LMFDB - Embedded newform 81.22.a.c.1.8

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			1.8
Root			$690.831$ 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)

$f(q)$	$=$	$q-741.831 q^{2} -1.54684e6 q^{4} +4.52810e6 q^{5} +1.01033e9 q^{7} +2.70323e9 q^{8} +O(q^{10})$	\(q-741.831 q^{2} -1.54684e6 q^{4} +4.52810e6 q^{5} +1.01033e9 q^{7} +2.70323e9 q^{8} -3.35909e9 q^{10} +1.02731e11 q^{11} +7.42741e11 q^{13} -7.49494e11 q^{14} +1.23862e12 q^{16} -1.18565e13 q^{17} +1.26218e13 q^{19} -7.00425e12 q^{20} -7.62087e13 q^{22} -1.31405e14 q^{23} -4.56333e14 q^{25} -5.50988e14 q^{26} -1.56282e15 q^{28} +2.03142e15 q^{29} -6.48553e15 q^{31} -6.58792e15 q^{32} +8.79551e15 q^{34} +4.57488e15 q^{35} +7.04380e14 q^{37} -9.36324e15 q^{38} +1.22405e16 q^{40} -1.12954e17 q^{41} -1.55432e17 q^{43} -1.58908e17 q^{44} +9.74806e16 q^{46} -3.26075e17 q^{47} +4.62222e17 q^{49} +3.38522e17 q^{50} -1.14890e18 q^{52} +1.06991e18 q^{53} +4.65175e17 q^{55} +2.73115e18 q^{56} -1.50697e18 q^{58} +1.51836e18 q^{59} +5.39606e18 q^{61} +4.81117e18 q^{62} +2.28955e18 q^{64} +3.36321e18 q^{65} -8.19132e18 q^{67} +1.83401e19 q^{68} -3.39379e18 q^{70} -2.08920e19 q^{71} +1.07276e19 q^{73} -5.22531e17 q^{74} -1.95239e19 q^{76} +1.03792e20 q^{77} -1.25979e20 q^{79} +5.60860e18 q^{80} +8.37929e19 q^{82} -2.09635e20 q^{83} -5.36874e19 q^{85} +1.15305e20 q^{86} +2.77704e20 q^{88} -2.23673e20 q^{89} +7.50414e20 q^{91} +2.03263e20 q^{92} +2.41892e20 q^{94} +5.71528e19 q^{95} -8.96523e20 q^{97} -3.42890e20 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−741.831	−0.512259	−0.256130	−	0.966642i	$-0.582447\pi$
$2$	−741.831	−0.512259	−0.256130	+	0.966642i	$0.582447\pi$
$3$	0	0
$3$	0	0
$4$	−1.54684e6	−0.737590
$5$	4.52810e6	0.207363	0.103682	−	0.994611i	$-0.466938\pi$
$5$	4.52810e6	0.207363	0.103682	+	0.994611i	$0.466938\pi$
$6$	0	0
$7$	1.01033e9	1.35187	0.675934	−	0.736963i	$-0.263741\pi$
$7$	1.01033e9	1.35187	0.675934	+	0.736963i	$0.263741\pi$
$8$	2.70323e9	0.890097
$9$	0	0
$10$	−3.35909e9	−0.106224
$11$	1.02731e11	1.19420	0.597099	−	0.802167i	$-0.296320\pi$
$11$	1.02731e11	1.19420	0.597099	+	0.802167i	$0.296320\pi$
$12$	0	0
$13$	7.42741e11	1.49428	0.747140	−	0.664667i	$-0.231426\pi$
$13$	7.42741e11	1.49428	0.747140	+	0.664667i	$0.231426\pi$
$14$	−7.49494e11	−0.692507
$15$	0	0
$16$	1.23862e12	0.281630
$17$	−1.18565e13	−1.42640	−0.713201	−	0.700959i	$-0.752756\pi$
$17$	−1.18565e13	−1.42640	−0.713201	+	0.700959i	$0.752756\pi$
$18$	0	0
$19$	1.26218e13	0.472290	0.236145	−	0.971718i	$-0.424116\pi$
$19$	1.26218e13	0.472290	0.236145	+	0.971718i	$0.424116\pi$
$20$	−7.00425e12	−0.152949
$21$	0	0
$22$	−7.62087e13	−0.611740
$23$	−1.31405e14	−0.661410	−0.330705	−	0.943734i	$-0.607287\pi$
$23$	−1.31405e14	−0.661410	−0.330705	+	0.943734i	$0.607287\pi$
$24$	0	0
$25$	−4.56333e14	−0.957001
$26$	−5.50988e14	−0.765459
$27$	0	0
$28$	−1.56282e15	−0.997124
$29$	2.03142e15	0.896645	0.448323	−	0.893872i	$-0.352022\pi$
$29$	2.03142e15	0.896645	0.448323	+	0.893872i	$0.352022\pi$
$30$	0	0
$31$	−6.48553e15	−1.42118	−0.710588	−	0.703608i	$-0.751571\pi$
$31$	−6.48553e15	−1.42118	−0.710588	+	0.703608i	$0.751571\pi$
$32$	−6.58792e15	−1.03436
$33$	0	0
$34$	8.79551e15	0.730688
$35$	4.57488e15	0.280327
$36$	0	0
$37$	7.04380e14	0.0240818	0.0120409	−	0.999928i	$-0.496167\pi$
$37$	7.04380e14	0.0240818	0.0120409	+	0.999928i	$0.496167\pi$
$38$	−9.36324e15	−0.241935
$39$	0	0
$40$	1.22405e16	0.184573
$41$	−1.12954e17	−1.31423	−0.657115	−	0.753790i	$-0.728224\pi$
$41$	−1.12954e17	−1.31423	−0.657115	+	0.753790i	$0.728224\pi$
$42$	0	0
$43$	−1.55432e17	−1.09679	−0.548394	−	0.836220i	$-0.684761\pi$
$43$	−1.55432e17	−1.09679	−0.548394	+	0.836220i	$0.684761\pi$
$44$	−1.58908e17	−0.880829
$45$	0	0
$46$	9.74806e16	0.338814
$47$	−3.26075e17	−0.904253	−0.452126	−	0.891954i	$-0.649334\pi$
$47$	−3.26075e17	−0.904253	−0.452126	+	0.891954i	$0.649334\pi$
$48$	0	0
$49$	4.62222e17	0.827545
$50$	3.38522e17	0.490233
$51$	0	0
$52$	−1.14890e18	−1.10217
$53$	1.06991e18	0.840332	0.420166	−	0.907447i	$-0.361972\pi$
$53$	1.06991e18	0.840332	0.420166	+	0.907447i	$0.361972\pi$
$54$	0	0
$55$	4.65175e17	0.247633
$56$	2.73115e18	1.20329
$57$	0	0
$58$	−1.50697e18	−0.459315
$59$	1.51836e18	0.386749	0.193374	−	0.981125i	$-0.438057\pi$
$59$	1.51836e18	0.386749	0.193374	+	0.981125i	$0.438057\pi$
$60$	0	0
$61$	5.39606e18	0.968532	0.484266	−	0.874921i	$-0.339087\pi$
$61$	5.39606e18	0.968532	0.484266	+	0.874921i	$0.339087\pi$
$62$	4.81117e18	0.728011
$63$	0	0
$64$	2.28955e18	0.248233
$65$	3.36321e18	0.309858
$66$	0	0
$67$	−8.19132e18	−0.548995	−0.274497	−	0.961588i	$-0.588511\pi$
$67$	−8.19132e18	−0.548995	−0.274497	+	0.961588i	$0.588511\pi$
$68$	1.83401e19	1.05210
$69$	0	0
$70$	−3.39379e18	−0.143600
$71$	−2.08920e19	−0.761671	−0.380835	−	0.924643i	$-0.624364\pi$
$71$	−2.08920e19	−0.761671	−0.380835	+	0.924643i	$0.624364\pi$
$72$	0	0
$73$	1.07276e19	0.292154	0.146077	−	0.989273i	$-0.453335\pi$
$73$	1.07276e19	0.292154	0.146077	+	0.989273i	$0.453335\pi$
$74$	−5.22531e17	−0.0123361
$75$	0	0
$76$	−1.95239e19	−0.348356
$77$	1.03792e20	1.61440
$78$	0	0
$79$	−1.25979e20	−1.49697	−0.748487	−	0.663149i	$-0.769220\pi$
$79$	−1.25979e20	−1.49697	−0.748487	+	0.663149i	$0.769220\pi$
$80$	5.60860e18	0.0583996
$81$	0	0
$82$	8.37929e19	0.673227
$83$	−2.09635e20	−1.48301	−0.741503	−	0.670949i	$-0.765887\pi$
$83$	−2.09635e20	−1.48301	−0.741503	+	0.670949i	$0.765887\pi$
$84$	0	0
$85$	−5.36874e19	−0.295783
$86$	1.15305e20	0.561840
$87$	0	0
$88$	2.77704e20	1.06295
$89$	−2.23673e20	−0.760359	−0.380180	−	0.924913i	$-0.624138\pi$
$89$	−2.23673e20	−0.760359	−0.380180	+	0.924913i	$0.624138\pi$
$90$	0	0
$91$	7.50414e20	2.02007
$92$	2.03263e20	0.487850
$93$	0	0
$94$	2.41892e20	0.463212
$95$	5.71528e19	0.0979354
$96$	0	0
$97$	−8.96523e20	−1.23441	−0.617203	−	0.786804i	$-0.711734\pi$
$97$	−8.96523e20	−1.23441	−0.617203	+	0.786804i	$0.711734\pi$
$98$	−3.42890e20	−0.423918
$99$	0	0
$100$	7.05874e20	0.705874
$101$	−4.04734e20	−0.364582	−0.182291	−	0.983245i	$-0.558351\pi$
$101$	−4.04734e20	−0.364582	−0.182291	+	0.983245i	$0.558351\pi$
$102$	0	0
$103$	−1.90573e21	−1.39723	−0.698617	−	0.715495i	$-0.746201\pi$
$103$	−1.90573e21	−1.39723	−0.698617	+	0.715495i	$0.746201\pi$
$104$	2.00780e21	1.33005
$105$	0	0
$106$	−7.93693e20	−0.430468
$107$	−2.48386e20	−0.122067	−0.0610333	−	0.998136i	$-0.519440\pi$
$107$	−2.48386e20	−0.122067	−0.0610333	+	0.998136i	$0.519440\pi$
$108$	0	0
$109$	1.24903e21	0.505353	0.252677	−	0.967551i	$-0.418689\pi$
$109$	1.24903e21	0.505353	0.252677	+	0.967551i	$0.418689\pi$
$110$	−3.45081e20	−0.126852
$111$	0	0
$112$	1.25142e21	0.380726
$113$	1.63792e21	0.453909	0.226954	−	0.973905i	$-0.427123\pi$
$113$	1.63792e21	0.453909	0.226954	+	0.973905i	$0.427123\pi$
$114$	0	0
$115$	−5.95017e20	−0.137152
$116$	−3.14228e21	−0.661357
$117$	0	0
$118$	−1.12637e21	−0.198116
$119$	−1.19790e22	−1.92831
$120$	0	0
$121$	3.15332e21	0.426110
$122$	−4.00297e21	−0.496139
$123$	0	0
$124$	1.00321e22	1.04825
$125$	−4.22549e21	−0.405810
$126$	0	0
$127$	1.14930e22	0.934314	0.467157	−	0.884174i	$-0.345278\pi$
$127$	1.14930e22	0.934314	0.467157	+	0.884174i	$0.345278\pi$
$128$	1.21174e22	0.907205
$129$	0	0
$130$	−2.49493e21	−0.158728
$131$	−1.18605e22	−0.696231	−0.348116	−	0.937452i	$-0.613178\pi$
$131$	−1.18605e22	−0.696231	−0.348116	+	0.937452i	$0.613178\pi$
$132$	0	0
$133$	1.27522e22	0.638473
$134$	6.07657e21	0.281228
$135$	0	0
$136$	−3.20507e22	−1.26964
$137$	4.48355e22	1.64458	0.822291	−	0.569067i	$-0.192695\pi$
$137$	4.48355e22	1.64458	0.822291	+	0.569067i	$0.192695\pi$
$138$	0	0
$139$	4.43192e22	1.39616	0.698082	−	0.716018i	$-0.254037\pi$
$139$	4.43192e22	1.39616	0.698082	+	0.716018i	$0.254037\pi$
$140$	−7.07660e21	−0.206767
$141$	0	0
$142$	1.54983e22	0.390173
$143$	7.63022e22	1.78447
$144$	0	0
$145$	9.19848e21	0.185931
$146$	−7.95806e21	−0.149659
$147$	0	0
$148$	−1.08956e21	−0.0177625
$149$	−7.10501e22	−1.07922	−0.539609	−	0.841916i	$-0.681428\pi$
$149$	−7.10501e22	−1.07922	−0.539609	+	0.841916i	$0.681428\pi$
$150$	0	0
$151$	1.07587e22	0.142070	0.0710351	−	0.997474i	$-0.477370\pi$
$151$	1.07587e22	0.142070	0.0710351	+	0.997474i	$0.477370\pi$
$152$	3.41196e22	0.420384
$153$	0	0
$154$	−7.69960e22	−0.826991
$155$	−2.93672e22	−0.294699
$156$	0	0
$157$	7.66567e22	0.672363	0.336182	−	0.941797i	$-0.390864\pi$
$157$	7.66567e22	0.672363	0.336182	+	0.941797i	$0.390864\pi$
$158$	9.34553e22	0.766839
$159$	0	0
$160$	−2.98308e22	−0.214489
$161$	−1.32763e23	−0.894139
$162$	0	0
$163$	4.25220e22	0.251561	0.125781	−	0.992058i	$-0.459856\pi$
$163$	4.25220e22	0.251561	0.125781	+	0.992058i	$0.459856\pi$
$164$	1.74722e23	0.969364
$165$	0	0
$166$	1.55513e23	0.759684
$167$	−2.27698e23	−1.04433	−0.522163	−	0.852846i	$-0.674875\pi$
$167$	−2.27698e23	−1.04433	−0.522163	+	0.852846i	$0.674875\pi$
$168$	0	0
$169$	3.04599e23	1.23287
$170$	3.98270e22	0.151518
$171$	0	0
$172$	2.40429e23	0.808980
$173$	−4.19413e23	−1.32788	−0.663939	−	0.747787i	$-0.731116\pi$
$173$	−4.19413e23	−1.32788	−0.663939	+	0.747787i	$0.731116\pi$
$174$	0	0
$175$	−4.61048e23	−1.29374
$176$	1.27244e23	0.336322
$177$	0	0
$178$	1.65928e23	0.389501
$179$	−7.94323e23	−1.75809	−0.879044	−	0.476741i	$-0.841818\pi$
$179$	−7.94323e23	−1.75809	−0.879044	+	0.476741i	$0.841818\pi$
$180$	0	0
$181$	−2.16814e22	−0.0427034	−0.0213517	−	0.999772i	$-0.506797\pi$
$181$	−2.16814e22	−0.0427034	−0.0213517	+	0.999772i	$0.506797\pi$
$182$	−5.56680e23	−1.03480
$183$	0	0
$184$	−3.55218e23	−0.588719
$185$	3.18950e21	0.00499367
$186$	0	0
$187$	−1.21802e24	−1.70341
$188$	5.04385e23	0.666968
$189$	0	0
$190$	−4.23977e22	−0.0501683
$191$	4.11512e23	0.460821	0.230411	−	0.973094i	$-0.425993\pi$
$191$	4.11512e23	0.460821	0.230411	+	0.973094i	$0.425993\pi$
$192$	0	0
$193$	3.96731e23	0.398240	0.199120	−	0.979975i	$-0.436192\pi$
$193$	3.96731e23	0.398240	0.199120	+	0.979975i	$0.436192\pi$
$194$	6.65069e23	0.632337
$195$	0	0
$196$	−7.14983e23	−0.610389
$197$	−1.24453e24	−1.00719	−0.503595	−	0.863940i	$-0.667990\pi$
$197$	−1.24453e24	−1.00719	−0.503595	+	0.863940i	$0.667990\pi$
$198$	0	0
$199$	2.10803e24	1.53433	0.767167	−	0.641447i	$-0.221666\pi$
$199$	2.10803e24	1.53433	0.767167	+	0.641447i	$0.221666\pi$
$200$	−1.23357e24	−0.851823
$201$	0	0
$202$	3.00244e23	0.186760
$203$	2.05240e24	1.21215
$204$	0	0
$205$	−5.11468e23	−0.272523
$206$	1.41373e24	0.715747
$207$	0	0
$208$	9.19974e23	0.420834
$209$	1.29664e24	0.564008
$210$	0	0
$211$	−1.82020e24	−0.716398	−0.358199	−	0.933645i	$-0.616609\pi$
$211$	−1.82020e24	−0.716398	−0.358199	+	0.933645i	$0.616609\pi$
$212$	−1.65498e24	−0.619821
$213$	0	0
$214$	1.84260e23	0.0625298
$215$	−7.03814e23	−0.227433
$216$	0	0
$217$	−6.55253e24	−1.92124
$218$	−9.26570e23	−0.258872
$219$	0	0
$220$	−7.19550e23	−0.182651
$221$	−8.80629e24	−2.13145
$222$	0	0
$223$	2.88268e24	0.634738	0.317369	−	0.948302i	$-0.397201\pi$
$223$	2.88268e24	0.634738	0.317369	+	0.948302i	$0.397201\pi$
$224$	−6.65598e24	−1.39832
$225$	0	0
$226$	−1.21506e24	−0.232519
$227$	−3.16940e24	−0.579036	−0.289518	−	0.957173i	$-0.593495\pi$
$227$	−3.16940e24	−0.579036	−0.289518	+	0.957173i	$0.593495\pi$
$228$	0	0
$229$	−3.15880e24	−0.526320	−0.263160	−	0.964752i	$-0.584765\pi$
$229$	−3.15880e24	−0.526320	−0.263160	+	0.964752i	$0.584765\pi$
$230$	4.41402e23	0.0702574
$231$	0	0
$232$	5.49138e24	0.798101
$233$	6.04545e24	0.839830	0.419915	−	0.907563i	$-0.362060\pi$
$233$	6.04545e24	0.839830	0.419915	+	0.907563i	$0.362060\pi$
$234$	0	0
$235$	−1.47650e24	−0.187509
$236$	−2.34866e24	−0.285262
$237$	0	0
$238$	8.88637e24	0.987794
$239$	3.23426e23	0.0344031	0.0172015	−	0.999852i	$-0.494524\pi$
$239$	3.23426e23	0.0344031	0.0172015	+	0.999852i	$0.494524\pi$
$240$	0	0
$241$	−1.18018e25	−1.15019	−0.575096	−	0.818086i	$-0.695035\pi$
$241$	−1.18018e25	−1.15019	−0.575096	+	0.818086i	$0.695035\pi$
$242$	−2.33923e24	−0.218279
$243$	0	0
$244$	−8.34684e24	−0.714379
$245$	2.09299e24	0.171602
$246$	0	0
$247$	9.37472e24	0.705733
$248$	−1.75319e25	−1.26498
$249$	0	0
$250$	3.13460e24	0.207880
$251$	−6.92669e24	−0.440506	−0.220253	−	0.975443i	$-0.570688\pi$
$251$	−6.92669e24	−0.440506	−0.220253	+	0.975443i	$0.570688\pi$
$252$	0	0
$253$	−1.34993e25	−0.789855
$254$	−8.52583e24	−0.478611
$255$	0	0
$256$	−1.37906e25	−0.712957
$257$	−2.43846e25	−1.21009	−0.605046	−	0.796191i	$-0.706845\pi$
$257$	−2.43846e25	−1.21009	−0.605046	+	0.796191i	$0.706845\pi$
$258$	0	0
$259$	7.11656e23	0.0325554
$260$	−5.20234e24	−0.228549
$261$	0	0
$262$	8.79847e24	0.356651
$263$	−1.58491e25	−0.617261	−0.308631	−	0.951182i	$-0.599871\pi$
$263$	−1.58491e25	−0.617261	−0.308631	+	0.951182i	$0.599871\pi$
$264$	0	0
$265$	4.84467e24	0.174254
$266$	−9.45997e24	−0.327064
$267$	0	0
$268$	1.26706e25	0.404933
$269$	−2.84423e25	−0.874110	−0.437055	−	0.899435i	$-0.643978\pi$
$269$	−2.84423e25	−0.874110	−0.437055	+	0.899435i	$0.643978\pi$
$270$	0	0
$271$	4.48162e25	1.27426	0.637129	−	0.770757i	$-0.280122\pi$
$271$	4.48162e25	1.27426	0.637129	+	0.770757i	$0.280122\pi$
$272$	−1.46857e25	−0.401717
$273$	0	0
$274$	−3.32603e25	−0.842453
$275$	−4.68794e25	−1.14285
$276$	0	0
$277$	2.55923e25	0.578191	0.289096	−	0.957300i	$-0.406645\pi$
$277$	2.55923e25	0.578191	0.289096	+	0.957300i	$0.406645\pi$
$278$	−3.28774e25	−0.715199
$279$	0	0
$280$	1.23669e25	0.249518
$281$	−7.50185e25	−1.45798	−0.728991	−	0.684523i	$-0.760010\pi$
$281$	−7.50185e25	−1.45798	−0.728991	+	0.684523i	$0.760010\pi$
$282$	0	0
$283$	9.43219e25	1.70159	0.850795	−	0.525498i	$-0.176121\pi$
$283$	9.43219e25	1.70159	0.850795	+	0.525498i	$0.176121\pi$
$284$	3.23166e25	0.561801
$285$	0	0
$286$	−5.66033e25	−0.914110
$287$	−1.14121e26	−1.77667
$288$	0	0
$289$	7.14843e25	1.03463
$290$	−6.82371e24	−0.0952449
$291$	0	0
$292$	−1.65939e25	−0.215490
$293$	1.36527e26	1.71044	0.855219	−	0.518267i	$-0.173423\pi$
$293$	1.36527e26	1.71044	0.855219	+	0.518267i	$0.173423\pi$
$294$	0	0
$295$	6.87529e24	0.0801974
$296$	1.90410e24	0.0214351
$297$	0	0
$298$	5.27072e25	0.552839
$299$	−9.76001e25	−0.988332
$300$	0	0
$301$	−1.57038e26	−1.48271
$302$	−7.98115e24	−0.0727768
$303$	0	0
$304$	1.56336e25	0.133011
$305$	2.44339e25	0.200838
$306$	0	0
$307$	−1.56009e26	−1.19728	−0.598641	−	0.801017i	$-0.704292\pi$
$307$	−1.56009e26	−1.19728	−0.598641	+	0.801017i	$0.704292\pi$
$308$	−1.60549e26	−1.19076
$309$	0	0
$310$	2.17855e25	0.150963
$311$	−2.45639e26	−1.64556	−0.822780	−	0.568360i	$-0.807578\pi$
$311$	−2.45639e26	−1.64556	−0.822780	+	0.568360i	$0.807578\pi$
$312$	0	0
$313$	−9.13635e25	−0.572212	−0.286106	−	0.958198i	$-0.592361\pi$
$313$	−9.13635e25	−0.572212	−0.286106	+	0.958198i	$0.592361\pi$
$314$	−5.68663e25	−0.344424
$315$	0	0
$316$	1.94870e26	1.10415
$317$	2.84345e26	1.55856	0.779280	−	0.626676i	$-0.215585\pi$
$317$	2.84345e26	1.55856	0.779280	+	0.626676i	$0.215585\pi$
$318$	0	0
$319$	2.08689e26	1.07077
$320$	1.03673e25	0.0514744
$321$	0	0
$322$	9.84876e25	0.458031
$323$	−1.49650e26	−0.673675
$324$	0	0
$325$	−3.38937e26	−1.43003
$326$	−3.15441e25	−0.128865
$327$	0	0
$328$	−3.05340e26	−1.16979
$329$	−3.29443e26	−1.22243
$330$	0	0
$331$	1.85942e26	0.647415	0.323707	−	0.946157i	$-0.395071\pi$
$331$	1.85942e26	0.647415	0.323707	+	0.946157i	$0.395071\pi$
$332$	3.24271e26	1.09385
$333$	0	0
$334$	1.68913e26	0.534966
$335$	−3.70911e25	−0.113841
$336$	0	0
$337$	4.32007e26	1.24559	0.622797	−	0.782383i	$-0.285996\pi$
$337$	4.32007e26	1.24559	0.622797	+	0.782383i	$0.285996\pi$
$338$	−2.25961e26	−0.631551
$339$	0	0
$340$	8.30457e25	0.218167
$341$	−6.66263e26	−1.69717
$342$	0	0
$343$	−9.73192e25	−0.233136
$344$	−4.20169e26	−0.976247
$345$	0	0
$346$	3.11134e26	0.680218
$347$	−8.47485e26	−1.79752	−0.898758	−	0.438445i	$-0.855529\pi$
$347$	−8.47485e26	−1.79752	−0.898758	+	0.438445i	$0.855529\pi$
$348$	0	0
$349$	−6.56582e26	−1.31106	−0.655530	−	0.755170i	$-0.727555\pi$
$349$	−6.56582e26	−1.31106	−0.655530	+	0.755170i	$0.727555\pi$
$350$	3.42019e26	0.662729
$351$	0	0
$352$	−6.76781e26	−1.23524
$353$	−4.17419e26	−0.739500	−0.369750	−	0.929131i	$-0.620557\pi$
$353$	−4.17419e26	−0.739500	−0.369750	+	0.929131i	$0.620557\pi$
$354$	0	0
$355$	−9.46011e25	−0.157942
$356$	3.45986e26	0.560834
$357$	0	0
$358$	5.89254e26	0.900597
$359$	−2.22280e26	−0.329920	−0.164960	−	0.986300i	$-0.552749\pi$
$359$	−2.22280e26	−0.329920	−0.164960	+	0.986300i	$0.552749\pi$
$360$	0	0
$361$	−5.54900e26	−0.776943
$362$	1.60839e25	0.0218752
$363$	0	0
$364$	−1.16077e27	−1.48998
$365$	4.85757e25	0.0605820
$366$	0	0
$367$	1.23955e26	0.145972	0.0729860	−	0.997333i	$-0.476747\pi$
$367$	1.23955e26	0.145972	0.0729860	+	0.997333i	$0.476747\pi$
$368$	−1.62761e26	−0.186273
$369$	0	0
$370$	−2.36607e24	−0.00255806
$371$	1.08096e27	1.13602
$372$	0	0
$373$	−1.47998e26	−0.146999	−0.0734993	−	0.997295i	$-0.523417\pi$
$373$	−1.47998e26	−0.146999	−0.0734993	+	0.997295i	$0.523417\pi$
$374$	9.03567e26	0.872587
$375$	0	0
$376$	−8.81454e26	−0.804873
$377$	1.50882e27	1.33984
$378$	0	0
$379$	2.85402e26	0.239742	0.119871	−	0.992789i	$-0.461752\pi$
$379$	2.85402e26	0.239742	0.119871	+	0.992789i	$0.461752\pi$
$380$	−8.84062e25	−0.0722362
$381$	0	0
$382$	−3.05272e26	−0.236060
$383$	1.32928e27	1.00006	0.500032	−	0.866007i	$-0.333321\pi$
$383$	1.32928e27	1.00006	0.500032	+	0.866007i	$0.333321\pi$
$384$	0	0
$385$	4.69980e26	0.334766
$386$	−2.94307e26	−0.204002
$387$	0	0
$388$	1.38678e27	0.910486
$389$	2.52780e27	1.61537	0.807684	−	0.589616i	$-0.200721\pi$
$389$	2.52780e27	1.61537	0.807684	+	0.589616i	$0.200721\pi$
$390$	0	0
$391$	1.55801e27	0.943437
$392$	1.24949e27	0.736595
$393$	0	0
$394$	9.23234e26	0.515942
$395$	−5.70447e26	−0.310417
$396$	0	0
$397$	3.42058e27	1.76522	0.882612	−	0.470102i	$-0.155783\pi$
$397$	3.42058e27	1.76522	0.882612	+	0.470102i	$0.155783\pi$
$398$	−1.56380e27	−0.785977
$399$	0	0
$400$	−5.65224e26	−0.269520
$401$	3.30849e26	0.153679	0.0768394	−	0.997043i	$-0.475517\pi$
$401$	3.30849e26	0.153679	0.0768394	+	0.997043i	$0.475517\pi$
$402$	0	0
$403$	−4.81707e27	−2.12364
$404$	6.26058e26	0.268912
$405$	0	0
$406$	−1.52254e27	−0.620933
$407$	7.23613e25	0.0287584
$408$	0	0
$409$	−1.48907e27	−0.562107	−0.281054	−	0.959692i	$-0.590684\pi$
$409$	−1.48907e27	−0.562107	−0.281054	+	0.959692i	$0.590684\pi$
$410$	3.79423e26	0.139602
$411$	0	0
$412$	2.94785e27	1.03059
$413$	1.53405e27	0.522833
$414$	0	0
$415$	−9.49247e26	−0.307521
$416$	−4.89312e27	−1.54563
$417$	0	0
$418$	−9.61891e26	−0.288918
$419$	4.26583e27	1.24956	0.624778	−	0.780802i	$-0.285189\pi$
$419$	4.26583e27	1.24956	0.624778	+	0.780802i	$0.285189\pi$
$420$	0	0
$421$	−2.73428e27	−0.761870	−0.380935	−	0.924602i	$-0.624398\pi$
$421$	−2.73428e27	−0.761870	−0.380935	+	0.924602i	$0.624398\pi$
$422$	1.35028e27	0.366981
$423$	0	0
$424$	2.89221e27	0.747977
$425$	5.41051e27	1.36507
$426$	0	0
$427$	5.45181e27	1.30933
$428$	3.84213e26	0.0900352
$429$	0	0
$430$	5.22111e26	0.116505
$431$	−2.23842e27	−0.487450	−0.243725	−	0.969844i	$-0.578369\pi$
$431$	−2.23842e27	−0.487450	−0.243725	+	0.969844i	$0.578369\pi$
$432$	0	0
$433$	−3.97149e27	−0.823817	−0.411909	−	0.911225i	$-0.635138\pi$
$433$	−3.97149e27	−0.823817	−0.411909	+	0.911225i	$0.635138\pi$
$434$	4.86087e27	0.984174
$435$	0	0
$436$	−1.93205e27	−0.372744
$437$	−1.65857e27	−0.312377
$438$	0	0
$439$	8.39564e27	1.50722	0.753609	−	0.657323i	$-0.228311\pi$
$439$	8.39564e27	1.50722	0.753609	+	0.657323i	$0.228311\pi$
$440$	1.25747e27	0.220417
$441$	0	0
$442$	6.53278e27	1.09185
$443$	6.40200e27	1.04490	0.522452	−	0.852668i	$-0.325017\pi$
$443$	6.40200e27	1.04490	0.522452	+	0.852668i	$0.325017\pi$
$444$	0	0
$445$	−1.01282e27	−0.157670
$446$	−2.13846e27	−0.325151
$447$	0	0
$448$	2.31320e27	0.335579
$449$	1.07791e28	1.52755	0.763775	−	0.645483i	$-0.223344\pi$
$449$	1.07791e28	1.52755	0.763775	+	0.645483i	$0.223344\pi$
$450$	0	0
$451$	−1.16038e28	−1.56945
$452$	−2.53360e27	−0.334799
$453$	0	0
$454$	2.35116e27	0.296616
$455$	3.39795e27	0.418887
$456$	0	0
$457$	8.94205e27	1.05273	0.526365	−	0.850259i	$-0.323555\pi$
$457$	8.94205e27	1.05273	0.526365	+	0.850259i	$0.323555\pi$
$458$	2.34330e27	0.269612
$459$	0	0
$460$	9.20396e26	0.101162
$461$	6.67509e27	0.717129	0.358564	−	0.933505i	$-0.383266\pi$
$461$	6.67509e27	0.717129	0.358564	+	0.933505i	$0.383266\pi$
$462$	0	0
$463$	6.07852e27	0.624018	0.312009	−	0.950079i	$-0.398998\pi$
$463$	6.07852e27	0.624018	0.312009	+	0.950079i	$0.398998\pi$
$464$	2.51616e27	0.252522
$465$	0	0
$466$	−4.48470e27	−0.430211
$467$	−6.21286e26	−0.0582726	−0.0291363	−	0.999575i	$-0.509276\pi$
$467$	−6.21286e26	−0.0582726	−0.0291363	+	0.999575i	$0.509276\pi$
$468$	0	0
$469$	−8.27594e27	−0.742168
$470$	1.09531e27	0.0960530
$471$	0	0
$472$	4.10447e27	0.344244
$473$	−1.59677e28	−1.30978
$474$	0	0
$475$	−5.75975e27	−0.451981
$476$	1.85295e28	1.42230
$477$	0	0
$478$	−2.39928e26	−0.0176233
$479$	1.32197e26	0.00949942	0.00474971	−	0.999989i	$-0.498488\pi$
$479$	1.32197e26	0.00949942	0.00474971	+	0.999989i	$0.498488\pi$
$480$	0	0
$481$	5.23171e26	0.0359849
$482$	8.75496e27	0.589196
$483$	0	0
$484$	−4.87768e27	−0.314295
$485$	−4.05955e27	−0.255970
$486$	0	0
$487$	1.20180e28	0.725734	0.362867	−	0.931841i	$-0.381798\pi$
$487$	1.20180e28	0.725734	0.362867	+	0.931841i	$0.381798\pi$
$488$	1.45868e28	0.862087
$489$	0	0
$490$	−1.55264e27	−0.0879049
$491$	1.70302e28	0.943765	0.471882	−	0.881662i	$-0.343575\pi$
$491$	1.70302e28	0.943765	0.471882	+	0.881662i	$0.343575\pi$
$492$	0	0
$493$	−2.40855e28	−1.27898
$494$	−6.95446e27	−0.361518
$495$	0	0
$496$	−8.03311e27	−0.400245
$497$	−2.11078e28	−1.02968
$498$	0	0
$499$	−1.10316e28	−0.515921	−0.257960	−	0.966155i	$-0.583050\pi$
$499$	−1.10316e28	−0.515921	−0.257960	+	0.966155i	$0.583050\pi$
$500$	6.53616e27	0.299321
$501$	0	0
$502$	5.13844e27	0.225653
$503$	−4.92022e27	−0.211602	−0.105801	−	0.994387i	$-0.533741\pi$
$503$	−4.92022e27	−0.211602	−0.105801	+	0.994387i	$0.533741\pi$
$504$	0	0
$505$	−1.83268e27	−0.0756008
$506$	1.00142e28	0.404611
$507$	0	0
$508$	−1.77778e28	−0.689141
$509$	−2.35381e28	−0.893789	−0.446894	−	0.894587i	$-0.647470\pi$
$509$	−2.35381e28	−0.893789	−0.446894	+	0.894587i	$0.647470\pi$
$510$	0	0
$511$	1.08384e28	0.394954
$512$	−1.51818e28	−0.541985
$513$	0	0
$514$	1.80893e28	0.619881
$515$	−8.62932e27	−0.289735
$516$	0	0
$517$	−3.34979e28	−1.07986
$518$	−5.27929e26	−0.0166768
$519$	0	0
$520$	9.09151e27	0.275804
$521$	−2.36824e28	−0.704091	−0.352046	−	0.935983i	$-0.614514\pi$
$521$	−2.36824e28	−0.704091	−0.352046	+	0.935983i	$0.614514\pi$
$522$	0	0
$523$	1.27206e28	0.363278	0.181639	−	0.983365i	$-0.441860\pi$
$523$	1.27206e28	0.363278	0.181639	+	0.983365i	$0.441860\pi$
$524$	1.83462e28	0.513533
$525$	0	0
$526$	1.17573e28	0.316198
$527$	7.68956e28	2.02717
$528$	0	0
$529$	−2.22042e28	−0.562537
$530$	−3.59392e27	−0.0892632
$531$	0	0
$532$	−1.97256e28	−0.470931
$533$	−8.38956e28	−1.96383
$534$	0	0
$535$	−1.12472e27	−0.0253121
$536$	−2.21430e28	−0.488659
$537$	0	0
$538$	2.10994e28	0.447771
$539$	4.74843e28	0.988253
$540$	0	0
$541$	5.60089e28	1.12121	0.560604	−	0.828084i	$-0.310569\pi$
$541$	5.60089e28	1.12121	0.560604	+	0.828084i	$0.310569\pi$
$542$	−3.32460e28	−0.652750
$543$	0	0
$544$	7.81096e28	1.47542
$545$	5.65574e27	0.104792
$546$	0	0
$547$	−3.02308e28	−0.538993	−0.269497	−	0.963001i	$-0.586857\pi$
$547$	−3.02308e28	−0.538993	−0.269497	+	0.963001i	$0.586857\pi$
$548$	−6.93532e28	−1.21303
$549$	0	0
$550$	3.47766e28	0.585435
$551$	2.56402e28	0.423476
$552$	0	0
$553$	−1.27281e29	−2.02371
$554$	−1.89851e28	−0.296184
$555$	0	0
$556$	−6.85547e28	−1.02980
$557$	−7.95003e28	−1.17190	−0.585948	−	0.810349i	$-0.699278\pi$
$557$	−7.95003e28	−1.17190	−0.585948	+	0.810349i	$0.699278\pi$
$558$	0	0
$559$	−1.15446e29	−1.63891
$560$	5.66654e27	0.0789485
$561$	0	0
$562$	5.56511e28	0.746865
$563$	−1.32050e29	−1.73940	−0.869701	−	0.493578i	$-0.835689\pi$
$563$	−1.32050e29	−1.73940	−0.869701	+	0.493578i	$0.835689\pi$
$564$	0	0
$565$	7.41666e27	0.0941239
$566$	−6.99709e28	−0.871655
$567$	0	0
$568$	−5.64758e28	−0.677961
$569$	−9.10488e28	−1.07299	−0.536495	−	0.843904i	$-0.680252\pi$
$569$	−9.10488e28	−1.07299	−0.536495	+	0.843904i	$0.680252\pi$
$570$	0	0
$571$	1.20863e29	1.37282	0.686408	−	0.727216i	$-0.259186\pi$
$571$	1.20863e29	1.37282	0.686408	+	0.727216i	$0.259186\pi$
$572$	−1.18027e29	−1.31621
$573$	0	0
$574$	8.46585e28	0.910114
$575$	5.99647e28	0.632970
$576$	0	0
$577$	1.19037e29	1.21153	0.605766	−	0.795643i	$-0.292867\pi$
$577$	1.19037e29	1.21153	0.605766	+	0.795643i	$0.292867\pi$
$578$	−5.30292e28	−0.529996
$579$	0	0
$580$	−1.42286e28	−0.137141
$581$	−2.11800e29	−2.00483
$582$	0	0
$583$	1.09913e29	1.00352
$584$	2.89991e28	0.260046
$585$	0	0
$586$	−1.01280e29	−0.876188
$587$	5.85051e28	0.497157	0.248578	−	0.968612i	$-0.420037\pi$
$587$	5.85051e28	0.497157	0.248578	+	0.968612i	$0.420037\pi$
$588$	0	0
$589$	−8.18591e28	−0.671207
$590$	−5.10031e27	−0.0410819
$591$	0	0
$592$	8.72459e26	0.00678214
$593$	5.86446e28	0.447871	0.223936	−	0.974604i	$-0.428109\pi$
$593$	5.86446e28	0.447871	0.223936	+	0.974604i	$0.428109\pi$
$594$	0	0
$595$	−5.42420e28	−0.399860
$596$	1.09903e29	0.796020
$597$	0	0
$598$	7.24028e28	0.506282
$599$	2.05350e29	1.41095	0.705477	−	0.708733i	$-0.250733\pi$
$599$	2.05350e29	1.41095	0.705477	+	0.708733i	$0.250733\pi$
$600$	0	0
$601$	1.36564e29	0.906052	0.453026	−	0.891497i	$-0.350344\pi$
$601$	1.36564e29	0.906052	0.453026	+	0.891497i	$0.350344\pi$
$602$	1.16496e29	0.759533
$603$	0	0
$604$	−1.66420e28	−0.104790
$605$	1.42786e28	0.0883595
$606$	0	0
$607$	−1.08095e29	−0.646137	−0.323069	−	0.946376i	$-0.604714\pi$
$607$	−1.08095e29	−0.646137	−0.323069	+	0.946376i	$0.604714\pi$
$608$	−8.31514e28	−0.488520
$609$	0	0
$610$	−1.81258e28	−0.102881
$611$	−2.42189e29	−1.35121
$612$	0	0
$613$	−1.01861e29	−0.549127	−0.274564	−	0.961569i	$-0.588533\pi$
$613$	−1.01861e29	−0.549127	−0.274564	+	0.961569i	$0.588533\pi$
$614$	1.15732e29	0.613319
$615$	0	0
$616$	2.80573e29	1.43697
$617$	1.09657e29	0.552131	0.276065	−	0.961139i	$-0.410969\pi$
$617$	1.09657e29	0.552131	0.276065	+	0.961139i	$0.410969\pi$
$618$	0	0
$619$	−2.30570e29	−1.12215	−0.561076	−	0.827764i	$-0.689613\pi$
$619$	−2.30570e29	−1.12215	−0.561076	+	0.827764i	$0.689613\pi$
$620$	4.54263e28	0.217367
$621$	0	0
$622$	1.82223e29	0.842954
$623$	−2.25984e29	−1.02790
$624$	0	0
$625$	1.98463e29	0.872851
$626$	6.77763e28	0.293121
$627$	0	0
$628$	−1.18576e29	−0.495929
$629$	−8.35146e27	−0.0343503
$630$	0	0
$631$	1.86894e29	0.743511	0.371755	−	0.928331i	$-0.378756\pi$
$631$	1.86894e29	0.743511	0.371755	+	0.928331i	$0.378756\pi$
$632$	−3.40550e29	−1.33245
$633$	0	0
$634$	−2.10936e29	−0.798387
$635$	5.20413e28	0.193742
$636$	0	0
$637$	3.43311e29	1.23658
$638$	−1.54812e29	−0.548513
$639$	0	0
$640$	5.48689e28	0.188121
$641$	−9.35142e28	−0.315405	−0.157702	−	0.987487i	$-0.550409\pi$
$641$	−9.35142e28	−0.315405	−0.157702	+	0.987487i	$0.550409\pi$
$642$	0	0
$643$	−3.51910e29	−1.14872	−0.574362	−	0.818601i	$-0.694750\pi$
$643$	−3.51910e29	−1.14872	−0.574362	+	0.818601i	$0.694750\pi$
$644$	2.05363e29	0.659508
$645$	0	0
$646$	1.11015e29	0.345097
$647$	−2.27859e28	−0.0696900	−0.0348450	−	0.999393i	$-0.511094\pi$
$647$	−2.27859e28	−0.0696900	−0.0348450	+	0.999393i	$0.511094\pi$
$648$	0	0
$649$	1.55982e29	0.461855
$650$	2.51434e29	0.732545
$651$	0	0
$652$	−6.57746e28	−0.185549
$653$	−3.91723e29	−1.08740	−0.543702	−	0.839278i	$-0.682978\pi$
$653$	−3.91723e29	−1.08740	−0.543702	+	0.839278i	$0.682978\pi$
$654$	0	0
$655$	−5.37055e28	−0.144373
$656$	−1.39907e29	−0.370126
$657$	0	0
$658$	2.44391e29	0.626201
$659$	−3.68927e28	−0.0930344	−0.0465172	−	0.998917i	$-0.514812\pi$
$659$	−3.68927e28	−0.0930344	−0.0465172	+	0.998917i	$0.514812\pi$
$660$	0	0
$661$	7.11650e28	0.173840	0.0869202	−	0.996215i	$-0.472297\pi$
$661$	7.11650e28	0.173840	0.0869202	+	0.996215i	$0.472297\pi$
$662$	−1.37937e29	−0.331644
$663$	0	0
$664$	−5.66689e29	−1.32002
$665$	5.77432e28	0.132396
$666$	0	0
$667$	−2.66939e29	−0.593050
$668$	3.52212e29	0.770285
$669$	0	0
$670$	2.75153e28	0.0583163
$671$	5.54341e29	1.15662
$672$	0	0
$673$	−6.93220e29	−1.40189	−0.700944	−	0.713217i	$-0.747238\pi$
$673$	−6.93220e29	−1.40189	−0.700944	+	0.713217i	$0.747238\pi$
$674$	−3.20476e29	−0.638068
$675$	0	0
$676$	−4.71166e29	−0.909355
$677$	−2.86167e29	−0.543798	−0.271899	−	0.962326i	$-0.587652\pi$
$677$	−2.86167e29	−0.543798	−0.271899	+	0.962326i	$0.587652\pi$
$678$	0	0
$679$	−9.05785e29	−1.66875
$680$	−1.45129e29	−0.263276
$681$	0	0
$682$	4.94254e29	0.869390
$683$	4.89536e29	0.847945	0.423972	−	0.905675i	$-0.360635\pi$
$683$	4.89536e29	0.847945	0.423972	+	0.905675i	$0.360635\pi$
$684$	0	0
$685$	2.03020e29	0.341026
$686$	7.21944e28	0.119426
$687$	0	0
$688$	−1.92522e29	−0.308888
$689$	7.94667e29	1.25569
$690$	0	0
$691$	−8.47823e29	−1.29953	−0.649764	−	0.760136i	$-0.725132\pi$
$691$	−8.47823e29	−1.29953	−0.649764	+	0.760136i	$0.725132\pi$
$692$	6.48765e29	0.979430
$693$	0	0
$694$	6.28691e29	0.920795
$695$	2.00682e29	0.289513
$696$	0	0
$697$	1.33924e30	1.87462
$698$	4.87073e29	0.671602
$699$	0	0
$700$	7.13166e29	0.954248
$701$	−8.15562e28	−0.107502	−0.0537512	−	0.998554i	$-0.517118\pi$
$701$	−8.15562e28	−0.107502	−0.0537512	+	0.998554i	$0.517118\pi$
$702$	0	0
$703$	8.89054e27	0.0113736
$704$	2.35207e29	0.296440
$705$	0	0
$706$	3.09654e29	0.378816
$707$	−4.08915e29	−0.492866
$708$	0	0
$709$	9.39238e29	1.09898	0.549490	−	0.835500i	$-0.314822\pi$
$709$	9.39238e29	1.09898	0.549490	+	0.835500i	$0.314822\pi$
$710$	7.01780e28	0.0809075
$711$	0	0
$712$	−6.04639e29	−0.676794
$713$	8.52234e29	0.939980
$714$	0	0
$715$	3.45504e29	0.370033
$716$	1.22869e30	1.29675
$717$	0	0
$718$	1.64894e29	0.169005
$719$	1.24077e30	1.25325	0.626625	−	0.779321i	$-0.284436\pi$
$719$	1.24077e30	1.25325	0.626625	+	0.779321i	$0.284436\pi$
$720$	0	0
$721$	−1.92541e30	−1.88888
$722$	4.11642e29	0.397996
$723$	0	0
$724$	3.35376e28	0.0314976
$725$	−9.27004e29	−0.858090
$726$	0	0
$727$	−1.90176e28	−0.0171019	−0.00855095	−	0.999963i	$-0.502722\pi$
$727$	−1.90176e28	−0.0171019	−0.00855095	+	0.999963i	$0.502722\pi$
$728$	2.02854e30	1.79806
$729$	0	0
$730$	−3.60349e28	−0.0310337
$731$	1.84288e30	1.56446
$732$	0	0
$733$	−1.97041e30	−1.62542	−0.812709	−	0.582669i	$-0.802008\pi$
$733$	−1.97041e30	−1.62542	−0.812709	+	0.582669i	$0.802008\pi$
$734$	−9.19535e28	−0.0747756
$735$	0	0
$736$	8.65688e29	0.684139
$737$	−8.41499e29	−0.655609
$738$	0	0
$739$	−8.44088e29	−0.639177	−0.319589	−	0.947556i	$-0.603545\pi$
$739$	−8.44088e29	−0.639177	−0.319589	+	0.947556i	$0.603545\pi$
$740$	−4.93365e27	−0.00368328
$741$	0	0
$742$	−8.01892e29	−0.581936
$743$	−8.92978e29	−0.638938	−0.319469	−	0.947597i	$-0.603504\pi$
$743$	−8.92978e29	−0.638938	−0.319469	+	0.947597i	$0.603504\pi$
$744$	0	0
$745$	−3.21722e29	−0.223790
$746$	1.09790e29	0.0753014
$747$	0	0
$748$	1.88409e30	1.25642
$749$	−2.50952e29	−0.165018
$750$	0	0
$751$	1.91667e30	1.22554	0.612770	−	0.790262i	$-0.290055\pi$
$751$	1.91667e30	1.22554	0.612770	+	0.790262i	$0.290055\pi$
$752$	−4.03883e29	−0.254664
$753$	0	0
$754$	−1.11929e30	−0.686345
$755$	4.87166e28	0.0294601
$756$	0	0
$757$	−6.81322e29	−0.400724	−0.200362	−	0.979722i	$-0.564212\pi$
$757$	−6.81322e29	−0.400724	−0.200362	+	0.979722i	$0.564212\pi$
$758$	−2.11720e29	−0.122810
$759$	0	0
$760$	1.54497e29	0.0871720
$761$	1.07855e30	0.600205	0.300103	−	0.953907i	$-0.402979\pi$
$761$	1.07855e30	0.600205	0.300103	+	0.953907i	$0.402979\pi$
$762$	0	0
$763$	1.26193e30	0.683171
$764$	−6.36543e29	−0.339897
$765$	0	0
$766$	−9.86098e29	−0.512293
$767$	1.12775e30	0.577911
$768$	0	0
$769$	3.48759e30	1.73900	0.869498	−	0.493937i	$-0.164443\pi$
$769$	3.48759e30	1.73900	0.869498	+	0.493937i	$0.164443\pi$
$770$	−3.48646e29	−0.171487
$771$	0	0
$772$	−6.13679e29	−0.293738
$773$	−5.50505e29	−0.259942	−0.129971	−	0.991518i	$-0.541488\pi$
$773$	−5.50505e29	−0.259942	−0.129971	+	0.991518i	$0.541488\pi$
$774$	0	0
$775$	2.95957e30	1.36007
$776$	−2.42350e30	−1.09874
$777$	0	0
$778$	−1.87520e30	−0.827487
$779$	−1.42568e30	−0.620698
$780$	0	0
$781$	−2.14625e30	−0.909586
$782$	−1.15578e30	−0.483285
$783$	0	0
$784$	5.72517e29	0.233061
$785$	3.47110e29	0.139423
$786$	0	0
$787$	1.85602e30	0.725852	0.362926	−	0.931818i	$-0.381778\pi$
$787$	1.85602e30	0.725852	0.362926	+	0.931818i	$0.381778\pi$
$788$	1.92509e30	0.742893
$789$	0	0
$790$	4.23175e29	0.159014
$791$	1.65484e30	0.613624
$792$	0	0
$793$	4.00788e30	1.44726
$794$	−2.53749e30	−0.904253
$795$	0	0
$796$	−3.26079e30	−1.13171
$797$	3.69097e30	1.26424	0.632118	−	0.774872i	$-0.282186\pi$
$797$	3.69097e30	1.26424	0.632118	+	0.774872i	$0.282186\pi$
$798$	0	0
$799$	3.86610e30	1.28983
$800$	3.00629e30	0.989887
$801$	0	0
$802$	−2.45434e29	−0.0787234
$803$	1.10205e30	0.348890
$804$	0	0
$805$	−6.01164e29	−0.185411
$806$	3.57345e30	1.08785
$807$	0	0
$808$	−1.09409e30	−0.324513
$809$	−6.24191e30	−1.82750	−0.913751	−	0.406275i	$-0.866827\pi$
$809$	−6.24191e30	−1.82750	−0.913751	+	0.406275i	$0.866827\pi$
$810$	0	0
$811$	8.51871e28	0.0243027	0.0121514	−	0.999926i	$-0.496132\pi$
$811$	8.51871e28	0.0243027	0.0121514	+	0.999926i	$0.496132\pi$
$812$	−3.17474e30	−0.894066
$813$	0	0
$814$	−5.36799e28	−0.0147318
$815$	1.92544e29	0.0521645
$816$	0	0
$817$	−1.96184e30	−0.518001
$818$	1.10464e30	0.287945
$819$	0	0
$820$	7.91159e29	0.201010
$821$	1.98591e30	0.498146	0.249073	−	0.968485i	$-0.419874\pi$
$821$	1.98591e30	0.498146	0.249073	+	0.968485i	$0.419874\pi$
$822$	0	0
$823$	−3.60804e30	−0.882213	−0.441106	−	0.897455i	$-0.645414\pi$
$823$	−3.60804e30	−0.882213	−0.441106	+	0.897455i	$0.645414\pi$
$824$	−5.15160e30	−1.24367
$825$	0	0
$826$	−1.13800e30	−0.267826
$827$	−6.64241e30	−1.54354	−0.771770	−	0.635902i	$-0.780628\pi$
$827$	−6.64241e30	−1.54354	−0.771770	+	0.635902i	$0.780628\pi$
$828$	0	0
$829$	−2.86158e30	−0.648312	−0.324156	−	0.946004i	$-0.605080\pi$
$829$	−2.86158e30	−0.648312	−0.324156	+	0.946004i	$0.605080\pi$
$830$	7.04181e29	0.157530
$831$	0	0
$832$	1.70054e30	0.370930
$833$	−5.48032e30	−1.18041
$834$	0	0
$835$	−1.03104e30	−0.216555
$836$	−2.00570e30	−0.416007
$837$	0	0
$838$	−3.16452e30	−0.640097
$839$	−3.67726e30	−0.734554	−0.367277	−	0.930112i	$-0.619710\pi$
$839$	−3.67726e30	−0.734554	−0.367277	+	0.930112i	$0.619710\pi$
$840$	0	0
$841$	−1.00618e30	−0.196028
$842$	2.02837e30	0.390275
$843$	0	0
$844$	2.81556e30	0.528408
$845$	1.37926e30	0.255652
$846$	0	0
$847$	3.18590e30	0.576045
$848$	1.32521e30	0.236662
$849$	0	0
$850$	−4.01368e30	−0.699269
$851$	−9.25593e28	−0.0159279
$852$	0	0
$853$	−4.25124e29	−0.0713758	−0.0356879	−	0.999363i	$-0.511362\pi$
$853$	−4.25124e29	−0.0713758	−0.0356879	+	0.999363i	$0.511362\pi$
$854$	−4.04432e30	−0.670715
$855$	0	0
$856$	−6.71443e29	−0.108651
$857$	−1.04210e31	−1.66576	−0.832880	−	0.553453i	$-0.813310\pi$
$857$	−1.04210e31	−1.66576	−0.832880	+	0.553453i	$0.813310\pi$
$858$	0	0
$859$	1.42713e30	0.222606	0.111303	−	0.993787i	$-0.464498\pi$
$859$	1.42713e30	0.222606	0.111303	+	0.993787i	$0.464498\pi$
$860$	1.08869e30	0.167753
$861$	0	0
$862$	1.66053e30	0.249701
$863$	4.41053e30	0.655205	0.327602	−	0.944816i	$-0.393759\pi$
$863$	4.41053e30	0.655205	0.327602	+	0.944816i	$0.393759\pi$
$864$	0	0
$865$	−1.89915e30	−0.275353
$866$	2.94618e30	0.422008
$867$	0	0
$868$	1.01357e31	1.41709
$869$	−1.29419e31	−1.78769
$870$	0	0
$871$	−6.08402e30	−0.820352
$872$	3.37641e30	0.449814
$873$	0	0
$874$	1.23038e30	0.160018
$875$	−4.26914e30	−0.548601
$876$	0	0
$877$	9.38187e30	1.17705	0.588523	−	0.808480i	$-0.299709\pi$
$877$	9.38187e30	1.17705	0.588523	+	0.808480i	$0.299709\pi$
$878$	−6.22814e30	−0.772087
$879$	0	0
$880$	5.76175e29	0.0697407
$881$	6.89368e30	0.824526	0.412263	−	0.911065i	$-0.364739\pi$
$881$	6.89368e30	0.824526	0.412263	+	0.911065i	$0.364739\pi$
$882$	0	0
$883$	−6.77660e30	−0.791452	−0.395726	−	0.918369i	$-0.629507\pi$
$883$	−6.77660e30	−0.791452	−0.395726	+	0.918369i	$0.629507\pi$
$884$	1.36219e31	1.57213
$885$	0	0
$886$	−4.74920e30	−0.535262
$887$	−9.49731e30	−1.05780	−0.528899	−	0.848685i	$-0.677395\pi$
$887$	−9.49731e30	−1.05780	−0.528899	+	0.848685i	$0.677395\pi$
$888$	0	0
$889$	1.16117e31	1.26307
$890$	7.51338e29	0.0807682
$891$	0	0
$892$	−4.45904e30	−0.468177
$893$	−4.11565e30	−0.427069
$894$	0	0
$895$	−3.59678e30	−0.364562
$896$	1.22426e31	1.22642
$897$	0	0
$898$	−7.99626e30	−0.782502
$899$	−1.31748e31	−1.27429
$900$	0	0
$901$	−1.26854e31	−1.19865
$902$	8.60809e30	0.803967
$903$	0	0
$904$	4.42766e30	0.404023
$905$	−9.81756e28	−0.00885510
$906$	0	0
$907$	−3.34399e30	−0.294705	−0.147353	−	0.989084i	$-0.547075\pi$
$907$	−3.34399e30	−0.294705	−0.147353	+	0.989084i	$0.547075\pi$
$908$	4.90255e30	0.427091
$909$	0	0
$910$	−2.52070e30	−0.214579
$911$	−9.08692e30	−0.764670	−0.382335	−	0.924024i	$-0.624880\pi$
$911$	−9.08692e30	−0.764670	−0.382335	+	0.924024i	$0.624880\pi$
$912$	0	0
$913$	−2.15359e31	−1.77100
$914$	−6.63349e30	−0.539271
$915$	0	0
$916$	4.88616e30	0.388208
$917$	−1.19830e31	−0.941212
$918$	0	0
$919$	1.85421e31	1.42346	0.711732	−	0.702451i	$-0.247911\pi$
$919$	1.85421e31	1.42346	0.711732	+	0.702451i	$0.247911\pi$
$920$	−1.60847e30	−0.122079
$921$	0	0
$922$	−4.95179e30	−0.367356
$923$	−1.55173e31	−1.13815
$924$	0	0
$925$	−3.21432e29	−0.0230463
$926$	−4.50923e30	−0.319659
$927$	0	0
$928$	−1.33828e31	−0.927458
$929$	−1.70088e31	−1.16549	−0.582745	−	0.812655i	$-0.698021\pi$
$929$	−1.70088e31	−1.16549	−0.582745	+	0.812655i	$0.698021\pi$
$930$	0	0
$931$	5.83407e30	0.390841
$932$	−9.35133e30	−0.619450
$933$	0	0
$934$	4.60889e29	0.0298507
$935$	−5.51534e30	−0.353224
$936$	0	0
$937$	1.63493e30	0.102384	0.0511922	−	0.998689i	$-0.483698\pi$
$937$	1.63493e30	0.102384	0.0511922	+	0.998689i	$0.483698\pi$
$938$	6.13935e30	0.380183
$939$	0	0
$940$	2.28391e30	0.138304
$941$	2.04048e31	1.22192	0.610958	−	0.791663i	$-0.290784\pi$
$941$	2.04048e31	1.22192	0.610958	+	0.791663i	$0.290784\pi$
$942$	0	0
$943$	1.48428e31	0.869246
$944$	1.88067e30	0.108920
$945$	0	0
$946$	1.18453e31	0.670948
$947$	−9.56566e30	−0.535846	−0.267923	−	0.963440i	$-0.586337\pi$
$947$	−9.56566e30	−0.535846	−0.267923	+	0.963440i	$0.586337\pi$
$948$	0	0
$949$	7.96782e30	0.436560
$950$	4.27276e30	0.231532
$951$	0	0
$952$	−3.23818e31	−1.71638
$953$	2.48157e30	0.130092	0.0650460	−	0.997882i	$-0.479281\pi$
$953$	2.48157e30	0.130092	0.0650460	+	0.997882i	$0.479281\pi$
$954$	0	0
$955$	1.86337e30	0.0955573
$956$	−5.00288e29	−0.0253754
$957$	0	0
$958$	−9.80675e28	−0.00486617
$959$	4.52986e31	2.22326
$960$	0	0
$961$	2.12366e31	1.01974
$962$	−3.88105e29	−0.0184336
$963$	0	0
$964$	1.82555e31	0.848370
$965$	1.79644e30	0.0825802
$966$	0	0
$967$	−1.01162e30	−0.0455031	−0.0227516	−	0.999741i	$-0.507243\pi$
$967$	−1.01162e30	−0.0455031	−0.0227516	+	0.999741i	$0.507243\pi$
$968$	8.52414e30	0.379280
$969$	0	0
$970$	3.01150e30	0.131123
$971$	−2.54874e30	−0.109780	−0.0548901	−	0.998492i	$-0.517481\pi$
$971$	−2.54874e30	−0.109780	−0.0548901	+	0.998492i	$0.517481\pi$
$972$	0	0
$973$	4.47771e31	1.88743
$974$	−8.91531e30	−0.371764
$975$	0	0
$976$	6.68367e30	0.272767
$977$	−2.28875e31	−0.924070	−0.462035	−	0.886862i	$-0.652881\pi$
$977$	−2.28875e31	−0.924070	−0.462035	+	0.886862i	$0.652881\pi$
$978$	0	0
$979$	−2.29781e31	−0.908020
$980$	−3.23752e30	−0.126572
$981$	0	0
$982$	−1.26335e31	−0.483452
$983$	−2.63464e31	−0.997493	−0.498746	−	0.866748i	$-0.666206\pi$
$983$	−2.63464e31	−0.997493	−0.498746	+	0.866748i	$0.666206\pi$
$984$	0	0
$985$	−5.63538e30	−0.208854
$986$	1.78674e31	0.655168
$987$	0	0
$988$	−1.45012e31	−0.520542
$989$	2.04246e31	0.725426
$990$	0	0
$991$	9.61199e29	0.0334226	0.0167113	−	0.999860i	$-0.494680\pi$
$991$	9.61199e29	0.0334226	0.0167113	+	0.999860i	$0.494680\pi$
$992$	4.27262e31	1.47001
$993$	0	0
$994$	1.56584e31	0.527462
$995$	9.54539e30	0.318164
$996$	0	0
$997$	4.83759e30	0.157881	0.0789405	−	0.996879i	$-0.474846\pi$
$997$	4.83759e30	0.157881	0.0789405	+	0.996879i	$0.474846\pi$
$998$	8.18359e30	0.264285
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	81.22.a.c.1.8		20
3.2	odd	2		81.22.a.d.1.13		20
9.2	odd	6		27.22.c.a.10.8		40
9.4	even	3		9.22.c.a.7.13	yes	40
9.5	odd	6		27.22.c.a.19.8		40
9.7	even	3		9.22.c.a.4.13	✓	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
9.22.c.a.4.13	✓	40	9.7	even	3
9.22.c.a.7.13	yes	40	9.4	even	3
27.22.c.a.10.8		40	9.2	odd	6
27.22.c.a.19.8		40	9.5	odd	6
81.22.a.c.1.8		20	1.1	even	1	trivial
81.22.a.d.1.13		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)

\(f(q)\)	\(=\)	\(q-741.831 q^{2} -1.54684e6 q^{4} +4.52810e6 q^{5} +1.01033e9 q^{7} +2.70323e9 q^{8} +O(q^{10})\)	\(q-741.831 q^{2} -1.54684e6 q^{4} +4.52810e6 q^{5} +1.01033e9 q^{7} +2.70323e9 q^{8} -3.35909e9 q^{10} +1.02731e11 q^{11} +7.42741e11 q^{13} -7.49494e11 q^{14} +1.23862e12 q^{16} -1.18565e13 q^{17} +1.26218e13 q^{19} -7.00425e12 q^{20} -7.62087e13 q^{22} -1.31405e14 q^{23} -4.56333e14 q^{25} -5.50988e14 q^{26} -1.56282e15 q^{28} +2.03142e15 q^{29} -6.48553e15 q^{31} -6.58792e15 q^{32} +8.79551e15 q^{34} +4.57488e15 q^{35} +7.04380e14 q^{37} -9.36324e15 q^{38} +1.22405e16 q^{40} -1.12954e17 q^{41} -1.55432e17 q^{43} -1.58908e17 q^{44} +9.74806e16 q^{46} -3.26075e17 q^{47} +4.62222e17 q^{49} +3.38522e17 q^{50} -1.14890e18 q^{52} +1.06991e18 q^{53} +4.65175e17 q^{55} +2.73115e18 q^{56} -1.50697e18 q^{58} +1.51836e18 q^{59} +5.39606e18 q^{61} +4.81117e18 q^{62} +2.28955e18 q^{64} +3.36321e18 q^{65} -8.19132e18 q^{67} +1.83401e19 q^{68} -3.39379e18 q^{70} -2.08920e19 q^{71} +1.07276e19 q^{73} -5.22531e17 q^{74} -1.95239e19 q^{76} +1.03792e20 q^{77} -1.25979e20 q^{79} +5.60860e18 q^{80} +8.37929e19 q^{82} -2.09635e20 q^{83} -5.36874e19 q^{85} +1.15305e20 q^{86} +2.77704e20 q^{88} -2.23673e20 q^{89} +7.50414e20 q^{91} +2.03263e20 q^{92} +2.41892e20 q^{94} +5.71528e19 q^{95} -8.96523e20 q^{97} -3.42890e20 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 1023 q^{2} + 19922945 q^{4} - 32234853 q^{5} + 189623959 q^{7} - 648135831 q^{8}+O(q^{10}) \) 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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