LMFDB - Embedded newform 58.22.a.b.1.6

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			1.6
Root			$4563.21$ 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)

$f(q)$	$=$	\(q-1024.00 q^{2} +7985.21 q^{3} +1.04858e6 q^{4} +1.71413e7 q^{5} -8.17686e6 q^{6} -1.67627e8 q^{7} -1.07374e9 q^{8} -1.03966e10 q^{9} -1.75526e10 q^{10} -6.71435e9 q^{11} +8.37310e9 q^{12} -1.89944e11 q^{13} +1.71650e11 q^{14} +1.36877e11 q^{15} +1.09951e12 q^{16} -1.26077e13 q^{17} +1.06461e13 q^{18} -3.38044e13 q^{19} +1.79739e13 q^{20} -1.33854e12 q^{21} +6.87550e12 q^{22} -3.41915e14 q^{23} -8.57406e12 q^{24} -1.83014e14 q^{25} +1.94503e14 q^{26} -1.66547e14 q^{27} -1.75770e14 q^{28} +4.20707e14 q^{29} -1.40162e14 q^{30} +5.11025e15 q^{31} -1.12590e15 q^{32} -5.36155e13 q^{33} +1.29103e16 q^{34} -2.87334e15 q^{35} -1.09016e16 q^{36} +6.84893e15 q^{37} +3.46157e16 q^{38} -1.51674e15 q^{39} -1.84053e16 q^{40} +9.55917e16 q^{41} +1.37066e15 q^{42} +1.19036e17 q^{43} -7.04051e15 q^{44} -1.78211e17 q^{45} +3.50121e17 q^{46} -1.08716e17 q^{47} +8.77984e15 q^{48} -5.30447e17 q^{49} +1.87407e17 q^{50} -1.00675e17 q^{51} -1.99171e17 q^{52} +2.33836e18 q^{53} +1.70544e17 q^{54} -1.15092e17 q^{55} +1.79988e17 q^{56} -2.69935e17 q^{57} -4.30804e17 q^{58} +2.66487e18 q^{59} +1.43526e17 q^{60} -5.56832e18 q^{61} -5.23290e18 q^{62} +1.74275e18 q^{63} +1.15292e18 q^{64} -3.25588e18 q^{65} +5.49023e16 q^{66} -1.16958e17 q^{67} -1.32202e19 q^{68} -2.73026e18 q^{69} +2.94230e18 q^{70} -1.33973e18 q^{71} +1.11633e19 q^{72} -8.30393e18 q^{73} -7.01330e18 q^{74} -1.46141e18 q^{75} -3.54465e19 q^{76} +1.12551e18 q^{77} +1.55315e18 q^{78} +2.74545e19 q^{79} +1.88470e19 q^{80} +1.07422e20 q^{81} -9.78859e19 q^{82} +9.28407e19 q^{83} -1.40356e18 q^{84} -2.16112e20 q^{85} -1.21892e20 q^{86} +3.35944e18 q^{87} +7.20948e18 q^{88} -1.38363e20 q^{89} +1.82488e20 q^{90} +3.18398e19 q^{91} -3.58523e20 q^{92} +4.08065e19 q^{93} +1.11325e20 q^{94} -5.79450e20 q^{95} -8.99055e18 q^{96} +8.40173e19 q^{97} +5.43178e20 q^{98} +6.98064e19 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	7985.21	0.0780752	0.0390376	−	0.999238i	$-0.487571\pi$
$3$	7985.21	0.0780752	0.0390376	+	0.999238i	$0.487571\pi$
$4$	1.04858e6	0.500000
$5$	1.71413e7	0.784978	0.392489	−	0.919757i	$-0.371614\pi$
$5$	1.71413e7	0.784978	0.392489	+	0.919757i	$0.371614\pi$
$6$	−8.17686e6	−0.0552075
$7$	−1.67627e8	−0.224293	−0.112146	−	0.993692i	$-0.535773\pi$
$7$	−1.67627e8	−0.224293	−0.112146	+	0.993692i	$0.535773\pi$
$8$	−1.07374e9	−0.353553
$9$	−1.03966e10	−0.993904
$10$	−1.75526e10	−0.555063
$11$	−6.71435e9	−0.0780514	−0.0390257	−	0.999238i	$-0.512425\pi$
$11$	−6.71435e9	−0.0780514	−0.0390257	+	0.999238i	$0.512425\pi$
$12$	8.37310e9	0.0390376
$13$	−1.89944e11	−0.382138	−0.191069	−	0.981577i	$-0.561195\pi$
$13$	−1.89944e11	−0.382138	−0.191069	+	0.981577i	$0.561195\pi$
$14$	1.71650e11	0.158599
$15$	1.36877e11	0.0612874
$16$	1.09951e12	0.250000
$17$	−1.26077e13	−1.51678	−0.758390	−	0.651800i	$-0.774014\pi$
$17$	−1.26077e13	−1.51678	−0.758390	+	0.651800i	$0.774014\pi$
$18$	1.06461e13	0.702796
$19$	−3.38044e13	−1.26491	−0.632456	−	0.774596i	$-0.717953\pi$
$19$	−3.38044e13	−1.26491	−0.632456	+	0.774596i	$0.717953\pi$
$20$	1.79739e13	0.392489
$21$	−1.33854e12	−0.0175117
$22$	6.87550e12	0.0551907
$23$	−3.41915e14	−1.72098	−0.860489	−	0.509469i	$-0.829842\pi$
$23$	−3.41915e14	−1.72098	−0.860489	+	0.509469i	$0.829842\pi$
$24$	−8.57406e12	−0.0276038
$25$	−1.83014e14	−0.383809
$26$	1.94503e14	0.270213
$27$	−1.66547e14	−0.155675
$28$	−1.75770e14	−0.112146
$29$	4.20707e14	0.185695
$29$	4.20707e14	0.185695
$30$	−1.40162e14	−0.0433367
$31$	5.11025e15	1.11981	0.559906	−	0.828556i	$-0.310837\pi$
$31$	5.11025e15	1.11981	0.559906	+	0.828556i	$0.310837\pi$
$32$	−1.12590e15	−0.176777
$33$	−5.36155e13	−0.00609388
$34$	1.29103e16	1.07253
$35$	−2.87334e15	−0.176065
$36$	−1.09016e16	−0.496952
$37$	6.84893e15	0.234156	0.117078	−	0.993123i	$-0.462647\pi$
$37$	6.84893e15	0.234156	0.117078	+	0.993123i	$0.462647\pi$
$38$	3.46157e16	0.894428
$39$	−1.51674e15	−0.0298355
$40$	−1.84053e16	−0.277532
$41$	9.55917e16	1.11222	0.556109	−	0.831110i	$-0.312294\pi$
$41$	9.55917e16	1.11222	0.556109	+	0.831110i	$0.312294\pi$
$42$	1.37066e15	0.0123826
$43$	1.19036e17	0.839958	0.419979	−	0.907534i	$-0.362037\pi$
$43$	1.19036e17	0.839958	0.419979	+	0.907534i	$0.362037\pi$
$44$	−7.04051e15	−0.0390257
$45$	−1.78211e17	−0.780193
$46$	3.50121e17	1.21692
$47$	−1.08716e17	−0.301484	−0.150742	−	0.988573i	$-0.548166\pi$
$47$	−1.08716e17	−0.301484	−0.150742	+	0.988573i	$0.548166\pi$
$48$	8.77984e15	0.0195188
$49$	−5.30447e17	−0.949693
$50$	1.87407e17	0.271394
$51$	−1.00675e17	−0.118423
$52$	−1.99171e17	−0.191069
$53$	2.33836e18	1.83660	0.918300	−	0.395884i	$-0.129562\pi$
$53$	2.33836e18	1.83660	0.918300	+	0.395884i	$0.129562\pi$
$54$	1.70544e17	0.110079
$55$	−1.15092e17	−0.0612687
$56$	1.79988e17	0.0792994
$57$	−2.69935e17	−0.0987583
$58$	−4.30804e17	−0.131306
$59$	2.66487e18	0.678780	0.339390	−	0.940646i	$-0.389779\pi$
$59$	2.66487e18	0.678780	0.339390	+	0.940646i	$0.389779\pi$
$60$	1.43526e17	0.0306437
$61$	−5.56832e18	−0.999450	−0.499725	−	0.866184i	$-0.666566\pi$
$61$	−5.56832e18	−0.999450	−0.499725	+	0.866184i	$0.666566\pi$
$62$	−5.23290e18	−0.791826
$63$	1.74275e18	0.222925
$64$	1.15292e18	0.125000
$65$	−3.25588e18	−0.299970
$66$	5.49023e16	0.00430903
$67$	−1.16958e17	−0.00783869	−0.00391935	−	0.999992i	$-0.501248\pi$
$67$	−1.16958e17	−0.00783869	−0.00391935	+	0.999992i	$0.501248\pi$
$68$	−1.32202e19	−0.758390
$69$	−2.73026e18	−0.134366
$70$	2.94230e18	0.124497
$71$	−1.33973e18	−0.0488432	−0.0244216	−	0.999702i	$-0.507774\pi$
$71$	−1.33973e18	−0.0488432	−0.0244216	+	0.999702i	$0.507774\pi$
$72$	1.11633e19	0.351398
$73$	−8.30393e18	−0.226148	−0.113074	−	0.993587i	$-0.536070\pi$
$73$	−8.30393e18	−0.226148	−0.113074	+	0.993587i	$0.536070\pi$
$74$	−7.01330e18	−0.165573
$75$	−1.46141e18	−0.0299660
$76$	−3.54465e19	−0.632456
$77$	1.12551e18	0.0175064
$78$	1.55315e18	0.0210969
$79$	2.74545e19	0.326234	0.163117	−	0.986607i	$-0.447845\pi$
$79$	2.74545e19	0.326234	0.163117	+	0.986607i	$0.447845\pi$
$80$	1.88470e19	0.196245
$81$	1.07422e20	0.981750
$82$	−9.78859e19	−0.786456
$83$	9.28407e19	0.656778	0.328389	−	0.944543i	$-0.393494\pi$
$83$	9.28407e19	0.656778	0.328389	+	0.944543i	$0.393494\pi$
$84$	−1.40356e18	−0.00875585
$85$	−2.16112e20	−1.19064
$86$	−1.21892e20	−0.593940
$87$	3.35944e18	0.0144982
$88$	7.20948e18	0.0275953
$89$	−1.38363e20	−0.470353	−0.235176	−	0.971953i	$-0.575567\pi$
$89$	−1.38363e20	−0.470353	−0.235176	+	0.971953i	$0.575567\pi$
$90$	1.82488e20	0.551680
$91$	3.18398e19	0.0857108
$92$	−3.58523e20	−0.860489
$93$	4.08065e19	0.0874295
$94$	1.11325e20	0.213182
$95$	−5.79450e20	−0.992928
$96$	−8.99055e18	−0.0138019
$97$	8.40173e19	0.115682	0.0578410	−	0.998326i	$-0.481578\pi$
$97$	8.40173e19	0.115682	0.0578410	+	0.998326i	$0.481578\pi$
$98$	5.43178e20	0.671534
$99$	6.98064e19	0.0775756

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.1.6	✓	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
58.22.a.b.1.6	✓	12	1.1	even	1	trivial

Overview	Random
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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)

\(f(q)\)	\(=\)	\(q-1024.00 q^{2} +7985.21 q^{3} +1.04858e6 q^{4} +1.71413e7 q^{5} -8.17686e6 q^{6} -1.67627e8 q^{7} -1.07374e9 q^{8} -1.03966e10 q^{9} -1.75526e10 q^{10} -6.71435e9 q^{11} +8.37310e9 q^{12} -1.89944e11 q^{13} +1.71650e11 q^{14} +1.36877e11 q^{15} +1.09951e12 q^{16} -1.26077e13 q^{17} +1.06461e13 q^{18} -3.38044e13 q^{19} +1.79739e13 q^{20} -1.33854e12 q^{21} +6.87550e12 q^{22} -3.41915e14 q^{23} -8.57406e12 q^{24} -1.83014e14 q^{25} +1.94503e14 q^{26} -1.66547e14 q^{27} -1.75770e14 q^{28} +4.20707e14 q^{29} -1.40162e14 q^{30} +5.11025e15 q^{31} -1.12590e15 q^{32} -5.36155e13 q^{33} +1.29103e16 q^{34} -2.87334e15 q^{35} -1.09016e16 q^{36} +6.84893e15 q^{37} +3.46157e16 q^{38} -1.51674e15 q^{39} -1.84053e16 q^{40} +9.55917e16 q^{41} +1.37066e15 q^{42} +1.19036e17 q^{43} -7.04051e15 q^{44} -1.78211e17 q^{45} +3.50121e17 q^{46} -1.08716e17 q^{47} +8.77984e15 q^{48} -5.30447e17 q^{49} +1.87407e17 q^{50} -1.00675e17 q^{51} -1.99171e17 q^{52} +2.33836e18 q^{53} +1.70544e17 q^{54} -1.15092e17 q^{55} +1.79988e17 q^{56} -2.69935e17 q^{57} -4.30804e17 q^{58} +2.66487e18 q^{59} +1.43526e17 q^{60} -5.56832e18 q^{61} -5.23290e18 q^{62} +1.74275e18 q^{63} +1.15292e18 q^{64} -3.25588e18 q^{65} +5.49023e16 q^{66} -1.16958e17 q^{67} -1.32202e19 q^{68} -2.73026e18 q^{69} +2.94230e18 q^{70} -1.33973e18 q^{71} +1.11633e19 q^{72} -8.30393e18 q^{73} -7.01330e18 q^{74} -1.46141e18 q^{75} -3.54465e19 q^{76} +1.12551e18 q^{77} +1.55315e18 q^{78} +2.74545e19 q^{79} +1.88470e19 q^{80} +1.07422e20 q^{81} -9.78859e19 q^{82} +9.28407e19 q^{83} -1.40356e18 q^{84} -2.16112e20 q^{85} -1.21892e20 q^{86} +3.35944e18 q^{87} +7.20948e18 q^{88} -1.38363e20 q^{89} +1.82488e20 q^{90} +3.18398e19 q^{91} -3.58523e20 q^{92} +4.08065e19 q^{93} +1.11325e20 q^{94} -5.79450e20 q^{95} -8.99055e18 q^{96} +8.40173e19 q^{97} +5.43178e20 q^{98} +6.98064e19 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 12288 q^{2} + 41066 q^{3} + 12582912 q^{4} + 32000498 q^{5} - 42051584 q^{6} + 442380608 q^{7} - 12884901888 q^{8} + 45829788394 q^{9} - 32768509952 q^{10} - 75612722022 q^{11} + 43060822016 q^{12}+ \cdots - 77\!\cdots\!40 q^{99}+O(q^{100}) \) 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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