LMFDB - Embedded newform 847.2.n.f.807.1

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			807.1
Character	$\chi$	$=$	847.807
Dual form			847.2.n.f.487.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.71690 + 0.764415i) q^{2} +(-0.638441 + 0.135705i) q^{3} +(1.02517 - 1.13856i) q^{4} +(-0.369204 - 3.51274i) q^{5} +(0.992406 - 0.721025i) q^{6} +(2.35514 - 1.20553i) q^{7} +(0.271745 - 0.836345i) q^{8} +(-2.35145 + 1.04693i) q^{9} +(3.31908 + 5.74881i) q^{10} +(-0.500000 + 0.866025i) q^{12} +(3.56896 + 2.59300i) q^{13} +(-3.12203 + 3.87009i) q^{14} +(0.712410 + 2.19257i) q^{15} +(0.493048 + 4.69104i) q^{16} +(4.79517 + 2.13495i) q^{17} +(3.23692 - 3.59496i) q^{18} +(-1.21461 - 1.34896i) q^{19} +(-4.37797 - 3.18078i) q^{20} +(-1.34002 + 1.08926i) q^{21} +(3.16637 - 5.48432i) q^{23} +(-0.0599970 + 0.570834i) q^{24} +(-7.31229 + 1.55428i) q^{25} +(-8.10968 - 1.72377i) q^{26} +(2.94333 - 2.13845i) q^{27} +(1.04184 - 3.91735i) q^{28} +(-0.593706 - 1.82724i) q^{29} +(-2.89917 - 3.21986i) q^{30} +(-0.153438 + 1.45987i) q^{31} +(-3.55303 - 6.15403i) q^{32} -9.86484 q^{34} +(-5.10424 - 7.82792i) q^{35} +(-1.21863 + 3.75055i) q^{36} +(-4.35605 - 0.925906i) q^{37} +(3.11654 + 1.38757i) q^{38} +(-2.63045 - 1.17115i) q^{39} +(-3.03819 - 0.645788i) q^{40} +(-0.0874885 + 0.269262i) q^{41} +(1.46804 - 2.89449i) q^{42} +3.41147 q^{43} +(4.54576 + 7.87349i) q^{45} +(-1.24406 + 11.8365i) q^{46} +(-3.04747 - 3.38456i) q^{47} +(-0.951379 - 2.92804i) q^{48} +(4.09339 - 5.67839i) q^{49} +(11.3664 - 8.25817i) q^{50} +(-3.35116 - 0.712310i) q^{51} +(6.61108 - 1.40523i) q^{52} +(0.756203 - 7.19479i) q^{53} +(-3.41875 + 5.92145i) q^{54} +(-0.368241 - 2.29731i) q^{56} +(0.958517 + 0.696404i) q^{57} +(2.41611 + 2.68336i) q^{58} +(6.38339 - 7.08948i) q^{59} +(3.22672 + 1.43663i) q^{60} +(-0.119994 - 1.14167i) q^{61} +(-0.852507 - 2.62375i) q^{62} +(-4.27588 + 5.30041i) q^{63} +(3.17238 + 2.30487i) q^{64} +(7.79086 - 13.4942i) q^{65} +(0.347296 + 0.601535i) q^{67} +(7.34663 - 3.27093i) q^{68} +(-1.27729 + 3.93110i) q^{69} +(14.7473 + 9.53802i) q^{70} +(-7.65419 + 5.56110i) q^{71} +(0.236602 + 2.25112i) q^{72} +(-1.57065 + 1.74438i) q^{73} +(8.18669 - 1.74013i) q^{74} +(4.45754 - 1.98462i) q^{75} -2.78106 q^{76} +5.41147 q^{78} +(11.3455 - 5.05135i) q^{79} +(16.2964 - 3.46390i) q^{80} +(3.57804 - 3.97382i) q^{81} +(-0.0556184 - 0.529174i) q^{82} +(-9.16839 + 6.66122i) q^{83} +(-0.133552 + 2.64238i) q^{84} +(5.72912 - 17.6324i) q^{85} +(-5.85717 + 2.60778i) q^{86} +(0.627011 + 1.08602i) q^{87} +(1.73396 - 3.00330i) q^{89} +(-13.8232 - 10.0432i) q^{90} +(11.5313 + 1.80440i) q^{91} +(-2.99819 - 9.22747i) q^{92} +(-0.100150 - 0.952862i) q^{93} +(7.81943 + 3.48143i) q^{94} +(-4.29011 + 4.76465i) q^{95} +(3.10353 + 3.44682i) 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 $\left(\mathbb{Z}/847\mathbb{Z}\right)^\times$.

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

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 $

$2$	−1.71690	+	0.764415i	−1.21403	+	0.540523i	−0.910980	−	0.412450i	$-0.864673\pi$
$2$	−1.71690	+	0.764415i	−1.21403	+	0.540523i	−0.303054	+	0.952973i	$0.598006\pi$
$3$	−0.638441	+	0.135705i	−0.368604	+	0.0783492i	−0.388490	−	0.921453i	$-0.627003\pi$
$3$	−0.638441	+	0.135705i	−0.368604	+	0.0783492i	0.0198858	+	0.999802i	$0.493670\pi$
$4$	1.02517	−	1.13856i	0.512584	−	0.569282i
$5$	−0.369204	−	3.51274i	−0.165113	−	1.57094i	−0.692562	−	0.721358i	$-0.743518\pi$
$5$	−0.369204	−	3.51274i	−0.165113	−	1.57094i	0.527449	−	0.849587i	$-0.323149\pi$
$6$	0.992406	−	0.721025i	0.405148	−	0.294357i
$7$	2.35514	−	1.20553i	0.890160	−	0.455648i
$7$	2.35514	−	1.20553i	0.890160	−	0.455648i
$8$	0.271745	−	0.836345i	0.0960764	−	0.295693i
$9$	−2.35145	+	1.04693i	−0.783815	+	0.348977i
$10$	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	$0.490461\pi$
$14$	−3.12203	+	3.87009i	−0.834397	+	1.03432i
$15$	0.712410	+	2.19257i	0.183943	+	0.566120i
$16$	0.493048	+	4.69104i	0.123262	+	1.17276i
$17$	4.79517	+	2.13495i	1.16300	+	0.517801i	0.895196	−	0.445672i	$-0.147035\pi$
$17$	4.79517	+	2.13495i	1.16300	+	0.517801i	0.267804	+	0.963473i	$0.413702\pi$
$18$	3.23692	−	3.59496i	0.762949	−	0.847340i
$19$	−1.21461	−	1.34896i	−0.278651	−	0.309473i	0.587531	−	0.809201i	$-0.300100\pi$
$19$	−1.21461	−	1.34896i	−0.278651	−	0.309473i	−0.866182	+	0.499728i	$0.833433\pi$
$20$	−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	−0.320319	−	0.947310i	$-0.603790\pi$
$23$	3.16637	−	5.48432i	0.660235	−	1.14356i	0.980554	−	0.196250i	$-0.0628765\pi$
$24$	−0.0599970	+	0.570834i	−0.0122468	+	0.116521i
$25$	−7.31229	+	1.55428i	−1.46246	+	0.310855i
$26$	−8.10968	−	1.72377i	−1.59044	−	0.338058i
$27$	2.94333	−	2.13845i	0.566444	−	0.411546i
$28$	1.04184	−	3.91735i	0.196890	−	0.740310i
$29$	−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	$0.957088\pi$
$30$	−2.89917	−	3.21986i	−0.529314	−	0.587863i
$31$	−0.153438	+	1.45987i	−0.0275584	+	0.262200i	0.972064	+	0.234716i	$0.0754162\pi$
$31$	−0.153438	+	1.45987i	−0.0275584	+	0.262200i	−0.999622	+	0.0274839i	$0.991251\pi$
$32$	−3.55303	−	6.15403i	−0.628094	−	1.08789i
$33$		0			0
$34$	−9.86484			−1.69181
$35$	−5.10424	−	7.82792i	−0.862774	−	1.32316i
$36$	−1.21863	+	3.75055i	−0.203105	+	0.625092i
$37$	−4.35605	−	0.925906i	−0.716130	−	0.152218i	−0.164584	−	0.986363i	$-0.552628\pi$
$37$	−4.35605	−	0.925906i	−0.716130	−	0.152218i	−0.551545	+	0.834145i	$0.685962\pi$
$38$	3.11654	+	1.38757i	0.505569	+	0.225094i
$39$	−2.63045	−	1.17115i	−0.421209	−	0.187534i
$40$	−3.03819	−	0.645788i	−0.480380	−	0.102108i
$41$	−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	$0.107038\pi$
$42$	1.46804	−	2.89449i	0.226524	−	0.446630i
$43$	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
$46$	−1.24406	+	11.8365i	−0.183427	+	1.74519i
$47$	−3.04747	−	3.38456i	−0.444520	−	0.493689i	0.478691	−	0.877983i	$-0.341111\pi$
$47$	−3.04747	−	3.38456i	−0.444520	−	0.493689i	−0.923211	+	0.384294i	$0.874445\pi$
$48$	−0.951379	−	2.92804i	−0.137320	−	0.422626i
$49$	4.09339	−	5.67839i	0.584771	−	0.811199i
$50$	11.3664	−	8.25817i	1.60745	−	1.16788i
$51$	−3.35116	−	0.712310i	−0.469256	−	0.0997434i
$52$	6.61108	−	1.40523i	0.916791	−	0.194870i
$53$	0.756203	−	7.19479i	0.103872	−	0.988281i	−0.811139	−	0.584853i	$-0.801152\pi$
$53$	0.756203	−	7.19479i	0.103872	−	0.988281i	0.915012	−	0.403427i	$-0.132181\pi$
$54$	−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
$58$	2.41611	+	2.68336i	0.317250	+	0.352342i
$59$	6.38339	−	7.08948i	0.831047	−	0.922971i	−0.166967	−	0.985962i	$-0.553397\pi$
$59$	6.38339	−	7.08948i	0.831047	−	0.922971i	0.998014	+	0.0629914i	$0.0200641\pi$
$60$	3.22672	+	1.43663i	0.416568	+	0.185468i
$61$	−0.119994	−	1.14167i	−0.0153637	−	0.146176i	0.984151	−	0.177334i	$-0.0567471\pi$
$61$	−0.119994	−	1.14167i	−0.0153637	−	0.146176i	−0.999514	+	0.0311581i	$0.990080\pi$
$62$	−0.852507	−	2.62375i	−0.108268	−	0.333216i
$63$	−4.27588	+	5.30041i	−0.538711	+	0.667789i
$64$	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	0.886460	−	0.462805i	$-0.153157\pi$
$67$	0.347296	+	0.601535i	0.0424290	+	0.0734892i	−0.844031	+	0.536294i	$0.819824\pi$
$68$	7.34663	−	3.27093i	0.890910	−	0.396659i
$69$	−1.27729	+	3.93110i	−0.153768	+	0.473249i
$70$	14.7473	+	9.53802i	1.76264	+	1.14001i
$71$	−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	$0.489742\pi$
$72$	0.236602	+	2.25112i	0.0278838	+	0.265297i
$73$	−1.57065	+	1.74438i	−0.183830	+	0.204164i	−0.828015	−	0.560705i	$-0.810530\pi$
$73$	−1.57065	+	1.74438i	−0.183830	+	0.204164i	0.644185	+	0.764870i	$0.277197\pi$
$74$	8.18669	−	1.74013i	0.951683	−	0.202287i
$75$	4.45754	−	1.98462i	0.514712	−	0.229165i
$76$	−2.78106			−0.319009
$77$		0			0
$78$	5.41147			0.612729
$79$	11.3455	−	5.05135i	1.27647	−	0.568321i	0.347224	−	0.937782i	$-0.387124\pi$
$79$	11.3455	−	5.05135i	1.27647	−	0.568321i	0.929246	+	0.369461i	$0.120458\pi$
$80$	16.2964	−	3.46390i	1.82199	−	0.387276i
$81$	3.57804	−	3.97382i	0.397560	−	0.441535i
$82$	−0.0556184	−	0.529174i	−0.00614203	−	0.0584375i
$83$	−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	$0.513666\pi$
$84$	−0.133552	+	2.64238i	−0.0145717	+	0.288307i
$85$	5.72912	−	17.6324i	0.621411	−	1.91251i
$86$	−5.85717	+	2.60778i	−0.631595	+	0.281204i
$87$	0.627011	+	1.08602i	0.0672227	+	0.116433i
$88$		0			0
$89$	1.73396	−	3.00330i	0.183799	−	0.318349i	−0.759372	−	0.650656i	$-0.774494\pi$
$89$	1.73396	−	3.00330i	0.183799	−	0.318349i	0.943171	+	0.332307i	$0.107827\pi$
$90$	−13.8232	−	10.0432i	−1.45710	−	1.05864i
$91$	11.5313	+	1.80440i	1.20881	+	0.189152i
$92$	−2.99819	−	9.22747i	−0.312582	−	0.962030i
$93$	−0.100150	−	0.952862i	−0.0103851	−	0.0988072i
$94$	7.81943	+	3.48143i	0.806512	+	0.359082i
$95$	−4.29011	+	4.76465i	−0.440156	+	0.488843i
$96$	3.10353	+	3.44682i	0.316753	+	0.351790i
$97$	−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
$101$	0.700585	−	6.66562i	0.0697108	−	0.663254i	−0.902747	−	0.430173i	$-0.858453\pi$
$101$	0.700585	−	6.66562i	0.0697108	−	0.663254i	0.972457	−	0.233081i	$-0.0748807\pi$
$102$	6.29811	−	1.33870i	0.623606	−	0.132552i
$103$	−2.19982	−	0.467587i	−0.216755	−	0.0460727i	0.0982540	−	0.995161i	$-0.468674\pi$
$103$	−2.19982	−	0.467587i	−0.216755	−	0.0460727i	−0.315009	+	0.949089i	$0.602008\pi$
$104$	3.13849	−	2.28025i	0.307754	−	0.223596i
$105$	4.32104	+	4.30499i	0.421690	+	0.420124i
$106$	4.20148	+	12.9308i	0.408084	+	1.25595i
$107$	7.71647	+	8.57001i	0.745980	+	0.828494i	0.989969	−	0.141284i	$-0.0451229\pi$
$107$	7.71647	+	8.57001i	0.745980	+	0.828494i	−0.243990	+	0.969778i	$0.578456\pi$
$108$	0.582639	−	5.54344i	0.0560645	−	0.533418i
$109$	−5.99273	−	10.3797i	−0.573999	−	0.994196i	−0.996150	−	0.0876698i	$-0.972058\pi$
$109$	−5.99273	−	10.3797i	−0.573999	−	0.994196i	0.422151	−	0.906526i	$-0.361275\pi$
$110$		0			0
$111$	2.90673			0.275894
$112$	6.81639	+	10.4537i	0.644088	+	0.987781i
$113$	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	$0.0243127\pi$
$114$	−2.17802	−	0.462953i	−0.203991	−	0.0433595i
$115$	−20.4340	−	9.09782i	−1.90548	−	0.848376i
$116$	−2.68908	−	1.19725i	−0.249675	−	0.111162i
$117$	−11.1069	−	2.36084i	−1.02683	−	0.218260i
$118$	−5.54037	+	17.0515i	−0.510032	+	1.56972i
$119$	13.8671	−	0.752617i	1.27119	−	0.0689922i
$120$	2.02734			0.185070
$121$		0			0
$122$	1.07873	+	1.86841i	0.0976632	+	0.169158i
$123$	0.0193161	−	0.183780i	0.00174167	−	0.0165709i
$124$	1.50485	+	1.67131i	0.135140	+	0.150088i
$125$	2.70211	+	8.31625i	0.241684	+	0.743828i
$126$	3.28957	−	12.3688i	0.293058	−	1.10190i
$127$	−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	$0.517581\pi$
$128$	6.69302	+	1.42265i	0.591585	+	0.125745i
$129$	−2.17802	+	0.462953i	−0.191764	+	0.0407608i
$130$	−3.06102	+	29.1236i	−0.268469	+	2.55431i
$131$	2.55690	−	4.42869i	0.223398	−	0.386936i	−0.732440	−	0.680832i	$-0.761618\pi$
$131$	2.55690	−	4.42869i	0.223398	−	0.386936i	0.955838	+	0.293896i	$0.0949518\pi$
$132$		0			0
$133$	−4.48680	−	1.71275i	−0.389055	−	0.148514i
$134$	−1.05610	−	0.767299i	−0.0912329	−	0.0662846i
$135$	−8.59852	−	9.54963i	−0.740043	−	0.821901i
$136$	3.08862	−	3.43026i	0.264847	−	0.294142i
$137$	18.0036	+	8.01572i	1.53815	+	0.684829i	0.988591	−	0.150626i	$-0.0481288\pi$
$137$	18.0036	+	8.01572i	1.53815	+	0.684829i	0.549560	+	0.835454i	$0.314795\pi$
$138$	−0.812005	−	7.72571i	−0.0691224	−	0.657656i
$139$	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	$0.828034\pi$
$140$	−14.1453	−	2.21342i	−1.19549	−	0.187068i
$141$	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
$145$	−6.19942	+	2.76016i	−0.514834	+	0.229219i
$146$	1.36322	−	4.19556i	0.112821	−	0.347227i
$147$	−1.84280	+	4.18081i	−0.151992	+	0.344827i
$148$	−5.51988	+	4.01043i	−0.453731	+	0.329655i
$149$	−1.77860	−	16.9223i	−0.145709	−	1.38633i	−0.786015	−	0.618207i	$-0.787859\pi$
$149$	−1.77860	−	16.9223i	−0.145709	−	1.38633i	0.640307	−	0.768119i	$-0.278807\pi$
$150$	−6.13609	+	6.81482i	−0.501010	+	0.556428i
$151$	1.27425	−	0.270850i	0.103697	−	0.0220415i	−0.155771	−	0.987793i	$-0.549786\pi$
$151$	1.27425	−	0.270850i	0.103697	−	0.0220415i	0.259468	+	0.965752i	$0.416453\pi$
$152$	−1.45826	+	0.649260i	−0.118281	+	0.0526620i
$153$	−13.5107			−1.09228
$154$		0			0
$155$	5.18479			0.416453
$156$	−4.03008	+	1.79431i	−0.322665	+	0.143660i
$157$	−13.3953	+	2.84727i	−1.06906	+	0.227237i	−0.708653	−	0.705557i	$-0.750697\pi$
$157$	−13.3953	+	2.84727i	−1.06906	+	0.227237i	−0.360411	+	0.932794i	$0.617364\pi$
$158$	−15.6178	+	17.3454i	−1.24249	+	1.37992i
$159$	0.493576	+	4.69607i	0.0391432	+	0.372422i
$160$	−20.3057	+	14.7530i	−1.60531	+	1.16633i
$161$	0.845749	−	16.7335i	0.0666544	−	1.31879i
$162$	−3.10551	+	9.55777i	−0.243992	+	0.750929i
$163$	14.9864	−	6.67238i	1.17383	−	0.522621i	0.275222	−	0.961381i	$-0.411249\pi$
$163$	14.9864	−	6.67238i	1.17383	−	0.522621i	0.898604	+	0.438760i	$0.144582\pi$
$164$	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	$0.803367\pi$
$168$	0.546856	+	1.41672i	0.0421908	+	0.109303i
$169$	1.99659	+	6.14488i	0.153584	+	0.472683i
$170$	3.64214	+	34.6526i	0.279339	+	2.65773i
$171$	4.26836	+	1.90040i	0.326410	+	0.145327i
$172$	3.49733	−	3.88418i	0.266669	−	0.296166i
$173$	−12.8703	−	14.2940i	−0.978514	−	1.08675i	−0.996216	−	0.0869065i	$-0.972302\pi$
$173$	−12.8703	−	14.2940i	−0.978514	−	1.08675i	0.0177026	−	0.999843i	$-0.494365\pi$
$174$	−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
$178$	−0.681269	+	6.48184i	−0.0510632	+	0.485834i
$179$	1.29868	−	0.276044i	0.0970681	−	0.0206325i	−0.159122	−	0.987259i	$-0.550866\pi$
$179$	1.29868	−	0.276044i	0.0970681	−	0.0206325i	0.256190	+	0.966627i	$0.417533\pi$
$180$	13.6246	+	2.89601i	1.01552	+	0.215855i
$181$	−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	$0.527777\pi$
$182$	−21.1775	+	5.71675i	−1.56978	+	0.423754i
$183$	0.231539	+	0.712603i	0.0171158	+	0.0526771i
$184$	−3.72634	−	4.13852i	−0.274709	−	0.305096i
$185$	−1.64420	+	15.6435i	−0.120884	+	1.15013i
$186$	0.900330	+	1.55942i	0.0660154	+	0.114342i
$187$		0			0
$188$	−6.97771			−0.508902
$189$	4.35399	−	8.58464i	0.316706	−	0.624441i
$190$	3.72354	−	11.4599i	0.270134	−	0.831387i
$191$	−15.2128	−	3.23357i	−1.10076	−	0.233973i	−0.378502	−	0.925600i	$-0.623561\pi$
$191$	−15.2128	−	3.23357i	−1.10076	−	0.233973i	−0.722255	+	0.691627i	$0.756894\pi$
$192$	−2.33816	−	1.04101i	−0.168742	−	0.0751287i
$193$	4.76774	+	2.12273i	0.343189	+	0.152798i	0.571092	−	0.820886i	$-0.306520\pi$
$193$	4.76774	+	2.12273i	0.343189	+	0.152798i	−0.227902	+	0.973684i	$0.573187\pi$
$194$	28.2132	+	5.99690i	2.02559	+	0.430552i
$195$	−3.14278	+	9.67248i	−0.225059	+	0.692660i
$196$	−2.26880	−	10.4819i	−0.162057	−	0.748707i
$197$	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	0.953094	−	0.302674i	$-0.0978794\pi$
$199$	3.02481	+	5.23913i	0.214423	+	0.371392i	−0.738671	+	0.674067i	$0.764546\pi$
$200$	−0.687168	+	6.53797i	−0.0485901	+	0.462304i
$201$	−0.303359	−	0.336915i	−0.0213973	−	0.0237641i
$202$	3.89246	+	11.9798i	0.273873	+	0.842893i
$203$	−3.60106	−	3.58768i	−0.252745	−	0.251806i
$204$	−4.24651	+	3.08527i	−0.297315	+	0.216012i
$205$	0.978148	+	0.207912i	0.0683168	+	0.0145212i
$206$	4.13432	−	0.878777i	0.288052	−	0.0612273i
$207$	−1.70385	+	16.2111i	−0.118426	+	1.12675i
$208$	−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	$0.603253\pi$
$212$	−7.41650	−	8.23685i	−0.509367	−	0.565709i
$213$	4.13208	−	4.58914i	0.283125	−	0.314443i
$214$	−19.7995	−	8.81530i	−1.35347	−	0.602601i
$215$	−1.25953	−	11.9836i	−0.0858992	−	0.817276i
$216$	−0.988651	−	3.04275i	−0.0672692	−	0.207033i
$217$	1.39855	+	3.62318i	0.0949396	+	0.245957i
$218$	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
$222$	−4.99057	+	2.22194i	−0.334945	+	0.149127i
$223$	−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	$0.102362\pi$
$224$	−15.7868	−	10.2103i	−1.05480	−	0.682207i
$225$	15.5672	−	11.3103i	1.03782	−	0.754017i
$226$	0.983767	+	9.35992i	0.0654392	+	0.622612i
$227$	6.49033	−	7.20824i	0.430778	−	0.478428i	−0.488202	−	0.872730i	$-0.662347\pi$
$227$	6.49033	−	7.20824i	0.430778	−	0.478428i	0.918981	+	0.394303i	$0.129014\pi$
$228$	1.77554	−	0.377403i	0.117588	−	0.0249941i
$229$	21.6461	−	9.63746i	1.43041	−	0.636861i	0.462152	−	0.886801i	$-0.347077\pi$
$229$	21.6461	−	9.63746i	1.43041	−	0.636861i	0.968261	+	0.249939i	$0.0804107\pi$
$230$	42.0378			2.77189
$231$		0			0
$232$	−1.68954			−0.110924
$233$	−19.0813	+	8.49556i	−1.25006	+	0.556563i	−0.921668	−	0.387979i	$-0.873173\pi$
$233$	−19.0813	+	8.49556i	−1.25006	+	0.556563i	−0.328392	+	0.944542i	$0.606507\pi$
$234$	20.8741	−	4.43694i	1.36459	−	0.290052i
$235$	−10.7639	+	11.9546i	−0.702162	+	0.779830i
$236$	−1.52777	−	14.5358i	−0.0994496	−	0.946200i
$237$	−6.55795	+	4.76463i	−0.425984	+	0.309496i
$238$	−23.2331	+	11.8924i	−1.50598	+	0.770867i
$239$	−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	$0.938417\pi$
$240$	−9.93420	+	4.42299i	−0.641250	+	0.285503i
$241$	14.7699	+	25.5822i	0.951414	+	1.64790i	0.742369	+	0.669991i	$0.233702\pi$
$241$	14.7699	+	25.5822i	0.951414	+	1.64790i	0.209045	+	0.977906i	$0.432965\pi$
$242$		0			0
$243$	−7.20233	+	12.4748i	−0.462030	+	0.800259i
$244$	−1.42288	−	1.03378i	−0.0910903	−	0.0661809i
$245$	−21.4580	−	12.2825i	−1.37090	−	0.784703i
$246$	0.107320	+	0.330298i	0.00684250	+	0.0210591i
$247$	−0.837037	−	7.96387i	−0.0532594	−	0.506729i
$248$	1.17926	+	0.525040i	0.0748830	+	0.0333401i
$249$	4.94951	−	5.49699i	0.313662	−	0.348357i
$250$	−10.9963	−	12.2127i	−0.695469	−	0.772397i
$251$	−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
$255$	−1.26490	+	12.0347i	−0.0792111	+	0.753644i
$256$	−20.2499	+	4.30426i	−1.26562	+	0.269016i
$257$	8.47119	+	1.80061i	0.528418	+	0.112319i	0.464393	−	0.885629i	$-0.346273\pi$
$257$	8.47119	+	1.80061i	0.528418	+	0.112319i	0.0640259	+	0.997948i	$0.479606\pi$
$258$	3.38557	−	2.45976i	0.210776	−	0.153138i
$259$	−11.3753	+	3.07070i	−0.706828	+	0.190804i
$260$	−7.37703	−	22.7042i	−0.457504	−	1.40805i
$261$	3.30906	+	3.67509i	0.204826	+	0.227482i
$262$	−1.00460	+	9.55817i	−0.0620646	+	0.590505i
$263$	−2.91740	−	5.05309i	−0.179895	−	0.311587i	0.761950	−	0.647636i	$-0.224242\pi$
$263$	−2.91740	−	5.05309i	−0.179895	−	0.311587i	−0.941844	+	0.336049i	$0.890909\pi$
$264$		0			0
$265$	−25.5526			−1.56969
$266$	9.01265	−	0.489150i	0.552601	−	0.0299917i
$267$	−0.699466	+	2.15273i	−0.0428066	+	0.131745i
$268$	1.04092	+	0.221255i	0.0635845	+	0.0135153i
$269$	−20.0809	−	8.94061i	−1.22436	−	0.545119i	−0.310274	−	0.950647i	$-0.600421\pi$
$269$	−20.0809	−	8.94061i	−1.22436	−	0.545119i	−0.914083	+	0.405528i	$0.867088\pi$
$270$	22.0627	+	9.82295i	1.34269	+	0.597806i
$271$	9.63675	+	2.04836i	0.585391	+	0.124429i	0.491081	−	0.871114i	$-0.336602\pi$
$271$	9.63675	+	2.04836i	0.585391	+	0.124429i	0.0943104	+	0.995543i	$0.469935\pi$
$272$	−7.65088	+	23.5470i	−0.463903	+	1.42775i
$273$	−7.60694	+	0.412857i	−0.460393	+	0.0249872i
$274$	−37.0378			−2.23753
$275$		0			0
$276$	3.16637	+	5.48432i	0.190593	+	0.330117i
$277$	2.47096	−	23.5096i	0.148465	−	1.41255i	−0.625943	−	0.779869i	$-0.715286\pi$
$277$	2.47096	−	23.5096i	0.148465	−	1.41255i	0.774409	−	0.632686i	$-0.218048\pi$
$278$	−6.64719	−	7.38245i	−0.398672	−	0.442770i
$279$	−1.16758	−	3.59344i	−0.0699012	−	0.215134i
$280$	−7.93389	+	2.14171i	−0.474141	+	0.127992i
$281$	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	$0.138699\pi$
$282$	−5.46469	−	1.16156i	−0.325417	−	0.0691696i
$283$	16.6268	−	3.53413i	0.988360	−	0.210082i	0.314754	−	0.949173i	$-0.398078\pi$
$283$	16.6268	−	3.53413i	0.988360	−	0.210082i	0.673606	+	0.739091i	$0.264745\pi$
$284$	−1.51517	+	14.4158i	−0.0899086	+	0.855423i
$285$	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
$289$	7.06046	+	7.84143i	0.415321	+	0.461261i
$290$	8.53390	−	9.47786i	0.501128	−	0.556559i
$291$	9.15120	+	4.07438i	0.536453	+	0.238844i
$292$	0.375912	+	3.57657i	0.0219986	+	0.209303i
$293$	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	$0.768152\pi$
$294$	−0.0319533	−	8.58671i	−0.00186355	−	0.500787i
$295$	−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
$299$	25.5215	−	11.3629i	1.47595	−	0.657134i
$300$	2.31010	−	7.10977i	0.133374	−	0.410483i
$301$	8.03451	−	4.11263i	0.463101	−	0.237048i
$302$	−1.98073	+	1.43908i	−0.113978	+	0.0828098i
$303$	0.457274	+	4.35067i	0.0262697	+	0.249940i
$304$	5.72918	−	6.36289i	0.328591	−	0.364937i
$305$	−3.96608	+	0.843016i	−0.227097	+	0.0482709i
$306$	23.1966	−	10.3278i	1.32606	−	0.590401i
$307$	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
$310$	−8.90179	+	3.96333i	−0.505588	+	0.225102i
$311$	−3.37296	+	0.716944i	−0.191263	+	0.0406542i	−0.302547	−	0.953134i	$-0.597837\pi$
$311$	−3.37296	+	0.716944i	−0.191263	+	0.0406542i	0.111284	+	0.993789i	$0.464504\pi$
$312$	−1.69430	+	1.88171i	−0.0959207	+	0.106531i
$313$	2.03014	+	19.3155i	0.114750	+	1.09178i	0.888687	+	0.458514i	$0.151618\pi$
$313$	2.03014	+	19.3155i	0.114750	+	1.09178i	−0.773937	+	0.633263i	$0.781715\pi$
$314$	20.8220	−	15.1281i	1.17505	−	0.853727i
$315$	20.1976	+	13.0631i	1.13801	+	0.736024i
$316$	5.87977	−	18.0961i	0.330763	−	1.01798i
$317$	−29.9790	+	13.3475i	−1.68379	+	0.749672i	−0.683994	+	0.729487i	$0.739759\pi$
$317$	−29.9790	+	13.3475i	−1.68379	+	0.749672i	−0.999796	+	0.0201843i	$0.993575\pi$
$318$	−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
$322$	11.3393	+	29.3763i	0.631913	+	1.63708i
$323$	−2.94430	−	9.06164i	−0.163825	−	0.504203i
$324$	−0.856353	−	8.14765i	−0.0475752	−	0.452647i
$325$	−30.1275	−	13.4136i	−1.67117	−	0.744054i
$326$	−20.6298	+	22.9117i	−1.14258	+	1.26896i
$327$	5.23457	+	5.81358i	0.289473	+	0.321492i
$328$	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	−0.765298	−	0.643676i	$-0.777408\pi$
$331$	3.18004	−	5.50800i	0.174791	−	0.302747i	0.940089	+	0.340929i	$0.110742\pi$
$332$	−1.81490	+	17.2677i	−0.0996058	+	0.947686i
$333$	11.2124	−	2.38326i	0.614434	−	0.130602i
$334$	15.1593	+	3.22220i	0.829479	+	0.176311i
$335$	1.98481	−	1.44205i	0.108442	−	0.0787876i
$336$	−5.77048	−	5.74904i	−0.314805	−	0.313636i
$337$	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	$0.760839\pi$
$338$	−8.12519	−	9.02394i	−0.441952	−	0.490837i
$339$	−0.341659	+	3.25067i	−0.0185564	+	0.176552i
$340$	−14.2023	−	24.5992i	−0.770230	−	1.33408i
$341$		0			0
$342$	−8.78106			−0.474825
$343$	2.79506	−	18.3081i	0.150919	−	0.988546i
$344$	0.927051	−	2.85317i	0.0499832	−	0.153833i
$345$	14.2805	+	3.03542i	0.768838	+	0.163422i
$346$	33.0237	+	14.7031i	1.77536	+	0.790442i
$347$	18.0193	+	8.02273i	0.967329	+	0.430683i	0.828719	−	0.559665i	$-0.189070\pi$
$347$	18.0193	+	8.02273i	0.967329	+	0.430683i	0.138610	+	0.990347i	$0.455737\pi$
$348$	1.87929	+	0.399455i	0.100741	+	0.0214131i
$349$	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	$0.0504400\pi$
$350$	16.8140	−	33.1517i	0.898746	−	1.77203i
$351$	16.0496			0.856666
$352$		0			0
$353$	−16.5831	−	28.7227i	−0.882627	−	1.52876i	−0.848409	−	0.529341i	$-0.822439\pi$
$353$	−16.5831	−	28.7227i	−0.882627	−	1.52876i	−0.0342183	−	0.999414i	$-0.510894\pi$
$354$	1.22323	−	11.6382i	0.0650138	−	0.618565i
$355$	22.3606	+	24.8340i	1.18678	+	1.31805i
$356$	−1.64185	−	5.05310i	−0.0870180	−	0.267814i
$357$	−8.75116	+	2.36233i	−0.463161	+	0.125028i
$358$	−2.01870	+	1.46667i	−0.106692	+	0.0775160i
$359$	4.11778	+	0.875260i	0.217328	+	0.0461945i	0.315289	−	0.948996i	$-0.397899\pi$
$359$	4.11778	+	0.875260i	0.217328	+	0.0461945i	−0.0979608	+	0.995190i	$0.531232\pi$
$360$	7.82024	−	1.66224i	0.412163	−	0.0876079i
$361$	1.64162	−	15.6190i	0.0864011	−	0.822052i
$362$	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
$366$	−0.942254	−	1.04648i	−0.0492524	−	0.0547003i
$367$	−13.0071	+	14.4459i	−0.678965	+	0.754067i	−0.979881	−	0.199583i	$-0.936041\pi$
$367$	−13.0071	+	14.4459i	−0.678965	+	0.754067i	0.300915	+	0.953651i	$0.402708\pi$
$368$	27.2884	+	12.1496i	1.42250	+	0.633340i
$369$	−0.0761742	−	0.724749i	−0.00396547	−	0.0377289i
$370$	−9.13520	−	28.1152i	−0.474916	−	1.46164i
$371$	−6.89257	−	17.8564i	−0.357844	−	0.927057i
$372$	−1.18757	−	0.862817i	−0.0615724	−	0.0447350i
$373$	6.35710	−	11.0108i	0.329158	−	0.570118i	−0.653187	−	0.757197i	$-0.726568\pi$
$373$	6.35710	−	11.0108i	0.329158	−	0.570118i	0.982345	+	0.187078i	$0.0599018\pi$
$374$		0			0
$375$	−2.85369	−	4.94274i	−0.147364	−	0.255242i
$376$	−3.65880	+	1.62900i	−0.188688	+	0.0840093i
$377$	2.61912	−	8.06082i	0.134892	−	0.415154i
$378$	−0.913159	+	18.0673i	−0.0469678	+	0.929279i
$379$	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	$0.100755\pi$
$380$	1.02678	+	9.76914i	0.0526726	+	0.501146i
$381$	6.21680	−	6.90445i	0.318496	−	0.353726i
$382$	28.5906	−	6.07713i	1.46282	−	0.310933i
$383$	7.58115	−	3.37534i	0.387379	−	0.172472i	−0.203800	−	0.979012i	$-0.565329\pi$
$383$	7.58115	−	3.37534i	0.387379	−	0.172472i	0.591179	+	0.806540i	$0.298663\pi$
$384$	−4.46616			−0.227913
$385$		0			0
$386$	−9.80840			−0.499234
$387$	−8.02190	+	3.57158i	−0.407776	+	0.181554i
$388$	−22.9996	+	4.88872i	−1.16763	+	0.248187i
$389$	7.62783	−	8.47156i	0.386746	−	0.429525i	−0.518063	−	0.855343i	$-0.673347\pi$
$389$	7.62783	−	8.47156i	0.386746	−	0.429525i	0.904809	+	0.425817i	$0.140013\pi$
$390$	−1.99794	−	19.0091i	−0.101169	−	0.962563i
$391$	26.8921	−	19.5382i	1.35999	−	0.988090i
$392$	−3.63673	−	4.96656i	−0.183683	−	0.250849i
$393$	−1.03144	+	3.17444i	−0.0520291	+	0.160129i
$394$	−7.92962	+	3.53049i	−0.399488	+	0.177864i
$395$	−21.9329	−	37.9889i	−1.10356	−	1.91143i
$396$		0			0
$397$	−3.29086	+	5.69994i	−0.165163	+	0.286072i	−0.936713	−	0.350097i	$-0.886149\pi$
$397$	−3.29086	+	5.69994i	−0.165163	+	0.286072i	0.771550	+	0.636169i	$0.219482\pi$
$398$	−9.19819	−	6.68287i	−0.461063	−	0.334982i
$399$	3.09698	+	0.484608i	0.155043	+	0.0242608i
$400$	−10.8965	−	33.5359i	−0.544824	−	1.67680i
$401$	−0.437958	−	4.16689i	−0.0218706	−	0.208085i	−1.00000		8.74528e-5i	$-0.999972\pi$
$401$	−0.437958	−	4.16689i	−0.0218706	−	0.208085i	0.978129	−	0.207997i	$-0.0666945\pi$
$402$	0.778381	+	0.346558i	0.0388221	+	0.0172847i
$403$	−4.33306	+	4.81235i	−0.215845	+	0.239720i
$404$	−6.87101	−	7.63104i	−0.341846	−	0.379658i
$405$	−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
$409$	0.0808338	−	0.769082i	0.00399697	−	0.0380287i	−0.992342	−	0.123524i	$-0.960581\pi$
$409$	0.0808338	−	0.769082i	0.00399697	−	0.0380287i	0.996339	+	0.0854950i	$0.0272472\pi$
$410$	−1.83832	+	0.390746i	−0.0907880	+	0.0192976i
$411$	−12.5820	−	2.67439i	−0.620624	−	0.131918i
$412$	−2.78757	+	2.02529i	−0.137334	+	0.0997787i
$413$	6.48722	−	24.3921i	0.319215	−	1.20026i
$414$	−9.46663	−	29.1353i	−0.465259	−	1.43192i
$415$	26.7841	+	29.7468i	1.31478	+	1.46021i
$416$	3.27678	−	31.1765i	0.160657	−	1.52855i
$417$	−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	$0.390933\pi$
$420$	9.33130	−	0.506444i	0.455321	−	0.0247119i
$421$	−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	$0.145185\pi$
$422$	−15.9834	−	3.39738i	−0.778060	−	0.165382i
$423$	10.7094	+	4.76812i	0.520708	+	0.231834i
$424$	−5.81183	−	2.58760i	−0.282248	−	0.125665i
$425$	−38.3820	−	8.15835i	−1.86180	−	0.395738i
$426$	−3.58638	+	11.0377i	−0.173761	+	0.534780i
$427$	−1.65892	−	2.54413i	−0.0802806	−	0.123119i
$428$	17.6682			0.854024
$429$		0			0
$430$	11.3229	+	19.6119i	0.546041	+	0.945771i
$431$	−1.88214	+	17.9073i	−0.0906594	+	0.862567i	0.850811	+	0.525471i	$0.176111\pi$
$431$	−1.88214	+	17.9073i	−0.0906594	+	0.862567i	−0.941471	+	0.337095i	$0.890556\pi$
$432$	11.4828	+	12.7529i	0.552466	+	0.613575i
$433$	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	$0.882089\pi$
$434$	−5.17078	−	5.15158i	−0.248205	−	0.247284i
$435$	3.58339	−	2.60349i	0.171811	−	0.124828i
$436$	−17.9615	−	3.81784i	−0.860200	−	0.182841i
$437$	−11.2441	+	2.39000i	−0.537876	+	0.114329i
$438$	−0.300978	+	2.86361i	−0.0143813	+	0.136829i
$439$	−20.0167	+	34.6699i	−0.955343	+	1.65470i	−0.221762	+	0.975101i	$0.571181\pi$
$439$	−20.0167	+	34.6699i	−0.955343	+	1.65470i	−0.733581	+	0.679602i	$0.762152\pi$
$440$		0			0
$441$	−3.68051	+	17.6379i	−0.175262	+	0.839901i
$442$	−35.2072	−	25.5795i	−1.67464	−	1.21669i
$443$	12.6974	+	14.1019i	0.603271	+	0.670001i	0.964990	−	0.262287i	$-0.0844766\pi$
$443$	12.6974	+	14.1019i	0.603271	+	0.670001i	−0.361719	+	0.932287i	$0.617810\pi$
$444$	2.97988	−	3.30949i	0.141419	−	0.157062i
$445$	−11.1900	−	4.98211i	−0.530456	−	0.236174i
$446$	−0.0435389	−	0.414245i	−0.00206163	−	0.0196151i
$447$	3.43196	+	10.5625i	0.162326	+	0.499589i
$448$	10.2500	+	1.60389i	0.484266	+	0.0757769i
$449$	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
$453$	−0.776778	+	0.345844i	−0.0364962	+	0.0162492i
$454$	−5.63319	+	17.3372i	−0.264378	+	0.813673i
$455$	2.08097	−	41.1728i	0.0975572	−	1.93021i
$456$	0.842906	−	0.612407i	0.0394727	−	0.0286786i
$457$	1.21447	+	11.5549i	0.0568105	+	0.540516i	0.985502	+	0.169663i	$0.0542679\pi$
$457$	1.21447	+	11.5549i	0.0568105	+	0.540516i	−0.928692	+	0.370853i	$0.879065\pi$
$458$	−29.7972	+	33.0932i	−1.39233	+	1.54634i
$459$	18.6793	−	3.97040i	0.871873	−	0.185322i
$460$	−31.3068	+	13.9387i	−1.45968	+	0.649894i
$461$	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	$0.192912\pi$
$464$	8.27894	−	3.68602i	0.384340	−	0.171119i
$465$	−3.31018	+	0.703601i	−0.153506	+	0.0326287i
$466$	26.2667	−	29.1721i	1.21678	−	1.35137i
$467$	4.16711	+	39.6474i	0.192831	+	1.83466i	0.480574	+	0.876954i	$0.340428\pi$
$467$	4.16711	+	39.6474i	0.192831	+	1.83466i	−0.287743	+	0.957708i	$0.592905\pi$
$468$	−14.0744	+	10.2257i	−0.650590	+	0.472681i
$469$	1.54310	+	0.998024i	0.0712538	+	0.0460845i
$470$	9.34241	−	28.7530i	0.430933	−	1.32628i
$471$	8.16574	−	3.63562i	0.376257	−	0.167521i
$472$	−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
$476$	13.3592	−	16.5601i	0.612316	−	0.759031i
$477$	5.75428	+	17.7099i	0.263470	+	0.810879i
$478$	−2.95264	−	28.0925i	−0.135051	−	1.28492i
$479$	27.7535	+	12.3567i	1.26809	+	0.564590i	0.926866	−	0.375391i	$-0.122492\pi$
$479$	27.7535	+	12.3567i	1.26809	+	0.564590i	0.341224	+	0.939982i	$0.389158\pi$
$480$	10.9620	−	12.1745i	0.500342	−	0.555686i
$481$	−13.1457	−	14.5997i	−0.599391	−	0.665691i
$482$	−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
$486$	2.82979	−	26.9236i	0.128362	−	1.22128i
$487$	10.2031	−	2.16874i	0.462348	−	0.0982751i	0.0291523	−	0.999575i	$-0.490719\pi$
$487$	10.2031	−	2.16874i	0.462348	−	0.0982751i	0.433196	+	0.901300i	$0.357386\pi$
$488$	−0.987436	−	0.209886i	−0.0446991	−	0.00950109i
$489$	−8.66246	+	6.29364i	−0.391730	+	0.284608i
$490$	46.2303	+	4.68513i	2.08847	+	0.211653i
$491$	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	$0.825512\pi$
$492$	−0.189443	−	0.210398i	−0.00854076	−	0.00948548i
$493$	1.05414	−	10.0295i	0.0474761	−	0.451704i
$494$	7.52481	+	13.0334i	0.338557	+	0.586399i
$495$		0			0
$496$	−6.92396			−0.310895
$497$	−11.3226	+	22.3245i	−0.507890	+	1.00139i
$498$	−4.29585	+	13.2213i	−0.192502	+	0.592460i
$499$	35.7205	+	7.59262i	1.59907	+	0.339892i	0.919307	−	0.393542i	$-0.128750\pi$
$499$	35.7205	+	7.59262i	1.59907	+	0.339892i	0.679761	+	0.733434i	$0.262084\pi$
$500$	12.2387	+	5.44902i	0.547331	+	0.243688i
$501$	4.91705	+	2.18921i	0.219677	+	0.0978067i
$502$	6.93161	+	1.47336i	0.309373	+	0.0657592i
$503$	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	$-0.146460\pi$
$504$	3.27102	+	5.01647i	0.145703	+	0.223452i
$505$	−23.6732			−1.05345
$506$		0			0
$507$	−2.10859	−	3.65219i	−0.0936459	−	0.162199i
$508$	−2.27960	+	21.6889i	−0.101141	+	0.962291i
$509$	−7.73815	−	8.59409i	−0.342987	−	0.380926i	0.546829	−	0.837244i	$-0.315835\pi$
$509$	−7.73815	−	8.59409i	−0.342987	−	0.380926i	−0.889817	+	0.456318i	$0.849168\pi$
$510$	−7.02781	−	21.6294i	−0.311197	−	0.957765i
$511$	−1.59620	+	6.00173i	−0.0706116	+	0.265501i
$512$	20.4055	−	14.8255i	0.901803	−	0.655199i
$513$	−6.45969	−	1.37305i	−0.285202	−	0.0606217i
$514$	−15.9206	+	3.38404i	−0.702229	+	0.149263i
$515$	−0.830328	+	7.90005i	−0.0365886	+	0.348118i
$516$	−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
$520$	−9.16865	−	10.1828i	−0.402072	−	0.446546i
$521$	−20.4489	+	22.7108i	−0.895881	+	0.994977i	0.104118	+	0.994565i	$0.466798\pi$
$521$	−20.4489	+	22.7108i	−0.895881	+	0.994977i	−1.00000		0.000412263i	$0.999869\pi$
$522$	−8.49064	−	3.78027i	−0.371625	−	0.165458i
$523$	−0.465687	−	4.43071i	−0.0203631	−	0.193742i	0.979611	−	0.200902i	$-0.0643873\pi$
$523$	−0.465687	−	4.43071i	−0.0203631	−	0.193742i	−0.999974	+	0.00716066i	$0.997721\pi$
$524$	−2.42109	−	7.45135i	−0.105766	−	0.325514i
$525$	8.10562	−	10.0478i	0.353758	−	0.438521i
$526$	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
$530$	43.8714	−	19.5328i	1.90565	−	0.848451i
$531$	−7.58801	+	23.3535i	−0.329292	+	1.01346i
$532$	−6.54979	+	3.35265i	−0.283969	+	0.145356i
$533$	−1.01044	+	0.734126i	−0.0437669	+	0.0317985i
$534$	−0.444666	−	4.23072i	−0.0192426	−	0.183081i
$535$	27.2553	−	30.2700i	1.17835	−	1.30869i
$536$	0.597467	−	0.126995i	0.0258066	−	0.00548537i
$537$	−0.791671	+	0.352475i	−0.0341631	+	0.0152104i
$538$	41.3114			1.78106
$539$		0			0
$540$	−19.6878			−0.847227
$541$	15.2293	−	6.78052i	0.654759	−	0.291517i	−0.0523429	−	0.998629i	$-0.516669\pi$
$541$	15.2293	−	6.78052i	0.654759	−	0.291517i	0.707102	+	0.707112i	$0.250002\pi$
$542$	−18.1112	+	3.84965i	−0.777941	+	0.165357i
$543$	7.70971	−	8.56250i	0.330855	−	0.367452i
$544$	−3.89886	−	37.0952i	−0.167162	−	1.59044i
$545$	−34.2487	+	24.8831i	−1.46705	+	1.06588i
$546$	12.7448	−	6.52369i	0.545427	−	0.279188i
$547$	−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	$0.818217\pi$
$548$	27.5831	−	12.2808i	1.17829	−	0.524609i
$549$	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
$553$	20.6308	−	25.5740i	0.877309	−	1.08752i
$554$	13.7287	+	42.2525i	0.583276	+	1.79514i
$555$	−1.07317	−	10.2106i	−0.0455537	−	0.433415i
$556$	7.39819	+	3.29389i	0.313753	+	0.139692i
$557$	0.448277	−	0.497862i	0.0189941	−	0.0210951i	−0.733573	−	0.679611i	$-0.762149\pi$
$557$	0.448277	−	0.497862i	0.0189941	−	0.0210951i	0.752567	+	0.658516i	$0.228815\pi$
$558$	4.75151	+	5.27708i	0.201147	+	0.223397i
$559$	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
$563$	−1.36244	+	12.9627i	−0.0574200	+	0.546315i	0.927563	+	0.373666i	$0.121899\pi$
$563$	−1.36244	+	12.9627i	−0.0574200	+	0.546315i	−0.984983	+	0.172649i	$0.944767\pi$
$564$	4.45485	−	0.946908i	0.187583	−	0.0398720i
$565$	−17.3013	−	3.67750i	−0.727870	−	0.154713i
$566$	−25.8451	+	18.7775i	−1.08635	+	0.789279i
$567$	3.63624	−	13.6723i	0.152708	−	0.574184i
$568$	2.57101	+	7.91275i	0.107877	+	0.332012i
$569$	−18.3619	−	20.3930i	−0.769773	−	0.854920i	0.223013	−	0.974815i	$-0.428411\pi$
$569$	−18.3619	−	20.3930i	−0.769773	−	0.854920i	−0.992786	+	0.119896i	$0.961744\pi$
$570$	−0.822099	+	7.82175i	−0.0344340	+	0.327617i
$571$	8.11974	+	14.0638i	0.339800	+	0.588552i	0.984395	−	0.175973i	$-0.0563071\pi$
$571$	8.11974	+	14.0638i	0.339800	+	0.588552i	−0.644595	+	0.764525i	$0.722974\pi$
$572$		0			0
$573$	10.1513			0.424075
$574$	−0.768925	−	1.17923i	−0.0320943	−	0.0492201i
$575$	−14.6293	+	45.0244i	−0.610084	+	1.87765i
$576$	−9.87271	−	2.09851i	−0.411363	−	0.0874379i
$577$	21.6673	+	9.64690i	0.902022	+	0.401606i	0.804724	−	0.593649i	$-0.202313\pi$
$577$	21.6673	+	9.64690i	0.902022	+	0.401606i	0.0972978	+	0.995255i	$0.468980\pi$
$578$	−18.1162	−	8.06587i	−0.753536	−	0.335496i
$579$	−3.33198	−	0.708235i	−0.138472	−	0.0294332i
$580$	−3.21283	+	9.88806i	−0.133405	+	0.410580i
$581$	−13.5626	+	26.7409i	−0.562670	+	1.10940i
$582$	−18.8262			−0.780373
$583$		0			0
$584$	1.03209	+	1.78763i	0.0427081	+	0.0739727i
$585$	−4.19232	+	39.8873i	−0.173331	+	1.64914i
$586$	−17.3270	−	19.2436i	−0.715774	−	0.794947i
$587$	−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	$-0.471991\pi$
$588$	2.87093	+	6.38418i	0.118395	+	0.263279i
$589$	2.15568	−	1.56619i	0.0888231	−	0.0645338i
$590$	61.9430	+	13.1664i	2.55015	+	0.542052i
$591$	−2.94867	+	0.626760i	−0.121292	+	0.0257815i
$592$	2.19572	−	20.8909i	0.0902437	−	0.858611i
$593$	−21.4217	+	37.1035i	−0.879685	+	1.52366i	−0.0279992	+	0.999608i	$0.508914\pi$
$593$	−21.4217	+	37.1035i	−0.879685	+	1.52366i	−0.851686	+	0.524052i	$0.824420\pi$
$594$		0			0
$595$	−7.76352	−	48.4335i	−0.318273	−	1.98558i
$596$	−21.0905	−	15.3231i	−0.863899	−	0.627659i
$597$	−2.64214	−	2.93439i	−0.108136	−	0.120097i
$598$	−35.1320	+	39.0180i	−1.43665	+	1.59557i
$599$	−0.578369	−	0.257506i	−0.0236315	−	0.0105214i	0.394887	−	0.918730i	$-0.370784\pi$
$599$	−0.578369	−	0.257506i	−0.0236315	−	0.0105214i	−0.418518	+	0.908208i	$0.637450\pi$
$600$	−0.448517	−	4.26735i	−0.0183106	−	0.174214i
$601$	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	$0.877529\pi$
$602$	−10.6507	+	13.2027i	−0.434091	+	0.538102i
$603$	−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
$607$	−44.1013	+	19.6352i	−1.79002	+	0.796967i	−0.813487	+	0.581583i	$0.802433\pi$
$607$	−44.1013	+	19.6352i	−1.79002	+	0.796967i	−0.976530	+	0.215383i	$0.930900\pi$
$608$	−3.98601	+	12.2677i	−0.161654	+	0.497519i
$609$	2.78593	+	1.80184i	0.112891	+	0.0730143i
$610$	6.16496	−	4.47911i	0.249612	−	0.181354i
$611$	−2.10014	−	19.9815i	−0.0849624	−	0.808363i
$612$	−13.8508	+	15.3828i	−0.559884	+	0.621814i
$613$	−20.8497	+	4.43174i	−0.842112	+	0.178996i	−0.608719	−	0.793386i	$-0.708316\pi$
$613$	−20.8497	+	4.43174i	−0.842112	+	0.178996i	−0.233393	+	0.972382i	$0.574983\pi$
$614$	−19.9433	+	8.87934i	−0.804847	+	0.358341i
$615$	−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	$0.580461\pi$
$618$	−2.52026	+	1.12209i	−0.101380	+	0.0451372i
$619$	−35.5464	+	7.55561i	−1.42873	+	0.303686i	−0.856389	−	0.516331i	$-0.827297\pi$
$619$	−35.5464	+	7.55561i	−1.42873	+	0.303686i	−0.572340	+	0.820017i	$0.693964\pi$
$620$	5.31528	−	5.90322i	0.213467	−	0.237079i
$621$	−2.40829	−	22.9133i	−0.0966412	−	0.919480i
$622$	5.24300	−	3.80926i	0.210225	−	0.152738i
$623$	0.463145	−	9.16353i	0.0185555	−	0.367129i
$624$	4.19698	−	12.9170i	0.168014	−	0.517093i
$625$	−5.93155	+	2.64090i	−0.237262	+	0.105636i
$626$	−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
$630$	−44.6631	−	6.98877i	−1.77942	−	0.278439i
$631$	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	$0.797367\pi$
$632$	−1.14158	−	10.8614i	−0.0454098	−	0.432045i
$633$	−5.18436	−	2.30823i	−0.206060	−	0.0917438i
$634$	41.2681	−	45.8328i	1.63896	−	1.82025i
$635$	33.6420	+	37.3633i	1.33504	+	1.48272i
$636$	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
$640$	2.52630	−	24.0361i	0.0998606	−	0.950110i
$641$	12.2013	−	2.59347i	0.481923	−	0.102436i	0.0394571	−	0.999221i	$-0.487437\pi$
$641$	12.2013	−	2.59347i	0.481923	−	0.102436i	0.442466	+	0.896785i	$0.354104\pi$
$642$	13.8371	+	2.94116i	0.546106	+	0.116078i
$643$	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	$0.0412490\pi$
$644$	−18.1851	−	18.1176i	−0.716595	−	0.713933i
$645$	2.43037	+	7.47990i	0.0956957	+	0.294521i
$646$	11.9819	+	13.3073i	0.471423	+	0.523568i
$647$	−2.13852	+	20.3467i	−0.0840739	+	0.799910i	0.868518	+	0.495658i	$0.165073\pi$
$647$	−2.13852	+	20.3467i	−0.0840739	+	0.799910i	−0.952592	+	0.304252i	$0.901594\pi$
$648$	−2.35117	−	4.07234i	−0.0923626	−	0.159977i
$649$		0			0
$650$	61.9796			2.43104
$651$	−1.38457	−	2.12339i	−0.0542656	−	0.0832223i
$652$	7.76665	−	23.9033i	0.304165	−	0.936125i
$653$	15.2194	+	3.23499i	0.595582	+	0.126595i	0.495833	−	0.868418i	$-0.334863\pi$
$653$	15.2194	+	3.23499i	0.595582	+	0.126595i	0.0997488	+	0.995013i	$0.468196\pi$
$654$	−13.4312	−	5.97998i	−0.525203	−	0.233836i
$655$	−16.5008	−	7.34665i	−0.644741	−	0.287057i
$656$	−1.30625	−	0.277653i	−0.0510007	−	0.0108405i
$657$	1.86705	−	5.74618i	0.0728404	−	0.224180i
$658$	22.6128	−	1.22728i	0.881540	−	0.0478444i
$659$	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	0.600020	−	0.799985i	$-0.295159\pi$
$661$	−10.0988	−	17.4916i	−0.392798	−	0.680345i	−0.992817	+	0.119640i	$0.961826\pi$
$662$	−1.24943	+	11.8876i	−0.0485607	+	0.462024i
$663$	−10.1131	−	11.2317i	−0.392761	−	0.436205i
$664$	3.07962	+	9.47809i	0.119512	+	0.367821i
$665$	−4.35990	+	16.3933i	−0.169070	+	0.635705i
$666$	−17.4288	+	12.6627i	−0.675351	+	0.490671i
$667$	−11.9011	−	2.52965i	−0.460811	−	0.0979485i
$668$	−12.3580	+	2.62676i	−0.478144	+	0.101633i
$669$	0.0151209	−	0.143866i	0.000584608	−	0.00556217i
$670$	−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	$0.651181\pi$
$674$	−19.5485	−	21.7108i	−0.752981	−	0.836270i
$675$	−18.1987	+	20.2117i	−0.700470	+	0.777950i
$676$	9.04317	+	4.02628i	0.347814	+	0.154857i
$677$	3.76892	+	35.8589i	0.144852	+	1.37817i	0.789528	+	0.613715i	$0.210325\pi$
$677$	3.76892	+	35.8589i	0.144852	+	1.37817i	−0.644676	+	0.764456i	$0.723008\pi$
$678$	−1.89826	−	5.84225i	−0.0729023	−	0.224370i
$679$	−40.1170	−	6.27741i	−1.53955	−	0.240905i
$680$	−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	0.959681	−	0.281090i	$-0.0906959\pi$
$683$	6.17840	+	10.7013i	0.236410	+	0.409474i	−0.723272	+	0.690564i	$0.757363\pi$
$684$	6.53951	−	2.91158i	0.250044	−	0.111327i
$685$	21.5101	−	66.2014i	0.821860	−	2.52942i
$686$	9.19616	+	33.5699i	0.351111	+	1.28170i
$687$	−12.5119	+	9.09042i	−0.477358	+	0.346821i
$688$	1.68202	+	16.0034i	0.0641265	+	0.610123i
$689$	21.3549	−	23.7171i	0.813559	−	0.903548i
$690$	−26.8386	+	5.70472i	−1.02173	+	0.217175i
$691$	7.30836	−	3.25389i	0.278023	−	0.123784i	−0.262988	−	0.964799i	$-0.584708\pi$
$691$	7.30836	−	3.25389i	0.278023	−	0.123784i	0.541012	+	0.841015i	$0.318041\pi$
$692$	−29.4688			−1.12024
$693$		0			0
$694$	−37.0702			−1.40716
$695$	17.0558	−	7.59375i	0.646965	−	0.288047i
$696$	1.07867	−	0.229279i	0.0408869	−	0.00869078i
$697$	−0.994382	+	1.10437i	−0.0376649	+	0.0418311i
$698$	1.13820	+	10.8292i	0.0430814	+	0.409892i
$699$	11.0294	−	8.01334i	0.417171	−	0.303092i
$700$	−1.52962	+	30.2641i	−0.0578141	+	1.14388i
$701$	−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	$0.177472\pi$
$702$	−27.5557	+	12.2686i	−1.04002	+	0.463048i
$703$	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
$707$	−6.38563	−	16.5431i	−0.240156	−	0.622166i
$708$	2.94797	+	9.07292i	0.110791	+	0.340981i
$709$	−0.491809	−	4.67925i	−0.0184703	−	0.175733i	0.981398	−	0.191986i	$-0.0614929\pi$
$709$	−0.491809	−	4.67925i	−0.0184703	−	0.175733i	−0.999868	+	0.0162533i	$0.994826\pi$
$710$	−57.3746	−	25.5448i	−2.15323	−	0.958679i
$711$	−21.3900	+	23.7560i	−0.802186	+	0.890918i
$712$	−2.04060	−	2.26632i	−0.0764747	−	0.0849338i
$713$	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
$717$	1.02544	−	9.75641i	0.0382958	−	0.364360i
$718$	−7.73889	+	1.64495i	−0.288813	+	0.0613890i
$719$	−51.4719	−	10.9407i	−1.91958	−	0.408019i	−0.999882	−	0.0153924i	$-0.995100\pi$
$719$	−51.4719	−	10.9407i	−1.91958	−	0.408019i	−0.919698	−	0.392627i	$-0.871566\pi$
$720$	−34.6936	+	25.2064i	−1.29295	+	0.939385i
$721$	−5.74459	+	1.55072i	−0.213940	+	0.0577518i
$722$	9.12088	+	28.0712i	0.339444	+	1.04470i
$723$	−12.9013	−	14.3284i	−0.479806	−	0.532879i
$724$	−2.82703	+	26.8974i	−0.105066	+	0.999632i
$725$	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	$0.636289\pi$
$728$	4.64268	−	9.15385i	0.172069	−	0.339264i
$729$	−2.05185	+	6.31493i	−0.0759943	+	0.233886i
$730$	−15.2412	−	3.23962i	−0.564103	−	0.119904i
$731$	16.3586	+	7.28332i	0.605045	+	0.269383i
$732$	1.04871	+	0.466916i	0.0387614	+	0.0172577i
$733$	−29.5555	−	6.28221i	−1.09166	−	0.232039i	−0.373298	−	0.927712i	$-0.621773\pi$
$733$	−29.5555	−	6.28221i	−1.09166	−	0.232039i	−0.718359	+	0.695673i	$0.755106\pi$
$734$	11.2893	−	34.7450i	0.416697	−	1.28246i
$735$	15.3665	+	4.92972i	0.566800	+	0.181836i
$736$	−45.0009			−1.65876
$737$		0			0
$738$	0.684793	+	1.18610i	0.0252076	+	0.0436608i
$739$	1.33499	−	12.7016i	0.0491085	−	0.467236i	−0.942139	−	0.335222i	$-0.891189\pi$
$739$	1.33499	−	12.7016i	0.0491085	−	0.467236i	0.991248	−	0.132014i	$-0.0421445\pi$
$740$	16.1256	+	17.9092i	0.592787	+	0.658357i
$741$	1.61513	+	4.97087i	0.0593334	+	0.182609i
$742$	25.4836	+	25.3889i	0.935531	+	0.932056i
$743$	−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	$0.541445\pi$
$744$	−0.824137	−	0.175176i	−0.0302143	−	0.00642225i
$745$	−58.7869	+	12.4955i	−2.15378	+	0.457801i
$746$	−2.49769	+	23.7640i	−0.0914471	+	0.870061i
$747$	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
$751$	24.6138	+	27.3363i	0.898169	+	0.997517i	0.999996	+	0.00271535i	$0.000864325\pi$
$751$	24.6138	+	27.3363i	0.898169	+	0.997517i	−0.101828	+	0.994802i	$0.532469\pi$
$752$	14.3746	−	15.9646i	0.524187	−	0.582168i
$753$	2.24833	+	1.00102i	0.0819337	+	0.0364792i
$754$	1.66504	+	15.8418i	0.0606370	+	0.576923i
$755$	−1.42189	−	4.37611i	−0.0517477	−	0.159263i
$756$	−5.31059	−	13.7580i	−0.193144	−	0.500373i
$757$	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
$761$	−9.30974	+	4.14496i	−0.337478	+	0.150255i	−0.568477	−	0.822699i	$-0.692467\pi$
$761$	−9.30974	+	4.14496i	−0.337478	+	0.150255i	0.230999	+	0.972954i	$0.425801\pi$
$762$	−5.39578	+	16.6065i	−0.195468	+	0.601590i
$763$	−26.6268	−	17.2213i	−0.963954	−	0.623452i
$764$	−19.2773	+	14.0057i	−0.697427	+	0.506710i
$765$	4.98821	+	47.4597i	0.180349	+	1.71591i
$766$	−10.4359	+	11.5903i	−0.377066	+	0.418774i
$767$	41.1651	−	8.74990i	1.48638	−	0.315941i
$768$	12.3443	−	5.49602i	0.445436	−	0.198321i
$769$	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
$772$	7.30460	−	3.25222i	0.262898	−	0.117050i
$773$	10.5464	−	2.24170i	0.379327	−	0.0806284i	−0.0143023	−	0.999898i	$-0.504553\pi$
$773$	10.5464	−	2.24170i	0.379327	−	0.0806284i	0.393629	+	0.919269i	$0.371219\pi$
$774$	11.0427	−	12.2641i	0.396920	−	0.440824i
$775$	−1.14705	−	10.9135i	−0.0412034	−	0.392024i
$776$	−10.9186	+	7.93286i	−0.391956	+	0.284773i
$777$	6.84576	−	3.50415i	0.245590	−	0.125711i
$778$	−6.62046	+	20.3757i	−0.237355	+	0.730504i
$779$	0.469488	−	0.209030i	0.0168212	−	0.00748927i
$780$	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
$784$	28.6558	+	16.4026i	1.02342	+	0.585806i
$785$	14.9473	+	46.0031i	0.533492	+	1.64192i
$786$	−0.655708	−	6.23865i	−0.0233883	−	0.222525i
$787$	19.5017	+	8.68273i	0.695161	+	0.309506i	0.723727	−	0.690086i	$-0.242427\pi$
$787$	19.5017	+	8.68273i	0.695161	+	0.309506i	−0.0285658	+	0.999592i	$0.509094\pi$
$788$	4.73479	−	5.25852i	0.168670	−	0.187327i
$789$	2.54832	+	2.83019i	0.0907225	+	0.100758i
$790$	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
$794$	1.29297	−	12.3018i	0.0458859	−	0.436575i
$795$	16.3138	−	3.46761i	0.578592	−	0.122984i
$796$	9.06603	+	1.92704i	0.321337	+	0.0683023i
$797$	−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	$0.545132\pi$
$798$	−5.68766	+	1.53535i	−0.201341	+	0.0543509i
$799$	−7.38730	−	22.7358i	−0.261344	−	0.804333i
$800$	35.5459	+	39.4777i	1.25674	+	1.39575i
$801$	−0.933055	+	8.87743i	−0.0329679	+	0.313668i
$802$	3.93717	+	6.81937i	0.139026	+	0.240800i
$803$		0			0
$804$	−0.694593			−0.0244964
$805$	−59.0927	+	3.20718i	−2.08275	+	0.113038i
$806$	3.76081	−	11.5746i	0.132469	−	0.407698i
$807$	14.0338	+	2.98297i	0.494012	+	0.105006i
$808$	−5.38438	−	2.39728i	−0.189422	−	0.0843360i
$809$	−2.96592	−	1.32051i	−0.104276	−	0.0464268i	0.353936	−	0.935270i	$-0.384843\pi$
$809$	−2.96592	−	1.32051i	−0.104276	−	0.0464268i	−0.458212	+	0.888843i	$0.651510\pi$
$810$	34.7205	+	7.38007i	1.21995	+	0.259309i
$811$	−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	$0.900500\pi$
$812$	−7.77649	+	0.422059i	−0.272901	+	0.0148114i
$813$	−6.43047			−0.225526
$814$		0			0
$815$	−28.9714	−	50.1799i	−1.01482	−	1.75772i
$816$	1.68919	−	16.0716i	0.0591336	−	0.562619i
$817$	−4.14361	−	4.60195i	−0.144967	−	0.161002i
$818$	0.449114	+	1.38223i	0.0157029	+	0.0483286i
$819$	−29.0044	+	7.82958i	−1.01350	+	0.273588i
$820$	1.23949	−	0.900539i	0.0432847	−	0.0314482i
$821$	−23.6688	−	5.03096i	−0.826047	−	0.175582i	−0.224556	−	0.974461i	$-0.572093\pi$
$821$	−23.6688	−	5.03096i	−0.826047	−	0.175582i	−0.601491	+	0.798879i	$0.705427\pi$
$822$	23.6464	−	5.02620i	0.824763	−	0.175309i
$823$	4.88306	−	46.4592i	0.170213	−	1.61947i	−0.492307	−	0.870422i	$-0.663846\pi$
$823$	4.88306	−	46.4592i	0.170213	−	1.61947i	0.662519	−	0.749045i	$-0.269487\pi$
$824$	−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	$0.689483\pi$
$828$	16.7106	+	18.5590i	0.580733	+	0.644970i
$829$	34.1056	−	37.8782i	1.18454	−	1.31556i	0.246454	−	0.969154i	$-0.420735\pi$
$829$	34.1056	−	37.8782i	1.18454	−	1.31556i	0.938084	−	0.346408i	$-0.112599\pi$
$830$	−68.7247	−	30.5982i	−2.38547	−	1.06208i
$831$	1.61280	+	15.3448i	0.0559475	+	0.532305i
$832$	5.34556	+	16.4519i	0.185324	+	0.570369i
$833$	31.7516	−	18.4897i	1.10013	−	0.640629i
$834$	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
$838$	−23.6154	+	10.5143i	−0.815781	+	0.363209i
$839$	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	$-0.165729\pi$
$840$	4.77468	−	2.44402i	0.164742	−	0.0843267i
$841$	20.4752	−	14.8761i	0.706040	−	0.512968i
$842$	−1.14053	−	10.8514i	−0.0393052	−	0.373964i
$843$	−7.10637	+	7.89243i	−0.244757	+	0.271830i
$844$	13.0298	−	2.76957i	0.448504	−	0.0953325i
$845$	20.8482	−	9.28222i	0.717200	−	0.319318i
$846$	−22.0318			−0.757468
$847$		0			0
$848$	34.1239			1.17182
$849$	−10.1356	+	4.51267i	−0.347854	+	0.154874i
$850$	72.1346	−	15.3327i	2.47420	−	0.525906i
$851$	−18.8708	+	20.9582i	−0.646884	+	0.718438i
$852$	−0.988955	−	9.40928i	−0.0338810	−	0.322356i
$853$	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	$-0.0537673\pi$
$854$	4.79297	+	3.09993i	0.164012	+	0.106077i
$855$	5.09971	−	15.6953i	0.174406	−	0.536767i
$856$	9.26440	−	4.12478i	0.316651	−	0.140982i
$857$	−0.489018	−	0.847004i	−0.0167045	−	0.0289331i	0.857552	−	0.514397i	$-0.171984\pi$
$857$	−0.489018	−	0.847004i	−0.0167045	−	0.0289331i	−0.874257	+	0.485464i	$0.838651\pi$
$858$		0			0
$859$	17.0073	−	29.4576i	0.580283	−	1.00508i	−0.415163	−	0.909747i	$-0.636275\pi$
$859$	17.0073	−	29.4576i	0.580283	−	1.00508i	0.995446	−	0.0953319i	$-0.0303912\pi$
$860$	−14.9353	−	10.8512i	−0.509291	−	0.370022i
$861$	−0.176060	−	0.456115i	−0.00600012	−	0.0155443i
$862$	−10.4572	−	32.1839i	−0.356173	−	1.09619i
$863$	2.37233	+	22.5712i	0.0807550	+	0.768333i	0.957705	+	0.287751i	$0.0929076\pi$
$863$	2.37233	+	22.5712i	0.0807550	+	0.768333i	−0.876950	+	0.480581i	$0.840426\pi$
$864$	−23.6179	−	10.5154i	−0.803496	−	0.357740i
$865$	−45.4592	+	50.4875i	−1.54566	+	1.71663i
$866$	−2.94329	−	3.26886i	−0.100017	−	0.111080i
$867$	−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
$871$	−0.320294	+	3.04739i	−0.0108527	+	0.103257i
$872$	−10.3095	+	2.19135i	−0.349124	+	0.0742086i
$873$	38.6404	+	8.21326i	1.30778	+	0.277977i
$874$	17.4780	−	12.6985i	0.591202	−	0.429534i
$875$	16.3894	+	16.3285i	0.554061	+	0.552003i
$876$	−0.725354	−	2.23241i	−0.0245075	−	0.0754262i
$877$	0.821984	+	0.912906i	0.0277564	+	0.0308266i	0.756863	−	0.653573i	$-0.226731\pi$
$877$	0.821984	+	0.912906i	0.0277564	+	0.0308266i	−0.729107	+	0.684400i	$0.760064\pi$
$878$	7.86452	−	74.8259i	0.265415	−	2.52525i
$879$	−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	$0.450821\pi$
$882$	−7.16361	−	33.0961i	−0.241211	−	1.11440i
$883$	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	$-0.172000\pi$
$884$	34.7013	+	7.37600i	1.16713	+	0.248082i
$885$	20.0918	+	8.94544i	0.675378	+	0.300698i
$886$	−32.5799	−	14.5055i	−1.09454	−	0.487322i
$887$	−22.5149	−	4.78568i	−0.755975	−	0.160687i	−0.186227	−	0.982507i	$-0.559626\pi$
$887$	−22.5149	−	4.78568i	−0.755975	−	0.160687i	−0.569748	+	0.821819i	$0.692959\pi$
$888$	0.789888	−	2.43103i	0.0265069	−	0.0815799i
$889$	−17.0352	+	33.5877i	−0.571341	+	1.12650i
$890$	23.0205			0.771650
$891$		0			0
$892$	0.169778	+	0.294064i	0.00568458	+	0.00984598i
$893$	−0.864151	+	8.22185i	−0.0289177	+	0.275134i
$894$	−13.9665	−	15.5113i	−0.467109	−	0.518777i
$895$	−1.44915	−	4.46002i	−0.0484397	−	0.149082i
$896$	17.4781	−	4.71811i	0.583901	−	0.157621i
$897$	−14.7520	+	10.7179i	−0.492554	+	0.357861i
$898$	−57.9752	−	12.3230i	−1.93466	−	0.411224i
$899$	2.75863	−	0.586365i	0.0920055	−	0.0195564i
$900$	3.08157	−	29.3192i	0.102719	−	0.977307i
$901$	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
$905$	41.7209	+	46.3358i	1.38685	+	1.54025i
$906$	1.06928	−	1.18756i	0.0355246	−	0.0394541i
$907$	−25.8724	−	11.5191i	−0.859080	−	0.382487i	−0.0705681	−	0.997507i	$-0.522481\pi$
$907$	−25.8724	−	11.5191i	−0.859080	−	0.382487i	−0.788511	+	0.615020i	$0.789148\pi$
$908$	−1.55337	−	14.7793i	−0.0515503	−	0.490469i
$909$	5.33106	+	16.4073i	0.176820	+	0.544196i
$910$	27.9003	+	72.2805i	0.924885	+	2.39607i
$911$	−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
$915$	2.41770	−	1.07643i	0.0799268	−	0.0355857i
$916$	11.2180	−	34.5255i	0.370653	−	1.14075i
$917$	0.682958	−	13.5126i	0.0225533	−	0.446226i
$918$	−29.0355	+	21.0955i	−0.958313	+	0.696255i
$919$	2.27808	+	21.6745i	0.0751469	+	0.714975i	0.965623	+	0.259945i	$0.0837045\pi$
$919$	2.27808	+	21.6745i	0.0751469	+	0.714975i	−0.890476	+	0.455029i	$0.849629\pi$
$920$	−13.1618	+	14.6176i	−0.433930	+	0.481928i
$921$	−7.41604	+	1.57633i	−0.244367	+	0.0519418i
$922$	−22.2831	+	9.92107i	−0.733854	+	0.326733i
$923$	−41.7374			−1.37380
$924$		0			0
$925$	33.2918			1.09463
$926$	−60.7278	+	27.0377i	−1.99564	+	0.888516i
$927$	5.66230	−	1.20356i	0.185974	−	0.0395301i
$928$	−9.13544	+	10.1459i	−0.299886	+	0.333057i
$929$	−3.87436	−	36.8621i	−0.127114	−	1.20941i	−0.853119	−	0.521716i	$-0.825292\pi$
$929$	−3.87436	−	36.8621i	−0.127114	−	1.20941i	0.726005	−	0.687689i	$-0.241375\pi$
$930$	5.14542	−	3.73837i	0.168725	−	0.122586i
$931$	−12.6318	+	1.37520i	−0.413991	+	0.0450704i
$932$	−9.88883	+	30.4347i	−0.323919	+	0.996922i
$933$	2.05614	−	0.915452i	0.0673150	−	0.0299706i
$934$	−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	$0.474492\pi$
$938$	−3.41226	−	0.533943i	−0.111414	−	0.0174338i
$939$	−3.91733	−	12.0563i	−0.127837	−	0.393443i
$940$	2.57620	+	24.5109i	0.0840263	+	0.799457i
$941$	−12.5082	−	5.56900i	−0.407755	−	0.181544i	0.192601	−	0.981277i	$-0.438308\pi$
$941$	−12.5082	−	5.56900i	−0.407755	−	0.181544i	−0.600356	+	0.799733i	$0.704974\pi$
$942$	−11.2407	+	12.4840i	−0.366241	+	0.406751i
$943$	1.19970	+	1.33240i	0.0390675	+	0.0433889i
$944$	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	−0.174000	−	0.984746i	$-0.555669\pi$
$947$	23.5667	−	40.8187i	0.765815	−	1.32643i	0.939815	−	0.341685i	$-0.110998\pi$
$948$	−1.29816	+	12.3512i	−0.0421623	+	0.401148i
$949$	−10.1288	+	2.15293i	−0.328793	+	0.0698872i
$950$	−24.9457	−	5.30237i	−0.809345	−	0.172032i
$951$	17.3285	−	12.5899i	0.561915	−	0.408255i
$952$	3.13886	−	11.8022i	0.101731	−	0.382510i
$953$	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	$0.756511\pi$
$954$	−23.4172	−	26.0075i	−0.758161	−	0.842023i
$955$	−5.74209	+	54.6323i	−0.185810	+	1.76786i
$956$	11.5137	+	19.9423i	0.372379	+	0.644979i
$957$		0			0
$958$	−57.0958			−1.84468
$959$	52.0642	−	2.82572i	1.68124	−	0.0912472i
$960$	−2.79356	+	8.59768i	−0.0901616	+	0.277489i
$961$	28.2149	+	5.99726i	0.910158	+	0.193460i
$962$	33.7301	+	15.0176i	1.08750	+	0.484187i
$963$	−27.1171	−	12.0733i	−0.873836	−	0.389057i
$964$	44.2687	+	9.40959i	1.42580	+	0.303063i
$965$	5.69635	−	17.5316i	0.183372	−	0.564361i
$966$	−11.2260	−	17.2163i	−0.361189	−	0.553924i
$967$	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
$970$	10.6491	−	101.320i	0.341923	−	3.25318i
$971$	10.7606	+	11.9508i	0.345323	+	0.383520i	0.890639	−	0.454710i	$-0.150257\pi$
$971$	10.7606	+	11.9508i	0.345323	+	0.383520i	−0.545316	+	0.838230i	$0.683591\pi$
$972$	6.81977	+	20.9891i	0.218744	+	0.673225i
$973$	9.90722	+	9.87042i	0.317611	+	0.316431i
$974$	−15.8600	+	11.5229i	−0.508186	+	0.369219i
$975$	21.0549	+	4.47536i	0.674297	+	0.143326i
$976$	5.29645	−	1.12579i	0.169535	−	0.0360358i
$977$	−2.86700	+	27.2776i	−0.0917233	+	0.872689i	0.847826	+	0.530275i	$0.177911\pi$
$977$	−2.86700	+	27.2776i	−0.0917233	+	0.872689i	−0.939549	+	0.342414i	$0.888755\pi$
$978$	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
$982$	−12.9230	−	14.3525i	−0.412390	−	0.458006i
$983$	−4.99583	+	5.54844i	−0.159342	+	0.176968i	−0.817529	−	0.575887i	$-0.804657\pi$
$983$	−4.99583	+	5.54844i	−0.159342	+	0.176968i	0.658187	+	0.752854i	$0.271324\pi$
$984$	−0.148455	−	0.0660963i	−0.00473256	−	0.00210707i
$985$	−1.70519	−	16.2238i	−0.0543318	−	0.516933i
$986$	5.85682	+	18.0254i	0.186519	+	0.574047i
$987$	7.77036	+	1.21589i	0.247333	+	0.0387022i
$988$	−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	0.991837	−	0.127514i	$-0.0406998\pi$
$991$	12.1352	+	21.0188i	0.385488	+	0.667685i	−0.606349	+	0.795199i	$0.707366\pi$
$992$	9.52926	−	4.24270i	0.302554	−	0.134706i
$993$	−1.28281	+	3.94808i	−0.0407087	+	0.125288i
$994$	2.37469	−	46.9843i	0.0753206	−	1.49025i
$995$	17.2869	−	12.5597i	0.548033	−	0.398169i
$996$	−1.18459	−	11.2707i	−0.0375353	−	0.357125i
$997$	22.1590	−	24.6101i	0.701784	−	0.779410i	−0.281875	−	0.959451i	$-0.590956\pi$
$997$	22.1590	−	24.6101i	0.701784	−	0.779410i	0.983659	+	0.180041i	$0.0576231\pi$
$998$	−67.1325	+	14.2695i	−2.12504	+	0.451692i
$999$	−14.8013	+	6.58996i	−0.468292	+	0.208497i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
77.2.e.a.23.1	✓	6	11.6	odd	10
77.2.e.a.67.1	yes	6	77.39	odd	30
539.2.a.g.1.3		3	77.61	even	30
539.2.a.j.1.3		3	77.72	odd	30
539.2.e.m.67.1		6	77.17	even	30
539.2.e.m.177.1		6	77.6	even	10
693.2.i.h.100.3		6	33.17	even	10
693.2.i.h.298.3		6	231.116	even	30
847.2.e.c.485.3		6	11.5	even	5
847.2.e.c.606.3		6	77.60	even	15
847.2.n.f.9.1		24	11.4	even	5	inner
847.2.n.f.81.3		24	7.4	even	3	inner
847.2.n.f.130.3		24	77.4	even	15	inner
847.2.n.f.366.3		24	11.3	even	5	inner
847.2.n.f.487.1		24	77.25	even	15	inner
847.2.n.f.632.3		24	11.9	even	5	inner
847.2.n.f.753.1		24	77.53	even	15	inner
847.2.n.f.807.1		24	1.1	even	1	trivial
847.2.n.g.9.3		24	11.7	odd	10
847.2.n.g.81.1		24	77.32	odd	6
847.2.n.g.130.1		24	77.18	odd	30
847.2.n.g.366.1		24	11.8	odd	10
847.2.n.g.487.3		24	77.74	odd	30
847.2.n.g.632.1		24	11.2	odd	10
847.2.n.g.753.3		24	77.46	odd	30
847.2.n.g.807.3		24	11.10	odd	2
1232.2.q.m.177.2		6	44.39	even	10
1232.2.q.m.529.2		6	308.39	even	30
4851.2.a.bj.1.1		3	231.149	even	30
4851.2.a.bk.1.1		3	231.215	odd	30
5929.2.a.u.1.1		3	77.5	odd	30
5929.2.a.x.1.1		3	77.16	even	15
8624.2.a.ch.1.2		3	308.303	even	30
8624.2.a.co.1.2		3	308.215	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+(-1.71690 + 0.764415i) q^{2} +(-0.638441 + 0.135705i) q^{3} +(1.02517 - 1.13856i) q^{4} +(-0.369204 - 3.51274i) q^{5} +(0.992406 - 0.721025i) q^{6} +(2.35514 - 1.20553i) q^{7} +(0.271745 - 0.836345i) q^{8} +(-2.35145 + 1.04693i) q^{9} +(3.31908 + 5.74881i) q^{10} +(-0.500000 + 0.866025i) q^{12} +(3.56896 + 2.59300i) q^{13} +(-3.12203 + 3.87009i) q^{14} +(0.712410 + 2.19257i) q^{15} +(0.493048 + 4.69104i) q^{16} +(4.79517 + 2.13495i) q^{17} +(3.23692 - 3.59496i) q^{18} +(-1.21461 - 1.34896i) q^{19} +(-4.37797 - 3.18078i) q^{20} +(-1.34002 + 1.08926i) q^{21} +(3.16637 - 5.48432i) q^{23} +(-0.0599970 + 0.570834i) q^{24} +(-7.31229 + 1.55428i) q^{25} +(-8.10968 - 1.72377i) q^{26} +(2.94333 - 2.13845i) q^{27} +(1.04184 - 3.91735i) q^{28} +(-0.593706 - 1.82724i) q^{29} +(-2.89917 - 3.21986i) q^{30} +(-0.153438 + 1.45987i) q^{31} +(-3.55303 - 6.15403i) q^{32} -9.86484 q^{34} +(-5.10424 - 7.82792i) q^{35} +(-1.21863 + 3.75055i) q^{36} +(-4.35605 - 0.925906i) q^{37} +(3.11654 + 1.38757i) q^{38} +(-2.63045 - 1.17115i) q^{39} +(-3.03819 - 0.645788i) q^{40} +(-0.0874885 + 0.269262i) q^{41} +(1.46804 - 2.89449i) q^{42} +3.41147 q^{43} +(4.54576 + 7.87349i) q^{45} +(-1.24406 + 11.8365i) q^{46} +(-3.04747 - 3.38456i) q^{47} +(-0.951379 - 2.92804i) q^{48} +(4.09339 - 5.67839i) q^{49} +(11.3664 - 8.25817i) q^{50} +(-3.35116 - 0.712310i) q^{51} +(6.61108 - 1.40523i) q^{52} +(0.756203 - 7.19479i) q^{53} +(-3.41875 + 5.92145i) q^{54} +(-0.368241 - 2.29731i) q^{56} +(0.958517 + 0.696404i) q^{57} +(2.41611 + 2.68336i) q^{58} +(6.38339 - 7.08948i) q^{59} +(3.22672 + 1.43663i) q^{60} +(-0.119994 - 1.14167i) q^{61} +(-0.852507 - 2.62375i) q^{62} +(-4.27588 + 5.30041i) q^{63} +(3.17238 + 2.30487i) q^{64} +(7.79086 - 13.4942i) q^{65} +(0.347296 + 0.601535i) q^{67} +(7.34663 - 3.27093i) q^{68} +(-1.27729 + 3.93110i) q^{69} +(14.7473 + 9.53802i) q^{70} +(-7.65419 + 5.56110i) q^{71} +(0.236602 + 2.25112i) q^{72} +(-1.57065 + 1.74438i) q^{73} +(8.18669 - 1.74013i) q^{74} +(4.45754 - 1.98462i) q^{75} -2.78106 q^{76} +5.41147 q^{78} +(11.3455 - 5.05135i) q^{79} +(16.2964 - 3.46390i) q^{80} +(3.57804 - 3.97382i) q^{81} +(-0.0556184 - 0.529174i) q^{82} +(-9.16839 + 6.66122i) q^{83} +(-0.133552 + 2.64238i) q^{84} +(5.72912 - 17.6324i) q^{85} +(-5.85717 + 2.60778i) q^{86} +(0.627011 + 1.08602i) q^{87} +(1.73396 - 3.00330i) q^{89} +(-13.8232 - 10.0432i) q^{90} +(11.5313 + 1.80440i) q^{91} +(-2.99819 - 9.22747i) q^{92} +(-0.100150 - 0.952862i) q^{93} +(7.81943 + 3.48143i) q^{94} +(-4.29011 + 4.76465i) q^{95} +(3.10353 + 3.44682i) 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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