LMFDB - Embedded newform 3330.2.d.r.1999.6

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			1999.6
Root			$0.299503i$ of defining polynomial
Character	$\chi$	$=$	3330.1999
Dual form			3330.2.d.r.1999.13

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-1.00000i q^{2} -1.00000 q^{4} +(1.89211 + 1.19161i) q^{5} -1.91030i q^{7} +1.00000i q^{8} +(1.19161 - 1.89211i) q^{10} -6.34148 q^{11} +1.16014i q^{13} -1.91030 q^{14} +1.00000 q^{16} +0.561130i q^{17} -0.439651 q^{19} +(-1.89211 - 1.19161i) q^{20} +6.34148i q^{22} +1.39252i q^{23} +(2.16014 + 4.50930i) q^{25} +1.16014 q^{26} +1.91030i q^{28} +5.86153 q^{29} +6.09391 q^{31} -1.00000i q^{32} +0.561130 q^{34} +(2.27633 - 3.61449i) q^{35} +1.00000i q^{37} +0.439651i q^{38} +(-1.19161 + 1.89211i) q^{40} +4.97226 q^{41} -4.94129i q^{43} +6.34148 q^{44} +1.39252 q^{46} +6.69678i q^{47} +3.35076 q^{49} +(4.50930 - 2.16014i) q^{50} -1.16014i q^{52} -9.13473i q^{53} +(-11.9988 - 7.55656i) q^{55} +1.91030 q^{56} -5.86153i q^{58} +5.51090 q^{59} +13.3222 q^{61} -6.09391i q^{62} -1.00000 q^{64} +(-1.38243 + 2.19510i) q^{65} -5.03975i q^{67} -0.561130i q^{68} +(-3.61449 - 2.27633i) q^{70} +3.59783 q^{71} -5.07193i q^{73} +1.00000 q^{74} +0.439651 q^{76} +12.1141i q^{77} +0.343246 q^{79} +(1.89211 + 1.19161i) q^{80} -4.97226i q^{82} +12.8462i q^{83} +(-0.668647 + 1.06172i) q^{85} -4.94129 q^{86} -6.34148i q^{88} +4.77883 q^{89} +2.21620 q^{91} -1.39252i q^{92} +6.69678 q^{94} +(-0.831867 - 0.523892i) q^{95} +10.8281i q^{97} -3.35076i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$5$	1.89211	+	1.19161i	0.846176	+	0.532904i
$5$	1.89211	+	1.19161i	0.846176	+	0.532904i
$6$		0			0
$7$		−	1.91030i		−	0.722025i	−0.932561	−	0.361012i	$-0.882431\pi$
$7$		−	1.91030i		−	0.722025i	0.932561	−	0.361012i	$-0.117569\pi$
$8$			1.00000i			0.353553i
$9$		0			0
$10$	1.19161	−	1.89211i	0.376820	−	0.598337i
$11$	−6.34148			−1.91203			−0.956014	−	0.293322i	$-0.905239\pi$
$11$	−6.34148			−1.91203			−0.956014	+	0.293322i	$0.905239\pi$
$12$		0			0
$13$			1.16014i			0.321764i	0.986974	+	0.160882i	$0.0514338\pi$
$13$			1.16014i			0.321764i	−0.986974	+	0.160882i	$0.948566\pi$
$14$	−1.91030			−0.510549
$15$		0			0
$16$	1.00000			0.250000
$17$			0.561130i			0.136094i	0.997682	+	0.0680470i	$0.0216768\pi$
$17$			0.561130i			0.136094i	−0.997682	+	0.0680470i	$0.978323\pi$
$18$		0			0
$19$	−0.439651			−0.100863			−0.0504315	−	0.998728i	$-0.516060\pi$
$19$	−0.439651			−0.100863			−0.0504315	+	0.998728i	$0.516060\pi$
$20$	−1.89211	−	1.19161i	−0.423088	−	0.266452i
$21$		0			0
$22$			6.34148i			1.35201i
$23$			1.39252i			0.290361i	0.989405	+	0.145181i	$0.0463763\pi$
$23$			1.39252i			0.290361i	−0.989405	+	0.145181i	$0.953624\pi$
$24$		0			0
$25$	2.16014	+	4.50930i	0.432027	+	0.901861i
$26$	1.16014			0.227521
$27$		0			0
$28$			1.91030i			0.361012i
$29$	5.86153			1.08846			0.544229	−	0.838937i	$-0.316822\pi$
$29$	5.86153			1.08846			0.544229	+	0.838937i	$0.316822\pi$
$30$		0			0
$31$	6.09391			1.09450			0.547250	−	0.836969i	$-0.315675\pi$
$31$	6.09391			1.09450			0.547250	+	0.836969i	$0.315675\pi$
$32$		−	1.00000i		−	0.176777i
$33$		0			0
$34$	0.561130			0.0962330
$35$	2.27633	−	3.61449i	0.384770	−	0.610960i
$36$		0			0
$37$			1.00000i			0.164399i
$37$			1.00000i			0.164399i
$38$			0.439651i			0.0713209i
$39$		0			0
$40$	−1.19161	+	1.89211i	−0.188410	+	0.299168i
$41$	4.97226			0.776536			0.388268	−	0.921546i	$-0.373073\pi$
$41$	4.97226			0.776536			0.388268	+	0.921546i	$0.373073\pi$
$42$		0			0
$43$		−	4.94129i		−	0.753540i	−0.926307	−	0.376770i	$-0.877035\pi$
$43$		−	4.94129i		−	0.753540i	0.926307	−	0.376770i	$-0.122965\pi$
$44$	6.34148			0.956014
$45$		0			0
$46$	1.39252			0.205316
$47$			6.69678i			0.976826i	0.872612	+	0.488413i	$0.162424\pi$
$47$			6.69678i			0.976826i	−0.872612	+	0.488413i	$0.837576\pi$
$48$		0			0
$49$	3.35076			0.478680
$50$	4.50930	−	2.16014i	0.637712	−	0.305489i
$51$		0			0
$52$		−	1.16014i		−	0.160882i
$53$		−	9.13473i		−	1.25475i	−0.778717	−	0.627376i	$-0.784129\pi$
$53$		−	9.13473i		−	1.25475i	0.778717	−	0.627376i	$-0.215871\pi$
$54$		0			0
$55$	−11.9988	−	7.55656i	−1.61791	−	1.01893i
$56$	1.91030			0.255274
$57$		0			0
$58$		−	5.86153i		−	0.769656i
$59$	5.51090			0.717458			0.358729	−	0.933442i	$-0.383210\pi$
$59$	5.51090			0.717458			0.358729	+	0.933442i	$0.383210\pi$
$60$		0			0
$61$	13.3222			1.70573			0.852867	−	0.522128i	$-0.174862\pi$
$61$	13.3222			1.70573			0.852867	+	0.522128i	$0.174862\pi$
$62$		−	6.09391i		−	0.773928i
$63$		0			0
$64$	−1.00000			−0.125000
$65$	−1.38243	+	2.19510i	−0.171469	+	0.272269i
$66$		0			0
$67$		−	5.03975i		−	0.615704i	−0.951434	−	0.307852i	$-0.900390\pi$
$67$		−	5.03975i		−	0.615704i	0.951434	−	0.307852i	$-0.0996102\pi$
$68$		−	0.561130i		−	0.0680470i
$69$		0			0
$70$	−3.61449	−	2.27633i	−0.432014	−	0.272073i
$71$	3.59783			0.426984			0.213492	−	0.976945i	$-0.431516\pi$
$71$	3.59783			0.426984			0.213492	+	0.976945i	$0.431516\pi$
$72$		0			0
$73$		−	5.07193i		−	0.593624i	−0.954936	−	0.296812i	$-0.904077\pi$
$73$		−	5.07193i		−	0.593624i	0.954936	−	0.296812i	$-0.0959235\pi$
$74$	1.00000			0.116248
$75$		0			0
$76$	0.439651			0.0504315
$77$			12.1141i			1.38053i
$78$		0			0
$79$	0.343246			0.0386182			0.0193091	−	0.999814i	$-0.493853\pi$
$79$	0.343246			0.0386182			0.0193091	+	0.999814i	$0.493853\pi$
$80$	1.89211	+	1.19161i	0.211544	+	0.133226i
$81$		0			0
$82$		−	4.97226i		−	0.549094i
$83$			12.8462i			1.41005i	0.709182	+	0.705025i	$0.249064\pi$
$83$			12.8462i			1.41005i	−0.709182	+	0.705025i	$0.750936\pi$
$84$		0			0
$85$	−0.668647	+	1.06172i	−0.0725250	+	0.115159i
$86$	−4.94129			−0.532833
$87$		0			0
$88$		−	6.34148i		−	0.676004i
$89$	4.77883			0.506555			0.253277	−	0.967394i	$-0.418492\pi$
$89$	4.77883			0.506555			0.253277	+	0.967394i	$0.418492\pi$
$90$		0			0
$91$	2.21620			0.232321
$92$		−	1.39252i		−	0.145181i
$93$		0			0
$94$	6.69678			0.690721
$95$	−0.831867	−	0.523892i	−0.0853478	−	0.0537502i
$96$		0			0
$97$			10.8281i			1.09943i	0.835352	+	0.549715i	$0.185264\pi$
$97$			10.8281i			1.09943i	−0.835352	+	0.549715i	$0.814736\pi$
$98$		−	3.35076i		−	0.338478i
$99$		0			0
$100$	−2.16014	−	4.50930i	−0.216014	−	0.450930i
$101$	3.94778			0.392819			0.196409	−	0.980522i	$-0.437072\pi$
$101$	3.94778			0.392819			0.196409	+	0.980522i	$0.437072\pi$
$102$		0			0
$103$		−	8.24163i		−	0.812072i	−0.913857	−	0.406036i	$-0.866911\pi$
$103$		−	8.24163i		−	0.812072i	0.913857	−	0.406036i	$-0.133089\pi$
$104$	−1.16014			−0.113761
$105$		0			0
$106$	−9.13473			−0.887243
$107$			11.3883i			1.10094i	0.834853	+	0.550472i	$0.185552\pi$
$107$			11.3883i			1.10094i	−0.834853	+	0.550472i	$0.814448\pi$
$108$		0			0
$109$	7.24702			0.694138			0.347069	−	0.937840i	$-0.387177\pi$
$109$	7.24702			0.694138			0.347069	+	0.937840i	$0.387177\pi$
$110$	−7.55656	+	11.9988i	−0.720490	+	1.14404i
$111$		0			0
$112$		−	1.91030i		−	0.180506i
$113$		−	3.74166i		−	0.351986i	−0.984391	−	0.175993i	$-0.943686\pi$
$113$		−	3.74166i		−	0.351986i	0.984391	−	0.175993i	$-0.0563136\pi$
$114$		0			0
$115$	−1.65934	+	2.63480i	−0.154735	+	0.245697i
$116$	−5.86153			−0.544229
$117$		0			0
$118$		−	5.51090i		−	0.507319i
$119$	1.07193			0.0982632
$120$		0			0
$121$	29.2143			2.65585
$122$		−	13.3222i		−	1.20614i
$123$		0			0
$124$	−6.09391			−0.547250
$125$	−1.28612	+	11.1061i	−0.115034	+	0.993362i
$126$		0			0
$127$		−	4.72570i		−	0.419338i	−0.977772	−	0.209669i	$-0.932761\pi$
$127$		−	4.72570i		−	0.419338i	0.977772	−	0.209669i	$-0.0672386\pi$
$128$			1.00000i			0.0883883i
$129$		0			0
$130$	2.19510	+	1.38243i	0.192523	+	0.121247i
$131$	−17.1887			−1.50178			−0.750890	−	0.660428i	$-0.770375\pi$
$131$	−17.1887			−1.50178			−0.750890	+	0.660428i	$0.770375\pi$
$132$		0			0
$133$			0.839865i			0.0728255i
$134$	−5.03975			−0.435368
$135$		0			0
$136$	−0.561130			−0.0481165
$137$			22.2907i			1.90442i	0.305443	+	0.952210i	$0.401195\pi$
$137$			22.2907i			1.90442i	−0.305443	+	0.952210i	$0.598805\pi$
$138$		0			0
$139$	6.19400			0.525368			0.262684	−	0.964882i	$-0.415392\pi$
$139$	6.19400			0.525368			0.262684	+	0.964882i	$0.415392\pi$
$140$	−2.27633	+	3.61449i	−0.192385	+	0.305480i
$141$		0			0
$142$		−	3.59783i		−	0.301923i
$143$		−	7.35697i		−	0.615221i
$144$		0			0
$145$	11.0906	+	6.98465i	0.921027	+	0.580043i
$146$	−5.07193			−0.419756
$147$		0			0
$148$		−	1.00000i		−	0.0821995i
$149$	1.52154			0.124649			0.0623247	−	0.998056i	$-0.480149\pi$
$149$	1.52154			0.124649			0.0623247	+	0.998056i	$0.480149\pi$
$150$		0			0
$151$	2.53077			0.205951			0.102976	−	0.994684i	$-0.467164\pi$
$151$	2.53077			0.205951			0.102976	+	0.994684i	$0.467164\pi$
$152$		−	0.439651i		−	0.0356604i
$153$		0			0
$154$	12.1141			0.976183
$155$	11.5303	+	7.26156i	0.926139	+	0.583263i
$156$		0			0
$157$		−	10.5701i		−	0.843585i	−0.906692	−	0.421792i	$-0.861401\pi$
$157$		−	10.5701i		−	0.843585i	0.906692	−	0.421792i	$-0.138599\pi$
$158$		−	0.343246i		−	0.0273072i
$159$		0			0
$160$	1.19161	−	1.89211i	0.0942050	−	0.149584i
$161$	2.66013			0.209648
$162$		0			0
$163$		−	4.37570i		−	0.342732i	−0.985207	−	0.171366i	$-0.945182\pi$
$163$		−	4.37570i		−	0.342732i	0.985207	−	0.171366i	$-0.0548180\pi$
$164$	−4.97226			−0.388268
$165$		0			0
$166$	12.8462			0.997057
$167$			14.7422i			1.14078i	0.821373	+	0.570392i	$0.193209\pi$
$167$			14.7422i			1.14078i	−0.821373	+	0.570392i	$0.806791\pi$
$168$		0			0
$169$	11.6541			0.896468
$170$	1.06172	+	0.668647i	0.0814300	+	0.0512829i
$171$		0			0
$172$			4.94129i			0.376770i
$173$			13.1708i			1.00136i	0.865633	+	0.500679i	$0.166916\pi$
$173$			13.1708i			1.00136i	−0.865633	+	0.500679i	$0.833084\pi$
$174$		0			0
$175$	8.61411	−	4.12650i	0.651166	−	0.311934i
$176$	−6.34148			−0.478007
$177$		0			0
$178$		−	4.77883i		−	0.358188i
$179$	2.72305			0.203531			0.101765	−	0.994808i	$-0.467551\pi$
$179$	2.72305			0.203531			0.101765	+	0.994808i	$0.467551\pi$
$180$		0			0
$181$	−10.9553			−0.814302			−0.407151	−	0.913361i	$-0.633478\pi$
$181$	−10.9553			−0.814302			−0.407151	+	0.913361i	$0.633478\pi$
$182$		−	2.21620i		−	0.164276i
$183$		0			0
$184$	−1.39252			−0.102658
$185$	−1.19161	+	1.89211i	−0.0876089	+	0.139110i
$186$		0			0
$187$		−	3.55839i		−	0.260215i
$188$		−	6.69678i		−	0.488413i
$189$		0			0
$190$	−0.523892	+	0.831867i	−0.0380072	+	0.0603500i
$191$	−19.1443			−1.38524			−0.692618	−	0.721304i	$-0.743543\pi$
$191$	−19.1443			−1.38524			−0.692618	+	0.721304i	$0.743543\pi$
$192$		0			0
$193$		−	2.79550i		−	0.201225i	−0.994926	−	0.100612i	$-0.967920\pi$
$193$		−	2.79550i		−	0.201225i	0.994926	−	0.100612i	$-0.0320802\pi$
$194$	10.8281			0.777415
$195$		0			0
$196$	−3.35076			−0.239340
$197$		−	19.5186i		−	1.39064i	−0.718701	−	0.695320i	$-0.755263\pi$
$197$		−	19.5186i		−	1.39064i	0.718701	−	0.695320i	$-0.244737\pi$
$198$		0			0
$199$	2.19757			0.155781			0.0778907	−	0.996962i	$-0.475181\pi$
$199$	2.19757			0.155781			0.0778907	+	0.996962i	$0.475181\pi$
$200$	−4.50930	+	2.16014i	−0.318856	+	0.152745i
$201$		0			0
$202$		−	3.94778i		−	0.277765i
$203$		−	11.1973i		−	0.785894i
$204$		0			0
$205$	9.40805	+	5.92499i	0.657086	+	0.413819i
$206$	−8.24163			−0.574222
$207$		0			0
$208$			1.16014i			0.0804409i
$209$	2.78804			0.192853
$210$		0			0
$211$	12.0625			0.830417			0.415208	−	0.909726i	$-0.363709\pi$
$211$	12.0625			0.830417			0.415208	+	0.909726i	$0.363709\pi$
$212$			9.13473i			0.627376i
$213$		0			0
$214$	11.3883			0.778486
$215$	5.88809	−	9.34945i	0.401564	−	0.637628i
$216$		0			0
$217$		−	11.6412i		−	0.790256i
$218$		−	7.24702i		−	0.490830i
$219$		0			0
$220$	11.9988	+	7.55656i	0.808956	+	0.509463i
$221$	−0.650986			−0.0437901
$222$		0			0
$223$		−	16.4112i		−	1.09898i	−0.835502	−	0.549488i	$-0.814823\pi$
$223$		−	16.4112i		−	1.09898i	0.835502	−	0.549488i	$-0.185177\pi$
$224$	−1.91030			−0.127637
$225$		0			0
$226$	−3.74166			−0.248892
$227$		−	17.2720i		−	1.14638i	−0.819422	−	0.573191i	$-0.805705\pi$
$227$		−	17.2720i		−	1.14638i	0.819422	−	0.573191i	$-0.194295\pi$
$228$		0			0
$229$	−16.6738			−1.10184			−0.550919	−	0.834559i	$-0.685723\pi$
$229$	−16.6738			−1.10184			−0.550919	+	0.834559i	$0.685723\pi$
$230$	2.63480	+	1.65934i	0.173734	+	0.109414i
$231$		0			0
$232$			5.86153i			0.384828i
$233$		−	7.78278i		−	0.509867i	−0.966959	−	0.254933i	$-0.917946\pi$
$233$		−	7.78278i		−	0.509867i	0.966959	−	0.254933i	$-0.0820536\pi$
$234$		0			0
$235$	−7.97995	+	12.6710i	−0.520555	+	0.826567i
$236$	−5.51090			−0.358729
$237$		0			0
$238$		−	1.07193i		−	0.0694826i
$239$	1.24406			0.0804713			0.0402356	−	0.999190i	$-0.487189\pi$
$239$	1.24406			0.0804713			0.0402356	+	0.999190i	$0.487189\pi$
$240$		0			0
$241$	−1.63717			−0.105459			−0.0527297	−	0.998609i	$-0.516792\pi$
$241$	−1.63717			−0.105459			−0.0527297	+	0.998609i	$0.516792\pi$
$242$		−	29.2143i		−	1.87797i
$243$		0			0
$244$	−13.3222			−0.852867
$245$	6.34000	+	3.99280i	0.405048	+	0.255090i
$246$		0			0
$247$		−	0.510055i		−	0.0324540i
$248$			6.09391i			0.386964i
$249$		0			0
$250$	11.1061	+	1.28612i	0.702413	+	0.0813415i
$251$	4.88816			0.308538			0.154269	−	0.988029i	$-0.450698\pi$
$251$	4.88816			0.308538			0.154269	+	0.988029i	$0.450698\pi$
$252$		0			0
$253$		−	8.83065i		−	0.555178i
$254$	−4.72570			−0.296516
$255$		0			0
$256$	1.00000			0.0625000
$257$			24.2278i			1.51129i	0.654982	+	0.755644i	$0.272676\pi$
$257$			24.2278i			1.51129i	−0.654982	+	0.755644i	$0.727324\pi$
$258$		0			0
$259$	1.91030			0.118700
$260$	1.38243	−	2.19510i	0.0857345	−	0.136134i
$261$		0			0
$262$			17.1887i			1.06192i
$263$			13.0441i			0.804337i	0.915566	+	0.402168i	$0.131743\pi$
$263$			13.0441i			0.804337i	−0.915566	+	0.402168i	$0.868257\pi$
$264$		0			0
$265$	10.8850	−	17.2839i	0.668662	−	1.06174i
$266$	0.839865			0.0514954
$267$		0			0
$268$			5.03975i			0.307852i
$269$	26.9155			1.64107			0.820533	−	0.571598i	$-0.193676\pi$
$269$	26.9155			1.64107			0.820533	+	0.571598i	$0.193676\pi$
$270$		0			0
$271$	−12.2502			−0.744144			−0.372072	−	0.928204i	$-0.621353\pi$
$271$	−12.2502			−0.744144			−0.372072	+	0.928204i	$0.621353\pi$
$272$			0.561130i			0.0340235i
$273$		0			0
$274$	22.2907			1.34663
$275$	−13.6984	−	28.5956i	−0.826047	−	1.72438i
$276$		0			0
$277$			11.1047i			0.667214i	0.942712	+	0.333607i	$0.108266\pi$
$277$			11.1047i			0.667214i	−0.942712	+	0.333607i	$0.891734\pi$
$278$		−	6.19400i		−	0.371491i
$279$		0			0
$280$	3.61449	+	2.27633i	0.216007	+	0.136037i
$281$	8.83875			0.527276			0.263638	−	0.964622i	$-0.415078\pi$
$281$	8.83875			0.527276			0.263638	+	0.964622i	$0.415078\pi$
$282$		0			0
$283$		−	14.7442i		−	0.876452i	−0.898865	−	0.438226i	$-0.855607\pi$
$283$		−	14.7442i		−	0.876452i	0.898865	−	0.438226i	$-0.144393\pi$
$284$	−3.59783			−0.213492
$285$		0			0
$286$	−7.35697			−0.435027
$287$		−	9.49850i		−	0.560679i
$288$		0			0
$289$	16.6851			0.981478
$290$	6.98465	−	11.0906i	0.410153	−	0.651264i
$291$		0			0
$292$			5.07193i			0.296812i
$293$			5.57403i			0.325638i	0.986656	+	0.162819i	$0.0520587\pi$
$293$			5.57403i			0.325638i	−0.986656	+	0.162819i	$0.947941\pi$
$294$		0			0
$295$	10.4272	+	6.56683i	0.607095	+	0.382336i
$296$	−1.00000			−0.0581238
$297$		0			0
$298$		−	1.52154i		−	0.0881405i
$299$	−1.61551			−0.0934276
$300$		0			0
$301$	−9.43934			−0.544075
$302$		−	2.53077i		−	0.145629i
$303$		0			0
$304$	−0.439651			−0.0252157
$305$	25.2070	+	15.8749i	1.44335	+	0.908992i
$306$		0			0
$307$			16.4137i			0.936777i	0.883523	+	0.468389i	$0.155165\pi$
$307$			16.4137i			0.936777i	−0.883523	+	0.468389i	$0.844835\pi$
$308$		−	12.1141i		−	0.690266i
$309$		0			0
$310$	7.26156	−	11.5303i	0.412429	−	0.654879i
$311$	3.72790			0.211390			0.105695	−	0.994399i	$-0.466293\pi$
$311$	3.72790			0.211390			0.105695	+	0.994399i	$0.466293\pi$
$312$		0			0
$313$			21.3300i			1.20564i	0.797876	+	0.602822i	$0.205957\pi$
$313$			21.3300i			1.20564i	−0.797876	+	0.602822i	$0.794043\pi$
$314$	−10.5701			−0.596505
$315$		0			0
$316$	−0.343246			−0.0193091
$317$		−	16.7437i		−	0.940418i	−0.882555	−	0.470209i	$-0.844179\pi$
$317$		−	16.7437i		−	0.940418i	0.882555	−	0.470209i	$-0.155821\pi$
$318$		0			0
$319$	−37.1707			−2.08116
$320$	−1.89211	−	1.19161i	−0.105772	−	0.0666130i
$321$		0			0
$322$		−	2.66013i		−	0.148243i
$323$		−	0.246701i		−	0.0137268i
$324$		0			0
$325$	−5.23140	+	2.50605i	−0.290186	+	0.139011i
$326$	−4.37570			−0.242348
$327$		0			0
$328$			4.97226i			0.274547i
$329$	12.7929			0.705293
$330$		0			0
$331$	−13.8978			−0.763895			−0.381947	−	0.924184i	$-0.624746\pi$
$331$	−13.8978			−0.763895			−0.381947	+	0.924184i	$0.624746\pi$
$332$		−	12.8462i		−	0.705025i
$333$		0			0
$334$	14.7422			0.806656
$335$	6.00542	−	9.53575i	0.328111	−	0.520994i
$336$		0			0
$337$			1.64957i			0.0898576i	0.998990	+	0.0449288i	$0.0143061\pi$
$337$			1.64957i			0.0898576i	−0.998990	+	0.0449288i	$0.985694\pi$
$338$		−	11.6541i		−	0.633899i
$339$		0			0
$340$	0.668647	−	1.06172i	0.0362625	−	0.0575797i
$341$	−38.6444			−2.09271
$342$		0			0
$343$		−	19.7730i		−	1.06764i
$344$	4.94129			0.266417
$345$		0			0
$346$	13.1708			0.708067
$347$		−	13.9455i		−	0.748632i	−0.927301	−	0.374316i	$-0.877877\pi$
$347$		−	13.9455i		−	0.748632i	0.927301	−	0.374316i	$-0.122123\pi$
$348$		0			0
$349$	−2.06031			−0.110286			−0.0551429	−	0.998478i	$-0.517561\pi$
$349$	−2.06031			−0.110286			−0.0551429	+	0.998478i	$0.517561\pi$
$350$	−4.12650	−	8.61411i	−0.220571	−	0.460444i
$351$		0			0
$352$			6.34148i			0.338002i
$353$		−	19.3839i		−	1.03170i	−0.856678	−	0.515851i	$-0.827476\pi$
$353$		−	19.3839i		−	1.03170i	0.856678	−	0.515851i	$-0.172524\pi$
$354$		0			0
$355$	6.80748	+	4.28721i	0.361303	+	0.227541i
$356$	−4.77883			−0.253277
$357$		0			0
$358$		−	2.72305i		−	0.143918i
$359$	34.3855			1.81480			0.907398	−	0.420273i	$-0.138066\pi$
$359$	34.3855			1.81480			0.907398	+	0.420273i	$0.138066\pi$
$360$		0			0
$361$	−18.8067			−0.989827
$362$			10.9553i			0.575799i
$363$		0			0
$364$	−2.21620			−0.116161
$365$	6.04375	−	9.59662i	0.316344	−	0.502310i
$366$		0			0
$367$		−	21.4179i		−	1.11800i	−0.829167	−	0.559002i	$-0.811185\pi$
$367$		−	21.4179i		−	1.11800i	0.829167	−	0.559002i	$-0.188815\pi$
$368$			1.39252i			0.0725903i
$369$		0			0
$370$	1.89211	+	1.19161i	0.0983659	+	0.0619488i
$371$	−17.4501			−0.905962
$372$		0			0
$373$		−	35.1439i		−	1.81968i	−0.414956	−	0.909841i	$-0.636203\pi$
$373$		−	35.1439i		−	1.81968i	0.414956	−	0.909841i	$-0.363797\pi$
$374$	−3.55839			−0.184000
$375$		0			0
$376$	−6.69678			−0.345360
$377$			6.80016i			0.350226i
$378$		0			0
$379$	21.8115			1.12038			0.560190	−	0.828364i	$-0.310728\pi$
$379$	21.8115			1.12038			0.560190	+	0.828364i	$0.310728\pi$
$380$	0.831867	+	0.523892i	0.0426739	+	0.0268751i
$381$		0			0
$382$			19.1443i			0.979510i
$383$			25.0363i			1.27929i	0.768669	+	0.639647i	$0.220920\pi$
$383$			25.0363i			1.27929i	−0.768669	+	0.639647i	$0.779080\pi$
$384$		0			0
$385$	−14.4353	+	22.9212i	−0.735690	+	1.16817i
$386$	−2.79550			−0.142287
$387$		0			0
$388$		−	10.8281i		−	0.549715i
$389$	34.4660			1.74750			0.873748	−	0.486380i	$-0.161683\pi$
$389$	34.4660			1.74750			0.873748	+	0.486380i	$0.161683\pi$
$390$		0			0
$391$	−0.781386			−0.0395164
$392$			3.35076i			0.169239i
$393$		0			0
$394$	−19.5186			−0.983330
$395$	0.649458	+	0.409015i	0.0326778	+	0.0205798i
$396$		0			0
$397$		−	36.3469i		−	1.82420i	−0.409972	−	0.912098i	$-0.634461\pi$
$397$		−	36.3469i		−	1.82420i	0.409972	−	0.912098i	$-0.365539\pi$
$398$		−	2.19757i		−	0.110154i
$399$		0			0
$400$	2.16014	+	4.50930i	0.108007	+	0.225465i
$401$	−34.9811			−1.74687			−0.873436	−	0.486938i	$-0.838114\pi$
$401$	−34.9811			−1.74687			−0.873436	+	0.486938i	$0.838114\pi$
$402$		0			0
$403$			7.06976i			0.352170i
$404$	−3.94778			−0.196409
$405$		0			0
$406$	−11.1973			−0.555711
$407$		−	6.34148i		−	0.314335i
$408$		0			0
$409$	−10.6254			−0.525393			−0.262697	−	0.964878i	$-0.584612\pi$
$409$	−10.6254			−0.525393			−0.262697	+	0.964878i	$0.584612\pi$
$410$	5.92499	−	9.40805i	0.292614	−	0.464630i
$411$		0			0
$412$			8.24163i			0.406036i
$413$		−	10.5275i		−	0.518022i
$414$		0			0
$415$	−15.3076	+	24.3063i	−0.751422	+	1.19315i
$416$	1.16014			0.0568803
$417$		0			0
$418$		−	2.78804i		−	0.136367i
$419$	−38.0309			−1.85793			−0.928967	−	0.370164i	$-0.879302\pi$
$419$	−38.0309			−1.85793			−0.928967	+	0.370164i	$0.879302\pi$
$420$		0			0
$421$	−4.85797			−0.236763			−0.118381	−	0.992968i	$-0.537771\pi$
$421$	−4.85797			−0.236763			−0.118381	+	0.992968i	$0.537771\pi$
$422$		−	12.0625i		−	0.587193i
$423$		0			0
$424$	9.13473			0.443622
$425$	−2.53030	+	1.21212i	−0.122738	+	0.0587963i
$426$		0			0
$427$		−	25.4494i		−	1.23158i
$428$		−	11.3883i		−	0.550472i
$429$		0			0
$430$	−9.34945	−	5.88809i	−0.450871	−	0.283949i
$431$	−18.4965			−0.890945			−0.445473	−	0.895296i	$-0.646964\pi$
$431$	−18.4965			−0.890945			−0.445473	+	0.895296i	$0.646964\pi$
$432$		0			0
$433$			8.29687i			0.398722i	0.979926	+	0.199361i	$0.0638866\pi$
$433$			8.29687i			0.398722i	−0.979926	+	0.199361i	$0.936113\pi$
$434$	−11.6412			−0.558795
$435$		0			0
$436$	−7.24702			−0.347069
$437$		−	0.612224i		−	0.0292867i
$438$		0			0
$439$	−11.2675			−0.537767			−0.268884	−	0.963173i	$-0.586655\pi$
$439$	−11.2675			−0.537767			−0.268884	+	0.963173i	$0.586655\pi$
$440$	7.55656	−	11.9988i	0.360245	−	0.572018i
$441$		0			0
$442$			0.650986i			0.0309643i
$443$			35.1510i			1.67007i	0.550195	+	0.835036i	$0.314553\pi$
$443$			35.1510i			1.67007i	−0.550195	+	0.835036i	$0.685447\pi$
$444$		0			0
$445$	9.04205	+	5.69449i	0.428634	+	0.269945i
$446$	−16.4112			−0.777093
$447$		0			0
$448$			1.91030i			0.0902531i
$449$	−21.0162			−0.991818			−0.495909	−	0.868374i	$-0.665165\pi$
$449$	−21.0162			−0.991818			−0.495909	+	0.868374i	$0.665165\pi$
$450$		0			0
$451$	−31.5315			−1.48476
$452$			3.74166i			0.175993i
$453$		0			0
$454$	−17.2720			−0.810615
$455$	4.19329	+	2.64085i	0.196585	+	0.123805i
$456$		0			0
$457$			33.7686i			1.57963i	0.613347	+	0.789813i	$0.289823\pi$
$457$			33.7686i			1.57963i	−0.613347	+	0.789813i	$0.710177\pi$
$458$			16.6738i			0.779116i
$459$		0			0
$460$	1.65934	−	2.63480i	0.0773673	−	0.122848i
$461$	−0.263532			−0.0122739			−0.00613694	−	0.999981i	$-0.501953\pi$
$461$	−0.263532			−0.0122739			−0.00613694	+	0.999981i	$0.501953\pi$
$462$		0			0
$463$			4.73741i			0.220166i	0.993922	+	0.110083i	$0.0351117\pi$
$463$			4.73741i			0.220166i	−0.993922	+	0.110083i	$0.964888\pi$
$464$	5.86153			0.272115
$465$		0			0
$466$	−7.78278			−0.360530
$467$		−	2.52474i		−	0.116831i	−0.998292	−	0.0584155i	$-0.981395\pi$
$467$		−	2.52474i		−	0.116831i	0.998292	−	0.0584155i	$-0.0186048\pi$
$468$		0			0
$469$	−9.62743			−0.444554
$470$	12.6710	+	7.97995i	0.584471	+	0.368088i
$471$		0			0
$472$			5.51090i			0.253660i
$473$			31.3351i			1.44079i
$474$		0			0
$475$	−0.949706	−	1.98252i	−0.0435755	−	0.0909643i
$476$	−1.07193			−0.0491316
$477$		0			0
$478$		−	1.24406i		−	0.0569018i
$479$	11.9387			0.545493			0.272746	−	0.962086i	$-0.412068\pi$
$479$	11.9387			0.545493			0.272746	+	0.962086i	$0.412068\pi$
$480$		0			0
$481$	−1.16014			−0.0528976
$482$			1.63717i			0.0745710i
$483$		0			0
$484$	−29.2143			−1.32792
$485$	−12.9029	+	20.4880i	−0.585891	+	0.930311i
$486$		0			0
$487$			9.65874i			0.437679i	0.975761	+	0.218840i	$0.0702271\pi$
$487$			9.65874i			0.437679i	−0.975761	+	0.218840i	$0.929773\pi$
$488$			13.3222i			0.603068i
$489$		0			0
$490$	3.99280	−	6.34000i	0.180376	−	0.286412i
$491$	24.9302			1.12508			0.562542	−	0.826769i	$-0.309823\pi$
$491$	24.9302			1.12508			0.562542	+	0.826769i	$0.309823\pi$
$492$		0			0
$493$			3.28908i			0.148133i
$494$	−0.510055			−0.0229485
$495$		0			0
$496$	6.09391			0.273625
$497$		−	6.87293i		−	0.308293i
$498$		0			0
$499$	27.4315			1.22800			0.614001	−	0.789305i	$-0.289559\pi$
$499$	27.4315			1.22800			0.614001	+	0.789305i	$0.289559\pi$
$500$	1.28612	−	11.1061i	0.0575171	−	0.496681i
$501$		0			0
$502$		−	4.88816i		−	0.218169i
$503$			17.8719i			0.796867i	0.917197	+	0.398434i	$0.130446\pi$
$503$			17.8719i			0.796867i	−0.917197	+	0.398434i	$0.869554\pi$
$504$		0			0
$505$	7.46962	+	4.70421i	0.332394	+	0.209335i
$506$	−8.83065			−0.392570
$507$		0			0
$508$			4.72570i			0.209669i
$509$	−25.0765			−1.11150			−0.555749	−	0.831350i	$-0.687568\pi$
$509$	−25.0765			−1.11150			−0.555749	+	0.831350i	$0.687568\pi$
$510$		0			0
$511$	−9.68889			−0.428611
$512$		−	1.00000i		−	0.0441942i
$513$		0			0
$514$	24.2278			1.06864
$515$	9.82080	−	15.5940i	0.432756	−	0.687156i
$516$		0			0
$517$		−	42.4675i		−	1.86772i
$518$		−	1.91030i		−	0.0839337i
$519$		0			0
$520$	−2.19510	−	1.38243i	−0.0962615	−	0.0606235i
$521$	−25.4597			−1.11541			−0.557704	−	0.830040i	$-0.688318\pi$
$521$	−25.4597			−1.11541			−0.557704	+	0.830040i	$0.688318\pi$
$522$		0			0
$523$			34.0240i			1.48777i	0.668309	+	0.743883i	$0.267018\pi$
$523$			34.0240i			1.48777i	−0.668309	+	0.743883i	$0.732982\pi$
$524$	17.1887			0.750890
$525$		0			0
$526$	13.0441			0.568752
$527$			3.41948i			0.148955i
$528$		0			0
$529$	21.0609			0.915690
$530$	−17.2839	−	10.8850i	−0.750764	−	0.472815i
$531$		0			0
$532$		−	0.839865i		−	0.0364128i
$533$			5.76849i			0.249861i
$534$		0			0
$535$	−13.5704	+	21.5478i	−0.586698	+	0.931593i
$536$	5.03975			0.217684
$537$		0			0
$538$		−	26.9155i		−	1.16041i
$539$	−21.2488			−0.915249
$540$		0			0
$541$	−13.4605			−0.578713			−0.289357	−	0.957221i	$-0.593441\pi$
$541$	−13.4605			−0.578713			−0.289357	+	0.957221i	$0.593441\pi$
$542$			12.2502i			0.526190i
$543$		0			0
$544$	0.561130			0.0240582
$545$	13.7121	+	8.63561i	0.587363	+	0.369909i
$546$		0			0
$547$			36.8248i			1.57451i	0.616625	+	0.787257i	$0.288499\pi$
$547$			36.8248i			1.57451i	−0.616625	+	0.787257i	$0.711501\pi$
$548$		−	22.2907i		−	0.952210i
$549$		0			0
$550$	−28.5956	+	13.6984i	−1.21932	+	0.584104i
$551$	−2.57703			−0.109785
$552$		0			0
$553$		−	0.655702i		−	0.0278833i
$554$	11.1047			0.471792
$555$		0			0
$556$	−6.19400			−0.262684
$557$		−	13.0767i		−	0.554076i	−0.960859	−	0.277038i	$-0.910647\pi$
$557$		−	13.0767i		−	0.554076i	0.960859	−	0.277038i	$-0.0893528\pi$
$558$		0			0
$559$	5.73257			0.242462
$560$	2.27633	−	3.61449i	0.0961925	−	0.152740i
$561$		0			0
$562$		−	8.83875i		−	0.372840i
$563$		−	15.2034i		−	0.640746i	−0.947292	−	0.320373i	$-0.896192\pi$
$563$		−	15.2034i		−	0.640746i	0.947292	−	0.320373i	$-0.103808\pi$
$564$		0			0
$565$	4.45860	−	7.07962i	0.187575	−	0.297842i
$566$	−14.7442			−0.619745
$567$		0			0
$568$			3.59783i			0.150962i
$569$	−5.54918			−0.232634			−0.116317	−	0.993212i	$-0.537109\pi$
$569$	−5.54918			−0.232634			−0.116317	+	0.993212i	$0.537109\pi$
$570$		0			0
$571$	29.2853			1.22555			0.612776	−	0.790256i	$-0.290053\pi$
$571$	29.2853			1.22555			0.612776	+	0.790256i	$0.290053\pi$
$572$			7.35697i			0.307610i
$573$		0			0
$574$	−9.49850			−0.396460
$575$	−6.27931	+	3.00804i	−0.261865	+	0.125444i
$576$		0			0
$577$			24.8613i			1.03499i	0.855686	+	0.517495i	$0.173135\pi$
$577$			24.8613i			1.03499i	−0.855686	+	0.517495i	$0.826865\pi$
$578$		−	16.6851i		−	0.694010i
$579$		0			0
$580$	−11.0906	−	6.98465i	−0.460513	−	0.290022i
$581$	24.5400			1.01809
$582$		0			0
$583$			57.9277i			2.39912i
$584$	5.07193			0.209878
$585$		0			0
$586$	5.57403			0.230261
$587$		−	39.7598i		−	1.64106i	−0.571602	−	0.820531i	$-0.693678\pi$
$587$		−	39.7598i		−	1.64106i	0.571602	−	0.820531i	$-0.306322\pi$
$588$		0			0
$589$	−2.67920			−0.110394
$590$	6.56683	−	10.4272i	0.270352	−	0.429281i
$591$		0			0
$592$			1.00000i			0.0410997i
$593$		−	2.63964i		−	0.108397i	−0.998530	−	0.0541985i	$-0.982740\pi$
$593$		−	2.63964i		−	0.108397i	0.998530	−	0.0541985i	$-0.0172604\pi$
$594$		0			0
$595$	2.02820	+	1.27732i	0.0831480	+	0.0523649i
$596$	−1.52154			−0.0623247
$597$		0			0
$598$			1.61551i			0.0660633i
$599$	5.65888			0.231216			0.115608	−	0.993295i	$-0.463118\pi$
$599$	5.65888			0.231216			0.115608	+	0.993295i	$0.463118\pi$
$600$		0			0
$601$	−0.689606			−0.0281296			−0.0140648	−	0.999901i	$-0.504477\pi$
$601$	−0.689606			−0.0281296			−0.0140648	+	0.999901i	$0.504477\pi$
$602$			9.43934i			0.384719i
$603$		0			0
$604$	−2.53077			−0.102976
$605$	55.2766	+	34.8121i	2.24731	+	1.41531i
$606$		0			0
$607$			13.1141i			0.532287i	0.963933	+	0.266143i	$0.0857495\pi$
$607$			13.1141i			0.532287i	−0.963933	+	0.266143i	$0.914251\pi$
$608$			0.439651i			0.0178302i
$609$		0			0
$610$	15.8749	−	25.2070i	0.642755	−	1.02060i
$611$	−7.76917			−0.314307
$612$		0			0
$613$		−	17.3742i		−	0.701738i	−0.936425	−	0.350869i	$-0.885886\pi$
$613$		−	17.3742i		−	0.701738i	0.936425	−	0.350869i	$-0.114114\pi$
$614$	16.4137			0.662401
$615$		0			0
$616$	−12.1141			−0.488092
$617$			43.5176i			1.75195i	0.482354	+	0.875976i	$0.339782\pi$
$617$			43.5176i			1.75195i	−0.482354	+	0.875976i	$0.660218\pi$
$618$		0			0
$619$	−18.9790			−0.762830			−0.381415	−	0.924404i	$-0.624563\pi$
$619$	−18.9790			−0.762830			−0.381415	+	0.924404i	$0.624563\pi$
$620$	−11.5303	−	7.26156i	−0.463069	−	0.291631i
$621$		0			0
$622$		−	3.72790i		−	0.149475i
$623$		−	9.12898i		−	0.365745i
$624$		0			0
$625$	−15.6676	+	19.4814i	−0.626705	+	0.779256i
$626$	21.3300			0.852519
$627$		0			0
$628$			10.5701i			0.421792i
$629$	−0.561130			−0.0223737
$630$		0			0
$631$	−1.86790			−0.0743600			−0.0371800	−	0.999309i	$-0.511837\pi$
$631$	−1.86790			−0.0743600			−0.0371800	+	0.999309i	$0.511837\pi$
$632$			0.343246i			0.0136536i
$633$		0			0
$634$	−16.7437			−0.664976
$635$	5.63118	−	8.94152i	0.223467	−	0.354833i
$636$		0			0
$637$			3.88733i			0.154022i
$638$			37.1707i			1.47160i
$639$		0			0
$640$	−1.19161	+	1.89211i	−0.0471025	+	0.0747921i
$641$	14.0944			0.556696			0.278348	−	0.960480i	$-0.410213\pi$
$641$	14.0944			0.556696			0.278348	+	0.960480i	$0.410213\pi$
$642$		0			0
$643$			14.3894i			0.567463i	0.958904	+	0.283732i	$0.0915725\pi$
$643$			14.3894i			0.567463i	−0.958904	+	0.283732i	$0.908428\pi$
$644$	−2.66013			−0.104824
$645$		0			0
$646$	−0.246701			−0.00970634
$647$		−	22.5927i		−	0.888212i	−0.895974	−	0.444106i	$-0.853521\pi$
$647$		−	22.5927i		−	0.888212i	0.895974	−	0.444106i	$-0.146479\pi$
$648$		0			0
$649$	−34.9472			−1.37180
$650$	2.50605	+	5.23140i	0.0982953	+	0.205192i
$651$		0			0
$652$			4.37570i			0.171366i
$653$			5.82479i			0.227942i	0.993484	+	0.113971i	$0.0363570\pi$
$653$			5.82479i			0.227942i	−0.993484	+	0.113971i	$0.963643\pi$
$654$		0			0
$655$	−32.5228	−	20.4822i	−1.27077	−	0.800304i
$656$	4.97226			0.194134
$657$		0			0
$658$		−	12.7929i		−	0.498717i
$659$	22.9392			0.893585			0.446793	−	0.894638i	$-0.352566\pi$
$659$	22.9392			0.893585			0.446793	+	0.894638i	$0.352566\pi$
$660$		0			0
$661$	34.2691			1.33291			0.666456	−	0.745545i	$-0.267811\pi$
$661$	34.2691			1.33291			0.666456	+	0.745545i	$0.267811\pi$
$662$			13.8978i			0.540155i
$663$		0			0
$664$	−12.8462			−0.498528
$665$	−1.00079	+	1.58911i	−0.0388090	+	0.0616232i
$666$		0			0
$667$			8.16231i			0.316046i
$668$		−	14.7422i		−	0.570392i
$669$		0			0
$670$	−9.53575	−	6.00542i	−0.368398	−	0.232010i
$671$	−84.4825			−3.26141
$672$		0			0
$673$		−	14.5326i		−	0.560190i	−0.959972	−	0.280095i	$-0.909634\pi$
$673$		−	14.5326i		−	0.560190i	0.959972	−	0.280095i	$-0.0903660\pi$
$674$	1.64957			0.0635389
$675$		0			0
$676$	−11.6541			−0.448234
$677$			32.2679i			1.24016i	0.784539	+	0.620079i	$0.212899\pi$
$677$			32.2679i			1.24016i	−0.784539	+	0.620079i	$0.787101\pi$
$678$		0			0
$679$	20.6850			0.793816
$680$	−1.06172	−	0.668647i	−0.0407150	−	0.0256415i
$681$		0			0
$682$			38.6444i			1.47977i
$683$		−	7.04046i		−	0.269396i	−0.990887	−	0.134698i	$-0.956994\pi$
$683$		−	7.04046i		−	0.269396i	0.990887	−	0.134698i	$-0.0430064\pi$
$684$		0			0
$685$	−26.5618	+	42.1763i	−1.01487	+	1.61147i
$686$	−19.7730			−0.754938
$687$		0			0
$688$		−	4.94129i		−	0.188385i
$689$	10.5975			0.403733
$690$		0			0
$691$	19.0846			0.726014			0.363007	−	0.931786i	$-0.381750\pi$
$691$	19.0846			0.726014			0.363007	+	0.931786i	$0.381750\pi$
$692$		−	13.1708i		−	0.500679i
$693$		0			0
$694$	−13.9455			−0.529363
$695$	11.7197	+	7.38082i	0.444554	+	0.279971i
$696$		0			0
$697$			2.79008i			0.105682i
$698$			2.06031i			0.0779838i
$699$		0			0
$700$	−8.61411	+	4.12650i	−0.325583	+	0.155967i
$701$	−1.59801			−0.0603561			−0.0301781	−	0.999545i	$-0.509607\pi$
$701$	−1.59801			−0.0603561			−0.0301781	+	0.999545i	$0.509607\pi$
$702$		0			0
$703$		−	0.439651i		−	0.0165818i
$704$	6.34148			0.239003
$705$		0			0
$706$	−19.3839			−0.729524
$707$		−	7.54144i		−	0.283625i
$708$		0			0
$709$	−18.5069			−0.695041			−0.347520	−	0.937672i	$-0.612976\pi$
$709$	−18.5069			−0.695041			−0.347520	+	0.937672i	$0.612976\pi$
$710$	4.28721	−	6.80748i	0.160896	−	0.255480i
$711$		0			0
$712$			4.77883i			0.179094i
$713$			8.48591i			0.317800i
$714$		0			0
$715$	8.76663	−	13.9202i	0.327853	−	0.520585i
$716$	−2.72305			−0.101765
$717$		0			0
$718$		−	34.3855i		−	1.28325i
$719$	10.8584			0.404949			0.202475	−	0.979287i	$-0.435102\pi$
$719$	10.8584			0.404949			0.202475	+	0.979287i	$0.435102\pi$
$720$		0			0
$721$	−15.7440			−0.586336
$722$			18.8067i			0.699913i
$723$		0			0
$724$	10.9553			0.407151
$725$	12.6617	+	26.4314i	0.470243	+	0.981638i
$726$		0			0
$727$		−	40.1183i		−	1.48791i	−0.668232	−	0.743953i	$-0.732949\pi$
$727$		−	40.1183i		−	1.48791i	0.668232	−	0.743953i	$-0.267051\pi$
$728$			2.21620i			0.0821380i
$729$		0			0
$730$	−9.59662	−	6.04375i	−0.355187	−	0.223689i
$731$	2.77271			0.102552
$732$		0			0
$733$		−	3.99598i		−	0.147595i	−0.997273	−	0.0737974i	$-0.976488\pi$
$733$		−	3.99598i		−	0.147595i	0.997273	−	0.0737974i	$-0.0235118\pi$
$734$	−21.4179			−0.790548
$735$		0			0
$736$	1.39252			0.0513291
$737$			31.9595i			1.17724i
$738$		0			0
$739$	46.2713			1.70212			0.851059	−	0.525069i	$-0.175961\pi$
$739$	46.2713			1.70212			0.851059	+	0.525069i	$0.175961\pi$
$740$	1.19161	−	1.89211i	0.0438044	−	0.0695552i
$741$		0			0
$742$			17.4501i			0.640612i
$743$		−	45.9938i		−	1.68735i	−0.536855	−	0.843674i	$-0.680388\pi$
$743$		−	45.9938i		−	1.68735i	0.536855	−	0.843674i	$-0.319612\pi$
$744$		0			0
$745$	2.87892	+	1.81308i	0.105475	+	0.0664262i
$746$	−35.1439			−1.28671
$747$		0			0
$748$			3.55839i			0.130108i
$749$	21.7550			0.794910
$750$		0			0
$751$	−4.06992			−0.148514			−0.0742568	−	0.997239i	$-0.523658\pi$
$751$	−4.06992			−0.148514			−0.0742568	+	0.997239i	$0.523658\pi$
$752$			6.69678i			0.244207i
$753$		0			0
$754$	6.80016			0.247647
$755$	4.78849	+	3.01569i	0.174271	+	0.109752i
$756$		0			0
$757$		−	41.5068i		−	1.50859i	−0.656536	−	0.754295i	$-0.727979\pi$
$757$		−	41.5068i		−	1.50859i	0.656536	−	0.754295i	$-0.272021\pi$
$758$		−	21.8115i		−	0.792228i
$759$		0			0
$760$	0.523892	−	0.831867i	0.0190036	−	0.0301750i
$761$	−2.87865			−0.104351			−0.0521755	−	0.998638i	$-0.516616\pi$
$761$	−2.87865			−0.104351			−0.0521755	+	0.998638i	$0.516616\pi$
$762$		0			0
$763$		−	13.8440i		−	0.501185i
$764$	19.1443			0.692618
$765$		0			0
$766$	25.0363			0.904598
$767$			6.39338i			0.230852i
$768$		0			0
$769$	−36.7760			−1.32618			−0.663088	−	0.748542i	$-0.730754\pi$
$769$	−36.7760			−1.32618			−0.663088	+	0.748542i	$0.730754\pi$
$770$	22.9212	+	14.4353i	0.826022	+	0.520212i
$771$		0			0
$772$			2.79550i			0.100612i
$773$			31.1721i			1.12118i	0.828093	+	0.560591i	$0.189426\pi$
$773$			31.1721i			1.12118i	−0.828093	+	0.560591i	$0.810574\pi$
$774$		0			0
$775$	13.1637	+	27.4793i	0.472853	+	0.987086i
$776$	−10.8281			−0.388707
$777$		0			0
$778$		−	34.4660i		−	1.23567i
$779$	−2.18606			−0.0783237
$780$		0			0
$781$	−22.8156			−0.816405
$782$			0.781386i			0.0279423i
$783$		0			0
$784$	3.35076			0.119670
$785$	12.5954	−	19.9997i	0.449550	−	0.713821i
$786$		0			0
$787$			22.3107i			0.795289i	0.917540	+	0.397644i	$0.130172\pi$
$787$			22.3107i			0.795289i	−0.917540	+	0.397644i	$0.869828\pi$
$788$			19.5186i			0.695320i
$789$		0			0
$790$	0.409015	−	0.649458i	0.0145521	−	0.0231067i
$791$	−7.14769			−0.254143
$792$		0			0
$793$			15.4556i			0.548843i
$794$	−36.3469			−1.28990
$795$		0			0
$796$	−2.19757			−0.0778907
$797$		−	32.0844i		−	1.13649i	−0.822860	−	0.568243i	$-0.807623\pi$
$797$		−	32.0844i		−	1.13649i	0.822860	−	0.568243i	$-0.192377\pi$
$798$		0			0
$799$	−3.75777			−0.132940
$800$	4.50930	−	2.16014i	0.159428	−	0.0763723i
$801$		0			0
$802$			34.9811i			1.23523i
$803$			32.1635i			1.13503i
$804$		0			0
$805$	5.03326	+	3.16984i	0.177399	+	0.111722i
$806$	7.06976			0.249022
$807$		0			0
$808$			3.94778i			0.138882i
$809$	11.9477			0.420057			0.210029	−	0.977695i	$-0.432644\pi$
$809$	11.9477			0.420057			0.210029	+	0.977695i	$0.432644\pi$
$810$		0			0
$811$	38.7527			1.36079			0.680396	−	0.732845i	$-0.261808\pi$
$811$	38.7527			1.36079			0.680396	+	0.732845i	$0.261808\pi$
$812$			11.1973i			0.392947i
$813$		0			0
$814$	−6.34148			−0.222269
$815$	5.21413	−	8.27930i	0.182643	−	0.290011i
$816$		0			0
$817$			2.17245i			0.0760043i
$818$			10.6254i			0.371509i
$819$		0			0
$820$	−9.40805	−	5.92499i	−0.328543	−	0.206910i
$821$	11.0047			0.384065			0.192033	−	0.981389i	$-0.438492\pi$
$821$	11.0047			0.384065			0.192033	+	0.981389i	$0.438492\pi$
$822$		0			0
$823$			31.6372i			1.10280i	0.834240	+	0.551402i	$0.185907\pi$
$823$			31.6372i			1.10280i	−0.834240	+	0.551402i	$0.814093\pi$
$824$	8.24163			0.287111
$825$		0			0
$826$	−10.5275			−0.366297
$827$		−	4.74477i		−	0.164992i	−0.996591	−	0.0824960i	$-0.973711\pi$
$827$		−	4.74477i		−	0.164992i	0.996591	−	0.0824960i	$-0.0262892\pi$
$828$		0			0
$829$	−46.6435			−1.62000			−0.809998	−	0.586432i	$-0.800532\pi$
$829$	−46.6435			−1.62000			−0.809998	+	0.586432i	$0.800532\pi$
$830$	24.3063	+	15.3076i	0.843685	+	0.531335i
$831$		0			0
$832$		−	1.16014i		−	0.0402204i
$833$			1.88021i			0.0651455i
$834$		0			0
$835$	−17.5669	+	27.8938i	−0.607928	+	0.965304i
$836$	−2.78804			−0.0964263
$837$		0			0
$838$			38.0309i			1.31376i
$839$	−35.1217			−1.21254			−0.606268	−	0.795261i	$-0.707334\pi$
$839$	−35.1217			−1.21254			−0.606268	+	0.795261i	$0.707334\pi$
$840$		0			0
$841$	5.35749			0.184741
$842$			4.85797i			0.167417i
$843$		0			0
$844$	−12.0625			−0.415208
$845$	22.0508	+	13.8871i	0.758570	+	0.477731i
$846$		0			0
$847$		−	55.8081i		−	1.91759i
$848$		−	9.13473i		−	0.313688i
$849$		0			0
$850$	1.21212	+	2.53030i	0.0415752	+	0.0867887i
$851$	−1.39252			−0.0477351
$852$		0			0
$853$			13.8610i			0.474591i	0.971438	+	0.237295i	$0.0762609\pi$
$853$			13.8610i			0.474591i	−0.971438	+	0.237295i	$0.923739\pi$
$854$	−25.4494			−0.870860
$855$		0			0
$856$	−11.3883			−0.389243
$857$			22.0303i			0.752541i	0.926510	+	0.376271i	$0.122794\pi$
$857$			22.0303i			0.752541i	−0.926510	+	0.376271i	$0.877206\pi$
$858$		0			0
$859$	−19.7323			−0.673256			−0.336628	−	0.941638i	$-0.609287\pi$
$859$	−19.7323			−0.673256			−0.336628	+	0.941638i	$0.609287\pi$
$860$	−5.88809	+	9.34945i	−0.200782	+	0.318814i
$861$		0			0
$862$			18.4965i			0.629993i
$863$		−	35.7875i		−	1.21822i	−0.793086	−	0.609110i	$-0.791527\pi$
$863$		−	35.7875i		−	1.21822i	0.793086	−	0.609110i	$-0.208473\pi$
$864$		0			0
$865$	−15.6945	+	24.9206i	−0.533628	+	0.847325i
$866$	8.29687			0.281939
$867$		0			0
$868$			11.6412i			0.395128i
$869$	−2.17669			−0.0738390
$870$		0			0
$871$	5.84680			0.198111
$872$			7.24702i			0.245415i
$873$		0			0
$874$	−0.612224			−0.0207088
$875$	21.2160	+	2.45688i	0.717232	+	0.0830576i
$876$		0			0
$877$			39.4320i			1.33152i	0.746165	+	0.665761i	$0.231893\pi$
$877$			39.4320i			1.33152i	−0.746165	+	0.665761i	$0.768107\pi$
$878$			11.2675i			0.380259i
$879$		0			0
$880$	−11.9988	−	7.55656i	−0.404478	−	0.254732i
$881$	−8.28585			−0.279157			−0.139579	−	0.990211i	$-0.544575\pi$
$881$	−8.28585			−0.279157			−0.139579	+	0.990211i	$0.544575\pi$
$882$		0			0
$883$			6.07448i			0.204422i	0.994763	+	0.102211i	$0.0325918\pi$
$883$			6.07448i			0.204422i	−0.994763	+	0.102211i	$0.967408\pi$
$884$	0.650986			0.0218950
$885$		0			0
$886$	35.1510			1.18092
$887$			17.0227i			0.571568i	0.958294	+	0.285784i	$0.0922539\pi$
$887$			17.0227i			0.571568i	−0.958294	+	0.285784i	$0.907746\pi$
$888$		0			0
$889$	−9.02749			−0.302772
$890$	5.69449	−	9.04205i	0.190880	−	0.303090i
$891$		0			0
$892$			16.4112i			0.549488i
$893$		−	2.94425i		−	0.0985256i
$894$		0			0
$895$	5.15231	+	3.24482i	0.172223	+	0.108462i
$896$	1.91030			0.0638186
$897$		0			0
$898$			21.0162i			0.701321i
$899$	35.7196			1.19132
$900$		0			0
$901$	5.12577			0.170764
$902$			31.5315i			1.04988i
$903$		0			0
$904$	3.74166			0.124446
$905$	−20.7286	−	13.0545i	−0.689043	−	0.433945i
$906$		0			0
$907$		−	47.5075i		−	1.57746i	−0.614739	−	0.788731i	$-0.710739\pi$
$907$		−	47.5075i		−	1.57746i	0.614739	−	0.788731i	$-0.289261\pi$
$908$			17.2720i			0.573191i
$909$		0			0
$910$	2.64085	−	4.19329i	0.0875433	−	0.139006i
$911$	−13.3434			−0.442088			−0.221044	−	0.975264i	$-0.570946\pi$
$911$	−13.3434			−0.442088			−0.221044	+	0.975264i	$0.570946\pi$
$912$		0			0
$913$		−	81.4637i		−	2.69606i
$914$	33.7686			1.11696
$915$		0			0
$916$	16.6738			0.550919
$917$			32.8354i			1.08432i
$918$		0			0
$919$	−21.0558			−0.694566			−0.347283	−	0.937760i	$-0.612896\pi$
$919$	−21.0558			−0.694566			−0.347283	+	0.937760i	$0.612896\pi$
$920$	−2.63480	−	1.65934i	−0.0868668	−	0.0547069i
$921$		0			0
$922$			0.263532i			0.00867895i
$923$			4.17397i			0.137388i
$924$		0			0
$925$	−4.50930	+	2.16014i	−0.148265	+	0.0710248i
$926$	4.73741			0.155681
$927$		0			0
$928$		−	5.86153i		−	0.192414i
$929$	−38.2577			−1.25519			−0.627597	−	0.778539i	$-0.715961\pi$
$929$	−38.2577			−1.25519			−0.627597	+	0.778539i	$0.715961\pi$
$930$		0			0
$931$	−1.47317			−0.0482811
$932$			7.78278i			0.254933i
$933$		0			0
$934$	−2.52474			−0.0826120
$935$	4.24021	−	6.73286i	0.138670	−	0.220188i
$936$		0			0
$937$			20.2830i			0.662615i	0.943523	+	0.331308i	$0.107490\pi$
$937$			20.2830i			0.662615i	−0.943523	+	0.331308i	$0.892510\pi$
$938$			9.62743i			0.314347i
$939$		0			0
$940$	7.97995	−	12.6710i	0.260277	−	0.413283i
$941$	−25.1260			−0.819084			−0.409542	−	0.912291i	$-0.634311\pi$
$941$	−25.1260			−0.819084			−0.409542	+	0.912291i	$0.634311\pi$
$942$		0			0
$943$			6.92398i			0.225476i
$944$	5.51090			0.179364
$945$		0			0
$946$	31.3351			1.01879
$947$		−	52.5869i		−	1.70884i	−0.519580	−	0.854422i	$-0.673912\pi$
$947$		−	52.5869i		−	1.70884i	0.519580	−	0.854422i	$-0.326088\pi$
$948$		0			0
$949$	5.88412			0.191007
$950$	−1.98252	+	0.949706i	−0.0643215	+	0.0308125i
$951$		0			0
$952$			1.07193i			0.0347413i
$953$		−	32.9016i		−	1.06579i	−0.846182	−	0.532894i	$-0.821105\pi$
$953$		−	32.9016i		−	1.06579i	0.846182	−	0.532894i	$-0.178895\pi$
$954$		0			0
$955$	−36.2231	−	22.8126i	−1.17215	−	0.738198i
$956$	−1.24406			−0.0402356
$957$		0			0
$958$		−	11.9387i		−	0.385722i
$959$	42.5818			1.37504
$960$		0			0
$961$	6.13579			0.197929
$962$			1.16014i			0.0374043i
$963$		0			0
$964$	1.63717			0.0527297
$965$	3.33115	−	5.28939i	0.107233	−	0.170271i
$966$		0			0
$967$			26.5880i			0.855013i	0.904012	+	0.427506i	$0.140608\pi$
$967$			26.5880i			0.855013i	−0.904012	+	0.427506i	$0.859392\pi$
$968$			29.2143i			0.938984i
$969$		0			0
$970$	20.4880	+	12.9029i	0.657829	+	0.414287i
$971$	−46.4529			−1.49074			−0.745372	−	0.666649i	$-0.767728\pi$
$971$	−46.4529			−1.49074			−0.745372	+	0.666649i	$0.767728\pi$
$972$		0			0
$973$		−	11.8324i		−	0.379329i
$974$	9.65874			0.309486
$975$		0			0
$976$	13.3222			0.426434
$977$		−	40.4082i		−	1.29277i	−0.763010	−	0.646386i	$-0.776279\pi$
$977$		−	40.4082i		−	1.29277i	0.763010	−	0.646386i	$-0.223721\pi$
$978$		0			0
$979$	−30.3048			−0.968546
$980$	−6.34000	−	3.99280i	−0.202524	−	0.127545i
$981$		0			0
$982$		−	24.9302i		−	0.795554i
$983$			30.0599i			0.958761i	0.877607	+	0.479380i	$0.159139\pi$
$983$			30.0599i			0.958761i	−0.877607	+	0.479380i	$0.840861\pi$
$984$		0			0
$985$	23.2585	−	36.9312i	0.741077	−	1.17673i
$986$	3.28908			0.104746
$987$		0			0
$988$			0.510055i			0.0162270i
$989$	6.88086			0.218799
$990$		0			0
$991$	−54.3782			−1.72738			−0.863691	−	0.504022i	$-0.831853\pi$
$991$	−54.3782			−1.72738			−0.863691	+	0.504022i	$0.831853\pi$
$992$		−	6.09391i		−	0.193482i
$993$		0			0
$994$	−6.87293			−0.217996
$995$	4.15803	+	2.61864i	0.131818	+	0.0830165i
$996$		0			0
$997$			0.230743i			0.00730769i	0.999993	+	0.00365385i	$0.00116306\pi$
$997$			0.230743i			0.00730769i	−0.999993	+	0.00365385i	$0.998837\pi$
$998$		−	27.4315i		−	0.868329i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3330.2.d.r.1999.6	yes	14
3.2	odd	2		3330.2.d.q.1999.9	yes	14
5.4	even	2	inner	3330.2.d.r.1999.13	yes	14
15.14	odd	2		3330.2.d.q.1999.2	✓	14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3330.2.d.q.1999.2	✓	14	15.14	odd	2
3330.2.d.q.1999.9	yes	14	3.2	odd	2
3330.2.d.r.1999.6	yes	14	1.1	even	1	trivial
3330.2.d.r.1999.13	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)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} -1.00000 q^{4} +(1.89211 + 1.19161i) q^{5} -1.91030i q^{7} +1.00000i q^{8} +(1.19161 - 1.89211i) q^{10} -6.34148 q^{11} +1.16014i q^{13} -1.91030 q^{14} +1.00000 q^{16} +0.561130i q^{17} -0.439651 q^{19} +(-1.89211 - 1.19161i) q^{20} +6.34148i q^{22} +1.39252i q^{23} +(2.16014 + 4.50930i) q^{25} +1.16014 q^{26} +1.91030i q^{28} +5.86153 q^{29} +6.09391 q^{31} -1.00000i q^{32} +0.561130 q^{34} +(2.27633 - 3.61449i) q^{35} +1.00000i q^{37} +0.439651i q^{38} +(-1.19161 + 1.89211i) q^{40} +4.97226 q^{41} -4.94129i q^{43} +6.34148 q^{44} +1.39252 q^{46} +6.69678i q^{47} +3.35076 q^{49} +(4.50930 - 2.16014i) q^{50} -1.16014i q^{52} -9.13473i q^{53} +(-11.9988 - 7.55656i) q^{55} +1.91030 q^{56} -5.86153i q^{58} +5.51090 q^{59} +13.3222 q^{61} -6.09391i q^{62} -1.00000 q^{64} +(-1.38243 + 2.19510i) q^{65} -5.03975i q^{67} -0.561130i q^{68} +(-3.61449 - 2.27633i) q^{70} +3.59783 q^{71} -5.07193i q^{73} +1.00000 q^{74} +0.439651 q^{76} +12.1141i q^{77} +0.343246 q^{79} +(1.89211 + 1.19161i) q^{80} -4.97226i q^{82} +12.8462i q^{83} +(-0.668647 + 1.06172i) q^{85} -4.94129 q^{86} -6.34148i q^{88} +4.77883 q^{89} +2.21620 q^{91} -1.39252i q^{92} +6.69678 q^{94} +(-0.831867 - 0.523892i) q^{95} +10.8281i q^{97} -3.35076i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q - 14 q^{4} + 4 q^{5} - 6 q^{10} - 12 q^{11} + 12 q^{14} + 14 q^{16} + 4 q^{19} - 4 q^{20} + 10 q^{25} - 4 q^{26} + 16 q^{29} + 12 q^{31} - 12 q^{34} + 8 q^{35} + 6 q^{40} - 56 q^{41} + 12 q^{44} - 8 q^{46}+ \cdots - 12 q^{95}+O(q^{100}) \) 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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