LMFDB - Embedded newform 112.2.m.a.29.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [112,2,Mod(29,112)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(112, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 3, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("112.29");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 112 = 2^{4} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	112.m (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$0.894324502638$
Analytic rank:	$1$
Dimension:	$2$
Coefficient field:	$\Q(i)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} + 1 $ x^2 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			29.1
Root			$-1.00000i$ of defining polynomial
Character	$\chi$	$=$	112.29
Dual form			112.2.m.a.85.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.00000 - 1.00000i) q^{2} +(-2.00000 - 2.00000i) q^{3} +2.00000i q^{4} +(-2.00000 + 2.00000i) q^{5} +4.00000i q^{6} -1.00000i q^{7} +(2.00000 - 2.00000i) q^{8} +5.00000i q^{9} +O(q^{10})$	\(q+(-1.00000 - 1.00000i) q^{2} +(-2.00000 - 2.00000i) q^{3} +2.00000i q^{4} +(-2.00000 + 2.00000i) q^{5} +4.00000i q^{6} -1.00000i q^{7} +(2.00000 - 2.00000i) q^{8} +5.00000i q^{9} +4.00000 q^{10} +(-3.00000 + 3.00000i) q^{11} +(4.00000 - 4.00000i) q^{12} +(-1.00000 + 1.00000i) q^{14} +8.00000 q^{15} -4.00000 q^{16} -6.00000 q^{17} +(5.00000 - 5.00000i) q^{18} +(-4.00000 - 4.00000i) q^{19} +(-4.00000 - 4.00000i) q^{20} +(-2.00000 + 2.00000i) q^{21} +6.00000 q^{22} -2.00000i q^{23} -8.00000 q^{24} -3.00000i q^{25} +(4.00000 - 4.00000i) q^{27} +2.00000 q^{28} +(-1.00000 - 1.00000i) q^{29} +(-8.00000 - 8.00000i) q^{30} +4.00000 q^{31} +(4.00000 + 4.00000i) q^{32} +12.0000 q^{33} +(6.00000 + 6.00000i) q^{34} +(2.00000 + 2.00000i) q^{35} -10.0000 q^{36} +(3.00000 - 3.00000i) q^{37} +8.00000i q^{38} +8.00000i q^{40} -2.00000i q^{41} +4.00000 q^{42} +(-5.00000 + 5.00000i) q^{43} +(-6.00000 - 6.00000i) q^{44} +(-10.0000 - 10.0000i) q^{45} +(-2.00000 + 2.00000i) q^{46} -8.00000 q^{47} +(8.00000 + 8.00000i) q^{48} -1.00000 q^{49} +(-3.00000 + 3.00000i) q^{50} +(12.0000 + 12.0000i) q^{51} +(7.00000 - 7.00000i) q^{53} -8.00000 q^{54} -12.0000i q^{55} +(-2.00000 - 2.00000i) q^{56} +16.0000i q^{57} +2.00000i q^{58} +(2.00000 - 2.00000i) q^{59} +16.0000i q^{60} +(6.00000 + 6.00000i) q^{61} +(-4.00000 - 4.00000i) q^{62} +5.00000 q^{63} -8.00000i q^{64} +(-12.0000 - 12.0000i) q^{66} +(-5.00000 - 5.00000i) q^{67} -12.0000i q^{68} +(-4.00000 + 4.00000i) q^{69} -4.00000i q^{70} +8.00000i q^{71} +(10.0000 + 10.0000i) q^{72} +10.0000i q^{73} -6.00000 q^{74} +(-6.00000 + 6.00000i) q^{75} +(8.00000 - 8.00000i) q^{76} +(3.00000 + 3.00000i) q^{77} -14.0000 q^{79} +(8.00000 - 8.00000i) q^{80} -1.00000 q^{81} +(-2.00000 + 2.00000i) q^{82} +(-4.00000 - 4.00000i) q^{84} +(12.0000 - 12.0000i) q^{85} +10.0000 q^{86} +4.00000i q^{87} +12.0000i q^{88} -6.00000i q^{89} +20.0000i q^{90} +4.00000 q^{92} +(-8.00000 - 8.00000i) q^{93} +(8.00000 + 8.00000i) q^{94} +16.0000 q^{95} -16.0000i q^{96} -6.00000 q^{97} +(1.00000 + 1.00000i) q^{98} +(-15.0000 - 15.0000i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{2} - 4 q^{3} - 4 q^{5} + 4 q^{8}+O(q^{10}) $ 2 * q - 2 * q^2 - 4 * q^3 - 4 * q^5 + 4 * q^8	$ 2 q - 2 q^{2} - 4 q^{3} - 4 q^{5} + 4 q^{8} + 8 q^{10} - 6 q^{11} + 8 q^{12} - 2 q^{14} + 16 q^{15} - 8 q^{16} - 12 q^{17} + 10 q^{18} - 8 q^{19} - 8 q^{20} - 4 q^{21} + 12 q^{22} - 16 q^{24} + 8 q^{27} + 4 q^{28} - 2 q^{29} - 16 q^{30} + 8 q^{31} + 8 q^{32} + 24 q^{33} + 12 q^{34} + 4 q^{35} - 20 q^{36} + 6 q^{37} + 8 q^{42} - 10 q^{43} - 12 q^{44} - 20 q^{45} - 4 q^{46} - 16 q^{47} + 16 q^{48} - 2 q^{49} - 6 q^{50} + 24 q^{51} + 14 q^{53} - 16 q^{54} - 4 q^{56} + 4 q^{59} + 12 q^{61} - 8 q^{62} + 10 q^{63} - 24 q^{66} - 10 q^{67} - 8 q^{69} + 20 q^{72} - 12 q^{74} - 12 q^{75} + 16 q^{76} + 6 q^{77} - 28 q^{79} + 16 q^{80} - 2 q^{81} - 4 q^{82} - 8 q^{84} + 24 q^{85} + 20 q^{86} + 8 q^{92} - 16 q^{93} + 16 q^{94} + 32 q^{95} - 12 q^{97} + 2 q^{98} - 30 q^{99}+O(q^{100}) $ 2 * q - 2 * q^2 - 4 * q^3 - 4 * q^5 + 4 * q^8 + 8 * q^10 - 6 * q^11 + 8 * q^12 - 2 * q^14 + 16 * q^15 - 8 * q^16 - 12 * q^17 + 10 * q^18 - 8 * q^19 - 8 * q^20 - 4 * q^21 + 12 * q^22 - 16 * q^24 + 8 * q^27 + 4 * q^28 - 2 * q^29 - 16 * q^30 + 8 * q^31 + 8 * q^32 + 24 * q^33 + 12 * q^34 + 4 * q^35 - 20 * q^36 + 6 * q^37 + 8 * q^42 - 10 * q^43 - 12 * q^44 - 20 * q^45 - 4 * q^46 - 16 * q^47 + 16 * q^48 - 2 * q^49 - 6 * q^50 + 24 * q^51 + 14 * q^53 - 16 * q^54 - 4 * q^56 + 4 * q^59 + 12 * q^61 - 8 * q^62 + 10 * q^63 - 24 * q^66 - 10 * q^67 - 8 * q^69 + 20 * q^72 - 12 * q^74 - 12 * q^75 + 16 * q^76 + 6 * q^77 - 28 * q^79 + 16 * q^80 - 2 * q^81 - 4 * q^82 - 8 * q^84 + 24 * q^85 + 20 * q^86 + 8 * q^92 - 16 * q^93 + 16 * q^94 + 32 * q^95 - 12 * q^97 + 2 * q^98 - 30 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/112\mathbb{Z}\right)^\times$.

$n$	$15$	$17$	$85$
$\chi(n)$	$1$	$1$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$	−1.00000	−	1.00000i	−0.707107	−	0.707107i
$2$	−1.00000	−	1.00000i	−0.707107	−	0.707107i
$3$	−2.00000	−	2.00000i	−1.15470	−	1.15470i	−0.985599	−	0.169102i	$-0.945913\pi$
$3$	−2.00000	−	2.00000i	−1.15470	−	1.15470i	−0.169102	−	0.985599i	$-0.554087\pi$
$4$			2.00000i			1.00000i
$5$	−2.00000	+	2.00000i	−0.894427	+	0.894427i	−0.994936	−	0.100509i	$-0.967953\pi$
$5$	−2.00000	+	2.00000i	−0.894427	+	0.894427i	0.100509	+	0.994936i	$0.467953\pi$
$6$			4.00000i			1.63299i
$7$		−	1.00000i		−	0.377964i
$7$		−	1.00000i		−	0.377964i
$8$	2.00000	−	2.00000i	0.707107	−	0.707107i
$9$			5.00000i			1.66667i
$10$	4.00000			1.26491
$11$	−3.00000	+	3.00000i	−0.904534	+	0.904534i	−0.995824	−	0.0912903i	$-0.970901\pi$
$11$	−3.00000	+	3.00000i	−0.904534	+	0.904534i	0.0912903	+	0.995824i	$0.470901\pi$
$12$	4.00000	−	4.00000i	1.15470	−	1.15470i
$13$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$13$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$14$	−1.00000	+	1.00000i	−0.267261	+	0.267261i
$15$	8.00000			2.06559
$16$	−4.00000			−1.00000
$17$	−6.00000			−1.45521			−0.727607	−	0.685994i	$-0.759367\pi$
$17$	−6.00000			−1.45521			−0.727607	+	0.685994i	$0.759367\pi$
$18$	5.00000	−	5.00000i	1.17851	−	1.17851i
$19$	−4.00000	−	4.00000i	−0.917663	−	0.917663i	0.0791961	−	0.996859i	$-0.474765\pi$
$19$	−4.00000	−	4.00000i	−0.917663	−	0.917663i	−0.996859	+	0.0791961i	$0.974765\pi$
$20$	−4.00000	−	4.00000i	−0.894427	−	0.894427i
$21$	−2.00000	+	2.00000i	−0.436436	+	0.436436i
$22$	6.00000			1.27920
$23$		−	2.00000i		−	0.417029i	−0.978019	−	0.208514i	$-0.933137\pi$
$23$		−	2.00000i		−	0.417029i	0.978019	−	0.208514i	$-0.0668628\pi$
$24$	−8.00000			−1.63299
$25$		−	3.00000i		−	0.600000i
$26$		0			0
$27$	4.00000	−	4.00000i	0.769800	−	0.769800i
$28$	2.00000			0.377964
$29$	−1.00000	−	1.00000i	−0.185695	−	0.185695i	0.608137	−	0.793832i	$-0.291917\pi$
$29$	−1.00000	−	1.00000i	−0.185695	−	0.185695i	−0.793832	+	0.608137i	$0.791917\pi$
$30$	−8.00000	−	8.00000i	−1.46059	−	1.46059i
$31$	4.00000			0.718421			0.359211	−	0.933257i	$-0.383046\pi$
$31$	4.00000			0.718421			0.359211	+	0.933257i	$0.383046\pi$
$32$	4.00000	+	4.00000i	0.707107	+	0.707107i
$33$	12.0000			2.08893
$34$	6.00000	+	6.00000i	1.02899	+	1.02899i
$35$	2.00000	+	2.00000i	0.338062	+	0.338062i
$36$	−10.0000			−1.66667
$37$	3.00000	−	3.00000i	0.493197	−	0.493197i	−0.416115	−	0.909312i	$-0.636609\pi$
$37$	3.00000	−	3.00000i	0.493197	−	0.493197i	0.909312	+	0.416115i	$0.136609\pi$
$38$			8.00000i			1.29777i
$39$		0			0
$40$			8.00000i			1.26491i
$41$		−	2.00000i		−	0.312348i	−0.987730	−	0.156174i	$-0.950084\pi$
$41$		−	2.00000i		−	0.312348i	0.987730	−	0.156174i	$-0.0499160\pi$
$42$	4.00000			0.617213
$43$	−5.00000	+	5.00000i	−0.762493	+	0.762493i	−0.976772	−	0.214280i	$-0.931260\pi$
$43$	−5.00000	+	5.00000i	−0.762493	+	0.762493i	0.214280	+	0.976772i	$0.431260\pi$
$44$	−6.00000	−	6.00000i	−0.904534	−	0.904534i
$45$	−10.0000	−	10.0000i	−1.49071	−	1.49071i
$46$	−2.00000	+	2.00000i	−0.294884	+	0.294884i
$47$	−8.00000			−1.16692			−0.583460	−	0.812142i	$-0.698301\pi$
$47$	−8.00000			−1.16692			−0.583460	+	0.812142i	$0.698301\pi$
$48$	8.00000	+	8.00000i	1.15470	+	1.15470i
$49$	−1.00000			−0.142857
$50$	−3.00000	+	3.00000i	−0.424264	+	0.424264i
$51$	12.0000	+	12.0000i	1.68034	+	1.68034i
$52$		0			0
$53$	7.00000	−	7.00000i	0.961524	−	0.961524i	−0.0377628	−	0.999287i	$-0.512023\pi$
$53$	7.00000	−	7.00000i	0.961524	−	0.961524i	0.999287	+	0.0377628i	$0.0120231\pi$
$54$	−8.00000			−1.08866
$55$		−	12.0000i		−	1.61808i
$56$	−2.00000	−	2.00000i	−0.267261	−	0.267261i
$57$			16.0000i			2.11925i
$58$			2.00000i			0.262613i
$59$	2.00000	−	2.00000i	0.260378	−	0.260378i	−0.564830	−	0.825208i	$-0.691058\pi$
$59$	2.00000	−	2.00000i	0.260378	−	0.260378i	0.825208	+	0.564830i	$0.191058\pi$
$60$			16.0000i			2.06559i
$61$	6.00000	+	6.00000i	0.768221	+	0.768221i	0.977793	−	0.209572i	$-0.0672070\pi$
$61$	6.00000	+	6.00000i	0.768221	+	0.768221i	−0.209572	+	0.977793i	$0.567207\pi$
$62$	−4.00000	−	4.00000i	−0.508001	−	0.508001i
$63$	5.00000			0.629941
$64$		−	8.00000i		−	1.00000i
$65$		0			0
$66$	−12.0000	−	12.0000i	−1.47710	−	1.47710i
$67$	−5.00000	−	5.00000i	−0.610847	−	0.610847i	0.332320	−	0.943167i	$-0.392169\pi$
$67$	−5.00000	−	5.00000i	−0.610847	−	0.610847i	−0.943167	+	0.332320i	$0.892169\pi$
$68$		−	12.0000i		−	1.45521i
$69$	−4.00000	+	4.00000i	−0.481543	+	0.481543i
$70$		−	4.00000i		−	0.478091i
$71$			8.00000i			0.949425i	0.880141	+	0.474713i	$0.157448\pi$
$71$			8.00000i			0.949425i	−0.880141	+	0.474713i	$0.842552\pi$
$72$	10.0000	+	10.0000i	1.17851	+	1.17851i
$73$			10.0000i			1.17041i	0.810885	+	0.585206i	$0.198986\pi$
$73$			10.0000i			1.17041i	−0.810885	+	0.585206i	$0.801014\pi$
$74$	−6.00000			−0.697486
$75$	−6.00000	+	6.00000i	−0.692820	+	0.692820i
$76$	8.00000	−	8.00000i	0.917663	−	0.917663i
$77$	3.00000	+	3.00000i	0.341882	+	0.341882i
$78$		0			0
$79$	−14.0000			−1.57512			−0.787562	−	0.616236i	$-0.788657\pi$
$79$	−14.0000			−1.57512			−0.787562	+	0.616236i	$0.788657\pi$
$80$	8.00000	−	8.00000i	0.894427	−	0.894427i
$81$	−1.00000			−0.111111
$82$	−2.00000	+	2.00000i	−0.220863	+	0.220863i
$83$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$83$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$84$	−4.00000	−	4.00000i	−0.436436	−	0.436436i
$85$	12.0000	−	12.0000i	1.30158	−	1.30158i
$86$	10.0000			1.07833
$87$			4.00000i			0.428845i
$88$			12.0000i			1.27920i
$89$		−	6.00000i		−	0.635999i	−0.948091	−	0.317999i	$-0.896989\pi$
$89$		−	6.00000i		−	0.635999i	0.948091	−	0.317999i	$-0.103011\pi$
$90$			20.0000i			2.10819i
$91$		0			0
$92$	4.00000			0.417029
$93$	−8.00000	−	8.00000i	−0.829561	−	0.829561i
$94$	8.00000	+	8.00000i	0.825137	+	0.825137i
$95$	16.0000			1.64157
$96$		−	16.0000i		−	1.63299i
$97$	−6.00000			−0.609208			−0.304604	−	0.952479i	$-0.598524\pi$
$97$	−6.00000			−0.609208			−0.304604	+	0.952479i	$0.598524\pi$
$98$	1.00000	+	1.00000i	0.101015	+	0.101015i
$99$	−15.0000	−	15.0000i	−1.50756	−	1.50756i
$100$	6.00000			0.600000
$101$	2.00000	−	2.00000i	0.199007	−	0.199007i	−0.600567	−	0.799574i	$-0.705058\pi$
$101$	2.00000	−	2.00000i	0.199007	−	0.199007i	0.799574	+	0.600567i	$0.205058\pi$
$102$		−	24.0000i		−	2.37635i
$103$		0			0		1.00000			$0$
$103$		0			0		−1.00000			$\pi$
$104$		0			0
$105$		−	8.00000i		−	0.780720i
$106$	−14.0000			−1.35980
$107$	5.00000	−	5.00000i	0.483368	−	0.483368i	−0.422837	−	0.906206i	$-0.638966\pi$
$107$	5.00000	−	5.00000i	0.483368	−	0.483368i	0.906206	+	0.422837i	$0.138966\pi$
$108$	8.00000	+	8.00000i	0.769800	+	0.769800i
$109$	−3.00000	−	3.00000i	−0.287348	−	0.287348i	0.548683	−	0.836031i	$-0.315129\pi$
$109$	−3.00000	−	3.00000i	−0.287348	−	0.287348i	−0.836031	+	0.548683i	$0.815129\pi$
$110$	−12.0000	+	12.0000i	−1.14416	+	1.14416i
$111$	−12.0000			−1.13899
$112$			4.00000i			0.377964i
$113$	−12.0000			−1.12887			−0.564433	−	0.825479i	$-0.690905\pi$
$113$	−12.0000			−1.12887			−0.564433	+	0.825479i	$0.690905\pi$
$114$	16.0000	−	16.0000i	1.49854	−	1.49854i
$115$	4.00000	+	4.00000i	0.373002	+	0.373002i
$116$	2.00000	−	2.00000i	0.185695	−	0.185695i
$117$		0			0
$118$	−4.00000			−0.368230
$119$			6.00000i			0.550019i
$120$	16.0000	−	16.0000i	1.46059	−	1.46059i
$121$		−	7.00000i		−	0.636364i
$122$		−	12.0000i		−	1.08643i
$123$	−4.00000	+	4.00000i	−0.360668	+	0.360668i
$124$			8.00000i			0.718421i
$125$	−4.00000	−	4.00000i	−0.357771	−	0.357771i
$126$	−5.00000	−	5.00000i	−0.445435	−	0.445435i
$127$	8.00000			0.709885			0.354943	−	0.934888i	$-0.384500\pi$
$127$	8.00000			0.709885			0.354943	+	0.934888i	$0.384500\pi$
$128$	−8.00000	+	8.00000i	−0.707107	+	0.707107i
$129$	20.0000			1.76090
$130$		0			0
$131$	12.0000	+	12.0000i	1.04844	+	1.04844i	0.998765	+	0.0496797i	$0.0158200\pi$
$131$	12.0000	+	12.0000i	1.04844	+	1.04844i	0.0496797	+	0.998765i	$0.484180\pi$
$132$			24.0000i			2.08893i
$133$	−4.00000	+	4.00000i	−0.346844	+	0.346844i
$134$			10.0000i			0.863868i
$135$			16.0000i			1.37706i
$136$	−12.0000	+	12.0000i	−1.02899	+	1.02899i
$137$		−	12.0000i		−	1.02523i	−0.858619	−	0.512615i	$-0.828677\pi$
$137$		−	12.0000i		−	1.02523i	0.858619	−	0.512615i	$-0.171323\pi$
$138$	8.00000			0.681005
$139$	−12.0000	+	12.0000i	−1.01783	+	1.01783i	−0.0179885	+	0.999838i	$0.505726\pi$
$139$	−12.0000	+	12.0000i	−1.01783	+	1.01783i	−0.999838	+	0.0179885i	$0.994274\pi$
$140$	−4.00000	+	4.00000i	−0.338062	+	0.338062i
$141$	16.0000	+	16.0000i	1.34744	+	1.34744i
$142$	8.00000	−	8.00000i	0.671345	−	0.671345i
$143$		0			0
$144$		−	20.0000i		−	1.66667i
$145$	4.00000			0.332182
$146$	10.0000	−	10.0000i	0.827606	−	0.827606i
$147$	2.00000	+	2.00000i	0.164957	+	0.164957i
$148$	6.00000	+	6.00000i	0.493197	+	0.493197i
$149$	−13.0000	+	13.0000i	−1.06500	+	1.06500i	−0.0672664	+	0.997735i	$0.521428\pi$
$149$	−13.0000	+	13.0000i	−1.06500	+	1.06500i	−0.997735	+	0.0672664i	$0.978572\pi$
$150$	12.0000			0.979796
$151$			6.00000i			0.488273i	0.969741	+	0.244137i	$0.0785045\pi$
$151$			6.00000i			0.488273i	−0.969741	+	0.244137i	$0.921495\pi$
$152$	−16.0000			−1.29777
$153$		−	30.0000i		−	2.42536i
$154$		−	6.00000i		−	0.483494i
$155$	−8.00000	+	8.00000i	−0.642575	+	0.642575i
$156$		0			0
$157$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$157$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$158$	14.0000	+	14.0000i	1.11378	+	1.11378i
$159$	−28.0000			−2.22054
$160$	−16.0000			−1.26491
$161$	−2.00000			−0.157622
$162$	1.00000	+	1.00000i	0.0785674	+	0.0785674i
$163$	−5.00000	−	5.00000i	−0.391630	−	0.391630i	0.483638	−	0.875268i	$-0.339315\pi$
$163$	−5.00000	−	5.00000i	−0.391630	−	0.391630i	−0.875268	+	0.483638i	$0.839315\pi$
$164$	4.00000			0.312348
$165$	−24.0000	+	24.0000i	−1.86840	+	1.86840i
$166$		0			0
$167$		0			0		1.00000			$0$
$167$		0			0		−1.00000			$\pi$
$168$			8.00000i			0.617213i
$169$		−	13.0000i		−	1.00000i
$170$	−24.0000			−1.84072
$171$	20.0000	−	20.0000i	1.52944	−	1.52944i
$172$	−10.0000	−	10.0000i	−0.762493	−	0.762493i
$173$	16.0000	+	16.0000i	1.21646	+	1.21646i	0.968864	+	0.247593i	$0.0796397\pi$
$173$	16.0000	+	16.0000i	1.21646	+	1.21646i	0.247593	+	0.968864i	$0.420360\pi$
$174$	4.00000	−	4.00000i	0.303239	−	0.303239i
$175$	−3.00000			−0.226779
$176$	12.0000	−	12.0000i	0.904534	−	0.904534i
$177$	−8.00000			−0.601317
$178$	−6.00000	+	6.00000i	−0.449719	+	0.449719i
$179$	5.00000	+	5.00000i	0.373718	+	0.373718i	0.868829	−	0.495112i	$-0.164873\pi$
$179$	5.00000	+	5.00000i	0.373718	+	0.373718i	−0.495112	+	0.868829i	$0.664873\pi$
$180$	20.0000	−	20.0000i	1.49071	−	1.49071i
$181$	4.00000	−	4.00000i	0.297318	−	0.297318i	−0.542645	−	0.839962i	$-0.682577\pi$
$181$	4.00000	−	4.00000i	0.297318	−	0.297318i	0.839962	+	0.542645i	$0.182577\pi$
$182$		0			0
$183$		−	24.0000i		−	1.77413i
$184$	−4.00000	−	4.00000i	−0.294884	−	0.294884i
$185$			12.0000i			0.882258i
$186$			16.0000i			1.17318i
$187$	18.0000	−	18.0000i	1.31629	−	1.31629i
$188$		−	16.0000i		−	1.16692i
$189$	−4.00000	−	4.00000i	−0.290957	−	0.290957i
$190$	−16.0000	−	16.0000i	−1.16076	−	1.16076i
$191$	22.0000			1.59186			0.795932	−	0.605386i	$-0.206981\pi$
$191$	22.0000			1.59186			0.795932	+	0.605386i	$0.206981\pi$
$192$	−16.0000	+	16.0000i	−1.15470	+	1.15470i
$193$	−24.0000			−1.72756			−0.863779	−	0.503871i	$-0.831909\pi$
$193$	−24.0000			−1.72756			−0.863779	+	0.503871i	$0.831909\pi$
$194$	6.00000	+	6.00000i	0.430775	+	0.430775i
$195$		0			0
$196$		−	2.00000i		−	0.142857i
$197$	−11.0000	+	11.0000i	−0.783718	+	0.783718i	−0.980456	−	0.196738i	$-0.936965\pi$
$197$	−11.0000	+	11.0000i	−0.783718	+	0.783718i	0.196738	+	0.980456i	$0.436965\pi$
$198$			30.0000i			2.13201i
$199$			20.0000i			1.41776i	0.705328	+	0.708881i	$0.250800\pi$
$199$			20.0000i			1.41776i	−0.705328	+	0.708881i	$0.749200\pi$
$200$	−6.00000	−	6.00000i	−0.424264	−	0.424264i
$201$			20.0000i			1.41069i
$202$	−4.00000			−0.281439
$203$	−1.00000	+	1.00000i	−0.0701862	+	0.0701862i
$204$	−24.0000	+	24.0000i	−1.68034	+	1.68034i
$205$	4.00000	+	4.00000i	0.279372	+	0.279372i
$206$		0			0
$207$	10.0000			0.695048
$208$		0			0
$209$	24.0000			1.66011
$210$	−8.00000	+	8.00000i	−0.552052	+	0.552052i
$211$	−9.00000	−	9.00000i	−0.619586	−	0.619586i	0.325840	−	0.945425i	$-0.394353\pi$
$211$	−9.00000	−	9.00000i	−0.619586	−	0.619586i	−0.945425	+	0.325840i	$0.894353\pi$
$212$	14.0000	+	14.0000i	0.961524	+	0.961524i
$213$	16.0000	−	16.0000i	1.09630	−	1.09630i
$214$	−10.0000			−0.683586
$215$		−	20.0000i		−	1.36399i
$216$		−	16.0000i		−	1.08866i
$217$		−	4.00000i		−	0.271538i
$218$			6.00000i			0.406371i
$219$	20.0000	−	20.0000i	1.35147	−	1.35147i
$220$	24.0000			1.61808
$221$		0			0
$222$	12.0000	+	12.0000i	0.805387	+	0.805387i
$223$	4.00000			0.267860			0.133930	−	0.990991i	$-0.457240\pi$
$223$	4.00000			0.267860			0.133930	+	0.990991i	$0.457240\pi$
$224$	4.00000	−	4.00000i	0.267261	−	0.267261i
$225$	15.0000			1.00000
$226$	12.0000	+	12.0000i	0.798228	+	0.798228i
$227$	4.00000	+	4.00000i	0.265489	+	0.265489i	0.827280	−	0.561790i	$-0.189887\pi$
$227$	4.00000	+	4.00000i	0.265489	+	0.265489i	−0.561790	+	0.827280i	$0.689887\pi$
$228$	−32.0000			−2.11925
$229$	12.0000	−	12.0000i	0.792982	−	0.792982i	−0.188996	−	0.981978i	$-0.560523\pi$
$229$	12.0000	−	12.0000i	0.792982	−	0.792982i	0.981978	+	0.188996i	$0.0605232\pi$
$230$		−	8.00000i		−	0.527504i
$231$		−	12.0000i		−	0.789542i
$232$	−4.00000			−0.262613
$233$			8.00000i			0.524097i	0.965055	+	0.262049i	$0.0843981\pi$
$233$			8.00000i			0.524097i	−0.965055	+	0.262049i	$0.915602\pi$
$234$		0			0
$235$	16.0000	−	16.0000i	1.04372	−	1.04372i
$236$	4.00000	+	4.00000i	0.260378	+	0.260378i
$237$	28.0000	+	28.0000i	1.81880	+	1.81880i
$238$	6.00000	−	6.00000i	0.388922	−	0.388922i
$239$	−8.00000			−0.517477			−0.258738	−	0.965947i	$-0.583307\pi$
$239$	−8.00000			−0.517477			−0.258738	+	0.965947i	$0.583307\pi$
$240$	−32.0000			−2.06559
$241$	−22.0000			−1.41714			−0.708572	−	0.705638i	$-0.750660\pi$
$241$	−22.0000			−1.41714			−0.708572	+	0.705638i	$0.750660\pi$
$242$	−7.00000	+	7.00000i	−0.449977	+	0.449977i
$243$	−10.0000	−	10.0000i	−0.641500	−	0.641500i
$244$	−12.0000	+	12.0000i	−0.768221	+	0.768221i
$245$	2.00000	−	2.00000i	0.127775	−	0.127775i
$246$	8.00000			0.510061
$247$		0			0
$248$	8.00000	−	8.00000i	0.508001	−	0.508001i
$249$		0			0
$250$			8.00000i			0.505964i
$251$	4.00000	−	4.00000i	0.252478	−	0.252478i	−0.569508	−	0.821986i	$-0.692866\pi$
$251$	4.00000	−	4.00000i	0.252478	−	0.252478i	0.821986	+	0.569508i	$0.192866\pi$
$252$			10.0000i			0.629941i
$253$	6.00000	+	6.00000i	0.377217	+	0.377217i
$254$	−8.00000	−	8.00000i	−0.501965	−	0.501965i
$255$	−48.0000			−3.00588
$256$	16.0000			1.00000
$257$	−10.0000			−0.623783			−0.311891	−	0.950118i	$-0.600963\pi$
$257$	−10.0000			−0.623783			−0.311891	+	0.950118i	$0.600963\pi$
$258$	−20.0000	−	20.0000i	−1.24515	−	1.24515i
$259$	−3.00000	−	3.00000i	−0.186411	−	0.186411i
$260$		0			0
$261$	5.00000	−	5.00000i	0.309492	−	0.309492i
$262$		−	24.0000i		−	1.48272i
$263$		−	24.0000i		−	1.47990i	−0.672660	−	0.739952i	$-0.734848\pi$
$263$		−	24.0000i		−	1.47990i	0.672660	−	0.739952i	$-0.265152\pi$
$264$	24.0000	−	24.0000i	1.47710	−	1.47710i
$265$			28.0000i			1.72003i
$266$	8.00000			0.490511
$267$	−12.0000	+	12.0000i	−0.734388	+	0.734388i
$268$	10.0000	−	10.0000i	0.610847	−	0.610847i
$269$	−16.0000	−	16.0000i	−0.975537	−	0.975537i	0.0241706	−	0.999708i	$-0.492306\pi$
$269$	−16.0000	−	16.0000i	−0.975537	−	0.975537i	−0.999708	+	0.0241706i	$0.992306\pi$
$270$	16.0000	−	16.0000i	0.973729	−	0.973729i
$271$	16.0000			0.971931			0.485965	−	0.873978i	$-0.338468\pi$
$271$	16.0000			0.971931			0.485965	+	0.873978i	$0.338468\pi$
$272$	24.0000			1.45521
$273$		0			0
$274$	−12.0000	+	12.0000i	−0.724947	+	0.724947i
$275$	9.00000	+	9.00000i	0.542720	+	0.542720i
$276$	−8.00000	−	8.00000i	−0.481543	−	0.481543i
$277$	1.00000	−	1.00000i	0.0600842	−	0.0600842i	−0.676426	−	0.736510i	$-0.736472\pi$
$277$	1.00000	−	1.00000i	0.0600842	−	0.0600842i	0.736510	+	0.676426i	$0.236472\pi$
$278$	24.0000			1.43942
$279$			20.0000i			1.19737i
$280$	8.00000			0.478091
$281$		−	24.0000i		−	1.43172i	−0.698244	−	0.715860i	$-0.746035\pi$
$281$		−	24.0000i		−	1.43172i	0.698244	−	0.715860i	$-0.253965\pi$
$282$		−	32.0000i		−	1.90557i
$283$	−6.00000	+	6.00000i	−0.356663	+	0.356663i	−0.862581	−	0.505918i	$-0.831154\pi$
$283$	−6.00000	+	6.00000i	−0.356663	+	0.356663i	0.505918	+	0.862581i	$0.331154\pi$
$284$	−16.0000			−0.949425
$285$	−32.0000	−	32.0000i	−1.89552	−	1.89552i
$286$		0			0
$287$	−2.00000			−0.118056
$288$	−20.0000	+	20.0000i	−1.17851	+	1.17851i
$289$	19.0000			1.11765
$290$	−4.00000	−	4.00000i	−0.234888	−	0.234888i
$291$	12.0000	+	12.0000i	0.703452	+	0.703452i
$292$	−20.0000			−1.17041
$293$	−10.0000	+	10.0000i	−0.584206	+	0.584206i	−0.936056	−	0.351850i	$-0.885553\pi$
$293$	−10.0000	+	10.0000i	−0.584206	+	0.584206i	0.351850	+	0.936056i	$0.385553\pi$
$294$		−	4.00000i		−	0.233285i
$295$			8.00000i			0.465778i
$296$		−	12.0000i		−	0.697486i
$297$			24.0000i			1.39262i
$298$	26.0000			1.50614
$299$		0			0
$300$	−12.0000	−	12.0000i	−0.692820	−	0.692820i
$301$	5.00000	+	5.00000i	0.288195	+	0.288195i
$302$	6.00000	−	6.00000i	0.345261	−	0.345261i
$303$	−8.00000			−0.459588
$304$	16.0000	+	16.0000i	0.917663	+	0.917663i
$305$	−24.0000			−1.37424
$306$	−30.0000	+	30.0000i	−1.71499	+	1.71499i
$307$	−8.00000	−	8.00000i	−0.456584	−	0.456584i	0.440948	−	0.897532i	$-0.354642\pi$
$307$	−8.00000	−	8.00000i	−0.456584	−	0.456584i	−0.897532	+	0.440948i	$0.854642\pi$
$308$	−6.00000	+	6.00000i	−0.341882	+	0.341882i
$309$		0			0
$310$	16.0000			0.908739
$311$			4.00000i			0.226819i	0.993548	+	0.113410i	$0.0361772\pi$
$311$			4.00000i			0.226819i	−0.993548	+	0.113410i	$0.963823\pi$
$312$		0			0
$313$			2.00000i			0.113047i	0.998401	+	0.0565233i	$0.0180015\pi$
$313$			2.00000i			0.113047i	−0.998401	+	0.0565233i	$0.981998\pi$
$314$		0			0
$315$	−10.0000	+	10.0000i	−0.563436	+	0.563436i
$316$		−	28.0000i		−	1.57512i
$317$	−15.0000	−	15.0000i	−0.842484	−	0.842484i	0.146697	−	0.989181i	$-0.453136\pi$
$317$	−15.0000	−	15.0000i	−0.842484	−	0.842484i	−0.989181	+	0.146697i	$0.953136\pi$
$318$	28.0000	+	28.0000i	1.57016	+	1.57016i
$319$	6.00000			0.335936
$320$	16.0000	+	16.0000i	0.894427	+	0.894427i
$321$	−20.0000			−1.11629
$322$	2.00000	+	2.00000i	0.111456	+	0.111456i
$323$	24.0000	+	24.0000i	1.33540	+	1.33540i
$324$		−	2.00000i		−	0.111111i
$325$		0			0
$326$			10.0000i			0.553849i
$327$			12.0000i			0.663602i
$328$	−4.00000	−	4.00000i	−0.220863	−	0.220863i
$329$			8.00000i			0.441054i
$330$	48.0000			2.64231
$331$	−15.0000	+	15.0000i	−0.824475	+	0.824475i	−0.986746	−	0.162272i	$-0.948118\pi$
$331$	−15.0000	+	15.0000i	−0.824475	+	0.824475i	0.162272	+	0.986746i	$0.448118\pi$
$332$		0			0
$333$	15.0000	+	15.0000i	0.821995	+	0.821995i
$334$		0			0
$335$	20.0000			1.09272
$336$	8.00000	−	8.00000i	0.436436	−	0.436436i
$337$	−8.00000			−0.435788			−0.217894	−	0.975972i	$-0.569919\pi$
$337$	−8.00000			−0.435788			−0.217894	+	0.975972i	$0.569919\pi$
$338$	−13.0000	+	13.0000i	−0.707107	+	0.707107i
$339$	24.0000	+	24.0000i	1.30350	+	1.30350i
$340$	24.0000	+	24.0000i	1.30158	+	1.30158i
$341$	−12.0000	+	12.0000i	−0.649836	+	0.649836i
$342$	−40.0000			−2.16295
$343$			1.00000i			0.0539949i
$344$			20.0000i			1.07833i
$345$		−	16.0000i		−	0.861411i
$346$		−	32.0000i		−	1.72033i
$347$	−13.0000	+	13.0000i	−0.697877	+	0.697877i	−0.963952	−	0.266076i	$-0.914273\pi$
$347$	−13.0000	+	13.0000i	−0.697877	+	0.697877i	0.266076	+	0.963952i	$0.414273\pi$
$348$	−8.00000			−0.428845
$349$	16.0000	+	16.0000i	0.856460	+	0.856460i	0.990919	−	0.134459i	$-0.0429296\pi$
$349$	16.0000	+	16.0000i	0.856460	+	0.856460i	−0.134459	+	0.990919i	$0.542930\pi$
$350$	3.00000	+	3.00000i	0.160357	+	0.160357i
$351$		0			0
$352$	−24.0000			−1.27920
$353$	18.0000			0.958043			0.479022	−	0.877803i	$-0.340992\pi$
$353$	18.0000			0.958043			0.479022	+	0.877803i	$0.340992\pi$
$354$	8.00000	+	8.00000i	0.425195	+	0.425195i
$355$	−16.0000	−	16.0000i	−0.849192	−	0.849192i
$356$	12.0000			0.635999
$357$	12.0000	−	12.0000i	0.635107	−	0.635107i
$358$		−	10.0000i		−	0.528516i
$359$		−	22.0000i		−	1.16112i	−0.814219	−	0.580558i	$-0.802835\pi$
$359$		−	22.0000i		−	1.16112i	0.814219	−	0.580558i	$-0.197165\pi$
$360$	−40.0000			−2.10819
$361$			13.0000i			0.684211i
$362$	−8.00000			−0.420471
$363$	−14.0000	+	14.0000i	−0.734809	+	0.734809i
$364$		0			0
$365$	−20.0000	−	20.0000i	−1.04685	−	1.04685i
$366$	−24.0000	+	24.0000i	−1.25450	+	1.25450i
$367$	−16.0000			−0.835193			−0.417597	−	0.908633i	$-0.637127\pi$
$367$	−16.0000			−0.835193			−0.417597	+	0.908633i	$0.637127\pi$
$368$			8.00000i			0.417029i
$369$	10.0000			0.520579
$370$	12.0000	−	12.0000i	0.623850	−	0.623850i
$371$	−7.00000	−	7.00000i	−0.363422	−	0.363422i
$372$	16.0000	−	16.0000i	0.829561	−	0.829561i
$373$	5.00000	−	5.00000i	0.258890	−	0.258890i	−0.565712	−	0.824603i	$-0.691399\pi$
$373$	5.00000	−	5.00000i	0.258890	−	0.258890i	0.824603	+	0.565712i	$0.191399\pi$
$374$	−36.0000			−1.86152
$375$			16.0000i			0.826236i
$376$	−16.0000	+	16.0000i	−0.825137	+	0.825137i
$377$		0			0
$378$			8.00000i			0.411476i
$379$	17.0000	−	17.0000i	0.873231	−	0.873231i	−0.119592	−	0.992823i	$-0.538159\pi$
$379$	17.0000	−	17.0000i	0.873231	−	0.873231i	0.992823	+	0.119592i	$0.0381586\pi$
$380$			32.0000i			1.64157i
$381$	−16.0000	−	16.0000i	−0.819705	−	0.819705i
$382$	−22.0000	−	22.0000i	−1.12562	−	1.12562i
$383$	−16.0000			−0.817562			−0.408781	−	0.912633i	$-0.634046\pi$
$383$	−16.0000			−0.817562			−0.408781	+	0.912633i	$0.634046\pi$
$384$	32.0000			1.63299
$385$	−12.0000			−0.611577
$386$	24.0000	+	24.0000i	1.22157	+	1.22157i
$387$	−25.0000	−	25.0000i	−1.27082	−	1.27082i
$388$		−	12.0000i		−	0.609208i
$389$	19.0000	−	19.0000i	0.963338	−	0.963338i	−0.0360131	−	0.999351i	$-0.511466\pi$
$389$	19.0000	−	19.0000i	0.963338	−	0.963338i	0.999351	+	0.0360131i	$0.0114658\pi$
$390$		0			0
$391$			12.0000i			0.606866i
$392$	−2.00000	+	2.00000i	−0.101015	+	0.101015i
$393$		−	48.0000i		−	2.42128i
$394$	22.0000			1.10834
$395$	28.0000	−	28.0000i	1.40883	−	1.40883i
$396$	30.0000	−	30.0000i	1.50756	−	1.50756i
$397$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$397$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$398$	20.0000	−	20.0000i	1.00251	−	1.00251i
$399$	16.0000			0.801002
$400$			12.0000i			0.600000i
$401$	−4.00000			−0.199750			−0.0998752	−	0.995000i	$-0.531844\pi$
$401$	−4.00000			−0.199750			−0.0998752	+	0.995000i	$0.531844\pi$
$402$	20.0000	−	20.0000i	0.997509	−	0.997509i
$403$		0			0
$404$	4.00000	+	4.00000i	0.199007	+	0.199007i
$405$	2.00000	−	2.00000i	0.0993808	−	0.0993808i
$406$	2.00000			0.0992583
$407$			18.0000i			0.892227i
$408$	48.0000			2.37635
$409$		−	10.0000i		−	0.494468i	−0.968956	−	0.247234i	$-0.920478\pi$
$409$		−	10.0000i		−	0.494468i	0.968956	−	0.247234i	$-0.0795217\pi$
$410$		−	8.00000i		−	0.395092i
$411$	−24.0000	+	24.0000i	−1.18383	+	1.18383i
$412$		0			0
$413$	−2.00000	−	2.00000i	−0.0984136	−	0.0984136i
$414$	−10.0000	−	10.0000i	−0.491473	−	0.491473i
$415$		0			0
$416$		0			0
$417$	48.0000			2.35057
$418$	−24.0000	−	24.0000i	−1.17388	−	1.17388i
$419$	−10.0000	−	10.0000i	−0.488532	−	0.488532i	0.419311	−	0.907843i	$-0.362272\pi$
$419$	−10.0000	−	10.0000i	−0.488532	−	0.488532i	−0.907843	+	0.419311i	$0.862272\pi$
$420$	16.0000			0.780720
$421$	−25.0000	+	25.0000i	−1.21843	+	1.21843i	−0.250242	+	0.968183i	$0.580510\pi$
$421$	−25.0000	+	25.0000i	−1.21843	+	1.21843i	−0.968183	+	0.250242i	$0.919490\pi$
$422$			18.0000i			0.876226i
$423$		−	40.0000i		−	1.94487i
$424$		−	28.0000i		−	1.35980i
$425$			18.0000i			0.873128i
$426$	−32.0000			−1.55041
$427$	6.00000	−	6.00000i	0.290360	−	0.290360i
$428$	10.0000	+	10.0000i	0.483368	+	0.483368i
$429$		0			0
$430$	−20.0000	+	20.0000i	−0.964486	+	0.964486i
$431$		0			0			−	1.00000i	$-0.5\pi$
$431$		0			0				1.00000i	$0.5\pi$
$432$	−16.0000	+	16.0000i	−0.769800	+	0.769800i
$433$	−2.00000			−0.0961139			−0.0480569	−	0.998845i	$-0.515303\pi$
$433$	−2.00000			−0.0961139			−0.0480569	+	0.998845i	$0.515303\pi$
$434$	−4.00000	+	4.00000i	−0.192006	+	0.192006i
$435$	−8.00000	−	8.00000i	−0.383571	−	0.383571i
$436$	6.00000	−	6.00000i	0.287348	−	0.287348i
$437$	−8.00000	+	8.00000i	−0.382692	+	0.382692i
$438$	−40.0000			−1.91127
$439$			24.0000i			1.14546i	0.819745	+	0.572729i	$0.194115\pi$
$439$			24.0000i			1.14546i	−0.819745	+	0.572729i	$0.805885\pi$
$440$	−24.0000	−	24.0000i	−1.14416	−	1.14416i
$441$		−	5.00000i		−	0.238095i
$442$		0			0
$443$	−17.0000	+	17.0000i	−0.807694	+	0.807694i	−0.984284	−	0.176590i	$-0.943493\pi$
$443$	−17.0000	+	17.0000i	−0.807694	+	0.807694i	0.176590	+	0.984284i	$0.443493\pi$
$444$		−	24.0000i		−	1.13899i
$445$	12.0000	+	12.0000i	0.568855	+	0.568855i
$446$	−4.00000	−	4.00000i	−0.189405	−	0.189405i
$447$	52.0000			2.45952
$448$	−8.00000			−0.377964
$449$	34.0000			1.60456			0.802280	−	0.596948i	$-0.203620\pi$
$449$	34.0000			1.60456			0.802280	+	0.596948i	$0.203620\pi$
$450$	−15.0000	−	15.0000i	−0.707107	−	0.707107i
$451$	6.00000	+	6.00000i	0.282529	+	0.282529i
$452$		−	24.0000i		−	1.12887i
$453$	12.0000	−	12.0000i	0.563809	−	0.563809i
$454$		−	8.00000i		−	0.375459i
$455$		0			0
$456$	32.0000	+	32.0000i	1.49854	+	1.49854i
$457$			26.0000i			1.21623i	0.793849	+	0.608114i	$0.208074\pi$
$457$			26.0000i			1.21623i	−0.793849	+	0.608114i	$0.791926\pi$
$458$	−24.0000			−1.12145
$459$	−24.0000	+	24.0000i	−1.12022	+	1.12022i
$460$	−8.00000	+	8.00000i	−0.373002	+	0.373002i
$461$	−28.0000	−	28.0000i	−1.30409	−	1.30409i	−0.925609	−	0.378481i	$-0.876447\pi$
$461$	−28.0000	−	28.0000i	−1.30409	−	1.30409i	−0.378481	−	0.925609i	$-0.623553\pi$
$462$	−12.0000	+	12.0000i	−0.558291	+	0.558291i
$463$	14.0000			0.650635			0.325318	−	0.945605i	$-0.394529\pi$
$463$	14.0000			0.650635			0.325318	+	0.945605i	$0.394529\pi$
$464$	4.00000	+	4.00000i	0.185695	+	0.185695i
$465$	32.0000			1.48396
$466$	8.00000	−	8.00000i	0.370593	−	0.370593i
$467$	−16.0000	−	16.0000i	−0.740392	−	0.740392i	0.232262	−	0.972653i	$-0.425387\pi$
$467$	−16.0000	−	16.0000i	−0.740392	−	0.740392i	−0.972653	+	0.232262i	$0.925387\pi$
$468$		0			0
$469$	−5.00000	+	5.00000i	−0.230879	+	0.230879i
$470$	−32.0000			−1.47605
$471$		0			0
$472$		−	8.00000i		−	0.368230i
$473$		−	30.0000i		−	1.37940i
$474$		−	56.0000i		−	2.57217i
$475$	−12.0000	+	12.0000i	−0.550598	+	0.550598i
$476$	−12.0000			−0.550019
$477$	35.0000	+	35.0000i	1.60254	+	1.60254i
$478$	8.00000	+	8.00000i	0.365911	+	0.365911i
$479$	−8.00000			−0.365529			−0.182765	−	0.983157i	$-0.558505\pi$
$479$	−8.00000			−0.365529			−0.182765	+	0.983157i	$0.558505\pi$
$480$	32.0000	+	32.0000i	1.46059	+	1.46059i
$481$		0			0
$482$	22.0000	+	22.0000i	1.00207	+	1.00207i
$483$	4.00000	+	4.00000i	0.182006	+	0.182006i
$484$	14.0000			0.636364
$485$	12.0000	−	12.0000i	0.544892	−	0.544892i
$486$			20.0000i			0.907218i
$487$			2.00000i			0.0906287i	0.998973	+	0.0453143i	$0.0144289\pi$
$487$			2.00000i			0.0906287i	−0.998973	+	0.0453143i	$0.985571\pi$
$488$	24.0000			1.08643
$489$			20.0000i			0.904431i
$490$	−4.00000			−0.180702
$491$	−11.0000	+	11.0000i	−0.496423	+	0.496423i	−0.910323	−	0.413900i	$-0.864166\pi$
$491$	−11.0000	+	11.0000i	−0.496423	+	0.496423i	0.413900	+	0.910323i	$0.364166\pi$
$492$	−8.00000	−	8.00000i	−0.360668	−	0.360668i
$493$	6.00000	+	6.00000i	0.270226	+	0.270226i
$494$		0			0
$495$	60.0000			2.69680
$496$	−16.0000			−0.718421
$497$	8.00000			0.358849
$498$		0			0
$499$	−15.0000	−	15.0000i	−0.671492	−	0.671492i	0.286568	−	0.958060i	$-0.407486\pi$
$499$	−15.0000	−	15.0000i	−0.671492	−	0.671492i	−0.958060	+	0.286568i	$0.907486\pi$
$500$	8.00000	−	8.00000i	0.357771	−	0.357771i
$501$		0			0
$502$	−8.00000			−0.357057
$503$		−	8.00000i		−	0.356702i	−0.983967	−	0.178351i	$-0.942924\pi$
$503$		−	8.00000i		−	0.356702i	0.983967	−	0.178351i	$-0.0570763\pi$
$504$	10.0000	−	10.0000i	0.445435	−	0.445435i
$505$			8.00000i			0.355995i
$506$		−	12.0000i		−	0.533465i
$507$	−26.0000	+	26.0000i	−1.15470	+	1.15470i
$508$			16.0000i			0.709885i
$509$	−12.0000	−	12.0000i	−0.531891	−	0.531891i	0.389244	−	0.921135i	$-0.372736\pi$
$509$	−12.0000	−	12.0000i	−0.531891	−	0.531891i	−0.921135	+	0.389244i	$0.872736\pi$
$510$	48.0000	+	48.0000i	2.12548	+	2.12548i
$511$	10.0000			0.442374
$512$	−16.0000	−	16.0000i	−0.707107	−	0.707107i
$513$	−32.0000			−1.41283
$514$	10.0000	+	10.0000i	0.441081	+	0.441081i
$515$		0			0
$516$			40.0000i			1.76090i
$517$	24.0000	−	24.0000i	1.05552	−	1.05552i
$518$			6.00000i			0.263625i
$519$		−	64.0000i		−	2.80929i
$520$		0			0
$521$		−	6.00000i		−	0.262865i	−0.991325	−	0.131432i	$-0.958042\pi$
$521$		−	6.00000i		−	0.262865i	0.991325	−	0.131432i	$-0.0419576\pi$
$522$	−10.0000			−0.437688
$523$	26.0000	−	26.0000i	1.13690	−	1.13690i	0.147898	−	0.989003i	$-0.452749\pi$
$523$	26.0000	−	26.0000i	1.13690	−	1.13690i	0.989003	−	0.147898i	$-0.0472507\pi$
$524$	−24.0000	+	24.0000i	−1.04844	+	1.04844i
$525$	6.00000	+	6.00000i	0.261861	+	0.261861i
$526$	−24.0000	+	24.0000i	−1.04645	+	1.04645i
$527$	−24.0000			−1.04546
$528$	−48.0000			−2.08893
$529$	19.0000			0.826087
$530$	28.0000	−	28.0000i	1.21624	−	1.21624i
$531$	10.0000	+	10.0000i	0.433963	+	0.433963i
$532$	−8.00000	−	8.00000i	−0.346844	−	0.346844i
$533$		0			0
$534$	24.0000			1.03858
$535$			20.0000i			0.864675i
$536$	−20.0000			−0.863868
$537$		−	20.0000i		−	0.863064i
$538$			32.0000i			1.37962i
$539$	3.00000	−	3.00000i	0.129219	−	0.129219i
$540$	−32.0000			−1.37706
$541$	−29.0000	−	29.0000i	−1.24681	−	1.24681i	−0.957122	−	0.289685i	$-0.906449\pi$
$541$	−29.0000	−	29.0000i	−1.24681	−	1.24681i	−0.289685	−	0.957122i	$-0.593551\pi$
$542$	−16.0000	−	16.0000i	−0.687259	−	0.687259i
$543$	−16.0000			−0.686626
$544$	−24.0000	−	24.0000i	−1.02899	−	1.02899i
$545$	12.0000			0.514024
$546$		0			0
$547$	19.0000	+	19.0000i	0.812381	+	0.812381i	0.984990	−	0.172609i	$-0.0552197\pi$
$547$	19.0000	+	19.0000i	0.812381	+	0.812381i	−0.172609	+	0.984990i	$0.555220\pi$
$548$	24.0000			1.02523
$549$	−30.0000	+	30.0000i	−1.28037	+	1.28037i
$550$		−	18.0000i		−	0.767523i
$551$			8.00000i			0.340811i
$552$			16.0000i			0.681005i
$553$			14.0000i			0.595341i
$554$	−2.00000			−0.0849719
$555$	24.0000	−	24.0000i	1.01874	−	1.01874i
$556$	−24.0000	−	24.0000i	−1.01783	−	1.01783i
$557$	15.0000	+	15.0000i	0.635570	+	0.635570i	0.949460	−	0.313889i	$-0.101632\pi$
$557$	15.0000	+	15.0000i	0.635570	+	0.635570i	−0.313889	+	0.949460i	$0.601632\pi$
$558$	20.0000	−	20.0000i	0.846668	−	0.846668i
$559$		0			0
$560$	−8.00000	−	8.00000i	−0.338062	−	0.338062i
$561$	−72.0000			−3.03984
$562$	−24.0000	+	24.0000i	−1.01238	+	1.01238i
$563$	−22.0000	−	22.0000i	−0.927189	−	0.927189i	0.0703340	−	0.997523i	$-0.477593\pi$
$563$	−22.0000	−	22.0000i	−0.927189	−	0.927189i	−0.997523	+	0.0703340i	$0.977593\pi$
$564$	−32.0000	+	32.0000i	−1.34744	+	1.34744i
$565$	24.0000	−	24.0000i	1.00969	−	1.00969i
$566$	12.0000			0.504398
$567$			1.00000i			0.0419961i
$568$	16.0000	+	16.0000i	0.671345	+	0.671345i
$569$			46.0000i			1.92842i	0.265139	+	0.964210i	$0.414582\pi$
$569$			46.0000i			1.92842i	−0.265139	+	0.964210i	$0.585418\pi$
$570$			64.0000i			2.68067i
$571$	−21.0000	+	21.0000i	−0.878823	+	0.878823i	−0.993413	−	0.114590i	$-0.963445\pi$
$571$	−21.0000	+	21.0000i	−0.878823	+	0.878823i	0.114590	+	0.993413i	$0.463445\pi$
$572$		0			0
$573$	−44.0000	−	44.0000i	−1.83813	−	1.83813i
$574$	2.00000	+	2.00000i	0.0834784	+	0.0834784i
$575$	−6.00000			−0.250217
$576$	40.0000			1.66667
$577$	−26.0000			−1.08239			−0.541197	−	0.840896i	$-0.682029\pi$
$577$	−26.0000			−1.08239			−0.541197	+	0.840896i	$0.682029\pi$
$578$	−19.0000	−	19.0000i	−0.790296	−	0.790296i
$579$	48.0000	+	48.0000i	1.99481	+	1.99481i
$580$			8.00000i			0.332182i
$581$		0			0
$582$		−	24.0000i		−	0.994832i
$583$			42.0000i			1.73946i
$584$	20.0000	+	20.0000i	0.827606	+	0.827606i
$585$		0			0
$586$	20.0000			0.826192
$587$	8.00000	−	8.00000i	0.330195	−	0.330195i	−0.522465	−	0.852661i	$-0.674988\pi$
$587$	8.00000	−	8.00000i	0.330195	−	0.330195i	0.852661	+	0.522465i	$0.174988\pi$
$588$	−4.00000	+	4.00000i	−0.164957	+	0.164957i
$589$	−16.0000	−	16.0000i	−0.659269	−	0.659269i
$590$	8.00000	−	8.00000i	0.329355	−	0.329355i
$591$	44.0000			1.80992
$592$	−12.0000	+	12.0000i	−0.493197	+	0.493197i
$593$	−22.0000			−0.903432			−0.451716	−	0.892162i	$-0.649188\pi$
$593$	−22.0000			−0.903432			−0.451716	+	0.892162i	$0.649188\pi$
$594$	24.0000	−	24.0000i	0.984732	−	0.984732i
$595$	−12.0000	−	12.0000i	−0.491952	−	0.491952i
$596$	−26.0000	−	26.0000i	−1.06500	−	1.06500i
$597$	40.0000	−	40.0000i	1.63709	−	1.63709i
$598$		0			0
$599$			8.00000i			0.326871i	0.986554	+	0.163436i	$0.0522576\pi$
$599$			8.00000i			0.326871i	−0.986554	+	0.163436i	$0.947742\pi$
$600$			24.0000i			0.979796i
$601$			10.0000i			0.407909i	0.978980	+	0.203954i	$0.0653794\pi$
$601$			10.0000i			0.407909i	−0.978980	+	0.203954i	$0.934621\pi$
$602$		−	10.0000i		−	0.407570i
$603$	25.0000	−	25.0000i	1.01808	−	1.01808i
$604$	−12.0000			−0.488273
$605$	14.0000	+	14.0000i	0.569181	+	0.569181i
$606$	8.00000	+	8.00000i	0.324978	+	0.324978i
$607$	20.0000			0.811775			0.405887	−	0.913923i	$-0.366962\pi$
$607$	20.0000			0.811775			0.405887	+	0.913923i	$0.366962\pi$
$608$		−	32.0000i		−	1.29777i
$609$	4.00000			0.162088
$610$	24.0000	+	24.0000i	0.971732	+	0.971732i
$611$		0			0
$612$	60.0000			2.42536
$613$	−15.0000	+	15.0000i	−0.605844	+	0.605844i	−0.941857	−	0.336013i	$-0.890921\pi$
$613$	−15.0000	+	15.0000i	−0.605844	+	0.605844i	0.336013	+	0.941857i	$0.390921\pi$
$614$			16.0000i			0.645707i
$615$		−	16.0000i		−	0.645182i
$616$	12.0000			0.483494
$617$			6.00000i			0.241551i	0.992680	+	0.120775i	$0.0385381\pi$
$617$			6.00000i			0.241551i	−0.992680	+	0.120775i	$0.961462\pi$
$618$		0			0
$619$	18.0000	−	18.0000i	0.723481	−	0.723481i	−0.245831	−	0.969313i	$-0.579061\pi$
$619$	18.0000	−	18.0000i	0.723481	−	0.723481i	0.969313	+	0.245831i	$0.0790610\pi$
$620$	−16.0000	−	16.0000i	−0.642575	−	0.642575i
$621$	−8.00000	−	8.00000i	−0.321029	−	0.321029i
$622$	4.00000	−	4.00000i	0.160385	−	0.160385i
$623$	−6.00000			−0.240385
$624$		0			0
$625$	31.0000			1.24000
$626$	2.00000	−	2.00000i	0.0799361	−	0.0799361i
$627$	−48.0000	−	48.0000i	−1.91694	−	1.91694i
$628$		0			0
$629$	−18.0000	+	18.0000i	−0.717707	+	0.717707i
$630$	20.0000			0.796819
$631$		0			0		1.00000			$0$
$631$		0			0		−1.00000			$\pi$
$632$	−28.0000	+	28.0000i	−1.11378	+	1.11378i
$633$			36.0000i			1.43087i
$634$			30.0000i			1.19145i
$635$	−16.0000	+	16.0000i	−0.634941	+	0.634941i
$636$		−	56.0000i		−	2.22054i
$637$		0			0
$638$	−6.00000	−	6.00000i	−0.237542	−	0.237542i
$639$	−40.0000			−1.58238
$640$		−	32.0000i		−	1.26491i
$641$	44.0000			1.73790			0.868948	−	0.494904i	$-0.164797\pi$
$641$	44.0000			1.73790			0.868948	+	0.494904i	$0.164797\pi$
$642$	20.0000	+	20.0000i	0.789337	+	0.789337i
$643$	26.0000	+	26.0000i	1.02534	+	1.02534i	0.999670	+	0.0256694i	$0.00817173\pi$
$643$	26.0000	+	26.0000i	1.02534	+	1.02534i	0.0256694	+	0.999670i	$0.491828\pi$
$644$		−	4.00000i		−	0.157622i
$645$	−40.0000	+	40.0000i	−1.57500	+	1.57500i
$646$		−	48.0000i		−	1.88853i
$647$			24.0000i			0.943537i	0.881722	+	0.471769i	$0.156384\pi$
$647$			24.0000i			0.943537i	−0.881722	+	0.471769i	$0.843616\pi$
$648$	−2.00000	+	2.00000i	−0.0785674	+	0.0785674i
$649$			12.0000i			0.471041i
$650$		0			0
$651$	−8.00000	+	8.00000i	−0.313545	+	0.313545i
$652$	10.0000	−	10.0000i	0.391630	−	0.391630i
$653$	25.0000	+	25.0000i	0.978326	+	0.978326i	0.999770	−	0.0214444i	$-0.00682650\pi$
$653$	25.0000	+	25.0000i	0.978326	+	0.978326i	−0.0214444	+	0.999770i	$0.506827\pi$
$654$	12.0000	−	12.0000i	0.469237	−	0.469237i
$655$	−48.0000			−1.87552
$656$			8.00000i			0.312348i
$657$	−50.0000			−1.95069
$658$	8.00000	−	8.00000i	0.311872	−	0.311872i
$659$	17.0000	+	17.0000i	0.662226	+	0.662226i	0.955904	−	0.293678i	$-0.0948794\pi$
$659$	17.0000	+	17.0000i	0.662226	+	0.662226i	−0.293678	+	0.955904i	$0.594879\pi$
$660$	−48.0000	−	48.0000i	−1.86840	−	1.86840i
$661$	30.0000	−	30.0000i	1.16686	−	1.16686i	0.183924	−	0.982940i	$-0.441120\pi$
$661$	30.0000	−	30.0000i	1.16686	−	1.16686i	0.982940	−	0.183924i	$-0.0588801\pi$
$662$	30.0000			1.16598
$663$		0			0
$664$		0			0
$665$		−	16.0000i		−	0.620453i
$666$		−	30.0000i		−	1.16248i
$667$	−2.00000	+	2.00000i	−0.0774403	+	0.0774403i
$668$		0			0
$669$	−8.00000	−	8.00000i	−0.309298	−	0.309298i
$670$	−20.0000	−	20.0000i	−0.772667	−	0.772667i
$671$	−36.0000			−1.38976
$672$	−16.0000			−0.617213
$673$	26.0000			1.00223			0.501113	−	0.865382i	$-0.332924\pi$
$673$	26.0000			1.00223			0.501113	+	0.865382i	$0.332924\pi$
$674$	8.00000	+	8.00000i	0.308148	+	0.308148i
$675$	−12.0000	−	12.0000i	−0.461880	−	0.461880i
$676$	26.0000			1.00000
$677$	8.00000	−	8.00000i	0.307465	−	0.307465i	−0.536460	−	0.843925i	$-0.680239\pi$
$677$	8.00000	−	8.00000i	0.307465	−	0.307465i	0.843925	+	0.536460i	$0.180239\pi$
$678$		−	48.0000i		−	1.84343i
$679$			6.00000i			0.230259i
$680$		−	48.0000i		−	1.84072i
$681$		−	16.0000i		−	0.613121i
$682$	24.0000			0.919007
$683$	5.00000	−	5.00000i	0.191320	−	0.191320i	−0.604946	−	0.796266i	$-0.706805\pi$
$683$	5.00000	−	5.00000i	0.191320	−	0.191320i	0.796266	+	0.604946i	$0.206805\pi$
$684$	40.0000	+	40.0000i	1.52944	+	1.52944i
$685$	24.0000	+	24.0000i	0.916993	+	0.916993i
$686$	1.00000	−	1.00000i	0.0381802	−	0.0381802i
$687$	−48.0000			−1.83131
$688$	20.0000	−	20.0000i	0.762493	−	0.762493i
$689$		0			0
$690$	−16.0000	+	16.0000i	−0.609110	+	0.609110i
$691$	12.0000	+	12.0000i	0.456502	+	0.456502i	0.897505	−	0.441004i	$-0.145377\pi$
$691$	12.0000	+	12.0000i	0.456502	+	0.456502i	−0.441004	+	0.897505i	$0.645377\pi$
$692$	−32.0000	+	32.0000i	−1.21646	+	1.21646i
$693$	−15.0000	+	15.0000i	−0.569803	+	0.569803i
$694$	26.0000			0.986947
$695$		−	48.0000i		−	1.82074i
$696$	8.00000	+	8.00000i	0.303239	+	0.303239i
$697$			12.0000i			0.454532i
$698$		−	32.0000i		−	1.21122i
$699$	16.0000	−	16.0000i	0.605176	−	0.605176i
$700$		−	6.00000i		−	0.226779i
$701$	13.0000	+	13.0000i	0.491003	+	0.491003i	0.908622	−	0.417619i	$-0.137135\pi$
$701$	13.0000	+	13.0000i	0.491003	+	0.491003i	−0.417619	+	0.908622i	$0.637135\pi$
$702$		0			0
$703$	−24.0000			−0.905177
$704$	24.0000	+	24.0000i	0.904534	+	0.904534i
$705$	−64.0000			−2.41038
$706$	−18.0000	−	18.0000i	−0.677439	−	0.677439i
$707$	−2.00000	−	2.00000i	−0.0752177	−	0.0752177i
$708$		−	16.0000i		−	0.601317i
$709$	−31.0000	+	31.0000i	−1.16423	+	1.16423i	−0.180689	+	0.983540i	$0.557833\pi$
$709$	−31.0000	+	31.0000i	−1.16423	+	1.16423i	−0.983540	+	0.180689i	$0.942167\pi$
$710$			32.0000i			1.20094i
$711$		−	70.0000i		−	2.62521i
$712$	−12.0000	−	12.0000i	−0.449719	−	0.449719i
$713$		−	8.00000i		−	0.299602i
$714$	−24.0000			−0.898177
$715$		0			0
$716$	−10.0000	+	10.0000i	−0.373718	+	0.373718i
$717$	16.0000	+	16.0000i	0.597531	+	0.597531i
$718$	−22.0000	+	22.0000i	−0.821033	+	0.821033i
$719$	−8.00000			−0.298350			−0.149175	−	0.988811i	$-0.547662\pi$
$719$	−8.00000			−0.298350			−0.149175	+	0.988811i	$0.547662\pi$
$720$	40.0000	+	40.0000i	1.49071	+	1.49071i
$721$		0			0
$722$	13.0000	−	13.0000i	0.483810	−	0.483810i
$723$	44.0000	+	44.0000i	1.63638	+	1.63638i
$724$	8.00000	+	8.00000i	0.297318	+	0.297318i
$725$	−3.00000	+	3.00000i	−0.111417	+	0.111417i
$726$	28.0000			1.03918
$727$		−	44.0000i		−	1.63187i	−0.578144	−	0.815935i	$-0.696223\pi$
$727$		−	44.0000i		−	1.63187i	0.578144	−	0.815935i	$-0.303777\pi$
$728$		0			0
$729$			43.0000i			1.59259i
$730$			40.0000i			1.48047i
$731$	30.0000	−	30.0000i	1.10959	−	1.10959i
$732$	48.0000			1.77413
$733$	−2.00000	−	2.00000i	−0.0738717	−	0.0738717i	0.669206	−	0.743077i	$-0.266635\pi$
$733$	−2.00000	−	2.00000i	−0.0738717	−	0.0738717i	−0.743077	+	0.669206i	$0.766635\pi$
$734$	16.0000	+	16.0000i	0.590571	+	0.590571i
$735$	−8.00000			−0.295084
$736$	8.00000	−	8.00000i	0.294884	−	0.294884i
$737$	30.0000			1.10506
$738$	−10.0000	−	10.0000i	−0.368105	−	0.368105i
$739$	−5.00000	−	5.00000i	−0.183928	−	0.183928i	0.609137	−	0.793065i	$-0.291516\pi$
$739$	−5.00000	−	5.00000i	−0.183928	−	0.183928i	−0.793065	+	0.609137i	$0.791516\pi$
$740$	−24.0000			−0.882258
$741$		0			0
$742$			14.0000i			0.513956i
$743$			6.00000i			0.220119i	0.993925	+	0.110059i	$0.0351041\pi$
$743$			6.00000i			0.220119i	−0.993925	+	0.110059i	$0.964896\pi$
$744$	−32.0000			−1.17318
$745$		−	52.0000i		−	1.90513i
$746$	−10.0000			−0.366126
$747$		0			0
$748$	36.0000	+	36.0000i	1.31629	+	1.31629i
$749$	−5.00000	−	5.00000i	−0.182696	−	0.182696i
$750$	16.0000	−	16.0000i	0.584237	−	0.584237i
$751$	40.0000			1.45962			0.729810	−	0.683650i	$-0.239608\pi$
$751$	40.0000			1.45962			0.729810	+	0.683650i	$0.239608\pi$
$752$	32.0000			1.16692
$753$	−16.0000			−0.583072
$754$		0			0
$755$	−12.0000	−	12.0000i	−0.436725	−	0.436725i
$756$	8.00000	−	8.00000i	0.290957	−	0.290957i
$757$	33.0000	−	33.0000i	1.19941	−	1.19941i	0.225061	−	0.974345i	$-0.427742\pi$
$757$	33.0000	−	33.0000i	1.19941	−	1.19941i	0.974345	−	0.225061i	$-0.0722580\pi$
$758$	−34.0000			−1.23494
$759$		−	24.0000i		−	0.871145i
$760$	32.0000	−	32.0000i	1.16076	−	1.16076i
$761$		−	18.0000i		−	0.652499i	−0.945284	−	0.326250i	$-0.894215\pi$
$761$		−	18.0000i		−	0.652499i	0.945284	−	0.326250i	$-0.105785\pi$
$762$			32.0000i			1.15924i
$763$	−3.00000	+	3.00000i	−0.108607	+	0.108607i
$764$			44.0000i			1.59186i
$765$	60.0000	+	60.0000i	2.16930	+	2.16930i
$766$	16.0000	+	16.0000i	0.578103	+	0.578103i
$767$		0			0
$768$	−32.0000	−	32.0000i	−1.15470	−	1.15470i
$769$	−30.0000			−1.08183			−0.540914	−	0.841078i	$-0.681921\pi$
$769$	−30.0000			−1.08183			−0.540914	+	0.841078i	$0.681921\pi$
$770$	12.0000	+	12.0000i	0.432450	+	0.432450i
$771$	20.0000	+	20.0000i	0.720282	+	0.720282i
$772$		−	48.0000i		−	1.72756i
$773$	−30.0000	+	30.0000i	−1.07903	+	1.07903i	−0.0824280	+	0.996597i	$0.526267\pi$
$773$	−30.0000	+	30.0000i	−1.07903	+	1.07903i	−0.996597	+	0.0824280i	$0.973733\pi$
$774$			50.0000i			1.79721i
$775$		−	12.0000i		−	0.431053i
$776$	−12.0000	+	12.0000i	−0.430775	+	0.430775i
$777$			12.0000i			0.430498i
$778$	−38.0000			−1.36237
$779$	−8.00000	+	8.00000i	−0.286630	+	0.286630i
$780$		0			0
$781$	−24.0000	−	24.0000i	−0.858788	−	0.858788i
$782$	12.0000	−	12.0000i	0.429119	−	0.429119i
$783$	−8.00000			−0.285897
$784$	4.00000			0.142857
$785$		0			0
$786$	−48.0000	+	48.0000i	−1.71210	+	1.71210i
$787$	−12.0000	−	12.0000i	−0.427754	−	0.427754i	0.460109	−	0.887863i	$-0.347810\pi$
$787$	−12.0000	−	12.0000i	−0.427754	−	0.427754i	−0.887863	+	0.460109i	$0.847810\pi$
$788$	−22.0000	−	22.0000i	−0.783718	−	0.783718i
$789$	−48.0000	+	48.0000i	−1.70885	+	1.70885i
$790$	−56.0000			−1.99239
$791$			12.0000i			0.426671i
$792$	−60.0000			−2.13201
$793$		0			0
$794$		0			0
$795$	56.0000	−	56.0000i	1.98612	−	1.98612i
$796$	−40.0000			−1.41776
$797$	8.00000	+	8.00000i	0.283375	+	0.283375i	0.834453	−	0.551079i	$-0.185784\pi$
$797$	8.00000	+	8.00000i	0.283375	+	0.283375i	−0.551079	+	0.834453i	$0.685784\pi$
$798$	−16.0000	−	16.0000i	−0.566394	−	0.566394i
$799$	48.0000			1.69812
$800$	12.0000	−	12.0000i	0.424264	−	0.424264i
$801$	30.0000			1.06000
$802$	4.00000	+	4.00000i	0.141245	+	0.141245i
$803$	−30.0000	−	30.0000i	−1.05868	−	1.05868i
$804$	−40.0000			−1.41069
$805$	4.00000	−	4.00000i	0.140981	−	0.140981i
$806$		0			0
$807$			64.0000i			2.25291i
$808$		−	8.00000i		−	0.281439i
$809$		−	38.0000i		−	1.33601i	−0.744157	−	0.668004i	$-0.767149\pi$
$809$		−	38.0000i		−	1.33601i	0.744157	−	0.668004i	$-0.232851\pi$
$810$	−4.00000			−0.140546
$811$	30.0000	−	30.0000i	1.05344	−	1.05344i	0.0549536	−	0.998489i	$-0.482499\pi$
$811$	30.0000	−	30.0000i	1.05344	−	1.05344i	0.998489	−	0.0549536i	$-0.0175011\pi$
$812$	−2.00000	−	2.00000i	−0.0701862	−	0.0701862i
$813$	−32.0000	−	32.0000i	−1.12229	−	1.12229i
$814$	18.0000	−	18.0000i	0.630900	−	0.630900i
$815$	20.0000			0.700569
$816$	−48.0000	−	48.0000i	−1.68034	−	1.68034i
$817$	40.0000			1.39942
$818$	−10.0000	+	10.0000i	−0.349642	+	0.349642i
$819$		0			0
$820$	−8.00000	+	8.00000i	−0.279372	+	0.279372i
$821$	−7.00000	+	7.00000i	−0.244302	+	0.244302i	−0.818627	−	0.574325i	$-0.805264\pi$
$821$	−7.00000	+	7.00000i	−0.244302	+	0.244302i	0.574325	+	0.818627i	$0.305264\pi$
$822$	48.0000			1.67419
$823$			40.0000i			1.39431i	0.716919	+	0.697156i	$0.245552\pi$
$823$			40.0000i			1.39431i	−0.716919	+	0.697156i	$0.754448\pi$
$824$		0			0
$825$		−	36.0000i		−	1.25336i
$826$			4.00000i			0.139178i
$827$	−13.0000	+	13.0000i	−0.452054	+	0.452054i	−0.896036	−	0.443982i	$-0.853566\pi$
$827$	−13.0000	+	13.0000i	−0.452054	+	0.452054i	0.443982	+	0.896036i	$0.353566\pi$
$828$			20.0000i			0.695048i
$829$	−2.00000	−	2.00000i	−0.0694629	−	0.0694629i	0.671522	−	0.740985i	$-0.265641\pi$
$829$	−2.00000	−	2.00000i	−0.0694629	−	0.0694629i	−0.740985	+	0.671522i	$0.765641\pi$
$830$		0			0
$831$	−4.00000			−0.138758
$832$		0			0
$833$	6.00000			0.207888
$834$	−48.0000	−	48.0000i	−1.66210	−	1.66210i
$835$		0			0
$836$			48.0000i			1.66011i
$837$	16.0000	−	16.0000i	0.553041	−	0.553041i
$838$			20.0000i			0.690889i
$839$			24.0000i			0.828572i	0.910147	+	0.414286i	$0.135969\pi$
$839$			24.0000i			0.828572i	−0.910147	+	0.414286i	$0.864031\pi$
$840$	−16.0000	−	16.0000i	−0.552052	−	0.552052i
$841$		−	27.0000i		−	0.931034i
$842$	50.0000			1.72311
$843$	−48.0000	+	48.0000i	−1.65321	+	1.65321i
$844$	18.0000	−	18.0000i	0.619586	−	0.619586i
$845$	26.0000	+	26.0000i	0.894427	+	0.894427i
$846$	−40.0000	+	40.0000i	−1.37523	+	1.37523i
$847$	−7.00000			−0.240523
$848$	−28.0000	+	28.0000i	−0.961524	+	0.961524i
$849$	24.0000			0.823678
$850$	18.0000	−	18.0000i	0.617395	−	0.617395i
$851$	−6.00000	−	6.00000i	−0.205677	−	0.205677i
$852$	32.0000	+	32.0000i	1.09630	+	1.09630i
$853$	−4.00000	+	4.00000i	−0.136957	+	0.136957i	−0.772262	−	0.635304i	$-0.780875\pi$
$853$	−4.00000	+	4.00000i	−0.136957	+	0.136957i	0.635304	+	0.772262i	$0.280875\pi$
$854$	−12.0000			−0.410632
$855$			80.0000i			2.73594i
$856$		−	20.0000i		−	0.683586i
$857$			18.0000i			0.614868i	0.951569	+	0.307434i	$0.0994704\pi$
$857$			18.0000i			0.614868i	−0.951569	+	0.307434i	$0.900530\pi$
$858$		0			0
$859$	−4.00000	+	4.00000i	−0.136478	+	0.136478i	−0.772046	−	0.635567i	$-0.780766\pi$
$859$	−4.00000	+	4.00000i	−0.136478	+	0.136478i	0.635567	+	0.772046i	$0.280766\pi$
$860$	40.0000			1.36399
$861$	4.00000	+	4.00000i	0.136320	+	0.136320i
$862$		0			0
$863$	6.00000			0.204242			0.102121	−	0.994772i	$-0.467437\pi$
$863$	6.00000			0.204242			0.102121	+	0.994772i	$0.467437\pi$
$864$	32.0000			1.08866
$865$	−64.0000			−2.17607
$866$	2.00000	+	2.00000i	0.0679628	+	0.0679628i
$867$	−38.0000	−	38.0000i	−1.29055	−	1.29055i
$868$	8.00000			0.271538
$869$	42.0000	−	42.0000i	1.42475	−	1.42475i
$870$			16.0000i			0.542451i
$871$		0			0
$872$	−12.0000			−0.406371
$873$		−	30.0000i		−	1.01535i
$874$	16.0000			0.541208
$875$	−4.00000	+	4.00000i	−0.135225	+	0.135225i
$876$	40.0000	+	40.0000i	1.35147	+	1.35147i
$877$	−21.0000	−	21.0000i	−0.709120	−	0.709120i	0.257230	−	0.966350i	$-0.417190\pi$
$877$	−21.0000	−	21.0000i	−0.709120	−	0.709120i	−0.966350	+	0.257230i	$0.917190\pi$
$878$	24.0000	−	24.0000i	0.809961	−	0.809961i
$879$	40.0000			1.34917
$880$			48.0000i			1.61808i
$881$	30.0000			1.01073			0.505363	−	0.862907i	$-0.331359\pi$
$881$	30.0000			1.01073			0.505363	+	0.862907i	$0.331359\pi$
$882$	−5.00000	+	5.00000i	−0.168359	+	0.168359i
$883$	−17.0000	−	17.0000i	−0.572096	−	0.572096i	0.360618	−	0.932714i	$-0.382566\pi$
$883$	−17.0000	−	17.0000i	−0.572096	−	0.572096i	−0.932714	+	0.360618i	$0.882566\pi$
$884$		0			0
$885$	16.0000	−	16.0000i	0.537834	−	0.537834i
$886$	34.0000			1.14225
$887$			24.0000i			0.805841i	0.915235	+	0.402921i	$0.132005\pi$
$887$			24.0000i			0.805841i	−0.915235	+	0.402921i	$0.867995\pi$
$888$	−24.0000	+	24.0000i	−0.805387	+	0.805387i
$889$		−	8.00000i		−	0.268311i
$890$		−	24.0000i		−	0.804482i
$891$	3.00000	−	3.00000i	0.100504	−	0.100504i
$892$			8.00000i			0.267860i
$893$	32.0000	+	32.0000i	1.07084	+	1.07084i
$894$	−52.0000	−	52.0000i	−1.73914	−	1.73914i
$895$	−20.0000			−0.668526
$896$	8.00000	+	8.00000i	0.267261	+	0.267261i
$897$		0			0
$898$	−34.0000	−	34.0000i	−1.13459	−	1.13459i
$899$	−4.00000	−	4.00000i	−0.133407	−	0.133407i
$900$			30.0000i			1.00000i
$901$	−42.0000	+	42.0000i	−1.39922	+	1.39922i
$902$		−	12.0000i		−	0.399556i
$903$		−	20.0000i		−	0.665558i
$904$	−24.0000	+	24.0000i	−0.798228	+	0.798228i
$905$			16.0000i			0.531858i
$906$	−24.0000			−0.797347
$907$	−9.00000	+	9.00000i	−0.298840	+	0.298840i	−0.840559	−	0.541719i	$-0.817774\pi$
$907$	−9.00000	+	9.00000i	−0.298840	+	0.298840i	0.541719	+	0.840559i	$0.317774\pi$
$908$	−8.00000	+	8.00000i	−0.265489	+	0.265489i
$909$	10.0000	+	10.0000i	0.331679	+	0.331679i
$910$		0			0
$911$		0			0			−	1.00000i	$-0.5\pi$
$911$		0			0				1.00000i	$0.5\pi$
$912$		−	64.0000i		−	2.11925i
$913$		0			0
$914$	26.0000	−	26.0000i	0.860004	−	0.860004i
$915$	48.0000	+	48.0000i	1.58683	+	1.58683i
$916$	24.0000	+	24.0000i	0.792982	+	0.792982i
$917$	12.0000	−	12.0000i	0.396275	−	0.396275i
$918$	48.0000			1.58424
$919$		−	56.0000i		−	1.84727i	−0.383274	−	0.923635i	$-0.625203\pi$
$919$		−	56.0000i		−	1.84727i	0.383274	−	0.923635i	$-0.374797\pi$
$920$	16.0000			0.527504
$921$			32.0000i			1.05444i
$922$			56.0000i			1.84426i
$923$		0			0
$924$	24.0000			0.789542
$925$	−9.00000	−	9.00000i	−0.295918	−	0.295918i
$926$	−14.0000	−	14.0000i	−0.460069	−	0.460069i
$927$		0			0
$928$		−	8.00000i		−	0.262613i
$929$	−30.0000			−0.984268			−0.492134	−	0.870519i	$-0.663783\pi$
$929$	−30.0000			−0.984268			−0.492134	+	0.870519i	$0.663783\pi$
$930$	−32.0000	−	32.0000i	−1.04932	−	1.04932i
$931$	4.00000	+	4.00000i	0.131095	+	0.131095i
$932$	−16.0000			−0.524097
$933$	8.00000	−	8.00000i	0.261908	−	0.261908i
$934$			32.0000i			1.04707i
$935$			72.0000i			2.35465i
$936$		0			0
$937$		−	50.0000i		−	1.63343i	−0.577042	−	0.816714i	$-0.695793\pi$
$937$		−	50.0000i		−	1.63343i	0.577042	−	0.816714i	$-0.304207\pi$
$938$	10.0000			0.326512
$939$	4.00000	−	4.00000i	0.130535	−	0.130535i
$940$	32.0000	+	32.0000i	1.04372	+	1.04372i
$941$	26.0000	+	26.0000i	0.847576	+	0.847576i	0.989830	−	0.142254i	$-0.0454351\pi$
$941$	26.0000	+	26.0000i	0.847576	+	0.847576i	−0.142254	+	0.989830i	$0.545435\pi$
$942$		0			0
$943$	−4.00000			−0.130258
$944$	−8.00000	+	8.00000i	−0.260378	+	0.260378i
$945$	16.0000			0.520480
$946$	−30.0000	+	30.0000i	−0.975384	+	0.975384i
$947$	13.0000	+	13.0000i	0.422443	+	0.422443i	0.886044	−	0.463601i	$-0.153443\pi$
$947$	13.0000	+	13.0000i	0.422443	+	0.422443i	−0.463601	+	0.886044i	$0.653443\pi$
$948$	−56.0000	+	56.0000i	−1.81880	+	1.81880i
$949$		0			0
$950$	24.0000			0.778663
$951$			60.0000i			1.94563i
$952$	12.0000	+	12.0000i	0.388922	+	0.388922i
$953$			16.0000i			0.518291i	0.965838	+	0.259145i	$0.0834409\pi$
$953$			16.0000i			0.518291i	−0.965838	+	0.259145i	$0.916559\pi$
$954$		−	70.0000i		−	2.26633i
$955$	−44.0000	+	44.0000i	−1.42381	+	1.42381i
$956$		−	16.0000i		−	0.517477i
$957$	−12.0000	−	12.0000i	−0.387905	−	0.387905i
$958$	8.00000	+	8.00000i	0.258468	+	0.258468i
$959$	−12.0000			−0.387500
$960$		−	64.0000i		−	2.06559i
$961$	−15.0000			−0.483871
$962$		0			0
$963$	25.0000	+	25.0000i	0.805614	+	0.805614i
$964$		−	44.0000i		−	1.41714i
$965$	48.0000	−	48.0000i	1.54517	−	1.54517i
$966$		−	8.00000i		−	0.257396i
$967$			38.0000i			1.22200i	0.791632	+	0.610999i	$0.209232\pi$
$967$			38.0000i			1.22200i	−0.791632	+	0.610999i	$0.790768\pi$
$968$	−14.0000	−	14.0000i	−0.449977	−	0.449977i
$969$		−	96.0000i		−	3.08396i
$970$	−24.0000			−0.770594
$971$	26.0000	−	26.0000i	0.834380	−	0.834380i	−0.153733	−	0.988112i	$-0.549129\pi$
$971$	26.0000	−	26.0000i	0.834380	−	0.834380i	0.988112	+	0.153733i	$0.0491295\pi$
$972$	20.0000	−	20.0000i	0.641500	−	0.641500i
$973$	12.0000	+	12.0000i	0.384702	+	0.384702i
$974$	2.00000	−	2.00000i	0.0640841	−	0.0640841i
$975$		0			0
$976$	−24.0000	−	24.0000i	−0.768221	−	0.768221i
$977$	−34.0000			−1.08776			−0.543878	−	0.839164i	$-0.683045\pi$
$977$	−34.0000			−1.08776			−0.543878	+	0.839164i	$0.683045\pi$
$978$	20.0000	−	20.0000i	0.639529	−	0.639529i
$979$	18.0000	+	18.0000i	0.575282	+	0.575282i
$980$	4.00000	+	4.00000i	0.127775	+	0.127775i
$981$	15.0000	−	15.0000i	0.478913	−	0.478913i
$982$	22.0000			0.702048
$983$		−	48.0000i		−	1.53096i	−0.643458	−	0.765481i	$-0.722501\pi$
$983$		−	48.0000i		−	1.53096i	0.643458	−	0.765481i	$-0.277499\pi$
$984$			16.0000i			0.510061i
$985$		−	44.0000i		−	1.40196i
$986$		−	12.0000i		−	0.382158i
$987$	16.0000	−	16.0000i	0.509286	−	0.509286i
$988$		0			0
$989$	10.0000	+	10.0000i	0.317982	+	0.317982i
$990$	−60.0000	−	60.0000i	−1.90693	−	1.90693i
$991$	−10.0000			−0.317660			−0.158830	−	0.987306i	$-0.550772\pi$
$991$	−10.0000			−0.317660			−0.158830	+	0.987306i	$0.550772\pi$
$992$	16.0000	+	16.0000i	0.508001	+	0.508001i
$993$	60.0000			1.90404
$994$	−8.00000	−	8.00000i	−0.253745	−	0.253745i
$995$	−40.0000	−	40.0000i	−1.26809	−	1.26809i
$996$		0			0
$997$	30.0000	−	30.0000i	0.950110	−	0.950110i	−0.0487037	−	0.998813i	$-0.515509\pi$
$997$	30.0000	−	30.0000i	0.950110	−	0.950110i	0.998813	+	0.0487037i	$0.0155090\pi$
$998$			30.0000i			0.949633i
$999$		−	24.0000i		−	0.759326i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	112.2.m.a.29.1	✓	2
4.3	odd	2		448.2.m.b.337.1		2
7.2	even	3		784.2.x.g.557.1		4
7.3	odd	6		784.2.x.b.765.1		4
7.4	even	3		784.2.x.g.765.1		4
7.5	odd	6		784.2.x.b.557.1		4
7.6	odd	2		784.2.m.c.589.1		2
8.3	odd	2		896.2.m.a.673.1		2
8.5	even	2		896.2.m.d.673.1		2
16.3	odd	4		896.2.m.a.225.1		2
16.5	even	4	inner	112.2.m.a.85.1	yes	2
16.11	odd	4		448.2.m.b.113.1		2
16.13	even	4		896.2.m.d.225.1		2
32.5	even	8		7168.2.a.q.1.2		2
32.11	odd	8		7168.2.a.i.1.2		2
32.21	even	8		7168.2.a.q.1.1		2
32.27	odd	8		7168.2.a.i.1.1		2
112.5	odd	12		784.2.x.b.165.1		4
112.37	even	12		784.2.x.g.165.1		4
112.53	even	12		784.2.x.g.373.1		4
112.69	odd	4		784.2.m.c.197.1		2
112.101	odd	12		784.2.x.b.373.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
112.2.m.a.29.1	✓	2	1.1	even	1	trivial
112.2.m.a.85.1	yes	2	16.5	even	4	inner
448.2.m.b.113.1		2	16.11	odd	4
448.2.m.b.337.1		2	4.3	odd	2
784.2.m.c.197.1		2	112.69	odd	4
784.2.m.c.589.1		2	7.6	odd	2
784.2.x.b.165.1		4	112.5	odd	12
784.2.x.b.373.1		4	112.101	odd	12
784.2.x.b.557.1		4	7.5	odd	6
784.2.x.b.765.1		4	7.3	odd	6
784.2.x.g.165.1		4	112.37	even	12
784.2.x.g.373.1		4	112.53	even	12
784.2.x.g.557.1		4	7.2	even	3
784.2.x.g.765.1		4	7.4	even	3
896.2.m.a.225.1		2	16.3	odd	4
896.2.m.a.673.1		2	8.3	odd	2
896.2.m.d.225.1		2	16.13	even	4
896.2.m.d.673.1		2	8.5	even	2
7168.2.a.i.1.1		2	32.27	odd	8
7168.2.a.i.1.2		2	32.11	odd	8
7168.2.a.q.1.1		2	32.21	even	8
7168.2.a.q.1.2		2	32.5	even	8

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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 112 = 2^{4} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	112.m (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.00000 - 1.00000i) q^{2} +(-2.00000 - 2.00000i) q^{3} +2.00000i q^{4} +(-2.00000 + 2.00000i) q^{5} +4.00000i q^{6} -1.00000i q^{7} +(2.00000 - 2.00000i) q^{8} +5.00000i q^{9} +O(q^{10})\)	\(q+(-1.00000 - 1.00000i) q^{2} +(-2.00000 - 2.00000i) q^{3} +2.00000i q^{4} +(-2.00000 + 2.00000i) q^{5} +4.00000i q^{6} -1.00000i q^{7} +(2.00000 - 2.00000i) q^{8} +5.00000i q^{9} +4.00000 q^{10} +(-3.00000 + 3.00000i) q^{11} +(4.00000 - 4.00000i) q^{12} +(-1.00000 + 1.00000i) q^{14} +8.00000 q^{15} -4.00000 q^{16} -6.00000 q^{17} +(5.00000 - 5.00000i) q^{18} +(-4.00000 - 4.00000i) q^{19} +(-4.00000 - 4.00000i) q^{20} +(-2.00000 + 2.00000i) q^{21} +6.00000 q^{22} -2.00000i q^{23} -8.00000 q^{24} -3.00000i q^{25} +(4.00000 - 4.00000i) q^{27} +2.00000 q^{28} +(-1.00000 - 1.00000i) q^{29} +(-8.00000 - 8.00000i) q^{30} +4.00000 q^{31} +(4.00000 + 4.00000i) q^{32} +12.0000 q^{33} +(6.00000 + 6.00000i) q^{34} +(2.00000 + 2.00000i) q^{35} -10.0000 q^{36} +(3.00000 - 3.00000i) q^{37} +8.00000i q^{38} +8.00000i q^{40} -2.00000i q^{41} +4.00000 q^{42} +(-5.00000 + 5.00000i) q^{43} +(-6.00000 - 6.00000i) q^{44} +(-10.0000 - 10.0000i) q^{45} +(-2.00000 + 2.00000i) q^{46} -8.00000 q^{47} +(8.00000 + 8.00000i) q^{48} -1.00000 q^{49} +(-3.00000 + 3.00000i) q^{50} +(12.0000 + 12.0000i) q^{51} +(7.00000 - 7.00000i) q^{53} -8.00000 q^{54} -12.0000i q^{55} +(-2.00000 - 2.00000i) q^{56} +16.0000i q^{57} +2.00000i q^{58} +(2.00000 - 2.00000i) q^{59} +16.0000i q^{60} +(6.00000 + 6.00000i) q^{61} +(-4.00000 - 4.00000i) q^{62} +5.00000 q^{63} -8.00000i q^{64} +(-12.0000 - 12.0000i) q^{66} +(-5.00000 - 5.00000i) q^{67} -12.0000i q^{68} +(-4.00000 + 4.00000i) q^{69} -4.00000i q^{70} +8.00000i q^{71} +(10.0000 + 10.0000i) q^{72} +10.0000i q^{73} -6.00000 q^{74} +(-6.00000 + 6.00000i) q^{75} +(8.00000 - 8.00000i) q^{76} +(3.00000 + 3.00000i) q^{77} -14.0000 q^{79} +(8.00000 - 8.00000i) q^{80} -1.00000 q^{81} +(-2.00000 + 2.00000i) q^{82} +(-4.00000 - 4.00000i) q^{84} +(12.0000 - 12.0000i) q^{85} +10.0000 q^{86} +4.00000i q^{87} +12.0000i q^{88} -6.00000i q^{89} +20.0000i q^{90} +4.00000 q^{92} +(-8.00000 - 8.00000i) q^{93} +(8.00000 + 8.00000i) q^{94} +16.0000 q^{95} -16.0000i q^{96} -6.00000 q^{97} +(1.00000 + 1.00000i) q^{98} +(-15.0000 - 15.0000i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{2} - 4 q^{3} - 4 q^{5} + 4 q^{8}+O(q^{10}) \) 2 * q - 2 * q^2 - 4 * q^3 - 4 * q^5 + 4 * q^8	\( 2 q - 2 q^{2} - 4 q^{3} - 4 q^{5} + 4 q^{8} + 8 q^{10} - 6 q^{11} + 8 q^{12} - 2 q^{14} + 16 q^{15} - 8 q^{16} - 12 q^{17} + 10 q^{18} - 8 q^{19} - 8 q^{20} - 4 q^{21} + 12 q^{22} - 16 q^{24} + 8 q^{27} + 4 q^{28} - 2 q^{29} - 16 q^{30} + 8 q^{31} + 8 q^{32} + 24 q^{33} + 12 q^{34} + 4 q^{35} - 20 q^{36} + 6 q^{37} + 8 q^{42} - 10 q^{43} - 12 q^{44} - 20 q^{45} - 4 q^{46} - 16 q^{47} + 16 q^{48} - 2 q^{49} - 6 q^{50} + 24 q^{51} + 14 q^{53} - 16 q^{54} - 4 q^{56} + 4 q^{59} + 12 q^{61} - 8 q^{62} + 10 q^{63} - 24 q^{66} - 10 q^{67} - 8 q^{69} + 20 q^{72} - 12 q^{74} - 12 q^{75} + 16 q^{76} + 6 q^{77} - 28 q^{79} + 16 q^{80} - 2 q^{81} - 4 q^{82} - 8 q^{84} + 24 q^{85} + 20 q^{86} + 8 q^{92} - 16 q^{93} + 16 q^{94} + 32 q^{95} - 12 q^{97} + 2 q^{98} - 30 q^{99}+O(q^{100}) \) 2 * q - 2 * q^2 - 4 * q^3 - 4 * q^5 + 4 * q^8 + 8 * q^10 - 6 * q^11 + 8 * q^12 - 2 * q^14 + 16 * q^15 - 8 * q^16 - 12 * q^17 + 10 * q^18 - 8 * q^19 - 8 * q^20 - 4 * q^21 + 12 * q^22 - 16 * q^24 + 8 * q^27 + 4 * q^28 - 2 * q^29 - 16 * q^30 + 8 * q^31 + 8 * q^32 + 24 * q^33 + 12 * q^34 + 4 * q^35 - 20 * q^36 + 6 * q^37 + 8 * q^42 - 10 * q^43 - 12 * q^44 - 20 * q^45 - 4 * q^46 - 16 * q^47 + 16 * q^48 - 2 * q^49 - 6 * q^50 + 24 * q^51 + 14 * q^53 - 16 * q^54 - 4 * q^56 + 4 * q^59 + 12 * q^61 - 8 * q^62 + 10 * q^63 - 24 * q^66 - 10 * q^67 - 8 * q^69 + 20 * q^72 - 12 * q^74 - 12 * q^75 + 16 * q^76 + 6 * q^77 - 28 * q^79 + 16 * q^80 - 2 * q^81 - 4 * q^82 - 8 * q^84 + 24 * q^85 + 20 * q^86 + 8 * q^92 - 16 * q^93 + 16 * q^94 + 32 * q^95 - 12 * q^97 + 2 * q^98 - 30 * q^99

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