LMFDB - Embedded newform 104.2.r.a.29.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [104,2,Mod(29,104)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("104.29"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(104, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 3, 2])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 104 = 2^{3} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	104.r (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$0.830444181021$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			29.6
Character	$\chi$	$=$	104.29
Dual form			104.2.r.a.61.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.262058 + 1.38972i) q^{2} +(2.64382 - 1.52641i) q^{3} +(-1.86265 - 0.728375i) q^{4} -0.497079i q^{5} +(1.42845 + 4.07418i) q^{6} +(-0.845740 + 1.46486i) q^{7} +(1.50036 - 2.39769i) q^{8} +(3.15986 - 5.47304i) q^{9} +(0.690801 + 0.130263i) q^{10} +(-3.29345 + 1.90148i) q^{11} +(-6.03632 + 0.917478i) q^{12} +(-1.15864 + 3.41432i) q^{13} +(-1.81412 - 1.55922i) q^{14} +(-0.758746 - 1.31419i) q^{15} +(2.93894 + 2.71342i) q^{16} +(-1.69983 + 2.94419i) q^{17} +(6.77793 + 5.82558i) q^{18} +(-1.05470 - 0.608933i) q^{19} +(-0.362060 + 0.925884i) q^{20} +5.16378i q^{21} +(-1.77945 - 5.07528i) q^{22} +(-4.43183 - 7.67616i) q^{23} +(0.306826 - 8.62923i) q^{24} +4.75291 q^{25} +(-4.44132 - 2.50493i) q^{26} -10.1345i q^{27} +(2.64229 - 2.11252i) q^{28} +(0.342961 - 0.198009i) q^{29} +(2.02519 - 0.710053i) q^{30} +2.08430 q^{31} +(-4.54107 + 3.37323i) q^{32} +(-5.80487 + 10.0543i) q^{33} +(-3.64615 - 3.13383i) q^{34} +(0.728152 + 0.420399i) q^{35} +(-9.87214 + 7.89280i) q^{36} +(8.53399 - 4.92710i) q^{37} +(1.12264 - 1.30617i) q^{38} +(2.14843 + 10.7954i) q^{39} +(-1.19184 - 0.745797i) q^{40} +(-2.30090 - 3.98527i) q^{41} +(-7.17622 - 1.35321i) q^{42} +(-2.68011 - 1.54736i) q^{43} +(7.51955 - 1.14292i) q^{44} +(-2.72053 - 1.57070i) q^{45} +(11.8291 - 4.14741i) q^{46} -3.97467 q^{47} +(11.9118 + 2.68776i) q^{48} +(2.06945 + 3.58439i) q^{49} +(-1.24554 + 6.60522i) q^{50} +10.3785i q^{51} +(4.64504 - 5.51576i) q^{52} +5.68458i q^{53} +(14.0841 + 2.65583i) q^{54} +(0.945183 + 1.63711i) q^{55} +(2.24337 + 4.22565i) q^{56} -3.71793 q^{57} +(0.185301 + 0.528511i) q^{58} +(5.36063 + 3.09496i) q^{59} +(0.456058 + 3.00052i) q^{60} +(3.53620 + 2.04163i) q^{61} +(-0.546207 + 2.89659i) q^{62} +(5.34484 + 9.25753i) q^{63} +(-3.49783 - 7.19480i) q^{64} +(1.69718 + 0.575933i) q^{65} +(-12.4515 - 10.7020i) q^{66} +(-6.67080 + 3.85139i) q^{67} +(5.31066 - 4.24588i) q^{68} +(-23.4339 - 13.5296i) q^{69} +(-0.775056 + 0.901760i) q^{70} +(3.83307 - 6.63908i) q^{71} +(-8.38172 - 15.7879i) q^{72} +6.02464 q^{73} +(4.61090 + 13.1511i) q^{74} +(12.5659 - 7.25490i) q^{75} +(1.52101 + 1.90245i) q^{76} -6.43262i q^{77} +(-15.5656 + 0.156696i) q^{78} -9.36611 q^{79} +(1.34878 - 1.46088i) q^{80} +(-5.98985 - 10.3747i) q^{81} +(6.14138 - 2.15323i) q^{82} +7.17235i q^{83} +(3.76117 - 9.61833i) q^{84} +(1.46349 + 0.844947i) q^{85} +(2.85275 - 3.31911i) q^{86} +(0.604486 - 1.04700i) q^{87} +(-0.382219 + 10.7496i) q^{88} +(-6.31322 - 10.9348i) q^{89} +(2.89577 - 3.36916i) q^{90} +(-4.02161 - 4.58487i) q^{91} +(2.66383 + 17.5260i) q^{92} +(5.51051 - 3.18150i) q^{93} +(1.04159 - 5.52368i) q^{94} +(-0.302688 + 0.524270i) q^{95} +(-6.85683 + 15.8498i) q^{96} +(0.832515 - 1.44196i) q^{97} +(-5.52362 + 1.93664i) q^{98} +24.0336i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - q^{2} - q^{4} - 8 q^{6} - 2 q^{7} - 10 q^{8} + 6 q^{9} - 3 q^{10} - 12 q^{12} + 8 q^{14} + 4 q^{15} - q^{16} + 6 q^{18} - 11 q^{20} - 2 q^{22} - 14 q^{23} - 18 q^{24} - 12 q^{25} - 3 q^{26} - 4 q^{28}+ \cdots - 17 q^{98}+O(q^{100}) $ 24 * q - q^2 - q^4 - 8 * q^6 - 2 * q^7 - 10 * q^8 + 6 * q^9 - 3 * q^10 - 12 * q^12 + 8 * q^14 + 4 * q^15 - q^16 + 6 * q^18 - 11 * q^20 - 2 * q^22 - 14 * q^23 - 18 * q^24 - 12 * q^25 - 3 * q^26 - 4 * q^28 + 14 * q^30 - 8 * q^31 - 21 * q^32 - 14 * q^33 + 14 * q^34 + 5 * q^36 + 12 * q^38 - 34 * q^39 + 54 * q^40 - 4 * q^41 + 22 * q^42 + 24 * q^46 - 8 * q^47 - 8 * q^48 + 6 * q^49 + 32 * q^50 - 4 * q^52 + 22 * q^54 + 8 * q^55 + 8 * q^56 - 52 * q^57 + 33 * q^58 + 56 * q^60 - 14 * q^62 + 32 * q^63 + 26 * q^64 + 30 * q^65 - 104 * q^66 + 23 * q^68 - 16 * q^70 + 30 * q^71 + 17 * q^72 - 12 * q^73 - 7 * q^74 + 14 * q^76 - 8 * q^78 - 48 * q^79 + 29 * q^80 + 8 * q^81 - q^82 + 60 * q^84 - 96 * q^86 - 26 * q^87 + 4 * q^88 - 22 * q^89 - 50 * q^90 - 80 * q^92 - 42 * q^94 + 60 * q^95 - 40 * q^96 + 2 * q^97 - 17 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/104\mathbb{Z}\right)^\times$.

$n$	$41$	$53$	$79$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$-1$	$1$

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 $

$2$	−0.262058	+	1.38972i	−0.185303	+	0.982681i
$2$	−0.262058	+	1.38972i	−0.185303	+	0.982681i
$3$	2.64382	−	1.52641i	1.52641	−	0.881274i	0.526902	−	0.849926i	$-0.323353\pi$
$3$	2.64382	−	1.52641i	1.52641	−	0.881274i	0.999509	−	0.0313478i	$-0.00997994\pi$
$4$	−1.86265	−	0.728375i	−0.931326	−	0.364188i
$5$		−	0.497079i		−	0.222300i	−0.993804	−	0.111150i	$-0.964547\pi$
$5$		−	0.497079i		−	0.222300i	0.993804	−	0.111150i	$-0.0354534\pi$
$6$	1.42845	+	4.07418i	0.583163	+	1.66328i
$7$	−0.845740	+	1.46486i	−0.319660	+	0.553667i	−0.980417	−	0.196933i	$-0.936902\pi$
$7$	−0.845740	+	1.46486i	−0.319660	+	0.553667i	0.660757	+	0.750600i	$0.270235\pi$
$8$	1.50036	−	2.39769i	0.530458	−	0.847711i
$9$	3.15986	−	5.47304i	1.05329	−	1.82435i
$10$	0.690801	+	0.130263i	0.218450	+	0.0411929i
$11$	−3.29345	+	1.90148i	−0.993014	+	0.573317i	−0.906174	−	0.422905i	$-0.861010\pi$
$11$	−3.29345	+	1.90148i	−0.993014	+	0.573317i	−0.0868401	+	0.996222i	$0.527677\pi$
$12$	−6.03632	+	0.917478i	−1.74253	+	0.264853i
$13$	−1.15864	+	3.41432i	−0.321348	+	0.946961i
$13$	−1.15864	+	3.41432i	−0.321348	+	0.946961i
$14$	−1.81412	−	1.55922i	−0.484844	−	0.416720i
$15$	−0.758746	−	1.31419i	−0.195907	−	0.339322i
$16$	2.93894	+	2.71342i	0.734735	+	0.678354i
$17$	−1.69983	+	2.94419i	−0.412269	+	0.714070i	−0.995137	−	0.0984962i	$-0.968597\pi$
$17$	−1.69983	+	2.94419i	−0.412269	+	0.714070i	0.582869	+	0.812566i	$0.301930\pi$
$18$	6.77793	+	5.82558i	1.59757	+	1.37310i
$19$	−1.05470	−	0.608933i	−0.241966	−	0.139699i	0.374114	−	0.927383i	$-0.377947\pi$
$19$	−1.05470	−	0.608933i	−0.241966	−	0.139699i	−0.616080	+	0.787684i	$0.711280\pi$
$20$	−0.362060	+	0.925884i	−0.0809590	+	0.207034i
$21$			5.16378i			1.12683i
$22$	−1.77945	−	5.07528i	−0.379379	−	1.08205i
$23$	−4.43183	−	7.67616i	−0.924101	−	1.60059i	−0.793001	−	0.609220i	$-0.791483\pi$
$23$	−4.43183	−	7.67616i	−0.924101	−	1.60059i	−0.131099	−	0.991369i	$-0.541851\pi$
$24$	0.306826	−	8.62923i	0.0626307	−	1.76143i
$25$	4.75291			0.950583
$26$	−4.44132	−	2.50493i	−0.871015	−	0.491257i
$27$		−	10.1345i		−	1.95039i
$28$	2.64229	−	2.11252i	0.499346	−	0.399228i
$29$	0.342961	−	0.198009i	0.0636863	−	0.0367693i	−0.467819	−	0.883824i	$-0.654960\pi$
$29$	0.342961	−	0.198009i	0.0636863	−	0.0367693i	0.531505	+	0.847055i	$0.321627\pi$
$30$	2.02519	−	0.710053i	0.369747	−	0.129637i
$31$	2.08430			0.374351			0.187176	−	0.982326i	$-0.440067\pi$
$31$	2.08430			0.374351			0.187176	+	0.982326i	$0.440067\pi$
$32$	−4.54107	+	3.37323i	−0.802755	+	0.596309i
$33$	−5.80487	+	10.0543i	−1.01050	+	1.75023i
$34$	−3.64615	−	3.13383i	−0.625309	−	0.537448i
$35$	0.728152	+	0.420399i	0.123080	+	0.0710604i
$36$	−9.87214	+	7.89280i	−1.64536	+	1.31547i
$37$	8.53399	−	4.92710i	1.40298	−	0.810011i	0.408283	−	0.912856i	$-0.366128\pi$
$37$	8.53399	−	4.92710i	1.40298	−	0.810011i	0.994697	+	0.102845i	$0.0327944\pi$
$38$	1.12264	−	1.30617i	0.182116	−	0.211888i
$39$	2.14843	+	10.7954i	0.344024	+	1.72865i
$40$	−1.19184	−	0.745797i	−0.188446	−	0.117921i
$41$	−2.30090	−	3.98527i	−0.359339	−	0.622394i	0.628511	−	0.777801i	$-0.283665\pi$
$41$	−2.30090	−	3.98527i	−0.359339	−	0.622394i	−0.987851	+	0.155406i	$0.950331\pi$
$42$	−7.17622	−	1.35321i	−1.10732	−	0.208805i
$43$	−2.68011	−	1.54736i	−0.408713	−	0.235971i	0.281524	−	0.959554i	$-0.409160\pi$
$43$	−2.68011	−	1.54736i	−0.408713	−	0.235971i	−0.690237	+	0.723584i	$0.742494\pi$
$44$	7.51955	−	1.14292i	1.13361	−	0.172301i
$45$	−2.72053	−	1.57070i	−0.405553	−	0.234146i
$46$	11.8291	−	4.14741i	1.74411	−	0.611503i
$47$	−3.97467			−0.579765			−0.289882	−	0.957062i	$-0.593616\pi$
$47$	−3.97467			−0.579765			−0.289882	+	0.957062i	$0.593616\pi$
$48$	11.9118	+	2.68776i	1.71932	+	0.387945i
$49$	2.06945	+	3.58439i	0.295636	+	0.512056i
$50$	−1.24554	+	6.60522i	−0.176146	+	0.934120i
$51$			10.3785i			1.45329i
$52$	4.64504	−	5.51576i	0.644151	−	0.764899i
$53$			5.68458i			0.780837i	0.920637	+	0.390419i	$0.127670\pi$
$53$			5.68458i			0.780837i	−0.920637	+	0.390419i	$0.872330\pi$
$54$	14.0841	+	2.65583i	1.91661	+	0.361413i
$55$	0.945183	+	1.63711i	0.127449	+	0.220747i
$56$	2.24337	+	4.22565i	0.299784	+	0.564676i
$57$	−3.71793			−0.492452
$58$	0.185301	+	0.528511i	0.0243313	+	0.0693968i
$59$	5.36063	+	3.09496i	0.697895	+	0.402930i	0.806563	−	0.591148i	$-0.201325\pi$
$59$	5.36063	+	3.09496i	0.697895	+	0.402930i	−0.108668	+	0.994078i	$0.534659\pi$
$60$	0.456058	+	3.00052i	0.0588769	+	0.387366i
$61$	3.53620	+	2.04163i	0.452764	+	0.261404i	0.708997	−	0.705211i	$-0.249148\pi$
$61$	3.53620	+	2.04163i	0.452764	+	0.261404i	−0.256233	+	0.966615i	$0.582481\pi$
$62$	−0.546207	+	2.89659i	−0.0693684	+	0.367868i
$63$	5.34484	+	9.25753i	0.673386	+	1.16634i
$64$	−3.49783	−	7.19480i	−0.437229	−	0.899350i
$65$	1.69718	+	0.575933i	0.210510	+	0.0714357i
$66$	−12.4515	−	10.7020i	−1.53267	−	1.31732i
$67$	−6.67080	+	3.85139i	−0.814969	+	0.470522i	−0.848678	−	0.528909i	$-0.822601\pi$
$67$	−6.67080	+	3.85139i	−0.814969	+	0.470522i	0.0337098	+	0.999432i	$0.489268\pi$
$68$	5.31066	−	4.24588i	0.644012	−	0.514889i
$69$	−23.4339	−	13.5296i	−2.82111	−	1.62877i
$70$	−0.775056	+	0.901760i	−0.0926369	+	0.107781i
$71$	3.83307	−	6.63908i	0.454902	−	0.787913i	−0.543781	−	0.839227i	$-0.683008\pi$
$71$	3.83307	−	6.63908i	0.454902	−	0.787913i	0.998683	+	0.0513141i	$0.0163410\pi$
$72$	−8.38172	−	15.7879i	−0.987795	−	1.86062i
$73$	6.02464			0.705131			0.352566	−	0.935787i	$-0.385309\pi$
$73$	6.02464			0.705131			0.352566	+	0.935787i	$0.385309\pi$
$74$	4.61090	+	13.1511i	0.536006	+	1.52878i
$75$	12.5659	−	7.25490i	1.45098	−	0.837723i
$76$	1.52101	+	1.90245i	0.174472	+	0.218226i
$77$		−	6.43262i		−	0.733065i
$78$	−15.5656	+	0.156696i	−1.76246	+	0.0177423i
$79$	−9.36611			−1.05377			−0.526885	−	0.849937i	$-0.676640\pi$
$79$	−9.36611			−1.05377			−0.526885	+	0.849937i	$0.676640\pi$
$80$	1.34878	−	1.46088i	0.150798	−	0.163332i
$81$	−5.98985	−	10.3747i	−0.665539	−	1.15275i
$82$	6.14138	−	2.15323i	0.678202	−	0.237785i
$83$			7.17235i			0.787268i	0.919267	+	0.393634i	$0.128782\pi$
$83$			7.17235i			0.787268i	−0.919267	+	0.393634i	$0.871218\pi$
$84$	3.76117	−	9.61833i	0.410377	−	1.04945i
$85$	1.46349	+	0.844947i	0.158738	+	0.0916474i
$86$	2.85275	−	3.31911i	0.307620	−	0.357909i
$87$	0.604486	−	1.04700i	0.0648077	−	0.112250i
$88$	−0.382219	+	10.7496i	−0.0407447	+	1.14591i
$89$	−6.31322	−	10.9348i	−0.669200	−	1.15909i	−0.978128	−	0.208003i	$-0.933304\pi$
$89$	−6.31322	−	10.9348i	−0.669200	−	1.15909i	0.308929	−	0.951085i	$-0.400030\pi$
$90$	2.89577	−	3.36916i	0.305241	−	0.355141i
$91$	−4.02161	−	4.58487i	−0.421579	−	0.480625i
$92$	2.66383	+	17.5260i	0.277724	+	1.82722i
$93$	5.51051	−	3.18150i	0.571413	−	0.329906i
$94$	1.04159	−	5.52368i	0.107432	−	0.569724i
$95$	−0.302688	+	0.524270i	−0.0310551	+	0.0537890i
$96$	−6.85683	+	15.8498i	−0.699822	+	1.61766i
$97$	0.832515	−	1.44196i	0.0845291	−	0.146409i	−0.820661	−	0.571415i	$-0.806395\pi$
$97$	0.832515	−	1.44196i	0.0845291	−	0.146409i	0.905190	+	0.425006i	$0.139728\pi$
$98$	−5.52362	+	1.93664i	−0.557970	+	0.195630i
$99$			24.0336i			2.41547i
$100$	−8.85302	−	3.46190i	−0.885302	−	0.346190i
$101$	6.79643	−	3.92392i	0.676270	−	0.390444i	−0.122178	−	0.992508i	$-0.538988\pi$
$101$	6.79643	−	3.92392i	0.676270	−	0.390444i	0.798448	+	0.602064i	$0.205655\pi$
$102$	−14.4233	−	2.71978i	−1.42812	−	0.269298i
$103$	13.2316			1.30375			0.651873	−	0.758328i	$-0.273983\pi$
$103$	13.2316			1.30375			0.651873	+	0.758328i	$0.273983\pi$
$104$	6.44810	+	7.90076i	0.632289	+	0.774733i
$105$	2.56681			0.250495
$106$	−7.89998	−	1.48969i	−0.767314	−	0.144691i
$107$	7.63683	−	4.40913i	0.738281	−	0.426247i	−0.0831632	−	0.996536i	$-0.526502\pi$
$107$	7.63683	−	4.40913i	0.738281	−	0.426247i	0.821444	+	0.570289i	$0.193169\pi$
$108$	−7.38173	+	18.8771i	−0.710307	+	1.81645i
$109$		−	3.65580i		−	0.350162i	−0.984554	−	0.175081i	$-0.943981\pi$
$109$		−	3.65580i		−	0.350162i	0.984554	−	0.175081i	$-0.0560188\pi$
$110$	−2.52281	+	0.884525i	−0.240541	+	0.0843362i
$111$	15.0416	−	26.0528i	1.42768	−	2.47282i
$112$	−6.46037	+	2.01030i	−0.610447	+	0.189956i
$113$	−5.71030	+	9.89054i	−0.537180	+	0.930423i	0.461874	+	0.886945i	$0.347177\pi$
$113$	−5.71030	+	9.89054i	−0.537180	+	0.930423i	−0.999054	+	0.0434779i	$0.986156\pi$
$114$	0.974313	−	5.16689i	0.0912527	−	0.483923i
$115$	−3.81565	+	2.20297i	−0.355811	+	0.205428i
$116$	−0.783042	+	0.119017i	−0.0727036	+	0.0110504i
$117$	15.0256	+	17.1300i	1.38911	+	1.58367i
$118$	−5.70593	+	6.63872i	−0.525274	+	0.611144i
$119$	−2.87522	−	4.98003i	−0.263571	−	0.456519i
$120$	−4.28941	−	0.152517i	−0.391567	−	0.0139228i
$121$	1.73123	−	2.99858i	0.157384	−	0.272598i
$122$	−3.76398	+	4.37931i	−0.340775	+	0.396484i
$123$	−12.1663	−	7.02422i	−1.09700	−	0.633353i
$124$	−3.88232	−	1.51815i	−0.348643	−	0.136334i
$125$		−	4.84796i		−	0.433615i
$126$	−14.2660	+	5.00183i	−1.27092	+	0.445598i
$127$	6.38026	+	11.0509i	0.566157	+	0.980612i	0.996941	+	0.0781574i	$0.0249037\pi$
$127$	6.38026	+	11.0509i	0.566157	+	0.980612i	−0.430784	+	0.902455i	$0.641763\pi$
$128$	10.9154	−	2.97556i	0.964795	−	0.263005i
$129$	−9.44764			−0.831818
$130$	−1.24515	+	2.20769i	−0.109207	+	0.193627i
$131$		−	11.2798i		−	0.985523i	−0.870165	−	0.492761i	$-0.835988\pi$
$131$		−	11.2798i		−	0.985523i	0.870165	−	0.492761i	$-0.164012\pi$
$132$	18.1358	−	14.4996i	1.57852	−	1.26203i
$133$	1.78401	−	1.03000i	0.154693	−	0.0893121i
$134$	−3.60422	−	10.2798i	−0.311357	−	0.888044i
$135$	−5.03765			−0.433572
$136$	4.50889	+	8.49300i	0.386634	+	0.728269i
$137$	−3.69961	+	6.40791i	−0.316079	+	0.547465i	−0.979666	−	0.200634i	$-0.935700\pi$
$137$	−3.69961	+	6.40791i	−0.316079	+	0.547465i	0.663587	+	0.748099i	$0.269033\pi$
$138$	24.9434	−	29.0211i	2.12332	−	2.47044i
$139$	−10.2330	−	5.90805i	−0.867956	−	0.501115i	−0.00128744	−	0.999999i	$-0.500410\pi$
$139$	−10.2330	−	5.90805i	−0.867956	−	0.501115i	−0.866668	+	0.498885i	$0.833743\pi$
$140$	−1.05009	−	1.31342i	−0.0887485	−	0.111005i
$141$	−10.5083	+	6.06697i	−0.884959	+	0.510931i
$142$	8.22198	+	7.06673i	0.689973	+	0.593026i
$143$	−2.67633	−	13.4480i	−0.223806	−	1.12458i
$144$	24.1373	−	7.51091i	2.01144	−	0.625909i
$145$	−0.0984260	−	0.170479i	−0.00817383	−	0.0141575i
$146$	−1.57881	+	8.37258i	−0.130663	+	0.692919i
$147$	10.9425	+	6.31766i	0.902523	+	0.521072i
$148$	−19.4846	+	2.96153i	−1.60163	+	0.243436i
$149$	−10.6954	−	6.17498i	−0.876199	−	0.505874i	−0.00679591	−	0.999977i	$-0.502163\pi$
$149$	−10.6954	−	6.17498i	−0.876199	−	0.505874i	−0.869403	+	0.494103i	$0.835497\pi$
$150$	6.78931	+	19.3642i	0.554344	+	1.58108i
$151$	−17.6993			−1.44035			−0.720175	−	0.693792i	$-0.755939\pi$
$151$	−17.6993			−1.44035			−0.720175	+	0.693792i	$0.755939\pi$
$152$	−3.04247	+	1.61523i	−0.246777	+	0.131013i
$153$	10.7424	+	18.6064i	0.868474	+	1.50424i
$154$	8.93955	+	1.68572i	0.720369	+	0.135839i
$155$		−	1.03606i		−	0.0832184i
$156$	3.86133	−	21.6729i	0.309154	−	1.73522i
$157$			2.70138i			0.215594i	0.994173	+	0.107797i	$0.0343796\pi$
$157$			2.70138i			0.215594i	−0.994173	+	0.107797i	$0.965620\pi$
$158$	2.45446	−	13.0163i	0.195267	−	1.03552i
$159$	8.67701	+	15.0290i	0.688131	+	1.19188i
$160$	1.67676	+	2.25727i	0.132560	+	0.178453i
$161$	14.9927			1.18159
$162$	15.9877	−	5.60544i	1.25611	−	0.440405i
$163$	1.86997	+	1.07963i	0.146467	+	0.0845630i	0.571443	−	0.820642i	$-0.306384\pi$
$163$	1.86997	+	1.07963i	0.146467	+	0.0845630i	−0.424975	+	0.905205i	$0.639717\pi$
$164$	1.38300	+	9.09908i	0.107994	+	0.710519i
$165$	4.99779	+	2.88548i	0.389078	+	0.224634i
$166$	−9.96757	−	1.87957i	−0.773634	−	0.145883i
$167$	3.70257	+	6.41303i	0.286513	+	0.496255i	0.972975	−	0.230910i	$-0.0741704\pi$
$167$	3.70257	+	6.41303i	0.286513	+	0.496255i	−0.686462	+	0.727166i	$0.740837\pi$
$168$	12.3812	+	7.74754i	0.955227	+	0.597736i
$169$	−10.3151	−	7.91190i	−0.793471	−	0.608607i
$170$	−1.55776	+	1.81242i	−0.119475	+	0.139006i
$171$	−6.66543	+	3.84829i	−0.509718	+	0.294286i
$172$	3.86505	+	4.83432i	0.294707	+	0.368614i
$173$	3.65801	+	2.11195i	0.278113	+	0.160569i	0.632569	−	0.774504i	$-0.282000\pi$
$173$	3.65801	+	2.11195i	0.278113	+	0.160569i	−0.354456	+	0.935073i	$0.615334\pi$
$174$	1.29663	+	1.11444i	0.0982971	+	0.0844856i
$175$	−4.01973	+	6.96237i	−0.303863	+	0.526306i
$176$	−14.8388	−	3.34819i	−1.11851	−	0.252379i
$177$	18.8967			1.42037
$178$	16.8508	−	5.90806i	1.26302	−	0.442828i
$179$	−0.388283	+	0.224175i	−0.0290216	+	0.0167557i	−0.514441	−	0.857526i	$-0.672000\pi$
$179$	−0.388283	+	0.224175i	−0.0290216	+	0.0167557i	0.485419	+	0.874282i	$0.338667\pi$
$180$	3.92334	+	4.90723i	0.292429	+	0.365763i
$181$		−	1.46266i		−	0.108718i	−0.998521	−	0.0543592i	$-0.982688\pi$
$181$		−	1.46266i		−	0.108718i	0.998521	−	0.0543592i	$-0.0173116\pi$
$182$	7.42558	−	4.38741i	0.550421	−	0.325217i
$183$	12.4655			0.921473
$184$	−25.0544	−	0.890850i	−1.84703	−	0.0656743i
$185$	−2.44916	−	4.24207i	−0.180066	−	0.311883i
$186$	2.97732	+	8.49181i	0.218308	+	0.622650i
$187$		−	12.9287i		−	0.945442i
$188$	7.40342	+	2.89505i	0.539950	+	0.211143i
$189$	14.8457	+	8.57116i	1.07986	+	0.623460i
$190$	−0.649268	−	0.558041i	−0.0471029	−	0.0404845i
$191$	−4.12331	+	7.14178i	−0.298352	+	0.516761i	−0.975759	−	0.218847i	$-0.929770\pi$
$191$	−4.12331	+	7.14178i	−0.298352	+	0.516761i	0.677407	+	0.735609i	$0.263104\pi$
$192$	−20.2299	−	13.6826i	−1.45996	−	0.987459i
$193$	−6.31137	−	10.9316i	−0.454302	−	0.786875i	0.544345	−	0.838861i	$-0.316778\pi$
$193$	−6.31137	−	10.9316i	−0.454302	−	0.786875i	−0.998648	+	0.0519863i	$0.983445\pi$
$194$	1.78575	+	1.53484i	0.128210	+	0.110195i
$195$	5.36616	−	1.06794i	0.384279	−	0.0764766i
$196$	−1.24388	−	8.18381i	−0.0888486	−	0.584558i
$197$	−15.2949	+	8.83050i	−1.08971	+	0.629147i	−0.933500	−	0.358576i	$-0.883262\pi$
$197$	−15.2949	+	8.83050i	−1.08971	+	0.629147i	−0.156214	+	0.987723i	$0.549929\pi$
$198$	−33.4000	−	6.29820i	−2.37364	−	0.447593i
$199$	−9.92096	+	17.1836i	−0.703278	+	1.21811i	0.264032	+	0.964514i	$0.414948\pi$
$199$	−9.92096	+	17.1836i	−0.703278	+	1.21811i	−0.967309	+	0.253599i	$0.918386\pi$
$200$	7.13109	−	11.3960i	0.504244	−	0.805820i
$201$	−11.7576	+	20.3648i	−0.829318	+	1.43642i
$202$	3.67210	+	10.4734i	0.258368	+	0.736908i
$203$			0.669856i			0.0470147i
$204$	7.55947	−	19.3316i	0.529269	−	1.35348i
$205$	−1.98099	+	1.14373i	−0.138358	+	0.0798813i
$206$	−3.46744	+	18.3882i	−0.241588	+	1.28117i
$207$	−56.0158			−3.89337
$208$	−12.6696	+	6.89061i	−0.878481	+	0.477778i
$209$	4.63149			0.320367
$210$	−0.672652	+	3.56715i	−0.0464174	+	0.246156i
$211$	13.0695	−	7.54568i	0.899742	−	0.519466i	0.0226255	−	0.999744i	$-0.492797\pi$
$211$	13.0695	−	7.54568i	0.899742	−	0.519466i	0.877116	+	0.480278i	$0.159464\pi$
$212$	4.14051	−	10.5884i	0.284371	−	0.727214i
$213$		−	23.4034i		−	1.60357i
$214$	4.12617	+	11.7685i	0.282059	+	0.804479i
$215$	−0.769161	+	1.33223i	−0.0524563	+	0.0908570i
$216$	−24.2994	−	15.2054i	−1.65337	−	1.03460i
$217$	−1.76277	+	3.05321i	−0.119665	+	0.207266i
$218$	5.08055	+	0.958032i	0.344098	+	0.0648861i
$219$	15.9281	−	9.19608i	1.07632	−	0.621414i
$220$	−0.568120	−	3.73781i	−0.0383026	−	0.252003i
$221$	−8.08291	−	9.21499i	−0.543715	−	0.619867i
$222$	32.2643	+	27.7309i	2.16544	+	1.86118i
$223$	4.97902	+	8.62392i	0.333420	+	0.577500i	0.983180	−	0.182639i	$-0.0584640\pi$
$223$	4.97902	+	8.62392i	0.333420	+	0.577500i	−0.649760	+	0.760139i	$0.725131\pi$
$224$	−1.10077	−	9.50492i	−0.0735483	−	0.635074i
$225$	15.0185	−	26.0129i	1.00124	−	1.73419i
$226$	−12.2487	−	10.5276i	−0.814769	−	0.700287i
$227$	1.19973	+	0.692666i	0.0796291	+	0.0459739i	0.539286	−	0.842123i	$-0.318694\pi$
$227$	1.19973	+	0.692666i	0.0796291	+	0.0459739i	−0.459657	+	0.888097i	$0.652028\pi$
$228$	6.92520	+	2.70805i	0.458633	+	0.179345i
$229$			22.8190i			1.50793i	0.656917	+	0.753963i	$0.271860\pi$
$229$			22.8190i			1.50793i	−0.656917	+	0.753963i	$0.728140\pi$
$230$	−2.06159	−	5.88000i	−0.135937	−	0.387716i
$231$	−9.81882	−	17.0067i	−0.646031	−	1.11896i
$232$	0.0398021	−	1.11940i	0.00261313	−	0.0734922i
$233$	4.47546			0.293197			0.146599	−	0.989196i	$-0.453167\pi$
$233$	4.47546			0.293197			0.146599	+	0.989196i	$0.453167\pi$
$234$	−27.7435	+	16.3923i	−1.81365	+	1.07160i
$235$			1.97572i			0.128882i
$236$	−7.73069	−	9.66939i	−0.503225	−	0.629423i
$237$	−24.7623	+	14.2965i	−1.60849	+	0.928660i
$238$	7.67433	−	2.69070i	0.497453	−	0.174412i
$239$	18.4932			1.19623			0.598114	−	0.801411i	$-0.295917\pi$
$239$	18.4932			1.19623			0.598114	+	0.801411i	$0.295917\pi$
$240$	1.33603	−	5.92111i	0.0862403	−	0.382206i
$241$	6.87454	−	11.9070i	0.442828	−	0.767000i	−0.555070	−	0.831803i	$-0.687309\pi$
$241$	6.87454	−	11.9070i	0.442828	−	0.767000i	0.997898	+	0.0648032i	$0.0206420\pi$
$242$	3.71350	+	3.19173i	0.238713	+	0.205172i
$243$	−5.34194	−	3.08417i	−0.342685	−	0.197849i
$244$	−5.09964	−	6.37852i	−0.326471	−	0.408343i
$245$	1.78172	−	1.02868i	0.113830	−	0.0657199i
$246$	12.9500	−	15.0670i	0.825661	−	0.960639i
$247$	3.30111	−	2.89556i	0.210044	−	0.184240i
$248$	3.12720	−	4.99750i	0.198577	−	0.317342i
$249$	10.9480	+	18.9624i	0.693799	+	1.20169i
$250$	6.73732	+	1.27045i	0.426105	+	0.0803502i
$251$	−3.45759	−	1.99624i	−0.218241	−	0.126002i	0.386894	−	0.922124i	$-0.373548\pi$
$251$	−3.45759	−	1.99624i	−0.218241	−	0.126002i	−0.605136	+	0.796122i	$0.706881\pi$
$252$	−3.21261	−	21.1366i	−0.202376	−	1.33148i
$253$	29.1921	+	16.8540i	1.83529	+	1.05960i
$254$	−17.0297	+	5.97080i	−1.06854	+	0.374641i
$255$	5.15895			0.323066
$256$	1.27473	+	15.9491i	0.0796706	+	0.996821i
$257$	−3.41417	−	5.91352i	−0.212970	−	0.368875i	0.739673	−	0.672967i	$-0.234980\pi$
$257$	−3.41417	−	5.91352i	−0.212970	−	0.368875i	−0.952643	+	0.304092i	$0.901647\pi$
$258$	2.47583	−	13.1296i	0.154138	−	0.817413i
$259$			16.6682i			1.03571i
$260$	−2.74177	−	2.30895i	−0.170037	−	0.143195i
$261$		−	2.50272i		−	0.154915i
$262$	15.6758	+	2.95597i	0.968455	+	0.182620i
$263$	5.96177	+	10.3261i	0.367619	+	0.636734i	0.989193	−	0.146621i	$-0.0468398\pi$
$263$	5.96177	+	10.3261i	0.367619	+	0.636734i	−0.621574	+	0.783355i	$0.713507\pi$
$264$	15.3978	+	29.0034i	0.947667	+	1.78504i
$265$	2.82568			0.173580
$266$	0.963896	+	2.74919i	0.0591003	+	0.168564i
$267$	−33.3820	−	19.2731i	−2.04295	−	1.17950i
$268$	15.2306	−	2.31495i	0.930359	−	0.141408i
$269$	−18.3269	−	10.5811i	−1.11741	−	0.645139i	−0.176674	−	0.984270i	$-0.556534\pi$
$269$	−18.3269	−	10.5811i	−1.11741	−	0.645139i	−0.940739	+	0.339131i	$0.889867\pi$
$270$	1.32016	−	7.00093i	0.0803421	−	0.426063i
$271$	−10.8551	−	18.8016i	−0.659402	−	1.14212i	−0.980771	−	0.195164i	$-0.937476\pi$
$271$	−10.8551	−	18.8016i	−0.659402	−	1.14212i	0.321368	−	0.946954i	$-0.395857\pi$
$272$	−12.9845	+	4.04045i	−0.787301	+	0.244988i
$273$	−17.6308	−	5.98294i	−1.06706	−	0.362104i
$274$	−7.93570	−	6.82067i	−0.479413	−	0.412052i
$275$	−15.6535	+	9.03755i	−0.943942	+	0.544985i
$276$	33.7946	+	42.2696i	2.03420	+	2.54433i
$277$	−1.51540	−	0.874918i	−0.0910517	−	0.0525687i	0.453783	−	0.891112i	$-0.350074\pi$
$277$	−1.51540	−	0.874918i	−0.0910517	−	0.0525687i	−0.544835	+	0.838544i	$0.683408\pi$
$278$	10.8922	−	12.6728i	0.653271	−	0.760066i
$279$	6.58609	−	11.4074i	0.394299	−	0.682946i
$280$	2.10048	−	1.11513i	0.125528	−	0.0666420i
$281$	−16.9779			−1.01282			−0.506408	−	0.862294i	$-0.669027\pi$
$281$	−16.9779			−1.01282			−0.506408	+	0.862294i	$0.669027\pi$
$282$	−5.67762	−	16.1935i	−0.338097	−	0.964310i
$283$	−14.3699	+	8.29645i	−0.854200	+	0.493173i	−0.862066	−	0.506796i	$-0.830830\pi$
$283$	−14.3699	+	8.29645i	−0.854200	+	0.493173i	0.00786548	+	0.999969i	$0.497496\pi$
$284$	−11.9754	+	9.57437i	−0.710610	+	0.568134i
$285$			1.84810i			0.109472i
$286$	19.3904	−	0.195198i	1.14658	−	0.0115423i
$287$	7.78383			0.459465
$288$	4.11270	+	35.5124i	0.242343	+	2.09259i
$289$	2.72118	+	4.71322i	0.160069	+	0.277248i
$290$	0.262711	−	0.0921093i	0.0154269	−	0.00540885i
$291$		−	5.08304i		−	0.297973i
$292$	−11.2218	−	4.38820i	−0.656707	−	0.256800i
$293$	19.9026	+	11.4908i	1.16272	+	0.671299i	0.951955	−	0.306237i	$-0.0990699\pi$
$293$	19.9026	+	11.4908i	1.16272	+	0.671299i	0.210769	+	0.977536i	$0.432403\pi$
$294$	−11.6474	+	13.5514i	−0.679288	+	0.790336i
$295$	1.53844	−	2.66465i	0.0895714	−	0.155142i
$296$	0.990405	−	27.8543i	0.0575661	−	1.61900i
$297$	19.2705	+	33.3776i	1.11819	+	1.93676i
$298$	11.3843	−	13.2454i	0.659475	−	0.767285i
$299$	31.3437	−	6.23781i	1.81265	−	0.360742i
$300$	−28.6901	+	4.36069i	−1.65642	+	0.251765i
$301$	4.53335	−	2.61733i	0.261298	−	0.150860i
$302$	4.63825	−	24.5971i	0.266901	−	1.41541i
$303$	11.9790	−	20.7483i	0.688177	−	1.19196i
$304$	−1.44742	−	4.65147i	−0.0830152	−	0.266780i
$305$	1.01485	−	1.75777i	0.0581101	−	0.100650i
$306$	−28.6729	+	10.0530i	−1.63912	+	0.574693i
$307$		−	14.1283i		−	0.806346i	−0.915124	−	0.403173i	$-0.867907\pi$
$307$		−	14.1283i		−	0.806346i	0.915124	−	0.403173i	$-0.132093\pi$
$308$	−4.68536	+	11.9817i	−0.266973	+	0.682722i
$309$	34.9819	−	20.1968i	1.99005	−	1.14896i
$310$	1.43983	+	0.271508i	0.0817771	+	0.0154206i
$311$	18.5022			1.04917			0.524583	−	0.851359i	$-0.324221\pi$
$311$	18.5022			1.04917			0.524583	+	0.851359i	$0.324221\pi$
$312$	29.1074	+	11.0457i	1.64788	+	0.625341i
$313$	−30.0763			−1.70001			−0.850007	−	0.526772i	$-0.823402\pi$
$313$	−30.0763			−1.70001			−0.850007	+	0.526772i	$0.823402\pi$
$314$	−3.75417	−	0.707918i	−0.211860	−	0.0399501i
$315$	4.60172	−	2.65680i	0.259278	−	0.149694i
$316$	17.4458	+	6.82204i	0.981403	+	0.383770i
$317$			29.4608i			1.65469i	0.561698	+	0.827343i	$0.310148\pi$
$317$			29.4608i			1.65469i	−0.561698	+	0.827343i	$0.689852\pi$
$318$	−23.1600	+	8.12015i	−1.29875	+	0.455355i
$319$	−0.753019	+	1.30427i	−0.0421609	+	0.0730249i
$320$	−3.57638	+	1.73870i	−0.199926	+	0.0971962i
$321$	13.4603	−	23.3139i	0.751280	−	1.30125i
$322$	−3.92896	+	20.8357i	−0.218952	+	1.16113i
$323$	3.58563	−	2.07016i	0.199510	−	0.115187i
$324$	3.60031	+	23.6873i	0.200017	+	1.31596i
$325$	−5.50689	+	16.2280i	−0.305467	+	0.900165i
$326$	−1.99042	+	2.31581i	−0.110239	+	0.128261i
$327$	−5.58026	−	9.66529i	−0.308589	−	0.534492i
$328$	−13.0076	−	0.462507i	−0.718225	−	0.0255377i
$329$	3.36153	−	5.82234i	0.185327	−	0.320996i
$330$	−5.31972	+	6.18938i	−0.292841	+	0.340714i
$331$	5.82316	+	3.36200i	0.320070	+	0.184792i	0.651424	−	0.758714i	$-0.274172\pi$
$331$	5.82316	+	3.36200i	0.320070	+	0.184792i	−0.331354	+	0.943507i	$0.607505\pi$
$332$	5.22416	−	13.3596i	0.286713	−	0.733203i
$333$		−	62.2758i		−	3.41269i
$334$	−9.88262	+	3.46495i	−0.540753	+	0.189594i
$335$	1.91444	+	3.31591i	0.104597	+	0.181168i
$336$	−14.0115	+	15.1760i	−0.764390	+	0.827921i
$337$	24.6061			1.34038			0.670191	−	0.742189i	$-0.266212\pi$
$337$	24.6061			1.34038			0.670191	+	0.742189i	$0.266212\pi$
$338$	13.6985	−	12.2618i	0.745100	−	0.666953i
$339$			34.8651i			1.89361i
$340$	−2.11054	−	2.63981i	−0.114460	−	0.143164i
$341$	−6.86454	+	3.96325i	−0.371736	+	0.214622i
$342$	−3.60132	−	10.2716i	−0.194737	−	0.555422i
$343$	−18.8412			−1.01733
$344$	−7.73123	+	4.10447i	−0.416840	+	0.221298i
$345$	−6.72527	+	11.6485i	−0.362076	+	0.627134i
$346$	−3.89364	+	4.53016i	−0.209323	+	0.243543i
$347$	24.0795	+	13.9023i	1.29265	+	0.746314i	0.979124	−	0.203264i	$-0.0651551\pi$
$347$	24.0795	+	13.9023i	1.29265	+	0.746314i	0.313530	+	0.949578i	$0.398488\pi$
$348$	−1.88855	+	1.50990i	−0.101237	+	0.0809393i
$349$	−1.80201	+	1.04039i	−0.0964596	+	0.0556910i	−0.547454	−	0.836836i	$-0.684403\pi$
$349$	−1.80201	+	1.04039i	−0.0964596	+	0.0556910i	0.450994	+	0.892527i	$0.351069\pi$
$350$	−8.62235	−	7.41084i	−0.460884	−	0.396126i
$351$	34.6024	+	11.7422i	1.84694	+	0.626752i
$352$	8.54167	−	19.7443i	0.455273	−	1.05238i
$353$	9.53154	+	16.5091i	0.507312	+	0.878691i	0.999964	+	0.00846439i	$0.00269433\pi$
$353$	9.53154	+	16.5091i	0.507312	+	0.878691i	−0.492652	+	0.870227i	$0.663972\pi$
$354$	−4.95204	+	26.2612i	−0.263198	+	1.39577i
$355$	−3.30014	−	1.90534i	−0.175153	−	0.101125i
$356$	3.79468	+	24.9661i	0.201117	+	1.32320i
$357$	−15.2031	−	8.77754i	−0.804636	−	0.464557i
$358$	−0.209789	−	0.598352i	−0.0110877	−	0.0316239i
$359$	−6.51007			−0.343588			−0.171794	−	0.985133i	$-0.554956\pi$
$359$	−6.51007			−0.343588			−0.171794	+	0.985133i	$0.554956\pi$
$360$	−7.84782	+	4.16637i	−0.413617	+	0.219587i
$361$	−8.75840	−	15.1700i	−0.460968	−	0.798421i
$362$	2.03268	+	0.383301i	0.106836	+	0.0201458i
$363$		−	10.5703i		−	0.554795i
$364$	4.15135	+	11.4692i	0.217590	+	0.601152i
$365$		−	2.99472i		−	0.156751i
$366$	−3.26667	+	17.3235i	−0.170752	+	0.905514i
$367$	2.78509	+	4.82392i	0.145381	+	0.251806i	0.929515	−	0.368785i	$-0.120226\pi$
$367$	2.78509	+	4.82392i	0.145381	+	0.251806i	−0.784134	+	0.620591i	$0.786893\pi$
$368$	7.80373	−	34.5852i	0.406798	−	1.80288i
$369$	−29.0820			−1.51395
$370$	6.53711	−	2.29198i	0.339848	−	0.119154i
$371$	−8.32714	−	4.80768i	−0.432323	−	0.249602i
$372$	−12.5815	+	1.91230i	−0.652320	+	0.0991480i
$373$	−14.8322	−	8.56338i	−0.767982	−	0.443395i	0.0641721	−	0.997939i	$-0.479559\pi$
$373$	−14.8322	−	8.56338i	−0.767982	−	0.443395i	−0.832154	+	0.554544i	$0.812893\pi$
$374$	17.9673	+	3.38808i	0.929068	+	0.175193i
$375$	−7.39998	−	12.8171i	−0.382134	−	0.661875i
$376$	−5.96343	+	9.53002i	−0.307541	+	0.491473i
$377$	0.278698	+	1.40040i	0.0143537	+	0.0721242i
$378$	−15.8019	+	18.3852i	−0.812765	+	0.945634i
$379$	10.6206	−	6.13180i	0.545543	−	0.314969i	−0.201780	−	0.979431i	$-0.564672\pi$
$379$	10.6206	−	6.13180i	0.545543	−	0.314969i	0.747322	+	0.664462i	$0.231339\pi$
$380$	0.945667	−	0.756063i	0.0485117	−	0.0387852i
$381$	33.7365	+	19.4778i	1.72838	+	0.997878i
$382$	−8.84454	−	7.60181i	−0.452526	−	0.388943i
$383$	−1.62701	+	2.81807i	−0.0831365	+	0.143997i	−0.904596	−	0.426271i	$-0.859827\pi$
$383$	−1.62701	+	2.81807i	−0.0831365	+	0.143997i	0.821459	+	0.570267i	$0.193160\pi$
$384$	24.3164	−	24.5282i	1.24089	−	1.25170i
$385$	−3.19752			−0.162961
$386$	16.8458	−	5.90633i	0.857431	−	0.300624i
$387$	−16.9375	+	9.77890i	−0.860984	+	0.497089i
$388$	−2.60097	+	2.07948i	−0.132044	+	0.105570i
$389$		−	17.9829i		−	0.911769i	−0.890039	−	0.455884i	$-0.849323\pi$
$389$		−	17.9829i		−	0.911769i	0.890039	−	0.455884i	$-0.150677\pi$
$390$	0.0778900	+	7.73733i	0.00394411	+	0.391795i
$391$	30.1334			1.52391
$392$	11.6992	+	0.415983i	0.590898	+	0.0210103i
$393$	−17.2176	−	29.8218i	−0.868515	−	1.50431i
$394$	−8.26379	−	23.5697i	−0.416324	−	1.18743i
$395$			4.65569i			0.234253i
$396$	17.5055	−	44.7662i	0.879683	−	2.24959i
$397$	−17.9828	−	10.3824i	−0.902532	−	0.521077i	−0.0245115	−	0.999700i	$-0.507803\pi$
$397$	−17.9828	−	10.3824i	−0.902532	−	0.521077i	−0.878021	+	0.478622i	$0.841136\pi$
$398$	−21.2806	−	18.2905i	−1.06670	−	0.916818i
$399$	3.14440	−	5.44626i	0.157417	−	0.272654i
$400$	13.9685	+	12.8966i	0.698426	+	0.644832i
$401$	1.17622	+	2.03728i	0.0587377	+	0.101737i	0.893899	−	0.448268i	$-0.147959\pi$
$401$	1.17622	+	2.03728i	0.0587377	+	0.101737i	−0.835161	+	0.550005i	$0.814626\pi$
$402$	−25.2202	−	21.6766i	−1.25787	−	1.08113i
$403$	−2.41494	+	7.11646i	−0.120297	+	0.354496i
$404$	−15.5175	+	2.35854i	−0.772022	+	0.117342i
$405$	−5.15705	+	2.97742i	−0.256256	+	0.147949i
$406$	−0.930913	−	0.175541i	−0.0462004	−	0.00871195i
$407$	−18.7376	+	32.4544i	−0.928786	+	1.60870i
$408$	24.8845	+	15.5715i	1.23197	+	0.770907i
$409$	18.1089	−	31.3655i	0.895426	−	1.55092i	0.0621499	−	0.998067i	$-0.480204\pi$
$409$	18.1089	−	31.3655i	0.895426	−	1.55092i	0.833276	−	0.552857i	$-0.186462\pi$
$410$	−1.07033	−	3.05275i	−0.0528596	−	0.150764i
$411$			22.5885i			1.11421i
$412$	−24.6458	−	9.63755i	−1.21421	−	0.474808i
$413$	−9.06740	+	5.23506i	−0.446177	+	0.257601i
$414$	14.6794	−	77.8464i	0.721453	−	3.82594i
$415$	3.56522			0.175010
$416$	−6.25585	−	19.4130i	−0.306718	−	0.951800i
$417$	−36.0725			−1.76648
$418$	−1.21372	+	6.43648i	−0.0593649	+	0.314819i
$419$	−20.6067	+	11.8973i	−1.00671	+	0.581222i	−0.910225	−	0.414113i	$-0.864092\pi$
$419$	−20.6067	+	11.8973i	−1.00671	+	0.581222i	−0.0964800	+	0.995335i	$0.530758\pi$
$420$	−4.78107	−	1.86960i	−0.233292	−	0.0912270i
$421$		−	19.8220i		−	0.966067i	−0.875602	−	0.483033i	$-0.839535\pi$
$421$		−	19.8220i		−	0.966067i	0.875602	−	0.483033i	$-0.160465\pi$
$422$	7.06143	+	20.1404i	0.343745	+	0.980418i
$423$	−12.5594	+	21.7535i	−0.610658	+	1.05769i
$424$	13.6299	+	8.52892i	0.661925	+	0.414201i
$425$	−8.07913	+	13.9935i	−0.391895	+	0.678783i
$426$	32.5242	+	6.13304i	1.57580	+	0.297147i
$427$	−5.98141	+	3.45337i	−0.289461	+	0.167120i
$428$	−17.4363	+	2.65019i	−0.842813	+	0.128102i
$429$	−27.6029	−	31.4690i	−1.33268	−	1.51934i
$430$	−1.64986	−	1.41804i	−0.0795632	−	0.0683839i
$431$	0.190576	+	0.330088i	0.00917975	+	0.0158998i	0.870579	−	0.492029i	$-0.163745\pi$
$431$	0.190576	+	0.330088i	0.00917975	+	0.0158998i	−0.861399	+	0.507929i	$0.830411\pi$
$432$	27.4992	−	29.7847i	1.32305	−	1.43302i
$433$	−1.76379	+	3.05497i	−0.0847622	+	0.146813i	−0.905290	−	0.424794i	$-0.860346\pi$
$433$	−1.76379	+	3.05497i	−0.0847622	+	0.146813i	0.820528	+	0.571607i	$0.193680\pi$
$434$	−3.78117	−	3.24988i	−0.181502	−	0.155999i
$435$	−0.520441	−	0.300477i	−0.0249532	−	0.0144068i
$436$	−2.66280	+	6.80949i	−0.127525	+	0.326115i
$437$			10.7948i			0.516383i
$438$	8.60591	+	24.5455i	0.411206	+	1.17283i
$439$	3.20727	+	5.55516i	0.153075	+	0.265133i	0.932356	−	0.361541i	$-0.117749\pi$
$439$	3.20727	+	5.55516i	0.153075	+	0.265133i	−0.779282	+	0.626674i	$0.784416\pi$
$440$	5.34339	+	0.189993i	0.254736	+	0.00905756i
$441$	26.1567			1.24556
$442$	14.9245	−	8.81813i	0.709884	−	0.419436i
$443$			17.5752i			0.835023i	0.908672	+	0.417512i	$0.137098\pi$
$443$			17.5752i			0.835023i	−0.908672	+	0.417512i	$0.862902\pi$
$444$	−46.9934	+	37.5713i	−2.23021	+	1.78306i
$445$	−5.43546	+	3.13816i	−0.257666	+	0.148763i
$446$	−13.2896	+	4.65949i	−0.629283	+	0.220633i
$447$	−37.7022			−1.78325
$448$	13.4977	+	0.961078i	0.637705	+	0.0454067i
$449$	−18.1700	+	31.4714i	−0.857498	+	1.48523i	0.0168107	+	0.999859i	$0.494649\pi$
$449$	−18.1700	+	31.4714i	−0.857498	+	1.48523i	−0.874308	+	0.485371i	$0.838685\pi$
$450$	32.2149	+	27.6885i	1.51863	+	1.30525i
$451$	15.1558	+	8.75020i	0.713658	+	0.412031i
$452$	17.8403	−	14.2634i	0.839138	−	0.670893i
$453$	−46.7938	+	27.0164i	−2.19857	+	1.26934i
$454$	−1.27701	+	1.48578i	−0.0599332	+	0.0697309i
$455$	−2.27904	+	1.99905i	−0.106843	+	0.0937171i
$456$	−5.57824	+	8.91444i	−0.261225	+	0.417457i
$457$	−6.58332	−	11.4026i	−0.307955	−	0.533393i	0.669960	−	0.742397i	$-0.266311\pi$
$457$	−6.58332	−	11.4026i	−0.307955	−	0.533393i	−0.977915	+	0.209004i	$0.932978\pi$
$458$	−31.7121	−	5.97991i	−1.48181	−	0.279423i
$459$	29.8379	+	17.2269i	1.39271	+	0.804083i
$460$	8.71182	−	1.32413i	0.406191	−	0.0617381i
$461$	12.7594	+	7.36666i	0.594266	+	0.343099i	0.766782	−	0.641907i	$-0.221857\pi$
$461$	12.7594	+	7.36666i	0.594266	+	0.343099i	−0.172517	+	0.985007i	$0.555190\pi$
$462$	26.2077	−	9.18868i	1.21929	−	0.427496i
$463$	−5.65151			−0.262648			−0.131324	−	0.991339i	$-0.541923\pi$
$463$	−5.65151			−0.262648			−0.131324	+	0.991339i	$0.541923\pi$
$464$	1.54522	+	0.348661i	0.0717352	+	0.0161862i
$465$	−1.58145	−	2.73916i	−0.0733381	−	0.127025i
$466$	−1.17283	+	6.21965i	−0.0543303	+	0.288120i
$467$		−	29.5883i		−	1.36918i	−0.728926	−	0.684592i	$-0.759980\pi$
$467$		−	29.5883i		−	1.36918i	0.728926	−	0.684592i	$-0.240020\pi$
$468$	−15.5103	−	42.8515i	−0.716964	−	1.98081i
$469$		−	13.0291i		−	0.601628i
$470$	−2.74570	−	0.517753i	−0.126650	−	0.0238822i
$471$	4.12342	+	7.14196i	0.189997	+	0.329084i
$472$	15.4636	−	8.20957i	0.711772	−	0.377876i
$473$	11.7691			0.541144
$474$	−13.3790	−	38.1593i	−0.614520	−	1.75271i
$475$	−5.01291	−	2.89421i	−0.230008	−	0.132795i
$476$	1.72821	+	11.3703i	0.0792122	+	0.521157i
$477$	31.1119	+	17.9625i	1.42452	+	0.822445i
$478$	−4.84630	+	25.7004i	−0.221665	+	1.17551i
$479$	7.57479	+	13.1199i	0.346101	+	0.599464i	0.985553	−	0.169367i	$-0.0541722\pi$
$479$	7.57479	+	13.1199i	0.346101	+	0.599464i	−0.639452	+	0.768831i	$0.720839\pi$
$480$	7.87858	+	3.40838i	0.359606	+	0.155571i
$481$	6.93491	+	34.8465i	0.316205	+	1.58886i
$482$	14.7459	+	12.6740i	0.671660	+	0.577286i
$483$	39.6380	−	22.8850i	1.80359	−	1.04130i
$484$	−5.40877	+	4.32432i	−0.245853	+	0.196560i
$485$	−0.716766	−	0.413825i	−0.0325467	−	0.0187908i
$486$	5.68603	−	6.61557i	0.257924	−	0.300088i
$487$	15.0531	−	26.0728i	0.682122	−	1.18147i	−0.292210	−	0.956354i	$-0.594391\pi$
$487$	15.0531	−	26.0728i	0.682122	−	1.18147i	0.974332	−	0.225116i	$-0.0722761\pi$
$488$	10.2008	−	5.41554i	0.461767	−	0.245150i
$489$	6.59183			0.298093
$490$	0.962662	+	2.74567i	0.0434886	+	0.124037i
$491$	−23.2315	+	13.4127i	−1.04842	+	0.605307i	−0.922208	−	0.386695i	$-0.873617\pi$
$491$	−23.2315	+	13.4127i	−1.04842	+	0.605307i	−0.126216	+	0.992003i	$0.540283\pi$
$492$	17.5453	+	21.9453i	0.791004	+	0.989371i
$493$			1.34632i			0.0606353i
$494$	3.15894	+	5.34642i	0.142127	+	0.240547i
$495$	11.9466			0.536959
$496$	6.12563	+	5.65557i	0.275049	+	0.253943i
$497$	6.48356	+	11.2299i	0.290828	+	0.503728i
$498$	−29.2215	+	10.2454i	−1.30945	+	0.459106i
$499$		−	18.5109i		−	0.828660i	−0.910127	−	0.414330i	$-0.864016\pi$
$499$		−	18.5109i		−	0.828660i	0.910127	−	0.414330i	$-0.135984\pi$
$500$	−3.53114	+	9.03007i	−0.157917	+	0.403837i
$501$	19.5778	+	11.3033i	0.874674	+	0.504993i
$502$	3.68031	−	4.28196i	0.164260	−	0.191113i
$503$	7.36468	−	12.7560i	0.328375	−	0.568762i	−0.653815	−	0.756655i	$-0.726832\pi$
$503$	7.36468	−	12.7560i	0.328375	−	0.568762i	0.982190	+	0.187893i	$0.0601658\pi$
$504$	30.2159	+	1.07437i	1.34592	+	0.0478564i
$505$	−1.95050	−	3.37836i	−0.0867959	−	0.150335i
$506$	−31.0724	+	36.1521i	−1.38134	+	1.60716i
$507$	−39.3482	−	5.17251i	−1.74751	−	0.229719i
$508$	−3.83498	−	25.2313i	−0.170150	−	1.11946i
$509$	28.9656	−	16.7233i	1.28388	−	0.741248i	0.306324	−	0.951927i	$-0.400901\pi$
$509$	28.9656	−	16.7233i	1.28388	−	0.741248i	0.977555	+	0.210680i	$0.0675677\pi$
$510$	−1.35194	+	7.16950i	−0.0598650	+	0.317471i
$511$	−5.09528	+	8.82528i	−0.225402	+	0.390408i
$512$	−22.4989	−	2.40808i	−0.994321	−	0.106423i
$513$	−6.17124	+	10.6889i	−0.272467	+	0.471926i
$514$	9.11285	−	3.19506i	0.401951	−	0.140928i
$515$		−	6.57713i		−	0.289823i
$516$	17.5977	+	6.88143i	0.774694	+	0.302938i
$517$	13.0904	−	7.55773i	0.575714	−	0.332389i
$518$	−23.1641	−	4.36803i	−1.01777	−	0.191920i
$519$	12.8948			0.566020
$520$	3.92730	−	3.20521i	0.172223	−	0.140558i
$521$	29.7885			1.30506			0.652530	−	0.757763i	$-0.273708\pi$
$521$	29.7885			1.30506			0.652530	+	0.757763i	$0.273708\pi$
$522$	3.47808	+	0.655858i	0.152232	+	0.0287061i
$523$	−1.49190	+	0.861351i	−0.0652364	+	0.0376642i	−0.532263	−	0.846579i	$-0.678658\pi$
$523$	−1.49190	+	0.861351i	−0.0652364	+	0.0376642i	0.467027	+	0.884243i	$0.345325\pi$
$524$	−8.21594	+	21.0104i	−0.358915	+	0.917843i
$525$			24.5430i			1.07115i
$526$	−15.9127	+	5.57917i	−0.693828	+	0.243263i
$527$	−3.54295	+	6.13656i	−0.154333	+	0.267313i
$528$	−44.3418	+	13.7980i	−1.92973	+	0.600482i
$529$	−27.7822	+	48.1203i	−1.20792	+	2.09218i
$530$	−0.740493	+	3.92691i	−0.0321650	+	0.170574i
$531$	33.8777	−	19.5593i	1.47017	−	0.848801i
$532$	−4.07321	+	0.619099i	−0.176596	+	0.0268414i
$533$	16.2729	−	3.23852i	0.704856	−	0.140276i
$534$	35.5323	−	41.3411i	1.53763	−	1.78900i
$535$	−2.19168	−	3.79611i	−0.0947547	−	0.164120i
$536$	−0.774174	+	21.7730i	−0.0334392	+	0.940450i
$537$	−0.684367	+	1.18536i	−0.0295326	+	0.0511520i
$538$	19.5074	−	22.6965i	0.841026	−	0.978515i
$539$	−13.6313	−	7.87002i	−0.587141	−	0.338986i
$540$	9.38338	+	3.66930i	0.403796	+	0.157901i
$541$		−	36.6856i		−	1.57724i	−0.614883	−	0.788618i	$-0.710797\pi$
$541$		−	36.6856i		−	1.57724i	0.614883	−	0.788618i	$-0.289203\pi$
$542$	28.9737	−	10.1585i	1.24453	−	0.436345i
$543$	−2.23261	−	3.86700i	−0.0958107	−	0.165949i
$544$	−2.21240	−	19.1037i	−0.0948560	−	0.819063i
$545$	−1.81722			−0.0778412
$546$	12.9349	−	22.9340i	0.553563	−	0.981486i
$547$		−	33.7227i		−	1.44188i	−0.692999	−	0.720939i	$-0.743711\pi$
$547$		−	33.7227i		−	1.44188i	0.692999	−	0.720939i	$-0.256289\pi$
$548$	11.5584	−	9.24100i	0.493752	−	0.394756i
$549$	22.3478	−	12.9025i	0.953781	−	0.550666i
$550$	−8.45756	−	24.1224i	−0.360631	−	1.02858i
$551$	−0.482297			−0.0205465
$552$	−67.5991	+	35.8880i	−2.87721	+	1.52750i
$553$	7.92129	−	13.7201i	0.336848	−	0.583437i
$554$	1.61302	−	1.87671i	0.0685305	−	0.0797337i
$555$	−12.9503	−	7.47684i	−0.549708	−	0.317374i
$556$	14.7573	+	18.4581i	0.625850	+	0.782800i
$557$	2.44793	−	1.41331i	0.103722	−	0.0598839i	−0.447242	−	0.894413i	$-0.647594\pi$
$557$	2.44793	−	1.41331i	0.103722	−	0.0598839i	0.550964	+	0.834529i	$0.314260\pi$
$558$	14.1272	+	12.1422i	0.598053	+	0.514022i
$559$	8.38846	−	7.35792i	0.354794	−	0.311207i
$560$	0.999278	+	3.21131i	0.0422272	+	0.135703i
$561$	−19.7345	−	34.1812i	−0.833193	−	1.44313i
$562$	4.44919	−	23.5945i	0.187678	−	0.995275i
$563$	−7.06225	−	4.07739i	−0.297638	−	0.171842i	0.343743	−	0.939064i	$-0.388305\pi$
$563$	−7.06225	−	4.07739i	−0.297638	−	0.171842i	−0.641381	+	0.767222i	$0.721638\pi$
$564$	23.9923	−	3.64667i	1.01026	−	0.153552i
$565$	4.91637	+	2.83847i	0.206833	+	0.119415i
$566$	−7.76402	−	22.1443i	−0.326346	−	0.930793i
$567$	20.2634			0.850983
$568$	−10.1675	−	19.1515i	−0.426617	−	0.803580i
$569$	−15.0669	−	26.0967i	−0.631638	−	1.09403i	−0.987217	−	0.159382i	$-0.949050\pi$
$569$	−15.0669	−	26.0967i	−0.631638	−	1.09403i	0.355579	−	0.934646i	$-0.384284\pi$
$570$	−2.56835	−	0.484310i	−0.107576	−	0.0202855i
$571$			32.3914i			1.35554i	0.735276	+	0.677768i	$0.237053\pi$
$571$			32.3914i			1.35554i	−0.735276	+	0.677768i	$0.762947\pi$
$572$	−4.81012	+	26.9983i	−0.201121	+	1.12886i
$573$			25.1755i			1.05172i
$574$	−2.03982	+	10.8174i	−0.0851402	+	0.451508i
$575$	−21.0641	−	36.4841i	−0.878434	−	1.52149i
$576$	−50.4301	−	3.59079i	−2.10125	−	0.149616i
$577$	15.3547			0.639225			0.319612	−	0.947548i	$-0.396447\pi$
$577$	15.3547			0.639225			0.319612	+	0.947548i	$0.396447\pi$
$578$	−7.26317	+	2.54654i	−0.302108	+	0.105922i
$579$	−33.3723	−	19.2675i	−1.38690	−	0.800730i
$580$	0.0591608	+	0.389233i	0.00245652	+	0.0161620i
$581$	−10.5065	−	6.06594i	−0.435884	−	0.251658i
$582$	7.06401	+	1.33205i	0.292813	+	0.0552153i
$583$	−10.8091	−	18.7219i	−0.447667	−	0.775382i
$584$	9.03914	−	14.4452i	0.374042	−	0.597748i
$585$	8.51496	−	7.46889i	0.352050	−	0.308800i
$586$	−21.1846	+	24.6479i	−0.875129	+	1.01819i
$587$	−0.529297	+	0.305590i	−0.0218464	+	0.0126130i	−0.510883	−	0.859650i	$-0.670682\pi$
$587$	−0.529297	+	0.305590i	−0.0218464	+	0.0126130i	0.489037	+	0.872263i	$0.337348\pi$
$588$	−15.7804	−	19.7378i	−0.650775	−	0.813975i
$589$	−2.19832	−	1.26920i	−0.0905800	−	0.0522964i
$590$	3.29997	+	2.83630i	0.135858	+	0.116768i
$591$	−26.9579	+	46.6925i	−1.10890	+	1.92067i
$592$	38.4502	+	8.67583i	1.58029	+	0.356574i
$593$	39.5530			1.62425			0.812123	−	0.583486i	$-0.198312\pi$
$593$	39.5530			1.62425			0.812123	+	0.583486i	$0.198312\pi$
$594$	−51.4355	+	18.0338i	−2.11042	+	0.739937i
$595$	−2.47547	+	1.42921i	−0.101484	+	0.0585919i
$596$	15.4241	+	19.2921i	0.631794	+	0.790234i
$597$			60.5738i			2.47912i
$598$	0.454955	+	45.1937i	0.0186045	+	1.84811i
$599$	−18.3132			−0.748257			−0.374128	−	0.927377i	$-0.622058\pi$
$599$	−18.3132			−0.748257			−0.374128	+	0.927377i	$0.622058\pi$
$600$	1.45832	−	41.0140i	0.0595356	−	1.67439i
$601$	5.87056	+	10.1681i	0.239465	+	0.414766i	0.960561	−	0.278069i	$-0.0896945\pi$
$601$	5.87056	+	10.1681i	0.239465	+	0.414766i	−0.721096	+	0.692836i	$0.756361\pi$
$602$	2.44936	+	6.98599i	0.0998285	+	0.284728i
$603$			48.6794i			1.98238i
$604$	32.9677	+	12.8917i	1.34144	+	0.524558i
$605$	−1.49053	−	0.860557i	−0.0605986	−	0.0349866i
$606$	25.6951	+	22.0848i	1.04379	+	0.897132i
$607$	17.0834	−	29.5893i	0.693393	−	1.20099i	−0.277326	−	0.960776i	$-0.589448\pi$
$607$	17.0834	−	29.5893i	0.693393	−	1.20099i	0.970719	−	0.240216i	$-0.0772184\pi$
$608$	6.84355	−	0.792555i	0.277543	−	0.0321423i
$609$	1.02247	+	1.77098i	0.0414328	+	0.0717637i
$610$	2.17686	+	1.87100i	0.0881386	+	0.0757544i
$611$	4.60519	−	13.5708i	0.186306	−	0.549015i
$612$	−6.45694	−	42.4818i	−0.261006	−	1.71723i
$613$	−17.1561	+	9.90507i	−0.692928	+	0.400062i	−0.804708	−	0.593671i	$-0.797678\pi$
$613$	−17.1561	+	9.90507i	−0.692928	+	0.400062i	0.111780	+	0.993733i	$0.464345\pi$
$614$	19.6344	+	3.70244i	0.792381	+	0.149418i
$615$	−3.49159	+	6.04761i	−0.140795	+	0.243863i
$616$	−15.4234	−	9.65125i	−0.621427	−	0.388860i
$617$	3.28645	−	5.69230i	0.132308	−	0.229164i	−0.792258	−	0.610186i	$-0.791095\pi$
$617$	3.28645	−	5.69230i	0.132308	−	0.229164i	0.924566	+	0.381023i	$0.124428\pi$
$618$	18.9007	+	53.9079i	0.760296	+	2.16849i
$619$		−	12.1233i		−	0.487277i	−0.969866	−	0.243638i	$-0.921659\pi$
$619$		−	12.1233i		−	0.487277i	0.969866	−	0.243638i	$-0.0783410\pi$
$620$	−0.754640	+	1.92982i	−0.0303071	+	0.0775034i
$621$	−77.7941	+	44.9144i	−3.12177	+	1.80235i
$622$	−4.84866	+	25.7130i	−0.194414	+	1.03100i
$623$	21.3574			0.855664
$624$	−22.9783	+	37.5566i	−0.919869	+	1.50347i
$625$	21.3547			0.854190
$626$	7.88174	−	41.7977i	0.315017	−	1.67057i
$627$	12.2448	−	7.06956i	0.489011	−	0.282331i
$628$	1.96762	−	5.03173i	0.0785165	−	0.200788i
$629$			33.5009i			1.33577i
$630$	2.48630	+	7.09134i	0.0990566	+	0.282526i
$631$	7.76063	−	13.4418i	0.308946	−	0.535110i	−0.669186	−	0.743095i	$-0.733357\pi$
$631$	7.76063	−	13.4418i	0.308946	−	0.535110i	0.978132	+	0.207985i	$0.0666905\pi$
$632$	−14.0526	+	22.4570i	−0.558980	+	0.893293i
$633$	23.0356	−	39.8989i	0.915584	−	1.58584i
$634$	−40.9424	−	7.72045i	−1.62603	−	0.306618i
$635$	5.49319	−	3.17149i	0.217990	−	0.125857i
$636$	−5.21548	−	34.3139i	−0.206807	−	1.36064i
$637$	−14.6360	+	2.91276i	−0.579899	+	0.115408i
$638$	−1.61523	−	1.38828i	−0.0639477	−	0.0549625i
$639$	−24.2239	−	41.9571i	−0.958284	−	1.65980i
$640$	−1.47909	−	5.42581i	−0.0584660	−	0.214474i
$641$	−5.10157	+	8.83618i	−0.201500	+	0.349008i	−0.949012	−	0.315240i	$-0.897915\pi$
$641$	−5.10157	+	8.83618i	−0.201500	+	0.349008i	0.747512	+	0.664248i	$0.231248\pi$
$642$	28.8724	+	24.8156i	1.13950	+	0.979395i
$643$	35.8102	+	20.6750i	1.41222	+	0.815343i	0.995597	−	0.0937380i	$-0.0298816\pi$
$643$	35.8102	+	20.6750i	1.41222	+	0.815343i	0.416619	+	0.909081i	$0.363215\pi$
$644$	−27.9262	−	10.9203i	−1.10045	−	0.430320i
$645$			4.69622i			0.184913i
$646$	1.93731	+	5.52552i	0.0762223	+	0.217399i
$647$	−2.36752	−	4.10066i	−0.0930767	−	0.161214i	0.815728	−	0.578436i	$-0.196337\pi$
$647$	−2.36752	−	4.10066i	−0.0930767	−	0.161214i	−0.908804	+	0.417223i	$0.863004\pi$
$648$	−33.8623	−	1.20403i	−1.33024	−	0.0472987i
$649$	−23.5400			−0.924026
$650$	−21.1092	−	11.9057i	−0.827971	−	0.466980i
$651$			10.7629i			0.421830i
$652$	−2.69673	−	3.37301i	−0.105612	−	0.132097i
$653$	−11.0711	+	6.39190i	−0.433245	+	0.250134i	−0.700728	−	0.713428i	$-0.747141\pi$
$653$	−11.0711	+	6.39190i	−0.433245	+	0.250134i	0.267483	+	0.963563i	$0.413808\pi$
$654$	14.8944	−	5.22214i	0.582418	−	0.204202i
$655$	−5.60696			−0.219082
$656$	4.05150	−	17.9558i	0.158185	−	0.701054i
$657$	19.0370	−	32.9731i	0.742705	−	1.28640i
$658$	7.21052	+	6.19738i	0.281095	+	0.241599i
$659$	−26.7651	−	15.4528i	−1.04262	−	0.601957i	−0.122046	−	0.992524i	$-0.538946\pi$
$659$	−26.7651	−	15.4528i	−1.04262	−	0.601957i	−0.920574	+	0.390567i	$0.872279\pi$
$660$	−7.20743	−	9.01490i	−0.280549	−	0.350905i
$661$	37.1109	−	21.4260i	1.44345	−	0.833374i	0.445368	−	0.895348i	$-0.353073\pi$
$661$	37.1109	−	21.4260i	1.44345	−	0.833374i	0.998078	+	0.0619739i	$0.0197396\pi$
$662$	−6.19825	+	7.21153i	−0.240902	+	0.280284i
$663$	−35.4356	−	12.0249i	−1.37621	−	0.467010i
$664$	17.1971	+	10.7611i	0.667376	+	0.417613i
$665$	−0.511990	−	0.886792i	−0.0198541	−	0.0343883i
$666$	86.5461	+	16.3199i	3.35359	+	0.632382i
$667$	−3.03989	−	1.75508i	−0.117705	−	0.0679571i
$668$	−2.22550	−	14.6421i	−0.0861070	−	0.566520i
$669$	26.3273	+	15.2001i	1.01787	+	0.587668i
$670$	−5.10989	+	1.79158i	−0.197412	+	0.0692149i
$671$	−15.5284			−0.599469
$672$	−17.4187	−	23.4491i	−0.671939	−	0.904568i
$673$	−1.93359	−	3.34907i	−0.0745343	−	0.129097i	0.826349	−	0.563158i	$-0.190414\pi$
$673$	−1.93359	−	3.34907i	−0.0745343	−	0.129097i	−0.900884	+	0.434061i	$0.857080\pi$
$674$	−6.44823	+	34.1957i	−0.248377	+	1.31717i
$675$		−	48.1684i		−	1.85400i
$676$	13.4507	+	22.2504i	0.517333	+	0.855784i
$677$		−	35.0468i		−	1.34696i	−0.739206	−	0.673479i	$-0.764799\pi$
$677$		−	35.0468i		−	1.34696i	0.739206	−	0.673479i	$-0.235201\pi$
$678$	−48.4527	−	9.13667i	−1.86082	−	0.350892i
$679$	1.40818	+	2.43904i	0.0540411	+	0.0936018i
$680$	4.22169	−	2.24127i	0.161894	−	0.0859489i
$681$	4.22917			0.162062
$682$	−3.70890	−	10.5784i	−0.142021	−	0.405068i
$683$	27.6732	+	15.9771i	1.05889	+	0.611348i	0.925124	−	0.379665i	$-0.123961\pi$
$683$	27.6732	+	15.9771i	1.05889	+	0.611348i	0.133763	+	0.991013i	$0.457294\pi$
$684$	15.2184	−	2.31308i	0.581889	−	0.0884430i
$685$	3.18524	+	1.83900i	0.121702	+	0.0702645i
$686$	4.93749	−	26.1840i	0.188514	−	0.999711i
$687$	34.8312	+	60.3295i	1.32889	+	2.30171i
$688$	−3.67804	−	11.8199i	−0.140224	−	0.450628i
$689$	−19.4090	−	6.58636i	−0.739423	−	0.250920i
$690$	−14.4258	−	12.3988i	−0.549180	−	0.472015i
$691$	5.89675	−	3.40449i	0.224323	−	0.129513i	−0.383627	−	0.923488i	$-0.625325\pi$
$691$	5.89675	−	3.40449i	0.224323	−	0.129513i	0.607950	+	0.793975i	$0.291992\pi$
$692$	−5.27530	−	6.59824i	−0.200537	−	0.250827i
$693$	−35.2060	−	20.3262i	−1.33736	−	0.772127i
$694$	−25.6305	+	29.8206i	−0.972921	+	1.13197i
$695$	−2.93677	+	5.08663i	−0.111398	+	0.192947i
$696$	−1.60343	−	3.02025i	−0.0607780	−	0.114482i
$697$	15.6445			0.592577
$698$	−0.973624	−	2.77694i	−0.0368522	−	0.105109i
$699$	11.8323	−	6.83139i	0.447540	−	0.258387i
$700$	12.5586	−	10.0406i	0.474669	−	0.379499i
$701$		−	39.0001i		−	1.47301i	−0.676431	−	0.736506i	$-0.736474\pi$
$701$		−	39.0001i		−	1.47301i	0.676431	−	0.736506i	$-0.263526\pi$
$702$	−25.3862	+	45.0106i	−0.958142	+	1.69882i
$703$	−12.0011			−0.452630
$704$	25.2007	+	17.0447i	0.949787	+	0.642396i
$705$	3.01576	+	5.22345i	0.113580	+	0.196727i
$706$	−25.4409	+	8.91984i	−0.957480	+	0.335703i
$707$			13.2745i			0.499237i
$708$	−35.1980	−	13.7639i	−1.32282	−	0.517279i
$709$	−11.4006	−	6.58214i	−0.428159	−	0.247198i	0.270403	−	0.962747i	$-0.412843\pi$
$709$	−11.4006	−	6.58214i	−0.428159	−	0.247198i	−0.698562	+	0.715550i	$0.746176\pi$
$710$	3.51272	−	4.08697i	0.131830	−	0.153381i
$711$	−29.5956	+	51.2611i	−1.10992	+	1.92244i
$712$	−35.6904	−	1.26903i	−1.33755	−	0.0475589i
$713$	−9.23726	−	15.9994i	−0.345938	−	0.599182i
$714$	16.1824	−	18.8279i	0.605612	−	0.704617i
$715$	−6.68472	+	1.33035i	−0.249994	+	0.0497522i
$716$	0.886520	−	0.134745i	0.0331308	−	0.00503565i
$717$	48.8928	−	28.2283i	1.82594	−	1.05420i
$718$	1.70602	−	9.04719i	0.0636680	−	0.337638i
$719$	4.83129	−	8.36804i	0.180177	−	0.312075i	−0.761764	−	0.647855i	$-0.775666\pi$
$719$	4.83129	−	8.36804i	0.180177	−	0.312075i	0.941941	+	0.335779i	$0.109000\pi$
$720$	−3.73351	−	11.9981i	−0.139140	−	0.447144i
$721$	−11.1905	+	19.3825i	−0.416755	+	0.721841i
$722$	23.3773	−	8.19632i	0.870012	−	0.305035i
$723$		−	41.9735i		−	1.56101i
$724$	−1.06536	+	2.72442i	−0.0395939	+	0.101252i
$725$	1.63007	−	0.941119i	0.0605391	−	0.0349523i
$726$	14.6897	+	2.77002i	0.545187	+	0.102805i
$727$	−34.2293			−1.26949			−0.634747	−	0.772720i	$-0.718896\pi$
$727$	−34.2293			−1.26949			−0.634747	+	0.772720i	$0.718896\pi$
$728$	−17.0270	+	2.76361i	−0.631061	+	0.102426i
$729$	17.1083			0.633639
$730$	4.16183	+	0.784791i	0.154036	+	0.0290464i
$731$	9.11145	−	5.26050i	0.336999	−	0.194566i
$732$	−23.2188	−	9.07952i	−0.858191	−	0.335589i
$733$		−	4.21648i		−	0.155739i	−0.996964	−	0.0778697i	$-0.975188\pi$
$733$		−	4.21648i		−	0.155739i	0.996964	−	0.0778697i	$-0.0248118\pi$
$734$	−7.43376	+	2.60635i	−0.274385	+	0.0962023i
$735$	3.14037	−	5.43928i	0.115834	−	0.200631i
$736$	46.0187	+	19.9083i	1.69627	+	0.733831i
$737$	14.6467	−	25.3688i	0.539517	−	0.934470i
$738$	7.62118	−	40.4159i	0.280539	−	1.48773i
$739$	−36.8643	+	21.2836i	−1.35608	+	0.782931i	−0.989092	−	0.147297i	$-0.952943\pi$
$739$	−36.8643	+	21.2836i	−1.35608	+	0.782931i	−0.366983	+	0.930228i	$0.619609\pi$
$740$	1.47211	+	9.68540i	0.0541159	+	0.356042i
$741$	4.30772	−	12.6942i	0.158248	−	0.466333i
$742$	8.86352	−	10.3125i	0.325390	−	0.378584i
$743$	20.6614	+	35.7866i	0.757994	+	1.31288i	0.943872	+	0.330311i	$0.107154\pi$
$743$	20.6614	+	35.7866i	0.757994	+	1.31288i	−0.185878	+	0.982573i	$0.559513\pi$
$744$	0.639518	−	17.9859i	0.0234459	−	0.659395i
$745$	−3.06945	+	5.31644i	−0.112456	+	0.194779i
$746$	15.7876	−	18.3685i	0.578025	−	0.672520i
$747$	39.2546	+	22.6636i	1.43625	+	0.829219i
$748$	−9.41696	+	24.0817i	−0.344318	+	0.880514i
$749$			14.9159i			0.545015i
$750$	19.7515	−	6.92508i	0.721222	−	0.252868i
$751$	6.54731	+	11.3403i	0.238915	+	0.413812i	0.960403	−	0.278614i	$-0.0898750\pi$
$751$	6.54731	+	11.3403i	0.238915	+	0.413812i	−0.721488	+	0.692427i	$0.756542\pi$
$752$	−11.6813	−	10.7849i	−0.425973	−	0.393286i
$753$	−12.1883			−0.444168
$754$	−2.01920	+	0.0203268i	−0.0735349	+	0.000740260i
$755$			8.79795i			0.320190i
$756$	−21.4093	−	26.7783i	−0.778649	−	0.973917i
$757$	−0.284326	+	0.164156i	−0.0103340	+	0.00596635i	−0.505158	−	0.863027i	$-0.668566\pi$
$757$	−0.284326	+	0.164156i	−0.0103340	+	0.00596635i	0.494824	+	0.868993i	$0.335232\pi$
$758$	5.73828	+	16.3665i	0.208424	+	0.594459i
$759$	102.905			3.73521
$760$	0.802897	+	1.51235i	0.0291241	+	0.0548586i
$761$	8.81782	−	15.2729i	0.319646	−	0.553642i	−0.660768	−	0.750590i	$-0.729769\pi$
$761$	8.81782	−	15.2729i	0.319646	−	0.553642i	0.980414	+	0.196947i	$0.0631028\pi$
$762$	−35.9097	+	41.7801i	−1.30087	+	1.51353i
$763$	5.35525	+	3.09186i	0.193873	+	0.111933i
$764$	12.8822	−	10.2993i	0.466061	−	0.372617i
$765$	9.24886	−	5.33983i	0.334393	−	0.193062i
$766$	−3.48996	−	2.99959i	−0.126097	−	0.108380i
$767$	−16.7782	+	14.7170i	−0.605826	+	0.531399i
$768$	27.7151	+	40.2209i	1.00008	+	1.45135i
$769$	25.0216	+	43.3387i	0.902302	+	1.56283i	0.824499	+	0.565864i	$0.191457\pi$
$769$	25.0216	+	43.3387i	0.902302	+	1.56283i	0.0778027	+	0.996969i	$0.475210\pi$
$770$	0.837935	−	4.44366i	0.0301971	−	0.160138i
$771$	−18.0529	−	10.4229i	−0.650160	−	0.375370i
$772$	3.79357	+	24.9588i	0.136533	+	0.898288i
$773$	−13.1919	−	7.61633i	−0.474479	−	0.273940i	0.243634	−	0.969867i	$-0.421660\pi$
$773$	−13.1919	−	7.61633i	−0.474479	−	0.273940i	−0.718113	+	0.695927i	$0.754994\pi$
$774$	−9.15132	−	26.1011i	−0.328937	−	0.938185i
$775$	9.90649			0.355852
$776$	−2.20830	−	4.15957i	−0.0792732	−	0.149320i
$777$	25.4425	+	44.0677i	0.912745	+	1.58092i
$778$	24.9912	+	4.71256i	0.895978	+	0.168953i
$779$			5.60437i			0.200797i
$780$	−10.7731	−	1.91938i	−0.385740	−	0.0687249i
$781$			29.1540i			1.04321i
$782$	−7.89669	+	41.8770i	−0.282385	+	1.49752i
$783$	−2.00672	−	3.47575i	−0.0717144	−	0.124213i
$784$	−3.64396	+	16.1496i	−0.130142	+	0.576771i
$785$	1.34280			0.0479265
$786$	45.9561	−	16.1127i	1.63920	−	0.574720i
$787$	47.6148	+	27.4904i	1.69728	+	0.979927i	0.948320	+	0.317316i	$0.102781\pi$
$787$	47.6148	+	27.4904i	1.69728	+	0.979927i	0.748963	+	0.662611i	$0.230552\pi$
$788$	34.9209	−	5.30774i	1.24401	−	0.189080i
$789$	31.5237	+	18.2002i	1.12227	+	0.647945i
$790$	−6.47012	−	1.22006i	−0.230196	−	0.0434078i
$791$	−9.65886	−	16.7296i	−0.343429	−	0.594837i
$792$	57.6251	+	36.0591i	2.04762	+	1.28130i
$793$	−11.0679	+	9.70822i	−0.393034	+	0.344749i
$794$	19.1412	−	22.2703i	0.679295	−	0.790345i
$795$	7.47060	−	4.31315i	0.264955	−	0.152972i
$796$	30.9954	−	24.7809i	1.09860	−	0.878335i
$797$	43.7170	+	25.2400i	1.54853	+	0.894047i	0.998254	+	0.0590673i	$0.0188126\pi$
$797$	43.7170	+	25.2400i	1.54853	+	0.894047i	0.550281	+	0.834980i	$0.314521\pi$
$798$	6.74477	+	5.79707i	0.238762	+	0.205214i
$799$	6.75624	−	11.7022i	0.239019	−	0.413992i
$800$	−21.5833	+	16.0327i	−0.763085	+	0.566841i
$801$	−79.7955			−2.81944
$802$	−3.13949	+	1.10074i	−0.110859	+	0.0388684i
$803$	−19.8419	+	11.4557i	−0.700205	+	0.404264i
$804$	36.7335	−	29.3685i	1.29549	−	1.03575i
$805$		−	7.45255i		−	0.262668i
$806$	−9.25704	−	5.22102i	−0.326065	−	0.183903i
$807$	−64.6042			−2.27417
$808$	0.788753	−	22.1830i	0.0277482	−	0.780396i
$809$	2.20857	+	3.82536i	0.0776493	+	0.134493i	0.902235	−	0.431244i	$-0.141925\pi$
$809$	2.20857	+	3.82536i	0.0776493	+	0.134493i	−0.824586	+	0.565737i	$0.808592\pi$
$810$	−2.78634	−	7.94712i	−0.0979022	−	0.279233i
$811$		−	2.09970i		−	0.0737305i	−0.999320	−	0.0368652i	$-0.988263\pi$
$811$		−	2.09970i		−	0.0737305i	0.999320	−	0.0368652i	$-0.0117372\pi$
$812$	0.487906	−	1.24771i	0.0171222	−	0.0437860i
$813$	−57.3981	−	33.1388i	−2.01304	−	1.16223i
$814$	−40.1922	−	34.5449i	−1.40874	−	1.21080i
$815$	0.536660	−	0.929523i	0.0187984	−	0.0325598i
$816$	−28.1613	+	30.5019i	−0.985843	+	1.06778i
$817$	1.88448	+	3.26402i	0.0659296	+	0.114193i
$818$	38.8437	+	33.3859i	1.35814	+	1.16731i
$819$	−37.8009	+	7.52287i	−1.32087	+	0.262870i
$820$	4.52296	−	0.687458i	0.157949	−	0.0240071i
$821$	−18.0251	+	10.4068i	−0.629079	+	0.363199i	−0.780395	−	0.625286i	$-0.784982\pi$
$821$	−18.0251	+	10.4068i	−0.629079	+	0.363199i	0.151316	+	0.988485i	$0.451649\pi$
$822$	−31.3917	−	5.91950i	−1.09491	−	0.206466i
$823$	3.91287	−	6.77729i	0.136394	−	0.236241i	−0.789735	−	0.613448i	$-0.789782\pi$
$823$	3.91287	−	6.77729i	0.136394	−	0.236241i	0.926129	+	0.377207i	$0.123115\pi$
$824$	19.8521	−	31.7252i	0.691582	−	1.10520i
$825$	−27.5900	+	47.7874i	−0.960562	+	1.66374i
$826$	−4.89910	−	13.9730i	−0.170461	−	0.486184i
$827$		−	25.1308i		−	0.873884i	−0.899490	−	0.436942i	$-0.856062\pi$
$827$		−	25.1308i		−	0.873884i	0.899490	−	0.436942i	$-0.143938\pi$
$828$	104.338	+	40.8005i	3.62600	+	1.41792i
$829$	−43.4669	+	25.0957i	−1.50967	+	0.871608i	−0.509733	+	0.860333i	$0.670256\pi$
$829$	−43.4669	+	25.0957i	−1.50967	+	0.871608i	−0.999936	+	0.0112755i	$0.996411\pi$
$830$	−0.934295	+	4.95467i	−0.0324299	+	0.171979i
$831$	−5.34194			−0.185310
$832$	28.6180	−	3.60657i	0.992152	−	0.125035i
$833$	−14.0708			−0.487525
$834$	9.45308	−	50.1307i	0.327333	−	1.73588i
$835$	3.18778	−	1.84047i	0.110318	−	0.0636920i
$836$	−8.62685	−	3.37346i	−0.298366	−	0.116674i
$837$		−	21.1233i		−	0.730130i
$838$	−11.1338	−	31.7554i	−0.384610	−	1.09697i
$839$	24.4177	−	42.2926i	0.842991	−	1.46010i	−0.0443634	−	0.999015i	$-0.514126\pi$
$839$	24.4177	−	42.2926i	0.842991	−	1.46010i	0.887354	−	0.461088i	$-0.152541\pi$
$840$	3.85114	−	6.15441i	0.132877	−	0.212347i
$841$	−14.4216	+	24.9789i	−0.497296	+	0.861342i
$842$	27.5471	+	5.19452i	0.949336	+	0.179015i
$843$	−44.8865	+	25.9152i	−1.54597	+	0.892568i
$844$	−29.8400	+	4.53547i	−1.02714	+	0.156117i
$845$	−3.93283	+	5.12743i	−0.135294	+	0.176389i
$846$	−26.9400	−	23.1547i	−0.926217	−	0.796076i
$847$	2.92834	+	5.07203i	0.100619	+	0.174277i
$848$	−15.4246	+	16.7066i	−0.529684	+	0.573708i
$849$	−25.3276	+	43.8687i	−0.869240	+	1.50557i
$850$	−17.3298	−	14.8948i	−0.594408	−	0.510889i
$851$	−75.6424	−	43.6722i	−2.59299	−	1.49706i
$852$	−17.0464	+	43.5923i	−0.584001	+	1.49345i
$853$			47.8014i			1.63669i	0.574728	+	0.818345i	$0.305108\pi$
$853$			47.8014i			1.63669i	−0.574728	+	0.818345i	$0.694892\pi$
$854$	−3.23175	−	9.21748i	−0.110588	−	0.315416i
$855$	1.91290	+	3.31324i	0.0654198	+	0.113310i
$856$	0.886286	−	24.9260i	0.0302926	−	0.851955i
$857$	−34.4402			−1.17646			−0.588228	−	0.808695i	$-0.700174\pi$
$857$	−34.4402			−1.17646			−0.588228	+	0.808695i	$0.700174\pi$
$858$	50.9667	−	30.1137i	1.73997	−	1.02807i
$859$		−	18.3183i		−	0.625012i	−0.949916	−	0.312506i	$-0.898832\pi$
$859$		−	18.3183i		−	0.625012i	0.949916	−	0.312506i	$-0.101168\pi$
$860$	2.40304	−	1.92123i	0.0819429	−	0.0655135i
$861$	20.5791	−	11.8813i	0.701333	−	0.404915i
$862$	−0.508673	+	0.178346i	−0.0173255	+	0.00607449i
$863$	−24.5989			−0.837356			−0.418678	−	0.908135i	$-0.637506\pi$
$863$	−24.5989			−0.837356			−0.418678	+	0.908135i	$0.637506\pi$
$864$	34.1861	+	46.0215i	1.16303	+	1.56568i
$865$	1.04981	−	1.81832i	0.0356945	−	0.0618247i
$866$	−3.78334	−	3.25175i	−0.128563	−	0.110499i
$867$	14.3886	+	8.30727i	0.488663	+	0.282130i
$868$	5.50732	−	4.40311i	0.186931	−	0.149451i
$869$	30.8469	−	17.8094i	1.04641	−	0.604144i
$870$	0.553965	−	0.644526i	0.0187812	−	0.0218515i
$871$	−5.42084	−	27.2386i	−0.183678	−	0.922945i
$872$	−8.76548	−	5.48502i	−0.296837	−	0.185746i
$873$	−5.26126	−	9.11277i	−0.178067	−	0.308421i
$874$	−15.0017	−	2.82885i	−0.507440	−	0.0956873i
$875$	7.10161	+	4.10012i	0.240078	+	0.138609i
$876$	−36.3667	+	5.52748i	−1.22872	+	0.186756i
$877$	−28.4988	−	16.4538i	−0.962337	−	0.555605i	−0.0654453	−	0.997856i	$-0.520847\pi$
$877$	−28.4988	−	16.4538i	−0.962337	−	0.555605i	−0.896891	+	0.442251i	$0.854180\pi$
$878$	−8.56061	+	3.00144i	−0.288907	+	0.101294i
$879$	70.1587			2.36639
$880$	−1.66431	+	7.37603i	−0.0561040	+	0.248646i
$881$	18.9830	+	32.8795i	0.639553	+	1.10774i	0.985531	+	0.169495i	$0.0542138\pi$
$881$	18.9830	+	32.8795i	0.639553	+	1.10774i	−0.345978	+	0.938243i	$0.612453\pi$
$882$	−6.85456	+	36.3505i	−0.230805	+	1.22398i
$883$			57.4770i			1.93425i	0.254295	+	0.967127i	$0.418157\pi$
$883$			57.4770i			1.93425i	−0.254295	+	0.967127i	$0.581843\pi$
$884$	8.34367	+	23.0517i	0.280628	+	0.775312i
$885$		−	9.39316i		−	0.315748i
$886$	−24.4246	−	4.60572i	−0.820562	−	0.154732i
$887$	8.29035	+	14.3593i	0.278363	+	0.482138i	0.970978	−	0.239169i	$-0.0768750\pi$
$887$	8.29035	+	14.3593i	0.278363	+	0.482138i	−0.692615	+	0.721307i	$0.743542\pi$
$888$	−39.8987	−	75.1536i	−1.33891	−	2.52199i
$889$	−21.5842			−0.723910
$890$	−2.93677	−	8.37616i	−0.0984407	−	0.280769i
$891$	39.4546	+	22.7791i	1.32178	+	0.763129i
$892$	−2.99273	−	19.6899i	−0.100204	−	0.659268i
$893$	4.19209	+	2.42031i	0.140283	+	0.0809924i
$894$	9.88016	−	52.3956i	0.330442	−	1.75237i
$895$	0.111433	+	0.193007i	0.00372479	+	0.00645152i
$896$	−4.87280	+	18.5061i	−0.162789	+	0.618246i
$897$	73.3457	−	64.3350i	2.44894	−	2.14808i
$898$	−38.9749	−	33.4987i	−1.30061	−	1.11786i
$899$	0.714834	−	0.412710i	0.0238410	−	0.0137646i
$900$	−46.9214	+	37.5138i	−1.56405	+	1.25046i
$901$	−16.7365	−	9.66280i	−0.557573	−	0.321915i
$902$	−16.1320	+	18.7693i	−0.537138	+	0.624948i
$903$	7.99024	−	13.8395i	0.265899	−	0.460550i
$904$	15.1469	+	28.5309i	0.503779	+	0.948924i
$905$	−0.727055			−0.0241681
$906$	−25.2826	−	72.1103i	−0.839959	−	2.39570i
$907$	13.4171	−	7.74635i	0.445507	−	0.257213i	−0.260424	−	0.965494i	$-0.583862\pi$
$907$	13.4171	−	7.74635i	0.445507	−	0.257213i	0.705931	+	0.708281i	$0.250529\pi$
$908$	−1.73016	−	2.16405i	−0.0574175	−	0.0718166i
$909$		−	49.5961i		−	1.64500i
$910$	−2.18089	−	3.69110i	−0.0722958	−	0.122359i
$911$	−3.26320			−0.108115			−0.0540574	−	0.998538i	$-0.517215\pi$
$911$	−3.26320			−0.108115			−0.0540574	+	0.998538i	$0.517215\pi$
$912$	−10.9268	−	10.0883i	−0.361821	−	0.334057i
$913$	−13.6381	−	23.6218i	−0.451354	−	0.781768i
$914$	17.5717	−	6.16083i	0.581221	−	0.203782i
$915$		−	6.19631i		−	0.204844i
$916$	16.6208	−	42.5039i	0.549168	−	1.40437i
$917$	16.5234	+	9.53979i	0.545651	+	0.315032i
$918$	−31.7599	+	36.9519i	−1.04823	+	1.21959i
$919$	−12.7268	+	22.0434i	−0.419817	+	0.727144i	−0.995921	−	0.0902323i	$-0.971239\pi$
$919$	−12.7268	+	22.0434i	−0.419817	+	0.727144i	0.576104	+	0.817377i	$0.304572\pi$
$920$	−0.442822	+	12.4540i	−0.0145994	+	0.410596i
$921$	−21.5656	−	37.3527i	−0.710611	−	1.23081i
$922$	−13.5813	+	15.8016i	−0.447277	+	0.520397i
$923$	18.2268	+	20.7796i	0.599942	+	0.683969i
$924$	5.90178	+	38.8293i	0.194154	+	1.27739i
$925$	40.5613	−	23.4181i	1.33365	−	0.769982i
$926$	1.48102	−	7.85403i	0.0486695	−	0.258099i
$927$	41.8099	−	72.4169i	1.37322	−	2.37848i
$928$	−0.889480	+	2.05606i	−0.0291986	+	0.0674935i
$929$	19.1596	−	33.1853i	0.628605	−	1.08878i	−0.359227	−	0.933250i	$-0.616960\pi$
$929$	19.1596	−	33.1853i	0.628605	−	1.08878i	0.987832	−	0.155525i	$-0.0497070\pi$
$930$	4.22110	−	1.47996i	0.138415	−	0.0485299i
$931$		−	5.04062i		−	0.165200i
$932$	−8.33623	−	3.25982i	−0.273062	−	0.106779i
$933$	48.9166	−	28.2420i	1.60146	−	0.924602i
$934$	41.1195	+	7.75386i	1.34547	+	0.253714i
$935$	−6.42659			−0.210172
$936$	63.6162	−	10.3254i	2.07936	−	0.337497i
$937$	−33.4565			−1.09298			−0.546488	−	0.837467i	$-0.684035\pi$
$937$	−33.4565			−1.09298			−0.546488	+	0.837467i	$0.684035\pi$
$938$	18.1068	+	3.41438i	0.591208	+	0.111483i
$939$	−79.5164	+	45.9088i	−2.59492	+	1.49818i
$940$	1.43907	−	3.68008i	0.0469372	−	0.120031i
$941$		−	3.09842i		−	0.101006i	−0.998724	−	0.0505028i	$-0.983918\pi$
$941$		−	3.09842i		−	0.101006i	0.998724	−	0.0505028i	$-0.0160824\pi$
$942$	−11.0059	+	3.85879i	−0.358592	+	0.125726i
$943$	−20.3944	+	35.3241i	−0.664132	+	1.15031i
$944$	7.35665	+	23.6415i	0.239438	+	0.769466i
$945$	4.26054	−	7.37947i	0.138595	−	0.240054i
$946$	−3.08418	+	16.3558i	−0.100275	+	0.531772i
$947$	−1.23979	+	0.715796i	−0.0402879	+	0.0232602i	−0.520009	−	0.854161i	$-0.674071\pi$
$947$	−1.23979	+	0.715796i	−0.0402879	+	0.0232602i	0.479721	+	0.877421i	$0.340738\pi$
$948$	56.5368	−	8.59320i	1.83623	−	0.279094i
$949$	−6.98036	+	20.5700i	−0.226592	+	0.667732i
$950$	5.33581	−	6.20810i	0.173117	−	0.201417i
$951$	44.9693	+	77.8892i	1.45823	+	2.52573i
$952$	−16.2544	−	0.577953i	−0.526809	−	0.0187316i
$953$	−14.0065	+	24.2600i	−0.453716	+	0.785859i	−0.998613	−	0.0526434i	$-0.983235\pi$
$953$	−14.0065	+	24.2600i	−0.453716	+	0.785859i	0.544897	+	0.838503i	$0.316569\pi$
$954$	−33.1160	+	38.5297i	−1.07217	+	1.24745i
$955$	3.55003	+	2.04961i	0.114876	+	0.0663238i
$956$	−34.4465	−	13.4700i	−1.11408	−	0.435651i
$957$			4.59766i			0.148621i
$958$	−20.2181	+	7.08867i	−0.653216	+	0.229024i
$959$	−6.25781	−	10.8388i	−0.202075	−	0.350005i
$960$	−6.80134	+	10.0558i	−0.219512	+	0.324551i
$961$	−26.6557			−0.859861
$962$	−50.2443	+	0.505798i	−1.61994	+	0.0163076i
$963$		−	55.7289i		−	1.79584i
$964$	−21.4777	+	17.1714i	−0.691749	+	0.553055i
$965$	−5.43387	+	3.13725i	−0.174923	+	0.100992i
$966$	21.4163	+	61.0830i	0.689059	+	1.96531i
$967$	36.4058			1.17073			0.585366	−	0.810769i	$-0.300951\pi$
$967$	36.4058			1.17073			0.585366	+	0.810769i	$0.300951\pi$
$968$	−4.59219	−	8.64990i	−0.147599	−	0.278018i
$969$	6.31983	−	10.9463i	0.203022	−	0.351645i
$970$	0.762936	−	0.887659i	0.0244964	−	0.0285010i
$971$	40.8856	+	23.6053i	1.31208	+	0.757531i	0.982441	−	0.186575i	$-0.0597386\pi$
$971$	40.8856	+	23.6053i	1.31208	+	0.757531i	0.329642	+	0.944106i	$0.393072\pi$
$972$	7.70373	+	9.63566i	0.247097	+	0.309064i
$973$	17.3090	−	9.99335i	0.554901	−	0.320372i
$974$	32.2891	+	27.7522i	1.03461	+	0.889239i
$975$	10.2113	+	51.3096i	0.327023	+	1.64322i
$976$	4.85290	+	15.5954i	0.155337	+	0.499197i
$977$	−29.7141	−	51.4663i	−0.950638	−	1.64655i	−0.744049	−	0.668125i	$-0.767097\pi$
$977$	−29.7141	−	51.4663i	−0.950638	−	1.64655i	−0.206589	−	0.978428i	$-0.566236\pi$
$978$	−1.72744	+	9.16080i	−0.0552374	+	0.292930i
$979$	41.5846	+	24.0089i	1.32905	+	0.767327i
$980$	−4.06799	+	0.618307i	−0.129947	+	0.0197511i
$981$	−20.0083	−	11.5518i	−0.638817	−	0.368821i
$982$	−12.5519	−	35.8002i	−0.400548	−	1.14243i
$983$	−30.8865			−0.985126			−0.492563	−	0.870277i	$-0.663940\pi$
$983$	−30.8865			−0.985126			−0.492563	+	0.870277i	$0.663940\pi$
$984$	−35.0958	+	18.6322i	−1.11881	+	0.593972i
$985$	4.38945	+	7.60275i	0.139860	+	0.242244i
$986$	−1.87101	−	0.352815i	−0.0595852	−	0.0112359i
$987$		−	20.5243i		−	0.653296i
$988$	−8.25787	+	2.98897i	−0.262718	+	0.0950920i
$989$			27.4306i			0.872242i
$990$	−3.13070	+	16.6024i	−0.0995001	+	0.527660i
$991$	−22.5422	−	39.0441i	−0.716075	−	1.24028i	−0.962543	−	0.271127i	$-0.912604\pi$
$991$	−22.5422	−	39.0441i	−0.716075	−	1.24028i	0.246468	−	0.969151i	$-0.420730\pi$
$992$	−9.46494	+	7.03083i	−0.300512	+	0.223229i
$993$	20.5272			0.651410
$994$	−17.3054	+	6.06747i	−0.548895	+	0.192449i
$995$	8.54160	+	4.93149i	0.270787	+	0.156339i
$996$	−6.58047	−	43.2946i	−0.208510	−	1.37184i
$997$	−45.6473	−	26.3545i	−1.44566	−	0.834655i	−0.447446	−	0.894311i	$-0.647666\pi$
$997$	−45.6473	−	26.3545i	−1.44566	−	0.834655i	−0.998219	+	0.0596564i	$0.981000\pi$
$998$	25.7249	+	4.85092i	0.814309	+	0.153553i
$999$	−49.9338	−	86.4879i	−1.57984	−	2.73635i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	104.2.r.a.29.6	✓	24
3.2	odd	2		936.2.be.a.757.7		24
4.3	odd	2		416.2.z.a.81.1		24
8.3	odd	2		416.2.z.a.81.12		24
8.5	even	2	inner	104.2.r.a.29.12	yes	24
13.9	even	3	inner	104.2.r.a.61.12	yes	24
24.5	odd	2		936.2.be.a.757.1		24
39.35	odd	6		936.2.be.a.685.1		24
52.35	odd	6		416.2.z.a.113.12		24
104.35	odd	6		416.2.z.a.113.1		24
104.61	even	6	inner	104.2.r.a.61.6	yes	24
312.269	odd	6		936.2.be.a.685.7		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
104.2.r.a.29.6	✓	24	1.1	even	1	trivial
104.2.r.a.29.12	yes	24	8.5	even	2	inner
104.2.r.a.61.6	yes	24	104.61	even	6	inner
104.2.r.a.61.12	yes	24	13.9	even	3	inner
416.2.z.a.81.1		24	4.3	odd	2
416.2.z.a.81.12		24	8.3	odd	2
416.2.z.a.113.1		24	104.35	odd	6
416.2.z.a.113.12		24	52.35	odd	6
936.2.be.a.685.1		24	39.35	odd	6
936.2.be.a.685.7		24	312.269	odd	6
936.2.be.a.757.1		24	24.5	odd	2
936.2.be.a.757.7		24	3.2	odd	2

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:	\( N \)	\(=\)	\( 104 = 2^{3} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	104.r (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.262058 + 1.38972i) q^{2} +(2.64382 - 1.52641i) q^{3} +(-1.86265 - 0.728375i) q^{4} -0.497079i q^{5} +(1.42845 + 4.07418i) q^{6} +(-0.845740 + 1.46486i) q^{7} +(1.50036 - 2.39769i) q^{8} +(3.15986 - 5.47304i) q^{9} +(0.690801 + 0.130263i) q^{10} +(-3.29345 + 1.90148i) q^{11} +(-6.03632 + 0.917478i) q^{12} +(-1.15864 + 3.41432i) q^{13} +(-1.81412 - 1.55922i) q^{14} +(-0.758746 - 1.31419i) q^{15} +(2.93894 + 2.71342i) q^{16} +(-1.69983 + 2.94419i) q^{17} +(6.77793 + 5.82558i) q^{18} +(-1.05470 - 0.608933i) q^{19} +(-0.362060 + 0.925884i) q^{20} +5.16378i q^{21} +(-1.77945 - 5.07528i) q^{22} +(-4.43183 - 7.67616i) q^{23} +(0.306826 - 8.62923i) q^{24} +4.75291 q^{25} +(-4.44132 - 2.50493i) q^{26} -10.1345i q^{27} +(2.64229 - 2.11252i) q^{28} +(0.342961 - 0.198009i) q^{29} +(2.02519 - 0.710053i) q^{30} +2.08430 q^{31} +(-4.54107 + 3.37323i) q^{32} +(-5.80487 + 10.0543i) q^{33} +(-3.64615 - 3.13383i) q^{34} +(0.728152 + 0.420399i) q^{35} +(-9.87214 + 7.89280i) q^{36} +(8.53399 - 4.92710i) q^{37} +(1.12264 - 1.30617i) q^{38} +(2.14843 + 10.7954i) q^{39} +(-1.19184 - 0.745797i) q^{40} +(-2.30090 - 3.98527i) q^{41} +(-7.17622 - 1.35321i) q^{42} +(-2.68011 - 1.54736i) q^{43} +(7.51955 - 1.14292i) q^{44} +(-2.72053 - 1.57070i) q^{45} +(11.8291 - 4.14741i) q^{46} -3.97467 q^{47} +(11.9118 + 2.68776i) q^{48} +(2.06945 + 3.58439i) q^{49} +(-1.24554 + 6.60522i) q^{50} +10.3785i q^{51} +(4.64504 - 5.51576i) q^{52} +5.68458i q^{53} +(14.0841 + 2.65583i) q^{54} +(0.945183 + 1.63711i) q^{55} +(2.24337 + 4.22565i) q^{56} -3.71793 q^{57} +(0.185301 + 0.528511i) q^{58} +(5.36063 + 3.09496i) q^{59} +(0.456058 + 3.00052i) q^{60} +(3.53620 + 2.04163i) q^{61} +(-0.546207 + 2.89659i) q^{62} +(5.34484 + 9.25753i) q^{63} +(-3.49783 - 7.19480i) q^{64} +(1.69718 + 0.575933i) q^{65} +(-12.4515 - 10.7020i) q^{66} +(-6.67080 + 3.85139i) q^{67} +(5.31066 - 4.24588i) q^{68} +(-23.4339 - 13.5296i) q^{69} +(-0.775056 + 0.901760i) q^{70} +(3.83307 - 6.63908i) q^{71} +(-8.38172 - 15.7879i) q^{72} +6.02464 q^{73} +(4.61090 + 13.1511i) q^{74} +(12.5659 - 7.25490i) q^{75} +(1.52101 + 1.90245i) q^{76} -6.43262i q^{77} +(-15.5656 + 0.156696i) q^{78} -9.36611 q^{79} +(1.34878 - 1.46088i) q^{80} +(-5.98985 - 10.3747i) q^{81} +(6.14138 - 2.15323i) q^{82} +7.17235i q^{83} +(3.76117 - 9.61833i) q^{84} +(1.46349 + 0.844947i) q^{85} +(2.85275 - 3.31911i) q^{86} +(0.604486 - 1.04700i) q^{87} +(-0.382219 + 10.7496i) q^{88} +(-6.31322 - 10.9348i) q^{89} +(2.89577 - 3.36916i) q^{90} +(-4.02161 - 4.58487i) q^{91} +(2.66383 + 17.5260i) q^{92} +(5.51051 - 3.18150i) q^{93} +(1.04159 - 5.52368i) q^{94} +(-0.302688 + 0.524270i) q^{95} +(-6.85683 + 15.8498i) q^{96} +(0.832515 - 1.44196i) q^{97} +(-5.52362 + 1.93664i) q^{98} +24.0336i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - q^{2} - q^{4} - 8 q^{6} - 2 q^{7} - 10 q^{8} + 6 q^{9} - 3 q^{10} - 12 q^{12} + 8 q^{14} + 4 q^{15} - q^{16} + 6 q^{18} - 11 q^{20} - 2 q^{22} - 14 q^{23} - 18 q^{24} - 12 q^{25} - 3 q^{26} - 4 q^{28}+ \cdots - 17 q^{98}+O(q^{100}) \) 24 * q - q^2 - q^4 - 8 * q^6 - 2 * q^7 - 10 * q^8 + 6 * q^9 - 3 * q^10 - 12 * q^12 + 8 * q^14 + 4 * q^15 - q^16 + 6 * q^18 - 11 * q^20 - 2 * q^22 - 14 * q^23 - 18 * q^24 - 12 * q^25 - 3 * q^26 - 4 * q^28 + 14 * q^30 - 8 * q^31 - 21 * q^32 - 14 * q^33 + 14 * q^34 + 5 * q^36 + 12 * q^38 - 34 * q^39 + 54 * q^40 - 4 * q^41 + 22 * q^42 + 24 * q^46 - 8 * q^47 - 8 * q^48 + 6 * q^49 + 32 * q^50 - 4 * q^52 + 22 * q^54 + 8 * q^55 + 8 * q^56 - 52 * q^57 + 33 * q^58 + 56 * q^60 - 14 * q^62 + 32 * q^63 + 26 * q^64 + 30 * q^65 - 104 * q^66 + 23 * q^68 - 16 * q^70 + 30 * q^71 + 17 * q^72 - 12 * q^73 - 7 * q^74 + 14 * q^76 - 8 * q^78 - 48 * q^79 + 29 * q^80 + 8 * q^81 - q^82 + 60 * q^84 - 96 * q^86 - 26 * q^87 + 4 * q^88 - 22 * q^89 - 50 * q^90 - 80 * q^92 - 42 * q^94 + 60 * q^95 - 40 * q^96 + 2 * q^97 - 17 * q^98

Introduction

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