LMFDB - Embedded newform 847.2.n.g.9.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [847,2,Mod(9,847)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("847.9"); S:= CuspForms(chi, 2); N := Newforms(S);

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

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

Newform invariants

comment:select newform

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

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

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

Embedding invariants

Embedding label			9.3
Character	$\chi$	$=$	847.9
Dual form			847.2.n.g.753.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.25755 + 1.39666i) q^{2} +(0.596274 + 0.265478i) q^{3} +(-0.160147 + 1.52370i) q^{4} +(-3.45490 - 0.734363i) q^{5} +(0.379065 + 1.16664i) q^{6} +(1.19676 - 2.35961i) q^{7} +(0.711438 - 0.516890i) q^{8} +(-1.72233 - 1.91284i) q^{9} +(-3.31908 - 5.74881i) q^{10} +(-0.500000 + 0.866025i) q^{12} +(1.36322 - 4.19556i) q^{13} +(4.80055 - 1.29588i) q^{14} +(-1.86511 - 1.35508i) q^{15} +(4.61381 + 0.980695i) q^{16} +(-3.51225 + 3.90075i) q^{17} +(0.505656 - 4.81100i) q^{18} +(-0.189741 - 1.80526i) q^{19} +(1.67224 - 5.14662i) q^{20} +(1.34002 - 1.08926i) q^{21} +(3.16637 - 5.48432i) q^{23} +(0.561435 - 0.119337i) q^{24} +(6.82935 + 3.04062i) q^{25} +(7.57408 - 3.37220i) q^{26} +(-1.12425 - 3.46009i) q^{27} +(3.40367 + 2.20138i) q^{28} +(-1.55434 - 1.12930i) q^{29} +(-0.452896 - 4.30901i) q^{30} +(-1.43583 + 0.305196i) q^{31} +(3.55303 + 6.15403i) q^{32} -9.86484 q^{34} +(-5.86749 + 7.27338i) q^{35} +(3.19041 - 2.31797i) q^{36} +(4.06835 - 1.81135i) q^{37} +(2.28272 - 2.53522i) q^{38} +(1.92668 - 2.13980i) q^{39} +(-2.83753 + 1.26335i) q^{40} +(-0.229048 + 0.166413i) q^{41} +(3.20648 + 0.501742i) q^{42} -3.41147 q^{43} +(4.54576 + 7.87349i) q^{45} +(11.6416 - 2.47450i) q^{46} +(0.476062 + 4.52943i) q^{47} +(2.49074 + 1.80963i) q^{48} +(-4.13554 - 5.64777i) q^{49} +(4.34157 + 13.3620i) q^{50} +(-3.12983 + 1.39349i) q^{51} +(6.17444 + 2.74904i) q^{52} +(7.07633 - 1.50412i) q^{53} +(3.41875 - 5.92145i) q^{54} +(-0.368241 - 2.29731i) q^{56} +(0.366121 - 1.12680i) q^{57} +(-0.377433 - 3.59103i) q^{58} +(-0.997184 + 9.48757i) q^{59} +(2.36343 - 2.62485i) q^{60} +(1.12287 + 0.238673i) q^{61} +(-2.23189 - 1.62156i) q^{62} +(-6.57477 + 1.77482i) q^{63} +(-1.21174 + 3.72935i) q^{64} +(-7.79086 + 13.4942i) q^{65} +(0.347296 + 0.601535i) q^{67} +(-5.38107 - 5.97629i) q^{68} +(3.34400 - 2.42956i) q^{69} +(-17.5371 + 0.951803i) q^{70} +(2.92364 + 8.99804i) q^{71} +(-2.21405 - 0.470612i) q^{72} +(-0.245359 + 2.33444i) q^{73} +(7.64600 + 3.40422i) q^{74} +(3.26495 + 3.62609i) q^{75} +2.78106 q^{76} +5.41147 q^{78} +(-8.31008 - 9.22928i) q^{79} +(-15.2201 - 6.77641i) q^{80} +(-0.558945 + 5.31800i) q^{81} +(-0.520461 - 0.110628i) q^{82} +(-3.50201 - 10.7781i) q^{83} +(1.44511 + 2.21623i) q^{84} +(14.9990 - 10.8974i) q^{85} +(-4.29011 - 4.76465i) q^{86} +(-0.627011 - 1.08602i) q^{87} +(1.73396 - 3.00330i) q^{89} +(-5.28001 + 16.2502i) q^{90} +(-8.26845 - 8.23774i) q^{91} +(7.84935 + 5.70289i) q^{92} +(-0.937174 - 0.199202i) q^{93} +(-5.72738 + 6.36090i) q^{94} +(-0.670182 + 6.37635i) q^{95} +(0.484819 + 4.61275i) q^{96} +(4.74258 - 14.5961i) 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 $\left(\mathbb{Z}/847\mathbb{Z}\right)^\times$.

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

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 $

$2$	1.25755	+	1.39666i	0.889225	+	0.987585i	0.999980	−	0.00626319i	$-0.00199365\pi$
$2$	1.25755	+	1.39666i	0.889225	+	0.987585i	−0.110755	+	0.993848i	$0.535327\pi$
$3$	0.596274	+	0.265478i	0.344259	+	0.153274i	0.571581	−	0.820546i	$-0.306330\pi$
$3$	0.596274	+	0.265478i	0.344259	+	0.153274i	−0.227322	+	0.973820i	$0.572997\pi$
$4$	−0.160147	+	1.52370i	−0.0800734	+	0.761848i
$5$	−3.45490	−	0.734363i	−1.54508	−	0.328417i	−0.645014	−	0.764171i	$-0.723149\pi$
$5$	−3.45490	−	0.734363i	−1.54508	−	0.328417i	−0.900066	+	0.435754i	$0.856482\pi$
$6$	0.379065	+	1.16664i	0.154753	+	0.476280i
$7$	1.19676	−	2.35961i	0.452332	−	0.891850i
$7$	1.19676	−	2.35961i	0.452332	−	0.891850i
$8$	0.711438	−	0.516890i	0.251531	−	0.182748i
$9$	−1.72233	−	1.91284i	−0.574109	−	0.637613i
$10$	−3.31908	−	5.74881i	−1.04958	−	1.81793i
$11$		0			0
$11$		0			0
$12$	−0.500000	+	0.866025i	−0.144338	+	0.250000i
$13$	1.36322	−	4.19556i	0.378089	−	1.16364i	−0.563281	−	0.826265i	$-0.690461\pi$
$13$	1.36322	−	4.19556i	0.378089	−	1.16364i	0.941371	−	0.337374i	$-0.109539\pi$
$14$	4.80055	−	1.29588i	1.28300	−	0.346339i
$15$	−1.86511	−	1.35508i	−0.481570	−	0.349881i
$16$	4.61381	+	0.980695i	1.15345	+	0.245174i
$17$	−3.51225	+	3.90075i	−0.851845	+	0.946070i	−0.999074	−	0.0430328i	$-0.986298\pi$
$17$	−3.51225	+	3.90075i	−0.851845	+	0.946070i	0.147229	+	0.989102i	$0.452965\pi$
$18$	0.505656	−	4.81100i	0.119184	−	1.13396i
$19$	−0.189741	−	1.80526i	−0.0435295	−	0.414156i	−0.994489	−	0.104840i	$-0.966567\pi$
$19$	−0.189741	−	1.80526i	−0.0435295	−	0.414156i	0.950960	−	0.309315i	$-0.100100\pi$
$20$	1.67224	−	5.14662i	0.373924	−	1.15082i
$21$	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	$-0.0628765\pi$
$24$	0.561435	−	0.119337i	0.114602	−	0.0243595i
$25$	6.82935	+	3.04062i	1.36587	+	0.608124i
$26$	7.57408	−	3.37220i	1.48540	−	0.661342i
$27$	−1.12425	−	3.46009i	−0.216362	−	0.665895i
$28$	3.40367	+	2.20138i	0.643234	+	0.416022i
$29$	−1.55434	−	1.12930i	−0.288634	−	0.209705i	0.434040	−	0.900893i	$-0.357088\pi$
$29$	−1.55434	−	1.12930i	−0.288634	−	0.209705i	−0.722675	+	0.691188i	$0.757088\pi$
$30$	−0.452896	−	4.30901i	−0.0826870	−	0.786715i
$31$	−1.43583	+	0.305196i	−0.257883	+	0.0548148i	−0.335039	−	0.942204i	$-0.608749\pi$
$31$	−1.43583	+	0.305196i	−0.257883	+	0.0548148i	0.0771556	+	0.997019i	$0.475416\pi$
$32$	3.55303	+	6.15403i	0.628094	+	1.08789i
$33$		0			0
$34$	−9.86484			−1.69181
$35$	−5.86749	+	7.27338i	−0.991788	+	1.22943i
$36$	3.19041	−	2.31797i	0.531735	−	0.386328i
$37$	4.06835	−	1.81135i	0.668833	−	0.297783i	−0.0440886	−	0.999028i	$-0.514038\pi$
$37$	4.06835	−	1.81135i	0.668833	−	0.297783i	0.712921	+	0.701244i	$0.247372\pi$
$38$	2.28272	−	2.53522i	0.370306	−	0.411267i
$39$	1.92668	−	2.13980i	0.308516	−	0.342642i
$40$	−2.83753	+	1.26335i	−0.448653	+	0.199753i
$41$	−0.229048	+	0.166413i	−0.0357712	+	0.0259893i	−0.605527	−	0.795825i	$-0.707038\pi$
$41$	−0.229048	+	0.166413i	−0.0357712	+	0.0259893i	0.569756	+	0.821814i	$0.307038\pi$
$42$	3.20648	+	0.501742i	0.494770	+	0.0774205i
$43$	−3.41147			−0.520245			−0.260122	−	0.965576i	$-0.583763\pi$
$43$	−3.41147			−0.520245			−0.260122	+	0.965576i	$0.583763\pi$
$44$		0			0
$45$	4.54576	+	7.87349i	0.677642	+	1.17371i
$46$	11.6416	−	2.47450i	1.71646	−	0.364845i
$47$	0.476062	+	4.52943i	0.0694408	+	0.660685i	0.972776	+	0.231749i	$0.0744448\pi$
$47$	0.476062	+	4.52943i	0.0694408	+	0.660685i	−0.903335	+	0.428936i	$0.858889\pi$
$48$	2.49074	+	1.80963i	0.359508	+	0.261198i
$49$	−4.13554	−	5.64777i	−0.590792	−	0.806824i
$50$	4.34157	+	13.3620i	0.613991	+	1.88967i
$51$	−3.12983	+	1.39349i	−0.438263	+	0.195127i
$52$	6.17444	+	2.74904i	0.856241	+	0.381223i
$53$	7.07633	−	1.50412i	0.972009	−	0.206607i	0.305573	−	0.952169i	$-0.401152\pi$
$53$	7.07633	−	1.50412i	0.972009	−	0.206607i	0.666436	+	0.745562i	$0.267819\pi$
$54$	3.41875	−	5.92145i	0.465233	−	0.805807i
$55$		0			0
$56$	−0.368241	−	2.29731i	−0.0492083	−	0.306991i
$57$	0.366121	−	1.12680i	0.0484939	−	0.149249i
$58$	−0.377433	−	3.59103i	−0.0495594	−	0.471526i
$59$	−0.997184	+	9.48757i	−0.129822	+	1.23518i	0.714614	+	0.699520i	$0.246603\pi$
$59$	−0.997184	+	9.48757i	−0.129822	+	1.23518i	−0.844436	+	0.535657i	$0.820064\pi$
$60$	2.36343	−	2.62485i	0.305117	−	0.338867i
$61$	1.12287	+	0.238673i	0.143769	+	0.0305590i	0.279234	−	0.960223i	$-0.409920\pi$
$61$	1.12287	+	0.238673i	0.143769	+	0.0305590i	−0.135465	+	0.990782i	$0.543253\pi$
$62$	−2.23189	−	1.62156i	−0.283451	−	0.205939i
$63$	−6.57477	+	1.77482i	−0.828343	+	0.223606i
$64$	−1.21174	+	3.72935i	−0.151468	+	0.466169i
$65$	−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	$0.819824\pi$
$68$	−5.38107	−	5.97629i	−0.652551	−	0.724731i
$69$	3.34400	−	2.42956i	0.402570	−	0.292484i
$70$	−17.5371	+	0.951803i	−2.09608	+	0.113762i
$71$	2.92364	+	8.99804i	0.346972	+	1.06787i	0.960519	+	0.278213i	$0.0897422\pi$
$71$	2.92364	+	8.99804i	0.346972	+	1.06787i	−0.613547	+	0.789658i	$0.710258\pi$
$72$	−2.21405	−	0.470612i	−0.260929	−	0.0554621i
$73$	−0.245359	+	2.33444i	−0.0287171	+	0.273225i	0.970736	+	0.240150i	$0.0771967\pi$
$73$	−0.245359	+	2.33444i	−0.0287171	+	0.273225i	−0.999453	+	0.0330750i	$0.989470\pi$
$74$	7.64600	+	3.40422i	0.888829	+	0.395732i
$75$	3.26495	+	3.62609i	0.377003	+	0.418705i
$76$	2.78106			0.319009
$77$		0			0
$78$	5.41147			0.612729
$79$	−8.31008	−	9.22928i	−0.934957	−	1.03837i	−0.999182	−	0.0404392i	$-0.987124\pi$
$79$	−8.31008	−	9.22928i	−0.934957	−	1.03837i	0.0642253	−	0.997935i	$-0.479542\pi$
$80$	−15.2201	−	6.77641i	−1.70166	−	0.757626i
$81$	−0.558945	+	5.31800i	−0.0621050	+	0.590889i
$82$	−0.520461	−	0.110628i	−0.0574754	−	0.0122168i
$83$	−3.50201	−	10.7781i	−0.384396	−	1.18305i	−0.936918	−	0.349550i	$-0.886334\pi$
$83$	−3.50201	−	10.7781i	−0.384396	−	1.18305i	0.552522	−	0.833498i	$-0.313666\pi$
$84$	1.44511	+	2.21623i	0.157674	+	0.241810i
$85$	14.9990	−	10.8974i	1.62687	−	1.18199i
$86$	−4.29011	−	4.76465i	−0.462615	−	0.513786i
$87$	−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	$0.107827\pi$
$90$	−5.28001	+	16.2502i	−0.556562	+	1.71292i
$91$	−8.26845	−	8.23774i	−0.866769	−	0.863550i
$92$	7.84935	+	5.70289i	0.818352	+	0.594567i
$93$	−0.937174	−	0.199202i	−0.0971804	−	0.0206563i
$94$	−5.72738	+	6.36090i	−0.590734	+	0.656076i
$95$	−0.670182	+	6.37635i	−0.0687592	+	0.654200i
$96$	0.484819	+	4.61275i	0.0494817	+	0.470787i
$97$	4.74258	−	14.5961i	0.481536	−	1.48201i	−0.355401	−	0.934714i	$-0.615656\pi$
$97$	4.74258	−	14.5961i	0.481536	−	1.48201i	0.836936	−	0.547300i	$-0.184344\pi$
$98$	2.68732	−	12.8783i	0.271460	−	1.30090i
$99$		0			0
$100$	−5.72668	+	9.91890i	−0.572668	+	0.991890i
$101$	−6.55587	+	1.39349i	−0.652334	+	0.138658i	−0.522179	−	0.852836i	$-0.674881\pi$
$101$	−6.55587	+	1.39349i	−0.652334	+	0.138658i	−0.130155	+	0.991494i	$0.541547\pi$
$102$	−5.88215	−	2.61890i	−0.582420	−	0.259310i
$103$	2.05454	−	0.914739i	0.202440	−	0.0901319i	−0.303013	−	0.952987i	$-0.597992\pi$
$103$	2.05454	−	0.914739i	0.202440	−	0.0901319i	0.505452	+	0.862855i	$0.331326\pi$
$104$	−1.19880	−	3.68951i	−0.117552	−	0.361787i
$105$	−5.42956	+	2.77924i	−0.529871	+	0.271226i
$106$	10.9996	+	7.99169i	1.06838	+	0.776221i
$107$	1.20543	+	11.4689i	0.116533	+	1.10874i	0.883946	+	0.467589i	$0.154877\pi$
$107$	1.20543	+	11.4689i	0.116533	+	1.10874i	−0.767413	+	0.641153i	$0.778456\pi$
$108$	5.45217	−	1.15890i	0.524636	−	0.111515i
$109$	5.99273	+	10.3797i	0.573999	+	0.994196i	0.996150	+	0.0876698i	$0.0279420\pi$
$109$	5.99273	+	10.3797i	0.573999	+	0.994196i	−0.422151	+	0.906526i	$0.638725\pi$
$110$		0			0
$111$	2.90673			0.275894
$112$	7.83567	−	9.71314i	0.740401	−	0.917806i
$113$	−4.05135	+	2.94348i	−0.381119	+	0.276899i	−0.761806	−	0.647805i	$-0.775687\pi$
$113$	−4.05135	+	2.94348i	−0.381119	+	0.276899i	0.380688	+	0.924704i	$0.375687\pi$
$114$	2.03417	−	0.905673i	0.190518	−	0.0848240i
$115$	−14.9670	+	16.6225i	−1.39568	+	1.55006i
$116$	1.96963	−	2.18749i	0.182875	−	0.203104i
$117$	−10.3733	+	4.61851i	−0.959016	+	0.426981i
$118$	−14.5049	+	10.5384i	−1.33528	+	0.970139i
$119$	5.00094	+	12.9558i	0.458435	+	1.18766i
$120$	−2.02734			−0.185070
$121$		0			0
$122$	1.07873	+	1.86841i	0.0976632	+	0.169158i
$123$	−0.180754	+	0.0384205i	−0.0162981	+	0.00346426i
$124$	−0.235081	−	2.23665i	−0.0211109	−	0.200857i
$125$	−7.07422	−	5.13973i	−0.632738	−	0.459711i
$126$	−10.7469	−	6.95075i	−0.957413	−	0.619222i
$127$	−4.39868	−	13.5377i	−0.390320	−	1.20128i	−0.932547	−	0.361048i	$-0.882419\pi$
$127$	−4.39868	−	13.5377i	−0.390320	−	1.20128i	0.542227	−	0.840232i	$-0.317581\pi$
$128$	6.25098	−	2.78312i	0.552514	−	0.245995i
$129$	−2.03417	−	0.905673i	−0.179099	−	0.0797401i
$130$	−28.6441	+	6.08850i	−2.51226	+	0.533996i
$131$	−2.55690	+	4.42869i	−0.223398	+	0.386936i	−0.955838	−	0.293896i	$-0.905048\pi$
$131$	−2.55690	+	4.42869i	−0.223398	+	0.386936i	0.732440	+	0.680832i	$0.238382\pi$
$132$		0			0
$133$	−4.48680	−	1.71275i	−0.389055	−	0.148514i
$134$	−0.403393	+	1.24152i	−0.0348479	+	0.107251i
$135$	1.34322	+	12.7799i	0.115606	+	1.09992i
$136$	−0.482489	+	4.59058i	−0.0413731	+	0.393639i
$137$	13.1868	−	14.6454i	1.12663	−	1.25124i	0.162238	−	0.986752i	$-0.448129\pi$
$137$	13.1868	−	14.6454i	1.12663	−	1.25124i	0.964388	−	0.264493i	$-0.0852046\pi$
$138$	7.59851	+	1.61511i	0.646828	+	0.137488i
$139$	4.27631	+	3.10692i	0.362712	+	0.263525i	0.754182	−	0.656665i	$-0.228034\pi$
$139$	4.27631	+	3.10692i	0.362712	+	0.263525i	−0.391471	+	0.920191i	$0.628034\pi$
$140$	−10.1428	−	10.1051i	−0.857220	−	0.854036i
$141$	−0.918602	+	2.82717i	−0.0773603	+	0.238090i
$142$	−8.89053	+	15.3988i	−0.746077	+	1.29224i
$143$		0			0
$144$	−6.07057	−	10.5145i	−0.505881	−	0.876212i
$145$	4.54079	+	5.04306i	0.377092	+	0.418804i
$146$	−3.56896	+	2.59300i	−0.295369	+	0.214598i
$147$	−0.966557	−	4.46552i	−0.0797203	−	0.368310i
$148$	2.10841	+	6.48901i	0.173310	+	0.533393i
$149$	16.6437	+	3.53772i	1.36350	+	0.289821i	0.830842	−	0.556509i	$-0.187859\pi$
$149$	16.6437	+	3.53772i	1.36350	+	0.289821i	0.532659	+	0.846330i	$0.321193\pi$
$150$	−0.958552	+	9.12001i	−0.0782654	+	0.744646i
$151$	1.19009	+	0.529864i	0.0968484	+	0.0431197i	0.454589	−	0.890701i	$-0.349786\pi$
$151$	1.19009	+	0.529864i	0.0968484	+	0.0431197i	−0.357741	+	0.933821i	$0.616453\pi$
$152$	−1.06811	−	1.18626i	−0.0866352	−	0.0962182i
$153$	13.5107			1.09228
$154$		0			0
$155$	5.18479			0.416453
$156$	2.95185	+	3.27836i	0.236337	+	0.262479i
$157$	12.5106	+	5.57009i	0.998457	+	0.444542i	0.839861	−	0.542802i	$-0.182636\pi$
$157$	12.5106	+	5.57009i	0.998457	+	0.444542i	0.158596	+	0.987344i	$0.449303\pi$
$158$	2.43975	−	23.2126i	0.194096	−	1.84670i
$159$	4.61875	+	0.981745i	0.366291	+	0.0778575i
$160$	−7.75610	−	23.8708i	−0.613173	−	1.88715i
$161$	−9.15149	−	14.0348i	−0.721238	−	1.10610i
$162$	−8.13032	+	5.90702i	−0.638778	+	0.464100i
$163$	10.9769	+	12.1910i	0.859774	+	0.954876i	0.999376	−	0.0353316i	$-0.0112487\pi$
$163$	10.9769	+	12.1910i	0.859774	+	0.954876i	−0.139601	+	0.990208i	$0.544582\pi$
$164$	−0.216881	−	0.375650i	−0.0169356	−	0.0293333i
$165$		0			0
$166$	10.6493	−	18.4451i	0.826546	−	1.43162i
$167$	−2.54824	+	7.84268i	−0.197189	+	0.606885i	0.802755	+	0.596309i	$0.203367\pi$
$167$	−2.54824	+	7.84268i	−0.197189	+	0.606885i	−0.999944	+	0.0105762i	$0.996633\pi$
$168$	0.390313	−	1.46759i	0.0301133	−	0.113227i
$169$	−5.22714	−	3.79774i	−0.402088	−	0.292134i
$170$	34.0821	+	7.24437i	2.61398	+	0.555618i
$171$	−3.12638	+	3.47220i	−0.239080	+	0.265526i
$172$	0.546337	−	5.19805i	0.0416578	−	0.396348i
$173$	−2.01054	−	19.1291i	−0.152859	−	1.45436i	−0.754874	−	0.655870i	$-0.772302\pi$
$173$	−2.01054	−	19.1291i	−0.152859	−	1.45436i	0.602015	−	0.798485i	$-0.294365\pi$
$174$	0.728289	−	2.24144i	0.0552114	−	0.169923i
$175$	15.3478	−	12.4757i	1.16018	−	0.943076i
$176$		0			0
$177$	−3.11334	+	5.39246i	−0.234013	+	0.405322i
$178$	6.37512	−	1.35507i	0.477835	−	0.101567i
$179$	−1.21291	−	0.540023i	−0.0906572	−	0.0403632i	0.360907	−	0.932602i	$-0.382467\pi$
$179$	−1.21291	−	0.540023i	−0.0906572	−	0.0403632i	−0.451564	+	0.892239i	$0.649134\pi$
$180$	−12.7248	+	5.66544i	−0.948450	+	0.422277i
$181$	5.45499	+	16.7887i	0.405466	+	1.24790i	0.920506	+	0.390729i	$0.127777\pi$
$181$	5.45499	+	16.7887i	0.405466	+	1.24790i	−0.515040	+	0.857166i	$0.672223\pi$
$182$	1.10726	−	21.9076i	0.0820755	−	1.62390i
$183$	0.606176	+	0.440413i	0.0448098	+	0.0325563i
$184$	−0.582111	−	5.53842i	−0.0429138	−	0.408298i
$185$	−15.3859	+	3.27038i	−1.13120	+	0.240443i
$186$	−0.900330	−	1.55942i	−0.0660154	−	0.114342i
$187$		0			0
$188$	−6.97771			−0.508902
$189$	−9.50993	−	1.48809i	−0.691746	−	0.108243i
$190$	−9.74836	+	7.08259i	−0.707220	+	0.513825i
$191$	14.2080	−	6.32582i	1.02806	−	0.457720i	0.177788	−	0.984069i	$-0.443106\pi$
$191$	14.2080	−	6.32582i	1.02806	−	0.457720i	0.850269	+	0.526348i	$0.176439\pi$
$192$	−1.71259	+	1.90203i	−0.123596	+	0.137267i
$193$	−3.49215	+	3.87843i	−0.251371	+	0.279175i	−0.855603	−	0.517633i	$-0.826813\pi$
$193$	−3.49215	+	3.87843i	−0.251371	+	0.279175i	0.604232	+	0.796808i	$0.293480\pi$
$194$	26.3498	−	11.7317i	1.89181	−	0.842287i
$195$	−8.22790	+	5.97792i	−0.589212	+	0.428088i
$196$	9.26778	−	5.39684i	0.661984	−	0.385488i
$197$	−4.61856			−0.329058			−0.164529	−	0.986372i	$-0.552610\pi$
$197$	−4.61856			−0.329058			−0.164529	+	0.986372i	$0.552610\pi$
$198$		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	$0.764546\pi$
$200$	6.43032	−	1.36681i	0.454692	−	0.0966478i
$201$	0.0473894	+	0.450880i	0.00334259	+	0.0318026i
$202$	−10.1906	−	7.40390i	−0.717008	−	0.520937i
$203$	−4.52488	+	2.31615i	−0.317584	+	0.162562i
$204$	−1.62202	−	4.99207i	−0.113564	−	0.349515i
$205$	0.913545	−	0.406737i	0.0638048	−	0.0284077i
$206$	3.86127	+	1.71915i	0.269027	+	0.119779i
$207$	−15.9442	+	3.38903i	−1.10820	+	0.235554i
$208$	10.4042	−	18.0206i	0.721401	−	1.24950i
$209$		0			0
$210$	−10.7096	−	4.08819i	−0.739033	−	0.282112i
$211$	2.68678	−	8.26905i	0.184965	−	0.569265i	−0.814982	−	0.579486i	$-0.803253\pi$
$211$	2.68678	−	8.26905i	0.184965	−	0.569265i	0.999948	+	0.0102209i	$0.00325346\pi$
$212$	1.15857	+	11.0231i	0.0795709	+	0.757067i
$213$	−0.645494	+	6.14147i	−0.0442285	+	0.420806i
$214$	−14.5022	+	16.1064i	−0.991352	+	1.10101i
$215$	11.7863	+	2.50526i	0.803820	+	0.170857i
$216$	−2.58832	−	1.88053i	−0.176113	−	0.127954i
$217$	−0.998201	+	3.75326i	−0.0677623	+	0.254788i
$218$	−6.96069	+	21.4228i	−0.471438	+	1.45094i
$219$	−0.766044	+	1.32683i	−0.0517645	+	0.0896587i
$220$		0			0
$221$	11.5778	+	20.0534i	0.778810	+	1.34894i
$222$	3.65537	+	4.05970i	0.245332	+	0.272469i
$223$	0.179302	−	0.130270i	0.0120069	−	0.00872355i	−0.581766	−	0.813356i	$-0.697638\pi$
$223$	0.179302	−	0.130270i	0.0120069	−	0.00872355i	0.593773	+	0.804633i	$0.297638\pi$
$224$	18.7733	−	1.01889i	1.25434	−	0.0680777i
$225$	−5.94616	−	18.3004i	−0.396410	−	1.22003i
$226$	−9.20581	−	1.95676i	−0.612361	−	0.130161i
$227$	1.01389	−	9.64651i	0.0672942	−	0.640261i	−0.907942	−	0.419096i	$-0.862347\pi$
$227$	1.01389	−	9.64651i	0.0672942	−	0.640261i	0.975236	−	0.221166i	$-0.0709861\pi$
$228$	1.65827	+	0.738311i	0.109822	+	0.0488959i
$229$	15.8548	+	17.6085i	1.04771	+	1.16360i	0.986210	+	0.165496i	$0.0529226\pi$
$229$	15.8548	+	17.6085i	1.04771	+	1.16360i	0.0615028	+	0.998107i	$0.480411\pi$
$230$	−42.0378			−2.77189
$231$		0			0
$232$	−1.68954			−0.110924
$233$	13.9762	+	15.5222i	0.915612	+	1.01689i	0.999791	+	0.0204398i	$0.00650665\pi$
$233$	13.9762	+	15.5222i	0.915612	+	1.01689i	−0.0841788	+	0.996451i	$0.526827\pi$
$234$	−19.4955	−	8.67996i	−1.27446	−	0.567427i
$235$	1.68149	−	15.9983i	0.109689	−	1.04362i
$236$	−14.2965	−	3.03881i	−0.930621	−	0.197810i
$237$	−2.50491	−	7.70933i	−0.162712	−	0.500775i
$238$	−11.8058	+	23.2772i	−0.765258	+	1.50884i
$239$	−12.1595	+	8.83443i	−0.786536	+	0.571452i	−0.906933	−	0.421274i	$-0.861583\pi$
$239$	−12.1595	+	8.83443i	−0.786536	+	0.571452i	0.120398	+	0.992726i	$0.461583\pi$
$240$	−7.27635	−	8.08120i	−0.469686	−	0.521639i
$241$	−14.7699	−	25.5822i	−0.951414	−	1.64790i	−0.742369	−	0.669991i	$-0.766298\pi$
$241$	−14.7699	−	25.5822i	−0.951414	−	1.64790i	−0.209045	−	0.977906i	$-0.567035\pi$
$242$		0			0
$243$	−7.20233	+	12.4748i	−0.462030	+	0.800259i
$244$	−0.543490	+	1.67269i	−0.0347934	+	0.107083i
$245$	10.1404	+	22.5495i	0.647846	+	1.44063i
$246$	−0.280969	−	0.204136i	−0.0179139	−	0.0130152i
$247$	−7.83275	−	1.66490i	−0.498386	−	0.105935i
$248$	−0.863754	+	0.959295i	−0.0548484	+	0.0609153i
$249$	0.773189	−	7.35641i	0.0489989	−	0.466193i
$250$	−1.71780	−	16.3437i	−0.108643	−	1.03367i
$251$	1.16519	−	3.58608i	0.0735461	−	0.226352i	−0.907526	−	0.419997i	$-0.862031\pi$
$251$	1.16519	−	3.58608i	0.0735461	−	0.226352i	0.981072	+	0.193645i	$0.0620311\pi$
$252$	−1.65136	−	10.3022i	−0.104026	−	0.648976i
$253$		0			0
$254$	13.3760	−	23.1679i	0.839284	−	1.45368i
$255$	11.8366	−	2.51594i	0.741235	−	0.157554i
$256$	18.9125	+	8.42040i	1.18203	+	0.526275i
$257$	−7.91171	+	3.52252i	−0.493519	+	0.219729i	−0.638377	−	0.769724i	$-0.720394\pi$
$257$	−7.91171	+	3.52252i	−0.493519	+	0.219729i	0.144858	+	0.989452i	$0.453727\pi$
$258$	−1.29317	−	3.97997i	−0.0805094	−	0.247782i
$259$	0.594754	−	11.7675i	0.0369562	−	0.731195i
$260$	−19.3133	−	14.0319i	−1.19776	−	0.870225i
$261$	0.516926	+	4.91823i	0.0319969	+	0.304431i
$262$	−9.40080	+	1.99820i	−0.580783	+	0.123449i
$263$	2.91740	+	5.05309i	0.179895	+	0.311587i	0.941844	−	0.336049i	$-0.109091\pi$
$263$	2.91740	+	5.05309i	0.179895	+	0.311587i	−0.761950	+	0.647636i	$0.775758\pi$
$264$		0			0
$265$	−25.5526			−1.56969
$266$	−3.25027	−	8.42038i	−0.199287	−	0.516287i
$267$	1.83122	−	1.33046i	0.112069	−	0.0814230i
$268$	−0.972175	+	0.432840i	−0.0593850	+	0.0264399i
$269$	−14.7084	+	16.3353i	−0.896786	+	0.995982i	0.103213	+	0.994659i	$0.467088\pi$
$269$	−14.7084	+	16.3353i	−0.896786	+	0.995982i	−0.999999	+	0.00132242i	$0.999579\pi$
$270$	−16.1599	+	17.9474i	−0.983462	+	1.09225i
$271$	9.00029	−	4.00719i	0.546729	−	0.243419i	−0.114735	−	0.993396i	$-0.536602\pi$
$271$	9.00029	−	4.00719i	0.546729	−	0.243419i	0.661464	+	0.749977i	$0.269935\pi$
$272$	−20.0303	+	14.5528i	−1.21451	+	0.882396i
$273$	−2.74332	−	7.10705i	−0.166034	−	0.430138i
$274$	37.0378			2.23753
$275$		0			0
$276$	3.16637	+	5.48432i	0.190593	+	0.330117i
$277$	−23.1225	+	4.91484i	−1.38930	+	0.295304i	−0.841025	−	0.540996i	$-0.818048\pi$
$277$	−23.1225	+	4.91484i	−1.38930	+	0.295304i	−0.548272	+	0.836300i	$0.684714\pi$
$278$	1.03839	+	9.87965i	0.0622787	+	0.592542i
$279$	3.05677	+	2.22087i	0.183004	+	0.132960i
$280$	−0.414821	+	8.20740i	−0.0247903	+	0.490486i
$281$	5.02810	+	15.4749i	0.299951	+	0.923154i	0.981513	+	0.191394i	$0.0613009\pi$
$281$	5.02810	+	15.4749i	0.299951	+	0.923154i	−0.681562	+	0.731760i	$0.738699\pi$
$282$	−5.10377	+	2.27234i	−0.303925	+	0.135316i
$283$	15.5287	+	6.91381i	0.923084	+	0.410983i	0.812552	−	0.582889i	$-0.198078\pi$
$283$	15.5287	+	6.91381i	0.923084	+	0.410983i	0.110532	+	0.993873i	$0.464745\pi$
$284$	−14.1785	+	3.01373i	−0.841339	+	0.178832i
$285$	−2.09240	+	3.62414i	−0.123943	+	0.214675i
$286$		0			0
$287$	0.118555	+	0.739620i	0.00699810	+	0.0436584i
$288$	5.65219	−	17.3956i	0.333058	−	1.02505i
$289$	−1.10295	−	10.4939i	−0.0648795	−	0.617287i
$290$	−1.33313	+	12.6839i	−0.0782839	+	0.744821i
$291$	6.70284	−	7.44426i	0.392927	−	0.436390i
$292$	−3.51768	−	0.747706i	−0.205857	−	0.0437562i
$293$	11.1469	+	8.09872i	0.651211	+	0.473132i	0.863683	−	0.504035i	$-0.168152\pi$
$293$	11.1469	+	8.09872i	0.651211	+	0.473132i	−0.212473	+	0.977167i	$0.568152\pi$
$294$	5.02129	−	6.96558i	0.292848	−	0.406241i
$295$	10.4125	−	32.0463i	0.606239	−	1.86581i
$296$	1.95811	−	3.39155i	0.113813	−	0.197130i
$297$		0			0
$298$	15.9893	+	27.6943i	0.926237	+	1.60429i
$299$	−18.6933	−	20.7611i	−1.08106	−	1.20064i
$300$	−6.04793	+	4.39408i	−0.349177	+	0.253692i
$301$	−4.08271	+	8.04976i	−0.235323	+	0.463980i
$302$	0.756570	+	2.32848i	0.0435357	+	0.133989i
$303$	−4.27904	−	0.909538i	−0.245824	−	0.0522516i
$304$	0.894985	−	8.51521i	0.0513309	−	0.488381i
$305$	−3.70414	−	1.64919i	−0.212098	−	0.0944322i
$306$	16.9905	+	18.8698i	0.971281	+	1.07872i
$307$	−11.6159			−0.662953			−0.331476	−	0.943464i	$-0.607547\pi$
$307$	−11.6159			−0.662953			−0.331476	+	0.943464i	$0.607547\pi$
$308$		0			0
$309$	1.46791			0.0835065
$310$	6.52016	+	7.24137i	0.370320	+	0.411282i
$311$	3.15019	+	1.40255i	0.178631	+	0.0795316i	0.494103	−	0.869403i	$-0.335496\pi$
$311$	3.15019	+	1.40255i	0.178631	+	0.0795316i	−0.315473	+	0.948935i	$0.602163\pi$
$312$	0.264675	−	2.51822i	0.0149843	−	0.142566i
$313$	18.9975	+	4.03804i	1.07380	+	0.228244i	0.710692	−	0.703503i	$-0.248382\pi$
$313$	18.9975	+	4.03804i	1.07380	+	0.228244i	0.363109	+	0.931747i	$0.381715\pi$
$314$	7.95330	+	24.4777i	0.448831	+	1.38136i
$315$	24.0185	−	1.30358i	1.35329	−	0.0734481i
$316$	15.3934	−	11.1840i	0.865949	−	0.629149i
$317$	−21.9583	−	24.3871i	−1.23330	−	1.36972i	−0.905150	−	0.425093i	$-0.860241\pi$
$317$	−21.9583	−	24.3871i	−1.23330	−	1.36972i	−0.328150	−	0.944625i	$-0.606425\pi$
$318$	4.43717	+	7.68540i	0.248824	+	0.430976i
$319$		0			0
$320$	6.92514	−	11.9947i	0.387127	−	0.670524i
$321$	−2.32598	+	7.15864i	−0.129824	+	0.399556i
$322$	8.09331	−	30.4310i	0.451023	−	1.69585i
$323$	7.70829	+	5.60040i	0.428901	+	0.311615i
$324$	−8.01351	−	1.70332i	−0.445195	−	0.0946291i
$325$	22.0670	−	24.5079i	1.22406	−	1.35945i
$326$	−3.22268	+	30.6618i	−0.178488	+	1.69820i
$327$	0.817721	+	7.78009i	0.0452201	+	0.430240i
$328$	−0.0769361	+	0.236785i	−0.00424808	+	0.0130743i
$329$	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	$0.110742\pi$
$332$	16.9834	−	3.60992i	0.932083	−	0.198120i
$333$	−10.4718	−	4.66236i	−0.573853	−	0.255496i
$334$	−14.1581	+	6.30358i	−0.774695	+	0.344917i
$335$	−0.758131	−	2.33329i	−0.0414211	−	0.127481i
$336$	7.25084	−	3.71150i	0.395566	−	0.202479i
$337$	12.5761	+	9.13705i	0.685062	+	0.497727i	0.875033	−	0.484063i	$-0.160839\pi$
$337$	12.5761	+	9.13705i	0.685062	+	0.497727i	−0.189971	+	0.981790i	$0.560839\pi$
$338$	−1.26928	−	12.0764i	−0.0690397	−	0.656869i
$339$	−3.19714	+	0.679574i	−0.173645	+	0.0369094i
$340$	14.2023	+	24.5992i	0.770230	+	1.33408i
$341$		0			0
$342$	−8.78106			−0.474825
$343$	−18.2758	+	2.99927i	−0.986800	+	0.161945i
$344$	−2.42705	+	1.76336i	−0.130858	+	0.0950738i
$345$	−13.3374	+	5.93818i	−0.718060	+	0.319701i
$346$	24.1883	−	26.8639i	1.30037	−	1.44421i
$347$	−13.1983	+	14.6583i	−0.708524	+	0.786896i	−0.984709	−	0.174209i	$-0.944263\pi$
$347$	−13.1983	+	14.6583i	−0.708524	+	0.786896i	0.276184	+	0.961105i	$0.410930\pi$
$348$	1.75517	−	0.781453i	0.0940871	−	0.0418903i
$349$	4.68733	−	3.40554i	0.250907	−	0.182294i	−0.455222	−	0.890378i	$-0.650440\pi$
$349$	4.68733	−	3.40554i	0.250907	−	0.182294i	0.706129	+	0.708084i	$0.250440\pi$
$350$	36.7249	+	5.74663i	1.96303	+	0.307171i
$351$	−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	$-0.510894\pi$
$354$	−11.4466	+	2.43305i	−0.608380	+	0.129315i
$355$	−3.49308	−	33.2344i	−0.185393	−	1.76390i
$356$	4.29843	+	3.12299i	0.227816	+	0.165518i
$357$	−0.457551	+	9.05285i	−0.0242162	+	0.479127i
$358$	−0.771075	−	2.37313i	−0.0407526	−	0.125424i
$359$	3.84582	−	1.71227i	0.202974	−	0.0903700i	−0.302732	−	0.953076i	$-0.597899\pi$
$359$	3.84582	−	1.71227i	0.202974	−	0.0903700i	0.505706	+	0.862706i	$0.331232\pi$
$360$	7.30375	+	3.25184i	0.384941	+	0.171387i
$361$	15.3618	−	3.26526i	0.808517	−	0.171856i
$362$	−16.5881	+	28.7315i	−0.871852	+	1.51009i
$363$		0			0
$364$	13.8760	−	11.2794i	0.727299	−	0.591199i
$365$	2.56202	−	7.88508i	0.134102	−	0.412724i
$366$	0.147195	+	1.40046i	0.00769398	+	0.0732033i
$367$	2.03191	−	19.3323i	0.106065	−	1.00914i	−0.803988	−	0.594646i	$-0.797292\pi$
$367$	2.03191	−	19.3323i	0.106065	−	1.00914i	0.910052	−	0.414493i	$-0.136041\pi$
$368$	19.9875	−	22.1983i	1.04192	−	1.15717i
$369$	0.712816	+	0.151514i	0.0371077	+	0.00788749i
$370$	−23.9163	−	17.3762i	−1.24335	−	0.903344i
$371$	4.91951	−	18.4975i	0.255408	−	0.960341i
$372$	0.453609	−	1.39607i	0.0235186	−	0.0723827i
$373$	−6.35710	+	11.0108i	−0.329158	+	0.570118i	−0.982345	−	0.187078i	$-0.940098\pi$
$373$	−6.35710	+	11.0108i	−0.329158	+	0.570118i	0.653187	+	0.757197i	$0.273432\pi$
$374$		0			0
$375$	−2.85369	−	4.94274i	−0.147364	−	0.255242i
$376$	2.67990	+	2.97633i	0.138205	+	0.153493i
$377$	−6.85695	+	4.98186i	−0.353151	+	0.256579i
$378$	−9.88090	−	15.1535i	−0.508219	−	0.779410i
$379$	−7.04901	−	21.6946i	−0.362084	−	1.11438i	−0.951787	−	0.306759i	$-0.900755\pi$
$379$	−7.04901	−	21.6946i	−0.362084	−	1.11438i	0.589704	−	0.807620i	$-0.299245\pi$
$380$	−9.60829	−	2.04231i	−0.492895	−	0.104768i
$381$	0.971159	−	9.23996i	0.0497540	−	0.473378i
$382$	26.7024	+	11.8887i	1.36621	+	0.608277i
$383$	5.55285	+	6.16706i	0.283737	+	0.315122i	0.868118	−	0.496357i	$-0.165329\pi$
$383$	5.55285	+	6.16706i	0.283737	+	0.315122i	−0.584381	+	0.811479i	$0.698663\pi$
$384$	4.46616			0.227913
$385$		0			0
$386$	−9.80840			−0.499234
$387$	5.87568	+	6.52560i	0.298677	+	0.331715i
$388$	21.4806	+	9.56377i	1.09051	+	0.485527i
$389$	−1.19158	+	11.3372i	−0.0604157	+	0.574817i	0.921879	+	0.387477i	$0.126653\pi$
$389$	−1.19158	+	11.3372i	−0.0604157	+	0.574817i	−0.982295	+	0.187340i	$0.940013\pi$
$390$	−18.6961	−	3.97398i	−0.946715	−	0.201231i
$391$	10.2719	+	31.6135i	0.519470	+	1.59876i
$392$	−5.86145	−	1.88042i	−0.296048	−	0.0949754i
$393$	−2.70034	+	1.96191i	−0.136214	+	0.0989653i
$394$	−5.80808	−	6.45053i	−0.292607	−	0.324973i
$395$	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	$0.219482\pi$
$398$	−3.51340	+	10.8131i	−0.176111	+	0.542013i
$399$	−2.22066	−	2.21242i	−0.111172	−	0.110759i
$400$	28.5274	+	20.7263i	1.42637	+	1.03632i
$401$	−4.09829	−	0.871118i	−0.204659	−	0.0435015i	0.104441	−	0.994531i	$-0.466695\pi$
$401$	−4.09829	−	0.871118i	−0.204659	−	0.0435015i	−0.309100	+	0.951029i	$0.600028\pi$
$402$	−0.570129	+	0.633192i	−0.0284354	+	0.0315808i
$403$	−0.676890	+	6.44018i	−0.0337183	+	0.320808i
$404$	−1.07336	−	10.2123i	−0.0534016	−	0.508082i
$405$	5.83644	−	17.9627i	0.290015	−	0.892575i
$406$	−8.92514	−	3.40700i	−0.442947	−	0.169087i
$407$		0			0
$408$	−1.50640	+	2.60916i	−0.0745777	+	0.129172i
$409$	−0.756420	+	0.160782i	−0.0374025	+	0.00795016i	−0.226575	−	0.973994i	$-0.572753\pi$
$409$	−0.756420	+	0.160782i	−0.0374025	+	0.00795016i	0.189172	+	0.981944i	$0.439419\pi$
$410$	1.71690	+	0.764415i	0.0847918	+	0.0377518i
$411$	11.7510	−	5.23189i	0.579635	−	0.258070i
$412$	1.06476	+	3.27698i	0.0524568	+	0.161445i
$413$	21.1936	+	13.7073i	1.04287	+	0.674492i
$414$	−24.7839	−	18.0066i	−1.21806	−	0.884976i
$415$	4.18409	+	39.8090i	0.205389	+	1.95415i
$416$	30.6632	−	6.51766i	1.50339	−	0.319555i
$417$	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	$0.390933\pi$
$420$	−3.36519	−	8.71809i	−0.164204	−	0.425399i
$421$	4.69692	−	3.41251i	0.228914	−	0.166316i	−0.467416	−	0.884037i	$-0.654815\pi$
$421$	4.69692	−	3.41251i	0.228914	−	0.166316i	0.696330	+	0.717722i	$0.254815\pi$
$422$	14.9278	−	6.64628i	0.726673	−	0.323536i
$423$	7.84413	−	8.71179i	0.381395	−	0.423582i
$424$	4.25690	−	4.72777i	0.206734	−	0.229601i
$425$	−35.8470	+	15.9601i	−1.73884	+	0.774180i
$426$	−9.38926	+	6.82170i	−0.454911	+	0.330512i
$427$	1.90698	−	2.36390i	0.0922853	−	0.114397i
$428$	−17.6682			−0.854024
$429$		0			0
$430$	11.3229	+	19.6119i	0.546041	+	0.945771i
$431$	17.6125	−	3.74366i	0.848365	−	0.180326i	0.236838	−	0.971549i	$-0.423889\pi$
$431$	17.6125	−	3.74366i	0.848365	−	0.180326i	0.611527	+	0.791224i	$0.290556\pi$
$432$	−1.79379	−	17.0667i	−0.0863036	−	0.821124i
$433$	−1.89350	−	1.37571i	−0.0909956	−	0.0661122i	0.541357	−	0.840793i	$-0.317911\pi$
$433$	−1.89350	−	1.37571i	−0.0909956	−	0.0661122i	−0.632353	+	0.774681i	$0.717911\pi$
$434$	−6.49730	+	3.32578i	−0.311880	+	0.159643i
$435$	1.36874	+	4.21253i	0.0656258	+	0.201976i
$436$	−16.7752	+	7.46881i	−0.803388	+	0.357691i
$437$	−10.5014	−	4.67554i	−0.502352	−	0.223661i
$438$	−2.81646	+	0.598658i	−0.134576	+	0.0286050i
$439$	20.0167	−	34.6699i	0.955343	−	1.65470i	0.221762	−	0.975101i	$-0.428819\pi$
$439$	20.0167	−	34.6699i	0.955343	−	1.65470i	0.733581	−	0.679602i	$-0.237848\pi$
$440$		0			0
$441$	−3.68051	+	17.6379i	−0.175262	+	0.839901i
$442$	−13.4479	+	41.3885i	−0.639654	+	1.96865i
$443$	−1.98353	−	18.8720i	−0.0942402	−	0.896636i	−0.934862	−	0.355013i	$-0.884477\pi$
$443$	−1.98353	−	18.8720i	−0.0942402	−	0.896636i	0.840621	−	0.541623i	$-0.182190\pi$
$444$	−0.465503	+	4.42897i	−0.0220918	+	0.210189i
$445$	−8.19616	+	9.10276i	−0.388535	+	0.431512i
$446$	0.407424	+	0.0866007i	0.0192921	+	0.00410066i
$447$	8.98500	+	6.52798i	0.424976	+	0.308763i
$448$	7.34967	+	7.32237i	0.347239	+	0.345949i
$449$	−9.74551	+	29.9936i	−0.459919	+	1.41549i	0.405342	+	0.914165i	$0.367152\pi$
$449$	−9.74551	+	29.9936i	−0.459919	+	1.41549i	−0.865262	+	0.501321i	$0.832848\pi$
$450$	18.0817	−	31.3185i	0.852380	−	1.47637i
$451$		0			0
$452$	−3.83615	−	6.64441i	−0.180437	−	0.312527i
$453$	0.568955	+	0.631888i	0.0267318	+	0.0296887i
$454$	14.7479	−	10.7150i	0.692152	−	0.502878i
$455$	22.5172	+	34.5327i	1.05562	+	1.61892i
$456$	−0.321961	−	0.990895i	−0.0150772	−	0.0464029i
$457$	−11.3647	−	2.41563i	−0.531616	−	0.112999i	−0.0657205	−	0.997838i	$-0.520935\pi$
$457$	−11.3647	−	2.41563i	−0.531616	−	0.112999i	−0.465896	+	0.884840i	$0.654268\pi$
$458$	−4.65478	+	44.2873i	−0.217504	+	2.06941i
$459$	17.4456	+	7.76728i	0.814290	+	0.362545i
$460$	−22.9308	−	25.4672i	−1.06915	−	1.18741i
$461$	−12.9786			−0.604476			−0.302238	−	0.953233i	$-0.597734\pi$
$461$	−12.9786			−0.604476			−0.302238	+	0.953233i	$0.597734\pi$
$462$		0			0
$463$	35.3705			1.64381			0.821904	−	0.569626i	$-0.192912\pi$
$463$	35.3705			1.64381			0.821904	+	0.569626i	$0.192912\pi$
$464$	−6.06394	−	6.73469i	−0.281512	−	0.312650i
$465$	3.09156	+	1.37645i	0.143368	+	0.0638314i
$466$	−4.10326	+	39.0399i	−0.190080	+	1.80849i
$467$	38.9946	+	8.28856i	1.80446	+	0.383549i	0.982539	−	0.186059i	$-0.0595715\pi$
$467$	38.9946	+	8.28856i	1.80446	+	0.383549i	0.821917	+	0.569608i	$0.192905\pi$
$468$	−5.37595	−	16.5455i	−0.248503	−	0.764814i
$469$	1.83502	−	0.0995932i	0.0847333	−	0.00459879i
$470$	24.4587	−	17.7703i	1.12820	−	0.819684i
$471$	5.98103	+	6.64261i	0.275591	+	0.306075i
$472$	4.19459	+	7.26525i	0.193072	+	0.334410i
$473$		0			0
$474$	7.61721	−	13.1934i	0.349870	−	0.605993i
$475$	4.19332	−	12.9057i	0.192403	−	0.592154i
$476$	−20.5416	+	5.54508i	−0.941521	+	0.254158i
$477$	−15.0649	−	10.9453i	−0.689775	−	0.501151i
$478$	−27.6299	−	5.87293i	−1.26376	−	0.268621i
$479$	−20.3282	+	22.5768i	−0.928819	+	1.03156i	0.0706010	+	0.997505i	$0.477508\pi$
$479$	−20.3282	+	22.5768i	−0.928819	+	1.03156i	−0.999420	+	0.0340534i	$0.989158\pi$
$480$	1.71242	−	16.2926i	0.0781611	−	0.743654i
$481$	−2.05356	−	19.5383i	−0.0936341	−	0.890869i
$482$	17.1556	−	52.7995i	0.781417	−	2.40495i
$483$	−1.73086	−	10.7981i	−0.0787567	−	0.491332i
$484$		0			0
$485$	−27.1040	+	46.9455i	−1.23073	+	2.13169i
$486$	−26.4803	+	5.62857i	−1.20117	+	0.255317i
$487$	−9.52926	−	4.24270i	−0.431812	−	0.192255i	0.179308	−	0.983793i	$-0.442614\pi$
$487$	−9.52926	−	4.24270i	−0.431812	−	0.192255i	−0.611120	+	0.791538i	$0.709281\pi$
$488$	0.922220	−	0.410599i	0.0417469	−	0.0185869i
$489$	3.30876	+	10.1833i	0.149627	+	0.460506i
$490$	−18.7418	+	42.5198i	−0.846667	+	1.92085i
$491$	8.31371	+	6.04026i	0.375193	+	0.272593i	0.759361	−	0.650670i	$-0.225512\pi$
$491$	8.31371	+	6.04026i	0.375193	+	0.272593i	−0.384168	+	0.923263i	$0.625512\pi$
$492$	−0.0295940	−	0.281568i	−0.00133420	−	0.0126940i
$493$	9.86434	−	2.09673i	0.444267	−	0.0944319i
$494$	−7.52481	−	13.0334i	−0.338557	−	0.586399i
$495$		0			0
$496$	−6.92396			−0.310895
$497$	24.7308	+	3.86982i	1.10933	+	0.173585i
$498$	11.2467	−	8.17120i	0.503976	−	0.366160i
$499$	−33.3613	+	14.8534i	−1.49346	+	0.664930i	−0.981040	−	0.193807i	$-0.937916\pi$
$499$	−33.3613	+	14.8534i	−1.49346	+	0.664930i	−0.512417	+	0.858737i	$0.671250\pi$
$500$	8.96429	−	9.95586i	0.400895	−	0.445239i
$501$	−3.60151	+	3.99989i	−0.160904	+	0.178702i
$502$	6.47381	−	2.88233i	0.288940	−	0.128644i
$503$	25.3730	−	18.4346i	1.13133	−	0.821957i	0.145440	−	0.989367i	$-0.453540\pi$
$503$	25.3730	−	18.4346i	1.13133	−	0.821957i	0.985887	+	0.167410i	$0.0535403\pi$
$504$	−3.76015	+	4.66110i	−0.167490	+	0.207622i
$505$	23.6732			1.05345
$506$		0			0
$507$	−2.10859	−	3.65219i	−0.0936459	−	0.162199i
$508$	21.3318	−	4.53422i	0.946447	−	0.201174i
$509$	1.20882	+	11.5011i	0.0535799	+	0.509779i	0.988094	+	0.153852i	$0.0491680\pi$
$509$	1.20882	+	11.5011i	0.0535799	+	0.509779i	−0.934514	+	0.355926i	$0.884165\pi$
$510$	18.3990	+	13.3677i	0.814723	+	0.591931i
$511$	5.21473	+	3.37271i	0.230686	+	0.149200i
$512$	7.79420	+	23.9881i	0.344458	+	1.06013i
$513$	−6.03306	+	2.68609i	−0.266366	+	0.118594i
$514$	−14.8692	−	6.62017i	−0.655850	−	0.292003i
$515$	−7.76998	+	1.65156i	−0.342386	+	0.0727764i
$516$	1.70574	−	2.95442i	0.0750909	−	0.130061i
$517$		0			0
$518$	17.1830	−	13.9676i	0.754979	−	0.613700i
$519$	3.87952	−	11.9399i	0.170292	−	0.524104i
$520$	1.43228	+	13.6273i	0.0628098	+	0.597595i
$521$	3.19443	−	30.3930i	0.139950	−	1.33154i	−0.668824	−	0.743421i	$-0.733202\pi$
$521$	3.19443	−	30.3930i	0.139950	−	1.33154i	0.808775	−	0.588119i	$-0.200131\pi$
$522$	−6.21900	+	6.90690i	−0.272198	+	0.302307i
$523$	4.35776	+	0.926271i	0.190552	+	0.0405030i	0.302199	−	0.953245i	$-0.402279\pi$
$523$	4.35776	+	0.926271i	0.190552	+	0.0405030i	−0.111647	+	0.993748i	$0.535613\pi$
$524$	−6.33849	−	4.60518i	−0.276898	−	0.201178i
$525$	12.4635	−	3.36446i	0.543952	−	0.146837i
$526$	−3.38863	+	10.4291i	−0.147751	+	0.454732i
$527$	3.85251	−	6.67274i	0.167818	−	0.290669i
$528$		0			0
$529$	−8.55185	−	14.8122i	−0.371820	−	0.644010i
$530$	−32.1338	−	35.6882i	−1.39580	−	1.55020i
$531$	19.8657	−	14.4332i	0.862096	−	0.626350i
$532$	3.32825	−	6.56222i	0.144298	−	0.284508i
$533$	0.385953	+	1.18784i	0.0167175	+	0.0514511i
$534$	4.16106	+	0.884461i	0.180067	+	0.0382744i
$535$	4.25769	−	40.5092i	0.184076	−	1.75137i
$536$	0.558007	+	0.248441i	0.0241022	+	0.0107310i
$537$	−0.579863	−	0.644003i	−0.0250229	−	0.0277908i
$538$	−41.3114			−1.78106
$539$		0			0
$540$	−19.6878			−0.847227
$541$	−11.1548	−	12.3886i	−0.479581	−	0.532629i	0.453997	−	0.891003i	$-0.349998\pi$
$541$	−11.1548	−	12.3886i	−0.479581	−	0.532629i	−0.933578	+	0.358374i	$0.883331\pi$
$542$	16.9150	+	7.53105i	0.726562	+	0.323486i
$543$	−1.20438	+	11.4589i	−0.0516847	+	0.491747i
$544$	−36.4844	−	7.75501i	−1.56426	−	0.332493i
$545$	−13.0818	−	40.2617i	−0.560364	−	1.72462i
$546$	6.47622	−	12.7690i	0.277157	−	0.546462i
$547$	−29.2929	+	21.2825i	−1.25247	+	0.909976i	−0.998363	−	0.0571994i	$-0.981783\pi$
$547$	−29.2929	+	21.2825i	−1.25247	+	0.909976i	−0.254111	+	0.967175i	$0.581783\pi$
$548$	20.2034	+	22.4381i	0.863045	+	0.958509i
$549$	−1.47741	−	2.55894i	−0.0630542	−	0.109213i
$550$		0			0
$551$	−1.74376	+	3.02027i	−0.0742865	+	0.128668i
$552$	1.12323	−	3.45696i	0.0478080	−	0.147138i
$553$	−31.7227	+	8.56335i	−1.34898	+	0.364151i
$554$	−35.9422	−	26.1135i	−1.52704	−	1.10946i
$555$	−10.0425	−	2.13459i	−0.426279	−	0.0906083i
$556$	−5.41884	+	6.01823i	−0.229810	+	0.255230i
$557$	0.0700278	−	0.666270i	0.00296717	−	0.0282308i	−0.992938	−	0.118633i	$-0.962149\pi$
$557$	0.0700278	−	0.666270i	0.00296717	−	0.0282308i	0.995905	+	0.0904026i	$0.0288154\pi$
$558$	0.742258	+	7.06211i	0.0314223	+	0.298963i
$559$	−4.65059	+	14.3130i	−0.196699	+	0.605377i
$560$	−34.2044	+	27.8038i	−1.44540	+	1.17492i
$561$		0			0
$562$	−15.2900	+	26.4830i	−0.644969	+	1.11712i
$563$	12.7493	−	2.70995i	0.537320	−	0.114211i	0.0687443	−	0.997634i	$-0.478101\pi$
$563$	12.7493	−	2.70995i	0.537320	−	0.114211i	0.468575	+	0.883423i	$0.344767\pi$
$564$	−4.16063	−	1.85243i	−0.175194	−	0.0780015i
$565$	16.1586	−	7.19427i	0.679797	−	0.302665i
$566$	9.87193	+	30.3827i	0.414948	+	1.27708i
$567$	11.8795	+	7.68325i	0.498892	+	0.322666i
$568$	6.73099	+	4.89035i	0.282426	+	0.205194i
$569$	−2.86842	−	27.2912i	−0.120250	−	1.14411i	−0.873654	−	0.486547i	$-0.838256\pi$
$569$	−2.86842	−	27.2912i	−0.120250	−	1.14411i	0.753404	−	0.657558i	$-0.228411\pi$
$570$	−7.69297	+	1.63519i	−0.322223	+	0.0684906i
$571$	−8.11974	−	14.0638i	−0.339800	−	0.588552i	0.644595	−	0.764525i	$-0.277026\pi$
$571$	−8.11974	−	14.0638i	−0.339800	−	0.588552i	−0.984395	+	0.175973i	$0.943693\pi$
$572$		0			0
$573$	10.1513			0.424075
$574$	−0.883904	+	1.09569i	−0.0368935	+	0.0457333i
$575$	38.3000	−	27.8266i	1.59722	−	1.16045i
$576$	9.22066	−	4.10530i	0.384194	−	0.171054i
$577$	15.8703	−	17.6258i	0.660690	−	0.733770i	−0.315921	−	0.948786i	$-0.602313\pi$
$577$	15.8703	−	17.6258i	0.660690	−	0.733770i	0.976611	+	0.215015i	$0.0689801\pi$
$578$	13.2693	−	14.7371i	0.551931	−	0.612981i
$579$	−3.11192	+	1.38552i	−0.129327	+	0.0575801i
$580$	−8.41129	+	6.11116i	−0.349260	+	0.253752i
$581$	−29.6232	−	4.63536i	−1.22898	−	0.192307i
$582$	18.8262			0.780373
$583$		0			0
$584$	1.03209	+	1.78763i	0.0427081	+	0.0739727i
$585$	39.2306	−	8.33871i	1.62198	−	0.344763i
$586$	2.70675	+	25.7530i	0.111815	+	1.06385i
$587$	36.0744	+	26.2096i	1.48895	+	1.08178i	0.974533	+	0.224244i	$0.0719914\pi$
$587$	36.0744	+	26.2096i	1.48895	+	1.08178i	0.514416	+	0.857541i	$0.328009\pi$
$588$	6.95888	−	0.757600i	0.286979	−	0.0312429i
$589$	0.823395	+	2.53415i	0.0339274	+	0.104418i
$590$	57.8520	−	25.7574i	2.38173	−	1.06041i
$591$	−2.75393	−	1.22613i	−0.113281	−	0.0504361i
$592$	20.5470	−	4.36739i	0.844475	−	0.179499i
$593$	21.4217	−	37.1035i	0.879685	−	1.52366i	0.0279992	−	0.999608i	$-0.491086\pi$
$593$	21.4217	−	37.1035i	0.879685	−	1.52366i	0.851686	−	0.524052i	$-0.175580\pi$
$594$		0			0
$595$	−7.76352	−	48.4335i	−0.318273	−	1.98558i
$596$	−8.05584	+	24.7933i	−0.329980	+	1.01557i
$597$	0.412743	+	3.92698i	0.0168924	+	0.160721i
$598$	5.48815	−	52.2163i	0.224427	−	2.13528i
$599$	−0.423629	+	0.470487i	−0.0173090	+	0.0192236i	−0.751737	−	0.659463i	$-0.770784\pi$
$599$	−0.423629	+	0.470487i	−0.0173090	+	0.0192236i	0.734428	+	0.678686i	$0.237450\pi$
$600$	4.19709	+	0.892120i	0.171346	+	0.0364206i
$601$	2.79792	+	2.03281i	0.114129	+	0.0829199i	0.643386	−	0.765542i	$-0.277529\pi$
$601$	2.79792	+	2.03281i	0.114129	+	0.0829199i	−0.529257	+	0.848462i	$0.677529\pi$
$602$	−16.3770	+	4.42087i	−0.667475	+	0.180181i
$603$	0.552481	−	1.70036i	0.0224988	−	0.0692441i
$604$	−0.997941	+	1.72848i	−0.0406056	+	0.0703310i
$605$		0			0
$606$	−4.11081	−	7.12014i	−0.166990	−	0.289236i
$607$	32.3022	+	35.8752i	1.31111	+	1.45613i	0.804500	+	0.593953i	$0.202433\pi$
$607$	32.3022	+	35.8752i	1.31111	+	1.45613i	0.506606	+	0.862178i	$0.330900\pi$
$608$	10.4355	−	7.58183i	0.423215	−	0.307484i
$609$	−3.31296	+	0.179806i	−0.134248	+	0.00728612i
$610$	−2.35481	−	7.24735i	−0.0953433	−	0.293436i
$611$	19.6525	+	4.17726i	0.795054	+	0.168994i
$612$	−2.16370	+	20.5863i	−0.0874625	+	0.832150i
$613$	−19.4727	−	8.66980i	−0.786495	−	0.350170i	−0.0261234	−	0.999659i	$-0.508316\pi$
$613$	−19.4727	−	8.66980i	−0.786495	−	0.350170i	−0.760371	+	0.649489i	$0.774983\pi$
$614$	−14.6076	−	16.2234i	−0.589514	−	0.654722i
$615$	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	$0.580461\pi$
$618$	1.84598	+	2.05017i	0.0742561	+	0.0824698i
$619$	33.1987	+	14.7810i	1.33437	+	0.594099i	0.945026	−	0.326994i	$-0.106036\pi$
$619$	33.1987	+	14.7810i	1.33437	+	0.594099i	0.389342	+	0.921093i	$0.372703\pi$
$620$	−0.830328	+	7.90005i	−0.0333468	+	0.317274i
$621$	−22.5361	−	4.79019i	−0.904341	−	0.192224i
$622$	2.00265	+	6.16352i	0.0802989	+	0.247134i
$623$	−5.01150	−	7.68568i	−0.200781	−	0.307920i
$624$	10.9878	−	7.98313i	0.439866	−	0.319581i
$625$	−4.34459	−	4.82516i	−0.173784	−	0.193006i
$626$	18.2506	+	31.6110i	0.729441	+	1.26343i
$627$		0			0
$628$	−10.4907	+	18.1704i	−0.418623	+	0.725077i
$629$	−7.22345	+	22.2315i	−0.288018	+	0.886428i
$630$	32.0253	+	31.9063i	1.27592	+	1.27118i
$631$	−12.8792	−	9.35726i	−0.512711	−	0.372507i	0.301140	−	0.953580i	$-0.402633\pi$
$631$	−12.8792	−	9.35726i	−0.512711	−	0.372507i	−0.813851	+	0.581073i	$0.802633\pi$
$632$	−10.6826	−	2.27066i	−0.424932	−	0.0903220i
$633$	3.79731	−	4.21734i	0.150930	−	0.167624i
$634$	6.44671	−	61.3363i	0.256031	−	2.43598i
$635$	5.25540	+	50.0018i	0.208554	+	1.98426i
$636$	−2.23556	+	6.88034i	−0.0886457	+	0.272823i
$637$	−29.3332	+	9.65177i	−1.16222	+	0.382417i
$638$		0			0
$639$	12.1763	−	21.0900i	0.481688	−	0.834309i
$640$	−23.6404	+	5.02491i	−0.934467	+	0.198627i
$641$	−11.3955	−	5.07359i	−0.450094	−	0.200395i	0.169155	−	0.985589i	$-0.445896\pi$
$641$	−11.3955	−	5.07359i	−0.450094	−	0.200395i	−0.619249	+	0.785195i	$0.712563\pi$
$642$	−12.9232	+	5.75378i	−0.510038	+	0.227084i
$643$	−11.3820	−	35.0303i	−0.448864	−	1.38146i	−0.878190	−	0.478311i	$-0.841249\pi$
$643$	−11.3820	−	35.0303i	−0.448864	−	1.38146i	0.429326	−	0.903149i	$-0.358751\pi$
$644$	22.8504	−	11.6965i	0.900431	−	0.460905i
$645$	6.36279	+	4.62284i	0.250534	+	0.182024i
$646$	1.87176	+	17.8086i	0.0736435	+	0.700671i
$647$	−20.0117	+	4.25361i	−0.786740	+	0.167227i	−0.583728	−	0.811950i	$-0.698406\pi$
$647$	−20.0117	+	4.25361i	−0.786740	+	0.167227i	−0.203012	+	0.979176i	$0.565073\pi$
$648$	2.35117	+	4.07234i	0.0923626	+	0.159977i
$649$		0			0
$650$	61.9796			2.43104
$651$	−1.59161	+	1.97297i	−0.0623801	+	0.0773268i
$652$	−20.3334	+	14.7730i	−0.796316	+	0.578557i
$653$	−14.2142	+	6.32859i	−0.556246	+	0.247657i	−0.665552	−	0.746351i	$-0.731804\pi$
$653$	−14.2142	+	6.32859i	−0.556246	+	0.247657i	0.109306	+	0.994008i	$0.465137\pi$
$654$	−9.83778	+	10.9260i	−0.384688	+	0.427239i
$655$	12.0861	−	13.4230i	0.472244	−	0.524480i
$656$	−1.21998	+	0.543171i	−0.0476323	+	0.0212073i
$657$	4.88799	−	3.55133i	0.190699	−	0.138551i
$658$	8.15497	+	21.1268i	0.317914	+	0.823610i
$659$	−23.6673			−0.921945			−0.460973	−	0.887414i	$-0.652499\pi$
$659$	−23.6673			−0.921945			−0.460973	+	0.887414i	$0.652499\pi$
$660$		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	$0.961826\pi$
$662$	11.6919	−	2.48518i	0.454417	−	0.0965893i
$663$	1.57982	+	15.0310i	0.0613552	+	0.583756i
$664$	−8.06254	−	5.85778i	−0.312887	−	0.227326i
$665$	14.2437	+	9.21232i	0.552346	+	0.357238i
$666$	−6.65719	−	20.4887i	−0.257961	−	0.793922i
$667$	−11.1151	+	4.94874i	−0.430377	+	0.191616i
$668$	−11.5418	−	5.13873i	−0.446564	−	0.198823i
$669$	0.141497	−	0.0300761i	0.00547059	−	0.00116281i
$670$	2.30541	−	3.99308i	0.0890657	−	0.154266i
$671$		0			0
$672$	11.4645	+	4.37636i	0.442253	+	0.168822i
$673$	2.44937	−	7.53838i	0.0944163	−	0.290583i	−0.892685	−	0.450681i	$-0.851181\pi$
$673$	2.44937	−	7.53838i	0.0944163	−	0.290583i	0.987101	+	0.160098i	$0.0511810\pi$
$674$	3.05378	+	29.0548i	0.117627	+	1.11915i
$675$	2.84292	−	27.0486i	0.109424	−	1.04110i
$676$	6.62371	−	7.35638i	0.254758	−	0.282938i
$677$	−35.2685	−	7.49655i	−1.35548	−	0.288116i	−0.527824	−	0.849354i	$-0.676992\pi$
$677$	−35.2685	−	7.49655i	−1.35548	−	0.288116i	−0.827655	+	0.561237i	$0.810325\pi$
$678$	−4.96971	−	3.61071i	−0.190861	−	0.138668i
$679$	−28.7655	−	28.6587i	−1.10392	−	1.09982i
$680$	5.03811	−	15.5057i	0.193203	−	0.594616i
$681$	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	$0.757363\pi$
$684$	−4.78989	−	5.31972i	−0.183146	−	0.203404i
$685$	−56.3142	+	40.9147i	−2.15166	+	1.56327i
$686$	−27.1717	−	21.7532i	−1.03742	−	0.830543i
$687$	4.77912	+	14.7086i	0.182335	+	0.561168i
$688$	−15.7399	−	3.34561i	−0.600077	−	0.127550i
$689$	3.33597	−	31.7396i	0.127090	−	1.20918i
$690$	−25.0660	−	11.1601i	−0.954248	−	0.424859i
$691$	5.35304	+	5.94516i	0.203639	+	0.226164i	0.836310	−	0.548256i	$-0.184708\pi$
$691$	5.35304	+	5.94516i	0.203639	+	0.226164i	−0.632671	+	0.774421i	$0.718041\pi$
$692$	29.4688			1.12024
$693$		0			0
$694$	−37.0702			−1.40716
$695$	−12.4926	−	13.8745i	−0.473872	−	0.526289i
$696$	−1.00743	−	0.448537i	−0.0381865	−	0.0170017i
$697$	0.155338	−	1.47794i	0.00588384	−	0.0559810i
$698$	10.6509	+	2.26393i	0.403144	+	0.0856908i
$699$	4.21286	+	12.9659i	0.159345	+	0.490414i
$700$	16.5513	+	25.3833i	0.625581	+	0.959398i
$701$	−10.3240	+	7.50081i	−0.389931	+	0.283302i	−0.765427	−	0.643522i	$-0.777472\pi$
$701$	−10.3240	+	7.50081i	−0.389931	+	0.283302i	0.375496	+	0.926824i	$0.377472\pi$
$702$	−20.1833	−	22.4158i	−0.761769	−	0.846030i
$703$	−4.04189	−	7.00076i	−0.152443	−	0.264039i
$704$		0			0
$705$	5.24985	−	9.09300i	0.197721	−	0.342462i
$706$	19.2616	−	59.2812i	0.724921	−	2.23108i
$707$	−4.55769	+	17.1370i	−0.171409	+	0.644503i
$708$	−7.71788	−	5.60737i	−0.290056	−	0.210738i
$709$	−4.60221	−	0.978229i	−0.172839	−	0.0367382i	0.120679	−	0.992692i	$-0.461493\pi$
$709$	−4.60221	−	0.978229i	−0.172839	−	0.0367382i	−0.293518	+	0.955953i	$0.594826\pi$
$710$	42.0243	−	46.6727i	1.57714	−	1.75159i
$711$	−3.34144	+	31.7917i	−0.125314	+	1.19228i
$712$	−0.318773	−	3.03292i	−0.0119465	−	0.113664i
$713$	−2.87259	+	8.84094i	−0.107580	+	0.331096i
$714$	−13.2191	+	10.7454i	−0.494712	+	0.402137i
$715$		0			0
$716$	1.01707	−	1.76162i	0.0380098	−	0.0658350i
$717$	−9.59578	+	2.03965i	−0.358361	+	0.0761720i
$718$	7.22777	+	3.21801i	0.269738	+	0.120095i
$719$	48.0725	−	21.4032i	1.79280	−	0.798206i	0.817969	−	0.575263i	$-0.195100\pi$
$719$	48.0725	−	21.4032i	1.79280	−	0.798206i	0.974831	−	0.222943i	$-0.0715664\pi$
$720$	13.2518	+	40.7847i	0.493864	+	1.51996i
$721$	0.300354	−	5.94263i	0.0111858	−	0.221315i
$722$	23.8788	+	17.3489i	0.888676	+	0.645661i
$723$	−2.01539	−	19.1751i	−0.0749531	−	0.713131i
$724$	−26.4545	+	5.62308i	−0.983174	+	0.208980i
$725$	−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	$0.636289\pi$
$728$	−10.1405	−	1.58676i	−0.375832	−	0.0588093i
$729$	5.37180	−	3.90284i	0.198956	−	0.144550i
$730$	14.2346	−	6.33766i	0.526846	−	0.234567i
$731$	11.9819	−	13.3073i	0.443168	−	0.492188i
$732$	−0.768132	+	0.853097i	−0.0283910	+	0.0315314i
$733$	−27.6035	+	12.2899i	−1.01956	+	0.453936i	−0.847299	−	0.531116i	$-0.821773\pi$
$733$	−27.6035	+	12.2899i	−1.01956	+	0.453936i	−0.172258	+	0.985052i	$0.555106\pi$
$734$	29.5558	−	21.4736i	1.09093	−	0.792604i
$735$	0.0600525	+	16.1377i	0.00221507	+	0.595249i
$736$	45.0009			1.65876
$737$		0			0
$738$	0.684793	+	1.18610i	0.0252076	+	0.0436608i
$739$	−12.4925	+	2.65536i	−0.459543	+	0.0976789i	−0.431866	−	0.901938i	$-0.642145\pi$
$739$	−12.4925	+	2.65536i	−0.459543	+	0.0976789i	−0.0276776	+	0.999617i	$0.508811\pi$
$740$	−2.51906	−	23.9672i	−0.0926024	−	0.881053i
$741$	−4.22847	−	3.07217i	−0.155337	−	0.112859i
$742$	32.0211	−	16.3907i	1.17553	−	0.601722i
$743$	−11.5878	−	35.6635i	−0.425115	−	1.30837i	−0.902884	−	0.429884i	$-0.858555\pi$
$743$	−11.5878	−	35.6635i	−0.425115	−	1.30837i	0.477770	−	0.878485i	$-0.341445\pi$
$744$	−0.769706	+	0.342695i	−0.0282188	+	0.0125638i
$745$	−54.9043	−	24.4450i	−2.01154	−	0.895594i
$746$	−23.3727	+	4.96802i	−0.855736	+	0.181892i
$747$	−14.5851	+	25.2622i	−0.533642	+	0.924295i
$748$		0			0
$749$	28.5048	+	10.8812i	1.04154	+	0.397589i
$750$	3.31463	−	10.2014i	0.121033	−	0.372502i
$751$	−3.84505	−	36.5832i	−0.140308	−	1.33494i	−0.807418	−	0.589980i	$-0.799136\pi$
$751$	−3.84505	−	36.5832i	−0.140308	−	1.33494i	0.667110	−	0.744959i	$-0.267531\pi$
$752$	−2.24553	+	21.3648i	−0.0818860	+	0.779093i
$753$	1.64680	−	1.82896i	0.0600127	−	0.0666509i
$754$	−15.5809	−	3.31183i	−0.567424	−	0.120610i
$755$	−3.72255	−	2.70459i	−0.135477	−	0.0984300i
$756$	3.79039	−	14.2519i	0.137855	−	0.518338i
$757$	−0.701858	+	2.16010i	−0.0255094	+	0.0785100i	−0.963001	−	0.269499i	$-0.913142\pi$
$757$	−0.701858	+	2.16010i	−0.0255094	+	0.0785100i	0.937491	+	0.348009i	$0.113142\pi$
$758$	21.4354	−	37.1272i	0.778569	−	1.34852i
$759$		0			0
$760$	2.81908	+	4.88279i	0.102259	+	0.177117i
$761$	6.81896	+	7.57322i	0.247187	+	0.274529i	0.853951	−	0.520353i	$-0.174199\pi$
$761$	6.81896	+	7.57322i	0.247187	+	0.274529i	−0.606764	+	0.794882i	$0.707533\pi$
$762$	14.1263	−	10.2634i	0.511743	−	0.371803i
$763$	31.6639	−	1.71852i	1.14631	−	0.0622145i
$764$	7.36326	+	22.6618i	0.266393	+	0.819874i
$765$	−46.6783	−	9.92178i	−1.68766	−	0.358723i
$766$	−1.63025	+	15.5108i	−0.0589035	+	0.560429i
$767$	38.4463	+	17.1174i	1.38822	+	0.618073i
$768$	9.04162	+	10.0417i	0.326261	+	0.362350i
$769$	−27.7802			−1.00178			−0.500891	−	0.865511i	$-0.666994\pi$
$769$	−27.7802			−1.00178			−0.500891	+	0.865511i	$0.666994\pi$
$770$		0			0
$771$	−5.65270			−0.203577
$772$	−5.35029	−	5.94210i	−0.192561	−	0.213861i
$773$	−9.84984	−	4.38543i	−0.354274	−	0.157733i	0.221880	−	0.975074i	$-0.428781\pi$
$773$	−9.84984	−	4.38543i	−0.354274	−	0.157733i	−0.576154	+	0.817341i	$0.695447\pi$
$774$	−1.72503	+	16.4126i	−0.0620050	+	0.589938i
$775$	−10.7338	−	2.28154i	−0.385569	−	0.0819553i
$776$	−4.17055	−	12.8356i	−0.149714	−	0.460772i
$777$	3.47865	−	6.85875i	0.124796	−	0.246056i
$778$	−17.3326	+	12.5929i	−0.621404	+	0.451476i
$779$	0.343879	+	0.381916i	0.0123207	+	0.0136836i
$780$	−7.79086	−	13.4942i	−0.278958	−	0.483169i
$781$		0			0
$782$	−31.2358	+	54.1019i	−1.11699	+	1.93468i
$783$	−2.16000	+	6.64779i	−0.0771920	+	0.237572i
$784$	−13.5419	−	30.1134i	−0.483638	−	1.07548i
$785$	−39.1326	−	28.4315i	−1.39670	−	1.01476i
$786$	−6.13593	−	1.30423i	−0.218861	−	0.0465204i
$787$	−14.2841	+	15.8641i	−0.509174	+	0.565495i	−0.941841	−	0.336059i	$-0.890906\pi$
$787$	−14.2841	+	15.8641i	−0.509174	+	0.565495i	0.432667	+	0.901554i	$0.357573\pi$
$788$	0.739647	−	7.03727i	0.0263488	−	0.250693i
$789$	0.398086	+	3.78754i	0.0141722	+	0.134840i
$790$	−25.4756	+	78.4057i	−0.906380	+	2.78955i
$791$	2.09698	+	13.0822i	0.0745601	+	0.465151i
$792$		0			0
$793$	2.53209	−	4.38571i	0.0899171	−	0.155741i
$794$	−12.0993	+	2.57178i	−0.429387	+	0.0912691i
$795$	−15.2364	−	6.78367i	−0.540379	−	0.240592i
$796$	−8.46726	+	3.76987i	−0.300114	+	0.133619i
$797$	12.1473	+	37.3857i	0.430281	+	1.32427i	0.897846	+	0.440310i	$0.145132\pi$
$797$	12.1473	+	37.3857i	0.430281	+	1.32427i	−0.467565	+	0.883959i	$0.654868\pi$
$798$	0.297377	−	5.88374i	0.0105270	−	0.208282i
$799$	−19.3402	−	14.0515i	−0.684207	−	0.497105i
$800$	5.55281	+	52.8315i	0.196322	+	1.86787i
$801$	−8.73127	+	1.85589i	−0.308504	+	0.0655746i
$802$	−3.93717	−	6.81937i	−0.139026	−	0.240800i
$803$		0			0
$804$	−0.694593			−0.0244964
$805$	21.3109	+	55.2095i	0.751110	+	1.94588i
$806$	−9.84593	+	7.15349i	−0.346808	+	0.251971i
$807$	−13.1069	+	5.83557i	−0.461385	+	0.205422i
$808$	−3.94381	+	4.38005i	−0.138743	+	0.154089i
$809$	2.17240	−	2.41270i	0.0763776	−	0.0848260i	−0.703745	−	0.710453i	$-0.748490\pi$
$809$	2.17240	−	2.41270i	0.0763776	−	0.0848260i	0.780122	+	0.625627i	$0.215157\pi$
$810$	32.4274	−	14.4376i	1.13938	−	0.507286i
$811$	−27.0257	+	19.6353i	−0.949001	+	0.689489i	−0.950570	−	0.310509i	$-0.899500\pi$
$811$	−27.0257	+	19.6353i	−0.949001	+	0.689489i	0.00156966	+	0.999999i	$0.499500\pi$
$812$	−2.80447	−	7.26546i	−0.0984176	−	0.254968i
$813$	6.43047			0.225526
$814$		0			0
$815$	−28.9714	−	50.1799i	−1.01482	−	1.75772i
$816$	−15.8070	+	3.35988i	−0.553356	+	0.117619i
$817$	0.647296	+	6.15861i	0.0226460	+	0.215462i
$818$	−1.17580	−	0.854265i	−0.0411107	−	0.0298687i
$819$	−1.51648	+	30.0043i	−0.0529903	+	1.04844i
$820$	0.473442	+	1.45710i	0.0165333	+	0.0508842i
$821$	−22.1056	+	9.84204i	−0.771491	+	0.343490i	−0.754444	−	0.656365i	$-0.772093\pi$
$821$	−22.1056	+	9.84204i	−0.771491	+	0.343490i	−0.0170470	+	0.999855i	$0.505427\pi$
$822$	22.0847	+	9.83273i	0.770292	+	0.342956i
$823$	45.6943	−	9.71262i	1.59280	−	0.338561i	0.675689	−	0.737187i	$-0.263846\pi$
$823$	45.6943	−	9.71262i	1.59280	−	0.338561i	0.917114	+	0.398626i	$0.130513\pi$
$824$	0.988856	−	1.71275i	0.0344484	−	0.0596664i
$825$		0			0
$826$	7.50774	+	46.8378i	0.261228	+	1.62970i
$827$	0.587107	−	1.80693i	0.0204157	−	0.0628331i	−0.940330	−	0.340265i	$-0.889483\pi$
$827$	0.587107	−	1.80693i	0.0204157	−	0.0628331i	0.960745	+	0.277432i	$0.0894833\pi$
$828$	−2.61045	−	24.8368i	−0.0907195	−	0.863138i
$829$	−5.32782	+	50.6909i	−0.185043	+	1.76057i	0.370269	+	0.928924i	$0.379265\pi$
$829$	−5.32782	+	50.6909i	−0.185043	+	1.76057i	−0.555312	+	0.831642i	$0.687401\pi$
$830$	−50.3377	+	55.9057i	−1.74725	+	1.94052i
$831$	−15.0922	−	3.20794i	−0.523541	−	0.111282i
$832$	13.9949	+	10.1679i	0.485185	+	0.352507i
$833$	36.5556	+	3.70466i	1.26657	+	0.128359i
$834$	−2.00367	+	6.16665i	−0.0693813	+	0.213534i
$835$	14.5633	−	25.2244i	0.503984	−	0.872926i
$836$		0			0
$837$	2.67024	+	4.62500i	0.0922972	+	0.159863i
$838$	17.2972	+	19.2105i	0.597523	+	0.663616i
$839$	−34.7366	+	25.2376i	−1.19924	+	0.871298i	−0.994210	−	0.107457i	$-0.965729\pi$
$839$	−34.7366	+	25.2376i	−1.19924	+	0.871298i	−0.205030	+	0.978756i	$0.565729\pi$
$840$	−2.42624	+	4.78374i	−0.0837131	+	0.165055i
$841$	−7.82082	−	24.0700i	−0.269683	−	0.830000i
$842$	10.6727	+	2.26856i	0.367807	+	0.0781797i
$843$	−1.11012	+	10.5621i	−0.0382347	+	0.363779i
$844$	12.1692	+	5.41809i	0.418882	+	0.186498i
$845$	15.2704	+	16.9595i	0.525316	+	0.583423i
$846$	22.0318			0.757468
$847$		0			0
$848$	34.1239			1.17182
$849$	7.42388	+	8.24506i	0.254787	+	0.282970i
$850$	−67.3704	−	29.9952i	−2.31079	−	1.02883i
$851$	2.94791	−	28.0475i	0.101053	−	0.961457i
$852$	−9.25436	−	1.96707i	−0.317049	−	0.0673908i
$853$	16.1789	+	49.7935i	0.553954	+	1.70490i	0.698689	+	0.715426i	$0.253767\pi$
$853$	16.1789	+	49.7935i	0.553954	+	1.70490i	−0.144734	+	0.989471i	$0.546233\pi$
$854$	5.69969	−	0.309343i	0.195039	−	0.0105855i
$855$	13.3512	−	9.70022i	0.456601	−	0.331740i
$856$	6.78575	+	7.53634i	0.231932	+	0.257587i
$857$	0.489018	+	0.847004i	0.0167045	+	0.0289331i	0.874257	−	0.485464i	$-0.161349\pi$
$857$	0.489018	+	0.847004i	0.0167045	+	0.0289331i	−0.857552	+	0.514397i	$0.828016\pi$
$858$		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	$-0.0303912\pi$
$860$	−5.70479	+	17.5576i	−0.194532	+	0.598708i
$861$	−0.125662	+	0.472490i	−0.00428254	+	0.0161024i
$862$	27.3773	+	19.8908i	0.932474	+	0.677482i
$863$	22.1996	+	4.71867i	0.755682	+	0.160625i	0.569615	−	0.821912i	$-0.307092\pi$
$863$	22.1996	+	4.71867i	0.755682	+	0.160625i	0.186067	+	0.982537i	$0.440426\pi$
$864$	17.2990	−	19.2125i	0.588525	−	0.653623i
$865$	−7.10142	+	67.5655i	−0.241456	+	2.29730i
$866$	−0.459787	−	4.37458i	−0.0156242	−	0.148654i
$867$	2.12824	−	6.55005i	0.0722788	−	0.222451i
$868$	−5.55896	−	2.12203i	−0.188684	−	0.0720263i
$869$		0			0
$870$	−4.16220	+	7.20914i	−0.141112	+	0.244413i
$871$	2.99722	−	0.637078i	0.101557	−	0.0215866i
$872$	9.62861	+	4.28693i	0.326066	+	0.145174i
$873$	−36.0883	+	16.0676i	−1.22141	+	0.543805i
$874$	−6.67601	−	20.5466i	−0.225819	−	0.695000i
$875$	−20.5939	+	10.5414i	−0.696201	+	0.356365i
$876$	−1.89900	−	1.37971i	−0.0641614	−	0.0466160i
$877$	0.128407	+	1.22171i	0.00433598	+	0.0412541i	0.996476	−	0.0838789i	$-0.0267309\pi$
$877$	0.128407	+	1.22171i	0.00433598	+	0.0412541i	−0.992140	+	0.125133i	$0.960064\pi$
$878$	73.5939	−	15.6429i	2.48367	−	0.527921i
$879$	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	$0.450821\pi$
$882$	−29.2626	+	17.0402i	−0.985321	+	0.573775i
$883$	−36.2647	+	26.3478i	−1.22040	+	0.886676i	−0.996134	−	0.0878512i	$-0.972000\pi$
$883$	−36.2647	+	26.3478i	−1.22040	+	0.886676i	−0.224271	+	0.974527i	$0.572000\pi$
$884$	−32.4095	+	14.4296i	−1.09005	+	0.485321i
$885$	14.7163	−	16.3441i	0.494684	−	0.549402i
$886$	23.8633	−	26.5029i	0.801703	−	0.890381i
$887$	−21.0278	+	9.36220i	−0.706046	+	0.314352i	−0.728164	−	0.685403i	$-0.759626\pi$
$887$	−21.0278	+	9.36220i	−0.706046	+	0.314352i	0.0221175	+	0.999755i	$0.492959\pi$
$888$	2.06795	−	1.50246i	0.0693960	−	0.0504192i
$889$	−37.2080	−	5.82222i	−1.24792	−	0.195271i
$890$	−23.0205			−0.771650
$891$		0			0
$892$	0.169778	+	0.294064i	0.00568458	+	0.00984598i
$893$	8.08648	−	1.71884i	0.270604	−	0.0575186i
$894$	2.18178	+	20.7582i	0.0729696	+	0.694259i
$895$	3.79392	+	2.75644i	0.126817	+	0.0921377i
$896$	0.913834	−	18.0806i	0.0305291	−	0.604031i
$897$	−5.63475	−	17.3420i	−0.188139	−	0.579031i
$898$	−54.1462	+	24.1075i	−1.80688	+	0.804476i
$899$	2.57644	+	1.14710i	0.0859289	+	0.0382580i
$900$	28.8365	−	6.12938i	0.961216	−	0.204313i
$901$	−18.9866	+	32.8858i	−0.632536	+	1.09559i
$902$		0			0
$903$	−4.57145	+	3.71599i	−0.152128	+	0.123661i
$904$	−1.36083	+	4.18820i	−0.0452605	+	0.139297i
$905$	−6.51745	−	62.0094i	−0.216647	−	2.06126i
$906$	−0.167039	+	1.58927i	−0.00554949	+	0.0527999i
$907$	−18.9504	+	21.0465i	−0.629237	+	0.698838i	−0.970492	−	0.241132i	$-0.922481\pi$
$907$	−18.9504	+	21.0465i	−0.629237	+	0.698838i	0.341255	+	0.939971i	$0.389148\pi$
$908$	14.5360	+	3.08972i	0.482393	+	0.102536i
$909$	13.9569	+	10.1403i	0.462921	+	0.336332i
$910$	−19.9136	+	74.8755i	−0.660129	+	2.48210i
$911$	0.919621	−	2.83030i	0.0304684	−	0.0937721i	−0.934666	−	0.355527i	$-0.884301\pi$
$911$	0.919621	−	2.83030i	0.0304684	−	0.0937721i	0.965134	+	0.261755i	$0.0843013\pi$
$912$	2.79426	−	4.83981i	0.0925273	−	0.160262i
$913$		0			0
$914$	−10.9179	−	18.9103i	−0.361131	−	0.625497i
$915$	−1.77086	−	1.96674i	−0.0585428	−	0.0650183i
$916$	−29.3691	+	21.3379i	−0.970383	+	0.705024i
$917$	7.38999	+	11.3334i	0.244039	+	0.374261i
$918$	11.0906	+	34.1332i	0.366043	+	1.12656i
$919$	−21.3176	−	4.53120i	−0.703203	−	0.149470i	−0.157586	−	0.987505i	$-0.550371\pi$
$919$	−21.3176	−	4.53120i	−0.703203	−	0.149470i	−0.545617	+	0.838035i	$0.683705\pi$
$920$	−2.05607	+	19.5622i	−0.0677866	+	0.644946i
$921$	−6.92624	−	3.08376i	−0.228228	−	0.101613i
$922$	−16.3213	−	18.1267i	−0.537515	−	0.596971i
$923$	41.7374			1.37380
$924$		0			0
$925$	33.2918			1.09463
$926$	44.4803	+	49.4004i	1.46171	+	1.62340i
$927$	−5.28833	−	2.35452i	−0.173692	−	0.0773325i
$928$	1.42710	−	13.5779i	0.0468467	−	0.445717i
$929$	−36.2551	−	7.70627i	−1.18949	−	0.252835i	−0.429683	−	0.902980i	$-0.641375\pi$
$929$	−36.2551	−	7.70627i	−1.18949	−	0.252835i	−0.759810	+	0.650145i	$0.774708\pi$
$930$	1.96538	+	6.04880i	0.0644472	+	0.198348i
$931$	−9.41103	+	8.53736i	−0.308434	+	0.279801i
$932$	−25.8893	+	18.8097i	−0.848032	+	0.616131i
$933$	1.50603	+	1.67261i	0.0493052	+	0.0547589i
$934$	37.4616	+	64.8853i	1.22578	+	2.12311i
$935$		0			0
$936$	−4.99273	+	8.64766i	−0.163192	+	0.282657i
$937$	12.3094	−	37.8844i	0.402130	−	1.23763i	−0.521138	−	0.853472i	$-0.674492\pi$
$937$	12.3094	−	37.8844i	0.402130	−	1.23763i	0.923268	−	0.384156i	$-0.125508\pi$
$938$	2.44673	+	2.43765i	0.0798887	+	0.0795919i
$939$	10.2557	+	7.45120i	0.334682	+	0.243161i
$940$	24.1073	+	5.12417i	0.786294	+	0.167132i
$941$	9.16167	−	10.1751i	0.298662	−	0.331698i	−0.575071	−	0.818103i	$-0.695026\pi$
$941$	9.16167	−	10.1751i	0.298662	−	0.331698i	0.873733	+	0.486406i	$0.161692\pi$
$942$	−1.75596	+	16.7069i	−0.0572124	+	0.544340i
$943$	0.187411	+	1.78310i	0.00610294	+	0.0580656i
$944$	−13.9052	+	42.7959i	−0.452576	+	1.39289i
$945$	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	$-0.110998\pi$
$948$	12.1478	−	2.58210i	0.394543	−	0.0838627i
$949$	9.45980	+	4.21177i	0.307078	+	0.136720i
$950$	23.2981	−	10.3730i	0.755892	−	0.336545i
$951$	−6.61890	−	20.3709i	−0.214633	−	0.660571i
$952$	10.2546	+	6.63230i	0.332352	+	0.214954i
$953$	21.7617	+	15.8108i	0.704932	+	0.512163i	0.881535	−	0.472119i	$-0.156511\pi$
$953$	21.7617	+	15.8108i	0.704932	+	0.512163i	−0.176603	+	0.984282i	$0.556511\pi$
$954$	−3.65813	−	34.8048i	−0.118436	−	1.12685i
$955$	−53.7328	+	11.4213i	−1.73875	+	0.369583i
$956$	−11.5137	−	19.9423i	−0.372379	−	0.644979i
$957$		0			0
$958$	−57.0958			−1.84468
$959$	−18.7761	−	48.6428i	−0.606313	−	1.57076i
$960$	7.31362	−	5.31366i	0.236046	−	0.171498i
$961$	−26.3514	+	11.7324i	−0.850046	+	0.378465i
$962$	24.7058	−	27.4385i	0.796546	−	0.884654i
$963$	19.8620	−	22.0590i	0.640045	−	0.710842i
$964$	41.3449	−	18.4079i	1.33163	−	0.592880i
$965$	14.9132	−	10.8351i	0.480074	−	0.348794i
$966$	12.9046	−	15.9966i	0.415199	−	0.514683i
$967$	−39.4270			−1.26789			−0.633943	−	0.773380i	$-0.718565\pi$
$967$	−39.4270			−1.26789			−0.633943	+	0.773380i	$0.718565\pi$
$968$		0			0
$969$	3.10947	+	5.38576i	0.0998906	+	0.173016i
$970$	−99.6515	+	21.1816i	−3.19962	+	0.680099i
$971$	−1.68097	−	15.9933i	−0.0539447	−	0.513250i	−0.987814	−	0.155636i	$-0.950257\pi$
$971$	−1.68097	−	15.9933i	−0.0539447	−	0.513250i	0.933870	−	0.357614i	$-0.116409\pi$
$972$	−17.8544	−	12.9720i	−0.572680	−	0.416076i
$973$	12.4488	−	6.37220i	0.399091	−	0.204283i
$974$	−6.05797	−	18.6445i	−0.194110	−	0.597409i
$975$	19.6643	−	8.75512i	0.629762	−	0.280388i
$976$	4.94664	+	2.20239i	0.158338	+	0.0704967i
$977$	−26.8285	+	5.70258i	−0.858321	+	0.182442i	−0.615992	−	0.787753i	$-0.711245\pi$
$977$	−26.8285	+	5.70258i	−0.858321	+	0.182442i	−0.242329	+	0.970194i	$0.577911\pi$
$978$	−10.0617	+	17.4273i	−0.321736	+	0.557263i
$979$		0			0
$980$	−35.9825	+	11.8396i	−1.14942	+	0.378204i
$981$	9.53326	−	29.3404i	0.304374	−	0.936766i
$982$	2.01877	+	19.2073i	0.0644217	+	0.612931i
$983$	0.780426	−	7.42526i	0.0248917	−	0.236829i	−0.975001	−	0.222199i	$-0.928676\pi$
$983$	0.780426	−	7.42526i	0.0248917	−	0.236829i	0.999893	−	0.0146296i	$-0.00465690\pi$
$984$	−0.108736	+	0.120764i	−0.00346639	+	0.00384981i
$985$	15.9567	+	3.39169i	0.508422	+	0.108068i
$986$	15.3333	+	11.1403i	0.488313	+	0.354780i
$987$	5.57167	+	5.55098i	0.177348	+	0.176690i
$988$	3.79120	−	11.6681i	0.120614	−	0.371212i
$989$	−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	$0.707366\pi$
$992$	−6.97975	−	7.75180i	−0.221607	−	0.246120i
$993$	3.35843	−	2.44005i	0.106577	−	0.0774325i
$994$	25.6955	+	39.4069i	0.815012	+	1.24991i
$995$	−6.60302	−	20.3220i	−0.209330	−	0.644251i
$996$	11.0851	+	2.35621i	0.351245	+	0.0746594i
$997$	3.46158	−	32.9348i	0.109629	−	1.04305i	−0.791993	−	0.610530i	$-0.790956\pi$
$997$	3.46158	−	32.9348i	0.109629	−	1.04305i	0.901622	−	0.432524i	$-0.142377\pi$
$998$	−62.6987	−	27.9153i	−1.98469	−	0.883642i
$999$	−10.8413	−	12.0405i	−0.343003	−	0.380943i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	847.2.n.g.9.3		24
7.4	even	3	inner	847.2.n.g.130.1		24
11.2	odd	10		847.2.n.f.366.3		24
11.3	even	5	inner	847.2.n.g.807.3		24
11.4	even	5		77.2.e.a.23.1	✓	6
11.5	even	5	inner	847.2.n.g.632.1		24
11.6	odd	10		847.2.n.f.632.3		24
11.7	odd	10		847.2.e.c.485.3		6
11.8	odd	10		847.2.n.f.807.1		24
11.9	even	5	inner	847.2.n.g.366.1		24
11.10	odd	2		847.2.n.f.9.1		24
33.26	odd	10		693.2.i.h.100.3		6
44.15	odd	10		1232.2.q.m.177.2		6
77.4	even	15		77.2.e.a.67.1	yes	6
77.18	odd	30		847.2.e.c.606.3		6
77.25	even	15	inner	847.2.n.g.81.1		24
77.26	odd	30		539.2.a.g.1.3		3
77.32	odd	6		847.2.n.f.130.3		24
77.37	even	15		539.2.a.j.1.3		3
77.39	odd	30		847.2.n.f.753.1		24
77.40	even	30		5929.2.a.u.1.1		3
77.46	odd	30		847.2.n.f.487.1		24
77.48	odd	10		539.2.e.m.177.1		6
77.51	odd	30		5929.2.a.x.1.1		3
77.53	even	15	inner	847.2.n.g.487.3		24
77.59	odd	30		539.2.e.m.67.1		6
77.60	even	15	inner	847.2.n.g.753.3		24
77.74	odd	30		847.2.n.f.81.3		24
231.26	even	30		4851.2.a.bk.1.1		3
231.158	odd	30		693.2.i.h.298.3		6
231.191	odd	30		4851.2.a.bj.1.1		3
308.103	even	30		8624.2.a.co.1.2		3
308.191	odd	30		8624.2.a.ch.1.2		3
308.235	odd	30		1232.2.q.m.529.2		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
77.2.e.a.23.1	✓	6	11.4	even	5
77.2.e.a.67.1	yes	6	77.4	even	15
539.2.a.g.1.3		3	77.26	odd	30
539.2.a.j.1.3		3	77.37	even	15
539.2.e.m.67.1		6	77.59	odd	30
539.2.e.m.177.1		6	77.48	odd	10
693.2.i.h.100.3		6	33.26	odd	10
693.2.i.h.298.3		6	231.158	odd	30
847.2.e.c.485.3		6	11.7	odd	10
847.2.e.c.606.3		6	77.18	odd	30
847.2.n.f.9.1		24	11.10	odd	2
847.2.n.f.81.3		24	77.74	odd	30
847.2.n.f.130.3		24	77.32	odd	6
847.2.n.f.366.3		24	11.2	odd	10
847.2.n.f.487.1		24	77.46	odd	30
847.2.n.f.632.3		24	11.6	odd	10
847.2.n.f.753.1		24	77.39	odd	30
847.2.n.f.807.1		24	11.8	odd	10
847.2.n.g.9.3		24	1.1	even	1	trivial
847.2.n.g.81.1		24	77.25	even	15	inner
847.2.n.g.130.1		24	7.4	even	3	inner
847.2.n.g.366.1		24	11.9	even	5	inner
847.2.n.g.487.3		24	77.53	even	15	inner
847.2.n.g.632.1		24	11.5	even	5	inner
847.2.n.g.753.3		24	77.60	even	15	inner
847.2.n.g.807.3		24	11.3	even	5	inner
1232.2.q.m.177.2		6	44.15	odd	10
1232.2.q.m.529.2		6	308.235	odd	30
4851.2.a.bj.1.1		3	231.191	odd	30
4851.2.a.bk.1.1		3	231.26	even	30
5929.2.a.u.1.1		3	77.40	even	30
5929.2.a.x.1.1		3	77.51	odd	30
8624.2.a.ch.1.2		3	308.191	odd	30
8624.2.a.co.1.2		3	308.103	even	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+(1.25755 + 1.39666i) q^{2} +(0.596274 + 0.265478i) q^{3} +(-0.160147 + 1.52370i) q^{4} +(-3.45490 - 0.734363i) q^{5} +(0.379065 + 1.16664i) q^{6} +(1.19676 - 2.35961i) q^{7} +(0.711438 - 0.516890i) q^{8} +(-1.72233 - 1.91284i) q^{9} +(-3.31908 - 5.74881i) q^{10} +(-0.500000 + 0.866025i) q^{12} +(1.36322 - 4.19556i) q^{13} +(4.80055 - 1.29588i) q^{14} +(-1.86511 - 1.35508i) q^{15} +(4.61381 + 0.980695i) q^{16} +(-3.51225 + 3.90075i) q^{17} +(0.505656 - 4.81100i) q^{18} +(-0.189741 - 1.80526i) q^{19} +(1.67224 - 5.14662i) q^{20} +(1.34002 - 1.08926i) q^{21} +(3.16637 - 5.48432i) q^{23} +(0.561435 - 0.119337i) q^{24} +(6.82935 + 3.04062i) q^{25} +(7.57408 - 3.37220i) q^{26} +(-1.12425 - 3.46009i) q^{27} +(3.40367 + 2.20138i) q^{28} +(-1.55434 - 1.12930i) q^{29} +(-0.452896 - 4.30901i) q^{30} +(-1.43583 + 0.305196i) q^{31} +(3.55303 + 6.15403i) q^{32} -9.86484 q^{34} +(-5.86749 + 7.27338i) q^{35} +(3.19041 - 2.31797i) q^{36} +(4.06835 - 1.81135i) q^{37} +(2.28272 - 2.53522i) q^{38} +(1.92668 - 2.13980i) q^{39} +(-2.83753 + 1.26335i) q^{40} +(-0.229048 + 0.166413i) q^{41} +(3.20648 + 0.501742i) q^{42} -3.41147 q^{43} +(4.54576 + 7.87349i) q^{45} +(11.6416 - 2.47450i) q^{46} +(0.476062 + 4.52943i) q^{47} +(2.49074 + 1.80963i) q^{48} +(-4.13554 - 5.64777i) q^{49} +(4.34157 + 13.3620i) q^{50} +(-3.12983 + 1.39349i) q^{51} +(6.17444 + 2.74904i) q^{52} +(7.07633 - 1.50412i) q^{53} +(3.41875 - 5.92145i) q^{54} +(-0.368241 - 2.29731i) q^{56} +(0.366121 - 1.12680i) q^{57} +(-0.377433 - 3.59103i) q^{58} +(-0.997184 + 9.48757i) q^{59} +(2.36343 - 2.62485i) q^{60} +(1.12287 + 0.238673i) q^{61} +(-2.23189 - 1.62156i) q^{62} +(-6.57477 + 1.77482i) q^{63} +(-1.21174 + 3.72935i) q^{64} +(-7.79086 + 13.4942i) q^{65} +(0.347296 + 0.601535i) q^{67} +(-5.38107 - 5.97629i) q^{68} +(3.34400 - 2.42956i) q^{69} +(-17.5371 + 0.951803i) q^{70} +(2.92364 + 8.99804i) q^{71} +(-2.21405 - 0.470612i) q^{72} +(-0.245359 + 2.33444i) q^{73} +(7.64600 + 3.40422i) q^{74} +(3.26495 + 3.62609i) q^{75} +2.78106 q^{76} +5.41147 q^{78} +(-8.31008 - 9.22928i) q^{79} +(-15.2201 - 6.77641i) q^{80} +(-0.558945 + 5.31800i) q^{81} +(-0.520461 - 0.110628i) q^{82} +(-3.50201 - 10.7781i) q^{83} +(1.44511 + 2.21623i) q^{84} +(14.9990 - 10.8974i) q^{85} +(-4.29011 - 4.76465i) q^{86} +(-0.627011 - 1.08602i) q^{87} +(1.73396 - 3.00330i) q^{89} +(-5.28001 + 16.2502i) q^{90} +(-8.26845 - 8.23774i) q^{91} +(7.84935 + 5.70289i) q^{92} +(-0.937174 - 0.199202i) q^{93} +(-5.72738 + 6.36090i) q^{94} +(-0.670182 + 6.37635i) q^{95} +(0.484819 + 4.61275i) q^{96} +(4.74258 - 14.5961i) 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

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