LMFDB - Embedded newform 168.2.ba.c.5.21

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			5.21
Character	$\chi$	$=$	168.5
Dual form			168.2.ba.c.101.21

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.30261 - 0.550645i) q^{2} +(-0.618109 - 1.61801i) q^{3} +(1.39358 - 1.43455i) q^{4} +(2.46958 + 1.42581i) q^{5} +(-1.69610 - 1.76727i) q^{6} +(-1.02032 + 2.44110i) q^{7} +(1.02536 - 2.63603i) q^{8} +(-2.23588 + 2.00021i) q^{9} +O(q^{10})$	\(q+(1.30261 - 0.550645i) q^{2} +(-0.618109 - 1.61801i) q^{3} +(1.39358 - 1.43455i) 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} +(-2.23588 + 2.00021i) q^{9} +(4.00201 + 0.497414i) q^{10} +(-2.42621 - 4.20231i) q^{11} +(-3.18249 - 1.36811i) q^{12} -2.75221 q^{13} +(0.0151045 + 3.74163i) q^{14} +(0.780502 - 4.87710i) q^{15} +(-0.115871 - 3.99832i) q^{16} +(1.75366 + 3.03743i) q^{17} +(-1.81107 + 3.83667i) q^{18} +(-3.14493 + 5.44717i) q^{19} +(5.48696 - 1.55575i) q^{20} +(4.58037 + 0.142013i) q^{21} +(-5.47438 - 4.13799i) q^{22} +(3.15865 + 1.82365i) q^{23} +(-4.89889 - 0.0296875i) q^{24} +(1.56588 + 2.71219i) q^{25} +(-3.58505 + 1.51549i) q^{26} +(4.61837 + 2.38132i) q^{27} +(2.07998 + 4.86556i) q^{28} +3.90427 q^{29} +(-1.66886 - 6.78274i) q^{30} +(-0.858051 + 0.495396i) q^{31} +(-2.35259 - 5.14445i) q^{32} +(-5.29970 + 6.52310i) 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} +(-1.09715 + 8.82727i) q^{38} +(1.70117 + 4.45309i) q^{39} +(6.29069 - 5.04791i) q^{40} -2.10659 q^{41} +(6.04464 - 2.33717i) q^{42} -5.11768i q^{43} +(-9.40954 - 2.37574i) q^{44} +(-8.37361 + 1.75172i) q^{45} +(5.11867 + 0.636204i) 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} +(3.83063 - 4.71490i) q^{51} +(-3.83543 + 3.94819i) q^{52} +(-1.00417 - 1.73927i) q^{53} +(7.32719 + 0.558850i) q^{54} -13.8373i q^{55} +(5.38860 + 5.19259i) q^{56} +(10.7575 + 1.72156i) q^{57} +(5.08574 - 2.14987i) q^{58} +(-0.890996 + 0.514417i) q^{59} +(-5.90876 - 7.91630i) q^{60} +(-1.24347 + 2.15376i) q^{61} +(-0.844918 + 1.11779i) q^{62} +(-2.60139 - 7.49885i) q^{63} +(-5.89727 - 5.40576i) q^{64} +(-6.79681 - 3.92414i) q^{65} +(-3.31153 + 11.4153i) q^{66} +(-5.02777 + 2.90279i) q^{67} +(6.80122 + 1.71719i) q^{68} +(0.998281 - 6.23793i) q^{69} +(-5.29756 + 9.26178i) q^{70} +9.75277i q^{71} +(2.98001 + 7.94478i) q^{72} +(0.291019 - 0.168020i) q^{73} +(-1.72612 - 0.214540i) q^{74} +(3.42045 - 4.21004i) 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} +(5.41471 - 10.0394i) q^{80} +(0.998337 - 8.94446i) q^{81} +(-2.74407 + 1.15999i) q^{82} -0.138115i q^{83} +(6.58684 - 6.37287i) q^{84} +10.0016i q^{85} +(-2.81803 - 6.66634i) q^{86} +(-2.41327 - 6.31714i) q^{87} +(-13.5651 + 2.08666i) 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} +(1.33192 + 1.08212i) q^{93} +(1.95806 - 15.7538i) q^{94} +(-15.5333 + 8.96815i) q^{95} +(-6.86958 + 6.98633i) q^{96} -11.0953i q^{97} +(-9.14908 - 3.78077i) 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 $

$2$	1.30261	−	0.550645i	0.921084	−	0.389365i
$2$	1.30261	−	0.550645i	0.921084	−	0.389365i
$3$	−0.618109	−	1.61801i	−0.356866	−	0.934156i
$3$	−0.618109	−	1.61801i	−0.356866	−	0.934156i
$4$	1.39358	−	1.43455i	0.696790	−	0.717275i
$5$	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
$9$	−2.23588	+	2.00021i	−0.745294	+	0.666736i
$10$	4.00201	+	0.497414i	1.26555	+	0.157296i
$11$	−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	$-0.427860\pi$
$12$	−3.18249	−	1.36811i	−0.918707	−	0.394939i
$13$	−2.75221			−0.763326			−0.381663	−	0.924302i	$-0.624649\pi$
$13$	−2.75221			−0.763326			−0.381663	+	0.924302i	$0.624649\pi$
$14$	0.0151045	+	3.74163i	0.00403685	+	0.999992i
$15$	0.780502	−	4.87710i	0.201525	−	1.25926i
$16$	−0.115871	−	3.99832i	−0.0289677	−	0.999580i
$17$	1.75366	+	3.03743i	0.425326	+	0.736686i	0.996451	−	0.0841773i	$-0.0268262\pi$
$17$	1.75366	+	3.03743i	0.425326	+	0.736686i	−0.571125	+	0.820863i	$0.693493\pi$
$18$	−1.81107	+	3.83667i	−0.426874	+	0.904311i
$19$	−3.14493	+	5.44717i	−0.721496	+	1.24967i	0.238905	+	0.971043i	$0.423212\pi$
$19$	−3.14493	+	5.44717i	−0.721496	+	1.24967i	−0.960400	+	0.278624i	$0.910122\pi$
$20$	5.48696	−	1.55575i	1.22692	−	0.347877i
$21$	4.58037	+	0.142013i	0.999520	+	0.0309899i
$22$	−5.47438	−	4.13799i	−1.16714	−	0.882223i
$23$	3.15865	+	1.82365i	0.658624	+	0.380257i	0.791753	−	0.610842i	$-0.209169\pi$
$23$	3.15865	+	1.82365i	0.658624	+	0.380257i	−0.133128	+	0.991099i	$0.542502\pi$
$24$	−4.89889	−	0.0296875i	−0.999982	−	0.00605994i
$25$	1.56588	+	2.71219i	0.313177	+	0.542438i
$26$	−3.58505	+	1.51549i	−0.703087	+	0.297212i
$27$	4.61837	+	2.38132i	0.888805	+	0.458286i
$28$	2.07998	+	4.86556i	0.393080	+	0.919504i
$29$	3.90427			0.725005			0.362503	−	0.931983i	$-0.381922\pi$
$29$	3.90427			0.725005			0.362503	+	0.931983i	$0.381922\pi$
$30$	−1.66886	−	6.78274i	−0.304691	−	1.23835i
$31$	−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	$0.361693\pi$
$32$	−2.35259	−	5.14445i	−0.415883	−	0.909418i
$33$	−5.29970	+	6.52310i	−0.922560	+	1.13553i
$34$	3.95689	+	2.99094i	0.678600	+	0.512942i
$35$	−6.00030	+	4.57370i	−1.01424	+	0.773097i
$36$	−0.246481	+	5.99494i	−0.0410801	+	0.999156i
$37$	−1.06516	−	0.614970i	−0.175111	−	0.101100i	0.409883	−	0.912138i	$-0.365570\pi$
$37$	−1.06516	−	0.614970i	−0.175111	−	0.101100i	−0.584994	+	0.811038i	$0.698903\pi$
$38$	−1.09715	+	8.82727i	−0.177981	+	1.43197i
$39$	1.70117	+	4.45309i	0.272405	+	0.713065i
$40$	6.29069	−	5.04791i	0.994646	−	0.798144i
$41$	−2.10659			−0.328995			−0.164497	−	0.986378i	$-0.552600\pi$
$41$	−2.10659			−0.328995			−0.164497	+	0.986378i	$0.552600\pi$
$42$	6.04464	−	2.33717i	0.932708	−	0.360634i
$43$		−	5.11768i		−	0.780439i	−0.920722	−	0.390220i	$-0.872399\pi$
$43$		−	5.11768i		−	0.780439i	0.920722	−	0.390220i	$-0.127601\pi$
$44$	−9.40954	−	2.37574i	−1.41854	−	0.358157i
$45$	−8.37361	+	1.75172i	−1.24826	+	0.261132i
$46$	5.11867	+	0.636204i	0.754706	+	0.0938032i
$47$	5.61268	−	9.72145i	0.818693	−	1.41802i	−0.0879518	−	0.996125i	$-0.528032\pi$
$47$	5.61268	−	9.72145i	0.818693	−	1.41802i	0.906645	−	0.421894i	$-0.138635\pi$
$48$	−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
$51$	3.83063	−	4.71490i	0.536395	−	0.660218i
$52$	−3.83543	+	3.94819i	−0.531878	+	0.547515i
$53$	−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	$0.877379\pi$
$54$	7.32719	+	0.558850i	0.997104	+	0.0760499i
$55$		−	13.8373i		−	1.86582i
$56$	5.38860	+	5.19259i	0.720082	+	0.693889i
$57$	10.7575	+	1.72156i	1.42486	+	0.228026i
$58$	5.08574	−	2.14987i	0.667791	−	0.282292i
$59$	−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	$0.354667\pi$
$60$	−5.90876	−	7.91630i	−0.762817	−	1.02199i
$61$	−1.24347	+	2.15376i	−0.159211	+	0.275761i	−0.934584	−	0.355742i	$-0.884228\pi$
$61$	−1.24347	+	2.15376i	−0.159211	+	0.275761i	0.775374	+	0.631503i	$0.217562\pi$
$62$	−0.844918	+	1.11779i	−0.107305	+	0.141959i
$63$	−2.60139	−	7.49885i	−0.327745	−	0.944766i
$64$	−5.89727	−	5.40576i	−0.737159	−	0.675720i
$65$	−6.79681	−	3.92414i	−0.843040	−	0.486729i
$66$	−3.31153	+	11.4153i	−0.407621	+	1.40513i
$67$	−5.02777	+	2.90279i	−0.614240	+	0.354632i	−0.774623	−	0.632423i	$-0.782060\pi$
$67$	−5.02777	+	2.90279i	−0.614240	+	0.354632i	0.160383	+	0.987055i	$0.448727\pi$
$68$	6.80122	+	1.71719i	0.824769	+	0.208240i
$69$	0.998281	−	6.23793i	0.120179	−	0.750958i
$70$	−5.29756	+	9.26178i	−0.633179	+	1.10699i
$71$			9.75277i			1.15744i	0.815526	+	0.578720i	$0.196448\pi$
$71$			9.75277i			1.15744i	−0.815526	+	0.578720i	$0.803552\pi$
$72$	2.98001	+	7.94478i	0.351198	+	0.936301i
$73$	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	$0.327073\pi$
$74$	−1.72612	−	0.214540i	−0.200657	−	0.0249398i
$75$	3.42045	−	4.21004i	0.394960	−	0.486133i
$76$	3.43154	+	12.1026i	0.393624	+	1.38827i
$77$	12.7338	−	1.63491i	1.45115	−	0.186316i
$78$	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	$0.268710\pi$
$80$	5.41471	−	10.0394i	0.605383	−	1.12244i
$81$	0.998337	−	8.94446i	0.110926	−	0.993829i
$82$	−2.74407	+	1.15999i	−0.303032	+	0.128099i
$83$		−	0.138115i		−	0.0151600i	−0.999971	−	0.00758002i	$-0.997587\pi$
$83$		−	0.138115i		−	0.0151600i	0.999971	−	0.00758002i	$-0.00241282\pi$
$84$	6.58684	−	6.37287i	0.718683	−	0.695337i
$85$			10.0016i			1.08482i
$86$	−2.81803	−	6.66634i	−0.303876	−	0.718850i
$87$	−2.41327	−	6.31714i	−0.258729	−	0.677268i
$88$	−13.5651	+	2.08666i	−1.44605	+	0.222438i
$89$	0.580993	−	1.00631i	0.0615852	−	0.106669i	−0.833589	−	0.552385i	$-0.813718\pi$
$89$	0.580993	−	1.00631i	0.0615852	−	0.106669i	0.895174	+	0.445717i	$0.147051\pi$
$90$	−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
$93$	1.33192	+	1.08212i	0.138114	+	0.112211i
$94$	1.95806	−	15.7538i	0.201958	−	1.62488i
$95$	−15.5333	+	8.96815i	−1.59368	+	0.920113i
$96$	−6.86958	+	6.98633i	−0.701124	+	0.713040i
$97$		−	11.0953i		−	1.12656i	−0.826266	−	0.563280i	$-0.809539\pi$
$97$		−	11.0953i		−	1.12656i	0.826266	−	0.563280i	$-0.190461\pi$
$98$	−9.14908	−	3.78077i	−0.924197	−	0.381916i
$99$	13.8302	+	4.54296i	1.38999	+	0.456585i
$100$	6.07296	+	1.53331i	0.607296	+	0.153331i
$101$	−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	$0.448522\pi$
$102$	2.39357	−	8.25099i	0.236999	−	0.816970i
$103$	1.50519	+	0.869021i	0.148311	+	0.0856271i	0.572319	−	0.820031i	$-0.306044\pi$
$103$	1.50519	+	0.869021i	0.148311	+	0.0856271i	−0.424008	+	0.905658i	$0.639377\pi$
$104$	−2.82201	+	7.25490i	−0.276721	+	0.711402i
$105$	11.1091	+	6.88147i	1.08414	+	0.671563i
$106$	−2.26576	−	1.71265i	−0.220070	−	0.166347i
$107$	0.532028	−	0.921500i	0.0514331	−	0.0890847i	−0.839163	−	0.543881i	$-0.816954\pi$
$107$	0.532028	−	0.921500i	0.0514331	−	0.0890847i	0.890596	+	0.454796i	$0.150288\pi$
$108$	9.85219	−	3.30672i	0.948027	−	0.318189i
$109$	7.85874	−	4.53725i	0.752731	−	0.434589i	−0.0739489	−	0.997262i	$-0.523560\pi$
$109$	7.85874	−	4.53725i	0.752731	−	0.434589i	0.826680	+	0.562673i	$0.190227\pi$
$110$	−7.61942	−	18.0245i	−0.726484	−	1.71857i
$111$	−0.336640	+	2.10355i	−0.0319524	+	0.199660i
$112$	9.87851	+	3.79670i	0.933432	+	0.358755i
$113$		−	16.8126i		−	1.58159i	−0.612078	−	0.790797i	$-0.709666\pi$
$113$		−	16.8126i		−	1.58159i	0.612078	−	0.790797i	$-0.290334\pi$
$114$	14.9607	−	3.68103i	1.40120	−	0.344760i
$115$	5.20036	+	9.00729i	0.484936	+	0.839934i
$116$	5.44092	−	5.60088i	0.505176	−	0.520028i
$117$	6.15362	−	5.50499i	0.568902	−	0.508937i
$118$	−0.877358	+	1.16071i	−0.0807674	+	0.106852i
$119$	−9.20396	+	1.18172i	−0.843726	+	0.108328i
$120$	−12.0559	−	7.05821i	−1.10055	−	0.644324i
$121$	−6.27296	+	10.8651i	−0.570269	+	0.987735i
$122$	−0.433803	+	3.49022i	−0.0392747	+	0.315990i
$123$	1.30211	+	3.40848i	0.117407	+	0.307332i
$124$	−0.485092	+	1.92129i	−0.0435626	+	0.172537i
$125$		−	5.32750i		−	0.476506i
$126$	−7.51780	−	8.33562i	−0.669739	−	0.742596i
$127$	15.6371			1.38756			0.693782	−	0.720185i	$-0.255943\pi$
$127$	15.6371			1.38756			0.693782	+	0.720185i	$0.255943\pi$
$128$	−10.6585	−	3.79429i	−0.942086	−	0.335371i
$129$	−8.28044	+	3.16329i	−0.729052	+	0.278512i
$130$	−11.0144	−	1.36899i	−0.966026	−	0.120068i
$131$	−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
$135$	8.01011	+	12.4658i	0.689400	+	1.07288i
$136$	9.80489	−	1.50824i	0.840763	−	0.129330i
$137$	17.0704	−	9.85557i	1.45842	−	0.842019i	0.459485	−	0.888185i	$-0.348034\pi$
$137$	17.0704	−	9.85557i	1.45842	−	0.842019i	0.998934	+	0.0461669i	$0.0147006\pi$
$138$	−2.13451	−	8.67528i	−0.181702	−	0.738489i
$139$	0.111832			0.00948546			0.00474273	−	0.999989i	$-0.498490\pi$
$139$	0.111832			0.00948546			0.00474273	+	0.999989i	$0.498490\pi$
$140$	−1.80069	+	14.9816i	−0.152186	+	1.26617i
$141$	−19.1986	−	3.07243i	−1.61681	−	0.258745i
$142$	5.37032	+	12.7040i	0.450667	+	1.06610i
$143$	6.67743	+	11.5657i	0.558395	+	0.967169i
$144$	8.25655	+	8.70801i	0.688046	+	0.725667i
$145$	9.64192	+	5.56676i	0.800718	+	0.462295i
$146$	0.286564	−	0.379112i	0.0237162	−	0.0313755i
$147$	−5.02010	+	11.0362i	−0.414051	+	0.910254i
$148$	−2.36659	+	0.671015i	−0.194532	+	0.0551571i
$149$	−5.49834	+	9.52340i	−0.450441	+	0.780187i	−0.998413	−	0.0563094i	$-0.982067\pi$
$149$	−5.49834	+	9.52340i	−0.450441	+	0.780187i	0.547972	+	0.836497i	$0.315400\pi$
$150$	2.13727	−	7.36749i	0.174508	−	0.601553i
$151$	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	$0.723202\pi$
$152$	11.1342	+	13.8754i	0.903103	+	1.12545i
$153$	−9.99648	−	3.28365i	−0.808168	−	0.265468i
$154$	15.6868	−	9.14143i	1.26408	−	0.736638i
$155$	−2.82537			−0.226939
$156$	8.75890	+	3.76533i	0.701273	+	0.301468i
$157$	5.42198	+	9.39114i	0.432721	+	0.749495i	0.997107	−	0.0760165i	$-0.0242202\pi$
$157$	5.42198	+	9.39114i	0.432721	+	0.749495i	−0.564386	+	0.825511i	$0.690887\pi$
$158$	−0.977103	+	7.86142i	−0.0777342	+	0.625421i
$159$	−2.19346	+	2.69980i	−0.173953	+	0.214108i
$160$	1.52510	−	16.0590i	0.120570	−	1.26957i
$161$	−7.67452	+	5.84987i	−0.604837	+	0.461035i
$162$	−3.62478	−	12.2009i	−0.284790	−	0.958590i
$163$	−10.0621	−	5.80934i	−0.788122	−	0.455022i	0.0511792	−	0.998689i	$-0.483702\pi$
$163$	−10.0621	−	5.80934i	−0.788122	−	0.455022i	−0.839301	+	0.543667i	$0.817035\pi$
$164$	−2.93571	+	3.02202i	−0.229240	+	0.235980i
$165$	−22.3888	+	8.55294i	−1.74296	+	0.665846i
$166$	−0.0760521	−	0.179909i	−0.00590279	−	0.0139637i
$167$	−7.75061			−0.599761			−0.299880	−	0.953977i	$-0.596947\pi$
$167$	−7.75061			−0.599761			−0.299880	+	0.953977i	$0.596947\pi$
$168$	5.07089	−	11.9284i	0.391228	−	0.920294i
$169$	−5.42533			−0.417333
$170$	5.50732	+	13.0281i	0.422392	+	0.999213i
$171$	−3.86379	−	18.4697i	−0.295472	−	1.41242i
$172$	−7.34158	−	7.13190i	−0.559790	−	0.543802i
$173$	−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
$177$	1.38306	+	1.12367i	0.103957	+	0.0844603i
$178$	0.202687	−	1.63075i	0.0151921	−	0.122230i
$179$	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	$0.533883\pi$
$180$	−9.15636	+	14.4535i	−0.682475	+	1.07730i
$181$	9.37049			0.696503			0.348251	−	0.937401i	$-0.386776\pi$
$181$	9.37049			0.696503			0.348251	+	0.937401i	$0.386776\pi$
$182$	−0.0415708	−	10.2977i	−0.00308144	−	0.763320i
$183$	4.25340	+	0.680689i	0.314420	+	0.0503180i
$184$	8.04594	−	6.45639i	0.593155	−	0.475971i
$185$	−1.75366	−	3.03743i	−0.128932	−	0.223317i
$186$	2.33084	+	0.676166i	0.170905	+	0.0495789i
$187$	8.50950	−	14.7389i	0.622276	−	1.07781i
$188$	−6.12419	−	21.5993i	−0.446652	−	1.57529i
$189$	−10.5252	+	8.84418i	−0.765598	+	0.643319i
$190$	−15.2955	+	20.2353i	−1.10966	+	1.46803i
$191$	7.70657	+	4.44939i	0.557628	+	0.321947i	0.752193	−	0.658943i	$-0.228996\pi$
$191$	7.70657	+	4.44939i	0.557628	+	0.321947i	−0.194565	+	0.980890i	$0.562329\pi$
$192$	−5.10139	+	12.8832i	−0.368161	+	0.929762i
$193$	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	$0.652957\pi$
$194$	−6.10958	−	14.4529i	−0.438643	−	1.03766i
$195$	−2.14811	+	13.4228i	−0.153829	+	0.961228i
$196$	−13.9995	+	0.113031i	−0.999967	+	0.00807364i
$197$	2.74394			0.195497			0.0977487	−	0.995211i	$-0.468836\pi$
$197$	2.74394			0.195497			0.0977487	+	0.995211i	$0.468836\pi$
$198$	20.5169	−	1.69784i	1.45807	−	0.120660i
$199$	−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	$0.642734\pi$
$200$	8.75500	−	1.34674i	0.619072	−	0.0952287i
$201$	7.80443	+	6.34072i	0.550482	+	0.447240i
$202$	−6.06823	+	8.02801i	−0.426959	+	0.564849i
$203$	−3.98360	+	9.53071i	−0.279594	+	0.668925i
$204$	−1.42548	−	12.0658i	−0.0998035	−	0.844776i
$205$	−5.20240	−	3.00361i	−0.363352	−	0.209781i
$206$	2.43919	+	0.303170i	0.169947	+	0.0211228i
$207$	−10.7100	+	2.24050i	−0.744399	+	0.155725i
$208$	0.318901	+	11.0042i	0.0221118	+	0.763006i
$209$	30.5210			2.11118
$210$	18.2601	+	2.84668i	1.26007	+	0.196440i
$211$			20.3918i			1.40383i	0.712259	+	0.701916i	$0.247672\pi$
$211$			20.3918i			1.40383i	−0.712259	+	0.701916i	$0.752328\pi$
$212$	−3.89445	−	0.983280i	−0.267472	−	0.0675320i
$213$	15.7800	−	6.02828i	1.08123	−	0.413051i
$214$	0.185605	−	1.49331i	0.0126877	−	0.102081i
$215$	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
$219$	−0.451738	−	0.367015i	−0.0305256	−	0.0248006i
$220$	−19.8503	−	19.2833i	−1.33830	−	1.30008i
$221$	−4.82645	−	8.35966i	−0.324662	−	0.562332i
$222$	0.719800	+	2.92547i	0.0483098	+	0.196345i
$223$			11.4666i			0.767860i	0.923362	+	0.383930i	$0.125430\pi$
$223$			11.4666i			0.767860i	−0.923362	+	0.383930i	$0.874570\pi$
$224$	14.9585	−	0.493938i	0.999455	−	0.0330026i
$225$	−8.92608	−	2.93204i	−0.595072	−	0.195470i
$226$	−9.25776	−	21.9002i	−0.615817	−	1.45678i
$227$	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	$0.0847567\pi$
$228$	17.4610	−	13.0330i	1.15639	−	0.863131i
$229$	−1.13465	+	1.96528i	−0.0749800	+	0.129869i	−0.901078	−	0.433658i	$-0.857223\pi$
$229$	−1.13465	+	1.96528i	−0.0749800	+	0.129869i	0.826098	+	0.563527i	$0.190556\pi$
$230$	11.7339	+	8.86942i	0.773707	+	0.584832i
$231$	−10.5162	−	19.5927i	−0.691912	−	1.28911i
$232$	4.00329	−	10.2918i	0.262829	−	0.675688i
$233$	−22.5624	−	13.0264i	−1.47811	−	0.853389i	−0.478420	−	0.878131i	$-0.658790\pi$
$233$	−22.5624	−	13.0264i	−1.47811	−	0.853389i	−0.999694	+	0.0247423i	$0.992123\pi$
$234$	4.98446	−	10.5593i	0.325844	−	0.690284i
$235$	27.7219	−	16.0053i	1.80838	−	1.04407i
$236$	−0.503717	+	1.99506i	−0.0327892	+	0.129867i
$237$	9.58042	+	1.53319i	0.622315	+	0.0995916i
$238$	−11.3385	+	6.60743i	−0.734963	+	0.428296i
$239$			8.32874i			0.538742i	0.963037	+	0.269371i	$0.0868157\pi$
$239$			8.32874i			0.538742i	−0.963037	+	0.269371i	$0.913184\pi$
$240$	−19.5907	−	2.55559i	−1.26457	−	0.164962i
$241$	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	$0.258771\pi$
$242$	−2.18841	+	17.6071i	−0.140676	+	1.13183i
$243$	−15.0893	+	3.91334i	−0.967977	+	0.251041i
$244$	1.35680	+	4.78527i	0.0868601	+	0.306345i
$245$	−5.04265	−	19.3139i	−0.322163	−	1.23392i
$246$	3.57300	+	3.72292i	0.227806	+	0.237365i
$247$	8.65550	−	14.9918i	0.550736	−	0.953904i
$248$	0.426065	+	2.76981i	0.0270551	+	0.175883i
$249$	−0.223470	+	0.0853699i	−0.0141618	+	0.00541010i
$250$	−2.93356	−	6.93965i	−0.185535	−	0.438902i
$251$		−	8.41270i		−	0.531005i	−0.964110	−	0.265502i	$-0.914462\pi$
$251$		−	8.41270i		−	0.531005i	0.964110	−	0.265502i	$-0.0855378\pi$
$252$	−14.3827	−	6.71842i	−0.906027	−	0.423220i
$253$		−	17.6982i		−	1.11268i
$254$	20.3690	−	8.61047i	1.27806	−	0.540269i
$255$	16.1826	−	6.18207i	1.01339	−	0.387136i
$256$	−15.9731	+	0.926576i	−0.998322	+	0.0579110i
$257$	−15.1284	+	26.2032i	−0.943685	+	1.63451i	−0.185321	+	0.982678i	$0.559332\pi$
$257$	−15.1284	+	26.2032i	−0.943685	+	1.63451i	−0.758364	+	0.651832i	$0.774001\pi$
$258$	−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
$261$	−8.72950	+	7.80936i	−0.540342	+	0.483387i
$262$	−14.1514	−	1.75889i	−0.874276	−	0.108665i
$263$	20.9078	−	12.0711i	1.28923	−	0.744338i	0.310714	−	0.950504i	$-0.399432\pi$
$263$	20.9078	−	12.0711i	1.28923	−	0.744338i	0.978517	+	0.206166i	$0.0660986\pi$
$264$	11.7610	+	20.6587i	0.723837	+	1.27145i
$265$		−	5.72701i		−	0.351808i
$266$	−20.4288	−	11.6849i	−1.25257	−	0.716445i
$267$	−1.98733	−	0.318041i	−0.121623	−	0.0194638i
$268$	−2.84241	+	11.2579i	−0.173628	+	0.687683i
$269$	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	$0.123377\pi$
$270$	17.2983	+	11.8273i	1.05274	+	0.719788i
$271$	−1.57903	−	0.911656i	−0.0959195	−	0.0553791i	0.451273	−	0.892386i	$-0.350970\pi$
$271$	−1.57903	−	0.911656i	−0.0959195	−	0.0553791i	−0.547192	+	0.837007i	$0.684303\pi$
$272$	11.9414	−	7.36366i	0.724056	−	0.446487i
$273$	−12.6062	−	0.390851i	−0.762959	−	0.0236554i
$274$	16.8091	−	22.2377i	1.01547	−	1.34343i
$275$	7.59832	−	13.1607i	0.458196	−	0.793618i
$276$	−7.55744	−	10.1251i	−0.454904	−	0.609461i
$277$	11.4072	−	6.58598i	0.685395	−	0.395713i	−0.116490	−	0.993192i	$-0.537164\pi$
$277$	11.4072	−	6.58598i	0.685395	−	0.395713i	0.801885	+	0.597479i	$0.203831\pi$
$278$	0.145673	−	0.0615797i	0.00873690	−	0.00369331i
$279$	0.927606	−	2.82393i	0.0555343	−	0.169064i
$280$	5.90393	+	20.5066i	0.352827	+	1.22551i
$281$			15.3821i			0.917618i	0.888535	+	0.458809i	$0.151724\pi$
$281$			15.3821i			0.917618i	−0.888535	+	0.458809i	$0.848276\pi$
$282$	−26.7001	+	6.56944i	−1.58997	+	0.391205i
$283$	4.64882	+	8.05200i	0.276344	+	0.478641i	0.970473	−	0.241209i	$-0.0775438\pi$
$283$	4.64882	+	8.05200i	0.276344	+	0.478641i	−0.694129	+	0.719850i	$0.744210\pi$
$284$	13.9908	+	13.5913i	0.830204	+	0.806493i
$285$	24.1118	+	19.5897i	1.42826	+	1.16039i
$286$	15.0667	+	11.3886i	0.890910	+	0.673424i
$287$	2.14939	−	5.14240i	0.126875	−	0.303546i
$288$	15.5501	+	6.79670i	0.916297	+	0.400500i
$289$	2.34933	−	4.06916i	0.138196	−	0.239362i
$290$	15.6250	+	1.94204i	0.917529	+	0.114041i
$291$	−17.9523	+	6.85812i	−1.05238	+	0.402030i
$292$	0.164525	−	0.651630i	0.00962810	−	0.0381338i
$293$			17.8462i			1.04258i	0.853378	+	0.521292i	$0.174550\pi$
$293$			17.8462i			1.04258i	−0.853378	+	0.521292i	$0.825450\pi$
$294$	−0.462177	+	17.1402i	−0.0269547	+	0.999637i
$295$	−2.93385			−0.170815
$296$	−2.71325	+	2.17722i	−0.157704	+	0.126548i
$297$	−1.19805	−	25.1854i	−0.0695179	−	1.46141i
$298$	−1.91817	+	15.4329i	−0.111117	+	0.894004i
$299$	−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
$303$	9.56593	+	7.77185i	0.549548	+	0.446481i
$304$	22.1440	+	11.9433i	1.27004	+	0.684993i
$305$	−6.14172	+	3.54592i	−0.351674	+	0.203039i
$306$	−14.8296	+	1.22720i	−0.847754	+	0.0701544i
$307$	−17.6654			−1.00822			−0.504110	−	0.863640i	$-0.668179\pi$
$307$	−17.6654			−1.00822			−0.504110	+	0.863640i	$0.668179\pi$
$308$	15.4001	−	20.5456i	0.877504	−	1.17069i
$309$	0.475709	−	2.97255i	0.0270622	−	0.169103i
$310$	−3.68035	+	1.55578i	−0.209030	+	0.0883621i
$311$	−4.15091	−	7.18958i	−0.235376	−	0.407684i	0.724006	−	0.689794i	$-0.242299\pi$
$311$	−4.15091	−	7.18958i	−0.235376	−	0.407684i	−0.959382	+	0.282110i	$0.908966\pi$
$312$	13.4828	+	0.0817063i	0.763312	+	0.00462571i
$313$	−23.0954	−	13.3342i	−1.30543	−	0.753691i	−0.324101	−	0.946023i	$-0.605062\pi$
$313$	−23.0954	−	13.3342i	−1.30543	−	0.753691i	−0.981330	+	0.192332i	$0.938395\pi$
$314$	12.2339	+	9.24740i	0.690399	+	0.521861i
$315$	4.26761	−	22.2281i	0.240452	−	1.25241i
$316$	3.05607	+	10.7784i	0.171917	+	0.606332i
$317$	−14.4097	+	24.9584i	−0.809331	+	1.40180i	0.103996	+	0.994578i	$0.466837\pi$
$317$	−14.4097	+	24.9584i	−0.809331	+	1.40180i	−0.913328	+	0.407225i	$0.866496\pi$
$318$	−1.37059	+	4.72461i	−0.0768586	+	0.264943i
$319$	−9.47258	−	16.4070i	−0.530362	−	0.918615i
$320$	−6.85618	−	21.7584i	−0.383272	−	1.21633i
$321$	−1.81984	−	0.291237i	−0.101574	−	0.0162553i
$322$	−6.77570	+	11.8460i	−0.377595	+	0.660154i
$323$	−22.0606			−1.22748
$324$	−11.4400	−	13.8970i	−0.635556	−	0.772054i
$325$	−4.30964	−	7.46452i	−0.239056	−	0.414057i
$326$	−16.3058	−	2.02666i	−0.903096	−	0.112247i
$327$	−12.1988	−	9.91097i	−0.674598	−	0.548078i
$328$	−2.16002	+	5.55304i	−0.119267	+	0.306615i
$329$	18.0043	+	23.6200i	0.992608	+	1.30222i
$330$	−24.4542	+	23.4694i	−1.34616	+	1.29195i
$331$	−2.24514	−	1.29623i	−0.123404	−	0.0712472i	0.437027	−	0.899448i	$-0.356031\pi$
$331$	−2.24514	−	1.29623i	−0.123404	−	0.0712472i	−0.560431	+	0.828201i	$0.689365\pi$
$332$	−0.198132	−	0.192474i	−0.0108739	−	0.0105634i
$333$	3.61164	−	0.755539i	0.197916	−	0.0414033i
$334$	−10.0960	+	4.26784i	−0.552430	+	0.233526i
$335$	−16.5553			−0.904513
$336$	0.0370842	−	18.3303i	0.00202311	−	0.999998i
$337$	11.1713			0.608541			0.304271	−	0.952586i	$-0.401587\pi$
$337$	11.1713			0.608541			0.304271	+	0.952586i	$0.401587\pi$
$338$	−7.06709	+	2.98743i	−0.384399	+	0.162495i
$339$	−27.2028	+	10.3920i	−1.47746	+	0.564416i
$340$	14.3478	+	13.9380i	0.778117	+	0.755894i
$341$	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
$345$	11.3594	−	13.9817i	0.611572	−	0.752749i
$346$	−1.42685	−	0.177345i	−0.0767079	−	0.00953410i
$347$	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	$0.706336\pi$
$348$	−12.4253	−	5.34148i	−0.666068	−	0.286333i
$349$	−22.8018			−1.22055			−0.610275	−	0.792189i	$-0.708941\pi$
$349$	−22.8018			−1.22055			−0.610275	+	0.792189i	$0.708941\pi$
$350$	−10.1244	+	5.89992i	−0.541169	+	0.315364i
$351$	−12.7107	−	6.55390i	−0.678448	−	0.349821i
$352$	−15.9107	+	22.3678i	−0.848043	+	1.19221i
$353$	2.06060	+	3.56907i	0.109675	+	0.189962i	0.915639	−	0.402003i	$-0.131686\pi$
$353$	2.06060	+	3.56907i	0.109675	+	0.189962i	−0.805964	+	0.591965i	$0.798352\pi$
$354$	2.42033	+	0.702127i	0.128639	+	0.0373176i
$355$	−13.9056	+	24.0852i	−0.738034	+	1.27831i
$356$	−0.633942	−	2.23584i	−0.0335989	−	0.118499i
$357$	7.60108	+	14.1616i	0.402292	+	0.749513i
$358$	24.3919	+	18.4374i	1.28915	+	0.974449i
$359$	−9.83790	−	5.67992i	−0.519225	−	0.299775i	0.217393	−	0.976084i	$-0.430245\pi$
$359$	−9.83790	−	5.67992i	−0.519225	−	0.299775i	−0.736617	+	0.676310i	$0.763578\pi$
$360$	−3.96838	+	23.8692i	−0.209152	+	1.25802i
$361$	−10.2811	−	17.8074i	−0.541112	−	0.937234i
$362$	12.2061	−	5.15981i	0.641537	−	0.271194i
$363$	21.4571	+	3.43387i	1.12621	+	0.180232i
$364$	−5.72456	−	13.3910i	−0.300048	−	0.701882i
$365$	0.958259			0.0501576
$366$	5.91533	−	1.45544i	0.309200	−	0.0760772i
$367$	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	$0.0724275\pi$
$368$	6.92553	−	12.8406i	0.361018	−	0.669363i
$369$	4.71010	−	4.21363i	0.245198	−	0.219353i
$370$	−3.95689	−	2.99094i	−0.205709	−	0.155492i
$371$	5.27029	−	0.676664i	0.273620	−	0.0351306i
$372$	3.40850	−	0.402687i	0.176723	−	0.0208783i
$373$	27.1273	+	15.6619i	1.40460	+	0.810944i	0.994860	−	0.101259i	$-0.0322872\pi$
$373$	27.1273	+	15.6619i	1.40460	+	0.810944i	0.409737	+	0.912204i	$0.365621\pi$
$374$	2.96865	−	23.8847i	0.153505	−	1.23505i
$375$	−8.61992	+	3.29298i	−0.445131	+	0.170049i
$376$	−19.8710	−	24.7632i	−1.02477	−	1.27706i
$377$	−10.7454			−0.553416
$378$	−8.84026	+	17.3162i	−0.454694	+	0.890648i
$379$		−	28.8128i		−	1.48001i	−0.672600	−	0.740006i	$-0.734822\pi$
$379$		−	28.8128i		−	1.48001i	0.672600	−	0.740006i	$-0.265178\pi$
$380$	−8.78162	+	34.7811i	−0.450488	+	1.78423i
$381$	−9.66541	−	25.3008i	−0.495174	−	1.29620i
$382$	12.4887	+	1.55223i	0.638977	+	0.0794190i
$383$	12.6701	−	21.9453i	0.647413	−	1.12135i	−0.336325	−	0.941746i	$-0.609184\pi$
$383$	12.6701	−	21.9453i	0.647413	−	1.12135i	0.983738	−	0.179607i	$-0.0574826\pi$
$384$	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
$387$	10.2364	+	11.4425i	0.520347	+	0.581657i
$388$	−15.9168	−	15.4622i	−0.808053	−	0.784975i
$389$	−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	$0.869057\pi$
$390$	4.59306	+	18.6675i	0.232579	+	0.945267i
$391$			12.7923i			0.646932i
$392$	−18.1737	+	7.85602i	−0.917910	+	0.396789i
$393$	−2.75991	+	17.2458i	−0.139219	+	0.869934i
$394$	3.57427	−	1.51093i	0.180069	−	0.0761198i
$395$	−13.8337	+	7.98689i	−0.696049	+	0.401864i
$396$	25.7906	−	13.5092i	1.29603	−	0.678861i
$397$	−8.01775	+	13.8871i	−0.402399	+	0.696976i	−0.994015	−	0.109244i	$-0.965157\pi$
$397$	−8.01775	+	13.8871i	−0.402399	+	0.696976i	0.591616	+	0.806220i	$0.298490\pi$
$398$	−19.8737	+	26.2921i	−0.996180	+	1.31790i
$399$	−15.1785	+	24.5035i	−0.759876	+	1.22671i
$400$	10.6628	−	6.57517i	0.533139	−	0.328759i
$401$	6.53545	+	3.77324i	0.326365	+	0.188427i	0.654226	−	0.756299i	$-0.272994\pi$
$401$	6.53545	+	3.77324i	0.326365	+	0.188427i	−0.327861	+	0.944726i	$0.606328\pi$
$402$	13.6576	+	3.96201i	0.681180	+	0.197607i
$403$	2.36154	−	1.36343i	0.117637	−	0.0679175i
$404$	−3.48395	+	13.7988i	−0.173333	+	0.686516i
$405$	15.2186	−	20.6656i	0.756218	−	1.02688i
$406$	0.0589722	+	14.6083i	0.00292674	+	0.725000i
$407$			5.96817i			0.295831i
$408$	−8.50083	−	14.9321i	−0.420854	−	0.739250i
$409$	−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	$0.578136\pi$
$410$	−8.43062	−	1.04785i	−0.416359	−	0.0517496i
$411$	−26.4977	−	21.5281i	−1.30704	−	1.06190i
$412$	3.34425	−	0.948219i	0.164760	−	0.0467154i
$413$	−0.346643	−	2.69988i	−0.0170572	−	0.132852i
$414$	−12.7173	+	8.81592i	−0.625020	+	0.433279i
$415$	0.196926	−	0.341085i	0.00966670	−	0.0167432i
$416$	6.47483	+	14.1586i	0.317454	+	0.694183i
$417$	−0.0691243	−	0.180945i	−0.00338503	−	0.00886090i
$418$	39.7569	−	16.8062i	1.94457	−	0.822019i
$419$		−	19.5661i		−	0.955866i	−0.878396	−	0.477933i	$-0.841386\pi$
$419$		−	19.5661i		−	0.955866i	0.878396	−	0.477933i	$-0.158614\pi$
$420$	25.3533	−	6.34671i	1.23711	−	0.309688i
$421$			26.0983i			1.27195i	0.771708	+	0.635977i	$0.219403\pi$
$421$			26.0983i			1.27195i	−0.771708	+	0.635977i	$0.780597\pi$
$422$	11.2287	+	26.5626i	0.546603	+	1.29305i
$423$	6.89562	+	32.9625i	0.335277	+	1.60269i
$424$	−5.61439	+	0.863632i	−0.272659	+	0.0419417i
$425$	−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
$429$	14.5859	−	17.9530i	0.704214	−	0.866777i
$430$	2.54561	−	20.4810i	0.122760	−	0.987683i
$431$	10.4072	−	6.00858i	0.501296	−	0.289423i	−0.227953	−	0.973672i	$-0.573203\pi$
$431$	10.4072	−	6.00858i	0.501296	−	0.289423i	0.729248	+	0.684249i	$0.239870\pi$
$432$	8.98616	−	18.7416i	0.432347	−	0.901707i
$433$			35.6343i			1.71247i	0.516583	+	0.856237i	$0.327204\pi$
$433$			35.6343i			1.71247i	−0.516583	+	0.856237i	$0.672796\pi$
$434$	−1.86655	−	3.20302i	−0.0895972	−	0.153750i
$435$	3.04729	−	19.0415i	0.146107	−	0.912972i
$436$	4.44287	−	17.5968i	0.212775	−	0.842733i
$437$	−19.8674	+	11.4705i	−0.950389	+	0.548707i
$438$	−0.790533	−	0.229330i	−0.0377732	−	0.0109578i
$439$	−11.6950	−	6.75210i	−0.558171	−	0.322260i	0.194240	−	0.980954i	$-0.437776\pi$
$439$	−11.6950	−	6.75210i	−0.558171	−	0.322260i	−0.752411	+	0.658694i	$0.771109\pi$
$440$	−36.4754	−	14.1882i	−1.73890	−	0.676396i
$441$	20.9597	+	1.30095i	0.998079	+	0.0619500i
$442$	−10.8902	−	8.23170i	−0.517993	−	0.391542i
$443$	11.7659	−	20.3791i	0.559014	−	0.968241i	−0.438565	−	0.898700i	$-0.644513\pi$
$443$	11.7659	−	20.3791i	0.559014	−	0.968241i	0.997579	−	0.0695416i	$-0.0221536\pi$
$444$	2.54852	+	3.41439i	0.120947	+	0.162040i
$445$	2.86962	−	1.65678i	0.136033	−	0.0785387i
$446$	6.31402	+	14.9365i	0.298978	+	0.707263i
$447$	18.8075	+	3.00984i	0.889563	+	0.142360i
$448$	19.2131	−	8.88022i	0.907732	−	0.419551i
$449$		−	30.6292i		−	1.44548i	−0.691120	−	0.722740i	$-0.742883\pi$
$449$		−	30.6292i		−	1.44548i	0.691120	−	0.722740i	$-0.257117\pi$
$450$	−13.2417	+	1.09579i	−0.624220	+	0.0516562i
$451$	5.11103	+	8.85257i	0.240669	+	0.416851i
$452$	−24.1185	−	23.4297i	−1.13444	−	1.10204i
$453$	9.10281	−	11.2041i	0.427687	−	0.526416i
$454$	18.0888	−	23.9307i	0.848948	−	1.12312i
$455$	16.5141	−	12.5878i	0.774193	−	0.590125i
$456$	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	$0.0790950\pi$
$458$	−0.395839	+	3.18478i	−0.0184964	+	0.148815i
$459$	0.865951	+	18.2040i	0.0404191	+	0.849691i
$460$	20.1685	+	5.09219i	0.940362	+	0.237425i
$461$			30.8362i			1.43618i	0.695948	+	0.718092i	$0.254985\pi$
$461$			30.8362i			1.43618i	−0.695948	+	0.718092i	$0.745015\pi$
$462$	−24.4871	−	19.7310i	−1.13924	−	0.917969i
$463$	−32.3199			−1.50203			−0.751016	−	0.660284i	$-0.770436\pi$
$463$	−32.3199			−1.50203			−0.751016	+	0.660284i	$0.770436\pi$
$464$	−0.452391	−	15.6105i	−0.0210017	−	0.724701i
$465$	1.74639	+	4.57146i	0.0809867	+	0.211996i
$466$	−36.5629	−	4.54444i	−1.69375	−	0.210517i
$467$	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
$471$	11.8435	−	14.5775i	0.545722	−	0.671698i
$472$	0.442424	+	2.87615i	0.0203642	+	0.132386i
$473$	−21.5061	+	12.4166i	−0.988852	+	0.570914i
$474$	13.3238	−	3.27826i	0.611981	−	0.150575i
$475$	−19.6984			−0.903823
$476$	−11.1312	+	14.8504i	−0.510199	+	0.680665i
$477$	5.72409	+	1.88025i	0.262088	+	0.0860910i
$478$	4.58618	+	10.8491i	0.209767	+	0.496226i
$479$	−17.6827	−	30.6273i	−0.807943	−	1.39940i	−0.914286	−	0.405068i	$-0.867248\pi$
$479$	−17.6827	−	30.6273i	−0.807943	−	1.39940i	0.106344	−	0.994329i	$-0.466086\pi$
$480$	−26.9262	+	7.45857i	−1.22901	+	0.340436i
$481$	2.93154	+	1.69253i	0.133667	+	0.0771726i
$482$	6.14559	−	8.13034i	0.279924	−	0.370327i
$483$	14.2088	+	8.80156i	0.646524	+	0.400485i
$484$	6.84464	+	24.1402i	0.311120	+	1.09728i
$485$	15.8198	−	27.4008i	0.718342	−	1.24421i
$486$	−17.5005	+	13.4064i	−0.793841	+	0.608126i
$487$	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	$0.566251\pi$
$488$	4.40236	+	5.48621i	0.199286	+	0.248349i
$489$	−3.18008	+	19.8713i	−0.143808	+	0.898610i
$490$	−17.2037	−	22.3818i	−0.777185	−	1.01111i
$491$	22.5295			1.01674			0.508371	−	0.861138i	$-0.330248\pi$
$491$	22.5295			1.01674			0.508371	+	0.861138i	$0.330248\pi$
$492$	6.70422	+	2.88205i	0.302250	+	0.129933i
$493$	6.84678	+	11.8590i	0.308363	+	0.534101i
$494$	3.01959	−	24.2945i	0.135858	−	1.09306i
$495$	27.6774	+	30.9385i	1.24401	+	1.39058i
$496$	2.08018	+	3.37336i	0.0934027	+	0.151468i
$497$	−23.8075	−	9.95092i	−1.06791	−	0.446360i
$498$	−0.244086	+	0.234256i	−0.0109377	+	0.0104973i
$499$	11.3117	+	6.53084i	0.506383	+	0.292361i	0.731346	−	0.682007i	$-0.238893\pi$
$499$	11.3117	+	6.53084i	0.506383	+	0.292361i	−0.224962	+	0.974367i	$0.572226\pi$
$500$	−7.64256	−	7.42429i	−0.341786	−	0.332024i
$501$	4.79073	+	12.5405i	0.214034	+	0.560270i
$502$	−4.63241	−	10.9585i	−0.206755	−	0.489100i
$503$	−2.77607			−0.123779			−0.0618894	−	0.998083i	$-0.519713\pi$
$503$	−2.77607			−0.123779			−0.0618894	+	0.998083i	$0.519713\pi$
$504$	−22.4345	−	0.831688i	−0.999314	−	0.0370463i
$505$	−20.2919			−0.902978
$506$	−9.74542	−	23.0538i	−0.433237	−	1.02487i
$507$	3.35345	+	8.77822i	0.148932	+	0.389854i
$508$	21.7915	−	22.4321i	0.966841	−	0.995265i
$509$	−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
$513$	−27.4959	+	17.6680i	−1.21397	+	0.780059i
$514$	−5.27775	+	42.4629i	−0.232792	+	1.87296i
$515$	2.47812	+	4.29223i	0.109199	+	0.189138i
$516$	−7.00156	+	16.2870i	−0.308226	+	0.716995i
$517$	−54.4701			−2.39559
$518$	2.28490	−	3.99471i	0.100393	−	0.175518i
$519$	−0.278275	+	1.73885i	−0.0122149	+	0.0763270i
$520$	−17.3133	+	13.8929i	−0.759239	+	0.609244i
$521$	2.92633	+	5.06856i	0.128205	+	0.222058i	0.922981	−	0.384845i	$-0.125745\pi$
$521$	2.92633	+	5.06856i	0.128205	+	0.222058i	−0.794776	+	0.606903i	$0.792412\pi$
$522$	−7.07093	+	14.9794i	−0.309486	+	0.655630i
$523$	−9.81038	+	16.9921i	−0.428978	+	0.743012i	−0.996783	−	0.0801516i	$-0.974460\pi$
$523$	−9.81038	+	16.9921i	−0.428978	+	0.743012i	0.567805	+	0.823163i	$0.307793\pi$
$524$	−19.4023	+	5.50125i	−0.847591	+	0.240323i
$525$	6.78717	+	12.6452i	0.296216	+	0.551883i
$526$	20.5878	−	27.2367i	0.897670	−	1.18758i
$527$	−3.00947	−	1.73752i	−0.131094	−	0.0756874i
$528$	26.6955	+	20.4341i	1.16177	+	0.889279i
$529$	−4.84862	−	8.39806i	−0.210810	−	0.365133i
$530$	−3.15355	−	7.46006i	−0.136982	−	0.324044i
$531$	0.963222	−	2.93235i	0.0418003	−	0.127253i
$532$	−33.0449	−	3.97179i	−1.43268	−	0.172199i
$533$	5.79779			0.251130
$534$	−2.76384	+	0.680032i	−0.119603	+	0.0294279i
$535$	2.62777	−	1.51715i	0.113609	−	0.0655919i
$536$	2.49654	+	16.2297i	0.107834	+	0.701018i
$537$	23.6136	−	29.0647i	1.01900	−	1.25423i
$538$	17.1418	−	22.6779i	0.739036	−	0.977712i
$539$	−9.00148	+	32.7525i	−0.387721	+	1.41075i
$540$	29.0455	+	5.88117i	1.24992	+	0.253085i
$541$	−35.5120	−	20.5029i	−1.52678	−	0.881488i	−0.999494	−	0.0318007i	$-0.989876\pi$
$541$	−35.5120	−	20.5029i	−1.52678	−	0.881488i	−0.527287	−	0.849687i	$-0.676791\pi$
$542$	−2.55886	−	0.318043i	−0.109913	−	0.0136611i
$543$	−5.79199	−	15.1615i	−0.248558	−	0.650642i
$544$	11.5003	−	16.1675i	0.493070	−	0.693174i
$545$	25.8771			1.10845
$546$	−16.6361	+	6.43239i	−0.711960	+	0.275281i
$547$			13.0813i			0.559315i	0.960100	+	0.279658i	$0.0902209\pi$
$547$			13.0813i			0.559315i	−0.960100	+	0.279658i	$0.909779\pi$
$548$	9.65058	−	38.2228i	0.412252	−	1.63280i
$549$	−1.52771	−	7.30276i	−0.0652010	−	0.311674i
$550$	2.65078	−	21.3272i	0.113029	−	0.909394i
$551$	−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
$555$	−3.83063	+	4.71490i	−0.162601	+	0.200136i
$556$	0.155847	−	0.160429i	0.00660937	−	0.00680369i
$557$	−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	$-0.471020\pi$
$558$	−0.346674	−	4.18926i	−0.0146759	−	0.177345i
$559$			14.0849i			0.595730i
$560$	18.9824	+	23.4612i	0.802153	+	0.991416i
$561$	−29.1074	−	4.65817i	−1.22891	−	0.196668i
$562$	8.47007	+	20.0368i	0.357288	+	0.845203i
$563$	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	$0.257034\pi$
$564$	−31.1623	+	23.2597i	−1.31217	+	0.979409i
$565$	23.9716	−	41.5200i	1.00849	−	1.74676i
$566$	10.4894	+	7.92875i	0.440902	+	0.333270i
$567$	20.8157	+	11.5632i	0.874176	+	0.485609i
$568$	25.7086	+	10.0001i	1.07871	+	0.419595i
$569$	26.7497	+	15.4440i	1.12141	+	0.647445i	0.941760	−	0.336286i	$-0.109171\pi$
$569$	26.7497	+	15.4440i	1.12141	+	0.647445i	0.179648	+	0.983731i	$0.442504\pi$
$570$	42.1952	+	12.2406i	1.76736	+	0.512703i
$571$	−6.49082	+	3.74748i	−0.271633	+	0.156827i	−0.629629	−	0.776896i	$-0.716793\pi$
$571$	−6.49082	+	3.74748i	−0.271633	+	0.156827i	0.357997	+	0.933723i	$0.383460\pi$
$572$	25.8971	+	6.53855i	1.08281	+	0.273390i
$573$	2.43564	−	15.2195i	0.101750	−	0.635803i
$574$	−0.0318191	−	7.88209i	−0.00132810	−	0.328992i
$575$			11.4225i			0.476350i
$576$	23.9982	+	0.290872i	0.999927	+	0.0121197i
$577$	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	$0.187091\pi$
$578$	0.819596	−	6.59418i	0.0340907	−	0.274282i
$579$	16.2905	−	20.0510i	0.677010	−	0.833292i
$580$	21.4226	−	6.07409i	0.889524	−	0.252213i
$581$	0.337151	+	0.140921i	0.0139874	+	0.00584637i
$582$	−19.6084	+	18.8188i	−0.812795	+	0.780064i
$583$	−4.87263	+	8.43964i	−0.201804	+	0.349534i
$584$	−0.144505	−	0.939414i	−0.00597967	−	0.0388732i
$585$	23.0459	−	4.82112i	0.952833	−	0.199329i
$586$	9.82690	+	23.2466i	0.405946	+	0.960307i
$587$		−	15.2002i		−	0.627381i	−0.949525	−	0.313691i	$-0.898435\pi$
$587$		−	15.2002i		−	0.627381i	0.949525	−	0.313691i	$-0.101565\pi$
$588$	8.83613	+	22.5815i	0.364396	+	0.931244i
$589$		−	6.23194i		−	0.256783i
$590$	−3.82166	+	1.61551i	−0.157335	+	0.0665095i
$591$	−1.69605	−	4.43970i	−0.0697663	−	0.182625i
$592$	−2.33543	+	4.33010i	−0.0959854	+	0.177966i
$593$	−4.55071	+	7.88206i	−0.186875	+	0.323678i	−0.944207	−	0.329353i	$-0.893169\pi$
$593$	−4.55071	+	7.88206i	−0.186875	+	0.323678i	0.757332	+	0.653031i	$0.226503\pi$
$594$	−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
$597$	31.3288	+	25.4531i	1.28220	+	1.04173i
$598$	−14.0877	−	1.75097i	−0.576087	−	0.0716024i
$599$	−37.6136	+	21.7162i	−1.53685	+	0.887302i	−0.537831	+	0.843053i	$0.680756\pi$
$599$	−37.6136	+	21.7162i	−1.53685	+	0.887302i	−0.999021	+	0.0442488i	$0.985911\pi$
$600$	−7.59057	−	13.3332i	−0.309884	−	0.544326i
$601$			15.5284i			0.633415i	0.948523	+	0.316708i	$0.102577\pi$
$601$			15.5284i			0.633415i	−0.948523	+	0.316708i	$0.897423\pi$
$602$	19.1485	−	0.0773002i	0.780433	−	0.00315052i
$603$	5.43533	−	16.5469i	0.221344	−	0.673841i
$604$	16.1619	+	4.08059i	0.657618	+	0.166037i
$605$	−30.9831	+	17.8881i	−1.25964	+	0.727256i
$606$	16.7402	+	4.85625i	0.680024	+	0.197272i
$607$	1.01612	+	0.586656i	0.0412430	+	0.0238116i	0.520480	−	0.853874i	$-0.325753\pi$
$607$	1.01612	+	0.586656i	0.0412430	+	0.0238116i	−0.479237	+	0.877686i	$0.659086\pi$
$608$	35.4214	+	3.36394i	1.43653	+	0.136426i
$609$	17.8830	+	0.554459i	0.724657	+	0.0224678i
$610$	−6.04771	+	8.00086i	−0.244865	+	0.323945i
$611$	−15.4473	+	26.7555i	−0.624930	+	1.08241i
$612$	−18.6415	+	9.76443i	−0.753536	+	0.394704i
$613$	−35.7276	+	20.6273i	−1.44302	+	0.833131i	−0.998050	−	0.0624126i	$-0.980121\pi$
$613$	−35.7276	+	20.6273i	−1.44302	+	0.833131i	−0.444974	+	0.895543i	$0.646787\pi$
$614$	−23.0112	+	9.72739i	−0.928655	+	0.392565i
$615$	−1.64420	+	10.2741i	−0.0663006	+	0.414291i
$616$	8.74702	−	35.2429i	0.352427	−	1.41998i
$617$		−	15.3232i		−	0.616887i	−0.951243	−	0.308444i	$-0.900192\pi$
$617$		−	15.3232i		−	0.616887i	0.951243	−	0.308444i	$-0.0998081\pi$
$618$	−1.01716	−	4.13402i	−0.0409161	−	0.166295i
$619$	−7.95796	−	13.7836i	−0.319857	−	0.554009i	0.660601	−	0.750738i	$-0.270302\pi$
$619$	−7.95796	−	13.7836i	−0.319857	−	0.554009i	−0.980458	+	0.196728i	$0.936968\pi$
$620$	−3.93738	+	4.05313i	−0.158129	+	0.162778i
$621$	10.2451	+	15.9440i	0.411122	+	0.639812i
$622$	−9.36592	−	7.07954i	−0.375539	−	0.283864i
$623$	1.86370	+	2.44502i	0.0746677	+	0.0979575i
$624$	17.6078	−	7.31780i	0.704875	−	0.292946i
$625$	15.4254	−	26.7176i	0.617017	−	1.06871i
$626$	−37.4267	−	4.65180i	−1.49587	−	0.185923i
$627$	−18.8653	−	49.3831i	−0.753407	−	1.97217i
$628$	21.0280	+	5.30920i	0.839110	+	0.211860i
$629$		−	4.31380i		−	0.172002i
$630$	−6.68078	−	31.3045i	−0.266169	−	1.24720i
$631$	−27.9268			−1.11175			−0.555875	−	0.831266i	$-0.687617\pi$
$631$	−27.9268			−1.11175			−0.555875	+	0.831266i	$0.687617\pi$
$632$	9.91594	+	12.3572i	0.394435	+	0.491544i
$633$	32.9941	−	12.6044i	1.31140	−	0.500980i
$634$	−5.02703	+	40.4457i	−0.199649	+	1.60630i
$635$	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
$639$	−19.5076	−	21.8060i	−0.771708	−	0.862634i
$640$	−20.9121	−	24.5673i	−0.826622	−	0.971108i
$641$	7.03036	−	4.05898i	0.277683	−	0.160320i	−0.354691	−	0.934984i	$-0.615414\pi$
$641$	7.03036	−	4.05898i	0.277683	−	0.160320i	0.632374	+	0.774663i	$0.282081\pi$
$642$	−2.53091	+	0.622720i	−0.0998871	+	0.0245768i
$643$	21.5611			0.850285			0.425143	−	0.905126i	$-0.360224\pi$
$643$	21.5611			0.850285			0.425143	+	0.905126i	$0.360224\pi$
$644$	−2.30312	+	19.1618i	−0.0907558	+	0.755079i
$645$	−24.9595	−	3.99436i	−0.982778	−	0.157278i
$646$	−28.7363	+	12.1475i	−1.13061	+	0.477939i
$647$	19.5173	+	33.8049i	0.767304	+	1.32901i	0.939020	+	0.343863i	$0.111736\pi$
$647$	19.5173	+	33.8049i	0.767304	+	1.32901i	−0.171716	+	0.985147i	$0.554931\pi$
$648$	−22.5542	−	11.8029i	−0.886011	−	0.463663i
$649$	4.32348	+	2.49616i	0.169712	+	0.0979830i
$650$	−9.72408	−	7.35027i	−0.381410	−	0.288301i
$651$	−4.00055	+	2.14725i	−0.156794	+	0.0841572i
$652$	−22.3561	+	6.33877i	−0.875531	+	0.248245i
$653$	−8.53952	+	14.7909i	−0.334177	+	0.578812i	−0.983326	−	0.181849i	$-0.941792\pi$
$653$	−8.53952	+	14.7909i	−0.334177	+	0.578812i	0.649149	+	0.760661i	$0.275125\pi$
$654$	−21.3478	−	6.19288i	−0.834763	−	0.242161i
$655$	−14.3772	−	24.9021i	−0.561765	−	0.973006i
$656$	0.244092	+	8.42284i	0.00953021	+	0.328857i
$657$	−0.314609	+	0.957770i	−0.0122741	+	0.0373662i
$658$	36.4588	+	20.8537i	1.42131	+	0.812962i
$659$	−6.99022			−0.272300			−0.136150	−	0.990688i	$-0.543473\pi$
$659$	−6.99022			−0.272300			−0.136150	+	0.990688i	$0.543473\pi$
$660$	−18.9309	+	44.0370i	−0.736885	+	1.71414i
$661$	23.0740	+	39.9653i	0.897474	+	1.55447i	0.830712	+	0.556702i	$0.187933\pi$
$661$	23.0740	+	39.9653i	0.897474	+	1.55447i	0.0667617	+	0.997769i	$0.478733\pi$
$662$	−3.63830	−	0.452207i	−0.141406	−	0.0175755i
$663$	−10.5427	+	12.9764i	−0.409444	+	0.503962i
$664$	−0.364074	−	0.141617i	−0.0141288	−	0.00549582i
$665$	−6.04325	−	47.0686i	−0.234347	−	1.82524i
$666$	4.28852	−	2.97290i	0.166177	−	0.115198i
$667$	12.3322	+	7.12002i	0.477506	+	0.275688i
$668$	−10.8011	+	11.1186i	−0.417907	+	0.430193i
$669$	18.5530	−	7.08760i	0.717301	−	0.274023i
$670$	−21.5651	+	9.11610i	−0.833133	+	0.352186i
$671$	12.0677			0.465869
$672$	−10.0452	−	23.8976i	−0.387501	−	0.921869i
$673$	8.04494			0.310110			0.155055	−	0.987906i	$-0.450445\pi$
$673$	8.04494			0.310110			0.155055	+	0.987906i	$0.450445\pi$
$674$	14.5519	−	6.15144i	0.560517	−	0.236945i
$675$	0.773227	+	16.2548i	0.0297615	+	0.625646i
$676$	−7.56063	+	7.78291i	−0.290794	+	0.299343i
$677$	−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
$681$	−28.5150	−	23.1671i	−1.09270	−	0.887764i
$682$	6.74725	+	0.838621i	0.258365	+	0.0321125i
$683$	−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	$-0.445998\pi$
$684$	−31.8803	−	20.1963i	−1.21897	−	0.772223i
$685$	56.2088			2.14763
$686$	18.5642	−	18.4762i	0.708784	−	0.705425i
$687$	3.88117	+	0.621119i	0.148076	+	0.0236972i
$688$	−20.4621	+	0.592989i	−0.780112	+	0.0226075i
$689$	2.76368	+	4.78683i	0.105288	+	0.182364i
$690$	7.09796	−	24.4677i	0.270215	−	0.931470i
$691$	17.2791	−	29.9282i	0.657326	−	1.13852i	−0.323979	−	0.946064i	$-0.605021\pi$
$691$	17.2791	−	29.9282i	0.657326	−	1.13852i	0.981305	−	0.192458i	$-0.0616460\pi$
$692$	−1.95628	+	0.554678i	−0.0743667	+	0.0210857i
$693$	−25.2010	+	29.1256i	−0.957307	+	1.10639i
$694$	16.3280	+	12.3420i	0.619801	+	0.468497i
$695$	0.276178	+	0.159451i	0.0104760	+	0.00604834i
$696$	−19.1266	−	0.115908i	−0.724992	−	0.00439349i
$697$	−3.69426	−	6.39864i	−0.139930	−	0.242366i
$698$	−29.7018	+	12.5557i	−1.12423	+	0.475240i
$699$	−7.13078	+	44.5579i	−0.269711	+	1.68533i
$700$	−9.93931	+	13.2602i	−0.375671	+	0.501189i
$701$	29.6534			1.11999			0.559997	−	0.828495i	$-0.310802\pi$
$701$	29.6534			1.11999			0.559997	+	0.828495i	$0.310802\pi$
$702$	−20.1660	−	1.53807i	−0.761115	−	0.0580508i
$703$	6.69969	−	3.86807i	0.252684	−	0.145887i
$704$	−8.40869	+	37.8977i	−0.316915	+	1.42832i
$705$	−43.0318	−	34.9612i	−1.62067	−	1.31672i
$706$	4.64945	+	3.51444i	0.174984	+	0.132268i
$707$	−2.39755	−	18.6736i	−0.0901692	−	0.702295i
$708$	3.53937	−	0.418148i	0.133018	−	0.0157150i
$709$	−9.81381	−	5.66601i	−0.368565	−	0.212791i	0.304266	−	0.952587i	$-0.401589\pi$
$709$	−9.81381	−	5.66601i	−0.368565	−	0.212791i	−0.672832	+	0.739796i	$0.734922\pi$
$710$	−4.85116	+	39.0307i	−0.182061	+	1.46480i
$711$	−3.44103	−	16.4488i	−0.129049	−	0.616880i
$712$	−2.05693	−	2.56335i	−0.0770868	−	0.0960654i
$713$	−3.61371			−0.135335
$714$	17.6993	+	14.2616i	0.662378	+	0.533726i
$715$			38.0831i			1.42423i
$716$	41.9256	+	10.5855i	1.56683	+	0.395598i
$717$	13.4759	−	5.14807i	0.503269	−	0.192258i
$718$	−15.9426	−	1.98152i	−0.594971	−	0.0739495i
$719$	−8.51080	+	14.7411i	−0.317399	+	0.549752i	−0.979945	−	0.199270i	$-0.936143\pi$
$719$	−8.51080	+	14.7411i	−0.317399	+	0.549752i	0.662545	+	0.749022i	$0.269476\pi$
$720$	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
$723$	−9.68787	−	7.87092i	−0.360296	−	0.292723i
$724$	13.0585	−	13.4424i	0.485316	−	0.499584i
$725$	6.11364	+	10.5891i	0.227055	+	0.393271i
$726$	29.8411	−	7.34228i	1.10751	−	0.272497i
$727$		−	42.1153i		−	1.56197i	−0.624550	−	0.780985i	$-0.714718\pi$
$727$		−	42.1153i		−	1.56197i	0.624550	−	0.780985i	$-0.285282\pi$
$728$	−14.8306	−	14.2911i	−0.549658	−	0.529663i
$729$	15.6586	+	21.9956i	0.579949	+	0.814653i
$730$	1.24824	−	0.527661i	0.0461993	−	0.0195296i
$731$	15.5446	−	8.97469i	0.574939	−	0.331941i
$732$	6.90394	−	5.15312i	0.255177	−	0.190465i
$733$	−20.3500	+	35.2472i	−0.751644	+	1.30189i	0.195382	+	0.980727i	$0.437405\pi$
$733$	−20.3500	+	35.2472i	−0.751644	+	1.30189i	−0.947026	+	0.321158i	$0.895928\pi$
$734$	23.8815	−	31.5941i	0.881481	−	1.16616i
$735$	−28.1332	+	20.0972i	−1.03771	+	0.741295i
$736$	1.95064	−	20.5398i	0.0719017	−	0.757107i
$737$	24.3968	+	14.0855i	0.898669	+	0.518847i
$738$	3.81520	−	8.08230i	0.140439	−	0.297513i
$739$	7.63741	−	4.40946i	0.280947	−	0.162205i	−0.352905	−	0.935659i	$-0.614806\pi$
$739$	7.63741	−	4.40946i	0.280947	−	0.162205i	0.633852	+	0.773454i	$0.281473\pi$
$740$	−6.80122	−	1.71719i	−0.250018	−	0.0631251i
$741$	−29.6068	−	4.73810i	−1.08763	−	0.174058i
$742$	6.49252	−	3.78349i	0.238348	−	0.138896i
$743$		−	16.3412i		−	0.599502i	−0.954017	−	0.299751i	$-0.903096\pi$
$743$		−	16.3412i		−	0.599502i	0.954017	−	0.299751i	$-0.0969036\pi$
$744$	4.21821	−	2.40142i	0.154647	−	0.0880402i
$745$	−27.1572	+	15.6792i	−0.994962	+	0.574441i
$746$	43.9604	+	5.46388i	1.60950	+	0.200047i
$747$	0.276258	+	0.308808i	0.0101077	+	0.0112987i
$748$	−9.28501	−	32.7471i	−0.339494	−	1.19735i
$749$	1.70663	+	2.23895i	0.0623590	+	0.0818096i
$750$	−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	$0.0943219\pi$
$752$	−39.5198	−	21.3149i	−1.44114	−	0.777273i
$753$	−13.6118	+	5.19997i	−0.496041	+	0.189497i
$754$	−13.9970	+	5.91690i	−0.509742	+	0.215481i
$755$			23.7670i			0.864969i
$756$	−1.98034	+	27.4240i	−0.0720241	+	0.997403i
$757$		−	29.0246i		−	1.05492i	−0.849581	−	0.527459i	$-0.823145\pi$
$757$		−	29.0246i		−	1.05492i	0.849581	−	0.527459i	$-0.176855\pi$
$758$	−15.8656	−	37.5318i	−0.576265	−	1.36322i
$759$	−28.6358	+	10.9394i	−1.03941	+	0.397075i
$760$	7.71305	+	50.1418i	0.279782	+	1.81883i
$761$	15.5050	−	26.8554i	0.562055	−	0.973507i	−0.435262	−	0.900304i	$-0.643344\pi$
$761$	15.5050	−	26.8554i	0.562055	−	0.973507i	0.997317	−	0.0732037i	$-0.0233223\pi$
$762$	−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
$765$	−20.0052	−	22.3624i	−0.723291	−	0.808513i
$766$	4.42015	−	35.5629i	0.159706	−	1.28494i
$767$	2.45221	−	1.41578i	0.0885442	−	0.0511210i
$768$	11.3724	+	25.2719i	0.410365	+	0.911922i
$769$		−	42.3916i		−	1.52868i	−0.644813	−	0.764340i	$-0.723065\pi$
$769$		−	42.3916i		−	1.52868i	0.644813	−	0.764340i	$-0.276935\pi$
$770$	51.7739	−	0.209005i	1.86580	−	0.00753203i
$771$	51.7479	+	8.28143i	1.86366	+	0.298248i
$772$	28.9235	+	7.30267i	1.04098	+	0.262829i
$773$	2.88336	−	1.66471i	0.103707	−	0.0598754i	−0.447249	−	0.894409i	$-0.647596\pi$
$773$	2.88336	−	1.66471i	0.103707	−	0.0598754i	0.550957	+	0.834534i	$0.314263\pi$
$774$	19.6348	+	9.26851i	0.705760	+	0.333150i
$775$	−2.68722	−	1.55147i	−0.0965277	−	0.0557303i
$776$	−29.2476	−	11.3767i	−1.04993	−	0.408400i
$777$	−4.79149	−	2.96806i	−0.171894	−	0.106478i
$778$	−4.98397	−	3.76730i	−0.178684	−	0.135064i
$779$	6.62508	−	11.4750i	0.237368	−	0.411134i
$780$	16.2621	+	21.7873i	0.582278	+	0.780112i
$781$	40.9842	−	23.6622i	1.46653	−	0.846701i
$782$	7.04399	+	16.6633i	0.251893	+	0.595878i
$783$	18.0314	+	9.29733i	0.644388	+	0.332260i
$784$	−19.3473	+	20.2406i	−0.690976	+	0.722878i
$785$			30.9229i			1.10369i
$786$	5.90121	+	23.9842i	0.210489	+	0.855489i
$787$	−11.2617	−	19.5059i	−0.401437	−	0.695309i	0.592463	−	0.805598i	$-0.298156\pi$
$787$	−11.2617	−	19.5059i	−0.401437	−	0.695309i	−0.993900	+	0.110289i	$0.964822\pi$
$788$	3.82389	−	3.93631i	0.136221	−	0.140225i
$789$	−32.4545	−	26.3677i	−1.15541	−	0.938714i
$790$	−13.6220	+	18.0212i	−0.484647	+	0.641167i
$791$	41.0411	+	17.1542i	1.45925	+	0.609932i
$792$	26.1563	−	31.7986i	0.929424	−	1.12992i
$793$	3.42230	−	5.92761i	0.121530	−	0.210495i
$794$	−2.79710	+	22.5045i	−0.0992654	+	0.798653i
$795$	−9.26634	+	3.53992i	−0.328643	+	0.125548i
$796$	−11.4101	+	45.1916i	−0.404420	+	1.60178i
$797$		−	20.3781i		−	0.721831i	−0.932599	−	0.360915i	$-0.882464\pi$
$797$		−	20.3781i		−	0.721831i	0.932599	−	0.360915i	$-0.117536\pi$
$798$	−6.27895	+	40.2764i	−0.222272	+	1.42577i
$799$	39.3710			1.39285
$800$	10.2688	−	14.4363i	0.363058	−	0.510400i
$801$	0.713797	+	3.41210i	0.0252208	+	0.120561i
$802$	10.5909	+	1.31635i	0.373976	+	0.0464818i
$803$	−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
$807$	−27.0222	−	21.9542i	−0.951228	−	0.772826i
$808$	3.06002	+	19.8929i	0.107651	+	0.699828i
$809$	−5.45505	+	3.14948i	−0.191789	+	0.110730i	−0.592820	−	0.805335i	$-0.701985\pi$
$809$	−5.45505	+	3.14948i	−0.191789	+	0.110730i	0.401031	+	0.916065i	$0.368652\pi$
$810$	8.44446	−	35.2993i	0.296708	−	1.24029i
$811$	9.32889			0.327582			0.163791	−	0.986495i	$-0.447628\pi$
$811$	9.32889			0.327582			0.163791	+	0.986495i	$0.447628\pi$
$812$	8.12083	+	18.9965i	0.284985	+	0.666646i
$813$	−0.499048	+	3.11839i	−0.0175024	+	0.109367i
$814$	3.28635	+	7.77420i	0.115186	+	0.272485i
$815$	−16.5660	−	28.6932i	−0.580283	−	1.00508i
$816$	−19.2955	−	14.7698i	−0.675479	−	0.517045i
$817$	27.8769	+	16.0947i	0.975290	+	0.563084i
$818$	−23.9883	+	31.7355i	−0.838732	+	1.10961i
$819$	7.15958	+	20.6384i	0.250176	+	0.721165i
$820$	−11.5588	+	3.27734i	−0.403650	+	0.114450i
$821$	21.8378	−	37.8241i	0.762143	−	1.32007i	−0.179600	−	0.983740i	$-0.557480\pi$
$821$	21.8378	−	37.8241i	0.762143	−	1.32007i	0.941744	−	0.336331i	$-0.109186\pi$
$822$	−46.3705	−	13.4519i	−1.61736	−	0.469188i
$823$	12.0388	+	20.8519i	0.419647	+	0.726850i	0.995904	−	0.0904188i	$-0.0288205\pi$
$823$	12.0388	+	20.8519i	0.419647	+	0.726850i	−0.576257	+	0.817269i	$0.695487\pi$
$824$	3.83412	−	3.07665i	0.133568	−	0.107180i
$825$	−25.9906	−	4.15938i	−0.904877	−	0.144811i
$826$	−1.93821	−	3.32601i	−0.0674391	−	0.115727i
$827$	−40.9864			−1.42524			−0.712618	−	0.701553i	$-0.752490\pi$
$827$	−40.9864			−1.42524			−0.712618	+	0.701553i	$0.752490\pi$
$828$	−11.7112	+	18.4864i	−0.406992	+	0.642447i
$829$	−8.07095	−	13.9793i	−0.280316	−	0.485521i	0.691147	−	0.722714i	$-0.257106\pi$
$829$	−8.07095	−	13.9793i	−0.280316	−	0.485521i	−0.971462	+	0.237194i	$0.923772\pi$
$830$	0.0687001	−	0.552737i	0.00238462	−	0.0191858i
$831$	−17.7071	−	14.3861i	−0.614251	−	0.499049i
$832$	16.2305	+	14.8778i	0.562692	+	0.515794i
$833$	6.50627	−	23.6735i	0.225429	−	0.820238i
$834$	−0.189678	−	0.197637i	−0.00656802	−	0.00684361i
$835$	−19.1408	−	11.0509i	−0.662393	−	0.382433i
$836$	42.5334	−	43.7839i	1.47105	−	1.51430i
$837$	−5.14249	+	0.244624i	−0.177751	+	0.00845546i
$838$	−10.7740	−	25.4870i	−0.372181	−	0.880432i
$839$	−40.8898			−1.41167			−0.705836	−	0.708375i	$-0.749429\pi$
$839$	−40.8898			−1.41167			−0.705836	+	0.708375i	$0.749429\pi$
$840$	29.5306	−	22.2279i	1.01890	−	0.766937i
$841$	−13.7566			−0.474367
$842$	14.3709	+	33.9959i	0.495255	+	1.17158i
$843$	24.8883	−	9.50780i	0.857198	−	0.327466i
$844$	29.2531	+	28.4177i	1.00693	+	0.978176i
$845$	−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
$849$	10.1547	−	12.4988i	0.348508	−	0.428959i
$850$	−1.91598	+	15.4153i	−0.0657176	+	0.528740i
$851$	−2.24298	−	3.88495i	−0.0768882	−	0.133174i
$852$	13.3429	−	31.0381i	0.457119	−	1.06335i
$853$	23.3041			0.797917			0.398958	−	0.916969i	$-0.369372\pi$
$853$	23.3041			0.797917			0.398958	+	0.916969i	$0.369372\pi$
$854$	−8.07735	−	4.62009i	−0.276401	−	0.158096i
$855$	16.7924	−	51.1216i	0.574290	−	1.74832i
$856$	−1.88358	−	2.34731i	−0.0643793	−	0.0802294i
$857$	3.23327	+	5.60019i	0.110447	+	0.191299i	0.915950	−	0.401292i	$-0.131439\pi$
$857$	3.23327	+	5.60019i	0.110447	+	0.191299i	−0.805504	+	0.592591i	$0.798105\pi$
$858$	9.11402	−	31.4173i	0.311148	−	1.07257i
$859$	1.10393	−	1.91207i	0.0376657	−	0.0652390i	−0.846578	−	0.532265i	$-0.821341\pi$
$859$	1.10393	−	1.91207i	0.0376657	−	0.0652390i	0.884244	+	0.467026i	$0.154674\pi$
$860$	−7.96186	−	28.0805i	−0.271497	−	0.957538i
$861$	−9.64899	−	0.299165i	−0.328837	−	0.0101955i
$862$	10.2479	−	13.5575i	0.349044	−	0.461770i
$863$	21.2034	+	12.2418i	0.721771	+	0.416715i	0.815404	−	0.578892i	$-0.196515\pi$
$863$	21.2034	+	12.2418i	0.721771	+	0.416715i	−0.0936330	+	0.995607i	$0.529848\pi$
$864$	1.38546	−	29.3612i	0.0471342	−	0.998889i
$865$	−1.44962	−	2.51082i	−0.0492886	−	0.0853704i
$866$	19.6218	+	46.4175i	0.666778	+	1.57733i
$867$	−8.03607	−	1.28604i	−0.272919	−	0.0436764i
$868$	−4.19511	−	3.14448i	−0.142391	−	0.106731i
$869$	27.1815			0.922068
$870$	−6.51570	−	26.4817i	−0.220903	−	0.897812i
$871$	13.8375	−	7.98908i	0.468866	−	0.270700i
$872$	−3.90225	−	25.3682i	−0.132147	−	0.859074i
$873$	22.1929	+	24.8078i	0.751117	+	0.839618i
$874$	−19.5634	+	25.8815i	−0.661740	+	0.875453i
$875$	13.0049	+	5.43574i	0.439647	+	0.183761i
$876$	−1.15604	+	0.136576i	−0.0390588	+	0.00461448i
$877$	−15.3248	−	8.84776i	−0.517481	−	0.298768i	0.218422	−	0.975854i	$-0.429909\pi$
$877$	−15.3248	−	8.84776i	−0.517481	−	0.298768i	−0.735903	+	0.677087i	$0.763242\pi$
$878$	−18.9520	−	2.35556i	−0.639599	−	0.0794964i
$879$	28.8752	−	11.0309i	0.973936	−	0.372062i
$880$	−55.3258	+	1.60333i	−1.86503	+	0.0540484i
$881$	−55.0445			−1.85450			−0.927249	−	0.374446i	$-0.877833\pi$
$881$	−55.0445			−1.85450			−0.927249	+	0.374446i	$0.877833\pi$
$882$	28.0186	−	9.84671i	0.943436	−	0.331556i
$883$		−	49.3732i		−	1.66154i	−0.556616	−	0.830770i	$-0.687900\pi$
$883$		−	49.3732i		−	1.66154i	0.556616	−	0.830770i	$-0.312100\pi$
$884$	−18.7184	−	4.72606i	−0.629568	−	0.158955i
$885$	1.81344	+	4.74698i	0.0609581	+	0.159568i
$886$	4.10469	−	33.0249i	0.137900	−	1.10949i
$887$	12.2514	−	21.2201i	0.411363	−	0.712502i	−0.583676	−	0.811987i	$-0.698386\pi$
$887$	12.2514	−	21.2201i	0.411363	−	0.712502i	0.995039	+	0.0994850i	$0.0317195\pi$
$888$	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
$891$	−40.0096	+	17.5058i	−1.34037	+	0.586466i
$892$	16.4494	+	15.9796i	0.550767	+	0.535037i
$893$	35.3029	+	61.1465i	1.18137	+	2.04619i
$894$	26.1561	−	6.43561i	0.874792	−	0.215239i
$895$			61.6540i			2.06087i
$896$	20.1373	−	22.1470i	0.672738	−	0.739880i
$897$	−2.74748	+	17.1681i	−0.0917357	+	0.573226i
$898$	−16.8658	−	39.8978i	−0.562819	−	1.33141i
$899$	−3.35007	+	1.93416i	−0.111731	+	0.0645079i
$900$	−16.6454	+	8.71887i	−0.554846	+	0.290629i
$901$	3.52194	−	6.10018i	0.117333	−	0.203226i
$902$	11.5323	+	8.71707i	0.383984	+	0.290247i
$903$	0.726780	−	23.4409i	0.0241857	−	0.780065i
$904$	−44.3184	−	17.2390i	−1.47401	−	0.573359i
$905$	23.1412	+	13.3606i	0.769239	+	0.444120i
$906$	5.68790	−	19.6070i	0.188968	−	0.651399i
$907$	−6.23747	+	3.60121i	−0.207112	+	0.119576i	−0.599968	−	0.800024i	$-0.704820\pi$
$907$	−6.23747	+	3.60121i	−0.207112	+	0.119576i	0.392857	+	0.919600i	$0.371487\pi$
$908$	10.3853	−	41.1328i	0.344648	−	1.36504i
$909$	6.66211	−	20.2816i	0.220968	−	0.672697i
$910$	14.5800	−	25.4904i	0.483322	−	0.844998i
$911$			13.3025i			0.440730i	0.975417	+	0.220365i	$0.0707248\pi$
$911$			13.3025i			0.440730i	−0.975417	+	0.220365i	$0.929275\pi$
$912$	5.63688	−	43.2113i	0.186656	−	1.43087i
$913$	−0.580401	+	0.335095i	−0.0192085	+	0.0110900i
$914$	2.02598	−	16.3003i	0.0670134	−	0.539166i
$915$	9.53358	+	7.74557i	0.315170	+	0.256061i
$916$	1.23806	+	4.36649i	0.0409066	+	0.144273i
$917$	21.2175	−	16.1729i	0.700663	−	0.534077i
$918$	11.1519	+	23.2359i	0.368069	+	0.766898i
$919$	−3.29521	+	5.70747i	−0.108699	+	0.188272i	−0.915243	−	0.402901i	$-0.868002\pi$
$919$	−3.29521	+	5.70747i	−0.108699	+	0.188272i	0.806544	+	0.591173i	$0.201335\pi$
$920$	29.0757	−	4.47256i	0.958597	−	0.147456i
$921$	10.9192	+	28.5828i	0.359799	+	0.941834i
$922$	16.9798	+	40.1675i	0.559200	+	1.32285i
$923$		−	26.8417i		−	0.883505i
$924$	−42.7618	−	12.2181i	−1.40676	−	0.401945i
$925$		−	3.85188i		−	0.126649i
$926$	−42.1002	+	17.7968i	−1.38350	+	0.584839i
$927$	−5.10364	+	1.06766i	−0.167626	+	0.0350666i
$928$	−9.18516	−	20.0853i	−0.301518	−	0.659333i
$929$	6.17532	−	10.6960i	0.202606	−	0.350923i	−0.746762	−	0.665092i	$-0.768392\pi$
$929$	6.17532	−	10.6960i	0.202606	−	0.350923i	0.949367	+	0.314169i	$0.101726\pi$
$930$	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
$933$	−9.06707	+	11.1601i	−0.296842	+	0.365366i
$934$	47.6027	+	5.91659i	1.55761	+	0.193597i
$935$	42.0298	−	24.2659i	1.37452	−	0.793580i
$936$	−8.20163	−	21.8657i	−0.268079	−	0.714703i
$937$			11.2161i			0.366413i	0.983074	+	0.183206i	$0.0586476\pi$
$937$			11.2161i			0.366413i	−0.983074	+	0.183206i	$0.941352\pi$
$938$	−10.9371	−	18.7682i	−0.357108	−	0.612804i
$939$	−7.29923	+	45.6105i	−0.238201	+	1.48844i
$940$	15.6724	−	62.0731i	0.511176	−	2.02460i
$941$	−8.10816	+	4.68125i	−0.264318	+	0.152604i	−0.626303	−	0.779580i	$-0.715433\pi$
$941$	−8.10816	+	4.68125i	−0.264318	+	0.152604i	0.361985	+	0.932184i	$0.382099\pi$
$942$	7.40045	−	25.5104i	0.241120	−	0.831175i
$943$	−6.65399	−	3.84168i	−0.216684	−	0.125102i
$944$	2.16004	+	3.50288i	0.0703035	+	0.114009i
$945$	−38.6030	+	6.83439i	−1.25576	+	0.222323i
$946$	−21.1769	+	28.0162i	−0.688521	+	0.910884i
$947$	−19.4899	+	33.7574i	−0.633335	+	1.09697i	0.353530	+	0.935423i	$0.384981\pi$
$947$	−19.4899	+	33.7574i	−0.633335	+	1.09697i	−0.986865	+	0.161546i	$0.948352\pi$
$948$	15.5505	−	11.6070i	0.505057	−	0.376977i
$949$	−0.800945	+	0.462426i	−0.0259998	+	0.0150110i
$950$	−25.6593	+	10.8468i	−0.832496	+	0.351917i
$951$	49.2896	+	7.88801i	1.59832	+	0.255786i
$952$	−6.32235	+	25.4736i	−0.204908	+	0.825603i
$953$			0.425521i			0.0137840i	0.999976	+	0.00689198i	$0.00219380\pi$
$953$			0.425521i			0.0137840i	−0.999976	+	0.00689198i	$0.997806\pi$
$954$	8.49161	−	0.702708i	0.274926	−	0.0227510i
$955$	12.6880	+	21.9763i	0.410574	+	0.711135i
$956$	11.9480	+	11.6068i	0.386426	+	0.375390i
$957$	−20.6915	+	25.4680i	−0.668861	+	0.823263i
$958$	−39.8984	−	30.1585i	−1.28906	−	0.974378i
$959$	6.64124	+	51.7262i	0.214457	+	1.67033i
$960$	−30.9673	+	24.5424i	−0.999464	+	0.792102i
$961$	−15.0092	+	25.9966i	−0.484167	+	0.838601i
$962$	4.75063	+	0.590461i	0.153167	+	0.0190372i
$963$	0.653639	+	3.12453i	0.0210632	+	0.100687i
$964$	3.52836	−	13.9747i	0.113641	−	0.450095i
$965$			42.5337i			1.36921i
$966$	23.3551	+	3.64097i	0.751437	+	0.117146i
$967$	−25.1685			−0.809365			−0.404682	−	0.914457i	$-0.632618\pi$
$967$	−25.1685			−0.809365			−0.404682	+	0.914457i	$0.632618\pi$
$968$	22.2086	+	27.6763i	0.713811	+	0.889551i
$969$	13.6358	+	35.6941i	0.438046	+	1.14666i
$970$	5.51897	−	44.4036i	0.177203	−	1.42571i
$971$	11.2476	+	6.49383i	0.360954	+	0.208397i	0.669499	−	0.742813i	$-0.266509\pi$
$971$	11.2476	+	6.49383i	0.360954	+	0.208397i	−0.308545	+	0.951210i	$0.599842\pi$
$972$	−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
$975$	−9.41381	+	11.5869i	−0.301483	+	0.371078i
$976$	8.75551	+	4.72225i	0.280257	+	0.151156i
$977$	−33.4781	+	19.3286i	−1.07106	+	0.618377i	−0.928471	−	0.371405i	$-0.878876\pi$
$977$	−33.4781	+	19.3286i	−1.07106	+	0.618377i	−0.142589	+	0.989782i	$0.545543\pi$
$978$	6.79962	+	27.6356i	0.217428	+	0.883689i
$979$	−5.63844			−0.180205
$980$	−34.7342	−	19.6816i	−1.10954	−	0.628705i
$981$	−8.49578	+	25.8639i	−0.271249	+	0.825770i
$982$	29.3471	−	12.4058i	0.936504	−	0.395884i
$983$	−24.2049	−	41.9241i	−0.772017	−	1.33717i	−0.936456	−	0.350785i	$-0.885915\pi$
$983$	−24.2049	−	41.9241i	−0.772017	−	1.33717i	0.164439	−	0.986387i	$-0.447419\pi$
$984$	10.3200	+	0.0625395i	0.328989	+	0.00199369i
$985$	6.77637	+	3.91234i	0.215913	+	0.124657i
$986$	15.4488	+	11.6775i	0.491989	+	0.371886i
$987$	27.0887	−	43.7308i	0.862244	−	1.39197i
$988$	−9.44432	−	33.3090i	−0.300464	−	1.05970i
$989$	9.33285	−	16.1650i	0.296767	−	0.514016i
$990$	53.0890	+	25.0603i	1.68728	+	0.796469i
$991$	8.16959	+	14.1502i	0.259516	+	0.449494i	0.966112	−	0.258122i	$-0.0831037\pi$
$991$	8.16959	+	14.1502i	0.259516	+	0.449494i	−0.706597	+	0.707617i	$0.749770\pi$
$992$	4.56718	+	3.24873i	0.145008	+	0.103147i
$993$	−0.709567	+	4.43385i	−0.0225174	+	0.140704i
$994$	−36.4912	+	0.147311i	−1.15743	+	0.00467242i
$995$	−66.4569			−2.10682
$996$	−0.188956	+	0.439549i	−0.00598730	+	0.0139276i
$997$	−4.94566	−	8.56614i	−0.156631	−	0.271292i	0.777021	−	0.629475i	$-0.216730\pi$
$997$	−4.94566	−	8.56614i	−0.156631	−	0.271292i	−0.933652	+	0.358182i	$0.883397\pi$
$998$	18.3310	+	2.27837i	0.580256	+	0.0721206i
$999$	−3.45485	−	5.37664i	−0.109307	−	0.170109i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	168.2.ba.c.5.21	yes	48
3.2	odd	2	inner	168.2.ba.c.5.4	✓	48
4.3	odd	2		672.2.bi.c.593.17		48
7.3	odd	6	inner	168.2.ba.c.101.11	yes	48
8.3	odd	2		672.2.bi.c.593.8		48
8.5	even	2	inner	168.2.ba.c.5.14	yes	48
12.11	even	2		672.2.bi.c.593.18		48
21.17	even	6	inner	168.2.ba.c.101.14	yes	48
24.5	odd	2	inner	168.2.ba.c.5.11	yes	48
24.11	even	2		672.2.bi.c.593.7		48
28.3	even	6		672.2.bi.c.17.7		48
56.3	even	6		672.2.bi.c.17.18		48
56.45	odd	6	inner	168.2.ba.c.101.4	yes	48
84.59	odd	6		672.2.bi.c.17.8		48
168.59	odd	6		672.2.bi.c.17.17		48
168.101	even	6	inner	168.2.ba.c.101.21	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
168.2.ba.c.5.4	✓	48	3.2	odd	2	inner
168.2.ba.c.5.11	yes	48	24.5	odd	2	inner
168.2.ba.c.5.14	yes	48	8.5	even	2	inner
168.2.ba.c.5.21	yes	48	1.1	even	1	trivial
168.2.ba.c.101.4	yes	48	56.45	odd	6	inner
168.2.ba.c.101.11	yes	48	7.3	odd	6	inner
168.2.ba.c.101.14	yes	48	21.17	even	6	inner
168.2.ba.c.101.21	yes	48	168.101	even	6	inner
672.2.bi.c.17.7		48	28.3	even	6
672.2.bi.c.17.8		48	84.59	odd	6
672.2.bi.c.17.17		48	168.59	odd	6
672.2.bi.c.17.18		48	56.3	even	6
672.2.bi.c.593.7		48	24.11	even	2
672.2.bi.c.593.8		48	8.3	odd	2
672.2.bi.c.593.17		48	4.3	odd	2
672.2.bi.c.593.18		48	12.11	even	2

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)

\(f(q)\)	\(=\)	\(q+(1.30261 - 0.550645i) q^{2} +(-0.618109 - 1.61801i) q^{3} +(1.39358 - 1.43455i) q^{4} +(2.46958 + 1.42581i) q^{5} +(-1.69610 - 1.76727i) q^{6} +(-1.02032 + 2.44110i) q^{7} +(1.02536 - 2.63603i) q^{8} +(-2.23588 + 2.00021i) q^{9} +O(q^{10})\)	\(q+(1.30261 - 0.550645i) q^{2} +(-0.618109 - 1.61801i) q^{3} +(1.39358 - 1.43455i) 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} +(-2.23588 + 2.00021i) q^{9} +(4.00201 + 0.497414i) q^{10} +(-2.42621 - 4.20231i) q^{11} +(-3.18249 - 1.36811i) q^{12} -2.75221 q^{13} +(0.0151045 + 3.74163i) q^{14} +(0.780502 - 4.87710i) q^{15} +(-0.115871 - 3.99832i) q^{16} +(1.75366 + 3.03743i) q^{17} +(-1.81107 + 3.83667i) q^{18} +(-3.14493 + 5.44717i) q^{19} +(5.48696 - 1.55575i) q^{20} +(4.58037 + 0.142013i) q^{21} +(-5.47438 - 4.13799i) q^{22} +(3.15865 + 1.82365i) q^{23} +(-4.89889 - 0.0296875i) q^{24} +(1.56588 + 2.71219i) q^{25} +(-3.58505 + 1.51549i) q^{26} +(4.61837 + 2.38132i) q^{27} +(2.07998 + 4.86556i) q^{28} +3.90427 q^{29} +(-1.66886 - 6.78274i) q^{30} +(-0.858051 + 0.495396i) q^{31} +(-2.35259 - 5.14445i) q^{32} +(-5.29970 + 6.52310i) 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} +(-1.09715 + 8.82727i) q^{38} +(1.70117 + 4.45309i) q^{39} +(6.29069 - 5.04791i) q^{40} -2.10659 q^{41} +(6.04464 - 2.33717i) q^{42} -5.11768i q^{43} +(-9.40954 - 2.37574i) q^{44} +(-8.37361 + 1.75172i) q^{45} +(5.11867 + 0.636204i) 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} +(3.83063 - 4.71490i) q^{51} +(-3.83543 + 3.94819i) q^{52} +(-1.00417 - 1.73927i) q^{53} +(7.32719 + 0.558850i) q^{54} -13.8373i q^{55} +(5.38860 + 5.19259i) q^{56} +(10.7575 + 1.72156i) q^{57} +(5.08574 - 2.14987i) q^{58} +(-0.890996 + 0.514417i) q^{59} +(-5.90876 - 7.91630i) q^{60} +(-1.24347 + 2.15376i) q^{61} +(-0.844918 + 1.11779i) q^{62} +(-2.60139 - 7.49885i) q^{63} +(-5.89727 - 5.40576i) q^{64} +(-6.79681 - 3.92414i) q^{65} +(-3.31153 + 11.4153i) q^{66} +(-5.02777 + 2.90279i) q^{67} +(6.80122 + 1.71719i) q^{68} +(0.998281 - 6.23793i) q^{69} +(-5.29756 + 9.26178i) q^{70} +9.75277i q^{71} +(2.98001 + 7.94478i) q^{72} +(0.291019 - 0.168020i) q^{73} +(-1.72612 - 0.214540i) q^{74} +(3.42045 - 4.21004i) 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} +(5.41471 - 10.0394i) q^{80} +(0.998337 - 8.94446i) q^{81} +(-2.74407 + 1.15999i) q^{82} -0.138115i q^{83} +(6.58684 - 6.37287i) q^{84} +10.0016i q^{85} +(-2.81803 - 6.66634i) q^{86} +(-2.41327 - 6.31714i) q^{87} +(-13.5651 + 2.08666i) 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} +(1.33192 + 1.08212i) q^{93} +(1.95806 - 15.7538i) q^{94} +(-15.5333 + 8.96815i) q^{95} +(-6.86958 + 6.98633i) q^{96} -11.0953i q^{97} +(-9.14908 - 3.78077i) 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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