LMFDB - Embedded newform 81.22.a.c.1.4

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			1.4
Root			$1931.83$ 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)

$f(q)$	$=$	$q-1982.83 q^{2} +1.83448e6 q^{4} -1.02434e7 q^{5} -9.51290e8 q^{7} +5.20838e8 q^{8} +O(q^{10})$	\(q-1982.83 q^{2} +1.83448e6 q^{4} -1.02434e7 q^{5} -9.51290e8 q^{7} +5.20838e8 q^{8} +2.03109e10 q^{10} +8.67734e10 q^{11} +5.25839e11 q^{13} +1.88625e12 q^{14} -4.87992e12 q^{16} -9.08695e12 q^{17} -8.79971e12 q^{19} -1.87913e13 q^{20} -1.72057e14 q^{22} +3.86072e13 q^{23} -3.71910e14 q^{25} -1.04265e15 q^{26} -1.74512e15 q^{28} -2.89780e14 q^{29} +6.04185e15 q^{31} +8.58379e15 q^{32} +1.80179e16 q^{34} +9.74443e15 q^{35} -4.41709e16 q^{37} +1.74484e16 q^{38} -5.33514e15 q^{40} +8.86265e16 q^{41} +7.26915e16 q^{43} +1.59184e17 q^{44} -7.65517e16 q^{46} -7.19545e17 q^{47} +3.46406e17 q^{49} +7.37436e17 q^{50} +9.64640e17 q^{52} +5.36630e17 q^{53} -8.88854e17 q^{55} -4.95468e17 q^{56} +5.74586e17 q^{58} -5.37267e18 q^{59} +2.17239e18 q^{61} -1.19800e19 q^{62} -6.78630e18 q^{64} -5.38637e18 q^{65} +1.82952e19 q^{67} -1.66698e19 q^{68} -1.93216e19 q^{70} -1.88011e19 q^{71} +7.15740e19 q^{73} +8.75835e19 q^{74} -1.61429e19 q^{76} -8.25467e19 q^{77} -7.42100e19 q^{79} +4.99869e19 q^{80} -1.75732e20 q^{82} +4.29574e19 q^{83} +9.30811e19 q^{85} -1.44135e20 q^{86} +4.51949e19 q^{88} -1.01476e20 q^{89} -5.00225e20 q^{91} +7.08241e19 q^{92} +1.42674e21 q^{94} +9.01388e19 q^{95} +9.96482e20 q^{97} -6.86866e20 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−1982.83	−1.36921	−0.684607	−	0.728912i	$-0.740026\pi$
$2$	−1982.83	−1.36921	−0.684607	+	0.728912i	$0.740026\pi$
$3$	0	0
$3$	0	0
$4$	1.83448e6	0.874748
$5$	−1.02434e7	−0.469093	−0.234546	−	0.972105i	$-0.575360\pi$
$5$	−1.02434e7	−0.469093	−0.234546	+	0.972105i	$0.575360\pi$
$6$	0	0
$7$	−9.51290e8	−1.27287	−0.636434	−	0.771331i	$-0.719591\pi$
$7$	−9.51290e8	−1.27287	−0.636434	+	0.771331i	$0.719591\pi$
$8$	5.20838e8	0.171497
$9$	0	0
$10$	2.03109e10	0.642288
$11$	8.67734e10	1.00870	0.504352	−	0.863498i	$-0.331731\pi$
$11$	8.67734e10	1.00870	0.504352	+	0.863498i	$0.331731\pi$
$12$	0	0
$13$	5.25839e11	1.05791	0.528954	−	0.848651i	$-0.322585\pi$
$13$	5.25839e11	1.05791	0.528954	+	0.848651i	$0.322585\pi$
$14$	1.88625e12	1.74283
$15$	0	0
$16$	−4.87992e12	−1.10956
$17$	−9.08695e12	−1.09321	−0.546606	−	0.837390i	$-0.684080\pi$
$17$	−9.08695e12	−1.09321	−0.546606	+	0.837390i	$0.684080\pi$
$18$	0	0
$19$	−8.79971e12	−0.329273	−0.164636	−	0.986354i	$-0.552645\pi$
$19$	−8.79971e12	−0.329273	−0.164636	+	0.986354i	$0.552645\pi$
$20$	−1.87913e13	−0.410338
$21$	0	0
$22$	−1.72057e14	−1.38113
$23$	3.86072e13	0.194324	0.0971620	−	0.995269i	$-0.469024\pi$
$23$	3.86072e13	0.194324	0.0971620	+	0.995269i	$0.469024\pi$
$24$	0	0
$25$	−3.71910e14	−0.779952
$26$	−1.04265e15	−1.44850
$27$	0	0
$28$	−1.74512e15	−1.11344
$29$	−2.89780e14	−0.127906	−0.0639528	−	0.997953i	$-0.520371\pi$
$29$	−2.89780e14	−0.127906	−0.0639528	+	0.997953i	$0.520371\pi$
$30$	0	0
$31$	6.04185e15	1.32395	0.661975	−	0.749526i	$-0.269718\pi$
$31$	6.04185e15	1.32395	0.661975	+	0.749526i	$0.269718\pi$
$32$	8.58379e15	1.34773
$33$	0	0
$34$	1.80179e16	1.49684
$35$	9.74443e15	0.597093
$36$	0	0
$37$	−4.41709e16	−1.51014	−0.755071	−	0.655642i	$-0.772398\pi$
$37$	−4.41709e16	−1.51014	−0.755071	+	0.655642i	$0.772398\pi$
$38$	1.74484e16	0.450845
$39$	0	0
$40$	−5.33514e15	−0.0804482
$41$	8.86265e16	1.03118	0.515589	−	0.856836i	$-0.327573\pi$
$41$	8.86265e16	1.03118	0.515589	+	0.856836i	$0.327573\pi$
$42$	0	0
$43$	7.26915e16	0.512938	0.256469	−	0.966552i	$-0.417441\pi$
$43$	7.26915e16	0.512938	0.256469	+	0.966552i	$0.417441\pi$
$44$	1.59184e17	0.882361
$45$	0	0
$46$	−7.65517e16	−0.266071
$47$	−7.19545e17	−1.99540	−0.997701	−	0.0677735i	$-0.978410\pi$
$47$	−7.19545e17	−1.99540	−0.997701	+	0.0677735i	$0.978410\pi$
$48$	0	0
$49$	3.46406e17	0.620193
$50$	7.37436e17	1.06792
$51$	0	0
$52$	9.64640e17	0.925402
$53$	5.36630e17	0.421481	0.210740	−	0.977542i	$-0.432413\pi$
$53$	5.36630e17	0.421481	0.210740	+	0.977542i	$0.432413\pi$
$54$	0	0
$55$	−8.88854e17	−0.473175
$56$	−4.95468e17	−0.218294
$57$	0	0
$58$	5.74586e17	0.175130
$59$	−5.37267e18	−1.36850	−0.684249	−	0.729249i	$-0.739870\pi$
$59$	−5.37267e18	−1.36850	−0.684249	+	0.729249i	$0.739870\pi$
$60$	0	0
$61$	2.17239e18	0.389919	0.194959	−	0.980811i	$-0.437543\pi$
$61$	2.17239e18	0.389919	0.194959	+	0.980811i	$0.437543\pi$
$62$	−1.19800e19	−1.81277
$63$	0	0
$64$	−6.78630e18	−0.735772
$65$	−5.38637e18	−0.496256
$66$	0	0
$67$	1.82952e19	1.22618	0.613088	−	0.790015i	$-0.289927\pi$
$67$	1.82952e19	1.22618	0.613088	+	0.790015i	$0.289927\pi$
$68$	−1.66698e19	−0.956284
$69$	0	0
$70$	−1.93216e19	−0.817548
$71$	−1.88011e19	−0.685442	−0.342721	−	0.939437i	$-0.611349\pi$
$71$	−1.88011e19	−0.685442	−0.342721	+	0.939437i	$0.611349\pi$
$72$	0	0
$73$	7.15740e19	1.94924	0.974619	−	0.223869i	$-0.0718689\pi$
$73$	7.15740e19	1.94924	0.974619	+	0.223869i	$0.0718689\pi$
$74$	8.75835e19	2.06771
$75$	0	0
$76$	−1.61429e19	−0.288030
$77$	−8.25467e19	−1.28395
$78$	0	0
$79$	−7.42100e19	−0.881816	−0.440908	−	0.897552i	$-0.645344\pi$
$79$	−7.42100e19	−0.881816	−0.440908	+	0.897552i	$0.645344\pi$
$80$	4.99869e19	0.520488
$81$	0	0
$82$	−1.75732e20	−1.41190
$83$	4.29574e19	0.303891	0.151946	−	0.988389i	$-0.451446\pi$
$83$	4.29574e19	0.303891	0.151946	+	0.988389i	$0.451446\pi$
$84$	0	0
$85$	9.30811e19	0.512817
$86$	−1.44135e20	−0.702322
$87$	0	0
$88$	4.51949e19	0.172990
$89$	−1.01476e20	−0.344958	−0.172479	−	0.985013i	$-0.555178\pi$
$89$	−1.01476e20	−0.344958	−0.172479	+	0.985013i	$0.555178\pi$
$90$	0	0
$91$	−5.00225e20	−1.34658
$92$	7.08241e19	0.169984
$93$	0	0
$94$	1.42674e21	2.73213
$95$	9.01388e19	0.154459
$96$	0	0
$97$	9.96482e20	1.37204	0.686019	−	0.727584i	$-0.259357\pi$
$97$	9.96482e20	1.37204	0.686019	+	0.727584i	$0.259357\pi$
$98$	−6.86866e20	−0.849177
$99$	0	0
$100$	−6.82261e20	−0.682261
$101$	9.40501e20	0.847198	0.423599	−	0.905850i	$-0.360767\pi$
$101$	9.40501e20	0.847198	0.423599	+	0.905850i	$0.360767\pi$
$102$	0	0
$103$	−4.34162e19	−0.0318318	−0.0159159	−	0.999873i	$-0.505066\pi$
$103$	−4.34162e19	−0.0318318	−0.0159159	+	0.999873i	$0.505066\pi$
$104$	2.73877e20	0.181428
$105$	0	0
$106$	−1.06405e21	−0.577098
$107$	1.58939e21	0.781088	0.390544	−	0.920584i	$-0.372287\pi$
$107$	1.58939e21	0.781088	0.390544	+	0.920584i	$0.372287\pi$
$108$	0	0
$109$	−3.48277e20	−0.140911	−0.0704557	−	0.997515i	$-0.522445\pi$
$109$	−3.48277e20	−0.140911	−0.0704557	+	0.997515i	$0.522445\pi$
$110$	1.76245e21	0.647878
$111$	0	0
$112$	4.64221e21	1.41233
$113$	−4.49798e21	−1.24651	−0.623253	−	0.782020i	$-0.714189\pi$
$113$	−4.49798e21	−1.24651	−0.623253	+	0.782020i	$0.714189\pi$
$114$	0	0
$115$	−3.95469e20	−0.0911559
$116$	−5.31595e20	−0.111885
$117$	0	0
$118$	1.06531e22	1.87377
$119$	8.64432e21	1.39151
$120$	0	0
$121$	1.29378e20	0.0174829
$122$	−4.30748e21	−0.533882
$123$	0	0
$124$	1.10836e22	1.15812
$125$	8.69405e21	0.834962
$126$	0	0
$127$	1.85658e22	1.50930	0.754650	−	0.656128i	$-0.227807\pi$
$127$	1.85658e22	1.50930	0.754650	+	0.656128i	$0.227807\pi$
$128$	−4.54540e21	−0.340304
$129$	0	0
$130$	1.06803e22	0.679481
$131$	2.91946e22	1.71378	0.856889	−	0.515501i	$-0.172394\pi$
$131$	2.91946e22	1.71378	0.856889	+	0.515501i	$0.172394\pi$
$132$	0	0
$133$	8.37108e21	0.419121
$134$	−3.62764e22	−1.67890
$135$	0	0
$136$	−4.73283e21	−0.187483
$137$	−2.54051e22	−0.931871	−0.465935	−	0.884819i	$-0.654282\pi$
$137$	−2.54051e22	−0.931871	−0.465935	+	0.884819i	$0.654282\pi$
$138$	0	0
$139$	8.12181e21	0.255857	0.127929	−	0.991783i	$-0.459167\pi$
$139$	8.12181e21	0.255857	0.127929	+	0.991783i	$0.459167\pi$
$140$	1.78759e22	0.522306
$141$	0	0
$142$	3.72795e22	0.938517
$143$	4.56289e22	1.06711
$144$	0	0
$145$	2.96833e21	0.0599996
$146$	−1.41919e23	−2.66892
$147$	0	0
$148$	−8.10306e22	−1.32099
$149$	−8.46647e22	−1.28602	−0.643008	−	0.765859i	$-0.722314\pi$
$149$	−8.46647e22	−1.28602	−0.643008	+	0.765859i	$0.722314\pi$
$150$	0	0
$151$	1.42695e23	1.88430	0.942152	−	0.335185i	$-0.108799\pi$
$151$	1.42695e23	1.88430	0.942152	+	0.335185i	$0.108799\pi$
$152$	−4.58322e21	−0.0564694
$153$	0	0
$154$	1.63676e23	1.75800
$155$	−6.18890e22	−0.621055
$156$	0	0
$157$	1.74777e23	1.53298	0.766491	−	0.642255i	$-0.222001\pi$
$157$	1.74777e23	1.53298	0.766491	+	0.642255i	$0.222001\pi$
$158$	1.47146e23	1.20740
$159$	0	0
$160$	−8.79270e22	−0.632212
$161$	−3.67267e22	−0.247349
$162$	0	0
$163$	2.02629e23	1.19876	0.599378	−	0.800466i	$-0.295414\pi$
$163$	2.02629e23	1.19876	0.599378	+	0.800466i	$0.295414\pi$
$164$	1.62583e23	0.902020
$165$	0	0
$166$	−8.51775e22	−0.416092
$167$	2.13757e22	0.0980385	0.0490193	−	0.998798i	$-0.484390\pi$
$167$	2.13757e22	0.0980385	0.0490193	+	0.998798i	$0.484390\pi$
$168$	0	0
$169$	2.94422e22	0.119168
$170$	−1.84564e23	−0.702157
$171$	0	0
$172$	1.33351e23	0.448691
$173$	3.91056e23	1.23810	0.619048	−	0.785353i	$-0.287519\pi$
$173$	3.91056e23	1.23810	0.619048	+	0.785353i	$0.287519\pi$
$174$	0	0
$175$	3.53794e23	0.992776
$176$	−4.23447e23	−1.11922
$177$	0	0
$178$	2.01209e23	0.472321
$179$	8.21918e23	1.81916	0.909582	−	0.415525i	$-0.136402\pi$
$179$	8.21918e23	1.81916	0.909582	+	0.415525i	$0.136402\pi$
$180$	0	0
$181$	−7.25876e23	−1.42968	−0.714838	−	0.699290i	$-0.753500\pi$
$181$	−7.25876e23	−1.42968	−0.714838	+	0.699290i	$0.753500\pi$
$182$	9.91864e23	1.84375
$183$	0	0
$184$	2.01081e22	0.0333261
$185$	4.52460e23	0.708397
$186$	0	0
$187$	−7.88506e23	−1.10273
$188$	−1.31999e24	−1.74547
$189$	0	0
$190$	−1.78730e23	−0.211488
$191$	−1.75688e24	−1.96740	−0.983699	−	0.179823i	$-0.942448\pi$
$191$	−1.75688e24	−1.96740	−0.983699	+	0.179823i	$0.942448\pi$
$192$	0	0
$193$	1.25951e24	1.26430	0.632151	−	0.774845i	$-0.282172\pi$
$193$	1.25951e24	1.26430	0.632151	+	0.774845i	$0.282172\pi$
$194$	−1.97586e24	−1.87861
$195$	0	0
$196$	6.35475e23	0.542512
$197$	−9.65242e22	−0.0781162	−0.0390581	−	0.999237i	$-0.512436\pi$
$197$	−9.65242e22	−0.0781162	−0.0390581	+	0.999237i	$0.512436\pi$
$198$	0	0
$199$	−1.00060e24	−0.728286	−0.364143	−	0.931343i	$-0.618638\pi$
$199$	−1.00060e24	−0.728286	−0.364143	+	0.931343i	$0.618638\pi$
$200$	−1.93705e23	−0.133760
$201$	0	0
$202$	−1.86486e24	−1.16000
$203$	2.75665e23	0.162807
$204$	0	0
$205$	−9.07836e23	−0.483718
$206$	8.60872e22	0.0435846
$207$	0	0
$208$	−2.56605e24	−1.17382
$209$	−7.63581e23	−0.332138
$210$	0	0
$211$	−9.80401e23	−0.385867	−0.192934	−	0.981212i	$-0.561800\pi$
$211$	−9.80401e23	−0.385867	−0.192934	+	0.981212i	$0.561800\pi$
$212$	9.84435e23	0.368689
$213$	0	0
$214$	−3.15149e24	−1.06948
$215$	−7.44607e23	−0.240615
$216$	0	0
$217$	−5.74755e24	−1.68521
$218$	6.90575e23	0.192938
$219$	0	0
$220$	−1.63058e24	−0.413909
$221$	−4.77827e24	−1.15652
$222$	0	0
$223$	−2.01061e24	−0.442717	−0.221359	−	0.975193i	$-0.571049\pi$
$223$	−2.01061e24	−0.442717	−0.221359	+	0.975193i	$0.571049\pi$
$224$	−8.16567e24	−1.71549
$225$	0	0
$226$	8.91876e24	1.70673
$227$	−1.48594e24	−0.271474	−0.135737	−	0.990745i	$-0.543340\pi$
$227$	−1.48594e24	−0.271474	−0.135737	+	0.990745i	$0.543340\pi$
$228$	0	0
$229$	−2.85440e24	−0.475600	−0.237800	−	0.971314i	$-0.576426\pi$
$229$	−2.85440e24	−0.475600	−0.237800	+	0.971314i	$0.576426\pi$
$230$	7.84149e23	0.124812
$231$	0	0
$232$	−1.50929e23	−0.0219355
$233$	5.64192e24	0.783772	0.391886	−	0.920014i	$-0.371823\pi$
$233$	5.64192e24	0.783772	0.391886	+	0.920014i	$0.371823\pi$
$234$	0	0
$235$	7.37057e24	0.936028
$236$	−9.85605e24	−1.19709
$237$	0	0
$238$	−1.71403e25	−1.90528
$239$	−5.37400e24	−0.571637	−0.285818	−	0.958284i	$-0.592265\pi$
$239$	−5.37400e24	−0.571637	−0.285818	+	0.958284i	$0.592265\pi$
$240$	0	0
$241$	4.11925e23	0.0401457	0.0200729	−	0.999799i	$-0.493610\pi$
$241$	4.11925e23	0.0401457	0.0200729	+	0.999799i	$0.493610\pi$
$242$	−2.56535e23	−0.0239378
$243$	0	0
$244$	3.98520e24	0.341080
$245$	−3.54837e24	−0.290928
$246$	0	0
$247$	−4.62723e24	−0.348340
$248$	3.14682e24	0.227054
$249$	0	0
$250$	−1.72389e25	−1.14324
$251$	−9.06680e24	−0.576607	−0.288304	−	0.957539i	$-0.593091\pi$
$251$	−9.06680e24	−0.576607	−0.288304	+	0.957539i	$0.593091\pi$
$252$	0	0
$253$	3.35008e24	0.196015
$254$	−3.68130e25	−2.06655
$255$	0	0
$256$	2.32447e25	1.20172
$257$	9.16702e24	0.454915	0.227458	−	0.973788i	$-0.426959\pi$
$257$	9.16702e24	0.454915	0.227458	+	0.973788i	$0.426959\pi$
$258$	0	0
$259$	4.20193e25	1.92221
$260$	−9.88118e24	−0.434099
$261$	0	0
$262$	−5.78881e25	−2.34653
$263$	−1.97814e25	−0.770411	−0.385206	−	0.922831i	$-0.625869\pi$
$263$	−1.97814e25	−0.770411	−0.385206	+	0.922831i	$0.625869\pi$
$264$	0	0
$265$	−5.49690e24	−0.197714
$266$	−1.65985e25	−0.573866
$267$	0	0
$268$	3.35622e25	1.07259
$269$	−1.02928e25	−0.316327	−0.158163	−	0.987413i	$-0.550557\pi$
$269$	−1.02928e25	−0.316327	−0.158163	+	0.987413i	$0.550557\pi$
$270$	0	0
$271$	4.42626e25	1.25852	0.629258	−	0.777196i	$-0.283359\pi$
$271$	4.42626e25	1.25852	0.629258	+	0.777196i	$0.283359\pi$
$272$	4.43435e25	1.21299
$273$	0	0
$274$	5.03742e25	1.27593
$275$	−3.22719e25	−0.786741
$276$	0	0
$277$	−7.57773e24	−0.171199	−0.0855996	−	0.996330i	$-0.527281\pi$
$277$	−7.57773e24	−0.171199	−0.0855996	+	0.996330i	$0.527281\pi$
$278$	−1.61042e25	−0.350323
$279$	0	0
$280$	5.07527e24	0.102400
$281$	2.30632e24	0.0448232	0.0224116	−	0.999749i	$-0.492866\pi$
$281$	2.30632e24	0.0448232	0.0224116	+	0.999749i	$0.492866\pi$
$282$	0	0
$283$	9.96523e24	0.179775	0.0898876	−	0.995952i	$-0.471349\pi$
$283$	9.96523e24	0.179775	0.0898876	+	0.995952i	$0.471349\pi$
$284$	−3.44902e25	−0.599589
$285$	0	0
$286$	−9.04744e25	−1.46111
$287$	−8.43095e25	−1.31255
$288$	0	0
$289$	1.34807e25	0.195112
$290$	−5.88571e24	−0.0821523
$291$	0	0
$292$	1.31301e26	1.70509
$293$	−9.07826e25	−1.13735	−0.568673	−	0.822563i	$-0.692543\pi$
$293$	−9.07826e25	−1.13735	−0.568673	+	0.822563i	$0.692543\pi$
$294$	0	0
$295$	5.50343e25	0.641952
$296$	−2.30059e25	−0.258986
$297$	0	0
$298$	1.67876e26	1.76083
$299$	2.03012e25	0.205577
$300$	0	0
$301$	−6.91507e25	−0.652903
$302$	−2.82941e26	−2.58002
$303$	0	0
$304$	4.29418e25	0.365349
$305$	−2.22526e25	−0.182908
$306$	0	0
$307$	−2.92837e25	−0.224736	−0.112368	−	0.993667i	$-0.535844\pi$
$307$	−2.92837e25	−0.224736	−0.112368	+	0.993667i	$0.535844\pi$
$308$	−1.51430e26	−1.12313
$309$	0	0
$310$	1.22716e26	0.850358
$311$	−7.77185e25	−0.520643	−0.260322	−	0.965522i	$-0.583829\pi$
$311$	−7.77185e25	−0.520643	−0.260322	+	0.965522i	$0.583829\pi$
$312$	0	0
$313$	1.19250e26	0.746864	0.373432	−	0.927658i	$-0.378181\pi$
$313$	1.19250e26	0.746864	0.373432	+	0.927658i	$0.378181\pi$
$314$	−3.46553e26	−2.09898
$315$	0	0
$316$	−1.36137e26	−0.771366
$317$	−4.56316e25	−0.250117	−0.125059	−	0.992149i	$-0.539912\pi$
$317$	−4.56316e25	−0.250117	−0.125059	+	0.992149i	$0.539912\pi$
$318$	0	0
$319$	−2.51452e25	−0.129019
$320$	6.95147e25	0.345145
$321$	0	0
$322$	7.28229e25	0.338673
$323$	7.99625e25	0.359965
$324$	0	0
$325$	−1.95565e26	−0.825117
$326$	−4.01779e26	−1.64136
$327$	0	0
$328$	4.61601e25	0.176844
$329$	6.84496e26	2.53988
$330$	0	0
$331$	−2.60518e26	−0.907077	−0.453538	−	0.891237i	$-0.649838\pi$
$331$	−2.60518e26	−0.907077	−0.453538	+	0.891237i	$0.649838\pi$
$332$	7.88045e25	0.265828
$333$	0	0
$334$	−4.23844e25	−0.134236
$335$	−1.87405e26	−0.575190
$336$	0	0
$337$	−4.59742e26	−1.32556	−0.662781	−	0.748813i	$-0.730624\pi$
$337$	−4.59742e26	−1.32556	−0.662781	+	0.748813i	$0.730624\pi$
$338$	−5.83789e25	−0.163166
$339$	0	0
$340$	1.70755e26	0.448586
$341$	5.24272e26	1.33547
$342$	0	0
$343$	2.01806e26	0.483444
$344$	3.78605e25	0.0879676
$345$	0	0
$346$	−7.75398e26	−1.69522
$347$	−2.10744e26	−0.446987	−0.223493	−	0.974705i	$-0.571746\pi$
$347$	−2.10744e26	−0.446987	−0.223493	+	0.974705i	$0.571746\pi$
$348$	0	0
$349$	3.34411e26	0.667749	0.333875	−	0.942617i	$-0.391644\pi$
$349$	3.34411e26	0.667749	0.333875	+	0.942617i	$0.391644\pi$
$350$	−7.01515e26	−1.35932
$351$	0	0
$352$	7.44844e26	1.35946
$353$	−5.00558e26	−0.886789	−0.443394	−	0.896327i	$-0.646226\pi$
$353$	−5.00558e26	−0.886789	−0.443394	+	0.896327i	$0.646226\pi$
$354$	0	0
$355$	1.92587e26	0.321536
$356$	−1.86155e26	−0.301751
$357$	0	0
$358$	−1.62973e27	−2.49083
$359$	7.99086e26	1.18605	0.593023	−	0.805185i	$-0.297934\pi$
$359$	7.99086e26	1.18605	0.593023	+	0.805185i	$0.297934\pi$
$360$	0	0
$361$	−6.36775e26	−0.891580
$362$	1.43929e27	1.95753
$363$	0	0
$364$	−9.17653e26	−1.17791
$365$	−7.33160e26	−0.914373
$366$	0	0
$367$	−4.46698e26	−0.526042	−0.263021	−	0.964790i	$-0.584719\pi$
$367$	−4.46698e26	−0.526042	−0.263021	+	0.964790i	$0.584719\pi$
$368$	−1.88400e26	−0.215615
$369$	0	0
$370$	−8.97152e26	−0.969947
$371$	−5.10490e26	−0.536490
$372$	0	0
$373$	−1.33252e27	−1.32352	−0.661761	−	0.749714i	$-0.730191\pi$
$373$	−1.33252e27	−1.32352	−0.661761	+	0.749714i	$0.730191\pi$
$374$	1.56348e27	1.50987
$375$	0	0
$376$	−3.74766e26	−0.342206
$377$	−1.52378e26	−0.135312
$378$	0	0
$379$	−8.18217e26	−0.687317	−0.343658	−	0.939095i	$-0.611666\pi$
$379$	−8.18217e26	−0.687317	−0.343658	+	0.939095i	$0.611666\pi$
$380$	1.65358e26	0.135113
$381$	0	0
$382$	3.48361e27	2.69379
$383$	−1.44791e27	−1.08931	−0.544657	−	0.838659i	$-0.683340\pi$
$383$	−1.44791e27	−1.08931	−0.544657	+	0.838659i	$0.683340\pi$
$384$	0	0
$385$	8.45557e26	0.602290
$386$	−2.49741e27	−1.73110
$387$	0	0
$388$	1.82802e27	1.20019
$389$	5.33912e26	0.341192	0.170596	−	0.985341i	$-0.445431\pi$
$389$	5.33912e26	0.341192	0.170596	+	0.985341i	$0.445431\pi$
$390$	0	0
$391$	−3.50822e26	−0.212437
$392$	1.80422e26	0.106362
$393$	0	0
$394$	1.91392e26	0.106958
$395$	7.60162e26	0.413653
$396$	0	0
$397$	−2.65812e27	−1.37175	−0.685874	−	0.727720i	$-0.740580\pi$
$397$	−2.65812e27	−1.37175	−0.685874	+	0.727720i	$0.740580\pi$
$398$	1.98402e27	0.997180
$399$	0	0
$400$	1.81489e27	0.865407
$401$	−1.28013e27	−0.594617	−0.297309	−	0.954781i	$-0.596089\pi$
$401$	−1.28013e27	−0.594617	−0.297309	+	0.954781i	$0.596089\pi$
$402$	0	0
$403$	3.17704e27	1.40062
$404$	1.72533e27	0.741084
$405$	0	0
$406$	−5.46598e26	−0.222918
$407$	−3.83286e27	−1.52329
$408$	0	0
$409$	1.59574e27	0.602374	0.301187	−	0.953565i	$-0.402617\pi$
$409$	1.59574e27	0.602374	0.301187	+	0.953565i	$0.402617\pi$
$410$	1.80009e27	0.662313
$411$	0	0
$412$	−7.96461e25	−0.0278448
$413$	5.11097e27	1.74192
$414$	0	0
$415$	−4.40030e26	−0.142553
$416$	4.51369e27	1.42578
$417$	0	0
$418$	1.51405e27	0.454769
$419$	3.39709e27	0.995084	0.497542	−	0.867440i	$-0.334236\pi$
$419$	3.39709e27	0.995084	0.497542	+	0.867440i	$0.334236\pi$
$420$	0	0
$421$	−2.70761e27	−0.754438	−0.377219	−	0.926124i	$-0.623120\pi$
$421$	−2.70761e27	−0.754438	−0.377219	+	0.926124i	$0.623120\pi$
$422$	1.94397e27	0.528335
$423$	0	0
$424$	2.79497e26	0.0722829
$425$	3.37953e27	0.852653
$426$	0	0
$427$	−2.06657e27	−0.496315
$428$	2.91570e27	0.683255
$429$	0	0
$430$	1.47643e27	0.329454
$431$	2.25771e26	0.0491650	0.0245825	−	0.999698i	$-0.492174\pi$
$431$	2.25771e26	0.0491650	0.0245825	+	0.999698i	$0.492174\pi$
$432$	0	0
$433$	5.59341e27	1.16026	0.580128	−	0.814525i	$-0.303003\pi$
$433$	5.59341e27	1.16026	0.580128	+	0.814525i	$0.303003\pi$
$434$	1.13964e28	2.30742
$435$	0	0
$436$	−6.38906e26	−0.123262
$437$	−3.39732e26	−0.0639855
$438$	0	0
$439$	−1.20421e27	−0.216185	−0.108093	−	0.994141i	$-0.534474\pi$
$439$	−1.20421e27	−0.216185	−0.108093	+	0.994141i	$0.534474\pi$
$440$	−4.62949e26	−0.0811484
$441$	0	0
$442$	9.47452e27	1.58352
$443$	−5.09084e27	−0.830903	−0.415451	−	0.909615i	$-0.636376\pi$
$443$	−5.09084e27	−0.830903	−0.415451	+	0.909615i	$0.636376\pi$
$444$	0	0
$445$	1.03945e27	0.161817
$446$	3.98670e27	0.606174
$447$	0	0
$448$	6.45574e27	0.936540
$449$	−3.77519e27	−0.534998	−0.267499	−	0.963558i	$-0.586197\pi$
$449$	−3.77519e27	−0.534998	−0.267499	+	0.963558i	$0.586197\pi$
$450$	0	0
$451$	7.69043e27	1.04015
$452$	−8.25146e27	−1.09038
$453$	0	0
$454$	2.94636e27	0.371706
$455$	5.12400e27	0.631669
$456$	0	0
$457$	8.97959e27	1.05715	0.528575	−	0.848887i	$-0.322727\pi$
$457$	8.97959e27	1.05715	0.528575	+	0.848887i	$0.322727\pi$
$458$	5.65980e27	0.651199
$459$	0	0
$460$	−7.25479e26	−0.0797384
$461$	1.03690e28	1.11398	0.556992	−	0.830518i	$-0.311956\pi$
$461$	1.03690e28	1.11398	0.556992	+	0.830518i	$0.311956\pi$
$462$	0	0
$463$	−4.56649e27	−0.468794	−0.234397	−	0.972141i	$-0.575312\pi$
$463$	−4.56649e27	−0.468794	−0.234397	+	0.972141i	$0.575312\pi$
$464$	1.41410e27	0.141920
$465$	0	0
$466$	−1.11870e28	−1.07315
$467$	9.25506e27	0.868064	0.434032	−	0.900897i	$-0.357090\pi$
$467$	9.25506e27	0.868064	0.434032	+	0.900897i	$0.357090\pi$
$468$	0	0
$469$	−1.74041e28	−1.56076
$470$	−1.46146e28	−1.28162
$471$	0	0
$472$	−2.79829e27	−0.234694
$473$	6.30769e27	0.517403
$474$	0	0
$475$	3.27270e27	0.256817
$476$	1.58578e28	1.21722
$477$	0	0
$478$	1.06558e28	0.782693
$479$	−7.49323e27	−0.538451	−0.269226	−	0.963077i	$-0.586768\pi$
$479$	−7.49323e27	−0.538451	−0.269226	+	0.963077i	$0.586768\pi$
$480$	0	0
$481$	−2.32268e28	−1.59759
$482$	−8.16779e26	−0.0549681
$483$	0	0
$484$	2.37341e26	0.0152931
$485$	−1.02073e28	−0.643613
$486$	0	0
$487$	5.44040e27	0.328531	0.164266	−	0.986416i	$-0.447475\pi$
$487$	5.44040e27	0.328531	0.164266	+	0.986416i	$0.447475\pi$
$488$	1.13146e27	0.0668701
$489$	0	0
$490$	7.03584e27	0.398343
$491$	1.09503e28	0.606834	0.303417	−	0.952858i	$-0.401873\pi$
$491$	1.09503e28	0.606834	0.303417	+	0.952858i	$0.401873\pi$
$492$	0	0
$493$	2.63322e27	0.139828
$494$	9.17503e27	0.476952
$495$	0	0
$496$	−2.94837e28	−1.46901
$497$	1.78853e28	0.872477
$498$	0	0
$499$	1.69149e28	0.791067	0.395534	−	0.918451i	$-0.370560\pi$
$499$	1.69149e28	0.791067	0.395534	+	0.918451i	$0.370560\pi$
$500$	1.59490e28	0.730381
$501$	0	0
$502$	1.79780e28	0.789499
$503$	−1.50401e28	−0.646827	−0.323414	−	0.946258i	$-0.604831\pi$
$503$	−1.50401e28	−0.646827	−0.323414	+	0.946258i	$0.604831\pi$
$504$	0	0
$505$	−9.63391e27	−0.397414
$506$	−6.64265e27	−0.268387
$507$	0	0
$508$	3.40586e28	1.32026
$509$	−7.64106e27	−0.290146	−0.145073	−	0.989421i	$-0.546342\pi$
$509$	−7.64106e27	−0.290146	−0.145073	+	0.989421i	$0.546342\pi$
$510$	0	0
$511$	−6.80876e28	−2.48112
$512$	−3.65579e28	−1.30511
$513$	0	0
$514$	−1.81767e28	−0.622876
$515$	4.44729e26	0.0149321
$516$	0	0
$517$	−6.24374e28	−2.01277
$518$	−8.33173e28	−2.63192
$519$	0	0
$520$	−2.80543e27	−0.0851067
$521$	−2.10509e28	−0.625856	−0.312928	−	0.949777i	$-0.601310\pi$
$521$	−2.10509e28	−0.625856	−0.312928	+	0.949777i	$0.601310\pi$
$522$	0	0
$523$	−2.92433e28	−0.835138	−0.417569	−	0.908645i	$-0.637118\pi$
$523$	−2.92433e28	−0.835138	−0.417569	+	0.908645i	$0.637118\pi$
$524$	5.35570e28	1.49912
$525$	0	0
$526$	3.92233e28	1.05486
$527$	−5.49019e28	−1.44736
$528$	0	0
$529$	−3.79811e28	−0.962238
$530$	1.08994e28	0.270712
$531$	0	0
$532$	1.53566e28	0.366625
$533$	4.66033e28	1.09089
$534$	0	0
$535$	−1.62807e28	−0.366402
$536$	9.52885e27	0.210286
$537$	0	0
$538$	2.04090e28	0.433119
$539$	3.00589e28	0.625591
$540$	0	0
$541$	−3.57924e28	−0.716506	−0.358253	−	0.933625i	$-0.616627\pi$
$541$	−3.57924e28	−0.716506	−0.358253	+	0.933625i	$0.616627\pi$
$542$	−8.77653e28	−1.72318
$543$	0	0
$544$	−7.80004e28	−1.47336
$545$	3.56753e27	0.0661005
$546$	0	0
$547$	−4.96222e28	−0.884726	−0.442363	−	0.896836i	$-0.645860\pi$
$547$	−4.96222e28	−0.884726	−0.442363	+	0.896836i	$0.645860\pi$
$548$	−4.66052e28	−0.815152
$549$	0	0
$550$	6.39899e28	1.07722
$551$	2.54998e27	0.0421158
$552$	0	0
$553$	7.05952e28	1.12244
$554$	1.50254e28	0.234408
$555$	0	0
$556$	1.48993e28	0.223810
$557$	2.30026e28	0.339076	0.169538	−	0.985524i	$-0.445772\pi$
$557$	2.30026e28	0.339076	0.169538	+	0.985524i	$0.445772\pi$
$558$	0	0
$559$	3.82240e28	0.542641
$560$	−4.75520e28	−0.662513
$561$	0	0
$562$	−4.57304e27	−0.0613725
$563$	5.62134e28	0.740461	0.370230	−	0.928940i	$-0.379279\pi$
$563$	5.62134e28	0.740461	0.370230	+	0.928940i	$0.379279\pi$
$564$	0	0
$565$	4.60746e28	0.584727
$566$	−1.97594e28	−0.246151
$567$	0	0
$568$	−9.79233e27	−0.117552
$569$	−8.17427e28	−0.963319	−0.481660	−	0.876358i	$-0.659966\pi$
$569$	−8.17427e28	−0.963319	−0.481660	+	0.876358i	$0.659966\pi$
$570$	0	0
$571$	6.28184e28	0.713523	0.356762	−	0.934195i	$-0.383881\pi$
$571$	6.28184e28	0.713523	0.356762	+	0.934195i	$0.383881\pi$
$572$	8.37052e28	0.933456
$573$	0	0
$574$	1.67172e29	1.79717
$575$	−1.43584e28	−0.151563
$576$	0	0
$577$	−1.12097e29	−1.14090	−0.570449	−	0.821333i	$-0.693231\pi$
$577$	−1.12097e29	−1.14090	−0.570449	+	0.821333i	$0.693231\pi$
$578$	−2.67299e28	−0.267150
$579$	0	0
$580$	5.44534e27	0.0524845
$581$	−4.08650e28	−0.386814
$582$	0	0
$583$	4.65652e28	0.425149
$584$	3.72784e28	0.334289
$585$	0	0
$586$	1.80007e29	1.55727
$587$	−1.68937e29	−1.43557	−0.717784	−	0.696266i	$-0.754843\pi$
$587$	−1.68937e29	−1.43557	−0.717784	+	0.696266i	$0.754843\pi$
$588$	0	0
$589$	−5.31665e28	−0.435941
$590$	−1.09124e29	−0.878970
$591$	0	0
$592$	2.15550e29	1.67560
$593$	−2.13722e29	−1.63221	−0.816104	−	0.577906i	$-0.803870\pi$
$593$	−2.13722e29	−1.63221	−0.816104	+	0.577906i	$0.803870\pi$
$594$	0	0
$595$	−8.85471e28	−0.652749
$596$	−1.55316e29	−1.12494
$597$	0	0
$598$	−4.02539e28	−0.281479
$599$	−6.63059e28	−0.455586	−0.227793	−	0.973710i	$-0.573151\pi$
$599$	−6.63059e28	−0.455586	−0.227793	+	0.973710i	$0.573151\pi$
$600$	0	0
$601$	−2.56590e29	−1.70238	−0.851192	−	0.524854i	$-0.824120\pi$
$601$	−2.56590e29	−1.70238	−0.851192	+	0.524854i	$0.824120\pi$
$602$	1.37114e29	0.893964
$603$	0	0
$604$	2.61771e29	1.64829
$605$	−1.32527e27	−0.00820109
$606$	0	0
$607$	6.37131e28	0.380845	0.190422	−	0.981702i	$-0.439014\pi$
$607$	6.37131e28	0.380845	0.190422	+	0.981702i	$0.439014\pi$
$608$	−7.55348e28	−0.443772
$609$	0	0
$610$	4.41232e28	0.250440
$611$	−3.78365e29	−2.11095
$612$	0	0
$613$	2.43258e29	1.31139	0.655694	−	0.755027i	$-0.272376\pi$
$613$	2.43258e29	1.31139	0.655694	+	0.755027i	$0.272376\pi$
$614$	5.80647e28	0.307712
$615$	0	0
$616$	−4.29934e28	−0.220194
$617$	2.30434e28	0.116025	0.0580127	−	0.998316i	$-0.481524\pi$
$617$	2.30434e28	0.116025	0.0580127	+	0.998316i	$0.481524\pi$
$618$	0	0
$619$	−3.66125e29	−1.78188	−0.890938	−	0.454125i	$-0.849952\pi$
$619$	−3.66125e29	−1.78188	−0.890938	+	0.454125i	$0.849952\pi$
$620$	−1.13534e29	−0.543267
$621$	0	0
$622$	1.54103e29	0.712872
$623$	9.65326e28	0.439086
$624$	0	0
$625$	8.82841e28	0.388278
$626$	−2.36452e29	−1.02262
$627$	0	0
$628$	3.20624e29	1.34097
$629$	4.01379e29	1.65091
$630$	0	0
$631$	−8.86516e28	−0.352678	−0.176339	−	0.984330i	$-0.556425\pi$
$631$	−8.86516e28	−0.352678	−0.176339	+	0.984330i	$0.556425\pi$
$632$	−3.86514e28	−0.151229
$633$	0	0
$634$	9.04800e28	0.342464
$635$	−1.90177e29	−0.708001
$636$	0	0
$637$	1.82154e29	0.656107
$638$	4.98588e28	0.176654
$639$	0	0
$640$	4.65603e28	0.159634
$641$	2.13941e29	0.721581	0.360790	−	0.932647i	$-0.382507\pi$
$641$	2.13941e29	0.721581	0.360790	+	0.932647i	$0.382507\pi$
$642$	0	0
$643$	−2.22607e29	−0.726647	−0.363323	−	0.931663i	$-0.618358\pi$
$643$	−2.22607e29	−0.726647	−0.363323	+	0.931663i	$0.618358\pi$
$644$	−6.73743e28	−0.216368
$645$	0	0
$646$	−1.58552e29	−0.492869
$647$	1.83534e29	0.561333	0.280666	−	0.959805i	$-0.409445\pi$
$647$	1.83534e29	0.561333	0.280666	+	0.959805i	$0.409445\pi$
$648$	0	0
$649$	−4.66205e29	−1.38041
$650$	3.87773e29	1.12976
$651$	0	0
$652$	3.71718e29	1.04861
$653$	4.04588e29	1.12312	0.561558	−	0.827437i	$-0.310202\pi$
$653$	4.04588e29	1.12312	0.561558	+	0.827437i	$0.310202\pi$
$654$	0	0
$655$	−2.99052e29	−0.803921
$656$	−4.32490e29	−1.14416
$657$	0	0
$658$	−1.35724e30	−3.47764
$659$	−1.05672e29	−0.266479	−0.133240	−	0.991084i	$-0.542538\pi$
$659$	−1.05672e29	−0.266479	−0.133240	+	0.991084i	$0.542538\pi$
$660$	0	0
$661$	3.72335e29	0.909532	0.454766	−	0.890611i	$-0.349723\pi$
$661$	3.72335e29	0.909532	0.454766	+	0.890611i	$0.349723\pi$
$662$	5.16564e29	1.24198
$663$	0	0
$664$	2.23739e28	0.0521166
$665$	−8.57482e28	−0.196606
$666$	0	0
$667$	−1.11876e28	−0.0248551
$668$	3.92132e28	0.0857589
$669$	0	0
$670$	3.71593e29	0.787558
$671$	1.88505e29	0.393312
$672$	0	0
$673$	5.57345e29	1.12711	0.563554	−	0.826079i	$-0.309434\pi$
$673$	5.57345e29	1.12711	0.563554	+	0.826079i	$0.309434\pi$
$674$	9.11591e29	1.81498
$675$	0	0
$676$	5.40110e28	0.104242
$677$	9.43636e29	1.79318	0.896589	−	0.442863i	$-0.146037\pi$
$677$	9.43636e29	1.79318	0.896589	+	0.442863i	$0.146037\pi$
$678$	0	0
$679$	−9.47943e29	−1.74642
$680$	4.84802e28	0.0879469
$681$	0	0
$682$	−1.03954e30	−1.82855
$683$	−2.26004e29	−0.391469	−0.195735	−	0.980657i	$-0.562709\pi$
$683$	−2.26004e29	−0.391469	−0.195735	+	0.980657i	$0.562709\pi$
$684$	0	0
$685$	2.60235e29	0.437134
$686$	−4.00148e29	−0.661938
$687$	0	0
$688$	−3.54729e29	−0.569138
$689$	2.82181e29	0.445888
$690$	0	0
$691$	1.59020e29	0.243743	0.121872	−	0.992546i	$-0.461110\pi$
$691$	1.59020e29	0.243743	0.121872	+	0.992546i	$0.461110\pi$
$692$	7.17383e29	1.08302
$693$	0	0
$694$	4.17869e29	0.612021
$695$	−8.31948e28	−0.120021
$696$	0	0
$697$	−8.05345e29	−1.12730
$698$	−6.63081e29	−0.914292
$699$	0	0
$700$	6.49028e29	0.868429
$701$	8.48451e28	0.111838	0.0559188	−	0.998435i	$-0.482191\pi$
$701$	8.48451e28	0.111838	0.0559188	+	0.998435i	$0.482191\pi$
$702$	0	0
$703$	3.88691e29	0.497249
$704$	−5.88870e29	−0.742176
$705$	0	0
$706$	9.92524e29	1.21420
$707$	−8.94689e29	−1.07837
$708$	0	0
$709$	−1.48138e30	−1.73333	−0.866663	−	0.498894i	$-0.833740\pi$
$709$	−1.48138e30	−1.73333	−0.866663	+	0.498894i	$0.833740\pi$
$710$	−3.81868e29	−0.440251
$711$	0	0
$712$	−5.28523e28	−0.0591594
$713$	2.33259e29	0.257275
$714$	0	0
$715$	−4.67394e29	−0.500576
$716$	1.50779e30	1.59131
$717$	0	0
$718$	−1.58445e30	−1.62395
$719$	−3.93222e29	−0.397178	−0.198589	−	0.980083i	$-0.563636\pi$
$719$	−3.93222e29	−0.397178	−0.198589	+	0.980083i	$0.563636\pi$
$720$	0	0
$721$	4.13014e28	0.0405177
$722$	1.26262e30	1.22076
$723$	0	0
$724$	−1.33160e30	−1.25061
$725$	1.07772e29	0.0997603
$726$	0	0
$727$	1.86883e30	1.68058	0.840289	−	0.542139i	$-0.182385\pi$
$727$	1.86883e30	1.68058	0.840289	+	0.542139i	$0.182385\pi$
$728$	−2.60536e29	−0.230934
$729$	0	0
$730$	1.45373e30	1.25197
$731$	−6.60544e29	−0.560750
$732$	0	0
$733$	−1.56464e30	−1.29069	−0.645347	−	0.763890i	$-0.723287\pi$
$733$	−1.56464e30	−1.29069	−0.645347	+	0.763890i	$0.723287\pi$
$734$	8.85729e29	0.720265
$735$	0	0
$736$	3.31396e29	0.261897
$737$	1.58754e30	1.23685
$738$	0	0
$739$	−9.06934e29	−0.686766	−0.343383	−	0.939195i	$-0.611573\pi$
$739$	−9.06934e29	−0.686766	−0.343383	+	0.939195i	$0.611573\pi$
$740$	8.30027e29	0.619668
$741$	0	0
$742$	1.01222e30	0.734569
$743$	−5.31590e29	−0.380359	−0.190180	−	0.981749i	$-0.560907\pi$
$743$	−5.31590e29	−0.380359	−0.190180	+	0.981749i	$0.560907\pi$
$744$	0	0
$745$	8.67253e29	0.603260
$746$	2.64217e30	1.81219
$747$	0	0
$748$	−1.44650e30	−0.964607
$749$	−1.51197e30	−0.994222
$750$	0	0
$751$	7.95212e29	0.508468	0.254234	−	0.967143i	$-0.418177\pi$
$751$	7.95212e29	0.508468	0.254234	+	0.967143i	$0.418177\pi$
$752$	3.51132e30	2.21403
$753$	0	0
$754$	3.02140e29	0.185272
$755$	−1.46168e30	−0.883913
$756$	0	0
$757$	1.04161e30	0.612630	0.306315	−	0.951930i	$-0.400904\pi$
$757$	1.04161e30	0.612630	0.306315	+	0.951930i	$0.400904\pi$
$758$	1.62239e30	0.941084
$759$	0	0
$760$	4.69477e28	0.0264894
$761$	1.41338e30	0.786539	0.393269	−	0.919423i	$-0.371344\pi$
$761$	1.41338e30	0.786539	0.393269	+	0.919423i	$0.371344\pi$
$762$	0	0
$763$	3.31312e29	0.179362
$764$	−3.22296e30	−1.72098
$765$	0	0
$766$	2.87096e30	1.49150
$767$	−2.82516e30	−1.44774
$768$	0	0
$769$	3.24769e30	1.61938	0.809688	−	0.586861i	$-0.199637\pi$
$769$	3.24769e30	1.61938	0.809688	+	0.586861i	$0.199637\pi$
$770$	−1.67660e30	−0.824664
$771$	0	0
$772$	2.31055e30	1.10595
$773$	3.03297e30	1.43213	0.716067	−	0.698031i	$-0.245940\pi$
$773$	3.03297e30	1.43213	0.716067	+	0.698031i	$0.245940\pi$
$774$	0	0
$775$	−2.24702e30	−1.03262
$776$	5.19005e29	0.235301
$777$	0	0
$778$	−1.05866e30	−0.467165
$779$	−7.79888e29	−0.339538
$780$	0	0
$781$	−1.63144e30	−0.691408
$782$	6.95621e29	0.290872
$783$	0	0
$784$	−1.69043e30	−0.688144
$785$	−1.79031e30	−0.719111
$786$	0	0
$787$	3.69463e30	1.44489	0.722447	−	0.691427i	$-0.243017\pi$
$787$	3.69463e30	1.44489	0.722447	+	0.691427i	$0.243017\pi$
$788$	−1.77072e29	−0.0683319
$789$	0	0
$790$	−1.50727e30	−0.566380
$791$	4.27889e30	1.58664
$792$	0	0
$793$	1.14233e30	0.412498
$794$	5.27061e30	1.87822
$795$	0	0
$796$	−1.83557e30	−0.637067
$797$	−5.77690e28	−0.0197871	−0.00989356	−	0.999951i	$-0.503149\pi$
$797$	−5.77690e28	−0.0197871	−0.00989356	+	0.999951i	$0.503149\pi$
$798$	0	0
$799$	6.53846e30	2.18140
$800$	−3.19240e30	−1.05117
$801$	0	0
$802$	2.53828e30	0.814158
$803$	6.21072e30	1.96620
$804$	0	0
$805$	3.76205e29	0.116029
$806$	−6.29954e30	−1.91774
$807$	0	0
$808$	4.89849e29	0.145292
$809$	−1.52694e30	−0.447056	−0.223528	−	0.974697i	$-0.571757\pi$
$809$	−1.52694e30	−0.447056	−0.223528	+	0.974697i	$0.571757\pi$
$810$	0	0
$811$	3.21814e30	0.918092	0.459046	−	0.888412i	$-0.348191\pi$
$811$	3.21814e30	0.918092	0.459046	+	0.888412i	$0.348191\pi$
$812$	5.05701e29	0.142415
$813$	0	0
$814$	7.59992e30	2.08571
$815$	−2.07560e30	−0.562328
$816$	0	0
$817$	−6.39664e29	−0.168896
$818$	−3.16408e30	−0.824779
$819$	0	0
$820$	−1.66541e30	−0.423131
$821$	−6.21750e30	−1.55960	−0.779799	−	0.626030i	$-0.784679\pi$
$821$	−6.21750e30	−1.55960	−0.779799	+	0.626030i	$0.784679\pi$
$822$	0	0
$823$	2.59262e30	0.633929	0.316965	−	0.948437i	$-0.397336\pi$
$823$	2.59262e30	0.633929	0.316965	+	0.948437i	$0.397336\pi$
$824$	−2.26128e28	−0.00545907
$825$	0	0
$826$	−1.01342e31	−2.38506
$827$	−7.60849e30	−1.76804	−0.884018	−	0.467454i	$-0.845171\pi$
$827$	−7.60849e30	−1.76804	−0.884018	+	0.467454i	$0.845171\pi$
$828$	0	0
$829$	−2.02047e28	−0.00457752	−0.00228876	−	0.999997i	$-0.500729\pi$
$829$	−2.02047e28	−0.00457752	−0.00228876	+	0.999997i	$0.500729\pi$
$830$	8.72506e29	0.195186
$831$	0	0
$832$	−3.56850e30	−0.778378
$833$	−3.14778e30	−0.678003
$834$	0	0
$835$	−2.18959e29	−0.0459891
$836$	−1.40077e30	−0.290537
$837$	0	0
$838$	−6.73587e30	−1.36248
$839$	2.31080e30	0.461595	0.230798	−	0.973002i	$-0.425866\pi$
$839$	2.31080e30	0.461595	0.230798	+	0.973002i	$0.425866\pi$
$840$	0	0
$841$	−5.04887e30	−0.983640
$842$	5.36873e30	1.03299
$843$	0	0
$844$	−1.79852e30	−0.337536
$845$	−3.01587e29	−0.0559008
$846$	0	0
$847$	−1.23076e29	−0.0222534
$848$	−2.61871e30	−0.467660
$849$	0	0
$850$	−6.70104e30	−1.16746
$851$	−1.70532e30	−0.293457
$852$	0	0
$853$	1.67813e30	0.281747	0.140874	−	0.990028i	$-0.455009\pi$
$853$	1.67813e30	0.281747	0.140874	+	0.990028i	$0.455009\pi$
$854$	4.09766e30	0.679561
$855$	0	0
$856$	8.27813e29	0.133955
$857$	−5.99035e30	−0.957533	−0.478766	−	0.877942i	$-0.658916\pi$
$857$	−5.99035e30	−0.957533	−0.478766	+	0.877942i	$0.658916\pi$
$858$	0	0
$859$	2.30587e30	0.359671	0.179836	−	0.983697i	$-0.442443\pi$
$859$	2.30587e30	0.359671	0.179836	+	0.983697i	$0.442443\pi$
$860$	−1.36597e30	−0.210478
$861$	0	0
$862$	−4.47666e29	−0.0673175
$863$	5.11930e30	0.760496	0.380248	−	0.924884i	$-0.375839\pi$
$863$	5.11930e30	0.760496	0.380248	+	0.924884i	$0.375839\pi$
$864$	0	0
$865$	−4.00573e30	−0.580782
$866$	−1.10908e31	−1.58864
$867$	0	0
$868$	−1.05437e31	−1.47414
$869$	−6.43946e30	−0.889491
$870$	0	0
$871$	9.62035e30	1.29718
$872$	−1.81396e29	−0.0241659
$873$	0	0
$874$	6.73633e29	0.0876099
$875$	−8.27056e30	−1.06280
$876$	0	0
$877$	−6.87157e30	−0.862105	−0.431052	−	0.902327i	$-0.641858\pi$
$877$	−6.87157e30	−0.862105	−0.431052	+	0.902327i	$0.641858\pi$
$878$	2.38776e30	0.296004
$879$	0	0
$880$	4.33753e30	0.525018
$881$	−5.75159e30	−0.687924	−0.343962	−	0.938984i	$-0.611769\pi$
$881$	−5.75159e30	−0.687924	−0.343962	+	0.938984i	$0.611769\pi$
$882$	0	0
$883$	4.44146e30	0.518726	0.259363	−	0.965780i	$-0.416487\pi$
$883$	4.44146e30	0.518726	0.259363	+	0.965780i	$0.416487\pi$
$884$	−8.76564e30	−1.01166
$885$	0	0
$886$	1.00943e31	1.13768
$887$	4.85663e30	0.540925	0.270463	−	0.962730i	$-0.412823\pi$
$887$	4.85663e30	0.540925	0.270463	+	0.962730i	$0.412823\pi$
$888$	0	0
$889$	−1.76615e31	−1.92114
$890$	−2.06106e30	−0.221562
$891$	0	0
$892$	−3.68842e30	−0.387266
$893$	6.33179e30	0.657031
$894$	0	0
$895$	−8.41923e30	−0.853356
$896$	4.32399e30	0.433163
$897$	0	0
$898$	7.48558e30	0.732527
$899$	−1.75081e30	−0.169341
$900$	0	0
$901$	−4.87632e30	−0.460768
$902$	−1.52488e31	−1.42419
$903$	0	0
$904$	−2.34272e30	−0.213773
$905$	7.43543e30	0.670650
$906$	0	0
$907$	−1.25564e31	−1.10660	−0.553298	−	0.832984i	$-0.686631\pi$
$907$	−1.25564e31	−1.10660	−0.553298	+	0.832984i	$0.686631\pi$
$908$	−2.72592e30	−0.237471
$909$	0	0
$910$	−1.01600e31	−0.864890
$911$	−5.33864e30	−0.449249	−0.224625	−	0.974445i	$-0.572116\pi$
$911$	−5.33864e30	−0.449249	−0.224625	+	0.974445i	$0.572116\pi$
$912$	0	0
$913$	3.72756e30	0.306536
$914$	−1.78050e31	−1.44746
$915$	0	0
$916$	−5.23633e30	−0.416030
$917$	−2.77726e31	−2.18141
$918$	0	0
$919$	1.80818e31	1.38813	0.694063	−	0.719914i	$-0.255819\pi$
$919$	1.80818e31	1.38813	0.694063	+	0.719914i	$0.255819\pi$
$920$	−2.05975e29	−0.0156330
$921$	0	0
$922$	−2.05601e31	−1.52528
$923$	−9.88636e30	−0.725134
$924$	0	0
$925$	1.64276e31	1.17784
$926$	9.05459e30	0.641880
$927$	0	0
$928$	−2.48741e30	−0.172383
$929$	2.43205e31	1.66651	0.833254	−	0.552890i	$-0.186475\pi$
$929$	2.43205e31	1.66651	0.833254	+	0.552890i	$0.186475\pi$
$930$	0	0
$931$	−3.04828e30	−0.204213
$932$	1.03500e31	0.685602
$933$	0	0
$934$	−1.83512e31	−1.18857
$935$	8.07697e30	0.517281
$936$	0	0
$937$	1.65121e31	1.03404	0.517018	−	0.855974i	$-0.327042\pi$
$937$	1.65121e31	1.03404	0.517018	+	0.855974i	$0.327042\pi$
$938$	3.45094e31	2.13701
$939$	0	0
$940$	1.35212e31	0.818788
$941$	−1.09085e31	−0.653241	−0.326620	−	0.945156i	$-0.605910\pi$
$941$	−1.09085e31	−0.653241	−0.326620	+	0.945156i	$0.605910\pi$
$942$	0	0
$943$	3.42162e30	0.200382
$944$	2.62182e31	1.51844
$945$	0	0
$946$	−1.25071e31	−0.708435
$947$	2.89763e31	1.62318	0.811592	−	0.584225i	$-0.198601\pi$
$947$	2.89763e31	1.62318	0.811592	+	0.584225i	$0.198601\pi$
$948$	0	0
$949$	3.76364e31	2.06211
$950$	−6.48923e30	−0.351637
$951$	0	0
$952$	4.50229e30	0.238641
$953$	−1.18340e31	−0.620376	−0.310188	−	0.950675i	$-0.600392\pi$
$953$	−1.18340e31	−0.620376	−0.310188	+	0.950675i	$0.600392\pi$
$954$	0	0
$955$	1.79964e31	0.922892
$956$	−9.85849e30	−0.500038
$957$	0	0
$958$	1.48578e31	0.737255
$959$	2.41677e31	1.18615
$960$	0	0
$961$	1.56784e31	0.752845
$962$	4.60548e31	2.18744
$963$	0	0
$964$	7.55668e29	0.0351174
$965$	−1.29017e31	−0.593075
$966$	0	0
$967$	2.41768e31	1.08748	0.543739	−	0.839254i	$-0.317008\pi$
$967$	2.41768e31	1.08748	0.543739	+	0.839254i	$0.317008\pi$
$968$	6.73848e28	0.00299827
$969$	0	0
$970$	2.02395e31	0.881244
$971$	−2.60921e31	−1.12384	−0.561922	−	0.827190i	$-0.689938\pi$
$971$	−2.60921e31	−1.12384	−0.561922	+	0.827190i	$0.689938\pi$
$972$	0	0
$973$	−7.72619e30	−0.325672
$974$	−1.07874e31	−0.449830
$975$	0	0
$976$	−1.06011e31	−0.432640
$977$	−1.30979e31	−0.528822	−0.264411	−	0.964410i	$-0.585177\pi$
$977$	−1.30979e31	−0.528822	−0.264411	+	0.964410i	$0.585177\pi$
$978$	0	0
$979$	−8.80538e30	−0.347960
$980$	−6.50942e30	−0.254489
$981$	0	0
$982$	−2.17126e31	−0.830885
$983$	−2.83479e31	−1.07327	−0.536636	−	0.843814i	$-0.680305\pi$
$983$	−2.83479e31	−1.07327	−0.536636	+	0.843814i	$0.680305\pi$
$984$	0	0
$985$	9.88735e29	0.0366437
$986$	−5.22123e30	−0.191454
$987$	0	0
$988$	−8.48856e30	−0.304709
$989$	2.80642e30	0.0996762
$990$	0	0
$991$	−2.80586e31	−0.975646	−0.487823	−	0.872942i	$-0.662209\pi$
$991$	−2.80586e31	−0.975646	−0.487823	+	0.872942i	$0.662209\pi$
$992$	5.18619e31	1.78433
$993$	0	0
$994$	−3.54636e31	−1.19461
$995$	1.02495e31	0.341634
$996$	0	0
$997$	5.09168e30	0.166174	0.0830868	−	0.996542i	$-0.473522\pi$
$997$	5.09168e30	0.166174	0.0830868	+	0.996542i	$0.473522\pi$
$998$	−3.35394e31	−1.08314
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	81.22.a.c.1.4		20
3.2	odd	2		81.22.a.d.1.17		20
9.2	odd	6		27.22.c.a.10.4		40
9.4	even	3		9.22.c.a.7.17	yes	40
9.5	odd	6		27.22.c.a.19.4		40
9.7	even	3		9.22.c.a.4.17	✓	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
9.22.c.a.4.17	✓	40	9.7	even	3
9.22.c.a.7.17	yes	40	9.4	even	3
27.22.c.a.10.4		40	9.2	odd	6
27.22.c.a.19.4		40	9.5	odd	6
81.22.a.c.1.4		20	1.1	even	1	trivial
81.22.a.d.1.17		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)

\(f(q)\)	\(=\)	\(q-1982.83 q^{2} +1.83448e6 q^{4} -1.02434e7 q^{5} -9.51290e8 q^{7} +5.20838e8 q^{8} +O(q^{10})\)	\(q-1982.83 q^{2} +1.83448e6 q^{4} -1.02434e7 q^{5} -9.51290e8 q^{7} +5.20838e8 q^{8} +2.03109e10 q^{10} +8.67734e10 q^{11} +5.25839e11 q^{13} +1.88625e12 q^{14} -4.87992e12 q^{16} -9.08695e12 q^{17} -8.79971e12 q^{19} -1.87913e13 q^{20} -1.72057e14 q^{22} +3.86072e13 q^{23} -3.71910e14 q^{25} -1.04265e15 q^{26} -1.74512e15 q^{28} -2.89780e14 q^{29} +6.04185e15 q^{31} +8.58379e15 q^{32} +1.80179e16 q^{34} +9.74443e15 q^{35} -4.41709e16 q^{37} +1.74484e16 q^{38} -5.33514e15 q^{40} +8.86265e16 q^{41} +7.26915e16 q^{43} +1.59184e17 q^{44} -7.65517e16 q^{46} -7.19545e17 q^{47} +3.46406e17 q^{49} +7.37436e17 q^{50} +9.64640e17 q^{52} +5.36630e17 q^{53} -8.88854e17 q^{55} -4.95468e17 q^{56} +5.74586e17 q^{58} -5.37267e18 q^{59} +2.17239e18 q^{61} -1.19800e19 q^{62} -6.78630e18 q^{64} -5.38637e18 q^{65} +1.82952e19 q^{67} -1.66698e19 q^{68} -1.93216e19 q^{70} -1.88011e19 q^{71} +7.15740e19 q^{73} +8.75835e19 q^{74} -1.61429e19 q^{76} -8.25467e19 q^{77} -7.42100e19 q^{79} +4.99869e19 q^{80} -1.75732e20 q^{82} +4.29574e19 q^{83} +9.30811e19 q^{85} -1.44135e20 q^{86} +4.51949e19 q^{88} -1.01476e20 q^{89} -5.00225e20 q^{91} +7.08241e19 q^{92} +1.42674e21 q^{94} +9.01388e19 q^{95} +9.96482e20 q^{97} -6.86866e20 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 1023 q^{2} + 19922945 q^{4} - 32234853 q^{5} + 189623959 q^{7} - 648135831 q^{8}+O(q^{10}) \) 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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