LMFDB - Embedded newform 56.2.e.b.27.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [56,2,Mod(27,56)] 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("56.27"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(56, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 1, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 56 = 2^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	56.e (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$0.447162251319$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(i, \sqrt{6})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 9 $ x^4 + 9
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			27.4
Root			$1.22474 + 1.22474i$ of defining polynomial
Character	$\chi$	$=$	56.27
Dual form			56.2.e.b.27.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.00000 + 1.00000i) q^{2} +2.44949i q^{3} -2.00000i q^{4} -2.44949 q^{5} +(-2.44949 - 2.44949i) q^{6} +(2.44949 + 1.00000i) q^{7} +(2.00000 + 2.00000i) q^{8} -3.00000 q^{9} +(2.44949 - 2.44949i) q^{10} +2.00000 q^{11} +4.89898 q^{12} +2.44949 q^{13} +(-3.44949 + 1.44949i) q^{14} -6.00000i q^{15} -4.00000 q^{16} -4.89898i q^{17} +(3.00000 - 3.00000i) q^{18} -2.44949i q^{19} +4.89898i q^{20} +(-2.44949 + 6.00000i) q^{21} +(-2.00000 + 2.00000i) q^{22} +4.00000i q^{23} +(-4.89898 + 4.89898i) q^{24} +1.00000 q^{25} +(-2.44949 + 2.44949i) q^{26} +(2.00000 - 4.89898i) q^{28} -4.00000i q^{29} +(6.00000 + 6.00000i) q^{30} -4.89898 q^{31} +(4.00000 - 4.00000i) q^{32} +4.89898i q^{33} +(4.89898 + 4.89898i) q^{34} +(-6.00000 - 2.44949i) q^{35} +6.00000i q^{36} -8.00000i q^{37} +(2.44949 + 2.44949i) q^{38} +6.00000i q^{39} +(-4.89898 - 4.89898i) q^{40} +(-3.55051 - 8.44949i) q^{42} -6.00000 q^{43} -4.00000i q^{44} +7.34847 q^{45} +(-4.00000 - 4.00000i) q^{46} +4.89898 q^{47} -9.79796i q^{48} +(5.00000 + 4.89898i) q^{49} +(-1.00000 + 1.00000i) q^{50} +12.0000 q^{51} -4.89898i q^{52} +4.00000i q^{53} -4.89898 q^{55} +(2.89898 + 6.89898i) q^{56} +6.00000 q^{57} +(4.00000 + 4.00000i) q^{58} -2.44949i q^{59} -12.0000 q^{60} +7.34847 q^{61} +(4.89898 - 4.89898i) q^{62} +(-7.34847 - 3.00000i) q^{63} +8.00000i q^{64} -6.00000 q^{65} +(-4.89898 - 4.89898i) q^{66} -2.00000 q^{67} -9.79796 q^{68} -9.79796 q^{69} +(8.44949 - 3.55051i) q^{70} -10.0000i q^{71} +(-6.00000 - 6.00000i) q^{72} +14.6969i q^{73} +(8.00000 + 8.00000i) q^{74} +2.44949i q^{75} -4.89898 q^{76} +(4.89898 + 2.00000i) q^{77} +(-6.00000 - 6.00000i) q^{78} +6.00000i q^{79} +9.79796 q^{80} -9.00000 q^{81} +2.44949i q^{83} +(12.0000 + 4.89898i) q^{84} +12.0000i q^{85} +(6.00000 - 6.00000i) q^{86} +9.79796 q^{87} +(4.00000 + 4.00000i) q^{88} -14.6969i q^{89} +(-7.34847 + 7.34847i) q^{90} +(6.00000 + 2.44949i) q^{91} +8.00000 q^{92} -12.0000i q^{93} +(-4.89898 + 4.89898i) q^{94} +6.00000i q^{95} +(9.79796 + 9.79796i) q^{96} -4.89898i q^{97} +(-9.89898 + 0.101021i) q^{98} -6.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{2} + 8 q^{8} - 12 q^{9} + 8 q^{11} - 4 q^{14} - 16 q^{16} + 12 q^{18} - 8 q^{22} + 4 q^{25} + 8 q^{28} + 24 q^{30} + 16 q^{32} - 24 q^{35} - 24 q^{42} - 24 q^{43} - 16 q^{46} + 20 q^{49} - 4 q^{50}+ \cdots - 24 q^{99}+O(q^{100}) $ 4 * q - 4 * q^2 + 8 * q^8 - 12 * q^9 + 8 * q^11 - 4 * q^14 - 16 * q^16 + 12 * q^18 - 8 * q^22 + 4 * q^25 + 8 * q^28 + 24 * q^30 + 16 * q^32 - 24 * q^35 - 24 * q^42 - 24 * q^43 - 16 * q^46 + 20 * q^49 - 4 * q^50 + 48 * q^51 - 8 * q^56 + 24 * q^57 + 16 * q^58 - 48 * q^60 - 24 * q^65 - 8 * q^67 + 24 * q^70 - 24 * q^72 + 32 * q^74 - 24 * q^78 - 36 * q^81 + 48 * q^84 + 24 * q^86 + 16 * q^88 + 24 * q^91 + 32 * q^92 - 20 * q^98 - 24 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/56\mathbb{Z}\right)^\times$.

$n$	$15$	$17$	$29$
$\chi(n)$	$-1$	$-1$	$-1$

Coefficient data

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

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

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

$2$	−1.00000	+	1.00000i	−0.707107	+	0.707107i
$2$	−1.00000	+	1.00000i	−0.707107	+	0.707107i
$3$			2.44949i			1.41421i	0.707107	+	0.707107i	$0.250000\pi$
$3$			2.44949i			1.41421i	−0.707107	+	0.707107i	$0.750000\pi$
$4$		−	2.00000i		−	1.00000i
$5$	−2.44949			−1.09545			−0.547723	−	0.836660i	$-0.684505\pi$
$5$	−2.44949			−1.09545			−0.547723	+	0.836660i	$0.684505\pi$
$6$	−2.44949	−	2.44949i	−1.00000	−	1.00000i
$7$	2.44949	+	1.00000i	0.925820	+	0.377964i
$7$	2.44949	+	1.00000i	0.925820	+	0.377964i
$8$	2.00000	+	2.00000i	0.707107	+	0.707107i
$9$	−3.00000			−1.00000
$10$	2.44949	−	2.44949i	0.774597	−	0.774597i
$11$	2.00000			0.603023			0.301511	−	0.953463i	$-0.402509\pi$
$11$	2.00000			0.603023			0.301511	+	0.953463i	$0.402509\pi$
$12$	4.89898			1.41421
$13$	2.44949			0.679366			0.339683	−	0.940540i	$-0.389680\pi$
$13$	2.44949			0.679366			0.339683	+	0.940540i	$0.389680\pi$
$14$	−3.44949	+	1.44949i	−0.921915	+	0.387392i
$15$		−	6.00000i		−	1.54919i
$16$	−4.00000			−1.00000
$17$		−	4.89898i		−	1.18818i	−0.804400	−	0.594089i	$-0.797513\pi$
$17$		−	4.89898i		−	1.18818i	0.804400	−	0.594089i	$-0.202487\pi$
$18$	3.00000	−	3.00000i	0.707107	−	0.707107i
$19$		−	2.44949i		−	0.561951i	−0.959715	−	0.280976i	$-0.909342\pi$
$19$		−	2.44949i		−	0.561951i	0.959715	−	0.280976i	$-0.0906580\pi$
$20$			4.89898i			1.09545i
$21$	−2.44949	+	6.00000i	−0.534522	+	1.30931i
$22$	−2.00000	+	2.00000i	−0.426401	+	0.426401i
$23$			4.00000i			0.834058i	0.908893	+	0.417029i	$0.136929\pi$
$23$			4.00000i			0.834058i	−0.908893	+	0.417029i	$0.863071\pi$
$24$	−4.89898	+	4.89898i	−1.00000	+	1.00000i
$25$	1.00000			0.200000
$26$	−2.44949	+	2.44949i	−0.480384	+	0.480384i
$27$		0			0
$28$	2.00000	−	4.89898i	0.377964	−	0.925820i
$29$		−	4.00000i		−	0.742781i	−0.928477	−	0.371391i	$-0.878881\pi$
$29$		−	4.00000i		−	0.742781i	0.928477	−	0.371391i	$-0.121119\pi$
$30$	6.00000	+	6.00000i	1.09545	+	1.09545i
$31$	−4.89898			−0.879883			−0.439941	−	0.898027i	$-0.645001\pi$
$31$	−4.89898			−0.879883			−0.439941	+	0.898027i	$0.645001\pi$
$32$	4.00000	−	4.00000i	0.707107	−	0.707107i
$33$			4.89898i			0.852803i
$34$	4.89898	+	4.89898i	0.840168	+	0.840168i
$35$	−6.00000	−	2.44949i	−1.01419	−	0.414039i
$36$			6.00000i			1.00000i
$37$		−	8.00000i		−	1.31519i	−0.753371	−	0.657596i	$-0.771573\pi$
$37$		−	8.00000i		−	1.31519i	0.753371	−	0.657596i	$-0.228427\pi$
$38$	2.44949	+	2.44949i	0.397360	+	0.397360i
$39$			6.00000i			0.960769i
$40$	−4.89898	−	4.89898i	−0.774597	−	0.774597i
$41$		0			0		1.00000			$0$
$41$		0			0		−1.00000			$\pi$
$42$	−3.55051	−	8.44949i	−0.547856	−	1.30378i
$43$	−6.00000			−0.914991			−0.457496	−	0.889212i	$-0.651253\pi$
$43$	−6.00000			−0.914991			−0.457496	+	0.889212i	$0.651253\pi$
$44$		−	4.00000i		−	0.603023i
$45$	7.34847			1.09545
$46$	−4.00000	−	4.00000i	−0.589768	−	0.589768i
$47$	4.89898			0.714590			0.357295	−	0.933992i	$-0.383699\pi$
$47$	4.89898			0.714590			0.357295	+	0.933992i	$0.383699\pi$
$48$		−	9.79796i		−	1.41421i
$49$	5.00000	+	4.89898i	0.714286	+	0.699854i
$50$	−1.00000	+	1.00000i	−0.141421	+	0.141421i
$51$	12.0000			1.68034
$52$		−	4.89898i		−	0.679366i
$53$			4.00000i			0.549442i	0.961524	+	0.274721i	$0.0885855\pi$
$53$			4.00000i			0.549442i	−0.961524	+	0.274721i	$0.911414\pi$
$54$		0			0
$55$	−4.89898			−0.660578
$56$	2.89898	+	6.89898i	0.387392	+	0.921915i
$57$	6.00000			0.794719
$58$	4.00000	+	4.00000i	0.525226	+	0.525226i
$59$		−	2.44949i		−	0.318896i	−0.987206	−	0.159448i	$-0.949029\pi$
$59$		−	2.44949i		−	0.318896i	0.987206	−	0.159448i	$-0.0509715\pi$
$60$	−12.0000			−1.54919
$61$	7.34847			0.940875			0.470438	−	0.882433i	$-0.344096\pi$
$61$	7.34847			0.940875			0.470438	+	0.882433i	$0.344096\pi$
$62$	4.89898	−	4.89898i	0.622171	−	0.622171i
$63$	−7.34847	−	3.00000i	−0.925820	−	0.377964i
$64$			8.00000i			1.00000i
$65$	−6.00000			−0.744208
$66$	−4.89898	−	4.89898i	−0.603023	−	0.603023i
$67$	−2.00000			−0.244339			−0.122169	−	0.992509i	$-0.538985\pi$
$67$	−2.00000			−0.244339			−0.122169	+	0.992509i	$0.538985\pi$
$68$	−9.79796			−1.18818
$69$	−9.79796			−1.17954
$70$	8.44949	−	3.55051i	1.00991	−	0.424367i
$71$		−	10.0000i		−	1.18678i	−0.804914	−	0.593391i	$-0.797789\pi$
$71$		−	10.0000i		−	1.18678i	0.804914	−	0.593391i	$-0.202211\pi$
$72$	−6.00000	−	6.00000i	−0.707107	−	0.707107i
$73$			14.6969i			1.72015i	0.510171	+	0.860073i	$0.329582\pi$
$73$			14.6969i			1.72015i	−0.510171	+	0.860073i	$0.670418\pi$
$74$	8.00000	+	8.00000i	0.929981	+	0.929981i
$75$			2.44949i			0.282843i
$76$	−4.89898			−0.561951
$77$	4.89898	+	2.00000i	0.558291	+	0.227921i
$78$	−6.00000	−	6.00000i	−0.679366	−	0.679366i
$79$			6.00000i			0.675053i	0.941316	+	0.337526i	$0.109590\pi$
$79$			6.00000i			0.675053i	−0.941316	+	0.337526i	$0.890410\pi$
$80$	9.79796			1.09545
$81$	−9.00000			−1.00000
$82$		0			0
$83$			2.44949i			0.268866i	0.990923	+	0.134433i	$0.0429214\pi$
$83$			2.44949i			0.268866i	−0.990923	+	0.134433i	$0.957079\pi$
$84$	12.0000	+	4.89898i	1.30931	+	0.534522i
$85$			12.0000i			1.30158i
$86$	6.00000	−	6.00000i	0.646997	−	0.646997i
$87$	9.79796			1.05045
$88$	4.00000	+	4.00000i	0.426401	+	0.426401i
$89$		−	14.6969i		−	1.55787i	−0.627103	−	0.778936i	$-0.715760\pi$
$89$		−	14.6969i		−	1.55787i	0.627103	−	0.778936i	$-0.284240\pi$
$90$	−7.34847	+	7.34847i	−0.774597	+	0.774597i
$91$	6.00000	+	2.44949i	0.628971	+	0.256776i
$92$	8.00000			0.834058
$93$		−	12.0000i		−	1.24434i
$94$	−4.89898	+	4.89898i	−0.505291	+	0.505291i
$95$			6.00000i			0.615587i
$96$	9.79796	+	9.79796i	1.00000	+	1.00000i
$97$		−	4.89898i		−	0.497416i	−0.968579	−	0.248708i	$-0.919994\pi$
$97$		−	4.89898i		−	0.497416i	0.968579	−	0.248708i	$-0.0800060\pi$
$98$	−9.89898	+	0.101021i	−0.999948	+	0.0102046i
$99$	−6.00000			−0.603023
$100$		−	2.00000i		−	0.200000i
$101$	−17.1464			−1.70613			−0.853067	−	0.521802i	$-0.825260\pi$
$101$	−17.1464			−1.70613			−0.853067	+	0.521802i	$0.825260\pi$
$102$	−12.0000	+	12.0000i	−1.18818	+	1.18818i
$103$	−9.79796			−0.965422			−0.482711	−	0.875780i	$-0.660348\pi$
$103$	−9.79796			−0.965422			−0.482711	+	0.875780i	$0.660348\pi$
$104$	4.89898	+	4.89898i	0.480384	+	0.480384i
$105$	6.00000	−	14.6969i	0.585540	−	1.43427i
$106$	−4.00000	−	4.00000i	−0.388514	−	0.388514i
$107$	−2.00000			−0.193347			−0.0966736	−	0.995316i	$-0.530820\pi$
$107$	−2.00000			−0.193347			−0.0966736	+	0.995316i	$0.530820\pi$
$108$		0			0
$109$		−	4.00000i		−	0.383131i	−0.981480	−	0.191565i	$-0.938644\pi$
$109$		−	4.00000i		−	0.383131i	0.981480	−	0.191565i	$-0.0613564\pi$
$110$	4.89898	−	4.89898i	0.467099	−	0.467099i
$111$	19.5959			1.85996
$112$	−9.79796	−	4.00000i	−0.925820	−	0.377964i
$113$	4.00000			0.376288			0.188144	−	0.982141i	$-0.439753\pi$
$113$	4.00000			0.376288			0.188144	+	0.982141i	$0.439753\pi$
$114$	−6.00000	+	6.00000i	−0.561951	+	0.561951i
$115$		−	9.79796i		−	0.913664i
$116$	−8.00000			−0.742781
$117$	−7.34847			−0.679366
$118$	2.44949	+	2.44949i	0.225494	+	0.225494i
$119$	4.89898	−	12.0000i	0.449089	−	1.10004i
$120$	12.0000	−	12.0000i	1.09545	−	1.09545i
$121$	−7.00000			−0.636364
$122$	−7.34847	+	7.34847i	−0.665299	+	0.665299i
$123$		0			0
$124$			9.79796i			0.879883i
$125$	9.79796			0.876356
$126$	10.3485	−	4.34847i	0.921915	−	0.387392i
$127$			12.0000i			1.06483i	0.846484	+	0.532414i	$0.178715\pi$
$127$			12.0000i			1.06483i	−0.846484	+	0.532414i	$0.821285\pi$
$128$	−8.00000	−	8.00000i	−0.707107	−	0.707107i
$129$		−	14.6969i		−	1.29399i
$130$	6.00000	−	6.00000i	0.526235	−	0.526235i
$131$			12.2474i			1.07006i	0.844832	+	0.535032i	$0.179701\pi$
$131$			12.2474i			1.07006i	−0.844832	+	0.535032i	$0.820299\pi$
$132$	9.79796			0.852803
$133$	2.44949	−	6.00000i	0.212398	−	0.520266i
$134$	2.00000	−	2.00000i	0.172774	−	0.172774i
$135$		0			0
$136$	9.79796	−	9.79796i	0.840168	−	0.840168i
$137$	−2.00000			−0.170872			−0.0854358	−	0.996344i	$-0.527228\pi$
$137$	−2.00000			−0.170872			−0.0854358	+	0.996344i	$0.527228\pi$
$138$	9.79796	−	9.79796i	0.834058	−	0.834058i
$139$		−	2.44949i		−	0.207763i	−0.994590	−	0.103882i	$-0.966874\pi$
$139$		−	2.44949i		−	0.207763i	0.994590	−	0.103882i	$-0.0331263\pi$
$140$	−4.89898	+	12.0000i	−0.414039	+	1.01419i
$141$			12.0000i			1.01058i
$142$	10.0000	+	10.0000i	0.839181	+	0.839181i
$143$	4.89898			0.409673
$144$	12.0000			1.00000
$145$			9.79796i			0.813676i
$146$	−14.6969	−	14.6969i	−1.21633	−	1.21633i
$147$	−12.0000	+	12.2474i	−0.989743	+	1.01015i
$148$	−16.0000			−1.31519
$149$			16.0000i			1.31077i	0.755295	+	0.655386i	$0.227494\pi$
$149$			16.0000i			1.31077i	−0.755295	+	0.655386i	$0.772506\pi$
$150$	−2.44949	−	2.44949i	−0.200000	−	0.200000i
$151$		−	20.0000i		−	1.62758i	−0.581161	−	0.813788i	$-0.697401\pi$
$151$		−	20.0000i		−	1.62758i	0.581161	−	0.813788i	$-0.302599\pi$
$152$	4.89898	−	4.89898i	0.397360	−	0.397360i
$153$			14.6969i			1.18818i
$154$	−6.89898	+	2.89898i	−0.555936	+	0.233606i
$155$	12.0000			0.963863
$156$	12.0000			0.960769
$157$	−7.34847			−0.586472			−0.293236	−	0.956040i	$-0.594732\pi$
$157$	−7.34847			−0.586472			−0.293236	+	0.956040i	$0.594732\pi$
$158$	−6.00000	−	6.00000i	−0.477334	−	0.477334i
$159$	−9.79796			−0.777029
$160$	−9.79796	+	9.79796i	−0.774597	+	0.774597i
$161$	−4.00000	+	9.79796i	−0.315244	+	0.772187i
$162$	9.00000	−	9.00000i	0.707107	−	0.707107i
$163$	14.0000			1.09656			0.548282	−	0.836293i	$-0.315282\pi$
$163$	14.0000			1.09656			0.548282	+	0.836293i	$0.315282\pi$
$164$		0			0
$165$		−	12.0000i		−	0.934199i
$166$	−2.44949	−	2.44949i	−0.190117	−	0.190117i
$167$	−19.5959			−1.51638			−0.758189	−	0.652035i	$-0.773915\pi$
$167$	−19.5959			−1.51638			−0.758189	+	0.652035i	$0.773915\pi$
$168$	−16.8990	+	7.10102i	−1.30378	+	0.547856i
$169$	−7.00000			−0.538462
$170$	−12.0000	−	12.0000i	−0.920358	−	0.920358i
$171$			7.34847i			0.561951i
$172$			12.0000i			0.914991i
$173$	2.44949			0.186231			0.0931156	−	0.995655i	$-0.470317\pi$
$173$	2.44949			0.186231			0.0931156	+	0.995655i	$0.470317\pi$
$174$	−9.79796	+	9.79796i	−0.742781	+	0.742781i
$175$	2.44949	+	1.00000i	0.185164	+	0.0755929i
$176$	−8.00000			−0.603023
$177$	6.00000			0.450988
$178$	14.6969	+	14.6969i	1.10158	+	1.10158i
$179$	10.0000			0.747435			0.373718	−	0.927543i	$-0.378083\pi$
$179$	10.0000			0.747435			0.373718	+	0.927543i	$0.378083\pi$
$180$		−	14.6969i		−	1.09545i
$181$	7.34847			0.546207			0.273104	−	0.961985i	$-0.411950\pi$
$181$	7.34847			0.546207			0.273104	+	0.961985i	$0.411950\pi$
$182$	−8.44949	+	3.55051i	−0.626318	+	0.263181i
$183$			18.0000i			1.33060i
$184$	−8.00000	+	8.00000i	−0.589768	+	0.589768i
$185$			19.5959i			1.44072i
$186$	12.0000	+	12.0000i	0.879883	+	0.879883i
$187$		−	9.79796i		−	0.716498i
$188$		−	9.79796i		−	0.714590i
$189$		0			0
$190$	−6.00000	−	6.00000i	−0.435286	−	0.435286i
$191$			10.0000i			0.723575i	0.932261	+	0.361787i	$0.117833\pi$
$191$			10.0000i			0.723575i	−0.932261	+	0.361787i	$0.882167\pi$
$192$	−19.5959			−1.41421
$193$	24.0000			1.72756			0.863779	−	0.503871i	$-0.168091\pi$
$193$	24.0000			1.72756			0.863779	+	0.503871i	$0.168091\pi$
$194$	4.89898	+	4.89898i	0.351726	+	0.351726i
$195$		−	14.6969i		−	1.05247i
$196$	9.79796	−	10.0000i	0.699854	−	0.714286i
$197$		−	8.00000i		−	0.569976i	−0.958531	−	0.284988i	$-0.908010\pi$
$197$		−	8.00000i		−	0.569976i	0.958531	−	0.284988i	$-0.0919897\pi$
$198$	6.00000	−	6.00000i	0.426401	−	0.426401i
$199$		0			0			−	1.00000i	$-0.5\pi$
$199$		0			0				1.00000i	$0.5\pi$
$200$	2.00000	+	2.00000i	0.141421	+	0.141421i
$201$		−	4.89898i		−	0.345547i
$202$	17.1464	−	17.1464i	1.20642	−	1.20642i
$203$	4.00000	−	9.79796i	0.280745	−	0.687682i
$204$		−	24.0000i		−	1.68034i
$205$		0			0
$206$	9.79796	−	9.79796i	0.682656	−	0.682656i
$207$		−	12.0000i		−	0.834058i
$208$	−9.79796			−0.679366
$209$		−	4.89898i		−	0.338869i
$210$	8.69694	+	20.6969i	0.600146	+	1.42822i
$211$	−18.0000			−1.23917			−0.619586	−	0.784929i	$-0.712699\pi$
$211$	−18.0000			−1.23917			−0.619586	+	0.784929i	$0.712699\pi$
$212$	8.00000			0.549442
$213$	24.4949			1.67836
$214$	2.00000	−	2.00000i	0.136717	−	0.136717i
$215$	14.6969			1.00232
$216$		0			0
$217$	−12.0000	−	4.89898i	−0.814613	−	0.332564i
$218$	4.00000	+	4.00000i	0.270914	+	0.270914i
$219$	−36.0000			−2.43265
$220$			9.79796i			0.660578i
$221$		−	12.0000i		−	0.807207i
$222$	−19.5959	+	19.5959i	−1.31519	+	1.31519i
$223$	−9.79796			−0.656120			−0.328060	−	0.944657i	$-0.606395\pi$
$223$	−9.79796			−0.656120			−0.328060	+	0.944657i	$0.606395\pi$
$224$	13.7980	−	5.79796i	0.921915	−	0.387392i
$225$	−3.00000			−0.200000
$226$	−4.00000	+	4.00000i	−0.266076	+	0.266076i
$227$			7.34847i			0.487735i	0.969809	+	0.243868i	$0.0784162\pi$
$227$			7.34847i			0.487735i	−0.969809	+	0.243868i	$0.921584\pi$
$228$		−	12.0000i		−	0.794719i
$229$	12.2474			0.809334			0.404667	−	0.914464i	$-0.367387\pi$
$229$	12.2474			0.809334			0.404667	+	0.914464i	$0.367387\pi$
$230$	9.79796	+	9.79796i	0.646058	+	0.646058i
$231$	−4.89898	+	12.0000i	−0.322329	+	0.789542i
$232$	8.00000	−	8.00000i	0.525226	−	0.525226i
$233$	14.0000			0.917170			0.458585	−	0.888650i	$-0.348356\pi$
$233$	14.0000			0.917170			0.458585	+	0.888650i	$0.348356\pi$
$234$	7.34847	−	7.34847i	0.480384	−	0.480384i
$235$	−12.0000			−0.782794
$236$	−4.89898			−0.318896
$237$	−14.6969			−0.954669
$238$	7.10102	+	16.8990i	0.460291	+	1.09540i
$239$		−	4.00000i		−	0.258738i	−0.991596	−	0.129369i	$-0.958705\pi$
$239$		−	4.00000i		−	0.258738i	0.991596	−	0.129369i	$-0.0412952\pi$
$240$			24.0000i			1.54919i
$241$		−	24.4949i		−	1.57786i	−0.614486	−	0.788928i	$-0.710637\pi$
$241$		−	24.4949i		−	1.57786i	0.614486	−	0.788928i	$-0.289363\pi$
$242$	7.00000	−	7.00000i	0.449977	−	0.449977i
$243$		−	22.0454i		−	1.41421i
$244$		−	14.6969i		−	0.940875i
$245$	−12.2474	−	12.0000i	−0.782461	−	0.766652i
$246$		0			0
$247$		−	6.00000i		−	0.381771i
$248$	−9.79796	−	9.79796i	−0.622171	−	0.622171i
$249$	−6.00000			−0.380235
$250$	−9.79796	+	9.79796i	−0.619677	+	0.619677i
$251$			12.2474i			0.773052i	0.922278	+	0.386526i	$0.126325\pi$
$251$			12.2474i			0.773052i	−0.922278	+	0.386526i	$0.873675\pi$
$252$	−6.00000	+	14.6969i	−0.377964	+	0.925820i
$253$			8.00000i			0.502956i
$254$	−12.0000	−	12.0000i	−0.752947	−	0.752947i
$255$	−29.3939			−1.84072
$256$	16.0000			1.00000
$257$			19.5959i			1.22236i	0.791492	+	0.611180i	$0.209305\pi$
$257$			19.5959i			1.22236i	−0.791492	+	0.611180i	$0.790695\pi$
$258$	14.6969	+	14.6969i	0.914991	+	0.914991i
$259$	8.00000	−	19.5959i	0.497096	−	1.21763i
$260$			12.0000i			0.744208i
$261$			12.0000i			0.742781i
$262$	−12.2474	−	12.2474i	−0.756650	−	0.756650i
$263$			14.0000i			0.863277i	0.902047	+	0.431638i	$0.142064\pi$
$263$			14.0000i			0.863277i	−0.902047	+	0.431638i	$0.857936\pi$
$264$	−9.79796	+	9.79796i	−0.603023	+	0.603023i
$265$		−	9.79796i		−	0.601884i
$266$	3.55051	+	8.44949i	0.217696	+	0.518071i
$267$	36.0000			2.20316
$268$			4.00000i			0.244339i
$269$	12.2474			0.746740			0.373370	−	0.927682i	$-0.378202\pi$
$269$	12.2474			0.746740			0.373370	+	0.927682i	$0.378202\pi$
$270$		0			0
$271$	19.5959			1.19037			0.595184	−	0.803590i	$-0.297079\pi$
$271$	19.5959			1.19037			0.595184	+	0.803590i	$0.297079\pi$
$272$			19.5959i			1.18818i
$273$	−6.00000	+	14.6969i	−0.363137	+	0.889499i
$274$	2.00000	−	2.00000i	0.120824	−	0.120824i
$275$	2.00000			0.120605
$276$			19.5959i			1.17954i
$277$			12.0000i			0.721010i	0.932757	+	0.360505i	$0.117396\pi$
$277$			12.0000i			0.721010i	−0.932757	+	0.360505i	$0.882604\pi$
$278$	2.44949	+	2.44949i	0.146911	+	0.146911i
$279$	14.6969			0.879883
$280$	−7.10102	−	16.8990i	−0.424367	−	1.00991i
$281$	2.00000			0.119310			0.0596550	−	0.998219i	$-0.481000\pi$
$281$	2.00000			0.119310			0.0596550	+	0.998219i	$0.481000\pi$
$282$	−12.0000	−	12.0000i	−0.714590	−	0.714590i
$283$			2.44949i			0.145607i	0.997346	+	0.0728035i	$0.0231946\pi$
$283$			2.44949i			0.145607i	−0.997346	+	0.0728035i	$0.976805\pi$
$284$	−20.0000			−1.18678
$285$	−14.6969			−0.870572
$286$	−4.89898	+	4.89898i	−0.289683	+	0.289683i
$287$		0			0
$288$	−12.0000	+	12.0000i	−0.707107	+	0.707107i
$289$	−7.00000			−0.411765
$290$	−9.79796	−	9.79796i	−0.575356	−	0.575356i
$291$	12.0000			0.703452
$292$	29.3939			1.72015
$293$	2.44949			0.143101			0.0715504	−	0.997437i	$-0.477205\pi$
$293$	2.44949			0.143101			0.0715504	+	0.997437i	$0.477205\pi$
$294$	−0.247449	−	24.2474i	−0.0144315	−	1.41414i
$295$			6.00000i			0.349334i
$296$	16.0000	−	16.0000i	0.929981	−	0.929981i
$297$		0			0
$298$	−16.0000	−	16.0000i	−0.926855	−	0.926855i
$299$			9.79796i			0.566631i
$300$	4.89898			0.282843
$301$	−14.6969	−	6.00000i	−0.847117	−	0.345834i
$302$	20.0000	+	20.0000i	1.15087	+	1.15087i
$303$		−	42.0000i		−	2.41284i
$304$			9.79796i			0.561951i
$305$	−18.0000			−1.03068
$306$	−14.6969	−	14.6969i	−0.840168	−	0.840168i
$307$			31.8434i			1.81740i	0.417453	+	0.908698i	$0.362923\pi$
$307$			31.8434i			1.81740i	−0.417453	+	0.908698i	$0.637077\pi$
$308$	4.00000	−	9.79796i	0.227921	−	0.558291i
$309$		−	24.0000i		−	1.36531i
$310$	−12.0000	+	12.0000i	−0.681554	+	0.681554i
$311$	−4.89898			−0.277796			−0.138898	−	0.990307i	$-0.544356\pi$
$311$	−4.89898			−0.277796			−0.138898	+	0.990307i	$0.544356\pi$
$312$	−12.0000	+	12.0000i	−0.679366	+	0.679366i
$313$		−	9.79796i		−	0.553813i	−0.960897	−	0.276907i	$-0.910691\pi$
$313$		−	9.79796i		−	0.553813i	0.960897	−	0.276907i	$-0.0893093\pi$
$314$	7.34847	−	7.34847i	0.414698	−	0.414698i
$315$	18.0000	+	7.34847i	1.01419	+	0.414039i
$316$	12.0000			0.675053
$317$			32.0000i			1.79730i	0.438667	+	0.898650i	$0.355451\pi$
$317$			32.0000i			1.79730i	−0.438667	+	0.898650i	$0.644549\pi$
$318$	9.79796	−	9.79796i	0.549442	−	0.549442i
$319$		−	8.00000i		−	0.447914i
$320$		−	19.5959i		−	1.09545i
$321$		−	4.89898i		−	0.273434i
$322$	−5.79796	−	13.7980i	−0.323108	−	0.768930i
$323$	−12.0000			−0.667698
$324$			18.0000i			1.00000i
$325$	2.44949			0.135873
$326$	−14.0000	+	14.0000i	−0.775388	+	0.775388i
$327$	9.79796			0.541828
$328$		0			0
$329$	12.0000	+	4.89898i	0.661581	+	0.270089i
$330$	12.0000	+	12.0000i	0.660578	+	0.660578i
$331$	−18.0000			−0.989369			−0.494685	−	0.869072i	$-0.664716\pi$
$331$	−18.0000			−0.989369			−0.494685	+	0.869072i	$0.664716\pi$
$332$	4.89898			0.268866
$333$			24.0000i			1.31519i
$334$	19.5959	−	19.5959i	1.07224	−	1.07224i
$335$	4.89898			0.267660
$336$	9.79796	−	24.0000i	0.534522	−	1.30931i
$337$	−12.0000			−0.653682			−0.326841	−	0.945079i	$-0.605984\pi$
$337$	−12.0000			−0.653682			−0.326841	+	0.945079i	$0.605984\pi$
$338$	7.00000	−	7.00000i	0.380750	−	0.380750i
$339$			9.79796i			0.532152i
$340$	24.0000			1.30158
$341$	−9.79796			−0.530589
$342$	−7.34847	−	7.34847i	−0.397360	−	0.397360i
$343$	7.34847	+	17.0000i	0.396780	+	0.917914i
$344$	−12.0000	−	12.0000i	−0.646997	−	0.646997i
$345$	24.0000			1.29212
$346$	−2.44949	+	2.44949i	−0.131685	+	0.131685i
$347$	−22.0000			−1.18102			−0.590511	−	0.807030i	$-0.701074\pi$
$347$	−22.0000			−1.18102			−0.590511	+	0.807030i	$0.701074\pi$
$348$		−	19.5959i		−	1.05045i
$349$	−12.2474			−0.655591			−0.327795	−	0.944749i	$-0.606306\pi$
$349$	−12.2474			−0.655591			−0.327795	+	0.944749i	$0.606306\pi$
$350$	−3.44949	+	1.44949i	−0.184383	+	0.0774785i
$351$		0			0
$352$	8.00000	−	8.00000i	0.426401	−	0.426401i
$353$		−	9.79796i		−	0.521493i	−0.965407	−	0.260746i	$-0.916031\pi$
$353$		−	9.79796i		−	0.521493i	0.965407	−	0.260746i	$-0.0839686\pi$
$354$	−6.00000	+	6.00000i	−0.318896	+	0.318896i
$355$			24.4949i			1.30005i
$356$	−29.3939			−1.55787
$357$	29.3939	+	12.0000i	1.55569	+	0.635107i
$358$	−10.0000	+	10.0000i	−0.528516	+	0.528516i
$359$		−	4.00000i		−	0.211112i	−0.994413	−	0.105556i	$-0.966338\pi$
$359$		−	4.00000i		−	0.211112i	0.994413	−	0.105556i	$-0.0336622\pi$
$360$	14.6969	+	14.6969i	0.774597	+	0.774597i
$361$	13.0000			0.684211
$362$	−7.34847	+	7.34847i	−0.386227	+	0.386227i
$363$		−	17.1464i		−	0.899954i
$364$	4.89898	−	12.0000i	0.256776	−	0.628971i
$365$		−	36.0000i		−	1.88433i
$366$	−18.0000	−	18.0000i	−0.940875	−	0.940875i
$367$	29.3939			1.53435			0.767174	−	0.641439i	$-0.221662\pi$
$367$	29.3939			1.53435			0.767174	+	0.641439i	$0.221662\pi$
$368$		−	16.0000i		−	0.834058i
$369$		0			0
$370$	−19.5959	−	19.5959i	−1.01874	−	1.01874i
$371$	−4.00000	+	9.79796i	−0.207670	+	0.508685i
$372$	−24.0000			−1.24434
$373$		−	36.0000i		−	1.86401i	−0.362446	−	0.932005i	$-0.618058\pi$
$373$		−	36.0000i		−	1.86401i	0.362446	−	0.932005i	$-0.381942\pi$
$374$	9.79796	+	9.79796i	0.506640	+	0.506640i
$375$			24.0000i			1.23935i
$376$	9.79796	+	9.79796i	0.505291	+	0.505291i
$377$		−	9.79796i		−	0.504621i
$378$		0			0
$379$	30.0000			1.54100			0.770498	−	0.637442i	$-0.220007\pi$
$379$	30.0000			1.54100			0.770498	+	0.637442i	$0.220007\pi$
$380$	12.0000			0.615587
$381$	−29.3939			−1.50589
$382$	−10.0000	−	10.0000i	−0.511645	−	0.511645i
$383$	−34.2929			−1.75228			−0.876142	−	0.482054i	$-0.839891\pi$
$383$	−34.2929			−1.75228			−0.876142	+	0.482054i	$0.839891\pi$
$384$	19.5959	−	19.5959i	1.00000	−	1.00000i
$385$	−12.0000	−	4.89898i	−0.611577	−	0.249675i
$386$	−24.0000	+	24.0000i	−1.22157	+	1.22157i
$387$	18.0000			0.914991
$388$	−9.79796			−0.497416
$389$			16.0000i			0.811232i	0.914044	+	0.405616i	$0.132943\pi$
$389$			16.0000i			0.811232i	−0.914044	+	0.405616i	$0.867057\pi$
$390$	14.6969	+	14.6969i	0.744208	+	0.744208i
$391$	19.5959			0.991008
$392$	0.202041	+	19.7980i	0.0102046	+	0.999948i
$393$	−30.0000			−1.51330
$394$	8.00000	+	8.00000i	0.403034	+	0.403034i
$395$		−	14.6969i		−	0.739483i
$396$			12.0000i			0.603023i
$397$	−31.8434			−1.59817			−0.799086	−	0.601216i	$-0.794683\pi$
$397$	−31.8434			−1.59817			−0.799086	+	0.601216i	$0.794683\pi$
$398$		0			0
$399$	14.6969	+	6.00000i	0.735767	+	0.300376i
$400$	−4.00000			−0.200000
$401$	32.0000			1.59800			0.799002	−	0.601329i	$-0.205362\pi$
$401$	32.0000			1.59800			0.799002	+	0.601329i	$0.205362\pi$
$402$	4.89898	+	4.89898i	0.244339	+	0.244339i
$403$	−12.0000			−0.597763
$404$			34.2929i			1.70613i
$405$	22.0454			1.09545
$406$	5.79796	+	13.7980i	0.287748	+	0.684781i
$407$		−	16.0000i		−	0.793091i
$408$	24.0000	+	24.0000i	1.18818	+	1.18818i
$409$			9.79796i			0.484478i	0.970217	+	0.242239i	$0.0778818\pi$
$409$			9.79796i			0.484478i	−0.970217	+	0.242239i	$0.922118\pi$
$410$		0			0
$411$		−	4.89898i		−	0.241649i
$412$			19.5959i			0.965422i
$413$	2.44949	−	6.00000i	0.120532	−	0.295241i
$414$	12.0000	+	12.0000i	0.589768	+	0.589768i
$415$		−	6.00000i		−	0.294528i
$416$	9.79796	−	9.79796i	0.480384	−	0.480384i
$417$	6.00000			0.293821
$418$	4.89898	+	4.89898i	0.239617	+	0.239617i
$419$		−	26.9444i		−	1.31632i	−0.752878	−	0.658160i	$-0.771335\pi$
$419$		−	26.9444i		−	1.31632i	0.752878	−	0.658160i	$-0.228665\pi$
$420$	−29.3939	−	12.0000i	−1.43427	−	0.585540i
$421$		0			0		1.00000			$0$
$421$		0			0		−1.00000			$\pi$
$422$	18.0000	−	18.0000i	0.876226	−	0.876226i
$423$	−14.6969			−0.714590
$424$	−8.00000	+	8.00000i	−0.388514	+	0.388514i
$425$		−	4.89898i		−	0.237635i
$426$	−24.4949	+	24.4949i	−1.18678	+	1.18678i
$427$	18.0000	+	7.34847i	0.871081	+	0.355617i
$428$			4.00000i			0.193347i
$429$			12.0000i			0.579365i
$430$	−14.6969	+	14.6969i	−0.708749	+	0.708749i
$431$			20.0000i			0.963366i	0.876346	+	0.481683i	$0.159974\pi$
$431$			20.0000i			0.963366i	−0.876346	+	0.481683i	$0.840026\pi$
$432$		0			0
$433$			14.6969i			0.706290i	0.935569	+	0.353145i	$0.114888\pi$
$433$			14.6969i			0.706290i	−0.935569	+	0.353145i	$0.885112\pi$
$434$	16.8990	−	7.10102i	0.811177	−	0.340860i
$435$	−24.0000			−1.15071
$436$	−8.00000			−0.383131
$437$	9.79796			0.468700
$438$	36.0000	−	36.0000i	1.72015	−	1.72015i
$439$	−24.4949			−1.16908			−0.584539	−	0.811366i	$-0.698725\pi$
$439$	−24.4949			−1.16908			−0.584539	+	0.811366i	$0.698725\pi$
$440$	−9.79796	−	9.79796i	−0.467099	−	0.467099i
$441$	−15.0000	−	14.6969i	−0.714286	−	0.699854i
$442$	12.0000	+	12.0000i	0.570782	+	0.570782i
$443$	−26.0000			−1.23530			−0.617649	−	0.786454i	$-0.711915\pi$
$443$	−26.0000			−1.23530			−0.617649	+	0.786454i	$0.711915\pi$
$444$		−	39.1918i		−	1.85996i
$445$			36.0000i			1.70656i
$446$	9.79796	−	9.79796i	0.463947	−	0.463947i
$447$	−39.1918			−1.85371
$448$	−8.00000	+	19.5959i	−0.377964	+	0.925820i
$449$	−10.0000			−0.471929			−0.235965	−	0.971762i	$-0.575825\pi$
$449$	−10.0000			−0.471929			−0.235965	+	0.971762i	$0.575825\pi$
$450$	3.00000	−	3.00000i	0.141421	−	0.141421i
$451$		0			0
$452$		−	8.00000i		−	0.376288i
$453$	48.9898			2.30174
$454$	−7.34847	−	7.34847i	−0.344881	−	0.344881i
$455$	−14.6969	−	6.00000i	−0.689003	−	0.281284i
$456$	12.0000	+	12.0000i	0.561951	+	0.561951i
$457$	−12.0000			−0.561336			−0.280668	−	0.959805i	$-0.590556\pi$
$457$	−12.0000			−0.561336			−0.280668	+	0.959805i	$0.590556\pi$
$458$	−12.2474	+	12.2474i	−0.572286	+	0.572286i
$459$		0			0
$460$	−19.5959			−0.913664
$461$	7.34847			0.342252			0.171126	−	0.985249i	$-0.445259\pi$
$461$	7.34847			0.342252			0.171126	+	0.985249i	$0.445259\pi$
$462$	−7.10102	−	16.8990i	−0.330369	−	0.786212i
$463$		−	6.00000i		−	0.278844i	−0.990233	−	0.139422i	$-0.955476\pi$
$463$		−	6.00000i		−	0.278844i	0.990233	−	0.139422i	$-0.0445244\pi$
$464$			16.0000i			0.742781i
$465$			29.3939i			1.36311i
$466$	−14.0000	+	14.0000i	−0.648537	+	0.648537i
$467$		−	41.6413i		−	1.92693i	−0.267833	−	0.963465i	$-0.586308\pi$
$467$		−	41.6413i		−	1.92693i	0.267833	−	0.963465i	$-0.413692\pi$
$468$			14.6969i			0.679366i
$469$	−4.89898	−	2.00000i	−0.226214	−	0.0923514i
$470$	12.0000	−	12.0000i	0.553519	−	0.553519i
$471$		−	18.0000i		−	0.829396i
$472$	4.89898	−	4.89898i	0.225494	−	0.225494i
$473$	−12.0000			−0.551761
$474$	14.6969	−	14.6969i	0.675053	−	0.675053i
$475$		−	2.44949i		−	0.112390i
$476$	−24.0000	−	9.79796i	−1.10004	−	0.449089i
$477$		−	12.0000i		−	0.549442i
$478$	4.00000	+	4.00000i	0.182956	+	0.182956i
$479$	24.4949			1.11920			0.559600	−	0.828763i	$-0.310955\pi$
$479$	24.4949			1.11920			0.559600	+	0.828763i	$0.310955\pi$
$480$	−24.0000	−	24.0000i	−1.09545	−	1.09545i
$481$		−	19.5959i		−	0.893497i
$482$	24.4949	+	24.4949i	1.11571	+	1.11571i
$483$	−24.0000	−	9.79796i	−1.09204	−	0.445823i
$484$			14.0000i			0.636364i
$485$			12.0000i			0.544892i
$486$	22.0454	+	22.0454i	1.00000	+	1.00000i
$487$		−	28.0000i		−	1.26880i	−0.773004	−	0.634401i	$-0.781247\pi$
$487$		−	28.0000i		−	1.26880i	0.773004	−	0.634401i	$-0.218753\pi$
$488$	14.6969	+	14.6969i	0.665299	+	0.665299i
$489$			34.2929i			1.55078i
$490$	24.2474	−	0.247449i	1.09539	−	0.0111786i
$491$	2.00000			0.0902587			0.0451294	−	0.998981i	$-0.485630\pi$
$491$	2.00000			0.0902587			0.0451294	+	0.998981i	$0.485630\pi$
$492$		0			0
$493$	−19.5959			−0.882556
$494$	6.00000	+	6.00000i	0.269953	+	0.269953i
$495$	14.6969			0.660578
$496$	19.5959			0.879883
$497$	10.0000	−	24.4949i	0.448561	−	1.09875i
$498$	6.00000	−	6.00000i	0.268866	−	0.268866i
$499$	30.0000			1.34298			0.671492	−	0.741012i	$-0.265654\pi$
$499$	30.0000			1.34298			0.671492	+	0.741012i	$0.265654\pi$
$500$		−	19.5959i		−	0.876356i
$501$		−	48.0000i		−	2.14448i
$502$	−12.2474	−	12.2474i	−0.546630	−	0.546630i
$503$	14.6969			0.655304			0.327652	−	0.944798i	$-0.393743\pi$
$503$	14.6969			0.655304			0.327652	+	0.944798i	$0.393743\pi$
$504$	−8.69694	−	20.6969i	−0.387392	−	0.921915i
$505$	42.0000			1.86898
$506$	−8.00000	−	8.00000i	−0.355643	−	0.355643i
$507$		−	17.1464i		−	0.761500i
$508$	24.0000			1.06483
$509$	36.7423			1.62858			0.814288	−	0.580461i	$-0.197128\pi$
$509$	36.7423			1.62858			0.814288	+	0.580461i	$0.197128\pi$
$510$	29.3939	−	29.3939i	1.30158	−	1.30158i
$511$	−14.6969	+	36.0000i	−0.650154	+	1.59255i
$512$	−16.0000	+	16.0000i	−0.707107	+	0.707107i
$513$		0			0
$514$	−19.5959	−	19.5959i	−0.864339	−	0.864339i
$515$	24.0000			1.05757
$516$	−29.3939			−1.29399
$517$	9.79796			0.430914
$518$	11.5959	+	27.5959i	0.509495	+	1.21250i
$519$			6.00000i			0.263371i
$520$	−12.0000	−	12.0000i	−0.526235	−	0.526235i
$521$		0			0		1.00000			$0$
$521$		0			0		−1.00000			$\pi$
$522$	−12.0000	−	12.0000i	−0.525226	−	0.525226i
$523$			26.9444i			1.17820i	0.808062	+	0.589098i	$0.200517\pi$
$523$			26.9444i			1.17820i	−0.808062	+	0.589098i	$0.799483\pi$
$524$	24.4949			1.07006
$525$	−2.44949	+	6.00000i	−0.106904	+	0.261861i
$526$	−14.0000	−	14.0000i	−0.610429	−	0.610429i
$527$			24.0000i			1.04546i
$528$		−	19.5959i		−	0.852803i
$529$	7.00000			0.304348
$530$	9.79796	+	9.79796i	0.425596	+	0.425596i
$531$			7.34847i			0.318896i
$532$	−12.0000	−	4.89898i	−0.520266	−	0.212398i
$533$		0			0
$534$	−36.0000	+	36.0000i	−1.55787	+	1.55787i
$535$	4.89898			0.211801
$536$	−4.00000	−	4.00000i	−0.172774	−	0.172774i
$537$			24.4949i			1.05703i
$538$	−12.2474	+	12.2474i	−0.528025	+	0.528025i
$539$	10.0000	+	9.79796i	0.430730	+	0.422028i
$540$		0			0
$541$		0			0		1.00000			$0$
$541$		0			0		−1.00000			$\pi$
$542$	−19.5959	+	19.5959i	−0.841717	+	0.841717i
$543$			18.0000i			0.772454i
$544$	−19.5959	−	19.5959i	−0.840168	−	0.840168i
$545$			9.79796i			0.419698i
$546$	−8.69694	−	20.6969i	−0.372195	−	0.885747i
$547$	−2.00000			−0.0855138			−0.0427569	−	0.999086i	$-0.513614\pi$
$547$	−2.00000			−0.0855138			−0.0427569	+	0.999086i	$0.513614\pi$
$548$			4.00000i			0.170872i
$549$	−22.0454			−0.940875
$550$	−2.00000	+	2.00000i	−0.0852803	+	0.0852803i
$551$	−9.79796			−0.417407
$552$	−19.5959	−	19.5959i	−0.834058	−	0.834058i
$553$	−6.00000	+	14.6969i	−0.255146	+	0.624977i
$554$	−12.0000	−	12.0000i	−0.509831	−	0.509831i
$555$	−48.0000			−2.03749
$556$	−4.89898			−0.207763
$557$		−	28.0000i		−	1.18640i	−0.805056	−	0.593199i	$-0.797865\pi$
$557$		−	28.0000i		−	1.18640i	0.805056	−	0.593199i	$-0.202135\pi$
$558$	−14.6969	+	14.6969i	−0.622171	+	0.622171i
$559$	−14.6969			−0.621614
$560$	24.0000	+	9.79796i	1.01419	+	0.414039i
$561$	24.0000			1.01328
$562$	−2.00000	+	2.00000i	−0.0843649	+	0.0843649i
$563$		−	22.0454i		−	0.929103i	−0.885546	−	0.464552i	$-0.846216\pi$
$563$		−	22.0454i		−	0.929103i	0.885546	−	0.464552i	$-0.153784\pi$
$564$	24.0000			1.01058
$565$	−9.79796			−0.412203
$566$	−2.44949	−	2.44949i	−0.102960	−	0.102960i
$567$	−22.0454	−	9.00000i	−0.925820	−	0.377964i
$568$	20.0000	−	20.0000i	0.839181	−	0.839181i
$569$	−20.0000			−0.838444			−0.419222	−	0.907884i	$-0.637697\pi$
$569$	−20.0000			−0.838444			−0.419222	+	0.907884i	$0.637697\pi$
$570$	14.6969	−	14.6969i	0.615587	−	0.615587i
$571$	2.00000			0.0836974			0.0418487	−	0.999124i	$-0.486675\pi$
$571$	2.00000			0.0836974			0.0418487	+	0.999124i	$0.486675\pi$
$572$		−	9.79796i		−	0.409673i
$573$	−24.4949			−1.02329
$574$		0			0
$575$			4.00000i			0.166812i
$576$		−	24.0000i		−	1.00000i
$577$			19.5959i			0.815789i	0.913029	+	0.407894i	$0.133737\pi$
$577$			19.5959i			0.815789i	−0.913029	+	0.407894i	$0.866263\pi$
$578$	7.00000	−	7.00000i	0.291162	−	0.291162i
$579$			58.7878i			2.44314i
$580$	19.5959			0.813676
$581$	−2.44949	+	6.00000i	−0.101622	+	0.248922i
$582$	−12.0000	+	12.0000i	−0.497416	+	0.497416i
$583$			8.00000i			0.331326i
$584$	−29.3939	+	29.3939i	−1.21633	+	1.21633i
$585$	18.0000			0.744208
$586$	−2.44949	+	2.44949i	−0.101187	+	0.101187i
$587$			7.34847i			0.303304i	0.988434	+	0.151652i	$0.0484593\pi$
$587$			7.34847i			0.303304i	−0.988434	+	0.151652i	$0.951541\pi$
$588$	24.4949	+	24.0000i	1.01015	+	0.989743i
$589$			12.0000i			0.494451i
$590$	−6.00000	−	6.00000i	−0.247016	−	0.247016i
$591$	19.5959			0.806068
$592$			32.0000i			1.31519i
$593$		−	9.79796i		−	0.402354i	−0.979555	−	0.201177i	$-0.935523\pi$
$593$		−	9.79796i		−	0.402354i	0.979555	−	0.201177i	$-0.0644766\pi$
$594$		0			0
$595$	−12.0000	+	29.3939i	−0.491952	+	1.20503i
$596$	32.0000			1.31077
$597$		0			0
$598$	−9.79796	−	9.79796i	−0.400668	−	0.400668i
$599$		−	14.0000i		−	0.572024i	−0.958226	−	0.286012i	$-0.907670\pi$
$599$		−	14.0000i		−	0.572024i	0.958226	−	0.286012i	$-0.0923298\pi$
$600$	−4.89898	+	4.89898i	−0.200000	+	0.200000i
$601$		−	24.4949i		−	0.999168i	−0.866266	−	0.499584i	$-0.833486\pi$
$601$		−	24.4949i		−	0.999168i	0.866266	−	0.499584i	$-0.166514\pi$
$602$	20.6969	−	8.69694i	0.843544	−	0.354461i
$603$	6.00000			0.244339
$604$	−40.0000			−1.62758
$605$	17.1464			0.697101
$606$	42.0000	+	42.0000i	1.70613	+	1.70613i
$607$	29.3939			1.19306			0.596530	−	0.802591i	$-0.296546\pi$
$607$	29.3939			1.19306			0.596530	+	0.802591i	$0.296546\pi$
$608$	−9.79796	−	9.79796i	−0.397360	−	0.397360i
$609$	24.0000	+	9.79796i	0.972529	+	0.397033i
$610$	18.0000	−	18.0000i	0.728799	−	0.728799i
$611$	12.0000			0.485468
$612$	29.3939			1.18818
$613$			24.0000i			0.969351i	0.874694	+	0.484675i	$0.161062\pi$
$613$			24.0000i			0.969351i	−0.874694	+	0.484675i	$0.838938\pi$
$614$	−31.8434	−	31.8434i	−1.28509	−	1.28509i
$615$		0			0
$616$	5.79796	+	13.7980i	0.233606	+	0.555936i
$617$	−32.0000			−1.28827			−0.644136	−	0.764911i	$-0.722783\pi$
$617$	−32.0000			−1.28827			−0.644136	+	0.764911i	$0.722783\pi$
$618$	24.0000	+	24.0000i	0.965422	+	0.965422i
$619$			22.0454i			0.886080i	0.896502	+	0.443040i	$0.146100\pi$
$619$			22.0454i			0.886080i	−0.896502	+	0.443040i	$0.853900\pi$
$620$		−	24.0000i		−	0.963863i
$621$		0			0
$622$	4.89898	−	4.89898i	0.196431	−	0.196431i
$623$	14.6969	−	36.0000i	0.588820	−	1.44231i
$624$		−	24.0000i		−	0.960769i
$625$	−29.0000			−1.16000
$626$	9.79796	+	9.79796i	0.391605	+	0.391605i
$627$	12.0000			0.479234
$628$			14.6969i			0.586472i
$629$	−39.1918			−1.56268
$630$	−25.3485	+	10.6515i	−1.00991	+	0.424367i
$631$		−	30.0000i		−	1.19428i	−0.802137	−	0.597141i	$-0.796303\pi$
$631$		−	30.0000i		−	1.19428i	0.802137	−	0.597141i	$-0.203697\pi$
$632$	−12.0000	+	12.0000i	−0.477334	+	0.477334i
$633$		−	44.0908i		−	1.75245i
$634$	−32.0000	−	32.0000i	−1.27088	−	1.27088i
$635$		−	29.3939i		−	1.16646i
$636$			19.5959i			0.777029i
$637$	12.2474	+	12.0000i	0.485262	+	0.475457i
$638$	8.00000	+	8.00000i	0.316723	+	0.316723i
$639$			30.0000i			1.18678i
$640$	19.5959	+	19.5959i	0.774597	+	0.774597i
$641$	−8.00000			−0.315981			−0.157991	−	0.987441i	$-0.550502\pi$
$641$	−8.00000			−0.315981			−0.157991	+	0.987441i	$0.550502\pi$
$642$	4.89898	+	4.89898i	0.193347	+	0.193347i
$643$		−	22.0454i		−	0.869386i	−0.900579	−	0.434693i	$-0.856857\pi$
$643$		−	22.0454i		−	0.869386i	0.900579	−	0.434693i	$-0.143143\pi$
$644$	19.5959	+	8.00000i	0.772187	+	0.315244i
$645$			36.0000i			1.41750i
$646$	12.0000	−	12.0000i	0.472134	−	0.472134i
$647$	−19.5959			−0.770395			−0.385198	−	0.922834i	$-0.625867\pi$
$647$	−19.5959			−0.770395			−0.385198	+	0.922834i	$0.625867\pi$
$648$	−18.0000	−	18.0000i	−0.707107	−	0.707107i
$649$		−	4.89898i		−	0.192302i
$650$	−2.44949	+	2.44949i	−0.0960769	+	0.0960769i
$651$	12.0000	−	29.3939i	0.470317	−	1.15204i
$652$		−	28.0000i		−	1.09656i
$653$		−	16.0000i		−	0.626128i	−0.949732	−	0.313064i	$-0.898644\pi$
$653$		−	16.0000i		−	0.626128i	0.949732	−	0.313064i	$-0.101356\pi$
$654$	−9.79796	+	9.79796i	−0.383131	+	0.383131i
$655$		−	30.0000i		−	1.17220i
$656$		0			0
$657$		−	44.0908i		−	1.72015i
$658$	−16.8990	+	7.10102i	−0.658791	+	0.276827i
$659$	10.0000			0.389545			0.194772	−	0.980848i	$-0.437603\pi$
$659$	10.0000			0.389545			0.194772	+	0.980848i	$0.437603\pi$
$660$	−24.0000			−0.934199
$661$	31.8434			1.23856			0.619282	−	0.785169i	$-0.287424\pi$
$661$	31.8434			1.23856			0.619282	+	0.785169i	$0.287424\pi$
$662$	18.0000	−	18.0000i	0.699590	−	0.699590i
$663$	29.3939			1.14156
$664$	−4.89898	+	4.89898i	−0.190117	+	0.190117i
$665$	−6.00000	+	14.6969i	−0.232670	+	0.569923i
$666$	−24.0000	−	24.0000i	−0.929981	−	0.929981i
$667$	16.0000			0.619522
$668$			39.1918i			1.51638i
$669$		−	24.0000i		−	0.927894i
$670$	−4.89898	+	4.89898i	−0.189264	+	0.189264i
$671$	14.6969			0.567369
$672$	14.2020	+	33.7980i	0.547856	+	1.30378i
$673$	−6.00000			−0.231283			−0.115642	−	0.993291i	$-0.536892\pi$
$673$	−6.00000			−0.231283			−0.115642	+	0.993291i	$0.536892\pi$
$674$	12.0000	−	12.0000i	0.462223	−	0.462223i
$675$		0			0
$676$			14.0000i			0.538462i
$677$	−31.8434			−1.22384			−0.611920	−	0.790920i	$-0.709603\pi$
$677$	−31.8434			−1.22384			−0.611920	+	0.790920i	$0.709603\pi$
$678$	−9.79796	−	9.79796i	−0.376288	−	0.376288i
$679$	4.89898	−	12.0000i	0.188006	−	0.460518i
$680$	−24.0000	+	24.0000i	−0.920358	+	0.920358i
$681$	−18.0000			−0.689761
$682$	9.79796	−	9.79796i	0.375183	−	0.375183i
$683$	14.0000			0.535695			0.267848	−	0.963461i	$-0.413688\pi$
$683$	14.0000			0.535695			0.267848	+	0.963461i	$0.413688\pi$
$684$	14.6969			0.561951
$685$	4.89898			0.187180
$686$	−24.3485	−	9.65153i	−0.929629	−	0.368497i
$687$			30.0000i			1.14457i
$688$	24.0000			0.914991
$689$			9.79796i			0.373273i
$690$	−24.0000	+	24.0000i	−0.913664	+	0.913664i
$691$		−	36.7423i		−	1.39774i	−0.715246	−	0.698872i	$-0.753686\pi$
$691$		−	36.7423i		−	1.39774i	0.715246	−	0.698872i	$-0.246314\pi$
$692$		−	4.89898i		−	0.186231i
$693$	−14.6969	−	6.00000i	−0.558291	−	0.227921i
$694$	22.0000	−	22.0000i	0.835109	−	0.835109i
$695$			6.00000i			0.227593i
$696$	19.5959	+	19.5959i	0.742781	+	0.742781i
$697$		0			0
$698$	12.2474	−	12.2474i	0.463573	−	0.463573i
$699$			34.2929i			1.29707i
$700$	2.00000	−	4.89898i	0.0755929	−	0.185164i
$701$			40.0000i			1.51078i	0.655276	+	0.755390i	$0.272552\pi$
$701$			40.0000i			1.51078i	−0.655276	+	0.755390i	$0.727448\pi$
$702$		0			0
$703$	−19.5959			−0.739074
$704$			16.0000i			0.603023i
$705$		−	29.3939i		−	1.10704i
$706$	9.79796	+	9.79796i	0.368751	+	0.368751i
$707$	−42.0000	−	17.1464i	−1.57957	−	0.644858i
$708$		−	12.0000i		−	0.450988i
$709$		−	4.00000i		−	0.150223i	−0.997175	−	0.0751116i	$-0.976069\pi$
$709$		−	4.00000i		−	0.150223i	0.997175	−	0.0751116i	$-0.0239313\pi$
$710$	−24.4949	−	24.4949i	−0.919277	−	0.919277i
$711$		−	18.0000i		−	0.675053i
$712$	29.3939	−	29.3939i	1.10158	−	1.10158i
$713$		−	19.5959i		−	0.733873i
$714$	−41.3939	+	17.3939i	−1.54913	+	0.650949i
$715$	−12.0000			−0.448775
$716$		−	20.0000i		−	0.747435i
$717$	9.79796			0.365911
$718$	4.00000	+	4.00000i	0.149279	+	0.149279i
$719$	−24.4949			−0.913506			−0.456753	−	0.889594i	$-0.650988\pi$
$719$	−24.4949			−0.913506			−0.456753	+	0.889594i	$0.650988\pi$
$720$	−29.3939			−1.09545
$721$	−24.0000	−	9.79796i	−0.893807	−	0.364895i
$722$	−13.0000	+	13.0000i	−0.483810	+	0.483810i
$723$	60.0000			2.23142
$724$		−	14.6969i		−	0.546207i
$725$		−	4.00000i		−	0.148556i
$726$	17.1464	+	17.1464i	0.636364	+	0.636364i
$727$	29.3939			1.09016			0.545079	−	0.838385i	$-0.316500\pi$
$727$	29.3939			1.09016			0.545079	+	0.838385i	$0.316500\pi$
$728$	7.10102	+	16.8990i	0.263181	+	0.626318i
$729$	27.0000			1.00000
$730$	36.0000	+	36.0000i	1.33242	+	1.33242i
$731$			29.3939i			1.08717i
$732$	36.0000			1.33060
$733$	−22.0454			−0.814266			−0.407133	−	0.913369i	$-0.633471\pi$
$733$	−22.0454			−0.814266			−0.407133	+	0.913369i	$0.633471\pi$
$734$	−29.3939	+	29.3939i	−1.08495	+	1.08495i
$735$	29.3939	−	30.0000i	1.08421	−	1.10657i
$736$	16.0000	+	16.0000i	0.589768	+	0.589768i
$737$	−4.00000			−0.147342
$738$		0			0
$739$	−50.0000			−1.83928			−0.919640	−	0.392763i	$-0.871519\pi$
$739$	−50.0000			−1.83928			−0.919640	+	0.392763i	$0.871519\pi$
$740$	39.1918			1.44072
$741$	14.6969			0.539906
$742$	−5.79796	−	13.7980i	−0.212850	−	0.506539i
$743$			44.0000i			1.61420i	0.590412	+	0.807102i	$0.298965\pi$
$743$			44.0000i			1.61420i	−0.590412	+	0.807102i	$0.701035\pi$
$744$	24.0000	−	24.0000i	0.879883	−	0.879883i
$745$		−	39.1918i		−	1.43588i
$746$	36.0000	+	36.0000i	1.31805	+	1.31805i
$747$		−	7.34847i		−	0.268866i
$748$	−19.5959			−0.716498
$749$	−4.89898	−	2.00000i	−0.179005	−	0.0730784i
$750$	−24.0000	−	24.0000i	−0.876356	−	0.876356i
$751$			20.0000i			0.729810i	0.931045	+	0.364905i	$0.118899\pi$
$751$			20.0000i			0.729810i	−0.931045	+	0.364905i	$0.881101\pi$
$752$	−19.5959			−0.714590
$753$	−30.0000			−1.09326
$754$	9.79796	+	9.79796i	0.356821	+	0.356821i
$755$			48.9898i			1.78292i
$756$		0			0
$757$		−	8.00000i		−	0.290765i	−0.989376	−	0.145382i	$-0.953559\pi$
$757$		−	8.00000i		−	0.290765i	0.989376	−	0.145382i	$-0.0464413\pi$
$758$	−30.0000	+	30.0000i	−1.08965	+	1.08965i
$759$	−19.5959			−0.711287
$760$	−12.0000	+	12.0000i	−0.435286	+	0.435286i
$761$			48.9898i			1.77588i	0.459961	+	0.887939i	$0.347864\pi$
$761$			48.9898i			1.77588i	−0.459961	+	0.887939i	$0.652136\pi$
$762$	29.3939	−	29.3939i	1.06483	−	1.06483i
$763$	4.00000	−	9.79796i	0.144810	−	0.354710i
$764$	20.0000			0.723575
$765$		−	36.0000i		−	1.30158i
$766$	34.2929	−	34.2929i	1.23905	−	1.23905i
$767$		−	6.00000i		−	0.216647i
$768$			39.1918i			1.41421i
$769$			34.2929i			1.23663i	0.785930	+	0.618316i	$0.212185\pi$
$769$			34.2929i			1.23663i	−0.785930	+	0.618316i	$0.787815\pi$
$770$	16.8990	−	7.10102i	0.608997	−	0.255903i
$771$	−48.0000			−1.72868
$772$		−	48.0000i		−	1.72756i
$773$	−22.0454			−0.792918			−0.396459	−	0.918052i	$-0.629761\pi$
$773$	−22.0454			−0.792918			−0.396459	+	0.918052i	$0.629761\pi$
$774$	−18.0000	+	18.0000i	−0.646997	+	0.646997i
$775$	−4.89898			−0.175977
$776$	9.79796	−	9.79796i	0.351726	−	0.351726i
$777$	48.0000	+	19.5959i	1.72199	+	0.703000i
$778$	−16.0000	−	16.0000i	−0.573628	−	0.573628i
$779$		0			0
$780$	−29.3939			−1.05247
$781$		−	20.0000i		−	0.715656i
$782$	−19.5959	+	19.5959i	−0.700749	+	0.700749i
$783$		0			0
$784$	−20.0000	−	19.5959i	−0.714286	−	0.699854i
$785$	18.0000			0.642448
$786$	30.0000	−	30.0000i	1.07006	−	1.07006i
$787$			7.34847i			0.261945i	0.991386	+	0.130972i	$0.0418099\pi$
$787$			7.34847i			0.261945i	−0.991386	+	0.130972i	$0.958190\pi$
$788$	−16.0000			−0.569976
$789$	−34.2929			−1.22086
$790$	14.6969	+	14.6969i	0.522894	+	0.522894i
$791$	9.79796	+	4.00000i	0.348375	+	0.142224i
$792$	−12.0000	−	12.0000i	−0.426401	−	0.426401i
$793$	18.0000			0.639199
$794$	31.8434	−	31.8434i	1.13008	−	1.13008i
$795$	24.0000			0.851192
$796$		0			0
$797$	41.6413			1.47501			0.737506	−	0.675341i	$-0.236003\pi$
$797$	41.6413			1.47501			0.737506	+	0.675341i	$0.236003\pi$
$798$	−20.6969	+	8.69694i	−0.732664	+	0.307868i
$799$		−	24.0000i		−	0.849059i
$800$	4.00000	−	4.00000i	0.141421	−	0.141421i
$801$			44.0908i			1.55787i
$802$	−32.0000	+	32.0000i	−1.12996	+	1.12996i
$803$			29.3939i			1.03729i
$804$	−9.79796			−0.345547
$805$	9.79796	−	24.0000i	0.345333	−	0.845889i
$806$	12.0000	−	12.0000i	0.422682	−	0.422682i
$807$			30.0000i			1.05605i
$808$	−34.2929	−	34.2929i	−1.20642	−	1.20642i
$809$	20.0000			0.703163			0.351581	−	0.936157i	$-0.385644\pi$
$809$	20.0000			0.703163			0.351581	+	0.936157i	$0.385644\pi$
$810$	−22.0454	+	22.0454i	−0.774597	+	0.774597i
$811$		−	36.7423i		−	1.29020i	−0.764099	−	0.645099i	$-0.776816\pi$
$811$		−	36.7423i		−	1.29020i	0.764099	−	0.645099i	$-0.223184\pi$
$812$	−19.5959	−	8.00000i	−0.687682	−	0.280745i
$813$			48.0000i			1.68343i
$814$	16.0000	+	16.0000i	0.560800	+	0.560800i
$815$	−34.2929			−1.20123
$816$	−48.0000			−1.68034
$817$			14.6969i			0.514181i
$818$	−9.79796	−	9.79796i	−0.342578	−	0.342578i
$819$	−18.0000	−	7.34847i	−0.628971	−	0.256776i
$820$		0			0
$821$			20.0000i			0.698005i	0.937122	+	0.349002i	$0.113479\pi$
$821$			20.0000i			0.698005i	−0.937122	+	0.349002i	$0.886521\pi$
$822$	4.89898	+	4.89898i	0.170872	+	0.170872i
$823$			54.0000i			1.88232i	0.337959	+	0.941161i	$0.390263\pi$
$823$			54.0000i			1.88232i	−0.337959	+	0.941161i	$0.609737\pi$
$824$	−19.5959	−	19.5959i	−0.682656	−	0.682656i
$825$			4.89898i			0.170561i
$826$	3.55051	+	8.44949i	0.123538	+	0.293995i
$827$	−22.0000			−0.765015			−0.382507	−	0.923952i	$-0.624939\pi$
$827$	−22.0000			−0.765015			−0.382507	+	0.923952i	$0.624939\pi$
$828$	−24.0000			−0.834058
$829$	36.7423			1.27611			0.638057	−	0.769989i	$-0.279738\pi$
$829$	36.7423			1.27611			0.638057	+	0.769989i	$0.279738\pi$
$830$	6.00000	+	6.00000i	0.208263	+	0.208263i
$831$	−29.3939			−1.01966
$832$			19.5959i			0.679366i
$833$	24.0000	−	24.4949i	0.831551	−	0.848698i
$834$	−6.00000	+	6.00000i	−0.207763	+	0.207763i
$835$	48.0000			1.66111
$836$	−9.79796			−0.338869
$837$		0			0
$838$	26.9444	+	26.9444i	0.930778	+	0.930778i
$839$		0			0			−	1.00000i	$-0.5\pi$
$839$		0			0				1.00000i	$0.5\pi$
$840$	41.3939	−	17.3939i	1.42822	−	0.600146i
$841$	13.0000			0.448276
$842$		0			0
$843$			4.89898i			0.168730i
$844$			36.0000i			1.23917i
$845$	17.1464			0.589855
$846$	14.6969	−	14.6969i	0.505291	−	0.505291i
$847$	−17.1464	−	7.00000i	−0.589158	−	0.240523i
$848$		−	16.0000i		−	0.549442i
$849$	−6.00000			−0.205919
$850$	4.89898	+	4.89898i	0.168034	+	0.168034i
$851$	32.0000			1.09695
$852$		−	48.9898i		−	1.67836i
$853$	2.44949			0.0838689			0.0419345	−	0.999120i	$-0.486648\pi$
$853$	2.44949			0.0838689			0.0419345	+	0.999120i	$0.486648\pi$
$854$	−25.3485	+	10.6515i	−0.867407	+	0.364488i
$855$		−	18.0000i		−	0.615587i
$856$	−4.00000	−	4.00000i	−0.136717	−	0.136717i
$857$		−	29.3939i		−	1.00408i	−0.864846	−	0.502038i	$-0.832584\pi$
$857$		−	29.3939i		−	1.00408i	0.864846	−	0.502038i	$-0.167416\pi$
$858$	−12.0000	−	12.0000i	−0.409673	−	0.409673i
$859$		−	26.9444i		−	0.919331i	−0.888092	−	0.459665i	$-0.847969\pi$
$859$		−	26.9444i		−	0.919331i	0.888092	−	0.459665i	$-0.152031\pi$
$860$		−	29.3939i		−	1.00232i
$861$		0			0
$862$	−20.0000	−	20.0000i	−0.681203	−	0.681203i
$863$		−	46.0000i		−	1.56586i	−0.622111	−	0.782929i	$-0.713725\pi$
$863$		−	46.0000i		−	1.56586i	0.622111	−	0.782929i	$-0.286275\pi$
$864$		0			0
$865$	−6.00000			−0.204006
$866$	−14.6969	−	14.6969i	−0.499422	−	0.499422i
$867$		−	17.1464i		−	0.582323i
$868$	−9.79796	+	24.0000i	−0.332564	+	0.814613i
$869$			12.0000i			0.407072i
$870$	24.0000	−	24.0000i	0.813676	−	0.813676i
$871$	−4.89898			−0.165996
$872$	8.00000	−	8.00000i	0.270914	−	0.270914i
$873$			14.6969i			0.497416i
$874$	−9.79796	+	9.79796i	−0.331421	+	0.331421i
$875$	24.0000	+	9.79796i	0.811348	+	0.331231i
$876$			72.0000i			2.43265i
$877$		−	48.0000i		−	1.62084i	−0.585846	−	0.810422i	$-0.699238\pi$
$877$		−	48.0000i		−	1.62084i	0.585846	−	0.810422i	$-0.300762\pi$
$878$	24.4949	−	24.4949i	0.826663	−	0.826663i
$879$			6.00000i			0.202375i
$880$	19.5959			0.660578
$881$			48.9898i			1.65051i	0.564762	+	0.825254i	$0.308968\pi$
$881$			48.9898i			1.65051i	−0.564762	+	0.825254i	$0.691032\pi$
$882$	29.6969	−	0.303062i	0.999948	−	0.0102046i
$883$	−6.00000			−0.201916			−0.100958	−	0.994891i	$-0.532191\pi$
$883$	−6.00000			−0.201916			−0.100958	+	0.994891i	$0.532191\pi$
$884$	−24.0000			−0.807207
$885$	−14.6969			−0.494032
$886$	26.0000	−	26.0000i	0.873487	−	0.873487i
$887$	29.3939			0.986950			0.493475	−	0.869760i	$-0.335726\pi$
$887$	29.3939			0.986950			0.493475	+	0.869760i	$0.335726\pi$
$888$	39.1918	+	39.1918i	1.31519	+	1.31519i
$889$	−12.0000	+	29.3939i	−0.402467	+	0.985839i
$890$	−36.0000	−	36.0000i	−1.20672	−	1.20672i
$891$	−18.0000			−0.603023
$892$			19.5959i			0.656120i
$893$		−	12.0000i		−	0.401565i
$894$	39.1918	−	39.1918i	1.31077	−	1.31077i
$895$	−24.4949			−0.818774
$896$	−11.5959	−	27.5959i	−0.387392	−	0.921915i
$897$	−24.0000			−0.801337
$898$	10.0000	−	10.0000i	0.333704	−	0.333704i
$899$			19.5959i			0.653560i
$900$			6.00000i			0.200000i
$901$	19.5959			0.652835
$902$		0			0
$903$	14.6969	−	36.0000i	0.489083	−	1.19800i
$904$	8.00000	+	8.00000i	0.266076	+	0.266076i
$905$	−18.0000			−0.598340
$906$	−48.9898	+	48.9898i	−1.62758	+	1.62758i
$907$	−42.0000			−1.39459			−0.697294	−	0.716786i	$-0.745613\pi$
$907$	−42.0000			−1.39459			−0.697294	+	0.716786i	$0.745613\pi$
$908$	14.6969			0.487735
$909$	51.4393			1.70613
$910$	20.6969	−	8.69694i	0.686097	−	0.288301i
$911$		−	20.0000i		−	0.662630i	−0.943520	−	0.331315i	$-0.892508\pi$
$911$		−	20.0000i		−	0.662630i	0.943520	−	0.331315i	$-0.107492\pi$
$912$	−24.0000			−0.794719
$913$			4.89898i			0.162133i
$914$	12.0000	−	12.0000i	0.396925	−	0.396925i
$915$		−	44.0908i		−	1.45760i
$916$		−	24.4949i		−	0.809334i
$917$	−12.2474	+	30.0000i	−0.404446	+	0.990687i
$918$		0			0
$919$			46.0000i			1.51740i	0.651440	+	0.758700i	$0.274165\pi$
$919$			46.0000i			1.51740i	−0.651440	+	0.758700i	$0.725835\pi$
$920$	19.5959	−	19.5959i	0.646058	−	0.646058i
$921$	−78.0000			−2.57019
$922$	−7.34847	+	7.34847i	−0.242009	+	0.242009i
$923$		−	24.4949i		−	0.806259i
$924$	24.0000	+	9.79796i	0.789542	+	0.322329i
$925$		−	8.00000i		−	0.263038i
$926$	6.00000	+	6.00000i	0.197172	+	0.197172i
$927$	29.3939			0.965422
$928$	−16.0000	−	16.0000i	−0.525226	−	0.525226i
$929$		−	14.6969i		−	0.482191i	−0.970501	−	0.241095i	$-0.922493\pi$
$929$		−	14.6969i		−	0.482191i	0.970501	−	0.241095i	$-0.0775067\pi$
$930$	−29.3939	−	29.3939i	−0.963863	−	0.963863i
$931$	12.0000	−	12.2474i	0.393284	−	0.401394i
$932$		−	28.0000i		−	0.917170i
$933$		−	12.0000i		−	0.392862i
$934$	41.6413	+	41.6413i	1.36255	+	1.36255i
$935$			24.0000i			0.784884i
$936$	−14.6969	−	14.6969i	−0.480384	−	0.480384i
$937$		−	4.89898i		−	0.160043i	−0.996793	−	0.0800213i	$-0.974501\pi$
$937$		−	4.89898i		−	0.160043i	0.996793	−	0.0800213i	$-0.0254988\pi$
$938$	6.89898	−	2.89898i	0.225260	−	0.0946550i
$939$	24.0000			0.783210
$940$			24.0000i			0.782794i
$941$	31.8434			1.03806			0.519032	−	0.854755i	$-0.326293\pi$
$941$	31.8434			1.03806			0.519032	+	0.854755i	$0.326293\pi$
$942$	18.0000	+	18.0000i	0.586472	+	0.586472i
$943$		0			0
$944$			9.79796i			0.318896i
$945$		0			0
$946$	12.0000	−	12.0000i	0.390154	−	0.390154i
$947$	−22.0000			−0.714904			−0.357452	−	0.933932i	$-0.616354\pi$
$947$	−22.0000			−0.714904			−0.357452	+	0.933932i	$0.616354\pi$
$948$			29.3939i			0.954669i
$949$			36.0000i			1.16861i
$950$	2.44949	+	2.44949i	0.0794719	+	0.0794719i
$951$	−78.3837			−2.54176
$952$	33.7980	−	14.2020i	1.09540	−	0.460291i
$953$	34.0000			1.10137			0.550684	−	0.834714i	$-0.314367\pi$
$953$	34.0000			1.10137			0.550684	+	0.834714i	$0.314367\pi$
$954$	12.0000	+	12.0000i	0.388514	+	0.388514i
$955$		−	24.4949i		−	0.792636i
$956$	−8.00000			−0.258738
$957$	19.5959			0.633446
$958$	−24.4949	+	24.4949i	−0.791394	+	0.791394i
$959$	−4.89898	−	2.00000i	−0.158196	−	0.0645834i
$960$	48.0000			1.54919
$961$	−7.00000			−0.225806
$962$	19.5959	+	19.5959i	0.631798	+	0.631798i
$963$	6.00000			0.193347
$964$	−48.9898			−1.57786
$965$	−58.7878			−1.89244
$966$	33.7980	−	14.2020i	1.08743	−	0.456943i
$967$			12.0000i			0.385894i	0.981209	+	0.192947i	$0.0618045\pi$
$967$			12.0000i			0.385894i	−0.981209	+	0.192947i	$0.938195\pi$
$968$	−14.0000	−	14.0000i	−0.449977	−	0.449977i
$969$		−	29.3939i		−	0.944267i
$970$	−12.0000	−	12.0000i	−0.385297	−	0.385297i
$971$			36.7423i			1.17912i	0.807725	+	0.589559i	$0.200698\pi$
$971$			36.7423i			1.17912i	−0.807725	+	0.589559i	$0.799302\pi$
$972$	−44.0908			−1.41421
$973$	2.44949	−	6.00000i	0.0785270	−	0.192351i
$974$	28.0000	+	28.0000i	0.897178	+	0.897178i
$975$			6.00000i			0.192154i
$976$	−29.3939			−0.940875
$977$	38.0000			1.21573			0.607864	−	0.794041i	$-0.292027\pi$
$977$	38.0000			1.21573			0.607864	+	0.794041i	$0.292027\pi$
$978$	−34.2929	−	34.2929i	−1.09656	−	1.09656i
$979$		−	29.3939i		−	0.939432i
$980$	−24.0000	+	24.4949i	−0.766652	+	0.782461i
$981$			12.0000i			0.383131i
$982$	−2.00000	+	2.00000i	−0.0638226	+	0.0638226i
$983$	39.1918			1.25003			0.625013	−	0.780615i	$-0.285094\pi$
$983$	39.1918			1.25003			0.625013	+	0.780615i	$0.285094\pi$
$984$		0			0
$985$			19.5959i			0.624378i
$986$	19.5959	−	19.5959i	0.624061	−	0.624061i
$987$	−12.0000	+	29.3939i	−0.381964	+	0.935617i
$988$	−12.0000			−0.381771
$989$		−	24.0000i		−	0.763156i
$990$	−14.6969	+	14.6969i	−0.467099	+	0.467099i
$991$		−	10.0000i		−	0.317660i	−0.987306	−	0.158830i	$-0.949228\pi$
$991$		−	10.0000i		−	0.317660i	0.987306	−	0.158830i	$-0.0507723\pi$
$992$	−19.5959	+	19.5959i	−0.622171	+	0.622171i
$993$		−	44.0908i		−	1.39918i
$994$	14.4949	+	34.4949i	0.459750	+	1.09411i
$995$		0			0
$996$			12.0000i			0.380235i
$997$	−31.8434			−1.00849			−0.504245	−	0.863561i	$-0.668229\pi$
$997$	−31.8434			−1.00849			−0.504245	+	0.863561i	$0.668229\pi$
$998$	−30.0000	+	30.0000i	−0.949633	+	0.949633i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	56.2.e.b.27.4	yes	4
3.2	odd	2		504.2.p.f.307.2		4
4.3	odd	2		224.2.e.b.111.1		4
7.2	even	3		392.2.m.f.227.3		8
7.3	odd	6		392.2.m.f.19.1		8
7.4	even	3		392.2.m.f.19.2		8
7.5	odd	6		392.2.m.f.227.4		8
7.6	odd	2	inner	56.2.e.b.27.3	yes	4
8.3	odd	2	inner	56.2.e.b.27.2	yes	4
8.5	even	2		224.2.e.b.111.2		4
12.11	even	2		2016.2.p.e.559.3		4
16.3	odd	4		1792.2.f.f.1791.4		4
16.5	even	4		1792.2.f.e.1791.3		4
16.11	odd	4		1792.2.f.e.1791.1		4
16.13	even	4		1792.2.f.f.1791.2		4
21.20	even	2		504.2.p.f.307.1		4
24.5	odd	2		2016.2.p.e.559.2		4
24.11	even	2		504.2.p.f.307.3		4
28.3	even	6		1568.2.q.e.1391.3		8
28.11	odd	6		1568.2.q.e.1391.2		8
28.19	even	6		1568.2.q.e.815.1		8
28.23	odd	6		1568.2.q.e.815.4		8
28.27	even	2		224.2.e.b.111.4		4
56.3	even	6		392.2.m.f.19.3		8
56.5	odd	6		1568.2.q.e.815.2		8
56.11	odd	6		392.2.m.f.19.4		8
56.13	odd	2		224.2.e.b.111.3		4
56.19	even	6		392.2.m.f.227.2		8
56.27	even	2	inner	56.2.e.b.27.1	✓	4
56.37	even	6		1568.2.q.e.815.3		8
56.45	odd	6		1568.2.q.e.1391.4		8
56.51	odd	6		392.2.m.f.227.1		8
56.53	even	6		1568.2.q.e.1391.1		8
84.83	odd	2		2016.2.p.e.559.1		4
112.13	odd	4		1792.2.f.f.1791.3		4
112.27	even	4		1792.2.f.e.1791.4		4
112.69	odd	4		1792.2.f.e.1791.2		4
112.83	even	4		1792.2.f.f.1791.1		4
168.83	odd	2		504.2.p.f.307.4		4
168.125	even	2		2016.2.p.e.559.4		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
56.2.e.b.27.1	✓	4	56.27	even	2	inner
56.2.e.b.27.2	yes	4	8.3	odd	2	inner
56.2.e.b.27.3	yes	4	7.6	odd	2	inner
56.2.e.b.27.4	yes	4	1.1	even	1	trivial
224.2.e.b.111.1		4	4.3	odd	2
224.2.e.b.111.2		4	8.5	even	2
224.2.e.b.111.3		4	56.13	odd	2
224.2.e.b.111.4		4	28.27	even	2
392.2.m.f.19.1		8	7.3	odd	6
392.2.m.f.19.2		8	7.4	even	3
392.2.m.f.19.3		8	56.3	even	6
392.2.m.f.19.4		8	56.11	odd	6
392.2.m.f.227.1		8	56.51	odd	6
392.2.m.f.227.2		8	56.19	even	6
392.2.m.f.227.3		8	7.2	even	3
392.2.m.f.227.4		8	7.5	odd	6
504.2.p.f.307.1		4	21.20	even	2
504.2.p.f.307.2		4	3.2	odd	2
504.2.p.f.307.3		4	24.11	even	2
504.2.p.f.307.4		4	168.83	odd	2
1568.2.q.e.815.1		8	28.19	even	6
1568.2.q.e.815.2		8	56.5	odd	6
1568.2.q.e.815.3		8	56.37	even	6
1568.2.q.e.815.4		8	28.23	odd	6
1568.2.q.e.1391.1		8	56.53	even	6
1568.2.q.e.1391.2		8	28.11	odd	6
1568.2.q.e.1391.3		8	28.3	even	6
1568.2.q.e.1391.4		8	56.45	odd	6
1792.2.f.e.1791.1		4	16.11	odd	4
1792.2.f.e.1791.2		4	112.69	odd	4
1792.2.f.e.1791.3		4	16.5	even	4
1792.2.f.e.1791.4		4	112.27	even	4
1792.2.f.f.1791.1		4	112.83	even	4
1792.2.f.f.1791.2		4	16.13	even	4
1792.2.f.f.1791.3		4	112.13	odd	4
1792.2.f.f.1791.4		4	16.3	odd	4
2016.2.p.e.559.1		4	84.83	odd	2
2016.2.p.e.559.2		4	24.5	odd	2
2016.2.p.e.559.3		4	12.11	even	2
2016.2.p.e.559.4		4	168.125	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 56 = 2^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	56.e (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.00000 + 1.00000i) q^{2} +2.44949i q^{3} -2.00000i q^{4} -2.44949 q^{5} +(-2.44949 - 2.44949i) q^{6} +(2.44949 + 1.00000i) q^{7} +(2.00000 + 2.00000i) q^{8} -3.00000 q^{9} +(2.44949 - 2.44949i) q^{10} +2.00000 q^{11} +4.89898 q^{12} +2.44949 q^{13} +(-3.44949 + 1.44949i) q^{14} -6.00000i q^{15} -4.00000 q^{16} -4.89898i q^{17} +(3.00000 - 3.00000i) q^{18} -2.44949i q^{19} +4.89898i q^{20} +(-2.44949 + 6.00000i) q^{21} +(-2.00000 + 2.00000i) q^{22} +4.00000i q^{23} +(-4.89898 + 4.89898i) q^{24} +1.00000 q^{25} +(-2.44949 + 2.44949i) q^{26} +(2.00000 - 4.89898i) q^{28} -4.00000i q^{29} +(6.00000 + 6.00000i) q^{30} -4.89898 q^{31} +(4.00000 - 4.00000i) q^{32} +4.89898i q^{33} +(4.89898 + 4.89898i) q^{34} +(-6.00000 - 2.44949i) q^{35} +6.00000i q^{36} -8.00000i q^{37} +(2.44949 + 2.44949i) q^{38} +6.00000i q^{39} +(-4.89898 - 4.89898i) q^{40} +(-3.55051 - 8.44949i) q^{42} -6.00000 q^{43} -4.00000i q^{44} +7.34847 q^{45} +(-4.00000 - 4.00000i) q^{46} +4.89898 q^{47} -9.79796i q^{48} +(5.00000 + 4.89898i) q^{49} +(-1.00000 + 1.00000i) q^{50} +12.0000 q^{51} -4.89898i q^{52} +4.00000i q^{53} -4.89898 q^{55} +(2.89898 + 6.89898i) q^{56} +6.00000 q^{57} +(4.00000 + 4.00000i) q^{58} -2.44949i q^{59} -12.0000 q^{60} +7.34847 q^{61} +(4.89898 - 4.89898i) q^{62} +(-7.34847 - 3.00000i) q^{63} +8.00000i q^{64} -6.00000 q^{65} +(-4.89898 - 4.89898i) q^{66} -2.00000 q^{67} -9.79796 q^{68} -9.79796 q^{69} +(8.44949 - 3.55051i) q^{70} -10.0000i q^{71} +(-6.00000 - 6.00000i) q^{72} +14.6969i q^{73} +(8.00000 + 8.00000i) q^{74} +2.44949i q^{75} -4.89898 q^{76} +(4.89898 + 2.00000i) q^{77} +(-6.00000 - 6.00000i) q^{78} +6.00000i q^{79} +9.79796 q^{80} -9.00000 q^{81} +2.44949i q^{83} +(12.0000 + 4.89898i) q^{84} +12.0000i q^{85} +(6.00000 - 6.00000i) q^{86} +9.79796 q^{87} +(4.00000 + 4.00000i) q^{88} -14.6969i q^{89} +(-7.34847 + 7.34847i) q^{90} +(6.00000 + 2.44949i) q^{91} +8.00000 q^{92} -12.0000i q^{93} +(-4.89898 + 4.89898i) q^{94} +6.00000i q^{95} +(9.79796 + 9.79796i) q^{96} -4.89898i q^{97} +(-9.89898 + 0.101021i) q^{98} -6.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{2} + 8 q^{8} - 12 q^{9} + 8 q^{11} - 4 q^{14} - 16 q^{16} + 12 q^{18} - 8 q^{22} + 4 q^{25} + 8 q^{28} + 24 q^{30} + 16 q^{32} - 24 q^{35} - 24 q^{42} - 24 q^{43} - 16 q^{46} + 20 q^{49} - 4 q^{50}+ \cdots - 24 q^{99}+O(q^{100}) \) 4 * q - 4 * q^2 + 8 * q^8 - 12 * q^9 + 8 * q^11 - 4 * q^14 - 16 * q^16 + 12 * q^18 - 8 * q^22 + 4 * q^25 + 8 * q^28 + 24 * q^30 + 16 * q^32 - 24 * q^35 - 24 * q^42 - 24 * q^43 - 16 * q^46 + 20 * q^49 - 4 * q^50 + 48 * q^51 - 8 * q^56 + 24 * q^57 + 16 * q^58 - 48 * q^60 - 24 * q^65 - 8 * q^67 + 24 * q^70 - 24 * q^72 + 32 * q^74 - 24 * q^78 - 36 * q^81 + 48 * q^84 + 24 * q^86 + 16 * q^88 + 24 * q^91 + 32 * q^92 - 20 * q^98 - 24 * q^99

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