LMFDB - Embedded newform 666.2.k.a.175.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [666,2,Mod(175,666)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("666.175"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(666, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([2, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 666 = 2 \cdot 3^{2} \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	666.k (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$5.31803677462$
Analytic rank:	$0$
Dimension:	$76$
Relative dimension:	$38$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			175.3
Character	$\chi$	$=$	666.175
Dual form			666.2.k.a.529.22

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-1.00000i q^{2} +(-1.52025 + 0.829972i) q^{3} -1.00000 q^{4} +1.89632i q^{5} +(0.829972 + 1.52025i) q^{6} +(1.11313 - 1.92800i) q^{7} +1.00000i q^{8} +(1.62229 - 2.52352i) q^{9} +1.89632 q^{10} +(-2.76965 - 4.79717i) q^{11} +(1.52025 - 0.829972i) q^{12} +5.43478i q^{13} +(-1.92800 - 1.11313i) q^{14} +(-1.57389 - 2.88287i) q^{15} +1.00000 q^{16} +(3.62888 + 2.09514i) q^{17} +(-2.52352 - 1.62229i) q^{18} +(-1.61653 + 0.933303i) q^{19} -1.89632i q^{20} +(-0.0920473 + 3.85489i) q^{21} +(-4.79717 + 2.76965i) q^{22} +(3.25875 + 1.88144i) q^{23} +(-0.829972 - 1.52025i) q^{24} +1.40397 q^{25} +5.43478 q^{26} +(-0.371833 + 5.18283i) q^{27} +(-1.11313 + 1.92800i) q^{28} +(0.737932 - 0.426045i) q^{29} +(-2.88287 + 1.57389i) q^{30} +(8.96141 + 5.17387i) q^{31} -1.00000i q^{32} +(8.19207 + 4.99415i) q^{33} +(2.09514 - 3.62888i) q^{34} +(3.65610 + 2.11085i) q^{35} +(-1.62229 + 2.52352i) q^{36} +(5.85749 - 1.64006i) q^{37} +(0.933303 + 1.61653i) q^{38} +(-4.51071 - 8.26220i) q^{39} -1.89632 q^{40} -0.675259 q^{41} +(3.85489 + 0.0920473i) q^{42} +(-0.810841 + 0.468139i) q^{43} +(2.76965 + 4.79717i) q^{44} +(4.78540 + 3.07639i) q^{45} +(1.88144 - 3.25875i) q^{46} +(-0.0673590 - 0.116669i) q^{47} +(-1.52025 + 0.829972i) q^{48} +(1.02189 + 1.76996i) q^{49} -1.40397i q^{50} +(-7.25570 - 0.173252i) q^{51} -5.43478i q^{52} +(-3.86220 + 6.68953i) q^{53} +(5.18283 + 0.371833i) q^{54} +(9.09698 - 5.25214i) q^{55} +(1.92800 + 1.11313i) q^{56} +(1.68291 - 2.76052i) q^{57} +(-0.426045 - 0.737932i) q^{58} +(6.14162 - 3.54587i) q^{59} +(1.57389 + 2.88287i) q^{60} +(7.04003 + 4.06456i) q^{61} +(5.17387 - 8.96141i) q^{62} +(-3.05952 - 5.93678i) q^{63} -1.00000 q^{64} -10.3061 q^{65} +(4.99415 - 8.19207i) q^{66} -5.30839 q^{67} +(-3.62888 - 2.09514i) q^{68} +(-6.51563 - 0.155581i) q^{69} +(2.11085 - 3.65610i) q^{70} +(-4.15409 - 7.19510i) q^{71} +(2.52352 + 1.62229i) q^{72} +3.91572 q^{73} +(-1.64006 - 5.85749i) q^{74} +(-2.13438 + 1.16526i) q^{75} +(1.61653 - 0.933303i) q^{76} -12.3319 q^{77} +(-8.26220 + 4.51071i) q^{78} +(11.2792 + 6.51206i) q^{79} +1.89632i q^{80} +(-3.73633 - 8.18779i) q^{81} +0.675259i q^{82} +0.546832 q^{83} +(0.0920473 - 3.85489i) q^{84} +(-3.97305 + 6.88153i) q^{85} +(0.468139 + 0.810841i) q^{86} +(-0.768233 + 1.26016i) q^{87} +(4.79717 - 2.76965i) q^{88} +(-14.8691 - 8.58470i) q^{89} +(3.07639 - 4.78540i) q^{90} +(10.4782 + 6.04961i) q^{91} +(-3.25875 - 1.88144i) q^{92} +(-17.9177 - 0.427840i) q^{93} +(-0.116669 + 0.0673590i) q^{94} +(-1.76984 - 3.06545i) q^{95} +(0.829972 + 1.52025i) q^{96} +(-2.72439 + 1.57293i) q^{97} +(1.76996 - 1.02189i) q^{98} +(-16.5990 - 0.793153i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 76 q + 4 q^{3} - 76 q^{4} - 2 q^{7} - 4 q^{9} - 4 q^{11} - 4 q^{12} + 12 q^{15} + 76 q^{16} + 6 q^{21} + 12 q^{23} - 100 q^{25} - 24 q^{26} + 4 q^{27} + 2 q^{28} + 18 q^{29} - 12 q^{30} + 6 q^{31} - 32 q^{33}+ \cdots - 76 q^{99}+O(q^{100}) $ 76 * q + 4 * q^3 - 76 * q^4 - 2 * q^7 - 4 * q^9 - 4 * q^11 - 4 * q^12 + 12 * q^15 + 76 * q^16 + 6 * q^21 + 12 * q^23 - 100 * q^25 - 24 * q^26 + 4 * q^27 + 2 * q^28 + 18 * q^29 - 12 * q^30 + 6 * q^31 - 32 * q^33 - 18 * q^35 + 4 * q^36 + 10 * q^37 + 12 * q^38 + 24 * q^39 + 72 * q^41 + 6 * q^42 + 6 * q^43 + 4 * q^44 + 12 * q^45 - 20 * q^47 + 4 * q^48 - 36 * q^49 - 18 * q^51 + 14 * q^53 + 36 * q^54 + 42 * q^57 - 6 * q^59 - 12 * q^60 - 16 * q^62 + 46 * q^63 - 76 * q^64 + 32 * q^65 + 40 * q^67 + 6 * q^69 + 2 * q^71 + 28 * q^73 - 2 * q^74 - 78 * q^75 - 24 * q^77 - 2 * q^78 + 6 * q^79 - 28 * q^81 - 64 * q^83 - 6 * q^84 - 12 * q^85 + 4 * q^86 - 78 * q^87 + 60 * q^89 - 16 * q^90 + 42 * q^91 - 12 * q^92 + 6 * q^93 - 14 * q^95 - 12 * q^97 - 24 * q^98 - 76 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/666\mathbb{Z}\right)^\times$.

$n$	$371$	$631$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$		−	1.00000i		−	0.707107i
$2$		−	1.00000i		−	0.707107i
$3$	−1.52025	+	0.829972i	−0.877714	+	0.479184i
$3$	−1.52025	+	0.829972i	−0.877714	+	0.479184i
$4$	−1.00000			−0.500000
$5$			1.89632i			0.848060i	0.905648	+	0.424030i	$0.139385\pi$
$5$			1.89632i			0.848060i	−0.905648	+	0.424030i	$0.860615\pi$
$6$	0.829972	+	1.52025i	0.338835	+	0.620638i
$7$	1.11313	−	1.92800i	0.420723	−	0.728714i	−0.575287	−	0.817951i	$-0.695110\pi$
$7$	1.11313	−	1.92800i	0.420723	−	0.728714i	0.996010	+	0.0892377i	$0.0284431\pi$
$8$			1.00000i			0.353553i
$9$	1.62229	−	2.52352i	0.540765	−	0.841174i
$10$	1.89632			0.599669
$11$	−2.76965	−	4.79717i	−0.835081	−	1.44640i	−0.893965	−	0.448138i	$-0.852087\pi$
$11$	−2.76965	−	4.79717i	−0.835081	−	1.44640i	0.0588837	−	0.998265i	$-0.481246\pi$
$12$	1.52025	−	0.829972i	0.438857	−	0.239592i
$13$			5.43478i			1.50734i	0.657255	+	0.753668i	$0.271718\pi$
$13$			5.43478i			1.50734i	−0.657255	+	0.753668i	$0.728282\pi$
$14$	−1.92800	−	1.11313i	−0.515278	−	0.297496i
$15$	−1.57389	−	2.88287i	−0.406377	−	0.744354i
$16$	1.00000			0.250000
$17$	3.62888	+	2.09514i	0.880134	+	0.508145i	0.870703	−	0.491810i	$-0.163665\pi$
$17$	3.62888	+	2.09514i	0.880134	+	0.508145i	0.00943127	+	0.999956i	$0.496998\pi$
$18$	−2.52352	−	1.62229i	−0.594800	−	0.382378i
$19$	−1.61653	+	0.933303i	−0.370857	+	0.214114i	−0.673833	−	0.738884i	$-0.735353\pi$
$19$	−1.61653	+	0.933303i	−0.370857	+	0.214114i	0.302976	+	0.952998i	$0.402020\pi$
$20$		−	1.89632i		−	0.424030i
$21$	−0.0920473	+	3.85489i	−0.0200864	+	0.841206i
$22$	−4.79717	+	2.76965i	−1.02276	+	0.590491i
$23$	3.25875	+	1.88144i	0.679495	+	0.392307i	0.799665	−	0.600447i	$-0.205010\pi$
$23$	3.25875	+	1.88144i	0.679495	+	0.392307i	−0.120170	+	0.992753i	$0.538344\pi$
$24$	−0.829972	−	1.52025i	−0.169417	−	0.310319i
$25$	1.40397			0.280794
$26$	5.43478			1.06585
$27$	−0.371833	+	5.18283i	−0.0715593	+	0.997436i
$28$	−1.11313	+	1.92800i	−0.210362	+	0.364357i
$29$	0.737932	−	0.426045i	0.137031	−	0.0791146i	−0.429917	−	0.902868i	$-0.641457\pi$
$29$	0.737932	−	0.426045i	0.137031	−	0.0791146i	0.566948	+	0.823754i	$0.308124\pi$
$30$	−2.88287	+	1.57389i	−0.526338	+	0.287352i
$31$	8.96141	+	5.17387i	1.60952	+	0.929255i	0.989478	+	0.144684i	$0.0462165\pi$
$31$	8.96141	+	5.17387i	1.60952	+	0.929255i	0.620039	+	0.784571i	$0.287117\pi$
$32$		−	1.00000i		−	0.176777i
$33$	8.19207	+	4.99415i	1.42606	+	0.869370i
$34$	2.09514	−	3.62888i	0.359313	−	0.622349i
$35$	3.65610	+	2.11085i	0.617993	+	0.356798i
$36$	−1.62229	+	2.52352i	−0.270382	+	0.420587i
$37$	5.85749	−	1.64006i	0.962965	−	0.269625i
$37$	5.85749	−	1.64006i	0.962965	−	0.269625i
$38$	0.933303	+	1.61653i	0.151402	+	0.262236i
$39$	−4.51071	−	8.26220i	−0.722292	−	1.32301i
$40$	−1.89632			−0.299834
$41$	−0.675259			−0.105458			−0.0527288	−	0.998609i	$-0.516792\pi$
$41$	−0.675259			−0.105458			−0.0527288	+	0.998609i	$0.516792\pi$
$42$	3.85489	+	0.0920473i	0.594823	+	0.0142032i
$43$	−0.810841	+	0.468139i	−0.123652	+	0.0713906i	−0.560550	−	0.828120i	$-0.689410\pi$
$43$	−0.810841	+	0.468139i	−0.123652	+	0.0713906i	0.436898	+	0.899511i	$0.356077\pi$
$44$	2.76965	+	4.79717i	0.417540	+	0.723201i
$45$	4.78540	+	3.07639i	0.713366	+	0.458601i
$46$	1.88144	−	3.25875i	0.277403	−	0.480476i
$47$	−0.0673590	−	0.116669i	−0.00982532	−	0.0170179i	0.861071	−	0.508485i	$-0.169794\pi$
$47$	−0.0673590	−	0.116669i	−0.00982532	−	0.0170179i	−0.870896	+	0.491467i	$0.836461\pi$
$48$	−1.52025	+	0.829972i	−0.219429	+	0.119796i
$49$	1.02189	+	1.76996i	0.145984	+	0.252852i
$50$		−	1.40397i		−	0.198552i
$51$	−7.25570	−	0.173252i	−1.01600	−	0.0242601i
$52$		−	5.43478i		−	0.753668i
$53$	−3.86220	+	6.68953i	−0.530515	+	0.918878i	0.468852	+	0.883277i	$0.344668\pi$
$53$	−3.86220	+	6.68953i	−0.530515	+	0.918878i	−0.999366	+	0.0356012i	$0.988665\pi$
$54$	5.18283	+	0.371833i	0.705294	+	0.0506001i
$55$	9.09698	−	5.25214i	1.22664	−	0.708199i
$56$	1.92800	+	1.11313i	0.257639	+	0.148748i
$57$	1.68291	−	2.76052i	0.222906	−	0.365640i
$58$	−0.426045	−	0.737932i	−0.0559425	−	0.0968953i
$59$	6.14162	−	3.54587i	0.799571	−	0.461633i	−0.0437501	−	0.999043i	$-0.513931\pi$
$59$	6.14162	−	3.54587i	0.799571	−	0.461633i	0.843321	+	0.537410i	$0.180597\pi$
$60$	1.57389	+	2.88287i	0.203189	+	0.372177i
$61$	7.04003	+	4.06456i	0.901384	+	0.520414i	0.877649	−	0.479304i	$-0.159111\pi$
$61$	7.04003	+	4.06456i	0.901384	+	0.520414i	0.0237349	+	0.999718i	$0.492444\pi$
$62$	5.17387	−	8.96141i	0.657082	−	1.13810i
$63$	−3.05952	−	5.93678i	−0.385463	−	0.747964i
$64$	−1.00000			−0.125000
$65$	−10.3061			−1.27831
$66$	4.99415	−	8.19207i	0.614738	−	1.00837i
$67$	−5.30839			−0.648524			−0.324262	−	0.945967i	$-0.605116\pi$
$67$	−5.30839			−0.648524			−0.324262	+	0.945967i	$0.605116\pi$
$68$	−3.62888	−	2.09514i	−0.440067	−	0.254073i
$69$	−6.51563	−	0.155581i	−0.784390	−	0.0187297i
$70$	2.11085	−	3.65610i	0.252295	−	0.436987i
$71$	−4.15409	−	7.19510i	−0.493000	−	0.853901i	0.506968	−	0.861965i	$-0.330766\pi$
$71$	−4.15409	−	7.19510i	−0.493000	−	0.853901i	−0.999967	+	0.00806416i	$0.997433\pi$
$72$	2.52352	+	1.62229i	0.297400	+	0.191189i
$73$	3.91572			0.458301			0.229150	−	0.973391i	$-0.426405\pi$
$73$	3.91572			0.458301			0.229150	+	0.973391i	$0.426405\pi$
$74$	−1.64006	−	5.85749i	−0.190654	−	0.680919i
$75$	−2.13438	+	1.16526i	−0.246457	+	0.134552i
$76$	1.61653	−	0.933303i	0.185429	−	0.107057i
$77$	−12.3319			−1.40535
$78$	−8.26220	+	4.51071i	−0.935510	+	0.510738i
$79$	11.2792	+	6.51206i	1.26901	+	0.732664i	0.974801	−	0.223076i	$-0.0716099\pi$
$79$	11.2792	+	6.51206i	1.26901	+	0.732664i	0.294211	+	0.955741i	$0.404943\pi$
$80$			1.89632i			0.212015i
$81$	−3.73633	−	8.18779i	−0.415147	−	0.909754i
$82$			0.675259i			0.0745698i
$83$	0.546832			0.0600226			0.0300113	−	0.999550i	$-0.490446\pi$
$83$	0.546832			0.0600226			0.0300113	+	0.999550i	$0.490446\pi$
$84$	0.0920473	−	3.85489i	0.0100432	−	0.420603i
$85$	−3.97305	+	6.88153i	−0.430938	+	0.746406i
$86$	0.468139	+	0.810841i	0.0504808	+	0.0874353i
$87$	−0.768233	+	1.26016i	−0.0823632	+	0.135103i
$88$	4.79717	−	2.76965i	0.511380	−	0.295246i
$89$	−14.8691	−	8.58470i	−1.57613	−	0.909976i	−0.995393	−	0.0958816i	$-0.969433\pi$
$89$	−14.8691	−	8.58470i	−1.57613	−	0.909976i	−0.580732	−	0.814095i	$-0.697234\pi$
$90$	3.07639	−	4.78540i	0.324280	−	0.504426i
$91$	10.4782	+	6.04961i	1.09842	+	0.634171i
$92$	−3.25875	−	1.88144i	−0.339748	−	0.196153i
$93$	−17.9177	−	0.427840i	−1.85798	−	0.0443649i
$94$	−0.116669	+	0.0673590i	−0.0120335	+	0.00694755i
$95$	−1.76984	−	3.06545i	−0.181582	−	0.314509i
$96$	0.829972	+	1.52025i	0.0847086	+	0.155159i
$97$	−2.72439	+	1.57293i	−0.276620	+	0.159706i	−0.631892	−	0.775056i	$-0.717721\pi$
$97$	−2.72439	+	1.57293i	−0.276620	+	0.159706i	0.355272	+	0.934763i	$0.384388\pi$
$98$	1.76996	−	1.02189i	0.178793	−	0.103226i
$99$	−16.5990	−	0.793153i	−1.66826	−	0.0797149i
$100$	−1.40397			−0.140397
$101$	2.49327	+	4.31847i	0.248090	+	0.429704i	0.962996	−	0.269516i	$-0.0868639\pi$
$101$	2.49327	+	4.31847i	0.248090	+	0.429704i	−0.714906	+	0.699221i	$0.753531\pi$
$102$	−0.173252	+	7.25570i	−0.0171545	+	0.718421i
$103$	15.0092	+	8.66559i	1.47890	+	0.853846i	0.999715	−	0.0238653i	$-0.00759730\pi$
$103$	15.0092	+	8.66559i	1.47890	+	0.853846i	0.479190	+	0.877711i	$0.340931\pi$
$104$	−5.43478			−0.532924
$105$	−7.31011	−	0.174551i	−0.713393	−	0.0170344i
$106$	6.68953	+	3.86220i	0.649745	+	0.375130i
$107$	0.539016	+	0.933602i	0.0521086	+	0.0902547i	0.890903	−	0.454193i	$-0.150072\pi$
$107$	0.539016	+	0.933602i	0.0521086	+	0.0902547i	−0.838795	+	0.544448i	$0.816739\pi$
$108$	0.371833	−	5.18283i	0.0357796	−	0.498718i
$109$	−8.26092	−	4.76944i	−0.791253	−	0.456830i	0.0491508	−	0.998791i	$-0.484349\pi$
$109$	−8.26092	−	4.76944i	−0.791253	−	0.456830i	−0.840403	+	0.541962i	$0.817682\pi$
$110$	−5.25214	−	9.09698i	−0.500772	−	0.867363i
$111$	−7.54362	+	7.35485i	−0.716008	+	0.698092i
$112$	1.11313	−	1.92800i	0.105181	−	0.182178i
$113$	4.87888	−	2.81682i	0.458967	−	0.264985i	−0.252643	−	0.967560i	$-0.581300\pi$
$113$	4.87888	−	2.81682i	0.458967	−	0.264985i	0.711610	+	0.702575i	$0.247966\pi$
$114$	−2.76052	−	1.68291i	−0.258547	−	0.157619i
$115$	−3.56781	+	6.17962i	−0.332700	+	0.576253i
$116$	−0.737932	+	0.426045i	−0.0685153	+	0.0395573i
$117$	13.7148	+	8.81681i	1.26793	+	0.815114i
$118$	−3.54587	−	6.14162i	−0.326424	−	0.565382i
$119$	8.07883	−	4.66431i	0.740585	−	0.427577i
$120$	2.88287	−	1.57389i	0.263169	−	0.143676i
$121$	−9.84192	+	17.0467i	−0.894720	+	1.54970i
$122$	4.06456	−	7.04003i	0.367988	−	0.637375i
$123$	1.02656	−	0.560445i	0.0925617	−	0.0505337i
$124$	−8.96141	−	5.17387i	−0.804758	−	0.464627i
$125$			12.1440i			1.08619i
$126$	−5.93678	+	3.05952i	−0.528890	+	0.272563i
$127$	4.23844	−	7.34120i	0.376101	−	0.651426i	−0.614390	−	0.789002i	$-0.710598\pi$
$127$	4.23844	−	7.34120i	0.376101	−	0.651426i	0.990491	+	0.137576i	$0.0439313\pi$
$128$			1.00000i			0.0883883i
$129$	0.844135	−	1.38466i	0.0743220	−	0.121913i
$130$			10.3061i			0.903903i
$131$	−11.3862	+	6.57382i	−0.994815	+	0.574357i	−0.906710	−	0.421754i	$-0.861415\pi$
$131$	−11.3862	+	6.57382i	−0.994815	+	0.574357i	−0.0881052	+	0.996111i	$0.528081\pi$
$132$	−8.19207	−	4.99415i	−0.713028	−	0.434685i
$133$			4.15555i			0.360331i
$134$			5.30839i			0.458575i
$135$	−9.82831	−	0.705114i	−0.845886	−	0.0606866i
$136$	−2.09514	+	3.62888i	−0.179657	+	0.311174i
$137$	3.34296	+	5.79018i	0.285608	+	0.494688i	0.972757	−	0.231829i	$-0.0744710\pi$
$137$	3.34296	+	5.79018i	0.285608	+	0.494688i	−0.687148	+	0.726517i	$0.741138\pi$
$138$	−0.155581	+	6.51563i	−0.0132439	+	0.554648i
$139$	−11.0240	−	19.0941i	−0.935044	−	1.61954i	−0.774555	−	0.632506i	$-0.782026\pi$
$139$	−11.0240	−	19.0941i	−0.935044	−	1.61954i	−0.160489	−	0.987038i	$-0.551307\pi$
$140$	−3.65610	−	2.11085i	−0.308996	−	0.178399i
$141$	0.199234	+	0.121460i	0.0167786	+	0.0102288i
$142$	−7.19510	+	4.15409i	−0.603799	+	0.348604i
$143$	26.0716	−	15.0524i	2.18022	−	1.25875i
$144$	1.62229	−	2.52352i	0.135191	−	0.210293i
$145$	0.807918	+	1.39936i	0.0670940	+	0.116210i
$146$		−	3.91572i		−	0.324068i
$147$	−3.02254	−	1.84264i	−0.249295	−	0.151979i
$148$	−5.85749	+	1.64006i	−0.481483	+	0.134812i
$149$	5.63355	−	9.75759i	0.461518	−	0.799373i	−0.537519	−	0.843252i	$-0.680638\pi$
$149$	5.63355	−	9.75759i	0.461518	−	0.799373i	0.999037	+	0.0438789i	$0.0139716\pi$
$150$	1.16526	+	2.13438i	0.0951428	+	0.174272i
$151$	1.63513	−	2.83213i	0.133065	−	0.230476i	−0.791792	−	0.610791i	$-0.790851\pi$
$151$	1.63513	−	2.83213i	0.133065	−	0.230476i	0.924857	+	0.380316i	$0.124185\pi$
$152$	−0.933303	−	1.61653i	−0.0757009	−	0.131118i
$153$	11.1742	−	5.75864i	0.903384	−	0.465559i
$154$			12.3319i			0.993733i
$155$	−9.81132	+	16.9937i	−0.788064	+	1.36497i
$156$	4.51071	+	8.26220i	0.361146	+	0.661505i
$157$	−9.56053	−	16.5593i	−0.763013	−	1.32158i	−0.941290	−	0.337598i	$-0.890386\pi$
$157$	−9.56053	−	16.5593i	−0.763013	−	1.32158i	0.178277	−	0.983980i	$-0.442948\pi$
$158$	6.51206	−	11.2792i	0.518072	−	0.897327i
$159$	0.319375	−	13.3753i	0.0253281	−	1.06073i
$160$	1.89632			0.149917
$161$	7.25480	−	4.18856i	0.571759	−	0.330105i
$162$	−8.18779	+	3.73633i	−0.643293	+	0.293554i
$163$	−0.279305	−	0.161257i	−0.0218768	−	0.0126306i	0.489022	−	0.872272i	$-0.337354\pi$
$163$	−0.279305	−	0.161257i	−0.0218768	−	0.0126306i	−0.510899	+	0.859641i	$0.670687\pi$
$164$	0.675259			0.0527288
$165$	−9.47051	+	15.5348i	−0.737278	+	1.20938i
$166$		−	0.546832i		−	0.0424424i
$167$		−	3.26030i		−	0.252290i	−0.992012	−	0.126145i	$-0.959740\pi$
$167$		−	3.26030i		−	0.252290i	0.992012	−	0.126145i	$-0.0402604\pi$
$168$	−3.85489	−	0.0920473i	−0.297411	−	0.00710160i
$169$	−16.5368			−1.27206
$170$	6.88153	+	3.97305i	0.527789	+	0.304719i
$171$	−0.267273	+	5.59344i	−0.0204389	+	0.427741i
$172$	0.810841	−	0.468139i	0.0618261	−	0.0356953i
$173$	3.92574			0.298469			0.149234	−	0.988802i	$-0.452319\pi$
$173$	3.92574			0.298469			0.149234	+	0.988802i	$0.452319\pi$
$174$	1.26016	+	0.768233i	0.0955322	+	0.0582396i
$175$	1.56280	−	2.70685i	0.118137	−	0.204619i
$176$	−2.76965	−	4.79717i	−0.208770	−	0.361601i
$177$	−6.39380	+	10.4880i	−0.480588	+	0.788323i
$178$	−8.58470	+	14.8691i	−0.643450	+	1.11449i
$179$		−	12.8330i		−	0.959184i	−0.877492	−	0.479592i	$-0.840785\pi$
$179$		−	12.8330i		−	0.959184i	0.877492	−	0.479592i	$-0.159215\pi$
$180$	−4.78540	−	3.07639i	−0.356683	−	0.229300i
$181$	6.73368	+	11.6631i	0.500510	+	0.866910i	1.00000		0.000589523i	$0.000187651\pi$
$181$	6.73368	+	11.6631i	0.500510	+	0.866910i	−0.499489	+	0.866320i	$0.666479\pi$
$182$	6.04961	−	10.4782i	0.448427	−	0.776698i
$183$	−14.0761	−	0.336109i	−1.04053	−	0.0248459i
$184$	−1.88144	+	3.25875i	−0.138701	+	0.240238i
$185$	3.11009	+	11.1077i	0.228658	+	0.816652i
$186$	−0.427840	+	17.9177i	−0.0313707	+	1.31379i
$187$		−	23.2112i		−	1.69737i
$188$	0.0673590	+	0.116669i	0.00491266	+	0.00850897i
$189$	9.57858	+	6.48605i	0.696739	+	0.471791i
$190$	−3.06545	+	1.76984i	−0.222391	+	0.128398i
$191$	−5.10962	+	2.95004i	−0.369719	+	0.213457i	−0.673336	−	0.739337i	$-0.735139\pi$
$191$	−5.10962	+	2.95004i	−0.369719	+	0.213457i	0.303617	+	0.952794i	$0.401806\pi$
$192$	1.52025	−	0.829972i	0.109714	−	0.0598981i
$193$	3.88379	+	2.24231i	0.279562	+	0.161405i	0.633225	−	0.773968i	$-0.281731\pi$
$193$	3.88379	+	2.24231i	0.279562	+	0.161405i	−0.353663	+	0.935373i	$0.615064\pi$
$194$	1.57293	+	2.72439i	0.112929	+	0.195600i
$195$	15.6678	−	8.55376i	1.12199	−	0.612547i
$196$	−1.02189	−	1.76996i	−0.0729921	−	0.126426i
$197$	1.65739	−	2.87068i	0.118084	−	0.204527i	−0.800924	−	0.598766i	$-0.795658\pi$
$197$	1.65739	−	2.87068i	0.118084	−	0.204527i	0.919008	+	0.394238i	$0.128991\pi$
$198$	−0.793153	+	16.5990i	−0.0563670	+	1.17964i
$199$			25.8485i			1.83235i	0.400775	+	0.916177i	$0.368741\pi$
$199$			25.8485i			1.83235i	−0.400775	+	0.916177i	$0.631259\pi$
$200$			1.40397i			0.0992758i
$201$	8.07006	−	4.40582i	0.569218	−	0.310762i
$202$	4.31847	−	2.49327i	0.303847	−	0.175426i
$203$		−	1.89697i		−	0.133141i
$204$	7.25570	+	0.173252i	0.508001	+	0.0121301i
$205$		−	1.28051i		−	0.0894344i
$206$	8.66559	−	15.0092i	0.603760	−	1.04574i
$207$	10.0345	−	5.17127i	0.697445	−	0.359428i
$208$			5.43478i			0.376834i
$209$	8.95444	+	5.16985i	0.619391	+	0.357606i
$210$	−0.174551	+	7.31011i	−0.0120452	+	0.504445i
$211$	3.80417	−	6.58901i	0.261890	−	0.453606i	−0.704854	−	0.709352i	$-0.748988\pi$
$211$	3.80417	−	6.58901i	0.261890	−	0.453606i	0.966744	+	0.255746i	$0.0823210\pi$
$212$	3.86220	−	6.68953i	0.265257	−	0.459439i
$213$	12.2870	+	7.49054i	0.841889	+	0.513243i
$214$	0.933602	−	0.539016i	0.0638197	−	0.0368463i
$215$	−0.887742	−	1.53761i	−0.0605435	−	0.104864i
$216$	−5.18283	−	0.371833i	−0.352647	−	0.0253000i
$217$	19.9504	−	11.5184i	1.35432	−	0.781918i
$218$	−4.76944	+	8.26092i	−0.323027	+	0.559500i
$219$	−5.95286	+	3.24994i	−0.402257	+	0.219611i
$220$	−9.09698	+	5.25214i	−0.613318	+	0.354099i
$221$	−11.3866	+	19.7222i	−0.765946	+	1.32666i
$222$	7.35485	+	7.54362i	0.493625	+	0.506294i
$223$	−13.6919	−	23.7151i	−0.916880	−	1.58808i	−0.804125	−	0.594460i	$-0.797366\pi$
$223$	−13.6919	−	23.7151i	−0.916880	−	1.58808i	−0.112755	−	0.993623i	$-0.535967\pi$
$224$	−1.92800	−	1.11313i	−0.128820	−	0.0743740i
$225$	2.27765	−	3.54295i	0.151844	−	0.236197i
$226$	−2.81682	−	4.87888i	−0.187372	−	0.324538i
$227$	−23.4310	−	13.5279i	−1.55517	−	0.897879i	−0.997707	−	0.0676785i	$-0.978441\pi$
$227$	−23.4310	−	13.5279i	−1.55517	−	0.897879i	−0.557465	−	0.830201i	$-0.688226\pi$
$228$	−1.68291	+	2.76052i	−0.111453	+	0.182820i
$229$	−25.4025			−1.67864			−0.839322	−	0.543634i	$-0.817048\pi$
$229$	−25.4025			−1.67864			−0.839322	+	0.543634i	$0.817048\pi$
$230$	6.17962	+	3.56781i	0.407472	+	0.235254i
$231$	18.7475	−	10.2351i	1.23350	−	0.673422i
$232$	0.426045	+	0.737932i	0.0279713	+	0.0484476i
$233$	−14.6671			−0.960872			−0.480436	−	0.877030i	$-0.659522\pi$
$233$	−14.6671			−0.960872			−0.480436	+	0.877030i	$0.659522\pi$
$234$	8.81681	−	13.7148i	0.576373	−	0.896564i
$235$	0.221242	−	0.127734i	0.0144322	−	0.00833246i
$236$	−6.14162	+	3.54587i	−0.399786	+	0.230816i
$237$	−22.5520	−	0.538498i	−1.46491	−	0.0349792i
$238$	−4.66431	−	8.07883i	−0.302343	−	0.523673i
$239$	−19.1753	+	11.0709i	−1.24035	+	0.716115i	−0.969165	−	0.246413i	$-0.920748\pi$
$239$	−19.1753	+	11.0709i	−1.24035	+	0.716115i	−0.271183	+	0.962528i	$0.587415\pi$
$240$	−1.57389	−	2.88287i	−0.101594	−	0.186089i
$241$	17.3437	+	10.0134i	1.11721	+	0.645019i	0.940686	−	0.339278i	$-0.110183\pi$
$241$	17.3437	+	10.0134i	1.11721	+	0.645019i	0.176520	+	0.984297i	$0.443516\pi$
$242$	17.0467	+	9.84192i	1.09580	+	0.632663i
$243$	12.4758	+	9.34640i	0.800321	+	0.599572i
$244$	−7.04003	−	4.06456i	−0.450692	−	0.260207i
$245$	−3.35642	+	1.93783i	−0.214434	+	0.123803i
$246$	−0.560445	−	1.02656i	−0.0357327	−	0.0654510i
$247$	−5.07230	−	8.78548i	−0.322743	−	0.559006i
$248$	−5.17387	+	8.96141i	−0.328541	+	0.569050i
$249$	−0.831318	+	0.453855i	−0.0526827	+	0.0287619i
$250$	12.1440			0.768053
$251$			9.72954i			0.614123i	0.951690	+	0.307062i	$0.0993458\pi$
$251$			9.72954i			0.614123i	−0.951690	+	0.307062i	$0.900654\pi$
$252$	3.05952	+	5.93678i	0.192731	+	0.373982i
$253$		−	20.8437i		−	1.31043i
$254$	−7.34120	−	4.23844i	−0.460628	−	0.265944i
$255$	0.328541	−	13.7591i	0.0205740	−	0.861630i
$256$	1.00000			0.0625000
$257$	21.2000	−	12.2398i	1.32242	−	0.763498i	0.338303	−	0.941037i	$-0.390147\pi$
$257$	21.2000	−	12.2398i	1.32242	−	0.763498i	0.984114	+	0.177540i	$0.0568138\pi$
$258$	−1.38466	−	0.844135i	−0.0862053	−	0.0525536i
$259$	3.35810	−	13.1188i	0.208662	−	0.815163i
$260$	10.3061			0.639156
$261$	0.122008	−	2.55336i	0.00755210	−	0.158049i
$262$	6.57382	+	11.3862i	0.406132	+	0.703441i
$263$	5.18456	−	8.97992i	0.319694	−	0.553725i	−0.660730	−	0.750623i	$-0.729753\pi$
$263$	5.18456	−	8.97992i	0.319694	−	0.553725i	0.980424	+	0.196898i	$0.0630867\pi$
$264$	−4.99415	+	8.19207i	−0.307369	+	0.504187i
$265$	−12.6855	−	7.32397i	−0.779264	−	0.449908i
$266$	4.15555			0.254793
$267$	29.7298	+	0.709889i	1.81943	+	0.0434445i
$268$	5.30839			0.324262
$269$	−7.17096			−0.437221			−0.218611	−	0.975812i	$-0.570152\pi$
$269$	−7.17096			−0.437221			−0.218611	+	0.975812i	$0.570152\pi$
$270$	−0.705114	+	9.82831i	−0.0429119	+	0.598132i
$271$	−13.8195	+	23.9360i	−0.839474	+	1.45401i	0.0508618	+	0.998706i	$0.483803\pi$
$271$	−13.8195	+	23.9360i	−0.839474	+	1.45401i	−0.890335	+	0.455305i	$0.849530\pi$
$272$	3.62888	+	2.09514i	0.220033	+	0.127036i
$273$	−20.9505	−	0.500257i	−1.26798	−	0.0302769i
$274$	5.79018	−	3.34296i	0.349797	−	0.201956i
$275$	−3.88851	−	6.73510i	−0.234486	−	0.406142i
$276$	6.51563	+	0.155581i	0.392195	+	0.00936485i
$277$	13.9488	+	8.05335i	0.838103	+	0.483879i	0.856619	−	0.515949i	$-0.172561\pi$
$277$	13.9488	+	8.05335i	0.838103	+	0.483879i	−0.0185158	+	0.999829i	$0.505894\pi$
$278$	−19.0941	+	11.0240i	−1.14519	+	0.661176i
$279$	27.5944	−	14.2208i	1.65203	−	0.851375i
$280$	−2.11085	+	3.65610i	−0.126147	+	0.218493i
$281$		−	12.6912i		−	0.757092i	−0.925582	−	0.378546i	$-0.876424\pi$
$281$		−	12.6912i		−	0.757092i	0.925582	−	0.378546i	$-0.123576\pi$
$282$	0.121460	−	0.199234i	0.00723282	−	0.0118642i
$283$			23.2610i			1.38272i	0.722510	+	0.691361i	$0.242988\pi$
$283$			23.2610i			1.38272i	−0.722510	+	0.691361i	$0.757012\pi$
$284$	4.15409	+	7.19510i	0.246500	+	0.426950i
$285$	5.23483	+	3.19133i	0.310085	+	0.189038i
$286$	−15.0524	−	26.0716i	−0.890069	−	1.54165i
$287$	−0.751650	+	1.30190i	−0.0443685	+	0.0768484i
$288$	−2.52352	−	1.62229i	−0.148700	−	0.0955946i
$289$	0.279202	+	0.483593i	0.0164237	+	0.0284466i
$290$	1.39936	−	0.807918i	0.0821730	−	0.0474426i
$291$	2.83625	−	4.65240i	0.166264	−	0.272728i
$292$	−3.91572			−0.229150
$293$	18.1212			1.05865			0.529325	−	0.848419i	$-0.322445\pi$
$293$	18.1212			1.05865			0.529325	+	0.848419i	$0.322445\pi$
$294$	−1.84264	+	3.02254i	−0.107465	+	0.176278i
$295$	6.72410	+	11.6465i	0.391492	+	0.678084i
$296$	1.64006	+	5.85749i	0.0953268	+	0.340460i
$297$	25.8928	−	12.5709i	1.50245	−	0.729436i
$298$	−9.75759	−	5.63355i	−0.565242	−	0.326343i
$299$	−10.2252	+	17.7106i	−0.591339	+	1.02423i
$300$	2.13438	−	1.16526i	0.123229	−	0.0672761i
$301$			2.08440i			0.120143i
$302$	−2.83213	−	1.63513i	−0.162971	−	0.0940912i
$303$	−7.37459	−	4.49579i	−0.423659	−	0.258277i
$304$	−1.61653	+	0.933303i	−0.0927143	+	0.0535286i
$305$	−7.70771	+	13.3502i	−0.441342	+	0.764428i
$306$	−5.75864	−	11.1742i	−0.329200	−	0.638789i
$307$	20.8256			1.18858			0.594291	−	0.804250i	$-0.297433\pi$
$307$	20.8256			1.18858			0.594291	+	0.804250i	$0.297433\pi$
$308$	12.3319			0.702675
$309$	−30.0099	−	0.716578i	−1.70721	−	0.0407647i
$310$	16.9937	+	9.81132i	0.965177	+	0.557245i
$311$	−21.0315	+	12.1426i	−1.19259	+	0.688541i	−0.958893	−	0.283769i	$-0.908415\pi$
$311$	−21.0315	+	12.1426i	−1.19259	+	0.688541i	−0.233695	+	0.972310i	$0.575082\pi$
$312$	8.26220	−	4.51071i	0.467755	−	0.255369i
$313$		−	4.57113i		−	0.258376i	−0.991620	−	0.129188i	$-0.958763\pi$
$313$		−	4.57113i		−	0.258376i	0.991620	−	0.129188i	$-0.0412370\pi$
$314$	−16.5593	+	9.56053i	−0.934497	+	0.539532i
$315$	11.2580	−	5.80182i	0.634318	−	0.326896i
$316$	−11.2792	−	6.51206i	−0.634506	−	0.366332i
$317$	30.2100			1.69676			0.848382	−	0.529384i	$-0.177577\pi$
$317$	30.2100			1.69676			0.848382	+	0.529384i	$0.177577\pi$
$318$	−13.3753	−	0.319375i	−0.750047	−	0.0179097i
$319$	−4.08763	−	2.35999i	−0.228863	−	0.132134i
$320$		−	1.89632i		−	0.106007i
$321$	−1.59430	−	0.971937i	−0.0889851	−	0.0542482i
$322$	−4.18856	−	7.25480i	−0.233420	−	0.404294i
$323$	−7.82159			−0.435205
$324$	3.73633	+	8.18779i	0.207574	+	0.454877i
$325$			7.63028i			0.423252i
$326$	−0.161257	+	0.279305i	−0.00893118	+	0.0154693i
$327$	16.5171	+	0.394397i	0.913399	+	0.0218102i
$328$		−	0.675259i		−	0.0372849i
$329$	−0.299917			−0.0165349
$330$	15.5348	+	9.47051i	0.855161	+	0.521334i
$331$		−	26.1062i		−	1.43492i	−0.696597	−	0.717462i	$-0.745304\pi$
$331$		−	26.1062i		−	1.43492i	0.696597	−	0.717462i	$-0.254696\pi$
$332$	−0.546832			−0.0300113
$333$	5.36383	−	17.4422i	0.293936	−	0.955825i
$334$	−3.26030			−0.178396
$335$		−	10.0664i		−	0.549987i
$336$	−0.0920473	+	3.85489i	−0.00502159	+	0.210302i
$337$	−15.1007			−0.822586			−0.411293	−	0.911503i	$-0.634923\pi$
$337$	−15.1007			−0.822586			−0.411293	+	0.911503i	$0.634923\pi$
$338$			16.5368i			0.899485i
$339$	−5.07922	+	8.33160i	−0.275865	+	0.452510i
$340$	3.97305	−	6.88153i	0.215469	−	0.373203i
$341$		−	57.3193i		−	3.10401i
$342$	5.59344	+	0.267273i	0.302458	+	0.0144525i
$343$	20.1338			1.08712
$344$	−0.468139	−	0.810841i	−0.0252404	−	0.0437176i
$345$	0.295030	−	12.3557i	0.0158839	−	0.665210i
$346$		−	3.92574i		−	0.211049i
$347$	29.0976	+	16.7995i	1.56204	+	0.901844i	0.997051	+	0.0767453i	$0.0244528\pi$
$347$	29.0976	+	16.7995i	1.56204	+	0.901844i	0.564989	+	0.825099i	$0.308881\pi$
$348$	0.768233	−	1.26016i	0.0411816	−	0.0675515i
$349$	1.51202			0.0809363			0.0404682	−	0.999181i	$-0.487115\pi$
$349$	1.51202			0.0809363			0.0404682	+	0.999181i	$0.487115\pi$
$350$	−2.70685	−	1.56280i	−0.144687	−	0.0835352i
$351$	−28.1675	−	2.02083i	−1.50347	−	0.107864i
$352$	−4.79717	+	2.76965i	−0.255690	+	0.147623i
$353$		−	1.24530i		−	0.0662806i	−0.999451	−	0.0331403i	$-0.989449\pi$
$353$		−	1.24530i		−	0.0662806i	0.999451	−	0.0331403i	$-0.0105508\pi$
$354$	10.4880	+	6.39380i	0.557429	+	0.339827i
$355$	13.6442	−	7.87749i	0.724159	−	0.418094i
$356$	14.8691	+	8.58470i	0.788063	+	0.454988i
$357$	−8.41056	+	13.7961i	−0.445134	+	0.730167i
$358$	−12.8330			−0.678245
$359$	19.0620			1.00605			0.503027	−	0.864271i	$-0.332220\pi$
$359$	19.0620			1.00605			0.503027	+	0.864271i	$0.332220\pi$
$360$	−3.07639	+	4.78540i	−0.162140	+	0.252213i
$361$	−7.75789	+	13.4371i	−0.408310	+	0.707214i
$362$	11.6631	−	6.73368i	0.612998	−	0.353914i
$363$	0.813852	−	34.0837i	0.0427161	−	1.78893i
$364$	−10.4782	−	6.04961i	−0.549208	−	0.317086i
$365$			7.42546i			0.388666i
$366$	−0.336109	+	14.0761i	−0.0175687	+	0.735767i
$367$	9.51586	−	16.4819i	0.496724	−	0.860351i	−0.503269	−	0.864130i	$-0.667870\pi$
$367$	9.51586	−	16.4819i	0.496724	−	0.860351i	0.999993	+	0.00377897i	$0.00120289\pi$
$368$	3.25875	+	1.88144i	0.169874	+	0.0980767i
$369$	−1.09547	+	1.70403i	−0.0570278	+	0.0887082i
$370$	11.1077	−	3.11009i	0.577460	−	0.161686i
$371$	8.59826	+	14.8926i	0.446399	+	0.773186i
$372$	17.9177	+	0.427840i	0.928990	+	0.0221825i
$373$	−10.5325			−0.545351			−0.272675	−	0.962106i	$-0.587908\pi$
$373$	−10.5325			−0.545351			−0.272675	+	0.962106i	$0.587908\pi$
$374$	−23.2112			−1.20022
$375$	−10.0792	−	18.4618i	−0.520486	−	0.953365i
$376$	0.116669	−	0.0673590i	0.00601675	−	0.00347377i
$377$	2.31546	+	4.01050i	0.119252	+	0.206551i
$378$	6.48605	−	9.57858i	0.333606	−	0.492669i
$379$	11.1637	−	19.3360i	0.573439	−	0.993226i	−0.422770	−	0.906237i	$-0.638942\pi$
$379$	11.1637	−	19.3360i	0.573439	−	0.993226i	0.996209	−	0.0869888i	$-0.0277244\pi$
$380$	1.76984	+	3.06545i	0.0907909	+	0.157255i
$381$	−0.350487	+	14.6782i	−0.0179560	+	0.751987i
$382$	2.95004	+	5.10962i	0.150937	+	0.261431i
$383$		−	24.1700i		−	1.23503i	−0.786559	−	0.617515i	$-0.788139\pi$
$383$		−	24.1700i		−	1.23503i	0.786559	−	0.617515i	$-0.211861\pi$
$384$	−0.829972	−	1.52025i	−0.0423543	−	0.0775797i
$385$		−	23.3852i		−	1.19182i
$386$	2.24231	−	3.88379i	0.114131	−	0.197680i
$387$	−0.134063	+	2.80564i	−0.00681478	+	0.142618i
$388$	2.72439	−	1.57293i	0.138310	−	0.0798532i
$389$	21.2000	+	12.2398i	1.07488	+	0.620584i	0.929511	−	0.368793i	$-0.120229\pi$
$389$	21.2000	+	12.2398i	1.07488	+	0.620584i	0.145371	+	0.989377i	$0.453562\pi$
$390$	−8.55376	−	15.6678i	−0.433136	−	0.793369i
$391$	7.88374	+	13.6550i	0.398698	+	0.690565i
$392$	−1.76996	+	1.02189i	−0.0893967	+	0.0516132i
$393$	11.8537	−	19.4440i	0.597941	−	0.980821i
$394$	−2.87068	−	1.65739i	−0.144623	−	0.0834980i
$395$	−12.3490	+	21.3890i	−0.621343	+	1.07620i
$396$	16.5990	+	0.793153i	0.834129	+	0.0398575i
$397$	−19.8487			−0.996177			−0.498089	−	0.867126i	$-0.665965\pi$
$397$	−19.8487			−0.996177			−0.498089	+	0.867126i	$0.665965\pi$
$398$	25.8485			1.29567
$399$	−3.44899	−	6.31745i	−0.172665	−	0.316268i
$400$	1.40397			0.0701986
$401$	23.9198	+	13.8101i	1.19450	+	0.689644i	0.959324	−	0.282309i	$-0.0911002\pi$
$401$	23.9198	+	13.8101i	1.19450	+	0.689644i	0.235175	+	0.971953i	$0.424434\pi$
$402$	−4.40582	−	8.07006i	−0.219742	−	0.402498i
$403$	−28.1189	+	48.7033i	−1.40070	+	2.42608i
$404$	−2.49327	−	4.31847i	−0.124045	−	0.214852i
$405$	15.5267	−	7.08527i	0.771526	−	0.352070i
$406$	−1.89697			−0.0941452
$407$	−24.0909	−	23.5570i	−1.19414	−	1.16768i
$408$	0.173252	−	7.25570i	0.00857725	−	0.359211i
$409$	11.5527	−	6.66997i	0.571246	−	0.329809i	−0.186401	−	0.982474i	$-0.559682\pi$
$409$	11.5527	−	6.66997i	0.571246	−	0.329809i	0.757647	+	0.652665i	$0.226349\pi$
$410$	−1.28051			−0.0632397
$411$	−9.88781	−	6.02793i	−0.487730	−	0.297336i
$412$	−15.0092	−	8.66559i	−0.739452	−	0.426923i
$413$		−	15.7880i		−	0.776878i
$414$	−5.17127	−	10.0345i	−0.254154	−	0.493168i
$415$			1.03697i			0.0509027i
$416$	5.43478			0.266462
$417$	32.6068	+	19.8782i	1.59676	+	0.973438i
$418$	5.16985	−	8.95444i	0.252865	−	0.437976i
$419$	7.29695	+	12.6387i	0.356479	+	0.617440i	0.987370	−	0.158432i	$-0.0506437\pi$
$419$	7.29695	+	12.6387i	0.356479	+	0.617440i	−0.630891	+	0.775872i	$0.717310\pi$
$420$	7.31011	+	0.174551i	0.356697	+	0.00851722i
$421$	−13.5592	+	7.82842i	−0.660836	+	0.381534i	−0.792595	−	0.609748i	$-0.791271\pi$
$421$	−13.5592	+	7.82842i	−0.660836	+	0.381534i	0.131759	+	0.991282i	$0.457937\pi$
$422$	−6.58901	−	3.80417i	−0.320748	−	0.185184i
$423$	−0.403693	−	0.0192898i	−0.0196282	−	0.000937902i
$424$	−6.68953	−	3.86220i	−0.324873	−	0.187565i
$425$	5.09485	+	2.94151i	0.247137	+	0.142684i
$426$	7.49054	−	12.2870i	0.362918	−	0.595306i
$427$	15.6729	−	9.04877i	0.758466	−	0.437900i
$428$	−0.539016	−	0.933602i	−0.0260543	−	0.0451274i
$429$	−27.1421	+	44.5221i	−1.31043	+	2.14955i
$430$	−1.53761	+	0.887742i	−0.0741503	+	0.0428107i
$431$	−12.3421	+	7.12573i	−0.594500	+	0.343235i	−0.766875	−	0.641797i	$-0.778189\pi$
$431$	−12.3421	+	7.12573i	−0.594500	+	0.343235i	0.172375	+	0.985031i	$0.444856\pi$
$432$	−0.371833	+	5.18283i	−0.0178898	+	0.249359i
$433$	25.4904			1.22499			0.612496	−	0.790474i	$-0.290166\pi$
$433$	25.4904			1.22499			0.612496	+	0.790474i	$0.290166\pi$
$434$	−11.5184	−	19.9504i	−0.552899	−	0.957650i
$435$	−2.38966	−	1.45681i	−0.114575	−	0.0698489i
$436$	8.26092	+	4.76944i	0.395626	+	0.228415i
$437$	−7.02381			−0.335994
$438$	3.24994	+	5.95286i	0.155288	+	0.284439i
$439$	−14.6428	−	8.45400i	−0.698861	−	0.403487i	0.108062	−	0.994144i	$-0.465535\pi$
$439$	−14.6428	−	8.45400i	−0.698861	−	0.403487i	−0.806923	+	0.590657i	$0.798869\pi$
$440$	5.25214	+	9.09698i	0.250386	+	0.433681i
$441$	6.12435	+	0.292642i	0.291636	+	0.0139353i
$442$	19.7222	+	11.3866i	0.938089	+	0.541606i
$443$	10.6960	+	18.5260i	0.508183	+	0.880199i	0.999955	+	0.00947466i	$0.00301592\pi$
$443$	10.6960	+	18.5260i	0.508183	+	0.880199i	−0.491772	+	0.870724i	$0.663651\pi$
$444$	7.54362	−	7.35485i	0.358004	−	0.349046i
$445$	16.2793	−	28.1966i	0.771714	−	1.33665i
$446$	−23.7151	+	13.6919i	−1.12294	+	0.648332i
$447$	−0.465851	+	19.5096i	−0.0220340	+	0.922773i
$448$	−1.11313	+	1.92800i	−0.0525904	+	0.0910892i
$449$	−26.5517	+	15.3296i	−1.25305	+	0.723450i	−0.971714	−	0.236159i	$-0.924111\pi$
$449$	−26.5517	+	15.3296i	−1.25305	+	0.723450i	−0.281338	+	0.959609i	$0.590778\pi$
$450$	−3.54295	−	2.27765i	−0.167016	−	0.107370i
$451$	1.87023	+	3.23933i	0.0880657	+	0.152534i
$452$	−4.87888	+	2.81682i	−0.229483	+	0.132492i
$453$	−0.135213	+	5.66265i	−0.00635286	+	0.266054i
$454$	−13.5279	+	23.4310i	−0.634896	+	1.09967i
$455$	−11.4720	+	19.8701i	−0.537815	+	0.931523i
$456$	2.76052	+	1.68291i	0.129273	+	0.0788093i
$457$	−11.2947	−	6.52102i	−0.528345	−	0.305040i	0.211997	−	0.977270i	$-0.432003\pi$
$457$	−11.2947	−	6.52102i	−0.528345	−	0.305040i	−0.740342	+	0.672230i	$0.765337\pi$
$458$			25.4025i			1.18698i
$459$	−12.2081	+	18.0289i	−0.569825	+	0.841515i
$460$	3.56781	−	6.17962i	0.166350	−	0.288126i
$461$			9.35518i			0.435714i	0.975981	+	0.217857i	$0.0699067\pi$
$461$			9.35518i			0.435714i	−0.975981	+	0.217857i	$0.930093\pi$
$462$	−10.2351	−	18.7475i	−0.476181	−	0.872214i
$463$		−	14.2872i		−	0.663984i	−0.943282	−	0.331992i	$-0.892279\pi$
$463$		−	14.2872i		−	0.663984i	0.943282	−	0.331992i	$-0.107721\pi$
$464$	0.737932	−	0.426045i	0.0342576	−	0.0197787i
$465$	0.811321	−	33.9777i	0.0376241	−	1.57568i
$466$			14.6671i			0.679439i
$467$			35.0057i			1.61987i	0.586519	+	0.809935i	$0.300498\pi$
$467$			35.0057i			1.61987i	−0.586519	+	0.809935i	$0.699502\pi$
$468$	−13.7148	−	8.81681i	−0.633966	−	0.407557i
$469$	−5.90892	+	10.2346i	−0.272849	+	0.472588i
$470$	−0.127734	−	0.221242i	−0.00589194	−	0.0102051i
$471$	28.2781	+	17.2393i	1.30299	+	0.794344i
$472$	3.54587	+	6.14162i	0.163212	+	0.282691i
$473$	4.49149	+	2.59316i	0.206519	+	0.119234i
$474$	−0.538498	+	22.5520i	−0.0247340	+	1.03585i
$475$	−2.26956	+	1.31033i	−0.104135	+	0.0601221i
$476$	−8.07883	+	4.66431i	−0.370293	+	0.213789i
$477$	10.6156	+	20.5987i	0.486053	+	0.943152i
$478$	11.0709	+	19.1753i	0.506370	+	0.877059i
$479$			18.6740i			0.853239i	0.904431	+	0.426619i	$0.140296\pi$
$479$			18.6740i			0.853239i	−0.904431	+	0.426619i	$0.859704\pi$
$480$	−2.88287	+	1.57389i	−0.131584	+	0.0718380i
$481$	8.91339	+	31.8342i	0.406416	+	1.45151i
$482$	10.0134	−	17.3437i	0.456098	−	0.789984i
$483$	−7.55270	+	12.3889i	−0.343660	+	0.563716i
$484$	9.84192	−	17.0467i	0.447360	−	0.774850i
$485$	−2.98277	−	5.16631i	−0.135441	−	0.234590i
$486$	9.34640	−	12.4758i	0.423961	−	0.565912i
$487$			13.2828i			0.601903i	0.953639	+	0.300951i	$0.0973042\pi$
$487$			13.2828i			0.601903i	−0.953639	+	0.300951i	$0.902696\pi$
$488$	−4.06456	+	7.04003i	−0.183994	+	0.318687i
$489$	0.558451	+	0.0133347i	0.0252540	+	0.000603016i
$490$	1.93783	+	3.35642i	0.0875422	+	0.151628i
$491$	7.39038	−	12.8005i	0.333523	−	0.577679i	−0.649677	−	0.760210i	$-0.725096\pi$
$491$	7.39038	−	12.8005i	0.333523	−	0.577679i	0.983200	+	0.182531i	$0.0584291\pi$
$492$	−1.02656	+	0.560445i	−0.0462808	+	0.0252668i
$493$	3.57049			0.160807
$494$	−8.78548	+	5.07230i	−0.395277	+	0.228213i
$495$	1.50407	−	31.4769i	0.0676030	−	1.41478i
$496$	8.96141	+	5.17387i	0.402379	+	0.232314i
$497$	−18.4962			−0.829666
$498$	0.453855	+	0.831318i	0.0203377	+	0.0372523i
$499$			17.6441i			0.789860i	0.918711	+	0.394930i	$0.129231\pi$
$499$			17.6441i			0.789860i	−0.918711	+	0.394930i	$0.870769\pi$
$500$		−	12.1440i		−	0.543095i
$501$	2.70596	+	4.95646i	0.120893	+	0.221438i
$502$	9.72954			0.434251
$503$	−37.5108	−	21.6569i	−1.67252	−	0.965632i	−0.966218	−	0.257725i	$-0.917027\pi$
$503$	−37.5108	−	21.6569i	−1.67252	−	0.965632i	−0.706306	−	0.707907i	$-0.749640\pi$
$504$	5.93678	−	3.05952i	0.264445	−	0.136282i
$505$	−8.18920	+	4.72804i	−0.364415	+	0.210395i
$506$	−20.8437			−0.926615
$507$	25.1401	−	13.7251i	1.11651	−	0.609553i
$508$	−4.23844	+	7.34120i	−0.188050	+	0.325713i
$509$	8.21539	+	14.2295i	0.364141	+	0.630710i	0.988638	−	0.150317i	$-0.0480294\pi$
$509$	8.21539	+	14.2295i	0.364141	+	0.630710i	−0.624497	+	0.781027i	$0.714696\pi$
$510$	−13.7591	−	0.328541i	−0.609264	−	0.0145480i
$511$	4.35870	−	7.54949i	0.192818	−	0.333970i
$512$		−	1.00000i		−	0.0441942i
$513$	−4.23607	−	8.72523i	−0.187027	−	0.385228i
$514$	−12.2398	−	21.2000i	−0.539874	−	0.935090i
$515$	−16.4327	+	28.4623i	−0.724113	+	1.25420i
$516$	−0.844135	+	1.38466i	−0.0371610	+	0.0609564i
$517$	−0.373122	+	0.646265i	−0.0164099	+	0.0284227i
$518$	−13.1188	−	3.35810i	−0.576408	−	0.147547i
$519$	−5.96809	+	3.25826i	−0.261970	+	0.143022i
$520$		−	10.3061i		−	0.451952i
$521$	−9.93752	−	17.2123i	−0.435371	−	0.754084i	0.561955	−	0.827168i	$-0.310049\pi$
$521$	−9.93752	−	17.2123i	−0.435371	−	0.754084i	−0.997326	+	0.0730835i	$0.976716\pi$
$522$	−2.55336	−	0.122008i	−0.111757	−	0.00534014i
$523$	−6.22307	+	3.59289i	−0.272116	+	0.157106i	−0.629849	−	0.776718i	$-0.716883\pi$
$523$	−6.22307	+	3.59289i	−0.272116	+	0.157106i	0.357733	+	0.933824i	$0.383550\pi$
$524$	11.3862	−	6.57382i	0.497408	−	0.287178i
$525$	−0.129232	+	5.41216i	−0.00564013	+	0.236206i
$526$	−8.97992	−	5.18456i	−0.391543	−	0.226057i
$527$	21.6799	+	37.5508i	0.944393	+	1.63574i
$528$	8.19207	+	4.99415i	0.356514	+	0.217343i
$529$	−4.42039	−	7.65633i	−0.192191	−	0.332884i
$530$	−7.32397	+	12.6855i	−0.318133	+	0.551023i
$531$	1.01544	−	21.2510i	0.0440664	−	0.922213i
$532$		−	4.15555i		−	0.180166i
$533$		−	3.66988i		−	0.158960i
$534$	0.709889	−	29.7298i	0.0307199	−	1.28653i
$535$	−1.77041	+	1.02215i	−0.0765414	+	0.0441912i
$536$		−	5.30839i		−	0.229288i
$537$	10.6510	+	19.5093i	0.459626	+	0.841889i
$538$			7.17096i			0.309162i
$539$	5.66055	−	9.80437i	0.243817	−	0.422304i
$540$	9.82831	+	0.705114i	0.422943	+	0.0303433i
$541$		−	25.2856i		−	1.08711i	−0.839373	−	0.543556i	$-0.817077\pi$
$541$		−	25.2856i		−	1.08711i	0.839373	−	0.543556i	$-0.182923\pi$
$542$	23.9360	+	13.8195i	1.02814	+	0.593597i
$543$	−19.9169	−	12.1420i	−0.854715	−	0.521062i
$544$	2.09514	−	3.62888i	0.0898283	−	0.155587i
$545$	9.04439	−	15.6653i	0.387419	−	0.671030i
$546$	−0.500257	+	20.9505i	−0.0214090	+	0.896598i
$547$	−8.21418	+	4.74246i	−0.351213	+	0.202773i	−0.665219	−	0.746648i	$-0.731662\pi$
$547$	−8.21418	+	4.74246i	−0.351213	+	0.202773i	0.314006	+	0.949421i	$0.398329\pi$
$548$	−3.34296	−	5.79018i	−0.142804	−	0.247344i
$549$	21.6780	−	11.1718i	0.925195	−	0.476799i
$550$	−6.73510	+	3.88851i	−0.287185	+	0.165807i
$551$	−0.795259	+	1.37743i	−0.0338792	+	0.0586805i
$552$	0.155581	−	6.51563i	0.00662195	−	0.277324i
$553$	25.1105	−	14.4975i	1.06781	−	0.616498i
$554$	8.05335	−	13.9488i	0.342154	−	0.592629i
$555$	−13.9472	−	14.3051i	−0.592024	−	0.607218i
$556$	11.0240	+	19.0941i	0.467522	+	0.809772i
$557$	25.0198	+	14.4452i	1.06012	+	0.612062i	0.925466	−	0.378830i	$-0.123674\pi$
$557$	25.0198	+	14.4452i	1.06012	+	0.612062i	0.134656	+	0.990892i	$0.457007\pi$
$558$	−14.2208	−	27.5944i	−0.602013	−	1.16816i
$559$	−2.54423	−	4.40674i	−0.107610	−	0.186385i
$560$	3.65610	+	2.11085i	0.154498	+	0.0891996i
$561$	19.2646	+	35.2867i	0.813353	+	1.48981i
$562$	−12.6912			−0.535345
$563$	−16.1957	−	9.35060i	−0.682568	−	0.394081i	0.118254	−	0.992983i	$-0.462270\pi$
$563$	−16.1957	−	9.35060i	−0.682568	−	0.394081i	−0.800822	+	0.598902i	$0.795604\pi$
$564$	−0.199234	−	0.121460i	−0.00838928	−	0.00511438i
$565$	5.34160	+	9.25192i	0.224723	+	0.389231i
$566$	23.2610			0.977732
$567$	−19.9450	−	1.91044i	−0.837612	−	0.0802310i
$568$	7.19510	−	4.15409i	0.301900	−	0.174302i
$569$	−2.39046	+	1.38014i	−0.100213	+	0.0578583i	−0.549269	−	0.835646i	$-0.685094\pi$
$569$	−2.39046	+	1.38014i	−0.100213	+	0.0578583i	0.449056	+	0.893504i	$0.351760\pi$
$570$	3.19133	−	5.23483i	0.133670	−	0.219263i
$571$	−10.3952	−	18.0049i	−0.435024	−	0.753483i	0.562274	−	0.826951i	$-0.309927\pi$
$571$	−10.3952	−	18.0049i	−0.435024	−	0.753483i	−0.997298	+	0.0734678i	$0.976593\pi$
$572$	−26.0716	+	15.0524i	−1.09011	+	0.629374i
$573$	5.31943	−	8.72562i	0.222222	−	0.364518i
$574$	1.30190	+	0.751650i	0.0543401	+	0.0313732i
$575$	4.57519	+	2.64148i	0.190798	+	0.110158i
$576$	−1.62229	+	2.52352i	−0.0675956	+	0.105147i
$577$	−22.8203	−	13.1753i	−0.950022	−	0.548496i	−0.0569344	−	0.998378i	$-0.518133\pi$
$577$	−22.8203	−	13.1753i	−0.950022	−	0.548496i	−0.893088	+	0.449882i	$0.851466\pi$
$578$	0.483593	−	0.279202i	0.0201148	−	0.0116133i
$579$	−7.76538	−	0.185422i	−0.322718	−	0.00770587i
$580$	−0.807918	−	1.39936i	−0.0335470	−	0.0581051i
$581$	0.608694	−	1.05429i	0.0252529	−	0.0437393i
$582$	−4.65240	−	2.83625i	−0.192848	−	0.117566i
$583$	42.7878			1.77209
$584$			3.91572i			0.162034i
$585$	−16.7195	+	26.0076i	−0.691266	+	1.07528i
$586$		−	18.1212i		−	0.748579i
$587$	−7.08791	−	4.09221i	−0.292550	−	0.168904i	0.346542	−	0.938035i	$-0.387356\pi$
$587$	−7.08791	−	4.09221i	−0.292550	−	0.168904i	−0.639091	+	0.769131i	$0.720689\pi$
$588$	3.02254	+	1.84264i	0.124648	+	0.0759893i
$589$	−19.3152			−0.795868
$590$	11.6465	−	6.72410i	0.479478	−	0.276827i
$591$	−0.137053	+	5.73972i	−0.00563762	+	0.236101i
$592$	5.85749	−	1.64006i	0.240741	−	0.0674062i
$593$	3.54132			0.145425			0.0727124	−	0.997353i	$-0.476834\pi$
$593$	3.54132			0.145425			0.0727124	+	0.997353i	$0.476834\pi$
$594$	−12.5709	−	25.8928i	−0.515789	−	1.06239i
$595$	8.84503	+	15.3200i	0.362611	+	0.628061i
$596$	−5.63355	+	9.75759i	−0.230759	+	0.399686i
$597$	−21.4535	−	39.2961i	−0.878035	−	1.60828i
$598$	17.7106	+	10.2252i	0.724239	+	0.418139i
$599$	12.7391			0.520506			0.260253	−	0.965540i	$-0.416194\pi$
$599$	12.7391			0.520506			0.260253	+	0.965540i	$0.416194\pi$
$600$	−1.16526	−	2.13438i	−0.0475714	−	0.0871358i
$601$	−36.7368			−1.49853			−0.749264	−	0.662272i	$-0.769592\pi$
$601$	−36.7368			−1.49853			−0.749264	+	0.662272i	$0.769592\pi$
$602$	2.08440			0.0849537
$603$	−8.61177	+	13.3958i	−0.350699	+	0.545521i
$604$	−1.63513	+	2.83213i	−0.0665325	+	0.115238i
$605$	−32.3260	−	18.6634i	−1.31424	−	0.758776i
$606$	−4.49579	+	7.37459i	−0.182629	+	0.299572i
$607$	−31.2598	+	18.0478i	−1.26880	+	0.732539i	−0.974760	−	0.223255i	$-0.928332\pi$
$607$	−31.2598	+	18.0478i	−1.26880	+	0.732539i	−0.294035	+	0.955795i	$0.594998\pi$
$608$	0.933303	+	1.61653i	0.0378504	+	0.0655589i
$609$	1.57443	+	2.88387i	0.0637993	+	0.116860i
$610$	13.3502	+	7.70771i	0.540532	+	0.312076i
$611$	0.634071	−	0.366081i	0.0256518	−	0.0148101i
$612$	−11.1742	+	5.75864i	−0.451692	+	0.232779i
$613$	−13.3492	+	23.1215i	−0.539168	+	0.933867i	0.459781	+	0.888033i	$0.347928\pi$
$613$	−13.3492	+	23.1215i	−0.539168	+	0.933867i	−0.998949	+	0.0458346i	$0.985405\pi$
$614$		−	20.8256i		−	0.840454i
$615$	1.06278	+	1.94668i	0.0428556	+	0.0784979i
$616$		−	12.3319i		−	0.496867i
$617$	−0.687451	−	1.19070i	−0.0276757	−	0.0479358i	0.851856	−	0.523776i	$-0.175477\pi$
$617$	−0.687451	−	1.19070i	−0.0276757	−	0.0479358i	−0.879532	+	0.475841i	$0.842144\pi$
$618$	−0.716578	+	30.0099i	−0.0288250	+	1.20718i
$619$	−11.4506	−	19.8330i	−0.460239	−	0.797157i	0.538733	−	0.842476i	$-0.318903\pi$
$619$	−11.4506	−	19.8330i	−0.460239	−	0.797157i	−0.998973	+	0.0453188i	$0.985570\pi$
$620$	9.81132	−	16.9937i	0.394032	−	0.682483i
$621$	−10.9629	+	16.1899i	−0.439925	+	0.649680i
$622$	12.1426	+	21.0315i	0.486872	+	0.843287i
$623$	−33.1025	+	19.1117i	−1.32622	+	0.765696i
$624$	−4.51071	−	8.26220i	−0.180573	−	0.330753i
$625$	−16.0090			−0.640360
$626$	−4.57113			−0.182699
$627$	−17.9038	−	0.427507i	−0.715008	−	0.0170730i
$628$	9.56053	+	16.5593i	0.381507	+	0.660789i
$629$	24.6923	+	6.32064i	0.984547	+	0.252021i
$630$	−5.80182	−	11.2580i	−0.231150	−	0.448531i
$631$	−32.1961	−	18.5884i	−1.28171	−	0.739993i	−0.304546	−	0.952498i	$-0.598505\pi$
$631$	−32.1961	−	18.5884i	−1.28171	−	0.739993i	−0.977160	+	0.212505i	$0.931838\pi$
$632$	−6.51206	+	11.2792i	−0.259036	+	0.448663i
$633$	−0.314576	+	13.1743i	−0.0125033	+	0.523630i
$634$		−	30.2100i		−	1.19979i
$635$	13.9213	+	8.03744i	0.552448	+	0.318956i
$636$	−0.319375	+	13.3753i	−0.0126640	+	0.530363i
$637$	−9.61937	+	5.55375i	−0.381133	+	0.220047i
$638$	−2.35999	+	4.08763i	−0.0934330	+	0.161831i
$639$	−24.8961	−	1.18962i	−0.984876	−	0.0470607i
$640$	−1.89632			−0.0749586
$641$	33.1798			1.31052			0.655262	−	0.755402i	$-0.272558\pi$
$641$	33.1798			1.31052			0.655262	+	0.755402i	$0.272558\pi$
$642$	−0.971937	+	1.59430i	−0.0383593	+	0.0629220i
$643$	−24.7305	−	14.2782i	−0.975277	−	0.563076i	−0.0744361	−	0.997226i	$-0.523716\pi$
$643$	−24.7305	−	14.2782i	−0.975277	−	0.563076i	−0.900841	+	0.434149i	$0.857049\pi$
$644$	−7.25480	+	4.18856i	−0.285879	+	0.165053i
$645$	2.62576	+	1.60075i	0.103389	+	0.0630295i
$646$			7.82159i			0.307736i
$647$	−27.5157	+	15.8862i	−1.08175	+	0.624550i	−0.931369	−	0.364077i	$-0.881384\pi$
$647$	−27.5157	+	15.8862i	−1.08175	+	0.624550i	−0.150384	+	0.988628i	$0.548051\pi$
$648$	8.18779	−	3.73633i	0.321647	−	0.146777i
$649$	−34.0203	−	19.6416i	−1.33541	−	0.771001i
$650$	7.63028			0.299284
$651$	−20.7696	+	34.0690i	−0.814024	+	1.33527i
$652$	0.279305	+	0.161257i	0.0109384	+	0.00631530i
$653$		−	36.5048i		−	1.42854i	−0.699869	−	0.714271i	$-0.746758\pi$
$653$		−	36.5048i		−	1.42854i	0.699869	−	0.714271i	$-0.253242\pi$
$654$	0.394397	−	16.5171i	0.0154221	−	0.645871i
$655$	−12.4661	−	21.5918i	−0.487089	−	0.843663i
$656$	−0.675259			−0.0263644
$657$	6.35245	−	9.88141i	0.247833	−	0.385511i
$658$			0.299917i			0.0116920i
$659$	−6.29718	+	10.9070i	−0.245303	+	0.424878i	−0.962217	−	0.272284i	$-0.912221\pi$
$659$	−6.29718	+	10.9070i	−0.245303	+	0.424878i	0.716914	+	0.697162i	$0.245554\pi$
$660$	9.47051	−	15.5348i	0.368639	−	0.604690i
$661$		−	4.96286i		−	0.193033i	−0.995331	−	0.0965165i	$-0.969230\pi$
$661$		−	4.96286i		−	0.193033i	0.995331	−	0.0965165i	$-0.0307701\pi$
$662$	−26.1062			−1.01464
$663$	0.941586	−	39.4331i	0.0365682	−	1.53146i
$664$			0.546832i			0.0212212i
$665$	−7.88024			−0.305583
$666$	−17.4422	−	5.36383i	−0.675870	−	0.207844i
$667$	3.20631			0.124149
$668$			3.26030i			0.126145i
$669$	40.4980	+	24.6889i	1.56574	+	0.954528i
$670$	−10.0664			−0.388899
$671$		−	45.0297i		−	1.73835i
$672$	3.85489	+	0.0920473i	0.148706	+	0.00355080i
$673$	14.1071	−	24.4342i	0.543789	−	0.941871i	−0.454893	−	0.890546i	$-0.650322\pi$
$673$	14.1071	−	24.4342i	0.543789	−	0.941871i	0.998682	−	0.0513247i	$-0.0163443\pi$
$674$			15.1007i			0.581656i
$675$	−0.522043	+	7.27655i	−0.0200934	+	0.280074i
$676$	16.5368			0.636032
$677$	−18.0801	−	31.3156i	−0.694874	−	1.20356i	−0.970223	−	0.242213i	$-0.922127\pi$
$677$	−18.0801	−	31.3156i	−0.694874	−	1.20356i	0.275349	−	0.961344i	$-0.411206\pi$
$678$	8.33160	+	5.07922i	0.319973	+	0.195066i
$679$			7.00347i			0.268769i
$680$	−6.88153	−	3.97305i	−0.263894	−	0.152360i
$681$	46.8487	+	1.11866i	1.79525	+	0.0428670i
$682$	−57.3193			−2.19487
$683$	−5.51639	−	3.18489i	−0.211079	−	0.121867i	0.390734	−	0.920504i	$-0.372221\pi$
$683$	−5.51639	−	3.18489i	−0.211079	−	0.121867i	−0.601813	+	0.798637i	$0.705555\pi$
$684$	0.267273	−	5.59344i	0.0102194	−	0.213870i
$685$	−10.9800	+	6.33932i	−0.419525	+	0.242213i
$686$		−	20.1338i		−	0.768711i
$687$	38.6180	−	21.0834i	1.47337	−	0.804380i
$688$	−0.810841	+	0.468139i	−0.0309130	+	0.0178476i
$689$	−36.3561	−	20.9902i	−1.38506	−	0.799664i
$690$	−12.3557	−	0.295030i	−0.470374	−	0.0112316i
$691$	16.5420			0.629285			0.314643	−	0.949210i	$-0.398115\pi$
$691$	16.5420			0.629285			0.314643	+	0.949210i	$0.398115\pi$
$692$	−3.92574			−0.149234
$693$	−20.0060	+	31.1198i	−0.759964	+	1.18214i
$694$	16.7995	−	29.0976i	0.637700	−	1.10453i
$695$	36.2086	−	20.9050i	1.37347	−	0.792973i
$696$	−1.26016	−	0.768233i	−0.0477661	−	0.0291198i
$697$	−2.45044	−	1.41476i	−0.0928169	−	0.0535878i
$698$		−	1.51202i		−	0.0572306i
$699$	22.2976	−	12.1733i	0.843371	−	0.460435i
$700$	−1.56280	+	2.70685i	−0.0590683	+	0.102309i
$701$	−28.3199	−	16.3505i	−1.06963	−	0.617550i	−0.141548	−	0.989931i	$-0.545208\pi$
$701$	−28.3199	−	16.3505i	−1.06963	−	0.617550i	−0.928080	+	0.372381i	$0.878541\pi$
$702$	−2.02083	+	28.1675i	−0.0762713	+	1.06312i
$703$	−7.93812	+	8.11802i	−0.299392	+	0.306177i
$704$	2.76965	+	4.79717i	0.104385	+	0.180800i
$705$	−0.230327	+	0.377812i	−0.00867460	+	0.0142292i
$706$	−1.24530			−0.0468675
$707$	11.1013			0.417508
$708$	6.39380	−	10.4880i	0.240294	−	0.394162i
$709$	14.8975	−	8.60106i	0.559486	−	0.323019i	−0.193453	−	0.981110i	$-0.561969\pi$
$709$	14.8975	−	8.60106i	0.559486	−	0.323019i	0.752939	+	0.658090i	$0.228635\pi$
$710$	−7.87749	−	13.6442i	−0.295637	−	0.512058i
$711$	34.7315	−	17.8989i	1.30253	−	0.671261i
$712$	8.58470	−	14.8691i	0.321725	−	0.557244i
$713$	19.4686	+	33.7207i	0.729106	+	1.26285i
$714$	13.7961	+	8.41056i	0.516306	+	0.314757i
$715$	28.5442	+	49.4401i	1.06749	+	1.84895i
$716$			12.8330i			0.479592i
$717$	19.9627	−	32.7454i	0.745520	−	1.22290i
$718$		−	19.0620i		−	0.711388i
$719$	7.15827	−	12.3985i	0.266959	−	0.462386i	−0.701116	−	0.713047i	$-0.747315\pi$
$719$	7.15827	−	12.3985i	0.266959	−	0.462386i	0.968075	+	0.250661i	$0.0806480\pi$
$720$	4.78540	+	3.07639i	0.178341	+	0.114650i
$721$	33.4144	−	19.2918i	1.24442	−	0.718465i
$722$	13.4371	+	7.75789i	0.500076	+	0.288719i
$723$	−34.6775	−	0.828032i	−1.28967	−	0.0307948i
$724$	−6.73368	−	11.6631i	−0.250255	−	0.433455i
$725$	1.03604	−	0.598156i	0.0384774	−	0.0222149i
$726$	−34.0837	−	0.813852i	−1.26496	−	0.0302049i
$727$	−4.86409	−	2.80828i	−0.180399	−	0.104153i	0.407081	−	0.913392i	$-0.366547\pi$
$727$	−4.86409	−	2.80828i	−0.180399	−	0.104153i	−0.587480	+	0.809239i	$0.699880\pi$
$728$	−6.04961	+	10.4782i	−0.224213	+	0.388349i
$729$	−26.7235	−	3.85430i	−0.989759	−	0.142752i
$730$	7.42546			0.274829
$731$	−3.92327			−0.145107
$732$	14.0761	+	0.336109i	0.520266	+	0.0124229i
$733$	8.93897			0.330168			0.165084	−	0.986279i	$-0.447210\pi$
$733$	8.93897			0.330168			0.165084	+	0.986279i	$0.447210\pi$
$734$	−16.4819	−	9.51586i	−0.608360	−	0.351237i
$735$	3.49424	−	5.73171i	0.128887	−	0.211417i
$736$	1.88144	−	3.25875i	0.0693507	−	0.120119i
$737$	14.7024	+	25.4653i	0.541570	+	0.938026i
$738$	1.70403	+	1.09547i	0.0627262	+	0.0403247i
$739$	4.81803			0.177234			0.0886171	−	0.996066i	$-0.471755\pi$
$739$	4.81803			0.177234			0.0886171	+	0.996066i	$0.471755\pi$
$740$	−3.11009	−	11.1077i	−0.114329	−	0.408326i
$741$	15.0028	+	9.14622i	0.551143	+	0.335995i
$742$	14.8926	−	8.59826i	0.546725	−	0.315652i
$743$	−28.8790			−1.05947			−0.529734	−	0.848164i	$-0.677708\pi$
$743$	−28.8790			−1.05947			−0.529734	+	0.848164i	$0.677708\pi$
$744$	0.427840	−	17.9177i	0.0156854	−	0.656895i
$745$	18.5035	+	10.6830i	0.677916	+	0.391395i
$746$			10.5325i			0.385621i
$747$	0.887122	−	1.37994i	0.0324581	−	0.0504894i
$748$			23.2112i			0.848685i
$749$	2.39997			0.0876931
$750$	−18.4618	+	10.0792i	−0.674131	+	0.368039i
$751$	7.58068	−	13.1301i	0.276623	−	0.479125i	−0.693920	−	0.720052i	$-0.744118\pi$
$751$	7.58068	−	13.1301i	0.276623	−	0.479125i	0.970543	+	0.240927i	$0.0774514\pi$
$752$	−0.0673590	−	0.116669i	−0.00245633	−	0.00425449i
$753$	−8.07525	−	14.7913i	−0.294278	−	0.539025i
$754$	4.01050	−	2.31546i	0.146054	−	0.0843242i
$755$	5.37062	+	3.10073i	0.195457	+	0.112847i
$756$	−9.57858	−	6.48605i	−0.348369	−	0.235895i
$757$	−12.9688	−	7.48753i	−0.471358	−	0.272139i	0.245450	−	0.969409i	$-0.421064\pi$
$757$	−12.9688	−	7.48753i	−0.471358	−	0.272139i	−0.716808	+	0.697270i	$0.754398\pi$
$758$	−19.3360	−	11.1637i	−0.702317	−	0.405483i
$759$	17.2997	+	31.6875i	0.627938	+	1.15018i
$760$	3.06545	−	1.76984i	0.111196	−	0.0641989i
$761$	9.33668	+	16.1716i	0.338454	+	0.586220i	0.984142	−	0.177381i	$-0.0567626\pi$
$761$	9.33668	+	16.1716i	0.338454	+	0.586220i	−0.645688	+	0.763601i	$0.723429\pi$
$762$	14.6782	+	0.350487i	0.531735	+	0.0126968i
$763$	−18.3909	+	10.6180i	−0.665796	+	0.384398i
$764$	5.10962	−	2.95004i	0.184860	−	0.106729i
$765$	10.9202	+	21.1899i	0.394822	+	0.766124i
$766$	−24.1700			−0.873299
$767$	19.2710	+	33.3784i	0.695836	+	1.20522i
$768$	−1.52025	+	0.829972i	−0.0548571	+	0.0299490i
$769$	−34.7959	−	20.0894i	−1.25477	−	0.724443i	−0.282718	−	0.959203i	$-0.591236\pi$
$769$	−34.7959	−	20.0894i	−1.25477	−	0.724443i	−0.972053	+	0.234760i	$0.924570\pi$
$770$	−23.3852			−0.842745
$771$	−22.0704	+	36.2029i	−0.794848	+	1.30381i
$772$	−3.88379	−	2.24231i	−0.139781	−	0.0807025i
$773$	11.9364	+	20.6744i	0.429322	+	0.743607i	0.996813	−	0.0797725i	$-0.0254194\pi$
$773$	11.9364	+	20.6744i	0.429322	+	0.743607i	−0.567492	+	0.823379i	$0.692086\pi$
$774$	2.80564	+	0.134063i	0.100846	+	0.00481878i
$775$	12.5816	+	7.26397i	0.451943	+	0.260929i
$776$	−1.57293	−	2.72439i	−0.0564647	−	0.0977998i
$777$	5.78310	+	22.7310i	0.207468	+	0.815468i
$778$	12.2398	−	21.2000i	0.438819	−	0.760057i
$779$	1.09157	−	0.630221i	0.0391097	−	0.0225800i
$780$	−15.6678	+	8.55376i	−0.560996	+	0.306274i
$781$	−23.0108	+	39.8558i	−0.823390	+	1.42615i
$782$	13.6550	−	7.88374i	0.488303	−	0.281922i
$783$	1.93373	+	3.98300i	0.0691060	+	0.142341i
$784$	1.02189	+	1.76996i	0.0364961	+	0.0632130i
$785$	31.4018	−	18.1298i	1.12078	−	0.647081i
$786$	−19.4440	−	11.8537i	−0.693545	−	0.422808i
$787$	−6.69133	+	11.5897i	−0.238520	+	0.413129i	−0.960290	−	0.279004i	$-0.909996\pi$
$787$	−6.69133	+	11.5897i	−0.238520	+	0.413129i	0.721770	+	0.692133i	$0.243329\pi$
$788$	−1.65739	+	2.87068i	−0.0590420	+	0.102264i
$789$	−0.428723	+	17.9547i	−0.0152630	+	0.639205i
$790$	21.3890	+	12.3490i	0.760987	+	0.439356i
$791$		−	12.5419i		−	0.445940i
$792$	0.793153	−	16.5990i	0.0281835	−	0.589818i
$793$	−22.0900	+	38.2610i	−0.784439	+	1.35869i
$794$			19.8487i			0.704404i
$795$	25.3638	+	0.605637i	0.899560	+	0.0214797i
$796$		−	25.8485i		−	0.916177i
$797$	13.7574	−	7.94287i	0.487314	−	0.281351i	−0.236146	−	0.971718i	$-0.575884\pi$
$797$	13.7574	−	7.94287i	0.487314	−	0.281351i	0.723459	+	0.690367i	$0.242551\pi$
$798$	−6.31745	+	3.44899i	−0.223635	+	0.122093i
$799$		−	0.564505i		−	0.0199708i
$800$		−	1.40397i		−	0.0496379i
$801$	−45.7858	+	23.5957i	−1.61776	+	0.833712i
$802$	13.8101	−	23.9198i	0.487652	−	0.844638i
$803$	−10.8452	−	18.7844i	−0.382718	−	0.662887i
$804$	−8.07006	+	4.40582i	−0.284609	+	0.155381i
$805$	7.94286	+	13.7574i	0.279949	+	0.484886i
$806$	48.7033	+	28.1189i	1.71550	+	0.990445i
$807$	10.9016	−	5.95169i	0.383755	−	0.209510i
$808$	−4.31847	+	2.49327i	−0.151923	+	0.0877130i
$809$	−27.2362	+	15.7249i	−0.957576	+	0.552856i	−0.895426	−	0.445210i	$-0.853129\pi$
$809$	−27.2362	+	15.7249i	−0.957576	+	0.552856i	−0.0621495	+	0.998067i	$0.519796\pi$
$810$	−7.08527	−	15.5267i	−0.248951	−	0.545551i
$811$	−12.2472	−	21.2128i	−0.430059	−	0.744883i	0.566819	−	0.823842i	$-0.308174\pi$
$811$	−12.2472	−	21.2128i	−0.430059	−	0.744883i	−0.996878	+	0.0789588i	$0.974840\pi$
$812$			1.89697i			0.0665707i
$813$	1.14277	−	47.8584i	0.0400785	−	1.67847i
$814$	−23.5570	+	24.0909i	−0.825672	+	0.844385i
$815$	0.305794	−	0.529651i	0.0107115	−	0.0185529i
$816$	−7.25570	−	0.173252i	−0.254000	−	0.00606503i
$817$	0.873832	−	1.51352i	0.0305715	−	0.0529514i
$818$	−6.66997	−	11.5527i	−0.233210	−	0.403932i
$819$	32.2651	−	16.6278i	1.12743	−	0.581022i
$820$			1.28051i			0.0447172i
$821$	24.0194	−	41.6028i	0.838281	−	1.45195i	−0.0530490	−	0.998592i	$-0.516894\pi$
$821$	24.0194	−	41.6028i	0.838281	−	1.45195i	0.891330	−	0.453354i	$-0.149773\pi$
$822$	−6.02793	+	9.88781i	−0.210248	+	0.344877i
$823$	−0.930692	−	1.61201i	−0.0324419	−	0.0561910i	0.849349	−	0.527832i	$-0.176995\pi$
$823$	−0.930692	−	1.61201i	−0.0324419	−	0.0561910i	−0.881790	+	0.471641i	$0.843662\pi$
$824$	−8.66559	+	15.0092i	−0.301880	+	0.522872i
$825$	11.5014	+	7.01165i	0.400428	+	0.244114i
$826$	−15.7880			−0.549336
$827$	28.6397	−	16.5351i	0.995900	−	0.574983i	0.0888677	−	0.996043i	$-0.471675\pi$
$827$	28.6397	−	16.5351i	0.995900	−	0.574983i	0.907033	+	0.421060i	$0.138342\pi$
$828$	−10.0345	+	5.17127i	−0.348723	+	0.179714i
$829$	28.3335	+	16.3583i	0.984063	+	0.568149i	0.903494	−	0.428600i	$-0.140993\pi$
$829$	28.3335	+	16.3583i	0.984063	+	0.568149i	0.0805684	+	0.996749i	$0.474326\pi$
$830$	1.03697			0.0359937
$831$	−27.8897	−	0.665951i	−0.967483	−	0.0231016i
$832$		−	5.43478i		−	0.188417i
$833$			8.56400i			0.296725i
$834$	19.8782	−	32.6068i	0.688325	−	1.12908i
$835$	6.18257			0.213957
$836$	−8.95444	−	5.16985i	−0.309696	−	0.178803i
$837$	−30.1475	+	44.5217i	−1.04205	+	1.53889i
$838$	12.6387	−	7.29695i	0.436596	−	0.252069i
$839$	−0.446602			−0.0154184			−0.00770920	−	0.999970i	$-0.502454\pi$
$839$	−0.446602			−0.0154184			−0.00770920	+	0.999970i	$0.502454\pi$
$840$	0.174551	−	7.31011i	0.00602258	−	0.252223i
$841$	−14.1370	+	24.4860i	−0.487482	+	0.844343i
$842$	7.82842	+	13.5592i	0.269785	+	0.467282i
$843$	10.5333	+	19.2937i	0.362787	+	0.664511i
$844$	−3.80417	+	6.58901i	−0.130945	+	0.226803i
$845$		−	31.3591i		−	1.07879i
$846$	−0.0192898	+	0.403693i	−0.000663197	+	0.0138793i
$847$	21.9106	+	37.9503i	0.752859	+	1.30399i
$848$	−3.86220	+	6.68953i	−0.132629	+	0.229720i
$849$	−19.3060	−	35.3624i	−0.662579	−	1.21363i
$850$	2.94151	−	5.09485i	0.100893	−	0.174752i
$851$	22.1737	+	5.67595i	0.760106	+	0.194569i
$852$	−12.2870	−	7.49054i	−0.420945	−	0.256622i
$853$		−	8.48276i		−	0.290444i	−0.989399	−	0.145222i	$-0.953610\pi$
$853$		−	8.48276i		−	0.290444i	0.989399	−	0.145222i	$-0.0463897\pi$
$854$	−9.04877	−	15.6729i	−0.309642	−	0.536316i
$855$	−10.6069	−	0.506835i	−0.362750	−	0.0173334i
$856$	−0.933602	+	0.539016i	−0.0319099	+	0.0184232i
$857$	−44.7964	+	25.8632i	−1.53021	+	0.883470i	−0.530863	+	0.847457i	$0.678132\pi$
$857$	−44.7964	+	25.8632i	−1.53021	+	0.883470i	−0.999351	+	0.0360124i	$0.988534\pi$
$858$	44.5221	+	27.1421i	1.51996	+	0.926617i
$859$	32.2873	+	18.6411i	1.10163	+	0.636025i	0.936648	−	0.350273i	$-0.113911\pi$
$859$	32.2873	+	18.6411i	1.10163	+	0.636025i	0.164979	+	0.986297i	$0.447244\pi$
$860$	0.887742	+	1.53761i	0.0302718	+	0.0524322i
$861$	0.0621557	−	2.60305i	0.00211826	−	0.0887116i
$862$	7.12573	+	12.3421i	0.242703	+	0.420375i
$863$	−13.4313	+	23.2637i	−0.457207	+	0.791906i	−0.998812	−	0.0487274i	$-0.984483\pi$
$863$	−13.4313	+	23.2637i	−0.457207	+	0.791906i	0.541605	+	0.840633i	$0.317817\pi$
$864$	5.18283	+	0.371833i	0.176324	+	0.0126500i
$865$			7.44446i			0.253119i
$866$		−	25.4904i		−	0.866200i
$867$	−0.825824	−	0.503450i	−0.0280465	−	0.0170980i
$868$	−19.9504	+	11.5184i	−0.677161	+	0.390959i
$869$		−	72.1445i		−	2.44734i
$870$	−1.45681	+	2.38966i	−0.0493906	+	0.0810171i
$871$		−	28.8500i		−	0.977543i
$872$	4.76944	−	8.26092i	0.161514	−	0.279750i
$873$	−0.450444	+	9.42680i	−0.0152452	+	0.319049i
$874$			7.02381i			0.237584i
$875$	23.4135	+	13.5178i	0.791522	+	0.456985i
$876$	5.95286	−	3.24994i	0.201129	−	0.109805i
$877$	−1.14079	+	1.97591i	−0.0385218	+	0.0667217i	−0.884644	−	0.466268i	$-0.845598\pi$
$877$	−1.14079	+	1.97591i	−0.0385218	+	0.0667217i	0.846122	+	0.532990i	$0.178932\pi$
$878$	−8.45400	+	14.6428i	−0.285309	+	0.494169i
$879$	−27.5486	+	15.0401i	−0.929192	+	0.507289i
$880$	9.09698	−	5.25214i	0.306659	−	0.177050i
$881$	12.4036	+	21.4836i	0.417887	+	0.723801i	0.995727	−	0.0923489i	$-0.0294375\pi$
$881$	12.4036	+	21.4836i	0.417887	+	0.723801i	−0.577840	+	0.816150i	$0.696104\pi$
$882$	0.292642	−	6.12435i	0.00985376	−	0.206218i
$883$	25.6069	−	14.7842i	0.861742	−	0.497527i	−0.00285334	−	0.999996i	$-0.500908\pi$
$883$	25.6069	−	14.7842i	0.861742	−	0.497527i	0.864595	+	0.502469i	$0.167575\pi$
$884$	11.3866	−	19.7222i	0.382973	−	0.663329i
$885$	−19.8885	−	12.1247i	−0.668546	−	0.407567i
$886$	18.5260	−	10.6960i	0.622394	−	0.359340i
$887$	16.8854	−	29.2464i	0.566957	−	0.981998i	−0.429908	−	0.902873i	$-0.641454\pi$
$887$	16.8854	−	29.2464i	0.566957	−	0.981998i	0.996865	−	0.0791256i	$-0.0252128\pi$
$888$	−7.35485	−	7.54362i	−0.246813	−	0.253147i
$889$	−9.43586	−	16.3434i	−0.316469	−	0.548140i
$890$	−28.1966	−	16.2793i	−0.945153	−	0.545684i
$891$	−28.9299	+	40.6011i	−0.969189	+	1.36019i
$892$	13.6919	+	23.7151i	0.458440	+	0.794041i
$893$	0.217775	+	0.125733i	0.00728758	+	0.00420748i
$894$	19.5096	+	0.465851i	0.652499	+	0.0155804i
$895$	24.3355			0.813445
$896$	1.92800	+	1.11313i	0.0644098	+	0.0371870i
$897$	0.845546	−	35.4110i	0.0282320	−	1.18234i
$898$	15.3296	+	26.5517i	0.511556	+	0.886042i
$899$	8.81722			0.294071
$900$	−2.27765	+	3.54295i	−0.0759218	+	0.118098i
$901$	−28.0310	+	16.1837i	−0.933848	+	0.539157i
$902$	3.23933	−	1.87023i	0.107858	−	0.0622718i
$903$	−1.72999	−	3.16880i	−0.0575705	−	0.105451i
$904$	2.81682	+	4.87888i	0.0936862	+	0.162269i
$905$	−22.1169	+	12.7692i	−0.735191	+	0.424463i
$906$	5.66265	+	0.135213i	0.188129	+	0.00449215i
$907$	15.9829	+	9.22772i	0.530703	+	0.306401i	0.741302	−	0.671171i	$-0.234208\pi$
$907$	15.9829	+	9.22772i	0.530703	+	0.306401i	−0.210600	+	0.977572i	$0.567542\pi$
$908$	23.4310	+	13.5279i	0.777586	+	0.448940i
$909$	14.9426	+	0.714006i	0.495614	+	0.0236821i
$910$	19.8701	+	11.4720i	0.658687	+	0.380293i
$911$	17.3249	−	10.0025i	0.573998	−	0.331398i	−0.184746	−	0.982786i	$-0.559146\pi$
$911$	17.3249	−	10.0025i	0.573998	−	0.331398i	0.758745	+	0.651388i	$0.225813\pi$
$912$	1.68291	−	2.76052i	0.0557266	−	0.0914101i
$913$	−1.51453	−	2.62325i	−0.0501237	−	0.0868168i
$914$	−6.52102	+	11.2947i	−0.215696	+	0.373597i
$915$	0.637369	−	26.6927i	0.0210708	−	0.882433i
$916$	25.4025			0.839322
$917$			29.2700i			0.966581i
$918$	18.0289	+	12.2081i	0.595041	+	0.402927i
$919$		−	23.2757i		−	0.767793i	−0.923376	−	0.383896i	$-0.874582\pi$
$919$		−	23.2757i		−	0.767793i	0.923376	−	0.383896i	$-0.125418\pi$
$920$	−6.17962	−	3.56781i	−0.203736	−	0.117627i
$921$	−31.6601	+	17.2847i	−1.04324	+	0.569550i
$922$	9.35518			0.308096
$923$	39.1038	−	22.5766i	1.28712	−	0.743117i
$924$	−18.7475	+	10.2351i	−0.616748	+	0.336711i
$925$	8.22375	−	2.30260i	0.270395	−	0.0757091i
$926$	−14.2872			−0.469508
$927$	46.2172	−	23.8180i	1.51797	−	0.782287i
$928$	−0.426045	−	0.737932i	−0.0139856	−	0.0242238i
$929$	−6.68198	+	11.5735i	−0.219229	+	0.379715i	−0.954572	−	0.297979i	$-0.903687\pi$
$929$	−6.68198	+	11.5735i	−0.219229	+	0.379715i	0.735344	+	0.677694i	$0.237021\pi$
$930$	−33.9777	−	0.811321i	−1.11417	−	0.0266043i
$931$	−3.30383	−	1.90747i	−0.108279	−	0.0625147i
$932$	14.6671			0.480436
$933$	21.8951	−	35.9152i	0.716813	−	1.17581i
$934$	35.0057			1.14542
$935$	44.0158			1.43947
$936$	−8.81681	+	13.7148i	−0.288186	+	0.448282i
$937$	27.4191	−	47.4913i	0.895743	−	1.55147i	0.0628599	−	0.998022i	$-0.479978\pi$
$937$	27.4191	−	47.4913i	0.895743	−	1.55147i	0.832883	−	0.553449i	$-0.186689\pi$
$938$	10.2346	+	5.90892i	0.334170	+	0.192933i
$939$	3.79391	+	6.94925i	0.123810	+	0.226780i
$940$	−0.221242	+	0.127734i	−0.00721612	+	0.00416623i
$941$	−19.6297	−	33.9996i	−0.639909	−	1.10836i	−0.985452	−	0.169952i	$-0.945639\pi$
$941$	−19.6297	−	33.9996i	−0.639909	−	1.10836i	0.345543	−	0.938403i	$-0.387695\pi$
$942$	17.2393	−	28.2781i	0.561686	−	0.921351i
$943$	−2.20050	−	1.27046i	−0.0716580	−	0.0413718i
$944$	6.14162	−	3.54587i	0.199893	−	0.115408i
$945$	−12.2996	+	18.1640i	−0.400107	+	0.590876i
$946$	2.59316	−	4.49149i	0.0843110	−	0.146031i
$947$			38.5831i			1.25378i	0.779107	+	0.626891i	$0.215673\pi$
$947$			38.5831i			1.25378i	−0.779107	+	0.626891i	$0.784327\pi$
$948$	22.5520	+	0.538498i	0.732456	+	0.0174896i
$949$			21.2811i			0.690813i
$950$	1.31033	+	2.26956i	0.0425128	+	0.0736342i
$951$	−45.9267	+	25.0735i	−1.48927	+	0.813063i
$952$	4.66431	+	8.07883i	0.151171	+	0.261836i
$953$	8.87267	−	15.3679i	0.287414	−	0.497815i	−0.685778	−	0.727811i	$-0.740538\pi$
$953$	8.87267	−	15.3679i	0.287414	−	0.497815i	0.973192	+	0.229996i	$0.0738712\pi$
$954$	20.5987	−	10.6156i	0.666909	−	0.343691i
$955$	−5.59422	−	9.68947i	−0.181025	−	0.313544i
$956$	19.1753	−	11.0709i	0.620174	−	0.358058i
$957$	8.17293	+	0.195153i	0.264193	+	0.00630842i
$958$	18.6740			0.603331
$959$	14.8846			0.480648
$960$	1.57389	+	2.88287i	0.0507971	+	0.0930443i
$961$	38.0379	+	65.8836i	1.22703	+	2.12528i
$962$	31.8342	−	8.91339i	1.02637	−	0.287379i
$963$	3.23041	+	0.154360i	0.104098	+	0.00497417i
$964$	−17.3437	−	10.0134i	−0.558603	−	0.322510i
$965$	−4.25214	+	7.36492i	−0.136881	+	0.237085i
$966$	12.3889	+	7.55270i	0.398607	+	0.243004i
$967$		−	24.0690i		−	0.774006i	−0.922079	−	0.387003i	$-0.873510\pi$
$967$		−	24.0690i		−	0.774006i	0.922079	−	0.387003i	$-0.126490\pi$
$968$	−17.0467	−	9.84192i	−0.547902	−	0.316331i
$969$	11.8907	−	6.49170i	0.381986	−	0.208544i
$970$	−5.16631	+	2.98277i	−0.165880	+	0.0957710i
$971$	13.6649	−	23.6684i	0.438529	−	0.759554i	−0.559047	−	0.829136i	$-0.688833\pi$
$971$	13.6649	−	23.6684i	0.438529	−	0.759554i	0.997576	+	0.0695813i	$0.0221663\pi$
$972$	−12.4758	−	9.34640i	−0.400160	−	0.299786i
$973$	−49.0845			−1.57358
$974$	13.2828			0.425610
$975$	−6.33291	−	11.5999i	−0.202816	−	0.371494i
$976$	7.04003	+	4.06456i	0.225346	+	0.130104i
$977$	2.06481	−	1.19212i	0.0660593	−	0.0381393i	−0.466607	−	0.884465i	$-0.654524\pi$
$977$	2.06481	−	1.19212i	0.0660593	−	0.0381393i	0.532666	+	0.846326i	$0.321190\pi$
$978$	0.0133347	−	0.558451i	0.000426397	−	0.0178573i
$979$			95.1064i			3.03961i
$980$	3.35642	−	1.93783i	0.107217	−	0.0619017i
$981$	−25.4374	+	13.1092i	−0.812155	+	0.418544i
$982$	−12.8005	−	7.39038i	−0.408481	−	0.235836i
$983$	−55.1188			−1.75802			−0.879008	−	0.476808i	$-0.841794\pi$
$983$	−55.1188			−1.75802			−0.879008	+	0.476808i	$0.841794\pi$
$984$	0.560445	+	1.02656i	0.0178663	+	0.0327255i
$985$	5.44373	+	3.14294i	0.173452	+	0.100142i
$986$		−	3.57049i		−	0.113708i
$987$	0.455947	−	0.248922i	0.0145130	−	0.00792329i
$988$	5.07230	+	8.78548i	0.161371	+	0.279503i
$989$	−3.52310			−0.112028
$990$	−31.4769	−	1.50407i	−1.00040	−	0.0478026i
$991$		−	35.3521i		−	1.12300i	−0.827478	−	0.561498i	$-0.810225\pi$
$991$		−	35.3521i		−	1.12300i	0.827478	−	0.561498i	$-0.189775\pi$
$992$	5.17387	−	8.96141i	0.164271	−	0.284525i
$993$	21.6674	+	39.6878i	0.687594	+	1.25945i
$994$			18.4962i			0.586662i
$995$	−49.0171			−1.55395
$996$	0.831318	−	0.453855i	0.0263413	−	0.0143809i
$997$			31.5146i			0.998078i	0.866579	+	0.499039i	$0.166314\pi$
$997$			31.5146i			0.998078i	−0.866579	+	0.499039i	$0.833686\pi$
$998$	17.6441			0.558515
$999$	6.32217	+	30.9682i	0.200025	+	0.979791i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	666.2.k.a.175.3	✓	76
3.2	odd	2		1998.2.k.a.1063.34		76
9.2	odd	6		1998.2.t.a.397.25		76
9.7	even	3		666.2.t.a.619.17	yes	76
37.11	even	6		666.2.t.a.85.17	yes	76
111.11	odd	6		1998.2.t.a.307.25		76
333.11	odd	6		1998.2.k.a.1639.5		76
333.196	even	6	inner	666.2.k.a.529.22	yes	76

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
666.2.k.a.175.3	✓	76	1.1	even	1	trivial
666.2.k.a.529.22	yes	76	333.196	even	6	inner
666.2.t.a.85.17	yes	76	37.11	even	6
666.2.t.a.619.17	yes	76	9.7	even	3
1998.2.k.a.1063.34		76	3.2	odd	2
1998.2.k.a.1639.5		76	333.11	odd	6
1998.2.t.a.307.25		76	111.11	odd	6
1998.2.t.a.397.25		76	9.2	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 666 = 2 \cdot 3^{2} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	666.k (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} +(-1.52025 + 0.829972i) q^{3} -1.00000 q^{4} +1.89632i q^{5} +(0.829972 + 1.52025i) q^{6} +(1.11313 - 1.92800i) q^{7} +1.00000i q^{8} +(1.62229 - 2.52352i) q^{9} +1.89632 q^{10} +(-2.76965 - 4.79717i) q^{11} +(1.52025 - 0.829972i) q^{12} +5.43478i q^{13} +(-1.92800 - 1.11313i) q^{14} +(-1.57389 - 2.88287i) q^{15} +1.00000 q^{16} +(3.62888 + 2.09514i) q^{17} +(-2.52352 - 1.62229i) q^{18} +(-1.61653 + 0.933303i) q^{19} -1.89632i q^{20} +(-0.0920473 + 3.85489i) q^{21} +(-4.79717 + 2.76965i) q^{22} +(3.25875 + 1.88144i) q^{23} +(-0.829972 - 1.52025i) q^{24} +1.40397 q^{25} +5.43478 q^{26} +(-0.371833 + 5.18283i) q^{27} +(-1.11313 + 1.92800i) q^{28} +(0.737932 - 0.426045i) q^{29} +(-2.88287 + 1.57389i) q^{30} +(8.96141 + 5.17387i) q^{31} -1.00000i q^{32} +(8.19207 + 4.99415i) q^{33} +(2.09514 - 3.62888i) q^{34} +(3.65610 + 2.11085i) q^{35} +(-1.62229 + 2.52352i) q^{36} +(5.85749 - 1.64006i) q^{37} +(0.933303 + 1.61653i) q^{38} +(-4.51071 - 8.26220i) q^{39} -1.89632 q^{40} -0.675259 q^{41} +(3.85489 + 0.0920473i) q^{42} +(-0.810841 + 0.468139i) q^{43} +(2.76965 + 4.79717i) q^{44} +(4.78540 + 3.07639i) q^{45} +(1.88144 - 3.25875i) q^{46} +(-0.0673590 - 0.116669i) q^{47} +(-1.52025 + 0.829972i) q^{48} +(1.02189 + 1.76996i) q^{49} -1.40397i q^{50} +(-7.25570 - 0.173252i) q^{51} -5.43478i q^{52} +(-3.86220 + 6.68953i) q^{53} +(5.18283 + 0.371833i) q^{54} +(9.09698 - 5.25214i) q^{55} +(1.92800 + 1.11313i) q^{56} +(1.68291 - 2.76052i) q^{57} +(-0.426045 - 0.737932i) q^{58} +(6.14162 - 3.54587i) q^{59} +(1.57389 + 2.88287i) q^{60} +(7.04003 + 4.06456i) q^{61} +(5.17387 - 8.96141i) q^{62} +(-3.05952 - 5.93678i) q^{63} -1.00000 q^{64} -10.3061 q^{65} +(4.99415 - 8.19207i) q^{66} -5.30839 q^{67} +(-3.62888 - 2.09514i) q^{68} +(-6.51563 - 0.155581i) q^{69} +(2.11085 - 3.65610i) q^{70} +(-4.15409 - 7.19510i) q^{71} +(2.52352 + 1.62229i) q^{72} +3.91572 q^{73} +(-1.64006 - 5.85749i) q^{74} +(-2.13438 + 1.16526i) q^{75} +(1.61653 - 0.933303i) q^{76} -12.3319 q^{77} +(-8.26220 + 4.51071i) q^{78} +(11.2792 + 6.51206i) q^{79} +1.89632i q^{80} +(-3.73633 - 8.18779i) q^{81} +0.675259i q^{82} +0.546832 q^{83} +(0.0920473 - 3.85489i) q^{84} +(-3.97305 + 6.88153i) q^{85} +(0.468139 + 0.810841i) q^{86} +(-0.768233 + 1.26016i) q^{87} +(4.79717 - 2.76965i) q^{88} +(-14.8691 - 8.58470i) q^{89} +(3.07639 - 4.78540i) q^{90} +(10.4782 + 6.04961i) q^{91} +(-3.25875 - 1.88144i) q^{92} +(-17.9177 - 0.427840i) q^{93} +(-0.116669 + 0.0673590i) q^{94} +(-1.76984 - 3.06545i) q^{95} +(0.829972 + 1.52025i) q^{96} +(-2.72439 + 1.57293i) q^{97} +(1.76996 - 1.02189i) q^{98} +(-16.5990 - 0.793153i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 76 q + 4 q^{3} - 76 q^{4} - 2 q^{7} - 4 q^{9} - 4 q^{11} - 4 q^{12} + 12 q^{15} + 76 q^{16} + 6 q^{21} + 12 q^{23} - 100 q^{25} - 24 q^{26} + 4 q^{27} + 2 q^{28} + 18 q^{29} - 12 q^{30} + 6 q^{31} - 32 q^{33}+ \cdots - 76 q^{99}+O(q^{100}) \) 76 * q + 4 * q^3 - 76 * q^4 - 2 * q^7 - 4 * q^9 - 4 * q^11 - 4 * q^12 + 12 * q^15 + 76 * q^16 + 6 * q^21 + 12 * q^23 - 100 * q^25 - 24 * q^26 + 4 * q^27 + 2 * q^28 + 18 * q^29 - 12 * q^30 + 6 * q^31 - 32 * q^33 - 18 * q^35 + 4 * q^36 + 10 * q^37 + 12 * q^38 + 24 * q^39 + 72 * q^41 + 6 * q^42 + 6 * q^43 + 4 * q^44 + 12 * q^45 - 20 * q^47 + 4 * q^48 - 36 * q^49 - 18 * q^51 + 14 * q^53 + 36 * q^54 + 42 * q^57 - 6 * q^59 - 12 * q^60 - 16 * q^62 + 46 * q^63 - 76 * q^64 + 32 * q^65 + 40 * q^67 + 6 * q^69 + 2 * q^71 + 28 * q^73 - 2 * q^74 - 78 * q^75 - 24 * q^77 - 2 * q^78 + 6 * q^79 - 28 * q^81 - 64 * q^83 - 6 * q^84 - 12 * q^85 + 4 * q^86 - 78 * q^87 + 60 * q^89 - 16 * q^90 + 42 * q^91 - 12 * q^92 + 6 * q^93 - 14 * q^95 - 12 * q^97 - 24 * q^98 - 76 * q^99

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