LMFDB - Embedded newform 3330.2.d.r.1999.4

Error: table mf_hecke_newspace_traces does not exist

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [3330,2,Mod(1999,3330)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("3330.1999"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(3330, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 1, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 3330 = 2 \cdot 3^{2} \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3330.d (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [14,0,0,-14,4,0,0,0,0,-6,-12,0,0,12] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(14)] == traces)

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

Self dual:	no
Analytic conductor:	$26.5901838731$
Analytic rank:	$0$
Dimension:	$14$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} + \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} + 20x^{12} + 154x^{10} + 580x^{8} + 1105x^{6} + 960x^{4} + 256x^{2} + 16 $ x^14 + 20x^12 + 154x^10 + 580x^8 + 1105x^6 + 960x^4 + 256x^2 + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{6} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			1999.4
Root			$1.79842i$ of defining polynomial
Character	$\chi$	$=$	3330.1999
Dual form			3330.2.d.r.1999.11

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-1.00000i q^{2} -1.00000 q^{4} +(1.13070 + 1.92912i) q^{5} +1.23431i q^{7} +1.00000i q^{8} +(1.92912 - 1.13070i) q^{10} +3.36649 q^{11} -3.44302i q^{13} +1.23431 q^{14} +1.00000 q^{16} -7.03986i q^{17} +4.40976 q^{19} +(-1.13070 - 1.92912i) q^{20} -3.36649i q^{22} -3.31926i q^{23} +(-2.44302 + 4.36253i) q^{25} -3.44302 q^{26} -1.23431i q^{28} +0.635565 q^{29} +0.759332 q^{31} -1.00000i q^{32} -7.03986 q^{34} +(-2.38114 + 1.39564i) q^{35} +1.00000i q^{37} -4.40976i q^{38} +(-1.92912 + 1.13070i) q^{40} -7.63407 q^{41} -8.35089i q^{43} -3.36649 q^{44} -3.31926 q^{46} +4.94420i q^{47} +5.47647 q^{49} +(4.36253 + 2.44302i) q^{50} +3.44302i q^{52} +9.85982i q^{53} +(3.80650 + 6.49437i) q^{55} -1.23431 q^{56} -0.635565i q^{58} +3.03345 q^{59} -7.27814 q^{61} -0.759332i q^{62} -1.00000 q^{64} +(6.64201 - 3.89304i) q^{65} -8.94445i q^{67} +7.03986i q^{68} +(1.39564 + 2.38114i) q^{70} +9.43709 q^{71} -12.6894i q^{73} +1.00000 q^{74} -4.40976 q^{76} +4.15530i q^{77} -1.67207 q^{79} +(1.13070 + 1.92912i) q^{80} +7.63407i q^{82} +1.86165i q^{83} +(13.5808 - 7.95999i) q^{85} -8.35089 q^{86} +3.36649i q^{88} +14.5766 q^{89} +4.24977 q^{91} +3.31926i q^{92} +4.94420 q^{94} +(4.98613 + 8.50696i) q^{95} -9.34055i q^{97} -5.47647i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q - 14 q^{4} + 4 q^{5} - 6 q^{10} - 12 q^{11} + 12 q^{14} + 14 q^{16} + 4 q^{19} - 4 q^{20} + 10 q^{25} - 4 q^{26} + 16 q^{29} + 12 q^{31} - 12 q^{34} + 8 q^{35} + 6 q^{40} - 56 q^{41} + 12 q^{44} - 8 q^{46}+ \cdots - 12 q^{95}+O(q^{100}) $ 14 * q - 14 * q^4 + 4 * q^5 - 6 * q^10 - 12 * q^11 + 12 * q^14 + 14 * q^16 + 4 * q^19 - 4 * q^20 + 10 * q^25 - 4 * q^26 + 16 * q^29 + 12 * q^31 - 12 * q^34 + 8 * q^35 + 6 * q^40 - 56 * q^41 + 12 * q^44 - 8 * q^46 + 18 * q^49 + 24 * q^50 - 12 * q^56 + 28 * q^59 + 12 * q^61 - 14 * q^64 - 12 * q^65 - 16 * q^70 - 48 * q^71 + 14 * q^74 - 4 * q^76 - 20 * q^79 + 4 * q^80 + 12 * q^85 - 12 * q^86 + 36 * q^89 - 32 * q^91 + 32 * q^94 - 12 * q^95

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/3330\mathbb{Z}\right)^\times$.

$n$	$371$	$631$	$667$
$\chi(n)$	$1$	$1$	$-1$

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 $

$2$		−	1.00000i		−	0.707107i
$2$		−	1.00000i		−	0.707107i
$3$		0			0
$3$		0			0
$4$	−1.00000			−0.500000
$5$	1.13070	+	1.92912i	0.505665	+	0.862730i
$5$	1.13070	+	1.92912i	0.505665	+	0.862730i
$6$		0			0
$7$			1.23431i			0.466527i	0.972414	+	0.233263i	$0.0749404\pi$
$7$			1.23431i			0.466527i	−0.972414	+	0.233263i	$0.925060\pi$
$8$			1.00000i			0.353553i
$9$		0			0
$10$	1.92912	−	1.13070i	0.610042	−	0.357560i
$11$	3.36649			1.01504			0.507518	−	0.861641i	$-0.330563\pi$
$11$	3.36649			1.01504			0.507518	+	0.861641i	$0.330563\pi$
$12$		0			0
$13$		−	3.44302i		−	0.954923i	−0.878653	−	0.477462i	$-0.841557\pi$
$13$		−	3.44302i		−	0.954923i	0.878653	−	0.477462i	$-0.158443\pi$
$14$	1.23431			0.329884
$15$		0			0
$16$	1.00000			0.250000
$17$		−	7.03986i		−	1.70742i	−0.520751	−	0.853709i	$-0.674348\pi$
$17$		−	7.03986i		−	1.70742i	0.520751	−	0.853709i	$-0.325652\pi$
$18$		0			0
$19$	4.40976			1.01167			0.505834	−	0.862631i	$-0.331185\pi$
$19$	4.40976			1.01167			0.505834	+	0.862631i	$0.331185\pi$
$20$	−1.13070	−	1.92912i	−0.252833	−	0.431365i
$21$		0			0
$22$		−	3.36649i		−	0.717738i
$23$		−	3.31926i		−	0.692113i	−0.938214	−	0.346057i	$-0.887521\pi$
$23$		−	3.31926i		−	0.692113i	0.938214	−	0.346057i	$-0.112479\pi$
$24$		0			0
$25$	−2.44302	+	4.36253i	−0.488605	+	0.872505i
$26$	−3.44302			−0.675233
$27$		0			0
$28$		−	1.23431i		−	0.233263i
$29$	0.635565			0.118022			0.0590108	−	0.998257i	$-0.481205\pi$
$29$	0.635565			0.118022			0.0590108	+	0.998257i	$0.481205\pi$
$30$		0			0
$31$	0.759332			0.136380			0.0681900	−	0.997672i	$-0.478278\pi$
$31$	0.759332			0.136380			0.0681900	+	0.997672i	$0.478278\pi$
$32$		−	1.00000i		−	0.176777i
$33$		0			0
$34$	−7.03986			−1.20733
$35$	−2.38114	+	1.39564i	−0.402486	+	0.235906i
$36$		0			0
$37$			1.00000i			0.164399i
$37$			1.00000i			0.164399i
$38$		−	4.40976i		−	0.715357i
$39$		0			0
$40$	−1.92912	+	1.13070i	−0.305021	+	0.178780i
$41$	−7.63407			−1.19224			−0.596121	−	0.802895i	$-0.703292\pi$
$41$	−7.63407			−1.19224			−0.596121	+	0.802895i	$0.703292\pi$
$42$		0			0
$43$		−	8.35089i		−	1.27350i	−0.771071	−	0.636750i	$-0.780279\pi$
$43$		−	8.35089i		−	1.27350i	0.771071	−	0.636750i	$-0.219721\pi$
$44$	−3.36649			−0.507518
$45$		0			0
$46$	−3.31926			−0.489398
$47$			4.94420i			0.721186i	0.932723	+	0.360593i	$0.117426\pi$
$47$			4.94420i			0.721186i	−0.932723	+	0.360593i	$0.882574\pi$
$48$		0			0
$49$	5.47647			0.782353
$50$	4.36253	+	2.44302i	0.616954	+	0.345496i
$51$		0			0
$52$			3.44302i			0.477462i
$53$			9.85982i			1.35435i	0.735822	+	0.677175i	$0.236796\pi$
$53$			9.85982i			1.35435i	−0.735822	+	0.677175i	$0.763204\pi$
$54$		0			0
$55$	3.80650	+	6.49437i	0.513268	+	0.875701i
$56$	−1.23431			−0.164942
$57$		0			0
$58$		−	0.635565i		−	0.0834538i
$59$	3.03345			0.394921			0.197461	−	0.980311i	$-0.436731\pi$
$59$	3.03345			0.394921			0.197461	+	0.980311i	$0.436731\pi$
$60$		0			0
$61$	−7.27814			−0.931871			−0.465935	−	0.884819i	$-0.654282\pi$
$61$	−7.27814			−0.931871			−0.465935	+	0.884819i	$0.654282\pi$
$62$		−	0.759332i		−	0.0964352i
$63$		0			0
$64$	−1.00000			−0.125000
$65$	6.64201	−	3.89304i	0.823840	−	0.482872i
$66$		0			0
$67$		−	8.94445i		−	1.09274i	−0.837545	−	0.546369i	$-0.816010\pi$
$67$		−	8.94445i		−	1.09274i	0.837545	−	0.546369i	$-0.183990\pi$
$68$			7.03986i			0.853709i
$69$		0			0
$70$	1.39564	+	2.38114i	0.166811	+	0.284601i
$71$	9.43709			1.11998			0.559988	−	0.828500i	$-0.310806\pi$
$71$	9.43709			1.11998			0.559988	+	0.828500i	$0.310806\pi$
$72$		0			0
$73$		−	12.6894i		−	1.48518i	−0.669745	−	0.742591i	$-0.733597\pi$
$73$		−	12.6894i		−	1.48518i	0.669745	−	0.742591i	$-0.266403\pi$
$74$	1.00000			0.116248
$75$		0			0
$76$	−4.40976			−0.505834
$77$			4.15530i			0.473541i
$78$		0			0
$79$	−1.67207			−0.188122			−0.0940610	−	0.995566i	$-0.529985\pi$
$79$	−1.67207			−0.188122			−0.0940610	+	0.995566i	$0.529985\pi$
$80$	1.13070	+	1.92912i	0.126416	+	0.215682i
$81$		0			0
$82$			7.63407i			0.843042i
$83$			1.86165i			0.204343i	0.994767	+	0.102171i	$0.0325790\pi$
$83$			1.86165i			0.204343i	−0.994767	+	0.102171i	$0.967421\pi$
$84$		0			0
$85$	13.5808	−	7.95999i	1.47304	−	0.863382i
$86$	−8.35089			−0.900500
$87$		0			0
$88$			3.36649i			0.358869i
$89$	14.5766			1.54512			0.772560	−	0.634941i	$-0.218976\pi$
$89$	14.5766			1.54512			0.772560	+	0.634941i	$0.218976\pi$
$90$		0			0
$91$	4.24977			0.445497
$92$			3.31926i			0.346057i
$93$		0			0
$94$	4.94420			0.509956
$95$	4.98613	+	8.50696i	0.511566	+	0.872796i
$96$		0			0
$97$		−	9.34055i		−	0.948390i	−0.880420	−	0.474195i	$-0.842739\pi$
$97$		−	9.34055i		−	0.948390i	0.880420	−	0.474195i	$-0.157261\pi$
$98$		−	5.47647i		−	0.553207i
$99$		0			0
$100$	2.44302	−	4.36253i	0.244302	−	0.436253i
$101$	1.79302			0.178412			0.0892062	−	0.996013i	$-0.471567\pi$
$101$	1.79302			0.178412			0.0892062	+	0.996013i	$0.471567\pi$
$102$		0			0
$103$		−	18.7262i		−	1.84514i	−0.385826	−	0.922572i	$-0.626083\pi$
$103$		−	18.7262i		−	1.84514i	0.385826	−	0.922572i	$-0.373917\pi$
$104$	3.44302			0.337616
$105$		0			0
$106$	9.85982			0.957670
$107$		−	3.51666i		−	0.339968i	−0.985447	−	0.169984i	$-0.945628\pi$
$107$		−	3.51666i		−	0.339968i	0.985447	−	0.169984i	$-0.0543716\pi$
$108$		0			0
$109$	6.41092			0.614055			0.307027	−	0.951701i	$-0.400666\pi$
$109$	6.41092			0.614055			0.307027	+	0.951701i	$0.400666\pi$
$110$	6.49437	−	3.80650i	0.619214	−	0.362935i
$111$		0			0
$112$			1.23431i			0.116632i
$113$			19.0839i			1.79526i	0.440750	+	0.897630i	$0.354713\pi$
$113$			19.0839i			1.79526i	−0.440750	+	0.897630i	$0.645287\pi$
$114$		0			0
$115$	6.40325	−	3.75309i	0.597106	−	0.349978i
$116$	−0.635565			−0.0590108
$117$		0			0
$118$		−	3.03345i		−	0.279251i
$119$	8.68940			0.796556
$120$		0			0
$121$	0.333261			0.0302964
$122$			7.27814i			0.658932i
$123$		0			0
$124$	−0.759332			−0.0681900
$125$	−11.1782	+	0.219827i	−0.999807	+	0.0196619i
$126$		0			0
$127$			16.3720i			1.45278i	0.687282	+	0.726390i	$0.258803\pi$
$127$			16.3720i			1.45278i	−0.687282	+	0.726390i	$0.741197\pi$
$128$			1.00000i			0.0883883i
$129$		0			0
$130$	−3.89304	−	6.64201i	−0.341442	−	0.582543i
$131$	16.3686			1.43013			0.715066	−	0.699057i	$-0.246397\pi$
$131$	16.3686			1.43013			0.715066	+	0.699057i	$0.246397\pi$
$132$		0			0
$133$			5.44302i			0.471970i
$134$	−8.94445			−0.772682
$135$		0			0
$136$	7.03986			0.603663
$137$		−	1.92605i		−	0.164554i	−0.996610	−	0.0822769i	$-0.973781\pi$
$137$		−	1.92605i		−	0.164554i	0.996610	−	0.0822769i	$-0.0262192\pi$
$138$		0			0
$139$	21.5940			1.83158			0.915788	−	0.401661i	$-0.131567\pi$
$139$	21.5940			1.83158			0.915788	+	0.401661i	$0.131567\pi$
$140$	2.38114	−	1.39564i	0.201243	−	0.117953i
$141$		0			0
$142$		−	9.43709i		−	0.791943i
$143$		−	11.5909i		−	0.969281i
$144$		0			0
$145$	0.718635	+	1.22608i	0.0596794	+	0.101821i
$146$	−12.6894			−1.05018
$147$		0			0
$148$		−	1.00000i		−	0.0821995i
$149$	21.3688			1.75060			0.875300	−	0.483581i	$-0.160664\pi$
$149$	21.3688			1.75060			0.875300	+	0.483581i	$0.160664\pi$
$150$		0			0
$151$	−11.5280			−0.938138			−0.469069	−	0.883162i	$-0.655410\pi$
$151$	−11.5280			−0.938138			−0.469069	+	0.883162i	$0.655410\pi$
$152$			4.40976i			0.357679i
$153$		0			0
$154$	4.15530			0.334844
$155$	0.858578	+	1.46484i	0.0689627	+	0.117659i
$156$		0			0
$157$		−	3.80302i		−	0.303514i	−0.988418	−	0.151757i	$-0.951507\pi$
$157$		−	3.80302i		−	0.303514i	0.988418	−	0.151757i	$-0.0484932\pi$
$158$			1.67207i			0.133022i
$159$		0			0
$160$	1.92912	−	1.13070i	0.152510	−	0.0893899i
$161$	4.09700			0.322889
$162$		0			0
$163$		−	1.70971i		−	0.133915i	−0.997756	−	0.0669573i	$-0.978671\pi$
$163$		−	1.70971i		−	0.133915i	0.997756	−	0.0669573i	$-0.0213291\pi$
$164$	7.63407			0.596121
$165$		0			0
$166$	1.86165			0.144492
$167$		−	22.1107i		−	1.71098i	−0.517820	−	0.855490i	$-0.673256\pi$
$167$		−	22.1107i		−	1.71098i	0.517820	−	0.855490i	$-0.326744\pi$
$168$		0			0
$169$	1.14559			0.0881220
$170$	−7.95999	−	13.5808i	−0.610503	−	1.04160i
$171$		0			0
$172$			8.35089i			0.636750i
$173$			12.5446i			0.953747i	0.878972	+	0.476874i	$0.158230\pi$
$173$			12.5446i			0.953747i	−0.878972	+	0.476874i	$0.841770\pi$
$174$		0			0
$175$	−5.38472	−	3.01546i	−0.407047	−	0.227947i
$176$	3.36649			0.253759
$177$		0			0
$178$		−	14.5766i		−	1.09257i
$179$	−19.8089			−1.48059			−0.740294	−	0.672283i	$-0.765314\pi$
$179$	−19.8089			−1.48059			−0.740294	+	0.672283i	$0.765314\pi$
$180$		0			0
$181$	5.07891			0.377512			0.188756	−	0.982024i	$-0.439554\pi$
$181$	5.07891			0.377512			0.188756	+	0.982024i	$0.439554\pi$
$182$		−	4.24977i		−	0.315014i
$183$		0			0
$184$	3.31926			0.244699
$185$	−1.92912	+	1.13070i	−0.141832	+	0.0831309i
$186$		0			0
$187$		−	23.6996i		−	1.73309i
$188$		−	4.94420i		−	0.360593i
$189$		0			0
$190$	8.50696	−	4.98613i	0.617160	−	0.361732i
$191$	−12.1697			−0.880566			−0.440283	−	0.897859i	$-0.645122\pi$
$191$	−12.1697			−0.880566			−0.440283	+	0.897859i	$0.645122\pi$
$192$		0			0
$193$		−	14.4442i		−	1.03972i	−0.854252	−	0.519860i	$-0.825984\pi$
$193$		−	14.4442i		−	1.03972i	0.854252	−	0.519860i	$-0.174016\pi$
$194$	−9.34055			−0.670613
$195$		0			0
$196$	−5.47647			−0.391176
$197$			20.4747i			1.45876i	0.684108	+	0.729381i	$0.260192\pi$
$197$			20.4747i			1.45876i	−0.684108	+	0.729381i	$0.739808\pi$
$198$		0			0
$199$	−18.0454			−1.27921			−0.639604	−	0.768705i	$-0.720902\pi$
$199$	−18.0454			−1.27921			−0.639604	+	0.768705i	$0.720902\pi$
$200$	−4.36253	−	2.44302i	−0.308477	−	0.172748i
$201$		0			0
$202$		−	1.79302i		−	0.126157i
$203$			0.784487i			0.0550602i
$204$		0			0
$205$	−8.63186	−	14.7271i	−0.602875	−	1.02858i
$206$	−18.7262			−1.30471
$207$		0			0
$208$		−	3.44302i		−	0.238731i
$209$	14.8454			1.02688
$210$		0			0
$211$	8.58522			0.591031			0.295516	−	0.955338i	$-0.404509\pi$
$211$	8.58522			0.591031			0.295516	+	0.955338i	$0.404509\pi$
$212$		−	9.85982i		−	0.677175i
$213$		0			0
$214$	−3.51666			−0.240394
$215$	16.1099	−	9.44237i	1.09869	−	0.643965i
$216$		0			0
$217$			0.937253i			0.0636249i
$218$		−	6.41092i		−	0.434202i
$219$		0			0
$220$	−3.80650	−	6.49437i	−0.256634	−	0.437850i
$221$	−24.2384			−1.63045
$222$		0			0
$223$			28.8602i			1.93262i	0.257379	+	0.966310i	$0.417141\pi$
$223$			28.8602i			1.93262i	−0.257379	+	0.966310i	$0.582859\pi$
$224$	1.23431			0.0824710
$225$		0			0
$226$	19.0839			1.26944
$227$			16.2253i			1.07691i	0.842654	+	0.538455i	$0.180992\pi$
$227$			16.2253i			1.07691i	−0.842654	+	0.538455i	$0.819008\pi$
$228$		0			0
$229$	15.6420			1.03365			0.516826	−	0.856090i	$-0.327113\pi$
$229$	15.6420			1.03365			0.516826	+	0.856090i	$0.327113\pi$
$230$	−3.75309	−	6.40325i	−0.247472	−	0.422218i
$231$		0			0
$232$			0.635565i			0.0417269i
$233$			13.8052i			0.904407i	0.891915	+	0.452203i	$0.149362\pi$
$233$			13.8052i			0.904407i	−0.891915	+	0.452203i	$0.850638\pi$
$234$		0			0
$235$	−9.53797	+	5.59042i	−0.622189	+	0.364679i
$236$	−3.03345			−0.197461
$237$		0			0
$238$		−	8.68940i		−	0.563250i
$239$	15.7337			1.01773			0.508864	−	0.860847i	$-0.330065\pi$
$239$	15.7337			1.01773			0.508864	+	0.860847i	$0.330065\pi$
$240$		0			0
$241$	25.4466			1.63916			0.819579	−	0.572966i	$-0.194207\pi$
$241$	25.4466			1.63916			0.819579	+	0.572966i	$0.194207\pi$
$242$		−	0.333261i		−	0.0214228i
$243$		0			0
$244$	7.27814			0.465935
$245$	6.19226	+	10.5648i	0.395609	+	0.674959i
$246$		0			0
$247$		−	15.1829i		−	0.966065i
$248$			0.759332i			0.0482176i
$249$		0			0
$250$	0.219827	+	11.1782i	0.0139031	+	0.706970i
$251$	−22.5978			−1.42636			−0.713179	−	0.700982i	$-0.752745\pi$
$251$	−22.5978			−1.42636			−0.713179	+	0.700982i	$0.752745\pi$
$252$		0			0
$253$		−	11.1743i		−	0.702519i
$254$	16.3720			1.02727
$255$		0			0
$256$	1.00000			0.0625000
$257$		−	0.382839i		−	0.0238809i	−0.999929	−	0.0119404i	$-0.996199\pi$
$257$		−	0.382839i		−	0.0238809i	0.999929	−	0.0119404i	$-0.00380085\pi$
$258$		0			0
$259$	−1.23431			−0.0766965
$260$	−6.64201	+	3.89304i	−0.411920	+	0.241436i
$261$		0			0
$262$		−	16.3686i		−	1.01126i
$263$			17.8935i			1.10336i	0.834055	+	0.551681i	$0.186013\pi$
$263$			17.8935i			1.10336i	−0.834055	+	0.551681i	$0.813987\pi$
$264$		0			0
$265$	−19.0208	+	11.1485i	−1.16844	+	0.684848i
$266$	5.44302			0.333733
$267$		0			0
$268$			8.94445i			0.546369i
$269$	23.7565			1.44846			0.724231	−	0.689558i	$-0.242195\pi$
$269$	23.7565			1.44846			0.724231	+	0.689558i	$0.242195\pi$
$270$		0			0
$271$	−19.7487			−1.19965			−0.599825	−	0.800131i	$-0.704763\pi$
$271$	−19.7487			−1.19965			−0.599825	+	0.800131i	$0.704763\pi$
$272$		−	7.03986i		−	0.426854i
$273$		0			0
$274$	−1.92605			−0.116357
$275$	−8.22442	+	14.6864i	−0.495951	+	0.885623i
$276$		0			0
$277$		−	18.7112i		−	1.12424i	−0.827054	−	0.562122i	$-0.809985\pi$
$277$		−	18.7112i		−	1.12424i	0.827054	−	0.562122i	$-0.190015\pi$
$278$		−	21.5940i		−	1.29512i
$279$		0			0
$280$	−1.39564	−	2.38114i	−0.0834055	−	0.142300i
$281$	−2.65311			−0.158271			−0.0791355	−	0.996864i	$-0.525216\pi$
$281$	−2.65311			−0.158271			−0.0791355	+	0.996864i	$0.525216\pi$
$282$		0			0
$283$		−	7.89107i		−	0.469076i	−0.972107	−	0.234538i	$-0.924642\pi$
$283$		−	7.89107i		−	0.469076i	0.972107	−	0.234538i	$-0.0753577\pi$
$284$	−9.43709			−0.559988
$285$		0			0
$286$	−11.5909			−0.685385
$287$		−	9.42283i		−	0.556212i
$288$		0			0
$289$	−32.5597			−1.91528
$290$	1.22608	−	0.718635i	0.0719981	−	0.0421997i
$291$		0			0
$292$			12.6894i			0.742591i
$293$		−	9.20656i		−	0.537853i	−0.963161	−	0.268927i	$-0.913331\pi$
$293$		−	9.20656i		−	0.537853i	0.963161	−	0.268927i	$-0.0866689\pi$
$294$		0			0
$295$	3.42993	+	5.85189i	0.199698	+	0.340710i
$296$	−1.00000			−0.0581238
$297$		0			0
$298$		−	21.3688i		−	1.23786i
$299$	−11.4283			−0.660915
$300$		0			0
$301$	10.3076			0.594121
$302$			11.5280i			0.663364i
$303$		0			0
$304$	4.40976			0.252917
$305$	−8.22941	−	14.0404i	−0.471215	−	0.803952i
$306$		0			0
$307$			10.5484i			0.602028i	0.953620	+	0.301014i	$0.0973251\pi$
$307$			10.5484i			0.602028i	−0.953620	+	0.301014i	$0.902675\pi$
$308$		−	4.15530i		−	0.236770i
$309$		0			0
$310$	1.46484	−	0.858578i	0.0831975	−	0.0487640i
$311$	−27.1869			−1.54163			−0.770813	−	0.637062i	$-0.780150\pi$
$311$	−27.1869			−1.54163			−0.770813	+	0.637062i	$0.780150\pi$
$312$		0			0
$313$		−	8.74232i		−	0.494145i	−0.968997	−	0.247073i	$-0.920531\pi$
$313$		−	8.74232i		−	0.494145i	0.968997	−	0.247073i	$-0.0794686\pi$
$314$	−3.80302			−0.214617
$315$		0			0
$316$	1.67207			0.0940610
$317$			4.74399i			0.266449i	0.991086	+	0.133225i	$0.0425332\pi$
$317$			4.74399i			0.266449i	−0.991086	+	0.133225i	$0.957467\pi$
$318$		0			0
$319$	2.13963			0.119796
$320$	−1.13070	−	1.92912i	−0.0632082	−	0.107841i
$321$		0			0
$322$		−	4.09700i		−	0.228317i
$323$		−	31.0441i		−	1.72734i
$324$		0			0
$325$	15.0203	+	8.41139i	0.833175	+	0.466580i
$326$	−1.70971			−0.0946920
$327$		0			0
$328$		−	7.63407i		−	0.421521i
$329$	−6.10270			−0.336453
$330$		0			0
$331$	8.82644			0.485145			0.242573	−	0.970133i	$-0.422009\pi$
$331$	8.82644			0.485145			0.242573	+	0.970133i	$0.422009\pi$
$332$		−	1.86165i		−	0.102171i
$333$		0			0
$334$	−22.1107			−1.20985
$335$	17.2549	−	10.1135i	0.942737	−	0.552560i
$336$		0			0
$337$		−	3.59908i		−	0.196054i	−0.995184	−	0.0980271i	$-0.968747\pi$
$337$		−	3.59908i		−	0.196054i	0.995184	−	0.0980271i	$-0.0312532\pi$
$338$		−	1.14559i		−	0.0623116i
$339$		0			0
$340$	−13.5808	+	7.95999i	−0.736520	+	0.431691i
$341$	2.55628			0.138430
$342$		0			0
$343$			15.3999i			0.831515i
$344$	8.35089			0.450250
$345$		0			0
$346$	12.5446			0.674401
$347$			13.6943i			0.735146i	0.929995	+	0.367573i	$0.119811\pi$
$347$			13.6943i			0.735146i	−0.929995	+	0.367573i	$0.880189\pi$
$348$		0			0
$349$	12.9295			0.692101			0.346050	−	0.938216i	$-0.387523\pi$
$349$	12.9295			0.692101			0.346050	+	0.938216i	$0.387523\pi$
$350$	−3.01546	+	5.38472i	−0.161183	+	0.287826i
$351$		0			0
$352$		−	3.36649i		−	0.179435i
$353$		−	19.5646i		−	1.04132i	−0.853765	−	0.520659i	$-0.825686\pi$
$353$		−	19.5646i		−	1.04132i	0.853765	−	0.520659i	$-0.174314\pi$
$354$		0			0
$355$	10.6705	+	18.2053i	0.566334	+	0.966237i
$356$	−14.5766			−0.772560
$357$		0			0
$358$			19.8089i			1.04693i
$359$	−22.1544			−1.16926			−0.584632	−	0.811299i	$-0.698761\pi$
$359$	−22.1544			−1.16926			−0.584632	+	0.811299i	$0.698761\pi$
$360$		0			0
$361$	0.445974			0.0234723
$362$		−	5.07891i		−	0.266941i
$363$		0			0
$364$	−4.24977			−0.222748
$365$	24.4794	−	14.3479i	1.28131	−	0.751005i
$366$		0			0
$367$			16.8362i			0.878843i	0.898281	+	0.439422i	$0.144817\pi$
$367$			16.8362i			0.878843i	−0.898281	+	0.439422i	$0.855183\pi$
$368$		−	3.31926i		−	0.173028i
$369$		0			0
$370$	1.13070	+	1.92912i	0.0587824	+	0.100290i
$371$	−12.1701			−0.631840
$372$		0			0
$373$		−	4.76106i		−	0.246518i	−0.992375	−	0.123259i	$-0.960665\pi$
$373$		−	4.76106i		−	0.246518i	0.992375	−	0.123259i	$-0.0393346\pi$
$374$	−23.6996			−1.22548
$375$		0			0
$376$	−4.94420			−0.254978
$377$		−	2.18827i		−	0.112701i
$378$		0			0
$379$	2.62236			0.134701			0.0673507	−	0.997729i	$-0.478545\pi$
$379$	2.62236			0.134701			0.0673507	+	0.997729i	$0.478545\pi$
$380$	−4.98613	−	8.50696i	−0.255783	−	0.436398i
$381$		0			0
$382$			12.1697i			0.622654i
$383$		−	26.7104i		−	1.36484i	−0.730962	−	0.682418i	$-0.760928\pi$
$383$		−	26.7104i		−	1.36484i	0.730962	−	0.682418i	$-0.239072\pi$
$384$		0			0
$385$	−8.01609	+	4.69841i	−0.408538	+	0.239453i
$386$	−14.4442			−0.735193
$387$		0			0
$388$			9.34055i			0.474195i
$389$	28.4487			1.44241			0.721204	−	0.692723i	$-0.243589\pi$
$389$	28.4487			1.44241			0.721204	+	0.692723i	$0.243589\pi$
$390$		0			0
$391$	−23.3671			−1.18173
$392$			5.47647i			0.276604i
$393$		0			0
$394$	20.4747			1.03150
$395$	−1.89061	−	3.22562i	−0.0951268	−	0.162298i
$396$		0			0
$397$			16.3501i			0.820587i	0.911953	+	0.410294i	$0.134574\pi$
$397$			16.3501i			0.820587i	−0.911953	+	0.410294i	$0.865426\pi$
$398$			18.0454i			0.904537i
$399$		0			0
$400$	−2.44302	+	4.36253i	−0.122151	+	0.218126i
$401$	−9.08493			−0.453680			−0.226840	−	0.973932i	$-0.572839\pi$
$401$	−9.08493			−0.453680			−0.226840	+	0.973932i	$0.572839\pi$
$402$		0			0
$403$		−	2.61440i		−	0.130232i
$404$	−1.79302			−0.0892062
$405$		0			0
$406$	0.784487			0.0389334
$407$			3.36649i			0.166871i
$408$		0			0
$409$	8.22234			0.406569			0.203284	−	0.979120i	$-0.434838\pi$
$409$	8.22234			0.406569			0.203284	+	0.979120i	$0.434838\pi$
$410$	−14.7271	+	8.63186i	−0.727317	+	0.426297i
$411$		0			0
$412$			18.7262i			0.922572i
$413$			3.74422i			0.184241i
$414$		0			0
$415$	−3.59135	+	2.10497i	−0.176292	+	0.103329i
$416$	−3.44302			−0.168808
$417$		0			0
$418$		−	14.8454i		−	0.726113i
$419$	−8.88285			−0.433956			−0.216978	−	0.976177i	$-0.569620\pi$
$419$	−8.88285			−0.433956			−0.216978	+	0.976177i	$0.569620\pi$
$420$		0			0
$421$	12.3712			0.602936			0.301468	−	0.953476i	$-0.402523\pi$
$421$	12.3712			0.602936			0.301468	+	0.953476i	$0.402523\pi$
$422$		−	8.58522i		−	0.417922i
$423$		0			0
$424$	−9.85982			−0.478835
$425$	30.7116	+	17.1986i	1.48973	+	0.834252i
$426$		0			0
$427$		−	8.98351i		−	0.434742i
$428$			3.51666i			0.169984i
$429$		0			0
$430$	−9.44237	−	16.1099i	−0.455352	−	0.776888i
$431$	−7.83341			−0.377322			−0.188661	−	0.982042i	$-0.560415\pi$
$431$	−7.83341			−0.377322			−0.188661	+	0.982042i	$0.560415\pi$
$432$		0			0
$433$		−	16.5213i		−	0.793963i	−0.917827	−	0.396981i	$-0.870058\pi$
$433$		−	16.5213i		−	0.793963i	0.917827	−	0.396981i	$-0.129942\pi$
$434$	0.937253			0.0449896
$435$		0			0
$436$	−6.41092			−0.307027
$437$		−	14.6371i		−	0.700189i
$438$		0			0
$439$	−18.6337			−0.889336			−0.444668	−	0.895695i	$-0.646678\pi$
$439$	−18.6337			−0.889336			−0.444668	+	0.895695i	$0.646678\pi$
$440$	−6.49437	+	3.80650i	−0.309607	+	0.181468i
$441$		0			0
$442$			24.2384i			1.15290i
$443$		−	1.02442i		−	0.0486718i	−0.999704	−	0.0243359i	$-0.992253\pi$
$443$		−	1.02442i		−	0.0486718i	0.999704	−	0.0243359i	$-0.00774712\pi$
$444$		0			0
$445$	16.4818	+	28.1201i	0.781314	+	1.33302i
$446$	28.8602			1.36657
$447$		0			0
$448$		−	1.23431i		−	0.0583158i
$449$	−11.4182			−0.538859			−0.269429	−	0.963020i	$-0.586835\pi$
$449$	−11.4182			−0.538859			−0.269429	+	0.963020i	$0.586835\pi$
$450$		0			0
$451$	−25.7000			−1.21017
$452$		−	19.0839i		−	0.897630i
$453$		0			0
$454$	16.2253			0.761491
$455$	4.80523	+	8.19833i	0.225272	+	0.384343i
$456$		0			0
$457$			32.5920i			1.52459i	0.647231	+	0.762294i	$0.275927\pi$
$457$			32.5920i			1.52459i	−0.647231	+	0.762294i	$0.724073\pi$
$458$		−	15.6420i		−	0.730903i
$459$		0			0
$460$	−6.40325	+	3.75309i	−0.298553	+	0.174989i
$461$	−7.68554			−0.357951			−0.178976	−	0.983854i	$-0.557278\pi$
$461$	−7.68554			−0.357951			−0.178976	+	0.983854i	$0.557278\pi$
$462$		0			0
$463$			0.229299i			0.0106564i	0.999986	+	0.00532822i	$0.00169603\pi$
$463$			0.229299i			0.0106564i	−0.999986	+	0.00532822i	$0.998304\pi$
$464$	0.635565			0.0295054
$465$		0			0
$466$	13.8052			0.639512
$467$			17.7416i			0.820985i	0.911864	+	0.410493i	$0.134643\pi$
$467$			17.7416i			0.820985i	−0.911864	+	0.410493i	$0.865357\pi$
$468$		0			0
$469$	11.0402			0.509791
$470$	5.59042	+	9.53797i	0.257867	+	0.439954i
$471$		0			0
$472$			3.03345i			0.139626i
$473$		−	28.1132i		−	1.29265i
$474$		0			0
$475$	−10.7731	+	19.2377i	−0.494306	+	0.882686i
$476$	−8.68940			−0.398278
$477$		0			0
$478$		−	15.7337i		−	0.719643i
$479$	−28.1920			−1.28813			−0.644063	−	0.764972i	$-0.722753\pi$
$479$	−28.1920			−1.28813			−0.644063	+	0.764972i	$0.722753\pi$
$480$		0			0
$481$	3.44302			0.156988
$482$		−	25.4466i		−	1.15906i
$483$		0			0
$484$	−0.333261			−0.0151482
$485$	18.0191	−	10.5614i	0.818204	−	0.479568i
$486$		0			0
$487$		−	26.8387i		−	1.21618i	−0.793869	−	0.608088i	$-0.791937\pi$
$487$		−	26.8387i		−	1.21618i	0.793869	−	0.608088i	$-0.208063\pi$
$488$		−	7.27814i		−	0.329466i
$489$		0			0
$490$	10.5648	−	6.19226i	0.477268	−	0.279738i
$491$	−22.4175			−1.01169			−0.505845	−	0.862624i	$-0.668819\pi$
$491$	−22.4175			−1.01169			−0.505845	+	0.862624i	$0.668819\pi$
$492$		0			0
$493$		−	4.47429i		−	0.201512i
$494$	−15.1829			−0.683111
$495$		0			0
$496$	0.759332			0.0340950
$497$			11.6483i			0.522499i
$498$		0			0
$499$	−31.6931			−1.41878			−0.709389	−	0.704817i	$-0.751029\pi$
$499$	−31.6931			−1.41878			−0.709389	+	0.704817i	$0.751029\pi$
$500$	11.1782	−	0.219827i	0.499903	−	0.00983097i
$501$		0			0
$502$			22.5978i			1.00859i
$503$		−	7.20775i		−	0.321378i	−0.987005	−	0.160689i	$-0.948628\pi$
$503$		−	7.20775i		−	0.321378i	0.987005	−	0.160689i	$-0.0513716\pi$
$504$		0			0
$505$	2.02737	+	3.45896i	0.0902169	+	0.153922i
$506$	−11.1743			−0.496756
$507$		0			0
$508$		−	16.3720i		−	0.726390i
$509$	30.8524			1.36751			0.683754	−	0.729713i	$-0.260346\pi$
$509$	30.8524			1.36751			0.683754	+	0.729713i	$0.260346\pi$
$510$		0			0
$511$	15.6627			0.692877
$512$		−	1.00000i		−	0.0441942i
$513$		0			0
$514$	−0.382839			−0.0168863
$515$	36.1250	−	21.1737i	1.59186	−	0.933025i
$516$		0			0
$517$			16.6446i			0.732029i
$518$			1.23431i			0.0542326i
$519$		0			0
$520$	3.89304	+	6.64201i	0.170721	+	0.291272i
$521$	−2.93822			−0.128726			−0.0643629	−	0.997927i	$-0.520502\pi$
$521$	−2.93822			−0.128726			−0.0643629	+	0.997927i	$0.520502\pi$
$522$		0			0
$523$			16.6208i			0.726775i	0.931638	+	0.363387i	$0.118380\pi$
$523$			16.6208i			0.726775i	−0.931638	+	0.363387i	$0.881620\pi$
$524$	−16.3686			−0.715066
$525$		0			0
$526$	17.8935			0.780194
$527$		−	5.34559i		−	0.232858i
$528$		0			0
$529$	11.9825			0.520979
$530$	11.1485	+	19.0208i	0.484261	+	0.826210i
$531$		0			0
$532$		−	5.44302i		−	0.235985i
$533$			26.2843i			1.13850i
$534$		0			0
$535$	6.78406	−	3.97629i	0.293301	−	0.171910i
$536$	8.94445			0.386341
$537$		0			0
$538$		−	23.7565i		−	1.02422i
$539$	18.4365			0.794116
$540$		0			0
$541$	3.00414			0.129158			0.0645791	−	0.997913i	$-0.479430\pi$
$541$	3.00414			0.129158			0.0645791	+	0.997913i	$0.479430\pi$
$542$			19.7487i			0.848281i
$543$		0			0
$544$	−7.03986			−0.301832
$545$	7.24884	+	12.3675i	0.310506	+	0.529763i
$546$		0			0
$547$		−	26.3147i		−	1.12513i	−0.826752	−	0.562567i	$-0.809814\pi$
$547$		−	26.3147i		−	1.12513i	0.826752	−	0.562567i	$-0.190186\pi$
$548$			1.92605i			0.0822769i
$549$		0			0
$550$	14.6864	+	8.22442i	0.626230	+	0.350690i
$551$	2.80269			0.119399
$552$		0			0
$553$		−	2.06385i		−	0.0877639i
$554$	−18.7112			−0.794961
$555$		0			0
$556$	−21.5940			−0.915788
$557$		−	12.5755i		−	0.532839i	−0.963857	−	0.266420i	$-0.914159\pi$
$557$		−	12.5755i		−	0.532839i	0.963857	−	0.266420i	$-0.0858407\pi$
$558$		0			0
$559$	−28.7523			−1.21609
$560$	−2.38114	+	1.39564i	−0.100622	+	0.0589766i
$561$		0			0
$562$			2.65311i			0.111914i
$563$			15.8495i			0.667977i	0.942577	+	0.333989i	$0.108395\pi$
$563$			15.8495i			0.667977i	−0.942577	+	0.333989i	$0.891605\pi$
$564$		0			0
$565$	−36.8151	+	21.5782i	−1.54882	+	0.907801i
$566$	−7.89107			−0.331687
$567$		0			0
$568$			9.43709i			0.395972i
$569$	−2.70072			−0.113220			−0.0566100	−	0.998396i	$-0.518029\pi$
$569$	−2.70072			−0.113220			−0.0566100	+	0.998396i	$0.518029\pi$
$570$		0			0
$571$	33.6184			1.40689			0.703443	−	0.710752i	$-0.251645\pi$
$571$	33.6184			1.40689			0.703443	+	0.710752i	$0.251645\pi$
$572$			11.5909i			0.484640i
$573$		0			0
$574$	−9.42283			−0.393301
$575$	14.4803	+	8.10903i	0.603872	+	0.338170i
$576$		0			0
$577$		−	18.3099i		−	0.762249i	−0.924524	−	0.381125i	$-0.875537\pi$
$577$		−	18.3099i		−	0.762249i	0.924524	−	0.381125i	$-0.124463\pi$
$578$			32.5597i			1.35430i
$579$		0			0
$580$	−0.718635	−	1.22608i	−0.0298397	−	0.0509103i
$581$	−2.29786			−0.0953312
$582$		0			0
$583$			33.1930i			1.37471i
$584$	12.6894			0.525091
$585$		0			0
$586$	−9.20656			−0.380320
$587$			16.7897i			0.692986i	0.938053	+	0.346493i	$0.112628\pi$
$587$			16.7897i			0.692986i	−0.938053	+	0.346493i	$0.887372\pi$
$588$		0			0
$589$	3.34847			0.137971
$590$	5.85189	−	3.42993i	0.240918	−	0.141208i
$591$		0			0
$592$			1.00000i			0.0410997i
$593$			29.5264i			1.21250i	0.795272	+	0.606252i	$0.207328\pi$
$593$			29.5264i			1.21250i	−0.795272	+	0.606252i	$0.792672\pi$
$594$		0			0
$595$	9.82512	+	16.7629i	0.402791	+	0.687212i
$596$	−21.3688			−0.875300
$597$		0			0
$598$			11.4283i			0.467337i
$599$	14.4857			0.591872			0.295936	−	0.955208i	$-0.404369\pi$
$599$	14.4857			0.591872			0.295936	+	0.955208i	$0.404369\pi$
$600$		0			0
$601$	−32.2637			−1.31606			−0.658032	−	0.752990i	$-0.728611\pi$
$601$	−32.2637			−1.31606			−0.658032	+	0.752990i	$0.728611\pi$
$602$		−	10.3076i		−	0.420107i
$603$		0			0
$604$	11.5280			0.469069
$605$	0.376819	+	0.642901i	0.0153199	+	0.0261376i
$606$		0			0
$607$		−	4.68289i		−	0.190072i	−0.995474	−	0.0950362i	$-0.969703\pi$
$607$		−	4.68289i		−	0.190072i	0.995474	−	0.0950362i	$-0.0302967\pi$
$608$		−	4.40976i		−	0.178839i
$609$		0			0
$610$	−14.0404	+	8.22941i	−0.568480	+	0.333199i
$611$	17.0230			0.688677
$612$		0			0
$613$			15.5305i			0.627271i	0.949543	+	0.313636i	$0.101547\pi$
$613$			15.5305i			0.627271i	−0.949543	+	0.313636i	$0.898453\pi$
$614$	10.5484			0.425698
$615$		0			0
$616$	−4.15530			−0.167422
$617$			33.7696i			1.35951i	0.733438	+	0.679757i	$0.237915\pi$
$617$			33.7696i			1.35951i	−0.733438	+	0.679757i	$0.762085\pi$
$618$		0			0
$619$	−23.7149			−0.953182			−0.476591	−	0.879125i	$-0.658128\pi$
$619$	−23.7149			−0.953182			−0.476591	+	0.879125i	$0.658128\pi$
$620$	−0.858578	−	1.46484i	−0.0344813	−	0.0588295i
$621$		0			0
$622$			27.1869i			1.09009i
$623$			17.9921i			0.720840i
$624$		0			0
$625$	−13.0633	−	21.3155i	−0.522531	−	0.852620i
$626$	−8.74232			−0.349413
$627$		0			0
$628$			3.80302i			0.151757i
$629$	7.03986			0.280698
$630$		0			0
$631$	−5.46438			−0.217533			−0.108767	−	0.994067i	$-0.534690\pi$
$631$	−5.46438			−0.217533			−0.108767	+	0.994067i	$0.534690\pi$
$632$		−	1.67207i		−	0.0665112i
$633$		0			0
$634$	4.74399			0.188408
$635$	−31.5836	+	18.5119i	−1.25336	+	0.734621i
$636$		0			0
$637$		−	18.8556i		−	0.747087i
$638$		−	2.13963i		−	0.0847086i
$639$		0			0
$640$	−1.92912	+	1.13070i	−0.0762552	+	0.0446949i
$641$	4.72202			0.186508			0.0932542	−	0.995642i	$-0.470273\pi$
$641$	4.72202			0.186508			0.0932542	+	0.995642i	$0.470273\pi$
$642$		0			0
$643$		−	26.5265i		−	1.04610i	−0.852301	−	0.523052i	$-0.824793\pi$
$643$		−	26.5265i		−	1.04610i	0.852301	−	0.523052i	$-0.175207\pi$
$644$	−4.09700			−0.161445
$645$		0			0
$646$	−31.0441			−1.22141
$647$		−	16.8901i		−	0.664017i	−0.943276	−	0.332009i	$-0.892274\pi$
$647$		−	16.8901i		−	0.664017i	0.943276	−	0.332009i	$-0.107726\pi$
$648$		0			0
$649$	10.2121			0.400859
$650$	8.41139	−	15.0203i	0.329922	−	0.589144i
$651$		0			0
$652$			1.70971i			0.0669573i
$653$		−	14.6814i		−	0.574528i	−0.957851	−	0.287264i	$-0.907254\pi$
$653$		−	14.6814i		−	0.574528i	0.957851	−	0.287264i	$-0.0927457\pi$
$654$		0			0
$655$	18.5080	+	31.5770i	0.723168	+	1.23382i
$656$	−7.63407			−0.298060
$657$		0			0
$658$			6.10270i			0.237908i
$659$	24.3591			0.948896			0.474448	−	0.880284i	$-0.342648\pi$
$659$	24.3591			0.948896			0.474448	+	0.880284i	$0.342648\pi$
$660$		0			0
$661$	−42.9547			−1.67075			−0.835373	−	0.549684i	$-0.814748\pi$
$661$	−42.9547			−1.67075			−0.835373	+	0.549684i	$0.814748\pi$
$662$		−	8.82644i		−	0.343049i
$663$		0			0
$664$	−1.86165			−0.0722460
$665$	−10.5003	+	6.15444i	−0.407183	+	0.238659i
$666$		0			0
$667$		−	2.10961i		−	0.0816843i
$668$			22.1107i			0.855490i
$669$		0			0
$670$	−10.1135	−	17.2549i	−0.390719	−	0.666616i
$671$	−24.5018			−0.945881
$672$		0			0
$673$		−	22.2378i		−	0.857205i	−0.903493	−	0.428602i	$-0.859006\pi$
$673$		−	22.2378i		−	0.857205i	0.903493	−	0.428602i	$-0.140994\pi$
$674$	−3.59908			−0.138631
$675$		0			0
$676$	−1.14559			−0.0440610
$677$		−	17.3025i		−	0.664987i	−0.943105	−	0.332494i	$-0.892110\pi$
$677$		−	17.3025i		−	0.664987i	0.943105	−	0.332494i	$-0.107890\pi$
$678$		0			0
$679$	11.5292			0.442449
$680$	7.95999	+	13.5808i	0.305252	+	0.520798i
$681$		0			0
$682$		−	2.55628i		−	0.0978851i
$683$			2.42928i			0.0929537i	0.998919	+	0.0464769i	$0.0147994\pi$
$683$			2.42928i			0.0929537i	−0.998919	+	0.0464769i	$0.985201\pi$
$684$		0			0
$685$	3.71559	−	2.17779i	0.141966	−	0.0832092i
$686$	15.3999			0.587970
$687$		0			0
$688$		−	8.35089i		−	0.318375i
$689$	33.9476			1.29330
$690$		0			0
$691$	−45.3655			−1.72578			−0.862892	−	0.505389i	$-0.831349\pi$
$691$	−45.3655			−1.72578			−0.862892	+	0.505389i	$0.831349\pi$
$692$		−	12.5446i		−	0.476874i
$693$		0			0
$694$	13.6943			0.519827
$695$	24.4164	+	41.6574i	0.926165	+	1.58016i
$696$		0			0
$697$			53.7428i			2.03565i
$698$		−	12.9295i		−	0.489389i
$699$		0			0
$700$	5.38472	+	3.01546i	0.203523	+	0.113974i
$701$	−49.1290			−1.85558			−0.927788	−	0.373109i	$-0.878292\pi$
$701$	−49.1290			−1.85558			−0.927788	+	0.373109i	$0.878292\pi$
$702$		0			0
$703$			4.40976i			0.166317i
$704$	−3.36649			−0.126879
$705$		0			0
$706$	−19.5646			−0.736323
$707$			2.21315i			0.0832341i
$708$		0			0
$709$	−11.3111			−0.424796			−0.212398	−	0.977183i	$-0.568127\pi$
$709$	−11.3111			−0.424796			−0.212398	+	0.977183i	$0.568127\pi$
$710$	18.2053	−	10.6705i	0.683233	−	0.400458i
$711$		0			0
$712$			14.5766i			0.546283i
$713$		−	2.52042i		−	0.0943904i
$714$		0			0
$715$	22.3603	−	13.1059i	0.836227	−	0.490132i
$716$	19.8089			0.740294
$717$		0			0
$718$			22.1544i			0.826794i
$719$	20.4566			0.762901			0.381451	−	0.924389i	$-0.375425\pi$
$719$	20.4566			0.762901			0.381451	+	0.924389i	$0.375425\pi$
$720$		0			0
$721$	23.1139			0.860808
$722$		−	0.445974i		−	0.0165974i
$723$		0			0
$724$	−5.07891			−0.188756
$725$	−1.55270	+	2.77267i	−0.0576659	+	0.102974i
$726$		0			0
$727$			40.0799i			1.48648i	0.669024	+	0.743241i	$0.266712\pi$
$727$			40.0799i			1.48648i	−0.669024	+	0.743241i	$0.733288\pi$
$728$			4.24977i			0.157507i
$729$		0			0
$730$	−14.3479	−	24.4794i	−0.531041	−	0.906023i
$731$	−58.7891			−2.17439
$732$		0			0
$733$			13.6671i			0.504806i	0.967622	+	0.252403i	$0.0812209\pi$
$733$			13.6671i			0.504806i	−0.967622	+	0.252403i	$0.918779\pi$
$734$	16.8362			0.621436
$735$		0			0
$736$	−3.31926			−0.122349
$737$		−	30.1114i		−	1.10917i
$738$		0			0
$739$	−36.2928			−1.33505			−0.667527	−	0.744586i	$-0.732647\pi$
$739$	−36.2928			−1.33505			−0.667527	+	0.744586i	$0.732647\pi$
$740$	1.92912	−	1.13070i	0.0709159	−	0.0415654i
$741$		0			0
$742$			12.1701i			0.446779i
$743$			37.8206i			1.38750i	0.720215	+	0.693751i	$0.244043\pi$
$743$			37.8206i			1.38750i	−0.720215	+	0.693751i	$0.755957\pi$
$744$		0			0
$745$	24.1617	+	41.2230i	0.885218	+	1.51029i
$746$	−4.76106			−0.174315
$747$		0			0
$748$			23.6996i			0.866545i
$749$	4.34066			0.158604
$750$		0			0
$751$	−4.25776			−0.155368			−0.0776840	−	0.996978i	$-0.524753\pi$
$751$	−4.25776			−0.155368			−0.0776840	+	0.996978i	$0.524753\pi$
$752$			4.94420i			0.180297i
$753$		0			0
$754$	−2.18827			−0.0796920
$755$	−13.0348	−	22.2390i	−0.474384	−	0.809359i
$756$		0			0
$757$			30.2524i			1.09954i	0.835315	+	0.549772i	$0.185285\pi$
$757$			30.2524i			1.09954i	−0.835315	+	0.549772i	$0.814715\pi$
$758$		−	2.62236i		−	0.0952483i
$759$		0			0
$760$	−8.50696	+	4.98613i	−0.308580	+	0.180866i
$761$	24.7344			0.896622			0.448311	−	0.893878i	$-0.352026\pi$
$761$	24.7344			0.896622			0.448311	+	0.893878i	$0.352026\pi$
$762$		0			0
$763$			7.91309i			0.286473i
$764$	12.1697			0.440283
$765$		0			0
$766$	−26.7104			−0.965085
$767$		−	10.4442i		−	0.377119i
$768$		0			0
$769$	13.1340			0.473624			0.236812	−	0.971555i	$-0.423897\pi$
$769$	13.1340			0.473624			0.236812	+	0.971555i	$0.423897\pi$
$770$	4.69841	+	8.01609i	0.169319	+	0.288880i
$771$		0			0
$772$			14.4442i			0.519860i
$773$			30.7387i			1.10559i	0.833316	+	0.552796i	$0.186439\pi$
$773$			30.7387i			1.10559i	−0.833316	+	0.552796i	$0.813561\pi$
$774$		0			0
$775$	−1.85507	+	3.31260i	−0.0666359	+	0.118992i
$776$	9.34055			0.335306
$777$		0			0
$778$		−	28.4487i		−	1.01994i
$779$	−33.6644			−1.20615
$780$		0			0
$781$	31.7699			1.13682
$782$			23.3671i			0.835607i
$783$		0			0
$784$	5.47647			0.195588
$785$	7.33650	−	4.30009i	0.261851	−	0.153477i
$786$		0			0
$787$		−	39.3548i		−	1.40285i	−0.712744	−	0.701424i	$-0.752548\pi$
$787$		−	39.3548i		−	1.40285i	0.712744	−	0.701424i	$-0.247452\pi$
$788$		−	20.4747i		−	0.729381i
$789$		0			0
$790$	−3.22562	+	1.89061i	−0.114762	+	0.0672648i
$791$	−23.5555			−0.837536
$792$		0			0
$793$			25.0588i			0.889865i
$794$	16.3501			0.580243
$795$		0			0
$796$	18.0454			0.639604
$797$			36.3497i			1.28757i	0.765206	+	0.643786i	$0.222637\pi$
$797$			36.3497i			1.28757i	−0.765206	+	0.643786i	$0.777363\pi$
$798$		0			0
$799$	34.8065			1.23137
$800$	4.36253	+	2.44302i	0.154239	+	0.0863739i
$801$		0			0
$802$			9.08493i			0.320800i
$803$		−	42.7187i		−	1.50751i
$804$		0			0
$805$	4.63249	+	7.90362i	0.163274	+	0.278566i
$806$	−2.61440			−0.0920882
$807$		0			0
$808$			1.79302i			0.0630783i
$809$	27.3642			0.962073			0.481036	−	0.876701i	$-0.340260\pi$
$809$	27.3642			0.962073			0.481036	+	0.876701i	$0.340260\pi$
$810$		0			0
$811$	21.7327			0.763138			0.381569	−	0.924340i	$-0.375384\pi$
$811$	21.7327			0.763138			0.381569	+	0.924340i	$0.375384\pi$
$812$		−	0.784487i		−	0.0275301i
$813$		0			0
$814$	3.36649			0.117995
$815$	3.29824	−	1.93317i	0.115532	−	0.0677160i
$816$		0			0
$817$		−	36.8254i		−	1.28836i
$818$		−	8.22234i		−	0.287488i
$819$		0			0
$820$	8.63186	+	14.7271i	0.301438	+	0.514291i
$821$	17.0859			0.596303			0.298152	−	0.954519i	$-0.403630\pi$
$821$	17.0859			0.596303			0.298152	+	0.954519i	$0.403630\pi$
$822$		0			0
$823$		−	4.74737i		−	0.165483i	−0.996571	−	0.0827414i	$-0.973632\pi$
$823$		−	4.74737i		−	0.165483i	0.996571	−	0.0827414i	$-0.0263676\pi$
$824$	18.7262			0.652357
$825$		0			0
$826$	3.74422			0.130278
$827$		−	14.9656i		−	0.520405i	−0.965554	−	0.260203i	$-0.916211\pi$
$827$		−	14.9656i		−	0.520405i	0.965554	−	0.260203i	$-0.0837894\pi$
$828$		0			0
$829$	−50.8537			−1.76622			−0.883111	−	0.469165i	$-0.844555\pi$
$829$	−50.8537			−1.76622			−0.883111	+	0.469165i	$0.844555\pi$
$830$	2.10497	+	3.59135i	0.0730646	+	0.124658i
$831$		0			0
$832$			3.44302i			0.119365i
$833$		−	38.5536i		−	1.33580i
$834$		0			0
$835$	42.6543	−	25.0007i	1.47611	−	0.865183i
$836$	−14.8454			−0.513439
$837$		0			0
$838$			8.88285i			0.306853i
$839$	−9.20967			−0.317953			−0.158977	−	0.987282i	$-0.550819\pi$
$839$	−9.20967			−0.317953			−0.158977	+	0.987282i	$0.550819\pi$
$840$		0			0
$841$	−28.5961			−0.986071
$842$		−	12.3712i		−	0.426340i
$843$		0			0
$844$	−8.58522			−0.295516
$845$	1.29532	+	2.20997i	0.0445602	+	0.0760254i
$846$		0			0
$847$			0.411348i			0.0141341i
$848$			9.85982i			0.338588i
$849$		0			0
$850$	17.1986	−	30.7116i	0.589906	−	1.05340i
$851$	3.31926			0.113783
$852$		0			0
$853$			3.39058i			0.116091i	0.998314	+	0.0580457i	$0.0184869\pi$
$853$			3.39058i			0.116091i	−0.998314	+	0.0580457i	$0.981513\pi$
$854$	−8.98351			−0.307409
$855$		0			0
$856$	3.51666			0.120197
$857$			6.65800i			0.227433i	0.993513	+	0.113716i	$0.0362755\pi$
$857$			6.65800i			0.227433i	−0.993513	+	0.113716i	$0.963724\pi$
$858$		0			0
$859$	41.7302			1.42382			0.711909	−	0.702272i	$-0.247831\pi$
$859$	41.7302			1.42382			0.711909	+	0.702272i	$0.247831\pi$
$860$	−16.1099	+	9.44237i	−0.549343	+	0.321982i
$861$		0			0
$862$			7.83341i			0.266807i
$863$		−	14.0899i		−	0.479624i	−0.970819	−	0.239812i	$-0.922914\pi$
$863$		−	14.0899i		−	0.479624i	0.970819	−	0.239812i	$-0.0770859\pi$
$864$		0			0
$865$	−24.2000	+	14.1842i	−0.822826	+	0.482277i
$866$	−16.5213			−0.561416
$867$		0			0
$868$		−	0.937253i		−	0.0318124i
$869$	−5.62899			−0.190950
$870$		0			0
$871$	−30.7959			−1.04348
$872$			6.41092i			0.217101i
$873$		0			0
$874$	−14.6371			−0.495108
$875$	−0.271336	−	13.7974i	−0.00917282	−	0.466436i
$876$		0			0
$877$		−	22.8145i		−	0.770391i	−0.922835	−	0.385196i	$-0.874134\pi$
$877$		−	22.8145i		−	0.770391i	0.922835	−	0.385196i	$-0.125866\pi$
$878$			18.6337i			0.628856i
$879$		0			0
$880$	3.80650	+	6.49437i	0.128317	+	0.218925i
$881$	35.0903			1.18222			0.591111	−	0.806590i	$-0.298689\pi$
$881$	35.0903			1.18222			0.591111	+	0.806590i	$0.298689\pi$
$882$		0			0
$883$		−	0.587522i		−	0.0197717i	−0.999951	−	0.00988585i	$-0.996853\pi$
$883$		−	0.587522i		−	0.0197717i	0.999951	−	0.00988585i	$-0.00314681\pi$
$884$	24.2384			0.815226
$885$		0			0
$886$	−1.02442			−0.0344162
$887$			28.9277i			0.971299i	0.874154	+	0.485649i	$0.161417\pi$
$887$			28.9277i			0.971299i	−0.874154	+	0.485649i	$0.838583\pi$
$888$		0			0
$889$	−20.2082			−0.677761
$890$	28.1201	−	16.4818i	0.942589	−	0.552473i
$891$		0			0
$892$		−	28.8602i		−	0.966310i
$893$			21.8027i			0.729601i
$894$		0			0
$895$	−22.3980	−	38.2138i	−0.748683	−	1.27735i
$896$	−1.23431			−0.0412355
$897$		0			0
$898$			11.4182i			0.381031i
$899$	0.482605			0.0160958
$900$		0			0
$901$	69.4118			2.31244
$902$			25.7000i			0.855717i
$903$		0			0
$904$	−19.0839			−0.634720
$905$	5.74273	+	9.79783i	0.190895	+	0.325691i
$906$		0			0
$907$			6.27428i			0.208334i	0.994560	+	0.104167i	$0.0332177\pi$
$907$			6.27428i			0.208334i	−0.994560	+	0.104167i	$0.966782\pi$
$908$		−	16.2253i		−	0.538455i
$909$		0			0
$910$	8.19833	−	4.80523i	0.271772	−	0.159292i
$911$	−24.6606			−0.817041			−0.408521	−	0.912749i	$-0.633955\pi$
$911$	−24.6606			−0.817041			−0.408521	+	0.912749i	$0.633955\pi$
$912$		0			0
$913$			6.26722i			0.207415i
$914$	32.5920			1.07805
$915$		0			0
$916$	−15.6420			−0.516826
$917$			20.2040i			0.667194i
$918$		0			0
$919$	28.1230			0.927691			0.463845	−	0.885916i	$-0.346469\pi$
$919$	28.1230			0.927691			0.463845	+	0.885916i	$0.346469\pi$
$920$	3.75309	+	6.40325i	0.123736	+	0.211109i
$921$		0			0
$922$			7.68554i			0.253110i
$923$		−	32.4921i		−	1.06949i
$924$		0			0
$925$	−4.36253	−	2.44302i	−0.143439	−	0.0803261i
$926$	0.229299			0.00753524
$927$		0			0
$928$		−	0.635565i		−	0.0208635i
$929$	−32.4655			−1.06516			−0.532579	−	0.846381i	$-0.678777\pi$
$929$	−32.4655			−1.06516			−0.532579	+	0.846381i	$0.678777\pi$
$930$		0			0
$931$	24.1499			0.791482
$932$		−	13.8052i		−	0.452203i
$933$		0			0
$934$	17.7416			0.580524
$935$	45.7195	−	26.7972i	1.49519	−	0.876363i
$936$		0			0
$937$		−	25.6809i		−	0.838959i	−0.907765	−	0.419479i	$-0.862213\pi$
$937$		−	25.6809i		−	0.838959i	0.907765	−	0.419479i	$-0.137787\pi$
$938$		−	11.0402i		−	0.360477i
$939$		0			0
$940$	9.53797	−	5.59042i	0.311094	−	0.182339i
$941$	14.5913			0.475662			0.237831	−	0.971307i	$-0.423564\pi$
$941$	14.5913			0.475662			0.237831	+	0.971307i	$0.423564\pi$
$942$		0			0
$943$			25.3394i			0.825166i
$944$	3.03345			0.0987303
$945$		0			0
$946$	−28.1132			−0.914039
$947$		−	46.7035i		−	1.51766i	−0.651290	−	0.758829i	$-0.725772\pi$
$947$		−	46.7035i		−	1.51766i	0.651290	−	0.758829i	$-0.274228\pi$
$948$		0			0
$949$	−43.6899			−1.41823
$950$	19.2377	+	10.7731i	0.624153	+	0.349527i
$951$		0			0
$952$			8.68940i			0.281625i
$953$			45.6196i			1.47777i	0.673834	+	0.738883i	$0.264646\pi$
$953$			45.6196i			1.47777i	−0.673834	+	0.738883i	$0.735354\pi$
$954$		0			0
$955$	−13.7603	−	23.4768i	−0.445272	−	0.759691i
$956$	−15.7337			−0.508864
$957$		0			0
$958$			28.1920i			0.910843i
$959$	2.37735			0.0767688
$960$		0			0
$961$	−30.4234			−0.981401
$962$		−	3.44302i		−	0.111008i
$963$		0			0
$964$	−25.4466			−0.819579
$965$	27.8647	−	16.3321i	0.896997	−	0.525750i
$966$		0			0
$967$		−	12.7855i		−	0.411154i	−0.978641	−	0.205577i	$-0.934093\pi$
$967$		−	12.7855i		−	0.411154i	0.978641	−	0.205577i	$-0.0659072\pi$
$968$			0.333261i			0.0107114i
$969$		0			0
$970$	−10.5614	−	18.0191i	−0.339106	−	0.578557i
$971$	6.30783			0.202428			0.101214	−	0.994865i	$-0.467727\pi$
$971$	6.30783			0.202428			0.101214	+	0.994865i	$0.467727\pi$
$972$		0			0
$973$			26.6537i			0.854479i
$974$	−26.8387			−0.859967
$975$		0			0
$976$	−7.27814			−0.232968
$977$		−	36.6913i		−	1.17386i	−0.809638	−	0.586929i	$-0.800337\pi$
$977$		−	36.6913i		−	1.17386i	0.809638	−	0.586929i	$-0.199663\pi$
$978$		0			0
$979$	49.0721			1.56835
$980$	−6.19226	−	10.5648i	−0.197804	−	0.337480i
$981$		0			0
$982$			22.4175i			0.715373i
$983$		−	3.96172i		−	0.126359i	−0.998002	−	0.0631796i	$-0.979876\pi$
$983$		−	3.96172i		−	0.126359i	0.998002	−	0.0631796i	$-0.0201241\pi$
$984$		0			0
$985$	−39.4982	+	23.1508i	−1.25852	+	0.737646i
$986$	−4.47429			−0.142491
$987$		0			0
$988$			15.1829i			0.483033i
$989$	−27.7188			−0.881405
$990$		0			0
$991$	−36.5320			−1.16048			−0.580239	−	0.814446i	$-0.697041\pi$
$991$	−36.5320			−1.16048			−0.580239	+	0.814446i	$0.697041\pi$
$992$		−	0.759332i		−	0.0241088i
$993$		0			0
$994$	11.6483			0.369463
$995$	−20.4040	−	34.8119i	−0.646851	−	1.10361i
$996$		0			0
$997$			45.1850i			1.43102i	0.698601	+	0.715511i	$0.253806\pi$
$997$			45.1850i			1.43102i	−0.698601	+	0.715511i	$0.746194\pi$
$998$			31.6931i			1.00323i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3330.2.d.r.1999.4	yes	14
3.2	odd	2		3330.2.d.q.1999.11	yes	14
5.4	even	2	inner	3330.2.d.r.1999.11	yes	14
15.14	odd	2		3330.2.d.q.1999.4	✓	14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3330.2.d.q.1999.4	✓	14	15.14	odd	2
3330.2.d.q.1999.11	yes	14	3.2	odd	2
3330.2.d.r.1999.4	yes	14	1.1	even	1	trivial
3330.2.d.r.1999.11	yes	14	5.4	even	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 3330 = 2 \cdot 3^{2} \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3330.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} -1.00000 q^{4} +(1.13070 + 1.92912i) q^{5} +1.23431i q^{7} +1.00000i q^{8} +(1.92912 - 1.13070i) q^{10} +3.36649 q^{11} -3.44302i q^{13} +1.23431 q^{14} +1.00000 q^{16} -7.03986i q^{17} +4.40976 q^{19} +(-1.13070 - 1.92912i) q^{20} -3.36649i q^{22} -3.31926i q^{23} +(-2.44302 + 4.36253i) q^{25} -3.44302 q^{26} -1.23431i q^{28} +0.635565 q^{29} +0.759332 q^{31} -1.00000i q^{32} -7.03986 q^{34} +(-2.38114 + 1.39564i) q^{35} +1.00000i q^{37} -4.40976i q^{38} +(-1.92912 + 1.13070i) q^{40} -7.63407 q^{41} -8.35089i q^{43} -3.36649 q^{44} -3.31926 q^{46} +4.94420i q^{47} +5.47647 q^{49} +(4.36253 + 2.44302i) q^{50} +3.44302i q^{52} +9.85982i q^{53} +(3.80650 + 6.49437i) q^{55} -1.23431 q^{56} -0.635565i q^{58} +3.03345 q^{59} -7.27814 q^{61} -0.759332i q^{62} -1.00000 q^{64} +(6.64201 - 3.89304i) q^{65} -8.94445i q^{67} +7.03986i q^{68} +(1.39564 + 2.38114i) q^{70} +9.43709 q^{71} -12.6894i q^{73} +1.00000 q^{74} -4.40976 q^{76} +4.15530i q^{77} -1.67207 q^{79} +(1.13070 + 1.92912i) q^{80} +7.63407i q^{82} +1.86165i q^{83} +(13.5808 - 7.95999i) q^{85} -8.35089 q^{86} +3.36649i q^{88} +14.5766 q^{89} +4.24977 q^{91} +3.31926i q^{92} +4.94420 q^{94} +(4.98613 + 8.50696i) q^{95} -9.34055i q^{97} -5.47647i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q - 14 q^{4} + 4 q^{5} - 6 q^{10} - 12 q^{11} + 12 q^{14} + 14 q^{16} + 4 q^{19} - 4 q^{20} + 10 q^{25} - 4 q^{26} + 16 q^{29} + 12 q^{31} - 12 q^{34} + 8 q^{35} + 6 q^{40} - 56 q^{41} + 12 q^{44} - 8 q^{46}+ \cdots - 12 q^{95}+O(q^{100}) \) 14 * q - 14 * q^4 + 4 * q^5 - 6 * q^10 - 12 * q^11 + 12 * q^14 + 14 * q^16 + 4 * q^19 - 4 * q^20 + 10 * q^25 - 4 * q^26 + 16 * q^29 + 12 * q^31 - 12 * q^34 + 8 * q^35 + 6 * q^40 - 56 * q^41 + 12 * q^44 - 8 * q^46 + 18 * q^49 + 24 * q^50 - 12 * q^56 + 28 * q^59 + 12 * q^61 - 14 * q^64 - 12 * q^65 - 16 * q^70 - 48 * q^71 + 14 * q^74 - 4 * q^76 - 20 * q^79 + 4 * q^80 + 12 * q^85 - 12 * q^86 + 36 * q^89 - 32 * q^91 + 32 * q^94 - 12 * q^95

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