LMFDB - Embedded newform 220.2.l.c.67.10

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [220,2,Mod(23,220)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(220, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([2, 3, 0])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("220.23"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$N$	$=$	$220 = 2^{2} \cdot 5 \cdot 11$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	220.l (of order $4$ , degree $2$ , minimal)

Newform invariants

comment:select newform

sage:traces = [28,-2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$1.75670884447$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$14$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			67.10
Character	$\chi$	$=$	220.67
Dual form			220.2.l.c.23.10

$q$ -expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.682007 + 1.23890i) q^{2} +(-1.16674 - 1.16674i) q^{3} +(-1.06973 + 1.68987i) q^{4} +(-2.21837 + 0.280768i) q^{5} +(0.649749 - 2.24120i) q^{6} +(-2.18012 + 2.18012i) q^{7} +(-2.82314 - 0.172785i) q^{8} -0.277416i q^{9} +(-1.86079 - 2.55685i) q^{10} +1.00000i q^{11} +(3.21975 - 0.723544i) q^{12} +(-2.68686 + 2.68686i) q^{13} +(-4.18780 - 1.21409i) q^{14} +(2.91586 + 2.26069i) q^{15} +(-1.71134 - 3.61543i) q^{16} +(-1.20447 - 1.20447i) q^{17} +(0.343690 - 0.189200i) q^{18} -0.758569 q^{19} +(1.89860 - 4.04911i) q^{20} +5.08728 q^{21} +(-1.23890 + 0.682007i) q^{22} +(4.06235 + 4.06235i) q^{23} +(3.09229 + 3.49548i) q^{24} +(4.84234 - 1.24569i) q^{25} +(-5.16119 - 1.49628i) q^{26} +(-3.82391 + 3.82391i) q^{27} +(-1.35198 - 6.01627i) q^{28} -3.39836i q^{29} +(-0.812127 + 5.15425i) q^{30} +4.55404i q^{31} +(3.31200 - 4.58592i) q^{32} +(1.16674 - 1.16674i) q^{33} +(0.670756 - 2.31367i) q^{34} +(4.22420 - 5.44842i) q^{35} +(0.468798 + 0.296761i) q^{36} +(4.42483 + 4.42483i) q^{37} +(-0.517349 - 0.939789i) q^{38} +6.26975 q^{39} +(6.31129 - 0.409346i) q^{40} +1.63221 q^{41} +(3.46956 + 6.30262i) q^{42} +(-7.31254 - 7.31254i) q^{43} +(-1.68987 - 1.06973i) q^{44} +(0.0778894 + 0.615412i) q^{45} +(-2.26228 + 7.80338i) q^{46} +(1.24068 - 1.24068i) q^{47} +(-2.22158 + 6.21498i) q^{48} -2.50582i q^{49} +(4.84579 + 5.14959i) q^{50} +2.81061i q^{51} +(-1.66623 - 7.41466i) q^{52} +(-4.89076 + 4.89076i) q^{53} +(-7.34536 - 2.12950i) q^{54} +(-0.280768 - 2.21837i) q^{55} +(6.53148 - 5.77810i) q^{56} +(0.885055 + 0.885055i) q^{57} +(4.21022 - 2.31771i) q^{58} +8.66327 q^{59} +(-6.93946 + 2.50909i) q^{60} -13.4356 q^{61} +(-5.64198 + 3.10588i) q^{62} +(0.604800 + 0.604800i) q^{63} +(7.94029 + 0.975594i) q^{64} +(5.20606 - 6.71482i) q^{65} +(2.24120 + 0.649749i) q^{66} +(-10.3953 + 10.3953i) q^{67} +(3.32385 - 0.746938i) q^{68} -9.47944i q^{69} +(9.63096 + 1.51750i) q^{70} -0.631635i q^{71} +(-0.0479333 + 0.783186i) q^{72} +(-11.0396 + 11.0396i) q^{73} +(-2.46415 + 8.49968i) q^{74} +(-7.10318 - 4.19637i) q^{75} +(0.811466 - 1.28188i) q^{76} +(-2.18012 - 2.18012i) q^{77} +(4.27601 + 7.76757i) q^{78} +9.62897 q^{79} +(4.81148 + 7.53987i) q^{80} +8.09079 q^{81} +(1.11318 + 2.02214i) q^{82} +(-4.44087 - 4.44087i) q^{83} +(-5.44203 + 8.59685i) q^{84} +(3.01013 + 2.33378i) q^{85} +(4.07229 - 14.0467i) q^{86} +(-3.96502 + 3.96502i) q^{87} +(0.172785 - 2.82314i) q^{88} +6.02286i q^{89} +(-0.709311 + 0.516212i) q^{90} -11.7153i q^{91} +(-11.2105 + 2.51922i) q^{92} +(5.31340 - 5.31340i) q^{93} +(2.38323 + 0.690925i) q^{94} +(1.68279 - 0.212981i) q^{95} +(-9.21485 + 1.48634i) q^{96} +(-1.24914 - 1.24914i) q^{97} +(3.10446 - 1.70899i) q^{98} +0.277416 q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$28 q - 2 q^{2} - 4 q^{3} + 4 q^{4} + 2 q^{5} - 12 q^{6} - 2 q^{7} - 14 q^{8} + 6 q^{10} - 8 q^{12} + 6 q^{13} - 20 q^{14} + 8 q^{15} + 8 q^{16} - 14 q^{17} + 34 q^{18} + 4 q^{19} + 8 q^{20} - 16 q^{21}+ \cdots - 20 q^{99}+O(q^{100})$ 28 * q - 2 * q^2 - 4 * q^3 + 4 * q^4 + 2 * q^5 - 12 * q^6 - 2 * q^7 - 14 * q^8 + 6 * q^10 - 8 * q^12 + 6 * q^13 - 20 * q^14 + 8 * q^15 + 8 * q^16 - 14 * q^17 + 34 * q^18 + 4 * q^19 + 8 * q^20 - 16 * q^21 - 2 * q^22 - 8 * q^23 + 28 * q^24 - 4 * q^25 + 4 * q^26 + 44 * q^27 - 28 * q^28 - 2 * q^32 + 4 * q^33 - 52 * q^34 - 10 * q^35 - 4 * q^36 + 20 * q^37 + 16 * q^38 + 32 * q^39 - 6 * q^40 + 12 * q^41 - 32 * q^42 + 2 * q^43 - 10 * q^45 + 4 * q^46 - 44 * q^47 - 36 * q^48 + 22 * q^50 + 24 * q^52 - 28 * q^53 - 40 * q^54 - 2 * q^55 + 4 * q^56 - 8 * q^57 + 28 * q^58 - 16 * q^59 - 48 * q^60 - 12 * q^61 - 24 * q^62 - 10 * q^63 + 28 * q^64 - 30 * q^65 + 16 * q^67 - 32 * q^68 + 72 * q^70 + 18 * q^72 + 22 * q^73 - 20 * q^74 - 56 * q^75 + 4 * q^76 - 2 * q^77 + 104 * q^78 - 20 * q^79 - 44 * q^80 + 12 * q^81 - 92 * q^82 + 2 * q^83 + 120 * q^84 - 14 * q^85 - 20 * q^86 - 48 * q^87 + 2 * q^88 + 70 * q^90 + 52 * q^92 - 20 * q^93 - 20 * q^94 + 92 * q^95 + 40 * q^96 + 16 * q^97 + 18 * q^98 - 20 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/220\mathbb{Z}\right)^\times$ .

$n$	$101$	$111$	$177$
$\chi(n)$	$1$	$-1$	$e\left(\frac{1}{4}\right)$

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

)

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

$2$	0.682007	+	1.23890i	0.482252	+	0.876033i
$2$	0.682007	+	1.23890i	0.482252	+	0.876033i
$3$	−1.16674	−	1.16674i	−0.673620	−	0.673620i	0.284929	−	0.958549i	$-0.408030\pi$
$3$	−1.16674	−	1.16674i	−0.673620	−	0.673620i	−0.958549	+	0.284929i	$0.908030\pi$
$4$	−1.06973	+	1.68987i	−0.534867	+	0.844936i
$5$	−2.21837	+	0.280768i	−0.992086	+	0.125563i
$5$	−2.21837	+	0.280768i	−0.992086	+	0.125563i
$6$	0.649749	−	2.24120i	0.265259	−	0.914968i
$7$	−2.18012	+	2.18012i	−0.824007	+	0.824007i	−0.986680	−	0.162673i	$-0.947988\pi$
$7$	−2.18012	+	2.18012i	−0.824007	+	0.824007i	0.162673	+	0.986680i	$0.447988\pi$
$8$	−2.82314	−	0.172785i	−0.998132	−	0.0610887i
$9$		−	0.277416i		−	0.0924720i
$10$	−1.86079	−	2.55685i	−0.588432	−	0.808547i
$11$			1.00000i			0.301511i
$11$			1.00000i			0.301511i
$12$	3.21975	−	0.723544i	0.929463	−	0.208869i
$13$	−2.68686	+	2.68686i	−0.745200	+	0.745200i	−0.973574	−	0.228374i	$-0.926659\pi$
$13$	−2.68686	+	2.68686i	−0.745200	+	0.745200i	0.228374	+	0.973574i	$0.426659\pi$
$14$	−4.18780	−	1.21409i	−1.11924	−	0.324478i
$15$	2.91586	+	2.26069i	0.752871	+	0.583707i
$16$	−1.71134	−	3.61543i	−0.427835	−	0.903857i
$17$	−1.20447	−	1.20447i	−0.292126	−	0.292126i	0.545794	−	0.837920i	$-0.316228\pi$
$17$	−1.20447	−	1.20447i	−0.292126	−	0.292126i	−0.837920	+	0.545794i	$0.816228\pi$
$18$	0.343690	−	0.189200i	0.0810085	−	0.0445948i
$19$	−0.758569			−0.174028			−0.0870138	−	0.996207i	$-0.527732\pi$
$19$	−0.758569			−0.174028			−0.0870138	+	0.996207i	$0.527732\pi$
$20$	1.89860	−	4.04911i	0.424541	−	0.905409i
$21$	5.08728			1.11014
$22$	−1.23890	+	0.682007i	−0.264134	+	0.145404i
$23$	4.06235	+	4.06235i	0.847058	+	0.847058i	0.989765	−	0.142707i	$-0.0455807\pi$
$23$	4.06235	+	4.06235i	0.847058	+	0.847058i	−0.142707	+	0.989765i	$0.545581\pi$
$24$	3.09229	+	3.49548i	0.631211	+	0.713513i
$25$	4.84234	−	1.24569i	0.968468	−	0.249139i
$26$	−5.16119	−	1.49628i	−1.01219	−	0.293446i
$27$	−3.82391	+	3.82391i	−0.735911	+	0.735911i
$28$	−1.35198	−	6.01627i	−0.255500	−	1.13697i
$29$		−	3.39836i		−	0.631060i	−0.948916	−	0.315530i	$-0.897818\pi$
$29$		−	3.39836i		−	0.631060i	0.948916	−	0.315530i	$-0.102182\pi$
$30$	−0.812127	+	5.15425i	−0.148273	+	0.941033i
$31$			4.55404i			0.817929i	0.912550	+	0.408965i	$0.134110\pi$
$31$			4.55404i			0.817929i	−0.912550	+	0.408965i	$0.865890\pi$
$32$	3.31200	−	4.58592i	0.585484	−	0.810684i
$33$	1.16674	−	1.16674i	0.203104	−	0.203104i
$34$	0.670756	−	2.31367i	0.115034	−	0.396790i
$35$	4.22420	−	5.44842i	0.714021	−	0.920950i
$36$	0.468798	+	0.296761i	0.0781330	+	0.0494602i
$37$	4.42483	+	4.42483i	0.727438	+	0.727438i	0.970109	−	0.242671i	$-0.0780235\pi$
$37$	4.42483	+	4.42483i	0.727438	+	0.727438i	−0.242671	+	0.970109i	$0.578024\pi$
$38$	−0.517349	−	0.939789i	−0.0839251	−	0.152454i
$39$	6.26975			1.00396
$40$	6.31129	−	0.409346i	0.997903	−	0.0647233i
$41$	1.63221			0.254908			0.127454	−	0.991844i	$-0.459319\pi$
$41$	1.63221			0.254908			0.127454	+	0.991844i	$0.459319\pi$
$42$	3.46956	+	6.30262i	0.535365	+	0.972515i
$43$	−7.31254	−	7.31254i	−1.11515	−	1.11515i	−0.992443	−	0.122710i	$-0.960842\pi$
$43$	−7.31254	−	7.31254i	−1.11515	−	1.11515i	−0.122710	−	0.992443i	$-0.539158\pi$
$44$	−1.68987	−	1.06973i	−0.254758	−	0.161268i
$45$	0.0778894	+	0.615412i	0.0116111	+	0.0917402i
$46$	−2.26228	+	7.80338i	−0.333555	+	1.15055i
$47$	1.24068	−	1.24068i	0.180972	−	0.180972i	−0.610807	−	0.791779i	$-0.709155\pi$
$47$	1.24068	−	1.24068i	0.180972	−	0.180972i	0.791779	+	0.610807i	$0.209155\pi$
$48$	−2.22158	+	6.21498i	−0.320658	+	0.897054i
$49$		−	2.50582i		−	0.357975i
$50$	4.84579	+	5.14959i	0.685299	+	0.728262i
$51$			2.81061i			0.393564i
$52$	−1.66623	−	7.41466i	−0.231064	−	1.02823i
$53$	−4.89076	+	4.89076i	−0.671798	+	0.671798i	−0.958130	−	0.286332i	$-0.907564\pi$
$53$	−4.89076	+	4.89076i	−0.671798	+	0.671798i	0.286332	+	0.958130i	$0.407564\pi$
$54$	−7.34536	−	2.12950i	−0.999577	−	0.289788i
$55$	−0.280768	−	2.21837i	−0.0378587	−	0.299125i
$56$	6.53148	−	5.77810i	0.872806	−	0.772130i
$57$	0.885055	+	0.885055i	0.117228	+	0.117228i
$58$	4.21022	−	2.31771i	0.552830	−	0.304330i
$59$	8.66327			1.12786			0.563931	−	0.825822i	$-0.309288\pi$
$59$	8.66327			1.12786			0.563931	+	0.825822i	$0.309288\pi$
$60$	−6.93946	+	2.50909i	−0.895881	+	0.323922i
$61$	−13.4356			−1.72026			−0.860129	−	0.510076i	$-0.829617\pi$
$61$	−13.4356			−1.72026			−0.860129	+	0.510076i	$0.829617\pi$
$62$	−5.64198	+	3.10588i	−0.716533	+	0.394448i
$63$	0.604800	+	0.604800i	0.0761976	+	0.0761976i
$64$	7.94029	+	0.975594i	0.992536	+	0.121949i
$65$	5.20606	−	6.71482i	0.645732	−	0.832871i
$66$	2.24120	+	0.649749i	0.275873	+	0.0799785i
$67$	−10.3953	+	10.3953i	−1.26998	+	1.26998i	−0.323886	+	0.946096i	$0.604990\pi$
$67$	−10.3953	+	10.3953i	−1.26998	+	1.26998i	−0.946096	+	0.323886i	$0.895010\pi$
$68$	3.32385	−	0.746938i	0.403077	−	0.0905795i
$69$		−	9.47944i		−	1.14119i
$70$	9.63096	+	1.51750i	1.15112	+	0.181376i
$71$		−	0.631635i		−	0.0749612i	−0.999297	−	0.0374806i	$-0.988067\pi$
$71$		−	0.631635i		−	0.0749612i	0.999297	−	0.0374806i	$-0.0119332\pi$
$72$	−0.0479333	+	0.783186i	−0.00564900	+	0.0922993i
$73$	−11.0396	+	11.0396i	−1.29209	+	1.29209i	−0.358592	+	0.933494i	$0.616743\pi$
$73$	−11.0396	+	11.0396i	−1.29209	+	1.29209i	−0.933494	+	0.358592i	$0.883257\pi$
$74$	−2.46415	+	8.49968i	−0.286451	+	0.988067i
$75$	−7.10318	−	4.19637i	−0.820204	−	0.484555i
$76$	0.811466	−	1.28188i	0.0930815	−	0.147042i
$77$	−2.18012	−	2.18012i	−0.248447	−	0.248447i
$78$	4.27601	+	7.76757i	0.484163	+	0.879504i
$79$	9.62897			1.08334			0.541672	−	0.840590i	$-0.317791\pi$
$79$	9.62897			1.08334			0.541672	+	0.840590i	$0.317791\pi$
$80$	4.81148	+	7.53987i	0.537940	+	0.842983i
$81$	8.09079			0.898977
$82$	1.11318	+	2.02214i	0.122930	+	0.223308i
$83$	−4.44087	−	4.44087i	−0.487449	−	0.487449i	0.420051	−	0.907500i	$-0.362012\pi$
$83$	−4.44087	−	4.44087i	−0.487449	−	0.487449i	−0.907500	+	0.420051i	$0.862012\pi$
$84$	−5.44203	+	8.59685i	−0.593774	+	0.937994i
$85$	3.01013	+	2.33378i	0.326494	+	0.253134i
$86$	4.07229	−	14.0467i	0.439126	−	1.51469i
$87$	−3.96502	+	3.96502i	−0.425095	+	0.425095i
$88$	0.172785	−	2.82314i	0.0184189	−	0.300948i
$89$			6.02286i			0.638422i	0.947684	+	0.319211i	$0.103418\pi$
$89$			6.02286i			0.638422i	−0.947684	+	0.319211i	$0.896582\pi$
$90$	−0.709311	+	0.516212i	−0.0747679	+	0.0544135i
$91$		−	11.7153i		−	1.22810i
$92$	−11.2105	+	2.51922i	−1.16877	+	0.262647i
$93$	5.31340	−	5.31340i	0.550973	−	0.550973i
$94$	2.38323	+	0.690925i	0.245812	+	0.0712634i
$95$	1.68279	−	0.212981i	0.172650	−	0.0218514i
$96$	−9.21485	+	1.48634i	−0.940487	+	0.151699i
$97$	−1.24914	−	1.24914i	−0.126831	−	0.126831i	0.640842	−	0.767673i	$-0.278585\pi$
$97$	−1.24914	−	1.24914i	−0.126831	−	0.126831i	−0.767673	+	0.640842i	$0.778585\pi$
$98$	3.10446	−	1.70899i	0.313598	−	0.172634i
$99$	0.277416			0.0278814
$100$	−3.07495	+	9.51550i	−0.307495	+	0.951550i
$101$	−9.45271			−0.940580			−0.470290	−	0.882512i	$-0.655851\pi$
$101$	−9.45271			−0.940580			−0.470290	+	0.882512i	$0.655851\pi$
$102$	−3.48206	+	1.91685i	−0.344775	+	0.189797i
$103$	−10.0850	−	10.0850i	−0.993705	−	0.993705i	0.00627506	−	0.999980i	$-0.498003\pi$
$103$	−10.0850	−	10.0850i	−0.993705	−	0.993705i	−0.999980	+	0.00627506i	$0.998003\pi$
$104$	8.04963	−	7.12113i	0.789331	−	0.698285i
$105$	−11.2855	+	1.42834i	−1.10135	+	0.139392i
$106$	−9.39469	−	2.72362i	−0.912493	−	0.264541i
$107$	13.6633	−	13.6633i	1.32088	−	1.32088i	0.407822	−	0.913061i	$-0.366288\pi$
$107$	13.6633	−	13.6633i	1.32088	−	1.32088i	0.913061	−	0.407822i	$-0.133712\pi$
$108$	−2.37136	−	10.5525i	−0.228184	−	1.01541i
$109$		−	6.38160i		−	0.611247i	−0.952153	−	0.305623i	$-0.901135\pi$
$109$		−	6.38160i		−	0.611247i	0.952153	−	0.305623i	$-0.0988648\pi$
$110$	2.55685	−	1.86079i	0.243786	−	0.177419i
$111$		−	10.3253i		−	0.980033i
$112$	11.6130	+	4.15113i	1.09732	+	0.392245i
$113$	13.6087	−	13.6087i	1.28019	−	1.28019i	0.339639	−	0.940556i	$-0.389695\pi$
$113$	13.6087	−	13.6087i	1.28019	−	1.28019i	0.940556	−	0.339639i	$-0.110305\pi$
$114$	−0.492879	+	1.70011i	−0.0461623	+	0.159230i
$115$	−10.1524	−	7.87122i	−0.946713	−	0.733995i
$116$	5.74280	+	3.63534i	0.533206	+	0.337533i
$117$	0.745377	+	0.745377i	0.0689101	+	0.0689101i
$118$	5.90841	+	10.7329i	0.543913	+	0.988044i
$119$	5.25176			0.481428
$120$	−7.84127	−	6.88606i	−0.715807	−	0.628609i
$121$	−1.00000			−0.0909091
$122$	−9.16320	−	16.6454i	−0.829597	−	1.50700i
$123$	−1.90437	−	1.90437i	−0.171711	−	0.171711i
$124$	−7.69574	−	4.87160i	−0.691098	−	0.437483i
$125$	−10.3924	+	4.12298i	−0.929520	+	0.368771i
$126$	−0.336807	+	1.16176i	−0.0300052	+	0.103498i
$127$	−8.01735	+	8.01735i	−0.711425	+	0.711425i	−0.966833	−	0.255408i	$-0.917790\pi$
$127$	−8.01735	+	8.01735i	−0.711425	+	0.711425i	0.255408	+	0.966833i	$0.417790\pi$
$128$	4.20667	+	10.5026i	0.371821	+	0.928305i
$129$			17.0637i			1.50238i
$130$	11.8695	+	1.87022i	1.04103	+	0.164029i
$131$			4.26635i			0.372752i	0.982478	+	0.186376i	$0.0596743\pi$
$131$			4.26635i			0.372752i	−0.982478	+	0.186376i	$0.940326\pi$
$132$	0.723544	+	3.21975i	0.0629764	+	0.280244i
$133$	1.65377	−	1.65377i	0.143400	−	0.143400i
$134$	−19.9683	−	5.78902i	−1.72500	−	0.500095i
$135$	7.40921	−	9.55647i	0.637684	−	0.822490i
$136$	3.19227	+	3.60850i	0.273735	+	0.309426i
$137$	8.22999	+	8.22999i	0.703136	+	0.703136i	0.965082	−	0.261947i	$-0.0843645\pi$
$137$	8.22999	+	8.22999i	0.703136	+	0.703136i	−0.261947	+	0.965082i	$0.584364\pi$
$138$	11.7441	−	6.46504i	0.999720	−	0.550341i
$139$	−1.78815			−0.151669			−0.0758343	−	0.997120i	$-0.524162\pi$
$139$	−1.78815			−0.151669			−0.0758343	+	0.997120i	$0.524162\pi$
$140$	4.68836	+	12.9667i	0.396239	+	1.09589i
$141$	−2.89512			−0.243813
$142$	0.782530	−	0.430779i	0.0656685	−	0.0361502i
$143$	−2.68686	−	2.68686i	−0.224686	−	0.224686i
$144$	−1.00298	+	0.474754i	−0.0835815	+	0.0395628i
$145$	0.954150	+	7.53883i	0.0792379	+	0.626066i
$146$	−21.2060	−	6.14784i	−1.75502	−	0.508799i
$147$	−2.92366	+	2.92366i	−0.241139	+	0.241139i
$148$	−12.2108	+	2.74401i	−1.00372	+	0.225556i
$149$			8.80481i			0.721318i	0.932698	+	0.360659i	$0.117448\pi$
$149$			8.80481i			0.721318i	−0.932698	+	0.360659i	$0.882552\pi$
$150$	0.354452	−	11.6621i	0.0289409	−	0.952203i
$151$			15.7849i			1.28456i	0.766472	+	0.642278i	$0.222010\pi$
$151$			15.7849i			1.28456i	−0.766472	+	0.642278i	$0.777990\pi$
$152$	2.14155	+	0.131069i	0.173703	+	0.0106311i
$153$	−0.334139	+	0.334139i	−0.0270135	+	0.0270135i
$154$	1.21409	−	4.18780i	0.0978339	−	0.337462i
$155$	−1.27863	−	10.1025i	−0.102702	−	0.811456i
$156$	−6.70696	+	10.5951i	−0.536986	+	0.848285i
$157$	12.7905	+	12.7905i	1.02079	+	1.02079i	0.999779	+	0.0210155i	$0.00668994\pi$
$157$	12.7905	+	12.7905i	1.02079	+	1.02079i	0.0210155	+	0.999779i	$0.493310\pi$
$158$	6.56703	+	11.9293i	0.522444	+	0.949045i
$159$	11.4125			0.905073
$160$	−6.05966	+	11.1032i	−0.479058	+	0.877783i
$161$	−17.7128			−1.39596
$162$	5.51798	+	10.0237i	0.433533	+	0.787533i
$163$	7.94254	+	7.94254i	0.622108	+	0.622108i	0.946070	−	0.323962i	$-0.105015\pi$
$163$	7.94254	+	7.94254i	0.622108	+	0.622108i	−0.323962	+	0.946070i	$0.605015\pi$
$164$	−1.74603	+	2.75822i	−0.136342	+	0.215381i
$165$	−2.26069	+	2.91586i	−0.175994	+	0.226999i
$166$	2.47308	−	8.53049i	0.191948	−	0.662094i
$167$	−0.855298	+	0.855298i	−0.0661849	+	0.0661849i	−0.739424	−	0.673240i	$-0.764902\pi$
$167$	−0.855298	+	0.855298i	−0.0661849	+	0.0661849i	0.673240	+	0.739424i	$0.264902\pi$
$168$	−14.3621	−	0.879005i	−1.10806	−	0.0678167i
$169$		−	1.43838i		−	0.110645i
$170$	−0.838384	+	5.32089i	−0.0643011	+	0.408094i
$171$			0.210439i			0.0160927i
$172$	20.1797	−	4.53480i	1.53869	−	0.345775i
$173$	11.9611	−	11.9611i	0.909383	−	0.909383i	−0.0868397	−	0.996222i	$-0.527677\pi$
$173$	11.9611	−	11.9611i	0.909383	−	0.909383i	0.996222	+	0.0868397i	$0.0276768\pi$
$174$	−7.61643	−	2.20808i	−0.577400	−	0.167394i
$175$	−7.84111	+	13.2726i	−0.592732	+	1.00332i
$176$	3.61543	−	1.71134i	0.272523	−	0.128997i
$177$	−10.1078	−	10.1078i	−0.759751	−	0.759751i
$178$	−7.46170	+	4.10763i	−0.559278	+	0.307880i
$179$	−24.8533			−1.85762			−0.928811	−	0.370553i	$-0.879168\pi$
$179$	−24.8533			−1.85762			−0.928811	+	0.370553i	$0.879168\pi$
$180$	−1.12329	−	0.526703i	−0.0837250	−	0.0392581i
$181$	22.4425			1.66813			0.834067	−	0.551663i	$-0.186006\pi$
$181$	22.4425			1.66813			0.834067	+	0.551663i	$0.186006\pi$
$182$	14.5141	−	7.98993i	1.07586	−	0.592253i
$183$	15.6760	+	15.6760i	1.15880	+	1.15880i
$184$	−10.7667	−	12.1705i	−0.793730	−	0.897221i
$185$	−11.0583	−	8.57357i	−0.813020	−	0.630341i
$186$	10.2065	+	2.95898i	0.748379	+	0.216963i
$187$	1.20447	−	1.20447i	0.0880793	−	0.0880793i
$188$	0.769397	+	3.42380i	0.0561140	+	0.249706i
$189$		−	16.6731i		−	1.21279i
$190$	1.41153	+	1.93954i	0.102403	+	0.140709i
$191$			2.73389i			0.197817i	0.995097	+	0.0989085i	$0.0315351\pi$
$191$			2.73389i			0.197817i	−0.995097	+	0.0989085i	$0.968465\pi$
$192$	−8.12602	−	10.4026i	−0.586445	−	0.750740i
$193$	3.26747	−	3.26747i	0.235197	−	0.235197i	−0.579661	−	0.814858i	$-0.696815\pi$
$193$	3.26747	−	3.26747i	0.235197	−	0.235197i	0.814858	+	0.579661i	$0.196815\pi$
$194$	0.695634	−	2.39948i	0.0499436	−	0.172272i
$195$	−13.9086	+	1.76034i	−0.996017	+	0.126061i
$196$	4.23453	+	2.68056i	0.302466	+	0.191469i
$197$	3.70741	+	3.70741i	0.264142	+	0.264142i	0.826734	−	0.562592i	$-0.190196\pi$
$197$	3.70741	+	3.70741i	0.264142	+	0.264142i	−0.562592	+	0.826734i	$0.690196\pi$
$198$	0.189200	+	0.343690i	0.0134458	+	0.0244250i
$199$	1.52889			0.108380			0.0541902	−	0.998531i	$-0.482742\pi$
$199$	1.52889			0.108380			0.0541902	+	0.998531i	$0.482742\pi$
$200$	−13.8859	+	2.68009i	−0.981879	+	0.189511i
$201$	24.2572			1.71097
$202$	−6.44681	−	11.7109i	−0.453596	−	0.823979i
$203$	7.40883	+	7.40883i	0.519998	+	0.519998i
$204$	−4.74957	−	3.00660i	−0.332537	−	0.210504i
$205$	−3.62084	+	0.458271i	−0.252891	+	0.0320070i
$206$	5.61624	−	19.3723i	0.391302	−	1.34973i
$207$	1.12696	−	1.12696i	0.0783292	−	0.0783292i
$208$	14.3123	+	5.11600i	0.992376	+	0.354731i
$209$		−	0.758569i		−	0.0524713i
$210$	−9.46634	−	13.0074i	−0.653239	−	0.897596i
$211$			28.2258i			1.94314i	0.236745	+	0.971572i	$0.423920\pi$
$211$			28.2258i			1.94314i	−0.236745	+	0.971572i	$0.576080\pi$
$212$	−3.03296	−	13.4966i	−0.208304	−	0.926949i
$213$	−0.736956	+	0.736956i	−0.0504954	+	0.0504954i
$214$	26.2459	+	7.60898i	1.79414	+	0.520139i
$215$	18.2751	+	14.1688i	1.24635	+	0.966305i
$216$	11.4562	−	10.1347i	0.779493	−	0.689581i
$217$	−9.92833	−	9.92833i	−0.673979	−	0.673979i
$218$	7.90615	−	4.35230i	0.535472	−	0.294775i
$219$	25.7608			1.74075
$220$	4.04911	+	1.89860i	0.272991	+	0.128004i
$221$	6.47246			0.435385
$222$	12.7920	−	7.04192i	0.858541	−	0.472623i
$223$	1.73371	+	1.73371i	0.116098	+	0.116098i	0.762769	−	0.646671i	$-0.223839\pi$
$223$	1.73371	+	1.73371i	0.116098	+	0.116098i	−0.646671	+	0.762769i	$0.723839\pi$
$224$	2.77731	+	17.2184i	0.185567	+	1.15045i
$225$	−0.345575	−	1.34334i	−0.0230384	−	0.0895562i
$226$	26.1409	+	7.57853i	1.73887	+	0.504116i
$227$	8.21233	−	8.21233i	0.545071	−	0.545071i	−0.379940	−	0.925011i	$-0.624055\pi$
$227$	8.21233	−	8.21233i	0.545071	−	0.545071i	0.925011	+	0.379940i	$0.124055\pi$
$228$	−2.44240	+	0.548858i	−0.161752	+	0.0363490i
$229$		−	12.2356i		−	0.808553i	−0.914637	−	0.404277i	$-0.867523\pi$
$229$		−	12.2356i		−	0.808553i	0.914637	−	0.404277i	$-0.132477\pi$
$230$	2.82765	−	17.9460i	0.186449	−	1.18332i
$231$			5.08728i			0.334718i
$232$	−0.587186	+	9.59407i	−0.0385507	+	0.629882i
$233$	−2.72493	+	2.72493i	−0.178516	+	0.178516i	−0.790709	−	0.612193i	$-0.790288\pi$
$233$	−2.72493	+	2.72493i	−0.178516	+	0.178516i	0.612193	+	0.790709i	$0.290288\pi$
$234$	−0.415093	+	1.43180i	−0.0271355	+	0.0935996i
$235$	−2.40395	+	3.10064i	−0.156817	+	0.202263i
$236$	−9.26739	+	14.6398i	−0.603256	+	0.952972i
$237$	−11.2345	−	11.2345i	−0.729762	−	0.729762i
$238$	3.58174	+	6.50639i	0.232169	+	0.421747i
$239$	2.84365			0.183940			0.0919701	−	0.995762i	$-0.470684\pi$
$239$	2.84365			0.183940			0.0919701	+	0.995762i	$0.470684\pi$
$240$	3.18333	−	14.4109i	0.205483	−	0.930218i
$241$	−4.90638			−0.316048			−0.158024	−	0.987435i	$-0.550512\pi$
$241$	−4.90638			−0.316048			−0.158024	+	0.987435i	$0.550512\pi$
$242$	−0.682007	−	1.23890i	−0.0438411	−	0.0796393i
$243$	2.03183	+	2.03183i	0.130342	+	0.130342i
$244$	14.3726	−	22.7045i	0.920109	−	1.45351i
$245$	0.703554	+	5.55885i	0.0449484	+	0.355142i
$246$	1.06053	−	3.65811i	0.0676166	−	0.233233i
$247$	2.03816	−	2.03816i	0.129685	−	0.129685i
$248$	0.786869	−	12.8567i	0.0499662	−	0.816401i
$249$			10.3627i			0.656711i
$250$	−12.1956	−	10.0632i	−0.771318	−	0.636450i
$251$			7.67142i			0.484216i	0.970249	+	0.242108i	$0.0778388\pi$
$251$			7.67142i			0.484216i	−0.970249	+	0.242108i	$0.922161\pi$
$252$	−1.66901	+	0.375060i	−0.105138	+	0.0236266i
$253$	−4.06235	+	4.06235i	−0.255398	+	0.255398i
$254$	−15.4006	−	4.46479i	−0.966318	−	0.280146i
$255$	−0.789128	−	6.23497i	−0.0494171	−	0.390449i
$256$	−10.1426	+	12.3745i	−0.633914	+	0.773404i
$257$	−11.3263	−	11.3263i	−0.706513	−	0.706513i	0.259287	−	0.965800i	$-0.416512\pi$
$257$	−11.3263	−	11.3263i	−0.706513	−	0.706513i	−0.965800	+	0.259287i	$0.916512\pi$
$258$	−21.1402	+	11.6376i	−1.31613	+	0.724524i
$259$	−19.2933			−1.19883
$260$	5.77810	+	15.9807i	0.358343	+	0.991078i
$261$	−0.942761			−0.0583554
$262$	−5.28556	+	2.90968i	−0.326543	+	0.179760i
$263$	−9.79931	−	9.79931i	−0.604251	−	0.604251i	0.337186	−	0.941438i	$-0.390525\pi$
$263$	−9.79931	−	9.79931i	−0.604251	−	0.604251i	−0.941438	+	0.337186i	$0.890525\pi$
$264$	−3.49548	+	3.09229i	−0.215132	+	0.190317i
$265$	9.47636	−	12.2227i	0.582128	−	0.750834i
$266$	3.17673	+	0.920968i	0.194778	+	0.0564682i
$267$	7.02714	−	7.02714i	0.430054	−	0.430054i
$268$	−6.44651	−	28.6868i	−0.393783	−	1.75233i
$269$			15.2457i			0.929548i	0.885429	+	0.464774i	$0.153864\pi$
$269$			15.2457i			0.929548i	−0.885429	+	0.464774i	$0.846136\pi$
$270$	16.8926	+	2.66168i	1.02805	+	0.161984i
$271$		−	6.70035i		−	0.407017i	−0.979073	−	0.203509i	$-0.934765\pi$
$271$		−	6.70035i		−	0.407017i	0.979073	−	0.203509i	$-0.0652345\pi$
$272$	−2.29341	+	6.41592i	−0.139058	+	0.389022i
$273$	−13.6688	+	13.6688i	−0.827272	+	0.827272i
$274$	−4.58320	+	15.8090i	−0.276881	+	0.955058i
$275$	1.24569	+	4.84234i	0.0751181	+	0.292004i
$276$	16.0190	+	10.1405i	0.964233	+	0.610385i
$277$	17.4946	+	17.4946i	1.05115	+	1.05115i	0.998620	+	0.0525262i	$0.0167273\pi$
$277$	17.4946	+	17.4946i	1.05115	+	1.05115i	0.0525262	+	0.998620i	$0.483273\pi$
$278$	−1.21953	−	2.21533i	−0.0731424	−	0.132867i
$279$	1.26336			0.0756356
$280$	−12.8669	+	14.6518i	−0.768947	+	0.875612i
$281$	−0.980883			−0.0585146			−0.0292573	−	0.999572i	$-0.509314\pi$
$281$	−0.980883			−0.0585146			−0.0292573	+	0.999572i	$0.509314\pi$
$282$	−1.97449	−	3.58676i	−0.117579	−	0.213588i
$283$	−6.47709	−	6.47709i	−0.385023	−	0.385023i	0.487885	−	0.872908i	$-0.337769\pi$
$283$	−6.47709	−	6.47709i	−0.385023	−	0.385023i	−0.872908	+	0.487885i	$0.837769\pi$
$284$	1.06738	+	0.675681i	0.0633375	+	0.0400943i
$285$	−2.21188	−	1.71489i	−0.131020	−	0.101581i
$286$	1.49628	−	5.16119i	0.0884772	−	0.305188i
$287$	−3.55840	+	3.55840i	−0.210046	+	0.210046i
$288$	−1.27221	−	0.918801i	−0.0749656	−	0.0541409i
$289$		−	14.0985i		−	0.829325i
$290$	−8.68910	+	6.32363i	−0.510242	+	0.371336i
$291$			2.91485i			0.170872i
$292$	−6.84609	−	30.4649i	−0.400637	−	1.78283i
$293$	−2.23641	+	2.23641i	−0.130652	+	0.130652i	−0.769409	−	0.638757i	$-0.779449\pi$
$293$	−2.23641	+	2.23641i	−0.130652	+	0.130652i	0.638757	+	0.769409i	$0.279449\pi$
$294$	−5.61606	−	1.62816i	−0.327536	−	0.0949560i
$295$	−19.2184	+	2.43237i	−1.11894	+	0.141618i
$296$	−11.7274	−	13.2565i	−0.681641	−	0.770517i
$297$	−3.82391	−	3.82391i	−0.221886	−	0.221886i
$298$	−10.9083	+	6.00494i	−0.631898	+	0.347857i
$299$	−21.8299			−1.26245
$300$	14.6898	−	7.51447i	0.848118	−	0.433848i
$301$	31.8844			1.83779
$302$	−19.5558	+	10.7654i	−1.12531	+	0.619479i
$303$	11.0289	+	11.0289i	0.633594	+	0.633594i
$304$	1.29817	+	2.74255i	0.0744551	+	0.157296i
$305$	29.8052	−	3.77229i	1.70664	−	0.216001i
$306$	−0.641848	−	0.186079i	−0.0366920	−	0.0106374i
$307$	18.5631	−	18.5631i	1.05945	−	1.05945i	0.0613318	−	0.998117i	$-0.480465\pi$
$307$	18.5631	−	18.5631i	1.05945	−	1.05945i	0.998117	−	0.0613318i	$-0.0195348\pi$
$308$	6.01627	−	1.35198i	0.342809	−	0.0770360i
$309$			23.5332i			1.33876i
$310$	11.6440	−	8.47409i	0.661334	−	0.481296i
$311$			25.1455i			1.42587i	0.701230	+	0.712935i	$0.252635\pi$
$311$			25.1455i			1.42587i	−0.701230	+	0.712935i	$0.747365\pi$
$312$	−17.7004	−	1.08332i	−1.00209	−	0.0613308i
$313$	1.22613	−	1.22613i	0.0693049	−	0.0693049i	−0.671605	−	0.740910i	$-0.734395\pi$
$313$	1.22613	−	1.22613i	0.0693049	−	0.0693049i	0.740910	+	0.671605i	$0.234395\pi$
$314$	−7.12292	+	24.5694i	−0.401970	+	1.38653i
$315$	−1.51148	−	1.17186i	−0.0851622	−	0.0660269i
$316$	−10.3004	+	16.2717i	−0.579445	+	0.915357i
$317$	−4.66060	−	4.66060i	−0.261766	−	0.261766i	0.564005	−	0.825771i	$-0.309260\pi$
$317$	−4.66060	−	4.66060i	−0.261766	−	0.261766i	−0.825771	+	0.564005i	$0.809260\pi$
$318$	7.78343	+	14.1390i	0.436473	+	0.792874i
$319$	3.39836			0.190272
$320$	−17.8884	+	0.0651461i	−0.999993	+	0.00364178i
$321$	−31.8832			−1.77955
$322$	−12.0802	−	21.9443i	−0.673206	−	1.22291i
$323$	0.913671	+	0.913671i	0.0508380	+	0.0508380i
$324$	−8.65499	+	13.6724i	−0.480833	+	0.759578i
$325$	−9.66367	+	16.3577i	−0.536044	+	0.907360i
$326$	−4.42313	+	15.2569i	−0.244974	+	0.845000i
$327$	−7.44570	+	7.44570i	−0.411748	+	0.411748i
$328$	−4.60796	−	0.282021i	−0.254432	−	0.0155720i
$329$			5.40967i			0.298245i
$330$	−5.15425	−	0.812127i	−0.283732	−	0.0447061i
$331$		−	18.8023i		−	1.03347i	−0.856146	−	0.516734i	$-0.827147\pi$
$331$		−	18.8023i		−	1.03347i	0.856146	−	0.516734i	$-0.172853\pi$
$332$	12.2551	−	2.75396i	0.672584	−	0.151143i
$333$	1.22752	−	1.22752i	0.0672676	−	0.0672676i
$334$	−1.64295	−	0.476307i	−0.0898980	−	0.0260624i
$335$	20.1419	−	25.9792i	1.10047	−	1.41939i
$336$	−8.70607	−	18.3927i	−0.474955	−	1.00340i
$337$	5.34610	+	5.34610i	0.291221	+	0.291221i	0.837562	−	0.546342i	$-0.183980\pi$
$337$	5.34610	+	5.34610i	0.291221	+	0.291221i	−0.546342	+	0.837562i	$0.683980\pi$
$338$	1.78201	−	0.980988i	0.0969286	−	0.0533587i
$339$	−31.7556			−1.72473
$340$	−7.16383	+	2.59021i	−0.388513	+	0.140474i
$341$	−4.55404			−0.246615
$342$	−0.260712	+	0.143521i	−0.0140977	+	0.00776072i
$343$	−9.79783	−	9.79783i	−0.529033	−	0.529033i
$344$	19.3809	+	21.9079i	1.04495	+	1.18119i
$345$	2.66152	+	21.0289i	0.143291	+	1.13216i
$346$	22.9761	+	6.66100i	1.23520	+	0.358098i
$347$	2.67879	−	2.67879i	0.143805	−	0.143805i	−0.631539	−	0.775344i	$-0.717577\pi$
$347$	2.67879	−	2.67879i	0.143805	−	0.143805i	0.775344	+	0.631539i	$0.217577\pi$
$348$	−2.45887	−	10.9419i	−0.131809	−	0.586547i
$349$			6.17389i			0.330481i	0.986253	+	0.165240i	$0.0528400\pi$
$349$			6.17389i			0.330481i	−0.986253	+	0.165240i	$0.947160\pi$
$350$	−21.7911	−	0.662311i	−1.16478	−	0.0354020i
$351$		−	20.5486i		−	1.09680i
$352$	4.58592	+	3.31200i	0.244430	+	0.176530i
$353$	0.680259	−	0.680259i	0.0362065	−	0.0362065i	−0.688772	−	0.724978i	$-0.741850\pi$
$353$	0.680259	−	0.680259i	0.0362065	−	0.0362065i	0.724978	+	0.688772i	$0.241850\pi$
$354$	5.62895	−	19.4162i	0.299175	−	1.03196i
$355$	0.177342	+	1.40120i	0.00941236	+	0.0743680i
$356$	−10.1779	−	6.44285i	−0.539426	−	0.341471i
$357$	−6.12746	−	6.12746i	−0.324299	−	0.324299i
$358$	−16.9501	−	30.7907i	−0.895842	−	1.62734i
$359$	−10.2380			−0.540343			−0.270171	−	0.962812i	$-0.587080\pi$
$359$	−10.2380			−0.540343			−0.270171	+	0.962812i	$0.587080\pi$
$360$	−0.113559	−	1.75085i	−0.00598510	−	0.0922781i
$361$	−18.4246			−0.969714
$362$	15.3059	+	27.8039i	0.804461	+	1.46134i
$363$	1.16674	+	1.16674i	0.0612382	+	0.0612382i
$364$	19.7974	+	12.5323i	1.03767	+	0.656869i
$365$	21.3904	−	27.5895i	1.11962	−	1.44410i
$366$	−8.72980	+	30.1120i	−0.456314	+	1.57398i
$367$	0.656087	−	0.656087i	0.0342475	−	0.0342475i	−0.689776	−	0.724023i	$-0.742291\pi$
$367$	0.656087	−	0.656087i	0.0342475	−	0.0342475i	0.724023	+	0.689776i	$0.242291\pi$
$368$	7.73506	−	21.6392i	0.403218	−	1.12802i
$369$		−	0.452801i		−	0.0235719i
$370$	3.07996	−	19.5473i	0.160119	−	1.01621i
$371$		−	21.3249i		−	1.10713i
$372$	3.29505	+	14.6629i	0.170840	+	0.760235i
$373$	−16.0294	+	16.0294i	−0.829973	+	0.829973i	−0.987513	−	0.157539i	$-0.949644\pi$
$373$	−16.0294	+	16.0294i	−0.829973	+	0.829973i	0.157539	+	0.987513i	$0.449644\pi$
$374$	2.31367	+	0.670756i	0.119637	+	0.0346840i
$375$	16.9357	+	7.31476i	0.874555	+	0.377732i
$376$	−3.71700	+	3.28826i	−0.191690	+	0.169579i
$377$	9.13091	+	9.13091i	0.470266	+	0.470266i
$378$	20.6563	−	11.3712i	1.06245	−	0.584871i
$379$	−10.5671			−0.542797			−0.271398	−	0.962467i	$-0.587486\pi$
$379$	−10.5671			−0.542797			−0.271398	+	0.962467i	$0.587486\pi$
$380$	−1.44022	+	3.07153i	−0.0738818	+	0.157566i
$381$	18.7084			0.958461
$382$	−3.38700	+	1.86453i	−0.173294	+	0.0953976i
$383$	9.17419	+	9.17419i	0.468779	+	0.468779i	0.901519	−	0.432740i	$-0.142453\pi$
$383$	9.17419	+	9.17419i	0.468779	+	0.468779i	−0.432740	+	0.901519i	$0.642453\pi$
$384$	7.34570	−	17.1619i	0.374859	−	0.875790i
$385$	5.44842	+	4.22420i	0.277677	+	0.215285i
$386$	6.27649	+	1.81962i	0.319465	+	0.0926163i
$387$	−2.02862	+	2.02862i	−0.103120	+	0.103120i
$388$	3.44713	−	0.774640i	0.175002	−	0.0393264i
$389$		−	32.0338i		−	1.62418i	−0.583533	−	0.812090i	$-0.698330\pi$
$389$		−	32.0338i		−	1.62418i	0.583533	−	0.812090i	$-0.301670\pi$
$390$	−11.6667	−	16.0308i	−0.590764	−	0.811751i
$391$		−	9.78592i		−	0.494895i
$392$	−0.432969	+	7.07431i	−0.0218682	+	0.357306i
$393$	4.97773	−	4.97773i	0.251093	−	0.251093i
$394$	−2.06462	+	7.12158i	−0.104014	+	0.358780i
$395$	−21.3606	+	2.70350i	−1.07477	+	0.136028i
$396$	−0.296761	+	0.468798i	−0.0149128	+	0.0235580i
$397$	−19.8777	−	19.8777i	−0.997631	−	0.997631i	0.00236570	−	0.999997i	$-0.499247\pi$
$397$	−19.8777	−	19.8777i	−0.997631	−	0.997631i	−0.999997	+	0.00236570i	$0.999247\pi$
$398$	1.04272	+	1.89414i	0.0522667	+	0.0949448i
$399$	−3.85905			−0.193194
$400$	−12.7906	−	15.3753i	−0.639530	−	0.768766i
$401$	1.54373			0.0770900			0.0385450	−	0.999257i	$-0.487728\pi$
$401$	1.54373			0.0770900			0.0385450	+	0.999257i	$0.487728\pi$
$402$	16.5436	+	30.0522i	0.825119	+	1.49887i
$403$	−12.2360	−	12.2360i	−0.609520	−	0.609520i
$404$	10.1119	−	15.9739i	0.503085	−	0.794730i
$405$	−17.9484	+	2.27163i	−0.891862	+	0.112878i
$406$	−4.12591	+	14.2317i	−0.204765	+	0.706305i
$407$	−4.42483	+	4.42483i	−0.219331	+	0.219331i
$408$	0.485631	−	7.93476i	0.0240423	−	0.392829i
$409$			23.7072i			1.17225i	0.810222	+	0.586123i	$0.199347\pi$
$409$			23.7072i			1.17225i	−0.810222	+	0.586123i	$0.800653\pi$
$410$	−3.03719	−	4.17331i	−0.149996	−	0.206105i
$411$		−	19.2046i		−	0.947292i
$412$	27.8306	−	6.25411i	1.37112	−	0.308118i
$413$	−18.8870	+	18.8870i	−0.929366	+	0.929366i
$414$	2.16478	+	0.627594i	0.106393	+	0.0308445i
$415$	11.0984	+	8.60465i	0.544797	+	0.422385i
$416$	3.42285	+	21.2206i	0.167819	+	1.04042i
$417$	2.08631	+	2.08631i	0.102167	+	0.102167i
$418$	0.939789	−	0.517349i	0.0459666	−	0.0253044i
$419$	8.70587			0.425310			0.212655	−	0.977127i	$-0.431789\pi$
$419$	8.70587			0.425310			0.212655	+	0.977127i	$0.431789\pi$
$420$	9.65873	−	20.5990i	0.471298	−	1.00513i
$421$	−17.2077			−0.838650			−0.419325	−	0.907836i	$-0.637733\pi$
$421$	−17.2077			−0.838650			−0.419325	+	0.907836i	$0.637733\pi$
$422$	−34.9689	+	19.2502i	−1.70226	+	0.937084i
$423$	−0.344186	−	0.344186i	−0.0167349	−	0.0167349i
$424$	14.6524	−	12.9623i	0.711583	−	0.629504i
$425$	−7.33283	−	4.33204i	−0.355695	−	0.210135i
$426$	−1.41562	−	0.410404i	−0.0685871	−	0.0198841i
$427$	29.2913	−	29.2913i	1.41750	−	1.41750i
$428$	8.47317	+	37.7054i	0.409566	+	1.82256i
$429$			6.26975i			0.302706i
$430$	−5.08998	+	32.3041i	−0.245461	+	1.55784i
$431$		−	5.51203i		−	0.265505i	−0.991149	−	0.132753i	$-0.957618\pi$
$431$		−	5.51203i		−	0.265505i	0.991149	−	0.132753i	$-0.0423816\pi$
$432$	20.3691	+	7.28105i	0.980007	+	0.350309i
$433$	18.5184	−	18.5184i	0.889938	−	0.889938i	−0.104579	−	0.994517i	$-0.533349\pi$
$433$	18.5184	−	18.5184i	0.889938	−	0.889938i	0.994517	+	0.104579i	$0.0333495\pi$
$434$	5.52900	−	19.0714i	0.265400	−	0.915456i
$435$	7.68264	−	9.90914i	0.368354	−	0.475107i
$436$	10.7841	+	6.82661i	0.516465	+	0.326935i
$437$	−3.08157	−	3.08157i	−0.147411	−	0.147411i
$438$	17.5690	+	31.9149i	0.839480	+	1.52495i
$439$	6.02886			0.287742			0.143871	−	0.989596i	$-0.454045\pi$
$439$	6.02886			0.287742			0.143871	+	0.989596i	$0.454045\pi$
$440$	0.409346	+	6.31129i	0.0195148	+	0.300879i
$441$	−0.695156			−0.0331027
$442$	4.41426	+	8.01871i	0.209965	+	0.381411i
$443$	9.54363	+	9.54363i	0.453432	+	0.453432i	0.896492	−	0.443060i	$-0.146107\pi$
$443$	9.54363	+	9.54363i	0.453432	+	0.453432i	−0.443060	+	0.896492i	$0.646107\pi$
$444$	17.4484	+	11.0453i	0.828066	+	0.524187i
$445$	−1.69102	−	13.3609i	−0.0801622	−	0.633369i
$446$	−0.965489	+	3.33030i	−0.0457172	+	0.157694i
$447$	10.2730	−	10.2730i	0.485894	−	0.485894i
$448$	−19.4377	+	15.1839i	−0.918344	+	0.717370i
$449$			2.70728i			0.127764i	0.997957	+	0.0638822i	$0.0203482\pi$
$449$			2.70728i			0.127764i	−0.997957	+	0.0638822i	$0.979652\pi$
$450$	1.42858	−	1.34430i	0.0673439	−	0.0633710i
$451$			1.63221i			0.0768577i
$452$	8.43927	+	37.5545i	0.396950	+	1.76642i
$453$	18.4169	−	18.4169i	0.865302	−	0.865302i
$454$	15.7751	+	4.57337i	0.740362	+	0.214639i
$455$	3.28928	+	25.9889i	0.154204	+	1.21838i
$456$	−2.34571	−	2.65156i	−0.109848	−	0.124171i
$457$	−23.1413	−	23.1413i	−1.08251	−	1.08251i	−0.996275	−	0.0862301i	$-0.972518\pi$
$457$	−23.1413	−	23.1413i	−1.08251	−	1.08251i	−0.0862301	−	0.996275i	$-0.527482\pi$
$458$	15.1587	−	8.34479i	0.708319	−	0.389926i
$459$	9.21154			0.429958
$460$	24.1617	−	8.73611i	1.12654	−	0.407323i
$461$	−5.77296			−0.268874			−0.134437	−	0.990922i	$-0.542923\pi$
$461$	−5.77296			−0.268874			−0.134437	+	0.990922i	$0.542923\pi$
$462$	−6.30262	+	3.46956i	−0.293224	+	0.161418i
$463$	9.39808	+	9.39808i	0.436766	+	0.436766i	0.890922	−	0.454156i	$-0.150059\pi$
$463$	9.39808	+	9.39808i	0.436766	+	0.436766i	−0.454156	+	0.890922i	$0.650059\pi$
$464$	−12.2865	+	5.81576i	−0.570388	+	0.269990i
$465$	−10.2953	+	13.2789i	−0.477431	+	0.615795i
$466$	−5.23433	−	1.51749i	−0.242476	−	0.0702963i
$467$	−12.2433	+	12.2433i	−0.566554	+	0.566554i	−0.931161	−	0.364607i	$-0.881203\pi$
$467$	−12.2433	+	12.2433i	−0.566554	+	0.566554i	0.364607	+	0.931161i	$0.381203\pi$
$468$	−2.05695	+	0.462238i	−0.0950824	+	0.0213669i
$469$		−	45.3257i		−	2.09295i
$470$	−5.48089	−	0.863593i	−0.252814	−	0.0398346i
$471$		−	29.8465i		−	1.37526i
$472$	−24.4577	−	1.49688i	−1.12576	−	0.0688997i
$473$	7.31254	−	7.31254i	0.336231	−	0.336231i
$474$	6.25641	−	21.5805i	0.287367	−	0.991225i
$475$	−3.67325	+	0.944943i	−0.168540	+	0.0433570i
$476$	−5.61798	+	8.87480i	−0.257500	+	0.406776i
$477$	1.35678	+	1.35678i	0.0621225	+	0.0621225i
$478$	1.93939	+	3.52299i	0.0887055	+	0.161138i
$479$	−15.8552			−0.724443			−0.362222	−	0.932092i	$-0.617982\pi$
$479$	−15.8552			−0.724443			−0.362222	+	0.932092i	$0.617982\pi$
$480$	20.0246	−	5.88449i	0.913996	−	0.268589i
$481$	−23.7778			−1.08417
$482$	−3.34619	−	6.07851i	−0.152415	−	0.276868i
$483$	20.6663	+	20.6663i	0.940349	+	0.940349i
$484$	1.06973	−	1.68987i	0.0486242	−	0.0768124i
$485$	3.12177	+	2.42034i	0.141752	+	0.109902i
$486$	−1.13151	+	3.90296i	−0.0513263	+	0.177042i
$487$	−11.2021	+	11.2021i	−0.507615	+	0.507615i	−0.913794	−	0.406179i	$-0.866861\pi$
$487$	−11.2021	+	11.2021i	−0.507615	+	0.507615i	0.406179	+	0.913794i	$0.366861\pi$
$488$	37.9308	+	2.32148i	1.71705	+	0.105088i
$489$		−	18.5338i		−	0.838129i
$490$	−6.40701	+	4.66280i	−0.289439	+	0.210644i
$491$			10.0076i			0.451639i	0.974169	+	0.225819i	$0.0725059\pi$
$491$			10.0076i			0.451639i	−0.974169	+	0.225819i	$0.927494\pi$
$492$	5.25531	−	1.18097i	0.236928	−	0.0532424i
$493$	−4.09322	+	4.09322i	−0.184349	+	0.184349i
$494$	3.91512	+	1.13503i	0.176149	+	0.0510676i
$495$	−0.615412	+	0.0778894i	−0.0276607	+	0.00350087i
$496$	16.4648	−	7.79351i	0.739291	−	0.349939i
$497$	1.37704	+	1.37704i	0.0617686	+	0.0617686i
$498$	−12.8383	+	7.06745i	−0.575300	+	0.316700i
$499$	13.5484			0.606509			0.303255	−	0.952910i	$-0.401927\pi$
$499$	13.5484			0.606509			0.303255	+	0.952910i	$0.401927\pi$
$500$	4.14973	−	21.9722i	0.185582	−	0.982629i
$501$	1.99583			0.0891670
$502$	−9.50410	+	5.23196i	−0.424189	+	0.233514i
$503$	−16.5958	−	16.5958i	−0.739970	−	0.739970i	0.232602	−	0.972572i	$-0.425276\pi$
$503$	−16.5958	−	16.5958i	−0.739970	−	0.739970i	−0.972572	+	0.232602i	$0.925276\pi$
$504$	−1.60294	−	1.81194i	−0.0714005	−	0.0807101i
$505$	20.9696	−	2.65401i	0.933136	−	0.118102i
$506$	−7.80338	−	2.26228i	−0.346902	−	0.100571i
$507$	−1.67823	+	1.67823i	−0.0745327	+	0.0745327i
$508$	−4.97188	−	22.1247i	−0.220591	−	0.981627i
$509$			31.0707i			1.37719i	0.725148	+	0.688593i	$0.241771\pi$
$509$			31.0707i			1.37719i	−0.725148	+	0.688593i	$0.758229\pi$
$510$	7.18630	−	5.22994i	0.318215	−	0.231586i
$511$		−	48.1352i		−	2.12938i
$512$	−22.2480	−	4.12621i	−0.983233	−	0.182354i
$513$	2.90069	−	2.90069i	0.128069	−	0.128069i
$514$	6.30749	−	21.7567i	0.278212	−	0.959646i
$515$	25.2038	+	19.5407i	1.11061	+	0.861068i
$516$	−28.8355	−	18.2536i	−1.26941	−	0.803572i
$517$	1.24068	+	1.24068i	0.0545652	+	0.0545652i
$518$	−13.1582	−	23.9024i	−0.578136	−	1.05021i
$519$	−27.9110			−1.22516
$520$	−15.8577	+	18.0574i	−0.695405	+	0.791869i
$521$	34.2806			1.50186			0.750930	−	0.660381i	$-0.229605\pi$
$521$	34.2806			1.50186			0.750930	+	0.660381i	$0.229605\pi$
$522$	−0.642969	−	1.16798i	−0.0281420	−	0.0511213i
$523$	4.41610	+	4.41610i	0.193103	+	0.193103i	0.797035	−	0.603933i	$-0.206400\pi$
$523$	4.41610	+	4.41610i	0.193103	+	0.193103i	−0.603933	+	0.797035i	$0.706400\pi$
$524$	−7.20958	−	4.56385i	−0.314952	−	0.199373i
$525$	24.6343	−	6.33719i	1.07513	−	0.276578i
$526$	5.45714	−	18.8235i	0.237943	−	0.820745i
$527$	5.48519	−	5.48519i	0.238938	−	0.238938i
$528$	−6.21498	−	2.22158i	−0.270472	−	0.0966819i
$529$			10.0053i			0.435014i
$530$	21.6056	+	3.40428i	0.938488	+	0.147872i
$531$		−	2.40333i		−	0.104296i
$532$	1.02557	+	4.56375i	0.0444640	+	0.197864i
$533$	−4.38551	+	4.38551i	−0.189957	+	0.189957i
$534$	13.4985	+	3.91335i	0.584135	+	0.169347i
$535$	−26.4741	+	34.1465i	−1.14458	+	1.47628i
$536$	31.1434	−	27.5512i	1.34519	−	1.19003i
$537$	28.9974	+	28.9974i	1.25133	+	1.25133i
$538$	−18.8879	+	10.3977i	−0.814314	+	0.448276i
$539$	2.50582			0.107934
$540$	8.22334	+	22.7435i	0.353876	+	0.978725i
$541$	−2.99477			−0.128755			−0.0643776	−	0.997926i	$-0.520506\pi$
$541$	−2.99477			−0.128755			−0.0643776	+	0.997926i	$0.520506\pi$
$542$	8.30105	−	4.56969i	0.356561	−	0.196285i
$543$	−26.1846	−	26.1846i	−1.12369	−	1.12369i
$544$	−9.51278	+	1.53440i	−0.407857	+	0.0657869i
$545$	1.79175	+	14.1568i	0.0767500	+	0.606409i
$546$	−26.2564	−	7.61202i	−1.12367	−	0.325764i
$547$	−12.3349	+	12.3349i	−0.527404	+	0.527404i	−0.919797	−	0.392394i	$-0.871647\pi$
$547$	−12.3349	+	12.3349i	−0.527404	+	0.527404i	0.392394	+	0.919797i	$0.371647\pi$
$548$	−22.7115	+	5.10374i	−0.970189	+	0.218021i
$549$			3.72726i			0.159076i
$550$	−5.14959	+	4.84579i	−0.219579	+	0.206625i
$551$			2.57789i			0.109822i
$552$	−1.63790	+	26.7618i	−0.0697139	+	1.13906i
$553$	−20.9923	+	20.9923i	−0.892683	+	0.892683i
$554$	−9.74255	+	33.6054i	−0.413921	+	1.42775i
$555$	2.89901	+	22.9053i	0.123056	+	0.972277i
$556$	1.91284	−	3.02174i	0.0811224	−	0.128150i
$557$	16.0243	+	16.0243i	0.678973	+	0.678973i	0.959768	−	0.280795i	$-0.0905980\pi$
$557$	16.0243	+	16.0243i	0.678973	+	0.678973i	−0.280795	+	0.959768i	$0.590598\pi$
$558$	0.861622	+	1.56518i	0.0364754	+	0.0662592i
$559$	39.2955			1.66202
$560$	−26.9274	−	5.94820i	−1.13789	−	0.251357i
$561$	−2.81061			−0.118664
$562$	−0.668969	−	1.21521i	−0.0282187	−	0.0512607i
$563$	18.2100	+	18.2100i	0.767461	+	0.767461i	0.977659	−	0.210198i	$-0.0674108\pi$
$563$	18.2100	+	18.2100i	0.767461	+	0.767461i	−0.210198	+	0.977659i	$0.567411\pi$
$564$	3.09701	−	4.89238i	0.130407	−	0.206007i
$565$	−26.3682	+	34.0099i	−1.10932	+	1.43081i
$566$	3.60703	−	12.4419i	0.151615	−	0.522970i
$567$	−17.6389	+	17.6389i	−0.740763	+	0.740763i
$568$	−0.109137	+	1.78320i	−0.00457929	+	0.0748212i
$569$			5.82173i			0.244060i	0.992526	+	0.122030i	$0.0389404\pi$
$569$			5.82173i			0.244060i	−0.992526	+	0.122030i	$0.961060\pi$
$570$	0.616054	−	3.90985i	0.0258036	−	0.163766i
$571$			22.1494i			0.926923i	0.886117	+	0.463461i	$0.153393\pi$
$571$			22.1494i			0.926923i	−0.886117	+	0.463461i	$0.846607\pi$
$572$	7.41466	−	1.66623i	0.310023	−	0.0696684i
$573$	3.18975	−	3.18975i	0.133254	−	0.133254i
$574$	−6.83535	−	1.98164i	−0.285302	−	0.0827121i
$575$	24.7317	+	14.6108i	1.03138	+	0.609313i
$576$	0.270646	−	2.20276i	0.0112769	−	0.0917819i
$577$	0.299763	+	0.299763i	0.0124793	+	0.0124793i	0.713319	−	0.700840i	$-0.247191\pi$
$577$	0.299763	+	0.299763i	0.0124793	+	0.0124793i	−0.700840	+	0.713319i	$0.747191\pi$
$578$	17.4666	−	9.61529i	0.726516	−	0.399943i
$579$	−7.62460			−0.316867
$580$	−13.7604	−	6.45215i	−0.571368	−	0.267911i
$581$	19.3632			0.803323
$582$	−3.61120	+	1.98795i	−0.149689	+	0.0824031i
$583$	−4.89076	−	4.89076i	−0.202555	−	0.202555i
$584$	33.0738	−	29.2589i	1.36861	−	1.21074i
$585$	−1.86280	−	1.44425i	−0.0770173	−	0.0597122i
$586$	−4.29592	−	1.24543i	−0.177463	−	0.0514484i
$587$	6.13158	−	6.13158i	0.253077	−	0.253077i	−0.569154	−	0.822231i	$-0.692729\pi$
$587$	6.13158	−	6.13158i	0.253077	−	0.253077i	0.822231	+	0.569154i	$0.192729\pi$
$588$	−1.81308	−	8.06814i	−0.0747700	−	0.332725i
$589$		−	3.45455i		−	0.142342i
$590$	−16.1205	−	22.1507i	−0.663670	−	0.911929i
$591$		−	8.65119i		−	0.355863i
$592$	8.42526	−	23.5700i	0.346276	−	0.968723i
$593$	1.76457	−	1.76457i	0.0724624	−	0.0724624i	−0.669947	−	0.742409i	$-0.733683\pi$
$593$	1.76457	−	1.76457i	0.0724624	−	0.0724624i	0.742409	+	0.669947i	$0.233683\pi$
$594$	2.12950	−	7.34536i	0.0873743	−	0.301384i
$595$	−11.6503	+	1.47452i	−0.477618	+	0.0604496i
$596$	−14.8790	−	9.41880i	−0.609468	−	0.385809i
$597$	−1.78383	−	1.78383i	−0.0730073	−	0.0730073i
$598$	−14.8881	−	27.0450i	−0.608821	−	1.10595i
$599$	−37.9941			−1.55240			−0.776198	−	0.630490i	$-0.782854\pi$
$599$	−37.9941			−1.55240			−0.776198	+	0.630490i	$0.782854\pi$
$600$	19.3282	+	13.0743i	0.789071	+	0.533755i
$601$	5.33565			0.217646			0.108823	−	0.994061i	$-0.465292\pi$
$601$	5.33565			0.217646			0.108823	+	0.994061i	$0.465292\pi$
$602$	21.7454	+	39.5015i	0.886276	+	1.60996i
$603$	2.88381	+	2.88381i	0.117438	+	0.117438i
$604$	−26.6744	−	16.8856i	−1.08537	−	0.687066i
$605$	2.21837	−	0.280768i	0.0901896	−	0.0114148i
$606$	−6.14189	+	21.1855i	−0.249497	+	0.860600i
$607$	20.9316	−	20.9316i	0.849586	−	0.849586i	−0.140495	−	0.990081i	$-0.544869\pi$
$607$	20.9316	−	20.9316i	0.849586	−	0.849586i	0.990081	+	0.140495i	$0.0448694\pi$
$608$	−2.51238	+	3.47874i	−0.101890	+	0.141081i
$609$		−	17.2884i		−	0.700562i
$610$	25.0009	+	34.3529i	1.01226	+	1.39091i
$611$			6.66707i			0.269721i
$612$	−0.207213	−	0.922091i	−0.00837607	−	0.0372733i
$613$	5.39906	−	5.39906i	0.218066	−	0.218066i	−0.589617	−	0.807683i	$-0.700721\pi$
$613$	5.39906	−	5.39906i	0.218066	−	0.218066i	0.807683	+	0.589617i	$0.200721\pi$
$614$	35.6578	+	10.3376i	1.43903	+	0.417191i
$615$	4.75928	+	3.68991i	0.191913	+	0.148792i
$616$	5.77810	+	6.53148i	0.232806	+	0.263161i
$617$	10.9003	+	10.9003i	0.438829	+	0.438829i	0.891618	−	0.452789i	$-0.149571\pi$
$617$	10.9003	+	10.9003i	0.438829	+	0.438829i	−0.452789	+	0.891618i	$0.649571\pi$
$618$	−29.1553	+	16.0498i	−1.17280	+	0.645619i
$619$	10.5326			0.423339			0.211670	−	0.977341i	$-0.432110\pi$
$619$	10.5326			0.423339			0.211670	+	0.977341i	$0.432110\pi$
$620$	18.4398	+	8.64631i	0.740560	+	0.347244i
$621$	−31.0681			−1.24672
$622$	−31.1527	+	17.1494i	−1.24911	+	0.687628i
$623$	−13.1305	−	13.1305i	−0.526064	−	0.526064i
$624$	−10.7297	−	22.6678i	−0.429531	−	0.907439i
$625$	21.8965	−	12.0641i	0.875860	−	0.482565i
$626$	2.35528	+	0.682820i	0.0941358	+	0.0272910i
$627$	−0.885055	+	0.885055i	−0.0353457	+	0.0353457i
$628$	−35.2968	+	7.93191i	−1.40850	+	0.316518i
$629$		−	10.6591i		−	0.425007i
$630$	0.420978	−	2.67178i	0.0167722	−	0.106446i
$631$		−	26.9699i		−	1.07366i	−0.843692	−	0.536828i	$-0.819623\pi$
$631$		−	26.9699i		−	1.07366i	0.843692	−	0.536828i	$-0.180377\pi$
$632$	−27.1840	−	1.66374i	−1.08132	−	0.0661801i
$633$	32.9323	−	32.9323i	1.30894	−	1.30894i
$634$	2.59545	−	8.95257i	0.103078	−	0.355552i
$635$	15.5345	−	20.0365i	0.616466	−	0.795123i
$636$	−12.2084	+	19.2857i	−0.484094	+	0.764729i
$637$	6.73279	+	6.73279i	0.266763	+	0.266763i
$638$	2.31771	+	4.21022i	0.0917589	+	0.166684i
$639$	−0.175226			−0.00693182
$640$	−12.2807	−	22.1175i	−0.485439	−	0.874271i
$641$	−19.0604			−0.752839			−0.376420	−	0.926449i	$-0.622845\pi$
$641$	−19.0604			−0.752839			−0.376420	+	0.926449i	$0.622845\pi$
$642$	−21.7446	−	39.5000i	−0.858190	−	1.55894i
$643$	27.8666	+	27.8666i	1.09895	+	1.09895i	0.994534	+	0.104417i	$0.0332976\pi$
$643$	27.8666	+	27.8666i	1.09895	+	1.09895i	0.104417	+	0.994534i	$0.466702\pi$
$644$	18.9480	−	29.9324i	0.746654	−	1.17950i
$645$	−4.79094	−	37.8537i	−0.188643	−	1.49049i
$646$	−0.508815	+	1.75507i	−0.0200190	+	0.0690525i
$647$	−27.6311	+	27.6311i	−1.08629	+	1.08629i	−0.0903845	+	0.995907i	$0.528810\pi$
$647$	−27.6311	+	27.6311i	−1.08629	+	1.08629i	−0.995907	+	0.0903845i	$0.971190\pi$
$648$	−22.8415	−	1.39797i	−0.897298	−	0.0549174i
$649$			8.66327i			0.340063i
$650$	−26.8562	−	0.816256i	−1.05338	−	0.0320162i
$651$			23.1677i			0.908012i
$652$	−21.9183	+	4.92548i	−0.858387	+	0.192897i
$653$	−16.4296	+	16.4296i	−0.642940	+	0.642940i	−0.951277	−	0.308337i	$-0.900227\pi$
$653$	−16.4296	+	16.4296i	−0.642940	+	0.642940i	0.308337	+	0.951277i	$0.400227\pi$
$654$	−14.3025	−	4.14644i	−0.559271	−	0.162139i
$655$	−1.19785	−	9.46434i	−0.0468039	−	0.369802i
$656$	−2.79326	−	5.90113i	−0.109059	−	0.230400i
$657$	3.06256	+	3.06256i	0.119482	+	0.119482i
$658$	−6.70203	+	3.68943i	−0.261272	+	0.143829i
$659$	−29.3260			−1.14238			−0.571189	−	0.820818i	$-0.693518\pi$
$659$	−29.3260			−1.14238			−0.571189	+	0.820818i	$0.693518\pi$
$660$	−2.50909	−	6.93946i	−0.0976663	−	0.270118i
$661$	−46.7121			−1.81689			−0.908445	−	0.418005i	$-0.862729\pi$
$661$	−46.7121			−1.81689			−0.908445	+	0.418005i	$0.862729\pi$
$662$	23.2941	−	12.8233i	0.905352	−	0.498392i
$663$	−7.55170	−	7.55170i	−0.293284	−	0.293284i
$664$	11.7699	+	13.3045i	0.456761	+	0.516316i
$665$	−3.20435	+	4.13300i	−0.124259	+	0.160271i
$666$	2.35795	+	0.683594i	0.0913686	+	0.0264887i
$667$	13.8053	−	13.8053i	0.534545	−	0.534545i
$668$	−0.530404	−	2.36029i	−0.0205220	−	0.0913222i
$669$		−	4.04560i		−	0.156412i
$670$	45.9224	+	7.23574i	1.77414	+	0.279541i
$671$		−	13.4356i		−	0.518677i
$672$	16.8491	−	23.3299i	0.649966	−	0.899969i
$673$	−11.6306	+	11.6306i	−0.448326	+	0.448326i	−0.894798	−	0.446472i	$-0.852680\pi$
$673$	−11.6306	+	11.6306i	−0.448326	+	0.448326i	0.446472	+	0.894798i	$0.352680\pi$
$674$	−2.97719	+	10.2693i	−0.114677	+	0.395560i
$675$	−13.7532	+	23.2801i	−0.529362	+	0.896050i
$676$	2.43069	+	1.53869i	0.0934879	+	0.0591803i
$677$	12.6714	+	12.6714i	0.487000	+	0.487000i	0.907358	−	0.420358i	$-0.138096\pi$
$677$	12.6714	+	12.6714i	0.487000	+	0.487000i	−0.420358	+	0.907358i	$0.638096\pi$
$678$	−21.6576	−	39.3420i	−0.831754	−	1.51092i
$679$	5.44654			0.209019
$680$	−8.09479	−	7.10870i	−0.310421	−	0.272606i
$681$	−19.1634			−0.734342
$682$	−3.10588	−	5.64198i	−0.118930	−	0.216043i
$683$	−6.70569	−	6.70569i	−0.256586	−	0.256586i	0.567078	−	0.823664i	$-0.308074\pi$
$683$	−6.70569	−	6.70569i	−0.256586	−	0.256586i	−0.823664	+	0.567078i	$0.808074\pi$
$684$	−0.355615	−	0.225114i	−0.0135973	−	0.00860744i
$685$	−20.5679	−	15.9465i	−0.785859	−	0.609283i
$686$	5.45632	−	18.8207i	0.208323	−	0.718577i
$687$	−14.2759	+	14.2759i	−0.544658	+	0.544658i
$688$	−13.9237	+	38.9522i	−0.530836	+	1.48504i
$689$		−	26.2816i		−	1.00125i
$690$	−24.2375	+	17.6392i	−0.922705	+	0.671513i
$691$			25.4431i			0.967899i	0.875096	+	0.483950i	$0.160798\pi$
$691$			25.4431i			0.967899i	−0.875096	+	0.483950i	$0.839202\pi$
$692$	7.41753	+	33.0078i	0.281972	+	1.25477i
$693$	−0.604800	+	0.604800i	−0.0229744	+	0.0229744i
$694$	5.14569	+	1.49179i	0.195328	+	0.0566276i
$695$	3.96677	−	0.502053i	0.150468	−	0.0190440i
$696$	11.8789	−	10.5087i	0.450270	−	0.398332i
$697$	−1.96594	−	1.96594i	−0.0744653	−	0.0744653i
$698$	−7.64881	+	4.21063i	−0.289512	+	0.159375i
$699$	6.35859			0.240504
$700$	−14.0412	−	27.4487i	−0.530706	−	1.03746i
$701$	2.58249			0.0975392			0.0487696	−	0.998810i	$-0.484470\pi$
$701$	2.58249			0.0975392			0.0487696	+	0.998810i	$0.484470\pi$
$702$	25.4576	−	14.0143i	0.960834	−	0.528934i
$703$	−3.35654	−	3.35654i	−0.126594	−	0.126594i
$704$	−0.975594	+	7.94029i	−0.0367691	+	0.299261i
$705$	6.42245	−	0.812856i	0.241883	−	0.0306139i
$706$	1.30671	+	0.378830i	0.0491788	+	0.0142574i
$707$	20.6080	−	20.6080i	0.775045	−	0.775045i
$708$	27.8936	−	6.26826i	1.04831	−	0.235576i
$709$			21.4440i			0.805347i	0.915344	+	0.402674i	$0.131919\pi$
$709$			21.4440i			0.805347i	−0.915344	+	0.402674i	$0.868081\pi$
$710$	−1.61499	+	1.17534i	−0.0606096	+	0.0441096i
$711$		−	2.67123i		−	0.100179i
$712$	1.04066	−	17.0034i	0.0390004	−	0.637229i
$713$	−18.5001	+	18.5001i	−0.692833	+	0.692833i
$714$	3.41232	−	11.7703i	0.127703	−	0.440491i
$715$	6.71482	+	5.20606i	0.251120	+	0.194696i
$716$	26.5864	−	41.9989i	0.993581	−	1.56957i
$717$	−3.31781	−	3.31781i	−0.123906	−	0.123906i
$718$	−6.98241	−	12.6839i	−0.260581	−	0.473358i
$719$	−34.4454			−1.28460			−0.642299	−	0.766455i	$-0.722019\pi$
$719$	−34.4454			−1.28460			−0.642299	+	0.766455i	$0.722019\pi$
$720$	2.09168	−	1.33478i	0.0779524	−	0.0497444i
$721$	43.9730			1.63764
$722$	−12.5657	−	22.8262i	−0.467646	−	0.849502i
$723$	5.72449	+	5.72449i	0.212896	+	0.212896i
$724$	−24.0074	+	37.9249i	−0.892230	+	1.40947i
$725$	−4.23332	−	16.4560i	−0.157222	−	0.611162i
$726$	−0.649749	+	2.24120i	−0.0241144	+	0.0831789i
$727$	−10.5267	+	10.5267i	−0.390414	+	0.390414i	−0.874835	−	0.484421i	$-0.839030\pi$
$727$	−10.5267	+	10.5267i	−0.390414	+	0.390414i	0.484421	+	0.874835i	$0.339030\pi$
$728$	−2.02423	+	33.0740i	−0.0750230	+	1.22581i
$729$		−	29.0136i		−	1.07458i
$730$	48.7689	+	7.68424i	1.80502	+	0.284407i
$731$			17.6154i			0.651530i
$732$	−43.2595	+	9.72128i	−1.59892	+	0.359309i
$733$	14.2088	−	14.2088i	0.524813	−	0.524813i	−0.394208	−	0.919021i	$-0.628981\pi$
$733$	14.2088	−	14.2088i	0.524813	−	0.524813i	0.919021	+	0.394208i	$0.128981\pi$
$734$	1.26028	+	0.365369i	0.0465178	+	0.0134860i
$735$	5.66489	−	7.30662i	0.208953	−	0.269509i
$736$	32.0841	−	5.17512i	1.18263	−	0.190758i
$737$	−10.3953	−	10.3953i	−0.382914	−	0.382914i
$738$	0.560974	−	0.308813i	0.0206497	−	0.0113676i
$739$	49.1754			1.80895			0.904474	−	0.426530i	$-0.140264\pi$
$739$	49.1754			1.80895			0.904474	+	0.426530i	$0.140264\pi$
$740$	26.3176	−	9.51563i	0.967455	−	0.349802i
$741$	−4.75603			−0.174717
$742$	26.4193	−	14.5437i	0.969884	−	0.533917i
$743$	−4.06425	−	4.06425i	−0.149103	−	0.149103i	0.628614	−	0.777717i	$-0.283622\pi$
$743$	−4.06425	−	4.06425i	−0.149103	−	0.149103i	−0.777717	+	0.628614i	$0.783622\pi$
$744$	−15.9186	+	14.0824i	−0.583603	+	0.516286i
$745$	−2.47211	−	19.5323i	−0.0905709	−	0.715609i
$746$	−30.7910	−	8.92665i	−1.12734	−	0.326828i
$747$	−1.23197	+	1.23197i	−0.0450754	+	0.0450754i
$748$	0.746938	+	3.32385i	0.0273107	+	0.121532i
$749$			59.5753i			2.17683i
$750$	2.48802	+	25.9703i	0.0908497	+	0.948301i
$751$		−	8.00983i		−	0.292283i	−0.989264	−	0.146141i	$-0.953315\pi$
$751$		−	8.00983i		−	0.292283i	0.989264	−	0.146141i	$-0.0466855\pi$
$752$	−6.60883	−	2.36237i	−0.240999	−	0.0861467i
$753$	8.95059	−	8.95059i	0.326177	−	0.326177i
$754$	−5.08492	+	17.5396i	−0.185182	+	0.638755i
$755$	−4.43188	−	35.0167i	−0.161293	−	1.27439i
$756$	28.1755	+	17.8358i	1.02473	+	0.648682i
$757$	18.0256	+	18.0256i	0.655151	+	0.655151i	0.954229	−	0.299078i	$-0.0966791\pi$
$757$	18.0256	+	18.0256i	0.655151	+	0.655151i	−0.299078	+	0.954229i	$0.596679\pi$
$758$	−7.20685	−	13.0916i	−0.261765	−	0.475508i
$759$	9.47944			0.344082
$760$	−4.78755	+	0.310517i	−0.173663	+	0.0112636i
$761$	−6.07320			−0.220153			−0.110077	−	0.993923i	$-0.535110\pi$
$761$	−6.07320			−0.220153			−0.110077	+	0.993923i	$0.535110\pi$
$762$	12.7593	+	23.1778i	0.462219	+	0.839643i
$763$	13.9126	+	13.9126i	0.503671	+	0.503671i
$764$	−4.61992	−	2.92453i	−0.167143	−	0.105806i
$765$	0.647428	−	0.835058i	0.0234078	−	0.0301916i
$766$	−5.10902	+	17.6227i	−0.184596	+	0.636736i
$767$	−23.2770	+	23.2770i	−0.840482	+	0.840482i
$768$	26.2717	−	2.60398i	0.947997	−	0.0939629i
$769$			26.6491i			0.960990i	0.876997	+	0.480495i	$0.159543\pi$
$769$			26.6491i			0.960990i	−0.876997	+	0.480495i	$0.840457\pi$
$770$	−1.51750	+	9.63096i	−0.0546868	+	0.347076i
$771$			26.4297i			0.951843i
$772$	2.02629	+	9.01692i	0.0729276	+	0.324526i
$773$	−12.5678	+	12.5678i	−0.452033	+	0.452033i	−0.896029	−	0.443996i	$-0.853560\pi$
$773$	−12.5678	+	12.5678i	−0.452033	+	0.452033i	0.443996	+	0.896029i	$0.353560\pi$
$774$	−3.89678	−	1.12972i	−0.140067	−	0.0406069i
$775$	5.67293	+	22.0522i	0.203778	+	0.792138i
$776$	3.31067	+	3.74233i	0.118846	+	0.134342i
$777$	22.5103	+	22.5103i	0.807554	+	0.807554i
$778$	39.6866	−	21.8473i	1.42283	−	0.783263i
$779$	−1.23814			−0.0443610
$780$	11.9038	−	25.3869i	0.426223	−	0.908997i
$781$	0.631635			0.0226017
$782$	12.1238	−	6.67407i	0.433545	−	0.238664i
$783$	12.9950	+	12.9950i	0.464404	+	0.464404i
$784$	−9.05963	+	4.28832i	−0.323558	+	0.153154i
$785$	−31.9653	−	24.7830i	−1.14089	−	0.884542i
$786$	9.56175	+	2.77205i	0.341056	+	0.0988759i
$787$	−4.43581	+	4.43581i	−0.158120	+	0.158120i	−0.781733	−	0.623613i	$-0.785664\pi$
$787$	−4.43581	+	4.43581i	−0.158120	+	0.158120i	0.623613	+	0.781733i	$0.285664\pi$
$788$	−10.2310	+	2.29911i	−0.364464	+	0.0819024i
$789$			22.8666i			0.814072i
$790$	−17.9175	−	24.6198i	−0.637475	−	0.875934i
$791$			59.3369i			2.10978i
$792$	−0.783186	−	0.0479333i	−0.0278293	−	0.00170324i
$793$	36.0996	−	36.0996i	1.28194	−	1.28194i
$794$	11.0697	−	38.1831i	0.392848	−	1.35507i
$795$	−25.3172	+	3.20427i	−0.897910	+	0.113644i
$796$	−1.63551	+	2.58364i	−0.0579691	+	0.0915746i
$797$	−22.0465	−	22.0465i	−0.780929	−	0.780929i	0.199059	−	0.979988i	$-0.436212\pi$
$797$	−22.0465	−	22.0465i	−0.780929	−	0.780929i	−0.979988	+	0.199059i	$0.936212\pi$
$798$	−2.63190	−	4.78097i	−0.0931682	−	0.169244i
$799$	−2.98872			−0.105733
$800$	10.3252	−	26.3323i	0.365050	−	0.930988i
$801$	1.67084			0.0590362
$802$	1.05283	+	1.91252i	0.0371768	+	0.0675334i
$803$	−11.0396	−	11.0396i	−0.389579	−	0.389579i
$804$	−25.9487	+	40.9916i	−0.915141	+	1.44566i
$805$	39.2935	−	4.97318i	1.38491	−	0.175281i
$806$	6.81413	−	23.5043i	0.240018	−	0.827902i
$807$	17.7879	−	17.7879i	0.626162	−	0.626162i
$808$	26.6864	+	1.63329i	0.938823	+	0.0574588i
$809$		−	9.01158i		−	0.316830i	−0.987373	−	0.158415i	$-0.949362\pi$
$809$		−	9.01158i		−	0.316830i	0.987373	−	0.158415i	$-0.0506384\pi$
$810$	−15.0552	−	20.6869i	−0.528987	−	0.726865i
$811$			25.0356i			0.879118i	0.898214	+	0.439559i	$0.144865\pi$
$811$			25.0356i			0.879118i	−0.898214	+	0.439559i	$0.855135\pi$
$812$	−20.4455	+	4.59451i	−0.717495	+	0.161236i
$813$	−7.81760	+	7.81760i	−0.274175	+	0.274175i
$814$	−8.49968	−	2.46415i	−0.297913	−	0.0863683i
$815$	−19.8495	−	15.3895i	−0.695298	−	0.539071i
$816$	10.1616	−	4.80991i	0.355725	−	0.168381i
$817$	5.54706	+	5.54706i	0.194067	+	0.194067i
$818$	−29.3708	+	16.1685i	−1.02693	+	0.565318i
$819$	−3.25002			−0.113565
$820$	3.09892	−	6.60899i	0.108219	−	0.230796i
$821$	19.3965			0.676944			0.338472	−	0.940976i	$-0.390090\pi$
$821$	19.3965			0.676944			0.338472	+	0.940976i	$0.390090\pi$
$822$	23.7925	−	13.0977i	0.829859	−	0.456833i
$823$	−19.9050	−	19.9050i	−0.693846	−	0.693846i	0.269230	−	0.963076i	$-0.413231\pi$
$823$	−19.9050	−	19.9050i	−0.693846	−	0.693846i	−0.963076	+	0.269230i	$0.913231\pi$
$824$	26.7289	+	30.2140i	0.931145	+	1.05255i
$825$	4.19637	−	7.10318i	0.146099	−	0.247301i
$826$	−36.2800	−	10.5180i	−1.26234	−	0.365967i
$827$	28.7284	−	28.7284i	0.998985	−	0.998985i	−0.00101496	−	0.999999i	$-0.500323\pi$
$827$	28.7284	−	28.7284i	0.998985	−	0.998985i	0.999999	+	0.00101496i	$0.000323070\pi$
$828$	0.698873	+	3.10997i	0.0242875	+	0.108079i
$829$			37.2557i			1.29394i	0.762514	+	0.646972i	$0.223965\pi$
$829$			37.2557i			1.29394i	−0.762514	+	0.646972i	$0.776035\pi$
$830$	−3.09112	+	19.6181i	−0.107294	+	0.680956i
$831$		−	40.8233i		−	1.41615i
$832$	−23.9557	+	18.7131i	−0.830514	+	0.648761i
$833$	−3.01818	+	3.01818i	−0.104574	+	0.104574i
$834$	−1.16185	+	4.00760i	−0.0402314	+	0.138772i
$835$	1.65723	−	2.13751i	0.0573507	−	0.0739715i
$836$	1.28188	+	0.811466i	0.0443349	+	0.0280651i
$837$	−17.4142	−	17.4142i	−0.601923	−	0.601923i
$838$	5.93746	+	10.7857i	0.205106	+	0.372585i
$839$	18.0996			0.624868			0.312434	−	0.949939i	$-0.398856\pi$
$839$	18.0996			0.624868			0.312434	+	0.949939i	$0.398856\pi$
$840$	32.1073	−	2.08246i	1.10781	−	0.0718516i
$841$	17.4511			0.601763
$842$	−11.7357	−	21.3185i	−0.404440	−	0.734684i
$843$	1.14444	+	1.14444i	0.0394166	+	0.0394166i
$844$	−47.6980	−	30.1941i	−1.64183	−	1.03932i
$845$	0.403852	+	3.19087i	0.0138929	+	0.109769i
$846$	0.191674	−	0.661147i	0.00658988	−	0.0227307i
$847$	2.18012	−	2.18012i	0.0749097	−	0.0749097i
$848$	26.0520	+	9.31243i	0.894628	+	0.319790i
$849$			15.1142i			0.518718i
$850$	0.365912	−	12.0391i	0.0125507	−	0.412938i
$851$			35.9504i			1.23236i
$852$	−0.457015	−	2.03371i	−0.0156571	−	0.0696737i
$853$	11.8955	−	11.8955i	0.407293	−	0.407293i	−0.473501	−	0.880793i	$-0.657010\pi$
$853$	11.8955	−	11.8955i	0.407293	−	0.407293i	0.880793	+	0.473501i	$0.157010\pi$
$854$	56.2658	+	16.3120i	1.92537	+	0.558187i
$855$	−0.0590845	−	0.466832i	−0.00202065	−	0.0159653i
$856$	−40.9344	+	36.2127i	−1.39911	+	1.23773i
$857$	−29.3661	−	29.3661i	−1.00313	−	1.00313i	−0.999995	−	0.00313143i	$-0.999003\pi$
$857$	−29.3661	−	29.3661i	−1.00313	−	1.00313i	−0.00313143	−	0.999995i	$-0.500997\pi$
$858$	−7.76757	+	4.27601i	−0.265181	+	0.145981i
$859$	12.6835			0.432754			0.216377	−	0.976310i	$-0.430576\pi$
$859$	12.6835			0.432754			0.216377	+	0.976310i	$0.430576\pi$
$860$	−43.4929	+	15.7257i	−1.48310	+	0.536241i
$861$	8.30350			0.282982
$862$	6.82884	−	3.75924i	0.232591	−	0.128040i
$863$	−24.8340	−	24.8340i	−0.845360	−	0.845360i	0.144190	−	0.989550i	$-0.453942\pi$
$863$	−24.8340	−	24.8340i	−0.845360	−	0.845360i	−0.989550	+	0.144190i	$0.953942\pi$
$864$	4.87137	+	30.2009i	0.165727	+	1.02746i
$865$	−23.1758	+	29.8923i	−0.788001	+	1.01637i
$866$	35.5721	+	10.3127i	1.20879	+	0.350441i
$867$	−16.4494	+	16.4494i	−0.558650	+	0.558650i
$868$	27.3983	−	6.15695i	0.929959	−	0.208981i
$869$			9.62897i			0.326641i
$870$	17.5160	+	2.75990i	0.593849	+	0.0935694i
$871$		−	55.8611i		−	1.89278i
$872$	−1.10265	+	18.0162i	−0.0373403	+	0.610105i
$873$	−0.346531	+	0.346531i	−0.0117283	+	0.0117283i
$874$	1.71610	−	5.91940i	0.0580478	−	0.200227i
$875$	13.6680	−	31.6451i	0.462062	−	1.06980i
$876$	−27.5571	+	43.5324i	−0.931070	+	1.47082i
$877$	−39.1193	−	39.1193i	−1.32097	−	1.32097i	−0.912995	−	0.407970i	$-0.866237\pi$
$877$	−39.1193	−	39.1193i	−1.32097	−	1.32097i	−0.407970	−	0.912995i	$-0.633763\pi$
$878$	4.11172	+	7.46913i	0.138764	+	0.252071i
$879$	5.21863			0.176020
$880$	−7.53987	+	4.81148i	−0.254169	+	0.162195i
$881$	20.0333			0.674939			0.337469	−	0.941337i	$-0.390429\pi$
$881$	20.0333			0.674939			0.337469	+	0.941337i	$0.390429\pi$
$882$	−0.474101	−	0.861227i	−0.0159638	−	0.0289990i
$883$	25.9099	+	25.9099i	0.871937	+	0.871937i	0.992683	−	0.120747i	$-0.0385289\pi$
$883$	25.9099	+	25.9099i	0.871937	+	0.871937i	−0.120747	+	0.992683i	$0.538529\pi$
$884$	−6.92380	+	10.9376i	−0.232873	+	0.367872i
$885$	25.2609	+	19.5850i	0.849134	+	0.658341i
$886$	−5.31476	+	18.3324i	−0.178553	+	0.615889i
$887$	−22.1814	+	22.1814i	−0.744777	+	0.744777i	−0.973493	−	0.228716i	$-0.926547\pi$
$887$	−22.1814	+	22.1814i	−0.744777	+	0.744777i	0.228716	+	0.973493i	$0.426547\pi$
$888$	−1.78406	+	29.1498i	−0.0598690	+	0.978203i
$889$		−	34.9576i		−	1.17244i
$890$	15.3995	−	11.2073i	0.516194	−	0.375668i
$891$			8.09079i			0.271052i
$892$	−4.78437	+	1.07515i	−0.160193	+	0.0359985i
$893$	−0.941143	+	0.941143i	−0.0314942	+	0.0314942i
$894$	19.7334	+	5.72092i	0.659983	+	0.191336i
$895$	55.1338	−	6.97800i	1.84292	−	0.233249i
$896$	−32.0679	−	13.7258i	−1.07131	−	0.458547i
$897$	25.4699	+	25.4699i	0.850415	+	0.850415i
$898$	−3.35404	+	1.84638i	−0.111926	+	0.0616146i
$899$	15.4763			0.516163
$900$	2.63975	+	0.853040i	0.0879917	+	0.0284347i
$901$	11.7815			0.392500
$902$	−2.02214	+	1.11318i	−0.0673298	+	0.0370647i
$903$	−37.2009	−	37.2009i	−1.23797	−	1.23797i
$904$	−40.7706	+	36.0678i	−1.35601	+	1.19960i
$905$	−49.7857	+	6.30111i	−1.65493	+	0.209456i
$906$	35.3771	+	10.2562i	1.17533	+	0.340740i
$907$	12.5576	−	12.5576i	0.416968	−	0.416968i	−0.467189	−	0.884157i	$-0.654733\pi$
$907$	12.5576	−	12.5576i	0.416968	−	0.416968i	0.884157	+	0.467189i	$0.154733\pi$
$908$	5.09279	+	22.6628i	0.169010	+	0.752091i
$909$			2.62233i			0.0869774i
$910$	−29.9543	+	21.7997i	−0.992975	+	0.722653i
$911$		−	15.5963i		−	0.516727i	−0.966048	−	0.258364i	$-0.916817\pi$
$911$		−	15.5963i		−	0.516727i	0.966048	−	0.258364i	$-0.0831832\pi$
$912$	1.68522	−	4.71448i	0.0558033	−	0.156112i
$913$	4.44087	−	4.44087i	0.146971	−	0.146971i
$914$	12.8872	−	44.4523i	0.426270	−	1.47035i
$915$	−39.1764	−	30.3738i	−1.29513	−	1.00413i
$916$	20.6767	+	13.0889i	0.683176	+	0.432468i
$917$	−9.30114	−	9.30114i	−0.307151	−	0.307151i
$918$	6.28233	+	11.4121i	0.207348	+	0.376657i
$919$	40.6104			1.33961			0.669807	−	0.742535i	$-0.266377\pi$
$919$	40.6104			1.33961			0.669807	+	0.742535i	$0.266377\pi$
$920$	27.3016	+	23.9758i	0.900106	+	0.790457i
$921$	−43.3167			−1.42733
$922$	−3.93720	−	7.15211i	−0.129665	−	0.235542i
$923$	1.69711	+	1.69711i	0.0558611	+	0.0558611i
$924$	−8.59685	−	5.44203i	−0.282816	−	0.179030i
$925$	26.9385	+	15.9145i	0.885733	+	0.523267i
$926$	−5.23370	+	18.0528i	−0.171990	+	0.593252i
$927$	−2.79774	+	2.79774i	−0.0918900	+	0.0918900i
$928$	−15.5846	−	11.2554i	−0.511591	−	0.369476i
$929$			14.4830i			0.475171i	0.971367	+	0.237585i	$0.0763560\pi$
$929$			14.4830i			0.475171i	−0.971367	+	0.237585i	$0.923644\pi$
$930$	−23.4726	−	3.69845i	−0.769698	−	0.121277i
$931$			1.90084i			0.0622975i
$932$	−1.68984	−	7.51974i	−0.0553525	−	0.246317i
$933$	29.3384	−	29.3384i	0.960495	−	0.960495i
$934$	−23.5183	−	6.81820i	−0.769542	−	0.223098i
$935$	−2.33378	+	3.01013i	−0.0763227	+	0.0984418i
$936$	−1.97552	−	2.23310i	−0.0645718	−	0.0729911i
$937$	−17.0283	−	17.0283i	−0.556290	−	0.556290i	0.371959	−	0.928249i	$-0.378686\pi$
$937$	−17.0283	−	17.0283i	−0.556290	−	0.556290i	−0.928249	+	0.371959i	$0.878686\pi$
$938$	56.1539	−	30.9125i	1.83349	−	1.00933i
$939$	−2.86116			−0.0933704
$940$	−2.66810	−	7.37923i	−0.0870238	−	0.240684i
$941$	39.7570			1.29604			0.648021	−	0.761623i	$-0.275597\pi$
$941$	39.7570			1.29604			0.648021	+	0.761623i	$0.275597\pi$
$942$	36.9768	−	20.3555i	1.20477	−	0.663219i
$943$	6.63059	+	6.63059i	0.215922	+	0.215922i
$944$	−14.8258	−	31.3214i	−0.482539	−	1.01943i
$945$	4.68127	+	36.9872i	0.152282	+	1.20319i
$946$	14.0467	+	4.07229i	0.456697	+	0.132401i
$947$	32.7101	−	32.7101i	1.06293	−	1.06293i	0.0650523	−	0.997882i	$-0.479279\pi$
$947$	32.7101	−	32.7101i	1.06293	−	1.06293i	0.997882	−	0.0650523i	$-0.0207214\pi$
$948$	31.0029	−	6.96699i	1.00693	−	0.226277i
$949$		−	59.3236i		−	1.92572i
$950$	−3.67587	−	3.90632i	−0.119261	−	0.126738i
$951$			10.8755i			0.352661i
$952$	−14.8265	−	0.907425i	−0.480529	−	0.0294098i
$953$	−35.3644	+	35.3644i	−1.14556	+	1.14556i	−0.158149	+	0.987415i	$0.550553\pi$
$953$	−35.3644	+	35.3644i	−1.14556	+	1.14556i	−0.987415	+	0.158149i	$0.949447\pi$
$954$	−0.755576	+	2.60624i	−0.0244627	+	0.0843801i
$955$	−0.767587	−	6.06477i	−0.0248385	−	0.196251i
$956$	−3.04194	+	4.80540i	−0.0983835	+	0.155418i
$957$	−3.96502	−	3.96502i	−0.128171	−	0.128171i
$958$	−10.8134	−	19.6430i	−0.349364	−	0.634636i
$959$	−35.8847			−1.15878
$960$	20.9472	+	20.7952i	0.676069	+	0.671162i
$961$	10.2608			0.330992
$962$	−16.2166	−	29.4582i	−0.522844	−	0.949771i
$963$	−3.79043	−	3.79043i	−0.122145	−	0.122145i
$964$	5.24852	−	8.29117i	0.169044	−	0.267040i
$965$	−6.33105	+	8.16585i	−0.203804	+	0.262868i
$966$	−11.5089	+	39.6980i	−0.370292	+	1.27726i
$967$	11.9686	−	11.9686i	0.384884	−	0.384884i	−0.487974	−	0.872858i	$-0.662264\pi$
$967$	11.9686	−	11.9686i	0.384884	−	0.384884i	0.872858	+	0.487974i	$0.162264\pi$
$968$	2.82314	+	0.172785i	0.0907393	+	0.00555352i
$969$		−	2.13204i		−	0.0684910i
$970$	−0.869478	+	5.51824i	−0.0279173	+	0.177180i
$971$		−	52.0304i		−	1.66974i	−0.550450	−	0.834868i	$-0.685544\pi$
$971$		−	52.0304i		−	1.66974i	0.550450	−	0.834868i	$-0.314456\pi$
$972$	−5.60706	+	1.26002i	−0.179847	+	0.0404152i
$973$	3.89837	−	3.89837i	0.124976	−	0.124976i
$974$	−21.5181	−	6.23833i	−0.689485	−	0.199889i
$975$	30.3602	−	7.81018i	0.972306	−	0.250126i
$976$	22.9930	+	48.5756i	0.735987	+	1.55487i
$977$	22.4148	+	22.4148i	0.717112	+	0.717112i	0.968013	−	0.250901i	$-0.0807268\pi$
$977$	22.4148	+	22.4148i	0.717112	+	0.717112i	−0.250901	+	0.968013i	$0.580727\pi$
$978$	22.9615	−	12.6402i	0.734228	−	0.404189i
$979$	−6.02286			−0.192491
$980$	−10.1464	−	4.75757i	−0.324114	−	0.151975i
$981$	−1.77036			−0.0565232
$982$	−12.3984	+	6.82528i	−0.395650	+	0.217804i
$983$	7.31758	+	7.31758i	0.233394	+	0.233394i	0.814108	−	0.580714i	$-0.197226\pi$
$983$	7.31758	+	7.31758i	0.233394	+	0.233394i	−0.580714	+	0.814108i	$0.697226\pi$
$984$	5.04726	+	5.70536i	0.160901	+	0.181880i
$985$	−9.26533	−	7.18349i	−0.295218	−	0.228885i
$986$	−7.86268	−	2.27947i	−0.250399	−	0.0725932i
$987$	6.31170	−	6.31170i	0.200904	−	0.200904i
$988$	1.26395	+	5.62453i	0.0402115	+	0.178940i
$989$		−	59.4122i		−	1.88920i
$990$	−0.516212	−	0.709311i	−0.0164063	−	0.0225434i
$991$			30.9389i			0.982805i	0.870933	+	0.491403i	$0.163516\pi$
$991$			30.9389i			0.982805i	−0.870933	+	0.491403i	$0.836484\pi$
$992$	20.8845	+	15.0830i	0.663082	+	0.478884i
$993$	−21.9375	+	21.9375i	−0.696165	+	0.696165i
$994$	−0.766859	+	2.64516i	−0.0243233	+	0.0838993i
$995$	−3.39166	+	0.429264i	−0.107523	+	0.0136086i
$996$	−17.5117	−	11.0853i	−0.554879	−	0.351253i
$997$	8.66091	+	8.66091i	0.274294	+	0.274294i	0.830826	−	0.556532i	$-0.187868\pi$
$997$	8.66091	+	8.66091i	0.274294	+	0.274294i	−0.556532	+	0.830826i	$0.687868\pi$
$998$	9.24009	+	16.7851i	0.292490	+	0.531322i
$999$	−33.8403			−1.07066

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Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	220.2.l.c.67.10	yes	28
4.3	odd	2		220.2.l.d.67.13	yes	28
5.3	odd	4		220.2.l.d.23.13	yes	28
20.3	even	4	inner	220.2.l.c.23.10	✓	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
220.2.l.c.23.10	✓	28	20.3	even	4	inner
220.2.l.c.67.10	yes	28	1.1	even	1	trivial
220.2.l.d.23.13	yes	28	5.3	odd	4
220.2.l.d.67.13	yes	28	4.3	odd	2

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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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

Coefficient data

Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	220.2.l.c.67.10

Level	$220$
Weight	$2$
Character	220.67
Analytic conductor	$1.757$
Analytic rank	$0$
Dimension	$28$
Inner twists	$2$