LMFDB - Embedded newform 220.2.l.d.23.13

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			23.13
Character	$\chi$	$=$	220.23
Dual form			220.2.l.d.67.13

$q$ -expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.23890 - 0.682007i) 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} +(0.172785 - 2.82314i) q^{8} +0.277416i q^{9} +(-2.93982 + 1.16510i) q^{10} +1.00000i q^{11} +(-0.723544 - 3.21975i) 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} +(0.189200 + 0.343690i) q^{18} +0.758569 q^{19} +(-2.84753 + 3.44842i) q^{20} +5.08728 q^{21} +(0.682007 + 1.23890i) 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} +(6.01627 - 1.35198i) q^{28} +3.39836i q^{29} +(-2.07064 + 4.78939i) q^{30} +4.55404i q^{31} +(-4.58592 - 3.31200i) 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} +(0.939789 - 0.517349i) q^{38} -6.26975 q^{39} +(-1.17595 + 6.21427i) q^{40} +1.63221 q^{41} +(6.30262 - 3.46956i) 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} +(-6.21498 - 2.22158i) q^{48} +2.50582i q^{49} +(6.84873 - 1.75922i) q^{50} +2.81061i q^{51} +(-7.41466 + 1.66623i) 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} +(2.31771 + 4.21022i) q^{58} -8.66327 q^{59} +(0.701087 + 7.34576i) q^{60} -13.4356 q^{61} +(3.10588 + 5.64198i) 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} +(0.746938 + 3.32385i) q^{68} +9.47944i q^{69} +(-8.94921 - 3.86909i) q^{70} -0.631635i q^{71} +(0.783186 + 0.0479333i) 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} +(-7.76757 + 4.27601i) q^{78} -9.62897 q^{79} +(2.78129 + 8.50085i) q^{80} +8.09079 q^{81} +(2.02214 - 1.11318i) 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} +(2.82314 + 0.172785i) q^{88} -6.02286i q^{89} +(-0.323218 - 0.815553i) q^{90} -11.7153i q^{91} +(2.51922 + 11.2105i) 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} +(1.70899 + 3.10446i) q^{98} -0.277416 q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$28 q + 2 q^{2} + 4 q^{3} - 4 q^{4} + 2 q^{5} - 12 q^{6} + 2 q^{7} + 2 q^{8} - 6 q^{10} + 8 q^{12} + 6 q^{13} + 20 q^{14} - 8 q^{15} + 8 q^{16} - 14 q^{17} - 6 q^{18} - 4 q^{19} + 8 q^{20} - 16 q^{21} - 2 q^{22}+ \cdots + 20 q^{99}+O(q^{100})$ 28 * q + 2 * q^2 + 4 * q^3 - 4 * q^4 + 2 * q^5 - 12 * q^6 + 2 * q^7 + 2 * q^8 - 6 * q^10 + 8 * q^12 + 6 * q^13 + 20 * q^14 - 8 * q^15 + 8 * q^16 - 14 * q^17 - 6 * 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 + 8 * q^28 - 24 * q^30 - 38 * q^32 + 4 * q^33 + 52 * q^34 + 10 * q^35 - 4 * q^36 + 20 * q^37 - 48 * q^38 - 32 * q^39 + 46 * q^40 + 12 * q^41 + 32 * q^42 - 2 * q^43 - 10 * q^45 + 4 * q^46 + 44 * q^47 + 44 * q^48 - 18 * q^50 - 52 * q^52 - 28 * q^53 + 40 * q^54 + 2 * q^55 + 4 * q^56 - 8 * q^57 - 36 * q^58 + 16 * q^59 - 32 * q^60 - 12 * q^61 + 20 * q^62 + 10 * q^63 - 28 * q^64 - 30 * q^65 - 16 * q^67 + 68 * q^68 - 40 * q^70 - 38 * q^72 + 22 * q^73 + 20 * q^74 + 56 * q^75 + 4 * q^76 - 2 * q^77 - 40 * q^78 + 20 * q^79 + 12 * q^80 + 12 * q^81 + 12 * q^82 - 2 * q^83 - 120 * q^84 - 14 * q^85 - 20 * q^86 + 48 * q^87 + 14 * q^88 - 10 * q^90 + 4 * q^92 - 20 * q^93 + 20 * q^94 - 92 * q^95 + 40 * q^96 + 16 * q^97 - 82 * q^98 + 20 * q^99

Character values

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

$n$	$101$	$111$	$177$
$\chi(n)$	$1$	$-1$	$e\left(\frac{3}{4}\right)$

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

)

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

$2$	1.23890	−	0.682007i	0.876033	−	0.482252i
$2$	1.23890	−	0.682007i	0.876033	−	0.482252i
$3$	1.16674	−	1.16674i	0.673620	−	0.673620i	−0.284929	−	0.958549i	$-0.591970\pi$
$3$	1.16674	−	1.16674i	0.673620	−	0.673620i	0.958549	+	0.284929i	$0.0919699\pi$
$4$	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	$-0.0520116\pi$
$7$	2.18012	+	2.18012i	0.824007	+	0.824007i	−0.162673	+	0.986680i	$0.552012\pi$
$8$	0.172785	−	2.82314i	0.0610887	−	0.998132i
$9$			0.277416i			0.0924720i
$10$	−2.93982	+	1.16510i	−0.929652	+	0.368438i
$11$			1.00000i			0.301511i
$11$			1.00000i			0.301511i
$12$	−0.723544	−	3.21975i	−0.208869	−	0.929463i
$13$	−2.68686	−	2.68686i	−0.745200	−	0.745200i	0.228374	−	0.973574i	$-0.426659\pi$
$13$	−2.68686	−	2.68686i	−0.745200	−	0.745200i	−0.973574	+	0.228374i	$0.926659\pi$
$14$	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	−0.837920	−	0.545794i	$-0.816228\pi$
$17$	−1.20447	+	1.20447i	−0.292126	+	0.292126i	0.545794	+	0.837920i	$0.316228\pi$
$18$	0.189200	+	0.343690i	0.0445948	+	0.0810085i
$19$	0.758569			0.174028			0.0870138	−	0.996207i	$-0.472268\pi$
$19$	0.758569			0.174028			0.0870138	+	0.996207i	$0.472268\pi$
$20$	−2.84753	+	3.44842i	−0.636726	+	0.771090i
$21$	5.08728			1.11014
$22$	0.682007	+	1.23890i	0.145404	+	0.264134i
$23$	−4.06235	+	4.06235i	−0.847058	+	0.847058i	−0.989765	−	0.142707i	$-0.954419\pi$
$23$	−4.06235	+	4.06235i	−0.847058	+	0.847058i	0.142707	+	0.989765i	$0.454419\pi$
$24$	−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
$28$	6.01627	−	1.35198i	1.13697	−	0.255500i
$29$			3.39836i			0.631060i	0.948916	+	0.315530i	$0.102182\pi$
$29$			3.39836i			0.631060i	−0.948916	+	0.315530i	$0.897818\pi$
$30$	−2.07064	+	4.78939i	−0.378046	+	0.874420i
$31$			4.55404i			0.817929i	0.912550	+	0.408965i	$0.134110\pi$
$31$			4.55404i			0.817929i	−0.912550	+	0.408965i	$0.865890\pi$
$32$	−4.58592	−	3.31200i	−0.810684	−	0.585484i
$33$	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	−0.242671	−	0.970109i	$-0.578024\pi$
$37$	4.42483	−	4.42483i	0.727438	−	0.727438i	0.970109	+	0.242671i	$0.0780235\pi$
$38$	0.939789	−	0.517349i	0.152454	−	0.0839251i
$39$	−6.26975			−1.00396
$40$	−1.17595	+	6.21427i	−0.185934	+	0.982562i
$41$	1.63221			0.254908			0.127454	−	0.991844i	$-0.459319\pi$
$41$	1.63221			0.254908			0.127454	+	0.991844i	$0.459319\pi$
$42$	6.30262	−	3.46956i	0.972515	−	0.535365i
$43$	7.31254	−	7.31254i	1.11515	−	1.11515i	0.122710	−	0.992443i	$-0.460842\pi$
$43$	7.31254	−	7.31254i	1.11515	−	1.11515i	0.992443	−	0.122710i	$-0.0391584\pi$
$44$	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	$-0.290845\pi$
$47$	−1.24068	−	1.24068i	−0.180972	−	0.180972i	−0.791779	+	0.610807i	$0.790845\pi$
$48$	−6.21498	−	2.22158i	−0.897054	−	0.320658i
$49$			2.50582i			0.357975i
$50$	6.84873	−	1.75922i	0.968557	−	0.248792i
$51$			2.81061i			0.393564i
$52$	−7.41466	+	1.66623i	−1.02823	+	0.231064i
$53$	−4.89076	−	4.89076i	−0.671798	−	0.671798i	0.286332	−	0.958130i	$-0.407564\pi$
$53$	−4.89076	−	4.89076i	−0.671798	−	0.671798i	−0.958130	+	0.286332i	$0.907564\pi$
$54$	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
$58$	2.31771	+	4.21022i	0.304330	+	0.552830i
$59$	−8.66327			−1.12786			−0.563931	−	0.825822i	$-0.690712\pi$
$59$	−8.66327			−1.12786			−0.563931	+	0.825822i	$0.690712\pi$
$60$	0.701087	+	7.34576i	0.0905099	+	0.948333i
$61$	−13.4356			−1.72026			−0.860129	−	0.510076i	$-0.829617\pi$
$61$	−13.4356			−1.72026			−0.860129	+	0.510076i	$0.829617\pi$
$62$	3.10588	+	5.64198i	0.394448	+	0.716533i
$63$	−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	0.946096	+	0.323886i	$0.104990\pi$
$67$	10.3953	+	10.3953i	1.26998	+	1.26998i	0.323886	+	0.946096i	$0.395010\pi$
$68$	0.746938	+	3.32385i	0.0905795	+	0.403077i
$69$			9.47944i			1.14119i
$70$	−8.94921	−	3.86909i	−1.06964	−	0.462445i
$71$		−	0.631635i		−	0.0749612i	−0.999297	−	0.0374806i	$-0.988067\pi$
$71$		−	0.631635i		−	0.0749612i	0.999297	−	0.0374806i	$-0.0119332\pi$
$72$	0.783186	+	0.0479333i	0.0922993	+	0.00564900i
$73$	−11.0396	−	11.0396i	−1.29209	−	1.29209i	−0.933494	−	0.358592i	$-0.883257\pi$
$73$	−11.0396	−	11.0396i	−1.29209	−	1.29209i	−0.358592	−	0.933494i	$-0.616743\pi$
$74$	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
$78$	−7.76757	+	4.27601i	−0.879504	+	0.484163i
$79$	−9.62897			−1.08334			−0.541672	−	0.840590i	$-0.682209\pi$
$79$	−9.62897			−1.08334			−0.541672	+	0.840590i	$0.682209\pi$
$80$	2.78129	+	8.50085i	0.310958	+	0.950424i
$81$	8.09079			0.898977
$82$	2.02214	−	1.11318i	0.223308	−	0.122930i
$83$	4.44087	−	4.44087i	0.487449	−	0.487449i	−0.420051	−	0.907500i	$-0.637988\pi$
$83$	4.44087	−	4.44087i	0.487449	−	0.487449i	0.907500	+	0.420051i	$0.137988\pi$
$84$	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
$88$	2.82314	+	0.172785i	0.300948	+	0.0184189i
$89$		−	6.02286i		−	0.638422i	−0.947684	−	0.319211i	$-0.896582\pi$
$89$		−	6.02286i		−	0.638422i	0.947684	−	0.319211i	$-0.103418\pi$
$90$	−0.323218	−	0.815553i	−0.0340702	−	0.0859669i
$91$		−	11.7153i		−	1.22810i
$92$	2.51922	+	11.2105i	0.262647	+	1.16877i
$93$	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	−0.767673	−	0.640842i	$-0.778585\pi$
$97$	−1.24914	+	1.24914i	−0.126831	+	0.126831i	0.640842	+	0.767673i	$0.278585\pi$
$98$	1.70899	+	3.10446i	0.172634	+	0.313598i
$99$	−0.277416			−0.0278814
$100$	7.28507	−	6.85038i	0.728507	−	0.685038i
$101$	−9.45271			−0.940580			−0.470290	−	0.882512i	$-0.655851\pi$
$101$	−9.45271			−0.940580			−0.470290	+	0.882512i	$0.655851\pi$
$102$	1.91685	+	3.48206i	0.189797	+	0.344775i
$103$	10.0850	−	10.0850i	0.993705	−	0.993705i	−0.00627506	−	0.999980i	$-0.501997\pi$
$103$	10.0850	−	10.0850i	0.993705	−	0.993705i	0.999980	+	0.00627506i	$0.00199743\pi$
$104$	−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	−0.913061	−	0.407822i	$-0.866288\pi$
$107$	−13.6633	−	13.6633i	−1.32088	−	1.32088i	−0.407822	−	0.913061i	$-0.633712\pi$
$108$	10.5525	−	2.37136i	1.01541	−	0.228184i
$109$			6.38160i			0.611247i	0.952153	+	0.305623i	$0.0988648\pi$
$109$			6.38160i			0.611247i	−0.952153	+	0.305623i	$0.901135\pi$
$110$	−1.16510	−	2.93982i	−0.111088	−	0.280301i
$111$		−	10.3253i		−	0.980033i
$112$	4.15113	−	11.6130i	0.392245	−	1.09732i
$113$	13.6087	+	13.6087i	1.28019	+	1.28019i	0.940556	+	0.339639i	$0.110305\pi$
$113$	13.6087	+	13.6087i	1.28019	+	1.28019i	0.339639	+	0.940556i	$0.389695\pi$
$114$	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
$118$	−10.7329	+	5.90841i	−0.988044	+	0.543913i
$119$	−5.25176			−0.481428
$120$	5.87843	+	8.62249i	0.536625	+	0.787122i
$121$	−1.00000			−0.0909091
$122$	−16.6454	+	9.16320i	−1.50700	+	0.829597i
$123$	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	$-0.0822098\pi$
$127$	8.01735	+	8.01735i	0.711425	+	0.711425i	−0.255408	+	0.966833i	$0.582210\pi$
$128$	−10.5026	+	4.20667i	−0.928305	+	0.371821i
$129$		−	17.0637i		−	1.50238i
$130$	11.0293	+	4.76841i	0.967336	+	0.418217i
$131$			4.26635i			0.372752i	0.982478	+	0.186376i	$0.0596743\pi$
$131$			4.26635i			0.372752i	−0.982478	+	0.186376i	$0.940326\pi$
$132$	3.21975	−	0.723544i	0.280244	−	0.0629764i
$133$	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	−0.261947	−	0.965082i	$-0.584364\pi$
$137$	8.22999	−	8.22999i	0.703136	−	0.703136i	0.965082	+	0.261947i	$0.0843645\pi$
$138$	6.46504	+	11.7441i	0.550341	+	0.999720i
$139$	1.78815			0.151669			0.0758343	−	0.997120i	$-0.475838\pi$
$139$	1.78815			0.151669			0.0758343	+	0.997120i	$0.475838\pi$
$140$	−13.7259	+	1.31001i	−1.16005	+	0.110716i
$141$	−2.89512			−0.243813
$142$	−0.430779	−	0.782530i	−0.0361502	−	0.0656685i
$143$	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
$148$	−2.74401	−	12.2108i	−0.225556	−	1.00372i
$149$		−	8.80481i		−	0.721318i	−0.932698	−	0.360659i	$-0.882552\pi$
$149$		−	8.80481i		−	0.721318i	0.932698	−	0.360659i	$-0.117448\pi$
$150$	5.93816	−	10.0433i	0.484848	−	0.820030i
$151$			15.7849i			1.28456i	0.766472	+	0.642278i	$0.222010\pi$
$151$			15.7849i			1.28456i	−0.766472	+	0.642278i	$0.777990\pi$
$152$	0.131069	−	2.14155i	0.0106311	−	0.173703i
$153$	−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	0.0210155	−	0.999779i	$-0.493310\pi$
$157$	12.7905	−	12.7905i	1.02079	−	1.02079i	0.999779	−	0.0210155i	$-0.00668994\pi$
$158$	−11.9293	+	6.56703i	−0.949045	+	0.522444i
$159$	−11.4125			−0.905073
$160$	9.24337	+	8.63482i	0.730753	+	0.682642i
$161$	−17.7128			−1.39596
$162$	10.0237	−	5.51798i	0.787533	−	0.433533i
$163$	−7.94254	+	7.94254i	−0.622108	+	0.622108i	−0.946070	−	0.323962i	$-0.894985\pi$
$163$	−7.94254	+	7.94254i	−0.622108	+	0.622108i	0.323962	+	0.946070i	$0.394985\pi$
$164$	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	$-0.235098\pi$
$167$	0.855298	+	0.855298i	0.0661849	+	0.0661849i	−0.673240	+	0.739424i	$0.735098\pi$
$168$	0.879005	−	14.3621i	0.0678167	−	1.10806i
$169$			1.43838i			0.110645i
$170$	2.13759	−	4.94424i	0.163946	−	0.379206i
$171$			0.210439i			0.0160927i
$172$	−4.53480	−	20.1797i	−0.345775	−	1.53869i
$173$	11.9611	+	11.9611i	0.909383	+	0.909383i	0.996222	−	0.0868397i	$-0.0276768\pi$
$173$	11.9611	+	11.9611i	0.909383	+	0.909383i	−0.0868397	+	0.996222i	$0.527677\pi$
$174$	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
$178$	−4.10763	−	7.46170i	−0.307880	−	0.559278i
$179$	24.8533			1.85762			0.928811	−	0.370553i	$-0.120832\pi$
$179$	24.8533			1.85762			0.928811	+	0.370553i	$0.120832\pi$
$180$	−0.956647	−	0.789950i	−0.0713042	−	0.0588794i
$181$	22.4425			1.66813			0.834067	−	0.551663i	$-0.186006\pi$
$181$	22.4425			1.66813			0.834067	+	0.551663i	$0.186006\pi$
$182$	−7.98993	−	14.5141i	−0.592253	−	1.07586i
$183$	−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
$188$	−3.42380	+	0.769397i	−0.249706	+	0.0561140i
$189$			16.6731i			1.21279i
$190$	−2.23005	+	0.883810i	−0.161785	+	0.0641183i
$191$			2.73389i			0.197817i	0.995097	+	0.0989085i	$0.0315351\pi$
$191$			2.73389i			0.197817i	−0.995097	+	0.0989085i	$0.968465\pi$
$192$	−10.4026	+	8.12602i	−0.750740	+	0.586445i
$193$	3.26747	+	3.26747i	0.235197	+	0.235197i	0.814858	−	0.579661i	$-0.196815\pi$
$193$	3.26747	+	3.26747i	0.235197	+	0.235197i	−0.579661	+	0.814858i	$0.696815\pi$
$194$	−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	−0.562592	−	0.826734i	$-0.690196\pi$
$197$	3.70741	−	3.70741i	0.264142	−	0.264142i	0.826734	+	0.562592i	$0.190196\pi$
$198$	−0.343690	+	0.189200i	−0.0244250	+	0.0134458i
$199$	−1.52889			−0.108380			−0.0541902	−	0.998531i	$-0.517258\pi$
$199$	−1.52889			−0.108380			−0.0541902	+	0.998531i	$0.517258\pi$
$200$	4.35346	−	13.4554i	0.307836	−	0.951440i
$201$	24.2572			1.71097
$202$	−11.7109	+	6.44681i	−0.823979	+	0.453596i
$203$	−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
$208$	−5.11600	+	14.3123i	−0.354731	+	0.992376i
$209$			0.758569i			0.0524713i
$210$	−14.9557	+	5.92720i	−1.03204	+	0.409016i
$211$			28.2258i			1.94314i	0.236745	+	0.971572i	$0.423920\pi$
$211$			28.2258i			1.94314i	−0.236745	+	0.971572i	$0.576080\pi$
$212$	−13.4966	+	3.03296i	−0.926949	+	0.208304i
$213$	−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
$218$	4.35230	+	7.90615i	0.294775	+	0.535472i
$219$	−25.7608			−1.74075
$220$	−3.44842	−	2.84753i	−0.232492	−	0.191980i
$221$	6.47246			0.435385
$222$	−7.04192	−	12.7920i	−0.472623	−	0.858541i
$223$	−1.73371	+	1.73371i	−0.116098	+	0.116098i	−0.762769	−	0.646671i	$-0.776161\pi$
$223$	−1.73371	+	1.73371i	−0.116098	+	0.116098i	0.646671	+	0.762769i	$0.276161\pi$
$224$	−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	$-0.375945\pi$
$227$	−8.21233	−	8.21233i	−0.545071	−	0.545071i	−0.925011	+	0.379940i	$0.875945\pi$
$228$	−0.548858	−	2.44240i	−0.0363490	−	0.161752i
$229$			12.2356i			0.808553i	0.914637	+	0.404277i	$0.132477\pi$
$229$			12.2356i			0.808553i	−0.914637	+	0.404277i	$0.867523\pi$
$230$	7.20952	−	16.6756i	0.475381	−	1.09956i
$231$			5.08728i			0.334718i
$232$	9.59407	+	0.587186i	0.629882	+	0.0385507i
$233$	−2.72493	−	2.72493i	−0.178516	−	0.178516i	0.612193	−	0.790709i	$-0.290288\pi$
$233$	−2.72493	−	2.72493i	−0.178516	−	0.178516i	−0.790709	+	0.612193i	$0.790288\pi$
$234$	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
$238$	−6.50639	+	3.58174i	−0.421747	+	0.232169i
$239$	−2.84365			−0.183940			−0.0919701	−	0.995762i	$-0.529316\pi$
$239$	−2.84365			−0.183940			−0.0919701	+	0.995762i	$0.529316\pi$
$240$	13.1634	+	6.67325i	0.849692	+	0.430757i
$241$	−4.90638			−0.316048			−0.158024	−	0.987435i	$-0.550512\pi$
$241$	−4.90638			−0.316048			−0.158024	+	0.987435i	$0.550512\pi$
$242$	−1.23890	+	0.682007i	−0.0796393	+	0.0438411i
$243$	−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
$248$	12.8567	+	0.786869i	0.816401	+	0.0499662i
$249$		−	10.3627i		−	0.656711i
$250$	−15.6870	+	1.97971i	−0.992131	+	0.125208i
$251$			7.67142i			0.484216i	0.970249	+	0.242108i	$0.0778388\pi$
$251$			7.67142i			0.484216i	−0.970249	+	0.242108i	$0.922161\pi$
$252$	0.375060	+	1.66901i	0.0236266	+	0.105138i
$253$	−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	−0.965800	−	0.259287i	$-0.916512\pi$
$257$	−11.3263	+	11.3263i	−0.706513	+	0.706513i	0.259287	+	0.965800i	$0.416512\pi$
$258$	−11.6376	−	21.1402i	−0.724524	−	1.31613i
$259$	19.2933			1.19883
$260$	16.9163	−	1.61451i	1.04910	−	0.100128i
$261$	−0.942761			−0.0583554
$262$	2.90968	+	5.28556i	0.179760	+	0.326543i
$263$	9.79931	−	9.79931i	0.604251	−	0.604251i	−0.337186	−	0.941438i	$-0.609475\pi$
$263$	9.79931	−	9.79931i	0.604251	−	0.604251i	0.941438	+	0.337186i	$0.109475\pi$
$264$	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
$268$	28.6868	−	6.44651i	1.75233	−	0.393783i
$269$		−	15.2457i		−	0.929548i	−0.885429	−	0.464774i	$-0.846136\pi$
$269$		−	15.2457i		−	0.929548i	0.885429	−	0.464774i	$-0.153864\pi$
$270$	−15.6968	−	6.78635i	−0.955279	−	0.413004i
$271$		−	6.70035i		−	0.407017i	−0.979073	−	0.203509i	$-0.934765\pi$
$271$		−	6.70035i		−	0.407017i	0.979073	−	0.203509i	$-0.0652345\pi$
$272$	6.41592	+	2.29341i	0.389022	+	0.139058i
$273$	−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	0.0525262	−	0.998620i	$-0.483273\pi$
$277$	17.4946	−	17.4946i	1.05115	−	1.05115i	0.998620	−	0.0525262i	$-0.0167273\pi$
$278$	2.21533	−	1.21953i	0.132867	−	0.0731424i
$279$	−1.26336			−0.0756356
$280$	−16.1115	+	10.9841i	−0.962849	+	0.656427i
$281$	−0.980883			−0.0585146			−0.0292573	−	0.999572i	$-0.509314\pi$
$281$	−0.980883			−0.0585146			−0.0292573	+	0.999572i	$0.509314\pi$
$282$	−3.58676	+	1.97449i	−0.213588	+	0.117579i
$283$	6.47709	−	6.47709i	0.385023	−	0.385023i	−0.487885	−	0.872908i	$-0.662231\pi$
$283$	6.47709	−	6.47709i	0.385023	−	0.385023i	0.872908	+	0.487885i	$0.162231\pi$
$284$	−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
$288$	0.918801	−	1.27221i	0.0541409	−	0.0749656i
$289$			14.0985i			0.829325i
$290$	−3.95944	−	9.99058i	−0.232506	−	0.586667i
$291$			2.91485i			0.170872i
$292$	−30.4649	+	6.84609i	−1.78283	+	0.400637i
$293$	−2.23641	−	2.23641i	−0.130652	−	0.130652i	0.638757	−	0.769409i	$-0.279449\pi$
$293$	−2.23641	−	2.23641i	−0.130652	−	0.130652i	−0.769409	+	0.638757i	$0.779449\pi$
$294$	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
$298$	−6.00494	−	10.9083i	−0.347857	−	0.631898i
$299$	21.8299			1.26245
$300$	0.507179	−	16.4925i	0.0292820	−	0.952192i
$301$	31.8844			1.83779
$302$	10.7654	+	19.5558i	0.619479	+	1.12531i
$303$	−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	−0.998117	−	0.0613318i	$-0.980465\pi$
$307$	−18.5631	−	18.5631i	−1.05945	−	1.05945i	−0.0613318	−	0.998117i	$-0.519535\pi$
$308$	1.35198	+	6.01627i	0.0770360	+	0.342809i
$309$		−	23.5332i		−	1.33876i
$310$	−5.30592	−	13.3880i	−0.301356	−	0.760390i
$311$			25.1455i			1.42587i	0.701230	+	0.712935i	$0.252635\pi$
$311$			25.1455i			1.42587i	−0.701230	+	0.712935i	$0.747365\pi$
$312$	−1.08332	+	17.7004i	−0.0613308	+	1.00209i
$313$	1.22613	+	1.22613i	0.0693049	+	0.0693049i	0.740910	−	0.671605i	$-0.234395\pi$
$313$	1.22613	+	1.22613i	0.0693049	+	0.0693049i	−0.671605	+	0.740910i	$0.734395\pi$
$314$	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	−0.825771	−	0.564005i	$-0.809260\pi$
$317$	−4.66060	+	4.66060i	−0.261766	+	0.261766i	0.564005	+	0.825771i	$0.309260\pi$
$318$	−14.1390	+	7.78343i	−0.792874	+	0.436473i
$319$	−3.39836			−0.190272
$320$	17.3406	+	4.39361i	0.969369	+	0.245610i
$321$	−31.8832			−1.77955
$322$	−21.9443	+	12.0802i	−1.22291	+	0.673206i
$323$	−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
$328$	0.282021	−	4.60796i	0.0155720	−	0.254432i
$329$		−	5.40967i		−	0.298245i
$330$	−4.78939	−	2.07064i	−0.263647	−	0.113985i
$331$		−	18.8023i		−	1.03347i	−0.856146	−	0.516734i	$-0.827147\pi$
$331$		−	18.8023i		−	1.03347i	0.856146	−	0.516734i	$-0.172853\pi$
$332$	−2.75396	−	12.2551i	−0.151143	−	0.672584i
$333$	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	−0.546342	−	0.837562i	$-0.683980\pi$
$337$	5.34610	−	5.34610i	0.291221	−	0.291221i	0.837562	+	0.546342i	$0.183980\pi$
$338$	0.980988	+	1.78201i	0.0533587	+	0.0969286i
$339$	31.7556			1.72473
$340$	−0.723754	−	7.58326i	−0.0392511	−	0.411260i
$341$	−4.55404			−0.246615
$342$	0.143521	+	0.260712i	0.00776072	+	0.0140977i
$343$	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	$-0.282423\pi$
$347$	−2.67879	−	2.67879i	−0.143805	−	0.143805i	−0.775344	+	0.631539i	$0.782423\pi$
$348$	10.9419	−	2.45887i	0.586547	−	0.131809i
$349$		−	6.17389i		−	0.330481i	−0.986253	−	0.165240i	$-0.947160\pi$
$349$		−	6.17389i		−	0.330481i	0.986253	−	0.165240i	$-0.0528400\pi$
$350$	18.7664	+	11.0957i	1.00310	+	0.593092i
$351$		−	20.5486i		−	1.09680i
$352$	3.31200	−	4.58592i	0.176530	−	0.244430i
$353$	0.680259	+	0.680259i	0.0362065	+	0.0362065i	0.724978	−	0.688772i	$-0.241850\pi$
$353$	0.680259	+	0.680259i	0.0362065	+	0.0362065i	−0.688772	+	0.724978i	$0.741850\pi$
$354$	−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
$358$	30.7907	−	16.9501i	1.62734	−	0.895842i
$359$	10.2380			0.540343			0.270171	−	0.962812i	$-0.412920\pi$
$359$	10.2380			0.540343			0.270171	+	0.962812i	$0.412920\pi$
$360$	−1.72394	−	0.326227i	−0.0908595	−	0.0171937i
$361$	−18.4246			−0.969714
$362$	27.8039	−	15.3059i	1.46134	−	0.804461i
$363$	−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	$-0.257709\pi$
$367$	−0.656087	−	0.656087i	−0.0342475	−	0.0342475i	−0.724023	+	0.689776i	$0.757709\pi$
$368$	21.6392	+	7.73506i	1.12802	+	0.403218i
$369$			0.452801i			0.0235719i
$370$	−7.85282	+	18.1636i	−0.408249	+	0.944280i
$371$		−	21.3249i		−	1.10713i
$372$	14.6629	−	3.29505i	0.760235	−	0.170840i
$373$	−16.0294	−	16.0294i	−0.829973	−	0.829973i	0.157539	−	0.987513i	$-0.449644\pi$
$373$	−16.0294	−	16.0294i	−0.829973	−	0.829973i	−0.987513	+	0.157539i	$0.949644\pi$
$374$	−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
$378$	11.3712	+	20.6563i	0.584871	+	1.06245i
$379$	10.5671			0.542797			0.271398	−	0.962467i	$-0.412514\pi$
$379$	10.5671			0.542797			0.271398	+	0.962467i	$0.412514\pi$
$380$	−2.16004	+	2.61586i	−0.110808	+	0.134191i
$381$	18.7084			0.958461
$382$	1.86453	+	3.38700i	0.0953976	+	0.173294i
$383$	−9.17419	+	9.17419i	−0.468779	+	0.468779i	−0.901519	−	0.432740i	$-0.857547\pi$
$383$	−9.17419	+	9.17419i	−0.468779	+	0.468779i	0.432740	+	0.901519i	$0.357547\pi$
$384$	−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
$388$	0.774640	+	3.44713i	0.0393264	+	0.175002i
$389$			32.0338i			1.62418i	0.583533	+	0.812090i	$0.301670\pi$
$389$			32.0338i			1.62418i	−0.583533	+	0.812090i	$0.698330\pi$
$390$	18.4319	−	7.30489i	0.933337	−	0.369898i
$391$		−	9.78592i		−	0.494895i
$392$	7.07431	+	0.432969i	0.357306	+	0.0218682i
$393$	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	−0.999997	−	0.00236570i	$-0.999247\pi$
$397$	−19.8777	+	19.8777i	−0.997631	+	0.997631i	0.00236570	+	0.999997i	$0.499247\pi$
$398$	−1.89414	+	1.04272i	−0.0949448	+	0.0522667i
$399$	3.85905			0.193194
$400$	−3.78318	−	19.6389i	−0.189159	−	0.981946i
$401$	1.54373			0.0770900			0.0385450	−	0.999257i	$-0.487728\pi$
$401$	1.54373			0.0770900			0.0385450	+	0.999257i	$0.487728\pi$
$402$	30.0522	−	16.5436i	1.49887	−	0.825119i
$403$	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
$408$	7.93476	+	0.485631i	0.392829	+	0.0240423i
$409$		−	23.7072i		−	1.17225i	−0.810222	−	0.586123i	$-0.800653\pi$
$409$		−	23.7072i		−	1.17225i	0.810222	−	0.586123i	$-0.199347\pi$
$410$	−4.79840	+	1.90169i	−0.236976	+	0.0939177i
$411$		−	19.2046i		−	0.947292i
$412$	−6.25411	−	27.8306i	−0.308118	−	1.37112i
$413$	−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
$418$	0.517349	+	0.939789i	0.0253044	+	0.0459666i
$419$	−8.70587			−0.425310			−0.212655	−	0.977127i	$-0.568211\pi$
$419$	−8.70587			−0.425310			−0.212655	+	0.977127i	$0.568211\pi$
$420$	−14.4862	+	17.5431i	−0.706852	+	0.856014i
$421$	−17.2077			−0.838650			−0.419325	−	0.907836i	$-0.637733\pi$
$421$	−17.2077			−0.838650			−0.419325	+	0.907836i	$0.637733\pi$
$422$	19.2502	+	34.9689i	0.937084	+	1.70226i
$423$	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
$428$	−37.7054	+	8.47317i	−1.82256	+	0.409566i
$429$		−	6.26975i		−	0.302706i
$430$	−12.9777	+	30.0174i	−0.625840	+	1.44757i
$431$		−	5.51203i		−	0.265505i	−0.991149	−	0.132753i	$-0.957618\pi$
$431$		−	5.51203i		−	0.265505i	0.991149	−	0.132753i	$-0.0423816\pi$
$432$	7.28105	−	20.3691i	0.350309	−	0.980007i
$433$	18.5184	+	18.5184i	0.889938	+	0.889938i	0.994517	−	0.104579i	$-0.0333495\pi$
$433$	18.5184	+	18.5184i	0.889938	+	0.889938i	−0.104579	+	0.994517i	$0.533349\pi$
$434$	−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
$438$	−31.9149	+	17.5690i	−1.52495	+	0.839480i
$439$	−6.02886			−0.287742			−0.143871	−	0.989596i	$-0.545955\pi$
$439$	−6.02886			−0.287742			−0.143871	+	0.989596i	$0.545955\pi$
$440$	−6.21427	−	1.17595i	−0.296254	−	0.0560611i
$441$	−0.695156			−0.0331027
$442$	8.01871	−	4.41426i	0.381411	−	0.209965i
$443$	−9.54363	+	9.54363i	−0.453432	+	0.453432i	−0.896492	−	0.443060i	$-0.853893\pi$
$443$	−9.54363	+	9.54363i	−0.453432	+	0.453432i	0.443060	+	0.896492i	$0.353893\pi$
$444$	−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
$448$	−15.1839	−	19.4377i	−0.717370	−	0.918344i
$449$		−	2.70728i		−	0.127764i	−0.997957	−	0.0638822i	$-0.979652\pi$
$449$		−	2.70728i		−	0.127764i	0.997957	−	0.0638822i	$-0.0203482\pi$
$450$	0.488037	+	1.89995i	0.0230063	+	0.0895644i
$451$			1.63221i			0.0768577i
$452$	37.5545	−	8.43927i	1.76642	−	0.396950i
$453$	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	−0.0862301	+	0.996275i	$0.527482\pi$
$457$	−23.1413	+	23.1413i	−1.08251	+	1.08251i	−0.996275	+	0.0862301i	$0.972518\pi$
$458$	8.34479	+	15.1587i	0.389926	+	0.708319i
$459$	−9.21154			−0.429958
$460$	−2.44103	−	25.5763i	−0.113814	−	1.19250i
$461$	−5.77296			−0.268874			−0.134437	−	0.990922i	$-0.542923\pi$
$461$	−5.77296			−0.268874			−0.134437	+	0.990922i	$0.542923\pi$
$462$	3.46956	+	6.30262i	0.161418	+	0.293224i
$463$	−9.39808	+	9.39808i	−0.436766	+	0.436766i	−0.890922	−	0.454156i	$-0.849941\pi$
$463$	−9.39808	+	9.39808i	−0.436766	+	0.436766i	0.454156	+	0.890922i	$0.349941\pi$
$464$	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	$-0.118797\pi$
$467$	12.2433	+	12.2433i	0.566554	+	0.566554i	−0.364607	+	0.931161i	$0.618797\pi$
$468$	−0.462238	−	2.05695i	−0.0213669	−	0.0950824i
$469$			45.3257i			2.09295i
$470$	5.09291	+	2.20186i	0.234918	+	0.101564i
$471$		−	29.8465i		−	1.37526i
$472$	−1.49688	+	24.4577i	−0.0688997	+	1.12576i
$473$	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
$478$	−3.52299	+	1.93939i	−0.161138	+	0.0887055i
$479$	15.8552			0.724443			0.362222	−	0.932092i	$-0.382018\pi$
$479$	15.8552			0.724443			0.362222	+	0.932092i	$0.382018\pi$
$480$	20.8593	−	0.710033i	0.952091	−	0.0324084i
$481$	−23.7778			−1.08417
$482$	−6.07851	+	3.34619i	−0.276868	+	0.152415i
$483$	−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	$-0.133139\pi$
$487$	11.2021	+	11.2021i	0.507615	+	0.507615i	−0.406179	+	0.913794i	$0.633139\pi$
$488$	−2.32148	+	37.9308i	−0.105088	+	1.71705i
$489$			18.5338i			0.838129i
$490$	−2.91954	−	7.36667i	−0.131891	−	0.332792i
$491$			10.0076i			0.451639i	0.974169	+	0.225819i	$0.0725059\pi$
$491$			10.0076i			0.451639i	−0.974169	+	0.225819i	$0.927494\pi$
$492$	−1.18097	−	5.25531i	−0.0532424	−	0.236928i
$493$	−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
$498$	−7.06745	−	12.8383i	−0.316700	−	0.575300i
$499$	−13.5484			−0.606509			−0.303255	−	0.952910i	$-0.598073\pi$
$499$	−13.5484			−0.606509			−0.303255	+	0.952910i	$0.598073\pi$
$500$	−18.0844	+	13.1513i	−0.808757	+	0.588143i
$501$	1.99583			0.0891670
$502$	5.23196	+	9.50410i	0.233514	+	0.424189i
$503$	16.5958	−	16.5958i	0.739970	−	0.739970i	−0.232602	−	0.972572i	$-0.574724\pi$
$503$	16.5958	−	16.5958i	0.739970	−	0.739970i	0.972572	+	0.232602i	$0.0747239\pi$
$504$	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
$508$	22.1247	−	4.97188i	0.981627	−	0.220591i
$509$		−	31.0707i		−	1.37719i	−0.725148	−	0.688593i	$-0.758229\pi$
$509$		−	31.0707i		−	1.37719i	0.725148	−	0.688593i	$-0.241771\pi$
$510$	−3.27465	−	8.26268i	−0.145004	−	0.365878i
$511$		−	48.1352i		−	2.12938i
$512$	−4.12621	+	22.2480i	−0.182354	+	0.983233i
$513$	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
$518$	23.9024	−	13.1582i	1.05021	−	0.578136i
$519$	27.9110			1.22516
$520$	19.8564	−	13.5372i	0.870763	−	0.593647i
$521$	34.2806			1.50186			0.750930	−	0.660381i	$-0.229605\pi$
$521$	34.2806			1.50186			0.750930	+	0.660381i	$0.229605\pi$
$522$	−1.16798	+	0.642969i	−0.0511213	+	0.0281420i
$523$	−4.41610	+	4.41610i	−0.193103	+	0.193103i	−0.797035	−	0.603933i	$-0.793600\pi$
$523$	−4.41610	+	4.41610i	−0.193103	+	0.193103i	0.603933	+	0.797035i	$0.293600\pi$
$524$	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
$528$	2.22158	−	6.21498i	0.0966819	−	0.270472i
$529$		−	10.0053i		−	0.435014i
$530$	20.0762	+	8.67972i	0.872054	+	0.377023i
$531$		−	2.40333i		−	0.104296i
$532$	4.56375	−	1.02557i	0.197864	−	0.0444640i
$533$	−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
$538$	−10.3977	−	18.8879i	−0.448276	−	0.814314i
$539$	−2.50582			−0.107934
$540$	−24.0751	+	2.29775i	−1.03603	+	0.0988796i
$541$	−2.99477			−0.128755			−0.0643776	−	0.997926i	$-0.520506\pi$
$541$	−2.99477			−0.128755			−0.0643776	+	0.997926i	$0.520506\pi$
$542$	−4.56969	−	8.30105i	−0.196285	−	0.356561i
$543$	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	$-0.128353\pi$
$547$	12.3349	+	12.3349i	0.527404	+	0.527404i	−0.392394	+	0.919797i	$0.628353\pi$
$548$	−5.10374	−	22.7115i	−0.218021	−	0.970189i
$549$		−	3.72726i		−	0.159076i
$550$	1.75922	+	6.84873i	0.0750135	+	0.292031i
$551$			2.57789i			0.109822i
$552$	26.7618	+	1.63790i	1.13906	+	0.0697139i
$553$	−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	−0.280795	−	0.959768i	$-0.590598\pi$
$557$	16.0243	−	16.0243i	0.678973	−	0.678973i	0.959768	+	0.280795i	$0.0905980\pi$
$558$	−1.56518	+	0.861622i	−0.0662592	+	0.0364754i
$559$	−39.2955			−1.66202
$560$	−12.4693	+	24.5964i	−0.526924	+	1.03939i
$561$	−2.81061			−0.118664
$562$	−1.21521	+	0.668969i	−0.0512607	+	0.0282187i
$563$	−18.2100	+	18.2100i	−0.767461	+	0.767461i	−0.977659	−	0.210198i	$-0.932589\pi$
$563$	−18.2100	+	18.2100i	−0.767461	+	0.767461i	0.210198	+	0.977659i	$0.432589\pi$
$564$	−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
$568$	−1.78320	−	0.109137i	−0.0748212	−	0.00457929i
$569$		−	5.82173i		−	0.244060i	−0.992526	−	0.122030i	$-0.961060\pi$
$569$		−	5.82173i		−	0.244060i	0.992526	−	0.122030i	$-0.0389404\pi$
$570$	−1.57072	+	3.63308i	−0.0657904	+	0.152173i
$571$			22.1494i			0.926923i	0.886117	+	0.463461i	$0.153393\pi$
$571$			22.1494i			0.926923i	−0.886117	+	0.463461i	$0.846607\pi$
$572$	−1.66623	−	7.41466i	−0.0696684	−	0.310023i
$573$	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	−0.700840	−	0.713319i	$-0.747191\pi$
$577$	0.299763	−	0.299763i	0.0124793	−	0.0124793i	0.713319	+	0.700840i	$0.247191\pi$
$578$	9.61529	+	17.4666i	0.399943	+	0.726516i
$579$	7.62460			0.316867
$580$	−11.7190	−	9.67693i	−0.486604	−	0.401813i
$581$	19.3632			0.803323
$582$	1.98795	+	3.61120i	0.0824031	+	0.149689i
$583$	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	$-0.307271\pi$
$587$	−6.13158	−	6.13158i	−0.253077	−	0.253077i	−0.822231	+	0.569154i	$0.807271\pi$
$588$	8.06814	−	1.81308i	0.332725	−	0.0747700i
$589$			3.45455i			0.142342i
$590$	25.4685	−	10.0936i	1.04852	−	0.415547i
$591$		−	8.65119i		−	0.355863i
$592$	−23.5700	−	8.42526i	−0.968723	−	0.346276i
$593$	1.76457	+	1.76457i	0.0724624	+	0.0724624i	0.742409	−	0.669947i	$-0.233683\pi$
$593$	1.76457	+	1.76457i	0.0724624	+	0.0724624i	−0.669947	+	0.742409i	$0.733683\pi$
$594$	−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
$598$	27.0450	−	14.8881i	1.10595	−	0.608821i
$599$	37.9941			1.55240			0.776198	−	0.630490i	$-0.217146\pi$
$599$	37.9941			1.55240			0.776198	+	0.630490i	$0.217146\pi$
$600$	−10.6196	−	20.7784i	−0.433544	−	0.848273i
$601$	5.33565			0.217646			0.108823	−	0.994061i	$-0.465292\pi$
$601$	5.33565			0.217646			0.108823	+	0.994061i	$0.465292\pi$
$602$	39.5015	−	21.7454i	1.60996	−	0.886276i
$603$	−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	$-0.455131\pi$
$607$	−20.9316	−	20.9316i	−0.849586	−	0.849586i	−0.990081	+	0.140495i	$0.955131\pi$
$608$	−3.47874	−	2.51238i	−0.141081	−	0.101890i
$609$			17.2884i			0.700562i
$610$	39.4984	−	15.6539i	1.59924	−	0.633808i
$611$			6.66707i			0.269721i
$612$	−0.922091	+	0.207213i	−0.0372733	+	0.00837607i
$613$	5.39906	+	5.39906i	0.218066	+	0.218066i	0.807683	−	0.589617i	$-0.200721\pi$
$613$	5.39906	+	5.39906i	0.218066	+	0.218066i	−0.589617	+	0.807683i	$0.700721\pi$
$614$	−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	−0.452789	−	0.891618i	$-0.649571\pi$
$617$	10.9003	−	10.9003i	0.438829	−	0.438829i	0.891618	+	0.452789i	$0.149571\pi$
$618$	−16.0498	−	29.1553i	−0.645619	−	1.17280i
$619$	−10.5326			−0.423339			−0.211670	−	0.977341i	$-0.567890\pi$
$619$	−10.5326			−0.423339			−0.211670	+	0.977341i	$0.567890\pi$
$620$	−15.7042	−	12.9677i	−0.630697	−	0.520797i
$621$	−31.0681			−1.24672
$622$	17.1494	+	31.1527i	0.687628	+	1.24911i
$623$	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
$628$	−7.93191	−	35.2968i	−0.316518	−	1.40850i
$629$			10.6591i			0.425007i
$630$	1.07335	−	2.48266i	0.0427632	−	0.0989114i
$631$		−	26.9699i		−	1.07366i	−0.843692	−	0.536828i	$-0.819623\pi$
$631$		−	26.9699i		−	1.07366i	0.843692	−	0.536828i	$-0.180377\pi$
$632$	−1.66374	+	27.1840i	−0.0661801	+	1.08132i
$633$	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
$638$	−4.21022	+	2.31771i	−0.166684	+	0.0917589i
$639$	0.175226			0.00693182
$640$	24.4797	−	6.38318i	0.967645	−	0.252317i
$641$	−19.0604			−0.752839			−0.376420	−	0.926449i	$-0.622845\pi$
$641$	−19.0604			−0.752839			−0.376420	+	0.926449i	$0.622845\pi$
$642$	−39.5000	+	21.7446i	−1.55894	+	0.858190i
$643$	−27.8666	+	27.8666i	−1.09895	+	1.09895i	−0.104417	+	0.994534i	$0.533298\pi$
$643$	−27.8666	+	27.8666i	−1.09895	+	1.09895i	−0.994534	+	0.104417i	$0.966702\pi$
$644$	−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	0.995907	+	0.0903845i	$0.0288096\pi$
$647$	27.6311	+	27.6311i	1.08629	+	1.08629i	0.0903845	+	0.995907i	$0.471190\pi$
$648$	1.39797	−	22.8415i	0.0549174	−	0.897298i
$649$		−	8.66327i		−	0.340063i
$650$	−23.1283	−	13.6748i	−0.907168	−	0.536369i
$651$			23.1677i			0.908012i
$652$	4.92548	+	21.9183i	0.192897	+	0.858387i
$653$	−16.4296	−	16.4296i	−0.642940	−	0.642940i	0.308337	−	0.951277i	$-0.400227\pi$
$653$	−16.4296	−	16.4296i	−0.642940	−	0.642940i	−0.951277	+	0.308337i	$0.900227\pi$
$654$	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
$658$	−3.68943	−	6.70203i	−0.143829	−	0.261272i
$659$	29.3260			1.14238			0.571189	−	0.820818i	$-0.306482\pi$
$659$	29.3260			1.14238			0.571189	+	0.820818i	$0.306482\pi$
$660$	−7.34576	+	0.701087i	−0.285933	+	0.0272898i
$661$	−46.7121			−1.81689			−0.908445	−	0.418005i	$-0.862729\pi$
$661$	−46.7121			−1.81689			−0.908445	+	0.418005i	$0.862729\pi$
$662$	−12.8233	−	23.2941i	−0.498392	−	0.905352i
$663$	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
$668$	2.36029	−	0.530404i	0.0913222	−	0.0205220i
$669$			4.04560i			0.156412i
$670$	−42.6717	−	18.4486i	−1.64855	−	0.712733i
$671$		−	13.4356i		−	0.518677i
$672$	−23.3299	−	16.8491i	−0.899969	−	0.649966i
$673$	−11.6306	−	11.6306i	−0.448326	−	0.448326i	0.446472	−	0.894798i	$-0.352680\pi$
$673$	−11.6306	−	11.6306i	−0.448326	−	0.448326i	−0.894798	+	0.446472i	$0.852680\pi$
$674$	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	−0.420358	−	0.907358i	$-0.638096\pi$
$677$	12.6714	−	12.6714i	0.487000	−	0.487000i	0.907358	+	0.420358i	$0.138096\pi$
$678$	39.3420	−	21.6576i	1.51092	−	0.831754i
$679$	−5.44654			−0.209019
$680$	−6.06849	−	8.90127i	−0.232716	−	0.341348i
$681$	−19.1634			−0.734342
$682$	−5.64198	+	3.10588i	−0.216043	+	0.118930i
$683$	6.70569	−	6.70569i	0.256586	−	0.256586i	−0.567078	−	0.823664i	$-0.691926\pi$
$683$	6.70569	−	6.70569i	0.256586	−	0.256586i	0.823664	+	0.567078i	$0.191926\pi$
$684$	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
$688$	−38.9522	−	13.9237i	−1.48504	−	0.530836i
$689$			26.2816i			1.00125i
$690$	−11.0445	−	27.8678i	−0.420457	−	1.06091i
$691$			25.4431i			0.967899i	0.875096	+	0.483950i	$0.160798\pi$
$691$			25.4431i			0.967899i	−0.875096	+	0.483950i	$0.839202\pi$
$692$	33.0078	−	7.41753i	1.25477	−	0.281972i
$693$	−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
$698$	−4.21063	−	7.64881i	−0.159375	−	0.289512i
$699$	−6.35859			−0.240504
$700$	30.8169	+	0.947689i	1.16477	+	0.0358193i
$701$	2.58249			0.0975392			0.0487696	−	0.998810i	$-0.484470\pi$
$701$	2.58249			0.0975392			0.0487696	+	0.998810i	$0.484470\pi$
$702$	−14.0143	−	25.4576i	−0.528934	−	0.960834i
$703$	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
$708$	6.26826	+	27.8936i	0.235576	+	1.04831i
$709$		−	21.4440i		−	0.805347i	−0.915344	−	0.402674i	$-0.868081\pi$
$709$		−	21.4440i		−	0.805347i	0.915344	−	0.402674i	$-0.131919\pi$
$710$	0.735919	+	1.85689i	0.0276185	+	0.0696879i
$711$		−	2.67123i		−	0.100179i
$712$	−17.0034	−	1.04066i	−0.637229	−	0.0390004i
$713$	−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
$718$	12.6839	−	6.98241i	0.473358	−	0.260581i
$719$	34.4454			1.28460			0.642299	−	0.766455i	$-0.277981\pi$
$719$	34.4454			1.28460			0.642299	+	0.766455i	$0.277981\pi$
$720$	−2.35827	+	0.771576i	−0.0878876	+	0.0287549i
$721$	43.9730			1.63764
$722$	−22.8262	+	12.5657i	−0.849502	+	0.467646i
$723$	−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	$-0.160970\pi$
$727$	10.5267	+	10.5267i	0.390414	+	0.390414i	−0.484421	+	0.874835i	$0.660970\pi$
$728$	−33.0740	−	2.02423i	−1.22581	−	0.0750230i
$729$			29.0136i			1.07458i
$730$	45.3167	+	19.5922i	1.67724	+	0.725138i
$731$			17.6154i			0.651530i
$732$	9.72128	+	43.2595i	0.359309	+	1.59892i
$733$	14.2088	+	14.2088i	0.524813	+	0.524813i	0.919021	−	0.394208i	$-0.128981\pi$
$733$	14.2088	+	14.2088i	0.524813	+	0.524813i	−0.394208	+	0.919021i	$0.628981\pi$
$734$	−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
$738$	0.308813	+	0.560974i	0.0113676	+	0.0206497i
$739$	−49.1754			−1.80895			−0.904474	−	0.426530i	$-0.859736\pi$
$739$	−49.1754			−1.80895			−0.904474	+	0.426530i	$0.859736\pi$
$740$	2.65884	+	27.8585i	0.0977410	+	1.02410i
$741$	−4.75603			−0.174717
$742$	−14.5437	−	26.4193i	−0.533917	−	0.969884i
$743$	4.06425	−	4.06425i	0.149103	−	0.149103i	−0.628614	−	0.777717i	$-0.716378\pi$
$743$	4.06425	−	4.06425i	0.149103	−	0.149103i	0.777717	+	0.628614i	$0.216378\pi$
$744$	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
$748$	−3.32385	+	0.746938i	−0.121532	+	0.0273107i
$749$		−	59.5753i		−	2.17683i
$750$	−15.9929	+	20.6125i	−0.583977	+	0.752661i
$751$		−	8.00983i		−	0.292283i	−0.989264	−	0.146141i	$-0.953315\pi$
$751$		−	8.00983i		−	0.292283i	0.989264	−	0.146141i	$-0.0466855\pi$
$752$	−2.36237	+	6.60883i	−0.0861467	+	0.240999i
$753$	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	−0.299078	−	0.954229i	$-0.596679\pi$
$757$	18.0256	−	18.0256i	0.655151	−	0.655151i	0.954229	+	0.299078i	$0.0966791\pi$
$758$	13.0916	−	7.20685i	0.475508	−	0.261765i
$759$	−9.47944			−0.344082
$760$	−0.892038	+	4.71395i	−0.0323576	+	0.170993i
$761$	−6.07320			−0.220153			−0.110077	−	0.993923i	$-0.535110\pi$
$761$	−6.07320			−0.220153			−0.110077	+	0.993923i	$0.535110\pi$
$762$	23.1778	−	12.7593i	0.839643	−	0.462219i
$763$	−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
$768$	2.60398	+	26.2717i	0.0939629	+	0.947997i
$769$		−	26.6491i		−	0.960990i	−0.876997	−	0.480495i	$-0.840457\pi$
$769$		−	26.6491i		−	0.960990i	0.876997	−	0.480495i	$-0.159543\pi$
$770$	3.86909	−	8.94921i	0.139432	−	0.322507i
$771$			26.4297i			0.951843i
$772$	9.01692	−	2.02629i	0.324526	−	0.0729276i
$773$	−12.5678	−	12.5678i	−0.452033	−	0.452033i	0.443996	−	0.896029i	$-0.353560\pi$
$773$	−12.5678	−	12.5678i	−0.452033	−	0.452033i	−0.896029	+	0.443996i	$0.853560\pi$
$774$	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
$778$	21.8473	+	39.6866i	0.783263	+	1.42283i
$779$	1.23814			0.0443610
$780$	17.8533	−	21.6207i	0.639250	−	0.774146i
$781$	0.631635			0.0226017
$782$	−6.67407	−	12.1238i	−0.238664	−	0.433545i
$783$	−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	$-0.214336\pi$
$787$	4.43581	+	4.43581i	0.158120	+	0.158120i	−0.623613	+	0.781733i	$0.714336\pi$
$788$	−2.29911	−	10.2310i	−0.0819024	−	0.364464i
$789$		−	22.8666i		−	0.814072i
$790$	28.3074	−	11.2187i	1.00713	−	0.399145i
$791$			59.3369i			2.10978i
$792$	−0.0479333	+	0.783186i	−0.00170324	+	0.0278293i
$793$	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	−0.979988	−	0.199059i	$-0.936212\pi$
$797$	−22.0465	+	22.0465i	−0.780929	+	0.780929i	0.199059	+	0.979988i	$0.436212\pi$
$798$	4.78097	−	2.63190i	0.169244	−	0.0931682i
$799$	2.98872			0.105733
$800$	−18.0809	−	21.7505i	−0.639255	−	0.768995i
$801$	1.67084			0.0590362
$802$	1.91252	−	1.05283i	0.0675334	−	0.0371768i
$803$	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
$808$	−1.63329	+	26.6864i	−0.0574588	+	0.938823i
$809$			9.01158i			0.316830i	0.987373	+	0.158415i	$0.0506384\pi$
$809$			9.01158i			0.316830i	−0.987373	+	0.158415i	$0.949362\pi$
$810$	−23.7855	+	9.42660i	−0.835736	+	0.331217i
$811$			25.0356i			0.879118i	0.898214	+	0.439559i	$0.144865\pi$
$811$			25.0356i			0.879118i	−0.898214	+	0.439559i	$0.855135\pi$
$812$	4.59451	+	20.4455i	0.161236	+	0.717495i
$813$	−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
$818$	−16.1685	−	29.3708i	−0.565318	−	1.02693i
$819$	3.25002			0.113565
$820$	−4.64776	+	5.62854i	−0.162307	+	0.196557i
$821$	19.3965			0.676944			0.338472	−	0.940976i	$-0.390090\pi$
$821$	19.3965			0.676944			0.338472	+	0.940976i	$0.390090\pi$
$822$	−13.0977	−	23.7925i	−0.456833	−	0.829859i
$823$	19.9050	−	19.9050i	0.693846	−	0.693846i	−0.269230	−	0.963076i	$-0.586769\pi$
$823$	19.9050	−	19.9050i	0.693846	−	0.693846i	0.963076	+	0.269230i	$0.0867693\pi$
$824$	−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	$-0.499677\pi$
$827$	−28.7284	−	28.7284i	−0.998985	−	0.998985i	−0.999999	+	0.00101496i	$0.999677\pi$
$828$	−3.10997	+	0.698873i	−0.108079	+	0.0242875i
$829$		−	37.2557i		−	1.29394i	−0.762514	−	0.646972i	$-0.776035\pi$
$829$		−	37.2557i		−	1.29394i	0.762514	−	0.646972i	$-0.223965\pi$
$830$	−7.88129	+	18.2294i	−0.273564	+	0.632753i
$831$		−	40.8233i		−	1.41615i
$832$	18.7131	+	23.9557i	0.648761	+	0.830514i
$833$	−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
$838$	−10.7857	+	5.93746i	−0.372585	+	0.205106i
$839$	−18.0996			−0.624868			−0.312434	−	0.949939i	$-0.601144\pi$
$839$	−18.0996			−0.624868			−0.312434	+	0.949939i	$0.601144\pi$
$840$	−5.98238	+	31.6137i	−0.206412	+	1.09078i
$841$	17.4511			0.601763
$842$	−21.3185	+	11.7357i	−0.734684	+	0.404440i
$843$	−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
$848$	−9.31243	+	26.0520i	−0.319790	+	0.894628i
$849$		−	15.1142i		−	0.518718i
$850$	−6.13015	+	10.3680i	−0.210262	+	0.355619i
$851$			35.9504i			1.23236i
$852$	−2.03371	+	0.457015i	−0.0696737	+	0.0156571i
$853$	11.8955	+	11.8955i	0.407293	+	0.407293i	0.880793	−	0.473501i	$-0.157010\pi$
$853$	11.8955	+	11.8955i	0.407293	+	0.407293i	−0.473501	+	0.880793i	$0.657010\pi$
$854$	−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	−0.00313143	+	0.999995i	$0.500997\pi$
$857$	−29.3661	+	29.3661i	−1.00313	+	1.00313i	−0.999995	+	0.00313143i	$0.999003\pi$
$858$	−4.27601	−	7.76757i	−0.145981	−	0.265181i
$859$	−12.6835			−0.432754			−0.216377	−	0.976310i	$-0.569424\pi$
$859$	−12.6835			−0.432754			−0.216377	+	0.976310i	$0.569424\pi$
$860$	4.39405	+	46.0394i	0.149836	+	1.56993i
$861$	8.30350			0.282982
$862$	−3.75924	−	6.82884i	−0.128040	−	0.232591i
$863$	24.8340	−	24.8340i	0.845360	−	0.845360i	−0.144190	−	0.989550i	$-0.546058\pi$
$863$	24.8340	−	24.8340i	0.845360	−	0.845360i	0.989550	+	0.144190i	$0.0460576\pi$
$864$	−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
$868$	6.15695	+	27.3983i	0.208981	+	0.929959i
$869$		−	9.62897i		−	0.326641i
$870$	−16.2761	−	7.03679i	−0.551812	−	0.238570i
$871$		−	55.8611i		−	1.89278i
$872$	18.0162	+	1.10265i	0.610105	+	0.0373403i
$873$	−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	−0.407970	+	0.912995i	$0.633763\pi$
$877$	−39.1193	+	39.1193i	−1.32097	+	1.32097i	−0.912995	+	0.407970i	$0.866237\pi$
$878$	−7.46913	+	4.11172i	−0.252071	+	0.138764i
$879$	−5.21863			−0.176020
$880$	−8.50085	+	2.78129i	−0.286563	+	0.0937574i
$881$	20.0333			0.674939			0.337469	−	0.941337i	$-0.390429\pi$
$881$	20.0333			0.674939			0.337469	+	0.941337i	$0.390429\pi$
$882$	−0.861227	+	0.474101i	−0.0289990	+	0.0159638i
$883$	−25.9099	+	25.9099i	−0.871937	+	0.871937i	−0.992683	−	0.120747i	$-0.961471\pi$
$883$	−25.9099	+	25.9099i	−0.871937	+	0.871937i	0.120747	+	0.992683i	$0.461471\pi$
$884$	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	$-0.0734527\pi$
$887$	22.1814	+	22.1814i	0.744777	+	0.744777i	−0.228716	+	0.973493i	$0.573453\pi$
$888$	−29.1498	−	1.78406i	−0.978203	−	0.0598690i
$889$			34.9576i			1.17244i
$890$	7.01725	+	17.7061i	0.235219	+	0.593510i
$891$			8.09079i			0.271052i
$892$	1.07515	+	4.78437i	0.0359985	+	0.160193i
$893$	−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
$898$	−1.84638	−	3.35404i	−0.0616146	−	0.111926i
$899$	−15.4763			−0.516163
$900$	1.90041	+	2.02100i	0.0633468	+	0.0673666i
$901$	11.7815			0.392500
$902$	1.11318	+	2.02214i	0.0370647	+	0.0673298i
$903$	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	$-0.345267\pi$
$907$	−12.5576	−	12.5576i	−0.416968	−	0.416968i	−0.884157	+	0.467189i	$0.845267\pi$
$908$	−22.6628	+	5.09279i	−0.752091	+	0.169010i
$909$		−	2.62233i		−	0.0869774i
$910$	13.6495	+	34.4409i	0.452478	+	1.14171i
$911$		−	15.5963i		−	0.516727i	−0.966048	−	0.258364i	$-0.916817\pi$
$911$		−	15.5963i		−	0.516727i	0.966048	−	0.258364i	$-0.0831832\pi$
$912$	−4.71448	−	1.68522i	−0.156112	−	0.0558033i
$913$	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
$918$	−11.4121	+	6.28233i	−0.376657	+	0.207348i
$919$	−40.6104			−1.33961			−0.669807	−	0.742535i	$-0.733623\pi$
$919$	−40.6104			−1.33961			−0.669807	+	0.742535i	$0.733623\pi$
$920$	−20.4674	−	30.0216i	−0.674790	−	0.989784i
$921$	−43.3167			−1.42733
$922$	−7.15211	+	3.93720i	−0.235542	+	0.129665i
$923$	−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
$928$	11.2554	−	15.5846i	0.369476	−	0.511591i
$929$		−	14.4830i		−	0.475171i	−0.971367	−	0.237585i	$-0.923644\pi$
$929$		−	14.4830i		−	0.475171i	0.971367	−	0.237585i	$-0.0763560\pi$
$930$	−21.8111	−	9.42977i	−0.715213	−	0.309215i
$931$			1.90084i			0.0622975i
$932$	−7.51974	+	1.68984i	−0.246317	+	0.0553525i
$933$	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	−0.928249	−	0.371959i	$-0.878686\pi$
$937$	−17.0283	+	17.0283i	−0.556290	+	0.556290i	0.371959	+	0.928249i	$0.378686\pi$
$938$	30.9125	+	56.1539i	1.00933	+	1.83349i
$939$	2.86116			0.0933704
$940$	7.81127	−	0.745516i	0.254776	−	0.0243161i
$941$	39.7570			1.29604			0.648021	−	0.761623i	$-0.275597\pi$
$941$	39.7570			1.29604			0.648021	+	0.761623i	$0.275597\pi$
$942$	−20.3555	−	36.9768i	−0.663219	−	1.20477i
$943$	−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	−0.997882	−	0.0650523i	$-0.979279\pi$
$947$	−32.7101	−	32.7101i	−1.06293	−	1.06293i	−0.0650523	−	0.997882i	$-0.520721\pi$
$948$	6.96699	+	31.0029i	0.226277	+	1.00693i
$949$			59.3236i			1.92572i
$950$	5.19523	−	1.33449i	0.168556	−	0.0432966i
$951$			10.8755i			0.352661i
$952$	−0.907425	+	14.8265i	−0.0294098	+	0.480529i
$953$	−35.3644	−	35.3644i	−1.14556	−	1.14556i	−0.987415	−	0.158149i	$-0.949447\pi$
$953$	−35.3644	−	35.3644i	−1.14556	−	1.14556i	−0.158149	−	0.987415i	$-0.550553\pi$
$954$	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
$958$	19.6430	−	10.8134i	0.634636	−	0.349364i
$959$	35.8847			1.15878
$960$	25.3583	−	15.1058i	0.818434	−	0.487538i
$961$	10.2608			0.330992
$962$	−29.4582	+	16.2166i	−0.949771	+	0.522844i
$963$	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	$-0.337736\pi$
$967$	−11.9686	−	11.9686i	−0.384884	−	0.384884i	−0.872858	+	0.487974i	$0.837736\pi$
$968$	−0.172785	+	2.82314i	−0.00555352	+	0.0907393i
$969$			2.13204i			0.0684910i
$970$	2.21687	−	5.12762i	0.0711793	−	0.164638i
$971$		−	52.0304i		−	1.66974i	−0.550450	−	0.834868i	$-0.685544\pi$
$971$		−	52.0304i		−	1.66974i	0.550450	−	0.834868i	$-0.314456\pi$
$972$	1.26002	+	5.60706i	0.0404152	+	0.179847i
$973$	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	−0.250901	−	0.968013i	$-0.580727\pi$
$977$	22.4148	−	22.4148i	0.717112	−	0.717112i	0.968013	+	0.250901i	$0.0807268\pi$
$978$	12.6402	+	22.9615i	0.404189	+	0.734228i
$979$	6.02286			0.192491
$980$	−8.64113	−	7.13540i	−0.276031	−	0.227932i
$981$	−1.77036			−0.0565232
$982$	6.82528	+	12.3984i	0.217804	+	0.395650i
$983$	−7.31758	+	7.31758i	−0.233394	+	0.233394i	−0.814108	−	0.580714i	$-0.802774\pi$
$983$	−7.31758	+	7.31758i	−0.233394	+	0.233394i	0.580714	+	0.814108i	$0.302774\pi$
$984$	−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
$988$	−5.62453	+	1.26395i	−0.178940	+	0.0402115i
$989$			59.4122i			1.88920i
$990$	0.815553	−	0.323218i	0.0259200	−	0.0102725i
$991$			30.9389i			0.982805i	0.870933	+	0.491403i	$0.163516\pi$
$991$			30.9389i			0.982805i	−0.870933	+	0.491403i	$0.836484\pi$
$992$	15.0830	−	20.8845i	0.478884	−	0.663082i
$993$	−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	−0.556532	−	0.830826i	$-0.687868\pi$
$997$	8.66091	−	8.66091i	0.274294	−	0.274294i	0.830826	+	0.556532i	$0.187868\pi$
$998$	−16.7851	+	9.24009i	−0.531322	+	0.292490i
$999$	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.d.23.13	yes	28
4.3	odd	2		220.2.l.c.23.10	✓	28
5.2	odd	4		220.2.l.c.67.10	yes	28
20.7	even	4	inner	220.2.l.d.67.13	yes	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
220.2.l.c.23.10	✓	28	4.3	odd	2
220.2.l.c.67.10	yes	28	5.2	odd	4
220.2.l.d.23.13	yes	28	1.1	even	1	trivial
220.2.l.d.67.13	yes	28	20.7	even	4	inner

Overview	Random
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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

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Modular forms

Varieties

Fields

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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.d.23.13

Level	$220$
Weight	$2$
Character	220.23
Analytic conductor	$1.757$
Analytic rank	$0$
Dimension	$28$
Inner twists	$2$