LMFDB - Embedded newform 147.2.e.a.79.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [147,2,Mod(67,147)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(147, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 4]))

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

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

chi := DirichletCharacter("147.67");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 147 = 3 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	147.e (of order $3$, degree $2$, not 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:	$1.17380090971$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 21)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			79.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	147.79
Dual form			147.2.e.a.67.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.00000 + 1.73205i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-1.00000 - 1.73205i) q^{4} +(-1.00000 + 1.73205i) q^{5} -2.00000 q^{6} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(-1.00000 + 1.73205i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-1.00000 - 1.73205i) q^{4} +(-1.00000 + 1.73205i) q^{5} -2.00000 q^{6} +(-0.500000 + 0.866025i) q^{9} +(-2.00000 - 3.46410i) q^{10} +(1.00000 + 1.73205i) q^{11} +(1.00000 - 1.73205i) q^{12} -1.00000 q^{13} -2.00000 q^{15} +(2.00000 - 3.46410i) q^{16} +(-1.00000 - 1.73205i) q^{18} +(0.500000 - 0.866025i) q^{19} +4.00000 q^{20} -4.00000 q^{22} +(0.500000 + 0.866025i) q^{25} +(1.00000 - 1.73205i) q^{26} -1.00000 q^{27} +4.00000 q^{29} +(2.00000 - 3.46410i) q^{30} +(4.50000 + 7.79423i) q^{31} +(4.00000 + 6.92820i) q^{32} +(-1.00000 + 1.73205i) q^{33} +2.00000 q^{36} +(-1.50000 + 2.59808i) q^{37} +(1.00000 + 1.73205i) q^{38} +(-0.500000 - 0.866025i) q^{39} +10.0000 q^{41} +5.00000 q^{43} +(2.00000 - 3.46410i) q^{44} +(-1.00000 - 1.73205i) q^{45} +(-3.00000 + 5.19615i) q^{47} +4.00000 q^{48} -2.00000 q^{50} +(1.00000 + 1.73205i) q^{52} +(-6.00000 - 10.3923i) q^{53} +(1.00000 - 1.73205i) q^{54} -4.00000 q^{55} +1.00000 q^{57} +(-4.00000 + 6.92820i) q^{58} +(-6.00000 - 10.3923i) q^{59} +(2.00000 + 3.46410i) q^{60} +(5.00000 - 8.66025i) q^{61} -18.0000 q^{62} -8.00000 q^{64} +(1.00000 - 1.73205i) q^{65} +(-2.00000 - 3.46410i) q^{66} +(2.50000 + 4.33013i) q^{67} -6.00000 q^{71} +(-1.50000 - 2.59808i) q^{73} +(-3.00000 - 5.19615i) q^{74} +(-0.500000 + 0.866025i) q^{75} -2.00000 q^{76} +2.00000 q^{78} +(0.500000 - 0.866025i) q^{79} +(4.00000 + 6.92820i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-10.0000 + 17.3205i) q^{82} -6.00000 q^{83} +(-5.00000 + 8.66025i) q^{86} +(2.00000 + 3.46410i) q^{87} +(8.00000 - 13.8564i) q^{89} +4.00000 q^{90} +(-4.50000 + 7.79423i) q^{93} +(-6.00000 - 10.3923i) q^{94} +(1.00000 + 1.73205i) q^{95} +(-4.00000 + 6.92820i) q^{96} +6.00000 q^{97} -2.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{2} + q^{3} - 2 q^{4} - 2 q^{5} - 4 q^{6} - q^{9}+O(q^{10}) $ 2 * q - 2 * q^2 + q^3 - 2 * q^4 - 2 * q^5 - 4 * q^6 - q^9	$ 2 q - 2 q^{2} + q^{3} - 2 q^{4} - 2 q^{5} - 4 q^{6} - q^{9} - 4 q^{10} + 2 q^{11} + 2 q^{12} - 2 q^{13} - 4 q^{15} + 4 q^{16} - 2 q^{18} + q^{19} + 8 q^{20} - 8 q^{22} + q^{25} + 2 q^{26} - 2 q^{27} + 8 q^{29} + 4 q^{30} + 9 q^{31} + 8 q^{32} - 2 q^{33} + 4 q^{36} - 3 q^{37} + 2 q^{38} - q^{39} + 20 q^{41} + 10 q^{43} + 4 q^{44} - 2 q^{45} - 6 q^{47} + 8 q^{48} - 4 q^{50} + 2 q^{52} - 12 q^{53} + 2 q^{54} - 8 q^{55} + 2 q^{57} - 8 q^{58} - 12 q^{59} + 4 q^{60} + 10 q^{61} - 36 q^{62} - 16 q^{64} + 2 q^{65} - 4 q^{66} + 5 q^{67} - 12 q^{71} - 3 q^{73} - 6 q^{74} - q^{75} - 4 q^{76} + 4 q^{78} + q^{79} + 8 q^{80} - q^{81} - 20 q^{82} - 12 q^{83} - 10 q^{86} + 4 q^{87} + 16 q^{89} + 8 q^{90} - 9 q^{93} - 12 q^{94} + 2 q^{95} - 8 q^{96} + 12 q^{97} - 4 q^{99}+O(q^{100}) $ 2 * q - 2 * q^2 + q^3 - 2 * q^4 - 2 * q^5 - 4 * q^6 - q^9 - 4 * q^10 + 2 * q^11 + 2 * q^12 - 2 * q^13 - 4 * q^15 + 4 * q^16 - 2 * q^18 + q^19 + 8 * q^20 - 8 * q^22 + q^25 + 2 * q^26 - 2 * q^27 + 8 * q^29 + 4 * q^30 + 9 * q^31 + 8 * q^32 - 2 * q^33 + 4 * q^36 - 3 * q^37 + 2 * q^38 - q^39 + 20 * q^41 + 10 * q^43 + 4 * q^44 - 2 * q^45 - 6 * q^47 + 8 * q^48 - 4 * q^50 + 2 * q^52 - 12 * q^53 + 2 * q^54 - 8 * q^55 + 2 * q^57 - 8 * q^58 - 12 * q^59 + 4 * q^60 + 10 * q^61 - 36 * q^62 - 16 * q^64 + 2 * q^65 - 4 * q^66 + 5 * q^67 - 12 * q^71 - 3 * q^73 - 6 * q^74 - q^75 - 4 * q^76 + 4 * q^78 + q^79 + 8 * q^80 - q^81 - 20 * q^82 - 12 * q^83 - 10 * q^86 + 4 * q^87 + 16 * q^89 + 8 * q^90 - 9 * q^93 - 12 * q^94 + 2 * q^95 - 8 * q^96 + 12 * q^97 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/147\mathbb{Z}\right)^\times$.

$n$	$50$	$52$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	−1.00000	+	1.73205i	−0.707107	+	1.22474i	0.258819	+	0.965926i	$0.416667\pi$
$2$	−1.00000	+	1.73205i	−0.707107	+	1.22474i	−0.965926	+	0.258819i	$0.916667\pi$
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$4$	−1.00000	−	1.73205i	−0.500000	−	0.866025i
$5$	−1.00000	+	1.73205i	−0.447214	+	0.774597i	−0.998203	−	0.0599153i	$-0.980917\pi$
$5$	−1.00000	+	1.73205i	−0.447214	+	0.774597i	0.550990	+	0.834512i	$0.314250\pi$
$6$	−2.00000			−0.816497
$7$		0			0
$7$		0			0
$8$		0			0
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	−2.00000	−	3.46410i	−0.632456	−	1.09545i
$11$	1.00000	+	1.73205i	0.301511	+	0.522233i	0.976478	−	0.215615i	$-0.0691756\pi$
$11$	1.00000	+	1.73205i	0.301511	+	0.522233i	−0.674967	+	0.737848i	$0.735842\pi$
$12$	1.00000	−	1.73205i	0.288675	−	0.500000i
$13$	−1.00000			−0.277350			−0.138675	−	0.990338i	$-0.544284\pi$
$13$	−1.00000			−0.277350			−0.138675	+	0.990338i	$0.544284\pi$
$14$		0			0
$15$	−2.00000			−0.516398
$16$	2.00000	−	3.46410i	0.500000	−	0.866025i
$17$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$17$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$18$	−1.00000	−	1.73205i	−0.235702	−	0.408248i
$19$	0.500000	−	0.866025i	0.114708	−	0.198680i	−0.802955	−	0.596040i	$-0.796740\pi$
$19$	0.500000	−	0.866025i	0.114708	−	0.198680i	0.917663	+	0.397360i	$0.130073\pi$
$20$	4.00000			0.894427
$21$		0			0
$22$	−4.00000			−0.852803
$23$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$23$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$24$		0			0
$25$	0.500000	+	0.866025i	0.100000	+	0.173205i
$26$	1.00000	−	1.73205i	0.196116	−	0.339683i
$27$	−1.00000			−0.192450
$28$		0			0
$29$	4.00000			0.742781			0.371391	−	0.928477i	$-0.378881\pi$
$29$	4.00000			0.742781			0.371391	+	0.928477i	$0.378881\pi$
$30$	2.00000	−	3.46410i	0.365148	−	0.632456i
$31$	4.50000	+	7.79423i	0.808224	+	1.39988i	0.914093	+	0.405505i	$0.132904\pi$
$31$	4.50000	+	7.79423i	0.808224	+	1.39988i	−0.105869	+	0.994380i	$0.533762\pi$
$32$	4.00000	+	6.92820i	0.707107	+	1.22474i
$33$	−1.00000	+	1.73205i	−0.174078	+	0.301511i
$34$		0			0
$35$		0			0
$36$	2.00000			0.333333
$37$	−1.50000	+	2.59808i	−0.246598	+	0.427121i	−0.962580	−	0.270998i	$-0.912646\pi$
$37$	−1.50000	+	2.59808i	−0.246598	+	0.427121i	0.715981	+	0.698119i	$0.245980\pi$
$38$	1.00000	+	1.73205i	0.162221	+	0.280976i
$39$	−0.500000	−	0.866025i	−0.0800641	−	0.138675i
$40$		0			0
$41$	10.0000			1.56174			0.780869	−	0.624695i	$-0.214777\pi$
$41$	10.0000			1.56174			0.780869	+	0.624695i	$0.214777\pi$
$42$		0			0
$43$	5.00000			0.762493			0.381246	−	0.924473i	$-0.375495\pi$
$43$	5.00000			0.762493			0.381246	+	0.924473i	$0.375495\pi$
$44$	2.00000	−	3.46410i	0.301511	−	0.522233i
$45$	−1.00000	−	1.73205i	−0.149071	−	0.258199i
$46$		0			0
$47$	−3.00000	+	5.19615i	−0.437595	+	0.757937i	−0.997503	−	0.0706177i	$-0.977503\pi$
$47$	−3.00000	+	5.19615i	−0.437595	+	0.757937i	0.559908	+	0.828554i	$0.310836\pi$
$48$	4.00000			0.577350
$49$		0			0
$50$	−2.00000			−0.282843
$51$		0			0
$52$	1.00000	+	1.73205i	0.138675	+	0.240192i
$53$	−6.00000	−	10.3923i	−0.824163	−	1.42749i	−0.902557	−	0.430570i	$-0.858312\pi$
$53$	−6.00000	−	10.3923i	−0.824163	−	1.42749i	0.0783936	−	0.996922i	$-0.475021\pi$
$54$	1.00000	−	1.73205i	0.136083	−	0.235702i
$55$	−4.00000			−0.539360
$56$		0			0
$57$	1.00000			0.132453
$58$	−4.00000	+	6.92820i	−0.525226	+	0.909718i
$59$	−6.00000	−	10.3923i	−0.781133	−	1.35296i	−0.931282	−	0.364299i	$-0.881308\pi$
$59$	−6.00000	−	10.3923i	−0.781133	−	1.35296i	0.150148	−	0.988663i	$-0.452025\pi$
$60$	2.00000	+	3.46410i	0.258199	+	0.447214i
$61$	5.00000	−	8.66025i	0.640184	−	1.10883i	−0.345207	−	0.938527i	$-0.612191\pi$
$61$	5.00000	−	8.66025i	0.640184	−	1.10883i	0.985391	−	0.170305i	$-0.0544754\pi$
$62$	−18.0000			−2.28600
$63$		0			0
$64$	−8.00000			−1.00000
$65$	1.00000	−	1.73205i	0.124035	−	0.214834i
$66$	−2.00000	−	3.46410i	−0.246183	−	0.426401i
$67$	2.50000	+	4.33013i	0.305424	+	0.529009i	0.977356	−	0.211604i	$-0.0678686\pi$
$67$	2.50000	+	4.33013i	0.305424	+	0.529009i	−0.671932	+	0.740613i	$0.734535\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−6.00000			−0.712069			−0.356034	−	0.934473i	$-0.615871\pi$
$71$	−6.00000			−0.712069			−0.356034	+	0.934473i	$0.615871\pi$
$72$		0			0
$73$	−1.50000	−	2.59808i	−0.175562	−	0.304082i	0.764794	−	0.644275i	$-0.222841\pi$
$73$	−1.50000	−	2.59808i	−0.175562	−	0.304082i	−0.940356	+	0.340193i	$0.889507\pi$
$74$	−3.00000	−	5.19615i	−0.348743	−	0.604040i
$75$	−0.500000	+	0.866025i	−0.0577350	+	0.100000i
$76$	−2.00000			−0.229416
$77$		0			0
$78$	2.00000			0.226455
$79$	0.500000	−	0.866025i	0.0562544	−	0.0974355i	−0.836527	−	0.547926i	$-0.815418\pi$
$79$	0.500000	−	0.866025i	0.0562544	−	0.0974355i	0.892781	+	0.450490i	$0.148751\pi$
$80$	4.00000	+	6.92820i	0.447214	+	0.774597i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	−10.0000	+	17.3205i	−1.10432	+	1.91273i
$83$	−6.00000			−0.658586			−0.329293	−	0.944228i	$-0.606810\pi$
$83$	−6.00000			−0.658586			−0.329293	+	0.944228i	$0.606810\pi$
$84$		0			0
$85$		0			0
$86$	−5.00000	+	8.66025i	−0.539164	+	0.933859i
$87$	2.00000	+	3.46410i	0.214423	+	0.371391i
$88$		0			0
$89$	8.00000	−	13.8564i	0.847998	−	1.46878i	−0.0349934	−	0.999388i	$-0.511141\pi$
$89$	8.00000	−	13.8564i	0.847998	−	1.46878i	0.882992	−	0.469389i	$-0.155526\pi$
$90$	4.00000			0.421637
$91$		0			0
$92$		0			0
$93$	−4.50000	+	7.79423i	−0.466628	+	0.808224i
$94$	−6.00000	−	10.3923i	−0.618853	−	1.07188i
$95$	1.00000	+	1.73205i	0.102598	+	0.177705i
$96$	−4.00000	+	6.92820i	−0.408248	+	0.707107i
$97$	6.00000			0.609208			0.304604	−	0.952479i	$-0.401476\pi$
$97$	6.00000			0.609208			0.304604	+	0.952479i	$0.401476\pi$
$98$		0			0
$99$	−2.00000			−0.201008
$100$	1.00000	−	1.73205i	0.100000	−	0.173205i
$101$	1.00000	+	1.73205i	0.0995037	+	0.172345i	0.911479	−	0.411346i	$-0.134941\pi$
$101$	1.00000	+	1.73205i	0.0995037	+	0.172345i	−0.811976	+	0.583691i	$0.801608\pi$
$102$		0			0
$103$	−3.50000	+	6.06218i	−0.344865	+	0.597324i	−0.985329	−	0.170664i	$-0.945409\pi$
$103$	−3.50000	+	6.06218i	−0.344865	+	0.597324i	0.640464	+	0.767988i	$0.278742\pi$
$104$		0			0
$105$		0			0
$106$	24.0000			2.33109
$107$	4.00000	−	6.92820i	0.386695	−	0.669775i	−0.605308	−	0.795991i	$-0.706950\pi$
$107$	4.00000	−	6.92820i	0.386695	−	0.669775i	0.992003	+	0.126217i	$0.0402834\pi$
$108$	1.00000	+	1.73205i	0.0962250	+	0.166667i
$109$	−4.50000	−	7.79423i	−0.431022	−	0.746552i	0.565940	−	0.824447i	$-0.308513\pi$
$109$	−4.50000	−	7.79423i	−0.431022	−	0.746552i	−0.996962	+	0.0778949i	$0.975180\pi$
$110$	4.00000	−	6.92820i	0.381385	−	0.660578i
$111$	−3.00000			−0.284747
$112$		0			0
$113$	10.0000			0.940721			0.470360	−	0.882474i	$-0.344124\pi$
$113$	10.0000			0.940721			0.470360	+	0.882474i	$0.344124\pi$
$114$	−1.00000	+	1.73205i	−0.0936586	+	0.162221i
$115$		0			0
$116$	−4.00000	−	6.92820i	−0.371391	−	0.643268i
$117$	0.500000	−	0.866025i	0.0462250	−	0.0800641i
$118$	24.0000			2.20938
$119$		0			0
$120$		0			0
$121$	3.50000	−	6.06218i	0.318182	−	0.551107i
$122$	10.0000	+	17.3205i	0.905357	+	1.56813i
$123$	5.00000	+	8.66025i	0.450835	+	0.780869i
$124$	9.00000	−	15.5885i	0.808224	−	1.39988i
$125$	−12.0000			−1.07331
$126$		0			0
$127$	−15.0000			−1.33103			−0.665517	−	0.746382i	$-0.731789\pi$
$127$	−15.0000			−1.33103			−0.665517	+	0.746382i	$0.731789\pi$
$128$		0			0
$129$	2.50000	+	4.33013i	0.220113	+	0.381246i
$130$	2.00000	+	3.46410i	0.175412	+	0.303822i
$131$	−7.00000	+	12.1244i	−0.611593	+	1.05931i	0.379379	+	0.925241i	$0.376138\pi$
$131$	−7.00000	+	12.1244i	−0.611593	+	1.05931i	−0.990972	+	0.134069i	$0.957196\pi$
$132$	4.00000			0.348155
$133$		0			0
$134$	−10.0000			−0.863868
$135$	1.00000	−	1.73205i	0.0860663	−	0.149071i
$136$		0			0
$137$	6.00000	+	10.3923i	0.512615	+	0.887875i	0.999893	+	0.0146279i	$0.00465636\pi$
$137$	6.00000	+	10.3923i	0.512615	+	0.887875i	−0.487278	+	0.873247i	$0.662010\pi$
$138$		0			0
$139$	3.00000			0.254457			0.127228	−	0.991873i	$-0.459392\pi$
$139$	3.00000			0.254457			0.127228	+	0.991873i	$0.459392\pi$
$140$		0			0
$141$	−6.00000			−0.505291
$142$	6.00000	−	10.3923i	0.503509	−	0.872103i
$143$	−1.00000	−	1.73205i	−0.0836242	−	0.144841i
$144$	2.00000	+	3.46410i	0.166667	+	0.288675i
$145$	−4.00000	+	6.92820i	−0.332182	+	0.575356i
$146$	6.00000			0.496564
$147$		0			0
$148$	6.00000			0.493197
$149$	6.00000	−	10.3923i	0.491539	−	0.851371i	−0.508413	−	0.861113i	$-0.669768\pi$
$149$	6.00000	−	10.3923i	0.491539	−	0.851371i	0.999953	+	0.00974235i	$0.00310113\pi$
$150$	−1.00000	−	1.73205i	−0.0816497	−	0.141421i
$151$	8.00000	+	13.8564i	0.651031	+	1.12762i	0.982873	+	0.184284i	$0.0589965\pi$
$151$	8.00000	+	13.8564i	0.651031	+	1.12762i	−0.331842	+	0.943335i	$0.607670\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−18.0000			−1.44579
$156$	−1.00000	+	1.73205i	−0.0800641	+	0.138675i
$157$	−7.00000	−	12.1244i	−0.558661	−	0.967629i	−0.997609	−	0.0691164i	$-0.977982\pi$
$157$	−7.00000	−	12.1244i	−0.558661	−	0.967629i	0.438948	−	0.898513i	$-0.355351\pi$
$158$	1.00000	+	1.73205i	0.0795557	+	0.137795i
$159$	6.00000	−	10.3923i	0.475831	−	0.824163i
$160$	−16.0000			−1.26491
$161$		0			0
$162$	2.00000			0.157135
$163$	−2.00000	+	3.46410i	−0.156652	+	0.271329i	−0.933659	−	0.358162i	$-0.883403\pi$
$163$	−2.00000	+	3.46410i	−0.156652	+	0.271329i	0.777007	+	0.629492i	$0.216737\pi$
$164$	−10.0000	−	17.3205i	−0.780869	−	1.35250i
$165$	−2.00000	−	3.46410i	−0.155700	−	0.269680i
$166$	6.00000	−	10.3923i	0.465690	−	0.806599i
$167$	14.0000			1.08335			0.541676	−	0.840587i	$-0.317790\pi$
$167$	14.0000			1.08335			0.541676	+	0.840587i	$0.317790\pi$
$168$		0			0
$169$	−12.0000			−0.923077
$170$		0			0
$171$	0.500000	+	0.866025i	0.0382360	+	0.0662266i
$172$	−5.00000	−	8.66025i	−0.381246	−	0.660338i
$173$	4.00000	−	6.92820i	0.304114	−	0.526742i	−0.672949	−	0.739689i	$-0.734973\pi$
$173$	4.00000	−	6.92820i	0.304114	−	0.526742i	0.977064	+	0.212947i	$0.0683062\pi$
$174$	−8.00000			−0.606478
$175$		0			0
$176$	8.00000			0.603023
$177$	6.00000	−	10.3923i	0.450988	−	0.781133i
$178$	16.0000	+	27.7128i	1.19925	+	2.07716i
$179$	−1.00000	−	1.73205i	−0.0747435	−	0.129460i	0.826231	−	0.563331i	$-0.190480\pi$
$179$	−1.00000	−	1.73205i	−0.0747435	−	0.129460i	−0.900975	+	0.433872i	$0.857147\pi$
$180$	−2.00000	+	3.46410i	−0.149071	+	0.258199i
$181$	−13.0000			−0.966282			−0.483141	−	0.875542i	$-0.660504\pi$
$181$	−13.0000			−0.966282			−0.483141	+	0.875542i	$0.660504\pi$
$182$		0			0
$183$	10.0000			0.739221
$184$		0			0
$185$	−3.00000	−	5.19615i	−0.220564	−	0.382029i
$186$	−9.00000	−	15.5885i	−0.659912	−	1.14300i
$187$		0			0
$188$	12.0000			0.875190
$189$		0			0
$190$	−4.00000			−0.290191
$191$	−5.00000	+	8.66025i	−0.361787	+	0.626634i	−0.988255	−	0.152813i	$-0.951167\pi$
$191$	−5.00000	+	8.66025i	−0.361787	+	0.626634i	0.626468	+	0.779447i	$0.284500\pi$
$192$	−4.00000	−	6.92820i	−0.288675	−	0.500000i
$193$	−5.50000	−	9.52628i	−0.395899	−	0.685717i	0.597317	−	0.802005i	$-0.296234\pi$
$193$	−5.50000	−	9.52628i	−0.395899	−	0.685717i	−0.993215	+	0.116289i	$0.962900\pi$
$194$	−6.00000	+	10.3923i	−0.430775	+	0.746124i
$195$	2.00000			0.143223
$196$		0			0
$197$	16.0000			1.13995			0.569976	−	0.821661i	$-0.306952\pi$
$197$	16.0000			1.13995			0.569976	+	0.821661i	$0.306952\pi$
$198$	2.00000	−	3.46410i	0.142134	−	0.246183i
$199$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$199$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$200$		0			0
$201$	−2.50000	+	4.33013i	−0.176336	+	0.305424i
$202$	−4.00000			−0.281439
$203$		0			0
$204$		0			0
$205$	−10.0000	+	17.3205i	−0.698430	+	1.20972i
$206$	−7.00000	−	12.1244i	−0.487713	−	0.844744i
$207$		0			0
$208$	−2.00000	+	3.46410i	−0.138675	+	0.240192i
$209$	2.00000			0.138343
$210$		0			0
$211$	4.00000			0.275371			0.137686	−	0.990476i	$-0.456034\pi$
$211$	4.00000			0.275371			0.137686	+	0.990476i	$0.456034\pi$
$212$	−12.0000	+	20.7846i	−0.824163	+	1.42749i
$213$	−3.00000	−	5.19615i	−0.205557	−	0.356034i
$214$	8.00000	+	13.8564i	0.546869	+	0.947204i
$215$	−5.00000	+	8.66025i	−0.340997	+	0.590624i
$216$		0			0
$217$		0			0
$218$	18.0000			1.21911
$219$	1.50000	−	2.59808i	0.101361	−	0.175562i
$220$	4.00000	+	6.92820i	0.269680	+	0.467099i
$221$		0			0
$222$	3.00000	−	5.19615i	0.201347	−	0.348743i
$223$	−16.0000			−1.07144			−0.535720	−	0.844396i	$-0.679960\pi$
$223$	−16.0000			−1.07144			−0.535720	+	0.844396i	$0.679960\pi$
$224$		0			0
$225$	−1.00000			−0.0666667
$226$	−10.0000	+	17.3205i	−0.665190	+	1.15214i
$227$	9.00000	+	15.5885i	0.597351	+	1.03464i	0.993210	+	0.116331i	$0.0371134\pi$
$227$	9.00000	+	15.5885i	0.597351	+	1.03464i	−0.395860	+	0.918311i	$0.629553\pi$
$228$	−1.00000	−	1.73205i	−0.0662266	−	0.114708i
$229$	−9.50000	+	16.4545i	−0.627778	+	1.08734i	0.360219	+	0.932868i	$0.382702\pi$
$229$	−9.50000	+	16.4545i	−0.627778	+	1.08734i	−0.987997	+	0.154475i	$0.950631\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−3.00000	+	5.19615i	−0.196537	+	0.340411i	−0.947403	−	0.320043i	$-0.896303\pi$
$233$	−3.00000	+	5.19615i	−0.196537	+	0.340411i	0.750867	+	0.660454i	$0.229636\pi$
$234$	1.00000	+	1.73205i	0.0653720	+	0.113228i
$235$	−6.00000	−	10.3923i	−0.391397	−	0.677919i
$236$	−12.0000	+	20.7846i	−0.781133	+	1.35296i
$237$	1.00000			0.0649570
$238$		0			0
$239$	6.00000			0.388108			0.194054	−	0.980991i	$-0.437836\pi$
$239$	6.00000			0.388108			0.194054	+	0.980991i	$0.437836\pi$
$240$	−4.00000	+	6.92820i	−0.258199	+	0.447214i
$241$	7.00000	+	12.1244i	0.450910	+	0.780998i	0.998443	−	0.0557856i	$-0.0177663\pi$
$241$	7.00000	+	12.1244i	0.450910	+	0.780998i	−0.547533	+	0.836784i	$0.684433\pi$
$242$	7.00000	+	12.1244i	0.449977	+	0.779383i
$243$	0.500000	−	0.866025i	0.0320750	−	0.0555556i
$244$	−20.0000			−1.28037
$245$		0			0
$246$	−20.0000			−1.27515
$247$	−0.500000	+	0.866025i	−0.0318142	+	0.0551039i
$248$		0			0
$249$	−3.00000	−	5.19615i	−0.190117	−	0.329293i
$250$	12.0000	−	20.7846i	0.758947	−	1.31453i
$251$	8.00000			0.504956			0.252478	−	0.967603i	$-0.418755\pi$
$251$	8.00000			0.504956			0.252478	+	0.967603i	$0.418755\pi$
$252$		0			0
$253$		0			0
$254$	15.0000	−	25.9808i	0.941184	−	1.63018i
$255$		0			0
$256$	−8.00000	−	13.8564i	−0.500000	−	0.866025i
$257$	13.0000	−	22.5167i	0.810918	−	1.40455i	−0.101305	−	0.994855i	$-0.532302\pi$
$257$	13.0000	−	22.5167i	0.810918	−	1.40455i	0.912222	−	0.409695i	$-0.134365\pi$
$258$	−10.0000			−0.622573
$259$		0			0
$260$	−4.00000			−0.248069
$261$	−2.00000	+	3.46410i	−0.123797	+	0.214423i
$262$	−14.0000	−	24.2487i	−0.864923	−	1.49809i
$263$	−2.00000	−	3.46410i	−0.123325	−	0.213606i	0.797752	−	0.602986i	$-0.206023\pi$
$263$	−2.00000	−	3.46410i	−0.123325	−	0.213606i	−0.921077	+	0.389380i	$0.872689\pi$
$264$		0			0
$265$	24.0000			1.47431
$266$		0			0
$267$	16.0000			0.979184
$268$	5.00000	−	8.66025i	0.305424	−	0.529009i
$269$	3.00000	+	5.19615i	0.182913	+	0.316815i	0.942871	−	0.333157i	$-0.108114\pi$
$269$	3.00000	+	5.19615i	0.182913	+	0.316815i	−0.759958	+	0.649972i	$0.774781\pi$
$270$	2.00000	+	3.46410i	0.121716	+	0.210819i
$271$	8.00000	−	13.8564i	0.485965	−	0.841717i	−0.513905	−	0.857847i	$-0.671801\pi$
$271$	8.00000	−	13.8564i	0.485965	−	0.841717i	0.999870	+	0.0161307i	$0.00513477\pi$
$272$		0			0
$273$		0			0
$274$	−24.0000			−1.44989
$275$	−1.00000	+	1.73205i	−0.0603023	+	0.104447i
$276$		0			0
$277$	−6.50000	−	11.2583i	−0.390547	−	0.676448i	0.601975	−	0.798515i	$-0.294381\pi$
$277$	−6.50000	−	11.2583i	−0.390547	−	0.676448i	−0.992522	+	0.122068i	$0.961047\pi$
$278$	−3.00000	+	5.19615i	−0.179928	+	0.311645i
$279$	−9.00000			−0.538816
$280$		0			0
$281$	−4.00000			−0.238620			−0.119310	−	0.992857i	$-0.538068\pi$
$281$	−4.00000			−0.238620			−0.119310	+	0.992857i	$0.538068\pi$
$282$	6.00000	−	10.3923i	0.357295	−	0.618853i
$283$	−5.50000	−	9.52628i	−0.326941	−	0.566279i	0.654962	−	0.755662i	$-0.272685\pi$
$283$	−5.50000	−	9.52628i	−0.326941	−	0.566279i	−0.981903	+	0.189383i	$0.939351\pi$
$284$	6.00000	+	10.3923i	0.356034	+	0.616670i
$285$	−1.00000	+	1.73205i	−0.0592349	+	0.102598i
$286$	4.00000			0.236525
$287$		0			0
$288$	−8.00000			−0.471405
$289$	8.50000	−	14.7224i	0.500000	−	0.866025i
$290$	−8.00000	−	13.8564i	−0.469776	−	0.813676i
$291$	3.00000	+	5.19615i	0.175863	+	0.304604i
$292$	−3.00000	+	5.19615i	−0.175562	+	0.304082i
$293$	−8.00000			−0.467365			−0.233682	−	0.972313i	$-0.575078\pi$
$293$	−8.00000			−0.467365			−0.233682	+	0.972313i	$0.575078\pi$
$294$		0			0
$295$	24.0000			1.39733
$296$		0			0
$297$	−1.00000	−	1.73205i	−0.0580259	−	0.100504i
$298$	12.0000	+	20.7846i	0.695141	+	1.20402i
$299$		0			0
$300$	2.00000			0.115470
$301$		0			0
$302$	−32.0000			−1.84139
$303$	−1.00000	+	1.73205i	−0.0574485	+	0.0995037i
$304$	−2.00000	−	3.46410i	−0.114708	−	0.198680i
$305$	10.0000	+	17.3205i	0.572598	+	0.991769i
$306$		0			0
$307$	17.0000			0.970241			0.485121	−	0.874447i	$-0.338776\pi$
$307$	17.0000			0.970241			0.485121	+	0.874447i	$0.338776\pi$
$308$		0			0
$309$	−7.00000			−0.398216
$310$	18.0000	−	31.1769i	1.02233	−	1.77073i
$311$	−3.00000	−	5.19615i	−0.170114	−	0.294647i	0.768345	−	0.640036i	$-0.221080\pi$
$311$	−3.00000	−	5.19615i	−0.170114	−	0.294647i	−0.938460	+	0.345389i	$0.887747\pi$
$312$		0			0
$313$	−0.500000	+	0.866025i	−0.0282617	+	0.0489506i	−0.879810	−	0.475325i	$-0.842331\pi$
$313$	−0.500000	+	0.866025i	−0.0282617	+	0.0489506i	0.851549	+	0.524276i	$0.175664\pi$
$314$	28.0000			1.58013
$315$		0			0
$316$	−2.00000			−0.112509
$317$	−12.0000	+	20.7846i	−0.673987	+	1.16738i	0.302777	+	0.953062i	$0.402086\pi$
$317$	−12.0000	+	20.7846i	−0.673987	+	1.16738i	−0.976764	+	0.214318i	$0.931247\pi$
$318$	12.0000	+	20.7846i	0.672927	+	1.16554i
$319$	4.00000	+	6.92820i	0.223957	+	0.387905i
$320$	8.00000	−	13.8564i	0.447214	−	0.774597i
$321$	8.00000			0.446516
$322$		0			0
$323$		0			0
$324$	−1.00000	+	1.73205i	−0.0555556	+	0.0962250i
$325$	−0.500000	−	0.866025i	−0.0277350	−	0.0480384i
$326$	−4.00000	−	6.92820i	−0.221540	−	0.383718i
$327$	4.50000	−	7.79423i	0.248851	−	0.431022i
$328$		0			0
$329$		0			0
$330$	8.00000			0.440386
$331$	12.5000	−	21.6506i	0.687062	−	1.19003i	−0.285722	−	0.958313i	$-0.592233\pi$
$331$	12.5000	−	21.6506i	0.687062	−	1.19003i	0.972784	−	0.231714i	$-0.0744333\pi$
$332$	6.00000	+	10.3923i	0.329293	+	0.570352i
$333$	−1.50000	−	2.59808i	−0.0821995	−	0.142374i
$334$	−14.0000	+	24.2487i	−0.766046	+	1.32683i
$335$	−10.0000			−0.546358
$336$		0			0
$337$	13.0000			0.708155			0.354078	−	0.935216i	$-0.384795\pi$
$337$	13.0000			0.708155			0.354078	+	0.935216i	$0.384795\pi$
$338$	12.0000	−	20.7846i	0.652714	−	1.13053i
$339$	5.00000	+	8.66025i	0.271563	+	0.470360i
$340$		0			0
$341$	−9.00000	+	15.5885i	−0.487377	+	0.844162i
$342$	−2.00000			−0.108148
$343$		0			0
$344$		0			0
$345$		0			0
$346$	8.00000	+	13.8564i	0.430083	+	0.744925i
$347$	−16.0000	−	27.7128i	−0.858925	−	1.48770i	−0.872955	−	0.487800i	$-0.837799\pi$
$347$	−16.0000	−	27.7128i	−0.858925	−	1.48770i	0.0140303	−	0.999902i	$-0.495534\pi$
$348$	4.00000	−	6.92820i	0.214423	−	0.371391i
$349$	14.0000			0.749403			0.374701	−	0.927146i	$-0.377745\pi$
$349$	14.0000			0.749403			0.374701	+	0.927146i	$0.377745\pi$
$350$		0			0
$351$	1.00000			0.0533761
$352$	−8.00000	+	13.8564i	−0.426401	+	0.738549i
$353$	17.0000	+	29.4449i	0.904819	+	1.56719i	0.821160	+	0.570697i	$0.193327\pi$
$353$	17.0000	+	29.4449i	0.904819	+	1.56719i	0.0836583	+	0.996495i	$0.473340\pi$
$354$	12.0000	+	20.7846i	0.637793	+	1.10469i
$355$	6.00000	−	10.3923i	0.318447	−	0.551566i
$356$	−32.0000			−1.69600
$357$		0			0
$358$	4.00000			0.211407
$359$	−10.0000	+	17.3205i	−0.527780	+	0.914141i	0.471696	+	0.881761i	$0.343642\pi$
$359$	−10.0000	+	17.3205i	−0.527780	+	0.914141i	−0.999476	+	0.0323801i	$0.989691\pi$
$360$		0			0
$361$	9.00000	+	15.5885i	0.473684	+	0.820445i
$362$	13.0000	−	22.5167i	0.683265	−	1.18345i
$363$	7.00000			0.367405
$364$		0			0
$365$	6.00000			0.314054
$366$	−10.0000	+	17.3205i	−0.522708	+	0.905357i
$367$	−4.50000	−	7.79423i	−0.234898	−	0.406855i	0.724345	−	0.689438i	$-0.242142\pi$
$367$	−4.50000	−	7.79423i	−0.234898	−	0.406855i	−0.959243	+	0.282582i	$0.908809\pi$
$368$		0			0
$369$	−5.00000	+	8.66025i	−0.260290	+	0.450835i
$370$	12.0000			0.623850
$371$		0			0
$372$	18.0000			0.933257
$373$	−11.5000	+	19.9186i	−0.595447	+	1.03135i	0.398036	+	0.917370i	$0.369692\pi$
$373$	−11.5000	+	19.9186i	−0.595447	+	1.03135i	−0.993484	+	0.113975i	$0.963641\pi$
$374$		0			0
$375$	−6.00000	−	10.3923i	−0.309839	−	0.536656i
$376$		0			0
$377$	−4.00000			−0.206010
$378$		0			0
$379$	3.00000			0.154100			0.0770498	−	0.997027i	$-0.475450\pi$
$379$	3.00000			0.154100			0.0770498	+	0.997027i	$0.475450\pi$
$380$	2.00000	−	3.46410i	0.102598	−	0.177705i
$381$	−7.50000	−	12.9904i	−0.384237	−	0.665517i
$382$	−10.0000	−	17.3205i	−0.511645	−	0.886194i
$383$	−6.00000	+	10.3923i	−0.306586	+	0.531022i	−0.977613	−	0.210411i	$-0.932520\pi$
$383$	−6.00000	+	10.3923i	−0.306586	+	0.531022i	0.671027	+	0.741433i	$0.265853\pi$
$384$		0			0
$385$		0			0
$386$	22.0000			1.11977
$387$	−2.50000	+	4.33013i	−0.127082	+	0.220113i
$388$	−6.00000	−	10.3923i	−0.304604	−	0.527589i
$389$	3.00000	+	5.19615i	0.152106	+	0.263455i	0.932002	−	0.362454i	$-0.118061\pi$
$389$	3.00000	+	5.19615i	0.152106	+	0.263455i	−0.779895	+	0.625910i	$0.784728\pi$
$390$	−2.00000	+	3.46410i	−0.101274	+	0.175412i
$391$		0			0
$392$		0			0
$393$	−14.0000			−0.706207
$394$	−16.0000	+	27.7128i	−0.806068	+	1.39615i
$395$	1.00000	+	1.73205i	0.0503155	+	0.0871489i
$396$	2.00000	+	3.46410i	0.100504	+	0.174078i
$397$	−4.50000	+	7.79423i	−0.225849	+	0.391181i	−0.956574	−	0.291491i	$-0.905849\pi$
$397$	−4.50000	+	7.79423i	−0.225849	+	0.391181i	0.730725	+	0.682672i	$0.239182\pi$
$398$		0			0
$399$		0			0
$400$	4.00000			0.200000
$401$	18.0000	−	31.1769i	0.898877	−	1.55690i	0.0699455	−	0.997551i	$-0.477717\pi$
$401$	18.0000	−	31.1769i	0.898877	−	1.55690i	0.828932	−	0.559350i	$-0.188949\pi$
$402$	−5.00000	−	8.66025i	−0.249377	−	0.431934i
$403$	−4.50000	−	7.79423i	−0.224161	−	0.388258i
$404$	2.00000	−	3.46410i	0.0995037	−	0.172345i
$405$	2.00000			0.0993808
$406$		0			0
$407$	−6.00000			−0.297409
$408$		0			0
$409$	2.50000	+	4.33013i	0.123617	+	0.214111i	0.921192	−	0.389109i	$-0.127217\pi$
$409$	2.50000	+	4.33013i	0.123617	+	0.214111i	−0.797574	+	0.603220i	$0.793884\pi$
$410$	−20.0000	−	34.6410i	−0.987730	−	1.71080i
$411$	−6.00000	+	10.3923i	−0.295958	+	0.512615i
$412$	14.0000			0.689730
$413$		0			0
$414$		0			0
$415$	6.00000	−	10.3923i	0.294528	−	0.510138i
$416$	−4.00000	−	6.92820i	−0.196116	−	0.339683i
$417$	1.50000	+	2.59808i	0.0734553	+	0.127228i
$418$	−2.00000	+	3.46410i	−0.0978232	+	0.169435i
$419$	−30.0000			−1.46560			−0.732798	−	0.680446i	$-0.761786\pi$
$419$	−30.0000			−1.46560			−0.732798	+	0.680446i	$0.761786\pi$
$420$		0			0
$421$	−7.00000			−0.341159			−0.170580	−	0.985344i	$-0.554564\pi$
$421$	−7.00000			−0.341159			−0.170580	+	0.985344i	$0.554564\pi$
$422$	−4.00000	+	6.92820i	−0.194717	+	0.337260i
$423$	−3.00000	−	5.19615i	−0.145865	−	0.252646i
$424$		0			0
$425$		0			0
$426$	12.0000			0.581402
$427$		0			0
$428$	−16.0000			−0.773389
$429$	1.00000	−	1.73205i	0.0482805	−	0.0836242i
$430$	−10.0000	−	17.3205i	−0.482243	−	0.835269i
$431$	9.00000	+	15.5885i	0.433515	+	0.750870i	0.997173	−	0.0751385i	$-0.0239399\pi$
$431$	9.00000	+	15.5885i	0.433515	+	0.750870i	−0.563658	+	0.826008i	$0.690607\pi$
$432$	−2.00000	+	3.46410i	−0.0962250	+	0.166667i
$433$	−31.0000			−1.48976			−0.744882	−	0.667196i	$-0.767494\pi$
$433$	−31.0000			−1.48976			−0.744882	+	0.667196i	$0.767494\pi$
$434$		0			0
$435$	−8.00000			−0.383571
$436$	−9.00000	+	15.5885i	−0.431022	+	0.746552i
$437$		0			0
$438$	3.00000	+	5.19615i	0.143346	+	0.248282i
$439$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$439$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−6.00000	+	10.3923i	−0.285069	+	0.493753i	−0.972626	−	0.232377i	$-0.925350\pi$
$443$	−6.00000	+	10.3923i	−0.285069	+	0.493753i	0.687557	+	0.726130i	$0.258683\pi$
$444$	3.00000	+	5.19615i	0.142374	+	0.246598i
$445$	16.0000	+	27.7128i	0.758473	+	1.31371i
$446$	16.0000	−	27.7128i	0.757622	−	1.31224i
$447$	12.0000			0.567581
$448$		0			0
$449$	−18.0000			−0.849473			−0.424736	−	0.905317i	$-0.639633\pi$
$449$	−18.0000			−0.849473			−0.424736	+	0.905317i	$0.639633\pi$
$450$	1.00000	−	1.73205i	0.0471405	−	0.0816497i
$451$	10.0000	+	17.3205i	0.470882	+	0.815591i
$452$	−10.0000	−	17.3205i	−0.470360	−	0.814688i
$453$	−8.00000	+	13.8564i	−0.375873	+	0.651031i
$454$	−36.0000			−1.68956
$455$		0			0
$456$		0			0
$457$	5.50000	−	9.52628i	0.257279	−	0.445621i	−0.708233	−	0.705979i	$-0.750507\pi$
$457$	5.50000	−	9.52628i	0.257279	−	0.445621i	0.965512	+	0.260358i	$0.0838407\pi$
$458$	−19.0000	−	32.9090i	−0.887812	−	1.53773i
$459$		0			0
$460$		0			0
$461$	−20.0000			−0.931493			−0.465746	−	0.884918i	$-0.654214\pi$
$461$	−20.0000			−0.931493			−0.465746	+	0.884918i	$0.654214\pi$
$462$		0			0
$463$	−17.0000			−0.790057			−0.395029	−	0.918669i	$-0.629265\pi$
$463$	−17.0000			−0.790057			−0.395029	+	0.918669i	$0.629265\pi$
$464$	8.00000	−	13.8564i	0.371391	−	0.643268i
$465$	−9.00000	−	15.5885i	−0.417365	−	0.722897i
$466$	−6.00000	−	10.3923i	−0.277945	−	0.481414i
$467$	3.00000	−	5.19615i	0.138823	−	0.240449i	−0.788228	−	0.615383i	$-0.789001\pi$
$467$	3.00000	−	5.19615i	0.138823	−	0.240449i	0.927052	+	0.374934i	$0.122335\pi$
$468$	−2.00000			−0.0924500
$469$		0			0
$470$	24.0000			1.10704
$471$	7.00000	−	12.1244i	0.322543	−	0.558661i
$472$		0			0
$473$	5.00000	+	8.66025i	0.229900	+	0.398199i
$474$	−1.00000	+	1.73205i	−0.0459315	+	0.0795557i
$475$	1.00000			0.0458831
$476$		0			0
$477$	12.0000			0.549442
$478$	−6.00000	+	10.3923i	−0.274434	+	0.475333i
$479$	−14.0000	−	24.2487i	−0.639676	−	1.10795i	−0.985504	−	0.169654i	$-0.945735\pi$
$479$	−14.0000	−	24.2487i	−0.639676	−	1.10795i	0.345827	−	0.938298i	$-0.387598\pi$
$480$	−8.00000	−	13.8564i	−0.365148	−	0.632456i
$481$	1.50000	−	2.59808i	0.0683941	−	0.118462i
$482$	−28.0000			−1.27537
$483$		0			0
$484$	−14.0000			−0.636364
$485$	−6.00000	+	10.3923i	−0.272446	+	0.471890i
$486$	1.00000	+	1.73205i	0.0453609	+	0.0785674i
$487$	−15.5000	−	26.8468i	−0.702372	−	1.21654i	−0.967632	−	0.252367i	$-0.918791\pi$
$487$	−15.5000	−	26.8468i	−0.702372	−	1.21654i	0.265260	−	0.964177i	$-0.414542\pi$
$488$		0			0
$489$	−4.00000			−0.180886
$490$		0			0
$491$	−28.0000			−1.26362			−0.631811	−	0.775122i	$-0.717688\pi$
$491$	−28.0000			−1.26362			−0.631811	+	0.775122i	$0.717688\pi$
$492$	10.0000	−	17.3205i	0.450835	−	0.780869i
$493$		0			0
$494$	−1.00000	−	1.73205i	−0.0449921	−	0.0779287i
$495$	2.00000	−	3.46410i	0.0898933	−	0.155700i
$496$	36.0000			1.61645
$497$		0			0
$498$	12.0000			0.537733
$499$	−18.5000	+	32.0429i	−0.828174	+	1.43444i	0.0712957	+	0.997455i	$0.477287\pi$
$499$	−18.5000	+	32.0429i	−0.828174	+	1.43444i	−0.899469	+	0.436984i	$0.856047\pi$
$500$	12.0000	+	20.7846i	0.536656	+	0.929516i
$501$	7.00000	+	12.1244i	0.312737	+	0.541676i
$502$	−8.00000	+	13.8564i	−0.357057	+	0.618442i
$503$	42.0000			1.87269			0.936344	−	0.351085i	$-0.114187\pi$
$503$	42.0000			1.87269			0.936344	+	0.351085i	$0.114187\pi$
$504$		0			0
$505$	−4.00000			−0.177998
$506$		0			0
$507$	−6.00000	−	10.3923i	−0.266469	−	0.461538i
$508$	15.0000	+	25.9808i	0.665517	+	1.15271i
$509$	1.00000	−	1.73205i	0.0443242	−	0.0767718i	−0.843012	−	0.537895i	$-0.819220\pi$
$509$	1.00000	−	1.73205i	0.0443242	−	0.0767718i	0.887336	+	0.461123i	$0.152553\pi$
$510$		0			0
$511$		0			0
$512$	32.0000			1.41421
$513$	−0.500000	+	0.866025i	−0.0220755	+	0.0382360i
$514$	26.0000	+	45.0333i	1.14681	+	1.98633i
$515$	−7.00000	−	12.1244i	−0.308457	−	0.534263i
$516$	5.00000	−	8.66025i	0.220113	−	0.381246i
$517$	−12.0000			−0.527759
$518$		0			0
$519$	8.00000			0.351161
$520$		0			0
$521$	6.00000	+	10.3923i	0.262865	+	0.455295i	0.967002	−	0.254769i	$-0.0819994\pi$
$521$	6.00000	+	10.3923i	0.262865	+	0.455295i	−0.704137	+	0.710064i	$0.748666\pi$
$522$	−4.00000	−	6.92820i	−0.175075	−	0.303239i
$523$	15.5000	−	26.8468i	0.677768	−	1.17393i	−0.297884	−	0.954602i	$-0.596281\pi$
$523$	15.5000	−	26.8468i	0.677768	−	1.17393i	0.975652	−	0.219326i	$-0.0703858\pi$
$524$	28.0000			1.22319
$525$		0			0
$526$	8.00000			0.348817
$527$		0			0
$528$	4.00000	+	6.92820i	0.174078	+	0.301511i
$529$	11.5000	+	19.9186i	0.500000	+	0.866025i
$530$	−24.0000	+	41.5692i	−1.04249	+	1.80565i
$531$	12.0000			0.520756
$532$		0			0
$533$	−10.0000			−0.433148
$534$	−16.0000	+	27.7128i	−0.692388	+	1.19925i
$535$	8.00000	+	13.8564i	0.345870	+	0.599065i
$536$		0			0
$537$	1.00000	−	1.73205i	0.0431532	−	0.0747435i
$538$	−12.0000			−0.517357
$539$		0			0
$540$	−4.00000			−0.172133
$541$	9.50000	−	16.4545i	0.408437	−	0.707433i	−0.586278	−	0.810110i	$-0.699407\pi$
$541$	9.50000	−	16.4545i	0.408437	−	0.707433i	0.994715	+	0.102677i	$0.0327407\pi$
$542$	16.0000	+	27.7128i	0.687259	+	1.19037i
$543$	−6.50000	−	11.2583i	−0.278942	−	0.483141i
$544$		0			0
$545$	18.0000			0.771035
$546$		0			0
$547$	28.0000			1.19719			0.598597	−	0.801050i	$-0.295725\pi$
$547$	28.0000			1.19719			0.598597	+	0.801050i	$0.295725\pi$
$548$	12.0000	−	20.7846i	0.512615	−	0.887875i
$549$	5.00000	+	8.66025i	0.213395	+	0.369611i
$550$	−2.00000	−	3.46410i	−0.0852803	−	0.147710i
$551$	2.00000	−	3.46410i	0.0852029	−	0.147576i
$552$		0			0
$553$		0			0
$554$	26.0000			1.10463
$555$	3.00000	−	5.19615i	0.127343	−	0.220564i
$556$	−3.00000	−	5.19615i	−0.127228	−	0.220366i
$557$	1.00000	+	1.73205i	0.0423714	+	0.0733893i	0.886433	−	0.462856i	$-0.153175\pi$
$557$	1.00000	+	1.73205i	0.0423714	+	0.0733893i	−0.844062	+	0.536246i	$0.819842\pi$
$558$	9.00000	−	15.5885i	0.381000	−	0.659912i
$559$	−5.00000			−0.211477
$560$		0			0
$561$		0			0
$562$	4.00000	−	6.92820i	0.168730	−	0.292249i
$563$	−13.0000	−	22.5167i	−0.547885	−	0.948964i	−0.998419	−	0.0562051i	$-0.982100\pi$
$563$	−13.0000	−	22.5167i	−0.547885	−	0.948964i	0.450535	−	0.892759i	$-0.351233\pi$
$564$	6.00000	+	10.3923i	0.252646	+	0.437595i
$565$	−10.0000	+	17.3205i	−0.420703	+	0.728679i
$566$	22.0000			0.924729
$567$		0			0
$568$		0			0
$569$	13.0000	−	22.5167i	0.544988	−	0.943948i	−0.453619	−	0.891196i	$-0.649867\pi$
$569$	13.0000	−	22.5167i	0.544988	−	0.943948i	0.998608	−	0.0527519i	$-0.0167993\pi$
$570$	−2.00000	−	3.46410i	−0.0837708	−	0.145095i
$571$	9.50000	+	16.4545i	0.397563	+	0.688599i	0.993425	−	0.114488i	$-0.0365228\pi$
$571$	9.50000	+	16.4545i	0.397563	+	0.688599i	−0.595862	+	0.803087i	$0.703189\pi$
$572$	−2.00000	+	3.46410i	−0.0836242	+	0.144841i
$573$	−10.0000			−0.417756
$574$		0			0
$575$		0			0
$576$	4.00000	−	6.92820i	0.166667	−	0.288675i
$577$	−8.50000	−	14.7224i	−0.353860	−	0.612903i	0.633062	−	0.774101i	$-0.281798\pi$
$577$	−8.50000	−	14.7224i	−0.353860	−	0.612903i	−0.986922	+	0.161198i	$0.948464\pi$
$578$	17.0000	+	29.4449i	0.707107	+	1.22474i
$579$	5.50000	−	9.52628i	0.228572	−	0.395899i
$580$	16.0000			0.664364
$581$		0			0
$582$	−12.0000			−0.497416
$583$	12.0000	−	20.7846i	0.496989	−	0.860811i
$584$		0			0
$585$	1.00000	+	1.73205i	0.0413449	+	0.0716115i
$586$	8.00000	−	13.8564i	0.330477	−	0.572403i
$587$	−16.0000			−0.660391			−0.330195	−	0.943913i	$-0.607115\pi$
$587$	−16.0000			−0.660391			−0.330195	+	0.943913i	$0.607115\pi$
$588$		0			0
$589$	9.00000			0.370839
$590$	−24.0000	+	41.5692i	−0.988064	+	1.71138i
$591$	8.00000	+	13.8564i	0.329076	+	0.569976i
$592$	6.00000	+	10.3923i	0.246598	+	0.427121i
$593$	−3.00000	+	5.19615i	−0.123195	+	0.213380i	−0.921026	−	0.389501i	$-0.872647\pi$
$593$	−3.00000	+	5.19615i	−0.123195	+	0.213380i	0.797831	+	0.602881i	$0.205981\pi$
$594$	4.00000			0.164122
$595$		0			0
$596$	−24.0000			−0.983078
$597$		0			0
$598$		0			0
$599$	−6.00000	−	10.3923i	−0.245153	−	0.424618i	0.717021	−	0.697051i	$-0.245505\pi$
$599$	−6.00000	−	10.3923i	−0.245153	−	0.424618i	−0.962175	+	0.272433i	$0.912172\pi$
$600$		0			0
$601$	9.00000			0.367118			0.183559	−	0.983009i	$-0.441238\pi$
$601$	9.00000			0.367118			0.183559	+	0.983009i	$0.441238\pi$
$602$		0			0
$603$	−5.00000			−0.203616
$604$	16.0000	−	27.7128i	0.651031	−	1.12762i
$605$	7.00000	+	12.1244i	0.284590	+	0.492925i
$606$	−2.00000	−	3.46410i	−0.0812444	−	0.140720i
$607$	11.5000	−	19.9186i	0.466771	−	0.808470i	−0.532509	−	0.846424i	$-0.678751\pi$
$607$	11.5000	−	19.9186i	0.466771	−	0.808470i	0.999279	+	0.0379540i	$0.0120840\pi$
$608$	8.00000			0.324443
$609$		0			0
$610$	−40.0000			−1.61955
$611$	3.00000	−	5.19615i	0.121367	−	0.210214i
$612$		0			0
$613$	−17.0000	−	29.4449i	−0.686624	−	1.18927i	−0.972924	−	0.231127i	$-0.925759\pi$
$613$	−17.0000	−	29.4449i	−0.686624	−	1.18927i	0.286300	−	0.958140i	$-0.407575\pi$
$614$	−17.0000	+	29.4449i	−0.686064	+	1.18830i
$615$	−20.0000			−0.806478
$616$		0			0
$617$	−6.00000			−0.241551			−0.120775	−	0.992680i	$-0.538538\pi$
$617$	−6.00000			−0.241551			−0.120775	+	0.992680i	$0.538538\pi$
$618$	7.00000	−	12.1244i	0.281581	−	0.487713i
$619$	−14.5000	−	25.1147i	−0.582804	−	1.00945i	−0.995145	−	0.0984169i	$-0.968622\pi$
$619$	−14.5000	−	25.1147i	−0.582804	−	1.00945i	0.412341	−	0.911030i	$-0.364711\pi$
$620$	18.0000	+	31.1769i	0.722897	+	1.25210i
$621$		0			0
$622$	12.0000			0.481156
$623$		0			0
$624$	−4.00000			−0.160128
$625$	9.50000	−	16.4545i	0.380000	−	0.658179i
$626$	−1.00000	−	1.73205i	−0.0399680	−	0.0692267i
$627$	1.00000	+	1.73205i	0.0399362	+	0.0691714i
$628$	−14.0000	+	24.2487i	−0.558661	+	0.967629i
$629$		0			0
$630$		0			0
$631$	8.00000			0.318475			0.159237	−	0.987240i	$-0.449096\pi$
$631$	8.00000			0.318475			0.159237	+	0.987240i	$0.449096\pi$
$632$		0			0
$633$	2.00000	+	3.46410i	0.0794929	+	0.137686i
$634$	−24.0000	−	41.5692i	−0.953162	−	1.65092i
$635$	15.0000	−	25.9808i	0.595257	−	1.03102i
$636$	−24.0000			−0.951662
$637$		0			0
$638$	−16.0000			−0.633446
$639$	3.00000	−	5.19615i	0.118678	−	0.205557i
$640$		0			0
$641$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$641$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$642$	−8.00000	+	13.8564i	−0.315735	+	0.546869i
$643$	19.0000			0.749287			0.374643	−	0.927169i	$-0.377765\pi$
$643$	19.0000			0.749287			0.374643	+	0.927169i	$0.377765\pi$
$644$		0			0
$645$	−10.0000			−0.393750
$646$		0			0
$647$	1.00000	+	1.73205i	0.0393141	+	0.0680939i	0.885013	−	0.465566i	$-0.154149\pi$
$647$	1.00000	+	1.73205i	0.0393141	+	0.0680939i	−0.845699	+	0.533660i	$0.820816\pi$
$648$		0			0
$649$	12.0000	−	20.7846i	0.471041	−	0.815867i
$650$	2.00000			0.0784465
$651$		0			0
$652$	8.00000			0.313304
$653$	−9.00000	+	15.5885i	−0.352197	+	0.610023i	−0.986634	−	0.162951i	$-0.947899\pi$
$653$	−9.00000	+	15.5885i	−0.352197	+	0.610023i	0.634437	+	0.772975i	$0.281232\pi$
$654$	9.00000	+	15.5885i	0.351928	+	0.609557i
$655$	−14.0000	−	24.2487i	−0.547025	−	0.947476i
$656$	20.0000	−	34.6410i	0.780869	−	1.35250i
$657$	3.00000			0.117041
$658$		0			0
$659$	36.0000			1.40236			0.701180	−	0.712984i	$-0.252657\pi$
$659$	36.0000			1.40236			0.701180	+	0.712984i	$0.252657\pi$
$660$	−4.00000	+	6.92820i	−0.155700	+	0.269680i
$661$	−20.5000	−	35.5070i	−0.797358	−	1.38106i	−0.921331	−	0.388778i	$-0.872897\pi$
$661$	−20.5000	−	35.5070i	−0.797358	−	1.38106i	0.123974	−	0.992286i	$-0.460436\pi$
$662$	25.0000	+	43.3013i	0.971653	+	1.68295i
$663$		0			0
$664$		0			0
$665$		0			0
$666$	6.00000			0.232495
$667$		0			0
$668$	−14.0000	−	24.2487i	−0.541676	−	0.938211i
$669$	−8.00000	−	13.8564i	−0.309298	−	0.535720i
$670$	10.0000	−	17.3205i	0.386334	−	0.669150i
$671$	20.0000			0.772091
$672$		0			0
$673$	−41.0000			−1.58043			−0.790217	−	0.612827i	$-0.790032\pi$
$673$	−41.0000			−1.58043			−0.790217	+	0.612827i	$0.790032\pi$
$674$	−13.0000	+	22.5167i	−0.500741	+	0.867309i
$675$	−0.500000	−	0.866025i	−0.0192450	−	0.0333333i
$676$	12.0000	+	20.7846i	0.461538	+	0.799408i
$677$	6.00000	−	10.3923i	0.230599	−	0.399409i	−0.727386	−	0.686229i	$-0.759265\pi$
$677$	6.00000	−	10.3923i	0.230599	−	0.399409i	0.957984	+	0.286820i	$0.0925982\pi$
$678$	−20.0000			−0.768095
$679$		0			0
$680$		0			0
$681$	−9.00000	+	15.5885i	−0.344881	+	0.597351i
$682$	−18.0000	−	31.1769i	−0.689256	−	1.19383i
$683$	6.00000	+	10.3923i	0.229584	+	0.397650i	0.957685	−	0.287819i	$-0.0929302\pi$
$683$	6.00000	+	10.3923i	0.229584	+	0.397650i	−0.728101	+	0.685470i	$0.759597\pi$
$684$	1.00000	−	1.73205i	0.0382360	−	0.0662266i
$685$	−24.0000			−0.916993
$686$		0			0
$687$	−19.0000			−0.724895
$688$	10.0000	−	17.3205i	0.381246	−	0.660338i
$689$	6.00000	+	10.3923i	0.228582	+	0.395915i
$690$		0			0
$691$	−18.5000	+	32.0429i	−0.703773	+	1.21897i	0.263359	+	0.964698i	$0.415170\pi$
$691$	−18.5000	+	32.0429i	−0.703773	+	1.21897i	−0.967132	+	0.254273i	$0.918164\pi$
$692$	−16.0000			−0.608229
$693$		0			0
$694$	64.0000			2.42941
$695$	−3.00000	+	5.19615i	−0.113796	+	0.197101i
$696$		0			0
$697$		0			0
$698$	−14.0000	+	24.2487i	−0.529908	+	0.917827i
$699$	−6.00000			−0.226941
$700$		0			0
$701$		0			0			−	1.00000i	$-0.5\pi$
$701$		0			0				1.00000i	$0.5\pi$
$702$	−1.00000	+	1.73205i	−0.0377426	+	0.0653720i
$703$	1.50000	+	2.59808i	0.0565736	+	0.0979883i
$704$	−8.00000	−	13.8564i	−0.301511	−	0.522233i
$705$	6.00000	−	10.3923i	0.225973	−	0.391397i
$706$	−68.0000			−2.55921
$707$		0			0
$708$	−24.0000			−0.901975
$709$	−15.0000	+	25.9808i	−0.563337	+	0.975728i	0.433865	+	0.900978i	$0.357149\pi$
$709$	−15.0000	+	25.9808i	−0.563337	+	0.975728i	−0.997202	+	0.0747503i	$0.976184\pi$
$710$	12.0000	+	20.7846i	0.450352	+	0.780033i
$711$	0.500000	+	0.866025i	0.0187515	+	0.0324785i
$712$		0			0
$713$		0			0
$714$		0			0
$715$	4.00000			0.149592
$716$	−2.00000	+	3.46410i	−0.0747435	+	0.129460i
$717$	3.00000	+	5.19615i	0.112037	+	0.194054i
$718$	−20.0000	−	34.6410i	−0.746393	−	1.29279i
$719$	−9.00000	+	15.5885i	−0.335643	+	0.581351i	−0.983608	−	0.180319i	$-0.942287\pi$
$719$	−9.00000	+	15.5885i	−0.335643	+	0.581351i	0.647965	+	0.761670i	$0.275620\pi$
$720$	−8.00000			−0.298142
$721$		0			0
$722$	−36.0000			−1.33978
$723$	−7.00000	+	12.1244i	−0.260333	+	0.450910i
$724$	13.0000	+	22.5167i	0.483141	+	0.836825i
$725$	2.00000	+	3.46410i	0.0742781	+	0.128654i
$726$	−7.00000	+	12.1244i	−0.259794	+	0.449977i
$727$	13.0000			0.482143			0.241072	−	0.970507i	$-0.422501\pi$
$727$	13.0000			0.482143			0.241072	+	0.970507i	$0.422501\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$	−6.00000	+	10.3923i	−0.222070	+	0.384636i
$731$		0			0
$732$	−10.0000	−	17.3205i	−0.369611	−	0.640184i
$733$	−7.50000	+	12.9904i	−0.277019	+	0.479811i	−0.970642	−	0.240527i	$-0.922680\pi$
$733$	−7.50000	+	12.9904i	−0.277019	+	0.479811i	0.693624	+	0.720338i	$0.256013\pi$
$734$	18.0000			0.664392
$735$		0			0
$736$		0			0
$737$	−5.00000	+	8.66025i	−0.184177	+	0.319005i
$738$	−10.0000	−	17.3205i	−0.368105	−	0.637577i
$739$	7.50000	+	12.9904i	0.275892	+	0.477859i	0.970360	−	0.241665i	$-0.0776935\pi$
$739$	7.50000	+	12.9904i	0.275892	+	0.477859i	−0.694468	+	0.719524i	$0.744360\pi$
$740$	−6.00000	+	10.3923i	−0.220564	+	0.382029i
$741$	−1.00000			−0.0367359
$742$		0			0
$743$	42.0000			1.54083			0.770415	−	0.637542i	$-0.220049\pi$
$743$	42.0000			1.54083			0.770415	+	0.637542i	$0.220049\pi$
$744$		0			0
$745$	12.0000	+	20.7846i	0.439646	+	0.761489i
$746$	−23.0000	−	39.8372i	−0.842090	−	1.45854i
$747$	3.00000	−	5.19615i	0.109764	−	0.190117i
$748$		0			0
$749$		0			0
$750$	24.0000			0.876356
$751$	−6.50000	+	11.2583i	−0.237188	+	0.410822i	−0.959906	−	0.280321i	$-0.909559\pi$
$751$	−6.50000	+	11.2583i	−0.237188	+	0.410822i	0.722718	+	0.691143i	$0.242893\pi$
$752$	12.0000	+	20.7846i	0.437595	+	0.757937i
$753$	4.00000	+	6.92820i	0.145768	+	0.252478i
$754$	4.00000	−	6.92820i	0.145671	−	0.252310i
$755$	−32.0000			−1.16460
$756$		0			0
$757$	−22.0000			−0.799604			−0.399802	−	0.916602i	$-0.630921\pi$
$757$	−22.0000			−0.799604			−0.399802	+	0.916602i	$0.630921\pi$
$758$	−3.00000	+	5.19615i	−0.108965	+	0.188733i
$759$		0			0
$760$		0			0
$761$	−24.0000	+	41.5692i	−0.869999	+	1.50688i	−0.00800331	+	0.999968i	$0.502548\pi$
$761$	−24.0000	+	41.5692i	−0.869999	+	1.50688i	−0.861996	+	0.506915i	$0.830786\pi$
$762$	30.0000			1.08679
$763$		0			0
$764$	20.0000			0.723575
$765$		0			0
$766$	−12.0000	−	20.7846i	−0.433578	−	0.750978i
$767$	6.00000	+	10.3923i	0.216647	+	0.375244i
$768$	8.00000	−	13.8564i	0.288675	−	0.500000i
$769$	49.0000			1.76699			0.883493	−	0.468445i	$-0.155186\pi$
$769$	49.0000			1.76699			0.883493	+	0.468445i	$0.155186\pi$
$770$		0			0
$771$	26.0000			0.936367
$772$	−11.0000	+	19.0526i	−0.395899	+	0.685717i
$773$	−17.0000	−	29.4449i	−0.611448	−	1.05906i	−0.990997	−	0.133887i	$-0.957254\pi$
$773$	−17.0000	−	29.4449i	−0.611448	−	1.05906i	0.379549	−	0.925172i	$-0.376079\pi$
$774$	−5.00000	−	8.66025i	−0.179721	−	0.311286i
$775$	−4.50000	+	7.79423i	−0.161645	+	0.279977i
$776$		0			0
$777$		0			0
$778$	−12.0000			−0.430221
$779$	5.00000	−	8.66025i	0.179144	−	0.310286i
$780$	−2.00000	−	3.46410i	−0.0716115	−	0.124035i
$781$	−6.00000	−	10.3923i	−0.214697	−	0.371866i
$782$		0			0
$783$	−4.00000			−0.142948
$784$		0			0
$785$	28.0000			0.999363
$786$	14.0000	−	24.2487i	0.499363	−	0.864923i
$787$	20.0000	+	34.6410i	0.712923	+	1.23482i	0.963755	+	0.266788i	$0.0859624\pi$
$787$	20.0000	+	34.6410i	0.712923	+	1.23482i	−0.250832	+	0.968031i	$0.580704\pi$
$788$	−16.0000	−	27.7128i	−0.569976	−	0.987228i
$789$	2.00000	−	3.46410i	0.0712019	−	0.123325i
$790$	−4.00000			−0.142314
$791$		0			0
$792$		0			0
$793$	−5.00000	+	8.66025i	−0.177555	+	0.307535i
$794$	−9.00000	−	15.5885i	−0.319398	−	0.553214i
$795$	12.0000	+	20.7846i	0.425596	+	0.737154i
$796$		0			0
$797$	8.00000			0.283375			0.141687	−	0.989911i	$-0.454747\pi$
$797$	8.00000			0.283375			0.141687	+	0.989911i	$0.454747\pi$
$798$		0			0
$799$		0			0
$800$	−4.00000	+	6.92820i	−0.141421	+	0.244949i
$801$	8.00000	+	13.8564i	0.282666	+	0.489592i
$802$	36.0000	+	62.3538i	1.27120	+	2.20179i
$803$	3.00000	−	5.19615i	0.105868	−	0.183368i
$804$	10.0000			0.352673
$805$		0			0
$806$	18.0000			0.634023
$807$	−3.00000	+	5.19615i	−0.105605	+	0.182913i
$808$		0			0
$809$	−15.0000	−	25.9808i	−0.527372	−	0.913435i	−0.999491	−	0.0319002i	$-0.989844\pi$
$809$	−15.0000	−	25.9808i	−0.527372	−	0.913435i	0.472119	−	0.881535i	$-0.343489\pi$
$810$	−2.00000	+	3.46410i	−0.0702728	+	0.121716i
$811$	−32.0000			−1.12367			−0.561836	−	0.827249i	$-0.689905\pi$
$811$	−32.0000			−1.12367			−0.561836	+	0.827249i	$0.689905\pi$
$812$		0			0
$813$	16.0000			0.561144
$814$	6.00000	−	10.3923i	0.210300	−	0.364250i
$815$	−4.00000	−	6.92820i	−0.140114	−	0.242684i
$816$		0			0
$817$	2.50000	−	4.33013i	0.0874639	−	0.151492i
$818$	−10.0000			−0.349642
$819$		0			0
$820$	40.0000			1.39686
$821$	−1.00000	+	1.73205i	−0.0349002	+	0.0604490i	−0.882948	−	0.469471i	$-0.844445\pi$
$821$	−1.00000	+	1.73205i	−0.0349002	+	0.0604490i	0.848048	+	0.529920i	$0.177778\pi$
$822$	−12.0000	−	20.7846i	−0.418548	−	0.724947i
$823$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$823$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$824$		0			0
$825$	−2.00000			−0.0696311
$826$		0			0
$827$	−30.0000			−1.04320			−0.521601	−	0.853189i	$-0.674665\pi$
$827$	−30.0000			−1.04320			−0.521601	+	0.853189i	$0.674665\pi$
$828$		0			0
$829$	20.5000	+	35.5070i	0.711994	+	1.23321i	0.964107	+	0.265513i	$0.0855412\pi$
$829$	20.5000	+	35.5070i	0.711994	+	1.23321i	−0.252113	+	0.967698i	$0.581125\pi$
$830$	12.0000	+	20.7846i	0.416526	+	0.721444i
$831$	6.50000	−	11.2583i	0.225483	−	0.390547i
$832$	8.00000			0.277350
$833$		0			0
$834$	−6.00000			−0.207763
$835$	−14.0000	+	24.2487i	−0.484490	+	0.839161i
$836$	−2.00000	−	3.46410i	−0.0691714	−	0.119808i
$837$	−4.50000	−	7.79423i	−0.155543	−	0.269408i
$838$	30.0000	−	51.9615i	1.03633	−	1.79498i
$839$	44.0000			1.51905			0.759524	−	0.650479i	$-0.225432\pi$
$839$	44.0000			1.51905			0.759524	+	0.650479i	$0.225432\pi$
$840$		0			0
$841$	−13.0000			−0.448276
$842$	7.00000	−	12.1244i	0.241236	−	0.417833i
$843$	−2.00000	−	3.46410i	−0.0688837	−	0.119310i
$844$	−4.00000	−	6.92820i	−0.137686	−	0.238479i
$845$	12.0000	−	20.7846i	0.412813	−	0.715012i
$846$	12.0000			0.412568
$847$		0			0
$848$	−48.0000			−1.64833
$849$	5.50000	−	9.52628i	0.188760	−	0.326941i
$850$		0			0
$851$		0			0
$852$	−6.00000	+	10.3923i	−0.205557	+	0.356034i
$853$	−35.0000			−1.19838			−0.599189	−	0.800608i	$-0.704510\pi$
$853$	−35.0000			−1.19838			−0.599189	+	0.800608i	$0.704510\pi$
$854$		0			0
$855$	−2.00000			−0.0683986
$856$		0			0
$857$	−16.0000	−	27.7128i	−0.546550	−	0.946652i	−0.998508	−	0.0546125i	$-0.982608\pi$
$857$	−16.0000	−	27.7128i	−0.546550	−	0.946652i	0.451958	−	0.892039i	$-0.350726\pi$
$858$	2.00000	+	3.46410i	0.0682789	+	0.118262i
$859$	−20.0000	+	34.6410i	−0.682391	+	1.18194i	0.291858	+	0.956462i	$0.405727\pi$
$859$	−20.0000	+	34.6410i	−0.682391	+	1.18194i	−0.974249	+	0.225475i	$0.927607\pi$
$860$	20.0000			0.681994
$861$		0			0
$862$	−36.0000			−1.22616
$863$	27.0000	−	46.7654i	0.919091	−	1.59191i	0.118291	−	0.992979i	$-0.462258\pi$
$863$	27.0000	−	46.7654i	0.919091	−	1.59191i	0.800799	−	0.598933i	$-0.204408\pi$
$864$	−4.00000	−	6.92820i	−0.136083	−	0.235702i
$865$	8.00000	+	13.8564i	0.272008	+	0.471132i
$866$	31.0000	−	53.6936i	1.05342	−	1.82458i
$867$	17.0000			0.577350
$868$		0			0
$869$	2.00000			0.0678454
$870$	8.00000	−	13.8564i	0.271225	−	0.469776i
$871$	−2.50000	−	4.33013i	−0.0847093	−	0.146721i
$872$		0			0
$873$	−3.00000	+	5.19615i	−0.101535	+	0.175863i
$874$		0			0
$875$		0			0
$876$	−6.00000			−0.202721
$877$	19.0000	−	32.9090i	0.641584	−	1.11126i	−0.343495	−	0.939155i	$-0.611611\pi$
$877$	19.0000	−	32.9090i	0.641584	−	1.11126i	0.985079	−	0.172102i	$-0.0550559\pi$
$878$		0			0
$879$	−4.00000	−	6.92820i	−0.134917	−	0.233682i
$880$	−8.00000	+	13.8564i	−0.269680	+	0.467099i
$881$	−24.0000			−0.808581			−0.404290	−	0.914631i	$-0.632481\pi$
$881$	−24.0000			−0.808581			−0.404290	+	0.914631i	$0.632481\pi$
$882$		0			0
$883$	−13.0000			−0.437485			−0.218742	−	0.975783i	$-0.570195\pi$
$883$	−13.0000			−0.437485			−0.218742	+	0.975783i	$0.570195\pi$
$884$		0			0
$885$	12.0000	+	20.7846i	0.403376	+	0.698667i
$886$	−12.0000	−	20.7846i	−0.403148	−	0.698273i
$887$	−17.0000	+	29.4449i	−0.570804	+	0.988662i	0.425679	+	0.904874i	$0.360035\pi$
$887$	−17.0000	+	29.4449i	−0.570804	+	0.988662i	−0.996484	+	0.0837878i	$0.973298\pi$
$888$		0			0
$889$		0			0
$890$	−64.0000			−2.14528
$891$	1.00000	−	1.73205i	0.0335013	−	0.0580259i
$892$	16.0000	+	27.7128i	0.535720	+	0.927894i
$893$	3.00000	+	5.19615i	0.100391	+	0.173883i
$894$	−12.0000	+	20.7846i	−0.401340	+	0.695141i
$895$	4.00000			0.133705
$896$		0			0
$897$		0			0
$898$	18.0000	−	31.1769i	0.600668	−	1.04039i
$899$	18.0000	+	31.1769i	0.600334	+	1.03981i
$900$	1.00000	+	1.73205i	0.0333333	+	0.0577350i
$901$		0			0
$902$	−40.0000			−1.33185
$903$		0			0
$904$		0			0
$905$	13.0000	−	22.5167i	0.432135	−	0.748479i
$906$	−16.0000	−	27.7128i	−0.531564	−	0.920697i
$907$	18.5000	+	32.0429i	0.614282	+	1.06397i	0.990510	+	0.137441i	$0.0438878\pi$
$907$	18.5000	+	32.0429i	0.614282	+	1.06397i	−0.376228	+	0.926527i	$0.622779\pi$
$908$	18.0000	−	31.1769i	0.597351	−	1.03464i
$909$	−2.00000			−0.0663358
$910$		0			0
$911$	−24.0000			−0.795155			−0.397578	−	0.917568i	$-0.630149\pi$
$911$	−24.0000			−0.795155			−0.397578	+	0.917568i	$0.630149\pi$
$912$	2.00000	−	3.46410i	0.0662266	−	0.114708i
$913$	−6.00000	−	10.3923i	−0.198571	−	0.343935i
$914$	11.0000	+	19.0526i	0.363848	+	0.630203i
$915$	−10.0000	+	17.3205i	−0.330590	+	0.572598i
$916$	38.0000			1.25556
$917$		0			0
$918$		0			0
$919$	−11.5000	+	19.9186i	−0.379350	+	0.657053i	−0.990968	−	0.134100i	$-0.957186\pi$
$919$	−11.5000	+	19.9186i	−0.379350	+	0.657053i	0.611618	+	0.791153i	$0.290519\pi$
$920$		0			0
$921$	8.50000	+	14.7224i	0.280085	+	0.485121i
$922$	20.0000	−	34.6410i	0.658665	−	1.14084i
$923$	6.00000			0.197492
$924$		0			0
$925$	−3.00000			−0.0986394
$926$	17.0000	−	29.4449i	0.558655	−	0.967618i
$927$	−3.50000	−	6.06218i	−0.114955	−	0.199108i
$928$	16.0000	+	27.7128i	0.525226	+	0.909718i
$929$	7.00000	−	12.1244i	0.229663	−	0.397787i	−0.728046	−	0.685529i	$-0.759571\pi$
$929$	7.00000	−	12.1244i	0.229663	−	0.397787i	0.957708	+	0.287742i	$0.0929044\pi$
$930$	36.0000			1.18049
$931$		0			0
$932$	12.0000			0.393073
$933$	3.00000	−	5.19615i	0.0982156	−	0.170114i
$934$	6.00000	+	10.3923i	0.196326	+	0.340047i
$935$		0			0
$936$		0			0
$937$	−15.0000			−0.490029			−0.245014	−	0.969519i	$-0.578793\pi$
$937$	−15.0000			−0.490029			−0.245014	+	0.969519i	$0.578793\pi$
$938$		0			0
$939$	−1.00000			−0.0326338
$940$	−12.0000	+	20.7846i	−0.391397	+	0.677919i
$941$	−2.00000	−	3.46410i	−0.0651981	−	0.112926i	0.831584	−	0.555399i	$-0.187435\pi$
$941$	−2.00000	−	3.46410i	−0.0651981	−	0.112926i	−0.896782	+	0.442473i	$0.854101\pi$
$942$	14.0000	+	24.2487i	0.456145	+	0.790066i
$943$		0			0
$944$	−48.0000			−1.56227
$945$		0			0
$946$	−20.0000			−0.650256
$947$	5.00000	−	8.66025i	0.162478	−	0.281420i	−0.773279	−	0.634066i	$-0.781385\pi$
$947$	5.00000	−	8.66025i	0.162478	−	0.281420i	0.935757	+	0.352646i	$0.114718\pi$
$948$	−1.00000	−	1.73205i	−0.0324785	−	0.0562544i
$949$	1.50000	+	2.59808i	0.0486921	+	0.0843371i
$950$	−1.00000	+	1.73205i	−0.0324443	+	0.0561951i
$951$	−24.0000			−0.778253
$952$		0			0
$953$	44.0000			1.42530			0.712650	−	0.701520i	$-0.247495\pi$
$953$	44.0000			1.42530			0.712650	+	0.701520i	$0.247495\pi$
$954$	−12.0000	+	20.7846i	−0.388514	+	0.672927i
$955$	−10.0000	−	17.3205i	−0.323592	−	0.560478i
$956$	−6.00000	−	10.3923i	−0.194054	−	0.336111i
$957$	−4.00000	+	6.92820i	−0.129302	+	0.223957i
$958$	56.0000			1.80928
$959$		0			0
$960$	16.0000			0.516398
$961$	−25.0000	+	43.3013i	−0.806452	+	1.39682i
$962$	3.00000	+	5.19615i	0.0967239	+	0.167531i
$963$	4.00000	+	6.92820i	0.128898	+	0.223258i
$964$	14.0000	−	24.2487i	0.450910	−	0.780998i
$965$	22.0000			0.708205
$966$		0			0
$967$	19.0000			0.610999			0.305499	−	0.952192i	$-0.401177\pi$
$967$	19.0000			0.610999			0.305499	+	0.952192i	$0.401177\pi$
$968$		0			0
$969$		0			0
$970$	−12.0000	−	20.7846i	−0.385297	−	0.667354i
$971$	18.0000	−	31.1769i	0.577647	−	1.00051i	−0.418101	−	0.908401i	$-0.637304\pi$
$971$	18.0000	−	31.1769i	0.577647	−	1.00051i	0.995748	−	0.0921142i	$-0.0293625\pi$
$972$	−2.00000			−0.0641500
$973$		0			0
$974$	62.0000			1.98661
$975$	0.500000	−	0.866025i	0.0160128	−	0.0277350i
$976$	−20.0000	−	34.6410i	−0.640184	−	1.10883i
$977$	9.00000	+	15.5885i	0.287936	+	0.498719i	0.973317	−	0.229465i	$-0.0736978\pi$
$977$	9.00000	+	15.5885i	0.287936	+	0.498719i	−0.685381	+	0.728184i	$0.740364\pi$
$978$	4.00000	−	6.92820i	0.127906	−	0.221540i
$979$	32.0000			1.02272
$980$		0			0
$981$	9.00000			0.287348
$982$	28.0000	−	48.4974i	0.893516	−	1.54761i
$983$	18.0000	+	31.1769i	0.574111	+	0.994389i	0.996138	+	0.0878058i	$0.0279855\pi$
$983$	18.0000	+	31.1769i	0.574111	+	0.994389i	−0.422027	+	0.906583i	$0.638681\pi$
$984$		0			0
$985$	−16.0000	+	27.7128i	−0.509802	+	0.883004i
$986$		0			0
$987$		0			0
$988$	2.00000			0.0636285
$989$		0			0
$990$	4.00000	+	6.92820i	0.127128	+	0.220193i
$991$	−8.50000	−	14.7224i	−0.270011	−	0.467673i	0.698853	−	0.715265i	$-0.253694\pi$
$991$	−8.50000	−	14.7224i	−0.270011	−	0.467673i	−0.968864	+	0.247592i	$0.920361\pi$
$992$	−36.0000	+	62.3538i	−1.14300	+	1.97974i
$993$	25.0000			0.793351
$994$		0			0
$995$		0			0
$996$	−6.00000	+	10.3923i	−0.190117	+	0.329293i
$997$	9.50000	+	16.4545i	0.300868	+	0.521119i	0.976333	−	0.216274i	$-0.0693903\pi$
$997$	9.50000	+	16.4545i	0.300868	+	0.521119i	−0.675465	+	0.737392i	$0.736057\pi$
$998$	−37.0000	−	64.0859i	−1.17121	−	2.02860i
$999$	1.50000	−	2.59808i	0.0474579	−	0.0821995i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	147.2.e.a.79.1		2
3.2	odd	2		441.2.e.e.226.1		2
4.3	odd	2		2352.2.q.c.961.1		2
7.2	even	3		147.2.a.b.1.1		1
7.3	odd	6		21.2.e.a.4.1	✓	2
7.4	even	3	inner	147.2.e.a.67.1		2
7.5	odd	6		147.2.a.c.1.1		1
7.6	odd	2		21.2.e.a.16.1	yes	2
21.2	odd	6		441.2.a.a.1.1		1
21.5	even	6		441.2.a.b.1.1		1
21.11	odd	6		441.2.e.e.361.1		2
21.17	even	6		63.2.e.b.46.1		2
21.20	even	2		63.2.e.b.37.1		2
28.3	even	6		336.2.q.f.193.1		2
28.11	odd	6		2352.2.q.c.1537.1		2
28.19	even	6		2352.2.a.d.1.1		1
28.23	odd	6		2352.2.a.w.1.1		1
28.27	even	2		336.2.q.f.289.1		2
35.3	even	12		525.2.r.e.424.1		4
35.9	even	6		3675.2.a.c.1.1		1
35.13	even	4		525.2.r.e.499.2		4
35.17	even	12		525.2.r.e.424.2		4
35.19	odd	6		3675.2.a.a.1.1		1
35.24	odd	6		525.2.i.e.151.1		2
35.27	even	4		525.2.r.e.499.1		4
35.34	odd	2		525.2.i.e.226.1		2
56.3	even	6		1344.2.q.c.193.1		2
56.5	odd	6		9408.2.a.bg.1.1		1
56.13	odd	2		1344.2.q.m.961.1		2
56.19	even	6		9408.2.a.cv.1.1		1
56.27	even	2		1344.2.q.c.961.1		2
56.37	even	6		9408.2.a.bz.1.1		1
56.45	odd	6		1344.2.q.m.193.1		2
56.51	odd	6		9408.2.a.k.1.1		1
63.13	odd	6		567.2.g.a.541.1		2
63.20	even	6		567.2.h.a.352.1		2
63.31	odd	6		567.2.h.f.298.1		2
63.34	odd	6		567.2.h.f.352.1		2
63.38	even	6		567.2.g.f.109.1		2
63.41	even	6		567.2.g.f.541.1		2
63.52	odd	6		567.2.g.a.109.1		2
63.59	even	6		567.2.h.a.298.1		2
84.23	even	6		7056.2.a.m.1.1		1
84.47	odd	6		7056.2.a.bp.1.1		1
84.59	odd	6		1008.2.s.d.865.1		2
84.83	odd	2		1008.2.s.d.289.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
21.2.e.a.4.1	✓	2	7.3	odd	6
21.2.e.a.16.1	yes	2	7.6	odd	2
63.2.e.b.37.1		2	21.20	even	2
63.2.e.b.46.1		2	21.17	even	6
147.2.a.b.1.1		1	7.2	even	3
147.2.a.c.1.1		1	7.5	odd	6
147.2.e.a.67.1		2	7.4	even	3	inner
147.2.e.a.79.1		2	1.1	even	1	trivial
336.2.q.f.193.1		2	28.3	even	6
336.2.q.f.289.1		2	28.27	even	2
441.2.a.a.1.1		1	21.2	odd	6
441.2.a.b.1.1		1	21.5	even	6
441.2.e.e.226.1		2	3.2	odd	2
441.2.e.e.361.1		2	21.11	odd	6
525.2.i.e.151.1		2	35.24	odd	6
525.2.i.e.226.1		2	35.34	odd	2
525.2.r.e.424.1		4	35.3	even	12
525.2.r.e.424.2		4	35.17	even	12
525.2.r.e.499.1		4	35.27	even	4
525.2.r.e.499.2		4	35.13	even	4
567.2.g.a.109.1		2	63.52	odd	6
567.2.g.a.541.1		2	63.13	odd	6
567.2.g.f.109.1		2	63.38	even	6
567.2.g.f.541.1		2	63.41	even	6
567.2.h.a.298.1		2	63.59	even	6
567.2.h.a.352.1		2	63.20	even	6
567.2.h.f.298.1		2	63.31	odd	6
567.2.h.f.352.1		2	63.34	odd	6
1008.2.s.d.289.1		2	84.83	odd	2
1008.2.s.d.865.1		2	84.59	odd	6
1344.2.q.c.193.1		2	56.3	even	6
1344.2.q.c.961.1		2	56.27	even	2
1344.2.q.m.193.1		2	56.45	odd	6
1344.2.q.m.961.1		2	56.13	odd	2
2352.2.a.d.1.1		1	28.19	even	6
2352.2.a.w.1.1		1	28.23	odd	6
2352.2.q.c.961.1		2	4.3	odd	2
2352.2.q.c.1537.1		2	28.11	odd	6
3675.2.a.a.1.1		1	35.19	odd	6
3675.2.a.c.1.1		1	35.9	even	6
7056.2.a.m.1.1		1	84.23	even	6
7056.2.a.bp.1.1		1	84.47	odd	6
9408.2.a.k.1.1		1	56.51	odd	6
9408.2.a.bg.1.1		1	56.5	odd	6
9408.2.a.bz.1.1		1	56.37	even	6
9408.2.a.cv.1.1		1	56.19	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 147 = 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	147.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.00000 + 1.73205i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-1.00000 - 1.73205i) q^{4} +(-1.00000 + 1.73205i) q^{5} -2.00000 q^{6} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(-1.00000 + 1.73205i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-1.00000 - 1.73205i) q^{4} +(-1.00000 + 1.73205i) q^{5} -2.00000 q^{6} +(-0.500000 + 0.866025i) q^{9} +(-2.00000 - 3.46410i) q^{10} +(1.00000 + 1.73205i) q^{11} +(1.00000 - 1.73205i) q^{12} -1.00000 q^{13} -2.00000 q^{15} +(2.00000 - 3.46410i) q^{16} +(-1.00000 - 1.73205i) q^{18} +(0.500000 - 0.866025i) q^{19} +4.00000 q^{20} -4.00000 q^{22} +(0.500000 + 0.866025i) q^{25} +(1.00000 - 1.73205i) q^{26} -1.00000 q^{27} +4.00000 q^{29} +(2.00000 - 3.46410i) q^{30} +(4.50000 + 7.79423i) q^{31} +(4.00000 + 6.92820i) q^{32} +(-1.00000 + 1.73205i) q^{33} +2.00000 q^{36} +(-1.50000 + 2.59808i) q^{37} +(1.00000 + 1.73205i) q^{38} +(-0.500000 - 0.866025i) q^{39} +10.0000 q^{41} +5.00000 q^{43} +(2.00000 - 3.46410i) q^{44} +(-1.00000 - 1.73205i) q^{45} +(-3.00000 + 5.19615i) q^{47} +4.00000 q^{48} -2.00000 q^{50} +(1.00000 + 1.73205i) q^{52} +(-6.00000 - 10.3923i) q^{53} +(1.00000 - 1.73205i) q^{54} -4.00000 q^{55} +1.00000 q^{57} +(-4.00000 + 6.92820i) q^{58} +(-6.00000 - 10.3923i) q^{59} +(2.00000 + 3.46410i) q^{60} +(5.00000 - 8.66025i) q^{61} -18.0000 q^{62} -8.00000 q^{64} +(1.00000 - 1.73205i) q^{65} +(-2.00000 - 3.46410i) q^{66} +(2.50000 + 4.33013i) q^{67} -6.00000 q^{71} +(-1.50000 - 2.59808i) q^{73} +(-3.00000 - 5.19615i) q^{74} +(-0.500000 + 0.866025i) q^{75} -2.00000 q^{76} +2.00000 q^{78} +(0.500000 - 0.866025i) q^{79} +(4.00000 + 6.92820i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-10.0000 + 17.3205i) q^{82} -6.00000 q^{83} +(-5.00000 + 8.66025i) q^{86} +(2.00000 + 3.46410i) q^{87} +(8.00000 - 13.8564i) q^{89} +4.00000 q^{90} +(-4.50000 + 7.79423i) q^{93} +(-6.00000 - 10.3923i) q^{94} +(1.00000 + 1.73205i) q^{95} +(-4.00000 + 6.92820i) q^{96} +6.00000 q^{97} -2.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{2} + q^{3} - 2 q^{4} - 2 q^{5} - 4 q^{6} - q^{9}+O(q^{10}) \) 2 * q - 2 * q^2 + q^3 - 2 * q^4 - 2 * q^5 - 4 * q^6 - q^9	\( 2 q - 2 q^{2} + q^{3} - 2 q^{4} - 2 q^{5} - 4 q^{6} - q^{9} - 4 q^{10} + 2 q^{11} + 2 q^{12} - 2 q^{13} - 4 q^{15} + 4 q^{16} - 2 q^{18} + q^{19} + 8 q^{20} - 8 q^{22} + q^{25} + 2 q^{26} - 2 q^{27} + 8 q^{29} + 4 q^{30} + 9 q^{31} + 8 q^{32} - 2 q^{33} + 4 q^{36} - 3 q^{37} + 2 q^{38} - q^{39} + 20 q^{41} + 10 q^{43} + 4 q^{44} - 2 q^{45} - 6 q^{47} + 8 q^{48} - 4 q^{50} + 2 q^{52} - 12 q^{53} + 2 q^{54} - 8 q^{55} + 2 q^{57} - 8 q^{58} - 12 q^{59} + 4 q^{60} + 10 q^{61} - 36 q^{62} - 16 q^{64} + 2 q^{65} - 4 q^{66} + 5 q^{67} - 12 q^{71} - 3 q^{73} - 6 q^{74} - q^{75} - 4 q^{76} + 4 q^{78} + q^{79} + 8 q^{80} - q^{81} - 20 q^{82} - 12 q^{83} - 10 q^{86} + 4 q^{87} + 16 q^{89} + 8 q^{90} - 9 q^{93} - 12 q^{94} + 2 q^{95} - 8 q^{96} + 12 q^{97} - 4 q^{99}+O(q^{100}) \) 2 * q - 2 * q^2 + q^3 - 2 * q^4 - 2 * q^5 - 4 * q^6 - q^9 - 4 * q^10 + 2 * q^11 + 2 * q^12 - 2 * q^13 - 4 * q^15 + 4 * q^16 - 2 * q^18 + q^19 + 8 * q^20 - 8 * q^22 + q^25 + 2 * q^26 - 2 * q^27 + 8 * q^29 + 4 * q^30 + 9 * q^31 + 8 * q^32 - 2 * q^33 + 4 * q^36 - 3 * q^37 + 2 * q^38 - q^39 + 20 * q^41 + 10 * q^43 + 4 * q^44 - 2 * q^45 - 6 * q^47 + 8 * q^48 - 4 * q^50 + 2 * q^52 - 12 * q^53 + 2 * q^54 - 8 * q^55 + 2 * q^57 - 8 * q^58 - 12 * q^59 + 4 * q^60 + 10 * q^61 - 36 * q^62 - 16 * q^64 + 2 * q^65 - 4 * q^66 + 5 * q^67 - 12 * q^71 - 3 * q^73 - 6 * q^74 - q^75 - 4 * q^76 + 4 * q^78 + q^79 + 8 * q^80 - q^81 - 20 * q^82 - 12 * q^83 - 10 * q^86 + 4 * q^87 + 16 * q^89 + 8 * q^90 - 9 * q^93 - 12 * q^94 + 2 * q^95 - 8 * q^96 + 12 * q^97 - 4 * q^99

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