LMFDB - Embedded newform 9.76.a.c.1.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [9,76,Mod(1,9)] 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("9.1"); S:= CuspForms(chi, 76); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(9, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0])) N = Newforms(chi, 76, names="a")

Level:	$ N $	$=$	$ 9 = 3^{2} $
Weight:	$ k $	$=$	$ 76 $
Character orbit:	$[\chi]$	$=$	9.a (trivial)

Newform invariants

comment:select newform

sage:traces = [6,57080822040] 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:	$320.605553540$
Analytic rank:	$1$
Dimension:	$6$
Coefficient field:	$\mathbb{Q}[x]/(x^{6} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 3 x^{5} + \cdots - 67\!\cdots\!50 $ x^6 - 3x^5 - 38457853073924058692x^4 - 10276556354621685339901678086x^3 + 371187556674475060057870954681799784505x^2 + 52686123927652036687598761277591247931691204025*x - 675344021115865838575279495800656435684060652010336995750
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	multiple of $ 2^{58}\cdot 3^{36}\cdot 5^{7}\cdot 7^{3}\cdot 11\cdot 13\cdot 19 $
Twist minimal:	no (minimal twist has level 1)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$3.19848e9$ of defining polynomial
Character	$\chi$	$=$	9.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-2.20777e11 q^{2} +1.09637e22 q^{4} +2.30711e25 q^{5} +1.96027e31 q^{7} +5.92020e33 q^{8} -5.09358e36 q^{10} -9.40509e38 q^{11} +1.14147e42 q^{13} -4.32784e42 q^{14} -1.72124e45 q^{16} -1.79040e46 q^{17} +1.43901e48 q^{19} +2.52945e47 q^{20} +2.07643e50 q^{22} +1.23136e51 q^{23} -2.59375e52 q^{25} -2.52010e53 q^{26} +2.14918e53 q^{28} +2.48097e54 q^{29} +1.95055e55 q^{31} +1.56352e56 q^{32} +3.95280e57 q^{34} +4.52257e56 q^{35} -2.65296e58 q^{37} -3.17702e59 q^{38} +1.36586e59 q^{40} -3.61594e59 q^{41} +8.98859e59 q^{43} -1.03115e61 q^{44} -2.71857e62 q^{46} -2.48355e62 q^{47} -2.02760e63 q^{49} +5.72641e63 q^{50} +1.25147e64 q^{52} -3.59994e64 q^{53} -2.16986e64 q^{55} +1.16052e65 q^{56} -5.47742e65 q^{58} +4.00811e66 q^{59} -1.59203e67 q^{61} -4.30637e66 q^{62} +3.05076e67 q^{64} +2.63349e67 q^{65} +1.61324e68 q^{67} -1.96294e68 q^{68} -9.98480e67 q^{70} -2.63303e69 q^{71} -2.52652e69 q^{73} +5.85713e69 q^{74} +1.57769e70 q^{76} -1.84365e70 q^{77} -9.29901e70 q^{79} -3.97110e70 q^{80} +7.98318e70 q^{82} +7.84087e71 q^{83} -4.13066e71 q^{85} -1.98448e71 q^{86} -5.56800e72 q^{88} -2.05618e73 q^{89} +2.23759e73 q^{91} +1.35003e73 q^{92} +5.48312e73 q^{94} +3.31997e73 q^{95} -4.10454e74 q^{97} +4.47648e74 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 57080822040 q^{2} + 17\!\cdots\!28 q^{4} + 38\!\cdots\!40 q^{5} + 19\!\cdots\!00 q^{7} - 44\!\cdots\!20 q^{8} + 13\!\cdots\!60 q^{10} + 94\!\cdots\!88 q^{11} + 53\!\cdots\!20 q^{13} - 82\!\cdots\!76 q^{14}+ \cdots + 16\!\cdots\!20 q^{98}+O(q^{100}) $ 6 * q + 57080822040 * q^2 + 172600466200162028593728 * q^4 + 38982947396479621874420940 * q^5 + 1924474634802918779239478643600 * q^7 - 4434903997968330342413437320645120 * q^8 + 133267935677460241037537052811576902960 * q^10 + 945659951949983071650740113735111214088 * q^11 + 533185179266852519941169625089098069764420 * q^13 - 8213946953162263647781694565284746353072576 * q^14 + 2681978005634517266622433394712415602648354816 * q^16 - 18261354095776132566172834671579513215483393580 * q^17 + 1061534856238354155312794852768417904375328867080 * q^19 - 9296557595621768320156983882258818695571369489280 * q^20 + 153315952874260268106194796405555863940172791589920 * q^22 - 1514929449877410771078348320690686508954384916853680 * q^23 + 19310380328261093150952553553121815533899364092239850 * q^25 - 117730941166816926498584842564210483616872200198362352 * q^26 + 1465885017268620651444113586751990931877154821040657920 * q^28 - 14718767377678125816030788545177391174717388984245534820 * q^29 - 41742874787360498453628839393549579933009794702042980288 * q^31 - 1174660148719991756036751189163540495635749096221862952960 * q^32 + 3034358950124956876257603978888653679838045546922892395856 * q^34 - 27299672493656883988453292135086250689495956464846953371360 * q^35 + 98517772547646219221591850851651469983797181732879949140340 * q^37 - 1257660981102762853948269222064665311191946222029530979162080 * q^38 + 8807901623729426290853411185831313455271917763097593104051200 * q^40 - 5039211762207387369185984529408567568647239506257650214613212 * q^41 + 27938749238581541451173935836639198120068956697568041153196600 * q^43 + 86388814623354110240559749283671522466589238091463431115801344 * q^44 - 824145803870667307795487213022331547039596870954611528203613888 * q^46 + 1386854970430427381646742231466788117324292253074354560479038880 * q^47 - 5707868790800975784856935495088511133239544554833878775910738442 * q^49 - 3144970672685230615695776810799603542575044196614572896663392600 * q^50 + 41677832028141179840113326797899392222702339479233001780216150400 * q^52 - 64283727174659970247345252518647455744441825702701764187054106260 * q^53 + 436876078674971654403803167180324983329224614451635548418098895120 * q^55 - 289950797286325881623798664040853221823087783432246887785270865920 * q^56 - 1763005756244374137396902189067511762184157619699352574614137403280 * q^58 + 2478360370933764187935912640189307752170553390931716617591182395560 * q^59 - 25641115321477658815889269525514418267074652297034046321782023152988 * q^61 + 29014701474354643819936101890527484086880802356768235703173807694080 * q^62 + 47683232974651133862719671893097862706511055838864188064811716968448 * q^64 - 122110621788131890149667214965152432737153070969379698276880591977720 * q^65 + 955579073553339181030887342220313909838725364297810737998207107813480 * q^67 - 1237210897217068882936524414359446185548686871817993659403939290386560 * q^68 - 3476902593928340346610001926714053112321275314411181267396530677050240 * q^70 + 255682319306096297182489045146623979225804710540351927309367569173488 * q^71 - 30605188898291905719532895918028188508004452865621142257485594115042020 * q^73 + 24065024027894599201472448362529876891121294631891709256708009194181584 * q^74 + 100020936372377387464010564774983213070641689274186088752725827576144640 * q^76 - 158930415774536768880543239288689183540801263714134710336228496440507200 * q^77 + 116627678166642324332643069323234092884951450625988452824960767925148320 * q^79 - 1239310052714502333188756625709169306278438274940582996524184215206748160 * q^80 - 2557649813228840791149140948716215474705151452500921688788291587877236080 * q^82 + 798780284119889426515570523310162377392459257634002033911814028088739960 * q^83 - 3615500806340871685633297735534398118961343923835923286123685237305018840 * q^85 - 7245194180836090971883743617494948296636529538939897523257528311698092832 * q^86 - 4827001398586167572057494186308233100206033194553368013345656010632181760 * q^88 - 53575610216125238704584826863934604186542249469498220298044079954014547260 * q^89 + 34502419684367451829908407139028781594042460695428817715772307436403470432 * q^91 - 187445224353587479072026786339601818260697439565538078689222489106585838080 * q^92 - 296189325151987924691405038954735773676385503565643130818482899021002578304 * q^94 - 194934959385332686251927514630723902507701573195047654345319995220933314800 * q^95 - 747928220344118582344222376208028579242743608466383778453296378427532508980 * q^97 + 1663265696927109513221859402309517858944410070626232817304447619248634722520 * q^98

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 $

$2$	−2.20777e11	−1.13587	−0.567936	−	0.823072i	$-0.692258\pi$
$2$	−2.20777e11	−1.13587	−0.567936	+	0.823072i	$0.692258\pi$
$3$	0	0
$3$	0	0
$4$	1.09637e22	0.290207
$5$	2.30711e25	0.141806	0.0709028	−	0.997483i	$-0.477412\pi$
$5$	2.30711e25	0.141806	0.0709028	+	0.997483i	$0.477412\pi$
$6$	0	0
$7$	1.96027e31	0.399153	0.199577	−	0.979882i	$-0.436043\pi$
$7$	1.96027e31	0.399153	0.199577	+	0.979882i	$0.436043\pi$
$8$	5.92020e33	0.806235
$9$	0	0
$10$	−5.09358e36	−0.161073
$11$	−9.40509e38	−0.833945	−0.416972	−	0.908919i	$-0.636909\pi$
$11$	−9.40509e38	−0.833945	−0.416972	+	0.908919i	$0.636909\pi$
$12$	0	0
$13$	1.14147e42	1.92570	0.962848	−	0.270042i	$-0.0870377\pi$
$13$	1.14147e42	1.92570	0.962848	+	0.270042i	$0.0870377\pi$
$14$	−4.32784e42	−0.453387
$15$	0	0
$16$	−1.72124e45	−1.20599
$17$	−1.79040e46	−1.29156	−0.645782	−	0.763522i	$-0.723469\pi$
$17$	−1.79040e46	−1.29156	−0.645782	+	0.763522i	$0.723469\pi$
$18$	0	0
$19$	1.43901e48	1.60253	0.801263	−	0.598312i	$-0.204162\pi$
$19$	1.43901e48	1.60253	0.801263	+	0.598312i	$0.204162\pi$
$20$	2.52945e47	0.0411529
$21$	0	0
$22$	2.07643e50	0.947255
$23$	1.23136e51	1.06070	0.530349	−	0.847779i	$-0.322061\pi$
$23$	1.23136e51	1.06070	0.530349	+	0.847779i	$0.322061\pi$
$24$	0	0
$25$	−2.59375e52	−0.979891
$26$	−2.52010e53	−2.18735
$27$	0	0
$28$	2.14918e53	0.115837
$29$	2.48097e54	0.358671	0.179336	−	0.983788i	$-0.442605\pi$
$29$	2.48097e54	0.358671	0.179336	+	0.983788i	$0.442605\pi$
$30$	0	0
$31$	1.95055e55	0.231256	0.115628	−	0.993293i	$-0.463112\pi$
$31$	1.95055e55	0.231256	0.115628	+	0.993293i	$0.463112\pi$
$32$	1.56352e56	0.563613
$33$	0	0
$34$	3.95280e57	1.46705
$35$	4.52257e56	0.0566022
$36$	0	0
$37$	−2.65296e58	−0.413205	−0.206603	−	0.978425i	$-0.566241\pi$
$37$	−2.65296e58	−0.413205	−0.206603	+	0.978425i	$0.566241\pi$
$38$	−3.17702e59	−1.82027
$39$	0	0
$40$	1.36586e59	0.114329
$41$	−3.61594e59	−0.119902	−0.0599511	−	0.998201i	$-0.519094\pi$
$41$	−3.61594e59	−0.119902	−0.0599511	+	0.998201i	$0.519094\pi$
$42$	0	0
$43$	8.98859e59	0.0499603	0.0249801	−	0.999688i	$-0.492048\pi$
$43$	8.98859e59	0.0499603	0.0249801	+	0.999688i	$0.492048\pi$
$44$	−1.03115e61	−0.242016
$45$	0	0
$46$	−2.71857e62	−1.20482
$47$	−2.48355e62	−0.491364	−0.245682	−	0.969350i	$-0.579012\pi$
$47$	−2.48355e62	−0.491364	−0.245682	+	0.969350i	$0.579012\pi$
$48$	0	0
$49$	−2.02760e63	−0.840677
$50$	5.72641e63	1.11303
$51$	0	0
$52$	1.25147e64	0.558850
$53$	−3.59994e64	−0.786955	−0.393477	−	0.919334i	$-0.628728\pi$
$53$	−3.59994e64	−0.786955	−0.393477	+	0.919334i	$0.628728\pi$
$54$	0	0
$55$	−2.16986e64	−0.118258
$56$	1.16052e65	0.321811
$57$	0	0
$58$	−5.47742e65	−0.407405
$59$	4.00811e66	1.57032	0.785162	−	0.619291i	$-0.212580\pi$
$59$	4.00811e66	1.57032	0.785162	+	0.619291i	$0.212580\pi$
$60$	0	0
$61$	−1.59203e67	−1.78683	−0.893413	−	0.449237i	$-0.851696\pi$
$61$	−1.59203e67	−1.78683	−0.893413	+	0.449237i	$0.851696\pi$
$62$	−4.30637e66	−0.262678
$63$	0	0
$64$	3.05076e67	0.565795
$65$	2.63349e67	0.273075
$66$	0	0
$67$	1.61324e68	0.536900	0.268450	−	0.963294i	$-0.413489\pi$
$67$	1.61324e68	0.536900	0.268450	+	0.963294i	$0.413489\pi$
$68$	−1.96294e68	−0.374821
$69$	0	0
$70$	−9.98480e67	−0.0642929
$71$	−2.63303e69	−0.996020	−0.498010	−	0.867171i	$-0.665936\pi$
$71$	−2.63303e69	−0.996020	−0.498010	+	0.867171i	$0.665936\pi$
$72$	0	0
$73$	−2.52652e69	−0.337221	−0.168611	−	0.985683i	$-0.553928\pi$
$73$	−2.52652e69	−0.337221	−0.168611	+	0.985683i	$0.553928\pi$
$74$	5.85713e69	0.469348
$75$	0	0
$76$	1.57769e70	0.465064
$77$	−1.84365e70	−0.332872
$78$	0	0
$79$	−9.29901e70	−0.641831	−0.320916	−	0.947108i	$-0.603991\pi$
$79$	−9.29901e70	−0.641831	−0.320916	+	0.947108i	$0.603991\pi$
$80$	−3.97110e70	−0.171016
$81$	0	0
$82$	7.98318e70	0.136194
$83$	7.84087e71	0.849055	0.424528	−	0.905415i	$-0.360440\pi$
$83$	7.84087e71	0.849055	0.424528	+	0.905415i	$0.360440\pi$
$84$	0	0
$85$	−4.13066e71	−0.183151
$86$	−1.98448e71	−0.0567485
$87$	0	0
$88$	−5.56800e72	−0.672355
$89$	−2.05618e73	−1.62531	−0.812656	−	0.582744i	$-0.801979\pi$
$89$	−2.05618e73	−1.62531	−0.812656	+	0.582744i	$0.801979\pi$
$90$	0	0
$91$	2.23759e73	0.768648
$92$	1.35003e73	0.307822
$93$	0	0
$94$	5.48312e73	0.558127
$95$	3.31997e73	0.227247
$96$	0	0
$97$	−4.10454e74	−1.28625	−0.643123	−	0.765763i	$-0.722362\pi$
$97$	−4.10454e74	−1.28625	−0.643123	+	0.765763i	$0.722362\pi$
$98$	4.47648e74	0.954902
$99$	0	0

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	9.76.a.c.1.2		6
3.2	odd	2		1.76.a.a.1.5	✓	6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1.76.a.a.1.5	✓	6	3.2	odd	2
9.76.a.c.1.2		6	1.1	even	1	trivial

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 9 = 3^{2} \)
Weight:	\( k \)	\(=\)	\( 76 \)
Character orbit:	\([\chi]\)	\(=\)	9.a (trivial)

\(f(q)\)	\(=\)	\(q-2.20777e11 q^{2} +1.09637e22 q^{4} +2.30711e25 q^{5} +1.96027e31 q^{7} +5.92020e33 q^{8} -5.09358e36 q^{10} -9.40509e38 q^{11} +1.14147e42 q^{13} -4.32784e42 q^{14} -1.72124e45 q^{16} -1.79040e46 q^{17} +1.43901e48 q^{19} +2.52945e47 q^{20} +2.07643e50 q^{22} +1.23136e51 q^{23} -2.59375e52 q^{25} -2.52010e53 q^{26} +2.14918e53 q^{28} +2.48097e54 q^{29} +1.95055e55 q^{31} +1.56352e56 q^{32} +3.95280e57 q^{34} +4.52257e56 q^{35} -2.65296e58 q^{37} -3.17702e59 q^{38} +1.36586e59 q^{40} -3.61594e59 q^{41} +8.98859e59 q^{43} -1.03115e61 q^{44} -2.71857e62 q^{46} -2.48355e62 q^{47} -2.02760e63 q^{49} +5.72641e63 q^{50} +1.25147e64 q^{52} -3.59994e64 q^{53} -2.16986e64 q^{55} +1.16052e65 q^{56} -5.47742e65 q^{58} +4.00811e66 q^{59} -1.59203e67 q^{61} -4.30637e66 q^{62} +3.05076e67 q^{64} +2.63349e67 q^{65} +1.61324e68 q^{67} -1.96294e68 q^{68} -9.98480e67 q^{70} -2.63303e69 q^{71} -2.52652e69 q^{73} +5.85713e69 q^{74} +1.57769e70 q^{76} -1.84365e70 q^{77} -9.29901e70 q^{79} -3.97110e70 q^{80} +7.98318e70 q^{82} +7.84087e71 q^{83} -4.13066e71 q^{85} -1.98448e71 q^{86} -5.56800e72 q^{88} -2.05618e73 q^{89} +2.23759e73 q^{91} +1.35003e73 q^{92} +5.48312e73 q^{94} +3.31997e73 q^{95} -4.10454e74 q^{97} +4.47648e74 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 57080822040 q^{2} + 17\!\cdots\!28 q^{4} + 38\!\cdots\!40 q^{5} + 19\!\cdots\!00 q^{7} - 44\!\cdots\!20 q^{8} + 13\!\cdots\!60 q^{10} + 94\!\cdots\!88 q^{11} + 53\!\cdots\!20 q^{13} - 82\!\cdots\!76 q^{14}+ \cdots + 16\!\cdots\!20 q^{98}+O(q^{100}) \) 6 * q + 57080822040 * q^2 + 172600466200162028593728 * q^4 + 38982947396479621874420940 * q^5 + 1924474634802918779239478643600 * q^7 - 4434903997968330342413437320645120 * q^8 + 133267935677460241037537052811576902960 * q^10 + 945659951949983071650740113735111214088 * q^11 + 533185179266852519941169625089098069764420 * q^13 - 8213946953162263647781694565284746353072576 * q^14 + 2681978005634517266622433394712415602648354816 * q^16 - 18261354095776132566172834671579513215483393580 * q^17 + 1061534856238354155312794852768417904375328867080 * q^19 - 9296557595621768320156983882258818695571369489280 * q^20 + 153315952874260268106194796405555863940172791589920 * q^22 - 1514929449877410771078348320690686508954384916853680 * q^23 + 19310380328261093150952553553121815533899364092239850 * q^25 - 117730941166816926498584842564210483616872200198362352 * q^26 + 1465885017268620651444113586751990931877154821040657920 * q^28 - 14718767377678125816030788545177391174717388984245534820 * q^29 - 41742874787360498453628839393549579933009794702042980288 * q^31 - 1174660148719991756036751189163540495635749096221862952960 * q^32 + 3034358950124956876257603978888653679838045546922892395856 * q^34 - 27299672493656883988453292135086250689495956464846953371360 * q^35 + 98517772547646219221591850851651469983797181732879949140340 * q^37 - 1257660981102762853948269222064665311191946222029530979162080 * q^38 + 8807901623729426290853411185831313455271917763097593104051200 * q^40 - 5039211762207387369185984529408567568647239506257650214613212 * q^41 + 27938749238581541451173935836639198120068956697568041153196600 * q^43 + 86388814623354110240559749283671522466589238091463431115801344 * q^44 - 824145803870667307795487213022331547039596870954611528203613888 * q^46 + 1386854970430427381646742231466788117324292253074354560479038880 * q^47 - 5707868790800975784856935495088511133239544554833878775910738442 * q^49 - 3144970672685230615695776810799603542575044196614572896663392600 * q^50 + 41677832028141179840113326797899392222702339479233001780216150400 * q^52 - 64283727174659970247345252518647455744441825702701764187054106260 * q^53 + 436876078674971654403803167180324983329224614451635548418098895120 * q^55 - 289950797286325881623798664040853221823087783432246887785270865920 * q^56 - 1763005756244374137396902189067511762184157619699352574614137403280 * q^58 + 2478360370933764187935912640189307752170553390931716617591182395560 * q^59 - 25641115321477658815889269525514418267074652297034046321782023152988 * q^61 + 29014701474354643819936101890527484086880802356768235703173807694080 * q^62 + 47683232974651133862719671893097862706511055838864188064811716968448 * q^64 - 122110621788131890149667214965152432737153070969379698276880591977720 * q^65 + 955579073553339181030887342220313909838725364297810737998207107813480 * q^67 - 1237210897217068882936524414359446185548686871817993659403939290386560 * q^68 - 3476902593928340346610001926714053112321275314411181267396530677050240 * q^70 + 255682319306096297182489045146623979225804710540351927309367569173488 * q^71 - 30605188898291905719532895918028188508004452865621142257485594115042020 * q^73 + 24065024027894599201472448362529876891121294631891709256708009194181584 * q^74 + 100020936372377387464010564774983213070641689274186088752725827576144640 * q^76 - 158930415774536768880543239288689183540801263714134710336228496440507200 * q^77 + 116627678166642324332643069323234092884951450625988452824960767925148320 * q^79 - 1239310052714502333188756625709169306278438274940582996524184215206748160 * q^80 - 2557649813228840791149140948716215474705151452500921688788291587877236080 * q^82 + 798780284119889426515570523310162377392459257634002033911814028088739960 * q^83 - 3615500806340871685633297735534398118961343923835923286123685237305018840 * q^85 - 7245194180836090971883743617494948296636529538939897523257528311698092832 * q^86 - 4827001398586167572057494186308233100206033194553368013345656010632181760 * q^88 - 53575610216125238704584826863934604186542249469498220298044079954014547260 * q^89 + 34502419684367451829908407139028781594042460695428817715772307436403470432 * q^91 - 187445224353587479072026786339601818260697439565538078689222489106585838080 * q^92 - 296189325151987924691405038954735773676385503565643130818482899021002578304 * q^94 - 194934959385332686251927514630723902507701573195047654345319995220933314800 * q^95 - 747928220344118582344222376208028579242743608466383778453296378427532508980 * q^97 + 1663265696927109513221859402309517858944410070626232817304447619248634722520 * q^98

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