LMFDB - Embedded newform 80.20.c.d.49.12

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			49.12
Character	$\chi$	$=$	80.49
Dual form			80.20.c.d.49.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-14155.3i q^{3} +(-2.17015e6 + 3.78998e6i) q^{5} -1.89772e8i q^{7} +9.61890e8 q^{9} +O(q^{10})$	\(q-14155.3i q^{3} +(-2.17015e6 + 3.78998e6i) q^{5} -1.89772e8i q^{7} +9.61890e8 q^{9} +6.57781e9 q^{11} -5.98927e10i q^{13} +(5.36482e10 + 3.07191e10i) q^{15} -8.66349e11i q^{17} +1.80776e12 q^{19} -2.68628e12 q^{21} -2.01397e12i q^{23} +(-9.65436e12 - 1.64497e13i) q^{25} -3.00679e13i q^{27} +7.93026e13 q^{29} +3.23570e13 q^{31} -9.31106e13i q^{33} +(7.19232e14 + 4.11835e14i) q^{35} -6.92096e13i q^{37} -8.47798e14 q^{39} +2.70752e15 q^{41} -1.55823e15i q^{43} +(-2.08745e15 + 3.64554e15i) q^{45} +1.13107e16i q^{47} -2.46146e16 q^{49} -1.22634e16 q^{51} +1.55711e16i q^{53} +(-1.42748e16 + 2.49297e16i) q^{55} -2.55893e16i q^{57} +1.03785e16 q^{59} +7.24902e16 q^{61} -1.82540e17i q^{63} +(2.26992e17 + 1.29976e17i) q^{65} -3.74671e16i q^{67} -2.85083e16 q^{69} +3.34962e17 q^{71} -6.81911e17i q^{73} +(-2.32849e17 + 1.36660e17i) q^{75} -1.24828e18i q^{77} +1.19213e18 q^{79} +6.92347e17 q^{81} +5.37397e17i q^{83} +(3.28344e18 + 1.88011e18i) q^{85} -1.12255e18i q^{87} -3.93785e18 q^{89} -1.13660e19 q^{91} -4.58022e17i q^{93} +(-3.92311e18 + 6.85136e18i) q^{95} -8.66554e17i q^{97} +6.32712e18 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$		−	14155.3i		−	0.415209i	−0.978213	−	0.207604i	$-0.933433\pi$
$3$		−	14155.3i		−	0.415209i	0.978213	−	0.207604i	$-0.0665666\pi$
$4$		0			0
$5$	−2.17015e6	+	3.78998e6i	−0.496907	+	0.867804i
$5$	−2.17015e6	+	3.78998e6i	−0.496907	+	0.867804i
$6$		0			0
$7$		−	1.89772e8i		−	1.77747i	−0.458425	−	0.888733i	$-0.651586\pi$
$7$		−	1.89772e8i		−	1.77747i	0.458425	−	0.888733i	$-0.348414\pi$
$8$		0			0
$9$	9.61890e8			0.827602
$10$		0			0
$11$	6.57781e9			0.841106			0.420553	−	0.907268i	$-0.361836\pi$
$11$	6.57781e9			0.841106			0.420553	+	0.907268i	$0.361836\pi$
$12$		0			0
$13$		−	5.98927e10i		−	1.56644i	−0.621748	−	0.783218i	$-0.713577\pi$
$13$		−	5.98927e10i		−	1.56644i	0.621748	−	0.783218i	$-0.286423\pi$
$14$		0			0
$15$	5.36482e10	+	3.07191e10i	0.360320	+	0.206320i
$16$		0			0
$17$		−	8.66349e11i		−	1.77185i	−0.463824	−	0.885927i	$-0.653523\pi$
$17$		−	8.66349e11i		−	1.77185i	0.463824	−	0.885927i	$-0.346477\pi$
$18$		0			0
$19$	1.80776e12			1.28523			0.642615	−	0.766189i	$-0.277849\pi$
$19$	1.80776e12			1.28523			0.642615	+	0.766189i	$0.277849\pi$
$20$		0			0
$21$	−2.68628e12			−0.738019
$22$		0			0
$23$		−	2.01397e12i		−	0.233152i	−0.993182	−	0.116576i	$-0.962808\pi$
$23$		−	2.01397e12i		−	0.233152i	0.993182	−	0.116576i	$-0.0371919\pi$
$24$		0			0
$25$	−9.65436e12	−	1.64497e13i	−0.506166	−	0.862436i
$26$		0			0
$27$		−	3.00679e13i		−	0.758836i
$28$		0			0
$29$	7.93026e13			1.01510			0.507548	−	0.861624i	$-0.330552\pi$
$29$	7.93026e13			1.01510			0.507548	+	0.861624i	$0.330552\pi$
$30$		0			0
$31$	3.23570e13			0.219802			0.109901	−	0.993943i	$-0.464947\pi$
$31$	3.23570e13			0.219802			0.109901	+	0.993943i	$0.464947\pi$
$32$		0			0
$33$		−	9.31106e13i		−	0.349234i
$34$		0			0
$35$	7.19232e14	+	4.11835e14i	1.54249	+	0.883236i
$36$		0			0
$37$		−	6.92096e13i		−	0.0875487i	−0.999041	−	0.0437744i	$-0.986062\pi$
$37$		−	6.92096e13i		−	0.0875487i	0.999041	−	0.0437744i	$-0.0139383\pi$
$38$		0			0
$39$	−8.47798e14			−0.650397
$40$		0			0
$41$	2.70752e15			1.29159			0.645795	−	0.763511i	$-0.276526\pi$
$41$	2.70752e15			1.29159			0.645795	+	0.763511i	$0.276526\pi$
$42$		0			0
$43$		−	1.55823e15i		−	0.472804i	−0.971655	−	0.236402i	$-0.924032\pi$
$43$		−	1.55823e15i		−	0.472804i	0.971655	−	0.236402i	$-0.0759682\pi$
$44$		0			0
$45$	−2.08745e15	+	3.64554e15i	−0.411241	+	0.718196i
$46$		0			0
$47$			1.13107e16i			1.47421i	0.675778	+	0.737106i	$0.263808\pi$
$47$			1.13107e16i			1.47421i	−0.675778	+	0.737106i	$0.736192\pi$
$48$		0			0
$49$	−2.46146e16			−2.15939
$50$		0			0
$51$	−1.22634e16			−0.735689
$52$		0			0
$53$			1.55711e16i			0.648186i	0.946025	+	0.324093i	$0.105059\pi$
$53$			1.55711e16i			0.648186i	−0.946025	+	0.324093i	$0.894941\pi$
$54$		0			0
$55$	−1.42748e16	+	2.49297e16i	−0.417951	+	0.729915i
$56$		0			0
$57$		−	2.55893e16i		−	0.533639i
$58$		0			0
$59$	1.03785e16			0.155969			0.0779846	−	0.996955i	$-0.475152\pi$
$59$	1.03785e16			0.155969			0.0779846	+	0.996955i	$0.475152\pi$
$60$		0			0
$61$	7.24902e16			0.793681			0.396840	−	0.917888i	$-0.370107\pi$
$61$	7.24902e16			0.793681			0.396840	+	0.917888i	$0.370107\pi$
$62$		0			0
$63$		−	1.82540e17i		−	1.47103i
$64$		0			0
$65$	2.26992e17	+	1.29976e17i	1.35936	+	0.778373i
$66$		0			0
$67$		−	3.74671e16i		−	0.168244i	−0.996455	−	0.0841219i	$-0.973191\pi$
$67$		−	3.74671e16i		−	0.168244i	0.996455	−	0.0841219i	$-0.0268085\pi$
$68$		0			0
$69$	−2.85083e16			−0.0968067
$70$		0			0
$71$	3.34962e17			0.867045			0.433523	−	0.901143i	$-0.357270\pi$
$71$	3.34962e17			0.867045			0.433523	+	0.901143i	$0.357270\pi$
$72$		0			0
$73$		−	6.81911e17i		−	1.35569i	−0.735204	−	0.677845i	$-0.762914\pi$
$73$		−	6.81911e17i		−	1.35569i	0.735204	−	0.677845i	$-0.237086\pi$
$74$		0			0
$75$	−2.32849e17	+	1.36660e17i	−0.358091	+	0.210165i
$76$		0			0
$77$		−	1.24828e18i		−	1.49504i
$78$		0			0
$79$	1.19213e18			1.11910			0.559548	−	0.828798i	$-0.310975\pi$
$79$	1.19213e18			1.11910			0.559548	+	0.828798i	$0.310975\pi$
$80$		0			0
$81$	6.92347e17			0.512526
$82$		0			0
$83$			5.37397e17i			0.315539i	0.987476	+	0.157770i	$0.0504303\pi$
$83$			5.37397e17i			0.315539i	−0.987476	+	0.157770i	$0.949570\pi$
$84$		0			0
$85$	3.28344e18	+	1.88011e18i	1.53762	+	0.880447i
$86$		0			0
$87$		−	1.12255e18i		−	0.421476i
$88$		0			0
$89$	−3.93785e18			−1.19139			−0.595695	−	0.803211i	$-0.703123\pi$
$89$	−3.93785e18			−1.19139			−0.595695	+	0.803211i	$0.703123\pi$
$90$		0			0
$91$	−1.13660e19			−2.78429
$92$		0			0
$93$		−	4.58022e17i		−	0.0912637i
$94$		0			0
$95$	−3.92311e18	+	6.85136e18i	−0.638640	+	1.11533i
$96$		0			0
$97$		−	8.66554e17i		−	0.115735i	−0.998324	−	0.0578675i	$-0.981570\pi$
$97$		−	8.66554e17i		−	0.115735i	0.998324	−	0.0578675i	$-0.0184301\pi$
$98$		0			0
$99$	6.32712e18			0.696100
$100$		0			0
$101$	8.66490e18			0.788335			0.394167	−	0.919039i	$-0.371033\pi$
$101$	8.66490e18			0.788335			0.394167	+	0.919039i	$0.371033\pi$
$102$		0			0
$103$			1.64258e19i			1.24043i	0.784431	+	0.620216i	$0.212955\pi$
$103$			1.64258e19i			1.24043i	−0.784431	+	0.620216i	$0.787045\pi$
$104$		0			0
$105$	5.82964e18	−	1.01809e19i	0.366727	−	0.640456i
$106$		0			0
$107$		−	1.31685e19i		−	0.692451i	−0.938151	−	0.346226i	$-0.887463\pi$
$107$		−	1.31685e19i		−	0.692451i	0.938151	−	0.346226i	$-0.112537\pi$
$108$		0			0
$109$	3.95782e19			1.74544			0.872719	−	0.488223i	$-0.162355\pi$
$109$	3.95782e19			1.74544			0.872719	+	0.488223i	$0.162355\pi$
$110$		0			0
$111$	−9.79681e17			−0.0363510
$112$		0			0
$113$			8.24243e18i			0.258113i	0.991637	+	0.129057i	$0.0411949\pi$
$113$			8.24243e18i			0.258113i	−0.991637	+	0.129057i	$0.958805\pi$
$114$		0			0
$115$	7.63291e18	+	4.37063e18i	0.202330	+	0.115855i
$116$		0			0
$117$		−	5.76102e19i		−	1.29638i
$118$		0			0
$119$	−1.64409e20			−3.14941
$120$		0			0
$121$	−1.78916e19			−0.292541
$122$		0			0
$123$		−	3.83257e19i		−	0.536279i
$124$		0			0
$125$	8.32953e19	−	8.91514e17i	0.999943	−	0.0107024i
$126$		0			0
$127$			1.69690e20i			1.75195i	0.482360	+	0.875973i	$0.339780\pi$
$127$			1.69690e20i			1.75195i	−0.482360	+	0.875973i	$0.660220\pi$
$128$		0			0
$129$	−2.20572e19			−0.196312
$130$		0			0
$131$	−5.58878e19			−0.429773			−0.214887	−	0.976639i	$-0.568938\pi$
$131$	−5.58878e19			−0.429773			−0.214887	+	0.976639i	$0.568938\pi$
$132$		0			0
$133$		−	3.43062e20i		−	2.28445i
$134$		0			0
$135$	1.13957e20	+	6.52520e19i	0.658521	+	0.377071i
$136$		0			0
$137$			2.60264e20i			1.30788i	0.756546	+	0.653940i	$0.226885\pi$
$137$			2.60264e20i			1.30788i	−0.756546	+	0.653940i	$0.773115\pi$
$138$		0			0
$139$	−2.77589e20			−1.21552			−0.607760	−	0.794121i	$-0.707932\pi$
$139$	−2.77589e20			−1.21552			−0.607760	+	0.794121i	$0.707932\pi$
$140$		0			0
$141$	1.60106e20			0.612105
$142$		0			0
$143$		−	3.93963e20i		−	1.31754i
$144$		0			0
$145$	−1.72099e20	+	3.00555e20i	−0.504408	+	0.880903i
$146$		0			0
$147$			3.48427e20i			0.896596i
$148$		0			0
$149$	3.26255e20			0.738394			0.369197	−	0.929351i	$-0.379633\pi$
$149$	3.26255e20			0.738394			0.369197	+	0.929351i	$0.379633\pi$
$150$		0			0
$151$	8.62345e19			0.171949			0.0859746	−	0.996297i	$-0.472600\pi$
$151$	8.62345e19			0.171949			0.0859746	+	0.996297i	$0.472600\pi$
$152$		0			0
$153$		−	8.33332e20i		−	1.46639i
$154$		0			0
$155$	−7.02196e19	+	1.22632e20i	−0.109221	+	0.190745i
$156$		0			0
$157$			1.17610e20i			0.161957i	0.996716	+	0.0809783i	$0.0258045\pi$
$157$			1.17610e20i			0.161957i	−0.996716	+	0.0809783i	$0.974196\pi$
$158$		0			0
$159$	2.20414e20			0.269132
$160$		0			0
$161$	−3.82196e20			−0.414420
$162$		0			0
$163$		−	1.89033e21i		−	1.82287i	−0.411448	−	0.911433i	$-0.634977\pi$
$163$		−	1.89033e21i		−	1.82287i	0.411448	−	0.911433i	$-0.365023\pi$
$164$		0			0
$165$	3.52887e20	+	2.02064e20i	0.303067	+	0.173537i
$166$		0			0
$167$		−	9.40304e20i		−	0.720215i	−0.932911	−	0.360107i	$-0.882740\pi$
$167$		−	9.40304e20i		−	0.720215i	0.932911	−	0.360107i	$-0.117260\pi$
$168$		0			0
$169$	−2.12522e21			−1.45372
$170$		0			0
$171$	1.73886e21			1.06366
$172$		0			0
$173$		−	5.47816e19i		−	0.0300052i	−0.999887	−	0.0150026i	$-0.995224\pi$
$173$		−	5.47816e19i		−	0.0300052i	0.999887	−	0.0150026i	$-0.00477566\pi$
$174$		0			0
$175$	−3.12169e21	+	1.83213e21i	−1.53295	+	0.899694i
$176$		0			0
$177$		−	1.46910e20i		−	0.0647598i
$178$		0			0
$179$	4.60482e21			1.82435			0.912176	−	0.409798i	$-0.134401\pi$
$179$	4.60482e21			1.82435			0.912176	+	0.409798i	$0.134401\pi$
$180$		0			0
$181$	−3.10117e21			−1.10555			−0.552776	−	0.833330i	$-0.686431\pi$
$181$	−3.10117e21			−1.10555			−0.552776	+	0.833330i	$0.686431\pi$
$182$		0			0
$183$		−	1.02612e21i		−	0.329543i
$184$		0			0
$185$	2.62303e20	+	1.50195e20i	0.0759751	+	0.0435036i
$186$		0			0
$187$		−	5.69867e21i		−	1.49032i
$188$		0			0
$189$	−5.70606e21			−1.34881
$190$		0			0
$191$	3.10424e21			0.663955			0.331977	−	0.943287i	$-0.392284\pi$
$191$	3.10424e21			0.663955			0.331977	+	0.943287i	$0.392284\pi$
$192$		0			0
$193$		−	5.48192e21i		−	1.06203i	−0.847362	−	0.531016i	$-0.821810\pi$
$193$		−	5.48192e21i		−	1.06203i	0.847362	−	0.531016i	$-0.178190\pi$
$194$		0			0
$195$	1.83985e21	−	3.21314e21i	0.323187	−	0.564417i
$196$		0			0
$197$		−	4.17661e21i		−	0.665878i	−0.942948	−	0.332939i	$-0.891960\pi$
$197$		−	4.17661e21i		−	0.665878i	0.942948	−	0.332939i	$-0.108040\pi$
$198$		0			0
$199$	−7.05428e21			−1.02176			−0.510880	−	0.859652i	$-0.670680\pi$
$199$	−7.05428e21			−1.02176			−0.510880	+	0.859652i	$0.670680\pi$
$200$		0			0
$201$	−5.30357e20			−0.0698563
$202$		0			0
$203$		−	1.50494e22i		−	1.80430i
$204$		0			0
$205$	−5.87573e21	+	1.02614e22i	−0.641801	+	1.12085i
$206$		0			0
$207$		−	1.93722e21i		−	0.192957i
$208$		0			0
$209$	1.18911e22			1.08101
$210$		0			0
$211$	−1.20003e22			−0.996576			−0.498288	−	0.867011i	$-0.666038\pi$
$211$	−1.20003e22			−0.996576			−0.498288	+	0.867011i	$0.666038\pi$
$212$		0			0
$213$		−	4.74148e21i		−	0.360005i
$214$		0			0
$215$	5.90565e21	+	3.38159e21i	0.410301	+	0.234940i
$216$		0			0
$217$		−	6.14045e21i		−	0.390691i
$218$		0			0
$219$	−9.65264e21			−0.562895
$220$		0			0
$221$	−5.18880e22			−2.77550
$222$		0			0
$223$			1.02181e22i			0.501734i	0.968022	+	0.250867i	$0.0807157\pi$
$223$			1.02181e22i			0.501734i	−0.968022	+	0.250867i	$0.919284\pi$
$224$		0			0
$225$	−9.28643e21	−	1.58228e22i	−0.418904	−	0.713753i
$226$		0			0
$227$			1.89378e22i			0.785386i	0.919670	+	0.392693i	$0.128457\pi$
$227$			1.89378e22i			0.785386i	−0.919670	+	0.392693i	$0.871543\pi$
$228$		0			0
$229$	2.00136e22			0.763638			0.381819	−	0.924237i	$-0.375298\pi$
$229$	2.00136e22			0.763638			0.381819	+	0.924237i	$0.375298\pi$
$230$		0			0
$231$	−1.76698e22			−0.620752
$232$		0			0
$233$		−	3.29845e22i		−	1.06765i	−0.845595	−	0.533825i	$-0.820754\pi$
$233$		−	3.29845e22i		−	1.06765i	0.845595	−	0.533825i	$-0.179246\pi$
$234$		0			0
$235$	−4.28673e22	−	2.45459e22i	−1.27933	−	0.732546i
$236$		0			0
$237$		−	1.68750e22i		−	0.464658i
$238$		0			0
$239$	−4.25676e22			−1.08218			−0.541090	−	0.840965i	$-0.681988\pi$
$239$	−4.25676e22			−1.08218			−0.541090	+	0.840965i	$0.681988\pi$
$240$		0			0
$241$	4.73100e22			1.11120			0.555598	−	0.831451i	$-0.312489\pi$
$241$	4.73100e22			1.11120			0.555598	+	0.831451i	$0.312489\pi$
$242$		0			0
$243$		−	4.47472e22i		−	0.971642i
$244$		0			0
$245$	5.34175e22	−	9.32888e22i	1.07301	−	1.87392i
$246$		0			0
$247$		−	1.08272e23i		−	2.01323i
$248$		0			0
$249$	7.60700e21			0.131015
$250$		0			0
$251$	1.52660e22			0.243683			0.121841	−	0.992550i	$-0.461120\pi$
$251$	1.52660e22			0.243683			0.121841	+	0.992550i	$0.461120\pi$
$252$		0			0
$253$		−	1.32475e22i		−	0.196105i
$254$		0			0
$255$	2.66135e22	−	4.64780e22i	0.365569	−	0.638434i
$256$		0			0
$257$		−	1.17833e23i		−	1.50281i	−0.659842	−	0.751404i	$-0.729377\pi$
$257$		−	1.17833e23i		−	1.50281i	0.659842	−	0.751404i	$-0.270623\pi$
$258$		0			0
$259$	−1.31341e22			−0.155615
$260$		0			0
$261$	7.62804e22			0.840094
$262$		0			0
$263$			1.34177e23i			1.37436i	0.726488	+	0.687179i	$0.241151\pi$
$263$			1.34177e23i			1.37436i	−0.726488	+	0.687179i	$0.758849\pi$
$264$		0			0
$265$	−5.90143e22	−	3.37918e22i	−0.562498	−	0.322088i
$266$		0			0
$267$			5.57413e22i			0.494675i
$268$		0			0
$269$	−1.36288e23			−1.12670			−0.563352	−	0.826217i	$-0.690488\pi$
$269$	−1.36288e23			−1.12670			−0.563352	+	0.826217i	$0.690488\pi$
$270$		0			0
$271$	−1.66068e23			−1.27961			−0.639804	−	0.768538i	$-0.720984\pi$
$271$	−1.66068e23			−1.27961			−0.639804	+	0.768538i	$0.720984\pi$
$272$		0			0
$273$			1.60889e23i			1.15606i
$274$		0			0
$275$	−6.35045e22	−	1.08203e23i	−0.425739	−	0.725400i
$276$		0			0
$277$		−	4.45973e22i		−	0.279094i	−0.990215	−	0.139547i	$-0.955435\pi$
$277$		−	4.45973e22i		−	0.279094i	0.990215	−	0.139547i	$-0.0445646\pi$
$278$		0			0
$279$	3.11238e22			0.181909
$280$		0			0
$281$	5.71913e22			0.312334			0.156167	−	0.987731i	$-0.450086\pi$
$281$	5.71913e22			0.312334			0.156167	+	0.987731i	$0.450086\pi$
$282$		0			0
$283$			1.82798e23i			0.933253i	0.884454	+	0.466627i	$0.154531\pi$
$283$			1.82798e23i			0.933253i	−0.884454	+	0.466627i	$0.845469\pi$
$284$		0			0
$285$	9.69829e22	+	5.55327e22i	0.463094	+	0.265169i
$286$		0			0
$287$		−	5.13812e23i		−	2.29576i
$288$		0			0
$289$	−5.11488e23			−2.13947
$290$		0			0
$291$	−1.22663e22			−0.0480541
$292$		0			0
$293$			6.28884e22i			0.230849i	0.993316	+	0.115424i	$0.0368228\pi$
$293$			6.28884e22i			0.230849i	−0.993316	+	0.115424i	$0.963177\pi$
$294$		0			0
$295$	−2.25228e22	+	3.93341e22i	−0.0775022	+	0.135351i
$296$		0			0
$297$		−	1.97781e23i		−	0.638261i
$298$		0			0
$299$	−1.20622e23			−0.365217
$300$		0			0
$301$	−2.95709e23			−0.840393
$302$		0			0
$303$		−	1.22654e23i		−	0.327323i
$304$		0			0
$305$	−1.57315e23	+	2.74736e23i	−0.394386	+	0.688759i
$306$		0			0
$307$			4.83801e23i			1.13986i	0.821693	+	0.569931i	$0.193030\pi$
$307$			4.83801e23i			1.13986i	−0.821693	+	0.569931i	$0.806970\pi$
$308$		0			0
$309$	2.32512e23			0.515038
$310$		0			0
$311$	8.84270e23			1.84230			0.921152	−	0.389204i	$-0.127250\pi$
$311$	8.84270e23			1.84230			0.921152	+	0.389204i	$0.127250\pi$
$312$		0			0
$313$		−	1.81562e23i		−	0.355922i	−0.984038	−	0.177961i	$-0.943050\pi$
$313$		−	1.81562e23i		−	0.355922i	0.984038	−	0.177961i	$-0.0569501\pi$
$314$		0			0
$315$	6.91822e23	+	3.96140e23i	1.27657	+	0.730967i
$316$		0			0
$317$			5.12554e21i			0.00890588i	0.999990	+	0.00445294i	$0.00141742\pi$
$317$			5.12554e21i			0.00890588i	−0.999990	+	0.00445294i	$0.998583\pi$
$318$		0			0
$319$	5.21637e23			0.853802
$320$		0			0
$321$	−1.86403e23			−0.287512
$322$		0			0
$323$		−	1.56615e24i		−	2.27724i
$324$		0			0
$325$	−9.85215e23	+	5.78226e23i	−1.35095	+	0.792877i
$326$		0			0
$327$		−	5.60240e23i		−	0.724721i
$328$		0			0
$329$	2.14646e24			2.62036
$330$		0			0
$331$	−5.82491e23			−0.671310			−0.335655	−	0.941985i	$-0.608958\pi$
$331$	−5.82491e23			−0.671310			−0.335655	+	0.941985i	$0.608958\pi$
$332$		0			0
$333$		−	6.65720e22i		−	0.0724555i
$334$		0			0
$335$	1.41999e23	+	8.13093e22i	0.146003	+	0.0836016i
$336$		0			0
$337$			1.65965e24i			1.61262i	0.591495	+	0.806309i	$0.298538\pi$
$337$			1.65965e24i			1.61262i	−0.591495	+	0.806309i	$0.701462\pi$
$338$		0			0
$339$	1.16674e23			0.107171
$340$		0			0
$341$	2.12838e23			0.184877
$342$		0			0
$343$			2.50798e24i			2.06077i
$344$		0			0
$345$	6.18675e22	−	1.08046e23i	0.0481040	−	0.0840092i
$346$		0			0
$347$			1.10638e24i			0.814279i	0.913366	+	0.407139i	$0.133474\pi$
$347$			1.10638e24i			0.814279i	−0.913366	+	0.407139i	$0.866526\pi$
$348$		0			0
$349$	−2.39693e24			−1.67037			−0.835186	−	0.549968i	$-0.814640\pi$
$349$	−2.39693e24			−1.67037			−0.835186	+	0.549968i	$0.814640\pi$
$350$		0			0
$351$	−1.80085e24			−1.18867
$352$		0			0
$353$		−	1.17504e24i		−	0.734838i	−0.930056	−	0.367419i	$-0.880242\pi$
$353$		−	1.17504e24i		−	0.734838i	0.930056	−	0.367419i	$-0.119758\pi$
$354$		0			0
$355$	−7.26920e23	+	1.26950e24i	−0.430841	+	0.752425i
$356$		0			0
$357$			2.32725e24i			1.30766i
$358$		0			0
$359$	1.20007e24			0.639456			0.319728	−	0.947509i	$-0.396408\pi$
$359$	1.20007e24			0.639456			0.319728	+	0.947509i	$0.396408\pi$
$360$		0			0
$361$	1.28957e24			0.651817
$362$		0			0
$363$			2.53260e23i			0.121466i
$364$		0			0
$365$	2.58443e24	+	1.47985e24i	1.17647	+	0.673653i
$366$		0			0
$367$			2.48254e24i			1.07292i	0.843925	+	0.536461i	$0.180239\pi$
$367$			2.48254e24i			1.07292i	−0.843925	+	0.536461i	$0.819761\pi$
$368$		0			0
$369$	2.60433e24			1.06892
$370$		0			0
$371$	2.95497e24			1.15213
$372$		0			0
$373$			2.33585e23i			0.0865388i	0.999063	+	0.0432694i	$0.0137774\pi$
$373$			2.33585e23i			0.0865388i	−0.999063	+	0.0432694i	$0.986223\pi$
$374$		0			0
$375$	−1.26196e22	−	1.17907e24i	−0.00444375	−	0.415185i
$376$		0			0
$377$		−	4.74965e24i		−	1.59008i
$378$		0			0
$379$	1.03992e24			0.331076			0.165538	−	0.986203i	$-0.447064\pi$
$379$	1.03992e24			0.331076			0.165538	+	0.986203i	$0.447064\pi$
$380$		0			0
$381$	2.40201e24			0.727423
$382$		0			0
$383$			4.26400e24i			1.22865i	0.789052	+	0.614326i	$0.210572\pi$
$383$			4.26400e24i			1.22865i	−0.789052	+	0.614326i	$0.789428\pi$
$384$		0			0
$385$	4.73097e24	+	2.70897e24i	1.29740	+	0.742895i
$386$		0			0
$387$		−	1.49884e24i		−	0.391293i
$388$		0			0
$389$	1.37420e24			0.341609			0.170805	−	0.985305i	$-0.445363\pi$
$389$	1.37420e24			0.341609			0.170805	+	0.985305i	$0.445363\pi$
$390$		0			0
$391$	−1.74480e24			−0.413111
$392$		0			0
$393$			7.91107e23i			0.178446i
$394$		0			0
$395$	−2.58711e24	+	4.51816e24i	−0.556087	+	0.971155i
$396$		0			0
$397$		−	1.05893e24i		−	0.216948i	−0.994099	−	0.108474i	$-0.965404\pi$
$397$		−	1.05893e24i		−	0.216948i	0.994099	−	0.108474i	$-0.0345965\pi$
$398$		0			0
$399$	−4.85614e24			−0.948525
$400$		0			0
$401$	−2.00918e24			−0.374238			−0.187119	−	0.982337i	$-0.559915\pi$
$401$	−2.00918e24			−0.374238			−0.187119	+	0.982337i	$0.559915\pi$
$402$		0			0
$403$		−	1.93795e24i		−	0.344306i
$404$		0			0
$405$	−1.50250e24	+	2.62398e24i	−0.254678	+	0.444772i
$406$		0			0
$407$		−	4.55247e23i		−	0.0736377i
$408$		0			0
$409$	−6.87280e23			−0.106111			−0.0530557	−	0.998592i	$-0.516896\pi$
$409$	−6.87280e23			−0.106111			−0.0530557	+	0.998592i	$0.516896\pi$
$410$		0			0
$411$	3.68410e24			0.543043
$412$		0			0
$413$		−	1.96954e24i		−	0.277230i
$414$		0			0
$415$	−2.03672e24	−	1.16623e24i	−0.273826	−	0.156794i
$416$		0			0
$417$			3.92935e24i			0.504695i
$418$		0			0
$419$	−1.49163e24			−0.183075			−0.0915373	−	0.995802i	$-0.529178\pi$
$419$	−1.49163e24			−0.183075			−0.0915373	+	0.995802i	$0.529178\pi$
$420$		0			0
$421$	8.94549e24			1.04936			0.524680	−	0.851300i	$-0.324185\pi$
$421$	8.94549e24			1.04936			0.524680	+	0.851300i	$0.324185\pi$
$422$		0			0
$423$			1.08796e25i			1.22006i
$424$		0			0
$425$	−1.42511e25	+	8.36404e24i	−1.52811	+	0.896853i
$426$		0			0
$427$		−	1.37566e25i		−	1.41074i
$428$		0			0
$429$	−5.57665e24			−0.547053
$430$		0			0
$431$	2.17546e24			0.204182			0.102091	−	0.994775i	$-0.467447\pi$
$431$	2.17546e24			0.204182			0.102091	+	0.994775i	$0.467447\pi$
$432$		0			0
$433$			5.84716e24i			0.525182i	0.964907	+	0.262591i	$0.0845770\pi$
$433$			5.84716e24i			0.525182i	−0.964907	+	0.262591i	$0.915423\pi$
$434$		0			0
$435$	4.25444e24	+	2.43611e24i	0.365759	+	0.209435i
$436$		0			0
$437$		−	3.64077e24i		−	0.299654i
$438$		0			0
$439$	6.15456e24			0.485048			0.242524	−	0.970145i	$-0.422025\pi$
$439$	6.15456e24			0.485048			0.242524	+	0.970145i	$0.422025\pi$
$440$		0			0
$441$	−2.36765e25			−1.78711
$442$		0			0
$443$			1.97906e25i			1.43095i	0.698639	+	0.715474i	$0.253789\pi$
$443$			1.97906e25i			1.43095i	−0.698639	+	0.715474i	$0.746211\pi$
$444$		0			0
$445$	8.54573e24	−	1.49243e25i	0.592010	−	1.03389i
$446$		0			0
$447$		−	4.61824e24i		−	0.306588i
$448$		0			0
$449$	5.53211e24			0.352006			0.176003	−	0.984390i	$-0.443683\pi$
$449$	5.53211e24			0.352006			0.176003	+	0.984390i	$0.443683\pi$
$450$		0			0
$451$	1.78095e25			1.08636
$452$		0			0
$453$		−	1.22067e24i		−	0.0713948i
$454$		0			0
$455$	2.46659e25	−	4.30768e25i	1.38353	−	2.41621i
$456$		0			0
$457$		−	1.31217e24i		−	0.0705968i	−0.999377	−	0.0352984i	$-0.988762\pi$
$457$		−	1.31217e24i		−	0.0705968i	0.999377	−	0.0352984i	$-0.0112382\pi$
$458$		0			0
$459$	−2.60493e25			−1.34455
$460$		0			0
$461$	−1.04116e25			−0.515656			−0.257828	−	0.966191i	$-0.583007\pi$
$461$	−1.04116e25			−0.515656			−0.257828	+	0.966191i	$0.583007\pi$
$462$		0			0
$463$			8.51780e24i			0.404863i	0.979296	+	0.202432i	$0.0648844\pi$
$463$			8.51780e24i			0.404863i	−0.979296	+	0.202432i	$0.935116\pi$
$464$		0			0
$465$	1.73589e24	+	9.93977e23i	0.0791990	+	0.0453496i
$466$		0			0
$467$		−	3.61231e25i		−	1.58225i	−0.611656	−	0.791124i	$-0.709496\pi$
$467$		−	3.61231e25i		−	1.58225i	0.611656	−	0.791124i	$-0.290504\pi$
$468$		0			0
$469$	−7.11021e24			−0.299048
$470$		0			0
$471$	1.66481e24			0.0672458
$472$		0			0
$473$		−	1.02497e25i		−	0.397678i
$474$		0			0
$475$	−1.74527e25	−	2.97370e25i	−0.650540	−	1.10843i
$476$		0			0
$477$			1.49777e25i			0.536440i
$478$		0			0
$479$	1.27137e25			0.437606			0.218803	−	0.975769i	$-0.429785\pi$
$479$	1.27137e25			0.437606			0.218803	+	0.975769i	$0.429785\pi$
$480$		0			0
$481$	−4.14515e24			−0.137139
$482$		0			0
$483$			5.41009e24i			0.172071i
$484$		0			0
$485$	3.28422e24	+	1.88056e24i	0.100435	+	0.0575095i
$486$		0			0
$487$		−	1.11079e25i		−	0.326668i	−0.986571	−	0.163334i	$-0.947775\pi$
$487$		−	1.11079e25i		−	0.326668i	0.986571	−	0.163334i	$-0.0522249\pi$
$488$		0			0
$489$	−2.67581e25			−0.756870
$490$		0			0
$491$	−4.31912e25			−1.17522			−0.587612	−	0.809143i	$-0.699932\pi$
$491$	−4.31912e25			−1.17522			−0.587612	+	0.809143i	$0.699932\pi$
$492$		0			0
$493$		−	6.87038e25i		−	1.79860i
$494$		0			0
$495$	−1.37308e25	+	2.39796e25i	−0.345897	+	0.604079i
$496$		0			0
$497$		−	6.35666e25i		−	1.54114i
$498$		0			0
$499$	8.16489e25			1.90544			0.952719	−	0.303852i	$-0.0982727\pi$
$499$	8.16489e25			1.90544			0.952719	+	0.303852i	$0.0982727\pi$
$500$		0			0
$501$	−1.33103e25			−0.299039
$502$		0			0
$503$		−	4.31190e25i		−	0.932766i	−0.884583	−	0.466383i	$-0.845557\pi$
$503$		−	4.31190e25i		−	0.932766i	0.884583	−	0.466383i	$-0.154443\pi$
$504$		0			0
$505$	−1.88042e25	+	3.28398e25i	−0.391729	+	0.684120i
$506$		0			0
$507$			3.00831e25i			0.603597i
$508$		0			0
$509$	−2.58241e25			−0.499122			−0.249561	−	0.968359i	$-0.580286\pi$
$509$	−2.58241e25			−0.499122			−0.249561	+	0.968359i	$0.580286\pi$
$510$		0			0
$511$	−1.29408e26			−2.40969
$512$		0			0
$513$		−	5.43556e25i		−	0.975279i
$514$		0			0
$515$	−6.22534e25	−	3.56465e25i	−1.07645	−	0.616379i
$516$		0			0
$517$			7.43996e25i			1.23997i
$518$		0			0
$519$	−7.75448e23			−0.0124584
$520$		0			0
$521$	1.21001e26			1.87427			0.937134	−	0.348969i	$-0.113468\pi$
$521$	1.21001e26			1.87427			0.937134	+	0.348969i	$0.113468\pi$
$522$		0			0
$523$			5.73600e25i			0.856728i	0.903606	+	0.428364i	$0.140910\pi$
$523$			5.73600e25i			0.856728i	−0.903606	+	0.428364i	$0.859090\pi$
$524$		0			0
$525$	2.59343e25	+	4.41884e25i	0.373561	+	0.636494i
$526$		0			0
$527$		−	2.80324e25i		−	0.389457i
$528$		0			0
$529$	7.05594e25			0.945640
$530$		0			0
$531$	9.98293e24			0.129080
$532$		0			0
$533$		−	1.62161e26i		−	2.02319i
$534$		0			0
$535$	4.99082e25	+	2.85776e25i	0.600912	+	0.344084i
$536$		0			0
$537$		−	6.51825e25i		−	0.757487i
$538$		0			0
$539$	−1.61910e26			−1.81627
$540$		0			0
$541$	−4.14663e25			−0.449078			−0.224539	−	0.974465i	$-0.572088\pi$
$541$	−4.14663e25			−0.449078			−0.224539	+	0.974465i	$0.572088\pi$
$542$		0			0
$543$			4.38979e25i			0.459035i
$544$		0			0
$545$	−8.58908e25	+	1.50000e26i	−0.867321	+	1.51470i
$546$		0			0
$547$		−	1.50177e25i		−	0.146462i	−0.997315	−	0.0732310i	$-0.976669\pi$
$547$		−	1.50177e25i		−	0.146462i	0.997315	−	0.0732310i	$-0.0233310\pi$
$548$		0			0
$549$	6.97276e25			0.656851
$550$		0			0
$551$	1.43360e26			1.30463
$552$		0			0
$553$		−	2.26234e26i		−	1.98915i
$554$		0			0
$555$	2.12606e24	−	3.71297e24i	0.0180631	−	0.0315455i
$556$		0			0
$557$			1.40480e26i			1.15343i	0.816947	+	0.576713i	$0.195665\pi$
$557$			1.40480e26i			1.15343i	−0.816947	+	0.576713i	$0.804335\pi$
$558$		0			0
$559$	−9.33266e25			−0.740616
$560$		0			0
$561$	−8.06663e25			−0.618792
$562$		0			0
$563$			1.92150e26i			1.42499i	0.701678	+	0.712494i	$0.252434\pi$
$563$			1.92150e26i			1.42499i	−0.701678	+	0.712494i	$0.747566\pi$
$564$		0			0
$565$	−3.12386e25	−	1.78873e25i	−0.223992	−	0.128258i
$566$		0			0
$567$		−	1.31388e26i		−	0.910998i
$568$		0			0
$569$	−5.14824e25			−0.345217			−0.172608	−	0.984991i	$-0.555220\pi$
$569$	−5.14824e25			−0.345217			−0.172608	+	0.984991i	$0.555220\pi$
$570$		0			0
$571$	−5.77123e24			−0.0374305			−0.0187152	−	0.999825i	$-0.505958\pi$
$571$	−5.77123e24			−0.0374305			−0.0187152	+	0.999825i	$0.505958\pi$
$572$		0			0
$573$		−	4.39414e25i		−	0.275680i
$574$		0			0
$575$	−3.31292e25	+	1.94436e25i	−0.201079	+	0.118014i
$576$		0			0
$577$			2.11504e26i			1.24207i	0.783781	+	0.621037i	$0.213288\pi$
$577$			2.11504e26i			1.24207i	−0.783781	+	0.621037i	$0.786712\pi$
$578$		0			0
$579$	−7.75980e25			−0.440965
$580$		0			0
$581$	1.01983e26			0.560860
$582$		0			0
$583$			1.02424e26i			0.545193i
$584$		0			0
$585$	2.18341e26	+	1.25023e26i	1.12501	+	0.644183i
$586$		0			0
$587$			1.56348e25i			0.0779883i	0.999239	+	0.0389941i	$0.0124154\pi$
$587$			1.56348e25i			0.0779883i	−0.999239	+	0.0389941i	$0.987585\pi$
$588$		0			0
$589$	5.84936e25			0.282496
$590$		0			0
$591$	−5.91210e25			−0.276478
$592$		0			0
$593$			2.48930e26i			1.12735i	0.825998	+	0.563673i	$0.190612\pi$
$593$			2.48930e26i			1.12735i	−0.825998	+	0.563673i	$0.809388\pi$
$594$		0			0
$595$	3.56793e26	−	6.23106e26i	1.56497	−	2.73307i
$596$		0			0
$597$			9.98553e25i			0.424243i
$598$		0			0
$599$	3.85523e26			1.58670			0.793351	−	0.608764i	$-0.208334\pi$
$599$	3.85523e26			1.58670			0.793351	+	0.608764i	$0.208334\pi$
$600$		0			0
$601$	4.66265e25			0.185920			0.0929599	−	0.995670i	$-0.470367\pi$
$601$	4.66265e25			0.185920			0.0929599	+	0.995670i	$0.470367\pi$
$602$		0			0
$603$		−	3.60392e25i		−	0.139239i
$604$		0			0
$605$	3.88274e25	−	6.78086e25i	0.145366	−	0.253868i
$606$		0			0
$607$			4.87283e26i			1.76803i	0.467461	+	0.884014i	$0.345169\pi$
$607$			4.87283e26i			1.76803i	−0.467461	+	0.884014i	$0.654831\pi$
$608$		0			0
$609$	−2.13029e26			−0.749160
$610$		0			0
$611$	6.77429e26			2.30926
$612$		0			0
$613$		−	4.13173e26i		−	1.36539i	−0.730702	−	0.682697i	$-0.760807\pi$
$613$		−	4.13173e26i		−	1.36539i	0.730702	−	0.682697i	$-0.239193\pi$
$614$		0			0
$615$	1.45253e26	+	8.31726e25i	0.465385	+	0.266481i
$616$		0			0
$617$		−	1.03592e26i		−	0.321822i	−0.986969	−	0.160911i	$-0.948557\pi$
$617$		−	1.03592e26i		−	0.321822i	0.986969	−	0.160911i	$-0.0514432\pi$
$618$		0			0
$619$	2.16657e26			0.652696			0.326348	−	0.945250i	$-0.394182\pi$
$619$	2.16657e26			0.652696			0.326348	+	0.945250i	$0.394182\pi$
$620$		0			0
$621$	−6.05560e25			−0.176924
$622$		0			0
$623$			7.47294e26i			2.11765i
$624$		0			0
$625$	−1.77385e26	+	3.17622e26i	−0.487591	+	0.873072i
$626$		0			0
$627$		−	1.68321e26i		−	0.448847i
$628$		0			0
$629$	−5.99596e25			−0.155124
$630$		0			0
$631$	−4.79909e26			−1.20470			−0.602351	−	0.798231i	$-0.705769\pi$
$631$	−4.79909e26			−1.20470			−0.602351	+	0.798231i	$0.705769\pi$
$632$		0			0
$633$			1.69868e26i			0.413787i
$634$		0			0
$635$	−6.43121e26	−	3.68253e26i	−1.52034	−	0.870555i
$636$		0			0
$637$			1.47424e27i			3.38254i
$638$		0			0
$639$	3.22197e26			0.717568
$640$		0			0
$641$	−6.76552e26			−1.46268			−0.731341	−	0.682012i	$-0.761105\pi$
$641$	−6.76552e26			−1.46268			−0.731341	+	0.682012i	$0.761105\pi$
$642$		0			0
$643$			5.15280e26i			1.08153i	0.841173	+	0.540766i	$0.181866\pi$
$643$			5.15280e26i			1.08153i	−0.841173	+	0.540766i	$0.818134\pi$
$644$		0			0
$645$	4.78674e25	−	8.35961e25i	0.0975490	−	0.170360i
$646$		0			0
$647$		−	1.74214e26i		−	0.344740i	−0.985032	−	0.172370i	$-0.944857\pi$
$647$		−	1.74214e26i		−	0.344740i	0.985032	−	0.172370i	$-0.0551425\pi$
$648$		0			0
$649$	6.82675e25			0.131187
$650$		0			0
$651$	−8.69198e25			−0.162218
$652$		0			0
$653$			1.86720e26i			0.338466i	0.985576	+	0.169233i	$0.0541290\pi$
$653$			1.86720e26i			0.338466i	−0.985576	+	0.169233i	$0.945871\pi$
$654$		0			0
$655$	1.21285e26	−	2.11813e26i	0.213558	−	0.372959i
$656$		0			0
$657$		−	6.55923e26i		−	1.12197i
$658$		0			0
$659$	1.53611e25			0.0255276			0.0127638	−	0.999919i	$-0.495937\pi$
$659$	1.53611e25			0.0255276			0.0127638	+	0.999919i	$0.495937\pi$
$660$		0			0
$661$	2.28629e26			0.369163			0.184581	−	0.982817i	$-0.440907\pi$
$661$	2.28629e26			0.369163			0.184581	+	0.982817i	$0.440907\pi$
$662$		0			0
$663$			7.34489e26i			1.15241i
$664$		0			0
$665$	1.30020e27	+	7.44498e26i	1.98246	+	1.13516i
$666$		0			0
$667$		−	1.59713e26i		−	0.236671i
$668$		0			0
$669$	1.44640e26			0.208324
$670$		0			0
$671$	4.76826e26			0.667569
$672$		0			0
$673$		−	5.61335e26i		−	0.763975i	−0.924167	−	0.381988i	$-0.875240\pi$
$673$		−	5.61335e26i		−	0.763975i	0.924167	−	0.381988i	$-0.124760\pi$
$674$		0			0
$675$	−4.94607e26	+	2.90287e26i	−0.654447	+	0.384097i
$676$		0			0
$677$			6.36984e26i			0.819476i	0.912203	+	0.409738i	$0.134380\pi$
$677$			6.36984e26i			0.819476i	−0.912203	+	0.409738i	$0.865620\pi$
$678$		0			0
$679$	−1.64448e26			−0.205715
$680$		0			0
$681$	2.68069e26			0.326099
$682$		0			0
$683$			8.90920e26i			1.05400i	0.849864	+	0.527002i	$0.176684\pi$
$683$			8.90920e26i			1.05400i	−0.849864	+	0.527002i	$0.823316\pi$
$684$		0			0
$685$	−9.86393e26	−	5.64812e26i	−1.13498	−	0.649895i
$686$		0			0
$687$		−	2.83298e26i		−	0.317069i
$688$		0			0
$689$	9.32598e26			1.01534
$690$		0			0
$691$	−1.80598e27			−1.91281			−0.956404	−	0.292046i	$-0.905664\pi$
$691$	−1.80598e27			−1.91281			−0.956404	+	0.292046i	$0.905664\pi$
$692$		0			0
$693$		−	1.20071e27i		−	1.23729i
$694$		0			0
$695$	6.02411e26	−	1.05206e27i	0.604001	−	1.05483i
$696$		0			0
$697$		−	2.34566e27i		−	2.28851i
$698$		0			0
$699$	−4.66905e26			−0.443298
$700$		0			0
$701$	−9.01636e26			−0.833125			−0.416563	−	0.909107i	$-0.636765\pi$
$701$	−9.01636e26			−0.833125			−0.416563	+	0.909107i	$0.636765\pi$
$702$		0			0
$703$		−	1.25114e26i		−	0.112520i
$704$		0			0
$705$	−3.47455e26	+	6.06798e26i	−0.304160	+	0.531187i
$706$		0			0
$707$		−	1.64436e27i		−	1.40124i
$708$		0			0
$709$	1.34606e27			1.11667			0.558335	−	0.829616i	$-0.311440\pi$
$709$	1.34606e27			1.11667			0.558335	+	0.829616i	$0.311440\pi$
$710$		0			0
$711$	1.14670e27			0.926166
$712$		0			0
$713$		−	6.51661e25i		−	0.0512473i
$714$		0			0
$715$	1.49311e27	+	8.54960e26i	1.14336	+	0.654694i
$716$		0			0
$717$			6.02557e26i			0.449330i
$718$		0			0
$719$	−1.37600e27			−0.999295			−0.499648	−	0.866229i	$-0.666537\pi$
$719$	−1.37600e27			−0.999295			−0.499648	+	0.866229i	$0.666537\pi$
$720$		0			0
$721$	3.11716e27			2.20483
$722$		0			0
$723$		−	6.69686e26i		−	0.461378i
$724$		0			0
$725$	−7.65616e26	−	1.30450e27i	−0.513807	−	0.875454i
$726$		0			0
$727$			1.87639e27i			1.22673i	0.789801	+	0.613363i	$0.210184\pi$
$727$			1.87639e27i			1.22673i	−0.789801	+	0.613363i	$0.789816\pi$
$728$		0			0
$729$	1.71280e26			0.109092
$730$		0			0
$731$	−1.34997e27			−0.837739
$732$		0			0
$733$		−	6.36662e26i		−	0.384965i	−0.981300	−	0.192483i	$-0.938346\pi$
$733$		−	6.36662e26i		−	0.384965i	0.981300	−	0.192483i	$-0.0616539\pi$
$734$		0			0
$735$	−1.32053e27	−	7.56139e26i	−0.778069	−	0.445525i
$736$		0			0
$737$		−	2.46451e26i		−	0.141511i
$738$		0			0
$739$	−1.19863e27			−0.670753			−0.335376	−	0.942084i	$-0.608863\pi$
$739$	−1.19863e27			−0.670753			−0.335376	+	0.942084i	$0.608863\pi$
$740$		0			0
$741$	−1.53261e27			−0.835911
$742$		0			0
$743$			1.70309e27i			0.905407i	0.891661	+	0.452704i	$0.149540\pi$
$743$			1.70309e27i			0.905407i	−0.891661	+	0.452704i	$0.850460\pi$
$744$		0			0
$745$	−7.08024e26	+	1.23650e27i	−0.366913	+	0.640781i
$746$		0			0
$747$			5.16917e26i			0.261141i
$748$		0			0
$749$	−2.49901e27			−1.23081
$750$		0			0
$751$	−1.89809e26			−0.0911460			−0.0455730	−	0.998961i	$-0.514511\pi$
$751$	−1.89809e26			−0.0911460			−0.0455730	+	0.998961i	$0.514511\pi$
$752$		0			0
$753$		−	2.16094e26i		−	0.101179i
$754$		0			0
$755$	−1.87142e26	+	3.26827e26i	−0.0854428	+	0.149218i
$756$		0			0
$757$			1.00860e27i			0.449063i	0.974467	+	0.224531i	$0.0720852\pi$
$757$			1.00860e27i			0.449063i	−0.974467	+	0.224531i	$0.927915\pi$
$758$		0			0
$759$	−1.87522e26			−0.0814247
$760$		0			0
$761$	−3.87591e27			−1.64142			−0.820709	−	0.571346i	$-0.806421\pi$
$761$	−3.87591e27			−1.64142			−0.820709	+	0.571346i	$0.806421\pi$
$762$		0			0
$763$		−	7.51085e27i		−	3.10246i
$764$		0			0
$765$	3.15831e27	+	1.80846e27i	1.27254	+	0.728660i
$766$		0			0
$767$		−	6.21595e26i		−	0.244316i
$768$		0			0
$769$	−4.22383e27			−1.61959			−0.809797	−	0.586710i	$-0.800423\pi$
$769$	−4.22383e27			−1.61959			−0.809797	+	0.586710i	$0.800423\pi$
$770$		0			0
$771$	−1.66796e27			−0.623979
$772$		0			0
$773$		−	4.57129e27i		−	1.66853i	−0.551364	−	0.834265i	$-0.685892\pi$
$773$		−	4.57129e27i		−	1.66853i	0.551364	−	0.834265i	$-0.314108\pi$
$774$		0			0
$775$	−3.12386e26	−	5.32261e26i	−0.111256	−	0.189565i
$776$		0			0
$777$			1.85916e26i			0.0646127i
$778$		0			0
$779$	4.89454e27			1.65999
$780$		0			0
$781$	2.20332e27			0.729276
$782$		0			0
$783$		−	2.38447e27i		−	0.770291i
$784$		0			0
$785$	−4.45740e26	−	2.55232e26i	−0.140547	−	0.0804774i
$786$		0			0
$787$		−	3.15350e27i		−	0.970582i	−0.874353	−	0.485291i	$-0.838714\pi$
$787$		−	3.15350e27i		−	0.970582i	0.874353	−	0.485291i	$-0.161286\pi$
$788$		0			0
$789$	1.89932e27			0.570645
$790$		0			0
$791$	1.56419e27			0.458787
$792$		0			0
$793$		−	4.34164e27i		−	1.24325i
$794$		0			0
$795$	−4.78332e26	+	8.35363e26i	−0.133734	+	0.233554i
$796$		0			0
$797$			1.55380e26i			0.0424172i	0.999775	+	0.0212086i	$0.00675141\pi$
$797$			1.55380e26i			0.0424172i	−0.999775	+	0.0212086i	$0.993249\pi$
$798$		0			0
$799$	9.79901e27			2.61209
$800$		0			0
$801$	−3.78777e27			−0.985996
$802$		0			0
$803$		−	4.48548e27i		−	1.14028i
$804$		0			0
$805$	8.29424e26	−	1.44851e27i	0.205928	−	0.359635i
$806$		0			0
$807$			1.92919e27i			0.467817i
$808$		0			0
$809$	−2.62754e27			−0.622354			−0.311177	−	0.950352i	$-0.600723\pi$
$809$	−2.62754e27			−0.622354			−0.311177	+	0.950352i	$0.600723\pi$
$810$		0			0
$811$	−5.23012e27			−1.21008			−0.605040	−	0.796195i	$-0.706843\pi$
$811$	−5.23012e27			−1.21008			−0.605040	+	0.796195i	$0.706843\pi$
$812$		0			0
$813$			2.35073e27i			0.531304i
$814$		0			0
$815$	7.16430e27	+	4.10230e27i	1.58189	+	0.905795i
$816$		0			0
$817$		−	2.81690e27i		−	0.607662i
$818$		0			0
$819$	−1.09328e28			−2.30428
$820$		0			0
$821$	−2.67180e27			−0.550229			−0.275115	−	0.961411i	$-0.588716\pi$
$821$	−2.67180e27			−0.550229			−0.275115	+	0.961411i	$0.588716\pi$
$822$		0			0
$823$			6.84884e27i			1.37822i	0.724656	+	0.689111i	$0.241999\pi$
$823$			6.84884e27i			1.37822i	−0.724656	+	0.689111i	$0.758001\pi$
$824$		0			0
$825$	−1.53164e27	+	8.98924e26i	−0.301192	+	0.176771i
$826$		0			0
$827$		−	8.50280e27i		−	1.63403i	−0.576618	−	0.817014i	$-0.695628\pi$
$827$		−	8.50280e27i		−	1.63403i	0.576618	−	0.817014i	$-0.304372\pi$
$828$		0			0
$829$	−1.55632e27			−0.292301			−0.146151	−	0.989262i	$-0.546688\pi$
$829$	−1.55632e27			−0.292301			−0.146151	+	0.989262i	$0.546688\pi$
$830$		0			0
$831$	−6.31287e26			−0.115882
$832$		0			0
$833$			2.13248e28i			3.82612i
$834$		0			0
$835$	3.56373e27	+	2.04060e27i	0.625005	+	0.357880i
$836$		0			0
$837$		−	9.72907e26i		−	0.166794i
$838$		0			0
$839$	−6.93323e27			−1.16198			−0.580988	−	0.813912i	$-0.697334\pi$
$839$	−6.93323e27			−1.16198			−0.580988	+	0.813912i	$0.697334\pi$
$840$		0			0
$841$	1.85649e26			0.0304180
$842$		0			0
$843$		−	8.09558e26i		−	0.129684i
$844$		0			0
$845$	4.61205e27	−	8.05454e27i	0.722363	−	1.26154i
$846$		0			0
$847$			3.39532e27i			0.519982i
$848$		0			0
$849$	2.58755e27			0.387495
$850$		0			0
$851$	−1.39386e26			−0.0204122
$852$		0			0
$853$			7.88064e27i			1.12862i	0.825565	+	0.564308i	$0.190857\pi$
$853$			7.88064e27i			1.12862i	−0.825565	+	0.564308i	$0.809143\pi$
$854$		0			0
$855$	−3.77360e27	+	6.59025e27i	−0.528540	+	0.923047i
$856$		0			0
$857$		−	9.02811e27i		−	1.23674i	−0.785886	−	0.618371i	$-0.787793\pi$
$857$		−	9.02811e27i		−	1.23674i	0.785886	−	0.618371i	$-0.212207\pi$
$858$		0			0
$859$	6.27018e27			0.840127			0.420064	−	0.907495i	$-0.362008\pi$
$859$	6.27018e27			0.840127			0.420064	+	0.907495i	$0.362008\pi$
$860$		0			0
$861$	−7.27315e27			−0.953219
$862$		0			0
$863$			7.26270e27i			0.931099i	0.885022	+	0.465549i	$0.154143\pi$
$863$			7.26270e27i			0.931099i	−0.885022	+	0.465549i	$0.845857\pi$
$864$		0			0
$865$	2.07621e26	+	1.18884e26i	0.0260386	+	0.0149098i
$866$		0			0
$867$			7.24025e27i			0.888326i
$868$		0			0
$869$	7.84162e27			0.941278
$870$		0			0
$871$	−2.24401e27			−0.263543
$872$		0			0
$873$		−	8.33530e26i		−	0.0957824i
$874$		0			0
$875$	−1.69185e26	−	1.58071e28i	−0.0190232	−	1.77736i
$876$		0			0
$877$		−	9.78094e27i		−	1.07618i	−0.842888	−	0.538089i	$-0.819146\pi$
$877$		−	9.78094e27i		−	1.07618i	0.842888	−	0.538089i	$-0.180854\pi$
$878$		0			0
$879$	8.90202e26			0.0958505
$880$		0			0
$881$	−2.73002e27			−0.287670			−0.143835	−	0.989602i	$-0.545943\pi$
$881$	−2.73002e27			−0.287670			−0.143835	+	0.989602i	$0.545943\pi$
$882$		0			0
$883$		−	1.52332e27i		−	0.157096i	−0.996910	−	0.0785480i	$-0.974972\pi$
$883$		−	1.52332e27i		−	0.157096i	0.996910	−	0.0785480i	$-0.0250284\pi$
$884$		0			0
$885$	5.56785e26	+	3.18817e26i	0.0561988	+	0.0321796i
$886$		0			0
$887$			5.92554e27i			0.585401i	0.956204	+	0.292701i	$0.0945539\pi$
$887$			5.92554e27i			0.585401i	−0.956204	+	0.292701i	$0.905446\pi$
$888$		0			0
$889$	3.22024e28			3.11402
$890$		0			0
$891$	4.55413e27			0.431089
$892$		0			0
$893$			2.04470e28i			1.89470i
$894$		0			0
$895$	−9.99316e27	+	1.74522e28i	−0.906534	+	1.58318i
$896$		0			0
$897$			1.70744e27i			0.151641i
$898$		0			0
$899$	2.56599e27			0.223120
$900$		0			0
$901$	1.34900e28			1.14849
$902$		0			0
$903$			4.18584e27i			0.348938i
$904$		0			0
$905$	6.73001e27	−	1.17534e28i	0.549357	−	0.959402i
$906$		0			0
$907$			8.28730e25i			0.00662436i	0.999995	+	0.00331218i	$0.00105430\pi$
$907$			8.28730e25i			0.00662436i	−0.999995	+	0.00331218i	$0.998946\pi$
$908$		0			0
$909$	8.33468e27			0.652427
$910$		0			0
$911$	1.54117e28			1.18148			0.590740	−	0.806862i	$-0.298836\pi$
$911$	1.54117e28			1.18148			0.590740	+	0.806862i	$0.298836\pi$
$912$		0			0
$913$			3.53489e27i			0.265402i
$914$		0			0
$915$	3.88896e27	+	2.22683e27i	0.285979	+	0.163752i
$916$		0			0
$917$			1.06059e28i			0.763908i
$918$		0			0
$919$	4.70381e27			0.331858			0.165929	−	0.986138i	$-0.446938\pi$
$919$	4.70381e27			0.331858			0.165929	+	0.986138i	$0.446938\pi$
$920$		0			0
$921$	6.84833e27			0.473280
$922$		0			0
$923$		−	2.00618e28i		−	1.35817i
$924$		0			0
$925$	−1.13847e27	+	6.68174e26i	−0.0755052	+	0.0443142i
$926$		0			0
$927$			1.57998e28i			1.02658i
$928$		0			0
$929$	−5.56651e27			−0.354351			−0.177175	−	0.984179i	$-0.556696\pi$
$929$	−5.56651e27			−0.354351			−0.177175	+	0.984179i	$0.556696\pi$
$930$		0			0
$931$	−4.44973e28			−2.77531
$932$		0			0
$933$		−	1.25171e28i		−	0.764940i
$934$		0			0
$935$	2.15978e28	+	1.23670e28i	1.29330	+	0.740549i
$936$		0			0
$937$			1.26870e28i			0.744444i	0.928144	+	0.372222i	$0.121404\pi$
$937$			1.26870e28i			0.744444i	−0.928144	+	0.372222i	$0.878596\pi$
$938$		0			0
$939$	−2.57007e27			−0.147782
$940$		0			0
$941$	−2.75974e28			−1.55513			−0.777564	−	0.628804i	$-0.783545\pi$
$941$	−2.75974e28			−1.55513			−0.777564	+	0.628804i	$0.783545\pi$
$942$		0			0
$943$		−	5.45287e27i		−	0.301137i
$944$		0			0
$945$	1.23830e28	−	2.16258e28i	0.670231	−	1.17050i
$946$		0			0
$947$			1.35118e28i			0.716784i	0.933571	+	0.358392i	$0.116675\pi$
$947$			1.35118e28i			0.716784i	−0.933571	+	0.358392i	$0.883325\pi$
$948$		0			0
$949$	−4.08415e28			−2.12360
$950$		0			0
$951$	7.25535e25			0.00369780
$952$		0			0
$953$			3.47564e27i			0.173641i	0.996224	+	0.0868204i	$0.0276706\pi$
$953$			3.47564e27i			0.173641i	−0.996224	+	0.0868204i	$0.972329\pi$
$954$		0			0
$955$	−6.73668e27	+	1.17650e28i	−0.329924	+	0.576182i
$956$		0			0
$957$		−	7.38392e27i		−	0.354506i
$958$		0			0
$959$	4.93908e28			2.32471
$960$		0			0
$961$	−2.06237e28			−0.951687
$962$		0			0
$963$		−	1.26666e28i		−	0.573074i
$964$		0			0
$965$	2.07763e28	+	1.18966e28i	0.921636	+	0.527732i
$966$		0			0
$967$			2.17676e28i			0.946801i	0.880847	+	0.473400i	$0.156974\pi$
$967$			2.17676e28i			0.946801i	−0.880847	+	0.473400i	$0.843026\pi$
$968$		0			0
$969$	−2.21693e28			−0.945530
$970$		0			0
$971$	−1.33361e28			−0.557758			−0.278879	−	0.960326i	$-0.589963\pi$
$971$	−1.33361e28			−0.557758			−0.278879	+	0.960326i	$0.589963\pi$
$972$		0			0
$973$			5.26788e28i			2.16055i
$974$		0			0
$975$	8.18495e27	+	1.39460e28i	0.329209	+	0.560926i
$976$		0			0
$977$			3.49042e28i			1.37683i	0.725319	+	0.688413i	$0.241692\pi$
$977$			3.49042e28i			1.37683i	−0.725319	+	0.688413i	$0.758308\pi$
$978$		0			0
$979$	−2.59024e28			−1.00208
$980$		0			0
$981$	3.80699e28			1.44453
$982$		0			0
$983$		−	5.05289e28i		−	1.88053i	−0.340437	−	0.940267i	$-0.610575\pi$
$983$		−	5.05289e28i		−	1.88053i	0.340437	−	0.940267i	$-0.389425\pi$
$984$		0			0
$985$	1.58292e28	+	9.06388e27i	0.577851	+	0.330879i
$986$		0			0
$987$		−	3.03837e28i		−	1.08800i
$988$		0			0
$989$	−3.13823e27			−0.110235
$990$		0			0
$991$	−1.66641e28			−0.574224			−0.287112	−	0.957897i	$-0.592695\pi$
$991$	−1.66641e28			−0.574224			−0.287112	+	0.957897i	$0.592695\pi$
$992$		0			0
$993$			8.24532e27i			0.278734i
$994$		0			0
$995$	1.53089e28	−	2.67356e28i	0.507720	−	0.886686i
$996$		0			0
$997$		−	3.15659e28i		−	1.02710i	−0.858059	−	0.513551i	$-0.828330\pi$
$997$		−	3.15659e28i		−	1.02710i	0.858059	−	0.513551i	$-0.171670\pi$
$998$		0			0
$999$	−2.08099e27			−0.0664351

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	80.20.c.d.49.12		28
4.3	odd	2		40.20.c.a.9.17	yes	28
5.4	even	2	inner	80.20.c.d.49.17		28
20.19	odd	2		40.20.c.a.9.12	✓	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
40.20.c.a.9.12	✓	28	20.19	odd	2
40.20.c.a.9.17	yes	28	4.3	odd	2
80.20.c.d.49.12		28	1.1	even	1	trivial
80.20.c.d.49.17		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)

\(f(q)\)	\(=\)	\(q-14155.3i q^{3} +(-2.17015e6 + 3.78998e6i) q^{5} -1.89772e8i q^{7} +9.61890e8 q^{9} +O(q^{10})\)	\(q-14155.3i q^{3} +(-2.17015e6 + 3.78998e6i) q^{5} -1.89772e8i q^{7} +9.61890e8 q^{9} +6.57781e9 q^{11} -5.98927e10i q^{13} +(5.36482e10 + 3.07191e10i) q^{15} -8.66349e11i q^{17} +1.80776e12 q^{19} -2.68628e12 q^{21} -2.01397e12i q^{23} +(-9.65436e12 - 1.64497e13i) q^{25} -3.00679e13i q^{27} +7.93026e13 q^{29} +3.23570e13 q^{31} -9.31106e13i q^{33} +(7.19232e14 + 4.11835e14i) q^{35} -6.92096e13i q^{37} -8.47798e14 q^{39} +2.70752e15 q^{41} -1.55823e15i q^{43} +(-2.08745e15 + 3.64554e15i) q^{45} +1.13107e16i q^{47} -2.46146e16 q^{49} -1.22634e16 q^{51} +1.55711e16i q^{53} +(-1.42748e16 + 2.49297e16i) q^{55} -2.55893e16i q^{57} +1.03785e16 q^{59} +7.24902e16 q^{61} -1.82540e17i q^{63} +(2.26992e17 + 1.29976e17i) q^{65} -3.74671e16i q^{67} -2.85083e16 q^{69} +3.34962e17 q^{71} -6.81911e17i q^{73} +(-2.32849e17 + 1.36660e17i) q^{75} -1.24828e18i q^{77} +1.19213e18 q^{79} +6.92347e17 q^{81} +5.37397e17i q^{83} +(3.28344e18 + 1.88011e18i) q^{85} -1.12255e18i q^{87} -3.93785e18 q^{89} -1.13660e19 q^{91} -4.58022e17i q^{93} +(-3.92311e18 + 6.85136e18i) q^{95} -8.66554e17i q^{97} +6.32712e18 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - 3935164 q^{5} - 10352560732 q^{9}+O(q^{10}) \) 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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