LMFDB - Embedded newform 168.2.ba.c.101.11

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			101.11
Character	$\chi$	$=$	168.101
Dual form			168.2.ba.c.5.11

$q$-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 $\left(\mathbb{Z}/168\mathbb{Z}\right)^\times$.

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

Coefficient data

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

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

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

$2$	−0.174432	+	1.40341i	−0.123342	+	0.992364i
$2$	−0.174432	+	1.40341i	−0.123342	+	0.992364i
$3$	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	0.167049	−	0.985949i	$-0.446576\pi$
$5$	2.46958	−	1.42581i	1.10443	−	0.637643i	0.937381	+	0.348306i	$0.113243\pi$
$6$	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	0.224701	+	0.974428i	$0.427860\pi$
$11$	−2.42621	+	4.20231i	−0.731529	+	1.26705i	−0.956230	+	0.292617i	$0.905474\pi$
$12$	−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	−0.996451	−	0.0841773i	$-0.973174\pi$
$17$	−1.75366	+	3.03743i	−0.425326	+	0.736686i	0.571125	+	0.820863i	$0.306507\pi$
$18$	4.22819	−	0.349896i	0.996593	−	0.0824713i
$19$	3.14493	+	5.44717i	0.721496	+	1.24967i	0.960400	+	0.278624i	$0.0898784\pi$
$19$	3.14493	+	5.44717i	0.721496	+	1.24967i	−0.238905	+	0.971043i	$0.576788\pi$
$20$	−5.48696	+	1.55575i	−1.22692	+	0.347877i
$21$	−4.39594	−	1.29450i	−0.959272	−	0.282484i
$22$	−5.47438	−	4.13799i	−1.16714	−	0.882223i
$23$	−3.15865	+	1.82365i	−0.658624	+	0.380257i	−0.791753	−	0.610842i	$-0.790831\pi$
$23$	−3.15865	+	1.82365i	−0.658624	+	0.380257i	0.133128	+	0.991099i	$0.457498\pi$
$24$	−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	0.420962	−	0.907078i	$-0.361693\pi$
$31$	−0.858051	−	0.495396i	−0.154111	−	0.0889758i	−0.575072	+	0.818103i	$0.695026\pi$
$32$	−3.27893	+	4.60963i	−0.579638	+	0.814874i
$33$	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	−0.409883	−	0.912138i	$-0.634430\pi$
$37$	1.06516	−	0.614970i	0.175111	−	0.101100i	0.584994	+	0.811038i	$0.301097\pi$
$38$	−8.19322	+	3.46348i	−1.32912	+	0.561850i
$39$	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	$-0.872399\pi$
$43$		−	5.11768i		−	0.780439i	0.920722	−	0.390220i	$-0.127601\pi$
$44$	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	−0.906645	−	0.421894i	$-0.861365\pi$
$47$	−5.61268	−	9.72145i	−0.818693	−	1.41802i	0.0879518	−	0.996125i	$-0.471968\pi$
$48$	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	−0.926714	−	0.375767i	$-0.877379\pi$
$53$	−1.00417	+	1.73927i	−0.137933	+	0.238907i	0.788781	+	0.614674i	$0.210712\pi$
$54$	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	0.440879	−	0.897567i	$-0.354667\pi$
$59$	−0.890996	−	0.514417i	−0.115998	−	0.0669714i	−0.556876	+	0.830595i	$0.688000\pi$
$60$	−3.90134	+	9.07528i	−0.503661	+	1.17161i
$61$	1.24347	+	2.15376i	0.159211	+	0.275761i	0.934584	−	0.355742i	$-0.115772\pi$
$61$	1.24347	+	2.15376i	0.159211	+	0.275761i	−0.775374	+	0.631503i	$0.782438\pi$
$62$	0.844918	−	1.11779i	0.107305	−	0.141959i
$63$	−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	0.774623	−	0.632423i	$-0.217940\pi$
$67$	5.02777	+	2.90279i	0.614240	+	0.354632i	−0.160383	+	0.987055i	$0.551273\pi$
$68$	4.88774	−	5.03144i	0.592725	−	0.610151i
$69$	−0.998281	+	6.23793i	−0.120179	+	0.750958i
$70$	7.46545	−	7.62311i	0.892292	−	0.911136i
$71$			9.75277i			1.15744i	0.815526	+	0.578720i	$0.196448\pi$
$71$			9.75277i			1.15744i	−0.815526	+	0.578720i	$0.803552\pi$
$72$	−8.37039	−	1.39162i	−0.986460	−	0.164004i
$73$	0.291019	+	0.168020i	0.0340612	+	0.0196652i	0.516934	−	0.856025i	$-0.327073\pi$
$73$	0.291019	+	0.168020i	0.0340612	+	0.0196652i	−0.482873	+	0.875691i	$0.660407\pi$
$74$	0.677260	+	1.60213i	0.0787299	+	0.186244i
$75$	−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	0.664346	−	0.747426i	$-0.268710\pi$
$79$	−2.80082	−	4.85116i	−0.315117	−	0.545798i	−0.979462	+	0.201627i	$0.935377\pi$
$80$	11.4017	−	0.330420i	1.27475	−	0.0369421i
$81$	−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	$0.00241282\pi$
$83$			0.138115i			0.0151600i	−0.999971	+	0.00758002i	$0.997587\pi$
$84$	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	0.833589	−	0.552385i	$-0.186282\pi$
$89$	−0.580993	−	1.00631i	−0.0615852	−	0.106669i	−0.895174	+	0.445717i	$0.852949\pi$
$90$	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	$0.190461\pi$
$97$			11.0953i			1.12656i	−0.826266	+	0.563280i	$0.809539\pi$
$98$	−6.13311	−	7.77078i	−0.619538	−	0.784967i
$99$	13.8302	+	4.54296i	1.38999	+	0.456585i
$100$	−4.36437	+	4.49268i	−0.436437	+	0.449268i
$101$	−6.16256	−	3.55796i	−0.613198	−	0.354030i	0.161018	−	0.986951i	$-0.448522\pi$
$101$	−6.16256	−	3.55796i	−0.613198	−	0.354030i	−0.774216	+	0.632922i	$0.781856\pi$
$102$	−8.34235	+	2.05260i	−0.826016	+	0.203238i
$103$	1.50519	−	0.869021i	0.148311	−	0.0856271i	−0.424008	−	0.905658i	$-0.639377\pi$
$103$	1.50519	−	0.869021i	0.148311	−	0.0856271i	0.572319	+	0.820031i	$0.306044\pi$
$104$	2.82201	−	7.25490i	0.276721	−	0.711402i
$105$	−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	0.890596	−	0.454796i	$-0.150288\pi$
$107$	0.532028	+	0.921500i	0.0514331	+	0.0890847i	−0.839163	+	0.543881i	$0.816954\pi$
$108$	7.78980	+	6.87889i	0.749573	+	0.661921i
$109$	−7.85874	−	4.53725i	−0.752731	−	0.434589i	0.0739489	−	0.997262i	$-0.476440\pi$
$109$	−7.85874	−	4.53725i	−0.752731	−	0.434589i	−0.826680	+	0.562673i	$0.809773\pi$
$110$	−19.4194	−	2.41366i	−1.85157	−	0.230133i
$111$	0.336640	−	2.10355i	0.0319524	−	0.199660i
$112$	1.04308	−	10.5315i	0.0985616	−	0.995131i
$113$		−	16.8126i		−	1.58159i	−0.612078	−	0.790797i	$-0.709666\pi$
$113$		−	16.8126i		−	1.58159i	0.612078	−	0.790797i	$-0.290334\pi$
$114$	−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	−0.830361	−	0.557225i	$-0.811866\pi$
$131$	−8.73260	+	5.04177i	−0.762971	+	0.440502i	0.0673904	+	0.997727i	$0.478533\pi$
$132$	−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	−0.459485	−	0.888185i	$-0.651966\pi$
$137$	−17.0704	−	9.85557i	−1.45842	−	0.842019i	−0.998934	+	0.0461669i	$0.985299\pi$
$138$	−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	0.547972	−	0.836497i	$-0.315400\pi$
$149$	−5.49834	−	9.52340i	−0.450441	−	0.780187i	−0.998413	+	0.0563094i	$0.982067\pi$
$150$	7.44907	−	1.83281i	0.608214	−	0.149648i
$151$	4.16727	−	7.21792i	0.339127	−	0.587386i	−0.645141	−	0.764063i	$-0.723202\pi$
$151$	4.16727	−	7.21792i	0.339127	−	0.587386i	0.984269	+	0.176677i	$0.0565349\pi$
$152$	17.5836	−	2.70479i	1.42622	−	0.219387i
$153$	9.99648	+	3.28365i	0.808168	+	0.265468i
$154$	−4.51563	+	17.5856i	−0.363880	+	1.41708i
$155$	−2.82537			−0.226939
$156$	−7.64032	+	5.70276i	−0.611715	+	0.456587i
$157$	−5.42198	+	9.39114i	−0.432721	+	0.749495i	−0.997107	−	0.0760165i	$-0.975780\pi$
$157$	−5.42198	+	9.39114i	−0.432721	+	0.749495i	0.564386	+	0.825511i	$0.309113\pi$
$158$	7.29674	−	3.08451i	0.580498	−	0.245391i
$159$	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	−0.0511792	−	0.998689i	$-0.516298\pi$
$163$	10.0621	−	5.80934i	0.788122	−	0.455022i	0.839301	+	0.543667i	$0.182965\pi$
$164$	−4.08500	−	1.03139i	−0.318985	−	0.0805379i
$165$	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	−0.533098	−	0.846054i	$-0.678972\pi$
$173$	−0.880487	+	0.508349i	−0.0669422	+	0.0386491i	0.466155	+	0.884703i	$0.345639\pi$
$174$	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	−0.106244	−	0.994340i	$-0.533883\pi$
$179$	10.8103	−	18.7240i	0.808002	−	1.39950i	0.914246	−	0.405160i	$-0.132784\pi$
$180$	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	−0.752193	−	0.658943i	$-0.771004\pi$
$191$	−7.70657	+	4.44939i	−0.557628	+	0.321947i	0.194565	+	0.980890i	$0.437671\pi$
$192$	−13.7078	+	2.02365i	−0.989278	+	0.146044i
$193$	7.45779	−	12.9173i	0.536824	−	0.929806i	−0.462249	−	0.886750i	$-0.652957\pi$
$193$	7.45779	−	12.9173i	0.536824	−	0.929806i	0.999073	−	0.0430556i	$-0.0137093\pi$
$194$	−15.5713	−	1.93538i	−1.11796	−	0.138952i
$195$	2.14811	−	13.4228i	0.153829	−	0.961228i
$196$	11.9754	−	7.25183i	0.855388	−	0.517988i
$197$	2.74394			0.195497			0.0977487	−	0.995211i	$-0.468836\pi$
$197$	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	−0.433535	−	0.901137i	$-0.642734\pi$
$199$	−20.1826	−	11.6525i	−1.43071	−	0.826021i	−0.997175	+	0.0751162i	$0.976067\pi$
$200$	−5.54381	−	6.90869i	−0.392007	−	0.488518i
$201$	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	$0.247672\pi$
$211$			20.3918i			1.40383i	−0.712259	+	0.701916i	$0.752328\pi$
$212$	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	$-0.874570\pi$
$223$		−	11.4666i		−	0.767860i	0.923362	−	0.383930i	$-0.125430\pi$
$224$	14.5981	+	3.30090i	0.975376	+	0.220550i
$225$	−8.92608	−	2.93204i	−0.595072	−	0.195470i
$226$	23.5950	+	2.93265i	1.56952	+	0.195077i
$227$	18.3699	+	10.6059i	1.21926	+	0.703938i	0.964759	−	0.263136i	$-0.0847567\pi$
$227$	18.3699	+	10.6059i	1.21926	+	0.703938i	0.254497	+	0.967073i	$0.418090\pi$
$228$	−20.0174	−	8.60521i	−1.32569	−	0.569894i
$229$	1.13465	+	1.96528i	0.0749800	+	0.129869i	0.901078	−	0.433658i	$-0.142777\pi$
$229$	1.13465	+	1.96528i	0.0749800	+	0.129869i	−0.826098	+	0.563527i	$0.809444\pi$
$230$	−11.7339	−	8.86942i	−0.773707	−	0.584832i
$231$	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	0.478420	−	0.878131i	$-0.341210\pi$
$233$	22.5624	−	13.0264i	1.47811	−	0.853389i	0.999694	+	0.0247423i	$0.00787651\pi$
$234$	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	$0.0868157\pi$
$239$			8.32874i			0.538742i	−0.963037	+	0.269371i	$0.913184\pi$
$240$	12.0085	−	15.6882i	0.775147	−	1.01267i
$241$	6.24112	+	3.60331i	0.402026	+	0.232110i	0.687358	−	0.726319i	$-0.258771\pi$
$241$	6.24112	+	3.60331i	0.402026	+	0.232110i	−0.285332	+	0.958429i	$0.592104\pi$
$242$	16.3424	−	6.90835i	1.05053	−	0.444085i
$243$	−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	$0.0855378\pi$
$251$			8.41270i			0.531005i	−0.964110	+	0.265502i	$0.914462\pi$
$252$	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	0.758364	+	0.651832i	$0.225999\pi$
$257$	15.1284	+	26.2032i	0.943685	+	1.63451i	0.185321	+	0.982678i	$0.440668\pi$
$258$	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	−0.310714	−	0.950504i	$-0.600568\pi$
$263$	−20.9078	−	12.0711i	−1.28923	−	0.744338i	−0.978517	+	0.206166i	$0.933901\pi$
$264$	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	0.925819	−	0.377966i	$-0.123377\pi$
$269$	17.4083	+	10.0507i	1.06140	+	0.612800i	0.135581	+	0.990766i	$0.456710\pi$
$270$	1.59363	−	20.8944i	0.0969853	−	1.27159i
$271$	−1.57903	+	0.911656i	−0.0959195	+	0.0553791i	−0.547192	−	0.837007i	$-0.684303\pi$
$271$	−1.57903	+	0.911656i	−0.0959195	+	0.0553791i	0.451273	+	0.892386i	$0.350970\pi$
$272$	−11.9414	+	7.36366i	−0.724056	+	0.446487i
$273$	−12.0985	−	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	0.116490	−	0.993192i	$-0.462836\pi$
$277$	−11.4072	−	6.58598i	−0.685395	−	0.395713i	−0.801885	+	0.597479i	$0.796169\pi$
$278$	0.0195070	−	0.156947i	0.00116995	−	0.00941303i
$279$	−0.927606	+	2.82393i	−0.0555343	+	0.169064i
$280$	−18.2089	+	11.1273i	−1.08819	+	0.664981i
$281$			15.3821i			0.917618i	0.888535	+	0.458809i	$0.151724\pi$
$281$			15.3821i			0.917618i	−0.888535	+	0.458809i	$0.848276\pi$
$282$	7.66074	−	26.4077i	0.456190	−	1.57255i
$283$	−4.64882	+	8.05200i	−0.276344	+	0.478641i	−0.970473	−	0.241209i	$-0.922456\pi$
$283$	−4.64882	+	8.05200i	−0.276344	+	0.478641i	0.694129	+	0.719850i	$0.255790\pi$
$284$	4.77496	−	18.9121i	0.283342	−	1.12222i
$285$	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	$-0.825450\pi$
$293$		−	17.8462i		−	1.04258i	0.853378	−	0.521292i	$-0.174550\pi$
$294$	−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	−0.724006	−	0.689794i	$-0.757701\pi$
$311$	4.15091	−	7.18958i	0.235376	−	0.407684i	0.959382	+	0.282110i	$0.0910344\pi$
$312$	−6.67063	−	11.7173i	−0.377650	−	0.663360i
$313$	−23.0954	+	13.3342i	−1.30543	+	0.753691i	−0.981330	−	0.192332i	$-0.938395\pi$
$313$	−23.0954	+	13.3342i	−1.30543	+	0.753691i	−0.324101	+	0.946023i	$0.605062\pi$
$314$	−12.2339	−	9.24740i	−0.690399	−	0.521861i
$315$	−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	−0.913328	−	0.407225i	$-0.866496\pi$
$317$	−14.4097	−	24.9584i	−0.809331	−	1.40180i	0.103996	−	0.994578i	$-0.466837\pi$
$318$	−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	−0.437027	−	0.899448i	$-0.643969\pi$
$331$	2.24514	−	1.29623i	0.123404	−	0.0712472i	0.560431	+	0.828201i	$0.310635\pi$
$332$	0.0676209	−	0.267825i	0.00371118	−	0.0146988i
$333$	−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	−0.603772	−	0.797157i	$-0.706336\pi$
$347$	7.23643	−	12.5339i	0.388472	−	0.672853i	0.992244	+	0.124304i	$0.0396697\pi$
$348$	−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	−0.915639	−	0.402003i	$-0.868314\pi$
$353$	−2.06060	+	3.56907i	−0.109675	+	0.189962i	0.805964	+	0.591965i	$0.201648\pi$
$354$	−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	−0.217393	−	0.976084i	$-0.569755\pi$
$359$	9.83790	−	5.67992i	0.519225	−	0.299775i	0.736617	+	0.676310i	$0.236422\pi$
$360$	−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	0.974225	−	0.225580i	$-0.0724275\pi$
$367$	24.2527	+	14.0023i	1.26598	+	0.730914i	0.291755	+	0.956493i	$0.405761\pi$
$368$	−14.5831	+	0.422615i	−0.760194	+	0.0220303i
$369$	−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	−0.994860	−	0.101259i	$-0.967713\pi$
$373$	−27.1273	+	15.6619i	−1.40460	+	0.810944i	−0.409737	+	0.912204i	$0.634379\pi$
$374$	22.1691	−	9.37143i	1.14634	−	0.484585i
$375$	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	$-0.734822\pi$
$379$		−	28.8128i		−	1.48001i	0.672600	−	0.740006i	$-0.265178\pi$
$380$	−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	−0.983738	−	0.179607i	$-0.942517\pi$
$383$	−12.6701	−	21.9453i	−0.647413	−	1.12135i	0.336325	−	0.941746i	$-0.390816\pi$
$384$	−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	−0.916574	−	0.399865i	$-0.869057\pi$
$389$	−2.20886	+	3.82586i	−0.111994	+	0.193979i	0.804580	+	0.593844i	$0.202390\pi$
$390$	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	0.994015	−	0.109244i	$-0.0348430\pi$
$397$	8.01775	+	13.8871i	0.402399	+	0.696976i	−0.591616	+	0.806220i	$0.701510\pi$
$398$	19.8737	−	26.2921i	0.996180	−	1.31790i
$399$	−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	−0.654226	−	0.756299i	$-0.727006\pi$
$401$	−6.53545	+	3.77324i	−0.326365	+	0.188427i	0.327861	+	0.944726i	$0.393672\pi$
$402$	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	−0.243013	−	0.970023i	$-0.578136\pi$
$409$	−24.3612	−	14.0650i	−1.20458	−	0.695467i	−0.961571	+	0.274556i	$0.911469\pi$
$410$	3.30784	+	7.82505i	0.163363	+	0.386452i
$411$	−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	$0.158614\pi$
$419$			19.5661i			0.955866i	−0.878396	+	0.477933i	$0.841386\pi$
$420$	26.1342	+	0.263882i	1.27522	+	0.0128761i
$421$			26.0983i			1.27195i	0.771708	+	0.635977i	$0.219403\pi$
$421$			26.0983i			1.27195i	−0.771708	+	0.635977i	$0.780597\pi$
$422$	−28.6182	−	3.55699i	−1.39311	−	0.173151i
$423$	−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	0.227953	−	0.973672i	$-0.426797\pi$
$431$	−10.4072	−	6.00858i	−0.501296	−	0.289423i	−0.729248	+	0.684249i	$0.760130\pi$
$432$	−11.7377	−	17.1531i	−0.564728	−	0.825277i
$433$		−	35.6343i		−	1.71247i	−0.516583	−	0.856237i	$-0.672796\pi$
$433$		−	35.6343i		−	1.71247i	0.516583	−	0.856237i	$-0.327204\pi$
$434$	−3.59072	−	0.922027i	−0.172360	−	0.0442587i
$435$	3.04729	−	19.0415i	0.146107	−	0.912972i
$436$	13.0178	+	12.6460i	0.623440	+	0.605635i
$437$	−19.8674	−	11.4705i	−0.950389	−	0.548707i
$438$	0.196661	+	0.799287i	0.00939683	+	0.0381914i
$439$	−11.6950	+	6.75210i	−0.558171	+	0.322260i	−0.752411	−	0.658694i	$-0.771109\pi$
$439$	−11.6950	+	6.75210i	−0.558171	+	0.322260i	0.194240	+	0.980954i	$0.437776\pi$
$440$	36.4754	+	14.1882i	1.73890	+	0.676396i
$441$	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	0.997579	+	0.0695416i	$0.0221536\pi$
$443$	11.7659	+	20.3791i	0.559014	+	0.968241i	−0.438565	+	0.898700i	$0.644513\pi$
$444$	−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	$-0.742883\pi$
$449$		−	30.6292i		−	1.44548i	0.691120	−	0.722740i	$-0.257117\pi$
$450$	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	0.969286	−	0.245935i	$-0.0790950\pi$
$457$	5.80736	+	10.0587i	0.271657	+	0.470524i	−0.697629	+	0.716459i	$0.745762\pi$
$458$	−2.95602	+	1.24958i	−0.138126	+	0.0583892i
$459$	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	$-0.745015\pi$
$461$		−	30.8362i		−	1.43618i	0.695948	−	0.718092i	$-0.254985\pi$
$462$	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	0.369778	−	0.929120i	$-0.379434\pi$
$467$	29.3749	−	16.9596i	1.35931	−	0.784797i	0.989531	+	0.144323i	$0.0461004\pi$
$468$	−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	−0.106344	−	0.994329i	$-0.533914\pi$
$479$	17.6827	−	30.6273i	0.807943	−	1.39940i	0.914286	−	0.405068i	$-0.132752\pi$
$480$	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	−0.206634	−	0.978418i	$-0.566251\pi$
$487$	16.4191	−	28.4386i	0.744018	−	1.28868i	0.950652	−	0.310259i	$-0.100416\pi$
$488$	6.95238	−	1.06945i	0.314720	−	0.0484117i
$489$	3.18008	−	19.8713i	0.143808	−	0.898610i
$490$	−26.2259	−	10.4459i	−1.18476	−	0.471897i
$491$	22.5295			1.01674			0.508371	−	0.861138i	$-0.330248\pi$
$491$	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	−0.731346	−	0.682007i	$-0.761107\pi$
$499$	−11.3117	+	6.53084i	−0.506383	+	0.292361i	0.224962	+	0.974367i	$0.427774\pi$
$500$	2.60834	−	10.3308i	0.116649	−	0.462007i
$501$	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	−0.962484	−	0.271339i	$-0.912534\pi$
$509$	−27.2704	+	15.7446i	−1.20874	+	0.697866i	−0.246255	+	0.969205i	$0.579200\pi$
$510$	−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	−0.922981	−	0.384845i	$-0.874255\pi$
$521$	−2.92633	+	5.06856i	−0.128205	+	0.222058i	0.794776	+	0.606903i	$0.207588\pi$
$522$	16.5080	−	1.36609i	0.722536	−	0.0597922i
$523$	9.81038	+	16.9921i	0.428978	+	0.743012i	0.996783	−	0.0801516i	$-0.0255405\pi$
$523$	9.81038	+	16.9921i	0.428978	+	0.743012i	−0.567805	+	0.823163i	$0.692207\pi$
$524$	19.4023	−	5.50125i	0.847591	−	0.240323i
$525$	−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	0.527287	−	0.849687i	$-0.323209\pi$
$541$	35.5120	−	20.5029i	1.52678	−	0.881488i	0.999494	−	0.0318007i	$-0.0101242\pi$
$542$	−1.00400	−	2.37506i	−0.0431254	−	0.102018i
$543$	−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	$0.0902209\pi$
$547$			13.0813i			0.559315i	−0.960100	+	0.279658i	$0.909779\pi$
$548$	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	0.0909180	+	0.995858i	$0.471020\pi$
$557$	−19.2814	+	33.3964i	−0.816980	+	1.41505i	−0.907898	+	0.419192i	$0.862313\pi$
$558$	−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	0.691309	−	0.722559i	$-0.257034\pi$
$563$	9.75701	+	5.63321i	0.411209	+	0.237411i	−0.280100	+	0.959971i	$0.590368\pi$
$564$	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	−0.941760	−	0.336286i	$-0.890829\pi$
$569$	−26.7497	+	15.4440i	−1.12141	+	0.647445i	−0.179648	+	0.983731i	$0.557496\pi$
$570$	10.4969	+	42.6624i	0.439667	+	1.78693i
$571$	6.49082	+	3.74748i	0.271633	+	0.156827i	0.629629	−	0.776896i	$-0.283207\pi$
$571$	6.49082	+	3.74748i	0.271633	+	0.156827i	−0.357997	+	0.933723i	$0.616540\pi$
$572$	18.6111	−	19.1582i	0.778168	−	0.801046i
$573$	−2.43564	+	15.2195i	−0.101750	+	0.635803i
$574$	7.59184	−	2.11949i	0.316877	−	0.0884659i
$575$			11.4225i			0.476350i
$576$	−12.2510	+	20.6376i	−0.510459	+	0.859902i
$577$	18.4495	+	10.6518i	0.768064	+	0.443442i	0.832184	−	0.554500i	$-0.187091\pi$
$577$	18.4495	+	10.6518i	0.768064	+	0.443442i	−0.0641196	+	0.997942i	$0.520424\pi$
$578$	−6.12052	+	2.58730i	−0.254580	+	0.107617i
$579$	−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	$0.101565\pi$
$587$			15.2002i			0.627381i	−0.949525	+	0.313691i	$0.898435\pi$
$588$	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	0.944207	−	0.329353i	$-0.106831\pi$
$593$	4.55071	+	7.88206i	0.186875	+	0.323678i	−0.757332	+	0.653031i	$0.773497\pi$
$594$	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	0.999021	+	0.0442488i	$0.0140894\pi$
$599$	37.6136	+	21.7162i	1.53685	+	0.887302i	0.537831	+	0.843053i	$0.319244\pi$
$600$	−15.3422	−	0.0929744i	−0.626342	−	0.00379566i
$601$		−	15.5284i		−	0.633415i	−0.948523	−	0.316708i	$-0.897423\pi$
$601$		−	15.5284i		−	0.633415i	0.948523	−	0.316708i	$-0.102577\pi$
$602$	−5.14902	−	18.4434i	−0.209858	−	0.751695i
$603$	5.43533	−	16.5469i	0.221344	−	0.673841i
$604$	−11.6148	+	11.9563i	−0.472601	+	0.486496i
$605$	−30.9831	−	17.8881i	−1.25964	−	0.727256i
$606$	−4.16446	−	16.9256i	−0.169170	−	0.687554i
$607$	1.01612	−	0.586656i	0.0412430	−	0.0238116i	−0.479237	−	0.877686i	$-0.659086\pi$
$607$	1.01612	−	0.586656i	0.0412430	−	0.0238116i	0.520480	+	0.853874i	$0.325753\pi$
$608$	−35.4214	−	3.36394i	−1.43653	−	0.136426i
$609$	−17.1629	−	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	0.998050	−	0.0624126i	$-0.0198795\pi$
$613$	35.7276	+	20.6273i	1.44302	+	0.833131i	0.444974	+	0.895543i	$0.353213\pi$
$614$	−3.08141	+	24.7919i	−0.124356	+	1.00052i
$615$	1.64420	−	10.2741i	0.0663006	−	0.414291i
$616$	17.3664	−	31.8901i	0.699711	−	1.28489i
$617$		−	15.3232i		−	0.616887i	−0.951243	−	0.308444i	$-0.900192\pi$
$617$		−	15.3232i		−	0.616887i	0.951243	−	0.308444i	$-0.0998081\pi$
$618$	4.08874	+	1.18613i	0.164473	+	0.0477130i
$619$	7.95796	−	13.7836i	0.319857	−	0.554009i	−0.660601	−	0.750738i	$-0.729698\pi$
$619$	7.95796	−	13.7836i	0.319857	−	0.554009i	0.980458	+	0.196728i	$0.0630316\pi$
$620$	5.47881	+	1.38330i	0.220034	+	0.0555547i
$621$	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	0.354691	−	0.934984i	$-0.384586\pi$
$641$	−7.03036	−	4.05898i	−0.277683	−	0.160320i	−0.632374	+	0.774663i	$0.717919\pi$
$642$	−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	0.171716	+	0.985147i	$0.445069\pi$
$647$	−19.5173	+	33.8049i	−0.767304	+	1.32901i	−0.939020	+	0.343863i	$0.888264\pi$
$648$	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	0.649149	−	0.760661i	$-0.275125\pi$
$653$	−8.53952	−	14.7909i	−0.334177	−	0.578812i	−0.983326	+	0.181849i	$0.941792\pi$
$654$	−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	−0.0667617	+	0.997769i	$0.521267\pi$
$661$	−23.0740	+	39.9653i	−0.897474	+	1.55447i	−0.830712	+	0.556702i	$0.812067\pi$
$662$	1.42753	+	3.37696i	0.0554823	+	0.131249i
$663$	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	−0.654903	−	0.755713i	$-0.727291\pi$
$677$	−8.53140	+	4.92561i	−0.327888	+	0.189306i	0.327015	+	0.945019i	$0.393957\pi$
$678$	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	0.168839	+	0.985644i	$0.445998\pi$
$683$	−20.1018	+	34.8173i	−0.769173	+	1.33225i	−0.938012	+	0.346603i	$0.887335\pi$
$684$	−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	−0.981305	−	0.192458i	$-0.938354\pi$
$691$	−17.2791	−	29.9282i	−0.657326	−	1.13852i	0.323979	−	0.946064i	$-0.394979\pi$
$692$	1.95628	−	0.554678i	0.0743667	−	0.0210857i
$693$	−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	−0.304266	−	0.952587i	$-0.598411\pi$
$709$	9.81381	−	5.66601i	0.368565	−	0.212791i	0.672832	+	0.739796i	$0.265078\pi$
$710$	−36.2272	+	15.3141i	−1.35958	+	0.574729i
$711$	−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	0.979945	−	0.199270i	$-0.0638572\pi$
$719$	8.51080	+	14.7411i	0.317399	+	0.549752i	−0.662545	+	0.749022i	$0.730524\pi$
$720$	−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	$0.285282\pi$
$727$			42.1153i			1.56197i	−0.624550	+	0.780985i	$0.714718\pi$
$728$	−20.5893	+	0.513497i	−0.763089	+	0.0190315i
$729$	15.6586	+	21.9956i	0.579949	+	0.814653i
$730$	−0.167151	+	1.34483i	−0.00618653	+	0.0497746i
$731$	15.5446	+	8.97469i	0.574939	+	0.331941i
$732$	−7.91470	−	3.40242i	−0.292536	−	0.125757i
$733$	20.3500	+	35.2472i	0.751644	+	1.30189i	0.947026	+	0.321158i	$0.104072\pi$
$733$	20.3500	+	35.2472i	0.751644	+	1.30189i	−0.195382	+	0.980727i	$0.562595\pi$
$734$	−23.8815	+	31.5941i	−0.881481	+	1.16616i
$735$	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	0.352905	−	0.935659i	$-0.385194\pi$
$739$	−7.63741	−	4.40946i	−0.280947	−	0.162205i	−0.633852	+	0.773454i	$0.718527\pi$
$740$	−4.88774	+	5.03144i	−0.179677	+	0.184959i
$741$	29.6068	+	4.73810i	1.08763	+	0.174058i
$742$	−1.86895	+	7.27837i	−0.0686112	+	0.267197i
$743$		−	16.3412i		−	0.599502i	−0.954017	−	0.299751i	$-0.903096\pi$
$743$		−	16.3412i		−	0.599502i	0.954017	−	0.299751i	$-0.0969036\pi$
$744$	−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	0.956417	−	0.292004i	$-0.0943219\pi$
$751$	6.17492	+	10.6953i	0.225326	+	0.390276i	−0.731091	+	0.682280i	$0.760989\pi$
$752$	−1.30069	−	44.8826i	−0.0474313	−	1.63670i
$753$	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	$-0.823145\pi$
$757$		−	29.0246i		−	1.05492i	0.849581	−	0.527459i	$-0.176855\pi$
$758$	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	−0.997317	−	0.0732037i	$-0.976678\pi$
$761$	−15.5050	−	26.8554i	−0.562055	−	0.973507i	0.435262	−	0.900304i	$-0.356656\pi$
$762$	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	$0.276935\pi$
$769$			42.3916i			1.52868i	−0.644813	+	0.764340i	$0.723065\pi$
$770$	13.9220	+	49.8674i	0.501714	+	1.79710i
$771$	51.7479	+	8.28143i	1.86366	+	0.298248i
$772$	−20.7861	+	21.3972i	−0.748107	+	0.770101i
$773$	2.88336	+	1.66471i	0.103707	+	0.0598754i	0.550957	−	0.834534i	$-0.314263\pi$
$773$	2.88336	+	1.66471i	0.103707	+	0.0598754i	−0.447249	+	0.894409i	$0.647596\pi$
$774$	−1.79066	−	21.6385i	−0.0643639	−	0.777781i
$775$	−2.68722	+	1.55147i	−0.0965277	+	0.0557303i
$776$	29.2476	+	11.3767i	1.04993	+	0.408400i
$777$	−5.47845	+	1.32452i	−0.196538	+	0.0475168i
$778$	−4.98397	−	3.76730i	−0.178684	−	0.135064i
$779$	6.62508	+	11.4750i	0.237368	+	0.411134i
$780$	−10.7373	+	24.9771i	−0.384457	+	0.894324i
$781$	−40.9842	−	23.6622i	−1.46653	−	0.846701i
$782$	17.9528	+	2.23137i	0.641992	+	0.0797938i
$783$	−18.0314	−	9.29733i	−0.644388	−	0.332260i
$784$	−26.7726	+	8.19919i	−0.956165	+	0.292828i
$785$			30.9229i			1.10369i
$786$	−23.7215	−	6.88151i	−0.846120	−	0.245455i
$787$	11.2617	−	19.5059i	0.401437	−	0.695309i	−0.592463	−	0.805598i	$-0.701844\pi$
$787$	11.2617	−	19.5059i	0.401437	−	0.695309i	0.993900	+	0.110289i	$0.0351777\pi$
$788$	−5.32089	−	1.34343i	−0.189549	−	0.0478578i
$789$	−39.0623	+	14.9226i	−1.39065	+	0.531257i
$790$	13.6220	−	18.0212i	0.484647	−	0.641167i
$791$	−41.0411	+	17.1542i	−1.45925	+	0.609932i
$792$	26.1563	−	31.7986i	0.929424	−	1.12992i
$793$	3.42230	+	5.92761i	0.121530	+	0.210495i
$794$	−20.8880	+	8.82987i	−0.741287	+	0.313360i
$795$	7.69883	+	6.25492i	0.273049	+	0.221839i
$796$	33.4321	+	32.4773i	1.18497	+	1.15113i
$797$			20.3781i			0.721831i	0.932599	+	0.360915i	$0.117536\pi$
$797$			20.3781i			0.721831i	−0.932599	+	0.360915i	$0.882464\pi$
$798$	40.5004	−	4.61909i	1.43370	−	0.163514i
$799$	39.3710			1.39285
$800$	7.36777	+	16.1112i	0.260490	+	0.569617i
$801$	−2.59807	+	2.32422i	−0.0917981	+	0.0821221i
$802$	−4.15544	−	9.83012i	−0.146734	−	0.347114i
$803$	−1.41214	+	0.815301i	−0.0498335	+	0.0287714i
$804$	−19.9722	+	2.35955i	−0.704365	+	0.0832150i
$805$	27.2937	+	3.50430i	0.961976	+	0.123510i
$806$	2.32539	−	3.07639i	0.0819084	−	0.108361i
$807$	32.5241	−	12.4248i	1.14490	−	0.437374i
$808$	−15.6977	+	12.5965i	−0.552244	+	0.443143i
$809$	5.45505	+	3.14948i	0.191789	+	0.110730i	0.592820	−	0.805335i	$-0.298015\pi$
$809$	5.45505	+	3.14948i	0.191789	+	0.110730i	−0.401031	+	0.916065i	$0.631348\pi$
$810$	−26.3478	−	24.9627i	−0.925768	−	0.877101i
$811$	−9.32889			−0.327582			−0.163791	−	0.986495i	$-0.552372\pi$
$811$	−9.32889			−0.327582			−0.163791	+	0.986495i	$0.552372\pi$
$812$	3.05854	+	20.4318i	0.107334	+	0.717016i
$813$	−0.499048	+	3.11839i	−0.0175024	+	0.109367i
$814$	−8.37582	−	1.04104i	−0.293572	−	0.0364884i
$815$	16.5660	−	28.6932i	0.580283	−	1.00508i
$816$	−3.14322	+	24.0953i	−0.110035	+	0.843505i
$817$	27.8769	−	16.0947i	0.975290	−	0.563084i
$818$	23.9883	−	31.7355i	0.838732	−	1.10961i
$819$	−18.0032	+	12.3729i	−0.629082	+	0.432345i
$820$	−11.5588	+	3.27734i	−0.403650	+	0.114450i
$821$	21.8378	+	37.8241i	0.762143	+	1.32007i	0.941744	+	0.336331i	$0.109186\pi$
$821$	21.8378	+	37.8241i	0.762143	+	1.32007i	−0.179600	+	0.983740i	$0.557480\pi$
$822$	−11.5356	−	46.8840i	−0.402350	−	1.63527i
$823$	12.0388	−	20.8519i	0.419647	−	0.726850i	−0.576257	−	0.817269i	$-0.695487\pi$
$823$	12.0388	−	20.8519i	0.419647	−	0.726850i	0.995904	+	0.0904188i	$0.0288205\pi$
$824$	−0.747400	−	4.85877i	−0.0260369	−	0.169263i
$825$	25.9906	+	4.15938i	0.904877	+	0.144811i
$826$	−3.72858	−	0.957428i	−0.129734	−	0.0333132i
$827$	−40.9864			−1.42524			−0.712618	−	0.701553i	$-0.752490\pi$
$827$	−40.9864			−1.42524			−0.712618	+	0.701553i	$0.752490\pi$
$828$	−10.1541	−	19.3854i	−0.352879	−	0.673689i
$829$	8.07095	−	13.9793i	0.280316	−	0.485521i	−0.691147	−	0.722714i	$-0.742894\pi$
$829$	8.07095	−	13.9793i	0.280316	−	0.485521i	0.971462	+	0.237194i	$0.0762275\pi$
$830$	−0.513034	+	0.216872i	−0.0178077	+	0.00752774i
$831$	−21.3123	+	8.14170i	−0.739315	+	0.282433i
$832$	−16.2305	−	14.8778i	−0.562692	−	0.515794i
$833$	−6.50627	−	23.6735i	−0.225429	−	0.820238i
$834$	−0.189678	−	0.197637i	−0.00656802	−	0.00684361i
$835$	19.1408	−	11.0509i	0.662393	−	0.382433i
$836$	59.1847	+	14.9431i	2.04694	+	0.516817i
$837$	2.78310	+	4.33122i	0.0961979	+	0.149709i
$838$	−27.4593	−	3.41295i	−0.948567	−	0.117898i
$839$	40.8898			1.41167			0.705836	−	0.708375i	$-0.250571\pi$
$839$	40.8898			1.41167			0.705836	+	0.708375i	$0.250571\pi$
$840$	−4.92898	+	36.6312i	−0.170066	+	1.26390i
$841$	−13.7566			−0.474367
$842$	−36.6268	−	4.55238i	−1.26224	−	0.156885i
$843$	20.6781	+	16.8000i	0.712193	+	0.578622i
$844$	9.98385	−	39.5428i	0.343658	−	1.36112i
$845$	−13.3983	+	7.73551i	−0.460915	+	0.266110i
$846$	−27.1330	−	39.1402i	−0.932850	−	1.34567i
$847$	−20.1223	+	26.3987i	−0.691411	+	0.907071i
$848$	−6.83780	+	4.21651i	−0.234811	+	0.144796i
$849$	5.74696	+	15.0436i	0.197235	+	0.516296i
$850$	−14.3080	+	6.04836i	−0.490761	+	0.207457i
$851$	−2.24298	+	3.88495i	−0.0768882	+	0.133174i
$852$	−20.2084	−	27.0743i	−0.692328	−	0.927551i
$853$	−23.3041			−0.797917			−0.398958	−	0.916969i	$-0.630628\pi$
$853$	−23.3041			−0.797917			−0.398958	+	0.916969i	$0.630628\pi$
$854$	6.64824	+	6.51074i	0.227498	+	0.222793i
$855$	16.7924	−	51.1216i	0.574290	−	1.74832i
$856$	2.97462	−	0.457570i	0.101670	−	0.0156394i
$857$	−3.23327	+	5.60019i	−0.110447	+	0.191299i	−0.915950	−	0.401292i	$-0.868561\pi$
$857$	−3.23327	+	5.60019i	−0.110447	+	0.191299i	0.805504	+	0.592591i	$0.201895\pi$
$858$	−31.7652	+	7.81570i	−1.08445	+	0.266824i
$859$	−1.10393	−	1.91207i	−0.0376657	−	0.0652390i	0.846578	−	0.532265i	$-0.178659\pi$
$859$	−1.10393	−	1.91207i	−0.0376657	−	0.0652390i	−0.884244	+	0.467026i	$0.845326\pi$
$860$	7.96186	+	28.0805i	0.271497	+	0.957538i
$861$	−9.26045	−	2.72699i	−0.315595	−	0.0929356i
$862$	10.2479	−	13.5575i	0.349044	−	0.461770i
$863$	−21.2034	+	12.2418i	−0.721771	+	0.416715i	−0.815404	−	0.578892i	$-0.803485\pi$
$863$	−21.2034	+	12.2418i	−0.721771	+	0.416715i	0.0936330	+	0.995607i	$0.470152\pi$
$864$	26.1203	−	13.4808i	0.888630	−	0.458625i
$865$	−1.44962	+	2.51082i	−0.0492886	+	0.0853704i
$866$	50.0097	+	6.21575i	1.69940	+	0.211220i
$867$	8.03607	+	1.28604i	0.272919	+	0.0436764i
$868$	1.92032	−	4.87843i	0.0651799	−	0.165585i
$869$	27.1815			0.922068
$870$	26.1916	+	7.59807i	0.887980	+	0.257599i
$871$	13.8375	+	7.98908i	0.468866	+	0.270700i
$872$	−20.0183	+	16.0635i	−0.677907	+	0.543980i
$873$	32.5807	−	6.81574i	1.10269	−	0.230678i
$874$	19.5634	−	25.8815i	0.661740	−	0.875453i
$875$	13.0049	−	5.43574i	0.439647	−	0.183761i
$876$	−1.15604	+	0.136576i	−0.0390588	+	0.00461448i
$877$	15.3248	−	8.84776i	0.517481	−	0.298768i	−0.218422	−	0.975854i	$-0.570091\pi$
$877$	15.3248	−	8.84776i	0.517481	−	0.298768i	0.735903	+	0.677087i	$0.236758\pi$
$878$	−7.43602	−	17.5907i	−0.250954	−	0.593657i
$879$	−23.9906	−	19.4912i	−0.809183	−	0.657422i
$880$	−26.2744	+	48.7152i	−0.885710	+	1.64219i
$881$	55.0445			1.85450			0.927249	−	0.374446i	$-0.122167\pi$
$881$	55.0445			1.85450			0.927249	+	0.374446i	$0.122167\pi$
$882$	−19.0509	+	22.7830i	−0.641476	+	0.767143i
$883$		−	49.3732i		−	1.66154i	−0.556616	−	0.830770i	$-0.687900\pi$
$883$		−	49.3732i		−	1.66154i	0.556616	−	0.830770i	$-0.312100\pi$
$884$	13.4521	−	13.8476i	0.452443	−	0.465744i
$885$	−3.20429	+	3.94398i	−0.107711	+	0.132575i
$886$	−30.6527	+	12.9577i	−1.02980	+	0.435321i
$887$	−12.2514	−	21.2201i	−0.411363	−	0.712502i	0.583676	−	0.811987i	$-0.301614\pi$
$887$	−12.2514	−	21.2201i	−0.411363	−	0.712502i	−0.995039	+	0.0994850i	$0.968280\pi$
$888$	−5.19984	−	3.04429i	−0.174495	−	0.102160i
$889$	−15.9547	−	38.1716i	−0.535105	−	1.28023i
$890$	2.82570	−	3.73827i	0.0947176	−	0.125307i
$891$	4.84434	−	43.4022i	0.162292	−	1.45403i
$892$	−5.61404	+	22.2354i	−0.187972	+	0.744496i
$893$	35.3029	−	61.1465i	1.18137	−	2.04619i
$894$	7.50467	−	25.8697i	0.250994	−	0.865212i
$895$		−	61.6540i		−	2.06087i
$896$	−26.6917	−	13.5481i	−0.891708	−	0.452612i
$897$	−2.74748	+	17.1681i	−0.0917357	+	0.573226i
$898$	42.9854	+	5.34270i	1.43444	+	0.178288i
$899$	−3.35007	−	1.93416i	−0.111731	−	0.0645079i
$900$	15.8734	+	10.0559i	0.529115	+	0.335196i
$901$	−3.52194	−	6.10018i	−0.117333	−	0.203226i
$902$	−11.5323	−	8.71707i	−0.383984	−	0.290247i
$903$	−6.62485	+	22.4970i	−0.220461	+	0.748654i
$904$	−44.3184	−	17.2390i	−1.47401	−	0.573359i
$905$	−23.1412	+	13.3606i	−0.769239	+	0.444120i
$906$	19.8241	−	4.87764i	0.658612	−	0.162049i
$907$	6.23747	+	3.60121i	0.207112	+	0.119576i	0.599968	−	0.800024i	$-0.295180\pi$
$907$	6.23747	+	3.60121i	0.207112	+	0.119576i	−0.392857	+	0.919600i	$0.628513\pi$
$908$	−30.4294	−	29.5603i	−1.00983	−	0.980994i
$909$	−6.66211	+	20.2816i	−0.220968	+	0.672697i
$910$	20.5465	−	20.9804i	0.681109	−	0.695494i
$911$			13.3025i			0.440730i	0.975417	+	0.220365i	$0.0707248\pi$
$911$			13.3025i			0.440730i	−0.975417	+	0.220365i	$0.929275\pi$
$912$	34.6036	+	26.4873i	1.14584	+	0.877083i
$913$	−0.580401	−	0.335095i	−0.0192085	−	0.0110900i
$914$	−15.1294	+	6.39559i	−0.500438	+	0.211547i
$915$	11.4746	−	4.38354i	0.379340	−	0.144915i
$916$	−1.23806	−	4.36649i	−0.0409066	−	0.144273i
$917$	21.2175	+	16.1729i	0.700663	+	0.534077i
$918$	11.1519	+	23.2359i	0.368069	+	0.766898i
$919$	−3.29521	−	5.70747i	−0.108699	−	0.188272i	0.806544	−	0.591173i	$-0.201335\pi$
$919$	−3.29521	−	5.70747i	−0.108699	−	0.188272i	−0.915243	+	0.402901i	$0.868002\pi$
$920$	18.4112	+	22.9440i	0.606999	+	0.756442i
$921$	19.2938	−	23.7477i	0.635753	−	0.782512i
$922$	43.2760	+	5.37881i	1.42522	+	0.177142i
$923$			26.8417i			0.883505i
$924$	−38.7374	+	21.8465i	−1.27437	+	0.718699i
$925$		−	3.85188i		−	0.126649i
$926$	5.63762	−	45.3582i	0.185264	−	1.49056i
$927$	−3.47644	−	3.88606i	−0.114181	−	0.127635i
$928$	−12.8018	+	17.9972i	−0.420240	+	0.590788i
$929$	−6.17532	−	10.6960i	−0.202606	−	0.350923i	0.746762	−	0.665092i	$-0.231608\pi$
$929$	−6.17532	−	10.6960i	−0.202606	−	0.350923i	−0.949367	+	0.314169i	$0.898274\pi$
$930$	−4.79211	−	4.99319i	−0.157140	−	0.163733i
$931$	−42.6009	−	11.1226i	−1.39619	−	0.364529i
$932$	−50.1296	+	14.2136i	−1.64205	+	0.465581i
$933$	−5.13143	−	13.4324i	−0.167995	−	0.439756i
$934$	18.6775	+	44.1835i	0.611145	+	1.44573i
$935$	−42.0298	−	24.2659i	−1.37452	−	0.793580i
$936$	−23.0371	−	3.83004i	−0.752990	−	0.125189i
$937$		−	11.2161i		−	0.366413i	−0.983074	−	0.183206i	$-0.941352\pi$
$937$		−	11.2161i		−	0.366413i	0.983074	−	0.183206i	$-0.0586476\pi$
$938$	21.0399	+	5.40264i	0.686977	+	0.176402i
$939$	−7.29923	+	45.6105i	−0.238201	+	1.48844i
$940$	45.9207	+	44.6092i	1.49777	+	1.45499i
$941$	−8.10816	−	4.68125i	−0.264318	−	0.152604i	0.361985	−	0.932184i	$-0.382099\pi$
$941$	−8.10816	−	4.68125i	−0.264318	−	0.152604i	−0.626303	+	0.779580i	$0.715433\pi$
$942$	−25.7929	+	6.34623i	−0.840378	+	0.206771i
$943$	−6.65399	+	3.84168i	−0.216684	+	0.125102i
$944$	−2.16004	−	3.50288i	−0.0703035	−	0.114009i
$945$	16.8201	+	35.4117i	0.547159	+	1.15194i
$946$	−21.1769	+	28.0162i	−0.688521	+	0.910884i
$947$	−19.4899	−	33.7574i	−0.633335	−	1.09697i	−0.986865	−	0.161546i	$-0.948352\pi$
$947$	−19.4899	−	33.7574i	−0.633335	−	1.09697i	0.353530	−	0.935423i	$-0.384981\pi$
$948$	17.8272	+	7.66366i	0.579000	+	0.248904i
$949$	0.800945	+	0.462426i	0.0259998	+	0.0150110i
$950$	−3.43602	+	27.6450i	−0.111479	+	0.896922i
$951$	−49.2896	−	7.88801i	−1.59832	−	0.255786i
$952$	12.5524	−	23.0502i	0.406826	−	0.747061i
$953$			0.425521i			0.0137840i	0.999976	+	0.00689198i	$0.00219380\pi$
$953$			0.425521i			0.0137840i	−0.999976	+	0.00689198i	$0.997806\pi$
$954$	−3.63724	+	7.70530i	−0.117760	+	0.249468i
$955$	−12.6880	+	21.9763i	−0.410574	+	0.711135i
$956$	4.07775	−	16.1507i	0.131884	−	0.522350i
$957$	11.7102	+	30.6534i	0.378536	+	0.990882i
$958$	39.8984	+	30.1585i	1.28906	+	0.974378i
$959$	−6.64124	+	51.7262i	−0.214457	+	1.67033i
$960$	−30.9673	+	24.5424i	−0.999464	+	0.792102i
$961$	−15.0092	−	25.9966i	−0.484167	−	0.838601i
$962$	1.86396	+	4.40940i	0.0600966	+	0.142165i
$963$	2.37910	−	2.12833i	0.0766656	−	0.0685846i
$964$	−10.3383	−	10.0430i	−0.332973	−	0.323463i
$965$		−	42.5337i		−	1.36921i
$966$	2.67847	+	23.4849i	0.0861784	+	0.755615i
$967$	−25.1685			−0.809365			−0.404682	−	0.914457i	$-0.632618\pi$
$967$	−25.1685			−0.809365			−0.404682	+	0.914457i	$0.632618\pi$
$968$	−35.0727	+	5.39505i	−1.12728	+	0.173403i
$969$	−24.0941	+	29.6560i	−0.774014	+	0.952689i
$970$	−41.2142	+	17.4222i	−1.32331	+	0.559395i
$971$	11.2476	−	6.49383i	0.360954	−	0.208397i	−0.308545	−	0.951210i	$-0.599842\pi$
$971$	11.2476	−	6.49383i	0.360954	−	0.208397i	0.669499	+	0.742813i	$0.266509\pi$
$972$	15.4142	−	27.0999i	0.494411	−	0.869228i
$973$	0.114104	+	0.272993i	0.00365801	+	0.00875174i
$974$	37.0472	+	28.0033i	1.18707	+	0.897285i
$975$	−5.32766	−	13.9461i	−0.170622	−	0.446631i
$976$	0.288164	+	9.94362i	0.00922392	+	0.318288i
$977$	33.4781	+	19.3286i	1.07106	+	0.618377i	0.928471	−	0.371405i	$-0.121124\pi$
$977$	33.4781	+	19.3286i	1.07106	+	0.618377i	0.142589	+	0.989782i	$0.454457\pi$
$978$	27.3329	+	7.92915i	0.874011	+	0.253546i
$979$	5.63844			0.180205
$980$	19.2345	−	34.9837i	0.614425	−	1.11751i
$981$	−8.49578	+	25.8639i	−0.271249	+	0.825770i
$982$	−3.92986	+	31.6182i	−0.125407	+	1.00898i
$983$	24.2049	−	41.9241i	0.772017	−	1.33717i	−0.164439	−	0.986387i	$-0.552581\pi$
$983$	24.2049	−	41.9241i	0.772017	−	1.33717i	0.936456	−	0.350785i	$-0.114085\pi$
$984$	−5.10582	−	8.96863i	−0.162768	−	0.285909i
$985$	6.77637	−	3.91234i	0.215913	−	0.124657i
$986$	−15.4488	−	11.6775i	−0.491989	−	0.371886i
$987$	12.0886	+	50.0005i	0.384783	+	1.59153i
$988$	−9.44432	−	33.3090i	−0.300464	−	1.05970i
$989$	9.33285	+	16.1650i	0.296767	+	0.514016i
$990$	4.84161	+	58.5066i	0.153876	+	1.85946i
$991$	8.16959	−	14.1502i	0.259516	−	0.449494i	−0.706597	−	0.707617i	$-0.749770\pi$
$991$	8.16959	−	14.1502i	0.259516	−	0.449494i	0.966112	+	0.258122i	$0.0831037\pi$
$992$	5.09708	−	2.33093i	0.161832	−	0.0740071i
$993$	0.709567	−	4.43385i	0.0225174	−	0.140704i
$994$	9.81249	+	35.1475i	0.311233	+	1.11481i
$995$	−66.4569			−2.10682
$996$	−0.286183	−	0.383415i	−0.00906804	−	0.0121490i
$997$	4.94566	−	8.56614i	0.156631	−	0.271292i	−0.777021	−	0.629475i	$-0.783270\pi$
$997$	4.94566	−	8.56614i	0.156631	−	0.271292i	0.933652	+	0.358182i	$0.116603\pi$
$998$	−7.19235	−	17.0143i	−0.227670	−	0.538577i
$999$	−6.38373	+	0.303669i	−0.201972	+	0.00960767i

Twists

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

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-0.174432 + 1.40341i) q^{2} +(1.09218 - 1.34430i) q^{3} +(-1.93915 - 0.489600i) q^{4} +(2.46958 - 1.42581i) q^{5} +(1.69610 + 1.76727i) q^{6} +(-1.02032 - 2.44110i) q^{7} +(1.02536 - 2.63603i) q^{8} +(-0.614290 - 2.93643i) q^{9} +O(q^{10})\)	\(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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