LMFDB - Embedded newform 81.22.a.c.1.7

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			1.7
Root			$1036.31$ 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)

$f(q)$	$=$	$q-1087.31 q^{2} -914902. q^{4} -1.49670e6 q^{5} -7.63950e7 q^{7} +3.27505e9 q^{8} +O(q^{10})$	\(q-1087.31 q^{2} -914902. q^{4} -1.49670e6 q^{5} -7.63950e7 q^{7} +3.27505e9 q^{8} +1.62738e9 q^{10} +1.45840e11 q^{11} -6.28503e11 q^{13} +8.30652e10 q^{14} -1.64231e12 q^{16} +8.35511e12 q^{17} -8.83024e12 q^{19} +1.36934e12 q^{20} -1.58574e14 q^{22} +8.45230e13 q^{23} -4.74597e14 q^{25} +6.83380e14 q^{26} +6.98939e13 q^{28} -1.39915e15 q^{29} -7.21913e15 q^{31} -5.08256e15 q^{32} -9.08462e15 q^{34} +1.14341e14 q^{35} +1.51491e16 q^{37} +9.60123e15 q^{38} -4.90177e15 q^{40} +7.57169e16 q^{41} +1.45314e17 q^{43} -1.33429e17 q^{44} -9.19029e16 q^{46} +2.38738e17 q^{47} -5.52710e17 q^{49} +5.16036e17 q^{50} +5.75019e17 q^{52} -1.10036e18 q^{53} -2.18279e17 q^{55} -2.50197e17 q^{56} +1.52131e18 q^{58} -1.24578e18 q^{59} +1.77729e18 q^{61} +7.84945e18 q^{62} +8.97051e18 q^{64} +9.40682e17 q^{65} -3.50739e18 q^{67} -7.64411e18 q^{68} -1.24324e17 q^{70} +4.49616e19 q^{71} -6.36022e19 q^{73} -1.64718e19 q^{74} +8.07881e18 q^{76} -1.11414e19 q^{77} +2.99543e19 q^{79} +2.45805e18 q^{80} -8.23279e19 q^{82} +2.77762e19 q^{83} -1.25051e19 q^{85} -1.58002e20 q^{86} +4.77633e20 q^{88} +3.84218e20 q^{89} +4.80145e19 q^{91} -7.73303e19 q^{92} -2.59583e20 q^{94} +1.32162e19 q^{95} +9.03672e20 q^{97} +6.00968e20 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−1087.31	−0.750827	−0.375413	−	0.926858i	$-0.622499\pi$
$2$	−1087.31	−0.750827	−0.375413	+	0.926858i	$0.622499\pi$
$3$	0	0
$3$	0	0
$4$	−914902.	−0.436259
$5$	−1.49670e6	−0.0685410	−0.0342705	−	0.999413i	$-0.510911\pi$
$5$	−1.49670e6	−0.0685410	−0.0342705	+	0.999413i	$0.510911\pi$
$6$	0	0
$7$	−7.63950e7	−0.102220	−0.0511099	−	0.998693i	$-0.516276\pi$
$7$	−7.63950e7	−0.102220	−0.0511099	+	0.998693i	$0.516276\pi$
$8$	3.27505e9	1.07838
$9$	0	0
$10$	1.62738e9	0.0514624
$11$	1.45840e11	1.69533	0.847664	−	0.530534i	$-0.178009\pi$
$11$	1.45840e11	1.69533	0.847664	+	0.530534i	$0.178009\pi$
$12$	0	0
$13$	−6.28503e11	−1.26445	−0.632226	−	0.774784i	$-0.717859\pi$
$13$	−6.28503e11	−1.26445	−0.632226	+	0.774784i	$0.717859\pi$
$14$	8.30652e10	0.0767494
$15$	0	0
$16$	−1.64231e12	−0.373418
$17$	8.35511e12	1.00517	0.502584	−	0.864528i	$-0.332383\pi$
$17$	8.35511e12	1.00517	0.502584	+	0.864528i	$0.332383\pi$
$18$	0	0
$19$	−8.83024e12	−0.330415	−0.165207	−	0.986259i	$-0.552829\pi$
$19$	−8.83024e12	−0.330415	−0.165207	+	0.986259i	$0.552829\pi$
$20$	1.36934e12	0.0299017
$21$	0	0
$22$	−1.58574e14	−1.27290
$23$	8.45230e13	0.425434	0.212717	−	0.977114i	$-0.431769\pi$
$23$	8.45230e13	0.425434	0.212717	+	0.977114i	$0.431769\pi$
$24$	0	0
$25$	−4.74597e14	−0.995302
$26$	6.83380e14	0.949384
$27$	0	0
$28$	6.98939e13	0.0445944
$29$	−1.39915e15	−0.617568	−0.308784	−	0.951132i	$-0.599922\pi$
$29$	−1.39915e15	−0.617568	−0.308784	+	0.951132i	$0.599922\pi$
$30$	0	0
$31$	−7.21913e15	−1.58193	−0.790964	−	0.611862i	$-0.790421\pi$
$31$	−7.21913e15	−1.58193	−0.790964	+	0.611862i	$0.790421\pi$
$32$	−5.08256e15	−0.798009
$33$	0	0
$34$	−9.08462e15	−0.754707
$35$	1.14341e14	0.00700625
$36$	0	0
$37$	1.51491e16	0.517928	0.258964	−	0.965887i	$-0.416619\pi$
$37$	1.51491e16	0.517928	0.258964	+	0.965887i	$0.416619\pi$
$38$	9.60123e15	0.248084
$39$	0	0
$40$	−4.90177e15	−0.0739134
$41$	7.57169e16	0.880972	0.440486	−	0.897759i	$-0.354806\pi$
$41$	7.57169e16	0.880972	0.440486	+	0.897759i	$0.354806\pi$
$42$	0	0
$43$	1.45314e17	1.02539	0.512694	−	0.858571i	$-0.328648\pi$
$43$	1.45314e17	1.02539	0.512694	+	0.858571i	$0.328648\pi$
$44$	−1.33429e17	−0.739603
$45$	0	0
$46$	−9.19029e16	−0.319427
$47$	2.38738e17	0.662054	0.331027	−	0.943621i	$-0.392605\pi$
$47$	2.38738e17	0.662054	0.331027	+	0.943621i	$0.392605\pi$
$48$	0	0
$49$	−5.52710e17	−0.989551
$50$	5.16036e17	0.747299
$51$	0	0
$52$	5.75019e17	0.551629
$53$	−1.10036e18	−0.864247	−0.432124	−	0.901814i	$-0.642236\pi$
$53$	−1.10036e18	−0.864247	−0.432124	+	0.901814i	$0.642236\pi$
$54$	0	0
$55$	−2.18279e17	−0.116199
$56$	−2.50197e17	−0.110232
$57$	0	0
$58$	1.52131e18	0.463686
$59$	−1.24578e18	−0.317319	−0.158660	−	0.987333i	$-0.550717\pi$
$59$	−1.24578e18	−0.317319	−0.158660	+	0.987333i	$0.550717\pi$
$60$	0	0
$61$	1.77729e18	0.319004	0.159502	−	0.987198i	$-0.449011\pi$
$61$	1.77729e18	0.319004	0.159502	+	0.987198i	$0.449011\pi$
$62$	7.84945e18	1.18775
$63$	0	0
$64$	8.97051e18	0.972585
$65$	9.40682e17	0.0866668
$66$	0	0
$67$	−3.50739e18	−0.235071	−0.117535	−	0.993069i	$-0.537499\pi$
$67$	−3.50739e18	−0.235071	−0.117535	+	0.993069i	$0.537499\pi$
$68$	−7.64411e18	−0.438514
$69$	0	0
$70$	−1.24324e17	−0.00526048
$71$	4.49616e19	1.63919	0.819594	−	0.572945i	$-0.194199\pi$
$71$	4.49616e19	1.63919	0.819594	+	0.572945i	$0.194199\pi$
$72$	0	0
$73$	−6.36022e19	−1.73214	−0.866068	−	0.499927i	$-0.833360\pi$
$73$	−6.36022e19	−1.73214	−0.866068	+	0.499927i	$0.833360\pi$
$74$	−1.64718e19	−0.388874
$75$	0	0
$76$	8.07881e18	0.144147
$77$	−1.11414e19	−0.173296
$78$	0	0
$79$	2.99543e19	0.355938	0.177969	−	0.984036i	$-0.443047\pi$
$79$	2.99543e19	0.355938	0.177969	+	0.984036i	$0.443047\pi$
$80$	2.45805e18	0.0255945
$81$	0	0
$82$	−8.23279e19	−0.661457
$83$	2.77762e19	0.196495	0.0982477	−	0.995162i	$-0.468676\pi$
$83$	2.77762e19	0.196495	0.0982477	+	0.995162i	$0.468676\pi$
$84$	0	0
$85$	−1.25051e19	−0.0688952
$86$	−1.58002e20	−0.769889
$87$	0	0
$88$	4.77633e20	1.82821
$89$	3.84218e20	1.30612	0.653060	−	0.757307i	$-0.273485\pi$
$89$	3.84218e20	1.30612	0.653060	+	0.757307i	$0.273485\pi$
$90$	0	0
$91$	4.80145e19	0.129252
$92$	−7.73303e19	−0.185600
$93$	0	0
$94$	−2.59583e20	−0.497088
$95$	1.32162e19	0.0226470
$96$	0	0
$97$	9.03672e20	1.24425	0.622125	−	0.782918i	$-0.286269\pi$
$97$	9.03672e20	1.24425	0.622125	+	0.782918i	$0.286269\pi$
$98$	6.00968e20	0.742981
$99$	0	0
$100$	4.34210e20	0.434210
$101$	−1.05997e21	−0.954812	−0.477406	−	0.878683i	$-0.658423\pi$
$101$	−1.05997e21	−0.954812	−0.477406	+	0.878683i	$0.658423\pi$
$102$	0	0
$103$	−9.46566e20	−0.694001	−0.347000	−	0.937865i	$-0.612800\pi$
$103$	−9.46566e20	−0.694001	−0.347000	+	0.937865i	$0.612800\pi$
$104$	−2.05838e21	−1.36356
$105$	0	0
$106$	1.19644e21	0.648900
$107$	2.82220e20	0.138694	0.0693471	−	0.997593i	$-0.477908\pi$
$107$	2.82220e20	0.138694	0.0693471	+	0.997593i	$0.477908\pi$
$108$	0	0
$109$	−4.40584e21	−1.78259	−0.891293	−	0.453427i	$-0.850201\pi$
$109$	−4.40584e21	−1.78259	−0.891293	+	0.453427i	$0.850201\pi$
$110$	2.37338e20	0.0872456
$111$	0	0
$112$	1.25464e20	0.0381708
$113$	2.69663e18	0.000747304 0	0.000373652	−	1.00000i	$-0.499881\pi$
$113$	2.69663e18	0.000747304 0	0.000373652		1.00000i	$0.499881\pi$
$114$	0	0
$115$	−1.26506e20	−0.0291597
$116$	1.28008e21	0.269420
$117$	0	0
$118$	1.35456e21	0.238252
$119$	−6.38288e20	−0.102748
$120$	0	0
$121$	1.38691e22	1.87413
$122$	−1.93247e21	−0.239517
$123$	0	0
$124$	6.60480e21	0.690131
$125$	1.42401e21	0.136760
$126$	0	0
$127$	1.87156e22	1.52148	0.760738	−	0.649059i	$-0.224837\pi$
$127$	1.87156e22	1.52148	0.760738	+	0.649059i	$0.224837\pi$
$128$	9.05151e20	0.0677667
$129$	0	0
$130$	−1.02282e21	−0.0650717
$131$	7.63354e21	0.448103	0.224051	−	0.974577i	$-0.428072\pi$
$131$	7.63354e21	0.448103	0.224051	+	0.974577i	$0.428072\pi$
$132$	0	0
$133$	6.74586e20	0.0337750
$134$	3.81363e21	0.176497
$135$	0	0
$136$	2.73634e22	1.08395
$137$	−7.77555e21	−0.285210	−0.142605	−	0.989780i	$-0.545548\pi$
$137$	−7.77555e21	−0.285210	−0.142605	+	0.989780i	$0.545548\pi$
$138$	0	0
$139$	4.84988e21	0.152783	0.0763917	−	0.997078i	$-0.475660\pi$
$139$	4.84988e21	0.152783	0.0763917	+	0.997078i	$0.475660\pi$
$140$	−1.04610e20	−0.00305654
$141$	0	0
$142$	−4.88873e22	−1.23075
$143$	−9.16609e22	−2.14366
$144$	0	0
$145$	2.09411e21	0.0423287
$146$	6.91555e22	1.30053
$147$	0	0
$148$	−1.38600e22	−0.225951
$149$	1.29752e23	1.97087	0.985433	−	0.170065i	$-0.0543979\pi$
$149$	1.29752e23	1.97087	0.985433	+	0.170065i	$0.0543979\pi$
$150$	0	0
$151$	3.28966e22	0.434404	0.217202	−	0.976127i	$-0.430307\pi$
$151$	3.28966e22	0.434404	0.217202	+	0.976127i	$0.430307\pi$
$152$	−2.89194e22	−0.356313
$153$	0	0
$154$	1.21142e22	0.130115
$155$	1.08049e22	0.108427
$156$	0	0
$157$	1.83400e23	1.60862	0.804309	−	0.594211i	$-0.202536\pi$
$157$	1.83400e23	1.60862	0.804309	+	0.594211i	$0.202536\pi$
$158$	−3.25697e22	−0.267248
$159$	0	0
$160$	7.60709e21	0.0546964
$161$	−6.45713e21	−0.0434878
$162$	0	0
$163$	2.55148e23	1.50946	0.754732	−	0.656033i	$-0.227767\pi$
$163$	2.55148e23	1.50946	0.754732	+	0.656033i	$0.227767\pi$
$164$	−6.92735e22	−0.384332
$165$	0	0
$166$	−3.02014e22	−0.147534
$167$	−2.06402e23	−0.946654	−0.473327	−	0.880887i	$-0.656947\pi$
$167$	−2.06402e23	−0.946654	−0.473327	+	0.880887i	$0.656947\pi$
$168$	0	0
$169$	1.47952e23	0.598838
$170$	1.35970e22	0.0517284
$171$	0	0
$172$	−1.32948e23	−0.447335
$173$	−2.99304e23	−0.947609	−0.473804	−	0.880630i	$-0.657120\pi$
$173$	−2.99304e23	−0.947609	−0.473804	+	0.880630i	$0.657120\pi$
$174$	0	0
$175$	3.62568e22	0.101740
$176$	−2.39515e23	−0.633066
$177$	0	0
$178$	−4.17765e23	−0.980669
$179$	6.83646e23	1.51312	0.756562	−	0.653922i	$-0.226877\pi$
$179$	6.83646e23	1.51312	0.756562	+	0.653922i	$0.226877\pi$
$180$	0	0
$181$	−3.38448e23	−0.666603	−0.333301	−	0.942820i	$-0.608163\pi$
$181$	−3.38448e23	−0.666603	−0.333301	+	0.942820i	$0.608163\pi$
$182$	−5.22068e22	−0.0970459
$183$	0	0
$184$	2.76817e23	0.458781
$185$	−2.26737e22	−0.0354993
$186$	0	0
$187$	1.21851e24	1.70409
$188$	−2.18422e23	−0.288827
$189$	0	0
$190$	−1.43702e22	−0.0170039
$191$	3.92569e23	0.439608	0.219804	−	0.975544i	$-0.429458\pi$
$191$	3.92569e23	0.439608	0.219804	+	0.975544i	$0.429458\pi$
$192$	0	0
$193$	−1.98300e24	−1.99054	−0.995270	−	0.0971436i	$-0.969029\pi$
$193$	−1.98300e24	−1.99054	−0.995270	+	0.0971436i	$0.969029\pi$
$194$	−9.82575e23	−0.934216
$195$	0	0
$196$	5.05675e23	0.431701
$197$	−1.13444e24	−0.918094	−0.459047	−	0.888412i	$-0.651809\pi$
$197$	−1.13444e24	−0.918094	−0.459047	+	0.888412i	$0.651809\pi$
$198$	0	0
$199$	−2.34252e24	−1.70501	−0.852504	−	0.522720i	$-0.824917\pi$
$199$	−2.34252e24	−1.70501	−0.852504	+	0.522720i	$0.824917\pi$
$200$	−1.55433e24	−1.07332
$201$	0	0
$202$	1.15252e24	0.716898
$203$	1.06888e23	0.0631277
$204$	0	0
$205$	−1.13326e23	−0.0603827
$206$	1.02921e24	0.521074
$207$	0	0
$208$	1.03220e24	0.472169
$209$	−1.28780e24	−0.560161
$210$	0	0
$211$	−2.86420e24	−1.12730	−0.563648	−	0.826015i	$-0.690602\pi$
$211$	−2.86420e24	−1.12730	−0.563648	+	0.826015i	$0.690602\pi$
$212$	1.00672e24	0.377036
$213$	0	0
$214$	−3.06862e23	−0.104135
$215$	−2.17492e23	−0.0702811
$216$	0	0
$217$	5.51505e23	0.161705
$218$	4.79053e24	1.33841
$219$	0	0
$220$	1.99704e23	0.0506931
$221$	−5.25121e24	−1.27099
$222$	0	0
$223$	−7.00427e24	−1.54228	−0.771138	−	0.636669i	$-0.780312\pi$
$223$	−7.00427e24	−1.54228	−0.771138	+	0.636669i	$0.780312\pi$
$224$	3.88282e23	0.0815724
$225$	0	0
$226$	−2.93208e21	−0.000561096 0
$227$	−8.60008e24	−1.57120	−0.785599	−	0.618736i	$-0.787645\pi$
$227$	−8.60008e24	−1.57120	−0.785599	+	0.618736i	$0.787645\pi$
$228$	0	0
$229$	4.14286e24	0.690284	0.345142	−	0.938550i	$-0.387831\pi$
$229$	4.14286e24	0.690284	0.345142	+	0.938550i	$0.387831\pi$
$230$	1.37551e23	0.0218939
$231$	0	0
$232$	−4.58227e24	−0.665974
$233$	−6.95020e24	−0.965517	−0.482758	−	0.875754i	$-0.660365\pi$
$233$	−6.95020e24	−0.965517	−0.482758	+	0.875754i	$0.660365\pi$
$234$	0	0
$235$	−3.57319e23	−0.0453779
$236$	1.13977e24	0.138434
$237$	0	0
$238$	6.94019e23	0.0771460
$239$	1.18448e25	1.25994	0.629970	−	0.776619i	$-0.283067\pi$
$239$	1.18448e25	1.25994	0.629970	+	0.776619i	$0.283067\pi$
$240$	0	0
$241$	−2.66786e24	−0.260006	−0.130003	−	0.991514i	$-0.541499\pi$
$241$	−2.66786e24	−0.260006	−0.130003	+	0.991514i	$0.541499\pi$
$242$	−1.50800e25	−1.40715
$243$	0	0
$244$	−1.62605e24	−0.139168
$245$	8.27242e23	0.0678248
$246$	0	0
$247$	5.54983e24	0.417794
$248$	−2.36430e25	−1.70592
$249$	0	0
$250$	−1.54835e24	−0.102683
$251$	−2.70218e25	−1.71846	−0.859231	−	0.511588i	$-0.829058\pi$
$251$	−2.70218e25	−1.71846	−0.859231	+	0.511588i	$0.829058\pi$
$252$	0	0
$253$	1.23268e25	0.721250
$254$	−2.03497e25	−1.14236
$255$	0	0
$256$	−1.97967e25	−1.02347
$257$	3.90081e24	0.193578	0.0967892	−	0.995305i	$-0.469143\pi$
$257$	3.90081e24	0.193578	0.0967892	+	0.995305i	$0.469143\pi$
$258$	0	0
$259$	−1.15732e24	−0.0529425
$260$	−8.60633e23	−0.0378092
$261$	0	0
$262$	−8.30005e24	−0.336447
$263$	1.28724e24	0.0501330	0.0250665	−	0.999686i	$-0.492020\pi$
$263$	1.28724e24	0.0501330	0.0250665	+	0.999686i	$0.492020\pi$
$264$	0	0
$265$	1.64691e24	0.0592364
$266$	−7.33486e23	−0.0253591
$267$	0	0
$268$	3.20892e24	0.102552
$269$	2.65509e24	0.0815981	0.0407991	−	0.999167i	$-0.487010\pi$
$269$	2.65509e24	0.0815981	0.0407991	+	0.999167i	$0.487010\pi$
$270$	0	0
$271$	2.50507e25	0.712267	0.356133	−	0.934435i	$-0.384095\pi$
$271$	2.50507e25	0.712267	0.356133	+	0.934435i	$0.384095\pi$
$272$	−1.37217e25	−0.375348
$273$	0	0
$274$	8.45446e24	0.214144
$275$	−6.92152e25	−1.68736
$276$	0	0
$277$	4.10365e25	0.927113	0.463557	−	0.886067i	$-0.346573\pi$
$277$	4.10365e25	0.927113	0.463557	+	0.886067i	$0.346573\pi$
$278$	−5.27334e24	−0.114714
$279$	0	0
$280$	3.74471e23	0.00755542
$281$	−9.04139e25	−1.75719	−0.878596	−	0.477566i	$-0.841519\pi$
$281$	−9.04139e25	−1.75719	−0.878596	+	0.477566i	$0.841519\pi$
$282$	0	0
$283$	2.26061e25	0.407819	0.203909	−	0.978990i	$-0.434635\pi$
$283$	2.26061e25	0.407819	0.203909	+	0.978990i	$0.434635\pi$
$284$	−4.11354e25	−0.715111
$285$	0	0
$286$	9.96641e25	1.60952
$287$	−5.78439e24	−0.0900528
$288$	0	0
$289$	7.15930e23	0.0103620
$290$	−2.27695e24	−0.0317815
$291$	0	0
$292$	5.81898e25	0.755660
$293$	−6.08065e25	−0.761798	−0.380899	−	0.924617i	$-0.624385\pi$
$293$	−6.08065e25	−0.761798	−0.380899	+	0.924617i	$0.624385\pi$
$294$	0	0
$295$	1.86457e24	0.0217494
$296$	4.96140e25	0.558524
$297$	0	0
$298$	−1.41081e26	−1.47978
$299$	−5.31230e25	−0.537941
$300$	0	0
$301$	−1.11012e25	−0.104815
$302$	−3.57689e25	−0.326162
$303$	0	0
$304$	1.45020e25	0.123383
$305$	−2.66008e24	−0.0218648
$306$	0	0
$307$	5.19438e25	0.398640	0.199320	−	0.979934i	$-0.436127\pi$
$307$	5.19438e25	0.398640	0.199320	+	0.979934i	$0.436127\pi$
$308$	1.01933e25	0.0756021
$309$	0	0
$310$	−1.17483e25	−0.0814099
$311$	−7.51953e25	−0.503740	−0.251870	−	0.967761i	$-0.581046\pi$
$311$	−7.51953e25	−0.503740	−0.251870	+	0.967761i	$0.581046\pi$
$312$	0	0
$313$	−1.28110e26	−0.802360	−0.401180	−	0.915999i	$-0.631400\pi$
$313$	−1.28110e26	−0.802360	−0.401180	+	0.915999i	$0.631400\pi$
$314$	−1.99413e26	−1.20779
$315$	0	0
$316$	−2.74052e25	−0.155281
$317$	−6.03321e25	−0.330694	−0.165347	−	0.986235i	$-0.552874\pi$
$317$	−6.03321e25	−0.330694	−0.165347	+	0.986235i	$0.552874\pi$
$318$	0	0
$319$	−2.04052e26	−1.04698
$320$	−1.34262e25	−0.0666620
$321$	0	0
$322$	7.02092e24	0.0326518
$323$	−7.37776e25	−0.332122
$324$	0	0
$325$	2.98286e26	1.25851
$326$	−2.77426e26	−1.13335
$327$	0	0
$328$	2.47976e26	0.950024
$329$	−1.82384e25	−0.0676751
$330$	0	0
$331$	1.11637e26	0.388699	0.194350	−	0.980932i	$-0.437740\pi$
$331$	1.11637e26	0.388699	0.194350	+	0.980932i	$0.437740\pi$
$332$	−2.54125e25	−0.0857230
$333$	0	0
$334$	2.24424e26	0.710773
$335$	5.24952e24	0.0161120
$336$	0	0
$337$	−2.47858e26	−0.714642	−0.357321	−	0.933982i	$-0.616310\pi$
$337$	−2.47858e26	−0.714642	−0.357321	+	0.933982i	$0.616310\pi$
$338$	−1.60870e26	−0.449624
$339$	0	0
$340$	1.14410e25	0.0300562
$341$	−1.05284e27	−2.68189
$342$	0	0
$343$	8.48943e25	0.203372
$344$	4.75910e26	1.10576
$345$	0	0
$346$	3.25438e26	0.711490
$347$	6.70624e26	1.42239	0.711197	−	0.702993i	$-0.248153\pi$
$347$	6.70624e26	1.42239	0.711197	+	0.702993i	$0.248153\pi$
$348$	0	0
$349$	−8.42950e26	−1.68320	−0.841598	−	0.540105i	$-0.818385\pi$
$349$	−8.42950e26	−1.68320	−0.841598	+	0.540105i	$0.818385\pi$
$350$	−3.94225e25	−0.0763888
$351$	0	0
$352$	−7.41241e26	−1.35289
$353$	−5.87900e26	−1.04152	−0.520762	−	0.853702i	$-0.674352\pi$
$353$	−5.87900e26	−1.04152	−0.520762	+	0.853702i	$0.674352\pi$
$354$	0	0
$355$	−6.72941e25	−0.112352
$356$	−3.51522e26	−0.569807
$357$	0	0
$358$	−7.43338e26	−1.13609
$359$	5.07228e26	0.752855	0.376428	−	0.926446i	$-0.377152\pi$
$359$	5.07228e26	0.752855	0.376428	+	0.926446i	$0.377152\pi$
$360$	0	0
$361$	−6.36236e26	−0.890826
$362$	3.67999e26	0.500503
$363$	0	0
$364$	−4.39286e25	−0.0563874
$365$	9.51935e25	0.118722
$366$	0	0
$367$	−1.94101e26	−0.228578	−0.114289	−	0.993448i	$-0.536459\pi$
$367$	−1.94101e26	−0.228578	−0.114289	+	0.993448i	$0.536459\pi$
$368$	−1.38813e26	−0.158865
$369$	0	0
$370$	2.46534e25	0.0266538
$371$	8.40619e25	0.0883432
$372$	0	0
$373$	−7.72051e26	−0.766838	−0.383419	−	0.923575i	$-0.625253\pi$
$373$	−7.72051e26	−0.766838	−0.383419	+	0.923575i	$0.625253\pi$
$374$	−1.32490e27	−1.27947
$375$	0	0
$376$	7.81877e26	0.713947
$377$	8.79369e26	0.780885
$378$	0	0
$379$	1.30910e27	1.09966	0.549832	−	0.835275i	$-0.314692\pi$
$379$	1.30910e27	1.09966	0.549832	+	0.835275i	$0.314692\pi$
$380$	−1.20916e25	−0.00987996
$381$	0	0
$382$	−4.26845e26	−0.330069
$383$	1.73808e27	1.30762	0.653811	−	0.756658i	$-0.273169\pi$
$383$	1.73808e27	1.30762	0.653811	+	0.756658i	$0.273169\pi$
$384$	0	0
$385$	1.66754e25	0.0118779
$386$	2.15614e27	1.49455
$387$	0	0
$388$	−8.26772e26	−0.542816
$389$	−1.70522e27	−1.08971	−0.544855	−	0.838531i	$-0.683415\pi$
$389$	−1.70522e27	−1.08971	−0.544855	+	0.838531i	$0.683415\pi$
$390$	0	0
$391$	7.06199e26	0.427633
$392$	−1.81015e27	−1.06711
$393$	0	0
$394$	1.23349e27	0.689329
$395$	−4.48327e25	−0.0243964
$396$	0	0
$397$	−6.15766e26	−0.317772	−0.158886	−	0.987297i	$-0.550790\pi$
$397$	−6.15766e26	−0.317772	−0.158886	+	0.987297i	$0.550790\pi$
$398$	2.54706e27	1.28017
$399$	0	0
$400$	7.79436e26	0.371664
$401$	3.12208e27	1.45020	0.725100	−	0.688644i	$-0.241794\pi$
$401$	3.12208e27	1.45020	0.725100	+	0.688644i	$0.241794\pi$
$402$	0	0
$403$	4.53724e27	2.00027
$404$	9.69766e26	0.416546
$405$	0	0
$406$	−1.16221e26	−0.0473979
$407$	2.20935e27	0.878057
$408$	0	0
$409$	−2.81037e27	−1.06089	−0.530443	−	0.847721i	$-0.677974\pi$
$409$	−2.81037e27	−1.06089	−0.530443	+	0.847721i	$0.677974\pi$
$410$	1.23220e26	0.0453370
$411$	0	0
$412$	8.66015e26	0.302764
$413$	9.51716e25	0.0324363
$414$	0	0
$415$	−4.15727e25	−0.0134680
$416$	3.19441e27	1.00904
$417$	0	0
$418$	1.40024e27	0.420584
$419$	1.37007e27	0.401324	0.200662	−	0.979661i	$-0.435691\pi$
$419$	1.37007e27	0.401324	0.200662	+	0.979661i	$0.435691\pi$
$420$	0	0
$421$	−4.46468e27	−1.24402	−0.622012	−	0.783008i	$-0.713684\pi$
$421$	−4.46468e27	−1.24402	−0.622012	+	0.783008i	$0.713684\pi$
$422$	3.11428e27	0.846403
$423$	0	0
$424$	−3.60373e27	−0.931988
$425$	−3.96531e27	−1.00045
$426$	0	0
$427$	−1.35776e26	−0.0326085
$428$	−2.58204e26	−0.0605066
$429$	0	0
$430$	2.36482e26	0.0527690
$431$	3.12532e24	0.000680586 0	0.000340293	−	1.00000i	$-0.499892\pi$
$431$	3.12532e24	0.000680586 0	0.000340293		1.00000i	$0.499892\pi$
$432$	0	0
$433$	2.60020e27	0.539366	0.269683	−	0.962949i	$-0.413081\pi$
$433$	2.60020e27	0.539366	0.269683	+	0.962949i	$0.413081\pi$
$434$	−5.99659e26	−0.121412
$435$	0	0
$436$	4.03092e27	0.777670
$437$	−7.46358e26	−0.140570
$438$	0	0
$439$	4.56289e26	0.0819148	0.0409574	−	0.999161i	$-0.486959\pi$
$439$	4.56289e26	0.0819148	0.0409574	+	0.999161i	$0.486959\pi$
$440$	−7.14874e26	−0.125307
$441$	0	0
$442$	5.70971e27	0.954290
$443$	4.84549e27	0.790858	0.395429	−	0.918497i	$-0.370596\pi$
$443$	4.84549e27	0.790858	0.395429	+	0.918497i	$0.370596\pi$
$444$	0	0
$445$	−5.75060e26	−0.0895227
$446$	7.61583e27	1.15798
$447$	0	0
$448$	−6.85302e26	−0.0994175
$449$	1.13093e28	1.60269	0.801344	−	0.598204i	$-0.204119\pi$
$449$	1.13093e28	1.60269	0.801344	+	0.598204i	$0.204119\pi$
$450$	0	0
$451$	1.10425e28	1.49354
$452$	−2.46715e24	−0.000326018 0
$453$	0	0
$454$	9.35098e27	1.17970
$455$	−7.18634e25	−0.00885907
$456$	0	0
$457$	−1.11724e28	−1.31530	−0.657651	−	0.753323i	$-0.728450\pi$
$457$	−1.11724e28	−1.31530	−0.657651	+	0.753323i	$0.728450\pi$
$458$	−4.50459e27	−0.518284
$459$	0	0
$460$	1.15740e26	0.0127212
$461$	1.32751e28	1.42619	0.713095	−	0.701068i	$-0.247293\pi$
$461$	1.32751e28	1.42619	0.713095	+	0.701068i	$0.247293\pi$
$462$	0	0
$463$	3.25866e27	0.334533	0.167266	−	0.985912i	$-0.446506\pi$
$463$	3.25866e27	0.334533	0.167266	+	0.985912i	$0.446506\pi$
$464$	2.29784e27	0.230611
$465$	0	0
$466$	7.55704e27	0.724936
$467$	−1.56716e28	−1.46989	−0.734945	−	0.678127i	$-0.762792\pi$
$467$	−1.56716e28	−1.46989	−0.734945	+	0.678127i	$0.762792\pi$
$468$	0	0
$469$	2.67947e26	0.0240289
$470$	3.88518e26	0.0340709
$471$	0	0
$472$	−4.08000e27	−0.342191
$473$	2.11926e28	1.73837
$474$	0	0
$475$	4.19080e27	0.328863
$476$	5.83972e26	0.0448248
$477$	0	0
$478$	−1.28790e28	−0.945997
$479$	2.28170e27	0.163959	0.0819796	−	0.996634i	$-0.473876\pi$
$479$	2.28170e27	0.163959	0.0819796	+	0.996634i	$0.473876\pi$
$480$	0	0
$481$	−9.52126e27	−0.654894
$482$	2.90080e27	0.195219
$483$	0	0
$484$	−1.26888e28	−0.817609
$485$	−1.35253e27	−0.0852822
$486$	0	0
$487$	−1.11454e28	−0.673039	−0.336519	−	0.941677i	$-0.609250\pi$
$487$	−1.11454e28	−0.673039	−0.336519	+	0.941677i	$0.609250\pi$
$488$	5.82072e27	0.344008
$489$	0	0
$490$	−8.99471e26	−0.0509247
$491$	−6.83361e27	−0.378700	−0.189350	−	0.981910i	$-0.560638\pi$
$491$	−6.83361e27	−0.378700	−0.189350	+	0.981910i	$0.560638\pi$
$492$	0	0
$493$	−1.16900e28	−0.620759
$494$	−6.03440e27	−0.313691
$495$	0	0
$496$	1.18561e28	0.590721
$497$	−3.43484e27	−0.167558
$498$	0	0
$499$	−2.26089e28	−1.05736	−0.528682	−	0.848820i	$-0.677314\pi$
$499$	−2.26089e28	−1.05736	−0.528682	+	0.848820i	$0.677314\pi$
$500$	−1.30283e27	−0.0596629
$501$	0	0
$502$	2.93811e28	1.29027
$503$	3.80663e28	1.63710	0.818552	−	0.574432i	$-0.194777\pi$
$503$	3.80663e28	1.63710	0.818552	+	0.574432i	$0.194777\pi$
$504$	0	0
$505$	1.58645e27	0.0654438
$506$	−1.34031e28	−0.541534
$507$	0	0
$508$	−1.71230e28	−0.663758
$509$	−2.15480e28	−0.818221	−0.409111	−	0.912485i	$-0.634161\pi$
$509$	−2.15480e28	−0.818221	−0.409111	+	0.912485i	$0.634161\pi$
$510$	0	0
$511$	4.85889e27	0.177059
$512$	1.96270e28	0.700679
$513$	0	0
$514$	−4.24140e27	−0.145344
$515$	1.41673e27	0.0475675
$516$	0	0
$517$	3.48175e28	1.12240
$518$	1.25836e27	0.0397506
$519$	0	0
$520$	3.08078e27	0.0934599
$521$	2.70198e28	0.803316	0.401658	−	0.915790i	$-0.368434\pi$
$521$	2.70198e28	0.803316	0.401658	+	0.915790i	$0.368434\pi$
$522$	0	0
$523$	−4.90637e28	−1.40118	−0.700588	−	0.713566i	$-0.747079\pi$
$523$	−4.90637e28	−1.40118	−0.700588	+	0.713566i	$0.747079\pi$
$524$	−6.98395e27	−0.195489
$525$	0	0
$526$	−1.39963e27	−0.0376412
$527$	−6.03166e28	−1.59010
$528$	0	0
$529$	−3.23275e28	−0.819006
$530$	−1.79071e27	−0.0444762
$531$	0	0
$532$	−6.17180e26	−0.0147346
$533$	−4.75883e28	−1.11395
$534$	0	0
$535$	−4.22400e26	−0.00950624
$536$	−1.14869e28	−0.253496
$537$	0	0
$538$	−2.88691e27	−0.0612660
$539$	−8.06072e28	−1.67761
$540$	0	0
$541$	−5.54856e28	−1.11073	−0.555366	−	0.831606i	$-0.687422\pi$
$541$	−5.54856e28	−1.11073	−0.555366	+	0.831606i	$0.687422\pi$
$542$	−2.72380e28	−0.534789
$543$	0	0
$544$	−4.24654e28	−0.802133
$545$	6.59424e27	0.122180
$546$	0	0
$547$	6.25466e28	1.11516	0.557580	−	0.830123i	$-0.311730\pi$
$547$	6.25466e28	1.11516	0.557580	+	0.830123i	$0.311730\pi$
$548$	7.11387e27	0.124426
$549$	0	0
$550$	7.52586e28	1.26692
$551$	1.23548e28	0.204054
$552$	0	0
$553$	−2.28836e27	−0.0363839
$554$	−4.46195e28	−0.696101
$555$	0	0
$556$	−4.43717e27	−0.0666532
$557$	−6.38782e28	−0.941614	−0.470807	−	0.882236i	$-0.656037\pi$
$557$	−6.38782e28	−0.941614	−0.470807	+	0.882236i	$0.656037\pi$
$558$	0	0
$559$	−9.13302e28	−1.29655
$560$	−1.87783e26	−0.00261626
$561$	0	0
$562$	9.83083e28	1.31935
$563$	−9.67287e27	−0.127414	−0.0637070	−	0.997969i	$-0.520292\pi$
$563$	−9.67287e27	−0.127414	−0.0637070	+	0.997969i	$0.520292\pi$
$564$	0	0
$565$	−4.03605e24	−5.12210e−5 0
$566$	−2.45799e28	−0.306201
$567$	0	0
$568$	1.47251e29	1.76767
$569$	−5.77269e28	−0.680299	−0.340149	−	0.940371i	$-0.610478\pi$
$569$	−5.77269e28	−0.680299	−0.340149	+	0.940371i	$0.610478\pi$
$570$	0	0
$571$	−9.40251e28	−1.06798	−0.533992	−	0.845490i	$-0.679309\pi$
$571$	−9.40251e28	−1.06798	−0.533992	+	0.845490i	$0.679309\pi$
$572$	8.38608e28	0.935192
$573$	0	0
$574$	6.28944e27	0.0676141
$575$	−4.01144e28	−0.423436
$576$	0	0
$577$	7.59710e28	0.773217	0.386609	−	0.922244i	$-0.373646\pi$
$577$	7.59710e28	0.773217	0.386609	+	0.922244i	$0.373646\pi$
$578$	−7.78440e26	−0.00778006
$579$	0	0
$580$	−1.91590e27	−0.0184663
$581$	−2.12196e27	−0.0200857
$582$	0	0
$583$	−1.60476e29	−1.46518
$584$	−2.08300e29	−1.86790
$585$	0	0
$586$	6.61157e28	0.571978
$587$	7.85941e28	0.667867	0.333934	−	0.942597i	$-0.391624\pi$
$587$	7.85941e28	0.667867	0.333934	+	0.942597i	$0.391624\pi$
$588$	0	0
$589$	6.37466e28	0.522693
$590$	−2.02737e27	−0.0163300
$591$	0	0
$592$	−2.48795e28	−0.193404
$593$	6.09013e28	0.465106	0.232553	−	0.972584i	$-0.425292\pi$
$593$	6.09013e28	0.465106	0.232553	+	0.972584i	$0.425292\pi$
$594$	0	0
$595$	9.55328e26	0.00704246
$596$	−1.18710e29	−0.859809
$597$	0	0
$598$	5.77613e28	0.403900
$599$	−1.60793e29	−1.10480	−0.552402	−	0.833578i	$-0.686289\pi$
$599$	−1.60793e29	−1.10480	−0.552402	+	0.833578i	$0.686289\pi$
$600$	0	0
$601$	4.33060e28	0.287320	0.143660	−	0.989627i	$-0.454113\pi$
$601$	4.33060e28	0.287320	0.143660	+	0.989627i	$0.454113\pi$
$602$	1.20705e28	0.0786979
$603$	0	0
$604$	−3.00972e28	−0.189513
$605$	−2.07579e28	−0.128455
$606$	0	0
$607$	9.80909e28	0.586337	0.293169	−	0.956061i	$-0.405290\pi$
$607$	9.80909e28	0.586337	0.293169	+	0.956061i	$0.405290\pi$
$608$	4.48802e28	0.263674
$609$	0	0
$610$	2.89234e27	0.0164167
$611$	−1.50047e29	−0.837135
$612$	0	0
$613$	2.23206e28	0.120329	0.0601645	−	0.998188i	$-0.480837\pi$
$613$	2.23206e28	0.120329	0.0601645	+	0.998188i	$0.480837\pi$
$614$	−5.64792e28	−0.299310
$615$	0	0
$616$	−3.64887e28	−0.186879
$617$	−8.31586e28	−0.418710	−0.209355	−	0.977840i	$-0.567136\pi$
$617$	−8.31586e28	−0.418710	−0.209355	+	0.977840i	$0.567136\pi$
$618$	0	0
$619$	1.60089e29	0.779128	0.389564	−	0.920999i	$-0.372626\pi$
$619$	1.60089e29	0.779128	0.389564	+	0.920999i	$0.372626\pi$
$620$	−9.88542e27	−0.0473023
$621$	0	0
$622$	8.17609e28	0.378222
$623$	−2.93523e28	−0.133511
$624$	0	0
$625$	2.24174e29	0.985928
$626$	1.39296e29	0.602433
$627$	0	0
$628$	−1.67793e29	−0.701775
$629$	1.26572e29	0.520604
$630$	0	0
$631$	−1.88236e29	−0.748850	−0.374425	−	0.927257i	$-0.622160\pi$
$631$	−1.88236e29	−0.748850	−0.374425	+	0.927257i	$0.622160\pi$
$632$	9.81016e28	0.383837
$633$	0	0
$634$	6.55998e28	0.248294
$635$	−2.80117e28	−0.104283
$636$	0	0
$637$	3.47380e29	1.25124
$638$	2.21868e29	0.786100
$639$	0	0
$640$	−1.35474e27	−0.00464480
$641$	1.69500e29	0.571689	0.285844	−	0.958276i	$-0.407726\pi$
$641$	1.69500e29	0.571689	0.285844	+	0.958276i	$0.407726\pi$
$642$	0	0
$643$	−1.34417e29	−0.438774	−0.219387	−	0.975638i	$-0.570406\pi$
$643$	−1.34417e29	−0.438774	−0.219387	+	0.975638i	$0.570406\pi$
$644$	5.90764e27	0.0189720
$645$	0	0
$646$	8.02194e28	0.249366
$647$	2.47036e29	0.755554	0.377777	−	0.925897i	$-0.376689\pi$
$647$	2.47036e29	0.755554	0.377777	+	0.925897i	$0.376689\pi$
$648$	0	0
$649$	−1.81685e29	−0.537960
$650$	−3.24330e29	−0.944924
$651$	0	0
$652$	−2.33436e29	−0.658518
$653$	−4.74335e29	−1.31673	−0.658365	−	0.752699i	$-0.728752\pi$
$653$	−4.74335e29	−1.31673	−0.658365	+	0.752699i	$0.728752\pi$
$654$	0	0
$655$	−1.14251e28	−0.0307134
$656$	−1.24351e29	−0.328971
$657$	0	0
$658$	1.98308e28	0.0508122
$659$	−2.85493e29	−0.719943	−0.359972	−	0.932963i	$-0.617214\pi$
$659$	−2.85493e29	−0.719943	−0.359972	+	0.932963i	$0.617214\pi$
$660$	0	0
$661$	−7.26484e29	−1.77464	−0.887321	−	0.461152i	$-0.847436\pi$
$661$	−7.26484e29	−1.77464	−0.887321	+	0.461152i	$0.847436\pi$
$662$	−1.21384e29	−0.291846
$663$	0	0
$664$	9.09682e28	0.211897
$665$	−1.00965e27	−0.00231497
$666$	0	0
$667$	−1.18260e29	−0.262734
$668$	1.88838e29	0.412987
$669$	0	0
$670$	−5.70787e27	−0.0120973
$671$	2.59201e29	0.540816
$672$	0	0
$673$	−6.71582e29	−1.35813	−0.679064	−	0.734079i	$-0.737614\pi$
$673$	−6.71582e29	−1.35813	−0.679064	+	0.734079i	$0.737614\pi$
$674$	2.69499e29	0.536572
$675$	0	0
$676$	−1.35361e29	−0.261249
$677$	5.03649e29	0.957077	0.478539	−	0.878067i	$-0.341167\pi$
$677$	5.03649e29	0.957077	0.478539	+	0.878067i	$0.341167\pi$
$678$	0	0
$679$	−6.90360e28	−0.127187
$680$	−4.09548e28	−0.0742953
$681$	0	0
$682$	1.14476e30	2.01363
$683$	3.19072e29	0.552677	0.276338	−	0.961060i	$-0.410879\pi$
$683$	3.19072e29	0.552677	0.276338	+	0.961060i	$0.410879\pi$
$684$	0	0
$685$	1.16377e28	0.0195486
$686$	−9.23067e28	−0.152697
$687$	0	0
$688$	−2.38651e29	−0.382899
$689$	6.91579e29	1.09280
$690$	0	0
$691$	−6.70036e29	−1.02702	−0.513510	−	0.858084i	$-0.671655\pi$
$691$	−6.70036e29	−1.02702	−0.513510	+	0.858084i	$0.671655\pi$
$692$	2.73834e29	0.413403
$693$	0	0
$694$	−7.29179e29	−1.06797
$695$	−7.25883e27	−0.0104719
$696$	0	0
$697$	6.32623e29	0.885525
$698$	9.16550e29	1.26379
$699$	0	0
$700$	−3.31715e28	−0.0443849
$701$	−5.28535e29	−0.696681	−0.348341	−	0.937368i	$-0.613255\pi$
$701$	−5.28535e29	−0.696681	−0.348341	+	0.937368i	$0.613255\pi$
$702$	0	0
$703$	−1.33770e29	−0.171131
$704$	1.30826e30	1.64885
$705$	0	0
$706$	6.39232e29	0.782004
$707$	8.09761e28	0.0976007
$708$	0	0
$709$	−3.14981e29	−0.368552	−0.184276	−	0.982875i	$-0.558994\pi$
$709$	−3.14981e29	−0.368552	−0.184276	+	0.982875i	$0.558994\pi$
$710$	7.31697e28	0.0843566
$711$	0	0
$712$	1.25833e30	1.40849
$713$	−6.10182e29	−0.673007
$714$	0	0
$715$	1.37189e29	0.146929
$716$	−6.25470e29	−0.660115
$717$	0	0
$718$	−5.51516e29	−0.565264
$719$	6.79762e29	0.686599	0.343300	−	0.939226i	$-0.388455\pi$
$719$	6.79762e29	0.686599	0.343300	+	0.939226i	$0.388455\pi$
$720$	0	0
$721$	7.23128e28	0.0709407
$722$	6.91788e29	0.668856
$723$	0	0
$724$	3.09647e29	0.290812
$725$	6.64031e29	0.614666
$726$	0	0
$727$	−1.01554e30	−0.913244	−0.456622	−	0.889661i	$-0.650941\pi$
$727$	−1.01554e30	−0.913244	−0.456622	+	0.889661i	$0.650941\pi$
$728$	1.57250e29	0.139383
$729$	0	0
$730$	−1.03505e29	−0.0891399
$731$	1.21411e30	1.03069
$732$	0	0
$733$	−2.56815e29	−0.211850	−0.105925	−	0.994374i	$-0.533780\pi$
$733$	−2.56815e29	−0.211850	−0.105925	+	0.994374i	$0.533780\pi$
$734$	2.11048e29	0.171622
$735$	0	0
$736$	−4.29593e29	−0.339501
$737$	−5.11518e29	−0.398522
$738$	0	0
$739$	1.41548e30	1.07186	0.535929	−	0.844263i	$-0.319961\pi$
$739$	1.41548e30	1.07186	0.535929	+	0.844263i	$0.319961\pi$
$740$	2.07442e28	0.0154869
$741$	0	0
$742$	−9.14016e28	−0.0663304
$743$	2.53033e30	1.81049	0.905243	−	0.424894i	$-0.139689\pi$
$743$	2.53033e30	1.81049	0.905243	+	0.424894i	$0.139689\pi$
$744$	0	0
$745$	−1.94200e29	−0.135085
$746$	8.39462e29	0.575762
$747$	0	0
$748$	−1.11482e30	−0.743425
$749$	−2.15602e28	−0.0141773
$750$	0	0
$751$	−1.34331e30	−0.858930	−0.429465	−	0.903084i	$-0.641298\pi$
$751$	−1.34331e30	−0.858930	−0.429465	+	0.903084i	$0.641298\pi$
$752$	−3.92081e29	−0.247223
$753$	0	0
$754$	−9.56149e29	−0.586309
$755$	−4.92365e28	−0.0297745
$756$	0	0
$757$	6.24143e29	0.367094	0.183547	−	0.983011i	$-0.441242\pi$
$757$	6.24143e29	0.367094	0.183547	+	0.983011i	$0.441242\pi$
$758$	−1.42340e30	−0.825657
$759$	0	0
$760$	4.32838e28	0.0244221
$761$	5.86059e28	0.0326139	0.0163070	−	0.999867i	$-0.494809\pi$
$761$	5.86059e28	0.0326139	0.0163070	+	0.999867i	$0.494809\pi$
$762$	0	0
$763$	3.36584e29	0.182216
$764$	−3.59162e29	−0.191783
$765$	0	0
$766$	−1.88984e30	−0.981797
$767$	7.82979e29	0.401235
$768$	0	0
$769$	−9.76093e29	−0.486704	−0.243352	−	0.969938i	$-0.578247\pi$
$769$	−9.76093e29	−0.486704	−0.243352	+	0.969938i	$0.578247\pi$
$770$	−1.81314e28	−0.00891824
$771$	0	0
$772$	1.81425e30	0.868392
$773$	−4.72527e29	−0.223122	−0.111561	−	0.993758i	$-0.535585\pi$
$773$	−4.72527e29	−0.223122	−0.111561	+	0.993758i	$0.535585\pi$
$774$	0	0
$775$	3.42618e30	1.57450
$776$	2.95957e30	1.34178
$777$	0	0
$778$	1.85411e30	0.818183
$779$	−6.68598e29	−0.291086
$780$	0	0
$781$	6.55719e30	2.77896
$782$	−7.67859e29	−0.321078
$783$	0	0
$784$	9.07721e29	0.369516
$785$	−2.74495e29	−0.110256
$786$	0	0
$787$	2.41003e30	0.942513	0.471257	−	0.881996i	$-0.343801\pi$
$787$	2.41003e30	0.942513	0.471257	+	0.881996i	$0.343801\pi$
$788$	1.03790e30	0.400527
$789$	0	0
$790$	4.87471e28	0.0183174
$791$	−2.06009e26	−7.63893e−5 0
$792$	0	0
$793$	−1.11703e30	−0.403365
$794$	6.69531e29	0.238592
$795$	0	0
$796$	2.14318e30	0.743826
$797$	−1.66543e30	−0.570446	−0.285223	−	0.958461i	$-0.592068\pi$
$797$	−1.66543e30	−0.570446	−0.285223	+	0.958461i	$0.592068\pi$
$798$	0	0
$799$	1.99468e30	0.665475
$800$	2.41217e30	0.794260
$801$	0	0
$802$	−3.39468e30	−1.08885
$803$	−9.27574e30	−2.93654
$804$	0	0
$805$	9.66441e27	0.00298070
$806$	−4.93341e30	−1.50186
$807$	0	0
$808$	−3.47144e30	−1.02965
$809$	7.54499e29	0.220902	0.110451	−	0.993882i	$-0.464771\pi$
$809$	7.54499e29	0.220902	0.110451	+	0.993882i	$0.464771\pi$
$810$	0	0
$811$	−1.44305e29	−0.0411683	−0.0205842	−	0.999788i	$-0.506553\pi$
$811$	−1.44305e29	−0.0411683	−0.0205842	+	0.999788i	$0.506553\pi$
$812$	−9.77919e28	−0.0275400
$813$	0	0
$814$	−2.40225e30	−0.659268
$815$	−3.81881e29	−0.103460
$816$	0	0
$817$	−1.28316e30	−0.338803
$818$	3.05575e30	0.796542
$819$	0	0
$820$	1.03682e29	0.0263425
$821$	2.45914e30	0.616850	0.308425	−	0.951249i	$-0.400198\pi$
$821$	2.45914e30	0.616850	0.308425	+	0.951249i	$0.400198\pi$
$822$	0	0
$823$	−6.39970e29	−0.156481	−0.0782405	−	0.996935i	$-0.524930\pi$
$823$	−6.39970e29	−0.156481	−0.0782405	+	0.996935i	$0.524930\pi$
$824$	−3.10005e30	−0.748398
$825$	0	0
$826$	−1.03481e29	−0.0243541
$827$	−6.16124e29	−0.143173	−0.0715863	−	0.997434i	$-0.522806\pi$
$827$	−6.16124e29	−0.143173	−0.0715863	+	0.997434i	$0.522806\pi$
$828$	0	0
$829$	4.68818e29	0.106214	0.0531070	−	0.998589i	$-0.483088\pi$
$829$	4.68818e29	0.106214	0.0531070	+	0.998589i	$0.483088\pi$
$830$	4.52025e28	0.0101121
$831$	0	0
$832$	−5.63800e30	−1.22979
$833$	−4.61795e30	−0.994665
$834$	0	0
$835$	3.08923e29	0.0648846
$836$	1.17821e30	0.244376
$837$	0	0
$838$	−1.48969e30	−0.301325
$839$	−5.57203e30	−1.11304	−0.556522	−	0.830833i	$-0.687865\pi$
$839$	−5.57203e30	−1.11304	−0.556522	+	0.830833i	$0.687865\pi$
$840$	0	0
$841$	−3.17523e30	−0.618610
$842$	4.85451e30	0.934046
$843$	0	0
$844$	2.62046e30	0.491793
$845$	−2.21440e29	−0.0410450
$846$	0	0
$847$	−1.05953e30	−0.191574
$848$	1.80713e30	0.322726
$849$	0	0
$850$	4.31153e30	0.751161
$851$	1.28045e30	0.220344
$852$	0	0
$853$	−8.49982e30	−1.42707	−0.713535	−	0.700620i	$-0.752907\pi$
$853$	−8.49982e30	−1.42707	−0.713535	+	0.700620i	$0.752907\pi$
$854$	1.47631e29	0.0244833
$855$	0	0
$856$	9.24284e29	0.149565
$857$	2.22224e30	0.355216	0.177608	−	0.984101i	$-0.443164\pi$
$857$	2.22224e30	0.355216	0.177608	+	0.984101i	$0.443164\pi$
$858$	0	0
$859$	8.49442e30	1.32497	0.662484	−	0.749076i	$-0.269502\pi$
$859$	8.49442e30	1.32497	0.662484	+	0.749076i	$0.269502\pi$
$860$	1.98984e29	0.0306608
$861$	0	0
$862$	−3.39820e27	−0.000511002 0
$863$	−1.24518e31	−1.84978	−0.924890	−	0.380234i	$-0.875843\pi$
$863$	−1.24518e31	−1.84978	−0.924890	+	0.380234i	$0.875843\pi$
$864$	0	0
$865$	4.47970e29	0.0649501
$866$	−2.82723e30	−0.404971
$867$	0	0
$868$	−5.04573e29	−0.0705451
$869$	4.36853e30	0.603431
$870$	0	0
$871$	2.20440e30	0.297235
$872$	−1.44293e31	−1.92231
$873$	0	0
$874$	8.11525e29	0.105544
$875$	−1.08788e29	−0.0139796
$876$	0	0
$877$	−4.40218e30	−0.552296	−0.276148	−	0.961115i	$-0.589058\pi$
$877$	−4.40218e30	−0.552296	−0.276148	+	0.961115i	$0.589058\pi$
$878$	−4.96129e29	−0.0615038
$879$	0	0
$880$	3.58482e29	0.0433910
$881$	−1.53729e31	−1.83870	−0.919348	−	0.393444i	$-0.871283\pi$
$881$	−1.53729e31	−1.83870	−0.919348	+	0.393444i	$0.871283\pi$
$882$	0	0
$883$	3.46064e30	0.404175	0.202087	−	0.979367i	$-0.435227\pi$
$883$	3.46064e30	0.404175	0.202087	+	0.979367i	$0.435227\pi$
$884$	4.80435e30	0.554480
$885$	0	0
$886$	−5.26856e30	−0.593797
$887$	−6.50229e30	−0.724216	−0.362108	−	0.932136i	$-0.617943\pi$
$887$	−6.50229e30	−0.724216	−0.362108	+	0.932136i	$0.617943\pi$
$888$	0	0
$889$	−1.42978e30	−0.155525
$890$	6.25271e29	0.0672160
$891$	0	0
$892$	6.40822e30	0.672832
$893$	−2.10811e30	−0.218752
$894$	0	0
$895$	−1.02322e30	−0.103711
$896$	−6.91490e28	−0.00692711
$897$	0	0
$898$	−1.22967e31	−1.20334
$899$	1.01006e31	0.976948
$900$	0	0
$901$	−9.19362e30	−0.868713
$902$	−1.20067e31	−1.12139
$903$	0	0
$904$	8.83158e27	0.000805879 0
$905$	5.06556e29	0.0456896
$906$	0	0
$907$	−7.60076e30	−0.669855	−0.334927	−	0.942244i	$-0.608712\pi$
$907$	−7.60076e30	−0.669855	−0.334927	+	0.942244i	$0.608712\pi$
$908$	7.86823e30	0.685450
$909$	0	0
$910$	7.81380e28	0.00665163
$911$	1.97731e30	0.166392	0.0831960	−	0.996533i	$-0.473487\pi$
$911$	1.97731e30	0.166392	0.0831960	+	0.996533i	$0.473487\pi$
$912$	0	0
$913$	4.05088e30	0.333124
$914$	1.21479e31	0.987563
$915$	0	0
$916$	−3.79032e30	−0.301143
$917$	−5.83164e29	−0.0458050
$918$	0	0
$919$	−5.18823e29	−0.0398297	−0.0199148	−	0.999802i	$-0.506340\pi$
$919$	−5.18823e29	−0.0398297	−0.0199148	+	0.999802i	$0.506340\pi$
$920$	−4.14312e29	−0.0314453
$921$	0	0
$922$	−1.44342e31	−1.07082
$923$	−2.82585e31	−2.07267
$924$	0	0
$925$	−7.18972e30	−0.515494
$926$	−3.54318e30	−0.251176
$927$	0	0
$928$	7.11126e30	0.492825
$929$	−1.49983e31	−1.02773	−0.513864	−	0.857872i	$-0.671786\pi$
$929$	−1.49983e31	−1.02773	−0.513864	+	0.857872i	$0.671786\pi$
$930$	0	0
$931$	4.88056e30	0.326962
$932$	6.35875e30	0.421216
$933$	0	0
$934$	1.70399e31	1.10363
$935$	−1.82375e30	−0.116800
$936$	0	0
$937$	1.01621e30	0.0636381	0.0318191	−	0.999494i	$-0.489870\pi$
$937$	1.01621e30	0.0636381	0.0318191	+	0.999494i	$0.489870\pi$
$938$	−2.91342e29	−0.0180415
$939$	0	0
$940$	3.26912e29	0.0197965
$941$	−1.53425e31	−0.918763	−0.459382	−	0.888239i	$-0.651929\pi$
$941$	−1.53425e31	−0.918763	−0.459382	+	0.888239i	$0.651929\pi$
$942$	0	0
$943$	6.39981e30	0.374796
$944$	2.04596e30	0.118493
$945$	0	0
$946$	−2.30430e31	−1.30521
$947$	1.98552e31	1.11224	0.556120	−	0.831102i	$-0.312289\pi$
$947$	1.98552e31	1.11224	0.556120	+	0.831102i	$0.312289\pi$
$948$	0	0
$949$	3.99742e31	2.19020
$950$	−4.55672e30	−0.246919
$951$	0	0
$952$	−2.09042e30	−0.110802
$953$	2.22129e31	1.16447	0.582237	−	0.813019i	$-0.302178\pi$
$953$	2.22129e31	1.16447	0.582237	+	0.813019i	$0.302178\pi$
$954$	0	0
$955$	−5.87559e29	−0.0301312
$956$	−1.08368e31	−0.549661
$957$	0	0
$958$	−2.48092e30	−0.123105
$959$	5.94013e29	0.0291542
$960$	0	0
$961$	3.12903e31	1.50250
$962$	1.03526e31	0.491712
$963$	0	0
$964$	2.44083e30	0.113430
$965$	2.96796e30	0.136434
$966$	0	0
$967$	−2.75032e31	−1.23710	−0.618550	−	0.785745i	$-0.712280\pi$
$967$	−2.75032e31	−1.23710	−0.618550	+	0.785745i	$0.712280\pi$
$968$	4.54218e31	2.02103
$969$	0	0
$970$	1.47062e30	0.0640321
$971$	−7.56268e30	−0.325742	−0.162871	−	0.986647i	$-0.552075\pi$
$971$	−7.56268e30	−0.325742	−0.162871	+	0.986647i	$0.552075\pi$
$972$	0	0
$973$	−3.70507e29	−0.0156175
$974$	1.21185e31	0.505335
$975$	0	0
$976$	−2.91887e30	−0.119122
$977$	−3.45274e31	−1.39402	−0.697012	−	0.717059i	$-0.745488\pi$
$977$	−3.45274e31	−1.39402	−0.697012	+	0.717059i	$0.745488\pi$
$978$	0	0
$979$	5.60344e31	2.21430
$980$	−7.56846e29	−0.0295892
$981$	0	0
$982$	7.43028e30	0.284338
$983$	−1.47808e31	−0.559609	−0.279805	−	0.960057i	$-0.590270\pi$
$983$	−1.47808e31	−0.559609	−0.279805	+	0.960057i	$0.590270\pi$
$984$	0	0
$985$	1.69792e30	0.0629271
$986$	1.27107e31	0.466082
$987$	0	0
$988$	−5.07755e30	−0.182266
$989$	1.22824e31	0.436235
$990$	0	0
$991$	3.79667e30	0.132017	0.0660085	−	0.997819i	$-0.478974\pi$
$991$	3.79667e30	0.132017	0.0660085	+	0.997819i	$0.478974\pi$
$992$	3.66917e31	1.26239
$993$	0	0
$994$	3.73474e30	0.125807
$995$	3.50606e30	0.116863
$996$	0	0
$997$	−7.58958e30	−0.247696	−0.123848	−	0.992301i	$-0.539523\pi$
$997$	−7.58958e30	−0.247696	−0.123848	+	0.992301i	$0.539523\pi$
$998$	2.45830e31	0.793897
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	81.22.a.c.1.7		20
3.2	odd	2		81.22.a.d.1.14		20
9.2	odd	6		27.22.c.a.10.7		40
9.4	even	3		9.22.c.a.7.14	yes	40
9.5	odd	6		27.22.c.a.19.7		40
9.7	even	3		9.22.c.a.4.14	✓	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
9.22.c.a.4.14	✓	40	9.7	even	3
9.22.c.a.7.14	yes	40	9.4	even	3
27.22.c.a.10.7		40	9.2	odd	6
27.22.c.a.19.7		40	9.5	odd	6
81.22.a.c.1.7		20	1.1	even	1	trivial
81.22.a.d.1.14		20	3.2	odd	2

Overview	Random
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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)

\(f(q)\)	\(=\)	\(q-1087.31 q^{2} -914902. q^{4} -1.49670e6 q^{5} -7.63950e7 q^{7} +3.27505e9 q^{8} +O(q^{10})\)	\(q-1087.31 q^{2} -914902. q^{4} -1.49670e6 q^{5} -7.63950e7 q^{7} +3.27505e9 q^{8} +1.62738e9 q^{10} +1.45840e11 q^{11} -6.28503e11 q^{13} +8.30652e10 q^{14} -1.64231e12 q^{16} +8.35511e12 q^{17} -8.83024e12 q^{19} +1.36934e12 q^{20} -1.58574e14 q^{22} +8.45230e13 q^{23} -4.74597e14 q^{25} +6.83380e14 q^{26} +6.98939e13 q^{28} -1.39915e15 q^{29} -7.21913e15 q^{31} -5.08256e15 q^{32} -9.08462e15 q^{34} +1.14341e14 q^{35} +1.51491e16 q^{37} +9.60123e15 q^{38} -4.90177e15 q^{40} +7.57169e16 q^{41} +1.45314e17 q^{43} -1.33429e17 q^{44} -9.19029e16 q^{46} +2.38738e17 q^{47} -5.52710e17 q^{49} +5.16036e17 q^{50} +5.75019e17 q^{52} -1.10036e18 q^{53} -2.18279e17 q^{55} -2.50197e17 q^{56} +1.52131e18 q^{58} -1.24578e18 q^{59} +1.77729e18 q^{61} +7.84945e18 q^{62} +8.97051e18 q^{64} +9.40682e17 q^{65} -3.50739e18 q^{67} -7.64411e18 q^{68} -1.24324e17 q^{70} +4.49616e19 q^{71} -6.36022e19 q^{73} -1.64718e19 q^{74} +8.07881e18 q^{76} -1.11414e19 q^{77} +2.99543e19 q^{79} +2.45805e18 q^{80} -8.23279e19 q^{82} +2.77762e19 q^{83} -1.25051e19 q^{85} -1.58002e20 q^{86} +4.77633e20 q^{88} +3.84218e20 q^{89} +4.80145e19 q^{91} -7.73303e19 q^{92} -2.59583e20 q^{94} +1.32162e19 q^{95} +9.03672e20 q^{97} +6.00968e20 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 1023 q^{2} + 19922945 q^{4} - 32234853 q^{5} + 189623959 q^{7} - 648135831 q^{8}+O(q^{10}) \) 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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