LMFDB - Embedded newform 847.2.n.f.81.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [847,2,Mod(9,847)] 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("847.9"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(847, base_ring=CyclotomicField(30)) chi = DirichletCharacter(H, H._module([10, 18])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 847 = 7 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	847.n (of order $15$, degree $8$, not minimal)

Newform invariants

comment:select newform

sage:traces = [24,0,3,0,6,-6] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(6)] == traces)

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

Self dual:	no
Analytic conductor:	$6.76332905120$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$3$ over $\Q(\zeta_{15})$
Twist minimal:	no (minimal twist has level 77)
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			81.3
Character	$\chi$	$=$	847.81
Dual form			847.2.n.f.366.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.196449 - 1.86909i) q^{2} +(0.436744 + 0.485053i) q^{3} +(-1.49861 - 0.318539i) q^{4} +(3.22672 + 1.43663i) q^{5} +(0.992406 - 0.721025i) q^{6} +(-2.61394 + 0.409024i) q^{7} +(0.271745 - 0.836345i) q^{8} +(0.269054 - 2.55988i) q^{9} +(3.31908 - 5.74881i) q^{10} +(-0.500000 - 0.866025i) q^{12} +(3.56896 + 2.59300i) q^{13} +(0.250995 + 4.96605i) q^{14} +(0.712410 + 2.19257i) q^{15} +(-4.30909 - 1.91853i) q^{16} +(-0.548667 - 5.22022i) q^{17} +(-4.73179 - 1.00577i) q^{18} +(1.77554 - 0.377403i) q^{19} +(-4.37797 - 3.18078i) q^{20} +(-1.34002 - 1.08926i) q^{21} +(3.16637 + 5.48432i) q^{23} +(0.524355 - 0.233458i) q^{24} +(5.00219 + 5.55549i) q^{25} +(5.54767 - 6.16131i) q^{26} +(2.94333 - 2.13845i) q^{27} +(4.04757 + 0.219677i) q^{28} +(-0.593706 - 1.82724i) q^{29} +(4.23807 - 0.900829i) q^{30} +(1.34100 - 0.597053i) q^{31} +(-3.55303 + 6.15403i) q^{32} -9.86484 q^{34} +(-9.02209 - 2.43546i) q^{35} +(-1.21863 + 3.75055i) q^{36} +(2.97988 - 3.30949i) q^{37} +(-0.356596 - 3.39279i) q^{38} +(0.300978 + 2.86361i) q^{39} +(2.07836 - 2.30826i) q^{40} +(-0.0874885 + 0.269262i) q^{41} +(-2.29918 + 2.29064i) q^{42} +3.41147 q^{43} +(4.54576 - 7.87349i) q^{45} +(10.8727 - 4.84085i) q^{46} +(4.45485 - 0.946908i) q^{47} +(-0.951379 - 2.92804i) q^{48} +(6.66540 - 2.13833i) q^{49} +(11.3664 - 8.25817i) q^{50} +(2.29246 - 2.54603i) q^{51} +(-4.52250 - 5.02275i) q^{52} +(-6.60897 + 2.94250i) q^{53} +(-3.41875 - 5.92145i) q^{54} +(-0.368241 + 2.29731i) q^{56} +(0.958517 + 0.696404i) q^{57} +(-3.53191 + 0.750731i) q^{58} +(-9.33136 - 1.98344i) q^{59} +(-0.369204 - 3.51274i) q^{60} +(1.04871 + 0.466916i) q^{61} +(-0.852507 - 2.62375i) q^{62} +(0.343759 + 6.80142i) q^{63} +(3.17238 + 2.30487i) q^{64} +(7.79086 + 13.4942i) q^{65} +(0.347296 - 0.601535i) q^{67} +(-0.840606 + 7.99783i) q^{68} +(-1.27729 + 3.93110i) q^{69} +(-6.32448 + 16.3846i) q^{70} +(-7.65419 + 5.56110i) q^{71} +(-2.06783 - 0.920656i) q^{72} +(2.29600 + 0.488030i) q^{73} +(-5.60035 - 6.21981i) q^{74} +(-0.510035 + 4.85266i) q^{75} -2.78106 q^{76} +5.41147 q^{78} +(-1.29816 + 12.3512i) q^{79} +(-11.1480 - 12.3811i) q^{80} +(-5.23045 - 1.11177i) q^{81} +(0.486087 + 0.216420i) q^{82} +(-9.16839 + 6.66122i) q^{83} +(1.66120 + 2.05923i) q^{84} +(5.72912 - 17.6324i) q^{85} +(0.670182 - 6.37635i) q^{86} +(0.627011 - 1.08602i) q^{87} +(1.73396 + 3.00330i) q^{89} +(-13.8232 - 10.0432i) q^{90} +(-10.3897 - 5.31816i) q^{91} +(-2.99819 - 9.22747i) q^{92} +(0.875278 + 0.389699i) q^{93} +(-0.894704 - 8.51254i) q^{94} +(6.27137 + 1.33302i) q^{95} +(-4.53680 + 0.964327i) q^{96} +(-12.4162 - 9.02091i) q^{97} +(-2.68732 - 12.8783i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 3 q^{3} + 6 q^{5} - 6 q^{6} + 6 q^{8} + 12 q^{10} - 12 q^{12} + 6 q^{13} + 12 q^{14} - 18 q^{15} - 6 q^{16} + 3 q^{17} + 12 q^{18} - 9 q^{19} - 12 q^{20} + 48 q^{21} - 6 q^{24} + 3 q^{25} + 9 q^{26}+ \cdots + 24 q^{98}+O(q^{100}) $ 24 * q + 3 * q^3 + 6 * q^5 - 6 * q^6 + 6 * q^8 + 12 * q^10 - 12 * q^12 + 6 * q^13 + 12 * q^14 - 18 * q^15 - 6 * q^16 + 3 * q^17 + 12 * q^18 - 9 * q^19 - 12 * q^20 + 48 * q^21 - 6 * q^24 + 3 * q^25 + 9 * q^26 - 12 * q^27 + 3 * q^28 - 6 * q^29 + 6 * q^30 + 9 * q^31 - 36 * q^32 - 48 * q^34 - 15 * q^35 - 6 * q^36 - 3 * q^39 - 3 * q^40 + 18 * q^41 + 18 * q^42 - 12 * q^45 + 24 * q^46 - 3 * q^47 + 36 * q^48 + 30 * q^50 + 18 * q^51 - 9 * q^52 + 9 * q^53 - 72 * q^54 + 12 * q^56 + 15 * q^58 + 6 * q^60 - 12 * q^61 - 6 * q^62 + 6 * q^63 + 6 * q^64 + 60 * q^65 + 21 * q^68 - 42 * q^69 - 45 * q^70 + 18 * q^71 - 12 * q^72 - 6 * q^73 - 18 * q^74 + 9 * q^75 + 72 * q^76 + 48 * q^78 + 3 * q^79 - 27 * q^80 + 15 * q^81 - 3 * q^82 - 30 * q^83 - 54 * q^85 - 9 * q^86 - 96 * q^87 + 60 * q^89 - 72 * q^90 - 9 * q^91 + 6 * q^92 + 6 * q^93 - 9 * q^95 - 3 * q^96 - 90 * q^97 + 24 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/847\mathbb{Z}\right)^\times$.

$n$	$122$	$365$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{5}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

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

$2$	0.196449	−	1.86909i	0.138911	−	1.32165i	−0.673772	−	0.738939i	$-0.735327\pi$
$2$	0.196449	−	1.86909i	0.138911	−	1.32165i	0.812683	−	0.582707i	$-0.198006\pi$
$3$	0.436744	+	0.485053i	0.252154	+	0.280046i	0.855911	−	0.517123i	$-0.172997\pi$
$3$	0.436744	+	0.485053i	0.252154	+	0.280046i	−0.603757	+	0.797168i	$0.706330\pi$
$4$	−1.49861	−	0.318539i	−0.749305	−	0.159270i
$5$	3.22672	+	1.43663i	1.44303	+	0.642480i	0.970996	−	0.239097i	$-0.0768514\pi$
$5$	3.22672	+	1.43663i	1.44303	+	0.642480i	0.472039	+	0.881578i	$0.343518\pi$
$6$	0.992406	−	0.721025i	0.405148	−	0.294357i
$7$	−2.61394	+	0.409024i	−0.987978	+	0.154596i
$7$	−2.61394	+	0.409024i	−0.987978	+	0.154596i
$8$	0.271745	−	0.836345i	0.0960764	−	0.295693i
$9$	0.269054	−	2.55988i	0.0896847	−	0.853292i
$10$	3.31908	−	5.74881i	1.04958	−	1.81793i
$11$		0			0
$11$		0			0
$12$	−0.500000	−	0.866025i	−0.144338	−	0.250000i
$13$	3.56896	+	2.59300i	0.989851	+	0.719169i	0.959888	−	0.280382i	$-0.0904613\pi$
$13$	3.56896	+	2.59300i	0.989851	+	0.719169i	0.0299623	+	0.999551i	$0.490461\pi$
$14$	0.250995	+	4.96605i	0.0670813	+	1.32723i
$15$	0.712410	+	2.19257i	0.183943	+	0.566120i
$16$	−4.30909	−	1.91853i	−1.07727	−	0.479632i
$17$	−0.548667	−	5.22022i	−0.133071	−	1.26609i	−0.833562	−	0.552426i	$-0.813702\pi$
$17$	−0.548667	−	5.22022i	−0.133071	−	1.26609i	0.700490	−	0.713662i	$-0.252965\pi$
$18$	−4.73179	−	1.00577i	−1.11529	−	0.237063i
$19$	1.77554	−	0.377403i	0.407337	−	0.0865822i	0.000313752	−	1.00000i	$-0.499900\pi$
$19$	1.77554	−	0.377403i	0.407337	−	0.0865822i	0.407023	+	0.913418i	$0.366567\pi$
$20$	−4.37797	−	3.18078i	−0.978945	−	0.711245i
$21$	−1.34002	−	1.08926i	−0.292417	−	0.237697i
$22$		0			0
$23$	3.16637	+	5.48432i	0.660235	+	1.14356i	0.980554	+	0.196250i	$0.0628765\pi$
$23$	3.16637	+	5.48432i	0.660235	+	1.14356i	−0.320319	+	0.947310i	$0.603790\pi$
$24$	0.524355	−	0.233458i	0.107034	−	0.0476544i
$25$	5.00219	+	5.55549i	1.00044	+	1.11110i
$26$	5.54767	−	6.16131i	1.08799	−	1.20833i
$27$	2.94333	−	2.13845i	0.566444	−	0.411546i
$28$	4.04757	+	0.219677i	0.764919	+	0.0415150i
$29$	−0.593706	−	1.82724i	−0.110249	−	0.339310i	0.880678	−	0.473716i	$-0.157088\pi$
$29$	−0.593706	−	1.82724i	−0.110249	−	0.339310i	−0.990926	+	0.134406i	$0.957088\pi$
$30$	4.23807	−	0.900829i	0.773762	−	0.164468i
$31$	1.34100	−	0.597053i	0.240851	−	0.107234i	−0.282762	−	0.959190i	$-0.591251\pi$
$31$	1.34100	−	0.597053i	0.240851	−	0.107234i	0.523613	+	0.851956i	$0.324584\pi$
$32$	−3.55303	+	6.15403i	−0.628094	+	1.08789i
$33$		0			0
$34$	−9.86484			−1.69181
$35$	−9.02209	−	2.43546i	−1.52501	−	0.411668i
$36$	−1.21863	+	3.75055i	−0.203105	+	0.625092i
$37$	2.97988	−	3.30949i	0.489890	−	0.544077i	−0.446618	−	0.894725i	$-0.647372\pi$
$37$	2.97988	−	3.30949i	0.489890	−	0.544077i	0.936508	+	0.350647i	$0.114038\pi$
$38$	−0.356596	−	3.39279i	−0.0578475	−	0.550383i
$39$	0.300978	+	2.86361i	0.0481950	+	0.458545i
$40$	2.07836	−	2.30826i	0.328618	−	0.364968i
$41$	−0.0874885	+	0.269262i	−0.0136634	+	0.0420516i	−0.957656	−	0.287916i	$-0.907038\pi$
$41$	−0.0874885	+	0.269262i	−0.0136634	+	0.0420516i	0.943992	+	0.329967i	$0.107038\pi$
$42$	−2.29918	+	2.29064i	−0.354771	+	0.353453i
$43$	3.41147			0.520245			0.260122	−	0.965576i	$-0.416237\pi$
$43$	3.41147			0.520245			0.260122	+	0.965576i	$0.416237\pi$
$44$		0			0
$45$	4.54576	−	7.87349i	0.677642	−	1.17371i
$46$	10.8727	−	4.84085i	1.60310	−	0.713744i
$47$	4.45485	−	0.946908i	0.649807	−	0.138121i	0.128797	−	0.991671i	$-0.458889\pi$
$47$	4.45485	−	0.946908i	0.649807	−	0.138121i	0.521011	+	0.853550i	$0.325555\pi$
$48$	−0.951379	−	2.92804i	−0.137320	−	0.422626i
$49$	6.66540	−	2.13833i	0.952200	−	0.305476i
$50$	11.3664	−	8.25817i	1.60745	−	1.16788i
$51$	2.29246	−	2.54603i	0.321008	−	0.356516i
$52$	−4.52250	−	5.02275i	−0.627158	−	0.696529i
$53$	−6.60897	+	2.94250i	−0.907812	+	0.404184i	−0.806884	−	0.590710i	$-0.798848\pi$
$53$	−6.60897	+	2.94250i	−0.907812	+	0.404184i	−0.100928	+	0.994894i	$0.532181\pi$
$54$	−3.41875	−	5.92145i	−0.465233	−	0.805807i
$55$		0			0
$56$	−0.368241	+	2.29731i	−0.0492083	+	0.306991i
$57$	0.958517	+	0.696404i	0.126959	+	0.0922409i
$58$	−3.53191	+	0.750731i	−0.463762	+	0.0985758i
$59$	−9.33136	−	1.98344i	−1.21484	−	0.258222i	−0.444455	−	0.895801i	$-0.646603\pi$
$59$	−9.33136	−	1.98344i	−1.21484	−	0.258222i	−0.770385	+	0.637579i	$0.779936\pi$
$60$	−0.369204	−	3.51274i	−0.0476640	−	0.453493i
$61$	1.04871	+	0.466916i	0.134274	+	0.0597824i	0.472774	−	0.881184i	$-0.343253\pi$
$61$	1.04871	+	0.466916i	0.134274	+	0.0597824i	−0.338500	+	0.940966i	$0.609920\pi$
$62$	−0.852507	−	2.62375i	−0.108268	−	0.333216i
$63$	0.343759	+	6.80142i	0.0433096	+	0.856899i
$64$	3.17238	+	2.30487i	0.396547	+	0.288108i
$65$	7.79086	+	13.4942i	0.966337	+	1.67375i
$66$		0			0
$67$	0.347296	−	0.601535i	0.0424290	−	0.0734892i	−0.844031	−	0.536294i	$-0.819824\pi$
$67$	0.347296	−	0.601535i	0.0424290	−	0.0734892i	0.886460	+	0.462805i	$0.153157\pi$
$68$	−0.840606	+	7.99783i	−0.101938	+	0.969880i
$69$	−1.27729	+	3.93110i	−0.153768	+	0.473249i
$70$	−6.32448	+	16.3846i	−0.755920	+	1.95834i
$71$	−7.65419	+	5.56110i	−0.908386	+	0.659981i	−0.940606	−	0.339500i	$-0.889742\pi$
$71$	−7.65419	+	5.56110i	−0.908386	+	0.659981i	0.0322204	+	0.999481i	$0.489742\pi$
$72$	−2.06783	−	0.920656i	−0.243696	−	0.108500i
$73$	2.29600	+	0.488030i	0.268727	+	0.0571196i	0.340304	−	0.940315i	$-0.389470\pi$
$73$	2.29600	+	0.488030i	0.268727	+	0.0571196i	−0.0715774	+	0.997435i	$0.522803\pi$
$74$	−5.60035	−	6.21981i	−0.651027	−	0.723039i
$75$	−0.510035	+	4.85266i	−0.0588937	+	0.560336i
$76$	−2.78106			−0.319009
$77$		0			0
$78$	5.41147			0.612729
$79$	−1.29816	+	12.3512i	−0.146055	+	1.38962i	0.638531	+	0.769596i	$0.279542\pi$
$79$	−1.29816	+	12.3512i	−0.146055	+	1.38962i	−0.784586	+	0.620020i	$0.787124\pi$
$80$	−11.1480	−	12.3811i	−1.24639	−	1.38425i
$81$	−5.23045	−	1.11177i	−0.581161	−	0.123529i
$82$	0.486087	+	0.216420i	0.0536794	+	0.0238996i
$83$	−9.16839	+	6.66122i	−1.00636	+	0.731164i	−0.963443	−	0.267914i	$-0.913666\pi$
$83$	−9.16839	+	6.66122i	−1.00636	+	0.731164i	−0.0429184	+	0.999079i	$0.513666\pi$
$84$	1.66120	+	2.05923i	0.181251	+	0.224680i
$85$	5.72912	−	17.6324i	0.621411	−	1.91251i
$86$	0.670182	−	6.37635i	0.0722675	−	0.687580i
$87$	0.627011	−	1.08602i	0.0672227	−	0.116433i
$88$		0			0
$89$	1.73396	+	3.00330i	0.183799	+	0.318349i	0.943171	−	0.332307i	$-0.107827\pi$
$89$	1.73396	+	3.00330i	0.183799	+	0.318349i	−0.759372	+	0.650656i	$0.774494\pi$
$90$	−13.8232	−	10.0432i	−1.45710	−	1.05864i
$91$	−10.3897	−	5.31816i	−1.08913	−	0.557495i
$92$	−2.99819	−	9.22747i	−0.312582	−	0.962030i
$93$	0.875278	+	0.389699i	0.0907621	+	0.0404099i
$94$	−0.894704	−	8.51254i	−0.0922817	−	0.878002i
$95$	6.27137	+	1.33302i	0.643429	+	0.136765i
$96$	−4.53680	+	0.964327i	−0.463035	+	0.0984212i
$97$	−12.4162	−	9.02091i	−1.26068	−	0.915935i	−0.261886	−	0.965099i	$-0.584344\pi$
$97$	−12.4162	−	9.02091i	−1.26068	−	0.915935i	−0.998791	+	0.0491638i	$0.984344\pi$
$98$	−2.68732	−	12.8783i	−0.271460	−	1.30090i
$99$		0			0
$100$	−5.72668	−	9.91890i	−0.572668	−	0.991890i
$101$	−6.12289	+	2.72608i	−0.609250	+	0.271256i	−0.688083	−	0.725632i	$-0.741547\pi$
$101$	−6.12289	+	2.72608i	−0.609250	+	0.271256i	0.0788327	+	0.996888i	$0.474881\pi$
$102$	−4.30841	−	4.78497i	−0.426596	−	0.473783i
$103$	1.50485	−	1.67131i	0.148278	−	0.164679i	−0.664430	−	0.747350i	$-0.731326\pi$
$103$	1.50485	−	1.67131i	0.148278	−	0.164679i	0.812708	+	0.582671i	$0.197992\pi$
$104$	3.13849	−	2.28025i	0.307754	−	0.223596i
$105$	−2.75901	−	5.43987i	−0.269252	−	0.530877i
$106$	4.20148	+	12.9308i	0.408084	+	1.25595i
$107$	−11.2801	+	2.39766i	−1.09049	+	0.231790i	−0.717858	−	0.696190i	$-0.754877\pi$
$107$	−11.2801	+	2.39766i	−1.09049	+	0.231790i	−0.372629	+	0.927980i	$0.621544\pi$
$108$	−5.09208	+	2.26714i	−0.489986	+	0.218156i
$109$	−5.99273	+	10.3797i	−0.573999	+	0.994196i	0.422151	+	0.906526i	$0.361275\pi$
$109$	−5.99273	+	10.3797i	−0.573999	+	0.994196i	−0.996150	+	0.0876698i	$0.972058\pi$
$110$		0			0
$111$	2.90673			0.275894
$112$	12.0484	+	3.25241i	1.13847	+	0.307323i
$113$	1.54748	−	4.76264i	0.145574	−	0.448032i	−0.851510	−	0.524338i	$-0.824313\pi$
$113$	1.54748	−	4.76264i	0.145574	−	0.448032i	0.997084	+	0.0763064i	$0.0243127\pi$
$114$	1.48994	−	1.65475i	0.139546	−	0.154981i
$115$	2.33807	+	22.2453i	0.218027	+	2.07438i
$116$	0.307686	+	2.92744i	0.0285679	+	0.271806i
$117$	7.59800	−	8.43844i	0.702436	−	0.780134i
$118$	−5.54037	+	17.0515i	−0.510032	+	1.56972i
$119$	3.56938	+	13.4209i	0.327204	+	1.23029i
$120$	2.02734			0.185070
$121$		0			0
$122$	1.07873	−	1.86841i	0.0976632	−	0.169158i
$123$	−0.168816	+	0.0751619i	−0.0152217	+	0.00677712i
$124$	−2.19982	+	0.467587i	−0.197550	+	0.0419906i
$125$	2.70211	+	8.31625i	0.241684	+	0.743828i
$126$	12.7800	+	0.693618i	1.13853	+	0.0617924i
$127$	−11.5159	+	8.36678i	−1.02187	+	0.742432i	−0.966665	−	0.256043i	$-0.917581\pi$
$127$	−11.5159	+	8.36678i	−1.02187	+	0.742432i	−0.0552046	+	0.998475i	$0.517581\pi$
$128$	−4.57856	+	5.08500i	−0.404691	+	0.449455i
$129$	1.48994	+	1.65475i	0.131182	+	0.145692i
$130$	26.7523	−	11.9109i	2.34633	−	1.04465i
$131$	2.55690	+	4.42869i	0.223398	+	0.386936i	0.955838	−	0.293896i	$-0.0949518\pi$
$131$	2.55690	+	4.42869i	0.223398	+	0.386936i	−0.732440	+	0.680832i	$0.761618\pi$
$132$		0			0
$133$	−4.48680	+	1.71275i	−0.389055	+	0.148514i
$134$	−1.05610	−	0.767299i	−0.0912329	−	0.0662846i
$135$	12.5695	−	2.67173i	1.08181	−	0.229946i
$136$	−4.51500	−	0.959693i	−0.387158	−	0.0822930i
$137$	−2.05998	−	19.5994i	−0.175996	−	1.67449i	−0.624741	−	0.780832i	$-0.714795\pi$
$137$	−2.05998	−	19.5994i	−0.175996	−	1.67449i	0.448745	−	0.893660i	$-0.351871\pi$
$138$	7.09666	+	3.15964i	0.604108	+	0.268966i
$139$	1.63340	+	5.02710i	0.138544	+	0.426393i	0.996124	−	0.0879561i	$-0.0280335\pi$
$139$	1.63340	+	5.02710i	0.138544	+	0.426393i	−0.857581	+	0.514349i	$0.828034\pi$
$140$	12.7448	+	6.52369i	1.07713	+	0.551353i
$141$	2.40493	+	1.74729i	0.202532	+	0.147148i
$142$	8.89053	+	15.3988i	0.746077	+	1.29224i
$143$		0			0
$144$	−6.07057	+	10.5145i	−0.505881	+	0.876212i
$145$	0.709342	−	6.74894i	0.0589076	−	0.560469i
$146$	1.36322	−	4.19556i	0.112821	−	0.347227i
$147$	3.94828	+	2.29917i	0.325648	+	0.189632i
$148$	−5.51988	+	4.01043i	−0.453731	+	0.329655i
$149$	15.5444	+	6.92082i	1.27345	+	0.566976i	0.928391	−	0.371606i	$-0.121193\pi$
$149$	15.5444	+	6.92082i	1.27345	+	0.566976i	0.345058	+	0.938582i	$0.387859\pi$
$150$	8.96985	+	1.90660i	0.732385	+	0.155673i
$151$	−0.871689	−	0.968109i	−0.0709371	−	0.0787836i	0.706632	−	0.707582i	$-0.250214\pi$
$151$	−0.871689	−	0.968109i	−0.0709371	−	0.0787836i	−0.777569	+	0.628798i	$0.783547\pi$
$152$	0.166855	−	1.58752i	0.0135338	−	0.128765i
$153$	−13.5107			−1.09228
$154$		0			0
$155$	5.18479			0.416453
$156$	0.461125	−	4.38731i	0.0369195	−	0.351266i
$157$	9.16347	+	10.1771i	0.731325	+	0.812218i	0.988028	−	0.154272i	$-0.0493032\pi$
$157$	9.16347	+	10.1771i	0.731325	+	0.812218i	−0.256704	+	0.966490i	$0.582636\pi$
$158$	22.8304	+	4.85276i	1.81629	+	0.386065i
$159$	−4.31370	−	1.92058i	−0.342099	−	0.152312i
$160$	−20.3057	+	14.7530i	−1.60531	+	1.16633i
$161$	−10.5199	−	13.0406i	−0.829087	−	1.02774i
$162$	−3.10551	+	9.55777i	−0.243992	+	0.750929i
$163$	−1.71475	+	16.3148i	−0.134310	+	1.27787i	0.694969	+	0.719039i	$0.255418\pi$
$163$	−1.71475	+	16.3148i	−0.134310	+	1.27787i	−0.829279	+	0.558834i	$0.811249\pi$
$164$	0.216881	−	0.375650i	0.0169356	−	0.0293333i
$165$		0			0
$166$	10.6493	+	18.4451i	0.826546	+	1.43162i
$167$	−6.67138	−	4.84704i	−0.516247	−	0.375075i	0.298941	−	0.954272i	$-0.403367\pi$
$167$	−6.67138	−	4.84704i	−0.516247	−	0.375075i	−0.815188	+	0.579196i	$0.803367\pi$
$168$	−1.27514	+	0.824719i	−0.0983795	+	0.0636285i
$169$	1.99659	+	6.14488i	0.153584	+	0.472683i
$170$	−31.8311	−	14.1721i	−2.44133	−	1.08695i
$171$	−0.488389	−	4.64671i	−0.0373480	−	0.355343i
$172$	−5.11247	−	1.08669i	−0.389822	−	0.0828592i
$173$	18.8141	−	3.99906i	1.43041	−	0.304043i	0.573371	−	0.819296i	$-0.305635\pi$
$173$	18.8141	−	3.99906i	1.43041	−	0.304043i	0.857038	+	0.515253i	$0.172302\pi$
$174$	−1.90668	−	1.38529i	−0.144545	−	0.105018i
$175$	−15.3478	−	12.4757i	−1.16018	−	0.943076i
$176$		0			0
$177$	−3.11334	−	5.39246i	−0.234013	−	0.405322i
$178$	5.95407	−	2.65092i	0.446276	−	0.198695i
$179$	−0.888402	−	0.986670i	−0.0664023	−	0.0737472i	0.709028	−	0.705180i	$-0.249134\pi$
$179$	−0.888402	−	0.986670i	−0.0664023	−	0.0737472i	−0.775431	+	0.631433i	$0.782467\pi$
$180$	−9.32033	+	10.3513i	−0.694696	+	0.771539i
$181$	−14.2813	+	10.3760i	−1.06152	+	0.771242i	−0.974370	−	0.224953i	$-0.927777\pi$
$181$	−14.2813	+	10.3760i	−1.06152	+	0.771242i	−0.0871538	+	0.996195i	$0.527777\pi$
$182$	−11.9812	+	18.3744i	−0.888103	+	1.36200i
$183$	0.231539	+	0.712603i	0.0171158	+	0.0526771i
$184$	5.44723	−	1.15784i	0.401575	−	0.0853574i
$185$	14.3698	−	6.39784i	1.05649	−	0.470378i
$186$	0.900330	−	1.55942i	0.0660154	−	0.114342i
$187$		0			0
$188$	−6.97771			−0.508902
$189$	−6.81902	+	6.79369i	−0.496011	+	0.494168i
$190$	3.72354	−	11.4599i	0.270134	−	0.831387i
$191$	10.4067	−	11.5579i	0.753005	−	0.836297i	−0.237840	−	0.971304i	$-0.576439\pi$
$191$	10.4067	−	11.5579i	0.753005	−	0.836297i	0.990845	+	0.135008i	$0.0431059\pi$
$192$	0.267533	+	2.54541i	0.0193076	+	0.183699i
$193$	−0.545528	−	5.19035i	−0.0392680	−	0.373610i	−0.996454	−	0.0841369i	$-0.973187\pi$
$193$	−0.545528	−	5.19035i	−0.0392680	−	0.373610i	0.957186	−	0.289473i	$-0.0934800\pi$
$194$	−19.3001	+	21.4349i	−1.38566	+	1.53894i
$195$	−3.14278	+	9.67248i	−0.225059	+	0.692660i
$196$	−10.6700	+	1.08133i	−0.762141	+	0.0772379i
$197$	4.61856			0.329058			0.164529	−	0.986372i	$-0.447390\pi$
$197$	4.61856			0.329058			0.164529	+	0.986372i	$0.447390\pi$
$198$		0			0
$199$	3.02481	−	5.23913i	0.214423	−	0.371392i	−0.738671	−	0.674067i	$-0.764546\pi$
$199$	3.02481	−	5.23913i	0.214423	−	0.371392i	0.953094	+	0.302674i	$0.0978794\pi$
$200$	6.00563	−	2.67388i	0.424662	−	0.189072i
$201$	0.443456	−	0.0942595i	0.0312790	−	0.00664855i
$202$	3.89246	+	11.9798i	0.273873	+	0.842893i
$203$	2.29930	+	4.53346i	0.161379	+	0.318187i
$204$	−4.24651	+	3.08527i	−0.297315	+	0.216012i
$205$	−0.669131	+	0.743145i	−0.0467341	+	0.0519035i
$206$	−2.82820	−	3.14104i	−0.197050	−	0.218846i
$207$	14.8911	−	6.62995i	1.03500	−	0.460813i
$208$	−10.4042	−	18.0206i	−0.721401	−	1.24950i
$209$		0			0
$210$	−10.7096	+	4.08819i	−0.739033	+	0.282112i
$211$	7.03407	+	5.11055i	0.484246	+	0.351825i	0.802967	−	0.596023i	$-0.203253\pi$
$211$	7.03407	+	5.11055i	0.484246	+	0.351825i	−0.318721	+	0.947848i	$0.603253\pi$
$212$	10.8416	−	2.30445i	0.744602	−	0.158270i
$213$	−6.04035	−	1.28392i	−0.413878	−	0.0879725i
$214$	2.26547	+	21.5545i	0.154864	+	1.47344i
$215$	11.0079	+	4.90103i	0.750731	+	0.334247i
$216$	−0.988651	−	3.04275i	−0.0672692	−	0.207033i
$217$	−3.26110	+	2.10917i	−0.221378	+	0.143180i
$218$	18.2233	+	13.2400i	1.23424	+	0.896728i
$219$	0.766044	+	1.32683i	0.0517645	+	0.0896587i
$220$		0			0
$221$	11.5778	−	20.0534i	0.778810	−	1.34894i
$222$	0.571024	−	5.43293i	0.0383246	−	0.364635i
$223$	−0.0684872	+	0.210782i	−0.00458624	+	0.0141150i	−0.953323	−	0.301951i	$-0.902362\pi$
$223$	−0.0684872	+	0.210782i	−0.00458624	+	0.0141150i	0.948737	+	0.316066i	$0.102362\pi$
$224$	6.77028	−	17.5396i	0.452358	−	1.17191i
$225$	15.5672	−	11.3103i	1.03782	−	0.754017i
$226$	−8.59781	−	3.82799i	−0.571918	−	0.254634i
$227$	−9.48768	−	2.01667i	−0.629720	−	0.133851i	−0.118014	−	0.993012i	$-0.537653\pi$
$227$	−9.48768	−	2.01667i	−0.629720	−	0.133851i	−0.511706	+	0.859161i	$0.670986\pi$
$228$	−1.21461	−	1.34896i	−0.0804396	−	0.0893372i
$229$	−2.47676	+	23.5648i	−0.163669	+	1.55721i	0.536916	+	0.843636i	$0.319589\pi$
$229$	−2.47676	+	23.5648i	−0.163669	+	1.55721i	−0.700585	+	0.713569i	$0.747077\pi$
$230$	42.0378			2.77189
$231$		0			0
$232$	−1.68954			−0.110924
$233$	2.18330	−	20.7727i	0.143033	−	1.36087i	−0.653801	−	0.756666i	$-0.726827\pi$
$233$	2.18330	−	20.7727i	0.143033	−	1.36087i	0.796834	−	0.604199i	$-0.206507\pi$
$234$	−14.2796	−	15.8591i	−0.933485	−	1.03674i
$235$	15.7349	+	3.34456i	1.02643	+	0.218175i
$236$	13.3523	+	5.94481i	0.869158	+	0.386974i
$237$	−6.55795	+	4.76463i	−0.425984	+	0.309496i
$238$	25.7861	−	4.03495i	1.67147	−	0.261547i
$239$	−4.64453	+	14.2944i	−0.300430	+	0.924628i	0.680913	+	0.732364i	$0.261583\pi$
$239$	−4.64453	+	14.2944i	−0.300430	+	0.924628i	−0.981343	+	0.192264i	$0.938417\pi$
$240$	1.13668	−	10.8148i	0.0733722	−	0.698090i
$241$	14.7699	−	25.5822i	0.951414	−	1.64790i	0.209045	−	0.977906i	$-0.432965\pi$
$241$	14.7699	−	25.5822i	0.951414	−	1.64790i	0.742369	−	0.669991i	$-0.233702\pi$
$242$		0			0
$243$	−7.20233	−	12.4748i	−0.462030	−	0.800259i
$244$	−1.42288	−	1.03378i	−0.0910903	−	0.0661809i
$245$	24.5794	+	2.67591i	1.57032	+	0.170958i
$246$	0.107320	+	0.330298i	0.00684250	+	0.0210591i
$247$	7.31544	+	3.25704i	0.465470	+	0.207241i
$248$	−0.134932	−	1.28379i	−0.00856816	−	0.0815206i
$249$	−7.23529	−	1.53791i	−0.458518	−	0.0974609i
$250$	16.0746	−	3.41677i	1.01665	−	0.216096i
$251$	−3.05050	−	2.21632i	−0.192546	−	0.139893i	0.487336	−	0.873215i	$-0.337969\pi$
$251$	−3.05050	−	2.21632i	−0.192546	−	0.139893i	−0.679882	+	0.733322i	$0.737969\pi$
$252$	1.65136	−	10.3022i	0.104026	−	0.648976i
$253$		0			0
$254$	13.3760	+	23.1679i	0.839284	+	1.45368i
$255$	11.0548	−	4.92193i	0.692280	−	0.308223i
$256$	13.8526	+	15.3848i	0.865785	+	0.961552i
$257$	−5.79497	+	6.43596i	−0.361480	+	0.401464i	−0.896261	−	0.443526i	$-0.853727\pi$
$257$	−5.79497	+	6.43596i	−0.361480	+	0.401464i	0.534781	+	0.844991i	$0.320394\pi$
$258$	3.38557	−	2.45976i	0.210776	−	0.153138i
$259$	−6.43558	+	9.86967i	−0.399887	+	0.613272i
$260$	−7.37703	−	22.7042i	−0.457504	−	1.40805i
$261$	−4.83725	+	1.02819i	−0.299418	+	0.0636433i
$262$	8.77992	−	3.90907i	0.542425	−	0.241503i
$263$	−2.91740	+	5.05309i	−0.179895	+	0.311587i	−0.941844	−	0.336049i	$-0.890909\pi$
$263$	−2.91740	+	5.05309i	−0.179895	+	0.311587i	0.761950	+	0.647636i	$0.224242\pi$
$264$		0			0
$265$	−25.5526			−1.56969
$266$	2.31985	+	8.72269i	0.142239	+	0.534823i
$267$	−0.699466	+	2.15273i	−0.0428066	+	0.131745i
$268$	−0.712074	+	0.790838i	−0.0434968	+	0.0483081i
$269$	2.29767	+	21.8609i	0.140092	+	1.33288i	0.808239	+	0.588855i	$0.200421\pi$
$269$	2.29767	+	21.8609i	0.140092	+	1.33288i	−0.668147	+	0.744029i	$0.732912\pi$
$270$	−2.52443	−	24.0183i	−0.153632	−	1.46171i
$271$	−6.59230	+	7.32150i	−0.400454	+	0.444749i	−0.909321	−	0.416096i	$-0.863398\pi$
$271$	−6.59230	+	7.32150i	−0.400454	+	0.444749i	0.508867	+	0.860845i	$0.330065\pi$
$272$	−7.65088	+	23.5470i	−0.463903	+	1.42775i
$273$	−1.95802	−	7.36221i	−0.118505	−	0.445581i
$274$	−37.0378			−2.23753
$275$		0			0
$276$	3.16637	−	5.48432i	0.190593	−	0.330117i
$277$	−21.5954	+	9.61488i	−1.29754	+	0.577702i	−0.935126	−	0.354315i	$-0.884714\pi$
$277$	−21.5954	+	9.61488i	−1.29754	+	0.577702i	−0.362415	+	0.932017i	$0.618048\pi$
$278$	9.71698	−	2.06541i	0.582786	−	0.123875i
$279$	−1.16758	−	3.59344i	−0.0699012	−	0.215134i
$280$	−4.48859	+	6.88375i	−0.268245	+	0.411383i
$281$	13.1637	−	9.56401i	0.785282	−	0.570541i	−0.121278	−	0.992619i	$-0.538699\pi$
$281$	13.1637	−	9.56401i	0.785282	−	0.570541i	0.906560	+	0.422078i	$0.138699\pi$
$282$	3.73828	−	4.15178i	0.222611	−	0.247235i
$283$	−11.3740	−	12.6322i	−0.676117	−	0.750904i	0.303268	−	0.952905i	$-0.401922\pi$
$283$	−11.3740	−	12.6322i	−0.676117	−	0.750904i	−0.979385	+	0.202001i	$0.935255\pi$
$284$	13.2421	−	5.89575i	0.785772	−	0.349848i
$285$	2.09240	+	3.62414i	0.123943	+	0.214675i
$286$		0			0
$287$	0.118555	−	0.739620i	0.00699810	−	0.0436584i
$288$	14.7976	+	10.7511i	0.871958	+	0.633514i
$289$	−10.3211	+	2.19382i	−0.607124	+	0.129048i
$290$	−12.4750	−	2.65165i	−0.732558	−	0.155710i
$291$	−1.04709	−	9.96236i	−0.0613813	−	0.584004i
$292$	−3.28535	−	1.46273i	−0.192261	−	0.0856000i
$293$	4.25775	+	13.1040i	0.248740	+	0.765544i	0.994999	+	0.0998879i	$0.0318484\pi$
$293$	4.25775	+	13.1040i	0.248740	+	0.765544i	−0.746258	+	0.665657i	$0.768152\pi$
$294$	5.07299	−	6.92801i	0.295863	−	0.404050i
$295$	−27.2603	−	19.8057i	−1.58715	−	1.15313i
$296$	−1.95811	−	3.39155i	−0.113813	−	0.197130i
$297$		0			0
$298$	15.9893	−	27.6943i	0.926237	−	1.60429i
$299$	−2.92019	+	27.7837i	−0.168879	+	1.60677i
$300$	2.31010	−	7.10977i	0.133374	−	0.410483i
$301$	−8.91740	+	1.39537i	−0.513990	+	0.0804280i
$302$	−1.98073	+	1.43908i	−0.113978	+	0.0828098i
$303$	−3.99643	−	1.77933i	−0.229589	−	0.102220i
$304$	−8.37502	−	1.78016i	−0.480340	−	0.102099i
$305$	2.71311	+	3.01322i	0.155352	+	0.172536i
$306$	−2.65417	+	25.2528i	−0.151729	+	1.44361i
$307$	11.6159			0.662953			0.331476	−	0.943464i	$-0.392453\pi$
$307$	11.6159			0.662953			0.331476	+	0.943464i	$0.392453\pi$
$308$		0			0
$309$	1.46791			0.0835065
$310$	1.01855	−	9.69084i	0.0578497	−	0.550403i
$311$	2.30737	+	2.56259i	0.130839	+	0.145311i	0.805004	−	0.593269i	$-0.202163\pi$
$311$	2.30737	+	2.56259i	0.130839	+	0.145311i	−0.674165	+	0.738581i	$0.735496\pi$
$312$	2.47676	+	0.526451i	0.140219	+	0.0298044i
$313$	−17.7428	−	7.89960i	−1.00288	−	0.446512i	−0.161453	−	0.986880i	$-0.551618\pi$
$313$	−17.7428	−	7.89960i	−1.00288	−	0.446512i	−0.841428	+	0.540369i	$0.818285\pi$
$314$	20.8220	−	15.1281i	1.17505	−	0.853727i
$315$	−8.66191	+	22.4402i	−0.488044	+	1.26436i
$316$	5.87977	−	18.0961i	0.330763	−	1.01798i
$317$	3.43022	−	32.6364i	0.192660	−	1.83304i	−0.289758	−	0.957100i	$-0.593575\pi$
$317$	3.43022	−	32.6364i	0.192660	−	1.83304i	0.482418	−	0.875941i	$-0.339759\pi$
$318$	−4.43717	+	7.68540i	−0.248824	+	0.430976i
$319$		0			0
$320$	6.92514	+	11.9947i	0.387127	+	0.670524i
$321$	−6.08950	−	4.42428i	−0.339883	−	0.246939i
$322$	−26.4407	+	17.1009i	−1.47348	+	0.952996i
$323$	−2.94430	−	9.06164i	−0.163825	−	0.504203i
$324$	7.48425	+	3.33220i	0.415792	+	0.185122i
$325$	3.44721	+	32.7980i	0.191217	+	1.81930i
$326$	30.1570	+	6.41006i	1.67024	+	0.355020i
$327$	−7.65200	+	1.62648i	−0.423156	+	0.0899447i
$328$	0.201421	+	0.146341i	0.0111216	+	0.00808033i
$329$	−11.2574	+	4.29731i	−0.620642	+	0.236918i
$330$		0			0
$331$	3.18004	+	5.50800i	0.174791	+	0.302747i	0.940089	−	0.340929i	$-0.110742\pi$
$331$	3.18004	+	5.50800i	0.174791	+	0.302747i	−0.765298	+	0.643676i	$0.777408\pi$
$332$	15.8617	−	7.06208i	0.870523	−	0.387582i
$333$	−7.67015	−	8.51856i	−0.420322	−	0.466814i
$334$	−10.3701	+	11.5172i	−0.567429	+	0.630194i
$335$	1.98481	−	1.44205i	0.108442	−	0.0787876i
$336$	3.68449	+	7.26460i	0.201005	+	0.396316i
$337$	4.80363	+	14.7841i	0.261671	+	0.805339i	0.992442	+	0.122717i	$0.0391606\pi$
$337$	4.80363	+	14.7841i	0.261671	+	0.805339i	−0.730771	+	0.682622i	$0.760839\pi$
$338$	11.8776	−	2.52465i	0.646054	−	0.137323i
$339$	2.98599	−	1.32945i	0.162177	−	0.0722057i
$340$	−14.2023	+	24.5992i	−0.770230	+	1.33408i
$341$		0			0
$342$	−8.78106			−0.474825
$343$	−16.5483	+	8.31578i	−0.893527	+	0.449010i
$344$	0.927051	−	2.85317i	0.0499832	−	0.153833i
$345$	−9.76902	+	10.8496i	−0.525946	+	0.584122i
$346$	−3.77859	−	35.9509i	−0.203138	−	1.93273i
$347$	−2.06178	−	19.6166i	−0.110682	−	1.05307i	−0.899043	−	0.437860i	$-0.855737\pi$
$347$	−2.06178	−	19.6166i	−0.110682	−	1.05307i	0.788361	−	0.615213i	$-0.210930\pi$
$348$	−1.28558	+	1.42779i	−0.0689145	+	0.0765373i
$349$	1.79040	−	5.51028i	0.0958379	−	0.294959i	−0.891633	−	0.452758i	$-0.850440\pi$
$349$	1.79040	−	5.51028i	0.0958379	−	0.294959i	0.987471	+	0.157800i	$0.0504400\pi$
$350$	−26.3333	+	26.2355i	−1.40757	+	1.40235i
$351$	16.0496			0.856666
$352$		0			0
$353$	−16.5831	+	28.7227i	−0.882627	+	1.52876i	−0.0342183	+	0.999414i	$0.510894\pi$
$353$	−16.5831	+	28.7227i	−0.882627	+	1.52876i	−0.848409	+	0.529341i	$0.822439\pi$
$354$	−10.6906	+	4.75977i	−0.568200	+	0.252979i
$355$	−32.6872	+	6.94788i	−1.73486	+	0.368755i
$356$	−1.64185	−	5.05310i	−0.0870180	−	0.267814i
$357$	−4.95096	+	7.59285i	−0.262033	+	0.401856i
$358$	−2.01870	+	1.46667i	−0.106692	+	0.0775160i
$359$	−2.81689	+	3.12847i	−0.148670	+	0.165114i	−0.812880	−	0.582432i	$-0.802101\pi$
$359$	−2.81689	+	3.12847i	−0.148670	+	0.165114i	0.664210	+	0.747546i	$0.268768\pi$
$360$	−5.34966	−	5.94140i	−0.281952	−	0.313139i
$361$	−14.3473	+	6.38781i	−0.755118	+	0.336200i
$362$	16.5881	+	28.7315i	0.871852	+	1.51009i
$363$		0			0
$364$	13.8760	+	11.2794i	0.727299	+	0.591199i
$365$	6.70745	+	4.87324i	0.351084	+	0.255077i
$366$	1.37740	−	0.292776i	0.0719981	−	0.0153037i
$367$	19.0140	+	4.04156i	0.992524	+	0.210968i	0.675428	−	0.737426i	$-0.263959\pi$
$367$	19.0140	+	4.04156i	0.992524	+	0.210968i	0.317096	+	0.948393i	$0.397292\pi$
$368$	−3.12235	−	29.7072i	−0.162764	−	1.54859i
$369$	0.665738	+	0.296406i	0.0346569	+	0.0154303i
$370$	−9.13520	−	28.1152i	−0.474916	−	1.46164i
$371$	16.0719	−	10.3948i	0.834413	−	0.539669i
$372$	−1.18757	−	0.862817i	−0.0615724	−	0.0447350i
$373$	6.35710	+	11.0108i	0.329158	+	0.570118i	0.982345	−	0.187078i	$-0.0599018\pi$
$373$	6.35710	+	11.0108i	0.329158	+	0.570118i	−0.653187	+	0.757197i	$0.726568\pi$
$374$		0			0
$375$	−2.85369	+	4.94274i	−0.147364	+	0.255242i
$376$	0.418642	−	3.98311i	0.0215898	−	0.205413i
$377$	2.61912	−	8.06082i	0.134892	−	0.415154i
$378$	11.3584	+	14.0800i	0.584214	+	0.724196i
$379$	18.4546	−	13.4080i	0.947947	−	0.688724i	−0.00237342	−	0.999997i	$-0.500755\pi$
$379$	18.4546	−	13.4080i	0.947947	−	0.688724i	0.950320	+	0.311273i	$0.100755\pi$
$380$	−8.97371	−	3.99535i	−0.460342	−	0.204957i
$381$	−9.08783	−	1.93168i	−0.465584	−	0.0989629i
$382$	−19.5583	−	21.7217i	−1.00069	−	1.11138i
$383$	−0.867440	+	8.25314i	−0.0443241	+	0.421716i	0.949750	+	0.313010i	$0.101337\pi$
$383$	−0.867440	+	8.25314i	−0.0443241	+	0.421716i	−0.994074	+	0.108706i	$0.965329\pi$
$384$	−4.46616			−0.227913
$385$		0			0
$386$	−9.80840			−0.499234
$387$	0.917871	−	8.73296i	0.0466580	−	0.443921i
$388$	15.7336	+	17.4739i	0.798750	+	0.887102i
$389$	−11.1505	−	2.37011i	−0.565353	−	0.120170i	−0.0836361	−	0.996496i	$-0.526653\pi$
$389$	−11.1505	−	2.37011i	−0.565353	−	0.120170i	−0.481717	+	0.876327i	$0.659987\pi$
$390$	17.4613	+	7.77429i	0.884189	+	0.393666i
$391$	26.8921	−	19.5382i	1.35999	−	0.988090i
$392$	0.0229067	−	6.15565i	0.00115696	−	0.310907i
$393$	−1.03144	+	3.17444i	−0.0520291	+	0.160129i
$394$	0.907312	−	8.63249i	0.0457097	−	0.434899i
$395$	−21.9329	+	37.9889i	−1.10356	+	1.91143i
$396$		0			0
$397$	−3.29086	−	5.69994i	−0.165163	−	0.286072i	0.771550	−	0.636169i	$-0.219482\pi$
$397$	−3.29086	−	5.69994i	−0.165163	−	0.286072i	−0.936713	+	0.350097i	$0.886149\pi$
$398$	−9.19819	−	6.68287i	−0.461063	−	0.334982i
$399$	−2.79036	−	1.42830i	−0.139693	−	0.0715046i
$400$	−10.8965	−	33.5359i	−0.544824	−	1.67680i
$401$	3.82761	+	1.70416i	0.191142	+	0.0851019i	0.500076	−	0.865982i	$-0.333305\pi$
$401$	3.82761	+	1.70416i	0.191142	+	0.0851019i	−0.308934	+	0.951084i	$0.599972\pi$
$402$	−0.0890629	−	0.847377i	−0.00444205	−	0.0422633i
$403$	6.33414	+	1.34636i	0.315526	+	0.0670672i
$404$	10.0442	−	2.13496i	0.499717	−	0.106218i
$405$	−15.2800	−	11.1016i	−0.759270	−	0.551642i
$406$	8.92514	−	3.40700i	0.442947	−	0.169087i
$407$		0			0
$408$	−1.50640	−	2.60916i	−0.0745777	−	0.129172i
$409$	−0.706462	+	0.314537i	−0.0349323	+	0.0155529i	−0.424128	−	0.905602i	$-0.639419\pi$
$409$	−0.706462	+	0.314537i	−0.0349323	+	0.0155529i	0.389196	+	0.921155i	$0.372753\pi$
$410$	1.25755	+	1.39666i	0.0621062	+	0.0689759i
$411$	8.60708	−	9.55913i	0.424556	−	0.471517i
$412$	−2.78757	+	2.02529i	−0.137334	+	0.0997787i
$413$	25.2029	+	1.36786i	1.24015	+	0.0673078i
$414$	−9.46663	−	29.1353i	−0.465259	−	1.43192i
$415$	−39.1536	+	8.32235i	−1.92197	+	0.408528i
$416$	−28.6380	+	12.7505i	−1.40410	+	0.625143i
$417$	−1.72503	+	2.98784i	−0.0844752	+	0.146315i
$418$		0			0
$419$	13.7547			0.671959			0.335979	−	0.941869i	$-0.390933\pi$
$419$	13.7547			0.671959			0.335979	+	0.941869i	$0.390933\pi$
$420$	2.40187	+	9.03109i	0.117199	+	0.440672i
$421$	−1.79406	+	5.52156i	−0.0874373	+	0.269104i	−0.985209	−	0.171357i	$-0.945185\pi$
$421$	−1.79406	+	5.52156i	−0.0874373	+	0.269104i	0.897772	+	0.440461i	$0.145185\pi$
$422$	10.9339	−	12.1434i	0.532255	−	0.591129i
$423$	−1.22537	−	11.6586i	−0.0595797	−	0.566863i
$424$	0.664994	+	6.32699i	0.0322950	+	0.307266i
$425$	26.2563	−	29.1606i	1.27362	−	1.41450i
$426$	−3.58638	+	11.0377i	−0.173761	+	0.534780i
$427$	−2.93225	−	0.791544i	−0.141901	−	0.0383055i
$428$	17.6682			0.854024
$429$		0			0
$430$	11.3229	−	19.6119i	0.546041	−	0.945771i
$431$	16.4493	−	7.32369i	0.792334	−	0.352770i	0.0296661	−	0.999560i	$-0.490556\pi$
$431$	16.4493	−	7.32369i	0.792334	−	0.352770i	0.762668	+	0.646790i	$0.223889\pi$
$432$	−16.7857	+	3.56792i	−0.807605	+	0.171662i
$433$	0.723251	+	2.22594i	0.0347572	+	0.106972i	0.966930	−	0.255042i	$-0.0820893\pi$
$433$	0.723251	+	2.22594i	0.0347572	+	0.106972i	−0.932173	+	0.362014i	$0.882089\pi$
$434$	3.30158	+	6.50963i	0.158481	+	0.312472i
$435$	3.58339	−	2.60349i	0.171811	−	0.124828i
$436$	12.2871	−	13.6462i	0.588445	−	0.653535i
$437$	7.69183	+	8.54264i	0.367950	+	0.408650i
$438$	2.63045	−	1.17115i	0.125688	−	0.0559598i
$439$	−20.0167	−	34.6699i	−0.955343	−	1.65470i	−0.733581	−	0.679602i	$-0.762152\pi$
$439$	−20.0167	−	34.6699i	−0.955343	−	1.65470i	−0.221762	−	0.975101i	$-0.571181\pi$
$440$		0			0
$441$	−3.68051	−	17.6379i	−0.175262	−	0.839901i
$442$	−35.2072	−	25.5795i	−1.67464	−	1.21669i
$443$	−18.5613	+	3.94532i	−0.881873	+	0.187448i	−0.626525	−	0.779401i	$-0.715523\pi$
$443$	−18.5613	+	3.94532i	−0.881873	+	0.187448i	−0.255348	+	0.966849i	$0.582190\pi$
$444$	−4.35605	−	0.925906i	−0.206729	−	0.0439416i
$445$	1.28037	+	12.1819i	0.0606952	+	0.577476i
$446$	0.380516	+	0.169417i	0.0180180	+	0.00802211i
$447$	3.43196	+	10.5625i	0.162326	+	0.499589i
$448$	−9.23516	−	4.72721i	−0.436320	−	0.223340i
$449$	25.5141	+	18.5371i	1.20408	+	0.874818i	0.994680	−	0.103011i	$-0.0328477\pi$
$449$	25.5141	+	18.5371i	1.20408	+	0.874818i	0.209404	+	0.977829i	$0.432848\pi$
$450$	−18.0817	−	31.3185i	−0.852380	−	1.47637i
$451$		0			0
$452$	−3.83615	+	6.64441i	−0.180437	+	0.312527i
$453$	0.0888794	−	0.845631i	0.00417592	−	0.0397312i
$454$	−5.63319	+	17.3372i	−0.264378	+	0.813673i
$455$	−25.8843	−	32.0863i	−1.21347	−	1.50423i
$456$	0.842906	−	0.612407i	0.0394727	−	0.0286786i
$457$	−10.6141	−	4.72569i	−0.496506	−	0.221059i	0.143178	−	0.989697i	$-0.454268\pi$
$457$	−10.6141	−	4.72569i	−0.496506	−	0.221059i	−0.639684	+	0.768638i	$0.720935\pi$
$458$	43.5582	+	9.25857i	2.03534	+	0.432625i
$459$	−12.7781	−	14.1915i	−0.596431	−	0.662403i
$460$	3.58214	−	34.0818i	0.167018	−	1.58907i
$461$	12.9786			0.604476			0.302238	−	0.953233i	$-0.402266\pi$
$461$	12.9786			0.604476			0.302238	+	0.953233i	$0.402266\pi$
$462$		0			0
$463$	35.3705			1.64381			0.821904	−	0.569626i	$-0.192912\pi$
$463$	35.3705			1.64381			0.821904	+	0.569626i	$0.192912\pi$
$464$	−0.947281	+	9.01278i	−0.0439764	+	0.418408i
$465$	2.26443	+	2.51490i	0.105010	+	0.116626i
$466$	−38.3971	−	8.16156i	−1.77871	−	0.378077i
$467$	−36.4192	−	16.2149i	−1.68528	−	0.750335i	−0.999752	−	0.0222882i	$-0.992905\pi$
$467$	−36.4192	−	16.2149i	−1.68528	−	0.750335i	−0.685528	−	0.728047i	$-0.740428\pi$
$468$	−14.0744	+	10.2257i	−0.650590	+	0.472681i
$469$	−0.661771	+	1.71443i	−0.0305577	+	0.0791651i
$470$	9.34241	−	28.7530i	0.430933	−	1.32628i
$471$	−0.934329	+	8.88954i	−0.0430516	+	0.409609i
$472$	−4.19459	+	7.26525i	−0.193072	+	0.334410i
$473$		0			0
$474$	7.61721	+	13.1934i	0.349870	+	0.605993i
$475$	10.9782	+	7.97616i	0.503717	+	0.365971i
$476$	−1.07401	−	21.2497i	−0.0492271	−	0.973979i
$477$	5.75428	+	17.7099i	0.263470	+	0.810879i
$478$	25.8051	+	11.4892i	1.18030	+	0.525503i
$479$	−3.17558	−	30.2136i	−0.145096	−	1.38049i	−0.788532	−	0.614994i	$-0.789158\pi$
$479$	−3.17558	−	30.2136i	−0.145096	−	1.38049i	0.643436	−	0.765500i	$-0.277508\pi$
$480$	−16.0244	−	3.40609i	−0.731410	−	0.155466i
$481$	19.2166	−	4.08461i	0.876201	−	0.186242i
$482$	−44.9140	−	32.6319i	−2.04578	−	1.48634i
$483$	1.73086	−	10.7981i	0.0787567	−	0.491332i
$484$		0			0
$485$	−27.1040	−	46.9455i	−1.23073	−	2.13169i
$486$	−24.7314	+	11.0111i	−1.12184	+	0.499476i
$487$	−6.97975	−	7.75180i	−0.316283	−	0.351268i	0.563951	−	0.825808i	$-0.309281\pi$
$487$	−6.97975	−	7.75180i	−0.316283	−	0.351268i	−0.880233	+	0.474541i	$0.842614\pi$
$488$	0.675484	−	0.750201i	0.0305777	−	0.0339600i
$489$	−8.66246	+	6.29364i	−0.391730	+	0.284608i
$490$	9.83012	−	45.4154i	0.444080	−	2.05166i
$491$	3.17555	+	9.77335i	0.143311	+	0.441065i	0.996790	−	0.0800618i	$-0.0255118\pi$
$491$	3.17555	+	9.77335i	0.143311	+	0.441065i	−0.853479	+	0.521127i	$0.825512\pi$
$492$	0.276932	−	0.0588637i	0.0124850	−	0.00265378i
$493$	−9.21284	+	4.10182i	−0.414926	+	0.184737i
$494$	7.52481	−	13.0334i	0.338557	−	0.586399i
$495$		0			0
$496$	−6.92396			−0.310895
$497$	17.7330	−	17.6671i	0.795434	−	0.792480i
$498$	−4.29585	+	13.2213i	−0.192502	+	0.592460i
$499$	−24.4356	+	27.1385i	−1.09389	+	1.21489i	−0.118836	+	0.992914i	$0.537916\pi$
$499$	−24.4356	+	27.1385i	−1.09389	+	1.21489i	−0.975053	+	0.221973i	$0.928750\pi$
$500$	−1.40036	−	13.3235i	−0.0626260	−	0.595847i
$501$	−0.562612	−	5.35289i	−0.0251356	−	0.239150i
$502$	−4.74177	+	5.26627i	−0.211636	+	0.235045i
$503$	9.69163	−	29.8278i	0.432128	−	1.32995i	−0.463872	−	0.885902i	$-0.653540\pi$
$503$	9.69163	−	29.8278i	0.432128	−	1.32995i	0.896001	−	0.444053i	$-0.146460\pi$
$504$	5.78175	+	1.56075i	0.257540	+	0.0695214i
$505$	−23.6732			−1.05345
$506$		0			0
$507$	−2.10859	+	3.65219i	−0.0936459	+	0.162199i
$508$	19.9230	−	8.87028i	0.883939	−	0.393555i
$509$	11.3118	−	2.40439i	0.501385	−	0.106573i	0.0497255	−	0.998763i	$-0.484165\pi$
$509$	11.3118	−	2.40439i	0.501385	−	0.106573i	0.451660	+	0.892190i	$0.350832\pi$
$510$	−7.02781	−	21.6294i	−0.311197	−	0.957765i
$511$	−6.20124	−	0.336564i	−0.274327	−	0.0148887i
$512$	20.4055	−	14.8255i	0.901803	−	0.655199i
$513$	4.41894	−	4.90773i	0.195101	−	0.216682i
$514$	10.8910	+	12.0957i	0.480380	+	0.533517i
$515$	7.25681	−	3.23094i	0.319773	−	0.142372i
$516$	−1.70574	−	2.95442i	−0.0750909	−	0.130061i
$517$		0			0
$518$	17.1830	+	13.9676i	0.754979	+	0.613700i
$519$	10.1567	+	7.37928i	0.445830	+	0.323914i
$520$	13.4029	−	2.84888i	0.587756	−	0.124931i
$521$	29.8925	+	6.35386i	1.30962	+	0.278368i	0.809259	−	0.587452i	$-0.199869\pi$
$521$	29.8925	+	6.35386i	1.30962	+	0.278368i	0.500357	+	0.865819i	$0.333202\pi$
$522$	0.971504	+	9.24324i	0.0425216	+	0.404566i
$523$	4.06995	+	1.81206i	0.177967	+	0.0792358i	0.493786	−	0.869584i	$-0.335613\pi$
$523$	4.06995	+	1.81206i	0.177967	+	0.0792358i	−0.315819	+	0.948819i	$0.602279\pi$
$524$	−2.42109	−	7.45135i	−0.105766	−	0.325514i
$525$	−0.651650	−	12.8932i	−0.0284403	−	0.562705i
$526$	8.87156	+	6.44557i	0.386818	+	0.281040i
$527$	−3.85251	−	6.67274i	−0.167818	−	0.290669i
$528$		0			0
$529$	−8.55185	+	14.8122i	−0.371820	+	0.644010i
$530$	−5.01979	+	47.7601i	−0.218046	+	2.07457i
$531$	−7.58801	+	23.3535i	−0.329292	+	1.01346i
$532$	7.26953	−	1.13752i	0.315174	−	0.0493177i
$533$	−1.01044	+	0.734126i	−0.0437669	+	0.0317985i
$534$	3.88624	+	1.73027i	0.168174	+	0.0748760i
$535$	−39.8423	−	8.46873i	−1.72253	−	0.366135i
$536$	−0.408715	−	0.453924i	−0.0176538	−	0.0196065i
$537$	0.0905835	−	0.861845i	0.00390897	−	0.0371913i
$538$	41.3114			1.78106
$539$		0			0
$540$	−19.6878			−0.847227
$541$	−1.74255	+	16.5792i	−0.0749179	+	0.712797i	0.891010	+	0.453984i	$0.149998\pi$
$541$	−1.74255	+	16.5792i	−0.0749179	+	0.712797i	−0.965928	+	0.258812i	$0.916669\pi$
$542$	12.3895	+	13.7599i	0.532174	+	0.591039i
$543$	−11.2702	−	2.39556i	−0.483651	−	0.102803i
$544$	34.0748	+	15.1711i	1.46095	+	0.650455i
$545$	−34.2487	+	24.8831i	−1.46705	+	1.06588i
$546$	−14.1453	+	2.21342i	−0.605362	+	0.0947257i
$547$	−11.1889	+	34.4359i	−0.478402	+	1.47237i	0.362911	+	0.931824i	$0.381783\pi$
$547$	−11.1889	+	34.4359i	−0.478402	+	1.47237i	−0.841313	+	0.540548i	$0.818217\pi$
$548$	−3.15608	+	30.0281i	−0.134821	+	1.28274i
$549$	1.47741	−	2.55894i	0.0630542	−	0.109213i
$550$		0			0
$551$	−1.74376	−	3.02027i	−0.0742865	−	0.128668i
$552$	2.94066	+	2.13652i	0.125163	+	0.0909362i
$553$	−1.65861	−	32.8163i	−0.0705312	−	1.39549i
$554$	13.7287	+	42.2525i	0.583276	+	1.79514i
$555$	9.37920	+	4.17589i	0.398125	+	0.177257i
$556$	−0.846506	−	8.05396i	−0.0358998	−	0.341564i
$557$	−0.655300	−	0.139288i	−0.0277660	−	0.00590184i	0.194008	−	0.981000i	$-0.437851\pi$
$557$	−0.655300	−	0.139288i	−0.0277660	−	0.00590184i	−0.221774	+	0.975098i	$0.571185\pi$
$558$	−6.94584	+	1.47638i	−0.294041	+	0.0625003i
$559$	12.1754	+	8.84595i	0.514965	+	0.374144i
$560$	34.2044	+	27.8038i	1.44540	+	1.17492i
$561$		0			0
$562$	−15.2900	−	26.4830i	−0.644969	−	1.11712i
$563$	11.9073	−	5.30147i	0.501832	−	0.223430i	−0.140178	−	0.990126i	$-0.544767\pi$
$563$	11.9073	−	5.30147i	0.501832	−	0.223430i	0.642010	+	0.766696i	$0.278101\pi$
$564$	−3.04747	−	3.38456i	−0.128322	−	0.142516i
$565$	11.8354	−	13.1446i	0.497921	−	0.552997i
$566$	−25.8451	+	18.7775i	−1.08635	+	0.789279i
$567$	14.1268	+	0.766715i	0.593271	+	0.0321990i
$568$	2.57101	+	7.91275i	0.107877	+	0.332012i
$569$	26.8418	−	5.70541i	1.12527	−	0.239183i	0.392560	−	0.919726i	$-0.371589\pi$
$569$	26.8418	−	5.70541i	1.12527	−	0.239183i	0.732708	+	0.680543i	$0.238256\pi$
$570$	7.18489	−	3.19892i	0.300942	−	0.133988i
$571$	8.11974	−	14.0638i	0.339800	−	0.588552i	−0.644595	−	0.764525i	$-0.722974\pi$
$571$	8.11974	−	14.0638i	0.339800	−	0.588552i	0.984395	+	0.175973i	$0.0563071\pi$
$572$		0			0
$573$	10.1513			0.424075
$574$	−1.35913	−	0.366888i	−0.0567288	−	0.0153136i
$575$	−14.6293	+	45.0244i	−0.610084	+	1.87765i
$576$	6.75372	−	7.50076i	0.281405	−	0.312532i
$577$	−2.47919	−	23.5879i	−0.103210	−	0.981977i	−0.916477	−	0.400087i	$-0.868980\pi$
$577$	−2.47919	−	23.5879i	−0.103210	−	0.981977i	0.813267	−	0.581890i	$-0.197687\pi$
$578$	2.07287	+	19.7221i	0.0862201	+	0.820329i
$579$	2.27934	−	2.53146i	0.0947262	−	0.105204i
$580$	−3.21283	+	9.88806i	−0.133405	+	0.410580i
$581$	21.2410	−	21.1621i	0.881227	−	0.877954i
$582$	−18.8262			−0.780373
$583$		0			0
$584$	1.03209	−	1.78763i	0.0427081	−	0.0739727i
$585$	36.6396	−	16.3130i	1.51486	−	0.674459i
$586$	25.3290	−	5.38385i	1.04633	−	0.222405i
$587$	−13.7792	−	42.4080i	−0.568728	−	1.75036i	−0.656606	−	0.754234i	$-0.728009\pi$
$587$	−13.7792	−	42.4080i	−0.568728	−	1.75036i	0.0878782	−	0.996131i	$-0.471991\pi$
$588$	−5.18455	−	4.70324i	−0.213807	−	0.193958i
$589$	2.15568	−	1.56619i	0.0888231	−	0.0645338i
$590$	−42.3740	+	47.0610i	−1.74451	+	1.93747i
$591$	2.01713	+	2.24025i	0.0829735	+	0.0921514i
$592$	−19.1899	+	8.54390i	−0.788701	+	0.351152i
$593$	−21.4217	−	37.1035i	−0.879685	−	1.52366i	−0.851686	−	0.524052i	$-0.824420\pi$
$593$	−21.4217	−	37.1035i	−0.879685	−	1.52366i	−0.0279992	−	0.999608i	$-0.508914\pi$
$594$		0			0
$595$	−7.76352	+	48.4335i	−0.318273	+	1.98558i
$596$	−21.0905	−	15.3231i	−0.863899	−	0.627659i
$597$	3.86233	−	0.820963i	0.158075	−	0.0335998i
$598$	51.3566	+	10.9162i	2.10013	+	0.446396i
$599$	0.0661773	+	0.629635i	0.00270393	+	0.0257262i	0.995791	−	0.0916566i	$-0.0292162\pi$
$599$	0.0661773	+	0.629635i	0.00270393	+	0.0257262i	−0.993087	+	0.117383i	$0.962550\pi$
$600$	3.91990	+	1.74525i	0.160029	+	0.0712495i
$601$	1.06871	+	3.28915i	0.0435936	+	0.134167i	0.970484	−	0.241164i	$-0.0775291\pi$
$601$	1.06871	+	3.28915i	0.0435936	+	0.134167i	−0.926891	+	0.375331i	$0.877529\pi$
$602$	0.856263	+	16.9415i	0.0348987	+	0.690486i
$603$	−1.44641	−	1.05088i	−0.0589025	−	0.0427952i
$604$	0.997941	+	1.72848i	0.0406056	+	0.0703310i
$605$		0			0
$606$	−4.11081	+	7.12014i	−0.166990	+	0.289236i
$607$	5.04610	−	48.0104i	0.204815	−	1.94868i	−0.0969224	−	0.995292i	$-0.530900\pi$
$607$	5.04610	−	48.0104i	0.204815	−	1.94868i	0.301737	−	0.953391i	$-0.402433\pi$
$608$	−3.98601	+	12.2677i	−0.161654	+	0.497519i
$609$	−1.19477	+	3.09525i	−0.0484144	+	0.125426i
$610$	6.16496	−	4.47911i	0.249612	−	0.181354i
$611$	18.3545	+	8.17196i	0.742544	+	0.330602i
$612$	20.2473	+	4.30370i	0.818449	+	0.173967i
$613$	14.2629	+	15.8405i	0.576072	+	0.639792i	0.958805	−	0.284067i	$-0.0916837\pi$
$613$	14.2629	+	15.8405i	0.576072	+	0.639792i	−0.382733	+	0.923859i	$0.625017\pi$
$614$	2.28193	−	21.7111i	0.0920911	−	0.876189i
$615$	−0.652704			−0.0263196
$616$		0			0
$617$	−12.4243			−0.500182			−0.250091	−	0.968222i	$-0.580461\pi$
$617$	−12.4243			−0.500182			−0.250091	+	0.968222i	$0.580461\pi$
$618$	0.288370	−	2.74366i	0.0115999	−	0.110366i
$619$	24.3165	+	27.0062i	0.977364	+	1.08547i	0.996325	+	0.0856525i	$0.0272975\pi$
$619$	24.3165	+	27.0062i	0.977364	+	1.08547i	−0.0189611	+	0.999820i	$0.506036\pi$
$620$	−7.76998	−	1.65156i	−0.312050	−	0.0663282i
$621$	21.0477	+	9.37102i	0.844613	+	0.376046i
$622$	5.24300	−	3.80926i	0.210225	−	0.152738i
$623$	−5.76088	−	7.14122i	−0.230805	−	0.286107i
$624$	4.19698	−	12.9170i	0.168014	−	0.517093i
$625$	0.678692	−	6.45732i	0.0271477	−	0.258293i
$626$	−18.2506	+	31.6110i	−0.729441	+	1.26343i
$627$		0			0
$628$	−10.4907	−	18.1704i	−0.418623	−	0.725077i
$629$	−18.9112	−	13.7398i	−0.754040	−	0.547842i
$630$	40.2411	+	20.5982i	1.60324	+	0.820654i
$631$	4.91940	+	15.1404i	0.195838	+	0.602728i	0.999966	+	0.00827144i	$0.00263291\pi$
$631$	4.91940	+	15.1404i	0.195838	+	0.602728i	−0.804127	+	0.594457i	$0.797367\pi$
$632$	9.97708	+	4.44208i	0.396867	+	0.176697i
$633$	0.593198	+	5.64390i	0.0235775	+	0.224325i
$634$	−60.3264	−	12.8228i	−2.39587	−	0.509258i
$635$	−49.1786	+	10.4532i	−1.95159	+	0.414824i
$636$	5.85277	+	4.25229i	0.232077	+	0.168614i
$637$	29.3332	+	9.65177i	1.16222	+	0.382417i
$638$		0			0
$639$	12.1763	+	21.0900i	0.481688	+	0.834309i
$640$	−22.0790	+	9.83021i	−0.872750	+	0.388573i
$641$	−8.34667	−	9.26991i	−0.329674	−	0.366140i	0.555406	−	0.831579i	$-0.312563\pi$
$641$	−8.34667	−	9.26991i	−0.329674	−	0.366140i	−0.885080	+	0.465440i	$0.845896\pi$
$642$	−9.46566	+	10.5127i	−0.373580	+	0.414902i
$643$	29.7986	−	21.6499i	1.17514	−	0.853790i	0.183525	−	0.983015i	$-0.441249\pi$
$643$	29.7986	−	21.6499i	1.17514	−	0.853790i	0.991615	+	0.129225i	$0.0412490\pi$
$644$	11.6113	+	22.8937i	0.457551	+	0.902140i
$645$	2.43037	+	7.47990i	0.0956957	+	0.294521i
$646$	−17.5154	+	3.72302i	−0.689135	+	0.146480i
$647$	18.6900	−	8.32132i	0.734779	−	0.327145i	−0.00500634	−	0.999987i	$-0.501594\pi$
$647$	18.6900	−	8.32132i	0.734779	−	0.327145i	0.739786	+	0.672843i	$0.234927\pi$
$648$	−2.35117	+	4.07234i	−0.0923626	+	0.159977i
$649$		0			0
$650$	61.9796			2.43104
$651$	−2.44732	−	0.660641i	−0.0959181	−	0.0258926i
$652$	7.76665	−	23.9033i	0.304165	−	0.936125i
$653$	−10.4113	+	11.5629i	−0.407425	+	0.452492i	−0.911581	−	0.411121i	$-0.865137\pi$
$653$	−10.4113	+	11.5629i	−0.407425	+	0.452492i	0.504155	+	0.863613i	$0.331804\pi$
$654$	1.53681	+	14.6218i	0.0600941	+	0.571757i
$655$	1.88804	+	17.9635i	0.0737717	+	0.701891i
$656$	0.893582	−	0.992423i	0.0348885	−	0.0387476i
$657$	1.86705	−	5.74618i	0.0728404	−	0.224180i
$658$	5.82054	+	21.8853i	0.226908	+	0.853179i
$659$	23.6673			0.921945			0.460973	−	0.887414i	$-0.347501\pi$
$659$	23.6673			0.921945			0.460973	+	0.887414i	$0.347501\pi$
$660$		0			0
$661$	−10.0988	+	17.4916i	−0.392798	+	0.680345i	−0.992817	−	0.119640i	$-0.961826\pi$
$661$	−10.0988	+	17.4916i	−0.392798	+	0.680345i	0.600020	+	0.799985i	$0.295159\pi$
$662$	10.9197	−	4.86175i	0.424405	−	0.188957i
$663$	14.7835	−	3.14234i	0.574145	−	0.122038i
$664$	3.07962	+	9.47809i	0.119512	+	0.367821i
$665$	−16.9382	−	0.919301i	−0.656837	−	0.0356489i
$666$	−17.4288	+	12.6627i	−0.675351	+	0.490671i
$667$	8.14128	−	9.04180i	0.315231	−	0.350100i
$668$	8.45382	+	9.38892i	0.327088	+	0.363268i
$669$	−0.132152	+	0.0588378i	−0.00510928	+	0.00227480i
$670$	−2.30541	−	3.99308i	−0.0890657	−	0.154266i
$671$		0			0
$672$	11.4645	−	4.37636i	0.442253	−	0.168822i
$673$	6.41253	+	4.65898i	0.247185	+	0.179590i	0.704478	−	0.709726i	$-0.251181\pi$
$673$	6.41253	+	4.65898i	0.247185	+	0.179590i	−0.457293	+	0.889316i	$0.651181\pi$
$674$	28.5764	−	6.07410i	1.10072	−	0.233966i
$675$	26.6033	+	5.65470i	1.02396	+	0.217649i
$676$	−1.03473	−	9.84476i	−0.0397971	−	0.378645i
$677$	−32.9392	−	14.6655i	−1.26596	−	0.563640i	−0.339700	−	0.940534i	$-0.610325\pi$
$677$	−32.9392	−	14.6655i	−1.26596	−	0.563640i	−0.926256	+	0.376894i	$0.876992\pi$
$678$	−1.89826	−	5.84225i	−0.0729023	−	0.224370i
$679$	36.1451	+	18.5016i	1.38712	+	0.710027i
$680$	−13.1899	−	9.58305i	−0.505811	−	0.367493i
$681$	−3.16550	−	5.48280i	−0.121302	−	0.210101i
$682$		0			0
$683$	6.17840	−	10.7013i	0.236410	−	0.409474i	−0.723272	−	0.690564i	$-0.757363\pi$
$683$	6.17840	−	10.7013i	0.236410	−	0.409474i	0.959681	+	0.281090i	$0.0906959\pi$
$684$	−0.748255	+	7.11917i	−0.0286102	+	0.272208i
$685$	21.5101	−	66.2014i	0.821860	−	2.52942i
$686$	12.2920	+	32.5640i	0.469312	+	1.24330i
$687$	−12.5119	+	9.09042i	−0.477358	+	0.346821i
$688$	−14.7003	−	6.54501i	−0.560445	−	0.249526i
$689$	−31.2171	−	6.63539i	−1.18928	−	0.252788i
$690$	18.3597	+	20.3906i	0.698943	+	0.776255i
$691$	−0.836228	+	7.95618i	−0.0318116	+	0.302667i	0.967035	+	0.254645i	$0.0819585\pi$
$691$	−0.836228	+	7.95618i	−0.0318116	+	0.302667i	−0.998846	+	0.0480224i	$0.984708\pi$
$692$	−29.4688			−1.12024
$693$		0			0
$694$	−37.0702			−1.40716
$695$	−1.95154	+	18.5677i	−0.0740261	+	0.704312i
$696$	−0.737897	−	0.819517i	−0.0279699	−	0.0310637i
$697$	1.45361	+	0.308974i	0.0550593	+	0.0117032i
$698$	−9.94749	−	4.42891i	−0.376518	−	0.167637i
$699$	11.0294	−	8.01334i	0.417171	−	0.303092i
$700$	19.0263	+	23.5851i	0.719126	+	0.891433i
$701$	−3.94341	+	12.1366i	−0.148940	+	0.458392i	−0.997497	−	0.0707137i	$-0.977472\pi$
$701$	−3.94341	+	12.1366i	−0.148940	+	0.458392i	0.848556	+	0.529105i	$0.177472\pi$
$702$	3.15294	−	29.9982i	0.119000	−	1.13221i
$703$	4.04189	−	7.00076i	0.152443	−	0.264039i
$704$		0			0
$705$	5.24985	+	9.09300i	0.197721	+	0.342462i
$706$	50.4276	+	36.6378i	1.89787	+	1.37888i
$707$	14.8898	−	9.63024i	0.559990	−	0.362182i
$708$	2.94797	+	9.07292i	0.110791	+	0.340981i
$709$	4.29825	+	1.91370i	0.161424	+	0.0718707i	0.485858	−	0.874038i	$-0.338507\pi$
$709$	4.29825	+	1.91370i	0.161424	+	0.0718707i	−0.324434	+	0.945908i	$0.605174\pi$
$710$	6.56484	+	62.4602i	0.246374	+	2.34409i
$711$	31.2682	+	6.64627i	1.17265	+	0.249255i
$712$	2.98299	−	0.634054i	0.111792	−	0.0237622i
$713$	7.52055	+	5.46400i	0.281647	+	0.204628i
$714$	13.2191	+	10.7454i	0.494712	+	0.402137i
$715$		0			0
$716$	1.01707	+	1.76162i	0.0380098	+	0.0658350i
$717$	−8.96202	+	3.99015i	−0.334693	+	0.149015i
$718$	5.29401	+	5.87960i	0.197571	+	0.219425i
$719$	35.2109	−	39.1057i	1.31314	−	1.45839i	0.513271	−	0.858227i	$-0.328434\pi$
$719$	35.2109	−	39.1057i	1.31314	−	1.45839i	0.799874	−	0.600168i	$-0.204900\pi$
$720$	−34.6936	+	25.2064i	−1.29295	+	0.939385i
$721$	−3.25000	+	4.98423i	−0.121036	+	0.185623i
$722$	9.12088	+	28.0712i	0.339444	+	1.04470i
$723$	18.8594	−	4.00869i	0.701390	−	0.149085i
$724$	24.7073	−	11.0004i	0.918240	−	0.408827i
$725$	7.18139	−	12.4385i	0.266710	−	0.461955i
$726$		0			0
$727$	−22.3901			−0.830404			−0.415202	−	0.909729i	$-0.636289\pi$
$727$	−22.3901			−0.830404			−0.415202	+	0.909729i	$0.636289\pi$
$728$	−7.27116	+	7.24415i	−0.269487	+	0.268486i
$729$	−2.05185	+	6.31493i	−0.0759943	+	0.233886i
$730$	10.4262	−	11.5795i	0.385891	−	0.428576i
$731$	−1.87176	−	17.8086i	−0.0692296	−	0.658676i
$732$	−0.119994	−	1.14167i	−0.00443511	−	0.0421972i
$733$	20.2183	−	22.4547i	0.746779	−	0.829383i	−0.243291	−	0.969953i	$-0.578227\pi$
$733$	20.2183	−	22.4547i	0.746779	−	0.829383i	0.990071	+	0.140571i	$0.0448937\pi$
$734$	11.2893	−	34.7450i	0.416697	−	1.28246i
$735$	9.43694	+	13.0910i	0.348087	+	0.482869i
$736$	−45.0009			−1.65876
$737$		0			0
$738$	0.684793	−	1.18610i	0.0252076	−	0.0436608i
$739$	−11.6674	+	5.19466i	−0.429192	+	0.191089i	−0.609952	−	0.792439i	$-0.708811\pi$
$739$	−11.6674	+	5.19466i	−0.429192	+	0.191089i	0.180759	+	0.983527i	$0.442145\pi$
$740$	−23.5726	+	5.01052i	−0.866547	+	0.184190i
$741$	1.61513	+	4.97087i	0.0593334	+	0.182609i
$742$	−16.2714	−	32.0819i	−0.597343	−	1.17776i
$743$	−30.3372	+	22.0413i	−1.11296	+	0.808616i	−0.983128	−	0.182919i	$-0.941445\pi$
$743$	−30.3372	+	22.0413i	−1.11296	+	0.808616i	−0.129837	+	0.991535i	$0.541445\pi$
$744$	0.563775	−	0.626136i	0.0206690	−	0.0229552i
$745$	40.2149	+	44.6631i	1.47336	+	1.63633i
$746$	21.8290	−	9.71892i	0.799218	−	0.355835i
$747$	14.5851	+	25.2622i	0.533642	+	0.924295i
$748$		0			0
$749$	28.5048	−	10.8812i	1.04154	−	0.397589i
$750$	8.67782	+	6.30481i	0.316869	+	0.230219i
$751$	−35.9808	+	7.64797i	−1.31296	+	0.279078i	−0.810610	−	0.585586i	$-0.800864\pi$
$751$	−35.9808	+	7.64797i	−1.31296	+	0.279078i	−0.502350	+	0.864665i	$0.667531\pi$
$752$	−21.0130	−	4.46645i	−0.766266	−	0.162875i
$753$	−0.257255	−	2.44762i	−0.00937491	−	0.0891963i
$754$	−14.5519	−	6.47891i	−0.529948	−	0.235948i
$755$	−1.42189	−	4.37611i	−0.0517477	−	0.159263i
$756$	12.3831	−	8.00896i	0.450369	−	0.291283i
$757$	1.83749	+	1.33501i	0.0667846	+	0.0485219i	0.620677	−	0.784067i	$-0.286858\pi$
$757$	1.83749	+	1.33501i	0.0667846	+	0.0485219i	−0.553892	+	0.832588i	$0.686858\pi$
$758$	−21.4354	−	37.1272i	−0.778569	−	1.34852i
$759$		0			0
$760$	2.81908	−	4.88279i	0.102259	−	0.177117i
$761$	1.06523	−	10.1350i	0.0386144	−	0.367392i	−0.958102	−	0.286426i	$-0.907533\pi$
$761$	1.06523	−	10.1350i	0.0386144	−	0.367392i	0.996717	−	0.0809660i	$-0.0258005\pi$
$762$	−5.39578	+	16.6065i	−0.195468	+	0.601590i
$763$	11.4191	−	29.5831i	0.413399	−	1.07098i
$764$	−19.2773	+	14.0057i	−0.697427	+	0.506710i
$765$	−43.5954	−	19.4099i	−1.57620	−	0.701767i
$766$	15.2555	+	3.24265i	0.551202	+	0.117162i
$767$	−28.1602	−	31.2750i	−1.01680	−	1.12928i
$768$	−1.41244	+	13.4385i	−0.0509670	+	0.484919i
$769$	27.7802			1.00178			0.500891	−	0.865511i	$-0.333006\pi$
$769$	27.7802			1.00178			0.500891	+	0.865511i	$0.333006\pi$
$770$		0			0
$771$	−5.65270			−0.203577
$772$	−0.835797	+	7.95208i	−0.0300810	+	0.286202i
$773$	−7.21456	−	8.01258i	−0.259490	−	0.288193i	0.599296	−	0.800528i	$-0.295447\pi$
$773$	−7.21456	−	8.01258i	−0.259490	−	0.288193i	−0.858786	+	0.512335i	$0.828781\pi$
$774$	−16.1424	−	3.43117i	−0.580225	−	0.123331i
$775$	10.0249	+	4.46336i	0.360104	+	0.160329i
$776$	−10.9186	+	7.93286i	−0.391956	+	0.284773i
$777$	−7.59802	+	1.18892i	−0.272577	+	0.0426523i
$778$	−6.62046	+	20.3757i	−0.237355	+	0.730504i
$779$	−0.0537192	+	0.511104i	−0.00192469	+	0.0183122i
$780$	7.79086	−	13.4942i	0.278958	−	0.483169i
$781$		0			0
$782$	−31.2358	−	54.1019i	−1.11699	−	1.93468i
$783$	−5.65494	−	4.10856i	−0.202091	−	0.146828i
$784$	−32.8242	−	3.57351i	−1.17229	−	0.127625i
$785$	14.9473	+	46.0031i	0.533492	+	1.64192i
$786$	5.73068	+	2.55146i	0.204407	+	0.0910077i
$787$	−2.23140	−	21.2304i	−0.0795408	−	0.756780i	−0.959496	−	0.281723i	$-0.909094\pi$
$787$	−2.23140	−	21.2304i	−0.0795408	−	0.756780i	0.879955	−	0.475057i	$-0.157573\pi$
$788$	−6.92141	−	1.47119i	−0.246565	−	0.0524090i
$789$	−3.72518	+	0.791811i	−0.132620	+	0.0281892i
$790$	66.6959	+	48.4574i	2.37293	+	1.72404i
$791$	−2.09698	+	13.0822i	−0.0745601	+	0.465151i
$792$		0			0
$793$	2.53209	+	4.38571i	0.0899171	+	0.155741i
$794$	−11.3002	+	5.03116i	−0.401028	+	0.178549i
$795$	−11.1600	−	12.3944i	−0.395803	−	0.439584i
$796$	−6.20188	+	6.88789i	−0.219820	+	0.244135i
$797$	−31.8022	+	23.1056i	−1.12649	+	0.818443i	−0.985180	−	0.171522i	$-0.945132\pi$
$797$	−31.8022	+	23.1056i	−1.12649	+	0.818443i	−0.141310	+	0.989965i	$0.545132\pi$
$798$	−3.21779	+	4.93484i	−0.113909	+	0.174691i
$799$	−7.38730	−	22.7358i	−0.261344	−	0.804333i
$800$	−51.9616	+	11.0448i	−1.83712	+	0.390492i
$801$	8.15461	−	3.63066i	0.288129	−	0.128283i
$802$	3.93717	−	6.81937i	0.139026	−	0.240800i
$803$		0			0
$804$	−0.694593			−0.0244964
$805$	−15.2105	−	57.1916i	−0.536098	−	2.01574i
$806$	3.76081	−	11.5746i	0.132469	−	0.407698i
$807$	−9.60022	+	10.6621i	−0.337944	+	0.375324i
$808$	0.616084	+	5.86165i	0.0216738	+	0.206212i
$809$	0.339363	+	3.22882i	0.0119314	+	0.113519i	0.998867	−	0.0475984i	$-0.0151568\pi$
$809$	0.339363	+	3.22882i	0.0119314	+	0.113519i	−0.986935	+	0.161118i	$0.948490\pi$
$810$	−23.7516	+	26.3788i	−0.834546	+	0.926857i
$811$	−10.3229	+	31.7706i	−0.362486	+	1.11562i	0.589054	+	0.808093i	$0.299500\pi$
$811$	−10.3229	+	31.7706i	−0.362486	+	1.11562i	−0.951540	+	0.307524i	$0.900500\pi$
$812$	−2.00167	−	7.52631i	−0.0702447	−	0.264122i
$813$	−6.43047			−0.225526
$814$		0			0
$815$	−28.9714	+	50.1799i	−1.01482	+	1.75772i
$816$	−14.7630	+	6.57292i	−0.516809	+	0.230098i
$817$	6.05721	−	1.28750i	0.211915	−	0.0450439i
$818$	0.449114	+	1.38223i	0.0157029	+	0.0483286i
$819$	−16.4092	+	25.1654i	−0.573385	+	0.879349i
$820$	1.23949	−	0.900539i	0.0432847	−	0.0314482i
$821$	16.1913	−	17.9823i	0.565082	−	0.627587i	−0.391104	−	0.920346i	$-0.627907\pi$
$821$	16.1913	−	17.9823i	0.565082	−	0.627587i	0.956186	+	0.292759i	$0.0945735\pi$
$822$	−16.1760	−	17.9653i	−0.564204	−	0.626612i
$823$	−42.6764	+	19.0008i	−1.48761	+	0.662325i	−0.979951	−	0.199236i	$-0.936154\pi$
$823$	−42.6764	+	19.0008i	−1.48761	+	0.662325i	−0.507654	+	0.861561i	$0.669487\pi$
$824$	−0.988856	−	1.71275i	−0.0344484	−	0.0596664i
$825$		0			0
$826$	7.50774	−	46.8378i	0.261228	−	1.62970i
$827$	1.53707	+	1.11674i	0.0534491	+	0.0388330i	0.614189	−	0.789159i	$-0.289483\pi$
$827$	1.53707	+	1.11674i	0.0534491	+	0.0388330i	−0.560740	+	0.827992i	$0.689483\pi$
$828$	−24.4279	+	5.19230i	−0.848927	+	0.180445i
$829$	−49.8563	−	10.5973i	−1.73158	−	0.368059i	−0.769040	−	0.639200i	$-0.779265\pi$
$829$	−49.8563	−	10.5973i	−1.73158	−	0.368059i	−0.962539	+	0.271142i	$0.912599\pi$
$830$	7.86352	+	74.8164i	0.272947	+	2.59692i
$831$	−14.0954	−	6.27567i	−0.488963	−	0.217701i
$832$	5.34556	+	16.4519i	0.185324	+	0.570369i
$833$	−14.8196	−	33.6216i	−0.513470	−	1.16492i
$834$	5.24567	+	3.81120i	0.181643	+	0.131971i
$835$	−14.5633	−	25.2244i	−0.503984	−	0.872926i
$836$		0			0
$837$	2.67024	−	4.62500i	0.0922972	−	0.159863i
$838$	2.70209	−	25.7087i	0.0933422	−	0.888092i
$839$	13.2682	−	40.8353i	0.458069	−	1.40979i	−0.409426	−	0.912343i	$-0.634271\pi$
$839$	13.2682	−	40.8353i	0.458069	−	1.40979i	0.867494	−	0.497447i	$-0.165729\pi$
$840$	−5.29935	+	0.829231i	−0.182845	+	0.0286112i
$841$	20.4752	−	14.8761i	0.706040	−	0.512968i
$842$	9.96785	+	4.43797i	0.343515	+	0.152943i
$843$	10.3882	+	2.20809i	0.357790	+	0.0760505i
$844$	−8.91341	−	9.89935i	−0.306812	−	0.340750i
$845$	−2.38546	+	22.6962i	−0.0820625	+	0.780772i
$846$	−22.0318			−0.757468
$847$		0			0
$848$	34.1239			1.17182
$849$	1.15972	−	11.0340i	0.0398016	−	0.378687i
$850$	−49.3458	−	54.8040i	−1.69255	−	1.87976i
$851$	27.5857	+	5.86353i	0.945627	+	0.200999i
$852$	8.64315	+	3.84818i	0.296109	+	0.131836i
$853$	42.3569	−	30.7741i	1.45027	−	1.05368i	0.464504	−	0.885571i	$-0.346233\pi$
$853$	42.3569	−	30.7741i	1.45027	−	1.05368i	0.985768	−	0.168113i	$-0.0537673\pi$
$854$	−2.05550	+	5.32514i	−0.0703379	+	0.182222i
$855$	5.09971	−	15.6953i	0.174406	−	0.536767i
$856$	−1.06004	+	10.0856i	−0.0362314	+	0.344719i
$857$	−0.489018	+	0.847004i	−0.0167045	+	0.0289331i	−0.874257	−	0.485464i	$-0.838651\pi$
$857$	−0.489018	+	0.847004i	−0.0167045	+	0.0289331i	0.857552	+	0.514397i	$0.171984\pi$
$858$		0			0
$859$	17.0073	+	29.4576i	0.580283	+	1.00508i	0.995446	+	0.0953319i	$0.0303912\pi$
$859$	17.0073	+	29.4576i	0.580283	+	1.00508i	−0.415163	+	0.909747i	$0.636275\pi$
$860$	−14.9353	−	10.8512i	−0.509291	−	0.370022i
$861$	0.410533	−	0.265519i	0.0139909	−	0.00904886i
$862$	−10.4572	−	32.1839i	−0.356173	−	1.09619i
$863$	−20.7334	−	9.23110i	−0.705773	−	0.314230i	0.0222795	−	0.999752i	$-0.492908\pi$
$863$	−20.7334	−	9.23110i	−0.705773	−	0.314230i	−0.728052	+	0.685521i	$0.759574\pi$
$864$	2.70237	+	25.7114i	0.0919366	+	0.874718i
$865$	66.4531	+	14.1250i	2.25947	+	0.480266i
$866$	4.30256	−	0.914537i	0.146207	−	0.0310772i
$867$	−5.57180	−	4.04815i	−0.189228	−	0.137482i
$868$	5.55896	−	2.12203i	0.188684	−	0.0720263i
$869$		0			0
$870$	−4.16220	−	7.20914i	−0.141112	−	0.244413i
$871$	2.79927	−	1.24631i	0.0948495	−	0.0422297i
$872$	7.05252	+	7.83262i	0.238829	+	0.265246i
$873$	−26.4331	+	29.3569i	−0.894624	+	0.993580i
$874$	17.4780	−	12.6985i	0.591202	−	0.429534i
$875$	−10.4647	−	20.6330i	−0.353772	−	0.697522i
$876$	−0.725354	−	2.23241i	−0.0245075	−	0.0754262i
$877$	−1.20159	+	0.255406i	−0.0405749	+	0.00862446i	−0.228154	−	0.973625i	$-0.573269\pi$
$877$	−1.20159	+	0.255406i	−0.0405749	+	0.00862446i	0.187580	+	0.982249i	$0.439936\pi$
$878$	−68.7334	+	30.6021i	−2.31964	+	1.03277i
$879$	−4.49660	+	7.78833i	−0.151666	+	0.262694i
$880$		0			0
$881$	9.13516			0.307771			0.153886	−	0.988089i	$-0.450821\pi$
$881$	9.13516			0.307771			0.153886	+	0.988089i	$0.450821\pi$
$882$	−33.6899	+	3.41425i	−1.13440	+	0.114964i
$883$	13.8519	−	42.6317i	0.466153	−	1.43467i	−0.391374	−	0.920232i	$-0.628000\pi$
$883$	13.8519	−	42.6317i	0.466153	−	1.43467i	0.857527	−	0.514440i	$-0.172000\pi$
$884$	−23.7385	+	26.3642i	−0.798411	+	0.886725i
$885$	−2.29891	−	21.8727i	−0.0772772	−	0.735243i
$886$	3.72781	+	35.4678i	0.125238	+	1.19156i
$887$	15.4019	−	17.1056i	0.517147	−	0.574350i	−0.426842	−	0.904326i	$-0.640374\pi$
$887$	15.4019	−	17.1056i	0.517147	−	0.574350i	0.943989	+	0.329976i	$0.107041\pi$
$888$	0.789888	−	2.43103i	0.0265069	−	0.0815799i
$889$	26.6797	−	26.5806i	0.894807	−	0.891484i
$890$	23.0205			0.771650
$891$		0			0
$892$	0.169778	−	0.294064i	0.00568458	−	0.00984598i
$893$	7.55241	−	3.36255i	0.252732	−	0.112523i
$894$	20.4165	−	4.33965i	0.682829	−	0.145140i
$895$	−1.44915	−	4.46002i	−0.0484397	−	0.149082i
$896$	9.88820	−	15.1647i	0.330342	−	0.506616i
$897$	−14.7520	+	10.7179i	−0.492554	+	0.357861i
$898$	39.6597	−	44.0465i	1.32346	−	1.46985i
$899$	−1.88712	−	2.09586i	−0.0629390	−	0.0699009i
$900$	−26.9320	+	11.9909i	−0.897732	+	0.399696i
$901$	18.9866	+	32.8858i	0.632536	+	1.09559i
$902$		0			0
$903$	−4.57145	−	3.71599i	−0.152128	−	0.123661i
$904$	−3.56270	−	2.58845i	−0.118493	−	0.0860906i
$905$	−60.9884	+	12.9635i	−2.02732	+	0.430921i
$906$	−1.56310	−	0.332247i	−0.0519305	−	0.0110382i
$907$	2.96034	+	28.1657i	0.0982964	+	0.935228i	0.926879	+	0.375361i	$0.122481\pi$
$907$	2.96034	+	28.1657i	0.0982964	+	0.935228i	−0.828582	+	0.559867i	$0.810852\pi$
$908$	13.5759	+	6.04440i	0.450533	+	0.200590i
$909$	5.33106	+	16.4073i	0.176820	+	0.544196i
$910$	−65.0572	+	42.0767i	−2.15662	+	1.39483i
$911$	−2.40760	−	1.74922i	−0.0797673	−	0.0579544i	0.547187	−	0.837010i	$-0.315699\pi$
$911$	−2.40760	−	1.74922i	−0.0797673	−	0.0579544i	−0.626954	+	0.779056i	$0.715699\pi$
$912$	−2.79426	−	4.83981i	−0.0925273	−	0.160262i
$913$		0			0
$914$	−10.9179	+	18.9103i	−0.361131	+	0.625497i
$915$	−0.276635	+	2.63201i	−0.00914528	+	0.0870115i
$916$	11.2180	−	34.5255i	0.370653	−	1.14075i
$917$	−8.49504	−	10.5305i	−0.280531	−	0.347748i
$918$	−29.0355	+	21.0955i	−0.958313	+	0.696255i
$919$	−19.9097	−	8.86436i	−0.656760	−	0.292408i	0.0511713	−	0.998690i	$-0.483705\pi$
$919$	−19.9097	−	8.86436i	−0.656760	−	0.292408i	−0.707931	+	0.706282i	$0.750371\pi$
$920$	19.2401	+	4.08961i	0.634327	+	0.134830i
$921$	5.07316	+	5.63432i	0.167166	+	0.185657i
$922$	2.54965	−	24.2583i	0.0839681	−	0.798903i
$923$	−41.7374			−1.37380
$924$		0			0
$925$	33.2918			1.09463
$926$	6.94851	−	66.1107i	0.228342	−	2.17253i
$927$	−3.87346	−	4.30192i	−0.127221	−	0.141293i
$928$	13.3544	+	2.83856i	0.438378	+	0.0931802i
$929$	33.8607	+	15.0757i	1.11093	+	0.494619i	0.878379	−	0.477965i	$-0.158625\pi$
$929$	33.8607	+	15.0757i	1.11093	+	0.494619i	0.232553	+	0.972584i	$0.425292\pi$
$930$	5.14542	−	3.73837i	0.168725	−	0.122586i
$931$	11.0277	−	6.31223i	0.361417	−	0.206875i
$932$	−9.88883	+	30.4347i	−0.323919	+	0.996922i
$933$	−0.235265	+	2.23840i	−0.00770222	+	0.0732818i
$934$	−37.4616	+	64.8853i	−1.22578	+	2.12311i
$935$		0			0
$936$	−4.99273	−	8.64766i	−0.163192	−	0.282657i
$937$	32.2264	+	23.4138i	1.05279	+	0.764896i	0.972741	−	0.231894i	$-0.0744924\pi$
$937$	32.2264	+	23.4138i	1.05279	+	0.764896i	0.0800487	+	0.996791i	$0.474492\pi$
$938$	3.07442	+	1.57371i	0.100383	+	0.0513834i
$939$	−3.91733	−	12.0563i	−0.127837	−	0.393443i
$940$	−22.5151	−	10.0244i	−0.734363	−	0.326960i
$941$	1.43119	+	13.6169i	0.0466556	+	0.443898i	0.992767	+	0.120057i	$0.0383077\pi$
$941$	1.43119	+	13.6169i	0.0466556	+	0.443898i	−0.946111	+	0.323841i	$0.895026\pi$
$942$	16.4318	+	3.49269i	0.535377	+	0.113798i
$943$	−1.75374	+	0.372769i	−0.0571096	+	0.0121390i
$944$	36.4043	+	26.4493i	1.18486	+	0.860852i
$945$	−31.7631	+	12.1250i	−1.03325	+	0.394425i
$946$		0			0
$947$	23.5667	+	40.8187i	0.765815	+	1.32643i	0.939815	+	0.341685i	$0.110998\pi$
$947$	23.5667	+	40.8187i	0.765815	+	1.32643i	−0.174000	+	0.984746i	$0.555669\pi$
$948$	11.3455	−	5.05135i	0.368485	−	0.164060i
$949$	6.92887	+	7.69529i	0.224921	+	0.249800i
$950$	17.0648	−	18.9524i	0.553656	−	0.614898i
$951$	17.3285	−	12.5899i	0.561915	−	0.408255i
$952$	12.1945	+	0.661840i	0.395226	+	0.0214504i
$953$	8.31224	+	25.5825i	0.269260	+	0.828697i	0.990681	+	0.136201i	$0.0434892\pi$
$953$	8.31224	+	25.5825i	0.269260	+	0.828697i	−0.721421	+	0.692496i	$0.756511\pi$
$954$	34.2317	−	7.27618i	1.10829	−	0.235575i
$955$	50.1840	−	22.3434i	1.62392	−	0.723014i
$956$	11.5137	−	19.9423i	0.372379	−	0.644979i
$957$		0			0
$958$	−57.0958			−1.84468
$959$	13.4013	+	50.3892i	0.432751	+	1.62715i
$960$	−2.79356	+	8.59768i	−0.0901616	+	0.277489i
$961$	−19.3012	+	21.4362i	−0.622620	+	0.691490i
$962$	−3.85942	−	36.7199i	−0.124433	−	1.18390i
$963$	3.10275	+	29.5207i	0.0999849	+	0.951292i
$964$	−30.2833	+	33.6330i	−0.975359	+	1.08325i
$965$	5.69635	−	17.5316i	0.183372	−	0.564361i
$966$	−19.8426	−	5.35641i	−0.638427	−	0.172340i
$967$	39.4270			1.26789			0.633943	−	0.773380i	$-0.281435\pi$
$967$	39.4270			1.26789			0.633943	+	0.773380i	$0.281435\pi$
$968$		0			0
$969$	3.10947	−	5.38576i	0.0998906	−	0.173016i
$970$	−93.0699	+	41.4374i	−2.98830	+	1.33048i
$971$	−15.7300	+	3.34351i	−0.504800	+	0.107298i	−0.453270	−	0.891373i	$-0.649743\pi$
$971$	−15.7300	+	3.34351i	−0.504800	+	0.107298i	−0.0515291	+	0.998671i	$0.516409\pi$
$972$	6.81977	+	20.9891i	0.218744	+	0.673225i
$973$	−6.32583	−	12.4725i	−0.202797	−	0.399849i
$974$	−15.8600	+	11.5229i	−0.508186	+	0.369219i
$975$	−14.4032	+	15.9964i	−0.461272	+	0.512295i
$976$	−3.62319	−	4.02396i	−0.115975	−	0.128804i
$977$	25.0566	−	11.1559i	0.801632	−	0.356910i	0.0353185	−	0.999376i	$-0.488755\pi$
$977$	25.0566	−	11.1559i	0.801632	−	0.356910i	0.766314	+	0.642466i	$0.222089\pi$
$978$	10.0617	+	17.4273i	0.321736	+	0.557263i
$979$		0			0
$980$	−35.9825	−	11.8396i	−1.14942	−	0.378204i
$981$	24.9584	+	18.1333i	0.796861	+	0.578953i
$982$	18.8911	−	4.01543i	0.602840	−	0.128137i
$983$	7.30300	+	1.55230i	0.232930	+	0.0495107i	0.322897	−	0.946434i	$-0.395343\pi$
$983$	7.30300	+	1.55230i	0.232930	+	0.0495107i	−0.0899679	+	0.995945i	$0.528676\pi$
$984$	0.0169863	+	0.161614i	0.000541503	+	0.00515205i
$985$	14.9028	+	6.63516i	0.474843	+	0.211414i
$986$	5.85682	+	18.0254i	0.186519	+	0.574047i
$987$	−7.00104	−	3.58363i	−0.222845	−	0.114068i
$988$	−9.92548	−	7.21128i	−0.315772	−	0.229422i
$989$	10.8020	+	18.7096i	0.343484	+	0.594931i
$990$		0			0
$991$	12.1352	−	21.0188i	0.385488	−	0.667685i	−0.606349	−	0.795199i	$-0.707366\pi$
$991$	12.1352	−	21.0188i	0.385488	−	0.667685i	0.991837	+	0.127514i	$0.0406998\pi$
$992$	−1.09034	+	10.3739i	−0.0346185	+	0.329373i
$993$	−1.28281	+	3.94808i	−0.0407087	+	0.125288i
$994$	−29.5378	−	36.6153i	−0.936883	−	1.16137i
$995$	17.2869	−	12.5597i	0.548033	−	0.398169i
$996$	10.3530	+	4.60944i	0.328047	+	0.146056i
$997$	−32.3925	−	6.88524i	−1.02588	−	0.218058i	−0.335909	−	0.941894i	$-0.609044\pi$
$997$	−32.3925	−	6.88524i	−1.02588	−	0.218058i	−0.689971	+	0.723837i	$0.742377\pi$
$998$	45.9240	+	51.0037i	1.45370	+	1.61449i
$999$	1.69357	−	16.1133i	0.0535823	−	0.509801i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	847.2.n.f.81.3		24
7.2	even	3	inner	847.2.n.f.807.1		24
11.2	odd	10		847.2.n.g.753.3		24
11.3	even	5	inner	847.2.n.f.487.1		24
11.4	even	5	inner	847.2.n.f.130.3		24
11.5	even	5		847.2.e.c.606.3		6
11.6	odd	10		77.2.e.a.67.1	yes	6
11.7	odd	10		847.2.n.g.130.1		24
11.8	odd	10		847.2.n.g.487.3		24
11.9	even	5	inner	847.2.n.f.753.1		24
11.10	odd	2		847.2.n.g.81.1		24
33.17	even	10		693.2.i.h.298.3		6
44.39	even	10		1232.2.q.m.529.2		6
77.2	odd	30		847.2.n.g.632.1		24
77.6	even	10		539.2.e.m.67.1		6
77.9	even	15	inner	847.2.n.f.632.3		24
77.16	even	15		847.2.e.c.485.3		6
77.17	even	30		539.2.a.g.1.3		3
77.30	odd	30		847.2.n.g.366.1		24
77.37	even	15	inner	847.2.n.f.9.1		24
77.38	odd	30		5929.2.a.u.1.1		3
77.39	odd	30		539.2.a.j.1.3		3
77.51	odd	30		847.2.n.g.9.3		24
77.58	even	15	inner	847.2.n.f.366.3		24
77.60	even	15		5929.2.a.x.1.1		3
77.61	even	30		539.2.e.m.177.1		6
77.65	odd	6		847.2.n.g.807.3		24
77.72	odd	30		77.2.e.a.23.1	✓	6
231.17	odd	30		4851.2.a.bk.1.1		3
231.116	even	30		4851.2.a.bj.1.1		3
231.149	even	30		693.2.i.h.100.3		6
308.39	even	30		8624.2.a.ch.1.2		3
308.171	odd	30		8624.2.a.co.1.2		3
308.303	even	30		1232.2.q.m.177.2		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
77.2.e.a.23.1	✓	6	77.72	odd	30
77.2.e.a.67.1	yes	6	11.6	odd	10
539.2.a.g.1.3		3	77.17	even	30
539.2.a.j.1.3		3	77.39	odd	30
539.2.e.m.67.1		6	77.6	even	10
539.2.e.m.177.1		6	77.61	even	30
693.2.i.h.100.3		6	231.149	even	30
693.2.i.h.298.3		6	33.17	even	10
847.2.e.c.485.3		6	77.16	even	15
847.2.e.c.606.3		6	11.5	even	5
847.2.n.f.9.1		24	77.37	even	15	inner
847.2.n.f.81.3		24	1.1	even	1	trivial
847.2.n.f.130.3		24	11.4	even	5	inner
847.2.n.f.366.3		24	77.58	even	15	inner
847.2.n.f.487.1		24	11.3	even	5	inner
847.2.n.f.632.3		24	77.9	even	15	inner
847.2.n.f.753.1		24	11.9	even	5	inner
847.2.n.f.807.1		24	7.2	even	3	inner
847.2.n.g.9.3		24	77.51	odd	30
847.2.n.g.81.1		24	11.10	odd	2
847.2.n.g.130.1		24	11.7	odd	10
847.2.n.g.366.1		24	77.30	odd	30
847.2.n.g.487.3		24	11.8	odd	10
847.2.n.g.632.1		24	77.2	odd	30
847.2.n.g.753.3		24	11.2	odd	10
847.2.n.g.807.3		24	77.65	odd	6
1232.2.q.m.177.2		6	308.303	even	30
1232.2.q.m.529.2		6	44.39	even	10
4851.2.a.bj.1.1		3	231.116	even	30
4851.2.a.bk.1.1		3	231.17	odd	30
5929.2.a.u.1.1		3	77.38	odd	30
5929.2.a.x.1.1		3	77.60	even	15
8624.2.a.ch.1.2		3	308.39	even	30
8624.2.a.co.1.2		3	308.171	odd	30

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:	\( N \)	\(=\)	\( 847 = 7 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	847.n (of order \(15\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.196449 - 1.86909i) q^{2} +(0.436744 + 0.485053i) q^{3} +(-1.49861 - 0.318539i) q^{4} +(3.22672 + 1.43663i) q^{5} +(0.992406 - 0.721025i) q^{6} +(-2.61394 + 0.409024i) q^{7} +(0.271745 - 0.836345i) q^{8} +(0.269054 - 2.55988i) q^{9} +(3.31908 - 5.74881i) q^{10} +(-0.500000 - 0.866025i) q^{12} +(3.56896 + 2.59300i) q^{13} +(0.250995 + 4.96605i) q^{14} +(0.712410 + 2.19257i) q^{15} +(-4.30909 - 1.91853i) q^{16} +(-0.548667 - 5.22022i) q^{17} +(-4.73179 - 1.00577i) q^{18} +(1.77554 - 0.377403i) q^{19} +(-4.37797 - 3.18078i) q^{20} +(-1.34002 - 1.08926i) q^{21} +(3.16637 + 5.48432i) q^{23} +(0.524355 - 0.233458i) q^{24} +(5.00219 + 5.55549i) q^{25} +(5.54767 - 6.16131i) q^{26} +(2.94333 - 2.13845i) q^{27} +(4.04757 + 0.219677i) q^{28} +(-0.593706 - 1.82724i) q^{29} +(4.23807 - 0.900829i) q^{30} +(1.34100 - 0.597053i) q^{31} +(-3.55303 + 6.15403i) q^{32} -9.86484 q^{34} +(-9.02209 - 2.43546i) q^{35} +(-1.21863 + 3.75055i) q^{36} +(2.97988 - 3.30949i) q^{37} +(-0.356596 - 3.39279i) q^{38} +(0.300978 + 2.86361i) q^{39} +(2.07836 - 2.30826i) q^{40} +(-0.0874885 + 0.269262i) q^{41} +(-2.29918 + 2.29064i) q^{42} +3.41147 q^{43} +(4.54576 - 7.87349i) q^{45} +(10.8727 - 4.84085i) q^{46} +(4.45485 - 0.946908i) q^{47} +(-0.951379 - 2.92804i) q^{48} +(6.66540 - 2.13833i) q^{49} +(11.3664 - 8.25817i) q^{50} +(2.29246 - 2.54603i) q^{51} +(-4.52250 - 5.02275i) q^{52} +(-6.60897 + 2.94250i) q^{53} +(-3.41875 - 5.92145i) q^{54} +(-0.368241 + 2.29731i) q^{56} +(0.958517 + 0.696404i) q^{57} +(-3.53191 + 0.750731i) q^{58} +(-9.33136 - 1.98344i) q^{59} +(-0.369204 - 3.51274i) q^{60} +(1.04871 + 0.466916i) q^{61} +(-0.852507 - 2.62375i) q^{62} +(0.343759 + 6.80142i) q^{63} +(3.17238 + 2.30487i) q^{64} +(7.79086 + 13.4942i) q^{65} +(0.347296 - 0.601535i) q^{67} +(-0.840606 + 7.99783i) q^{68} +(-1.27729 + 3.93110i) q^{69} +(-6.32448 + 16.3846i) q^{70} +(-7.65419 + 5.56110i) q^{71} +(-2.06783 - 0.920656i) q^{72} +(2.29600 + 0.488030i) q^{73} +(-5.60035 - 6.21981i) q^{74} +(-0.510035 + 4.85266i) q^{75} -2.78106 q^{76} +5.41147 q^{78} +(-1.29816 + 12.3512i) q^{79} +(-11.1480 - 12.3811i) q^{80} +(-5.23045 - 1.11177i) q^{81} +(0.486087 + 0.216420i) q^{82} +(-9.16839 + 6.66122i) q^{83} +(1.66120 + 2.05923i) q^{84} +(5.72912 - 17.6324i) q^{85} +(0.670182 - 6.37635i) q^{86} +(0.627011 - 1.08602i) q^{87} +(1.73396 + 3.00330i) q^{89} +(-13.8232 - 10.0432i) q^{90} +(-10.3897 - 5.31816i) q^{91} +(-2.99819 - 9.22747i) q^{92} +(0.875278 + 0.389699i) q^{93} +(-0.894704 - 8.51254i) q^{94} +(6.27137 + 1.33302i) q^{95} +(-4.53680 + 0.964327i) q^{96} +(-12.4162 - 9.02091i) q^{97} +(-2.68732 - 12.8783i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 3 q^{3} + 6 q^{5} - 6 q^{6} + 6 q^{8} + 12 q^{10} - 12 q^{12} + 6 q^{13} + 12 q^{14} - 18 q^{15} - 6 q^{16} + 3 q^{17} + 12 q^{18} - 9 q^{19} - 12 q^{20} + 48 q^{21} - 6 q^{24} + 3 q^{25} + 9 q^{26}+ \cdots + 24 q^{98}+O(q^{100}) \) 24 * q + 3 * q^3 + 6 * q^5 - 6 * q^6 + 6 * q^8 + 12 * q^10 - 12 * q^12 + 6 * q^13 + 12 * q^14 - 18 * q^15 - 6 * q^16 + 3 * q^17 + 12 * q^18 - 9 * q^19 - 12 * q^20 + 48 * q^21 - 6 * q^24 + 3 * q^25 + 9 * q^26 - 12 * q^27 + 3 * q^28 - 6 * q^29 + 6 * q^30 + 9 * q^31 - 36 * q^32 - 48 * q^34 - 15 * q^35 - 6 * q^36 - 3 * q^39 - 3 * q^40 + 18 * q^41 + 18 * q^42 - 12 * q^45 + 24 * q^46 - 3 * q^47 + 36 * q^48 + 30 * q^50 + 18 * q^51 - 9 * q^52 + 9 * q^53 - 72 * q^54 + 12 * q^56 + 15 * q^58 + 6 * q^60 - 12 * q^61 - 6 * q^62 + 6 * q^63 + 6 * q^64 + 60 * q^65 + 21 * q^68 - 42 * q^69 - 45 * q^70 + 18 * q^71 - 12 * q^72 - 6 * q^73 - 18 * q^74 + 9 * q^75 + 72 * q^76 + 48 * q^78 + 3 * q^79 - 27 * q^80 + 15 * q^81 - 3 * q^82 - 30 * q^83 - 54 * q^85 - 9 * q^86 - 96 * q^87 + 60 * q^89 - 72 * q^90 - 9 * q^91 + 6 * q^92 + 6 * q^93 - 9 * q^95 - 3 * q^96 - 90 * q^97 + 24 * q^98

Introduction

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