LMFDB - Embedded newform 80.20.c.c.49.3

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:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 14903918288 x^{7} + 443569659980446 x^{6} + \cdots + 53\!\cdots\!00 $ x^10 - 14903918288x^7 + 443569659980446x^6 - 407914028595579828x^5 + 111063390167690425472x^4 + 2240737884939969545921560x^3 + 9026417197496381459207546025x^2 + 3113006936793203978513537653500*x + 536802807608455434230094922445000
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{69}\cdot 3^{6}\cdot 5^{18} $
Twist minimal:	no (minimal twist has level 10)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			49.3
Root			$1933.50 - 1933.50i$ of defining polynomial
Character	$\chi$	$=$	80.49
Dual form			80.20.c.c.49.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-43192.0i q^{3} +(3.01510e6 + 3.15954e6i) q^{5} +2.08285e8i q^{7} -7.03291e8 q^{9} +O(q^{10})$	\(q-43192.0i q^{3} +(3.01510e6 + 3.15954e6i) q^{5} +2.08285e8i q^{7} -7.03291e8 q^{9} -8.06882e9 q^{11} +5.42118e10i q^{13} +(1.36467e11 - 1.30228e11i) q^{15} +1.27965e11i q^{17} -3.24794e11 q^{19} +8.99624e12 q^{21} -4.42630e12i q^{23} +(-8.91860e11 + 1.90526e13i) q^{25} -1.98239e13i q^{27} +1.05364e14 q^{29} +1.18471e14 q^{31} +3.48509e14i q^{33} +(-6.58083e14 + 6.27998e14i) q^{35} +1.23582e15i q^{37} +2.34152e15 q^{39} +2.26871e15 q^{41} +2.39124e15i q^{43} +(-2.12049e15 - 2.22208e15i) q^{45} -2.93268e15i q^{47} -3.19836e16 q^{49} +5.52707e15 q^{51} +9.00554e14i q^{53} +(-2.43283e16 - 2.54937e16i) q^{55} +1.40285e16i q^{57} -7.94073e15 q^{59} +8.68976e16 q^{61} -1.46485e17i q^{63} +(-1.71284e17 + 1.63454e17i) q^{65} -2.07970e17i q^{67} -1.91181e17 q^{69} -2.68592e17 q^{71} -4.47519e17i q^{73} +(8.22922e17 + 3.85213e16i) q^{75} -1.68061e18i q^{77} -9.56550e17 q^{79} -1.67364e18 q^{81} +9.39729e17i q^{83} +(-4.04310e17 + 3.85827e17i) q^{85} -4.55087e18i q^{87} +1.39386e18 q^{89} -1.12915e19 q^{91} -5.11700e18i q^{93} +(-9.79285e17 - 1.02620e18i) q^{95} -1.03444e18i q^{97} +5.67473e18 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 2902670 q^{5} - 8718754970 q^{9}+O(q^{10}) $ 10 * q + 2902670 * q^5 - 8718754970 * q^9	$ 10 q + 2902670 q^{5} - 8718754970 q^{9} + 2965225880 q^{11} - 225010487480 q^{15} + 4196987836200 q^{19} - 501224287480 q^{21} + 19247576437650 q^{25} + 219360620418300 q^{29} + 667121586663680 q^{31} - 14\!\cdots\!60 q^{35}+ \cdots - 41\!\cdots\!60 q^{99}+O(q^{100}) $ 10 * q + 2902670 * q^5 - 8718754970 * q^9 + 2965225880 * q^11 - 225010487480 * q^15 + 4196987836200 * q^19 - 501224287480 * q^21 + 19247576437650 * q^25 + 219360620418300 * q^29 + 667121586663680 * q^31 - 1477908982965160 * q^35 + 3387373771795440 * q^39 + 3587345408194420 * q^41 - 13139237288012990 * q^45 - 30324198320796930 * q^49 - 106899828254155520 * q^51 + 99144934237329160 * q^55 + 332698279801897400 * q^59 + 533407565011656620 * q^61 - 682989395388761520 * q^65 - 95759593423262840 * q^69 - 1975827158504532720 * q^71 + 3881333883421828400 * q^75 + 2303771531732690400 * q^79 + 12793501534789009010 * q^81 - 6445103007057591040 * q^85 - 11076199503631707100 * q^89 - 7638137420731759920 * q^91 + 7279632536499161400 * q^95 - 41542573713793315160 * 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
$3$		−	43192.0i		−	1.26693i	−0.773772	−	0.633464i	$-0.781633\pi$
$3$		−	43192.0i		−	1.26693i	0.773772	−	0.633464i	$-0.218367\pi$
$4$		0			0
$5$	3.01510e6	+	3.15954e6i	0.690377	+	0.723450i
$5$	3.01510e6	+	3.15954e6i	0.690377	+	0.723450i
$6$		0			0
$7$			2.08285e8i			1.95086i	0.220312	+	0.975429i	$0.429292\pi$
$7$			2.08285e8i			1.95086i	−0.220312	+	0.975429i	$0.570708\pi$
$8$		0			0
$9$	−7.03291e8			−0.605106
$10$		0			0
$11$	−8.06882e9			−1.03176			−0.515881	−	0.856660i	$-0.672535\pi$
$11$	−8.06882e9			−1.03176			−0.515881	+	0.856660i	$0.672535\pi$
$12$		0			0
$13$			5.42118e10i			1.41786i	0.705281	+	0.708928i	$0.250821\pi$
$13$			5.42118e10i			1.41786i	−0.705281	+	0.708928i	$0.749179\pi$
$14$		0			0
$15$	1.36467e11	−	1.30228e11i	0.916559	−	0.874658i
$16$		0			0
$17$			1.27965e11i			0.261714i	0.991401	+	0.130857i	$0.0417728\pi$
$17$			1.27965e11i			0.261714i	−0.991401	+	0.130857i	$0.958227\pi$
$18$		0			0
$19$	−3.24794e11			−0.230913			−0.115457	−	0.993313i	$-0.536833\pi$
$19$	−3.24794e11			−0.230913			−0.115457	+	0.993313i	$0.536833\pi$
$20$		0			0
$21$	8.99624e12			2.47160
$22$		0			0
$23$		−	4.42630e12i		−	0.512420i	−0.966621	−	0.256210i	$-0.917526\pi$
$23$		−	4.42630e12i		−	0.512420i	0.966621	−	0.256210i	$-0.0824739\pi$
$24$		0			0
$25$	−8.91860e11	+	1.90526e13i	−0.0467592	+	0.998906i
$26$		0			0
$27$		−	1.98239e13i		−	0.500302i
$28$		0			0
$29$	1.05364e14			1.34868			0.674340	−	0.738421i	$-0.264428\pi$
$29$	1.05364e14			1.34868			0.674340	+	0.738421i	$0.264428\pi$
$30$		0			0
$31$	1.18471e14			0.804777			0.402389	−	0.915469i	$-0.368180\pi$
$31$	1.18471e14			0.804777			0.402389	+	0.915469i	$0.368180\pi$
$32$		0			0
$33$			3.48509e14i			1.30717i
$34$		0			0
$35$	−6.58083e14	+	6.27998e14i	−1.41135	+	1.34683i
$36$		0			0
$37$			1.23582e15i			1.56328i	0.623728	+	0.781642i	$0.285617\pi$
$37$			1.23582e15i			1.56328i	−0.623728	+	0.781642i	$0.714383\pi$
$38$		0			0
$39$	2.34152e15			1.79632
$40$		0			0
$41$	2.26871e15			1.08226			0.541132	−	0.840938i	$-0.317996\pi$
$41$	2.26871e15			1.08226			0.541132	+	0.840938i	$0.317996\pi$
$42$		0			0
$43$			2.39124e15i			0.725559i	0.931875	+	0.362779i	$0.118172\pi$
$43$			2.39124e15i			0.725559i	−0.931875	+	0.362779i	$0.881828\pi$
$44$		0			0
$45$	−2.12049e15	−	2.22208e15i	−0.417751	−	0.437764i
$46$		0			0
$47$		−	2.93268e15i		−	0.382239i	−0.981567	−	0.191119i	$-0.938788\pi$
$47$		−	2.93268e15i		−	0.382239i	0.981567	−	0.191119i	$-0.0612117\pi$
$48$		0			0
$49$	−3.19836e16			−2.80585
$50$		0			0
$51$	5.52707e15			0.331572
$52$		0			0
$53$			9.00554e14i			0.0374877i	0.999824	+	0.0187439i	$0.00596671\pi$
$53$			9.00554e14i			0.0374877i	−0.999824	+	0.0187439i	$0.994033\pi$
$54$		0			0
$55$	−2.43283e16	−	2.54937e16i	−0.712304	−	0.746428i
$56$		0			0
$57$			1.40285e16i			0.292550i
$58$		0			0
$59$	−7.94073e15			−0.119335			−0.0596673	−	0.998218i	$-0.519004\pi$
$59$	−7.94073e15			−0.119335			−0.0596673	+	0.998218i	$0.519004\pi$
$60$		0			0
$61$	8.68976e16			0.951424			0.475712	−	0.879601i	$-0.342190\pi$
$61$	8.68976e16			0.951424			0.475712	+	0.879601i	$0.342190\pi$
$62$		0			0
$63$		−	1.46485e17i		−	1.18048i
$64$		0			0
$65$	−1.71284e17	+	1.63454e17i	−1.02575	+	0.978855i
$66$		0			0
$67$		−	2.07970e17i		−	0.933878i	−0.884289	−	0.466939i	$-0.845357\pi$
$67$		−	2.07970e17i		−	0.933878i	0.884289	−	0.466939i	$-0.154643\pi$
$68$		0			0
$69$	−1.91181e17			−0.649199
$70$		0			0
$71$	−2.68592e17			−0.695246			−0.347623	−	0.937634i	$-0.613011\pi$
$71$	−2.68592e17			−0.695246			−0.347623	+	0.937634i	$0.613011\pi$
$72$		0			0
$73$		−	4.47519e17i		−	0.889701i	−0.895605	−	0.444851i	$-0.853257\pi$
$73$		−	4.47519e17i		−	0.889701i	0.895605	−	0.444851i	$-0.146743\pi$
$74$		0			0
$75$	8.22922e17	+	3.85213e16i	1.26554	+	0.0592405i
$76$		0			0
$77$		−	1.68061e18i		−	2.01282i
$78$		0			0
$79$	−9.56550e17			−0.897947			−0.448973	−	0.893545i	$-0.648210\pi$
$79$	−9.56550e17			−0.897947			−0.448973	+	0.893545i	$0.648210\pi$
$80$		0			0
$81$	−1.67364e18			−1.23895
$82$		0			0
$83$			9.39729e17i			0.551773i	0.961190	+	0.275887i	$0.0889714\pi$
$83$			9.39729e17i			0.551773i	−0.961190	+	0.275887i	$0.911029\pi$
$84$		0			0
$85$	−4.04310e17	+	3.85827e17i	−0.189337	+	0.180681i
$86$		0			0
$87$		−	4.55087e18i		−	1.70868i
$88$		0			0
$89$	1.39386e18			0.421710			0.210855	−	0.977517i	$-0.432375\pi$
$89$	1.39386e18			0.421710			0.210855	+	0.977517i	$0.432375\pi$
$90$		0			0
$91$	−1.12915e19			−2.76604
$92$		0			0
$93$		−	5.11700e18i		−	1.01959i
$94$		0			0
$95$	−9.79285e17	−	1.02620e18i	−0.159417	−	0.167054i
$96$		0			0
$97$		−	1.03444e18i		−	0.138158i	−0.997611	−	0.0690789i	$-0.977994\pi$
$97$		−	1.03444e18i		−	0.138158i	0.997611	−	0.0690789i	$-0.0220060\pi$
$98$		0			0
$99$	5.67473e18			0.624325
$100$		0			0
$101$	−4.20066e18			−0.382177			−0.191088	−	0.981573i	$-0.561202\pi$
$101$	−4.20066e18			−0.382177			−0.191088	+	0.981573i	$0.561202\pi$
$102$		0			0
$103$			1.21938e19i			0.920844i	0.887700	+	0.460422i	$0.152302\pi$
$103$			1.21938e19i			0.920844i	−0.887700	+	0.460422i	$0.847698\pi$
$104$		0			0
$105$	2.71245e19	+	2.84240e19i	1.70633	+	1.78808i
$106$		0			0
$107$			3.10285e19i			1.63161i	0.578331	+	0.815803i	$0.303704\pi$
$107$			3.10285e19i			1.63161i	−0.578331	+	0.815803i	$0.696296\pi$
$108$		0			0
$109$	−1.66625e19			−0.734833			−0.367416	−	0.930057i	$-0.619758\pi$
$109$	−1.66625e19			−0.734833			−0.367416	+	0.930057i	$0.619758\pi$
$110$		0			0
$111$	5.33775e19			1.98057
$112$		0			0
$113$			1.50444e19i			0.471118i	0.971860	+	0.235559i	$0.0756921\pi$
$113$			1.50444e19i			0.471118i	−0.971860	+	0.235559i	$0.924308\pi$
$114$		0			0
$115$	1.39851e19	−	1.33457e19i	0.370710	−	0.353763i
$116$		0			0
$117$		−	3.81267e19i		−	0.857953i
$118$		0			0
$119$	−2.66531e19			−0.510566
$120$		0			0
$121$	3.94671e18			0.0645319
$122$		0			0
$123$		−	9.79904e19i		−	1.37115i
$124$		0			0
$125$	−6.28865e19	+	5.46277e19i	−0.754940	+	0.655794i
$126$		0			0
$127$			5.54813e19i			0.572811i	0.958108	+	0.286406i	$0.0924605\pi$
$127$			5.54813e19i			0.572811i	−0.958108	+	0.286406i	$0.907540\pi$
$128$		0			0
$129$	1.03282e20			0.919231
$130$		0			0
$131$	3.22163e18			0.0247741			0.0123871	−	0.999923i	$-0.496057\pi$
$131$	3.22163e18			0.0247741			0.0123871	+	0.999923i	$0.496057\pi$
$132$		0			0
$133$		−	6.76496e19i		−	0.450479i
$134$		0			0
$135$	6.26342e19	−	5.97709e19i	0.361944	−	0.345397i
$136$		0			0
$137$			1.65123e20i			0.829778i	0.909872	+	0.414889i	$0.136180\pi$
$137$			1.65123e20i			0.829778i	−0.909872	+	0.414889i	$0.863820\pi$
$138$		0			0
$139$	−8.07694e19			−0.353677			−0.176838	−	0.984240i	$-0.556587\pi$
$139$	−8.07694e19			−0.353677			−0.176838	+	0.984240i	$0.556587\pi$
$140$		0			0
$141$	−1.26668e20			−0.484269
$142$		0			0
$143$		−	4.37425e20i		−	1.46289i
$144$		0			0
$145$	3.17681e20	+	3.32900e20i	0.931098	+	0.975703i
$146$		0			0
$147$			1.38144e21i			3.55481i
$148$		0			0
$149$	−4.65143e20			−1.05273			−0.526364	−	0.850259i	$-0.676445\pi$
$149$	−4.65143e20			−1.05273			−0.526364	+	0.850259i	$0.676445\pi$
$150$		0			0
$151$	−6.31893e20			−1.25998			−0.629988	−	0.776605i	$-0.716940\pi$
$151$	−6.31893e20			−1.25998			−0.629988	+	0.776605i	$0.716940\pi$
$152$		0			0
$153$		−	8.99967e19i		−	0.158364i
$154$		0			0
$155$	3.57201e20	+	3.74313e20i	0.555600	+	0.582216i
$156$		0			0
$157$		−	1.26928e21i		−	1.74788i	−0.486038	−	0.873938i	$-0.661558\pi$
$157$		−	1.26928e21i		−	1.74788i	0.486038	−	0.873938i	$-0.338442\pi$
$158$		0			0
$159$	3.88968e19			0.0474943
$160$		0			0
$161$	9.21930e20			0.999659
$162$		0			0
$163$		−	1.86977e21i		−	1.80304i	−0.432736	−	0.901521i	$-0.642452\pi$
$163$		−	1.86977e21i		−	1.80304i	0.432736	−	0.901521i	$-0.357548\pi$
$164$		0			0
$165$	−1.10113e21	+	1.05079e21i	−0.945670	+	0.902438i
$166$		0			0
$167$			9.25020e20i			0.708508i	0.935149	+	0.354254i	$0.115265\pi$
$167$			9.25020e20i			0.708508i	−0.935149	+	0.354254i	$0.884735\pi$
$168$		0			0
$169$	−1.47700e21			−1.01032
$170$		0			0
$171$	2.28425e20			0.139727
$172$		0			0
$173$		−	1.19860e21i		−	0.656501i	−0.944591	−	0.328251i	$-0.893541\pi$
$173$		−	1.19860e21i		−	0.656501i	0.944591	−	0.328251i	$-0.106459\pi$
$174$		0			0
$175$	−3.96837e21	−	1.85761e20i	−1.94872	−	0.0912205i
$176$		0			0
$177$			3.42976e20i			0.151188i
$178$		0			0
$179$	−4.58702e21			−1.81730			−0.908650	−	0.417558i	$-0.862886\pi$
$179$	−4.58702e21			−1.81730			−0.908650	+	0.417558i	$0.862886\pi$
$180$		0			0
$181$	−1.97622e21			−0.704511			−0.352256	−	0.935904i	$-0.614585\pi$
$181$	−1.97622e21			−0.704511			−0.352256	+	0.935904i	$0.614585\pi$
$182$		0			0
$183$		−	3.75328e21i		−	1.20539i
$184$		0			0
$185$	−3.90461e21	+	3.72611e21i	−1.13096	+	1.07925i
$186$		0			0
$187$		−	1.03253e21i		−	0.270026i
$188$		0			0
$189$	4.12900e21			0.976019
$190$		0			0
$191$	5.28606e21			1.13062			0.565308	−	0.824880i	$-0.308757\pi$
$191$	5.28606e21			1.13062			0.565308	+	0.824880i	$0.308757\pi$
$192$		0			0
$193$		−	3.11632e21i		−	0.603737i	−0.953350	−	0.301869i	$-0.902390\pi$
$193$		−	3.11632e21i		−	0.603737i	0.953350	−	0.301869i	$-0.0976104\pi$
$194$		0			0
$195$	7.05991e21	+	7.39812e21i	1.24014	+	1.29955i
$196$		0			0
$197$			8.74592e21i			1.39436i	0.716894	+	0.697182i	$0.245563\pi$
$197$			8.74592e21i			1.39436i	−0.716894	+	0.697182i	$0.754437\pi$
$198$		0			0
$199$	6.60021e21			0.955990			0.477995	−	0.878362i	$-0.341364\pi$
$199$	6.60021e21			0.955990			0.477995	+	0.878362i	$0.341364\pi$
$200$		0			0
$201$	−8.98265e21			−1.18316
$202$		0			0
$203$			2.19456e22i			2.63109i
$204$		0			0
$205$	6.84039e21	+	7.16808e21i	0.747170	+	0.782963i
$206$		0			0
$207$			3.11298e21i			0.310069i
$208$		0			0
$209$	2.62070e21			0.238247
$210$		0			0
$211$	−1.10420e22			−0.916988			−0.458494	−	0.888697i	$-0.651611\pi$
$211$	−1.10420e22			−0.916988			−0.458494	+	0.888697i	$0.651611\pi$
$212$		0			0
$213$			1.16010e22i			0.880826i
$214$		0			0
$215$	−7.55521e21	+	7.20982e21i	−0.524905	+	0.500909i
$216$		0			0
$217$			2.46757e22i			1.57001i
$218$		0			0
$219$	−1.93293e22			−1.12719
$220$		0			0
$221$	−6.93721e21			−0.371072
$222$		0			0
$223$		−	2.73728e21i		−	0.134407i	−0.997739	−	0.0672036i	$-0.978592\pi$
$223$		−	2.73728e21i		−	0.134407i	0.997739	−	0.0672036i	$-0.0214077\pi$
$224$		0			0
$225$	6.27238e20	−	1.33995e22i	0.0282943	−	0.604444i
$226$		0			0
$227$			1.24285e22i			0.515433i	0.966221	+	0.257716i	$0.0829700\pi$
$227$			1.24285e22i			0.515433i	−0.966221	+	0.257716i	$0.917030\pi$
$228$		0			0
$229$	−1.48359e22			−0.566078			−0.283039	−	0.959108i	$-0.591343\pi$
$229$	−1.48359e22			−0.566078			−0.283039	+	0.959108i	$0.591343\pi$
$230$		0			0
$231$	−7.25890e22			−2.55010
$232$		0			0
$233$		−	1.40623e22i		−	0.455171i	−0.973758	−	0.227586i	$-0.926917\pi$
$233$		−	1.40623e22i		−	0.455171i	0.973758	−	0.227586i	$-0.0730831\pi$
$234$		0			0
$235$	9.26590e21	−	8.84231e21i	0.276530	−	0.263889i
$236$		0			0
$237$			4.13154e22i			1.13763i
$238$		0			0
$239$	9.39243e21			0.238780			0.119390	−	0.992847i	$-0.461906\pi$
$239$	9.39243e21			0.238780			0.119390	+	0.992847i	$0.461906\pi$
$240$		0			0
$241$	−2.44048e22			−0.573209			−0.286605	−	0.958049i	$-0.592527\pi$
$241$	−2.44048e22			−0.573209			−0.286605	+	0.958049i	$0.592527\pi$
$242$		0			0
$243$			4.92475e22i			1.06936i
$244$		0			0
$245$	−9.64336e22	−	1.01053e23i	−1.93709	−	2.02989i
$246$		0			0
$247$		−	1.76077e22i		−	0.327402i
$248$		0			0
$249$	4.05888e22			0.699057
$250$		0			0
$251$	1.01347e23			1.61775			0.808874	−	0.587982i	$-0.200077\pi$
$251$	1.01347e23			1.61775			0.808874	+	0.587982i	$0.200077\pi$
$252$		0			0
$253$			3.57150e22i			0.528695i
$254$		0			0
$255$	1.66647e22	+	1.74630e22i	0.228910	+	0.239876i
$256$		0			0
$257$			8.73524e22i			1.11406i	0.830491	+	0.557032i	$0.188060\pi$
$257$			8.73524e22i			1.11406i	−0.830491	+	0.557032i	$0.811940\pi$
$258$		0			0
$259$	−2.57402e23			−3.04975
$260$		0			0
$261$	−7.41012e22			−0.816095
$262$		0			0
$263$			7.98635e22i			0.818030i	0.912528	+	0.409015i	$0.134128\pi$
$263$			7.98635e22i			0.818030i	−0.912528	+	0.409015i	$0.865872\pi$
$264$		0			0
$265$	−2.84533e21	+	2.71526e21i	−0.0271205	+	0.0258807i
$266$		0			0
$267$		−	6.02036e22i		−	0.534276i
$268$		0			0
$269$	−1.58322e23			−1.30886			−0.654431	−	0.756122i	$-0.727092\pi$
$269$	−1.58322e23			−1.30886			−0.654431	+	0.756122i	$0.727092\pi$
$270$		0			0
$271$	4.43865e21			0.0342013			0.0171006	−	0.999854i	$-0.494556\pi$
$271$	4.43865e21			0.0342013			0.0171006	+	0.999854i	$0.494556\pi$
$272$		0			0
$273$			4.87703e23i			3.50437i
$274$		0			0
$275$	7.19626e21	−	1.53732e23i	0.0482443	−	1.03063i
$276$		0			0
$277$		−	2.46343e23i		−	1.54164i	−0.637053	−	0.770820i	$-0.719847\pi$
$277$		−	2.46343e23i		−	1.54164i	0.637053	−	0.770820i	$-0.280153\pi$
$278$		0			0
$279$	−8.33196e22			−0.486975
$280$		0			0
$281$	6.37562e22			0.348187			0.174093	−	0.984729i	$-0.444301\pi$
$281$	6.37562e22			0.348187			0.174093	+	0.984729i	$0.444301\pi$
$282$		0			0
$283$		−	1.05073e22i		−	0.0536441i	−0.999640	−	0.0268220i	$-0.991461\pi$
$283$		−	1.05073e22i		−	0.0536441i	0.999640	−	0.0268220i	$-0.00853874\pi$
$284$		0			0
$285$	−4.43236e22	+	4.22973e22i	−0.211645	+	0.201970i
$286$		0			0
$287$			4.72538e23i			2.11134i
$288$		0			0
$289$	2.22697e23			0.931506
$290$		0			0
$291$	−4.46797e22			−0.175036
$292$		0			0
$293$		−	3.65971e23i		−	1.34340i	−0.740825	−	0.671698i	$-0.765565\pi$
$293$		−	3.65971e23i		−	1.34340i	0.740825	−	0.671698i	$-0.234435\pi$
$294$		0			0
$295$	−2.39421e22	−	2.50890e22i	−0.0823859	−	0.0863326i
$296$		0			0
$297$			1.59955e23i			0.516193i
$298$		0			0
$299$	2.39958e23			0.726538
$300$		0			0
$301$	−4.98058e23			−1.41546
$302$		0			0
$303$			1.81435e23i			0.484190i
$304$		0			0
$305$	2.62005e23	+	2.74556e23i	0.656841	+	0.688308i
$306$		0			0
$307$			3.02695e23i			0.713167i	0.934264	+	0.356583i	$0.116058\pi$
$307$			3.02695e23i			0.713167i	−0.934264	+	0.356583i	$0.883942\pi$
$308$		0			0
$309$	5.26676e23			1.16664
$310$		0			0
$311$	6.11936e23			1.27492			0.637459	−	0.770484i	$-0.279985\pi$
$311$	6.11936e23			1.27492			0.637459	+	0.770484i	$0.279985\pi$
$312$		0			0
$313$		−	2.01681e23i		−	0.395362i	−0.980266	−	0.197681i	$-0.936659\pi$
$313$		−	2.01681e23i		−	0.395362i	0.980266	−	0.197681i	$-0.0633410\pi$
$314$		0			0
$315$	4.62824e23	−	4.41666e23i	0.854015	−	0.814974i
$316$		0			0
$317$		−	1.77676e22i		−	0.0308720i	−0.999881	−	0.0154360i	$-0.995086\pi$
$317$		−	1.77676e22i		−	0.0308720i	0.999881	−	0.0154360i	$-0.00491363\pi$
$318$		0			0
$319$	−8.50159e23			−1.39152
$320$		0			0
$321$	1.34018e24			2.06713
$322$		0			0
$323$		−	4.15622e22i		−	0.0604331i
$324$		0			0
$325$	−1.03288e24	−	4.83494e22i	−1.41631	−	0.0662978i
$326$		0			0
$327$			7.19687e23i			0.930980i
$328$		0			0
$329$	6.10832e23			0.745694
$330$		0			0
$331$	−8.27231e23			−0.953368			−0.476684	−	0.879075i	$-0.658161\pi$
$331$	−8.27231e23			−0.953368			−0.476684	+	0.879075i	$0.658161\pi$
$332$		0			0
$333$		−	8.69139e23i		−	0.945952i
$334$		0			0
$335$	6.57089e23	−	6.27050e23i	0.675614	−	0.644728i
$336$		0			0
$337$			5.93914e23i			0.577084i	0.957467	+	0.288542i	$0.0931705\pi$
$337$			5.93914e23i			0.577084i	−0.957467	+	0.288542i	$0.906829\pi$
$338$		0			0
$339$	6.49799e23			0.596873
$340$		0			0
$341$	−9.55920e23			−0.830338
$342$		0			0
$343$		−	4.28748e24i		−	3.52296i
$344$		0			0
$345$	−5.76429e23	−	6.04043e23i	−0.448192	−	0.469663i
$346$		0			0
$347$		−	9.46719e21i		−	0.00696773i	−0.999994	−	0.00348386i	$-0.998891\pi$
$347$		−	9.46719e21i		−	0.00696773i	0.999994	−	0.00348386i	$-0.00110895\pi$
$348$		0			0
$349$	7.78170e23			0.542292			0.271146	−	0.962538i	$-0.412597\pi$
$349$	7.78170e23			0.542292			0.271146	+	0.962538i	$0.412597\pi$
$350$		0			0
$351$	1.07469e24			0.709357
$352$		0			0
$353$		−	2.76550e24i		−	1.72947i	−0.502224	−	0.864737i	$-0.667485\pi$
$353$		−	2.76550e24i		−	1.72947i	0.502224	−	0.864737i	$-0.332515\pi$
$354$		0			0
$355$	−8.09830e23	−	8.48626e23i	−0.479982	−	0.502975i
$356$		0			0
$357$			1.15120e24i			0.646851i
$358$		0			0
$359$	−5.17573e23			−0.275787			−0.137894	−	0.990447i	$-0.544033\pi$
$359$	−5.17573e23			−0.275787			−0.137894	+	0.990447i	$0.544033\pi$
$360$		0			0
$361$	−1.87293e24			−0.946679
$362$		0			0
$363$		−	1.70467e23i		−	0.0817572i
$364$		0			0
$365$	1.41395e24	−	1.34931e24i	0.643654	−	0.614229i
$366$		0			0
$367$			2.75239e24i			1.18955i	0.803892	+	0.594775i	$0.202759\pi$
$367$			2.75239e24i			1.18955i	−0.803892	+	0.594775i	$0.797241\pi$
$368$		0			0
$369$	−1.59557e24			−0.654884
$370$		0			0
$371$	−1.87572e23			−0.0731333
$372$		0			0
$373$		−	2.84949e24i		−	1.05568i	−0.849343	−	0.527842i	$-0.823001\pi$
$373$		−	2.84949e24i		−	1.05568i	0.849343	−	0.527842i	$-0.176999\pi$
$374$		0			0
$375$	2.35948e24	+	2.71620e24i	0.830844	+	0.956454i
$376$		0			0
$377$			5.71195e24i			1.91224i
$378$		0			0
$379$	5.49548e24			1.74958			0.874788	−	0.484506i	$-0.161000\pi$
$379$	5.49548e24			1.74958			0.874788	+	0.484506i	$0.161000\pi$
$380$		0			0
$381$	2.39635e24			0.725710
$382$		0			0
$383$		−	4.78864e24i		−	1.37982i	−0.723894	−	0.689912i	$-0.757649\pi$
$383$		−	4.78864e24i		−	1.37982i	0.723894	−	0.689912i	$-0.242351\pi$
$384$		0			0
$385$	5.30995e24	−	5.06720e24i	1.45617	−	1.38961i
$386$		0			0
$387$		−	1.68174e24i		−	0.439040i
$388$		0			0
$389$	5.45472e24			1.35597			0.677986	−	0.735074i	$-0.262853\pi$
$389$	5.45472e24			1.35597			0.677986	+	0.735074i	$0.262853\pi$
$390$		0			0
$391$	5.66411e23			0.134107
$392$		0			0
$393$		−	1.39149e23i		−	0.0313870i
$394$		0			0
$395$	−2.88409e24	−	3.02226e24i	−0.619922	−	0.649619i
$396$		0			0
$397$			5.07640e23i			0.104003i	0.998647	+	0.0520015i	$0.0165601\pi$
$397$			5.07640e23i			0.104003i	−0.998647	+	0.0520015i	$0.983440\pi$
$398$		0			0
$399$	−2.92192e24			−0.570724
$400$		0			0
$401$	4.10057e24			0.763787			0.381894	−	0.924206i	$-0.375272\pi$
$401$	4.10057e24			0.763787			0.381894	+	0.924206i	$0.375272\pi$
$402$		0			0
$403$			6.42252e24i			1.14106i
$404$		0			0
$405$	−5.04619e24	−	5.28793e24i	−0.855344	−	0.896320i
$406$		0			0
$407$		−	9.97158e24i		−	1.61294i
$408$		0			0
$409$	3.32374e24			0.513163			0.256581	−	0.966523i	$-0.417404\pi$
$409$	3.32374e24			0.513163			0.256581	+	0.966523i	$0.417404\pi$
$410$		0			0
$411$	7.13200e24			1.05127
$412$		0			0
$413$		−	1.65393e24i		−	0.232805i
$414$		0			0
$415$	−2.96911e24	+	2.83337e24i	−0.399180	+	0.380931i
$416$		0			0
$417$			3.48860e24i			0.448083i
$418$		0			0
$419$	−7.54102e24			−0.925543			−0.462771	−	0.886478i	$-0.653145\pi$
$419$	−7.54102e24			−0.925543			−0.462771	+	0.886478i	$0.653145\pi$
$420$		0			0
$421$	2.77469e24			0.325487			0.162744	−	0.986668i	$-0.447966\pi$
$421$	2.77469e24			0.325487			0.162744	+	0.986668i	$0.447966\pi$
$422$		0			0
$423$			2.06253e24i			0.231295i
$424$		0			0
$425$	−2.43807e24	−	1.14127e23i	−0.261427	−	0.0122375i
$426$		0			0
$427$			1.80994e25i			1.85609i
$428$		0			0
$429$	−1.88933e25			−1.85338
$430$		0			0
$431$	6.87641e24			0.645398			0.322699	−	0.946502i	$-0.395410\pi$
$431$	6.87641e24			0.645398			0.322699	+	0.946502i	$0.395410\pi$
$432$		0			0
$433$			3.34344e24i			0.300302i	0.988663	+	0.150151i	$0.0479760\pi$
$433$			3.34344e24i			0.300302i	−0.988663	+	0.150151i	$0.952024\pi$
$434$		0			0
$435$	1.43786e25	−	1.37213e25i	1.23615	−	1.17963i
$436$		0			0
$437$			1.43763e24i			0.118325i
$438$		0			0
$439$	1.84873e25			1.45700			0.728502	−	0.685044i	$-0.240217\pi$
$439$	1.84873e25			1.45700			0.728502	+	0.685044i	$0.240217\pi$
$440$		0			0
$441$	2.24938e25			1.69784
$442$		0			0
$443$			7.38035e24i			0.533632i	0.963748	+	0.266816i	$0.0859716\pi$
$443$			7.38035e24i			0.533632i	−0.963748	+	0.266816i	$0.914028\pi$
$444$		0			0
$445$	4.20262e24	+	4.40395e24i	0.291139	+	0.305086i
$446$		0			0
$447$			2.00905e25i			1.33373i
$448$		0			0
$449$	−3.08050e25			−1.96011			−0.980057	−	0.198718i	$-0.936322\pi$
$449$	−3.08050e25			−1.96011			−0.980057	+	0.198718i	$0.936322\pi$
$450$		0			0
$451$	−1.83058e25			−1.11664
$452$		0			0
$453$			2.72928e25i			1.59630i
$454$		0			0
$455$	−3.40449e25	−	3.56759e25i	−1.90961	−	2.00109i
$456$		0			0
$457$			1.67496e25i			0.901155i	0.892737	+	0.450577i	$0.148782\pi$
$457$			1.67496e25i			0.901155i	−0.892737	+	0.450577i	$0.851218\pi$
$458$		0			0
$459$	2.53676e24			0.130936
$460$		0			0
$461$	−2.99493e25			−1.48329			−0.741647	−	0.670791i	$-0.765955\pi$
$461$	−2.99493e25			−1.48329			−0.741647	+	0.670791i	$0.765955\pi$
$462$		0			0
$463$			1.95872e25i			0.931008i	0.885046	+	0.465504i	$0.154127\pi$
$463$			1.95872e25i			0.931008i	−0.885046	+	0.465504i	$0.845873\pi$
$464$		0			0
$465$	1.61674e25	−	1.54283e25i	0.737625	−	0.703905i
$466$		0			0
$467$		−	1.31967e25i		−	0.578037i	−0.957323	−	0.289019i	$-0.906671\pi$
$467$		−	1.31967e25i		−	0.578037i	0.957323	−	0.289019i	$-0.0933289\pi$
$468$		0			0
$469$	4.33170e25			1.82186
$470$		0			0
$471$	−5.48228e25			−2.21443
$472$		0			0
$473$		−	1.92945e25i		−	0.748604i
$474$		0			0
$475$	2.89671e23	−	6.18818e24i	0.0107973	−	0.230661i
$476$		0			0
$477$		−	6.33352e23i		−	0.0226841i
$478$		0			0
$479$	2.67518e25			0.920802			0.460401	−	0.887711i	$-0.347706\pi$
$479$	2.67518e25			0.920802			0.460401	+	0.887711i	$0.347706\pi$
$480$		0			0
$481$	−6.69959e25			−2.21651
$482$		0			0
$483$		−	3.98200e25i		−	1.26650i
$484$		0			0
$485$	3.26836e24	−	3.11895e24i	0.0999502	−	0.0953809i
$486$		0			0
$487$			5.86617e25i			1.72516i	0.505920	+	0.862581i	$0.331153\pi$
$487$			5.86617e25i			1.72516i	−0.505920	+	0.862581i	$0.668847\pi$
$488$		0			0
$489$	−8.07592e25			−2.28432
$490$		0			0
$491$	−1.96325e25			−0.534197			−0.267098	−	0.963669i	$-0.586065\pi$
$491$	−1.96325e25			−0.534197			−0.267098	+	0.963669i	$0.586065\pi$
$492$		0			0
$493$			1.34828e25i			0.352968i
$494$		0			0
$495$	1.71099e25	+	1.79295e25i	0.431020	+	0.451668i
$496$		0			0
$497$		−	5.59435e25i		−	1.35633i
$498$		0			0
$499$	−7.20078e25			−1.68044			−0.840222	−	0.542242i	$-0.817575\pi$
$499$	−7.20078e25			−1.68044			−0.840222	+	0.542242i	$0.817575\pi$
$500$		0			0
$501$	3.99535e25			0.897628
$502$		0			0
$503$		−	2.80080e23i		−	0.00605880i	−0.999995	−	0.00302940i	$-0.999036\pi$
$503$		−	2.80080e23i		−	0.00605880i	0.999995	−	0.00302940i	$-0.000964289\pi$
$504$		0			0
$505$	−1.26654e25	−	1.32721e25i	−0.263846	−	0.276486i
$506$		0			0
$507$			6.37947e25i			1.28000i
$508$		0			0
$509$	4.20773e25			0.813260			0.406630	−	0.913593i	$-0.366704\pi$
$509$	4.20773e25			0.813260			0.406630	+	0.913593i	$0.366704\pi$
$510$		0			0
$511$	9.32113e25			1.73568
$512$		0			0
$513$			6.43867e24i			0.115526i
$514$		0			0
$515$	−3.85268e25	+	3.67655e25i	−0.666184	+	0.635730i
$516$		0			0
$517$			2.36632e25i			0.394379i
$518$		0			0
$519$	−5.17699e25			−0.831740
$520$		0			0
$521$	−6.76164e24			−0.104735			−0.0523677	−	0.998628i	$-0.516677\pi$
$521$	−6.76164e24			−0.104735			−0.0523677	+	0.998628i	$0.516677\pi$
$522$		0			0
$523$		−	1.21973e25i		−	0.182179i	−0.995843	−	0.0910894i	$-0.970965\pi$
$523$		−	1.21973e25i		−	0.182179i	0.995843	−	0.0910894i	$-0.0290349\pi$
$524$		0			0
$525$	−8.02339e24	+	1.71402e26i	−0.115570	+	2.46889i
$526$		0			0
$527$			1.51601e25i			0.210621i
$528$		0			0
$529$	5.50234e25			0.737426
$530$		0			0
$531$	5.58465e24			0.0722101
$532$		0			0
$533$			1.22991e26i			1.53449i
$534$		0			0
$535$	−9.80357e25	+	9.35540e25i	−1.18038	+	1.12642i
$536$		0			0
$537$			1.98123e26i			2.30239i
$538$		0			0
$539$	2.58070e26			2.89497
$540$		0			0
$541$	1.42631e26			1.54469			0.772343	−	0.635206i	$-0.219085\pi$
$541$	1.42631e26			1.54469			0.772343	+	0.635206i	$0.219085\pi$
$542$		0			0
$543$			8.53568e25i			0.892565i
$544$		0			0
$545$	−5.02391e25	−	5.26458e25i	−0.507311	−	0.531614i
$546$		0			0
$547$		−	1.70841e26i		−	1.66615i	−0.553163	−	0.833073i	$-0.686579\pi$
$547$		−	1.70841e26i		−	1.66615i	0.553163	−	0.833073i	$-0.313421\pi$
$548$		0			0
$549$	−6.11143e25			−0.575712
$550$		0			0
$551$	−3.42214e25			−0.311428
$552$		0			0
$553$		−	1.99235e26i		−	1.75177i
$554$		0			0
$555$	1.60938e26	+	1.68648e26i	1.36734	+	1.43284i
$556$		0			0
$557$		−	1.59134e26i		−	1.30659i	−0.757104	−	0.653294i	$-0.773386\pi$
$557$		−	1.59134e26i		−	1.30659i	0.757104	−	0.653294i	$-0.226614\pi$
$558$		0			0
$559$	−1.29633e26			−1.02874
$560$		0			0
$561$	−4.45969e25			−0.342103
$562$		0			0
$563$		−	1.24671e26i		−	0.924562i	−0.886733	−	0.462281i	$-0.847031\pi$
$563$		−	1.24671e26i		−	0.924562i	0.886733	−	0.462281i	$-0.152969\pi$
$564$		0			0
$565$	−4.75334e25	+	4.53604e25i	−0.340830	+	0.325249i
$566$		0			0
$567$		−	3.48594e26i		−	2.41702i
$568$		0			0
$569$	−1.31042e26			−0.878705			−0.439352	−	0.898315i	$-0.644792\pi$
$569$	−1.31042e26			−0.878705			−0.439352	+	0.898315i	$0.644792\pi$
$570$		0			0
$571$	−1.62155e26			−1.05169			−0.525846	−	0.850580i	$-0.676251\pi$
$571$	−1.62155e26			−1.05169			−0.525846	+	0.850580i	$0.676251\pi$
$572$		0			0
$573$		−	2.28316e26i		−	1.43241i
$574$		0			0
$575$	8.43326e25	+	3.94764e24i	0.511860	+	0.0239603i
$576$		0			0
$577$			8.42365e24i			0.0494687i	0.999694	+	0.0247343i	$0.00787399\pi$
$577$			8.42365e24i			0.0494687i	−0.999694	+	0.0247343i	$0.992126\pi$
$578$		0			0
$579$	−1.34600e26			−0.764891
$580$		0			0
$581$	−1.95731e26			−1.07643
$582$		0			0
$583$		−	7.26641e24i		−	0.0386784i
$584$		0			0
$585$	1.20463e26	−	1.14956e26i	0.620686	−	0.592311i
$586$		0			0
$587$		−	2.19200e25i		−	0.109340i	−0.998504	−	0.0546699i	$-0.982589\pi$
$587$		−	2.19200e25i		−	0.109340i	0.998504	−	0.0546699i	$-0.0174107\pi$
$588$		0			0
$589$	−3.84786e25			−0.185834
$590$		0			0
$591$	3.77754e26			1.76656
$592$		0			0
$593$			2.48422e25i			0.112505i	0.998417	+	0.0562524i	$0.0179152\pi$
$593$			2.48422e25i			0.112505i	−0.998417	+	0.0562524i	$0.982085\pi$
$594$		0			0
$595$	−8.03618e25	−	8.42116e25i	−0.352483	−	0.369369i
$596$		0			0
$597$		−	2.85077e26i		−	1.21117i
$598$		0			0
$599$	−3.32173e26			−1.36713			−0.683565	−	0.729890i	$-0.739571\pi$
$599$	−3.32173e26			−1.36713			−0.683565	+	0.729890i	$0.739571\pi$
$600$		0			0
$601$	2.53258e26			1.00985			0.504924	−	0.863164i	$-0.331521\pi$
$601$	2.53258e26			1.00985			0.504924	+	0.863164i	$0.331521\pi$
$602$		0			0
$603$			1.46264e26i			0.565095i
$604$		0			0
$605$	1.18997e25	+	1.24698e25i	0.0445513	+	0.0466856i
$606$		0			0
$607$		−	1.40197e26i		−	0.508680i	−0.967115	−	0.254340i	$-0.918142\pi$
$607$		−	1.40197e26i		−	0.508680i	0.967115	−	0.254340i	$-0.0818582\pi$
$608$		0			0
$609$	9.47875e26			3.33340
$610$		0			0
$611$	1.58986e26			0.541959
$612$		0			0
$613$		−	6.82804e25i		−	0.225643i	−0.993615	−	0.112821i	$-0.964011\pi$
$613$		−	6.82804e25i		−	0.225643i	0.993615	−	0.112821i	$-0.0359888\pi$
$614$		0			0
$615$	3.09604e26	−	2.95450e26i	0.991958	−	0.946610i
$616$		0			0
$617$			3.30908e26i			1.02801i	0.857787	+	0.514006i	$0.171839\pi$
$617$			3.30908e26i			1.02801i	−0.857787	+	0.514006i	$0.828161\pi$
$618$		0			0
$619$	−5.09639e24			−0.0153533			−0.00767665	−	0.999971i	$-0.502444\pi$
$619$	−5.09639e24			−0.0153533			−0.00767665	+	0.999971i	$0.502444\pi$
$620$		0			0
$621$	−8.77463e25			−0.256365
$622$		0			0
$623$			2.90319e26i			0.822696i
$624$		0			0
$625$	−3.62207e26	−	3.39846e25i	−0.995627	−	0.0934160i
$626$		0			0
$627$		−	1.13193e26i		−	0.301842i
$628$		0			0
$629$	−1.58141e26			−0.409133
$630$		0			0
$631$	−2.18125e26			−0.547554			−0.273777	−	0.961793i	$-0.588273\pi$
$631$	−2.18125e26			−0.547554			−0.273777	+	0.961793i	$0.588273\pi$
$632$		0			0
$633$			4.76926e26i			1.16176i
$634$		0			0
$635$	−1.75295e26	+	1.67282e26i	−0.414400	+	0.395456i
$636$		0			0
$637$		−	1.73389e27i		−	3.97829i
$638$		0			0
$639$	1.88898e26			0.420697
$640$		0			0
$641$	2.36210e26			0.510677			0.255339	−	0.966852i	$-0.417813\pi$
$641$	2.36210e26			0.510677			0.255339	+	0.966852i	$0.417813\pi$
$642$		0			0
$643$		−	3.22770e26i		−	0.677468i	−0.940882	−	0.338734i	$-0.890001\pi$
$643$		−	3.22770e26i		−	0.677468i	0.940882	−	0.338734i	$-0.109999\pi$
$644$		0			0
$645$	3.11407e26	+	3.26325e26i	0.634616	+	0.665017i
$646$		0			0
$647$		−	8.05361e25i		−	0.159368i	−0.996820	−	0.0796838i	$-0.974609\pi$
$647$		−	8.05361e25i		−	0.159368i	0.996820	−	0.0796838i	$-0.0253911\pi$
$648$		0			0
$649$	6.40723e25			0.123125
$650$		0			0
$651$	1.06579e27			1.98909
$652$		0			0
$653$			9.62412e26i			1.74456i	0.489007	+	0.872280i	$0.337359\pi$
$653$			9.62412e26i			1.74456i	−0.489007	+	0.872280i	$0.662641\pi$
$654$		0			0
$655$	9.71352e24	+	1.01789e25i	0.0171035	+	0.0179228i
$656$		0			0
$657$			3.14736e26i			0.538363i
$658$		0			0
$659$	7.10178e26			1.18020			0.590101	−	0.807330i	$-0.299088\pi$
$659$	7.10178e26			1.18020			0.590101	+	0.807330i	$0.299088\pi$
$660$		0			0
$661$	−5.58871e26			−0.902397			−0.451199	−	0.892424i	$-0.649003\pi$
$661$	−5.58871e26			−0.902397			−0.451199	+	0.892424i	$0.649003\pi$
$662$		0			0
$663$			2.99632e26i			0.470122i
$664$		0			0
$665$	2.13741e26	−	2.03970e26i	0.325899	−	0.311000i
$666$		0			0
$667$		−	4.66370e26i		−	0.691091i
$668$		0			0
$669$	−1.18229e26			−0.170284
$670$		0			0
$671$	−7.01160e26			−0.981643
$672$		0			0
$673$		−	9.30277e25i		−	0.126610i	−0.997994	−	0.0633052i	$-0.979836\pi$
$673$		−	9.30277e25i		−	0.126610i	0.997994	−	0.0633052i	$-0.0201642\pi$
$674$		0			0
$675$	3.77696e26	+	1.76801e25i	0.499755	+	0.0233937i
$676$		0			0
$677$		−	1.13084e27i		−	1.45481i	−0.686206	−	0.727407i	$-0.740725\pi$
$677$		−	1.13084e27i		−	1.45481i	0.686206	−	0.727407i	$-0.259275\pi$
$678$		0			0
$679$	2.15459e26			0.269526
$680$		0			0
$681$	5.36811e26			0.653016
$682$		0			0
$683$		−	6.79696e25i		−	0.0804115i	−0.999191	−	0.0402058i	$-0.987199\pi$
$683$		−	6.79696e25i		−	0.0804115i	0.999191	−	0.0402058i	$-0.0128013\pi$
$684$		0			0
$685$	−5.21712e26	+	4.97862e26i	−0.600303	+	0.572860i
$686$		0			0
$687$			6.40792e26i			0.717180i
$688$		0			0
$689$	−4.88207e25			−0.0531522
$690$		0			0
$691$	−6.31024e26			−0.668350			−0.334175	−	0.942511i	$-0.608458\pi$
$691$	−6.31024e26			−0.668350			−0.334175	+	0.942511i	$0.608458\pi$
$692$		0			0
$693$			1.18196e27i			1.21797i
$694$		0			0
$695$	−2.43528e26	−	2.55194e26i	−0.244170	−	0.255867i
$696$		0			0
$697$			2.90316e26i			0.283243i
$698$		0			0
$699$	−6.07379e26			−0.576669
$700$		0			0
$701$	1.94723e27			1.79927			0.899636	−	0.436641i	$-0.143832\pi$
$701$	1.94723e27			1.79927			0.899636	+	0.436641i	$0.143832\pi$
$702$		0			0
$703$		−	4.01386e26i		−	0.360983i
$704$		0			0
$705$	−3.81917e26	−	4.00213e26i	−0.334328	−	0.350344i
$706$		0			0
$707$		−	8.74932e26i		−	0.745573i
$708$		0			0
$709$	8.15682e26			0.676678			0.338339	−	0.941024i	$-0.390135\pi$
$709$	8.15682e26			0.676678			0.338339	+	0.941024i	$0.390135\pi$
$710$		0			0
$711$	6.72734e26			0.543353
$712$		0			0
$713$		−	5.24388e26i		−	0.412384i
$714$		0			0
$715$	1.38206e27	−	1.31888e27i	1.05833	−	1.00995i
$716$		0			0
$717$		−	4.05678e26i		−	0.302517i
$718$		0			0
$719$	−1.06484e27			−0.773319			−0.386659	−	0.922223i	$-0.626371\pi$
$719$	−1.06484e27			−0.773319			−0.386659	+	0.922223i	$0.626371\pi$
$720$		0			0
$721$	−2.53978e27			−1.79644
$722$		0			0
$723$			1.05409e27i			0.726214i
$724$		0			0
$725$	−9.39695e25	+	2.00745e27i	−0.0630632	+	1.34721i
$726$		0			0
$727$			2.38416e27i			1.55868i	0.626599	+	0.779342i	$0.284446\pi$
$727$			2.38416e27i			1.55868i	−0.626599	+	0.779342i	$0.715554\pi$
$728$		0			0
$729$	1.81891e26			0.115851
$730$		0			0
$731$	−3.05995e26			−0.189889
$732$		0			0
$733$		−	2.19360e27i		−	1.32639i	−0.748448	−	0.663193i	$-0.769201\pi$
$733$		−	2.19360e27i		−	1.32639i	0.748448	−	0.663193i	$-0.230799\pi$
$734$		0			0
$735$	−4.36470e27	+	4.16517e27i	−2.57173	+	2.45416i
$736$		0			0
$737$			1.67807e27i			0.963540i
$738$		0			0
$739$	−1.15117e27			−0.644194			−0.322097	−	0.946707i	$-0.604388\pi$
$739$	−1.15117e27			−0.644194			−0.322097	+	0.946707i	$0.604388\pi$
$740$		0			0
$741$	−7.60511e26			−0.414794
$742$		0			0
$743$			1.22060e27i			0.648903i	0.945902	+	0.324451i	$0.105180\pi$
$743$			1.22060e27i			0.648903i	−0.945902	+	0.324451i	$0.894820\pi$
$744$		0			0
$745$	−1.40245e27	−	1.46964e27i	−0.726780	−	0.761596i
$746$		0			0
$747$		−	6.60903e26i		−	0.333881i
$748$		0			0
$749$	−6.46276e27			−3.18303
$750$		0			0
$751$	−1.03596e27			−0.497468			−0.248734	−	0.968572i	$-0.580015\pi$
$751$	−1.03596e27			−0.497468			−0.248734	+	0.968572i	$0.580015\pi$
$752$		0			0
$753$		−	4.37739e27i		−	2.04957i
$754$		0			0
$755$	−1.90522e27	−	1.99649e27i	−0.869859	−	0.911530i
$756$		0			0
$757$			3.63469e27i			1.61829i	0.587609	+	0.809145i	$0.300069\pi$
$757$			3.63469e27i			1.61829i	−0.587609	+	0.809145i	$0.699931\pi$
$758$		0			0
$759$	1.54260e27			0.669819
$760$		0			0
$761$	2.66230e27			1.12746			0.563732	−	0.825958i	$-0.309365\pi$
$761$	2.66230e27			1.12746			0.563732	+	0.825958i	$0.309365\pi$
$762$		0			0
$763$		−	3.47054e27i		−	1.43355i
$764$		0			0
$765$	2.84348e26	−	2.71349e26i	0.114569	−	0.109331i
$766$		0			0
$767$		−	4.30481e26i		−	0.169199i
$768$		0			0
$769$	−2.42037e27			−0.928073			−0.464037	−	0.885816i	$-0.653599\pi$
$769$	−2.42037e27			−0.928073			−0.464037	+	0.885816i	$0.653599\pi$
$770$		0			0
$771$	3.77293e27			1.41144
$772$		0			0
$773$		−	2.26005e26i		−	0.0824920i	−0.999149	−	0.0412460i	$-0.986867\pi$
$773$		−	2.26005e26i		−	0.0824920i	0.999149	−	0.0412460i	$-0.0131327\pi$
$774$		0			0
$775$	−1.05660e26	+	2.25718e27i	−0.0376307	+	0.803897i
$776$		0			0
$777$			1.11177e28i			3.86381i
$778$		0			0
$779$	−7.36864e26			−0.249909
$780$		0			0
$781$	2.16722e27			0.717328
$782$		0			0
$783$		−	2.08871e27i		−	0.674748i
$784$		0			0
$785$	4.01033e27	−	3.82700e27i	1.26450	−	1.20669i
$786$		0			0
$787$			1.54109e27i			0.474317i	0.971471	+	0.237158i	$0.0762160\pi$
$787$			1.54109e27i			0.474317i	−0.971471	+	0.237158i	$0.923784\pi$
$788$		0			0
$789$	3.44947e27			1.03638
$790$		0			0
$791$	−3.13352e27			−0.919085
$792$		0			0
$793$			4.71087e27i			1.34898i
$794$		0			0
$795$	1.17278e26	+	1.22896e26i	0.0327889	+	0.0343597i
$796$		0			0
$797$		−	1.83594e27i		−	0.501193i	−0.968092	−	0.250596i	$-0.919373\pi$
$797$		−	1.83594e27i		−	0.501193i	0.968092	−	0.250596i	$-0.0806267\pi$
$798$		0			0
$799$	3.75280e26			0.100037
$800$		0			0
$801$	−9.80289e26			−0.255179
$802$		0			0
$803$			3.61095e27i			0.917959i
$804$		0			0
$805$	2.77971e27	+	2.91287e27i	0.690142	+	0.723203i
$806$		0			0
$807$			6.83824e27i			1.65823i
$808$		0			0
$809$	−3.38086e27			−0.800785			−0.400393	−	0.916344i	$-0.631126\pi$
$809$	−3.38086e27			−0.800785			−0.400393	+	0.916344i	$0.631126\pi$
$810$		0			0
$811$	3.29137e27			0.761515			0.380757	−	0.924675i	$-0.375663\pi$
$811$	3.29137e27			0.761515			0.380757	+	0.924675i	$0.375663\pi$
$812$		0			0
$813$		−	1.91714e26i		−	0.0433306i
$814$		0			0
$815$	5.90760e27	−	5.63754e27i	1.30441	−	1.24478i
$816$		0			0
$817$		−	7.76660e26i		−	0.167541i
$818$		0			0
$819$	7.94121e27			1.67375
$820$		0			0
$821$	−6.67368e27			−1.37438			−0.687188	−	0.726479i	$-0.741155\pi$
$821$	−6.67368e27			−1.37438			−0.687188	+	0.726479i	$0.741155\pi$
$822$		0			0
$823$		−	9.66964e26i		−	0.194586i	−0.995256	−	0.0972931i	$-0.968982\pi$
$823$		−	9.66964e26i		−	0.194586i	0.995256	−	0.0972931i	$-0.0310184\pi$
$824$		0			0
$825$	−6.64001e27	−	3.10821e26i	−1.30574	−	0.0611221i
$826$		0			0
$827$			2.86949e27i			0.551445i	0.961237	+	0.275722i	$0.0889170\pi$
$827$			2.86949e27i			0.551445i	−0.961237	+	0.275722i	$0.911083\pi$
$828$		0			0
$829$	2.07117e27			0.388999			0.194500	−	0.980903i	$-0.437692\pi$
$829$	2.07117e27			0.388999			0.194500	+	0.980903i	$0.437692\pi$
$830$		0			0
$831$	−1.06401e28			−1.95315
$832$		0			0
$833$		−	4.09278e27i		−	0.734329i
$834$		0			0
$835$	−2.92263e27	+	2.78902e27i	−0.512570	+	0.489137i
$836$		0			0
$837$		−	2.34855e27i		−	0.402632i
$838$		0			0
$839$	−8.37219e27			−1.40314			−0.701569	−	0.712602i	$-0.747517\pi$
$839$	−8.37219e27			−1.40314			−0.701569	+	0.712602i	$0.747517\pi$
$840$		0			0
$841$	4.99821e27			0.818940
$842$		0			0
$843$		−	2.75376e27i		−	0.441127i
$844$		0			0
$845$	−4.45330e27	−	4.66664e27i	−0.697499	−	0.730913i
$846$		0			0
$847$			8.22039e26i			0.125893i
$848$		0			0
$849$	−4.53834e26			−0.0679632
$850$		0			0
$851$	5.47009e27			0.801058
$852$		0			0
$853$			1.10526e28i			1.58289i	0.611241	+	0.791445i	$0.290671\pi$
$853$			1.10526e28i			1.58289i	−0.611241	+	0.791445i	$0.709329\pi$
$854$		0			0
$855$	6.88723e26	+	7.21716e26i	0.0964642	+	0.101085i
$856$		0			0
$857$		−	1.29183e28i		−	1.76966i	−0.465917	−	0.884828i	$-0.654276\pi$
$857$		−	1.29183e28i		−	1.76966i	0.465917	−	0.884828i	$-0.345724\pi$
$858$		0			0
$859$	5.49824e27			0.736696			0.368348	−	0.929688i	$-0.379923\pi$
$859$	5.49824e27			0.736696			0.368348	+	0.929688i	$0.379923\pi$
$860$		0			0
$861$	2.04099e28			2.67492
$862$		0			0
$863$			4.72445e27i			0.605688i	0.953040	+	0.302844i	$0.0979361\pi$
$863$			4.72445e27i			0.605688i	−0.953040	+	0.302844i	$0.902064\pi$
$864$		0			0
$865$	3.78701e27	−	3.61389e27i	0.474946	−	0.453233i
$866$		0			0
$867$		−	9.61876e27i		−	1.18015i
$868$		0			0
$869$	7.71823e27			0.926467
$870$		0			0
$871$	1.12744e28			1.32410
$872$		0			0
$873$			7.27515e26i			0.0836001i
$874$		0			0
$875$	−1.13781e28	−	1.30983e28i	−1.27936	−	1.47278i
$876$		0			0
$877$			4.47817e27i			0.492725i	0.969178	+	0.246363i	$0.0792354\pi$
$877$			4.47817e27i			0.492725i	−0.969178	+	0.246363i	$0.920765\pi$
$878$		0			0
$879$	−1.58070e28			−1.70199
$880$		0			0
$881$	−3.79218e27			−0.399593			−0.199796	−	0.979837i	$-0.564028\pi$
$881$	−3.79218e27			−0.399593			−0.199796	+	0.979837i	$0.564028\pi$
$882$		0			0
$883$		−	1.20844e28i		−	1.24623i	−0.782130	−	0.623116i	$-0.785867\pi$
$883$		−	1.20844e28i		−	1.24623i	0.782130	−	0.623116i	$-0.214133\pi$
$884$		0			0
$885$	−1.08365e27	+	1.03411e27i	−0.109377	+	0.104377i
$886$		0			0
$887$			1.24023e28i			1.22526i	0.790369	+	0.612631i	$0.209889\pi$
$887$			1.24023e28i			1.22526i	−0.790369	+	0.612631i	$0.790111\pi$
$888$		0			0
$889$	−1.15559e28			−1.11747
$890$		0			0
$891$	1.35043e28			1.27830
$892$		0			0
$893$			9.52516e26i			0.0882639i
$894$		0			0
$895$	−1.38303e28	−	1.44929e28i	−1.25462	−	1.31473i
$896$		0			0
$897$		−	1.03643e28i		−	0.920471i
$898$		0			0
$899$	1.24825e28			1.08539
$900$		0			0
$901$	−1.15239e26			−0.00981105
$902$		0			0
$903$			2.15122e28i			1.79329i
$904$		0			0
$905$	−5.95849e27	−	6.24393e27i	−0.486379	−	0.509679i
$906$		0			0
$907$		−	1.66588e27i		−	0.133161i	−0.997781	−	0.0665803i	$-0.978791\pi$
$907$		−	1.66588e27i		−	0.133161i	0.997781	−	0.0665803i	$-0.0212088\pi$
$908$		0			0
$909$	2.95429e27			0.231257
$910$		0			0
$911$	1.24680e28			0.955815			0.477908	−	0.878410i	$-0.341395\pi$
$911$	1.24680e28			0.955815			0.477908	+	0.878410i	$0.341395\pi$
$912$		0			0
$913$		−	7.58250e27i		−	0.569298i
$914$		0			0
$915$	1.18586e28	−	1.13165e28i	0.872036	−	0.832170i
$916$		0			0
$917$			6.71016e26i			0.0483308i
$918$		0			0
$919$	4.88830e27			0.344874			0.172437	−	0.985021i	$-0.444836\pi$
$919$	4.88830e27			0.344874			0.172437	+	0.985021i	$0.444836\pi$
$920$		0			0
$921$	1.30740e28			0.903531
$922$		0			0
$923$		−	1.45608e28i		−	0.985759i
$924$		0			0
$925$	−2.35456e28	−	1.10218e27i	−1.56157	−	0.0730978i
$926$		0			0
$927$		−	8.57581e27i		−	0.557208i
$928$		0			0
$929$	6.92502e27			0.440830			0.220415	−	0.975406i	$-0.429259\pi$
$929$	6.92502e27			0.440830			0.220415	+	0.975406i	$0.429259\pi$
$930$		0			0
$931$	1.03881e28			0.647908
$932$		0			0
$933$		−	2.64308e28i		−	1.61523i
$934$		0			0
$935$	3.26230e27	−	3.11317e27i	0.195350	−	0.186420i
$936$		0			0
$937$		−	1.70882e28i		−	1.00270i	−0.865246	−	0.501348i	$-0.832838\pi$
$937$		−	1.70882e28i		−	1.00270i	0.865246	−	0.501348i	$-0.167162\pi$
$938$		0			0
$939$	−8.71104e27			−0.500895
$940$		0			0
$941$	−2.35344e27			−0.132618			−0.0663089	−	0.997799i	$-0.521122\pi$
$941$	−2.35344e27			−0.132618			−0.0663089	+	0.997799i	$0.521122\pi$
$942$		0			0
$943$		−	1.00420e28i		−	0.554574i
$944$		0			0
$945$	1.24494e28	+	1.30457e28i	0.673821	+	0.706101i
$946$		0			0
$947$		−	1.17827e28i		−	0.625060i	−0.949908	−	0.312530i	$-0.898824\pi$
$947$		−	1.17827e28i		−	0.625060i	0.949908	−	0.312530i	$-0.101176\pi$
$948$		0			0
$949$	2.42608e28			1.26147
$950$		0			0
$951$	−7.67418e26			−0.0391126
$952$		0			0
$953$			1.46936e28i			0.734081i	0.930205	+	0.367041i	$0.119629\pi$
$953$			1.46936e28i			0.734081i	−0.930205	+	0.367041i	$0.880371\pi$
$954$		0			0
$955$	1.59380e28	+	1.67015e28i	0.780551	+	0.817944i
$956$		0			0
$957$			3.67201e28i			1.76295i
$958$		0			0
$959$	−3.43926e28			−1.61878
$960$		0			0
$961$	−7.63530e27			−0.352334
$962$		0			0
$963$		−	2.18221e28i		−	0.987294i
$964$		0			0
$965$	9.84613e27	−	9.39601e27i	0.436774	−	0.416806i
$966$		0			0
$967$			1.02025e28i			0.443768i	0.975073	+	0.221884i	$0.0712207\pi$
$967$			1.02025e28i			0.443768i	−0.975073	+	0.221884i	$0.928779\pi$
$968$		0			0
$969$	−1.79516e27			−0.0765644
$970$		0			0
$971$	3.31985e28			1.38847			0.694233	−	0.719750i	$-0.255744\pi$
$971$	3.31985e28			1.38847			0.694233	+	0.719750i	$0.255744\pi$
$972$		0			0
$973$		−	1.68230e28i		−	0.689973i
$974$		0			0
$975$	−2.08831e27	+	4.46121e28i	−0.0839945	+	1.79436i
$976$		0			0
$977$			2.60461e28i			1.02741i	0.857966	+	0.513706i	$0.171728\pi$
$977$			2.60461e28i			1.02741i	−0.857966	+	0.513706i	$0.828272\pi$
$978$		0			0
$979$	−1.12468e28			−0.435104
$980$		0			0
$981$	1.17186e28			0.444652
$982$		0			0
$983$			4.59224e28i			1.70909i	0.519374	+	0.854547i	$0.326165\pi$
$983$			4.59224e28i			1.70909i	−0.519374	+	0.854547i	$0.673835\pi$
$984$		0			0
$985$	−2.76331e28	+	2.63698e28i	−1.00875	+	0.962637i
$986$		0			0
$987$		−	2.63831e28i		−	0.944740i
$988$		0			0
$989$	1.05843e28			0.371791
$990$		0			0
$991$	−3.05172e28			−1.05159			−0.525794	−	0.850612i	$-0.676232\pi$
$991$	−3.05172e28			−1.05159			−0.525794	+	0.850612i	$0.676232\pi$
$992$		0			0
$993$			3.57298e28i			1.20785i
$994$		0			0
$995$	1.99003e28	+	2.08536e28i	0.659994	+	0.691611i
$996$		0			0
$997$		−	2.30016e28i		−	0.748435i	−0.927341	−	0.374217i	$-0.877911\pi$
$997$		−	2.30016e28i		−	0.748435i	0.927341	−	0.374217i	$-0.122089\pi$
$998$		0			0
$999$	2.44987e28			0.782114

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	80.20.c.c.49.3		10
4.3	odd	2		10.20.b.a.9.4	✓	10
5.4	even	2	inner	80.20.c.c.49.8		10
12.11	even	2		90.20.c.b.19.7		10
20.3	even	4		50.20.a.k.1.2		5
20.7	even	4		50.20.a.l.1.4		5
20.19	odd	2		10.20.b.a.9.7	yes	10
60.59	even	2		90.20.c.b.19.2		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
10.20.b.a.9.4	✓	10	4.3	odd	2
10.20.b.a.9.7	yes	10	20.19	odd	2
50.20.a.k.1.2		5	20.3	even	4
50.20.a.l.1.4		5	20.7	even	4
80.20.c.c.49.3		10	1.1	even	1	trivial
80.20.c.c.49.8		10	5.4	even	2	inner
90.20.c.b.19.2		10	60.59	even	2
90.20.c.b.19.7		10	12.11	even	2

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)

\(f(q)\)	\(=\)	\(q-43192.0i q^{3} +(3.01510e6 + 3.15954e6i) q^{5} +2.08285e8i q^{7} -7.03291e8 q^{9} +O(q^{10})\)	\(q-43192.0i q^{3} +(3.01510e6 + 3.15954e6i) q^{5} +2.08285e8i q^{7} -7.03291e8 q^{9} -8.06882e9 q^{11} +5.42118e10i q^{13} +(1.36467e11 - 1.30228e11i) q^{15} +1.27965e11i q^{17} -3.24794e11 q^{19} +8.99624e12 q^{21} -4.42630e12i q^{23} +(-8.91860e11 + 1.90526e13i) q^{25} -1.98239e13i q^{27} +1.05364e14 q^{29} +1.18471e14 q^{31} +3.48509e14i q^{33} +(-6.58083e14 + 6.27998e14i) q^{35} +1.23582e15i q^{37} +2.34152e15 q^{39} +2.26871e15 q^{41} +2.39124e15i q^{43} +(-2.12049e15 - 2.22208e15i) q^{45} -2.93268e15i q^{47} -3.19836e16 q^{49} +5.52707e15 q^{51} +9.00554e14i q^{53} +(-2.43283e16 - 2.54937e16i) q^{55} +1.40285e16i q^{57} -7.94073e15 q^{59} +8.68976e16 q^{61} -1.46485e17i q^{63} +(-1.71284e17 + 1.63454e17i) q^{65} -2.07970e17i q^{67} -1.91181e17 q^{69} -2.68592e17 q^{71} -4.47519e17i q^{73} +(8.22922e17 + 3.85213e16i) q^{75} -1.68061e18i q^{77} -9.56550e17 q^{79} -1.67364e18 q^{81} +9.39729e17i q^{83} +(-4.04310e17 + 3.85827e17i) q^{85} -4.55087e18i q^{87} +1.39386e18 q^{89} -1.12915e19 q^{91} -5.11700e18i q^{93} +(-9.79285e17 - 1.02620e18i) q^{95} -1.03444e18i q^{97} +5.67473e18 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 2902670 q^{5} - 8718754970 q^{9}+O(q^{10}) \) 10 * q + 2902670 * q^5 - 8718754970 * q^9	\( 10 q + 2902670 q^{5} - 8718754970 q^{9} + 2965225880 q^{11} - 225010487480 q^{15} + 4196987836200 q^{19} - 501224287480 q^{21} + 19247576437650 q^{25} + 219360620418300 q^{29} + 667121586663680 q^{31} - 14\!\cdots\!60 q^{35}+ \cdots - 41\!\cdots\!60 q^{99}+O(q^{100}) \) 10 * q + 2902670 * q^5 - 8718754970 * q^9 + 2965225880 * q^11 - 225010487480 * q^15 + 4196987836200 * q^19 - 501224287480 * q^21 + 19247576437650 * q^25 + 219360620418300 * q^29 + 667121586663680 * q^31 - 1477908982965160 * q^35 + 3387373771795440 * q^39 + 3587345408194420 * q^41 - 13139237288012990 * q^45 - 30324198320796930 * q^49 - 106899828254155520 * q^51 + 99144934237329160 * q^55 + 332698279801897400 * q^59 + 533407565011656620 * q^61 - 682989395388761520 * q^65 - 95759593423262840 * q^69 - 1975827158504532720 * q^71 + 3881333883421828400 * q^75 + 2303771531732690400 * q^79 + 12793501534789009010 * q^81 - 6445103007057591040 * q^85 - 11076199503631707100 * q^89 - 7638137420731759920 * q^91 + 7279632536499161400 * q^95 - 41542573713793315160 * q^99

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