LMFDB - Embedded newform 58.22.a.b.1.9

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [58,22,Mod(1,58)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("58.1"); S:= CuspForms(chi, 22); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(58, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0])) N = Newforms(chi, 22, names="a")

Level:	$ N $	$=$	$ 58 = 2 \cdot 29 $
Weight:	$ k $	$=$	$ 22 $
Character orbit:	$[\chi]$	$=$	58.a (trivial)

Newform invariants

comment:select newform

sage:traces = [12,-12288] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	yes
Analytic conductor:	$162.096859686$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 2 x^{11} - 85606746065 x^{10} + 168391612240800 x^{9} + \cdots - 43\!\cdots\!52 $ x^12 - 2x^11 - 85606746065x^10 + 168391612240800x^9 + 2757451572807239631894x^8 - 9555058037278166472042924x^7 - 41080125611886905801364859902282x^6 + 219676398182820150688852409537061672x^5 + 275643374302867319301523239182483426388837x^4 - 2552366829028681148436422955846851460551806114x^3 - 642653898637251875288116099694392871957038148316709x^2 + 12480988287776125933764548171660251753177162704735793256*x - 43448541674489152601942422286507508998272701751075093301052
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	multiple of $ 2^{32}\cdot 3^{8}\cdot 5^{3}\cdot 7^{3} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.9
Root			$104736.$ of defining polynomial
Character	$\chi$	$=$	58.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-1024.00 q^{2} +108158. q^{3} +1.04858e6 q^{4} -2.17418e7 q^{5} -1.10753e8 q^{6} +4.76282e8 q^{7} -1.07374e9 q^{8} +1.23770e9 q^{9} +2.22636e10 q^{10} -1.19118e11 q^{11} +1.13411e11 q^{12} -3.28609e11 q^{13} -4.87713e11 q^{14} -2.35154e12 q^{15} +1.09951e12 q^{16} +8.70093e12 q^{17} -1.26741e12 q^{18} -3.75713e13 q^{19} -2.27979e13 q^{20} +5.15135e13 q^{21} +1.21977e14 q^{22} +2.03083e13 q^{23} -1.16133e14 q^{24} -4.13259e12 q^{25} +3.36495e14 q^{26} -9.97499e14 q^{27} +4.99418e14 q^{28} +4.20707e14 q^{29} +2.40797e15 q^{30} -4.21793e15 q^{31} -1.12590e15 q^{32} -1.28835e16 q^{33} -8.90975e15 q^{34} -1.03552e16 q^{35} +1.29782e15 q^{36} +4.61890e16 q^{37} +3.84730e16 q^{38} -3.55415e16 q^{39} +2.33450e16 q^{40} -1.30476e17 q^{41} -5.27498e16 q^{42} -6.13614e16 q^{43} -1.24904e17 q^{44} -2.69098e16 q^{45} -2.07957e16 q^{46} +6.83569e17 q^{47} +1.18920e17 q^{48} -3.31701e17 q^{49} +4.23178e15 q^{50} +9.41071e17 q^{51} -3.44571e17 q^{52} +1.30769e18 q^{53} +1.02144e18 q^{54} +2.58983e18 q^{55} -5.11404e17 q^{56} -4.06362e18 q^{57} -4.30804e17 q^{58} +2.23088e18 q^{59} -2.46576e18 q^{60} +9.45038e18 q^{61} +4.31916e18 q^{62} +5.89495e17 q^{63} +1.15292e18 q^{64} +7.14454e18 q^{65} +1.31927e19 q^{66} +1.27847e19 q^{67} +9.12359e18 q^{68} +2.19650e18 q^{69} +1.06037e19 q^{70} -1.82966e19 q^{71} -1.32897e18 q^{72} -5.69729e19 q^{73} -4.72975e19 q^{74} -4.46971e17 q^{75} -3.93963e19 q^{76} -5.67337e19 q^{77} +3.63945e19 q^{78} +1.02156e20 q^{79} -2.39053e19 q^{80} -1.20834e20 q^{81} +1.33608e20 q^{82} -5.14783e19 q^{83} +5.40158e19 q^{84} -1.89174e20 q^{85} +6.28341e19 q^{86} +4.55027e19 q^{87} +1.27902e20 q^{88} +6.50060e19 q^{89} +2.75557e19 q^{90} -1.56511e20 q^{91} +2.12948e19 q^{92} -4.56201e20 q^{93} -6.99975e20 q^{94} +8.16866e20 q^{95} -1.21775e20 q^{96} -3.45116e19 q^{97} +3.39662e20 q^{98} -1.47432e20 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 12288 q^{2} + 41066 q^{3} + 12582912 q^{4} + 32000498 q^{5} - 42051584 q^{6} + 442380608 q^{7} - 12884901888 q^{8} + 45829788394 q^{9} - 32768509952 q^{10} - 75612722022 q^{11} + 43060822016 q^{12}+ \cdots - 77\!\cdots\!40 q^{99}+O(q^{100}) $ 12 * q - 12288 * q^2 + 41066 * q^3 + 12582912 * q^4 + 32000498 * q^5 - 42051584 * q^6 + 442380608 * q^7 - 12884901888 * q^8 + 45829788394 * q^9 - 32768509952 * q^10 - 75612722022 * q^11 + 43060822016 * q^12 + 1106340906306 * q^13 - 452997742592 * q^14 + 1765515734274 * q^15 + 13194139533312 * q^16 + 21318462894400 * q^17 - 46929703315456 * q^18 - 64137907734512 * q^19 + 33554954190848 * q^20 - 128443192005240 * q^21 + 77427427350528 * q^22 - 92442371463100 * q^23 - 44094281744384 * q^24 + 1051521588244678 * q^25 - 1132893088057344 * q^26 + 394367717882726 * q^27 + 463869688414208 * q^28 + 5048486799602412 * q^29 - 1807888111896576 * q^30 + 667598339910262 * q^31 - 13510798882111488 * q^32 + 4201639353560358 * q^33 - 21830106003865600 * q^34 + 7107310943840024 * q^35 + 48056016195026944 * q^36 + 28910323697160228 * q^37 + 65677217520140288 * q^38 + 225314095106008122 * q^39 - 34360273091428352 * q^40 + 114917975551005484 * q^41 + 131525828613365760 * q^42 + 203268895640575250 * q^43 - 79285685606940672 * q^44 + 792851894167749996 * q^45 + 94660988378214400 * q^46 + 1050843994052953634 * q^47 + 45152544506249216 * q^48 + 1737975087532848780 * q^49 - 1076758106362550272 * q^50 + 2268747312849354956 * q^51 + 1160082522170720256 * q^52 + 1243305464914490870 * q^53 - 403832543111911424 * q^54 + 1883810806035056562 * q^55 - 475002560936148992 * q^56 - 491546347093854212 * q^57 - 5169650482792869888 * q^58 + 2566690023566975892 * q^59 + 1851277426582093824 * q^60 - 11920971254026911592 * q^61 - 683620700068108288 * q^62 + 2930768167479272136 * q^63 + 13835058055282163712 * q^64 - 4017336204912291950 * q^65 - 4302478698045806592 * q^66 + 27467580398508962728 * q^67 + 22354028547958374400 * q^68 - 29416524647657806036 * q^69 - 7277886406492184576 * q^70 + 39394008523302335116 * q^71 - 49209360583707590656 * q^72 - 105436578371427269044 * q^73 - 29604171465892073472 * q^74 - 283509646740931456276 * q^75 - 67253470740623654912 * q^76 - 275397747965407922232 * q^77 - 230721633388552316928 * q^78 - 436842923520537104882 * q^79 + 35184919645622632448 * q^80 - 431897364305527243016 * q^81 - 117676006964229615616 * q^82 - 156371463675503224156 * q^83 - 134682448500086538240 * q^84 - 102757376758180914100 * q^85 - 208147349135949056000 * q^86 + 17276763242706054266 * q^87 + 81188542061507248128 * q^88 - 371114169124003188548 * q^89 - 811880339627775995904 * q^90 + 294733199359386364888 * q^91 - 96932852099291545600 * q^92 - 490543681961018456926 * q^93 - 1076064249910224521216 * q^94 - 872483370018144298908 * q^95 - 46236205574399197184 * q^96 - 579594350488340562436 * q^97 - 1779686489633637150720 * q^98 - 779201899240987231740 * q^99

Coefficient data

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

Currently showing only $a_p$; display all $a_n$ Currently showing all $a_n$; display 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 $

$2$	−1024.00	−0.707107
$2$	−1024.00	−0.707107
$3$	108158.	1.05751	0.528754	−	0.848775i	$-0.322659\pi$
$3$	108158.	1.05751	0.528754	+	0.848775i	$0.322659\pi$
$4$	1.04858e6	0.500000
$5$	−2.17418e7	−0.995657	−0.497829	−	0.867275i	$-0.665869\pi$
$5$	−2.17418e7	−0.995657	−0.497829	+	0.867275i	$0.665869\pi$
$6$	−1.10753e8	−0.747771
$7$	4.76282e8	0.637287	0.318643	−	0.947875i	$-0.396773\pi$
$7$	4.76282e8	0.637287	0.318643	+	0.947875i	$0.396773\pi$
$8$	−1.07374e9	−0.353553
$9$	1.23770e9	0.118323
$10$	2.22636e10	0.704036
$11$	−1.19118e11	−1.38469	−0.692346	−	0.721566i	$-0.743423\pi$
$11$	−1.19118e11	−1.38469	−0.692346	+	0.721566i	$0.743423\pi$
$12$	1.13411e11	0.528754
$13$	−3.28609e11	−0.661110	−0.330555	−	0.943787i	$-0.607236\pi$
$13$	−3.28609e11	−0.661110	−0.330555	+	0.943787i	$0.607236\pi$
$14$	−4.87713e11	−0.450630
$15$	−2.35154e12	−1.05292
$16$	1.09951e12	0.250000
$17$	8.70093e12	1.04677	0.523386	−	0.852096i	$-0.324669\pi$
$17$	8.70093e12	1.04677	0.523386	+	0.852096i	$0.324669\pi$
$18$	−1.26741e12	−0.0836671
$19$	−3.75713e13	−1.40586	−0.702932	−	0.711257i	$-0.748126\pi$
$19$	−3.75713e13	−1.40586	−0.702932	+	0.711257i	$0.748126\pi$
$20$	−2.27979e13	−0.497829
$21$	5.15135e13	0.673936
$22$	1.21977e14	0.979125
$23$	2.03083e13	0.102219	0.0511095	−	0.998693i	$-0.483724\pi$
$23$	2.03083e13	0.102219	0.0511095	+	0.998693i	$0.483724\pi$
$24$	−1.16133e14	−0.373886
$25$	−4.13259e12	−0.00866668
$26$	3.36495e14	0.467476
$27$	−9.97499e14	−0.932380
$28$	4.99418e14	0.318643
$29$	4.20707e14	0.185695
$29$	4.20707e14	0.185695
$30$	2.40797e15	0.744524
$31$	−4.21793e15	−0.924276	−0.462138	−	0.886808i	$-0.652918\pi$
$31$	−4.21793e15	−0.924276	−0.462138	+	0.886808i	$0.652918\pi$
$32$	−1.12590e15	−0.176777
$33$	−1.28835e16	−1.46432
$34$	−8.90975e15	−0.740179
$35$	−1.03552e16	−0.634519
$36$	1.29782e15	0.0591616
$37$	4.61890e16	1.57914	0.789570	−	0.613661i	$-0.210304\pi$
$37$	4.61890e16	1.57914	0.789570	+	0.613661i	$0.210304\pi$
$38$	3.84730e16	0.994096
$39$	−3.55415e16	−0.699129
$40$	2.33450e16	0.352018
$41$	−1.30476e17	−1.51810	−0.759051	−	0.651032i	$-0.774336\pi$
$41$	−1.30476e17	−1.51810	−0.759051	+	0.651032i	$0.774336\pi$
$42$	−5.27498e16	−0.476545
$43$	−6.13614e16	−0.432989	−0.216494	−	0.976284i	$-0.569462\pi$
$43$	−6.13614e16	−0.432989	−0.216494	+	0.976284i	$0.569462\pi$
$44$	−1.24904e17	−0.692346
$45$	−2.69098e16	−0.117809
$46$	−2.07957e16	−0.0722797
$47$	6.83569e17	1.89564	0.947818	−	0.318812i	$-0.103284\pi$
$47$	6.83569e17	1.89564	0.947818	+	0.318812i	$0.103284\pi$
$48$	1.18920e17	0.264377
$49$	−3.31701e17	−0.593866
$50$	4.23178e15	0.00612827
$51$	9.41071e17	1.10697
$52$	−3.44571e17	−0.330555
$53$	1.30769e18	1.02709	0.513545	−	0.858063i	$-0.328332\pi$
$53$	1.30769e18	1.02709	0.513545	+	0.858063i	$0.328332\pi$
$54$	1.02144e18	0.659292
$55$	2.58983e18	1.37868
$56$	−5.11404e17	−0.225315
$57$	−4.06362e18	−1.48671
$58$	−4.30804e17	−0.131306
$59$	2.23088e18	0.568239	0.284119	−	0.958789i	$-0.408299\pi$
$59$	2.23088e18	0.568239	0.284119	+	0.958789i	$0.408299\pi$
$60$	−2.46576e18	−0.526458
$61$	9.45038e18	1.69624	0.848118	−	0.529808i	$-0.177736\pi$
$61$	9.45038e18	1.69624	0.848118	+	0.529808i	$0.177736\pi$
$62$	4.31916e18	0.653562
$63$	5.89495e17	0.0754058
$64$	1.15292e18	0.125000
$65$	7.14454e18	0.658239
$66$	1.31927e19	1.03543
$67$	1.27847e19	0.856852	0.428426	−	0.903577i	$-0.359068\pi$
$67$	1.27847e19	0.856852	0.428426	+	0.903577i	$0.359068\pi$
$68$	9.12359e18	0.523386
$69$	2.19650e18	0.108097
$70$	1.06037e19	0.448673
$71$	−1.82966e19	−0.667048	−0.333524	−	0.942742i	$-0.608238\pi$
$71$	−1.82966e19	−0.667048	−0.333524	+	0.942742i	$0.608238\pi$
$72$	−1.32897e18	−0.0418335
$73$	−5.69729e19	−1.55159	−0.775797	−	0.630982i	$-0.782652\pi$
$73$	−5.69729e19	−1.55159	−0.775797	+	0.630982i	$0.782652\pi$
$74$	−4.72975e19	−1.11662
$75$	−4.46971e17	−0.00916508
$76$	−3.93963e19	−0.702932
$77$	−5.67337e19	−0.882446
$78$	3.63945e19	0.494359
$79$	1.02156e20	1.21388	0.606942	−	0.794746i	$-0.292396\pi$
$79$	1.02156e20	1.21388	0.606942	+	0.794746i	$0.292396\pi$
$80$	−2.39053e19	−0.248914
$81$	−1.20834e20	−1.10432
$82$	1.33608e20	1.07346
$83$	−5.14783e19	−0.364170	−0.182085	−	0.983283i	$-0.558285\pi$
$83$	−5.14783e19	−0.364170	−0.182085	+	0.983283i	$0.558285\pi$
$84$	5.40158e19	0.336968
$85$	−1.89174e20	−1.04223
$86$	6.28341e19	0.306169
$87$	4.55027e19	0.196374
$88$	1.27902e20	0.489563
$89$	6.50060e19	0.220983	0.110491	−	0.993877i	$-0.464758\pi$
$89$	6.50060e19	0.220983	0.110491	+	0.993877i	$0.464758\pi$
$90$	2.75557e19	0.0833037
$91$	−1.56511e20	−0.421317
$92$	2.12948e19	0.0511095
$93$	−4.56201e20	−0.977429
$94$	−6.99975e20	−1.34042
$95$	8.16866e20	1.39976
$96$	−1.21775e20	−0.186943
$97$	−3.45116e19	−0.0475183	−0.0237592	−	0.999718i	$-0.507563\pi$
$97$	−3.45116e19	−0.0475183	−0.0237592	+	0.999718i	$0.507563\pi$
$98$	3.39662e20	0.419926
$99$	−1.47432e20	−0.163841

Currently showing only $a_p$; display all $a_n$ Currently showing all $a_n$; display only $a_p$

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	58.22.a.b.1.9	✓	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
58.22.a.b.1.9	✓	12	1.1	even	1	trivial

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Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 58 = 2 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 22 \)
Character orbit:	\([\chi]\)	\(=\)	58.a (trivial)

\(f(q)\)	\(=\)	\(q-1024.00 q^{2} +108158. q^{3} +1.04858e6 q^{4} -2.17418e7 q^{5} -1.10753e8 q^{6} +4.76282e8 q^{7} -1.07374e9 q^{8} +1.23770e9 q^{9} +2.22636e10 q^{10} -1.19118e11 q^{11} +1.13411e11 q^{12} -3.28609e11 q^{13} -4.87713e11 q^{14} -2.35154e12 q^{15} +1.09951e12 q^{16} +8.70093e12 q^{17} -1.26741e12 q^{18} -3.75713e13 q^{19} -2.27979e13 q^{20} +5.15135e13 q^{21} +1.21977e14 q^{22} +2.03083e13 q^{23} -1.16133e14 q^{24} -4.13259e12 q^{25} +3.36495e14 q^{26} -9.97499e14 q^{27} +4.99418e14 q^{28} +4.20707e14 q^{29} +2.40797e15 q^{30} -4.21793e15 q^{31} -1.12590e15 q^{32} -1.28835e16 q^{33} -8.90975e15 q^{34} -1.03552e16 q^{35} +1.29782e15 q^{36} +4.61890e16 q^{37} +3.84730e16 q^{38} -3.55415e16 q^{39} +2.33450e16 q^{40} -1.30476e17 q^{41} -5.27498e16 q^{42} -6.13614e16 q^{43} -1.24904e17 q^{44} -2.69098e16 q^{45} -2.07957e16 q^{46} +6.83569e17 q^{47} +1.18920e17 q^{48} -3.31701e17 q^{49} +4.23178e15 q^{50} +9.41071e17 q^{51} -3.44571e17 q^{52} +1.30769e18 q^{53} +1.02144e18 q^{54} +2.58983e18 q^{55} -5.11404e17 q^{56} -4.06362e18 q^{57} -4.30804e17 q^{58} +2.23088e18 q^{59} -2.46576e18 q^{60} +9.45038e18 q^{61} +4.31916e18 q^{62} +5.89495e17 q^{63} +1.15292e18 q^{64} +7.14454e18 q^{65} +1.31927e19 q^{66} +1.27847e19 q^{67} +9.12359e18 q^{68} +2.19650e18 q^{69} +1.06037e19 q^{70} -1.82966e19 q^{71} -1.32897e18 q^{72} -5.69729e19 q^{73} -4.72975e19 q^{74} -4.46971e17 q^{75} -3.93963e19 q^{76} -5.67337e19 q^{77} +3.63945e19 q^{78} +1.02156e20 q^{79} -2.39053e19 q^{80} -1.20834e20 q^{81} +1.33608e20 q^{82} -5.14783e19 q^{83} +5.40158e19 q^{84} -1.89174e20 q^{85} +6.28341e19 q^{86} +4.55027e19 q^{87} +1.27902e20 q^{88} +6.50060e19 q^{89} +2.75557e19 q^{90} -1.56511e20 q^{91} +2.12948e19 q^{92} -4.56201e20 q^{93} -6.99975e20 q^{94} +8.16866e20 q^{95} -1.21775e20 q^{96} -3.45116e19 q^{97} +3.39662e20 q^{98} -1.47432e20 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 12288 q^{2} + 41066 q^{3} + 12582912 q^{4} + 32000498 q^{5} - 42051584 q^{6} + 442380608 q^{7} - 12884901888 q^{8} + 45829788394 q^{9} - 32768509952 q^{10} - 75612722022 q^{11} + 43060822016 q^{12}+ \cdots - 77\!\cdots\!40 q^{99}+O(q^{100}) \) 12 * q - 12288 * q^2 + 41066 * q^3 + 12582912 * q^4 + 32000498 * q^5 - 42051584 * q^6 + 442380608 * q^7 - 12884901888 * q^8 + 45829788394 * q^9 - 32768509952 * q^10 - 75612722022 * q^11 + 43060822016 * q^12 + 1106340906306 * q^13 - 452997742592 * q^14 + 1765515734274 * q^15 + 13194139533312 * q^16 + 21318462894400 * q^17 - 46929703315456 * q^18 - 64137907734512 * q^19 + 33554954190848 * q^20 - 128443192005240 * q^21 + 77427427350528 * q^22 - 92442371463100 * q^23 - 44094281744384 * q^24 + 1051521588244678 * q^25 - 1132893088057344 * q^26 + 394367717882726 * q^27 + 463869688414208 * q^28 + 5048486799602412 * q^29 - 1807888111896576 * q^30 + 667598339910262 * q^31 - 13510798882111488 * q^32 + 4201639353560358 * q^33 - 21830106003865600 * q^34 + 7107310943840024 * q^35 + 48056016195026944 * q^36 + 28910323697160228 * q^37 + 65677217520140288 * q^38 + 225314095106008122 * q^39 - 34360273091428352 * q^40 + 114917975551005484 * q^41 + 131525828613365760 * q^42 + 203268895640575250 * q^43 - 79285685606940672 * q^44 + 792851894167749996 * q^45 + 94660988378214400 * q^46 + 1050843994052953634 * q^47 + 45152544506249216 * q^48 + 1737975087532848780 * q^49 - 1076758106362550272 * q^50 + 2268747312849354956 * q^51 + 1160082522170720256 * q^52 + 1243305464914490870 * q^53 - 403832543111911424 * q^54 + 1883810806035056562 * q^55 - 475002560936148992 * q^56 - 491546347093854212 * q^57 - 5169650482792869888 * q^58 + 2566690023566975892 * q^59 + 1851277426582093824 * q^60 - 11920971254026911592 * q^61 - 683620700068108288 * q^62 + 2930768167479272136 * q^63 + 13835058055282163712 * q^64 - 4017336204912291950 * q^65 - 4302478698045806592 * q^66 + 27467580398508962728 * q^67 + 22354028547958374400 * q^68 - 29416524647657806036 * q^69 - 7277886406492184576 * q^70 + 39394008523302335116 * q^71 - 49209360583707590656 * q^72 - 105436578371427269044 * q^73 - 29604171465892073472 * q^74 - 283509646740931456276 * q^75 - 67253470740623654912 * q^76 - 275397747965407922232 * q^77 - 230721633388552316928 * q^78 - 436842923520537104882 * q^79 + 35184919645622632448 * q^80 - 431897364305527243016 * q^81 - 117676006964229615616 * q^82 - 156371463675503224156 * q^83 - 134682448500086538240 * q^84 - 102757376758180914100 * q^85 - 208147349135949056000 * q^86 + 17276763242706054266 * q^87 + 81188542061507248128 * q^88 - 371114169124003188548 * q^89 - 811880339627775995904 * q^90 + 294733199359386364888 * q^91 - 96932852099291545600 * q^92 - 490543681961018456926 * q^93 - 1076064249910224521216 * q^94 - 872483370018144298908 * q^95 - 46236205574399197184 * q^96 - 579594350488340562436 * q^97 - 1779686489633637150720 * q^98 - 779201899240987231740 * q^99

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