0.321385	+	0.152396i
$544$	21.2950	−	8.33655i	0.913017	−	0.357426i
$545$	6.81777	+	18.7317i	0.292041	+	0.802377i
$546$	0.285526	−	0.351419i	0.0122194	−	0.0150393i
$547$	21.9345	−	3.86764i	0.937850	−	0.165368i	0.316226	−	0.948684i	$-0.397584\pi$
$547$	21.9345	−	3.86764i	0.937850	−	0.165368i	0.621624	+	0.783316i	$0.286473\pi$
$548$	−10.6932	+	9.81628i	−0.456791	+	0.419331i
$549$	−5.28596	−	1.00254i	−0.225599	−	0.0427872i
$550$	0.688672	−	1.56704i	0.0293651	−	0.0668190i
$551$	34.5551	+	12.5770i	1.47210	+	0.535799i
$552$	4.94794	−	16.6591i	0.210598	−	0.709058i
$553$	1.66720	+	1.39895i	0.0708967	+	0.0594894i
$554$	31.1825	+	20.8151i	1.32482	+	0.884351i
$555$	12.1261	−	5.55956i	0.514725	−	0.235990i
$556$	3.90967	−	29.9054i	0.165807	−	1.26827i
$557$	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	$0.666231\pi$
$558$	−8.57004	−	30.8259i	−0.362799	−	1.30497i
$559$	0.00425420	−	0.00245616i	0.000179933	−	0.000103885i
$560$	−0.565413	−	0.804399i	−0.0238931	−	0.0339921i
$561$	−8.17187	−	2.24624i	−0.345017	−	0.0948364i
$562$	5.00367	+	10.1349i	0.211067	+	0.427515i
$563$	5.59927	−	31.7550i	0.235981	−	1.33831i	−0.604557	−	0.796562i	$-0.706650\pi$
$563$	5.59927	−	31.7550i	0.235981	−	1.33831i	0.840538	−	0.541753i	$-0.182239\pi$
$564$	−4.98678	+	5.38186i	−0.209981	+	0.226617i
$565$	−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	$0.583111\pi$
$570$	10.6766	−	9.25042i	0.447194	−	0.387457i
$571$	−23.2461	−	4.09892i	−0.972820	−	0.171534i	−0.335421	−	0.942068i	$-0.608879\pi$
$571$	−23.2461	−	4.09892i	−0.972820	−	0.171534i	−0.637399	+	0.770534i	$0.719990\pi$
$572$	1.53443	−	0.979486i	0.0641576	−	0.0409544i
$573$	6.14261	−	22.3469i	0.256611	−	0.933556i
$574$	−0.332785	−	1.13982i	−0.0138902	−	0.0475752i
$575$	−1.77367	−	3.07209i	−0.0739672	−	0.128115i
$576$	23.3769	+	5.43312i	0.974039	+	0.226380i
$577$	−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	$0.206286\pi$
$578$	0.902587	+	0.220430i	0.0375427	+	0.00916868i
$579$	5.59707	+	12.2079i	0.232606	+	0.507344i
$580$	11.3169	+	5.87822i	0.469908	+	0.244080i
$581$	−2.19089	+	2.61100i	−0.0908935	+	0.108323i
$582$	−2.01756	+	3.62577i	−0.0836305	+	0.150293i
$583$	0.231444	−	0.635887i	0.00958543	−	0.0263358i
$584$	−7.93227	+	40.1623i	−0.328239	+	1.66193i
$585$	1.70938	+	1.47233i	0.0706740	+	0.0608733i
$586$	12.3677	−	9.07697i	0.510906	−	0.374966i
$587$	−2.33966	−	13.2689i	−0.0965681	−	0.547665i	−0.994256	−	0.107032i	$-0.965865\pi$
$587$	−2.33966	−	13.2689i	−0.0965681	−	0.547665i	0.897687	−	0.440633i	$-0.145246\pi$
$588$	−20.2027	−	13.0286i	−0.833143	−	0.537292i
$589$	−40.8690	+	14.8751i	−1.68398	+	0.612918i
$590$	−8.88368	−	0.578241i	−0.365735	−	0.0238058i
$591$	5.94494	−	12.5372i	0.244542	−	0.515711i
$592$	12.9692	−	27.9441i	0.533031	−	1.14850i
$593$		−	1.15177i		−	0.0472976i	−0.999720	−	0.0236488i	$-0.992472\pi$
$593$		−	1.15177i		−	0.0472976i	0.999720	−	0.0236488i	$-0.00752835\pi$
$594$	−5.73694	−	6.79667i	−0.235390	−	0.278871i
$595$			0.993718i			0.0407385i
$596$	−11.1539	−	8.54273i	−0.456883	−	0.349924i
$597$	−15.9597	+	1.29261i	−0.653185	+	0.0529030i
$598$	0.245043	−	3.76466i	0.0100206	−	0.153948i
$599$	−15.0200	+	5.46685i	−0.613702	+	0.223369i	−0.630122	−	0.776496i	$-0.716995\pi$
$599$	−15.0200	+	5.46685i	−0.613702	+	0.223369i	0.0164201	+	0.999865i	$0.494773\pi$
$600$	4.08717	−	2.70093i	0.166858	−	0.110265i
$601$	−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	$-0.271770\pi$
$602$	0.00134356	+	0.00183065i	5.47593e−5	+	7.46116e-5i
$603$	−14.6534	−	26.1539i	−0.596732	−	1.06507i
$604$	−0.902626	−	0.283702i	−0.0367273	−	0.0115437i
$605$	3.26118	−	8.96002i	0.132586	−	0.364277i
$606$	−0.453282	−	28.6549i	−0.0184133	−	1.16402i
$607$	−25.8106	+	30.7598i	−1.04762	+	1.24850i	−0.0798109	+	0.996810i	$0.525432\pi$
$607$	−25.8106	+	30.7598i	−1.04762	+	1.24850i	−0.967807	+	0.251693i	$0.919013\pi$
$608$	4.89011	−	32.2554i	0.198320	−	1.30813i
$609$	−2.70279	−	0.254041i	−0.109523	−	0.0102943i
$610$	−0.601718	+	2.46383i	−0.0243629	+	0.0997577i
$611$	−0.796392	+	1.37939i	−0.0322186	+	0.0558042i
$612$	−16.1713	−	18.0787i	−0.653686	−	0.730786i
$613$	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	$0.673752\pi$
$614$	−21.7530	+	6.35106i	−0.877879	+	0.256308i
$615$	5.72444	−	1.49435i	0.230832	−	0.0602580i
$616$	0.527602	+	0.655558i	0.0212577	+	0.0264132i
$617$	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	$0.454267\pi$
$618$	−24.5098	+	4.72262i	−0.985929	+	0.189972i
$619$	−6.32644	−	7.53956i	−0.254281	−	0.303040i	0.623769	−	0.781608i	$-0.285600\pi$
$619$	−6.32644	−	7.53956i	−0.254281	−	0.303040i	−0.878050	+	0.478568i	$0.841156\pi$
$620$	−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
$624$	5.21005	+	0.0242038i	0.208569	+	0.000968927i
$625$	0.173648	−	0.984808i	0.00694593	−	0.0393923i
$626$	3.98094	−	1.96541i	0.159110	−	0.0785538i
$627$	−8.60403	+	8.49374i	−0.343612	+	0.339207i
$628$	16.3328	+	39.3304i	0.651749	+	1.56945i
$629$	−26.9642	+	15.5678i	−1.07513	+	0.620728i
$630$	−0.590142	+	0.859841i	−0.0235118	+	0.0342569i
$631$	−32.2698	−	18.6310i	−1.28464	−	0.741687i	−0.306947	−	0.951726i	$-0.599308\pi$
$631$	−32.2698	−	18.6310i	−1.28464	−	0.741687i	−0.977693	+	0.210039i	$0.932641\pi$
$632$	−0.512412	+	25.0375i	−0.0203827	+	0.995939i
$633$	29.2535	+	20.7660i	1.16272	+	0.825375i
$634$	−9.48823	+	14.2140i	−0.376826	+	0.564511i
$635$	11.9466	+	10.0244i	0.474088	+	0.397807i
$636$	1.54304	−	1.17048i	0.0611857	−	0.0464124i
$637$	−4.90393	−	1.78489i	−0.194301	−	0.0707198i
$638$	−9.99184	−	4.39113i	−0.395581	−	0.173847i
$639$	15.3556	+	18.7871i	0.607460	+	0.743207i
$640$	3.13158	−	10.8717i	0.123787	−	0.429740i
$641$	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	$0.267194\pi$
$642$	4.43488	−	27.7073i	0.175031	−	1.09352i
$643$	−10.1102	−	27.7775i	−0.398707	−	1.09544i	−0.962915	−	0.269806i	$-0.913041\pi$
$643$	−10.1102	−	27.7775i	−0.398707	−	1.09544i	0.564208	−	0.825633i	$-0.309182\pi$
$644$	1.74221	−	0.0776417i	0.0686525	−	0.00305951i
$645$	−0.00930968	+	0.00642961i	−0.000366568	+	0.000253166i
$646$	−22.7897	+	23.8279i	−0.896648	+	0.937497i
$647$	−26.4918			−1.04150			−0.520749	−	0.853710i	$-0.674347\pi$
$647$	−26.4918			−1.04150			−0.520749	+	0.853710i	$0.674347\pi$
$648$	−3.25622	−	25.2467i	−0.127917	−	0.991785i
$649$	7.61916			0.299078
$650$	0.735083	−	0.768572i	0.0288323	−	0.0301459i
$651$	2.64190	−	1.82460i	0.103544	−	0.0715116i
$652$	−5.94249	+	0.264828i	−0.232726	+	0.0103715i
$653$	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	$0.508409\pi$
$654$	7.71722	−	48.2140i	0.301767	−	1.88532i
$655$	−12.8879	+	2.27248i	−0.503570	+	0.0887930i
$656$	7.81659	−	11.2062i	0.305187	−	0.437530i
$657$	42.8554	−	6.98777i	1.67195	−	0.272619i
$658$	−0.674059	−	0.296230i	−0.0262776	−	0.0115483i
$659$	1.02802	+	0.374169i	0.0400460	+	0.0145756i	0.361966	−	0.932191i	$-0.382106\pi$
$659$	1.02802	+	0.374169i	0.0400460	+	0.0145756i	−0.321919	+	0.946767i	$0.604328\pi$
$660$	−3.34046	+	2.53391i	−0.130027	+	0.0986322i
$661$	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	$0.562468\pi$
$662$	2.12915	−	3.18962i	0.0827519	−	0.123968i
$663$	−4.29380	−	3.04802i	−0.166757	−	0.118375i
$664$	−39.2112	−	0.802488i	−1.52169	−	0.0311426i
$665$	1.22769	+	0.708808i	0.0476078	+	0.0274864i
$666$	−32.5767	−	2.54286i	−1.26232	−	0.0985338i
$667$	−19.5884	+	11.3093i	−0.758464	+	0.437900i
$668$	12.8951	+	31.0523i	0.498927	+	1.20145i
$669$	−10.8442	+	10.7052i	−0.419260	+	0.413886i
$670$	−12.6721	+	6.25627i	−0.489564	+	0.241701i
$671$	0.376927	−	2.13766i	0.0145511	−	0.0825235i
$672$	0.252154	+	2.39519i	0.00972703	+	0.0923963i
$673$	−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	$0.984728\pi$
$678$	9.47316	−	1.82532i	0.363815	−	0.0701009i
$679$	−0.410061	−	0.0723048i	−0.0157367	−	0.00277480i
$680$	−8.90777	+	7.16909i	−0.341597	+	0.274922i
$681$	16.6588	−	4.34872i	0.638365	−	0.166643i
$682$	12.3911	−	3.61774i	0.474479	−	0.138530i
$683$	−11.0324	−	19.1086i	−0.422141	−	0.731170i	0.574007	−	0.818850i	$-0.305388\pi$
$683$	−11.0324	−	19.1086i	−0.422141	−	0.731170i	−0.996149	+	0.0876798i	$0.972055\pi$
$684$	−33.8701	+	7.08357i	−1.29506	+	0.270847i
$685$	3.62891	−	6.28546i	0.138654	−	0.240155i
$686$	1.14964	−	4.70741i	0.0438936	−	0.179730i
$687$	−1.06163	−	0.0997848i	−0.0405036	−	0.00380703i
$688$	−0.00671710	+	0.0252508i	−0.000256087	+	0.000962676i
$689$	0.270257	−	0.322079i	0.0102960	−	0.0122702i
$690$	0.137434	+	8.68810i	0.00523203	+	0.330750i
$691$	−5.57347	+	15.3130i	−0.212025	+	0.582533i	−0.999425	−	0.0339088i	$-0.989204\pi$
$691$	−5.57347	+	15.3130i	−0.212025	+	0.582533i	0.787400	+	0.616442i	$0.211427\pi$
$692$	−9.90772	−	3.11407i	−0.376635	−	0.118379i
$693$	0.456207	−	0.767144i	0.0173299	−	0.0291414i
$694$	9.63258	+	13.1248i	0.365648	+	0.498209i
$695$	2.61860	+	14.8508i	0.0993293	+	0.563325i
$696$	−17.2218	−	26.0608i	−0.652789	−	0.987831i
$697$	−12.9760	+	4.72286i	−0.491500	+	0.178891i
$698$	0.383142	−	5.88632i	0.0145022	−	0.222800i
$699$	47.9783	−	3.88588i	1.81471	−	0.146977i
$700$	0.390296	+	0.298926i	0.0147518	+	0.0112983i
$701$		−	8.06276i		−	0.304526i	−0.988340	−	0.152263i	$-0.951344\pi$
$701$		−	8.06276i		−	0.304526i	0.988340	−	0.152263i	$-0.0486561\pi$
$702$	−1.90519	−	5.18735i	−0.0719068	−	0.195784i
$703$			44.4173i			1.67523i
$704$	−2.07014	+	9.45892i	−0.0780214	+	0.356497i
$705$	1.57180	−	3.31474i	0.0591974	−	0.124840i
$706$	46.8388	+	3.04875i	1.76280	+	0.114741i
$707$	2.70247	−	0.983617i	0.101637	−	0.0369927i
$708$	18.3261	+	11.8185i	0.688739	+	0.444166i
$709$	−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	$0.947589\pi$
$710$	9.22127	−	6.76771i	0.346068	−	0.253988i
$711$	25.0751	−	8.76194i	0.940390	−	0.328598i
$712$	8.82750	+	1.74348i	0.330824	+	0.0653396i
$713$	9.14958	−	25.1383i	0.342655	−	0.941436i
$714$	1.18356	−	2.12698i	0.0442935	−	0.0796003i
$715$	−0.585065	+	0.697254i	−0.0218802	+	0.0260758i
$716$	−16.0133	−	8.31766i	−0.598447	−	0.310846i
$717$	−11.7056	−	25.5314i	−0.437152	−	0.953486i
$718$	40.1875	+	9.81460i	1.49978	+	0.366277i
$719$	−23.3686	+	40.4756i	−0.871503	+	1.50949i	−0.0110603	+	0.999939i	$0.503521\pi$
$719$	−23.3686	+	40.4756i	−0.871503	+	1.50949i	−0.860442	+	0.509548i	$0.829813\pi$
$720$	−11.9652	+	0.913161i	−0.445917	+	0.0340315i
$721$	−1.25241	−	2.16924i	−0.0466423	−	0.0807868i
$722$	5.65199	+	19.3586i	0.210345	+	0.720452i
$723$	−11.4375	+	41.6098i	−0.425365	+	1.54749i
$724$	−8.06706	+	5.14952i	−0.299810	+	0.191381i
$725$	−6.27936	−	1.10722i	−0.233210	−	0.0411212i
$726$	−17.6520	+	15.2941i	−0.655129	+	0.567616i
$727$	8.80102	+	10.4886i	0.326412	+	0.389002i	0.904147	−	0.427222i	$-0.140508\pi$
$727$	8.80102	+	10.4886i	0.326412	+	0.389002i	−0.577735	+	0.816224i	$0.696063\pi$
$728$	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
$732$	4.22246	−	4.55699i	0.156067	−	0.168431i
$733$	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	$-0.114767\pi$
$734$	2.16747	+	4.39020i	0.0800028	+	0.162045i
$735$	11.5898	+	3.18575i	0.427497	+	0.117508i
$736$	13.2650	+	15.0571i	0.488953	+	0.555013i
$737$	10.4747	−	6.04754i	0.385839	−	0.222764i
$738$	−14.0326	−	3.61949i	−0.516546	−	0.133235i
$739$	−6.47095	−	3.73600i	−0.238038	−	0.137431i	0.376237	−	0.926524i	$-0.377218\pi$
$739$	−6.47095	−	3.73600i	−0.238038	−	0.137431i	−0.614275	+	0.789092i	$0.710551\pi$
$740$	−1.99678	+	15.2736i	−0.0734031	+	0.561467i
$741$	−6.82840	+	3.13067i	−0.250848	+	0.115008i
$742$	0.161649	+	0.107905i	0.00593431	+	0.00396131i
$743$	−34.1696	−	28.6717i	−1.25356	−	1.05186i	−0.996337	−	0.0855095i	$-0.972748\pi$
$743$	−34.1696	−	28.6717i	−1.25356	−	1.05186i	−0.257223	−	0.966352i	$-0.582807\pi$
$744$	35.4156	+	10.5188i	1.29840	+	0.385639i
$745$	6.60111	+	2.40261i	0.241846	+	0.0880247i
$746$	10.1508	−	23.0978i	0.371648	−	0.845670i
$747$	13.7221	+	39.2701i	0.502064	+	1.43682i
$748$	7.20906	−	6.61787i	0.263589	−	0.241973i
$749$	2.77306	−	0.488966i	0.101326	−	0.0178664i
$750$	−1.54463	+	1.90109i	−0.0564018	+	0.0694179i
$751$	4.73072	+	12.9976i	0.172627	+	0.474288i	0.995590	−	0.0938060i	$-0.0299033\pi$
$751$	4.73072	+	12.9976i	0.172627	+	0.474288i	−0.822964	+	0.568094i	$0.807681\pi$
$752$	−2.20751	−	8.17945i	−0.0804995	−	0.298274i
$753$	−7.98089	−	3.78442i	−0.290840	−	0.137912i
$754$	−4.90059	−	4.68706i	−0.178469	−	0.170693i
$755$	0.473080			0.0172172
$756$	2.28726	−	1.13754i	0.0831868	−	0.0413721i
$757$	−34.6538			−1.25951			−0.629756	−	0.776793i	$-0.716845\pi$
$757$	−34.6538			−1.25951			−0.629756	+	0.776793i	$0.716845\pi$
$758$	17.3555	+	16.5993i	0.630382	+	0.602914i
$759$	−0.600343	−	7.41234i	−0.0217911	−	0.269051i
$760$	2.50326	+	16.1188i	0.0908026	+	0.584689i
$761$	−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	$-0.232986\pi$
$762$	−13.6314	−	35.6854i	−0.493814	−	1.29275i
$763$	4.82547	−	0.850860i	0.174694	−	0.0308032i
$764$	18.0973	+	19.7140i	0.654738	+	0.713228i
$765$	10.4240	+	6.19897i	0.376881	+	0.224124i
$766$	3.72018	−	8.46511i	0.134416	−	0.305857i
$767$	4.44844	+	1.61910i	0.160624	+	0.0584623i
$768$	−19.6515	+	19.5402i	−0.709113	+	0.705095i
$769$	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	$0.684086\pi$
$770$	−0.349946	−	0.233598i	−0.0126112	−	0.00841828i
$771$	4.12621	−	43.8995i	0.148602	−	1.58100i
$772$	−15.3766	−	2.01025i	−0.553416	−	0.0723506i
$773$	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	$0.312540\pi$
$774$	0.0275846	−	0.00267392i	0.000991508	−	9.61121e-5i
$775$	6.53096	−	3.77065i	0.234599	−	0.135446i
$776$	−2.31020	−	4.19746i	−0.0829314	−	0.150680i
$777$	−0.828232	−	3.17273i	−0.0297127	−	0.113821i
$778$	13.2151	+	26.7672i	0.473786	+	0.959651i
$779$	−3.42074	+	19.4000i	−0.122561	+	0.695075i
$780$	−2.48879	+	0.769558i	−0.0891130	+	0.0275546i
$781$	−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
$786$	30.2921	+	10.4859i	1.08048	+	0.374019i
$787$	25.5084	+	4.49783i	0.909278	+	0.160330i	0.608675	−	0.793419i	$-0.291701\pi$
$787$	25.5084	+	4.49783i	0.909278	+	0.160330i	0.300602	+	0.953750i	$0.402812\pi$
$788$	8.62069	+	13.5049i	0.307099	+	0.481091i
$789$	8.46370	+	8.57360i	0.301316	+	0.305228i
$790$	−3.50927	−	12.0196i	−0.124854	−	0.427637i
$791$	0.484063	+	0.838423i	0.0172113	+	0.0298109i
$792$	10.1680	−	1.44502i	0.361304	−	0.0513465i
$793$	0.674329	−	1.16797i	0.0239461	−	0.0414759i
$794$	−7.09961	−	1.73387i	−0.251956	−	0.0615327i
$795$	−0.560542	+	0.789647i	−0.0198804	+	0.0280059i
$796$	8.52245	−	16.4076i	0.302070	−	0.581553i
$797$	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	$0.0847976\pi$
$798$	−1.78357	−	2.97938i	−0.0631375	−	0.105469i
$799$	−2.92852	+	8.04605i	−0.103604	+	0.284649i
$800$	0.136163	+	5.65522i	0.00481409	+	0.199942i
$801$	−1.53588	−	9.41945i	−0.0542677	−	0.332820i
$802$	−33.5571	+	24.6284i	−1.18494	+	0.869659i
$803$	3.04203	+	17.2522i	0.107351	+	0.608818i
$804$	34.5751	+	1.70182i	1.21937	+	0.0600185i
$805$	−0.819382	+	0.298231i	−0.0288794	+	0.0105112i
$806$	8.00330	+	0.520937i	0.281904	+	0.0183492i
$807$	2.23497	+	3.23609i	0.0786745	+	0.113916i
$808$	28.3139	+	17.1289i	0.996080	+	0.602593i
$809$		−	26.8566i		−	0.944229i	−0.881537	−	0.472115i	$-0.843491\pi$
$809$		−	26.8566i		−	0.944229i	0.881537	−	0.472115i	$-0.156509\pi$
$810$	5.33825	+	11.5544i	0.187567	+	0.405979i
$811$			41.4068i			1.45399i	0.686644	+	0.726994i	$0.259083\pi$
$811$			41.4068i			1.45399i	−0.686644	+	0.726994i	$0.740917\pi$
$812$	1.90602	−	2.48862i	0.0668882	−	0.0873334i
$813$	−22.2819	−	32.2629i	−0.781462	−	1.13151i
$814$	0.856278	−	13.1552i	0.0300125	−	0.461090i
$815$	2.79483	−	1.01723i	0.0978985	−	0.0356321i
$816$	27.6051	−	4.73540i	0.966371	−	0.165772i
$817$	−0.00654174	−	0.0371001i	−0.000228867	−	0.00129797i
$818$	20.0102	+	27.2647i	0.699641	+	0.953287i
$819$	0.429377	−	0.350951i	0.0150036	−	0.0122632i
$820$	−2.04840	+	6.51719i	−0.0715332	+	0.227590i
$821$	−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	$0.906711\pi$
$822$	−15.2536	+	9.13139i	−0.532032	+	0.318494i
$823$	−24.1949	+	28.8343i	−0.843380	+	1.00510i	0.156468	+	0.987683i	$0.449989\pi$
$823$	−24.1949	+	28.8343i	−0.843380	+	1.00510i	−0.999848	+	0.0174181i	$0.994455\pi$
$824$	10.4098	−	26.8765i	0.362644	−	0.936288i
$825$	1.21349	−	1.70947i	0.0422483	−	0.0595161i
$826$	−0.519170	+	2.12583i	−0.0180642	+	0.0739670i
$827$	−11.8331	+	20.4955i	−0.411476	+	0.712697i	−0.995051	−	0.0993619i	$-0.968320\pi$
$827$	−11.8331	+	20.4955i	−0.411476	+	0.712697i	0.583576	+	0.812059i	$0.301653\pi$
$828$	10.0537	−	18.7599i	0.349390	−	0.651952i
$829$	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	$0.614820\pi$
$830$	18.8238	−	5.49586i	0.653385	−	0.190764i
$831$	32.2586	+	32.6774i	1.11904	+	1.13357i
$832$	−3.21870	+	5.08267i	−0.111589	+	0.176210i
$833$	−27.6281	−	4.87158i	−0.957256	−	0.168790i
$834$	12.0830	−	34.9060i	0.418400	−	1.20870i
$835$	−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	−0.221393	−	0.975185i	$-0.571060\pi$
$839$	20.2912	−	17.0264i	0.700531	−	0.587816i	0.921925	+	0.387369i	$0.126616\pi$
$840$	−0.479368	−	1.10469i	−0.0165398	−	0.0381153i
$841$	−2.02411	+	11.4793i	−0.0697967	+	0.395837i
$842$	7.65545	−	3.77955i	0.263824	−	0.130252i
$843$	3.49652	+	13.3942i	0.120426	+	0.461320i
$844$	−38.2570	+	15.8870i	−1.31686	+	0.546854i
$845$	10.7686	−	6.21724i	0.370450	−	0.213879i
$846$	−7.31231	+	5.22289i	−0.251403	+	0.179567i
$847$	−2.02979	−	1.17190i	−0.0697444	−	0.0402669i
$848$	0.198933	+	2.22750i	0.00683139	+	0.0764927i
$849$	−0.180991	+	1.92560i	−0.00621161	+	0.0660864i
$850$	3.17414	−	4.75509i	0.108872	−	0.163098i
$851$	−20.9290	−	17.5615i	−0.717435	−	0.602000i
$852$	−27.7981	+	3.50290i	−0.952346	+	0.120007i
$853$	−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	$0.753935\pi$
$854$	0.570747	+	0.250827i	0.0195306	+	0.00858313i
$855$	15.0939	−	8.45672i	0.516199	−	0.289214i
$856$	24.3891	+	21.3304i	0.833604	+	0.729057i
$857$	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	$0.111689\pi$
$858$	2.08275	−	0.795585i	0.0711038	−	0.0271608i
$859$	16.3264	+	44.8564i	0.557049	+	1.53048i	0.823896	+	0.566740i	$0.191796\pi$
$859$	16.3264	+	44.8564i	0.557049	+	1.53048i	−0.266848	+	0.963739i	$0.585982\pi$
$860$	−0.000581643	−	0.0130515i	−1.98338e−5	−	0.000445053i
$861$	−0.117400	−	1.44952i	−0.00400100	−	0.0493997i
$862$	−36.6045	+	38.2721i	−1.24675	+	1.30355i
$863$	36.7547			1.25114			0.625572	−	0.780166i	$-0.284866\pi$
$863$	36.7547			1.25114			0.625572	+	0.780166i	$0.284866\pi$
$864$	26.6983	+	12.2965i	0.908293	+	0.418335i
$865$	5.19279			0.176560
$866$	−37.8202	+	39.5432i	−1.28518	+	1.34373i
$867$	1.02819	+	0.487551i	0.0349191	+	0.0165581i
$868$	0.165059	+	3.70376i	0.00560246	+	0.125714i
$869$	3.66522	+	10.0701i	0.124334	+	0.341605i
$870$	12.1218	+	9.84890i	0.410967	+	0.333909i
$871$	7.40074	−	1.30495i	0.250764	−	0.0442165i
$872$	42.4401	+	37.1174i	1.43720	+	1.25695i
$873$	−3.31649	+	3.85045i	−0.112246	+	0.130318i
$874$	−26.4871	−	11.6404i	−0.895941	−	0.393741i
$875$	−0.230985	−	0.0840715i	−0.00780870	−	0.00284214i
$876$	−19.4440	+	46.2150i	−0.656950	+	1.56146i
$877$	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	$0.664735\pi$
$878$	31.0132	−	46.4599i	1.04664	−	1.56795i
$879$	17.0795	−	7.83058i	0.576078	−	0.264119i
$880$	−0.430660	−	4.82221i	−0.0145176	−	0.162557i
$881$	−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	$0.788946\pi$
$882$	−21.0128	−	20.6228i	−0.707539	−	0.694406i
$883$	−43.7766	+	25.2744i	−1.47320	+	0.850552i	−0.999545	−	0.0301587i	$-0.990399\pi$
$883$	−43.7766	+	25.2744i	−1.47320	+	0.850552i	−0.473654	+	0.880711i	$0.657065\pi$
$884$	5.61532	−	2.33188i	0.188864	−	0.0784297i
$885$	−10.5133	−	2.88985i	−0.353401	−	0.0971412i
$886$	−1.56616	+	0.773225i	−0.0526163	+	0.0259770i
$887$	6.48419	−	36.7737i	0.217718	−	1.23474i	−0.658410	−	0.752659i	$-0.728771\pi$
$887$	6.48419	−	36.7737i	0.217718	−	1.23474i	0.876128	−	0.482079i	$-0.160118\pi$
$888$	22.4654	−	30.3137i	0.753888	−	1.01726i
$889$	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
$894$	−11.2676	−	13.0048i	−0.376844	−	0.434945i
$895$	8.88527	+	1.56671i	0.297002	+	0.0523695i
$896$	−2.49808	−	1.22212i	−0.0834551	−	0.0408283i
$897$	1.22464	−	4.45526i	0.0408895	−	0.148757i
$898$	45.5092	−	13.2870i	1.51866	−	0.443393i
$899$	−24.0426	−	41.6429i	−0.801864	−	1.38887i
$900$	5.57043	−	2.22943i	0.185681	−	0.0743142i
$901$	1.13011	−	1.95740i	0.0376493	−	0.0652105i
$902$	1.38712	−	5.67981i	0.0461862	−	0.189117i
$903$	0.00115907	+	0.00252808i	3.85714e−5	+	8.41291e-5i
$904$	−4.02345	+	10.3879i	−0.133818	+	0.345497i
$905$	3.07591	−	3.66573i	0.102247	−	0.121853i
$906$	−1.01259	−	0.563457i	−0.0336412	−	0.0187196i
$907$	7.11240	−	19.5412i	0.236163	−	0.648854i	−0.763831	−	0.645417i	$-0.776684\pi$
$907$	7.11240	−	19.5412i	0.236163	−	0.648854i	0.999994	−	0.00343704i	$-0.00109405\pi$
$908$	−5.96107	+	18.9657i	−0.197825	+	0.629400i
$909$	6.54035	−	34.4846i	0.216930	−	1.14378i
$910$	−0.154675	−	0.210751i	−0.00512743	−	0.00698631i
$911$	5.45823	+	30.9552i	0.180839	+	1.02559i	0.931186	+	0.364546i	$0.118776\pi$
$911$	5.45823	+	30.9552i	0.180839	+	1.02559i	−0.750346	+	0.661045i	$0.770113\pi$
$912$	13.8400	−	37.4825i	0.458290	−	1.24117i
$913$	−15.7708	+	5.74010i	−0.521937	+	0.189970i
$914$	−2.79542	+	42.9468i	−0.0924643	+	1.42055i
$915$	−1.33089	+	2.80670i	−0.0439979	+	0.0927865i
$916$	0.748664	−	0.977504i	0.0247366	−	0.0322976i
$917$			3.21682i			0.106229i
$918$	−14.9286	−	25.6838i	−0.492718	−	0.847693i
$919$		−	50.8721i		−	1.67812i	−0.544042	−	0.839058i	$-0.683107\pi$
$919$		−	50.8721i		−	1.67812i	0.544042	−	0.839058i	$-0.316893\pi$
$920$	−8.58471	−	5.19344i	−0.283030	−	0.171223i
$921$	−27.6635	+	2.24054i	−0.911545	+	0.0738282i
$922$	−40.7484	−	2.65233i	−1.34198	−	0.0873498i
$923$	−5.71553	+	2.08028i	−0.188129	+	0.0684733i
$924$	0.470809	+	0.916798i	0.0154885	+	0.0301604i
$925$	−1.33740	−	7.58476i	−0.0439734	−	0.249385i
$926$	10.2952	−	7.55592i	0.338322	−	0.248303i
$927$	−30.5679	−	0.394378i	−1.00398	−	0.0129531i
$928$	36.0590	−	0.868208i	1.18369	−	0.0285003i
$929$	−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	$0.113987\pi$
$930$	−18.4700	+	0.292171i	−0.605656	+	0.00958068i
$931$	−25.7254	+	30.6583i	−0.843116	+	1.00479i
$932$	−25.6204	+	49.3250i	−0.839224	+	1.61569i
$933$	−35.2934	−	3.31731i	−1.15546	−	0.108604i
$934$	51.4639	+	12.5685i	1.68395	+	0.411255i
$935$	−2.44651	+	4.23748i	−0.0800095	+	0.138581i
$936$	6.24365	+	1.31706i	0.204080	+	0.0430496i
$937$	−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	$-0.388283\pi$
$938$	0.973586	+	3.33462i	0.0317887	+	0.108879i
$939$	5.26116	−	1.37341i	0.171691	−	0.0448196i
$940$	2.27925	+	3.57059i	0.0743410	+	0.116460i
$941$	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	$0.429104\pi$
$942$	9.86845	+	51.2160i	0.321532	+	1.66871i
$943$	−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	−0.541981	−	0.840391i	$-0.682325\pi$
$947$	5.89399	−	4.94565i	0.191529	−	0.160712i	0.733510	+	0.679679i	$0.237881\pi$
$948$	−6.80445	+	29.9067i	−0.220998	+	0.971324i
$949$	−1.89007	+	10.7191i	−0.0613544	+	0.347958i
$950$	−3.61060	−	7.31326i	−0.117143	−	0.237273i
$951$	−14.8954	+	14.7045i	−0.483018	+	0.476826i
$952$	1.35523	+	2.46235i	0.0439233	+	0.0798052i
$953$	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	$0.226830\pi$
$954$	2.14030	−	1.02255i	0.0692948	−	0.0331064i
$955$	−11.5879	−	6.69027i	−0.374975	−	0.216492i
$956$	32.1582	+	4.20419i	1.04007	+	0.135973i
$957$	−10.9000	−	7.73750i	−0.352346	−	0.250118i
$958$	39.5085	+	26.3729i	1.27646	+	0.852071i
$959$	−1.36665	−	1.14676i	−0.0441314	−	0.0370307i
$960$	6.44414	−	12.2667i	0.207984	−	0.395908i
$961$	24.3110	+	8.84849i	0.784227	+	0.285435i
$962$	3.29547	−	7.49870i	0.106250	−	0.241768i
$963$	12.1696	−	32.1394i	0.392160	−	1.03568i
$964$	−33.6971	−	36.7074i	−1.08531	−	1.18226i
$965$	7.63593	−	1.34642i	0.245809	−	0.0433428i
$966$	2.10903	+	0.337575i	0.0678569	+	0.0108613i
$967$	−4.84704	−	13.3171i	−0.155870	−	0.428250i	0.837036	−	0.547147i	$-0.184286\pi$
$967$	−4.84704	−	13.3171i	−0.155870	−	0.428250i	−0.992907	+	0.118897i	$0.962064\pi$
$968$	−4.13873	−	26.6497i	−0.133024	−	0.856555i
$969$	−33.2278	+	22.9483i	−1.06743	+	0.737207i
$970$	1.73124	+	1.65581i	0.0555869	+	0.0531649i
$971$	31.0109			0.995187			0.497593	−	0.867410i	$-0.334217\pi$
$971$	31.0109			0.995187			0.497593	+	0.867410i	$0.334217\pi$
$972$	2.33556	−	31.0893i	0.0749130	−	0.997190i
$973$	3.70678			0.118834
$974$	35.1800	+	33.6471i	1.12724	+	1.07812i
$975$	1.07176	−	0.740200i	0.0343239	−	0.0237054i
$976$	1.86916	+	6.92579i	0.0598305	+	0.221689i
$977$	−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	$-0.302185\pi$
$978$	−7.19369	−	1.15143i	−0.230029	−	0.0368188i
$979$	3.79197	−	0.668626i	0.121192	−	0.0213694i
$980$	−10.2243	+	9.38585i	−0.326604	+	0.299820i
$981$	21.1766	−	55.9265i	0.676116	−	1.78560i
$982$	−12.8892	+	29.3287i	−0.411309	+	0.935917i
$983$	−13.8628	−	5.04565i	−0.442155	−	0.160931i	0.111343	−	0.993782i	$-0.464485\pi$
$983$	−13.8628	−	5.04565i	−0.442155	−	0.160931i	−0.553498	+	0.832851i	$0.686707\pi$
$984$	12.1467	−	11.5098i	0.387222	−	0.366920i
$985$	−6.13670	−	5.14930i	−0.195532	−	0.164070i
$986$	−30.3195	−	20.2391i	−0.965571	−	0.644544i
$987$	−0.735323	−	0.521980i	−0.0234056	−	0.0166148i
$988$	1.12442	−	8.60077i	0.0357725	−	0.273627i
$989$	0.0200676	+	0.0115860i	0.000638112	+	0.000368414i
$990$	−4.63343	+	2.21368i	−0.147260	+	0.0703553i
$991$	2.11784	−	1.22274i	0.0672754	−	0.0388415i	−0.465985	−	0.884793i	$-0.654300\pi$
$991$	2.11784	−	1.22274i	0.0672754	−	0.0388415i	0.533260	+	0.845951i	$0.320967\pi$
$992$	−32.0100	+	28.2000i	−1.01632	+	0.895352i
$993$	3.34253	−	3.29969i	0.106072	−	0.104712i
$994$	−1.24469	−	2.52111i	−0.0394791	−	0.0799646i
$995$	−1.60529	+	9.10404i	−0.0508911	+	0.288618i
$996$	−46.8368	−	10.6564i	−1.48408	−	0.337662i
$997$	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.491.20	yes	432
4.3	odd	2	inner	540.2.be.a.491.60	yes	432
27.11	odd	18	inner	540.2.be.a.11.60	yes	432
108.11	even	18	inner	540.2.be.a.11.20	✓	432

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
540.2.be.a.11.20	✓	432	108.11	even	18	inner
540.2.be.a.11.60	yes	432	27.11	odd	18	inner
540.2.be.a.491.20	yes	432	1.1	even	1	trivial
540.2.be.a.491.60	yes	432	4.3	odd	2	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 $\F_{q}$
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+(-0.977486 + 1.02202i) q^{2} +(-1.42519 + 0.984291i) q^{3} +(-0.0890420 - 1.99802i) q^{4} +(0.342020 + 0.939693i) q^{5} +(0.387142 - 2.41870i) q^{6} +(0.242074 - 0.0426842i) q^{7} +(2.12905 + 1.86203i) q^{8} +(1.06234 - 2.80561i) q^{9} +(-1.29470 - 0.568986i) q^{10} +(1.13736 + 0.413964i) q^{11} +(2.09353 + 2.75991i) q^{12} +(0.576076 + 0.483385i) q^{13} +(-0.193000 + 0.289128i) q^{14} +(-1.41238 - 1.00259i) q^{15} +(-3.98414 + 0.355815i) q^{16} +(3.50104 + 2.02132i) q^{17} +(1.82896 + 3.82817i) q^{18} +(4.99450 - 2.88358i) q^{19} +(1.84707 - 0.767034i) q^{20} +(-0.302989 + 0.299105i) q^{21} +(-1.53483 + 0.757756i) q^{22} +(-0.615990 + 3.49345i) q^{23} +(-4.86708 - 0.558150i) 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} +(2.40525 - 0.463450i) q^{30} +(-7.42673 - 1.30953i) q^{31} +(3.53080 - 4.41967i) q^{32} +(-2.02841 + 0.529512i) q^{33} +(-5.48805 + 1.60231i) q^{34} +(0.122904 + 0.212877i) q^{35} +(-5.70024 - 1.87276i) q^{36} +(-3.85088 + 6.66992i) q^{37} +(-1.93499 + 7.92313i) q^{38} +(-1.29681 - 0.121890i) q^{39} +(-1.02156 + 2.63750i) q^{40} +(-2.19561 + 2.61663i) q^{41} +(-0.00952332 - 0.602030i) q^{42} +(0.00223415 - 0.00613829i) q^{43} +(0.725835 - 2.30932i) q^{44} +(2.99975 + 0.0387019i) q^{45} +(-2.96825 - 4.04435i) q^{46} +(0.367791 + 2.08585i) q^{47} +(5.32794 - 4.42866i) q^{48} +(-6.52107 + 2.37348i) q^{49} +(0.0918572 - 1.41123i) q^{50} +(-6.97922 + 0.565264i) q^{51} +(0.914517 - 1.19405i) q^{52} -0.559092i q^{53} +(-6.37465 - 3.65566i) q^{54} +1.21035i q^{55} +(0.594867 + 0.359873i) q^{56} +(-4.27984 + 9.02569i) q^{57} +(-8.99831 - 0.585703i) q^{58} +(5.91537 - 2.15302i) q^{59} +(-1.87744 + 2.91122i) q^{60} +(-0.311420 - 1.76615i) q^{61} +(8.59790 - 6.31021i) q^{62} +(0.137411 - 0.724510i) q^{63} +(1.06568 + 7.92870i) q^{64} +(-0.257204 + 0.706662i) q^{65} +(1.44158 - 2.59067i) q^{66} +(6.42340 - 7.65512i) q^{67} +(3.72690 - 7.17511i) q^{68} +(-2.56067 - 5.58515i) q^{69} +(-0.337701 - 0.0824734i) q^{70} +(-4.04403 + 7.00447i) q^{71} +(7.48590 - 3.99515i) q^{72} +(7.23690 + 12.5347i) q^{73} +(-3.05260 - 10.4554i) q^{74} +(0.459070 - 1.67011i) q^{75} +(-6.20616 - 9.72234i) q^{76} +(0.292995 + 0.0516629i) q^{77} +(1.39219 - 1.20622i) 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} +(0.624595 + 0.578743i) q^{84} +(-0.701999 + 3.98123i) q^{85} +(0.00408959 + 0.00828344i) q^{86} +(-10.6490 - 2.92714i) q^{87} +(1.65067 + 2.99914i) q^{88} +(2.75507 - 1.59064i) q^{89} +(-2.97177 + 3.02797i) q^{90} +(0.160086 + 0.0924257i) q^{91} +(7.03482 + 0.919694i) q^{92} +(11.8735 - 5.44373i) q^{93} +(-2.49128 - 1.66300i) q^{94} +(4.41790 + 3.70706i) q^{95} +(-0.681819 + 9.77421i) q^{96} +(-1.59179 - 0.579364i) q^{97} +(3.94852 - 8.98469i) 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

Related objects

Downloads

Learn more