LMFDB - Embedded newform 80.20.c.a.49.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [80,20,Mod(49,80)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(80, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0, 1]))

N = Newforms(chi, 20, names="a")

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

chi := DirichletCharacter("80.49");

S:= CuspForms(chi, 20);

N := Newforms(S);

Level:	$ N $	$=$	$ 80 = 2^{4} \cdot 5 $
Weight:	$ k $	$=$	$ 20 $
Character orbit:	$[\chi]$	$=$	80.c (of order $2$, degree $1$, not minimal)

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:	no
Analytic conductor:	$183.053357245$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 726881x^{6} + 160513523376x^{4} + 10607307647230976x^{2} + 32429098232548950016 $ x^8 + 726881x^6 + 160513523376x^4 + 10607307647230976*x^2 + 32429098232548950016
Coefficient ring:	$\Z[a_1, \ldots, a_{17}]$
Coefficient ring index:	$ 2^{34}\cdot 3^{8}\cdot 5^{13} $
Twist minimal:	no (minimal twist has level 5)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			49.5
Root			$-607.943i$ of defining polynomial
Character	$\chi$	$=$	80.49
Dual form			80.20.c.a.49.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+18754.1i q^{3} +(4.05746e6 - 1.61570e6i) q^{5} +1.79878e8i q^{7} +8.10544e8 q^{9} +O(q^{10})$	\(q+18754.1i q^{3} +(4.05746e6 - 1.61570e6i) q^{5} +1.79878e8i q^{7} +8.10544e8 q^{9} +3.61960e9 q^{11} +7.48125e9i q^{13} +(3.03011e10 + 7.60942e10i) q^{15} -2.32175e11i q^{17} -2.12840e12 q^{19} -3.37345e12 q^{21} +6.69298e12i q^{23} +(1.38525e13 - 1.31113e13i) q^{25} +3.69983e13i q^{27} -7.26252e13 q^{29} -2.51555e14 q^{31} +6.78825e13i q^{33} +(2.90628e14 + 7.29846e14i) q^{35} +2.00511e14i q^{37} -1.40304e14 q^{39} -2.32187e15 q^{41} -1.85667e15i q^{43} +(3.28875e15 - 1.30960e15i) q^{45} -9.40833e15i q^{47} -2.09570e16 q^{49} +4.35425e15 q^{51} -1.66277e16i q^{53} +(1.46864e16 - 5.84819e15i) q^{55} -3.99164e16i q^{57} +1.59149e15 q^{59} -4.33362e16 q^{61} +1.45799e17i q^{63} +(1.20875e16 + 3.03549e16i) q^{65} +2.54117e17i q^{67} -1.25521e17 q^{69} +2.27564e17 q^{71} +8.76951e17i q^{73} +(2.45891e17 + 2.59792e17i) q^{75} +6.51085e17i q^{77} -5.76500e17 q^{79} +2.48193e17 q^{81} -5.61483e17i q^{83} +(-3.75125e17 - 9.42042e17i) q^{85} -1.36202e18i q^{87} +2.36138e18 q^{89} -1.34571e18 q^{91} -4.71769e18i q^{93} +(-8.63592e18 + 3.43886e18i) q^{95} +1.90922e18i q^{97} +2.93385e18 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 147000 q^{5} + 345358584 q^{9}+O(q^{10}) $ 8 * q + 147000 * q^5 + 345358584 * q^9	$ 8 q + 147000 q^{5} + 345358584 q^{9} + 3379575264 q^{11} + 242324628000 q^{15} - 4547188380640 q^{19} - 2983154334624 q^{21} + 17715709625000 q^{25} - 188222300345040 q^{29} - 72115006686976 q^{31} + 299115755916000 q^{35} - 30\!\cdots\!28 q^{39}+ \cdots + 16\!\cdots\!72 q^{99}+O(q^{100}) $ 8 * q + 147000 * q^5 + 345358584 * q^9 + 3379575264 * q^11 + 242324628000 * q^15 - 4547188380640 * q^19 - 2983154334624 * q^21 + 17715709625000 * q^25 - 188222300345040 * q^29 - 72115006686976 * q^31 + 299115755916000 * q^35 - 3011653788049728 * q^39 - 3314269428857904 * q^41 + 10198157211261000 * q^45 - 11129258011816744 * q^49 + 46867071411404544 * q^51 - 69821226326124000 * q^55 - 259648032778012320 * q^59 - 582893562753226064 * q^61 + 747545324689032000 * q^65 + 302144302523815008 * q^69 + 2617007600602926144 * q^71 - 2877932428209000000 * q^75 - 3935092091109861760 * q^79 - 8328177293660704152 * q^81 + 3752387009219584000 * q^85 + 2120141101636921680 * q^89 + 3358638219973817664 * q^91 - 6106065789884820000 * q^95 + 16256944625235082272 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/80\mathbb{Z}\right)^\times$.

$n$	$17$	$21$	$31$
$\chi(n)$	$-1$	$1$	$1$

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 $

$2$		0			0
$2$		0			0
$3$			18754.1i			0.550104i	0.961429	+	0.275052i	$0.0886951\pi$
$3$			18754.1i			0.550104i	−0.961429	+	0.275052i	$0.911305\pi$
$4$		0			0
$5$	4.05746e6	−	1.61570e6i	0.929051	−	0.369952i
$5$	4.05746e6	−	1.61570e6i	0.929051	−	0.369952i
$6$		0			0
$7$			1.79878e8i			1.68479i	0.538861	+	0.842395i	$0.318855\pi$
$7$			1.79878e8i			1.68479i	−0.538861	+	0.842395i	$0.681145\pi$
$8$		0			0
$9$	8.10544e8			0.697385
$10$		0			0
$11$	3.61960e9			0.462840			0.231420	−	0.972854i	$-0.425663\pi$
$11$	3.61960e9			0.462840			0.231420	+	0.972854i	$0.425663\pi$
$12$		0			0
$13$			7.48125e9i			0.195665i	0.995203	+	0.0978323i	$0.0311909\pi$
$13$			7.48125e9i			0.195665i	−0.995203	+	0.0978323i	$0.968809\pi$
$14$		0			0
$15$	3.03011e10	+	7.60942e10i	0.203512	+	0.511075i
$16$		0			0
$17$		−	2.32175e11i		−	0.474844i	−0.971407	−	0.237422i	$-0.923698\pi$
$17$		−	2.32175e11i		−	0.474844i	0.971407	−	0.237422i	$-0.0763024\pi$
$18$		0			0
$19$	−2.12840e12			−1.51319			−0.756597	−	0.653881i	$-0.773140\pi$
$19$	−2.12840e12			−1.51319			−0.756597	+	0.653881i	$0.773140\pi$
$20$		0			0
$21$	−3.37345e12			−0.926810
$22$		0			0
$23$			6.69298e12i			0.774828i	0.921906	+	0.387414i	$0.126632\pi$
$23$			6.69298e12i			0.774828i	−0.921906	+	0.387414i	$0.873368\pi$
$24$		0			0
$25$	1.38525e13	−	1.31113e13i	0.726271	−	0.687409i
$26$		0			0
$27$			3.69983e13i			0.933739i
$28$		0			0
$29$	−7.26252e13			−0.929622			−0.464811	−	0.885410i	$-0.653878\pi$
$29$	−7.26252e13			−0.929622			−0.464811	+	0.885410i	$0.653878\pi$
$30$		0			0
$31$	−2.51555e14			−1.70882			−0.854410	−	0.519600i	$-0.826081\pi$
$31$	−2.51555e14			−1.70882			−0.854410	+	0.519600i	$0.826081\pi$
$32$		0			0
$33$			6.78825e13i			0.254610i
$34$		0			0
$35$	2.90628e14	+	7.29846e14i	0.623291	+	1.56525i
$36$		0			0
$37$			2.00511e14i			0.253643i	0.991926	+	0.126821i	$0.0404775\pi$
$37$			2.00511e14i			0.253643i	−0.991926	+	0.126821i	$0.959522\pi$
$38$		0			0
$39$	−1.40304e14			−0.107636
$40$		0			0
$41$	−2.32187e15			−1.10762			−0.553811	−	0.832642i	$-0.686827\pi$
$41$	−2.32187e15			−1.10762			−0.553811	+	0.832642i	$0.686827\pi$
$42$		0			0
$43$		−	1.85667e15i		−	0.563359i	−0.959508	−	0.281680i	$-0.909108\pi$
$43$		−	1.85667e15i		−	0.563359i	0.959508	−	0.281680i	$-0.0908916\pi$
$44$		0			0
$45$	3.28875e15	−	1.30960e15i	0.647906	−	0.257999i
$46$		0			0
$47$		−	9.40833e15i		−	1.22626i	−0.789982	−	0.613130i	$-0.789910\pi$
$47$		−	9.40833e15i		−	1.22626i	0.789982	−	0.613130i	$-0.210090\pi$
$48$		0			0
$49$	−2.09570e16			−1.83851
$50$		0			0
$51$	4.35425e15			0.261214
$52$		0			0
$53$		−	1.66277e16i		−	0.692167i	−0.938204	−	0.346084i	$-0.887511\pi$
$53$		−	1.66277e16i		−	0.692167i	0.938204	−	0.346084i	$-0.112489\pi$
$54$		0			0
$55$	1.46864e16	−	5.84819e15i	0.430001	−	0.171229i
$56$		0			0
$57$		−	3.99164e16i		−	0.832415i
$58$		0			0
$59$	1.59149e15			0.0239171			0.0119586	−	0.999928i	$-0.496193\pi$
$59$	1.59149e15			0.0239171			0.0119586	+	0.999928i	$0.496193\pi$
$60$		0			0
$61$	−4.33362e16			−0.474479			−0.237240	−	0.971451i	$-0.576243\pi$
$61$	−4.33362e16			−0.474479			−0.237240	+	0.971451i	$0.576243\pi$
$62$		0			0
$63$			1.45799e17i			1.17495i
$64$		0			0
$65$	1.20875e16	+	3.03549e16i	0.0723865	+	0.181782i
$66$		0			0
$67$			2.54117e17i			1.14110i	0.821263	+	0.570550i	$0.193270\pi$
$67$			2.54117e17i			1.14110i	−0.821263	+	0.570550i	$0.806730\pi$
$68$		0			0
$69$	−1.25521e17			−0.426236
$70$		0			0
$71$	2.27564e17			0.589047			0.294524	−	0.955644i	$-0.404839\pi$
$71$	2.27564e17			0.589047			0.294524	+	0.955644i	$0.404839\pi$
$72$		0			0
$73$			8.76951e17i			1.74344i	0.490000	+	0.871722i	$0.336997\pi$
$73$			8.76951e17i			1.74344i	−0.490000	+	0.871722i	$0.663003\pi$
$74$		0			0
$75$	2.45891e17	+	2.59792e17i	0.378147	+	0.399525i
$76$		0			0
$77$			6.51085e17i			0.779787i
$78$		0			0
$79$	−5.76500e17			−0.541181			−0.270590	−	0.962695i	$-0.587219\pi$
$79$	−5.76500e17			−0.541181			−0.270590	+	0.962695i	$0.587219\pi$
$80$		0			0
$81$	2.48193e17			0.183731
$82$		0			0
$83$		−	5.61483e17i		−	0.329682i	−0.986320	−	0.164841i	$-0.947289\pi$
$83$		−	5.61483e17i		−	0.329682i	0.986320	−	0.164841i	$-0.0527110\pi$
$84$		0			0
$85$	−3.75125e17	−	9.42042e17i	−0.175670	−	0.441154i
$86$		0			0
$87$		−	1.36202e18i		−	0.511389i
$88$		0			0
$89$	2.36138e18			0.714431			0.357215	−	0.934022i	$-0.383726\pi$
$89$	2.36138e18			0.714431			0.357215	+	0.934022i	$0.383726\pi$
$90$		0			0
$91$	−1.34571e18			−0.329654
$92$		0			0
$93$		−	4.71769e18i		−	0.940029i
$94$		0			0
$95$	−8.63592e18	+	3.43886e18i	−1.40583	+	0.559810i
$96$		0			0
$97$			1.90922e18i			0.254991i	0.991839	+	0.127496i	$0.0406939\pi$
$97$			1.90922e18i			0.254991i	−0.991839	+	0.127496i	$0.959306\pi$
$98$		0			0
$99$	2.93385e18			0.322777
$100$		0			0
$101$	5.27814e18			0.480206			0.240103	−	0.970747i	$-0.422819\pi$
$101$	5.27814e18			0.480206			0.240103	+	0.970747i	$0.422819\pi$
$102$		0			0
$103$		−	5.05461e18i		−	0.381710i	−0.981618	−	0.190855i	$-0.938874\pi$
$103$		−	5.05461e18i		−	0.381710i	0.981618	−	0.190855i	$-0.0611261\pi$
$104$		0			0
$105$	−1.36876e19	+	5.45048e18i	−0.861054	+	0.342875i
$106$		0			0
$107$		−	5.80087e18i		−	0.305033i	−0.988301	−	0.152517i	$-0.951262\pi$
$107$		−	5.80087e18i		−	0.305033i	0.988301	−	0.152517i	$-0.0487378\pi$
$108$		0			0
$109$	−4.20726e17			−0.0185544			−0.00927722	−	0.999957i	$-0.502953\pi$
$109$	−4.20726e17			−0.0185544			−0.00927722	+	0.999957i	$0.502953\pi$
$110$		0			0
$111$	−3.76042e18			−0.139530
$112$		0			0
$113$			1.52582e19i			0.477813i	0.971043	+	0.238907i	$0.0767890\pi$
$113$			1.52582e19i			0.477813i	−0.971043	+	0.238907i	$0.923211\pi$
$114$		0			0
$115$	1.08139e19	+	2.71565e19i	0.286649	+	0.719855i
$116$		0			0
$117$			6.06388e18i			0.136454i
$118$		0			0
$119$	4.17631e19			0.800012
$120$		0			0
$121$	−4.80576e19			−0.785780
$122$		0			0
$123$		−	4.35447e19i		−	0.609308i
$124$		0			0
$125$	3.50222e19	−	7.55800e19i	0.420434	−	0.907323i
$126$		0			0
$127$		−	5.60376e19i		−	0.578554i	−0.957245	−	0.289277i	$-0.906585\pi$
$127$		−	5.60376e19i		−	0.578554i	0.957245	−	0.289277i	$-0.0934149\pi$
$128$		0			0
$129$	3.48203e19			0.309907
$130$		0			0
$131$	8.10990e19			0.623646			0.311823	−	0.950140i	$-0.399060\pi$
$131$	8.10990e19			0.623646			0.311823	+	0.950140i	$0.399060\pi$
$132$		0			0
$133$		−	3.82852e20i		−	2.54941i
$134$		0			0
$135$	5.97781e19	+	1.50119e20i	0.345439	+	0.867491i
$136$		0			0
$137$			3.62932e20i			1.82381i	0.410401	+	0.911905i	$0.365389\pi$
$137$			3.62932e20i			1.82381i	−0.410401	+	0.911905i	$0.634611\pi$
$138$		0			0
$139$	−1.66383e20			−0.728564			−0.364282	−	0.931289i	$-0.618686\pi$
$139$	−1.66383e20			−0.728564			−0.364282	+	0.931289i	$0.618686\pi$
$140$		0			0
$141$	1.76445e20			0.674571
$142$		0			0
$143$			2.70792e19i			0.0905613i
$144$		0			0
$145$	−2.94674e20	+	1.17340e20i	−0.863666	+	0.343916i
$146$		0			0
$147$		−	3.93031e20i		−	1.01137i
$148$		0			0
$149$	−1.41978e20			−0.321330			−0.160665	−	0.987009i	$-0.551364\pi$
$149$	−1.41978e20			−0.321330			−0.160665	+	0.987009i	$0.551364\pi$
$150$		0			0
$151$	−4.28309e20			−0.854036			−0.427018	−	0.904243i	$-0.640436\pi$
$151$	−4.28309e20			−0.854036			−0.427018	+	0.904243i	$0.640436\pi$
$152$		0			0
$153$		−	1.88188e20i		−	0.331149i
$154$		0			0
$155$	−1.02067e21	+	4.06437e20i	−1.58758	+	0.632182i
$156$		0			0
$157$			7.80079e20i			1.07422i	0.843513	+	0.537108i	$0.180483\pi$
$157$			7.80079e20i			1.07422i	−0.843513	+	0.537108i	$0.819517\pi$
$158$		0			0
$159$	3.11838e20			0.380764
$160$		0			0
$161$	−1.20392e21			−1.30542
$162$		0			0
$163$		−	1.09860e21i		−	1.05939i	−0.848188	−	0.529696i	$-0.822306\pi$
$163$		−	1.09860e21i		−	1.05939i	0.848188	−	0.529696i	$-0.177694\pi$
$164$		0			0
$165$	1.09678e20	+	2.75431e20i	0.0941936	+	0.236546i
$166$		0			0
$167$			3.21947e19i			0.0246591i	0.999924	+	0.0123296i	$0.00392472\pi$
$167$			3.21947e19i			0.0246591i	−0.999924	+	0.0123296i	$0.996075\pi$
$168$		0			0
$169$	1.40595e21			0.961715
$170$		0			0
$171$	−1.72516e21			−1.05528
$172$		0			0
$173$		−	2.65247e21i		−	1.45282i	−0.687261	−	0.726410i	$-0.741187\pi$
$173$		−	2.65247e21i		−	1.45282i	0.687261	−	0.726410i	$-0.258813\pi$
$174$		0			0
$175$	2.35843e21	+	2.49176e21i	1.15814	+	1.22361i
$176$		0			0
$177$			2.98470e19i			0.0131569i
$178$		0			0
$179$	−1.15403e21			−0.457206			−0.228603	−	0.973520i	$-0.573416\pi$
$179$	−1.15403e21			−0.457206			−0.228603	+	0.973520i	$0.573416\pi$
$180$		0			0
$181$	−7.70360e20			−0.274629			−0.137315	−	0.990527i	$-0.543847\pi$
$181$	−7.70360e20			−0.274629			−0.137315	+	0.990527i	$0.543847\pi$
$182$		0			0
$183$		−	8.12733e20i		−	0.261013i
$184$		0			0
$185$	3.23966e20	+	8.13568e20i	0.0938358	+	0.235647i
$186$		0			0
$187$		−	8.40382e20i		−	0.219777i
$188$		0			0
$189$	−6.65516e21			−1.57315
$190$		0			0
$191$	3.70311e21			0.792044			0.396022	−	0.918241i	$-0.370390\pi$
$191$	3.70311e21			0.792044			0.396022	+	0.918241i	$0.370390\pi$
$192$		0			0
$193$		−	5.44930e21i		−	1.05571i	−0.849333	−	0.527857i	$-0.822996\pi$
$193$		−	5.44930e21i		−	1.05571i	0.849333	−	0.527857i	$-0.177004\pi$
$194$		0			0
$195$	−5.69280e20	+	2.26690e20i	−0.0999993	+	0.0398202i
$196$		0			0
$197$			5.28276e21i			0.842231i	0.907007	+	0.421116i	$0.138361\pi$
$197$			5.28276e21i			0.842231i	−0.907007	+	0.421116i	$0.861639\pi$
$198$		0			0
$199$	−1.12121e22			−1.62398			−0.811991	−	0.583670i	$-0.801616\pi$
$199$	−1.12121e22			−1.62398			−0.811991	+	0.583670i	$0.801616\pi$
$200$		0			0
$201$	−4.76575e21			−0.627724
$202$		0			0
$203$		−	1.30636e22i		−	1.56622i
$204$		0			0
$205$	−9.42091e21	+	3.75145e21i	−1.02904	+	0.409767i
$206$		0			0
$207$			5.42496e21i			0.540354i
$208$		0			0
$209$	−7.70398e21			−0.700366
$210$		0			0
$211$	−1.02283e22			−0.849416			−0.424708	−	0.905330i	$-0.639623\pi$
$211$	−1.02283e22			−0.849416			−0.424708	+	0.905330i	$0.639623\pi$
$212$		0			0
$213$			4.26777e21i			0.324037i
$214$		0			0
$215$	−2.99983e21	−	7.53339e21i	−0.208416	−	0.523390i
$216$		0			0
$217$		−	4.52490e22i		−	2.87900i
$218$		0			0
$219$	−1.64465e22			−0.959077
$220$		0			0
$221$	1.73696e21			0.0929102
$222$		0			0
$223$		−	9.30478e21i		−	0.456888i	−0.973557	−	0.228444i	$-0.926636\pi$
$223$		−	9.30478e21i		−	0.456888i	0.973557	−	0.228444i	$-0.0733638\pi$
$224$		0			0
$225$	1.12281e22	−	1.06273e22i	0.506490	−	0.479389i
$226$		0			0
$227$		−	7.54698e20i		−	0.0312988i	−0.999878	−	0.0156494i	$-0.995018\pi$
$227$		−	7.54698e20i		−	0.0312988i	0.999878	−	0.0156494i	$-0.00498156\pi$
$228$		0			0
$229$	6.69932e21			0.255619			0.127810	−	0.991799i	$-0.459205\pi$
$229$	6.69932e21			0.255619			0.127810	+	0.991799i	$0.459205\pi$
$230$		0			0
$231$	−1.22105e22			−0.428964
$232$		0			0
$233$			2.31221e22i			0.748421i	0.927344	+	0.374211i	$0.122086\pi$
$233$			2.31221e22i			0.748421i	−0.927344	+	0.374211i	$0.877914\pi$
$234$		0			0
$235$	−1.52010e22	−	3.81739e22i	−0.453658	−	1.13926i
$236$		0			0
$237$		−	1.08118e22i		−	0.297706i
$238$		0			0
$239$	−4.10044e22			−1.04244			−0.521220	−	0.853423i	$-0.674523\pi$
$239$	−4.10044e22			−1.04244			−0.521220	+	0.853423i	$0.674523\pi$
$240$		0			0
$241$	−5.88872e22			−1.38312			−0.691559	−	0.722320i	$-0.743076\pi$
$241$	−5.88872e22			−1.38312			−0.691559	+	0.722320i	$0.743076\pi$
$242$		0			0
$243$			4.76563e22i			1.03481i
$244$		0			0
$245$	−8.50324e22	+	3.38603e22i	−1.70807	+	0.680162i
$246$		0			0
$247$		−	1.59231e22i		−	0.296079i
$248$		0			0
$249$	1.05301e22			0.181359
$250$		0			0
$251$	−2.44560e22			−0.390378			−0.195189	−	0.980766i	$-0.562532\pi$
$251$	−2.44560e22			−0.390378			−0.195189	+	0.980766i	$0.562532\pi$
$252$		0			0
$253$			2.42260e22i			0.358621i
$254$		0			0
$255$	1.76672e22	−	7.03515e21i	0.242681	−	0.0966366i
$256$		0			0
$257$			5.03201e22i			0.641767i	0.947119	+	0.320883i	$0.103980\pi$
$257$			5.03201e22i			0.641767i	−0.947119	+	0.320883i	$0.896020\pi$
$258$		0			0
$259$	−3.60675e22			−0.427335
$260$		0			0
$261$	−5.88659e22			−0.648304
$262$		0			0
$263$			6.26756e22i			0.641976i	0.947083	+	0.320988i	$0.104015\pi$
$263$			6.26756e22i			0.641976i	−0.947083	+	0.320988i	$0.895985\pi$
$264$		0			0
$265$	−2.68654e22	−	6.74662e22i	−0.256069	−	0.643059i
$266$		0			0
$267$			4.42856e22i			0.393011i
$268$		0			0
$269$	−2.88988e22			−0.238910			−0.119455	−	0.992840i	$-0.538115\pi$
$269$	−2.88988e22			−0.238910			−0.119455	+	0.992840i	$0.538115\pi$
$270$		0			0
$271$	−2.97029e22			−0.228871			−0.114435	−	0.993431i	$-0.536506\pi$
$271$	−2.97029e22			−0.228871			−0.114435	+	0.993431i	$0.536506\pi$
$272$		0			0
$273$		−	2.52376e22i		−	0.181344i
$274$		0			0
$275$	5.01406e22	−	4.74576e22i	0.336147	−	0.318160i
$276$		0			0
$277$		−	3.03186e23i		−	1.89737i	−0.316223	−	0.948685i	$-0.602415\pi$
$277$		−	3.03186e23i		−	1.89737i	0.316223	−	0.948685i	$-0.397585\pi$
$278$		0			0
$279$	−2.03896e23			−1.19171
$280$		0			0
$281$	−2.50158e23			−1.36617			−0.683084	−	0.730340i	$-0.739362\pi$
$281$	−2.50158e23			−1.36617			−0.683084	+	0.730340i	$0.739362\pi$
$282$		0			0
$283$		−	1.87699e22i		−	0.0958276i	−0.998851	−	0.0479138i	$-0.984743\pi$
$283$		−	1.87699e22i		−	0.0958276i	0.998851	−	0.0479138i	$-0.0152573\pi$
$284$		0			0
$285$	−6.44929e22	−	1.61959e23i	−0.307954	−	0.773356i
$286$		0			0
$287$		−	4.17652e23i		−	1.86611i
$288$		0			0
$289$	1.85167e23			0.774523
$290$		0			0
$291$	−3.58058e22			−0.140272
$292$		0			0
$293$			1.83821e23i			0.674764i	0.941368	+	0.337382i	$0.109541\pi$
$293$			1.83821e23i			0.674764i	−0.941368	+	0.337382i	$0.890459\pi$
$294$		0			0
$295$	6.45740e21	−	2.57136e21i	0.0222202	−	0.00884819i
$296$		0			0
$297$			1.33919e23i			0.432171i
$298$		0			0
$299$	−5.00719e22			−0.151606
$300$		0			0
$301$	3.33974e23			0.949142
$302$		0			0
$303$			9.89869e22i			0.264164i
$304$		0			0
$305$	−1.75835e23	+	7.00183e22i	−0.440815	+	0.175535i
$306$		0			0
$307$		−	3.57199e23i		−	0.841580i	−0.907158	−	0.420790i	$-0.861753\pi$
$307$		−	3.57199e23i		−	0.841580i	0.907158	−	0.420790i	$-0.138247\pi$
$308$		0			0
$309$	9.47948e22			0.209981
$310$		0			0
$311$	2.61658e22			0.0545143			0.0272571	−	0.999628i	$-0.491323\pi$
$311$	2.61658e22			0.0545143			0.0272571	+	0.999628i	$0.491323\pi$
$312$		0			0
$313$		−	2.90894e23i		−	0.570247i	−0.958491	−	0.285124i	$-0.907965\pi$
$313$		−	2.90894e23i		−	0.570247i	0.958491	−	0.285124i	$-0.0920347\pi$
$314$		0			0
$315$	2.35567e23	+	5.91572e23i	0.434674	+	1.09159i
$316$		0			0
$317$			1.00748e24i			1.75055i	0.483628	+	0.875273i	$0.339319\pi$
$317$			1.00748e24i			1.75055i	−0.483628	+	0.875273i	$0.660681\pi$
$318$		0			0
$319$	−2.62874e23			−0.430266
$320$		0			0
$321$	1.08790e23			0.167800
$322$		0			0
$323$			4.94162e23i			0.718532i
$324$		0			0
$325$	9.80888e22	+	1.03634e23i	0.134502	+	0.142105i
$326$		0			0
$327$		−	7.89036e21i		−	0.0102069i
$328$		0			0
$329$	1.69235e24			2.06599
$330$		0			0
$331$	1.24050e24			1.42965			0.714827	−	0.699302i	$-0.246506\pi$
$331$	1.24050e24			1.42965			0.714827	+	0.699302i	$0.246506\pi$
$332$		0			0
$333$			1.62523e23i			0.176887i
$334$		0			0
$335$	4.10577e23	+	1.03107e24i	0.422152	+	1.06014i
$336$		0			0
$337$		−	1.24721e24i		−	1.21187i	−0.795513	−	0.605937i	$-0.792799\pi$
$337$		−	1.24721e24i		−	1.21187i	0.795513	−	0.605937i	$-0.207201\pi$
$338$		0			0
$339$	−2.86155e23			−0.262847
$340$		0			0
$341$	−9.10528e23			−0.790909
$342$		0			0
$343$		−	1.71929e24i		−	1.41272i
$344$		0			0
$345$	−5.09297e23	+	2.02805e23i	−0.395995	+	0.157687i
$346$		0			0
$347$			8.82339e23i			0.649390i	0.945819	+	0.324695i	$0.105262\pi$
$347$			8.82339e23i			0.649390i	−0.945819	+	0.324695i	$0.894738\pi$
$348$		0			0
$349$	−6.79957e23			−0.473849			−0.236925	−	0.971528i	$-0.576139\pi$
$349$	−6.79957e23			−0.473849			−0.236925	+	0.971528i	$0.576139\pi$
$350$		0			0
$351$	−2.76793e23			−0.182700
$352$		0			0
$353$		−	1.70063e24i		−	1.06353i	−0.846892	−	0.531765i	$-0.821529\pi$
$353$		−	1.70063e24i		−	1.06353i	0.846892	−	0.531765i	$-0.178471\pi$
$354$		0			0
$355$	9.23334e23	−	3.67676e23i	0.547255	−	0.217919i
$356$		0			0
$357$			7.83231e23i			0.440090i
$358$		0			0
$359$	1.87542e24			0.999311			0.499656	−	0.866224i	$-0.333460\pi$
$359$	1.87542e24			0.999311			0.499656	+	0.866224i	$0.333460\pi$
$360$		0			0
$361$	2.55168e24			1.28976
$362$		0			0
$363$		−	9.01278e23i		−	0.432261i
$364$		0			0
$365$	1.41689e24	+	3.55820e24i	0.644991	+	1.61975i
$366$		0			0
$367$			1.73965e24i			0.751856i	0.926649	+	0.375928i	$0.122676\pi$
$367$			1.73965e24i			0.751856i	−0.926649	+	0.375928i	$0.877324\pi$
$368$		0			0
$369$	−1.88198e24			−0.772439
$370$		0			0
$371$	2.99095e24			1.16616
$372$		0			0
$373$			1.95284e24i			0.723491i	0.932277	+	0.361746i	$0.117819\pi$
$373$			1.95284e24i			0.723491i	−0.932277	+	0.361746i	$0.882181\pi$
$374$		0			0
$375$	1.41744e24	+	6.56810e23i	0.499122	+	0.231283i
$376$		0			0
$377$		−	5.43327e23i		−	0.181894i
$378$		0			0
$379$	−3.86854e24			−1.23161			−0.615806	−	0.787897i	$-0.711170\pi$
$379$	−3.86854e24			−1.23161			−0.615806	+	0.787897i	$0.711170\pi$
$380$		0			0
$381$	1.05094e24			0.318265
$382$		0			0
$383$			5.32239e24i			1.53362i	0.641874	+	0.766810i	$0.278157\pi$
$383$			5.32239e24i			1.53362i	−0.641874	+	0.766810i	$0.721843\pi$
$384$		0			0
$385$	1.05196e24	+	2.64175e24i	0.288484	+	0.724462i
$386$		0			0
$387$		−	1.50492e24i		−	0.392878i
$388$		0			0
$389$	4.85730e24			1.20746			0.603731	−	0.797188i	$-0.293680\pi$
$389$	4.85730e24			1.20746			0.603731	+	0.797188i	$0.293680\pi$
$390$		0			0
$391$	1.55395e24			0.367923
$392$		0			0
$393$			1.52094e24i			0.343071i
$394$		0			0
$395$	−2.33913e24	+	9.31451e23i	−0.502784	+	0.200211i
$396$		0			0
$397$		−	5.78732e24i		−	1.18568i	−0.805320	−	0.592841i	$-0.798006\pi$
$397$		−	5.78732e24i		−	1.18568i	0.805320	−	0.592841i	$-0.201994\pi$
$398$		0			0
$399$	7.18006e24			1.40244
$400$		0			0
$401$	6.31326e24			1.17593			0.587966	−	0.808886i	$-0.299929\pi$
$401$	6.31326e24			1.17593			0.587966	+	0.808886i	$0.299929\pi$
$402$		0			0
$403$		−	1.88194e24i		−	0.334355i
$404$		0			0
$405$	1.00704e24	−	4.01006e23i	0.170695	−	0.0679717i
$406$		0			0
$407$			7.25772e23i			0.117396i
$408$		0			0
$409$	5.68097e24			0.877104			0.438552	−	0.898706i	$-0.355491\pi$
$409$	5.68097e24			0.877104			0.438552	+	0.898706i	$0.355491\pi$
$410$		0			0
$411$	−6.80647e24			−1.00329
$412$		0			0
$413$			2.86273e23i			0.0402953i
$414$		0			0
$415$	−9.07188e23	−	2.27820e24i	−0.121966	−	0.306291i
$416$		0			0
$417$		−	3.12036e24i		−	0.400786i
$418$		0			0
$419$	1.23198e25			1.51207			0.756033	−	0.654533i	$-0.227135\pi$
$419$	1.23198e25			1.51207			0.756033	+	0.654533i	$0.227135\pi$
$420$		0			0
$421$	−8.35914e24			−0.980577			−0.490289	−	0.871560i	$-0.663109\pi$
$421$	−8.35914e24			−0.980577			−0.490289	+	0.871560i	$0.663109\pi$
$422$		0			0
$423$		−	7.62586e24i		−	0.855176i
$424$		0			0
$425$	−3.04411e24	−	3.21621e24i	−0.326412	−	0.344865i
$426$		0			0
$427$		−	7.79520e24i		−	0.799397i
$428$		0			0
$429$	−5.07846e23			−0.0498182
$430$		0			0
$431$	3.01638e23			0.0283108			0.0141554	−	0.999900i	$-0.495494\pi$
$431$	3.01638e23			0.0283108			0.0141554	+	0.999900i	$0.495494\pi$
$432$		0			0
$433$			1.90272e25i			1.70899i	0.519461	+	0.854494i	$0.326133\pi$
$433$			1.90272e25i			1.70899i	−0.519461	+	0.854494i	$0.673867\pi$
$434$		0			0
$435$	−2.20062e24	−	5.52636e24i	−0.189189	−	0.475106i
$436$		0			0
$437$		−	1.42454e25i		−	1.17247i
$438$		0			0
$439$	−5.53042e24			−0.435858			−0.217929	−	0.975965i	$-0.569930\pi$
$439$	−5.53042e24			−0.435858			−0.217929	+	0.975965i	$0.569930\pi$
$440$		0			0
$441$	−1.69866e25			−1.28215
$442$		0			0
$443$			2.30459e25i			1.66632i	0.553031	+	0.833161i	$0.313471\pi$
$443$			2.30459e25i			1.66632i	−0.553031	+	0.833161i	$0.686529\pi$
$444$		0			0
$445$	9.58119e24	−	3.81527e24i	0.663742	−	0.264305i
$446$		0			0
$447$		−	2.66267e24i		−	0.176765i
$448$		0			0
$449$	−2.60186e25			−1.65556			−0.827778	−	0.561056i	$-0.810395\pi$
$449$	−2.60186e25			−1.65556			−0.827778	+	0.561056i	$0.810395\pi$
$450$		0			0
$451$	−8.40425e24			−0.512651
$452$		0			0
$453$		−	8.03256e24i		−	0.469809i
$454$		0			0
$455$	−5.46016e24	+	2.17426e24i	−0.306265	+	0.121956i
$456$		0			0
$457$			2.31329e25i			1.24459i	0.782783	+	0.622295i	$0.213800\pi$
$457$			2.31329e25i			1.24459i	−0.782783	+	0.622295i	$0.786200\pi$
$458$		0			0
$459$	8.59008e24			0.443380
$460$		0			0
$461$	2.86383e25			1.41837			0.709184	−	0.705023i	$-0.249063\pi$
$461$	2.86383e25			1.41837			0.709184	+	0.705023i	$0.249063\pi$
$462$		0			0
$463$			2.65604e25i			1.26245i	0.775598	+	0.631227i	$0.217448\pi$
$463$			2.65604e25i			1.26245i	−0.775598	+	0.631227i	$0.782552\pi$
$464$		0			0
$465$	−7.62237e24	−	1.91418e25i	−0.347766	−	0.873335i
$466$		0			0
$467$		−	1.59314e25i		−	0.697819i	−0.937156	−	0.348909i	$-0.886552\pi$
$467$		−	1.59314e25i		−	0.697819i	0.937156	−	0.348909i	$-0.113448\pi$
$468$		0			0
$469$	−4.57100e25			−1.92251
$470$		0			0
$471$	−1.46297e25			−0.590931
$472$		0			0
$473$		−	6.72043e24i		−	0.260745i
$474$		0			0
$475$	−2.94837e25	+	2.79061e25i	−1.09899	+	1.04018i
$476$		0			0
$477$		−	1.34775e25i		−	0.482707i
$478$		0			0
$479$	−3.55269e25			−1.22284			−0.611420	−	0.791306i	$-0.709401\pi$
$479$	−3.55269e25			−1.22284			−0.611420	+	0.791306i	$0.709401\pi$
$480$		0			0
$481$	−1.50008e24			−0.0496289
$482$		0			0
$483$		−	2.25784e25i		−	0.718118i
$484$		0			0
$485$	3.08473e24	+	7.74660e24i	0.0943345	+	0.236900i
$486$		0			0
$487$		−	5.62096e25i		−	1.65305i	−0.562902	−	0.826524i	$-0.690315\pi$
$487$		−	5.62096e25i		−	1.65305i	0.562902	−	0.826524i	$-0.309685\pi$
$488$		0			0
$489$	2.06032e25			0.582776
$490$		0			0
$491$	5.81507e25			1.58227			0.791135	−	0.611642i	$-0.209491\pi$
$491$	5.81507e25			1.58227			0.791135	+	0.611642i	$0.209491\pi$
$492$		0			0
$493$			1.68618e25i			0.441425i
$494$		0			0
$495$	1.19040e25	−	4.74022e24i	0.299877	−	0.119412i
$496$		0			0
$497$			4.09337e25i			0.992420i
$498$		0			0
$499$	−1.33885e25			−0.312447			−0.156224	−	0.987722i	$-0.549932\pi$
$499$	−1.33885e25			−0.312447			−0.156224	+	0.987722i	$0.549932\pi$
$500$		0			0
$501$	−6.03784e23			−0.0135651
$502$		0			0
$503$		−	5.92007e25i		−	1.28065i	−0.768103	−	0.640326i	$-0.778799\pi$
$503$		−	5.92007e25i		−	1.28065i	0.768103	−	0.640326i	$-0.221201\pi$
$504$		0			0
$505$	2.14158e25	−	8.52789e24i	0.446136	−	0.177653i
$506$		0			0
$507$			2.63674e25i			0.529044i
$508$		0			0
$509$	−4.36448e25			−0.843555			−0.421777	−	0.906699i	$-0.638594\pi$
$509$	−4.36448e25			−0.843555			−0.421777	+	0.906699i	$0.638594\pi$
$510$		0			0
$511$	−1.57744e26			−2.93734
$512$		0			0
$513$		−	7.87472e25i		−	1.41293i
$514$		0			0
$515$	−8.16673e24	−	2.05089e25i	−0.141215	−	0.354628i
$516$		0			0
$517$		−	3.40544e25i		−	0.567562i
$518$		0			0
$519$	4.97447e25			0.799203
$520$		0			0
$521$	−7.24724e25			−1.12257			−0.561286	−	0.827622i	$-0.689693\pi$
$521$	−7.24724e25			−1.12257			−0.561286	+	0.827622i	$0.689693\pi$
$522$		0			0
$523$			3.62351e25i			0.541207i	0.962691	+	0.270604i	$0.0872232\pi$
$523$			3.62351e25i			0.541207i	−0.962691	+	0.270604i	$0.912777\pi$
$524$		0			0
$525$	−4.67307e25	+	4.42302e25i	−0.673115	+	0.637097i
$526$		0			0
$527$			5.84047e25i			0.811423i
$528$		0			0
$529$	2.98194e25			0.399641
$530$		0			0
$531$	1.28997e24			0.0166794
$532$		0			0
$533$		−	1.73705e25i		−	0.216722i
$534$		0			0
$535$	−9.37246e24	−	2.35368e25i	−0.112848	−	0.283391i
$536$		0			0
$537$		−	2.16428e25i		−	0.251511i
$538$		0			0
$539$	−7.58561e25			−0.850937
$540$		0			0
$541$	−4.47583e24			−0.0484730			−0.0242365	−	0.999706i	$-0.507715\pi$
$541$	−4.47583e24			−0.0484730			−0.0242365	+	0.999706i	$0.507715\pi$
$542$		0			0
$543$		−	1.44474e25i		−	0.151075i
$544$		0			0
$545$	−1.70708e24	+	6.79768e23i	−0.0172380	+	0.00686426i
$546$		0			0
$547$			2.13519e25i			0.208237i	0.994565	+	0.104118i	$0.0332021\pi$
$547$			2.13519e25i			0.208237i	−0.994565	+	0.104118i	$0.966798\pi$
$548$		0			0
$549$	−3.51259e25			−0.330895
$550$		0			0
$551$	1.54576e26			1.40670
$552$		0			0
$553$		−	1.03699e26i		−	0.911775i
$554$		0			0
$555$	−1.52578e25	+	6.07571e24i	−0.129631	+	0.0516195i
$556$		0			0
$557$		−	7.41228e25i		−	0.608593i	−0.952577	−	0.304297i	$-0.901579\pi$
$557$		−	7.41228e25i		−	0.608593i	0.952577	−	0.304297i	$-0.0984214\pi$
$558$		0			0
$559$	1.38902e25			0.110229
$560$		0			0
$561$	1.57606e25			0.120900
$562$		0			0
$563$		−	2.39164e26i		−	1.77364i	−0.462116	−	0.886820i	$-0.652910\pi$
$563$		−	2.39164e26i		−	1.77364i	0.462116	−	0.886820i	$-0.347090\pi$
$564$		0			0
$565$	2.46527e25	+	6.19096e25i	0.176768	+	0.443913i
$566$		0			0
$567$			4.46444e25i			0.309548i
$568$		0			0
$569$	−1.08135e26			−0.725102			−0.362551	−	0.931964i	$-0.618094\pi$
$569$	−1.08135e26			−0.725102			−0.362551	+	0.931964i	$0.618094\pi$
$570$		0			0
$571$	9.51568e25			0.617158			0.308579	−	0.951199i	$-0.400147\pi$
$571$	9.51568e25			0.617158			0.308579	+	0.951199i	$0.400147\pi$
$572$		0			0
$573$			6.94485e25i			0.435707i
$574$		0			0
$575$	8.77536e25	+	9.27147e25i	0.532624	+	0.562735i
$576$		0			0
$577$			2.21789e26i			1.30248i	0.758873	+	0.651238i	$0.225750\pi$
$577$			2.21789e26i			1.30248i	−0.758873	+	0.651238i	$0.774250\pi$
$578$		0			0
$579$	1.02197e26			0.580753
$580$		0			0
$581$	1.00998e26			0.555444
$582$		0			0
$583$		−	6.01856e25i		−	0.320362i
$584$		0			0
$585$	9.79741e24	+	2.46040e25i	0.0504813	+	0.126772i
$586$		0			0
$587$			3.00717e26i			1.50002i	0.661429	+	0.750008i	$0.269950\pi$
$587$			3.00717e26i			1.50002i	−0.661429	+	0.750008i	$0.730050\pi$
$588$		0			0
$589$	5.35410e26			2.58578
$590$		0			0
$591$	−9.90735e25			−0.463315
$592$		0			0
$593$			2.27900e26i			1.03211i	0.856557	+	0.516053i	$0.172599\pi$
$593$			2.27900e26i			1.03211i	−0.856557	+	0.516053i	$0.827401\pi$
$594$		0			0
$595$	1.69452e26	−	6.74766e25i	0.743252	−	0.295966i
$596$		0			0
$597$		−	2.10273e26i		−	0.893360i
$598$		0			0
$599$	−9.07164e25			−0.373363			−0.186681	−	0.982420i	$-0.559773\pi$
$599$	−9.07164e25			−0.373363			−0.186681	+	0.982420i	$0.559773\pi$
$600$		0			0
$601$	9.37859e25			0.373964			0.186982	−	0.982363i	$-0.440129\pi$
$601$	9.37859e25			0.373964			0.186982	+	0.982363i	$0.440129\pi$
$602$		0			0
$603$			2.05973e26i			0.795786i
$604$		0			0
$605$	−1.94992e26	+	7.76466e25i	−0.730029	+	0.290701i
$606$		0			0
$607$			2.25098e26i			0.816732i	0.912818	+	0.408366i	$0.133901\pi$
$607$			2.25098e26i			0.816732i	−0.912818	+	0.408366i	$0.866099\pi$
$608$		0			0
$609$	2.44997e26			0.861583
$610$		0			0
$611$	7.03860e25			0.239936
$612$		0			0
$613$			8.30040e25i			0.274299i	0.990550	+	0.137150i	$0.0437941\pi$
$613$			8.30040e25i			0.274299i	−0.990550	+	0.137150i	$0.956206\pi$
$614$		0			0
$615$	−7.03552e25	−	1.76681e26i	−0.225415	−	0.566078i
$616$		0			0
$617$			4.41321e26i			1.37103i	0.728061	+	0.685513i	$0.240422\pi$
$617$			4.41321e26i			1.37103i	−0.728061	+	0.685513i	$0.759578\pi$
$618$		0			0
$619$	−2.41336e26			−0.727044			−0.363522	−	0.931586i	$-0.618426\pi$
$619$	−2.41336e26			−0.727044			−0.363522	+	0.931586i	$0.618426\pi$
$620$		0			0
$621$	−2.47629e26			−0.723487
$622$		0			0
$623$			4.24758e26i			1.20366i
$624$		0			0
$625$	1.99865e25	−	3.63248e26i	0.0549383	−	0.998490i
$626$		0			0
$627$		−	1.44481e26i		−	0.385275i
$628$		0			0
$629$	4.65538e25			0.120441
$630$		0			0
$631$	1.75895e26			0.441545			0.220773	−	0.975325i	$-0.429142\pi$
$631$	1.75895e26			0.441545			0.220773	+	0.975325i	$0.429142\pi$
$632$		0			0
$633$		−	1.91823e26i		−	0.467268i
$634$		0			0
$635$	−9.05399e25	−	2.27370e26i	−0.214037	−	0.537506i
$636$		0			0
$637$		−	1.56785e26i		−	0.359732i
$638$		0			0
$639$	1.84451e26			0.410793
$640$		0			0
$641$	6.26722e26			1.35495			0.677475	−	0.735546i	$-0.263074\pi$
$641$	6.26722e26			1.35495			0.677475	+	0.735546i	$0.263074\pi$
$642$		0			0
$643$			4.06756e25i			0.0853748i	0.999088	+	0.0426874i	$0.0135919\pi$
$643$			4.06756e25i			0.0853748i	−0.999088	+	0.0426874i	$0.986408\pi$
$644$		0			0
$645$	1.41282e26	−	5.62592e25i	0.287919	−	0.114651i
$646$		0			0
$647$		−	5.94304e26i		−	1.17603i	−0.808851	−	0.588014i	$-0.799910\pi$
$647$		−	5.94304e26i		−	1.17603i	0.808851	−	0.588014i	$-0.200090\pi$
$648$		0			0
$649$	5.76055e24			0.0110698
$650$		0			0
$651$	8.48606e26			1.58375
$652$		0			0
$653$			4.38542e26i			0.794944i	0.917614	+	0.397472i	$0.130112\pi$
$653$			4.38542e26i			0.794944i	−0.917614	+	0.397472i	$0.869888\pi$
$654$		0			0
$655$	3.29056e26	−	1.31032e26i	0.579399	−	0.230719i
$656$		0			0
$657$			7.10807e26i			1.21585i
$658$		0			0
$659$	5.41264e26			0.899493			0.449747	−	0.893156i	$-0.351514\pi$
$659$	5.41264e26			0.899493			0.449747	+	0.893156i	$0.351514\pi$
$660$		0			0
$661$	7.96736e24			0.0128647			0.00643236	−	0.999979i	$-0.497953\pi$
$661$	7.96736e24			0.0128647			0.00643236	+	0.999979i	$0.497953\pi$
$662$		0			0
$663$			3.25752e25i			0.0511103i
$664$		0			0
$665$	−6.18574e26	−	1.55341e27i	−0.943161	−	2.36853i
$666$		0			0
$667$		−	4.86079e26i		−	0.720297i
$668$		0			0
$669$	1.74503e26			0.251336
$670$		0			0
$671$	−1.56860e26			−0.219608
$672$		0			0
$673$		−	3.41589e26i		−	0.464902i	−0.972608	−	0.232451i	$-0.925325\pi$
$673$		−	3.41589e26i		−	0.464902i	0.972608	−	0.232451i	$-0.0746745\pi$
$674$		0			0
$675$	4.85095e26	+	5.12519e26i	0.641860	+	0.678147i
$676$		0			0
$677$		−	3.34901e26i		−	0.430849i	−0.976521	−	0.215424i	$-0.930887\pi$
$677$		−	3.34901e26i		−	0.430849i	0.976521	−	0.215424i	$-0.0691135\pi$
$678$		0			0
$679$	−3.43426e26			−0.429606
$680$		0			0
$681$	1.41537e25			0.0172176
$682$		0			0
$683$			1.09285e27i			1.29290i	0.762956	+	0.646450i	$0.223747\pi$
$683$			1.09285e27i			1.29290i	−0.762956	+	0.646450i	$0.776253\pi$
$684$		0			0
$685$	5.86389e26	+	1.47258e27i	0.674723	+	1.69441i
$686$		0			0
$687$			1.25640e26i			0.140617i
$688$		0			0
$689$	1.24396e26			0.135433
$690$		0			0
$691$	2.01449e26			0.213365			0.106682	−	0.994293i	$-0.465977\pi$
$691$	2.01449e26			0.213365			0.106682	+	0.994293i	$0.465977\pi$
$692$		0			0
$693$			5.27733e26i			0.543812i
$694$		0			0
$695$	−6.75092e26	+	2.68824e26i	−0.676873	+	0.269534i
$696$		0			0
$697$			5.39081e26i			0.525948i
$698$		0			0
$699$	−4.33635e26			−0.411710
$700$		0			0
$701$	−4.28823e26			−0.396239			−0.198120	−	0.980178i	$-0.563483\pi$
$701$	−4.28823e26			−0.396239			−0.198120	+	0.980178i	$0.563483\pi$
$702$		0			0
$703$		−	4.26769e26i		−	0.383811i
$704$		0			0
$705$	7.15919e26	−	2.85082e26i	0.626711	−	0.249559i
$706$		0			0
$707$			9.49418e26i			0.809046i
$708$		0			0
$709$	−1.91128e27			−1.58557			−0.792783	−	0.609504i	$-0.791369\pi$
$709$	−1.91128e27			−1.58557			−0.792783	+	0.609504i	$0.791369\pi$
$710$		0			0
$711$	−4.67279e26			−0.377411
$712$		0			0
$713$		−	1.68365e27i		−	1.32404i
$714$		0			0
$715$	4.37518e25	+	1.09873e26i	0.0335034	+	0.0841361i
$716$		0			0
$717$		−	7.69003e26i		−	0.573451i
$718$		0			0
$719$	−2.62640e27			−1.90737			−0.953687	−	0.300799i	$-0.902747\pi$
$719$	−2.62640e27			−1.90737			−0.953687	+	0.300799i	$0.902747\pi$
$720$		0			0
$721$	9.09210e26			0.643101
$722$		0			0
$723$		−	1.10438e27i		−	0.760859i
$724$		0			0
$725$	−1.00604e27	+	9.52209e26i	−0.675157	+	0.639030i
$726$		0			0
$727$		−	7.24253e25i		−	0.0473493i	−0.999720	−	0.0236747i	$-0.992463\pi$
$727$		−	7.24253e25i		−	0.0473493i	0.999720	−	0.0236747i	$-0.00753658\pi$
$728$		0			0
$729$	−6.05287e26			−0.385523
$730$		0			0
$731$	−4.31074e26			−0.267508
$732$		0			0
$733$			1.12113e27i			0.677901i	0.940804	+	0.338951i	$0.110072\pi$
$733$			1.12113e27i			0.677901i	−0.940804	+	0.338951i	$0.889928\pi$
$734$		0			0
$735$	−6.35020e26	−	1.59471e27i	−0.374160	−	0.939619i
$736$		0			0
$737$			9.19804e26i			0.528146i
$738$		0			0
$739$	2.25754e27			1.26332			0.631661	−	0.775245i	$-0.282373\pi$
$739$	2.25754e27			1.26332			0.631661	+	0.775245i	$0.282373\pi$
$740$		0			0
$741$	2.98624e26			0.162874
$742$		0			0
$743$		−	2.84762e27i		−	1.51387i	−0.653491	−	0.756934i	$-0.726696\pi$
$743$		−	2.84762e27i		−	1.51387i	0.653491	−	0.756934i	$-0.273304\pi$
$744$		0			0
$745$	−5.76069e26	+	2.29393e26i	−0.298532	+	0.118877i
$746$		0			0
$747$		−	4.55106e26i		−	0.229915i
$748$		0			0
$749$	1.04345e27			0.513917
$750$		0			0
$751$	−1.75682e27			−0.843623			−0.421812	−	0.906684i	$-0.638606\pi$
$751$	−1.75682e27			−0.843623			−0.421812	+	0.906684i	$0.638606\pi$
$752$		0			0
$753$		−	4.58652e26i		−	0.214749i
$754$		0			0
$755$	−1.73785e27	+	6.92018e26i	−0.793442	+	0.315952i
$756$		0			0
$757$		−	3.07775e27i		−	1.37032i	−0.728392	−	0.685160i	$-0.759732\pi$
$757$		−	3.07775e27i		−	1.37032i	0.728392	−	0.685160i	$-0.240268\pi$
$758$		0			0
$759$	−4.54337e26			−0.197279
$760$		0			0
$761$	−3.44812e27			−1.46025			−0.730127	−	0.683312i	$-0.760539\pi$
$761$	−3.44812e27			−1.46025			−0.730127	+	0.683312i	$0.760539\pi$
$762$		0			0
$763$		−	7.56792e25i		−	0.0312603i
$764$		0			0
$765$	−3.04056e26	−	7.63566e26i	−0.122509	−	0.307654i
$766$		0			0
$767$			1.19063e25i			0.00467973i
$768$		0			0
$769$	−3.66284e27			−1.40449			−0.702243	−	0.711937i	$-0.747818\pi$
$769$	−3.66284e27			−1.40449			−0.702243	+	0.711937i	$0.747818\pi$
$770$		0			0
$771$	−9.43711e26			−0.353039
$772$		0			0
$773$		−	1.93533e27i		−	0.706399i	−0.935548	−	0.353199i	$-0.885094\pi$
$773$		−	1.93533e27i		−	0.706399i	0.935548	−	0.353199i	$-0.114906\pi$
$774$		0			0
$775$	−3.48466e27	+	3.29820e27i	−1.24107	+	1.17466i
$776$		0			0
$777$		−	6.76415e26i		−	0.235079i
$778$		0			0
$779$	4.94188e27			1.67605
$780$		0			0
$781$	8.23693e26			0.272634
$782$		0			0
$783$		−	2.68701e27i		−	0.868024i
$784$		0			0
$785$	1.26037e27	+	3.16514e27i	0.397409	+	0.998002i
$786$		0			0
$787$			4.47507e27i			1.37733i	0.725077	+	0.688667i	$0.241804\pi$
$787$			4.47507e27i			1.37733i	−0.725077	+	0.688667i	$0.758196\pi$
$788$		0			0
$789$	−1.17543e27			−0.353154
$790$		0			0
$791$	−2.74461e27			−0.805015
$792$		0			0
$793$		−	3.24209e26i		−	0.0928388i
$794$		0			0
$795$	1.26527e27	−	5.03837e26i	0.353749	−	0.140865i
$796$		0			0
$797$		−	2.99623e27i		−	0.817939i	−0.912548	−	0.408969i	$-0.865888\pi$
$797$		−	2.99623e27i		−	0.817939i	0.912548	−	0.408969i	$-0.134112\pi$
$798$		0			0
$799$	−2.18438e27			−0.582283
$800$		0			0
$801$	1.91400e27			0.498233
$802$		0			0
$803$			3.17421e27i			0.806935i
$804$		0			0
$805$	−4.88485e27	+	1.94517e27i	−1.21280	+	0.482944i
$806$		0			0
$807$		−	5.41973e26i		−	0.131425i
$808$		0			0
$809$	−8.97271e26			−0.212526			−0.106263	−	0.994338i	$-0.533889\pi$
$809$	−8.97271e26			−0.212526			−0.106263	+	0.994338i	$0.533889\pi$
$810$		0			0
$811$	7.80812e27			1.80654			0.903271	−	0.429070i	$-0.141159\pi$
$811$	7.80812e27			1.80654			0.903271	+	0.429070i	$0.141159\pi$
$812$		0			0
$813$		−	5.57052e26i		−	0.125903i
$814$		0			0
$815$	−1.77500e27	−	4.45752e27i	−0.391924	−	0.984228i
$816$		0			0
$817$			3.95175e27i			0.852472i
$818$		0			0
$819$	−1.09076e27			−0.229895
$820$		0			0
$821$	5.65133e27			1.16383			0.581917	−	0.813248i	$-0.302303\pi$
$821$	5.65133e27			1.16383			0.581917	+	0.813248i	$0.302303\pi$
$822$		0			0
$823$			4.23337e27i			0.851898i	0.904747	+	0.425949i	$0.140060\pi$
$823$			4.23337e27i			0.851898i	−0.904747	+	0.425949i	$0.859940\pi$
$824$		0			0
$825$	8.90027e26	+	9.40344e26i	0.175021	+	0.184916i
$826$		0			0
$827$		−	8.60057e27i		−	1.65282i	−0.563071	−	0.826408i	$-0.690380\pi$
$827$		−	8.60057e27i		−	1.65282i	0.563071	−	0.826408i	$-0.309620\pi$
$828$		0			0
$829$	−2.40358e27			−0.451431			−0.225715	−	0.974193i	$-0.572472\pi$
$829$	−2.40358e27			−0.451431			−0.225715	+	0.974193i	$0.572472\pi$
$830$		0			0
$831$	5.68600e27			1.04375
$832$		0			0
$833$			4.86570e27i			0.873008i
$834$		0			0
$835$	5.20170e25	+	1.30629e26i	0.00912271	+	0.0229096i
$836$		0			0
$837$		−	9.30708e27i		−	1.59559i
$838$		0			0
$839$	−2.28307e27			−0.382632			−0.191316	−	0.981529i	$-0.561275\pi$
$839$	−2.28307e27			−0.382632			−0.191316	+	0.981529i	$0.561275\pi$
$840$		0			0
$841$	−8.28845e26			−0.135804
$842$		0			0
$843$		−	4.69150e27i		−	0.751535i
$844$		0			0
$845$	5.70459e27	−	2.27160e27i	0.893482	−	0.355789i
$846$		0			0
$847$		−	8.64448e27i		−	1.32387i
$848$		0			0
$849$	3.52013e26			0.0527152
$850$		0			0
$851$	−1.34202e27			−0.196530
$852$		0			0
$853$		−	3.07333e27i		−	0.440142i	−0.975484	−	0.220071i	$-0.929371\pi$
$853$		−	3.07333e27i		−	0.440142i	0.975484	−	0.220071i	$-0.0706289\pi$
$854$		0			0
$855$	−6.99979e27	+	2.78735e27i	−0.980408	+	0.390403i
$856$		0			0
$857$			4.56647e27i			0.625551i	0.949827	+	0.312775i	$0.101259\pi$
$857$			4.56647e27i			0.625551i	−0.949827	+	0.312775i	$0.898741\pi$
$858$		0			0
$859$	−5.09546e27			−0.682728			−0.341364	−	0.939931i	$-0.610889\pi$
$859$	−5.09546e27			−0.682728			−0.341364	+	0.939931i	$0.610889\pi$
$860$		0			0
$861$	7.83271e27			1.02655
$862$		0			0
$863$			4.49338e27i			0.576064i	0.957621	+	0.288032i	$0.0930010\pi$
$863$			4.49338e27i			0.576064i	−0.957621	+	0.288032i	$0.906999\pi$
$864$		0			0
$865$	−4.28559e27	−	1.07623e28i	−0.537474	−	1.34974i
$866$		0			0
$867$			3.47265e27i			0.426069i
$868$		0			0
$869$	−2.08670e27			−0.250480
$870$		0			0
$871$	−1.90111e27			−0.223273
$872$		0			0
$873$			1.54751e27i			0.177827i
$874$		0			0
$875$	1.35952e28	+	6.29970e27i	1.52865	+	0.708343i
$876$		0			0
$877$			1.20133e28i			1.32180i	0.750473	+	0.660901i	$0.229826\pi$
$877$			1.20133e28i			1.32180i	−0.750473	+	0.660901i	$0.770174\pi$
$878$		0			0
$879$	−3.44740e27			−0.371191
$880$		0			0
$881$	5.81954e27			0.613221			0.306611	−	0.951835i	$-0.400805\pi$
$881$	5.81954e27			0.613221			0.306611	+	0.951835i	$0.400805\pi$
$882$		0			0
$883$			1.68577e28i			1.73849i	0.494386	+	0.869243i	$0.335393\pi$
$883$			1.68577e28i			1.73849i	−0.494386	+	0.869243i	$0.664607\pi$
$884$		0			0
$885$	4.82237e25	+	1.21103e26i	0.00486743	+	0.0122234i
$886$		0			0
$887$			8.09385e26i			0.0799614i	0.999200	+	0.0399807i	$0.0127296\pi$
$887$			8.09385e26i			0.0799614i	−0.999200	+	0.0399807i	$0.987270\pi$
$888$		0			0
$889$	1.00799e28			0.974742
$890$		0			0
$891$	8.98362e26			0.0850380
$892$		0			0
$893$			2.00247e28i			1.85557i
$894$		0			0
$895$	−4.68242e27	+	1.86456e27i	−0.424768	+	0.169144i
$896$		0			0
$897$		−	9.39055e26i		−	0.0833994i
$898$		0			0
$899$	1.82692e28			1.58856
$900$		0			0
$901$	−3.86054e27			−0.328672
$902$		0			0
$903$			6.26340e27i			0.522127i
$904$		0			0
$905$	−3.12571e27	+	1.24467e27i	−0.255145	+	0.101600i
$906$		0			0
$907$		−	2.84041e27i		−	0.227045i	−0.993535	−	0.113522i	$-0.963787\pi$
$907$		−	2.84041e27i		−	0.227045i	0.993535	−	0.113522i	$-0.0362134\pi$
$908$		0			0
$909$	4.27816e27			0.334889
$910$		0			0
$911$	1.43331e28			1.09879			0.549397	−	0.835561i	$-0.314857\pi$
$911$	1.43331e28			1.09879			0.549397	+	0.835561i	$0.314857\pi$
$912$		0			0
$913$		−	2.03235e27i		−	0.152590i
$914$		0			0
$915$	−1.31313e27	−	3.29763e27i	−0.0965624	−	0.242494i
$916$		0			0
$917$			1.45879e28i			1.05071i
$918$		0			0
$919$	1.84550e27			0.130202			0.0651009	−	0.997879i	$-0.479263\pi$
$919$	1.84550e27			0.130202			0.0651009	+	0.997879i	$0.479263\pi$
$920$		0			0
$921$	6.69896e27			0.462957
$922$		0			0
$923$			1.70247e27i			0.115256i
$924$		0			0
$925$	2.62896e27	+	2.77759e27i	0.174356	+	0.184213i
$926$		0			0
$927$		−	4.09698e27i		−	0.266199i
$928$		0			0
$929$	1.47827e28			0.941033			0.470516	−	0.882391i	$-0.344068\pi$
$929$	1.47827e28			0.941033			0.470516	+	0.882391i	$0.344068\pi$
$930$		0			0
$931$	4.46050e28			2.78203
$932$		0			0
$933$			4.90717e26i			0.0299886i
$934$		0			0
$935$	−1.35781e27	−	3.40982e27i	−0.0813069	−	0.204184i
$936$		0			0
$937$		−	2.62877e28i		−	1.54250i	−0.636531	−	0.771251i	$-0.719631\pi$
$937$		−	2.62877e28i		−	1.54250i	0.636531	−	0.771251i	$-0.280369\pi$
$938$		0			0
$939$	5.45546e27			0.313696
$940$		0			0
$941$	5.29025e27			0.298109			0.149054	−	0.988829i	$-0.452377\pi$
$941$	5.29025e27			0.298109			0.149054	+	0.988829i	$0.452377\pi$
$942$		0			0
$943$		−	1.55403e28i		−	0.858217i
$944$		0			0
$945$	−2.70030e28	+	1.07527e28i	−1.46154	+	0.581992i
$946$		0			0
$947$			2.77520e28i			1.47221i	0.676868	+	0.736105i	$0.263337\pi$
$947$			2.77520e28i			1.47221i	−0.676868	+	0.736105i	$0.736663\pi$
$948$		0			0
$949$	−6.56069e27			−0.341130
$950$		0			0
$951$	−1.88944e28			−0.962984
$952$		0			0
$953$		−	4.86733e27i		−	0.243169i	−0.992581	−	0.121585i	$-0.961202\pi$
$953$		−	4.86733e27i		−	0.243169i	0.992581	−	0.121585i	$-0.0387976\pi$
$954$		0			0
$955$	1.50252e28	−	5.98311e27i	0.735849	−	0.293018i
$956$		0			0
$957$		−	4.92998e27i		−	0.236691i
$958$		0			0
$959$	−6.52833e28			−3.07274
$960$		0			0
$961$	4.16091e28			1.92006
$962$		0			0
$963$		−	4.70186e27i		−	0.212726i
$964$		0			0
$965$	−8.80443e27	−	2.21103e28i	−0.390564	−	0.980812i
$966$		0			0
$967$		−	1.90521e28i		−	0.828689i	−0.910120	−	0.414345i	$-0.864011\pi$
$967$		−	1.90521e28i		−	0.828689i	0.910120	−	0.414345i	$-0.135989\pi$
$968$		0			0
$969$	−9.26759e27			−0.395267
$970$		0			0
$971$	4.36106e28			1.82394			0.911968	−	0.410261i	$-0.134562\pi$
$971$	4.36106e28			1.82394			0.911968	+	0.410261i	$0.134562\pi$
$972$		0			0
$973$		−	2.99285e28i		−	1.22748i
$974$		0			0
$975$	−1.94357e27	+	1.83957e27i	−0.0781728	+	0.0739899i
$976$		0			0
$977$		−	1.33368e28i		−	0.526081i	−0.964785	−	0.263041i	$-0.915275\pi$
$977$		−	1.33368e28i		−	0.526081i	0.964785	−	0.263041i	$-0.0847254\pi$
$978$		0			0
$979$	8.54724e27			0.330667
$980$		0			0
$981$	−3.41017e26			−0.0129396
$982$		0			0
$983$		−	3.76958e28i		−	1.40293i	−0.712706	−	0.701463i	$-0.752531\pi$
$983$		−	3.76958e28i		−	1.40293i	0.712706	−	0.701463i	$-0.247469\pi$
$984$		0			0
$985$	8.53535e27	+	2.14346e28i	0.311585	+	0.782476i
$986$		0			0
$987$			3.17385e28i			1.13651i
$988$		0			0
$989$	1.24267e28			0.436507
$990$		0			0
$991$	−2.77322e28			−0.955620			−0.477810	−	0.878463i	$-0.658569\pi$
$991$	−2.77322e28			−0.955620			−0.477810	+	0.878463i	$0.658569\pi$
$992$		0			0
$993$			2.32645e28i			0.786459i
$994$		0			0
$995$	−4.54925e28	+	1.81153e28i	−1.50876	+	0.600796i
$996$		0			0
$997$			4.18648e28i			1.36221i	0.732184	+	0.681107i	$0.238501\pi$
$997$			4.18648e28i			1.36221i	−0.732184	+	0.681107i	$0.761499\pi$
$998$		0			0
$999$	−7.41857e27			−0.236836

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	80.20.c.a.49.5		8
4.3	odd	2		5.20.b.a.4.8	yes	8
5.4	even	2	inner	80.20.c.a.49.4		8
12.11	even	2		45.20.b.b.19.1		8
20.3	even	4		25.20.a.f.1.8		8
20.7	even	4		25.20.a.f.1.1		8
20.19	odd	2		5.20.b.a.4.1	✓	8
60.59	even	2		45.20.b.b.19.8		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5.20.b.a.4.1	✓	8	20.19	odd	2
5.20.b.a.4.8	yes	8	4.3	odd	2
25.20.a.f.1.1		8	20.7	even	4
25.20.a.f.1.8		8	20.3	even	4
45.20.b.b.19.1		8	12.11	even	2
45.20.b.b.19.8		8	60.59	even	2
80.20.c.a.49.4		8	5.4	even	2	inner
80.20.c.a.49.5		8	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 80 = 2^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 20 \)
Character orbit:	\([\chi]\)	\(=\)	80.c (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+18754.1i q^{3} +(4.05746e6 - 1.61570e6i) q^{5} +1.79878e8i q^{7} +8.10544e8 q^{9} +O(q^{10})\)	\(q+18754.1i q^{3} +(4.05746e6 - 1.61570e6i) q^{5} +1.79878e8i q^{7} +8.10544e8 q^{9} +3.61960e9 q^{11} +7.48125e9i q^{13} +(3.03011e10 + 7.60942e10i) q^{15} -2.32175e11i q^{17} -2.12840e12 q^{19} -3.37345e12 q^{21} +6.69298e12i q^{23} +(1.38525e13 - 1.31113e13i) q^{25} +3.69983e13i q^{27} -7.26252e13 q^{29} -2.51555e14 q^{31} +6.78825e13i q^{33} +(2.90628e14 + 7.29846e14i) q^{35} +2.00511e14i q^{37} -1.40304e14 q^{39} -2.32187e15 q^{41} -1.85667e15i q^{43} +(3.28875e15 - 1.30960e15i) q^{45} -9.40833e15i q^{47} -2.09570e16 q^{49} +4.35425e15 q^{51} -1.66277e16i q^{53} +(1.46864e16 - 5.84819e15i) q^{55} -3.99164e16i q^{57} +1.59149e15 q^{59} -4.33362e16 q^{61} +1.45799e17i q^{63} +(1.20875e16 + 3.03549e16i) q^{65} +2.54117e17i q^{67} -1.25521e17 q^{69} +2.27564e17 q^{71} +8.76951e17i q^{73} +(2.45891e17 + 2.59792e17i) q^{75} +6.51085e17i q^{77} -5.76500e17 q^{79} +2.48193e17 q^{81} -5.61483e17i q^{83} +(-3.75125e17 - 9.42042e17i) q^{85} -1.36202e18i q^{87} +2.36138e18 q^{89} -1.34571e18 q^{91} -4.71769e18i q^{93} +(-8.63592e18 + 3.43886e18i) q^{95} +1.90922e18i q^{97} +2.93385e18 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 147000 q^{5} + 345358584 q^{9}+O(q^{10}) \) 8 * q + 147000 * q^5 + 345358584 * q^9	\( 8 q + 147000 q^{5} + 345358584 q^{9} + 3379575264 q^{11} + 242324628000 q^{15} - 4547188380640 q^{19} - 2983154334624 q^{21} + 17715709625000 q^{25} - 188222300345040 q^{29} - 72115006686976 q^{31} + 299115755916000 q^{35} - 30\!\cdots\!28 q^{39}+ \cdots + 16\!\cdots\!72 q^{99}+O(q^{100}) \) 8 * q + 147000 * q^5 + 345358584 * q^9 + 3379575264 * q^11 + 242324628000 * q^15 - 4547188380640 * q^19 - 2983154334624 * q^21 + 17715709625000 * q^25 - 188222300345040 * q^29 - 72115006686976 * q^31 + 299115755916000 * q^35 - 3011653788049728 * q^39 - 3314269428857904 * q^41 + 10198157211261000 * q^45 - 11129258011816744 * q^49 + 46867071411404544 * q^51 - 69821226326124000 * q^55 - 259648032778012320 * q^59 - 582893562753226064 * q^61 + 747545324689032000 * q^65 + 302144302523815008 * q^69 + 2617007600602926144 * q^71 - 2877932428209000000 * q^75 - 3935092091109861760 * q^79 - 8328177293660704152 * q^81 + 3752387009219584000 * q^85 + 2120141101636921680 * q^89 + 3358638219973817664 * q^91 - 6106065789884820000 * q^95 + 16256944625235082272 * q^99

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