LMFDB - Embedded newform 168.2.ba.c.5.14

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			5.14
Character	$\chi$	$=$	168.5
Dual form			168.2.ba.c.101.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.174432 + 1.40341i) q^{2} +(0.618109 + 1.61801i) q^{3} +(-1.93915 + 0.489600i) q^{4} +(-2.46958 - 1.42581i) q^{5} +(-2.16291 + 1.14970i) q^{6} +(-1.02032 + 2.44110i) q^{7} +(-1.02536 - 2.63603i) q^{8} +(-2.23588 + 2.00021i) q^{9} +O(q^{10})$	\(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}+O(q^{10}) $ 48 * q + 6 * q^4 - 4 * q^7 - 14 * q^9	$ 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}+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

Display 100 coefficients 10 coefficients

Character values

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

$n$	$73$	$85$	$113$	$127$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$	$-1$	$1$

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	−0.167049	−	0.985949i	$-0.553424\pi$
$5$	−2.46958	−	1.42581i	−1.10443	−	0.637643i	−0.937381	+	0.348306i	$0.886757\pi$
$6$	−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	0.956230	+	0.292617i	$0.0945262\pi$
$11$	2.42621	+	4.20231i	0.731529	+	1.26705i	−0.224701	+	0.974428i	$0.572140\pi$
$12$	−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	0.996451	−	0.0841773i	$-0.0268262\pi$
$17$	1.75366	+	3.03743i	0.425326	+	0.736686i	−0.571125	+	0.820863i	$0.693493\pi$
$18$	−3.19713	−	2.78897i	−0.753571	−	0.657367i
$19$	3.14493	−	5.44717i	0.721496	−	1.24967i	−0.238905	−	0.971043i	$-0.576788\pi$
$19$	3.14493	−	5.44717i	0.721496	−	1.24967i	0.960400	−	0.278624i	$-0.0898784\pi$
$20$	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	0.791753	−	0.610842i	$-0.209169\pi$
$23$	3.15865	+	1.82365i	0.658624	+	0.380257i	−0.133128	+	0.991099i	$0.542502\pi$
$24$	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	−0.575072	−	0.818103i	$-0.695026\pi$
$31$	−0.858051	+	0.495396i	−0.154111	+	0.0889758i	0.420962	+	0.907078i	$0.361693\pi$
$32$	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	0.584994	−	0.811038i	$-0.301097\pi$
$37$	1.06516	+	0.614970i	0.175111	+	0.101100i	−0.409883	+	0.912138i	$0.634430\pi$
$38$	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	$0.127601\pi$
$43$			5.11768i			0.780439i	−0.920722	+	0.390220i	$0.872399\pi$
$44$	−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	−0.0879518	−	0.996125i	$-0.528032\pi$
$47$	5.61268	−	9.72145i	0.818693	−	1.41802i	0.906645	−	0.421894i	$-0.138635\pi$
$48$	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	0.926714	−	0.375767i	$-0.122621\pi$
$53$	1.00417	+	1.73927i	0.137933	+	0.238907i	−0.788781	+	0.614674i	$0.789288\pi$
$54$	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	−0.440879	−	0.897567i	$-0.645333\pi$
$59$	0.890996	−	0.514417i	0.115998	−	0.0669714i	0.556876	+	0.830595i	$0.312000\pi$
$60$	0.874321	+	9.83955i	0.112874	+	1.27028i
$61$	1.24347	−	2.15376i	0.159211	−	0.275761i	−0.775374	−	0.631503i	$-0.782438\pi$
$61$	1.24347	−	2.15376i	0.159211	−	0.275761i	0.934584	+	0.355742i	$0.115772\pi$
$62$	−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	−0.160383	−	0.987055i	$-0.551273\pi$
$67$	5.02777	−	2.90279i	0.614240	−	0.354632i	0.774623	+	0.632423i	$0.217940\pi$
$68$	−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	$0.196448\pi$
$71$			9.75277i			1.15744i	−0.815526	+	0.578720i	$0.803552\pi$
$72$	7.56519	+	3.84291i	0.891566	+	0.452891i
$73$	0.291019	−	0.168020i	0.0340612	−	0.0196652i	−0.482873	−	0.875691i	$-0.660407\pi$
$73$	0.291019	−	0.168020i	0.0340612	−	0.0196652i	0.516934	+	0.856025i	$0.327073\pi$
$74$	−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	−0.979462	−	0.201627i	$-0.935377\pi$
$79$	−2.80082	+	4.85116i	−0.315117	+	0.545798i	0.664346	+	0.747426i	$0.268710\pi$
$80$	−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	$0.00241282\pi$
$83$			0.138115i			0.0151600i	−0.999971	+	0.00758002i	$0.997587\pi$
$84$	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	−0.833589	−	0.552385i	$-0.813718\pi$
$89$	0.580993	−	1.00631i	0.0615852	−	0.106669i	0.895174	+	0.445717i	$0.147051\pi$
$90$	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	$-0.809539\pi$
$97$		−	11.0953i		−	1.12656i	0.826266	−	0.563280i	$-0.190461\pi$
$98$	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	−0.161018	−	0.986951i	$-0.551478\pi$
$101$	6.16256	−	3.55796i	0.613198	−	0.354030i	0.774216	+	0.632922i	$0.218144\pi$
$102$	−7.28515	−	4.55353i	−0.721337	−	0.450867i
$103$	1.50519	+	0.869021i	0.148311	+	0.0856271i	0.572319	−	0.820031i	$-0.306044\pi$
$103$	1.50519	+	0.869021i	0.148311	+	0.0856271i	−0.424008	+	0.905658i	$0.639377\pi$
$104$	−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	−0.890596	−	0.454796i	$-0.849712\pi$
$107$	−0.532028	+	0.921500i	−0.0514331	+	0.0890847i	0.839163	+	0.543881i	$0.183046\pi$
$108$	10.1216	+	2.35658i	0.973950	+	0.226762i
$109$	−7.85874	+	4.53725i	−0.752731	+	0.434589i	−0.826680	−	0.562673i	$-0.809773\pi$
$109$	−7.85874	+	4.53725i	−0.752731	+	0.434589i	0.0739489	+	0.997262i	$0.476440\pi$
$110$	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	$-0.709666\pi$
$113$		−	16.8126i		−	1.58159i	0.612078	−	0.790797i	$-0.290334\pi$
$114$	−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	0.830361	−	0.557225i	$-0.188134\pi$
$131$	8.73260	+	5.04177i	0.762971	+	0.440502i	−0.0673904	+	0.997727i	$0.521467\pi$
$132$	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	0.459485	−	0.888185i	$-0.348034\pi$
$137$	17.0704	−	9.85557i	1.45842	−	0.842019i	0.998934	+	0.0461669i	$0.0147006\pi$
$138$	−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	−0.547972	−	0.836497i	$-0.684600\pi$
$149$	5.49834	−	9.52340i	0.450441	−	0.780187i	0.998413	+	0.0563094i	$0.0179333\pi$
$150$	−6.50507	−	4.06595i	−0.531136	−	0.331983i
$151$	4.16727	+	7.21792i	0.339127	+	0.587386i	0.984269	−	0.176677i	$-0.0565349\pi$
$151$	4.16727	+	7.21792i	0.339127	+	0.587386i	−0.645141	+	0.764063i	$0.723202\pi$
$152$	−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	0.564386	−	0.825511i	$-0.309113\pi$
$157$	−5.42198	−	9.39114i	−0.432721	−	0.749495i	−0.997107	+	0.0760165i	$0.975780\pi$
$158$	−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	0.839301	−	0.543667i	$-0.182965\pi$
$163$	10.0621	+	5.80934i	0.788122	+	0.455022i	−0.0511792	+	0.998689i	$0.516298\pi$
$164$	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	0.533098	−	0.846054i	$-0.321028\pi$
$173$	0.880487	+	0.508349i	0.0669422	+	0.0386491i	−0.466155	+	0.884703i	$0.654361\pi$
$174$	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	−0.914246	−	0.405160i	$-0.867216\pi$
$179$	−10.8103	−	18.7240i	−0.808002	−	1.39950i	0.106244	−	0.994340i	$-0.466117\pi$
$180$	−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	0.752193	−	0.658943i	$-0.228996\pi$
$191$	7.70657	+	4.44939i	0.557628	+	0.321947i	−0.194565	+	0.980890i	$0.562329\pi$
$192$	−12.3917	−	6.20046i	−0.894294	−	0.447480i
$193$	7.45779	+	12.9173i	0.536824	+	0.929806i	0.999073	+	0.0430556i	$0.0137093\pi$
$193$	7.45779	+	12.9173i	0.536824	+	0.929806i	−0.462249	+	0.886750i	$0.652957\pi$
$194$	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	−0.997175	−	0.0751162i	$-0.976067\pi$
$199$	−20.1826	+	11.6525i	−1.43071	+	0.826021i	−0.433535	+	0.901137i	$0.642734\pi$
$200$	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	$-0.752328\pi$
$211$		−	20.3918i		−	1.40383i	0.712259	−	0.701916i	$-0.247672\pi$
$212$	−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	$0.125430\pi$
$223$			11.4666i			0.767860i	−0.923362	+	0.383930i	$0.874570\pi$
$224$	−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	−0.964759	−	0.263136i	$-0.915243\pi$
$227$	−18.3699	+	10.6059i	−1.21926	+	0.703938i	−0.254497	+	0.967073i	$0.581910\pi$
$228$	−21.7032	+	1.92850i	−1.43733	+	0.127718i
$229$	1.13465	−	1.96528i	0.0749800	−	0.129869i	−0.826098	−	0.563527i	$-0.809444\pi$
$229$	1.13465	−	1.96528i	0.0749800	−	0.129869i	0.901078	+	0.433658i	$0.142777\pi$
$230$	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	−0.478420	−	0.878131i	$-0.658790\pi$
$233$	−22.5624	−	13.0264i	−1.47811	−	0.853389i	−0.999694	+	0.0247423i	$0.992123\pi$
$234$	−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	$0.0868157\pi$
$239$			8.32874i			0.538742i	−0.963037	+	0.269371i	$0.913184\pi$
$240$	−6.51288	−	18.6523i	−0.420405	−	1.20400i
$241$	6.24112	−	3.60331i	0.402026	−	0.232110i	−0.285332	−	0.958429i	$-0.592104\pi$
$241$	6.24112	−	3.60331i	0.402026	−	0.232110i	0.687358	+	0.726319i	$0.258771\pi$
$242$	−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	$0.0855378\pi$
$251$			8.41270i			0.531005i	−0.964110	+	0.265502i	$0.914462\pi$
$252$	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	−0.185321	+	0.982678i	$0.559332\pi$
$257$	−15.1284	+	26.2032i	−0.943685	+	1.63451i	−0.758364	+	0.651832i	$0.774001\pi$
$258$	−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	0.310714	−	0.950504i	$-0.399432\pi$
$263$	20.9078	−	12.0711i	1.28923	−	0.744338i	0.978517	+	0.206166i	$0.0660986\pi$
$264$	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	−0.925819	−	0.377966i	$-0.876623\pi$
$269$	−17.4083	+	10.0507i	−1.06140	+	0.612800i	−0.135581	+	0.990766i	$0.543290\pi$
$270$	−16.0975	+	13.4159i	−0.979660	+	0.816468i
$271$	−1.57903	−	0.911656i	−0.0959195	−	0.0553791i	0.451273	−	0.892386i	$-0.350970\pi$
$271$	−1.57903	−	0.911656i	−0.0959195	−	0.0553791i	−0.547192	+	0.837007i	$0.684303\pi$
$272$	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	−0.801885	−	0.597479i	$-0.796169\pi$
$277$	−11.4072	+	6.58598i	−0.685395	+	0.395713i	0.116490	+	0.993192i	$0.462836\pi$
$278$	−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	$0.151724\pi$
$281$			15.3821i			0.917618i	−0.888535	+	0.458809i	$0.848276\pi$
$282$	−0.963049	+	27.4795i	−0.0573487	+	1.63638i
$283$	−4.64882	−	8.05200i	−0.276344	−	0.478641i	0.694129	−	0.719850i	$-0.255790\pi$
$283$	−4.64882	−	8.05200i	−0.276344	−	0.478641i	−0.970473	+	0.241209i	$0.922456\pi$
$284$	−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	$-0.825450\pi$
$293$		−	17.8462i		−	1.04258i	0.853378	−	0.521292i	$-0.174550\pi$
$294$	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	0.724006	−	0.689794i	$-0.242299\pi$
$311$	−4.15091	−	7.18958i	−0.235376	−	0.407684i	−0.959382	+	0.282110i	$0.908966\pi$
$312$	9.99416	−	9.05035i	0.565808	−	0.512375i
$313$	−23.0954	−	13.3342i	−1.30543	−	0.753691i	−0.324101	−	0.946023i	$-0.605062\pi$
$313$	−23.0954	−	13.3342i	−1.30543	−	0.753691i	−0.981330	+	0.192332i	$0.938395\pi$
$314$	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	−0.103996	−	0.994578i	$-0.533163\pi$
$317$	14.4097	−	24.9584i	0.809331	−	1.40180i	0.913328	−	0.407225i	$-0.133504\pi$
$318$	−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	0.560431	−	0.828201i	$-0.310635\pi$
$331$	2.24514	+	1.29623i	0.123404	+	0.0712472i	−0.437027	+	0.899448i	$0.643969\pi$
$332$	−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	0.603772	−	0.797157i	$-0.293664\pi$
$347$	−7.23643	−	12.5339i	−0.388472	−	0.672853i	−0.992244	+	0.124304i	$0.960330\pi$
$348$	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	0.915639	−	0.402003i	$-0.131686\pi$
$353$	2.06060	+	3.56907i	0.109675	+	0.189962i	−0.805964	+	0.591965i	$0.798352\pi$
$354$	−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	0.217393	−	0.976084i	$-0.430245\pi$
$359$	−9.83790	−	5.67992i	−0.519225	−	0.299775i	−0.736617	+	0.676310i	$0.763578\pi$
$360$	−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	0.291755	−	0.956493i	$-0.405761\pi$
$367$	24.2527	−	14.0023i	1.26598	−	0.730914i	0.974225	+	0.225580i	$0.0724275\pi$
$368$	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	−0.409737	−	0.912204i	$-0.634379\pi$
$373$	−27.1273	−	15.6619i	−1.40460	−	0.810944i	−0.994860	+	0.101259i	$0.967713\pi$
$374$	−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	$0.265178\pi$
$379$			28.8128i			1.48001i	−0.672600	+	0.740006i	$0.734822\pi$
$380$	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	−0.336325	−	0.941746i	$-0.609184\pi$
$383$	12.6701	−	21.9453i	0.647413	−	1.12135i	0.983738	−	0.179607i	$-0.0574826\pi$
$384$	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	0.916574	−	0.399865i	$-0.130943\pi$
$389$	2.20886	+	3.82586i	0.111994	+	0.193979i	−0.804580	+	0.593844i	$0.797610\pi$
$390$	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	−0.591616	−	0.806220i	$-0.701510\pi$
$397$	8.01775	−	13.8871i	0.402399	−	0.696976i	0.994015	+	0.109244i	$0.0348430\pi$
$398$	−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	0.654226	−	0.756299i	$-0.272994\pi$
$401$	6.53545	+	3.77324i	0.326365	+	0.188427i	−0.327861	+	0.944726i	$0.606328\pi$
$402$	−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	−0.961571	−	0.274556i	$-0.911469\pi$
$409$	−24.3612	+	14.0650i	−1.20458	+	0.695467i	−0.243013	+	0.970023i	$0.578136\pi$
$410$	−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	$0.158614\pi$
$419$			19.5661i			0.955866i	−0.878396	+	0.477933i	$0.841386\pi$
$420$	−24.9114	−	7.90516i	−1.21555	−	0.385732i
$421$		−	26.0983i		−	1.27195i	−0.771708	−	0.635977i	$-0.780597\pi$
$421$		−	26.0983i		−	1.27195i	0.771708	−	0.635977i	$-0.219403\pi$
$422$	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	−0.227953	−	0.973672i	$-0.573203\pi$
$431$	10.4072	−	6.00858i	0.501296	−	0.289423i	0.729248	+	0.684249i	$0.239870\pi$
$432$	−20.7810	+	0.385775i	−0.999828	+	0.0185606i
$433$			35.6343i			1.71247i	0.516583	+	0.856237i	$0.327204\pi$
$433$			35.6343i			1.71247i	−0.516583	+	0.856237i	$0.672796\pi$
$434$	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	0.194240	−	0.980954i	$-0.437776\pi$
$439$	−11.6950	−	6.75210i	−0.558171	−	0.322260i	−0.752411	+	0.658694i	$0.771109\pi$
$440$	−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	0.438565	+	0.898700i	$0.355487\pi$
$443$	−11.7659	+	20.3791i	−0.559014	+	0.968241i	−0.997579	+	0.0695416i	$0.977846\pi$
$444$	−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	$-0.742883\pi$
$449$		−	30.6292i		−	1.44548i	0.691120	−	0.722740i	$-0.257117\pi$
$450$	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	−0.697629	−	0.716459i	$-0.745762\pi$
$457$	5.80736	−	10.0587i	0.271657	−	0.470524i	0.969286	+	0.245935i	$0.0790950\pi$
$458$	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	$-0.745015\pi$
$461$		−	30.8362i		−	1.43618i	0.695948	−	0.718092i	$-0.254985\pi$
$462$	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	−0.369778	−	0.929120i	$-0.620566\pi$
$467$	−29.3749	−	16.9596i	−1.35931	−	0.784797i	−0.989531	+	0.144323i	$0.953900\pi$
$468$	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	−0.914286	−	0.405068i	$-0.867248\pi$
$479$	−17.6827	−	30.6273i	−0.807943	−	1.39940i	0.106344	−	0.994329i	$-0.466086\pi$
$480$	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	0.950652	+	0.310259i	$0.100416\pi$
$487$	16.4191	+	28.4386i	0.744018	+	1.28868i	−0.206634	+	0.978418i	$0.566251\pi$
$488$	−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	0.224962	−	0.974367i	$-0.427774\pi$
$499$	−11.3117	−	6.53084i	−0.506383	−	0.292361i	−0.731346	+	0.682007i	$0.761107\pi$
$500$	−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	0.962484	−	0.271339i	$-0.0874665\pi$
$509$	27.2704	+	15.7446i	1.20874	+	0.697866i	0.246255	+	0.969205i	$0.420800\pi$
$510$	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	0.922981	−	0.384845i	$-0.125745\pi$
$521$	2.92633	+	5.06856i	0.128205	+	0.222058i	−0.794776	+	0.606903i	$0.792412\pi$
$522$	12.4825	+	10.8889i	0.546343	+	0.476594i
$523$	9.81038	−	16.9921i	0.428978	−	0.743012i	−0.567805	−	0.823163i	$-0.692207\pi$
$523$	9.81038	−	16.9921i	0.428978	−	0.743012i	0.996783	+	0.0801516i	$0.0255405\pi$
$524$	−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	0.999494	+	0.0318007i	$0.0101242\pi$
$541$	35.5120	+	20.5029i	1.52678	+	0.881488i	0.527287	+	0.849687i	$0.323209\pi$
$542$	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	$-0.909779\pi$
$547$		−	13.0813i		−	0.559315i	0.960100	−	0.279658i	$-0.0902209\pi$
$548$	−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	0.907898	+	0.419192i	$0.137687\pi$
$557$	19.2814	+	33.3964i	0.816980	+	1.41505i	−0.0909180	+	0.995858i	$0.528980\pi$
$558$	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	−0.691309	−	0.722559i	$-0.742966\pi$
$563$	−9.75701	+	5.63321i	−0.411209	+	0.237411i	0.280100	+	0.959971i	$0.409632\pi$
$564$	−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	0.941760	−	0.336286i	$-0.109171\pi$
$569$	26.7497	+	15.4440i	1.12141	+	0.647445i	0.179648	+	0.983731i	$0.442504\pi$
$570$	23.2866	−	37.2559i	0.975367	−	1.56048i
$571$	6.49082	−	3.74748i	0.271633	−	0.156827i	−0.357997	−	0.933723i	$-0.616540\pi$
$571$	6.49082	−	3.74748i	0.271633	−	0.156827i	0.629629	+	0.776896i	$0.283207\pi$
$572$	−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	−0.0641196	−	0.997942i	$-0.520424\pi$
$577$	18.4495	−	10.6518i	0.768064	−	0.443442i	0.832184	+	0.554500i	$0.187091\pi$
$578$	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	$0.101565\pi$
$587$			15.2002i			0.627381i	−0.949525	+	0.313691i	$0.898435\pi$
$588$	−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	−0.944207	−	0.329353i	$-0.893169\pi$
$593$	−4.55071	+	7.88206i	−0.186875	+	0.323678i	0.757332	+	0.653031i	$0.226503\pi$
$594$	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	−0.537831	+	0.843053i	$0.680756\pi$
$599$	−37.6136	+	21.7162i	−1.53685	+	0.887302i	−0.999021	+	0.0442488i	$0.985911\pi$
$600$	14.6050	+	4.69959i	0.596245	+	0.191860i
$601$			15.5284i			0.633415i	0.948523	+	0.316708i	$0.102577\pi$
$601$			15.5284i			0.633415i	−0.948523	+	0.316708i	$0.897423\pi$
$602$	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	0.520480	−	0.853874i	$-0.325753\pi$
$607$	1.01612	+	0.586656i	0.0412430	+	0.0238116i	−0.479237	+	0.877686i	$0.659086\pi$
$608$	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	0.444974	−	0.895543i	$-0.353213\pi$
$613$	35.7276	−	20.6273i	1.44302	−	0.833131i	0.998050	+	0.0624126i	$0.0198795\pi$
$614$	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	$-0.900192\pi$
$617$		−	15.3232i		−	0.616887i	0.951243	−	0.308444i	$-0.0998081\pi$
$618$	−4.25470	−	0.149110i	−0.171149	−	0.00599810i
$619$	7.95796	+	13.7836i	0.319857	+	0.554009i	0.980458	−	0.196728i	$-0.0630316\pi$
$619$	7.95796	+	13.7836i	0.319857	+	0.554009i	−0.660601	+	0.750738i	$0.729698\pi$
$620$	−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	−0.354691	−	0.934984i	$-0.615414\pi$
$641$	7.03036	−	4.05898i	0.277683	−	0.160320i	0.632374	+	0.774663i	$0.282081\pi$
$642$	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	0.939020	+	0.343863i	$0.111736\pi$
$647$	19.5173	+	33.8049i	0.767304	+	1.32901i	−0.171716	+	0.985147i	$0.554931\pi$
$648$	−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	−0.649149	−	0.760661i	$-0.724875\pi$
$653$	8.53952	−	14.7909i	0.334177	−	0.578812i	0.983326	+	0.181849i	$0.0582083\pi$
$654$	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	−0.830712	−	0.556702i	$-0.812067\pi$
$661$	−23.0740	−	39.9653i	−0.897474	−	1.55447i	−0.0667617	−	0.997769i	$-0.521267\pi$
$662$	−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	0.654903	−	0.755713i	$-0.272709\pi$
$677$	8.53140	+	4.92561i	0.327888	+	0.189306i	−0.327015	+	0.945019i	$0.606043\pi$
$678$	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	0.938012	+	0.346603i	$0.112665\pi$
$683$	20.1018	+	34.8173i	0.769173	+	1.33225i	−0.168839	+	0.985644i	$0.554002\pi$
$684$	−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	0.323979	+	0.946064i	$0.394979\pi$
$691$	−17.2791	+	29.9282i	−0.657326	+	1.13852i	−0.981305	+	0.192458i	$0.938354\pi$
$692$	−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	0.672832	−	0.739796i	$-0.265078\pi$
$709$	9.81381	+	5.66601i	0.368565	+	0.212791i	−0.304266	+	0.952587i	$0.598411\pi$
$710$	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	−0.979945	−	0.199270i	$-0.936143\pi$
$719$	−8.51080	+	14.7411i	−0.317399	+	0.549752i	0.662545	+	0.749022i	$0.269476\pi$
$720$	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	$-0.714718\pi$
$727$		−	42.1153i		−	1.56197i	0.624550	−	0.780985i	$-0.285282\pi$
$728$	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	−0.195382	−	0.980727i	$-0.562595\pi$
$733$	20.3500	−	35.2472i	0.751644	−	1.30189i	0.947026	−	0.321158i	$-0.104072\pi$
$734$	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	−0.633852	−	0.773454i	$-0.718527\pi$
$739$	−7.63741	+	4.40946i	−0.280947	+	0.162205i	0.352905	+	0.935659i	$0.385194\pi$
$740$	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	$-0.903096\pi$
$743$		−	16.3412i		−	0.599502i	0.954017	−	0.299751i	$-0.0969036\pi$
$744$	−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	−0.731091	−	0.682280i	$-0.760989\pi$
$751$	6.17492	−	10.6953i	0.225326	−	0.390276i	0.956417	+	0.292004i	$0.0943219\pi$
$752$	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	$0.176855\pi$
$757$			29.0246i			1.05492i	−0.849581	+	0.527459i	$0.823145\pi$
$758$	−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	−0.435262	−	0.900304i	$-0.643344\pi$
$761$	15.5050	−	26.8554i	0.562055	−	0.973507i	0.997317	−	0.0732037i	$-0.0233223\pi$
$762$	−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	$-0.723065\pi$
$769$		−	42.3916i		−	1.52868i	0.644813	−	0.764340i	\(-0.27693

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)

\(f(q)\)	\(=\)	\(q+(0.174432 + 1.40341i) q^{2} +(0.618109 + 1.61801i) q^{3} +(-1.93915 + 0.489600i) q^{4} +(-2.46958 - 1.42581i) q^{5} +(-2.16291 + 1.14970i) q^{6} +(-1.02032 + 2.44110i) q^{7} +(-1.02536 - 2.63603i) q^{8} +(-2.23588 + 2.00021i) q^{9} +O(q^{10})\)	\(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})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 6 q^{4} - 4 q^{7} - 14 q^{9}+O(q^{10}) \) 48 * q + 6 * q^4 - 4 * q^7 - 14 * q^9	\( 48 q + 6 q^{4} - 4 q^{7} - 14 q^{9} - 30 q^{10} - 18 q^{12} + 4 q^{15} + 6 q^{16} - 36 q^{22} - 12 q^{24} - 8 q^{25} - 10 q^{28} + 22 q^{30} + 48 q^{31} - 42 q^{33} + 52 q^{36} - 8 q^{39} - 18 q^{40} + 12 q^{42} - 8 q^{46} - 36 q^{49} - 48 q^{52} + 60 q^{54} + 4 q^{57} + 30 q^{58} - 32 q^{60} - 6 q^{63} - 60 q^{64} + 54 q^{66} + 42 q^{70} + 42 q^{72} - 36 q^{73} - 68 q^{78} - 56 q^{79} + 42 q^{81} + 48 q^{82} + 48 q^{84} - 132 q^{87} + 6 q^{88} + 48 q^{94} + 90 q^{96}+O(q^{100}) \) 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

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