LMFDB - Embedded newform 728.2.c.b.365.15

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [728,2,Mod(365,728)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(728, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 1, 0, 0])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("728.365"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 728 = 2^{3} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	728.c (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [38] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$5.81310926715$
Analytic rank:	$0$
Dimension:	$38$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			365.15
Character	$\chi$	$=$	728.365
Dual form			728.2.c.b.365.16

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.581532 - 1.28912i) q^{2} +2.40918i q^{3} +(-1.32364 + 1.49933i) q^{4} -0.687773i q^{5} +(3.10571 - 1.40101i) q^{6} +1.00000 q^{7} +(2.70254 + 0.834421i) q^{8} -2.80413 q^{9} +(-0.886619 + 0.399962i) q^{10} +3.21615i q^{11} +(-3.61214 - 3.18888i) q^{12} -1.00000i q^{13} +(-0.581532 - 1.28912i) q^{14} +1.65697 q^{15} +(-0.495951 - 3.96913i) q^{16} +6.73233 q^{17} +(1.63069 + 3.61485i) q^{18} +4.13763i q^{19} +(1.03119 + 0.910364i) q^{20} +2.40918i q^{21} +(4.14598 - 1.87029i) q^{22} -7.04171 q^{23} +(-2.01027 + 6.51091i) q^{24} +4.52697 q^{25} +(-1.28912 + 0.581532i) q^{26} +0.471879i q^{27} +(-1.32364 + 1.49933i) q^{28} -4.45687i q^{29} +(-0.963579 - 2.13602i) q^{30} -8.29157 q^{31} +(-4.82826 + 2.94752i) q^{32} -7.74826 q^{33} +(-3.91507 - 8.67876i) q^{34} -0.687773i q^{35} +(3.71166 - 4.20431i) q^{36} +7.82265i q^{37} +(5.33388 - 2.40616i) q^{38} +2.40918 q^{39} +(0.573892 - 1.85874i) q^{40} -4.81888 q^{41} +(3.10571 - 1.40101i) q^{42} +12.7017i q^{43} +(-4.82205 - 4.25702i) q^{44} +1.92861i q^{45} +(4.09498 + 9.07758i) q^{46} +7.90753 q^{47} +(9.56235 - 1.19483i) q^{48} +1.00000 q^{49} +(-2.63258 - 5.83579i) q^{50} +16.2194i q^{51} +(1.49933 + 1.32364i) q^{52} +10.0261i q^{53} +(0.608307 - 0.274413i) q^{54} +2.21198 q^{55} +(2.70254 + 0.834421i) q^{56} -9.96828 q^{57} +(-5.74542 + 2.59181i) q^{58} +3.97386i q^{59} +(-2.19323 + 2.48433i) q^{60} -2.07834i q^{61} +(4.82182 + 10.6888i) q^{62} -2.80413 q^{63} +(6.60748 + 4.51012i) q^{64} -0.687773 q^{65} +(4.50586 + 9.98841i) q^{66} -11.4528i q^{67} +(-8.91119 + 10.0940i) q^{68} -16.9647i q^{69} +(-0.886619 + 0.399962i) q^{70} +11.8606 q^{71} +(-7.57829 - 2.33983i) q^{72} -16.8777 q^{73} +(10.0843 - 4.54912i) q^{74} +10.9063i q^{75} +(-6.20365 - 5.47673i) q^{76} +3.21615i q^{77} +(-1.40101 - 3.10571i) q^{78} +0.900413 q^{79} +(-2.72986 + 0.341102i) q^{80} -9.54924 q^{81} +(2.80233 + 6.21210i) q^{82} +2.06372i q^{83} +(-3.61214 - 3.18888i) q^{84} -4.63031i q^{85} +(16.3740 - 7.38644i) q^{86} +10.7374 q^{87} +(-2.68362 + 8.69177i) q^{88} +11.8949 q^{89} +(2.48620 - 1.12155i) q^{90} -1.00000i q^{91} +(9.32069 - 10.5578i) q^{92} -19.9759i q^{93} +(-4.59848 - 10.1937i) q^{94} +2.84575 q^{95} +(-7.10109 - 11.6321i) q^{96} -8.07789 q^{97} +(-0.581532 - 1.28912i) q^{98} -9.01850i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 38 q + 8 q^{4} + 14 q^{6} + 38 q^{7} - 6 q^{8} - 46 q^{9} - 4 q^{12} - 8 q^{15} - 4 q^{16} + 20 q^{17} + 4 q^{18} - 24 q^{20} + 10 q^{22} + 12 q^{23} + 10 q^{24} - 50 q^{25} + 8 q^{28} + 4 q^{30} + 16 q^{31}+ \cdots + 82 q^{96}+O(q^{100}) $ 38 * q + 8 * q^4 + 14 * q^6 + 38 * q^7 - 6 * q^8 - 46 * q^9 - 4 * q^12 - 8 * q^15 - 4 * q^16 + 20 * q^17 + 4 * q^18 - 24 * q^20 + 10 * q^22 + 12 * q^23 + 10 * q^24 - 50 * q^25 + 8 * q^28 + 4 * q^30 + 16 * q^31 + 10 * q^32 - 8 * q^33 - 4 * q^34 - 38 * q^36 - 28 * q^38 + 8 * q^39 + 4 * q^40 + 8 * q^41 + 14 * q^42 - 40 * q^44 - 16 * q^46 + 4 * q^48 + 38 * q^49 + 24 * q^50 - 4 * q^52 - 14 * q^54 - 6 * q^56 + 8 * q^57 - 24 * q^58 + 44 * q^60 - 12 * q^62 - 46 * q^63 + 32 * q^64 + 20 * q^65 - 76 * q^66 - 52 * q^68 + 42 * q^72 + 50 * q^74 - 28 * q^76 - 12 * q^79 - 16 * q^80 + 62 * q^81 - 4 * q^84 + 44 * q^86 - 56 * q^87 - 6 * q^88 + 48 * q^90 + 2 * q^92 - 48 * q^94 + 82 * q^96

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/728\mathbb{Z}\right)^\times$.

$n$	$183$	$365$	$521$	$561$
$\chi(n)$	$1$	$-1$	$1$	$1$

Coefficient data

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

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

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

$2$	−0.581532	−	1.28912i	−0.411205	−	0.911543i
$2$	−0.581532	−	1.28912i	−0.411205	−	0.911543i
$3$			2.40918i			1.39094i	0.718556	+	0.695469i	$0.244804\pi$
$3$			2.40918i			1.39094i	−0.718556	+	0.695469i	$0.755196\pi$
$4$	−1.32364	+	1.49933i	−0.661820	+	0.749663i
$5$		−	0.687773i		−	0.307581i	−0.988103	−	0.153791i	$-0.950852\pi$
$5$		−	0.687773i		−	0.307581i	0.988103	−	0.153791i	$-0.0491481\pi$
$6$	3.10571	−	1.40101i	1.26790	−	0.571962i
$7$	1.00000			0.377964
$7$	1.00000			0.377964
$8$	2.70254	+	0.834421i	0.955493	+	0.295012i
$9$	−2.80413			−0.934711
$10$	−0.886619	+	0.399962i	−0.280373	+	0.126479i
$11$			3.21615i			0.969704i	0.874596	+	0.484852i	$0.161127\pi$
$11$			3.21615i			0.969704i	−0.874596	+	0.484852i	$0.838873\pi$
$12$	−3.61214	−	3.18888i	−1.04273	−	0.920552i
$13$		−	1.00000i		−	0.277350i
$13$		−	1.00000i		−	0.277350i
$14$	−0.581532	−	1.28912i	−0.155421	−	0.344531i
$15$	1.65697			0.427827
$16$	−0.495951	−	3.96913i	−0.123988	−	0.992284i
$17$	6.73233			1.63283			0.816415	−	0.577466i	$-0.195958\pi$
$17$	6.73233			1.63283			0.816415	+	0.577466i	$0.195958\pi$
$18$	1.63069	+	3.61485i	0.384358	+	0.852029i
$19$			4.13763i			0.949237i	0.880192	+	0.474618i	$0.157414\pi$
$19$			4.13763i			0.949237i	−0.880192	+	0.474618i	$0.842586\pi$
$20$	1.03119	+	0.910364i	0.230582	+	0.203564i
$21$			2.40918i			0.525725i
$22$	4.14598	−	1.87029i	0.883927	−	0.398748i
$23$	−7.04171			−1.46830			−0.734149	−	0.678988i	$-0.762419\pi$
$23$	−7.04171			−1.46830			−0.734149	+	0.678988i	$0.762419\pi$
$24$	−2.01027	+	6.51091i	−0.410344	+	1.32903i
$25$	4.52697			0.905394
$26$	−1.28912	+	0.581532i	−0.252816	+	0.114048i
$27$			0.471879i			0.0908132i
$28$	−1.32364	+	1.49933i	−0.250145	+	0.283346i
$29$		−	4.45687i		−	0.827620i	−0.910363	−	0.413810i	$-0.864198\pi$
$29$		−	4.45687i		−	0.827620i	0.910363	−	0.413810i	$-0.135802\pi$
$30$	−0.963579	−	2.13602i	−0.175925	−	0.389982i
$31$	−8.29157			−1.48921			−0.744605	−	0.667505i	$-0.767362\pi$
$31$	−8.29157			−1.48921			−0.744605	+	0.667505i	$0.767362\pi$
$32$	−4.82826	+	2.94752i	−0.853525	+	0.521053i
$33$	−7.74826			−1.34880
$34$	−3.91507	−	8.67876i	−0.671428	−	1.48839i
$35$		−	0.687773i		−	0.116255i
$36$	3.71166	−	4.20431i	0.618611	−	0.700718i
$37$			7.82265i			1.28604i	0.765851	+	0.643018i	$0.222318\pi$
$37$			7.82265i			1.28604i	−0.765851	+	0.643018i	$0.777682\pi$
$38$	5.33388	−	2.40616i	0.865270	−	0.390331i
$39$	2.40918			0.385777
$40$	0.573892	−	1.85874i	0.0907402	−	0.293892i
$41$	−4.81888			−0.752583			−0.376291	−	0.926501i	$-0.622801\pi$
$41$	−4.81888			−0.752583			−0.376291	+	0.926501i	$0.622801\pi$
$42$	3.10571	−	1.40101i	0.479221	−	0.216181i
$43$			12.7017i			1.93699i	0.249032	+	0.968495i	$0.419887\pi$
$43$			12.7017i			1.93699i	−0.249032	+	0.968495i	$0.580113\pi$
$44$	−4.82205	−	4.25702i	−0.726951	−	0.641770i
$45$			1.92861i			0.287500i
$46$	4.09498	+	9.07758i	0.603772	+	1.33842i
$47$	7.90753			1.15343			0.576716	−	0.816945i	$-0.304334\pi$
$47$	7.90753			1.15343			0.576716	+	0.816945i	$0.304334\pi$
$48$	9.56235	−	1.19483i	1.38021	−	0.172459i
$49$	1.00000			0.142857
$50$	−2.63258	−	5.83579i	−0.372303	−	0.825305i
$51$			16.2194i			2.27117i
$52$	1.49933	+	1.32364i	0.207919	+	0.183556i
$53$			10.0261i			1.37719i	0.725147	+	0.688594i	$0.241772\pi$
$53$			10.0261i			1.37719i	−0.725147	+	0.688594i	$0.758228\pi$
$54$	0.608307	−	0.274413i	0.0827801	−	0.0373429i
$55$	2.21198			0.298263
$56$	2.70254	+	0.834421i	0.361143	+	0.111504i
$57$	−9.96828			−1.32033
$58$	−5.74542	+	2.59181i	−0.754411	+	0.340322i
$59$			3.97386i			0.517352i	0.965964	+	0.258676i	$0.0832862\pi$
$59$			3.97386i			0.517352i	−0.965964	+	0.258676i	$0.916714\pi$
$60$	−2.19323	+	2.48433i	−0.283144	+	0.320726i
$61$		−	2.07834i		−	0.266104i	−0.991109	−	0.133052i	$-0.957522\pi$
$61$		−	2.07834i		−	0.266104i	0.991109	−	0.133052i	$-0.0424777\pi$
$62$	4.82182	+	10.6888i	0.612371	+	1.35748i
$63$	−2.80413			−0.353287
$64$	6.60748	+	4.51012i	0.825936	+	0.563765i
$65$	−0.687773			−0.0853077
$66$	4.50586	+	9.98841i	0.554633	+	1.22949i
$67$		−	11.4528i		−	1.39918i	−0.714543	−	0.699591i	$-0.753365\pi$
$67$		−	11.4528i		−	1.39918i	0.714543	−	0.699591i	$-0.246635\pi$
$68$	−8.91119	+	10.0940i	−1.08064	+	1.22407i
$69$		−	16.9647i		−	2.04231i
$70$	−0.886619	+	0.399962i	−0.105971	+	0.0478046i
$71$	11.8606			1.40759			0.703797	−	0.710401i	$-0.251486\pi$
$71$	11.8606			1.40759			0.703797	+	0.710401i	$0.251486\pi$
$72$	−7.57829	−	2.33983i	−0.893110	−	0.275751i
$73$	−16.8777			−1.97538			−0.987691	−	0.156420i	$-0.950005\pi$
$73$	−16.8777			−1.97538			−0.987691	+	0.156420i	$0.950005\pi$
$74$	10.0843	−	4.54912i	1.17228	−	0.528825i
$75$			10.9063i			1.25935i
$76$	−6.20365	−	5.47673i	−0.711607	−	0.628224i
$77$			3.21615i			0.366514i
$78$	−1.40101	−	3.10571i	−0.158634	−	0.351652i
$79$	0.900413			0.101304			0.0506522	−	0.998716i	$-0.483870\pi$
$79$	0.900413			0.101304			0.0506522	+	0.998716i	$0.483870\pi$
$80$	−2.72986	+	0.341102i	−0.305208	+	0.0381363i
$81$	−9.54924			−1.06103
$82$	2.80233	+	6.21210i	0.309466	+	0.686011i
$83$			2.06372i			0.226522i	0.993565	+	0.113261i	$0.0361297\pi$
$83$			2.06372i			0.226522i	−0.993565	+	0.113261i	$0.963870\pi$
$84$	−3.61214	−	3.18888i	−0.394117	−	0.347936i
$85$		−	4.63031i		−	0.502228i
$86$	16.3740	−	7.38644i	1.76565	−	0.796501i
$87$	10.7374			1.15117
$88$	−2.68362	+	8.69177i	−0.286075	+	0.926546i
$89$	11.8949			1.26085			0.630427	−	0.776249i	$-0.282880\pi$
$89$	11.8949			1.26085			0.630427	+	0.776249i	$0.282880\pi$
$90$	2.48620	−	1.12155i	0.262068	−	0.118221i
$91$		−	1.00000i		−	0.104828i
$92$	9.32069	−	10.5578i	0.971749	−	1.10073i
$93$		−	19.9759i		−	2.07140i
$94$	−4.59848	−	10.1937i	−0.474297	−	1.05140i
$95$	2.84575			0.291968
$96$	−7.10109	−	11.6321i	−0.724752	−	1.18720i
$97$	−8.07789			−0.820185			−0.410093	−	0.912044i	$-0.634504\pi$
$97$	−8.07789			−0.820185			−0.410093	+	0.912044i	$0.634504\pi$
$98$	−0.581532	−	1.28912i	−0.0587436	−	0.130220i
$99$		−	9.01850i		−	0.906393i
$100$	−5.99208	+	6.78740i	−0.599208	+	0.678740i
$101$			7.62035i			0.758254i	0.925345	+	0.379127i	$0.123776\pi$
$101$			7.62035i			0.758254i	−0.925345	+	0.379127i	$0.876224\pi$
$102$	20.9087	−	9.43209i	2.07027	−	0.933916i
$103$	−5.04500			−0.497098			−0.248549	−	0.968619i	$-0.579954\pi$
$103$	−5.04500			−0.497098			−0.248549	+	0.968619i	$0.579954\pi$
$104$	0.834421	−	2.70254i	0.0818217	−	0.265006i
$105$	1.65697			0.161703
$106$	12.9248	−	5.83049i	1.25537	−	0.566307i
$107$		−	16.1219i		−	1.55856i	−0.626675	−	0.779281i	$-0.715585\pi$
$107$		−	16.1219i		−	1.55856i	0.626675	−	0.779281i	$-0.284415\pi$
$108$	−0.707500	−	0.624599i	−0.0680793	−	0.0601020i
$109$		−	11.1382i		−	1.06685i	−0.845848	−	0.533424i	$-0.820905\pi$
$109$		−	11.1382i		−	1.06685i	0.845848	−	0.533424i	$-0.179095\pi$
$110$	−1.28634	−	2.85149i	−0.122647	−	0.271879i
$111$	−18.8462			−1.78880
$112$	−0.495951	−	3.96913i	−0.0468630	−	0.375048i
$113$	19.2899			1.81464			0.907320	−	0.420442i	$-0.138125\pi$
$113$	19.2899			1.81464			0.907320	+	0.420442i	$0.138125\pi$
$114$	5.79687	+	12.8503i	0.542927	+	1.20354i
$115$			4.84309i			0.451621i
$116$	6.68230	+	5.89930i	0.620436	+	0.547736i
$117$			2.80413i			0.259242i
$118$	5.12276	−	2.31093i	0.471589	−	0.212738i
$119$	6.73233			0.617152
$120$	4.47802	+	1.38261i	0.408786	+	0.126214i
$121$	0.656411			0.0596738
$122$	−2.67922	+	1.20862i	−0.242565	+	0.109423i
$123$		−	11.6095i		−	1.04680i
$124$	10.9751	−	12.4318i	0.985590	−	1.11641i
$125$		−	6.55239i		−	0.586063i
$126$	1.63069	+	3.61485i	0.145274	+	0.322037i
$127$	12.8222			1.13778			0.568892	−	0.822412i	$-0.307372\pi$
$127$	12.8222			1.13778			0.568892	+	0.822412i	$0.307372\pi$
$128$	1.97160	−	11.1406i	0.174266	−	0.984699i
$129$	−30.6006			−2.69424
$130$	0.399962	+	0.886619i	0.0350790	+	0.0777616i
$131$			3.98575i			0.348237i	0.984725	+	0.174118i	$0.0557075\pi$
$131$			3.98575i			0.348237i	−0.984725	+	0.174118i	$0.944292\pi$
$132$	10.2559	−	11.6172i	0.892663	−	1.01114i
$133$			4.13763i			0.358778i
$134$	−14.7640	+	6.66017i	−1.27541	+	0.575351i
$135$	0.324546			0.0279324
$136$	18.1944	+	5.61760i	1.56016	+	0.481705i
$137$	5.92401			0.506122			0.253061	−	0.967450i	$-0.418563\pi$
$137$	5.92401			0.506122			0.253061	+	0.967450i	$0.418563\pi$
$138$	−21.8695	+	9.86553i	−1.86166	+	0.839810i
$139$		−	3.12806i		−	0.265318i	−0.991162	−	0.132659i	$-0.957648\pi$
$139$		−	3.12806i		−	0.265318i	0.991162	−	0.132659i	$-0.0423516\pi$
$140$	1.03119	+	0.910364i	0.0871519	+	0.0769398i
$141$			19.0506i			1.60435i
$142$	−6.89732	−	15.2897i	−0.578811	−	1.28308i
$143$	3.21615			0.268948
$144$	1.39071	+	11.1300i	0.115893	+	0.927498i
$145$	−3.06531			−0.254560
$146$	9.81490	+	21.7573i	0.812287	+	1.80064i
$147$			2.40918i			0.198706i
$148$	−11.7287	−	10.3544i	−0.964093	−	0.851125i
$149$			2.20901i			0.180969i	0.995898	+	0.0904846i	$0.0288416\pi$
$149$			2.20901i			0.180969i	−0.995898	+	0.0904846i	$0.971158\pi$
$150$	14.0594	−	6.34235i	1.14795	−	0.517850i
$151$	−4.94770			−0.402638			−0.201319	−	0.979526i	$-0.564523\pi$
$151$	−4.94770			−0.402638			−0.201319	+	0.979526i	$0.564523\pi$
$152$	−3.45252	+	11.1821i	−0.280037	+	0.906990i
$153$	−18.8783			−1.52622
$154$	4.14598	−	1.87029i	0.334093	−	0.150712i
$155$			5.70272i			0.458053i
$156$	−3.18888	+	3.61214i	−0.255315	+	0.289203i
$157$		−	20.8723i		−	1.66579i	−0.553430	−	0.832895i	$-0.686681\pi$
$157$		−	20.8723i		−	1.66579i	0.553430	−	0.832895i	$-0.313319\pi$
$158$	−0.523619	−	1.16074i	−0.0416569	−	0.0923432i
$159$	−24.1546			−1.91558
$160$	2.02722	+	3.32075i	0.160266	+	0.262528i
$161$	−7.04171			−0.554964
$162$	5.55319	+	12.3101i	0.436300	+	0.967171i
$163$		−	11.1250i		−	0.871374i	−0.900098	−	0.435687i	$-0.856505\pi$
$163$		−	11.1250i		−	0.871374i	0.900098	−	0.435687i	$-0.143495\pi$
$164$	6.37847	−	7.22507i	0.498075	−	0.564183i
$165$			5.32904i			0.414865i
$166$	2.66037	−	1.20012i	0.206485	−	0.0931472i
$167$	−5.73008			−0.443407			−0.221703	−	0.975114i	$-0.571162\pi$
$167$	−5.73008			−0.443407			−0.221703	+	0.975114i	$0.571162\pi$
$168$	−2.01027	+	6.51091i	−0.155095	+	0.502327i
$169$	−1.00000			−0.0769231
$170$	−5.96901	+	2.69268i	−0.457802	+	0.206519i
$171$		−	11.6025i		−	0.887262i
$172$	−19.0440	−	16.8125i	−1.45209	−	1.28194i
$173$		−	8.86006i		−	0.673618i	−0.941573	−	0.336809i	$-0.890652\pi$
$173$		−	8.86006i		−	0.673618i	0.941573	−	0.336809i	$-0.109348\pi$
$174$	−6.24414	−	13.8417i	−0.473367	−	1.04934i
$175$	4.52697			0.342207
$176$	12.7653	−	1.59505i	0.962222	−	0.120231i
$177$	−9.57373			−0.719605
$178$	−6.91725	−	15.3339i	−0.518470	−	1.14932i
$179$		−	5.50445i		−	0.411422i	−0.978613	−	0.205711i	$-0.934049\pi$
$179$		−	5.50445i		−	0.411422i	0.978613	−	0.205711i	$-0.0659507\pi$
$180$	−2.89161	−	2.55278i	−0.215528	−	0.190273i
$181$			14.5090i			1.07845i	0.842163	+	0.539223i	$0.181282\pi$
$181$			14.5090i			1.07845i	−0.842163	+	0.539223i	$0.818718\pi$
$182$	−1.28912	+	0.581532i	−0.0955556	+	0.0431060i
$183$	5.00708			0.370134
$184$	−19.0305	−	5.87575i	−1.40295	−	0.433166i
$185$	5.38021			0.395561
$186$	−25.7512	+	11.6166i	−1.88817	+	0.851771i
$187$			21.6522i			1.58336i
$188$	−10.4667	+	11.8560i	−0.763364	+	0.864684i
$189$			0.471879i			0.0343242i
$190$	−1.65489	−	3.66850i	−0.120059	−	0.266141i
$191$	17.4734			1.26433			0.632165	−	0.774834i	$-0.282166\pi$
$191$	17.4734			1.26433			0.632165	+	0.774834i	$0.282166\pi$
$192$	−10.8657	+	15.9186i	−0.784162	+	1.14883i
$193$	5.20134			0.374401			0.187200	−	0.982322i	$-0.440059\pi$
$193$	5.20134			0.374401			0.187200	+	0.982322i	$0.440059\pi$
$194$	4.69755	+	10.4133i	0.337265	+	0.747634i
$195$		−	1.65697i		−	0.118658i
$196$	−1.32364	+	1.49933i	−0.0945458	+	0.107095i
$197$		−	5.95897i		−	0.424559i	−0.977209	−	0.212279i	$-0.931911\pi$
$197$		−	5.95897i		−	0.424559i	0.977209	−	0.212279i	$-0.0680887\pi$
$198$	−11.6259	+	5.24455i	−0.826216	+	0.372714i
$199$	12.1075			0.858276			0.429138	−	0.903239i	$-0.358817\pi$
$199$	12.1075			0.858276			0.429138	+	0.903239i	$0.358817\pi$
$200$	12.2343	+	3.77740i	0.865098	+	0.267102i
$201$	27.5918			1.94618
$202$	9.82352	−	4.43148i	0.691180	−	0.311798i
$203$		−	4.45687i		−	0.312811i
$204$	−24.3181	−	21.4686i	−1.70261	−	1.50310i
$205$			3.31429i			0.231480i
$206$	2.93383	+	6.50359i	0.204409	+	0.453126i
$207$	19.7459			1.37243
$208$	−3.96913	+	0.495951i	−0.275210	+	0.0343880i
$209$	−13.3072			−0.920479
$210$	−0.963579	−	2.13602i	−0.0664933	−	0.147399i
$211$			9.71594i			0.668873i	0.942418	+	0.334437i	$0.108546\pi$
$211$			9.71594i			0.668873i	−0.942418	+	0.334437i	$0.891454\pi$
$212$	−15.0324	−	13.2709i	−1.03243	−	0.911451i
$213$			28.5743i			1.95788i
$214$	−20.7830	+	9.37540i	−1.42070	+	0.640889i
$215$	8.73588			0.595782
$216$	−0.393746	+	1.27527i	−0.0267910	+	0.0867714i
$217$	−8.29157			−0.562869
$218$	−14.3585	+	6.47723i	−0.972478	+	0.438694i
$219$		−	40.6613i		−	2.74763i
$220$	−2.92786	+	3.31647i	−0.197396	+	0.223596i
$221$		−	6.73233i		−	0.452866i
$222$	10.9596	+	24.2949i	0.735563	+	1.63057i
$223$	−19.4803			−1.30450			−0.652249	−	0.758005i	$-0.726174\pi$
$223$	−19.4803			−1.30450			−0.652249	+	0.758005i	$0.726174\pi$
$224$	−4.82826	+	2.94752i	−0.322602	+	0.196939i
$225$	−12.6942			−0.846281
$226$	−11.2177	−	24.8669i	−0.746189	−	1.65412i
$227$			5.75489i			0.381966i	0.981593	+	0.190983i	$0.0611675\pi$
$227$			5.75489i			0.381966i	−0.981593	+	0.190983i	$0.938833\pi$
$228$	13.1944	−	14.9457i	0.873822	−	0.989802i
$229$			4.51943i			0.298652i	0.988788	+	0.149326i	$0.0477104\pi$
$229$			4.51943i			0.298652i	−0.988788	+	0.149326i	$0.952290\pi$
$230$	6.24331	−	2.81642i	0.411672	−	0.185709i
$231$	−7.74826			−0.509798
$232$	3.71891	−	12.0449i	0.244158	−	0.790786i
$233$	2.03939			0.133605			0.0668025	−	0.997766i	$-0.478720\pi$
$233$	2.03939			0.133605			0.0668025	+	0.997766i	$0.478720\pi$
$234$	3.61485	−	1.63069i	0.236310	−	0.106602i
$235$		−	5.43858i		−	0.354774i
$236$	−5.95810	−	5.25996i	−0.387840	−	0.342394i
$237$			2.16925i			0.140908i
$238$	−3.91507	−	8.67876i	−0.253776	−	0.562560i
$239$	8.01616			0.518522			0.259261	−	0.965807i	$-0.416521\pi$
$239$	8.01616			0.518522			0.259261	+	0.965807i	$0.416521\pi$
$240$	−0.821774	−	6.57672i	−0.0530453	−	0.424526i
$241$	3.51113			0.226172			0.113086	−	0.993585i	$-0.463927\pi$
$241$	3.51113			0.226172			0.113086	+	0.993585i	$0.463927\pi$
$242$	−0.381724	−	0.846190i	−0.0245382	−	0.0543952i
$243$		−	21.5902i		−	1.38501i
$244$	3.11610	+	2.75097i	0.199488	+	0.176113i
$245$		−	0.687773i		−	0.0439402i
$246$	−14.9660	+	6.75132i	−0.954200	+	0.430448i
$247$	4.13763			0.263271
$248$	−22.4083	−	6.91866i	−1.42293	−	0.439335i
$249$	−4.97186			−0.315079
$250$	−8.44679	+	3.81042i	−0.534222	+	0.240992i
$251$		−	12.4594i		−	0.786430i	−0.919447	−	0.393215i	$-0.871363\pi$
$251$		−	12.4594i		−	0.786430i	0.919447	−	0.393215i	$-0.128637\pi$
$252$	3.71166	−	4.20431i	0.233813	−	0.264846i
$253$		−	22.6472i		−	1.42381i
$254$	−7.45651	−	16.5293i	−0.467863	−	1.03714i
$255$	11.1552			0.698568
$256$	−15.5081	+	3.93699i	−0.969254	+	0.246062i
$257$	1.98847			0.124037			0.0620186	−	0.998075i	$-0.480246\pi$
$257$	1.98847			0.124037			0.0620186	+	0.998075i	$0.480246\pi$
$258$	17.7952	+	39.4478i	1.10788	+	2.45591i
$259$			7.82265i			0.486076i
$260$	0.910364	−	1.03119i	0.0564584	−	0.0639520i
$261$			12.4977i			0.773586i
$262$	5.13809	−	2.31784i	0.317433	−	0.143197i
$263$	25.0187			1.54272			0.771360	−	0.636399i	$-0.219577\pi$
$263$	25.0187			1.54272			0.771360	+	0.636399i	$0.219577\pi$
$264$	−20.9400	−	6.46531i	−1.28877	−	0.397912i
$265$	6.89566			0.423597
$266$	5.33388	−	2.40616i	0.327041	−	0.147531i
$267$			28.6569i			1.75377i
$268$	17.1715	+	15.1594i	1.04891	+	0.926008i
$269$			16.1113i			0.982326i	0.871068	+	0.491163i	$0.163428\pi$
$269$			16.1113i			0.982326i	−0.871068	+	0.491163i	$0.836572\pi$
$270$	−0.188734	−	0.418377i	−0.0114860	−	0.0254616i
$271$	−16.8822			−1.02552			−0.512759	−	0.858532i	$-0.671377\pi$
$271$	−16.8822			−1.02552			−0.512759	+	0.858532i	$0.671377\pi$
$272$	−3.33891	−	26.7215i	−0.202451	−	1.62023i
$273$	2.40918			0.145810
$274$	−3.44500	−	7.63673i	−0.208120	−	0.461352i
$275$			14.5594i			0.877964i
$276$	25.4356	+	22.4552i	1.53105	+	1.35164i
$277$			6.69730i			0.402402i	0.979550	+	0.201201i	$0.0644844\pi$
$277$			6.69730i			0.402402i	−0.979550	+	0.201201i	$0.935516\pi$
$278$	−4.03243	+	1.81907i	−0.241849	+	0.109100i
$279$	23.2507			1.39198
$280$	0.573892	−	1.85874i	0.0342966	−	0.111081i
$281$	−22.9392			−1.36844			−0.684218	−	0.729278i	$-0.739856\pi$
$281$	−22.9392			−1.36844			−0.684218	+	0.729278i	$0.739856\pi$
$282$	24.5585	−	11.0786i	1.46244	−	0.659718i
$283$			1.57480i			0.0936120i	0.998904	+	0.0468060i	$0.0149043\pi$
$283$			1.57480i			0.0936120i	−0.998904	+	0.0468060i	$0.985096\pi$
$284$	−15.6992	+	17.7829i	−0.931575	+	1.05522i
$285$			6.85591i			0.406109i
$286$	−1.87029	−	4.14598i	−0.110593	−	0.245157i
$287$	−4.81888			−0.284450
$288$	13.5391	−	8.26523i	0.797799	−	0.487033i
$289$	28.3243			1.66613
$290$	1.78258	+	3.95155i	0.104677	+	0.232043i
$291$		−	19.4611i		−	1.14083i
$292$	22.3400	−	25.3051i	1.30735	−	1.48087i
$293$		−	27.8609i		−	1.62765i	−0.581111	−	0.813825i	$-0.697382\pi$
$293$		−	27.8609i		−	1.62765i	0.581111	−	0.813825i	$-0.302618\pi$
$294$	3.10571	−	1.40101i	0.181129	−	0.0817088i
$295$	2.73311			0.159128
$296$	−6.52738	+	21.1411i	−0.379396	+	1.22880i
$297$	−1.51763			−0.0880619
$298$	2.84767	−	1.28461i	0.164961	−	0.0744155i
$299$			7.04171i			0.407233i
$300$	−16.3520	−	14.4360i	−0.944085	−	0.833462i
$301$			12.7017i			0.732114i
$302$	2.87725	+	6.37816i	0.165567	+	0.367022i
$303$	−18.3588			−1.05468
$304$	16.4228	−	2.05206i	0.941912	−	0.117694i
$305$	−1.42942			−0.0818485
$306$	10.9784	+	24.3364i	0.627591	+	1.39122i
$307$		−	21.6337i		−	1.23470i	−0.786689	−	0.617349i	$-0.788207\pi$
$307$		−	21.6337i		−	1.23470i	0.786689	−	0.617349i	$-0.211793\pi$
$308$	−4.82205	−	4.25702i	−0.274762	−	0.242566i
$309$		−	12.1543i		−	0.691433i
$310$	7.35146	−	3.31631i	0.417535	−	0.188354i
$311$	12.6974			0.720006			0.360003	−	0.932951i	$-0.382776\pi$
$311$	12.6974			0.720006			0.360003	+	0.932951i	$0.382776\pi$
$312$	6.51091	+	2.01027i	0.368607	+	0.113809i
$313$	23.8266			1.34676			0.673380	−	0.739297i	$-0.264842\pi$
$313$	23.8266			1.34676			0.673380	+	0.739297i	$0.264842\pi$
$314$	−26.9068	+	12.1379i	−1.51844	+	0.684982i
$315$			1.92861i			0.108665i
$316$	−1.19182	+	1.35001i	−0.0670453	+	0.0759441i
$317$			0.958688i			0.0538453i	0.999638	+	0.0269226i	$0.00857078\pi$
$317$			0.958688i			0.0538453i	−0.999638	+	0.0269226i	$0.991429\pi$
$318$	14.0467	+	31.1381i	0.787699	+	1.74614i
$319$	14.3339			0.802547
$320$	3.10193	−	4.54445i	0.173403	−	0.254042i
$321$	38.8405			2.16786
$322$	4.09498	+	9.07758i	0.228204	+	0.505874i
$323$			27.8559i			1.54994i
$324$	12.6398	−	14.3174i	0.702209	−	0.795412i
$325$		−	4.52697i		−	0.251111i
$326$	−14.3414	+	6.46952i	−0.794295	+	0.358314i
$327$	26.8339			1.48392
$328$	−13.0232	−	4.02097i	−0.719088	−	0.222021i
$329$	7.90753			0.435956
$330$	6.86975	−	3.09901i	0.378168	−	0.170595i
$331$		−	6.17550i		−	0.339436i	−0.985493	−	0.169718i	$-0.945714\pi$
$331$		−	6.17550i		−	0.339436i	0.985493	−	0.169718i	$-0.0542857\pi$
$332$	−3.09418	−	2.73162i	−0.169815	−	0.149917i
$333$		−	21.9358i		−	1.20207i
$334$	3.33223	+	7.38674i	0.182331	+	0.404184i
$335$	−7.87693			−0.430362
$336$	9.56235	−	1.19483i	0.521669	−	0.0651835i
$337$	−6.59480			−0.359242			−0.179621	−	0.983736i	$-0.557487\pi$
$337$	−6.59480			−0.359242			−0.179621	+	0.983736i	$0.557487\pi$
$338$	0.581532	+	1.28912i	0.0316312	+	0.0701187i
$339$			46.4727i			2.52405i
$340$	6.94234	+	6.12887i	0.376501	+	0.332385i
$341$		−	26.6669i		−	1.44409i
$342$	−14.9569	+	6.74720i	−0.808777	+	0.364847i
$343$	1.00000			0.0539949
$344$	−10.5986	+	34.3269i	−0.571436	+	1.85078i
$345$	−11.6679			−0.628177
$346$	−11.4216	+	5.15241i	−0.614032	+	0.276995i
$347$		−	10.6595i		−	0.572233i	−0.958195	−	0.286117i	$-0.907636\pi$
$347$		−	10.6595i		−	0.572233i	0.958195	−	0.286117i	$-0.0923645\pi$
$348$	−14.2124	+	16.0988i	−0.761867	+	0.862988i
$349$			20.7465i			1.11053i	0.831673	+	0.555266i	$0.187384\pi$
$349$			20.7465i			1.11053i	−0.831673	+	0.555266i	$0.812616\pi$
$350$	−2.63258	−	5.83579i	−0.140717	−	0.311936i
$351$	0.471879			0.0251871
$352$	−9.47965	−	15.5284i	−0.505267	−	0.827666i
$353$	5.86613			0.312223			0.156111	−	0.987739i	$-0.450104\pi$
$353$	5.86613			0.312223			0.156111	+	0.987739i	$0.450104\pi$
$354$	5.56743	+	12.3416i	0.295906	+	0.655951i
$355$		−	8.15740i		−	0.432950i
$356$	−15.7445	+	17.8343i	−0.834459	+	0.945215i
$357$			16.2194i			0.858420i
$358$	−7.09587	+	3.20101i	−0.375029	+	0.169179i
$359$	32.1557			1.69711			0.848556	−	0.529105i	$-0.177472\pi$
$359$	32.1557			1.69711			0.848556	+	0.529105i	$0.177472\pi$
$360$	−1.60927	+	5.21214i	−0.0848159	+	0.274704i
$361$	1.88004			0.0989492
$362$	18.7038	−	8.43745i	0.983049	−	0.443462i
$363$			1.58141i			0.0830025i
$364$	1.49933	+	1.32364i	0.0785860	+	0.0693776i
$365$			11.6080i			0.607590i
$366$	−2.91178	−	6.45470i	−0.152201	−	0.337393i
$367$	−0.00587334			−0.000306586			−0.000153293	−	1.00000i	$-0.500049\pi$
$367$	−0.00587334			−0.000306586			−0.000153293		1.00000i	$0.500049\pi$
$368$	3.49234	+	27.9495i	0.182051	+	1.45697i
$369$	13.5128			0.703447
$370$	−3.12876	−	6.93571i	−0.162657	−	0.360570i
$371$			10.0261i			0.520528i
$372$	29.9503	+	26.4409i	1.55285	+	1.37090i
$373$		−	22.2332i		−	1.15119i	−0.817734	−	0.575596i	$-0.804770\pi$
$373$		−	22.2332i		−	1.15119i	0.817734	−	0.575596i	$-0.195230\pi$
$374$	27.9121	−	12.5914i	1.44330	−	0.651087i
$375$	15.7859			0.815178
$376$	21.3704	+	6.59820i	1.10210	+	0.340276i
$377$	−4.45687			−0.229541
$378$	0.608307	−	0.274413i	0.0312879	−	0.0141143i
$379$		−	4.20029i		−	0.215754i	−0.994164	−	0.107877i	$-0.965595\pi$
$379$		−	4.20029i		−	0.215754i	0.994164	−	0.107877i	$-0.0344053\pi$
$380$	−3.76675	+	4.26670i	−0.193230	+	0.218877i
$381$			30.8909i			1.58259i
$382$	−10.1613	−	22.5252i	−0.519899	−	1.15249i
$383$	3.25784			0.166468			0.0832339	−	0.996530i	$-0.473475\pi$
$383$	3.25784			0.166468			0.0832339	+	0.996530i	$0.473475\pi$
$384$	26.8397	+	4.74993i	1.36966	+	0.242394i
$385$	2.21198			0.112733
$386$	−3.02475	−	6.70514i	−0.153956	−	0.341282i
$387$		−	35.6172i		−	1.81053i
$388$	10.6922	−	12.1114i	0.542815	−	0.614862i
$389$			20.0798i			1.01809i	0.860741	+	0.509043i	$0.170001\pi$
$389$			20.0798i			1.01809i	−0.860741	+	0.509043i	$0.829999\pi$
$390$	−2.13602	+	0.963579i	−0.108162	+	0.0487927i
$391$	−47.4071			−2.39748
$392$	2.70254	+	0.834421i	0.136499	+	0.0421446i
$393$	−9.60238			−0.484376
$394$	−7.68180	+	3.46533i	−0.387004	+	0.174581i
$395$		−	0.619279i		−	0.0311593i
$396$	13.5217	+	11.9372i	0.679489	+	0.599869i
$397$		−	23.0645i		−	1.15758i	−0.815478	−	0.578788i	$-0.803526\pi$
$397$		−	23.0645i		−	1.15758i	0.815478	−	0.578788i	$-0.196474\pi$
$398$	−7.04089	−	15.6079i	−0.352928	−	0.782355i
$399$	−9.96828			−0.499038
$400$	−2.24515	−	17.9682i	−0.112258	−	0.898408i
$401$	6.25670			0.312445			0.156222	−	0.987722i	$-0.450068\pi$
$401$	6.25670			0.312445			0.156222	+	0.987722i	$0.450068\pi$
$402$	−16.0455	−	35.5691i	−0.800279	−	1.77402i
$403$			8.29157i			0.413033i
$404$	−11.4254	−	10.0866i	−0.568434	−	0.501828i
$405$			6.56770i			0.326352i
$406$	−5.74542	+	2.59181i	−0.285141	+	0.128630i
$407$	−25.1588			−1.24707
$408$	−13.5338	+	43.8336i	−0.670022	+	2.17009i
$409$	20.2811			1.00284			0.501418	−	0.865205i	$-0.332812\pi$
$409$	20.2811			1.00284			0.501418	+	0.865205i	$0.332812\pi$
$410$	4.27251	−	1.92737i	0.211004	−	0.0951860i
$411$			14.2720i			0.703985i
$412$	6.67776	−	7.56409i	0.328990	−	0.372656i
$413$			3.97386i			0.195541i
$414$	−11.4829	−	25.4547i	−0.564352	−	1.25103i
$415$	1.41937			0.0696740
$416$	2.94752	+	4.82826i	0.144514	+	0.236725i
$417$	7.53604			0.369042
$418$	7.73857	+	17.1545i	0.378506	+	0.839056i
$419$			31.6138i			1.54444i	0.635357	+	0.772219i	$0.280853\pi$
$419$			31.6138i			1.54444i	−0.635357	+	0.772219i	$0.719147\pi$
$420$	−2.19323	+	2.48433i	−0.107019	+	0.121223i
$421$			1.28516i			0.0626348i	0.999509	+	0.0313174i	$0.00997027\pi$
$421$			1.28516i			0.0626348i	−0.999509	+	0.0313174i	$0.990030\pi$
$422$	12.5250	−	5.65013i	0.609706	−	0.275044i
$423$	−22.1738			−1.07812
$424$	−8.36597	+	27.0959i	−0.406287	+	1.31589i
$425$	30.4771			1.47835
$426$	36.8356	−	16.6169i	1.78469	−	0.805090i
$427$		−	2.07834i		−	0.100578i
$428$	24.1719	+	21.3396i	1.16840	+	1.03149i
$429$			7.74826i			0.374090i
$430$	−5.08019	−	11.2616i	−0.244989	−	0.543081i
$431$	13.9878			0.673770			0.336885	−	0.941546i	$-0.390627\pi$
$431$	13.9878			0.673770			0.336885	+	0.941546i	$0.390627\pi$
$432$	1.87295	−	0.234029i	0.0901125	−	0.0112597i
$433$	−12.4382			−0.597740			−0.298870	−	0.954294i	$-0.596610\pi$
$433$	−12.4382			−0.597740			−0.298870	+	0.954294i	$0.596610\pi$
$434$	4.82182	+	10.6888i	0.231455	+	0.513079i
$435$		−	7.38488i		−	0.354078i
$436$	16.6998	+	14.7430i	0.799776	+	0.706062i
$437$		−	29.1360i		−	1.39376i
$438$	−52.4171	+	23.6458i	−2.50459	+	1.12984i
$439$	−29.1671			−1.39207			−0.696034	−	0.718008i	$-0.745054\pi$
$439$	−29.1671			−1.39207			−0.696034	+	0.718008i	$0.745054\pi$
$440$	5.97796	+	1.84572i	0.284988	+	0.0879912i
$441$	−2.80413			−0.133530
$442$	−8.67876	+	3.91507i	−0.412806	+	0.186221i
$443$		−	7.38931i		−	0.351077i	−0.984473	−	0.175538i	$-0.943833\pi$
$443$		−	7.38931i		−	0.351077i	0.984473	−	0.175538i	$-0.0561666\pi$
$444$	24.9455	−	28.2565i	1.18386	−	1.34099i
$445$		−	8.18097i		−	0.387815i
$446$	11.3284	+	25.1124i	0.536416	+	1.18910i
$447$	−5.32190			−0.251717
$448$	6.60748	+	4.51012i	0.312174	+	0.213083i
$449$	−18.4074			−0.868700			−0.434350	−	0.900744i	$-0.643022\pi$
$449$	−18.4074			−0.868700			−0.434350	+	0.900744i	$0.643022\pi$
$450$	7.38210	+	16.3643i	0.347995	+	0.771422i
$451$		−	15.4982i		−	0.729783i
$452$	−25.5329	+	28.9218i	−1.20097	+	1.36037i
$453$		−	11.9199i		−	0.560045i
$454$	7.41872	−	3.34665i	0.348178	−	0.157066i
$455$	−0.687773			−0.0322433
$456$	−26.9397	−	8.31774i	−1.26157	−	0.389514i
$457$	21.1297			0.988405			0.494202	−	0.869347i	$-0.335460\pi$
$457$	21.1297			0.988405			0.494202	+	0.869347i	$0.335460\pi$
$458$	5.82607	−	2.62819i	0.272234	−	0.122807i
$459$			3.17685i			0.148283i
$460$	−7.26137	−	6.41052i	−0.338563	−	0.298892i
$461$		−	10.0573i		−	0.468415i	−0.972187	−	0.234207i	$-0.924751\pi$
$461$		−	10.0573i		−	0.468415i	0.972187	−	0.234207i	$-0.0752494\pi$
$462$	4.50586	+	9.98841i	0.209632	+	0.464703i
$463$	−35.0391			−1.62840			−0.814202	−	0.580582i	$-0.802825\pi$
$463$	−35.0391			−1.62840			−0.814202	+	0.580582i	$0.802825\pi$
$464$	−17.6899	+	2.21039i	−0.821234	+	0.102615i
$465$	−13.7389			−0.637124
$466$	−1.18597	−	2.62901i	−0.0549391	−	0.121787i
$467$			22.2151i			1.02799i	0.857792	+	0.513996i	$0.171835\pi$
$467$			22.2151i			1.02799i	−0.857792	+	0.513996i	$0.828165\pi$
$468$	−4.20431	−	3.71166i	−0.194344	−	0.171572i
$469$		−	11.4528i		−	0.528841i
$470$	−7.01096	+	3.16271i	−0.323392	+	0.145885i
$471$	50.2851			2.31701
$472$	−3.31587	+	10.7395i	−0.152625	+	0.494327i
$473$	−40.8505			−1.87831
$474$	2.79642	−	1.26149i	0.128444	−	0.0579422i
$475$			18.7309i			0.859433i
$476$	−8.91119	+	10.0940i	−0.408444	+	0.462656i
$477$		−	28.1145i		−	1.28727i
$478$	−4.66165	−	10.3338i	−0.213219	−	0.472655i
$479$	−26.9888			−1.23315			−0.616574	−	0.787297i	$-0.711480\pi$
$479$	−26.9888			−1.23315			−0.616574	+	0.787297i	$0.711480\pi$
$480$	−8.00027	+	4.88394i	−0.365161	+	0.222920i
$481$	7.82265			0.356682
$482$	−2.04183	−	4.52625i	−0.0930029	−	0.206165i
$483$		−	16.9647i		−	0.771922i
$484$	−0.868853	+	0.984174i	−0.0394933	+	0.0447352i
$485$			5.55575i			0.252274i
$486$	−27.8322	+	12.5554i	−1.26250	+	0.569523i
$487$	4.49681			0.203770			0.101885	−	0.994796i	$-0.467513\pi$
$487$	4.49681			0.203770			0.101885	+	0.994796i	$0.467513\pi$
$488$	1.73421	−	5.61679i	0.0785038	−	0.254260i
$489$	26.8020			1.21203
$490$	−0.886619	+	0.399962i	−0.0400534	+	0.0180684i
$491$		−	41.3602i		−	1.86656i	−0.359152	−	0.933279i	$-0.616934\pi$
$491$		−	41.3602i		−	1.86656i	0.359152	−	0.933279i	$-0.383066\pi$
$492$	17.4065	+	15.3669i	0.784744	+	0.692791i
$493$		−	30.0051i		−	1.35136i
$494$	−2.40616	−	5.33388i	−0.108258	−	0.239983i
$495$	−6.20268			−0.278790
$496$	4.11221	+	32.9104i	0.184644	+	1.47772i
$497$	11.8606			0.532021
$498$	2.89130	+	6.40930i	0.129562	+	0.287208i
$499$			2.02432i			0.0906210i	0.998973	+	0.0453105i	$0.0144277\pi$
$499$			2.02432i			0.0906210i	−0.998973	+	0.0453105i	$0.985572\pi$
$500$	9.82416	+	8.67301i	0.439350	+	0.387869i
$501$		−	13.8048i		−	0.616752i
$502$	−16.0616	+	7.24554i	−0.716865	+	0.323384i
$503$	−13.6836			−0.610123			−0.305062	−	0.952333i	$-0.598677\pi$
$503$	−13.6836			−0.610123			−0.305062	+	0.952333i	$0.598677\pi$
$504$	−7.57829	−	2.33983i	−0.337564	−	0.104224i
$505$	5.24107			0.233225
$506$	−29.1948	+	13.1701i	−1.29787	+	0.585480i
$507$		−	2.40918i		−	0.106995i
$508$	−16.9720	+	19.2246i	−0.753009	+	0.852954i
$509$		−	15.2121i		−	0.674265i	−0.941457	−	0.337133i	$-0.890543\pi$
$509$		−	15.2121i		−	0.674265i	0.941457	−	0.337133i	$-0.109457\pi$
$510$	−6.48713	−	14.3804i	−0.287255	−	0.636775i
$511$	−16.8777			−0.746624
$512$	14.0937	+	17.7022i	0.622859	+	0.782334i
$513$	−1.95246			−0.0862032
$514$	−1.15636	−	2.56337i	−0.0510048	−	0.113065i
$515$			3.46981i			0.152898i
$516$	40.5042	−	45.8803i	1.78310	−	2.01977i
$517$			25.4318i			1.11849i
$518$	10.0843	−	4.54912i	0.443079	−	0.199877i
$519$	21.3455			0.936961
$520$	−1.85874	−	0.573892i	−0.0815109	−	0.0251668i
$521$	26.9487			1.18064			0.590322	−	0.807168i	$-0.299001\pi$
$521$	26.9487			1.18064			0.590322	+	0.807168i	$0.299001\pi$
$522$	16.1109	−	7.26779i	0.705156	−	0.318103i
$523$		−	0.627284i		−	0.0274292i	−0.999906	−	0.0137146i	$-0.995634\pi$
$523$		−	0.627284i		−	0.0274292i	0.999906	−	0.0137146i	$-0.00436563\pi$
$524$	−5.97593	−	5.27570i	−0.261060	−	0.230470i
$525$			10.9063i			0.475989i
$526$	−14.5492	−	32.2520i	−0.634375	−	1.40625i
$527$	−55.8216			−2.43163
$528$	3.84276	+	30.7539i	0.167235	+	1.33839i
$529$	26.5857			1.15590
$530$	−4.01005	−	8.88931i	−0.174185	−	0.386127i
$531$		−	11.1432i		−	0.483575i
$532$	−6.20365	−	5.47673i	−0.268962	−	0.237446i
$533$			4.81888i			0.208729i
$534$	36.9420	−	16.6649i	1.59864	−	0.721160i
$535$	−11.0882			−0.479384
$536$	9.55646	−	30.9517i	0.412776	−	1.33691i
$537$	13.2612			0.572263
$538$	20.7694	−	9.36927i	0.895432	−	0.403938i
$539$			3.21615i			0.138529i
$540$	−0.429582	+	0.486599i	−0.0184863	+	0.0209399i
$541$			7.91671i			0.340366i	0.985412	+	0.170183i	$0.0544359\pi$
$541$			7.91671i			0.340366i	−0.985412	+	0.170183i	$0.945564\pi$
$542$	9.81753	+	21.7631i	0.421699	+	0.934804i
$543$	−34.9547			−1.50005
$544$	−32.5055	+	19.8437i	−1.39366	+	0.850790i
$545$	−7.66056			−0.328142
$546$	−1.40101	−	3.10571i	−0.0599579	−	0.132912i
$547$		−	29.4627i		−	1.25973i	−0.776704	−	0.629866i	$-0.783110\pi$
$547$		−	29.4627i		−	1.25973i	0.776704	−	0.629866i	$-0.216890\pi$
$548$	−7.84125	+	8.88201i	−0.334962	+	0.379421i
$549$			5.82793i			0.248730i
$550$	18.7687	−	8.46675i	0.800302	−	0.361024i
$551$	18.4409			0.785608
$552$	14.1557	−	45.8479i	0.602507	−	1.95142i
$553$	0.900413			0.0382894
$554$	8.63360	−	3.89470i	0.366806	−	0.165470i
$555$			12.9619i			0.550201i
$556$	4.68997	+	4.14042i	0.198899	+	0.175593i
$557$		−	6.15890i		−	0.260961i	−0.991451	−	0.130480i	$-0.958348\pi$
$557$		−	6.15890i		−	0.260961i	0.991451	−	0.130480i	$-0.0416520\pi$
$558$	−13.5210	−	29.9728i	−0.572390	−	1.26885i
$559$	12.7017			0.537224
$560$	−2.72986	+	0.341102i	−0.115358	+	0.0144142i
$561$	−52.1639			−2.20236
$562$	13.3399	+	29.5712i	0.562708	+	1.24739i
$563$		−	27.4626i		−	1.15741i	−0.815536	−	0.578706i	$-0.803558\pi$
$563$		−	27.4626i		−	1.15741i	0.815536	−	0.578706i	$-0.196442\pi$
$564$	−28.5631	−	25.2162i	−1.20272	−	1.06179i
$565$		−	13.2671i		−	0.558149i
$566$	2.03010	−	0.915795i	0.0853313	−	0.0384937i
$567$	−9.54924			−0.401030
$568$	32.0538	+	9.89673i	1.34495	+	0.415258i
$569$	−25.1770			−1.05547			−0.527737	−	0.849408i	$-0.676959\pi$
$569$	−25.1770			−1.05547			−0.527737	+	0.849408i	$0.676959\pi$
$570$	8.83806	−	3.98693i	0.370186	−	0.166994i
$571$			34.0974i			1.42693i	0.700689	+	0.713467i	$0.252876\pi$
$571$			34.0974i			1.42693i	−0.700689	+	0.713467i	$0.747124\pi$
$572$	−4.25702	+	4.82205i	−0.177995	+	0.201620i
$573$			42.0965i			1.75861i
$574$	2.80233	+	6.21210i	0.116967	+	0.259288i
$575$	−31.8776			−1.32939
$576$	−18.5283	−	12.6470i	−0.772011	−	0.526957i
$577$	−34.3580			−1.43034			−0.715170	−	0.698950i	$-0.753651\pi$
$577$	−34.3580			−1.43034			−0.715170	+	0.698950i	$0.753651\pi$
$578$	−16.4715	−	36.5133i	−0.685123	−	1.51875i
$579$			12.5310i			0.520769i
$580$	4.05737	−	4.59590i	0.168473	−	0.190834i
$581$			2.06372i			0.0856174i
$582$	−25.0876	+	11.3172i	−1.03991	+	0.469114i
$583$	−32.2453			−1.33547
$584$	−45.6126	−	14.0831i	−1.88746	−	0.582762i
$585$	1.92861			0.0797380
$586$	−35.9159	+	16.2020i	−1.48367	+	0.669298i
$587$		−	4.39822i		−	0.181534i	−0.995872	−	0.0907669i	$-0.971068\pi$
$587$		−	4.39822i		−	0.181534i	0.995872	−	0.0907669i	$-0.0289318\pi$
$588$	−3.61214	−	3.18888i	−0.148962	−	0.131507i
$589$		−	34.3074i		−	1.41361i
$590$	−1.58939	−	3.52330i	−0.0654342	−	0.145052i
$591$	14.3562			0.590536
$592$	31.0492	−	3.87965i	1.27611	−	0.159453i
$593$	−1.50359			−0.0617451			−0.0308725	−	0.999523i	$-0.509829\pi$
$593$	−1.50359			−0.0617451			−0.0308725	+	0.999523i	$0.509829\pi$
$594$	0.882552	+	1.95640i	0.0362115	+	0.0802722i
$595$		−	4.63031i		−	0.189824i
$596$	−3.31203	−	2.92394i	−0.135666	−	0.119769i
$597$			29.1691i			1.19381i
$598$	9.07758	−	4.09498i	0.371210	−	0.167456i
$599$	13.7500			0.561809			0.280904	−	0.959736i	$-0.409366\pi$
$599$	13.7500			0.561809			0.280904	+	0.959736i	$0.409366\pi$
$600$	−9.10042	+	29.4747i	−0.371523	+	1.20330i
$601$	7.31520			0.298393			0.149197	−	0.988808i	$-0.452331\pi$
$601$	7.31520			0.298393			0.149197	+	0.988808i	$0.452331\pi$
$602$	16.3740	−	7.38644i	0.667353	−	0.301049i
$603$			32.1152i			1.30783i
$604$	6.54898	−	7.41821i	0.266474	−	0.301843i
$605$		−	0.451462i		−	0.0183545i
$606$	10.6762	+	23.6666i	0.433692	+	0.961390i
$607$	−19.5840			−0.794889			−0.397445	−	0.917626i	$-0.630103\pi$
$607$	−19.5840			−0.794889			−0.397445	+	0.917626i	$0.630103\pi$
$608$	−12.1957	−	19.9776i	−0.494602	−	0.810197i
$609$	10.7374			0.435101
$610$	0.831255	+	1.84269i	0.0336565	+	0.0746084i
$611$		−	7.90753i		−	0.319904i
$612$	24.9881	−	28.3048i	1.01009	−	1.14415i
$613$			44.5486i			1.79930i	0.436610	+	0.899651i	$0.356179\pi$
$613$			44.5486i			1.79930i	−0.436610	+	0.899651i	$0.643821\pi$
$614$	−27.8883	+	12.5807i	−1.12548	+	0.507715i
$615$	−7.98472			−0.321975
$616$	−2.68362	+	8.69177i	−0.108126	+	0.350201i
$617$	−17.9533			−0.722772			−0.361386	−	0.932416i	$-0.617696\pi$
$617$	−17.9533			−0.722772			−0.361386	+	0.932416i	$0.617696\pi$
$618$	−15.6683	+	7.06811i	−0.630271	+	0.284321i
$619$		−	14.7130i		−	0.591365i	−0.955286	−	0.295683i	$-0.904453\pi$
$619$		−	14.7130i		−	0.591365i	0.955286	−	0.295683i	$-0.0955471\pi$
$620$	−8.55023	−	7.54835i	−0.343385	−	0.303149i
$621$		−	3.32284i		−	0.133341i
$622$	−7.38397	−	16.3685i	−0.296070	−	0.656316i
$623$	11.8949			0.476558
$624$	−1.19483	−	9.56235i	−0.0478316	−	0.382800i
$625$	18.1283			0.725132
$626$	−13.8559	−	30.7153i	−0.553795	−	1.22763i
$627$		−	32.0594i		−	1.28033i
$628$	31.2944	+	27.6274i	1.24878	+	1.10245i
$629$			52.6647i			2.09988i
$630$	2.48620	−	1.12155i	0.0990524	−	0.0446835i
$631$	17.9131			0.713110			0.356555	−	0.934274i	$-0.383951\pi$
$631$	17.9131			0.713110			0.356555	+	0.934274i	$0.383951\pi$
$632$	2.43340	+	0.751323i	0.0967956	+	0.0298860i
$633$	−23.4074			−0.930362
$634$	1.23586	−	0.557508i	0.0490823	−	0.0221415i
$635$		−	8.81874i		−	0.349961i
$636$	31.9720	−	36.2156i	1.26777	−	1.43604i
$637$		−	1.00000i		−	0.0396214i
$638$	−8.33565	−	18.4781i	−0.330012	−	0.731556i
$639$	−33.2587			−1.31569
$640$	−7.66219	−	1.35601i	−0.302875	−	0.0536011i
$641$	46.0544			1.81904			0.909520	−	0.415660i	$-0.136449\pi$
$641$	46.0544			1.81904			0.909520	+	0.415660i	$0.136449\pi$
$642$	−22.5870	−	50.0699i	−0.891437	−	1.97610i
$643$			20.1393i			0.794215i	0.917772	+	0.397107i	$0.129986\pi$
$643$			20.1393i			0.794215i	−0.917772	+	0.397107i	$0.870014\pi$
$644$	9.32069	−	10.5578i	0.367287	−	0.416036i
$645$			21.0463i			0.828696i
$646$	35.9095	−	16.1991i	1.41284	−	0.637345i
$647$	3.30439			0.129909			0.0649544	−	0.997888i	$-0.479310\pi$
$647$	3.30439			0.129909			0.0649544	+	0.997888i	$0.479310\pi$
$648$	−25.8072	−	7.96808i	−1.01380	−	0.313016i
$649$	−12.7805			−0.501679
$650$	−5.83579	+	2.63258i	−0.228898	+	0.103258i
$651$		−	19.9759i		−	0.782916i
$652$	16.6799	+	14.7254i	0.653236	+	0.576693i
$653$		−	13.9169i		−	0.544610i	−0.962211	−	0.272305i	$-0.912214\pi$
$653$		−	13.9169i		−	0.544610i	0.962211	−	0.272305i	$-0.0877860\pi$
$654$	−15.6048	−	34.5921i	−0.610196	−	1.35266i
$655$	2.74129			0.107111
$656$	2.38993	+	19.1268i	0.0933111	+	0.746776i
$657$	47.3272			1.84641
$658$	−4.59848	−	10.1937i	−0.179267	−	0.397393i
$659$			23.5824i			0.918638i	0.888271	+	0.459319i	$0.151907\pi$
$659$			23.5824i			0.918638i	−0.888271	+	0.459319i	$0.848093\pi$
$660$	−7.98997	−	7.05374i	−0.311009	−	0.274566i
$661$			47.2373i			1.83732i	0.395050	+	0.918660i	$0.370727\pi$
$661$			47.2373i			1.83732i	−0.395050	+	0.918660i	$0.629273\pi$
$662$	−7.96094	+	3.59125i	−0.309411	+	0.139578i
$663$	16.2194			0.629908
$664$	−1.72201	+	5.57729i	−0.0668269	+	0.216441i
$665$	2.84575			0.110353
$666$	−28.2777	+	12.7563i	−1.09574	+	0.494298i
$667$			31.3840i			1.21519i
$668$	7.58457	−	8.59125i	0.293456	−	0.332405i
$669$		−	46.9315i		−	1.81448i
$670$	4.58069	+	10.1543i	0.176967	+	0.392294i
$671$	6.68423			0.258042
$672$	−7.10109	−	11.6321i	−0.273931	−	0.448720i
$673$	−8.68063			−0.334614			−0.167307	−	0.985905i	$-0.553507\pi$
$673$	−8.68063			−0.334614			−0.167307	+	0.985905i	$0.553507\pi$
$674$	3.83509	+	8.50147i	0.147722	+	0.327464i
$675$			2.13618i			0.0822217i
$676$	1.32364	−	1.49933i	0.0509093	−	0.0576663i
$677$		−	9.39355i		−	0.361024i	−0.983573	−	0.180512i	$-0.942225\pi$
$677$		−	9.39355i		−	0.361024i	0.983573	−	0.180512i	$-0.0577754\pi$
$678$	59.9087	−	27.0254i	2.30078	−	1.03790i
$679$	−8.07789			−0.310001
$680$	3.86363	−	12.5136i	0.148163	−	0.479876i
$681$	−13.8646			−0.531291
$682$	−34.3767	+	15.5077i	−1.31635	+	0.593819i
$683$			7.64309i			0.292455i	0.989251	+	0.146227i	$0.0467131\pi$
$683$			7.64309i			0.292455i	−0.989251	+	0.146227i	$0.953287\pi$
$684$	17.3959	+	15.3575i	0.665147	+	0.587208i
$685$		−	4.07437i		−	0.155674i
$686$	−0.581532	−	1.28912i	−0.0222030	−	0.0492187i
$687$	−10.8881			−0.415407
$688$	50.4147	−	6.29942i	1.92204	−	0.240163i
$689$	10.0261			0.381963
$690$	6.78524	+	15.0412i	0.258310	+	0.572610i
$691$		−	38.5172i		−	1.46526i	−0.680626	−	0.732631i	$-0.738292\pi$
$691$		−	38.5172i		−	1.46526i	0.680626	−	0.732631i	$-0.261708\pi$
$692$	13.2841	+	11.7275i	0.504986	+	0.445814i
$693$		−	9.01850i		−	0.342584i
$694$	−13.7414	+	6.19886i	−0.521615	+	0.235305i
$695$	−2.15139			−0.0816070
$696$	29.0183	+	8.95950i	1.09993	+	0.339609i
$697$	−32.4423			−1.22884
$698$	26.7446	−	12.0647i	1.01230	−	0.456657i
$699$			4.91326i			0.185836i
$700$	−5.99208	+	6.78740i	−0.226479	+	0.256540i
$701$		−	18.4756i		−	0.697814i	−0.937157	−	0.348907i	$-0.886553\pi$
$701$		−	18.4756i		−	0.697814i	0.937157	−	0.348907i	$-0.113447\pi$
$702$	−0.274413	−	0.608307i	−0.0103571	−	0.0229591i
$703$	−32.3672			−1.22075
$704$	−14.5052	+	21.2506i	−0.546685	+	0.800913i
$705$	13.1025			0.493469
$706$	−3.41134	−	7.56212i	−0.128388	−	0.284604i
$707$			7.62035i			0.286593i
$708$	12.6722	−	14.3541i	0.476249	−	0.539461i
$709$			2.94207i			0.110492i	0.998473	+	0.0552459i	$0.0175943\pi$
$709$			2.94207i			0.110492i	−0.998473	+	0.0552459i	$0.982406\pi$
$710$	−10.5158	+	4.74379i	−0.394652	+	0.178031i
$711$	−2.52488			−0.0946903
$712$	32.1464	+	9.92533i	1.20474	+	0.371967i
$713$	58.3868			2.18660
$714$	20.9087	−	9.43209i	0.782487	−	0.352987i
$715$		−	2.21198i		−	0.0827232i
$716$	8.25296	+	7.28591i	0.308428	+	0.272287i
$717$			19.3123i			0.721233i
$718$	−18.6996	−	41.4524i	−0.697862	−	1.54699i
$719$	−4.53648			−0.169182			−0.0845911	−	0.996416i	$-0.526958\pi$
$719$	−4.53648			−0.169182			−0.0845911	+	0.996416i	$0.526958\pi$
$720$	7.65490	−	0.956494i	0.285281	−	0.0356464i
$721$	−5.04500			−0.187885
$722$	−1.09330	−	2.42358i	−0.0406885	−	0.0901965i
$723$			8.45892i			0.314591i
$724$	−21.7537	−	19.2047i	−0.808470	−	0.713737i
$725$		−	20.1761i		−	0.749322i
$726$	2.03862	−	0.919641i	0.0756604	−	0.0341311i
$727$	−0.575488			−0.0213437			−0.0106718	−	0.999943i	$-0.503397\pi$
$727$	−0.575488			−0.0213437			−0.0106718	+	0.999943i	$0.503397\pi$
$728$	0.834421	−	2.70254i	0.0309257	−	0.100163i
$729$	23.3668			0.865437
$730$	14.9641	−	6.75042i	0.553844	−	0.249844i
$731$			85.5120i			3.16278i
$732$	−6.62757	+	7.50724i	−0.244962	+	0.277475i
$733$			4.34048i			0.160319i	0.996782	+	0.0801597i	$0.0255430\pi$
$733$			4.34048i			0.160319i	−0.996782	+	0.0801597i	$0.974457\pi$
$734$	0.00341554	+	0.00757142i	0.000126070	+	0.000279466i
$735$	1.65697			0.0611181
$736$	33.9992	−	20.7556i	1.25323	−	0.765060i
$737$	36.8339			1.35679
$738$	−7.85812	−	17.4195i	−0.289261	−	0.641222i
$739$		−	5.99047i		−	0.220363i	−0.993911	−	0.110181i	$-0.964857\pi$
$739$		−	5.99047i		−	0.220363i	0.993911	−	0.110181i	$-0.0351432\pi$
$740$	−7.12146	+	8.06668i	−0.261790	+	0.296537i
$741$			9.96828i			0.366194i
$742$	12.9248	−	5.83049i	0.474484	−	0.214044i
$743$	14.2196			0.521665			0.260833	−	0.965384i	$-0.416003\pi$
$743$	14.2196			0.521665			0.260833	+	0.965384i	$0.416003\pi$
$744$	16.6683	−	53.9856i	0.611089	−	1.97921i
$745$	1.51930			0.0556628
$746$	−28.6612	+	12.9293i	−1.04936	+	0.473377i
$747$		−	5.78694i		−	0.211733i
$748$	−32.4636	−	28.6597i	−1.18699	−	1.04790i
$749$		−	16.1219i		−	0.589081i
$750$	−9.17999	−	20.3498i	−0.335206	−	0.743070i
$751$	4.72032			0.172247			0.0861234	−	0.996284i	$-0.472552\pi$
$751$	4.72032			0.172247			0.0861234	+	0.996284i	$0.472552\pi$
$752$	−3.92175	−	31.3860i	−0.143011	−	1.14453i
$753$	30.0169			1.09388
$754$	2.59181	+	5.74542i	0.0943883	+	0.209236i
$755$			3.40289i			0.123844i
$756$	−0.707500	−	0.624599i	−0.0257315	−	0.0227164i
$757$			34.5160i			1.25451i	0.778816	+	0.627253i	$0.215821\pi$
$757$			34.5160i			1.25451i	−0.778816	+	0.627253i	$0.784179\pi$
$758$	−5.41466	+	2.44260i	−0.196669	+	0.0887193i
$759$	54.5610			1.98044
$760$	7.69076	+	2.37455i	0.278973	+	0.0861340i
$761$	13.0455			0.472900			0.236450	−	0.971644i	$-0.424016\pi$
$761$	13.0455			0.472900			0.236450	+	0.971644i	$0.424016\pi$
$762$	39.8219	−	17.9640i	1.44260	−	0.650769i
$763$		−	11.1382i		−	0.403231i
$764$	−23.1285	+	26.1983i	−0.836759	+	0.947821i
$765$			12.9840i			0.469438i
$766$	−1.89454	−	4.19973i	−0.0684525	−	0.151743i
$767$	3.97386			0.143488
$768$	−9.48491	−	37.3617i	−0.342257	−	1.34817i
$769$	15.5443			0.560541			0.280271	−	0.959921i	$-0.409576\pi$
$769$	15.5443			0.560541			0.280271	+	0.959921i	$0.409576\pi$
$770$	−1.28634	−	2.85149i	−0.0463563	−	0.102761i
$771$			4.79057i			0.172528i
$772$	−6.88471	+	7.79850i	−0.247786	+	0.280674i
$773$		−	36.8531i		−	1.32551i	−0.748834	−	0.662757i	$-0.769386\pi$
$773$		−	36.8531i		−	1.32551i	0.748834	−	0.662757i	$-0.230614\pi$
$774$	−45.9148	+	20.7126i	−1.65037	+	0.744498i
$775$	−37.5357			−1.34832
$776$	−21.8308	−	6.74036i	−0.783682	−	0.241965i
$777$	−18.8462			−0.676102
$778$	25.8852	−	11.6770i	0.928029	−	0.418643i
$779$		−	19.9387i		−	0.714379i
$780$	2.48433	+	2.19323i	0.0889533	+	0.0785301i
$781$			38.1454i			1.36495i
$782$	27.5688	+	61.1133i	0.985857	+	2.18541i
$783$	2.10311			0.0751588
$784$	−0.495951	−	3.96913i	−0.0177125	−	0.141755i
$785$	−14.3554			−0.512366
$786$	5.58409	+	12.3786i	0.199178	+	0.441529i
$787$		−	19.8020i		−	0.705866i	−0.935649	−	0.352933i	$-0.885184\pi$
$787$		−	19.8020i		−	0.705866i	0.935649	−	0.352933i	$-0.114816\pi$
$788$	8.93443	+	7.88753i	0.318276	+	0.280982i
$789$			60.2745i			2.14583i
$790$	−0.798323	+	0.360131i	−0.0284031	+	0.0128129i
$791$	19.2899			0.685869
$792$	7.52522	−	24.3729i	0.267397	−	0.866053i
$793$	−2.07834			−0.0738039
$794$	−29.7329	+	13.4128i	−1.05518	+	0.476001i
$795$			16.6129i			0.589198i
$796$	−16.0259	+	18.1530i	−0.568025	+	0.643418i
$797$		−	14.0956i		−	0.499292i	−0.968337	−	0.249646i	$-0.919686\pi$
$797$		−	14.0956i		−	0.499292i	0.968337	−	0.249646i	$-0.0803143\pi$
$798$	5.79687	+	12.8503i	0.205207	+	0.454894i
$799$	53.2361			1.88336
$800$	−21.8574	+	13.3433i	−0.772776	+	0.471758i
$801$	−33.3548			−1.17853
$802$	−3.63847	−	8.06562i	−0.128479	−	0.284807i
$803$		−	54.2810i		−	1.91554i
$804$	−36.5217	+	41.3691i	−1.28802	+	1.45898i
$805$			4.84309i			0.170697i
$806$	10.6888	−	4.82182i	0.376497	−	0.169841i
$807$	−38.8151			−1.36636
$808$	−6.35858	+	20.5943i	−0.223694	+	0.724506i
$809$	−13.6176			−0.478770			−0.239385	−	0.970925i	$-0.576946\pi$
$809$	−13.6176			−0.478770			−0.239385	+	0.970925i	$0.576946\pi$
$810$	8.46653	−	3.81933i	0.297484	−	0.134198i
$811$		−	18.9691i		−	0.666095i	−0.942910	−	0.333047i	$-0.891923\pi$
$811$		−	18.9691i		−	0.666095i	0.942910	−	0.333047i	$-0.108077\pi$
$812$	6.68230	+	5.89930i	0.234503	+	0.207025i
$813$		−	40.6721i		−	1.42643i
$814$	14.6306	+	32.4326i	0.512804	+	1.13676i
$815$	−7.65144			−0.268018
$816$	64.3769	−	8.04402i	2.25364	−	0.281597i
$817$	−52.5549			−1.83866
$818$	−11.7941	−	26.1447i	−0.412371	−	0.914127i
$819$			2.80413i			0.0979843i
$820$	−4.96921	−	4.38694i	−0.173532	−	0.153198i
$821$		−	6.42394i		−	0.224197i	−0.993697	−	0.112099i	$-0.964243\pi$
$821$		−	6.42394i		−	0.224197i	0.993697	−	0.112099i	$-0.0357572\pi$
$822$	18.3982	−	8.29961i	0.641712	−	0.289482i
$823$	−9.99062			−0.348251			−0.174125	−	0.984723i	$-0.555710\pi$
$823$	−9.99062			−0.348251			−0.174125	+	0.984723i	$0.555710\pi$
$824$	−13.6343	−	4.20965i	−0.474974	−	0.146650i
$825$	−35.0761			−1.22119
$826$	5.12276	−	2.31093i	0.178244	−	0.0804074i
$827$			36.5643i			1.27147i	0.771909	+	0.635733i	$0.219302\pi$
$827$			36.5643i			1.27147i	−0.771909	+	0.635733i	$0.780698\pi$
$828$	−26.1365	+	29.6055i	−0.908305	+	1.02886i
$829$		−	45.0922i		−	1.56612i	−0.621948	−	0.783059i	$-0.713658\pi$
$829$		−	45.0922i		−	1.56612i	0.621948	−	0.783059i	$-0.286342\pi$
$830$	−0.825408	−	1.82973i	−0.0286503	−	0.0635109i
$831$	−16.1350			−0.559716
$832$	4.51012	−	6.60748i	0.156360	−	0.229073i
$833$	6.73233			0.233261
$834$	−4.38245	−	9.71483i	−0.151752	−	0.336397i
$835$			3.94099i			0.136384i
$836$	17.6140	−	19.9518i	0.609192	−	0.690049i
$837$		−	3.91262i		−	0.135240i
$838$	40.7539	−	18.3845i	1.40782	−	0.635081i
$839$	16.0522			0.554184			0.277092	−	0.960843i	$-0.410629\pi$
$839$	16.0522			0.554184			0.277092	+	0.960843i	$0.410629\pi$
$840$	4.47802	+	1.38261i	0.154506	+	0.0477045i
$841$	9.13630			0.315045
$842$	1.65672	−	0.747361i	0.0570943	−	0.0257558i
$843$		−	55.2645i		−	1.90341i
$844$	−14.5674	−	12.8604i	−0.501429	−	0.442674i
$845$			0.687773i			0.0236601i
$846$	12.8948	+	28.5845i	0.443331	+	0.982757i
$847$	0.656411			0.0225546
$848$	39.7949	−	4.97245i	1.36656	−	0.170754i
$849$	−3.79396			−0.130209
$850$	−17.7234	−	39.2885i	−0.607907	−	1.34758i
$851$		−	55.0848i		−	1.88828i
$852$	−42.8422	−	37.8221i	−1.46775	−	1.29576i
$853$		−	32.9867i		−	1.12944i	−0.825282	−	0.564721i	$-0.808984\pi$
$853$		−	32.9867i		−	1.12944i	0.825282	−	0.564721i	$-0.191016\pi$
$854$	−2.67922	+	1.20862i	−0.0916809	+	0.0413581i
$855$	−7.97985			−0.272905
$856$	13.4524	−	43.5701i	0.459795	−	1.48920i
$857$	8.97007			0.306412			0.153206	−	0.988194i	$-0.451040\pi$
$857$	8.97007			0.306412			0.153206	+	0.988194i	$0.451040\pi$
$858$	9.98841	−	4.50586i	0.340999	−	0.153828i
$859$			7.46952i			0.254857i	0.991848	+	0.127428i	$0.0406723\pi$
$859$			7.46952i			0.254857i	−0.991848	+	0.127428i	$0.959328\pi$
$860$	−11.5632	+	13.0979i	−0.394301	+	0.446635i
$861$		−	11.6095i		−	0.395652i
$862$	−8.13437	−	18.0319i	−0.277058	−	0.614170i
$863$	−4.42663			−0.150684			−0.0753421	−	0.997158i	$-0.524005\pi$
$863$	−4.42663			−0.150684			−0.0753421	+	0.997158i	$0.524005\pi$
$864$	−1.39087	−	2.27836i	−0.0473184	−	0.0775113i
$865$	−6.09371			−0.207192
$866$	7.23320	+	16.0342i	0.245794	+	0.544866i
$867$			68.2382i			2.31749i
$868$	10.9751	−	12.4318i	0.372518	−	0.421962i
$869$			2.89586i			0.0982352i
$870$	−9.51997	+	4.29455i	−0.322757	+	0.145599i
$871$	−11.4528			−0.388064
$872$	9.29396	−	30.1015i	0.314733	−	1.01937i
$873$	22.6515			0.766636
$874$	−37.5597	+	16.9435i	−1.27047	+	0.573123i
$875$		−	6.55239i		−	0.221511i
$876$	60.9645	+	53.8209i	2.05980	+	1.81844i
$877$			27.9884i			0.945100i	0.881304	+	0.472550i	$0.156666\pi$
$877$			27.9884i			0.945100i	−0.881304	+	0.472550i	$0.843334\pi$
$878$	16.9616	+	37.5998i	0.572426	+	1.26893i
$879$	67.1218			2.26396
$880$	−1.09703	−	8.77963i	−0.0369809	−	0.295961i
$881$	−13.3354			−0.449280			−0.224640	−	0.974442i	$-0.572121\pi$
$881$	−13.3354			−0.449280			−0.224640	+	0.974442i	$0.572121\pi$
$882$	1.63069	+	3.61485i	0.0549083	+	0.121718i
$883$		−	2.41618i		−	0.0813110i	−0.999173	−	0.0406555i	$-0.987055\pi$
$883$		−	2.41618i		−	0.0813110i	0.999173	−	0.0406555i	$-0.0129446\pi$
$884$	10.0940	+	8.91119i	0.339496	+	0.299716i
$885$			6.58455i			0.221337i
$886$	−9.52568	+	4.29712i	−0.320021	+	0.144365i
$887$	−40.2075			−1.35004			−0.675018	−	0.737801i	$-0.735864\pi$
$887$	−40.2075			−1.35004			−0.675018	+	0.737801i	$0.735864\pi$
$888$	−50.9326	−	15.7256i	−1.70918	−	0.527717i
$889$	12.8222			0.430042
$890$	−10.5462	+	4.75750i	−0.353510	+	0.159472i
$891$		−	30.7117i		−	1.02888i
$892$	25.7849	−	29.2073i	0.863343	−	0.977933i
$893$			32.7184i			1.09488i
$894$	3.09486	+	6.86055i	0.103507	+	0.229451i
$895$	−3.78581			−0.126546
$896$	1.97160	−	11.1406i	0.0658665	−	0.372181i
$897$	−16.9647			−0.566436
$898$	10.7045	+	23.7293i	0.357214	+	0.791858i
$899$			36.9545i			1.23250i
$900$	16.8026	−	19.0328i	0.560086	−	0.634425i
$901$			67.4989i			2.24871i
$902$	−19.9790	+	9.01271i	−0.665228	+	0.300091i
$903$	−30.6006			−1.01833
$904$	52.1317	+	16.0959i	1.73388	+	0.535341i
$905$	9.97889			0.331710
$906$	−15.3661	+	6.93180i	−0.510505	+	0.230294i
$907$		−	27.7295i		−	0.920742i	−0.887727	−	0.460371i	$-0.847716\pi$
$907$		−	27.7295i		−	0.920742i	0.887727	−	0.460371i	$-0.152284\pi$
$908$	−8.62845	−	7.61741i	−0.286345	−	0.252793i
$909$		−	21.3685i		−	0.708748i
$910$	0.399962	+	0.886619i	0.0132586	+	0.0293911i
$911$	14.4713			0.479456			0.239728	−	0.970840i	$-0.422942\pi$
$911$	14.4713			0.479456			0.239728	+	0.970840i	$0.422942\pi$
$912$	4.94378	+	39.5654i	0.163705	+	1.31014i
$913$	−6.63721			−0.219660
$914$	−12.2876	−	27.2386i	−0.406437	−	0.900973i
$915$		−	3.44373i		−	0.113846i
$916$	−6.77610	−	5.98210i	−0.223888	−	0.197654i
$917$			3.98575i			0.131621i
$918$	4.09532	−	1.84744i	0.135166	−	0.0609746i
$919$	−31.3587			−1.03443			−0.517214	−	0.855856i	$-0.673031\pi$
$919$	−31.3587			−1.03443			−0.517214	+	0.855856i	$0.673031\pi$
$920$	−4.04118	+	13.0887i	−0.133234	+	0.431521i
$921$	52.1193			1.71739
$922$	−12.9650	+	5.84864i	−0.426980	+	0.192615i
$923$		−	11.8606i		−	0.390397i
$924$	10.2559	−	11.6172i	0.337395	−	0.382177i
$925$			35.4129i			1.16437i
$926$	20.3764	+	45.1694i	0.669608	+	1.48436i
$927$	14.1468			0.464643
$928$	13.1367	+	21.5190i	0.431234	+	0.706394i
$929$	−48.9015			−1.60441			−0.802203	−	0.597052i	$-0.796339\pi$
$929$	−48.9015			−1.60441			−0.802203	+	0.597052i	$0.796339\pi$
$930$	7.98959	+	17.7110i	0.261989	+	0.580766i
$931$			4.13763i			0.135605i
$932$	−2.69942	+	3.05771i	−0.0884225	+	0.100159i
$933$			30.5904i			1.00148i
$934$	28.6378	−	12.9188i	0.937059	−	0.422716i
$935$	14.8918			0.487013
$936$	−2.33983	+	7.57829i	−0.0764796	+	0.247704i
$937$	16.8418			0.550198			0.275099	−	0.961416i	$-0.411289\pi$
$937$	16.8418			0.550198			0.275099	+	0.961416i	$0.411289\pi$
$938$	−14.7640	+	6.66017i	−0.482062	+	0.217462i
$939$			57.4025i			1.87326i
$940$	8.15420	+	7.19873i	0.265961	+	0.234797i
$941$			25.4756i			0.830480i	0.909712	+	0.415240i	$0.136302\pi$
$941$			25.4756i			0.830480i	−0.909712	+	0.415240i	$0.863698\pi$
$942$	−29.2424	−	64.8233i	−0.952768	−	2.11206i
$943$	33.9332			1.10502
$944$	15.7728	−	1.97084i	0.513360	−	0.0641453i
$945$	0.324546			0.0105575
$946$	23.7559	+	52.6610i	0.772370	+	1.71216i
$947$		−	48.9591i		−	1.59096i	−0.605981	−	0.795479i	$-0.707219\pi$
$947$		−	48.9591i		−	1.59096i	0.605981	−	0.795479i	$-0.292781\pi$
$948$	−3.25242	−	2.87131i	−0.105634	−	0.0932559i
$949$			16.8777i			0.547872i
$950$	24.1463	−	10.8926i	0.783410	−	0.353404i
$951$	−2.30965			−0.0748955
$952$	18.1944	+	5.61760i	0.589684	+	0.182067i
$953$	−53.9832			−1.74869			−0.874344	−	0.485307i	$-0.838708\pi$
$953$	−53.9832			−1.74869			−0.874344	+	0.485307i	$0.838708\pi$
$954$	−36.2428	+	16.3495i	−1.17340	+	0.529333i
$955$		−	12.0177i		−	0.388884i
$956$	−10.6105	+	12.0188i	−0.343168	+	0.388717i
$957$			34.5330i			1.11629i
$958$	15.6948	+	34.7917i	0.507077	+	1.12407i
$959$	5.92401			0.191296
$960$	10.9484	+	7.47311i	0.353357	+	0.241194i
$961$	37.7502			1.21775
$962$	−4.54912	−	10.0843i	−0.146670	−	0.325131i
$963$			45.2079i			1.45680i
$964$	−4.64747	+	5.26432i	−0.149685	+	0.169552i
$965$		−	3.57734i		−	0.115159i
$966$	−21.8695	+	9.86553i	−0.703640	+	0.317418i
$967$	−4.69531			−0.150991			−0.0754955	−	0.997146i	$-0.524054\pi$
$967$	−4.69531			−0.150991			−0.0754955	+	0.997146i	$0.524054\pi$
$968$	1.77398	+	0.547723i	0.0570179	+	0.0176045i
$969$	−67.1097			−2.15588
$970$	7.16201	−	3.23085i	0.229958	−	0.103736i
$971$		−	43.6293i		−	1.40013i	−0.714079	−	0.700065i	$-0.753154\pi$
$971$		−	43.6293i		−	1.40013i	0.714079	−	0.700065i	$-0.246846\pi$
$972$	32.3707	+	28.5776i	1.03829	+	0.916628i
$973$		−	3.12806i		−	0.100281i
$974$	−2.61504	−	5.79691i	−0.0837913	−	0.185745i
$975$	10.9063			0.349280
$976$	−8.24919	+	1.03075i	−0.264050	+	0.0329936i
$977$	−24.1270			−0.771892			−0.385946	−	0.922521i	$-0.626125\pi$
$977$	−24.1270			−0.771892			−0.385946	+	0.922521i	$0.626125\pi$
$978$	−15.5862	−	34.5509i	−0.498392	−	1.10482i
$979$			38.2556i			1.22266i
$980$	1.03119	+	0.910364i	0.0329403	+	0.0290805i
$981$			31.2330i			0.997195i
$982$	−53.3181	+	24.0523i	−1.70145	+	0.767539i
$983$	−53.7433			−1.71415			−0.857073	−	0.515196i	$-0.827719\pi$
$983$	−53.7433			−1.71415			−0.857073	+	0.515196i	$0.827719\pi$
$984$	9.68724	−	31.3753i	0.308818	−	1.00021i
$985$	−4.09842			−0.130586
$986$	−38.6801	+	17.4490i	−1.23183	+	0.555688i
$987$			19.0506i			0.606388i
$988$	−5.47673	+	6.20365i	−0.174238	+	0.197364i
$989$		−	89.4416i		−	2.84408i
$990$	3.60706	+	7.99597i	0.114640	+	0.254129i
$991$	−43.0179			−1.36651			−0.683255	−	0.730180i	$-0.739436\pi$
$991$	−43.0179			−1.36651			−0.683255	+	0.730180i	$0.739436\pi$
$992$	40.0339	−	24.4396i	1.27108	−	0.775957i
$993$	14.8779			0.472135
$994$	−6.89732	−	15.2897i	−0.218770	−	0.484960i
$995$		−	8.32719i		−	0.263990i
$996$	6.58096	−	7.45443i	0.208526	−	0.236203i
$997$			47.1795i			1.49419i	0.664717	+	0.747095i	$0.268552\pi$
$997$			47.1795i			1.49419i	−0.664717	+	0.747095i	$0.731448\pi$
$998$	2.60958	−	1.17721i	0.0826049	−	0.0372638i
$999$	−3.69135			−0.116789

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	728.2.c.b.365.15	✓	38
4.3	odd	2		2912.2.c.b.1457.6		38
8.3	odd	2		2912.2.c.b.1457.33		38
8.5	even	2	inner	728.2.c.b.365.16	yes	38

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
728.2.c.b.365.15	✓	38	1.1	even	1	trivial
728.2.c.b.365.16	yes	38	8.5	even	2	inner
2912.2.c.b.1457.6		38	4.3	odd	2
2912.2.c.b.1457.33		38	8.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 728 = 2^{3} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	728.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.581532 - 1.28912i) q^{2} +2.40918i q^{3} +(-1.32364 + 1.49933i) q^{4} -0.687773i q^{5} +(3.10571 - 1.40101i) q^{6} +1.00000 q^{7} +(2.70254 + 0.834421i) q^{8} -2.80413 q^{9} +(-0.886619 + 0.399962i) q^{10} +3.21615i q^{11} +(-3.61214 - 3.18888i) q^{12} -1.00000i q^{13} +(-0.581532 - 1.28912i) q^{14} +1.65697 q^{15} +(-0.495951 - 3.96913i) q^{16} +6.73233 q^{17} +(1.63069 + 3.61485i) q^{18} +4.13763i q^{19} +(1.03119 + 0.910364i) q^{20} +2.40918i q^{21} +(4.14598 - 1.87029i) q^{22} -7.04171 q^{23} +(-2.01027 + 6.51091i) q^{24} +4.52697 q^{25} +(-1.28912 + 0.581532i) q^{26} +0.471879i q^{27} +(-1.32364 + 1.49933i) q^{28} -4.45687i q^{29} +(-0.963579 - 2.13602i) q^{30} -8.29157 q^{31} +(-4.82826 + 2.94752i) q^{32} -7.74826 q^{33} +(-3.91507 - 8.67876i) q^{34} -0.687773i q^{35} +(3.71166 - 4.20431i) q^{36} +7.82265i q^{37} +(5.33388 - 2.40616i) q^{38} +2.40918 q^{39} +(0.573892 - 1.85874i) q^{40} -4.81888 q^{41} +(3.10571 - 1.40101i) q^{42} +12.7017i q^{43} +(-4.82205 - 4.25702i) q^{44} +1.92861i q^{45} +(4.09498 + 9.07758i) q^{46} +7.90753 q^{47} +(9.56235 - 1.19483i) q^{48} +1.00000 q^{49} +(-2.63258 - 5.83579i) q^{50} +16.2194i q^{51} +(1.49933 + 1.32364i) q^{52} +10.0261i q^{53} +(0.608307 - 0.274413i) q^{54} +2.21198 q^{55} +(2.70254 + 0.834421i) q^{56} -9.96828 q^{57} +(-5.74542 + 2.59181i) q^{58} +3.97386i q^{59} +(-2.19323 + 2.48433i) q^{60} -2.07834i q^{61} +(4.82182 + 10.6888i) q^{62} -2.80413 q^{63} +(6.60748 + 4.51012i) q^{64} -0.687773 q^{65} +(4.50586 + 9.98841i) q^{66} -11.4528i q^{67} +(-8.91119 + 10.0940i) q^{68} -16.9647i q^{69} +(-0.886619 + 0.399962i) q^{70} +11.8606 q^{71} +(-7.57829 - 2.33983i) q^{72} -16.8777 q^{73} +(10.0843 - 4.54912i) q^{74} +10.9063i q^{75} +(-6.20365 - 5.47673i) q^{76} +3.21615i q^{77} +(-1.40101 - 3.10571i) q^{78} +0.900413 q^{79} +(-2.72986 + 0.341102i) q^{80} -9.54924 q^{81} +(2.80233 + 6.21210i) q^{82} +2.06372i q^{83} +(-3.61214 - 3.18888i) q^{84} -4.63031i q^{85} +(16.3740 - 7.38644i) q^{86} +10.7374 q^{87} +(-2.68362 + 8.69177i) q^{88} +11.8949 q^{89} +(2.48620 - 1.12155i) q^{90} -1.00000i q^{91} +(9.32069 - 10.5578i) q^{92} -19.9759i q^{93} +(-4.59848 - 10.1937i) q^{94} +2.84575 q^{95} +(-7.10109 - 11.6321i) q^{96} -8.07789 q^{97} +(-0.581532 - 1.28912i) q^{98} -9.01850i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 38 q + 8 q^{4} + 14 q^{6} + 38 q^{7} - 6 q^{8} - 46 q^{9} - 4 q^{12} - 8 q^{15} - 4 q^{16} + 20 q^{17} + 4 q^{18} - 24 q^{20} + 10 q^{22} + 12 q^{23} + 10 q^{24} - 50 q^{25} + 8 q^{28} + 4 q^{30} + 16 q^{31}+ \cdots + 82 q^{96}+O(q^{100}) \) 38 * q + 8 * q^4 + 14 * q^6 + 38 * q^7 - 6 * q^8 - 46 * q^9 - 4 * q^12 - 8 * q^15 - 4 * q^16 + 20 * q^17 + 4 * q^18 - 24 * q^20 + 10 * q^22 + 12 * q^23 + 10 * q^24 - 50 * q^25 + 8 * q^28 + 4 * q^30 + 16 * q^31 + 10 * q^32 - 8 * q^33 - 4 * q^34 - 38 * q^36 - 28 * q^38 + 8 * q^39 + 4 * q^40 + 8 * q^41 + 14 * q^42 - 40 * q^44 - 16 * q^46 + 4 * q^48 + 38 * q^49 + 24 * q^50 - 4 * q^52 - 14 * q^54 - 6 * q^56 + 8 * q^57 - 24 * q^58 + 44 * q^60 - 12 * q^62 - 46 * q^63 + 32 * q^64 + 20 * q^65 - 76 * q^66 - 52 * q^68 + 42 * q^72 + 50 * q^74 - 28 * q^76 - 12 * q^79 - 16 * q^80 + 62 * q^81 - 4 * q^84 + 44 * q^86 - 56 * q^87 - 6 * q^88 + 48 * q^90 + 2 * q^92 - 48 * q^94 + 82 * q^96

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