LMFDB - Embedded newform 26.2.c.a.3.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [26,2,Mod(3,26)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(26, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2]))

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

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

chi := DirichletCharacter("26.3");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 26 = 2 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	26.c (of order $3$, 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:	$0.207611045255$
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:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			3.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	26.3
Dual form			26.2.c.a.9.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} -1.00000 q^{5} +(-2.00000 + 3.46410i) q^{7} +1.00000 q^{8} +(1.50000 - 2.59808i) q^{9} +O(q^{10})$	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} -1.00000 q^{5} +(-2.00000 + 3.46410i) q^{7} +1.00000 q^{8} +(1.50000 - 2.59808i) q^{9} +(0.500000 + 0.866025i) q^{10} +(-2.00000 - 3.46410i) q^{11} +(3.50000 - 0.866025i) q^{13} +4.00000 q^{14} +(-0.500000 - 0.866025i) q^{16} +(-1.50000 + 2.59808i) q^{17} -3.00000 q^{18} +(0.500000 - 0.866025i) q^{20} +(-2.00000 + 3.46410i) q^{22} +(2.00000 + 3.46410i) q^{23} -4.00000 q^{25} +(-2.50000 - 2.59808i) q^{26} +(-2.00000 - 3.46410i) q^{28} +(0.500000 + 0.866025i) q^{29} +4.00000 q^{31} +(-0.500000 + 0.866025i) q^{32} +3.00000 q^{34} +(2.00000 - 3.46410i) q^{35} +(1.50000 + 2.59808i) q^{36} +(-1.50000 - 2.59808i) q^{37} -1.00000 q^{40} +(4.50000 + 7.79423i) q^{41} +(4.00000 - 6.92820i) q^{43} +4.00000 q^{44} +(-1.50000 + 2.59808i) q^{45} +(2.00000 - 3.46410i) q^{46} -8.00000 q^{47} +(-4.50000 - 7.79423i) q^{49} +(2.00000 + 3.46410i) q^{50} +(-1.00000 + 3.46410i) q^{52} -9.00000 q^{53} +(2.00000 + 3.46410i) q^{55} +(-2.00000 + 3.46410i) q^{56} +(0.500000 - 0.866025i) q^{58} +(2.00000 - 3.46410i) q^{59} +(-3.50000 + 6.06218i) q^{61} +(-2.00000 - 3.46410i) q^{62} +(6.00000 + 10.3923i) q^{63} +1.00000 q^{64} +(-3.50000 + 0.866025i) q^{65} +(-2.00000 - 3.46410i) q^{67} +(-1.50000 - 2.59808i) q^{68} -4.00000 q^{70} +(4.00000 - 6.92820i) q^{71} +(1.50000 - 2.59808i) q^{72} +11.0000 q^{73} +(-1.50000 + 2.59808i) q^{74} +16.0000 q^{77} -4.00000 q^{79} +(0.500000 + 0.866025i) q^{80} +(-4.50000 - 7.79423i) q^{81} +(4.50000 - 7.79423i) q^{82} +(1.50000 - 2.59808i) q^{85} -8.00000 q^{86} +(-2.00000 - 3.46410i) q^{88} +(3.00000 + 5.19615i) q^{89} +3.00000 q^{90} +(-4.00000 + 13.8564i) q^{91} -4.00000 q^{92} +(4.00000 + 6.92820i) q^{94} +(-1.00000 + 1.73205i) q^{97} +(-4.50000 + 7.79423i) q^{98} -12.0000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - q^{2} - q^{4} - 2 q^{5} - 4 q^{7} + 2 q^{8} + 3 q^{9}+O(q^{10}) $ 2 * q - q^2 - q^4 - 2 * q^5 - 4 * q^7 + 2 * q^8 + 3 * q^9	$ 2 q - q^{2} - q^{4} - 2 q^{5} - 4 q^{7} + 2 q^{8} + 3 q^{9} + q^{10} - 4 q^{11} + 7 q^{13} + 8 q^{14} - q^{16} - 3 q^{17} - 6 q^{18} + q^{20} - 4 q^{22} + 4 q^{23} - 8 q^{25} - 5 q^{26} - 4 q^{28} + q^{29} + 8 q^{31} - q^{32} + 6 q^{34} + 4 q^{35} + 3 q^{36} - 3 q^{37} - 2 q^{40} + 9 q^{41} + 8 q^{43} + 8 q^{44} - 3 q^{45} + 4 q^{46} - 16 q^{47} - 9 q^{49} + 4 q^{50} - 2 q^{52} - 18 q^{53} + 4 q^{55} - 4 q^{56} + q^{58} + 4 q^{59} - 7 q^{61} - 4 q^{62} + 12 q^{63} + 2 q^{64} - 7 q^{65} - 4 q^{67} - 3 q^{68} - 8 q^{70} + 8 q^{71} + 3 q^{72} + 22 q^{73} - 3 q^{74} + 32 q^{77} - 8 q^{79} + q^{80} - 9 q^{81} + 9 q^{82} + 3 q^{85} - 16 q^{86} - 4 q^{88} + 6 q^{89} + 6 q^{90} - 8 q^{91} - 8 q^{92} + 8 q^{94} - 2 q^{97} - 9 q^{98} - 24 q^{99}+O(q^{100}) $ 2 * q - q^2 - q^4 - 2 * q^5 - 4 * q^7 + 2 * q^8 + 3 * q^9 + q^10 - 4 * q^11 + 7 * q^13 + 8 * q^14 - q^16 - 3 * q^17 - 6 * q^18 + q^20 - 4 * q^22 + 4 * q^23 - 8 * q^25 - 5 * q^26 - 4 * q^28 + q^29 + 8 * q^31 - q^32 + 6 * q^34 + 4 * q^35 + 3 * q^36 - 3 * q^37 - 2 * q^40 + 9 * q^41 + 8 * q^43 + 8 * q^44 - 3 * q^45 + 4 * q^46 - 16 * q^47 - 9 * q^49 + 4 * q^50 - 2 * q^52 - 18 * q^53 + 4 * q^55 - 4 * q^56 + q^58 + 4 * q^59 - 7 * q^61 - 4 * q^62 + 12 * q^63 + 2 * q^64 - 7 * q^65 - 4 * q^67 - 3 * q^68 - 8 * q^70 + 8 * q^71 + 3 * q^72 + 22 * q^73 - 3 * q^74 + 32 * q^77 - 8 * q^79 + q^80 - 9 * q^81 + 9 * q^82 + 3 * q^85 - 16 * q^86 - 4 * q^88 + 6 * q^89 + 6 * q^90 - 8 * q^91 - 8 * q^92 + 8 * q^94 - 2 * q^97 - 9 * q^98 - 24 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/26\mathbb{Z}\right)^\times$.

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

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 $

$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$3$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$3$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	−1.00000			−0.447214			−0.223607	−	0.974679i	$-0.571783\pi$
$5$	−1.00000			−0.447214			−0.223607	+	0.974679i	$0.571783\pi$
$6$		0			0
$7$	−2.00000	+	3.46410i	−0.755929	+	1.30931i	0.188982	+	0.981981i	$0.439481\pi$
$7$	−2.00000	+	3.46410i	−0.755929	+	1.30931i	−0.944911	+	0.327327i	$0.893852\pi$
$8$	1.00000			0.353553
$9$	1.50000	−	2.59808i	0.500000	−	0.866025i
$10$	0.500000	+	0.866025i	0.158114	+	0.273861i
$11$	−2.00000	−	3.46410i	−0.603023	−	1.04447i	−0.992361	−	0.123371i	$-0.960630\pi$
$11$	−2.00000	−	3.46410i	−0.603023	−	1.04447i	0.389338	−	0.921095i	$-0.372704\pi$
$12$		0			0
$13$	3.50000	−	0.866025i	0.970725	−	0.240192i
$13$	3.50000	−	0.866025i	0.970725	−	0.240192i
$14$	4.00000			1.06904
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−1.50000	+	2.59808i	−0.363803	+	0.630126i	−0.988583	−	0.150675i	$-0.951855\pi$
$17$	−1.50000	+	2.59808i	−0.363803	+	0.630126i	0.624780	+	0.780801i	$0.285189\pi$
$18$	−3.00000			−0.707107
$19$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$19$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$20$	0.500000	−	0.866025i	0.111803	−	0.193649i
$21$		0			0
$22$	−2.00000	+	3.46410i	−0.426401	+	0.738549i
$23$	2.00000	+	3.46410i	0.417029	+	0.722315i	0.995639	−	0.0932891i	$-0.0297381\pi$
$23$	2.00000	+	3.46410i	0.417029	+	0.722315i	−0.578610	+	0.815604i	$0.696405\pi$
$24$		0			0
$25$	−4.00000			−0.800000
$26$	−2.50000	−	2.59808i	−0.490290	−	0.509525i
$27$		0			0
$28$	−2.00000	−	3.46410i	−0.377964	−	0.654654i
$29$	0.500000	+	0.866025i	0.0928477	+	0.160817i	0.908708	−	0.417432i	$-0.137070\pi$
$29$	0.500000	+	0.866025i	0.0928477	+	0.160817i	−0.815861	+	0.578249i	$0.803736\pi$
$30$		0			0
$31$	4.00000			0.718421			0.359211	−	0.933257i	$-0.383046\pi$
$31$	4.00000			0.718421			0.359211	+	0.933257i	$0.383046\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$		0			0
$34$	3.00000			0.514496
$35$	2.00000	−	3.46410i	0.338062	−	0.585540i
$36$	1.50000	+	2.59808i	0.250000	+	0.433013i
$37$	−1.50000	−	2.59808i	−0.246598	−	0.427121i	0.715981	−	0.698119i	$-0.245980\pi$
$37$	−1.50000	−	2.59808i	−0.246598	−	0.427121i	−0.962580	+	0.270998i	$0.912646\pi$
$38$		0			0
$39$		0			0
$40$	−1.00000			−0.158114
$41$	4.50000	+	7.79423i	0.702782	+	1.21725i	0.967486	+	0.252924i	$0.0813924\pi$
$41$	4.50000	+	7.79423i	0.702782	+	1.21725i	−0.264704	+	0.964330i	$0.585274\pi$
$42$		0			0
$43$	4.00000	−	6.92820i	0.609994	−	1.05654i	−0.381246	−	0.924473i	$-0.624505\pi$
$43$	4.00000	−	6.92820i	0.609994	−	1.05654i	0.991241	−	0.132068i	$-0.0421616\pi$
$44$	4.00000			0.603023
$45$	−1.50000	+	2.59808i	−0.223607	+	0.387298i
$46$	2.00000	−	3.46410i	0.294884	−	0.510754i
$47$	−8.00000			−1.16692			−0.583460	−	0.812142i	$-0.698301\pi$
$47$	−8.00000			−1.16692			−0.583460	+	0.812142i	$0.698301\pi$
$48$		0			0
$49$	−4.50000	−	7.79423i	−0.642857	−	1.11346i
$50$	2.00000	+	3.46410i	0.282843	+	0.489898i
$51$		0			0
$52$	−1.00000	+	3.46410i	−0.138675	+	0.480384i
$53$	−9.00000			−1.23625			−0.618123	−	0.786082i	$-0.712106\pi$
$53$	−9.00000			−1.23625			−0.618123	+	0.786082i	$0.712106\pi$
$54$		0			0
$55$	2.00000	+	3.46410i	0.269680	+	0.467099i
$56$	−2.00000	+	3.46410i	−0.267261	+	0.462910i
$57$		0			0
$58$	0.500000	−	0.866025i	0.0656532	−	0.113715i
$59$	2.00000	−	3.46410i	0.260378	−	0.450988i	−0.705965	−	0.708247i	$-0.749486\pi$
$59$	2.00000	−	3.46410i	0.260378	−	0.450988i	0.966342	+	0.257260i	$0.0828195\pi$
$60$		0			0
$61$	−3.50000	+	6.06218i	−0.448129	+	0.776182i	−0.998264	−	0.0588933i	$-0.981243\pi$
$61$	−3.50000	+	6.06218i	−0.448129	+	0.776182i	0.550135	+	0.835076i	$0.314576\pi$
$62$	−2.00000	−	3.46410i	−0.254000	−	0.439941i
$63$	6.00000	+	10.3923i	0.755929	+	1.30931i
$64$	1.00000			0.125000
$65$	−3.50000	+	0.866025i	−0.434122	+	0.107417i
$66$		0			0
$67$	−2.00000	−	3.46410i	−0.244339	−	0.423207i	0.717607	−	0.696449i	$-0.245238\pi$
$67$	−2.00000	−	3.46410i	−0.244339	−	0.423207i	−0.961946	+	0.273241i	$0.911904\pi$
$68$	−1.50000	−	2.59808i	−0.181902	−	0.315063i
$69$		0			0
$70$	−4.00000			−0.478091
$71$	4.00000	−	6.92820i	0.474713	−	0.822226i	−0.524868	−	0.851184i	$-0.675885\pi$
$71$	4.00000	−	6.92820i	0.474713	−	0.822226i	0.999581	+	0.0289572i	$0.00921865\pi$
$72$	1.50000	−	2.59808i	0.176777	−	0.306186i
$73$	11.0000			1.28745			0.643726	−	0.765256i	$-0.277388\pi$
$73$	11.0000			1.28745			0.643726	+	0.765256i	$0.277388\pi$
$74$	−1.50000	+	2.59808i	−0.174371	+	0.302020i
$75$		0			0
$76$		0			0
$77$	16.0000			1.82337
$78$		0			0
$79$	−4.00000			−0.450035			−0.225018	−	0.974355i	$-0.572244\pi$
$79$	−4.00000			−0.450035			−0.225018	+	0.974355i	$0.572244\pi$
$80$	0.500000	+	0.866025i	0.0559017	+	0.0968246i
$81$	−4.50000	−	7.79423i	−0.500000	−	0.866025i
$82$	4.50000	−	7.79423i	0.496942	−	0.860729i
$83$		0			0			−	1.00000i	$-0.5\pi$
$83$		0			0				1.00000i	$0.5\pi$
$84$		0			0
$85$	1.50000	−	2.59808i	0.162698	−	0.281801i
$86$	−8.00000			−0.862662
$87$		0			0
$88$	−2.00000	−	3.46410i	−0.213201	−	0.369274i
$89$	3.00000	+	5.19615i	0.317999	+	0.550791i	0.980071	−	0.198650i	$-0.0636557\pi$
$89$	3.00000	+	5.19615i	0.317999	+	0.550791i	−0.662071	+	0.749441i	$0.730322\pi$
$90$	3.00000			0.316228
$91$	−4.00000	+	13.8564i	−0.419314	+	1.45255i
$92$	−4.00000			−0.417029
$93$		0			0
$94$	4.00000	+	6.92820i	0.412568	+	0.714590i
$95$		0			0
$96$		0			0
$97$	−1.00000	+	1.73205i	−0.101535	+	0.175863i	−0.912317	−	0.409484i	$-0.865709\pi$
$97$	−1.00000	+	1.73205i	−0.101535	+	0.175863i	0.810782	+	0.585348i	$0.199042\pi$
$98$	−4.50000	+	7.79423i	−0.454569	+	0.787336i
$99$	−12.0000			−1.20605
$100$	2.00000	−	3.46410i	0.200000	−	0.346410i
$101$	−3.50000	−	6.06218i	−0.348263	−	0.603209i	0.637678	−	0.770303i	$-0.279895\pi$
$101$	−3.50000	−	6.06218i	−0.348263	−	0.603209i	−0.985941	+	0.167094i	$0.946562\pi$
$102$		0			0
$103$	−8.00000			−0.788263			−0.394132	−	0.919054i	$-0.628955\pi$
$103$	−8.00000			−0.788263			−0.394132	+	0.919054i	$0.628955\pi$
$104$	3.50000	−	0.866025i	0.343203	−	0.0849208i
$105$		0			0
$106$	4.50000	+	7.79423i	0.437079	+	0.757042i
$107$	2.00000	+	3.46410i	0.193347	+	0.334887i	0.946357	−	0.323122i	$-0.104732\pi$
$107$	2.00000	+	3.46410i	0.193347	+	0.334887i	−0.753010	+	0.658009i	$0.771399\pi$
$108$		0			0
$109$	−2.00000			−0.191565			−0.0957826	−	0.995402i	$-0.530535\pi$
$109$	−2.00000			−0.191565			−0.0957826	+	0.995402i	$0.530535\pi$
$110$	2.00000	−	3.46410i	0.190693	−	0.330289i
$111$		0			0
$112$	4.00000			0.377964
$113$	0.500000	−	0.866025i	0.0470360	−	0.0814688i	−0.841549	−	0.540181i	$-0.818356\pi$
$113$	0.500000	−	0.866025i	0.0470360	−	0.0814688i	0.888585	+	0.458712i	$0.151689\pi$
$114$		0			0
$115$	−2.00000	−	3.46410i	−0.186501	−	0.323029i
$116$	−1.00000			−0.0928477
$117$	3.00000	−	10.3923i	0.277350	−	0.960769i
$118$	−4.00000			−0.368230
$119$	−6.00000	−	10.3923i	−0.550019	−	0.952661i
$120$		0			0
$121$	−2.50000	+	4.33013i	−0.227273	+	0.393648i
$122$	7.00000			0.633750
$123$		0			0
$124$	−2.00000	+	3.46410i	−0.179605	+	0.311086i
$125$	9.00000			0.804984
$126$	6.00000	−	10.3923i	0.534522	−	0.925820i
$127$	4.00000	+	6.92820i	0.354943	+	0.614779i	0.987108	−	0.160055i	$-0.0511671\pi$
$127$	4.00000	+	6.92820i	0.354943	+	0.614779i	−0.632166	+	0.774833i	$0.717834\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$		0			0
$130$	2.50000	+	2.59808i	0.219265	+	0.227866i
$131$	20.0000			1.74741			0.873704	−	0.486458i	$-0.161711\pi$
$131$	20.0000			1.74741			0.873704	+	0.486458i	$0.161711\pi$
$132$		0			0
$133$		0			0
$134$	−2.00000	+	3.46410i	−0.172774	+	0.299253i
$135$		0			0
$136$	−1.50000	+	2.59808i	−0.128624	+	0.222783i
$137$	4.50000	−	7.79423i	0.384461	−	0.665906i	−0.607233	−	0.794524i	$-0.707721\pi$
$137$	4.50000	−	7.79423i	0.384461	−	0.665906i	0.991694	+	0.128618i	$0.0410540\pi$
$138$		0			0
$139$	−8.00000	+	13.8564i	−0.678551	+	1.17529i	0.296866	+	0.954919i	$0.404058\pi$
$139$	−8.00000	+	13.8564i	−0.678551	+	1.17529i	−0.975417	+	0.220366i	$0.929275\pi$
$140$	2.00000	+	3.46410i	0.169031	+	0.292770i
$141$		0			0
$142$	−8.00000			−0.671345
$143$	−10.0000	−	10.3923i	−0.836242	−	0.869048i
$144$	−3.00000			−0.250000
$145$	−0.500000	−	0.866025i	−0.0415227	−	0.0719195i
$146$	−5.50000	−	9.52628i	−0.455183	−	0.788400i
$147$		0			0
$148$	3.00000			0.246598
$149$	−7.50000	+	12.9904i	−0.614424	+	1.06421i	0.376061	+	0.926595i	$0.377278\pi$
$149$	−7.50000	+	12.9904i	−0.614424	+	1.06421i	−0.990485	+	0.137619i	$0.956055\pi$
$150$		0			0
$151$	12.0000			0.976546			0.488273	−	0.872691i	$-0.337627\pi$
$151$	12.0000			0.976546			0.488273	+	0.872691i	$0.337627\pi$
$152$		0			0
$153$	4.50000	+	7.79423i	0.363803	+	0.630126i
$154$	−8.00000	−	13.8564i	−0.644658	−	1.11658i
$155$	−4.00000			−0.321288
$156$		0			0
$157$	11.0000			0.877896			0.438948	−	0.898513i	$-0.355351\pi$
$157$	11.0000			0.877896			0.438948	+	0.898513i	$0.355351\pi$
$158$	2.00000	+	3.46410i	0.159111	+	0.275589i
$159$		0			0
$160$	0.500000	−	0.866025i	0.0395285	−	0.0684653i
$161$	−16.0000			−1.26098
$162$	−4.50000	+	7.79423i	−0.353553	+	0.612372i
$163$	−4.00000	+	6.92820i	−0.313304	+	0.542659i	−0.979076	−	0.203497i	$-0.934769\pi$
$163$	−4.00000	+	6.92820i	−0.313304	+	0.542659i	0.665771	+	0.746156i	$0.268103\pi$
$164$	−9.00000			−0.702782
$165$		0			0
$166$		0			0
$167$	−6.00000	−	10.3923i	−0.464294	−	0.804181i	0.534875	−	0.844931i	$-0.320359\pi$
$167$	−6.00000	−	10.3923i	−0.464294	−	0.804181i	−0.999169	+	0.0407502i	$0.987025\pi$
$168$		0			0
$169$	11.5000	−	6.06218i	0.884615	−	0.466321i
$170$	−3.00000			−0.230089
$171$		0			0
$172$	4.00000	+	6.92820i	0.304997	+	0.528271i
$173$	−7.00000	+	12.1244i	−0.532200	+	0.921798i	0.467093	+	0.884208i	$0.345301\pi$
$173$	−7.00000	+	12.1244i	−0.532200	+	0.921798i	−0.999293	+	0.0375896i	$0.988032\pi$
$174$		0			0
$175$	8.00000	−	13.8564i	0.604743	−	1.04745i
$176$	−2.00000	+	3.46410i	−0.150756	+	0.261116i
$177$		0			0
$178$	3.00000	−	5.19615i	0.224860	−	0.389468i
$179$	12.0000	+	20.7846i	0.896922	+	1.55351i	0.831408	+	0.555663i	$0.187536\pi$
$179$	12.0000	+	20.7846i	0.896922	+	1.55351i	0.0655145	+	0.997852i	$0.479131\pi$
$180$	−1.50000	−	2.59808i	−0.111803	−	0.193649i
$181$	−21.0000			−1.56092			−0.780459	−	0.625207i	$-0.785014\pi$
$181$	−21.0000			−1.56092			−0.780459	+	0.625207i	$0.785014\pi$
$182$	14.0000	−	3.46410i	1.03775	−	0.256776i
$183$		0			0
$184$	2.00000	+	3.46410i	0.147442	+	0.255377i
$185$	1.50000	+	2.59808i	0.110282	+	0.191014i
$186$		0			0
$187$	12.0000			0.877527
$188$	4.00000	−	6.92820i	0.291730	−	0.505291i
$189$		0			0
$190$		0			0
$191$	10.0000	−	17.3205i	0.723575	−	1.25327i	−0.235983	−	0.971757i	$-0.575831\pi$
$191$	10.0000	−	17.3205i	0.723575	−	1.25327i	0.959558	−	0.281511i	$-0.0908356\pi$
$192$		0			0
$193$	−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	$0.962900\pi$
$194$	2.00000			0.143592
$195$		0			0
$196$	9.00000			0.642857
$197$	−3.00000	−	5.19615i	−0.213741	−	0.370211i	0.739141	−	0.673550i	$-0.235232\pi$
$197$	−3.00000	−	5.19615i	−0.213741	−	0.370211i	−0.952882	+	0.303340i	$0.901898\pi$
$198$	6.00000	+	10.3923i	0.426401	+	0.738549i
$199$	2.00000	−	3.46410i	0.141776	−	0.245564i	−0.786389	−	0.617731i	$-0.788052\pi$
$199$	2.00000	−	3.46410i	0.141776	−	0.245564i	0.928166	+	0.372168i	$0.121385\pi$
$200$	−4.00000			−0.282843
$201$		0			0
$202$	−3.50000	+	6.06218i	−0.246259	+	0.426533i
$203$	−4.00000			−0.280745
$204$		0			0
$205$	−4.50000	−	7.79423i	−0.314294	−	0.544373i
$206$	4.00000	+	6.92820i	0.278693	+	0.482711i
$207$	12.0000			0.834058
$208$	−2.50000	−	2.59808i	−0.173344	−	0.180144i
$209$		0			0
$210$		0			0
$211$	−10.0000	−	17.3205i	−0.688428	−	1.19239i	−0.972346	−	0.233544i	$-0.924968\pi$
$211$	−10.0000	−	17.3205i	−0.688428	−	1.19239i	0.283918	−	0.958849i	$-0.408366\pi$
$212$	4.50000	−	7.79423i	0.309061	−	0.535310i
$213$		0			0
$214$	2.00000	−	3.46410i	0.136717	−	0.236801i
$215$	−4.00000	+	6.92820i	−0.272798	+	0.472500i
$216$		0			0
$217$	−8.00000	+	13.8564i	−0.543075	+	0.940634i
$218$	1.00000	+	1.73205i	0.0677285	+	0.117309i
$219$		0			0
$220$	−4.00000			−0.269680
$221$	−3.00000	+	10.3923i	−0.201802	+	0.699062i
$222$		0			0
$223$	−6.00000	−	10.3923i	−0.401790	−	0.695920i	0.592152	−	0.805826i	$-0.298278\pi$
$223$	−6.00000	−	10.3923i	−0.401790	−	0.695920i	−0.993942	+	0.109906i	$0.964945\pi$
$224$	−2.00000	−	3.46410i	−0.133631	−	0.231455i
$225$	−6.00000	+	10.3923i	−0.400000	+	0.692820i
$226$	−1.00000			−0.0665190
$227$	−12.0000	+	20.7846i	−0.796468	+	1.37952i	0.125435	+	0.992102i	$0.459967\pi$
$227$	−12.0000	+	20.7846i	−0.796468	+	1.37952i	−0.921903	+	0.387421i	$0.873366\pi$
$228$		0			0
$229$	6.00000			0.396491			0.198246	−	0.980152i	$-0.436476\pi$
$229$	6.00000			0.396491			0.198246	+	0.980152i	$0.436476\pi$
$230$	−2.00000	+	3.46410i	−0.131876	+	0.228416i
$231$		0			0
$232$	0.500000	+	0.866025i	0.0328266	+	0.0568574i
$233$	10.0000			0.655122			0.327561	−	0.944830i	$-0.393773\pi$
$233$	10.0000			0.655122			0.327561	+	0.944830i	$0.393773\pi$
$234$	−10.5000	+	2.59808i	−0.686406	+	0.169842i
$235$	8.00000			0.521862
$236$	2.00000	+	3.46410i	0.130189	+	0.225494i
$237$		0			0
$238$	−6.00000	+	10.3923i	−0.388922	+	0.673633i
$239$	−12.0000			−0.776215			−0.388108	−	0.921614i	$-0.626871\pi$
$239$	−12.0000			−0.776215			−0.388108	+	0.921614i	$0.626871\pi$
$240$		0			0
$241$	−1.50000	+	2.59808i	−0.0966235	+	0.167357i	−0.910285	−	0.413982i	$-0.864138\pi$
$241$	−1.50000	+	2.59808i	−0.0966235	+	0.167357i	0.813662	+	0.581339i	$0.197471\pi$
$242$	5.00000			0.321412
$243$		0			0
$244$	−3.50000	−	6.06218i	−0.224065	−	0.388091i
$245$	4.50000	+	7.79423i	0.287494	+	0.497955i
$246$		0			0
$247$		0			0
$248$	4.00000			0.254000
$249$		0			0
$250$	−4.50000	−	7.79423i	−0.284605	−	0.492950i
$251$	6.00000	−	10.3923i	0.378717	−	0.655956i	−0.612159	−	0.790735i	$-0.709699\pi$
$251$	6.00000	−	10.3923i	0.378717	−	0.655956i	0.990876	+	0.134778i	$0.0430322\pi$
$252$	−12.0000			−0.755929
$253$	8.00000	−	13.8564i	0.502956	−	0.871145i
$254$	4.00000	−	6.92820i	0.250982	−	0.434714i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−7.50000	−	12.9904i	−0.467837	−	0.810318i	0.531487	−	0.847066i	$-0.321633\pi$
$257$	−7.50000	−	12.9904i	−0.467837	−	0.810318i	−0.999325	+	0.0367485i	$0.988300\pi$
$258$		0			0
$259$	12.0000			0.745644
$260$	1.00000	−	3.46410i	0.0620174	−	0.214834i
$261$	3.00000			0.185695
$262$	−10.0000	−	17.3205i	−0.617802	−	1.07006i
$263$	12.0000	+	20.7846i	0.739952	+	1.28163i	0.952517	+	0.304487i	$0.0984850\pi$
$263$	12.0000	+	20.7846i	0.739952	+	1.28163i	−0.212565	+	0.977147i	$0.568182\pi$
$264$		0			0
$265$	9.00000			0.552866
$266$		0			0
$267$		0			0
$268$	4.00000			0.244339
$269$	9.00000	−	15.5885i	0.548740	−	0.950445i	−0.449622	−	0.893219i	$-0.648441\pi$
$269$	9.00000	−	15.5885i	0.548740	−	0.950445i	0.998361	−	0.0572259i	$-0.0182255\pi$
$270$		0			0
$271$	10.0000	+	17.3205i	0.607457	+	1.05215i	0.991658	+	0.128897i	$0.0411435\pi$
$271$	10.0000	+	17.3205i	0.607457	+	1.05215i	−0.384201	+	0.923249i	$0.625523\pi$
$272$	3.00000			0.181902
$273$		0			0
$274$	−9.00000			−0.543710
$275$	8.00000	+	13.8564i	0.482418	+	0.835573i
$276$		0			0
$277$	4.50000	−	7.79423i	0.270379	−	0.468310i	−0.698580	−	0.715532i	$-0.746184\pi$
$277$	4.50000	−	7.79423i	0.270379	−	0.468310i	0.968959	+	0.247222i	$0.0795177\pi$
$278$	16.0000			0.959616
$279$	6.00000	−	10.3923i	0.359211	−	0.622171i
$280$	2.00000	−	3.46410i	0.119523	−	0.207020i
$281$	−5.00000			−0.298275			−0.149137	−	0.988816i	$-0.547650\pi$
$281$	−5.00000			−0.298275			−0.149137	+	0.988816i	$0.547650\pi$
$282$		0			0
$283$	−14.0000	−	24.2487i	−0.832214	−	1.44144i	−0.896279	−	0.443491i	$-0.853740\pi$
$283$	−14.0000	−	24.2487i	−0.832214	−	1.44144i	0.0640654	−	0.997946i	$-0.479593\pi$
$284$	4.00000	+	6.92820i	0.237356	+	0.411113i
$285$		0			0
$286$	−4.00000	+	13.8564i	−0.236525	+	0.819346i
$287$	−36.0000			−2.12501
$288$	1.50000	+	2.59808i	0.0883883	+	0.153093i
$289$	4.00000	+	6.92820i	0.235294	+	0.407541i
$290$	−0.500000	+	0.866025i	−0.0293610	+	0.0508548i
$291$		0			0
$292$	−5.50000	+	9.52628i	−0.321863	+	0.557483i
$293$	2.50000	−	4.33013i	0.146052	−	0.252969i	−0.783713	−	0.621123i	$-0.786677\pi$
$293$	2.50000	−	4.33013i	0.146052	−	0.252969i	0.929765	+	0.368154i	$0.120010\pi$
$294$		0			0
$295$	−2.00000	+	3.46410i	−0.116445	+	0.201688i
$296$	−1.50000	−	2.59808i	−0.0871857	−	0.151010i
$297$		0			0
$298$	15.0000			0.868927
$299$	10.0000	+	10.3923i	0.578315	+	0.601003i
$300$		0			0
$301$	16.0000	+	27.7128i	0.922225	+	1.59734i
$302$	−6.00000	−	10.3923i	−0.345261	−	0.598010i
$303$		0			0
$304$		0			0
$305$	3.50000	−	6.06218i	0.200409	−	0.347119i
$306$	4.50000	−	7.79423i	0.257248	−	0.445566i
$307$	−28.0000			−1.59804			−0.799022	−	0.601302i	$-0.794649\pi$
$307$	−28.0000			−1.59804			−0.799022	+	0.601302i	$0.794649\pi$
$308$	−8.00000	+	13.8564i	−0.455842	+	0.789542i
$309$		0			0
$310$	2.00000	+	3.46410i	0.113592	+	0.196748i
$311$	−24.0000			−1.36092			−0.680458	−	0.732787i	$-0.738219\pi$
$311$	−24.0000			−1.36092			−0.680458	+	0.732787i	$0.738219\pi$
$312$		0			0
$313$	−22.0000			−1.24351			−0.621757	−	0.783210i	$-0.713581\pi$
$313$	−22.0000			−1.24351			−0.621757	+	0.783210i	$0.713581\pi$
$314$	−5.50000	−	9.52628i	−0.310383	−	0.537599i
$315$	−6.00000	−	10.3923i	−0.338062	−	0.585540i
$316$	2.00000	−	3.46410i	0.112509	−	0.194871i
$317$	3.00000			0.168497			0.0842484	−	0.996445i	$-0.473151\pi$
$317$	3.00000			0.168497			0.0842484	+	0.996445i	$0.473151\pi$
$318$		0			0
$319$	2.00000	−	3.46410i	0.111979	−	0.193952i
$320$	−1.00000			−0.0559017
$321$		0			0
$322$	8.00000	+	13.8564i	0.445823	+	0.772187i
$323$		0			0
$324$	9.00000			0.500000
$325$	−14.0000	+	3.46410i	−0.776580	+	0.192154i
$326$	8.00000			0.443079
$327$		0			0
$328$	4.50000	+	7.79423i	0.248471	+	0.430364i
$329$	16.0000	−	27.7128i	0.882109	−	1.52786i
$330$		0			0
$331$	−4.00000	+	6.92820i	−0.219860	+	0.380808i	−0.954765	−	0.297361i	$-0.903893\pi$
$331$	−4.00000	+	6.92820i	−0.219860	+	0.380808i	0.734905	+	0.678170i	$0.237227\pi$
$332$		0			0
$333$	−9.00000			−0.493197
$334$	−6.00000	+	10.3923i	−0.328305	+	0.568642i
$335$	2.00000	+	3.46410i	0.109272	+	0.189264i
$336$		0			0
$337$	23.0000			1.25289			0.626445	−	0.779466i	$-0.284509\pi$
$337$	23.0000			1.25289			0.626445	+	0.779466i	$0.284509\pi$
$338$	−11.0000	−	6.92820i	−0.598321	−	0.376845i
$339$		0			0
$340$	1.50000	+	2.59808i	0.0813489	+	0.140900i
$341$	−8.00000	−	13.8564i	−0.433224	−	0.750366i
$342$		0			0
$343$	8.00000			0.431959
$344$	4.00000	−	6.92820i	0.215666	−	0.373544i
$345$		0			0
$346$	14.0000			0.752645
$347$	−6.00000	+	10.3923i	−0.322097	+	0.557888i	−0.980921	−	0.194409i	$-0.937721\pi$
$347$	−6.00000	+	10.3923i	−0.322097	+	0.557888i	0.658824	+	0.752297i	$0.271054\pi$
$348$		0			0
$349$	1.00000	+	1.73205i	0.0535288	+	0.0927146i	0.891548	−	0.452926i	$-0.149620\pi$
$349$	1.00000	+	1.73205i	0.0535288	+	0.0927146i	−0.838019	+	0.545640i	$0.816286\pi$
$350$	−16.0000			−0.855236
$351$		0			0
$352$	4.00000			0.213201
$353$	−3.50000	−	6.06218i	−0.186286	−	0.322657i	0.757723	−	0.652576i	$-0.226312\pi$
$353$	−3.50000	−	6.06218i	−0.186286	−	0.322657i	−0.944009	+	0.329919i	$0.892979\pi$
$354$		0			0
$355$	−4.00000	+	6.92820i	−0.212298	+	0.367711i
$356$	−6.00000			−0.317999
$357$		0			0
$358$	12.0000	−	20.7846i	0.634220	−	1.09850i
$359$	24.0000			1.26667			0.633336	−	0.773877i	$-0.281685\pi$
$359$	24.0000			1.26667			0.633336	+	0.773877i	$0.281685\pi$
$360$	−1.50000	+	2.59808i	−0.0790569	+	0.136931i
$361$	9.50000	+	16.4545i	0.500000	+	0.866025i
$362$	10.5000	+	18.1865i	0.551868	+	0.955863i
$363$		0			0
$364$	−10.0000	−	10.3923i	−0.524142	−	0.544705i
$365$	−11.0000			−0.575766
$366$		0			0
$367$	14.0000	+	24.2487i	0.730794	+	1.26577i	0.956544	+	0.291587i	$0.0941834\pi$
$367$	14.0000	+	24.2487i	0.730794	+	1.26577i	−0.225750	+	0.974185i	$0.572483\pi$
$368$	2.00000	−	3.46410i	0.104257	−	0.180579i
$369$	27.0000			1.40556
$370$	1.50000	−	2.59808i	0.0779813	−	0.135068i
$371$	18.0000	−	31.1769i	0.934513	−	1.61862i
$372$		0			0
$373$	6.50000	−	11.2583i	0.336557	−	0.582934i	−0.647225	−	0.762299i	$-0.724071\pi$
$373$	6.50000	−	11.2583i	0.336557	−	0.582934i	0.983783	+	0.179364i	$0.0574041\pi$
$374$	−6.00000	−	10.3923i	−0.310253	−	0.537373i
$375$		0			0
$376$	−8.00000			−0.412568
$377$	2.50000	+	2.59808i	0.128757	+	0.133808i
$378$		0			0
$379$	4.00000	+	6.92820i	0.205466	+	0.355878i	0.950281	−	0.311393i	$-0.100796\pi$
$379$	4.00000	+	6.92820i	0.205466	+	0.355878i	−0.744815	+	0.667271i	$0.767462\pi$
$380$		0			0
$381$		0			0
$382$	−20.0000			−1.02329
$383$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$383$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$384$		0			0
$385$	−16.0000			−0.815436
$386$	−5.50000	+	9.52628i	−0.279943	+	0.484875i
$387$	−12.0000	−	20.7846i	−0.609994	−	1.05654i
$388$	−1.00000	−	1.73205i	−0.0507673	−	0.0879316i
$389$	−9.00000			−0.456318			−0.228159	−	0.973624i	$-0.573271\pi$
$389$	−9.00000			−0.456318			−0.228159	+	0.973624i	$0.573271\pi$
$390$		0			0
$391$	−12.0000			−0.606866
$392$	−4.50000	−	7.79423i	−0.227284	−	0.393668i
$393$		0			0
$394$	−3.00000	+	5.19615i	−0.151138	+	0.261778i
$395$	4.00000			0.201262
$396$	6.00000	−	10.3923i	0.301511	−	0.522233i
$397$	−7.00000	+	12.1244i	−0.351320	+	0.608504i	−0.986481	−	0.163876i	$-0.947600\pi$
$397$	−7.00000	+	12.1244i	−0.351320	+	0.608504i	0.635161	+	0.772380i	$0.280934\pi$
$398$	−4.00000			−0.200502
$399$		0			0
$400$	2.00000	+	3.46410i	0.100000	+	0.173205i
$401$	−1.50000	−	2.59808i	−0.0749064	−	0.129742i	0.826139	−	0.563466i	$-0.190532\pi$
$401$	−1.50000	−	2.59808i	−0.0749064	−	0.129742i	−0.901046	+	0.433724i	$0.857199\pi$
$402$		0			0
$403$	14.0000	−	3.46410i	0.697390	−	0.172559i
$404$	7.00000			0.348263
$405$	4.50000	+	7.79423i	0.223607	+	0.387298i
$406$	2.00000	+	3.46410i	0.0992583	+	0.171920i
$407$	−6.00000	+	10.3923i	−0.297409	+	0.515127i
$408$		0			0
$409$	−15.5000	+	26.8468i	−0.766426	+	1.32749i	0.173064	+	0.984911i	$0.444633\pi$
$409$	−15.5000	+	26.8468i	−0.766426	+	1.32749i	−0.939490	+	0.342578i	$0.888700\pi$
$410$	−4.50000	+	7.79423i	−0.222239	+	0.384930i
$411$		0			0
$412$	4.00000	−	6.92820i	0.197066	−	0.341328i
$413$	8.00000	+	13.8564i	0.393654	+	0.681829i
$414$	−6.00000	−	10.3923i	−0.294884	−	0.510754i
$415$		0			0
$416$	−1.00000	+	3.46410i	−0.0490290	+	0.169842i
$417$		0			0
$418$		0			0
$419$	−6.00000	−	10.3923i	−0.293119	−	0.507697i	0.681426	−	0.731887i	$-0.261360\pi$
$419$	−6.00000	−	10.3923i	−0.293119	−	0.507697i	−0.974546	+	0.224189i	$0.928027\pi$
$420$		0			0
$421$	−5.00000			−0.243685			−0.121843	−	0.992549i	$-0.538880\pi$
$421$	−5.00000			−0.243685			−0.121843	+	0.992549i	$0.538880\pi$
$422$	−10.0000	+	17.3205i	−0.486792	+	0.843149i
$423$	−12.0000	+	20.7846i	−0.583460	+	1.01058i
$424$	−9.00000			−0.437079
$425$	6.00000	−	10.3923i	0.291043	−	0.504101i
$426$		0			0
$427$	−14.0000	−	24.2487i	−0.677507	−	1.17348i
$428$	−4.00000			−0.193347
$429$		0			0
$430$	8.00000			0.385794
$431$	12.0000	+	20.7846i	0.578020	+	1.00116i	0.995706	+	0.0925683i	$0.0295076\pi$
$431$	12.0000	+	20.7846i	0.578020	+	1.00116i	−0.417687	+	0.908591i	$0.637159\pi$
$432$		0			0
$433$	2.50000	−	4.33013i	0.120142	−	0.208093i	−0.799681	−	0.600425i	$-0.794998\pi$
$433$	2.50000	−	4.33013i	0.120142	−	0.208093i	0.919824	+	0.392332i	$0.128332\pi$
$434$	16.0000			0.768025
$435$		0			0
$436$	1.00000	−	1.73205i	0.0478913	−	0.0829502i
$437$		0			0
$438$		0			0
$439$	−4.00000	−	6.92820i	−0.190910	−	0.330665i	0.754642	−	0.656136i	$-0.227810\pi$
$439$	−4.00000	−	6.92820i	−0.190910	−	0.330665i	−0.945552	+	0.325471i	$0.894477\pi$
$440$	2.00000	+	3.46410i	0.0953463	+	0.165145i
$441$	−27.0000			−1.28571
$442$	10.5000	−	2.59808i	0.499434	−	0.123578i
$443$	24.0000			1.14027			0.570137	−	0.821549i	$-0.306890\pi$
$443$	24.0000			1.14027			0.570137	+	0.821549i	$0.306890\pi$
$444$		0			0
$445$	−3.00000	−	5.19615i	−0.142214	−	0.246321i
$446$	−6.00000	+	10.3923i	−0.284108	+	0.492090i
$447$		0			0
$448$	−2.00000	+	3.46410i	−0.0944911	+	0.163663i
$449$	−17.0000	+	29.4449i	−0.802280	+	1.38959i	0.115833	+	0.993269i	$0.463046\pi$
$449$	−17.0000	+	29.4449i	−0.802280	+	1.38959i	−0.918112	+	0.396320i	$0.870287\pi$
$450$	12.0000			0.565685
$451$	18.0000	−	31.1769i	0.847587	−	1.46806i
$452$	0.500000	+	0.866025i	0.0235180	+	0.0407344i
$453$		0			0
$454$	24.0000			1.12638
$455$	4.00000	−	13.8564i	0.187523	−	0.649598i
$456$		0			0
$457$	−15.5000	−	26.8468i	−0.725059	−	1.25584i	−0.958950	−	0.283577i	$-0.908479\pi$
$457$	−15.5000	−	26.8468i	−0.725059	−	1.25584i	0.233890	−	0.972263i	$-0.424854\pi$
$458$	−3.00000	−	5.19615i	−0.140181	−	0.242800i
$459$		0			0
$460$	4.00000			0.186501
$461$	16.5000	−	28.5788i	0.768482	−	1.33105i	−0.169904	−	0.985461i	$-0.554346\pi$
$461$	16.5000	−	28.5788i	0.768482	−	1.33105i	0.938386	−	0.345589i	$-0.112321\pi$
$462$		0			0
$463$	16.0000			0.743583			0.371792	−	0.928316i	$-0.378744\pi$
$463$	16.0000			0.743583			0.371792	+	0.928316i	$0.378744\pi$
$464$	0.500000	−	0.866025i	0.0232119	−	0.0402042i
$465$		0			0
$466$	−5.00000	−	8.66025i	−0.231621	−	0.401179i
$467$	20.0000			0.925490			0.462745	−	0.886492i	$-0.346865\pi$
$467$	20.0000			0.925490			0.462745	+	0.886492i	$0.346865\pi$
$468$	7.50000	+	7.79423i	0.346688	+	0.360288i
$469$	16.0000			0.738811
$470$	−4.00000	−	6.92820i	−0.184506	−	0.319574i
$471$		0			0
$472$	2.00000	−	3.46410i	0.0920575	−	0.159448i
$473$	−32.0000			−1.47136
$474$		0			0
$475$		0			0
$476$	12.0000			0.550019
$477$	−13.5000	+	23.3827i	−0.618123	+	1.07062i
$478$	6.00000	+	10.3923i	0.274434	+	0.475333i
$479$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$479$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$480$		0			0
$481$	−7.50000	−	7.79423i	−0.341971	−	0.355386i
$482$	3.00000			0.136646
$483$		0			0
$484$	−2.50000	−	4.33013i	−0.113636	−	0.196824i
$485$	1.00000	−	1.73205i	0.0454077	−	0.0786484i
$486$		0			0
$487$	8.00000	−	13.8564i	0.362515	−	0.627894i	−0.625859	−	0.779936i	$-0.715252\pi$
$487$	8.00000	−	13.8564i	0.362515	−	0.627894i	0.988374	+	0.152042i	$0.0485850\pi$
$488$	−3.50000	+	6.06218i	−0.158438	+	0.274422i
$489$		0			0
$490$	4.50000	−	7.79423i	0.203289	−	0.352107i
$491$	4.00000	+	6.92820i	0.180517	+	0.312665i	0.942057	−	0.335453i	$-0.108889\pi$
$491$	4.00000	+	6.92820i	0.180517	+	0.312665i	−0.761539	+	0.648119i	$0.775556\pi$
$492$		0			0
$493$	−3.00000			−0.135113
$494$		0			0
$495$	12.0000			0.539360
$496$	−2.00000	−	3.46410i	−0.0898027	−	0.155543i
$497$	16.0000	+	27.7128i	0.717698	+	1.24309i
$498$		0			0
$499$	−32.0000			−1.43252			−0.716258	−	0.697835i	$-0.754147\pi$
$499$	−32.0000			−1.43252			−0.716258	+	0.697835i	$0.754147\pi$
$500$	−4.50000	+	7.79423i	−0.201246	+	0.348569i
$501$		0			0
$502$	−12.0000			−0.535586
$503$	−8.00000	+	13.8564i	−0.356702	+	0.617827i	−0.987408	−	0.158196i	$-0.949432\pi$
$503$	−8.00000	+	13.8564i	−0.356702	+	0.617827i	0.630705	+	0.776022i	$0.282766\pi$
$504$	6.00000	+	10.3923i	0.267261	+	0.462910i
$505$	3.50000	+	6.06218i	0.155748	+	0.269763i
$506$	−16.0000			−0.711287
$507$		0			0
$508$	−8.00000			−0.354943
$509$	−21.5000	−	37.2391i	−0.952971	−	1.65059i	−0.738945	−	0.673766i	$-0.764676\pi$
$509$	−21.5000	−	37.2391i	−0.952971	−	1.65059i	−0.214026	−	0.976828i	$-0.568658\pi$
$510$		0			0
$511$	−22.0000	+	38.1051i	−0.973223	+	1.68567i
$512$	1.00000			0.0441942
$513$		0			0
$514$	−7.50000	+	12.9904i	−0.330811	+	0.572981i
$515$	8.00000			0.352522
$516$		0			0
$517$	16.0000	+	27.7128i	0.703679	+	1.21881i
$518$	−6.00000	−	10.3923i	−0.263625	−	0.456612i
$519$		0			0
$520$	−3.50000	+	0.866025i	−0.153485	+	0.0379777i
$521$	39.0000			1.70862			0.854311	−	0.519763i	$-0.173980\pi$
$521$	39.0000			1.70862			0.854311	+	0.519763i	$0.173980\pi$
$522$	−1.50000	−	2.59808i	−0.0656532	−	0.113715i
$523$	−18.0000	−	31.1769i	−0.787085	−	1.36327i	−0.927746	−	0.373213i	$-0.878256\pi$
$523$	−18.0000	−	31.1769i	−0.787085	−	1.36327i	0.140660	−	0.990058i	$-0.455077\pi$
$524$	−10.0000	+	17.3205i	−0.436852	+	0.756650i
$525$		0			0
$526$	12.0000	−	20.7846i	0.523225	−	0.906252i
$527$	−6.00000	+	10.3923i	−0.261364	+	0.452696i
$528$		0			0
$529$	3.50000	−	6.06218i	0.152174	−	0.263573i
$530$	−4.50000	−	7.79423i	−0.195468	−	0.338560i
$531$	−6.00000	−	10.3923i	−0.260378	−	0.450988i
$532$		0			0
$533$	22.5000	+	23.3827i	0.974583	+	1.01282i
$534$		0			0
$535$	−2.00000	−	3.46410i	−0.0864675	−	0.149766i
$536$	−2.00000	−	3.46410i	−0.0863868	−	0.149626i
$537$		0			0
$538$	−18.0000			−0.776035
$539$	−18.0000	+	31.1769i	−0.775315	+	1.34288i
$540$		0			0
$541$	−25.0000			−1.07483			−0.537417	−	0.843317i	$-0.680600\pi$
$541$	−25.0000			−1.07483			−0.537417	+	0.843317i	$0.680600\pi$
$542$	10.0000	−	17.3205i	0.429537	−	0.743980i
$543$		0			0
$544$	−1.50000	−	2.59808i	−0.0643120	−	0.111392i
$545$	2.00000			0.0856706
$546$		0			0
$547$	16.0000			0.684111			0.342055	−	0.939680i	$-0.388877\pi$
$547$	16.0000			0.684111			0.342055	+	0.939680i	$0.388877\pi$
$548$	4.50000	+	7.79423i	0.192230	+	0.332953i
$549$	10.5000	+	18.1865i	0.448129	+	0.776182i
$550$	8.00000	−	13.8564i	0.341121	−	0.590839i
$551$		0			0
$552$		0			0
$553$	8.00000	−	13.8564i	0.340195	−	0.589234i
$554$	−9.00000			−0.382373
$555$		0			0
$556$	−8.00000	−	13.8564i	−0.339276	−	0.587643i
$557$	−19.5000	−	33.7750i	−0.826242	−	1.43109i	−0.900967	−	0.433888i	$-0.857141\pi$
$557$	−19.5000	−	33.7750i	−0.826242	−	1.43109i	0.0747252	−	0.997204i	$-0.476192\pi$
$558$	−12.0000			−0.508001
$559$	8.00000	−	27.7128i	0.338364	−	1.17213i
$560$	−4.00000			−0.169031
$561$		0			0
$562$	2.50000	+	4.33013i	0.105456	+	0.182655i
$563$	2.00000	−	3.46410i	0.0842900	−	0.145994i	−0.820798	−	0.571218i	$-0.806471\pi$
$563$	2.00000	−	3.46410i	0.0842900	−	0.145994i	0.905088	+	0.425223i	$0.139804\pi$
$564$		0			0
$565$	−0.500000	+	0.866025i	−0.0210352	+	0.0364340i
$566$	−14.0000	+	24.2487i	−0.588464	+	1.01925i
$567$	36.0000			1.51186
$568$	4.00000	−	6.92820i	0.167836	−	0.290701i
$569$	−5.00000	−	8.66025i	−0.209611	−	0.363057i	0.741981	−	0.670421i	$-0.233886\pi$
$569$	−5.00000	−	8.66025i	−0.209611	−	0.363057i	−0.951592	+	0.307364i	$0.900553\pi$
$570$		0			0
$571$	12.0000			0.502184			0.251092	−	0.967963i	$-0.419210\pi$
$571$	12.0000			0.502184			0.251092	+	0.967963i	$0.419210\pi$
$572$	14.0000	−	3.46410i	0.585369	−	0.144841i
$573$		0			0
$574$	18.0000	+	31.1769i	0.751305	+	1.30130i
$575$	−8.00000	−	13.8564i	−0.333623	−	0.577852i
$576$	1.50000	−	2.59808i	0.0625000	−	0.108253i
$577$	39.0000			1.62359			0.811796	−	0.583942i	$-0.198490\pi$
$577$	39.0000			1.62359			0.811796	+	0.583942i	$0.198490\pi$
$578$	4.00000	−	6.92820i	0.166378	−	0.288175i
$579$		0			0
$580$	1.00000			0.0415227
$581$		0			0
$582$		0			0
$583$	18.0000	+	31.1769i	0.745484	+	1.29122i
$584$	11.0000			0.455183
$585$	−3.00000	+	10.3923i	−0.124035	+	0.429669i
$586$	−5.00000			−0.206548
$587$	8.00000	+	13.8564i	0.330195	+	0.571915i	0.982550	−	0.185999i	$-0.0595520\pi$
$587$	8.00000	+	13.8564i	0.330195	+	0.571915i	−0.652355	+	0.757914i	$0.726219\pi$
$588$		0			0
$589$		0			0
$590$	4.00000			0.164677
$591$		0			0
$592$	−1.50000	+	2.59808i	−0.0616496	+	0.106780i
$593$	−1.00000			−0.0410651			−0.0205325	−	0.999789i	$-0.506536\pi$
$593$	−1.00000			−0.0410651			−0.0205325	+	0.999789i	$0.506536\pi$
$594$		0			0
$595$	6.00000	+	10.3923i	0.245976	+	0.426043i
$596$	−7.50000	−	12.9904i	−0.307212	−	0.532107i
$597$		0			0
$598$	4.00000	−	13.8564i	0.163572	−	0.566631i
$599$	−44.0000			−1.79779			−0.898896	−	0.438163i	$-0.855629\pi$
$599$	−44.0000			−1.79779			−0.898896	+	0.438163i	$0.855629\pi$
$600$		0			0
$601$	−9.50000	−	16.4545i	−0.387513	−	0.671192i	0.604601	−	0.796528i	$-0.293332\pi$
$601$	−9.50000	−	16.4545i	−0.387513	−	0.671192i	−0.992114	+	0.125336i	$0.959999\pi$
$602$	16.0000	−	27.7128i	0.652111	−	1.12949i
$603$	−12.0000			−0.488678
$604$	−6.00000	+	10.3923i	−0.244137	+	0.422857i
$605$	2.50000	−	4.33013i	0.101639	−	0.176045i
$606$		0			0
$607$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$607$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$608$		0			0
$609$		0			0
$610$	−7.00000			−0.283422
$611$	−28.0000	+	6.92820i	−1.13276	+	0.280285i
$612$	−9.00000			−0.363803
$613$	−5.50000	−	9.52628i	−0.222143	−	0.384763i	0.733316	−	0.679888i	$-0.237972\pi$
$613$	−5.50000	−	9.52628i	−0.222143	−	0.384763i	−0.955458	+	0.295126i	$0.904638\pi$
$614$	14.0000	+	24.2487i	0.564994	+	0.978598i
$615$		0			0
$616$	16.0000			0.644658
$617$	14.5000	−	25.1147i	0.583748	−	1.01108i	−0.411282	−	0.911508i	$-0.634919\pi$
$617$	14.5000	−	25.1147i	0.583748	−	1.01108i	0.995030	−	0.0995732i	$-0.0317477\pi$
$618$		0			0
$619$	4.00000			0.160774			0.0803868	−	0.996764i	$-0.474384\pi$
$619$	4.00000			0.160774			0.0803868	+	0.996764i	$0.474384\pi$
$620$	2.00000	−	3.46410i	0.0803219	−	0.139122i
$621$		0			0
$622$	12.0000	+	20.7846i	0.481156	+	0.833387i
$623$	−24.0000			−0.961540
$624$		0			0
$625$	11.0000			0.440000
$626$	11.0000	+	19.0526i	0.439648	+	0.761493i
$627$		0			0
$628$	−5.50000	+	9.52628i	−0.219474	+	0.380140i
$629$	9.00000			0.358854
$630$	−6.00000	+	10.3923i	−0.239046	+	0.414039i
$631$	4.00000	−	6.92820i	0.159237	−	0.275807i	−0.775356	−	0.631524i	$-0.782430\pi$
$631$	4.00000	−	6.92820i	0.159237	−	0.275807i	0.934594	+	0.355716i	$0.115763\pi$
$632$	−4.00000			−0.159111
$633$		0			0
$634$	−1.50000	−	2.59808i	−0.0595726	−	0.103183i
$635$	−4.00000	−	6.92820i	−0.158735	−	0.274937i
$636$		0			0
$637$	−22.5000	−	23.3827i	−0.891482	−	0.926456i
$638$	−4.00000			−0.158362
$639$	−12.0000	−	20.7846i	−0.474713	−	0.822226i
$640$	0.500000	+	0.866025i	0.0197642	+	0.0342327i
$641$	−9.50000	+	16.4545i	−0.375227	+	0.649913i	−0.990361	−	0.138510i	$-0.955769\pi$
$641$	−9.50000	+	16.4545i	−0.375227	+	0.649913i	0.615134	+	0.788423i	$0.289102\pi$
$642$		0			0
$643$	−22.0000	+	38.1051i	−0.867595	+	1.50272i	−0.00314839	+	0.999995i	$0.501002\pi$
$643$	−22.0000	+	38.1051i	−0.867595	+	1.50272i	−0.864447	+	0.502724i	$0.832331\pi$
$644$	8.00000	−	13.8564i	0.315244	−	0.546019i
$645$		0			0
$646$		0			0
$647$	−14.0000	−	24.2487i	−0.550397	−	0.953315i	−0.998246	−	0.0592060i	$-0.981143\pi$
$647$	−14.0000	−	24.2487i	−0.550397	−	0.953315i	0.447849	−	0.894109i	$-0.352190\pi$
$648$	−4.50000	−	7.79423i	−0.176777	−	0.306186i
$649$	−16.0000			−0.628055
$650$	10.0000	+	10.3923i	0.392232	+	0.407620i
$651$		0			0
$652$	−4.00000	−	6.92820i	−0.156652	−	0.271329i
$653$	9.00000	+	15.5885i	0.352197	+	0.610023i	0.986634	−	0.162951i	$-0.0521013\pi$
$653$	9.00000	+	15.5885i	0.352197	+	0.610023i	−0.634437	+	0.772975i	$0.718768\pi$
$654$		0			0
$655$	−20.0000			−0.781465
$656$	4.50000	−	7.79423i	0.175695	−	0.304314i
$657$	16.5000	−	28.5788i	0.643726	−	1.11497i
$658$	−32.0000			−1.24749
$659$	−24.0000	+	41.5692i	−0.934907	+	1.61931i	−0.160108	+	0.987099i	$0.551184\pi$
$659$	−24.0000	+	41.5692i	−0.934907	+	1.61931i	−0.774799	+	0.632207i	$0.782149\pi$
$660$		0			0
$661$	24.5000	+	42.4352i	0.952940	+	1.65054i	0.739014	+	0.673690i	$0.235292\pi$
$661$	24.5000	+	42.4352i	0.952940	+	1.65054i	0.213925	+	0.976850i	$0.431375\pi$
$662$	8.00000			0.310929
$663$		0			0
$664$		0			0
$665$		0			0
$666$	4.50000	+	7.79423i	0.174371	+	0.302020i
$667$	−2.00000	+	3.46410i	−0.0774403	+	0.134131i
$668$	12.0000			0.464294
$669$		0			0
$670$	2.00000	−	3.46410i	0.0772667	−	0.133830i
$671$	28.0000			1.08093
$672$		0			0
$673$	14.5000	+	25.1147i	0.558934	+	0.968102i	0.997586	+	0.0694449i	$0.0221228\pi$
$673$	14.5000	+	25.1147i	0.558934	+	0.968102i	−0.438652	+	0.898657i	$0.644544\pi$
$674$	−11.5000	−	19.9186i	−0.442963	−	0.767235i
$675$		0			0
$676$	−0.500000	+	12.9904i	−0.0192308	+	0.499630i
$677$	6.00000			0.230599			0.115299	−	0.993331i	$-0.463217\pi$
$677$	6.00000			0.230599			0.115299	+	0.993331i	$0.463217\pi$
$678$		0			0
$679$	−4.00000	−	6.92820i	−0.153506	−	0.265880i
$680$	1.50000	−	2.59808i	0.0575224	−	0.0996317i
$681$		0			0
$682$	−8.00000	+	13.8564i	−0.306336	+	0.530589i
$683$	22.0000	−	38.1051i	0.841807	−	1.45805i	−0.0465592	−	0.998916i	$-0.514826\pi$
$683$	22.0000	−	38.1051i	0.841807	−	1.45805i	0.888366	−	0.459136i	$-0.151841\pi$
$684$		0			0
$685$	−4.50000	+	7.79423i	−0.171936	+	0.297802i
$686$	−4.00000	−	6.92820i	−0.152721	−	0.264520i
$687$		0			0
$688$	−8.00000			−0.304997
$689$	−31.5000	+	7.79423i	−1.20005	+	0.296936i
$690$		0			0
$691$	10.0000	+	17.3205i	0.380418	+	0.658903i	0.991122	−	0.132956i	$-0.0424468\pi$
$691$	10.0000	+	17.3205i	0.380418	+	0.658903i	−0.610704	+	0.791859i	$0.709113\pi$
$692$	−7.00000	−	12.1244i	−0.266100	−	0.460899i
$693$	24.0000	−	41.5692i	0.911685	−	1.57908i
$694$	12.0000			0.455514
$695$	8.00000	−	13.8564i	0.303457	−	0.525603i
$696$		0			0
$697$	−27.0000			−1.02270
$698$	1.00000	−	1.73205i	0.0378506	−	0.0655591i
$699$		0			0
$700$	8.00000	+	13.8564i	0.302372	+	0.523723i
$701$	30.0000			1.13308			0.566542	−	0.824033i	$-0.308281\pi$
$701$	30.0000			1.13308			0.566542	+	0.824033i	$0.308281\pi$
$702$		0			0
$703$		0			0
$704$	−2.00000	−	3.46410i	−0.0753778	−	0.130558i
$705$		0			0
$706$	−3.50000	+	6.06218i	−0.131724	+	0.228153i
$707$	28.0000			1.05305
$708$		0			0
$709$	6.50000	−	11.2583i	0.244113	−	0.422815i	−0.717769	−	0.696281i	$-0.754837\pi$
$709$	6.50000	−	11.2583i	0.244113	−	0.422815i	0.961882	+	0.273466i	$0.0881700\pi$
$710$	8.00000			0.300235
$711$	−6.00000	+	10.3923i	−0.225018	+	0.389742i
$712$	3.00000	+	5.19615i	0.112430	+	0.194734i
$713$	8.00000	+	13.8564i	0.299602	+	0.518927i
$714$		0			0
$715$	10.0000	+	10.3923i	0.373979	+	0.388650i
$716$	−24.0000			−0.896922
$717$		0			0
$718$	−12.0000	−	20.7846i	−0.447836	−	0.775675i
$719$	14.0000	−	24.2487i	0.522112	−	0.904324i	−0.477557	−	0.878601i	$-0.658478\pi$
$719$	14.0000	−	24.2487i	0.522112	−	0.904324i	0.999669	−	0.0257237i	$-0.00818900\pi$
$720$	3.00000			0.111803
$721$	16.0000	−	27.7128i	0.595871	−	1.03208i
$722$	9.50000	−	16.4545i	0.353553	−	0.612372i
$723$		0			0
$724$	10.5000	−	18.1865i	0.390229	−	0.675897i
$725$	−2.00000	−	3.46410i	−0.0742781	−	0.128654i
$726$		0			0
$727$	28.0000			1.03846			0.519231	−	0.854634i	$-0.326218\pi$
$727$	28.0000			1.03846			0.519231	+	0.854634i	$0.326218\pi$
$728$	−4.00000	+	13.8564i	−0.148250	+	0.513553i
$729$	−27.0000			−1.00000
$730$	5.50000	+	9.52628i	0.203564	+	0.352583i
$731$	12.0000	+	20.7846i	0.443836	+	0.768747i
$732$		0			0
$733$	−1.00000			−0.0369358			−0.0184679	−	0.999829i	$-0.505879\pi$
$733$	−1.00000			−0.0369358			−0.0184679	+	0.999829i	$0.505879\pi$
$734$	14.0000	−	24.2487i	0.516749	−	0.895036i
$735$		0			0
$736$	−4.00000			−0.147442
$737$	−8.00000	+	13.8564i	−0.294684	+	0.510407i
$738$	−13.5000	−	23.3827i	−0.496942	−	0.860729i
$739$	12.0000	+	20.7846i	0.441427	+	0.764574i	0.997796	−	0.0663614i	$-0.0211390\pi$
$739$	12.0000	+	20.7846i	0.441427	+	0.764574i	−0.556369	+	0.830936i	$0.687806\pi$
$740$	−3.00000			−0.110282
$741$		0			0
$742$	−36.0000			−1.32160
$743$	4.00000	+	6.92820i	0.146746	+	0.254171i	0.930023	−	0.367502i	$-0.119787\pi$
$743$	4.00000	+	6.92820i	0.146746	+	0.254171i	−0.783277	+	0.621673i	$0.786453\pi$
$744$		0			0
$745$	7.50000	−	12.9904i	0.274779	−	0.475931i
$746$	−13.0000			−0.475964
$747$		0			0
$748$	−6.00000	+	10.3923i	−0.219382	+	0.379980i
$749$	−16.0000			−0.584627
$750$		0			0
$751$	−12.0000	−	20.7846i	−0.437886	−	0.758441i	0.559640	−	0.828736i	$-0.310939\pi$
$751$	−12.0000	−	20.7846i	−0.437886	−	0.758441i	−0.997526	+	0.0702946i	$0.977606\pi$
$752$	4.00000	+	6.92820i	0.145865	+	0.252646i
$753$		0			0
$754$	1.00000	−	3.46410i	0.0364179	−	0.126155i
$755$	−12.0000			−0.436725
$756$		0			0
$757$	−3.00000	−	5.19615i	−0.109037	−	0.188857i	0.806343	−	0.591448i	$-0.201443\pi$
$757$	−3.00000	−	5.19615i	−0.109037	−	0.188857i	−0.915380	+	0.402590i	$0.868110\pi$
$758$	4.00000	−	6.92820i	0.145287	−	0.251644i
$759$		0			0
$760$		0			0
$761$	−21.0000	+	36.3731i	−0.761249	+	1.31852i	0.180957	+	0.983491i	$0.442080\pi$
$761$	−21.0000	+	36.3731i	−0.761249	+	1.31852i	−0.942207	+	0.335032i	$0.891253\pi$
$762$		0			0
$763$	4.00000	−	6.92820i	0.144810	−	0.250818i
$764$	10.0000	+	17.3205i	0.361787	+	0.626634i
$765$	−4.50000	−	7.79423i	−0.162698	−	0.281801i
$766$		0			0
$767$	4.00000	−	13.8564i	0.144432	−	0.500326i
$768$		0			0
$769$	15.0000	+	25.9808i	0.540914	+	0.936890i	0.998852	+	0.0479061i	$0.0152548\pi$
$769$	15.0000	+	25.9808i	0.540914	+	0.936890i	−0.457938	+	0.888984i	$0.651412\pi$
$770$	8.00000	+	13.8564i	0.288300	+	0.499350i
$771$		0			0
$772$	11.0000			0.395899
$773$	−19.0000	+	32.9090i	−0.683383	+	1.18365i	0.290560	+	0.956857i	$0.406159\pi$
$773$	−19.0000	+	32.9090i	−0.683383	+	1.18365i	−0.973942	+	0.226796i	$0.927175\pi$
$774$	−12.0000	+	20.7846i	−0.431331	+	0.747087i
$775$	−16.0000			−0.574737
$776$	−1.00000	+	1.73205i	−0.0358979	+	0.0621770i
$777$		0			0
$778$	4.50000	+	7.79423i	0.161333	+	0.279437i
$779$		0			0
$780$		0			0
$781$	−32.0000			−1.14505
$782$	6.00000	+	10.3923i	0.214560	+	0.371628i
$783$		0			0
$784$	−4.50000	+	7.79423i	−0.160714	+	0.278365i
$785$	−11.0000			−0.392607
$786$		0			0
$787$	2.00000	−	3.46410i	0.0712923	−	0.123482i	−0.828176	−	0.560469i	$-0.810621\pi$
$787$	2.00000	−	3.46410i	0.0712923	−	0.123482i	0.899468	+	0.436987i	$0.143954\pi$
$788$	6.00000			0.213741
$789$		0			0
$790$	−2.00000	−	3.46410i	−0.0711568	−	0.123247i
$791$	2.00000	+	3.46410i	0.0711118	+	0.123169i
$792$	−12.0000			−0.426401
$793$	−7.00000	+	24.2487i	−0.248577	+	0.861097i
$794$	14.0000			0.496841
$795$		0			0
$796$	2.00000	+	3.46410i	0.0708881	+	0.122782i
$797$	−15.0000	+	25.9808i	−0.531327	+	0.920286i	0.468004	+	0.883726i	$0.344973\pi$
$797$	−15.0000	+	25.9808i	−0.531327	+	0.920286i	−0.999331	+	0.0365596i	$0.988360\pi$
$798$		0			0
$799$	12.0000	−	20.7846i	0.424529	−	0.735307i
$800$	2.00000	−	3.46410i	0.0707107	−	0.122474i
$801$	18.0000			0.635999
$802$	−1.50000	+	2.59808i	−0.0529668	+	0.0917413i
$803$	−22.0000	−	38.1051i	−0.776363	−	1.34470i
$804$		0			0
$805$	16.0000			0.563926
$806$	−10.0000	−	10.3923i	−0.352235	−	0.366053i
$807$		0			0
$808$	−3.50000	−	6.06218i	−0.123130	−	0.213267i
$809$	−19.5000	−	33.7750i	−0.685583	−	1.18747i	−0.973253	−	0.229736i	$-0.926214\pi$
$809$	−19.5000	−	33.7750i	−0.685583	−	1.18747i	0.287670	−	0.957730i	$-0.407120\pi$
$810$	4.50000	−	7.79423i	0.158114	−	0.273861i
$811$	−28.0000			−0.983213			−0.491606	−	0.870817i	$-0.663590\pi$
$811$	−28.0000			−0.983213			−0.491606	+	0.870817i	$0.663590\pi$
$812$	2.00000	−	3.46410i	0.0701862	−	0.121566i
$813$		0			0
$814$	12.0000			0.420600
$815$	4.00000	−	6.92820i	0.140114	−	0.242684i
$816$		0			0
$817$		0			0
$818$	31.0000			1.08389
$819$	30.0000	+	31.1769i	1.04828	+	1.08941i
$820$	9.00000			0.314294
$821$	−19.0000	−	32.9090i	−0.663105	−	1.14853i	−0.979795	−	0.200002i	$-0.935905\pi$
$821$	−19.0000	−	32.9090i	−0.663105	−	1.14853i	0.316691	−	0.948529i	$-0.397428\pi$
$822$		0			0
$823$	−6.00000	+	10.3923i	−0.209147	+	0.362253i	−0.951446	−	0.307816i	$-0.900402\pi$
$823$	−6.00000	+	10.3923i	−0.209147	+	0.362253i	0.742299	+	0.670069i	$0.233735\pi$
$824$	−8.00000			−0.278693
$825$		0			0
$826$	8.00000	−	13.8564i	0.278356	−	0.482126i
$827$	−12.0000			−0.417281			−0.208640	−	0.977992i	$-0.566904\pi$
$827$	−12.0000			−0.417281			−0.208640	+	0.977992i	$0.566904\pi$
$828$	−6.00000	+	10.3923i	−0.208514	+	0.361158i
$829$	−3.50000	−	6.06218i	−0.121560	−	0.210548i	0.798823	−	0.601566i	$-0.205456\pi$
$829$	−3.50000	−	6.06218i	−0.121560	−	0.210548i	−0.920383	+	0.391018i	$0.872123\pi$
$830$		0			0
$831$		0			0
$832$	3.50000	−	0.866025i	0.121341	−	0.0300240i
$833$	27.0000			0.935495
$834$		0			0
$835$	6.00000	+	10.3923i	0.207639	+	0.359641i
$836$		0			0
$837$		0			0
$838$	−6.00000	+	10.3923i	−0.207267	+	0.358996i
$839$	20.0000	−	34.6410i	0.690477	−	1.19594i	−0.281205	−	0.959648i	$-0.590734\pi$
$839$	20.0000	−	34.6410i	0.690477	−	1.19594i	0.971682	−	0.236293i	$-0.0759325\pi$
$840$		0			0
$841$	14.0000	−	24.2487i	0.482759	−	0.836162i
$842$	2.50000	+	4.33013i	0.0861557	+	0.149226i
$843$		0			0
$844$	20.0000			0.688428
$845$	−11.5000	+	6.06218i	−0.395612	+	0.208545i
$846$	24.0000			0.825137
$847$	−10.0000	−	17.3205i	−0.343604	−	0.595140i
$848$	4.50000	+	7.79423i	0.154531	+	0.267655i
$849$		0			0
$850$	−12.0000			−0.411597
$851$	6.00000	−	10.3923i	0.205677	−	0.356244i
$852$		0			0
$853$	7.00000			0.239675			0.119838	−	0.992793i	$-0.461763\pi$
$853$	7.00000			0.239675			0.119838	+	0.992793i	$0.461763\pi$
$854$	−14.0000	+	24.2487i	−0.479070	+	0.829774i
$855$		0			0
$856$	2.00000	+	3.46410i	0.0683586	+	0.118401i
$857$	−17.0000			−0.580709			−0.290354	−	0.956919i	$-0.593773\pi$
$857$	−17.0000			−0.580709			−0.290354	+	0.956919i	$0.593773\pi$
$858$		0			0
$859$	20.0000			0.682391			0.341196	−	0.939992i	$-0.389168\pi$
$859$	20.0000			0.682391			0.341196	+	0.939992i	$0.389168\pi$
$860$	−4.00000	−	6.92820i	−0.136399	−	0.236250i
$861$		0			0
$862$	12.0000	−	20.7846i	0.408722	−	0.707927i
$863$	52.0000			1.77010			0.885050	−	0.465495i	$-0.154124\pi$
$863$	52.0000			1.77010			0.885050	+	0.465495i	$0.154124\pi$
$864$		0			0
$865$	7.00000	−	12.1244i	0.238007	−	0.412240i
$866$	−5.00000			−0.169907
$867$		0			0
$868$	−8.00000	−	13.8564i	−0.271538	−	0.470317i
$869$	8.00000	+	13.8564i	0.271381	+	0.470046i
$870$		0			0
$871$	−10.0000	−	10.3923i	−0.338837	−	0.352130i
$872$	−2.00000			−0.0677285
$873$	3.00000	+	5.19615i	0.101535	+	0.175863i
$874$		0			0
$875$	−18.0000	+	31.1769i	−0.608511	+	1.05397i
$876$		0			0
$877$	−7.50000	+	12.9904i	−0.253257	+	0.438654i	−0.964421	−	0.264373i	$-0.914835\pi$
$877$	−7.50000	+	12.9904i	−0.253257	+	0.438654i	0.711164	+	0.703027i	$0.248168\pi$
$878$	−4.00000	+	6.92820i	−0.134993	+	0.233816i
$879$		0			0
$880$	2.00000	−	3.46410i	0.0674200	−	0.116775i
$881$	4.50000	+	7.79423i	0.151609	+	0.262594i	0.931819	−	0.362923i	$-0.118221\pi$
$881$	4.50000	+	7.79423i	0.151609	+	0.262594i	−0.780210	+	0.625517i	$0.784888\pi$
$882$	13.5000	+	23.3827i	0.454569	+	0.787336i
$883$	16.0000			0.538443			0.269221	−	0.963078i	$-0.413234\pi$
$883$	16.0000			0.538443			0.269221	+	0.963078i	$0.413234\pi$
$884$	−7.50000	−	7.79423i	−0.252252	−	0.262148i
$885$		0			0
$886$	−12.0000	−	20.7846i	−0.403148	−	0.698273i
$887$	10.0000	+	17.3205i	0.335767	+	0.581566i	0.983632	−	0.180190i	$-0.0576711\pi$
$887$	10.0000	+	17.3205i	0.335767	+	0.581566i	−0.647865	+	0.761755i	$0.724338\pi$
$888$		0			0
$889$	−32.0000			−1.07325
$890$	−3.00000	+	5.19615i	−0.100560	+	0.174175i
$891$	−18.0000	+	31.1769i	−0.603023	+	1.04447i
$892$	12.0000			0.401790
$893$		0			0
$894$		0			0
$895$	−12.0000	−	20.7846i	−0.401116	−	0.694753i
$896$	4.00000			0.133631
$897$		0			0
$898$	34.0000			1.13459
$899$	2.00000	+	3.46410i	0.0667037	+	0.115534i
$900$	−6.00000	−	10.3923i	−0.200000	−	0.346410i
$901$	13.5000	−	23.3827i	0.449750	−	0.778990i
$902$	−36.0000			−1.19867
$903$		0			0
$904$	0.500000	−	0.866025i	0.0166298	−	0.0288036i
$905$	21.0000			0.698064
$906$		0			0
$907$	12.0000	+	20.7846i	0.398453	+	0.690142i	0.993535	−	0.113523i	$-0.0362137\pi$
$907$	12.0000	+	20.7846i	0.398453	+	0.690142i	−0.595082	+	0.803665i	$0.702880\pi$
$908$	−12.0000	−	20.7846i	−0.398234	−	0.689761i
$909$	−21.0000			−0.696526
$910$	−14.0000	+	3.46410i	−0.464095	+	0.114834i
$911$	−12.0000			−0.397578			−0.198789	−	0.980042i	$-0.563701\pi$
$911$	−12.0000			−0.397578			−0.198789	+	0.980042i	$0.563701\pi$
$912$		0			0
$913$		0			0
$914$	−15.5000	+	26.8468i	−0.512694	+	0.888013i
$915$		0			0
$916$	−3.00000	+	5.19615i	−0.0991228	+	0.171686i
$917$	−40.0000	+	69.2820i	−1.32092	+	2.28789i
$918$		0			0
$919$	24.0000	−	41.5692i	0.791687	−	1.37124i	−0.133235	−	0.991084i	$-0.542536\pi$
$919$	24.0000	−	41.5692i	0.791687	−	1.37124i	0.924922	−	0.380158i	$-0.124130\pi$
$920$	−2.00000	−	3.46410i	−0.0659380	−	0.114208i
$921$		0			0
$922$	−33.0000			−1.08680
$923$	8.00000	−	27.7128i	0.263323	−	0.912178i
$924$		0			0
$925$	6.00000	+	10.3923i	0.197279	+	0.341697i
$926$	−8.00000	−	13.8564i	−0.262896	−	0.455350i
$927$	−12.0000	+	20.7846i	−0.394132	+	0.682656i
$928$	−1.00000			−0.0328266
$929$	10.5000	−	18.1865i	0.344494	−	0.596681i	−0.640768	−	0.767735i	$-0.721384\pi$
$929$	10.5000	−	18.1865i	0.344494	−	0.596681i	0.985262	+	0.171054i	$0.0547172\pi$
$930$		0			0
$931$		0			0
$932$	−5.00000	+	8.66025i	−0.163780	+	0.283676i
$933$		0			0
$934$	−10.0000	−	17.3205i	−0.327210	−	0.566744i
$935$	−12.0000			−0.392442
$936$	3.00000	−	10.3923i	0.0980581	−	0.339683i
$937$	−21.0000			−0.686040			−0.343020	−	0.939328i	$-0.611450\pi$
$937$	−21.0000			−0.686040			−0.343020	+	0.939328i	$0.611450\pi$
$938$	−8.00000	−	13.8564i	−0.261209	−	0.452428i
$939$		0			0
$940$	−4.00000	+	6.92820i	−0.130466	+	0.225973i
$941$	46.0000			1.49956			0.749779	−	0.661689i	$-0.230160\pi$
$941$	46.0000			1.49956			0.749779	+	0.661689i	$0.230160\pi$
$942$		0			0
$943$	−18.0000	+	31.1769i	−0.586161	+	1.01526i
$944$	−4.00000			−0.130189
$945$		0			0
$946$	16.0000	+	27.7128i	0.520205	+	0.901021i
$947$	−12.0000	−	20.7846i	−0.389948	−	0.675409i	0.602494	−	0.798123i	$-0.294174\pi$
$947$	−12.0000	−	20.7846i	−0.389948	−	0.675409i	−0.992442	+	0.122714i	$0.960840\pi$
$948$		0			0
$949$	38.5000	−	9.52628i	1.24976	−	0.309236i
$950$		0			0
$951$		0			0
$952$	−6.00000	−	10.3923i	−0.194461	−	0.336817i
$953$	11.0000	−	19.0526i	0.356325	−	0.617173i	−0.631019	−	0.775768i	$-0.717363\pi$
$953$	11.0000	−	19.0526i	0.356325	−	0.617173i	0.987344	+	0.158595i	$0.0506963\pi$
$954$	27.0000			0.874157
$955$	−10.0000	+	17.3205i	−0.323592	+	0.560478i
$956$	6.00000	−	10.3923i	0.194054	−	0.336111i
$957$		0			0
$958$		0			0
$959$	18.0000	+	31.1769i	0.581250	+	1.00676i
$960$		0			0
$961$	−15.0000			−0.483871
$962$	−3.00000	+	10.3923i	−0.0967239	+	0.335061i
$963$	12.0000			0.386695
$964$	−1.50000	−	2.59808i	−0.0483117	−	0.0836784i
$965$	5.50000	+	9.52628i	0.177051	+	0.306662i
$966$		0			0
$967$	−40.0000			−1.28631			−0.643157	−	0.765735i	$-0.722376\pi$
$967$	−40.0000			−1.28631			−0.643157	+	0.765735i	$0.722376\pi$
$968$	−2.50000	+	4.33013i	−0.0803530	+	0.139176i
$969$		0			0
$970$	−2.00000			−0.0642161
$971$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$971$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$972$		0			0
$973$	−32.0000	−	55.4256i	−1.02587	−	1.77686i
$974$	−16.0000			−0.512673
$975$		0			0
$976$	7.00000			0.224065
$977$	22.5000	+	38.9711i	0.719839	+	1.24680i	0.961063	+	0.276328i	$0.0891176\pi$
$977$	22.5000	+	38.9711i	0.719839	+	1.24680i	−0.241225	+	0.970469i	$0.577549\pi$
$978$		0			0
$979$	12.0000	−	20.7846i	0.383522	−	0.664279i
$980$	−9.00000			−0.287494
$981$	−3.00000	+	5.19615i	−0.0957826	+	0.165900i
$982$	4.00000	−	6.92820i	0.127645	−	0.221088i
$983$	−52.0000			−1.65854			−0.829271	−	0.558846i	$-0.811244\pi$
$983$	−52.0000			−1.65854			−0.829271	+	0.558846i	$0.811244\pi$
$984$		0			0
$985$	3.00000	+	5.19615i	0.0955879	+	0.165563i
$986$	1.50000	+	2.59808i	0.0477697	+	0.0827396i
$987$		0			0
$988$		0			0
$989$	32.0000			1.01754
$990$	−6.00000	−	10.3923i	−0.190693	−	0.330289i
$991$	12.0000	+	20.7846i	0.381193	+	0.660245i	0.991233	−	0.132125i	$-0.0421802\pi$
$991$	12.0000	+	20.7846i	0.381193	+	0.660245i	−0.610040	+	0.792370i	$0.708847\pi$
$992$	−2.00000	+	3.46410i	−0.0635001	+	0.109985i
$993$		0			0
$994$	16.0000	−	27.7128i	0.507489	−	0.878997i
$995$	−2.00000	+	3.46410i	−0.0634043	+	0.109819i
$996$		0			0
$997$	12.5000	−	21.6506i	0.395879	−	0.685682i	−0.597334	−	0.801993i	$-0.703773\pi$
$997$	12.5000	−	21.6506i	0.395879	−	0.685682i	0.993213	+	0.116310i	$0.0371066\pi$
$998$	16.0000	+	27.7128i	0.506471	+	0.877234i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	26.2.c.a.3.1	✓	2
3.2	odd	2		234.2.h.c.55.1		2
4.3	odd	2		208.2.i.b.81.1		2
5.2	odd	4		650.2.o.c.549.2		4
5.3	odd	4		650.2.o.c.549.1		4
5.4	even	2		650.2.e.c.601.1		2
7.2	even	3		1274.2.h.b.263.1		2
7.3	odd	6		1274.2.e.m.471.1		2
7.4	even	3		1274.2.e.n.471.1		2
7.5	odd	6		1274.2.h.a.263.1		2
7.6	odd	2		1274.2.g.a.393.1		2
8.3	odd	2		832.2.i.f.705.1		2
8.5	even	2		832.2.i.e.705.1		2
12.11	even	2		1872.2.t.k.289.1		2
13.2	odd	12		338.2.b.b.337.1		2
13.3	even	3		338.2.a.e.1.1		1
13.4	even	6		338.2.c.e.191.1		2
13.5	odd	4		338.2.e.b.23.1		4
13.6	odd	12		338.2.e.b.147.2		4
13.7	odd	12		338.2.e.b.147.1		4
13.8	odd	4		338.2.e.b.23.2		4
13.9	even	3	inner	26.2.c.a.9.1	yes	2
13.10	even	6		338.2.a.c.1.1		1
13.11	odd	12		338.2.b.b.337.2		2
13.12	even	2		338.2.c.e.315.1		2
39.2	even	12		3042.2.b.e.1351.2		2
39.11	even	12		3042.2.b.e.1351.1		2
39.23	odd	6		3042.2.a.k.1.1		1
39.29	odd	6		3042.2.a.e.1.1		1
39.35	odd	6		234.2.h.c.217.1		2
52.3	odd	6		2704.2.a.h.1.1		1
52.11	even	12		2704.2.f.g.337.1		2
52.15	even	12		2704.2.f.g.337.2		2
52.23	odd	6		2704.2.a.i.1.1		1
52.35	odd	6		208.2.i.b.113.1		2
65.9	even	6		650.2.e.c.451.1		2
65.22	odd	12		650.2.o.c.399.1		4
65.29	even	6		8450.2.a.f.1.1		1
65.48	odd	12		650.2.o.c.399.2		4
65.49	even	6		8450.2.a.s.1.1		1
91.9	even	3		1274.2.e.n.165.1		2
91.48	odd	6		1274.2.g.a.295.1		2
91.61	odd	6		1274.2.e.m.165.1		2
91.74	even	3		1274.2.h.b.373.1		2
91.87	odd	6		1274.2.h.a.373.1		2
104.35	odd	6		832.2.i.f.321.1		2
104.61	even	6		832.2.i.e.321.1		2
156.35	even	6		1872.2.t.k.1153.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
26.2.c.a.3.1	✓	2	1.1	even	1	trivial
26.2.c.a.9.1	yes	2	13.9	even	3	inner
208.2.i.b.81.1		2	4.3	odd	2
208.2.i.b.113.1		2	52.35	odd	6
234.2.h.c.55.1		2	3.2	odd	2
234.2.h.c.217.1		2	39.35	odd	6
338.2.a.c.1.1		1	13.10	even	6
338.2.a.e.1.1		1	13.3	even	3
338.2.b.b.337.1		2	13.2	odd	12
338.2.b.b.337.2		2	13.11	odd	12
338.2.c.e.191.1		2	13.4	even	6
338.2.c.e.315.1		2	13.12	even	2
338.2.e.b.23.1		4	13.5	odd	4
338.2.e.b.23.2		4	13.8	odd	4
338.2.e.b.147.1		4	13.7	odd	12
338.2.e.b.147.2		4	13.6	odd	12
650.2.e.c.451.1		2	65.9	even	6
650.2.e.c.601.1		2	5.4	even	2
650.2.o.c.399.1		4	65.22	odd	12
650.2.o.c.399.2		4	65.48	odd	12
650.2.o.c.549.1		4	5.3	odd	4
650.2.o.c.549.2		4	5.2	odd	4
832.2.i.e.321.1		2	104.61	even	6
832.2.i.e.705.1		2	8.5	even	2
832.2.i.f.321.1		2	104.35	odd	6
832.2.i.f.705.1		2	8.3	odd	2
1274.2.e.m.165.1		2	91.61	odd	6
1274.2.e.m.471.1		2	7.3	odd	6
1274.2.e.n.165.1		2	91.9	even	3
1274.2.e.n.471.1		2	7.4	even	3
1274.2.g.a.295.1		2	91.48	odd	6
1274.2.g.a.393.1		2	7.6	odd	2
1274.2.h.a.263.1		2	7.5	odd	6
1274.2.h.a.373.1		2	91.87	odd	6
1274.2.h.b.263.1		2	7.2	even	3
1274.2.h.b.373.1		2	91.74	even	3
1872.2.t.k.289.1		2	12.11	even	2
1872.2.t.k.1153.1		2	156.35	even	6
2704.2.a.h.1.1		1	52.3	odd	6
2704.2.a.i.1.1		1	52.23	odd	6
2704.2.f.g.337.1		2	52.11	even	12
2704.2.f.g.337.2		2	52.15	even	12
3042.2.a.e.1.1		1	39.29	odd	6
3042.2.a.k.1.1		1	39.23	odd	6
3042.2.b.e.1351.1		2	39.11	even	12
3042.2.b.e.1351.2		2	39.2	even	12
8450.2.a.f.1.1		1	65.29	even	6
8450.2.a.s.1.1		1	65.49	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:	\( N \)	\(=\)	\( 26 = 2 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	26.c (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} -1.00000 q^{5} +(-2.00000 + 3.46410i) q^{7} +1.00000 q^{8} +(1.50000 - 2.59808i) q^{9} +O(q^{10})\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} -1.00000 q^{5} +(-2.00000 + 3.46410i) q^{7} +1.00000 q^{8} +(1.50000 - 2.59808i) q^{9} +(0.500000 + 0.866025i) q^{10} +(-2.00000 - 3.46410i) q^{11} +(3.50000 - 0.866025i) q^{13} +4.00000 q^{14} +(-0.500000 - 0.866025i) q^{16} +(-1.50000 + 2.59808i) q^{17} -3.00000 q^{18} +(0.500000 - 0.866025i) q^{20} +(-2.00000 + 3.46410i) q^{22} +(2.00000 + 3.46410i) q^{23} -4.00000 q^{25} +(-2.50000 - 2.59808i) q^{26} +(-2.00000 - 3.46410i) q^{28} +(0.500000 + 0.866025i) q^{29} +4.00000 q^{31} +(-0.500000 + 0.866025i) q^{32} +3.00000 q^{34} +(2.00000 - 3.46410i) q^{35} +(1.50000 + 2.59808i) q^{36} +(-1.50000 - 2.59808i) q^{37} -1.00000 q^{40} +(4.50000 + 7.79423i) q^{41} +(4.00000 - 6.92820i) q^{43} +4.00000 q^{44} +(-1.50000 + 2.59808i) q^{45} +(2.00000 - 3.46410i) q^{46} -8.00000 q^{47} +(-4.50000 - 7.79423i) q^{49} +(2.00000 + 3.46410i) q^{50} +(-1.00000 + 3.46410i) q^{52} -9.00000 q^{53} +(2.00000 + 3.46410i) q^{55} +(-2.00000 + 3.46410i) q^{56} +(0.500000 - 0.866025i) q^{58} +(2.00000 - 3.46410i) q^{59} +(-3.50000 + 6.06218i) q^{61} +(-2.00000 - 3.46410i) q^{62} +(6.00000 + 10.3923i) q^{63} +1.00000 q^{64} +(-3.50000 + 0.866025i) q^{65} +(-2.00000 - 3.46410i) q^{67} +(-1.50000 - 2.59808i) q^{68} -4.00000 q^{70} +(4.00000 - 6.92820i) q^{71} +(1.50000 - 2.59808i) q^{72} +11.0000 q^{73} +(-1.50000 + 2.59808i) q^{74} +16.0000 q^{77} -4.00000 q^{79} +(0.500000 + 0.866025i) q^{80} +(-4.50000 - 7.79423i) q^{81} +(4.50000 - 7.79423i) q^{82} +(1.50000 - 2.59808i) q^{85} -8.00000 q^{86} +(-2.00000 - 3.46410i) q^{88} +(3.00000 + 5.19615i) q^{89} +3.00000 q^{90} +(-4.00000 + 13.8564i) q^{91} -4.00000 q^{92} +(4.00000 + 6.92820i) q^{94} +(-1.00000 + 1.73205i) q^{97} +(-4.50000 + 7.79423i) q^{98} -12.0000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - q^{2} - q^{4} - 2 q^{5} - 4 q^{7} + 2 q^{8} + 3 q^{9}+O(q^{10}) \) 2 * q - q^2 - q^4 - 2 * q^5 - 4 * q^7 + 2 * q^8 + 3 * q^9	\( 2 q - q^{2} - q^{4} - 2 q^{5} - 4 q^{7} + 2 q^{8} + 3 q^{9} + q^{10} - 4 q^{11} + 7 q^{13} + 8 q^{14} - q^{16} - 3 q^{17} - 6 q^{18} + q^{20} - 4 q^{22} + 4 q^{23} - 8 q^{25} - 5 q^{26} - 4 q^{28} + q^{29} + 8 q^{31} - q^{32} + 6 q^{34} + 4 q^{35} + 3 q^{36} - 3 q^{37} - 2 q^{40} + 9 q^{41} + 8 q^{43} + 8 q^{44} - 3 q^{45} + 4 q^{46} - 16 q^{47} - 9 q^{49} + 4 q^{50} - 2 q^{52} - 18 q^{53} + 4 q^{55} - 4 q^{56} + q^{58} + 4 q^{59} - 7 q^{61} - 4 q^{62} + 12 q^{63} + 2 q^{64} - 7 q^{65} - 4 q^{67} - 3 q^{68} - 8 q^{70} + 8 q^{71} + 3 q^{72} + 22 q^{73} - 3 q^{74} + 32 q^{77} - 8 q^{79} + q^{80} - 9 q^{81} + 9 q^{82} + 3 q^{85} - 16 q^{86} - 4 q^{88} + 6 q^{89} + 6 q^{90} - 8 q^{91} - 8 q^{92} + 8 q^{94} - 2 q^{97} - 9 q^{98} - 24 q^{99}+O(q^{100}) \) 2 * q - q^2 - q^4 - 2 * q^5 - 4 * q^7 + 2 * q^8 + 3 * q^9 + q^10 - 4 * q^11 + 7 * q^13 + 8 * q^14 - q^16 - 3 * q^17 - 6 * q^18 + q^20 - 4 * q^22 + 4 * q^23 - 8 * q^25 - 5 * q^26 - 4 * q^28 + q^29 + 8 * q^31 - q^32 + 6 * q^34 + 4 * q^35 + 3 * q^36 - 3 * q^37 - 2 * q^40 + 9 * q^41 + 8 * q^43 + 8 * q^44 - 3 * q^45 + 4 * q^46 - 16 * q^47 - 9 * q^49 + 4 * q^50 - 2 * q^52 - 18 * q^53 + 4 * q^55 - 4 * q^56 + q^58 + 4 * q^59 - 7 * q^61 - 4 * q^62 + 12 * q^63 + 2 * q^64 - 7 * q^65 - 4 * q^67 - 3 * q^68 - 8 * q^70 + 8 * q^71 + 3 * q^72 + 22 * q^73 - 3 * q^74 + 32 * q^77 - 8 * q^79 + q^80 - 9 * q^81 + 9 * q^82 + 3 * q^85 - 16 * q^86 - 4 * q^88 + 6 * q^89 + 6 * q^90 - 8 * q^91 - 8 * q^92 + 8 * q^94 - 2 * q^97 - 9 * q^98 - 24 * q^99

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