LMFDB - Embedded newform 714.2.bh.b.151.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [714,2,Mod(25,714)] 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("714.25"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(714, base_ring=CyclotomicField(24)) chi = DirichletCharacter(H, H._module([0, 16, 15])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 714 = 2 \cdot 3 \cdot 7 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	714.bh (of order $24$, degree $8$, minimal)

Newform invariants

comment:select newform

sage:traces = [96,0,0,0,8,0,0,0,0,8] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(10)] == traces)

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

Self dual:	no
Analytic conductor:	$5.70131870432$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$12$ over $\Q(\zeta_{24})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{24}]$

Embedding invariants

Embedding label			151.2
Character	$\chi$	$=$	714.151
Dual form			714.2.bh.b.331.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.258819 - 0.965926i) q^{2} +(-0.991445 - 0.130526i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(-0.652971 - 0.501042i) q^{5} +(-0.382683 + 0.923880i) q^{6} +(2.38359 + 1.14825i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(0.965926 + 0.258819i) q^{9} +(-0.652971 + 0.501042i) q^{10} +(0.317254 + 0.413454i) q^{11} +(0.793353 + 0.608761i) q^{12} +5.83540i q^{13} +(1.72605 - 2.00518i) q^{14} +(0.581986 + 0.581986i) q^{15} +(0.500000 + 0.866025i) q^{16} +(3.66667 - 1.88561i) q^{17} +(0.500000 - 0.866025i) q^{18} +(-0.584289 + 2.18060i) q^{19} +(0.314968 + 0.760401i) q^{20} +(-2.21332 - 1.44955i) q^{21} +(0.481477 - 0.199434i) q^{22} +(3.98042 - 0.524033i) q^{23} +(0.793353 - 0.608761i) q^{24} +(-1.11877 - 4.17530i) q^{25} +(5.63657 + 1.51031i) q^{26} +(-0.923880 - 0.382683i) q^{27} +(-1.49012 - 2.18621i) q^{28} +(0.134450 - 0.0556910i) q^{29} +(0.712784 - 0.411526i) q^{30} +(4.76875 + 0.627818i) q^{31} +(0.965926 - 0.258819i) q^{32} +(-0.260573 - 0.451326i) q^{33} +(-0.872358 - 4.02976i) q^{34} +(-0.981092 - 1.94406i) q^{35} +(-0.707107 - 0.707107i) q^{36} +(0.421853 - 0.549770i) q^{37} +(1.95507 + 1.12876i) q^{38} +(0.761673 - 5.78548i) q^{39} +(0.816011 - 0.107430i) q^{40} +(4.13388 + 1.71231i) q^{41} +(-1.97301 + 1.76273i) q^{42} +(2.30375 - 2.30375i) q^{43} +(-0.0680233 - 0.516688i) q^{44} +(-0.501042 - 0.652971i) q^{45} +(0.524033 - 3.98042i) q^{46} +(4.54751 - 2.62551i) q^{47} +(-0.382683 - 0.923880i) q^{48} +(4.36302 + 5.47394i) q^{49} -4.32259 q^{50} +(-3.88142 + 1.39088i) q^{51} +(2.91770 - 5.05361i) q^{52} +(2.88190 - 0.772204i) q^{53} +(-0.608761 + 0.793353i) q^{54} -0.428931i q^{55} +(-2.49739 + 0.873515i) q^{56} +(0.863915 - 2.08568i) q^{57} +(-0.0189952 - 0.144283i) q^{58} +(-2.35567 - 8.79150i) q^{59} +(-0.213022 - 0.795007i) q^{60} +(1.91085 + 14.5144i) q^{61} +(1.84067 - 4.44377i) q^{62} +(2.00518 + 1.72605i) q^{63} -1.00000i q^{64} +(2.92378 - 3.81035i) q^{65} +(-0.503389 + 0.134883i) q^{66} +(0.901540 - 1.56151i) q^{67} +(-4.11824 - 0.200347i) q^{68} -4.01477 q^{69} +(-2.13174 + 0.444503i) q^{70} +(-0.822380 - 1.98540i) q^{71} +(-0.866025 + 0.500000i) q^{72} +(0.320424 - 2.43386i) q^{73} +(-0.421853 - 0.549770i) q^{74} +(0.564211 + 4.28560i) q^{75} +(1.59631 - 1.59631i) q^{76} +(0.281454 + 1.34979i) q^{77} +(-5.39121 - 2.23311i) q^{78} +(-3.62697 + 0.477500i) q^{79} +(0.107430 - 0.816011i) q^{80} +(0.866025 + 0.500000i) q^{81} +(2.72389 - 3.54984i) q^{82} +(3.72085 + 3.72085i) q^{83} +(1.19202 + 2.36201i) q^{84} +(-3.33900 - 0.605906i) q^{85} +(-1.62900 - 2.82151i) q^{86} +(-0.140569 + 0.0376653i) q^{87} +(-0.516688 - 0.0680233i) q^{88} +(-2.79672 + 1.61469i) q^{89} +(-0.760401 + 0.314968i) q^{90} +(-6.70053 + 13.9092i) q^{91} +(-3.70917 - 1.53639i) q^{92} +(-4.64601 - 1.24489i) q^{93} +(-1.35906 - 5.07209i) q^{94} +(1.47409 - 1.13111i) q^{95} +(-0.991445 + 0.130526i) q^{96} +(-13.9878 + 5.79395i) q^{97} +(6.41666 - 2.79759i) q^{98} +(0.199434 + 0.481477i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q + 8 q^{5} + 8 q^{10} + 16 q^{14} + 16 q^{15} + 48 q^{16} + 8 q^{17} + 48 q^{18} - 8 q^{19} + 16 q^{22} + 24 q^{25} + 32 q^{28} - 32 q^{29} - 16 q^{33} - 48 q^{37} - 16 q^{39} + 128 q^{41} + 16 q^{42}+ \cdots + 160 q^{97}+O(q^{100}) $ 96 * q + 8 * q^5 + 8 * q^10 + 16 * q^14 + 16 * q^15 + 48 * q^16 + 8 * q^17 + 48 * q^18 - 8 * q^19 + 16 * q^22 + 24 * q^25 + 32 * q^28 - 32 * q^29 - 16 * q^33 - 48 * q^37 - 16 * q^39 + 128 * q^41 + 16 * q^42 + 48 * q^43 - 8 * q^44 - 8 * q^46 - 112 * q^49 + 64 * q^50 - 16 * q^52 - 40 * q^53 + 16 * q^57 + 16 * q^58 - 24 * q^59 + 8 * q^60 - 56 * q^70 + 24 * q^73 + 48 * q^74 - 16 * q^76 + 16 * q^77 + 32 * q^78 - 56 * q^79 - 8 * q^80 - 80 * q^83 + 80 * q^85 + 16 * q^86 - 24 * q^87 + 16 * q^90 - 40 * q^91 + 16 * q^92 - 8 * q^93 - 8 * q^94 + 80 * q^95 + 160 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/714\mathbb{Z}\right)^\times$.

$n$	$239$	$409$	$547$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{3}{8}\right)$

Coefficient data

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

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

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

$2$	0.258819	−	0.965926i	0.183013	−	0.683013i
$2$	0.258819	−	0.965926i	0.183013	−	0.683013i
$3$	−0.991445	−	0.130526i	−0.572411	−	0.0753593i
$3$	−0.991445	−	0.130526i	−0.572411	−	0.0753593i
$4$	−0.866025	−	0.500000i	−0.433013	−	0.250000i
$5$	−0.652971	−	0.501042i	−0.292018	−	0.224073i	0.452354	−	0.891838i	$-0.350584\pi$
$5$	−0.652971	−	0.501042i	−0.292018	−	0.224073i	−0.744372	+	0.667765i	$0.767251\pi$
$6$	−0.382683	+	0.923880i	−0.156230	+	0.377172i
$7$	2.38359	+	1.14825i	0.900913	+	0.434000i
$7$	2.38359	+	1.14825i	0.900913	+	0.434000i
$8$	−0.707107	+	0.707107i	−0.250000	+	0.250000i
$9$	0.965926	+	0.258819i	0.321975	+	0.0862730i
$10$	−0.652971	+	0.501042i	−0.206488	+	0.158444i
$11$	0.317254	+	0.413454i	0.0956557	+	0.124661i	0.838729	−	0.544549i	$-0.183299\pi$
$11$	0.317254	+	0.413454i	0.0956557	+	0.124661i	−0.743073	+	0.669210i	$0.766633\pi$
$12$	0.793353	+	0.608761i	0.229021	+	0.175734i
$13$			5.83540i			1.61845i	0.587499	+	0.809225i	$0.300113\pi$
$13$			5.83540i			1.61845i	−0.587499	+	0.809225i	$0.699887\pi$
$14$	1.72605	−	2.00518i	0.461306	−	0.535908i
$15$	0.581986	+	0.581986i	0.150268	+	0.150268i
$16$	0.500000	+	0.866025i	0.125000	+	0.216506i
$17$	3.66667	−	1.88561i	0.889298	−	0.457328i
$17$	3.66667	−	1.88561i	0.889298	−	0.457328i
$18$	0.500000	−	0.866025i	0.117851	−	0.204124i
$19$	−0.584289	+	2.18060i	−0.134045	+	0.500263i	0.865955	+	0.500122i	$0.166712\pi$
$19$	−0.584289	+	2.18060i	−0.134045	+	0.500263i	−1.00000		0.000140942i	$0.999955\pi$
$20$	0.314968	+	0.760401i	0.0704291	+	0.170031i
$21$	−2.21332	−	1.44955i	−0.482987	−	0.316318i
$22$	0.481477	−	0.199434i	0.102651	−	0.0425195i
$23$	3.98042	−	0.524033i	0.829976	−	0.109268i	0.296446	−	0.955050i	$-0.404199\pi$
$23$	3.98042	−	0.524033i	0.829976	−	0.109268i	0.533530	+	0.845781i	$0.320865\pi$
$24$	0.793353	−	0.608761i	0.161943	−	0.124263i
$25$	−1.11877	−	4.17530i	−0.223753	−	0.835059i
$26$	5.63657	+	1.51031i	1.10542	+	0.296197i
$27$	−0.923880	−	0.382683i	−0.177801	−	0.0736475i
$28$	−1.49012	−	2.18621i	−0.281607	−	0.413156i
$29$	0.134450	−	0.0556910i	0.0249667	−	0.0103416i	−0.370165	−	0.928966i	$-0.620699\pi$
$29$	0.134450	−	0.0556910i	0.0249667	−	0.0103416i	0.395132	+	0.918624i	$0.370699\pi$
$30$	0.712784	−	0.411526i	0.130136	−	0.0751340i
$31$	4.76875	+	0.627818i	0.856494	+	0.112760i	0.545969	−	0.837806i	$-0.316162\pi$
$31$	4.76875	+	0.627818i	0.856494	+	0.112760i	0.310525	+	0.950565i	$0.399495\pi$
$32$	0.965926	−	0.258819i	0.170753	−	0.0457532i
$33$	−0.260573	−	0.451326i	−0.0453600	−	0.0785658i
$34$	−0.872358	−	4.02976i	−0.149608	−	0.691099i
$35$	−0.981092	−	1.94406i	−0.165835	−	0.328606i
$36$	−0.707107	−	0.707107i	−0.117851	−	0.117851i
$37$	0.421853	−	0.549770i	0.0693523	−	0.0903816i	−0.757389	−	0.652964i	$-0.773525\pi$
$37$	0.421853	−	0.549770i	0.0693523	−	0.0903816i	0.826741	+	0.562582i	$0.190192\pi$
$38$	1.95507	+	1.12876i	0.317154	+	0.183109i
$39$	0.761673	−	5.78548i	0.121965	−	0.926418i
$40$	0.816011	−	0.107430i	0.129023	−	0.0169862i
$41$	4.13388	+	1.71231i	0.645603	+	0.267418i	0.681366	−	0.731943i	$-0.261386\pi$
$41$	4.13388	+	1.71231i	0.645603	+	0.267418i	−0.0357631	+	0.999360i	$0.511386\pi$
$42$	−1.97301	+	1.76273i	−0.304442	+	0.271996i
$43$	2.30375	−	2.30375i	0.351319	−	0.351319i	−0.509281	−	0.860600i	$-0.670089\pi$
$43$	2.30375	−	2.30375i	0.351319	−	0.351319i	0.860600	+	0.509281i	$0.170089\pi$
$44$	−0.0680233	−	0.516688i	−0.0102549	−	0.0778937i
$45$	−0.501042	−	0.652971i	−0.0746910	−	0.0973392i
$46$	0.524033	−	3.98042i	0.0772644	−	0.586882i
$47$	4.54751	−	2.62551i	0.663322	−	0.382969i	−0.130219	−	0.991485i	$-0.541568\pi$
$47$	4.54751	−	2.62551i	0.663322	−	0.382969i	0.793542	+	0.608516i	$0.208235\pi$
$48$	−0.382683	−	0.923880i	−0.0552356	−	0.133351i
$49$	4.36302	+	5.47394i	0.623289	+	0.781992i
$50$	−4.32259			−0.611306
$51$	−3.88142	+	1.39088i	−0.543508	+	0.194763i
$52$	2.91770	−	5.05361i	0.404612	−	0.700809i
$53$	2.88190	−	0.772204i	0.395860	−	0.106070i	−0.0553970	−	0.998464i	$-0.517642\pi$
$53$	2.88190	−	0.772204i	0.395860	−	0.106070i	0.451257	+	0.892394i	$0.350976\pi$
$54$	−0.608761	+	0.793353i	−0.0828419	+	0.107962i
$55$		−	0.428931i		−	0.0578371i
$56$	−2.49739	+	0.873515i	−0.333728	+	0.116728i
$57$	0.863915	−	2.08568i	0.114428	−	0.276254i
$58$	−0.0189952	−	0.144283i	−0.00249419	−	0.0189452i
$59$	−2.35567	−	8.79150i	−0.306683	−	1.14456i	−0.931487	−	0.363774i	$-0.881488\pi$
$59$	−2.35567	−	8.79150i	−0.306683	−	1.14456i	0.624805	−	0.780781i	$-0.285179\pi$
$60$	−0.213022	−	0.795007i	−0.0275010	−	0.102635i
$61$	1.91085	+	14.5144i	0.244660	+	1.85837i	0.468124	+	0.883663i	$0.344930\pi$
$61$	1.91085	+	14.5144i	0.244660	+	1.85837i	−0.223465	+	0.974712i	$0.571737\pi$
$62$	1.84067	−	4.44377i	0.233765	−	0.564360i
$63$	2.00518	+	1.72605i	0.252629	+	0.217462i
$64$		−	1.00000i		−	0.125000i
$65$	2.92378	−	3.81035i	0.362651	−	0.472616i
$66$	−0.503389	+	0.134883i	−0.0619629	+	0.0166029i
$67$	0.901540	−	1.56151i	0.110141	−	0.190769i	−0.805686	−	0.592343i	$-0.798203\pi$
$67$	0.901540	−	1.56151i	0.110141	−	0.190769i	0.915827	+	0.401573i	$0.131537\pi$
$68$	−4.11824	−	0.200347i	−0.499409	−	0.0242956i
$69$	−4.01477			−0.483322
$70$	−2.13174	+	0.444503i	−0.254792	+	0.0531283i
$71$	−0.822380	−	1.98540i	−0.0975985	−	0.235624i	0.867538	−	0.497371i	$-0.165701\pi$
$71$	−0.822380	−	1.98540i	−0.0975985	−	0.235624i	−0.965136	+	0.261747i	$0.915701\pi$
$72$	−0.866025	+	0.500000i	−0.102062	+	0.0589256i
$73$	0.320424	−	2.43386i	0.0375028	−	0.284862i	−0.962409	−	0.271603i	$-0.912446\pi$
$73$	0.320424	−	2.43386i	0.0375028	−	0.284862i	0.999912	−	0.0132588i	$-0.00422052\pi$
$74$	−0.421853	−	0.549770i	−0.0490395	−	0.0639095i
$75$	0.564211	+	4.28560i	0.0651494	+	0.494859i
$76$	1.59631	−	1.59631i	0.183109	−	0.183109i
$77$	0.281454	+	1.34979i	0.0320747	+	0.153823i
$78$	−5.39121	−	2.23311i	−0.610434	−	0.252850i
$79$	−3.62697	+	0.477500i	−0.408066	+	0.0537230i	−0.331766	−	0.943362i	$-0.607644\pi$
$79$	−3.62697	+	0.477500i	−0.408066	+	0.0537230i	−0.0763009	+	0.997085i	$0.524311\pi$
$80$	0.107430	−	0.816011i	0.0120110	−	0.0912328i
$81$	0.866025	+	0.500000i	0.0962250	+	0.0555556i
$82$	2.72389	−	3.54984i	0.300803	−	0.392014i
$83$	3.72085	+	3.72085i	0.408416	+	0.408416i	0.881186	−	0.472770i	$-0.156746\pi$
$83$	3.72085	+	3.72085i	0.408416	+	0.408416i	−0.472770	+	0.881186i	$0.656746\pi$
$84$	1.19202	+	2.36201i	0.130060	+	0.257717i
$85$	−3.33900	−	0.605906i	−0.362166	−	0.0657198i
$86$	−1.62900	−	2.82151i	−0.175659	−	0.304251i
$87$	−0.140569	+	0.0376653i	−0.0150706	+	0.00403815i
$88$	−0.516688	−	0.0680233i	−0.0550792	−	0.00725131i
$89$	−2.79672	+	1.61469i	−0.296452	+	0.171157i	−0.640848	−	0.767668i	$-0.721417\pi$
$89$	−2.79672	+	1.61469i	−0.296452	+	0.171157i	0.344396	+	0.938825i	$0.388084\pi$
$90$	−0.760401	+	0.314968i	−0.0801533	+	0.0332006i
$91$	−6.70053	+	13.9092i	−0.702406	+	1.45808i
$92$	−3.70917	−	1.53639i	−0.386707	−	0.160179i
$93$	−4.64601	−	1.24489i	−0.481769	−	0.129090i
$94$	−1.35906	−	5.07209i	−0.140176	−	0.523146i
$95$	1.47409	−	1.13111i	0.151239	−	0.116050i
$96$	−0.991445	+	0.130526i	−0.101189	+	0.0133218i
$97$	−13.9878	+	5.79395i	−1.42025	+	0.588286i	−0.954923	−	0.296854i	$-0.904063\pi$
$97$	−13.9878	+	5.79395i	−1.42025	+	0.588286i	−0.465325	+	0.885140i	$0.654063\pi$
$98$	6.41666	−	2.79759i	0.648180	−	0.282600i
$99$	0.199434	+	0.481477i	0.0200439	+	0.0483903i
$100$	−1.11877	+	4.17530i	−0.111877	+	0.417530i
$101$	−2.26806	+	3.92839i	−0.225680	+	0.390890i	−0.956523	−	0.291656i	$-0.905794\pi$
$101$	−2.26806	+	3.92839i	−0.225680	+	0.390890i	0.730843	+	0.682546i	$0.239127\pi$
$102$	0.338905	+	4.10915i	0.0335566	+	0.406867i
$103$	5.79872	+	10.0437i	0.571364	+	0.989632i	0.996426	+	0.0844679i	$0.0269190\pi$
$103$	5.79872	+	10.0437i	0.571364	+	0.989632i	−0.425062	+	0.905164i	$0.639748\pi$
$104$	−4.12625	−	4.12625i	−0.404612	−	0.404612i
$105$	0.718949	+	2.05548i	0.0701622	+	0.200595i
$106$		−	2.98357i		−	0.289790i
$107$	−8.24956	−	6.33011i	−0.797515	−	0.611955i	0.127520	−	0.991836i	$-0.459298\pi$
$107$	−8.24956	−	6.33011i	−0.797515	−	0.611955i	−0.925035	+	0.379881i	$0.875965\pi$
$108$	0.608761	+	0.793353i	0.0585781	+	0.0763405i
$109$	−9.08610	+	6.97201i	−0.870290	+	0.667797i	−0.944166	−	0.329470i	$-0.893130\pi$
$109$	−9.08610	+	6.97201i	−0.870290	+	0.667797i	0.0738758	+	0.997267i	$0.476463\pi$
$110$	−0.414316	−	0.111016i	−0.0395034	−	0.0105849i
$111$	−0.490004	+	0.490004i	−0.0465091	+	0.0465091i
$112$	0.197378	+	2.63838i	0.0186505	+	0.249303i
$113$	−3.38848	+	8.18051i	−0.318761	+	0.769558i	0.680559	+	0.732693i	$0.261737\pi$
$113$	−3.38848	+	8.18051i	−0.318761	+	0.769558i	−0.999320	+	0.0368647i	$0.988263\pi$
$114$	−1.79101	−	1.37429i	−0.167743	−	0.128714i
$115$	−2.86167	−	1.65218i	−0.266852	−	0.154067i
$116$	−0.144283	−	0.0189952i	−0.0133963	−	0.00176366i
$117$	−1.51031	+	5.63657i	−0.139629	+	0.521101i
$118$	−9.10163			−0.837873
$119$	10.9050	−	0.284259i	0.999660	−	0.0260580i
$120$	−0.823052			−0.0751340
$121$	2.77672	−	10.3628i	0.252429	−	0.942077i
$122$	14.5144	+	1.91085i	1.31407	+	0.173001i
$123$	−3.87501	−	2.23724i	−0.349398	−	0.201725i
$124$	−3.81595	−	2.92808i	−0.342683	−	0.262950i
$125$	−2.93632	+	7.08890i	−0.262632	+	0.634051i
$126$	2.18621	−	1.49012i	0.194763	−	0.132751i
$127$	6.12431	−	6.12431i	0.543444	−	0.543444i	−0.381093	−	0.924537i	$-0.624452\pi$
$127$	6.12431	−	6.12431i	0.543444	−	0.543444i	0.924537	+	0.381093i	$0.124452\pi$
$128$	−0.965926	−	0.258819i	−0.0853766	−	0.0228766i
$129$	−2.58474	+	1.98334i	−0.227574	+	0.174624i
$130$	−2.92378	−	3.81035i	−0.256433	−	0.334190i
$131$	13.9919	+	10.7364i	1.22248	+	0.938041i	0.999325	−	0.0367420i	$-0.0116980\pi$
$131$	13.9919	+	10.7364i	1.22248	+	0.938041i	0.223154	+	0.974783i	$0.428365\pi$
$132$			0.521147i			0.0453600i
$133$	−3.89659	+	4.52674i	−0.337877	+	0.392518i
$134$	−1.27497	−	1.27497i	−0.110141	−	0.110141i
$135$	0.411526	+	0.712784i	0.0354185	+	0.0613467i
$136$	−1.25940	+	3.92606i	−0.107992	+	0.336657i
$137$	−3.84637	+	6.66211i	−0.328617	+	0.569182i	−0.982238	−	0.187641i	$-0.939916\pi$
$137$	−3.84637	+	6.66211i	−0.328617	+	0.569182i	0.653620	+	0.756823i	$0.273249\pi$
$138$	−1.03910	+	3.87797i	−0.0884540	+	0.330115i
$139$	−3.93002	−	9.48790i	−0.333340	−	0.804753i	−0.998323	−	0.0578945i	$-0.981561\pi$
$139$	−3.93002	−	9.48790i	−0.333340	−	0.804753i	0.664983	−	0.746858i	$-0.268439\pi$
$140$	−0.122378	+	2.17415i	−0.0103428	+	0.183749i
$141$	−4.85130	+	2.00947i	−0.408553	+	0.169228i
$142$	−2.13060	+	0.280498i	−0.178796	+	0.0235389i
$143$	−2.41267	+	1.85131i	−0.201757	+	0.154814i
$144$	0.258819	+	0.965926i	0.0215683	+	0.0804938i
$145$	−0.115696	−	0.0310005i	−0.00960799	−	0.00257445i
$146$	−2.26800	−	0.939436i	−0.187701	−	0.0777483i
$147$	−3.61120	−	5.99660i	−0.297847	−	0.494591i
$148$	−0.640221	+	0.265188i	−0.0526258	+	0.0217983i
$149$	19.9355	−	11.5098i	1.63318	−	0.942917i	0.650076	−	0.759869i	$-0.274737\pi$
$149$	19.9355	−	11.5098i	1.63318	−	0.942917i	0.983104	−	0.183048i	$-0.0585964\pi$
$150$	4.28560	+	0.564211i	0.349918	+	0.0460676i
$151$	−6.71970	+	1.80054i	−0.546841	+	0.146526i	−0.521654	−	0.853157i	$-0.674685\pi$
$151$	−6.71970	+	1.80054i	−0.546841	+	0.146526i	−0.0251871	+	0.999683i	$0.508018\pi$
$152$	−1.12876	−	1.95507i	−0.0915545	−	0.158577i
$153$	4.02976	−	0.872358i	0.325787	−	0.0705259i
$154$	1.37665	+	0.0774884i	0.110933	+	0.00624419i
$155$	−2.79930	−	2.79930i	−0.224845	−	0.224845i
$156$	−3.55237	+	4.62954i	−0.284417	+	0.370660i
$157$	3.66335	+	2.11504i	0.292367	+	0.168798i	0.639009	−	0.769199i	$-0.279345\pi$
$157$	3.66335	+	2.11504i	0.292367	+	0.168798i	−0.346642	+	0.937998i	$0.612678\pi$
$158$	−0.477500	+	3.62697i	−0.0379879	+	0.288547i
$159$	−2.95804	+	0.389434i	−0.234588	+	0.0308841i
$160$	−0.760401	−	0.314968i	−0.0601150	−	0.0249004i
$161$	10.0894	+	3.32146i	0.795159	+	0.261768i
$162$	0.707107	−	0.707107i	0.0555556	−	0.0555556i
$163$	0.438871	+	3.33355i	0.0343750	+	0.261104i	0.999999	+	0.00116243i	$0.000370014\pi$
$163$	0.438871	+	3.33355i	0.0343750	+	0.261104i	−0.965624	+	0.259942i	$0.916297\pi$
$164$	−2.72389	−	3.54984i	−0.212700	−	0.277196i
$165$	−0.0559867	+	0.425262i	−0.00435856	+	0.0331066i
$166$	4.55709	−	2.63104i	0.353699	−	0.204208i
$167$	−8.21171	−	19.8248i	−0.635441	−	1.53409i	−0.832691	−	0.553737i	$-0.813201\pi$
$167$	−8.21171	−	19.8248i	−0.635441	−	1.53409i	0.197250	−	0.980353i	$-0.436799\pi$
$168$	2.59004	−	0.540067i	0.199826	−	0.0416671i
$169$	−21.0519			−1.61938
$170$	−1.44946	+	3.06841i	−0.111168	+	0.235336i
$171$	−1.12876	+	1.95507i	−0.0863184	+	0.149508i
$172$	−3.14698	+	0.843231i	−0.239955	+	0.0642958i
$173$	−8.93614	+	11.6458i	−0.679402	+	0.885414i	−0.998047	−	0.0624597i	$-0.980105\pi$
$173$	−8.93614	+	11.6458i	−0.679402	+	0.885414i	0.318645	+	0.947874i	$0.396772\pi$
$174$			0.145528i			0.0110324i
$175$	2.12762	−	11.2368i	0.160833	−	0.849425i
$176$	−0.199434	+	0.481477i	−0.0150329	+	0.0362927i
$177$	1.18800	+	9.02376i	0.0892956	+	0.678267i
$178$	0.835825	+	3.11934i	0.0626477	+	0.233804i
$179$	−4.13618	−	15.4364i	−0.309153	−	1.15377i	−0.929312	−	0.369297i	$-0.879599\pi$
$179$	−4.13618	−	15.4364i	−0.309153	−	1.15377i	0.620159	−	0.784476i	$-0.287068\pi$
$180$	0.107430	+	0.816011i	0.00800735	+	0.0608219i
$181$	−4.66144	+	11.2537i	−0.346482	+	0.836482i	0.650548	+	0.759466i	$0.274539\pi$
$181$	−4.66144	+	11.2537i	−0.346482	+	0.836482i	−0.997030	+	0.0770167i	$0.975461\pi$
$182$	11.7010	+	10.0722i	0.867339	+	0.746600i
$183$		−	14.6396i		−	1.08219i
$184$	−2.44404	+	3.18513i	−0.180177	+	0.234811i
$185$	−0.550916	+	0.147618i	−0.0405042	+	0.0108531i
$186$	−2.40495	+	4.16550i	−0.176340	+	0.305429i
$187$	1.94288	+	0.917779i	0.142077	+	0.0671147i
$188$	−5.25101			−0.382969
$189$	−1.76273	−	1.97301i	−0.128220	−	0.143515i
$190$	−0.711047	−	1.71662i	−0.0515848	−	0.124537i
$191$	16.7556	−	9.67386i	1.21239	−	0.699976i	0.249114	−	0.968474i	$-0.419861\pi$
$191$	16.7556	−	9.67386i	1.21239	−	0.699976i	0.963280	+	0.268498i	$0.0865274\pi$
$192$	−0.130526	+	0.991445i	−0.00941992	+	0.0715514i
$193$	2.85978	+	3.72693i	0.205851	+	0.268271i	0.884857	−	0.465862i	$-0.154256\pi$
$193$	2.85978	+	3.72693i	0.205851	+	0.268271i	−0.679006	+	0.734133i	$0.737589\pi$
$194$	1.97621	+	15.0108i	0.141883	+	1.07771i
$195$	−3.39612	+	3.39612i	−0.243201	+	0.243201i
$196$	−1.04152	−	6.92208i	−0.0743940	−	0.494435i
$197$	−9.36208	−	3.87790i	−0.667021	−	0.276289i	0.0233688	−	0.999727i	$-0.492561\pi$
$197$	−9.36208	−	3.87790i	−0.667021	−	0.276289i	−0.690389	+	0.723438i	$0.742561\pi$
$198$	0.516688	−	0.0680233i	0.0367194	−	0.00483421i
$199$	−1.91803	+	14.5689i	−0.135966	+	1.03276i	0.778370	+	0.627806i	$0.216047\pi$
$199$	−1.91803	+	14.5689i	−0.135966	+	1.03276i	−0.914336	+	0.404957i	$0.867287\pi$
$200$	3.74347	+	2.16129i	0.264703	+	0.152826i
$201$	−1.09765	+	1.43048i	−0.0774219	+	0.100898i
$202$	3.20752	+	3.20752i	0.225680	+	0.225680i
$203$	0.384421	+	0.0216382i	0.0269811	+	0.00151871i
$204$	4.05685	+	0.736170i	0.284036	+	0.0515422i
$205$	−1.84136	−	3.18934i	−0.128606	−	0.222753i
$206$	11.2023	−	3.00164i	0.780498	−	0.209134i
$207$	3.98042	+	0.524033i	0.276659	+	0.0364228i
$208$	−5.05361	+	2.91770i	−0.350405	+	0.202306i
$209$	−1.08694	+	0.450227i	−0.0751854	+	0.0311428i
$210$	2.17152	−	0.162452i	0.149849	−	0.0112103i
$211$	−1.98321	−	0.821472i	−0.136530	−	0.0565524i	0.313373	−	0.949630i	$-0.398541\pi$
$211$	−1.98321	−	0.821472i	−0.136530	−	0.0565524i	−0.449902	+	0.893078i	$0.648541\pi$
$212$	−2.88190	−	0.772204i	−0.197930	−	0.0530352i
$213$	0.556197	+	2.07576i	0.0381100	+	0.142229i
$214$	−8.24956	+	6.33011i	−0.563928	+	0.432717i
$215$	−2.65856	+	0.350006i	−0.181312	+	0.0238702i
$216$	0.923880	−	0.382683i	0.0628620	−	0.0260383i
$217$	10.6459	+	6.97221i	0.722689	+	0.473304i
$218$	4.38279	+	10.5810i	0.296840	+	0.716635i
$219$	−0.635366	+	2.37122i	−0.0429340	+	0.160232i
$220$	−0.214466	+	0.371465i	−0.0144593	+	0.0250442i
$221$	11.0033	+	21.3965i	0.740163	+	1.43928i
$222$	0.346485	+	0.600130i	0.0232545	+	0.0402781i
$223$	−7.80662	−	7.80662i	−0.522770	−	0.522770i	0.395637	−	0.918407i	$-0.370524\pi$
$223$	−7.80662	−	7.80662i	−0.522770	−	0.522770i	−0.918407	+	0.395637i	$0.870524\pi$
$224$	2.59956	+	0.492210i	0.173691	+	0.0328872i
$225$		−	4.32259i		−	0.288172i
$226$	7.02477	+	5.39029i	0.467281	+	0.358557i
$227$	−2.47345	−	3.22346i	−0.164168	−	0.213948i	0.704024	−	0.710176i	$-0.251385\pi$
$227$	−2.47345	−	3.22346i	−0.164168	−	0.213948i	−0.868192	+	0.496228i	$0.834718\pi$
$228$	−1.79101	+	1.37429i	−0.118613	+	0.0910146i
$229$	23.0915	+	6.18734i	1.52593	+	0.408871i	0.921688	−	0.387932i	$-0.126810\pi$
$229$	23.0915	+	6.18734i	1.52593	+	0.408871i	0.604239	+	0.796803i	$0.293477\pi$
$230$	−2.33654	+	2.33654i	−0.154067	+	0.154067i
$231$	−0.102863	−	1.37498i	−0.00676788	−	0.0904672i
$232$	−0.0556910	+	0.134450i	−0.00365629	+	0.00882707i
$233$	−10.3565	−	7.94679i	−0.678474	−	0.520611i	0.211064	−	0.977472i	$-0.432307\pi$
$233$	−10.3565	−	7.94679i	−0.678474	−	0.520611i	−0.889538	+	0.456861i	$0.848974\pi$
$234$	5.05361	+	2.91770i	0.330365	+	0.190736i
$235$	−4.28488	−	0.564115i	−0.279515	−	0.0367988i
$236$	−2.35567	+	8.79150i	−0.153341	+	0.572278i
$237$	3.65827			0.237630
$238$	2.54785	−	10.6070i	0.165153	−	0.687550i
$239$	−2.34830			−0.151899			−0.0759495	−	0.997112i	$-0.524199\pi$
$239$	−2.34830			−0.151899			−0.0759495	+	0.997112i	$0.524199\pi$
$240$	−0.213022	+	0.795007i	−0.0137505	+	0.0513175i
$241$	10.2324	+	1.34712i	0.659125	+	0.0867755i	0.452667	−	0.891680i	$-0.350473\pi$
$241$	10.2324	+	1.34712i	0.659125	+	0.0867755i	0.206459	+	0.978455i	$0.433806\pi$
$242$	−9.29107	−	5.36420i	−0.597253	−	0.344824i
$243$	−0.793353	−	0.608761i	−0.0508936	−	0.0390521i
$244$	5.60234	−	13.5252i	0.358653	−	0.865865i
$245$	−0.106249	−	5.76039i	−0.00678803	−	0.368018i
$246$	−3.16393	+	3.16393i	−0.201725	+	0.201725i
$247$	−12.7247	−	3.40956i	−0.809650	−	0.216945i
$248$	−3.81595	+	2.92808i	−0.242313	+	0.185934i
$249$	−3.20335	−	4.17468i	−0.203004	−	0.264560i
$250$	6.08738	+	4.67101i	0.385000	+	0.295421i
$251$			5.09722i			0.321734i	0.986976	+	0.160867i	$0.0514289\pi$
$251$			5.09722i			0.321734i	−0.986976	+	0.160867i	$0.948571\pi$
$252$	−0.873515	−	2.49739i	−0.0550263	−	0.157321i
$253$	1.47947	+	1.47947i	0.0930134	+	0.0930134i
$254$	−4.33054	−	7.50071i	−0.271722	−	0.470637i
$255$	3.23135	+	1.03655i	0.202355	+	0.0649113i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−5.49838	+	20.5202i	−0.342980	+	1.28002i	0.551975	+	0.833861i	$0.313874\pi$
$257$	−5.49838	+	20.5202i	−0.342980	+	1.28002i	−0.894955	+	0.446157i	$0.852792\pi$
$258$	1.24678	+	3.01000i	0.0776212	+	0.187394i
$259$	1.63680	−	0.826032i	0.101706	−	0.0513271i
$260$	−4.43725	+	1.83797i	−0.275186	+	0.113986i
$261$	0.144283	−	0.0189952i	0.00893087	−	0.00117577i
$262$	13.9919	−	10.7364i	0.864423	−	0.663295i
$263$	−6.11122	−	22.8074i	−0.376834	−	1.40636i	−0.850647	−	0.525738i	$-0.823789\pi$
$263$	−6.11122	−	22.8074i	−0.376834	−	1.40636i	0.473813	−	0.880626i	$-0.342877\pi$
$264$	0.503389	+	0.134883i	0.0309815	+	0.00830146i
$265$	−2.26871	−	0.939729i	−0.139366	−	0.0577271i
$266$	3.36398	+	4.93542i	0.206259	+	0.302610i
$267$	2.98356	−	1.23583i	0.182591	−	0.0756316i
$268$	−1.56151	+	0.901540i	−0.0953846	+	0.0550703i
$269$	−17.0313	−	2.24221i	−1.03842	−	0.136710i	−0.408011	−	0.912977i	$-0.633778\pi$
$269$	−17.0313	−	2.24221i	−1.03842	−	0.136710i	−0.630404	+	0.776267i	$0.717111\pi$
$270$	0.795007	−	0.213022i	0.0483826	−	0.0129641i
$271$	−16.0884	−	27.8659i	−0.977301	−	1.69274i	−0.672123	−	0.740440i	$-0.734617\pi$
$271$	−16.0884	−	27.8659i	−0.977301	−	1.69274i	−0.305178	−	0.952295i	$-0.598716\pi$
$272$	3.46632	+	2.23262i	0.210177	+	0.135373i
$273$	8.45872	−	12.9156i	0.511945	−	0.781689i
$274$	5.43959	+	5.43959i	0.328617	+	0.328617i
$275$	1.37136	−	1.78719i	0.0826960	−	0.107772i
$276$	3.47689	+	2.00739i	0.209284	+	0.120830i
$277$	−2.77481	+	21.0768i	−0.166722	+	1.26638i	0.679549	+	0.733630i	$0.262175\pi$
$277$	−2.77481	+	21.0768i	−0.166722	+	1.26638i	−0.846272	+	0.532752i	$0.821158\pi$
$278$	−10.1818	+	1.34045i	−0.610662	+	0.0803951i
$279$	4.44377	+	1.84067i	0.266042	+	0.110198i
$280$	2.06839	+	0.680920i	0.123610	+	0.0406927i
$281$	1.35815	−	1.35815i	0.0810205	−	0.0810205i	−0.665435	−	0.746456i	$-0.731754\pi$
$281$	1.35815	−	1.35815i	0.0810205	−	0.0810205i	0.746456	+	0.665435i	$0.231754\pi$
$282$	0.685394	+	5.20609i	0.0408146	+	0.310018i
$283$	−11.4179	−	14.8801i	−0.678723	−	0.884529i	0.319282	−	0.947660i	$-0.396558\pi$
$283$	−11.4179	−	14.8801i	−0.678723	−	0.884529i	−0.998005	+	0.0631307i	$0.979892\pi$
$284$	−0.280498	+	2.13060i	−0.0166445	+	0.126428i
$285$	−1.60912	+	0.929028i	−0.0953163	+	0.0550309i
$286$	1.16378	+	2.80961i	0.0688157	+	0.166136i
$287$	7.88731	+	8.82819i	0.465573	+	0.521111i
$288$	1.00000			0.0589256
$289$	9.88893	−	13.8278i	0.581702	−	0.813402i
$290$	−0.0598884	+	0.103730i	−0.00351677	+	0.00609122i
$291$	14.6244	−	3.91860i	0.857298	−	0.229712i
$292$	−1.49443	+	1.94757i	−0.0874547	+	0.113973i
$293$		−	6.36234i		−	0.371692i	−0.982579	−	0.185846i	$-0.940497\pi$
$293$		−	6.36234i		−	0.371692i	0.982579	−	0.185846i	$-0.0595025\pi$
$294$	−6.72692	+	1.93612i	−0.392322	+	0.112917i
$295$	−2.86673	+	6.92089i	−0.166907	+	0.402950i
$296$	0.0904507	+	0.687042i	0.00525734	+	0.0399335i
$297$	−0.134883	−	0.503389i	−0.00782669	−	0.0292096i
$298$	−5.95789	−	22.2352i	−0.345132	−	1.28805i
$299$	3.05794	+	23.2274i	0.176845	+	1.34327i
$300$	1.65418	−	3.99355i	0.0955042	−	0.230568i
$301$	8.13650	−	2.84591i	0.468980	−	0.164035i
$302$			6.95674i			0.400315i
$303$	2.76141	−	3.59875i	0.158639	−	0.206743i
$304$	−2.18060	+	0.584289i	−0.125066	+	0.0335113i
$305$	6.02458	−	10.4349i	0.344967	−	0.597500i
$306$	0.200347	−	4.11824i	0.0114530	−	0.235424i
$307$	20.7435			1.18390			0.591948	−	0.805976i	$-0.298359\pi$
$307$	20.7435			1.18390			0.591948	+	0.805976i	$0.298359\pi$
$308$	0.431150	−	1.30968i	0.0245671	−	0.0746261i
$309$	−4.43814	−	10.7146i	−0.252477	−	0.609534i
$310$	−3.42842	+	1.97940i	−0.194721	+	0.112422i
$311$	3.76398	−	28.5903i	0.213436	−	1.62121i	−0.464146	−	0.885759i	$-0.653639\pi$
$311$	3.76398	−	28.5903i	0.213436	−	1.62121i	0.677582	−	0.735448i	$-0.263028\pi$
$312$	3.55237	+	4.62954i	0.201113	+	0.262096i
$313$	−3.39207	−	25.7653i	−0.191731	−	1.45634i	−0.768718	−	0.639588i	$-0.779105\pi$
$313$	−3.39207	−	25.7653i	−0.191731	−	1.45634i	0.576987	−	0.816753i	$-0.304228\pi$
$314$	2.99111	−	2.99111i	0.168798	−	0.168798i
$315$	−0.444503	−	2.13174i	−0.0250449	−	0.120110i
$316$	3.37980	+	1.39996i	0.190129	+	0.0787539i
$317$	−17.7245	+	2.33348i	−0.995509	+	0.131061i	−0.610639	−	0.791909i	$-0.709087\pi$
$317$	−17.7245	+	2.33348i	−0.995509	+	0.131061i	−0.384871	+	0.922971i	$0.625754\pi$
$318$	−0.389434	+	2.95804i	−0.0218384	+	0.165879i
$319$	0.0656805	+	0.0379206i	0.00367740	+	0.00212315i
$320$	−0.501042	+	0.652971i	−0.0280091	+	0.0365022i
$321$	7.35274	+	7.35274i	0.410390	+	0.410390i
$322$	5.81962	−	8.88599i	0.324315	−	0.495197i
$323$	1.96936	+	9.09727i	0.109578	+	0.506185i
$324$	−0.500000	−	0.866025i	−0.0277778	−	0.0481125i
$325$	24.3645	−	6.52846i	1.35150	−	0.362134i
$326$	3.33355	+	0.438871i	0.184629	+	0.0243068i
$327$	9.91839	−	5.72639i	0.548488	−	0.316670i
$328$	−4.13388	+	1.71231i	−0.228255	+	0.0945464i
$329$	13.8542	−	1.03643i	0.763804	−	0.0571404i
$330$	0.396281	+	0.164145i	0.0218145	+	0.00903587i
$331$	−2.90710	−	0.778955i	−0.159789	−	0.0428152i	0.178038	−	0.984024i	$-0.443025\pi$
$331$	−2.90710	−	0.778955i	−0.159789	−	0.0428152i	−0.337826	+	0.941208i	$0.609692\pi$
$332$	−1.36193	−	5.08277i	−0.0747454	−	0.278953i
$333$	0.549770	−	0.421853i	0.0301272	−	0.0231174i
$334$	−21.2747	+	2.80086i	−1.16410	+	0.153256i
$335$	−1.37106	+	0.567913i	−0.0749092	+	0.0310284i
$336$	0.148688	−	2.64157i	0.00811160	−	0.144109i
$337$	−6.91104	−	16.6847i	−0.376468	−	0.908875i	−0.992622	−	0.121249i	$-0.961310\pi$
$337$	−6.91104	−	16.6847i	−0.376468	−	0.908875i	0.616154	−	0.787626i	$-0.288690\pi$
$338$	−5.44864	+	20.3346i	−0.296367	+	1.10606i
$339$	4.42726	−	7.66824i	0.240456	−	0.416482i
$340$	2.58871	+	2.19423i	0.140392	+	0.118999i
$341$	1.25333	+	2.17084i	0.0678718	+	0.117557i
$342$	1.59631	+	1.59631i	0.0863184	+	0.0863184i
$343$	4.11418	+	18.0575i	0.222145	+	0.975014i
$344$			3.25800i			0.175659i
$345$	2.62153	+	2.01157i	0.141138	+	0.108299i
$346$	8.93614	+	11.6458i	0.480410	+	0.626082i
$347$	−6.87189	+	5.27299i	−0.368902	+	0.283069i	−0.776531	−	0.630079i	$-0.783022\pi$
$347$	−6.87189	+	5.27299i	−0.368902	+	0.283069i	0.407629	+	0.913148i	$0.366356\pi$
$348$	0.140569	+	0.0376653i	0.00753528	+	0.00201907i
$349$	−7.48198	+	7.48198i	−0.400501	+	0.400501i	−0.878410	−	0.477909i	$-0.841395\pi$
$349$	−7.48198	+	7.48198i	−0.400501	+	0.400501i	0.477909	+	0.878410i	$0.341395\pi$
$350$	−10.3033	−	4.96343i	−0.550733	−	0.265306i
$351$	2.23311	−	5.39121i	0.119195	−	0.287761i
$352$	0.413454	+	0.317254i	0.0220372	+	0.0169097i
$353$	−16.3512	−	9.44039i	−0.870288	−	0.502461i	−0.00284423	−	0.999996i	$-0.500905\pi$
$353$	−16.3512	−	9.44039i	−0.870288	−	0.502461i	−0.867444	+	0.497535i	$0.834239\pi$
$354$	9.02376	+	1.18800i	0.479607	+	0.0631415i
$355$	−0.457780	+	1.70846i	−0.0242964	+	0.0906755i
$356$	3.22938			0.171157
$357$	−10.8488	−	1.14156i	−0.574180	−	0.0604179i
$358$	−15.9810			−0.844620
$359$	4.89825	−	18.2805i	0.258520	−	0.964809i	−0.707579	−	0.706635i	$-0.750212\pi$
$359$	4.89825	−	18.2805i	0.258520	−	0.964809i	0.966098	−	0.258174i	$-0.0831208\pi$
$360$	0.816011	+	0.107430i	0.0430075	+	0.00566205i
$361$	12.0409	+	6.95180i	0.633730	+	0.365884i
$362$	9.66379	+	7.41528i	0.507917	+	0.389739i
$363$	−4.10558	+	9.91175i	−0.215487	+	0.520232i
$364$	12.7574	−	8.69547i	0.668672	−	0.455767i
$365$	−1.42870	+	1.42870i	−0.0747814	+	0.0747814i
$366$	−14.1408	−	3.78901i	−0.739150	−	0.198055i
$367$	−7.55430	+	5.79662i	−0.394331	+	0.302581i	−0.786828	−	0.617172i	$-0.788278\pi$
$367$	−7.55430	+	5.79662i	−0.394331	+	0.302581i	0.392497	+	0.919753i	$0.371611\pi$
$368$	2.44404	+	3.18513i	0.127404	+	0.166037i
$369$	3.54984	+	2.72389i	0.184797	+	0.141800i
$370$			0.570350i			0.0296511i
$371$	7.75597	+	1.46854i	0.402670	+	0.0762429i
$372$	3.40112	+	3.40112i	0.176340	+	0.176340i
$373$	−16.4708	−	28.5283i	−0.852825	−	1.47714i	−0.878648	−	0.477470i	$-0.841554\pi$
$373$	−16.4708	−	28.5283i	−0.852825	−	1.47714i	0.0258223	−	0.999667i	$-0.491780\pi$
$374$	1.38936	−	1.63914i	0.0718421	−	0.0847578i
$375$	3.83649	−	6.64499i	0.198115	−	0.343146i
$376$	−1.35906	+	5.07209i	−0.0700882	+	0.261573i
$377$	0.324979	+	0.784570i	0.0167373	+	0.0404074i
$378$	−2.36201	+	1.19202i	−0.121489	+	0.0613108i
$379$	24.0340	−	9.95520i	1.23454	−	0.511364i	0.332537	−	0.943090i	$-0.392095\pi$
$379$	24.0340	−	9.95520i	1.23454	−	0.511364i	0.902005	+	0.431726i	$0.142095\pi$
$380$	−1.84216	+	0.242525i	−0.0945008	+	0.0124413i
$381$	−6.87129	+	5.27253i	−0.352027	+	0.270120i
$382$	−5.00756	−	18.6885i	−0.256209	−	0.956185i
$383$	−31.2460	−	8.37234i	−1.59660	−	0.427806i	−0.652583	−	0.757717i	$-0.726315\pi$
$383$	−31.2460	−	8.37234i	−1.59660	−	0.427806i	−0.944012	+	0.329911i	$0.892981\pi$
$384$	0.923880	+	0.382683i	0.0471465	+	0.0195287i
$385$	0.492522	−	1.02240i	0.0251013	−	0.0521062i
$386$	4.34011	−	1.79773i	0.220906	−	0.0915021i
$387$	2.82151	−	1.62900i	0.143425	−	0.0828066i
$388$	15.0108	+	1.97621i	0.762057	+	0.100327i
$389$	−29.4540	+	7.89219i	−1.49338	+	0.400150i	−0.910877	−	0.412679i	$-0.864593\pi$
$389$	−29.4540	+	7.89219i	−1.49338	+	0.400150i	−0.582503	+	0.812829i	$0.697926\pi$
$390$	2.40142	+	4.15938i	0.121601	+	0.210619i
$391$	13.6068	−	9.42699i	0.688124	−	0.476744i
$392$	−6.95578	−	0.785540i	−0.351320	−	0.0396758i
$393$	−12.4708	−	12.4708i	−0.629070	−	0.629070i
$394$	−6.16885	+	8.03940i	−0.310782	+	0.405019i
$395$	2.60756	+	1.50547i	0.131200	+	0.0757486i
$396$	0.0680233	−	0.516688i	0.00341830	−	0.0259646i
$397$	17.4333	−	2.29514i	0.874954	−	0.115190i	0.320345	−	0.947301i	$-0.396201\pi$
$397$	17.4333	−	2.29514i	0.874954	−	0.115190i	0.554609	+	0.832111i	$0.312868\pi$
$398$	13.5761	+	5.62339i	0.680506	+	0.281875i
$399$	4.45411	−	3.97940i	0.222984	−	0.199219i
$400$	3.05653	−	3.05653i	0.152826	−	0.152826i
$401$	3.73586	+	28.3767i	0.186560	+	1.41706i	0.786782	+	0.617231i	$0.211746\pi$
$401$	3.73586	+	28.3767i	0.186560	+	1.41706i	−0.600222	+	0.799833i	$0.704921\pi$
$402$	1.09765	+	1.43048i	0.0547456	+	0.0713458i
$403$	−3.66357	+	27.8276i	−0.182496	+	1.38619i
$404$	3.92839	−	2.26806i	0.195445	−	0.112840i
$405$	−0.314968	−	0.760401i	−0.0156509	−	0.0377846i
$406$	0.120396	−	0.365722i	0.00597518	−	0.0181505i
$407$	0.361139			0.0179010
$408$	1.76108	−	3.72808i	0.0871863	−	0.184568i
$409$	11.0793	−	19.1899i	0.547836	−	0.948880i	−0.450587	−	0.892733i	$-0.648785\pi$
$409$	11.0793	−	19.1899i	0.547836	−	0.948880i	0.998423	−	0.0561469i	$-0.0178815\pi$
$410$	−3.55724	+	0.953160i	−0.175680	+	0.0470732i
$411$	4.68304	−	6.10306i	0.230997	−	0.301042i
$412$		−	11.5974i		−	0.571364i
$413$	4.47991	−	23.6603i	0.220442	−	1.16424i
$414$	1.53639	−	3.70917i	0.0755093	−	0.182296i
$415$	−0.565304	−	4.29391i	−0.0277497	−	0.210780i
$416$	1.51031	+	5.63657i	0.0740492	+	0.276355i
$417$	2.65797	+	9.91970i	0.130162	+	0.485770i
$418$	0.153564	+	1.16643i	0.00751106	+	0.0570521i
$419$	6.47099	−	15.6224i	0.316129	−	0.763202i	−0.683324	−	0.730115i	$-0.739466\pi$
$419$	6.47099	−	15.6224i	0.316129	−	0.763202i	0.999452	−	0.0330867i	$-0.0105337\pi$
$420$	0.405115	−	2.13958i	0.0197676	−	0.104401i
$421$		−	25.3125i		−	1.23366i	−0.787097	−	0.616829i	$-0.788417\pi$
$421$		−	25.3125i		−	1.23366i	0.787097	−	0.616829i	$-0.211583\pi$
$422$	−1.30677	+	1.70302i	−0.0636127	+	0.0829017i
$423$	5.07209	−	1.35906i	0.246613	−	0.0660798i
$424$	−1.49178	+	2.58384i	−0.0724474	+	0.125483i
$425$	−11.9751	−	13.1999i	−0.580880	−	0.640288i
$426$	2.14898			0.104119
$427$	−12.1115	+	36.7905i	−0.586117	+	1.78042i
$428$	3.97927	+	9.60681i	0.192345	+	0.464363i
$429$	2.63367	−	1.52055i	0.127155	−	0.0734129i
$430$	−0.350006	+	2.65856i	−0.0168788	+	0.128207i
$431$	14.7313	+	19.1982i	0.709580	+	0.924743i	0.999478	−	0.0323146i	$-0.0102878\pi$
$431$	14.7313	+	19.1982i	0.709580	+	0.924743i	−0.289897	+	0.957058i	$0.593621\pi$
$432$	−0.130526	−	0.991445i	−0.00627994	−	0.0477009i
$433$	−1.52328	+	1.52328i	−0.0732041	+	0.0732041i	−0.742761	−	0.669557i	$-0.766484\pi$
$433$	−1.52328	+	1.52328i	−0.0732041	+	0.0732041i	0.669557	+	0.742761i	$0.266484\pi$
$434$	9.48999	−	8.47858i	0.455534	−	0.406985i
$435$	0.110659	+	0.0458366i	0.00530571	+	0.00219770i
$436$	11.3548	−	1.49489i	0.543796	−	0.0715921i
$437$	−1.18301	+	8.98588i	−0.0565912	+	0.429853i
$438$	2.12597	+	1.22743i	0.101583	+	0.0586490i
$439$	7.63668	−	9.95231i	0.364479	−	0.474998i	−0.574731	−	0.818343i	$-0.694893\pi$
$439$	7.63668	−	9.95231i	0.364479	−	0.474998i	0.939209	+	0.343345i	$0.111560\pi$
$440$	0.303300	+	0.303300i	0.0144593	+	0.0144593i
$441$	2.79759	+	6.41666i	0.133219	+	0.305555i
$442$	23.5153	−	5.09056i	1.11851	−	0.242133i
$443$	−3.81756	−	6.61221i	−0.181378	−	0.314156i	0.760972	−	0.648785i	$-0.224722\pi$
$443$	−3.81756	−	6.61221i	−0.181378	−	0.314156i	−0.942350	+	0.334629i	$0.891389\pi$
$444$	0.669358	−	0.179354i	0.0317663	−	0.00851176i
$445$	2.63521	+	0.346932i	0.124921	+	0.0164461i
$446$	−9.56112	+	5.52012i	−0.452732	+	0.261385i
$447$	−21.2673	+	8.80920i	−1.00591	+	0.416661i
$448$	1.14825	−	2.38359i	0.0542499	−	0.112614i
$449$	−7.63521	−	3.16261i	−0.360328	−	0.149253i	0.195173	−	0.980769i	$-0.437473\pi$
$449$	−7.63521	−	3.16261i	−0.360328	−	0.149253i	−0.555501	+	0.831516i	$0.687473\pi$
$450$	−4.17530	−	1.11877i	−0.196825	−	0.0527392i
$451$	0.603530	+	2.25240i	0.0284191	+	0.106062i
$452$	7.02477	−	5.39029i	0.330417	−	0.253538i
$453$	6.89723	−	0.908037i	0.324060	−	0.0426633i
$454$	−3.75379	+	1.55487i	−0.176174	+	0.0729738i
$455$	11.3444	−	5.72507i	0.531832	−	0.268395i
$456$	0.863915	+	2.08568i	0.0404565	+	0.0976707i
$457$	−7.90717	+	29.5100i	−0.369882	+	1.38042i	0.490799	+	0.871273i	$0.336705\pi$
$457$	−7.90717	+	29.5100i	−0.369882	+	1.38042i	−0.860681	+	0.509145i	$0.829962\pi$
$458$	11.9530	−	20.7032i	0.558528	−	0.967399i
$459$	−4.10915	+	0.338905i	−0.191799	+	0.0158187i
$460$	1.65218	+	2.86167i	0.0770335	+	0.133426i
$461$	2.53233	+	2.53233i	0.117942	+	0.117942i	0.763615	−	0.645672i	$-0.223423\pi$
$461$	2.53233	+	2.53233i	0.117942	+	0.117942i	−0.645672	+	0.763615i	$0.723423\pi$
$462$	−1.35475	−	0.256514i	−0.0630289	−	0.0119341i
$463$			21.0221i			0.976979i	0.872570	+	0.488489i	$0.162452\pi$
$463$			21.0221i			0.976979i	−0.872570	+	0.488489i	$0.837548\pi$
$464$	0.115455	+	0.0885916i	0.00535986	+	0.00411276i
$465$	2.40997	+	3.14073i	0.111759	+	0.145648i
$466$	−10.3565	+	7.94679i	−0.479754	+	0.368128i
$467$	−25.7455	−	6.89849i	−1.19136	−	0.319224i	−0.391937	−	0.919992i	$-0.628195\pi$
$467$	−25.7455	−	6.89849i	−1.19136	−	0.319224i	−0.799423	+	0.600768i	$0.794861\pi$
$468$	4.12625	−	4.12625i	0.190736	−	0.190736i
$469$	3.94192	−	2.68681i	0.182021	−	0.124065i
$470$	−1.65390	+	3.99287i	−0.0762888	+	0.184178i
$471$	−3.35594	−	2.57511i	−0.154634	−	0.118655i
$472$	7.88224	+	4.55081i	0.362809	+	0.209468i
$473$	1.68337	+	0.221620i	0.0774014	+	0.0101901i
$474$	0.946830	−	3.53362i	0.0434893	−	0.162304i
$475$	9.75832			0.447742
$476$	−9.58614	−	5.20633i	−0.439380	−	0.238632i
$477$	2.98357			0.136608
$478$	−0.607785	+	2.26828i	−0.0277994	+	0.103749i
$479$	−3.53387	−	0.465243i	−0.161467	−	0.0212575i	0.0493594	−	0.998781i	$-0.484282\pi$
$479$	−3.53387	−	0.465243i	−0.161467	−	0.0212575i	−0.210826	+	0.977524i	$0.567615\pi$
$480$	0.712784	+	0.411526i	0.0325340	+	0.0187835i
$481$	3.20813	+	2.46168i	0.146278	+	0.112243i
$482$	3.94955	−	9.53506i	0.179897	−	0.434310i
$483$	−9.56958	−	4.60998i	−0.435431	−	0.209761i
$484$	−7.58613	+	7.58613i	−0.344824	+	0.344824i
$485$	12.0367	+	3.22521i	0.546556	+	0.146449i
$486$	−0.793353	+	0.608761i	−0.0359872	+	0.0276140i
$487$	9.06142	+	11.8091i	0.410612	+	0.535120i	0.952180	−	0.305537i	$-0.0988359\pi$
$487$	9.06142	+	11.8091i	0.410612	+	0.535120i	−0.541568	+	0.840657i	$0.682169\pi$
$488$	−11.6144	−	8.91203i	−0.525759	−	0.403429i
$489$		−	3.36232i		−	0.152049i
$490$	−5.59160	−	1.38827i	−0.252603	−	0.0627156i
$491$	1.36875	+	1.36875i	0.0617709	+	0.0617709i	0.737317	−	0.675547i	$-0.236092\pi$
$491$	1.36875	+	1.36875i	0.0617709	+	0.0617709i	−0.675547	+	0.737317i	$0.736092\pi$
$492$	2.23724	+	3.87501i	0.100862	+	0.174699i
$493$	0.387972	−	0.457721i	0.0174734	−	0.0206147i
$494$	−6.58677	+	11.4086i	−0.296353	+	0.513298i
$495$	0.111016	−	0.414316i	0.00498978	−	0.0186221i
$496$	1.84067	+	4.44377i	0.0826485	+	0.199531i
$497$	0.319528	−	5.67669i	0.0143328	−	0.254634i
$498$	−4.86152	+	2.01371i	−0.217850	+	0.0902364i
$499$	40.8335	−	5.37584i	1.82796	−	0.240656i	0.863401	−	0.504519i	$-0.168330\pi$
$499$	40.8335	−	5.37584i	1.82796	−	0.240656i	0.964560	+	0.263864i	$0.0849969\pi$
$500$	6.08738	−	4.67101i	0.272236	−	0.208894i
$501$	5.55380	+	20.7271i	0.248125	+	0.926017i
$502$	4.92353	+	1.31926i	0.219748	+	0.0588813i
$503$	32.9055	+	13.6299i	1.46718	+	0.607727i	0.966215	−	0.257738i	$-0.0829771\pi$
$503$	32.9055	+	13.6299i	1.46718	+	0.607727i	0.500969	+	0.865465i	$0.332977\pi$
$504$	−2.63838	+	0.197378i	−0.117523	+	0.00879191i
$505$	3.44927	−	1.42873i	0.153491	−	0.0635779i
$506$	1.81197	−	1.04614i	0.0805520	−	0.0465067i
$507$	20.8718	+	2.74783i	0.926950	+	0.122035i
$508$	−8.36596	+	2.24165i	−0.371179	+	0.0994572i
$509$	−4.53356	−	7.85235i	−0.200946	−	0.348049i	0.747887	−	0.663826i	$-0.231068\pi$
$509$	−4.53356	−	7.85235i	−0.200946	−	0.348049i	−0.948834	+	0.315776i	$0.897735\pi$
$510$	1.83757	−	2.85296i	0.0813688	−	0.126331i
$511$	3.55846	−	5.43341i	0.157417	−	0.240360i
$512$	0.707107	+	0.707107i	0.0312500	+	0.0312500i
$513$	1.37429	−	1.79101i	0.0606764	−	0.0790750i
$514$	18.3979	+	10.6221i	0.811499	+	0.468519i
$515$	1.24591	−	9.46363i	0.0549014	−	0.417017i
$516$	3.23012	−	0.425254i	0.142198	−	0.0187208i
$517$	2.52824	+	1.04723i	0.111192	+	0.0460572i
$518$	−0.374250	−	1.79482i	−0.0164436	−	0.0788600i
$519$	10.3798	−	10.3798i	0.455622	−	0.455622i
$520$	0.626897	+	4.76175i	0.0274912	+	0.208817i
$521$	−22.1191	−	28.8261i	−0.969055	−	1.26290i	−0.964822	−	0.262905i	$-0.915319\pi$
$521$	−22.1191	−	28.8261i	−0.969055	−	1.26290i	−0.00423288	−	0.999991i	$-0.501347\pi$
$522$	0.0189952	−	0.144283i	0.000831396	−	0.00631508i
$523$	−18.9092	+	10.9172i	−0.826843	+	0.477378i	−0.852770	−	0.522286i	$-0.825079\pi$
$523$	−18.9092	+	10.9172i	−0.826843	+	0.477378i	0.0259276	+	0.999664i	$0.491746\pi$
$524$	−6.74917	−	16.2939i	−0.294839	−	0.711804i
$525$	−3.57612	+	10.8630i	−0.156075	+	0.474100i
$526$	−23.6119			−1.02953
$527$	18.6693	−	6.69002i	0.813246	−	0.291422i
$528$	0.260573	−	0.451326i	0.0113400	−	0.0196415i
$529$	−6.64712	+	1.78109i	−0.289005	+	0.0774387i
$530$	−1.49489	+	1.94818i	−0.0649340	+	0.0846237i
$531$		−	9.10163i		−	0.394977i
$532$	5.63791	−	1.97198i	0.244434	−	0.0854960i
$533$	−9.99201	+	24.1228i	−0.432802	+	1.04488i
$534$	−0.421519	−	3.20175i	−0.0182409	−	0.138553i
$535$	2.21507	+	8.26676i	0.0957659	+	0.357403i
$536$	0.466671	+	1.74164i	0.0201571	+	0.0752275i
$537$	2.08593	+	15.8442i	0.0900147	+	0.683730i
$538$	−6.57383	+	15.8706i	−0.283418	+	0.684231i
$539$	−0.879035	+	3.54054i	−0.0378627	+	0.152502i
$540$		−	0.823052i		−	0.0354185i
$541$	5.00140	−	6.51795i	0.215027	−	0.280229i	−0.673369	−	0.739307i	$-0.735153\pi$
$541$	5.00140	−	6.51795i	0.215027	−	0.280229i	0.888396	+	0.459078i	$0.151820\pi$
$542$	−31.0804	+	8.32797i	−1.33502	+	0.357717i
$543$	6.09047	−	10.5490i	0.261367	−	0.452701i
$544$	3.05370	−	2.77037i	0.130926	−	0.118778i
$545$	9.42623			0.403775
$546$	−10.2863	−	11.5133i	−0.440211	−	0.492724i
$547$	−9.61793	−	23.2197i	−0.411233	−	0.992805i	−0.984807	−	0.173651i	$-0.944444\pi$
$547$	−9.61793	−	23.2197i	−0.411233	−	0.992805i	0.573574	−	0.819154i	$-0.305556\pi$
$548$	6.66211	−	3.84637i	0.284591	−	0.164309i
$549$	−1.91085	+	14.5144i	−0.0815532	+	0.619458i
$550$	−1.37136	−	1.78719i	−0.0584749	−	0.0762060i
$551$	0.0428819	+	0.325721i	0.00182683	+	0.0138762i
$552$	2.83887	−	2.83887i	0.120830	−	0.120830i
$553$	−9.19352	−	3.02653i	−0.390948	−	0.128701i
$554$	19.6404	+	8.13534i	0.834442	+	0.345637i
$555$	0.565471	−	0.0744457i	0.0240029	−	0.00316004i
$556$	−1.34045	+	10.1818i	−0.0568480	+	0.431803i
$557$	1.79863	+	1.03844i	0.0762104	+	0.0440001i	0.537621	−	0.843187i	$-0.319323\pi$
$557$	1.79863	+	1.03844i	0.0762104	+	0.0440001i	−0.461411	+	0.887187i	$0.652656\pi$
$558$	2.92808	−	3.81595i	0.123956	−	0.161542i
$559$	13.4433	+	13.4433i	0.568592	+	0.568592i
$560$	1.19306	−	1.82168i	0.0504159	−	0.0769800i
$561$	−1.80646	−	1.16352i	−0.0762689	−	0.0491240i
$562$	−0.960358	−	1.66339i	−0.0405103	−	0.0701658i
$563$	−36.1726	+	9.69241i	−1.52449	+	0.408486i	−0.921218	−	0.389048i	$-0.872804\pi$
$563$	−36.1726	+	9.69241i	−1.52449	+	0.408486i	−0.603274	+	0.797534i	$0.706138\pi$
$564$	5.20609	+	0.685394i	0.219216	+	0.0288603i
$565$	6.31136	−	3.64387i	0.265521	−	0.153299i
$566$	−17.3282	+	7.17758i	−0.728359	+	0.301696i
$567$	1.49012	+	2.18621i	0.0625793	+	0.0918124i
$568$	1.98540	+	0.822380i	0.0833056	+	0.0345063i
$569$	42.7666	+	11.4593i	1.79287	+	0.480398i	0.992828	−	0.119548i	$-0.0381446\pi$
$569$	42.7666	+	11.4593i	1.79287	+	0.480398i	0.800041	+	0.599946i	$0.204811\pi$
$570$	0.480900	+	1.79474i	0.0201427	+	0.0751736i
$571$	−23.3917	+	17.9491i	−0.978914	+	0.751147i	−0.968555	−	0.248800i	$-0.919964\pi$
$571$	−23.3917	+	17.9491i	−0.978914	+	0.751147i	−0.0103586	+	0.999946i	$0.503297\pi$
$572$	3.01508	−	0.396943i	0.126067	−	0.0165970i
$573$	−17.8750	+	7.40405i	−0.746737	+	0.309309i
$574$	10.5688	−	5.33365i	0.441132	−	0.222622i
$575$	−6.64116	−	16.0332i	−0.276956	−	0.668630i
$576$	0.258819	−	0.965926i	0.0107841	−	0.0402469i
$577$	16.2624	−	28.1672i	0.677011	−	1.17262i	−0.298866	−	0.954295i	$-0.596608\pi$
$577$	16.2624	−	28.1672i	0.677011	−	1.17262i	0.975877	−	0.218322i	$-0.0700584\pi$
$578$	−10.7972	−	13.1309i	−0.449105	−	0.546173i
$579$	−2.34885	−	4.06833i	−0.0976148	−	0.169074i
$580$	0.0846950	+	0.0846950i	0.00351677	+	0.00351677i
$581$	4.59650	+	13.1415i	0.190695	+	0.545200i
$582$		−	15.1403i		−	0.627586i
$583$	1.23357	+	0.946549i	0.0510891	+	0.0392020i
$584$	1.49443	+	1.94757i	0.0618398	+	0.0805912i
$585$	3.81035	−	2.92378i	0.157539	−	0.120884i
$586$	−6.14555	−	1.64669i	−0.253870	−	0.0680243i
$587$	−25.6702	+	25.6702i	−1.05952	+	1.05952i	−0.0614094	+	0.998113i	$0.519560\pi$
$587$	−25.6702	+	25.6702i	−1.05952	+	1.05952i	−0.998113	+	0.0614094i	$0.980440\pi$
$588$	0.129092	+	6.99881i	0.00532367	+	0.288626i
$589$	−4.15535	+	10.0319i	−0.171218	+	0.413357i
$590$	5.94310	+	4.56030i	0.244674	+	0.187745i
$591$	8.77582	+	5.06672i	0.360989	+	0.208417i
$592$	0.687042	+	0.0904507i	0.0282372	+	0.00371750i
$593$	−3.47343	+	12.9630i	−0.142637	+	0.532328i	0.857212	+	0.514963i	$0.172194\pi$
$593$	−3.47343	+	12.9630i	−0.142637	+	0.532328i	−0.999849	+	0.0173650i	$0.994472\pi$
$594$	−0.521147			−0.0213829
$595$	−7.26308	−	5.27826i	−0.297757	−	0.216388i
$596$	−23.0195			−0.942917
$597$	3.80325	−	14.1939i	0.155657	−	0.580918i
$598$	23.2274	+	3.05794i	0.949838	+	0.125049i
$599$	−21.9454	−	12.6702i	−0.896664	−	0.517689i	−0.0205476	−	0.999789i	$-0.506541\pi$
$599$	−21.9454	−	12.6702i	−0.896664	−	0.517689i	−0.876116	+	0.482100i	$0.839874\pi$
$600$	−3.42934	−	2.63142i	−0.140002	−	0.107427i
$601$	6.00011	−	14.4856i	0.244750	−	0.590878i	−0.752993	−	0.658028i	$-0.771391\pi$
$601$	6.00011	−	14.4856i	0.244750	−	0.590878i	0.997743	+	0.0671502i	$0.0213907\pi$
$602$	−0.643057	−	8.59583i	−0.0262090	−	0.350340i
$603$	1.27497	−	1.27497i	0.0519208	−	0.0519208i
$604$	6.71970	+	1.80054i	0.273421	+	0.0732628i
$605$	−7.00534	+	5.37539i	−0.284808	+	0.218541i
$606$	−2.76141	−	3.59875i	−0.112175	−	0.146189i
$607$	33.3412	+	25.5836i	1.35328	+	1.03841i	0.994473	+	0.104995i	$0.0334828\pi$
$607$	33.3412	+	25.5836i	1.35328	+	1.03841i	0.358806	+	0.933412i	$0.383184\pi$
$608$			2.25752i			0.0915545i
$609$	−0.378308	−	0.0716302i	−0.0153298	−	0.00290260i
$610$	−8.52005	−	8.52005i	−0.344967	−	0.344967i
$611$	15.3209	+	26.5365i	0.619817	+	1.07355i
$612$	−3.92606	−	1.25940i	−0.158701	−	0.0509081i
$613$	24.5322	−	42.4910i	0.990845	−	1.71619i	0.378507	−	0.925598i	$-0.376438\pi$
$613$	24.5322	−	42.4910i	0.990845	−	1.71619i	0.612338	−	0.790596i	$-0.290229\pi$
$614$	5.36882	−	20.0367i	0.216668	−	0.808616i
$615$	1.40932	+	3.40240i	0.0568292	+	0.137198i
$616$	−1.15347	−	0.755430i	−0.0464745	−	0.0304371i
$617$	−34.6802	+	14.3650i	−1.39617	+	0.578314i	−0.948755	−	0.316012i	$-0.897656\pi$
$617$	−34.6802	+	14.3650i	−1.39617	+	0.578314i	−0.447417	+	0.894325i	$0.647656\pi$
$618$	−11.4982	+	1.51377i	−0.462526	+	0.0608927i
$619$	−37.2177	+	28.5581i	−1.49591	+	1.14785i	−0.544971	+	0.838455i	$0.683459\pi$
$619$	−37.2177	+	28.5581i	−1.49591	+	1.14785i	−0.950934	+	0.309393i	$0.899874\pi$
$620$	1.02461	+	3.82391i	0.0411495	+	0.153572i
$621$	−3.87797	−	1.03910i	−0.155618	−	0.0416976i
$622$	−26.6419	−	11.0354i	−1.06824	−	0.442481i
$623$	−8.52032	+	0.637408i	−0.341360	+	0.0255372i
$624$	5.39121	−	2.23311i	0.215821	−	0.0893960i
$625$	−13.2482	+	7.64883i	−0.529927	+	0.305953i
$626$	−25.7653	−	3.39207i	−1.02979	−	0.135574i
$627$	1.13641	−	0.304500i	0.0453839	−	0.0121606i
$628$	−2.11504	−	3.66335i	−0.0843992	−	0.146184i
$629$	0.510144	−	2.81128i	0.0203408	−	0.112093i
$630$	−2.17415	−	0.122378i	−0.0866202	−	0.00487566i
$631$	26.7440	+	26.7440i	1.06466	+	1.06466i	0.997760	+	0.0669005i	$0.0213110\pi$
$631$	26.7440	+	26.7440i	1.06466	+	1.06466i	0.0669005	+	0.997760i	$0.478689\pi$
$632$	2.22701	−	2.90230i	0.0885859	−	0.115447i
$633$	1.85902	+	1.07330i	0.0738893	+	0.0426600i
$634$	−2.33348	+	17.7245i	−0.0926743	+	0.703931i
$635$	−7.06753	+	0.930458i	−0.280466	+	0.0369241i
$636$	2.75646	+	1.14176i	0.109301	+	0.0452738i
$637$	−31.9427	+	25.4600i	−1.26561	+	1.00876i
$638$	0.0536279	−	0.0536279i	0.00212315	−	0.00212315i
$639$	−0.280498	−	2.13060i	−0.0110963	−	0.0842851i
$640$	0.501042	+	0.652971i	0.0198054	+	0.0258110i
$641$	−4.47755	+	34.0103i	−0.176852	+	1.34333i	0.640841	+	0.767674i	$0.278586\pi$
$641$	−4.47755	+	34.0103i	−0.176852	+	1.34333i	−0.817693	+	0.575654i	$0.804747\pi$
$642$	9.00523	−	5.19917i	0.355408	−	0.205195i
$643$	5.93004	+	14.3164i	0.233858	+	0.564583i	0.996625	−	0.0820906i	$-0.0261597\pi$
$643$	5.93004	+	14.3164i	0.233858	+	0.564583i	−0.762767	+	0.646673i	$0.776160\pi$
$644$	−7.07697	−	7.92119i	−0.278872	−	0.312138i
$645$	2.68150			0.105584
$646$	9.29699	+	0.452286i	0.365785	+	0.0177950i
$647$	−10.5367	+	18.2500i	−0.414239	+	0.717483i	−0.995348	−	0.0963428i	$-0.969285\pi$
$647$	−10.5367	+	18.2500i	−0.414239	+	0.717483i	0.581109	+	0.813825i	$0.302619\pi$
$648$	−0.965926	+	0.258819i	−0.0379452	+	0.0101674i
$649$	2.88753	−	3.76310i	0.113345	−	0.147715i
$650$		−	25.2240i		−	0.989368i
$651$	−9.64474	−	8.30213i	−0.378007	−	0.325386i
$652$	1.28670	−	3.10638i	0.0503912	−	0.121655i
$653$	0.656879	+	4.98949i	0.0257057	+	0.195254i	0.999479	−	0.0322649i	$-0.0102720\pi$
$653$	0.656879	+	4.98949i	0.0257057	+	0.195254i	−0.973774	+	0.227519i	$0.926939\pi$
$654$	−2.96420	−	11.0625i	−0.115909	−	0.432579i
$655$	−3.75694	−	14.0211i	−0.146796	−	0.547849i
$656$	0.584036	+	4.43620i	0.0228028	+	0.173204i
$657$	0.939436	−	2.26800i	0.0366509	−	0.0884831i
$658$	2.58460	−	13.6503i	0.100758	−	0.532145i
$659$			7.46366i			0.290743i	0.989377	+	0.145371i	$0.0464377\pi$
$659$			7.46366i			0.290743i	−0.989377	+	0.145371i	$0.953562\pi$
$660$	0.261117	−	0.340294i	0.0101640	−	0.0132459i
$661$	−11.7378	+	3.14514i	−0.456548	+	0.122332i	−0.479762	−	0.877399i	$-0.659277\pi$
$661$	−11.7378	+	3.14514i	−0.456548	+	0.122332i	0.0232138	+	0.999731i	$0.492610\pi$
$662$	−1.50483	+	2.60643i	−0.0584867	+	0.101302i
$663$	−8.11637	−	22.6497i	−0.315214	−	0.879640i
$664$	−5.26207			−0.204208
$665$	4.81245	−	1.00347i	0.186619	−	0.0389131i
$666$	−0.265188	−	0.640221i	−0.0102758	−	0.0248081i
$667$	0.505984	−	0.292130i	0.0195918	−	0.0113113i
$668$	−2.80086	+	21.2747i	−0.108369	+	0.823141i
$669$	6.72087	+	8.75881i	0.259844	+	0.338635i
$670$	0.193705	+	1.47133i	0.00748346	+	0.0568425i
$671$	−5.39479	+	5.39479i	−0.208264	+	0.208264i
$672$	−2.51308	−	0.827310i	−0.0969441	−	0.0319142i
$673$	−15.9858	−	6.62155i	−0.616208	−	0.255242i	0.0526721	−	0.998612i	$-0.483226\pi$
$673$	−15.9858	−	6.62155i	−0.616208	−	0.255242i	−0.668880	+	0.743370i	$0.733226\pi$
$674$	−17.9049	+	2.35723i	−0.689672	+	0.0907970i
$675$	−0.564211	+	4.28560i	−0.0217165	+	0.164953i
$676$	18.2315	+	10.5260i	0.701212	+	0.404845i
$677$	−6.93072	+	9.03228i	−0.266369	+	0.347139i	−0.907318	−	0.420444i	$-0.861874\pi$
$677$	−6.93072	+	9.03228i	−0.266369	+	0.347139i	0.640949	+	0.767583i	$0.278541\pi$
$678$	−6.26109	−	6.26109i	−0.240456	−	0.240456i
$679$	−39.9942	−	2.25118i	−1.53484	−	0.0863925i
$680$	2.78947	−	1.93259i	0.106971	−	0.0741114i
$681$	2.03154	+	3.51873i	0.0778487	+	0.134838i
$682$	2.42125	−	0.648773i	0.0927146	−	0.0248428i
$683$	−20.5826	−	2.70975i	−0.787570	−	0.103686i	−0.273996	−	0.961731i	$-0.588346\pi$
$683$	−20.5826	−	2.70975i	−0.787570	−	0.103686i	−0.513574	+	0.858045i	$0.671679\pi$
$684$	1.95507	−	1.12876i	0.0747539	−	0.0431592i
$685$	5.84957	−	2.42297i	0.223500	−	0.0925769i
$686$	18.5070	+	0.699634i	0.706602	+	0.0267122i
$687$	−22.0863	−	9.14845i	−0.842645	−	0.349035i
$688$	3.14698	+	0.843231i	0.119978	+	0.0321479i
$689$	4.50612	+	16.8171i	0.171670	+	0.640679i
$690$	2.62153	−	2.01157i	0.0998000	−	0.0765792i
$691$	−12.4042	+	1.63304i	−0.471878	+	0.0621239i	−0.362715	−	0.931900i	$-0.618150\pi$
$691$	−12.4042	+	1.63304i	−0.471878	+	0.0621239i	−0.109163	+	0.994024i	$0.534817\pi$
$692$	13.5618	−	5.61749i	0.515543	−	0.213545i
$693$	−0.0774884	+	1.37665i	−0.00294354	+	0.0522945i
$694$	3.31474	+	8.00249i	0.125826	+	0.303770i
$695$	−2.18765	+	8.16443i	−0.0829824	+	0.309694i
$696$	0.0727638	−	0.126031i	0.00275810	−	0.00477718i
$697$	18.3863	−	1.51642i	0.696431	−	0.0574386i
$698$	5.29056	+	9.16351i	0.200251	+	0.346844i
$699$	9.23059	+	9.23059i	0.349133	+	0.349133i
$700$	−7.46099	+	8.66757i	−0.281999	+	0.327603i
$701$			25.6627i			0.969267i	0.874717	+	0.484634i	$0.161047\pi$
$701$			25.6627i			0.969267i	−0.874717	+	0.484634i	$0.838953\pi$
$702$	−4.62954	−	3.55237i	−0.174731	−	0.134075i
$703$	0.952342	+	1.24112i	0.0359183	+	0.0468096i
$704$	0.413454	−	0.317254i	0.0155826	−	0.0119570i
$705$	4.17459	+	1.11858i	0.157224	+	0.0421281i
$706$	−13.3507	+	13.3507i	−0.502461	+	0.502461i
$707$	−9.91693	+	6.75938i	−0.372964	+	0.254213i
$708$	3.48304	−	8.40881i	0.130901	−	0.316022i
$709$	−4.19814	−	3.22135i	−0.157665	−	0.120980i	0.526916	−	0.849917i	$-0.323348\pi$
$709$	−4.19814	−	3.22135i	−0.157665	−	0.120980i	−0.684581	+	0.728937i	$0.740015\pi$
$710$	1.53176	+	0.884362i	0.0574859	+	0.0331895i
$711$	−3.62697	−	0.477500i	−0.136022	−	0.0179077i
$712$	0.835825	−	3.11934i	0.0313239	−	0.116902i
$713$	19.3107			0.723190
$714$	−3.91054	+	10.1837i	−0.146348	+	0.381115i
$715$	2.50299			0.0936064
$716$	−4.13618	+	15.4364i	−0.154576	+	0.576886i
$717$	2.32821	+	0.306515i	0.0869486	+	0.0114470i
$718$	−16.3899	−	9.46269i	−0.611664	−	0.353145i
$719$	−20.4287	−	15.6755i	−0.761863	−	0.584598i	0.153064	−	0.988216i	$-0.451086\pi$
$719$	−20.4287	−	15.6755i	−0.761863	−	0.584598i	−0.914928	+	0.403618i	$0.867753\pi$
$720$	0.314968	−	0.760401i	0.0117382	−	0.0283385i
$721$	2.28908	+	30.5984i	0.0852497	+	1.13954i
$722$	9.83134	−	9.83134i	0.365884	−	0.365884i
$723$	−9.96900	−	2.67119i	−0.370751	−	0.0993425i
$724$	9.66379	−	7.41528i	0.359152	−	0.275587i
$725$	−0.382945	−	0.499063i	−0.0142222	−	0.0185347i
$726$	8.51142	+	6.53104i	0.315888	+	0.242390i
$727$		−	22.7877i		−	0.845148i	−0.906328	−	0.422574i	$-0.861127\pi$
$727$		−	22.7877i		−	0.845148i	0.906328	−	0.422574i	$-0.138873\pi$
$728$	−5.09731	−	14.5733i	−0.188919	−	0.540122i
$729$	0.707107	+	0.707107i	0.0261891	+	0.0261891i
$730$	1.01024	+	1.74979i	0.0373907	+	0.0647626i
$731$	4.10311	−	12.7911i	0.151759	−	0.473095i
$732$	−7.31981	+	12.6783i	−0.270548	+	0.468603i
$733$	10.3630	−	38.6752i	0.382766	−	1.42850i	−0.458894	−	0.888491i	$-0.651754\pi$
$733$	10.3630	−	38.6752i	0.382766	−	1.42850i	0.841659	−	0.540009i	$-0.181579\pi$
$734$	3.64391	+	8.79717i	0.134499	+	0.324709i
$735$	−0.646541	+	5.72497i	−0.0238480	+	0.211169i
$736$	3.70917	−	1.53639i	0.136722	−	0.0566320i
$737$	0.931630	−	0.122651i	0.0343170	−	0.00451792i
$738$	3.54984	−	2.72389i	0.130671	−	0.100268i
$739$	−2.36795	−	8.83729i	−0.0871063	−	0.325085i	0.908598	−	0.417671i	$-0.137153\pi$
$739$	−2.36795	−	8.83729i	−0.0871063	−	0.325085i	−0.995705	+	0.0925857i	$0.970487\pi$
$740$	0.550916	+	0.147618i	0.0202521	+	0.00542653i
$741$	12.1708	+	5.04129i	0.447104	+	0.185197i
$742$	3.42590	−	7.11161i	0.125769	−	0.261075i
$743$	−6.54720	+	2.71194i	−0.240193	+	0.0994914i	−0.499533	−	0.866295i	$-0.666495\pi$
$743$	−6.54720	+	2.71194i	−0.240193	+	0.0994914i	0.259340	+	0.965786i	$0.416495\pi$
$744$	4.16550	−	2.40495i	0.152715	−	0.0881698i
$745$	−18.7842	−	2.47299i	−0.688200	−	0.0906032i
$746$	−31.8191	+	8.52591i	−1.16498	+	0.312156i
$747$	2.63104	+	4.55709i	0.0962646	+	0.166735i
$748$	−1.22369	−	1.76626i	−0.0447426	−	0.0645809i
$749$	−12.3950	−	24.5610i	−0.452904	−	0.897439i
$750$	−5.42561	−	5.42561i	−0.198115	−	0.198115i
$751$	−17.5816	+	22.9128i	−0.641561	+	0.836098i	−0.995054	−	0.0993388i	$-0.968327\pi$
$751$	−17.5816	+	22.9128i	−0.641561	+	0.836098i	0.353493	+	0.935437i	$0.384994\pi$
$752$	4.54751	+	2.62551i	0.165831	+	0.0957423i
$753$	0.665320	−	5.05361i	0.0242456	−	0.184164i
$754$	0.841947	−	0.110844i	0.0306619	−	0.00403672i
$755$	5.28991	+	2.19115i	0.192520	+	0.0797443i
$756$	0.540067	+	2.59004i	0.0196420	+	0.0941990i
$757$	26.9319	−	26.9319i	0.978858	−	0.978858i	−0.0209233	−	0.999781i	$-0.506661\pi$
$757$	26.9319	−	26.9319i	0.978858	−	0.978858i	0.999781	+	0.0209233i	$0.00666058\pi$
$758$	−3.39553	−	25.7916i	−0.123331	−	0.936794i
$759$	−1.27370	−	1.65992i	−0.0462325	−	0.0602513i
$760$	−0.242525	+	1.84216i	−0.00879731	+	0.0668222i
$761$	13.9349	−	8.04533i	0.505140	−	0.291643i	−0.225693	−	0.974198i	$-0.572465\pi$
$761$	13.9349	−	8.04533i	0.505140	−	0.291643i	0.730834	+	0.682555i	$0.239131\pi$
$762$	3.31445	+	8.00179i	0.120070	+	0.289874i
$763$	−29.6632	+	6.18526i	−1.07388	+	0.223922i
$764$	−19.3477			−0.699976
$765$	−3.06841	−	1.44946i	−0.110939	−	0.0524053i
$766$	−16.1741	+	28.0144i	−0.584394	+	1.01220i
$767$	51.3019	−	13.7463i	1.85241	−	0.496350i
$768$	0.608761	−	0.793353i	0.0219668	−	0.0286277i
$769$			16.8986i			0.609379i	0.952452	+	0.304690i	$0.0985527\pi$
$769$			16.8986i			0.609379i	−0.952452	+	0.304690i	$0.901447\pi$
$770$	−0.860085	−	0.740356i	−0.0309953	−	0.0266806i
$771$	8.12977	−	19.6270i	0.292787	−	0.706849i
$772$	−0.613173	−	4.65751i	−0.0220686	−	0.167627i
$773$	−11.0788	−	41.3467i	−0.398477	−	1.48714i	−0.815777	−	0.578367i	$-0.803690\pi$
$773$	−11.0788	−	41.3467i	−0.398477	−	1.48714i	0.417300	−	0.908769i	$-0.362976\pi$
$774$	−0.843231	−	3.14698i	−0.0303093	−	0.113116i
$775$	−2.71380	−	20.6133i	−0.0974825	−	0.740453i
$776$	5.79395	−	13.9878i	0.207991	−	0.502134i
$777$	−1.73062	+	0.605320i	−0.0620856	+	0.0217157i
$778$			30.4931i			1.09323i
$779$	−6.14923	+	8.01383i	−0.220319	+	0.287125i
$780$	4.63919	−	1.24307i	0.166110	−	0.0445089i
$781$	0.559968	−	0.969892i	0.0200372	−	0.0347055i
$782$	−5.58408	−	15.5830i	−0.199686	−	0.557248i
$783$	−0.145528			−0.00520073
$784$	−2.55906	+	6.51546i	−0.0913951	+	0.232695i
$785$	−1.33234	−	3.21655i	−0.0475533	−	0.114804i
$786$	−15.2736	+	8.81821i	−0.544791	+	0.314535i
$787$	−0.998353	+	7.58324i	−0.0355874	+	0.270313i	0.964395	+	0.264464i	$0.0851952\pi$
$787$	−0.998353	+	7.58324i	−0.0355874	+	0.270313i	−0.999983	+	0.00584906i	$0.998138\pi$
$788$	6.16885	+	8.03940i	0.219756	+	0.286392i
$789$	3.08198	+	23.4099i	0.109721	+	0.833416i
$790$	2.12906	−	2.12906i	0.0757486	−	0.0757486i
$791$	−17.4701	+	15.6082i	−0.621164	+	0.554963i
$792$	−0.481477	−	0.199434i	−0.0171085	−	0.00708659i
$793$	−84.6972	+	11.1506i	−3.00769	+	0.395969i
$794$	2.29514	−	17.4333i	0.0814515	−	0.618686i
$795$	2.12664	+	1.22782i	0.0754241	+	0.0435461i
$796$	8.94552	−	11.6580i	0.317065	−	0.413208i
$797$	−27.1246	−	27.1246i	−0.960801	−	0.960801i	0.0384591	−	0.999260i	$-0.487755\pi$
$797$	−27.1246	−	27.1246i	−0.960801	−	0.960801i	−0.999260	+	0.0384591i	$0.987755\pi$
$798$	−2.69100	−	5.33228i	−0.0952604	−	0.188761i
$799$	11.7235	−	18.2017i	0.414749	−	0.643930i
$800$	−2.16129	−	3.74347i	−0.0764132	−	0.132352i
$801$	−3.11934	+	0.835825i	−0.110216	+	0.0295324i
$802$	28.3767	+	3.73586i	1.00202	+	0.131918i
$803$	1.10795	−	0.639672i	0.0390985	−	0.0225735i
$804$	1.66583	−	0.690009i	0.0587492	−	0.0243347i
$805$	−4.92392	−	7.22405i	−0.173545	−	0.254614i
$806$	25.9312	+	10.7411i	0.913387	+	0.378337i
$807$	16.5929	+	4.44606i	0.584098	+	0.156509i
$808$	−1.17403	−	4.38156i	−0.0413024	−	0.154143i
$809$	23.6087	−	18.1156i	0.830036	−	0.636909i	−0.103805	−	0.994598i	$-0.533102\pi$
$809$	23.6087	−	18.1156i	0.830036	−	0.636909i	0.933841	+	0.357688i	$0.116435\pi$
$810$	−0.816011	+	0.107430i	−0.0286717	+	0.00377470i
$811$	38.4155	−	15.9122i	1.34895	−	0.558754i	0.412950	−	0.910754i	$-0.364498\pi$
$811$	38.4155	−	15.9122i	1.34895	−	0.558754i	0.936000	+	0.352000i	$0.114498\pi$
$812$	−0.322100	−	0.210950i	−0.0113035	−	0.00740289i
$813$	12.3135	+	29.7275i	0.431854	+	1.04259i
$814$	0.0934697	−	0.348834i	0.00327611	−	0.0122266i
$815$	1.38368	−	2.39661i	0.0484683	−	0.0839495i
$816$	−3.14525	−	2.66597i	−0.110106	−	0.0933276i
$817$	3.67749	+	6.36961i	0.128659	+	0.222844i
$818$	−15.6685	−	15.6685i	−0.547836	−	0.547836i
$819$	−10.0722	+	11.7010i	−0.351951	+	0.408868i
$820$			3.68273i			0.128606i
$821$	11.7024	+	8.97955i	0.408416	+	0.313388i	0.792457	−	0.609927i	$-0.208801\pi$
$821$	11.7024	+	8.97955i	0.408416	+	0.313388i	−0.384042	+	0.923316i	$0.625468\pi$
$822$	−4.68304	−	6.10306i	−0.163340	−	0.212869i
$823$	−12.0774	+	9.26729i	−0.420991	+	0.323038i	−0.797438	−	0.603400i	$-0.793812\pi$
$823$	−12.0774	+	9.26729i	−0.420991	+	0.323038i	0.376448	+	0.926438i	$0.377145\pi$
$824$	−11.2023	−	3.00164i	−0.390249	−	0.104567i
$825$	−1.59290	+	1.59290i	−0.0554577	+	0.0554577i
$826$	−21.6946	−	10.4510i	−0.754850	−	0.363636i
$827$	−14.3792	+	34.7144i	−0.500013	+	1.20714i	0.449464	+	0.893299i	$0.351615\pi$
$827$	−14.3792	+	34.7144i	−0.500013	+	1.20714i	−0.949476	+	0.313839i	$0.898385\pi$
$828$	−3.18513	−	2.44404i	−0.110691	−	0.0849362i
$829$	3.32147	+	1.91765i	0.115359	+	0.0666027i	0.556569	−	0.830801i	$-0.312117\pi$
$829$	3.32147	+	1.91765i	0.115359	+	0.0666027i	−0.441210	+	0.897404i	$0.645451\pi$
$830$	−4.29391	−	0.565304i	−0.149044	−	0.0196220i
$831$	5.50215	−	20.5343i	0.190867	−	0.712326i
$832$	5.83540			0.202306
$833$	26.3195	+	11.8442i	0.911916	+	0.410376i
$834$	10.2696			0.355608
$835$	−4.57107	+	17.0595i	−0.158188	+	0.590367i
$836$	1.16643	+	0.153564i	0.0403420	+	0.00531112i
$837$	−4.16550	−	2.40495i	−0.143981	−	0.0831273i
$838$	−13.4152	−	10.2939i	−0.463421	−	0.355596i
$839$	−5.02073	+	12.1211i	−0.173335	+	0.418467i	−0.986542	−	0.163507i	$-0.947719\pi$
$839$	−5.02073	+	12.1211i	−0.173335	+	0.418467i	0.813207	+	0.581974i	$0.197719\pi$
$840$	−1.96182	−	0.945074i	−0.0676892	−	0.0326081i
$841$	−20.4911	+	20.4911i	−0.706590	+	0.706590i
$842$	−24.4500	−	6.55137i	−0.842604	−	0.225775i
$843$	−1.52381	+	1.16926i	−0.0524827	+	0.0402714i
$844$	1.30677	+	1.70302i	0.0449810	+	0.0586203i
$845$	13.7463	+	10.5479i	0.472887	+	0.362859i
$846$		−	5.25101i		−	0.180533i
$847$	18.5177	−	21.5124i	0.636277	−	0.739175i
$848$	2.10970	+	2.10970i	0.0724474	+	0.0724474i
$849$	9.37797	+	16.2431i	0.321851	+	0.557462i
$850$	−15.8495	+	8.15072i	−0.543633	+	0.279567i
$851$	1.39106	−	2.40938i	0.0476849	−	0.0825926i
$852$	0.556197	−	2.07576i	0.0190550	−	0.0711143i
$853$	−15.1148	−	36.4904i	−0.517521	−	1.24941i	−0.939421	−	0.342765i	$-0.888637\pi$
$853$	−15.1148	−	36.4904i	−0.517521	−	1.24941i	0.421900	−	0.906642i	$-0.361363\pi$
$854$	32.4022	+	21.2209i	1.10878	+	0.726164i
$855$	1.71662	−	0.711047i	0.0587072	−	0.0243173i
$856$	10.3094	−	1.35726i	0.352367	−	0.0463901i
$857$	−36.6126	+	28.0939i	−1.25066	+	0.959668i	−0.999965	−	0.00839694i	$-0.997327\pi$
$857$	−36.6126	+	28.0939i	−1.25066	+	0.959668i	−0.250699	+	0.968065i	$0.580660\pi$
$858$	−0.787095	−	2.93748i	−0.0268710	−	0.100284i
$859$	−10.5108	−	2.81636i	−0.358624	−	0.0960931i	0.0750082	−	0.997183i	$-0.476102\pi$
$859$	−10.5108	−	2.81636i	−0.358624	−	0.0960931i	−0.433632	+	0.901090i	$0.642768\pi$
$860$	2.47738	+	1.02617i	0.0844781	+	0.0349920i
$861$	−6.66752	−	9.78216i	−0.227229	−	0.333375i
$862$	22.3567	−	9.26046i	0.761474	−	0.315413i
$863$	28.2127	−	16.2886i	0.960372	−	0.554471i	0.0640846	−	0.997944i	$-0.479587\pi$
$863$	28.2127	−	16.2886i	0.960372	−	0.554471i	0.896288	+	0.443473i	$0.146254\pi$
$864$	−0.991445	−	0.130526i	−0.0337296	−	0.00444059i
$865$	11.6701	−	3.12699i	0.396795	−	0.106321i
$866$	1.07712	+	1.86563i	0.0366020	+	0.0633966i
$867$	−11.6092	+	12.4188i	−0.394270	+	0.421764i
$868$	−5.73349	−	11.3610i	−0.194607	−	0.385619i
$869$	−1.34810	−	1.34810i	−0.0457310	−	0.0457310i
$870$	0.0729155	−	0.0950253i	0.00247207	−	0.00322166i
$871$	9.11206	+	5.26085i	0.308750	+	0.178257i
$872$	1.49489	−	11.3548i	0.0506233	−	0.384522i
$873$	−15.0108	+	1.97621i	−0.508038	+	0.0668845i
$874$	8.37351	+	3.46842i	0.283238	+	0.117321i
$875$	−15.1389	+	13.5254i	−0.511787	+	0.457242i
$876$	1.73585	−	1.73585i	0.0586490	−	0.0586490i
$877$	−4.81561	−	36.5782i	−0.162612	−	1.23516i	−0.856909	−	0.515469i	$-0.827618\pi$
$877$	−4.81561	−	36.5782i	−0.162612	−	1.23516i	0.694297	−	0.719689i	$-0.255715\pi$
$878$	−7.63668	−	9.95231i	−0.257725	−	0.335874i
$879$	−0.830452	+	6.30791i	−0.0280104	+	0.212760i
$880$	0.371465	−	0.214466i	0.0125221	−	0.00722963i
$881$	5.30389	+	12.8047i	0.178693	+	0.431402i	0.987693	−	0.156406i	$-0.0499909\pi$
$881$	5.30389	+	12.8047i	0.178693	+	0.431402i	−0.809000	+	0.587808i	$0.799991\pi$
$882$	6.92208	−	1.04152i	0.233079	−	0.0350697i
$883$	4.41942			0.148725			0.0743626	−	0.997231i	$-0.476308\pi$
$883$	4.41942			0.148725			0.0743626	+	0.997231i	$0.476308\pi$
$884$	1.16910	−	24.0316i	0.0393212	−	0.808269i
$885$	3.74556	−	6.48749i	0.125906	−	0.218075i
$886$	−7.37496	+	1.97611i	−0.247767	+	0.0663889i
$887$	36.1091	−	47.0583i	1.21243	−	1.58006i	0.533694	−	0.845678i	$-0.320804\pi$
$887$	36.1091	−	47.0583i	1.21243	−	1.58006i	0.678732	−	0.734386i	$-0.262530\pi$
$888$		−	0.692970i		−	0.0232545i
$889$	21.6301	−	7.56558i	0.725451	−	0.253741i
$890$	1.01715	−	2.45562i	0.0340950	−	0.0823127i
$891$	0.0680233	+	0.516688i	0.00227887	+	0.0173097i
$892$	2.85742	+	10.6640i	0.0956736	+	0.357059i
$893$	3.06811	+	11.4503i	0.102670	+	0.383171i
$894$	3.00465	+	22.8226i	0.100491	+	0.763302i
$895$	−5.03350	+	12.1519i	−0.168251	+	0.406195i
$896$	−2.00518	−	1.72605i	−0.0669885	−	0.0576632i
$897$		−	23.4278i		−	0.782232i
$898$	−5.03098	+	6.55651i	−0.167886	+	0.218793i
$899$	0.676123	−	0.181167i	0.0225500	−	0.00604224i
$900$	−2.16129	+	3.74347i	−0.0720431	+	0.124782i
$901$	9.11091	−	8.26557i	0.303529	−	0.275366i
$902$	2.33186			0.0776424
$903$	−8.43835	+	1.75954i	−0.280811	+	0.0585537i
$904$	−3.38848	−	8.18051i	−0.112699	−	0.272080i
$905$	8.68238	−	5.01277i	0.288612	−	0.166630i
$906$	0.908037	−	6.89723i	0.0301675	−	0.229145i
$907$	−14.6212	−	19.0547i	−0.485488	−	0.632700i	0.484808	−	0.874620i	$-0.338889\pi$
$907$	−14.6212	−	19.0547i	−0.485488	−	0.632700i	−0.970296	+	0.241920i	$0.922223\pi$
$908$	0.530338	+	4.02832i	0.0175999	+	0.133684i
$909$	−3.20752	+	3.20752i	−0.106387	+	0.106387i
$910$	−2.59386	−	12.4396i	−0.0859855	−	0.412368i
$911$	48.1503	+	19.9445i	1.59529	+	0.660791i	0.990740	−	0.135776i	$-0.0433528\pi$
$911$	48.1503	+	19.9445i	1.59529	+	0.660791i	0.604550	+	0.796567i	$0.293353\pi$
$912$	2.23821	−	0.294665i	0.0741144	−	0.00975734i
$913$	−0.357944	+	2.71885i	−0.0118462	+	0.0899809i
$914$	26.4579	+	15.2755i	0.875150	+	0.505268i
$915$	−7.33507	+	9.55925i	−0.242490	+	0.316019i
$916$	−16.9041	−	16.9041i	−0.558528	−	0.558528i
$917$	21.0229	+	41.6574i	0.694238	+	1.37565i
$918$	−0.736170	+	4.05685i	−0.0242972	+	0.133896i
$919$	10.7640	+	18.6438i	0.355071	+	0.615001i	0.987130	−	0.159919i	$-0.0511233\pi$
$919$	10.7640	+	18.6438i	0.355071	+	0.615001i	−0.632059	+	0.774920i	$0.717790\pi$
$920$	3.19177	−	0.855233i	0.105230	−	0.0281962i
$921$	−20.5661	−	2.70758i	−0.677675	−	0.0892177i
$922$	3.10145	−	1.79063i	0.102141	−	0.0589711i
$923$	11.5856	−	4.79892i	0.381345	−	0.157958i
$924$	−0.598409	+	1.24220i	−0.0196862	+	0.0408654i
$925$	−2.76741	−	1.14630i	−0.0909918	−	0.0376901i
$926$	20.3058	+	5.44091i	0.667289	+	0.178799i
$927$	3.00164	+	11.2023i	0.0985867	+	0.367930i
$928$	0.115455	−	0.0885916i	0.00378999	−	0.00290816i
$929$	7.13953	−	0.939937i	0.234240	−	0.0308383i	−0.0124921	−	0.999922i	$-0.503976\pi$
$929$	7.13953	−	0.939937i	0.234240	−	0.0308383i	0.246732	+	0.969084i	$0.420643\pi$
$930$	3.65746	−	1.51497i	0.119933	−	0.0496778i
$931$	−14.4857	+	6.31562i	−0.474750	+	0.206986i
$932$	4.99556	+	12.0603i	0.163635	+	0.395050i
$933$	−7.46356	+	27.8544i	−0.244346	+	0.911912i
$934$	−13.3269	+	23.0828i	−0.436068	+	0.755292i
$935$	−0.808798	−	1.57275i	−0.0264505	−	0.0514344i
$936$	−2.91770	−	5.05361i	−0.0953681	−	0.165182i
$937$	33.9519	+	33.9519i	1.10916	+	1.10916i	0.993261	+	0.115899i	$0.0369750\pi$
$937$	33.9519	+	33.9519i	1.10916	+	1.10916i	0.115899	+	0.993261i	$0.463025\pi$
$938$	−1.57502	−	4.50300i	−0.0514261	−	0.147028i
$939$			25.9876i			0.848074i
$940$	3.42876	+	2.63098i	0.111834	+	0.0858131i
$941$	−13.8154	−	18.0046i	−0.450369	−	0.586932i	0.511896	−	0.859047i	$-0.328943\pi$
$941$	−13.8154	−	18.0046i	−0.450369	−	0.586932i	−0.962265	+	0.272116i	$0.912277\pi$
$942$	−3.35594	+	2.57511i	−0.109343	+	0.0839015i
$943$	17.3519	+	4.64943i	0.565055	+	0.151406i
$944$	6.43582	−	6.43582i	0.209468	−	0.209468i
$945$	0.162452	+	2.17152i	0.00528458	+	0.0706397i
$946$	0.649756	−	1.56865i	0.0211254	−	0.0510012i
$947$	4.67316	+	3.58584i	0.151857	+	0.116524i	0.681896	−	0.731449i	$-0.261156\pi$
$947$	4.67316	+	3.58584i	0.151857	+	0.116524i	−0.530038	+	0.847974i	$0.677822\pi$
$948$	−3.16816	−	1.82914i	−0.102897	−	0.0594076i
$949$	14.2026	+	1.86980i	0.461035	+	0.0606964i
$950$	2.52564	−	9.42581i	0.0819425	−	0.305814i
$951$	17.8775			0.579717
$952$	−7.51000	+	7.91201i	−0.243401	+	0.256430i
$953$	−5.11357			−0.165645			−0.0828225	−	0.996564i	$-0.526393\pi$
$953$	−5.11357			−0.165645			−0.0828225	+	0.996564i	$0.526393\pi$
$954$	0.772204	−	2.88190i	0.0250010	−	0.0933051i
$955$	−15.7880	−	2.07852i	−0.510886	−	0.0672594i
$956$	2.03369	+	1.17415i	0.0657742	+	0.0379747i
$957$	−0.0601689	−	0.0461692i	−0.00194498	−	0.00149244i
$958$	−1.36402	+	3.29304i	−0.0440696	+	0.106393i
$959$	−16.8180	+	11.4631i	−0.543081	+	0.370164i
$960$	0.581986	−	0.581986i	0.0187835	−	0.0187835i
$961$	−7.59684	−	2.03557i	−0.245059	−	0.0656634i
$962$	3.20813	−	2.46168i	0.103434	−	0.0793679i
$963$	−6.33011	−	8.24956i	−0.203985	−	0.265838i
$964$	−8.18794	−	6.28283i	−0.263716	−	0.202356i
$965$		−	3.86645i		−	0.124465i
$966$	−6.92969	+	8.05035i	−0.222959	+	0.259016i
$967$	4.47884	+	4.47884i	0.144030	+	0.144030i	0.775445	−	0.631415i	$-0.217526\pi$
$967$	4.47884	+	4.47884i	0.144030	+	0.144030i	−0.631415	+	0.775445i	$0.717526\pi$
$968$	5.36420	+	9.29107i	0.172412	+	0.298626i
$969$	−0.765084	−	9.27649i	−0.0245781	−	0.298004i
$970$	6.23063	−	10.7918i	0.200054	−	0.346503i
$971$	14.0714	−	52.5153i	0.451574	−	1.68530i	−0.246396	−	0.969169i	$-0.579246\pi$
$971$	14.0714	−	52.5153i	0.451574	−	1.68530i	0.697970	−	0.716127i	$-0.254087\pi$
$972$	0.382683	+	0.923880i	0.0122746	+	0.0296334i
$973$	1.52697	−	27.1279i	0.0489525	−	0.869682i
$974$	13.7520	−	5.69625i	0.440641	−	0.182519i
$975$	−25.0082	+	3.29240i	−0.800904	+	0.105441i
$976$	−11.6144	+	8.91203i	−0.371767	+	0.285267i
$977$	−4.61981	−	17.2414i	−0.147801	−	0.551600i	−0.999615	−	0.0277556i	$-0.991164\pi$
$977$	−4.61981	−	17.2414i	−0.147801	−	0.551600i	0.851814	−	0.523844i	$-0.175503\pi$
$978$	−3.24775	−	0.870232i	−0.103852	−	0.0278270i
$979$	−1.55487	−	0.644049i	−0.0496939	−	0.0205839i
$980$	−2.78818	+	5.04177i	−0.0890651	+	0.161053i
$981$	−10.5810	+	4.38279i	−0.337825	+	0.139932i
$982$	1.67637	−	0.967853i	0.0534951	−	0.0308854i
$983$	0.749187	+	0.0986323i	0.0238953	+	0.00314588i	0.142464	−	0.989800i	$-0.454497\pi$
$983$	0.749187	+	0.0986323i	0.0238953	+	0.00314588i	−0.118569	+	0.992946i	$0.537831\pi$
$984$	4.32201	−	1.15808i	0.137781	−	0.0369182i
$985$	4.17018	+	7.22296i	0.132873	+	0.230143i
$986$	−0.341710	−	0.493219i	−0.0108823	−	0.0157073i
$987$	−13.8709	−	0.780763i	−0.441516	−	0.0248520i
$988$	9.31509	+	9.31509i	0.296353	+	0.296353i
$989$	7.96267	−	10.3771i	0.253198	−	0.329974i
$990$	−0.371465	−	0.214466i	−0.0118059	−	0.00681616i
$991$	−1.15196	+	8.75003i	−0.0365933	+	0.277954i	0.963359	+	0.268214i	$0.0864336\pi$
$991$	−1.15196	+	8.75003i	−0.0365933	+	0.277954i	−0.999953	+	0.00973951i	$0.996900\pi$
$992$	4.76875	−	0.627818i	0.151408	−	0.0199333i
$993$	2.78055	+	1.15174i	0.0882382	+	0.0365495i
$994$	−5.40056	−	1.77788i	−0.171295	−	0.0563908i
$995$	8.55206	−	8.55206i	0.271118	−	0.271118i
$996$	0.686839	+	5.21706i	0.0217633	+	0.165309i
$997$	−25.4633	−	33.1844i	−0.806431	−	1.05096i	−0.997589	−	0.0694025i	$-0.977891\pi$
$997$	−25.4633	−	33.1844i	−0.806431	−	1.05096i	0.191157	−	0.981559i	$-0.438776\pi$
$998$	5.37584	−	40.8335i	0.170169	−	1.29256i
$999$	−0.600130	+	0.346485i	−0.0189873	+	0.0109623i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	714.2.bh.b.151.2	yes	96
7.2	even	3	inner	714.2.bh.b.457.8	yes	96
17.8	even	8	inner	714.2.bh.b.25.8	✓	96
119.93	even	24	inner	714.2.bh.b.331.2	yes	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
714.2.bh.b.25.8	✓	96	17.8	even	8	inner
714.2.bh.b.151.2	yes	96	1.1	even	1	trivial
714.2.bh.b.331.2	yes	96	119.93	even	24	inner
714.2.bh.b.457.8	yes	96	7.2	even	3	inner

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:	\( N \)	\(=\)	\( 714 = 2 \cdot 3 \cdot 7 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	714.bh (of order \(24\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.258819 - 0.965926i) q^{2} +(-0.991445 - 0.130526i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(-0.652971 - 0.501042i) q^{5} +(-0.382683 + 0.923880i) q^{6} +(2.38359 + 1.14825i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(0.965926 + 0.258819i) q^{9} +(-0.652971 + 0.501042i) q^{10} +(0.317254 + 0.413454i) q^{11} +(0.793353 + 0.608761i) q^{12} +5.83540i q^{13} +(1.72605 - 2.00518i) q^{14} +(0.581986 + 0.581986i) q^{15} +(0.500000 + 0.866025i) q^{16} +(3.66667 - 1.88561i) q^{17} +(0.500000 - 0.866025i) q^{18} +(-0.584289 + 2.18060i) q^{19} +(0.314968 + 0.760401i) q^{20} +(-2.21332 - 1.44955i) q^{21} +(0.481477 - 0.199434i) q^{22} +(3.98042 - 0.524033i) q^{23} +(0.793353 - 0.608761i) q^{24} +(-1.11877 - 4.17530i) q^{25} +(5.63657 + 1.51031i) q^{26} +(-0.923880 - 0.382683i) q^{27} +(-1.49012 - 2.18621i) q^{28} +(0.134450 - 0.0556910i) q^{29} +(0.712784 - 0.411526i) q^{30} +(4.76875 + 0.627818i) q^{31} +(0.965926 - 0.258819i) q^{32} +(-0.260573 - 0.451326i) q^{33} +(-0.872358 - 4.02976i) q^{34} +(-0.981092 - 1.94406i) q^{35} +(-0.707107 - 0.707107i) q^{36} +(0.421853 - 0.549770i) q^{37} +(1.95507 + 1.12876i) q^{38} +(0.761673 - 5.78548i) q^{39} +(0.816011 - 0.107430i) q^{40} +(4.13388 + 1.71231i) q^{41} +(-1.97301 + 1.76273i) q^{42} +(2.30375 - 2.30375i) q^{43} +(-0.0680233 - 0.516688i) q^{44} +(-0.501042 - 0.652971i) q^{45} +(0.524033 - 3.98042i) q^{46} +(4.54751 - 2.62551i) q^{47} +(-0.382683 - 0.923880i) q^{48} +(4.36302 + 5.47394i) q^{49} -4.32259 q^{50} +(-3.88142 + 1.39088i) q^{51} +(2.91770 - 5.05361i) q^{52} +(2.88190 - 0.772204i) q^{53} +(-0.608761 + 0.793353i) q^{54} -0.428931i q^{55} +(-2.49739 + 0.873515i) q^{56} +(0.863915 - 2.08568i) q^{57} +(-0.0189952 - 0.144283i) q^{58} +(-2.35567 - 8.79150i) q^{59} +(-0.213022 - 0.795007i) q^{60} +(1.91085 + 14.5144i) q^{61} +(1.84067 - 4.44377i) q^{62} +(2.00518 + 1.72605i) q^{63} -1.00000i q^{64} +(2.92378 - 3.81035i) q^{65} +(-0.503389 + 0.134883i) q^{66} +(0.901540 - 1.56151i) q^{67} +(-4.11824 - 0.200347i) q^{68} -4.01477 q^{69} +(-2.13174 + 0.444503i) q^{70} +(-0.822380 - 1.98540i) q^{71} +(-0.866025 + 0.500000i) q^{72} +(0.320424 - 2.43386i) q^{73} +(-0.421853 - 0.549770i) q^{74} +(0.564211 + 4.28560i) q^{75} +(1.59631 - 1.59631i) q^{76} +(0.281454 + 1.34979i) q^{77} +(-5.39121 - 2.23311i) q^{78} +(-3.62697 + 0.477500i) q^{79} +(0.107430 - 0.816011i) q^{80} +(0.866025 + 0.500000i) q^{81} +(2.72389 - 3.54984i) q^{82} +(3.72085 + 3.72085i) q^{83} +(1.19202 + 2.36201i) q^{84} +(-3.33900 - 0.605906i) q^{85} +(-1.62900 - 2.82151i) q^{86} +(-0.140569 + 0.0376653i) q^{87} +(-0.516688 - 0.0680233i) q^{88} +(-2.79672 + 1.61469i) q^{89} +(-0.760401 + 0.314968i) q^{90} +(-6.70053 + 13.9092i) q^{91} +(-3.70917 - 1.53639i) q^{92} +(-4.64601 - 1.24489i) q^{93} +(-1.35906 - 5.07209i) q^{94} +(1.47409 - 1.13111i) q^{95} +(-0.991445 + 0.130526i) q^{96} +(-13.9878 + 5.79395i) q^{97} +(6.41666 - 2.79759i) q^{98} +(0.199434 + 0.481477i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q + 8 q^{5} + 8 q^{10} + 16 q^{14} + 16 q^{15} + 48 q^{16} + 8 q^{17} + 48 q^{18} - 8 q^{19} + 16 q^{22} + 24 q^{25} + 32 q^{28} - 32 q^{29} - 16 q^{33} - 48 q^{37} - 16 q^{39} + 128 q^{41} + 16 q^{42}+ \cdots + 160 q^{97}+O(q^{100}) \) 96 * q + 8 * q^5 + 8 * q^10 + 16 * q^14 + 16 * q^15 + 48 * q^16 + 8 * q^17 + 48 * q^18 - 8 * q^19 + 16 * q^22 + 24 * q^25 + 32 * q^28 - 32 * q^29 - 16 * q^33 - 48 * q^37 - 16 * q^39 + 128 * q^41 + 16 * q^42 + 48 * q^43 - 8 * q^44 - 8 * q^46 - 112 * q^49 + 64 * q^50 - 16 * q^52 - 40 * q^53 + 16 * q^57 + 16 * q^58 - 24 * q^59 + 8 * q^60 - 56 * q^70 + 24 * q^73 + 48 * q^74 - 16 * q^76 + 16 * q^77 + 32 * q^78 - 56 * q^79 - 8 * q^80 - 80 * q^83 + 80 * q^85 + 16 * q^86 - 24 * q^87 + 16 * q^90 - 40 * q^91 + 16 * q^92 - 8 * q^93 - 8 * q^94 + 80 * q^95 + 160 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more