LMFDB - Embedded newform 58.22.a.b.1.7

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			1.7
Root			$15802.7$ 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)

$f(q)$	$=$	\(q-1024.00 q^{2} +19224.7 q^{3} +1.04858e6 q^{4} -1.85439e7 q^{5} -1.96861e7 q^{6} -1.12639e9 q^{7} -1.07374e9 q^{8} -1.00908e10 q^{9} +1.89890e10 q^{10} +2.44974e10 q^{11} +2.01586e10 q^{12} +8.45154e11 q^{13} +1.15342e12 q^{14} -3.56502e11 q^{15} +1.09951e12 q^{16} +4.80247e12 q^{17} +1.03329e13 q^{18} -3.06054e13 q^{19} -1.94447e13 q^{20} -2.16546e13 q^{21} -2.50853e13 q^{22} -2.87069e14 q^{23} -2.06424e13 q^{24} -1.32961e14 q^{25} -8.65438e14 q^{26} -3.95090e14 q^{27} -1.18111e15 q^{28} +4.20707e14 q^{29} +3.65058e14 q^{30} -4.92141e15 q^{31} -1.12590e15 q^{32} +4.70956e14 q^{33} -4.91773e15 q^{34} +2.08877e16 q^{35} -1.05809e16 q^{36} -4.04594e16 q^{37} +3.13399e16 q^{38} +1.62479e16 q^{39} +1.99114e16 q^{40} -5.87779e16 q^{41} +2.21743e16 q^{42} -8.01236e16 q^{43} +2.56874e16 q^{44} +1.87122e17 q^{45} +2.93958e17 q^{46} -5.08607e17 q^{47} +2.11378e16 q^{48} +7.10209e17 q^{49} +1.36152e17 q^{50} +9.23263e16 q^{51} +8.86208e17 q^{52} -2.52920e18 q^{53} +4.04572e17 q^{54} -4.54277e17 q^{55} +1.20945e18 q^{56} -5.88380e17 q^{57} -4.30804e17 q^{58} -1.07073e18 q^{59} -3.73819e17 q^{60} +3.09141e18 q^{61} +5.03953e18 q^{62} +1.13661e19 q^{63} +1.15292e18 q^{64} -1.56725e19 q^{65} -4.82259e17 q^{66} +2.10021e19 q^{67} +5.03576e18 q^{68} -5.51882e18 q^{69} -2.13890e19 q^{70} +5.81169e18 q^{71} +1.08349e19 q^{72} -6.83431e19 q^{73} +4.14305e19 q^{74} -2.55613e18 q^{75} -3.20921e19 q^{76} -2.75936e19 q^{77} -1.66378e19 q^{78} -9.36862e19 q^{79} -2.03892e19 q^{80} +9.79574e19 q^{81} +6.01886e19 q^{82} +1.46086e20 q^{83} -2.27064e19 q^{84} -8.90567e19 q^{85} +8.20466e19 q^{86} +8.08799e18 q^{87} -2.63039e19 q^{88} -4.97327e20 q^{89} -1.91613e20 q^{90} -9.51973e20 q^{91} -3.01013e20 q^{92} -9.46129e19 q^{93} +5.20814e20 q^{94} +5.67543e20 q^{95} -2.16451e19 q^{96} +7.60391e20 q^{97} -7.27254e20 q^{98} -2.47197e20 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	19224.7	0.187969	0.0939847	−	0.995574i	$-0.470040\pi$
$3$	19224.7	0.187969	0.0939847	+	0.995574i	$0.470040\pi$
$4$	1.04858e6	0.500000
$5$	−1.85439e7	−0.849212	−0.424606	−	0.905378i	$-0.639587\pi$
$5$	−1.85439e7	−0.849212	−0.424606	+	0.905378i	$0.639587\pi$
$6$	−1.96861e7	−0.132914
$7$	−1.12639e9	−1.50716	−0.753580	−	0.657356i	$-0.771675\pi$
$7$	−1.12639e9	−1.50716	−0.753580	+	0.657356i	$0.771675\pi$
$8$	−1.07374e9	−0.353553
$9$	−1.00908e10	−0.964667
$10$	1.89890e10	0.600484
$11$	2.44974e10	0.284771	0.142386	−	0.989811i	$-0.454523\pi$
$11$	2.44974e10	0.284771	0.142386	+	0.989811i	$0.454523\pi$
$12$	2.01586e10	0.0939847
$13$	8.45154e11	1.70032	0.850160	−	0.526525i	$-0.176505\pi$
$13$	8.45154e11	1.70032	0.850160	+	0.526525i	$0.176505\pi$
$14$	1.15342e12	1.06572
$15$	−3.56502e11	−0.159626
$16$	1.09951e12	0.250000
$17$	4.80247e12	0.577765	0.288883	−	0.957365i	$-0.406716\pi$
$17$	4.80247e12	0.577765	0.288883	+	0.957365i	$0.406716\pi$
$18$	1.03329e13	0.682123
$19$	−3.06054e13	−1.14521	−0.572605	−	0.819832i	$-0.694067\pi$
$19$	−3.06054e13	−1.14521	−0.572605	+	0.819832i	$0.694067\pi$
$20$	−1.94447e13	−0.424606
$21$	−2.16546e13	−0.283300
$22$	−2.50853e13	−0.201364
$23$	−2.87069e14	−1.44492	−0.722460	−	0.691413i	$-0.756989\pi$
$23$	−2.87069e14	−1.44492	−0.722460	+	0.691413i	$0.756989\pi$
$24$	−2.06424e13	−0.0664572
$25$	−1.32961e14	−0.278839
$26$	−8.65438e14	−1.20231
$27$	−3.95090e14	−0.369298
$28$	−1.18111e15	−0.753580
$29$	4.20707e14	0.185695
$29$	4.20707e14	0.185695
$30$	3.65058e14	0.112873
$31$	−4.92141e15	−1.07843	−0.539215	−	0.842168i	$-0.681279\pi$
$31$	−4.92141e15	−1.07843	−0.539215	+	0.842168i	$0.681279\pi$
$32$	−1.12590e15	−0.176777
$33$	4.70956e14	0.0535283
$34$	−4.91773e15	−0.408542
$35$	2.08877e16	1.27990
$36$	−1.05809e16	−0.482334
$37$	−4.04594e16	−1.38325	−0.691627	−	0.722255i	$-0.743106\pi$
$37$	−4.04594e16	−1.38325	−0.691627	+	0.722255i	$0.743106\pi$
$38$	3.13399e16	0.809785
$39$	1.62479e16	0.319608
$40$	1.99114e16	0.300242
$41$	−5.87779e16	−0.683886	−0.341943	−	0.939721i	$-0.611085\pi$
$41$	−5.87779e16	−0.683886	−0.341943	+	0.939721i	$0.611085\pi$
$42$	2.21743e16	0.200323
$43$	−8.01236e16	−0.565382	−0.282691	−	0.959211i	$-0.591227\pi$
$43$	−8.01236e16	−0.565382	−0.282691	+	0.959211i	$0.591227\pi$
$44$	2.56874e16	0.142386
$45$	1.87122e17	0.819207
$46$	2.93958e17	1.02171
$47$	−5.08607e17	−1.41044	−0.705221	−	0.708988i	$-0.749152\pi$
$47$	−5.08607e17	−1.41044	−0.705221	+	0.708988i	$0.749152\pi$
$48$	2.11378e16	0.0469924
$49$	7.10209e17	1.27153
$50$	1.36152e17	0.197169
$51$	9.23263e16	0.108602
$52$	8.86208e17	0.850160
$53$	−2.52920e18	−1.98649	−0.993244	−	0.116042i	$-0.962979\pi$
$53$	−2.52920e18	−1.98649	−0.993244	+	0.116042i	$0.962979\pi$
$54$	4.04572e17	0.261133
$55$	−4.54277e17	−0.241831
$56$	1.20945e18	0.532862
$57$	−5.88380e17	−0.215264
$58$	−4.30804e17	−0.131306
$59$	−1.07073e18	−0.272731	−0.136365	−	0.990659i	$-0.543542\pi$
$59$	−1.07073e18	−0.272731	−0.136365	+	0.990659i	$0.543542\pi$
$60$	−3.73819e17	−0.0798130
$61$	3.09141e18	0.554873	0.277436	−	0.960744i	$-0.410515\pi$
$61$	3.09141e18	0.554873	0.277436	+	0.960744i	$0.410515\pi$
$62$	5.03953e18	0.762565
$63$	1.13661e19	1.45391
$64$	1.15292e18	0.125000
$65$	−1.56725e19	−1.44393
$66$	−4.82259e17	−0.0378502
$67$	2.10021e19	1.40759	0.703797	−	0.710401i	$-0.251486\pi$
$67$	2.10021e19	1.40759	0.703797	+	0.710401i	$0.251486\pi$
$68$	5.03576e18	0.288883
$69$	−5.51882e18	−0.271601
$70$	−2.13890e19	−0.905025
$71$	5.81169e18	0.211880	0.105940	−	0.994373i	$-0.466215\pi$
$71$	5.81169e18	0.211880	0.105940	+	0.994373i	$0.466215\pi$
$72$	1.08349e19	0.341061
$73$	−6.83431e19	−1.86125	−0.930625	−	0.365973i	$-0.880736\pi$
$73$	−6.83431e19	−1.86125	−0.930625	+	0.365973i	$0.880736\pi$
$74$	4.14305e19	0.978108
$75$	−2.55613e18	−0.0524131
$76$	−3.20921e19	−0.572605
$77$	−2.75936e19	−0.429196
$78$	−1.66378e19	−0.225997
$79$	−9.36862e19	−1.11325	−0.556623	−	0.830765i	$-0.687903\pi$
$79$	−9.36862e19	−1.11325	−0.556623	+	0.830765i	$0.687903\pi$
$80$	−2.03892e19	−0.212303
$81$	9.79574e19	0.895251
$82$	6.01886e19	0.483581
$83$	1.46086e20	1.03345	0.516724	−	0.856152i	$-0.327151\pi$
$83$	1.46086e20	1.03345	0.516724	+	0.856152i	$0.327151\pi$
$84$	−2.27064e19	−0.141650
$85$	−8.90567e19	−0.490645
$86$	8.20466e19	0.399785
$87$	8.08799e18	0.0349051
$88$	−2.63039e19	−0.100682
$89$	−4.97327e20	−1.69063	−0.845313	−	0.534272i	$-0.820586\pi$
$89$	−4.97327e20	−1.69063	−0.845313	+	0.534272i	$0.820586\pi$
$90$	−1.91613e20	−0.579267
$91$	−9.51973e20	−2.56265
$92$	−3.01013e20	−0.722460
$93$	−9.46129e19	−0.202712
$94$	5.20814e20	0.997333
$95$	5.67543e20	0.972526
$96$	−2.16451e19	−0.0332286
$97$	7.60391e20	1.04697	0.523485	−	0.852035i	$-0.324632\pi$
$97$	7.60391e20	1.04697	0.523485	+	0.852035i	$0.324632\pi$
$98$	−7.27254e20	−0.899109
$99$	−2.47197e20	−0.274710

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.1.7	✓	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
58.22.a.b.1.7	✓	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)

\(f(q)\)	\(=\)	\(q-1024.00 q^{2} +19224.7 q^{3} +1.04858e6 q^{4} -1.85439e7 q^{5} -1.96861e7 q^{6} -1.12639e9 q^{7} -1.07374e9 q^{8} -1.00908e10 q^{9} +1.89890e10 q^{10} +2.44974e10 q^{11} +2.01586e10 q^{12} +8.45154e11 q^{13} +1.15342e12 q^{14} -3.56502e11 q^{15} +1.09951e12 q^{16} +4.80247e12 q^{17} +1.03329e13 q^{18} -3.06054e13 q^{19} -1.94447e13 q^{20} -2.16546e13 q^{21} -2.50853e13 q^{22} -2.87069e14 q^{23} -2.06424e13 q^{24} -1.32961e14 q^{25} -8.65438e14 q^{26} -3.95090e14 q^{27} -1.18111e15 q^{28} +4.20707e14 q^{29} +3.65058e14 q^{30} -4.92141e15 q^{31} -1.12590e15 q^{32} +4.70956e14 q^{33} -4.91773e15 q^{34} +2.08877e16 q^{35} -1.05809e16 q^{36} -4.04594e16 q^{37} +3.13399e16 q^{38} +1.62479e16 q^{39} +1.99114e16 q^{40} -5.87779e16 q^{41} +2.21743e16 q^{42} -8.01236e16 q^{43} +2.56874e16 q^{44} +1.87122e17 q^{45} +2.93958e17 q^{46} -5.08607e17 q^{47} +2.11378e16 q^{48} +7.10209e17 q^{49} +1.36152e17 q^{50} +9.23263e16 q^{51} +8.86208e17 q^{52} -2.52920e18 q^{53} +4.04572e17 q^{54} -4.54277e17 q^{55} +1.20945e18 q^{56} -5.88380e17 q^{57} -4.30804e17 q^{58} -1.07073e18 q^{59} -3.73819e17 q^{60} +3.09141e18 q^{61} +5.03953e18 q^{62} +1.13661e19 q^{63} +1.15292e18 q^{64} -1.56725e19 q^{65} -4.82259e17 q^{66} +2.10021e19 q^{67} +5.03576e18 q^{68} -5.51882e18 q^{69} -2.13890e19 q^{70} +5.81169e18 q^{71} +1.08349e19 q^{72} -6.83431e19 q^{73} +4.14305e19 q^{74} -2.55613e18 q^{75} -3.20921e19 q^{76} -2.75936e19 q^{77} -1.66378e19 q^{78} -9.36862e19 q^{79} -2.03892e19 q^{80} +9.79574e19 q^{81} +6.01886e19 q^{82} +1.46086e20 q^{83} -2.27064e19 q^{84} -8.90567e19 q^{85} +8.20466e19 q^{86} +8.08799e18 q^{87} -2.63039e19 q^{88} -4.97327e20 q^{89} -1.91613e20 q^{90} -9.51973e20 q^{91} -3.01013e20 q^{92} -9.46129e19 q^{93} +5.20814e20 q^{94} +5.67543e20 q^{95} -2.16451e19 q^{96} +7.60391e20 q^{97} -7.27254e20 q^{98} -2.47197e20 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 12288 q^{2} + 41066 q^{3} + 12582912 q^{4} + 32000498 q^{5} - 42051584 q^{6} + 442380608 q^{7} - 12884901888 q^{8} + 45829788394 q^{9} - 32768509952 q^{10} - 75612722022 q^{11} + 43060822016 q^{12}+ \cdots - 77\!\cdots\!40 q^{99}+O(q^{100}) \) 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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