LMFDB - Embedded newform 80.20.c.d.49.16

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:	$28$
Twist minimal:	no (minimal twist has level 40)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			49.16
Character	$\chi$	$=$	80.49
Dual form			80.20.c.d.49.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+7086.75i q^{3} +(3.46294e6 + 2.66112e6i) q^{5} -8.07683e7i q^{7} +1.11204e9 q^{9} +O(q^{10})$	\(q+7086.75i q^{3} +(3.46294e6 + 2.66112e6i) q^{5} -8.07683e7i q^{7} +1.11204e9 q^{9} -1.18624e10 q^{11} +5.69632e10i q^{13} +(-1.88587e10 + 2.45410e10i) q^{15} -6.43121e11i q^{17} -2.02839e12 q^{19} +5.72385e11 q^{21} -4.89514e12i q^{23} +(4.91036e12 + 1.84306e13i) q^{25} +1.61174e13i q^{27} +8.54240e13 q^{29} +1.78399e14 q^{31} -8.40659e13i q^{33} +(2.14934e14 - 2.79695e14i) q^{35} -4.42635e14i q^{37} -4.03684e14 q^{39} -2.92385e15 q^{41} +1.00677e15i q^{43} +(3.85092e15 + 2.95927e15i) q^{45} -7.76229e15i q^{47} +4.87537e15 q^{49} +4.55764e15 q^{51} -4.30061e16i q^{53} +(-4.10787e16 - 3.15673e16i) q^{55} -1.43747e16i q^{57} +7.84706e16 q^{59} +4.14592e16 q^{61} -8.98176e16i q^{63} +(-1.51586e17 + 1.97260e17i) q^{65} +3.97441e17i q^{67} +3.46907e16 q^{69} -4.02265e17 q^{71} +6.89262e16i q^{73} +(-1.30613e17 + 3.47985e16i) q^{75} +9.58106e17i q^{77} -1.39960e17 q^{79} +1.17826e18 q^{81} -3.15223e18i q^{83} +(1.71142e18 - 2.22709e18i) q^{85} +6.05379e17i q^{87} -5.27072e18 q^{89} +4.60082e18 q^{91} +1.26427e18i q^{93} +(-7.02417e18 - 5.39778e18i) q^{95} +8.01437e18i q^{97} -1.31915e19 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q - 3935164 q^{5} - 10352560732 q^{9}+O(q^{10}) $ 28 * q - 3935164 * q^5 - 10352560732 * q^9	$ 28 q - 3935164 q^{5} - 10352560732 q^{9} - 18570995888 q^{11} - 79041415120 q^{15} + 1685869130672 q^{19} + 140419722832 q^{21} - 29558822439924 q^{25} + 160448197635496 q^{29} - 64251929934720 q^{31} + 88899634227664 q^{35} - 45\!\cdots\!04 q^{39}+ \cdots + 24\!\cdots\!92 q^{99}+O(q^{100}) $ 28 * q - 3935164 * q^5 - 10352560732 * q^9 - 18570995888 * q^11 - 79041415120 * q^15 + 1685869130672 * q^19 + 140419722832 * q^21 - 29558822439924 * q^25 + 160448197635496 * q^29 - 64251929934720 * q^31 + 88899634227664 * q^35 - 4563253596731104 * q^39 + 87868042694936 * q^41 + 3557698140217852 * q^45 - 28923781405647564 * q^49 - 14937379593456000 * q^51 - 28335039172010704 * q^55 + 83879503376835216 * q^59 + 2336306250785000 * q^61 + 23503427909569568 * q^65 - 46927873937137712 * q^69 - 104881848512783264 * q^71 - 1094024007292275040 * q^75 + 795721739900308672 * q^79 + 3593102866196377132 * q^81 + 834124526841485952 * q^85 + 1582238786752844568 * q^89 - 11017818924975052064 * q^91 - 30914057837649668144 * q^95 + 24571127463084047792 * 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
$3$			7086.75i			0.207872i	0.994584	+	0.103936i	$0.0331437\pi$
$3$			7086.75i			0.207872i	−0.994584	+	0.103936i	$0.966856\pi$
$4$		0			0
$5$	3.46294e6	+	2.66112e6i	0.792920	+	0.609326i
$5$	3.46294e6	+	2.66112e6i	0.792920	+	0.609326i
$6$		0			0
$7$		−	8.07683e7i		−	0.756501i	−0.925703	−	0.378251i	$-0.876526\pi$
$7$		−	8.07683e7i		−	0.756501i	0.925703	−	0.378251i	$-0.123474\pi$
$8$		0			0
$9$	1.11204e9			0.956789
$10$		0			0
$11$	−1.18624e10			−1.51685			−0.758424	−	0.651762i	$-0.774030\pi$
$11$	−1.18624e10			−1.51685			−0.758424	+	0.651762i	$0.774030\pi$
$12$		0			0
$13$			5.69632e10i			1.48982i	0.667167	+	0.744908i	$0.267507\pi$
$13$			5.69632e10i			1.48982i	−0.667167	+	0.744908i	$0.732493\pi$
$14$		0			0
$15$	−1.88587e10	+	2.45410e10i	−0.126662	+	0.164826i
$16$		0			0
$17$		−	6.43121e11i		−	1.31531i	−0.753320	−	0.657655i	$-0.771549\pi$
$17$		−	6.43121e11i		−	1.31531i	0.753320	−	0.657655i	$-0.228451\pi$
$18$		0			0
$19$	−2.02839e12			−1.44209			−0.721043	−	0.692890i	$-0.756337\pi$
$19$	−2.02839e12			−1.44209			−0.721043	+	0.692890i	$0.756337\pi$
$20$		0			0
$21$	5.72385e11			0.157255
$22$		0			0
$23$		−	4.89514e12i		−	0.566697i	−0.959017	−	0.283348i	$-0.908555\pi$
$23$		−	4.89514e12i		−	0.566697i	0.959017	−	0.283348i	$-0.0914453\pi$
$24$		0			0
$25$	4.91036e12	+	1.84306e13i	0.257444	+	0.966293i
$26$		0			0
$27$			1.61174e13i			0.406761i
$28$		0			0
$29$	8.54240e13			1.09345			0.546725	−	0.837312i	$-0.315874\pi$
$29$	8.54240e13			1.09345			0.546725	+	0.837312i	$0.315874\pi$
$30$		0			0
$31$	1.78399e14			1.21187			0.605937	−	0.795513i	$-0.292798\pi$
$31$	1.78399e14			1.21187			0.605937	+	0.795513i	$0.292798\pi$
$32$		0			0
$33$		−	8.40659e13i		−	0.315310i
$34$		0			0
$35$	2.14934e14	−	2.79695e14i	0.460956	−	0.599845i
$36$		0			0
$37$		−	4.42635e14i		−	0.559924i	−0.960011	−	0.279962i	$-0.909678\pi$
$37$		−	4.42635e14i		−	0.559924i	0.960011	−	0.279962i	$-0.0903219\pi$
$38$		0			0
$39$	−4.03684e14			−0.309691
$40$		0			0
$41$	−2.92385e15			−1.39479			−0.697395	−	0.716687i	$-0.745657\pi$
$41$	−2.92385e15			−1.39479			−0.697395	+	0.716687i	$0.745657\pi$
$42$		0			0
$43$			1.00677e15i			0.305479i	0.988267	+	0.152739i	$0.0488095\pi$
$43$			1.00677e15i			0.305479i	−0.988267	+	0.152739i	$0.951190\pi$
$44$		0			0
$45$	3.85092e15	+	2.95927e15i	0.758657	+	0.582996i
$46$		0			0
$47$		−	7.76229e15i		−	1.01172i	−0.862616	−	0.505860i	$-0.831175\pi$
$47$		−	7.76229e15i		−	1.01172i	0.862616	−	0.505860i	$-0.168825\pi$
$48$		0			0
$49$	4.87537e15			0.427706
$50$		0			0
$51$	4.55764e15			0.273416
$52$		0			0
$53$		−	4.30061e16i		−	1.79023i	−0.445832	−	0.895116i	$-0.647092\pi$
$53$		−	4.30061e16i		−	1.79023i	0.445832	−	0.895116i	$-0.352908\pi$
$54$		0			0
$55$	−4.10787e16	−	3.15673e16i	−1.20274	−	0.924255i
$56$		0			0
$57$		−	1.43747e16i		−	0.299769i
$58$		0			0
$59$	7.84706e16			1.17927			0.589635	−	0.807670i	$-0.299272\pi$
$59$	7.84706e16			1.17927			0.589635	+	0.807670i	$0.299272\pi$
$60$		0			0
$61$	4.14592e16			0.453928			0.226964	−	0.973903i	$-0.427120\pi$
$61$	4.14592e16			0.453928			0.226964	+	0.973903i	$0.427120\pi$
$62$		0			0
$63$		−	8.98176e16i		−	0.723812i
$64$		0			0
$65$	−1.51586e17	+	1.97260e17i	−0.907784	+	1.18131i
$66$		0			0
$67$			3.97441e17i			1.78469i	0.451358	+	0.892343i	$0.350940\pi$
$67$			3.97441e17i			1.78469i	−0.451358	+	0.892343i	$0.649060\pi$
$68$		0			0
$69$	3.46907e16			0.117800
$70$		0			0
$71$	−4.02265e17			−1.04126			−0.520628	−	0.853783i	$-0.674302\pi$
$71$	−4.02265e17			−1.04126			−0.520628	+	0.853783i	$0.674302\pi$
$72$		0			0
$73$			6.89262e16i			0.137030i	0.997650	+	0.0685152i	$0.0218262\pi$
$73$			6.89262e16i			0.137030i	−0.997650	+	0.0685152i	$0.978174\pi$
$74$		0			0
$75$	−1.30613e17	+	3.47985e16i	−0.200865	+	0.0535154i
$76$		0			0
$77$			9.58106e17i			1.14750i
$78$		0			0
$79$	−1.39960e17			−0.131385			−0.0656924	−	0.997840i	$-0.520926\pi$
$79$	−1.39960e17			−0.131385			−0.0656924	+	0.997840i	$0.520926\pi$
$80$		0			0
$81$	1.17826e18			0.872235
$82$		0			0
$83$		−	3.15223e18i		−	1.85087i	−0.378909	−	0.925434i	$-0.623701\pi$
$83$		−	3.15223e18i		−	1.85087i	0.378909	−	0.925434i	$-0.376299\pi$
$84$		0			0
$85$	1.71142e18	−	2.22709e18i	0.801452	−	1.04293i
$86$		0			0
$87$			6.05379e17i			0.227297i
$88$		0			0
$89$	−5.27072e18			−1.59465			−0.797324	−	0.603551i	$-0.793752\pi$
$89$	−5.27072e18			−1.59465			−0.797324	+	0.603551i	$0.793752\pi$
$90$		0			0
$91$	4.60082e18			1.12705
$92$		0			0
$93$			1.26427e18i			0.251914i
$94$		0			0
$95$	−7.02417e18	−	5.39778e18i	−1.14346	−	0.878701i
$96$		0			0
$97$			8.01437e18i			1.07038i	0.844732	+	0.535190i	$0.179760\pi$
$97$			8.01437e18i			1.07038i	−0.844732	+	0.535190i	$0.820240\pi$
$98$		0			0
$99$	−1.31915e19			−1.45130
$100$		0			0
$101$	1.98372e19			1.80480			0.902398	−	0.430903i	$-0.141805\pi$
$101$	1.98372e19			1.80480			0.902398	+	0.430903i	$0.141805\pi$
$102$		0			0
$103$		−	1.87418e17i		−	0.0141533i	−0.999975	−	0.00707665i	$-0.997747\pi$
$103$		−	1.87418e17i		−	0.0141533i	0.999975	−	0.00707665i	$-0.00225259\pi$
$104$		0			0
$105$	1.98213e18	+	1.52319e18i	0.124691	+	0.0958197i
$106$		0			0
$107$		−	2.49193e19i		−	1.31036i	−0.755475	−	0.655178i	$-0.772594\pi$
$107$		−	2.49193e19i		−	1.31036i	0.755475	−	0.655178i	$-0.227406\pi$
$108$		0			0
$109$	1.21452e19			0.535616			0.267808	−	0.963472i	$-0.413701\pi$
$109$	1.21452e19			0.535616			0.267808	+	0.963472i	$0.413701\pi$
$110$		0			0
$111$	3.13684e18			0.116392
$112$		0			0
$113$			8.86387e18i			0.277574i	0.990322	+	0.138787i	$0.0443203\pi$
$113$			8.86387e18i			0.277574i	−0.990322	+	0.138787i	$0.955680\pi$
$114$		0			0
$115$	1.30266e19	−	1.69516e19i	0.345303	−	0.449345i
$116$		0			0
$117$			6.33454e19i			1.42544i
$118$		0			0
$119$	−5.19438e19			−0.995033
$120$		0			0
$121$	7.95574e19			1.30083
$122$		0			0
$123$		−	2.07206e19i		−	0.289937i
$124$		0			0
$125$	−3.20418e19	+	7.68910e19i	−0.384655	+	0.923061i
$126$		0			0
$127$		−	3.11680e19i		−	0.321791i	−0.986971	−	0.160895i	$-0.948562\pi$
$127$		−	3.11680e19i		−	0.321791i	0.986971	−	0.160895i	$-0.0514382\pi$
$128$		0			0
$129$	−7.13475e18			−0.0635004
$130$		0			0
$131$	−3.59697e19			−0.276605			−0.138302	−	0.990390i	$-0.544165\pi$
$131$	−3.59697e19			−0.276605			−0.138302	+	0.990390i	$0.544165\pi$
$132$		0			0
$133$			1.63829e20i			1.09094i
$134$		0			0
$135$	−4.28904e19	+	5.58135e19i	−0.247850	+	0.322529i
$136$		0			0
$137$		−	1.75270e20i		−	0.880771i	−0.897809	−	0.440386i	$-0.854842\pi$
$137$		−	1.75270e20i		−	0.880771i	0.897809	−	0.440386i	$-0.145158\pi$
$138$		0			0
$139$	−2.03316e20			−0.890287			−0.445144	−	0.895459i	$-0.646847\pi$
$139$	−2.03316e20			−0.890287			−0.445144	+	0.895459i	$0.646847\pi$
$140$		0			0
$141$	5.50094e19			0.210308
$142$		0			0
$143$		−	6.75721e20i		−	2.25982i
$144$		0			0
$145$	2.95818e20	+	2.27324e20i	0.867019	+	0.666268i
$146$		0			0
$147$			3.45506e19i			0.0889079i
$148$		0			0
$149$	3.21713e20			0.728113			0.364056	−	0.931377i	$-0.381392\pi$
$149$	3.21713e20			0.728113			0.364056	+	0.931377i	$0.381392\pi$
$150$		0			0
$151$	3.97551e20			0.792706			0.396353	−	0.918098i	$-0.370276\pi$
$151$	3.97551e20			0.792706			0.396353	+	0.918098i	$0.370276\pi$
$152$		0			0
$153$		−	7.15176e20i		−	1.25847i
$154$		0			0
$155$	6.17786e20	+	4.74743e20i	0.960919	+	0.738426i
$156$		0			0
$157$		−	1.80456e20i		−	0.248500i	−0.992251	−	0.124250i	$-0.960348\pi$
$157$		−	1.80456e20i		−	0.248500i	0.992251	−	0.124250i	$-0.0396524\pi$
$158$		0			0
$159$	3.04774e20			0.372139
$160$		0			0
$161$	−3.95372e20			−0.428707
$162$		0			0
$163$			8.96853e20i			0.864846i	0.901671	+	0.432423i	$0.142341\pi$
$163$			8.96853e20i			0.864846i	−0.901671	+	0.432423i	$0.857659\pi$
$164$		0			0
$165$	2.23710e20	−	2.91115e20i	0.192126	−	0.250015i
$166$		0			0
$167$		−	1.29535e21i		−	0.992158i	−0.868277	−	0.496079i	$-0.834773\pi$
$167$		−	1.29535e21i		−	0.992158i	0.868277	−	0.496079i	$-0.165227\pi$
$168$		0			0
$169$	−1.78289e21			−1.21955
$170$		0			0
$171$	−2.25564e21			−1.37977
$172$		0			0
$173$		−	2.51650e21i		−	1.37835i	−0.724595	−	0.689175i	$-0.757973\pi$
$173$		−	2.51650e21i		−	1.37835i	0.724595	−	0.689175i	$-0.242027\pi$
$174$		0			0
$175$	1.48861e21	−	3.96601e20i	0.731002	−	0.194757i
$176$		0			0
$177$			5.56102e20i			0.245137i
$178$		0			0
$179$	4.28504e21			1.69766			0.848831	−	0.528665i	$-0.177307\pi$
$179$	4.28504e21			1.69766			0.848831	+	0.528665i	$0.177307\pi$
$180$		0			0
$181$	7.88628e20			0.281142			0.140571	−	0.990071i	$-0.455106\pi$
$181$	7.88628e20			0.281142			0.140571	+	0.990071i	$0.455106\pi$
$182$		0			0
$183$			2.93811e20i			0.0943589i
$184$		0			0
$185$	1.17790e21	−	1.53282e21i	0.341176	−	0.443975i
$186$		0			0
$187$			7.62896e21i			1.99512i
$188$		0			0
$189$	1.30178e21			0.307715
$190$		0			0
$191$	4.59583e21			0.982986			0.491493	−	0.870882i	$-0.336451\pi$
$191$	4.59583e21			0.982986			0.491493	+	0.870882i	$0.336451\pi$
$192$		0			0
$193$		−	3.32958e21i		−	0.645053i	−0.946560	−	0.322526i	$-0.895468\pi$
$193$		−	3.32958e21i		−	0.645053i	0.946560	−	0.322526i	$-0.104532\pi$
$194$		0			0
$195$	−1.39793e21	−	1.07425e21i	−0.245560	−	0.188703i
$196$		0			0
$197$		−	3.21629e21i		−	0.512775i	−0.966574	−	0.256387i	$-0.917468\pi$
$197$		−	3.21629e21i		−	0.512775i	0.966574	−	0.256387i	$-0.0825323\pi$
$198$		0			0
$199$	8.66329e21			1.25481			0.627406	−	0.778692i	$-0.284117\pi$
$199$	8.66329e21			1.25481			0.627406	+	0.778692i	$0.284117\pi$
$200$		0			0
$201$	−2.81656e21			−0.370986
$202$		0			0
$203$		−	6.89956e21i		−	0.827197i
$204$		0			0
$205$	−1.01251e22	−	7.78072e21i	−1.10596	−	0.849881i
$206$		0			0
$207$		−	5.44359e21i		−	0.542210i
$208$		0			0
$209$	2.40615e22			2.18743
$210$		0			0
$211$	1.49329e22			1.24011			0.620057	−	0.784557i	$-0.287110\pi$
$211$	1.49329e22			1.24011			0.620057	+	0.784557i	$0.287110\pi$
$212$		0			0
$213$		−	2.85075e21i		−	0.216448i
$214$		0			0
$215$	−2.67914e21	+	3.48639e21i	−0.186136	+	0.242220i
$216$		0			0
$217$		−	1.44090e22i		−	0.916784i
$218$		0			0
$219$	−4.88463e20			−0.0284848
$220$		0			0
$221$	3.66342e22			1.95957
$222$		0			0
$223$		−	2.67509e22i		−	1.31354i	−0.754091	−	0.656770i	$-0.771922\pi$
$223$		−	2.67509e22i		−	1.31354i	0.754091	−	0.656770i	$-0.228078\pi$
$224$		0			0
$225$	5.46051e21	+	2.04955e22i	0.246320	+	0.924539i
$226$		0			0
$227$		−	1.53288e22i		−	0.635716i	−0.948138	−	0.317858i	$-0.897036\pi$
$227$		−	1.53288e22i		−	0.635716i	0.948138	−	0.317858i	$-0.102964\pi$
$228$		0			0
$229$	−9.82714e21			−0.374965			−0.187482	−	0.982268i	$-0.560033\pi$
$229$	−9.82714e21			−0.374965			−0.187482	+	0.982268i	$0.560033\pi$
$230$		0			0
$231$	−6.78986e21			−0.238532
$232$		0			0
$233$		−	1.63644e22i		−	0.529688i	−0.964291	−	0.264844i	$-0.914680\pi$
$233$		−	1.63644e22i		−	0.529688i	0.964291	−	0.264844i	$-0.0853204\pi$
$234$		0			0
$235$	2.06564e22	−	2.68803e22i	0.616467	−	0.802212i
$236$		0			0
$237$		−	9.91859e20i		−	0.0273112i
$238$		0			0
$239$	−6.41647e20			−0.0163123			−0.00815617	−	0.999967i	$-0.502596\pi$
$239$	−6.41647e20			−0.0163123			−0.00815617	+	0.999967i	$0.502596\pi$
$240$		0			0
$241$	3.60258e22			0.846160			0.423080	−	0.906092i	$-0.360949\pi$
$241$	3.60258e22			0.846160			0.423080	+	0.906092i	$0.360949\pi$
$242$		0			0
$243$			2.70827e22i			0.588074i
$244$		0			0
$245$	1.68831e22	+	1.29740e22i	0.339136	+	0.260612i
$246$		0			0
$247$		−	1.15543e23i		−	2.14844i
$248$		0			0
$249$	2.23390e22			0.384743
$250$		0			0
$251$	4.55399e22			0.726929			0.363464	−	0.931608i	$-0.381594\pi$
$251$	4.55399e22			0.726929			0.363464	+	0.931608i	$0.381594\pi$
$252$		0			0
$253$			5.80681e22i			0.859593i
$254$		0			0
$255$	1.57828e22	+	1.21284e22i	0.216797	+	0.166599i
$256$		0			0
$257$			3.60490e22i			0.459758i	0.973219	+	0.229879i	$0.0738330\pi$
$257$			3.60490e22i			0.459758i	−0.973219	+	0.229879i	$0.926167\pi$
$258$		0			0
$259$	−3.57509e22			−0.423583
$260$		0			0
$261$	9.49949e22			1.04620
$262$		0			0
$263$			1.64108e22i			0.168093i	0.996462	+	0.0840465i	$0.0267844\pi$
$263$			1.64108e22i			0.168093i	−0.996462	+	0.0840465i	$0.973216\pi$
$264$		0			0
$265$	1.14444e23	−	1.48927e23i	1.09084	−	1.41951i
$266$		0			0
$267$		−	3.73523e22i		−	0.331482i
$268$		0			0
$269$	1.24461e23			1.02894			0.514468	−	0.857510i	$-0.327990\pi$
$269$	1.24461e23			1.02894			0.514468	+	0.857510i	$0.327990\pi$
$270$		0			0
$271$	−1.10267e22			−0.0849644			−0.0424822	−	0.999097i	$-0.513527\pi$
$271$	−1.10267e22			−0.0849644			−0.0424822	+	0.999097i	$0.513527\pi$
$272$		0			0
$273$			3.26049e22i			0.234281i
$274$		0			0
$275$	−5.82486e22	−	2.18631e23i	−0.390504	−	1.46572i
$276$		0			0
$277$		−	1.25840e23i		−	0.787516i	−0.919214	−	0.393758i	$-0.871175\pi$
$277$		−	1.25840e23i		−	0.787516i	0.919214	−	0.393758i	$-0.128825\pi$
$278$		0			0
$279$	1.98387e23			1.15951
$280$		0			0
$281$	−2.92010e23			−1.59473			−0.797366	−	0.603496i	$-0.793774\pi$
$281$	−2.92010e23			−1.59473			−0.797366	+	0.603496i	$0.793774\pi$
$282$		0			0
$283$		−	2.10209e23i		−	1.07320i	−0.843838	−	0.536599i	$-0.819709\pi$
$283$		−	2.10209e23i		−	1.07320i	0.843838	−	0.536599i	$-0.180291\pi$
$284$		0			0
$285$	3.82527e22	−	4.97786e22i	0.182657	−	0.237693i
$286$		0			0
$287$			2.36155e23i			1.05516i
$288$		0			0
$289$	−1.74532e23			−0.730038
$290$		0			0
$291$	−5.67959e22			−0.222502
$292$		0			0
$293$		−	1.77889e23i		−	0.652991i	−0.945199	−	0.326495i	$-0.894132\pi$
$293$		−	1.77889e23i		−	0.652991i	0.945199	−	0.326495i	$-0.105868\pi$
$294$		0			0
$295$	2.71739e23	+	2.08820e23i	0.935066	+	0.718559i
$296$		0			0
$297$		−	1.91191e23i		−	0.616995i
$298$		0			0
$299$	2.78843e23			0.844274
$300$		0			0
$301$	8.13153e22			0.231095
$302$		0			0
$303$			1.40582e23i			0.375166i
$304$		0			0
$305$	1.43570e23	+	1.10328e23i	0.359929	+	0.276590i
$306$		0			0
$307$			4.30057e23i			1.01324i	0.862170	+	0.506619i	$0.169105\pi$
$307$			4.30057e23i			1.01324i	−0.862170	+	0.506619i	$0.830895\pi$
$308$		0			0
$309$	1.32819e21			0.00294207
$310$		0			0
$311$	2.33580e23			0.486644			0.243322	−	0.969946i	$-0.421763\pi$
$311$	2.33580e23			0.486644			0.243322	+	0.969946i	$0.421763\pi$
$312$		0			0
$313$		−	4.80623e23i		−	0.942179i	−0.882085	−	0.471090i	$-0.843861\pi$
$313$		−	4.80623e23i		−	0.942179i	0.882085	−	0.471090i	$-0.156139\pi$
$314$		0			0
$315$	2.39015e23	−	3.11032e23i	0.441038	−	0.573925i
$316$		0			0
$317$			8.27759e23i			1.43827i	0.694870	+	0.719136i	$0.255462\pi$
$317$			8.27759e23i			1.43827i	−0.694870	+	0.719136i	$0.744538\pi$
$318$		0			0
$319$	−1.01333e24			−1.65860
$320$		0			0
$321$	1.76597e23			0.272386
$322$		0			0
$323$			1.30450e24i			1.89679i
$324$		0			0
$325$	−1.04987e24	+	2.79710e23i	−1.43960	+	0.383545i
$326$		0			0
$327$			8.60702e22i			0.111339i
$328$		0			0
$329$	−6.26947e23			−0.765367
$330$		0			0
$331$	7.52356e23			0.867076			0.433538	−	0.901135i	$-0.357265\pi$
$331$	7.52356e23			0.867076			0.433538	+	0.901135i	$0.357265\pi$
$332$		0			0
$333$		−	4.92227e23i		−	0.535730i
$334$		0			0
$335$	−1.05764e24	+	1.37631e24i	−1.08746	+	1.41511i
$336$		0			0
$337$		−	3.22807e23i		−	0.313660i	−0.987626	−	0.156830i	$-0.949873\pi$
$337$		−	3.22807e23i		−	0.313660i	0.987626	−	0.156830i	$-0.0501274\pi$
$338$		0			0
$339$	−6.28161e22			−0.0576997
$340$		0			0
$341$	−2.11625e24			−1.83823
$342$		0			0
$343$		−	1.31445e24i		−	1.08006i
$344$		0			0
$345$	1.20132e23	+	9.23160e22i	0.0934062	+	0.0717787i
$346$		0			0
$347$		−	8.83861e23i		−	0.650510i	−0.945626	−	0.325255i	$-0.894550\pi$
$347$		−	8.83861e23i		−	0.650510i	0.945626	−	0.325255i	$-0.105450\pi$
$348$		0			0
$349$	1.64754e24			1.14814			0.574069	−	0.818807i	$-0.305364\pi$
$349$	1.64754e24			1.14814			0.574069	+	0.818807i	$0.305364\pi$
$350$		0			0
$351$	−9.18100e23			−0.605999
$352$		0			0
$353$			1.16016e24i			0.725533i	0.931880	+	0.362766i	$0.118168\pi$
$353$			1.16016e24i			0.725533i	−0.931880	+	0.362766i	$0.881832\pi$
$354$		0			0
$355$	−1.39302e24	−	1.07048e24i	−0.825633	−	0.634464i
$356$		0			0
$357$		−	3.68113e23i		−	0.206839i
$358$		0			0
$359$	1.43972e24			0.767151			0.383576	−	0.923509i	$-0.374693\pi$
$359$	1.43972e24			0.767151			0.383576	+	0.923509i	$0.374693\pi$
$360$		0			0
$361$	2.13593e24			1.07961
$362$		0			0
$363$			5.63804e23i			0.270405i
$364$		0			0
$365$	−1.83421e23	+	2.38687e23i	−0.0834962	+	0.108654i
$366$		0			0
$367$			3.38230e23i			0.146179i	0.997325	+	0.0730894i	$0.0232858\pi$
$367$			3.38230e23i			0.146179i	−0.997325	+	0.0730894i	$0.976714\pi$
$368$		0			0
$369$	−3.25144e24			−1.33452
$370$		0			0
$371$	−3.47353e24			−1.35431
$372$		0			0
$373$			1.79179e24i			0.663825i	0.943310	+	0.331913i	$0.107694\pi$
$373$			1.79179e24i			0.663825i	−0.943310	+	0.331913i	$0.892306\pi$
$374$		0			0
$375$	−5.44907e23	−	2.27072e23i	−0.191878	−	0.0799588i
$376$		0			0
$377$			4.86603e24i			1.62904i
$378$		0			0
$379$	−3.79319e24			−1.20763			−0.603813	−	0.797126i	$-0.706352\pi$
$379$	−3.79319e24			−1.20763			−0.603813	+	0.797126i	$0.706352\pi$
$380$		0			0
$381$	2.20880e23			0.0668912
$382$		0			0
$383$		−	1.62307e24i		−	0.467679i	−0.972275	−	0.233839i	$-0.924871\pi$
$383$		−	1.62307e24i		−	0.467679i	0.972275	−	0.233839i	$-0.0751290\pi$
$384$		0			0
$385$	−2.54964e24	+	3.31786e24i	−0.699200	+	0.909874i
$386$		0			0
$387$			1.11957e24i			0.292279i
$388$		0			0
$389$	1.48667e24			0.369568			0.184784	−	0.982779i	$-0.440841\pi$
$389$	1.48667e24			0.369568			0.184784	+	0.982779i	$0.440841\pi$
$390$		0			0
$391$	−3.14817e24			−0.745382
$392$		0			0
$393$		−	2.54909e23i		−	0.0574983i
$394$		0			0
$395$	−4.84671e23	−	3.72449e23i	−0.104178	−	0.0800562i
$396$		0			0
$397$			4.69658e24i			0.962214i	0.876662	+	0.481107i	$0.159765\pi$
$397$			4.69658e24i			0.962214i	−0.876662	+	0.481107i	$0.840235\pi$
$398$		0			0
$399$	−1.16102e24			−0.226776
$400$		0			0
$401$	−6.80430e22			−0.0126739			−0.00633697	−	0.999980i	$-0.502017\pi$
$401$	−6.80430e22			−0.0126739			−0.00633697	+	0.999980i	$0.502017\pi$
$402$		0			0
$403$			1.01622e25i			1.80547i
$404$		0			0
$405$	4.08024e24	+	3.13549e24i	0.691613	+	0.531475i
$406$		0			0
$407$			5.25071e24i			0.849320i
$408$		0			0
$409$	−4.73292e24			−0.730732			−0.365366	−	0.930864i	$-0.619056\pi$
$409$	−4.73292e24			−0.730732			−0.365366	+	0.930864i	$0.619056\pi$
$410$		0			0
$411$	1.24210e24			0.183087
$412$		0			0
$413$		−	6.33794e24i		−	0.892119i
$414$		0			0
$415$	8.38845e24	−	1.09160e25i	1.12778	−	1.46759i
$416$		0			0
$417$		−	1.44085e24i		−	0.185066i
$418$		0			0
$419$	−1.43553e24			−0.176190			−0.0880948	−	0.996112i	$-0.528078\pi$
$419$	−1.43553e24			−0.176190			−0.0880948	+	0.996112i	$0.528078\pi$
$420$		0			0
$421$	−1.11032e25			−1.30247			−0.651237	−	0.758875i	$-0.725749\pi$
$421$	−1.11032e25			−1.30247			−0.651237	+	0.758875i	$0.725749\pi$
$422$		0			0
$423$		−	8.63197e24i		−	0.968002i
$424$		0			0
$425$	1.18531e25	−	3.15795e24i	1.27097	−	0.338619i
$426$		0			0
$427$		−	3.34859e24i		−	0.343397i
$428$		0			0
$429$	4.78867e24			0.469754
$430$		0			0
$431$	−8.62012e24			−0.809057			−0.404528	−	0.914525i	$-0.632564\pi$
$431$	−8.62012e24			−0.809057			−0.404528	+	0.914525i	$0.632564\pi$
$432$		0			0
$433$		−	1.34341e25i		−	1.20663i	−0.797504	−	0.603314i	$-0.793847\pi$
$433$		−	1.34341e25i		−	1.20663i	0.797504	−	0.603314i	$-0.206153\pi$
$434$		0			0
$435$	−1.61099e24	+	2.09639e24i	−0.138498	+	0.180229i
$436$		0			0
$437$			9.92924e24i			0.817226i
$438$		0			0
$439$	−1.07513e24			−0.0847318			−0.0423659	−	0.999102i	$-0.513490\pi$
$439$	−1.07513e24			−0.0847318			−0.0423659	+	0.999102i	$0.513490\pi$
$440$		0			0
$441$	5.42161e24			0.409224
$442$		0			0
$443$			1.95210e25i			1.41145i	0.708485	+	0.705726i	$0.249379\pi$
$443$			1.95210e25i			1.41145i	−0.708485	+	0.705726i	$0.750621\pi$
$444$		0			0
$445$	−1.82522e25	−	1.40260e25i	−1.26443	−	0.971661i
$446$		0			0
$447$			2.27990e24i			0.151354i
$448$		0			0
$449$	−1.58065e25			−1.00576			−0.502881	−	0.864356i	$-0.667727\pi$
$449$	−1.58065e25			−1.00576			−0.502881	+	0.864356i	$0.667727\pi$
$450$		0			0
$451$	3.46839e25			2.11568
$452$		0			0
$453$			2.81735e24i			0.164781i
$454$		0			0
$455$	1.59324e25	+	1.22434e25i	0.893659	+	0.686739i
$456$		0			0
$457$		−	1.93069e25i		−	1.03875i	−0.854547	−	0.519373i	$-0.826165\pi$
$457$		−	1.93069e25i		−	1.03875i	0.854547	−	0.519373i	$-0.173835\pi$
$458$		0			0
$459$	1.03654e25			0.535017
$460$		0			0
$461$	8.45846e24			0.418921			0.209461	−	0.977817i	$-0.432829\pi$
$461$	8.45846e24			0.418921			0.209461	+	0.977817i	$0.432829\pi$
$462$		0			0
$463$			2.83455e25i			1.34730i	0.739049	+	0.673652i	$0.235275\pi$
$463$			2.83455e25i			1.34730i	−0.739049	+	0.673652i	$0.764725\pi$
$464$		0			0
$465$	−3.36438e24	+	4.37810e24i	−0.153498	+	0.199748i
$466$		0			0
$467$		−	4.04727e25i		−	1.77277i	−0.462950	−	0.886384i	$-0.653209\pi$
$467$		−	4.04727e25i		−	1.77277i	0.462950	−	0.886384i	$-0.346791\pi$
$468$		0			0
$469$	3.21006e25			1.35012
$470$		0			0
$471$	1.27885e24			0.0516560
$472$		0			0
$473$		−	1.19427e25i		−	0.463365i
$474$		0			0
$475$	−9.96010e24	−	3.73843e25i	−0.371257	−	1.39348i
$476$		0			0
$477$		−	4.78245e25i		−	1.71288i
$478$		0			0
$479$	2.78316e25			0.957967			0.478984	−	0.877824i	$-0.341005\pi$
$479$	2.78316e25			0.957967			0.478984	+	0.877824i	$0.341005\pi$
$480$		0			0
$481$	2.52139e25			0.834184
$482$		0			0
$483$		−	2.80191e24i		−	0.0891160i
$484$		0			0
$485$	−2.13272e25	+	2.77532e25i	−0.652210	+	0.848725i
$486$		0			0
$487$			1.52695e25i			0.449054i	0.974468	+	0.224527i	$0.0720837\pi$
$487$			1.52695e25i			0.449054i	−0.974468	+	0.224527i	$0.927916\pi$
$488$		0			0
$489$	−6.35577e24			−0.179777
$490$		0			0
$491$	1.56357e24			0.0425444			0.0212722	−	0.999774i	$-0.493228\pi$
$491$	1.56357e24			0.0425444			0.0212722	+	0.999774i	$0.493228\pi$
$492$		0			0
$493$		−	5.49380e25i		−	1.43823i
$494$		0			0
$495$	−4.56812e25	−	3.51041e25i	−1.15077	−	0.884317i
$496$		0			0
$497$			3.24903e25i			0.787712i
$498$		0			0
$499$	1.61893e25			0.377809			0.188905	−	0.981995i	$-0.439506\pi$
$499$	1.61893e25			0.377809			0.188905	+	0.981995i	$0.439506\pi$
$500$		0			0
$501$	9.17983e24			0.206242
$502$		0			0
$503$			6.75580e25i			1.46144i	0.682678	+	0.730720i	$0.260815\pi$
$503$			6.75580e25i			1.46144i	−0.682678	+	0.730720i	$0.739185\pi$
$504$		0			0
$505$	6.86951e25	+	5.27893e25i	1.43106	+	1.09971i
$506$		0			0
$507$		−	1.26349e25i		−	0.253511i
$508$		0			0
$509$	2.16326e25			0.418110			0.209055	−	0.977904i	$-0.432961\pi$
$509$	2.16326e25			0.418110			0.209055	+	0.977904i	$0.432961\pi$
$510$		0			0
$511$	5.56705e24			0.103664
$512$		0			0
$513$		−	3.26923e25i		−	0.586585i
$514$		0			0
$515$	4.98742e23	−	6.49016e23i	0.00862397	−	0.0112224i
$516$		0			0
$517$			9.20794e25i			1.53462i
$518$		0			0
$519$	1.78338e25			0.286520
$520$		0			0
$521$	−3.25280e25			−0.503848			−0.251924	−	0.967747i	$-0.581063\pi$
$521$	−3.25280e25			−0.503848			−0.251924	+	0.967747i	$0.581063\pi$
$522$		0			0
$523$		−	1.04500e26i		−	1.56081i	−0.625274	−	0.780405i	$-0.715013\pi$
$523$		−	1.04500e26i		−	1.56081i	0.625274	−	0.780405i	$-0.284987\pi$
$524$		0			0
$525$	2.81062e24	+	1.05494e25i	0.0404844	+	0.151955i
$526$		0			0
$527$		−	1.14732e26i		−	1.59399i
$528$		0			0
$529$	5.06531e25			0.678855
$530$		0			0
$531$	8.72624e25			1.12831
$532$		0			0
$533$		−	1.66552e26i		−	2.07798i
$534$		0			0
$535$	6.63132e25	−	8.62938e25i	0.798434	−	1.03901i
$536$		0			0
$537$			3.03670e25i			0.352896i
$538$		0			0
$539$	−5.78336e25			−0.648765
$540$		0			0
$541$	9.64006e25			1.04401			0.522006	−	0.852942i	$-0.325184\pi$
$541$	9.64006e25			1.04401			0.522006	+	0.852942i	$0.325184\pi$
$542$		0			0
$543$			5.58881e24i			0.0584415i
$544$		0			0
$545$	4.20581e25	+	3.23199e25i	0.424701	+	0.326365i
$546$		0			0
$547$			7.70409e25i			0.751349i	0.926752	+	0.375675i	$0.122589\pi$
$547$			7.70409e25i			0.751349i	−0.926752	+	0.375675i	$0.877411\pi$
$548$		0			0
$549$	4.61042e25			0.434314
$550$		0			0
$551$	−1.73273e26			−1.57685
$552$		0			0
$553$			1.13043e25i			0.0993928i
$554$		0			0
$555$	1.08627e25	+	8.34752e24i	0.0922899	+	0.0709209i
$556$		0			0
$557$			1.40298e26i			1.15193i	0.817474	+	0.575965i	$0.195374\pi$
$557$			1.40298e26i			1.15193i	−0.817474	+	0.575965i	$0.804626\pi$
$558$		0			0
$559$	−5.73490e25			−0.455107
$560$		0			0
$561$	−5.40645e25			−0.414730
$562$		0			0
$563$			6.21221e25i			0.460698i	0.973108	+	0.230349i	$0.0739867\pi$
$563$			6.21221e25i			0.460698i	−0.973108	+	0.230349i	$0.926013\pi$
$564$		0			0
$565$	−2.35878e25	+	3.06950e25i	−0.169133	+	0.220094i
$566$		0			0
$567$		−	9.51661e25i		−	0.659847i
$568$		0			0
$569$	5.62107e25			0.376923			0.188461	−	0.982081i	$-0.439650\pi$
$569$	5.62107e25			0.376923			0.188461	+	0.982081i	$0.439650\pi$
$570$		0			0
$571$	−1.43689e26			−0.931923			−0.465961	−	0.884805i	$-0.654291\pi$
$571$	−1.43689e26			−0.931923			−0.465961	+	0.884805i	$0.654291\pi$
$572$		0			0
$573$			3.25695e25i			0.204335i
$574$		0			0
$575$	9.02203e25	−	2.40369e25i	0.547595	−	0.145893i
$576$		0			0
$577$		−	9.16044e25i		−	0.537955i	−0.963146	−	0.268978i	$-0.913314\pi$
$577$		−	9.16044e25i		−	0.537955i	0.963146	−	0.268978i	$-0.0866857\pi$
$578$		0			0
$579$	2.35959e25			0.134088
$580$		0			0
$581$	−2.54600e26			−1.40018
$582$		0			0
$583$			5.10156e26i			2.71551i
$584$		0			0
$585$	−1.68570e26	+	2.19361e26i	−0.868558	+	1.13026i
$586$		0			0
$587$		−	5.25608e24i		−	0.0262180i	−0.999914	−	0.0131090i	$-0.995827\pi$
$587$		−	5.25608e24i		−	0.0262180i	0.999914	−	0.0131090i	$-0.00417284\pi$
$588$		0			0
$589$	−3.61863e26			−1.74763
$590$		0			0
$591$	2.27931e25			0.106591
$592$		0			0
$593$		−	3.62425e26i		−	1.64134i	−0.571402	−	0.820670i	$-0.693600\pi$
$593$		−	3.62425e26i		−	1.64134i	0.571402	−	0.820670i	$-0.306400\pi$
$594$		0			0
$595$	−1.79878e26	−	1.38229e26i	−0.788982	−	0.606299i
$596$		0			0
$597$			6.13946e25i			0.260840i
$598$		0			0
$599$	2.27698e25			0.0937140			0.0468570	−	0.998902i	$-0.485079\pi$
$599$	2.27698e25			0.0937140			0.0468570	+	0.998902i	$0.485079\pi$
$600$		0			0
$601$	−9.64462e25			−0.384572			−0.192286	−	0.981339i	$-0.561590\pi$
$601$	−9.64462e25			−0.384572			−0.192286	+	0.981339i	$0.561590\pi$
$602$		0			0
$603$			4.41970e26i			1.70757i
$604$		0			0
$605$	2.75502e26	+	2.11712e26i	1.03145	+	0.792628i
$606$		0			0
$607$		−	1.68085e26i		−	0.609869i	−0.952373	−	0.304934i	$-0.901365\pi$
$607$		−	1.68085e26i		−	0.609869i	0.952373	−	0.304934i	$-0.0986345\pi$
$608$		0			0
$609$	4.88955e25			0.171951
$610$		0			0
$611$	4.42165e26			1.50728
$612$		0			0
$613$		−	2.31579e26i		−	0.765288i	−0.923896	−	0.382644i	$-0.875014\pi$
$613$		−	2.31579e26i		−	0.765288i	0.923896	−	0.382644i	$-0.124986\pi$
$614$		0			0
$615$	5.51400e25	−	7.17541e25i	0.176666	−	0.229897i
$616$		0			0
$617$		−	3.14264e26i		−	0.976305i	−0.872758	−	0.488153i	$-0.837671\pi$
$617$		−	3.14264e26i		−	0.976305i	0.872758	−	0.488153i	$-0.162329\pi$
$618$		0			0
$619$	−1.01992e26			−0.307259			−0.153630	−	0.988128i	$-0.549096\pi$
$619$	−1.01992e26			−0.307259			−0.153630	+	0.988128i	$0.549096\pi$
$620$		0			0
$621$	7.88970e25			0.230510
$622$		0			0
$623$			4.25707e26i			1.20635i
$624$		0			0
$625$	−3.15575e26	+	1.81001e26i	−0.867445	+	0.497533i
$626$		0			0
$627$			1.70518e26i			0.454704i
$628$		0			0
$629$	−2.84668e26			−0.736473
$630$		0			0
$631$	−4.52274e26			−1.13533			−0.567666	−	0.823259i	$-0.692154\pi$
$631$	−4.52274e26			−1.13533			−0.567666	+	0.823259i	$0.692154\pi$
$632$		0			0
$633$			1.05826e26i			0.257785i
$634$		0			0
$635$	8.29418e25	−	1.07933e26i	0.196075	−	0.255154i
$636$		0			0
$637$			2.77717e26i			0.637203i
$638$		0			0
$639$	−4.47334e26			−0.996263
$640$		0			0
$641$	−4.43417e25			−0.0958653			−0.0479326	−	0.998851i	$-0.515263\pi$
$641$	−4.43417e25			−0.0958653			−0.0479326	+	0.998851i	$0.515263\pi$
$642$		0			0
$643$			1.10309e26i			0.231530i	0.993277	+	0.115765i	$0.0369319\pi$
$643$			1.10309e26i			0.231530i	−0.993277	+	0.115765i	$0.963068\pi$
$644$		0			0
$645$	−2.47072e25	−	1.89864e25i	−0.0503507	−	0.0386924i
$646$		0			0
$647$			1.08191e26i			0.214092i	0.994254	+	0.107046i	$0.0341392\pi$
$647$			1.08191e26i			0.214092i	−0.994254	+	0.107046i	$0.965861\pi$
$648$		0			0
$649$	−9.30850e26			−1.78877
$650$		0			0
$651$	1.02113e26			0.190574
$652$		0			0
$653$		−	5.60353e26i		−	1.01575i	−0.861431	−	0.507875i	$-0.830431\pi$
$653$		−	5.60353e26i		−	1.01575i	0.861431	−	0.507875i	$-0.169569\pi$
$654$		0			0
$655$	−1.24561e26	−	9.57198e25i	−0.219326	−	0.168543i
$656$		0			0
$657$			7.66487e25i			0.131109i
$658$		0			0
$659$	3.12890e26			0.519972			0.259986	−	0.965612i	$-0.416282\pi$
$659$	3.12890e26			0.519972			0.259986	+	0.965612i	$0.416282\pi$
$660$		0			0
$661$	5.06982e26			0.818613			0.409306	−	0.912397i	$-0.365771\pi$
$661$	5.06982e26			0.818613			0.409306	+	0.912397i	$0.365771\pi$
$662$		0			0
$663$			2.59618e26i			0.407339i
$664$		0			0
$665$	−4.35970e26	+	5.67330e26i	−0.664738	+	0.865028i
$666$		0			0
$667$		−	4.18163e26i		−	0.619655i
$668$		0			0
$669$	1.89577e26			0.273048
$670$		0			0
$671$	−4.91805e26			−0.688540
$672$		0			0
$673$		−	1.75314e26i		−	0.238601i	−0.992858	−	0.119301i	$-0.961935\pi$
$673$		−	1.75314e26i		−	0.238601i	0.992858	−	0.119301i	$-0.0380653\pi$
$674$		0			0
$675$	−2.97053e26	+	7.91422e25i	−0.393051	+	0.104718i
$676$		0			0
$677$			7.00965e26i			0.901788i	0.892578	+	0.450894i	$0.148895\pi$
$677$			7.00965e26i			0.901788i	−0.892578	+	0.450894i	$0.851105\pi$
$678$		0			0
$679$	6.47307e26			0.809744
$680$		0			0
$681$	1.08632e26			0.132147
$682$		0			0
$683$			2.45445e26i			0.290373i	0.989404	+	0.145187i	$0.0463783\pi$
$683$			2.45445e26i			0.290373i	−0.989404	+	0.145187i	$0.953622\pi$
$684$		0			0
$685$	4.66416e26	−	6.06950e26i	0.536677	−	0.698381i
$686$		0			0
$687$		−	6.96425e25i		−	0.0779445i
$688$		0			0
$689$	2.44977e27			2.66712
$690$		0			0
$691$	−7.98402e26			−0.845629			−0.422815	−	0.906216i	$-0.638958\pi$
$691$	−7.98402e26			−0.845629			−0.422815	+	0.906216i	$0.638958\pi$
$692$		0			0
$693$			1.06545e27i			1.09791i
$694$		0			0
$695$	−7.04069e26	−	5.41047e26i	−0.705927	−	0.542475i
$696$		0			0
$697$			1.88039e27i			1.83458i
$698$		0			0
$699$	1.15971e26			0.110107
$700$		0			0
$701$	−1.93020e27			−1.78353			−0.891767	−	0.452495i	$-0.850534\pi$
$701$	−1.93020e27			−1.78353			−0.891767	+	0.452495i	$0.850534\pi$
$702$		0			0
$703$			8.97834e26i			0.807459i
$704$		0			0
$705$	1.90494e26	+	1.46387e26i	0.166757	+	0.128146i
$706$		0			0
$707$		−	1.60222e27i		−	1.36533i
$708$		0			0
$709$	7.64614e26			0.634312			0.317156	−	0.948373i	$-0.397272\pi$
$709$	7.64614e26			0.634312			0.317156	+	0.948373i	$0.397272\pi$
$710$		0			0
$711$	−1.55641e26			−0.125708
$712$		0			0
$713$		−	8.73291e26i		−	0.686765i
$714$		0			0
$715$	1.79817e27	−	2.33998e27i	1.37697	−	1.79186i
$716$		0			0
$717$		−	4.54720e24i		−	0.00339088i
$718$		0			0
$719$	−9.69205e26			−0.703868			−0.351934	−	0.936025i	$-0.614476\pi$
$719$	−9.69205e26			−0.703868			−0.351934	+	0.936025i	$0.614476\pi$
$720$		0			0
$721$	−1.51374e25			−0.0107070
$722$		0			0
$723$			2.55306e26i			0.175893i
$724$		0			0
$725$	4.19463e26	+	1.57441e27i	0.281502	+	1.05659i
$726$		0			0
$727$			1.46350e27i			0.956787i	0.878145	+	0.478394i	$0.158781\pi$
$727$			1.46350e27i			0.956787i	−0.878145	+	0.478394i	$0.841219\pi$
$728$		0			0
$729$	1.17752e27			0.749991
$730$		0			0
$731$	6.47476e26			0.401799
$732$		0			0
$733$		−	2.47647e27i		−	1.49743i	−0.662893	−	0.748714i	$-0.730672\pi$
$733$		−	2.47647e27i		−	1.49743i	0.662893	−	0.748714i	$-0.269328\pi$
$734$		0			0
$735$	−9.19432e25	+	1.19646e26i	−0.0541739	+	0.0704969i
$736$		0			0
$737$		−	4.71460e27i		−	2.70710i
$738$		0			0
$739$	6.89258e26			0.385709			0.192854	−	0.981227i	$-0.438226\pi$
$739$	6.89258e26			0.385709			0.192854	+	0.981227i	$0.438226\pi$
$740$		0			0
$741$	8.18828e26			0.446601
$742$		0			0
$743$		−	3.49215e27i		−	1.85652i	−0.371931	−	0.928260i	$-0.621304\pi$
$743$		−	3.49215e27i		−	1.85652i	0.371931	−	0.928260i	$-0.378696\pi$
$744$		0			0
$745$	1.11407e27	+	8.56117e26i	0.577335	+	0.443658i
$746$		0			0
$747$		−	3.50540e27i		−	1.77089i
$748$		0			0
$749$	−2.01269e27			−0.991286
$750$		0			0
$751$	6.36739e26			0.305761			0.152880	−	0.988245i	$-0.451145\pi$
$751$	6.36739e26			0.305761			0.152880	+	0.988245i	$0.451145\pi$
$752$		0			0
$753$			3.22730e26i			0.151108i
$754$		0			0
$755$	1.37669e27	+	1.05793e27i	0.628552	+	0.483016i
$756$		0			0
$757$			1.30336e27i			0.580302i	0.956981	+	0.290151i	$0.0937055\pi$
$757$			1.30336e27i			0.580302i	−0.956981	+	0.290151i	$0.906294\pi$
$758$		0			0
$759$	−4.11515e26			−0.178685
$760$		0			0
$761$	−1.17194e26			−0.0496308			−0.0248154	−	0.999692i	$-0.507900\pi$
$761$	−1.17194e26			−0.0496308			−0.0248154	+	0.999692i	$0.507900\pi$
$762$		0			0
$763$		−	9.80950e26i		−	0.405195i
$764$		0			0
$765$	1.90317e27	−	2.47661e27i	0.766820	−	0.997869i
$766$		0			0
$767$			4.46994e27i			1.75689i
$768$		0			0
$769$	−1.43696e27			−0.550990			−0.275495	−	0.961303i	$-0.588842\pi$
$769$	−1.43696e27			−0.550990			−0.275495	+	0.961303i	$0.588842\pi$
$770$		0			0
$771$	−2.55471e26			−0.0955706
$772$		0			0
$773$		−	2.24130e27i		−	0.818078i	−0.912517	−	0.409039i	$-0.865864\pi$
$773$		−	2.24130e27i		−	0.818078i	0.912517	−	0.409039i	$-0.134136\pi$
$774$		0			0
$775$	8.76005e26	+	3.28801e27i	0.311990	+	1.17103i
$776$		0			0
$777$		−	2.53358e26i		−	0.0880510i
$778$		0			0
$779$	5.93070e27			2.01141
$780$		0			0
$781$	4.77183e27			1.57943
$782$		0			0
$783$			1.37681e27i			0.444773i
$784$		0			0
$785$	4.80217e26	−	6.24909e26i	0.151417	−	0.197040i
$786$		0			0
$787$		−	2.47335e27i		−	0.761246i	−0.924730	−	0.380623i	$-0.875710\pi$
$787$		−	2.47335e27i		−	0.761246i	0.924730	−	0.380623i	$-0.124290\pi$
$788$		0			0
$789$	−1.16299e26			−0.0349418
$790$		0			0
$791$	7.15920e26			0.209985
$792$		0			0
$793$			2.36165e27i			0.676270i
$794$		0			0
$795$	1.05541e27	+	8.11040e26i	0.295076	+	0.226754i
$796$		0			0
$797$		−	1.11223e27i		−	0.303627i	−0.988409	−	0.151813i	$-0.951489\pi$
$797$		−	1.11223e27i		−	0.303627i	0.988409	−	0.151813i	$-0.0485112\pi$
$798$		0			0
$799$	−4.99209e27			−1.33072
$800$		0			0
$801$	−5.86125e27			−1.52574
$802$		0			0
$803$		−	8.17630e26i		−	0.207854i
$804$		0			0
$805$	−1.36915e27	−	1.05213e27i	−0.339930	−	0.261222i
$806$		0			0
$807$			8.82027e26i			0.213887i
$808$		0			0
$809$	−6.66167e26			−0.157787			−0.0788936	−	0.996883i	$-0.525139\pi$
$809$	−6.66167e26			−0.157787			−0.0788936	+	0.996883i	$0.525139\pi$
$810$		0			0
$811$	4.41128e27			1.02063			0.510313	−	0.859989i	$-0.329530\pi$
$811$	4.41128e27			1.02063			0.510313	+	0.859989i	$0.329530\pi$
$812$		0			0
$813$		−	7.81434e25i		−	0.0176617i
$814$		0			0
$815$	−2.38663e27	+	3.10574e27i	−0.526973	+	0.685754i
$816$		0			0
$817$		−	2.04212e27i		−	0.440527i
$818$		0			0
$819$	5.11630e27			1.07835
$820$		0			0
$821$	−2.76676e27			−0.569785			−0.284892	−	0.958559i	$-0.591958\pi$
$821$	−2.76676e27			−0.569785			−0.284892	+	0.958559i	$0.591958\pi$
$822$		0			0
$823$		−	7.35067e26i		−	0.147920i	−0.997261	−	0.0739602i	$-0.976436\pi$
$823$		−	7.35067e26i		−	0.147920i	0.997261	−	0.0739602i	$-0.0235638\pi$
$824$		0			0
$825$	1.54938e27	−	4.12794e26i	0.304682	−	0.0811747i
$826$		0			0
$827$			9.68559e27i			1.86133i	0.365869	+	0.930666i	$0.380772\pi$
$827$			9.68559e27i			1.86133i	−0.365869	+	0.930666i	$0.619228\pi$
$828$		0			0
$829$	3.35722e27			0.630538			0.315269	−	0.949002i	$-0.397905\pi$
$829$	3.35722e27			0.630538			0.315269	+	0.949002i	$0.397905\pi$
$830$		0			0
$831$	8.91794e26			0.163702
$832$		0			0
$833$		−	3.13545e27i		−	0.562565i
$834$		0			0
$835$	3.44708e27	−	4.48571e27i	0.604547	−	0.786702i
$836$		0			0
$837$			2.87534e27i			0.492943i
$838$		0			0
$839$	9.58548e26			0.160648			0.0803240	−	0.996769i	$-0.474405\pi$
$839$	9.58548e26			0.160648			0.0803240	+	0.996769i	$0.474405\pi$
$840$		0			0
$841$	1.19401e27			0.195634
$842$		0			0
$843$		−	2.06940e27i		−	0.331500i
$844$		0			0
$845$	−6.17403e27	−	4.74448e27i	−0.967008	−	0.743105i
$846$		0			0
$847$		−	6.42572e27i		−	0.984078i
$848$		0			0
$849$	1.48970e27			0.223087
$850$		0			0
$851$	−2.16676e27			−0.317307
$852$		0			0
$853$			1.03132e28i			1.47699i	0.674258	+	0.738496i	$0.264464\pi$
$853$			1.03132e28i			1.47699i	−0.674258	+	0.738496i	$0.735536\pi$
$854$		0			0
$855$	−7.81115e27	−	6.00254e27i	−1.09405	−	0.840731i
$856$		0			0
$857$			6.29893e27i			0.862877i	0.902142	+	0.431439i	$0.141994\pi$
$857$			6.29893e27i			0.862877i	−0.902142	+	0.431439i	$0.858006\pi$
$858$		0			0
$859$	−9.50512e27			−1.27357			−0.636785	−	0.771042i	$-0.719736\pi$
$859$	−9.50512e27			−1.27357			−0.636785	+	0.771042i	$0.719736\pi$
$860$		0			0
$861$	−1.67357e27			−0.219338
$862$		0			0
$863$		−	7.14276e26i		−	0.0915721i	−0.998951	−	0.0457861i	$-0.985421\pi$
$863$		−	7.14276e26i		−	0.0915721i	0.998951	−	0.0457861i	$-0.0145793\pi$
$864$		0			0
$865$	6.69672e27	−	8.71449e27i	0.839864	−	1.09292i
$866$		0			0
$867$		−	1.23686e27i		−	0.151754i
$868$		0			0
$869$	1.66026e27			0.199291
$870$		0			0
$871$	−2.26395e28			−2.65885
$872$		0			0
$873$			8.91229e27i			1.02413i
$874$		0			0
$875$	6.21035e27	+	2.58796e27i	0.698297	+	0.290992i
$876$		0			0
$877$		−	8.38771e27i		−	0.922884i	−0.887170	−	0.461442i	$-0.847332\pi$
$877$		−	8.38771e27i		−	0.922884i	0.887170	−	0.461442i	$-0.152668\pi$
$878$		0			0
$879$	1.26066e27			0.135738
$880$		0			0
$881$	2.30230e27			0.242600			0.121300	−	0.992616i	$-0.461294\pi$
$881$	2.30230e27			0.242600			0.121300	+	0.992616i	$0.461294\pi$
$882$		0			0
$883$		−	1.33295e28i		−	1.37463i	−0.726358	−	0.687317i	$-0.758788\pi$
$883$		−	1.33295e28i		−	1.37463i	0.726358	−	0.687317i	$-0.241212\pi$
$884$		0			0
$885$	−1.47985e27	+	1.92574e27i	−0.149368	+	0.194374i
$886$		0			0
$887$			1.28401e28i			1.26851i	0.773123	+	0.634257i	$0.218694\pi$
$887$			1.28401e28i			1.26851i	−0.773123	+	0.634257i	$0.781306\pi$
$888$		0			0
$889$	−2.51739e27			−0.243435
$890$		0			0
$891$	−1.39770e28			−1.32305
$892$		0			0
$893$			1.57449e28i			1.45899i
$894$		0			0
$895$	1.48388e28	+	1.14030e28i	1.34611	+	1.03443i
$896$		0			0
$897$			1.97609e27i			0.175501i
$898$		0			0
$899$	1.52396e28			1.32512
$900$		0			0
$901$	−2.76581e28			−2.35471
$902$		0			0
$903$			5.76262e26i			0.0480381i
$904$		0			0
$905$	2.73097e27	+	2.09864e27i	0.222923	+	0.171307i
$906$		0			0
$907$			3.27529e27i			0.261807i	0.991395	+	0.130903i	$0.0417878\pi$
$907$			3.27529e27i			0.261807i	−0.991395	+	0.130903i	$0.958212\pi$
$908$		0			0
$909$	2.20598e28			1.72681
$910$		0			0
$911$	−9.71001e27			−0.744381			−0.372190	−	0.928156i	$-0.621393\pi$
$911$	−9.71001e27			−0.744381			−0.372190	+	0.928156i	$0.621393\pi$
$912$		0			0
$913$			3.73930e28i			2.80748i
$914$		0			0
$915$	−7.81867e26	+	1.01745e27i	−0.0574953	+	0.0748190i
$916$		0			0
$917$			2.90522e27i			0.209252i
$918$		0			0
$919$	−2.16218e28			−1.52544			−0.762720	−	0.646729i	$-0.776136\pi$
$919$	−2.16218e28			−1.52544			−0.762720	+	0.646729i	$0.776136\pi$
$920$		0			0
$921$	−3.04771e27			−0.210623
$922$		0			0
$923$		−	2.29143e28i		−	1.55128i
$924$		0			0
$925$	8.15802e27	−	2.17350e27i	0.541051	−	0.144149i
$926$		0			0
$927$		−	2.08416e26i		−	0.0135417i
$928$		0			0
$929$	−2.26327e28			−1.44074			−0.720372	−	0.693588i	$-0.756029\pi$
$929$	−2.26327e28			−1.44074			−0.720372	+	0.693588i	$0.756029\pi$
$930$		0			0
$931$	−9.88914e27			−0.616789
$932$		0			0
$933$			1.65532e27i			0.101160i
$934$		0			0
$935$	−2.03016e28	+	2.64186e28i	−1.21568	+	1.58197i
$936$		0			0
$937$		−	4.55406e27i		−	0.267222i	−0.991034	−	0.133611i	$-0.957343\pi$
$937$		−	4.55406e27i		−	0.267222i	0.991034	−	0.133611i	$-0.0426573\pi$
$938$		0			0
$939$	3.40606e27			0.195852
$940$		0			0
$941$	−2.14054e28			−1.20621			−0.603104	−	0.797663i	$-0.706069\pi$
$941$	−2.14054e28			−1.20621			−0.603104	+	0.797663i	$0.706069\pi$
$942$		0			0
$943$			1.43127e28i			0.790423i
$944$		0			0
$945$	4.50797e27	+	3.46418e27i	0.243994	+	0.187499i
$946$		0			0
$947$		−	7.71447e27i		−	0.409243i	−0.978841	−	0.204621i	$-0.934404\pi$
$947$		−	7.71447e27i		−	0.409243i	0.978841	−	0.204621i	$-0.0655963\pi$
$948$		0			0
$949$	−3.92626e27			−0.204150
$950$		0			0
$951$	−5.86612e27			−0.298976
$952$		0			0
$953$		−	3.74963e28i		−	1.87329i	−0.350274	−	0.936647i	$-0.613911\pi$
$953$		−	3.74963e28i		−	1.87329i	0.350274	−	0.936647i	$-0.386089\pi$
$954$		0			0
$955$	1.59151e28	+	1.22301e28i	0.779429	+	0.598959i
$956$		0			0
$957$		−	7.18125e27i		−	0.344776i
$958$		0			0
$959$	−1.41563e28			−0.666304
$960$		0			0
$961$	1.01557e28			0.468639
$962$		0			0
$963$		−	2.77112e28i		−	1.25373i
$964$		0			0
$965$	8.86042e27	−	1.15301e28i	0.393047	−	0.511475i
$966$		0			0
$967$		−	3.50843e27i		−	0.152602i	−0.997085	−	0.0763012i	$-0.975689\pi$
$967$		−	3.50843e27i		−	0.152602i	0.997085	−	0.0763012i	$-0.0243111\pi$
$968$		0			0
$969$	−9.24465e27			−0.394289
$970$		0			0
$971$	3.64618e28			1.52495			0.762475	−	0.647017i	$-0.223984\pi$
$971$	3.64618e28			1.52495			0.762475	+	0.647017i	$0.223984\pi$
$972$		0			0
$973$			1.64215e28i			0.673504i
$974$		0			0
$975$	−1.98223e27	−	7.44014e27i	−0.0797281	−	0.299252i
$976$		0			0
$977$		−	3.23132e26i		−	0.0127462i	−0.999980	−	0.00637312i	$-0.997971\pi$
$977$		−	3.23132e26i		−	0.0127462i	0.999980	−	0.00637312i	$-0.00202864\pi$
$978$		0			0
$979$	6.25234e28			2.41884
$980$		0			0
$981$	1.35060e28			0.512472
$982$		0			0
$983$			4.67175e28i			1.73869i	0.494208	+	0.869344i	$0.335458\pi$
$983$			4.67175e28i			1.73869i	−0.494208	+	0.869344i	$0.664542\pi$
$984$		0			0
$985$	8.55895e27	−	1.11378e28i	0.312447	−	0.406589i
$986$		0			0
$987$		−	4.44302e27i		−	0.159098i
$988$		0			0
$989$	4.92829e27			0.173114
$990$		0			0
$991$	−4.06585e28			−1.40104			−0.700522	−	0.713631i	$-0.747049\pi$
$991$	−4.06585e28			−1.40104			−0.700522	+	0.713631i	$0.747049\pi$
$992$		0			0
$993$			5.33176e27i			0.180241i
$994$		0			0
$995$	3.00004e28	+	2.30541e28i	0.994965	+	0.764589i
$996$		0			0
$997$		−	2.94446e28i		−	0.958080i	−0.877793	−	0.479040i	$-0.840985\pi$
$997$		−	2.94446e28i		−	0.958080i	0.877793	−	0.479040i	$-0.159015\pi$
$998$		0			0
$999$	7.13413e27			0.227755

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	80.20.c.d.49.16		28
4.3	odd	2		40.20.c.a.9.13	✓	28
5.4	even	2	inner	80.20.c.d.49.13		28
20.19	odd	2		40.20.c.a.9.16	yes	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
40.20.c.a.9.13	✓	28	4.3	odd	2
40.20.c.a.9.16	yes	28	20.19	odd	2
80.20.c.d.49.13		28	5.4	even	2	inner
80.20.c.d.49.16		28	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)

\(f(q)\)	\(=\)	\(q+7086.75i q^{3} +(3.46294e6 + 2.66112e6i) q^{5} -8.07683e7i q^{7} +1.11204e9 q^{9} +O(q^{10})\)	\(q+7086.75i q^{3} +(3.46294e6 + 2.66112e6i) q^{5} -8.07683e7i q^{7} +1.11204e9 q^{9} -1.18624e10 q^{11} +5.69632e10i q^{13} +(-1.88587e10 + 2.45410e10i) q^{15} -6.43121e11i q^{17} -2.02839e12 q^{19} +5.72385e11 q^{21} -4.89514e12i q^{23} +(4.91036e12 + 1.84306e13i) q^{25} +1.61174e13i q^{27} +8.54240e13 q^{29} +1.78399e14 q^{31} -8.40659e13i q^{33} +(2.14934e14 - 2.79695e14i) q^{35} -4.42635e14i q^{37} -4.03684e14 q^{39} -2.92385e15 q^{41} +1.00677e15i q^{43} +(3.85092e15 + 2.95927e15i) q^{45} -7.76229e15i q^{47} +4.87537e15 q^{49} +4.55764e15 q^{51} -4.30061e16i q^{53} +(-4.10787e16 - 3.15673e16i) q^{55} -1.43747e16i q^{57} +7.84706e16 q^{59} +4.14592e16 q^{61} -8.98176e16i q^{63} +(-1.51586e17 + 1.97260e17i) q^{65} +3.97441e17i q^{67} +3.46907e16 q^{69} -4.02265e17 q^{71} +6.89262e16i q^{73} +(-1.30613e17 + 3.47985e16i) q^{75} +9.58106e17i q^{77} -1.39960e17 q^{79} +1.17826e18 q^{81} -3.15223e18i q^{83} +(1.71142e18 - 2.22709e18i) q^{85} +6.05379e17i q^{87} -5.27072e18 q^{89} +4.60082e18 q^{91} +1.26427e18i q^{93} +(-7.02417e18 - 5.39778e18i) q^{95} +8.01437e18i q^{97} -1.31915e19 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - 3935164 q^{5} - 10352560732 q^{9}+O(q^{10}) \) 28 * q - 3935164 * q^5 - 10352560732 * q^9	\( 28 q - 3935164 q^{5} - 10352560732 q^{9} - 18570995888 q^{11} - 79041415120 q^{15} + 1685869130672 q^{19} + 140419722832 q^{21} - 29558822439924 q^{25} + 160448197635496 q^{29} - 64251929934720 q^{31} + 88899634227664 q^{35} - 45\!\cdots\!04 q^{39}+ \cdots + 24\!\cdots\!92 q^{99}+O(q^{100}) \) 28 * q - 3935164 * q^5 - 10352560732 * q^9 - 18570995888 * q^11 - 79041415120 * q^15 + 1685869130672 * q^19 + 140419722832 * q^21 - 29558822439924 * q^25 + 160448197635496 * q^29 - 64251929934720 * q^31 + 88899634227664 * q^35 - 4563253596731104 * q^39 + 87868042694936 * q^41 + 3557698140217852 * q^45 - 28923781405647564 * q^49 - 14937379593456000 * q^51 - 28335039172010704 * q^55 + 83879503376835216 * q^59 + 2336306250785000 * q^61 + 23503427909569568 * q^65 - 46927873937137712 * q^69 - 104881848512783264 * q^71 - 1094024007292275040 * q^75 + 795721739900308672 * q^79 + 3593102866196377132 * q^81 + 834124526841485952 * q^85 + 1582238786752844568 * q^89 - 11017818924975052064 * q^91 - 30914057837649668144 * q^95 + 24571127463084047792 * q^99

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