LMFDB - Embedded newform 80.12.c.c.49.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [80,12,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, 12, names="a")

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

chi := DirichletCharacter("80.49");

S:= CuspForms(chi, 12);

N := Newforms(S);

Level:	$ N $	$=$	$ 80 = 2^{4} \cdot 5 $
Weight:	$ k $	$=$	$ 12 $
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:	$61.4674544448$
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} - 2x^{5} + 2x^{4} + 198x^{3} + 3568321x^{2} - 6762620x + 6408200 $ x^6 - 2x^5 + 2x^4 + 198x^3 + 3568321x^2 - 6762620*x + 6408200
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{25}\cdot 5^{5} $
Twist minimal:	no (minimal twist has level 10)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			49.4
Root			$0.947541 + 0.947541i$ of defining polynomial
Character	$\chi$	$=$	80.49
Dual form			80.12.c.c.49.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+100.951i q^{3} +(2827.02 - 6390.31i) q^{5} +15908.8i q^{7} +166956. q^{9} +O(q^{10})$	\(q+100.951i q^{3} +(2827.02 - 6390.31i) q^{5} +15908.8i q^{7} +166956. q^{9} -623805. q^{11} -1.54230e6i q^{13} +(645107. + 285390. i) q^{15} -1.11817e6i q^{17} +1.45889e7 q^{19} -1.60601e6 q^{21} +6.03368e6i q^{23} +(-3.28441e7 - 3.61310e7i) q^{25} +3.47375e7i q^{27} +2.91997e7 q^{29} -2.33031e8 q^{31} -6.29736e7i q^{33} +(1.01662e8 + 4.49744e7i) q^{35} +6.65053e8i q^{37} +1.55696e8 q^{39} -6.63914e8 q^{41} -4.11150e8i q^{43} +(4.71987e8 - 1.06690e9i) q^{45} -2.47761e9i q^{47} +1.72424e9 q^{49} +1.12880e8 q^{51} -3.69178e9i q^{53} +(-1.76351e9 + 3.98631e9i) q^{55} +1.47277e9i q^{57} +1.25820e9 q^{59} -4.05784e9 q^{61} +2.65607e9i q^{63} +(-9.85577e9 - 4.36011e9i) q^{65} -1.84180e10i q^{67} -6.09105e8 q^{69} -3.19489e9 q^{71} -1.51712e10i q^{73} +(3.64746e9 - 3.31564e9i) q^{75} -9.92398e9i q^{77} -4.26826e10 q^{79} +2.60690e10 q^{81} -5.86787e10i q^{83} +(-7.14544e9 - 3.16108e9i) q^{85} +2.94773e9i q^{87} -3.40792e10 q^{89} +2.45361e10 q^{91} -2.35247e10i q^{93} +(4.12432e10 - 9.32279e10i) q^{95} -1.37873e11i q^{97} -1.04148e11 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 530 q^{5} - 496022 q^{9}+O(q^{10}) $ 6 * q + 530 * q^5 - 496022 * q^9	$ 6 q + 530 q^{5} - 496022 q^{9} + 642728 q^{11} + 698680 q^{15} + 24109080 q^{19} + 125471192 q^{21} - 181718850 q^{25} - 256409820 q^{29} - 458481792 q^{31} + 697136360 q^{35} - 1318797936 q^{39} - 164768948 q^{41} + 3174067390 q^{45} - 675514158 q^{49} + 13060087168 q^{51} - 3688644360 q^{55} - 17663962360 q^{59} - 5020792428 q^{61} - 19996916880 q^{65} + 23117013976 q^{69} - 56788418832 q^{71} + 95499160400 q^{75} - 2602550880 q^{79} - 7039907074 q^{81} - 85024210560 q^{85} + 249448412540 q^{89} + 184446766128 q^{91} - 104896380600 q^{95} - 520781125736 q^{99}+O(q^{100}) $ 6 * q + 530 * q^5 - 496022 * q^9 + 642728 * q^11 + 698680 * q^15 + 24109080 * q^19 + 125471192 * q^21 - 181718850 * q^25 - 256409820 * q^29 - 458481792 * q^31 + 697136360 * q^35 - 1318797936 * q^39 - 164768948 * q^41 + 3174067390 * q^45 - 675514158 * q^49 + 13060087168 * q^51 - 3688644360 * q^55 - 17663962360 * q^59 - 5020792428 * q^61 - 19996916880 * q^65 + 23117013976 * q^69 - 56788418832 * q^71 + 95499160400 * q^75 - 2602550880 * q^79 - 7039907074 * q^81 - 85024210560 * q^85 + 249448412540 * q^89 + 184446766128 * q^91 - 104896380600 * q^95 - 520781125736 * 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
$3$			100.951i			0.239852i	0.992783	+	0.119926i	$0.0382657\pi$
$3$			100.951i			0.239852i	−0.992783	+	0.119926i	$0.961734\pi$
$4$		0			0
$5$	2827.02	−	6390.31i	0.404570	−	0.914507i
$5$	2827.02	−	6390.31i	0.404570	−	0.914507i
$6$		0			0
$7$			15908.8i			0.357765i	0.983870	+	0.178883i	$0.0572482\pi$
$7$			15908.8i			0.357765i	−0.983870	+	0.178883i	$0.942752\pi$
$8$		0			0
$9$	166956.			0.942471
$10$		0			0
$11$	−623805.			−1.16786			−0.583928	−	0.811806i	$-0.698485\pi$
$11$	−623805.			−1.16786			−0.583928	+	0.811806i	$0.698485\pi$
$12$		0			0
$13$		−	1.54230e6i		−	1.15207i	−0.817424	−	0.576037i	$-0.804599\pi$
$13$		−	1.54230e6i		−	1.15207i	0.817424	−	0.576037i	$-0.195401\pi$
$14$		0			0
$15$	645107.	+	285390.i	0.219346	+	0.0970368i
$16$		0			0
$17$		−	1.11817e6i		−	0.191002i	−0.995429	−	0.0955010i	$-0.969555\pi$
$17$		−	1.11817e6i		−	0.191002i	0.995429	−	0.0955010i	$-0.0304453\pi$
$18$		0			0
$19$	1.45889e7			1.35170			0.675848	−	0.737041i	$-0.263777\pi$
$19$	1.45889e7			1.35170			0.675848	+	0.737041i	$0.263777\pi$
$20$		0			0
$21$	−1.60601e6			−0.0858106
$22$		0			0
$23$			6.03368e6i			0.195470i	0.995212	+	0.0977348i	$0.0311597\pi$
$23$			6.03368e6i			0.195470i	−0.995212	+	0.0977348i	$0.968840\pi$
$24$		0			0
$25$	−3.28441e7	−	3.61310e7i	−0.672647	−	0.739964i
$26$		0			0
$27$			3.47375e7i			0.465905i
$28$		0			0
$29$	2.91997e7			0.264356			0.132178	−	0.991226i	$-0.457803\pi$
$29$	2.91997e7			0.264356			0.132178	+	0.991226i	$0.457803\pi$
$30$		0			0
$31$	−2.33031e8			−1.46192			−0.730962	−	0.682418i	$-0.760928\pi$
$31$	−2.33031e8			−1.46192			−0.730962	+	0.682418i	$0.760928\pi$
$32$		0			0
$33$		−	6.29736e7i		−	0.280112i
$34$		0			0
$35$	1.01662e8	+	4.49744e7i	0.327179	+	0.144741i
$36$		0			0
$37$			6.65053e8i			1.57669i	0.615232	+	0.788346i	$0.289062\pi$
$37$			6.65053e8i			1.57669i	−0.615232	+	0.788346i	$0.710938\pi$
$38$		0			0
$39$	1.55696e8			0.276327
$40$		0			0
$41$	−6.63914e8			−0.894954			−0.447477	−	0.894295i	$-0.647677\pi$
$41$	−6.63914e8			−0.894954			−0.447477	+	0.894295i	$0.647677\pi$
$42$		0			0
$43$		−	4.11150e8i		−	0.426505i	−0.976997	−	0.213252i	$-0.931594\pi$
$43$		−	4.11150e8i		−	0.426505i	0.976997	−	0.213252i	$-0.0684057\pi$
$44$		0			0
$45$	4.71987e8	−	1.06690e9i	0.381295	−	0.861897i
$46$		0			0
$47$		−	2.47761e9i		−	1.57578i	−0.615818	−	0.787888i	$-0.711175\pi$
$47$		−	2.47761e9i		−	1.57578i	0.615818	−	0.787888i	$-0.288825\pi$
$48$		0			0
$49$	1.72424e9			0.872004
$50$		0			0
$51$	1.12880e8			0.0458122
$52$		0			0
$53$		−	3.69178e9i		−	1.21260i	−0.795235	−	0.606302i	$-0.792652\pi$
$53$		−	3.69178e9i		−	1.21260i	0.795235	−	0.606302i	$-0.207348\pi$
$54$		0			0
$55$	−1.76351e9	+	3.98631e9i	−0.472479	+	1.06801i
$56$		0			0
$57$			1.47277e9i			0.324207i
$58$		0			0
$59$	1.25820e9			0.229121			0.114561	−	0.993416i	$-0.463454\pi$
$59$	1.25820e9			0.229121			0.114561	+	0.993416i	$0.463454\pi$
$60$		0			0
$61$	−4.05784e9			−0.615150			−0.307575	−	0.951524i	$-0.599517\pi$
$61$	−4.05784e9			−0.615150			−0.307575	+	0.951524i	$0.599517\pi$
$62$		0			0
$63$			2.65607e9i			0.337183i
$64$		0			0
$65$	−9.85577e9	−	4.36011e9i	−1.05358	−	0.466094i
$66$		0			0
$67$		−	1.84180e10i		−	1.66660i	−0.552821	−	0.833300i	$-0.686449\pi$
$67$		−	1.84180e10i		−	1.66660i	0.552821	−	0.833300i	$-0.313551\pi$
$68$		0			0
$69$	−6.09105e8			−0.0468837
$70$		0			0
$71$	−3.19489e9			−0.210153			−0.105076	−	0.994464i	$-0.533509\pi$
$71$	−3.19489e9			−0.210153			−0.105076	+	0.994464i	$0.533509\pi$
$72$		0			0
$73$		−	1.51712e10i		−	0.856535i	−0.903652	−	0.428267i	$-0.859124\pi$
$73$		−	1.51712e10i		−	0.856535i	0.903652	−	0.428267i	$-0.140876\pi$
$74$		0			0
$75$	3.64746e9	−	3.31564e9i	0.177482	−	0.161336i
$76$		0			0
$77$		−	9.92398e9i		−	0.417818i
$78$		0			0
$79$	−4.26826e10			−1.56064			−0.780319	−	0.625382i	$-0.784943\pi$
$79$	−4.26826e10			−1.56064			−0.780319	+	0.625382i	$0.784943\pi$
$80$		0			0
$81$	2.60690e10			0.830723
$82$		0			0
$83$		−	5.86787e10i		−	1.63512i	−0.575840	−	0.817562i	$-0.695325\pi$
$83$		−	5.86787e10i		−	1.63512i	0.575840	−	0.817562i	$-0.304675\pi$
$84$		0			0
$85$	−7.14544e9	−	3.16108e9i	−0.174673	−	0.0772736i
$86$		0			0
$87$			2.94773e9i			0.0634063i
$88$		0			0
$89$	−3.40792e10			−0.646910			−0.323455	−	0.946244i	$-0.604844\pi$
$89$	−3.40792e10			−0.646910			−0.323455	+	0.946244i	$0.604844\pi$
$90$		0			0
$91$	2.45361e10			0.412172
$92$		0			0
$93$		−	2.35247e10i		−	0.350645i
$94$		0			0
$95$	4.12432e10	−	9.32279e10i	0.546855	−	1.23614i
$96$		0			0
$97$		−	1.37873e11i		−	1.63017i	−0.579339	−	0.815087i	$-0.696689\pi$
$97$		−	1.37873e11i		−	1.63017i	0.579339	−	0.815087i	$-0.303311\pi$
$98$		0			0
$99$	−1.04148e11			−1.10067
$100$		0			0
$101$	−2.07552e11			−1.96499			−0.982493	−	0.186302i	$-0.940350\pi$
$101$	−2.07552e11			−1.96499			−0.982493	+	0.186302i	$0.940350\pi$
$102$		0			0
$103$		−	2.57852e10i		−	0.219162i	−0.993978	−	0.109581i	$-0.965049\pi$
$103$		−	2.57852e10i		−	0.219162i	0.993978	−	0.109581i	$-0.0349509\pi$
$104$		0			0
$105$	−4.54021e9	+	1.02629e10i	−0.0347164	+	0.0784744i
$106$		0			0
$107$			1.05201e11i			0.725119i	0.931961	+	0.362559i	$0.118097\pi$
$107$			1.05201e11i			0.725119i	−0.931961	+	0.362559i	$0.881903\pi$
$108$		0			0
$109$	2.37343e11			1.47751			0.738757	−	0.673972i	$-0.235413\pi$
$109$	2.37343e11			1.47751			0.738757	+	0.673972i	$0.235413\pi$
$110$		0			0
$111$	−6.71377e10			−0.378172
$112$		0			0
$113$			1.77970e10i			0.0908689i	0.998967	+	0.0454344i	$0.0144672\pi$
$113$			1.77970e10i			0.0908689i	−0.998967	+	0.0454344i	$0.985533\pi$
$114$		0			0
$115$	3.85571e10	+	1.70573e10i	0.178758	+	0.0790811i
$116$		0			0
$117$		−	2.57496e11i		−	1.08580i
$118$		0			0
$119$	1.77887e10			0.0683338
$120$		0			0
$121$	1.03821e11			0.363886
$122$		0			0
$123$		−	6.70227e10i		−	0.214656i
$124$		0			0
$125$	−3.23739e11	+	1.07741e11i	−0.948835	+	0.315773i
$126$		0			0
$127$		−	5.56375e11i		−	1.49433i	−0.664637	−	0.747167i	$-0.731414\pi$
$127$		−	5.56375e11i		−	1.49433i	0.664637	−	0.747167i	$-0.268586\pi$
$128$		0			0
$129$	4.15059e10			0.102298
$130$		0			0
$131$	7.67575e10			0.173832			0.0869158	−	0.996216i	$-0.472299\pi$
$131$	7.67575e10			0.173832			0.0869158	+	0.996216i	$0.472299\pi$
$132$		0			0
$133$			2.32093e11i			0.483590i
$134$		0			0
$135$	2.21983e11	+	9.82034e10i	0.426074	+	0.188491i
$136$		0			0
$137$			5.87391e11i			1.03983i	0.854217	+	0.519917i	$0.174037\pi$
$137$			5.87391e11i			1.03983i	−0.854217	+	0.519917i	$0.825963\pi$
$138$		0			0
$139$	−2.71414e11			−0.443660			−0.221830	−	0.975085i	$-0.571203\pi$
$139$	−2.71414e11			−0.443660			−0.221830	+	0.975085i	$0.571203\pi$
$140$		0			0
$141$	2.50117e11			0.377953
$142$		0			0
$143$			9.62094e11i			1.34545i
$144$		0			0
$145$	8.25481e10	−	1.86595e11i	0.106951	−	0.241756i
$146$		0			0
$147$			1.74063e11i			0.209152i
$148$		0			0
$149$	4.91446e11			0.548215			0.274108	−	0.961699i	$-0.411618\pi$
$149$	4.91446e11			0.548215			0.274108	+	0.961699i	$0.411618\pi$
$150$		0			0
$151$	3.53354e11			0.366300			0.183150	−	0.983085i	$-0.441371\pi$
$151$	3.53354e11			0.366300			0.183150	+	0.983085i	$0.441371\pi$
$152$		0			0
$153$		−	1.86685e11i		−	0.180014i
$154$		0			0
$155$	−6.58783e11	+	1.48914e12i	−0.591450	+	1.33694i
$156$		0			0
$157$			1.61767e12i			1.35345i	0.736236	+	0.676725i	$0.236601\pi$
$157$			1.61767e12i			1.35345i	−0.736236	+	0.676725i	$0.763399\pi$
$158$		0			0
$159$	3.72688e11			0.290845
$160$		0			0
$161$	−9.59885e10			−0.0699322
$162$		0			0
$163$			2.86025e11i			0.194703i	0.995250	+	0.0973513i	$0.0310370\pi$
$163$			2.86025e11i			0.194703i	−0.995250	+	0.0973513i	$0.968963\pi$
$164$		0			0
$165$	−4.02421e11	−	1.78027e11i	−0.256165	−	0.113325i
$166$		0			0
$167$			8.22338e11i			0.489903i	0.969535	+	0.244951i	$0.0787720\pi$
$167$			8.22338e11i			0.489903i	−0.969535	+	0.244951i	$0.921228\pi$
$168$		0			0
$169$	−5.86526e11			−0.327273
$170$		0			0
$171$	2.43571e12			1.27393
$172$		0			0
$173$			5.03556e11i			0.247055i	0.992341	+	0.123528i	$0.0394208\pi$
$173$			5.03556e11i			0.247055i	−0.992341	+	0.123528i	$0.960579\pi$
$174$		0			0
$175$	5.74801e11	−	5.22510e11i	0.264733	−	0.240650i
$176$		0			0
$177$			1.27017e11i			0.0549551i
$178$		0			0
$179$	1.28718e12			0.523536			0.261768	−	0.965131i	$-0.415694\pi$
$179$	1.28718e12			0.523536			0.261768	+	0.965131i	$0.415694\pi$
$180$		0			0
$181$	1.43456e12			0.548890			0.274445	−	0.961603i	$-0.411506\pi$
$181$	1.43456e12			0.548890			0.274445	+	0.961603i	$0.411506\pi$
$182$		0			0
$183$		−	4.09642e11i		−	0.147545i
$184$		0			0
$185$	4.24990e12	+	1.88012e12i	1.44190	+	0.637882i
$186$		0			0
$187$			6.97518e11i			0.223063i
$188$		0			0
$189$	−5.52631e11			−0.166685
$190$		0			0
$191$	−6.04865e12			−1.72177			−0.860885	−	0.508800i	$-0.830089\pi$
$191$	−6.04865e12			−1.72177			−0.860885	+	0.508800i	$0.830089\pi$
$192$		0			0
$193$			3.02913e12i			0.814241i	0.913375	+	0.407120i	$0.133467\pi$
$193$			3.02913e12i			0.814241i	−0.913375	+	0.407120i	$0.866533\pi$
$194$		0			0
$195$	4.40156e11	−	9.94949e11i	0.111793	−	0.252703i
$196$		0			0
$197$		−	5.19664e12i		−	1.24784i	−0.781489	−	0.623920i	$-0.785539\pi$
$197$		−	5.19664e12i		−	1.24784i	0.781489	−	0.623920i	$-0.214461\pi$
$198$		0			0
$199$	5.20023e11			0.118122			0.0590610	−	0.998254i	$-0.481189\pi$
$199$	5.20023e11			0.118122			0.0590610	+	0.998254i	$0.481189\pi$
$200$		0			0
$201$	1.85931e12			0.399737
$202$		0			0
$203$			4.64532e11i			0.0945774i
$204$		0			0
$205$	−1.87690e12	+	4.24262e12i	−0.362071	+	0.818442i
$206$		0			0
$207$			1.00736e12i			0.184224i
$208$		0			0
$209$	−9.10066e12			−1.57859
$210$		0			0
$211$	2.82884e12			0.465645			0.232822	−	0.972519i	$-0.425204\pi$
$211$	2.82884e12			0.465645			0.232822	+	0.972519i	$0.425204\pi$
$212$		0			0
$213$		−	3.22527e11i		−	0.0504056i
$214$		0			0
$215$	−2.62738e12	−	1.16233e12i	−0.390042	−	0.172551i
$216$		0			0
$217$		−	3.70724e12i		−	0.523025i
$218$		0			0
$219$	1.53155e12			0.205441
$220$		0			0
$221$	−1.72455e12			−0.220048
$222$		0			0
$223$		−	6.97675e12i		−	0.847182i	−0.905854	−	0.423591i	$-0.860769\pi$
$223$		−	6.97675e12i		−	0.847182i	0.905854	−	0.423591i	$-0.139231\pi$
$224$		0			0
$225$	−5.48351e12	−	6.03229e12i	−0.633950	−	0.697395i
$226$		0			0
$227$			3.33075e12i			0.366775i	0.983041	+	0.183388i	$0.0587063\pi$
$227$			3.33075e12i			0.366775i	−0.983041	+	0.183388i	$0.941294\pi$
$228$		0			0
$229$	4.95393e12			0.519822			0.259911	−	0.965633i	$-0.416307\pi$
$229$	4.95393e12			0.519822			0.259911	+	0.965633i	$0.416307\pi$
$230$		0			0
$231$	1.00183e12			0.100214
$232$		0			0
$233$		−	1.20602e13i		−	1.15053i	−0.817968	−	0.575264i	$-0.804899\pi$
$233$		−	1.20602e13i		−	1.15053i	0.817968	−	0.575264i	$-0.195101\pi$
$234$		0			0
$235$	−1.58327e13	−	7.00424e12i	−1.44106	−	0.637511i
$236$		0			0
$237$		−	4.30885e12i		−	0.374322i
$238$		0			0
$239$	4.41187e12			0.365961			0.182980	−	0.983117i	$-0.441426\pi$
$239$	4.41187e12			0.365961			0.182980	+	0.983117i	$0.441426\pi$
$240$		0			0
$241$	2.16312e12			0.171390			0.0856952	−	0.996321i	$-0.472689\pi$
$241$	2.16312e12			0.171390			0.0856952	+	0.996321i	$0.472689\pi$
$242$		0			0
$243$			8.78532e12i			0.665156i
$244$		0			0
$245$	4.87445e12	−	1.10184e13i	0.352786	−	0.797454i
$246$		0			0
$247$		−	2.25005e13i		−	1.55725i
$248$		0			0
$249$	5.92366e12			0.392188
$250$		0			0
$251$	1.06811e13			0.676723			0.338361	−	0.941016i	$-0.390127\pi$
$251$	1.06811e13			0.676723			0.338361	+	0.941016i	$0.390127\pi$
$252$		0			0
$253$		−	3.76384e12i		−	0.228280i
$254$		0			0
$255$	3.19113e11	−	7.21338e11i	0.0185342	−	0.0418955i
$256$		0			0
$257$			2.32150e13i			1.29162i	0.763496	+	0.645812i	$0.223481\pi$
$257$			2.32150e13i			1.29162i	−0.763496	+	0.645812i	$0.776519\pi$
$258$		0			0
$259$	−1.05802e13			−0.564085
$260$		0			0
$261$	4.87506e12			0.249148
$262$		0			0
$263$		−	3.54305e13i		−	1.73628i	−0.496317	−	0.868141i	$-0.665315\pi$
$263$		−	3.54305e13i		−	1.73628i	0.496317	−	0.868141i	$-0.334685\pi$
$264$		0			0
$265$	−2.35916e13	−	1.04367e13i	−1.10893	−	0.490583i
$266$		0			0
$267$		−	3.44032e12i		−	0.155163i
$268$		0			0
$269$	−2.98211e13			−1.29088			−0.645441	−	0.763810i	$-0.723326\pi$
$269$	−2.98211e13			−1.29088			−0.645441	+	0.763810i	$0.723326\pi$
$270$		0			0
$271$	−5.87087e12			−0.243989			−0.121995	−	0.992531i	$-0.538929\pi$
$271$	−5.87087e12			−0.243989			−0.121995	+	0.992531i	$0.538929\pi$
$272$		0			0
$273$			2.47694e12i			0.0988601i
$274$		0			0
$275$	2.04883e13	+	2.25387e13i	0.785554	+	0.864171i
$276$		0			0
$277$			1.03428e13i			0.381066i	0.981681	+	0.190533i	$0.0610215\pi$
$277$			1.03428e13i			0.381066i	−0.981681	+	0.190533i	$0.938978\pi$
$278$		0			0
$279$	−3.89059e13			−1.37782
$280$		0			0
$281$	1.50495e13			0.512432			0.256216	−	0.966620i	$-0.417524\pi$
$281$	1.50495e13			0.512432			0.256216	+	0.966620i	$0.417524\pi$
$282$		0			0
$283$			5.55117e13i			1.81785i	0.416955	+	0.908927i	$0.363097\pi$
$283$			5.55117e13i			1.81785i	−0.416955	+	0.908927i	$0.636903\pi$
$284$		0			0
$285$	9.41144e12	+	4.16354e12i	0.296489	+	0.131164i
$286$		0			0
$287$		−	1.05621e13i		−	0.320183i
$288$		0			0
$289$	3.30216e13			0.963518
$290$		0			0
$291$	1.39184e13			0.391000
$292$		0			0
$293$		−	5.82419e12i		−	0.157566i	−0.996892	−	0.0787832i	$-0.974897\pi$
$293$		−	5.82419e12i		−	0.157566i	0.996892	−	0.0787832i	$-0.0251035\pi$
$294$		0			0
$295$	3.55696e12	−	8.04032e12i	0.0926954	−	0.209533i
$296$		0			0
$297$		−	2.16694e13i		−	0.544110i
$298$		0			0
$299$	9.30574e12			0.225195
$300$		0			0
$301$	6.54090e12			0.152589
$302$		0			0
$303$		−	2.09525e13i		−	0.471305i
$304$		0			0
$305$	−1.14716e13	+	2.59309e13i	−0.248871	+	0.562559i
$306$		0			0
$307$			7.34987e13i			1.53822i	0.639117	+	0.769110i	$0.279300\pi$
$307$			7.34987e13i			1.53822i	−0.639117	+	0.769110i	$0.720700\pi$
$308$		0			0
$309$	2.60304e12			0.0525664
$310$		0			0
$311$	5.27276e13			1.02768			0.513838	−	0.857887i	$-0.328223\pi$
$311$	5.27276e13			1.02768			0.513838	+	0.857887i	$0.328223\pi$
$312$		0			0
$313$			1.10252e12i			0.0207440i	0.999946	+	0.0103720i	$0.00330157\pi$
$313$			1.10252e12i			0.0207440i	−0.999946	+	0.0103720i	$0.996698\pi$
$314$		0			0
$315$	1.69731e13	+	7.50875e12i	0.308357	+	0.136414i
$316$		0			0
$317$		−	9.68269e12i		−	0.169891i	−0.996386	−	0.0849455i	$-0.972928\pi$
$317$		−	9.68269e12i		−	0.169891i	0.996386	−	0.0849455i	$-0.0270716\pi$
$318$		0			0
$319$	−1.82149e13			−0.308730
$320$		0			0
$321$	−1.06201e13			−0.173921
$322$		0			0
$323$		−	1.63129e13i		−	0.258177i
$324$		0			0
$325$	−5.57249e13	+	5.06554e13i	−0.852493	+	0.774938i
$326$		0			0
$327$			2.39600e13i			0.354384i
$328$		0			0
$329$	3.94158e13			0.563758
$330$		0			0
$331$	8.90833e13			1.23237			0.616187	−	0.787600i	$-0.288677\pi$
$331$	8.90833e13			1.23237			0.616187	+	0.787600i	$0.288677\pi$
$332$		0			0
$333$			1.11035e14i			1.48599i
$334$		0			0
$335$	−1.17697e14	−	5.20681e13i	−1.52412	−	0.674256i
$336$		0			0
$337$			4.89653e13i			0.613655i	0.951765	+	0.306827i	$0.0992674\pi$
$337$			4.89653e13i			0.613655i	−0.951765	+	0.306827i	$0.900733\pi$
$338$		0			0
$339$	−1.79662e12			−0.0217951
$340$		0			0
$341$	1.45366e14			1.70731
$342$		0			0
$343$			5.88874e13i			0.669738i
$344$		0			0
$345$	−1.72195e12	+	3.89237e12i	−0.0189677	+	0.0428755i
$346$		0			0
$347$			1.41507e14i			1.50997i	0.655744	+	0.754983i	$0.272355\pi$
$347$			1.41507e14i			1.50997i	−0.655744	+	0.754983i	$0.727645\pi$
$348$		0			0
$349$	−1.17661e13			−0.121645			−0.0608223	−	0.998149i	$-0.519372\pi$
$349$	−1.17661e13			−0.121645			−0.0608223	+	0.998149i	$0.519372\pi$
$350$		0			0
$351$	5.35756e13			0.536757
$352$		0			0
$353$			2.34718e13i			0.227921i	0.993485	+	0.113961i	$0.0363538\pi$
$353$			2.34718e13i			0.227921i	−0.993485	+	0.113961i	$0.963646\pi$
$354$		0			0
$355$	−9.03202e12	+	2.04164e13i	−0.0850215	+	0.192186i
$356$		0			0
$357$			1.79578e12i			0.0163900i
$358$		0			0
$359$	−1.12805e14			−0.998413			−0.499207	−	0.866483i	$-0.666375\pi$
$359$	−1.12805e14			−0.998413			−0.499207	+	0.866483i	$0.666375\pi$
$360$		0			0
$361$	9.63471e13			0.827083
$362$		0			0
$363$			1.04808e13i			0.0872786i
$364$		0			0
$365$	−9.69489e13	−	4.28893e13i	−0.783307	−	0.346528i
$366$		0			0
$367$		−	1.66738e14i		−	1.30729i	−0.756802	−	0.653645i	$-0.773239\pi$
$367$		−	1.66738e14i		−	1.30729i	0.756802	−	0.653645i	$-0.226761\pi$
$368$		0			0
$369$	−1.10844e14			−0.843469
$370$		0			0
$371$	5.87318e13			0.433827
$372$		0			0
$373$		−	1.39847e14i		−	1.00290i	−0.865188	−	0.501448i	$-0.832801\pi$
$373$		−	1.39847e14i		−	1.00290i	0.865188	−	0.501448i	$-0.167199\pi$
$374$		0			0
$375$	−1.08765e13	−	3.26818e13i	−0.0757388	−	0.227580i
$376$		0			0
$377$		−	4.50347e13i		−	0.304558i
$378$		0			0
$379$	2.46176e14			1.61708			0.808539	−	0.588443i	$-0.200259\pi$
$379$	2.46176e14			1.61708			0.808539	+	0.588443i	$0.200259\pi$
$380$		0			0
$381$	5.61666e13			0.358419
$382$		0			0
$383$		−	1.19986e14i		−	0.743941i	−0.928245	−	0.371970i	$-0.878682\pi$
$383$		−	1.19986e14i		−	0.743941i	0.928245	−	0.371970i	$-0.121318\pi$
$384$		0			0
$385$	−6.34173e13	−	2.80553e13i	−0.382097	−	0.169036i
$386$		0			0
$387$		−	6.86439e13i		−	0.401968i
$388$		0			0
$389$	−9.66133e13			−0.549939			−0.274969	−	0.961453i	$-0.588668\pi$
$389$	−9.66133e13			−0.549939			−0.274969	+	0.961453i	$0.588668\pi$
$390$		0			0
$391$	6.74666e12			0.0373351
$392$		0			0
$393$			7.74873e12i			0.0416938i
$394$		0			0
$395$	−1.20664e14	+	2.72755e14i	−0.631387	+	1.42721i
$396$		0			0
$397$		−	3.07115e13i		−	0.156298i	−0.996942	−	0.0781489i	$-0.975099\pi$
$397$		−	3.07115e13i		−	0.156298i	0.996942	−	0.0781489i	$-0.0249010\pi$
$398$		0			0
$399$	−2.34299e13			−0.115990
$400$		0			0
$401$	1.38014e14			0.664707			0.332354	−	0.943155i	$-0.392157\pi$
$401$	1.38014e14			0.664707			0.332354	+	0.943155i	$0.392157\pi$
$402$		0			0
$403$			3.59404e14i			1.68424i
$404$		0			0
$405$	7.36974e13	−	1.66589e14i	0.336085	−	0.759702i
$406$		0			0
$407$		−	4.14863e14i		−	1.84135i
$408$		0			0
$409$	−1.98577e14			−0.857927			−0.428963	−	0.903322i	$-0.641121\pi$
$409$	−1.98577e14			−0.857927			−0.428963	+	0.903322i	$0.641121\pi$
$410$		0			0
$411$	−5.92976e13			−0.249406
$412$		0			0
$413$			2.00165e13i			0.0819715i
$414$		0			0
$415$	−3.74975e14	−	1.65886e14i	−1.49533	−	0.661522i
$416$		0			0
$417$		−	2.73995e13i		−	0.106413i
$418$		0			0
$419$	−3.42176e14			−1.29441			−0.647205	−	0.762316i	$-0.724062\pi$
$419$	−3.42176e14			−1.29441			−0.647205	+	0.762316i	$0.724062\pi$
$420$		0			0
$421$	−3.12187e13			−0.115044			−0.0575219	−	0.998344i	$-0.518320\pi$
$421$	−3.12187e13			−0.115044			−0.0575219	+	0.998344i	$0.518320\pi$
$422$		0			0
$423$		−	4.13652e14i		−	1.48512i
$424$		0			0
$425$	−4.04006e13	+	3.67252e13i	−0.141334	+	0.128477i
$426$		0			0
$427$		−	6.45553e13i		−	0.220079i
$428$		0			0
$429$	−9.71242e13			−0.322710
$430$		0			0
$431$	4.22057e14			1.36693			0.683465	−	0.729983i	$-0.260472\pi$
$431$	4.22057e14			1.36693			0.683465	+	0.729983i	$0.260472\pi$
$432$		0			0
$433$		−	3.63091e14i		−	1.14639i	−0.819419	−	0.573194i	$-0.805704\pi$
$433$		−	3.63091e14i		−	1.14639i	0.819419	−	0.573194i	$-0.194296\pi$
$434$		0			0
$435$	1.88369e13	+	8.33329e12i	0.0579855	+	0.0256523i
$436$		0			0
$437$			8.80250e13i			0.264215i
$438$		0			0
$439$	−8.98176e13			−0.262910			−0.131455	−	0.991322i	$-0.541965\pi$
$439$	−8.98176e13			−0.262910			−0.131455	+	0.991322i	$0.541965\pi$
$440$		0			0
$441$	2.87872e14			0.821839
$442$		0			0
$443$		−	2.31585e14i		−	0.644895i	−0.946587	−	0.322448i	$-0.895494\pi$
$443$		−	2.31585e14i		−	0.644895i	0.946587	−	0.322448i	$-0.104506\pi$
$444$		0			0
$445$	−9.63424e13	+	2.17777e14i	−0.261720	+	0.591604i
$446$		0			0
$447$			4.96118e13i			0.131490i
$448$		0			0
$449$	−5.36475e14			−1.38738			−0.693689	−	0.720275i	$-0.744016\pi$
$449$	−5.36475e14			−1.38738			−0.693689	+	0.720275i	$0.744016\pi$
$450$		0			0
$451$	4.14153e14			1.04518
$452$		0			0
$453$			3.56714e13i			0.0878578i
$454$		0			0
$455$	6.93640e13	−	1.56793e14i	0.166752	−	0.376934i
$456$		0			0
$457$		−	1.86645e14i		−	0.438002i	−0.975725	−	0.219001i	$-0.929720\pi$
$457$		−	1.86645e14i		−	0.438002i	0.975725	−	0.219001i	$-0.0702799\pi$
$458$		0			0
$459$	3.88423e13			0.0889888
$460$		0			0
$461$	4.16181e14			0.930951			0.465476	−	0.885061i	$-0.345883\pi$
$461$	4.16181e14			0.930951			0.465476	+	0.885061i	$0.345883\pi$
$462$		0			0
$463$			9.23323e13i			0.201678i	0.994903	+	0.100839i	$0.0321527\pi$
$463$			9.23323e13i			0.201678i	−0.994903	+	0.100839i	$0.967847\pi$
$464$		0			0
$465$	−1.50330e14	−	6.65047e13i	−0.320667	−	0.141860i
$466$		0			0
$467$			6.81230e14i			1.41922i	0.704592	+	0.709612i	$0.251130\pi$
$467$			6.81230e14i			1.41922i	−0.704592	+	0.709612i	$0.748870\pi$
$468$		0			0
$469$	2.93008e14			0.596252
$470$		0			0
$471$	−1.63305e14			−0.324627
$472$		0			0
$473$			2.56477e14i			0.498096i
$474$		0			0
$475$	−4.79161e14	−	5.27114e14i	−0.909214	−	1.00021i
$476$		0			0
$477$		−	6.16365e14i		−	1.14284i
$478$		0			0
$479$	−2.62125e14			−0.474966			−0.237483	−	0.971392i	$-0.576322\pi$
$479$	−2.62125e14			−0.474966			−0.237483	+	0.971392i	$0.576322\pi$
$480$		0			0
$481$	1.02571e15			1.81647
$482$		0			0
$483$		−	9.69012e12i		−	0.0167734i
$484$		0			0
$485$	−8.81050e14	−	3.89769e14i	−1.49081	−	0.659519i
$486$		0			0
$487$			5.11692e14i			0.846446i	0.906025	+	0.423223i	$0.139101\pi$
$487$			5.11692e14i			0.846446i	−0.906025	+	0.423223i	$0.860899\pi$
$488$		0			0
$489$	−2.88744e13			−0.0466998
$490$		0			0
$491$	1.06861e15			1.68994			0.844971	−	0.534812i	$-0.179618\pi$
$491$	1.06861e15			1.68994			0.844971	+	0.534812i	$0.179618\pi$
$492$		0			0
$493$		−	3.26502e13i		−	0.0504925i
$494$		0			0
$495$	−2.94428e14	+	6.65538e14i	−0.445298	+	1.00657i
$496$		0			0
$497$		−	5.08269e13i		−	0.0751854i
$498$		0			0
$499$	1.64668e14			0.238263			0.119132	−	0.992878i	$-0.461989\pi$
$499$	1.64668e14			0.238263			0.119132	+	0.992878i	$0.461989\pi$
$500$		0			0
$501$	−8.30157e13			−0.117504
$502$		0			0
$503$		−	1.55884e14i		−	0.215862i	−0.994158	−	0.107931i	$-0.965577\pi$
$503$		−	1.55884e14i		−	0.215862i	0.994158	−	0.107931i	$-0.0344226\pi$
$504$		0			0
$505$	−5.86753e14	+	1.32632e15i	−0.794973	+	1.79699i
$506$		0			0
$507$		−	5.92103e13i		−	0.0784971i
$508$		0			0
$509$	5.27594e14			0.684466			0.342233	−	0.939615i	$-0.388817\pi$
$509$	5.27594e14			0.684466			0.342233	+	0.939615i	$0.388817\pi$
$510$		0			0
$511$	2.41356e14			0.306438
$512$		0			0
$513$			5.06783e14i			0.629762i
$514$		0			0
$515$	−1.64775e14	−	7.28952e13i	−0.200425	−	0.0886664i
$516$		0			0
$517$			1.54554e15i			1.84028i
$518$		0			0
$519$	−5.08344e13			−0.0592567
$520$		0			0
$521$	−8.60186e14			−0.981713			−0.490857	−	0.871240i	$-0.663316\pi$
$521$	−8.60186e14			−0.981713			−0.490857	+	0.871240i	$0.663316\pi$
$522$		0			0
$523$			1.14697e15i			1.28171i	0.767661	+	0.640857i	$0.221421\pi$
$523$			1.14697e15i			1.28171i	−0.767661	+	0.640857i	$0.778579\pi$
$524$		0			0
$525$	5.27478e13	+	5.80267e13i	0.0577202	+	0.0634967i
$526$		0			0
$527$			2.60568e14i			0.279230i
$528$		0			0
$529$	9.16404e14			0.961792
$530$		0			0
$531$	2.10065e14			0.215940
$532$		0			0
$533$			1.02395e15i			1.03105i
$534$		0			0
$535$	6.72267e14	+	2.97405e14i	0.663126	+	0.293361i
$536$		0			0
$537$			1.29942e14i			0.125571i
$538$		0			0
$539$	−1.07559e15			−1.01837
$540$		0			0
$541$	1.24370e15			1.15380			0.576898	−	0.816816i	$-0.304263\pi$
$541$	1.24370e15			1.15380			0.576898	+	0.816816i	$0.304263\pi$
$542$		0			0
$543$			1.44820e14i			0.131652i
$544$		0			0
$545$	6.70974e14	−	1.51670e15i	0.597757	−	1.35120i
$546$		0			0
$547$		−	1.40219e15i		−	1.22427i	−0.790755	−	0.612133i	$-0.790312\pi$
$547$		−	1.40219e15i		−	1.22427i	0.790755	−	0.612133i	$-0.209688\pi$
$548$		0			0
$549$	−6.77481e14			−0.579761
$550$		0			0
$551$	4.25993e14			0.357329
$552$		0			0
$553$		−	6.79029e14i		−	0.558342i
$554$		0			0
$555$	−1.89799e14	+	4.29031e14i	−0.152997	+	0.345841i
$556$		0			0
$557$		−	4.54370e14i		−	0.359092i	−0.983750	−	0.179546i	$-0.942537\pi$
$557$		−	4.54370e14i		−	0.359092i	0.983750	−	0.179546i	$-0.0574629\pi$
$558$		0			0
$559$	−6.34116e14			−0.491365
$560$		0			0
$561$	−7.04150e13			−0.0535020
$562$		0			0
$563$		−	3.40271e14i		−	0.253530i	−0.991933	−	0.126765i	$-0.959541\pi$
$563$		−	3.40271e14i		−	0.253530i	0.991933	−	0.126765i	$-0.0404594\pi$
$564$		0			0
$565$	1.13728e14	+	5.03124e13i	0.0831002	+	0.0367628i
$566$		0			0
$567$			4.14726e14i			0.297204i
$568$		0			0
$569$	1.02622e15			0.721311			0.360656	−	0.932699i	$-0.382553\pi$
$569$	1.02622e15			0.721311			0.360656	+	0.932699i	$0.382553\pi$
$570$		0			0
$571$	1.81645e15			1.25235			0.626174	−	0.779683i	$-0.284620\pi$
$571$	1.81645e15			1.25235			0.626174	+	0.779683i	$0.284620\pi$
$572$		0			0
$573$		−	6.10616e14i		−	0.412970i
$574$		0			0
$575$	2.18003e14	−	1.98171e14i	0.144640	−	0.131482i
$576$		0			0
$577$			2.60905e15i			1.69830i	0.528148	+	0.849152i	$0.322887\pi$
$577$			2.60905e15i			1.69830i	−0.528148	+	0.849152i	$0.677113\pi$
$578$		0			0
$579$	−3.05793e14			−0.195297
$580$		0			0
$581$	9.33507e14			0.584990
$582$		0			0
$583$			2.30295e15i			1.41614i
$584$		0			0
$585$	−1.64548e15	−	7.27945e14i	−0.992968	−	0.439280i
$586$		0			0
$587$		−	2.46315e14i		−	0.145875i	−0.997337	−	0.0729375i	$-0.976763\pi$
$587$		−	2.46315e14i		−	0.145875i	0.997337	−	0.0729375i	$-0.0232374\pi$
$588$		0			0
$589$	−3.39968e15			−1.97608
$590$		0			0
$591$	5.24605e14			0.299296
$592$		0			0
$593$		−	1.31447e15i		−	0.736121i	−0.929802	−	0.368060i	$-0.880022\pi$
$593$		−	1.31447e15i		−	0.736121i	0.929802	−	0.368060i	$-0.119978\pi$
$594$		0			0
$595$	5.02889e13	−	1.13675e14i	0.0276458	−	0.0624918i
$596$		0			0
$597$			5.24968e13i			0.0283318i
$598$		0			0
$599$	2.18539e15			1.15793			0.578963	−	0.815354i	$-0.303458\pi$
$599$	2.18539e15			1.15793			0.578963	+	0.815354i	$0.303458\pi$
$600$		0			0
$601$	9.81120e14			0.510402			0.255201	−	0.966888i	$-0.417858\pi$
$601$	9.81120e14			0.510402			0.255201	+	0.966888i	$0.417858\pi$
$602$		0			0
$603$		−	3.07500e15i		−	1.57072i
$604$		0			0
$605$	2.93503e14	−	6.63448e14i	0.147217	−	0.332776i
$606$		0			0
$607$			1.08458e15i			0.534225i	0.963665	+	0.267112i	$0.0860695\pi$
$607$			1.08458e15i			0.534225i	−0.963665	+	0.267112i	$0.913930\pi$
$608$		0			0
$609$	−4.68949e13			−0.0226846
$610$		0			0
$611$	−3.82121e15			−1.81541
$612$		0			0
$613$			7.52110e13i			0.0350953i	0.999846	+	0.0175476i	$0.00558588\pi$
$613$			7.52110e13i			0.0350953i	−0.999846	+	0.0175476i	$0.994414\pi$
$614$		0			0
$615$	−4.28296e14	−	1.89474e14i	−0.196305	−	0.0868435i
$616$		0			0
$617$		−	2.63722e15i		−	1.18735i	−0.804705	−	0.593675i	$-0.797677\pi$
$617$		−	2.63722e15i		−	1.18735i	0.804705	−	0.593675i	$-0.202323\pi$
$618$		0			0
$619$	−1.97316e15			−0.872696			−0.436348	−	0.899778i	$-0.643728\pi$
$619$	−1.97316e15			−0.872696			−0.436348	+	0.899778i	$0.643728\pi$
$620$		0			0
$621$	−2.09595e14			−0.0910703
$622$		0			0
$623$		−	5.42158e14i		−	0.231442i
$624$		0			0
$625$	−2.26719e14	+	2.37338e15i	−0.0950929	+	0.995468i
$626$		0			0
$627$		−	9.18719e14i		−	0.378627i
$628$		0			0
$629$	7.43641e14			0.301151
$630$		0			0
$631$	4.42271e14			0.176006			0.0880028	−	0.996120i	$-0.471952\pi$
$631$	4.42271e14			0.176006			0.0880028	+	0.996120i	$0.471952\pi$
$632$		0			0
$633$			2.85574e14i			0.111686i
$634$		0			0
$635$	−3.55541e15	−	1.57288e15i	−1.36658	−	0.604562i
$636$		0			0
$637$		−	2.65929e15i		−	1.00461i
$638$		0			0
$639$	−5.33406e14			−0.198063
$640$		0			0
$641$	−6.82035e14			−0.248936			−0.124468	−	0.992224i	$-0.539722\pi$
$641$	−6.82035e14			−0.248936			−0.124468	+	0.992224i	$0.539722\pi$
$642$		0			0
$643$		−	2.75748e15i		−	0.989356i	−0.869076	−	0.494678i	$-0.835286\pi$
$643$		−	2.75748e15i		−	0.989356i	0.869076	−	0.494678i	$-0.164714\pi$
$644$		0			0
$645$	1.17338e14	−	2.65236e14i	0.0413866	−	0.0935522i
$646$		0			0
$647$		−	6.27496e14i		−	0.217589i	−0.994064	−	0.108795i	$-0.965301\pi$
$647$		−	6.27496e14i		−	0.217589i	0.994064	−	0.108795i	$-0.0346991\pi$
$648$		0			0
$649$	−7.84874e14			−0.267580
$650$		0			0
$651$	3.74249e14			0.125449
$652$		0			0
$653$			8.70491e14i			0.286908i	0.989657	+	0.143454i	$0.0458208\pi$
$653$			8.70491e14i			0.286908i	−0.989657	+	0.143454i	$0.954179\pi$
$654$		0			0
$655$	2.16995e14	−	4.90504e14i	0.0703270	−	0.158970i
$656$		0			0
$657$		−	2.53293e15i		−	0.807259i
$658$		0			0
$659$	3.46426e15			1.08578			0.542889	−	0.839805i	$-0.317330\pi$
$659$	3.46426e15			1.08578			0.542889	+	0.839805i	$0.317330\pi$
$660$		0			0
$661$	−1.96770e15			−0.606528			−0.303264	−	0.952907i	$-0.598076\pi$
$661$	−1.96770e15			−0.606528			−0.303264	+	0.952907i	$0.598076\pi$
$662$		0			0
$663$		−	1.74095e14i		−	0.0527790i
$664$		0			0
$665$	1.48314e15	+	6.56129e14i	0.442246	+	0.195646i
$666$		0			0
$667$			1.76182e14i			0.0516736i
$668$		0			0
$669$	7.04309e14			0.203198
$670$		0			0
$671$	2.53130e15			0.718406
$672$		0			0
$673$		−	8.57604e14i		−	0.239444i	−0.992807	−	0.119722i	$-0.961800\pi$
$673$		−	8.57604e14i		−	0.239444i	0.992807	−	0.119722i	$-0.0382003\pi$
$674$		0			0
$675$	1.25510e15	−	1.14092e15i	0.344753	−	0.313390i
$676$		0			0
$677$		−	2.11042e15i		−	0.570336i	−0.958478	−	0.285168i	$-0.907951\pi$
$677$		−	2.11042e15i		−	0.570336i	0.958478	−	0.285168i	$-0.0920494\pi$
$678$		0			0
$679$	2.19339e15			0.583219
$680$		0			0
$681$	−3.36242e14			−0.0879717
$682$		0			0
$683$		−	3.30397e15i		−	0.850593i	−0.905054	−	0.425296i	$-0.860170\pi$
$683$		−	3.30397e15i		−	0.850593i	0.905054	−	0.425296i	$-0.139830\pi$
$684$		0			0
$685$	3.75361e15	+	1.66056e15i	0.950936	+	0.420685i
$686$		0			0
$687$			5.00103e14i			0.124680i
$688$		0			0
$689$	−5.69383e15			−1.39701
$690$		0			0
$691$	−7.09703e15			−1.71375			−0.856875	−	0.515524i	$-0.827597\pi$
$691$	−7.09703e15			−1.71375			−0.856875	+	0.515524i	$0.827597\pi$
$692$		0			0
$693$		−	1.65687e15i		−	0.393781i
$694$		0			0
$695$	−7.67292e14	+	1.73442e15i	−0.179492	+	0.405731i
$696$		0			0
$697$			7.42367e14i			0.170938i
$698$		0			0
$699$	1.21749e15			0.275956
$700$		0			0
$701$	−5.37565e15			−1.19945			−0.599725	−	0.800206i	$-0.704723\pi$
$701$	−5.37565e15			−1.19945			−0.599725	+	0.800206i	$0.704723\pi$
$702$		0			0
$703$			9.70243e15i			2.13121i
$704$		0			0
$705$	7.07084e14	−	1.59832e15i	0.152908	−	0.345641i
$706$		0			0
$707$		−	3.30190e15i		−	0.703003i
$708$		0			0
$709$	6.48992e15			1.36046			0.680229	−	0.733000i	$-0.261880\pi$
$709$	6.48992e15			1.36046			0.680229	+	0.733000i	$0.261880\pi$
$710$		0			0
$711$	−7.12612e15			−1.47086
$712$		0			0
$713$		−	1.40604e15i		−	0.285762i
$714$		0			0
$715$	6.14808e15	+	2.71986e15i	1.23043	+	0.544330i
$716$		0			0
$717$			4.45382e14i			0.0877763i
$718$		0			0
$719$	−1.27151e15			−0.246781			−0.123391	−	0.992358i	$-0.539377\pi$
$719$	−1.27151e15			−0.246781			−0.123391	+	0.992358i	$0.539377\pi$
$720$		0			0
$721$	4.10211e14			0.0784086
$722$		0			0
$723$			2.18368e14i			0.0411083i
$724$		0			0
$725$	−9.59037e14	−	1.05502e15i	−0.177818	−	0.195614i
$726$		0			0
$727$			8.04231e15i			1.46873i	0.678755	+	0.734364i	$0.262520\pi$
$727$			8.04231e15i			1.46873i	−0.678755	+	0.734364i	$0.737480\pi$
$728$		0			0
$729$	3.73115e15			0.671184
$730$		0			0
$731$	−4.59735e14			−0.0814632
$732$		0			0
$733$			6.66245e15i			1.16295i	0.813563	+	0.581477i	$0.197525\pi$
$733$			6.66245e15i			1.16295i	−0.813563	+	0.581477i	$0.802475\pi$
$734$		0			0
$735$	1.11232e15	+	4.92080e14i	0.191271	+	0.0846165i
$736$		0			0
$737$			1.14893e16i			1.94635i
$738$		0			0
$739$	4.29592e15			0.716989			0.358494	−	0.933532i	$-0.383290\pi$
$739$	4.29592e15			0.716989			0.358494	+	0.933532i	$0.383290\pi$
$740$		0			0
$741$	2.27145e15			0.373510
$742$		0			0
$743$		−	1.83929e15i		−	0.297998i	−0.988837	−	0.148999i	$-0.952395\pi$
$743$		−	1.83929e15i		−	0.297998i	0.988837	−	0.148999i	$-0.0476051\pi$
$744$		0			0
$745$	1.38933e15	−	3.14049e15i	0.221791	−	0.501347i
$746$		0			0
$747$		−	9.79675e15i		−	1.54106i
$748$		0			0
$749$	−1.67362e15			−0.259422
$750$		0			0
$751$	7.02545e15			1.07314			0.536568	−	0.843857i	$-0.319721\pi$
$751$	7.02545e15			1.07314			0.536568	+	0.843857i	$0.319721\pi$
$752$		0			0
$753$			1.07827e15i			0.162313i
$754$		0			0
$755$	9.98939e14	−	2.25805e15i	0.148194	−	0.334984i
$756$		0			0
$757$			6.85179e15i			1.00179i	0.865508	+	0.500895i	$0.166996\pi$
$757$			6.85179e15i			1.00179i	−0.865508	+	0.500895i	$0.833004\pi$
$758$		0			0
$759$	3.79963e14			0.0547534
$760$		0			0
$761$	−4.99642e15			−0.709649			−0.354824	−	0.934933i	$-0.615459\pi$
$761$	−4.99642e15			−0.709649			−0.354824	+	0.934933i	$0.615459\pi$
$762$		0			0
$763$			3.77585e15i			0.528603i
$764$		0			0
$765$	−1.19297e15	−	5.27761e14i	−0.164624	−	0.0728281i
$766$		0			0
$767$		−	1.94053e15i		−	0.263964i
$768$		0			0
$769$	2.45456e15			0.329138			0.164569	−	0.986366i	$-0.447377\pi$
$769$	2.45456e15			0.329138			0.164569	+	0.986366i	$0.447377\pi$
$770$		0			0
$771$	−2.34357e15			−0.309798
$772$		0			0
$773$		−	3.34228e15i		−	0.435568i	−0.975997	−	0.217784i	$-0.930117\pi$
$773$		−	3.34228e15i		−	0.435568i	0.975997	−	0.217784i	$-0.0698829\pi$
$774$		0			0
$775$	7.65369e15	+	8.41966e15i	0.983358	+	1.08177i
$776$		0			0
$777$		−	1.06808e15i		−	0.135297i
$778$		0			0
$779$	−9.68581e15			−1.20971
$780$		0			0
$781$	1.99299e15			0.245428
$782$		0			0
$783$			1.01432e15i			0.123165i
$784$		0			0
$785$	1.03374e16	+	4.57318e15i	1.23774	+	0.547565i
$786$		0			0
$787$			6.92298e15i			0.817395i	0.912670	+	0.408698i	$0.134017\pi$
$787$			6.92298e15i			0.817395i	−0.912670	+	0.408698i	$0.865983\pi$
$788$		0			0
$789$	3.57674e15			0.416451
$790$		0			0
$791$	−2.83129e14			−0.0325097
$792$		0			0
$793$			6.25840e15i			0.708698i
$794$		0			0
$795$	1.05360e15	−	2.38160e15i	0.117667	−	0.265980i
$796$		0			0
$797$		−	1.92200e15i		−	0.211706i	−0.994382	−	0.105853i	$-0.966243\pi$
$797$		−	1.92200e15i		−	0.211706i	0.994382	−	0.105853i	$-0.0337573\pi$
$798$		0			0
$799$	−2.77038e15			−0.300976
$800$		0			0
$801$	−5.68972e15			−0.609694
$802$		0			0
$803$			9.46388e15i			1.00031i
$804$		0			0
$805$	−2.71361e14	+	6.13397e14i	−0.0282924	+	0.0639535i
$806$		0			0
$807$		−	3.01047e15i		−	0.309620i
$808$		0			0
$809$	9.00708e15			0.913834			0.456917	−	0.889509i	$-0.348954\pi$
$809$	9.00708e15			0.913834			0.456917	+	0.889509i	$0.348954\pi$
$810$		0			0
$811$	−6.65720e15			−0.666311			−0.333156	−	0.942872i	$-0.608113\pi$
$811$	−6.65720e15			−0.666311			−0.333156	+	0.942872i	$0.608113\pi$
$812$		0			0
$813$		−	5.92669e14i		−	0.0585213i
$814$		0			0
$815$	1.82779e15	+	8.08597e14i	0.178057	+	0.0787708i
$816$		0			0
$817$		−	5.99825e15i		−	0.576505i
$818$		0			0
$819$	4.09645e15			0.388460
$820$		0			0
$821$	−1.71399e16			−1.60369			−0.801847	−	0.597530i	$-0.796149\pi$
$821$	−1.71399e16			−1.60369			−0.801847	+	0.597530i	$0.796149\pi$
$822$		0			0
$823$		−	8.06228e15i		−	0.744318i	−0.928169	−	0.372159i	$-0.878618\pi$
$823$		−	8.06228e15i		−	0.744318i	0.928169	−	0.372159i	$-0.121382\pi$
$824$		0			0
$825$	−2.27530e15	+	2.06831e15i	−0.207273	+	0.188417i
$826$		0			0
$827$			1.42703e16i			1.28279i	0.767213	+	0.641393i	$0.221643\pi$
$827$			1.42703e16i			1.28279i	−0.767213	+	0.641393i	$0.778357\pi$
$828$		0			0
$829$	1.25323e15			0.111168			0.0555842	−	0.998454i	$-0.482298\pi$
$829$	1.25323e15			0.111168			0.0555842	+	0.998454i	$0.482298\pi$
$830$		0			0
$831$	−1.04412e15			−0.0913993
$832$		0			0
$833$		−	1.92799e15i		−	0.166554i
$834$		0			0
$835$	5.25500e15	+	2.32476e15i	0.448020	+	0.198200i
$836$		0			0
$837$		−	8.09491e15i		−	0.681118i
$838$		0			0
$839$	−1.10625e15			−0.0918678			−0.0459339	−	0.998944i	$-0.514626\pi$
$839$	−1.10625e15			−0.0918678			−0.0459339	+	0.998944i	$0.514626\pi$
$840$		0			0
$841$	−1.13479e16			−0.930116
$842$		0			0
$843$			1.51926e15i			0.122908i
$844$		0			0
$845$	−1.65812e15	+	3.74809e15i	−0.132405	+	0.299294i
$846$		0			0
$847$			1.65166e15i			0.130186i
$848$		0			0
$849$	−5.60395e15			−0.436016
$850$		0			0
$851$	−4.01272e15			−0.308195
$852$		0			0
$853$			1.53821e16i			1.16626i	0.812378	+	0.583131i	$0.198173\pi$
$853$			1.53821e16i			1.16626i	−0.812378	+	0.583131i	$0.801827\pi$
$854$		0			0
$855$	6.88580e15	−	1.55650e16i	0.515395	−	1.16502i
$856$		0			0
$857$		−	1.34229e16i		−	0.991862i	−0.868362	−	0.495931i	$-0.834827\pi$
$857$		−	1.34229e16i		−	0.991862i	0.868362	−	0.495931i	$-0.165173\pi$
$858$		0			0
$859$	2.30497e16			1.68152			0.840760	−	0.541408i	$-0.182109\pi$
$859$	2.30497e16			1.68152			0.840760	+	0.541408i	$0.182109\pi$
$860$		0			0
$861$	1.06625e15			0.0767966
$862$		0			0
$863$		−	2.37761e16i		−	1.69076i	−0.534166	−	0.845379i	$-0.679374\pi$
$863$		−	2.37761e16i		−	1.69076i	0.534166	−	0.845379i	$-0.320626\pi$
$864$		0			0
$865$	3.21788e15	+	1.42356e15i	0.225934	+	0.0999511i
$866$		0			0
$867$			3.33356e15i			0.231102i
$868$		0			0
$869$	2.66256e16			1.82260
$870$		0			0
$871$	−2.84061e16			−1.92005
$872$		0			0
$873$		−	2.30187e16i		−	1.53639i
$874$		0			0
$875$	−1.71403e15	−	5.15030e15i	−0.112973	−	0.339460i
$876$		0			0
$877$			7.60940e15i			0.495282i	0.968852	+	0.247641i	$0.0796553\pi$
$877$			7.60940e15i			0.495282i	−0.968852	+	0.247641i	$0.920345\pi$
$878$		0			0
$879$	5.87957e14			0.0377926
$880$		0			0
$881$	−1.17608e15			−0.0746565			−0.0373282	−	0.999303i	$-0.511885\pi$
$881$	−1.17608e15			−0.0746565			−0.0373282	+	0.999303i	$0.511885\pi$
$882$		0			0
$883$		−	6.74481e15i		−	0.422849i	−0.977394	−	0.211425i	$-0.932190\pi$
$883$		−	6.74481e15i		−	0.422849i	0.977394	−	0.211425i	$-0.0678103\pi$
$884$		0			0
$885$	8.11677e14	+	3.59078e14i	0.0502568	+	0.0222332i
$886$		0			0
$887$		−	1.45784e16i		−	0.891519i	−0.895153	−	0.445759i	$-0.852934\pi$
$887$		−	1.45784e16i		−	0.891519i	0.895153	−	0.445759i	$-0.147066\pi$
$888$		0			0
$889$	8.85126e15			0.534620
$890$		0			0
$891$	−1.62619e16			−0.970164
$892$		0			0
$893$		−	3.61457e16i		−	2.12997i
$894$		0			0
$895$	3.63887e15	−	8.22546e15i	0.211807	−	0.478778i
$896$		0			0
$897$			9.39422e14i			0.0540135i
$898$		0			0
$899$	−6.80444e15			−0.386469
$900$		0			0
$901$	−4.12803e15			−0.231610
$902$		0			0
$903$			6.60309e14i			0.0365986i
$904$		0			0
$905$	4.05551e15	−	9.16726e15i	0.222064	−	0.501964i
$906$		0			0
$907$			5.14712e15i			0.278435i	0.990262	+	0.139218i	$0.0444588\pi$
$907$			5.14712e15i			0.278435i	−0.990262	+	0.139218i	$0.955541\pi$
$908$		0			0
$909$	−3.46520e16			−1.85194
$910$		0			0
$911$	−1.22053e16			−0.644462			−0.322231	−	0.946661i	$-0.604433\pi$
$911$	−1.22053e16			−0.644462			−0.322231	+	0.946661i	$0.604433\pi$
$912$		0			0
$913$			3.66040e16i			1.90959i
$914$		0			0
$915$	−2.61774e15	−	1.15807e15i	−0.134931	−	0.0596922i
$916$		0			0
$917$			1.22112e15i			0.0621909i
$918$		0			0
$919$	−1.21787e15			−0.0612864			−0.0306432	−	0.999530i	$-0.509756\pi$
$919$	−1.21787e15			−0.0612864			−0.0306432	+	0.999530i	$0.509756\pi$
$920$		0			0
$921$	−7.41975e15			−0.368945
$922$		0			0
$923$			4.92748e15i			0.242112i
$924$		0			0
$925$	2.40291e16	−	2.18431e16i	1.16670	−	1.06056i
$926$		0			0
$927$		−	4.30499e15i		−	0.206554i
$928$		0			0
$929$	−1.51088e16			−0.716380			−0.358190	−	0.933649i	$-0.616606\pi$
$929$	−1.51088e16			−0.716380			−0.358190	+	0.933649i	$0.616606\pi$
$930$		0			0
$931$	2.51548e16			1.17868
$932$		0			0
$933$			5.32290e15i			0.246490i
$934$		0			0
$935$	4.45736e15	+	1.97190e15i	0.203992	+	0.0902444i
$936$		0			0
$937$			1.74345e16i			0.788572i	0.918988	+	0.394286i	$0.129008\pi$
$937$			1.74345e16i			0.788572i	−0.918988	+	0.394286i	$0.870992\pi$
$938$		0			0
$939$	−1.11300e14			−0.00497549
$940$		0			0
$941$	−3.26895e16			−1.44433			−0.722164	−	0.691722i	$-0.756853\pi$
$941$	−3.26895e16			−1.44433			−0.722164	+	0.691722i	$0.756853\pi$
$942$		0			0
$943$		−	4.00585e15i		−	0.174936i
$944$		0			0
$945$	−1.56230e15	+	3.53149e15i	−0.0674355	+	0.152434i
$946$		0			0
$947$		−	2.42336e16i		−	1.03393i	−0.856005	−	0.516967i	$-0.827061\pi$
$947$		−	2.42336e16i		−	1.03393i	0.856005	−	0.516967i	$-0.172939\pi$
$948$		0			0
$949$	−2.33986e16			−0.986791
$950$		0			0
$951$	9.77476e14			0.0407486
$952$		0			0
$953$		−	3.07149e16i		−	1.26572i	−0.774266	−	0.632860i	$-0.781881\pi$
$953$		−	3.07149e16i		−	1.26572i	0.774266	−	0.632860i	$-0.218119\pi$
$954$		0			0
$955$	−1.70996e16	+	3.86528e16i	−0.696576	+	1.57457i
$956$		0			0
$957$		−	1.83881e15i		−	0.0740494i
$958$		0			0
$959$	−9.34468e15			−0.372016
$960$		0			0
$961$	2.88950e16			1.13722
$962$		0			0
$963$			1.75639e16i			0.683404i
$964$		0			0
$965$	1.93571e16	+	8.56340e15i	0.744629	+	0.329417i
$966$		0			0
$967$		−	2.20548e15i		−	0.0838799i	−0.999120	−	0.0419399i	$-0.986646\pi$
$967$		−	2.20548e15i		−	0.0838799i	0.999120	−	0.0419399i	$-0.0133538\pi$
$968$		0			0
$969$	1.64680e15			0.0619241
$970$		0			0
$971$	2.99429e16			1.11324			0.556619	−	0.830768i	$-0.312098\pi$
$971$	2.99429e16			1.11324			0.556619	+	0.830768i	$0.312098\pi$
$972$		0			0
$973$		−	4.31787e15i		−	0.158726i
$974$		0			0
$975$	−5.11370e15	−	5.62547e15i	−0.185870	−	0.204472i
$976$		0			0
$977$		−	1.87713e16i		−	0.674644i	−0.941389	−	0.337322i	$-0.890479\pi$
$977$		−	1.87713e16i		−	0.674644i	0.941389	−	0.337322i	$-0.109521\pi$
$978$		0			0
$979$	2.12588e16			0.755497
$980$		0			0
$981$	3.96259e16			1.39251
$982$		0			0
$983$			1.90327e16i			0.661388i	0.943738	+	0.330694i	$0.107283\pi$
$983$			1.90327e16i			0.661388i	−0.943738	+	0.330694i	$0.892717\pi$
$984$		0			0
$985$	−3.32082e16	−	1.46910e16i	−1.14116	−	0.504838i
$986$		0			0
$987$			3.97905e15i			0.135218i
$988$		0			0
$989$	2.48075e15			0.0833687
$990$		0			0
$991$	−3.63443e16			−1.20790			−0.603950	−	0.797023i	$-0.706407\pi$
$991$	−3.63443e16			−1.20790			−0.603950	+	0.797023i	$0.706407\pi$
$992$		0			0
$993$			8.99303e15i			0.295587i
$994$		0			0
$995$	1.47011e15	−	3.32311e15i	0.0477886	−	0.108023i
$996$		0			0
$997$			2.46615e16i			0.792858i	0.918065	+	0.396429i	$0.129751\pi$
$997$			2.46615e16i			0.792858i	−0.918065	+	0.396429i	$0.870249\pi$
$998$		0			0
$999$	−2.31023e16			−0.734589

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	80.12.c.c.49.4		6
4.3	odd	2		10.12.b.a.9.5	yes	6
5.4	even	2	inner	80.12.c.c.49.3		6
12.11	even	2		90.12.c.b.19.1		6
20.3	even	4		50.12.a.j.1.2		3
20.7	even	4		50.12.a.i.1.2		3
20.19	odd	2		10.12.b.a.9.2	✓	6
60.59	even	2		90.12.c.b.19.4		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
10.12.b.a.9.2	✓	6	20.19	odd	2
10.12.b.a.9.5	yes	6	4.3	odd	2
50.12.a.i.1.2		3	20.7	even	4
50.12.a.j.1.2		3	20.3	even	4
80.12.c.c.49.3		6	5.4	even	2	inner
80.12.c.c.49.4		6	1.1	even	1	trivial
90.12.c.b.19.1		6	12.11	even	2
90.12.c.b.19.4		6	60.59	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:	\( k \)	\(=\)	\( 12 \)
Character orbit:	\([\chi]\)	\(=\)	80.c (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+100.951i q^{3} +(2827.02 - 6390.31i) q^{5} +15908.8i q^{7} +166956. q^{9} +O(q^{10})\)	\(q+100.951i q^{3} +(2827.02 - 6390.31i) q^{5} +15908.8i q^{7} +166956. q^{9} -623805. q^{11} -1.54230e6i q^{13} +(645107. + 285390. i) q^{15} -1.11817e6i q^{17} +1.45889e7 q^{19} -1.60601e6 q^{21} +6.03368e6i q^{23} +(-3.28441e7 - 3.61310e7i) q^{25} +3.47375e7i q^{27} +2.91997e7 q^{29} -2.33031e8 q^{31} -6.29736e7i q^{33} +(1.01662e8 + 4.49744e7i) q^{35} +6.65053e8i q^{37} +1.55696e8 q^{39} -6.63914e8 q^{41} -4.11150e8i q^{43} +(4.71987e8 - 1.06690e9i) q^{45} -2.47761e9i q^{47} +1.72424e9 q^{49} +1.12880e8 q^{51} -3.69178e9i q^{53} +(-1.76351e9 + 3.98631e9i) q^{55} +1.47277e9i q^{57} +1.25820e9 q^{59} -4.05784e9 q^{61} +2.65607e9i q^{63} +(-9.85577e9 - 4.36011e9i) q^{65} -1.84180e10i q^{67} -6.09105e8 q^{69} -3.19489e9 q^{71} -1.51712e10i q^{73} +(3.64746e9 - 3.31564e9i) q^{75} -9.92398e9i q^{77} -4.26826e10 q^{79} +2.60690e10 q^{81} -5.86787e10i q^{83} +(-7.14544e9 - 3.16108e9i) q^{85} +2.94773e9i q^{87} -3.40792e10 q^{89} +2.45361e10 q^{91} -2.35247e10i q^{93} +(4.12432e10 - 9.32279e10i) q^{95} -1.37873e11i q^{97} -1.04148e11 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 530 q^{5} - 496022 q^{9}+O(q^{10}) \) 6 * q + 530 * q^5 - 496022 * q^9	\( 6 q + 530 q^{5} - 496022 q^{9} + 642728 q^{11} + 698680 q^{15} + 24109080 q^{19} + 125471192 q^{21} - 181718850 q^{25} - 256409820 q^{29} - 458481792 q^{31} + 697136360 q^{35} - 1318797936 q^{39} - 164768948 q^{41} + 3174067390 q^{45} - 675514158 q^{49} + 13060087168 q^{51} - 3688644360 q^{55} - 17663962360 q^{59} - 5020792428 q^{61} - 19996916880 q^{65} + 23117013976 q^{69} - 56788418832 q^{71} + 95499160400 q^{75} - 2602550880 q^{79} - 7039907074 q^{81} - 85024210560 q^{85} + 249448412540 q^{89} + 184446766128 q^{91} - 104896380600 q^{95} - 520781125736 q^{99}+O(q^{100}) \) 6 * q + 530 * q^5 - 496022 * q^9 + 642728 * q^11 + 698680 * q^15 + 24109080 * q^19 + 125471192 * q^21 - 181718850 * q^25 - 256409820 * q^29 - 458481792 * q^31 + 697136360 * q^35 - 1318797936 * q^39 - 164768948 * q^41 + 3174067390 * q^45 - 675514158 * q^49 + 13060087168 * q^51 - 3688644360 * q^55 - 17663962360 * q^59 - 5020792428 * q^61 - 19996916880 * q^65 + 23117013976 * q^69 - 56788418832 * q^71 + 95499160400 * q^75 - 2602550880 * q^79 - 7039907074 * q^81 - 85024210560 * q^85 + 249448412540 * q^89 + 184446766128 * q^91 - 104896380600 * q^95 - 520781125736 * q^99

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