LMFDB - Newform orbit 153.3.p.b

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [153,3,Mod(10,153)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(153, base_ring=CyclotomicField(16))

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

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("153.10");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 153 = 3^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	153.p (of order $16$, degree $8$, 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:	$4.16894804471$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	$\Q(\zeta_{16})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 1 $ x^8 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 17)
Sato-Tate group:	$\mathrm{SU}(2)[C_{16}]$

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/153\mathbb{Z}\right)^\times$.

$n$	$37$	$137$
$\chi(n)$	$\zeta_{16}$	$1$

Embeddings

For each embedding $\iota_m$ of the coefficient field, the values $\iota_m(a_n)$ are shown below.

For more information on an embedded modular form you can click on its label.

comment: embeddings in the coefficient field

gp: mfembed(f)

Label

$\iota_m(\nu)$

$ a_{2} $

$ a_{3} $

$ a_{4} $

$ a_{5} $

$ a_{6} $

$ a_{7} $

$ a_{8} $

$ a_{9} $

$ a_{10} $

10.1

0.382683	+	0.923880i
−0.923880	+	0.382683i
0.923880	+	0.382683i
0.382683	−	0.923880i
−0.382683	+	0.923880i
−0.923880	−	0.382683i
0.923880	−	0.382683i
−0.382683	−	0.923880i

1.15851

−

2.79690i

−3.65205

−

3.65205i

−7.87510

1.56645i

−7.70353

−

1.53233i

−3.25778

1.34942i

−4.74219

23.8406i

28.1

3.23044

1.33809i

5.81684

5.81684i

−0.268761

−

0.179580i

5.55967

−

3.71485i

5.65512

13.6527i

−0.627922

−

0.939752i

37.1

−1.23044

0.509666i

−1.57420

1.57420i

−0.902812

−

1.35115i

4.92562

−

7.37170i

3.17331

−

7.66104i

1.79949

1.20238i

46.1

1.15851

2.79690i

−3.65205

3.65205i

−7.87510

−

1.56645i

−7.70353

1.53233i

−3.25778

−

1.34942i

−4.74219

−

23.8406i

73.1

0.841487

2.03153i

−0.590587

0.590587i

1.04667

−

5.26197i

1.21824

6.12453i

6.42935

2.66313i

11.5706

−

2.30154i

82.1

3.23044

−

1.33809i

5.81684

−

5.81684i

−0.268761

0.179580i

5.55967

3.71485i

5.65512

−

13.6527i

−0.627922

0.939752i

91.1

−1.23044

−

0.509666i

−1.57420

−

1.57420i

−0.902812

1.35115i

4.92562

7.37170i

3.17331

7.66104i

1.79949

−

1.20238i

109.1

0.841487

−

2.03153i

−0.590587

−

0.590587i

1.04667

5.26197i

1.21824

−

6.12453i

6.42935

−

2.66313i

11.5706

2.30154i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
17.e	odd	16	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	153.3.p.b		8
3.b	odd	2	1		17.3.e.a	✓	8
12.b	even	2	1		272.3.bh.c		8
15.d	odd	2	1		425.3.u.b		8
15.e	even	4	1		425.3.t.a		8
15.e	even	4	1		425.3.t.c		8
17.e	odd	16	1	inner	153.3.p.b		8
51.c	odd	2	1		289.3.e.c		8
51.f	odd	4	1		289.3.e.i		8
51.f	odd	4	1		289.3.e.m		8
51.g	odd	8	1		289.3.e.b		8
51.g	odd	8	1		289.3.e.d		8
51.g	odd	8	1		289.3.e.k		8
51.g	odd	8	1		289.3.e.l		8
51.i	even	16	1		17.3.e.a	✓	8
51.i	even	16	1		289.3.e.b		8
51.i	even	16	1		289.3.e.c		8
51.i	even	16	1		289.3.e.d		8
51.i	even	16	1		289.3.e.i		8
51.i	even	16	1		289.3.e.k		8
51.i	even	16	1		289.3.e.l		8
51.i	even	16	1		289.3.e.m		8
204.t	odd	16	1		272.3.bh.c		8
255.bc	odd	16	1		425.3.t.a		8
255.be	even	16	1		425.3.u.b		8
255.bj	odd	16	1		425.3.t.c		8

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
17.3.e.a	✓	8	3.b	odd	2	1
17.3.e.a	✓	8	51.i	even	16	1
153.3.p.b		8	1.a	even	1	1	trivial
153.3.p.b		8	17.e	odd	16	1	inner
272.3.bh.c		8	12.b	even	2	1
272.3.bh.c		8	204.t	odd	16	1
289.3.e.b		8	51.g	odd	8	1
289.3.e.b		8	51.i	even	16	1
289.3.e.c		8	51.c	odd	2	1
289.3.e.c		8	51.i	even	16	1
289.3.e.d		8	51.g	odd	8	1
289.3.e.d		8	51.i	even	16	1
289.3.e.i		8	51.f	odd	4	1
289.3.e.i		8	51.i	even	16	1
289.3.e.k		8	51.g	odd	8	1
289.3.e.k		8	51.i	even	16	1
289.3.e.l		8	51.g	odd	8	1
289.3.e.l		8	51.i	even	16	1
289.3.e.m		8	51.f	odd	4	1
289.3.e.m		8	51.i	even	16	1
425.3.t.a		8	15.e	even	4	1
425.3.t.a		8	255.bc	odd	16	1
425.3.t.c		8	15.e	even	4	1
425.3.t.c		8	255.bj	odd	16	1
425.3.u.b		8	15.d	odd	2	1
425.3.u.b		8	255.be	even	16	1

This newform subspace can be constructed as the kernel of the linear operator $ T_{2}^{8} - 8T_{2}^{7} + 32T_{2}^{6} - 72T_{2}^{5} + 64T_{2}^{4} + 120T_{2}^{3} - 192T_{2}^{2} + 248T_{2} + 961 $ T2^8 - 8*T2^7 + 32*T2^6 - 72*T2^5 + 64*T2^4 + 120*T2^3 - 192*T2^2 + 248*T2 + 961 acting on $S_{3}^{\mathrm{new}}(153, [\chi])$.

Hecke characteristic polynomials

$p$	$F_p(T)$
$2$	$ T^{8} - 8 T^{7} + \cdots + 961 $ T^8 - 8T^7 + 32T^6 - 72T^5 + 64T^4 + 120T^3 - 192T^2 + 248*T + 961
$3$	$ T^{8} $ T^8
$5$	$ T^{8} + 16 T^{7} + \cdots + 512 $ T^8 + 16T^7 + 96T^6 + 512T^5 + 2848T^4 + 5632T^3 + 7424T^2 + 3072*T + 512
$7$	$ T^{8} - 8 T^{7} + \cdots + 8454272 $ T^8 - 8T^7 + 24T^6 + 832T^5 - 5872T^4 + 17024T^3 + 189952T^2 - 1579008*T + 8454272
$11$	$ T^{8} - 8 T^{7} + \cdots + 27572738 $ T^8 - 8T^7 + 12T^6 + 432T^5 + 12502T^4 + 130472T^3 + 1210100T^2 + 9416168*T + 27572738
$13$	$ T^{8} - 16 T^{7} + \cdots + 9048064 $ T^8 - 16T^7 + 128T^6 + 2688T^5 + 129408T^4 - 1129472T^3 + 5120000T^2 + 9625600*T + 9048064
$17$	$ T^{8} + 6975757441 $ T^8 + 6975757441
$19$	$ T^{8} + 368 T^{6} + \cdots + 929296 $ T^8 + 368T^6 - 9888T^5 + 67712T^4 - 20544T^3 + 154432T^2 + 925440T + 929296
$23$	$ T^{8} - 56 T^{7} + \cdots + 859299968 $ T^8 - 56T^7 + 1032T^6 - 10912T^5 + 193840T^4 - 2371328T^3 + 25926272T^2 - 191029248*T + 859299968
$29$	$ T^{8} + \cdots + 4240836608 $ T^8 + 48T^7 + 624T^6 + 50688T^5 + 2924096T^4 + 55948800T^3 + 407177216T^2 + 17682432*T + 4240836608
$31$	$ T^{8} - 24 T^{7} + \cdots + 14536832 $ T^8 - 24T^7 + 232T^6 - 4512T^5 + 46000T^4 - 407808T^3 + 8906112T^2 + 19152384*T + 14536832
$37$	$ T^{8} + \cdots + 120057840128 $ T^8 - 32T^7 + 1024T^6 - 88192T^5 + 4247072T^4 - 110329856T^3 + 1831515392T^2 - 20619873280*T + 120057840128
$41$	$ T^{8} + \cdots + 59058658562 $ T^8 + 48T^7 + 1824T^6 + 56704T^5 + 1267458T^4 + 34847696T^3 + 851345876T^2 + 10891969944*T + 59058658562
$43$	$ T^{8} + \cdots + 6201305218564 $ T^8 + 232T^7 + 27932T^6 + 2135880T^5 + 106466248T^4 + 3383205408T^3 + 70877592744T^2 + 937586073968*T + 6201305218564
$47$	$ T^{8} + \cdots + 2259754549504 $ T^8 + 192T^7 + 18432T^6 + 907072T^5 + 25209440T^4 + 277465600T^3 + 2803712T^2 + 3559691264*T + 2259754549504
$53$	$ T^{8} + \cdots + 26754490624 $ T^8 - 32T^7 + 2272T^6 + 76032T^5 - 1916416T^4 - 38105088T^3 + 1142718976T^2 - 5213239296*T + 26754490624
$59$	$ T^{8} + \cdots + 2675455605124 $ T^8 - 48T^7 + 5988T^6 + 167784T^5 - 2594808T^4 - 145724880T^3 - 682934952T^2 + 57746117328*T + 2675455605124
$61$	$ T^{8} + \cdots + 106680004247552 $ T^8 + 160T^7 + 8384T^6 + 480256T^5 + 53458432T^4 + 2998558720T^3 + 96984055808T^2 + 3040094060544*T + 106680004247552
$67$	$ T^{8} + \cdots + 83643718741636 $ T^8 + 21304T^6 + 118064724T^4 + 200330319344*T^2 + 83643718741636
$71$	$ T^{8} + \cdots + 71246079996032 $ T^8 + 40T^7 - 12216T^6 - 1432352T^5 + 43290416T^4 + 6737847296T^3 + 458184132736T^2 + 3272841105408*T + 71246079996032
$73$	$ T^{8} + \cdots + 51301810562 $ T^8 - 48T^7 - 4096T^6 + 449272T^5 + 5936898T^4 - 577515296T^3 + 27962577292T^2 + 13800580712*T + 51301810562
$79$	$ T^{8} + \cdots + 3948319764608 $ T^8 + 136T^7 + 3800T^6 + 741152T^5 + 121806000T^4 + 5217092480T^3 + 94955734144T^2 + 467240282112*T + 3948319764608
$83$	$ T^{8} + \cdots + 10\!\cdots\!04 $ T^8 - 264T^7 + 35100T^6 - 5125992T^5 + 737320392T^4 - 61237522464T^3 + 2706769838376T^2 - 65499066502320*T + 1042256526864004
$89$	$ T^{8} + \cdots + 117588822570244 $ T^8 + 160T^7 + 12800T^6 - 64128T^5 + 72896012T^4 + 9469447872T^3 + 584098906112T^2 + 11720367113216*T + 117588822570244
$97$	$ T^{8} + \cdots + 21682310986562 $ T^8 - 48T^7 - 4444T^6 + 520800T^5 + 3432614T^4 - 652549016T^3 + 50830789412T^2 - 852254254440*T + 21682310986562
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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:	\( N \)	\(=\)	\( 153 = 3^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	153.p (of order \(16\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\( q + (\zeta_{16}^{7} - \zeta_{16}^{6} + \cdots + 1) q^{2}+ \cdots + (3 \zeta_{16}^{7} - 5 \zeta_{16}^{6} + \cdots + 3) q^{8}+O(q^{10}) \) q + (z^7 - z^6 + z^5 + z^4 - z^2 - z + 1) * q^2 + (2z^7 - 3z^6 + 2z^5 + 2z^3 - 2z) q^4 + (-2z^5 - 2z^4 + 2z^3 + 2z^2 - 2z - 2) q^5 + (z^7 - 5z^6 - 5z^5 + z^4 - z^3 + z^2 - z + 1) * q^7 + (3z^7 - 5z^6 - z^5 - 5z^4 + 3z^3 - 3z^2 + 3) q^8	\( q + (\zeta_{16}^{7} - \zeta_{16}^{6} + \cdots + 1) q^{2}+ \cdots + ( - 9 \zeta_{16}^{7} + 9 \zeta_{16}^{5} + \cdots + 15) q^{98}+O(q^{100}) \) q + (z^7 - z^6 + z^5 + z^4 - z^2 - z + 1) * q^2 + (2z^7 - 3z^6 + 2z^5 + 2z^3 - 2z) q^4 + (-2z^5 - 2z^4 + 2z^3 + 2z^2 - 2z - 2) q^5 + (z^7 - 5z^6 - 5z^5 + z^4 - z^3 + z^2 - z + 1) * q^7 + (3z^7 - 5z^6 - z^5 - 5z^4 + 3z^3 - 3z^2 + 3) q^8 + (6z^7 + 6z^6 - 6z^5 - 6z^4 + 2z^3 + 4z^2 + 4z + 2) q^10 + (z^7 + z^6 - 3z^5 + 6z^4 + 6z^3 - 3z^2 + z + 1) * q^11 + (-2z^7 + 2z^5 + 2z^4 + 10z^3 + 10z + 2) q^13 + (13z^7 - 3z^6 + z^5 + z^4 - 3z^3 + 13z^2 + z - 1) * q^14 + (4z^7 - 8z^6 + 4z^5 + 3z^4 + 4z^3 - 8z^2 + 4z) q^16 - 17z^7 q^17 + (-4z^7 + 7z^5 - 6z^4 + 6z^2 - 7z) q^19 + (2z^7 + 10z^6 + 4z^5 - 4z^4 - 10z^3 - 2z^2 + 10z + 10) q^20 + (6z^7 - 6z^6 - 13z^5 + 7z^4 - 3z^3 - 3z^2 + 7z - 13) q^22 + (-7z^7 - 7z^6 - 3z^5 + 5z^4 - 5z^3 + 3z^2 + 7z + 7) q^23 + (-16z^7 + 4z^6 - z^5 + 4z^4 - 16z^3 - 8z^2 + 8) q^25 + (-2z^7 + 6z^6 - 6z^4 + 2z^3 - 22z^2 + 12z - 22) * q^26 + (19z^7 + z^6 + 15z^5 - 7z^4 - 7z^3 + 15z^2 + z + 19) q^28 + (2z^7 + 2z^6 + 6z^5 + 8z^4 - 16z^3 + 16z^2 - 8z - 6) q^29 + (5z^7 - 5z^6 - 5z^5 - 5z^4 - 5z^3 + 5z^2 - 3z + 3) q^31 + (-11z^6 + z^5 + 11z^4 + 17z^3 + 11z^2 + z - 11) * q^32 + (-17z^7 + 17z^6 - 17z^5 + 17z^4 + 17z^3 - 17z - 17) * q^34 + (20z^6 + 8z^5 - 8z^3 - 20z^2 + 20) * q^35 + (-12z^7 + 2z^6 + 16z^5 - 16z^4 - 2z^3 + 12z^2 + 4z + 4) q^37 + (2z^7 + 2z^6 + 2z^5 - 15z^4 + 18z^3 - 18z + 15) * q^38 + (-8z^7 + 14z^6 + 6z^5 - 2z^4 + 2z^3 - 6z^2 - 14z + 8) q^40 + (-14z^7 - 6z^6 - 6z^5 - 14z^4 + 6z^3 + 5z^2 - 5z - 6) q^41 + (2z^7 - 14z^6 + 14z^4 - 2z^3 - 29z^2 + 22z - 29) * q^43 + (3z^7 + 15z^6 - 15z^5 - 3z^4 - 15z^3 + 8z^2 + 8z - 15) q^44 + (z^7 + z^6 + 11z^5 + 17z^4 - 9z^3 + 9z^2 - 17z - 11) q^46 + (22z^7 - 22z^5 - 24z^4 + 8z^3 - 2z^2 + 8z - 24) * q^47 + (2z^6 - 4z^5 - 10z^4 - 7z^3 - 10z^2 - 4z + 2) * q^49 + (-35z^7 + z^6 - z^5 + 57z^4 - z^3 + z^2 - 35z) q^50 + (-22z^7 + 34z^6 - 6z^5 + 6z^3 - 34z^2 + 22z - 48) * q^52 + (-2z^7 - 4z^6 + 18z^5 + 16z^4 - 16z^2 - 18z + 4) * q^53 + (-4z^7 + 32z^6 - 4z^5 - 28z^4 + 2z^3 - 2z + 28) * q^55 + (33z^7 - 33z^6 + 15z^5 - 17z^4 - 25z^3 - 25z^2 - 17z + 15) q^56 + (-4z^7 - 4z^4 - 30z^3 + 46z^2 - 46z + 30) q^58 + (10z^7 - 15z^6 + 42z^5 - 15z^4 + 10z^3 - 6z^2 + 6) * q^59 + (8z^7 - 36z^6 + 36z^5 - 8z^4 - 20z^3 - 12z^2 - 12z - 20) q^61 + (21z^7 - z^6 + 15z^5 - 7z^4 - 7z^3 + 15z^2 - z + 21) q^62 + (42z^7 - 42z^5 - 8z^4 - 10z^3 + 13z^2 - 10z - 8) * q^64 + (-8z^7 - 12z^5 - 12z^4 - 8z^2 - 12z + 12) q^65 + (-33z^7 + 4z^6 + 26z^5 + 42z^4 + 26z^3 + 4z^2 - 33z) q^67 + (34z^6 - 51z^5 + 34z^4 + 34z^2 - 34) * q^68 + (-36z^7 - 28z^6 + 16z^5 + 60z^4 - 60z^2 - 16z + 28) * q^70 + (-43z^7 - 35z^6 - 11z^5 + 11z^4 + 35z^3 + 43z^2 - 5z - 5) q^71 + (26z^7 - 26z^6 + 6z^5 - 6z^4 + 25z^3 + 25z^2 - 6z + 6) q^73 + (-20z^7 + 26z^6 + 28z^5 - 24z^4 + 24z^3 - 28z^2 - 26z + 20) q^74 + (21z^7 - 20z^6 + 12z^5 - 20z^4 + 21z^3 - 10z^2 + 10) * q^76 + (8z^7 - 10z^6 + 10z^4 - 8z^3 + 6z^2 + 66z + 6) * q^77 + (-17z^7 + 41z^6 - 3z^5 - 21z^4 - 21z^3 - 3z^2 + 41z - 17) q^79 + (30z^7 + 30z^6 - 30z^5 - 14z^4 + 8z^3 - 8z^2 + 14z + 30) q^80 + (8z^7 + 34z^6 - 17z^5 - 17z^4 + 34z^3 + 8z^2 + 8z - 8) q^82 + (33z^6 - 20z^5 - 42z^4 - 54z^3 - 42z^2 - 20z + 33) * q^83 + (34z^7 - 34z^4 - 34z^3 + 34z^2 + 34z - 34) q^85 + (-66z^7 - 8z^6 - 3z^5 + 3z^3 + 8z^2 + 66z - 104) * q^86 + (z^7 + 9z^6 - 40z^5 + 40z^4 - 9z^3 - z^2 + 33z + 33) q^88 + (29z^7 + 8z^6 + 29z^5 + 20z^4 - 46z^3 + 46z - 20) * q^89 + (-40z^7 - 68z^6 - 28z^4 + 28z^3 + 68z + 40) q^91 + (23z^7 + 3z^6 + 3z^5 + 23z^4 + 3z^3 + 31z^2 - 31z - 3) q^92 + (18z^7 + 54z^6 - 54z^4 - 18z^3 + 4z^2 + 110z + 4) * q^94 + (-2z^7 - 24z^6 + 24z^5 + 2z^4 - 34z^3 + 24z^2 + 24z - 34) q^95 + (-22z^7 - 22z^6 - 6z^5 - 13z^4 - 30z^3 + 30z^2 + 13z + 6) q^97 + (-9z^7 + 9z^5 + 15z^4 + 11z^3 - 9z^2 + 11z + 15) * q^98
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 8 q^{2} - 16 q^{5} + 8 q^{7} + 24 q^{8}+O(q^{10}) \) 8 * q + 8 * q^2 - 16 * q^5 + 8 * q^7 + 24 * q^8	\( 8 q + 8 q^{2} - 16 q^{5} + 8 q^{7} + 24 q^{8} + 16 q^{10} + 8 q^{11} + 16 q^{13} - 8 q^{14} + 80 q^{20} - 104 q^{22} + 56 q^{23} + 64 q^{25} - 176 q^{26} + 152 q^{28} - 48 q^{29} + 24 q^{31} - 88 q^{32} - 136 q^{34} + 160 q^{35} + 32 q^{37} + 120 q^{38} + 64 q^{40} - 48 q^{41} - 232 q^{43} - 120 q^{44} - 88 q^{46} - 192 q^{47} + 16 q^{49} - 384 q^{52} + 32 q^{53} + 224 q^{55} + 120 q^{56} + 240 q^{58} + 48 q^{59} - 160 q^{61} + 168 q^{62} - 64 q^{64} + 96 q^{65} - 272 q^{68} + 224 q^{70} - 40 q^{71} + 48 q^{73} + 160 q^{74} + 80 q^{76} + 48 q^{77} - 136 q^{79} + 240 q^{80} - 64 q^{82} + 264 q^{83} - 272 q^{85} - 832 q^{86} + 264 q^{88} - 160 q^{89} + 320 q^{91} - 24 q^{92} + 32 q^{94} - 272 q^{95} + 48 q^{97} + 120 q^{98}+O(q^{100}) \) 8 * q + 8 * q^2 - 16 * q^5 + 8 * q^7 + 24 * q^8 + 16 * q^10 + 8 * q^11 + 16 * q^13 - 8 * q^14 + 80 * q^20 - 104 * q^22 + 56 * q^23 + 64 * q^25 - 176 * q^26 + 152 * q^28 - 48 * q^29 + 24 * q^31 - 88 * q^32 - 136 * q^34 + 160 * q^35 + 32 * q^37 + 120 * q^38 + 64 * q^40 - 48 * q^41 - 232 * q^43 - 120 * q^44 - 88 * q^46 - 192 * q^47 + 16 * q^49 - 384 * q^52 + 32 * q^53 + 224 * q^55 + 120 * q^56 + 240 * q^58 + 48 * q^59 - 160 * q^61 + 168 * q^62 - 64 * q^64 + 96 * q^65 - 272 * q^68 + 224 * q^70 - 40 * q^71 + 48 * q^73 + 160 * q^74 + 80 * q^76 + 48 * q^77 - 136 * q^79 + 240 * q^80 - 64 * q^82 + 264 * q^83 - 272 * q^85 - 832 * q^86 + 264 * q^88 - 160 * q^89 + 320 * q^91 - 24 * q^92 + 32 * q^94 - 272 * q^95 + 48 * q^97 + 120 * q^98

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