LMFDB - Embedded newform 220.2.l.c.23.1

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			23.1
Character	$\chi$	$=$	220.23
Dual form			220.2.l.c.67.1

$q$ -expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.41380 - 0.0339977i) 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} +(-2.82107 - 0.203829i) q^{8} -5.13826i q^{9} +(0.734323 + 3.07584i) q^{10} -1.00000i q^{11} +(-4.22367 + 3.83584i) 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} +(-0.174689 + 7.26450i) q^{18} +3.13149 q^{19} +(-0.933619 - 4.37360i) q^{20} +2.33107 q^{21} +(-0.0339977 + 1.41380i) 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} +(-1.09871 - 1.20980i) q^{28} +3.78445i q^{29} +(-7.68589 - 4.72332i) q^{30} -4.05288i q^{31} +(-5.61603 - 0.678382i) 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} +(-4.42731 - 0.106463i) q^{38} -10.8705 q^{39} +(1.17126 + 6.21515i) q^{40} +6.81081 q^{41} +(-3.29567 - 0.0792508i) 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} +(-8.80633 + 7.25677i) q^{48} -6.33231i q^{49} +(6.22987 - 3.34496i) q^{50} +16.9540i q^{51} +(5.12365 + 5.64170i) 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} +(0.128662 - 5.35047i) q^{58} -6.72046 q^{59} +(10.7058 + 6.93915i) q^{60} +1.20808 q^{61} +(-0.137789 + 5.72999i) 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} +(8.79895 - 7.99099i) q^{68} +16.1957i q^{69} +(1.35291 - 2.20149i) q^{70} +5.72115i q^{71} +(-1.04733 + 14.4954i) 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} +(15.3688 + 0.369573i) q^{78} -9.31739 q^{79} +(-1.44464 - 8.82684i) q^{80} -1.98693 q^{81} +(-9.62915 - 0.231552i) 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} +(-0.203829 + 2.82107i) q^{88} -17.0439i q^{89} +(15.8044 - 3.77314i) q^{90} -3.11368i q^{91} +(8.40542 - 7.63359i) 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} +(-0.215284 + 8.95265i) q^{98} -5.13826 q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$28 q - 2 q^{2} - 4 q^{3} + 4 q^{4} + 2 q^{5} - 12 q^{6} - 2 q^{7} - 14 q^{8} + 6 q^{10} - 8 q^{12} + 6 q^{13} - 20 q^{14} + 8 q^{15} + 8 q^{16} - 14 q^{17} + 34 q^{18} + 4 q^{19} + 8 q^{20} - 16 q^{21}+ \cdots - 20 q^{99}+O(q^{100})$ 28 * q - 2 * q^2 - 4 * q^3 + 4 * q^4 + 2 * q^5 - 12 * q^6 - 2 * q^7 - 14 * q^8 + 6 * q^10 - 8 * q^12 + 6 * q^13 - 20 * q^14 + 8 * q^15 + 8 * q^16 - 14 * q^17 + 34 * q^18 + 4 * q^19 + 8 * q^20 - 16 * q^21 - 2 * q^22 - 8 * q^23 + 28 * q^24 - 4 * q^25 + 4 * q^26 + 44 * q^27 - 28 * q^28 - 2 * q^32 + 4 * q^33 - 52 * q^34 - 10 * q^35 - 4 * q^36 + 20 * q^37 + 16 * q^38 + 32 * q^39 - 6 * q^40 + 12 * q^41 - 32 * q^42 + 2 * q^43 - 10 * q^45 + 4 * q^46 - 44 * q^47 - 36 * q^48 + 22 * q^50 + 24 * q^52 - 28 * q^53 - 40 * q^54 - 2 * q^55 + 4 * q^56 - 8 * q^57 + 28 * q^58 - 16 * q^59 - 48 * q^60 - 12 * q^61 - 24 * q^62 - 10 * q^63 + 28 * q^64 - 30 * q^65 + 16 * q^67 - 32 * q^68 + 72 * q^70 + 18 * q^72 + 22 * q^73 - 20 * q^74 - 56 * q^75 + 4 * q^76 - 2 * q^77 + 104 * q^78 - 20 * q^79 - 44 * q^80 + 12 * q^81 - 92 * q^82 + 2 * q^83 + 120 * q^84 - 14 * q^85 - 20 * q^86 - 48 * q^87 + 2 * q^88 + 70 * q^90 + 52 * q^92 - 20 * q^93 - 20 * q^94 + 92 * q^95 + 40 * q^96 + 16 * q^97 + 18 * q^98 - 20 * q^99

Character values

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

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

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

)

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

$2$	−1.41380	−	0.0339977i	−0.999711	−	0.0240400i
$2$	−1.41380	−	0.0339977i	−0.999711	−	0.0240400i
$3$	−2.01721	+	2.01721i	−1.16464	+	1.16464i	−0.181187	+	0.983449i	$0.557994\pi$
$3$	−2.01721	+	2.01721i	−1.16464	+	1.16464i	−0.983449	+	0.181187i	$0.942006\pi$
$4$	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	0.589432	−	0.807818i	$-0.299352\pi$
$7$	−0.577795	−	0.577795i	−0.218386	−	0.218386i	−0.807818	+	0.589432i	$0.799352\pi$
$8$	−2.82107	−	0.203829i	−0.997400	−	0.0720644i
$9$		−	5.13826i		−	1.71275i
$10$	0.734323	+	3.07584i	0.232213	+	0.972665i
$11$		−	1.00000i		−	0.301511i
$11$		−	1.00000i		−	0.301511i
$12$	−4.22367	+	3.83584i	−1.21927	+	1.10731i
$13$	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	$-0.00617747\pi$
$18$	−0.174689	+	7.26450i	−0.0411746	+	1.71226i
$19$	3.13149			0.718413			0.359206	−	0.933258i	$-0.383047\pi$
$19$	3.13149			0.718413			0.359206	+	0.933258i	$0.383047\pi$
$20$	−0.933619	−	4.37360i	−0.208763	−	0.977966i
$21$	2.33107			0.508680
$22$	−0.0339977	+	1.41380i	−0.00724833	+	0.301424i
$23$	4.01439	−	4.01439i	0.837059	−	0.837059i	−0.151412	−	0.988471i	$-0.548382\pi$
$23$	4.01439	−	4.01439i	0.837059	−	0.837059i	0.988471	+	0.151412i	$0.0483820\pi$
$24$	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
$28$	−1.09871	−	1.20980i	−0.207637	−	0.228630i
$29$			3.78445i			0.702754i	0.936234	+	0.351377i	$0.114287\pi$
$29$			3.78445i			0.702754i	−0.936234	+	0.351377i	$0.885713\pi$
$30$	−7.68589	−	4.72332i	−1.40324	−	0.862356i
$31$		−	4.05288i		−	0.727919i	−0.931415	−	0.363960i	$-0.881425\pi$
$31$		−	4.05288i		−	0.727919i	0.931415	−	0.363960i	$-0.118575\pi$
$32$	−5.61603	−	0.678382i	−0.992783	−	0.119922i
$33$	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	$0.344436\pi$
$38$	−4.42731	−	0.106463i	−0.718205	−	0.0172706i
$39$	−10.8705			−1.74068
$40$	1.17126	+	6.21515i	0.185193	+	0.982702i
$41$	6.81081			1.06367			0.531835	−	0.846848i	$-0.321503\pi$
$41$	6.81081			1.06367			0.531835	+	0.846848i	$0.321503\pi$
$42$	−3.29567	−	0.0792508i	−0.508533	−	0.0122287i
$43$	8.76281	−	8.76281i	1.33632	−	1.33632i	0.436716	−	0.899599i	$-0.356141\pi$
$43$	8.76281	−	8.76281i	1.33632	−	1.33632i	0.899599	−	0.436716i	$-0.143859\pi$
$44$	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	0.335128	−	0.942173i	$-0.391220\pi$
$47$	−4.16169	−	4.16169i	−0.607045	−	0.607045i	−0.942173	+	0.335128i	$0.891220\pi$
$48$	−8.80633	+	7.25677i	−1.27108	+	1.04742i
$49$		−	6.33231i		−	0.904615i
$50$	6.22987	−	3.34496i	0.881036	−	0.473049i
$51$			16.9540i			2.37403i
$52$	5.12365	+	5.64170i	0.710523	+	0.782363i
$53$	−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
$58$	0.128662	−	5.35047i	0.0168942	−	0.702551i
$59$	−6.72046			−0.874929			−0.437464	−	0.899236i	$-0.644123\pi$
$59$	−6.72046			−0.874929			−0.437464	+	0.899236i	$0.644123\pi$
$60$	10.7058	+	6.93915i	1.38211	+	0.895841i
$61$	1.20808			0.154678			0.0773392	−	0.997005i	$-0.475358\pi$
$61$	1.20808			0.154678			0.0773392	+	0.997005i	$0.475358\pi$
$62$	−0.137789	+	5.72999i	−0.0174992	+	0.727709i
$63$	−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	0.940290	−	0.340373i	$-0.110553\pi$
$67$	4.91054	+	4.91054i	0.599917	+	0.599917i	−0.340373	+	0.940290i	$0.610553\pi$
$68$	8.79895	−	7.99099i	1.06703	−	0.969050i
$69$			16.1957i			1.94974i
$70$	1.35291	−	2.20149i	0.161704	−	0.263128i
$71$			5.72115i			0.678976i	0.940610	+	0.339488i	$0.110254\pi$
$71$			5.72115i			0.678976i	−0.940610	+	0.339488i	$0.889746\pi$
$72$	−1.04733	+	14.4954i	−0.123429	+	1.70830i
$73$	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
$78$	15.3688	+	0.369573i	1.74018	+	0.0418459i
$79$	−9.31739			−1.04829			−0.524144	−	0.851630i	$-0.675615\pi$
$79$	−9.31739			−1.04829			−0.524144	+	0.851630i	$0.675615\pi$
$80$	−1.44464	−	8.82684i	−0.161515	−	0.986870i
$81$	−1.98693			−0.220770
$82$	−9.62915	−	0.231552i	−1.06336	−	0.0255706i
$83$	−2.21189	+	2.21189i	−0.242787	+	0.242787i	−0.818002	−	0.575215i	$-0.804918\pi$
$83$	−2.21189	+	2.21189i	−0.242787	+	0.242787i	0.575215	+	0.818002i	$0.304918\pi$
$84$	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
$88$	−0.203829	+	2.82107i	−0.0217282	+	0.300727i
$89$		−	17.0439i		−	1.80665i	−0.428952	−	0.903327i	$-0.641117\pi$
$89$		−	17.0439i		−	1.80665i	0.428952	−	0.903327i	$-0.358883\pi$
$90$	15.8044	−	3.77314i	1.66593	−	0.397724i
$91$		−	3.11368i		−	0.326402i
$92$	8.40542	−	7.63359i	0.876325	−	0.795857i
$93$	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	$0.253017\pi$
$98$	−0.215284	+	8.95265i	−0.0217469	+	0.904354i
$99$	−5.13826			−0.516415
$100$	−8.92154	+	4.51732i	−0.892154	+	0.451732i
$101$	1.29902			0.129257			0.0646285	−	0.997909i	$-0.479414\pi$
$101$	1.29902			0.129257			0.0646285	+	0.997909i	$0.479414\pi$
$102$	0.576397	−	23.9696i	0.0570718	−	2.37335i
$103$	8.75492	−	8.75492i	0.862648	−	0.862648i	−0.128997	−	0.991645i	$-0.541176\pi$
$103$	8.75492	−	8.75492i	0.862648	−	0.862648i	0.991645	+	0.128997i	$0.0411758\pi$
$104$	−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	0.996889	−	0.0788177i	$-0.0251145\pi$
$107$	9.49660	+	9.49660i	0.918071	+	0.918071i	−0.0788177	+	0.996889i	$0.525114\pi$
$108$	8.20201	+	9.03131i	0.789239	+	0.869038i
$109$			14.0377i			1.34457i	0.740293	+	0.672284i	$0.234687\pi$
$109$			14.0377i			1.34457i	−0.740293	+	0.672284i	$0.765313\pi$
$110$	3.07584	−	0.734323i	0.293269	−	0.0700150i
$111$		−	10.1459i		−	0.963010i
$112$	−2.07858	−	2.52242i	−0.196407	−	0.238346i
$113$	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
$118$	9.50141	+	0.228480i	0.874676	+	0.0210333i
$119$	−4.85618			−0.445166
$120$	−14.8999	−	10.1746i	−1.36017	−	0.928808i
$121$	−1.00000			−0.0909091
$122$	−1.70799	−	0.0410718i	−0.154634	−	0.00371847i
$123$	−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	0.617349	−	0.786689i	$-0.288207\pi$
$127$	−1.90837	−	1.90837i	−0.169341	−	0.169341i	−0.786689	+	0.617349i	$0.788207\pi$
$128$	−11.1539	−	1.89508i	−0.985872	−	0.167503i
$129$			35.3528i			3.11264i
$130$	−6.30909	+	10.2663i	−0.553344	+	0.900413i
$131$			6.50809i			0.568614i	0.958733	+	0.284307i	$0.0917635\pi$
$131$			6.50809i			0.568614i	−0.958733	+	0.284307i	$0.908236\pi$
$132$	3.83584	+	4.22367i	0.333867	+	0.367623i
$133$	−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	$0.464740\pi$
$138$	0.550617	−	22.8976i	0.0468717	−	1.94917i
$139$	5.40889			0.458776			0.229388	−	0.973335i	$-0.426328\pi$
$139$	5.40889			0.458776			0.229388	+	0.973335i	$0.426328\pi$
$140$	−1.98760	+	3.06648i	−0.167983	+	0.259165i
$141$	16.7900			1.41397
$142$	0.194506	−	8.08860i	0.0163226	−	0.678780i
$143$	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
$148$	−5.26564	+	4.78212i	−0.432833	+	0.393088i
$149$			6.97727i			0.571601i	0.958289	+	0.285800i	$0.0922594\pi$
$149$			6.97727i			0.571601i	−0.958289	+	0.285800i	$0.907741\pi$
$150$	−5.81946	+	19.3144i	−0.475157	+	1.57702i
$151$			1.28022i			0.104183i	0.998642	+	0.0520916i	$0.0165888\pi$
$151$			1.28022i			0.104183i	−0.998642	+	0.0520916i	$0.983411\pi$
$152$	−8.83416	−	0.638288i	−0.716545	−	0.0517720i
$153$	−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	$0.129470\pi$
$158$	13.1730	+	0.316769i	1.04798	+	0.0252008i
$159$	29.9736			2.37706
$160$	1.74234	+	12.5285i	0.137744	+	0.990468i
$161$	−4.63899			−0.365604
$162$	2.80914	+	0.0675511i	0.220707	+	0.00530732i
$163$	−7.29898	+	7.29898i	−0.571700	+	0.571700i	−0.932603	−	0.360903i	$-0.882469\pi$
$163$	−7.29898	+	7.29898i	−0.571700	+	0.571700i	0.360903	+	0.932603i	$0.382469\pi$
$164$	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	0.943765	−	0.330617i	$-0.107257\pi$
$167$	7.92362	+	7.92362i	0.613148	+	0.613148i	−0.330617	+	0.943765i	$0.607257\pi$
$168$	−6.57611	−	0.475138i	−0.507358	−	0.0366577i
$169$			1.52014i			0.116934i
$170$	16.0116	+	9.83984i	1.22803	+	0.754681i
$171$		−	16.0904i		−	1.23046i
$172$	18.3477	−	16.6630i	1.39900	−	1.27054i
$173$	−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
$178$	−0.579455	+	24.0968i	−0.0434320	+	1.80613i
$179$	4.03496			0.301587			0.150793	−	0.988565i	$-0.451817\pi$
$179$	4.03496			0.301587			0.150793	+	0.988565i	$0.451817\pi$
$180$	−22.4727	+	4.79718i	−1.67501	+	0.357560i
$181$	−23.4754			−1.74491			−0.872455	−	0.488694i	$-0.837473\pi$
$181$	−23.4754			−1.74491			−0.872455	+	0.488694i	$0.837473\pi$
$182$	−0.105858	+	4.40214i	−0.00784671	+	0.326308i
$183$	−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
$188$	−7.91368	−	8.71383i	−0.577165	−	0.635521i
$189$		−	4.98442i		−	0.362563i
$190$	2.29953	+	9.63195i	0.166825	+	0.698775i
$191$			18.4065i			1.33185i	0.746019	+	0.665925i	$0.231963\pi$
$191$			18.4065i			1.33185i	−0.746019	+	0.665925i	$0.768037\pi$
$192$	−18.2899	+	13.6502i	−1.31996	+	0.985118i
$193$	−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	$0.457573\pi$
$198$	7.26450	+	0.174689i	0.516265	+	0.0124146i
$199$	10.4553			0.741155			0.370577	−	0.928802i	$-0.379160\pi$
$199$	10.4553			0.741155			0.370577	+	0.928802i	$0.379160\pi$
$200$	12.7669	−	6.08329i	0.902756	−	0.430154i
$201$	−19.8111			−1.39737
$202$	−1.83656	−	0.0441636i	−0.129220	−	0.00310734i
$203$	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
$208$	9.69311	+	11.7629i	0.672096	+	0.815611i
$209$		−	3.13149i		−	0.216610i
$210$	1.71176	+	7.16998i	0.118122	+	0.494775i
$211$		−	11.9700i		−	0.824050i	−0.911173	−	0.412025i	$-0.864822\pi$
$211$		−	11.9700i		−	0.824050i	0.911173	−	0.412025i	$-0.135178\pi$
$212$	−14.1275	−	15.5560i	−0.970284	−	1.06839i
$213$	−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
$218$	0.477249	−	19.8466i	0.0323234	−	1.34418i
$219$	−7.30087			−0.493347
$220$	−4.37360	+	0.933619i	−0.294868	+	0.0629446i
$221$	22.6460			1.52334
$222$	−0.344938	+	14.3444i	−0.0231507	+	0.962731i
$223$	−2.11226	+	2.11226i	−0.141447	+	0.141447i	−0.774285	−	0.632837i	$-0.781890\pi$
$223$	−2.11226	+	2.11226i	−0.141447	+	0.141447i	0.632837	+	0.774285i	$0.281890\pi$
$224$	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	0.379576	−	0.925160i	$-0.376070\pi$
$227$	−8.22005	−	8.22005i	−0.545584	−	0.545584i	−0.925160	+	0.379576i	$0.876070\pi$
$228$	−13.2264	+	12.0119i	−0.875939	+	0.795506i
$229$		−	20.8865i		−	1.38022i	−0.723705	−	0.690110i	$-0.757562\pi$
$229$		−	20.8865i		−	1.38022i	0.723705	−	0.690110i	$-0.242438\pi$
$230$	15.2955	+	9.39975i	1.00855	+	0.619801i
$231$		−	2.33107i		−	0.153373i
$232$	0.771380	−	10.6762i	0.0506436	−	0.700927i
$233$	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
$238$	6.86569	+	0.165099i	0.445037	+	0.0107018i
$239$	0.577502			0.0373555			0.0186778	−	0.999826i	$-0.494054\pi$
$239$	0.577502			0.0373555			0.0186778	+	0.999826i	$0.494054\pi$
$240$	20.7197	+	14.8914i	1.33745	+	0.961238i
$241$	9.18680			0.591774			0.295887	−	0.955223i	$-0.404385\pi$
$241$	9.18680			0.591774			0.295887	+	0.955223i	$0.404385\pi$
$242$	1.41380	+	0.0339977i	0.0908828	+	0.00218545i
$243$	−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
$248$	−0.826095	+	11.4335i	−0.0524571	+	0.726027i
$249$		−	8.92370i		−	0.565516i
$250$	−10.7909	−	11.5567i	−0.682474	−	0.730909i
$251$			13.7459i			0.867635i	0.901001	+	0.433817i	$0.142834\pi$
$251$			13.7459i			0.867635i	−0.901001	+	0.433817i	$0.857166\pi$
$252$	−6.21626	+	5.64545i	−0.391588	+	0.355630i
$253$	−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	$0.465321\pi$
$258$	1.20191	−	49.9820i	0.0748279	−	3.11174i
$259$	2.90613			0.180578
$260$	9.26886	−	14.3000i	0.574830	−	0.886851i
$261$	19.4455			1.20364
$262$	0.221260	−	9.20117i	0.0136695	−	0.568450i
$263$	0.819798	−	0.819798i	0.0505509	−	0.0505509i	−0.681379	−	0.731930i	$-0.738620\pi$
$263$	0.819798	−	0.819798i	0.0505509	−	0.0505509i	0.731930	+	0.681379i	$0.238620\pi$
$264$	−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
$268$	9.33766	+	10.2818i	0.570388	+	0.628060i
$269$		−	11.0294i		−	0.672475i	−0.941777	−	0.336237i	$-0.890846\pi$
$269$		−	11.0294i		−	0.672475i	0.941777	−	0.336237i	$-0.109154\pi$
$270$	−10.0997	+	16.4344i	−0.614647	+	1.00017i
$271$		−	4.95036i		−	0.300713i	−0.988632	−	0.150356i	$-0.951958\pi$
$271$		−	4.95036i		−	0.300713i	0.988632	−	0.150356i	$-0.0480421\pi$
$272$	18.3457	−	15.1176i	1.11237	−	0.916642i
$273$	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	$-0.0647306\pi$
$278$	−7.64711	−	0.183890i	−0.458643	−	0.0110290i
$279$	−20.8248			−1.24675
$280$	2.91433	−	4.26783i	0.174165	−	0.255052i
$281$	11.2306			0.669959			0.334980	−	0.942225i	$-0.391271\pi$
$281$	11.2306			0.669959			0.334980	+	0.942225i	$0.391271\pi$
$282$	−23.7378	−	0.570821i	−1.41356	−	0.0339919i
$283$	20.2259	−	20.2259i	1.20230	−	1.20230i	0.228841	−	0.973464i	$-0.426506\pi$
$283$	20.2259	−	20.2259i	1.20230	−	1.20230i	0.973464	−	0.228841i	$-0.0734936\pi$
$284$	−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
$288$	−3.48570	+	28.8566i	−0.205397	+	1.70039i
$289$		−	18.3194i		−	1.07761i
$290$	−11.6403	+	2.77901i	−0.683544	+	0.163189i
$291$		−	0.532661i		−	0.0312252i
$292$	3.44114	+	3.78907i	0.201378	+	0.221739i
$293$	−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
$298$	0.237211	−	9.86450i	0.0137413	−	0.571435i
$299$	21.6332			1.25108
$300$	8.88423	−	27.1090i	0.512931	−	1.56514i
$301$	−10.1262			−0.583665
$302$	0.0435246	−	1.80999i	0.00250456	−	0.104153i
$303$	−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	0.269149	−	0.963099i	$-0.413258\pi$
$307$	−12.1590	−	12.1590i	−0.693950	−	0.693950i	−0.963099	+	0.269149i	$0.913258\pi$
$308$	−1.20980	+	1.09871i	−0.0689347	+	0.0626048i
$309$			35.3210i			2.00934i
$310$	12.4660	−	2.97613i	0.708021	−	0.169033i
$311$		−	8.10871i		−	0.459803i	−0.973214	−	0.229902i	$-0.926160\pi$
$311$		−	8.10871i		−	0.459803i	0.973214	−	0.229902i	$-0.0738404\pi$
$312$	30.6666	+	2.21573i	1.73615	+	0.125441i
$313$	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	$0.232884\pi$
$318$	−42.3768	−	1.01903i	−2.37637	−	0.0571445i
$319$	3.78445			0.211888
$320$	−2.03739	−	17.7721i	−0.113894	−	0.993493i
$321$	−38.3133			−2.13844
$322$	6.55863	+	0.157715i	0.365498	+	0.00878911i
$323$	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
$328$	−19.2138	−	1.38824i	−1.06090	−	0.0766527i
$329$			4.80920i			0.265140i
$330$	−4.72332	+	7.68589i	−0.260010	+	0.423094i
$331$		−	1.01553i		−	0.0558186i	−0.999610	−	0.0279093i	$-0.991115\pi$
$331$		−	1.01553i		−	0.0558186i	0.999610	−	0.0279093i	$-0.00888495\pi$
$332$	−4.63131	+	4.20604i	−0.254176	+	0.230836i
$333$	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	$0.435451\pi$
$338$	0.0516813	−	2.14918i	0.00281109	−	0.116900i
$339$	−31.0527			−1.68655
$340$	−22.3027	−	14.4560i	−1.20954	−	0.783985i
$341$	−4.05288			−0.219476
$342$	−0.547036	+	22.7487i	−0.0295803	+	1.23011i
$343$	−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	$0.110777\pi$
$347$	23.8639	+	23.8639i	1.28108	+	1.28108i	0.341032	+	0.940052i	$0.389223\pi$
$348$	−14.5165	−	15.9843i	−0.778167	−	0.856847i
$349$			5.29742i			0.283565i	0.989898	+	0.141782i	$0.0452833\pi$
$349$			5.29742i			0.283565i	−0.989898	+	0.141782i	$0.954717\pi$
$350$	−5.53229	−	1.66689i	−0.295713	−	0.0890988i
$351$			23.2440i			1.24068i
$352$	−0.678382	+	5.61603i	−0.0361579	+	0.299335i
$353$	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
$358$	−5.70464	−	0.137179i	−0.301500	−	0.00725014i
$359$	−30.0479			−1.58587			−0.792934	−	0.609308i	$-0.791447\pi$
$359$	−30.0479			−1.58587			−0.792934	+	0.609308i	$0.791447\pi$
$360$	31.9351	−	6.01825i	1.68313	−	0.317190i
$361$	−9.19377			−0.483883
$362$	33.1896	+	0.798108i	1.74441	+	0.0419476i
$363$	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	0.997283	−	0.0736687i	$-0.0234707\pi$
$367$	17.6939	+	17.6939i	0.923614	+	0.923614i	−0.0736687	+	0.997283i	$0.523471\pi$
$368$	17.5252	−	14.4415i	0.913566	−	0.752816i
$369$		−	34.9957i		−	1.82180i
$370$	−9.58196	−	5.88854i	−0.498143	−	0.306131i
$371$			8.58542i			0.445733i
$372$	15.5462	+	17.1180i	0.806032	+	0.887529i
$373$	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
$378$	−0.169459	+	7.04700i	−0.00871602	+	0.362459i
$379$	−26.3215			−1.35205			−0.676023	−	0.736881i	$-0.736298\pi$
$379$	−26.3215			−1.35205			−0.676023	+	0.736881i	$0.736298\pi$
$380$	−2.92362	−	13.6959i	−0.149978	−	0.702584i
$381$	7.69916			0.394440
$382$	0.625779	−	26.0232i	0.0320177	−	1.33146i
$383$	3.16875	−	3.16875i	0.161916	−	0.161916i	−0.621499	−	0.783415i	$-0.713476\pi$
$383$	3.16875	−	3.16875i	0.161916	−	0.161916i	0.783415	+	0.621499i	$0.213476\pi$
$384$	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
$388$	−0.276446	+	0.251061i	−0.0140344	+	0.0127457i
$389$		−	5.27196i		−	0.267299i	−0.991029	−	0.133650i	$-0.957330\pi$
$389$		−	5.27196i		−	0.267299i	0.991029	−	0.133650i	$-0.0426697\pi$
$390$	−7.98249	−	33.4360i	−0.404209	−	1.69310i
$391$		−	33.7397i		−	1.70629i
$392$	−1.29071	+	17.8639i	−0.0651905	+	0.902263i
$393$	−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	$0.339688\pi$
$398$	−14.7817	−	0.355455i	−0.740940	−	0.0178173i
$399$	7.29971			0.365442
$400$	−18.2567	+	8.16654i	−0.912836	+	0.408327i
$401$	0.846108			0.0422526			0.0211263	−	0.999777i	$-0.493275\pi$
$401$	0.846108			0.0422526			0.0211263	+	0.999777i	$0.493275\pi$
$402$	28.0091	+	0.673533i	1.39697	+	0.0335928i
$403$	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
$408$	3.45571	−	47.8285i	0.171083	−	2.36786i
$409$		−	9.86215i		−	0.487652i	−0.969819	−	0.243826i	$-0.921597\pi$
$409$		−	9.86215i		−	0.487652i	0.969819	−	0.243826i	$-0.0784026\pi$
$410$	5.00134	+	20.9489i	0.246998	+	1.03459i
$411$		−	41.7121i		−	2.05751i
$412$	18.3312	−	16.6480i	0.903115	−	0.820187i
$413$	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
$418$	−0.106463	+	4.42731i	−0.00520729	+	0.216547i
$419$	19.9803			0.976102			0.488051	−	0.872815i	$-0.337708\pi$
$419$	19.9803			0.976102			0.488051	+	0.872815i	$0.337708\pi$
$420$	−2.17633	−	10.1951i	−0.106194	−	0.497472i
$421$	−15.5127			−0.756042			−0.378021	−	0.925797i	$-0.623395\pi$
$421$	−15.5127			−0.756042			−0.378021	+	0.925797i	$0.623395\pi$
$422$	−0.406953	+	16.9233i	−0.0198101	+	0.823812i
$423$	−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
$428$	18.0583	+	19.8842i	0.872882	+	0.961138i
$429$			10.8705i			0.524835i
$430$	33.3877	+	20.5182i	1.61010	+	0.989477i
$431$			19.1176i			0.920860i	0.887696	+	0.460430i	$0.152305\pi$
$431$			19.1176i			0.920860i	−0.887696	+	0.460430i	$0.847695\pi$
$432$	15.5169	+	18.8302i	0.746555	+	0.905969i
$433$	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
$438$	10.3220	+	0.248213i	0.493204	+	0.0118601i
$439$	7.24897			0.345975			0.172987	−	0.984924i	$-0.444658\pi$
$439$	7.24897			0.345975			0.172987	+	0.984924i	$0.444658\pi$
$440$	6.21515	−	1.17126i	0.296296	−	0.0558377i
$441$	−32.5370			−1.54938
$442$	−32.0170	−	0.769912i	−1.52290	−	0.0366210i
$443$	9.15600	−	9.15600i	0.435014	−	0.435014i	−0.455316	−	0.890330i	$-0.650474\pi$
$443$	9.15600	−	9.15600i	0.435014	−	0.435014i	0.890330	+	0.455316i	$0.150474\pi$
$444$	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
$448$	−3.90987	−	5.23883i	−0.184724	−	0.247512i
$449$			5.22383i			0.246528i	0.992374	+	0.123264i	$0.0393361\pi$
$449$			5.22383i			0.246528i	−0.992374	+	0.123264i	$0.960664\pi$
$450$	−17.1873	−	32.0107i	−0.810215	−	1.50900i
$451$		−	6.81081i		−	0.320708i
$452$	14.6362	+	16.1160i	0.688428	+	0.758035i
$453$	−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	$0.177933\pi$
$458$	−0.710093	+	29.5294i	−0.0331804	+	1.37982i
$459$	36.2521			1.69210
$460$	−21.3053	−	13.8094i	−0.993362	−	0.643868i
$461$	15.9739			0.743981			0.371990	−	0.928237i	$-0.378675\pi$
$461$	15.9739			0.743981			0.371990	+	0.928237i	$0.378675\pi$
$462$	−0.0792508	+	3.29567i	−0.00368708	+	0.153329i
$463$	−26.1957	+	26.1957i	−1.21742	+	1.21742i	−0.248887	+	0.968533i	$0.580065\pi$
$463$	−26.1957	+	26.1957i	−1.21742	+	1.21742i	−0.968533	+	0.248887i	$0.919935\pi$
$464$	−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	0.451879	−	0.892079i	$-0.350754\pi$
$467$	−9.51280	−	9.51280i	−0.440200	−	0.440200i	−0.892079	+	0.451879i	$0.850754\pi$
$468$	28.9885	−	26.3267i	1.33999	−	1.21695i
$469$		−	5.67456i		−	0.262027i
$470$	9.74465	−	15.8567i	0.449487	−	0.731415i
$471$			26.4279i			1.21773i
$472$	18.9589	+	1.36982i	0.872654	+	0.0630512i
$473$	−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
$478$	−0.816475	−	0.0196337i	−0.0373447	−	0.000898026i
$479$	1.08020			0.0493557			0.0246779	−	0.999695i	$-0.492144\pi$
$479$	1.08020			0.0493557			0.0246779	+	0.999695i	$0.492144\pi$
$480$	−28.7873	−	21.7580i	−1.31396	−	0.993113i
$481$	−13.5523			−0.617930
$482$	−12.9883	−	0.312330i	−0.591603	−	0.0142262i
$483$	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	0.773010	−	0.634393i	$-0.218750\pi$
$487$	3.05902	+	3.05902i	0.138617	+	0.138617i	−0.634393	+	0.773010i	$0.718750\pi$
$488$	−3.40808	−	0.246241i	−0.154276	−	0.0111468i
$489$		−	29.4471i		−	1.33165i
$490$	19.4771	−	4.64996i	0.879887	−	0.210064i
$491$		−	23.7862i		−	1.07346i	−0.843756	−	0.536728i	$-0.819660\pi$
$491$		−	23.7862i		−	1.07346i	0.843756	−	0.536728i	$-0.180340\pi$
$492$	−28.7666	+	26.1251i	−1.29690	+	1.17781i
$493$	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
$498$	−0.303385	+	12.6164i	−0.0135950	+	0.565353i
$499$	−25.3868			−1.13647			−0.568234	−	0.822867i	$-0.692373\pi$
$499$	−25.3868			−1.13647			−0.568234	+	0.822867i	$0.692373\pi$
$500$	14.8633	+	16.7058i	0.664706	+	0.747105i
$501$	−31.9672			−1.42819
$502$	0.467329	−	19.4340i	0.0208579	−	0.867384i
$503$	−23.4070	+	23.4070i	−1.04367	+	1.04367i	−0.0446651	+	0.999002i	$0.514222\pi$
$503$	−23.4070	+	23.4070i	−1.04367	+	1.04367i	−0.999002	+	0.0446651i	$0.985778\pi$
$504$	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
$508$	−3.62887	−	3.99579i	−0.161005	−	0.177284i
$509$		−	10.4107i		−	0.461445i	−0.973020	−	0.230722i	$-0.925891\pi$
$509$		−	10.4107i		−	0.461445i	0.973020	−	0.230722i	$-0.0741089\pi$
$510$	−52.1477	+	12.4497i	−2.30914	+	0.551283i
$511$		−	2.09121i		−	0.0925096i
$512$	−22.0998	−	4.85802i	−0.976681	−	0.214696i
$513$	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
$518$	−4.10870	−	0.0988017i	−0.180526	−	0.00434110i
$519$	49.6308			2.17855
$520$	−13.5905	+	19.9023i	−0.595984	+	0.872776i
$521$	18.1068			0.793271			0.396636	−	0.917976i	$-0.370178\pi$
$521$	18.1068			0.793271			0.396636	+	0.917976i	$0.370178\pi$
$522$	−27.4921	−	0.661101i	−1.20330	−	0.0289356i
$523$	−9.00519	+	9.00519i	−0.393769	+	0.393769i	−0.876029	−	0.482259i	$-0.839816\pi$
$523$	−9.00519	+	9.00519i	−0.393769	+	0.393769i	0.482259	+	0.876029i	$0.339816\pi$
$524$	−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
$528$	7.25677	+	8.80633i	0.315810	+	0.383246i
$529$		−	9.23070i		−	0.401335i
$530$	17.3962	−	28.3075i	0.755642	−	1.22960i
$531$			34.5314i			1.49854i
$532$	−3.44060	−	3.78847i	−0.149169	−	0.164251i
$533$	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
$538$	−0.374974	+	15.5934i	−0.0161663	+	0.672280i
$539$	−6.33231			−0.272752
$540$	14.8377	−	22.8917i	0.638514	−	0.985102i
$541$	10.2839			0.442137			0.221069	−	0.975258i	$-0.429046\pi$
$541$	10.2839			0.442137			0.221069	+	0.975258i	$0.429046\pi$
$542$	−0.168301	+	6.99884i	−0.00722913	+	0.300626i
$543$	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	0.551554	−	0.834139i	$-0.314035\pi$
$547$	−6.60913	−	6.60913i	−0.282586	−	0.282586i	−0.834139	+	0.551554i	$0.814035\pi$
$548$	−21.6482	+	19.6603i	−0.924764	+	0.839847i
$549$		−	6.20742i		−	0.264926i
$550$	−3.34496	−	6.22987i	−0.142629	−	0.265642i
$551$			11.8510i			0.504868i
$552$	3.30116	−	45.6894i	0.140507	−	1.94467i
$553$	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	$0.908274\pi$
$558$	29.4422	+	0.707994i	1.24639	+	0.0299718i
$559$	47.2219			1.99727
$560$	−4.26540	+	5.93480i	−0.180246	+	0.250791i
$561$	16.9540			0.715798
$562$	−15.8778	−	0.381813i	−0.669765	−	0.0161058i
$563$	10.2716	−	10.2716i	0.432896	−	0.432896i	−0.456716	−	0.889612i	$-0.650975\pi$
$563$	10.2716	−	10.2716i	0.432896	−	0.432896i	0.889612	+	0.456716i	$0.150975\pi$
$564$	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
$568$	1.16614	−	16.1398i	0.0489300	−	0.677211i
$569$			7.70852i			0.323158i	0.986860	+	0.161579i	$0.0516587\pi$
$569$			7.70852i			0.323158i	−0.986860	+	0.161579i	$0.948341\pi$
$570$	−24.0683	−	14.7910i	−1.00811	−	0.619528i
$571$			27.9383i			1.16918i	0.811329	+	0.584590i	$0.198745\pi$
$571$			27.9383i			1.16918i	−0.811329	+	0.584590i	$0.801255\pi$
$572$	5.64170	−	5.12365i	0.235891	−	0.214231i
$573$	−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	$0.277887\pi$
$578$	−0.622815	+	25.9000i	−0.0259057	+	1.07730i
$579$	6.89933			0.286726
$580$	16.5517	−	3.53323i	0.687270	−	0.146709i
$581$	2.55604			0.106042
$582$	−0.0181092	+	0.753079i	−0.000750652	+	0.0312161i
$583$	−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	0.721575	−	0.692336i	$-0.243419\pi$
$587$	0.708389	+	0.708389i	0.0292384	+	0.0292384i	−0.692336	+	0.721575i	$0.743419\pi$
$588$	24.2897	+	26.7456i	1.00169	+	1.10297i
$589$		−	12.6916i		−	0.522947i
$590$	−4.93499	−	20.6710i	−0.203170	−	0.851013i
$591$		−	48.5983i		−	1.99907i
$592$	−10.9788	+	9.04699i	−0.451226	+	0.371829i
$593$	−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
$598$	−30.5851	−	0.735478i	−1.25072	−	0.0300759i
$599$	36.9338			1.50908			0.754538	−	0.656257i	$-0.227861\pi$
$599$	36.9338			1.50908			0.754538	+	0.656257i	$0.227861\pi$
$600$	−13.4822	+	38.0248i	−0.550409	+	1.55235i
$601$	22.8410			0.931703			0.465851	−	0.884863i	$-0.345748\pi$
$601$	22.8410			0.931703			0.465851	+	0.884863i	$0.345748\pi$
$602$	14.3165	+	0.344268i	0.583496	+	0.0140313i
$603$	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	0.519585	−	0.854419i	$-0.326086\pi$
$607$	−8.24942	−	8.24942i	−0.334833	−	0.334833i	−0.854419	+	0.519585i	$0.826086\pi$
$608$	−17.5865	−	2.12435i	−0.713228	−	0.0861537i
$609$			8.82179i			0.357477i
$610$	0.887120	+	3.71585i	0.0359184	+	0.150450i
$611$		−	22.4269i		−	0.907297i
$612$	−41.0598	−	45.2113i	−1.65974	−	1.82756i
$613$	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	$0.138811\pi$
$618$	1.20083	−	49.9370i	0.0483045	−	2.00876i
$619$	5.24313			0.210739			0.105370	−	0.994433i	$-0.466397\pi$
$619$	5.24313			0.210739			0.105370	+	0.994433i	$0.466397\pi$
$620$	−17.7257	+	3.78385i	−0.711880	+	0.151963i
$621$	34.6307			1.38968
$622$	−0.275677	+	11.4641i	−0.0110537	+	0.459670i
$623$	−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
$628$	13.7158	−	12.4564i	0.547321	−	0.497063i
$629$			21.1365i			0.842767i
$630$	−11.3118	−	6.95162i	−0.450674	−	0.276959i
$631$			7.51569i			0.299195i	0.988747	+	0.149597i	$0.0477978\pi$
$631$			7.51569i			0.299195i	−0.988747	+	0.149597i	$0.952202\pi$
$632$	26.2850	+	1.89915i	1.04556	+	0.0755442i
$633$	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
$638$	−5.35047	−	0.128662i	−0.211827	−	0.00509379i
$639$	29.3968			1.16292
$640$	2.27626	+	25.1956i	0.0899770	+	0.995944i
$641$	7.27424			0.287315			0.143658	−	0.989627i	$-0.454114\pi$
$641$	7.27424			0.287315			0.143658	+	0.989627i	$0.454114\pi$
$642$	54.1675	+	1.30256i	2.13782	+	0.0514080i
$643$	−24.9810	+	24.9810i	−0.985153	+	0.985153i	−0.999891	−	0.0147379i	$-0.995309\pi$
$643$	−24.9810	+	24.9810i	−0.985153	+	0.985153i	0.0147379	+	0.999891i	$0.495309\pi$
$644$	−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	0.827763	−	0.561078i	$-0.189613\pi$
$647$	6.78345	+	6.78345i	0.266685	+	0.266685i	−0.561078	+	0.827763i	$0.689613\pi$
$648$	5.60529	+	0.404995i	0.220196	+	0.0159097i
$649$			6.72046i			0.263801i
$650$	25.7989	+	7.77325i	1.01192	+	0.304892i
$651$		−	9.44753i		−	0.370278i
$652$	−15.2828	+	13.8794i	−0.598519	+	0.543560i
$653$	−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
$658$	0.163502	−	6.79928i	0.00637396	−	0.265063i
$659$	−13.5226			−0.526766			−0.263383	−	0.964691i	$-0.584838\pi$
$659$	−13.5226			−0.526766			−0.263383	+	0.964691i	$0.584838\pi$
$660$	6.93915	−	10.7058i	0.270106	−	0.416721i
$661$	18.8632			0.733694			0.366847	−	0.930281i	$-0.380437\pi$
$661$	18.8632			0.733694			0.366847	+	0.930281i	$0.380437\pi$
$662$	−0.0345256	+	1.43576i	−0.00134188	+	0.0558024i
$663$	−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
$668$	15.0672	+	16.5906i	0.582968	+	0.641911i
$669$		−	8.52173i		−	0.329469i
$670$	−11.4981	+	18.7099i	−0.444210	+	0.722827i
$671$		−	1.20808i		−	0.0466373i
$672$	−13.0913	−	1.58135i	−0.505009	−	0.0610020i
$673$	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	$0.482122\pi$
$678$	43.9025	+	1.05572i	1.68606	+	0.0405447i
$679$	0.152572			0.00585517
$680$	31.0402	+	21.1962i	1.19034	+	0.812836i
$681$	33.1631			1.27081
$682$	5.72999	+	0.137789i	0.219412	+	0.00527620i
$683$	26.1744	−	26.1744i	1.00154	−	1.00154i	0.00153813	−	0.999999i	$-0.499510\pi$
$683$	26.1744	−	26.1744i	1.00154	−	1.00154i	0.999999	−	0.00153813i	$-0.000489602\pi$
$684$	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
$688$	38.2549	−	31.5236i	1.45846	−	1.20183i
$689$		−	40.0367i		−	1.52528i
$690$	−49.8154	+	11.8929i	−1.89644	+	0.452755i
$691$			15.4756i			0.588721i	0.955694	+	0.294361i	$0.0951067\pi$
$691$			15.4756i			0.588721i	−0.955694	+	0.294361i	$0.904893\pi$
$692$	−23.3927	−	25.7579i	−0.889256	−	0.979168i
$693$	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
$698$	0.180100	−	7.48952i	0.00681689	−	0.283483i
$699$	−20.2224			−0.764883
$700$	7.76490	+	2.54474i	0.293486	+	0.0961820i
$701$	−23.5564			−0.889712			−0.444856	−	0.895602i	$-0.646745\pi$
$701$	−23.5564			−0.889712			−0.444856	+	0.895602i	$0.646745\pi$
$702$	0.790243	−	32.8625i	0.0298258	−	1.24032i
$703$	−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
$708$	28.3850	−	25.7786i	1.06677	−	0.968818i
$709$			17.6845i			0.664157i	0.943252	+	0.332078i	$0.107750\pi$
$709$			17.6845i			0.664157i	−0.943252	+	0.332078i	$0.892250\pi$
$710$	−17.5973	+	4.20118i	−0.660416	+	0.157667i
$711$			47.8752i			1.79546i
$712$	−3.47405	+	48.0822i	−0.130195	+	1.80196i
$713$	−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
$718$	42.4819	+	1.02156i	1.58541	+	0.0381242i
$719$	−30.3312			−1.13116			−0.565581	−	0.824692i	$-0.691348\pi$
$719$	−30.3312			−1.13116			−0.565581	+	0.824692i	$0.691348\pi$
$720$	−45.3546	+	7.42291i	−1.69027	+	0.276636i
$721$	−10.1171			−0.376780
$722$	12.9982	+	0.312567i	0.483743	+	0.0116325i
$723$	−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	0.633677	−	0.773598i	$-0.281545\pi$
$727$	−3.77266	−	3.77266i	−0.139920	−	0.139920i	−0.773598	+	0.633677i	$0.781545\pi$
$728$	−0.634658	+	8.78392i	−0.0235220	+	0.325554i
$729$		−	41.9958i		−	1.55540i
$730$	−4.23731	+	6.89504i	−0.156830	+	0.255197i
$731$		−	73.6486i		−	2.72399i
$732$	−5.10252	+	4.63399i	−0.188595	+	0.171277i
$733$	−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
$738$	−1.18977	+	49.4771i	−0.0437961	+	1.82128i
$739$	−49.1757			−1.80896			−0.904479	−	0.426517i	$-0.859740\pi$
$739$	−49.1757			−1.80896			−0.904479	+	0.426517i	$0.859740\pi$
$740$	13.3468	+	8.65102i	0.490639	+	0.318018i
$741$	−34.0410			−1.25053
$742$	0.291884	−	12.1381i	0.0107154	−	0.445604i
$743$	7.28068	−	7.28068i	0.267102	−	0.267102i	−0.560829	−	0.827931i	$-0.689518\pi$
$743$	7.28068	−	7.28068i	0.267102	−	0.267102i	0.827931	+	0.560829i	$0.189518\pi$
$744$	−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
$748$	−7.99099	−	8.79895i	−0.292179	−	0.321721i
$749$		−	10.9742i		−	0.400988i
$750$	45.0797	+	1.54483i	1.64608	+	0.0564092i
$751$		−	8.47426i		−	0.309230i	−0.987975	−	0.154615i	$-0.950586\pi$
$751$		−	8.47426i		−	0.309230i	0.987975	−	0.154615i	$-0.0494137\pi$
$752$	−14.9714	−	18.1683i	−0.545951	−	0.662529i
$753$	−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	$0.412497\pi$
$758$	37.2135	+	0.894871i	1.35166	+	0.0325032i
$759$	16.1957			0.587868
$760$	3.66780	+	19.4627i	0.133045	+	0.705986i
$761$	34.5321			1.25179			0.625894	−	0.779908i	$-0.284734\pi$
$761$	34.5321			1.25179			0.625894	+	0.779908i	$0.284734\pi$
$762$	−10.8851	−	0.261754i	−0.394326	−	0.00948234i
$763$	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
$768$	−37.8498	+	25.5106i	−1.36579	+	0.920534i
$769$			30.6356i			1.10475i	0.833596	+	0.552375i	$0.186278\pi$
$769$			30.6356i			1.10475i	−0.833596	+	0.552375i	$0.813722\pi$
$770$	−2.20149	−	1.35291i	−0.0793362	−	0.0487556i
$771$		−	57.2607i		−	2.06219i
$772$	−3.25189	−	3.58068i	−0.117038	−	0.128872i
$773$	−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
$778$	−0.179235	+	7.45353i	−0.00642587	+	0.267222i
$779$	21.3280			0.764154
$780$	10.1489	+	47.5434i	0.363390	+	1.70233i
$781$	5.72115			0.204719
$782$	−1.14707	+	47.7014i	−0.0410192	+	1.70580i
$783$	−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	$0.142033\pi$
$787$	37.4133	+	37.4133i	1.33364	+	1.33364i	0.431551	+	0.902089i	$0.357967\pi$
$788$	−25.2220	+	22.9060i	−0.898497	+	0.815993i
$789$			3.30741i			0.117747i
$790$	−6.84197	−	28.6588i	−0.243427	−	1.01963i
$791$		−	8.89452i		−	0.316253i
$792$	14.4954	+	1.04733i	0.515072	+	0.0372151i
$793$	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	$0.0163900\pi$
$798$	−10.3204	−	0.248173i	−0.365337	−	0.00878523i
$799$	−34.9777			−1.23742
$800$	26.0891	−	10.9252i	0.922388	−	0.386265i
$801$	−87.5762			−3.09435
$802$	−1.19623	−	0.0287657i	−0.0422404	−	0.00101575i
$803$	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
$808$	−3.66462	−	0.264777i	−0.128921	−	0.00931483i
$809$			27.8007i			0.977421i	0.872446	+	0.488710i	$0.162532\pi$
$809$			27.8007i			0.977421i	−0.872446	+	0.488710i	$0.837468\pi$
$810$	−1.45905	−	6.11148i	−0.0512659	−	0.214736i
$811$		−	24.4103i		−	0.857163i	−0.903503	−	0.428582i	$-0.859013\pi$
$811$		−	24.4103i		−	0.857163i	0.903503	−	0.428582i	$-0.140987\pi$
$812$	4.57842	−	4.15801i	0.160671	−	0.145917i
$813$	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
$818$	−0.335290	+	13.9432i	−0.0117231	+	0.487511i
$819$	−15.9989			−0.559047
$820$	−6.35870	−	29.7877i	−0.222055	−	1.04023i
$821$	−6.73158			−0.234934			−0.117467	−	0.993077i	$-0.537477\pi$
$821$	−6.73158			−0.234934			−0.117467	+	0.993077i	$0.537477\pi$
$822$	−1.41812	+	58.9728i	−0.0494625	+	2.05691i
$823$	−34.4158	+	34.4158i	−1.19966	+	1.19966i	−0.225392	+	0.974268i	$0.572366\pi$
$823$	−34.4158	+	34.4158i	−1.19966	+	1.19966i	−0.974268	+	0.225392i	$0.927634\pi$
$824$	−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	0.713814	−	0.700335i	$-0.246966\pi$
$827$	0.387622	+	0.387622i	0.0134789	+	0.0134789i	−0.700335	+	0.713814i	$0.746966\pi$
$828$	−39.2234	−	43.1892i	−1.36311	−	1.50093i
$829$		−	21.1590i		−	0.734884i	−0.930046	−	0.367442i	$-0.880234\pi$
$829$		−	21.1590i		−	0.734884i	0.930046	−	0.367442i	$-0.119766\pi$
$830$	−8.42766	−	5.17918i	−0.292528	−	0.179772i
$831$			79.3232i			2.75169i
$832$	18.2330	+	24.4304i	0.632116	+	0.846973i
$833$	−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
$838$	−28.2482	−	0.679284i	−0.975820	−	0.0234655i
$839$	−35.8248			−1.23681			−0.618405	−	0.785859i	$-0.712221\pi$
$839$	−35.8248			−1.23681			−0.618405	+	0.785859i	$0.712221\pi$
$840$	2.73029	+	14.4879i	0.0942039	+	0.499881i
$841$	14.6780			0.506136
$842$	21.9319	+	0.527396i	0.755824	+	0.0181753i
$843$	−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
$848$	−26.7270	−	32.4341i	−0.917809	−	1.11379i
$849$			81.5997i			2.80049i
$850$	12.1234	−	40.2367i	0.415828	−	1.38011i
$851$			20.1912i			0.692144i
$852$	−21.9454	−	24.1643i	−0.751837	−	0.827855i
$853$	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	$0.953939\pi$
$858$	0.369573	−	15.3688i	0.0126170	−	0.524683i
$859$	22.2469			0.759053			0.379527	−	0.925181i	$-0.376087\pi$
$859$	22.2469			0.759053			0.379527	+	0.925181i	$0.376087\pi$
$860$	−46.5061	−	30.1439i	−1.58585	−	1.02790i
$861$	15.8764			0.541068
$862$	0.649952	−	27.0285i	0.0221375	−	0.920594i
$863$	36.4372	−	36.4372i	1.24034	−	1.24034i	0.280475	−	0.959861i	$-0.409508\pi$
$863$	36.4372	−	36.4372i	1.24034	−	1.24034i	0.959861	−	0.280475i	$-0.0904919\pi$
$864$	−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
$868$	−4.90317	+	4.45294i	−0.166425	+	0.151143i
$869$			9.31739i			0.316071i
$870$	17.8752	−	29.0868i	0.606025	−	0.986136i
$871$			26.4624i			0.896644i
$872$	2.86129	−	39.6014i	0.0968955	−	1.34107i
$873$	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	$0.259294\pi$
$878$	−10.2486	−	0.246448i	−0.345875	−	0.00831722i
$879$	23.4942			0.792439
$880$	−8.82684	+	1.44464i	−0.297553	+	0.0486987i
$881$	57.1296			1.92475			0.962373	−	0.271732i	$-0.0875964\pi$
$881$	57.1296			1.92475			0.962373	+	0.271732i	$0.0875964\pi$
$882$	46.0010	+	1.10618i	1.54893	+	0.0372471i
$883$	9.90424	−	9.90424i	0.333304	−	0.333304i	−0.520536	−	0.853840i	$-0.674268\pi$
$883$	9.90424	−	9.90424i	0.333304	−	0.333304i	0.853840	+	0.520536i	$0.174268\pi$
$884$	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	0.606044	−	0.795431i	$-0.292755\pi$
$887$	−5.64043	−	5.64043i	−0.189387	−	0.189387i	−0.795431	+	0.606044i	$0.792755\pi$
$888$	−2.06803	+	28.6224i	−0.0693987	+	0.960506i
$889$			2.20529i			0.0739632i
$890$	52.4244	−	12.5158i	1.75727	−	0.419529i
$891$			1.98693i			0.0665648i
$892$	−4.42269	+	4.01658i	−0.148083	+	0.134485i
$893$	−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
$898$	0.177598	−	7.38547i	0.00592652	−	0.246456i
$899$	15.3379			0.511548
$900$	23.2111	+	45.8412i	0.773705	+	1.52804i
$901$	−62.4423			−2.08026
$902$	−0.231552	+	9.62915i	−0.00770983	+	0.320616i
$903$	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	0.0628499	−	0.998023i	$-0.479981\pi$
$907$	−28.1641	−	28.1641i	−0.935173	−	0.935173i	−0.998023	+	0.0628499i	$0.979981\pi$
$908$	−15.6309	−	17.2113i	−0.518729	−	0.571177i
$909$		−	6.67469i		−	0.221385i
$910$	9.57717	−	2.28645i	0.317480	−	0.0757950i
$911$			19.5259i			0.646921i	0.946242	+	0.323460i	$0.104846\pi$
$911$			19.5259i			0.646921i	−0.946242	+	0.323460i	$0.895154\pi$
$912$	−27.5769	+	22.7245i	−0.913163	+	0.752484i
$913$	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
$918$	−51.2533	−	1.23249i	−1.69161	−	0.0406781i
$919$	−2.67588			−0.0882693			−0.0441346	−	0.999026i	$-0.514053\pi$
$919$	−2.67588			−0.0882693			−0.0441346	+	0.999026i	$0.514053\pi$
$920$	29.6520	+	20.2482i	0.977597	+	0.667562i
$921$	49.0544			1.61640
$922$	−22.5840	−	0.543077i	−0.743766	−	0.0178853i
$923$	−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
$928$	2.56730	−	21.2536i	0.0842758	−	0.697683i
$929$			41.6520i			1.36656i	0.730157	+	0.683279i	$0.239447\pi$
$929$			41.6520i			1.36656i	−0.730157	+	0.683279i	$0.760553\pi$
$930$	−19.1431	+	31.1500i	−0.627726	+	1.02145i
$931$		−	19.8295i		−	0.649887i
$932$	9.53151	+	10.4952i	0.312215	+	0.343783i
$933$	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	$0.436512\pi$
$938$	−0.192922	+	8.02273i	−0.00629913	+	0.261951i
$939$	−32.9434			−1.07507
$940$	−14.3161	+	22.0870i	−0.466940	+	0.720398i
$941$	−36.2569			−1.18194			−0.590970	−	0.806693i	$-0.701255\pi$
$941$	−36.2569			−1.18194			−0.590970	+	0.806693i	$0.701255\pi$
$942$	0.898488	−	37.3639i	0.0292743	−	1.21738i
$943$	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	0.746532	−	0.665349i	$-0.231717\pi$
$947$	2.49828	+	2.49828i	0.0811831	+	0.0811831i	−0.665349	+	0.746532i	$0.731717\pi$
$948$	39.3536	−	35.7400i	1.27815	−	1.16078i
$949$			9.75201i			0.316564i
$950$	19.5088	−	10.4747i	0.632948	−	0.339844i
$951$			5.45973i			0.177044i
$952$	13.6996	+	0.989830i	0.444008	+	0.0320806i
$953$	−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
$958$	−1.52720	−	0.0367244i	−0.0493414	−	0.00118651i
$959$	11.9477			0.385812
$960$	39.9600	+	31.7403i	1.28970	+	1.02441i
$961$	14.5741			0.470134
$962$	19.1603	+	0.460745i	0.617751	+	0.0148550i
$963$	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	0.343152	−	0.939280i	$-0.388505\pi$
$967$	−18.5375	−	18.5375i	−0.596127	−	0.596127i	−0.939280	+	0.343152i	$0.888505\pi$
$968$	2.82107	+	0.203829i	0.0906727	+	0.00655131i
$969$			53.0913i			1.70554i
$970$	−0.503053	−	0.309148i	−0.0161521	−	0.00992616i
$971$			23.3207i			0.748397i	0.927349	+	0.374199i	$0.122082\pi$
$971$			23.3207i			0.748397i	−0.927349	+	0.374199i	$0.877918\pi$
$972$	−18.7018	+	16.9845i	−0.599859	+	0.544778i
$973$	−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	$0.0662540\pi$
$978$	−1.00113	+	41.6325i	−0.0320127	+	1.33126i
$979$	−17.0439			−0.544727
$980$	−27.6950	+	5.91196i	−0.884683	+	0.188851i
$981$	72.1294			2.30291
$982$	−0.808675	+	33.6290i	−0.0258058	+	1.07314i
$983$	−32.7750	+	32.7750i	−1.04536	+	1.04536i	−0.0464400	+	0.998921i	$0.514788\pi$
$983$	−32.7750	+	32.7750i	−1.04536	+	1.04536i	−0.998921	+	0.0464400i	$0.985212\pi$
$984$	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
$988$	16.0447	+	17.6669i	0.510449	+	0.562060i
$989$		−	70.3547i		−	2.23715i
$990$	−3.77314	−	15.8044i	−0.119918	−	0.502298i
$991$		−	10.1064i		−	0.321041i	−0.987033	−	0.160520i	$-0.948683\pi$
$991$		−	10.1064i		−	0.321041i	0.987033	−	0.160520i	$-0.0513172\pi$
$992$	−2.74940	+	22.7611i	−0.0872937	+	0.722666i
$993$	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	$0.265588\pi$
$998$	35.8919	+	0.863091i	1.13614	+	0.0273207i
$999$	−21.6946			−0.686388

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instead) (See

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Twists

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

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

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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

Representations

Groups

Database

Properties

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Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

Coefficient data

Twists

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

Label	220.2.l.c.23.1

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