LMFDB - Embedded newform 220.2.l.d.23.8

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			23.8
Character	$\chi$	$=$	220.23
Dual form			220.2.l.d.67.8

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.0339977 + 1.41380i) q^{2} +(2.01721 - 2.01721i) q^{3} +(-1.99769 + 0.0961322i) q^{4} +(-0.571381 - 2.16183i) q^{5} +(2.92052 + 2.78336i) q^{6} +(0.577795 + 0.577795i) q^{7} +(-0.203829 - 2.82107i) q^{8} -5.13826i q^{9} +(3.03699 - 0.881318i) q^{10} +1.00000i q^{11} +(-3.83584 + 4.22367i) q^{12} +(2.69445 + 2.69445i) q^{13} +(-0.797245 + 0.836533i) q^{14} +(-5.51346 - 3.20828i) q^{15} +(3.98152 - 0.384084i) q^{16} +(4.20234 - 4.20234i) q^{17} +(7.26450 - 0.174689i) q^{18} -3.13149 q^{19} +(1.34926 + 4.26374i) q^{20} +2.33107 q^{21} +(-1.41380 + 0.0339977i) q^{22} +(-4.01439 + 4.01439i) q^{23} +(-6.10186 - 5.27953i) q^{24} +(-4.34705 + 2.47046i) q^{25} +(-3.71782 + 3.90103i) q^{26} +(-4.31332 - 4.31332i) q^{27} +(-1.20980 - 1.09871i) q^{28} +3.78445i q^{29} +(4.34843 - 7.90403i) q^{30} +4.05288i q^{31} +(0.678382 + 5.61603i) q^{32} +(2.01721 + 2.01721i) q^{33} +(6.08416 + 5.79842i) q^{34} +(0.918956 - 1.57924i) q^{35} +(0.493952 + 10.2646i) q^{36} +(-2.51485 + 2.51485i) q^{37} +(-0.106463 - 4.42731i) q^{38} +10.8705 q^{39} +(-5.98223 + 2.05255i) q^{40} +6.81081 q^{41} +(0.0792508 + 3.29567i) q^{42} +(-8.76281 + 8.76281i) q^{43} +(-0.0961322 - 1.99769i) q^{44} +(-11.1081 + 2.93590i) q^{45} +(-5.81205 - 5.53909i) q^{46} +(4.16169 + 4.16169i) q^{47} +(7.25677 - 8.80633i) q^{48} -6.33231i q^{49} +(-3.64054 - 6.06189i) q^{50} -16.9540i q^{51} +(-5.64170 - 5.12365i) q^{52} +(-7.42947 - 7.42947i) q^{53} +(5.95154 - 6.24483i) q^{54} +(2.16183 - 0.571381i) q^{55} +(1.51223 - 1.74777i) q^{56} +(-6.31687 + 6.31687i) q^{57} +(-5.35047 + 0.128662i) q^{58} +6.72046 q^{59} +(11.3226 + 5.87911i) q^{60} +1.20808 q^{61} +(-5.72999 + 0.137789i) q^{62} +(2.96886 - 2.96886i) q^{63} +(-7.91691 + 1.15003i) q^{64} +(4.28540 - 7.36451i) q^{65} +(-2.78336 + 2.92052i) q^{66} +(-4.91054 - 4.91054i) q^{67} +(-7.99099 + 8.79895i) q^{68} +16.1957i q^{69} +(2.26398 + 1.24553i) q^{70} -5.72115i q^{71} +(-14.4954 + 1.04733i) q^{72} +(1.80965 + 1.80965i) q^{73} +(-3.64100 - 3.47000i) q^{74} +(-3.78547 + 13.7523i) q^{75} +(6.25574 - 0.301037i) q^{76} +(-0.577795 + 0.577795i) q^{77} +(0.369573 + 15.3688i) q^{78} +9.31739 q^{79} +(-3.10529 - 8.38792i) q^{80} -1.98693 q^{81} +(0.231552 + 9.62915i) q^{82} +(2.21189 - 2.21189i) q^{83} +(-4.65674 + 0.224090i) q^{84} +(-11.4859 - 6.68363i) q^{85} +(-12.6868 - 12.0910i) q^{86} +(7.63402 + 7.63402i) q^{87} +(2.82107 - 0.203829i) q^{88} -17.0439i q^{89} +(-4.52844 - 15.6048i) q^{90} +3.11368i q^{91} +(7.63359 - 8.40542i) q^{92} +(8.17551 + 8.17551i) q^{93} +(-5.74233 + 6.02530i) q^{94} +(1.78927 + 6.76976i) q^{95} +(12.6971 + 9.96027i) q^{96} +(-0.132029 + 0.132029i) q^{97} +(8.95265 - 0.215284i) q^{98} +5.13826 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 $

$2$	0.0339977	+	1.41380i	0.0240400	+	0.999711i
$2$	0.0339977	+	1.41380i	0.0240400	+	0.999711i
$3$	2.01721	−	2.01721i	1.16464	−	1.16464i	0.181187	−	0.983449i	$-0.442006\pi$
$3$	2.01721	−	2.01721i	1.16464	−	1.16464i	0.983449	−	0.181187i	$-0.0579940\pi$
$4$	−1.99769	+	0.0961322i	−0.998844	+	0.0480661i
$5$	−0.571381	−	2.16183i	−0.255529	−	0.966801i
$5$	−0.571381	−	2.16183i	−0.255529	−	0.966801i
$6$	2.92052	+	2.78336i	1.19230	+	1.13630i
$7$	0.577795	+	0.577795i	0.218386	+	0.218386i	0.807818	−	0.589432i	$-0.200648\pi$
$7$	0.577795	+	0.577795i	0.218386	+	0.218386i	−0.589432	+	0.807818i	$0.700648\pi$
$8$	−0.203829	−	2.82107i	−0.0720644	−	0.997400i
$9$		−	5.13826i		−	1.71275i
$10$	3.03699	−	0.881318i	0.960379	−	0.278697i
$11$			1.00000i			0.301511i
$11$			1.00000i			0.301511i
$12$	−3.83584	+	4.22367i	−1.10731	+	1.21927i
$13$	2.69445	+	2.69445i	0.747306	+	0.747306i	0.973973	−	0.226666i	$-0.0727826\pi$
$13$	2.69445	+	2.69445i	0.747306	+	0.747306i	−0.226666	+	0.973973i	$0.572783\pi$
$14$	−0.797245	+	0.836533i	−0.213073	+	0.223573i
$15$	−5.51346	−	3.20828i	−1.42357	−	0.828373i
$16$	3.98152	−	0.384084i	0.995379	−	0.0960210i
$17$	4.20234	−	4.20234i	1.01922	−	1.01922i	0.0194059	−	0.999812i	$-0.493823\pi$
$17$	4.20234	−	4.20234i	1.01922	−	1.01922i	0.999812	−	0.0194059i	$-0.00617747\pi$
$18$	7.26450	−	0.174689i	1.71226	−	0.0411746i
$19$	−3.13149			−0.718413			−0.359206	−	0.933258i	$-0.616953\pi$
$19$	−3.13149			−0.718413			−0.359206	+	0.933258i	$0.616953\pi$
$20$	1.34926	+	4.26374i	0.301704	+	0.953402i
$21$	2.33107			0.508680
$22$	−1.41380	+	0.0339977i	−0.301424	+	0.00724833i
$23$	−4.01439	+	4.01439i	−0.837059	+	0.837059i	−0.988471	−	0.151412i	$-0.951618\pi$
$23$	−4.01439	+	4.01439i	−0.837059	+	0.837059i	0.151412	+	0.988471i	$0.451618\pi$
$24$	−6.10186	−	5.27953i	−1.24554	−	1.07768i
$25$	−4.34705	+	2.47046i	−0.869410	+	0.494092i
$26$	−3.71782	+	3.90103i	−0.729125	+	0.765056i
$27$	−4.31332	−	4.31332i	−0.830098	−	0.830098i
$28$	−1.20980	−	1.09871i	−0.228630	−	0.207637i
$29$			3.78445i			0.702754i	0.936234	+	0.351377i	$0.114287\pi$
$29$			3.78445i			0.702754i	−0.936234	+	0.351377i	$0.885713\pi$
$30$	4.34843	−	7.90403i	0.793911	−	1.44307i
$31$			4.05288i			0.727919i	0.931415	+	0.363960i	$0.118575\pi$
$31$			4.05288i			0.727919i	−0.931415	+	0.363960i	$0.881425\pi$
$32$	0.678382	+	5.61603i	0.119922	+	0.992783i
$33$	2.01721	+	2.01721i	0.351151	+	0.351151i
$34$	6.08416	+	5.79842i	1.04342	+	0.994421i
$35$	0.918956	−	1.57924i	0.155332	−	0.266940i
$36$	0.493952	+	10.2646i	0.0823253	+	1.71077i
$37$	−2.51485	+	2.51485i	−0.413438	+	0.413438i	−0.882934	−	0.469496i	$-0.844436\pi$
$37$	−2.51485	+	2.51485i	−0.413438	+	0.413438i	0.469496	+	0.882934i	$0.344436\pi$
$38$	−0.106463	−	4.42731i	−0.0172706	−	0.718205i
$39$	10.8705			1.74068
$40$	−5.98223	+	2.05255i	−0.945873	+	0.324537i
$41$	6.81081			1.06367			0.531835	−	0.846848i	$-0.321503\pi$
$41$	6.81081			1.06367			0.531835	+	0.846848i	$0.321503\pi$
$42$	0.0792508	+	3.29567i	0.0122287	+	0.508533i
$43$	−8.76281	+	8.76281i	−1.33632	+	1.33632i	−0.436716	+	0.899599i	$0.643859\pi$
$43$	−8.76281	+	8.76281i	−1.33632	+	1.33632i	−0.899599	+	0.436716i	$0.856141\pi$
$44$	−0.0961322	−	1.99769i	−0.0144925	−	0.301163i
$45$	−11.1081	+	2.93590i	−1.65589	+	0.437658i
$46$	−5.81205	−	5.53909i	−0.856940	−	0.816694i
$47$	4.16169	+	4.16169i	0.607045	+	0.607045i	0.942173	−	0.335128i	$-0.108780\pi$
$47$	4.16169	+	4.16169i	0.607045	+	0.607045i	−0.335128	+	0.942173i	$0.608780\pi$
$48$	7.25677	−	8.80633i	1.04742	−	1.27108i
$49$		−	6.33231i		−	0.904615i
$50$	−3.64054	−	6.06189i	−0.514850	−	0.857280i
$51$		−	16.9540i		−	2.37403i
$52$	−5.64170	−	5.12365i	−0.782363	−	0.710523i
$53$	−7.42947	−	7.42947i	−1.02052	−	1.02052i	−0.999785	−	0.0207307i	$-0.993401\pi$
$53$	−7.42947	−	7.42947i	−1.02052	−	1.02052i	−0.0207307	−	0.999785i	$-0.506599\pi$
$54$	5.95154	−	6.24483i	0.809903	−	0.849814i
$55$	2.16183	−	0.571381i	0.291502	−	0.0770449i
$56$	1.51223	−	1.74777i	0.202080	−	0.233556i
$57$	−6.31687	+	6.31687i	−0.836689	+	0.836689i
$58$	−5.35047	+	0.128662i	−0.702551	+	0.0168942i
$59$	6.72046			0.874929			0.437464	−	0.899236i	$-0.355877\pi$
$59$	6.72046			0.874929			0.437464	+	0.899236i	$0.355877\pi$
$60$	11.3226	+	5.87911i	1.46174	+	0.758990i
$61$	1.20808			0.154678			0.0773392	−	0.997005i	$-0.475358\pi$
$61$	1.20808			0.154678			0.0773392	+	0.997005i	$0.475358\pi$
$62$	−5.72999	+	0.137789i	−0.727709	+	0.0174992i
$63$	2.96886	−	2.96886i	0.374041	−	0.374041i
$64$	−7.91691	+	1.15003i	−0.989613	+	0.143754i
$65$	4.28540	−	7.36451i	0.531538	−	0.913456i
$66$	−2.78336	+	2.92052i	−0.342608	+	0.359491i
$67$	−4.91054	−	4.91054i	−0.599917	−	0.599917i	0.340373	−	0.940290i	$-0.389447\pi$
$67$	−4.91054	−	4.91054i	−0.599917	−	0.599917i	−0.940290	+	0.340373i	$0.889447\pi$
$68$	−7.99099	+	8.79895i	−0.969050	+	1.06703i
$69$			16.1957i			1.94974i
$70$	2.26398	+	1.24553i	0.270597	+	0.148870i
$71$		−	5.72115i		−	0.678976i	−0.940610	−	0.339488i	$-0.889746\pi$
$71$		−	5.72115i		−	0.678976i	0.940610	−	0.339488i	$-0.110254\pi$
$72$	−14.4954	+	1.04733i	−1.70830	+	0.123429i
$73$	1.80965	+	1.80965i	0.211803	+	0.211803i	0.805033	−	0.593230i	$-0.202148\pi$
$73$	1.80965	+	1.80965i	0.211803	+	0.211803i	−0.593230	+	0.805033i	$0.702148\pi$
$74$	−3.64100	−	3.47000i	−0.423258	−	0.403380i
$75$	−3.78547	+	13.7523i	−0.437109	+	1.58798i
$76$	6.25574	−	0.301037i	0.717583	−	0.0345313i
$77$	−0.577795	+	0.577795i	−0.0658458	+	0.0658458i
$78$	0.369573	+	15.3688i	0.0418459	+	1.74018i
$79$	9.31739			1.04829			0.524144	−	0.851630i	$-0.324385\pi$
$79$	9.31739			1.04829			0.524144	+	0.851630i	$0.324385\pi$
$80$	−3.10529	−	8.38792i	−0.347182	−	0.937798i
$81$	−1.98693			−0.220770
$82$	0.231552	+	9.62915i	0.0255706	+	1.06336i
$83$	2.21189	−	2.21189i	0.242787	−	0.242787i	−0.575215	−	0.818002i	$-0.695082\pi$
$83$	2.21189	−	2.21189i	0.242787	−	0.242787i	0.818002	+	0.575215i	$0.195082\pi$
$84$	−4.65674	+	0.224090i	−0.508092	+	0.0244503i
$85$	−11.4859	−	6.68363i	−1.24582	−	0.724941i
$86$	−12.6868	−	12.0910i	−1.36805	−	1.30380i
$87$	7.63402	+	7.63402i	0.818453	+	0.818453i
$88$	2.82107	−	0.203829i	0.300727	−	0.0217282i
$89$		−	17.0439i		−	1.80665i	−0.428952	−	0.903327i	$-0.641117\pi$
$89$		−	17.0439i		−	1.80665i	0.428952	−	0.903327i	$-0.358883\pi$
$90$	−4.52844	−	15.6048i	−0.477340	−	1.64489i
$91$			3.11368i			0.326402i
$92$	7.63359	−	8.40542i	0.795857	−	0.876325i
$93$	8.17551	+	8.17551i	0.847761	+	0.847761i
$94$	−5.74233	+	6.02530i	−0.592276	+	0.621463i
$95$	1.78927	+	6.76976i	0.183575	+	0.694563i
$96$	12.6971	+	9.96027i	1.29590	+	1.01657i
$97$	−0.132029	+	0.132029i	−0.0134055	+	0.0134055i	−0.713778	−	0.700372i	$-0.753017\pi$
$97$	−0.132029	+	0.132029i	−0.0134055	+	0.0134055i	0.700372	+	0.713778i	$0.253017\pi$
$98$	8.95265	−	0.215284i	0.904354	−	0.0217469i
$99$	5.13826			0.516415
$100$	8.44656	−	5.35310i	0.844656	−	0.535310i
$101$	1.29902			0.129257			0.0646285	−	0.997909i	$-0.479414\pi$
$101$	1.29902			0.129257			0.0646285	+	0.997909i	$0.479414\pi$
$102$	23.9696	−	0.576397i	2.37335	−	0.0570718i
$103$	−8.75492	+	8.75492i	−0.862648	+	0.862648i	−0.991645	−	0.128997i	$-0.958824\pi$
$103$	−8.75492	+	8.75492i	−0.862648	+	0.862648i	0.128997	+	0.991645i	$0.458824\pi$
$104$	7.05204	−	8.15045i	0.691509	−	0.799218i
$105$	−1.33193	−	5.03938i	−0.129983	−	0.491793i
$106$	10.2512	−	10.7564i	0.995688	−	1.04475i
$107$	−9.49660	−	9.49660i	−0.918071	−	0.918071i	0.0788177	−	0.996889i	$-0.474886\pi$
$107$	−9.49660	−	9.49660i	−0.918071	−	0.918071i	−0.996889	+	0.0788177i	$0.974886\pi$
$108$	9.03131	+	8.20201i	0.869038	+	0.789239i
$109$			14.0377i			1.34457i	0.740293	+	0.672284i	$0.234687\pi$
$109$			14.0377i			1.34457i	−0.740293	+	0.672284i	$0.765313\pi$
$110$	0.881318	+	3.03699i	0.0840304	+	0.289565i
$111$			10.1459i			0.963010i
$112$	2.52242	+	2.07858i	0.238346	+	0.196407i
$113$	7.69695	+	7.69695i	0.724069	+	0.724069i	0.969431	−	0.245363i	$-0.0789071\pi$
$113$	7.69695	+	7.69695i	0.724069	+	0.724069i	−0.245363	+	0.969431i	$0.578907\pi$
$114$	−9.14558	−	8.71606i	−0.856562	−	0.816334i
$115$	10.9722	+	6.38470i	1.02316	+	0.595377i
$116$	−0.363807	−	7.56015i	−0.0337786	−	0.701942i
$117$	13.8448	−	13.8448i	1.27995	−	1.27995i
$118$	0.228480	+	9.50141i	0.0210333	+	0.874676i
$119$	4.85618			0.445166
$120$	−7.92698	+	16.2078i	−0.723631	+	1.47956i
$121$	−1.00000			−0.0909091
$122$	0.0410718	+	1.70799i	0.00371847	+	0.154634i
$123$	13.7388	−	13.7388i	1.23879	−	1.23879i
$124$	−0.389612	−	8.09640i	−0.0349882	−	0.727078i
$125$	7.82454	+	7.98602i	0.699848	+	0.714292i
$126$	4.29832	+	4.09645i	0.382925	+	0.364941i
$127$	1.90837	+	1.90837i	0.169341	+	0.169341i	0.786689	−	0.617349i	$-0.211793\pi$
$127$	1.90837	+	1.90837i	0.169341	+	0.169341i	−0.617349	+	0.786689i	$0.711793\pi$
$128$	−1.89508	−	11.1539i	−0.167503	−	0.985872i
$129$			35.3528i			3.11264i
$130$	10.5577	+	5.80834i	0.925970	+	0.509425i
$131$		−	6.50809i		−	0.568614i	−0.958733	−	0.284307i	$-0.908236\pi$
$131$		−	6.50809i		−	0.568614i	0.958733	−	0.284307i	$-0.0917635\pi$
$132$	−4.22367	−	3.83584i	−0.367623	−	0.333867i
$133$	−1.80936	−	1.80936i	−0.156891	−	0.156891i
$134$	6.77559	−	7.10949i	0.585322	−	0.614166i
$135$	−6.86013	+	11.7892i	−0.590426	+	1.01465i
$136$	−12.7117	−	10.9986i	−1.09002	−	0.943118i
$137$	−10.3391	+	10.3391i	−0.883327	+	0.883327i	−0.993871	−	0.110545i	$-0.964740\pi$
$137$	−10.3391	+	10.3391i	−0.883327	+	0.883327i	0.110545	+	0.993871i	$0.464740\pi$
$138$	−22.8976	+	0.550617i	−1.94917	+	0.0468717i
$139$	−5.40889			−0.458776			−0.229388	−	0.973335i	$-0.573672\pi$
$139$	−5.40889			−0.458776			−0.229388	+	0.973335i	$0.573672\pi$
$140$	−1.68397	+	3.24316i	−0.142322	+	0.274097i
$141$	16.7900			1.41397
$142$	8.08860	−	0.194506i	0.678780	−	0.0163226i
$143$	−2.69445	+	2.69445i	−0.225321	+	0.225321i
$144$	−1.97352	−	20.4581i	−0.164460	−	1.70484i
$145$	8.18135	−	2.16236i	0.679424	−	0.179574i
$146$	−2.49696	+	2.62001i	−0.206650	+	0.216834i
$147$	−12.7736	−	12.7736i	−1.05355	−	1.05355i
$148$	4.78212	−	5.26564i	0.393088	−	0.432833i
$149$			6.97727i			0.571601i	0.958289	+	0.285800i	$0.0922594\pi$
$149$			6.97727i			0.571601i	−0.958289	+	0.285800i	$0.907741\pi$
$150$	−19.5718	−	4.88437i	−1.59803	−	0.398807i
$151$		−	1.28022i		−	0.104183i	−0.998642	−	0.0520916i	$-0.983411\pi$
$151$		−	1.28022i		−	0.104183i	0.998642	−	0.0520916i	$-0.0165888\pi$
$152$	0.638288	+	8.83416i	0.0517720	+	0.716545i
$153$	−21.5927	−	21.5927i	−1.74567	−	1.74567i
$154$	−0.836533	−	0.797245i	−0.0674097	−	0.0642439i
$155$	8.76166	−	2.31574i	0.703753	−	0.186005i
$156$	−21.7160	+	1.04501i	−1.73867	+	0.0836677i
$157$	6.55062	−	6.55062i	0.522796	−	0.522796i	−0.395619	−	0.918415i	$-0.629470\pi$
$157$	6.55062	−	6.55062i	0.522796	−	0.522796i	0.918415	+	0.395619i	$0.129470\pi$
$158$	0.316769	+	13.1730i	0.0252008	+	1.04798i
$159$	−29.9736			−2.37706
$160$	11.7533	−	4.67544i	0.929181	−	0.369626i
$161$	−4.63899			−0.365604
$162$	−0.0675511	−	2.80914i	−0.00530732	−	0.220707i
$163$	7.29898	−	7.29898i	0.571700	−	0.571700i	−0.360903	−	0.932603i	$-0.617531\pi$
$163$	7.29898	−	7.29898i	0.571700	−	0.571700i	0.932603	+	0.360903i	$0.117531\pi$
$164$	−13.6059	+	0.654738i	−1.06244	+	0.0511264i
$165$	3.20828	−	5.51346i	0.249764	−	0.429222i
$166$	3.20238	+	3.05199i	0.248553	+	0.236880i
$167$	−7.92362	−	7.92362i	−0.613148	−	0.613148i	0.330617	−	0.943765i	$-0.392743\pi$
$167$	−7.92362	−	7.92362i	−0.613148	−	0.613148i	−0.943765	+	0.330617i	$0.892743\pi$
$168$	−0.475138	−	6.57611i	−0.0366577	−	0.507358i
$169$			1.52014i			0.116934i
$170$	9.05885	−	16.4660i	0.694782	−	1.26289i
$171$			16.0904i			1.23046i
$172$	16.6630	−	18.3477i	1.27054	−	1.39900i
$173$	−12.3019	−	12.3019i	−0.935293	−	0.935293i	0.0627367	−	0.998030i	$-0.480017\pi$
$173$	−12.3019	−	12.3019i	−0.935293	−	0.935293i	−0.998030	+	0.0627367i	$0.980017\pi$
$174$	−10.5335	+	11.0526i	−0.798541	+	0.837892i
$175$	−3.93912	−	1.08428i	−0.297770	−	0.0819641i
$176$	0.384084	+	3.98152i	0.0289514	+	0.300118i
$177$	13.5566	−	13.5566i	1.01897	−	1.01897i
$178$	24.0968	−	0.579455i	1.80613	−	0.0434320i
$179$	−4.03496			−0.301587			−0.150793	−	0.988565i	$-0.548183\pi$
$179$	−4.03496			−0.301587			−0.150793	+	0.988565i	$0.548183\pi$
$180$	21.9082	−	6.93286i	1.63294	−	0.516745i
$181$	−23.4754			−1.74491			−0.872455	−	0.488694i	$-0.837473\pi$
$181$	−23.4754			−1.74491			−0.872455	+	0.488694i	$0.837473\pi$
$182$	−4.40214	+	0.105858i	−0.326308	+	0.00784671i
$183$	2.43694	−	2.43694i	0.180144	−	0.180144i
$184$	12.1431	+	10.5066i	0.895205	+	0.774560i
$185$	6.87361	+	3.99974i	0.505358	+	0.294067i
$186$	−11.2806	+	11.8365i	−0.827136	+	0.867896i
$187$	4.20234	+	4.20234i	0.307306	+	0.307306i
$188$	−8.71383	−	7.91368i	−0.635521	−	0.577165i
$189$		−	4.98442i		−	0.362563i
$190$	−9.51029	+	2.75984i	−0.689949	+	0.200220i
$191$		−	18.4065i		−	1.33185i	−0.746019	−	0.665925i	$-0.768037\pi$
$191$		−	18.4065i		−	1.33185i	0.746019	−	0.665925i	$-0.231963\pi$
$192$	−13.6502	+	18.2899i	−0.985118	+	1.31996i
$193$	−1.71012	−	1.71012i	−0.123097	−	0.123097i	0.642874	−	0.765972i	$-0.277742\pi$
$193$	−1.71012	−	1.71012i	−0.123097	−	0.123097i	−0.765972	+	0.642874i	$0.777742\pi$
$194$	−0.191152	−	0.182175i	−0.0137239	−	0.0130794i
$195$	−6.21122	−	23.5003i	−0.444794	−	1.68289i
$196$	0.608738	+	12.6500i	0.0434813	+	0.903570i
$197$	−12.0459	+	12.0459i	−0.858237	+	0.858237i	−0.991130	−	0.132894i	$-0.957573\pi$
$197$	−12.0459	+	12.0459i	−0.858237	+	0.858237i	0.132894	+	0.991130i	$0.457573\pi$
$198$	0.174689	+	7.26450i	0.0124146	+	0.516265i
$199$	−10.4553			−0.741155			−0.370577	−	0.928802i	$-0.620840\pi$
$199$	−10.4553			−0.741155			−0.370577	+	0.928802i	$0.620840\pi$
$200$	7.85540	+	11.7598i	0.555461	+	0.831543i
$201$	−19.8111			−1.39737
$202$	0.0441636	+	1.83656i	0.00310734	+	0.129220i
$203$	−2.18663	+	2.18663i	−0.153472	+	0.153472i
$204$	1.62982	+	33.8688i	0.114111	+	2.37129i
$205$	−3.89156	−	14.7238i	−0.271799	−	1.02836i
$206$	−12.6754	−	12.0801i	−0.883137	−	0.841661i
$207$	20.6270	+	20.6270i	1.43368	+	1.43368i
$208$	11.7629	+	9.69311i	0.815611	+	0.672096i
$209$		−	3.13149i		−	0.216610i
$210$	7.07941	−	2.05441i	0.488526	−	0.141768i
$211$			11.9700i			0.824050i	0.911173	+	0.412025i	$0.135178\pi$
$211$			11.9700i			0.824050i	−0.911173	+	0.412025i	$0.864822\pi$
$212$	15.5560	+	14.1275i	1.06839	+	0.970284i
$213$	−11.5408	−	11.5408i	−0.790760	−	0.790760i
$214$	13.1035	−	13.7492i	0.895736	−	0.939876i
$215$	23.9506	+	13.9368i	1.63342	+	0.950484i
$216$	−11.2890	+	13.0474i	−0.768119	+	0.887760i
$217$	−2.34173	+	2.34173i	−0.158967	+	0.158967i
$218$	−19.8466	+	0.477249i	−1.34418	+	0.0323234i
$219$	7.30087			0.493347
$220$	−4.26374	+	1.34926i	−0.287461	+	0.0909672i
$221$	22.6460			1.52334
$222$	−14.3444	+	0.344938i	−0.962731	+	0.0231507i
$223$	2.11226	−	2.11226i	0.141447	−	0.141447i	−0.632837	−	0.774285i	$-0.718110\pi$
$223$	2.11226	−	2.11226i	0.141447	−	0.141447i	0.774285	+	0.632837i	$0.218110\pi$
$224$	−2.85295	+	3.63688i	−0.190621	+	0.242999i
$225$	12.6939	+	22.3363i	0.846258	+	1.48908i
$226$	−10.6203	+	11.1437i	−0.706453	+	0.741266i
$227$	8.22005	+	8.22005i	0.545584	+	0.545584i	0.925160	−	0.379576i	$-0.123930\pi$
$227$	8.22005	+	8.22005i	0.545584	+	0.545584i	−0.379576	+	0.925160i	$0.623930\pi$
$228$	12.0119	−	13.2264i	0.795506	−	0.875939i
$229$		−	20.8865i		−	1.38022i	−0.723705	−	0.690110i	$-0.757562\pi$
$229$		−	20.8865i		−	1.38022i	0.723705	−	0.690110i	$-0.242438\pi$
$230$	−8.65369	+	15.7296i	−0.570608	+	1.03718i
$231$			2.33107i			0.153373i
$232$	10.6762	−	0.771380i	0.700927	−	0.0506436i
$233$	5.01248	+	5.01248i	0.328379	+	0.328379i	0.851970	−	0.523591i	$-0.175408\pi$
$233$	5.01248	+	5.01248i	0.328379	+	0.328379i	−0.523591	+	0.851970i	$0.675408\pi$
$234$	20.0445	+	19.1031i	1.31035	+	1.24881i
$235$	6.61897	−	11.3748i	0.431774	−	0.742009i
$236$	−13.4254	+	0.646052i	−0.873918	+	0.0420544i
$237$	18.7951	−	18.7951i	1.22087	−	1.22087i
$238$	0.165099	+	6.86569i	0.0107018	+	0.445037i
$239$	−0.577502			−0.0373555			−0.0186778	−	0.999826i	$-0.505946\pi$
$239$	−0.577502			−0.0373555			−0.0186778	+	0.999826i	$0.505946\pi$
$240$	−23.1842	−	10.6562i	−1.49653	−	0.687853i
$241$	9.18680			0.591774			0.295887	−	0.955223i	$-0.404385\pi$
$241$	9.18680			0.591774			0.295887	+	0.955223i	$0.404385\pi$
$242$	−0.0339977	−	1.41380i	−0.00218545	−	0.0908828i
$243$	8.93189	−	8.93189i	0.572981	−	0.572981i
$244$	−2.41336	+	0.116135i	−0.154500	+	0.00743479i
$245$	−13.6894	+	3.61816i	−0.874583	+	0.231156i
$246$	19.8911	+	18.9569i	1.26821	+	1.20865i
$247$	−8.43765	−	8.43765i	−0.536875	−	0.536875i
$248$	11.4335	−	0.826095i	0.726027	−	0.0524571i
$249$		−	8.92370i		−	0.565516i
$250$	−11.0247	+	11.3339i	−0.697261	+	0.716818i
$251$		−	13.7459i		−	0.867635i	−0.901001	−	0.433817i	$-0.857166\pi$
$251$		−	13.7459i		−	0.867635i	0.901001	−	0.433817i	$-0.142834\pi$
$252$	−5.64545	+	6.21626i	−0.355630	+	0.391588i
$253$	−4.01439	−	4.01439i	−0.252383	−	0.252383i
$254$	−2.63318	+	2.76294i	−0.165221	+	0.173363i
$255$	−36.6517	+	9.68719i	−2.29522	+	0.606635i
$256$	15.7050	−	3.05848i	0.981560	−	0.191155i
$257$	−14.1931	+	14.1931i	−0.885338	+	0.885338i	−0.994071	−	0.108733i	$-0.965321\pi$
$257$	−14.1931	+	14.1931i	−0.885338	+	0.885338i	0.108733	+	0.994071i	$0.465321\pi$
$258$	−49.9820	+	1.20191i	−3.11174	+	0.0748279i
$259$	−2.90613			−0.180578
$260$	−7.85292	+	15.1240i	−0.487018	+	0.937949i
$261$	19.4455			1.20364
$262$	9.20117	−	0.221260i	0.568450	−	0.0136695i
$263$	−0.819798	+	0.819798i	−0.0505509	+	0.0505509i	−0.731930	−	0.681379i	$-0.761380\pi$
$263$	−0.819798	+	0.819798i	−0.0505509	+	0.0505509i	0.681379	+	0.731930i	$0.261380\pi$
$264$	5.27953	−	6.10186i	0.324932	−	0.375543i
$265$	−11.8162	+	20.3063i	−0.725864	+	1.24741i
$266$	2.49657	−	2.61959i	0.153074	−	0.160618i
$267$	−34.3812	−	34.3812i	−2.10409	−	2.10409i
$268$	10.2818	+	9.33766i	0.628060	+	0.570388i
$269$		−	11.0294i		−	0.672475i	−0.941777	−	0.336237i	$-0.890846\pi$
$269$		−	11.0294i		−	0.672475i	0.941777	−	0.336237i	$-0.109154\pi$
$270$	−16.9009	−	9.29807i	−1.02855	−	0.565863i
$271$			4.95036i			0.300713i	0.988632	+	0.150356i	$0.0480421\pi$
$271$			4.95036i			0.300713i	−0.988632	+	0.150356i	$0.951958\pi$
$272$	15.1176	−	18.3457i	0.916642	−	1.11237i
$273$	6.28094	+	6.28094i	0.380140	+	0.380140i
$274$	−14.9689	−	14.2659i	−0.904306	−	0.861836i
$275$	−2.47046	−	4.34705i	−0.148974	−	0.262137i
$276$	−1.55693	−	32.3540i	−0.0937162	−	1.94748i
$277$	19.6616	−	19.6616i	1.18135	−	1.18135i	0.201958	−	0.979394i	$-0.435269\pi$
$277$	19.6616	−	19.6616i	1.18135	−	1.18135i	0.979394	−	0.201958i	$-0.0647306\pi$
$278$	−0.183890	−	7.64711i	−0.0110290	−	0.458643i
$279$	20.8248			1.24675
$280$	−4.64245	−	2.27055i	−0.277440	−	0.135691i
$281$	11.2306			0.669959			0.334980	−	0.942225i	$-0.391271\pi$
$281$	11.2306			0.669959			0.334980	+	0.942225i	$0.391271\pi$
$282$	0.570821	+	23.7378i	0.0339919	+	1.41356i
$283$	−20.2259	+	20.2259i	−1.20230	+	1.20230i	−0.228841	+	0.973464i	$0.573494\pi$
$283$	−20.2259	+	20.2259i	−1.20230	+	1.20230i	−0.973464	+	0.228841i	$0.926506\pi$
$284$	0.549987	+	11.4291i	0.0326357	+	0.678191i
$285$	17.2653	+	10.0467i	1.02271	+	0.595114i
$286$	−3.90103	−	3.71782i	−0.230673	−	0.219840i
$287$	3.93525	+	3.93525i	0.232290	+	0.232290i
$288$	28.8566	−	3.48570i	1.70039	−	0.205397i
$289$		−	18.3194i		−	1.07761i
$290$	3.33530	+	11.4933i	0.195856	+	0.674910i
$291$			0.532661i			0.0312252i
$292$	−3.78907	−	3.44114i	−0.221739	−	0.201378i
$293$	−5.82344	−	5.82344i	−0.340209	−	0.340209i	0.516237	−	0.856446i	$-0.327332\pi$
$293$	−5.82344	−	5.82344i	−0.340209	−	0.340209i	−0.856446	+	0.516237i	$0.827332\pi$
$294$	17.6251	−	18.4936i	1.02792	−	1.07857i
$295$	−3.83994	−	14.5285i	−0.223570	−	0.845882i
$296$	7.60716	+	6.58197i	0.442157	+	0.382569i
$297$	4.31332	−	4.31332i	0.250284	−	0.250284i
$298$	−9.86450	+	0.237211i	−0.571435	+	0.0137413i
$299$	−21.6332			−1.25108
$300$	6.24015	−	27.8368i	0.360275	−	1.60716i
$301$	−10.1262			−0.583665
$302$	1.80999	−	0.0435246i	0.104153	−	0.00250456i
$303$	2.62039	−	2.62039i	0.150537	−	0.150537i
$304$	−12.4681	+	1.20276i	−0.715093	+	0.0689828i
$305$	−0.690272	−	2.61166i	−0.0395249	−	0.149543i
$306$	29.7938	−	31.2620i	1.70320	−	1.78713i
$307$	12.1590	+	12.1590i	0.693950	+	0.693950i	0.963099	−	0.269149i	$-0.0867424\pi$
$307$	12.1590	+	12.1590i	0.693950	+	0.693950i	−0.269149	+	0.963099i	$0.586742\pi$
$308$	1.09871	−	1.20980i	0.0626048	−	0.0689347i
$309$			35.3210i			2.00934i
$310$	3.57188	+	12.3085i	0.202869	+	0.699078i
$311$			8.10871i			0.459803i	0.973214	+	0.229902i	$0.0738404\pi$
$311$			8.10871i			0.459803i	−0.973214	+	0.229902i	$0.926160\pi$
$312$	−2.21573	−	30.6666i	−0.125441	−	1.73615i
$313$	8.16560	+	8.16560i	0.461547	+	0.461547i	0.899162	−	0.437615i	$-0.144177\pi$
$313$	8.16560	+	8.16560i	0.461547	+	0.461547i	−0.437615	+	0.899162i	$0.644177\pi$
$314$	9.48400	+	9.03859i	0.535213	+	0.510077i
$315$	−8.11453	−	4.72183i	−0.457202	−	0.266045i
$316$	−18.6132	+	0.895700i	−1.04708	+	0.0503871i
$317$	1.35329	−	1.35329i	0.0760083	−	0.0760083i	−0.668081	−	0.744089i	$-0.732884\pi$
$317$	1.35329	−	1.35329i	0.0760083	−	0.0760083i	0.744089	+	0.668081i	$0.232884\pi$
$318$	−1.01903	−	42.3768i	−0.0571445	−	2.37637i
$319$	−3.78445			−0.211888
$320$	7.00975	+	16.4579i	0.391857	+	0.920026i
$321$	−38.3133			−2.13844
$322$	−0.157715	−	6.55863i	−0.00878911	−	0.365498i
$323$	−13.1596	+	13.1596i	−0.732219	+	0.732219i
$324$	3.96928	−	0.191008i	0.220515	−	0.0106116i
$325$	−18.3694	−	5.05638i	−1.01895	−	0.280477i
$326$	10.5675	+	10.0712i	0.585279	+	0.557791i
$327$	28.3170	+	28.3170i	1.56593	+	1.56593i
$328$	−1.38824	−	19.2138i	−0.0766527	−	1.06090i
$329$			4.80920i			0.265140i
$330$	7.90403	+	4.34843i	0.435103	+	0.239373i
$331$			1.01553i			0.0558186i	0.999610	+	0.0279093i	$0.00888495\pi$
$331$			1.01553i			0.0558186i	−0.999610	+	0.0279093i	$0.991115\pi$
$332$	−4.20604	+	4.63131i	−0.230836	+	0.254176i
$333$	12.9219	+	12.9219i	0.708117	+	0.708117i
$334$	10.9331	−	11.4718i	0.598231	−	0.627711i
$335$	−7.80998	+	13.4215i	−0.426705	+	0.733297i
$336$	9.28118	−	0.895325i	0.506330	−	0.0488440i
$337$	−14.2842	+	14.2842i	−0.778108	+	0.778108i	−0.979509	−	0.201401i	$-0.935451\pi$
$337$	−14.2842	+	14.2842i	−0.778108	+	0.778108i	0.201401	+	0.979509i	$0.435451\pi$
$338$	−2.14918	+	0.0516813i	−0.116900	+	0.00281109i
$339$	31.0527			1.68655
$340$	23.5878	+	12.2476i	1.27923	+	0.664221i
$341$	−4.05288			−0.219476
$342$	−22.7487	+	0.547036i	−1.23011	+	0.0295803i
$343$	7.70334	−	7.70334i	0.415941	−	0.415941i
$344$	26.5066	+	22.9344i	1.42914	+	1.23654i
$345$	35.0125	−	9.25393i	1.88501	−	0.498215i
$346$	16.9742	−	17.8107i	0.912539	−	0.957508i
$347$	−23.8639	−	23.8639i	−1.28108	−	1.28108i	−0.940052	−	0.341032i	$-0.889223\pi$
$347$	−23.8639	−	23.8639i	−1.28108	−	1.28108i	−0.341032	−	0.940052i	$-0.610777\pi$
$348$	−15.9843	−	14.5165i	−0.856847	−	0.778167i
$349$			5.29742i			0.283565i	0.989898	+	0.141782i	$0.0452833\pi$
$349$			5.29742i			0.283565i	−0.989898	+	0.141782i	$0.954717\pi$
$350$	1.39904	−	5.60601i	0.0747821	−	0.299654i
$351$		−	23.2440i		−	1.24068i
$352$	−5.61603	+	0.678382i	−0.299335	+	0.0361579i
$353$	21.0101	+	21.0101i	1.11825	+	1.11825i	0.991998	+	0.126255i	$0.0402958\pi$
$353$	21.0101	+	21.0101i	1.11825	+	1.11825i	0.126255	+	0.991998i	$0.459704\pi$
$354$	19.6272	+	18.7054i	1.04318	+	0.994183i
$355$	−12.3682	+	3.26896i	−0.656435	+	0.173498i
$356$	1.63847	+	34.0485i	0.0868388	+	1.80457i
$357$	9.79593	−	9.79593i	0.518456	−	0.518456i
$358$	−0.137179	−	5.70464i	−0.00725014	−	0.301500i
$359$	30.0479			1.58587			0.792934	−	0.609308i	$-0.208553\pi$
$359$	30.0479			1.58587			0.792934	+	0.609308i	$0.208553\pi$
$360$	10.5465	+	30.7382i	0.555851	+	1.62005i
$361$	−9.19377			−0.483883
$362$	−0.798108	−	33.1896i	−0.0419476	−	1.74441i
$363$	−2.01721	+	2.01721i	−0.105876	+	0.105876i
$364$	−0.299325	−	6.22016i	−0.0156889	−	0.326025i
$365$	2.87816	−	4.94615i	0.150650	−	0.258893i
$366$	3.52821	+	3.36251i	0.184423	+	0.175761i
$367$	−17.6939	−	17.6939i	−0.923614	−	0.923614i	0.0736687	−	0.997283i	$-0.476529\pi$
$367$	−17.6939	−	17.6939i	−0.923614	−	0.923614i	−0.997283	+	0.0736687i	$0.976529\pi$
$368$	−14.4415	+	17.5252i	−0.752816	+	0.913566i
$369$		−	34.9957i		−	1.82180i
$370$	−5.42117	+	9.85393i	−0.281833	+	0.512281i
$371$		−	8.58542i		−	0.445733i
$372$	−17.1180	−	15.5462i	−0.887529	−	0.806032i
$373$	7.55696	+	7.55696i	0.391285	+	0.391285i	0.875145	−	0.483861i	$-0.160766\pi$
$373$	7.55696	+	7.55696i	0.391285	+	0.391285i	−0.483861	+	0.875145i	$0.660766\pi$
$374$	−5.79842	+	6.08416i	−0.299829	+	0.314604i
$375$	31.8932	+	0.325741i	1.64696	+	0.0168212i
$376$	10.8922	−	12.5887i	0.561720	−	0.649213i
$377$	−10.1970	+	10.1970i	−0.525173	+	0.525173i
$378$	7.04700	−	0.169459i	0.362459	−	0.00871602i
$379$	26.3215			1.35205			0.676023	−	0.736881i	$-0.263702\pi$
$379$	26.3215			1.35205			0.676023	+	0.736881i	$0.263702\pi$
$380$	−4.22520	−	13.3519i	−0.216748	−	0.684936i
$381$	7.69916			0.394440
$382$	26.0232	−	0.625779i	1.33146	−	0.0320177i
$383$	−3.16875	+	3.16875i	−0.161916	+	0.161916i	−0.783415	−	0.621499i	$-0.786524\pi$
$383$	−3.16875	+	3.16875i	−0.161916	+	0.161916i	0.621499	+	0.783415i	$0.286524\pi$
$384$	−26.3224	−	18.6769i	−1.34326	−	0.953102i
$385$	1.57924	+	0.918956i	0.0804854	+	0.0468343i
$386$	2.35963	−	2.47591i	0.120102	−	0.126021i
$387$	45.0256	+	45.0256i	2.28878	+	2.28878i
$388$	0.251061	−	0.276446i	0.0127457	−	0.0140344i
$389$		−	5.27196i		−	0.267299i	−0.991029	−	0.133650i	$-0.957330\pi$
$389$		−	5.27196i		−	0.267299i	0.991029	−	0.133650i	$-0.0426697\pi$
$390$	33.0137	−	9.58040i	1.67171	−	0.485123i
$391$			33.7397i			1.70629i
$392$	−17.8639	+	1.29071i	−0.902263	+	0.0651905i
$393$	−13.1282	−	13.1282i	−0.662229	−	0.662229i
$394$	−17.4401	−	16.6211i	−0.878621	−	0.837357i
$395$	−5.32377	−	20.1426i	−0.267868	−	1.01349i
$396$	−10.2646	+	0.493952i	−0.515818	+	0.0248220i
$397$	−7.83485	+	7.83485i	−0.393220	+	0.393220i	−0.875833	−	0.482614i	$-0.839688\pi$
$397$	−7.83485	+	7.83485i	−0.393220	+	0.393220i	0.482614	+	0.875833i	$0.339688\pi$
$398$	−0.355455	−	14.7817i	−0.0178173	−	0.740940i
$399$	−7.29971			−0.365442
$400$	−16.3590	+	11.5058i	−0.817949	+	0.575290i
$401$	0.846108			0.0422526			0.0211263	−	0.999777i	$-0.493275\pi$
$401$	0.846108			0.0422526			0.0211263	+	0.999777i	$0.493275\pi$
$402$	−0.673533	−	28.0091i	−0.0335928	−	1.39697i
$403$	−10.9203	+	10.9203i	−0.543979	+	0.543979i
$404$	−2.59503	+	0.124877i	−0.129108	+	0.00621288i
$405$	1.13530	+	4.29542i	0.0564133	+	0.213441i
$406$	−3.16581	−	3.01713i	−0.157117	−	0.149738i
$407$	−2.51485	−	2.51485i	−0.124656	−	0.124656i
$408$	−47.8285	+	3.45571i	−2.36786	+	0.171083i
$409$		−	9.86215i		−	0.487652i	−0.969819	−	0.243826i	$-0.921597\pi$
$409$		−	9.86215i		−	0.487652i	0.969819	−	0.243826i	$-0.0784026\pi$
$410$	20.6843	−	6.00249i	1.02153	−	0.296442i
$411$			41.7121i			2.05751i
$412$	16.6480	−	18.3312i	0.820187	−	0.903115i
$413$	3.88304	+	3.88304i	0.191072	+	0.191072i
$414$	−28.4613	+	29.8638i	−1.39880	+	1.46773i
$415$	−6.04558	−	3.51791i	−0.296766	−	0.172687i
$416$	−13.3043	+	16.9600i	−0.652295	+	0.831532i
$417$	−10.9109	+	10.9109i	−0.534307	+	0.534307i
$418$	4.42731	−	0.106463i	0.216547	−	0.00520729i
$419$	−19.9803			−0.976102			−0.488051	−	0.872815i	$-0.662292\pi$
$419$	−19.9803			−0.976102			−0.488051	+	0.872815i	$0.662292\pi$
$420$	3.14522	+	9.93906i	0.153471	+	0.484976i
$421$	−15.5127			−0.756042			−0.378021	−	0.925797i	$-0.623395\pi$
$421$	−15.5127			−0.756042			−0.378021	+	0.925797i	$0.623395\pi$
$422$	−16.9233	+	0.406953i	−0.823812	+	0.0198101i
$423$	21.3838	−	21.3838i	1.03972	−	1.03972i
$424$	−19.4447	+	22.4734i	−0.944320	+	1.09141i
$425$	−7.88607	+	28.6495i	−0.382530	+	1.38970i
$426$	15.9240	−	16.7087i	0.771522	−	0.809541i
$427$	0.698021	+	0.698021i	0.0337796	+	0.0337796i
$428$	19.8842	+	18.0583i	0.961138	+	0.872882i
$429$			10.8705i			0.524835i
$430$	−18.8897	+	34.3353i	−0.910942	+	1.65580i
$431$		−	19.1176i		−	0.920860i	−0.887696	−	0.460430i	$-0.847695\pi$
$431$		−	19.1176i		−	0.920860i	0.887696	−	0.460430i	$-0.152305\pi$
$432$	−18.8302	−	15.5169i	−0.905969	−	0.746555i
$433$	14.9076	+	14.9076i	0.716413	+	0.716413i	0.967869	−	0.251456i	$-0.0809093\pi$
$433$	14.9076	+	14.9076i	0.716413	+	0.716413i	−0.251456	+	0.967869i	$0.580909\pi$
$434$	−3.39037	−	3.23114i	−0.162743	−	0.155100i
$435$	12.1415	−	20.8654i	0.582143	−	1.00042i
$436$	−1.34947	−	28.0430i	−0.0646281	−	1.34301i
$437$	12.5710	−	12.5710i	0.601354	−	0.601354i
$438$	0.248213	+	10.3220i	0.0118601	+	0.493204i
$439$	−7.24897			−0.345975			−0.172987	−	0.984924i	$-0.555342\pi$
$439$	−7.24897			−0.345975			−0.172987	+	0.984924i	$0.555342\pi$
$440$	−2.05255	−	5.98223i	−0.0978515	−	0.285191i
$441$	−32.5370			−1.54938
$442$	0.769912	+	32.0170i	0.0366210	+	1.52290i
$443$	−9.15600	+	9.15600i	−0.435014	+	0.435014i	−0.890330	−	0.455316i	$-0.849526\pi$
$443$	−9.15600	+	9.15600i	−0.435014	+	0.435014i	0.455316	+	0.890330i	$0.349526\pi$
$444$	−0.975351	−	20.2684i	−0.0462881	−	0.961897i
$445$	−36.8462	+	9.73858i	−1.74668	+	0.461653i
$446$	3.05813	+	2.91451i	0.144807	+	0.138006i
$447$	14.0746	+	14.0746i	0.665707	+	0.665707i
$448$	−5.23883	−	3.90987i	−0.247512	−	0.184724i
$449$			5.22383i			0.246528i	0.992374	+	0.123264i	$0.0393361\pi$
$449$			5.22383i			0.246528i	−0.992374	+	0.123264i	$0.960664\pi$
$450$	−31.1476	+	18.7060i	−1.46831	+	0.881810i
$451$			6.81081i			0.320708i
$452$	−16.1160	−	14.6362i	−0.758035	−	0.688428i
$453$	−2.58248	−	2.58248i	−0.121335	−	0.121335i
$454$	−11.3421	+	11.9010i	−0.532310	+	0.558542i
$455$	6.73126	−	1.77910i	0.315566	−	0.0834053i
$456$	19.1079	+	16.5328i	0.894810	+	0.774218i
$457$	6.78650	−	6.78650i	0.317459	−	0.317459i	−0.530331	−	0.847790i	$-0.677933\pi$
$457$	6.78650	−	6.78650i	0.317459	−	0.317459i	0.847790	+	0.530331i	$0.177933\pi$
$458$	29.5294	−	0.710093i	1.37982	−	0.0331804i
$459$	−36.2521			−1.69210
$460$	−22.5328	−	11.6999i	−1.05060	−	0.545509i
$461$	15.9739			0.743981			0.371990	−	0.928237i	$-0.378675\pi$
$461$	15.9739			0.743981			0.371990	+	0.928237i	$0.378675\pi$
$462$	−3.29567	+	0.0792508i	−0.153329	+	0.00368708i
$463$	26.1957	−	26.1957i	1.21742	−	1.21742i	0.248887	−	0.968533i	$-0.419935\pi$
$463$	26.1957	−	26.1957i	1.21742	−	1.21742i	0.968533	−	0.248887i	$-0.0800647\pi$
$464$	1.45355	+	15.0678i	0.0674792	+	0.699507i
$465$	13.0028	−	22.3454i	0.602989	−	1.03624i
$466$	−6.91626	+	7.25708i	−0.320389	+	0.336178i
$467$	9.51280	+	9.51280i	0.440200	+	0.440200i	0.892079	−	0.451879i	$-0.149246\pi$
$467$	9.51280	+	9.51280i	0.440200	+	0.440200i	−0.451879	+	0.892079i	$0.649246\pi$
$468$	−26.3267	+	28.9885i	−1.21695	+	1.33999i
$469$		−	5.67456i		−	0.262027i
$470$	16.3068	+	8.97122i	0.752175	+	0.413811i
$471$		−	26.4279i		−	1.21773i
$472$	−1.36982	−	18.9589i	−0.0630512	−	0.872654i
$473$	−8.76281	−	8.76281i	−0.402914	−	0.402914i
$474$	27.2116	+	25.9336i	1.24987	+	1.19117i
$475$	13.6127	−	7.73622i	0.624595	−	0.354962i
$476$	−9.70114	+	0.466835i	−0.444651	+	0.0213974i
$477$	−38.1745	+	38.1745i	−1.74789	+	1.74789i
$478$	−0.0196337	−	0.816475i	−0.000898026	−	0.0373447i
$479$	−1.08020			−0.0493557			−0.0246779	−	0.999695i	$-0.507856\pi$
$479$	−1.08020			−0.0493557			−0.0246779	+	0.999695i	$0.507856\pi$
$480$	14.2775	−	33.1402i	0.651677	−	1.51264i
$481$	−13.5523			−0.617930
$482$	0.312330	+	12.9883i	0.0142262	+	0.591603i
$483$	−9.35781	+	9.35781i	−0.425795	+	0.425795i
$484$	1.99769	−	0.0961322i	0.0908040	−	0.00436964i
$485$	0.360864	+	0.209986i	0.0163860	+	0.00953499i
$486$	12.9316	+	12.3243i	0.586590	+	0.559041i
$487$	−3.05902	−	3.05902i	−0.138617	−	0.138617i	0.634393	−	0.773010i	$-0.281250\pi$
$487$	−3.05902	−	3.05902i	−0.138617	−	0.138617i	−0.773010	+	0.634393i	$0.781250\pi$
$488$	−0.246241	−	3.40808i	−0.0111468	−	0.154276i
$489$		−	29.4471i		−	1.33165i
$490$	−5.58078	−	19.2311i	−0.252114	−	0.868773i
$491$			23.7862i			1.07346i	0.843756	+	0.536728i	$0.180340\pi$
$491$			23.7862i			1.07346i	−0.843756	+	0.536728i	$0.819660\pi$
$492$	−26.1251	+	28.7666i	−1.17781	+	1.29690i
$493$	15.9035	+	15.9035i	0.716260	+	0.716260i
$494$	11.6423	−	12.2160i	0.523813	−	0.549626i
$495$	−2.93590	−	11.1081i	−0.131959	−	0.499270i
$496$	1.55665	+	16.1366i	0.0698956	+	0.724556i
$497$	3.30565	−	3.30565i	0.148279	−	0.148279i
$498$	12.6164	−	0.303385i	0.565353	−	0.0135950i
$499$	25.3868			1.13647			0.568234	−	0.822867i	$-0.307627\pi$
$499$	25.3868			1.13647			0.568234	+	0.822867i	$0.307627\pi$
$500$	−16.3987	−	15.2014i	−0.733373	−	0.679827i
$501$	−31.9672			−1.42819
$502$	19.4340	−	0.467329i	0.867384	−	0.0208579i
$503$	23.4070	−	23.4070i	1.04367	−	1.04367i	0.0446651	−	0.999002i	$-0.485778\pi$
$503$	23.4070	−	23.4070i	1.04367	−	1.04367i	0.999002	−	0.0446651i	$-0.0142221\pi$
$504$	−8.98051	−	7.77023i	−0.400024	−	0.346114i
$505$	−0.742233	−	2.80826i	−0.0330289	−	0.124966i
$506$	5.53909	−	5.81205i	0.246242	−	0.258377i
$507$	3.06644	+	3.06644i	0.136186	+	0.136186i
$508$	−3.99579	−	3.62887i	−0.177284	−	0.161005i
$509$		−	10.4107i		−	0.461445i	−0.973020	−	0.230722i	$-0.925891\pi$
$509$		−	10.4107i		−	0.461445i	0.973020	−	0.230722i	$-0.0741089\pi$
$510$	−14.9419	−	51.4890i	−0.661637	−	2.27997i
$511$			2.09121i			0.0925096i
$512$	4.85802	+	22.0998i	0.214696	+	0.976681i
$513$	13.5071	+	13.5071i	0.596353	+	0.596353i
$514$	−20.5487	−	19.5837i	−0.906366	−	0.863799i
$515$	23.9291	+	13.9243i	1.05444	+	0.613577i
$516$	−3.39854	−	70.6239i	−0.149613	−	3.10904i
$517$	−4.16169	+	4.16169i	−0.183031	+	0.183031i
$518$	−0.0988017	−	4.10870i	−0.00434110	−	0.180526i
$519$	−49.6308			−2.17855
$520$	−21.6493	−	10.5883i	−0.949386	−	0.464329i
$521$	18.1068			0.793271			0.396636	−	0.917976i	$-0.370178\pi$
$521$	18.1068			0.793271			0.396636	+	0.917976i	$0.370178\pi$
$522$	0.661101	+	27.4921i	0.0289356	+	1.20330i
$523$	9.00519	−	9.00519i	0.393769	−	0.393769i	−0.482259	−	0.876029i	$-0.660184\pi$
$523$	9.00519	−	9.00519i	0.393769	−	0.393769i	0.876029	+	0.482259i	$0.160184\pi$
$524$	0.625637	+	13.0011i	0.0273311	+	0.567957i
$525$	−10.1333	+	5.75880i	−0.442251	+	0.251335i
$526$	−1.18691	−	1.13116i	−0.0517515	−	0.0493210i
$527$	17.0316	+	17.0316i	0.741908	+	0.741908i
$528$	8.80633	+	7.25677i	0.383246	+	0.315810i
$529$		−	9.23070i		−	0.401335i
$530$	−29.1109	−	16.0155i	−1.26450	−	0.695667i
$531$		−	34.5314i		−	1.49854i
$532$	3.78847	+	3.44060i	0.164251	+	0.149169i
$533$	18.3514	+	18.3514i	0.794887	+	0.794887i
$534$	47.4394	−	49.7772i	2.05290	−	2.15407i
$535$	−15.1039	+	25.9563i	−0.652999	+	1.12219i
$536$	−12.8521	+	14.8539i	−0.555125	+	0.641590i
$537$	−8.13935	+	8.13935i	−0.351239	+	0.351239i
$538$	15.5934	−	0.374974i	0.672280	−	0.0161663i
$539$	6.33231			0.272752
$540$	12.5711	−	24.2107i	0.540973	−	1.04186i
$541$	10.2839			0.442137			0.221069	−	0.975258i	$-0.429046\pi$
$541$	10.2839			0.442137			0.221069	+	0.975258i	$0.429046\pi$
$542$	−6.99884	+	0.168301i	−0.300626	+	0.00722913i
$543$	−47.3547	+	47.3547i	−2.03219	+	2.03219i
$544$	26.4513	+	20.7497i	1.13409	+	0.889635i
$545$	30.3472	−	8.02087i	1.29993	−	0.343576i
$546$	−8.66649	+	9.09357i	−0.370892	+	0.389169i
$547$	6.60913	+	6.60913i	0.282586	+	0.282586i	0.834139	−	0.551554i	$-0.185965\pi$
$547$	6.60913	+	6.60913i	0.282586	+	0.282586i	−0.551554	+	0.834139i	$0.685965\pi$
$548$	19.6603	−	21.6482i	0.839847	−	0.924764i
$549$		−	6.20742i		−	0.264926i
$550$	6.06189	−	3.64054i	0.258480	−	0.155233i
$551$		−	11.8510i		−	0.504868i
$552$	45.6894	−	3.30116i	1.94467	−	0.140507i
$553$	5.38354	+	5.38354i	0.228931	+	0.228931i
$554$	28.4661	+	27.1292i	1.20941	+	1.15261i
$555$	21.9338	−	5.79719i	0.931039	−	0.246077i
$556$	10.8053	−	0.519968i	0.458246	−	0.0220516i
$557$	−29.3349	+	29.3349i	−1.24296	+	1.24296i	−0.284195	+	0.958767i	$0.591726\pi$
$557$	−29.3349	+	29.3349i	−1.24296	+	1.24296i	−0.958767	+	0.284195i	$0.908274\pi$
$558$	0.707994	+	29.4422i	0.0299718	+	1.24639i
$559$	−47.2219			−1.99727
$560$	3.05228	−	6.64072i	0.128982	−	0.280621i
$561$	16.9540			0.715798
$562$	0.381813	+	15.8778i	0.0161058	+	0.669765i
$563$	−10.2716	+	10.2716i	−0.432896	+	0.432896i	−0.889612	−	0.456716i	$-0.849025\pi$
$563$	−10.2716	+	10.2716i	−0.432896	+	0.432896i	0.456716	+	0.889612i	$0.349025\pi$
$564$	−33.5412	+	1.61406i	−1.41234	+	0.0679641i
$565$	12.2416	−	21.0374i	0.515010	−	0.885051i
$566$	−29.2831	−	27.9078i	−1.23086	−	1.17305i
$567$	−1.14804	−	1.14804i	−0.0482132	−	0.0482132i
$568$	−16.1398	+	1.16614i	−0.677211	+	0.0489300i
$569$			7.70852i			0.323158i	0.986860	+	0.161579i	$0.0516587\pi$
$569$			7.70852i			0.323158i	−0.986860	+	0.161579i	$0.948341\pi$
$570$	−13.6171	+	24.7514i	−0.570356	+	1.03672i
$571$		−	27.9383i		−	1.16918i	−0.811329	−	0.584590i	$-0.801255\pi$
$571$		−	27.9383i		−	1.16918i	0.811329	−	0.584590i	$-0.198745\pi$
$572$	5.12365	−	5.64170i	0.214231	−	0.235891i
$573$	−37.1298	−	37.1298i	−1.55112	−	1.55112i
$574$	−5.42989	+	5.69747i	−0.226639	+	0.237808i
$575$	7.53337	−	27.3682i	0.314163	−	1.14133i
$576$	5.90916	+	40.6791i	0.246215	+	1.69496i
$577$	−2.97232	+	2.97232i	−0.123739	+	0.123739i	−0.766265	−	0.642525i	$-0.777887\pi$
$577$	−2.97232	+	2.97232i	−0.123739	+	0.123739i	0.642525	+	0.766265i	$0.277887\pi$
$578$	25.9000	−	0.622815i	1.07730	−	0.0259057i
$579$	−6.89933			−0.286726
$580$	−16.1359	+	5.10621i	−0.670007	+	0.212024i
$581$	2.55604			0.106042
$582$	−0.753079	+	0.0181092i	−0.0312161	+	0.000750652i
$583$	7.42947	−	7.42947i	0.307697	−	0.307697i
$584$	4.73629	−	5.47400i	0.195989	−	0.226516i
$585$	−37.8408	−	22.0195i	−1.56452	−	0.910394i
$586$	8.03522	−	8.43119i	0.331932	−	0.348289i
$587$	−0.708389	−	0.708389i	−0.0292384	−	0.0292384i	0.692336	−	0.721575i	$-0.256581\pi$
$587$	−0.708389	−	0.708389i	−0.0292384	−	0.0292384i	−0.721575	+	0.692336i	$0.756581\pi$
$588$	26.7456	+	24.2897i	1.10297	+	1.00169i
$589$		−	12.6916i		−	0.522947i
$590$	20.4099	−	5.92286i	0.840263	−	0.243840i
$591$			48.5983i			1.99907i
$592$	−9.04699	+	10.9788i	−0.371829	+	0.451226i
$593$	−20.0300	−	20.0300i	−0.822534	−	0.822534i	0.163937	−	0.986471i	$-0.447581\pi$
$593$	−20.0300	−	20.0300i	−0.822534	−	0.822534i	−0.986471	+	0.163937i	$0.947581\pi$
$594$	6.24483	+	5.95154i	0.256228	+	0.244195i
$595$	−2.77473	−	10.4983i	−0.113753	−	0.430387i
$596$	−0.670740	−	13.9384i	−0.0274746	−	0.570940i
$597$	−21.0905	+	21.0905i	−0.863175	+	0.863175i
$598$	−0.735478	−	30.5851i	−0.0300759	−	1.25072i
$599$	−36.9338			−1.50908			−0.754538	−	0.656257i	$-0.772139\pi$
$599$	−36.9338			−1.50908			−0.754538	+	0.656257i	$0.772139\pi$
$600$	39.5679	+	7.87597i	1.61535	+	0.321535i
$601$	22.8410			0.931703			0.465851	−	0.884863i	$-0.345748\pi$
$601$	22.8410			0.931703			0.465851	+	0.884863i	$0.345748\pi$
$602$	−0.344268	−	14.3165i	−0.0140313	−	0.583496i
$603$	−25.2316	+	25.2316i	−1.02751	+	1.02751i
$604$	0.123071	+	2.55749i	0.00500768	+	0.104063i
$605$	0.571381	+	2.16183i	0.0232299	+	0.0878910i
$606$	3.79381	+	3.61563i	0.154113	+	0.146875i
$607$	8.24942	+	8.24942i	0.334833	+	0.334833i	0.854419	−	0.519585i	$-0.173914\pi$
$607$	8.24942	+	8.24942i	0.334833	+	0.334833i	−0.519585	+	0.854419i	$0.673914\pi$
$608$	−2.12435	−	17.5865i	−0.0861537	−	0.713228i
$609$			8.82179i			0.357477i
$610$	3.66891	−	1.06470i	0.148550	−	0.0431085i
$611$			22.4269i			0.907297i
$612$	45.2113	+	41.0598i	1.82756	+	1.65974i
$613$	26.2623	+	26.2623i	1.06072	+	1.06072i	0.998033	+	0.0626907i	$0.0199682\pi$
$613$	26.2623	+	26.2623i	1.06072	+	1.06072i	0.0626907	+	0.998033i	$0.480032\pi$
$614$	−16.7770	+	17.6038i	−0.677066	+	0.710431i
$615$	−37.5511	−	21.8509i	−1.51421	−	0.881115i
$616$	1.74777	+	1.51223i	0.0704198	+	0.0609295i
$617$	12.0227	−	12.0227i	0.484014	−	0.484014i	−0.422397	−	0.906411i	$-0.638811\pi$
$617$	12.0227	−	12.0227i	0.484014	−	0.484014i	0.906411	+	0.422397i	$0.138811\pi$
$618$	−49.9370	+	1.20083i	−2.00876	+	0.0483045i
$619$	−5.24313			−0.210739			−0.105370	−	0.994433i	$-0.533603\pi$
$619$	−5.24313			−0.210739			−0.105370	+	0.994433i	$0.533603\pi$
$620$	−17.2804	+	5.46840i	−0.693999	+	0.219616i
$621$	34.6307			1.38968
$622$	−11.4641	+	0.275677i	−0.459670	+	0.0110537i
$623$	9.84790	−	9.84790i	0.394548	−	0.394548i
$624$	43.2813	−	4.17520i	1.73264	−	0.167142i
$625$	12.7937	−	21.4784i	0.511746	−	0.859137i
$626$	−11.2670	+	11.8222i	−0.450318	+	0.472509i
$627$	−6.31687	−	6.31687i	−0.252271	−	0.252271i
$628$	−12.4564	+	13.7158i	−0.497063	+	0.547321i
$629$			21.1365i			0.842767i
$630$	6.39987	−	11.6329i	0.254977	−	0.463466i
$631$		−	7.51569i		−	0.299195i	−0.988747	−	0.149597i	$-0.952202\pi$
$631$		−	7.51569i		−	0.299195i	0.988747	−	0.149597i	$-0.0477978\pi$
$632$	−1.89915	−	26.2850i	−0.0755442	−	1.04556i
$633$	24.1460	+	24.1460i	0.959718	+	0.959718i
$634$	1.95930	+	1.86728i	0.0778136	+	0.0741591i
$635$	3.03517	−	5.21599i	0.120447	−	0.206990i
$636$	59.8778	−	2.88142i	2.37431	−	0.114256i
$637$	17.0621	−	17.0621i	0.676025	−	0.676025i
$638$	−0.128662	−	5.35047i	−0.00509379	−	0.211827i
$639$	−29.3968			−1.16292
$640$	−23.0300	+	10.4699i	−0.910340	+	0.413861i
$641$	7.27424			0.287315			0.143658	−	0.989627i	$-0.454114\pi$
$641$	7.27424			0.287315			0.143658	+	0.989627i	$0.454114\pi$
$642$	−1.30256	−	54.1675i	−0.0514080	−	2.13782i
$643$	24.9810	−	24.9810i	0.985153	−	0.985153i	−0.0147379	−	0.999891i	$-0.504691\pi$
$643$	24.9810	−	24.9810i	0.985153	−	0.985153i	0.999891	+	0.0147379i	$0.00469139\pi$
$644$	9.26726	−	0.445956i	0.365181	−	0.0175731i
$645$	76.4269	−	20.1999i	3.00931	−	0.795371i
$646$	−19.0525	−	18.1577i	−0.749610	−	0.714405i
$647$	−6.78345	−	6.78345i	−0.266685	−	0.266685i	0.561078	−	0.827763i	$-0.310387\pi$
$647$	−6.78345	−	6.78345i	−0.266685	−	0.266685i	−0.827763	+	0.561078i	$0.810387\pi$
$648$	0.404995	+	5.60529i	0.0159097	+	0.220196i
$649$			6.72046i			0.263801i
$650$	6.52421	−	26.1427i	0.255901	−	1.02540i
$651$			9.44753i			0.370278i
$652$	−13.8794	+	15.2828i	−0.543560	+	0.598519i
$653$	−22.1899	−	22.1899i	−0.868357	−	0.868357i	0.123934	−	0.992291i	$-0.460449\pi$
$653$	−22.1899	−	22.1899i	−0.868357	−	0.868357i	−0.992291	+	0.123934i	$0.960449\pi$
$654$	−39.0720	+	40.9974i	−1.52783	+	1.60312i
$655$	−14.0694	+	3.71860i	−0.549737	+	0.145298i
$656$	27.1174	−	2.61592i	1.05875	−	0.102135i
$657$	9.29843	−	9.29843i	0.362766	−	0.362766i
$658$	−6.79928	+	0.163502i	−0.265063	+	0.00637396i
$659$	13.5226			0.526766			0.263383	−	0.964691i	$-0.415162\pi$
$659$	13.5226			0.526766			0.263383	+	0.964691i	$0.415162\pi$
$660$	−5.87911	+	11.3226i	−0.228844	+	0.440732i
$661$	18.8632			0.733694			0.366847	−	0.930281i	$-0.380437\pi$
$661$	18.8632			0.733694			0.366847	+	0.930281i	$0.380437\pi$
$662$	−1.43576	+	0.0345256i	−0.0558024	+	0.00134188i
$663$	45.6817	−	45.6817i	1.77413	−	1.77413i
$664$	−6.69076	−	5.78906i	−0.259652	−	0.224659i
$665$	−2.87770	+	4.94536i	−0.111592	+	0.191773i
$666$	−17.8298	+	18.7084i	−0.690890	+	0.724936i
$667$	−15.1923	−	15.1923i	−0.588247	−	0.588247i
$668$	16.5906	+	15.0672i	0.641911	+	0.582968i
$669$		−	8.52173i		−	0.329469i
$670$	−19.2410	−	10.5855i	−0.743343	−	0.408953i
$671$			1.20808i			0.0466373i
$672$	1.58135	+	13.0913i	0.0610020	+	0.505009i
$673$	11.4476	+	11.4476i	0.441273	+	0.441273i	0.892440	−	0.451167i	$-0.148992\pi$
$673$	11.4476	+	11.4476i	0.441273	+	0.441273i	−0.451167	+	0.892440i	$0.648992\pi$
$674$	−20.6807	−	19.7094i	−0.796589	−	0.759178i
$675$	29.4061	+	8.09432i	1.13184	+	0.311551i
$676$	−0.146135	−	3.03677i	−0.00562056	−	0.116799i
$677$	−24.5176	+	24.5176i	−0.942289	+	0.942289i	−0.998423	−	0.0561347i	$-0.982122\pi$
$677$	−24.5176	+	24.5176i	−0.942289	+	0.942289i	0.0561347	+	0.998423i	$0.482122\pi$
$678$	1.05572	+	43.9025i	0.0405447	+	1.68606i
$679$	−0.152572			−0.00585517
$680$	−16.5138	+	33.7649i	−0.633277	+	1.29482i
$681$	33.1631			1.27081
$682$	−0.137789	−	5.72999i	−0.00527620	−	0.219412i
$683$	−26.1744	+	26.1744i	−1.00154	+	1.00154i	−0.00153813	+	0.999999i	$0.500490\pi$
$683$	−26.1744	+	26.1744i	−1.00154	+	1.00154i	−0.999999	+	0.00153813i	$0.999510\pi$
$684$	−1.54681	−	32.1436i	−0.0591436	−	1.22904i
$685$	28.2589	+	16.4438i	1.07972	+	0.628286i
$686$	11.1529	+	10.6291i	0.425820	+	0.405822i
$687$	−42.1324	−	42.1324i	−1.60745	−	1.60745i
$688$	−31.5236	+	38.2549i	−1.20183	+	1.45846i
$689$		−	40.0367i		−	1.52528i
$690$	14.2736	+	49.1862i	0.543386	+	1.87249i
$691$		−	15.4756i		−	0.588721i	−0.955694	−	0.294361i	$-0.904893\pi$
$691$		−	15.4756i		−	0.588721i	0.955694	−	0.294361i	$-0.0951067\pi$
$692$	25.7579	+	23.3927i	0.979168	+	0.889256i
$693$	2.96886	+	2.96886i	0.112778	+	0.112778i
$694$	32.9276	−	34.5503i	1.24992	−	1.31151i
$695$	3.09053	+	11.6931i	0.117231	+	0.443545i
$696$	19.9801	−	23.0922i	0.757344	−	0.875306i
$697$	28.6213	−	28.6213i	1.08411	−	1.08411i
$698$	−7.48952	+	0.180100i	−0.283483	+	0.00681689i
$699$	20.2224			0.764883
$700$	7.97337	+	1.78738i	0.301365	+	0.0675568i
$701$	−23.5564			−0.889712			−0.444856	−	0.895602i	$-0.646745\pi$
$701$	−23.5564			−0.889712			−0.444856	+	0.895602i	$0.646745\pi$
$702$	32.8625	−	0.790243i	1.24032	−	0.0298258i
$703$	7.87521	−	7.87521i	0.297019	−	0.297019i
$704$	−1.15003	−	7.91691i	−0.0433435	−	0.298380i
$705$	−9.59347	−	36.2972i	−0.361311	−	1.36703i
$706$	−28.9898	+	30.4184i	−1.09105	+	1.14481i
$707$	0.750565	+	0.750565i	0.0282279	+	0.0282279i
$708$	−25.7786	+	28.3850i	−0.968818	+	1.06677i
$709$			17.6845i			0.664157i	0.943252	+	0.332078i	$0.107750\pi$
$709$			17.6845i			0.664157i	−0.943252	+	0.332078i	$0.892250\pi$
$710$	−5.04216	−	17.3751i	−0.189229	−	0.652074i
$711$		−	47.8752i		−	1.79546i
$712$	−48.0822	+	3.47405i	−1.80196	+	0.130195i
$713$	−16.2699	−	16.2699i	−0.609311	−	0.609311i
$714$	14.1826	+	13.5165i	0.530770	+	0.505842i
$715$	7.36451	+	4.28540i	0.275417	+	0.160265i
$716$	8.06059	−	0.387889i	0.301238	−	0.0144961i
$717$	−1.16494	+	1.16494i	−0.0435056	+	0.0435056i
$718$	1.02156	+	42.4819i	0.0381242	+	1.58541i
$719$	30.3312			1.13116			0.565581	−	0.824692i	$-0.308652\pi$
$719$	30.3312			1.13116			0.565581	+	0.824692i	$0.308652\pi$
$720$	−43.0993	+	15.9558i	−1.60622	+	0.594637i
$721$	−10.1171			−0.376780
$722$	−0.312567	−	12.9982i	−0.0116325	−	0.483743i
$723$	18.5317	−	18.5317i	0.689201	−	0.689201i
$724$	46.8965	−	2.25674i	1.74289	−	0.0838710i
$725$	−9.34932	−	16.4512i	−0.347225	−	0.610981i
$726$	−2.92052	−	2.78336i	−0.108391	−	0.103300i
$727$	3.77266	+	3.77266i	0.139920	+	0.139920i	0.773598	−	0.633677i	$-0.218455\pi$
$727$	3.77266	+	3.77266i	0.139920	+	0.139920i	−0.633677	+	0.773598i	$0.718455\pi$
$728$	8.78392	−	0.634658i	0.325554	−	0.0235220i
$729$		−	41.9958i		−	1.55540i
$730$	7.09074	+	3.90100i	0.262440	+	0.144382i
$731$			73.6486i			2.72399i
$732$	−4.63399	+	5.10252i	−0.171277	+	0.188595i
$733$	−24.8819	−	24.8819i	−0.919035	−	0.919035i	0.0779247	−	0.996959i	$-0.475171\pi$
$733$	−24.8819	−	24.8819i	−0.919035	−	0.919035i	−0.996959	+	0.0779247i	$0.975171\pi$
$734$	24.4142	−	25.6173i	0.901143	−	0.945551i
$735$	−20.3158	+	34.9129i	−0.749359	+	1.28778i
$736$	−25.2682	−	19.8217i	−0.931400	−	0.730636i
$737$	4.91054	−	4.91054i	0.180882	−	0.180882i
$738$	49.4771	−	1.18977i	1.82128	−	0.0437961i
$739$	49.1757			1.80896			0.904479	−	0.426517i	$-0.140260\pi$
$739$	49.1757			1.80896			0.904479	+	0.426517i	$0.140260\pi$
$740$	−14.1158	−	7.32947i	−0.518909	−	0.269437i
$741$	−34.0410			−1.25053
$742$	12.1381	−	0.291884i	0.445604	−	0.0107154i
$743$	−7.28068	+	7.28068i	−0.267102	+	0.267102i	−0.827931	−	0.560829i	$-0.810482\pi$
$743$	−7.28068	+	7.28068i	−0.267102	+	0.267102i	0.560829	+	0.827931i	$0.310482\pi$
$744$	21.3973	−	24.7301i	0.784463	−	0.906650i
$745$	15.0837	−	3.98668i	0.552624	−	0.146061i
$746$	−10.4271	+	10.9410i	−0.381765	+	0.400578i
$747$	−11.3653	−	11.3653i	−0.415834	−	0.415834i
$748$	−8.79895	−	7.99099i	−0.321721	−	0.292179i
$749$		−	10.9742i		−	0.400988i
$750$	0.623760	+	45.1018i	0.0227765	+	1.64689i
$751$			8.47426i			0.309230i	0.987975	+	0.154615i	$0.0494137\pi$
$751$			8.47426i			0.309230i	−0.987975	+	0.154615i	$0.950586\pi$
$752$	18.1683	+	14.9714i	0.662529	+	0.545951i
$753$	−27.7284	−	27.7284i	−1.01048	−	1.01048i
$754$	−14.7633	−	14.0699i	−0.537646	−	0.512396i
$755$	−2.76763	+	0.731495i	−0.100724	+	0.0266218i
$756$	0.479163	+	9.95732i	0.0174270	+	0.362144i
$757$	−19.0120	+	19.0120i	−0.691004	+	0.691004i	−0.962453	−	0.271449i	$-0.912497\pi$
$757$	−19.0120	+	19.0120i	−0.691004	+	0.691004i	0.271449	+	0.962453i	$0.412497\pi$
$758$	0.894871	+	37.2135i	0.0325032	+	1.35166i
$759$	−16.1957			−0.587868
$760$	18.7333	−	6.42754i	0.679527	−	0.233151i
$761$	34.5321			1.25179			0.625894	−	0.779908i	$-0.284734\pi$
$761$	34.5321			1.25179			0.625894	+	0.779908i	$0.284734\pi$
$762$	0.261754	+	10.8851i	0.00948234	+	0.394326i
$763$	−8.11091	+	8.11091i	−0.293635	+	0.293635i
$764$	1.76946	+	36.7705i	0.0640168	+	1.33031i
$765$	−34.3422	+	59.0175i	−1.24165	+	2.13378i
$766$	−4.58772	−	4.37226i	−0.165761	−	0.157976i
$767$	18.1079	+	18.1079i	0.653840	+	0.653840i
$768$	25.5106	−	37.8498i	0.920534	−	1.36579i
$769$			30.6356i			1.10475i	0.833596	+	0.552375i	$0.186278\pi$
$769$			30.6356i			1.10475i	−0.833596	+	0.552375i	$0.813722\pi$
$770$	−1.24553	+	2.26398i	−0.0448859	+	0.0815880i
$771$			57.2607i			2.06219i
$772$	3.58068	+	3.25189i	0.128872	+	0.117038i
$773$	−3.28135	−	3.28135i	−0.118022	−	0.118022i	0.645629	−	0.763651i	$-0.276595\pi$
$773$	−3.28135	−	3.28135i	−0.118022	−	0.118022i	−0.763651	+	0.645629i	$0.776595\pi$
$774$	−62.1266	+	65.1882i	−2.23310	+	2.34314i
$775$	−10.0125	−	17.6181i	−0.359659	−	0.632860i
$776$	0.399376	+	0.345553i	0.0143368	+	0.0124046i
$777$	−5.86227	+	5.86227i	−0.210308	+	0.210308i
$778$	7.45353	−	0.179235i	0.267222	−	0.00642587i
$779$	−21.3280			−0.764154
$780$	14.6672	+	46.3492i	0.525170	+	1.65957i
$781$	5.72115			0.204719
$782$	−47.7014	+	1.14707i	−1.70580	+	0.0410192i
$783$	16.3235	−	16.3235i	0.583355	−	0.583355i
$784$	−2.43214	−	25.2122i	−0.0868621	−	0.900435i
$785$	−17.9042	−	10.4184i	−0.639030	−	0.371850i
$786$	18.1143	−	19.0070i	0.646117	−	0.677957i
$787$	−37.4133	−	37.4133i	−1.33364	−	1.33364i	−0.902089	−	0.431551i	$-0.857967\pi$
$787$	−37.4133	−	37.4133i	−1.33364	−	1.33364i	−0.431551	−	0.902089i	$-0.642033\pi$
$788$	22.9060	−	25.2220i	0.815993	−	0.898497i
$789$			3.30741i			0.117747i
$790$	28.2968	−	8.21158i	1.00675	−	0.292155i
$791$			8.89452i			0.316253i
$792$	−1.04733	−	14.4954i	−0.0372151	−	0.515072i
$793$	3.25511	+	3.25511i	0.115592	+	0.115592i
$794$	−11.3433	−	10.8106i	−0.402559	−	0.383653i
$795$	17.1263	+	64.7979i	0.607408	+	2.29814i
$796$	20.8864	−	1.00509i	0.740298	−	0.0356244i
$797$	26.7408	−	26.7408i	0.947207	−	0.947207i	−0.0514680	−	0.998675i	$-0.516390\pi$
$797$	26.7408	−	26.7408i	0.947207	−	0.947207i	0.998675	+	0.0514680i	$0.0163900\pi$
$798$	−0.248173	−	10.3204i	−0.00878523	−	0.365337i
$799$	34.9777			1.23742
$800$	−16.8231	−	22.7372i	−0.594788	−	0.803883i
$801$	−87.5762			−3.09435
$802$	0.0287657	+	1.19623i	0.00101575	+	0.0422404i
$803$	−1.80965	+	1.80965i	−0.0638610	+	0.0638610i
$804$	39.5765	−	1.90449i	1.39576	−	0.0671661i
$805$	2.65063	+	10.0287i	0.0934224	+	0.353466i
$806$	−15.8104	−	15.0679i	−0.556899	−	0.530744i
$807$	−22.2486	−	22.2486i	−0.783188	−	0.783188i
$808$	−0.264777	−	3.66462i	−0.00931483	−	0.128921i
$809$			27.8007i			0.977421i	0.872446	+	0.488710i	$0.162532\pi$
$809$			27.8007i			0.977421i	−0.872446	+	0.488710i	$0.837468\pi$
$810$	−6.03429	+	1.75112i	−0.212023	+	0.0615281i
$811$			24.4103i			0.857163i	0.903503	+	0.428582i	$0.140987\pi$
$811$			24.4103i			0.857163i	−0.903503	+	0.428582i	$0.859013\pi$
$812$	4.15801	−	4.57842i	0.145917	−	0.160671i
$813$	9.98591	+	9.98591i	0.350221	+	0.350221i
$814$	3.47000	−	3.64100i	0.121624	−	0.127617i
$815$	−19.9497	−	11.6087i	−0.698807	−	0.406634i
$816$	−6.51176	−	67.5026i	−0.227957	−	2.36306i
$817$	27.4406	−	27.4406i	0.960026	−	0.960026i
$818$	13.9432	−	0.335290i	0.487511	−	0.0117231i
$819$	15.9989			0.559047
$820$	9.18957	+	29.0395i	0.320914	+	1.01410i
$821$	−6.73158			−0.234934			−0.117467	−	0.993077i	$-0.537477\pi$
$821$	−6.73158			−0.234934			−0.117467	+	0.993077i	$0.537477\pi$
$822$	−58.9728	+	1.41812i	−2.05691	+	0.0494625i
$823$	34.4158	−	34.4158i	1.19966	−	1.19966i	0.225392	−	0.974268i	$-0.427634\pi$
$823$	34.4158	−	34.4158i	1.19966	−	1.19966i	0.974268	−	0.225392i	$-0.0723662\pi$
$824$	26.4828	+	22.9138i	0.922571	+	0.798239i
$825$	−13.7523	−	3.78547i	−0.478795	−	0.131793i
$826$	−5.35785	+	5.62188i	−0.186424	+	0.195610i
$827$	−0.387622	−	0.387622i	−0.0134789	−	0.0134789i	0.700335	−	0.713814i	$-0.253034\pi$
$827$	−0.387622	−	0.387622i	−0.0134789	−	0.0134789i	−0.713814	+	0.700335i	$0.753034\pi$
$828$	−43.1892	−	39.2234i	−1.50093	−	1.36311i
$829$		−	21.1590i		−	0.734884i	−0.930046	−	0.367442i	$-0.880234\pi$
$829$		−	21.1590i		−	0.734884i	0.930046	−	0.367442i	$-0.119766\pi$
$830$	4.76810	−	8.66687i	0.165503	−	0.300831i
$831$		−	79.3232i		−	2.75169i
$832$	−24.4304	−	18.2330i	−0.846973	−	0.632116i
$833$	−26.6105	−	26.6105i	−0.922000	−	0.922000i
$834$	−15.7968	−	15.0549i	−0.546997	−	0.521308i
$835$	−12.6021	+	21.6570i	−0.436115	+	0.749470i
$836$	0.301037	+	6.25574i	0.0104116	+	0.216359i
$837$	17.4814	−	17.4814i	0.604244	−	0.604244i
$838$	−0.679284	−	28.2482i	−0.0234655	−	0.975820i
$839$	35.8248			1.23681			0.618405	−	0.785859i	$-0.287779\pi$
$839$	35.8248			1.23681			0.618405	+	0.785859i	$0.287779\pi$
$840$	−13.9450	+	4.78463i	−0.481147	+	0.165085i
$841$	14.6780			0.506136
$842$	−0.527396	−	21.9319i	−0.0181753	−	0.755824i
$843$	22.6544	−	22.6544i	0.780258	−	0.780258i
$844$	−1.15070	−	23.9124i	−0.0396088	−	0.823097i
$845$	3.28629	−	0.868580i	0.113052	−	0.0298800i
$846$	30.9596	+	29.5056i	1.06441	+	1.01442i
$847$	−0.577795	−	0.577795i	−0.0198533	−	0.0198533i
$848$	−32.4341	−	26.7270i	−1.11379	−	0.917809i
$849$			81.5997i			2.80049i
$850$	−40.7729	−	10.1753i	−1.39850	−	0.349011i
$851$		−	20.1912i		−	0.692144i
$852$	24.1643	+	21.9454i	0.827855	+	0.751837i
$853$	28.2283	+	28.2283i	0.966518	+	0.966518i	0.999457	−	0.0329397i	$-0.0104869\pi$
$853$	28.2283	+	28.2283i	0.966518	+	0.966518i	−0.0329397	+	0.999457i	$0.510487\pi$
$854$	−0.963134	+	1.01060i	−0.0329578	+	0.0345819i
$855$	34.7848	−	9.19375i	1.18961	−	0.314419i
$856$	−24.8549	+	28.7263i	−0.849524	+	0.981845i
$857$	−33.1900	+	33.1900i	−1.13375	+	1.13375i	−0.144202	+	0.989548i	$0.546061\pi$
$857$	−33.1900	+	33.1900i	−1.13375	+	1.13375i	−0.989548	+	0.144202i	$0.953939\pi$
$858$	−15.3688	+	0.369573i	−0.524683	+	0.0126170i
$859$	−22.2469			−0.759053			−0.379527	−	0.925181i	$-0.623913\pi$
$859$	−22.2469			−0.759053			−0.379527	+	0.925181i	$0.623913\pi$
$860$	−49.1857	−	25.5390i	−1.67722	−	0.870873i
$861$	15.8764			0.541068
$862$	27.0285	−	0.649952i	0.920594	−	0.0221375i
$863$	−36.4372	+	36.4372i	−1.24034	+	1.24034i	−0.280475	+	0.959861i	$0.590492\pi$
$863$	−36.4372	+	36.4372i	−1.24034	+	1.24034i	−0.959861	+	0.280475i	$0.909508\pi$
$864$	21.2976	−	27.1498i	0.724560	−	0.923655i
$865$	−19.5655	+	33.6236i	−0.665248	+	1.14324i
$866$	−20.5696	+	21.5832i	−0.698983	+	0.733429i
$867$	−36.9539	−	36.9539i	−1.25502	−	1.25502i
$868$	4.45294	−	4.90317i	0.151143	−	0.166425i
$869$			9.31739i			0.316071i
$870$	29.9124	+	16.4564i	1.01413	+	0.557924i
$871$		−	26.4624i		−	0.896644i
$872$	39.6014	−	2.86129i	1.34107	−	0.0968955i
$873$	0.678401	+	0.678401i	0.0229604	+	0.0229604i
$874$	18.2004	+	17.3456i	0.615637	+	0.586723i
$875$	−0.0933030	+	9.13526i	−0.00315422	+	0.308828i
$876$	−14.5849	+	0.701848i	−0.492777	+	0.0237133i
$877$	−1.22262	+	1.22262i	−0.0412851	+	0.0412851i	−0.727448	−	0.686163i	$-0.759294\pi$
$877$	−1.22262	+	1.22262i	−0.0412851	+	0.0412851i	0.686163	+	0.727448i	$0.259294\pi$
$878$	−0.246448	−	10.2486i	−0.00831722	−	0.345875i
$879$	−23.4942			−0.792439
$880$	8.38792	−	3.10529i	0.282757	−	0.104679i
$881$	57.1296			1.92475			0.962373	−	0.271732i	$-0.0875964\pi$
$881$	57.1296			1.92475			0.962373	+	0.271732i	$0.0875964\pi$
$882$	−1.10618	−	46.0010i	−0.0372471	−	1.54893i
$883$	−9.90424	+	9.90424i	−0.333304	+	0.333304i	−0.853840	−	0.520536i	$-0.825732\pi$
$883$	−9.90424	+	9.90424i	−0.333304	+	0.333304i	0.520536	+	0.853840i	$0.325732\pi$
$884$	−45.2397	+	2.17701i	−1.52158	+	0.0732208i
$885$	−37.0530	−	21.5611i	−1.24552	−	0.724767i
$886$	−13.2561	−	12.6335i	−0.445346	−	0.424431i
$887$	5.64043	+	5.64043i	0.189387	+	0.189387i	0.795431	−	0.606044i	$-0.207245\pi$
$887$	5.64043	+	5.64043i	0.189387	+	0.189387i	−0.606044	+	0.795431i	$0.707245\pi$
$888$	28.6224	−	2.06803i	0.960506	−	0.0693987i
$889$			2.20529i			0.0739632i
$890$	−15.0211	−	51.7622i	−0.503510	−	1.73507i
$891$		−	1.98693i		−	0.0665648i
$892$	−4.01658	+	4.42269i	−0.134485	+	0.148083i
$893$	−13.0323	−	13.0323i	−0.436109	−	0.436109i
$894$	−19.4203	+	20.3773i	−0.649511	+	0.681518i
$895$	2.30550	+	8.72290i	0.0770642	+	0.291575i
$896$	5.34968	−	7.53961i	0.178720	−	0.251881i
$897$	−43.6386	+	43.6386i	−1.45705	+	1.45705i
$898$	−7.38547	+	0.177598i	−0.246456	+	0.00592652i
$899$	−15.3379			−0.511548
$900$	−27.5056	−	43.4006i	−0.916854	−	1.44669i
$901$	−62.4423			−2.08026
$902$	−9.62915	+	0.231552i	−0.320616	+	0.00770983i
$903$	−20.4267	+	20.4267i	−0.679757	+	0.679757i
$904$	20.1448	−	23.2825i	0.670006	−	0.774365i
$905$	13.4134	+	50.7498i	0.445876	+	1.68698i
$906$	3.56332	−	3.73892i	0.118383	−	0.124217i
$907$	28.1641	+	28.1641i	0.935173	+	0.935173i	0.998023	−	0.0628499i	$-0.0200189\pi$
$907$	28.1641	+	28.1641i	0.935173	+	0.935173i	−0.0628499	+	0.998023i	$0.520019\pi$
$908$	−17.2113	−	15.6309i	−0.571177	−	0.518729i
$909$		−	6.67469i		−	0.221385i
$910$	2.74414	+	9.45620i	0.0909675	+	0.313470i
$911$		−	19.5259i		−	0.646921i	−0.946242	−	0.323460i	$-0.895154\pi$
$911$		−	19.5259i		−	0.646921i	0.946242	−	0.323460i	$-0.104846\pi$
$912$	−22.7245	+	27.5769i	−0.752484	+	0.913163i
$913$	2.21189	+	2.21189i	0.0732030	+	0.0732030i
$914$	9.82551	+	9.36406i	0.324999	+	0.309736i
$915$	−6.66069	−	3.87585i	−0.220196	−	0.128131i
$916$	2.00786	+	41.7247i	0.0663417	+	1.37862i
$917$	3.76034	−	3.76034i	0.124177	−	0.124177i
$918$	−1.23249	−	51.2533i	−0.0406781	−	1.69161i
$919$	2.67588			0.0882693			0.0441346	−	0.999026i	$-0.485947\pi$
$919$	2.67588			0.0882693			0.0441346	+	0.999026i	$0.485947\pi$
$920$	15.7753	−	32.2548i	0.520095	−	1.06341i
$921$	49.0544			1.61640
$922$	0.543077	+	22.5840i	0.0178853	+	0.743766i
$923$	15.4154	−	15.4154i	0.507403	−	0.507403i
$924$	−0.224090	−	4.65674i	−0.00737203	−	0.153196i
$925$	4.71933	−	17.1450i	0.155171	−	0.563723i
$926$	37.9263	+	36.1451i	1.24633	+	1.18780i
$927$	44.9851	+	44.9851i	1.47750	+	1.47750i
$928$	−21.2536	+	2.56730i	−0.697683	+	0.0842758i
$929$			41.6520i			1.36656i	0.730157	+	0.683279i	$0.239447\pi$
$929$			41.6520i			1.36656i	−0.730157	+	0.683279i	$0.760553\pi$
$930$	32.0341	+	17.6237i	1.05044	+	0.577903i
$931$			19.8295i			0.649887i
$932$	−10.4952	−	9.53151i	−0.343783	−	0.312215i
$933$	16.3570	+	16.3570i	0.535503	+	0.535503i
$934$	−13.1258	+	13.7727i	−0.429490	+	0.450655i
$935$	6.68363	−	11.4859i	0.218578	−	0.375629i
$936$	−41.8791	−	36.2352i	−1.36886	−	1.18438i
$937$	−23.9386	+	23.9386i	−0.782041	+	0.782041i	−0.980175	−	0.198134i	$-0.936512\pi$
$937$	−23.9386	+	23.9386i	−0.782041	+	0.782041i	0.198134	+	0.980175i	$0.436512\pi$
$938$	8.02273	−	0.192922i	0.261951	−	0.00629913i
$939$	32.9434			1.07507
$940$	−12.1292	+	23.3596i	−0.395609	+	0.761905i
$941$	−36.2569			−1.18194			−0.590970	−	0.806693i	$-0.701255\pi$
$941$	−36.2569			−1.18194			−0.590970	+	0.806693i	$0.701255\pi$
$942$	37.3639	−	0.898488i	1.21738	−	0.0292743i
$943$	−27.3413	+	27.3413i	−0.890354	+	0.890354i
$944$	26.7576	−	2.58122i	0.870886	−	0.0840116i
$945$	−10.7755	+	2.84800i	−0.350527	+	0.0926455i
$946$	12.0910	−	12.6868i	0.393112	−	0.412484i
$947$	−2.49828	−	2.49828i	−0.0811831	−	0.0811831i	0.665349	−	0.746532i	$-0.268283\pi$
$947$	−2.49828	−	2.49828i	−0.0811831	−	0.0811831i	−0.746532	+	0.665349i	$0.768283\pi$
$948$	−35.7400	+	39.3536i	−1.16078	+	1.27815i
$949$			9.75201i			0.316564i
$950$	11.4003	+	18.9827i	0.369875	+	0.615881i
$951$		−	5.45973i		−	0.177044i
$952$	−0.989830	−	13.6996i	−0.0320806	−	0.444008i
$953$	−11.1582	−	11.1582i	−0.361449	−	0.361449i	0.502897	−	0.864346i	$-0.332267\pi$
$953$	−11.1582	−	11.1582i	−0.361449	−	0.361449i	−0.864346	+	0.502897i	$0.832267\pi$
$954$	−55.2692	−	52.6735i	−1.78941	−	1.70537i
$955$	−39.7919	+	10.5171i	−1.28763	+	0.340326i
$956$	1.15367	−	0.0555165i	0.0373123	−	0.00179553i
$957$	−7.63402	+	7.63402i	−0.246773	+	0.246773i
$958$	−0.0367244	−	1.52720i	−0.00118651	−	0.0493414i
$959$	−11.9477			−0.385812
$960$	47.3392	+	19.0590i	1.52787	+	0.615125i
$961$	14.5741			0.470134
$962$	−0.460745	−	19.1603i	−0.0148550	−	0.617751i
$963$	−48.7960	+	48.7960i	−1.57243	+	1.57243i
$964$	−18.3524	+	0.883147i	−0.591090	+	0.0284442i
$965$	−2.71986	+	4.67412i	−0.0875555	+	0.150465i
$966$	−13.5483	−	12.9120i	−0.435908	−	0.415436i
$967$	18.5375	+	18.5375i	0.596127	+	0.596127i	0.939280	−	0.343152i	$-0.111495\pi$
$967$	18.5375	+	18.5375i	0.596127	+	0.596127i	−0.343152	+	0.939280i	$0.611495\pi$
$968$	0.203829	+	2.82107i	0.00655131	+	0.0906727i
$969$			53.0913i			1.70554i
$970$	−0.284611	+	0.517331i	−0.00913832	+	0.0166105i
$971$		−	23.3207i		−	0.748397i	−0.927349	−	0.374199i	$-0.877918\pi$
$971$		−	23.3207i		−	0.748397i	0.927349	−	0.374199i	$-0.122082\pi$
$972$	−16.9845	+	18.7018i	−0.544778	+	0.599859i
$973$	−3.12523	−	3.12523i	−0.100190	−	0.100190i
$974$	4.22085	−	4.42885i	0.135245	−	0.141910i
$975$	−47.2548	+	26.8552i	−1.51336	+	0.860056i
$976$	4.80998	−	0.464003i	0.153964	−	0.0148524i
$977$	24.1233	−	24.1233i	0.771773	−	0.771773i	−0.206643	−	0.978416i	$-0.566254\pi$
$977$	24.1233	−	24.1233i	0.771773	−	0.771773i	0.978416	+	0.206643i	$0.0662540\pi$
$978$	41.6325	−	1.00113i	1.33126	−	0.0320127i
$979$	17.0439			0.544727
$980$	26.9993	−	8.54394i	0.862462	−	0.272926i
$981$	72.1294			2.30291
$982$	−33.6290	+	0.808675i	−1.07314	+	0.0258058i
$983$	32.7750	−	32.7750i	1.04536	−	1.04536i	0.0464400	−	0.998921i	$-0.485212\pi$
$983$	32.7750	−	32.7750i	1.04536	−	1.04536i	0.998921	−	0.0464400i	$-0.0147876\pi$
$984$	−41.5586	−	35.9579i	−1.32484	−	1.14629i
$985$	32.9241	+	19.1585i	1.04905	+	0.610440i
$986$	−21.9438	+	23.0252i	−0.698834	+	0.733271i
$987$	9.70117	+	9.70117i	0.308792	+	0.308792i
$988$	17.6669	+	16.0447i	0.562060	+	0.510449i
$989$		−	70.3547i		−	2.23715i
$990$	15.6048	−	4.52844i	0.495954	−	0.143923i
$991$			10.1064i			0.321041i	0.987033	+	0.160520i	$0.0513172\pi$
$991$			10.1064i			0.321041i	−0.987033	+	0.160520i	$0.948683\pi$
$992$	−22.7611	+	2.74940i	−0.722666	+	0.0872937i
$993$	2.04853	+	2.04853i	0.0650083	+	0.0650083i
$994$	4.78593	+	4.56116i	0.151801	+	0.144671i
$995$	5.97394	+	22.6026i	0.189387	+	0.716549i
$996$	0.857854	+	17.8268i	0.0271822	+	0.564863i
$997$	−2.18583	+	2.18583i	−0.0692260	+	0.0692260i	−0.740872	−	0.671646i	$-0.765588\pi$
$997$	−2.18583	+	2.18583i	−0.0692260	+	0.0692260i	0.671646	+	0.740872i	$0.265588\pi$
$998$	0.863091	+	35.8919i	0.0273207	+	1.13614i
$999$	21.6946			0.686388

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	220.2.l.d.23.8	yes	28
4.3	odd	2		220.2.l.c.23.1	✓	28
5.2	odd	4		220.2.l.c.67.1	yes	28
20.7	even	4	inner	220.2.l.d.67.8	yes	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
220.2.l.c.23.1	✓	28	4.3	odd	2
220.2.l.c.67.1	yes	28	5.2	odd	4
220.2.l.d.23.8	yes	28	1.1	even	1	trivial
220.2.l.d.67.8	yes	28	20.7	even	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(0.0339977 + 1.41380i) q^{2} +(2.01721 - 2.01721i) q^{3} +(-1.99769 + 0.0961322i) q^{4} +(-0.571381 - 2.16183i) q^{5} +(2.92052 + 2.78336i) q^{6} +(0.577795 + 0.577795i) q^{7} +(-0.203829 - 2.82107i) q^{8} -5.13826i q^{9} +(3.03699 - 0.881318i) q^{10} +1.00000i q^{11} +(-3.83584 + 4.22367i) q^{12} +(2.69445 + 2.69445i) q^{13} +(-0.797245 + 0.836533i) q^{14} +(-5.51346 - 3.20828i) q^{15} +(3.98152 - 0.384084i) q^{16} +(4.20234 - 4.20234i) q^{17} +(7.26450 - 0.174689i) q^{18} -3.13149 q^{19} +(1.34926 + 4.26374i) q^{20} +2.33107 q^{21} +(-1.41380 + 0.0339977i) q^{22} +(-4.01439 + 4.01439i) q^{23} +(-6.10186 - 5.27953i) q^{24} +(-4.34705 + 2.47046i) q^{25} +(-3.71782 + 3.90103i) q^{26} +(-4.31332 - 4.31332i) q^{27} +(-1.20980 - 1.09871i) q^{28} +3.78445i q^{29} +(4.34843 - 7.90403i) q^{30} +4.05288i q^{31} +(0.678382 + 5.61603i) q^{32} +(2.01721 + 2.01721i) q^{33} +(6.08416 + 5.79842i) q^{34} +(0.918956 - 1.57924i) q^{35} +(0.493952 + 10.2646i) q^{36} +(-2.51485 + 2.51485i) q^{37} +(-0.106463 - 4.42731i) q^{38} +10.8705 q^{39} +(-5.98223 + 2.05255i) q^{40} +6.81081 q^{41} +(0.0792508 + 3.29567i) q^{42} +(-8.76281 + 8.76281i) q^{43} +(-0.0961322 - 1.99769i) q^{44} +(-11.1081 + 2.93590i) q^{45} +(-5.81205 - 5.53909i) q^{46} +(4.16169 + 4.16169i) q^{47} +(7.25677 - 8.80633i) q^{48} -6.33231i q^{49} +(-3.64054 - 6.06189i) q^{50} -16.9540i q^{51} +(-5.64170 - 5.12365i) q^{52} +(-7.42947 - 7.42947i) q^{53} +(5.95154 - 6.24483i) q^{54} +(2.16183 - 0.571381i) q^{55} +(1.51223 - 1.74777i) q^{56} +(-6.31687 + 6.31687i) q^{57} +(-5.35047 + 0.128662i) q^{58} +6.72046 q^{59} +(11.3226 + 5.87911i) q^{60} +1.20808 q^{61} +(-5.72999 + 0.137789i) q^{62} +(2.96886 - 2.96886i) q^{63} +(-7.91691 + 1.15003i) q^{64} +(4.28540 - 7.36451i) q^{65} +(-2.78336 + 2.92052i) q^{66} +(-4.91054 - 4.91054i) q^{67} +(-7.99099 + 8.79895i) q^{68} +16.1957i q^{69} +(2.26398 + 1.24553i) q^{70} -5.72115i q^{71} +(-14.4954 + 1.04733i) q^{72} +(1.80965 + 1.80965i) q^{73} +(-3.64100 - 3.47000i) q^{74} +(-3.78547 + 13.7523i) q^{75} +(6.25574 - 0.301037i) q^{76} +(-0.577795 + 0.577795i) q^{77} +(0.369573 + 15.3688i) q^{78} +9.31739 q^{79} +(-3.10529 - 8.38792i) q^{80} -1.98693 q^{81} +(0.231552 + 9.62915i) q^{82} +(2.21189 - 2.21189i) q^{83} +(-4.65674 + 0.224090i) q^{84} +(-11.4859 - 6.68363i) q^{85} +(-12.6868 - 12.0910i) q^{86} +(7.63402 + 7.63402i) q^{87} +(2.82107 - 0.203829i) q^{88} -17.0439i q^{89} +(-4.52844 - 15.6048i) q^{90} +3.11368i q^{91} +(7.63359 - 8.40542i) q^{92} +(8.17551 + 8.17551i) q^{93} +(-5.74233 + 6.02530i) q^{94} +(1.78927 + 6.76976i) q^{95} +(12.6971 + 9.96027i) q^{96} +(-0.132029 + 0.132029i) q^{97} +(8.95265 - 0.215284i) q^{98} +5.13826 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

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