LMFDB - Embedded newform 588.2.n.f.263.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [588,2,Mod(263,588)] 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("588.263"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(588, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 3, 4])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 588 = 2^{2} \cdot 3 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	588.n (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [24,0,0,4,0,-12] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(6)] == traces)

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

Self dual:	no
Analytic conductor:	$4.69520363885$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 84)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			263.6
Character	$\chi$	$=$	588.263
Dual form			588.2.n.f.275.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.300756 - 1.38186i) q^{2} +(1.73104 - 0.0590228i) q^{3} +(-1.81909 + 0.831208i) q^{4} +(0.301907 - 0.174306i) q^{5} +(-0.602184 - 2.37432i) q^{6} +(1.69572 + 2.26374i) q^{8} +(2.99303 - 0.204342i) q^{9} +(-0.331667 - 0.364770i) q^{10} +(1.95188 - 3.38076i) q^{11} +(-3.09987 + 1.54623i) q^{12} -2.93923 q^{13} +(0.512326 - 0.319551i) q^{15} +(2.61819 - 3.02409i) q^{16} +(3.38076 + 1.95188i) q^{17} +(-1.18255 - 4.07450i) q^{18} +(4.83098 - 2.78917i) q^{19} +(-0.404312 + 0.568026i) q^{20} +(-5.25879 - 1.68045i) q^{22} +(-1.09094 - 1.88957i) q^{23} +(3.06898 + 3.81856i) q^{24} +(-2.43923 + 4.22488i) q^{25} +(0.883993 + 4.06162i) q^{26} +(5.16901 - 0.530383i) q^{27} -9.75220i q^{29} +(-0.595661 - 0.611858i) q^{30} +(2.28553 + 1.31955i) q^{31} +(-4.96631 - 2.70846i) q^{32} +(3.17925 - 5.96745i) q^{33} +(1.68045 - 5.25879i) q^{34} +(-5.27475 + 2.85955i) q^{36} +(-0.319551 - 0.553478i) q^{37} +(-5.30720 - 5.83689i) q^{38} +(-5.08795 + 0.173482i) q^{39} +(0.906533 + 0.387866i) q^{40} +7.57031i q^{41} -2.51757i q^{43} +(-0.740538 + 7.77233i) q^{44} +(0.867999 - 0.583396i) q^{45} +(-2.28302 + 2.07583i) q^{46} +(-2.18189 - 3.77914i) q^{47} +(4.35371 - 5.38936i) q^{48} +(6.57182 + 2.10003i) q^{50} +(5.96745 + 3.17925i) q^{51} +(5.34674 - 2.44312i) q^{52} +(-1.49119 - 0.860938i) q^{53} +(-2.28753 - 6.98335i) q^{54} -1.36090i q^{55} +(8.19802 - 5.11331i) q^{57} +(-13.4762 + 2.93304i) q^{58} +(-4.12318 + 7.14155i) q^{59} +(-0.666355 + 1.00714i) q^{60} +(7.04795 + 12.2074i) q^{61} +(1.13605 - 3.55515i) q^{62} +(-2.24908 + 7.67735i) q^{64} +(-0.887375 + 0.512326i) q^{65} +(-9.20238 - 2.59854i) q^{66} +(0.553478 + 0.319551i) q^{67} +(-7.77233 - 0.740538i) q^{68} +(-2.00000 - 3.20654i) q^{69} -11.9341 q^{71} +(5.53792 + 6.42895i) q^{72} +(-3.93923 + 6.82295i) q^{73} +(-0.668724 + 0.608037i) q^{74} +(-3.97306 + 7.45743i) q^{75} +(-6.46962 + 9.08930i) q^{76} +(1.76996 + 6.97867i) q^{78} +(-3.46410 + 2.00000i) q^{79} +(0.263332 - 1.36936i) q^{80} +(8.91649 - 1.22321i) q^{81} +(10.4611 - 2.27682i) q^{82} -8.94358 q^{83} +1.36090 q^{85} +(-3.47894 + 0.757175i) q^{86} +(-0.575602 - 16.8815i) q^{87} +(10.9630 - 1.31425i) q^{88} +(9.12760 - 5.26982i) q^{89} +(-1.06723 - 1.02400i) q^{90} +(3.55515 + 2.53050i) q^{92} +(4.03424 + 2.14930i) q^{93} +(-4.56604 + 4.15167i) q^{94} +(0.972337 - 1.68414i) q^{95} +(-8.75677 - 4.39535i) q^{96} -2.00000 q^{97} +(5.15121 - 10.5176i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 4 q^{4} - 12 q^{6} + 4 q^{9} - 4 q^{10} + 6 q^{12} - 4 q^{16} + 8 q^{18} - 32 q^{22} - 2 q^{24} + 12 q^{25} - 20 q^{30} + 16 q^{33} + 64 q^{34} - 40 q^{36} + 16 q^{37} - 20 q^{40} - 24 q^{45} + 92 q^{48}+ \cdots - 48 q^{97}+O(q^{100}) $ 24 * q + 4 * q^4 - 12 * q^6 + 4 * q^9 - 4 * q^10 + 6 * q^12 - 4 * q^16 + 8 * q^18 - 32 * q^22 - 2 * q^24 + 12 * q^25 - 20 * q^30 + 16 * q^33 + 64 * q^34 - 40 * q^36 + 16 * q^37 - 20 * q^40 - 24 * q^45 + 92 * q^48 + 28 * q^52 - 10 * q^54 + 32 * q^57 + 32 * q^58 - 28 * q^60 + 16 * q^61 + 40 * q^64 + 12 * q^66 - 48 * q^69 + 32 * q^72 - 24 * q^73 - 120 * q^76 + 40 * q^78 - 28 * q^81 - 8 * q^82 + 80 * q^85 + 56 * q^88 - 160 * q^90 - 24 * q^93 + 34 * q^96 - 48 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/588\mathbb{Z}\right)^\times$.

$n$	$197$	$295$	$493$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−0.300756	−	1.38186i	−0.212667	−	0.977125i
$2$	−0.300756	−	1.38186i	−0.212667	−	0.977125i
$3$	1.73104	−	0.0590228i	0.999419	−	0.0340768i
$3$	1.73104	−	0.0590228i	0.999419	−	0.0340768i
$4$	−1.81909	+	0.831208i	−0.909546	+	0.415604i
$5$	0.301907	−	0.174306i	0.135017	−	0.0779520i	−0.430970	−	0.902366i	$-0.641829\pi$
$5$	0.301907	−	0.174306i	0.135017	−	0.0779520i	0.565987	+	0.824414i	$0.308495\pi$
$6$	−0.602184	−	2.37432i	−0.245841	−	0.969310i
$7$		0			0
$7$		0			0
$8$	1.69572	+	2.26374i	0.599527	+	0.800354i
$9$	2.99303	−	0.204342i	0.997678	−	0.0681141i
$10$	−0.331667	−	0.364770i	−0.104882	−	0.115350i
$11$	1.95188	−	3.38076i	0.588514	−	1.01934i	−0.405913	−	0.913912i	$-0.633046\pi$
$11$	1.95188	−	3.38076i	0.588514	−	1.01934i	0.994427	−	0.105425i	$-0.0336203\pi$
$12$	−3.09987	+	1.54623i	−0.894855	+	0.446357i
$13$	−2.93923			−0.815197			−0.407599	−	0.913161i	$-0.633634\pi$
$13$	−2.93923			−0.815197			−0.407599	+	0.913161i	$0.633634\pi$
$14$		0			0
$15$	0.512326	−	0.319551i	0.132282	−	0.0825077i
$16$	2.61819	−	3.02409i	0.654547	−	0.756022i
$17$	3.38076	+	1.95188i	0.819954	+	0.473401i	0.850401	−	0.526136i	$-0.176360\pi$
$17$	3.38076	+	1.95188i	0.819954	+	0.473401i	−0.0304464	+	0.999536i	$0.509693\pi$
$18$	−1.18255	−	4.07450i	−0.278729	−	0.960370i
$19$	4.83098	−	2.78917i	1.10830	−	0.639879i	0.169914	−	0.985459i	$-0.445651\pi$
$19$	4.83098	−	2.78917i	1.10830	−	0.639879i	0.938389	+	0.345580i	$0.112318\pi$
$20$	−0.404312	+	0.568026i	−0.0904068	+	0.127014i
$21$		0			0
$22$	−5.25879	−	1.68045i	−1.12118	−	0.358273i
$23$	−1.09094	−	1.88957i	−0.227477	−	0.394003i	0.729582	−	0.683893i	$-0.239714\pi$
$23$	−1.09094	−	1.88957i	−0.227477	−	0.394003i	−0.957060	+	0.289890i	$0.906381\pi$
$24$	3.06898	+	3.81856i	0.626452	+	0.779460i
$25$	−2.43923	+	4.22488i	−0.487847	+	0.844976i
$26$	0.883993	+	4.06162i	0.173365	+	0.796549i
$27$	5.16901	−	0.530383i	0.994777	−	0.102072i
$28$		0			0
$29$		−	9.75220i		−	1.81094i	−0.424412	−	0.905469i	$-0.639519\pi$
$29$		−	9.75220i		−	1.81094i	0.424412	−	0.905469i	$-0.360481\pi$
$30$	−0.595661	−	0.611858i	−0.108752	−	0.111709i
$31$	2.28553	+	1.31955i	0.410493	+	0.236998i	0.691002	−	0.722853i	$-0.257170\pi$
$31$	2.28553	+	1.31955i	0.410493	+	0.236998i	−0.280508	+	0.959852i	$0.590503\pi$
$32$	−4.96631	−	2.70846i	−0.877928	−	0.478793i
$33$	3.17925	−	5.96745i	0.553437	−	1.03880i
$34$	1.68045	−	5.25879i	0.288195	−	0.901874i
$35$		0			0
$36$	−5.27475	+	2.85955i	−0.879125	+	0.476592i
$37$	−0.319551	−	0.553478i	−0.0525338	−	0.0909913i	0.838563	−	0.544805i	$-0.183396\pi$
$37$	−0.319551	−	0.553478i	−0.0525338	−	0.0909913i	−0.891096	+	0.453814i	$0.850063\pi$
$38$	−5.30720	−	5.83689i	−0.860941	−	0.946869i
$39$	−5.08795	+	0.173482i	−0.814724	+	0.0277793i
$40$	0.906533	+	0.387866i	0.143335	+	0.0613270i
$41$			7.57031i			1.18228i	0.806567	+	0.591142i	$0.201323\pi$
$41$			7.57031i			1.18228i	−0.806567	+	0.591142i	$0.798677\pi$
$42$		0			0
$43$		−	2.51757i		−	0.383926i	−0.981402	−	0.191963i	$-0.938515\pi$
$43$		−	2.51757i		−	0.383926i	0.981402	−	0.191963i	$-0.0614854\pi$
$44$	−0.740538	+	7.77233i	−0.111640	+	1.17172i
$45$	0.867999	−	0.583396i	0.129394	−	0.0869675i
$46$	−2.28302	+	2.07583i	−0.336613	+	0.306065i
$47$	−2.18189	−	3.77914i	−0.318261	−	0.551244i	0.661864	−	0.749624i	$-0.269765\pi$
$47$	−2.18189	−	3.77914i	−0.318261	−	0.551244i	−0.980125	+	0.198379i	$0.936432\pi$
$48$	4.35371	−	5.38936i	0.628404	−	0.777887i
$49$		0			0
$50$	6.57182	+	2.10003i	0.929396	+	0.296989i
$51$	5.96745	+	3.17925i	0.835610	+	0.445184i
$52$	5.34674	−	2.44312i	0.741459	−	0.338799i
$53$	−1.49119	−	0.860938i	−0.204830	−	0.118259i	0.394076	−	0.919078i	$-0.371065\pi$
$53$	−1.49119	−	0.860938i	−0.204830	−	0.118259i	−0.598907	+	0.800819i	$0.704398\pi$
$54$	−2.28753	−	6.98335i	−0.311293	−	0.950314i
$55$		−	1.36090i		−	0.183504i
$56$		0			0
$57$	8.19802	−	5.11331i	1.08585	−	0.677275i
$58$	−13.4762	+	2.93304i	−1.76951	+	0.385126i
$59$	−4.12318	+	7.14155i	−0.536792	+	0.929751i	0.462282	+	0.886733i	$0.347031\pi$
$59$	−4.12318	+	7.14155i	−0.536792	+	0.929751i	−0.999074	+	0.0430181i	$0.986303\pi$
$60$	−0.666355	+	1.00714i	−0.0860260	+	0.130021i
$61$	7.04795	+	12.2074i	0.902398	+	1.56300i	0.824372	+	0.566048i	$0.191528\pi$
$61$	7.04795	+	12.2074i	0.902398	+	1.56300i	0.0780257	+	0.996951i	$0.475138\pi$
$62$	1.13605	−	3.55515i	0.144279	−	0.451505i
$63$		0			0
$64$	−2.24908	+	7.67735i	−0.281135	+	0.959668i
$65$	−0.887375	+	0.512326i	−0.110065	+	0.0635462i
$66$	−9.20238	−	2.59854i	−1.13273	−	0.319859i
$67$	0.553478	+	0.319551i	0.0676181	+	0.0390393i	0.533428	−	0.845846i	$-0.320904\pi$
$67$	0.553478	+	0.319551i	0.0676181	+	0.0390393i	−0.465810	+	0.884885i	$0.654237\pi$
$68$	−7.77233	−	0.740538i	−0.942533	−	0.0898034i
$69$	−2.00000	−	3.20654i	−0.240772	−	0.386022i
$70$		0			0
$71$	−11.9341			−1.41632			−0.708158	−	0.706054i	$-0.750474\pi$
$71$	−11.9341			−1.41632			−0.708158	+	0.706054i	$0.750474\pi$
$72$	5.53792	+	6.42895i	0.652650	+	0.757659i
$73$	−3.93923	+	6.82295i	−0.461053	+	0.798566i	−0.999014	−	0.0444032i	$-0.985861\pi$
$73$	−3.93923	+	6.82295i	−0.461053	+	0.798566i	0.537961	+	0.842970i	$0.319195\pi$
$74$	−0.668724	+	0.608037i	−0.0777376	+	0.0706829i
$75$	−3.97306	+	7.45743i	−0.458770	+	0.861109i
$76$	−6.46962	+	9.08930i	−0.742116	+	1.04261i
$77$		0			0
$78$	1.76996	+	6.97867i	0.200409	+	0.790179i
$79$	−3.46410	+	2.00000i	−0.389742	+	0.225018i	−0.682048	−	0.731307i	$-0.738911\pi$
$79$	−3.46410	+	2.00000i	−0.389742	+	0.225018i	0.292306	+	0.956325i	$0.405577\pi$
$80$	0.263332	−	1.36936i	0.0294414	−	0.153099i
$81$	8.91649	−	1.22321i	0.990721	−	0.135912i
$82$	10.4611	−	2.27682i	1.15524	−	0.251433i
$83$	−8.94358			−0.981685			−0.490843	−	0.871248i	$-0.663311\pi$
$83$	−8.94358			−0.981685			−0.490843	+	0.871248i	$0.663311\pi$
$84$		0			0
$85$	1.36090			0.147610
$86$	−3.47894	+	0.757175i	−0.375144	+	0.0816483i
$87$	−0.575602	−	16.8815i	−0.0617110	−	1.80989i
$88$	10.9630	−	1.31425i	1.16866	−	0.140100i
$89$	9.12760	−	5.26982i	0.967523	−	0.558600i	0.0690430	−	0.997614i	$-0.478005\pi$
$89$	9.12760	−	5.26982i	0.967523	−	0.558600i	0.898480	+	0.439014i	$0.144672\pi$
$90$	−1.06723	−	1.02400i	−0.112496	−	0.107939i
$91$		0			0
$92$	3.55515	+	2.53050i	0.370650	+	0.263823i
$93$	4.03424	+	2.14930i	0.418331	+	0.222872i
$94$	−4.56604	+	4.15167i	−0.470951	+	0.428212i
$95$	0.972337	−	1.68414i	0.0997597	−	0.172789i
$96$	−8.75677	−	4.39535i	−0.893734	−	0.448598i
$97$	−2.00000			−0.203069			−0.101535	−	0.994832i	$-0.532375\pi$
$97$	−2.00000			−0.203069			−0.101535	+	0.994832i	$0.532375\pi$
$98$		0			0
$99$	5.15121	−	10.5176i	0.517716	−	1.05706i
$100$	0.925439	−	9.71295i	0.0925439	−	0.971295i
$101$	2.68047	+	1.54757i	0.266717	+	0.153989i	0.627395	−	0.778701i	$-0.284121\pi$
$101$	2.68047	+	1.54757i	0.266717	+	0.153989i	−0.360678	+	0.932690i	$0.617455\pi$
$102$	2.59854	−	9.20238i	0.257294	−	0.911171i
$103$	−6.26948	+	3.61968i	−0.617750	+	0.356658i	−0.775992	−	0.630742i	$-0.782751\pi$
$103$	−6.26948	+	3.61968i	−0.617750	+	0.356658i	0.158243	+	0.987400i	$0.449417\pi$
$104$	−4.98412	−	6.65368i	−0.488733	−	0.652447i
$105$		0			0
$106$	−0.741214	+	2.31955i	−0.0719931	+	0.225295i
$107$	−5.50703	−	9.53846i	−0.532385	−	0.922118i	−0.999285	−	0.0378077i	$-0.987963\pi$
$107$	−5.50703	−	9.53846i	−0.532385	−	0.922118i	0.466900	−	0.884310i	$-0.345371\pi$
$108$	−8.96205	+	5.26134i	−0.862374	+	0.506273i
$109$	−0.699867	+	1.21220i	−0.0670351	+	0.116108i	−0.897595	−	0.440821i	$-0.854687\pi$
$109$	−0.699867	+	1.21220i	−0.0670351	+	0.116108i	0.830560	+	0.556929i	$0.188021\pi$
$110$	−1.88058	+	0.409299i	−0.179306	+	0.0390251i
$111$	−0.585825	−	0.939235i	−0.0556040	−	0.0891482i
$112$		0			0
$113$			8.83218i			0.830862i	0.909625	+	0.415431i	$0.136369\pi$
$113$			8.83218i			0.830862i	−0.909625	+	0.415431i	$0.863631\pi$
$114$	−9.53150	−	9.79068i	−0.892707	−	0.916981i
$115$	−0.658727	−	0.380316i	−0.0614266	−	0.0354646i
$116$	8.10611	+	17.7401i	0.752633	+	1.64713i
$117$	−8.79723	+	0.600610i	−0.813304	+	0.0555264i
$118$	11.1087	+	3.54980i	1.02264	+	0.326786i
$119$		0			0
$120$	1.59214	+	0.617907i	0.145342	+	0.0564069i
$121$	−2.11968	−	3.67140i	−0.192699	−	0.333764i
$122$	14.7493	−	13.4108i	1.33534	−	1.21415i
$123$	0.446821	+	13.1046i	0.0402885	+	1.18160i
$124$	−5.25441	−	0.500634i	−0.471860	−	0.0449582i
$125$			3.44375i			0.308019i
$126$		0			0
$127$			12.3960i			1.09997i	0.835174	+	0.549985i	$0.185367\pi$
$127$			12.3960i			1.09997i	−0.835174	+	0.549985i	$0.814633\pi$
$128$	11.2855	+	0.798907i	0.997504	+	0.0706140i
$129$	−0.148594	−	4.35803i	−0.0130830	−	0.383703i
$130$	0.974848	+	1.07215i	0.0854998	+	0.0940334i
$131$	−0.805238	−	1.39471i	−0.0703540	−	0.121857i	0.828702	−	0.559689i	$-0.189080\pi$
$131$	−0.805238	−	1.39471i	−0.0703540	−	0.121857i	−0.899056	+	0.437833i	$0.855746\pi$
$132$	−0.823160	+	13.4980i	−0.0716469	+	1.17485i
$133$		0			0
$134$	0.275113	−	0.860938i	0.0237662	−	0.0743737i
$135$	1.46811	−	1.06112i	0.126355	−	0.0913263i
$136$	1.31425	+	10.9630i	0.112696	+	0.940071i
$137$	3.77914	+	2.18189i	0.322874	+	0.186411i	0.652673	−	0.757640i	$-0.273648\pi$
$137$	3.77914	+	2.18189i	0.322874	+	0.186411i	−0.329799	+	0.944051i	$0.606981\pi$
$138$	−3.82949	+	3.72811i	−0.325988	+	0.317358i
$139$			16.8177i			1.42646i	0.700931	+	0.713230i	$0.252768\pi$
$139$			16.8177i			1.42646i	−0.700931	+	0.713230i	$0.747232\pi$
$140$		0			0
$141$	−4.00000	−	6.41308i	−0.336861	−	0.540079i
$142$	3.58925	+	16.4913i	0.301203	+	1.38392i
$143$	−5.73704	+	9.93684i	−0.479755	+	0.830961i
$144$	7.21837	−	9.58619i	0.601531	−	0.798850i
$145$	−1.69987	−	2.94426i	−0.141166	−	0.244507i
$146$	10.6131	+	3.39144i	0.878350	+	0.280677i
$147$		0			0
$148$	1.04135	+	0.741214i	0.0855982	+	0.0609274i
$149$	6.63421	−	3.83026i	0.543496	−	0.313788i	−0.202999	−	0.979179i	$-0.565069\pi$
$149$	6.63421	−	3.83026i	0.543496	−	0.313788i	0.746495	+	0.665391i	$0.231735\pi$
$150$	11.5001	+	3.24736i	0.938976	+	0.265146i
$151$	10.9458	+	6.31955i	0.890755	+	0.514278i	0.874189	−	0.485585i	$-0.161393\pi$
$151$	10.9458	+	6.31955i	0.890755	+	0.514278i	0.0165658	+	0.999863i	$0.494727\pi$
$152$	14.5059	+	6.20646i	1.17659	+	0.503411i
$153$	10.5176	+	5.15121i	0.850295	+	0.416451i
$154$		0			0
$155$	0.920022			0.0738980
$156$	9.11124	−	4.54472i	0.729483	−	0.363869i
$157$	−0.108719	+	0.188307i	−0.00867672	+	0.0150285i	−0.870331	−	0.492467i	$-0.836095\pi$
$157$	−0.108719	+	0.188307i	−0.00867672	+	0.0150285i	0.861654	+	0.507495i	$0.169429\pi$
$158$	3.80558	+	4.18540i	0.302755	+	0.332973i
$159$	−2.63213	−	1.40231i	−0.208741	−	0.111210i
$160$	−1.97146	+	0.0479539i	−0.155858	+	0.00379109i
$161$		0			0
$162$	−4.37199	−	11.9535i	−0.343496	−	0.939154i
$163$	4.53743	−	2.61968i	0.355399	−	0.205189i	−0.311662	−	0.950193i	$-0.600886\pi$
$163$	4.53743	−	2.61968i	0.355399	−	0.205189i	0.667060	+	0.745004i	$0.267552\pi$
$164$	−6.29250	−	13.7711i	−0.491362	−	1.07534i
$165$	−0.0803240	−	2.35578i	−0.00625322	−	0.183397i
$166$	2.68984	+	12.3588i	0.208772	+	0.959229i
$167$	11.4741			0.887891			0.443945	−	0.896054i	$-0.353578\pi$
$167$	11.4741			0.887891			0.443945	+	0.896054i	$0.353578\pi$
$168$		0			0
$169$	−4.36090			−0.335454
$170$	−0.409299	−	1.88058i	−0.0313918	−	0.144234i
$171$	13.8893	−	9.33524i	1.06214	−	0.713884i
$172$	2.09263	+	4.57969i	0.159561	+	0.349198i
$173$	−18.3642	+	10.6025i	−1.39620	+	0.806097i	−0.993992	−	0.109451i	$-0.965091\pi$
$173$	−18.3642	+	10.6025i	−1.39620	+	0.806097i	−0.402208	+	0.915548i	$0.631757\pi$
$174$	−23.1548	+	5.87262i	−1.75536	+	0.445202i
$175$		0			0
$176$	−5.11331	−	14.7541i	−0.385430	−	1.11213i
$177$	−6.71589	+	12.6057i	−0.504797	+	0.947503i
$178$	−10.0274	−	11.0282i	−0.751582	−	0.826595i
$179$	0.906046	−	1.56932i	0.0677211	−	0.117296i	−0.830177	−	0.557500i	$-0.811761\pi$
$179$	0.906046	−	1.56932i	0.0677211	−	0.117296i	0.897898	+	0.440204i	$0.145094\pi$
$180$	−1.09405	+	1.78274i	−0.0815454	+	0.132877i
$181$	7.53950			0.560407			0.280203	−	0.959941i	$-0.409598\pi$
$181$	7.53950			0.560407			0.280203	+	0.959941i	$0.409598\pi$
$182$		0			0
$183$	12.9208	+	20.7156i	0.955136	+	1.53134i
$184$	2.42757	−	5.67380i	0.178963	−	0.418278i
$185$	−0.192949	−	0.111399i	−0.0141859	−	0.00819023i
$186$	1.75672	−	6.22118i	0.128809	−	0.456159i
$187$	13.1977	−	7.61968i	0.965110	−	0.557206i
$188$	7.11030	+	5.06100i	0.518572	+	0.369111i
$189$		0			0
$190$	−2.61968	−	0.837122i	−0.190052	−	0.0607312i
$191$	0.815830	+	1.41306i	0.0590314	+	0.102245i	0.894031	−	0.448005i	$-0.147865\pi$
$191$	0.815830	+	1.41306i	0.0590314	+	0.102245i	−0.834999	+	0.550251i	$0.814532\pi$
$192$	−3.44011	+	13.4226i	−0.248269	+	0.968691i
$193$	7.57834	−	13.1261i	0.545501	−	0.944835i	−0.453075	−	0.891473i	$-0.649673\pi$
$193$	7.57834	−	13.1261i	0.545501	−	0.944835i	0.998575	−	0.0533622i	$-0.0169938\pi$
$194$	0.601512	+	2.76373i	0.0431861	+	0.198424i
$195$	−1.50585	+	0.939235i	−0.107836	+	0.0672600i
$196$		0			0
$197$			21.2263i			1.51231i	0.654393	+	0.756155i	$0.272924\pi$
$197$			21.2263i			1.51231i	−0.654393	+	0.756155i	$0.727076\pi$
$198$	−16.0831	−	3.95505i	−1.14298	−	0.281073i
$199$	−3.25361	−	1.87847i	−0.230642	−	0.133161i	0.380226	−	0.924894i	$-0.375846\pi$
$199$	−3.25361	−	1.87847i	−0.230642	−	0.133161i	−0.610868	+	0.791732i	$0.709179\pi$
$200$	−13.7003	+	1.64240i	−0.968758	+	0.116135i
$201$	0.976956	+	0.520489i	0.0689092	+	0.0367125i
$202$	1.33236	−	4.16948i	0.0937447	−	0.293364i
$203$		0			0
$204$	−13.4980	−	0.823160i	−0.945046	−	0.0576328i
$205$	1.31955	+	2.28553i	0.0921614	+	0.159628i
$206$	6.88749	+	7.57492i	0.479874	+	0.527769i
$207$	−3.65135	−	5.43262i	−0.253786	−	0.377593i
$208$	−7.69547	+	8.88850i	−0.533585	+	0.616307i
$209$		−	21.7765i		−	1.50631i
$210$		0			0
$211$		−	9.83963i		−	0.677388i	−0.940897	−	0.338694i	$-0.890015\pi$
$211$		−	9.83963i		−	0.677388i	0.940897	−	0.338694i	$-0.109985\pi$
$212$	3.42823	+	0.326637i	0.235452	+	0.0224335i
$213$	−20.6584	+	0.704383i	−1.41549	+	0.0482635i
$214$	−11.5246	+	10.4787i	−0.787804	+	0.716310i
$215$	−0.438828	−	0.760072i	−0.0299278	−	0.0518365i
$216$	9.96584	+	10.8019i	0.678090	+	0.734979i
$217$		0			0
$218$	1.88559	+	0.602542i	0.127708	+	0.0408093i
$219$	−6.41628	+	12.0433i	−0.433572	+	0.813814i
$220$	1.13119	+	2.47560i	0.0762648	+	0.166905i
$221$	−9.93684	−	5.73704i	−0.668424	−	0.385915i
$222$	−1.12170	+	1.09201i	−0.0752838	+	0.0732909i
$223$		−	22.9136i		−	1.53441i	−0.641403	−	0.767204i	$-0.721647\pi$
$223$		−	22.9136i		−	1.53441i	0.641403	−	0.767204i	$-0.278353\pi$
$224$		0			0
$225$	−6.43739	+	13.1436i	−0.429159	+	0.876243i
$226$	12.2049	−	2.65633i	0.811855	−	0.176697i
$227$	−6.76508	+	11.7175i	−0.449014	+	0.777715i	−0.998322	−	0.0579050i	$-0.981558\pi$
$227$	−6.76508	+	11.7175i	−0.449014	+	0.777715i	0.549308	+	0.835620i	$0.314891\pi$
$228$	−10.6627	+	16.1158i	−0.706156	+	1.06730i
$229$	−7.34809	−	12.7273i	−0.485575	−	0.841041i	0.514287	−	0.857618i	$-0.328056\pi$
$229$	−7.34809	−	12.7273i	−0.485575	−	0.841041i	−0.999863	+	0.0165769i	$0.994723\pi$
$230$	−0.327428	+	1.02465i	−0.0215900	+	0.0675636i
$231$		0			0
$232$	22.0765	−	16.5370i	1.44939	−	1.08571i
$233$	−14.8869	+	8.59497i	−0.975274	+	0.563075i	−0.900840	−	0.434151i	$-0.857048\pi$
$233$	−14.8869	+	8.59497i	−0.975274	+	0.563075i	−0.0744343	+	0.997226i	$0.523715\pi$
$234$	3.47578	+	11.9759i	0.227219	+	0.782891i
$235$	−1.31745	−	0.760632i	−0.0859412	−	0.0496182i
$236$	1.56432	−	16.4184i	0.101829	−	1.06874i
$237$	−5.87847	+	3.66655i	−0.381848	+	0.238168i
$238$		0			0
$239$	−14.5336			−0.940102			−0.470051	−	0.882639i	$-0.655764\pi$
$239$	−14.5336			−0.940102			−0.470051	+	0.882639i	$0.655764\pi$
$240$	0.375016	−	2.38596i	0.0242072	−	0.154013i
$241$	9.39604	−	16.2744i	0.605252	−	1.04833i	−0.386759	−	0.922181i	$-0.626406\pi$
$241$	9.39604	−	16.2744i	0.605252	−	1.04833i	0.992012	−	0.126147i	$-0.0402611\pi$
$242$	−4.43586	+	4.03331i	−0.285148	+	0.259271i
$243$	15.3626	−	2.64370i	0.985514	−	0.169593i
$244$	−22.9678	−	16.3481i	−1.47036	−	1.04658i
$245$		0			0
$246$	17.9743	−	4.55872i	1.14600	−	0.290653i
$247$	−14.1994	+	8.19802i	−0.903485	+	0.521628i
$248$	0.888488	+	7.41144i	0.0564191	+	0.470627i
$249$	−15.4817	+	0.527875i	−0.981115	+	0.0334527i
$250$	4.75879	−	1.03573i	0.300973	−	0.0655053i
$251$	−20.6405			−1.30281			−0.651407	−	0.758729i	$-0.725821\pi$
$251$	−20.6405			−1.30281			−0.651407	+	0.758729i	$0.725821\pi$
$252$		0			0
$253$	−8.51757			−0.535495
$254$	17.1296	−	3.72819i	1.07481	−	0.233927i
$255$	2.35578	−	0.0803240i	0.147524	−	0.00503008i
$256$	−2.29019	−	15.8352i	−0.143137	−	0.989703i
$257$	−4.17752	+	2.41189i	−0.260587	+	0.150450i	−0.624602	−	0.780943i	$-0.714739\pi$
$257$	−4.17752	+	2.41189i	−0.260587	+	0.150450i	0.364016	+	0.931393i	$0.381406\pi$
$258$	−5.97751	+	1.51604i	−0.372143	+	0.0943846i
$259$		0			0
$260$	1.18837	−	1.66956i	0.0736994	−	0.103542i
$261$	−1.99279	−	29.1887i	−0.123350	−	1.80673i
$262$	−1.68512	+	1.53220i	−0.104107	+	0.0946595i
$263$	7.22891	−	12.5208i	0.445754	−	0.772068i	−0.552351	−	0.833612i	$-0.686269\pi$
$263$	7.22891	−	12.5208i	0.445754	−	0.772068i	0.998104	+	0.0615439i	$0.0196024\pi$
$264$	18.8999	−	2.92210i	1.16321	−	0.179843i
$265$	−0.600267			−0.0368741
$266$		0			0
$267$	15.4892	−	9.66103i	0.947926	−	0.591246i
$268$	−1.27244	−	0.121237i	−0.0777267	−	0.00740571i
$269$	−4.08105	−	2.35619i	−0.248826	−	0.143660i	0.370401	−	0.928872i	$-0.379220\pi$
$269$	−4.08105	−	2.35619i	−0.248826	−	0.143660i	−0.619226	+	0.785212i	$0.712554\pi$
$270$	−1.90786	−	1.70959i	−0.116109	−	0.104042i
$271$	−13.5743	+	7.83712i	−0.824580	+	0.476071i	−0.851993	−	0.523553i	$-0.824606\pi$
$271$	−13.5743	+	7.83712i	−0.824580	+	0.476071i	0.0274135	+	0.999624i	$0.491273\pi$
$272$	14.7541	−	5.11331i	0.894600	−	0.310040i
$273$		0			0
$274$	1.87847	−	5.87847i	0.113483	−	0.355131i
$275$	9.52220	+	16.4929i	0.574210	+	0.994561i
$276$	6.30348	+	4.17057i	0.379425	+	0.251039i
$277$	−8.49815	+	14.7192i	−0.510605	+	0.884393i	0.489320	+	0.872104i	$0.337245\pi$
$277$	−8.49815	+	14.7192i	−0.510605	+	0.884393i	−0.999924	+	0.0122887i	$0.996088\pi$
$278$	23.2398	−	5.05803i	1.39383	−	0.303360i
$279$	7.11030	+	3.48243i	0.425683	+	0.208488i
$280$		0			0
$281$			5.75822i			0.343507i	0.985140	+	0.171753i	$0.0549432\pi$
$281$			5.75822i			0.343507i	−0.985140	+	0.171753i	$0.945057\pi$
$282$	−7.65897	+	7.45623i	−0.456085	+	0.444012i
$283$	4.83098	+	2.78917i	0.287172	+	0.165799i	0.636666	−	0.771140i	$-0.280313\pi$
$283$	4.83098	+	2.78917i	0.287172	+	0.165799i	−0.349494	+	0.936939i	$0.613646\pi$
$284$	21.7092	−	9.91971i	1.28820	−	0.588626i
$285$	1.58376	−	2.97271i	0.0938137	−	0.176088i
$286$	15.4568	+	4.93923i	0.913980	+	0.292063i
$287$		0			0
$288$	−15.4178	−	7.09169i	−0.908501	−	0.417882i
$289$	−0.880316	−	1.52475i	−0.0517833	−	0.0896913i
$290$	−3.55731	+	3.23449i	−0.208893	+	0.189936i
$291$	−3.46209	+	0.118046i	−0.202951	+	0.00691995i
$292$	1.49453	−	15.6859i	0.0874610	−	0.917948i
$293$		−	23.7712i		−	1.38873i	−0.719624	−	0.694364i	$-0.755686\pi$
$293$		−	23.7712i		−	1.38873i	0.719624	−	0.694364i	$-0.244314\pi$
$294$		0			0
$295$			2.87478i			0.167376i
$296$	0.711065	−	1.66192i	0.0413298	−	0.0965974i
$297$	8.29621	−	18.5104i	0.481395	−	1.07408i
$298$	−7.28818	−	8.01560i	−0.422193	−	0.464331i
$299$	3.20654	+	5.55389i	0.185439	+	0.321190i
$300$	1.02869	−	16.8682i	0.0593915	−	0.973885i
$301$		0			0
$302$	5.44074	−	17.0262i	0.313080	−	0.979749i
$303$	4.73136	+	2.52070i	0.271809	+	0.144811i
$304$	4.21373	−	21.9119i	0.241674	−	1.25673i
$305$	4.25565	+	2.45700i	0.243678	+	0.140687i
$306$	3.95505	−	16.0831i	0.226095	−	0.919410i
$307$		−	3.69987i		−	0.211163i	−0.994411	−	0.105581i	$-0.966330\pi$
$307$		−	3.69987i		−	0.211163i	0.994411	−	0.105581i	$-0.0336703\pi$
$308$		0			0
$309$	−10.6391	+	6.63588i	−0.605237	+	0.377502i
$310$	−0.276702	−	1.27134i	−0.0157156	−	0.0722075i
$311$	−3.79236	+	6.56857i	−0.215045	+	0.372469i	−0.953287	−	0.302067i	$-0.902323\pi$
$311$	−3.79236	+	6.56857i	−0.215045	+	0.372469i	0.738241	+	0.674537i	$0.235657\pi$
$312$	−9.02045	−	11.2236i	−0.510682	−	0.635413i
$313$	−7.81770	−	13.5407i	−0.441883	−	0.765363i	0.555946	−	0.831218i	$-0.312356\pi$
$313$	−7.81770	−	13.5407i	−0.441883	−	0.765363i	−0.997829	+	0.0658547i	$0.979023\pi$
$314$	0.292912	+	0.0936004i	0.0165300	+	0.00528217i
$315$		0			0
$316$	4.63910	−	6.51757i	0.260970	−	0.366642i
$317$	−12.0318	+	6.94659i	−0.675776	+	0.390159i	−0.798262	−	0.602311i	$-0.794247\pi$
$317$	−12.0318	+	6.94659i	−0.675776	+	0.390159i	0.122486	+	0.992470i	$0.460913\pi$
$318$	−1.14617	+	4.05900i	−0.0642740	+	0.227617i
$319$	−32.9698	−	19.0351i	−1.84596	−	1.06576i
$320$	0.659196	+	2.70987i	0.0368502	+	0.151486i
$321$	−10.0959	−	16.1865i	−0.563499	−	0.903440i
$322$		0			0
$323$	21.7765			1.21168
$324$	−15.2032	+	9.63658i	−0.844621	+	0.535365i
$325$	7.16948	−	12.4179i	0.397691	−	0.688822i
$326$	−4.98470	−	5.48222i	−0.276077	−	0.303632i
$327$	−1.13995	+	2.13969i	−0.0630395	+	0.118325i
$328$	−17.1373	+	12.8371i	−0.946247	+	0.708811i
$329$		0			0
$330$	−3.23120	+	0.819511i	−0.177872	+	0.0451126i
$331$	27.5359	−	15.8979i	1.51351	−	0.873827i	0.513638	−	0.858007i	$-0.328298\pi$
$331$	27.5359	−	15.8979i	1.51351	−	0.873827i	0.999875	−	0.0158198i	$-0.00503580\pi$
$332$	16.2692	−	7.43397i	0.892888	−	0.407992i
$333$	−1.06952	−	1.59128i	−0.0586096	−	0.0872016i
$334$	−3.45090	−	15.8556i	−0.188825	−	0.867580i
$335$	0.222798			0.0121728
$336$		0			0
$337$	−17.1178			−0.932468			−0.466234	−	0.884661i	$-0.654390\pi$
$337$	−17.1178			−0.932468			−0.466234	+	0.884661i	$0.654390\pi$
$338$	1.31157	+	6.02616i	0.0713399	+	0.327780i
$339$	0.521300	+	15.2889i	0.0283131	+	0.830379i
$340$	−2.47560	+	1.13119i	−0.134258	+	0.0613474i
$341$	8.92216	−	5.15121i	0.483162	−	0.278954i
$342$	−17.0773	−	16.3855i	−0.923437	−	0.886028i
$343$		0			0
$344$	5.69914	−	4.26909i	0.307277	−	0.230174i
$345$	−1.16273	−	0.619464i	−0.0625994	−	0.0333508i
$346$	20.1744	+	22.1880i	1.08458	+	1.19283i
$347$	−4.22398	+	7.31616i	−0.226755	+	0.392752i	−0.956845	−	0.290600i	$-0.906145\pi$
$347$	−4.22398	+	7.31616i	−0.226755	+	0.392752i	0.730089	+	0.683352i	$0.239478\pi$
$348$	15.0791	+	30.2305i	0.808325	+	1.62053i
$349$	17.4956			0.936520			0.468260	−	0.883591i	$-0.344881\pi$
$349$	17.4956			0.936520			0.468260	+	0.883591i	$0.344881\pi$
$350$		0			0
$351$	−15.1929	+	1.55892i	−0.810939	+	0.0832089i
$352$	−18.8503	+	11.5033i	−1.00472	+	0.613127i
$353$	7.15990	+	4.13377i	0.381083	+	0.220018i	0.678289	−	0.734795i	$-0.262722\pi$
$353$	7.15990	+	4.13377i	0.381083	+	0.220018i	−0.297206	+	0.954813i	$0.596055\pi$
$354$	19.4392	+	5.48920i	1.03318	+	0.291747i
$355$	−3.60298	+	2.08018i	−0.191226	+	0.110405i
$356$	−12.2236	+	17.1732i	−0.647850	+	0.910179i
$357$		0			0
$358$	−2.44108	−	0.780049i	−0.129015	−	0.0412269i
$359$	−12.5650	−	21.7633i	−0.663156	−	1.14862i	−0.979782	−	0.200070i	$-0.935883\pi$
$359$	−12.5650	−	21.7633i	−0.663156	−	1.14862i	0.316625	−	0.948551i	$-0.397450\pi$
$360$	2.79254	+	0.975652i	0.147180	+	0.0514214i
$361$	6.05892	−	10.4944i	0.318890	−	0.552334i
$362$	−2.26755	−	10.4186i	−0.119180	−	0.547587i
$363$	−3.88596	−	6.23025i	−0.203960	−	0.327003i
$364$		0			0
$365$			2.74653i			0.143760i
$366$	24.7401	−	24.0852i	1.29319	−	1.25895i
$367$	−18.8041	−	10.8565i	−0.981565	−	0.566707i	−0.0788227	−	0.996889i	$-0.525116\pi$
$367$	−18.8041	−	10.8565i	−0.981565	−	0.566707i	−0.902742	+	0.430182i	$0.858449\pi$
$368$	−8.57052	−	1.64814i	−0.446769	−	0.0859152i
$369$	1.54693	+	22.6582i	0.0805302	+	1.17954i
$370$	−0.0959078	+	0.300133i	−0.00498601	+	0.0156032i
$371$		0			0
$372$	−9.12516	−	0.556490i	−0.473118	−	0.0288526i
$373$	0.360898	+	0.625094i	0.0186866	+	0.0323662i	0.875217	−	0.483730i	$-0.160718\pi$
$373$	0.360898	+	0.625094i	0.0186866	+	0.0323662i	−0.856531	+	0.516096i	$0.827385\pi$
$374$	−14.4986	−	15.9457i	−0.749707	−	0.824534i
$375$	0.203260	+	5.96129i	0.0104963	+	0.307840i
$376$	4.85514	−	11.3476i	0.250385	−	0.585207i
$377$			28.6640i			1.47627i
$378$		0			0
$379$		−	18.2745i		−	0.938699i	−0.883013	−	0.469349i	$-0.844489\pi$
$379$		−	18.2745i		−	0.938699i	0.883013	−	0.469349i	$-0.155511\pi$
$380$	−0.368902	+	3.87181i	−0.0189243	+	0.198620i
$381$	0.731649	+	21.4581i	0.0374835	+	1.09933i
$382$	1.70729	−	1.55235i	0.0873525	−	0.0794252i
$383$	1.02465	+	1.77475i	0.0523573	+	0.0906855i	0.891016	−	0.453971i	$-0.149993\pi$
$383$	1.02465	+	1.77475i	0.0523573	+	0.0906855i	−0.838659	+	0.544657i	$0.816660\pi$
$384$	19.5828	+	0.716843i	0.999331	+	0.0365813i
$385$		0			0
$386$	−20.4177	−	6.52448i	−1.03923	−	0.332087i
$387$	−0.514446	−	7.53517i	−0.0261508	−	0.383034i
$388$	3.63818	−	1.66242i	0.184701	−	0.0843964i
$389$	−9.65328	−	5.57332i	−0.489441	−	0.282579i	0.234902	−	0.972019i	$-0.424523\pi$
$389$	−9.65328	−	5.57332i	−0.489441	−	0.282579i	−0.724342	+	0.689440i	$0.757857\pi$
$390$	1.75079	+	1.79839i	0.0886545	+	0.0910652i
$391$		−	8.51757i		−	0.430752i
$392$		0			0
$393$	−1.47622	−	2.36678i	−0.0744656	−	0.119389i
$394$	29.3318	−	6.38394i	1.47772	−	0.321618i
$395$	−0.697224	+	1.20763i	−0.0350811	+	0.0607623i
$396$	−0.628241	+	23.4142i	−0.0315703	+	1.17661i
$397$	−3.98719	−	6.90601i	−0.200111	−	0.346603i	0.748453	−	0.663188i	$-0.230797\pi$
$397$	−3.98719	−	6.90601i	−0.200111	−	0.346603i	−0.948564	+	0.316585i	$0.897464\pi$
$398$	−1.61725	+	5.06100i	−0.0810652	+	0.253685i
$399$		0			0
$400$	6.39002	+	18.4380i	0.319501	+	0.921899i
$401$	18.6004	−	10.7390i	0.928860	−	0.536278i	0.0424093	−	0.999100i	$-0.486497\pi$
$401$	18.6004	−	10.7390i	0.928860	−	0.536278i	0.886451	+	0.462823i	$0.153163\pi$
$402$	0.425419	−	1.50656i	0.0212180	−	0.0751404i
$403$	−6.71771	−	3.87847i	−0.334633	−	0.193200i
$404$	−6.16237	−	0.587144i	−0.306589	−	0.0292115i
$405$	2.47874	−	1.92349i	0.123169	−	0.0955790i
$406$		0			0
$407$	−2.49490			−0.123668
$408$	2.92210	+	18.8999i	0.144665	+	0.935684i
$409$	−18.4568	+	31.9681i	−0.912630	+	1.58072i	−0.102296	+	0.994754i	$0.532619\pi$
$409$	−18.4568	+	31.9681i	−0.912630	+	1.58072i	−0.810334	+	0.585968i	$0.800714\pi$
$410$	2.76143	−	2.51083i	0.136377	−	0.124001i
$411$	6.67064	+	3.55389i	0.329038	+	0.175300i
$412$	8.39604	−	11.7958i	0.413643	−	0.581136i
$413$		0			0
$414$	−6.40897	+	6.67956i	−0.314984	+	0.328282i
$415$	−2.70013	+	1.55892i	−0.132544	+	0.0765243i
$416$	14.5971	+	7.96081i	0.715684	+	0.390311i
$417$	0.992628	+	29.1122i	0.0486092	+	1.42563i
$418$	−30.0921	+	6.54942i	−1.47186	+	0.320343i
$419$	29.5773			1.44494			0.722472	−	0.691400i	$-0.243006\pi$
$419$	29.5773			1.44494			0.722472	+	0.691400i	$0.243006\pi$
$420$		0			0
$421$	36.8309			1.79503			0.897515	−	0.440985i	$-0.145371\pi$
$421$	36.8309			1.79503			0.897515	+	0.440985i	$0.145371\pi$
$422$	−13.5970	+	2.95933i	−0.661893	+	0.144058i
$423$	−7.30270	−	10.8652i	−0.355069	−	0.528286i
$424$	−0.579692	−	4.83558i	−0.0281523	−	0.234836i
$425$	−16.4929	+	9.52220i	−0.800024	+	0.461894i
$426$	7.18652	+	28.3353i	0.348188	+	1.37285i
$427$		0			0
$428$	17.9462	+	12.7738i	0.867464	+	0.617447i
$429$	−9.34457	+	17.5397i	−0.451160	+	0.846826i
$430$	−0.918335	+	0.834996i	−0.0442861	+	0.0402671i
$431$	2.33839	−	4.05022i	0.112636	−	0.195092i	−0.804196	−	0.594364i	$-0.797404\pi$
$431$	2.33839	−	4.05022i	0.112636	−	0.195092i	0.916832	+	0.399272i	$0.130737\pi$
$432$	11.9295	−	17.0202i	0.573959	−	0.818884i
$433$	−16.5564			−0.795650			−0.397825	−	0.917461i	$-0.630235\pi$
$433$	−16.5564			−0.795650			−0.397825	+	0.917461i	$0.630235\pi$
$434$		0			0
$435$	−3.11632	−	4.99631i	−0.149416	−	0.239555i
$436$	0.265527	−	2.78685i	0.0127165	−	0.133466i
$437$	−10.5407	−	6.08565i	−0.504228	−	0.291116i
$438$	18.5720	+	5.24431i	0.887404	+	0.250583i
$439$	−22.9313	+	13.2394i	−1.09445	+	0.631881i	−0.934758	−	0.355286i	$-0.884383\pi$
$439$	−22.9313	+	13.2394i	−1.09445	+	0.631881i	−0.159692	+	0.987167i	$0.551050\pi$
$440$	3.08073	−	2.30770i	0.146868	−	0.110015i
$441$		0			0
$442$	−4.93923	+	15.4568i	−0.234935	+	0.735205i
$443$	−2.30049	−	3.98457i	−0.109300	−	0.189313i	0.806187	−	0.591661i	$-0.201528\pi$
$443$	−2.30049	−	3.98457i	−0.109300	−	0.189313i	−0.915487	+	0.402348i	$0.868194\pi$
$444$	1.84637	+	1.22161i	0.0876247	+	0.0579751i
$445$	1.83712	−	3.18199i	0.0870879	−	0.150841i
$446$	−31.6635	+	6.89141i	−1.49931	+	0.326318i
$447$	11.2580	−	7.02193i	0.532487	−	0.332126i
$448$		0			0
$449$		−	17.0095i		−	0.802728i	−0.915919	−	0.401364i	$-0.868536\pi$
$449$		−	17.0095i		−	0.802728i	0.915919	−	0.401364i	$-0.131464\pi$
$450$	20.0988	+	4.94256i	0.947466	+	0.232994i
$451$	25.5934	+	14.7764i	1.20515	+	0.695791i
$452$	−7.34138	−	16.0665i	−0.345309	−	0.755706i
$453$	19.3206	+	10.2934i	0.907763	+	0.483625i
$454$	18.2266	+	5.82431i	0.855415	+	0.273348i
$455$		0			0
$456$	25.4768	+	9.88748i	1.19306	+	0.463024i
$457$	7.71559	+	13.3638i	0.360920	+	0.625132i	0.988113	−	0.153732i	$-0.0491293\pi$
$457$	7.71559	+	13.3638i	0.360920	+	0.625132i	−0.627192	+	0.778864i	$0.715796\pi$
$458$	−15.3773	+	13.9819i	−0.718536	+	0.653329i
$459$	18.5104	+	8.29621i	0.863993	+	0.387234i
$460$	1.51441	+	0.144291i	0.0706095	+	0.00672759i
$461$			33.3764i			1.55449i	0.629196	+	0.777247i	$0.283384\pi$
$461$			33.3764i			1.55449i	−0.629196	+	0.777247i	$0.716616\pi$
$462$		0			0
$463$			26.4787i			1.23057i	0.788304	+	0.615286i	$0.210959\pi$
$463$			26.4787i			1.23057i	−0.788304	+	0.615286i	$0.789041\pi$
$464$	−29.4915	−	25.5331i	−1.36911	−	1.18534i
$465$	1.59260	−	0.0543023i	0.0738550	−	0.00251821i
$466$	16.3544	+	17.9867i	0.757603	+	0.833217i
$467$	9.29557	+	16.1004i	0.430148	+	0.745038i	0.996886	−	0.0788602i	$-0.0251281\pi$
$467$	9.29557	+	16.1004i	0.430148	+	0.745038i	−0.566738	+	0.823898i	$0.691795\pi$
$468$	15.5037	−	8.40489i	0.716660	−	0.388516i
$469$		0			0
$470$	−0.654857	+	2.04930i	−0.0302063	+	0.0945274i
$471$	−0.177083	+	0.332385i	−0.00815956	+	0.0153155i
$472$	−23.1584	+	2.77624i	−1.06595	+	0.127787i
$473$	−8.51130	−	4.91400i	−0.391350	−	0.225946i
$474$	6.83466	+	7.02050i	0.313926	+	0.322462i
$475$			27.2137i			1.24865i
$476$		0			0
$477$	−4.63910	−	2.27210i	−0.212410	−	0.104032i
$478$	4.37108	+	20.0835i	0.199928	+	0.918597i
$479$	20.4388	−	35.4011i	0.933874	−	1.61752i	0.157245	−	0.987560i	$-0.449739\pi$
$479$	20.4388	−	35.4011i	0.933874	−	1.61752i	0.776629	−	0.629958i	$-0.216928\pi$
$480$	−3.40986	+	0.199372i	−0.155638	+	0.00910003i
$481$	0.939235	+	1.62680i	0.0428254	+	0.0741758i
$482$	−25.3149	−	8.08941i	−1.15306	−	0.368462i
$483$		0			0
$484$	6.90760	+	4.91671i	0.313982	+	0.223487i
$485$	−0.603814	+	0.348612i	−0.0274178	+	0.0158297i
$486$	−8.27364	−	20.4340i	−0.375300	−	0.926903i
$487$	18.5599	+	10.7156i	0.841032	+	0.485570i	0.857615	−	0.514293i	$-0.171945\pi$
$487$	18.5599	+	10.7156i	0.841032	+	0.485570i	−0.0165831	+	0.999862i	$0.505279\pi$
$488$	−15.6831	+	36.6551i	−0.709941	+	1.65930i
$489$	7.69987	−	4.80260i	0.348200	−	0.217181i
$490$		0			0
$491$	−1.63166			−0.0736358			−0.0368179	−	0.999322i	$-0.511722\pi$
$491$	−1.63166			−0.0736358			−0.0368179	+	0.999322i	$0.511722\pi$
$492$	−11.7054	−	23.4670i	−0.527721	−	1.05797i
$493$	19.0351	−	32.9698i	0.857300	−	1.48489i
$494$	15.5991	+	17.1560i	0.701837	+	0.771885i
$495$	−0.278089	−	4.07321i	−0.0124992	−	0.183077i
$496$	9.97438	−	3.45681i	0.447863	−	0.155215i
$497$		0			0
$498$	5.38568	+	21.2349i	0.241338	+	0.951558i
$499$	−7.69218	+	4.44108i	−0.344349	+	0.198810i	−0.662194	−	0.749333i	$-0.730374\pi$
$499$	−7.69218	+	4.44108i	−0.344349	+	0.198810i	0.317844	+	0.948143i	$0.397041\pi$
$500$	−2.86247	−	6.26450i	−0.128014	−	0.280157i
$501$	19.8621	−	0.677232i	0.887375	−	0.0302565i
$502$	6.20775	+	28.5223i	0.277065	+	1.27301i
$503$	−34.8967			−1.55597			−0.777983	−	0.628286i	$-0.783757\pi$
$503$	−34.8967			−1.55597			−0.777983	+	0.628286i	$0.783757\pi$
$504$		0			0
$505$	1.07900			0.0480150
$506$	2.56171	+	11.7701i	0.113882	+	0.523246i
$507$	−7.54891	+	0.257392i	−0.335259	+	0.0114312i
$508$	−10.3037	−	22.5495i	−0.457152	−	1.00047i
$509$	20.5865	−	11.8856i	0.912479	−	0.526820i	0.0312508	−	0.999512i	$-0.490051\pi$
$509$	20.5865	−	11.8856i	0.912479	−	0.526820i	0.881228	+	0.472692i	$0.156718\pi$
$510$	−0.819511	−	3.23120i	−0.0362886	−	0.143080i
$511$		0			0
$512$	−21.1934	+	7.92728i	−0.936623	+	0.350340i
$513$	23.4921	−	16.9795i	1.03720	−	0.749664i
$514$	4.58932	+	5.04737i	0.202426	+	0.222630i
$515$	−1.26186	+	2.18561i	−0.0556044	+	0.0963097i
$516$	3.89273	+	7.80414i	0.171368	+	0.343558i
$517$	−17.0351			−0.749205
$518$		0			0
$519$	−31.1634	+	19.4374i	−1.36792	+	0.853207i
$520$	−2.66451	−	1.14003i	−0.116847	−	0.0499936i
$521$	−4.96256	−	2.86513i	−0.217414	−	0.125524i	0.387338	−	0.921938i	$-0.373394\pi$
$521$	−4.96256	−	2.86513i	−0.217414	−	0.125524i	−0.604752	+	0.796414i	$0.706728\pi$
$522$	−39.7354	+	11.5324i	−1.73917	+	0.504761i
$523$	4.17225	−	2.40885i	0.182440	−	0.105332i	−0.405999	−	0.913874i	$-0.633076\pi$
$523$	4.17225	−	2.40885i	0.182440	−	0.105332i	0.588439	+	0.808542i	$0.299743\pi$
$524$	2.62410	+	1.86779i	0.114634	+	0.0815948i
$525$		0			0
$526$	−19.4762	−	6.22364i	−0.849204	−	0.271364i
$527$	5.15121	+	8.92216i	0.224390	+	0.388656i
$528$	−9.72220	−	25.2382i	−0.423105	−	1.09835i
$529$	9.11968	−	15.7958i	0.396508	−	0.686772i
$530$	0.180534	+	0.829486i	0.00784189	+	0.0360306i
$531$	−10.8815	+	22.2174i	−0.472216	+	0.964155i
$532$		0			0
$533$		−	22.2509i		−	0.963795i
$534$	−18.0087	−	18.4984i	−0.779313	−	0.800504i
$535$	−3.32522	−	1.91982i	−0.143762	−	0.0830009i
$536$	0.215162	+	1.79480i	0.00929358	+	0.0775236i
$537$	1.47578	−	2.77004i	0.0636846	−	0.119536i
$538$	−2.02854	+	6.34809i	−0.0874564	+	0.273685i
$539$		0			0
$540$	−1.78862	+	3.15057i	−0.0769700	+	0.135579i
$541$	6.01942	+	10.4259i	0.258795	+	0.448246i	0.965919	−	0.258843i	$-0.0833413\pi$
$541$	6.01942	+	10.4259i	0.258795	+	0.448246i	−0.707124	+	0.707089i	$0.750008\pi$
$542$	14.9124	+	16.4008i	0.640542	+	0.704473i
$543$	13.0512	−	0.445002i	0.560081	−	0.0190969i
$544$	−11.5033	−	18.8503i	−0.493200	−	0.808200i
$545$			0.487964i			0.0209021i
$546$		0			0
$547$		−	35.3097i		−	1.50973i	−0.655879	−	0.754866i	$-0.727702\pi$
$547$		−	35.3097i		−	1.50973i	0.655879	−	0.754866i	$-0.272298\pi$
$548$	−8.68820	−	0.827802i	−0.371142	−	0.0353619i
$549$	23.5892	+	35.0970i	1.00676	+	1.49790i
$550$	19.9271	−	18.1187i	0.849695	−	0.772585i
$551$	−27.2005	−	47.1127i	−1.15878	−	2.00707i
$552$	3.86735	−	9.96488i	0.164605	−	0.424133i
$553$		0			0
$554$	22.8958	+	7.31638i	0.972751	+	0.310843i
$555$	−0.340579	−	0.181449i	−0.0144568	−	0.00770207i
$556$	−13.9790	−	30.5929i	−0.592842	−	1.29743i
$557$	30.1308	+	17.3960i	1.27668	+	0.737093i	0.976237	−	0.216706i	$-0.0695314\pi$
$557$	30.1308	+	17.3960i	1.27668	+	0.737093i	0.300445	+	0.953799i	$0.402865\pi$
$558$	2.67377	−	10.8728i	0.113190	−	0.460283i
$559$			7.39973i			0.312975i
$560$		0			0
$561$	22.3960	−	13.9690i	0.945562	−	0.589771i
$562$	7.95707	−	1.73182i	0.335649	−	0.0730525i
$563$	6.43088	−	11.1386i	0.271029	−	0.469436i	−0.698096	−	0.716004i	$-0.745969\pi$
$563$	6.43088	−	11.1386i	0.271029	−	0.469436i	0.969126	+	0.246567i	$0.0793027\pi$
$564$	12.6070	+	8.34115i	0.530849	+	0.351226i
$565$	1.53950	+	2.66649i	0.0647673	+	0.112180i
$566$	2.40130	−	7.51461i	0.100934	−	0.315863i
$567$		0			0
$568$	−20.2369	−	27.0157i	−0.849120	−	1.13355i
$569$	13.5887	−	7.84543i	0.569667	−	0.328897i	−0.187349	−	0.982293i	$-0.559990\pi$
$569$	13.5887	−	7.84543i	0.569667	−	0.328897i	0.757016	+	0.653396i	$0.226656\pi$
$570$	−4.58420	−	1.29447i	−0.192011	−	0.0542196i
$571$	36.4003	+	21.0157i	1.52331	+	0.879481i	0.999620	+	0.0275690i	$0.00877659\pi$
$571$	36.4003	+	21.0157i	1.52331	+	0.879481i	0.523685	+	0.851912i	$0.324557\pi$
$572$	2.17662	−	22.8447i	0.0910089	−	0.955185i
$573$	1.49564	+	2.39792i	0.0624813	+	0.100174i
$574$		0			0
$575$	10.6443			0.443897
$576$	−5.16275	+	23.4381i	−0.215115	+	0.976589i
$577$	−19.3960	+	33.5949i	−0.807468	+	1.39858i	0.107145	+	0.994243i	$0.465829\pi$
$577$	−19.3960	+	33.5949i	−0.807468	+	1.39858i	−0.914612	+	0.404332i	$0.867504\pi$
$578$	−1.84224	+	1.67505i	−0.0766270	+	0.0696731i
$579$	12.3437	−	23.1691i	0.512987	−	0.962875i
$580$	5.53950	+	3.94293i	0.230015	+	0.163721i
$581$		0			0
$582$	1.20437	+	4.74863i	0.0499227	+	0.196837i
$583$	−5.82125	+	3.36090i	−0.241091	+	0.139194i
$584$	−22.1253	+	2.65239i	−0.915550	+	0.109757i
$585$	−2.55125	+	1.71474i	−0.105481	+	0.0708956i
$586$	−32.8485	+	7.14933i	−1.35696	+	0.295336i
$587$	−7.07471			−0.292004			−0.146002	−	0.989284i	$-0.546641\pi$
$587$	−7.07471			−0.292004			−0.146002	+	0.989284i	$0.546641\pi$
$588$		0			0
$589$	14.7218			0.606601
$590$	3.97255	−	0.864607i	0.163547	−	0.0355953i
$591$	1.25283	+	36.7436i	0.0515347	+	1.51143i
$592$	−2.51041	−	0.482760i	−0.103177	−	0.0198413i
$593$	15.9258	−	9.19477i	0.653994	−	0.377584i	−0.135991	−	0.990710i	$-0.543422\pi$
$593$	15.9258	−	9.19477i	0.653994	−	0.377584i	0.789985	+	0.613126i	$0.210088\pi$
$594$	−28.0740	−	5.89710i	−1.15189	−	0.241961i
$595$		0			0
$596$	−8.88449	+	12.4820i	−0.363923	+	0.511283i
$597$	−5.74301	−	3.05968i	−0.235046	−	0.125224i
$598$	6.71033	−	6.10137i	0.274406	−	0.249503i
$599$	−18.9258	+	32.7804i	−0.773287	+	1.33937i	0.162466	+	0.986714i	$0.448055\pi$
$599$	−18.9258	+	32.7804i	−0.773287	+	1.33937i	−0.935752	+	0.352658i	$0.885278\pi$
$600$	−23.6189	+	3.65170i	−0.964237	+	0.149080i
$601$	21.9488			0.895308			0.447654	−	0.894207i	$-0.352260\pi$
$601$	21.9488			0.895308			0.447654	+	0.894207i	$0.352260\pi$
$602$		0			0
$603$	1.72188	+	0.843327i	0.0701202	+	0.0343429i
$604$	−25.1642	−	2.39762i	−1.02392	−	0.0975577i
$605$	−1.27989	−	0.738947i	−0.0520351	−	0.0300425i
$606$	2.06028	−	7.29620i	0.0836933	−	0.296388i
$607$	22.4114	−	12.9392i	0.909651	−	0.525187i	0.0293323	−	0.999570i	$-0.490662\pi$
$607$	22.4114	−	12.9392i	0.909651	−	0.525187i	0.880319	+	0.474382i	$0.157329\pi$
$608$	−31.5465	+	0.767338i	−1.27938	+	0.0311197i
$609$		0			0
$610$	2.11533	−	6.61968i	0.0856470	−	0.268023i
$611$	6.41308	+	11.1078i	0.259445	+	0.449373i
$612$	−23.4142	−	0.628241i	−0.946461	−	0.0253951i
$613$	6.45681	−	11.1835i	0.260788	−	0.451698i	−0.705664	−	0.708547i	$-0.749351\pi$
$613$	6.45681	−	11.1835i	0.260788	−	0.451698i	0.966452	+	0.256849i	$0.0826843\pi$
$614$	−5.11271	+	1.11276i	−0.206332	+	0.0449073i
$615$	2.41910	+	3.87847i	0.0975475	+	0.156395i
$616$		0			0
$617$		−	26.4677i		−	1.06555i	−0.846257	−	0.532775i	$-0.821149\pi$
$617$		−	26.4677i		−	1.06555i	0.846257	−	0.532775i	$-0.178851\pi$
$618$	12.3697	+	12.7060i	0.497580	+	0.511110i
$619$	−29.7384	−	17.1695i	−1.19529	−	0.690100i	−0.235787	−	0.971805i	$-0.575767\pi$
$619$	−29.7384	−	17.1695i	−1.19529	−	0.690100i	−0.959501	+	0.281705i	$0.909100\pi$
$620$	−1.67360	+	0.764730i	−0.0672136	+	0.0307123i
$621$	−6.64130	−	9.18859i	−0.266506	−	0.368726i
$622$	10.2174	+	3.26499i	0.409682	+	0.130914i
$623$		0			0
$624$	−12.7966	+	15.8406i	−0.512273	+	0.634131i
$625$	−11.5959	−	20.0847i	−0.463836	−	0.803388i
$626$	−16.3601	+	14.8754i	−0.653882	+	0.594542i
$627$	−1.28531	−	37.6961i	−0.0513303	−	1.50544i
$628$	0.0412477	−	0.432916i	0.00164596	−	0.0172752i
$629$		−	2.49490i		−	0.0994782i
$630$		0			0
$631$			27.7569i			1.10499i	0.833517	+	0.552493i	$0.186323\pi$
$631$			27.7569i			1.10499i	−0.833517	+	0.552493i	$0.813677\pi$
$632$	−10.4016	−	4.45040i	−0.413755	−	0.177028i
$633$	−0.580763	−	17.0328i	−0.0230832	−	0.676995i
$634$	13.2179	+	14.5371i	0.524949	+	0.577343i
$635$	2.16070	+	3.74245i	0.0857449	+	0.148515i
$636$	5.95369	+	0.363081i	0.236079	+	0.0143971i
$637$		0			0
$638$	−16.3881	+	51.2847i	−0.648810	+	2.03038i
$639$	−35.7191	+	2.43864i	−1.41303	+	0.0964710i
$640$	3.54641	−	1.72593i	0.140184	−	0.0682233i
$641$	−6.03040	−	3.48165i	−0.238186	−	0.137517i	0.376156	−	0.926556i	$-0.377246\pi$
$641$	−6.03040	−	3.48165i	−0.238186	−	0.137517i	−0.614343	+	0.789039i	$0.710579\pi$
$642$	−19.3311	+	18.8193i	−0.762936	+	0.742740i
$643$		−	9.74373i		−	0.384255i	−0.981370	−	0.192128i	$-0.938461\pi$
$643$		−	9.74373i		−	0.384255i	0.981370	−	0.192128i	$-0.0615387\pi$
$644$		0			0
$645$	−0.804492	−	1.28982i	−0.0316768	−	0.0507865i
$646$	−6.54942	−	30.0921i	−0.257683	−	1.18396i
$647$	14.0948	−	24.4129i	0.554123	−	0.959770i	−0.443848	−	0.896102i	$-0.646387\pi$
$647$	14.0948	−	24.4129i	0.554123	−	0.959770i	0.997971	−	0.0636677i	$-0.0202798\pi$
$648$	17.8889	+	18.1104i	0.702742	+	0.711445i
$649$	16.0959	+	27.8789i	0.631820	+	1.09434i
$650$	−19.3161	−	6.17248i	−0.757641	−	0.242105i
$651$		0			0
$652$	−6.07649	+	8.53699i	−0.237974	+	0.334334i
$653$	−9.39867	+	5.42633i	−0.367799	+	0.212349i	−0.672496	−	0.740101i	$-0.734778\pi$
$653$	−9.39867	+	5.42633i	−0.367799	+	0.212349i	0.304698	+	0.952449i	$0.401445\pi$
$654$	3.29961	+	0.931734i	0.129025	+	0.0364337i
$655$	−0.486214	−	0.280716i	−0.0189979	−	0.0109685i
$656$	22.8933	+	19.8205i	0.893832	+	0.773860i
$657$	−10.3960	+	21.2263i	−0.405588	+	0.828116i
$658$		0			0
$659$	19.2248			0.748893			0.374446	−	0.927249i	$-0.377833\pi$
$659$	19.2248			0.748893			0.374446	+	0.927249i	$0.377833\pi$
$660$	2.10426	+	4.21861i	0.0819081	+	0.164209i
$661$	1.37371	−	2.37933i	0.0534311	−	0.0925454i	−0.838073	−	0.545558i	$-0.816318\pi$
$661$	1.37371	−	2.37933i	0.0534311	−	0.0925454i	0.891504	+	0.453013i	$0.149651\pi$
$662$	−30.2503	−	33.2695i	−1.17571	−	1.29306i
$663$	−17.5397	−	9.34457i	−0.681187	−	0.362913i
$664$	−15.1658	−	20.2460i	−0.588547	−	0.785696i
$665$		0			0
$666$	−1.87727	+	1.95652i	−0.0727426	+	0.0758138i
$667$	−18.4275	+	10.6391i	−0.713514	+	0.411948i
$668$	−20.8724	+	9.53734i	−0.807577	+	0.369011i
$669$	−1.35243	−	39.6645i	−0.0522878	−	1.53352i
$670$	−0.0670080	−	0.307877i	−0.00258875	−	0.0118943i
$671$	55.0271			2.12430
$672$		0			0
$673$	31.3097			1.20690			0.603449	−	0.797401i	$-0.293793\pi$
$673$	31.3097			1.20690			0.603449	+	0.797401i	$0.293793\pi$
$674$	5.14830	+	23.6545i	0.198305	+	0.911138i
$675$	−10.3676	+	23.1322i	−0.399050	+	0.890358i
$676$	7.93287	−	3.62481i	0.305110	−	0.139416i
$677$	18.1712	−	10.4911i	0.698376	−	0.403208i	−0.108366	−	0.994111i	$-0.534562\pi$
$677$	18.1712	−	10.4911i	0.698376	−	0.403208i	0.806742	+	0.590903i	$0.201229\pi$
$678$	20.9704	−	5.31860i	0.805363	−	0.204259i
$679$		0			0
$680$	2.30770	+	3.08073i	0.0884963	+	0.118140i
$681$	−11.0191	+	20.6827i	−0.422251	+	0.792564i
$682$	−9.80167	−	10.7800i	−0.375325	−	0.412786i
$683$	−7.91172	+	13.7035i	−0.302734	+	0.524350i	−0.976754	−	0.214363i	$-0.931233\pi$
$683$	−7.91172	+	13.7035i	−0.302734	+	0.524350i	0.674021	+	0.738713i	$0.264566\pi$
$684$	−17.5064	+	28.5266i	−0.669376	+	1.09074i
$685$	1.52126			0.0581245
$686$		0			0
$687$	−13.4711	−	21.5978i	−0.513953	−	0.824006i
$688$	−7.61335	−	6.59147i	−0.290256	−	0.251298i
$689$	4.38295	+	2.53050i	0.166977	+	0.0964043i
$690$	−0.506316	+	1.79304i	−0.0192751	+	0.0682600i
$691$	21.1390	−	12.2046i	0.804167	−	0.464286i	−0.0407593	−	0.999169i	$-0.512978\pi$
$691$	21.1390	−	12.2046i	0.804167	−	0.464286i	0.844926	+	0.534883i	$0.179644\pi$
$692$	24.5931	−	34.5514i	0.934891	−	1.31345i
$693$		0			0
$694$	11.3803	+	3.63659i	0.431991	+	0.138043i
$695$	2.93143	+	5.07738i	0.111195	+	0.192596i
$696$	37.2393	−	29.9293i	1.41155	−	1.13447i
$697$	−14.7764	+	25.5934i	−0.559694	+	0.969419i
$698$	−5.26192	−	24.1766i	−0.199167	−	0.915097i
$699$	−25.2626	+	15.7569i	−0.955520	+	0.595982i
$700$		0			0
$701$		−	21.4779i		−	0.811209i	−0.914049	−	0.405605i	$-0.867061\pi$
$701$		−	21.4779i		−	0.811209i	0.914049	−	0.405605i	$-0.132939\pi$
$702$	6.72358	+	20.5257i	0.253765	+	0.774693i
$703$	−3.08749	−	1.78256i	−0.116447	−	0.0672306i
$704$	21.5653	+	22.5889i	0.812774	+	0.851350i
$705$	−2.32546	−	1.23893i	−0.0875821	−	0.0466607i
$706$	3.55892	−	11.1373i	0.133942	−	0.419156i
$707$		0			0
$708$	1.73885	−	28.5132i	0.0653501	−	1.07159i
$709$	21.0959	+	36.5392i	0.792273	+	1.37226i	0.924556	+	0.381046i	$0.124436\pi$
$709$	21.0959	+	36.5392i	0.792273	+	1.37226i	−0.132283	+	0.991212i	$0.542231\pi$
$710$	3.95815	+	4.35320i	0.148547	+	0.163373i
$711$	−9.95948	+	6.69393i	−0.373510	+	0.251042i
$712$	27.4074	+	11.7264i	1.02713	+	0.439466i
$713$		−	5.75822i		−	0.215647i
$714$		0			0
$715$			4.00000i			0.149592i
$716$	−0.343751	+	3.60784i	−0.0128466	+	0.134831i
$717$	−25.1583	+	0.857815i	−0.939556	+	0.0320357i
$718$	−26.2948	+	23.9086i	−0.981314	+	0.892260i
$719$	9.52940	+	16.5054i	0.355387	+	0.615548i	0.987184	−	0.159586i	$-0.0510158\pi$
$719$	9.52940	+	16.5054i	0.355387	+	0.615548i	−0.631797	+	0.775134i	$0.717683\pi$
$720$	0.508344	−	4.15234i	0.0189449	−	0.154749i
$721$		0			0
$722$	−16.3240	−	5.21635i	−0.607517	−	0.194133i
$723$	15.3044	−	28.7263i	0.569177	−	1.06834i
$724$	−13.7150	+	6.26689i	−0.509716	+	0.232907i
$725$	41.2019	+	23.7879i	1.53020	+	0.883461i
$726$	−7.44062	+	7.24366i	−0.276147	+	0.268837i
$727$		−	3.72549i		−	0.138171i	−0.997611	−	0.0690854i	$-0.977992\pi$
$727$		−	3.72549i		−	0.138171i	0.997611	−	0.0690854i	$-0.0220081\pi$
$728$		0			0
$729$	26.4374	−	5.48311i	0.979163	−	0.203078i
$730$	3.79533	−	0.826036i	0.140471	−	0.0305729i
$731$	4.91400	−	8.51130i	0.181751	−	0.314802i
$732$	−40.7232	−	26.9437i	−1.50517	−	0.995866i
$733$	12.7090	+	22.0126i	0.469417	+	0.813054i	0.999389	−	0.0349611i	$-0.0111307\pi$
$733$	12.7090	+	22.0126i	0.469417	+	0.813054i	−0.529972	+	0.848015i	$0.677797\pi$
$734$	−9.34681	+	29.2498i	−0.344997	+	1.07963i
$735$		0			0
$736$	0.300133	+	12.3390i	0.0110631	+	0.454820i
$737$	2.16065	−	1.24745i	0.0795885	−	0.0459504i
$738$	30.8453	−	8.95225i	1.13543	−	0.329537i
$739$	−20.1868	−	11.6548i	−0.742582	−	0.428730i	0.0804256	−	0.996761i	$-0.474372\pi$
$739$	−20.1868	−	11.6548i	−0.742582	−	0.428730i	−0.823007	+	0.568031i	$0.807705\pi$
$740$	0.443588	+	0.0422645i	0.0163066	+	0.00155368i
$741$	−24.0959	+	15.0292i	−0.885185	+	0.552113i
$742$		0			0
$743$	−33.8576			−1.24211			−0.621057	−	0.783765i	$-0.713297\pi$
$743$	−33.8576			−1.24211			−0.621057	+	0.783765i	$0.713297\pi$
$744$	1.97546	+	12.7771i	0.0724238	+	0.468431i
$745$	1.33528	−	2.31277i	0.0489207	−	0.0847332i
$746$	0.755252	−	0.686713i	0.0276518	−	0.0251424i
$747$	−26.7684	+	1.82755i	−0.979405	+	0.0668666i
$748$	−17.6742	+	24.8309i	−0.646234	+	0.907908i
$749$		0			0
$750$	8.17655	−	2.07377i	0.298566	−	0.0757235i
$751$	41.7017	−	24.0765i	1.52172	−	0.878564i	0.522046	−	0.852918i	$-0.325169\pi$
$751$	41.7017	−	24.0765i	1.52172	−	0.878564i	0.999671	−	0.0256461i	$-0.00816430\pi$
$752$	−17.1410	−	3.29628i	−0.625069	−	0.120203i
$753$	−35.7296	+	1.21826i	−1.30206	+	0.0443958i
$754$	39.6097	−	8.62088i	1.44250	−	0.313954i
$755$	4.40614			0.160356
$756$		0			0
$757$	−11.3923			−0.414062			−0.207031	−	0.978334i	$-0.566380\pi$
$757$	−11.3923			−0.414062			−0.207031	+	0.978334i	$0.566380\pi$
$758$	−25.2529	+	5.49617i	−0.917226	+	0.199630i
$759$	−14.7443	+	0.502731i	−0.535184	+	0.0182480i
$760$	5.46127	−	0.654700i	0.198101	−	0.0237485i
$761$	−23.8583	+	13.7746i	−0.864861	+	0.499328i	−0.865637	−	0.500672i	$-0.833086\pi$
$761$	−23.8583	+	13.7746i	−0.864861	+	0.499328i	0.000776011		1.00000i	$0.499753\pi$
$762$	29.4321	−	7.46470i	1.06621	−	0.270417i
$763$		0			0
$764$	−2.65862	−	1.89236i	−0.0961853	−	0.0684632i
$765$	4.07321	−	0.278089i	0.147267	−	0.0100543i
$766$	2.14429	−	1.94970i	0.0774764	−	0.0704454i
$767$	12.1190	−	20.9907i	0.437591	−	0.757930i
$768$	−4.89907	−	27.2763i	−0.176780	−	0.984250i
$769$	−5.83461			−0.210401			−0.105201	−	0.994451i	$-0.533549\pi$
$769$	−5.83461			−0.210401			−0.105201	+	0.994451i	$0.533549\pi$
$770$		0			0
$771$	−7.08912	+	4.42166i	−0.255308	+	0.159242i
$772$	−2.87520	+	30.1767i	−0.103481	+	1.08608i
$773$	41.1952	+	23.7841i	1.48169	+	0.855454i	0.999784	−	0.0207689i	$-0.00661143\pi$
$773$	41.1952	+	23.7841i	1.48169	+	0.855454i	0.481906	+	0.876223i	$0.339945\pi$
$774$	−10.2579	+	2.97714i	−0.368711	+	0.107011i
$775$	−11.1499	+	6.43739i	−0.400516	+	0.231238i
$776$	−3.39144	−	4.52749i	−0.121745	−	0.162527i
$777$		0			0
$778$	−4.79829	+	15.0157i	−0.172027	+	0.538340i
$779$	21.1149	+	36.5720i	0.756519	+	1.31033i
$780$	1.95857	−	2.96023i	0.0701282	−	0.105993i
$781$	−23.2939	+	40.3463i	−0.833522	+	1.44370i
$782$	−11.7701	+	2.56171i	−0.420899	+	0.0916067i
$783$	−5.17240	−	50.4093i	−0.184846	−	1.80148i
$784$		0			0
$785$			0.0758015i			0.00270547i
$786$	−2.82659	+	2.75176i	−0.100821	+	0.0981522i
$787$	42.2774	+	24.4089i	1.50703	+	0.870082i	0.999967	+	0.00817024i	$0.00260070\pi$
$787$	42.2774	+	24.4089i	1.50703	+	0.870082i	0.507059	+	0.861911i	$0.330733\pi$
$788$	−17.6435	−	38.6125i	−0.628522	−	1.37551i
$789$	11.7746	−	22.1008i	0.419185	−	0.786809i
$790$	1.87847	+	0.600267i	0.0668330	+	0.0213565i
$791$		0			0
$792$	32.5441	−	6.17381i	1.15640	−	0.219377i
$793$	−20.7156	−	35.8805i	−0.735632	−	1.27415i
$794$	−8.34399	+	7.58678i	−0.296117	+	0.269245i
$795$	−1.03909	+	0.0354294i	−0.0368527	+	0.00125655i
$796$	7.48000	+	0.712686i	0.265122	+	0.0252605i
$797$		−	12.7292i		−	0.450890i	−0.974256	−	0.225445i	$-0.927616\pi$
$797$		−	12.7292i		−	0.450890i	0.974256	−	0.225445i	$-0.0723837\pi$
$798$		0			0
$799$		−	17.0351i		−	0.602660i
$800$	23.5569	−	14.3755i	0.832863	−	0.508250i
$801$	26.2423	−	17.6379i	0.927228	−	0.623204i
$802$	−20.4340	−	22.4734i	−0.721548	−	0.793564i
$803$	15.3778	+	26.6352i	0.542672	+	0.939936i
$804$	−2.20981	−	0.134763i	−0.0779339	−	0.00475273i
$805$		0			0
$806$	−3.33912	+	10.4494i	−0.117616	+	0.368065i
$807$	−7.20354	−	3.83780i	−0.253577	−	0.135097i
$808$	1.04202	+	8.69214i	0.0366581	+	0.305789i
$809$	−23.0201	−	13.2906i	−0.809342	−	0.467274i	0.0373853	−	0.999301i	$-0.488097\pi$
$809$	−23.0201	−	13.2906i	−0.809342	−	0.467274i	−0.846727	+	0.532027i	$0.821430\pi$
$810$	−3.40350	−	2.84677i	−0.119587	−	0.100025i
$811$			4.13977i			0.145367i	0.997355	+	0.0726835i	$0.0231563\pi$
$811$			4.13977i			0.145367i	−0.997355	+	0.0726835i	$0.976844\pi$
$812$		0			0
$813$	−23.0351	+	14.3676i	−0.807878	+	0.503894i
$814$	0.750357	+	3.44761i	0.0263000	+	0.120839i
$815$	0.913253	−	1.58180i	0.0319899	−	0.0554081i
$816$	25.2382	−	9.72220i	0.883515	−	0.340345i
$817$	−7.02193	−	12.1623i	−0.245666	−	0.425506i
$818$	49.7266	+	15.8902i	1.73865	+	0.555587i
$819$		0			0
$820$	−4.30013	−	3.06077i	−0.150167	−	0.106887i
$821$	25.5549	−	14.7541i	0.891871	−	0.514922i	0.0173172	−	0.999850i	$-0.494487\pi$
$821$	25.5549	−	14.7541i	0.891871	−	0.514922i	0.874554	+	0.484928i	$0.161154\pi$
$822$	2.90475	−	10.2868i	0.101315	−	0.358792i
$823$	−10.4596	−	6.03884i	−0.364598	−	0.210501i	0.306498	−	0.951871i	$-0.400843\pi$
$823$	−10.4596	−	6.03884i	−0.364598	−	0.210501i	−0.671096	+	0.741371i	$0.734176\pi$
$824$	−18.8253	−	8.05453i	−0.655811	−	0.280593i
$825$	17.4568	+	27.9880i	0.607768	+	0.974416i
$826$		0			0
$827$	11.9341			0.414989			0.207494	−	0.978236i	$-0.433469\pi$
$827$	11.9341			0.414989			0.207494	+	0.978236i	$0.433469\pi$
$828$	11.1578	+	6.84740i	0.387759	+	0.237964i
$829$	1.25218	−	2.16884i	0.0434900	−	0.0753269i	−0.843461	−	0.537190i	$-0.819486\pi$
$829$	1.25218	−	2.16884i	0.0434900	−	0.0753269i	0.886951	+	0.461863i	$0.152819\pi$
$830$	2.96629	+	3.26235i	0.102962	+	0.113238i
$831$	−13.8419	+	25.9812i	−0.480171	+	0.901279i
$832$	6.61057	−	22.5655i	0.229180	−	0.782319i
$833$		0			0
$834$	39.9305	−	10.1274i	1.38268	−	0.350682i
$835$	3.46410	−	2.00000i	0.119880	−	0.0692129i
$836$	18.1008	+	39.6135i	0.626029	+	1.37006i
$837$	12.5138	+	5.60857i	0.432540	+	0.193861i
$838$	−8.89555	−	40.8717i	−0.307292	−	1.41189i
$839$	1.64607			0.0568288			0.0284144	−	0.999596i	$-0.490954\pi$
$839$	1.64607			0.0568288			0.0284144	+	0.999596i	$0.490954\pi$
$840$		0			0
$841$	−66.1054			−2.27950
$842$	−11.0771	−	50.8953i	−0.381743	−	1.75397i
$843$	0.339866	+	9.96774i	0.0117056	+	0.343307i
$844$	8.17878	+	17.8992i	0.281525	+	0.616116i
$845$	−1.31658	+	0.760131i	−0.0452919	+	0.0261493i
$846$	−12.8179	+	13.3591i	−0.440690	+	0.459296i
$847$		0			0
$848$	−6.50776	+	2.25539i	−0.223477	+	0.0774503i
$849$	8.52727	+	4.54304i	0.292655	+	0.155917i
$850$	18.1187	+	19.9271i	0.621467	+	0.683494i
$851$	−0.697224	+	1.20763i	−0.0239005	+	0.0413969i
$852$	36.9941	−	18.4528i	1.26740	−	0.632182i
$853$	−15.1311			−0.518077			−0.259039	−	0.965867i	$-0.583406\pi$
$853$	−15.1311			−0.518077			−0.259039	+	0.965867i	$0.583406\pi$
$854$		0			0
$855$	2.56610	−	5.23937i	0.0877587	−	0.179183i
$856$	12.2543	−	28.6411i	0.418842	−	0.978931i
$857$	−42.3681	−	24.4612i	−1.44727	−	0.835579i	−0.448947	−	0.893558i	$-0.648201\pi$
$857$	−42.3681	−	24.4612i	−1.44727	−	0.835579i	−0.998318	+	0.0579792i	$0.981534\pi$
$858$	27.0480	+	7.63773i	0.923402	+	0.260748i
$859$	−13.9058	+	8.02854i	−0.474461	+	0.273930i	−0.718105	−	0.695935i	$-0.754990\pi$
$859$	−13.9058	+	8.02854i	−0.474461	+	0.273930i	0.243644	+	0.969865i	$0.421657\pi$
$860$	1.43005	+	1.01788i	0.0487641	+	0.0347095i
$861$		0			0
$862$	−6.30013	−	2.01321i	−0.214583	−	0.0685703i
$863$	−7.45171	−	12.9067i	−0.253659	−	0.439350i	0.710871	−	0.703322i	$-0.248301\pi$
$863$	−7.45171	−	12.9067i	−0.253659	−	0.439350i	−0.964530	+	0.263972i	$0.914967\pi$
$864$	−27.1074	−	11.3660i	−0.922214	−	0.386680i
$865$	−3.69617	+	6.40196i	−0.125674	+	0.217673i
$866$	4.97944	+	22.8787i	0.169208	+	0.777449i
$867$	−1.61386	−	2.58746i	−0.0548096	−	0.0878746i
$868$		0			0
$869$			15.6151i			0.529704i
$870$	−5.96696	+	5.80900i	−0.202299	+	0.196944i
$871$	−1.62680	−	0.939235i	−0.0551221	−	0.0318248i
$872$	−3.93090	+	0.471239i	−0.133117	+	0.0159582i
$873$	−5.98607	+	0.408684i	−0.202598	+	0.0138319i
$874$	−5.23937	+	16.3960i	−0.177224	+	0.554604i
$875$		0			0
$876$	1.66128	−	27.2412i	0.0561295	−	0.920395i
$877$	−5.93923	−	10.2871i	−0.200554	−	0.347369i	0.748153	−	0.663526i	$-0.230941\pi$
$877$	−5.93923	−	10.2871i	−0.200554	−	0.347369i	−0.948707	+	0.316157i	$0.897607\pi$
$878$	25.1917	+	27.7060i	0.850179	+	0.935033i
$879$	−1.40304	−	41.1490i	−0.0473234	−	1.38792i
$880$	−4.11547	−	3.56309i	−0.138733	−	0.120112i
$881$		−	36.4995i		−	1.22970i	−0.788644	−	0.614850i	$-0.789217\pi$
$881$		−	36.4995i		−	1.22970i	0.788644	−	0.614850i	$-0.210783\pi$
$882$		0			0
$883$		−	31.1178i		−	1.04720i	−0.851965	−	0.523599i	$-0.824589\pi$
$883$		−	31.1178i		−	1.04720i	0.851965	−	0.523599i	$-0.175411\pi$
$884$	22.8447	+	2.17662i	0.768350	+	0.0732075i
$885$	0.169677	+	4.97637i	0.00570364	+	0.167279i
$886$	−4.81424	+	4.37735i	−0.161738	+	0.147060i
$887$	28.4624	+	49.2983i	0.955674	+	1.65528i	0.732819	+	0.680424i	$0.238204\pi$
$887$	28.4624	+	49.2983i	0.955674	+	1.65528i	0.222855	+	0.974852i	$0.428462\pi$
$888$	1.13279	−	2.91884i	0.0380141	−	0.0979497i
$889$		0			0
$890$	−4.94960	−	1.58165i	−0.165911	−	0.0530170i
$891$	13.2686	−	32.5320i	0.444514	−	1.08986i
$892$	19.0460	+	41.6820i	0.637706	+	1.39562i
$893$	−21.0813	−	12.1713i	−0.705459	−	0.407297i
$894$	−13.0893	−	13.4452i	−0.437771	−	0.449674i
$895$		−	0.631717i		−	0.0211160i
$896$		0			0
$897$	5.87847	+	9.42477i	0.196276	+	0.314684i
$898$	−23.5048	+	5.11571i	−0.784365	+	0.170714i
$899$	12.8685	−	22.2889i	0.429189	−	0.743378i
$900$	0.785102	−	29.2603i	0.0261701	−	0.975343i
$901$	−3.36090	−	5.82125i	−0.111968	−	0.193934i
$902$	12.7215	−	39.8107i	0.423581	−	1.32555i
$903$		0			0
$904$	−19.9938	+	14.9769i	−0.664984	+	0.498124i
$905$	2.27623	−	1.31418i	0.0756643	−	0.0436848i
$906$	8.41323	−	29.7943i	0.279511	−	0.989848i
$907$	5.81050	+	3.35469i	0.192934	+	0.111391i	0.593356	−	0.804940i	$-0.297803\pi$
$907$	5.81050	+	3.35469i	0.192934	+	0.111391i	−0.400421	+	0.916331i	$0.631136\pi$
$908$	2.56665	−	26.9383i	0.0851773	−	0.893979i
$909$	8.33897	+	4.08419i	0.276586	+	0.135464i
$910$		0			0
$911$	50.1275			1.66080			0.830399	−	0.557169i	$-0.188112\pi$
$911$	50.1275			1.66080			0.830399	+	0.557169i	$0.188112\pi$
$912$	6.00085	−	38.1791i	0.198708	−	1.26424i
$913$	−17.4568	+	30.2361i	−0.577736	+	1.00067i
$914$	16.1464	−	14.6811i	0.534076	−	0.485609i
$915$	7.51174	+	4.00200i	0.248330	+	0.132302i
$916$	23.9458	+	17.0443i	0.791193	+	0.563158i
$917$		0			0
$918$	5.89710	−	28.0740i	0.194633	−	0.926580i
$919$	−14.7529	+	8.51757i	−0.486652	+	0.280969i	−0.723185	−	0.690655i	$-0.757322\pi$
$919$	−14.7529	+	8.51757i	−0.486652	+	0.280969i	0.236532	+	0.971624i	$0.423989\pi$
$920$	−0.256077	−	2.13610i	−0.00844260	−	0.0704250i
$921$	−0.218376	−	6.40464i	−0.00719575	−	0.211040i
$922$	46.1216	−	10.0382i	1.51893	−	0.330589i
$923$	35.0771			1.15458
$924$		0			0
$925$	3.11784			0.102514
$926$	36.5900	−	7.96364i	1.20242	−	0.261702i
$927$	−18.0251	+	12.1150i	−0.592022	+	0.397907i
$928$	−26.4135	+	48.4324i	−0.867065	+	1.58987i
$929$	20.2721	−	11.7041i	0.665105	−	0.383999i	−0.129114	−	0.991630i	$-0.541213\pi$
$929$	20.2721	−	11.7041i	0.665105	−	0.383999i	0.794219	+	0.607631i	$0.207880\pi$
$930$	−0.554023	−	2.18442i	−0.0181671	−	0.0716301i
$931$		0			0
$932$	19.9365	−	28.0092i	0.653040	−	0.917470i
$933$	−6.17706	+	11.5943i	−0.202228	+	0.379581i
$934$	19.4529	−	17.6875i	0.636517	−	0.578753i
$935$	2.65631	−	4.60087i	0.0868707	−	0.150464i
$936$	−16.2772	−	18.8962i	−0.532038	−	0.617642i
$937$	−48.5929			−1.58746			−0.793730	−	0.608270i	$-0.791864\pi$
$937$	−48.5929			−1.58746			−0.793730	+	0.608270i	$0.791864\pi$
$938$		0			0
$939$	−14.3320	−	22.9781i	−0.467707	−	0.749861i
$940$	3.02881	+	0.288582i	0.0987889	+	0.00941249i
$941$	12.6540	+	7.30579i	0.412509	+	0.238162i	0.691867	−	0.722025i	$-0.256788\pi$
$941$	12.6540	+	7.30579i	0.412509	+	0.238162i	−0.279358	+	0.960187i	$0.590122\pi$
$942$	0.512569	+	0.144738i	0.0167004	+	0.00471582i
$943$	14.3046	−	8.25879i	0.465823	−	0.268943i
$944$	10.8014	+	31.1668i	0.351556	+	1.01439i
$945$		0			0
$946$	−4.23065	+	13.2394i	−0.137550	+	0.430449i
$947$	−15.7125	−	27.2148i	−0.510587	−	0.884362i	−0.999925	−	0.0122681i	$-0.996095\pi$
$947$	−15.7125	−	27.2148i	−0.510587	−	0.884362i	0.489338	−	0.872094i	$-0.337238\pi$
$948$	7.64581	−	11.5560i	0.248324	−	0.375322i
$949$	11.5783	−	20.0543i	0.375849	−	0.650989i
$950$	37.6057	−	8.18470i	1.22009	−	0.265547i
$951$	−20.4177	+	12.7350i	−0.662088	+	0.412961i
$952$		0			0
$953$			14.0113i			0.453872i	0.973910	+	0.226936i	$0.0728708\pi$
$953$			14.0113i			0.453872i	−0.973910	+	0.226936i	$0.927129\pi$
$954$	−1.74450	+	7.09395i	−0.0564802	+	0.229675i
$955$	0.492609	+	0.284408i	0.0159405	+	0.00920323i
$956$	26.4380	−	12.0805i	0.855065	−	0.390710i
$957$	−58.1958	−	31.0047i	−1.88120	−	1.00224i
$958$	−55.0666	−	17.5966i	−1.77912	−	0.568520i
$959$		0			0
$960$	1.30104	+	4.65200i	0.0419909	+	0.150143i
$961$	−12.0176	−	20.8150i	−0.387664	−	0.671453i
$962$	1.96554	−	1.78717i	0.0633715	−	0.0576205i
$963$	−18.4318	−	27.4236i	−0.593958	−	0.883713i
$964$	−3.56483	+	37.4147i	−0.114815	+	1.20505i
$965$		−	5.28380i		−	0.170091i
$966$		0			0
$967$			35.9876i			1.15728i	0.815582	+	0.578641i	$0.196417\pi$
$967$			35.9876i			1.15728i	−0.815582	+	0.578641i	$0.803583\pi$
$968$	4.71672	−	11.0241i	0.151601	−	0.354328i
$969$	37.6961	−	1.28531i	1.21097	−	0.0412901i
$970$	0.663335	+	0.729540i	0.0212984	+	0.0234241i
$971$	−24.1922	−	41.9022i	−0.776365	−	1.34470i	−0.934024	−	0.357210i	$-0.883728\pi$
$971$	−24.1922	−	41.9022i	−0.776365	−	1.34470i	0.157659	−	0.987494i	$-0.449605\pi$
$972$	−25.7486	+	17.5787i	−0.825886	+	0.563837i
$973$		0			0
$974$	9.22546	−	28.8701i	0.295603	−	0.925057i
$975$	11.6778	−	21.9191i	0.373988	−	0.701974i
$976$	55.3691	+	10.6477i	1.77232	+	0.340824i
$977$	32.6000	+	18.8216i	1.04296	+	0.602156i	0.920672	−	0.390338i	$-0.127642\pi$
$977$	32.6000	+	18.8216i	1.04296	+	0.602156i	0.122293	+	0.992494i	$0.460975\pi$
$978$	−8.95232	−	9.19575i	−0.286264	−	0.294048i
$979$		−	41.1443i		−	1.31498i
$980$		0			0
$981$	−1.84702	+	3.77118i	−0.0589708	+	0.120405i
$982$	0.490732	+	2.25473i	0.0156599	+	0.0719514i
$983$	−2.67750	+	4.63756i	−0.0853989	+	0.147915i	−0.905561	−	0.424216i	$-0.860550\pi$
$983$	−2.67750	+	4.63756i	−0.0853989	+	0.147915i	0.820162	+	0.572131i	$0.193883\pi$
$984$	−28.9077	+	23.2331i	−0.921543	+	0.740645i
$985$	3.69987	+	6.40836i	0.117888	+	0.204187i
$986$	−51.2847	−	16.3881i	−1.63324	−	0.521903i
$987$		0			0
$988$	19.0157	−	26.7156i	0.604971	−	0.849936i
$989$	−4.75713	+	2.74653i	−0.151268	+	0.0873345i
$990$	−5.54499	+	1.60933i	−0.176231	+	0.0511477i
$991$	−44.1913	−	25.5139i	−1.40378	−	0.810475i	−0.409005	−	0.912532i	$-0.634124\pi$
$991$	−44.1913	−	25.5139i	−1.40378	−	0.810475i	−0.994779	+	0.102057i	$0.967458\pi$
$992$	−7.77669	−	12.7436i	−0.246910	−	0.404609i
$993$	46.7276	−	29.1452i	1.48286	−	0.924895i
$994$		0			0
$995$	−1.30971			−0.0415207
$996$	27.7239	−	13.8288i	0.878466	−	0.438182i
$997$	26.9653	−	46.7052i	0.853998	−	1.47917i	−0.0235729	−	0.999722i	$-0.507504\pi$
$997$	26.9653	−	46.7052i	0.853998	−	1.47917i	0.877571	−	0.479446i	$-0.159162\pi$
$998$	8.45044	+	9.29385i	0.267494	+	0.294192i
$999$	−1.94532	−	2.69145i	−0.0615471	−	0.0851538i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	588.2.n.f.263.6		24
3.2	odd	2	inner	588.2.n.f.263.7		24
4.3	odd	2	inner	588.2.n.f.263.10		24
7.2	even	3	inner	588.2.n.f.275.3		24
7.3	odd	6		588.2.e.c.491.12		12
7.4	even	3		84.2.e.a.71.12	yes	12
7.5	odd	6		588.2.n.g.275.3		24
7.6	odd	2		588.2.n.g.263.6		24
12.11	even	2	inner	588.2.n.f.263.3		24
21.2	odd	6	inner	588.2.n.f.275.10		24
21.5	even	6		588.2.n.g.275.10		24
21.11	odd	6		84.2.e.a.71.1	✓	12
21.17	even	6		588.2.e.c.491.1		12
21.20	even	2		588.2.n.g.263.7		24
28.3	even	6		588.2.e.c.491.2		12
28.11	odd	6		84.2.e.a.71.2	yes	12
28.19	even	6		588.2.n.g.275.7		24
28.23	odd	6	inner	588.2.n.f.275.7		24
28.27	even	2		588.2.n.g.263.10		24
56.11	odd	6		1344.2.h.h.575.3		12
56.53	even	6		1344.2.h.h.575.10		12
84.11	even	6		84.2.e.a.71.11	yes	12
84.23	even	6	inner	588.2.n.f.275.6		24
84.47	odd	6		588.2.n.g.275.6		24
84.59	odd	6		588.2.e.c.491.11		12
84.83	odd	2		588.2.n.g.263.3		24
168.11	even	6		1344.2.h.h.575.9		12
168.53	odd	6		1344.2.h.h.575.4		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
84.2.e.a.71.1	✓	12	21.11	odd	6
84.2.e.a.71.2	yes	12	28.11	odd	6
84.2.e.a.71.11	yes	12	84.11	even	6
84.2.e.a.71.12	yes	12	7.4	even	3
588.2.e.c.491.1		12	21.17	even	6
588.2.e.c.491.2		12	28.3	even	6
588.2.e.c.491.11		12	84.59	odd	6
588.2.e.c.491.12		12	7.3	odd	6
588.2.n.f.263.3		24	12.11	even	2	inner
588.2.n.f.263.6		24	1.1	even	1	trivial
588.2.n.f.263.7		24	3.2	odd	2	inner
588.2.n.f.263.10		24	4.3	odd	2	inner
588.2.n.f.275.3		24	7.2	even	3	inner
588.2.n.f.275.6		24	84.23	even	6	inner
588.2.n.f.275.7		24	28.23	odd	6	inner
588.2.n.f.275.10		24	21.2	odd	6	inner
588.2.n.g.263.3		24	84.83	odd	2
588.2.n.g.263.6		24	7.6	odd	2
588.2.n.g.263.7		24	21.20	even	2
588.2.n.g.263.10		24	28.27	even	2
588.2.n.g.275.3		24	7.5	odd	6
588.2.n.g.275.6		24	84.47	odd	6
588.2.n.g.275.7		24	28.19	even	6
588.2.n.g.275.10		24	21.5	even	6
1344.2.h.h.575.3		12	56.11	odd	6
1344.2.h.h.575.4		12	168.53	odd	6
1344.2.h.h.575.9		12	168.11	even	6
1344.2.h.h.575.10		12	56.53	even	6

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:	\( N \)	\(=\)	\( 588 = 2^{2} \cdot 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	588.n (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.300756 - 1.38186i) q^{2} +(1.73104 - 0.0590228i) q^{3} +(-1.81909 + 0.831208i) q^{4} +(0.301907 - 0.174306i) q^{5} +(-0.602184 - 2.37432i) q^{6} +(1.69572 + 2.26374i) q^{8} +(2.99303 - 0.204342i) q^{9} +(-0.331667 - 0.364770i) q^{10} +(1.95188 - 3.38076i) q^{11} +(-3.09987 + 1.54623i) q^{12} -2.93923 q^{13} +(0.512326 - 0.319551i) q^{15} +(2.61819 - 3.02409i) q^{16} +(3.38076 + 1.95188i) q^{17} +(-1.18255 - 4.07450i) q^{18} +(4.83098 - 2.78917i) q^{19} +(-0.404312 + 0.568026i) q^{20} +(-5.25879 - 1.68045i) q^{22} +(-1.09094 - 1.88957i) q^{23} +(3.06898 + 3.81856i) q^{24} +(-2.43923 + 4.22488i) q^{25} +(0.883993 + 4.06162i) q^{26} +(5.16901 - 0.530383i) q^{27} -9.75220i q^{29} +(-0.595661 - 0.611858i) q^{30} +(2.28553 + 1.31955i) q^{31} +(-4.96631 - 2.70846i) q^{32} +(3.17925 - 5.96745i) q^{33} +(1.68045 - 5.25879i) q^{34} +(-5.27475 + 2.85955i) q^{36} +(-0.319551 - 0.553478i) q^{37} +(-5.30720 - 5.83689i) q^{38} +(-5.08795 + 0.173482i) q^{39} +(0.906533 + 0.387866i) q^{40} +7.57031i q^{41} -2.51757i q^{43} +(-0.740538 + 7.77233i) q^{44} +(0.867999 - 0.583396i) q^{45} +(-2.28302 + 2.07583i) q^{46} +(-2.18189 - 3.77914i) q^{47} +(4.35371 - 5.38936i) q^{48} +(6.57182 + 2.10003i) q^{50} +(5.96745 + 3.17925i) q^{51} +(5.34674 - 2.44312i) q^{52} +(-1.49119 - 0.860938i) q^{53} +(-2.28753 - 6.98335i) q^{54} -1.36090i q^{55} +(8.19802 - 5.11331i) q^{57} +(-13.4762 + 2.93304i) q^{58} +(-4.12318 + 7.14155i) q^{59} +(-0.666355 + 1.00714i) q^{60} +(7.04795 + 12.2074i) q^{61} +(1.13605 - 3.55515i) q^{62} +(-2.24908 + 7.67735i) q^{64} +(-0.887375 + 0.512326i) q^{65} +(-9.20238 - 2.59854i) q^{66} +(0.553478 + 0.319551i) q^{67} +(-7.77233 - 0.740538i) q^{68} +(-2.00000 - 3.20654i) q^{69} -11.9341 q^{71} +(5.53792 + 6.42895i) q^{72} +(-3.93923 + 6.82295i) q^{73} +(-0.668724 + 0.608037i) q^{74} +(-3.97306 + 7.45743i) q^{75} +(-6.46962 + 9.08930i) q^{76} +(1.76996 + 6.97867i) q^{78} +(-3.46410 + 2.00000i) q^{79} +(0.263332 - 1.36936i) q^{80} +(8.91649 - 1.22321i) q^{81} +(10.4611 - 2.27682i) q^{82} -8.94358 q^{83} +1.36090 q^{85} +(-3.47894 + 0.757175i) q^{86} +(-0.575602 - 16.8815i) q^{87} +(10.9630 - 1.31425i) q^{88} +(9.12760 - 5.26982i) q^{89} +(-1.06723 - 1.02400i) q^{90} +(3.55515 + 2.53050i) q^{92} +(4.03424 + 2.14930i) q^{93} +(-4.56604 + 4.15167i) q^{94} +(0.972337 - 1.68414i) q^{95} +(-8.75677 - 4.39535i) q^{96} -2.00000 q^{97} +(5.15121 - 10.5176i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 4 q^{4} - 12 q^{6} + 4 q^{9} - 4 q^{10} + 6 q^{12} - 4 q^{16} + 8 q^{18} - 32 q^{22} - 2 q^{24} + 12 q^{25} - 20 q^{30} + 16 q^{33} + 64 q^{34} - 40 q^{36} + 16 q^{37} - 20 q^{40} - 24 q^{45} + 92 q^{48}+ \cdots - 48 q^{97}+O(q^{100}) \) 24 * q + 4 * q^4 - 12 * q^6 + 4 * q^9 - 4 * q^10 + 6 * q^12 - 4 * q^16 + 8 * q^18 - 32 * q^22 - 2 * q^24 + 12 * q^25 - 20 * q^30 + 16 * q^33 + 64 * q^34 - 40 * q^36 + 16 * q^37 - 20 * q^40 - 24 * q^45 + 92 * q^48 + 28 * q^52 - 10 * q^54 + 32 * q^57 + 32 * q^58 - 28 * q^60 + 16 * q^61 + 40 * q^64 + 12 * q^66 - 48 * q^69 + 32 * q^72 - 24 * q^73 - 120 * q^76 + 40 * q^78 - 28 * q^81 - 8 * q^82 + 80 * q^85 + 56 * q^88 - 160 * q^90 - 24 * q^93 + 34 * q^96 - 48 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more