LMFDB - Embedded newform 80.20.c.d.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:	$28$
Twist minimal:	no (minimal twist has level 40)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			49.5
Character	$\chi$	$=$	80.49
Dual form			80.20.c.d.49.24

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-46696.1i q^{3} +(3.00829e6 + 3.16602e6i) q^{5} -1.36132e8i q^{7} -1.01826e9 q^{9} +O(q^{10})$	\(q-46696.1i q^{3} +(3.00829e6 + 3.16602e6i) q^{5} -1.36132e8i q^{7} -1.01826e9 q^{9} -4.20583e9 q^{11} +1.12658e10i q^{13} +(1.47841e11 - 1.40475e11i) q^{15} +3.71149e11i q^{17} +9.33011e11 q^{19} -6.35682e12 q^{21} +8.82142e12i q^{23} +(-9.73835e11 + 1.90486e13i) q^{25} -6.72423e12i q^{27} +4.97962e12 q^{29} +1.42379e14 q^{31} +1.96396e14i q^{33} +(4.30996e14 - 4.09525e14i) q^{35} +5.39667e14i q^{37} +5.26070e14 q^{39} +4.36489e14 q^{41} -5.79397e15i q^{43} +(-3.06323e15 - 3.22383e15i) q^{45} +1.96290e15i q^{47} -7.13300e15 q^{49} +1.73312e16 q^{51} +3.50239e15i q^{53} +(-1.26524e16 - 1.33157e16i) q^{55} -4.35680e16i q^{57} -7.25059e16 q^{59} +1.49761e17 q^{61} +1.38618e17i q^{63} +(-3.56678e16 + 3.38909e16i) q^{65} +4.36924e17i q^{67} +4.11926e17 q^{69} +6.38198e17 q^{71} +8.15021e17i q^{73} +(8.89495e17 + 4.54743e16i) q^{75} +5.72547e17i q^{77} +5.55814e17 q^{79} -1.49748e18 q^{81} +1.74953e18i q^{83} +(-1.17506e18 + 1.11652e18i) q^{85} -2.32529e17i q^{87} +3.15965e18 q^{89} +1.53364e18 q^{91} -6.64855e18i q^{93} +(2.80677e18 + 2.95393e18i) q^{95} -2.55830e18i q^{97} +4.28263e18 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$		−	46696.1i		−	1.36971i	−0.728680	−	0.684855i	$-0.759866\pi$
$3$		−	46696.1i		−	1.36971i	0.728680	−	0.684855i	$-0.240134\pi$
$4$		0			0
$5$	3.00829e6	+	3.16602e6i	0.688819	+	0.724933i
$5$	3.00829e6	+	3.16602e6i	0.688819	+	0.724933i
$6$		0			0
$7$		−	1.36132e8i		−	1.27505i	−0.770428	−	0.637527i	$-0.779957\pi$
$7$		−	1.36132e8i		−	1.27505i	0.770428	−	0.637527i	$-0.220043\pi$
$8$		0			0
$9$	−1.01826e9			−0.876104
$10$		0			0
$11$	−4.20583e9			−0.537800			−0.268900	−	0.963168i	$-0.586660\pi$
$11$	−4.20583e9			−0.537800			−0.268900	+	0.963168i	$0.586660\pi$
$12$		0			0
$13$			1.12658e10i			0.294646i	0.989088	+	0.147323i	$0.0470657\pi$
$13$			1.12658e10i			0.294646i	−0.989088	+	0.147323i	$0.952934\pi$
$14$		0			0
$15$	1.47841e11	−	1.40475e11i	0.992948	−	0.943482i
$16$		0			0
$17$			3.71149e11i			0.759073i	0.925177	+	0.379536i	$0.123916\pi$
$17$			3.71149e11i			0.759073i	−0.925177	+	0.379536i	$0.876084\pi$
$18$		0			0
$19$	9.33011e11			0.663327			0.331663	−	0.943398i	$-0.392390\pi$
$19$	9.33011e11			0.663327			0.331663	+	0.943398i	$0.392390\pi$
$20$		0			0
$21$	−6.35682e12			−1.74645
$22$		0			0
$23$			8.82142e12i			1.02123i	0.859809	+	0.510616i	$0.170583\pi$
$23$			8.82142e12i			1.02123i	−0.859809	+	0.510616i	$0.829417\pi$
$24$		0			0
$25$	−9.73835e11	+	1.90486e13i	−0.0510570	+	0.998696i
$26$		0			0
$27$		−	6.72423e12i		−	0.169702i
$28$		0			0
$29$	4.97962e12			0.0637404			0.0318702	−	0.999492i	$-0.489854\pi$
$29$	4.97962e12			0.0637404			0.0318702	+	0.999492i	$0.489854\pi$
$30$		0			0
$31$	1.42379e14			0.967188			0.483594	−	0.875293i	$-0.339331\pi$
$31$	1.42379e14			0.967188			0.483594	+	0.875293i	$0.339331\pi$
$32$		0			0
$33$			1.96396e14i			0.736630i
$34$		0			0
$35$	4.30996e14	−	4.09525e14i	0.924329	−	0.878281i
$36$		0			0
$37$			5.39667e14i			0.682668i	0.939942	+	0.341334i	$0.110879\pi$
$37$			5.39667e14i			0.682668i	−0.939942	+	0.341334i	$0.889121\pi$
$38$		0			0
$39$	5.26070e14			0.403580
$40$		0			0
$41$	4.36489e14			0.208222			0.104111	−	0.994566i	$-0.466800\pi$
$41$	4.36489e14			0.208222			0.104111	+	0.994566i	$0.466800\pi$
$42$		0			0
$43$		−	5.79397e15i		−	1.75803i	−0.476794	−	0.879015i	$-0.658201\pi$
$43$		−	5.79397e15i		−	1.75803i	0.476794	−	0.879015i	$-0.341799\pi$
$44$		0			0
$45$	−3.06323e15	−	3.22383e15i	−0.603477	−	0.635117i
$46$		0			0
$47$			1.96290e15i			0.255841i	0.991784	+	0.127920i	$0.0408302\pi$
$47$			1.96290e15i			0.255841i	−0.991784	+	0.127920i	$0.959170\pi$
$48$		0			0
$49$	−7.13300e15			−0.625762
$50$		0			0
$51$	1.73312e16			1.03971
$52$		0			0
$53$			3.50239e15i			0.145795i	0.997339	+	0.0728977i	$0.0232247\pi$
$53$			3.50239e15i			0.145795i	−0.997339	+	0.0728977i	$0.976775\pi$
$54$		0			0
$55$	−1.26524e16	−	1.33157e16i	−0.370447	−	0.389869i
$56$		0			0
$57$		−	4.35680e16i		−	0.908565i
$58$		0			0
$59$	−7.25059e16			−1.08963			−0.544815	−	0.838556i	$-0.683400\pi$
$59$	−7.25059e16			−1.08963			−0.544815	+	0.838556i	$0.683400\pi$
$60$		0			0
$61$	1.49761e17			1.63971			0.819853	−	0.572574i	$-0.194055\pi$
$61$	1.49761e17			1.63971			0.819853	+	0.572574i	$0.194055\pi$
$62$		0			0
$63$			1.38618e17i			1.11708i
$64$		0			0
$65$	−3.56678e16	+	3.38909e16i	−0.213599	+	0.202958i
$66$		0			0
$67$			4.36924e17i			1.96198i	0.194056	+	0.980991i	$0.437836\pi$
$67$			4.36924e17i			1.96198i	−0.194056	+	0.980991i	$0.562164\pi$
$68$		0			0
$69$	4.11926e17			1.39879
$70$		0			0
$71$	6.38198e17			1.65197			0.825983	−	0.563696i	$-0.190621\pi$
$71$	6.38198e17			1.65197			0.825983	+	0.563696i	$0.190621\pi$
$72$		0			0
$73$			8.15021e17i			1.62032i	0.586207	+	0.810162i	$0.300621\pi$
$73$			8.15021e17i			1.62032i	−0.586207	+	0.810162i	$0.699379\pi$
$74$		0			0
$75$	8.89495e17	+	4.54743e16i	1.36792	+	0.0699333i
$76$		0			0
$77$			5.72547e17i			0.685724i
$78$		0			0
$79$	5.55814e17			0.521761			0.260881	−	0.965371i	$-0.415987\pi$
$79$	5.55814e17			0.521761			0.260881	+	0.965371i	$0.415987\pi$
$80$		0			0
$81$	−1.49748e18			−1.10855
$82$		0			0
$83$			1.74953e18i			1.02726i	0.858012	+	0.513630i	$0.171699\pi$
$83$			1.74953e18i			1.02726i	−0.858012	+	0.513630i	$0.828301\pi$
$84$		0			0
$85$	−1.17506e18	+	1.11652e18i	−0.550277	+	0.522864i
$86$		0			0
$87$		−	2.32529e17i		−	0.0873058i
$88$		0			0
$89$	3.15965e18			0.955947			0.477973	−	0.878374i	$-0.341371\pi$
$89$	3.15965e18			0.955947			0.477973	+	0.878374i	$0.341371\pi$
$90$		0			0
$91$	1.53364e18			0.375690
$92$		0			0
$93$		−	6.64855e18i		−	1.32477i
$94$		0			0
$95$	2.80677e18	+	2.95393e18i	0.456912	+	0.480868i
$96$		0			0
$97$		−	2.55830e18i		−	0.341680i	−0.985299	−	0.170840i	$-0.945352\pi$
$97$		−	2.55830e18i		−	0.341680i	0.985299	−	0.170840i	$-0.0546481\pi$
$98$		0			0
$99$	4.28263e18			0.471169
$100$		0			0
$101$	1.48871e18			0.135444			0.0677218	−	0.997704i	$-0.478427\pi$
$101$	1.48871e18			0.135444			0.0677218	+	0.997704i	$0.478427\pi$
$102$		0			0
$103$		−	1.17039e18i		−	0.0883849i	−0.999023	−	0.0441925i	$-0.985929\pi$
$103$		−	1.17039e18i		−	0.0883849i	0.999023	−	0.0441925i	$-0.0140715\pi$
$104$		0			0
$105$	−1.91232e19	−	2.01258e19i	−1.20299	−	1.26606i
$106$		0			0
$107$			2.41487e19i			1.26984i	0.772578	+	0.634919i	$0.218967\pi$
$107$			2.41487e19i			1.26984i	−0.772578	+	0.634919i	$0.781033\pi$
$108$		0			0
$109$	−7.94248e18			−0.350271			−0.175136	−	0.984544i	$-0.556036\pi$
$109$	−7.94248e18			−0.350271			−0.175136	+	0.984544i	$0.556036\pi$
$110$		0			0
$111$	2.52003e19			0.935057
$112$		0			0
$113$		−	4.18708e19i		−	1.31119i	−0.755111	−	0.655596i	$-0.772417\pi$
$113$		−	4.18708e19i		−	1.31119i	0.755111	−	0.655596i	$-0.227583\pi$
$114$		0			0
$115$	−2.79288e19	+	2.65374e19i	−0.740325	+	0.703444i
$116$		0			0
$117$		−	1.14716e19i		−	0.258141i
$118$		0			0
$119$	5.05252e19			0.967858
$120$		0			0
$121$	−4.34701e19			−0.710771
$122$		0			0
$123$		−	2.03823e19i		−	0.285204i
$124$		0			0
$125$	−6.32378e19	+	5.42206e19i	−0.759157	+	0.650908i
$126$		0			0
$127$		−	3.10874e19i		−	0.320959i	−0.987039	−	0.160480i	$-0.948696\pi$
$127$		−	3.10874e19i		−	0.320959i	0.987039	−	0.160480i	$-0.0513041\pi$
$128$		0			0
$129$	−2.70556e20			−2.40799
$130$		0			0
$131$	−7.45743e19			−0.573471			−0.286736	−	0.958010i	$-0.592570\pi$
$131$	−7.45743e19			−0.573471			−0.286736	+	0.958010i	$0.592570\pi$
$132$		0			0
$133$		−	1.27013e20i		−	0.845777i
$134$		0			0
$135$	2.12890e19	−	2.02284e19i	0.123023	−	0.116894i
$136$		0			0
$137$		−	3.19984e20i		−	1.60799i	−0.594638	−	0.803994i	$-0.702704\pi$
$137$		−	3.19984e20i		−	1.60799i	0.594638	−	0.803994i	$-0.297296\pi$
$138$		0			0
$139$	4.26872e20			1.86921			0.934604	−	0.355691i	$-0.115754\pi$
$139$	4.26872e20			1.86921			0.934604	+	0.355691i	$0.115754\pi$
$140$		0			0
$141$	9.16599e19			0.350427
$142$		0			0
$143$		−	4.73821e19i		−	0.158461i
$144$		0			0
$145$	1.49801e19	+	1.57655e19i	0.0439056	+	0.0462076i
$146$		0			0
$147$			3.33083e20i			0.857112i
$148$		0			0
$149$	6.79383e20			1.53761			0.768803	−	0.639486i	$-0.220853\pi$
$149$	6.79383e20			1.53761			0.768803	+	0.639486i	$0.220853\pi$
$150$		0			0
$151$	−5.21635e20			−1.04013			−0.520063	−	0.854128i	$-0.674091\pi$
$151$	−5.21635e20			−1.04013			−0.520063	+	0.854128i	$0.674091\pi$
$152$		0			0
$153$		−	3.77927e20i		−	0.665026i
$154$		0			0
$155$	4.28319e20	+	4.50775e20i	0.666217	+	0.701147i
$156$		0			0
$157$			6.59583e20i			0.908286i	0.890929	+	0.454143i	$0.150054\pi$
$157$			6.59583e20i			0.908286i	−0.890929	+	0.454143i	$0.849946\pi$
$158$		0			0
$159$	1.63548e20			0.199697
$160$		0			0
$161$	1.20088e21			1.30213
$162$		0			0
$163$		−	7.70274e20i		−	0.742784i	−0.928476	−	0.371392i	$-0.878881\pi$
$163$		−	7.70274e20i		−	0.742784i	0.928476	−	0.371392i	$-0.121119\pi$
$164$		0			0
$165$	−6.21792e20	+	5.90816e20i	−0.534008	+	0.507405i
$166$		0			0
$167$		−	7.50262e20i		−	0.574654i	−0.957833	−	0.287327i	$-0.907233\pi$
$167$		−	7.50262e20i		−	0.574654i	0.957833	−	0.287327i	$-0.0927667\pi$
$168$		0			0
$169$	1.33500e21			0.913184
$170$		0			0
$171$	−9.50049e20			−0.581143
$172$		0			0
$173$		−	7.58212e20i		−	0.415291i	−0.978204	−	0.207646i	$-0.933420\pi$
$173$		−	7.58212e20i		−	0.415291i	0.978204	−	0.207646i	$-0.0665801\pi$
$174$		0			0
$175$	2.59312e21	+	1.32570e20i	1.27339	+	0.0651004i
$176$		0			0
$177$			3.38574e21i			1.49248i
$178$		0			0
$179$	6.89624e20			0.273218			0.136609	−	0.990625i	$-0.456380\pi$
$179$	6.89624e20			0.273218			0.136609	+	0.990625i	$0.456380\pi$
$180$		0			0
$181$	4.19375e21			1.49505			0.747526	−	0.664233i	$-0.231242\pi$
$181$	4.19375e21			1.49505			0.747526	+	0.664233i	$0.231242\pi$
$182$		0			0
$183$		−	6.99326e21i		−	2.24592i
$184$		0			0
$185$	−1.70860e21	+	1.62348e21i	−0.494889	+	0.470235i
$186$		0			0
$187$		−	1.56099e21i		−	0.408229i
$188$		0			0
$189$	−9.15382e20			−0.216379
$190$		0			0
$191$	−2.55896e21			−0.547325			−0.273663	−	0.961826i	$-0.588235\pi$
$191$	−2.55896e21			−0.547325			−0.273663	+	0.961826i	$0.588235\pi$
$192$		0			0
$193$		−	2.08885e20i		−	0.0404680i	−0.999795	−	0.0202340i	$-0.993559\pi$
$193$		−	2.08885e20i		−	0.0404680i	0.999795	−	0.0202340i	$-0.00644113\pi$
$194$		0			0
$195$	1.58257e21	+	1.66555e21i	0.277993	+	0.292569i
$196$		0			0
$197$		−	6.98545e21i		−	1.11369i	−0.830615	−	0.556846i	$-0.812011\pi$
$197$		−	6.98545e21i		−	1.11369i	0.830615	−	0.556846i	$-0.187989\pi$
$198$		0			0
$199$	−9.10492e21			−1.31878			−0.659389	−	0.751802i	$-0.729185\pi$
$199$	−9.10492e21			−1.31878			−0.659389	+	0.751802i	$0.729185\pi$
$200$		0			0
$201$	2.04026e22			2.68734
$202$		0			0
$203$		−	6.77885e20i		−	0.0812725i
$204$		0			0
$205$	1.31309e21	+	1.38193e21i	0.143427	+	0.150947i
$206$		0			0
$207$		−	8.98252e21i		−	0.894705i
$208$		0			0
$209$	−3.92408e21			−0.356737
$210$		0			0
$211$	−2.19804e22			−1.82538			−0.912688	−	0.408657i	$-0.865997\pi$
$211$	−2.19804e22			−1.82538			−0.912688	+	0.408657i	$0.865997\pi$
$212$		0			0
$213$		−	2.98013e22i		−	2.26271i
$214$		0			0
$215$	1.83438e22	−	1.74300e22i	1.27445	−	1.21096i
$216$		0			0
$217$		−	1.93824e22i		−	1.23322i
$218$		0			0
$219$	3.80583e22			2.21937
$220$		0			0
$221$	−4.18130e21			−0.223658
$222$		0			0
$223$		−	2.34115e22i		−	1.14957i	−0.818306	−	0.574783i	$-0.805087\pi$
$223$		−	2.34115e22i		−	1.14957i	0.818306	−	0.574783i	$-0.194913\pi$
$224$		0			0
$225$	9.91619e20	−	1.93965e22i	0.0447312	−	0.874961i
$226$		0			0
$227$		−	1.46936e22i		−	0.609373i	−0.952453	−	0.304687i	$-0.901448\pi$
$227$		−	1.46936e22i		−	0.609373i	0.952453	−	0.304687i	$-0.0985517\pi$
$228$		0			0
$229$	−3.75179e22			−1.43153			−0.715766	−	0.698340i	$-0.753922\pi$
$229$	−3.75179e22			−1.43153			−0.715766	+	0.698340i	$0.753922\pi$
$230$		0			0
$231$	2.67357e22			0.939243
$232$		0			0
$233$			4.73030e22i			1.53111i	0.643368	+	0.765557i	$0.277537\pi$
$233$			4.73030e22i			1.53111i	−0.643368	+	0.765557i	$0.722463\pi$
$234$		0			0
$235$	−6.21459e21	+	5.90499e21i	−0.185467	+	0.176228i
$236$		0			0
$237$		−	2.59543e22i		−	0.714661i
$238$		0			0
$239$	4.03175e22			1.02497			0.512487	−	0.858695i	$-0.328724\pi$
$239$	4.03175e22			1.02497			0.512487	+	0.858695i	$0.328724\pi$
$240$		0			0
$241$	6.18640e22			1.45304			0.726518	−	0.687148i	$-0.241137\pi$
$241$	6.18640e22			1.45304			0.726518	+	0.687148i	$0.241137\pi$
$242$		0			0
$243$			6.21112e22i			1.34868i
$244$		0			0
$245$	−2.14581e22	−	2.25832e22i	−0.431037	−	0.453636i
$246$		0			0
$247$			1.05111e22i			0.195447i
$248$		0			0
$249$	8.16963e22			1.40705
$250$		0			0
$251$	1.05345e23			1.68156			0.840780	−	0.541377i	$-0.182097\pi$
$251$	1.05345e23			1.68156			0.840780	+	0.541377i	$0.182097\pi$
$252$		0			0
$253$		−	3.71014e22i		−	0.549219i
$254$		0			0
$255$	5.21373e22	+	5.48708e22i	0.716171	+	0.753720i
$256$		0			0
$257$		−	2.93863e22i		−	0.374783i	−0.982285	−	0.187391i	$-0.939997\pi$
$257$		−	2.93863e22i		−	0.374783i	0.982285	−	0.187391i	$-0.0600033\pi$
$258$		0			0
$259$	7.34659e22			0.870439
$260$		0			0
$261$	−5.07055e21			−0.0558432
$262$		0			0
$263$			1.16084e23i			1.18903i	0.804086	+	0.594514i	$0.202655\pi$
$263$			1.16084e23i			1.18903i	−0.804086	+	0.594514i	$0.797345\pi$
$264$		0			0
$265$	−1.10886e22	+	1.05362e22i	−0.105692	+	0.100427i
$266$		0			0
$267$		−	1.47543e23i		−	1.30937i
$268$		0			0
$269$	1.59811e23			1.32117			0.660586	−	0.750750i	$-0.270308\pi$
$269$	1.59811e23			1.32117			0.660586	+	0.750750i	$0.270308\pi$
$270$		0			0
$271$	6.82665e22			0.526017			0.263008	−	0.964794i	$-0.415285\pi$
$271$	6.82665e22			0.526017			0.263008	+	0.964794i	$0.415285\pi$
$272$		0			0
$273$		−	7.16149e22i		−	0.514586i
$274$		0			0
$275$	4.09578e21	−	8.01152e22i	0.0274585	−	0.537099i
$276$		0			0
$277$		−	2.78687e23i		−	1.74405i	−0.489464	−	0.872023i	$-0.662808\pi$
$277$		−	2.78687e23i		−	1.74405i	0.489464	−	0.872023i	$-0.337192\pi$
$278$		0			0
$279$	−1.44979e23			−0.847357
$280$		0			0
$281$	−1.68385e23			−0.919590			−0.459795	−	0.888025i	$-0.652077\pi$
$281$	−1.68385e23			−0.919590			−0.459795	+	0.888025i	$0.652077\pi$
$282$		0			0
$283$		−	2.69169e23i		−	1.37421i	−0.726557	−	0.687106i	$-0.758881\pi$
$283$		−	2.69169e23i		−	1.37421i	0.726557	−	0.687106i	$-0.241119\pi$
$284$		0			0
$285$	1.37937e23	−	1.31065e23i	0.658649	−	0.625837i
$286$		0			0
$287$		−	5.94201e22i		−	0.265494i
$288$		0			0
$289$	1.01321e23			0.423809
$290$		0			0
$291$	−1.19462e23			−0.468002
$292$		0			0
$293$			2.93125e23i			1.07600i	0.842946	+	0.537998i	$0.180819\pi$
$293$			2.93125e23i			1.07600i	−0.842946	+	0.537998i	$0.819181\pi$
$294$		0			0
$295$	−2.18119e23	−	2.29555e23i	−0.750558	−	0.789910i
$296$		0			0
$297$			2.82809e22i			0.0912657i
$298$		0			0
$299$	−9.93806e22			−0.300902
$300$		0			0
$301$	−7.88745e23			−2.24158
$302$		0			0
$303$		−	6.95171e22i		−	0.185518i
$304$		0			0
$305$	4.50526e23	+	4.74147e23i	1.12946	+	1.18868i
$306$		0			0
$307$		−	6.84464e23i		−	1.61263i	−0.591483	−	0.806317i	$-0.701457\pi$
$307$		−	6.84464e23i		−	1.61263i	0.591483	−	0.806317i	$-0.298543\pi$
$308$		0			0
$309$	−5.46528e22			−0.121062
$310$		0			0
$311$	1.96399e23			0.409181			0.204590	−	0.978848i	$-0.434414\pi$
$311$	1.96399e23			0.409181			0.204590	+	0.978848i	$0.434414\pi$
$312$		0			0
$313$			5.40367e23i			1.05930i	0.848217	+	0.529649i	$0.177676\pi$
$313$			5.40367e23i			1.05930i	−0.848217	+	0.529649i	$0.822324\pi$
$314$		0			0
$315$	−4.38867e23	+	4.17003e23i	−0.809808	+	0.769465i
$316$		0			0
$317$		−	2.21571e23i		−	0.384991i	−0.981298	−	0.192495i	$-0.938342\pi$
$317$		−	2.21571e23i		−	0.384991i	0.981298	−	0.192495i	$-0.0616580\pi$
$318$		0			0
$319$	−2.09434e22			−0.0342796
$320$		0			0
$321$	1.12765e24			1.73931
$322$		0			0
$323$			3.46286e23i			0.503513i
$324$		0			0
$325$	−2.14598e23	−	1.09711e22i	−0.294262	−	0.0150438i
$326$		0			0
$327$			3.70883e23i			0.479770i
$328$		0			0
$329$	2.67214e23			0.326211
$330$		0			0
$331$	3.86636e23			0.445590			0.222795	−	0.974865i	$-0.428482\pi$
$331$	3.86636e23			0.445590			0.222795	+	0.974865i	$0.428482\pi$
$332$		0			0
$333$		−	5.49522e23i		−	0.598088i
$334$		0			0
$335$	−1.38331e24	+	1.31439e24i	−1.42231	+	1.35145i
$336$		0			0
$337$			5.89165e23i			0.572470i	0.958159	+	0.286235i	$0.0924039\pi$
$337$			5.89165e23i			0.572470i	−0.958159	+	0.286235i	$0.907596\pi$
$338$		0			0
$339$	−1.95520e24			−1.79595
$340$		0			0
$341$	−5.98823e23			−0.520154
$342$		0			0
$343$		−	5.80725e23i		−	0.477173i
$344$		0			0
$345$	1.23919e24	+	1.30416e24i	0.963513	+	1.01403i
$346$		0			0
$347$		−	5.28403e23i		−	0.388897i	−0.980913	−	0.194449i	$-0.937708\pi$
$347$		−	5.28403e23i		−	0.388897i	0.980913	−	0.194449i	$-0.0622918\pi$
$348$		0			0
$349$	−2.10645e24			−1.46794			−0.733970	−	0.679181i	$-0.762335\pi$
$349$	−2.10645e24			−1.46794			−0.733970	+	0.679181i	$0.762335\pi$
$350$		0			0
$351$	7.57539e22			0.0500020
$352$		0			0
$353$			1.92106e24i			1.20138i	0.799482	+	0.600691i	$0.205108\pi$
$353$			1.92106e24i			1.20138i	−0.799482	+	0.600691i	$0.794892\pi$
$354$		0			0
$355$	1.91989e24	+	2.02054e24i	1.13790	+	1.19756i
$356$		0			0
$357$		−	2.35933e24i		−	1.32568i
$358$		0			0
$359$	1.84735e24			0.984358			0.492179	−	0.870494i	$-0.336201\pi$
$359$	1.84735e24			0.984358			0.492179	+	0.870494i	$0.336201\pi$
$360$		0			0
$361$	−1.10791e24			−0.559997
$362$		0			0
$363$			2.02988e24i			0.973550i
$364$		0			0
$365$	−2.58037e24	+	2.45182e24i	−1.17463	+	1.11611i
$366$		0			0
$367$		−	1.75157e24i		−	0.757006i	−0.925600	−	0.378503i	$-0.876439\pi$
$367$		−	1.75157e24i		−	0.757006i	0.925600	−	0.378503i	$-0.123561\pi$
$368$		0			0
$369$	−4.44460e23			−0.182424
$370$		0			0
$371$	4.76787e23			0.185897
$372$		0			0
$373$		−	1.07617e24i		−	0.398701i	−0.979928	−	0.199350i	$-0.936117\pi$
$373$		−	1.07617e24i		−	0.398701i	0.979928	−	0.199350i	$-0.0638832\pi$
$374$		0			0
$375$	2.53189e24	+	2.95296e24i	0.891554	+	1.03982i
$376$		0			0
$377$			5.60995e22i			0.0187809i
$378$		0			0
$379$	−8.79962e22			−0.0280150			−0.0140075	−	0.999902i	$-0.504459\pi$
$379$	−8.79962e22			−0.0280150			−0.0140075	+	0.999902i	$0.504459\pi$
$380$		0			0
$381$	−1.45166e24			−0.439621
$382$		0			0
$383$			7.44972e23i			0.214660i	0.994223	+	0.107330i	$0.0342302\pi$
$383$			7.44972e23i			0.214660i	−0.994223	+	0.107330i	$0.965770\pi$
$384$		0			0
$385$	−1.81269e24	+	1.72239e24i	−0.497104	+	0.472340i
$386$		0			0
$387$			5.89978e24i			1.54022i
$388$		0			0
$389$	−1.14402e23			−0.0284388			−0.0142194	−	0.999899i	$-0.504526\pi$
$389$	−1.14402e23			−0.0284388			−0.0142194	+	0.999899i	$0.504526\pi$
$390$		0			0
$391$	−3.27406e24			−0.775189
$392$		0			0
$393$			3.48233e24i			0.785489i
$394$		0			0
$395$	1.67205e24	+	1.75971e24i	0.359399	+	0.378242i
$396$		0			0
$397$		−	4.26893e24i		−	0.874600i	−0.899316	−	0.437300i	$-0.855935\pi$
$397$		−	4.26893e24i		−	0.874600i	0.899316	−	0.437300i	$-0.144065\pi$
$398$		0			0
$399$	−5.93099e24			−1.15847
$400$		0			0
$401$	−9.29204e23			−0.173077			−0.0865386	−	0.996249i	$-0.527581\pi$
$401$	−9.29204e23			−0.173077			−0.0865386	+	0.996249i	$0.527581\pi$
$402$		0			0
$403$			1.60402e24i			0.284978i
$404$		0			0
$405$	−4.50486e24	−	4.74105e24i	−0.763587	−	0.803622i
$406$		0			0
$407$		−	2.26975e24i		−	0.367139i
$408$		0			0
$409$	−4.13110e24			−0.637814			−0.318907	−	0.947786i	$-0.603316\pi$
$409$	−4.13110e24			−0.637814			−0.318907	+	0.947786i	$0.603316\pi$
$410$		0			0
$411$	−1.49420e25			−2.20248
$412$		0			0
$413$			9.87037e24i			1.38934i
$414$		0			0
$415$	−5.53905e24	+	5.26311e24i	−0.744695	+	0.707596i
$416$		0			0
$417$		−	1.99333e25i		−	2.56027i
$418$		0			0
$419$	1.14647e25			1.40711			0.703555	−	0.710641i	$-0.251595\pi$
$419$	1.14647e25			1.40711			0.703555	+	0.710641i	$0.251595\pi$
$420$		0			0
$421$	9.11773e24			1.06956			0.534782	−	0.844990i	$-0.320394\pi$
$421$	9.11773e24			1.06956			0.534782	+	0.844990i	$0.320394\pi$
$422$		0			0
$423$		−	1.99875e24i		−	0.224143i
$424$		0			0
$425$	−7.06987e24	−	3.61438e23i	−0.758083	−	0.0387560i
$426$		0			0
$427$		−	2.03873e25i		−	2.09071i
$428$		0			0
$429$	−2.21256e24			−0.217045
$430$		0			0
$431$	−2.52448e24			−0.236939			−0.118470	−	0.992958i	$-0.537799\pi$
$431$	−2.52448e24			−0.236939			−0.118470	+	0.992958i	$0.537799\pi$
$432$		0			0
$433$			6.89664e24i			0.619445i	0.950827	+	0.309722i	$0.100236\pi$
$433$			6.89664e24i			0.619445i	−0.950827	+	0.309722i	$0.899764\pi$
$434$		0			0
$435$	7.36189e23	−	6.99514e23i	0.0632909	−	0.0601379i
$436$		0			0
$437$			8.23049e24i			0.677410i
$438$		0			0
$439$	1.10125e25			0.867905			0.433953	−	0.900936i	$-0.357119\pi$
$439$	1.10125e25			0.867905			0.433953	+	0.900936i	$0.357119\pi$
$440$		0			0
$441$	7.26326e24			0.548233
$442$		0			0
$443$		−	1.45824e24i		−	0.105437i	−0.998609	−	0.0527184i	$-0.983211\pi$
$443$		−	1.45824e24i		−	0.105437i	0.998609	−	0.0527184i	$-0.0167886\pi$
$444$		0			0
$445$	9.50515e24	+	1.00035e25i	0.658474	+	0.692998i
$446$		0			0
$447$		−	3.17245e25i		−	2.10607i
$448$		0			0
$449$	−2.78192e24			−0.177013			−0.0885064	−	0.996076i	$-0.528209\pi$
$449$	−2.78192e24			−0.177013			−0.0885064	+	0.996076i	$0.528209\pi$
$450$		0			0
$451$	−1.83580e24			−0.111982
$452$		0			0
$453$			2.43583e25i			1.42467i
$454$		0			0
$455$	4.61363e24	+	4.85552e24i	0.258782	+	0.272350i
$456$		0			0
$457$		−	1.02707e25i		−	0.552582i	−0.961074	−	0.276291i	$-0.910895\pi$
$457$		−	1.02707e25i		−	0.552582i	0.961074	−	0.276291i	$-0.0891054\pi$
$458$		0			0
$459$	2.49569e24			0.128816
$460$		0			0
$461$	2.32322e25			1.15062			0.575308	−	0.817937i	$-0.304882\pi$
$461$	2.32322e25			1.15062			0.575308	+	0.817937i	$0.304882\pi$
$462$		0			0
$463$		−	3.82975e24i		−	0.182033i	−0.995849	−	0.0910166i	$-0.970988\pi$
$463$		−	3.82975e24i		−	0.182033i	0.995849	−	0.0910166i	$-0.0290116\pi$
$464$		0			0
$465$	2.10494e25	−	2.00008e25i	0.960367	−	0.912524i
$466$		0			0
$467$			2.16615e25i			0.948806i	0.880308	+	0.474403i	$0.157336\pi$
$467$			2.16615e25i			0.948806i	−0.880308	+	0.474403i	$0.842664\pi$
$468$		0			0
$469$	5.94792e25			2.50163
$470$		0			0
$471$	3.07999e25			1.24409
$472$		0			0
$473$			2.43685e25i			0.945469i
$474$		0			0
$475$	−9.08599e23	+	1.77726e25i	−0.0338675	+	0.662462i
$476$		0			0
$477$		−	3.56635e24i		−	0.127732i
$478$		0			0
$479$	−4.07862e25			−1.40387			−0.701933	−	0.712243i	$-0.747679\pi$
$479$	−4.07862e25			−1.40387			−0.701933	+	0.712243i	$0.747679\pi$
$480$		0			0
$481$	−6.07980e24			−0.201146
$482$		0			0
$483$		−	5.60762e25i		−	1.78353i
$484$		0			0
$485$	8.09961e24	−	7.69611e24i	0.247695	−	0.235356i
$486$		0			0
$487$			3.78705e25i			1.11372i	0.830607	+	0.556860i	$0.187994\pi$
$487$			3.78705e25i			1.11372i	−0.830607	+	0.556860i	$0.812006\pi$
$488$		0			0
$489$	−3.59687e25			−1.01740
$490$		0			0
$491$	6.11258e23			0.0166322			0.00831611	−	0.999965i	$-0.497353\pi$
$491$	6.11258e23			0.0166322			0.00831611	+	0.999965i	$0.497353\pi$
$492$		0			0
$493$			1.84818e24i			0.0483836i
$494$		0			0
$495$	1.28834e25	+	1.35589e25i	0.324550	+	0.341566i
$496$		0			0
$497$		−	8.68790e25i		−	2.10634i
$498$		0			0
$499$	2.52925e25			0.590252			0.295126	−	0.955458i	$-0.404638\pi$
$499$	2.52925e25			0.590252			0.295126	+	0.955458i	$0.404638\pi$
$500$		0			0
$501$	−3.50343e25			−0.787109
$502$		0			0
$503$		−	5.38408e24i		−	0.116470i	−0.998303	−	0.0582352i	$-0.981453\pi$
$503$		−	5.38408e24i		−	0.116470i	0.998303	−	0.0582352i	$-0.0185473\pi$
$504$		0			0
$505$	4.47849e24	+	4.71330e24i	0.0932961	+	0.0981876i
$506$		0			0
$507$		−	6.23393e25i		−	1.25080i
$508$		0			0
$509$	4.42894e25			0.856015			0.428007	−	0.903775i	$-0.359216\pi$
$509$	4.42894e25			0.856015			0.428007	+	0.903775i	$0.359216\pi$
$510$		0			0
$511$	1.10950e26			2.06600
$512$		0			0
$513$		−	6.27378e24i		−	0.112568i
$514$		0			0
$515$	3.70549e24	−	3.52089e24i	0.0640732	−	0.0608812i
$516$		0			0
$517$		−	8.25564e24i		−	0.137591i
$518$		0			0
$519$	−3.54055e25			−0.568829
$520$		0			0
$521$	−2.65646e25			−0.411476			−0.205738	−	0.978607i	$-0.565960\pi$
$521$	−2.65646e25			−0.411476			−0.205738	+	0.978607i	$0.565960\pi$
$522$		0			0
$523$		−	9.63495e25i		−	1.43907i	−0.694454	−	0.719537i	$-0.744354\pi$
$523$		−	9.63495e25i		−	1.43907i	0.694454	−	0.719537i	$-0.255646\pi$
$524$		0			0
$525$	6.19050e24	−	1.21089e26i	0.0891687	−	1.74418i
$526$		0			0
$527$			5.28439e25i			0.734166i
$528$		0			0
$529$	−3.20206e24			−0.0429142
$530$		0			0
$531$	7.38300e25			0.954629
$532$		0			0
$533$			4.91741e24i			0.0613519i
$534$		0			0
$535$	−7.64553e25	+	7.26465e25i	−0.920549	+	0.874689i
$536$		0			0
$537$		−	3.22027e25i		−	0.374229i
$538$		0			0
$539$	3.00002e25			0.336535
$540$		0			0
$541$	−1.24350e26			−1.34671			−0.673353	−	0.739321i	$-0.735146\pi$
$541$	−1.24350e26			−1.34671			−0.673353	+	0.739321i	$0.735146\pi$
$542$		0			0
$543$		−	1.95832e26i		−	2.04779i
$544$		0			0
$545$	−2.38933e25	−	2.51460e25i	−0.241273	−	0.253923i
$546$		0			0
$547$			7.17464e25i			0.699713i	0.936803	+	0.349857i	$0.113770\pi$
$547$			7.17464e25i			0.699713i	−0.936803	+	0.349857i	$0.886230\pi$
$548$		0			0
$549$	−1.52496e26			−1.43655
$550$		0			0
$551$	4.64604e24			0.0422807
$552$		0			0
$553$		−	7.56639e25i		−	0.665274i
$554$		0			0
$555$	7.58100e25	+	7.97847e25i	0.644085	+	0.677854i
$556$		0			0
$557$			1.00613e26i			0.826098i	0.910709	+	0.413049i	$0.135536\pi$
$557$			1.00613e26i			0.826098i	−0.910709	+	0.413049i	$0.864464\pi$
$558$		0			0
$559$	6.52739e25			0.517997
$560$		0			0
$561$	−7.28920e25			−0.559156
$562$		0			0
$563$		−	2.92181e25i		−	0.216682i	−0.994114	−	0.108341i	$-0.965446\pi$
$563$		−	2.92181e25i		−	0.216682i	0.994114	−	0.108341i	$-0.0345538\pi$
$564$		0			0
$565$	1.32564e26	−	1.25960e26i	0.950528	−	0.903174i
$566$		0			0
$567$			2.03855e26i			1.41346i
$568$		0			0
$569$	9.19083e25			0.616295			0.308147	−	0.951339i	$-0.400291\pi$
$569$	9.19083e25			0.616295			0.308147	+	0.951339i	$0.400291\pi$
$570$		0			0
$571$	−1.91490e26			−1.24195			−0.620973	−	0.783832i	$-0.713262\pi$
$571$	−1.91490e26			−1.24195			−0.620973	+	0.783832i	$0.713262\pi$
$572$		0			0
$573$			1.19493e26i			0.749677i
$574$		0			0
$575$	−1.68036e26	−	8.59061e24i	−1.01990	−	0.0521410i
$576$		0			0
$577$			3.58349e25i			0.210444i	0.994449	+	0.105222i	$0.0335553\pi$
$577$			3.58349e25i			0.210444i	−0.994449	+	0.105222i	$0.966445\pi$
$578$		0			0
$579$	−9.75410e24			−0.0554295
$580$		0			0
$581$	2.38167e26			1.30981
$582$		0			0
$583$		−	1.47305e25i		−	0.0784088i
$584$		0			0
$585$	3.63191e25	−	3.45098e25i	0.187135	−	0.177812i
$586$		0			0
$587$			3.33038e26i			1.66124i	0.556841	+	0.830619i	$0.312013\pi$
$587$			3.33038e26i			1.66124i	−0.556841	+	0.830619i	$0.687987\pi$
$588$		0			0
$589$	1.32841e26			0.641562
$590$		0			0
$591$	−3.26193e26			−1.52544
$592$		0			0
$593$			3.69358e26i			1.67274i	0.548165	+	0.836370i	$0.315326\pi$
$593$			3.69358e26i			1.67274i	−0.548165	+	0.836370i	$0.684674\pi$
$594$		0			0
$595$	1.51995e26	+	1.59964e26i	0.666679	+	0.701633i
$596$		0			0
$597$			4.25164e26i			1.80634i
$598$		0			0
$599$	2.26098e26			0.930555			0.465278	−	0.885165i	$-0.345954\pi$
$599$	2.26098e26			0.930555			0.465278	+	0.885165i	$0.345954\pi$
$600$		0			0
$601$	−2.89977e25			−0.115626			−0.0578131	−	0.998327i	$-0.518413\pi$
$601$	−2.89977e25			−0.115626			−0.0578131	+	0.998327i	$0.518413\pi$
$602$		0			0
$603$		−	4.44902e26i		−	1.71890i
$604$		0			0
$605$	−1.30771e26	−	1.37627e26i	−0.489592	−	0.515262i
$606$		0			0
$607$			2.14053e26i			0.776656i	0.921521	+	0.388328i	$0.126947\pi$
$607$			2.14053e26i			0.776656i	−0.921521	+	0.388328i	$0.873053\pi$
$608$		0			0
$609$	−3.16545e25			−0.111320
$610$		0			0
$611$	−2.21137e25			−0.0753825
$612$		0			0
$613$			5.58255e26i			1.84484i	0.386190	+	0.922419i	$0.373791\pi$
$613$			5.58255e26i			1.84484i	−0.386190	+	0.922419i	$0.626209\pi$
$614$		0			0
$615$	6.45308e25	−	6.13160e25i	0.206754	−	0.196454i
$616$		0			0
$617$			1.34243e26i			0.417044i	0.978018	+	0.208522i	$0.0668654\pi$
$617$			1.34243e26i			0.417044i	−0.978018	+	0.208522i	$0.933135\pi$
$618$		0			0
$619$	−2.57692e26			−0.776320			−0.388160	−	0.921592i	$-0.626889\pi$
$619$	−2.57692e26			−0.776320			−0.388160	+	0.921592i	$0.626889\pi$
$620$		0			0
$621$	5.93172e25			0.173305
$622$		0			0
$623$		−	4.30129e26i		−	1.21888i
$624$		0			0
$625$	−3.61901e26	−	3.71004e25i	−0.994786	−	0.101981i
$626$		0			0
$627$			1.83239e26i			0.488627i
$628$		0			0
$629$	−2.00297e26			−0.518195
$630$		0			0
$631$	4.23758e25			0.106375			0.0531874	−	0.998585i	$-0.483062\pi$
$631$	4.23758e25			0.106375			0.0531874	+	0.998585i	$0.483062\pi$
$632$		0			0
$633$			1.02640e27i			2.50024i
$634$		0			0
$635$	9.84233e25	−	9.35201e25i	0.232674	−	0.221083i
$636$		0			0
$637$		−	8.03591e25i		−	0.184379i
$638$		0			0
$639$	−6.49852e26			−1.44729
$640$		0			0
$641$	7.11047e26			1.53726			0.768630	−	0.639694i	$-0.220939\pi$
$641$	7.11047e26			1.53726			0.768630	+	0.639694i	$0.220939\pi$
$642$		0			0
$643$			2.33271e26i			0.489617i	0.969571	+	0.244809i	$0.0787252\pi$
$643$			2.33271e26i			0.489617i	−0.969571	+	0.244809i	$0.921275\pi$
$644$		0			0
$645$	−8.13911e26	−	8.56584e26i	−1.65867	−	1.74563i
$646$		0			0
$647$		−	4.09676e25i		−	0.0810681i	−0.999178	−	0.0405341i	$-0.987094\pi$
$647$		−	4.09676e25i		−	0.0810681i	0.999178	−	0.0405341i	$-0.0129059\pi$
$648$		0			0
$649$	3.04947e26			0.586004
$650$		0			0
$651$	−9.05080e26			−1.68915
$652$		0			0
$653$		−	9.92011e26i		−	1.79821i	−0.437730	−	0.899106i	$-0.644218\pi$
$653$		−	9.92011e26i		−	1.79821i	0.437730	−	0.899106i	$-0.355782\pi$
$654$		0			0
$655$	−2.24341e26	−	2.36103e26i	−0.395018	−	0.415729i
$656$		0			0
$657$		−	8.29905e26i		−	1.41957i
$658$		0			0
$659$	−4.05081e25			−0.0673178			−0.0336589	−	0.999433i	$-0.510716\pi$
$659$	−4.05081e25			−0.0673178			−0.0336589	+	0.999433i	$0.510716\pi$
$660$		0			0
$661$	−3.93464e26			−0.635317			−0.317659	−	0.948205i	$-0.602897\pi$
$661$	−3.93464e26			−0.635317			−0.317659	+	0.948205i	$0.602897\pi$
$662$		0			0
$663$			1.95250e26i			0.306346i
$664$		0			0
$665$	4.02124e26	−	3.82091e26i	0.613132	−	0.582588i
$666$		0			0
$667$			4.39273e25i			0.0650937i
$668$		0			0
$669$	−1.09323e27			−1.57457
$670$		0			0
$671$	−6.29870e26			−0.881835
$672$		0			0
$673$			9.36315e26i			1.27432i	0.770731	+	0.637161i	$0.219891\pi$
$673$			9.36315e26i			1.27432i	−0.770731	+	0.637161i	$0.780109\pi$
$674$		0			0
$675$	1.28087e26	+	6.54829e24i	0.169480	+	0.00866447i
$676$		0			0
$677$			1.38940e27i			1.78745i	0.448615	+	0.893725i	$0.351917\pi$
$677$			1.38940e27i			1.78745i	−0.448615	+	0.893725i	$0.648083\pi$
$678$		0			0
$679$	−3.48266e26			−0.435660
$680$		0			0
$681$	−6.86135e26			−0.834664
$682$		0			0
$683$		−	7.46696e26i		−	0.883379i	−0.897168	−	0.441689i	$-0.854379\pi$
$683$		−	7.46696e26i		−	0.883379i	0.897168	−	0.441689i	$-0.145621\pi$
$684$		0			0
$685$	1.01307e27	−	9.62605e26i	1.16568	−	1.10761i
$686$		0			0
$687$			1.75194e27i			1.96078i
$688$		0			0
$689$	−3.94573e25			−0.0429581
$690$		0			0
$691$	1.34374e27			1.42322			0.711612	−	0.702572i	$-0.247965\pi$
$691$	1.34374e27			1.42322			0.711612	+	0.702572i	$0.247965\pi$
$692$		0			0
$693$		−	5.83003e26i		−	0.600766i
$694$		0			0
$695$	1.28416e27	+	1.35148e27i	1.28755	+	1.35505i
$696$		0			0
$697$			1.62002e26i			0.158056i
$698$		0			0
$699$	2.20887e27			2.09718
$700$		0			0
$701$	−7.67269e26			−0.708968			−0.354484	−	0.935062i	$-0.615343\pi$
$701$	−7.67269e26			−0.708968			−0.354484	+	0.935062i	$0.615343\pi$
$702$		0			0
$703$			5.03516e26i			0.452832i
$704$		0			0
$705$	2.75740e26	+	2.90197e26i	0.241381	+	0.254037i
$706$		0			0
$707$		−	2.02662e26i		−	0.172698i
$708$		0			0
$709$	−1.12078e27			−0.929778			−0.464889	−	0.885369i	$-0.653906\pi$
$709$	−1.12078e27			−0.929778			−0.464889	+	0.885369i	$0.653906\pi$
$710$		0			0
$711$	−5.65964e26			−0.457117
$712$		0			0
$713$			1.25599e27i			0.987723i
$714$		0			0
$715$	1.50013e26	−	1.42539e26i	0.114874	−	0.109151i
$716$		0			0
$717$		−	1.88267e27i		−	1.40392i
$718$		0			0
$719$	4.32010e26			0.313740			0.156870	−	0.987619i	$-0.449860\pi$
$719$	4.32010e26			0.313740			0.156870	+	0.987619i	$0.449860\pi$
$720$		0			0
$721$	−1.59328e26			−0.112696
$722$		0			0
$723$		−	2.88881e27i		−	1.99024i
$724$		0			0
$725$	−4.84933e24	+	9.48548e25i	−0.00325440	+	0.0636573i
$726$		0			0
$727$		−	2.21678e25i		−	0.0144926i	−0.999974	−	0.00724628i	$-0.997693\pi$
$727$		−	2.21678e25i		−	0.0144926i	0.999974	−	0.00724628i	$-0.00230658\pi$
$728$		0			0
$729$	1.15988e27			0.738759
$730$		0			0
$731$	2.15043e27			1.33447
$732$		0			0
$733$		−	2.15813e26i		−	0.130494i	−0.997869	−	0.0652468i	$-0.979217\pi$
$733$		−	2.15813e26i		−	0.130494i	0.997869	−	0.0652468i	$-0.0207835\pi$
$734$		0			0
$735$	−1.05455e27	+	1.00201e27i	−0.621349	+	0.590395i
$736$		0			0
$737$		−	1.83763e27i		−	1.05515i
$738$		0			0
$739$	6.61344e26			0.370088			0.185044	−	0.982730i	$-0.440757\pi$
$739$	6.61344e26			0.370088			0.185044	+	0.982730i	$0.440757\pi$
$740$		0			0
$741$	4.90829e26			0.267705
$742$		0			0
$743$		−	1.52318e26i		−	0.0809763i	−0.999180	−	0.0404882i	$-0.987109\pi$
$743$		−	1.52318e26i		−	0.0809763i	0.999180	−	0.0404882i	$-0.0128913\pi$
$744$		0			0
$745$	2.04378e27	+	2.15094e27i	1.05913	+	1.11466i
$746$		0			0
$747$		−	1.78148e27i		−	0.899986i
$748$		0			0
$749$	3.28741e27			1.61911
$750$		0			0
$751$	3.37340e27			1.61990			0.809950	−	0.586498i	$-0.199494\pi$
$751$	3.37340e27			1.61990			0.809950	+	0.586498i	$0.199494\pi$
$752$		0			0
$753$		−	4.91918e27i		−	2.30325i
$754$		0			0
$755$	−1.56923e27	−	1.65150e27i	−0.716458	−	0.754022i
$756$		0			0
$757$			1.54430e26i			0.0687578i	0.999409	+	0.0343789i	$0.0109453\pi$
$757$			1.54430e26i			0.0687578i	−0.999409	+	0.0343789i	$0.989055\pi$
$758$		0			0
$759$	−1.73249e27			−0.752270
$760$		0			0
$761$	−3.62579e26			−0.153549			−0.0767747	−	0.997048i	$-0.524462\pi$
$761$	−3.62579e26			−0.153549			−0.0767747	+	0.997048i	$0.524462\pi$
$762$		0			0
$763$			1.08122e27i			0.446615i
$764$		0			0
$765$	1.19652e27	−	1.13691e27i	0.482100	−	0.458083i
$766$		0			0
$767$		−	8.16839e26i		−	0.321056i
$768$		0			0
$769$	1.92263e27			0.737218			0.368609	−	0.929584i	$-0.379834\pi$
$769$	1.92263e27			0.737218			0.368609	+	0.929584i	$0.379834\pi$
$770$		0			0
$771$	−1.37222e27			−0.513343
$772$		0			0
$773$			2.90361e27i			1.05982i	0.848053	+	0.529911i	$0.177775\pi$
$773$			2.90361e27i			1.05982i	−0.848053	+	0.529911i	$0.822225\pi$
$774$		0			0
$775$	−1.38654e26	+	2.71213e27i	−0.0493817	+	0.965926i
$776$		0			0
$777$		−	3.43057e27i		−	1.19225i
$778$		0			0
$779$	4.07249e26			0.138119
$780$		0			0
$781$	−2.68415e27			−0.888427
$782$		0			0
$783$		−	3.34841e25i		−	0.0108169i
$784$		0			0
$785$	−2.08825e27	+	1.98422e27i	−0.658447	+	0.625644i
$786$		0			0
$787$		−	2.86629e27i		−	0.882187i	−0.897461	−	0.441094i	$-0.854591\pi$
$787$		−	2.86629e27i		−	0.882187i	0.897461	−	0.441094i	$-0.145409\pi$
$788$		0			0
$789$	5.42066e27			1.62862
$790$		0			0
$791$	−5.69996e27			−1.67184
$792$		0			0
$793$			1.68718e27i			0.483134i
$794$		0			0
$795$	4.92000e26	+	5.17795e26i	0.137555	+	0.144767i
$796$		0			0
$797$			6.13305e27i			1.67426i	0.547005	+	0.837129i	$0.315768\pi$
$797$			6.13305e27i			1.67426i	−0.547005	+	0.837129i	$0.684232\pi$
$798$		0			0
$799$	−7.28530e26			−0.194202
$800$		0			0
$801$	−3.21735e27			−0.837509
$802$		0			0
$803$		−	3.42784e27i		−	0.871410i
$804$		0			0
$805$	3.61259e27	+	3.80200e27i	0.896929	+	0.943954i
$806$		0			0
$807$		−	7.46254e27i		−	1.80962i
$808$		0			0
$809$	−4.98029e26			−0.117963			−0.0589813	−	0.998259i	$-0.518785\pi$
$809$	−4.98029e26			−0.117963			−0.0589813	+	0.998259i	$0.518785\pi$
$810$		0			0
$811$	8.48208e27			1.96248			0.981238	−	0.192801i	$-0.0617571\pi$
$811$	8.48208e27			1.96248			0.981238	+	0.192801i	$0.0617571\pi$
$812$		0			0
$813$		−	3.18778e27i		−	0.720490i
$814$		0			0
$815$	2.43870e27	−	2.31721e27i	0.538469	−	0.511644i
$816$		0			0
$817$		−	5.40584e27i		−	1.16615i
$818$		0			0
$819$	−1.56164e27			−0.329143
$820$		0			0
$821$	5.82236e27			1.19906			0.599528	−	0.800354i	$-0.295355\pi$
$821$	5.82236e27			1.19906			0.599528	+	0.800354i	$0.295355\pi$
$822$		0			0
$823$			2.76066e27i			0.555539i	0.960648	+	0.277769i	$0.0895951\pi$
$823$			2.76066e27i			0.555539i	−0.960648	+	0.277769i	$0.910405\pi$
$824$		0			0
$825$	−3.74106e27	−	1.91257e26i	−0.735669	−	0.0376101i
$826$		0			0
$827$		−	7.77359e27i		−	1.49389i	−0.664885	−	0.746946i	$-0.731519\pi$
$827$		−	7.77359e27i		−	1.49389i	0.664885	−	0.746946i	$-0.268481\pi$
$828$		0			0
$829$	−5.84577e26			−0.109793			−0.0548963	−	0.998492i	$-0.517483\pi$
$829$	−5.84577e26			−0.109793			−0.0548963	+	0.998492i	$0.517483\pi$
$830$		0			0
$831$	−1.30136e28			−2.38884
$832$		0			0
$833$		−	2.64740e27i		−	0.474999i
$834$		0			0
$835$	2.37534e27	−	2.25701e27i	0.416586	−	0.395833i
$836$		0			0
$837$		−	9.57390e26i		−	0.164133i
$838$		0			0
$839$	−1.01089e27			−0.169421			−0.0847104	−	0.996406i	$-0.526997\pi$
$839$	−1.01089e27			−0.169421			−0.0847104	+	0.996406i	$0.526997\pi$
$840$		0			0
$841$	−6.07846e27			−0.995937
$842$		0			0
$843$			7.86294e27i			1.25957i
$844$		0			0
$845$	4.01608e27	+	4.22664e27i	0.629018	+	0.661997i
$846$		0			0
$847$			5.91767e27i			0.906271i
$848$		0			0
$849$	−1.25691e28			−1.88227
$850$		0			0
$851$	−4.76063e27			−0.697162
$852$		0			0
$853$		−	9.85920e26i		−	0.141197i	−0.997505	−	0.0705986i	$-0.977509\pi$
$853$		−	9.85920e26i		−	0.141197i	0.997505	−	0.0705986i	$-0.0224909\pi$
$854$		0			0
$855$	−2.85803e27	−	3.00787e27i	−0.400302	−	0.421290i
$856$		0			0
$857$		−	3.75260e27i		−	0.514061i	−0.966403	−	0.257030i	$-0.917256\pi$
$857$		−	3.75260e27i		−	0.514061i	0.966403	−	0.257030i	$-0.0827440\pi$
$858$		0			0
$859$	4.52630e27			0.606468			0.303234	−	0.952916i	$-0.401934\pi$
$859$	4.52630e27			0.606468			0.303234	+	0.952916i	$0.401934\pi$
$860$		0			0
$861$	−2.77468e27			−0.363650
$862$		0			0
$863$			1.15045e28i			1.47491i	0.675397	+	0.737454i	$0.263972\pi$
$863$			1.15045e28i			1.47491i	−0.675397	+	0.737454i	$0.736028\pi$
$864$		0			0
$865$	2.40051e27	−	2.28093e27i	0.301059	−	0.286061i
$866$		0			0
$867$		−	4.73129e27i		−	0.580495i
$868$		0			0
$869$	−2.33766e27			−0.280603
$870$		0			0
$871$	−4.92230e27			−0.578091
$872$		0			0
$873$			2.60502e27i			0.299347i
$874$		0			0
$875$	7.38116e27	+	8.60868e27i	0.829942	+	0.967966i
$876$		0			0
$877$		−	5.61761e27i		−	0.618096i	−0.951046	−	0.309048i	$-0.899990\pi$
$877$		−	5.61761e27i		−	0.618096i	0.951046	−	0.309048i	$-0.100010\pi$
$878$		0			0
$879$	1.36878e28			1.47380
$880$		0			0
$881$	1.84137e28			1.94031			0.970153	−	0.242492i	$-0.0779649\pi$
$881$	1.84137e28			1.94031			0.970153	+	0.242492i	$0.0779649\pi$
$882$		0			0
$883$			8.75205e27i			0.902574i	0.892379	+	0.451287i	$0.149035\pi$
$883$			8.75205e27i			0.902574i	−0.892379	+	0.451287i	$0.850965\pi$
$884$		0			0
$885$	−1.07193e28	+	1.01853e28i	−1.08195	+	1.02805i
$886$		0			0
$887$			1.23855e28i			1.22360i	0.791013	+	0.611799i	$0.209554\pi$
$887$			1.23855e28i			1.22360i	−0.791013	+	0.611799i	$0.790446\pi$
$888$		0			0
$889$	−4.23199e27			−0.409240
$890$		0			0
$891$	6.29815e27			0.596176
$892$		0			0
$893$			1.83141e27i			0.169706i
$894$		0			0
$895$	2.07459e27	+	2.18336e27i	0.188197	+	0.198065i
$896$		0			0
$897$			4.64068e27i			0.412149i
$898$		0			0
$899$	7.08994e26			0.0616489
$900$		0			0
$901$	−1.29991e27			−0.110669
$902$		0			0
$903$			3.68313e28i			3.07032i
$904$		0			0
$905$	1.26160e28	+	1.32775e28i	1.02982	+	1.08381i
$906$		0			0
$907$		−	3.19498e27i		−	0.255387i	−0.991814	−	0.127694i	$-0.959243\pi$
$907$		−	3.19498e27i		−	0.255387i	0.991814	−	0.127694i	$-0.0407574\pi$
$908$		0			0
$909$	−1.51590e27			−0.118663
$910$		0			0
$911$	−2.57209e28			−1.97179			−0.985896	−	0.167362i	$-0.946475\pi$
$911$	−2.57209e28			−1.97179			−0.985896	+	0.167362i	$0.946475\pi$
$912$		0			0
$913$		−	7.35823e27i		−	0.552460i
$914$		0			0
$915$	2.21408e28	−	2.10378e28i	1.62814	−	1.54703i
$916$		0			0
$917$			1.01519e28i			0.731207i
$918$		0			0
$919$	−1.15041e28			−0.811624			−0.405812	−	0.913957i	$-0.633011\pi$
$919$	−1.15041e28			−0.811624			−0.405812	+	0.913957i	$0.633011\pi$
$920$		0			0
$921$	−3.19618e28			−2.20884
$922$		0			0
$923$			7.18982e27i			0.486746i
$924$		0			0
$925$	−1.02799e28	−	5.25547e26i	−0.681778	−	0.0348550i
$926$		0			0
$927$			1.19177e27i			0.0774344i
$928$		0			0
$929$	6.84876e27			0.435976			0.217988	−	0.975951i	$-0.430051\pi$
$929$	6.84876e27			0.435976			0.217988	+	0.975951i	$0.430051\pi$
$930$		0			0
$931$	−6.65517e27			−0.415085
$932$		0			0
$933$		−	9.17105e27i		−	0.560459i
$934$		0			0
$935$	4.94211e27	−	4.69591e27i	0.295939	−	0.281196i
$936$		0			0
$937$			2.38924e28i			1.40196i	0.713183	+	0.700978i	$0.247253\pi$
$937$			2.38924e28i			1.40196i	−0.713183	+	0.700978i	$0.752747\pi$
$938$		0			0
$939$	2.52330e28			1.45093
$940$		0			0
$941$	−3.09356e28			−1.74324			−0.871621	−	0.490181i	$-0.836931\pi$
$941$	−3.09356e28			−1.74324			−0.871621	+	0.490181i	$0.836931\pi$
$942$		0			0
$943$			3.85045e27i			0.212643i
$944$		0			0
$945$	−2.75374e27	−	2.89811e27i	−0.149046	−	0.156860i
$946$		0			0
$947$		−	1.96100e28i		−	1.04029i	−0.854079	−	0.520144i	$-0.825878\pi$
$947$		−	1.96100e28i		−	1.04029i	0.854079	−	0.520144i	$-0.174122\pi$
$948$		0			0
$949$	−9.18188e27			−0.477422
$950$		0			0
$951$	−1.03465e28			−0.527325
$952$		0			0
$953$			5.52240e27i			0.275896i	0.990439	+	0.137948i	$0.0440507\pi$
$953$			5.52240e27i			0.275896i	−0.990439	+	0.137948i	$0.955949\pi$
$954$		0			0
$955$	−7.69809e27	−	8.10169e27i	−0.377008	−	0.396775i
$956$		0			0
$957$			9.77975e26i			0.0469531i
$958$		0			0
$959$	−4.35600e28			−2.05027
$960$		0			0
$961$	−1.39880e27			−0.0645482
$962$		0			0
$963$		−	2.45897e28i		−	1.11251i
$964$		0			0
$965$	6.61333e26	−	6.28386e26i	0.0293366	−	0.0278752i
$966$		0			0
$967$			1.58099e28i			0.687667i	0.939031	+	0.343833i	$0.111726\pi$
$967$			1.58099e28i			0.687667i	−0.939031	+	0.343833i	$0.888274\pi$
$968$		0			0
$969$	1.61702e28			0.689667
$970$		0			0
$971$	−2.23364e28			−0.934181			−0.467090	−	0.884210i	$-0.654698\pi$
$971$	−2.23364e28			−0.934181			−0.467090	+	0.884210i	$0.654698\pi$
$972$		0			0
$973$		−	5.81109e28i		−	2.38334i
$974$		0			0
$975$	−5.12305e26	+	1.00209e28i	−0.0206056	+	0.403054i
$976$		0			0
$977$			2.51328e28i			0.991385i	0.868498	+	0.495693i	$0.165086\pi$
$977$			2.51328e28i			0.991385i	−0.868498	+	0.495693i	$0.834914\pi$
$978$		0			0
$979$	−1.32889e28			−0.514109
$980$		0			0
$981$	8.08752e27			0.306874
$982$		0			0
$983$		−	8.32726e27i		−	0.309916i	−0.987921	−	0.154958i	$-0.950476\pi$
$983$		−	8.32726e27i		−	0.309916i	0.987921	−	0.154958i	$-0.0495242\pi$
$984$		0			0
$985$	2.21161e28	−	2.10143e28i	0.807353	−	0.767133i
$986$		0			0
$987$		−	1.24778e28i		−	0.446814i
$988$		0			0
$989$	5.11111e28			1.79536
$990$		0			0
$991$	−2.30436e28			−0.794055			−0.397028	−	0.917807i	$-0.629958\pi$
$991$	−2.30436e28			−0.794055			−0.397028	+	0.917807i	$0.629958\pi$
$992$		0			0
$993$		−	1.80544e28i		−	0.610329i
$994$		0			0
$995$	−2.73903e28	−	2.88263e28i	−0.908400	−	0.956027i
$996$		0			0
$997$		−	2.74239e28i		−	0.892331i	−0.894951	−	0.446165i	$-0.852789\pi$
$997$		−	2.74239e28i		−	0.892331i	0.894951	−	0.446165i	$-0.147211\pi$
$998$		0			0
$999$	3.62884e27			0.115850

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	80.20.c.d.49.5		28
4.3	odd	2		40.20.c.a.9.24	yes	28
5.4	even	2	inner	80.20.c.d.49.24		28
20.19	odd	2		40.20.c.a.9.5	✓	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
40.20.c.a.9.5	✓	28	20.19	odd	2
40.20.c.a.9.24	yes	28	4.3	odd	2
80.20.c.d.49.5		28	1.1	even	1	trivial
80.20.c.d.49.24		28	5.4	even	2	inner

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)

\(f(q)\)	\(=\)	\(q-46696.1i q^{3} +(3.00829e6 + 3.16602e6i) q^{5} -1.36132e8i q^{7} -1.01826e9 q^{9} +O(q^{10})\)	\(q-46696.1i q^{3} +(3.00829e6 + 3.16602e6i) q^{5} -1.36132e8i q^{7} -1.01826e9 q^{9} -4.20583e9 q^{11} +1.12658e10i q^{13} +(1.47841e11 - 1.40475e11i) q^{15} +3.71149e11i q^{17} +9.33011e11 q^{19} -6.35682e12 q^{21} +8.82142e12i q^{23} +(-9.73835e11 + 1.90486e13i) q^{25} -6.72423e12i q^{27} +4.97962e12 q^{29} +1.42379e14 q^{31} +1.96396e14i q^{33} +(4.30996e14 - 4.09525e14i) q^{35} +5.39667e14i q^{37} +5.26070e14 q^{39} +4.36489e14 q^{41} -5.79397e15i q^{43} +(-3.06323e15 - 3.22383e15i) q^{45} +1.96290e15i q^{47} -7.13300e15 q^{49} +1.73312e16 q^{51} +3.50239e15i q^{53} +(-1.26524e16 - 1.33157e16i) q^{55} -4.35680e16i q^{57} -7.25059e16 q^{59} +1.49761e17 q^{61} +1.38618e17i q^{63} +(-3.56678e16 + 3.38909e16i) q^{65} +4.36924e17i q^{67} +4.11926e17 q^{69} +6.38198e17 q^{71} +8.15021e17i q^{73} +(8.89495e17 + 4.54743e16i) q^{75} +5.72547e17i q^{77} +5.55814e17 q^{79} -1.49748e18 q^{81} +1.74953e18i q^{83} +(-1.17506e18 + 1.11652e18i) q^{85} -2.32529e17i q^{87} +3.15965e18 q^{89} +1.53364e18 q^{91} -6.64855e18i q^{93} +(2.80677e18 + 2.95393e18i) q^{95} -2.55830e18i q^{97} +4.28263e18 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - 3935164 q^{5} - 10352560732 q^{9}+O(q^{10}) \) 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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