LMFDB - Embedded newform 80.20.c.c.49.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [80,20,Mod(49,80)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(80, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 20, names="a")

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

chi := DirichletCharacter("80.49");

S:= CuspForms(chi, 20);

N := Newforms(S);

Level:	$ N $	$=$	$ 80 = 2^{4} \cdot 5 $
Weight:	$ k $	$=$	$ 20 $
Character orbit:	$[\chi]$	$=$	80.c (of order $2$, degree $1$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$183.053357245$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 14903918288 x^{7} + 443569659980446 x^{6} + \cdots + 53\!\cdots\!00 $ x^10 - 14903918288x^7 + 443569659980446x^6 - 407914028595579828x^5 + 111063390167690425472x^4 + 2240737884939969545921560x^3 + 9026417197496381459207546025x^2 + 3113006936793203978513537653500*x + 536802807608455434230094922445000
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{69}\cdot 3^{6}\cdot 5^{18} $
Twist minimal:	no (minimal twist has level 10)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			49.5
Root			$-180.677 + 180.677i$ of defining polynomial
Character	$\chi$	$=$	80.49
Dual form			80.20.c.c.49.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-908.466i q^{3} +(986770. - 4.25438e6i) q^{5} +4.96199e7i q^{7} +1.16144e9 q^{9} +O(q^{10})$	\(q-908.466i q^{3} +(986770. - 4.25438e6i) q^{5} +4.96199e7i q^{7} +1.16144e9 q^{9} +3.15919e9 q^{11} -5.24467e10i q^{13} +(-3.86496e9 - 8.96447e8i) q^{15} -3.26184e10i q^{17} +1.65953e12 q^{19} +4.50780e10 q^{21} -1.15711e13i q^{23} +(-1.71261e13 - 8.39619e12i) q^{25} -2.11100e12i q^{27} -1.19069e14 q^{29} +1.47537e14 q^{31} -2.87001e12i q^{33} +(2.11102e14 + 4.89634e13i) q^{35} +1.07730e14i q^{37} -4.76460e13 q^{39} +2.23018e15 q^{41} -1.65194e14i q^{43} +(1.14607e15 - 4.94119e15i) q^{45} +6.86224e15i q^{47} +8.93676e15 q^{49} -2.96327e13 q^{51} -3.03245e16i q^{53} +(3.11739e15 - 1.34404e16i) q^{55} -1.50762e15i q^{57} +1.09697e17 q^{59} -6.76315e15 q^{61} +5.76303e16i q^{63} +(-2.23128e17 - 5.17528e16i) q^{65} +2.45598e17i q^{67} -1.05119e16 q^{69} -5.52545e17 q^{71} +8.96373e16i q^{73} +(-7.62766e15 + 1.55584e16i) q^{75} +1.56758e17i q^{77} -4.12914e17 q^{79} +1.34797e18 q^{81} -9.58716e17i q^{83} +(-1.38771e17 - 3.21869e16i) q^{85} +1.08170e17i q^{87} -1.34938e18 q^{89} +2.60240e18 q^{91} -1.34033e17i q^{93} +(1.63757e18 - 7.06026e18i) q^{95} +6.64383e18i q^{97} +3.66919e18 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 2902670 q^{5} - 8718754970 q^{9}+O(q^{10}) $ 10 * q + 2902670 * q^5 - 8718754970 * q^9	$ 10 q + 2902670 q^{5} - 8718754970 q^{9} + 2965225880 q^{11} - 225010487480 q^{15} + 4196987836200 q^{19} - 501224287480 q^{21} + 19247576437650 q^{25} + 219360620418300 q^{29} + 667121586663680 q^{31} - 14\!\cdots\!60 q^{35}+ \cdots - 41\!\cdots\!60 q^{99}+O(q^{100}) $ 10 * q + 2902670 * q^5 - 8718754970 * q^9 + 2965225880 * q^11 - 225010487480 * q^15 + 4196987836200 * q^19 - 501224287480 * q^21 + 19247576437650 * q^25 + 219360620418300 * q^29 + 667121586663680 * q^31 - 1477908982965160 * q^35 + 3387373771795440 * q^39 + 3587345408194420 * q^41 - 13139237288012990 * q^45 - 30324198320796930 * q^49 - 106899828254155520 * q^51 + 99144934237329160 * q^55 + 332698279801897400 * q^59 + 533407565011656620 * q^61 - 682989395388761520 * q^65 - 95759593423262840 * q^69 - 1975827158504532720 * q^71 + 3881333883421828400 * q^75 + 2303771531732690400 * q^79 + 12793501534789009010 * q^81 - 6445103007057591040 * q^85 - 11076199503631707100 * q^89 - 7638137420731759920 * q^91 + 7279632536499161400 * q^95 - 41542573713793315160 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/80\mathbb{Z}\right)^\times$.

$n$	$17$	$21$	$31$
$\chi(n)$	$-1$	$1$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$		−	908.466i		−	0.0266475i	−0.999911	−	0.0133238i	$-0.995759\pi$
$3$		−	908.466i		−	0.0266475i	0.999911	−	0.0133238i	$-0.00424121\pi$
$4$		0			0
$5$	986770.	−	4.25438e6i	0.225944	−	0.974140i
$5$	986770.	−	4.25438e6i	0.225944	−	0.974140i
$6$		0			0
$7$			4.96199e7i			0.464755i	0.972626	+	0.232378i	$0.0746505\pi$
$7$			4.96199e7i			0.464755i	−0.972626	+	0.232378i	$0.925349\pi$
$8$		0			0
$9$	1.16144e9			0.999290
$10$		0			0
$11$	3.15919e9			0.403966			0.201983	−	0.979389i	$-0.435261\pi$
$11$	3.15919e9			0.403966			0.201983	+	0.979389i	$0.435261\pi$
$12$		0			0
$13$		−	5.24467e10i		−	1.37169i	−0.727747	−	0.685845i	$-0.759433\pi$
$13$		−	5.24467e10i		−	1.37169i	0.727747	−	0.685845i	$-0.240567\pi$
$14$		0			0
$15$	−3.86496e9	−	8.96447e8i	−0.0259584	−	0.00602085i
$16$		0			0
$17$		−	3.26184e10i		−	0.0667111i	−0.999444	−	0.0333555i	$-0.989381\pi$
$17$		−	3.26184e10i		−	0.0667111i	0.999444	−	0.0333555i	$-0.0106194\pi$
$18$		0			0
$19$	1.65953e12			1.17984			0.589922	−	0.807460i	$-0.299158\pi$
$19$	1.65953e12			1.17984			0.589922	+	0.807460i	$0.299158\pi$
$20$		0			0
$21$	4.50780e10			0.0123846
$22$		0			0
$23$		−	1.15711e13i		−	1.33955i	−0.742563	−	0.669776i	$-0.766390\pi$
$23$		−	1.15711e13i		−	1.33955i	0.742563	−	0.669776i	$-0.233610\pi$
$24$		0			0
$25$	−1.71261e13	−	8.39619e12i	−0.897899	−	0.440202i
$26$		0			0
$27$		−	2.11100e12i		−	0.0532761i
$28$		0			0
$29$	−1.19069e14			−1.52412			−0.762059	−	0.647508i	$-0.775811\pi$
$29$	−1.19069e14			−1.52412			−0.762059	+	0.647508i	$0.775811\pi$
$30$		0			0
$31$	1.47537e14			1.00223			0.501113	−	0.865382i	$-0.332924\pi$
$31$	1.47537e14			1.00223			0.501113	+	0.865382i	$0.332924\pi$
$32$		0			0
$33$		−	2.87001e12i		−	0.0107647i
$34$		0			0
$35$	2.11102e14	+	4.89634e13i	0.452737	+	0.105009i
$36$		0			0
$37$			1.07730e14i			0.136276i	0.997676	+	0.0681382i	$0.0217059\pi$
$37$			1.07730e14i			0.136276i	−0.997676	+	0.0681382i	$0.978294\pi$
$38$		0			0
$39$	−4.76460e13			−0.0365521
$40$		0			0
$41$	2.23018e15			1.06388			0.531940	−	0.846782i	$-0.321463\pi$
$41$	2.23018e15			1.06388			0.531940	+	0.846782i	$0.321463\pi$
$42$		0			0
$43$		−	1.65194e14i		−	0.0501239i	−0.999686	−	0.0250619i	$-0.992022\pi$
$43$		−	1.65194e14i		−	0.0501239i	0.999686	−	0.0250619i	$-0.00797830\pi$
$44$		0			0
$45$	1.14607e15	−	4.94119e15i	0.225784	−	0.973449i
$46$		0			0
$47$			6.86224e15i			0.894409i	0.894432	+	0.447205i	$0.147580\pi$
$47$			6.86224e15i			0.894409i	−0.894432	+	0.447205i	$0.852420\pi$
$48$		0			0
$49$	8.93676e15			0.784002
$50$		0			0
$51$	−2.96327e13			−0.00177768
$52$		0			0
$53$		−	3.03245e16i		−	1.26233i	−0.775649	−	0.631165i	$-0.782577\pi$
$53$		−	3.03245e16i		−	1.26233i	0.775649	−	0.631165i	$-0.217423\pi$
$54$		0			0
$55$	3.11739e15	−	1.34404e16i	0.0912737	−	0.393519i
$56$		0			0
$57$		−	1.50762e15i		−	0.0314399i
$58$		0			0
$59$	1.09697e17			1.64854			0.824272	−	0.566195i	$-0.191585\pi$
$59$	1.09697e17			1.64854			0.824272	+	0.566195i	$0.191585\pi$
$60$		0			0
$61$	−6.76315e15			−0.0740484			−0.0370242	−	0.999314i	$-0.511788\pi$
$61$	−6.76315e15			−0.0740484			−0.0370242	+	0.999314i	$0.511788\pi$
$62$		0			0
$63$			5.76303e16i			0.464425i
$64$		0			0
$65$	−2.23128e17	−	5.17528e16i	−1.33622	−	0.309925i
$66$		0			0
$67$			2.45598e17i			1.10284i	0.834226	+	0.551422i	$0.185915\pi$
$67$			2.45598e17i			1.10284i	−0.834226	+	0.551422i	$0.814085\pi$
$68$		0			0
$69$	−1.05119e16			−0.0356958
$70$		0			0
$71$	−5.52545e17			−1.43026			−0.715128	−	0.698994i	$-0.753631\pi$
$71$	−5.52545e17			−1.43026			−0.715128	+	0.698994i	$0.753631\pi$
$72$		0			0
$73$			8.96373e16i			0.178206i	0.996022	+	0.0891029i	$0.0284000\pi$
$73$			8.96373e16i			0.178206i	−0.996022	+	0.0891029i	$0.971600\pi$
$74$		0			0
$75$	−7.62766e15	+	1.55584e16i	−0.0117303	+	0.0239268i
$76$		0			0
$77$			1.56758e17i			0.187745i
$78$		0			0
$79$	−4.12914e17			−0.387617			−0.193808	−	0.981039i	$-0.562084\pi$
$79$	−4.12914e17			−0.387617			−0.193808	+	0.981039i	$0.562084\pi$
$80$		0			0
$81$	1.34797e18			0.997870
$82$		0			0
$83$		−	9.58716e17i		−	0.562922i	−0.959573	−	0.281461i	$-0.909181\pi$
$83$		−	9.58716e17i		−	0.562922i	0.959573	−	0.281461i	$-0.0908190\pi$
$84$		0			0
$85$	−1.38771e17	−	3.21869e16i	−0.0649859	−	0.0150730i
$86$		0			0
$87$			1.08170e17i			0.0406139i
$88$		0			0
$89$	−1.34938e18			−0.408254			−0.204127	−	0.978944i	$-0.565436\pi$
$89$	−1.34938e18			−0.408254			−0.204127	+	0.978944i	$0.565436\pi$
$90$		0			0
$91$	2.60240e18			0.637501
$92$		0			0
$93$		−	1.34033e17i		−	0.0267068i
$94$		0			0
$95$	1.63757e18	−	7.06026e18i	0.266579	−	1.14933i
$96$		0			0
$97$			6.64383e18i			0.887334i	0.896192	+	0.443667i	$0.146323\pi$
$97$			6.64383e18i			0.887334i	−0.896192	+	0.443667i	$0.853677\pi$
$98$		0			0
$99$	3.66919e18			0.403679
$100$		0			0
$101$	−9.46208e17			−0.0860862			−0.0430431	−	0.999073i	$-0.513705\pi$
$101$	−9.46208e17			−0.0860862			−0.0430431	+	0.999073i	$0.513705\pi$
$102$		0			0
$103$		−	1.08105e19i		−	0.816377i	−0.912898	−	0.408188i	$-0.866161\pi$
$103$		−	1.08105e19i		−	0.816377i	0.912898	−	0.408188i	$-0.133839\pi$
$104$		0			0
$105$	4.44816e16	−	1.91779e17i	0.00279822	−	0.0120643i
$106$		0			0
$107$			3.09312e19i			1.62649i	0.581923	+	0.813244i	$0.302301\pi$
$107$			3.09312e19i			1.62649i	−0.581923	+	0.813244i	$0.697699\pi$
$108$		0			0
$109$	2.37244e19			1.04627			0.523134	−	0.852250i	$-0.324763\pi$
$109$	2.37244e19			1.04627			0.523134	+	0.852250i	$0.324763\pi$
$110$		0			0
$111$	9.78692e16			0.00363143
$112$		0			0
$113$		−	7.84999e18i		−	0.245824i	−0.992418	−	0.122912i	$-0.960777\pi$
$113$		−	7.84999e18i		−	0.245824i	0.992418	−	0.122912i	$-0.0392233\pi$
$114$		0			0
$115$	−4.92278e19	−	1.14180e19i	−1.30491	−	0.302664i
$116$		0			0
$117$		−	6.09135e19i		−	1.37072i
$118$		0			0
$119$	1.61852e18			0.0310043
$120$		0			0
$121$	−5.11786e19			−0.836812
$122$		0			0
$123$		−	2.02604e18i		−	0.0283498i
$124$		0			0
$125$	−5.26201e19	+	6.45757e19i	−0.631694	+	0.775218i
$126$		0			0
$127$			6.81563e19i			0.703673i	0.936062	+	0.351836i	$0.114443\pi$
$127$			6.81563e19i			0.703673i	−0.936062	+	0.351836i	$0.885557\pi$
$128$		0			0
$129$	−1.50073e17			−0.00133568
$130$		0			0
$131$	6.98695e19			0.537292			0.268646	−	0.963239i	$-0.413424\pi$
$131$	6.98695e19			0.537292			0.268646	+	0.963239i	$0.413424\pi$
$132$		0			0
$133$			8.23455e19i			0.548339i
$134$		0			0
$135$	−8.98100e18	−	2.08307e18i	−0.0518984	−	0.0120374i
$136$		0			0
$137$		−	3.71652e20i		−	1.86763i	−0.357753	−	0.933816i	$-0.616457\pi$
$137$		−	3.71652e20i		−	1.86763i	0.357753	−	0.933816i	$-0.383543\pi$
$138$		0			0
$139$	2.22660e20			0.974994			0.487497	−	0.873125i	$-0.337910\pi$
$139$	2.22660e20			0.974994			0.487497	+	0.873125i	$0.337910\pi$
$140$		0			0
$141$	6.23411e18			0.0238338
$142$		0			0
$143$		−	1.65689e20i		−	0.554116i
$144$		0			0
$145$	−1.17494e20	+	5.06566e20i	−0.344365	+	1.48470i
$146$		0			0
$147$		−	8.11874e18i		−	0.0208917i
$148$		0			0
$149$	4.84970e20			1.09760			0.548802	−	0.835952i	$-0.315084\pi$
$149$	4.84970e20			1.09760			0.548802	+	0.835952i	$0.315084\pi$
$150$		0			0
$151$	−8.98470e20			−1.79152			−0.895762	−	0.444534i	$-0.853369\pi$
$151$	−8.98470e20			−1.79152			−0.895762	+	0.444534i	$0.853369\pi$
$152$		0			0
$153$		−	3.78842e19i		−	0.0666637i
$154$		0			0
$155$	1.45585e20	−	6.27680e20i	0.226447	−	0.976308i
$156$		0			0
$157$		−	8.32684e20i		−	1.14666i	−0.819326	−	0.573329i	$-0.805652\pi$
$157$		−	8.32684e20i		−	1.14666i	0.819326	−	0.573329i	$-0.194348\pi$
$158$		0			0
$159$	−2.75488e19			−0.0336379
$160$		0			0
$161$	5.74156e20			0.622564
$162$		0			0
$163$		−	1.83526e21i		−	1.76977i	−0.465814	−	0.884883i	$-0.654238\pi$
$163$		−	1.83526e21i		−	1.76977i	0.465814	−	0.884883i	$-0.345762\pi$
$164$		0			0
$165$	−1.22101e19	−	2.83204e18i	−0.0104863	−	0.00243222i
$166$		0			0
$167$			1.70782e21i			1.30809i	0.756457	+	0.654043i	$0.226928\pi$
$167$			1.70782e21i			1.30809i	−0.756457	+	0.654043i	$0.773072\pi$
$168$		0			0
$169$	−1.28873e21			−0.881535
$170$		0			0
$171$	1.92743e21			1.17901
$172$		0			0
$173$		−	3.35739e19i		−	0.0183892i	−0.999958	−	0.00919462i	$-0.997073\pi$
$173$		−	3.35739e19i		−	0.0183892i	0.999958	−	0.00919462i	$-0.00292678\pi$
$174$		0			0
$175$	4.16618e20	−	8.49793e20i	0.204586	−	0.417303i
$176$		0			0
$177$		−	9.96559e19i		−	0.0439296i
$178$		0			0
$179$	−1.85627e21			−0.735425			−0.367713	−	0.929940i	$-0.619859\pi$
$179$	−1.85627e21			−0.735425			−0.367713	+	0.929940i	$0.619859\pi$
$180$		0			0
$181$	−3.23615e21			−1.15367			−0.576835	−	0.816861i	$-0.695712\pi$
$181$	−3.23615e21			−1.15367			−0.576835	+	0.816861i	$0.695712\pi$
$182$		0			0
$183$			6.14409e18i			0.00197321i
$184$		0			0
$185$	4.58325e20	+	1.06305e20i	0.132752	+	0.0307909i
$186$		0			0
$187$		−	1.03048e20i		−	0.0269490i
$188$		0			0
$189$	1.04748e20			0.0247604
$190$		0			0
$191$	−3.35803e21			−0.718237			−0.359118	−	0.933292i	$-0.616923\pi$
$191$	−3.35803e21			−0.718237			−0.359118	+	0.933292i	$0.616923\pi$
$192$		0			0
$193$		−	1.02099e22i		−	1.97801i	−0.147891	−	0.989004i	$-0.547248\pi$
$193$		−	1.02099e22i		−	1.97801i	0.147891	−	0.989004i	$-0.452752\pi$
$194$		0			0
$195$	−4.70157e19	+	2.02704e20i	−0.00825874	+	0.0356069i
$196$		0			0
$197$		−	3.82443e21i		−	0.609730i	−0.952396	−	0.304865i	$-0.901389\pi$
$197$		−	3.82443e21i		−	0.609730i	0.952396	−	0.304865i	$-0.0986114\pi$
$198$		0			0
$199$	−5.27047e21			−0.763388			−0.381694	−	0.924289i	$-0.624659\pi$
$199$	−5.27047e21			−0.763388			−0.381694	+	0.924289i	$0.624659\pi$
$200$		0			0
$201$	2.23118e20			0.0293881
$202$		0			0
$203$		−	5.90820e21i		−	0.708342i
$204$		0			0
$205$	2.20067e21	−	9.48803e21i	0.240378	−	1.03637i
$206$		0			0
$207$		−	1.34391e22i		−	1.33860i
$208$		0			0
$209$	5.24275e21			0.476617
$210$		0			0
$211$	1.13252e22			0.940510			0.470255	−	0.882531i	$-0.344162\pi$
$211$	1.13252e22			0.940510			0.470255	+	0.882531i	$0.344162\pi$
$212$		0			0
$213$			5.01968e20i			0.0381127i
$214$		0			0
$215$	−7.02799e20	−	1.63009e20i	−0.0488277	−	0.0113252i
$216$		0			0
$217$			7.32078e21i			0.465790i
$218$		0			0
$219$	8.14324e19			0.00474874
$220$		0			0
$221$	−1.71073e21			−0.0915069
$222$		0			0
$223$		−	1.21988e22i		−	0.598992i	−0.954097	−	0.299496i	$-0.903181\pi$
$223$		−	1.21988e22i		−	0.598992i	0.954097	−	0.299496i	$-0.0968186\pi$
$224$		0			0
$225$	−1.98908e22	−	9.75164e21i	−0.897261	−	0.439890i
$226$		0			0
$227$		−	4.56122e22i		−	1.89163i	−0.324711	−	0.945813i	$-0.605267\pi$
$227$		−	4.56122e22i		−	1.89163i	0.324711	−	0.945813i	$-0.394733\pi$
$228$		0			0
$229$	−1.64239e22			−0.626672			−0.313336	−	0.949642i	$-0.601447\pi$
$229$	−1.64239e22			−0.626672			−0.313336	+	0.949642i	$0.601447\pi$
$230$		0			0
$231$	1.42410e20			0.00500295
$232$		0			0
$233$		−	3.19494e22i		−	1.03415i	−0.855941	−	0.517073i	$-0.827021\pi$
$233$		−	3.19494e22i		−	1.03415i	0.855941	−	0.517073i	$-0.172979\pi$
$234$		0			0
$235$	2.91946e22	+	6.77145e21i	0.871280	+	0.202086i
$236$		0			0
$237$			3.75118e20i			0.0103290i
$238$		0			0
$239$	−6.63222e22			−1.68608			−0.843041	−	0.537849i	$-0.819237\pi$
$239$	−6.63222e22			−1.68608			−0.843041	+	0.537849i	$0.819237\pi$
$240$		0			0
$241$	3.28176e22			0.770806			0.385403	−	0.922748i	$-0.374062\pi$
$241$	3.28176e22			0.770806			0.385403	+	0.922748i	$0.374062\pi$
$242$		0			0
$243$		−	3.67812e21i		−	0.0798669i
$244$		0			0
$245$	8.81853e21	−	3.80204e22i	0.177141	−	0.763728i
$246$		0			0
$247$		−	8.70366e22i		−	1.61838i
$248$		0			0
$249$	−8.70961e20			−0.0150005
$250$		0			0
$251$	−8.59947e22			−1.37269			−0.686343	−	0.727278i	$-0.740785\pi$
$251$	−8.59947e22			−1.37269			−0.686343	+	0.727278i	$0.740785\pi$
$252$		0			0
$253$		−	3.65552e22i		−	0.541134i
$254$		0			0
$255$	−2.92407e19	+	1.26069e20i	−0.000401657	+	0.00173171i
$256$		0			0
$257$		−	7.40568e22i		−	0.944497i	−0.881466	−	0.472248i	$-0.843443\pi$
$257$		−	7.40568e22i		−	0.944497i	0.881466	−	0.472248i	$-0.156557\pi$
$258$		0			0
$259$	−5.34556e21			−0.0633352
$260$		0			0
$261$	−1.38291e23			−1.52303
$262$		0			0
$263$			5.72414e22i			0.586314i	0.956064	+	0.293157i	$0.0947059\pi$
$263$			5.72414e22i			0.586314i	−0.956064	+	0.293157i	$0.905294\pi$
$264$		0			0
$265$	−1.29012e23	−	2.99233e22i	−1.22969	−	0.285216i
$266$		0			0
$267$			1.22587e21i			0.0108790i
$268$		0			0
$269$	2.17327e23			1.79667			0.898333	−	0.439316i	$-0.144779\pi$
$269$	2.17327e23			1.79667			0.898333	+	0.439316i	$0.144779\pi$
$270$		0			0
$271$	1.84385e23			1.42075			0.710373	−	0.703825i	$-0.248526\pi$
$271$	1.84385e23			1.42075			0.710373	+	0.703825i	$0.248526\pi$
$272$		0			0
$273$		−	2.36419e21i		−	0.0169878i
$274$		0			0
$275$	−5.41044e22	−	2.65251e22i	−0.362720	−	0.177827i
$276$		0			0
$277$		−	1.45405e23i		−	0.909959i	−0.890502	−	0.454979i	$-0.849647\pi$
$277$		−	1.45405e23i		−	0.909959i	0.890502	−	0.454979i	$-0.150353\pi$
$278$		0			0
$279$	1.71355e23			1.00151
$280$		0			0
$281$	−1.16696e23			−0.637303			−0.318652	−	0.947872i	$-0.603230\pi$
$281$	−1.16696e23			−0.637303			−0.318652	+	0.947872i	$0.603230\pi$
$282$		0			0
$283$		−	2.96619e23i		−	1.51436i	−0.653208	−	0.757179i	$-0.726577\pi$
$283$		−	2.96619e23i		−	1.51436i	0.653208	−	0.757179i	$-0.273423\pi$
$284$		0			0
$285$	−6.41400e21	−	1.48768e21i	−0.0306269	−	0.00710366i
$286$		0			0
$287$			1.10661e23i			0.494444i
$288$		0			0
$289$	2.38008e23			0.995550
$290$		0			0
$291$	6.03570e21			0.0236453
$292$		0			0
$293$		−	9.37098e22i		−	0.343987i	−0.985098	−	0.171994i	$-0.944979\pi$
$293$		−	9.37098e22i		−	0.343987i	0.985098	−	0.171994i	$-0.0550209\pi$
$294$		0			0
$295$	1.08246e23	−	4.66693e23i	0.372479	−	1.60591i
$296$		0			0
$297$		−	6.66904e21i		−	0.0215217i
$298$		0			0
$299$	−6.06865e23			−1.83745
$300$		0			0
$301$	8.19692e21			0.0232953
$302$		0			0
$303$			8.59598e20i			0.00229398i
$304$		0			0
$305$	−6.67368e21	+	2.87730e22i	−0.0167308	+	0.0721335i
$306$		0			0
$307$			6.56344e23i			1.54638i	0.634173	+	0.773191i	$0.281341\pi$
$307$			6.56344e23i			1.54638i	−0.634173	+	0.773191i	$0.718659\pi$
$308$		0			0
$309$	−9.82093e21			−0.0217544
$310$		0			0
$311$	−3.69779e23			−0.770405			−0.385202	−	0.922832i	$-0.625868\pi$
$311$	−3.69779e23			−0.770405			−0.385202	+	0.922832i	$0.625868\pi$
$312$		0			0
$313$			5.11458e23i			1.00262i	0.865266	+	0.501312i	$0.167149\pi$
$313$			5.11458e23i			1.00262i	−0.865266	+	0.501312i	$0.832851\pi$
$314$		0			0
$315$	2.45182e23	+	5.68679e22i	0.452415	+	0.104934i
$316$		0			0
$317$			2.18373e23i			0.379433i	0.981839	+	0.189717i	$0.0607569\pi$
$317$			2.18373e23i			0.379433i	−0.981839	+	0.189717i	$0.939243\pi$
$318$		0			0
$319$	−3.76162e23			−0.615691
$320$		0			0
$321$	2.80999e22			0.0433419
$322$		0			0
$323$		−	5.41311e22i		−	0.0787087i
$324$		0			0
$325$	−4.40353e23	+	8.98205e23i	−0.603822	+	1.23164i
$326$		0			0
$327$		−	2.15528e22i		−	0.0278805i
$328$		0			0
$329$	−3.40504e23			−0.415682
$330$		0			0
$331$	1.01065e24			1.16475			0.582376	−	0.812919i	$-0.302123\pi$
$331$	1.01065e24			1.16475			0.582376	+	0.812919i	$0.302123\pi$
$332$		0			0
$333$			1.25122e23i			0.136180i
$334$		0			0
$335$	1.04487e24	+	2.42349e23i	1.07433	+	0.249181i
$336$		0			0
$337$		−	8.10817e23i		−	0.787841i	−0.919144	−	0.393921i	$-0.871118\pi$
$337$		−	8.10817e23i		−	0.787841i	0.919144	−	0.393921i	$-0.128882\pi$
$338$		0			0
$339$	−7.13145e21			−0.00655060
$340$		0			0
$341$	4.66098e23			0.404865
$342$		0			0
$343$			1.00905e24i			0.829125i
$344$		0			0
$345$	−1.03729e22	+	4.47218e22i	−0.00806524	+	0.0347727i
$346$		0			0
$347$			5.03843e23i			0.370822i	0.982661	+	0.185411i	$0.0593616\pi$
$347$			5.03843e23i			0.370822i	−0.982661	+	0.185411i	$0.940638\pi$
$348$		0			0
$349$	5.76315e23			0.401623			0.200812	−	0.979630i	$-0.435642\pi$
$349$	5.76315e23			0.401623			0.200812	+	0.979630i	$0.435642\pi$
$350$		0			0
$351$	−1.10715e23			−0.0730783
$352$		0			0
$353$			3.71561e23i			0.232365i	0.993228	+	0.116182i	$0.0370657\pi$
$353$			3.71561e23i			0.232365i	−0.993228	+	0.116182i	$0.962934\pi$
$354$		0			0
$355$	−5.45235e23	+	2.35074e24i	−0.323158	+	1.39327i
$356$		0			0
$357$		−	1.47037e21i		−	0.000826188i
$358$		0			0
$359$	−4.66671e23			−0.248665			−0.124332	−	0.992241i	$-0.539679\pi$
$359$	−4.66671e23			−0.248665			−0.124332	+	0.992241i	$0.539679\pi$
$360$		0			0
$361$	7.75605e23			0.392033
$362$		0			0
$363$			4.64940e22i			0.0222989i
$364$		0			0
$365$	3.81351e23	+	8.84514e22i	0.173597	+	0.0402645i
$366$		0			0
$367$		−	4.13540e23i		−	0.178727i	−0.995999	−	0.0893635i	$-0.971517\pi$
$367$		−	4.13540e23i		−	0.178727i	0.995999	−	0.0893635i	$-0.0284833\pi$
$368$		0			0
$369$	2.59021e24			1.06313
$370$		0			0
$371$	1.50470e24			0.586674
$372$		0			0
$373$			2.27817e22i			0.00844021i	0.999991	+	0.00422010i	$0.00134330\pi$
$373$			2.27817e22i			0.00844021i	−0.999991	+	0.00422010i	$0.998657\pi$
$374$		0			0
$375$	5.86648e22	+	4.78036e22i	0.0206576	+	0.0168331i
$376$		0			0
$377$			6.24478e24i			2.09062i
$378$		0			0
$379$	3.28540e23			0.104596			0.0522981	−	0.998632i	$-0.483345\pi$
$379$	3.28540e23			0.104596			0.0522981	+	0.998632i	$0.483345\pi$
$380$		0			0
$381$	6.19177e22			0.0187511
$382$		0			0
$383$			6.00943e24i			1.73159i	0.500399	+	0.865795i	$0.333187\pi$
$383$			6.00943e24i			1.73159i	−0.500399	+	0.865795i	$0.666813\pi$
$384$		0			0
$385$	6.66910e23	+	1.54685e23i	0.182890	+	0.0424199i
$386$		0			0
$387$		−	1.91863e23i		−	0.0500883i
$388$		0			0
$389$	−4.99930e24			−1.24276			−0.621381	−	0.783508i	$-0.713428\pi$
$389$	−4.99930e24			−1.24276			−0.621381	+	0.783508i	$0.713428\pi$
$390$		0			0
$391$	−3.77430e23			−0.0893630
$392$		0			0
$393$		−	6.34741e22i		−	0.0143175i
$394$		0			0
$395$	−4.07451e23	+	1.75669e24i	−0.0875797	+	0.377593i
$396$		0			0
$397$			9.25380e24i			1.89588i	0.318452	+	0.947939i	$0.396837\pi$
$397$			9.25380e24i			1.89588i	−0.318452	+	0.947939i	$0.603163\pi$
$398$		0			0
$399$	7.48081e22			0.0146119
$400$		0			0
$401$	−9.45274e24			−1.76070			−0.880351	−	0.474322i	$-0.842693\pi$
$401$	−9.45274e24			−1.76070			−0.880351	+	0.474322i	$0.842693\pi$
$402$		0			0
$403$		−	7.73784e24i		−	1.37474i
$404$		0			0
$405$	1.33014e24	−	5.73480e24i	0.225463	−	0.972066i
$406$		0			0
$407$			3.40340e23i			0.0550510i
$408$		0			0
$409$	5.13613e24			0.792984			0.396492	−	0.918038i	$-0.370228\pi$
$409$	5.13613e24			0.792984			0.396492	+	0.918038i	$0.370228\pi$
$410$		0			0
$411$	−3.37633e23			−0.0497678
$412$		0			0
$413$			5.44315e24i			0.766169i
$414$		0			0
$415$	−4.07874e24	−	9.46032e23i	−0.548365	−	0.127189i
$416$		0			0
$417$		−	2.02279e23i		−	0.0259812i
$418$		0			0
$419$	7.63531e24			0.937116			0.468558	−	0.883433i	$-0.344774\pi$
$419$	7.63531e24			0.937116			0.468558	+	0.883433i	$0.344774\pi$
$420$		0			0
$421$	1.40251e25			1.64522			0.822611	−	0.568604i	$-0.192516\pi$
$421$	1.40251e25			1.64522			0.822611	+	0.568604i	$0.192516\pi$
$422$		0			0
$423$			7.97006e24i			0.893774i
$424$		0			0
$425$	−2.73870e23	+	5.58624e23i	−0.0293664	+	0.0598998i
$426$		0			0
$427$		−	3.35587e23i		−	0.0344144i
$428$		0			0
$429$	−1.50523e23			−0.0147658
$430$		0			0
$431$	−1.35223e25			−1.26916			−0.634578	−	0.772859i	$-0.718826\pi$
$431$	−1.35223e25			−1.26916			−0.634578	+	0.772859i	$0.718826\pi$
$432$		0			0
$433$		−	7.64294e24i		−	0.686476i	−0.939248	−	0.343238i	$-0.888476\pi$
$433$		−	7.64294e24i		−	0.686476i	0.939248	−	0.343238i	$-0.111524\pi$
$434$		0			0
$435$	4.60198e23	+	1.06739e23i	0.0395637	+	0.00917648i
$436$		0			0
$437$		−	1.92025e25i		−	1.58046i
$438$		0			0
$439$	1.07132e25			0.844322			0.422161	−	0.906521i	$-0.361272\pi$
$439$	1.07132e25			0.844322			0.422161	+	0.906521i	$0.361272\pi$
$440$		0			0
$441$	1.03795e25			0.783446
$442$		0			0
$443$			6.70085e24i			0.484501i	0.970214	+	0.242250i	$0.0778855\pi$
$443$			6.70085e24i			0.484501i	−0.970214	+	0.242250i	$0.922114\pi$
$444$		0			0
$445$	−1.33153e24	+	5.74079e24i	−0.0922425	+	0.397697i
$446$		0			0
$447$		−	4.40579e23i		−	0.0292484i
$448$		0			0
$449$	−1.76496e25			−1.12304			−0.561521	−	0.827463i	$-0.689783\pi$
$449$	−1.76496e25			−1.12304			−0.561521	+	0.827463i	$0.689783\pi$
$450$		0			0
$451$	7.04555e24			0.429772
$452$		0			0
$453$			8.16230e23i			0.0477397i
$454$		0			0
$455$	2.56797e24	−	1.10716e25i	0.144039	−	0.621015i
$456$		0			0
$457$		−	1.08665e25i		−	0.584638i	−0.956321	−	0.292319i	$-0.905573\pi$
$457$		−	1.08665e25i		−	0.584638i	0.956321	−	0.292319i	$-0.0944270\pi$
$458$		0			0
$459$	−6.88574e22			−0.00355411
$460$		0			0
$461$	−2.12712e25			−1.05350			−0.526749	−	0.850021i	$-0.676589\pi$
$461$	−2.12712e25			−1.05350			−0.526749	+	0.850021i	$0.676589\pi$
$462$		0			0
$463$		−	2.87367e25i		−	1.36590i	−0.730466	−	0.682949i	$-0.760697\pi$
$463$		−	2.87367e25i		−	1.36590i	0.730466	−	0.682949i	$-0.239303\pi$
$464$		0			0
$465$	−5.70226e23	−	1.32259e23i	−0.0260162	−	0.00603425i
$466$		0			0
$467$			8.37118e24i			0.366671i	0.983050	+	0.183335i	$0.0586894\pi$
$467$			8.37118e24i			0.366671i	−0.983050	+	0.183335i	$0.941311\pi$
$468$		0			0
$469$	−1.21866e25			−0.512553
$470$		0			0
$471$	−7.56465e23			−0.0305556
$472$		0			0
$473$		−	5.21879e23i		−	0.0202483i
$474$		0			0
$475$	−2.84211e25	−	1.39337e25i	−1.05938	−	0.519370i
$476$		0			0
$477$		−	3.52200e25i		−	1.26143i
$478$		0			0
$479$	1.95087e25			0.671493			0.335747	−	0.941952i	$-0.391011\pi$
$479$	1.95087e25			0.671493			0.335747	+	0.941952i	$0.391011\pi$
$480$		0			0
$481$	5.65009e24			0.186929
$482$		0			0
$483$		−	5.21601e23i		−	0.0165898i
$484$		0			0
$485$	2.82654e25	+	6.55594e24i	0.864388	+	0.200488i
$486$		0			0
$487$		−	2.06631e25i		−	0.607674i	−0.952724	−	0.303837i	$-0.901732\pi$
$487$		−	2.06631e25i		−	0.607674i	0.952724	−	0.303837i	$-0.0982678\pi$
$488$		0			0
$489$	−1.66727e24			−0.0471598
$490$		0			0
$491$	−1.21925e25			−0.331755			−0.165877	−	0.986146i	$-0.553046\pi$
$491$	−1.21925e25			−0.331755			−0.165877	+	0.986146i	$0.553046\pi$
$492$		0			0
$493$			3.88385e24i			0.101675i
$494$		0			0
$495$	3.62065e24	−	1.56101e25i	0.0912089	−	0.393240i
$496$		0			0
$497$		−	2.74172e25i		−	0.664719i
$498$		0			0
$499$	−5.63166e25			−1.31426			−0.657130	−	0.753777i	$-0.728230\pi$
$499$	−5.63166e25			−1.31426			−0.657130	+	0.753777i	$0.728230\pi$
$500$		0			0
$501$	1.55150e24			0.0348572
$502$		0			0
$503$		−	5.18100e25i		−	1.12077i	−0.828231	−	0.560387i	$-0.810653\pi$
$503$		−	5.18100e25i		−	1.12077i	0.828231	−	0.560387i	$-0.189347\pi$
$504$		0			0
$505$	−9.33690e23	+	4.02553e24i	−0.0194507	+	0.0838601i
$506$		0			0
$507$			1.17077e24i			0.0234907i
$508$		0			0
$509$	−2.18360e25			−0.422040			−0.211020	−	0.977482i	$-0.567679\pi$
$509$	−2.18360e25			−0.422040			−0.211020	+	0.977482i	$0.567679\pi$
$510$		0			0
$511$	−4.44779e24			−0.0828221
$512$		0			0
$513$		−	3.50326e24i		−	0.0628575i
$514$		0			0
$515$	−4.59918e25	−	1.06674e25i	−0.795265	−	0.184455i
$516$		0			0
$517$			2.16791e25i			0.361311i
$518$		0			0
$519$	−3.05007e22			−0.000490027
$520$		0			0
$521$	4.15334e25			0.643338			0.321669	−	0.946852i	$-0.395756\pi$
$521$	4.15334e25			0.643338			0.321669	+	0.946852i	$0.395756\pi$
$522$		0			0
$523$		−	1.37677e25i		−	0.205634i	−0.994700	−	0.102817i	$-0.967214\pi$
$523$		−	1.37677e25i		−	0.205634i	0.994700	−	0.102817i	$-0.0327856\pi$
$524$		0			0
$525$	−7.72008e23	−	3.78483e23i	−0.0111201	−	0.00545172i
$526$		0			0
$527$		−	4.81243e24i		−	0.0668595i
$528$		0			0
$529$	−5.92747e25			−0.794402
$530$		0			0
$531$	1.27406e26			1.64737
$532$		0			0
$533$		−	1.16965e26i		−	1.45932i
$534$		0			0
$535$	1.31593e26	+	3.05220e25i	1.58443	+	0.367495i
$536$		0			0
$537$			1.68636e24i			0.0195973i
$538$		0			0
$539$	2.82329e25			0.316710
$540$		0			0
$541$	−4.62801e25			−0.501211			−0.250605	−	0.968089i	$-0.580630\pi$
$541$	−4.62801e25			−0.501211			−0.250605	+	0.968089i	$0.580630\pi$
$542$		0			0
$543$			2.93993e24i			0.0307424i
$544$		0			0
$545$	2.34105e25	−	1.00933e26i	0.236398	−	1.01921i
$546$		0			0
$547$		−	9.37647e25i		−	0.914449i	−0.889351	−	0.457225i	$-0.848844\pi$
$547$		−	9.37647e25i		−	0.914449i	0.889351	−	0.457225i	$-0.151156\pi$
$548$		0			0
$549$	−7.85497e24			−0.0739958
$550$		0			0
$551$	−1.97598e26			−1.79822
$552$		0			0
$553$		−	2.04888e25i		−	0.180147i
$554$		0			0
$555$	9.65744e22	−	4.16373e23i	0.000820500	−	0.00353752i
$556$		0			0
$557$			7.66948e25i			0.629712i	0.949140	+	0.314856i	$0.101956\pi$
$557$			7.66948e25i			0.629712i	−0.949140	+	0.314856i	$0.898044\pi$
$558$		0			0
$559$	−8.66389e24			−0.0687544
$560$		0			0
$561$	−9.36152e22			−0.000718123
$562$		0			0
$563$			1.37590e26i			1.02037i	0.860065	+	0.510185i	$0.170423\pi$
$563$			1.37590e26i			1.02037i	−0.860065	+	0.510185i	$0.829577\pi$
$564$		0			0
$565$	−3.33969e25	−	7.74614e24i	−0.239467	−	0.0555425i
$566$		0			0
$567$			6.68864e25i			0.463766i
$568$		0			0
$569$	1.90506e26			1.27745			0.638724	−	0.769436i	$-0.279463\pi$
$569$	1.90506e26			1.27745			0.638724	+	0.769436i	$0.279463\pi$
$570$		0			0
$571$	−6.32898e24			−0.0410479			−0.0205240	−	0.999789i	$-0.506533\pi$
$571$	−6.32898e24			−0.0410479			−0.0205240	+	0.999789i	$0.506533\pi$
$572$		0			0
$573$			3.05066e24i			0.0191392i
$574$		0			0
$575$	−9.71531e25	+	1.98167e26i	−0.589674	+	1.20278i
$576$		0			0
$577$			2.98759e26i			1.75449i	0.480045	+	0.877244i	$0.340620\pi$
$577$			2.98759e26i			1.75449i	−0.480045	+	0.877244i	$0.659380\pi$
$578$		0			0
$579$	−9.27536e24			−0.0527090
$580$		0			0
$581$	4.75714e25			0.261621
$582$		0			0
$583$		−	9.58007e25i		−	0.509938i
$584$		0			0
$585$	−2.59149e26	−	6.01076e25i	−1.33527	−	0.309705i
$586$		0			0
$587$			6.25902e25i			0.312208i	0.987741	+	0.156104i	$0.0498936\pi$
$587$			6.25902e25i			0.312208i	−0.987741	+	0.156104i	$0.950106\pi$
$588$		0			0
$589$	2.44842e26			1.18247
$590$		0			0
$591$	−3.47437e24			−0.0162478
$592$		0			0
$593$			7.35832e25i			0.333242i	0.986021	+	0.166621i	$0.0532856\pi$
$593$			7.35832e25i			0.333242i	−0.986021	+	0.166621i	$0.946714\pi$
$594$		0			0
$595$	1.59711e24	−	6.88581e24i	0.00700524	−	0.0302026i
$596$		0			0
$597$			4.78805e24i			0.0203424i
$598$		0			0
$599$	1.06912e26			0.440018			0.220009	−	0.975498i	$-0.429391\pi$
$599$	1.06912e26			0.440018			0.220009	+	0.975498i	$0.429391\pi$
$600$		0			0
$601$	−1.65740e26			−0.660877			−0.330438	−	0.943828i	$-0.607197\pi$
$601$	−1.65740e26			−0.660877			−0.330438	+	0.943828i	$0.607197\pi$
$602$		0			0
$603$			2.85247e26i			1.10206i
$604$		0			0
$605$	−5.05015e25	+	2.17734e26i	−0.189073	+	0.815172i
$606$		0			0
$607$		−	2.46455e26i		−	0.894220i	−0.894479	−	0.447110i	$-0.852453\pi$
$607$		−	2.46455e26i		−	0.894220i	0.894479	−	0.447110i	$-0.147547\pi$
$608$		0			0
$609$	−5.36740e24			−0.0188755
$610$		0			0
$611$	3.59902e26			1.22685
$612$		0			0
$613$			4.86117e26i			1.60645i	0.595678	+	0.803224i	$0.296884\pi$
$613$			4.86117e26i			1.60645i	−0.595678	+	0.803224i	$0.703116\pi$
$614$		0			0
$615$	−8.61955e24	−	1.99924e24i	−0.0276167	−	0.00640546i
$616$		0			0
$617$		−	4.69129e25i		−	0.145742i	−0.997341	−	0.0728708i	$-0.976784\pi$
$617$		−	4.69129e25i		−	0.145742i	0.997341	−	0.0728708i	$-0.0232161\pi$
$618$		0			0
$619$	−1.70854e26			−0.514710			−0.257355	−	0.966317i	$-0.582851\pi$
$619$	−1.70854e26			−0.514710			−0.257355	+	0.966317i	$0.582851\pi$
$620$		0			0
$621$	−2.44266e25			−0.0713662
$622$		0			0
$623$		−	6.69563e25i		−	0.189738i
$624$		0			0
$625$	2.22806e26	+	2.87587e26i	0.612444	+	0.790514i
$626$		0			0
$627$		−	4.76286e24i		−	0.0127007i
$628$		0			0
$629$	3.51398e24			0.00909115
$630$		0			0
$631$	3.05761e26			0.767543			0.383771	−	0.923428i	$-0.374625\pi$
$631$	3.05761e26			0.767543			0.383771	+	0.923428i	$0.374625\pi$
$632$		0			0
$633$		−	1.02886e25i		−	0.0250623i
$634$		0			0
$635$	2.89963e26	+	6.72546e25i	0.685476	+	0.158991i
$636$		0			0
$637$		−	4.68704e26i		−	1.07541i
$638$		0			0
$639$	−6.41746e26			−1.42924
$640$		0			0
$641$	2.96145e25			0.0640254			0.0320127	−	0.999487i	$-0.489808\pi$
$641$	2.96145e25			0.0640254			0.0320127	+	0.999487i	$0.489808\pi$
$642$		0			0
$643$			4.99016e26i			1.04739i	0.851905	+	0.523697i	$0.175448\pi$
$643$			4.99016e26i			1.04739i	−0.851905	+	0.523697i	$0.824552\pi$
$644$		0			0
$645$	−1.48088e23	+	6.38469e23i	−0.000301788	+	0.00130114i
$646$		0			0
$647$			5.63321e26i			1.11472i	0.830271	+	0.557359i	$0.188185\pi$
$647$			5.63321e26i			1.11472i	−0.830271	+	0.557359i	$0.811815\pi$
$648$		0			0
$649$	3.46553e26			0.665955
$650$		0			0
$651$	6.65068e24			0.0124121
$652$		0			0
$653$			1.32602e26i			0.240366i	0.992752	+	0.120183i	$0.0383482\pi$
$653$			1.32602e26i			0.240366i	−0.992752	+	0.120183i	$0.961652\pi$
$654$		0			0
$655$	6.89451e25	−	2.97252e26i	0.121398	−	0.523398i
$656$		0			0
$657$			1.04108e26i			0.178079i
$658$		0			0
$659$	2.88667e26			0.479717			0.239859	−	0.970808i	$-0.422899\pi$
$659$	2.88667e26			0.479717			0.239859	+	0.970808i	$0.422899\pi$
$660$		0			0
$661$	6.21905e26			1.00418			0.502089	−	0.864816i	$-0.332565\pi$
$661$	6.21905e26			1.00418			0.502089	+	0.864816i	$0.332565\pi$
$662$		0			0
$663$			1.55414e24i			0.00243843i
$664$		0			0
$665$	3.50329e26	+	8.12561e25i	0.534159	+	0.123894i
$666$		0			0
$667$			1.37776e27i			2.04164i
$668$		0			0
$669$	−1.10822e25			−0.0159617
$670$		0			0
$671$	−2.13661e25			−0.0299130
$672$		0			0
$673$			3.42772e26i			0.466512i	0.972415	+	0.233256i	$0.0749380\pi$
$673$			3.42772e26i			0.466512i	−0.972415	+	0.233256i	$0.925062\pi$
$674$		0			0
$675$	−1.77244e25	+	3.61531e25i	−0.0234523	+	0.0478365i
$676$		0			0
$677$		−	6.64614e25i		−	0.0855022i	−0.999086	−	0.0427511i	$-0.986388\pi$
$677$		−	6.64614e25i		−	0.0855022i	0.999086	−	0.0427511i	$-0.0136122\pi$
$678$		0			0
$679$	−3.29666e26			−0.412393
$680$		0			0
$681$	−4.14371e25			−0.0504071
$682$		0			0
$683$		−	8.48673e26i		−	1.00402i	−0.864861	−	0.502012i	$-0.832593\pi$
$683$		−	8.48673e26i		−	1.00402i	0.864861	−	0.502012i	$-0.167407\pi$
$684$		0			0
$685$	−1.58115e27	−	3.66735e26i	−1.81934	−	0.421980i
$686$		0			0
$687$			1.49206e25i			0.0166992i
$688$		0			0
$689$	−1.59042e27			−1.73153
$690$		0			0
$691$	−1.77439e26			−0.187935			−0.0939673	−	0.995575i	$-0.529955\pi$
$691$	−1.77439e26			−0.187935			−0.0939673	+	0.995575i	$0.529955\pi$
$692$		0			0
$693$			1.82065e26i			0.187612i
$694$		0			0
$695$	2.19714e26	−	9.47282e26i	0.220294	−	0.949781i
$696$		0			0
$697$		−	7.27448e25i		−	0.0709726i
$698$		0			0
$699$	−2.90250e25			−0.0275574
$700$		0			0
$701$	−3.00150e26			−0.277343			−0.138671	−	0.990338i	$-0.544283\pi$
$701$	−3.00150e26			−0.277343			−0.138671	+	0.990338i	$0.544283\pi$
$702$		0			0
$703$			1.78781e26i			0.160785i
$704$		0			0
$705$	6.15163e24	−	2.65223e25i	0.00538510	−	0.0232175i
$706$		0			0
$707$		−	4.69507e25i		−	0.0400090i
$708$		0			0
$709$	2.90737e26			0.241191			0.120596	−	0.992702i	$-0.461520\pi$
$709$	2.90737e26			0.241191			0.120596	+	0.992702i	$0.461520\pi$
$710$		0			0
$711$	−4.79573e26			−0.387341
$712$		0			0
$713$		−	1.70717e27i		−	1.34253i
$714$		0			0
$715$	−7.04904e26	−	1.63497e26i	−0.539787	−	0.125199i
$716$		0			0
$717$			6.02514e25i			0.0449299i
$718$		0			0
$719$	1.53300e27			1.11331			0.556656	−	0.830743i	$-0.312084\pi$
$719$	1.53300e27			1.11331			0.556656	+	0.830743i	$0.312084\pi$
$720$		0			0
$721$	5.36414e26			0.379415
$722$		0			0
$723$		−	2.98137e25i		−	0.0205401i
$724$		0			0
$725$	2.03919e27	+	9.99728e26i	1.36850	+	0.670920i
$726$		0			0
$727$		−	2.28969e27i		−	1.49692i	−0.663179	−	0.748461i	$-0.730793\pi$
$727$		−	2.28969e27i		−	1.49692i	0.663179	−	0.748461i	$-0.269207\pi$
$728$		0			0
$729$	1.56336e27			0.995742
$730$		0			0
$731$	−5.38837e24			−0.00334382
$732$		0			0
$733$			2.56760e26i			0.155253i	0.996983	+	0.0776263i	$0.0247341\pi$
$733$			2.56760e26i			0.155253i	−0.996983	+	0.0776263i	$0.975266\pi$
$734$		0			0
$735$	−3.45402e25	−	8.01133e24i	−0.0203515	−	0.00472036i
$736$		0			0
$737$			7.75890e26i			0.445512i
$738$		0			0
$739$	−1.76577e27			−0.988127			−0.494064	−	0.869426i	$-0.664489\pi$
$739$	−1.76577e27			−0.988127			−0.494064	+	0.869426i	$0.664489\pi$
$740$		0			0
$741$	−7.90698e25			−0.0431258
$742$		0			0
$743$		−	2.45784e27i		−	1.30665i	−0.757078	−	0.653325i	$-0.773374\pi$
$743$		−	2.45784e27i		−	1.30665i	0.757078	−	0.653325i	$-0.226626\pi$
$744$		0			0
$745$	4.78554e26	−	2.06325e27i	0.247997	−	1.06922i
$746$		0			0
$747$		−	1.11349e27i		−	0.562522i
$748$		0			0
$749$	−1.53480e27			−0.755919
$750$		0			0
$751$	1.55185e27			0.745193			0.372597	−	0.927993i	$-0.378467\pi$
$751$	1.55185e27			0.745193			0.372597	+	0.927993i	$0.378467\pi$
$752$		0			0
$753$			7.81233e25i			0.0365787i
$754$		0			0
$755$	−8.86584e26	+	3.82244e27i	−0.404784	+	1.74520i
$756$		0			0
$757$		−	2.49568e27i		−	1.11116i	−0.831462	−	0.555582i	$-0.812496\pi$
$757$		−	2.49568e27i		−	1.11116i	0.831462	−	0.555582i	$-0.187504\pi$
$758$		0			0
$759$	−3.32092e25			−0.0144199
$760$		0			0
$761$	1.64660e27			0.697325			0.348662	−	0.937248i	$-0.386636\pi$
$761$	1.64660e27			0.697325			0.348662	+	0.937248i	$0.386636\pi$
$762$		0			0
$763$			1.17720e27i			0.486259i
$764$		0			0
$765$	−1.61174e26	−	3.73830e25i	−0.0649398	−	0.0150623i
$766$		0			0
$767$		−	5.75324e27i		−	2.26129i
$768$		0			0
$769$	−3.33096e27			−1.27723			−0.638615	−	0.769527i	$-0.720492\pi$
$769$	−3.33096e27			−1.27723			−0.638615	+	0.769527i	$0.720492\pi$
$770$		0			0
$771$	−6.72781e25			−0.0251685
$772$		0			0
$773$		−	4.83311e27i		−	1.76409i	−0.471163	−	0.882046i	$-0.656166\pi$
$773$		−	4.83311e27i		−	1.76409i	0.471163	−	0.882046i	$-0.343834\pi$
$774$		0			0
$775$	−2.52673e27	−	1.23875e27i	−0.899897	−	0.441182i
$776$		0			0
$777$			4.85626e24i			0.00168773i
$778$		0			0
$779$	3.70104e27			1.25521
$780$		0			0
$781$	−1.74559e27			−0.577774
$782$		0			0
$783$			2.51355e26i			0.0811990i
$784$		0			0
$785$	−3.54256e27	−	8.21668e26i	−1.11700	−	0.259080i
$786$		0			0
$787$			1.68622e27i			0.518983i	0.965745	+	0.259491i	$0.0835549\pi$
$787$			1.68622e27i			0.518983i	−0.965745	+	0.259491i	$0.916445\pi$
$788$		0			0
$789$	5.20019e25			0.0156238
$790$		0			0
$791$	3.89516e26			0.114248
$792$		0			0
$793$			3.54705e26i			0.101572i
$794$		0			0
$795$	−2.71843e25	+	1.17203e26i	−0.00760029	+	0.0327681i
$796$		0			0
$797$			2.98355e27i			0.814477i	0.913322	+	0.407239i	$0.133508\pi$
$797$			2.98355e27i			0.814477i	−0.913322	+	0.407239i	$0.866492\pi$
$798$		0			0
$799$	2.23835e26			0.0596670
$800$		0			0
$801$	−1.56722e27			−0.407964
$802$		0			0
$803$			2.83181e26i			0.0719890i
$804$		0			0
$805$	5.66560e26	−	2.44268e27i	0.140665	−	0.606465i
$806$		0			0
$807$		−	1.97434e26i		−	0.0478767i
$808$		0			0
$809$	8.47523e26			0.200743			0.100371	−	0.994950i	$-0.467997\pi$
$809$	8.47523e26			0.200743			0.100371	+	0.994950i	$0.467997\pi$
$810$		0			0
$811$	−1.93622e27			−0.447978			−0.223989	−	0.974592i	$-0.571908\pi$
$811$	−1.93622e27			−0.447978			−0.223989	+	0.974592i	$0.571908\pi$
$812$		0			0
$813$		−	1.67507e26i		−	0.0378593i
$814$		0			0
$815$	−7.80790e27	−	1.81098e27i	−1.72400	−	0.399868i
$816$		0			0
$817$		−	2.74144e26i		−	0.0591384i
$818$		0			0
$819$	3.02252e27			0.637048
$820$		0			0
$821$	6.51192e27			1.34106			0.670532	−	0.741881i	$-0.266066\pi$
$821$	6.51192e27			1.34106			0.670532	+	0.741881i	$0.266066\pi$
$822$		0			0
$823$		−	8.92133e26i		−	0.179528i	−0.995963	−	0.0897638i	$-0.971389\pi$
$823$		−	8.92133e26i		−	0.179528i	0.995963	−	0.0897638i	$-0.0286112\pi$
$824$		0			0
$825$	−2.40972e25	+	4.91520e25i	−0.00473864	+	0.00966559i
$826$		0			0
$827$			8.30658e27i			1.59632i	0.602446	+	0.798160i	$0.294193\pi$
$827$			8.30658e27i			1.59632i	−0.602446	+	0.798160i	$0.705807\pi$
$828$		0			0
$829$	−2.37854e27			−0.446727			−0.223364	−	0.974735i	$-0.571704\pi$
$829$	−2.37854e27			−0.446727			−0.223364	+	0.974735i	$0.571704\pi$
$830$		0			0
$831$	−1.32096e26			−0.0242481
$832$		0			0
$833$		−	2.91503e26i		−	0.0523016i
$834$		0			0
$835$	7.26573e27	+	1.68523e27i	1.27426	+	0.295554i
$836$		0			0
$837$		−	3.11451e26i		−	0.0533947i
$838$		0			0
$839$	−9.91481e27			−1.66167			−0.830837	−	0.556516i	$-0.812138\pi$
$839$	−9.91481e27			−1.66167			−0.830837	+	0.556516i	$0.812138\pi$
$840$		0			0
$841$	8.07421e27			1.32293
$842$		0			0
$843$			1.06014e26i			0.0169825i
$844$		0			0
$845$	−1.27168e27	+	5.48277e27i	−0.199178	+	0.858739i
$846$		0			0
$847$		−	2.53948e27i		−	0.388913i
$848$		0			0
$849$	−2.69469e26			−0.0403539
$850$		0			0
$851$	1.24656e27			0.182550
$852$		0			0
$853$			4.84613e27i			0.694032i	0.937859	+	0.347016i	$0.112805\pi$
$853$			4.84613e27i			0.694032i	−0.937859	+	0.347016i	$0.887195\pi$
$854$		0			0
$855$	1.90193e27	−	8.20004e27i	0.266390	−	1.14852i
$856$		0			0
$857$		−	7.31479e26i		−	0.100204i	−0.998744	−	0.0501019i	$-0.984045\pi$
$857$		−	7.31479e26i		−	0.100204i	0.998744	−	0.0501019i	$-0.0159546\pi$
$858$		0			0
$859$	8.86102e27			1.18727			0.593634	−	0.804735i	$-0.297693\pi$
$859$	8.86102e27			1.18727			0.593634	+	0.804735i	$0.297693\pi$
$860$		0			0
$861$	1.00532e26			0.0131757
$862$		0			0
$863$		−	7.74919e27i		−	0.993468i	−0.867903	−	0.496734i	$-0.834532\pi$
$863$		−	7.74919e27i		−	0.993468i	0.867903	−	0.496734i	$-0.165468\pi$
$864$		0			0
$865$	−1.42836e26	−	3.31297e25i	−0.0179137	−	0.00415494i
$866$		0			0
$867$		−	2.16223e26i		−	0.0265289i
$868$		0			0
$869$	−1.30447e27			−0.156584
$870$		0			0
$871$	1.28808e28			1.51276
$872$		0			0
$873$			7.71639e27i			0.886704i
$874$		0			0
$875$	−3.20424e27	−	2.61100e27i	−0.360287	−	0.293583i
$876$		0			0
$877$		−	3.99206e27i		−	0.439240i	−0.975586	−	0.219620i	$-0.929518\pi$
$877$		−	3.99206e27i		−	0.439240i	0.975586	−	0.219620i	$-0.0704817\pi$
$878$		0			0
$879$	−8.51321e25			−0.00916641
$880$		0			0
$881$	4.16852e26			0.0439249			0.0219624	−	0.999759i	$-0.493009\pi$
$881$	4.16852e26			0.0439249			0.0219624	+	0.999759i	$0.493009\pi$
$882$		0			0
$883$			1.15241e28i			1.18845i	0.804298	+	0.594226i	$0.202542\pi$
$883$			1.15241e28i			1.18845i	−0.804298	+	0.594226i	$0.797458\pi$
$884$		0			0
$885$	−4.23974e26	−	9.83375e25i	−0.0427936	−	0.00992563i
$886$		0			0
$887$			1.10477e28i			1.09144i	0.837969	+	0.545718i	$0.183743\pi$
$887$			1.10477e28i			1.09144i	−0.837969	+	0.545718i	$0.816257\pi$
$888$		0			0
$889$	−3.38191e27			−0.327036
$890$		0			0
$891$	4.25850e27			0.403105
$892$		0			0
$893$			1.13881e28i			1.05526i
$894$		0			0
$895$	−1.83172e27	+	7.89730e27i	−0.166165	+	0.716407i
$896$		0			0
$897$			5.51316e26i			0.0489635i
$898$		0			0
$899$	−1.75671e28			−1.52751
$900$		0			0
$901$	−9.89136e26			−0.0842113
$902$		0			0
$903$		−	7.44662e24i		−	0.000620763i
$904$		0			0
$905$	−3.19333e27	+	1.37678e28i	−0.260665	+	1.12384i
$906$		0			0
$907$			2.25805e28i			1.80495i	0.430743	+	0.902475i	$0.358252\pi$
$907$			2.25805e28i			1.80495i	−0.430743	+	0.902475i	$0.641748\pi$
$908$		0			0
$909$	−1.09896e27			−0.0860251
$910$		0			0
$911$	4.26118e27			0.326667			0.163333	−	0.986571i	$-0.447775\pi$
$911$	4.26118e27			0.326667			0.163333	+	0.986571i	$0.447775\pi$
$912$		0			0
$913$		−	3.02876e27i		−	0.227401i
$914$		0			0
$915$	2.61393e25	+	6.06281e24i	0.00192218	+	0.000445834i
$916$		0			0
$917$			3.46692e27i			0.249709i
$918$		0			0
$919$	−1.91791e28			−1.35310			−0.676552	−	0.736395i	$-0.736527\pi$
$919$	−1.91791e28			−1.35310			−0.676552	+	0.736395i	$0.736527\pi$
$920$		0			0
$921$	5.96266e26			0.0412073
$922$		0			0
$923$			2.89792e28i			1.96187i
$924$		0			0
$925$	9.04523e26	−	1.84499e27i	0.0599892	−	0.122362i
$926$		0			0
$927$		−	1.25557e28i		−	0.815797i
$928$		0			0
$929$	1.34000e28			0.853016			0.426508	−	0.904484i	$-0.359744\pi$
$929$	1.34000e28			0.853016			0.426508	+	0.904484i	$0.359744\pi$
$930$		0			0
$931$	1.48308e28			0.925001
$932$		0			0
$933$			3.35932e26i			0.0205294i
$934$		0			0
$935$	−4.38404e26	−	1.01684e26i	−0.0262521	−	0.00608896i
$936$		0			0
$937$		−	2.74084e27i		−	0.160826i	−0.996762	−	0.0804132i	$-0.974376\pi$
$937$		−	2.74084e27i		−	0.160826i	0.996762	−	0.0804132i	$-0.0256240\pi$
$938$		0			0
$939$	4.64642e26			0.0267175
$940$		0			0
$941$	1.24272e28			0.700282			0.350141	−	0.936697i	$-0.386134\pi$
$941$	1.24272e28			0.700282			0.350141	+	0.936697i	$0.386134\pi$
$942$		0			0
$943$		−	2.58056e28i		−	1.42512i
$944$		0			0
$945$	1.03362e26	−	4.45636e26i	0.00559446	−	0.0241201i
$946$		0			0
$947$			3.85591e27i			0.204551i	0.994756	+	0.102276i	$0.0326124\pi$
$947$			3.85591e27i			0.204551i	−0.994756	+	0.102276i	$0.967388\pi$
$948$		0			0
$949$	4.70118e27			0.244443
$950$		0			0
$951$	1.98384e26			0.0101110
$952$		0			0
$953$		−	7.95493e27i		−	0.397424i	−0.980058	−	0.198712i	$-0.936324\pi$
$953$		−	7.95493e27i		−	0.397424i	0.980058	−	0.198712i	$-0.0636758\pi$
$954$		0			0
$955$	−3.31360e27	+	1.42863e28i	−0.162281	+	0.699663i
$956$		0			0
$957$			3.41730e26i			0.0164066i
$958$		0			0
$959$	1.84413e28			0.867992
$960$		0			0
$961$	9.65741e25			0.00445644
$962$		0			0
$963$			3.59246e28i			1.62533i
$964$		0			0
$965$	−4.34369e28	−	1.00748e28i	−1.92686	−	0.446919i
$966$		0			0
$967$		−	3.11858e28i		−	1.35645i	−0.734853	−	0.678227i	$-0.762749\pi$
$967$		−	3.11858e28i		−	1.35645i	0.734853	−	0.678227i	$-0.237251\pi$
$968$		0			0
$969$	−4.91762e25			−0.00209739
$970$		0			0
$971$	3.27069e28			1.36791			0.683955	−	0.729525i	$-0.260259\pi$
$971$	3.27069e28			1.36791			0.683955	+	0.729525i	$0.260259\pi$
$972$		0			0
$973$			1.10484e28i			0.453134i
$974$		0			0
$975$	8.15988e26	+	4.00045e26i	0.0328201	+	0.0160903i
$976$		0			0
$977$			2.32952e28i			0.918898i	0.888204	+	0.459449i	$0.151953\pi$
$977$			2.32952e28i			0.918898i	−0.888204	+	0.459449i	$0.848047\pi$
$978$		0			0
$979$	−4.26295e27			−0.164921
$980$		0			0
$981$	2.75544e28			1.04553
$982$		0			0
$983$		−	4.39368e28i		−	1.63520i	−0.575789	−	0.817599i	$-0.695305\pi$
$983$		−	4.39368e28i		−	1.63520i	0.575789	−	0.817599i	$-0.304695\pi$
$984$		0			0
$985$	−1.62706e28	−	3.77383e27i	−0.593963	−	0.137765i
$986$		0			0
$987$			3.09336e26i			0.0110769i
$988$		0			0
$989$	−1.91148e27			−0.0671436
$990$		0			0
$991$	−1.81866e28			−0.626688			−0.313344	−	0.949640i	$-0.601449\pi$
$991$	−1.81866e28			−0.626688			−0.313344	+	0.949640i	$0.601449\pi$
$992$		0			0
$993$		−	9.18139e26i		−	0.0310378i
$994$		0			0
$995$	−5.20075e27	+	2.24226e28i	−0.172483	+	0.743647i
$996$		0			0
$997$			3.48687e28i			1.13457i	0.823521	+	0.567285i	$0.192006\pi$
$997$			3.48687e28i			1.13457i	−0.823521	+	0.567285i	$0.807994\pi$
$998$		0			0
$999$	2.27418e26			0.00726028

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	80.20.c.c.49.5		10
4.3	odd	2		10.20.b.a.9.3	✓	10
5.4	even	2	inner	80.20.c.c.49.6		10
12.11	even	2		90.20.c.b.19.8		10
20.3	even	4		50.20.a.k.1.3		5
20.7	even	4		50.20.a.l.1.3		5
20.19	odd	2		10.20.b.a.9.8	yes	10
60.59	even	2		90.20.c.b.19.3		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
10.20.b.a.9.3	✓	10	4.3	odd	2
10.20.b.a.9.8	yes	10	20.19	odd	2
50.20.a.k.1.3		5	20.3	even	4
50.20.a.l.1.3		5	20.7	even	4
80.20.c.c.49.5		10	1.1	even	1	trivial
80.20.c.c.49.6		10	5.4	even	2	inner
90.20.c.b.19.3		10	60.59	even	2
90.20.c.b.19.8		10	12.11	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 80 = 2^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 20 \)
Character orbit:	\([\chi]\)	\(=\)	80.c (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q-908.466i q^{3} +(986770. - 4.25438e6i) q^{5} +4.96199e7i q^{7} +1.16144e9 q^{9} +O(q^{10})\)	\(q-908.466i q^{3} +(986770. - 4.25438e6i) q^{5} +4.96199e7i q^{7} +1.16144e9 q^{9} +3.15919e9 q^{11} -5.24467e10i q^{13} +(-3.86496e9 - 8.96447e8i) q^{15} -3.26184e10i q^{17} +1.65953e12 q^{19} +4.50780e10 q^{21} -1.15711e13i q^{23} +(-1.71261e13 - 8.39619e12i) q^{25} -2.11100e12i q^{27} -1.19069e14 q^{29} +1.47537e14 q^{31} -2.87001e12i q^{33} +(2.11102e14 + 4.89634e13i) q^{35} +1.07730e14i q^{37} -4.76460e13 q^{39} +2.23018e15 q^{41} -1.65194e14i q^{43} +(1.14607e15 - 4.94119e15i) q^{45} +6.86224e15i q^{47} +8.93676e15 q^{49} -2.96327e13 q^{51} -3.03245e16i q^{53} +(3.11739e15 - 1.34404e16i) q^{55} -1.50762e15i q^{57} +1.09697e17 q^{59} -6.76315e15 q^{61} +5.76303e16i q^{63} +(-2.23128e17 - 5.17528e16i) q^{65} +2.45598e17i q^{67} -1.05119e16 q^{69} -5.52545e17 q^{71} +8.96373e16i q^{73} +(-7.62766e15 + 1.55584e16i) q^{75} +1.56758e17i q^{77} -4.12914e17 q^{79} +1.34797e18 q^{81} -9.58716e17i q^{83} +(-1.38771e17 - 3.21869e16i) q^{85} +1.08170e17i q^{87} -1.34938e18 q^{89} +2.60240e18 q^{91} -1.34033e17i q^{93} +(1.63757e18 - 7.06026e18i) q^{95} +6.64383e18i q^{97} +3.66919e18 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 2902670 q^{5} - 8718754970 q^{9}+O(q^{10}) \) 10 * q + 2902670 * q^5 - 8718754970 * q^9	\( 10 q + 2902670 q^{5} - 8718754970 q^{9} + 2965225880 q^{11} - 225010487480 q^{15} + 4196987836200 q^{19} - 501224287480 q^{21} + 19247576437650 q^{25} + 219360620418300 q^{29} + 667121586663680 q^{31} - 14\!\cdots\!60 q^{35}+ \cdots - 41\!\cdots\!60 q^{99}+O(q^{100}) \) 10 * q + 2902670 * q^5 - 8718754970 * q^9 + 2965225880 * q^11 - 225010487480 * q^15 + 4196987836200 * q^19 - 501224287480 * q^21 + 19247576437650 * q^25 + 219360620418300 * q^29 + 667121586663680 * q^31 - 1477908982965160 * q^35 + 3387373771795440 * q^39 + 3587345408194420 * q^41 - 13139237288012990 * q^45 - 30324198320796930 * q^49 - 106899828254155520 * q^51 + 99144934237329160 * q^55 + 332698279801897400 * q^59 + 533407565011656620 * q^61 - 682989395388761520 * q^65 - 95759593423262840 * q^69 - 1975827158504532720 * q^71 + 3881333883421828400 * q^75 + 2303771531732690400 * q^79 + 12793501534789009010 * q^81 - 6445103007057591040 * q^85 - 11076199503631707100 * q^89 - 7638137420731759920 * q^91 + 7279632536499161400 * q^95 - 41542573713793315160 * q^99

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