LMFDB - Embedded newform 81.22.a.c.1.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [81,22,Mod(1,81)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(81, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 22, names="a")

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

chi := DirichletCharacter("81.1");

S:= CuspForms(chi, 22);

N := Newforms(S);

Level:	$ N $	$=$	$ 81 = 3^{4} $
Weight:	$ k $	$=$	$ 22 $
Character orbit:	$[\chi]$	$=$	81.a (trivial)

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:	yes
Analytic conductor:	$226.376648873$
Analytic rank:	$1$
Dimension:	$20$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 3 x^{19} - 30906825 x^{18} + 1599806295 x^{17} + 397632537600480 x^{16} + \cdots + 18\!\cdots\!00 $ x^20 - 3x^19 - 30906825x^18 + 1599806295x^17 + 397632537600480x^16 - 39002822306934732x^15 - 2767501910687405017140x^14 + 391326176564192242210572x^13 + 11337389828314088384663968014x^12 - 2062014444300295623078414274842x^11 - 27853618399037107366577090329328670x^10 + 6152815999004060192586598873467670626x^9 + 39977296093180250047956449416351511766204x^8 - 10437440555436107068148091511291912219002012x^7 - 30979178049576561502756083124979860960535622468x^6 + 9412443148812104482026646046738359353628722883452x^5 + 10839091544581780684520015865967041645826136352388761x^4 - 3593653765955001665256902255875226615482416031331126139x^3 - 1035173030260593239029556168369420911667390769758792727969x^2 + 245833151533526228904784003201706226905806706020142118380223*x + 18500665156024978040775113037246170660034380741167330211264700
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	multiple of $ 2^{56}\cdot 3^{135}\cdot 5^{4}\cdot 7^{6} $
Twist minimal:	no (minimal twist has level 9)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.17
Root			$-1969.93$ of defining polynomial
Character	$\chi$	$=$	81.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1918.93 q^{2} +1.58515e6 q^{4} +1.00885e7 q^{5} +1.43926e9 q^{7} -9.82502e8 q^{8} +O(q^{10})$	\(q+1918.93 q^{2} +1.58515e6 q^{4} +1.00885e7 q^{5} +1.43926e9 q^{7} -9.82502e8 q^{8} +1.93592e10 q^{10} -1.78976e10 q^{11} -1.16791e10 q^{13} +2.76184e12 q^{14} -5.20965e12 q^{16} -8.88490e11 q^{17} -3.75758e13 q^{19} +1.59918e13 q^{20} -3.43443e13 q^{22} -2.58872e14 q^{23} -3.75059e14 q^{25} -2.24114e13 q^{26} +2.28144e15 q^{28} -2.84799e15 q^{29} +4.11887e15 q^{31} -7.93651e15 q^{32} -1.70495e15 q^{34} +1.45200e16 q^{35} +4.25896e15 q^{37} -7.21054e16 q^{38} -9.91201e15 q^{40} -1.25337e17 q^{41} -1.69863e17 q^{43} -2.83704e16 q^{44} -4.96757e17 q^{46} -5.56420e16 q^{47} +1.51292e18 q^{49} -7.19712e17 q^{50} -1.85131e16 q^{52} +8.15800e17 q^{53} -1.80561e17 q^{55} -1.41407e18 q^{56} -5.46510e18 q^{58} +4.14492e17 q^{59} -3.64695e18 q^{61} +7.90383e18 q^{62} -4.30419e18 q^{64} -1.17825e17 q^{65} -3.67422e18 q^{67} -1.40839e18 q^{68} +2.78629e19 q^{70} -3.18391e19 q^{71} +3.33473e19 q^{73} +8.17265e18 q^{74} -5.95632e19 q^{76} -2.57593e19 q^{77} +1.42618e20 q^{79} -5.25577e19 q^{80} -2.40512e20 q^{82} -2.05840e20 q^{83} -8.96356e18 q^{85} -3.25956e20 q^{86} +1.75844e19 q^{88} +3.19774e20 q^{89} -1.68092e19 q^{91} -4.10350e20 q^{92} -1.06773e20 q^{94} -3.79085e20 q^{95} +1.18447e20 q^{97} +2.90319e21 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 1023 q^{2} + 19922945 q^{4} - 32234853 q^{5} + 189623959 q^{7} - 648135831 q^{8}+O(q^{10}) $ 20 * q - 1023 * q^2 + 19922945 * q^4 - 32234853 * q^5 + 189623959 * q^7 - 648135831 * q^8	$ 20 q - 1023 q^{2} + 19922945 q^{4} - 32234853 q^{5} + 189623959 q^{7} - 648135831 q^{8} + 2097150 q^{10} - 146068576386 q^{11} + 177565977277 q^{13} - 1549677244440 q^{14} + 18691699769345 q^{16} - 9307801874799 q^{17} - 4884366861977 q^{19} - 76202257650204 q^{20} - 86758343554047 q^{22} - 356460494884095 q^{23} + 13\!\cdots\!29 q^{25}+ \cdots + 26\!\cdots\!43 q^{98}+O(q^{100}) $ 20 * q - 1023 * q^2 + 19922945 * q^4 - 32234853 * q^5 + 189623959 * q^7 - 648135831 * q^8 + 2097150 * q^10 - 146068576386 * q^11 + 177565977277 * q^13 - 1549677244440 * q^14 + 18691699769345 * q^16 - 9307801874799 * q^17 - 4884366861977 * q^19 - 76202257650204 * q^20 - 86758343554047 * q^22 - 356460494884095 * q^23 + 1379841857082329 * q^25 + 2254540119546732 * q^26 + 799738574143486 * q^28 + 2772828270755157 * q^29 - 3064842508546901 * q^31 - 9763241440878495 * q^32 - 5532390311666553 * q^34 - 28944789317551797 * q^35 + 15041349243939694 * q^37 - 38173338977409867 * q^38 + 43546396391926176 * q^40 - 4985514195953106 * q^41 + 41986108659289660 * q^43 + 154909775468547021 * q^44 - 370501619585816100 * q^46 - 971751895603333665 * q^47 + 1393736132530446381 * q^49 - 1504393427506051923 * q^50 + 892509168437820382 * q^52 - 3200468347464244650 * q^53 + 1763329427612189115 * q^55 - 9313401575284840590 * q^56 + 985520139125952432 * q^58 - 11335149505478767926 * q^59 + 333769931007960067 * q^61 - 30822195887206546926 * q^62 + 12804600562751272961 * q^64 - 24815104795645584999 * q^65 - 14325054629523996728 * q^67 - 98193137232148637751 * q^68 + 23664205955002266174 * q^70 - 108719113548124731960 * q^71 - 2415544298256170813 * q^73 - 284989967381657148240 * q^74 - 45502930505046158765 * q^76 - 209785238565183158133 * q^77 - 45386959469213650259 * q^79 - 499015504255192380624 * q^80 + 114258090814276483077 * q^82 - 224083700347690062915 * q^83 + 135764416394391341394 * q^85 + 210501162447733500423 * q^86 - 409557505702705259691 * q^88 + 140942904695660466360 * q^89 - 193584504929412672709 * q^91 - 160981359902419031922 * q^92 - 1246412695298803268064 * q^94 - 583111881346045719228 * q^95 + 658984791485125488346 * q^97 + 2671316103447781667343 * q^98

Display 100 coefficients 10 coefficients

Coefficient data

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

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See 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 $

$2$	1918.93	1.32509	0.662544	−	0.749023i	$-0.269477\pi$
$2$	1918.93	1.32509	0.662544	+	0.749023i	$0.269477\pi$
$3$	0	0
$3$	0	0
$4$	1.58515e6	0.755857
$5$	1.00885e7	0.462001	0.231001	−	0.972954i	$-0.425800\pi$
$5$	1.00885e7	0.462001	0.231001	+	0.972954i	$0.425800\pi$
$6$	0	0
$7$	1.43926e9	1.92579	0.962896	−	0.269873i	$-0.0869816\pi$
$7$	1.43926e9	1.92579	0.962896	+	0.269873i	$0.0869816\pi$
$8$	−9.82502e8	−0.323511
$9$	0	0
$10$	1.93592e10	0.612192
$11$	−1.78976e10	−0.208052	−0.104026	−	0.994575i	$-0.533173\pi$
$11$	−1.78976e10	−0.208052	−0.104026	+	0.994575i	$0.533173\pi$
$12$	0	0
$13$	−1.16791e10	−0.0234965	−0.0117483	−	0.999931i	$-0.503740\pi$
$13$	−1.16791e10	−0.0234965	−0.0117483	+	0.999931i	$0.503740\pi$
$14$	2.76184e12	2.55184
$15$	0	0
$16$	−5.20965e12	−1.18454
$17$	−8.88490e11	−0.106890	−0.0534452	−	0.998571i	$-0.517020\pi$
$17$	−8.88490e11	−0.106890	−0.0534452	+	0.998571i	$0.517020\pi$
$18$	0	0
$19$	−3.75758e13	−1.40603	−0.703016	−	0.711174i	$-0.748164\pi$
$19$	−3.75758e13	−1.40603	−0.703016	+	0.711174i	$0.748164\pi$
$20$	1.59918e13	0.349207
$21$	0	0
$22$	−3.43443e13	−0.275687
$23$	−2.58872e14	−1.30299	−0.651497	−	0.758651i	$-0.725859\pi$
$23$	−2.58872e14	−1.30299	−0.651497	+	0.758651i	$0.725859\pi$
$24$	0	0
$25$	−3.75059e14	−0.786555
$26$	−2.24114e13	−0.0311350
$27$	0	0
$28$	2.28144e15	1.45562
$29$	−2.84799e15	−1.25707	−0.628535	−	0.777781i	$-0.716345\pi$
$29$	−2.84799e15	−1.25707	−0.628535	+	0.777781i	$0.716345\pi$
$30$	0	0
$31$	4.11887e15	0.902569	0.451284	−	0.892380i	$-0.350966\pi$
$31$	4.11887e15	0.902569	0.451284	+	0.892380i	$0.350966\pi$
$32$	−7.93651e15	−1.24610
$33$	0	0
$34$	−1.70495e15	−0.141639
$35$	1.45200e16	0.889718
$36$	0	0
$37$	4.25896e15	0.145608	0.0728040	−	0.997346i	$-0.476805\pi$
$37$	4.25896e15	0.145608	0.0728040	+	0.997346i	$0.476805\pi$
$38$	−7.21054e16	−1.86312
$39$	0	0
$40$	−9.91201e15	−0.149462
$41$	−1.25337e17	−1.45830	−0.729150	−	0.684354i	$-0.760084\pi$
$41$	−1.25337e17	−1.45830	−0.729150	+	0.684354i	$0.760084\pi$
$42$	0	0
$43$	−1.69863e17	−1.19862	−0.599309	−	0.800518i	$-0.704558\pi$
$43$	−1.69863e17	−1.19862	−0.599309	+	0.800518i	$0.704558\pi$
$44$	−2.83704e16	−0.157258
$45$	0	0
$46$	−4.96757e17	−1.72658
$47$	−5.56420e16	−0.154303	−0.0771517	−	0.997019i	$-0.524583\pi$
$47$	−5.56420e16	−0.154303	−0.0771517	+	0.997019i	$0.524583\pi$
$48$	0	0
$49$	1.51292e18	2.70868
$50$	−7.19712e17	−1.04225
$51$	0	0
$52$	−1.85131e16	−0.0177600
$53$	8.15800e17	0.640748	0.320374	−	0.947291i	$-0.396191\pi$
$53$	8.15800e17	0.640748	0.320374	+	0.947291i	$0.396191\pi$
$54$	0	0
$55$	−1.80561e17	−0.0961203
$56$	−1.41407e18	−0.623014
$57$	0	0
$58$	−5.46510e18	−1.66573
$59$	4.14492e17	0.105577	0.0527886	−	0.998606i	$-0.483189\pi$
$59$	4.14492e17	0.105577	0.0527886	+	0.998606i	$0.483189\pi$
$60$	0	0
$61$	−3.64695e18	−0.654586	−0.327293	−	0.944923i	$-0.606136\pi$
$61$	−3.64695e18	−0.654586	−0.327293	+	0.944923i	$0.606136\pi$
$62$	7.90383e18	1.19598
$63$	0	0
$64$	−4.30419e18	−0.466661
$65$	−1.17825e17	−0.0108554
$66$	0	0
$67$	−3.67422e18	−0.246252	−0.123126	−	0.992391i	$-0.539292\pi$
$67$	−3.67422e18	−0.246252	−0.123126	+	0.992391i	$0.539292\pi$
$68$	−1.40839e18	−0.0807939
$69$	0	0
$70$	2.78629e19	1.17895
$71$	−3.18391e19	−1.16077	−0.580387	−	0.814340i	$-0.697099\pi$
$71$	−3.18391e19	−1.16077	−0.580387	+	0.814340i	$0.697099\pi$
$72$	0	0
$73$	3.33473e19	0.908179	0.454089	−	0.890956i	$-0.349965\pi$
$73$	3.33473e19	0.908179	0.454089	+	0.890956i	$0.349965\pi$
$74$	8.17265e18	0.192943
$75$	0	0
$76$	−5.95632e19	−1.06276
$77$	−2.57593e19	−0.400665
$78$	0	0
$79$	1.42618e20	1.69468	0.847341	−	0.531049i	$-0.178202\pi$
$79$	1.42618e20	1.69468	0.847341	+	0.531049i	$0.178202\pi$
$80$	−5.25577e19	−0.547257
$81$	0	0
$82$	−2.40512e20	−1.93238
$83$	−2.05840e20	−1.45616	−0.728082	−	0.685490i	$-0.759588\pi$
$83$	−2.05840e20	−1.45616	−0.728082	+	0.685490i	$0.759588\pi$
$84$	0	0
$85$	−8.96356e18	−0.0493835
$86$	−3.25956e20	−1.58827
$87$	0	0
$88$	1.75844e19	0.0673071
$89$	3.19774e20	1.08705	0.543523	−	0.839395i	$-0.317090\pi$
$89$	3.19774e20	1.08705	0.543523	+	0.839395i	$0.317090\pi$
$90$	0	0
$91$	−1.68092e19	−0.0452495
$92$	−4.10350e20	−0.984877
$93$	0	0
$94$	−1.06773e20	−0.204465
$95$	−3.79085e20	−0.649588
$96$	0	0
$97$	1.18447e20	0.163087	0.0815435	−	0.996670i	$-0.474015\pi$
$97$	1.18447e20	0.163087	0.0815435	+	0.996670i	$0.474015\pi$
$98$	2.90319e21	3.58923
$99$	0	0
$100$	−5.94523e20	−0.594523
$101$	1.12856e21	1.01660	0.508301	−	0.861180i	$-0.330274\pi$
$101$	1.12856e21	1.01660	0.508301	+	0.861180i	$0.330274\pi$
$102$	0	0
$103$	8.43842e20	0.618686	0.309343	−	0.950951i	$-0.399891\pi$
$103$	8.43842e20	0.618686	0.309343	+	0.950951i	$0.399891\pi$
$104$	1.14747e19	0.00760139
$105$	0	0
$106$	1.56546e21	0.849047
$107$	6.33311e20	0.311234	0.155617	−	0.987817i	$-0.450263\pi$
$107$	6.33311e20	0.311234	0.155617	+	0.987817i	$0.450263\pi$
$108$	0	0
$109$	−4.46747e21	−1.80752	−0.903760	−	0.428040i	$-0.859204\pi$
$109$	−4.46747e21	−1.80752	−0.903760	+	0.428040i	$0.859204\pi$
$110$	−3.46484e20	−0.127368
$111$	0	0
$112$	−7.49803e21	−2.28117
$113$	3.58005e21	0.992123	0.496061	−	0.868288i	$-0.334779\pi$
$113$	3.58005e21	0.992123	0.496061	+	0.868288i	$0.334779\pi$
$114$	0	0
$115$	−2.61163e21	−0.601984
$116$	−4.51448e21	−0.950165
$117$	0	0
$118$	7.95382e20	0.139899
$119$	−1.27877e21	−0.205849
$120$	0	0
$121$	−7.07993e21	−0.956714
$122$	−6.99825e21	−0.867383
$123$	0	0
$124$	6.52902e21	0.682213
$125$	−8.59438e21	−0.825390
$126$	0	0
$127$	−5.60955e21	−0.456026	−0.228013	−	0.973658i	$-0.573223\pi$
$127$	−5.60955e21	−0.456026	−0.228013	+	0.973658i	$0.573223\pi$
$128$	8.38462e21	0.627738
$129$	0	0
$130$	−2.26098e20	−0.0143844
$131$	3.13673e21	0.184131	0.0920657	−	0.995753i	$-0.470653\pi$
$131$	3.13673e21	0.184131	0.0920657	+	0.995753i	$0.470653\pi$
$132$	0	0
$133$	−5.40813e22	−2.70773
$134$	−7.05057e21	−0.326305
$135$	0	0
$136$	8.72943e20	0.0345802
$137$	−3.66042e22	−1.34266	−0.671328	−	0.741161i	$-0.734276\pi$
$137$	−3.66042e22	−1.34266	−0.671328	+	0.741161i	$0.734276\pi$
$138$	0	0
$139$	−6.78869e21	−0.213861	−0.106930	−	0.994267i	$-0.534102\pi$
$139$	−6.78869e21	−0.213861	−0.106930	+	0.994267i	$0.534102\pi$
$140$	2.30163e22	0.672500
$141$	0	0
$142$	−6.10970e22	−1.53813
$143$	2.09028e20	0.00488850
$144$	0	0
$145$	−2.87320e22	−0.580768
$146$	6.39913e22	1.20342
$147$	0	0
$148$	6.75108e21	0.110059
$149$	−7.01638e22	−1.06575	−0.532877	−	0.846192i	$-0.678889\pi$
$149$	−7.01638e22	−1.06575	−0.532877	+	0.846192i	$0.678889\pi$
$150$	0	0
$151$	−3.43798e22	−0.453988	−0.226994	−	0.973896i	$-0.572890\pi$
$151$	−3.43798e22	−0.453988	−0.226994	+	0.973896i	$0.572890\pi$
$152$	3.69183e22	0.454867
$153$	0	0
$154$	−4.94303e22	−0.530916
$155$	4.15534e22	0.416988
$156$	0	0
$157$	9.01120e22	0.790381	0.395191	−	0.918599i	$-0.370679\pi$
$157$	9.01120e22	0.790381	0.395191	+	0.918599i	$0.370679\pi$
$158$	2.73673e23	2.24560
$159$	0	0
$160$	−8.00677e22	−0.575702
$161$	−3.72583e23	−2.50929
$162$	0	0
$163$	2.91470e22	0.172434	0.0862171	−	0.996276i	$-0.472522\pi$
$163$	2.91470e22	0.172434	0.0862171	+	0.996276i	$0.472522\pi$
$164$	−1.98677e23	−1.10227
$165$	0	0
$166$	−3.94993e23	−1.92954
$167$	−3.95995e23	−1.81622	−0.908108	−	0.418737i	$-0.862473\pi$
$167$	−3.95995e23	−1.81622	−0.908108	+	0.418737i	$0.862473\pi$
$168$	0	0
$169$	−2.46928e23	−0.999448
$170$	−1.72005e22	−0.0654374
$171$	0	0
$172$	−2.69258e23	−0.905983
$173$	1.74766e23	0.553316	0.276658	−	0.960968i	$-0.410773\pi$
$173$	1.74766e23	0.553316	0.276658	+	0.960968i	$0.410773\pi$
$174$	0	0
$175$	−5.39806e23	−1.51474
$176$	9.32403e22	0.246445
$177$	0	0
$178$	6.13624e23	1.44043
$179$	8.15206e23	1.80431	0.902153	−	0.431416i	$-0.141986\pi$
$179$	8.15206e23	1.80431	0.902153	+	0.431416i	$0.141986\pi$
$180$	0	0
$181$	3.90557e23	0.769236	0.384618	−	0.923076i	$-0.374333\pi$
$181$	3.90557e23	0.769236	0.384618	+	0.923076i	$0.374333\pi$
$182$	−3.22558e22	−0.0599595
$183$	0	0
$184$	2.54342e23	0.421532
$185$	4.29667e22	0.0672711
$186$	0	0
$187$	1.59018e22	0.0222388
$188$	−8.82008e22	−0.116631
$189$	0	0
$190$	−7.27438e23	−0.860762
$191$	−8.48589e23	−0.950270	−0.475135	−	0.879913i	$-0.657601\pi$
$191$	−8.48589e23	−0.950270	−0.475135	+	0.879913i	$0.657601\pi$
$192$	0	0
$193$	9.80489e23	0.984217	0.492109	−	0.870534i	$-0.336226\pi$
$193$	9.80489e23	0.984217	0.492109	+	0.870534i	$0.336226\pi$
$194$	2.27291e23	0.216104
$195$	0	0
$196$	2.39820e24	2.04737
$197$	9.48861e23	0.767905	0.383952	−	0.923353i	$-0.374563\pi$
$197$	9.48861e23	0.767905	0.383952	+	0.923353i	$0.374563\pi$
$198$	0	0
$199$	−4.82519e23	−0.351202	−0.175601	−	0.984461i	$-0.556187\pi$
$199$	−4.82519e23	−0.351202	−0.175601	+	0.984461i	$0.556187\pi$
$200$	3.68496e23	0.254459
$201$	0	0
$202$	2.16563e24	1.34709
$203$	−4.09899e24	−2.42086
$204$	0	0
$205$	−1.26446e24	−0.673736
$206$	1.61927e24	0.819813
$207$	0	0
$208$	6.08440e22	0.0278325
$209$	6.72517e23	0.292528
$210$	0	0
$211$	−7.76646e23	−0.305673	−0.152837	−	0.988251i	$-0.548841\pi$
$211$	−7.76646e23	−0.305673	−0.152837	+	0.988251i	$0.548841\pi$
$212$	1.29316e24	0.484314
$213$	0	0
$214$	1.21528e24	0.412413
$215$	−1.71367e24	−0.553762
$216$	0	0
$217$	5.92812e24	1.73816
$218$	−8.57276e24	−2.39512
$219$	0	0
$220$	−2.86215e23	−0.0726532
$221$	1.03768e22	0.00251156
$222$	0	0
$223$	3.33639e24	0.734641	0.367321	−	0.930094i	$-0.380275\pi$
$223$	3.33639e24	0.734641	0.367321	+	0.930094i	$0.380275\pi$
$224$	−1.14227e25	−2.39974
$225$	0	0
$226$	6.86987e24	1.31465
$227$	1.29427e24	0.236458	0.118229	−	0.992986i	$-0.462278\pi$
$227$	1.29427e24	0.236458	0.118229	+	0.992986i	$0.462278\pi$
$228$	0	0
$229$	4.68549e24	0.780698	0.390349	−	0.920667i	$-0.372354\pi$
$229$	4.68549e24	0.780698	0.390349	+	0.920667i	$0.372354\pi$
$230$	−5.01155e24	−0.797682
$231$	0	0
$232$	2.79816e24	0.406676
$233$	−9.39232e24	−1.30478	−0.652388	−	0.757885i	$-0.726233\pi$
$233$	−9.39232e24	−1.30478	−0.652388	+	0.757885i	$0.726233\pi$
$234$	0	0
$235$	−5.61346e23	−0.0712883
$236$	6.57031e23	0.0798013
$237$	0	0
$238$	−2.45387e24	−0.272768
$239$	5.80655e24	0.617647	0.308824	−	0.951119i	$-0.400065\pi$
$239$	5.80655e24	0.617647	0.308824	+	0.951119i	$0.400065\pi$
$240$	0	0
$241$	−1.05193e25	−1.02520	−0.512599	−	0.858628i	$-0.671317\pi$
$241$	−1.05193e25	−1.02520	−0.512599	+	0.858628i	$0.671317\pi$
$242$	−1.35859e25	−1.26773
$243$	0	0
$244$	−5.78095e24	−0.494773
$245$	1.52631e25	1.25141
$246$	0	0
$247$	4.38851e23	0.0330369
$248$	−4.04680e24	−0.291991
$249$	0	0
$250$	−1.64920e25	−1.09371
$251$	1.24868e25	0.794103	0.397052	−	0.917796i	$-0.370033\pi$
$251$	1.24868e25	0.794103	0.397052	+	0.917796i	$0.370033\pi$
$252$	0	0
$253$	4.63318e24	0.271090
$254$	−1.07644e25	−0.604274
$255$	0	0
$256$	2.51160e25	1.29847
$257$	3.46865e25	1.72132	0.860662	−	0.509177i	$-0.170050\pi$
$257$	3.46865e25	1.72132	0.860662	+	0.509177i	$0.170050\pi$
$258$	0	0
$259$	6.12975e24	0.280411
$260$	−1.86770e23	−0.00820515
$261$	0	0
$262$	6.01916e24	0.243990
$263$	−4.29357e25	−1.67218	−0.836091	−	0.548591i	$-0.815164\pi$
$263$	−4.29357e25	−1.67218	−0.836091	+	0.548591i	$0.815164\pi$
$264$	0	0
$265$	8.23022e24	0.296026
$266$	−1.03778e26	−3.58797
$267$	0	0
$268$	−5.82417e24	−0.186131
$269$	3.27085e25	1.00522	0.502610	−	0.864513i	$-0.332373\pi$
$269$	3.27085e25	1.00522	0.502610	+	0.864513i	$0.332373\pi$
$270$	0	0
$271$	−2.87108e25	−0.816334	−0.408167	−	0.912907i	$-0.633832\pi$
$271$	−2.87108e25	−0.816334	−0.408167	+	0.912907i	$0.633832\pi$
$272$	4.62872e24	0.126616
$273$	0	0
$274$	−7.02409e25	−1.77914
$275$	6.71266e24	0.163644
$276$	0	0
$277$	−3.60016e23	−0.00813362	−0.00406681	−	0.999992i	$-0.501295\pi$
$277$	−3.60016e23	−0.00813362	−0.00406681	+	0.999992i	$0.501295\pi$
$278$	−1.30270e25	−0.283384
$279$	0	0
$280$	−1.42659e25	−0.287833
$281$	−7.31578e25	−1.42182	−0.710910	−	0.703283i	$-0.751717\pi$
$281$	−7.31578e25	−1.42182	−0.710910	+	0.703283i	$0.751717\pi$
$282$	0	0
$283$	−5.94047e25	−1.07167	−0.535837	−	0.844321i	$-0.680004\pi$
$283$	−5.94047e25	−1.07167	−0.535837	+	0.844321i	$0.680004\pi$
$284$	−5.04696e25	−0.877380
$285$	0	0
$286$	4.01110e23	0.00647770
$287$	−1.80392e26	−2.80838
$288$	0	0
$289$	−6.83025e25	−0.988574
$290$	−5.51348e25	−0.769568
$291$	0	0
$292$	5.28604e25	0.686453
$293$	−6.94779e25	−0.870436	−0.435218	−	0.900325i	$-0.643329\pi$
$293$	−6.94779e25	−0.870436	−0.435218	+	0.900325i	$0.643329\pi$
$294$	0	0
$295$	4.18162e24	0.0487768
$296$	−4.18444e24	−0.0471058
$297$	0	0
$298$	−1.34640e26	−1.41222
$299$	3.02339e24	0.0306158
$300$	0	0
$301$	−2.44477e26	−2.30829
$302$	−6.59724e25	−0.601574
$303$	0	0
$304$	1.95757e26	1.66550
$305$	−3.67924e25	−0.302419
$306$	0	0
$307$	4.34578e25	0.333514	0.166757	−	0.985998i	$-0.446670\pi$
$307$	4.34578e25	0.333514	0.166757	+	0.985998i	$0.446670\pi$
$308$	−4.08323e25	−0.302845
$309$	0	0
$310$	7.97381e25	0.552545
$311$	3.69095e25	0.247260	0.123630	−	0.992328i	$-0.460546\pi$
$311$	3.69095e25	0.247260	0.123630	+	0.992328i	$0.460546\pi$
$312$	0	0
$313$	1.65069e25	0.103384	0.0516918	−	0.998663i	$-0.483539\pi$
$313$	1.65069e25	0.103384	0.0516918	+	0.998663i	$0.483539\pi$
$314$	1.72919e26	1.04732
$315$	0	0
$316$	2.26070e26	1.28094
$317$	−1.87242e26	−1.02632	−0.513158	−	0.858294i	$-0.671525\pi$
$317$	−1.87242e26	−1.02632	−0.513158	+	0.858294i	$0.671525\pi$
$318$	0	0
$319$	5.09722e25	0.261536
$320$	−4.34229e25	−0.215598
$321$	0	0
$322$	−7.14962e26	−3.32503
$323$	3.33857e25	0.150291
$324$	0	0
$325$	4.38035e24	0.0184813
$326$	5.59310e25	0.228490
$327$	0	0
$328$	1.23143e26	0.471776
$329$	−8.00833e25	−0.297156
$330$	0	0
$331$	1.10813e26	0.385831	0.192915	−	0.981215i	$-0.438206\pi$
$331$	1.10813e26	0.385831	0.192915	+	0.981215i	$0.438206\pi$
$332$	−3.26287e26	−1.10065
$333$	0	0
$334$	−7.59888e26	−2.40664
$335$	−3.70674e25	−0.113769
$336$	0	0
$337$	5.04643e26	1.45502	0.727512	−	0.686095i	$-0.240677\pi$
$337$	5.04643e26	1.45502	0.727512	+	0.686095i	$0.240677\pi$
$338$	−4.73838e26	−1.32436
$339$	0	0
$340$	−1.42086e25	−0.0373269
$341$	−7.37180e25	−0.187781
$342$	0	0
$343$	1.37359e27	3.29055
$344$	1.66891e26	0.387766
$345$	0	0
$346$	3.35364e26	0.733192
$347$	4.69718e26	0.996272	0.498136	−	0.867099i	$-0.334018\pi$
$347$	4.69718e26	0.996272	0.498136	+	0.867099i	$0.334018\pi$
$348$	0	0
$349$	1.31480e26	0.262539	0.131269	−	0.991347i	$-0.458095\pi$
$349$	1.31480e26	0.262539	0.131269	+	0.991347i	$0.458095\pi$
$350$	−1.03585e27	−2.00717
$351$	0	0
$352$	1.42045e26	0.259255
$353$	−6.81592e26	−1.20751	−0.603754	−	0.797171i	$-0.706329\pi$
$353$	−6.81592e26	−1.20751	−0.603754	+	0.797171i	$0.706329\pi$
$354$	0	0
$355$	−3.21210e26	−0.536279
$356$	5.06888e26	0.821651
$357$	0	0
$358$	1.56432e27	2.39086
$359$	−7.00365e26	−1.03952	−0.519760	−	0.854313i	$-0.673979\pi$
$359$	−7.00365e26	−1.03952	−0.519760	+	0.854313i	$0.673979\pi$
$360$	0	0
$361$	6.97731e26	0.976927
$362$	7.49452e26	1.01930
$363$	0	0
$364$	−2.66451e25	−0.0342021
$365$	3.36426e26	0.419579
$366$	0	0
$367$	−6.83947e26	−0.805432	−0.402716	−	0.915325i	$-0.631934\pi$
$367$	−6.83947e26	−0.805432	−0.402716	+	0.915325i	$0.631934\pi$
$368$	1.34863e27	1.54344
$369$	0	0
$370$	8.24501e25	0.0891401
$371$	1.17415e27	1.23395
$372$	0	0
$373$	8.12611e26	0.807123	0.403562	−	0.914952i	$-0.367772\pi$
$373$	8.12611e26	0.807123	0.403562	+	0.914952i	$0.367772\pi$
$374$	3.05146e25	0.0294683
$375$	0	0
$376$	5.46684e25	0.0499188
$377$	3.32620e25	0.0295368
$378$	0	0
$379$	−1.08255e27	−0.909362	−0.454681	−	0.890654i	$-0.650247\pi$
$379$	−1.08255e27	−0.909362	−0.454681	+	0.890654i	$0.650247\pi$
$380$	−6.00905e26	−0.490996
$381$	0	0
$382$	−1.62838e27	−1.25919
$383$	−7.38183e25	−0.0555363	−0.0277681	−	0.999614i	$-0.508840\pi$
$383$	−7.38183e25	−0.0555363	−0.0277681	+	0.999614i	$0.508840\pi$
$384$	0	0
$385$	−2.59873e26	−0.185108
$386$	1.88149e27	1.30417
$387$	0	0
$388$	1.87755e26	0.123270
$389$	−5.83122e26	−0.372640	−0.186320	−	0.982489i	$-0.559656\pi$
$389$	−5.83122e26	−0.372640	−0.186320	+	0.982489i	$0.559656\pi$
$390$	0	0
$391$	2.30005e26	0.139278
$392$	−1.48645e27	−0.876286
$393$	0	0
$394$	1.82080e27	1.01754
$395$	1.43880e27	0.782945
$396$	0	0
$397$	2.64645e27	1.36572	0.682862	−	0.730547i	$-0.260735\pi$
$397$	2.64645e27	1.36572	0.682862	+	0.730547i	$0.260735\pi$
$398$	−9.25922e26	−0.465374
$399$	0	0
$400$	1.95392e27	0.931704
$401$	7.02503e25	0.0326311	0.0163156	−	0.999867i	$-0.494806\pi$
$401$	7.02503e25	0.0326311	0.0163156	+	0.999867i	$0.494806\pi$
$402$	0	0
$403$	−4.81047e25	−0.0212073
$404$	1.78894e27	0.768406
$405$	0	0
$406$	−7.86569e27	−3.20785
$407$	−7.62252e25	−0.0302941
$408$	0	0
$409$	−1.55437e27	−0.586760	−0.293380	−	0.955996i	$-0.594780\pi$
$409$	−1.55437e27	−0.586760	−0.293380	+	0.955996i	$0.594780\pi$
$410$	−2.42642e27	−0.892760
$411$	0	0
$412$	1.33761e27	0.467638
$413$	5.96561e26	0.203320
$414$	0	0
$415$	−2.07663e27	−0.672749
$416$	9.26912e25	0.0292792
$417$	0	0
$418$	1.29051e27	0.387625
$419$	3.25686e27	0.954007	0.477003	−	0.878901i	$-0.341723\pi$
$419$	3.25686e27	0.954007	0.477003	+	0.878901i	$0.341723\pi$
$420$	0	0
$421$	−4.42448e27	−1.23282	−0.616411	−	0.787425i	$-0.711414\pi$
$421$	−4.42448e27	−1.23282	−0.616411	+	0.787425i	$0.711414\pi$
$422$	−1.49033e27	−0.405044
$423$	0	0
$424$	−8.01525e26	−0.207289
$425$	3.33236e26	0.0840752
$426$	0	0
$427$	−5.24890e27	−1.26060
$428$	1.00389e27	0.235249
$429$	0	0
$430$	−3.28842e27	−0.733784
$431$	5.08936e27	1.10829	0.554143	−	0.832421i	$-0.313046\pi$
$431$	5.08936e27	1.10829	0.554143	+	0.832421i	$0.313046\pi$
$432$	0	0
$433$	7.54206e27	1.56447	0.782235	−	0.622983i	$-0.214080\pi$
$433$	7.54206e27	1.56447	0.782235	+	0.622983i	$0.214080\pi$
$434$	1.13757e28	2.30321
$435$	0	0
$436$	−7.08159e27	−1.36623
$437$	9.72731e27	1.83205
$438$	0	0
$439$	5.05560e27	0.907601	0.453800	−	0.891103i	$-0.350068\pi$
$439$	5.05560e27	0.907601	0.453800	+	0.891103i	$0.350068\pi$
$440$	1.77401e26	0.0310959
$441$	0	0
$442$	1.99123e25	0.00332803
$443$	2.30267e27	0.375832	0.187916	−	0.982185i	$-0.439827\pi$
$443$	2.30267e27	0.375832	0.187916	+	0.982185i	$0.439827\pi$
$444$	0	0
$445$	3.22605e27	0.502216
$446$	6.40230e27	0.973464
$447$	0	0
$448$	−6.19484e27	−0.898691
$449$	−6.87770e27	−0.974668	−0.487334	−	0.873216i	$-0.662031\pi$
$449$	−6.87770e27	−0.974668	−0.487334	+	0.873216i	$0.662031\pi$
$450$	0	0
$451$	2.24322e27	0.303402
$452$	5.67490e27	0.749903
$453$	0	0
$454$	2.48362e27	0.313327
$455$	−1.69581e26	−0.0209053
$456$	0	0
$457$	−3.63453e27	−0.427886	−0.213943	−	0.976846i	$-0.568631\pi$
$457$	−3.63453e27	−0.427886	−0.213943	+	0.976846i	$0.568631\pi$
$458$	8.99114e27	1.03449
$459$	0	0
$460$	−4.13983e27	−0.455014
$461$	2.08814e27	0.224336	0.112168	−	0.993689i	$-0.464221\pi$
$461$	2.08814e27	0.224336	0.112168	+	0.993689i	$0.464221\pi$
$462$	0	0
$463$	−1.23302e27	−0.126581	−0.0632906	−	0.997995i	$-0.520159\pi$
$463$	−1.23302e27	−0.126581	−0.0632906	+	0.997995i	$0.520159\pi$
$464$	1.48370e28	1.48905
$465$	0	0
$466$	−1.80232e28	−1.72894
$467$	−3.72155e27	−0.349057	−0.174529	−	0.984652i	$-0.555840\pi$
$467$	−3.72155e27	−0.349057	−0.174529	+	0.984652i	$0.555840\pi$
$468$	0	0
$469$	−5.28815e27	−0.474229
$470$	−1.07719e27	−0.0944633
$471$	0	0
$472$	−4.07239e26	−0.0341554
$473$	3.04015e27	0.249375
$474$	0	0
$475$	1.40931e28	1.10592
$476$	−2.02703e27	−0.155592
$477$	0	0
$478$	1.11424e28	0.818437
$479$	4.01585e27	0.288572	0.144286	−	0.989536i	$-0.453911\pi$
$479$	4.01585e27	0.288572	0.144286	+	0.989536i	$0.453911\pi$
$480$	0	0
$481$	−4.97408e25	−0.00342129
$482$	−2.01858e28	−1.35848
$483$	0	0
$484$	−1.12227e28	−0.723139
$485$	1.19495e27	0.0753463
$486$	0	0
$487$	−4.76670e27	−0.287848	−0.143924	−	0.989589i	$-0.545972\pi$
$487$	−4.76670e27	−0.287848	−0.143924	+	0.989589i	$0.545972\pi$
$488$	3.58314e27	0.211766
$489$	0	0
$490$	2.92889e28	1.65823
$491$	−1.70058e28	−0.942413	−0.471207	−	0.882023i	$-0.656181\pi$
$491$	−1.70058e28	−0.942413	−0.471207	+	0.882023i	$0.656181\pi$
$492$	0	0
$493$	2.53041e27	0.134369
$494$	8.42126e26	0.0437768
$495$	0	0
$496$	−2.14579e28	−1.06913
$497$	−4.58247e28	−2.23541
$498$	0	0
$499$	1.63082e28	0.762693	0.381346	−	0.924432i	$-0.375461\pi$
$499$	1.63082e28	0.762693	0.381346	+	0.924432i	$0.375461\pi$
$500$	−1.36234e28	−0.623877
$501$	0	0
$502$	2.39613e28	1.05226
$503$	−6.10168e27	−0.262413	−0.131207	−	0.991355i	$-0.541885\pi$
$503$	−6.10168e27	−0.262413	−0.131207	+	0.991355i	$0.541885\pi$
$504$	0	0
$505$	1.13855e28	0.469671
$506$	8.89077e27	0.359219
$507$	0	0
$508$	−8.89197e27	−0.344690
$509$	1.08400e28	0.411615	0.205807	−	0.978592i	$-0.434018\pi$
$509$	1.08400e28	0.411615	0.205807	+	0.978592i	$0.434018\pi$
$510$	0	0
$511$	4.79955e28	1.74896
$512$	3.06122e28	1.09285
$513$	0	0
$514$	6.65610e28	2.28091
$515$	8.51312e27	0.285833
$516$	0	0
$517$	9.95860e26	0.0321031
$518$	1.17626e28	0.371569
$519$	0	0
$520$	1.15763e26	0.00351185
$521$	6.28643e27	0.186899	0.0934497	−	0.995624i	$-0.470211\pi$
$521$	6.28643e27	0.186899	0.0934497	+	0.995624i	$0.470211\pi$
$522$	0	0
$523$	3.14604e28	0.898454	0.449227	−	0.893418i	$-0.351699\pi$
$523$	3.14604e28	0.898454	0.449227	+	0.893418i	$0.351699\pi$
$524$	4.97217e27	0.139177
$525$	0	0
$526$	−8.23907e28	−2.21579
$527$	−3.65957e27	−0.0964760
$528$	0	0
$529$	2.75429e28	0.697792
$530$	1.57932e28	0.392260
$531$	0	0
$532$	−8.57268e28	−2.04665
$533$	1.46382e27	0.0342650
$534$	0	0
$535$	6.38918e27	0.143791
$536$	3.60993e27	0.0796651
$537$	0	0
$538$	6.27653e28	1.33201
$539$	−2.70776e28	−0.563545
$540$	0	0
$541$	−1.83966e28	−0.368270	−0.184135	−	0.982901i	$-0.558948\pi$
$541$	−1.83966e28	−0.368270	−0.184135	+	0.982901i	$0.558948\pi$
$542$	−5.50941e28	−1.08171
$543$	0	0
$544$	7.05150e27	0.133197
$545$	−4.50702e28	−0.835076
$546$	0	0
$547$	−3.24549e28	−0.578646	−0.289323	−	0.957231i	$-0.593430\pi$
$547$	−3.24549e28	−0.578646	−0.289323	+	0.957231i	$0.593430\pi$
$548$	−5.80230e28	−1.01486
$549$	0	0
$550$	1.28811e28	0.216843
$551$	1.07015e29	1.76748
$552$	0	0
$553$	2.05263e29	3.26361
$554$	−6.90845e26	−0.0107778
$555$	0	0
$556$	−1.07611e28	−0.161648
$557$	1.37986e28	0.203402	0.101701	−	0.994815i	$-0.467571\pi$
$557$	1.37986e28	0.203402	0.101701	+	0.994815i	$0.467571\pi$
$558$	0	0
$559$	1.98385e27	0.0281634
$560$	−7.56441e28	−1.05390
$561$	0	0
$562$	−1.40385e29	−1.88404
$563$	1.51648e28	0.199756	0.0998778	−	0.995000i	$-0.468155\pi$
$563$	1.51648e28	0.199756	0.0998778	+	0.995000i	$0.468155\pi$
$564$	0	0
$565$	3.61174e28	0.458362
$566$	−1.13994e29	−1.42006
$567$	0	0
$568$	3.12820e28	0.375523
$569$	−9.58103e28	−1.12910	−0.564552	−	0.825398i	$-0.690951\pi$
$569$	−9.58103e28	−1.12910	−0.564552	+	0.825398i	$0.690951\pi$
$570$	0	0
$571$	7.57951e28	0.860919	0.430459	−	0.902610i	$-0.358352\pi$
$571$	7.57951e28	0.860919	0.430459	+	0.902610i	$0.358352\pi$
$572$	3.31340e26	0.00369501
$573$	0	0
$574$	−3.46159e29	−3.72135
$575$	9.70921e28	1.02488
$576$	0	0
$577$	4.37885e28	0.445671	0.222835	−	0.974856i	$-0.428469\pi$
$577$	4.37885e28	0.445671	0.222835	+	0.974856i	$0.428469\pi$
$578$	−1.31068e29	−1.30995
$579$	0	0
$580$	−4.55445e28	−0.438977
$581$	−2.96257e29	−2.80427
$582$	0	0
$583$	−1.46009e28	−0.133309
$584$	−3.27638e28	−0.293806
$585$	0	0
$586$	−1.33323e29	−1.15340
$587$	1.06943e29	0.908766	0.454383	−	0.890806i	$-0.349860\pi$
$587$	1.06943e29	0.908766	0.454383	+	0.890806i	$0.349860\pi$
$588$	0	0
$589$	−1.54770e29	−1.26904
$590$	8.02424e27	0.0646335
$591$	0	0
$592$	−2.21877e28	−0.172478
$593$	−5.57095e28	−0.425456	−0.212728	−	0.977111i	$-0.568235\pi$
$593$	−5.57095e28	−0.425456	−0.212728	+	0.977111i	$0.568235\pi$
$594$	0	0
$595$	−1.29009e28	−0.0951023
$596$	−1.11220e29	−0.805558
$597$	0	0
$598$	5.80167e27	0.0405687
$599$	6.50977e28	0.447285	0.223642	−	0.974671i	$-0.428205\pi$
$599$	6.50977e28	0.447285	0.223642	+	0.974671i	$0.428205\pi$
$600$	0	0
$601$	−9.78716e28	−0.649344	−0.324672	−	0.945827i	$-0.605254\pi$
$601$	−9.78716e28	−0.649344	−0.324672	+	0.945827i	$0.605254\pi$
$602$	−4.69135e29	−3.05868
$603$	0	0
$604$	−5.44970e28	−0.343150
$605$	−7.14261e28	−0.442003
$606$	0	0
$607$	−7.65865e28	−0.457795	−0.228897	−	0.973451i	$-0.573512\pi$
$607$	−7.65865e28	−0.457795	−0.228897	+	0.973451i	$0.573512\pi$
$608$	2.98220e29	1.75206
$609$	0	0
$610$	−7.06021e28	−0.400732
$611$	6.49849e26	0.00362560
$612$	0	0
$613$	1.41320e29	0.761847	0.380923	−	0.924607i	$-0.375606\pi$
$613$	1.41320e29	0.761847	0.380923	+	0.924607i	$0.375606\pi$
$614$	8.33925e28	0.441935
$615$	0	0
$616$	2.53086e28	0.129619
$617$	−1.53273e28	−0.0771742	−0.0385871	−	0.999255i	$-0.512286\pi$
$617$	−1.53273e28	−0.0771742	−0.0385871	+	0.999255i	$0.512286\pi$
$618$	0	0
$619$	2.64333e29	1.28647	0.643234	−	0.765670i	$-0.277592\pi$
$619$	2.64333e29	1.28647	0.643234	+	0.765670i	$0.277592\pi$
$620$	6.58682e28	0.315183
$621$	0	0
$622$	7.08268e28	0.327641
$623$	4.60237e29	2.09342
$624$	0	0
$625$	9.21372e28	0.405224
$626$	3.16757e28	0.136992
$627$	0	0
$628$	1.42841e29	0.597415
$629$	−3.78404e27	−0.0155641
$630$	0	0
$631$	−4.04710e29	−1.61004	−0.805019	−	0.593249i	$-0.797845\pi$
$631$	−4.04710e29	−1.61004	−0.805019	+	0.593249i	$0.797845\pi$
$632$	−1.40122e29	−0.548248
$633$	0	0
$634$	−3.59305e29	−1.35996
$635$	−5.65922e28	−0.210684
$636$	0	0
$637$	−1.76695e28	−0.0636445
$638$	9.78122e28	0.346558
$639$	0	0
$640$	8.45885e28	0.290016
$641$	−2.25664e29	−0.761118	−0.380559	−	0.924757i	$-0.624268\pi$
$641$	−2.25664e29	−0.761118	−0.380559	+	0.924757i	$0.624268\pi$
$642$	0	0
$643$	−2.38638e28	−0.0778978	−0.0389489	−	0.999241i	$-0.512401\pi$
$643$	−2.38638e28	−0.0778978	−0.0389489	+	0.999241i	$0.512401\pi$
$644$	−5.90599e29	−1.89667
$645$	0	0
$646$	6.40649e28	0.199149
$647$	3.52013e29	1.07662	0.538311	−	0.842746i	$-0.319062\pi$
$647$	3.52013e29	1.07662	0.538311	+	0.842746i	$0.319062\pi$
$648$	0	0
$649$	−7.41842e27	−0.0219655
$650$	8.40559e27	0.0244894
$651$	0	0
$652$	4.62022e28	0.130336
$653$	−7.92250e28	−0.219925	−0.109962	−	0.993936i	$-0.535073\pi$
$653$	−7.92250e28	−0.219925	−0.109962	+	0.993936i	$0.535073\pi$
$654$	0	0
$655$	3.16450e28	0.0850689
$656$	6.52959e29	1.72741
$657$	0	0
$658$	−1.53674e29	−0.393758
$659$	−6.58595e29	−1.66082	−0.830408	−	0.557156i	$-0.811893\pi$
$659$	−6.58595e29	−1.66082	−0.830408	+	0.557156i	$0.811893\pi$
$660$	0	0
$661$	5.76931e29	1.40932	0.704658	−	0.709547i	$-0.251101\pi$
$661$	5.76931e29	1.40932	0.704658	+	0.709547i	$0.251101\pi$
$662$	2.12643e29	0.511259
$663$	0	0
$664$	2.02238e29	0.471085
$665$	−5.45601e29	−1.25097
$666$	0	0
$667$	7.37264e29	1.63795
$668$	−6.27711e29	−1.37280
$669$	0	0
$670$	−7.11299e28	−0.150753
$671$	6.52717e28	0.136188
$672$	0	0
$673$	2.30962e29	0.467071	0.233536	−	0.972348i	$-0.424970\pi$
$673$	2.30962e29	0.467071	0.233536	+	0.972348i	$0.424970\pi$
$674$	9.68375e29	1.92803
$675$	0	0
$676$	−3.91417e29	−0.755440
$677$	2.82785e29	0.537372	0.268686	−	0.963228i	$-0.413411\pi$
$677$	2.82785e29	0.537372	0.268686	+	0.963228i	$0.413411\pi$
$678$	0	0
$679$	1.70475e29	0.314072
$680$	8.80672e27	0.0159761
$681$	0	0
$682$	−1.41460e29	−0.248827
$683$	6.52113e29	1.12955	0.564775	−	0.825245i	$-0.308963\pi$
$683$	6.52113e29	1.12955	0.564775	+	0.825245i	$0.308963\pi$
$684$	0	0
$685$	−3.69282e29	−0.620308
$686$	2.63583e30	4.36027
$687$	0	0
$688$	8.84928e29	1.41981
$689$	−9.52781e27	−0.0150554
$690$	0	0
$691$	1.20725e30	1.85045	0.925223	−	0.379424i	$-0.123878\pi$
$691$	1.20725e30	1.85045	0.925223	+	0.379424i	$0.123878\pi$
$692$	2.77030e29	0.418228
$693$	0	0
$694$	9.01357e29	1.32015
$695$	−6.84879e28	−0.0988038
$696$	0	0
$697$	1.11360e29	0.155878
$698$	2.52302e29	0.347887
$699$	0	0
$700$	−8.55673e29	−1.14493
$701$	−1.24828e30	−1.64541	−0.822705	−	0.568468i	$-0.807536\pi$
$701$	−1.24828e30	−1.64541	−0.822705	+	0.568468i	$0.807536\pi$
$702$	0	0
$703$	−1.60034e29	−0.204730
$704$	7.70346e28	0.0970897
$705$	0	0
$706$	−1.30793e30	−1.60005
$707$	1.62429e30	1.95776
$708$	0	0
$709$	6.98119e29	0.816853	0.408427	−	0.912791i	$-0.366078\pi$
$709$	6.98119e29	0.816853	0.408427	+	0.912791i	$0.366078\pi$
$710$	−6.16380e29	−0.710617
$711$	0	0
$712$	−3.14178e29	−0.351671
$713$	−1.06626e30	−1.17604
$714$	0	0
$715$	2.10879e27	0.00225849
$716$	1.29222e30	1.36380
$717$	0	0
$718$	−1.34395e30	−1.37745
$719$	−6.00175e29	−0.606212	−0.303106	−	0.952957i	$-0.598024\pi$
$719$	−6.00175e29	−0.606212	−0.303106	+	0.952957i	$0.598024\pi$
$720$	0	0
$721$	1.21451e30	1.19146
$722$	1.33890e30	1.29451
$723$	0	0
$724$	6.19090e29	0.581432
$725$	1.06816e30	0.988755
$726$	0	0
$727$	−8.90899e29	−0.801157	−0.400578	−	0.916263i	$-0.631191\pi$
$727$	−8.90899e29	−0.801157	−0.400578	+	0.916263i	$0.631191\pi$
$728$	1.65151e28	0.0146387
$729$	0	0
$730$	6.45578e29	0.555979
$731$	1.50922e29	0.128121
$732$	0	0
$733$	−1.86535e30	−1.53875	−0.769375	−	0.638797i	$-0.779432\pi$
$733$	−1.86535e30	−1.53875	−0.769375	+	0.638797i	$0.779432\pi$
$734$	−1.31245e30	−1.06727
$735$	0	0
$736$	2.05454e30	1.62367
$737$	6.57597e28	0.0512332
$738$	0	0
$739$	9.76021e29	0.739082	0.369541	−	0.929214i	$-0.379515\pi$
$739$	9.76021e29	0.739082	0.369541	+	0.929214i	$0.379515\pi$
$740$	6.81085e28	0.0508473
$741$	0	0
$742$	2.25311e30	1.63509
$743$	−1.30919e30	−0.936742	−0.468371	−	0.883532i	$-0.655159\pi$
$743$	−1.30919e30	−0.936742	−0.468371	+	0.883532i	$0.655159\pi$
$744$	0	0
$745$	−7.07850e29	−0.492380
$746$	1.55934e30	1.06951
$747$	0	0
$748$	2.52068e28	0.0168093
$749$	9.11499e29	0.599373
$750$	0	0
$751$	1.02067e30	0.652626	0.326313	−	0.945262i	$-0.394194\pi$
$751$	1.02067e30	0.652626	0.326313	+	0.945262i	$0.394194\pi$
$752$	2.89875e29	0.182778
$753$	0	0
$754$	6.38274e28	0.0391389
$755$	−3.46841e29	−0.209743
$756$	0	0
$757$	−1.30425e30	−0.767106	−0.383553	−	0.923519i	$-0.625300\pi$
$757$	−1.30425e30	−0.767106	−0.383553	+	0.923519i	$0.625300\pi$
$758$	−2.07734e30	−1.20498
$759$	0	0
$760$	3.72452e29	0.210149
$761$	−1.44355e30	−0.803329	−0.401664	−	0.915787i	$-0.631568\pi$
$761$	−1.44355e30	−0.803329	−0.401664	+	0.915787i	$0.631568\pi$
$762$	0	0
$763$	−6.42984e30	−3.48091
$764$	−1.34514e30	−0.718268
$765$	0	0
$766$	−1.41652e29	−0.0735904
$767$	−4.84089e27	−0.00248070
$768$	0	0
$769$	−4.69617e29	−0.234163	−0.117081	−	0.993122i	$-0.537354\pi$
$769$	−4.69617e29	−0.234163	−0.117081	+	0.993122i	$0.537354\pi$
$770$	−4.98679e29	−0.245284
$771$	0	0
$772$	1.55422e30	0.743927
$773$	1.85640e30	0.876572	0.438286	−	0.898835i	$-0.355586\pi$
$773$	1.85640e30	0.876572	0.438286	+	0.898835i	$0.355586\pi$
$774$	0	0
$775$	−1.54482e30	−0.709920
$776$	−1.16374e29	−0.0527604
$777$	0	0
$778$	−1.11897e30	−0.493780
$779$	4.70962e30	2.05042
$780$	0	0
$781$	5.69844e29	0.241502
$782$	4.41364e29	0.184555
$783$	0	0
$784$	−7.88178e30	−3.20853
$785$	9.09098e29	0.365157
$786$	0	0
$787$	−3.15728e30	−1.23475	−0.617374	−	0.786669i	$-0.711804\pi$
$787$	−3.15728e30	−1.23475	−0.617374	+	0.786669i	$0.711804\pi$
$788$	1.50408e30	0.580426
$789$	0	0
$790$	2.76096e30	1.03747
$791$	5.15262e30	1.91062
$792$	0	0
$793$	4.25931e28	0.0153805
$794$	5.07835e30	1.80970
$795$	0	0
$796$	−7.64864e29	−0.265459
$797$	−4.17512e30	−1.43007	−0.715034	−	0.699090i	$-0.753589\pi$
$797$	−4.17512e30	−1.43007	−0.715034	+	0.699090i	$0.753589\pi$
$798$	0	0
$799$	4.94374e28	0.0164936
$800$	2.97666e30	0.980130
$801$	0	0
$802$	1.34806e29	0.0432391
$803$	−5.96838e29	−0.188948
$804$	0	0
$805$	−3.75882e30	−1.15930
$806$	−9.23096e28	−0.0281015
$807$	0	0
$808$	−1.10881e30	−0.328882
$809$	−1.58248e30	−0.463318	−0.231659	−	0.972797i	$-0.574415\pi$
$809$	−1.58248e30	−0.463318	−0.231659	+	0.972797i	$0.574415\pi$
$810$	0	0
$811$	6.17280e30	1.76102	0.880508	−	0.474031i	$-0.157202\pi$
$811$	6.17280e30	1.76102	0.880508	+	0.474031i	$0.157202\pi$
$812$	−6.49751e30	−1.82982
$813$	0	0
$814$	−1.46271e29	−0.0401423
$815$	2.94050e29	0.0796648
$816$	0	0
$817$	6.38274e30	1.68529
$818$	−2.98274e30	−0.777509
$819$	0	0
$820$	−2.00436e30	−0.509248
$821$	1.86634e30	0.468154	0.234077	−	0.972218i	$-0.424793\pi$
$821$	1.86634e30	0.468154	0.234077	+	0.972218i	$0.424793\pi$
$822$	0	0
$823$	−9.55497e29	−0.233631	−0.116816	−	0.993154i	$-0.537269\pi$
$823$	−9.55497e29	−0.233631	−0.116816	+	0.993154i	$0.537269\pi$
$824$	−8.29076e29	−0.200151
$825$	0	0
$826$	1.14476e30	0.269416
$827$	−6.36744e30	−1.47964	−0.739821	−	0.672803i	$-0.765090\pi$
$827$	−6.36744e30	−1.47964	−0.739821	+	0.672803i	$0.765090\pi$
$828$	0	0
$829$	1.73773e30	0.393694	0.196847	−	0.980434i	$-0.436930\pi$
$829$	1.73773e30	0.393694	0.196847	+	0.980434i	$0.436930\pi$
$830$	−3.98490e30	−0.891451
$831$	0	0
$832$	5.02690e28	0.0109649
$833$	−1.34421e30	−0.289531
$834$	0	0
$835$	−3.99501e30	−0.839093
$836$	1.06604e30	0.221109
$837$	0	0
$838$	6.24969e30	1.26414
$839$	−6.90704e29	−0.137972	−0.0689861	−	0.997618i	$-0.521976\pi$
$839$	−6.90704e29	−0.137972	−0.0689861	+	0.997618i	$0.521976\pi$
$840$	0	0
$841$	2.97820e30	0.580225
$842$	−8.49028e30	−1.63360
$843$	0	0
$844$	−1.23110e30	−0.231045
$845$	−2.49114e30	−0.461746
$846$	0	0
$847$	−1.01898e31	−1.84243
$848$	−4.25003e30	−0.758989
$849$	0	0
$850$	6.39457e29	0.111407
$851$	−1.10252e30	−0.189726
$852$	0	0
$853$	−3.91355e30	−0.657061	−0.328531	−	0.944493i	$-0.606553\pi$
$853$	−3.91355e30	−0.657061	−0.328531	+	0.944493i	$0.606553\pi$
$854$	−1.00723e31	−1.67040
$855$	0	0
$856$	−6.22230e29	−0.100688
$857$	−9.77653e30	−1.56274	−0.781369	−	0.624069i	$-0.785478\pi$
$857$	−9.77653e30	−1.56274	−0.781369	+	0.624069i	$0.785478\pi$
$858$	0	0
$859$	2.87242e30	0.448043	0.224022	−	0.974584i	$-0.428081\pi$
$859$	2.87242e30	0.448043	0.224022	+	0.974584i	$0.428081\pi$
$860$	−2.71642e30	−0.418565
$861$	0	0
$862$	9.76614e30	1.46858
$863$	1.04420e30	0.155122	0.0775608	−	0.996988i	$-0.475287\pi$
$863$	1.04420e30	0.155122	0.0775608	+	0.996988i	$0.475287\pi$
$864$	0	0
$865$	1.76313e30	0.255633
$866$	1.44727e31	2.07306
$867$	0	0
$868$	9.39694e30	1.31380
$869$	−2.55251e30	−0.352582
$870$	0	0
$871$	4.29115e28	0.00578606
$872$	4.38930e30	0.584752
$873$	0	0
$874$	1.86660e31	2.42763
$875$	−1.23695e31	−1.58953
$876$	0	0
$877$	5.88930e30	0.738870	0.369435	−	0.929257i	$-0.379551\pi$
$877$	5.88930e30	0.738870	0.369435	+	0.929257i	$0.379551\pi$
$878$	9.70134e30	1.20265
$879$	0	0
$880$	9.40658e29	0.113858
$881$	−1.18650e31	−1.41913	−0.709563	−	0.704642i	$-0.751108\pi$
$881$	−1.18650e31	−1.41913	−0.709563	+	0.704642i	$0.751108\pi$
$882$	0	0
$883$	−3.58382e30	−0.418561	−0.209280	−	0.977856i	$-0.567112\pi$
$883$	−3.58382e30	−0.418561	−0.209280	+	0.977856i	$0.567112\pi$
$884$	1.64487e28	0.00189838
$885$	0	0
$886$	4.41868e30	0.498010
$887$	−1.13748e31	−1.26691	−0.633456	−	0.773779i	$-0.718364\pi$
$887$	−1.13748e31	−1.26691	−0.633456	+	0.773779i	$0.718364\pi$
$888$	0	0
$889$	−8.07360e30	−0.878211
$890$	6.19056e30	0.665480
$891$	0	0
$892$	5.28866e30	0.555284
$893$	2.09079e30	0.216956
$894$	0	0
$895$	8.22423e30	0.833591
$896$	1.20676e31	1.20889
$897$	0	0
$898$	−1.31978e31	−1.29152
$899$	−1.17305e31	−1.13459
$900$	0	0
$901$	−7.24830e29	−0.0684898
$902$	4.30459e30	0.402035
$903$	0	0
$904$	−3.51741e30	−0.320962
$905$	3.94015e30	0.355388
$906$	0	0
$907$	6.42730e30	0.566438	0.283219	−	0.959055i	$-0.408598\pi$
$907$	6.42730e30	0.566438	0.283219	+	0.959055i	$0.408598\pi$
$908$	2.05161e30	0.178728
$909$	0	0
$910$	−3.25414e29	−0.0277014
$911$	2.02085e30	0.170056	0.0850278	−	0.996379i	$-0.472902\pi$
$911$	2.02085e30	0.170056	0.0850278	+	0.996379i	$0.472902\pi$
$912$	0	0
$913$	3.68405e30	0.302958
$914$	−6.97441e30	−0.566986
$915$	0	0
$916$	7.42720e30	0.590096
$917$	4.51456e30	0.354599
$918$	0	0
$919$	−1.04014e30	−0.0798510	−0.0399255	−	0.999203i	$-0.512712\pi$
$919$	−1.04014e30	−0.0798510	−0.0399255	+	0.999203i	$0.512712\pi$
$920$	2.56594e30	0.194748
$921$	0	0
$922$	4.00699e30	0.297265
$923$	3.71852e29	0.0272742
$924$	0	0
$925$	−1.59736e30	−0.114529
$926$	−2.36608e30	−0.167731
$927$	0	0
$928$	2.26031e31	1.56644
$929$	1.20936e31	0.828684	0.414342	−	0.910121i	$-0.364012\pi$
$929$	1.20936e31	0.828684	0.414342	+	0.910121i	$0.364012\pi$
$930$	0	0
$931$	−5.68491e31	−3.80849
$932$	−1.48882e31	−0.986224
$933$	0	0
$934$	−7.14140e30	−0.462531
$935$	1.60426e29	0.0102743
$936$	0	0
$937$	−2.84764e31	−1.78328	−0.891638	−	0.452748i	$-0.850444\pi$
$937$	−2.84764e31	−1.78328	−0.891638	+	0.452748i	$0.850444\pi$
$938$	−1.01476e31	−0.628396
$939$	0	0
$940$	−8.89817e29	−0.0538838
$941$	2.38411e31	1.42770	0.713848	−	0.700301i	$-0.246951\pi$
$941$	2.38411e31	1.42770	0.713848	+	0.700301i	$0.246951\pi$
$942$	0	0
$943$	3.24461e31	1.90016
$944$	−2.15936e30	−0.125060
$945$	0	0
$946$	5.83383e30	0.330443
$947$	−3.03747e31	−1.70152	−0.850760	−	0.525555i	$-0.823858\pi$
$947$	−3.03747e31	−1.70152	−0.850760	+	0.525555i	$0.823858\pi$
$948$	0	0
$949$	−3.89467e29	−0.0213391
$950$	2.70438e31	1.46544
$951$	0	0
$952$	1.25639e30	0.0665943
$953$	−3.43245e30	−0.179941	−0.0899703	−	0.995944i	$-0.528677\pi$
$953$	−3.43245e30	−0.179941	−0.0899703	+	0.995944i	$0.528677\pi$
$954$	0	0
$955$	−8.56102e30	−0.439026
$956$	9.20424e30	0.466853
$957$	0	0
$958$	7.70614e30	0.382384
$959$	−5.26829e31	−2.58568
$960$	0	0
$961$	−3.86041e30	−0.185370
$962$	−9.54492e28	−0.00453351
$963$	0	0
$964$	−1.66746e31	−0.774903
$965$	9.89169e30	0.454709
$966$	0	0
$967$	1.94184e31	0.873445	0.436722	−	0.899596i	$-0.356139\pi$
$967$	1.94184e31	0.873445	0.436722	+	0.899596i	$0.356139\pi$
$968$	6.95604e30	0.309507
$969$	0	0
$970$	2.29303e30	0.0998405
$971$	1.81095e31	0.780016	0.390008	−	0.920811i	$-0.372472\pi$
$971$	1.81095e31	0.780016	0.390008	+	0.920811i	$0.372472\pi$
$972$	0	0
$973$	−9.77068e30	−0.411851
$974$	−9.14697e30	−0.381424
$975$	0	0
$976$	1.89993e31	0.775381
$977$	−2.12590e31	−0.858323	−0.429161	−	0.903228i	$-0.641191\pi$
$977$	−2.12590e31	−0.858323	−0.429161	+	0.903228i	$0.641191\pi$
$978$	0	0
$979$	−5.72319e30	−0.226162
$980$	2.41943e31	0.945888
$981$	0	0
$982$	−3.26330e31	−1.24878
$983$	3.74700e31	1.41864	0.709318	−	0.704888i	$-0.249003\pi$
$983$	3.74700e31	1.41864	0.709318	+	0.704888i	$0.249003\pi$
$984$	0	0
$985$	9.57262e30	0.354773
$986$	4.85568e30	0.178050
$987$	0	0
$988$	6.95644e29	0.0249712
$989$	4.39728e31	1.56179
$990$	0	0
$991$	−3.66143e31	−1.27314	−0.636572	−	0.771217i	$-0.719648\pi$
$991$	−3.66143e31	−1.27314	−0.636572	+	0.771217i	$0.719648\pi$
$992$	−3.26894e31	−1.12470
$993$	0	0
$994$	−8.79344e31	−2.96212
$995$	−4.86791e30	−0.162256
$996$	0	0
$997$	−4.25970e31	−1.39021	−0.695105	−	0.718909i	$-0.744642\pi$
$997$	−4.25970e31	−1.39021	−0.695105	+	0.718909i	$0.744642\pi$
$998$	3.12943e31	1.01063
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	81.22.a.c.1.17		20
3.2	odd	2		81.22.a.d.1.4		20
9.2	odd	6		27.22.c.a.10.17		40
9.4	even	3		9.22.c.a.7.4	yes	40
9.5	odd	6		27.22.c.a.19.17		40
9.7	even	3		9.22.c.a.4.4	✓	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
9.22.c.a.4.4	✓	40	9.7	even	3
9.22.c.a.7.4	yes	40	9.4	even	3
27.22.c.a.10.17		40	9.2	odd	6
27.22.c.a.19.17		40	9.5	odd	6
81.22.a.c.1.17		20	1.1	even	1	trivial
81.22.a.d.1.4		20	3.2	odd	2

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:	\( N \)	\(=\)	\( 81 = 3^{4} \)
Weight:	\( k \)	\(=\)	\( 22 \)
Character orbit:	\([\chi]\)	\(=\)	81.a (trivial)

\(f(q)\)	\(=\)	\(q+1918.93 q^{2} +1.58515e6 q^{4} +1.00885e7 q^{5} +1.43926e9 q^{7} -9.82502e8 q^{8} +O(q^{10})\)	\(q+1918.93 q^{2} +1.58515e6 q^{4} +1.00885e7 q^{5} +1.43926e9 q^{7} -9.82502e8 q^{8} +1.93592e10 q^{10} -1.78976e10 q^{11} -1.16791e10 q^{13} +2.76184e12 q^{14} -5.20965e12 q^{16} -8.88490e11 q^{17} -3.75758e13 q^{19} +1.59918e13 q^{20} -3.43443e13 q^{22} -2.58872e14 q^{23} -3.75059e14 q^{25} -2.24114e13 q^{26} +2.28144e15 q^{28} -2.84799e15 q^{29} +4.11887e15 q^{31} -7.93651e15 q^{32} -1.70495e15 q^{34} +1.45200e16 q^{35} +4.25896e15 q^{37} -7.21054e16 q^{38} -9.91201e15 q^{40} -1.25337e17 q^{41} -1.69863e17 q^{43} -2.83704e16 q^{44} -4.96757e17 q^{46} -5.56420e16 q^{47} +1.51292e18 q^{49} -7.19712e17 q^{50} -1.85131e16 q^{52} +8.15800e17 q^{53} -1.80561e17 q^{55} -1.41407e18 q^{56} -5.46510e18 q^{58} +4.14492e17 q^{59} -3.64695e18 q^{61} +7.90383e18 q^{62} -4.30419e18 q^{64} -1.17825e17 q^{65} -3.67422e18 q^{67} -1.40839e18 q^{68} +2.78629e19 q^{70} -3.18391e19 q^{71} +3.33473e19 q^{73} +8.17265e18 q^{74} -5.95632e19 q^{76} -2.57593e19 q^{77} +1.42618e20 q^{79} -5.25577e19 q^{80} -2.40512e20 q^{82} -2.05840e20 q^{83} -8.96356e18 q^{85} -3.25956e20 q^{86} +1.75844e19 q^{88} +3.19774e20 q^{89} -1.68092e19 q^{91} -4.10350e20 q^{92} -1.06773e20 q^{94} -3.79085e20 q^{95} +1.18447e20 q^{97} +2.90319e21 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 1023 q^{2} + 19922945 q^{4} - 32234853 q^{5} + 189623959 q^{7} - 648135831 q^{8}+O(q^{10}) \) 20 * q - 1023 * q^2 + 19922945 * q^4 - 32234853 * q^5 + 189623959 * q^7 - 648135831 * q^8	\( 20 q - 1023 q^{2} + 19922945 q^{4} - 32234853 q^{5} + 189623959 q^{7} - 648135831 q^{8} + 2097150 q^{10} - 146068576386 q^{11} + 177565977277 q^{13} - 1549677244440 q^{14} + 18691699769345 q^{16} - 9307801874799 q^{17} - 4884366861977 q^{19} - 76202257650204 q^{20} - 86758343554047 q^{22} - 356460494884095 q^{23} + 13\!\cdots\!29 q^{25}+ \cdots + 26\!\cdots\!43 q^{98}+O(q^{100}) \) 20 * q - 1023 * q^2 + 19922945 * q^4 - 32234853 * q^5 + 189623959 * q^7 - 648135831 * q^8 + 2097150 * q^10 - 146068576386 * q^11 + 177565977277 * q^13 - 1549677244440 * q^14 + 18691699769345 * q^16 - 9307801874799 * q^17 - 4884366861977 * q^19 - 76202257650204 * q^20 - 86758343554047 * q^22 - 356460494884095 * q^23 + 1379841857082329 * q^25 + 2254540119546732 * q^26 + 799738574143486 * q^28 + 2772828270755157 * q^29 - 3064842508546901 * q^31 - 9763241440878495 * q^32 - 5532390311666553 * q^34 - 28944789317551797 * q^35 + 15041349243939694 * q^37 - 38173338977409867 * q^38 + 43546396391926176 * q^40 - 4985514195953106 * q^41 + 41986108659289660 * q^43 + 154909775468547021 * q^44 - 370501619585816100 * q^46 - 971751895603333665 * q^47 + 1393736132530446381 * q^49 - 1504393427506051923 * q^50 + 892509168437820382 * q^52 - 3200468347464244650 * q^53 + 1763329427612189115 * q^55 - 9313401575284840590 * q^56 + 985520139125952432 * q^58 - 11335149505478767926 * q^59 + 333769931007960067 * q^61 - 30822195887206546926 * q^62 + 12804600562751272961 * q^64 - 24815104795645584999 * q^65 - 14325054629523996728 * q^67 - 98193137232148637751 * q^68 + 23664205955002266174 * q^70 - 108719113548124731960 * q^71 - 2415544298256170813 * q^73 - 284989967381657148240 * q^74 - 45502930505046158765 * q^76 - 209785238565183158133 * q^77 - 45386959469213650259 * q^79 - 499015504255192380624 * q^80 + 114258090814276483077 * q^82 - 224083700347690062915 * q^83 + 135764416394391341394 * q^85 + 210501162447733500423 * q^86 - 409557505702705259691 * q^88 + 140942904695660466360 * q^89 - 193584504929412672709 * q^91 - 160981359902419031922 * q^92 - 1246412695298803268064 * q^94 - 583111881346045719228 * q^95 + 658984791485125488346 * q^97 + 2671316103447781667343 * q^98

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