LMFDB - Embedded newform 80.20.c.d.49.9

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			49.9
Character	$\chi$	$=$	80.49
Dual form			80.20.c.d.49.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-22508.3i q^{3} +(4.34396e6 + 451090. i) q^{5} +7.05814e7i q^{7} +6.55637e8 q^{9} +O(q^{10})$	\(q-22508.3i q^{3} +(4.34396e6 + 451090. i) q^{5} +7.05814e7i q^{7} +6.55637e8 q^{9} +6.97971e9 q^{11} -1.18686e9i q^{13} +(1.01533e10 - 9.77753e10i) q^{15} +3.61783e11i q^{17} +1.01175e12 q^{19} +1.58867e12 q^{21} -4.01739e12i q^{23} +(1.86665e13 + 3.91904e12i) q^{25} -4.09178e13i q^{27} +2.17099e13 q^{29} -4.40484e13 q^{31} -1.57102e14i q^{33} +(-3.18386e13 + 3.06603e14i) q^{35} -4.82533e14i q^{37} -2.67143e13 q^{39} +2.23161e15 q^{41} -2.91450e15i q^{43} +(2.84806e15 + 2.95751e14i) q^{45} +3.97991e15i q^{47} +6.41716e15 q^{49} +8.14313e15 q^{51} +3.11857e16i q^{53} +(3.03196e16 + 3.14848e15i) q^{55} -2.27729e16i q^{57} -1.09550e16 q^{59} -5.75192e16 q^{61} +4.62757e16i q^{63} +(5.35383e14 - 5.15569e15i) q^{65} +7.22598e16i q^{67} -9.04247e16 q^{69} -1.18022e17 q^{71} +5.97537e17i q^{73} +(8.82110e16 - 4.20152e17i) q^{75} +4.92638e17i q^{77} -1.14602e18 q^{79} -1.58971e17 q^{81} +9.93477e17i q^{83} +(-1.63197e17 + 1.57157e18i) q^{85} -4.88654e17i q^{87} +4.02911e18 q^{89} +8.37705e16 q^{91} +9.91455e17i q^{93} +(4.39501e18 + 4.56392e17i) q^{95} +1.07209e19i q^{97} +4.57615e18 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$		−	22508.3i		−	0.660224i	−0.943942	−	0.330112i	$-0.892913\pi$
$3$		−	22508.3i		−	0.660224i	0.943942	−	0.330112i	$-0.107087\pi$
$4$		0			0
$5$	4.34396e6	+	451090.i	0.994652	+	0.103288i
$5$	4.34396e6	+	451090.i	0.994652	+	0.103288i
$6$		0			0
$7$			7.05814e7i			0.661087i	0.943791	+	0.330544i	$0.107232\pi$
$7$			7.05814e7i			0.661087i	−0.943791	+	0.330544i	$0.892768\pi$
$8$		0			0
$9$	6.55637e8			0.564104
$10$		0			0
$11$	6.97971e9			0.892497			0.446249	−	0.894909i	$-0.352760\pi$
$11$	6.97971e9			0.892497			0.446249	+	0.894909i	$0.352760\pi$
$12$		0			0
$13$		−	1.18686e9i		−	0.0310412i	−0.999880	−	0.0155206i	$-0.995059\pi$
$13$		−	1.18686e9i		−	0.0310412i	0.999880	−	0.0155206i	$-0.00494057\pi$
$14$		0			0
$15$	1.01533e10	−	9.77753e10i	0.0681930	−	0.656693i
$16$		0			0
$17$			3.61783e11i			0.739918i	0.929048	+	0.369959i	$0.120628\pi$
$17$			3.61783e11i			0.739918i	−0.929048	+	0.369959i	$0.879372\pi$
$18$		0			0
$19$	1.01175e12			0.719308			0.359654	−	0.933086i	$-0.382895\pi$
$19$	1.01175e12			0.719308			0.359654	+	0.933086i	$0.382895\pi$
$20$		0			0
$21$	1.58867e12			0.436466
$22$		0			0
$23$		−	4.01739e12i		−	0.465082i	−0.972587	−	0.232541i	$-0.925296\pi$
$23$		−	4.01739e12i		−	0.465082i	0.972587	−	0.232541i	$-0.0747040\pi$
$24$		0			0
$25$	1.86665e13	+	3.91904e12i	0.978663	+	0.205471i
$26$		0			0
$27$		−	4.09178e13i		−	1.03266i
$28$		0			0
$29$	2.17099e13			0.277893			0.138946	−	0.990300i	$-0.455628\pi$
$29$	2.17099e13			0.277893			0.138946	+	0.990300i	$0.455628\pi$
$30$		0			0
$31$	−4.40484e13			−0.299222			−0.149611	−	0.988745i	$-0.547802\pi$
$31$	−4.40484e13			−0.299222			−0.149611	+	0.988745i	$0.547802\pi$
$32$		0			0
$33$		−	1.57102e14i		−	0.589248i
$34$		0			0
$35$	−3.18386e13	+	3.06603e14i	−0.0682822	+	0.657552i
$36$		0			0
$37$		−	4.82533e14i		−	0.610394i	−0.952289	−	0.305197i	$-0.901278\pi$
$37$		−	4.82533e14i		−	0.610394i	0.952289	−	0.305197i	$-0.0987224\pi$
$38$		0			0
$39$	−2.67143e13			−0.0204942
$40$		0			0
$41$	2.23161e15			1.06456			0.532281	−	0.846568i	$-0.321335\pi$
$41$	2.23161e15			1.06456			0.532281	+	0.846568i	$0.321335\pi$
$42$		0			0
$43$		−	2.91450e15i		−	0.884330i	−0.896934	−	0.442165i	$-0.854211\pi$
$43$		−	2.91450e15i		−	0.884330i	0.896934	−	0.442165i	$-0.145789\pi$
$44$		0			0
$45$	2.84806e15	+	2.95751e14i	0.561087	+	0.0582650i
$46$		0			0
$47$			3.97991e15i			0.518733i	0.965779	+	0.259366i	$0.0835137\pi$
$47$			3.97991e15i			0.518733i	−0.965779	+	0.259366i	$0.916486\pi$
$48$		0			0
$49$	6.41716e15			0.562964
$50$		0			0
$51$	8.14313e15			0.488512
$52$		0			0
$53$			3.11857e16i			1.29818i	0.760712	+	0.649089i	$0.224850\pi$
$53$			3.11857e16i			1.29818i	−0.760712	+	0.649089i	$0.775150\pi$
$54$		0			0
$55$	3.03196e16	+	3.14848e15i	0.887724	+	0.0921840i
$56$		0			0
$57$		−	2.27729e16i		−	0.474905i
$58$		0			0
$59$	−1.09550e16			−0.164633			−0.0823166	−	0.996606i	$-0.526232\pi$
$59$	−1.09550e16			−0.164633			−0.0823166	+	0.996606i	$0.526232\pi$
$60$		0			0
$61$	−5.75192e16			−0.629766			−0.314883	−	0.949130i	$-0.601965\pi$
$61$	−5.75192e16			−0.629766			−0.314883	+	0.949130i	$0.601965\pi$
$62$		0			0
$63$			4.62757e16i			0.372922i
$64$		0			0
$65$	5.35383e14	−	5.15569e15i	0.00320618	−	0.0308752i
$66$		0			0
$67$			7.22598e16i			0.324479i	0.986751	+	0.162239i	$0.0518717\pi$
$67$			7.22598e16i			0.324479i	−0.986751	+	0.162239i	$0.948128\pi$
$68$		0			0
$69$	−9.04247e16			−0.307058
$70$		0			0
$71$	−1.18022e17			−0.305497			−0.152749	−	0.988265i	$-0.548812\pi$
$71$	−1.18022e17			−0.305497			−0.152749	+	0.988265i	$0.548812\pi$
$72$		0			0
$73$			5.97537e17i			1.18795i	0.804484	+	0.593975i	$0.202442\pi$
$73$			5.97537e17i			1.18795i	−0.804484	+	0.593975i	$0.797558\pi$
$74$		0			0
$75$	8.82110e16	−	4.20152e17i	0.135657	−	0.646137i
$76$		0			0
$77$			4.92638e17i			0.590019i
$78$		0			0
$79$	−1.14602e18			−1.07581			−0.537903	−	0.843007i	$-0.680783\pi$
$79$	−1.14602e18			−1.07581			−0.537903	+	0.843007i	$0.680783\pi$
$80$		0			0
$81$	−1.58971e17			−0.117682
$82$		0			0
$83$			9.93477e17i			0.583332i	0.956520	+	0.291666i	$0.0942096\pi$
$83$			9.93477e17i			0.583332i	−0.956520	+	0.291666i	$0.905790\pi$
$84$		0			0
$85$	−1.63197e17	+	1.57157e18i	−0.0764244	+	0.735960i
$86$		0			0
$87$		−	4.88654e17i		−	0.183471i
$88$		0			0
$89$	4.02911e18			1.21900			0.609501	−	0.792786i	$-0.291370\pi$
$89$	4.02911e18			1.21900			0.609501	+	0.792786i	$0.291370\pi$
$90$		0			0
$91$	8.37705e16			0.0205210
$92$		0			0
$93$			9.91455e17i			0.197554i
$94$		0			0
$95$	4.39501e18	+	4.56392e17i	0.715461	+	0.0742957i
$96$		0			0
$97$			1.07209e19i			1.43186i	0.698174	+	0.715928i	$0.253996\pi$
$97$			1.07209e19i			1.43186i	−0.698174	+	0.715928i	$0.746004\pi$
$98$		0			0
$99$	4.57615e18			0.503462
$100$		0			0
$101$	−5.70070e18			−0.518651			−0.259325	−	0.965790i	$-0.583500\pi$
$101$	−5.70070e18			−0.518651			−0.259325	+	0.965790i	$0.583500\pi$
$102$		0			0
$103$		−	2.10155e19i		−	1.58704i	−0.608546	−	0.793518i	$-0.708247\pi$
$103$		−	2.10155e19i		−	1.58704i	0.608546	−	0.793518i	$-0.291753\pi$
$104$		0			0
$105$	6.90112e18	+	7.16633e17i	0.434131	+	0.0450815i
$106$		0			0
$107$		−	3.07494e19i		−	1.61693i	−0.588546	−	0.808464i	$-0.700299\pi$
$107$		−	3.07494e19i		−	1.61693i	0.588546	−	0.808464i	$-0.299701\pi$
$108$		0			0
$109$	−3.23163e18			−0.142518			−0.0712589	−	0.997458i	$-0.522702\pi$
$109$	−3.23163e18			−0.142518			−0.0712589	+	0.997458i	$0.522702\pi$
$110$		0			0
$111$	−1.08610e19			−0.402997
$112$		0			0
$113$			4.30834e19i			1.34916i	0.738200	+	0.674582i	$0.235676\pi$
$113$			4.30834e19i			1.34916i	−0.738200	+	0.674582i	$0.764324\pi$
$114$		0			0
$115$	1.81221e18	−	1.74514e19i	0.0480372	−	0.462594i
$116$		0			0
$117$		−	7.78152e17i		−	0.0175105i
$118$		0			0
$119$	−2.55352e19			−0.489150
$120$		0			0
$121$	−1.24427e19			−0.203448
$122$		0			0
$123$		−	5.02297e19i		−	0.702849i
$124$		0			0
$125$	7.93188e19	+	2.54444e19i	0.952206	+	0.305455i
$126$		0			0
$127$		−	6.12778e19i		−	0.632657i	−0.948650	−	0.316328i	$-0.897550\pi$
$127$		−	6.12778e19i		−	0.632657i	0.948650	−	0.316328i	$-0.102450\pi$
$128$		0			0
$129$	−6.56006e19			−0.583856
$130$		0			0
$131$	−5.36675e19			−0.412699			−0.206350	−	0.978478i	$-0.566158\pi$
$131$	−5.36675e19			−0.412699			−0.206350	+	0.978478i	$0.566158\pi$
$132$		0			0
$133$			7.14109e19i			0.475526i
$134$		0			0
$135$	1.84576e19	−	1.77746e20i	0.106661	−	1.02714i
$136$		0			0
$137$			1.86444e20i			0.936922i	0.883484	+	0.468461i	$0.155191\pi$
$137$			1.86444e20i			0.936922i	−0.883484	+	0.468461i	$0.844809\pi$
$138$		0			0
$139$	−7.89872e19			−0.345873			−0.172936	−	0.984933i	$-0.555325\pi$
$139$	−7.89872e19			−0.345873			−0.172936	+	0.984933i	$0.555325\pi$
$140$		0			0
$141$	8.95812e19			0.342480
$142$		0			0
$143$		−	8.28397e18i		−	0.0277042i
$144$		0			0
$145$	9.43071e19	+	9.79314e18i	0.276406	+	0.0287029i
$146$		0			0
$147$		−	1.44440e20i		−	0.371682i
$148$		0			0
$149$	3.13441e19			0.0709393			0.0354696	−	0.999371i	$-0.488707\pi$
$149$	3.13441e19			0.0709393			0.0354696	+	0.999371i	$0.488707\pi$
$150$		0			0
$151$	9.44890e20			1.88408			0.942042	−	0.335496i	$-0.108904\pi$
$151$	9.44890e20			1.88408			0.942042	+	0.335496i	$0.108904\pi$
$152$		0			0
$153$			2.37198e20i			0.417391i
$154$		0			0
$155$	−1.91344e20	−	1.98698e19i	−0.297622	−	0.0309060i
$156$		0			0
$157$		−	7.52962e20i		−	1.03688i	−0.855115	−	0.518438i	$-0.826514\pi$
$157$		−	7.52962e20i		−	1.03688i	0.855115	−	0.518438i	$-0.173486\pi$
$158$		0			0
$159$	7.01937e20			0.857089
$160$		0			0
$161$	2.83553e20			0.307460
$162$		0			0
$163$			1.50887e21i			1.45502i	0.686095	+	0.727512i	$0.259324\pi$
$163$			1.50887e21i			1.45502i	−0.686095	+	0.727512i	$0.740676\pi$
$164$		0			0
$165$	7.08670e19	−	6.82444e20i	0.0608621	−	0.586097i
$166$		0			0
$167$			5.95618e20i			0.456206i	0.973637	+	0.228103i	$0.0732523\pi$
$167$			5.95618e20i			0.456206i	−0.973637	+	0.228103i	$0.926748\pi$
$168$		0			0
$169$	1.46051e21			0.999036
$170$		0			0
$171$	6.63342e20			0.405765
$172$		0			0
$173$			7.43625e20i			0.407301i	0.979044	+	0.203651i	$0.0652807\pi$
$173$			7.43625e20i			0.407301i	−0.979044	+	0.203651i	$0.934719\pi$
$174$		0			0
$175$	−2.76611e20	+	1.31751e21i	−0.135834	+	0.646982i
$176$		0			0
$177$			2.46578e20i			0.108695i
$178$		0			0
$179$	−3.13936e21			−1.24376			−0.621881	−	0.783111i	$-0.713631\pi$
$179$	−3.13936e21			−1.24376			−0.621881	+	0.783111i	$0.713631\pi$
$180$		0			0
$181$	−1.52540e21			−0.543796			−0.271898	−	0.962326i	$-0.587651\pi$
$181$	−1.52540e21			−0.543796			−0.271898	+	0.962326i	$0.587651\pi$
$182$		0			0
$183$			1.29466e21i			0.415787i
$184$		0			0
$185$	2.17666e20	−	2.09610e21i	0.0630462	−	0.607130i
$186$		0			0
$187$			2.52514e21i			0.660375i
$188$		0			0
$189$	2.88804e21			0.682678
$190$		0			0
$191$	7.02231e21			1.50198			0.750988	−	0.660316i	$-0.229578\pi$
$191$	7.02231e21			1.50198			0.750988	+	0.660316i	$0.229578\pi$
$192$		0			0
$193$		−	7.95648e21i		−	1.54144i	−0.637174	−	0.770720i	$-0.719897\pi$
$193$		−	7.95648e21i		−	1.54144i	0.637174	−	0.770720i	$-0.280103\pi$
$194$		0			0
$195$	−1.16046e20	−	1.20506e19i	−0.0203846	−	0.00211680i
$196$		0			0
$197$		−	7.80386e21i		−	1.24417i	−0.782949	−	0.622086i	$-0.786285\pi$
$197$		−	7.80386e21i		−	1.24417i	0.782949	−	0.622086i	$-0.213715\pi$
$198$		0			0
$199$	1.16760e22			1.69117			0.845587	−	0.533838i	$-0.179251\pi$
$199$	1.16760e22			1.69117			0.845587	+	0.533838i	$0.179251\pi$
$200$		0			0
$201$	1.62645e21			0.214229
$202$		0			0
$203$			1.53232e21i			0.183711i
$204$		0			0
$205$	9.69401e21	+	1.00666e21i	1.05887	+	0.109956i
$206$		0			0
$207$		−	2.63395e21i		−	0.262355i
$208$		0			0
$209$	7.06174e21			0.641981
$210$		0			0
$211$	9.08045e21			0.754091			0.377046	−	0.926195i	$-0.376940\pi$
$211$	9.08045e21			0.754091			0.377046	+	0.926195i	$0.376940\pi$
$212$		0			0
$213$			2.65647e21i			0.201697i
$214$		0			0
$215$	1.31471e21	−	1.26605e22i	0.0913404	−	0.879600i
$216$		0			0
$217$		−	3.10900e21i		−	0.197812i
$218$		0			0
$219$	1.34496e22			0.784313
$220$		0			0
$221$	4.29387e20			0.0229680
$222$		0			0
$223$		−	1.90916e21i		−	0.0937445i	−0.998901	−	0.0468723i	$-0.985075\pi$
$223$		−	1.90916e21i		−	0.0937445i	0.998901	−	0.0468723i	$-0.0149254\pi$
$224$		0			0
$225$	1.22385e22	+	2.56947e21i	0.552068	+	0.115907i
$226$		0			0
$227$		−	2.03319e22i		−	0.843202i	−0.906782	−	0.421601i	$-0.861468\pi$
$227$		−	2.03319e22i		−	0.843202i	0.906782	−	0.421601i	$-0.138532\pi$
$228$		0			0
$229$	3.56430e22			1.35999			0.679997	−	0.733214i	$-0.261981\pi$
$229$	3.56430e22			1.35999			0.679997	+	0.733214i	$0.261981\pi$
$230$		0			0
$231$	1.10885e22			0.389545
$232$		0			0
$233$			3.66502e22i			1.18630i	0.805092	+	0.593151i	$0.202116\pi$
$233$			3.66502e22i			1.18630i	−0.805092	+	0.593151i	$0.797884\pi$
$234$		0			0
$235$	−1.79530e21	+	1.72886e22i	−0.0535787	+	0.515959i
$236$		0			0
$237$			2.57949e22i			0.710273i
$238$		0			0
$239$	1.77590e22			0.451479			0.225740	−	0.974188i	$-0.427520\pi$
$239$	1.77590e22			0.451479			0.225740	+	0.974188i	$0.427520\pi$
$240$		0			0
$241$	2.90100e22			0.681374			0.340687	−	0.940177i	$-0.389340\pi$
$241$	2.90100e22			0.681374			0.340687	+	0.940177i	$0.389340\pi$
$242$		0			0
$243$		−	4.39791e22i		−	0.954963i
$244$		0			0
$245$	2.78759e22	+	2.89472e21i	0.559953	+	0.0581472i
$246$		0			0
$247$		−	1.20081e21i		−	0.0223282i
$248$		0			0
$249$	2.23615e22			0.385130
$250$		0			0
$251$	3.23501e22			0.516387			0.258194	−	0.966093i	$-0.416873\pi$
$251$	3.23501e22			0.516387			0.258194	+	0.966093i	$0.416873\pi$
$252$		0			0
$253$		−	2.80402e22i		−	0.415084i
$254$		0			0
$255$	3.53735e22	+	3.67329e21i	0.485899	+	0.0504572i
$256$		0			0
$257$			7.60208e22i			0.969544i	0.874641	+	0.484772i	$0.161097\pi$
$257$			7.60208e22i			0.969544i	−0.874641	+	0.484772i	$0.838903\pi$
$258$		0			0
$259$	3.40578e22			0.403524
$260$		0			0
$261$	1.42338e22			0.156760
$262$		0			0
$263$		−	8.19776e22i		−	0.839683i	−0.907597	−	0.419842i	$-0.862086\pi$
$263$		−	8.19776e22i		−	0.839683i	0.907597	−	0.419842i	$-0.137914\pi$
$264$		0			0
$265$	−1.40676e22	+	1.35469e23i	−0.134086	+	1.29124i
$266$		0			0
$267$		−	9.06885e22i		−	0.804814i
$268$		0			0
$269$	4.50666e21			0.0372570			0.0186285	−	0.999826i	$-0.494070\pi$
$269$	4.50666e21			0.0372570			0.0186285	+	0.999826i	$0.494070\pi$
$270$		0			0
$271$	7.71387e22			0.594380			0.297190	−	0.954818i	$-0.403951\pi$
$271$	7.71387e22			0.594380			0.297190	+	0.954818i	$0.403951\pi$
$272$		0			0
$273$		−	1.88553e21i		−	0.0135484i
$274$		0			0
$275$	1.30287e23	+	2.73538e22i	0.873455	+	0.183382i
$276$		0			0
$277$		−	7.07096e22i		−	0.442507i	−0.975216	−	0.221254i	$-0.928985\pi$
$277$		−	7.07096e22i		−	0.442507i	0.975216	−	0.221254i	$-0.0710149\pi$
$278$		0			0
$279$	−2.88797e22			−0.168793
$280$		0			0
$281$	3.09768e23			1.69171			0.845857	−	0.533409i	$-0.179089\pi$
$281$	3.09768e23			1.69171			0.845857	+	0.533409i	$0.179089\pi$
$282$		0			0
$283$			1.55115e23i			0.791924i	0.918267	+	0.395962i	$0.129589\pi$
$283$			1.55115e23i			0.791924i	−0.918267	+	0.395962i	$0.870411\pi$
$284$		0			0
$285$	1.02726e22	−	9.89244e22i	0.0490518	−	0.472365i
$286$		0			0
$287$			1.57510e23i			0.703768i
$288$		0			0
$289$	1.08185e23			0.452522
$290$		0			0
$291$	2.41309e23			0.945346
$292$		0			0
$293$		−	3.29580e23i		−	1.20981i	−0.796296	−	0.604907i	$-0.793210\pi$
$293$		−	3.29580e23i		−	1.20981i	0.796296	−	0.604907i	$-0.206790\pi$
$294$		0			0
$295$	−4.75880e22	−	4.94168e21i	−0.163753	−	0.0170046i
$296$		0			0
$297$		−	2.85595e23i		−	0.921646i
$298$		0			0
$299$	−4.76809e21			−0.0144367
$300$		0			0
$301$	2.05710e23			0.584619
$302$		0			0
$303$			1.28313e23i			0.342426i
$304$		0			0
$305$	−2.49861e23	−	2.59464e22i	−0.626398	−	0.0650471i
$306$		0			0
$307$		−	1.68067e23i		−	0.395975i	−0.980205	−	0.197987i	$-0.936560\pi$
$307$		−	1.68067e23i		−	0.395975i	0.980205	−	0.197987i	$-0.0634405\pi$
$308$		0			0
$309$	−4.73025e23			−1.04780
$310$		0			0
$311$	−8.21014e23			−1.71051			−0.855257	−	0.518204i	$-0.826601\pi$
$311$	−8.21014e23			−1.71051			−0.855257	+	0.518204i	$0.826601\pi$
$312$		0			0
$313$			2.92333e23i			0.573068i	0.958070	+	0.286534i	$0.0925032\pi$
$313$			2.92333e23i			0.573068i	−0.958070	+	0.286534i	$0.907497\pi$
$314$		0			0
$315$	−2.08745e22	+	2.01020e23i	−0.0385183	+	0.370928i
$316$		0			0
$317$		−	9.45142e23i		−	1.64223i	−0.570762	−	0.821115i	$-0.693352\pi$
$317$		−	9.45142e23i		−	1.64223i	0.570762	−	0.821115i	$-0.306648\pi$
$318$		0			0
$319$	1.51529e23			0.248019
$320$		0			0
$321$	−6.92117e23			−1.06753
$322$		0			0
$323$			3.66035e23i			0.532229i
$324$		0			0
$325$	4.65137e21	−	2.21546e22i	0.00637806	−	0.0303789i
$326$		0			0
$327$			7.27385e22i			0.0940937i
$328$		0			0
$329$	−2.80908e23			−0.342928
$330$		0			0
$331$	−7.61258e23			−0.877336			−0.438668	−	0.898649i	$-0.644549\pi$
$331$	−7.61258e23			−0.877336			−0.438668	+	0.898649i	$0.644549\pi$
$332$		0			0
$333$		−	3.16366e23i		−	0.344326i
$334$		0			0
$335$	−3.25957e22	+	3.13894e23i	−0.0335147	+	0.322743i
$336$		0			0
$337$			7.89860e23i			0.767478i	0.923442	+	0.383739i	$0.125364\pi$
$337$			7.89860e23i			0.767478i	−0.923442	+	0.383739i	$0.874636\pi$
$338$		0			0
$339$	9.69736e23			0.890751
$340$		0			0
$341$	−3.07445e23			−0.267055
$342$		0			0
$343$			1.25748e24i			1.03326i
$344$		0			0
$345$	−3.92801e23	−	4.07897e22i	−0.305416	−	0.0317153i
$346$		0			0
$347$		−	3.50264e23i		−	0.257789i	−0.991658	−	0.128895i	$-0.958857\pi$
$347$		−	3.50264e23i		−	0.257789i	0.991658	−	0.128895i	$-0.0411429\pi$
$348$		0			0
$349$	−1.12993e23			−0.0787427			−0.0393713	−	0.999225i	$-0.512536\pi$
$349$	−1.12993e23			−0.0787427			−0.0393713	+	0.999225i	$0.512536\pi$
$350$		0			0
$351$	−4.85639e22			−0.0320550
$352$		0			0
$353$			7.33053e23i			0.458433i	0.973375	+	0.229217i	$0.0736164\pi$
$353$			7.33053e23i			0.458433i	−0.973375	+	0.229217i	$0.926384\pi$
$354$		0			0
$355$	−5.12681e23	−	5.32384e22i	−0.303863	−	0.0315541i
$356$		0			0
$357$			5.74754e23i			0.322949i
$358$		0			0
$359$	−2.27478e24			−1.21211			−0.606056	−	0.795422i	$-0.707249\pi$
$359$	−2.27478e24			−1.21211			−0.606056	+	0.795422i	$0.707249\pi$
$360$		0			0
$361$	−9.54777e23			−0.482596
$362$		0			0
$363$			2.80065e23i			0.134321i
$364$		0			0
$365$	−2.69543e23	+	2.59568e24i	−0.122701	+	1.18160i
$366$		0			0
$367$		−	3.26196e24i		−	1.40978i	−0.709316	−	0.704890i	$-0.750996\pi$
$367$		−	3.26196e24i		−	1.40978i	0.709316	−	0.704890i	$-0.249004\pi$
$368$		0			0
$369$	1.46312e24			0.600524
$370$		0			0
$371$	−2.20113e24			−0.858209
$372$		0			0
$373$			1.77528e24i			0.657709i	0.944381	+	0.328855i	$0.106663\pi$
$373$			1.77528e24i			0.657709i	−0.944381	+	0.328855i	$0.893337\pi$
$374$		0			0
$375$	5.72712e23	−	1.78533e24i	0.201669	−	0.628670i
$376$		0			0
$377$		−	2.57667e22i		−	0.00862614i
$378$		0			0
$379$	−4.51524e24			−1.43750			−0.718752	−	0.695267i	$-0.755286\pi$
$379$	−4.51524e24			−1.43750			−0.718752	+	0.695267i	$0.755286\pi$
$380$		0			0
$381$	−1.37926e24			−0.417695
$382$		0			0
$383$		−	3.02571e23i		−	0.0871844i	−0.999049	−	0.0435922i	$-0.986120\pi$
$383$		−	3.02571e23i		−	0.0871844i	0.999049	−	0.0435922i	$-0.0138802\pi$
$384$		0			0
$385$	−2.22224e23	+	2.14000e24i	−0.0609417	+	0.586863i
$386$		0			0
$387$		−	1.91086e24i		−	0.498854i
$388$		0			0
$389$	−6.27798e24			−1.56063			−0.780313	−	0.625389i	$-0.784940\pi$
$389$	−6.27798e24			−1.56063			−0.780313	+	0.625389i	$0.784940\pi$
$390$		0			0
$391$	1.45342e24			0.344122
$392$		0			0
$393$			1.20796e24i			0.272474i
$394$		0			0
$395$	−4.97825e24	−	5.16957e23i	−1.07005	−	0.111117i
$396$		0			0
$397$		−	3.61967e24i		−	0.741582i	−0.928716	−	0.370791i	$-0.879087\pi$
$397$		−	3.61967e24i		−	0.741582i	0.928716	−	0.370791i	$-0.120913\pi$
$398$		0			0
$399$	1.60734e24			0.313953
$400$		0			0
$401$	−6.66605e24			−1.24164			−0.620822	−	0.783951i	$-0.713201\pi$
$401$	−6.66605e24			−1.24164			−0.620822	+	0.783951i	$0.713201\pi$
$402$		0			0
$403$			5.22794e22i			0.00928823i
$404$		0			0
$405$	−6.90565e23	−	7.17104e22i	−0.117053	−	0.0121551i
$406$		0			0
$407$		−	3.36794e24i		−	0.544775i
$408$		0			0
$409$	2.06875e24			0.319401			0.159701	−	0.987165i	$-0.448947\pi$
$409$	2.06875e24			0.319401			0.159701	+	0.987165i	$0.448947\pi$
$410$		0			0
$411$	4.19655e24			0.618579
$412$		0			0
$413$		−	7.73217e23i		−	0.108837i
$414$		0			0
$415$	−4.48148e23	+	4.31563e24i	−0.0602510	+	0.580212i
$416$		0			0
$417$			1.77787e24i			0.228353i
$418$		0			0
$419$	−7.04437e24			−0.864588			−0.432294	−	0.901733i	$-0.642296\pi$
$419$	−7.04437e24			−0.864588			−0.432294	+	0.901733i	$0.642296\pi$
$420$		0			0
$421$	4.28708e24			0.502900			0.251450	−	0.967870i	$-0.419093\pi$
$421$	4.28708e24			0.502900			0.251450	+	0.967870i	$0.419093\pi$
$422$		0			0
$423$			2.60938e24i			0.292619i
$424$		0			0
$425$	−1.41784e24	+	6.75323e24i	−0.152031	+	0.724130i
$426$		0			0
$427$		−	4.05979e24i		−	0.416331i
$428$		0			0
$429$	−1.86458e23			−0.0182910
$430$		0			0
$431$	−3.20930e23			−0.0301215			−0.0150607	−	0.999887i	$-0.504794\pi$
$431$	−3.20930e23			−0.0301215			−0.0150607	+	0.999887i	$0.504794\pi$
$432$		0			0
$433$		−	1.72040e25i		−	1.54524i	−0.634872	−	0.772618i	$-0.718947\pi$
$433$		−	1.72040e25i		−	1.54524i	0.634872	−	0.772618i	$-0.281053\pi$
$434$		0			0
$435$	2.20427e23	−	2.12269e24i	0.0189503	−	0.182490i
$436$		0			0
$437$		−	4.06460e24i		−	0.334537i
$438$		0			0
$439$	8.60936e24			0.678513			0.339256	−	0.940694i	$-0.389825\pi$
$439$	8.60936e24			0.678513			0.339256	+	0.940694i	$0.389825\pi$
$440$		0			0
$441$	4.20733e24			0.317570
$442$		0			0
$443$			1.87520e25i			1.35585i	0.735131	+	0.677925i	$0.237120\pi$
$443$			1.87520e25i			1.35585i	−0.735131	+	0.677925i	$0.762880\pi$
$444$		0			0
$445$	1.75023e25	+	1.81749e24i	1.21248	+	0.125908i
$446$		0			0
$447$		−	7.05504e23i		−	0.0468358i
$448$		0			0
$449$	5.20005e24			0.330878			0.165439	−	0.986220i	$-0.447096\pi$
$449$	5.20005e24			0.330878			0.165439	+	0.986220i	$0.447096\pi$
$450$		0			0
$451$	1.55760e25			0.950119
$452$		0			0
$453$		−	2.12679e25i		−	1.24392i
$454$		0			0
$455$	3.63896e23	+	3.77881e22i	0.0204112	+	0.00211956i
$456$		0			0
$457$		−	1.28310e25i		−	0.690327i	−0.938543	−	0.345164i	$-0.887823\pi$
$457$		−	1.28310e25i		−	0.690327i	0.938543	−	0.345164i	$-0.112177\pi$
$458$		0			0
$459$	1.48034e25			0.764083
$460$		0			0
$461$	6.32944e24			0.313478			0.156739	−	0.987640i	$-0.449902\pi$
$461$	6.32944e24			0.313478			0.156739	+	0.987640i	$0.449902\pi$
$462$		0			0
$463$			3.06484e25i			1.45676i	0.685173	+	0.728380i	$0.259727\pi$
$463$			3.06484e25i			1.45676i	−0.685173	+	0.728380i	$0.740273\pi$
$464$		0			0
$465$	−4.47236e23	+	4.30684e24i	−0.0204049	+	0.196497i
$466$		0			0
$467$			1.63484e25i			0.716084i	0.933705	+	0.358042i	$0.116556\pi$
$467$			1.63484e25i			0.716084i	−0.933705	+	0.358042i	$0.883444\pi$
$468$		0			0
$469$	−5.10020e24			−0.214509
$470$		0			0
$471$	−1.69479e25			−0.684570
$472$		0			0
$473$		−	2.03424e25i		−	0.789262i
$474$		0			0
$475$	1.88859e25	+	3.96510e24i	0.703961	+	0.147797i
$476$		0			0
$477$			2.04465e25i			0.732308i
$478$		0			0
$479$	−1.86744e24			−0.0642774			−0.0321387	−	0.999483i	$-0.510232\pi$
$479$	−1.86744e24			−0.0642774			−0.0321387	+	0.999483i	$0.510232\pi$
$480$		0			0
$481$	−5.72701e23			−0.0189474
$482$		0			0
$483$		−	6.38230e24i		−	0.202992i
$484$		0			0
$485$	−4.83609e24	+	4.65712e25i	−0.147893	+	1.42420i
$486$		0			0
$487$		−	2.43751e25i		−	0.716837i	−0.933561	−	0.358419i	$-0.883316\pi$
$487$		−	2.43751e25i		−	0.716837i	0.933561	−	0.358419i	$-0.116684\pi$
$488$		0			0
$489$	3.39622e25			0.960642
$490$		0			0
$491$	3.22918e25			0.878655			0.439327	−	0.898327i	$-0.355217\pi$
$491$	3.22918e25			0.878655			0.439327	+	0.898327i	$0.355217\pi$
$492$		0			0
$493$			7.85428e24i			0.205618i
$494$		0			0
$495$	1.98786e25	+	2.06426e24i	0.500769	+	0.0520014i
$496$		0			0
$497$		−	8.33013e24i		−	0.201960i
$498$		0			0
$499$	3.66392e25			0.855050			0.427525	−	0.904004i	$-0.359386\pi$
$499$	3.66392e25			0.855050			0.427525	+	0.904004i	$0.359386\pi$
$500$		0			0
$501$	1.34064e25			0.301198
$502$		0			0
$503$			1.16411e25i			0.251824i	0.992041	+	0.125912i	$0.0401857\pi$
$503$			1.16411e25i			0.251824i	−0.992041	+	0.125912i	$0.959814\pi$
$504$		0			0
$505$	−2.47636e25	−	2.57153e24i	−0.515877	−	0.0535702i
$506$		0			0
$507$		−	3.28737e25i		−	0.659588i
$508$		0			0
$509$	3.37945e25			0.653172			0.326586	−	0.945168i	$-0.394102\pi$
$509$	3.37945e25			0.653172			0.326586	+	0.945168i	$0.394102\pi$
$510$		0			0
$511$	−4.21750e25			−0.785338
$512$		0			0
$513$		−	4.13987e25i		−	0.742800i
$514$		0			0
$515$	9.47991e24	−	9.12907e25i	0.163921	−	1.57855i
$516$		0			0
$517$			2.77786e25i			0.462968i
$518$		0			0
$519$	1.67378e25			0.268910
$520$		0			0
$521$	6.32307e25			0.979421			0.489711	−	0.871885i	$-0.337102\pi$
$521$	6.32307e25			0.979421			0.489711	+	0.871885i	$0.337102\pi$
$522$		0			0
$523$			5.04142e25i			0.752986i	0.926419	+	0.376493i	$0.122870\pi$
$523$			5.04142e25i			0.752986i	−0.926419	+	0.376493i	$0.877130\pi$
$524$		0			0
$525$	2.96549e25	+	6.22606e24i	0.427153	+	0.0896808i
$526$		0			0
$527$		−	1.59360e25i		−	0.221400i
$528$		0			0
$529$	5.84761e25			0.783699
$530$		0			0
$531$	−7.18248e24			−0.0928703
$532$		0			0
$533$		−	2.64861e24i		−	0.0330453i
$534$		0			0
$535$	1.38708e25	−	1.33574e26i	0.167009	−	1.60828i
$536$		0			0
$537$			7.06618e25i			0.821162i
$538$		0			0
$539$	4.47899e25			0.502444
$540$		0			0
$541$	2.70919e25			0.293404			0.146702	−	0.989181i	$-0.453134\pi$
$541$	2.70919e25			0.293404			0.146702	+	0.989181i	$0.453134\pi$
$542$		0			0
$543$			3.43341e25i			0.359027i
$544$		0			0
$545$	−1.40381e25	−	1.45776e24i	−0.141756	−	0.0147203i
$546$		0			0
$547$		−	1.88673e26i		−	1.84005i	−0.391855	−	0.920027i	$-0.628166\pi$
$547$		−	1.88673e26i		−	1.84005i	0.391855	−	0.920027i	$-0.371834\pi$
$548$		0			0
$549$	−3.77117e25			−0.355254
$550$		0			0
$551$	2.19651e25			0.199891
$552$		0			0
$553$		−	8.08875e25i		−	0.711201i
$554$		0			0
$555$	−4.71798e25	−	4.89930e24i	−0.400842	−	0.0416246i
$556$		0			0
$557$			6.06520e25i			0.497991i	0.968505	+	0.248995i	$0.0801004\pi$
$557$			6.06520e25i			0.497991i	−0.968505	+	0.248995i	$0.919900\pi$
$558$		0			0
$559$	−3.45912e24			−0.0274507
$560$		0			0
$561$	5.68367e25			0.435995
$562$		0			0
$563$			1.73864e26i			1.28938i	0.764445	+	0.644689i	$0.223013\pi$
$563$			1.73864e26i			1.28938i	−0.764445	+	0.644689i	$0.776987\pi$
$564$		0			0
$565$	−1.94345e25	+	1.87153e26i	−0.139352	+	1.34195i
$566$		0			0
$567$		−	1.12204e25i		−	0.0777982i
$568$		0			0
$569$	−2.64344e26			−1.77257			−0.886285	−	0.463140i	$-0.846723\pi$
$569$	−2.64344e26			−1.77257			−0.886285	+	0.463140i	$0.846723\pi$
$570$		0			0
$571$	5.75861e25			0.373486			0.186743	−	0.982409i	$-0.440207\pi$
$571$	5.75861e25			0.373486			0.186743	+	0.982409i	$0.440207\pi$
$572$		0			0
$573$		−	1.58060e26i		−	0.991640i
$574$		0			0
$575$	1.57443e25	−	7.49907e25i	0.0955606	−	0.455159i
$576$		0			0
$577$			2.73815e26i			1.60800i	0.594628	+	0.804001i	$0.297299\pi$
$577$			2.73815e26i			1.60800i	−0.594628	+	0.804001i	$0.702701\pi$
$578$		0			0
$579$	−1.79087e26			−1.01770
$580$		0			0
$581$	−7.01210e25			−0.385633
$582$		0			0
$583$			2.17667e26i			1.15862i
$584$		0			0
$585$	3.51017e23	−	3.38026e24i	0.00180862	−	0.0174168i
$586$		0			0
$587$			2.98071e26i			1.48682i	0.668836	+	0.743410i	$0.266793\pi$
$587$			2.98071e26i			1.48682i	−0.668836	+	0.743410i	$0.733207\pi$
$588$		0			0
$589$	−4.45661e25			−0.215233
$590$		0			0
$591$	−1.75652e26			−0.821432
$592$		0			0
$593$		−	3.03693e26i		−	1.37536i	−0.726015	−	0.687679i	$-0.758630\pi$
$593$		−	3.03693e26i		−	1.37536i	0.726015	−	0.687679i	$-0.241370\pi$
$594$		0			0
$595$	−1.10924e26	−	1.15187e25i	−0.486534	−	0.0505232i
$596$		0			0
$597$		−	2.62806e26i		−	1.11655i
$598$		0			0
$599$	−1.22447e26			−0.503956			−0.251978	−	0.967733i	$-0.581081\pi$
$599$	−1.22447e26			−0.503956			−0.251978	+	0.967733i	$0.581081\pi$
$600$		0			0
$601$	−3.63124e26			−1.44793			−0.723964	−	0.689838i	$-0.757682\pi$
$601$	−3.63124e26			−1.44793			−0.723964	+	0.689838i	$0.757682\pi$
$602$		0			0
$603$			4.73762e25i			0.183040i
$604$		0			0
$605$	−5.40507e25	−	5.61279e24i	−0.202360	−	0.0210137i
$606$		0			0
$607$			3.15548e26i			1.14491i	0.819935	+	0.572456i	$0.194009\pi$
$607$			3.15548e26i			1.14491i	−0.819935	+	0.572456i	$0.805991\pi$
$608$		0			0
$609$	3.44899e25			0.121291
$610$		0			0
$611$	4.72362e24			0.0161021
$612$		0			0
$613$		−	3.06658e26i		−	1.01340i	−0.862123	−	0.506699i	$-0.830865\pi$
$613$		−	3.06658e26i		−	1.01340i	0.862123	−	0.506699i	$-0.169135\pi$
$614$		0			0
$615$	2.26581e25	−	2.18196e26i	0.0725957	−	0.699090i
$616$		0			0
$617$			2.73898e26i			0.850904i	0.904981	+	0.425452i	$0.139885\pi$
$617$			2.73898e26i			0.850904i	−0.904981	+	0.425452i	$0.860115\pi$
$618$		0			0
$619$	−1.32247e26			−0.398405			−0.199202	−	0.979958i	$-0.563835\pi$
$619$	−1.32247e26			−0.398405			−0.199202	+	0.979958i	$0.563835\pi$
$620$		0			0
$621$	−1.64383e26			−0.480271
$622$		0			0
$623$			2.84380e26i			0.805866i
$624$		0			0
$625$	3.33080e26	+	1.46310e26i	0.915564	+	0.402173i
$626$		0			0
$627$		−	1.58948e26i		−	0.423851i
$628$		0			0
$629$	1.74572e26			0.451642
$630$		0			0
$631$	−1.12452e26			−0.282286			−0.141143	−	0.989989i	$-0.545078\pi$
$631$	−1.12452e26			−0.282286			−0.141143	+	0.989989i	$0.545078\pi$
$632$		0			0
$633$		−	2.04386e26i		−	0.497869i
$634$		0			0
$635$	2.76418e25	−	2.66189e26i	0.0653456	−	0.629273i
$636$		0			0
$637$		−	7.61630e24i		−	0.0174751i
$638$		0			0
$639$	−7.73793e25			−0.172332
$640$		0			0
$641$	−7.39690e25			−0.159918			−0.0799592	−	0.996798i	$-0.525479\pi$
$641$	−7.39690e25			−0.159918			−0.0799592	+	0.996798i	$0.525479\pi$
$642$		0			0
$643$			7.13728e26i			1.49806i	0.662537	+	0.749029i	$0.269480\pi$
$643$			7.13728e26i			1.49806i	−0.662537	+	0.749029i	$0.730520\pi$
$644$		0			0
$645$	−2.84967e26	−	2.95918e25i	−0.580733	−	0.0603051i
$646$		0			0
$647$		−	1.21717e26i		−	0.240857i	−0.992722	−	0.120428i	$-0.961573\pi$
$647$		−	1.21717e26i		−	0.240857i	0.992722	−	0.120428i	$-0.0384268\pi$
$648$		0			0
$649$	−7.64626e25			−0.146935
$650$		0			0
$651$	−6.99783e25			−0.130600
$652$		0			0
$653$		−	9.44902e26i		−	1.71282i	−0.516297	−	0.856410i	$-0.672690\pi$
$653$		−	9.44902e26i		−	1.71282i	0.516297	−	0.856410i	$-0.327310\pi$
$654$		0			0
$655$	−2.33129e26	−	2.42089e25i	−0.410492	−	0.0426267i
$656$		0			0
$657$			3.91767e26i			0.670127i
$658$		0			0
$659$	2.64692e26			0.439875			0.219937	−	0.975514i	$-0.429415\pi$
$659$	2.64692e26			0.439875			0.219937	+	0.975514i	$0.429415\pi$
$660$		0			0
$661$	−1.09845e27			−1.77364			−0.886820	−	0.462114i	$-0.847091\pi$
$661$	−1.09845e27			−1.77364			−0.886820	+	0.462114i	$0.847091\pi$
$662$		0			0
$663$		−	9.66479e24i		−	0.0151640i
$664$		0			0
$665$	−3.22128e25	+	3.10206e26i	−0.0491159	+	0.472982i
$666$		0			0
$667$		−	8.72172e25i		−	0.129243i
$668$		0			0
$669$	−4.29720e25			−0.0618924
$670$		0			0
$671$	−4.01468e26			−0.562065
$672$		0			0
$673$		−	4.45661e26i		−	0.606543i	−0.952904	−	0.303272i	$-0.901921\pi$
$673$		−	4.45661e26i		−	0.606543i	0.952904	−	0.303272i	$-0.0980789\pi$
$674$		0			0
$675$	1.60359e26	−	7.63794e26i	0.212181	−	1.01063i
$676$		0			0
$677$			6.50039e26i			0.836271i	0.908385	+	0.418136i	$0.137316\pi$
$677$			6.50039e26i			0.836271i	−0.908385	+	0.418136i	$0.862684\pi$
$678$		0			0
$679$	−7.56696e26			−0.946582
$680$		0			0
$681$	−4.57636e26			−0.556702
$682$		0			0
$683$		−	3.00674e26i		−	0.355713i	−0.984056	−	0.177856i	$-0.943084\pi$
$683$		−	3.00674e26i		−	0.355713i	0.984056	−	0.177856i	$-0.0569162\pi$
$684$		0			0
$685$	−8.41032e25	+	8.09907e26i	−0.0967725	+	0.931911i
$686$		0			0
$687$		−	8.02265e26i		−	0.897901i
$688$		0			0
$689$	3.70132e25			0.0402971
$690$		0			0
$691$	4.53074e26			0.479875			0.239937	−	0.970788i	$-0.422873\pi$
$691$	4.53074e26			0.479875			0.239937	+	0.970788i	$0.422873\pi$
$692$		0			0
$693$			3.22991e26i			0.332832i
$694$		0			0
$695$	−3.43117e26	−	3.56304e25i	−0.344023	−	0.0357244i
$696$		0			0
$697$			8.07357e26i			0.787688i
$698$		0			0
$699$	8.24935e26			0.783225
$700$		0			0
$701$	1.97420e27			1.82419			0.912095	−	0.409978i	$-0.134464\pi$
$701$	1.97420e27			1.82419			0.912095	+	0.409978i	$0.134464\pi$
$702$		0			0
$703$		−	4.88204e26i		−	0.439062i
$704$		0			0
$705$	3.89137e26	+	4.04092e25i	0.340648	+	0.0353740i
$706$		0			0
$707$		−	4.02363e26i		−	0.342873i
$708$		0			0
$709$	4.25496e26			0.352985			0.176492	−	0.984302i	$-0.443525\pi$
$709$	4.25496e26			0.352985			0.176492	+	0.984302i	$0.443525\pi$
$710$		0			0
$711$	−7.51371e26			−0.606866
$712$		0			0
$713$			1.76959e26i			0.139163i
$714$		0			0
$715$	3.73682e24	−	3.59852e25i	0.00286151	−	0.0275561i
$716$		0			0
$717$		−	3.99725e26i		−	0.298077i
$718$		0			0
$719$	2.15252e26			0.156323			0.0781613	−	0.996941i	$-0.475095\pi$
$719$	2.15252e26			0.156323			0.0781613	+	0.996941i	$0.475095\pi$
$720$		0			0
$721$	1.48331e27			1.04917
$722$		0			0
$723$		−	6.52966e26i		−	0.449859i
$724$		0			0
$725$	4.05249e26	+	8.50820e25i	0.271963	+	0.0570988i
$726$		0			0
$727$		−	1.32836e26i		−	0.0868435i	−0.999057	−	0.0434218i	$-0.986174\pi$
$727$		−	1.32836e26i		−	0.0868435i	0.999057	−	0.0434218i	$-0.0138259\pi$
$728$		0			0
$729$	−1.17466e27			−0.748171
$730$		0			0
$731$	1.05442e27			0.654332
$732$		0			0
$733$			1.51731e27i			0.917456i	0.888577	+	0.458728i	$0.151695\pi$
$733$			1.51731e27i			0.917456i	−0.888577	+	0.458728i	$0.848305\pi$
$734$		0			0
$735$	6.51553e25	−	6.27440e26i	0.0383902	−	0.369694i
$736$		0			0
$737$			5.04353e26i			0.289596i
$738$		0			0
$739$	2.52020e27			1.41030			0.705152	−	0.709056i	$-0.250879\pi$
$739$	2.52020e27			1.41030			0.705152	+	0.709056i	$0.250879\pi$
$740$		0			0
$741$	−2.70283e25			−0.0147416
$742$		0			0
$743$			3.71912e27i			1.97718i	0.150623	+	0.988591i	$0.451872\pi$
$743$			3.71912e27i			1.97718i	−0.150623	+	0.988591i	$0.548128\pi$
$744$		0			0
$745$	1.36158e26	+	1.41390e25i	0.0705598	+	0.00732715i
$746$		0			0
$747$			6.51360e26i			0.329060i
$748$		0			0
$749$	2.17033e27			1.06893
$750$		0			0
$751$	−5.96593e26			−0.286483			−0.143241	−	0.989688i	$-0.545753\pi$
$751$	−5.96593e26			−0.286483			−0.143241	+	0.989688i	$0.545753\pi$
$752$		0			0
$753$		−	7.28147e26i		−	0.340931i
$754$		0			0
$755$	4.10457e27	+	4.26231e26i	1.87401	+	0.194603i
$756$		0			0
$757$		−	1.91312e27i		−	0.851786i	−0.904774	−	0.425893i	$-0.859960\pi$
$757$		−	1.91312e27i		−	0.851786i	0.904774	−	0.425893i	$-0.140040\pi$
$758$		0			0
$759$	−6.31138e26			−0.274049
$760$		0			0
$761$	1.15691e26			0.0489943			0.0244971	−	0.999700i	$-0.492202\pi$
$761$	1.15691e26			0.0489943			0.0244971	+	0.999700i	$0.492202\pi$
$762$		0			0
$763$		−	2.28093e26i		−	0.0942168i
$764$		0			0
$765$	−1.06998e26	+	1.03038e27i	−0.0431113	+	0.415158i
$766$		0			0
$767$			1.30021e25i			0.00511042i
$768$		0			0
$769$	3.10713e27			1.19140			0.595702	−	0.803205i	$-0.296874\pi$
$769$	3.10713e27			1.19140			0.595702	+	0.803205i	$0.296874\pi$
$770$		0			0
$771$	1.71110e27			0.640116
$772$		0			0
$773$		−	4.80152e26i		−	0.175256i	−0.996153	−	0.0876281i	$-0.972071\pi$
$773$		−	4.80152e26i		−	0.175256i	0.996153	−	0.0876281i	$-0.0279287\pi$
$774$		0			0
$775$	−8.22230e26	−	1.72627e26i	−0.292838	−	0.0614813i
$776$		0			0
$777$		−	7.66585e26i		−	0.266416i
$778$		0			0
$779$	2.25783e27			0.765748
$780$		0			0
$781$	−8.23757e26			−0.272655
$782$		0			0
$783$		−	8.88323e26i		−	0.286968i
$784$		0			0
$785$	3.39654e26	−	3.27084e27i	0.107096	−	1.03133i
$786$		0			0
$787$		−	1.47363e27i		−	0.453553i	−0.973947	−	0.226776i	$-0.927181\pi$
$787$		−	1.47363e27i		−	0.453553i	0.973947	−	0.226776i	$-0.0728186\pi$
$788$		0			0
$789$	−1.84518e27			−0.554379
$790$		0			0
$791$	−3.04089e27			−0.891916
$792$		0			0
$793$			6.82675e25i			0.0195487i
$794$		0			0
$795$	3.04919e27	+	3.16637e26i	0.852504	+	0.0885267i
$796$		0			0
$797$		−	5.13238e27i		−	1.40109i	−0.713610	−	0.700543i	$-0.752941\pi$
$797$		−	5.13238e27i		−	1.40109i	0.713610	−	0.700543i	$-0.247059\pi$
$798$		0			0
$799$	−1.43986e27			−0.383820
$800$		0			0
$801$	2.64163e27			0.687644
$802$		0			0
$803$			4.17064e27i			1.06024i
$804$		0			0
$805$	1.23174e27	+	1.27908e26i	0.305815	+	0.0317568i
$806$		0			0
$807$		−	1.01437e26i		−	0.0245980i
$808$		0			0
$809$	−2.09774e27			−0.496868			−0.248434	−	0.968649i	$-0.579916\pi$
$809$	−2.09774e27			−0.496868			−0.248434	+	0.968649i	$0.579916\pi$
$810$		0			0
$811$	−1.23103e27			−0.284821			−0.142411	−	0.989808i	$-0.545485\pi$
$811$	−1.23103e27			−0.284821			−0.142411	+	0.989808i	$0.545485\pi$
$812$		0			0
$813$		−	1.73626e27i		−	0.392424i
$814$		0			0
$815$	−6.80638e26	+	6.55448e27i	−0.150286	+	1.44724i
$816$		0			0
$817$		−	2.94876e27i		−	0.636106i
$818$		0			0
$819$	5.49230e25			0.0115760
$820$		0			0
$821$	−5.27699e27			−1.08674			−0.543371	−	0.839493i	$-0.682852\pi$
$821$	−5.27699e27			−1.08674			−0.543371	+	0.839493i	$0.682852\pi$
$822$		0			0
$823$		−	3.18176e27i		−	0.640279i	−0.947370	−	0.320140i	$-0.896270\pi$
$823$		−	3.18176e27i		−	0.640279i	0.947370	−	0.320140i	$-0.103730\pi$
$824$		0			0
$825$	6.15687e26	−	2.93254e27i	0.121073	−	0.576676i
$826$		0			0
$827$			1.20233e27i			0.231058i	0.993304	+	0.115529i	$0.0368564\pi$
$827$			1.20233e27i			0.231058i	−0.993304	+	0.115529i	$0.963144\pi$
$828$		0			0
$829$	3.53006e27			0.663000			0.331500	−	0.943455i	$-0.392445\pi$
$829$	3.53006e27			0.663000			0.331500	+	0.943455i	$0.392445\pi$
$830$		0			0
$831$	−1.59155e27			−0.292154
$832$		0			0
$833$			2.32162e27i			0.416547i
$834$		0			0
$835$	−2.68677e26	+	2.58734e27i	−0.0471205	+	0.453766i
$836$		0			0
$837$			1.80236e27i			0.308995i
$838$		0			0
$839$	−3.75481e27			−0.629288			−0.314644	−	0.949210i	$-0.601885\pi$
$839$	−3.75481e27			−0.629288			−0.314644	+	0.949210i	$0.601885\pi$
$840$		0			0
$841$	−5.63194e27			−0.922776
$842$		0			0
$843$		−	6.97237e27i		−	1.11691i
$844$		0			0
$845$	6.34441e27	+	6.58823e26i	0.993693	+	0.103188i
$846$		0			0
$847$		−	8.78224e26i		−	0.134497i
$848$		0			0
$849$	3.49139e27			0.522847
$850$		0			0
$851$	−1.93852e27			−0.283883
$852$		0			0
$853$			1.17710e28i			1.68577i	0.538092	+	0.842886i	$0.319145\pi$
$853$			1.17710e28i			1.68577i	−0.538092	+	0.842886i	$0.680855\pi$
$854$		0			0
$855$	2.88153e27	+	2.99227e26i	0.403595	+	0.0419105i
$856$		0			0
$857$		−	6.28476e27i		−	0.860936i	−0.902606	−	0.430468i	$-0.858348\pi$
$857$		−	6.28476e27i		−	0.860936i	0.902606	−	0.430468i	$-0.141652\pi$
$858$		0			0
$859$	1.24468e28			1.66771			0.833856	−	0.551982i	$-0.186128\pi$
$859$	1.24468e28			1.66771			0.833856	+	0.551982i	$0.186128\pi$
$860$		0			0
$861$	3.54528e27			0.464645
$862$		0			0
$863$		−	8.43872e27i		−	1.08187i	−0.841065	−	0.540934i	$-0.818071\pi$
$863$		−	8.43872e27i		−	1.08187i	0.841065	−	0.540934i	$-0.181929\pi$
$864$		0			0
$865$	−3.35442e26	+	3.23028e27i	−0.0420692	+	0.405123i
$866$		0			0
$867$		−	2.43507e27i		−	0.298766i
$868$		0			0
$869$	−7.99887e27			−0.960154
$870$		0			0
$871$	8.57626e25			0.0100722
$872$		0			0
$873$			7.02901e27i			0.807716i
$874$		0			0
$875$	−1.79590e27	+	5.59843e27i	−0.201933	+	0.629492i
$876$		0			0
$877$			9.70144e27i			1.06743i	0.845664	+	0.533716i	$0.179205\pi$
$877$			9.70144e27i			1.06743i	−0.845664	+	0.533716i	$0.820795\pi$
$878$		0			0
$879$	−7.41830e27			−0.798748
$880$		0			0
$881$	−1.65327e28			−1.74210			−0.871052	−	0.491192i	$-0.836561\pi$
$881$	−1.65327e28			−1.74210			−0.871052	+	0.491192i	$0.836561\pi$
$882$		0			0
$883$		−	1.21220e28i		−	1.25011i	−0.780582	−	0.625054i	$-0.785077\pi$
$883$		−	1.21220e28i		−	1.25011i	0.780582	−	0.625054i	$-0.214923\pi$
$884$		0			0
$885$	−1.11229e26	+	1.07113e27i	−0.0112268	+	0.108113i
$886$		0			0
$887$			1.27486e28i			1.25947i	0.776809	+	0.629736i	$0.216837\pi$
$887$			1.27486e28i			1.25947i	−0.776809	+	0.629736i	$0.783163\pi$
$888$		0			0
$889$	4.32507e27			0.418241
$890$		0			0
$891$	−1.10957e27			−0.105031
$892$		0			0
$893$			4.02669e27i			0.373129i
$894$		0			0
$895$	−1.36373e28	−	1.41614e27i	−1.23711	−	0.128465i
$896$		0			0
$897$			1.07322e26i			0.00953147i
$898$		0			0
$899$	−9.56287e26			−0.0831517
$900$		0			0
$901$	−1.12824e28			−0.960545
$902$		0			0
$903$		−	4.63018e27i		−	0.385980i
$904$		0			0
$905$	−6.62626e27	−	6.88092e26i	−0.540888	−	0.0561675i
$906$		0			0
$907$		−	5.33392e27i		−	0.426361i	−0.977013	−	0.213180i	$-0.931618\pi$
$907$		−	5.33392e27i		−	0.426361i	0.977013	−	0.213180i	$-0.0683822\pi$
$908$		0			0
$909$	−3.73759e27			−0.292573
$910$		0			0
$911$	−2.55689e28			−1.96014			−0.980071	−	0.198647i	$-0.936345\pi$
$911$	−2.55689e28			−1.96014			−0.980071	+	0.198647i	$0.936345\pi$
$912$		0			0
$913$			6.93418e27i			0.520622i
$914$		0			0
$915$	−5.84009e26	+	5.62396e27i	−0.0429457	+	0.413563i
$916$		0			0
$917$		−	3.78792e27i		−	0.272830i
$918$		0			0
$919$	−1.64999e28			−1.16408			−0.582040	−	0.813160i	$-0.697745\pi$
$919$	−1.64999e28			−1.16408			−0.582040	+	0.813160i	$0.697745\pi$
$920$		0			0
$921$	−3.78290e27			−0.261432
$922$		0			0
$923$			1.40076e26i			0.00948301i
$924$		0			0
$925$	1.89107e27	−	9.00721e27i	0.125418	−	0.597371i
$926$		0			0
$927$		−	1.37786e28i		−	0.895254i
$928$		0			0
$929$	1.77483e27			0.112982			0.0564908	−	0.998403i	$-0.482009\pi$
$929$	1.77483e27			0.112982			0.0564908	+	0.998403i	$0.482009\pi$
$930$		0			0
$931$	6.49258e27			0.404944
$932$		0			0
$933$			1.84796e28i			1.12932i
$934$		0			0
$935$	−1.13907e27	+	1.09691e28i	−0.0682086	+	0.656843i
$936$		0			0
$937$			5.57101e27i			0.326895i	0.986552	+	0.163447i	$0.0522614\pi$
$937$			5.57101e27i			0.326895i	−0.986552	+	0.163447i	$0.947739\pi$
$938$		0			0
$939$	6.57992e27			0.378353
$940$		0			0
$941$	−8.26284e27			−0.465616			−0.232808	−	0.972523i	$-0.574791\pi$
$941$	−8.26284e27			−0.465616			−0.232808	+	0.972523i	$0.574791\pi$
$942$		0			0
$943$		−	8.96523e27i		−	0.495108i
$944$		0			0
$945$	1.25455e28	+	1.30277e27i	0.679027	+	0.0705122i
$946$		0			0
$947$			1.07005e28i			0.567646i	0.958877	+	0.283823i	$0.0916028\pi$
$947$			1.07005e28i			0.567646i	−0.958877	+	0.283823i	$0.908397\pi$
$948$		0			0
$949$	7.09196e26			0.0368754
$950$		0			0
$951$	−2.12736e28			−1.08424
$952$		0			0
$953$			9.41803e27i			0.470519i	0.971933	+	0.235260i	$0.0755940\pi$
$953$			9.41803e27i			0.470519i	−0.971933	+	0.235260i	$0.924406\pi$
$954$		0			0
$955$	3.05046e28	+	3.16770e27i	1.49394	+	0.155136i
$956$		0			0
$957$		−	3.41066e27i		−	0.163748i
$958$		0			0
$959$	−1.31595e28			−0.619387
$960$		0			0
$961$	−1.97304e28			−0.910466
$962$		0			0
$963$		−	2.01604e28i		−	0.912116i
$964$		0			0
$965$	3.58909e27	−	3.45626e28i	0.159212	−	1.53319i
$966$		0			0
$967$			2.73555e28i			1.18985i	0.803781	+	0.594926i	$0.202818\pi$
$967$			2.73555e28i			1.18985i	−0.803781	+	0.594926i	$0.797182\pi$
$968$		0			0
$969$	8.23883e27			0.351390
$970$		0			0
$971$	1.92667e28			0.805795			0.402897	−	0.915245i	$-0.368003\pi$
$971$	1.92667e28			0.805795			0.402897	+	0.915245i	$0.368003\pi$
$972$		0			0
$973$		−	5.57503e27i		−	0.228652i
$974$		0			0
$975$	−4.98664e26	−	1.04694e26i	−0.0200569	−	0.00421095i
$976$		0			0
$977$		−	4.35338e28i		−	1.71723i	−0.512622	−	0.858615i	$-0.671326\pi$
$977$		−	4.35338e28i		−	1.71723i	0.512622	−	0.858615i	$-0.328674\pi$
$978$		0			0
$979$	2.81220e28			1.08796
$980$		0			0
$981$	−2.11877e27			−0.0803949
$982$		0			0
$983$			4.28821e27i			0.159594i	0.996811	+	0.0797972i	$0.0254273\pi$
$983$			4.28821e27i			0.159594i	−0.996811	+	0.0797972i	$0.974573\pi$
$984$		0			0
$985$	3.52025e27	−	3.38997e28i	0.128508	−	1.23752i
$986$		0			0
$987$			6.32276e27i			0.226409i
$988$		0			0
$989$	−1.17087e28			−0.411286
$990$		0			0
$991$	−5.37801e28			−1.85320			−0.926599	−	0.376051i	$-0.877282\pi$
$991$	−5.37801e28			−1.85320			−0.926599	+	0.376051i	$0.877282\pi$
$992$		0			0
$993$			1.71346e28i			0.579238i
$994$		0			0
$995$	5.07199e28	+	5.26691e27i	1.68213	+	0.174677i
$996$		0			0
$997$		−	5.79271e27i		−	0.188486i	−0.995549	−	0.0942428i	$-0.969957\pi$
$997$		−	5.79271e27i		−	0.188486i	0.995549	−	0.0942428i	$-0.0300430\pi$
$998$		0			0
$999$	−1.97442e28			−0.630329

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	80.20.c.d.49.9		28
4.3	odd	2		40.20.c.a.9.20	yes	28
5.4	even	2	inner	80.20.c.d.49.20		28
20.19	odd	2		40.20.c.a.9.9	✓	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
40.20.c.a.9.9	✓	28	20.19	odd	2
40.20.c.a.9.20	yes	28	4.3	odd	2
80.20.c.d.49.9		28	1.1	even	1	trivial
80.20.c.d.49.20		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)

\(f(q)\)	\(=\)	\(q-22508.3i q^{3} +(4.34396e6 + 451090. i) q^{5} +7.05814e7i q^{7} +6.55637e8 q^{9} +O(q^{10})\)	\(q-22508.3i q^{3} +(4.34396e6 + 451090. i) q^{5} +7.05814e7i q^{7} +6.55637e8 q^{9} +6.97971e9 q^{11} -1.18686e9i q^{13} +(1.01533e10 - 9.77753e10i) q^{15} +3.61783e11i q^{17} +1.01175e12 q^{19} +1.58867e12 q^{21} -4.01739e12i q^{23} +(1.86665e13 + 3.91904e12i) q^{25} -4.09178e13i q^{27} +2.17099e13 q^{29} -4.40484e13 q^{31} -1.57102e14i q^{33} +(-3.18386e13 + 3.06603e14i) q^{35} -4.82533e14i q^{37} -2.67143e13 q^{39} +2.23161e15 q^{41} -2.91450e15i q^{43} +(2.84806e15 + 2.95751e14i) q^{45} +3.97991e15i q^{47} +6.41716e15 q^{49} +8.14313e15 q^{51} +3.11857e16i q^{53} +(3.03196e16 + 3.14848e15i) q^{55} -2.27729e16i q^{57} -1.09550e16 q^{59} -5.75192e16 q^{61} +4.62757e16i q^{63} +(5.35383e14 - 5.15569e15i) q^{65} +7.22598e16i q^{67} -9.04247e16 q^{69} -1.18022e17 q^{71} +5.97537e17i q^{73} +(8.82110e16 - 4.20152e17i) q^{75} +4.92638e17i q^{77} -1.14602e18 q^{79} -1.58971e17 q^{81} +9.93477e17i q^{83} +(-1.63197e17 + 1.57157e18i) q^{85} -4.88654e17i q^{87} +4.02911e18 q^{89} +8.37705e16 q^{91} +9.91455e17i q^{93} +(4.39501e18 + 4.56392e17i) q^{95} +1.07209e19i q^{97} +4.57615e18 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - 3935164 q^{5} - 10352560732 q^{9}+O(q^{10}) \) 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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