LMFDB - Embedded newform 20.12.c.a.9.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [20,12,Mod(9,20)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(20, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1]))

N = Newforms(chi, 12, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("20.9");

S:= CuspForms(chi, 12);

N := Newforms(S);

Level:	$ N $	$=$	$ 20 = 2^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 12 $
Character orbit:	$[\chi]$	$=$	20.c (of order $2$, degree $1$, 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:	$15.3668636112$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	$\mathbb{Q}[x]/(x^{6} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} + 195547x^{4} + 7296096303x^{2} + 4158054148149 $ x^6 + 195547x^4 + 7296096303x^2 + 4158054148149
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{19}\cdot 5^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			9.4
Root			$24.0594i$ of defining polynomial
Character	$\chi$	$=$	20.9
Dual form			20.12.c.a.9.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+48.1188i q^{3} +(-2879.20 - 6366.97i) q^{5} +37910.4i q^{7} +174832. q^{9} +O(q^{10})$	\(q+48.1188i q^{3} +(-2879.20 - 6366.97i) q^{5} +37910.4i q^{7} +174832. q^{9} -668452. q^{11} +515134. i q^{13} +(306371. - 138544. i) q^{15} +1.14831e7i q^{17} -1.10559e7 q^{19} -1.82420e6 q^{21} +4.67316e7i q^{23} +(-3.22485e7 + 3.66636e7i) q^{25} +1.69368e7i q^{27} +1.68323e7 q^{29} -7.80518e7 q^{31} -3.21651e7i q^{33} +(2.41375e8 - 1.09152e8i) q^{35} -4.07086e8i q^{37} -2.47876e7 q^{39} +7.02415e8 q^{41} -9.99699e8i q^{43} +(-5.03375e8 - 1.11315e9i) q^{45} +4.52761e8i q^{47} +5.40126e8 q^{49} -5.52551e8 q^{51} +2.24663e9i q^{53} +(1.92461e9 + 4.25601e9i) q^{55} -5.31997e8i q^{57} -8.02972e9 q^{59} -2.42500e9 q^{61} +6.62794e9i q^{63} +(3.27984e9 - 1.48317e9i) q^{65} +1.19590e10i q^{67} -2.24867e9 q^{69} +1.02547e10 q^{71} -2.04028e10i q^{73} +(-1.76421e9 - 1.55176e9i) q^{75} -2.53413e10i q^{77} -2.27024e10 q^{79} +3.01559e10 q^{81} -8.74412e9i q^{83} +(7.31123e10 - 3.30620e10i) q^{85} +8.09952e8i q^{87} -6.71306e10 q^{89} -1.95289e10 q^{91} -3.75576e9i q^{93} +(3.18322e10 + 7.03927e10i) q^{95} -5.17927e10i q^{97} -1.16866e11 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 4126 q^{5} - 501494 q^{9}+O(q^{10}) $ 6 * q - 4126 * q^5 - 501494 * q^9	$ 6 q - 4126 q^{5} - 501494 q^{9} + 1298200 q^{11} - 3310648 q^{15} - 244824 q^{19} - 44518024 q^{21} + 34713726 q^{25} - 138940764 q^{29} + 214450176 q^{31} - 308845352 q^{35} + 542728176 q^{39} + 106601836 q^{41} + 3311255374 q^{45} - 4506920718 q^{49} + 571023872 q^{51} - 1741716600 q^{55} - 14817616328 q^{59} + 13263695412 q^{61} + 22042348848 q^{65} - 57831800072 q^{69} + 983424528 q^{71} + 97974745648 q^{75} - 158406142752 q^{79} + 113598783134 q^{81} + 109785881856 q^{85} - 288677471236 q^{89} + 228887753424 q^{91} + 348434078904 q^{95} - 1006608631000 q^{99}+O(q^{100}) $ 6 * q - 4126 * q^5 - 501494 * q^9 + 1298200 * q^11 - 3310648 * q^15 - 244824 * q^19 - 44518024 * q^21 + 34713726 * q^25 - 138940764 * q^29 + 214450176 * q^31 - 308845352 * q^35 + 542728176 * q^39 + 106601836 * q^41 + 3311255374 * q^45 - 4506920718 * q^49 + 571023872 * q^51 - 1741716600 * q^55 - 14817616328 * q^59 + 13263695412 * q^61 + 22042348848 * q^65 - 57831800072 * q^69 + 983424528 * q^71 + 97974745648 * q^75 - 158406142752 * q^79 + 113598783134 * q^81 + 109785881856 * q^85 - 288677471236 * q^89 + 228887753424 * q^91 + 348434078904 * q^95 - 1006608631000 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/20\mathbb{Z}\right)^\times$.

$n$	$11$	$17$
$\chi(n)$	$1$	$-1$

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
$3$			48.1188i			0.114327i	0.998365	+	0.0571634i	$0.0182056\pi$
$3$			48.1188i			0.114327i	−0.998365	+	0.0571634i	$0.981794\pi$
$4$		0			0
$5$	−2879.20	−	6366.97i	−0.412038	−	0.911167i
$5$	−2879.20	−	6366.97i	−0.412038	−	0.911167i
$6$		0			0
$7$			37910.4i			0.852549i	0.904594	+	0.426275i	$0.140174\pi$
$7$			37910.4i			0.852549i	−0.904594	+	0.426275i	$0.859826\pi$
$8$		0			0
$9$	174832.			0.986929
$10$		0			0
$11$	−668452.			−1.25144			−0.625720	−	0.780047i	$-0.715195\pi$
$11$	−668452.			−1.25144			−0.625720	+	0.780047i	$0.715195\pi$
$12$		0			0
$13$			515134.i			0.384797i	0.981317	+	0.192398i	$0.0616266\pi$
$13$			515134.i			0.384797i	−0.981317	+	0.192398i	$0.938373\pi$
$14$		0			0
$15$	306371.	−	138544.i	0.104171	−	0.0471069i
$16$		0			0
$17$			1.14831e7i			1.96150i	0.195268	+	0.980750i	$0.437442\pi$
$17$			1.14831e7i			1.96150i	−0.195268	+	0.980750i	$0.562558\pi$
$18$		0			0
$19$	−1.10559e7			−1.02435			−0.512176	−	0.858880i	$-0.671161\pi$
$19$	−1.10559e7			−1.02435			−0.512176	+	0.858880i	$0.671161\pi$
$20$		0			0
$21$	−1.82420e6			−0.0974692
$22$		0			0
$23$			4.67316e7i			1.51394i	0.653452	+	0.756968i	$0.273320\pi$
$23$			4.67316e7i			1.51394i	−0.653452	+	0.756968i	$0.726680\pi$
$24$		0			0
$25$	−3.22485e7	+	3.66636e7i	−0.660450	+	0.750870i
$26$		0			0
$27$			1.69368e7i			0.227159i
$28$		0			0
$29$	1.68323e7			0.152390			0.0761948	−	0.997093i	$-0.475723\pi$
$29$	1.68323e7			0.152390			0.0761948	+	0.997093i	$0.475723\pi$
$30$		0			0
$31$	−7.80518e7			−0.489659			−0.244830	−	0.969566i	$-0.578732\pi$
$31$	−7.80518e7			−0.489659			−0.244830	+	0.969566i	$0.578732\pi$
$32$		0			0
$33$		−	3.21651e7i		−	0.143073i
$34$		0			0
$35$	2.41375e8	−	1.09152e8i	0.776814	−	0.351282i
$36$		0			0
$37$		−	4.07086e8i		−	0.965109i	−0.875866	−	0.482555i	$-0.839709\pi$
$37$		−	4.07086e8i		−	0.965109i	0.875866	−	0.482555i	$-0.160291\pi$
$38$		0			0
$39$	−2.47876e7			−0.0439926
$40$		0			0
$41$	7.02415e8			0.946853			0.473427	−	0.880833i	$-0.343017\pi$
$41$	7.02415e8			0.946853			0.473427	+	0.880833i	$0.343017\pi$
$42$		0			0
$43$		−	9.99699e8i		−	1.03703i	−0.855067	−	0.518517i	$-0.826484\pi$
$43$		−	9.99699e8i		−	1.03703i	0.855067	−	0.518517i	$-0.173516\pi$
$44$		0			0
$45$	−5.03375e8	−	1.11315e9i	−0.406652	−	0.899257i
$46$		0			0
$47$			4.52761e8i			0.287959i	0.989581	+	0.143979i	$0.0459899\pi$
$47$			4.52761e8i			0.287959i	−0.989581	+	0.143979i	$0.954010\pi$
$48$		0			0
$49$	5.40126e8			0.273160
$50$		0			0
$51$	−5.52551e8			−0.224252
$52$		0			0
$53$			2.24663e9i			0.737929i	0.929443	+	0.368965i	$0.120288\pi$
$53$			2.24663e9i			0.737929i	−0.929443	+	0.368965i	$0.879712\pi$
$54$		0			0
$55$	1.92461e9	+	4.25601e9i	0.515641	+	1.14027i
$56$		0			0
$57$		−	5.31997e8i		−	0.117111i
$58$		0			0
$59$	−8.02972e9			−1.46222			−0.731112	−	0.682257i	$-0.760998\pi$
$59$	−8.02972e9			−1.46222			−0.731112	+	0.682257i	$0.760998\pi$
$60$		0			0
$61$	−2.42500e9			−0.367619			−0.183809	−	0.982962i	$-0.558843\pi$
$61$	−2.42500e9			−0.367619			−0.183809	+	0.982962i	$0.558843\pi$
$62$		0			0
$63$			6.62794e9i			0.841406i
$64$		0			0
$65$	3.27984e9	−	1.48317e9i	0.350614	−	0.158551i
$66$		0			0
$67$			1.19590e10i			1.08214i	0.840977	+	0.541071i	$0.181981\pi$
$67$			1.19590e10i			1.08214i	−0.840977	+	0.541071i	$0.818019\pi$
$68$		0			0
$69$	−2.24867e9			−0.173084
$70$		0			0
$71$	1.02547e10			0.674531			0.337265	−	0.941410i	$-0.390498\pi$
$71$	1.02547e10			0.674531			0.337265	+	0.941410i	$0.390498\pi$
$72$		0			0
$73$		−	2.04028e10i		−	1.15190i	−0.817486	−	0.575949i	$-0.804633\pi$
$73$		−	2.04028e10i		−	1.15190i	0.817486	−	0.575949i	$-0.195367\pi$
$74$		0			0
$75$	−1.76421e9	−	1.55176e9i	−0.0858446	−	0.0755071i
$76$		0			0
$77$		−	2.53413e10i		−	1.06691i
$78$		0			0
$79$	−2.27024e10			−0.830084			−0.415042	−	0.909802i	$-0.636233\pi$
$79$	−2.27024e10			−0.830084			−0.415042	+	0.909802i	$0.636233\pi$
$80$		0			0
$81$	3.01559e10			0.960959
$82$		0			0
$83$		−	8.74412e9i		−	0.243661i	−0.992551	−	0.121831i	$-0.961124\pi$
$83$		−	8.74412e9i		−	0.243661i	0.992551	−	0.121831i	$-0.0388765\pi$
$84$		0			0
$85$	7.31123e10	−	3.30620e10i	1.78725	−	0.808212i
$86$		0			0
$87$			8.09952e8i			0.0174222i
$88$		0			0
$89$	−6.71306e10			−1.27431			−0.637156	−	0.770735i	$-0.719889\pi$
$89$	−6.71306e10			−1.27431			−0.637156	+	0.770735i	$0.719889\pi$
$90$		0			0
$91$	−1.95289e10			−0.328058
$92$		0			0
$93$		−	3.75576e9i		−	0.0559811i
$94$		0			0
$95$	3.18322e10	+	7.03927e10i	0.422072	+	0.933356i
$96$		0			0
$97$		−	5.17927e10i		−	0.612385i	−0.951970	−	0.306192i	$-0.900945\pi$
$97$		−	5.17927e10i		−	0.612385i	0.951970	−	0.306192i	$-0.0990551\pi$
$98$		0			0
$99$	−1.16866e11			−1.23508
$100$		0			0
$101$	1.00903e11			0.955291			0.477646	−	0.878553i	$-0.341490\pi$
$101$	1.00903e11			0.955291			0.477646	+	0.878553i	$0.341490\pi$
$102$		0			0
$103$			1.82963e11i			1.55510i	0.628820	+	0.777551i	$0.283538\pi$
$103$			1.82963e11i			1.55510i	−0.628820	+	0.777551i	$0.716462\pi$
$104$		0			0
$105$	5.25225e9	+	1.16147e10i	0.0401610	+	0.0888107i
$106$		0			0
$107$			2.19901e11i			1.51571i	0.652424	+	0.757854i	$0.273752\pi$
$107$			2.19901e11i			1.51571i	−0.652424	+	0.757854i	$0.726248\pi$
$108$		0			0
$109$	−2.62384e11			−1.63340			−0.816698	−	0.577066i	$-0.804198\pi$
$109$	−2.62384e11			−1.63340			−0.816698	+	0.577066i	$0.804198\pi$
$110$		0			0
$111$	1.95885e10			0.110338
$112$		0			0
$113$		−	1.53875e11i		−	0.785661i	−0.919611	−	0.392831i	$-0.871496\pi$
$113$		−	1.53875e11i		−	0.785661i	0.919611	−	0.392831i	$-0.128504\pi$
$114$		0			0
$115$	2.97539e11	−	1.34550e11i	1.37945	−	0.623799i
$116$		0			0
$117$			9.00616e10i			0.379767i
$118$		0			0
$119$	−4.35327e11			−1.67227
$120$		0			0
$121$	1.61516e11			0.566104
$122$		0			0
$123$			3.37994e10i			0.108251i
$124$		0			0
$125$	3.26286e11	+	9.97637e10i	0.956298	+	0.292393i
$126$		0			0
$127$		−	6.51722e11i		−	1.75042i	−0.483744	−	0.875209i	$-0.660724\pi$
$127$		−	6.51722e11i		−	1.75042i	0.483744	−	0.875209i	$-0.339276\pi$
$128$		0			0
$129$	4.81043e10			0.118561
$130$		0			0
$131$	2.38727e11			0.540641			0.270320	−	0.962770i	$-0.412870\pi$
$131$	2.38727e11			0.540641			0.270320	+	0.962770i	$0.412870\pi$
$132$		0			0
$133$		−	4.19134e11i		−	0.873311i
$134$		0			0
$135$	1.07836e11	−	4.87644e10i	0.206980	−	0.0935982i
$136$		0			0
$137$			4.60682e10i			0.0815527i	0.999168	+	0.0407764i	$0.0129831\pi$
$137$			4.60682e10i			0.0815527i	−0.999168	+	0.0407764i	$0.987017\pi$
$138$		0			0
$139$	−1.94283e11			−0.317581			−0.158790	−	0.987312i	$-0.550759\pi$
$139$	−1.94283e11			−0.317581			−0.158790	+	0.987312i	$0.550759\pi$
$140$		0			0
$141$	−2.17863e10			−0.0329214
$142$		0			0
$143$		−	3.44342e11i		−	0.481551i
$144$		0			0
$145$	−4.84637e10	−	1.07171e11i	−0.0627903	−	0.138852i
$146$		0			0
$147$			2.59902e10i			0.0312295i
$148$		0			0
$149$	−9.99438e11			−1.11489			−0.557444	−	0.830214i	$-0.688218\pi$
$149$	−9.99438e11			−1.11489			−0.557444	+	0.830214i	$0.688218\pi$
$150$		0			0
$151$	9.91957e11			1.02830			0.514150	−	0.857700i	$-0.328108\pi$
$151$	9.91957e11			1.02830			0.514150	+	0.857700i	$0.328108\pi$
$152$		0			0
$153$			2.00760e12i			1.93586i
$154$		0			0
$155$	2.24727e11	+	4.96954e11i	0.201758	+	0.446161i
$156$		0			0
$157$			1.03373e12i			0.864890i	0.901660	+	0.432445i	$0.142349\pi$
$157$			1.03373e12i			0.864890i	−0.901660	+	0.432445i	$0.857651\pi$
$158$		0			0
$159$	−1.08105e11			−0.0843651
$160$		0			0
$161$	−1.77162e12			−1.29071
$162$		0			0
$163$		−	1.56832e12i		−	1.06759i	−0.845615	−	0.533793i	$-0.820766\pi$
$163$		−	1.56832e12i		−	1.06759i	0.845615	−	0.533793i	$-0.179234\pi$
$164$		0			0
$165$	−2.04794e11	+	9.26098e10i	−0.130364	+	0.0589516i
$166$		0			0
$167$			1.43110e12i			0.852570i	0.904589	+	0.426285i	$0.140178\pi$
$167$			1.43110e12i			0.852570i	−0.904589	+	0.426285i	$0.859822\pi$
$168$		0			0
$169$	1.52680e12			0.851931
$170$		0			0
$171$	−1.93292e12			−1.01096
$172$		0			0
$173$			1.51824e12i			0.744883i	0.928056	+	0.372442i	$0.121479\pi$
$173$			1.51824e12i			0.744883i	−0.928056	+	0.372442i	$0.878521\pi$
$174$		0			0
$175$	−1.38993e12	−	1.22256e12i	−0.640154	−	0.563066i
$176$		0			0
$177$		−	3.86380e11i		−	0.167171i
$178$		0			0
$179$	4.15357e12			1.68939			0.844695	−	0.535248i	$-0.179782\pi$
$179$	4.15357e12			1.68939			0.844695	+	0.535248i	$0.179782\pi$
$180$		0			0
$181$	2.68160e12			1.02604			0.513018	−	0.858378i	$-0.328528\pi$
$181$	2.68160e12			1.02604			0.513018	+	0.858378i	$0.328528\pi$
$182$		0			0
$183$		−	1.16688e11i		−	0.0420287i
$184$		0			0
$185$	−2.59190e12	+	1.17208e12i	−0.879375	+	0.397661i
$186$		0			0
$187$		−	7.67587e12i		−	2.45470i
$188$		0			0
$189$	−6.42081e11			−0.193664
$190$		0			0
$191$	−5.17048e11			−0.147180			−0.0735898	−	0.997289i	$-0.523446\pi$
$191$	−5.17048e11			−0.147180			−0.0735898	+	0.997289i	$0.523446\pi$
$192$		0			0
$193$		−	4.24382e12i		−	1.14075i	−0.821383	−	0.570377i	$-0.806797\pi$
$193$		−	4.24382e12i		−	1.14075i	0.821383	−	0.570377i	$-0.193203\pi$
$194$		0			0
$195$	7.13685e10	+	1.57822e11i	0.0181266	+	0.0400846i
$196$		0			0
$197$			1.46419e12i			0.351587i	0.984427	+	0.175793i	$0.0562491\pi$
$197$			1.46419e12i			0.351587i	−0.984427	+	0.175793i	$0.943751\pi$
$198$		0			0
$199$	6.37980e12			1.44916			0.724578	−	0.689192i	$-0.242035\pi$
$199$	6.37980e12			1.44916			0.724578	+	0.689192i	$0.242035\pi$
$200$		0			0
$201$	−5.75454e11			−0.123718
$202$		0			0
$203$			6.38121e11i			0.129920i
$204$		0			0
$205$	−2.02239e12	−	4.47226e12i	−0.390139	−	0.862741i
$206$		0			0
$207$			8.17016e12i			1.49415i
$208$		0			0
$209$	7.39034e12			1.28192
$210$		0			0
$211$	−7.17062e12			−1.18033			−0.590165	−	0.807283i	$-0.700937\pi$
$211$	−7.17062e12			−1.18033			−0.590165	+	0.807283i	$0.700937\pi$
$212$		0			0
$213$			4.93444e11i			0.0771169i
$214$		0			0
$215$	−6.36506e12	+	2.87833e12i	−0.944911	+	0.427297i
$216$		0			0
$217$		−	2.95898e12i		−	0.417458i
$218$		0			0
$219$	9.81759e11			0.131693
$220$		0			0
$221$	−5.91531e12			−0.754779
$222$		0			0
$223$			5.41171e12i			0.657140i	0.944480	+	0.328570i	$0.106567\pi$
$223$			5.41171e12i			0.657140i	−0.944480	+	0.328570i	$0.893433\pi$
$224$		0			0
$225$	−5.63806e12	+	6.40995e12i	−0.651817	+	0.741056i
$226$		0			0
$227$			7.75692e12i			0.854175i	0.904210	+	0.427088i	$0.140460\pi$
$227$			7.75692e12i			0.854175i	−0.904210	+	0.427088i	$0.859540\pi$
$228$		0			0
$229$	1.02073e13			1.07106			0.535530	−	0.844516i	$-0.320112\pi$
$229$	1.02073e13			1.07106			0.535530	+	0.844516i	$0.320112\pi$
$230$		0			0
$231$	1.21939e12			0.121977
$232$		0			0
$233$			4.05476e12i			0.386819i	0.981118	+	0.193410i	$0.0619546\pi$
$233$			4.05476e12i			0.386819i	−0.981118	+	0.193410i	$0.938045\pi$
$234$		0			0
$235$	2.88271e12	−	1.30359e12i	0.262379	−	0.118650i
$236$		0			0
$237$		−	1.09241e12i		−	0.0949009i
$238$		0			0
$239$	−1.54631e13			−1.28265			−0.641324	−	0.767270i	$-0.721615\pi$
$239$	−1.54631e13			−1.28265			−0.641324	+	0.767270i	$0.721615\pi$
$240$		0			0
$241$	7.88664e12			0.624883			0.312441	−	0.949937i	$-0.398853\pi$
$241$	7.88664e12			0.624883			0.312441	+	0.949937i	$0.398853\pi$
$242$		0			0
$243$			4.45137e12i			0.337023i
$244$		0			0
$245$	−1.55513e12	−	3.43897e12i	−0.112552	−	0.248894i
$246$		0			0
$247$		−	5.69527e12i		−	0.394168i
$248$		0			0
$249$	4.20757e11			0.0278570
$250$		0			0
$251$	2.66690e12			0.168967			0.0844833	−	0.996425i	$-0.473076\pi$
$251$	2.66690e12			0.168967			0.0844833	+	0.996425i	$0.473076\pi$
$252$		0			0
$253$		−	3.12378e13i		−	1.89460i
$254$		0			0
$255$	1.59090e12	+	3.51808e12i	0.0924003	+	0.204331i
$256$		0			0
$257$		−	2.24779e13i		−	1.25061i	−0.780380	−	0.625306i	$-0.784974\pi$
$257$		−	2.24779e13i		−	1.25061i	0.780380	−	0.625306i	$-0.215026\pi$
$258$		0			0
$259$	1.54328e13			0.822803
$260$		0			0
$261$	2.94282e12			0.150398
$262$		0			0
$263$			1.68484e13i			0.825663i	0.910807	+	0.412832i	$0.135460\pi$
$263$			1.68484e13i			0.825663i	−0.910807	+	0.412832i	$0.864540\pi$
$264$		0			0
$265$	1.43042e13	−	6.46850e12i	0.672377	−	0.304055i
$266$		0			0
$267$		−	3.23025e12i		−	0.145688i
$268$		0			0
$269$	−9.49100e12			−0.410842			−0.205421	−	0.978674i	$-0.565856\pi$
$269$	−9.49100e12			−0.410842			−0.205421	+	0.978674i	$0.565856\pi$
$270$		0			0
$271$	−2.03248e13			−0.844684			−0.422342	−	0.906436i	$-0.638792\pi$
$271$	−2.03248e13			−0.844684			−0.422342	+	0.906436i	$0.638792\pi$
$272$		0			0
$273$		−	9.39709e11i		−	0.0375058i
$274$		0			0
$275$	2.15566e13	−	2.45078e13i	0.826514	−	0.939670i
$276$		0			0
$277$			2.52920e13i			0.931848i	0.884825	+	0.465924i	$0.154278\pi$
$277$			2.52920e13i			0.931848i	−0.884825	+	0.465924i	$0.845722\pi$
$278$		0			0
$279$	−1.36459e13			−0.483259
$280$		0			0
$281$	4.27990e13			1.45730			0.728649	−	0.684887i	$-0.240149\pi$
$281$	4.27990e13			1.45730			0.728649	+	0.684887i	$0.240149\pi$
$282$		0			0
$283$		−	2.95638e13i		−	0.968131i	−0.875032	−	0.484066i	$-0.839160\pi$
$283$		−	2.95638e13i		−	0.968131i	0.875032	−	0.484066i	$-0.160840\pi$
$284$		0			0
$285$	−3.38721e12	+	1.53173e12i	−0.106708	+	0.0482541i
$286$		0			0
$287$			2.66289e13i			0.807239i
$288$		0			0
$289$	−9.75886e13			−2.84748
$290$		0			0
$291$	2.49221e12			0.0700120
$292$		0			0
$293$			5.26343e13i			1.42396i	0.702201	+	0.711979i	$0.252201\pi$
$293$			5.26343e13i			1.42396i	−0.702201	+	0.711979i	$0.747799\pi$
$294$		0			0
$295$	2.31192e13	+	5.11250e13i	0.602492	+	1.33233i
$296$		0			0
$297$		−	1.13214e13i		−	0.284276i
$298$		0			0
$299$	−2.40730e13			−0.582558
$300$		0			0
$301$	3.78990e13			0.884122
$302$		0			0
$303$			4.85533e12i			0.109215i
$304$		0			0
$305$	6.98206e12	+	1.54399e13i	0.151473	+	0.334962i
$306$		0			0
$307$		−	2.42511e13i		−	0.507540i	−0.967265	−	0.253770i	$-0.918329\pi$
$307$		−	2.42511e13i		−	0.507540i	0.967265	−	0.253770i	$-0.0816707\pi$
$308$		0			0
$309$	−8.80397e12			−0.177790
$310$		0			0
$311$	−4.92067e13			−0.959052			−0.479526	−	0.877528i	$-0.659191\pi$
$311$	−4.92067e13			−0.959052			−0.479526	+	0.877528i	$0.659191\pi$
$312$		0			0
$313$			7.99895e13i			1.50501i	0.658587	+	0.752505i	$0.271154\pi$
$313$			7.99895e13i			1.50501i	−0.658587	+	0.752505i	$0.728846\pi$
$314$		0			0
$315$	4.21999e13	−	1.90832e13i	0.766661	−	0.346691i
$316$		0			0
$317$			2.50298e13i			0.439168i	0.975594	+	0.219584i	$0.0704701\pi$
$317$			2.50298e13i			0.439168i	−0.975594	+	0.219584i	$0.929530\pi$
$318$		0			0
$319$	−1.12516e13			−0.190707
$320$		0			0
$321$	−1.05814e13			−0.173286
$322$		0			0
$323$		−	1.26956e14i		−	2.00927i
$324$		0			0
$325$	−1.88866e13	−	1.66123e13i	−0.288932	−	0.254139i
$326$		0			0
$327$		−	1.26256e13i		−	0.186741i
$328$		0			0
$329$	−1.71643e13			−0.245499
$330$		0			0
$331$	5.93818e13			0.821484			0.410742	−	0.911752i	$-0.365270\pi$
$331$	5.93818e13			0.821484			0.410742	+	0.911752i	$0.365270\pi$
$332$		0			0
$333$		−	7.11715e13i		−	0.952495i
$334$		0			0
$335$	7.61428e13	−	3.44325e13i	0.986013	−	0.445884i
$336$		0			0
$337$			4.04081e13i			0.506413i	0.967412	+	0.253206i	$0.0814851\pi$
$337$			4.04081e13i			0.506413i	−0.967412	+	0.253206i	$0.918515\pi$
$338$		0			0
$339$	7.40426e12			0.0898222
$340$		0			0
$341$	5.21739e13			0.612779
$342$		0			0
$343$			9.54377e13i			1.08543i
$344$		0			0
$345$	6.47437e12	+	1.43172e13i	0.0713169	+	0.157708i
$346$		0			0
$347$		−	1.49971e14i		−	1.60027i	−0.599817	−	0.800137i	$-0.704760\pi$
$347$		−	1.49971e14i		−	1.60027i	0.599817	−	0.800137i	$-0.295240\pi$
$348$		0			0
$349$	−5.65532e13			−0.584679			−0.292339	−	0.956315i	$-0.594434\pi$
$349$	−5.65532e13			−0.584679			−0.292339	+	0.956315i	$0.594434\pi$
$350$		0			0
$351$	−8.72471e12			−0.0874102
$352$		0			0
$353$		−	1.20648e14i		−	1.17154i	−0.810477	−	0.585771i	$-0.800792\pi$
$353$		−	1.20648e14i		−	1.17154i	0.810477	−	0.585771i	$-0.199208\pi$
$354$		0			0
$355$	−2.95253e13	−	6.52913e13i	−0.277932	−	0.614610i
$356$		0			0
$357$		−	2.09474e13i		−	0.191186i
$358$		0			0
$359$	4.86952e13			0.430989			0.215495	−	0.976505i	$-0.430864\pi$
$359$	4.86952e13			0.430989			0.215495	+	0.976505i	$0.430864\pi$
$360$		0			0
$361$	5.74285e12			0.0492989
$362$		0			0
$363$			7.77196e12i			0.0647209i
$364$		0			0
$365$	−1.29904e14	+	5.87438e13i	−1.04957	+	0.474625i
$366$		0			0
$367$			2.15711e14i			1.69126i	0.533773	+	0.845628i	$0.320774\pi$
$367$			2.15711e14i			1.69126i	−0.533773	+	0.845628i	$0.679226\pi$
$368$		0			0
$369$	1.22804e14			0.934477
$370$		0			0
$371$	−8.51708e13			−0.629121
$372$		0			0
$373$			1.74473e14i			1.25121i	0.780141	+	0.625604i	$0.215147\pi$
$373$			1.74473e14i			1.25121i	−0.780141	+	0.625604i	$0.784853\pi$
$374$		0			0
$375$	−4.80051e12	+	1.57005e13i	−0.0334284	+	0.109331i
$376$		0			0
$377$			8.67090e12i			0.0586391i
$378$		0			0
$379$	1.47245e14			0.967222			0.483611	−	0.875283i	$-0.339325\pi$
$379$	1.47245e14			0.967222			0.483611	+	0.875283i	$0.339325\pi$
$380$		0			0
$381$	3.13601e13			0.200120
$382$		0			0
$383$			1.37305e14i			0.851321i	0.904883	+	0.425661i	$0.139958\pi$
$383$			1.37305e14i			0.851321i	−0.904883	+	0.425661i	$0.860042\pi$
$384$		0			0
$385$	−1.61347e14	+	7.29627e13i	−0.972137	+	0.439609i
$386$		0			0
$387$		−	1.74779e14i		−	1.02348i
$388$		0			0
$389$	6.67406e13			0.379898			0.189949	−	0.981794i	$-0.439168\pi$
$389$	6.67406e13			0.379898			0.189949	+	0.981794i	$0.439168\pi$
$390$		0			0
$391$	−5.36622e14			−2.96959
$392$		0			0
$393$			1.14872e13i			0.0618097i
$394$		0			0
$395$	6.53647e13	+	1.44545e14i	0.342026	+	0.756345i
$396$		0			0
$397$			2.30205e13i			0.117157i	0.998283	+	0.0585784i	$0.0186568\pi$
$397$			2.30205e13i			0.117157i	−0.998283	+	0.0585784i	$0.981343\pi$
$398$		0			0
$399$	2.01682e13			0.0998429
$400$		0			0
$401$	2.75776e14			1.32820			0.664099	−	0.747644i	$-0.268815\pi$
$401$	2.75776e14			1.32820			0.664099	+	0.747644i	$0.268815\pi$
$402$		0			0
$403$		−	4.02071e13i		−	0.188419i
$404$		0			0
$405$	−8.68249e13	−	1.92002e14i	−0.395951	−	0.875594i
$406$		0			0
$407$			2.72117e14i			1.20778i
$408$		0			0
$409$	9.28256e13			0.401042			0.200521	−	0.979689i	$-0.435737\pi$
$409$	9.28256e13			0.401042			0.200521	+	0.979689i	$0.435737\pi$
$410$		0			0
$411$	−2.21675e12			−0.00932366
$412$		0			0
$413$		−	3.04410e14i		−	1.24662i
$414$		0			0
$415$	−5.56735e13	+	2.51761e13i	−0.222016	+	0.100398i
$416$		0			0
$417$		−	9.34869e12i		−	0.0363080i
$418$		0			0
$419$	4.36069e14			1.64960			0.824799	−	0.565427i	$-0.191288\pi$
$419$	4.36069e14			1.64960			0.824799	+	0.565427i	$0.191288\pi$
$420$		0			0
$421$	2.81056e14			1.03572			0.517859	−	0.855466i	$-0.326729\pi$
$421$	2.81056e14			1.03572			0.517859	+	0.855466i	$0.326729\pi$
$422$		0			0
$423$			7.91569e13i			0.284195i
$424$		0			0
$425$	−4.21010e14	−	3.70312e14i	−1.47283	−	1.29547i
$426$		0			0
$427$		−	9.19328e13i		−	0.313413i
$428$		0			0
$429$	1.65693e13			0.0550541
$430$		0			0
$431$	−3.11667e14			−1.00941			−0.504703	−	0.863293i	$-0.668398\pi$
$431$	−3.11667e14			−1.00941			−0.504703	+	0.863293i	$0.668398\pi$
$432$		0			0
$433$		−	2.16113e14i		−	0.682336i	−0.940002	−	0.341168i	$-0.889178\pi$
$433$		−	2.16113e14i		−	0.682336i	0.940002	−	0.341168i	$-0.110822\pi$
$434$		0			0
$435$	5.15694e12	−	2.33201e12i	0.0158745	−	0.00717861i
$436$		0			0
$437$		−	5.16660e14i		−	1.55081i
$438$		0			0
$439$	4.61302e14			1.35030			0.675151	−	0.737680i	$-0.264079\pi$
$439$	4.61302e14			1.35030			0.675151	+	0.737680i	$0.264079\pi$
$440$		0			0
$441$	9.44312e13			0.269590
$442$		0			0
$443$		−	6.79139e13i		−	0.189120i	−0.995519	−	0.0945602i	$-0.969856\pi$
$443$		−	6.79139e13i		−	0.189120i	0.995519	−	0.0945602i	$-0.0301445\pi$
$444$		0			0
$445$	1.93282e14	+	4.27419e14i	0.525064	+	1.16111i
$446$		0			0
$447$		−	4.80918e13i		−	0.127462i
$448$		0			0
$449$	1.56137e13			0.0403785			0.0201893	−	0.999796i	$-0.493573\pi$
$449$	1.56137e13			0.0403785			0.0201893	+	0.999796i	$0.493573\pi$
$450$		0			0
$451$	−4.69531e14			−1.18493
$452$		0			0
$453$			4.77318e13i			0.117562i
$454$		0			0
$455$	5.62277e13	+	1.24340e14i	0.135172	+	0.298916i
$456$		0			0
$457$			6.83470e13i			0.160391i	0.996779	+	0.0801955i	$0.0255545\pi$
$457$			6.83470e13i			0.160391i	−0.996779	+	0.0801955i	$0.974446\pi$
$458$		0			0
$459$	−1.94486e14			−0.445573
$460$		0			0
$461$	2.79469e14			0.625143			0.312571	−	0.949894i	$-0.398810\pi$
$461$	2.79469e14			0.625143			0.312571	+	0.949894i	$0.398810\pi$
$462$		0			0
$463$			1.19444e14i			0.260897i	0.991455	+	0.130448i	$0.0416417\pi$
$463$			1.19444e14i			0.260897i	−0.991455	+	0.130448i	$0.958358\pi$
$464$		0			0
$465$	−2.39128e13	+	1.08136e13i	−0.0510082	+	0.0230663i
$466$		0			0
$467$			4.90092e14i			1.02102i	0.859871	+	0.510511i	$0.170544\pi$
$467$			4.90092e14i			1.02102i	−0.859871	+	0.510511i	$0.829456\pi$
$468$		0			0
$469$	−4.53372e14			−0.922580
$470$		0			0
$471$	−4.97421e13			−0.0988801
$472$		0			0
$473$			6.68251e14i			1.29779i
$474$		0			0
$475$	3.56537e14	−	4.05349e14i	0.676534	−	0.769156i
$476$		0			0
$477$			3.92782e14i			0.728284i
$478$		0			0
$479$	−7.33341e14			−1.32880			−0.664401	−	0.747376i	$-0.731313\pi$
$479$	−7.33341e14			−1.32880			−0.664401	+	0.747376i	$0.731313\pi$
$480$		0			0
$481$	2.09704e14			0.371371
$482$		0			0
$483$		−	8.52480e13i		−	0.147562i
$484$		0			0
$485$	−3.29763e14	+	1.49122e14i	−0.557985	+	0.252326i
$486$		0			0
$487$		−	3.29193e14i		−	0.544555i	−0.962219	−	0.272277i	$-0.912223\pi$
$487$		−	3.29193e14i		−	0.544555i	0.962219	−	0.272277i	$-0.0877768\pi$
$488$		0			0
$489$	7.54658e13			0.122054
$490$		0			0
$491$	−1.85674e12			−0.00293632			−0.00146816	−	0.999999i	$-0.500467\pi$
$491$	−1.85674e12			−0.00293632			−0.00146816	+	0.999999i	$0.500467\pi$
$492$		0			0
$493$			1.93287e14i			0.298912i
$494$		0			0
$495$	3.36482e14	+	7.44086e14i	0.508901	+	1.12537i
$496$		0			0
$497$			3.88760e14i			0.575071i
$498$		0			0
$499$	−5.25505e13			−0.0760368			−0.0380184	−	0.999277i	$-0.512105\pi$
$499$	−5.25505e13			−0.0760368			−0.0380184	+	0.999277i	$0.512105\pi$
$500$		0			0
$501$	−6.88629e13			−0.0974716
$502$		0			0
$503$		−	1.66268e14i		−	0.230242i	−0.993352	−	0.115121i	$-0.963274\pi$
$503$		−	1.66268e14i		−	0.230242i	0.993352	−	0.115121i	$-0.0367255\pi$
$504$		0			0
$505$	−2.90520e14	−	6.42446e14i	−0.393616	−	0.870430i
$506$		0			0
$507$			7.34677e13i			0.0973986i
$508$		0			0
$509$	−7.71275e14			−1.00060			−0.500301	−	0.865851i	$-0.666777\pi$
$509$	−7.71275e14			−1.00060			−0.500301	+	0.865851i	$0.666777\pi$
$510$		0			0
$511$	7.73479e14			0.982050
$512$		0			0
$513$		−	1.87252e14i		−	0.232691i
$514$		0			0
$515$	1.16492e15	−	5.26787e14i	1.41696	−	0.640760i
$516$		0			0
$517$		−	3.02649e14i		−	0.360363i
$518$		0			0
$519$	−7.30562e13			−0.0851601
$520$		0			0
$521$	8.94795e14			1.02121			0.510606	−	0.859815i	$-0.329421\pi$
$521$	8.94795e14			1.02121			0.510606	+	0.859815i	$0.329421\pi$
$522$		0			0
$523$		−	1.18244e15i		−	1.32135i	−0.750672	−	0.660676i	$-0.770270\pi$
$523$		−	1.18244e15i		−	1.32135i	0.750672	−	0.660676i	$-0.229730\pi$
$524$		0			0
$525$	5.88279e13	−	6.68819e13i	0.0643735	−	0.0731867i
$526$		0			0
$527$		−	8.96273e14i		−	0.960466i
$528$		0			0
$529$	−1.23103e15			−1.29200
$530$		0			0
$531$	−1.40385e15			−1.44311
$532$		0			0
$533$			3.61838e14i			0.364346i
$534$		0			0
$535$	1.40010e15	−	6.33138e14i	1.38106	−	0.624529i
$536$		0			0
$537$			1.99865e14i			0.193143i
$538$		0			0
$539$	−3.61048e14			−0.341844
$540$		0			0
$541$	1.52355e15			1.41342			0.706710	−	0.707504i	$-0.250179\pi$
$541$	1.52355e15			1.41342			0.706710	+	0.707504i	$0.250179\pi$
$542$		0			0
$543$			1.29036e14i			0.117303i
$544$		0			0
$545$	7.55456e14	+	1.67059e15i	0.673021	+	1.48830i
$546$		0			0
$547$		−	1.59946e15i		−	1.39650i	−0.715852	−	0.698252i	$-0.753961\pi$
$547$		−	1.59946e15i		−	1.39650i	0.715852	−	0.698252i	$-0.246039\pi$
$548$		0			0
$549$	−4.23967e14			−0.362814
$550$		0			0
$551$	−1.86097e14			−0.156101
$552$		0			0
$553$		−	8.60657e14i		−	0.707688i
$554$		0			0
$555$	−5.63992e13	−	1.24719e14i	−0.0454633	−	0.100536i
$556$		0			0
$557$			2.32605e13i			0.0183829i	0.999958	+	0.00919147i	$0.00292578\pi$
$557$			2.32605e13i			0.0183829i	−0.999958	+	0.00919147i	$0.997074\pi$
$558$		0			0
$559$	5.14979e14			0.399047
$560$		0			0
$561$	3.69354e14			0.280638
$562$		0			0
$563$			2.13606e15i			1.59154i	0.605602	+	0.795768i	$0.292932\pi$
$563$			2.13606e15i			1.59154i	−0.605602	+	0.795768i	$0.707068\pi$
$564$		0			0
$565$	−9.79715e14	+	4.43036e14i	−0.715869	+	0.323722i
$566$		0			0
$567$			1.14322e15i			0.819265i
$568$		0			0
$569$	−1.82241e15			−1.28094			−0.640471	−	0.767982i	$-0.721261\pi$
$569$	−1.82241e15			−1.28094			−0.640471	+	0.767982i	$0.721261\pi$
$570$		0			0
$571$	−4.16662e14			−0.287267			−0.143633	−	0.989631i	$-0.545879\pi$
$571$	−4.16662e14			−0.287267			−0.143633	+	0.989631i	$0.545879\pi$
$572$		0			0
$573$		−	2.48798e13i		−	0.0168266i
$574$		0			0
$575$	−1.71335e15	−	1.50703e15i	−1.13677	−	0.999879i
$576$		0			0
$577$			1.40213e15i			0.912683i	0.889805	+	0.456342i	$0.150840\pi$
$577$			1.40213e15i			0.912683i	−0.889805	+	0.456342i	$0.849160\pi$
$578$		0			0
$579$	2.04208e14			0.130419
$580$		0			0
$581$	3.31493e14			0.207733
$582$		0			0
$583$		−	1.50177e15i		−	0.923475i
$584$		0			0
$585$	5.73420e14	−	2.59306e14i	0.346031	−	0.156478i
$586$		0			0
$587$			3.15423e15i			1.86803i	0.357231	+	0.934016i	$0.383721\pi$
$587$			3.15423e15i			1.86803i	−0.357231	+	0.934016i	$0.616279\pi$
$588$		0			0
$589$	8.62934e14			0.501584
$590$		0			0
$591$	−7.04550e13			−0.0401958
$592$		0			0
$593$			5.55270e14i			0.310959i	0.987839	+	0.155480i	$0.0496923\pi$
$593$			5.55270e14i			0.310959i	−0.987839	+	0.155480i	$0.950308\pi$
$594$		0			0
$595$	1.25339e15	+	2.77172e15i	0.689040	+	1.52372i
$596$		0			0
$597$			3.06989e14i			0.165677i
$598$		0			0
$599$	3.83208e14			0.203043			0.101521	−	0.994833i	$-0.467629\pi$
$599$	3.83208e14			0.203043			0.101521	+	0.994833i	$0.467629\pi$
$600$		0			0
$601$	−1.79521e15			−0.933913			−0.466956	−	0.884280i	$-0.654650\pi$
$601$	−1.79521e15			−0.933913			−0.466956	+	0.884280i	$0.654650\pi$
$602$		0			0
$603$			2.09082e15i			1.06800i
$604$		0			0
$605$	−4.65037e14	−	1.02837e15i	−0.233256	−	0.515815i
$606$		0			0
$607$		−	1.96383e15i		−	0.967312i	−0.875258	−	0.483656i	$-0.839309\pi$
$607$		−	1.96383e15i		−	0.967312i	0.875258	−	0.483656i	$-0.160691\pi$
$608$		0			0
$609$	−3.07056e13			−0.0148533
$610$		0			0
$611$	−2.33232e14			−0.110806
$612$		0			0
$613$			2.94637e14i			0.137485i	0.997634	+	0.0687423i	$0.0218986\pi$
$613$			2.94637e14i			0.137485i	−0.997634	+	0.0687423i	$0.978101\pi$
$614$		0			0
$615$	2.15200e14	−	9.73152e13i	0.0986344	−	0.0446034i
$616$		0			0
$617$		−	4.26614e15i		−	1.92073i	−0.278740	−	0.960367i	$-0.589917\pi$
$617$		−	4.26614e15i		−	1.92073i	0.278740	−	0.960367i	$-0.410083\pi$
$618$		0			0
$619$	6.19951e13			0.0274194			0.0137097	−	0.999906i	$-0.495636\pi$
$619$	6.19951e13			0.0274194			0.0137097	+	0.999906i	$0.495636\pi$
$620$		0			0
$621$	−7.91484e14			−0.343905
$622$		0			0
$623$		−	2.54495e15i		−	1.08641i
$624$		0			0
$625$	−3.04250e14	−	2.36469e15i	−0.127612	−	0.991824i
$626$		0			0
$627$			3.55614e14i			0.146557i
$628$		0			0
$629$	4.67459e15			1.89306
$630$		0			0
$631$	−6.14597e14			−0.244584			−0.122292	−	0.992494i	$-0.539025\pi$
$631$	−6.14597e14			−0.244584			−0.122292	+	0.992494i	$0.539025\pi$
$632$		0			0
$633$		−	3.45042e14i		−	0.134943i
$634$		0			0
$635$	−4.14950e15	+	1.87644e15i	−1.59492	+	0.721238i
$636$		0			0
$637$			2.78237e14i			0.105111i
$638$		0			0
$639$	1.79284e15			0.665714
$640$		0			0
$641$	3.03626e15			1.10820			0.554101	−	0.832449i	$-0.313062\pi$
$641$	3.03626e15			1.10820			0.554101	+	0.832449i	$0.313062\pi$
$642$		0			0
$643$			2.56693e14i			0.0920989i	0.998939	+	0.0460495i	$0.0146632\pi$
$643$			2.56693e14i			0.0920989i	−0.998939	+	0.0460495i	$0.985337\pi$
$644$		0			0
$645$	−1.38502e14	−	3.06279e14i	−0.0488515	−	0.108029i
$646$		0			0
$647$			6.91387e14i			0.239744i	0.992789	+	0.119872i	$0.0382484\pi$
$647$			6.91387e14i			0.239744i	−0.992789	+	0.119872i	$0.961752\pi$
$648$		0			0
$649$	5.36748e15			1.82989
$650$		0			0
$651$	1.42383e14			0.0477267
$652$		0			0
$653$		−	3.62496e15i		−	1.19476i	−0.801958	−	0.597381i	$-0.796208\pi$
$653$		−	3.62496e15i		−	1.19476i	0.801958	−	0.597381i	$-0.203792\pi$
$654$		0			0
$655$	−6.87342e14	−	1.51997e15i	−0.222764	−	0.492614i
$656$		0			0
$657$		−	3.56705e15i		−	1.13684i
$658$		0			0
$659$	−3.35320e14			−0.105097			−0.0525484	−	0.998618i	$-0.516734\pi$
$659$	−3.35320e14			−0.105097			−0.0525484	+	0.998618i	$0.516734\pi$
$660$		0			0
$661$	−4.78647e15			−1.47539			−0.737696	−	0.675134i	$-0.764086\pi$
$661$	−4.78647e15			−1.47539			−0.737696	+	0.675134i	$0.764086\pi$
$662$		0			0
$663$		−	2.84638e14i		−	0.0862915i
$664$		0			0
$665$	−2.66862e15	+	1.20677e15i	−0.795732	+	0.359837i
$666$		0			0
$667$			7.86602e14i			0.230708i
$668$		0			0
$669$	−2.60405e14			−0.0751287
$670$		0			0
$671$	1.62100e15			0.460053
$672$		0			0
$673$			5.37099e15i			1.49959i	0.661672	+	0.749794i	$0.269847\pi$
$673$			5.37099e15i			1.49959i	−0.661672	+	0.749794i	$0.730153\pi$
$674$		0			0
$675$	−6.20963e14	−	5.46187e14i	−0.170567	−	0.150027i
$676$		0			0
$677$			1.88943e15i			0.510614i	0.966860	+	0.255307i	$0.0821765\pi$
$677$			1.88943e15i			0.510614i	−0.966860	+	0.255307i	$0.917824\pi$
$678$		0			0
$679$	1.96348e15			0.522088
$680$		0			0
$681$	−3.73254e14			−0.0976551
$682$		0			0
$683$			2.72875e15i			0.702506i	0.936281	+	0.351253i	$0.114244\pi$
$683$			2.72875e15i			0.702506i	−0.936281	+	0.351253i	$0.885756\pi$
$684$		0			0
$685$	2.93315e14	−	1.32640e14i	0.0743082	−	0.0336028i
$686$		0			0
$687$			4.91161e14i			0.122451i
$688$		0			0
$689$	−1.15732e15			−0.283953
$690$		0			0
$691$	−3.25192e15			−0.785255			−0.392628	−	0.919697i	$-0.628434\pi$
$691$	−3.25192e15			−0.785255			−0.392628	+	0.919697i	$0.628434\pi$
$692$		0			0
$693$		−	4.43046e15i		−	1.05297i
$694$		0			0
$695$	5.59381e14	+	1.23700e15i	0.130855	+	0.289369i
$696$		0			0
$697$			8.06587e15i			1.85725i
$698$		0			0
$699$	−1.95110e14			−0.0442238
$700$		0			0
$701$	9.70371e14			0.216515			0.108258	−	0.994123i	$-0.465473\pi$
$701$	9.70371e14			0.216515			0.108258	+	0.994123i	$0.465473\pi$
$702$		0			0
$703$			4.50070e15i			0.988612i
$704$		0			0
$705$	6.27272e13	+	1.38713e14i	0.0135649	+	0.0299969i
$706$		0			0
$707$			3.82527e15i			0.814433i
$708$		0			0
$709$	5.98747e13			0.0125513			0.00627565	−	0.999980i	$-0.498002\pi$
$709$	5.98747e13			0.0125513			0.00627565	+	0.999980i	$0.498002\pi$
$710$		0			0
$711$	−3.96909e15			−0.819235
$712$		0			0
$713$		−	3.64749e15i		−	0.741313i
$714$		0			0
$715$	−2.19242e15	+	9.91430e14i	−0.438773	+	0.198417i
$716$		0			0
$717$		−	7.44065e14i		−	0.146641i
$718$		0			0
$719$	2.52757e15			0.490563			0.245281	−	0.969452i	$-0.421120\pi$
$719$	2.52757e15			0.490563			0.245281	+	0.969452i	$0.421120\pi$
$720$		0			0
$721$	−6.93621e15			−1.32580
$722$		0			0
$723$			3.79496e14i			0.0714408i
$724$		0			0
$725$	−5.42818e14	+	6.17134e14i	−0.100646	+	0.114425i
$726$		0			0
$727$		−	9.27966e15i		−	1.69470i	−0.531034	−	0.847350i	$-0.678196\pi$
$727$		−	9.27966e15i		−	1.69470i	0.531034	−	0.847350i	$-0.321804\pi$
$728$		0			0
$729$	5.12783e15			0.922428
$730$		0			0
$731$	1.14796e16			2.03414
$732$		0			0
$733$			7.72726e15i			1.34882i	0.738358	+	0.674410i	$0.235602\pi$
$733$			7.72726e15i			1.34882i	−0.738358	+	0.674410i	$0.764398\pi$
$734$		0			0
$735$	1.65479e14	−	7.48311e13i	0.0284553	−	0.0128677i
$736$		0			0
$737$		−	7.99404e15i		−	1.35424i
$738$		0			0
$739$	−6.45358e15			−1.07710			−0.538550	−	0.842594i	$-0.681028\pi$
$739$	−6.45358e15			−1.07710			−0.538550	+	0.842594i	$0.681028\pi$
$740$		0			0
$741$	2.74050e14			0.0450639
$742$		0			0
$743$		−	8.35693e15i		−	1.35397i	−0.735998	−	0.676984i	$-0.763287\pi$
$743$		−	8.35693e15i		−	1.35397i	0.735998	−	0.676984i	$-0.236713\pi$
$744$		0			0
$745$	2.87758e15	+	6.36339e15i	0.459376	+	1.01585i
$746$		0			0
$747$		−	1.52875e15i		−	0.240476i
$748$		0			0
$749$	−8.33652e15			−1.29222
$750$		0			0
$751$	1.02136e16			1.56012			0.780060	−	0.625705i	$-0.215189\pi$
$751$	1.02136e16			1.56012			0.780060	+	0.625705i	$0.215189\pi$
$752$		0			0
$753$			1.28328e14i			0.0193174i
$754$		0			0
$755$	−2.85604e15	−	6.31576e15i	−0.423698	−	0.936953i
$756$		0			0
$757$			7.28462e15i			1.06507i	0.846407	+	0.532537i	$0.178761\pi$
$757$			7.28462e15i			1.06507i	−0.846407	+	0.532537i	$0.821239\pi$
$758$		0			0
$759$	1.50313e15			0.216604
$760$		0			0
$761$	5.79601e14			0.0823216			0.0411608	−	0.999153i	$-0.486894\pi$
$761$	5.79601e14			0.0823216			0.0411608	+	0.999153i	$0.486894\pi$
$762$		0			0
$763$		−	9.94708e15i		−	1.39255i
$764$		0			0
$765$	1.27823e16	−	5.78028e15i	1.76389	−	0.797648i
$766$		0			0
$767$		−	4.13638e15i		−	0.562659i
$768$		0			0
$769$	−5.91169e15			−0.792714			−0.396357	−	0.918096i	$-0.629726\pi$
$769$	−5.91169e15			−0.792714			−0.396357	+	0.918096i	$0.629726\pi$
$770$		0			0
$771$	1.08161e15			0.142979
$772$		0			0
$773$			1.91827e15i			0.249990i	0.992157	+	0.124995i	$0.0398915\pi$
$773$			1.91827e15i			0.249990i	−0.992157	+	0.124995i	$0.960108\pi$
$774$		0			0
$775$	2.51706e15	−	2.86166e15i	0.323395	−	0.367670i
$776$		0			0
$777$			7.42608e14i			0.0940684i
$778$		0			0
$779$	−7.76584e15			−0.969912
$780$		0			0
$781$	−6.85477e15			−0.844135
$782$		0			0
$783$			2.85086e14i			0.0346167i
$784$		0			0
$785$	6.58176e15	−	2.97633e15i	0.788059	−	0.356367i
$786$		0			0
$787$			4.27027e15i			0.504190i	0.967703	+	0.252095i	$0.0811195\pi$
$787$			4.27027e15i			0.504190i	−0.967703	+	0.252095i	$0.918881\pi$
$788$		0			0
$789$	−8.10727e14			−0.0943954
$790$		0			0
$791$	5.83345e15			0.669815
$792$		0			0
$793$		−	1.24920e15i		−	0.141459i
$794$		0			0
$795$	3.11257e14	+	6.88303e14i	0.0347616	+	0.0768707i
$796$		0			0
$797$			9.86973e12i			0.00108714i	1.00000		0.000543569i	$0.000173023\pi$
$797$			9.86973e12i			0.00108714i	−1.00000		0.000543569i	$0.999827\pi$
$798$		0			0
$799$	−5.19907e15			−0.564831
$800$		0			0
$801$	−1.17365e16			−1.25766
$802$		0			0
$803$			1.36383e16i			1.44153i
$804$		0			0
$805$	5.10084e15	+	1.12798e16i	0.531819	+	1.17605i
$806$		0			0
$807$		−	4.56696e14i		−	0.0469702i
$808$		0			0
$809$	−6.90335e14			−0.0700395			−0.0350198	−	0.999387i	$-0.511149\pi$
$809$	−6.90335e14			−0.0700395			−0.0350198	+	0.999387i	$0.511149\pi$
$810$		0			0
$811$	1.10979e16			1.11077			0.555385	−	0.831593i	$-0.312571\pi$
$811$	1.10979e16			1.11077			0.555385	+	0.831593i	$0.312571\pi$
$812$		0			0
$813$		−	9.78004e14i		−	0.0965701i
$814$		0			0
$815$	−9.98546e15	+	4.51551e15i	−0.972750	+	0.439886i
$816$		0			0
$817$			1.10526e16i			1.06229i
$818$		0			0
$819$	−3.41428e15			−0.323770
$820$		0			0
$821$	7.24931e15			0.678281			0.339140	−	0.940736i	$-0.389864\pi$
$821$	7.24931e15			0.678281			0.339140	+	0.940736i	$0.389864\pi$
$822$		0			0
$823$			1.36021e15i			0.125576i	0.998027	+	0.0627882i	$0.0199993\pi$
$823$			1.36021e15i			0.125576i	−0.998027	+	0.0627882i	$0.980001\pi$
$824$		0			0
$825$	1.17929e15	+	1.03728e15i	0.107429	+	0.0944927i
$826$		0			0
$827$		−	2.78452e15i		−	0.250305i	−0.992138	−	0.125153i	$-0.960058\pi$
$827$		−	2.78452e15i		−	0.250305i	0.992138	−	0.125153i	$-0.0399420\pi$
$828$		0			0
$829$	−1.02828e16			−0.912142			−0.456071	−	0.889943i	$-0.650744\pi$
$829$	−1.02828e16			−0.912142			−0.456071	+	0.889943i	$0.650744\pi$
$830$		0			0
$831$	−1.21702e15			−0.106535
$832$		0			0
$833$			6.20230e15i			0.535803i
$834$		0			0
$835$	9.11179e15	−	4.12043e15i	0.776833	−	0.351291i
$836$		0			0
$837$		−	1.32195e15i		−	0.111231i
$838$		0			0
$839$	−2.23265e16			−1.85408			−0.927042	−	0.374958i	$-0.877657\pi$
$839$	−2.23265e16			−1.85408			−0.927042	+	0.374958i	$0.877657\pi$
$840$		0			0
$841$	−1.19172e16			−0.976777
$842$		0			0
$843$			2.05944e15i			0.166608i
$844$		0			0
$845$	−4.39596e15	−	9.72108e15i	−0.351028	−	0.776252i
$846$		0			0
$847$			6.12314e15i			0.482632i
$848$		0			0
$849$	1.42257e15			0.110683
$850$		0			0
$851$	1.90238e16			1.46111
$852$		0			0
$853$			5.79840e14i			0.0439632i	0.999758	+	0.0219816i	$0.00699752\pi$
$853$			5.79840e14i			0.0439632i	−0.999758	+	0.0219816i	$0.993002\pi$
$854$		0			0
$855$	5.56527e15	+	1.23069e16i	0.416555	+	0.921157i
$856$		0			0
$857$		−	6.64966e15i		−	0.491366i	−0.969350	−	0.245683i	$-0.920988\pi$
$857$		−	6.64966e15i		−	0.491366i	0.969350	−	0.245683i	$-0.0790122\pi$
$858$		0			0
$859$	3.26558e15			0.238231			0.119116	−	0.992880i	$-0.461994\pi$
$859$	3.26558e15			0.238231			0.119116	+	0.992880i	$0.461994\pi$
$860$		0			0
$861$	−1.28135e15			−0.0922890
$862$		0			0
$863$			1.60071e15i			0.113829i	0.998379	+	0.0569144i	$0.0181262\pi$
$863$			1.60071e15i			0.113829i	−0.998379	+	0.0569144i	$0.981874\pi$
$864$		0			0
$865$	9.66662e15	−	4.37133e15i	0.678713	−	0.306920i
$866$		0			0
$867$		−	4.69585e15i		−	0.325543i
$868$		0			0
$869$	1.51754e16			1.03880
$870$		0			0
$871$	−6.16050e15			−0.416405
$872$		0			0
$873$		−	9.05501e15i		−	0.604380i
$874$		0			0
$875$	−3.78208e15	+	1.23696e16i	−0.249280	+	0.815291i
$876$		0			0
$877$		−	2.99372e16i		−	1.94856i	−0.225345	−	0.974279i	$-0.572351\pi$
$877$		−	2.99372e16i		−	1.94856i	0.225345	−	0.974279i	$-0.427649\pi$
$878$		0			0
$879$	−2.53270e15			−0.162797
$880$		0			0
$881$	1.66913e16			1.05955			0.529777	−	0.848137i	$-0.322276\pi$
$881$	1.66913e16			1.05955			0.529777	+	0.848137i	$0.322276\pi$
$882$		0			0
$883$		−	2.78149e16i		−	1.74379i	−0.489692	−	0.871895i	$-0.662891\pi$
$883$		−	2.78149e16i		−	1.74379i	0.489692	−	0.871895i	$-0.337109\pi$
$884$		0			0
$885$	−2.46007e15	+	1.11247e15i	−0.152321	+	0.0688809i
$886$		0			0
$887$			2.86853e16i			1.75420i	0.480304	+	0.877102i	$0.340526\pi$
$887$			2.86853e16i			1.75420i	−0.480304	+	0.877102i	$0.659474\pi$
$888$		0			0
$889$	2.47071e16			1.49232
$890$		0			0
$891$	−2.01578e16			−1.20258
$892$		0			0
$893$		−	5.00568e15i		−	0.294972i
$894$		0			0
$895$	−1.19590e16	−	2.64457e16i	−0.696092	−	1.53932i
$896$		0			0
$897$		−	1.15837e15i		−	0.0666020i
$898$		0			0
$899$	−1.31379e15			−0.0746190
$900$		0			0
$901$	−2.57982e16			−1.44745
$902$		0			0
$903$			1.82366e15i			0.101079i
$904$		0			0
$905$	−7.72087e15	−	1.70737e16i	−0.422765	−	0.934889i
$906$		0			0
$907$		−	1.49291e16i		−	0.807594i	−0.914849	−	0.403797i	$-0.867690\pi$
$907$		−	1.49291e16i		−	0.807594i	0.914849	−	0.403797i	$-0.132310\pi$
$908$		0			0
$909$	1.76410e16			0.942805
$910$		0			0
$911$	2.00189e16			1.05703			0.528517	−	0.848923i	$-0.322748\pi$
$911$	2.00189e16			1.05703			0.528517	+	0.848923i	$0.322748\pi$
$912$		0			0
$913$			5.84502e15i			0.304928i
$914$		0			0
$915$	−7.42950e14	+	3.35969e14i	−0.0382951	+	0.0173174i
$916$		0			0
$917$			9.05023e15i			0.460923i
$918$		0			0
$919$	3.61370e16			1.81852			0.909258	−	0.416233i	$-0.136650\pi$
$919$	3.61370e16			1.81852			0.909258	+	0.416233i	$0.136650\pi$
$920$		0			0
$921$	1.16693e15			0.0580255
$922$		0			0
$923$			5.28254e15i			0.259557i
$924$		0			0
$925$	1.49252e16	+	1.31279e16i	0.724672	+	0.637406i
$926$		0			0
$927$			3.19877e16i			1.53478i
$928$		0			0
$929$	−2.45692e16			−1.16494			−0.582470	−	0.812852i	$-0.697914\pi$
$929$	−2.45692e16			−1.16494			−0.582470	+	0.812852i	$0.697914\pi$
$930$		0			0
$931$	−5.97159e15			−0.279812
$932$		0			0
$933$		−	2.36777e15i		−	0.109645i
$934$		0			0
$935$	−4.88720e16	+	2.21004e16i	−2.23664	+	1.01143i
$936$		0			0
$937$		−	1.14220e16i		−	0.516623i	−0.966062	−	0.258311i	$-0.916834\pi$
$937$		−	1.14220e16i		−	0.516623i	0.966062	−	0.258311i	$-0.0831660\pi$
$938$		0			0
$939$	−3.84900e15			−0.172063
$940$		0			0
$941$	2.27548e15			0.100538			0.0502689	−	0.998736i	$-0.483992\pi$
$941$	2.27548e15			0.100538			0.0502689	+	0.998736i	$0.483992\pi$
$942$		0			0
$943$			3.28250e16i			1.43348i
$944$		0			0
$945$	1.84868e15	+	4.08811e15i	0.0797970	+	0.176461i
$946$		0			0
$947$		−	2.72715e16i		−	1.16355i	−0.813351	−	0.581774i	$-0.802359\pi$
$947$		−	2.72715e16i		−	1.16355i	0.813351	−	0.581774i	$-0.197641\pi$
$948$		0			0
$949$	1.05102e16			0.443247
$950$		0			0
$951$	−1.20440e15			−0.0502087
$952$		0			0
$953$		−	1.90303e16i		−	0.784216i	−0.919919	−	0.392108i	$-0.871746\pi$
$953$		−	1.90303e16i		−	0.784216i	0.919919	−	0.392108i	$-0.128254\pi$
$954$		0			0
$955$	1.48869e15	+	3.29203e15i	0.0606436	+	0.134105i
$956$		0			0
$957$		−	5.41414e14i		−	0.0218029i
$958$		0			0
$959$	−1.74647e15			−0.0695277
$960$		0			0
$961$	−1.93164e16			−0.760234
$962$		0			0
$963$			3.84456e16i			1.49590i
$964$		0			0
$965$	−2.70203e16	+	1.22188e16i	−1.03942	+	0.470034i
$966$		0			0
$967$		−	4.77003e15i		−	0.181416i	−0.995878	−	0.0907079i	$-0.971087\pi$
$967$		−	4.77003e15i		−	0.181416i	0.995878	−	0.0907079i	$-0.0289130\pi$
$968$		0			0
$969$	6.10895e15			0.229713
$970$		0			0
$971$	1.07477e16			0.399584			0.199792	−	0.979838i	$-0.435973\pi$
$971$	1.07477e16			0.399584			0.199792	+	0.979838i	$0.435973\pi$
$972$		0			0
$973$		−	7.36536e15i		−	0.270753i
$974$		0			0
$975$	7.99364e14	−	9.08803e14i	0.0290549	−	0.0330327i
$976$		0			0
$977$			5.18984e16i			1.86524i	0.360864	+	0.932618i	$0.382482\pi$
$977$			5.18984e16i			1.86524i	−0.360864	+	0.932618i	$0.617518\pi$
$978$		0			0
$979$	4.48736e16			1.59473
$980$		0			0
$981$	−4.58730e16			−1.61205
$982$		0			0
$983$			2.15497e16i			0.748855i	0.927256	+	0.374427i	$0.122161\pi$
$983$			2.15497e16i			0.748855i	−0.927256	+	0.374427i	$0.877839\pi$
$984$		0			0
$985$	9.32245e15	−	4.21569e15i	0.320354	−	0.144867i
$986$		0			0
$987$		−	8.25928e14i		−	0.0280671i
$988$		0			0
$989$	4.67176e16			1.57000
$990$		0			0
$991$	−2.84227e16			−0.944627			−0.472314	−	0.881431i	$-0.656581\pi$
$991$	−2.84227e16			−0.944627			−0.472314	+	0.881431i	$0.656581\pi$
$992$		0			0
$993$			2.85738e15i			0.0939176i
$994$		0			0
$995$	−1.83687e16	−	4.06200e16i	−0.597107	−	1.32042i
$996$		0			0
$997$			1.03066e16i			0.331352i	0.986180	+	0.165676i	$0.0529806\pi$
$997$			1.03066e16i			0.331352i	−0.986180	+	0.165676i	$0.947019\pi$
$998$		0			0
$999$	6.89473e15			0.219234

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	20.12.c.a.9.4	yes	6
3.2	odd	2		180.12.d.a.109.4		6
4.3	odd	2		80.12.c.b.49.3		6
5.2	odd	4		100.12.a.f.1.4		6
5.3	odd	4		100.12.a.f.1.3		6
5.4	even	2	inner	20.12.c.a.9.3	✓	6
15.14	odd	2		180.12.d.a.109.3		6
20.19	odd	2		80.12.c.b.49.4		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
20.12.c.a.9.3	✓	6	5.4	even	2	inner
20.12.c.a.9.4	yes	6	1.1	even	1	trivial
80.12.c.b.49.3		6	4.3	odd	2
80.12.c.b.49.4		6	20.19	odd	2
100.12.a.f.1.3		6	5.3	odd	4
100.12.a.f.1.4		6	5.2	odd	4
180.12.d.a.109.3		6	15.14	odd	2
180.12.d.a.109.4		6	3.2	odd	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:	\( N \)	\(=\)	\( 20 = 2^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 12 \)
Character orbit:	\([\chi]\)	\(=\)	20.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+48.1188i q^{3} +(-2879.20 - 6366.97i) q^{5} +37910.4i q^{7} +174832. q^{9} +O(q^{10})\)	\(q+48.1188i q^{3} +(-2879.20 - 6366.97i) q^{5} +37910.4i q^{7} +174832. q^{9} -668452. q^{11} +515134. i q^{13} +(306371. - 138544. i) q^{15} +1.14831e7i q^{17} -1.10559e7 q^{19} -1.82420e6 q^{21} +4.67316e7i q^{23} +(-3.22485e7 + 3.66636e7i) q^{25} +1.69368e7i q^{27} +1.68323e7 q^{29} -7.80518e7 q^{31} -3.21651e7i q^{33} +(2.41375e8 - 1.09152e8i) q^{35} -4.07086e8i q^{37} -2.47876e7 q^{39} +7.02415e8 q^{41} -9.99699e8i q^{43} +(-5.03375e8 - 1.11315e9i) q^{45} +4.52761e8i q^{47} +5.40126e8 q^{49} -5.52551e8 q^{51} +2.24663e9i q^{53} +(1.92461e9 + 4.25601e9i) q^{55} -5.31997e8i q^{57} -8.02972e9 q^{59} -2.42500e9 q^{61} +6.62794e9i q^{63} +(3.27984e9 - 1.48317e9i) q^{65} +1.19590e10i q^{67} -2.24867e9 q^{69} +1.02547e10 q^{71} -2.04028e10i q^{73} +(-1.76421e9 - 1.55176e9i) q^{75} -2.53413e10i q^{77} -2.27024e10 q^{79} +3.01559e10 q^{81} -8.74412e9i q^{83} +(7.31123e10 - 3.30620e10i) q^{85} +8.09952e8i q^{87} -6.71306e10 q^{89} -1.95289e10 q^{91} -3.75576e9i q^{93} +(3.18322e10 + 7.03927e10i) q^{95} -5.17927e10i q^{97} -1.16866e11 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 4126 q^{5} - 501494 q^{9}+O(q^{10}) \) 6 * q - 4126 * q^5 - 501494 * q^9	\( 6 q - 4126 q^{5} - 501494 q^{9} + 1298200 q^{11} - 3310648 q^{15} - 244824 q^{19} - 44518024 q^{21} + 34713726 q^{25} - 138940764 q^{29} + 214450176 q^{31} - 308845352 q^{35} + 542728176 q^{39} + 106601836 q^{41} + 3311255374 q^{45} - 4506920718 q^{49} + 571023872 q^{51} - 1741716600 q^{55} - 14817616328 q^{59} + 13263695412 q^{61} + 22042348848 q^{65} - 57831800072 q^{69} + 983424528 q^{71} + 97974745648 q^{75} - 158406142752 q^{79} + 113598783134 q^{81} + 109785881856 q^{85} - 288677471236 q^{89} + 228887753424 q^{91} + 348434078904 q^{95} - 1006608631000 q^{99}+O(q^{100}) \) 6 * q - 4126 * q^5 - 501494 * q^9 + 1298200 * q^11 - 3310648 * q^15 - 244824 * q^19 - 44518024 * q^21 + 34713726 * q^25 - 138940764 * q^29 + 214450176 * q^31 - 308845352 * q^35 + 542728176 * q^39 + 106601836 * q^41 + 3311255374 * q^45 - 4506920718 * q^49 + 571023872 * q^51 - 1741716600 * q^55 - 14817616328 * q^59 + 13263695412 * q^61 + 22042348848 * q^65 - 57831800072 * q^69 + 983424528 * q^71 + 97974745648 * q^75 - 158406142752 * q^79 + 113598783134 * q^81 + 109785881856 * q^85 - 288677471236 * q^89 + 228887753424 * q^91 + 348434078904 * q^95 - 1006608631000 * q^99

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