LMFDB - Embedded newform 168.2.ba.c.101.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [168,2,Mod(5,168)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(168, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 3, 5]))

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

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

chi := DirichletCharacter("168.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 168 = 2^{3} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	168.ba (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.34148675396$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			101.14
Character	$\chi$	$=$	168.101
Dual form			168.2.ba.c.5.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.174432 - 1.40341i) q^{2} +(0.618109 - 1.61801i) q^{3} +(-1.93915 - 0.489600i) q^{4} +(-2.46958 + 1.42581i) q^{5} +(-2.16291 - 1.14970i) q^{6} +(-1.02032 - 2.44110i) q^{7} +(-1.02536 + 2.63603i) q^{8} +(-2.23588 - 2.00021i) q^{9} +(1.57023 + 3.71455i) q^{10} +(2.42621 - 4.20231i) q^{11} +(-1.99078 + 2.83492i) q^{12} +2.75221 q^{13} +(-3.60385 + 1.00612i) q^{14} +(0.780502 + 4.87710i) q^{15} +(3.52058 + 1.89881i) q^{16} +(1.75366 - 3.03743i) q^{17} +(-3.19713 + 2.78897i) q^{18} +(3.14493 + 5.44717i) q^{19} +(5.48696 - 1.55575i) q^{20} +(-4.58037 + 0.142013i) q^{21} +(-5.47438 - 4.13799i) q^{22} +(3.15865 - 1.82365i) q^{23} +(3.63132 + 3.28839i) q^{24} +(1.56588 - 2.71219i) q^{25} +(0.480073 - 3.86249i) q^{26} +(-4.61837 + 2.38132i) q^{27} +(0.783383 + 5.23319i) q^{28} -3.90427 q^{29} +(6.98074 - 0.244647i) q^{30} +(-0.858051 - 0.495396i) q^{31} +(3.27893 - 4.60963i) q^{32} +(-5.29970 - 6.52310i) q^{33} +(-3.95689 - 2.99094i) q^{34} +(6.00030 + 4.57370i) q^{35} +(3.35640 + 4.97339i) q^{36} +(1.06516 - 0.614970i) q^{37} +(8.19322 - 3.46348i) q^{38} +(1.70117 - 4.45309i) q^{39} +(-1.22627 - 7.97185i) q^{40} -2.10659 q^{41} +(-0.599659 + 6.45294i) q^{42} -5.11768i q^{43} +(-6.76223 + 6.96103i) q^{44} +(8.37361 + 1.75172i) q^{45} +(-2.00837 - 4.75100i) q^{46} +(5.61268 + 9.72145i) q^{47} +(5.24840 - 4.52265i) q^{48} +(-4.91791 + 4.98138i) q^{49} +(-3.53319 - 2.67068i) q^{50} +(-3.83063 - 4.71490i) q^{51} +(-5.33694 - 1.34748i) q^{52} +(1.00417 - 1.73927i) q^{53} +(2.53639 + 6.89686i) q^{54} +13.8373i q^{55} +(7.48099 - 0.186576i) q^{56} +(10.7575 - 1.72156i) q^{57} +(-0.681029 + 5.47932i) q^{58} +(0.890996 + 0.514417i) q^{59} +(0.874321 - 9.83955i) q^{60} +(1.24347 + 2.15376i) q^{61} +(-0.844918 + 1.11779i) q^{62} +(-2.60139 + 7.49885i) q^{63} +(-5.89727 - 5.40576i) q^{64} +(-6.79681 + 3.92414i) q^{65} +(-10.0791 + 6.29985i) q^{66} +(5.02777 + 2.90279i) q^{67} +(-4.88774 + 5.03144i) q^{68} +(-0.998281 - 6.23793i) q^{69} +(7.46545 - 7.62311i) q^{70} -9.75277i q^{71} +(7.56519 - 3.84291i) q^{72} +(0.291019 + 0.168020i) q^{73} +(-0.677260 - 1.60213i) q^{74} +(-3.42045 - 4.21004i) q^{75} +(-3.43154 - 12.1026i) q^{76} +(-12.7338 - 1.63491i) q^{77} +(-5.95280 - 3.16420i) q^{78} +(-2.80082 - 4.85116i) q^{79} +(-11.4017 + 0.330420i) q^{80} +(0.998337 + 8.94446i) q^{81} +(-0.367457 + 2.95643i) q^{82} -0.138115i q^{83} +(8.95155 + 1.96717i) q^{84} +10.0016i q^{85} +(-7.18223 - 0.892686i) q^{86} +(-2.41327 + 6.31714i) q^{87} +(8.58967 + 10.7044i) q^{88} +(0.580993 + 1.00631i) q^{89} +(3.91902 - 11.4461i) q^{90} +(-2.80813 - 6.71841i) q^{91} +(-7.01795 + 1.98985i) q^{92} +(-1.33192 + 1.08212i) q^{93} +(14.6223 - 6.18119i) q^{94} +(-15.5333 - 8.96815i) q^{95} +(-5.43167 - 8.15457i) q^{96} +11.0953i q^{97} +(6.13311 + 7.77078i) q^{98} +(-13.8302 + 4.54296i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 6 q^{4} - 4 q^{7} - 14 q^{9} - 30 q^{10} - 18 q^{12} + 4 q^{15} + 6 q^{16} - 36 q^{22} - 12 q^{24} - 8 q^{25} - 10 q^{28} + 22 q^{30} + 48 q^{31} - 42 q^{33} + 52 q^{36} - 8 q^{39} - 18 q^{40} + 12 q^{42}+ \cdots + 90 q^{96}+O(q^{100}) $ 48 * q + 6 * q^4 - 4 * q^7 - 14 * q^9 - 30 * q^10 - 18 * q^12 + 4 * q^15 + 6 * q^16 - 36 * q^22 - 12 * q^24 - 8 * q^25 - 10 * q^28 + 22 * q^30 + 48 * q^31 - 42 * q^33 + 52 * q^36 - 8 * q^39 - 18 * q^40 + 12 * q^42 - 8 * q^46 - 36 * q^49 - 48 * q^52 + 60 * q^54 + 4 * q^57 + 30 * q^58 - 32 * q^60 - 6 * q^63 - 60 * q^64 + 54 * q^66 + 42 * q^70 + 42 * q^72 - 36 * q^73 - 68 * q^78 - 56 * q^79 + 42 * q^81 + 48 * q^82 + 48 * q^84 - 132 * q^87 + 6 * q^88 + 48 * q^94 + 90 * q^96

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/168\mathbb{Z}\right)^\times$.

$n$	$73$	$85$	$113$	$127$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$-1$	$-1$	$1$

Coefficient data

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

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

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

$2$	0.174432	−	1.40341i	0.123342	−	0.992364i
$2$	0.174432	−	1.40341i	0.123342	−	0.992364i
$3$	0.618109	−	1.61801i	0.356866	−	0.934156i
$3$	0.618109	−	1.61801i	0.356866	−	0.934156i
$4$	−1.93915	−	0.489600i	−0.969574	−	0.244800i
$5$	−2.46958	+	1.42581i	−1.10443	+	0.637643i	−0.937381	−	0.348306i	$-0.886757\pi$
$5$	−2.46958	+	1.42581i	−1.10443	+	0.637643i	−0.167049	+	0.985949i	$0.553424\pi$
$6$	−2.16291	−	1.14970i	−0.883006	−	0.469361i
$7$	−1.02032	−	2.44110i	−0.385643	−	0.922648i
$7$	−1.02032	−	2.44110i	−0.385643	−	0.922648i
$8$	−1.02536	+	2.63603i	−0.362520	+	0.931976i
$9$	−2.23588	−	2.00021i	−0.745294	−	0.666736i
$10$	1.57023	+	3.71455i	0.496552	+	1.17464i
$11$	2.42621	−	4.20231i	0.731529	−	1.26705i	−0.224701	−	0.974428i	$-0.572140\pi$
$11$	2.42621	−	4.20231i	0.731529	−	1.26705i	0.956230	−	0.292617i	$-0.0945262\pi$
$12$	−1.99078	+	2.83492i	−0.574689	+	0.818372i
$13$	2.75221			0.763326			0.381663	−	0.924302i	$-0.375351\pi$
$13$	2.75221			0.763326			0.381663	+	0.924302i	$0.375351\pi$
$14$	−3.60385	+	1.00612i	−0.963169	+	0.268898i
$15$	0.780502	+	4.87710i	0.201525	+	1.25926i
$16$	3.52058	+	1.89881i	0.880146	+	0.474703i
$17$	1.75366	−	3.03743i	0.425326	−	0.736686i	−0.571125	−	0.820863i	$-0.693493\pi$
$17$	1.75366	−	3.03743i	0.425326	−	0.736686i	0.996451	+	0.0841773i	$0.0268262\pi$
$18$	−3.19713	+	2.78897i	−0.753571	+	0.657367i
$19$	3.14493	+	5.44717i	0.721496	+	1.24967i	0.960400	+	0.278624i	$0.0898784\pi$
$19$	3.14493	+	5.44717i	0.721496	+	1.24967i	−0.238905	+	0.971043i	$0.576788\pi$
$20$	5.48696	−	1.55575i	1.22692	−	0.347877i
$21$	−4.58037	+	0.142013i	−0.999520	+	0.0309899i
$22$	−5.47438	−	4.13799i	−1.16714	−	0.882223i
$23$	3.15865	−	1.82365i	0.658624	−	0.380257i	−0.133128	−	0.991099i	$-0.542502\pi$
$23$	3.15865	−	1.82365i	0.658624	−	0.380257i	0.791753	+	0.610842i	$0.209169\pi$
$24$	3.63132	+	3.28839i	0.741240	+	0.671240i
$25$	1.56588	−	2.71219i	0.313177	−	0.542438i
$26$	0.480073	−	3.86249i	0.0941501	−	0.757498i
$27$	−4.61837	+	2.38132i	−0.888805	+	0.458286i
$28$	0.783383	+	5.23319i	0.148045	+	0.988981i
$29$	−3.90427			−0.725005			−0.362503	−	0.931983i	$-0.618078\pi$
$29$	−3.90427			−0.725005			−0.362503	+	0.931983i	$0.618078\pi$
$30$	6.98074	−	0.244647i	1.27450	−	0.0446663i
$31$	−0.858051	−	0.495396i	−0.154111	−	0.0889758i	0.420962	−	0.907078i	$-0.361693\pi$
$31$	−0.858051	−	0.495396i	−0.154111	−	0.0889758i	−0.575072	+	0.818103i	$0.695026\pi$
$32$	3.27893	−	4.60963i	0.579638	−	0.814874i
$33$	−5.29970	−	6.52310i	−0.922560	−	1.13553i
$34$	−3.95689	−	2.99094i	−0.678600	−	0.512942i
$35$	6.00030	+	4.57370i	1.01424	+	0.773097i
$36$	3.35640	+	4.97339i	0.559400	+	0.828898i
$37$	1.06516	−	0.614970i	0.175111	−	0.101100i	−0.409883	−	0.912138i	$-0.634430\pi$
$37$	1.06516	−	0.614970i	0.175111	−	0.101100i	0.584994	+	0.811038i	$0.301097\pi$
$38$	8.19322	−	3.46348i	1.32912	−	0.561850i
$39$	1.70117	−	4.45309i	0.272405	−	0.713065i
$40$	−1.22627	−	7.97185i	−0.193890	−	1.26046i
$41$	−2.10659			−0.328995			−0.164497	−	0.986378i	$-0.552600\pi$
$41$	−2.10659			−0.328995			−0.164497	+	0.986378i	$0.552600\pi$
$42$	−0.599659	+	6.45294i	−0.0925294	+	0.995710i
$43$		−	5.11768i		−	0.780439i	−0.920722	−	0.390220i	$-0.872399\pi$
$43$		−	5.11768i		−	0.780439i	0.920722	−	0.390220i	$-0.127601\pi$
$44$	−6.76223	+	6.96103i	−1.01944	+	1.04942i
$45$	8.37361	+	1.75172i	1.24826	+	0.261132i
$46$	−2.00837	−	4.75100i	−0.296117	−	0.700497i
$47$	5.61268	+	9.72145i	0.818693	+	1.41802i	0.906645	+	0.421894i	$0.138635\pi$
$47$	5.61268	+	9.72145i	0.818693	+	1.41802i	−0.0879518	+	0.996125i	$0.528032\pi$
$48$	5.24840	−	4.52265i	0.757541	−	0.652788i
$49$	−4.91791	+	4.98138i	−0.702558	+	0.711626i
$50$	−3.53319	−	2.67068i	−0.499668	−	0.377691i
$51$	−3.83063	−	4.71490i	−0.536395	−	0.660218i
$52$	−5.33694	−	1.34748i	−0.740101	−	0.186862i
$53$	1.00417	−	1.73927i	0.137933	−	0.238907i	−0.788781	−	0.614674i	$-0.789288\pi$
$53$	1.00417	−	1.73927i	0.137933	−	0.238907i	0.926714	+	0.375767i	$0.122621\pi$
$54$	2.53639	+	6.89686i	0.345159	+	0.938544i
$55$			13.8373i			1.86582i
$56$	7.48099	−	0.186576i	0.999689	−	0.0249323i
$57$	10.7575	−	1.72156i	1.42486	−	0.228026i
$58$	−0.681029	+	5.47932i	−0.0894235	+	0.719469i
$59$	0.890996	+	0.514417i	0.115998	+	0.0669714i	0.556876	−	0.830595i	$-0.312000\pi$
$59$	0.890996	+	0.514417i	0.115998	+	0.0669714i	−0.440879	+	0.897567i	$0.645333\pi$
$60$	0.874321	−	9.83955i	0.112874	−	1.27028i
$61$	1.24347	+	2.15376i	0.159211	+	0.275761i	0.934584	−	0.355742i	$-0.115772\pi$
$61$	1.24347	+	2.15376i	0.159211	+	0.275761i	−0.775374	+	0.631503i	$0.782438\pi$
$62$	−0.844918	+	1.11779i	−0.107305	+	0.141959i
$63$	−2.60139	+	7.49885i	−0.327745	+	0.944766i
$64$	−5.89727	−	5.40576i	−0.737159	−	0.675720i
$65$	−6.79681	+	3.92414i	−0.843040	+	0.486729i
$66$	−10.0791	+	6.29985i	−1.24065	+	0.775458i
$67$	5.02777	+	2.90279i	0.614240	+	0.354632i	0.774623	−	0.632423i	$-0.217940\pi$
$67$	5.02777	+	2.90279i	0.614240	+	0.354632i	−0.160383	+	0.987055i	$0.551273\pi$
$68$	−4.88774	+	5.03144i	−0.592725	+	0.610151i
$69$	−0.998281	−	6.23793i	−0.120179	−	0.750958i
$70$	7.46545	−	7.62311i	0.892292	−	0.911136i
$71$		−	9.75277i		−	1.15744i	−0.815526	−	0.578720i	$-0.803552\pi$
$71$		−	9.75277i		−	1.15744i	0.815526	−	0.578720i	$-0.196448\pi$
$72$	7.56519	−	3.84291i	0.891566	−	0.452891i
$73$	0.291019	+	0.168020i	0.0340612	+	0.0196652i	0.516934	−	0.856025i	$-0.327073\pi$
$73$	0.291019	+	0.168020i	0.0340612	+	0.0196652i	−0.482873	+	0.875691i	$0.660407\pi$
$74$	−0.677260	−	1.60213i	−0.0787299	−	0.186244i
$75$	−3.42045	−	4.21004i	−0.394960	−	0.486133i
$76$	−3.43154	−	12.1026i	−0.393624	−	1.38827i
$77$	−12.7338	−	1.63491i	−1.45115	−	0.186316i
$78$	−5.95280	−	3.16420i	−0.674022	−	0.358276i
$79$	−2.80082	−	4.85116i	−0.315117	−	0.545798i	0.664346	−	0.747426i	$-0.268710\pi$
$79$	−2.80082	−	4.85116i	−0.315117	−	0.545798i	−0.979462	+	0.201627i	$0.935377\pi$
$80$	−11.4017	+	0.330420i	−1.27475	+	0.0369421i
$81$	0.998337	+	8.94446i	0.110926	+	0.993829i
$82$	−0.367457	+	2.95643i	−0.0405788	+	0.326483i
$83$		−	0.138115i		−	0.0151600i	−0.999971	−	0.00758002i	$-0.997587\pi$
$83$		−	0.138115i		−	0.0151600i	0.999971	−	0.00758002i	$-0.00241282\pi$
$84$	8.95155	+	1.96717i	0.976694	+	0.214636i
$85$			10.0016i			1.08482i
$86$	−7.18223	−	0.892686i	−0.774480	−	0.0962609i
$87$	−2.41327	+	6.31714i	−0.258729	+	0.677268i
$88$	8.58967	+	10.7044i	0.915662	+	1.14110i
$89$	0.580993	+	1.00631i	0.0615852	+	0.106669i	0.895174	−	0.445717i	$-0.147051\pi$
$89$	0.580993	+	1.00631i	0.0615852	+	0.106669i	−0.833589	+	0.552385i	$0.813718\pi$
$90$	3.91902	−	11.4461i	0.413101	−	1.20652i
$91$	−2.80813	−	6.71841i	−0.294372	−	0.704281i
$92$	−7.01795	+	1.98985i	−0.731671	+	0.207456i
$93$	−1.33192	+	1.08212i	−0.138114	+	0.112211i
$94$	14.6223	−	6.18119i	1.50817	−	0.637541i
$95$	−15.5333	−	8.96815i	−1.59368	−	0.920113i
$96$	−5.43167	−	8.15457i	−0.554367	−	0.832272i
$97$			11.0953i			1.12656i	0.826266	+	0.563280i	$0.190461\pi$
$97$			11.0953i			1.12656i	−0.826266	+	0.563280i	$0.809539\pi$
$98$	6.13311	+	7.77078i	0.619538	+	0.784967i
$99$	−13.8302	+	4.54296i	−1.38999	+	0.456585i
$100$	−4.36437	+	4.49268i	−0.436437	+	0.449268i
$101$	6.16256	+	3.55796i	0.613198	+	0.354030i	0.774216	−	0.632922i	$-0.218144\pi$
$101$	6.16256	+	3.55796i	0.613198	+	0.354030i	−0.161018	+	0.986951i	$0.551478\pi$
$102$	−7.28515	+	4.55353i	−0.721337	+	0.450867i
$103$	1.50519	−	0.869021i	0.148311	−	0.0856271i	−0.424008	−	0.905658i	$-0.639377\pi$
$103$	1.50519	−	0.869021i	0.148311	−	0.0856271i	0.572319	+	0.820031i	$0.306044\pi$
$104$	−2.82201	+	7.25490i	−0.276721	+	0.711402i
$105$	11.1091	−	6.88147i	1.08414	−	0.671563i
$106$	−2.26576	−	1.71265i	−0.220070	−	0.166347i
$107$	−0.532028	−	0.921500i	−0.0514331	−	0.0890847i	0.839163	−	0.543881i	$-0.183046\pi$
$107$	−0.532028	−	0.921500i	−0.0514331	−	0.0890847i	−0.890596	+	0.454796i	$0.849712\pi$
$108$	10.1216	−	2.35658i	0.973950	−	0.226762i
$109$	−7.85874	−	4.53725i	−0.752731	−	0.434589i	0.0739489	−	0.997262i	$-0.476440\pi$
$109$	−7.85874	−	4.53725i	−0.752731	−	0.434589i	−0.826680	+	0.562673i	$0.809773\pi$
$110$	19.4194	+	2.41366i	1.85157	+	0.230133i
$111$	−0.336640	−	2.10355i	−0.0319524	−	0.199660i
$112$	1.04308	−	10.5315i	0.0985616	−	0.995131i
$113$			16.8126i			1.58159i	0.612078	+	0.790797i	$0.290334\pi$
$113$			16.8126i			1.58159i	−0.612078	+	0.790797i	$0.709666\pi$
$114$	−0.539621	−	15.3975i	−0.0505401	−	1.44211i
$115$	−5.20036	+	9.00729i	−0.484936	+	0.839934i
$116$	7.57096	+	1.91153i	0.702946	+	0.177481i
$117$	−6.15362	−	5.50499i	−0.568902	−	0.508937i
$118$	0.877358	−	1.16071i	0.0807674	−	0.106852i
$119$	−9.20396	−	1.18172i	−0.843726	−	0.108328i
$120$	−13.6565	−	2.94337i	−1.24666	−	0.268691i
$121$	−6.27296	−	10.8651i	−0.570269	−	0.987735i
$122$	3.23952	−	1.36943i	0.293293	−	0.123982i
$123$	−1.30211	+	3.40848i	−0.117407	+	0.307332i
$124$	1.42134	+	1.38075i	0.127640	+	0.123995i
$125$		−	5.32750i		−	0.476506i
$126$	10.0702	+	4.95887i	0.897128	+	0.441771i
$127$	15.6371			1.38756			0.693782	−	0.720185i	$-0.255943\pi$
$127$	15.6371			1.38756			0.693782	+	0.720185i	$0.255943\pi$
$128$	−8.61519	+	7.33338i	−0.761483	+	0.648185i
$129$	−8.28044	−	3.16329i	−0.729052	−	0.278512i
$130$	4.32162	+	10.2232i	0.379031	+	0.896637i
$131$	8.73260	−	5.04177i	0.762971	−	0.440502i	−0.0673904	−	0.997727i	$-0.521467\pi$
$131$	8.73260	−	5.04177i	0.762971	−	0.440502i	0.830361	+	0.557225i	$0.188134\pi$
$132$	7.08319	+	15.2440i	0.616513	+	1.32682i
$133$	10.0883	−	13.2349i	0.874763	−	1.14761i
$134$	4.95082	−	6.54971i	0.427685	−	0.565809i
$135$	8.01011	−	12.4658i	0.689400	−	1.07288i
$136$	6.20862	+	7.73717i	0.532384	+	0.663457i
$137$	17.0704	+	9.85557i	1.45842	+	0.842019i	0.998934	−	0.0461669i	$-0.0147006\pi$
$137$	17.0704	+	9.85557i	1.45842	+	0.842019i	0.459485	+	0.888185i	$0.348034\pi$
$138$	−8.92853	+	0.312910i	−0.760047	+	0.0266366i
$139$	−0.111832			−0.00948546			−0.00474273	−	0.999989i	$-0.501510\pi$
$139$	−0.111832			−0.00948546			−0.00474273	+	0.999989i	$0.501510\pi$
$140$	−9.39618	−	11.8068i	−0.794122	−	0.997860i
$141$	19.1986	−	3.07243i	1.61681	−	0.258745i
$142$	−13.6872	−	1.70119i	−1.14860	−	0.142761i
$143$	6.67743	−	11.5657i	0.558395	−	0.967169i
$144$	−4.07359	−	11.2874i	−0.339466	−	0.940618i
$145$	9.64192	−	5.56676i	0.800718	−	0.462295i
$146$	0.286564	−	0.379112i	0.0237162	−	0.0313755i
$147$	5.02010	+	11.0362i	0.414051	+	0.910254i
$148$	−2.36659	+	0.671015i	−0.194532	+	0.0551571i
$149$	5.49834	+	9.52340i	0.450441	+	0.780187i	0.998413	−	0.0563094i	$-0.0179333\pi$
$149$	5.49834	+	9.52340i	0.450441	+	0.780187i	−0.547972	+	0.836497i	$0.684600\pi$
$150$	−6.50507	+	4.06595i	−0.531136	+	0.331983i
$151$	4.16727	−	7.21792i	0.339127	−	0.587386i	−0.645141	−	0.764063i	$-0.723202\pi$
$151$	4.16727	−	7.21792i	0.339127	−	0.587386i	0.984269	+	0.176677i	$0.0565349\pi$
$152$	−17.5836	+	2.70479i	−1.42622	+	0.219387i
$153$	−9.99648	+	3.28365i	−0.808168	+	0.265468i
$154$	−4.51563	+	17.5856i	−0.363880	+	1.41708i
$155$	2.82537			0.226939
$156$	−5.47905	+	7.80231i	−0.438675	+	0.624685i
$157$	−5.42198	+	9.39114i	−0.432721	+	0.749495i	−0.997107	−	0.0760165i	$-0.975780\pi$
$157$	−5.42198	+	9.39114i	−0.432721	+	0.749495i	0.564386	+	0.825511i	$0.309113\pi$
$158$	−7.29674	+	3.08451i	−0.580498	+	0.245391i
$159$	−2.19346	−	2.69980i	−0.173953	−	0.214108i
$160$	−1.52510	+	16.0590i	−0.120570	+	1.26957i
$161$	−7.67452	−	5.84987i	−0.604837	−	0.461035i
$162$	12.7269	+	0.159116i	0.999922	+	0.0125014i
$163$	10.0621	−	5.80934i	0.788122	−	0.455022i	−0.0511792	−	0.998689i	$-0.516298\pi$
$163$	10.0621	−	5.80934i	0.788122	−	0.455022i	0.839301	+	0.543667i	$0.182965\pi$
$164$	4.08500	+	1.03139i	0.318985	+	0.0805379i
$165$	22.3888	+	8.55294i	1.74296	+	0.665846i
$166$	−0.193832	−	0.0240916i	−0.0150443	−	0.00186987i
$167$	−7.75061			−0.599761			−0.299880	−	0.953977i	$-0.596947\pi$
$167$	−7.75061			−0.599761			−0.299880	+	0.953977i	$0.596947\pi$
$168$	4.32219	−	12.2196i	0.333464	−	0.942763i
$169$	−5.42533			−0.417333
$170$	14.0364	+	1.74459i	1.07654	+	0.133804i
$171$	3.86379	−	18.4697i	0.295472	−	1.41242i
$172$	−2.50562	+	9.92394i	−0.191052	+	0.756693i
$173$	0.880487	−	0.508349i	0.0669422	−	0.0386491i	−0.466155	−	0.884703i	$-0.654361\pi$
$173$	0.880487	−	0.508349i	0.0669422	−	0.0386491i	0.533098	+	0.846054i	$0.321028\pi$
$174$	8.44461	+	4.48872i	0.640184	+	0.340289i
$175$	−8.21842	−	1.05518i	−0.621254	−	0.0797642i
$176$	16.5211	−	10.1877i	1.24532	−	0.767925i
$177$	1.38306	−	1.12367i	0.103957	−	0.0844603i
$178$	1.51361	−	0.639843i	0.113450	−	0.0479582i
$179$	−10.8103	+	18.7240i	−0.808002	+	1.39950i	0.106244	+	0.994340i	$0.466117\pi$
$179$	−10.8103	+	18.7240i	−0.808002	+	1.39950i	−0.914246	+	0.405160i	$0.867216\pi$
$180$	−15.3800	−	7.49657i	−1.14636	−	0.558762i
$181$	−9.37049			−0.696503			−0.348251	−	0.937401i	$-0.613224\pi$
$181$	−9.37049			−0.696503			−0.348251	+	0.937401i	$0.613224\pi$
$182$	−9.91855	+	2.76906i	−0.735212	+	0.205257i
$183$	4.25340	−	0.680689i	0.314420	−	0.0503180i
$184$	1.56843	+	10.1962i	0.115626	+	0.751673i
$185$	−1.75366	+	3.03743i	−0.128932	+	0.223317i
$186$	1.28634	+	2.05800i	0.0943188	+	0.150900i
$187$	−8.50950	−	14.7389i	−0.622276	−	1.07781i
$188$	−6.12419	−	21.5993i	−0.446652	−	1.57529i
$189$	10.5252	+	8.84418i	0.765598	+	0.643319i
$190$	−15.2955	+	20.2353i	−1.10966	+	1.46803i
$191$	7.70657	−	4.44939i	0.557628	−	0.321947i	−0.194565	−	0.980890i	$-0.562329\pi$
$191$	7.70657	−	4.44939i	0.557628	−	0.321947i	0.752193	+	0.658943i	$0.228996\pi$
$192$	−12.3917	+	6.20046i	−0.894294	+	0.447480i
$193$	7.45779	−	12.9173i	0.536824	−	0.929806i	−0.462249	−	0.886750i	$-0.652957\pi$
$193$	7.45779	−	12.9173i	0.536824	−	0.929806i	0.999073	−	0.0430556i	$-0.0137093\pi$
$194$	15.5713	+	1.93538i	1.11796	+	0.138952i
$195$	2.14811	+	13.4228i	0.153829	+	0.961228i
$196$	11.9754	−	7.25183i	0.855388	−	0.517988i
$197$	−2.74394			−0.195497			−0.0977487	−	0.995211i	$-0.531164\pi$
$197$	−2.74394			−0.195497			−0.0977487	+	0.995211i	$0.531164\pi$
$198$	3.96323	+	20.2020i	0.281654	+	1.43569i
$199$	−20.1826	−	11.6525i	−1.43071	−	0.826021i	−0.433535	−	0.901137i	$-0.642734\pi$
$199$	−20.1826	−	11.6525i	−1.43071	−	0.826021i	−0.997175	+	0.0751162i	$0.976067\pi$
$200$	5.54381	+	6.90869i	0.392007	+	0.488518i
$201$	7.80443	−	6.34072i	0.550482	−	0.447240i
$202$	6.06823	−	8.02801i	0.426959	−	0.564849i
$203$	3.98360	+	9.53071i	0.279594	+	0.668925i
$204$	5.11973	+	11.0184i	0.358453	+	0.771440i
$205$	5.20240	−	3.00361i	0.363352	−	0.209781i
$206$	−0.957044	−	2.26399i	−0.0666804	−	0.157740i
$207$	−10.7100	−	2.24050i	−0.744399	−	0.155725i
$208$	9.68939	+	5.22594i	0.671838	+	0.362354i
$209$	30.5210			2.11118
$210$	−7.71978	−	16.7910i	−0.532715	−	1.15869i
$211$			20.3918i			1.40383i	0.712259	+	0.701916i	$0.247672\pi$
$211$			20.3918i			1.40383i	−0.712259	+	0.701916i	$0.752328\pi$
$212$	−2.79877	+	2.88105i	−0.192220	+	0.197872i
$213$	−15.7800	−	6.02828i	−1.08123	−	0.413051i
$214$	−1.38605	+	0.585917i	−0.0947484	+	0.0400525i
$215$	7.29686	+	12.6385i	0.497642	+	0.861941i
$216$	−1.54173	−	14.6158i	−0.104902	−	0.994483i
$217$	−0.333826	+	2.60005i	−0.0226616	+	0.176503i
$218$	−7.73845	+	10.2376i	−0.524114	+	0.693380i
$219$	0.451738	−	0.367015i	0.0305256	−	0.0248006i
$220$	6.77473	−	26.8325i	0.456752	−	1.80905i
$221$	4.82645	−	8.35966i	0.324662	−	0.562332i
$222$	−3.01088	+	0.105519i	−0.202077	+	0.00708199i
$223$		−	11.4666i		−	0.767860i	−0.923362	−	0.383930i	$-0.874570\pi$
$223$		−	11.4666i		−	0.767860i	0.923362	−	0.383930i	$-0.125430\pi$
$224$	−14.5981	−	3.30090i	−0.975376	−	0.220550i
$225$	−8.92608	+	2.93204i	−0.595072	+	0.195470i
$226$	23.5950	+	2.93265i	1.56952	+	0.195077i
$227$	−18.3699	−	10.6059i	−1.21926	−	0.703938i	−0.254497	−	0.967073i	$-0.581910\pi$
$227$	−18.3699	−	10.6059i	−1.21926	−	0.703938i	−0.964759	+	0.263136i	$0.915243\pi$
$228$	−21.7032	−	1.92850i	−1.43733	−	0.127718i
$229$	1.13465	+	1.96528i	0.0749800	+	0.129869i	0.901078	−	0.433658i	$-0.142777\pi$
$229$	1.13465	+	1.96528i	0.0749800	+	0.129869i	−0.826098	+	0.563527i	$0.809444\pi$
$230$	11.7339	+	8.86942i	0.773707	+	0.584832i
$231$	−10.5162	+	19.5927i	−0.691912	+	1.28911i
$232$	4.00329	−	10.2918i	0.262829	−	0.675688i
$233$	−22.5624	+	13.0264i	−1.47811	+	0.853389i	−0.999694	−	0.0247423i	$-0.992123\pi$
$233$	−22.5624	+	13.0264i	−1.47811	+	0.853389i	−0.478420	+	0.878131i	$0.658790\pi$
$234$	−8.79918	+	7.67584i	−0.575220	+	0.501785i
$235$	−27.7219	−	16.0053i	−1.80838	−	1.04407i
$236$	−1.47591	−	1.43376i	−0.0960738	−	0.0933300i
$237$	−9.58042	+	1.53319i	−0.622315	+	0.0995916i
$238$	−3.26390	+	12.7108i	−0.211567	+	0.823922i
$239$		−	8.32874i		−	0.538742i	−0.963037	−	0.269371i	$-0.913184\pi$
$239$		−	8.32874i		−	0.538742i	0.963037	−	0.269371i	$-0.0868157\pi$
$240$	−6.51288	+	18.6523i	−0.420405	+	1.20400i
$241$	6.24112	+	3.60331i	0.402026	+	0.232110i	0.687358	−	0.726319i	$-0.258771\pi$
$241$	6.24112	+	3.60331i	0.402026	+	0.232110i	−0.285332	+	0.958429i	$0.592104\pi$
$242$	−16.3424	+	6.90835i	−1.05053	+	0.444085i
$243$	15.0893	+	3.91334i	0.967977	+	0.251041i
$244$	−1.35680	−	4.78527i	−0.0868601	−	0.306345i
$245$	5.04265	−	19.3139i	0.322163	−	1.23392i
$246$	4.55638	+	2.42194i	0.290504	+	0.154417i
$247$	8.65550	+	14.9918i	0.550736	+	0.953904i
$248$	2.18569	−	1.75389i	0.138791	−	0.111372i
$249$	−0.223470	−	0.0853699i	−0.0141618	−	0.00541010i
$250$	−7.47669	−	0.929285i	−0.472867	−	0.0587731i
$251$		−	8.41270i		−	0.531005i	−0.964110	−	0.265502i	$-0.914462\pi$
$251$		−	8.41270i		−	0.531005i	0.964110	−	0.265502i	$-0.0855378\pi$
$252$	8.71592	−	13.2677i	0.549052	−	0.835788i
$253$		−	17.6982i		−	1.11268i
$254$	2.72760	−	21.9453i	0.171145	−	1.37697i
$255$	16.1826	+	6.18207i	1.01339	+	0.387136i
$256$	8.78901	+	13.3699i	0.549313	+	0.835616i
$257$	−15.1284	−	26.2032i	−0.943685	−	1.63451i	−0.758364	−	0.651832i	$-0.774001\pi$
$257$	−15.1284	−	26.2032i	−0.943685	−	1.63451i	−0.185321	−	0.982678i	$-0.559332\pi$
$258$	−5.88378	+	11.0691i	−0.366308	+	0.689133i
$259$	−2.58800	−	1.97269i	−0.160810	−	0.122577i
$260$	15.1013	−	4.28176i	0.936541	−	0.265544i
$261$	8.72950	+	7.80936i	0.540342	+	0.483387i
$262$	−5.55245	−	13.1349i	−0.343032	−	0.811478i
$263$	20.9078	+	12.0711i	1.28923	+	0.744338i	0.978517	−	0.206166i	$-0.0660986\pi$
$263$	20.9078	+	12.0711i	1.28923	+	0.744338i	0.310714	+	0.950504i	$0.399432\pi$
$264$	22.6292	−	7.28162i	1.39273	−	0.448153i
$265$			5.72701i			0.351808i
$266$	−16.8144	−	16.4666i	−1.03095	−	1.00963i
$267$	1.98733	−	0.318041i	0.121623	−	0.0194638i
$268$	−8.32839	−	8.09053i	−0.508737	−	0.494208i
$269$	−17.4083	−	10.0507i	−1.06140	−	0.612800i	−0.135581	−	0.990766i	$-0.543290\pi$
$269$	−17.4083	−	10.0507i	−1.06140	−	0.612800i	−0.925819	+	0.377966i	$0.876623\pi$
$270$	−16.0975	−	13.4159i	−0.979660	−	0.816468i
$271$	−1.57903	+	0.911656i	−0.0959195	+	0.0553791i	−0.547192	−	0.837007i	$-0.684303\pi$
$271$	−1.57903	+	0.911656i	−0.0959195	+	0.0553791i	0.451273	+	0.892386i	$0.350970\pi$
$272$	11.9414	−	7.36366i	0.724056	−	0.446487i
$273$	−12.6062	+	0.390851i	−0.762959	+	0.0236554i
$274$	16.8091	−	22.2377i	1.01547	−	1.34343i
$275$	−7.59832	−	13.1607i	−0.458196	−	0.793618i
$276$	−1.11828	+	12.5850i	−0.0673124	+	0.757529i
$277$	−11.4072	−	6.58598i	−0.685395	−	0.395713i	0.116490	−	0.993192i	$-0.462836\pi$
$277$	−11.4072	−	6.58598i	−0.685395	−	0.395713i	−0.801885	+	0.597479i	$0.796169\pi$
$278$	−0.0195070	+	0.156947i	−0.00116995	+	0.00941303i
$279$	0.927606	+	2.82393i	0.0555343	+	0.169064i
$280$	−18.2089	+	11.1273i	−1.08819	+	0.664981i
$281$		−	15.3821i		−	0.917618i	−0.888535	−	0.458809i	$-0.848276\pi$
$281$		−	15.3821i		−	0.917618i	0.888535	−	0.458809i	$-0.151724\pi$
$282$	−0.963049	−	27.4795i	−0.0573487	−	1.63638i
$283$	−4.64882	+	8.05200i	−0.276344	+	0.478641i	−0.970473	−	0.241209i	$-0.922456\pi$
$283$	−4.64882	+	8.05200i	−0.276344	+	0.478641i	0.694129	+	0.719850i	$0.255790\pi$
$284$	−4.77496	+	18.9121i	−0.283342	+	1.12222i
$285$	−24.1118	+	19.5897i	−1.42826	+	1.16039i
$286$	−15.0667	−	11.3886i	−0.890910	−	0.673424i
$287$	2.14939	+	5.14240i	0.126875	+	0.303546i
$288$	−16.5515	+	3.74805i	−0.975306	+	0.220856i
$289$	2.34933	+	4.06916i	0.138196	+	0.239362i
$290$	−6.13062	−	14.5026i	−0.360003	−	0.851624i
$291$	17.9523	+	6.85812i	1.05238	+	0.402030i
$292$	−0.482066	−	0.468298i	−0.0282108	−	0.0274051i
$293$			17.8462i			1.04258i	0.853378	+	0.521292i	$0.174550\pi$
$293$			17.8462i			1.04258i	−0.853378	+	0.521292i	$0.825450\pi$
$294$	16.3641	−	5.12022i	0.954373	−	0.298617i
$295$	−2.93385			−0.170815
$296$	0.528904	+	3.43835i	0.0307419	+	0.199850i
$297$	−1.19805	+	25.1854i	−0.0695179	+	1.46141i
$298$	14.3244	−	6.05527i	0.829788	−	0.350772i
$299$	8.69327	−	5.01906i	0.502745	−	0.290260i
$300$	4.57152	+	9.83854i	0.263937	+	0.568028i
$301$	−12.4928	+	5.22166i	−0.720071	+	0.300971i
$302$	−9.40283	−	7.10744i	−0.541072	−	0.408987i
$303$	9.56593	−	7.77185i	0.549548	−	0.446481i
$304$	0.728810	+	25.1489i	0.0418001	+	1.44239i
$305$	−6.14172	−	3.54592i	−0.351674	−	0.203039i
$306$	2.86462	+	14.6020i	0.163760	+	0.834740i
$307$	17.6654			1.00822			0.504110	−	0.863640i	$-0.331821\pi$
$307$	17.6654			1.00822			0.504110	+	0.863640i	$0.331821\pi$
$308$	23.8922	+	9.40479i	1.36138	+	0.535888i
$309$	−0.475709	−	2.97255i	−0.0270622	−	0.169103i
$310$	0.492834	−	3.96516i	0.0279911	−	0.225206i
$311$	−4.15091	+	7.18958i	−0.235376	+	0.407684i	−0.959382	−	0.282110i	$-0.908966\pi$
$311$	−4.15091	+	7.18958i	−0.235376	+	0.407684i	0.724006	+	0.689794i	$0.242299\pi$
$312$	9.99416	+	9.05035i	0.565808	+	0.512375i
$313$	−23.0954	+	13.3342i	−1.30543	+	0.753691i	−0.981330	−	0.192332i	$-0.938395\pi$
$313$	−23.0954	+	13.3342i	−1.30543	+	0.753691i	−0.324101	+	0.946023i	$0.605062\pi$
$314$	12.2339	+	9.24740i	0.690399	+	0.521861i
$315$	−4.26761	−	22.2281i	−0.240452	−	1.25241i
$316$	3.05607	+	10.7784i	0.171917	+	0.606332i
$317$	14.4097	+	24.9584i	0.809331	+	1.40180i	0.913328	+	0.407225i	$0.133504\pi$
$317$	14.4097	+	24.9584i	0.809331	+	1.40180i	−0.103996	+	0.994578i	$0.533163\pi$
$318$	−4.17155	+	2.60740i	−0.233929	+	0.146216i
$319$	−9.47258	+	16.4070i	−0.530362	+	0.918615i
$320$	22.2714	+	4.94155i	1.24501	+	0.276241i
$321$	−1.81984	+	0.291237i	−0.101574	+	0.0162553i
$322$	−9.54848	+	9.75014i	−0.532116	+	0.543354i
$323$	22.0606			1.22748
$324$	2.44329	−	17.8334i	0.135738	−	0.990745i
$325$	4.30964	−	7.46452i	0.239056	−	0.414057i
$326$	−6.39776	−	15.1346i	−0.354339	−	0.838227i
$327$	−12.1988	+	9.91097i	−0.674598	+	0.548078i
$328$	2.16002	−	5.55304i	0.119267	−	0.306615i
$329$	18.0043	−	23.6200i	0.992608	−	1.30222i
$330$	15.9086	−	29.9288i	0.875742	−	1.64753i
$331$	2.24514	−	1.29623i	0.123404	−	0.0712472i	−0.437027	−	0.899448i	$-0.643969\pi$
$331$	2.24514	−	1.29623i	0.123404	−	0.0712472i	0.560431	+	0.828201i	$0.310635\pi$
$332$	−0.0676209	+	0.267825i	−0.00371118	+	0.0146988i
$333$	−3.61164	−	0.755539i	−0.197916	−	0.0414033i
$334$	−1.35195	+	10.8773i	−0.0739756	+	0.595181i
$335$	−16.5553			−0.904513
$336$	−16.3952	−	8.19731i	−0.894434	−	0.447200i
$337$	11.1713			0.608541			0.304271	−	0.952586i	$-0.401587\pi$
$337$	11.1713			0.608541			0.304271	+	0.952586i	$0.401587\pi$
$338$	−0.946350	+	7.61399i	−0.0514747	+	0.414147i
$339$	27.2028	+	10.3920i	1.47746	+	0.564416i
$340$	4.89678	−	19.3945i	0.265565	−	1.05182i
$341$	−4.16362	+	2.40387i	−0.225473	+	0.130177i
$342$	−25.2467	−	8.64421i	−1.36519	−	0.467426i
$343$	17.1779	+	6.92250i	0.927517	+	0.373780i
$344$	13.4903	+	5.24747i	0.727351	+	0.282925i
$345$	11.3594	+	13.9817i	0.611572	+	0.752749i
$346$	−0.559840	−	1.32436i	−0.0300972	−	0.0711981i
$347$	−7.23643	+	12.5339i	−0.388472	+	0.672853i	−0.992244	−	0.124304i	$-0.960330\pi$
$347$	−7.23643	+	12.5339i	−0.388472	+	0.672853i	0.603772	+	0.797157i	$0.293664\pi$
$348$	7.77255	−	11.0683i	0.416653	−	0.593324i
$349$	22.8018			1.22055			0.610275	−	0.792189i	$-0.291059\pi$
$349$	22.8018			1.22055			0.610275	+	0.792189i	$0.291059\pi$
$350$	−2.91441	+	11.3498i	−0.155782	+	0.606672i
$351$	−12.7107	+	6.55390i	−0.678448	+	0.349821i
$352$	−11.4157	−	24.9630i	−0.608461	−	1.33053i
$353$	2.06060	−	3.56907i	0.109675	−	0.189962i	−0.805964	−	0.591965i	$-0.798352\pi$
$353$	2.06060	−	3.56907i	0.109675	−	0.189962i	0.915639	+	0.402003i	$0.131686\pi$
$354$	−1.33573	−	2.13701i	−0.0709931	−	0.113581i
$355$	13.9056	+	24.0852i	0.738034	+	1.27831i
$356$	−0.633942	−	2.23584i	−0.0335989	−	0.118499i
$357$	−7.60108	+	14.1616i	−0.402292	+	0.749513i
$358$	24.3919	+	18.4374i	1.28915	+	0.974449i
$359$	−9.83790	+	5.67992i	−0.519225	+	0.299775i	−0.736617	−	0.676310i	$-0.763578\pi$
$359$	−9.83790	+	5.67992i	−0.519225	+	0.299775i	0.217393	+	0.976084i	$0.430245\pi$
$360$	−13.2036	+	20.2769i	−0.695889	+	1.06869i
$361$	−10.2811	+	17.8074i	−0.541112	+	0.937234i
$362$	−1.63451	+	13.1507i	−0.0859080	+	0.691185i
$363$	−21.4571	+	3.43387i	−1.12621	+	0.180232i
$364$	2.15603	+	14.4029i	0.113007	+	0.754915i
$365$	−0.958259			−0.0501576
$366$	−0.213361	−	6.08802i	−0.0111526	−	0.318226i
$367$	24.2527	+	14.0023i	1.26598	+	0.730914i	0.974225	−	0.225580i	$-0.0724275\pi$
$367$	24.2527	+	14.0023i	1.26598	+	0.730914i	0.291755	+	0.956493i	$0.405761\pi$
$368$	14.5831	−	0.422615i	0.760194	−	0.0220303i
$369$	4.71010	+	4.21363i	0.245198	+	0.219353i
$370$	3.95689	+	2.99094i	0.205709	+	0.155492i
$371$	−5.27029	−	0.676664i	−0.273620	−	0.0351306i
$372$	3.11260	−	1.44629i	0.161381	−	0.0749864i
$373$	−27.1273	+	15.6619i	−1.40460	+	0.810944i	−0.994860	−	0.101259i	$-0.967713\pi$
$373$	−27.1273	+	15.6619i	−1.40460	+	0.810944i	−0.409737	+	0.912204i	$0.634379\pi$
$374$	−22.1691	+	9.37143i	−1.14634	+	0.484585i
$375$	−8.61992	−	3.29298i	−0.445131	−	0.170049i
$376$	−31.3810	+	4.82718i	−1.61835	+	0.248943i
$377$	−10.7454			−0.553416
$378$	14.2480	−	13.2286i	0.732837	−	0.680404i
$379$		−	28.8128i		−	1.48001i	−0.672600	−	0.740006i	$-0.734822\pi$
$379$		−	28.8128i		−	1.48001i	0.672600	−	0.740006i	$-0.265178\pi$
$380$	25.7305	+	24.9957i	1.31995	+	1.28225i
$381$	9.66541	−	25.3008i	0.495174	−	1.29620i
$382$	−4.90007	−	11.5916i	−0.250710	−	0.593080i
$383$	12.6701	+	21.9453i	0.647413	+	1.12135i	0.983738	+	0.179607i	$0.0574826\pi$
$383$	12.6701	+	21.9453i	0.647413	+	1.12135i	−0.336325	+	0.941746i	$0.609184\pi$
$384$	6.54032	+	18.4723i	0.333759	+	0.942658i
$385$	33.7781	−	14.1184i	1.72149	−	0.719540i
$386$	−16.8274	−	12.7196i	−0.856493	−	0.647409i
$387$	−10.2364	+	11.4425i	−0.520347	+	0.581657i
$388$	5.43227	−	21.5155i	0.275782	−	1.09228i
$389$	2.20886	−	3.82586i	0.111994	−	0.193979i	−0.804580	−	0.593844i	$-0.797610\pi$
$389$	2.20886	−	3.82586i	0.111994	−	0.193979i	0.916574	+	0.399865i	$0.130943\pi$
$390$	19.2125	−	0.673321i	0.972862	−	0.0340949i
$391$		−	12.7923i		−	0.646932i
$392$	−8.08843	−	18.0715i	−0.408527	−	0.912746i
$393$	−2.75991	−	17.2458i	−0.139219	−	0.869934i
$394$	−0.478629	+	3.85088i	−0.0241130	+	0.194005i
$395$	13.8337	+	7.98689i	0.696049	+	0.401864i
$396$	29.0431	−	2.03819i	1.45947	−	0.102423i
$397$	8.01775	+	13.8871i	0.402399	+	0.696976i	0.994015	−	0.109244i	$-0.0348430\pi$
$397$	8.01775	+	13.8871i	0.402399	+	0.696976i	−0.591616	+	0.806220i	$0.701510\pi$
$398$	−19.8737	+	26.2921i	−0.996180	+	1.31790i
$399$	−15.1785	−	24.5035i	−0.759876	−	1.22671i
$400$	10.6628	−	6.57517i	0.533139	−	0.328759i
$401$	6.53545	−	3.77324i	0.326365	−	0.188427i	−0.327861	−	0.944726i	$-0.606328\pi$
$401$	6.53545	−	3.77324i	0.326365	−	0.188427i	0.654226	+	0.756299i	$0.272994\pi$
$402$	−7.53732	−	12.0589i	−0.375928	−	0.601442i
$403$	−2.36154	−	1.36343i	−0.117637	−	0.0679175i
$404$	−10.2081	−	9.91659i	−0.507874	−	0.493369i
$405$	−15.2186	−	20.6656i	−0.756218	−	1.02688i
$406$	14.0704	−	3.92818i	0.698303	−	0.194952i
$407$		−	5.96817i		−	0.295831i
$408$	16.3564	−	5.26316i	0.809762	−	0.260565i
$409$	−24.3612	−	14.0650i	−1.20458	−	0.695467i	−0.243013	−	0.970023i	$-0.578136\pi$
$409$	−24.3612	−	14.0650i	−1.20458	−	0.695467i	−0.961571	+	0.274556i	$0.911469\pi$
$410$	−3.30784	−	7.82505i	−0.163363	−	0.386452i
$411$	26.4977	−	21.5281i	1.30704	−	1.06190i
$412$	−3.34425	+	0.948219i	−0.164760	+	0.0467154i
$413$	0.346643	−	2.69988i	0.0170572	−	0.132852i
$414$	−5.01252	+	14.6398i	−0.246352	+	0.719508i
$415$	0.196926	+	0.341085i	0.00966670	+	0.0167432i
$416$	9.02429	−	12.6867i	0.442452	−	0.622015i
$417$	−0.0691243	+	0.180945i	−0.00338503	+	0.00886090i
$418$	5.32383	−	42.8336i	0.260397	−	2.09506i
$419$		−	19.5661i		−	0.955866i	−0.878396	−	0.477933i	$-0.841386\pi$
$419$		−	19.5661i		−	0.955866i	0.878396	−	0.477933i	$-0.158614\pi$
$420$	−24.9114	+	7.90516i	−1.21555	+	0.385732i
$421$			26.0983i			1.27195i	0.771708	+	0.635977i	$0.219403\pi$
$421$			26.0983i			1.27195i	−0.771708	+	0.635977i	$0.780597\pi$
$422$	28.6182	+	3.55699i	1.39311	+	0.173151i
$423$	6.89562	−	32.9625i	0.335277	−	1.60269i
$424$	3.55512	+	4.43039i	0.172652	+	0.215159i
$425$	−5.49207	−	9.51254i	−0.266404	−	0.461426i
$426$	−11.2127	+	21.0944i	−0.543258	+	1.02203i
$427$	3.98880	−	5.23296i	0.193032	−	0.253241i
$428$	0.580514	+	2.04740i	0.0280602	+	0.0989650i
$429$	−14.5859	−	17.9530i	−0.704214	−	0.866777i
$430$	19.0099	−	8.03596i	0.916739	−	0.387528i
$431$	10.4072	+	6.00858i	0.501296	+	0.289423i	0.729248	−	0.684249i	$-0.239870\pi$
$431$	10.4072	+	6.00858i	0.501296	+	0.289423i	−0.227953	+	0.973672i	$0.573203\pi$
$432$	−20.7810	−	0.385775i	−0.999828	−	0.0185606i
$433$		−	35.6343i		−	1.71247i	−0.516583	−	0.856237i	$-0.672796\pi$
$433$		−	35.6343i		−	1.71247i	0.516583	−	0.856237i	$-0.327204\pi$
$434$	3.59072	+	0.922027i	0.172360	+	0.0442587i
$435$	−3.04729	−	19.0415i	−0.146107	−	0.912972i
$436$	13.0178	+	12.6460i	0.623440	+	0.605635i
$437$	19.8674	+	11.4705i	0.950389	+	0.548707i
$438$	−0.436277	−	0.697995i	−0.0208461	−	0.0333515i
$439$	−11.6950	+	6.75210i	−0.558171	+	0.322260i	−0.752411	−	0.658694i	$-0.771109\pi$
$439$	−11.6950	+	6.75210i	−0.558171	+	0.322260i	0.194240	+	0.980954i	$0.437776\pi$
$440$	−36.4754	−	14.1882i	−1.73890	−	0.676396i
$441$	20.9597	−	1.30095i	0.998079	−	0.0619500i
$442$	−10.8902	−	8.23170i	−0.517993	−	0.391542i
$443$	−11.7659	−	20.3791i	−0.559014	−	0.968241i	−0.997579	−	0.0695416i	$-0.977846\pi$
$443$	−11.7659	−	20.3791i	−0.559014	−	0.968241i	0.438565	−	0.898700i	$-0.355487\pi$
$444$	−0.377105	+	4.24391i	−0.0178966	+	0.201407i
$445$	−2.86962	−	1.65678i	−0.136033	−	0.0785387i
$446$	−16.0924	−	2.00014i	−0.761996	−	0.0947092i
$447$	18.8075	−	3.00984i	0.889563	−	0.142360i
$448$	−7.17890	+	19.9114i	−0.339171	+	0.940725i
$449$			30.6292i			1.44548i	0.691120	+	0.722740i	$0.257117\pi$
$449$			30.6292i			1.44548i	−0.691120	+	0.722740i	$0.742883\pi$
$450$	2.55788	+	13.0384i	0.120580	+	0.614638i
$451$	−5.11103	+	8.85257i	−0.240669	+	0.416851i
$452$	8.23144	−	32.6021i	0.387174	−	1.53347i
$453$	−9.10281	−	11.2041i	−0.427687	−	0.526416i
$454$	−18.0888	+	23.9307i	−0.848948	+	1.12312i
$455$	16.5141	+	12.5878i	0.774193	+	0.590125i
$456$	−6.49221	+	30.1222i	−0.304025	+	1.41060i
$457$	5.80736	+	10.0587i	0.271657	+	0.470524i	0.969286	−	0.245935i	$-0.0790950\pi$
$457$	5.80736	+	10.0587i	0.271657	+	0.470524i	−0.697629	+	0.716459i	$0.745762\pi$
$458$	2.95602	−	1.24958i	0.138126	−	0.0583892i
$459$	−0.865951	+	18.2040i	−0.0404191	+	0.849691i
$460$	14.4942	−	14.9204i	0.675797	−	0.695665i
$461$			30.8362i			1.43618i	0.695948	+	0.718092i	$0.254985\pi$
$461$			30.8362i			1.43618i	−0.695948	+	0.718092i	$0.745015\pi$
$462$	25.6624	+	18.1761i	1.19392	+	0.845629i
$463$	−32.3199			−1.50203			−0.751016	−	0.660284i	$-0.770436\pi$
$463$	−32.3199			−1.50203			−0.751016	+	0.660284i	$0.770436\pi$
$464$	−13.7453	−	7.41349i	−0.638111	−	0.344163i
$465$	1.74639	−	4.57146i	0.0809867	−	0.211996i
$466$	14.3459	+	33.9367i	0.664560	+	1.57209i
$467$	−29.3749	+	16.9596i	−1.35931	+	0.784797i	−0.989531	−	0.144323i	$-0.953900\pi$
$467$	−29.3749	+	16.9596i	−1.35931	+	0.784797i	−0.369778	+	0.929120i	$0.620566\pi$
$468$	9.23753	+	13.6878i	0.427005	+	0.632719i
$469$	1.95606	−	15.2350i	0.0903225	−	0.703489i
$470$	−27.2976	+	36.1135i	−1.25914	+	1.66579i
$471$	11.8435	+	14.5775i	0.545722	+	0.671698i
$472$	−2.26961	+	1.82123i	−0.104467	+	0.0838287i
$473$	−21.5061	−	12.4166i	−0.988852	−	0.570914i
$474$	0.480577	+	13.7127i	0.0220736	+	0.629847i
$475$	19.6984			0.903823
$476$	17.2693	+	6.79778i	0.791535	+	0.311576i
$477$	−5.72409	+	1.88025i	−0.262088	+	0.0860910i
$478$	−11.6887	−	1.45280i	−0.534628	−	0.0664494i
$479$	−17.6827	+	30.6273i	−0.807943	+	1.39940i	0.106344	+	0.994329i	$0.466086\pi$
$479$	−17.6827	+	30.6273i	−0.807943	+	1.39940i	−0.914286	+	0.405068i	$0.867248\pi$
$480$	25.0408	+	12.3938i	1.14295	+	0.565698i
$481$	2.93154	−	1.69253i	0.133667	−	0.0771726i
$482$	6.14559	−	8.13034i	0.279924	−	0.370327i
$483$	−14.2088	+	8.80156i	−0.646524	+	0.400485i
$484$	6.84464	+	24.1402i	0.311120	+	1.09728i
$485$	−15.8198	−	27.4008i	−0.718342	−	1.24421i
$486$	8.12408	−	20.4939i	0.368516	−	0.929621i
$487$	16.4191	−	28.4386i	0.744018	−	1.28868i	−0.206634	−	0.978418i	$-0.566251\pi$
$487$	16.4191	−	28.4386i	0.744018	−	1.28868i	0.950652	−	0.310259i	$-0.100416\pi$
$488$	−6.95238	+	1.06945i	−0.314720	+	0.0484117i
$489$	−3.18008	−	19.8713i	−0.143808	−	0.898610i
$490$	−26.2259	−	10.4459i	−1.18476	−	0.471897i
$491$	−22.5295			−1.01674			−0.508371	−	0.861138i	$-0.669752\pi$
$491$	−22.5295			−1.01674			−0.508371	+	0.861138i	$0.669752\pi$
$492$	4.19377	−	5.97203i	0.189070	−	0.269240i
$493$	−6.84678	+	11.8590i	−0.308363	+	0.534101i
$494$	22.5495	−	9.53222i	1.01455	−	0.428875i
$495$	27.6774	−	30.9385i	1.24401	−	1.39058i
$496$	−2.08018	−	3.37336i	−0.0934027	−	0.151468i
$497$	−23.8075	+	9.95092i	−1.06791	+	0.446360i
$498$	−0.158790	+	0.298730i	−0.00711554	+	0.0133864i
$499$	−11.3117	+	6.53084i	−0.506383	+	0.292361i	−0.731346	−	0.682007i	$-0.761107\pi$
$499$	−11.3117	+	6.53084i	−0.506383	+	0.292361i	0.224962	+	0.974367i	$0.427774\pi$
$500$	−2.60834	+	10.3308i	−0.116649	+	0.462007i
$501$	−4.79073	+	12.5405i	−0.214034	+	0.560270i
$502$	−11.8065	−	1.46744i	−0.526950	−	0.0654951i
$503$	−2.77607			−0.123779			−0.0618894	−	0.998083i	$-0.519713\pi$
$503$	−2.77607			−0.123779			−0.0618894	+	0.998083i	$0.519713\pi$
$504$	−17.0998	−	14.5464i	−0.761686	−	0.647947i
$505$	−20.2919			−0.902978
$506$	−24.8379	−	3.08712i	−1.10418	−	0.137239i
$507$	−3.35345	+	8.77822i	−0.148932	+	0.389854i
$508$	−30.3225	−	7.65590i	−1.34535	−	0.339676i
$509$	27.2704	−	15.7446i	1.20874	−	0.697866i	0.246255	−	0.969205i	$-0.420800\pi$
$509$	27.2704	−	15.7446i	1.20874	−	0.697866i	0.962484	+	0.271339i	$0.0874665\pi$
$510$	11.4988	−	21.6326i	0.509174	−	0.957906i
$511$	0.113221	−	0.881838i	0.00500861	−	0.0390102i
$512$	20.2965	−	10.0025i	0.896989	−	0.442052i
$513$	−27.4959	−	17.6680i	−1.21397	−	0.780059i
$514$	−39.4128	+	16.6608i	−1.73842	+	0.734875i
$515$	−2.47812	+	4.29223i	−0.109199	+	0.189138i
$516$	14.5082	+	10.1882i	0.638690	+	0.448510i
$517$	54.4701			2.39559
$518$	−3.21993	+	3.28794i	−0.141476	+	0.144464i
$519$	−0.278275	−	1.73885i	−0.0122149	−	0.0763270i
$520$	−3.37495	−	21.9402i	−0.148001	−	0.962142i
$521$	2.92633	−	5.06856i	0.128205	−	0.222058i	−0.794776	−	0.606903i	$-0.792412\pi$
$521$	2.92633	−	5.06856i	0.128205	−	0.222058i	0.922981	+	0.384845i	$0.125745\pi$
$522$	12.4825	−	10.8889i	0.546343	−	0.476594i
$523$	9.81038	+	16.9921i	0.428978	+	0.743012i	0.996783	−	0.0801516i	$-0.0255405\pi$
$523$	9.81038	+	16.9921i	0.428978	+	0.743012i	−0.567805	+	0.823163i	$0.692207\pi$
$524$	−19.4023	+	5.50125i	−0.847591	+	0.240323i
$525$	−6.78717	+	12.6452i	−0.296216	+	0.551883i
$526$	20.5878	−	27.2367i	0.897670	−	1.18758i
$527$	−3.00947	+	1.73752i	−0.131094	+	0.0756874i
$528$	−6.27189	−	33.0283i	−0.272949	−	1.43737i
$529$	−4.84862	+	8.39806i	−0.210810	+	0.365133i
$530$	8.03738	+	0.998973i	0.349121	+	0.0433926i
$531$	−0.963222	−	2.93235i	−0.0418003	−	0.127253i
$532$	−26.0424	+	20.7252i	−1.12908	+	0.898553i
$533$	−5.79779			−0.251130
$534$	−0.0996895	−	2.84453i	−0.00431398	−	0.123095i
$535$	2.62777	+	1.51715i	0.113609	+	0.0655919i
$536$	−12.8071	+	10.2769i	−0.553183	+	0.443896i
$537$	23.6136	+	29.0647i	1.01900	+	1.25423i
$538$	−17.1418	+	22.6779i	−0.739036	+	0.977712i
$539$	9.00148	+	32.7525i	0.387721	+	1.41075i
$540$	−21.6360	+	20.2513i	−0.931066	+	0.871475i
$541$	35.5120	−	20.5029i	1.52678	−	0.881488i	0.527287	−	0.849687i	$-0.323209\pi$
$541$	35.5120	−	20.5029i	1.52678	−	0.881488i	0.999494	−	0.0318007i	$-0.0101242\pi$
$542$	1.00400	+	2.37506i	0.0431254	+	0.102018i
$543$	−5.79199	+	15.1615i	−0.248558	+	0.650642i
$544$	−8.25130	−	18.0432i	−0.353772	−	0.773598i
$545$	25.8771			1.10845
$546$	−1.65039	+	17.7598i	−0.0706301	+	0.760051i
$547$			13.0813i			0.559315i	0.960100	+	0.279658i	$0.0902209\pi$
$547$			13.0813i			0.559315i	−0.960100	+	0.279658i	$0.909779\pi$
$548$	−28.2766	−	27.4691i	−1.20792	−	1.17342i
$549$	1.52771	−	7.30276i	0.0652010	−	0.311674i
$550$	−19.7953	+	8.36795i	−0.844073	+	0.356811i
$551$	−12.2787	−	21.2673i	−0.523088	−	0.906016i
$552$	17.4669	+	3.76463i	0.743442	+	0.160233i
$553$	−8.98443	+	11.7868i	−0.382057	+	0.501225i
$554$	−11.2326	+	14.8603i	−0.477229	+	0.631353i
$555$	3.83063	+	4.71490i	0.162601	+	0.200136i
$556$	0.216859	+	0.0547529i	0.00919685	+	0.00232204i
$557$	19.2814	−	33.3964i	0.816980	−	1.41505i	−0.0909180	−	0.995858i	$-0.528980\pi$
$557$	19.2814	−	33.3964i	0.816980	−	1.41505i	0.907898	−	0.419192i	$-0.137687\pi$
$558$	4.12495	−	0.809234i	0.174623	−	0.0342576i
$559$		−	14.0849i		−	0.595730i
$560$	12.4399	+	27.4956i	0.525684	+	1.16190i
$561$	−29.1074	+	4.65817i	−1.22891	+	0.196668i
$562$	−21.5874	−	2.68312i	−0.910611	−	0.113181i
$563$	−9.75701	−	5.63321i	−0.411209	−	0.237411i	0.280100	−	0.959971i	$-0.409632\pi$
$563$	−9.75701	−	5.63321i	−0.411209	−	0.237411i	−0.691309	+	0.722559i	$0.742966\pi$
$564$	−38.7332	−	3.44175i	−1.63096	−	0.144924i
$565$	−23.9716	−	41.5200i	−1.00849	−	1.74676i
$566$	10.4894	+	7.92875i	0.440902	+	0.333270i
$567$	20.8157	−	11.5632i	0.874176	−	0.485609i
$568$	25.7086	+	10.0001i	1.07871	+	0.419595i
$569$	26.7497	−	15.4440i	1.12141	−	0.647445i	0.179648	−	0.983731i	$-0.442504\pi$
$569$	26.7497	−	15.4440i	1.12141	−	0.647445i	0.941760	+	0.336286i	$0.109171\pi$
$570$	23.2866	+	37.2559i	0.975367	+	1.56048i
$571$	6.49082	+	3.74748i	0.271633	+	0.156827i	0.629629	−	0.776896i	$-0.283207\pi$
$571$	6.49082	+	3.74748i	0.271633	+	0.156827i	−0.357997	+	0.933723i	$0.616540\pi$
$572$	−18.6111	+	19.1582i	−0.778168	+	0.801046i
$573$	−2.43564	−	15.2195i	−0.101750	−	0.635803i
$574$	7.59184	−	2.11949i	0.316877	−	0.0884659i
$575$		−	11.4225i		−	0.476350i
$576$	2.37296	+	23.8824i	0.0988733	+	0.995100i
$577$	18.4495	+	10.6518i	0.768064	+	0.443442i	0.832184	−	0.554500i	$-0.187091\pi$
$577$	18.4495	+	10.6518i	0.768064	+	0.443442i	−0.0641196	+	0.997942i	$0.520424\pi$
$578$	6.12052	−	2.58730i	0.254580	−	0.107617i
$579$	−16.2905	−	20.0510i	−0.677010	−	0.833292i
$580$	−21.4226	+	6.07409i	−0.889524	+	0.252213i
$581$	−0.337151	+	0.140921i	−0.0139874	+	0.00584637i
$582$	12.7562	−	23.9982i	0.528763	−	0.994759i
$583$	−4.87263	−	8.43964i	−0.201804	−	0.349534i
$584$	−0.741304	+	0.594852i	−0.0306754	+	0.0246152i
$585$	23.0459	+	4.82112i	0.952833	+	0.199329i
$586$	25.0456	+	3.11294i	1.03462	+	0.128594i
$587$		−	15.2002i		−	0.627381i	−0.949525	−	0.313691i	$-0.898435\pi$
$587$		−	15.2002i		−	0.627381i	0.949525	−	0.313691i	$-0.101565\pi$
$588$	−4.33137	−	23.8587i	−0.178623	−	0.983918i
$589$		−	6.23194i		−	0.256783i
$590$	−0.511756	+	4.11741i	−0.0210687	+	0.169511i
$591$	−1.69605	+	4.43970i	−0.0697663	+	0.182625i
$592$	4.91769	−	0.142514i	0.202116	−	0.00585728i
$593$	−4.55071	−	7.88206i	−0.186875	−	0.323678i	0.757332	−	0.653031i	$-0.226503\pi$
$593$	−4.55071	−	7.88206i	−0.186875	−	0.323678i	−0.944207	+	0.329353i	$0.893169\pi$
$594$	35.1366	+	6.07449i	1.44167	+	0.249240i
$595$	24.4148	−	10.2048i	1.00091	−	0.418355i
$596$	−5.99943	−	21.1593i	−0.245746	−	0.866717i
$597$	−31.3288	+	25.4531i	−1.28220	+	1.04173i
$598$	−5.52745	−	13.0758i	−0.226034	−	0.534707i
$599$	−37.6136	−	21.7162i	−1.53685	−	0.887302i	−0.999021	−	0.0442488i	$-0.985911\pi$
$599$	−37.6136	−	21.7162i	−1.53685	−	0.887302i	−0.537831	−	0.843053i	$-0.680756\pi$
$600$	14.6050	−	4.69959i	0.596245	−	0.191860i
$601$		−	15.5284i		−	0.633415i	−0.948523	−	0.316708i	$-0.897423\pi$
$601$		−	15.5284i		−	0.633415i	0.948523	−	0.316708i	$-0.102577\pi$
$602$	5.14902	+	18.4434i	0.209858	+	0.751695i
$603$	−5.43533	−	16.5469i	−0.221344	−	0.673841i
$604$	−11.6148	+	11.9563i	−0.472601	+	0.486496i
$605$	30.9831	+	17.8881i	1.25964	+	0.727256i
$606$	−9.23853	−	14.7806i	−0.375290	−	0.600422i
$607$	1.01612	−	0.586656i	0.0412430	−	0.0238116i	−0.479237	−	0.877686i	$-0.659086\pi$
$607$	1.01612	−	0.586656i	0.0412430	−	0.0238116i	0.520480	+	0.853874i	$0.325753\pi$
$608$	35.4214	+	3.36394i	1.43653	+	0.136426i
$609$	17.8830	−	0.554459i	0.724657	−	0.0224678i
$610$	−6.04771	+	8.00086i	−0.244865	+	0.323945i
$611$	15.4473	+	26.7555i	0.624930	+	1.08241i
$612$	20.9923	−	1.47321i	0.848565	−	0.0595508i
$613$	35.7276	+	20.6273i	1.44302	+	0.833131i	0.998050	−	0.0624126i	$-0.0198795\pi$
$613$	35.7276	+	20.6273i	1.44302	+	0.833131i	0.444974	+	0.895543i	$0.353213\pi$
$614$	3.08141	−	24.7919i	0.124356	−	1.00052i
$615$	−1.64420	−	10.2741i	−0.0663006	−	0.414291i
$616$	17.3664	−	31.8901i	0.699711	−	1.28489i
$617$			15.3232i			0.616887i	0.951243	+	0.308444i	$0.0998081\pi$
$617$			15.3232i			0.616887i	−0.951243	+	0.308444i	$0.900192\pi$
$618$	−4.25470	+	0.149110i	−0.171149	+	0.00599810i
$619$	7.95796	−	13.7836i	0.319857	−	0.554009i	−0.660601	−	0.750738i	$-0.729698\pi$
$619$	7.95796	−	13.7836i	0.319857	−	0.554009i	0.980458	+	0.196728i	$0.0630316\pi$
$620$	−5.47881	−	1.38330i	−0.220034	−	0.0555547i
$621$	−10.2451	+	15.9440i	−0.411122	+	0.639812i
$622$	9.36592	+	7.07954i	0.375539	+	0.283864i
$623$	1.86370	−	2.44502i	0.0746677	−	0.0979575i
$624$	14.4447	−	12.4473i	0.578251	−	0.498290i
$625$	15.4254	+	26.7176i	0.617017	+	1.06871i
$626$	14.6848	+	34.7384i	0.586922	+	1.38842i
$627$	18.8653	−	49.3831i	0.753407	−	1.97217i
$628$	15.1119	−	15.5562i	0.603031	−	0.620760i
$629$		−	4.31380i		−	0.172002i
$630$	−31.9397	+	2.11194i	−1.27251	+	0.0841415i
$631$	−27.9268			−1.11175			−0.555875	−	0.831266i	$-0.687617\pi$
$631$	−27.9268			−1.11175			−0.555875	+	0.831266i	$0.687617\pi$
$632$	15.6596	−	2.40884i	0.622907	−	0.0958186i
$633$	32.9941	+	12.6044i	1.31140	+	0.500980i
$634$	37.5405	−	15.8693i	1.49092	−	0.630251i
$635$	−38.6170	+	22.2955i	−1.53247	+	0.884770i
$636$	2.93162	+	6.30923i	0.116246	+	0.250177i
$637$	−13.5351	+	13.7098i	−0.536281	+	0.543203i
$638$	21.3735	+	16.1559i	0.846184	+	0.639616i
$639$	−19.5076	+	21.8060i	−0.771708	+	0.862634i
$640$	10.8199	−	30.3940i	0.427693	−	1.20143i
$641$	7.03036	+	4.05898i	0.277683	+	0.160320i	0.632374	−	0.774663i	$-0.282081\pi$
$641$	7.03036	+	4.05898i	0.277683	+	0.160320i	−0.354691	+	0.934984i	$0.615414\pi$
$642$	0.0912878	+	2.60480i	0.00360284	+	0.102803i
$643$	−21.5611			−0.850285			−0.425143	−	0.905126i	$-0.639776\pi$
$643$	−21.5611			−0.850285			−0.425143	+	0.905126i	$0.639776\pi$
$644$	12.0179	+	15.1012i	0.473573	+	0.595071i
$645$	24.9595	−	3.99436i	0.982778	−	0.157278i
$646$	3.84806	−	30.9601i	0.151400	−	1.21811i
$647$	19.5173	−	33.8049i	0.767304	−	1.32901i	−0.171716	−	0.985147i	$-0.554931\pi$
$647$	19.5173	−	33.8049i	0.767304	−	1.32901i	0.939020	−	0.343863i	$-0.111736\pi$
$648$	−24.6015	−	6.53966i	−0.966437	−	0.256902i
$649$	4.32348	−	2.49616i	0.169712	−	0.0979830i
$650$	−9.72408	−	7.35027i	−0.381410	−	0.288301i
$651$	4.00055	+	2.14725i	0.156794	+	0.0841572i
$652$	−22.3561	+	6.33877i	−0.875531	+	0.248245i
$653$	8.53952	+	14.7909i	0.334177	+	0.578812i	0.983326	−	0.181849i	$-0.0582083\pi$
$653$	8.53952	+	14.7909i	0.334177	+	0.578812i	−0.649149	+	0.760661i	$0.724875\pi$
$654$	11.7813	+	18.8488i	0.460687	+	0.737048i
$655$	−14.3772	+	24.9021i	−0.561765	+	0.973006i
$656$	−7.41644	−	4.00003i	−0.289563	−	0.156175i
$657$	−0.314609	−	0.957770i	−0.0122741	−	0.0373662i
$658$	−30.0082	−	29.3876i	−1.16984	−	1.14565i
$659$	6.99022			0.272300			0.136150	−	0.990688i	$-0.456527\pi$
$659$	6.99022			0.272300			0.136150	+	0.990688i	$0.456527\pi$
$660$	−39.2276	−	27.5470i	−1.52693	−	1.07226i
$661$	−23.0740	+	39.9653i	−0.897474	+	1.55447i	−0.0667617	+	0.997769i	$0.521267\pi$
$661$	−23.0740	+	39.9653i	−0.897474	+	1.55447i	−0.830712	+	0.556702i	$0.812067\pi$
$662$	−1.42753	−	3.37696i	−0.0554823	−	0.131249i
$663$	−10.5427	−	12.9764i	−0.409444	−	0.503962i
$664$	0.364074	+	0.141617i	0.0141288	+	0.00549582i
$665$	−6.04325	+	47.0686i	−0.234347	+	1.82524i
$666$	−1.69032	+	4.93683i	−0.0654985	+	0.191298i
$667$	−12.3322	+	7.12002i	−0.477506	+	0.275688i
$668$	15.0296	+	3.79470i	0.581512	+	0.146821i
$669$	−18.5530	−	7.08760i	−0.717301	−	0.274023i
$670$	−2.88777	+	23.2340i	−0.111564	+	0.897607i
$671$	12.0677			0.465869
$672$	−14.3641	+	21.5795i	−0.554106	+	0.832446i
$673$	8.04494			0.310110			0.155055	−	0.987906i	$-0.450445\pi$
$673$	8.04494			0.310110			0.155055	+	0.987906i	$0.450445\pi$
$674$	1.94863	−	15.6780i	0.0750586	−	0.603894i
$675$	−0.773227	+	16.2548i	−0.0297615	+	0.625646i
$676$	10.5205	+	2.65624i	0.404635	+	0.102163i
$677$	8.53140	−	4.92561i	0.327888	−	0.189306i	−0.327015	−	0.945019i	$-0.606043\pi$
$677$	8.53140	−	4.92561i	0.327888	−	0.189306i	0.654903	+	0.755713i	$0.272709\pi$
$678$	19.3293	−	36.3642i	0.742339	−	1.39656i
$679$	27.0847	−	11.3207i	1.03942	−	0.434450i
$680$	−26.3644	−	10.2552i	−1.01103	−	0.393270i
$681$	−28.5150	+	23.1671i	−1.09270	+	0.887764i
$682$	2.64736	+	6.26260i	0.101372	+	0.239807i
$683$	20.1018	−	34.8173i	0.769173	−	1.33225i	−0.168839	−	0.985644i	$-0.554002\pi$
$683$	20.1018	−	34.8173i	0.769173	−	1.33225i	0.938012	−	0.346603i	$-0.112665\pi$
$684$	−16.5353	+	33.9238i	−0.632241	+	1.29711i
$685$	−56.2088			−2.14763
$686$	12.7115	−	22.9002i	0.485327	−	0.874332i
$687$	3.88117	−	0.621119i	0.148076	−	0.0236972i
$688$	9.71753	−	18.0172i	0.370477	−	0.686900i
$689$	2.76368	−	4.78683i	0.105288	−	0.182364i
$690$	21.6036	−	13.5032i	0.822434	−	0.514057i
$691$	−17.2791	−	29.9282i	−0.657326	−	1.13852i	−0.981305	−	0.192458i	$-0.938354\pi$
$691$	−17.2791	−	29.9282i	−0.657326	−	1.13852i	0.323979	−	0.946064i	$-0.394979\pi$
$692$	−1.95628	+	0.554678i	−0.0743667	+	0.0210857i
$693$	25.2010	+	29.1256i	0.957307	+	1.10639i
$694$	16.3280	+	12.3420i	0.619801	+	0.468497i
$695$	0.276178	−	0.159451i	0.0104760	−	0.00604834i
$696$	−14.1777	−	12.8388i	−0.537403	−	0.486653i
$697$	−3.69426	+	6.39864i	−0.139930	+	0.242366i
$698$	3.97735	−	32.0003i	0.150545	−	1.21123i
$699$	7.13078	+	44.5579i	0.269711	+	1.68533i
$700$	15.4201	+	6.06989i	0.582825	+	0.229420i
$701$	−29.6534			−1.11999			−0.559997	−	0.828495i	$-0.689198\pi$
$701$	−29.6534			−1.11999			−0.559997	+	0.828495i	$0.689198\pi$
$702$	6.98069	+	18.9816i	0.263469	+	0.716415i
$703$	6.69969	+	3.86807i	0.252684	+	0.145887i
$704$	−37.0247	+	11.6667i	−1.39542	+	0.439705i
$705$	−43.0318	+	34.9612i	−1.62067	+	1.31672i
$706$	−4.64945	−	3.51444i	−0.174984	−	0.132268i
$707$	2.39755	−	18.6736i	0.0901692	−	0.702295i
$708$	−3.23211	+	1.50182i	−0.121470	+	0.0564417i
$709$	9.81381	−	5.66601i	0.368565	−	0.212791i	−0.304266	−	0.952587i	$-0.598411\pi$
$709$	9.81381	−	5.66601i	0.368565	−	0.212791i	0.672832	+	0.739796i	$0.265078\pi$
$710$	36.2272	−	15.3141i	1.35958	−	0.574729i
$711$	−3.44103	+	16.4488i	−0.129049	+	0.616880i
$712$	−3.24839	+	0.499683i	−0.121738	+	0.0187264i
$713$	−3.61371			−0.135335
$714$	18.5488	+	13.1377i	0.694170	+	0.491666i
$715$			38.0831i			1.42423i
$716$	30.1301	−	31.0159i	1.12601	−	1.15912i
$717$	−13.4759	−	5.14807i	−0.503269	−	0.192258i
$718$	6.25524	+	14.7974i	0.233443	+	0.552235i
$719$	−8.51080	−	14.7411i	−0.317399	−	0.549752i	0.662545	−	0.749022i	$-0.269476\pi$
$719$	−8.51080	−	14.7411i	−0.317399	−	0.549752i	−0.979945	+	0.199270i	$0.936143\pi$
$720$	26.1538	+	22.0670i	0.974695	+	0.822389i
$721$	−3.65713	−	2.78763i	−0.136199	−	0.103817i
$722$	23.1979	+	17.5349i	0.863335	+	0.652580i
$723$	9.68787	−	7.87092i	0.360296	−	0.292723i
$724$	18.1708	+	4.58779i	0.675311	+	0.170504i
$725$	−6.11364	+	10.5891i	−0.227055	+	0.393271i
$726$	1.07634	+	30.7122i	0.0399468	+	1.13984i
$727$			42.1153i			1.56197i	0.624550	+	0.780985i	$0.285282\pi$
$727$			42.1153i			1.56197i	−0.624550	+	0.780985i	$0.714718\pi$
$728$	20.5893	−	0.513497i	0.763089	−	0.0190315i
$729$	15.6586	−	21.9956i	0.579949	−	0.814653i
$730$	−0.167151	+	1.34483i	−0.00618653	+	0.0497746i
$731$	−15.5446	−	8.97469i	−0.574939	−	0.331941i
$732$	−8.58123	−	0.762510i	−0.317172	−	0.0281832i
$733$	20.3500	+	35.2472i	0.751644	+	1.30189i	0.947026	+	0.321158i	$0.104072\pi$
$733$	20.3500	+	35.2472i	0.751644	+	1.30189i	−0.195382	+	0.980727i	$0.562595\pi$
$734$	23.8815	−	31.5941i	0.881481	−	1.16616i
$735$	−28.1332	−	20.0972i	−1.03771	−	0.741295i
$736$	1.95064	−	20.5398i	0.0719017	−	0.757107i
$737$	24.3968	−	14.0855i	0.898669	−	0.518847i
$738$	6.73506	−	5.87523i	0.247921	−	0.216270i
$739$	−7.63741	−	4.40946i	−0.280947	−	0.162205i	0.352905	−	0.935659i	$-0.385194\pi$
$739$	−7.63741	−	4.40946i	−0.280947	−	0.162205i	−0.633852	+	0.773454i	$0.718527\pi$
$740$	4.88774	−	5.03144i	0.179677	−	0.184959i
$741$	29.6068	−	4.73810i	1.08763	−	0.174058i
$742$	−1.86895	+	7.27837i	−0.0686112	+	0.267197i
$743$			16.3412i			0.599502i	0.954017	+	0.299751i	$0.0969036\pi$
$743$			16.3412i			0.599502i	−0.954017	+	0.299751i	$0.903096\pi$
$744$	−1.48680	−	4.62055i	−0.0545088	−	0.169398i
$745$	−27.1572	−	15.6792i	−0.994962	−	0.574441i
$746$	17.2483	+	40.8028i	0.631507	+	1.49390i
$747$	−0.276258	+	0.308808i	−0.0101077	+	0.0112987i
$748$	9.28501	+	32.7471i	0.339494	+	1.19735i
$749$	−1.70663	+	2.23895i	−0.0623590	+	0.0818096i
$750$	−6.12500	+	11.5229i	−0.223653	+	0.420758i
$751$	6.17492	+	10.6953i	0.225326	+	0.390276i	0.956417	−	0.292004i	$-0.0943219\pi$
$751$	6.17492	+	10.6953i	0.225326	+	0.390276i	−0.731091	+	0.682280i	$0.760989\pi$
$752$	1.30069	+	44.8826i	0.0474313	+	1.63670i
$753$	−13.6118	−	5.19997i	−0.496041	−	0.189497i
$754$	−1.87434	+	15.0802i	−0.0682593	+	0.549190i
$755$			23.7670i			0.864969i
$756$	−16.0799	−	22.3033i	−0.584819	−	0.811164i
$757$		−	29.0246i		−	1.05492i	−0.849581	−	0.527459i	$-0.823145\pi$
$757$		−	29.0246i		−	1.05492i	0.849581	−	0.527459i	$-0.176855\pi$
$758$	−40.4363	−	5.02586i	−1.46871	−	0.182548i
$759$	−28.6358	−	10.9394i	−1.03941	−	0.397075i
$760$	39.5675	−	31.7506i	1.43527	−	1.15171i
$761$	15.5050	+	26.8554i	0.562055	+	0.973507i	0.997317	+	0.0732037i	$0.0233223\pi$
$761$	15.5050	+	26.8554i	0.562055	+	0.973507i	−0.435262	+	0.900304i	$0.643344\pi$
$762$	−33.8216	−	17.9778i	−1.22523	−	0.651269i
$763$	−3.05745	+	23.8134i	−0.110687	+	0.862102i
$764$	−17.1226	+	4.85489i	−0.619474	+	0.175644i
$765$	20.0052	−	22.3624i	0.723291	−	0.808513i
$766$	33.0084	−	13.9535i	1.19264	−	0.504160i
$767$	2.45221	+	1.41578i	0.0885442	+	0.0511210i
$768$	27.0651	−	5.95663i	0.976627	−	0.214941i
$769$			42.3916i			1.52868i	0.644813	+	0.764340i	$0.276935\pi$
$769$			42.3916i			1.52868i	−0.644813	+	0.764340i	$0.723065\pi$
$770$	−13.9220	−	49.8674i	−0.501714	−	1.79710i
$771$	−51.7479	+	8.28143i	−1.86366	+	0.298248i
$772$	−20.7861	+	21.3972i	−0.748107	+	0.770101i
$773$	−2.88336	−	1.66471i	−0.103707	−	0.0598754i	0.447249	−	0.894409i	$-0.352404\pi$
$773$	−2.88336	−	1.66471i	−0.103707	−	0.0598754i	−0.550957	+	0.834534i	$0.685737\pi$
$774$	14.2731	+	16.3619i	0.513035	+	0.588116i
$775$	−2.68722	+	1.55147i	−0.0965277	+	0.0557303i
$776$	−29.2476	−	11.3767i	−1.04993	−	0.408400i
$777$	−4.79149	+	2.96806i	−0.171894	+	0.106478i
$778$	−4.98397	−	3.76730i	−0.178684	−	0.135064i
$779$	−6.62508	−	11.4750i	−0.237368	−	0.411134i
$780$	2.40632	−	27.0805i	0.0861600	−	0.969638i
$781$	−40.9842	−	23.6622i	−1.46653	−	0.846701i
$782$	−17.9528	−	2.23137i	−0.641992	−	0.0797938i
$783$	18.0314	−	9.29733i	0.644388	−	0.332260i
$784$	−26.7726	+	8.19919i	−0.956165	+	0.292828i
$785$		−	30.9229i		−	1.10369i
$786$	−24.6844	+	0.865090i	−0.880463	+	0.0308567i
$787$	11.2617	−	19.5059i	0.401437	−	0.695309i	−0.592463	−	0.805598i	$-0.701844\pi$
$787$	11.2617	−	19.5059i	0.401437	−	0.695309i	0.993900	+	0.110289i	$0.0351777\pi$
$788$	5.32089	+	1.34343i	0.189549	+	0.0478578i
$789$	32.4545	−	26.3677i	1.15541	−	0.938714i
$790$	13.6220	−	18.0212i	0.484647	−	0.641167i
$791$	41.0411	−	17.1542i	1.45925	−	0.609932i
$792$	2.20560	−	41.1150i	0.0783727	−	1.46096i
$793$	3.42230	+	5.92761i	0.121530	+	0.210495i
$794$	20.8880	−	8.82987i	0.741287	−	0.313360i
$795$	9.26634	+	3.53992i	0.328643	+	0.125548i
$796$	33.4321	+	32.4773i	1.18497	+	1.15113i
$797$		−	20.3781i		−	0.721831i	−0.932599	−	0.360915i	$-0.882464\pi$
$797$		−	20.3781i		−	0.721831i	0.932599	−	0.360915i	$-0.117536\pi$
$798$	−37.0362	+	17.0276i	−1.31107	+	0.602769i
$799$	39.3710			1.39285
$800$	−7.36777	−	16.1112i	−0.260490	−	0.569617i
$801$	0.713797	−	3.41210i	0.0252208	−	0.120561i
$802$	−4.15544	−	9.83012i	−0.146734	−	0.347114i
$803$	1.41214	−	0.815301i	0.0498335	−	0.0287714i
$804$	−18.2384	+	8.47454i	−0.643218	+	0.298874i
$805$	27.2937	+	3.50430i	0.961976	+	0.123510i
$806$	−2.32539	+	3.07639i	−0.0819084	+	0.108361i
$807$	−27.0222	+	21.9542i	−0.951228	+	0.772826i
$808$	−15.6977	+	12.5965i	−0.552244	+	0.443143i
$809$	−5.45505	−	3.14948i	−0.191789	−	0.110730i	0.401031	−	0.916065i	$-0.368652\pi$
$809$	−5.45505	−	3.14948i	−0.191789	−	0.110730i	−0.592820	+	0.805335i	$0.701985\pi$
$810$	−31.6570	+	17.7533i	−1.11231	+	0.623786i
$811$	−9.32889			−0.327582			−0.163791	−	0.986495i	$-0.552372\pi$
$811$	−9.32889			−0.327582			−0.163791	+	0.986495i	$0.552372\pi$
$812$	−3.05854	−	20.4318i	−0.107334	−	0.717016i
$813$	0.499048	+	3.11839i	0.0175024	+	0.109367i
$814$	−8.37582	−	1.04104i	−0.293572	−	0.0364884i
$815$	−16.5660	+	28.6932i	−0.580283	+	1.00508i
$816$	−4.53332	−	23.8729i	−0.158698	−	0.835717i
$817$	27.8769	−	16.0947i	0.975290	−	0.563084i
$818$	−23.9883	+	31.7355i	−0.838732	+	1.10961i
$819$	−7.15958	+	20.6384i	−0.250176	+	0.721165i
$820$	−11.5588	+	3.27734i	−0.403650	+	0.114450i
$821$	−21.8378	−	37.8241i	−0.762143	−	1.32007i	−0.941744	−	0.336331i	$-0.890814\pi$
$821$	−21.8378	−	37.8241i	−0.762143	−	1.32007i	0.179600	−	0.983740i	$-0.442520\pi$
$822$	−25.5908	−	40.9425i	−0.892582	−	1.42803i
$823$	12.0388	−	20.8519i	0.419647	−	0.726850i	−0.576257	−	0.817269i	$-0.695487\pi$
$823$	12.0388	−	20.8519i	0.419647	−	0.726850i	0.995904	+	0.0904188i	$0.0288205\pi$
$824$	0.747400	+	4.85877i	0.0260369	+	0.169263i
$825$	−25.9906	+	4.15938i	−0.904877	+	0.144811i
$826$	−3.72858	−	0.957428i	−0.129734	−	0.0333132i
$827$	40.9864			1.42524			0.712618	−	0.701553i	$-0.247510\pi$
$827$	40.9864			1.42524			0.712618	+	0.701553i	$0.247510\pi$
$828$	19.6714	+	9.58829i	0.683628	+	0.333216i
$829$	8.07095	−	13.9793i	0.280316	−	0.485521i	−0.691147	−	0.722714i	$-0.742894\pi$
$829$	8.07095	−	13.9793i	0.280316	−	0.485521i	0.971462	+	0.237194i	$0.0762275\pi$
$830$	0.513034	−	0.216872i	0.0178077	−	0.00752774i
$831$	−17.7071	+	14.3861i	−0.614251	+	0.499049i
$832$	−16.2305	−	14.8778i	−0.562692	−	0.515794i
$833$	6.50627	+	23.6735i	0.225429	+	0.820238i
$834$	0.241883	+	0.128573i	0.00837572	+	0.00445211i
$835$	19.1408	−	11.0509i	0.662393	−	0.382433i
$836$	−59.1847	−	14.9431i	−2.04694	−	0.516817i
$837$	5.14249	+	0.244624i	0.177751	+	0.00845546i
$838$	−27.4593	−	3.41295i	−0.948567	−	0.117898i
$839$	−40.8898			−1.41167			−0.705836	−	0.708375i	$-0.749429\pi$
$839$	−40.8898			−1.41167			−0.705836	+	0.708375i	$0.749429\pi$
$840$	6.74888	+	36.3399i	0.232858	+	1.25385i
$841$	−13.7566			−0.474367
$842$	36.6268	+	4.55238i	1.26224	+	0.156885i
$843$	−24.8883	−	9.50780i	−0.857198	−	0.327466i
$844$	9.98385	−	39.5428i	0.343658	−	1.36112i
$845$	13.3983	−	7.73551i	0.460915	−	0.266110i
$846$	−45.0573	−	15.4271i	−1.54910	−	0.530396i
$847$	−20.1223	+	26.3987i	−0.691411	+	0.907071i
$848$	6.83780	−	4.21651i	0.234811	−	0.144796i
$849$	10.1547	+	12.4988i	0.348508	+	0.428959i
$850$	−14.3080	+	6.04836i	−0.490761	+	0.207457i
$851$	2.24298	−	3.88495i	0.0768882	−	0.133174i
$852$	27.6484	+	19.4156i	0.947217	+	0.665168i
$853$	−23.3041			−0.797917			−0.398958	−	0.916969i	$-0.630628\pi$
$853$	−23.3041			−0.797917			−0.398958	+	0.916969i	$0.630628\pi$
$854$	−6.64824	−	6.51074i	−0.227498	−	0.222793i
$855$	16.7924	+	51.1216i	0.574290	+	1.74832i
$856$	2.97462	−	0.457570i	0.101670	−	0.0156394i
$857$	3.23327	−	5.60019i	0.110447	−	0.191299i	−0.805504	−	0.592591i	$-0.798105\pi$
$857$	3.23327	−	5.60019i	0.110447	−	0.191299i	0.915950	+	0.401292i	$0.131439\pi$
$858$	−27.7397	+	17.3385i	−0.947018	+	0.591927i
$859$	−1.10393	−	1.91207i	−0.0376657	−	0.0652390i	0.846578	−	0.532265i	$-0.178659\pi$
$859$	−1.10393	−	1.91207i	−0.0376657	−	0.0652390i	−0.884244	+	0.467026i	$0.845326\pi$
$860$	−7.96186	−	28.0805i	−0.271497	−	0.957538i
$861$	9.64899	−	0.299165i	0.328837	−	0.0101955i
$862$	10.2479	−	13.5575i	0.349044	−	0.461770i
$863$	21.2034	−	12.2418i	0.721771	−	0.416715i	−0.0936330	−	0.995607i	$-0.529848\pi$
$863$	21.2034	−	12.2418i	0.721771	−	0.416715i	0.815404	+	0.578892i	$0.196515\pi$
$864$	−4.16627	+	29.0971i	−0.141740	+	0.989904i
$865$	−1.44962	+	2.51082i	−0.0492886	+	0.0853704i
$866$	−50.0097	−	6.21575i	−1.69940	−	0.211220i
$867$	8.03607	−	1.28604i	0.272919	−	0.0436764i
$868$	1.92032	−	4.87843i	0.0651799	−	0.165585i
$869$	−27.1815			−0.922068
$870$	−27.2547	+	0.955170i	−0.924022	+	0.0323833i
$871$	13.8375	+	7.98908i	0.468866	+	0.270700i
$872$	20.0183	−	16.0635i	0.677907	−	0.543980i
$873$	22.1929	−	24.8078i	0.751117	−	0.839618i
$874$	19.5634	−	25.8815i	0.661740	−	0.875453i
$875$	−13.0049	+	5.43574i	−0.439647	+	0.183761i
$876$	−1.05568	+	0.490526i	−0.0356680	+	0.0165733i
$877$	15.3248	−	8.84776i	0.517481	−	0.298768i	−0.218422	−	0.975854i	$-0.570091\pi$
$877$	15.3248	−	8.84776i	0.517481	−	0.298768i	0.735903	+	0.677087i	$0.236758\pi$
$878$	7.43602	+	17.5907i	0.250954	+	0.593657i
$879$	28.8752	+	11.0309i	0.973936	+	0.372062i
$880$	−26.2744	+	48.7152i	−0.885710	+	1.64219i
$881$	−55.0445			−1.85450			−0.927249	−	0.374446i	$-0.877833\pi$
$881$	−55.0445			−1.85450			−0.927249	+	0.374446i	$0.877833\pi$
$882$	1.83026	−	29.6420i	0.0616280	−	0.998099i
$883$		−	49.3732i		−	1.66154i	−0.556616	−	0.830770i	$-0.687900\pi$
$883$		−	49.3732i		−	1.66154i	0.556616	−	0.830770i	$-0.312100\pi$
$884$	−13.4521	+	13.8476i	−0.452443	+	0.465744i
$885$	−1.81344	+	4.74698i	−0.0609581	+	0.159568i
$886$	−30.6527	+	12.9577i	−1.02980	+	0.435321i
$887$	12.2514	+	21.2201i	0.411363	+	0.712502i	0.995039	−	0.0994850i	$-0.0317195\pi$
$887$	12.2514	+	21.2201i	0.411363	+	0.712502i	−0.583676	+	0.811987i	$0.698386\pi$
$888$	5.89019	+	1.26951i	0.197662	+	0.0426019i
$889$	−15.9547	−	38.1716i	−0.535105	−	1.28023i
$890$	−2.82570	+	3.73827i	−0.0947176	+	0.125307i
$891$	40.0096	+	17.5058i	1.34037	+	0.586466i
$892$	−5.61404	+	22.2354i	−0.187972	+	0.744496i
$893$	−35.3029	+	61.1465i	−1.18137	+	2.04619i
$894$	−0.943429	−	26.9197i	−0.0315530	−	0.900330i
$895$		−	61.6540i		−	2.06087i
$896$	26.6917	+	13.5481i	0.891708	+	0.452612i
$897$	−2.74748	−	17.1681i	−0.0917357	−	0.573226i
$898$	42.9854	+	5.34270i	1.43444	+	0.178288i
$899$	3.35007	+	1.93416i	0.111731	+	0.0645079i
$900$	18.7445	−	1.31546i	0.624817	−	0.0438486i
$901$	−3.52194	−	6.10018i	−0.117333	−	0.203226i
$902$	11.5323	+	8.71707i	0.383984	+	0.290247i
$903$	0.726780	+	23.4409i	0.0241857	+	0.780065i
$904$	−44.3184	−	17.2390i	−1.47401	−	0.573359i
$905$	23.1412	−	13.3606i	0.769239	−	0.444120i
$906$	−17.3119	+	10.8207i	−0.575148	+	0.359492i
$907$	6.23747	+	3.60121i	0.207112	+	0.119576i	0.599968	−	0.800024i	$-0.295180\pi$
$907$	6.23747	+	3.60121i	0.207112	+	0.119576i	−0.392857	+	0.919600i	$0.628513\pi$
$908$	30.4294	+	29.5603i	1.00983	+	0.980994i
$909$	−6.66211	−	20.2816i	−0.220968	−	0.672697i
$910$	20.5465	−	20.9804i	0.681109	−	0.695494i
$911$		−	13.3025i		−	0.440730i	−0.975417	−	0.220365i	$-0.929275\pi$
$911$		−	13.3025i		−	0.440730i	0.975417	−	0.220365i	$-0.0707248\pi$
$912$	41.1415	+	14.3655i	1.36233	+	0.475690i
$913$	−0.580401	−	0.335095i	−0.0192085	−	0.0110900i
$914$	15.1294	−	6.39559i	0.500438	−	0.211547i
$915$	−9.53358	+	7.74557i	−0.315170	+	0.256061i
$916$	−1.23806	−	4.36649i	−0.0409066	−	0.144273i
$917$	−21.2175	−	16.1729i	−0.700663	−	0.534077i
$918$	25.3967	+	4.39065i	0.838217	+	0.144913i
$919$	−3.29521	−	5.70747i	−0.108699	−	0.188272i	0.806544	−	0.591173i	$-0.201335\pi$
$919$	−3.29521	−	5.70747i	−0.108699	−	0.188272i	−0.915243	+	0.402901i	$0.868002\pi$
$920$	−18.4112	−	22.9440i	−0.606999	−	0.756442i
$921$	10.9192	−	28.5828i	0.359799	−	0.941834i
$922$	43.2760	+	5.37881i	1.42522	+	0.177142i
$923$		−	26.8417i		−	0.883505i
$924$	29.9850	−	32.8445i	0.986433	−	1.08050i
$925$		−	3.85188i		−	0.126649i
$926$	−5.63762	+	45.3582i	−0.185264	+	1.49056i
$927$	−5.10364	−	1.06766i	−0.167626	−	0.0350666i
$928$	−12.8018	+	17.9972i	−0.420240	+	0.590788i
$929$	6.17532	+	10.6960i	0.202606	+	0.350923i	0.949367	−	0.314169i	$-0.101726\pi$
$929$	6.17532	+	10.6960i	0.202606	+	0.350923i	−0.746762	+	0.665092i	$0.768392\pi$
$930$	−6.11103	−	3.24831i	−0.200389	−	0.106516i
$931$	−42.6009	−	11.1226i	−1.39619	−	0.364529i
$932$	50.1296	−	14.2136i	1.64205	−	0.465581i
$933$	9.06707	+	11.1601i	0.296842	+	0.365366i
$934$	18.6775	+	44.1835i	0.611145	+	1.44573i
$935$	42.0298	+	24.2659i	1.37452	+	0.793580i
$936$	20.8210	−	10.5765i	0.680555	−	0.345704i
$937$		−	11.2161i		−	0.366413i	−0.983074	−	0.183206i	$-0.941352\pi$
$937$		−	11.2161i		−	0.366413i	0.983074	−	0.183206i	$-0.0586476\pi$
$938$	−21.0399	−	5.40264i	−0.686977	−	0.176402i
$939$	7.29923	+	45.6105i	0.238201	+	1.48844i
$940$	45.9207	+	44.6092i	1.49777	+	1.45499i
$941$	8.10816	+	4.68125i	0.264318	+	0.152604i	0.626303	−	0.779580i	$-0.284567\pi$
$941$	8.10816	+	4.68125i	0.264318	+	0.152604i	−0.361985	+	0.932184i	$0.617901\pi$
$942$	22.5242	−	14.0786i	0.733879	−	0.458706i
$943$	−6.65399	+	3.84168i	−0.216684	+	0.125102i
$944$	2.16004	+	3.50288i	0.0703035	+	0.114009i
$945$	−38.6030	−	6.83439i	−1.25576	−	0.222323i
$946$	−21.1769	+	28.0162i	−0.688521	+	0.910884i
$947$	19.4899	+	33.7574i	0.633335	+	1.09697i	0.986865	+	0.161546i	$0.0516480\pi$
$947$	19.4899	+	33.7574i	0.633335	+	1.09697i	−0.353530	+	0.935423i	$0.615019\pi$
$948$	19.3285	+	1.71749i	0.627760	+	0.0557814i
$949$	0.800945	+	0.462426i	0.0259998	+	0.0150110i
$950$	3.43602	−	27.6450i	0.111479	−	0.896922i
$951$	49.2896	−	7.88801i	1.59832	−	0.255786i
$952$	12.5524	−	23.0502i	0.406826	−	0.747061i
$953$		−	0.425521i		−	0.0137840i	−0.999976	−	0.00689198i	$-0.997806\pi$
$953$		−	0.425521i		−	0.0137840i	0.999976	−	0.00689198i	$-0.00219380\pi$
$954$	1.64031	+	8.36125i	0.0531071	+	0.270706i
$955$	−12.6880	+	21.9763i	−0.410574	+	0.711135i
$956$	−4.07775	+	16.1507i	−0.131884	+	0.522350i
$957$	20.6915	+	25.4680i	0.668861	+	0.823263i
$958$	39.8984	+	30.1585i	1.28906	+	0.974378i
$959$	6.64124	−	51.7262i	0.214457	−	1.67033i
$960$	21.7616	−	32.9808i	0.702353	−	1.06445i
$961$	−15.0092	−	25.9966i	−0.484167	−	0.838601i
$962$	−1.86396	−	4.40940i	−0.0600966	−	0.142165i
$963$	−0.653639	+	3.12453i	−0.0210632	+	0.100687i
$964$	−10.3383	−	10.0430i	−0.332973	−	0.323463i
$965$			42.5337i			1.36921i
$966$	9.87377	+	21.4761i	0.317683	+	0.690983i
$967$	−25.1685			−0.809365			−0.404682	−	0.914457i	$-0.632618\pi$
$967$	−25.1685			−0.809365			−0.404682	+	0.914457i	$0.632618\pi$
$968$	35.0727	−	5.39505i	1.12728	−	0.173403i
$969$	13.6358	−	35.6941i	0.438046	−	1.14666i
$970$	−41.2142	+	17.4222i	−1.32331	+	0.559395i
$971$	−11.2476	+	6.49383i	−0.360954	+	0.208397i	−0.669499	−	0.742813i	$-0.733491\pi$
$971$	−11.2476	+	6.49383i	−0.360954	+	0.208397i	0.308545	+	0.951210i	$0.400158\pi$
$972$	−27.3443	−	14.9762i	−0.877070	−	0.480363i
$973$	0.114104	+	0.272993i	0.00365801	+	0.00875174i
$974$	−37.0472	−	28.0033i	−1.18707	−	0.897285i
$975$	−9.41381	−	11.5869i	−0.301483	−	0.371078i
$976$	0.288164	+	9.94362i	0.00922392	+	0.318288i
$977$	−33.4781	−	19.3286i	−1.07106	−	0.618377i	−0.142589	−	0.989782i	$-0.545543\pi$
$977$	−33.4781	−	19.3286i	−1.07106	−	0.618377i	−0.928471	+	0.371405i	$0.878876\pi$
$978$	−28.4424	+	0.996792i	−0.909486	+	0.0318739i
$979$	5.63844			0.180205
$980$	−19.2345	+	34.9837i	−0.614425	+	1.11751i
$981$	8.49578	+	25.8639i	0.271249	+	0.825770i
$982$	−3.92986	+	31.6182i	−0.125407	+	1.00898i
$983$	−24.2049	+	41.9241i	−0.772017	+	1.33717i	0.164439	+	0.986387i	$0.447419\pi$
$983$	−24.2049	+	41.9241i	−0.772017	+	1.33717i	−0.936456	+	0.350785i	$0.885915\pi$
$984$	−7.64971	−	6.92731i	−0.243864	−	0.220834i
$985$	6.77637	−	3.91234i	0.215913	−	0.124657i
$986$	15.4488	+	11.6775i	0.491989	+	0.371886i
$987$	−27.0887	−	43.7308i	−0.862244	−	1.39197i
$988$	−9.44432	−	33.3090i	−0.300464	−	1.05970i
$989$	−9.33285	−	16.1650i	−0.296767	−	0.514016i
$990$	−38.5917	−	44.2395i	−1.22653	−	1.40603i
$991$	8.16959	−	14.1502i	0.259516	−	0.449494i	−0.706597	−	0.707617i	$-0.749770\pi$
$991$	8.16959	−	14.1502i	0.259516	−	0.449494i	0.966112	+	0.258122i	$0.0831037\pi$
$992$	−5.09708	+	2.33093i	−0.161832	+	0.0740071i
$993$	−0.709567	−	4.43385i	−0.0225174	−	0.140704i
$994$	9.81249	+	35.1475i	0.311233	+	1.11481i
$995$	66.4569			2.10682
$996$	0.391544	+	0.274956i	0.0124066	+	0.00871231i
$997$	4.94566	−	8.56614i	0.156631	−	0.271292i	−0.777021	−	0.629475i	$-0.783270\pi$
$997$	4.94566	−	8.56614i	0.156631	−	0.271292i	0.933652	+	0.358182i	$0.116603\pi$
$998$	7.19235	+	17.0143i	0.227670	+	0.538577i
$999$	−3.45485	+	5.37664i	−0.109307	+	0.170109i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	168.2.ba.c.101.14	yes	48
3.2	odd	2	inner	168.2.ba.c.101.11	yes	48
4.3	odd	2		672.2.bi.c.17.8		48
7.5	odd	6	inner	168.2.ba.c.5.4	✓	48
8.3	odd	2		672.2.bi.c.17.17		48
8.5	even	2	inner	168.2.ba.c.101.21	yes	48
12.11	even	2		672.2.bi.c.17.7		48
21.5	even	6	inner	168.2.ba.c.5.21	yes	48
24.5	odd	2	inner	168.2.ba.c.101.4	yes	48
24.11	even	2		672.2.bi.c.17.18		48
28.19	even	6		672.2.bi.c.593.18		48
56.5	odd	6	inner	168.2.ba.c.5.11	yes	48
56.19	even	6		672.2.bi.c.593.7		48
84.47	odd	6		672.2.bi.c.593.17		48
168.5	even	6	inner	168.2.ba.c.5.14	yes	48
168.131	odd	6		672.2.bi.c.593.8		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
168.2.ba.c.5.4	✓	48	7.5	odd	6	inner
168.2.ba.c.5.11	yes	48	56.5	odd	6	inner
168.2.ba.c.5.14	yes	48	168.5	even	6	inner
168.2.ba.c.5.21	yes	48	21.5	even	6	inner
168.2.ba.c.101.4	yes	48	24.5	odd	2	inner
168.2.ba.c.101.11	yes	48	3.2	odd	2	inner
168.2.ba.c.101.14	yes	48	1.1	even	1	trivial
168.2.ba.c.101.21	yes	48	8.5	even	2	inner
672.2.bi.c.17.7		48	12.11	even	2
672.2.bi.c.17.8		48	4.3	odd	2
672.2.bi.c.17.17		48	8.3	odd	2
672.2.bi.c.17.18		48	24.11	even	2
672.2.bi.c.593.7		48	56.19	even	6
672.2.bi.c.593.8		48	168.131	odd	6
672.2.bi.c.593.17		48	84.47	odd	6
672.2.bi.c.593.18		48	28.19	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 168 = 2^{3} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	168.ba (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.174432 - 1.40341i) q^{2} +(0.618109 - 1.61801i) q^{3} +(-1.93915 - 0.489600i) q^{4} +(-2.46958 + 1.42581i) q^{5} +(-2.16291 - 1.14970i) q^{6} +(-1.02032 - 2.44110i) q^{7} +(-1.02536 + 2.63603i) q^{8} +(-2.23588 - 2.00021i) q^{9} +(1.57023 + 3.71455i) q^{10} +(2.42621 - 4.20231i) q^{11} +(-1.99078 + 2.83492i) q^{12} +2.75221 q^{13} +(-3.60385 + 1.00612i) q^{14} +(0.780502 + 4.87710i) q^{15} +(3.52058 + 1.89881i) q^{16} +(1.75366 - 3.03743i) q^{17} +(-3.19713 + 2.78897i) q^{18} +(3.14493 + 5.44717i) q^{19} +(5.48696 - 1.55575i) q^{20} +(-4.58037 + 0.142013i) q^{21} +(-5.47438 - 4.13799i) q^{22} +(3.15865 - 1.82365i) q^{23} +(3.63132 + 3.28839i) q^{24} +(1.56588 - 2.71219i) q^{25} +(0.480073 - 3.86249i) q^{26} +(-4.61837 + 2.38132i) q^{27} +(0.783383 + 5.23319i) q^{28} -3.90427 q^{29} +(6.98074 - 0.244647i) q^{30} +(-0.858051 - 0.495396i) q^{31} +(3.27893 - 4.60963i) q^{32} +(-5.29970 - 6.52310i) q^{33} +(-3.95689 - 2.99094i) q^{34} +(6.00030 + 4.57370i) q^{35} +(3.35640 + 4.97339i) q^{36} +(1.06516 - 0.614970i) q^{37} +(8.19322 - 3.46348i) q^{38} +(1.70117 - 4.45309i) q^{39} +(-1.22627 - 7.97185i) q^{40} -2.10659 q^{41} +(-0.599659 + 6.45294i) q^{42} -5.11768i q^{43} +(-6.76223 + 6.96103i) q^{44} +(8.37361 + 1.75172i) q^{45} +(-2.00837 - 4.75100i) q^{46} +(5.61268 + 9.72145i) q^{47} +(5.24840 - 4.52265i) q^{48} +(-4.91791 + 4.98138i) q^{49} +(-3.53319 - 2.67068i) q^{50} +(-3.83063 - 4.71490i) q^{51} +(-5.33694 - 1.34748i) q^{52} +(1.00417 - 1.73927i) q^{53} +(2.53639 + 6.89686i) q^{54} +13.8373i q^{55} +(7.48099 - 0.186576i) q^{56} +(10.7575 - 1.72156i) q^{57} +(-0.681029 + 5.47932i) q^{58} +(0.890996 + 0.514417i) q^{59} +(0.874321 - 9.83955i) q^{60} +(1.24347 + 2.15376i) q^{61} +(-0.844918 + 1.11779i) q^{62} +(-2.60139 + 7.49885i) q^{63} +(-5.89727 - 5.40576i) q^{64} +(-6.79681 + 3.92414i) q^{65} +(-10.0791 + 6.29985i) q^{66} +(5.02777 + 2.90279i) q^{67} +(-4.88774 + 5.03144i) q^{68} +(-0.998281 - 6.23793i) q^{69} +(7.46545 - 7.62311i) q^{70} -9.75277i q^{71} +(7.56519 - 3.84291i) q^{72} +(0.291019 + 0.168020i) q^{73} +(-0.677260 - 1.60213i) q^{74} +(-3.42045 - 4.21004i) q^{75} +(-3.43154 - 12.1026i) q^{76} +(-12.7338 - 1.63491i) q^{77} +(-5.95280 - 3.16420i) q^{78} +(-2.80082 - 4.85116i) q^{79} +(-11.4017 + 0.330420i) q^{80} +(0.998337 + 8.94446i) q^{81} +(-0.367457 + 2.95643i) q^{82} -0.138115i q^{83} +(8.95155 + 1.96717i) q^{84} +10.0016i q^{85} +(-7.18223 - 0.892686i) q^{86} +(-2.41327 + 6.31714i) q^{87} +(8.58967 + 10.7044i) q^{88} +(0.580993 + 1.00631i) q^{89} +(3.91902 - 11.4461i) q^{90} +(-2.80813 - 6.71841i) q^{91} +(-7.01795 + 1.98985i) q^{92} +(-1.33192 + 1.08212i) q^{93} +(14.6223 - 6.18119i) q^{94} +(-15.5333 - 8.96815i) q^{95} +(-5.43167 - 8.15457i) q^{96} +11.0953i q^{97} +(6.13311 + 7.77078i) q^{98} +(-13.8302 + 4.54296i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 6 q^{4} - 4 q^{7} - 14 q^{9} - 30 q^{10} - 18 q^{12} + 4 q^{15} + 6 q^{16} - 36 q^{22} - 12 q^{24} - 8 q^{25} - 10 q^{28} + 22 q^{30} + 48 q^{31} - 42 q^{33} + 52 q^{36} - 8 q^{39} - 18 q^{40} + 12 q^{42}+ \cdots + 90 q^{96}+O(q^{100}) \) 48 * q + 6 * q^4 - 4 * q^7 - 14 * q^9 - 30 * q^10 - 18 * q^12 + 4 * q^15 + 6 * q^16 - 36 * q^22 - 12 * q^24 - 8 * q^25 - 10 * q^28 + 22 * q^30 + 48 * q^31 - 42 * q^33 + 52 * q^36 - 8 * q^39 - 18 * q^40 + 12 * q^42 - 8 * q^46 - 36 * q^49 - 48 * q^52 + 60 * q^54 + 4 * q^57 + 30 * q^58 - 32 * q^60 - 6 * q^63 - 60 * q^64 + 54 * q^66 + 42 * q^70 + 42 * q^72 - 36 * q^73 - 68 * q^78 - 56 * q^79 + 42 * q^81 + 48 * q^82 + 48 * q^84 - 132 * q^87 + 6 * q^88 + 48 * q^94 + 90 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more