LMFDB - Embedded newform 168.2.ba.c.5.11

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			5.11
Character	$\chi$	$=$	168.5
Dual form			168.2.ba.c.101.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.174432 - 1.40341i) q^{2} +(1.09218 + 1.34430i) q^{3} +(-1.93915 + 0.489600i) q^{4} +(2.46958 + 1.42581i) q^{5} +(1.69610 - 1.76727i) q^{6} +(-1.02032 + 2.44110i) q^{7} +(1.02536 + 2.63603i) q^{8} +(-0.614290 + 2.93643i) q^{9} +O(q^{10})$	\(q+(-0.174432 - 1.40341i) q^{2} +(1.09218 + 1.34430i) q^{3} +(-1.93915 + 0.489600i) q^{4} +(2.46958 + 1.42581i) q^{5} +(1.69610 - 1.76727i) q^{6} +(-1.02032 + 2.44110i) q^{7} +(1.02536 + 2.63603i) q^{8} +(-0.614290 + 2.93643i) q^{9} +(1.57023 - 3.71455i) q^{10} +(-2.42621 - 4.20231i) q^{11} +(-2.77607 - 2.07207i) 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} +(4.22819 + 0.349896i) q^{18} +(3.14493 - 5.44717i) q^{19} +(-5.48696 - 1.55575i) q^{20} +(-4.39594 + 1.29450i) q^{21} +(-5.47438 + 4.13799i) q^{22} +(-3.15865 - 1.82365i) q^{23} +(-2.42373 + 4.25741i) 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} +(6.70845 - 1.94609i) q^{30} +(-0.858051 + 0.495396i) q^{31} +(-3.27893 - 4.60963i) q^{32} +(2.99932 - 7.85123i) q^{33} +(-3.95689 + 2.99094i) q^{34} +(-6.00030 + 4.57370i) q^{35} +(-0.246481 - 5.99494i) q^{36} +(1.06516 + 0.614970i) q^{37} +(-8.19322 - 3.46348i) q^{38} +(3.00591 + 3.69980i) q^{39} +(-1.22627 + 7.97185i) q^{40} +2.10659 q^{41} +(2.58351 + 5.94352i) q^{42} +5.11768i q^{43} +(6.76223 + 6.96103i) q^{44} +(-5.70384 + 6.37590i) q^{45} +(-2.00837 + 4.75100i) q^{46} +(-5.61268 + 9.72145i) q^{47} +(6.39768 + 2.65888i) q^{48} +(-4.91791 - 4.98138i) q^{49} +(3.53319 - 2.67068i) q^{50} +(2.16791 - 5.67487i) q^{51} +(-5.33694 + 1.34748i) q^{52} +(-1.00417 - 1.73927i) q^{53} +(4.14757 + 6.06611i) 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} +(-3.90134 - 9.07528i) q^{60} +(1.24347 - 2.15376i) q^{61} +(0.844918 + 1.11779i) q^{62} +(-6.54135 - 4.49563i) q^{63} +(-5.89727 + 5.40576i) q^{64} +(6.79681 + 3.92414i) q^{65} +(-11.5417 - 2.83979i) 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} +(-8.37039 + 1.39162i) q^{72} +(0.291019 - 0.168020i) q^{73} +(0.677260 - 1.60213i) q^{74} +(-1.93577 + 5.06722i) q^{75} +(-3.43154 + 12.1026i) q^{76} +(12.7338 - 1.63491i) q^{77} +(4.66803 - 4.86390i) q^{78} +(-2.80082 + 4.85116i) q^{79} +(11.4017 + 0.330420i) q^{80} +(-8.24530 - 3.60764i) q^{81} +(-0.367457 - 2.95643i) q^{82} -0.138115i q^{83} +(7.89058 - 4.66248i) q^{84} -10.0016i q^{85} +(7.18223 - 0.892686i) q^{86} +(4.26417 + 5.24852i) q^{87} +(8.58967 - 10.7044i) q^{88} +(-0.580993 + 1.00631i) q^{89} +(9.94296 + 6.89270i) q^{90} +(-2.80813 + 6.71841i) q^{91} +(7.01795 + 1.98985i) q^{92} +(-1.60311 - 0.612418i) q^{93} +(14.6223 + 6.18119i) q^{94} +(15.5333 - 8.96815i) q^{95} +(2.61555 - 9.44240i) 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
$3$	1.09218	+	1.34430i	0.630570	+	0.776132i
$3$	1.09218	+	1.34430i	0.630570	+	0.776132i
$4$	−1.93915	+	0.489600i	−0.969574	+	0.244800i
$5$	2.46958	+	1.42581i	1.10443	+	0.637643i	0.937381	−	0.348306i	$-0.113243\pi$
$5$	2.46958	+	1.42581i	1.10443	+	0.637643i	0.167049	+	0.985949i	$0.446576\pi$
$6$	1.69610	−	1.76727i	0.692430	−	0.721485i
$7$	−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
$9$	−0.614290	+	2.93643i	−0.204763	+	0.978812i
$10$	1.57023	−	3.71455i	0.496552	−	1.17464i
$11$	−2.42621	−	4.20231i	−0.731529	−	1.26705i	−0.956230	−	0.292617i	$-0.905474\pi$
$11$	−2.42621	−	4.20231i	−0.731529	−	1.26705i	0.224701	−	0.974428i	$-0.427860\pi$
$12$	−2.77607	−	2.07207i	−0.801381	−	0.598154i
$13$	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	$-0.306507\pi$
$17$	−1.75366	−	3.03743i	−0.425326	−	0.736686i	−0.996451	+	0.0841773i	$0.973174\pi$
$18$	4.22819	+	0.349896i	0.996593	+	0.0824713i
$19$	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
$21$	−4.39594	+	1.29450i	−0.959272	+	0.282484i
$22$	−5.47438	+	4.13799i	−1.16714	+	0.882223i
$23$	−3.15865	−	1.82365i	−0.658624	−	0.380257i	0.133128	−	0.991099i	$-0.457498\pi$
$23$	−3.15865	−	1.82365i	−0.658624	−	0.380257i	−0.791753	+	0.610842i	$0.790831\pi$
$24$	−2.42373	+	4.25741i	−0.494743	+	0.869039i
$25$	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	$-0.381922\pi$
$29$	3.90427			0.725005			0.362503	+	0.931983i	$0.381922\pi$
$30$	6.70845	−	1.94609i	1.22479	−	0.355306i
$31$	−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
$33$	2.99932	−	7.85123i	0.522115	−	1.36672i
$34$	−3.95689	+	2.99094i	−0.678600	+	0.512942i
$35$	−6.00030	+	4.57370i	−1.01424	+	0.773097i
$36$	−0.246481	−	5.99494i	−0.0410801	−	0.999156i
$37$	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
$39$	3.00591	+	3.69980i	0.481330	+	0.592442i
$40$	−1.22627	+	7.97185i	−0.193890	+	1.26046i
$41$	2.10659			0.328995			0.164497	−	0.986378i	$-0.447400\pi$
$41$	2.10659			0.328995			0.164497	+	0.986378i	$0.447400\pi$
$42$	2.58351	+	5.94352i	0.398645	+	0.917105i
$43$			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
$45$	−5.70384	+	6.37590i	−0.850279	+	0.950463i
$46$	−2.00837	+	4.75100i	−0.296117	+	0.700497i
$47$	−5.61268	+	9.72145i	−0.818693	+	1.41802i	0.0879518	+	0.996125i	$0.471968\pi$
$47$	−5.61268	+	9.72145i	−0.818693	+	1.41802i	−0.906645	+	0.421894i	$0.861365\pi$
$48$	6.39768	+	2.65888i	0.923426	+	0.383776i
$49$	−4.91791	−	4.98138i	−0.702558	−	0.711626i
$50$	3.53319	−	2.67068i	0.499668	−	0.377691i
$51$	2.16791	−	5.67487i	0.303568	−	0.794641i
$52$	−5.33694	+	1.34748i	−0.740101	+	0.186862i
$53$	−1.00417	−	1.73927i	−0.137933	−	0.238907i	0.788781	−	0.614674i	$-0.210712\pi$
$53$	−1.00417	−	1.73927i	−0.137933	−	0.238907i	−0.926714	+	0.375767i	$0.877379\pi$
$54$	4.14757	+	6.06611i	0.564413	+	0.825492i
$55$		−	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	$-0.688000\pi$
$59$	−0.890996	+	0.514417i	−0.115998	+	0.0669714i	0.440879	+	0.897567i	$0.354667\pi$
$60$	−3.90134	−	9.07528i	−0.503661	−	1.17161i
$61$	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
$63$	−6.54135	−	4.49563i	−0.824133	−	0.566397i
$64$	−5.89727	+	5.40576i	−0.737159	+	0.675720i
$65$	6.79681	+	3.92414i	0.843040	+	0.486729i
$66$	−11.5417	−	2.83979i	−1.42069	−	0.349554i
$67$	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	$-0.803552\pi$
$71$		−	9.75277i		−	1.15744i	0.815526	−	0.578720i	$-0.196448\pi$
$72$	−8.37039	+	1.39162i	−0.986460	+	0.164004i
$73$	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
$75$	−1.93577	+	5.06722i	−0.223524	+	0.585112i
$76$	−3.43154	+	12.1026i	−0.393624	+	1.38827i
$77$	12.7338	−	1.63491i	1.45115	−	0.186316i
$78$	4.66803	−	4.86390i	0.528550	−	0.550728i
$79$	−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
$81$	−8.24530	−	3.60764i	−0.916144	−	0.400849i
$82$	−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	$-0.00241282\pi$
$84$	7.89058	−	4.66248i	0.860933	−	0.508718i
$85$		−	10.0016i		−	1.08482i
$86$	7.18223	−	0.892686i	0.774480	−	0.0962609i
$87$	4.26417	+	5.24852i	0.457167	+	0.562700i
$88$	8.58967	−	10.7044i	0.915662	−	1.14110i
$89$	−0.580993	+	1.00631i	−0.0615852	+	0.106669i	−0.895174	−	0.445717i	$-0.852949\pi$
$89$	−0.580993	+	1.00631i	−0.0615852	+	0.106669i	0.833589	+	0.552385i	$0.186282\pi$
$90$	9.94296	+	6.89270i	1.04808	+	0.726554i
$91$	−2.80813	+	6.71841i	−0.294372	+	0.704281i
$92$	7.01795	+	1.98985i	0.731671	+	0.207456i
$93$	−1.60311	−	0.612418i	−0.166234	−	0.0635048i
$94$	14.6223	+	6.18119i	1.50817	+	0.637541i
$95$	15.5333	−	8.96815i	1.59368	−	0.920113i
$96$	2.61555	−	9.44240i	0.266949	−	0.963711i
$97$		−	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	−0.774216	−	0.632922i	$-0.781856\pi$
$101$	−6.16256	+	3.55796i	−0.613198	+	0.354030i	0.161018	+	0.986951i	$0.448522\pi$
$102$	−8.34235	−	2.05260i	−0.826016	−	0.203238i
$103$	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
$105$	−12.7018	−	3.07091i	−1.23957	−	0.299690i
$106$	−2.26576	+	1.71265i	−0.220070	+	0.166347i
$107$	0.532028	−	0.921500i	0.0514331	−	0.0890847i	−0.839163	−	0.543881i	$-0.816954\pi$
$107$	0.532028	−	0.921500i	0.0514331	−	0.0890847i	0.890596	+	0.454796i	$0.150288\pi$
$108$	7.78980	−	6.87889i	0.749573	−	0.661921i
$109$	−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	$0.290334\pi$
$113$			16.8126i			1.58159i	−0.612078	+	0.790797i	$0.709666\pi$
$114$	−4.29251	−	14.7969i	−0.402030	−	1.38586i
$115$	−5.20036	−	9.00729i	−0.484936	−	0.839934i
$116$	−7.57096	+	1.91153i	−0.702946	+	0.177481i
$117$	−1.69066	+	8.08169i	−0.156301	+	0.747152i
$118$	0.877358	+	1.16071i	0.0807674	+	0.106852i
$119$	9.20396	−	1.18172i	0.843726	−	0.108328i
$120$	−12.0559	+	7.05821i	−1.10055	+	0.644324i
$121$	−6.27296	+	10.8651i	−0.570269	+	0.987735i
$122$	−3.23952	−	1.36943i	−0.293293	−	0.123982i
$123$	2.30078	+	2.83190i	0.207454	+	0.255343i
$124$	1.42134	−	1.38075i	0.127640	−	0.123995i
$125$		−	5.32750i		−	0.476506i
$126$	−5.16822	+	9.96441i	−0.460422	+	0.887700i
$127$	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
$129$	−6.87971	+	5.58943i	−0.605724	+	0.492122i
$130$	4.32162	−	10.2232i	0.379031	−	0.896637i
$131$	−8.73260	−	5.04177i	−0.762971	−	0.440502i	0.0673904	−	0.997727i	$-0.478533\pi$
$131$	−8.73260	−	5.04177i	−0.762971	−	0.440502i	−0.830361	+	0.557225i	$0.811866\pi$
$132$	−1.97216	+	16.6932i	−0.171655	+	1.45295i
$133$	10.0883	+	13.2349i	0.874763	+	1.14761i
$134$	−4.95082	−	6.54971i	−0.427685	−	0.565809i
$135$	−14.8007	−	0.704060i	−1.27385	−	0.0605958i
$136$	6.20862	−	7.73717i	0.532384	−	0.663457i
$137$	−17.0704	+	9.85557i	−1.45842	+	0.842019i	−0.998934	−	0.0461669i	$-0.985299\pi$
$137$	−17.0704	+	9.85557i	−1.45842	+	0.842019i	−0.459485	+	0.888185i	$0.651966\pi$
$138$	−8.58027	+	2.48909i	−0.730401	+	0.211886i
$139$	−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
$144$	3.41308	+	11.5044i	0.284424	+	0.958699i
$145$	9.64192	+	5.56676i	0.800718	+	0.462295i
$146$	−0.286564	−	0.379112i	−0.0237162	−	0.0313755i
$147$	1.32524	−	12.0517i	0.109304	−	0.994008i
$148$	−2.36659	−	0.671015i	−0.194532	−	0.0551571i
$149$	−5.49834	+	9.52340i	−0.450441	+	0.780187i	−0.998413	−	0.0563094i	$-0.982067\pi$
$149$	−5.49834	+	9.52340i	−0.450441	+	0.780187i	0.547972	+	0.836497i	$0.315400\pi$
$150$	7.44907	+	1.83281i	0.608214	+	0.149648i
$151$	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
$156$	−7.64032	−	5.70276i	−0.611715	−	0.456587i
$157$	−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
$159$	1.24137	−	3.24949i	0.0984470	−	0.257702i
$160$	−1.52510	−	16.0590i	−0.120570	−	1.26957i
$161$	7.67452	−	5.84987i	0.604837	−	0.461035i
$162$	−3.62478	+	12.2009i	−0.284790	+	0.958590i
$163$	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
$165$	18.6014	−	15.1128i	1.44812	−	1.17653i
$166$	−0.193832	+	0.0240916i	−0.0150443	+	0.00186987i
$167$	7.75061			0.599761			0.299880	−	0.953977i	$-0.403053\pi$
$167$	7.75061			0.599761			0.299880	+	0.953977i	$0.403053\pi$
$168$	−7.91976	−	10.2605i	−0.611023	−	0.791613i
$169$	−5.42533			−0.417333
$170$	−14.0364	+	1.74459i	−1.07654	+	0.133804i
$171$	14.0634	+	12.5810i	1.07545	+	0.962094i
$172$	−2.50562	−	9.92394i	−0.191052	−	0.756693i
$173$	−0.880487	−	0.508349i	−0.0669422	−	0.0386491i	0.466155	−	0.884703i	$-0.345639\pi$
$173$	−0.880487	−	0.508349i	−0.0669422	−	0.0386491i	−0.533098	+	0.846054i	$0.678972\pi$
$174$	6.62204	−	6.89990i	0.502016	−	0.523080i
$175$	−8.21842	+	1.05518i	−0.621254	+	0.0797642i
$176$	−16.5211	−	10.1877i	−1.24532	−	0.767925i
$177$	−1.66466	−	0.635932i	−0.125123	−	0.0477996i
$178$	1.51361	+	0.639843i	0.113450	+	0.0479582i
$179$	10.8103	+	18.7240i	0.808002	+	1.39950i	0.914246	+	0.405160i	$0.132784\pi$
$179$	10.8103	+	18.7240i	0.808002	+	1.39950i	−0.106244	+	0.994340i	$0.533883\pi$
$180$	7.93895	−	15.1564i	0.591734	−	1.12969i
$181$	−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
$186$	−0.579844	+	2.35665i	−0.0425162	+	0.172798i
$187$	−8.50950	+	14.7389i	−0.622276	+	1.07781i
$188$	6.12419	−	21.5993i	0.446652	−	1.57529i
$189$	−1.10084	−	13.7036i	−0.0800744	−	0.996789i
$190$	−15.2955	−	20.2353i	−1.10966	−	1.46803i
$191$	−7.70657	−	4.44939i	−0.557628	−	0.321947i	0.194565	−	0.980890i	$-0.437671\pi$
$191$	−7.70657	−	4.44939i	−0.557628	−	0.321947i	−0.752193	+	0.658943i	$0.771004\pi$
$192$	−13.7078	−	2.02365i	−0.989278	−	0.146044i
$193$	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	$-0.468836\pi$
$197$	2.74394			0.195497			0.0977487	+	0.995211i	$0.468836\pi$
$198$	−8.78808	−	18.6171i	−0.624542	−	1.32306i
$199$	−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
$201$	9.39344	+	3.58848i	0.662562	+	0.253112i
$202$	6.06823	+	8.02801i	0.426959	+	0.564849i
$203$	−3.98360	+	9.53071i	−0.279594	+	0.668925i
$204$	−1.42548	+	12.0658i	−0.0998035	+	0.844776i
$205$	5.20240	+	3.00361i	0.363352	+	0.209781i
$206$	0.957044	−	2.26399i	0.0666804	−	0.157740i
$207$	7.29535	−	8.15492i	0.507062	−	0.566806i
$208$	9.68939	−	5.22594i	0.671838	−	0.362354i
$209$	−30.5210			−2.11118
$210$	−2.09415	+	18.3616i	−0.144510	+	1.26707i
$211$		−	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
$213$	13.1107	−	10.6518i	0.898328	−	0.729847i
$214$	−1.38605	−	0.585917i	−0.0947484	−	0.0400525i
$215$	−7.29686	+	12.6385i	−0.497642	+	0.861941i
$216$	−11.0127	−	9.73242i	−0.749321	−	0.662207i
$217$	−0.333826	−	2.60005i	−0.0226616	−	0.176503i
$218$	7.73845	+	10.2376i	0.524114	+	0.693380i
$219$	0.543714	+	0.207709i	0.0367408	+	0.0140357i
$220$	6.77473	+	26.8325i	0.456752	+	1.80905i
$221$	−4.82645	−	8.35966i	−0.324662	−	0.562332i
$222$	2.89343	−	0.839371i	0.194195	−	0.0563349i
$223$			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	0.254497	−	0.967073i	$-0.418090\pi$
$227$	18.3699	−	10.6059i	1.21926	−	0.703938i	0.964759	+	0.263136i	$0.0847567\pi$
$228$	−20.0174	+	8.60521i	−1.32569	+	0.569894i
$229$	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
$231$	16.1054	+	15.3324i	1.05965	+	1.00880i
$232$	4.00329	+	10.2918i	0.262829	+	0.675688i
$233$	22.5624	+	13.0264i	1.47811	+	0.853389i	0.999694	−	0.0247423i	$-0.00787651\pi$
$233$	22.5624	+	13.0264i	1.47811	+	0.853389i	0.478420	+	0.878131i	$0.341210\pi$
$234$	11.6369	+	0.962988i	0.760726	+	0.0629525i
$235$	−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	$-0.0868157\pi$
$240$	12.0085	+	15.6882i	0.775147	+	1.01267i
$241$	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
$243$	−4.15558	−	15.0244i	−0.266581	−	0.963813i
$244$	−1.35680	+	4.78527i	−0.0868601	+	0.306345i
$245$	−5.04265	−	19.3139i	−0.322163	−	1.23392i
$246$	3.57300	−	3.72292i	0.227806	−	0.237365i
$247$	8.65550	−	14.9918i	0.550736	−	0.953904i
$248$	−2.18569	−	1.75389i	−0.138791	−	0.111372i
$249$	0.185668	−	0.150846i	0.0117662	−	0.00955947i
$250$	−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	$-0.0855378\pi$
$252$	14.8857	+	5.51505i	0.937711	+	0.347415i
$253$			17.6982i			1.11268i
$254$	−2.72760	−	21.9453i	−0.171145	−	1.37697i
$255$	13.4451	−	10.9235i	0.841967	−	0.684057i
$256$	8.78901	−	13.3699i	0.549313	−	0.835616i
$257$	15.1284	−	26.2032i	0.943685	−	1.63451i	0.185321	−	0.982678i	$-0.440668\pi$
$257$	15.1284	−	26.2032i	0.943685	−	1.63451i	0.758364	−	0.651832i	$-0.225999\pi$
$258$	9.04432	+	8.68011i	0.563075	+	0.540400i
$259$	−2.58800	+	1.97269i	−0.160810	+	0.122577i
$260$	−15.1013	−	4.28176i	−0.936541	−	0.265544i
$261$	−2.39836	+	11.4646i	−0.148454	+	0.709644i
$262$	−5.55245	+	13.1349i	−0.343032	+	0.811478i
$263$	−20.9078	+	12.0711i	−1.28923	+	0.744338i	−0.978517	−	0.206166i	$-0.933901\pi$
$263$	−20.9078	+	12.0711i	−1.28923	+	0.744338i	−0.310714	+	0.950504i	$0.600568\pi$
$264$	23.7714	−	0.144056i	1.46303	−	0.00886604i
$265$		−	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	$-0.456710\pi$
$269$	17.4083	−	10.0507i	1.06140	−	0.612800i	0.925819	+	0.377966i	$0.123377\pi$
$270$	1.59363	+	20.8944i	0.0969853	+	1.27159i
$271$	−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
$273$	−12.0985	+	3.56274i	−0.732237	+	0.215627i
$274$	16.8091	+	22.2377i	1.01547	+	1.34343i
$275$	7.59832	−	13.1607i	0.458196	−	0.793618i
$276$	4.98990	+	11.6075i	0.300357	+	0.698689i
$277$	−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	$-0.848276\pi$
$281$		−	15.3821i		−	0.917618i	0.888535	−	0.458809i	$-0.151724\pi$
$282$	7.66074	+	26.4077i	0.456190	+	1.57255i
$283$	−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
$285$	29.0210	+	11.0866i	1.71906	+	0.656713i
$286$	−15.0667	+	11.3886i	−0.890910	+	0.673424i
$287$	−2.14939	+	5.14240i	−0.126875	+	0.303546i
$288$	15.5501	−	6.79670i	0.916297	−	0.400500i
$289$	2.34933	−	4.06916i	0.138196	−	0.239362i
$290$	6.13062	−	14.5026i	0.360003	−	0.851624i
$291$	14.9154	−	12.1181i	0.874359	−	0.710374i
$292$	−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	$0.825450\pi$
$294$	−17.1447	+	0.242334i	−0.999900	+	0.0141332i
$295$	−2.93385			−0.170815
$296$	−0.528904	+	3.43835i	−0.0307419	+	0.199850i
$297$	21.2122	+	13.6302i	1.23086	+	0.790907i
$298$	14.3244	+	6.05527i	0.829788	+	0.350772i
$299$	−8.69327	−	5.01906i	−0.502745	−	0.290260i
$300$	1.27284	−	10.7738i	0.0734875	−	0.622028i
$301$	−12.4928	−	5.22166i	−0.720071	−	0.300971i
$302$	9.40283	−	7.10744i	0.541072	−	0.408987i
$303$	−11.5136	−	4.39841i	−0.661438	−	0.252682i
$304$	0.728810	−	25.1489i	0.0418001	−	1.44239i
$305$	6.14172	−	3.54592i	0.351674	−	0.203039i
$306$	−6.35203	−	13.4564i	−0.363121	−	0.769253i
$307$	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	$-0.0910344\pi$
$311$	4.15091	+	7.18958i	0.235376	+	0.407684i	−0.724006	+	0.689794i	$0.757701\pi$
$312$	−6.67063	+	11.7173i	−0.377650	+	0.663360i
$313$	−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
$315$	−9.74446	−	20.4291i	−0.549038	−	1.15105i
$316$	3.05607	−	10.7784i	0.171917	−	0.606332i
$317$	−14.4097	+	24.9584i	−0.809331	+	1.40180i	0.103996	+	0.994578i	$0.466837\pi$
$317$	−14.4097	+	24.9584i	−0.809331	+	1.40180i	−0.913328	+	0.407225i	$0.866496\pi$
$318$	−4.77692	−	1.17534i	−0.267876	−	0.0659099i
$319$	−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
$324$	17.7551	+	2.95885i	0.986397	+	0.164381i
$325$	4.30964	+	7.46452i	0.239056	+	0.414057i
$326$	6.39776	−	15.1346i	0.354339	−	0.838227i
$327$	−14.6826	−	5.60903i	−0.811948	−	0.310180i
$328$	2.16002	+	5.55304i	0.119267	+	0.306615i
$329$	−18.0043	−	23.6200i	−0.992608	−	1.30222i
$330$	−24.4542	−	23.4694i	−1.34616	−	1.29195i
$331$	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
$333$	−2.46013	+	2.75000i	−0.134815	+	0.150699i
$334$	−1.35195	−	10.8773i	−0.0739756	−	0.595181i
$335$	16.5553			0.904513
$336$	−13.0182	+	12.9045i	−0.710203	+	0.703996i
$337$	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
$339$	−22.6012	+	18.3623i	−1.22753	+	0.997306i
$340$	4.89678	+	19.3945i	0.265565	+	1.05182i
$341$	4.16362	+	2.40387i	0.225473	+	0.130177i
$342$	15.2033	−	21.9313i	0.822100	−	1.18591i
$343$	17.1779	−	6.92250i	0.927517	−	0.373780i
$344$	−13.4903	+	5.24747i	−0.727351	+	0.282925i
$345$	6.42878	−	16.8284i	0.346114	−	0.906012i
$346$	−0.559840	+	1.32436i	−0.0300972	+	0.0711981i
$347$	7.23643	+	12.5339i	0.388472	+	0.672853i	0.992244	−	0.124304i	$-0.0396697\pi$
$347$	7.23643	+	12.5339i	0.388472	+	0.672853i	−0.603772	+	0.797157i	$0.706336\pi$
$348$	−10.8385	−	8.08991i	−0.581006	−	0.433665i
$349$	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	$-0.201648\pi$
$353$	−2.06060	−	3.56907i	−0.109675	−	0.189962i	−0.915639	+	0.402003i	$0.868314\pi$
$354$	−0.602107	+	2.44713i	−0.0320016	+	0.130064i
$355$	13.9056	−	24.0852i	0.738034	−	1.27831i
$356$	0.633942	−	2.23584i	0.0335989	−	0.118499i
$357$	11.6410	+	11.0822i	0.616105	+	0.586535i
$358$	24.3919	−	18.4374i	1.28915	−	0.974449i
$359$	9.83790	+	5.67992i	0.519225	+	0.299775i	0.736617	−	0.676310i	$-0.236422\pi$
$359$	9.83790	+	5.67992i	0.519225	+	0.299775i	−0.217393	+	0.976084i	$0.569755\pi$
$360$	−22.6555	−	8.49788i	−1.19405	−	0.447878i
$361$	−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
$366$	−1.69722	−	5.85055i	−0.0887149	−	0.305813i
$367$	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
$369$	−1.29406	+	6.18587i	−0.0673660	+	0.322024i
$370$	3.95689	−	2.99094i	0.205709	−	0.155492i
$371$	5.27029	−	0.676664i	0.273620	−	0.0351306i
$372$	3.40850	+	0.402687i	0.176723	+	0.0208783i
$373$	−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
$375$	7.16176	−	5.81858i	0.369832	−	0.300470i
$376$	−31.3810	−	4.82718i	−1.61835	−	0.248943i
$377$	10.7454			0.553416
$378$	−19.0398	+	3.93528i	−0.979301	+	0.202409i
$379$			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
$381$	17.0785	+	21.0209i	0.874956	+	1.07693i
$382$	−4.90007	+	11.5916i	−0.250710	+	0.593080i
$383$	−12.6701	+	21.9453i	−0.647413	+	1.12135i	0.336325	+	0.941746i	$0.390816\pi$
$383$	−12.6701	+	21.9453i	−0.647413	+	1.12135i	−0.983738	+	0.179607i	$0.942517\pi$
$384$	−0.448937	+	19.5908i	−0.0229097	+	0.999738i
$385$	33.7781	+	14.1184i	1.72149	+	0.719540i
$386$	16.8274	−	12.7196i	0.856493	−	0.647409i
$387$	−15.0277	−	3.14374i	−0.763903	−	0.159805i
$388$	5.43227	+	21.5155i	0.275782	+	1.09228i
$389$	−2.20886	−	3.82586i	−0.111994	−	0.193979i	0.804580	−	0.593844i	$-0.202390\pi$
$389$	−2.20886	−	3.82586i	−0.111994	−	0.193979i	−0.916574	+	0.399865i	$0.869057\pi$
$390$	18.4631	−	5.35605i	0.934914	−	0.271214i
$391$			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
$396$	−24.5946	+	15.5807i	−1.23592	+	0.782962i
$397$	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
$399$	−6.77352	+	28.0165i	−0.339100	+	1.40258i
$400$	10.6628	+	6.57517i	0.533139	+	0.328759i
$401$	−6.53545	−	3.77324i	−0.326365	−	0.188427i	0.327861	−	0.944726i	$-0.393672\pi$
$401$	−6.53545	−	3.77324i	−0.326365	−	0.188427i	−0.654226	+	0.756299i	$0.727006\pi$
$402$	3.39761	−	13.8088i	0.169457	−	0.688723i
$403$	−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
$408$	17.1820	−	0.104124i	0.850636	−	0.00515490i
$409$	−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
$411$	−31.8927	−	12.1836i	−1.57315	−	0.600975i
$412$	−3.34425	−	0.948219i	−0.164760	−	0.0467154i
$413$	−0.346643	−	2.69988i	−0.0170572	−	0.132852i
$414$	−12.7173	−	8.81592i	−0.625020	−	0.433279i
$415$	0.196926	−	0.341085i	0.00966670	−	0.0167432i
$416$	−9.02429	−	12.6867i	−0.442452	−	0.622015i
$417$	−0.122140	−	0.150336i	−0.00598125	−	0.00736197i
$418$	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	$-0.158614\pi$
$420$	26.1342	−	0.263882i	1.27522	−	0.0128761i
$421$		−	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
$423$	−25.0986	−	22.4531i	−1.22033	−	1.09170i
$424$	3.55512	−	4.43039i	0.172652	−	0.215159i
$425$	5.49207	−	9.51254i	0.266404	−	0.461426i
$426$	−17.2358	−	16.5417i	−0.835076	−	0.801447i
$427$	3.98880	+	5.23296i	0.193032	+	0.253241i
$428$	−0.580514	+	2.04740i	−0.0280602	+	0.0989650i
$429$	8.25477	−	21.6082i	0.398544	−	1.04326i
$430$	19.0099	+	8.03596i	0.916739	+	0.387528i
$431$	−10.4072	+	6.00858i	−0.501296	+	0.289423i	−0.729248	−	0.684249i	$-0.760130\pi$
$431$	−10.4072	+	6.00858i	−0.501296	+	0.289423i	0.227953	+	0.973672i	$0.426797\pi$
$432$	−11.7377	+	17.1531i	−0.564728	+	0.825277i
$433$			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
$438$	0.196661	−	0.799287i	0.00939683	−	0.0381914i
$439$	−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
$441$	17.6485	−	11.3811i	0.840406	−	0.541957i
$442$	−10.8902	+	8.23170i	−0.517993	+	0.391542i
$443$	11.7659	−	20.3791i	0.559014	−	0.968241i	−0.438565	−	0.898700i	$-0.644513\pi$
$443$	11.7659	−	20.3791i	0.559014	−	0.968241i	0.997579	−	0.0695416i	$-0.0221536\pi$
$444$	−1.68269	−	3.91428i	−0.0798571	−	0.185763i
$445$	−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	$0.742883\pi$
$450$	5.67187	+	12.0155i	0.267374	+	0.566418i
$451$	−5.11103	−	8.85257i	−0.240669	−	0.416851i
$452$	−8.23144	−	32.6021i	−0.387174	−	1.53347i
$453$	−5.15165	+	13.4853i	−0.242046	+	0.633596i
$454$	−18.0888	−	23.9307i	−0.848948	−	1.12312i
$455$	−16.5141	+	12.5878i	−0.774193	+	0.590125i
$456$	15.5684	+	26.5917i	0.729055	+	1.24527i
$457$	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
$459$	15.3322	+	9.85194i	0.715644	+	0.459849i
$460$	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	$0.745015\pi$
$462$	18.7084	−	25.2770i	0.870394	−	1.17599i
$463$	−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
$465$	−3.08581	−	3.79815i	−0.143101	−	0.176135i
$466$	14.3459	−	33.9367i	0.664560	−	1.57209i
$467$	29.3749	+	16.9596i	1.35931	+	0.784797i	0.989531	−	0.144323i	$-0.0461004\pi$
$467$	29.3749	+	16.9596i	1.35931	+	0.784797i	0.369778	+	0.929120i	$0.379434\pi$
$468$	−0.678367	−	16.4993i	−0.0313575	−	0.762682i
$469$	1.95606	+	15.2350i	0.0903225	+	0.703489i
$470$	27.2976	+	36.1135i	1.25914	+	1.66579i
$471$	6.70275	−	17.5456i	0.308846	−	0.808458i
$472$	−2.26961	−	1.82123i	−0.104467	−	0.0838287i
$473$	21.5061	−	12.4166i	0.988852	−	0.570914i
$474$	3.82283	+	13.1779i	0.175589	+	0.605279i
$475$	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	$0.132752\pi$
$479$	17.6827	+	30.6273i	0.807943	+	1.39940i	−0.106344	+	0.994329i	$0.533914\pi$
$480$	19.9224	−	19.5895i	0.909329	−	0.894133i
$481$	2.93154	+	1.69253i	0.133667	+	0.0771726i
$482$	−6.14559	−	8.13034i	−0.279924	−	0.370327i
$483$	16.2459	+	3.92776i	0.739216	+	0.178719i
$484$	6.84464	−	24.1402i	0.311120	−	1.09728i
$485$	15.8198	−	27.4008i	0.718342	−	1.24421i
$486$	−20.3605	+	8.45273i	−0.923573	+	0.383424i
$487$	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	$-0.330248\pi$
$491$	22.5295			1.01674			0.508371	+	0.861138i	$0.330248\pi$
$492$	−5.84804	−	4.36500i	−0.263650	−	0.196789i
$493$	−6.84678	−	11.8590i	−0.308363	−	0.534101i
$494$	−22.5495	−	9.53222i	−1.01455	−	0.428875i
$495$	40.6322	+	8.50009i	1.82628	+	0.382051i
$496$	−2.08018	+	3.37336i	−0.0934027	+	0.151468i
$497$	23.8075	+	9.95092i	1.06791	+	0.446360i
$498$	−0.244086	−	0.234256i	−0.0109377	−	0.0104973i
$499$	−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
$501$	8.46506	+	10.4192i	0.378191	+	0.465494i
$502$	−11.8065	+	1.46744i	−0.526950	+	0.0654951i
$503$	2.77607			0.123779			0.0618894	−	0.998083i	$-0.480287\pi$
$503$	2.77607			0.123779			0.0618894	+	0.998083i	$0.480287\pi$
$504$	5.14336	−	21.8528i	0.229104	−	0.973402i
$505$	−20.2919			−0.902978
$506$	24.8379	−	3.08712i	1.10418	−	0.137239i
$507$	−5.92543	−	7.29328i	−0.263158	−	0.323906i
$508$	−30.3225	+	7.65590i	−1.34535	+	0.339676i
$509$	−27.2704	−	15.7446i	−1.20874	−	0.697866i	−0.246255	−	0.969205i	$-0.579200\pi$
$509$	−27.2704	−	15.7446i	−1.20874	−	0.697866i	−0.962484	+	0.271339i	$0.912534\pi$
$510$	−17.6755	−	16.9637i	−0.782684	−	0.751165i
$511$	0.113221	+	0.881838i	0.00500861	+	0.0390102i
$512$	−20.2965	−	10.0025i	−0.896989	−	0.442052i
$513$	−1.55295	+	32.6461i	−0.0685645	+	1.44136i
$514$	−39.4128	−	16.6608i	−1.73842	−	0.734875i
$515$	2.47812	+	4.29223i	0.109199	+	0.189138i
$516$	10.6042	−	14.2070i	0.466823	−	0.625429i
$517$	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	$-0.207588\pi$
$521$	−2.92633	−	5.06856i	−0.128205	−	0.222058i	−0.922981	+	0.384845i	$0.874255\pi$
$522$	16.5080	+	1.36609i	0.722536	+	0.0597922i
$523$	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
$525$	−10.3945	−	9.89558i	−0.453652	−	0.431879i
$526$	20.5878	+	27.2367i	0.897670	+	1.18758i
$527$	3.00947	+	1.73752i	0.131094	+	0.0756874i
$528$	−4.34866	−	33.3361i	−0.189251	−	1.45077i
$529$	−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
$534$	0.792997	+	2.73358i	0.0343163	+	0.118293i
$535$	2.62777	−	1.51715i	0.113609	−	0.0655919i
$536$	12.8071	+	10.2769i	0.553183	+	0.443896i
$537$	−13.3639	+	34.9823i	−0.576696	+	1.50960i
$538$	−17.1418	−	22.6779i	−0.739036	−	0.977712i
$539$	−9.00148	+	32.7525i	−0.387721	+	1.41075i
$540$	29.0455	−	5.88117i	1.24992	−	0.253085i
$541$	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
$543$	−10.2343	−	12.5968i	−0.439194	−	0.540579i
$544$	−8.25130	+	18.0432i	−0.353772	+	0.773598i
$545$	−25.8771			−1.10845
$546$	7.11038	+	16.3578i	0.304296	+	0.700050i
$547$		−	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
$549$	5.56053	+	4.97442i	0.237317	+	0.212303i
$550$	−19.7953	−	8.36795i	−0.844073	−	0.356811i
$551$	12.2787	−	21.2673i	0.523088	−	0.906016i
$552$	15.4197	−	9.02762i	0.656308	−	0.384241i
$553$	−8.98443	−	11.7868i	−0.382057	−	0.501225i
$554$	11.2326	+	14.8603i	0.477229	+	0.631353i
$555$	−2.16791	+	5.67487i	−0.0920227	+	0.240885i
$556$	0.216859	−	0.0547529i	0.00919685	−	0.00232204i
$557$	−19.2814	−	33.3964i	−0.816980	−	1.41505i	−0.907898	−	0.419192i	$-0.862313\pi$
$557$	−19.2814	−	33.3964i	−0.816980	−	1.41505i	0.0909180	−	0.995858i	$-0.471020\pi$
$558$	−3.80134	+	1.79440i	−0.160924	+	0.0759630i
$559$			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	$-0.590368\pi$
$563$	9.75701	−	5.63321i	0.411209	−	0.237411i	0.691309	+	0.722559i	$0.257034\pi$
$564$	35.7246	−	15.3575i	1.50428	−	0.646669i
$565$	−23.9716	+	41.5200i	−1.00849	+	1.74676i
$566$	−10.4894	+	7.92875i	−0.440902	+	0.333270i
$567$	17.2194	−	16.4466i	0.723148	−	0.690693i
$568$	25.7086	−	10.0001i	1.07871	−	0.419595i
$569$	−26.7497	−	15.4440i	−1.12141	−	0.647445i	−0.179648	−	0.983731i	$-0.557496\pi$
$569$	−26.7497	−	15.4440i	−1.12141	−	0.647445i	−0.941760	+	0.336286i	$0.890829\pi$
$570$	10.4969	−	42.6624i	0.439667	−	1.78693i
$571$	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
$576$	−12.2510	−	20.6376i	−0.510459	−	0.859902i
$577$	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
$579$	−9.21946	+	24.1335i	−0.383148	+	1.00295i
$580$	−21.4226	−	6.07409i	−0.889524	−	0.252213i
$581$	0.337151	+	0.140921i	0.0139874	+	0.00584637i
$582$	−19.6084	−	18.8188i	−0.812795	−	0.780064i
$583$	−4.87263	+	8.43964i	−0.201804	+	0.349534i
$584$	0.741304	+	0.594852i	0.0306754	+	0.0246152i
$585$	−15.6982	+	17.5478i	−0.649040	+	0.725513i
$586$	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	$-0.101565\pi$
$588$	3.33068	+	24.0189i	0.137355	+	0.990522i
$589$			6.23194i			0.256783i
$590$	0.511756	+	4.11741i	0.0210687	+	0.169511i
$591$	2.99687	+	3.68868i	0.123275	+	0.151732i
$592$	4.91769	+	0.142514i	0.202116	+	0.00585728i
$593$	4.55071	−	7.88206i	0.186875	−	0.323678i	−0.757332	−	0.653031i	$-0.773497\pi$
$593$	4.55071	−	7.88206i	0.186875	−	0.323678i	0.944207	+	0.329353i	$0.106831\pi$
$594$	15.4288	−	32.1470i	0.633052	−	1.31901i
$595$	24.4148	+	10.2048i	1.00091	+	0.418355i
$596$	5.99943	−	21.1593i	0.245746	−	0.866717i
$597$	−37.7075	−	14.4050i	−1.54326	−	0.589557i
$598$	−5.52745	+	13.0758i	−0.226034	+	0.534707i
$599$	37.6136	−	21.7162i	1.53685	−	0.887302i	0.537831	−	0.843053i	$-0.319244\pi$
$599$	37.6136	−	21.7162i	1.53685	−	0.887302i	0.999021	−	0.0442488i	$-0.0140894\pi$
$600$	−15.3422	+	0.0929744i	−0.626342	+	0.00379566i
$601$			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
$606$	−4.16446	+	16.9256i	−0.169170	+	0.687554i
$607$	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
$609$	−17.1629	+	5.05409i	−0.695478	+	0.204802i
$610$	−6.04771	−	8.00086i	−0.244865	−	0.323945i
$611$	−15.4473	+	26.7555i	−0.624930	+	1.08241i
$612$	−17.7770	+	11.2618i	−0.718592	+	0.455230i
$613$	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	$0.0998081\pi$
$617$			15.3232i			0.616887i	−0.951243	+	0.308444i	$0.900192\pi$
$618$	4.08874	−	1.18613i	0.164473	−	0.0477130i
$619$	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
$621$	18.9305	+	0.900509i	0.759655	+	0.0361362i
$622$	9.36592	−	7.07954i	0.375539	−	0.283864i
$623$	−1.86370	−	2.44502i	−0.0746677	−	0.0979575i
$624$	17.6078	+	7.31780i	0.704875	+	0.292946i
$625$	15.4254	−	26.7176i	0.617017	−	1.06871i
$626$	−14.6848	+	34.7384i	−0.586922	+	1.38842i
$627$	−33.3344	−	41.0294i	−1.33125	−	1.63856i
$628$	15.1119	+	15.5562i	0.603031	+	0.620760i
$629$		−	4.31380i		−	0.172002i
$630$	−26.9707	+	17.2390i	−1.07454	+	0.686818i
$631$	−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
$633$	27.4128	−	22.2715i	1.08956	−	0.885215i
$634$	37.5405	+	15.8693i	1.49092	+	0.630251i
$635$	38.6170	+	22.2955i	1.53247	+	0.884770i
$636$	−0.816245	+	6.90902i	−0.0323662	+	0.273960i
$637$	−13.5351	−	13.7098i	−0.536281	−	0.543203i
$638$	−21.3735	+	16.1559i	−0.846184	+	0.639616i
$639$	28.6384	+	5.99103i	1.13292	+	0.237001i
$640$	10.8199	+	30.3940i	0.427693	+	1.20143i
$641$	−7.03036	+	4.05898i	−0.277683	+	0.160320i	−0.632374	−	0.774663i	$-0.717919\pi$
$641$	−7.03036	+	4.05898i	−0.277683	+	0.160320i	0.354691	+	0.934984i	$0.384586\pi$
$642$	−0.726164	−	2.50319i	−0.0286594	−	0.0987932i
$643$	−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	$-0.888264\pi$
$647$	−19.5173	−	33.8049i	−0.767304	−	1.32901i	0.171716	−	0.985147i	$-0.445069\pi$
$648$	1.05544	−	25.4340i	0.0414615	−	0.999140i
$649$	4.32348	+	2.49616i	0.169712	+	0.0979830i
$650$	9.72408	−	7.35027i	0.381410	−	0.288301i
$651$	3.13065	−	3.28848i	0.122700	−	0.128886i
$652$	−22.3561	−	6.33877i	−0.875531	−	0.248245i
$653$	−8.53952	+	14.7909i	−0.334177	+	0.578812i	−0.983326	−	0.181849i	$-0.941792\pi$
$653$	−8.53952	+	14.7909i	−0.334177	+	0.578812i	0.649149	+	0.760661i	$0.275125\pi$
$654$	−5.31069	+	21.5841i	−0.207664	+	0.844007i
$655$	−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	$-0.543473\pi$
$659$	−6.99022			−0.272300			−0.136150	+	0.990688i	$0.543473\pi$
$660$	−28.6717	+	38.4132i	−1.11605	+	1.49523i
$661$	−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
$663$	5.96655	−	15.6184i	0.231722	−	0.606570i
$664$	0.364074	−	0.141617i	0.0141288	−	0.00549582i
$665$	6.04325	+	47.0686i	0.234347	+	1.82524i
$666$	4.28852	+	2.97290i	0.166177	+	0.115198i
$667$	−12.3322	−	7.12002i	−0.477506	−	0.275688i
$668$	−15.0296	+	3.79470i	−0.581512	+	0.146821i
$669$	−15.4145	+	12.5236i	−0.595961	+	0.484189i
$670$	−2.88777	−	23.2340i	−0.111564	−	0.897607i
$671$	−12.0677			−0.465869
$672$	20.3811	+	16.0191i	0.786219	+	0.617948i
$673$	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
$675$	−13.6904	−	8.79702i	−0.526945	−	0.338597i
$676$	10.5205	−	2.65624i	0.404635	−	0.102163i
$677$	−8.53140	−	4.92561i	−0.327888	−	0.189306i	0.327015	−	0.945019i	$-0.393957\pi$
$677$	−8.53140	−	4.92561i	−0.327888	−	0.189306i	−0.654903	+	0.755713i	$0.727291\pi$
$678$	29.7123	+	28.5158i	1.14110	+	1.09514i
$679$	27.0847	+	11.3207i	1.03942	+	0.434450i
$680$	26.3644	−	10.2552i	1.01103	−	0.393270i
$681$	34.3208	+	13.1112i	1.31518	+	0.502422i
$682$	2.64736	−	6.26260i	0.101372	−	0.239807i
$683$	−20.1018	−	34.8173i	−0.769173	−	1.33225i	−0.938012	−	0.346603i	$-0.887335\pi$
$683$	−20.1018	−	34.8173i	−0.769173	−	1.33225i	0.168839	−	0.985644i	$-0.445998\pi$
$684$	−33.4306	−	17.5110i	−1.27825	−	0.669550i
$685$	−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
$690$	−24.7386	−	6.08684i	−0.941784	−	0.231722i
$691$	−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
$693$	−3.02139	+	38.3961i	−0.114773	+	1.45855i
$694$	16.3280	−	12.3420i	0.619801	−	0.468497i
$695$	−0.276178	−	0.159451i	−0.0104760	−	0.00604834i
$696$	−9.46292	+	16.6221i	−0.358691	+	0.630058i
$697$	−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	$-0.310802\pi$
$701$	29.6534			1.11999			0.559997	+	0.828495i	$0.310802\pi$
$702$	11.4150	+	16.6952i	0.430831	+	0.630120i
$703$	6.69969	−	3.86807i	0.252684	−	0.145887i
$704$	37.0247	+	11.6667i	1.39542	+	0.439705i
$705$	−51.7932	−	19.7860i	−1.95064	−	0.745184i
$706$	−4.64945	+	3.51444i	−0.174984	+	0.132268i
$707$	−2.39755	−	18.6736i	−0.0901692	−	0.702295i
$708$	3.53937	+	0.418148i	0.133018	+	0.0157150i
$709$	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
$711$	−12.5246	−	11.2044i	−0.469709	−	0.420199i
$712$	−3.24839	−	0.499683i	−0.121738	−	0.0187264i
$713$	3.61371			0.135335
$714$	13.5224	−	18.2702i	0.506065	−	0.683745i
$715$		−	38.0831i		−	1.42423i
$716$	−30.1301	−	31.0159i	−1.12601	−	1.15912i
$717$	11.1963	−	9.09648i	0.418135	−	0.339714i
$718$	6.25524	−	14.7974i	0.233443	−	0.552235i
$719$	8.51080	−	14.7411i	0.317399	−	0.549752i	−0.662545	−	0.749022i	$-0.730524\pi$
$719$	8.51080	−	14.7411i	0.317399	−	0.549752i	0.979945	+	0.199270i	$0.0638572\pi$
$720$	−7.97421	+	33.2774i	−0.297181	+	1.24018i
$721$	−3.65713	+	2.78763i	−0.136199	+	0.103817i
$722$	−23.1979	+	17.5349i	−0.863335	+	0.652580i
$723$	11.6604	+	4.45448i	0.433653	+	0.165664i
$724$	18.1708	−	4.58779i	0.675311	−	0.170504i
$725$	6.11364	+	10.5891i	0.227055	+	0.393271i
$726$	8.56195	+	29.5143i	0.317764	+	1.09538i
$727$		−	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
$732$	−7.91470	+	3.40242i	−0.292536	+	0.125757i
$733$	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
$735$	20.4563	−	27.8731i	0.754541	−	1.02812i
$736$	1.95064	+	20.5398i	0.0719017	+	0.757107i
$737$	−24.3968	−	14.0855i	−0.898669	−	0.518847i
$738$	8.90707	+	0.737089i	0.327874	+	0.0271326i
$739$	−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	$0.0969036\pi$
$743$			16.3412i			0.599502i	−0.954017	+	0.299751i	$0.903096\pi$
$744$	−0.0294142	−	4.85378i	−0.00107838	−	0.177948i
$745$	−27.1572	+	15.6792i	−0.994962	+	0.574441i
$746$	−17.2483	+	40.8028i	−0.631507	+	1.49390i
$747$	0.405564	+	0.0848424i	0.0148388	+	0.00310422i
$748$	9.28501	−	32.7471i	0.339494	−	1.19735i
$749$	1.70663	+	2.23895i	0.0623590	+	0.0818096i
$750$	−9.41512	−	9.03598i	−0.343792	−	0.329947i
$751$	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
$753$	11.3092	−	9.18817i	0.412130	−	0.334836i
$754$	−1.87434	−	15.0802i	−0.0682593	−	0.549190i
$755$			23.7670i			0.864969i
$756$	8.84397	+	26.0343i	0.321652	+	0.946858i
$757$			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
$759$	−23.7917	+	19.3296i	−0.863583	+	0.701620i
$760$	39.5675	+	31.7506i	1.43527	+	1.15171i
$761$	−15.5050	+	26.8554i	−0.562055	+	0.973507i	0.435262	+	0.900304i	$0.356656\pi$
$761$	−15.5050	+	26.8554i	−0.562055	+	0.973507i	−0.997317	+	0.0732037i	$0.976678\pi$
$762$	26.5220	−	27.6349i	0.960792	−	1.00111i
$763$	−3.05745	−	23.8134i	−0.110687	−	0.862102i
$764$	17.1226	+	4.85489i	0.619474	+	0.175644i
$765$	29.3690	+	6.14387i	1.06184	+	0.222132i
$766$	33.0084	+	13.9535i	1.19264	+	0.504160i
$767$	−2.45221	+	1.41578i	−0.0885442	+	0.0511210i
$768$	27.5723	−	2.78721i	0.994930	−	0.100575i
$769$		−	42.3916i		−	1.52868i	−0.644813	−	0.764340i	$-0.723065\pi$
$769$		−	42.3916i		−	1.52868i	0.644813	−	0.764340i	$-0.276935\pi$

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)

\(f(q)\)	\(=\)	\(q+(-0.174432 - 1.40341i) q^{2} +(1.09218 + 1.34430i) q^{3} +(-1.93915 + 0.489600i) q^{4} +(2.46958 + 1.42581i) q^{5} +(1.69610 - 1.76727i) q^{6} +(-1.02032 + 2.44110i) q^{7} +(1.02536 + 2.63603i) q^{8} +(-0.614290 + 2.93643i) q^{9} +O(q^{10})\)	\(q+(-0.174432 - 1.40341i) q^{2} +(1.09218 + 1.34430i) q^{3} +(-1.93915 + 0.489600i) q^{4} +(2.46958 + 1.42581i) q^{5} +(1.69610 - 1.76727i) q^{6} +(-1.02032 + 2.44110i) q^{7} +(1.02536 + 2.63603i) q^{8} +(-0.614290 + 2.93643i) q^{9} +(1.57023 - 3.71455i) q^{10} +(-2.42621 - 4.20231i) q^{11} +(-2.77607 - 2.07207i) 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} +(4.22819 + 0.349896i) q^{18} +(3.14493 - 5.44717i) q^{19} +(-5.48696 - 1.55575i) q^{20} +(-4.39594 + 1.29450i) q^{21} +(-5.47438 + 4.13799i) q^{22} +(-3.15865 - 1.82365i) q^{23} +(-2.42373 + 4.25741i) 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} +(6.70845 - 1.94609i) q^{30} +(-0.858051 + 0.495396i) q^{31} +(-3.27893 - 4.60963i) q^{32} +(2.99932 - 7.85123i) q^{33} +(-3.95689 + 2.99094i) q^{34} +(-6.00030 + 4.57370i) q^{35} +(-0.246481 - 5.99494i) q^{36} +(1.06516 + 0.614970i) q^{37} +(-8.19322 - 3.46348i) q^{38} +(3.00591 + 3.69980i) q^{39} +(-1.22627 + 7.97185i) q^{40} +2.10659 q^{41} +(2.58351 + 5.94352i) q^{42} +5.11768i q^{43} +(6.76223 + 6.96103i) q^{44} +(-5.70384 + 6.37590i) q^{45} +(-2.00837 + 4.75100i) q^{46} +(-5.61268 + 9.72145i) q^{47} +(6.39768 + 2.65888i) q^{48} +(-4.91791 - 4.98138i) q^{49} +(3.53319 - 2.67068i) q^{50} +(2.16791 - 5.67487i) q^{51} +(-5.33694 + 1.34748i) q^{52} +(-1.00417 - 1.73927i) q^{53} +(4.14757 + 6.06611i) 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} +(-3.90134 - 9.07528i) q^{60} +(1.24347 - 2.15376i) q^{61} +(0.844918 + 1.11779i) q^{62} +(-6.54135 - 4.49563i) q^{63} +(-5.89727 + 5.40576i) q^{64} +(6.79681 + 3.92414i) q^{65} +(-11.5417 - 2.83979i) 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} +(-8.37039 + 1.39162i) q^{72} +(0.291019 - 0.168020i) q^{73} +(0.677260 - 1.60213i) q^{74} +(-1.93577 + 5.06722i) q^{75} +(-3.43154 + 12.1026i) q^{76} +(12.7338 - 1.63491i) q^{77} +(4.66803 - 4.86390i) q^{78} +(-2.80082 + 4.85116i) q^{79} +(11.4017 + 0.330420i) q^{80} +(-8.24530 - 3.60764i) q^{81} +(-0.367457 - 2.95643i) q^{82} -0.138115i q^{83} +(7.89058 - 4.66248i) q^{84} -10.0016i q^{85} +(7.18223 - 0.892686i) q^{86} +(4.26417 + 5.24852i) q^{87} +(8.58967 - 10.7044i) q^{88} +(-0.580993 + 1.00631i) q^{89} +(9.94296 + 6.89270i) q^{90} +(-2.80813 + 6.71841i) q^{91} +(7.01795 + 1.98985i) q^{92} +(-1.60311 - 0.612418i) q^{93} +(14.6223 + 6.18119i) q^{94} +(15.5333 - 8.96815i) q^{95} +(2.61555 - 9.44240i) 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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