LMFDB - Embedded newform 847.2.n.f.487.1

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			487.1
Character	$\chi$	$=$	847.487
Dual form			847.2.n.f.807.1

$q$-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 $\left(\mathbb{Z}/847\mathbb{Z}\right)^\times$.

$n$	$122$	$365$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{4}{5}\right)$

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	−0.303054	−	0.952973i	$-0.598006\pi$
$2$	−1.71690	−	0.764415i	−1.21403	−	0.540523i	−0.910980	+	0.412450i	$0.864673\pi$
$3$	−0.638441	−	0.135705i	−0.368604	−	0.0783492i	0.0198858	−	0.999802i	$-0.493670\pi$
$3$	−0.638441	−	0.135705i	−0.368604	−	0.0783492i	−0.388490	+	0.921453i	$0.627003\pi$
$4$	1.02517	+	1.13856i	0.512584	+	0.569282i
$5$	−0.369204	+	3.51274i	−0.165113	+	1.57094i	0.527449	+	0.849587i	$0.323149\pi$
$5$	−0.369204	+	3.51274i	−0.165113	+	1.57094i	−0.692562	+	0.721358i	$0.743518\pi$
$6$	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	0.0299623	−	0.999551i	$-0.490461\pi$
$13$	3.56896	−	2.59300i	0.989851	−	0.719169i	0.959888	+	0.280382i	$0.0904613\pi$
$14$	−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	0.267804	−	0.963473i	$-0.413702\pi$
$17$	4.79517	−	2.13495i	1.16300	−	0.517801i	0.895196	+	0.445672i	$0.147035\pi$
$18$	3.23692	+	3.59496i	0.762949	+	0.847340i
$19$	−1.21461	+	1.34896i	−0.278651	+	0.309473i	−0.866182	−	0.499728i	$-0.833433\pi$
$19$	−1.21461	+	1.34896i	−0.278651	+	0.309473i	0.587531	+	0.809201i	$0.300100\pi$
$20$	−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	$0.603790\pi$
$24$	−0.0599970	−	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	−0.990926	−	0.134406i	$-0.957088\pi$
$29$	−0.593706	+	1.82724i	−0.110249	+	0.339310i	0.880678	+	0.473716i	$0.157088\pi$
$30$	−2.89917	+	3.21986i	−0.529314	+	0.587863i
$31$	−0.153438	−	1.45987i	−0.0275584	−	0.262200i	−0.999622	−	0.0274839i	$-0.991251\pi$
$31$	−0.153438	−	1.45987i	−0.0275584	−	0.262200i	0.972064	−	0.234716i	$-0.0754162\pi$
$32$	−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	−0.551545	−	0.834145i	$-0.685962\pi$
$37$	−4.35605	+	0.925906i	−0.716130	+	0.152218i	−0.164584	+	0.986363i	$0.552628\pi$
$38$	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	0.943992	−	0.329967i	$-0.107038\pi$
$41$	−0.0874885	−	0.269262i	−0.0136634	−	0.0420516i	−0.957656	+	0.287916i	$0.907038\pi$
$42$	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	−0.923211	−	0.384294i	$-0.874445\pi$
$47$	−3.04747	+	3.38456i	−0.444520	+	0.493689i	0.478691	+	0.877983i	$0.341111\pi$
$48$	−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	0.915012	+	0.403427i	$0.132181\pi$
$53$	0.756203	+	7.19479i	0.103872	+	0.988281i	−0.811139	+	0.584853i	$0.801152\pi$
$54$	−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	0.998014	−	0.0629914i	$-0.0200641\pi$
$59$	6.38339	+	7.08948i	0.831047	+	0.922971i	−0.166967	+	0.985962i	$0.553397\pi$
$60$	3.22672	−	1.43663i	0.416568	−	0.185468i
$61$	−0.119994	+	1.14167i	−0.0153637	+	0.146176i	−0.999514	−	0.0311581i	$-0.990080\pi$
$61$	−0.119994	+	1.14167i	−0.0153637	+	0.146176i	0.984151	+	0.177334i	$0.0567471\pi$
$62$	−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	−0.844031	−	0.536294i	$-0.819824\pi$
$67$	0.347296	−	0.601535i	0.0424290	−	0.0734892i	0.886460	+	0.462805i	$0.153157\pi$
$68$	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	0.0322204	−	0.999481i	$-0.489742\pi$
$71$	−7.65419	−	5.56110i	−0.908386	−	0.659981i	−0.940606	+	0.339500i	$0.889742\pi$
$72$	0.236602	−	2.25112i	0.0278838	−	0.265297i
$73$	−1.57065	−	1.74438i	−0.183830	−	0.204164i	0.644185	−	0.764870i	$-0.277197\pi$
$73$	−1.57065	−	1.74438i	−0.183830	−	0.204164i	−0.828015	+	0.560705i	$0.810530\pi$
$74$	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	0.929246	−	0.369461i	$-0.120458\pi$
$79$	11.3455	+	5.05135i	1.27647	+	0.568321i	0.347224	+	0.937782i	$0.387124\pi$
$80$	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	−0.0429184	−	0.999079i	$-0.513666\pi$
$83$	−9.16839	−	6.66122i	−1.00636	−	0.731164i	−0.963443	+	0.267914i	$0.913666\pi$
$84$	−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	0.943171	−	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
$91$	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	−0.998791	−	0.0491638i	$-0.984344\pi$
$97$	−12.4162	+	9.02091i	−1.26068	+	0.915935i	−0.261886	+	0.965099i	$0.584344\pi$
$98$	−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	0.972457	+	0.233081i	$0.0748807\pi$
$101$	0.700585	+	6.66562i	0.0697108	+	0.663254i	−0.902747	+	0.430173i	$0.858453\pi$
$102$	6.29811	+	1.33870i	0.623606	+	0.132552i
$103$	−2.19982	+	0.467587i	−0.216755	+	0.0460727i	−0.315009	−	0.949089i	$-0.602008\pi$
$103$	−2.19982	+	0.467587i	−0.216755	+	0.0460727i	0.0982540	+	0.995161i	$0.468674\pi$
$104$	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	−0.243990	−	0.969778i	$-0.578456\pi$
$107$	7.71647	−	8.57001i	0.745980	−	0.828494i	0.989969	+	0.141284i	$0.0451229\pi$
$108$	0.582639	+	5.54344i	0.0560645	+	0.533418i
$109$	−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
$112$	6.81639	−	10.4537i	0.644088	−	0.987781i
$113$	1.54748	+	4.76264i	0.145574	+	0.448032i	0.997084	−	0.0763064i	$-0.0243127\pi$
$113$	1.54748	+	4.76264i	0.145574	+	0.448032i	−0.851510	+	0.524338i	$0.824313\pi$
$114$	−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	−0.0552046	−	0.998475i	$-0.517581\pi$
$127$	−11.5159	−	8.36678i	−1.02187	−	0.742432i	−0.966665	+	0.256043i	$0.917581\pi$
$128$	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	0.955838	−	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
$135$	−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	0.549560	−	0.835454i	$-0.314795\pi$
$137$	18.0036	−	8.01572i	1.53815	−	0.684829i	0.988591	+	0.150626i	$0.0481288\pi$
$138$	−0.812005	+	7.72571i	−0.0691224	+	0.657656i
$139$	1.63340	−	5.02710i	0.138544	−	0.426393i	−0.857581	−	0.514349i	$-0.828034\pi$
$139$	1.63340	−	5.02710i	0.138544	−	0.426393i	0.996124	+	0.0879561i	$0.0280335\pi$
$140$	−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	0.640307	+	0.768119i	$0.278807\pi$
$149$	−1.77860	+	16.9223i	−0.145709	+	1.38633i	−0.786015	+	0.618207i	$0.787859\pi$
$150$	−6.13609	−	6.81482i	−0.501010	−	0.556428i
$151$	1.27425	+	0.270850i	0.103697	+	0.0220415i	0.259468	−	0.965752i	$-0.416453\pi$
$151$	1.27425	+	0.270850i	0.103697	+	0.0220415i	−0.155771	+	0.987793i	$0.549786\pi$
$152$	−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	−0.360411	−	0.932794i	$-0.617364\pi$
$157$	−13.3953	−	2.84727i	−1.06906	−	0.227237i	−0.708653	+	0.705557i	$0.750697\pi$
$158$	−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	0.898604	−	0.438760i	$-0.144582\pi$
$163$	14.9864	+	6.67238i	1.17383	+	0.522621i	0.275222	+	0.961381i	$0.411249\pi$
$164$	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	−0.815188	−	0.579196i	$-0.803367\pi$
$167$	−6.67138	+	4.84704i	−0.516247	+	0.375075i	0.298941	+	0.954272i	$0.403367\pi$
$168$	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	0.0177026	+	0.999843i	$0.494365\pi$
$173$	−12.8703	+	14.2940i	−0.978514	+	1.08675i	−0.996216	+	0.0869065i	$0.972302\pi$
$174$	−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	0.256190	−	0.966627i	$-0.417533\pi$
$179$	1.29868	+	0.276044i	0.0970681	+	0.0206325i	−0.159122	+	0.987259i	$0.550866\pi$
$180$	13.6246	−	2.89601i	1.01552	−	0.215855i
$181$	−14.2813	−	10.3760i	−1.06152	−	0.771242i	−0.0871538	−	0.996195i	$-0.527777\pi$
$181$	−14.2813	−	10.3760i	−1.06152	−	0.771242i	−0.974370	+	0.224953i	$0.927777\pi$
$182$	−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	−0.722255	−	0.691627i	$-0.756894\pi$
$191$	−15.2128	+	3.23357i	−1.10076	+	0.233973i	−0.378502	+	0.925600i	$0.623561\pi$
$192$	−2.33816	+	1.04101i	−0.168742	+	0.0751287i
$193$	4.76774	−	2.12273i	0.343189	−	0.152798i	−0.227902	−	0.973684i	$-0.573187\pi$
$193$	4.76774	−	2.12273i	0.343189	−	0.152798i	0.571092	+	0.820886i	$0.306520\pi$
$194$	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	−0.738671	−	0.674067i	$-0.764546\pi$
$199$	3.02481	−	5.23913i	0.214423	−	0.371392i	0.953094	+	0.302674i	$0.0978794\pi$
$200$	−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	−0.318721	−	0.947848i	$-0.603253\pi$
$211$	7.03407	−	5.11055i	0.484246	−	0.351825i	0.802967	+	0.596023i	$0.203253\pi$
$212$	−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	0.948737	−	0.316066i	$-0.102362\pi$
$223$	−0.0684872	−	0.210782i	−0.00458624	−	0.0141150i	−0.953323	+	0.301951i	$0.902362\pi$
$224$	−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	0.918981	−	0.394303i	$-0.129014\pi$
$227$	6.49033	+	7.20824i	0.430778	+	0.478428i	−0.488202	+	0.872730i	$0.662347\pi$
$228$	1.77554	+	0.377403i	0.117588	+	0.0249941i
$229$	21.6461	+	9.63746i	1.43041	+	0.636861i	0.968261	−	0.249939i	$-0.0804107\pi$
$229$	21.6461	+	9.63746i	1.43041	+	0.636861i	0.462152	+	0.886801i	$0.347077\pi$
$230$	42.0378			2.77189
$231$		0			0
$232$	−1.68954			−0.110924
$233$	−19.0813	−	8.49556i	−1.25006	−	0.556563i	−0.328392	−	0.944542i	$-0.606507\pi$
$233$	−19.0813	−	8.49556i	−1.25006	−	0.556563i	−0.921668	+	0.387979i	$0.873173\pi$
$234$	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	−0.981343	−	0.192264i	$-0.938417\pi$
$239$	−4.64453	−	14.2944i	−0.300430	−	0.924628i	0.680913	−	0.732364i	$-0.261583\pi$
$240$	−9.93420	−	4.42299i	−0.641250	−	0.285503i
$241$	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
$245$	−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	−0.679882	−	0.733322i	$-0.737969\pi$
$251$	−3.05050	+	2.21632i	−0.192546	+	0.139893i	0.487336	+	0.873215i	$0.337969\pi$
$252$	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	0.0640259	−	0.997948i	$-0.479606\pi$
$257$	8.47119	−	1.80061i	0.528418	−	0.112319i	0.464393	+	0.885629i	$0.346273\pi$
$258$	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	−0.941844	−	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
$266$	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	−0.914083	−	0.405528i	$-0.867088\pi$
$269$	−20.0809	+	8.94061i	−1.22436	+	0.545119i	−0.310274	+	0.950647i	$0.600421\pi$
$270$	22.0627	−	9.82295i	1.34269	−	0.597806i
$271$	9.63675	−	2.04836i	0.585391	−	0.124429i	0.0943104	−	0.995543i	$-0.469935\pi$
$271$	9.63675	−	2.04836i	0.585391	−	0.124429i	0.491081	+	0.871114i	$0.336602\pi$
$272$	−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	0.774409	+	0.632686i	$0.218048\pi$
$277$	2.47096	+	23.5096i	0.148465	+	1.41255i	−0.625943	+	0.779869i	$0.715286\pi$
$278$	−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	0.906560	−	0.422078i	$-0.138699\pi$
$281$	13.1637	+	9.56401i	0.785282	+	0.570541i	−0.121278	+	0.992619i	$0.538699\pi$
$282$	−5.46469	+	1.16156i	−0.325417	+	0.0691696i
$283$	16.6268	+	3.53413i	0.988360	+	0.210082i	0.673606	−	0.739091i	$-0.264745\pi$
$283$	16.6268	+	3.53413i	0.988360	+	0.210082i	0.314754	+	0.949173i	$0.398078\pi$
$284$	−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	−0.746258	−	0.665657i	$-0.768152\pi$
$293$	4.25775	−	13.1040i	0.248740	−	0.765544i	0.994999	−	0.0998879i	$-0.0318484\pi$
$294$	−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	0.111284	−	0.993789i	$-0.464504\pi$
$311$	−3.37296	−	0.716944i	−0.191263	−	0.0406542i	−0.302547	+	0.953134i	$0.597837\pi$
$312$	−1.69430	−	1.88171i	−0.0959207	−	0.106531i
$313$	2.03014	−	19.3155i	0.114750	−	1.09178i	−0.773937	−	0.633263i	$-0.781715\pi$
$313$	2.03014	−	19.3155i	0.114750	−	1.09178i	0.888687	−	0.458514i	$-0.151618\pi$
$314$	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	−0.999796	−	0.0201843i	$-0.993575\pi$
$317$	−29.9790	−	13.3475i	−1.68379	−	0.749672i	−0.683994	−	0.729487i	$-0.739759\pi$
$318$	−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	0.940089	−	0.340929i	$-0.110742\pi$
$331$	3.18004	+	5.50800i	0.174791	+	0.302747i	−0.765298	+	0.643676i	$0.777408\pi$
$332$	−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	−0.730771	−	0.682622i	$-0.760839\pi$
$337$	4.80363	−	14.7841i	0.261671	−	0.805339i	0.992442	−	0.122717i	$-0.0391606\pi$
$338$	−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	0.138610	−	0.990347i	$-0.455737\pi$
$347$	18.0193	−	8.02273i	0.967329	−	0.430683i	0.828719	+	0.559665i	$0.189070\pi$
$348$	1.87929	−	0.399455i	0.100741	−	0.0214131i
$349$	1.79040	+	5.51028i	0.0958379	+	0.294959i	0.987471	−	0.157800i	$-0.0504400\pi$
$349$	1.79040	+	5.51028i	0.0958379	+	0.294959i	−0.891633	+	0.452758i	$0.850440\pi$
$350$	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	−0.0342183	+	0.999414i	$0.510894\pi$
$353$	−16.5831	+	28.7227i	−0.882627	+	1.52876i	−0.848409	+	0.529341i	$0.822439\pi$
$354$	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	−0.0979608	−	0.995190i	$-0.531232\pi$
$359$	4.11778	−	0.875260i	0.217328	−	0.0461945i	0.315289	+	0.948996i	$0.397899\pi$
$360$	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	0.300915	−	0.953651i	$-0.402708\pi$
$367$	−13.0071	−	14.4459i	−0.678965	−	0.754067i	−0.979881	+	0.199583i	$0.936041\pi$
$368$	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	0.982345	−	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
$376$	−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	0.950320	−	0.311273i	$-0.100755\pi$
$379$	18.4546	+	13.4080i	0.947947	+	0.688724i	−0.00237342	+	0.999997i	$0.500755\pi$
$380$	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	0.591179	−	0.806540i	$-0.298663\pi$
$383$	7.58115	+	3.37534i	0.387379	+	0.172472i	−0.203800	+	0.979012i	$0.565329\pi$
$384$	−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	0.904809	−	0.425817i	$-0.140013\pi$
$389$	7.62783	+	8.47156i	0.386746	+	0.429525i	−0.518063	+	0.855343i	$0.673347\pi$
$390$	−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	0.771550	−	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
$399$	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	0.978129	+	0.207997i	$0.0666945\pi$
$401$	−0.437958	+	4.16689i	−0.0218706	+	0.208085i	−1.00000		8.74528e-5i	$0.999972\pi$
$402$	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	0.996339	−	0.0854950i	$-0.0272472\pi$
$409$	0.0808338	+	0.769082i	0.00399697	+	0.0380287i	−0.992342	+	0.123524i	$0.960581\pi$
$410$	−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	0.897772	−	0.440461i	$-0.145185\pi$
$421$	−1.79406	−	5.52156i	−0.0874373	−	0.269104i	−0.985209	+	0.171357i	$0.945185\pi$
$422$	−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	−0.941471	−	0.337095i	$-0.890556\pi$
$431$	−1.88214	−	17.9073i	−0.0906594	−	0.862567i	0.850811	−	0.525471i	$-0.176111\pi$
$432$	11.4828	−	12.7529i	0.552466	−	0.613575i
$433$	0.723251	−	2.22594i	0.0347572	−	0.106972i	−0.932173	−	0.362014i	$-0.882089\pi$
$433$	0.723251	−	2.22594i	0.0347572	−	0.106972i	0.966930	+	0.255042i	$0.0820893\pi$
$434$	−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	−0.733581	−	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
$443$	12.6974	−	14.1019i	0.603271	−	0.670001i	−0.361719	−	0.932287i	$-0.617810\pi$
$443$	12.6974	−	14.1019i	0.603271	−	0.670001i	0.964990	+	0.262287i	$0.0844766\pi$
$444$	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	0.209404	−	0.977829i	$-0.432848\pi$
$449$	25.5141	−	18.5371i	1.20408	−	0.874818i	0.994680	+	0.103011i	$0.0328477\pi$
$450$	−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	−0.928692	−	0.370853i	$-0.879065\pi$
$457$	1.21447	−	11.5549i	0.0568105	−	0.540516i	0.985502	−	0.169663i	$-0.0542679\pi$
$458$	−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	−0.287743	−	0.957708i	$-0.592905\pi$
$467$	4.16711	−	39.6474i	0.192831	−	1.83466i	0.480574	−	0.876954i	$-0.340428\pi$
$468$	−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	0.341224	−	0.939982i	$-0.389158\pi$
$479$	27.7535	−	12.3567i	1.26809	−	0.564590i	0.926866	+	0.375391i	$0.122492\pi$
$480$	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	0.433196	−	0.901300i	$-0.357386\pi$
$487$	10.2031	+	2.16874i	0.462348	+	0.0982751i	0.0291523	+	0.999575i	$0.490719\pi$
$488$	−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	−0.853479	−	0.521127i	$-0.825512\pi$
$491$	3.17555	−	9.77335i	0.143311	−	0.441065i	0.996790	+	0.0800618i	$0.0255118\pi$
$492$	−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	0.679761	−	0.733434i	$-0.262084\pi$
$499$	35.7205	−	7.59262i	1.59907	−	0.339892i	0.919307	+	0.393542i	$0.128750\pi$
$500$	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	0.896001	+	0.444053i	$0.146460\pi$
$503$	9.69163	+	29.8278i	0.432128	+	1.32995i	−0.463872	+	0.885902i	$0.653540\pi$
$504$	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	−0.889817	−	0.456318i	$-0.849168\pi$
$509$	−7.73815	+	8.59409i	−0.342987	+	0.380926i	0.546829	+	0.837244i	$0.315835\pi$
$510$	−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	−1.00000		0.000412263i	$-0.999869\pi$
$521$	−20.4489	−	22.7108i	−0.895881	−	0.994977i	0.104118	−	0.994565i	$-0.466798\pi$
$522$	−8.49064	+	3.78027i	−0.371625	+	0.165458i
$523$	−0.465687	+	4.43071i	−0.0203631	+	0.193742i	−0.999974	−	0.00716066i	$-0.997721\pi$
$523$	−0.465687	+	4.43071i	−0.0203631	+	0.193742i	0.979611	+	0.200902i	$0.0643873\pi$
$524$	−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	0.707102	−	0.707112i	$-0.250002\pi$
$541$	15.2293	+	6.78052i	0.654759	+	0.291517i	−0.0523429	+	0.998629i	$0.516669\pi$
$542$	−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	−0.841313	−	0.540548i	$-0.818217\pi$
$547$	−11.1889	−	34.4359i	−0.478402	−	1.47237i	0.362911	−	0.931824i	$-0.381783\pi$
$548$	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	0.752567	−	0.658516i	$-0.228815\pi$
$557$	0.448277	+	0.497862i	0.0189941	+	0.0210951i	−0.733573	+	0.679611i	$0.762149\pi$
$558$	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	−0.984983	−	0.172649i	$-0.944767\pi$
$563$	−1.36244	−	12.9627i	−0.0574200	−	0.546315i	0.927563	−	0.373666i	$-0.121899\pi$
$564$	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	−0.992786	−	0.119896i	$-0.961744\pi$
$569$	−18.3619	+	20.3930i	−0.769773	+	0.854920i	0.223013	+	0.974815i	$0.428411\pi$
$570$	−0.822099	−	7.82175i	−0.0344340	−	0.327617i
$571$	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
$574$	−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	0.0972978	−	0.995255i	$-0.468980\pi$
$577$	21.6673	−	9.64690i	0.902022	−	0.401606i	0.804724	+	0.593649i	$0.202313\pi$
$578$	−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	0.0878782	+	0.996131i	$0.471991\pi$
$587$	−13.7792	+	42.4080i	−0.568728	+	1.75036i	−0.656606	+	0.754234i	$0.728009\pi$
$588$	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	−0.851686	−	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
$597$	−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	−0.418518	−	0.908208i	$-0.637450\pi$
$599$	−0.578369	+	0.257506i	−0.0236315	+	0.0105214i	0.394887	+	0.918730i	$0.370784\pi$
$600$	−0.448517	+	4.26735i	−0.0183106	+	0.174214i
$601$	1.06871	−	3.28915i	0.0435936	−	0.134167i	−0.926891	−	0.375331i	$-0.877529\pi$
$601$	1.06871	−	3.28915i	0.0435936	−	0.134167i	0.970484	+	0.241164i	$0.0775291\pi$
$602$	−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	−0.976530	−	0.215383i	$-0.930900\pi$
$607$	−44.1013	−	19.6352i	−1.79002	−	0.796967i	−0.813487	−	0.581583i	$-0.802433\pi$
$608$	−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	−0.233393	−	0.972382i	$-0.574983\pi$
$613$	−20.8497	−	4.43174i	−0.842112	−	0.178996i	−0.608719	+	0.793386i	$0.708316\pi$
$614$	−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	−0.572340	−	0.820017i	$-0.693964\pi$
$619$	−35.5464	−	7.55561i	−1.42873	−	0.303686i	−0.856389	+	0.516331i	$0.827297\pi$
$620$	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	−0.804127	−	0.594457i	$-0.797367\pi$
$631$	4.91940	−	15.1404i	0.195838	−	0.602728i	0.999966	−	0.00827144i	$-0.00263291\pi$
$632$	−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	0.442466	−	0.896785i	$-0.354104\pi$
$641$	12.2013	+	2.59347i	0.481923	+	0.102436i	0.0394571	+	0.999221i	$0.487437\pi$
$642$	13.8371	−	2.94116i	0.546106	−	0.116078i
$643$	29.7986	+	21.6499i	1.17514	+	0.853790i	0.991615	−	0.129225i	$-0.0412490\pi$
$643$	29.7986	+	21.6499i	1.17514	+	0.853790i	0.183525	+	0.983015i	$0.441249\pi$
$644$	−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	−0.952592	−	0.304252i	$-0.901594\pi$
$647$	−2.13852	−	20.3467i	−0.0840739	−	0.799910i	0.868518	−	0.495658i	$-0.165073\pi$
$648$	−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	0.0997488	−	0.995013i	$-0.468196\pi$
$653$	15.2194	−	3.23499i	0.595582	−	0.126595i	0.495833	+	0.868418i	$0.334863\pi$
$654$	−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	−0.992817	−	0.119640i	$-0.961826\pi$
$661$	−10.0988	+	17.4916i	−0.392798	+	0.680345i	0.600020	+	0.799985i	$0.295159\pi$
$662$	−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	−0.457293	−	0.889316i	$-0.651181\pi$
$673$	6.41253	−	4.65898i	0.247185	−	0.179590i	0.704478	+	0.709726i	$0.251181\pi$
$674$	−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	−0.644676	−	0.764456i	$-0.723008\pi$
$677$	3.76892	−	35.8589i	0.144852	−	1.37817i	0.789528	−	0.613715i	$-0.210325\pi$
$678$	−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	−0.723272	−	0.690564i	$-0.757363\pi$
$683$	6.17840	−	10.7013i	0.236410	−	0.409474i	0.959681	+	0.281090i	$0.0906959\pi$
$684$	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	0.541012	−	0.841015i	$-0.318041\pi$
$691$	7.30836	+	3.25389i	0.278023	+	0.123784i	−0.262988	+	0.964799i	$0.584708\pi$
$692$	−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	0.848556	−	0.529105i	$-0.177472\pi$
$701$	−3.94341	−	12.1366i	−0.148940	−	0.458392i	−0.997497	+	0.0707137i	$0.977472\pi$
$702$	−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	−0.999868	−	0.0162533i	$-0.994826\pi$
$709$	−0.491809	+	4.67925i	−0.0184703	+	0.175733i	0.981398	+	0.191986i	$0.0614929\pi$
$710$	−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	−0.919698	+	0.392627i	$0.871566\pi$
$719$	−51.4719	+	10.9407i	−1.91958	+	0.408019i	−0.999882	+	0.0153924i	$0.995100\pi$
$720$	−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	−0.718359	−	0.695673i	$-0.755106\pi$
$733$	−29.5555	+	6.28221i	−1.09166	+	0.232039i	−0.373298	+	0.927712i	$0.621773\pi$
$734$	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	0.991248	+	0.132014i	$0.0421445\pi$
$739$	1.33499	+	12.7016i	0.0491085	+	0.467236i	−0.942139	+	0.335222i	$0.891189\pi$
$740$	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	−0.129837	−	0.991535i	$-0.541445\pi$
$743$	−30.3372	−	22.0413i	−1.11296	−	0.808616i	−0.983128	+	0.182919i	$0.941445\pi$
$744$	−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	−0.101828	−	0.994802i	$-0.532469\pi$
$751$	24.6138	−	27.3363i	0.898169	−	0.997517i	0.999996	−	0.00271535i	$-0.000864325\pi$
$752$	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	−0.553892	−	0.832588i	$-0.686858\pi$
$757$	1.83749	−	1.33501i	0.0667846	−	0.0485219i	0.620677	+	0.784067i	$0.286858\pi$
$758$	−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	0.230999	−	0.972954i	$-0.425801\pi$
$761$	−9.30974	−	4.14496i	−0.337478	−	0.150255i	−0.568477	+	0.822699i	$0.692467\pi$
$762$	−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	0.393629	−	0.919269i	$-0.371219\pi$
$773$	10.5464	+	2.24170i	0.379327	+	0.0806284i	−0.0143023	+	0.999898i	$0.504553\pi$
$774$	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	−0.0285658	−	0.999592i	$-0.509094\pi$
$787$	19.5017	−	8.68273i	0.695161	−	0.309506i	0.723727	+	0.690086i	$0.242427\pi$
$788$	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	−0.141310	−	0.989965i	$-0.545132\pi$
$797$	−31.8022	−	23.1056i	−1.12649	−	0.818443i	−0.985180	+	0.171522i	$0.945132\pi$
$798$	−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	−0.458212	−	0.888843i	$-0.651510\pi$
$809$	−2.96592	+	1.32051i	−0.104276	+	0.0464268i	0.353936	+	0.935270i	$0.384843\pi$
$810$	34.7205	−	7.38007i	1.21995	−	0.259309i
$811$	−10.3229	−	31.7706i	−0.362486	−	1.11562i	−0.951540	−	0.307524i	$-0.900500\pi$
$811$	−10.3229	−	31.7706i	−0.362486	−	1.11562i	0.589054	−	0.808093i	$-0.299500\pi$
$812$	−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	−0.601491	−	0.798879i	$-0.705427\pi$
$821$	−23.6688	+	5.03096i	−0.826047	+	0.175582i	−0.224556	+	0.974461i	$0.572093\pi$
$822$	23.6464	+	5.02620i	0.824763	+	0.175309i
$823$	4.88306	+	46.4592i	0.170213	+	1.61947i	0.662519	+	0.749045i	$0.269487\pi$
$823$	4.88306	+	46.4592i	0.170213	+	1.61947i	−0.492307	+	0.870422i	$0.663846\pi$
$824$	−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	−0.560740	−	0.827992i	$-0.689483\pi$
$827$	1.53707	−	1.11674i	0.0534491	−	0.0388330i	0.614189	+	0.789159i	$0.289483\pi$
$828$	16.7106	−	18.5590i	0.580733	−	0.644970i
$829$	34.1056	+	37.8782i	1.18454	+	1.31556i	0.938084	+	0.346408i	$0.112599\pi$
$829$	34.1056	+	37.8782i	1.18454	+	1.31556i	0.246454	+	0.969154i	$0.420735\pi$
$830$	−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	0.867494	+	0.497447i	$0.165729\pi$
$839$	13.2682	+	40.8353i	0.458069	+	1.40979i	−0.409426	+	0.912343i	$0.634271\pi$
$840$	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	0.985768	+	0.168113i	$0.0537673\pi$
$853$	42.3569	+	30.7741i	1.45027	+	1.05368i	0.464504	+	0.885571i	$0.346233\pi$
$854$	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	−0.874257	−	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
$861$	−0.176060	+	0.456115i	−0.00600012	+	0.0155443i
$862$	−10.4572	+	32.1839i	−0.356173	+	1.09619i
$863$	2.37233	−	22.5712i	0.0807550	−	0.768333i	−0.876950	−	0.480581i	$-0.840426\pi$
$863$	2.37233	−	22.5712i	0.0807550	−	0.768333i	0.957705	−	0.287751i	$-0.0929076\pi$
$864$	−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	−0.729107	−	0.684400i	$-0.760064\pi$
$877$	0.821984	−	0.912906i	0.0277564	−	0.0308266i	0.756863	+	0.653573i	$0.226731\pi$
$878$	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	0.857527	+	0.514440i	$0.172000\pi$
$883$	13.8519	+	42.6317i	0.466153	+	1.43467i	−0.391374	+	0.920232i	$0.628000\pi$
$884$	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	−0.569748	−	0.821819i	$-0.692959\pi$
$887$	−22.5149	+	4.78568i	−0.755975	+	0.160687i	−0.186227	+	0.982507i	$0.559626\pi$
$888$	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	−0.788511	−	0.615020i	$-0.789148\pi$
$907$	−25.8724	+	11.5191i	−0.859080	+	0.382487i	−0.0705681	+	0.997507i	$0.522481\pi$
$908$	−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	−0.626954	−	0.779056i	$-0.715699\pi$
$911$	−2.40760	+	1.74922i	−0.0797673	+	0.0579544i	0.547187	+	0.837010i	$0.315699\pi$
$912$	−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	−0.890476	−	0.455029i	$-0.849629\pi$
$919$	2.27808	−	21.6745i	0.0751469	−	0.714975i	0.965623	−	0.259945i	$-0.0837045\pi$
$920$	−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	0.726005	+	0.687689i	$0.241375\pi$
$929$	−3.87436	+	36.8621i	−0.127114	+	1.20941i	−0.853119	+	0.521716i	$0.825292\pi$
$930$	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	0.0800487	−	0.996791i	$-0.474492\pi$
$937$	32.2264	−	23.4138i	1.05279	−	0.764896i	0.972741	+	0.231894i	$0.0744924\pi$
$938$	−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	−0.600356	−	0.799733i	$-0.704974\pi$
$941$	−12.5082	+	5.56900i	−0.407755	+	0.181544i	0.192601	+	0.981277i	$0.438308\pi$
$942$	−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	0.939815	+	0.341685i	$0.110998\pi$
$947$	23.5667	+	40.8187i	0.765815	+	1.32643i	−0.174000	+	0.984746i	$0.555669\pi$
$948$	−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	−0.721421	−	0.692496i	$-0.756511\pi$
$953$	8.31224	−	25.5825i	0.269260	−	0.828697i	0.990681	−	0.136201i	$-0.0434892\pi$
$954$	−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	−0.545316	−	0.838230i	$-0.683591\pi$
$971$	10.7606	−	11.9508i	0.345323	−	0.383520i	0.890639	+	0.454710i	$0.150257\pi$
$972$	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	−0.939549	−	0.342414i	$-0.888755\pi$
$977$	−2.86700	−	27.2776i	−0.0917233	−	0.872689i	0.847826	−	0.530275i	$-0.177911\pi$
$978$	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	0.658187	−	0.752854i	$-0.271324\pi$
$983$	−4.99583	−	5.54844i	−0.159342	−	0.176968i	−0.817529	+	0.575887i	$0.804657\pi$
$984$	−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	−0.606349	−	0.795199i	$-0.707366\pi$
$991$	12.1352	−	21.0188i	0.385488	−	0.667685i	0.991837	+	0.127514i	$0.0406998\pi$
$992$	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	0.983659	−	0.180041i	$-0.0576231\pi$
$997$	22.1590	+	24.6101i	0.701784	+	0.779410i	−0.281875	+	0.959451i	$0.590956\pi$
$998$	−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.487.1		24
7.2	even	3	inner	847.2.n.f.366.3		24
11.2	odd	10		77.2.e.a.67.1	yes	6
11.3	even	5	inner	847.2.n.f.753.1		24
11.4	even	5	inner	847.2.n.f.81.3		24
11.5	even	5	inner	847.2.n.f.130.3		24
11.6	odd	10		847.2.n.g.130.1		24
11.7	odd	10		847.2.n.g.81.1		24
11.8	odd	10		847.2.n.g.753.3		24
11.9	even	5		847.2.e.c.606.3		6
11.10	odd	2		847.2.n.g.487.3		24
33.2	even	10		693.2.i.h.298.3		6
44.35	even	10		1232.2.q.m.529.2		6
77.2	odd	30		77.2.e.a.23.1	✓	6
77.9	even	15		847.2.e.c.485.3		6
77.13	even	10		539.2.e.m.67.1		6
77.16	even	15	inner	847.2.n.f.9.1		24
77.24	even	30		539.2.a.g.1.3		3
77.30	odd	30		847.2.n.g.632.1		24
77.31	odd	30		5929.2.a.u.1.1		3
77.37	even	15	inner	847.2.n.f.807.1		24
77.46	odd	30		539.2.a.j.1.3		3
77.51	odd	30		847.2.n.g.807.3		24
77.53	even	15		5929.2.a.x.1.1		3
77.58	even	15	inner	847.2.n.f.632.3		24
77.65	odd	6		847.2.n.g.366.1		24
77.68	even	30		539.2.e.m.177.1		6
77.72	odd	30		847.2.n.g.9.3		24
231.2	even	30		693.2.i.h.100.3		6
231.101	odd	30		4851.2.a.bk.1.1		3
231.200	even	30		4851.2.a.bj.1.1		3
308.79	even	30		1232.2.q.m.177.2		6
308.123	even	30		8624.2.a.ch.1.2		3
308.255	odd	30		8624.2.a.co.1.2		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
77.2.e.a.23.1	✓	6	77.2	odd	30
77.2.e.a.67.1	yes	6	11.2	odd	10
539.2.a.g.1.3		3	77.24	even	30
539.2.a.j.1.3		3	77.46	odd	30
539.2.e.m.67.1		6	77.13	even	10
539.2.e.m.177.1		6	77.68	even	30
693.2.i.h.100.3		6	231.2	even	30
693.2.i.h.298.3		6	33.2	even	10
847.2.e.c.485.3		6	77.9	even	15
847.2.e.c.606.3		6	11.9	even	5
847.2.n.f.9.1		24	77.16	even	15	inner
847.2.n.f.81.3		24	11.4	even	5	inner
847.2.n.f.130.3		24	11.5	even	5	inner
847.2.n.f.366.3		24	7.2	even	3	inner
847.2.n.f.487.1		24	1.1	even	1	trivial
847.2.n.f.632.3		24	77.58	even	15	inner
847.2.n.f.753.1		24	11.3	even	5	inner
847.2.n.f.807.1		24	77.37	even	15	inner
847.2.n.g.9.3		24	77.72	odd	30
847.2.n.g.81.1		24	11.7	odd	10
847.2.n.g.130.1		24	11.6	odd	10
847.2.n.g.366.1		24	77.65	odd	6
847.2.n.g.487.3		24	11.10	odd	2
847.2.n.g.632.1		24	77.30	odd	30
847.2.n.g.753.3		24	11.8	odd	10
847.2.n.g.807.3		24	77.51	odd	30
1232.2.q.m.177.2		6	308.79	even	30
1232.2.q.m.529.2		6	44.35	even	10
4851.2.a.bj.1.1		3	231.200	even	30
4851.2.a.bk.1.1		3	231.101	odd	30
5929.2.a.u.1.1		3	77.31	odd	30
5929.2.a.x.1.1		3	77.53	even	15
8624.2.a.ch.1.2		3	308.123	even	30
8624.2.a.co.1.2		3	308.255	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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