LMFDB - Embedded newform 81.22.a.c.1.10

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			1.10
Root			$261.580$ 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)

$f(q)$	$=$	$q-312.580 q^{2} -1.99945e6 q^{4} -3.51534e7 q^{5} +1.24694e9 q^{7} +1.28051e9 q^{8} +O(q^{10})$	\(q-312.580 q^{2} -1.99945e6 q^{4} -3.51534e7 q^{5} +1.24694e9 q^{7} +1.28051e9 q^{8} +1.09883e10 q^{10} -8.81097e10 q^{11} -6.90753e11 q^{13} -3.89769e11 q^{14} +3.79288e12 q^{16} -5.45416e12 q^{17} +1.85213e13 q^{19} +7.02874e13 q^{20} +2.75413e13 q^{22} -6.83150e13 q^{23} +7.58927e14 q^{25} +2.15915e14 q^{26} -2.49319e15 q^{28} -1.16637e15 q^{29} +2.51215e15 q^{31} -3.87101e15 q^{32} +1.70486e15 q^{34} -4.38343e16 q^{35} +7.08944e15 q^{37} -5.78939e15 q^{38} -4.50145e16 q^{40} -1.46154e16 q^{41} +2.13132e16 q^{43} +1.76171e17 q^{44} +2.13539e16 q^{46} -4.19033e17 q^{47} +9.96319e17 q^{49} -2.37225e17 q^{50} +1.38112e18 q^{52} +3.61502e17 q^{53} +3.09736e18 q^{55} +1.59673e18 q^{56} +3.64583e17 q^{58} +3.75725e18 q^{59} +2.15687e18 q^{61} -7.85248e17 q^{62} -6.74425e18 q^{64} +2.42823e19 q^{65} +2.35787e19 q^{67} +1.09053e19 q^{68} +1.37017e19 q^{70} +5.47019e19 q^{71} -2.31502e19 q^{73} -2.21602e18 q^{74} -3.70324e19 q^{76} -1.09868e20 q^{77} -9.38404e19 q^{79} -1.33333e20 q^{80} +4.56849e18 q^{82} +1.28419e20 q^{83} +1.91732e20 q^{85} -6.66207e18 q^{86} -1.12826e20 q^{88} +2.53773e20 q^{89} -8.61329e20 q^{91} +1.36592e20 q^{92} +1.30981e20 q^{94} -6.51088e20 q^{95} +5.53931e20 q^{97} -3.11429e20 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−312.580	−0.215847	−0.107923	−	0.994159i	$-0.534420\pi$
$2$	−312.580	−0.215847	−0.107923	+	0.994159i	$0.534420\pi$
$3$	0	0
$3$	0	0
$4$	−1.99945e6	−0.953410
$5$	−3.51534e7	−1.60984	−0.804920	−	0.593383i	$-0.797792\pi$
$5$	−3.51534e7	−1.60984	−0.804920	+	0.593383i	$0.797792\pi$
$6$	0	0
$7$	1.24694e9	1.66846	0.834232	−	0.551413i	$-0.185911\pi$
$7$	1.24694e9	1.66846	0.834232	+	0.551413i	$0.185911\pi$
$8$	1.28051e9	0.421638
$9$	0	0
$10$	1.09883e10	0.347479
$11$	−8.81097e10	−1.02424	−0.512119	−	0.858915i	$-0.671139\pi$
$11$	−8.81097e10	−1.02424	−0.512119	+	0.858915i	$0.671139\pi$
$12$	0	0
$13$	−6.90753e11	−1.38969	−0.694844	−	0.719160i	$-0.744527\pi$
$13$	−6.90753e11	−1.38969	−0.694844	+	0.719160i	$0.744527\pi$
$14$	−3.89769e11	−0.360133
$15$	0	0
$16$	3.79288e12	0.862401
$17$	−5.45416e12	−0.656166	−0.328083	−	0.944649i	$-0.606403\pi$
$17$	−5.45416e12	−0.656166	−0.328083	+	0.944649i	$0.606403\pi$
$18$	0	0
$19$	1.85213e13	0.693041	0.346520	−	0.938042i	$-0.387363\pi$
$19$	1.85213e13	0.693041	0.346520	+	0.938042i	$0.387363\pi$
$20$	7.02874e13	1.53484
$21$	0	0
$22$	2.75413e13	0.221079
$23$	−6.83150e13	−0.343854	−0.171927	−	0.985110i	$-0.554999\pi$
$23$	−6.83150e13	−0.343854	−0.171927	+	0.985110i	$0.554999\pi$
$24$	0	0
$25$	7.58927e14	1.59159
$26$	2.15915e14	0.299960
$27$	0	0
$28$	−2.49319e15	−1.59073
$29$	−1.16637e15	−0.514822	−0.257411	−	0.966302i	$-0.582869\pi$
$29$	−1.16637e15	−0.514822	−0.257411	+	0.966302i	$0.582869\pi$
$30$	0	0
$31$	2.51215e15	0.550489	0.275244	−	0.961374i	$-0.411241\pi$
$31$	2.51215e15	0.550489	0.275244	+	0.961374i	$0.411241\pi$
$32$	−3.87101e15	−0.607784
$33$	0	0
$34$	1.70486e15	0.141631
$35$	−4.38343e16	−2.68596
$36$	0	0
$37$	7.08944e15	0.242378	0.121189	−	0.992629i	$-0.461329\pi$
$37$	7.08944e15	0.242378	0.121189	+	0.992629i	$0.461329\pi$
$38$	−5.78939e15	−0.149591
$39$	0	0
$40$	−4.50145e16	−0.678769
$41$	−1.46154e16	−0.170052	−0.0850258	−	0.996379i	$-0.527097\pi$
$41$	−1.46154e16	−0.170052	−0.0850258	+	0.996379i	$0.527097\pi$
$42$	0	0
$43$	2.13132e16	0.150394	0.0751968	−	0.997169i	$-0.476041\pi$
$43$	2.13132e16	0.150394	0.0751968	+	0.997169i	$0.476041\pi$
$44$	1.76171e17	0.976518
$45$	0	0
$46$	2.13539e16	0.0742198
$47$	−4.19033e17	−1.16204	−0.581020	−	0.813889i	$-0.697346\pi$
$47$	−4.19033e17	−1.16204	−0.581020	+	0.813889i	$0.697346\pi$
$48$	0	0
$49$	9.96319e17	1.78377
$50$	−2.37225e17	−0.343539
$51$	0	0
$52$	1.38112e18	1.32494
$53$	3.61502e17	0.283932	0.141966	−	0.989872i	$-0.454658\pi$
$53$	3.61502e17	0.283932	0.141966	+	0.989872i	$0.454658\pi$
$54$	0	0
$55$	3.09736e18	1.64886
$56$	1.59673e18	0.703487
$57$	0	0
$58$	3.64583e17	0.111123
$59$	3.75725e18	0.957025	0.478513	−	0.878081i	$-0.341176\pi$
$59$	3.75725e18	0.957025	0.478513	+	0.878081i	$0.341176\pi$
$60$	0	0
$61$	2.15687e18	0.387134	0.193567	−	0.981087i	$-0.437994\pi$
$61$	2.15687e18	0.387134	0.193567	+	0.981087i	$0.437994\pi$
$62$	−7.85248e17	−0.118821
$63$	0	0
$64$	−6.74425e18	−0.731213
$65$	2.42823e19	2.23718
$66$	0	0
$67$	2.35787e19	1.58028	0.790140	−	0.612927i	$-0.210008\pi$
$67$	2.35787e19	1.58028	0.790140	+	0.612927i	$0.210008\pi$
$68$	1.09053e19	0.625596
$69$	0	0
$70$	1.37017e19	0.579757
$71$	5.47019e19	1.99430	0.997148	−	0.0754665i	$-0.0240446\pi$
$71$	5.47019e19	1.99430	0.997148	+	0.0754665i	$0.0240446\pi$
$72$	0	0
$73$	−2.31502e19	−0.630471	−0.315236	−	0.949013i	$-0.602084\pi$
$73$	−2.31502e19	−0.630471	−0.315236	+	0.949013i	$0.602084\pi$
$74$	−2.21602e18	−0.0523166
$75$	0	0
$76$	−3.70324e19	−0.660752
$77$	−1.09868e20	−1.70890
$78$	0	0
$79$	−9.38404e19	−1.11508	−0.557539	−	0.830151i	$-0.688254\pi$
$79$	−9.38404e19	−1.11508	−0.557539	+	0.830151i	$0.688254\pi$
$80$	−1.33333e20	−1.38833
$81$	0	0
$82$	4.56849e18	0.0367051
$83$	1.28419e20	0.908466	0.454233	−	0.890883i	$-0.349913\pi$
$83$	1.28419e20	0.908466	0.454233	+	0.890883i	$0.349913\pi$
$84$	0	0
$85$	1.91732e20	1.05632
$86$	−6.66207e18	−0.0324620
$87$	0	0
$88$	−1.12826e20	−0.431857
$89$	2.53773e20	0.862680	0.431340	−	0.902189i	$-0.358041\pi$
$89$	2.53773e20	0.862680	0.431340	+	0.902189i	$0.358041\pi$
$90$	0	0
$91$	−8.61329e20	−2.31865
$92$	1.36592e20	0.327834
$93$	0	0
$94$	1.30981e20	0.250823
$95$	−6.51088e20	−1.11569
$96$	0	0
$97$	5.53931e20	0.762698	0.381349	−	0.924431i	$-0.375460\pi$
$97$	5.53931e20	0.762698	0.381349	+	0.924431i	$0.375460\pi$
$98$	−3.11429e20	−0.385022
$99$	0	0
$100$	−1.51743e21	−1.51743
$101$	2.02303e21	1.82233	0.911167	−	0.412038i	$-0.135183\pi$
$101$	2.02303e21	1.82233	0.911167	+	0.412038i	$0.135183\pi$
$102$	0	0
$103$	1.01137e21	0.741515	0.370757	−	0.928730i	$-0.379098\pi$
$103$	1.01137e21	0.741515	0.370757	+	0.928730i	$0.379098\pi$
$104$	−8.84519e20	−0.585945
$105$	0	0
$106$	−1.12998e20	−0.0612858
$107$	−5.82372e20	−0.286201	−0.143100	−	0.989708i	$-0.545707\pi$
$107$	−5.82372e20	−0.286201	−0.143100	+	0.989708i	$0.545707\pi$
$108$	0	0
$109$	3.80298e21	1.53867	0.769335	−	0.638845i	$-0.220588\pi$
$109$	3.80298e21	1.53867	0.769335	+	0.638845i	$0.220588\pi$
$110$	−9.68172e20	−0.355901
$111$	0	0
$112$	4.72950e21	1.43889
$113$	−2.81440e21	−0.779943	−0.389971	−	0.920827i	$-0.627515\pi$
$113$	−2.81440e21	−0.779943	−0.389971	+	0.920827i	$0.627515\pi$
$114$	0	0
$115$	2.40151e21	0.553549
$116$	2.33209e21	0.490836
$117$	0	0
$118$	−1.17444e21	−0.206571
$119$	−6.80102e21	−1.09479
$120$	0	0
$121$	3.63075e20	0.0490625
$122$	−6.74195e20	−0.0835617
$123$	0	0
$124$	−5.02291e21	−0.524841
$125$	−9.91643e21	−0.952358
$126$	0	0
$127$	7.23860e21	0.588458	0.294229	−	0.955735i	$-0.404937\pi$
$127$	7.23860e21	0.588458	0.294229	+	0.955735i	$0.404937\pi$
$128$	1.02262e22	0.765614
$129$	0	0
$130$	−7.59017e21	−0.482888
$131$	−1.02621e22	−0.602402	−0.301201	−	0.953561i	$-0.597387\pi$
$131$	−1.02621e22	−0.602402	−0.301201	+	0.953561i	$0.597387\pi$
$132$	0	0
$133$	2.30950e22	1.15631
$134$	−7.37021e21	−0.341098
$135$	0	0
$136$	−6.98412e21	−0.276664
$137$	−2.15290e22	−0.789691	−0.394846	−	0.918748i	$-0.629202\pi$
$137$	−2.15290e22	−0.789691	−0.394846	+	0.918748i	$0.629202\pi$
$138$	0	0
$139$	−3.26846e22	−1.02965	−0.514823	−	0.857297i	$-0.672142\pi$
$139$	−3.26846e22	−1.02965	−0.514823	+	0.857297i	$0.672142\pi$
$140$	8.76443e22	2.56082
$141$	0	0
$142$	−1.70987e22	−0.430463
$143$	6.08621e22	1.42337
$144$	0	0
$145$	4.10019e22	0.828781
$146$	7.23629e21	0.136085
$147$	0	0
$148$	−1.41750e22	−0.231086
$149$	4.81977e22	0.732100	0.366050	−	0.930595i	$-0.380710\pi$
$149$	4.81977e22	0.732100	0.366050	+	0.930595i	$0.380710\pi$
$150$	0	0
$151$	−1.12630e23	−1.48729	−0.743644	−	0.668575i	$-0.766904\pi$
$151$	−1.12630e23	−1.48729	−0.743644	+	0.668575i	$0.766904\pi$
$152$	2.37168e22	0.292212
$153$	0	0
$154$	3.43424e22	0.368862
$155$	−8.83108e22	−0.886199
$156$	0	0
$157$	−1.00217e23	−0.879012	−0.439506	−	0.898240i	$-0.644846\pi$
$157$	−1.00217e23	−0.879012	−0.439506	+	0.898240i	$0.644846\pi$
$158$	2.93326e22	0.240686
$159$	0	0
$160$	1.36079e23	0.978435
$161$	−8.51848e22	−0.573708
$162$	0	0
$163$	1.00338e23	0.593603	0.296802	−	0.954939i	$-0.404080\pi$
$163$	1.00338e23	0.593603	0.296802	+	0.954939i	$0.404080\pi$
$164$	2.92227e22	0.162129
$165$	0	0
$166$	−4.01411e22	−0.196090
$167$	−2.65401e23	−1.21725	−0.608624	−	0.793459i	$-0.708278\pi$
$167$	−2.65401e23	−1.21725	−0.608624	+	0.793459i	$0.708278\pi$
$168$	0	0
$169$	2.30075e23	0.931235
$170$	−5.99317e22	−0.228004
$171$	0	0
$172$	−4.26145e22	−0.143387
$173$	−2.07614e23	−0.657314	−0.328657	−	0.944449i	$-0.606596\pi$
$173$	−2.07614e23	−0.657314	−0.328657	+	0.944449i	$0.606596\pi$
$174$	0	0
$175$	9.46338e23	2.65550
$176$	−3.34190e23	−0.883303
$177$	0	0
$178$	−7.93242e22	−0.186207
$179$	−8.02544e23	−1.77628	−0.888142	−	0.459570i	$-0.848004\pi$
$179$	−8.02544e23	−1.77628	−0.888142	+	0.459570i	$0.848004\pi$
$180$	0	0
$181$	−2.04191e23	−0.402172	−0.201086	−	0.979574i	$-0.564447\pi$
$181$	−2.04191e23	−0.402172	−0.201086	+	0.979574i	$0.564447\pi$
$182$	2.69234e23	0.500473
$183$	0	0
$184$	−8.74783e22	−0.144982
$185$	−2.49218e23	−0.390190
$186$	0	0
$187$	4.80564e23	0.672070
$188$	8.37835e23	1.10790
$189$	0	0
$190$	2.03517e23	0.240817
$191$	3.05909e23	0.342564	0.171282	−	0.985222i	$-0.445209\pi$
$191$	3.05909e23	0.342564	0.171282	+	0.985222i	$0.445209\pi$
$192$	0	0
$193$	−4.27986e23	−0.429613	−0.214807	−	0.976657i	$-0.568912\pi$
$193$	−4.27986e23	−0.429613	−0.214807	+	0.976657i	$0.568912\pi$
$194$	−1.73148e23	−0.164626
$195$	0	0
$196$	−1.99209e24	−1.70067
$197$	3.17082e23	0.256612	0.128306	−	0.991735i	$-0.459046\pi$
$197$	3.17082e23	0.256612	0.128306	+	0.991735i	$0.459046\pi$
$198$	0	0
$199$	−2.18540e24	−1.59064	−0.795321	−	0.606188i	$-0.792698\pi$
$199$	−2.18540e24	−1.59064	−0.795321	+	0.606188i	$0.792698\pi$
$200$	9.71816e23	0.671072
$201$	0	0
$202$	−6.32358e23	−0.393345
$203$	−1.45439e24	−0.858962
$204$	0	0
$205$	5.13782e23	0.273756
$206$	−3.16134e23	−0.160054
$207$	0	0
$208$	−2.61994e24	−1.19847
$209$	−1.63191e24	−0.709838
$210$	0	0
$211$	3.14762e24	1.23884	0.619421	−	0.785059i	$-0.287367\pi$
$211$	3.14762e24	1.23884	0.619421	+	0.785059i	$0.287367\pi$
$212$	−7.22804e23	−0.270704
$213$	0	0
$214$	1.82038e23	0.0617756
$215$	−7.49231e23	−0.242110
$216$	0	0
$217$	3.13251e24	0.918471
$218$	−1.18873e24	−0.332117
$219$	0	0
$220$	−6.19300e24	−1.57204
$221$	3.76748e24	0.911867
$222$	0	0
$223$	6.07343e23	0.133731	0.0668657	−	0.997762i	$-0.478700\pi$
$223$	6.07343e23	0.133731	0.0668657	+	0.997762i	$0.478700\pi$
$224$	−4.82693e24	−1.01407
$225$	0	0
$226$	8.79726e23	0.168348
$227$	1.52876e24	0.279297	0.139649	−	0.990201i	$-0.455403\pi$
$227$	1.52876e24	0.279297	0.139649	+	0.990201i	$0.455403\pi$
$228$	0	0
$229$	2.04174e23	0.0340195	0.0170097	−	0.999855i	$-0.494585\pi$
$229$	2.04174e23	0.0340195	0.0170097	+	0.999855i	$0.494585\pi$
$230$	−7.50662e23	−0.119482
$231$	0	0
$232$	−1.49355e24	−0.217068
$233$	−3.28244e24	−0.455994	−0.227997	−	0.973662i	$-0.573218\pi$
$233$	−3.28244e24	−0.455994	−0.227997	+	0.973662i	$0.573218\pi$
$234$	0	0
$235$	1.47305e25	1.87070
$236$	−7.51241e24	−0.912438
$237$	0	0
$238$	2.12586e24	0.236307
$239$	−8.96342e24	−0.953446	−0.476723	−	0.879054i	$-0.658175\pi$
$239$	−8.96342e24	−0.953446	−0.476723	+	0.879054i	$0.658175\pi$
$240$	0	0
$241$	1.91406e24	0.186542	0.0932711	−	0.995641i	$-0.470268\pi$
$241$	1.91406e24	0.186542	0.0932711	+	0.995641i	$0.470268\pi$
$242$	−1.13490e23	−0.0105900
$243$	0	0
$244$	−4.31255e24	−0.369098
$245$	−3.50240e25	−2.87159
$246$	0	0
$247$	−1.27937e25	−0.963111
$248$	3.21685e24	0.232107
$249$	0	0
$250$	3.09968e24	0.205564
$251$	1.51084e25	0.960822	0.480411	−	0.877043i	$-0.340487\pi$
$251$	1.51084e25	0.960822	0.480411	+	0.877043i	$0.340487\pi$
$252$	0	0
$253$	6.01921e24	0.352188
$254$	−2.26264e24	−0.127017
$255$	0	0
$256$	1.09472e25	0.565957
$257$	2.23108e24	0.110718	0.0553590	−	0.998467i	$-0.482370\pi$
$257$	2.23108e24	0.110718	0.0553590	+	0.998467i	$0.482370\pi$
$258$	0	0
$259$	8.84012e24	0.404400
$260$	−4.85512e25	−2.13295
$261$	0	0
$262$	3.20771e24	0.130027
$263$	2.99012e25	1.16454	0.582269	−	0.812996i	$-0.302165\pi$
$263$	2.99012e25	1.16454	0.582269	+	0.812996i	$0.302165\pi$
$264$	0	0
$265$	−1.27080e25	−0.457085
$266$	−7.21903e24	−0.249587
$267$	0	0
$268$	−4.71443e25	−1.50665
$269$	−4.65710e25	−1.43125	−0.715627	−	0.698483i	$-0.753859\pi$
$269$	−4.65710e25	−1.43125	−0.715627	+	0.698483i	$0.753859\pi$
$270$	0	0
$271$	−2.16700e25	−0.616141	−0.308071	−	0.951363i	$-0.599683\pi$
$271$	−2.16700e25	−0.616141	−0.308071	+	0.951363i	$0.599683\pi$
$272$	−2.06870e25	−0.565878
$273$	0	0
$274$	6.72952e24	0.170452
$275$	−6.68689e25	−1.63016
$276$	0	0
$277$	7.22395e25	1.63206	0.816032	−	0.578007i	$-0.196169\pi$
$277$	7.22395e25	1.63206	0.816032	+	0.578007i	$0.196169\pi$
$278$	1.02165e25	0.222246
$279$	0	0
$280$	−5.61304e25	−1.13250
$281$	−7.39572e25	−1.43736	−0.718678	−	0.695343i	$-0.755252\pi$
$281$	−7.39572e25	−1.43736	−0.718678	+	0.695343i	$0.755252\pi$
$282$	0	0
$283$	2.64709e25	0.477541	0.238770	−	0.971076i	$-0.423256\pi$
$283$	2.64709e25	0.477541	0.238770	+	0.971076i	$0.423256\pi$
$284$	−1.09373e26	−1.90138
$285$	0	0
$286$	−1.90243e25	−0.307230
$287$	−1.82246e25	−0.283725
$288$	0	0
$289$	−3.93441e25	−0.569446
$290$	−1.28164e25	−0.178890
$291$	0	0
$292$	4.62876e25	0.601097
$293$	−5.77021e25	−0.722906	−0.361453	−	0.932390i	$-0.617719\pi$
$293$	−5.77021e25	−0.722906	−0.361453	+	0.932390i	$0.617719\pi$
$294$	0	0
$295$	−1.32080e26	−1.54066
$296$	9.07813e24	0.102196
$297$	0	0
$298$	−1.50656e25	−0.158021
$299$	4.71888e25	0.477850
$300$	0	0
$301$	2.65763e25	0.250926
$302$	3.52058e25	0.321027
$303$	0	0
$304$	7.02491e25	0.597679
$305$	−7.58215e25	−0.623224
$306$	0	0
$307$	2.04550e26	1.56980	0.784902	−	0.619620i	$-0.212713\pi$
$307$	2.04550e26	1.56980	0.784902	+	0.619620i	$0.212713\pi$
$308$	2.19675e26	1.62929
$309$	0	0
$310$	2.76042e25	0.191283
$311$	−1.18458e25	−0.0793561	−0.0396780	−	0.999213i	$-0.512633\pi$
$311$	−1.18458e25	−0.0793561	−0.0396780	+	0.999213i	$0.512633\pi$
$312$	0	0
$313$	2.24058e26	1.40328	0.701641	−	0.712531i	$-0.252451\pi$
$313$	2.24058e26	1.40328	0.701641	+	0.712531i	$0.252451\pi$
$314$	3.13258e25	0.189732
$315$	0	0
$316$	1.87629e26	1.06313
$317$	−2.94145e26	−1.61227	−0.806137	−	0.591728i	$-0.798446\pi$
$317$	−2.94145e26	−1.61227	−0.806137	+	0.591728i	$0.798446\pi$
$318$	0	0
$319$	1.02768e26	0.527300
$320$	2.37083e26	1.17714
$321$	0	0
$322$	2.66271e25	0.123833
$323$	−1.01018e26	−0.454750
$324$	0	0
$325$	−5.24231e26	−2.21181
$326$	−3.13637e25	−0.128127
$327$	0	0
$328$	−1.87152e25	−0.0717002
$329$	−5.22510e26	−1.93882
$330$	0	0
$331$	8.41531e25	0.293006	0.146503	−	0.989210i	$-0.453198\pi$
$331$	8.41531e25	0.293006	0.146503	+	0.989210i	$0.453198\pi$
$332$	−2.56766e26	−0.866140
$333$	0	0
$334$	8.29589e25	0.262739
$335$	−8.28871e26	−2.54400
$336$	0	0
$337$	−4.69889e26	−1.35482	−0.677409	−	0.735606i	$-0.736897\pi$
$337$	−4.69889e26	−1.35482	−0.677409	+	0.735606i	$0.736897\pi$
$338$	−7.19169e25	−0.201004
$339$	0	0
$340$	−3.83358e26	−1.00711
$341$	−2.21345e26	−0.563831
$342$	0	0
$343$	5.45878e26	1.30770
$344$	2.72918e25	0.0634116
$345$	0	0
$346$	6.48960e25	0.141879
$347$	4.61612e26	0.979078	0.489539	−	0.871981i	$-0.337165\pi$
$347$	4.61612e26	0.979078	0.489539	+	0.871981i	$0.337165\pi$
$348$	0	0
$349$	−4.24539e26	−0.847716	−0.423858	−	0.905729i	$-0.639324\pi$
$349$	−4.24539e26	−0.847716	−0.423858	+	0.905729i	$0.639324\pi$
$350$	−2.95806e26	−0.573182
$351$	0	0
$352$	3.41074e26	0.622515
$353$	−5.19071e26	−0.919586	−0.459793	−	0.888026i	$-0.652076\pi$
$353$	−5.19071e26	−0.919586	−0.459793	+	0.888026i	$0.652076\pi$
$354$	0	0
$355$	−1.92296e27	−3.21050
$356$	−5.07405e26	−0.822488
$357$	0	0
$358$	2.50859e26	0.383405
$359$	4.86811e26	0.722552	0.361276	−	0.932459i	$-0.382341\pi$
$359$	4.86811e26	0.722552	0.361276	+	0.932459i	$0.382341\pi$
$360$	0	0
$361$	−3.71171e26	−0.519694
$362$	6.38260e25	0.0868076
$363$	0	0
$364$	1.72218e27	2.21062
$365$	8.13810e26	1.01496
$366$	0	0
$367$	−7.67927e26	−0.904328	−0.452164	−	0.891935i	$-0.649348\pi$
$367$	−7.67927e26	−0.904328	−0.452164	+	0.891935i	$0.649348\pi$
$368$	−2.59110e26	−0.296540
$369$	0	0
$370$	7.79006e25	0.0842214
$371$	4.50772e26	0.473730
$372$	0	0
$373$	3.97987e26	0.395299	0.197649	−	0.980273i	$-0.436669\pi$
$373$	3.97987e26	0.395299	0.197649	+	0.980273i	$0.436669\pi$
$374$	−1.50215e26	−0.145064
$375$	0	0
$376$	−5.36578e26	−0.489960
$377$	8.05673e26	0.715442
$378$	0	0
$379$	−1.67323e27	−1.40554	−0.702770	−	0.711418i	$-0.748054\pi$
$379$	−1.67323e27	−1.40554	−0.702770	+	0.711418i	$0.748054\pi$
$380$	1.30181e27	1.06371
$381$	0	0
$382$	−9.56210e25	−0.0739414
$383$	−4.24048e26	−0.319027	−0.159514	−	0.987196i	$-0.550993\pi$
$383$	−4.24048e26	−0.319027	−0.159514	+	0.987196i	$0.550993\pi$
$384$	0	0
$385$	3.86223e27	2.75106
$386$	1.33780e26	0.0927307
$387$	0	0
$388$	−1.10756e27	−0.727164
$389$	2.72141e27	1.73909	0.869547	−	0.493850i	$-0.164411\pi$
$389$	2.72141e27	1.73909	0.869547	+	0.493850i	$0.164411\pi$
$390$	0	0
$391$	3.72601e26	0.225625
$392$	1.27580e27	0.752106
$393$	0	0
$394$	−9.91135e25	−0.0553889
$395$	3.29881e27	1.79510
$396$	0	0
$397$	3.31963e27	1.71313	0.856564	−	0.516040i	$-0.172595\pi$
$397$	3.31963e27	1.71313	0.856564	+	0.516040i	$0.172595\pi$
$398$	6.83110e26	0.343335
$399$	0	0
$400$	2.87852e27	1.37258
$401$	−5.58698e26	−0.259514	−0.129757	−	0.991546i	$-0.541420\pi$
$401$	−5.58698e26	−0.259514	−0.129757	+	0.991546i	$0.541420\pi$
$402$	0	0
$403$	−1.73528e27	−0.765008
$404$	−4.04494e27	−1.73743
$405$	0	0
$406$	4.54614e26	0.185404
$407$	−6.24649e26	−0.248253
$408$	0	0
$409$	−1.28901e26	−0.0486590	−0.0243295	−	0.999704i	$-0.507745\pi$
$409$	−1.28901e26	−0.0486590	−0.0243295	+	0.999704i	$0.507745\pi$
$410$	−1.60598e26	−0.0590894
$411$	0	0
$412$	−2.02218e27	−0.706968
$413$	4.68507e27	1.59676
$414$	0	0
$415$	−4.51436e27	−1.46248
$416$	2.67391e27	0.844631
$417$	0	0
$418$	5.10101e26	0.153216
$419$	5.79707e26	0.169809	0.0849046	−	0.996389i	$-0.472941\pi$
$419$	5.79707e26	0.169809	0.0849046	+	0.996389i	$0.472941\pi$
$420$	0	0
$421$	1.51313e27	0.421613	0.210807	−	0.977528i	$-0.432391\pi$
$421$	1.51313e27	0.421613	0.210807	+	0.977528i	$0.432391\pi$
$422$	−9.83881e26	−0.267400
$423$	0	0
$424$	4.62908e26	0.119716
$425$	−4.13931e27	−1.04434
$426$	0	0
$427$	2.68950e27	0.645920
$428$	1.16442e27	0.272867
$429$	0	0
$430$	2.34195e26	0.0522586
$431$	1.07105e27	0.233238	0.116619	−	0.993177i	$-0.462794\pi$
$431$	1.07105e27	0.233238	0.116619	+	0.993177i	$0.462794\pi$
$432$	0	0
$433$	1.64300e27	0.340811	0.170406	−	0.985374i	$-0.445492\pi$
$433$	1.64300e27	0.340811	0.170406	+	0.985374i	$0.445492\pi$
$434$	−9.79159e26	−0.198249
$435$	0	0
$436$	−7.60385e27	−1.46698
$437$	−1.26528e27	−0.238305
$438$	0	0
$439$	3.59793e27	0.645915	0.322957	−	0.946413i	$-0.395323\pi$
$439$	3.59793e27	0.645915	0.322957	+	0.946413i	$0.395323\pi$
$440$	3.96621e27	0.695221
$441$	0	0
$442$	−1.17764e27	−0.196824
$443$	1.05260e28	1.71800	0.858998	−	0.511978i	$-0.171087\pi$
$443$	1.05260e28	1.71800	0.858998	+	0.511978i	$0.171087\pi$
$444$	0	0
$445$	−8.92098e27	−1.38878
$446$	−1.89843e26	−0.0288655
$447$	0	0
$448$	−8.40968e27	−1.22000
$449$	−3.83730e27	−0.543801	−0.271900	−	0.962325i	$-0.587652\pi$
$449$	−3.83730e27	−0.543801	−0.271900	+	0.962325i	$0.587652\pi$
$450$	0	0
$451$	1.28776e27	0.174173
$452$	5.62725e27	0.743605
$453$	0	0
$454$	−4.77858e26	−0.0602855
$455$	3.02787e28	3.73265
$456$	0	0
$457$	−1.27376e27	−0.149957	−0.0749783	−	0.997185i	$-0.523889\pi$
$457$	−1.27376e27	−0.149957	−0.0749783	+	0.997185i	$0.523889\pi$
$458$	−6.38206e25	−0.00734300
$459$	0	0
$460$	−4.80168e27	−0.527760
$461$	−6.92340e27	−0.743806	−0.371903	−	0.928272i	$-0.621295\pi$
$461$	−6.92340e27	−0.743806	−0.371903	+	0.928272i	$0.621295\pi$
$462$	0	0
$463$	5.91972e27	0.607717	0.303858	−	0.952717i	$-0.401725\pi$
$463$	5.91972e27	0.607717	0.303858	+	0.952717i	$0.401725\pi$
$464$	−4.42390e27	−0.443983
$465$	0	0
$466$	1.02602e27	0.0984249
$467$	1.41157e28	1.32396	0.661979	−	0.749522i	$-0.269717\pi$
$467$	1.41157e28	1.32396	0.661979	+	0.749522i	$0.269717\pi$
$468$	0	0
$469$	2.94012e28	2.63664
$470$	−4.60445e27	−0.403785
$471$	0	0
$472$	4.81120e27	0.403518
$473$	−1.87790e27	−0.154039
$474$	0	0
$475$	1.40563e28	1.10303
$476$	1.35983e28	1.04378
$477$	0	0
$478$	2.80178e27	0.205798
$479$	−2.48079e28	−1.78265	−0.891327	−	0.453361i	$-0.850225\pi$
$479$	−2.48079e28	−1.78265	−0.891327	+	0.453361i	$0.850225\pi$
$480$	0	0
$481$	−4.89705e27	−0.336831
$482$	−5.98297e26	−0.0402646
$483$	0	0
$484$	−7.25948e26	−0.0467767
$485$	−1.94726e28	−1.22782
$486$	0	0
$487$	−3.65458e27	−0.220690	−0.110345	−	0.993893i	$-0.535196\pi$
$487$	−3.65458e27	−0.220690	−0.110345	+	0.993893i	$0.535196\pi$
$488$	2.76191e27	0.163230
$489$	0	0
$490$	1.09478e28	0.619824
$491$	−4.31431e27	−0.239087	−0.119543	−	0.992829i	$-0.538143\pi$
$491$	−4.31431e27	−0.239087	−0.119543	+	0.992829i	$0.538143\pi$
$492$	0	0
$493$	6.36156e27	0.337809
$494$	3.99904e27	0.207885
$495$	0	0
$496$	9.52829e27	0.474742
$497$	6.82101e28	3.32741
$498$	0	0
$499$	−5.39998e27	−0.252543	−0.126272	−	0.991996i	$-0.540301\pi$
$499$	−5.39998e27	−0.252543	−0.126272	+	0.991996i	$0.540301\pi$
$500$	1.98274e28	0.907988
$501$	0	0
$502$	−4.72257e27	−0.207391
$503$	5.28212e27	0.227166	0.113583	−	0.993528i	$-0.463767\pi$
$503$	5.28212e27	0.227166	0.113583	+	0.993528i	$0.463767\pi$
$504$	0	0
$505$	−7.11165e28	−2.93367
$506$	−1.88148e27	−0.0760187
$507$	0	0
$508$	−1.44732e28	−0.561042
$509$	−4.25052e28	−1.61401	−0.807004	−	0.590546i	$-0.798912\pi$
$509$	−4.25052e28	−1.61401	−0.807004	+	0.590546i	$0.798912\pi$
$510$	0	0
$511$	−2.88670e28	−1.05192
$512$	−2.48678e28	−0.887774
$513$	0	0
$514$	−6.97392e26	−0.0238981
$515$	−3.55532e28	−1.19372
$516$	0	0
$517$	3.69209e28	1.19021
$518$	−2.76324e27	−0.0872884
$519$	0	0
$520$	3.10939e28	0.943278
$521$	3.16788e28	0.941830	0.470915	−	0.882179i	$-0.343924\pi$
$521$	3.16788e28	0.941830	0.470915	+	0.882179i	$0.343924\pi$
$522$	0	0
$523$	8.06489e27	0.230320	0.115160	−	0.993347i	$-0.463262\pi$
$523$	8.06489e27	0.230320	0.115160	+	0.993347i	$0.463262\pi$
$524$	2.05184e28	0.574336
$525$	0	0
$526$	−9.34652e27	−0.251362
$527$	−1.37017e28	−0.361212
$528$	0	0
$529$	−3.48046e28	−0.881765
$530$	3.97228e27	0.0986604
$531$	0	0
$532$	−4.61772e28	−1.10244
$533$	1.00956e28	0.236319
$534$	0	0
$535$	2.04724e28	0.460738
$536$	3.01928e28	0.666305
$537$	0	0
$538$	1.45572e28	0.308932
$539$	−8.77854e28	−1.82701
$540$	0	0
$541$	3.46867e28	0.694371	0.347185	−	0.937796i	$-0.387137\pi$
$541$	3.46867e28	0.694371	0.347185	+	0.937796i	$0.387137\pi$
$542$	6.77359e27	0.132992
$543$	0	0
$544$	2.11131e28	0.398808
$545$	−1.33688e29	−2.47701
$546$	0	0
$547$	−9.88433e28	−1.76230	−0.881151	−	0.472835i	$-0.843230\pi$
$547$	−9.88433e28	−1.76230	−0.881151	+	0.472835i	$0.843230\pi$
$548$	4.30460e28	0.752899
$549$	0	0
$550$	2.09019e28	0.351865
$551$	−2.16027e28	−0.356793
$552$	0	0
$553$	−1.17014e29	−1.86047
$554$	−2.25806e28	−0.352276
$555$	0	0
$556$	6.53511e28	0.981675
$557$	−6.39055e28	−0.942016	−0.471008	−	0.882129i	$-0.656110\pi$
$557$	−6.39055e28	−0.942016	−0.471008	+	0.882129i	$0.656110\pi$
$558$	0	0
$559$	−1.47221e28	−0.209000
$560$	−1.66258e29	−2.31638
$561$	0	0
$562$	2.31175e28	0.310249
$563$	5.94803e28	0.783493	0.391746	−	0.920073i	$-0.371871\pi$
$563$	5.94803e28	0.783493	0.391746	+	0.920073i	$0.371871\pi$
$564$	0	0
$565$	9.89360e28	1.25558
$566$	−8.27426e27	−0.103076
$567$	0	0
$568$	7.00465e28	0.840870
$569$	−9.46463e28	−1.11538	−0.557692	−	0.830048i	$-0.688313\pi$
$569$	−9.46463e28	−1.11538	−0.557692	+	0.830048i	$0.688313\pi$
$570$	0	0
$571$	8.86752e28	1.00722	0.503608	−	0.863932i	$-0.332005\pi$
$571$	8.86752e28	1.00722	0.503608	+	0.863932i	$0.332005\pi$
$572$	−1.21690e29	−1.35706
$573$	0	0
$574$	5.69664e27	0.0612412
$575$	−5.18461e28	−0.547273
$576$	0	0
$577$	−6.12766e28	−0.623661	−0.311830	−	0.950138i	$-0.600942\pi$
$577$	−6.12766e28	−0.623661	−0.311830	+	0.950138i	$0.600942\pi$
$578$	1.22982e28	0.122913
$579$	0	0
$580$	−8.19810e28	−0.790168
$581$	1.60131e29	1.51574
$582$	0	0
$583$	−3.18519e28	−0.290814
$584$	−2.96442e28	−0.265830
$585$	0	0
$586$	1.80365e28	0.156037
$587$	3.20311e28	0.272190	0.136095	−	0.990696i	$-0.456545\pi$
$587$	3.20311e28	0.272190	0.136095	+	0.990696i	$0.456545\pi$
$588$	0	0
$589$	4.65284e28	0.381511
$590$	4.12856e28	0.332546
$591$	0	0
$592$	2.68894e28	0.209027
$593$	−1.89614e29	−1.44809	−0.724047	−	0.689750i	$-0.757720\pi$
$593$	−1.89614e29	−1.44809	−0.724047	+	0.689750i	$0.757720\pi$
$594$	0	0
$595$	2.39079e29	1.76244
$596$	−9.63686e28	−0.697991
$597$	0	0
$598$	−1.47503e28	−0.103142
$599$	−8.60609e26	−0.00591323	−0.00295661	−	0.999996i	$-0.500941\pi$
$599$	−8.60609e26	−0.00591323	−0.00295661	+	0.999996i	$0.500941\pi$
$600$	0	0
$601$	3.27930e28	0.217570	0.108785	−	0.994065i	$-0.465304\pi$
$601$	3.27930e28	0.217570	0.108785	+	0.994065i	$0.465304\pi$
$602$	−8.30721e27	−0.0541617
$603$	0	0
$604$	2.25197e29	1.41800
$605$	−1.27633e28	−0.0789828
$606$	0	0
$607$	−5.48036e28	−0.327588	−0.163794	−	0.986495i	$-0.552373\pi$
$607$	−5.48036e28	−0.327588	−0.163794	+	0.986495i	$0.552373\pi$
$608$	−7.16962e28	−0.421219
$609$	0	0
$610$	2.37003e28	0.134521
$611$	2.89449e29	1.61487
$612$	0	0
$613$	−2.63675e29	−1.42146	−0.710729	−	0.703466i	$-0.751635\pi$
$613$	−2.63675e29	−1.42146	−0.710729	+	0.703466i	$0.751635\pi$
$614$	−6.39381e28	−0.338838
$615$	0	0
$616$	−1.40687e29	−0.720538
$617$	1.14876e29	0.578410	0.289205	−	0.957267i	$-0.406609\pi$
$617$	1.14876e29	0.578410	0.289205	+	0.957267i	$0.406609\pi$
$618$	0	0
$619$	−1.15464e29	−0.561948	−0.280974	−	0.959715i	$-0.590657\pi$
$619$	−1.15464e29	−0.561948	−0.280974	+	0.959715i	$0.590657\pi$
$620$	1.76573e29	0.844911
$621$	0	0
$622$	3.70276e27	0.0171288
$623$	3.16440e29	1.43935
$624$	0	0
$625$	−1.32880e28	−0.0584413
$626$	−7.00360e28	−0.302894
$627$	0	0
$628$	2.00378e29	0.838059
$629$	−3.86669e28	−0.159041
$630$	0	0
$631$	−9.64140e28	−0.383559	−0.191779	−	0.981438i	$-0.561426\pi$
$631$	−9.64140e28	−0.383559	−0.191779	+	0.981438i	$0.561426\pi$
$632$	−1.20164e29	−0.470159
$633$	0	0
$634$	9.19437e28	0.348005
$635$	−2.54462e29	−0.947323
$636$	0	0
$637$	−6.88211e29	−2.47889
$638$	−3.21233e28	−0.113816
$639$	0	0
$640$	−3.59486e29	−1.23252
$641$	−2.14636e29	−0.723925	−0.361962	−	0.932193i	$-0.617893\pi$
$641$	−2.14636e29	−0.723925	−0.361962	+	0.932193i	$0.617893\pi$
$642$	0	0
$643$	4.10636e29	1.34042	0.670211	−	0.742170i	$-0.266203\pi$
$643$	4.10636e29	1.34042	0.670211	+	0.742170i	$0.266203\pi$
$644$	1.70322e29	0.546979
$645$	0	0
$646$	3.15762e28	0.0981564
$647$	−2.71708e29	−0.831011	−0.415506	−	0.909591i	$-0.636395\pi$
$647$	−2.71708e29	−0.831011	−0.415506	+	0.909591i	$0.636395\pi$
$648$	0	0
$649$	−3.31050e29	−0.980221
$650$	1.63864e29	0.477412
$651$	0	0
$652$	−2.00621e29	−0.565947
$653$	−4.91929e29	−1.36557	−0.682785	−	0.730619i	$-0.739232\pi$
$653$	−4.91929e29	−1.36557	−0.682785	+	0.730619i	$0.739232\pi$
$654$	0	0
$655$	3.60747e29	0.969771
$656$	−5.54345e28	−0.146653
$657$	0	0
$658$	1.63326e29	0.418489
$659$	3.80930e29	0.960613	0.480306	−	0.877101i	$-0.340526\pi$
$659$	3.80930e29	0.960613	0.480306	+	0.877101i	$0.340526\pi$
$660$	0	0
$661$	−2.55776e29	−0.624805	−0.312402	−	0.949950i	$-0.601134\pi$
$661$	−2.55776e29	−0.624805	−0.312402	+	0.949950i	$0.601134\pi$
$662$	−2.63045e28	−0.0632444
$663$	0	0
$664$	1.64442e29	0.383043
$665$	−8.11869e29	−1.86148
$666$	0	0
$667$	7.96805e28	0.177023
$668$	5.30654e29	1.16054
$669$	0	0
$670$	2.59088e29	0.549114
$671$	−1.90042e29	−0.396517
$672$	0	0
$673$	2.91045e29	0.588576	0.294288	−	0.955717i	$-0.404918\pi$
$673$	2.91045e29	0.588576	0.294288	+	0.955717i	$0.404918\pi$
$674$	1.46878e29	0.292433
$675$	0	0
$676$	−4.60023e29	−0.887849
$677$	−8.80454e29	−1.67311	−0.836557	−	0.547879i	$-0.815435\pi$
$677$	−8.80454e29	−1.67311	−0.836557	+	0.547879i	$0.815435\pi$
$678$	0	0
$679$	6.90720e29	1.27253
$680$	2.45516e29	0.445385
$681$	0	0
$682$	6.91880e28	0.121701
$683$	8.60467e29	1.49045	0.745224	−	0.666814i	$-0.232342\pi$
$683$	8.60467e29	1.49045	0.745224	+	0.666814i	$0.232342\pi$
$684$	0	0
$685$	7.56817e29	1.27128
$686$	−1.70631e29	−0.282263
$687$	0	0
$688$	8.08383e28	0.129700
$689$	−2.49709e29	−0.394577
$690$	0	0
$691$	5.86147e29	0.898436	0.449218	−	0.893422i	$-0.351703\pi$
$691$	5.86147e29	0.898436	0.449218	+	0.893422i	$0.351703\pi$
$692$	4.15113e29	0.626690
$693$	0	0
$694$	−1.44290e29	−0.211331
$695$	1.14898e30	1.65757
$696$	0	0
$697$	7.97148e28	0.111582
$698$	1.32702e29	0.182977
$699$	0	0
$700$	−1.89215e30	−2.53178
$701$	1.45516e30	1.91810	0.959052	−	0.283232i	$-0.0914065\pi$
$701$	1.45516e30	1.91810	0.959052	+	0.283232i	$0.0914065\pi$
$702$	0	0
$703$	1.31306e29	0.167978
$704$	5.94234e29	0.748935
$705$	0	0
$706$	1.62251e29	0.198490
$707$	2.52260e30	3.04050
$708$	0	0
$709$	1.08589e30	1.27058	0.635289	−	0.772274i	$-0.280881\pi$
$709$	1.08589e30	1.27058	0.635289	+	0.772274i	$0.280881\pi$
$710$	6.01078e29	0.692976
$711$	0	0
$712$	3.24959e29	0.363738
$713$	−1.71618e29	−0.189288
$714$	0	0
$715$	−2.13951e30	−2.29140
$716$	1.60464e30	1.69353
$717$	0	0
$718$	−1.52167e29	−0.155961
$719$	3.39337e29	0.342750	0.171375	−	0.985206i	$-0.445179\pi$
$719$	3.39337e29	0.342750	0.171375	+	0.985206i	$0.445179\pi$
$720$	0	0
$721$	1.26112e30	1.23719
$722$	1.16020e29	0.112174
$723$	0	0
$724$	4.08269e29	0.383435
$725$	−8.85189e29	−0.819383
$726$	0	0
$727$	−6.30236e29	−0.566751	−0.283375	−	0.959009i	$-0.591454\pi$
$727$	−6.30236e29	−0.566751	−0.283375	+	0.959009i	$0.591454\pi$
$728$	−1.10294e30	−0.977629
$729$	0	0
$730$	−2.54381e29	−0.219076
$731$	−1.16245e29	−0.0986832
$732$	0	0
$733$	−1.85636e30	−1.53134	−0.765669	−	0.643235i	$-0.777592\pi$
$733$	−1.85636e30	−1.53134	−0.765669	+	0.643235i	$0.777592\pi$
$734$	2.40038e29	0.195196
$735$	0	0
$736$	2.64448e29	0.208989
$737$	−2.07751e30	−1.61858
$738$	0	0
$739$	−5.78686e28	−0.0438204	−0.0219102	−	0.999760i	$-0.506975\pi$
$739$	−5.78686e28	−0.0438204	−0.0219102	+	0.999760i	$0.506975\pi$
$740$	4.98298e29	0.372012
$741$	0	0
$742$	−1.40902e29	−0.102253
$743$	3.57823e29	0.256027	0.128014	−	0.991772i	$-0.459140\pi$
$743$	3.57823e29	0.256027	0.128014	+	0.991772i	$0.459140\pi$
$744$	0	0
$745$	−1.69431e30	−1.17856
$746$	−1.24403e29	−0.0853241
$747$	0	0
$748$	−9.60862e29	−0.640758
$749$	−7.26184e29	−0.477516
$750$	0	0
$751$	1.34132e30	0.857657	0.428828	−	0.903386i	$-0.358926\pi$
$751$	1.34132e30	0.857657	0.428828	+	0.903386i	$0.358926\pi$
$752$	−1.58934e30	−1.00214
$753$	0	0
$754$	−2.51837e29	−0.154426
$755$	3.95932e30	2.39430
$756$	0	0
$757$	−2.27540e30	−1.33829	−0.669147	−	0.743130i	$-0.733340\pi$
$757$	−2.27540e30	−1.33829	−0.669147	+	0.743130i	$0.733340\pi$
$758$	5.23017e29	0.303381
$759$	0	0
$760$	−8.33727e29	−0.470415
$761$	3.12415e30	1.73857	0.869285	−	0.494311i	$-0.164579\pi$
$761$	3.12415e30	1.73857	0.869285	+	0.494311i	$0.164579\pi$
$762$	0	0
$763$	4.74209e30	2.56722
$764$	−6.11649e29	−0.326604
$765$	0	0
$766$	1.32549e29	0.0688611
$767$	−2.59533e30	−1.32997
$768$	0	0
$769$	2.03959e30	1.01699	0.508495	−	0.861065i	$-0.330202\pi$
$769$	2.03959e30	1.01699	0.508495	+	0.861065i	$0.330202\pi$
$770$	−1.20725e30	−0.593808
$771$	0	0
$772$	8.55734e29	0.409597
$773$	1.87277e30	0.884303	0.442151	−	0.896941i	$-0.354215\pi$
$773$	1.87277e30	0.884303	0.442151	+	0.896941i	$0.354215\pi$
$774$	0	0
$775$	1.90654e30	0.876150
$776$	7.09316e29	0.321582
$777$	0	0
$778$	−8.50657e29	−0.375378
$779$	−2.70697e29	−0.117853
$780$	0	0
$781$	−4.81977e30	−2.04263
$782$	−1.16467e29	−0.0487005
$783$	0	0
$784$	3.77892e30	1.53833
$785$	3.52297e30	1.41507
$786$	0	0
$787$	−4.46447e29	−0.174596	−0.0872982	−	0.996182i	$-0.527823\pi$
$787$	−4.46447e29	−0.174596	−0.0872982	+	0.996182i	$0.527823\pi$
$788$	−6.33989e29	−0.244656
$789$	0	0
$790$	−1.03114e30	−0.387466
$791$	−3.50940e30	−1.30131
$792$	0	0
$793$	−1.48987e30	−0.537996
$794$	−1.03765e30	−0.369774
$795$	0	0
$796$	4.36958e30	1.51653
$797$	−3.64984e30	−1.25015	−0.625074	−	0.780566i	$-0.714931\pi$
$797$	−3.64984e30	−1.25015	−0.625074	+	0.780566i	$0.714931\pi$
$798$	0	0
$799$	2.28547e30	0.762492
$800$	−2.93781e30	−0.967340
$801$	0	0
$802$	1.74638e29	0.0560153
$803$	2.03976e30	0.645752
$804$	0	0
$805$	2.99454e30	0.923578
$806$	5.42413e29	0.165125
$807$	0	0
$808$	2.59052e30	0.768364
$809$	1.55633e30	0.455661	0.227831	−	0.973701i	$-0.426837\pi$
$809$	1.55633e30	0.455661	0.227831	+	0.973701i	$0.426837\pi$
$810$	0	0
$811$	−3.10075e30	−0.884601	−0.442301	−	0.896867i	$-0.645838\pi$
$811$	−3.10075e30	−0.884601	−0.442301	+	0.896867i	$0.645838\pi$
$812$	2.90798e30	0.818943
$813$	0	0
$814$	1.95253e29	0.0535847
$815$	−3.52723e30	−0.955606
$816$	0	0
$817$	3.94748e29	0.104229
$818$	4.02920e28	0.0105029
$819$	0	0
$820$	−1.02728e30	−0.261002
$821$	−6.03994e30	−1.51506	−0.757530	−	0.652801i	$-0.773594\pi$
$821$	−6.03994e30	−1.51506	−0.757530	+	0.652801i	$0.773594\pi$
$822$	0	0
$823$	−1.94675e30	−0.476005	−0.238003	−	0.971265i	$-0.576493\pi$
$823$	−1.94675e30	−0.476005	−0.238003	+	0.971265i	$0.576493\pi$
$824$	1.29507e30	0.312651
$825$	0	0
$826$	−1.46446e30	−0.344656
$827$	8.99746e29	0.209080	0.104540	−	0.994521i	$-0.466663\pi$
$827$	8.99746e29	0.209080	0.104540	+	0.994521i	$0.466663\pi$
$828$	0	0
$829$	−4.20804e30	−0.953360	−0.476680	−	0.879077i	$-0.658160\pi$
$829$	−4.20804e30	−0.953360	−0.476680	+	0.879077i	$0.658160\pi$
$830$	1.41110e30	0.315673
$831$	0	0
$832$	4.65861e30	1.01616
$833$	−5.43408e30	−1.17045
$834$	0	0
$835$	9.32974e30	1.95957
$836$	3.26291e30	0.676767
$837$	0	0
$838$	−1.81205e29	−0.0366528
$839$	−1.34022e30	−0.267718	−0.133859	−	0.991000i	$-0.542737\pi$
$839$	−1.34022e30	−0.267718	−0.133859	+	0.991000i	$0.542737\pi$
$840$	0	0
$841$	−3.77243e30	−0.734959
$842$	−4.72974e29	−0.0910039
$843$	0	0
$844$	−6.29349e30	−1.18112
$845$	−8.08794e30	−1.49914
$846$	0	0
$847$	4.52733e29	0.0818590
$848$	1.37113e30	0.244863
$849$	0	0
$850$	1.29386e30	0.225419
$851$	−4.84315e29	−0.0833427
$852$	0	0
$853$	−8.82163e30	−1.48110	−0.740550	−	0.672002i	$-0.765435\pi$
$853$	−8.82163e30	−1.48110	−0.740550	+	0.672002i	$0.765435\pi$
$854$	−8.40683e29	−0.139420
$855$	0	0
$856$	−7.45735e29	−0.120673
$857$	−5.00809e30	−0.800522	−0.400261	−	0.916401i	$-0.631080\pi$
$857$	−5.00809e30	−0.800522	−0.400261	+	0.916401i	$0.631080\pi$
$858$	0	0
$859$	−1.09861e31	−1.71362	−0.856811	−	0.515630i	$-0.827558\pi$
$859$	−1.09861e31	−1.71362	−0.856811	+	0.515630i	$0.827558\pi$
$860$	1.49805e30	0.230830
$861$	0	0
$862$	−3.34789e29	−0.0503437
$863$	−1.17297e31	−1.74250	−0.871249	−	0.490841i	$-0.836690\pi$
$863$	−1.17297e31	−1.74250	−0.871249	+	0.490841i	$0.836690\pi$
$864$	0	0
$865$	7.29835e30	1.05817
$866$	−5.13568e29	−0.0735631
$867$	0	0
$868$	−6.26328e30	−0.875679
$869$	8.26825e30	1.14211
$870$	0	0
$871$	−1.62870e31	−2.19610
$872$	4.86977e30	0.648761
$873$	0	0
$874$	3.95502e29	0.0514373
$875$	−1.23652e31	−1.58898
$876$	0	0
$877$	−9.15533e30	−1.14863	−0.574313	−	0.818636i	$-0.694731\pi$
$877$	−9.15533e30	−1.14863	−0.574313	+	0.818636i	$0.694731\pi$
$878$	−1.12464e30	−0.139419
$879$	0	0
$880$	1.17479e31	1.42198
$881$	7.99561e30	0.956323	0.478161	−	0.878272i	$-0.341303\pi$
$881$	7.99561e30	0.956323	0.478161	+	0.878272i	$0.341303\pi$
$882$	0	0
$883$	7.40530e30	0.864879	0.432440	−	0.901663i	$-0.357653\pi$
$883$	7.40530e30	0.864879	0.432440	+	0.901663i	$0.357653\pi$
$884$	−7.53286e30	−0.869383
$885$	0	0
$886$	−3.29020e30	−0.370824
$887$	−9.84356e30	−1.09636	−0.548181	−	0.836359i	$-0.684680\pi$
$887$	−9.84356e30	−1.09636	−0.548181	+	0.836359i	$0.684680\pi$
$888$	0	0
$889$	9.02611e30	0.981821
$890$	2.78852e30	0.299763
$891$	0	0
$892$	−1.21435e30	−0.127501
$893$	−7.76105e30	−0.805341
$894$	0	0
$895$	2.82122e31	2.85953
$896$	1.27515e31	1.27740
$897$	0	0
$898$	1.19946e30	0.117378
$899$	−2.93010e30	−0.283404
$900$	0	0
$901$	−1.97169e30	−0.186307
$902$	−4.02528e29	−0.0375948
$903$	0	0
$904$	−3.60388e30	−0.328853
$905$	7.17802e30	0.647433
$906$	0	0
$907$	6.18628e30	0.545196	0.272598	−	0.962128i	$-0.412117\pi$
$907$	6.18628e30	0.545196	0.272598	+	0.962128i	$0.412117\pi$
$908$	−3.05667e30	−0.266285
$909$	0	0
$910$	−9.46450e30	−0.805681
$911$	1.72568e31	1.45217	0.726086	−	0.687604i	$-0.241337\pi$
$911$	1.72568e31	1.45217	0.726086	+	0.687604i	$0.241337\pi$
$912$	0	0
$913$	−1.13149e31	−0.930485
$914$	3.98150e29	0.0323677
$915$	0	0
$916$	−4.08234e29	−0.0324345
$917$	−1.27962e31	−1.00509
$918$	0	0
$919$	1.44973e31	1.11295	0.556473	−	0.830866i	$-0.312154\pi$
$919$	1.44973e31	1.11295	0.556473	+	0.830866i	$0.312154\pi$
$920$	3.07516e30	0.233397
$921$	0	0
$922$	2.16411e30	0.160548
$923$	−3.77855e31	−2.77145
$924$	0	0
$925$	5.38037e30	0.385766
$926$	−1.85039e30	−0.131174
$927$	0	0
$928$	4.51502e30	0.312901
$929$	5.04584e30	0.345755	0.172877	−	0.984943i	$-0.444694\pi$
$929$	5.04584e30	0.345755	0.172877	+	0.984943i	$0.444694\pi$
$930$	0	0
$931$	1.84531e31	1.23623
$932$	6.56305e30	0.434749
$933$	0	0
$934$	−4.41227e30	−0.285772
$935$	−1.68935e31	−1.08193
$936$	0	0
$937$	−7.65160e29	−0.0479167	−0.0239583	−	0.999713i	$-0.507627\pi$
$937$	−7.65160e29	−0.0479167	−0.0239583	+	0.999713i	$0.507627\pi$
$938$	−9.19023e30	−0.569111
$939$	0	0
$940$	−2.94528e31	−1.78354
$941$	4.40920e30	0.264039	0.132020	−	0.991247i	$-0.457854\pi$
$941$	4.40920e30	0.264039	0.132020	+	0.991247i	$0.457854\pi$
$942$	0	0
$943$	9.98452e29	0.0584729
$944$	1.42508e31	0.825340
$945$	0	0
$946$	5.86993e29	0.0332488
$947$	−3.27394e31	−1.83399	−0.916993	−	0.398904i	$-0.869391\pi$
$947$	−3.27394e31	−1.83399	−0.916993	+	0.398904i	$0.869391\pi$
$948$	0	0
$949$	1.59911e31	0.876159
$950$	−4.39372e30	−0.238086
$951$	0	0
$952$	−8.70880e30	−0.461605
$953$	−7.07540e30	−0.370916	−0.185458	−	0.982652i	$-0.559377\pi$
$953$	−7.07540e30	−0.370916	−0.185458	+	0.982652i	$0.559377\pi$
$954$	0	0
$955$	−1.07538e31	−0.551474
$956$	1.79219e31	0.909025
$957$	0	0
$958$	7.75445e30	0.384781
$959$	−2.68454e31	−1.31757
$960$	0	0
$961$	−1.45146e31	−0.696962
$962$	1.53072e30	0.0727038
$963$	0	0
$964$	−3.82706e30	−0.177851
$965$	1.50452e31	0.691608
$966$	0	0
$967$	3.09022e31	1.38999	0.694995	−	0.719014i	$-0.255406\pi$
$967$	3.09022e31	1.38999	0.694995	+	0.719014i	$0.255406\pi$
$968$	4.64922e29	0.0206866
$969$	0	0
$970$	6.08674e30	0.265022
$971$	−3.76184e30	−0.162031	−0.0810156	−	0.996713i	$-0.525816\pi$
$971$	−3.76184e30	−0.162031	−0.0810156	+	0.996713i	$0.525816\pi$
$972$	0	0
$973$	−4.07558e31	−1.71793
$974$	1.14235e30	0.0476354
$975$	0	0
$976$	8.18076e30	0.333865
$977$	9.99426e30	0.403513	0.201757	−	0.979436i	$-0.435335\pi$
$977$	9.99426e30	0.403513	0.201757	+	0.979436i	$0.435335\pi$
$978$	0	0
$979$	−2.23598e31	−0.883589
$980$	7.00287e31	2.73780
$981$	0	0
$982$	1.34856e30	0.0516061
$983$	4.18889e31	1.58594	0.792971	−	0.609259i	$-0.208533\pi$
$983$	4.18889e31	1.58594	0.792971	+	0.609259i	$0.208533\pi$
$984$	0	0
$985$	−1.11465e31	−0.413104
$986$	−1.98849e30	−0.0729150
$987$	0	0
$988$	2.55802e31	0.918240
$989$	−1.45601e30	−0.0517134
$990$	0	0
$991$	1.54921e31	0.538689	0.269344	−	0.963044i	$-0.413193\pi$
$991$	1.54921e31	0.538689	0.269344	+	0.963044i	$0.413193\pi$
$992$	−9.72457e30	−0.334578
$993$	0	0
$994$	−2.13211e31	−0.718212
$995$	7.68242e31	2.56068
$996$	0	0
$997$	1.34575e31	0.439202	0.219601	−	0.975590i	$-0.429525\pi$
$997$	1.34575e31	0.439202	0.219601	+	0.975590i	$0.429525\pi$
$998$	1.68792e30	0.0545107
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	81.22.a.c.1.10		20
3.2	odd	2		81.22.a.d.1.11		20
9.2	odd	6		27.22.c.a.10.10		40
9.4	even	3		9.22.c.a.7.11	yes	40
9.5	odd	6		27.22.c.a.19.10		40
9.7	even	3		9.22.c.a.4.11	✓	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
9.22.c.a.4.11	✓	40	9.7	even	3
9.22.c.a.7.11	yes	40	9.4	even	3
27.22.c.a.10.10		40	9.2	odd	6
27.22.c.a.19.10		40	9.5	odd	6
81.22.a.c.1.10		20	1.1	even	1	trivial
81.22.a.d.1.11		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)

\(f(q)\)	\(=\)	\(q-312.580 q^{2} -1.99945e6 q^{4} -3.51534e7 q^{5} +1.24694e9 q^{7} +1.28051e9 q^{8} +O(q^{10})\)	\(q-312.580 q^{2} -1.99945e6 q^{4} -3.51534e7 q^{5} +1.24694e9 q^{7} +1.28051e9 q^{8} +1.09883e10 q^{10} -8.81097e10 q^{11} -6.90753e11 q^{13} -3.89769e11 q^{14} +3.79288e12 q^{16} -5.45416e12 q^{17} +1.85213e13 q^{19} +7.02874e13 q^{20} +2.75413e13 q^{22} -6.83150e13 q^{23} +7.58927e14 q^{25} +2.15915e14 q^{26} -2.49319e15 q^{28} -1.16637e15 q^{29} +2.51215e15 q^{31} -3.87101e15 q^{32} +1.70486e15 q^{34} -4.38343e16 q^{35} +7.08944e15 q^{37} -5.78939e15 q^{38} -4.50145e16 q^{40} -1.46154e16 q^{41} +2.13132e16 q^{43} +1.76171e17 q^{44} +2.13539e16 q^{46} -4.19033e17 q^{47} +9.96319e17 q^{49} -2.37225e17 q^{50} +1.38112e18 q^{52} +3.61502e17 q^{53} +3.09736e18 q^{55} +1.59673e18 q^{56} +3.64583e17 q^{58} +3.75725e18 q^{59} +2.15687e18 q^{61} -7.85248e17 q^{62} -6.74425e18 q^{64} +2.42823e19 q^{65} +2.35787e19 q^{67} +1.09053e19 q^{68} +1.37017e19 q^{70} +5.47019e19 q^{71} -2.31502e19 q^{73} -2.21602e18 q^{74} -3.70324e19 q^{76} -1.09868e20 q^{77} -9.38404e19 q^{79} -1.33333e20 q^{80} +4.56849e18 q^{82} +1.28419e20 q^{83} +1.91732e20 q^{85} -6.66207e18 q^{86} -1.12826e20 q^{88} +2.53773e20 q^{89} -8.61329e20 q^{91} +1.36592e20 q^{92} +1.30981e20 q^{94} -6.51088e20 q^{95} +5.53931e20 q^{97} -3.11429e20 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 1023 q^{2} + 19922945 q^{4} - 32234853 q^{5} + 189623959 q^{7} - 648135831 q^{8}+O(q^{10}) \) 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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